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lfunc_lfunctions • Show schema
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{'Lhash': '1092013265925947401108011424601,2124469762400187299457207524705,2685961887553945194469701396769,3139802904583567884616130403496,3647900437863126382884575700342,3742718571757066382014425575593', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': 3, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5689731207859845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 0, 1, 0, 0, 1]], [3, [1, 0, 0, 1, 0, 0, 1]], [19, [1, -6, -12, 169, -228, -2166, 6859]]], 'bad_primes': [2, 3, 19], 'central_character': '114.1', 'coefficient_field': '1.1.1.1', 'conductor': 2194972623936, 'conductor_radical': 114, 'degree': 12, 'euler_factors': [[1, 0, 0, 1, 0, 0, 1], [1, 0, 0, 1, 0, 0, 1], [1, 3, 0, 0, -9, -15, 109, -75, -225, 0, 0, 9375, 15625], [1, -3, -6, 41, -9, -162, 519, -1134, -441, 14063, -14406, -50421, 117649], [1, -12, 66, -306, 1446, -5430, 17539, -59730, 174966, -407286, 966306, -1932612, 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-
lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5689731207859845, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 2194972623936, 'conductor_radical': 114, 'degree': 12, 'dirichlet_coefficients': [1, 0, 0, 0, -3, 0, 3, -1, 0, 0, 12, 0, -21, 0, 0, 0, 3, 0, 6, 0, 0, 0, -15, 0, 9, 0, -1, 0, 15, 0, 3, 0, 0, 0, -9, 0, 6, 0, 0, 3, -9, 0, -9, 0, 0, 0, -21, 0, 15, 0, 0, 0, 30, 0, -36, -3, 0, 0, 27, 0, -9, 0, 0, 0, 63, 0, -15, 0, 0, 0, 9, 0, 12, 0, 0, 0, 36, 0, 15, 0, 0, 0, -3, 0, -9, 0, 0, -12, -48, 0, -63, 0, 0, 0, -18, 0, 18, 0, 0, 0], 'euler11': [1, -12, 66, -306, 1446, -5430, 17539, -59730, 174966, -407286, 966306, -1932612, 1771561], 'euler13': [1, 21, 186, 800, 549, -13005, -74727, -169065, 92781, 1757600, 5312346, 7797153, 4826809], 'euler17': [1, -3, -18, 180, -423, -1785, 18649, -30345, -122247, 884340, -1503378, -4259571, 24137569], 'euler19': [1, -6, -12, 169, -228, -2166, 6859, 0, 0, 0, 0, 0, 0], 'euler2': [1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 15, 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-12545864790, 22164361129], 'euler59': [1, -27, 360, -3312, 30879, -316287, 2798533, -18660933, 107489799, -680215248, 4362249960, -19302956073, 42180533641], 'euler61': [1, 9, 72, 506, 6588, 59805, 418827, 3648105, 24513948, 114852386, 996900552, 7601366709, 51520374361], 'euler67': [1, 15, 156, 1472, 16461, 143415, 1174659, 9608805, 73893429, 442723136, 3143574876, 20251876605, 90458382169], 'euler7': [1, -3, -6, 41, -9, -162, 519, -1134, -441, 14063, -14406, -50421, 117649], 'euler71': [1, -9, 81, -9, 2916, 32418, -92555, 2301678, 14699556, -3221199, 2058346161, -16238064159, 128100283921], 'euler73': [1, -12, 246, -2623, 30177, -326385, 2687649, -23826105, 160813233, -1020391591, 6985967286, -24876859116, 151334226289], 'euler79': [1, -15, 105, -559, -6300, 127350, -1087083, 10060650, -39318300, -275608801, 4089758505, -46155845985, 243087455521], 'euler83': [1, 3, 30, 2727, 6369, 60420, 2990995, 5014860, 43876041, 1559263149, 1423749630, 11817121929, 326940373369], 'euler89': [1, 48, 1044, 11907, 43551, -760371, -12833135, -67673019, 344967471, 8394065883, 65502899604, 268034853552, 496981290961], 'euler97': [1, -18, 99, 551, -5967, -122661, 2662518, -11898117, -56143503, 502882823, 8764398819, -154572124626, 832972004929], 'euler_factors': [[1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 3, 0, 0, -9, -15, 109, -75, -225, 0, 0, 9375, 15625], [1, -3, -6, 41, -9, -162, 519, -1134, -441, 14063, -14406, -50421, 117649], [1, -12, 66, -306, 1446, -5430, 17539, -59730, 174966, -407286, 966306, -1932612, 1771561], [1, 21, 186, 800, 549, -13005, -74727, -169065, 92781, 1757600, 5312346, 7797153, 4826809], [1, -3, -18, 180, -423, -1785, 18649, -30345, -122247, 884340, -1503378, -4259571, 24137569], [1, -6, -12, 169, -228, -2166, 6859, 0, 0, 0, 0, 0, 0], [1, 15, 108, 522, 1881, 6855, 32347, 157665, 995049, 6351174, 30222828, 96545145, 148035889], [1, -15, 72, 36, -729, -13389, 142381, -388281, -613089, 878004, 50924232, -307667235, 594823321], [1, -3, -78, 77, 4365, -1404, -155145, -43524, 4194765, 2293907, -72034638, -85887453, 887503681], [1, -6, 213, -1018, 19170, -72270, 937053, -2673990, 26243730, -51564754, 399196293, -416063742, 2565726409], [1, 9, 27, 153, -1728, -21024, -78155, -861984, -2904768, 10544913, 76295547, 1042705809, 4750104241], [1, 9, 45, 209, -972, -25110, -174579, -1079730, -1797228, 16616963, 153846045, 1323075987, 6321363049], [1, 21, 261, 2673, 22680, 170022, 1202725, 7991034, 50100120, 277518879, 1273596741, 4816245147, 10779215329], [1, -30, 378, -2214, -3276, 201552, -2070449, 10682256, -9202284, -329613678, 2982601818, -12545864790, 22164361129], [1, -27, 360, -3312, 30879, -316287, 2798533, -18660933, 107489799, -680215248, 4362249960, -19302956073, 42180533641], [1, 9, 72, 506, 6588, 59805, 418827, 3648105, 24513948, 114852386, 996900552, 7601366709, 51520374361], [1, 15, 156, 1472, 16461, 143415, 1174659, 9608805, 73893429, 442723136, 3143574876, 20251876605, 90458382169], [1, -9, 81, -9, 2916, 32418, -92555, 2301678, 14699556, -3221199, 2058346161, -16238064159, 128100283921], [1, -12, 246, -2623, 30177, -326385, 2687649, -23826105, 160813233, -1020391591, 6985967286, -24876859116, 151334226289], [1, -15, 105, -559, -6300, 127350, -1087083, 10060650, -39318300, -275608801, 4089758505, -46155845985, 243087455521], [1, 3, 30, 2727, 6369, 60420, 2990995, 5014860, 43876041, 1559263149, 1423749630, 11817121929, 326940373369], [1, 48, 1044, 11907, 43551, -760371, -12833135, -67673019, 344967471, 8394065883, 65502899604, 268034853552, 496981290961], [1, -18, 99, 551, -5967, -122661, 2662518, -11898117, -56143503, 502882823, 8764398819, -154572124626, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/i/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '12-114e6-1.1-c1e6-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-114e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 760543505555790370, 'z1': {'__RealLiteral__': 0, 'data': '0.861446573471696353256315581864', 'prec': 107}}
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{'Lhash': '1092013265925947401108011424601,2124469762400187299457207524705,2685961887553945194469701396769,3139802904583567884616130403496,3647900437863126382884575700342,3742718571757066382014425575593', 'Lhash_array': ['1092013265925947401108011424601', '2124469762400187299457207524705', '2685961887553945194469701396769', '3139802904583567884616130403496', '3647900437863126382884575700342', '3742718571757066382014425575593'], 'label': '12-114e6-1.1-c1e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/i/b'}