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lfunc_lfunctions • Show schema
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{'Lhash': '4554002651937236633993113951980,5314102166269815070532313603729', 'a10': 18, 'a2': -3, 'a3': -3, 'a4': 4, 'a5': -6, 'a6': 9, 'a7': -5, 'a8': -3, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2530668812404866, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 3, 3]], [7, [1, 5, 7]]], 'bad_primes': [3, 7], 'central_character': '63.1', 'coefficient_field': '1.1.1.1', 'conductor': 3969, 'conductor_radical': 21, 'degree': 4, 'euler_factors': [[1, 3, 5, 6, 4], [1, 3, 3], [1, 6, 19, 30, 25], [1, 5, 7], [1, 0, -19, 0, 121], [1, 3, 16, 39, 169], [1, -3, -8, -51, 289], [1, 9, 46, 171, 361], [1, 0, -19, 0, 529], [1, 9, 56, 261, 841], [1, 6, 43, 186, 961], [1, 7, 12, 259, 1369], [1, -3, -32, -123, 1681], [1, 1, -42, 43, 1849], [1, 0, -47, 0, 2209], [1, 15, 128, 795, 2809], [1, 0, -59, 0, 3481], [1, -24, 253, -1464, 3721], [1, -4, -51, -268, 4489], [1, 0, -130, 0, 5041], [1, 9, 100, 657, 5329], [1, 8, -15, 632, 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'14.72518720460067095407821569932268', '15.06020113073052208804577183465849'], 'prelabel': '4-63e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7092654881876509, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1846074924137177523, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.59247465438609684224541002929', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.19208744532054610463242934762', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.52642751154064048615476871412', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 0.2530668812404866, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 3969, 'conductor_radical': 21, 'degree': 4, 'dirichlet_coefficients': [1, -3, -3, 4, -6, 9, -5, -3, 6, 18, 0, -12, -3, 15, 18, 3, 3, -18, -9, -24, 15, 0, 0, 9, 17, 9, -9, -20, -9, -54, -6, -6, 0, -9, 30, 24, -7, 27, 9, 18, 3, -45, -1, 0, -36, 0, 0, -9, 18, -51, -9, -12, -15, 27, 0, 15, 27, 27, 0, 72, 24, 18, -30, 5, 18, 0, 4, 12, 0, -90, 0, -18, -9, 21, -51, -36, 0, -27, -8, -18, 9, -9, -15, 60, -18, 3, 27, 0, 3, 108, 15, 0, 18, 0, 54, 18, -3, -54, 0, 68], 'euler11': [1, 0, -19, 0, 121], 'euler13': [1, 3, 16, 39, 169], 'euler17': [1, -3, -8, -51, 289], 'euler19': [1, 9, 46, 171, 361], 'euler2': [1, 3, 5, 6, 4], 'euler23': [1, 0, -19, 0, 529], 'euler29': [1, 9, 56, 261, 841], 'euler3': [1, 3, 3, 0, 0], 'euler31': [1, 6, 43, 186, 961], 'euler37': [1, 7, 12, 259, 1369], 'euler41': [1, -3, -32, -123, 1681], 'euler43': [1, 1, -42, 43, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, 6, 19, 30, 25], 'euler53': [1, 15, 128, 795, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, -24, 253, -1464, 3721], 'euler67': [1, -4, -51, -268, 4489], 'euler7': [1, 5, 7, 0, 0], 'euler71': [1, 0, -130, 0, 5041], 'euler73': [1, 9, 100, 657, 5329], 'euler79': [1, 8, -15, 632, 6241], 'euler83': [1, 15, 142, 1245, 6889], 'euler89': [1, -3, -80, -267, 7921], 'euler97': [1, 3, 100, 291, 9409], 'euler_factors': [[1, 3, 5, 6, 4], [1, 3, 3, 0, 0], [1, 6, 19, 30, 25], [1, 5, 7, 0, 0], [1, 0, -19, 0, 121], [1, 3, 16, 39, 169], [1, -3, -8, -51, 289], [1, 9, 46, 171, 361], [1, 0, -19, 0, 529], [1, 9, 56, 261, 841], [1, 6, 43, 186, 961], [1, 7, 12, 259, 1369], [1, -3, -32, -123, 1681], [1, 1, -42, 43, 1849], [1, 0, -47, 0, 2209], [1, 15, 128, 795, 2809], [1, 0, -59, 0, 3481], [1, -24, 253, -1464, 3721], [1, -4, -51, -268, 4489], [1, 0, -130, 0, 5041], [1, 9, 100, 657, 5329], [1, 8, -15, 632, 6241], [1, 15, 142, 1245, 6889], [1, -3, -80, -267, 7921], [1, 3, 100, 291, 9409]], 'index': 7, 'instance_types': ['G2Q', 'CMF'], 'instance_urls': ['Genus2Curve/Q/3969/b', 'ModularForm/GL2/Q/holomorphic/63/2/s/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': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-63e2-1.1-c1e2-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-63e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7092654881876509, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1846074924137177523, 'z1': {'__RealLiteral__': 0, 'data': '3.59247465438609684224541002929', 'prec': 103}}
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id: 9957693
{'Lhash': '4554002651937236633993113951980,5314102166269815070532313603729', 'Lhash_array': ['4554002651937236633993113951980', '5314102166269815070532313603729'], 'label': '4-63e2-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/2/s/a'}
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id: 1223214
{'Lhash': '1846074924137177523', 'Lhash_array': ['1846074924137177523'], 'label': '4-63e2-1.1-c1e2-0-7', 'type': 'G2Q', 'url': 'Genus2Curve/Q/3969/b'}