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Astronomical basis of the Hindu calendar

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126: 3716: 22: 3706: 1692:. Instead of referring to it as "2nd dina of kanyā masa" Hindus will refer to it as " bhādrapada māsa, śukla pakṣa, dvitiyā tithi", which is the tithi prevailing at sunrise on that sāvana dina. Even though the Moon moves into the trayodaśī arc soon after sunrise (at 6:54AM), that entire sāvana dina is considered to be dvādaśī tithi. 1782:
that a nakṣatra dina is divided into ghaṭikā (of 24 modern minutes each) and vighaṭikā (of 24 modern seconds each). These same units are used to subdivide a savana dina using sunrise as the starting point, i.e. the first 24 minutes after sunrise constitute the first ghaṭikā, the next 24 minutes the
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As seen above, both the cāndra māna and saura māna of the calendar define a varṣa comprising twelve māsa, but the duration of the varṣa differ; the cāndra māna varṣa is shorter than the saura māna varṣa by about eleven sāvana dina. As a result, unless explicitly synchronised, these two parts of the
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It is also possible that an entire tithi elapses between two sunrises, i.e. the Moon traverses a 12° arc in between two sunrises (it enters the arc after one sunrise and exits the arc before the next sunrise). In this such a case, neither sāvana dina will be associated with this tithi, i.e. this
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It is possible that two consecutive sunrises may have the same tithi, i.e. the Moon continues to remain within the same 12° arc across two consecutive sunrises. In such a case, two consecutive sāvana dina will be associated with the same tithi. The tithi associated with the second sāvana dina is
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bhādrapada māsa kṛṣṇa pakṣa is identified with pitṛpakṣa. This identification is not always correct. For instance, in the Gregorian year 2020, bhādrapada māsa kṛṣṇa pakṣa ended with the new moon on 17 September while autumnal equinox occurred five days later, on 22 September.
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Human life is regulated by the rising of the Sun and not by the movement of the Moon through a 12° arc. Hence, the position of the Moon at sunrise is used to determine the tithi prevailing at sunrise. This tithi is then associated with the entire sāvana dina.
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If a cāndramāsa does not witness a saṅkramaṇa, that cāndramāsa is designated as a adhikamāsa thus resulting in the cāndra māna varṣa "catching up" with the saura māna varṣa. This happens approximately once every two and a half (solar) years.
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Not everyone is in agreement with this definition. Mercier argues that Ketkar has interpreted a Sanskrit source in a way that is different from other authorities. Yet, this definition is widely used to create Hindu almanacs or
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aśvinī, bharaṇī etc. These names are identical to the names of the asterisms that are located within the respective arc segments. For example, revatī refers to both an asterism and the arc segment within which the asterism is
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As seen above, both the cāndra māna and sāvana māna of the calendar define the concept of a day as tithi and dina respectively. dina are not named and are not used for calendric purposes. The tithi takes precedence instead.
1003: 1882:. As a result of the precesstion of the equinoxes, that coincidence no longer exists thus making that definition incorrect. To illustrate, as per the Surya Siddhantha definition, the period from winter solstice (Dec 21) to 959:) is the time taken by the Sun to traverse a rāśi. Sauramāsa get their names from the corresponding rāśi. sauramāsa corresponds to the concept of a month. The moment in time when the Sun enters a rāśi is known as a 486: 490: 489: 485: 484: 1575:). There are twenty eight such nakṣatra and they are individually named. The name of a nakṣatra and its yogatārā are identical. For example, revatī is an asterism whose principal star is revatī (Zeta Piscium). 491: 1198:
is consecrated to the gods (deva) and the south celestial sphere is consecrated to the ancestors (pitṛ). Devayāna and pitṛyāṇa are not in active calendric use any longer but do form the basis for
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is the time taken by the Sun to orbit the Earth once and return to the starting point with respect to the fixed stars. The starting point is taken to be the position of the Sun when it is in
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The Surya Siddhantha defines uttarāyaṇa and dakṣiṇāyana using rāśi instead of the equinoxes and solstices. That definition assumed a coincidence of the winter solstice and
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In order to synchronise these two parts of the calendar, an additional cāndramāsa is introduced into some cāndra māna varṣa. Such a cāndramāsa is referred to as
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A sidereal rotation is defined with respect to the fixed stars, i.e. at the end of a sidereal rotation all the fixed stars are back in their starting position.
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Apart from the four māna explained above, the concept of nakṣatra is an important characteristic of the Hindu calendar. This term has multiple meanings:
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are defined in cāndra māna terms. Hence these annual festivals do not repeat on the same day on any solar calendar (neither saurana māna nor Gregorian).
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of the Earth on its axis. This definition is not used in practice but is required for defining the following smaller units of time. Ā
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Since a rāśi is a 30° arc of the ecliptic, a ṛtu can be considered as the time taken by the Sun to transit through two rāśi.
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Explains the various calendric elements of the Hindu calendar by means of astronomical simulations created using
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is a pakṣa during which the Sun crosses the equator and transitions overhead the southern hemisphere, i.e. the
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calendar will diverge over time, as the cāndra māna varṣa will keep "falling behind" the saura māna varṣa.
3038: 2662: 877: 732: 615:) is the time taken by the moon to move from a new moon to the next new moon (as per the amānta tradition 273: 3677: 3672: 3439: 2274: 3665: 3546: 3429: 3254: 3162: 2780: 2674: 2590: 1807: 1560: 348:. A geocentric model describes the Solar System as seen by an observer on the surface of the Earth. 206: 727:) is the time taken by the Moon to advance 12° with respect to the Earth-Sun axis. In other words a 3628: 3399: 3361: 3197: 3147: 2997: 2975: 2970: 2916: 2846: 2814: 1124: 251: 216: 3135: 2217: 1186:). Due to the axial tilt of the Earth, the Sun appears to be in the north celestial sphere during 3719: 3536: 3434: 3157: 3100: 3071: 2876: 2856: 2575: 2570: 2534: 2492: 1587: 1583: 263: 179: 3709: 3648: 3576: 3571: 3317: 3269: 3207: 3187: 3002: 2953: 2923: 2861: 2824: 2819: 2765: 2728: 2669: 2639: 2634: 2629: 2560: 2236: 1907:, that assumption is no longer true and hence those definitions of ṛtu are no longer accurate. 1796: 1759: 1741: 1652: 1564: 1542: 1484: 1446: 1427: 1413: 1396: 1382: 1365: 1353: 1324: 1286: 1229: 1179: 1167: 1159: 1151: 1098: 1068: 1045: 1029: 973: 963: 952: 940: 932: 915: 885: 834: 822: 810: 720: 608: 555: 531: 515: 449: 425: 413: 352: 1972::pitṛ), Hindus perform special religious rites in honour of their ancestors during pitṛpakṣa. 3556: 3296: 3286: 3182: 2987: 2982: 2911: 2871: 2851: 2841: 2797: 2723: 2701: 2696: 2691: 2657: 2585: 2565: 2423: 2352: 1904: 1195: 1128: 817:) of the Hindu calendar is defined by the movement of the Earth around the Sun. It contains 341: 211: 184: 862:
Animation that illustrates the twelve rāśi (and sauramāsa) that make up a saura māna varṣa.
420:) of the Hindu calendar is defined based on the movement of the Moon around the Earth. The 3586: 3581: 3512: 3376: 3341: 3291: 3249: 3167: 3152: 3088: 3076: 3066: 3012: 2943: 2933: 2866: 2829: 2770: 2733: 2686: 2681: 2428: 1823: 1332: 1094: 1090: 1064: 1060: 619:
or a full moon to the next full moon (as per the pūrṇimānta tradition). In other words a
3366: 3140: 2293:, the astronomy software that was used to create the animations featured in this article. 2453: 3551: 3409: 3274: 3259: 3217: 3192: 3130: 3125: 3048: 3033: 3007: 2960: 2938: 2928: 2834: 2802: 2787: 2755: 2738: 2706: 2580: 2539: 2529: 2468: 2463: 2377: 2372: 2328: 1336: 736: 656: 624: 476: 337: 226: 3734: 3279: 3232: 3222: 3177: 3172: 3017: 2992: 2965: 2906: 2889: 2760: 2743: 2624: 2595: 2458: 2418: 2392: 2230: 1294: 1171: 1143: 873: 830: 818: 1491:) is the time between two succeeding sunrises. dina corresponds to the concept of a 1135:, and towards the south from the tropic of Cancer to the tropic of Capricorn during 3616: 3591: 3466: 3394: 2884: 1586:(i.e. 360° divided by 13° 20'). Starting in the vicinity of revatī (Zeta Piscium), 345: 2433: 3596: 3522: 3491: 3486: 3404: 3242: 2894: 2402: 1639: 1492: 551: 527: 21: 2296: 3611: 3606: 3541: 3531: 3526: 3351: 2901: 2716: 2382: 1899:
The Surya Siddhanta defines ṛtu in terms of various rāśi assuming that makara
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tithi will be skipped over in the calendar. Such a tithi is referred to as a
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The four māna explained above are used in combination in the Hindu calendar.
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abhijit is an asterism for which there is no corresponding arc segment.
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Of these, only the last four are in active use and are explained here.
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An animation that illustrates a geocentric model of the Solar System.
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Translation of the Surya Siddhanta – a text-book of Hindu astronomy
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Since the south celestial sphere is consecrated to the ancestors (
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of the Earth, the Sun appears to move towards the north from the
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Animation that illustrates the twenty seven nakṣatra (asterism).
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is a 13° 20' arc of the ecliptic. There are twenty seven such
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Astronomical Computations for the History of Indian Astronomy
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around the Earth. In reality, this movement is caused by the
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but the Sun is moving towards the north during this period.
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in which the Moon is positioned at the time of full moon.
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All examples in this article assume the amānta tradition.
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The Orion or Researches into the Antiquity of the Vedas
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Burgess, Ebenezer (1935). Gangooly, Phanidarlal (ed.).
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Animation that illustrates uttarāyaṇa and dakṣiṇāyana.
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This is a common calendric technique and is known as
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Starting in the vicinity of Zeta Piscium ( 599:Animation that illustrates cāndra māna varṣa. 300: 8: 1598:is the time taken by the Moon to traverse a 1473:Animation that illustrates sāvana māna dina. 1024:These time periods are defined based on the 475:of the Hindu calendar defines the following 1688:To illustrate: consider the Gregorian date 1142:The time taken by the Sun to move from the 1059:The time taken by the Sun to move from the 765:numbers according by their position in the 755:corresponds to the concept of a lunar day. 3705: 3456: 2617: 2507: 2493: 2485: 2319: 2305: 2297: 468:) are important markers in this calendar. 307: 293: 120: 55:"Astronomical basis of the Hindu calendar" 530:of the moon is known as the bright side ( 106:Learn how and when to remove this message 2222:Journal of the Asiatic Society of Bombay 1607:Combining the different measures of time 1985: 1835: 1708:Animation that illustrates adhika tithi 171: 132: 1725:Animation that illustrates kṣaya tithi 1627:Animation that illustrates adhikamāsa. 1190:and the south celestial sphere during 1154:(ecliptic longitude 180°) is known as 1239:The six ṛtu of the year are known as 7: 2041: 2039: 2020: 2018: 2016: 44:adding citations to reliable sources 2224:(75, Part 1). British Indian Press. 526:to a full moon and vice versa. The 118:Applied astronomy of ancient India 14: 2216:Ketkar, Venkatesh Bapuji (1923). 1851:These names are derived from the 1343:is ~4 minutes short of 24 hours. 731:is the time taken for the Moon's 3715: 3714: 3704: 1453:) of the Hindu calendar defines 1194:. In Hindu tradition, the north 1067:is known as northward movement ( 670:In some instances an additional 124: 20: 3567:English and British regnal year 2218:"Indian and Foreign Chronology" 1886:(Jan 14) is considered part of 1199: 659:are designated by unique names 31:needs additional citations for 2179:Burgess 1935, p. 319 (XIV. 18) 2161:Burgess 1935, p. 314 (XIV. 15) 2143:Burgess 1935, p. 313 (XIV. 10) 1992:Burgess 1935, p. 285 (XII. 32) 1852: 678:, is added to synchronise the 1: 2250:Tilak, Bal Gangadhar (1955). 2134:Burgess 1935, p. 313 (XIV. 9) 2045:Burgess 1935, p. 104 (II. 64) 2010:Burgess 1935, p. 310 (XIV. 2) 2001:Burgess 1935, p. 310 (XIV. 1) 1774:Subdivisions of a sāvana dina 1097:is called southward movement 789:(new moon) and the fifteenth 651:is made up of 12 consecutive 1779: 1731:adhika tithi and kṣaya tithi 2283:, an online Hindu almanac ( 2116:Burgess 1935, p. 16 (I. 28) 1905:precession of the equinoxes 1113: 1083: 900: 793:of a śukla pakṣa is called 707:Animation that illustrates 570: 554:is known as the dark side ( 546: 464: 440: 364: 3762: 2170:Burgess 1935, p. 5 (I. 11) 2033:Burgess 1935, p. 7 (I. 13) 1783:second ghaṭikā and so on. 1637: 1510: 503: 3700: 2620: 2383:Agrahayana (Margashirsha) 2229:Mercier, Raymond (2018). 2211:. University of Calcutta. 2188:Burgess 1935, pp. 202–250 2098:Mercier (2018). pp. 74–75 1810:occurs within pitṛpakṣa. 1800: 1763: 1745: 1656: 1568: 1546: 1488: 1450: 1431: 1417: 1400: 1386: 1369: 1357: 1328: 1290: 1233: 1183: 1163: 1102: 1072: 1049: 1033: 977: 967: 956: 944: 936: 919: 889: 838: 826: 814: 724: 612: 559: 535: 519: 453: 429: 417: 356: 1955:As a result, almost all 739:) to increase by 12°. A 2635:Assamese (Bhāshkarābda) 747:and one thirtieth of a 682:with the solar year or 3666:Dungeons & Dragons 3072:Ethiopian and Eritrean 2089:Ketkar 1923. pp. 34–35 1726: 1709: 1628: 1594:In calendric terms, a 1531: 1474: 1314: 1219: 1016: 999: 863: 743:is one fifteenth of a 712: 600: 496: 333: 135:History of science and 3678:The Lord of the Rings 3385:Hanke–Henry Permanent 2125:Tilak 1955, pp. 20–31 1724: 1707: 1626: 1529: 1472: 1312: 1217: 1014: 997: 861: 706: 598: 494: 331: 159:Science in Bangladesh 2152:Burgess 1935, p. 207 2107:Burgess 1935, p. 230 2054:Burgess 1935, p. 106 1749:) (additional) tithi 627:of the Moon, or two 237:Traditional medicine 200:Units of measurement 40:improve this article 3390:International Fixed 3328:Proleptic Gregorian 2949:Slavic Native Faith 2071:. 18 September 2021 1125:Tropic of Capricorn 479:calendar elements: 195:Measurement systems 164:Science in Pakistan 139:Indian subcontinent 3060:Christian variants 2024:Burgess 1935, p. 8 1727: 1710: 1629: 1532: 1495:. The length of a 1475: 1315: 1220: 1148:ecliptic longitude 1017: 1000: 864: 713: 601: 497: 334: 137:technology in the 3728: 3727: 3710:List of calendars 3637: 3636: 3336:historiographical 3203:French Republican 3109: 3108: 2867:Manipuri (Meitei) 2482: 2481: 2242:978-81-215-1177-3 2069:www.wisdomlib.org 1884:makara saṅkramaṇa 1880:makara saṅkramaṇa 1737:referred to as a 1722: 1705: 1624: 1527: 1470: 1333:sidereal rotation 1310: 1215: 1174:is designated as 1111: 1081: 1020:Tropical elements 1012: 995: 898: 859: 845:Sidereal elements 709:cāndra māna tithi 704: 680:candra māna varṣa 657:twelve candramāsa 645:candra māna varṣa 639:Candra māna varṣa 596: 568: 544: 492: 462: 438: 329: 317: 316: 116: 115: 108: 90: 3753: 3718: 3717: 3708: 3707: 3572:Human (Holocene) 3557:Chinese Imperial 3457: 3377:Reform proposals 3332:Proleptic Julian 3094:Eastern Orthodox 2724:Germanic heathen 2702:Earthly Branches 2618: 2509: 2502: 2495: 2486: 2321: 2314: 2307: 2298: 2260: 2258: 2246: 2225: 2212: 2210: 2189: 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295: 269:Maritime history 154:Science in India 140: 128: 121: 111: 104: 100: 97: 91: 89: 48: 24: 16: 3761: 3760: 3756: 3755: 3754: 3752: 3751: 3750: 3746:Hindu astronomy 3731: 3730: 3729: 3724: 3696: 3633: 3587:Nirayana system 3513:Ab urbe condita 3501: 3453: 3451: 3444: 3423: 3421: 3414: 3371: 3322:anthropological 3306: 3105: 3089:Liturgical year 3055: 3022: 2614: 2612: 2605: 2544: 2518: 2513: 2483: 2478: 2407: 2331: 2325: 2267: 2256: 2249: 2243: 2228: 2215: 2208: 2201: 2198: 2193: 2192: 2187: 2183: 2178: 2174: 2169: 2165: 2160: 2156: 2151: 2147: 2142: 2138: 2133: 2129: 2124: 2120: 2115: 2111: 2106: 2102: 2097: 2093: 2088: 2084: 2074: 2072: 2063: 2062: 2058: 2053: 2049: 2044: 2037: 2032: 2028: 2023: 2014: 2009: 2005: 2000: 1996: 1991: 1987: 1982: 1977: 1976: 1967: 1963: 1957:Hindu festivals 1954: 1950: 1942: 1938: 1933: 1929: 1924: 1920: 1915: 1911: 1898: 1894: 1877: 1873: 1863: 1859: 1850: 1846: 1841: 1837: 1832: 1824:Nirayana system 1820: 1789: 1775: 1732: 1712: 1695: 1676: 1642: 1634: 1614: 1609: 1517: 1515: 1509: 1460: 1440: 1300: 1285:Nākṣatra māna ( 1283: 1205: 1095:winter solstice 1091:summer solstice 1065:summer solstice 1061:winter solstice 1022: 1002: 985: 849: 847: 827:निरयन; nirayana 803: 694: 692: 641: 586: 584: 508: 502: 482: 406: 381:prājāpatya māna 319: 313: 138: 136: 134: 119: 112: 101: 95: 92: 49: 47: 37: 25: 12: 11: 5: 3759: 3757: 3749: 3748: 3743: 3741:Hindu calendar 3733: 3732: 3726: 3725: 3723: 3722: 3712: 3701: 3698: 3697: 3695: 3694: 3682: 3670: 3658: 3645: 3643: 3639: 3638: 3635: 3634: 3632: 3631: 3626: 3625: 3624: 3619: 3614: 3609: 3599: 3594: 3589: 3584: 3579: 3574: 3569: 3564: 3562:Chinese Minguo 3559: 3554: 3552:Before Present 3549: 3544: 3539: 3534: 3529: 3520: 3515: 3509: 3507: 3503: 3502: 3500: 3499: 3494: 3489: 3484: 3479: 3474: 3469: 3463: 3461: 3454: 3449: 3446: 3445: 3443: 3442: 3437: 3432: 3426: 3424: 3419: 3416: 3415: 3413: 3412: 3407: 3402: 3397: 3392: 3387: 3381: 3379: 3373: 3372: 3370: 3369: 3364: 3359: 3358: 3357: 3349: 3348: 3347: 3339: 3338: 3337: 3325: 3324: 3323: 3314: 3312: 3308: 3307: 3305: 3304: 3299: 3294: 3289: 3284: 3277: 3272: 3267: 3262: 3257: 3252: 3247: 3246: 3245: 3240: 3230: 3225: 3220: 3215: 3210: 3205: 3200: 3195: 3190: 3185: 3180: 3175: 3170: 3165: 3160: 3155: 3150: 3145: 3144: 3143: 3138: 3128: 3123: 3117: 3115: 3111: 3110: 3107: 3106: 3104: 3103: 3098: 3097: 3096: 3086: 3085: 3084: 3074: 3069: 3063: 3061: 3057: 3056: 3054: 3053: 3052: 3051: 3049:Calendar round 3046: 3036: 3030: 3028: 3024: 3023: 3021: 3020: 3015: 3010: 3005: 3000: 2995: 2990: 2985: 2980: 2979: 2978: 2973: 2963: 2958: 2957: 2956: 2951: 2941: 2936: 2931: 2926: 2921: 2920: 2919: 2909: 2904: 2899: 2898: 2897: 2892: 2887: 2879: 2874: 2869: 2864: 2859: 2854: 2849: 2844: 2839: 2838: 2837: 2827: 2822: 2817: 2812: 2811: 2810: 2805: 2795: 2794: 2793: 2785: 2784: 2783: 2778: 2777: 2776: 2763: 2758: 2753: 2752: 2751: 2746: 2736: 2731: 2726: 2721: 2720: 2719: 2714: 2709: 2707:Heavenly Stems 2704: 2694: 2689: 2684: 2679: 2678: 2677: 2667: 2666: 2665: 2660: 2652: 2651: 2650: 2642: 2637: 2632: 2627: 2621: 2615: 2610: 2607: 2606: 2604: 2603: 2598: 2593: 2588: 2583: 2578: 2573: 2568: 2563: 2558: 2552: 2550: 2546: 2545: 2543: 2542: 2537: 2532: 2526: 2524: 2520: 2519: 2514: 2512: 2511: 2504: 2497: 2489: 2480: 2479: 2477: 2476: 2471: 2466: 2461: 2456: 2451: 2446: 2441: 2436: 2431: 2426: 2421: 2415: 2413: 2409: 2408: 2406: 2405: 2400: 2395: 2390: 2385: 2380: 2375: 2370: 2365: 2360: 2355: 2350: 2345: 2339: 2337: 2333: 2332: 2329:Hindu calendar 2327:Months of the 2326: 2324: 2323: 2316: 2309: 2301: 2295: 2294: 2288: 2278: 2266: 2265:External links 2263: 2262: 2261: 2247: 2241: 2226: 2213: 2197: 2194: 2191: 2190: 2181: 2172: 2163: 2154: 2145: 2136: 2127: 2118: 2109: 2100: 2091: 2082: 2056: 2047: 2035: 2026: 2012: 2003: 1994: 1984: 1983: 1981: 1978: 1975: 1974: 1961: 1948: 1936: 1927: 1918: 1909: 1892: 1871: 1857: 1844: 1834: 1833: 1831: 1828: 1827: 1826: 1819: 1816: 1787: 1773: 1767:) (lost) tithi 1730: 1675:dina and tithi 1674: 1638:Main article: 1632: 1608: 1605: 1604: 1603: 1592: 1588:they are named 1576: 1553: 1511:Main article: 1508: 1505: 1501:daytime length 1439: 1436: 1282: 1279: 1278: 1277: 1271: 1265: 1259: 1253: 1247: 1172:spring equinox 1144:spring equinox 1021: 1018: 846: 843: 802: 799: 737:ecliptic plane 691: 688: 674:, known as an 640: 637: 625:synodic period 583: 580: 504:Main article: 501: 498: 405: 402: 398: 397: 394: 391: 388: 385: 382: 379: 376: 373: 340:is based on a 338:Hindu calendar 315: 314: 312: 311: 304: 297: 289: 286: 285: 284: 283: 278: 277: 276: 271: 261: 260: 259: 249: 244: 239: 234: 232:Indian Alchemy 229: 224: 219: 214: 209: 204: 203: 202: 192: 187: 182: 174: 173: 169: 168: 167: 166: 161: 156: 151: 143: 142: 130: 129: 117: 114: 113: 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 3758: 3747: 3744: 3742: 3739: 3738: 3736: 3721: 3713: 3711: 3703: 3702: 3699: 3692: 3691: 3686: 3683: 3680: 3679: 3674: 3671: 3668: 3667: 3662: 3659: 3656: 3655: 3650: 3647: 3646: 3644: 3640: 3630: 3627: 3623: 3620: 3618: 3615: 3613: 3610: 3608: 3605: 3604: 3603: 3600: 3598: 3595: 3593: 3590: 3588: 3585: 3583: 3580: 3578: 3575: 3573: 3570: 3568: 3565: 3563: 3560: 3558: 3555: 3553: 3550: 3548: 3545: 3543: 3540: 3538: 3537:Anno Martyrum 3535: 3533: 3530: 3528: 3524: 3521: 3519: 3516: 3514: 3511: 3510: 3508: 3504: 3498: 3495: 3493: 3490: 3488: 3485: 3483: 3480: 3478: 3475: 3473: 3470: 3468: 3465: 3464: 3462: 3458: 3455: 3452:and numbering 3447: 3441: 3438: 3436: 3433: 3431: 3428: 3427: 3425: 3417: 3411: 3408: 3406: 3403: 3401: 3398: 3396: 3393: 3391: 3388: 3386: 3383: 3382: 3380: 3378: 3374: 3368: 3367:'Pataphysical 3365: 3363: 3360: 3355: 3354: 3353: 3350: 3345: 3344: 3343: 3340: 3335: 3334: 3333: 3329: 3326: 3321: 3320: 3319: 3316: 3315: 3313: 3309: 3303: 3300: 3298: 3295: 3293: 3290: 3288: 3285: 3283: 3282: 3278: 3276: 3273: 3271: 3268: 3266: 3263: 3261: 3258: 3256: 3253: 3251: 3248: 3244: 3241: 3239: 3236: 3235: 3234: 3231: 3229: 3226: 3224: 3221: 3219: 3216: 3214: 3211: 3209: 3206: 3204: 3201: 3199: 3196: 3194: 3191: 3189: 3186: 3184: 3181: 3179: 3176: 3174: 3171: 3169: 3166: 3164: 3161: 3159: 3156: 3154: 3151: 3149: 3146: 3142: 3139: 3137: 3136:Tōnalpōhualli 3134: 3133: 3132: 3129: 3127: 3124: 3122: 3119: 3118: 3116: 3112: 3102: 3099: 3095: 3092: 3091: 3090: 3087: 3083: 3080: 3079: 3078: 3075: 3073: 3070: 3068: 3065: 3064: 3062: 3058: 3050: 3047: 3045: 3042: 3041: 3040: 3037: 3035: 3032: 3031: 3029: 3025: 3019: 3016: 3014: 3011: 3009: 3006: 3004: 3001: 2999: 2996: 2994: 2991: 2989: 2986: 2984: 2981: 2977: 2974: 2972: 2969: 2968: 2967: 2964: 2962: 2959: 2955: 2952: 2950: 2947: 2946: 2945: 2942: 2940: 2937: 2935: 2932: 2930: 2927: 2925: 2922: 2918: 2915: 2914: 2913: 2910: 2908: 2905: 2903: 2900: 2896: 2893: 2891: 2890:Vikram Samvat 2888: 2886: 2883: 2882: 2880: 2878: 2875: 2873: 2870: 2868: 2865: 2863: 2860: 2858: 2855: 2853: 2850: 2848: 2845: 2843: 2840: 2836: 2833: 2832: 2831: 2828: 2826: 2823: 2821: 2818: 2816: 2813: 2809: 2806: 2804: 2801: 2800: 2799: 2796: 2791: 2790: 2789: 2786: 2782: 2779: 2774: 2773: 2772: 2769: 2768: 2767: 2764: 2762: 2759: 2757: 2754: 2750: 2747: 2745: 2744:Vikram Samvat 2742: 2741: 2740: 2737: 2735: 2732: 2730: 2727: 2725: 2722: 2718: 2715: 2713: 2710: 2708: 2705: 2703: 2700: 2699: 2698: 2695: 2693: 2690: 2688: 2685: 2683: 2680: 2676: 2673: 2672: 2671: 2668: 2664: 2661: 2659: 2656: 2655: 2653: 2648: 2647: 2646: 2643: 2641: 2638: 2636: 2633: 2631: 2628: 2626: 2623: 2622: 2619: 2616: 2608: 2602: 2599: 2597: 2594: 2592: 2589: 2587: 2584: 2582: 2579: 2577: 2574: 2572: 2569: 2567: 2564: 2562: 2559: 2557: 2554: 2553: 2551: 2547: 2541: 2538: 2536: 2533: 2531: 2528: 2527: 2525: 2521: 2517: 2510: 2505: 2503: 2498: 2496: 2491: 2490: 2487: 2475: 2472: 2470: 2467: 2465: 2462: 2460: 2457: 2455: 2452: 2450: 2447: 2445: 2442: 2440: 2437: 2435: 2432: 2430: 2427: 2425: 2422: 2420: 2417: 2416: 2414: 2410: 2404: 2401: 2399: 2396: 2394: 2391: 2389: 2386: 2384: 2381: 2379: 2376: 2374: 2371: 2369: 2366: 2364: 2361: 2359: 2356: 2354: 2351: 2349: 2346: 2344: 2341: 2340: 2338: 2334: 2330: 2322: 2317: 2315: 2310: 2308: 2303: 2302: 2299: 2292: 2289: 2286: 2282: 2279: 2276: 2272: 2269: 2268: 2264: 2259:. Tilak Bros. 2255: 2254: 2248: 2244: 2238: 2234: 2233: 2227: 2223: 2219: 2214: 2207: 2206: 2200: 2199: 2195: 2185: 2182: 2176: 2173: 2167: 2164: 2158: 2155: 2149: 2146: 2140: 2137: 2131: 2128: 2122: 2119: 2113: 2110: 2104: 2101: 2095: 2092: 2086: 2083: 2070: 2066: 2060: 2057: 2051: 2048: 2042: 2040: 2036: 2030: 2027: 2021: 2019: 2017: 2013: 2007: 2004: 1998: 1995: 1989: 1986: 1979: 1971: 1965: 1962: 1958: 1952: 1949: 1946: 1945:intercalation 1940: 1937: 1931: 1928: 1922: 1919: 1913: 1910: 1906: 1902: 1896: 1893: 1889: 1885: 1881: 1875: 1872: 1868: 1861: 1858: 1854: 1848: 1845: 1839: 1836: 1829: 1825: 1822: 1821: 1817: 1815: 1811: 1809: 1805: 1798: 1795: 1791: 1790: 1784: 1781: 1777: 1776: 1770: 1768: 1761: 1758: 1752: 1750: 1743: 1740: 1734: 1733: 1693: 1691: 1690:18th Sep 2021 1686: 1682: 1678: 1677: 1671: 1668: 1663: 1661: 1654: 1651: 1646: 1641: 1636: 1635: 1612: 1606: 1601: 1597: 1593: 1589: 1585: 1581: 1577: 1572: 1566: 1562: 1558: 1554: 1551: 1544: 1541: 1537: 1536: 1535: 1514: 1506: 1504: 1502: 1498: 1494: 1486: 1482: 1481: 1458: 1456: 1448: 1444: 1437: 1435: 1429: 1425: 1424: 1415: 1411: 1410: 1404: 1398: 1394: 1393: 1384: 1380: 1379: 1373: 1367: 1363: 1355: 1351: 1350: 1344: 1342: 1338: 1334: 1326: 1322: 1321: 1298: 1296: 1288: 1281:Nākṣatra māna 1280: 1275: 1272: 1269: 1266: 1263: 1260: 1257: 1254: 1251: 1248: 1245: 1242: 1241: 1240: 1237: 1231: 1227: 1226: 1203: 1201: 1197: 1193: 1189: 1181: 1177: 1173: 1169: 1161: 1157: 1153: 1149: 1145: 1140: 1138: 1134: 1130: 1126: 1122: 1119:. Due to the 1117: 1116: 1109: 1100: 1096: 1092: 1087: 1086: 1079: 1070: 1066: 1062: 1057: 1053: 1047: 1043: 1037: 1031: 1027: 1019: 983: 982: 975: 972: 965: 962: 954: 950: 942: 934: 930: 926: 922: 917: 912: 911: 905: 902: 896: 887: 883: 879: 875: 874:sidereal year 871: 870: 844: 842: 836: 832: 824: 820: 812: 808: 800: 798: 797:(full moon). 796: 792: 788: 784: 780: 776: 772: 768: 764: 760: 756: 754: 750: 746: 742: 738: 734: 730: 722: 718: 710: 689: 687: 685: 681: 677: 673: 668: 666: 662: 658: 654: 650: 646: 638: 636: 634: 630: 626: 622: 618: 610: 606: 581: 579: 577: 572: 566: 557: 553: 548: 542: 533: 529: 525: 517: 513: 507: 499: 480: 478: 474: 469: 466: 460: 451: 447: 442: 436: 427: 423: 415: 411: 403: 401: 396:nākṣatra māna 395: 392: 389: 386: 383: 380: 377: 374: 371: 370: 369: 366: 361: 354: 349: 347: 343: 339: 310: 305: 303: 298: 296: 291: 290: 288: 287: 282: 279: 275: 272: 270: 267: 266: 265: 262: 258: 255: 254: 253: 250: 248: 245: 243: 240: 238: 235: 233: 230: 228: 225: 223: 220: 218: 215: 213: 210: 208: 205: 201: 198: 197: 196: 193: 191: 188: 186: 183: 181: 178: 177: 176: 175: 170: 165: 162: 160: 157: 155: 152: 150: 147: 146: 145: 144: 141: 131: 127: 123: 122: 110: 107: 99: 88: 85: 81: 78: 74: 71: 67: 64: 60: 57: –  56: 52: 51:Find sources: 45: 41: 35: 34: 29:This article 27: 23: 18: 17: 3688: 3676: 3673:Middle-earth 3664: 3652: 3422:applications 3420:Displays and 3330: / 3311:By specialty 3280: 3141:Xiuhpōhualli 3039:Mesoamerican 2885:Nepal Sambat 2556:Astronomical 2287:: pañcāṅga). 2281:drikPanchang 2252: 2231: 2221: 2204: 2196:Bibliography 2184: 2175: 2166: 2157: 2148: 2139: 2130: 2121: 2112: 2103: 2094: 2085: 2073:. Retrieved 2068: 2059: 2050: 2029: 2006: 1997: 1988: 1964: 1951: 1939: 1930: 1921: 1912: 1900: 1895: 1887: 1883: 1879: 1874: 1866: 1860: 1847: 1838: 1812: 1803: 1793: 1792: 1786: 1785: 1778: 1772: 1771: 1766: 1756: 1753: 1748: 1738: 1735: 1729: 1728: 1687: 1683: 1679: 1673: 1672: 1666: 1664: 1659: 1650:adhikamāsa ( 1649: 1647: 1643: 1631: 1630: 1610: 1599: 1595: 1579: 1556: 1549: 1539: 1533: 1499:varies with 1496: 1479: 1478: 1476: 1442: 1441: 1422: 1421: 1408: 1407: 1405: 1391: 1390: 1377: 1376: 1374: 1361: 1348: 1347: 1345: 1340: 1319: 1318: 1316: 1297:in nature. 1291:नाक्षत्र मान 1284: 1276:(pre-winter) 1273: 1267: 1261: 1255: 1249: 1244:Śiśira ṛtu ( 1243: 1238: 1224: 1223: 1221: 1191: 1187: 1175: 1155: 1141: 1136: 1132: 1114: 1084: 1058: 1023: 980: 970: 961:saṅkramaṇa ( 960: 948: 939:), vṛṣabha ( 914: 909: 908: 906: 868: 867: 865: 841:) elements. 839:सायन; sāyana 806: 804: 794: 790: 786: 782: 778: 774: 770: 766: 758: 757: 752: 748: 744: 740: 728: 716: 714: 708: 683: 679: 675: 671: 669: 664: 660: 652: 644: 642: 632: 628: 620: 616: 604: 602: 575: 574:). During a 552:waning phase 528:waxing phase 511: 509: 472: 470: 409: 407: 399: 378:pitraya māna 350: 346:Solar System 335: 252:Architecture 102: 96:January 2022 93: 83: 76: 69: 62: 50: 38:Please help 33:verification 30: 3523:Anno Domini 3492:Regnal year 3487:Regnal name 3460:Terminology 3450:Year naming 3405:Symmetry454 3255:Pentecontad 3178:Culāsakaraj 3163:Cappadocian 2895:Yele Sambat 2781:Zoroastrian 2675:Bangladeshi 2613:limited use 2591:Solar Hijri 2586:Lunar Hijri 2549:In wide use 2403:Adhika-masa 1888:dakṣiṇāyana 1794:pitṛpakṣa ( 1640:Adhika-masa 1443:Sāvana māna 1438:Sāvana māna 1274:Hemanta ṛtu 1250:Vasanta ṛtu 1150:0°) to the 1137:dakṣiṇāyana 1115:dakṣiṇāyana 978:सङ्क्रान्ति 783:kṛṣṇa pakṣa 631:. During a 571:kṛṣṇa pakṣa 547:śukla pakṣa 473:candra māna 410:candra māna 404:Candra māna 393:candra māna 390:sāvana māna 372:brāhma māna 242:Agriculture 207:Cartography 180:Mathematics 3735:Categories 3629:Vietnamese 3542:Anno Mundi 3532:Anno Lucis 3527:Common Era 3430:Electronic 3400:Positivist 3362:Discordian 3352:Dreamspell 3287:Sexagenary 3228:Macedonian 3198:Florentine 3148:Babylonian 3114:Historical 3044:Long Count 2998:Vietnamese 2954:Macedonian 2917:Nanakshahi 2847:Lithuanian 2717:Solar term 2291:Stellarium 2275:Stellarium 2075:8 December 1980:References 1901:saṅkramaṇa 1633:adhikamāsa 1552:is a star. 1540:nakṣatra ( 1455:civil time 1268:Śarada ṛtu 1256:Grīṣma ṛtu 1133:uttarāyaṇa 1121:axial tilt 1085:uttarāyaṇa 947:) etc. A 878:opposition 807:saura māna 801:Saura māna 785:is called 749:cāndramāsa 733:elongation 676:adhikamāsa 672:candramāsa 653:candramāsa 649:lunar year 633:cāndramāsa 621:cāndramāsa 605:cāndramāsa 582:Candramāsa 560:कृष्ण पक्ष 550:) and the 536:शुक्ल पक्ष 418:चन्द्र मान 387:saura māna 384:guror māna 375:divya māna 274:Navigation 222:Metallurgy 172:By subject 149:Inventions 66:newspapers 3690:Star Trek 3654:Discworld 3649:Discworld 3642:Fictional 3518:Anka year 3497:Year zero 3477:Leap year 3435:Perpetual 3158:Byzantine 2877:Mongolian 2857:Malayalam 2601:Unix time 2576:Gregorian 2571:Ethiopian 2535:Lunisolar 2516:Calendars 2363:Shraavana 1788:pitṛpakṣa 1573::yogatārā 1569:योगतारा; 1513:Nakshatra 1493:solar day 1378:vighaṭikā 1262:Varṣā ṛtu 1200:pitṛpakṣa 1108:romanized 1103:दक्षिणायन 1078:romanized 1054:: viṣuvat 1050:विषुवत्; 1042:equinoxes 1026:solstices 949:sauramāsa 895:romanized 773:(first), 613:चन्द्रमास 565:romanized 541:romanized 459:romanized 446:full moon 435:romanized 264:Transport 247:Education 212:Geography 185:Astronomy 3720:Category 3685:Stardate 3661:Greyhawk 3592:Seleucid 3577:Japanese 3547:Assyrian 3482:New Year 3318:Holocene 3270:Rapa Nui 3243:Tzolkʼin 3208:Germanic 3188:Egyptian 2924:Romanian 2902:Nisg̱a'a 2862:Mandaean 2852:Maithili 2825:Javanese 2820:Japanese 2775:medieval 2729:Georgian 2640:Assyrian 2630:Armenian 2561:Buddhist 2398:Phalguna 2348:Vaisakha 1867:pañcāṅga 1853:nakṣatra 1818:See also 1801:पितृपक्ष 1797:Sanskrit 1760:Sanskrit 1742:Sanskrit 1739:adhika ( 1653:Sanskrit 1600:nakṣatra 1596:nakṣatra 1591:located. 1584:nakṣatra 1580:nakṣatra 1565:Sanskrit 1561:asterism 1557:nakṣatra 1543:Sanskrit 1507:nakṣatra 1485:Sanskrit 1451:सावन मान 1447:Sanskrit 1428:Sanskrit 1414:Sanskrit 1397:Sanskrit 1383:Sanskrit 1366:Sanskrit 1354:Sanskrit 1325:Sanskrit 1295:sidereal 1287:Sanskrit 1270:(autumn) 1258:(summer) 1252:(spring) 1230:Sanskrit 1192:pitṛyāṇa 1188:devayāna 1180:Sanskrit 1176:pitṛyāṇa 1160:Sanskrit 1156:devayāna 1099:Sanskrit 1073:उत्तरायण 1069:Sanskrit 1046:Sanskrit 1030:Sanskrit 974:Sanskrit 968:सङ्क्रमण 964:Sanskrit 953:Sanskrit 941:Sanskrit 933:Sanskrit 925:ecliptic 916:Sanskrit 886:Sanskrit 835:Sanskrit 831:tropical 823:Sanskrit 819:sidereal 811:Sanskrit 787:amāvāsya 771:prathama 763:Sanskrit 735:(on the 721:Sanskrit 665:vaiśākha 655:. These 609:Sanskrit 556:Sanskrit 532:Sanskrit 524:new moon 516:Sanskrit 454:पूर्णिमा 450:Sanskrit 441:amāvāsya 430:अमावास्य 426:Sanskrit 422:new moon 414:Sanskrit 353:Sanskrit 281:Military 217:Printing 190:Calendar 3617:Dvapara 3597:Spanish 3506:Systems 3356:New Age 3346:Martian 3302:Turkmen 3297:Swedish 3183:Coligny 3121:Arabian 3082:Revised 2988:Tripuri 2983:Tibetan 2939:Sesotho 2912:Punjabi 2872:Melanau 2842:Kurdish 2808:Tabular 2798:Islamic 2766:Iranian 2697:Chinese 2692:Burmese 2670:Bengali 2658:Pawukon 2611:In more 2566:Chinese 2523:Systems 2454:Vṛścika 2434:Karkaṭa 2429:Mithuna 2424:Vṛṣabha 2358:Ashadha 2353:Jyeshta 2343:Chaitra 1757:kṣaya ( 1657:अधिकमास 1547:नक्षत्र 1387:विघटिका 1349:ghaṭikā 1246:winter) 1184:पितृयाण 1170:to the 1131:during 1127:to the 1110::  1093:to the 1080::  1063:to the 1038:: ayana 897::  815:सौर मान 795:pūrṇimā 775:dvitīya 769:, i.e. 667:, etc. 623:is the 567::  543::  477:synodic 465:pūrṇimā 461::  437::  344:of the 257:Bridges 227:Coinage 80:scholar 3582:Korean 3342:Darian 3292:Soviet 3265:Qumran 3250:Muisca 3168:Celtic 3153:Bulgar 3101:Saints 3077:Julian 3067:Coptic 3013:Yoruba 2944:Slavic 2934:Somali 2881:Nepal 2830:Korean 2792:Gaelic 2771:Jalali 2734:Hebrew 2712:Minguo 2687:Borana 2682:Berber 2645:Baháʼí 2469:Kumbha 2464:Makara 2388:Pausha 2378:Kartik 2373:Ashvin 2368:Bhadra 2239:  1559:is an 1401:विनाडी 1392:vināḍī 1164:देवयान 1040:) and 957:सौरमास 890:चित्रा 829:) and 661:caitra 629:pakṣas 506:Paksha 444:) and 82:  75:  68:  61:  53:  3612:Treta 3607:Satya 3602:Yugas 3472:Epoch 3410:World 3275:Roman 3260:Pisan 3238:Haabʼ 3218:Hindu 3213:Greek 3193:Enoch 3131:Aztec 3126:Attic 3034:Runic 3027:Types 3008:Xhosa 3003:Wicca 2976:solar 2971:lunar 2961:Tamil 2929:Shona 2835:Juche 2803:Fasli 2788:Irish 2756:Hmong 2739:Hindu 2654:Bali 2649:Badí‘ 2581:Hindu 2540:Solar 2530:Lunar 2459:Dhanu 2444:Kanyā 2439:Siṃha 2419:Mesha 2412:Solar 2393:Magha 2336:Lunar 2257:(PDF) 2209:(PDF) 1830:Notes 1780:Above 1420:) or 1418:प्राण 1409:prāṇa 1389:) or 1360:) or 1358:घटिका 1034:अयन; 901:citrā 882:Spica 791:tithi 781:of a 779:tithi 767:pakṣa 761:have 759:Tithi 753:tithi 745:pakṣa 741:tithi 729:tithi 717:tithi 690:Tithi 576:pakṣa 512:pakṣa 500:Pakṣa 87:JSTOR 73:books 3622:Kali 3440:Wall 3281:Rumi 3233:Maya 3223:Inca 3173:Cham 3018:Zulu 2993:Tulu 2966:Thai 2907:Odia 2815:Jain 2761:Igbo 2749:Saka 2663:Saka 2625:Akan 2474:Mīna 2449:Tulā 2285:IAST 2237:ISBN 2077:2022 1970:IAST 1764:क्षय 1746:अधिक 1571:IAST 1497:dina 1480:dina 1370:नाडी 1362:nāḍī 1341:dina 1320:dina 1052:IAST 1036:IAST 945:वृषभ 929:IAST 920:राशि 910:rāśi 904:).. 805:The 751:. A 725:तिथि 520:पक्ष 471:The 408:The 365:māna 360:IAST 336:The 59:news 3467:Era 3395:Pax 2596:ISO 1489:दिन 1432:असु 1423:asu 1329:दिन 1234:ऋतु 1225:ṛtu 1056:). 937:मेष 880:to 872:or 647:or 368:): 357:मान 42:by 3737:: 2220:. 2067:. 2038:^ 2015:^ 1869:). 1799:: 1769:. 1762:: 1751:. 1744:: 1655:: 1578:A 1567:: 1555:A 1545:: 1538:A 1503:. 1487:: 1477:A 1457:. 1449:: 1430:: 1416:: 1406:A 1399:: 1385:: 1375:A 1368:: 1356:: 1346:A 1327:: 1317:A 1289:: 1232:: 1222:A 1202:. 1182:: 1162:: 1139:. 1105:, 1101:: 1075:, 1071:: 1048:: 1032:: 981:). 976:: 966:: 955:: 943:: 935:: 918:: 907:A 892:, 888:: 866:A 837:: 825:: 813:: 723:: 715:A 686:. 663:, 643:A 611:: 603:A 562:, 558:: 538:, 534:: 518:: 510:A 456:, 452:: 432:, 428:: 416:: 355:: 3693:) 3687:( 3681:) 3675:( 3669:) 3663:( 3657:) 3651:( 3525:/ 2508:e 2501:t 2494:v 2320:e 2313:t 2306:v 2277:. 2245:. 2079:. 1804:) 1667:. 1660:) 1550:) 1483:( 1445:( 1426:( 1412:( 1395:( 1381:( 1364:( 1352:( 1323:( 1228:( 1178:( 1158:( 1146:( 1044:( 1028:( 951:( 913:( 884:( 833:( 821:( 809:( 719:( 711:. 617:) 607:( 514:( 448:( 424:( 412:( 362:: 308:e 301:t 294:v 109:) 103:( 98:) 94:( 84:· 77:· 70:· 63:· 36:.

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