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lfunc_lfunctions • Show schema
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{'Lhash': '3180625551095116630929897876110,5743903882919995551462519500434', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.09698027875202321, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 1]], [13, [1, 2, 13]]], 'bad_primes': [3, 13], 'central_character': '39.1', 'coefficient_field': '1.1.1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 4], [1, 2, 1], [1, 0, -10, 0, 25], [1, 0, -2, 0, 49], [1, 0, -10, 0, 121], [1, 2, 13], [1, 12, 70, 204, 289], [1, 0, -26, 0, 361], [1, 0, 46, 0, 529], [1, -12, 94, -348, 841], [1, 0, -50, 0, 961], [1, 0, -26, 0, 1369], [1, 0, -34, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, -82, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, -10, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -26, 0, 4489], [1, 0, -130, 0, 5041], [1, 0, -146, 0, 5329], [1, 16, 222, 1264, 6241], [1, 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['2.50907115140597324194211607824721', '4.53114121658275230059828339895009', '4.86905381270888678414367702714244', '6.27213339115059087211963100444849', '6.74370882529777620950526970910339', '7.17583948104702118314526429719415', '8.644174139697889043440842449786057', '8.940367594292810735571675595474928', '10.21653240500991125494313664342996', '10.53459028746773639400487486073471', '11.32665602148099343374542466664582', '11.58516389668836280292342537270103', '12.34089512118979564148306677207497', '13.00091491120810677917759627525562', '13.46495961562743261746007621117813', '14.26255209441121924621344692766351', '15.10589552252558216865316324166816', '15.66671800979046012428842867774483', '15.86429046282199755109551449657059', '16.68934332216539481158586929182233'], 'prelabel': '4-39e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5580471018498292, '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': 1490356237652503274, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.50907115140597324194211607825', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.53114121658275230059828339895', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.86905381270888678414367702714', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.09698027875202321, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 1, 0, 0, 0, 0, 3, 0, 0, -2, -2, 0, 0, -3, -12, 0, 0, 0, 0, 0, 0, 0, 10, 0, -4, 0, 12, 0, 0, 0, 0, 0, 0, 3, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, 0, 6, 2, 0, 24, -2, 12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -7, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, -16, 0, 5, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, 2, 13, 0, 0], 'euler17': [1, 12, 70, 204, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, -1, 0, 4], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 0, -50, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 0, -34, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, -82, 0, 2209], 'euler5': [1, 0, -10, 0, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, -10, 0, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, -26, 0, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, -130, 0, 5041], 'euler73': [1, 0, -146, 0, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, 0, -154, 0, 6889], 'euler89': [1, 0, -130, 0, 7921], 'euler97': [1, 0, -2, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 4], [1, 2, 1, 0, 0], [1, 0, -10, 0, 25], [1, 0, -2, 0, 49], [1, 0, -10, 0, 121], [1, 2, 13, 0, 0], [1, 12, 70, 204, 289], [1, 0, -26, 0, 361], [1, 0, 46, 0, 529], [1, -12, 94, -348, 841], [1, 0, -50, 0, 961], [1, 0, -26, 0, 1369], [1, 0, -34, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, -82, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, -10, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -26, 0, 4489], [1, 0, -130, 0, 5041], [1, 0, -146, 0, 5329], [1, 16, 222, 1264, 6241], [1, 0, -154, 0, 6889], [1, 0, -130, 0, 7921], [1, 0, -2, 0, 9409]], 'index': 1, 'instance_types': ['ECNF', 'HMF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.13.1/9.1/a', 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-9.1-a', 'ModularForm/GL2/Q/holomorphic/39/2/b/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '4-39e2-1.1-c1e2-0-1', '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': '4-39e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5580471018498292, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1490356237652503274, 'z1': {'__RealLiteral__': 0, 'data': '2.50907115140597324194211607825', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9955913
{'Lhash': '3180625551095116630929897876110,5743903882919995551462519500434', 'Lhash_array': ['3180625551095116630929897876110', '5743903882919995551462519500434'], 'factors': ['2-39-13.12-c1-0-0', '2-39-13.12-c1-0-1'], 'label': '4-39e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/39/2/b/a'}
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id: 9530854
{'Lhash': '_3180625551095116630929897876110', 'Lhash_array': ['_3180625551095116630929897876110'], 'factors': ['4-39e2-1.1-c1e2-0-1'], 'label': '4-39e2-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-9.1-a'}
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id: 9530238
{'Lhash': '_3180625551095116630929897876110', 'Lhash_array': ['_3180625551095116630929897876110'], 'factors': ['4-39e2-1.1-c1e2-0-1'], 'label': '4-39e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/9.1/a'}