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lfunc_lfunctions • Show schema
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{'Lhash': '810400510740230270880482549719,1453118069519800469351803898446', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -4, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.66888685406058, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [31, [1, -2, 1]]], 'bad_primes': [3, 31], 'central_character': '837.1', 'coefficient_field': '1.1.1.1', 'conductor': 700569, 'conductor_radical': 93, 'degree': 4, 'euler_factors': [[1, 0, 4, 0, 4], [1], [1, 0, -2, 0, 25], [1, 2, 15, 14, 49], [1, 0, 10, 0, 121], [1, 2, 27, 26, 169], [1, 0, 22, 0, 289], [1, -10, 63, -190, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, -2, 1], [1, -10, 99, -370, 1369], [1, 0, 70, 0, 1681], [1, -16, 150, -688, 1849], [1, 0, -14, 0, 2209], [1, 0, 94, 0, 2809], [1, 0, -74, 0, 3481], [1, -10, 147, -610, 3721], [1, -10, 159, -670, 4489], [1, 0, 94, 0, 5041], [1, -22, 267, -1606, 5329], [1, 2, 159, 158, 6241], [1, 0, 154, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.66888685406058, 'bad_primes': [3, 31], 'central_character': '1.1', 'conductor': 700569, 'conductor_radical': 93, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 12, 0, 0, 10, 0, 0, 0, 0, 0, 2, 0, 0, 8, 0, 0, 2, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -11, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, -32, 0, 0, 10, 0, 0, 0, 0, 0, 22, 0, 0, -40, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 10, 0, 0, -8], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, 2, 27, 26, 169], 'euler17': [1, 0, 22, 0, 289], 'euler19': [1, -10, 63, -190, 361], 'euler2': [1, 0, 4, 0, 4], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -2, 1, 0, 0], 'euler37': [1, -10, 99, -370, 1369], 'euler41': [1, 0, 70, 0, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, 0, -14, 0, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 0, 94, 0, 2809], 'euler59': [1, 0, -74, 0, 3481], 'euler61': [1, -10, 147, -610, 3721], 'euler67': [1, -10, 159, -670, 4489], 'euler7': [1, 2, 15, 14, 49], 'euler71': [1, 0, 94, 0, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, 2, 159, 158, 6241], 'euler83': [1, 0, 154, 0, 6889], 'euler89': [1, 0, 70, 0, 7921], 'euler97': [1, -10, 219, -970, 9409], 'euler_factors': [[1, 0, 4, 0, 4], [1, 0, 0, 0, 0], [1, 0, -2, 0, 25], [1, 2, 15, 14, 49], [1, 0, 10, 0, 121], [1, 2, 27, 26, 169], [1, 0, 22, 0, 289], [1, -10, 63, -190, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, -2, 1, 0, 0], [1, -10, 99, -370, 1369], [1, 0, 70, 0, 1681], [1, -16, 150, -688, 1849], [1, 0, -14, 0, 2209], [1, 0, 94, 0, 2809], [1, 0, -74, 0, 3481], [1, -10, 147, -610, 3721], [1, -10, 159, -670, 4489], [1, 0, 94, 0, 5041], [1, -22, 267, -1606, 5329], [1, 2, 159, 158, 6241], [1, 0, 154, 0, 6889], [1, 0, 70, 0, 7921], [1, -10, 219, -970, 9409]], 'index': 4, 'instance_types': ['BMF', 'ECNF', 'CMF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/77841.2/a', 'EllipticCurve/2.0.3.1/77841.2/a', 'ModularForm/GL2/Q/holomorphic/837/2/a/c'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-837e2-1.1-c1e2-0-4', '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': 0, 'prelabel': '4-837e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5852424739627753, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 812304698749287168, 'z1': {'__RealLiteral__': 0, 'data': '0.63929328049410835138045782888', 'prec': 103}}
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lfunc_instances • Show schema
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id: 15723513
{'Lhash': '810400510740230270880482549719,1453118069519800469351803898446', 'Lhash_array': ['810400510740230270880482549719', '1453118069519800469351803898446'], 'factors': ['2-837-1.1-c1-0-2', '2-837-1.1-c1-0-10'], 'label': '4-837e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/837/2/a/c'}
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id: 9800625
{'Lhash': '_810400510740230270880482549719', 'Lhash_array': ['_810400510740230270880482549719'], 'factors': ['4-837e2-1.1-c1e2-0-4'], 'label': '4-837e2-1.1-c1e2-0-4', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/77841.2/a'}
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id: 9799749
{'Lhash': '_810400510740230270880482549719', 'Lhash_array': ['_810400510740230270880482549719'], 'factors': ['4-837e2-1.1-c1e2-0-4'], 'label': '4-837e2-1.1-c1e2-0-4', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/77841.2/a'}