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lfunc_lfunctions • Show schema
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{'Lhash': '1901505607009914088155956019048', 'a10': -1, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 1, 'a6': 0, 'a7': 0, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.27826216393724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, -1]], [31, [1, 1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '2790.1', 'coefficient_field': '1.1.1.1', 'conductor': 2790, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -1], [1, 0, 7], [1, 2, 11], [1, 0, 13], [1, 2, 17], [1, 4, 19], [1, -4, 23], [1, -4, 29], [1, 1], [1, 8, 37], [1, 6, 41], [1, -2, 43], [1, 0, 47], [1, 8, 53], [1, 8, 59], [1, 0, 61], [1, -4, 67], [1, 0, 71], [1, -6, 73], [1, 4, 79], [1, 6, 83], [1, -6, 89], [1, 2, 97], [1, 2, 101], [1, -8, 103], [1, -8, 107], [1, 18, 109], [1, 14, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, -1], 1]], [[[1, 0, 7], 1]], [[[1, 2, 11], 1]], [[[1, 0, 13], 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0.3073955617416827, -0.26146392270445895, -0.7751918985980382, -1.204285560804087, -1.5236101191546154, -1.7138005531188176, -1.7623732128916036, -1.664482600756707], 'positive_zeros': ['1.50002343442867035876074318729604', '2.44569227539742541309238526143207', '3.35246501897724533562865353409569', '4.62364450878552237809302992665157', '5.36013908964288749051473827733731', '6.38928498895932353355711112533627', '6.85566084303057349352756596640802', '7.82324426194698016701524671113378', '8.509196251671545492180031763811574'], 'prelabel': '2-2790-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.71998539869958, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 548296838954598446, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50002343442867035876074318730', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44569227539742541309238526143', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35246501897724533562865353410', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.27826216393724, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 2790, 'conductor_radical': 930, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 1, 0, 0, -1, 0, -1, -2, 0, 0, 0, 0, 1, -2, 0, -4, 1, 0, 2, 4, 0, 1, 0, 0, 0, 4, 0, -1, -1, 0, 2, 0, 0, -8, 4, 0, -1, -6, 0, 2, -2, 0, -4, 0, 0, -7, -1, 0, 0, -8, 0, -2, 0, 0, -4, -8, 0, 0, 1, 0, 1, 0, 0, 4, -2, 0, 0, 0, 0, 6, 8, 0, -4, 0, 0, -4, 1, 0, 6, -6, 0, -2, -2, 0, 2, 6, 0, 0, 4, 0, 0, -4, 0, -2, 7, 0, 1], 'euler11': [1, 2, 11], 'euler13': [1, 0, 13], 'euler17': [1, 2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, -4, 23], 'euler29': [1, -4, 29], 'euler3': [1, 0, 0], 'euler31': [1, 1, 0], 'euler37': [1, 8, 37], 'euler41': [1, 6, 41], 'euler43': [1, -2, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, 8, 53], 'euler59': [1, 8, 59], 'euler61': [1, 0, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, -6, 73], 'euler79': [1, 4, 79], 'euler83': [1, 6, 83], 'euler89': [1, -6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 0, 7], [1, 2, 11], [1, 0, 13], [1, 2, 17], [1, 4, 19], [1, -4, 23], [1, -4, 29], [1, 1, 0], [1, 8, 37], [1, 6, 41], [1, -2, 43], [1, 0, 47], [1, 8, 53], [1, 8, 59], [1, 0, 61], [1, -4, 67], [1, 0, 71], [1, -6, 73], [1, 4, 79], [1, 6, 83], [1, -6, 89], [1, 2, 97]], 'index': 39, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2790/h', 'ModularForm/GL2/Q/holomorphic/2790/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/2790/2/a/h'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-2790-1.1-c1-0-39', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-2790-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.71998539869958, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 548296838954598446, 'z1': {'__RealLiteral__': 0, 'data': '1.50002343442867035876074318730', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20041975
{'Lhash': '1901505607009914088155956019048', 'Lhash_array': ['1901505607009914088155956019048'], 'label': '2-2790-1.1-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2790/2/a/h'}
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id: 24558776
{'Lhash': '1901505607009914088155956019048', 'Lhash_array': ['1901505607009914088155956019048'], 'label': '2-2790-1.1-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2790/2/a/h/1/1'}
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id: 96001
{'Lhash': '548296838954598446', 'Lhash_array': ['548296838954598446'], 'label': '2-2790-1.1-c1-0-39', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2790/h'}