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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 3, 'A4': 1, 'A5': -5, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 6, 'Lhash': '1848677228270656187690228232341', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.7320508075688772, 0], 'a4': [0.5, 0], 'a5': [-2.23606797749979, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.928024889369617, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1, -3, 3]], [23, [1, 1]]], 'bad_primes': [2, 3, 23], 'central_character': '438012.1', 'coefficient_field': '1.1.1.1', 'conductor': 438012, 'conductor_radical': 138, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, -3, 3], [1, 5, 16, 25, 25], [1, 0, 2, 0, 49], [1, -3, 18, -33, 121], [1, 5, 32, 65, 169], [1, 5, 20, 85, 289], [1, 0, 16, 0, 361], [1, 1], [1, 0, -43, 0, 841], [1, 0, 13, 0, 961], [1, 0, -6, 0, 1369], [1, 0, -19, 0, 1681], [1, 0, -20, 0, 1849], [1, 0, -13, 0, 2209], [1, -9, 70, -477, 2809], 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-1.7803692734662626, -1.3380916519376707, -0.7284171470042355], 'positive_zeros': ['1.45834919175506091700881127846374', '2.39422209402380212499518383584259', '2.71439601719013453935072567898708', '3.48244561279109951222497999456047', '3.98366473405145155523022042405897', '4.12576730667187250286037975668089', '4.69254767982085797856428267091458', '5.38576310114245014632109805927795', '6.39745871931626390237679545426839', '6.81699084358108692939333787254474', '7.18397458027831275084905593908930', '7.66789484637525947828872256743135', '7.79693084013738314313676529375774', '8.281332014480734507686463382372257'], 'prelabel': '4-438012-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.2988469364547384, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1339400871586888764, 'z1': {'__RealLiteral__': 0, 'data': '1.45834919175506091700881127846374', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.39422209402380212499518383584259', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.71439601719013453935072567898708', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.928024889369617, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 438012, 'conductor_radical': 138, 'degree': 4, 'dirichlet_coefficients': [1, 0, 3, 1, -5, 0, 0, 0, 6, 0, 3, 3, -5, 0, -15, 1, -5, 0, 0, -5, 0, 0, -1, 0, 9, 0, 9, 0, 0, 0, 0, 0, 9, 0, 0, 6, 0, 0, -15, 0, 0, 0, 0, 3, -30, 0, 0, 3, -2, 0, -15, -5, 9, 0, -15, 0, 0, 0, 0, -15, 0, 0, 0, 1, 25, 0, 0, -5, -3, 0, 0, 0, -4, 0, 27, 0, 0, 0, 0, -5, 9, 0, -5, 0, 25, 0, 0, 0, -7, 0, 0, -1, 0, 0, 0, 0, 0, 0, 18, 9], 'euler11': [1, -3, 18, -33, 121], 'euler13': [1, 5, 32, 65, 169], 'euler17': [1, 5, 20, 85, 289], 'euler19': [1, 0, 16, 0, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 1, 0, 0, 0], 'euler29': [1, 0, -43, 0, 841], 'euler3': [1, -3, 3, 0, 0], 'euler31': [1, 0, 13, 0, 961], 'euler37': [1, 0, -6, 0, 1369], 'euler41': [1, 0, -19, 0, 1681], 'euler43': [1, 0, -20, 0, 1849], 'euler47': [1, 0, -13, 0, 2209], 'euler5': [1, 5, 16, 25, 25], 'euler53': [1, -9, 70, -477, 2809], 'euler59': [1, 0, 51, 0, 3481], 'euler61': [1, 0, -108, 0, 3721], 'euler67': [1, 0, 40, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 0, 73, 0, 5041], 'euler73': [1, 4, 134, 292, 5329], 'euler79': [1, 0, 92, 0, 6241], 'euler83': [1, 5, 130, 415, 6889], 'euler89': [1, 7, 58, 623, 7921], 'euler97': [1, 0, -40, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, -3, 3, 0, 0], [1, 5, 16, 25, 25], [1, 0, 2, 0, 49], [1, -3, 18, -33, 121], [1, 5, 32, 65, 169], [1, 5, 20, 85, 289], [1, 0, 16, 0, 361], [1, 1, 0, 0, 0], [1, 0, -43, 0, 841], [1, 0, 13, 0, 961], [1, 0, -6, 0, 1369], [1, 0, -19, 0, 1681], [1, 0, -20, 0, 1849], [1, 0, -13, 0, 2209], [1, -9, 70, -477, 2809], [1, 0, 51, 0, 3481], [1, 0, -108, 0, 3721], [1, 0, 40, 0, 4489], [1, 0, 73, 0, 5041], [1, 4, 134, 292, 5329], [1, 0, 92, 0, 6241], [1, 5, 130, 415, 6889], [1, 7, 58, 623, 7921], [1, 0, -40, 0, 9409]], 'index': 3, 'instance_types': ['ECNF', 'ECNF', 'HMF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.69.1/92.1/e', 'EllipticCurve/2.2.69.1/92.1/f', 'ModularForm/GL2/TotallyReal/2.2.69.1/holomorphic/2.2.69.1-92.1-f', 'ModularForm/GL2/TotallyReal/2.2.69.1/holomorphic/2.2.69.1-92.1-e'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-438012-1.1-c1e2-0-3', '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': 1, 'prelabel': '4-438012-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.2988469364547384, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1339400871586888764, 'z1': {'__RealLiteral__': 0, 'data': '1.45834919175506091700881127846374', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9949672
{'Lhash': '1848677228270656187690228232341', 'Lhash_array': ['1848677228270656187690228232341'], 'label': '4-438012-1.1-c1e2-0-3', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.69.1/holomorphic/2.2.69.1-92.1-e'}
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id: 9949625
{'Lhash': '1848677228270656187690228232341', 'Lhash_array': ['1848677228270656187690228232341'], 'label': '4-438012-1.1-c1e2-0-3', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.69.1/holomorphic/2.2.69.1-92.1-f'}
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id: 9949496
{'Lhash': '1848677228270656187690228232341', 'Lhash_array': ['1848677228270656187690228232341'], 'label': '4-438012-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.69.1/92.1/f'}
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id: 9949421
{'Lhash': '1848677228270656187690228232341', 'Lhash_array': ['1848677228270656187690228232341'], 'label': '4-438012-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.69.1/92.1/e'}