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lfunc_lfunctions • Show schema
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{'Lhash': '808723166250740971147940672964,849054788104013874205372600820', 'a10': 0, 'a2': 1, 'a3': -6, 'a4': -11, 'a5': 0, 'a6': -6, 'a7': 4, 'a8': -15, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2369.4090272065555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 6, 9]], [5, [1]], [11, [1, 22, 121]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': '1.1.1.1', 'conductor': 680625, 'conductor_radical': 165, 'degree': 4, 'euler_factors': [[1, -1, 12, -8, 64], [1, 6, 9], [1], [1, -4, 622, -1372, 117649], [1, 22, 121], [1, -90, 6402, -197730, 4826809], [1, -16, 1662, -78608, 24137569], [1, 170, 18886, 1166030, 47045881], [1, -124, 12878, -1508708, 148035889], [1, 158, 50106, 3853462, 594823321], [1, -60, 59870, -1787460, 887503681], [1, -372, 82590, -18842916, 2565726409], [1, -38, 37410, -2618998, 4750104241], [1, -516, 160230, -41025612, 6321363049], [1, 224, 21902, 23256352, 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'root_analytic_conductor': 6.976860021151064, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 271354243183710467, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63797008900176234647170914173', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.66978612872596675055054712958', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.71164066558505707530058870290', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 2369.4090272065555, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 680625, 'conductor_radical': 165, 'degree': 4, 'dirichlet_coefficients': [1, 1, -6, -11, 0, -6, 4, -15, 27, 0, -22, 66, 90, 4, 0, 61, 16, 27, -170, 0, -24, -22, 124, 90, 0, 90, -108, -44, -158, 0, 60, 89, 132, 16, 0, -297, 372, -170, -540, 0, 38, -24, 516, 242, 0, 124, -224, -366, -606, 0, -96, -990, -472, -108, 0, -60, 1020, -158, 248, 0, 72, 60, 108, -59, 0, 132, 744, -176, -744, 0, 2060, -405, 486, 372, 0, 1870, -88, -540, 642, 0, 405, 38, 286, 264, 0, 516, 948, 330, 244, 0, 360, -1364, -360, -224, 0, -534, 168, -606, -594, 0], 'euler11': [1, 22, 121, 0, 0], 'euler13': [1, -90, 6402, -197730, 4826809], 'euler17': [1, -16, 1662, -78608, 24137569], 'euler19': [1, 170, 18886, 1166030, 47045881], 'euler2': [1, -1, 12, -8, 64], 'euler23': [1, -124, 12878, -1508708, 148035889], 'euler29': [1, 158, 50106, 3853462, 594823321], 'euler3': [1, 6, 9, 0, 0], 'euler31': [1, -60, 59870, -1787460, 887503681], 'euler37': [1, -372, 82590, -18842916, 2565726409], 'euler41': [1, -38, 37410, -2618998, 4750104241], 'euler43': [1, -516, 160230, -41025612, 6321363049], 'euler47': [1, 224, 21902, 23256352, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 472, 190182, 70269944, 22164361129], 'euler59': [1, -248, 181334, -50933992, 42180533641], 'euler61': [1, -72, -107850, -16342632, 51520374361], 'euler67': [1, -744, 738822, -223767672, 90458382169], 'euler7': [1, -4, 622, -1372, 117649], 'euler71': [1, -2060, 1768494, -737296660, 128100283921], 'euler73': [1, -486, 822786, -189062262, 151334226289], 'euler79': [1, -642, 691166, -316531038, 243087455521], 'euler83': [1, -286, 392750, -163531082, 326940373369], 'euler89': [1, -244, 1355190, -172012436, 496981290961], 'euler97': [1, -168, 1053870, -153329064, 832972004929], 'euler_factors': [[1, -1, 12, -8, 64], [1, 6, 9, 0, 0], [1, 0, 0, 0, 0], [1, -4, 622, -1372, 117649], [1, 22, 121, 0, 0], [1, -90, 6402, -197730, 4826809], [1, -16, 1662, -78608, 24137569], [1, 170, 18886, 1166030, 47045881], [1, -124, 12878, -1508708, 148035889], [1, 158, 50106, 3853462, 594823321], [1, -60, 59870, -1787460, 887503681], [1, -372, 82590, -18842916, 2565726409], [1, -38, 37410, -2618998, 4750104241], [1, -516, 160230, -41025612, 6321363049], [1, 224, 21902, 23256352, 10779215329], [1, 472, 190182, 70269944, 22164361129], [1, -248, 181334, -50933992, 42180533641], [1, -72, -107850, -16342632, 51520374361], [1, -744, 738822, -223767672, 90458382169], [1, -2060, 1768494, -737296660, 128100283921], [1, -486, 822786, -189062262, 151334226289], [1, -642, 691166, -316531038, 243087455521], [1, -286, 392750, -163531082, 326940373369], [1, -244, 1355190, -172012436, 496981290961], [1, -168, 1053870, -153329064, 832972004929]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/4/a/m'], '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': '4-825e2-1.1-c3e2-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-825e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.976860021151064, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 271354243183710467, 'z1': {'__RealLiteral__': 0, 'data': '0.63797008900176234647170914173', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '808723166250740971147940672964,849054788104013874205372600820', 'Lhash_array': ['808723166250740971147940672964', '849054788104013874205372600820'], 'label': '4-825e2-1.1-c3e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/4/a/m'}