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lfunc_lfunctions • Show schema
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{'Lhash': '1562021337699541089741989911313,3115167475625969463700667566430,3198637153158898858876734052513,3818758864985571222042619735706', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.34529744132629725, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -2, 0, 9]]], 'bad_primes': [2, 3], 'central_character': '96.1', 'coefficient_field': '1.1.1.1', 'conductor': 84934656, 'conductor_radical': 6, 'degree': 8, 'euler_factors': [[1], [1, 0, -2, 0, 9], [1, 0, -4, 0, 54, 0, -100, 0, 625], [1, 0, -20, 0, 198, 0, -980, 0, 2401], [1, 0, 28, 0, 438, 0, 3388, 0, 14641], [1, 8, 76, 344, 1654, 4472, 12844, 17576, 28561], [1, 0, -68, 0, 1734, 0, -19652, 0, 83521], [1, 0, -4, 0, 726, 0, -1444, 0, 130321], [1, 0, 28, 0, 1254, 0, 14812, 0, 279841], [1, 0, -100, 0, 4182, 0, -84100, 0, 707281], [1, 0, -116, 0, 5286, 0, -111476, 0, 923521], [1, 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'13.94461742805014315394279729389458', '14.08812374946186900952054595031328', '14.71404074630410880159589972394966'], 'prelabel': '8-96e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8755363267188244, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 1889277004635868137, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23221756643219575807517130617', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45743383473735650058526571696', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.52327980011448913469364768265', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 0.34529744132629725, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 84934656, 'conductor_radical': 6, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0], 'euler11': [1, 0, 28, 0, 438, 0, 3388, 0, 14641], 'euler13': [1, 8, 76, 344, 1654, 4472, 12844, 17576, 28561], 'euler17': [1, 0, -68, 0, 1734, 0, -19652, 0, 83521], 'euler19': [1, 0, -4, 0, 726, 0, -1444, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 28, 0, 1254, 0, 14812, 0, 279841], 'euler29': [1, 0, -100, 0, 4182, 0, -84100, 0, 707281], 'euler3': [1, 0, -2, 0, 9, 0, 0, 0, 0], 'euler31': [1, 0, -116, 0, 5286, 0, -111476, 0, 923521], 'euler37': [1, -24, 364, -3528, 25494, -130536, 498316, -1215672, 1874161], 'euler41': [1, 0, -100, 0, 5862, 0, -168100, 0, 2825761], 'euler43': [1, 0, -164, 0, 10422, 0, -303236, 0, 3418801], 'euler47': [1, 0, -68, 0, 5574, 0, -150212, 0, 4879681], 'euler5': [1, 0, -4, 0, 54, 0, -100, 0, 625], 'euler53': [1, 0, -68, 0, 6774, 0, -191012, 0, 7890481], 'euler59': [1, 0, 220, 0, 19062, 0, 765820, 0, 12117361], 'euler61': [1, 8, 268, 1496, 25270, 91256, 997228, 1815848, 13845841], 'euler67': [1, 0, -260, 0, 25878, 0, -1167140, 0, 20151121], 'euler7': [1, 0, -20, 0, 198, 0, -980, 0, 2401], 'euler71': [1, 0, 220, 0, 22182, 0, 1109020, 0, 25411681], 'euler73': [1, 24, 508, 6120, 64806, 446760, 2707132, 9336408, 28398241], 'euler79': [1, 0, 76, 0, 13926, 0, 474316, 0, 38950081], 'euler83': [1, 0, 316, 0, 38742, 0, 2176924, 0, 47458321], 'euler89': [1, 0, 220, 0, 27942, 0, 1742620, 0, 62742241], 'euler97': [1, -40, 988, -15640, 182854, -1517080, 9296092, -36506920, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -2, 0, 9, 0, 0, 0, 0], [1, 0, -4, 0, 54, 0, -100, 0, 625], [1, 0, -20, 0, 198, 0, -980, 0, 2401], [1, 0, 28, 0, 438, 0, 3388, 0, 14641], [1, 8, 76, 344, 1654, 4472, 12844, 17576, 28561], [1, 0, -68, 0, 1734, 0, -19652, 0, 83521], [1, 0, -4, 0, 726, 0, -1444, 0, 130321], [1, 0, 28, 0, 1254, 0, 14812, 0, 279841], [1, 0, -100, 0, 4182, 0, -84100, 0, 707281], [1, 0, -116, 0, 5286, 0, -111476, 0, 923521], [1, -24, 364, -3528, 25494, -130536, 498316, -1215672, 1874161], [1, 0, -100, 0, 5862, 0, -168100, 0, 2825761], [1, 0, -164, 0, 10422, 0, -303236, 0, 3418801], [1, 0, -68, 0, 5574, 0, -150212, 0, 4879681], [1, 0, -68, 0, 6774, 0, -191012, 0, 7890481], [1, 0, 220, 0, 19062, 0, 765820, 0, 12117361], [1, 8, 268, 1496, 25270, 91256, 997228, 1815848, 13845841], [1, 0, -260, 0, 25878, 0, -1167140, 0, 20151121], [1, 0, 220, 0, 22182, 0, 1109020, 0, 25411681], [1, 24, 508, 6120, 64806, 446760, 2707132, 9336408, 28398241], [1, 0, 76, 0, 13926, 0, 474316, 0, 38950081], [1, 0, 316, 0, 38742, 0, 2176924, 0, 47458321], [1, 0, 220, 0, 27942, 0, 1742620, 0, 62742241], [1, -40, 988, -15640, 182854, -1517080, 9296092, -36506920, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/96/2/c/a'], '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': '8-96e4-1.1-c1e4-0-0', '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}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-96e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8755363267188244, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1889277004635868137, 'z1': {'__RealLiteral__': 0, 'data': '1.23221756643219575807517130617', 'prec': 103}}
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{'Lhash': '1562021337699541089741989911313,3115167475625969463700667566430,3198637153158898858876734052513,3818758864985571222042619735706', 'Lhash_array': ['1562021337699541089741989911313', '3115167475625969463700667566430', '3198637153158898858876734052513', '3818758864985571222042619735706'], 'label': '8-96e4-1.1-c1e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/96/2/c/a'}