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lfunc_lfunctions • Show schema
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{'Lhash': '1340983181895594265382446367884,3529273562380180225651125552466', 'a10': -8, 'a2': 2, 'a3': 0, 'a4': 2, 'a5': -4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.3102346112010315, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 2]], [5, [1, 4, 5]], [13, [1, -4, 13]]], 'bad_primes': [2, 5, 13], 'central_character': '260.1', 'coefficient_field': '1.1.1.1', 'conductor': 67600, 'conductor_radical': 130, 'degree': 4, 'euler_factors': [[1, -2, 2], [1, 0, 0, 0, 9], [1, 4, 5], [1, 0, 0, 0, 49], [1, 0, 22, 0, 121], [1, -4, 13], [1, -10, 50, -170, 289], [1, 0, -38, 0, 361], [1, 0, 0, 0, 529], [1, 0, -42, 0, 841], [1, 0, 62, 0, 961], [1, -14, 98, -518, 1369], [1, 0, 18, 0, 1681], [1, 0, 0, 0, 1849], [1, 0, 0, 0, 2209], [1, -10, 50, -530, 2809], [1, 0, -118, 0, 3481], [1, 24, 266, 1464, 3721], [1, 0, 0, 0, 4489], [1, 0, 142, 0, 5041], [1, -22, 242, -1606, 5329], [1, 0, 158, 0, 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'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4408714212424685, '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': 706228385348195489, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05784920675631122175991650457', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78410593719181404868377758581', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27607928396725695438596259054', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.3102346112010315, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 67600, 'conductor_radical': 130, 'degree': 4, 'dirichlet_coefficients': [1, 2, 0, 2, -4, 0, 0, 0, 0, -8, 0, 0, 4, 0, 0, -4, 10, 0, 0, -8, 0, 0, 0, 0, 11, 8, 0, 0, 0, 0, 0, -8, 0, 20, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 8, 10, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -8, -16, 0, 0, 20, 0, 0, 0, 0, 22, 28, 0, 0, 0, 0, 0, 16, -9, 0, 0, 0, -40, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 22], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, -4, 13, 0, 0], 'euler17': [1, -10, 50, -170, 289], 'euler19': [1, 0, -38, 0, 361], 'euler2': [1, -2, 2, 0, 0], 'euler23': [1, 0, 0, 0, 529], 'euler29': [1, 0, -42, 0, 841], 'euler3': [1, 0, 0, 0, 9], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, -14, 98, -518, 1369], 'euler41': [1, 0, 18, 0, 1681], 'euler43': [1, 0, 0, 0, 1849], 'euler47': [1, 0, 0, 0, 2209], 'euler5': [1, 4, 5, 0, 0], 'euler53': [1, -10, 50, -530, 2809], 'euler59': [1, 0, -118, 0, 3481], 'euler61': [1, 24, 266, 1464, 3721], 'euler67': [1, 0, 0, 0, 4489], 'euler7': [1, 0, 0, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -22, 242, -1606, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 0, 0, 6889], 'euler89': [1, -20, 278, -1780, 7921], 'euler97': [1, -26, 338, -2522, 9409], 'euler_factors': [[1, -2, 2, 0, 0], [1, 0, 0, 0, 9], [1, 4, 5, 0, 0], [1, 0, 0, 0, 49], [1, 0, 22, 0, 121], [1, -4, 13, 0, 0], [1, -10, 50, -170, 289], [1, 0, -38, 0, 361], [1, 0, 0, 0, 529], [1, 0, -42, 0, 841], [1, 0, 62, 0, 961], [1, -14, 98, -518, 1369], [1, 0, 18, 0, 1681], [1, 0, 0, 0, 1849], [1, 0, 0, 0, 2209], [1, -10, 50, -530, 2809], [1, 0, -118, 0, 3481], [1, 24, 266, 1464, 3721], [1, 0, 0, 0, 4489], [1, 0, 142, 0, 5041], [1, -22, 242, -1606, 5329], [1, 0, 158, 0, 6241], [1, 0, 0, 0, 6889], [1, -20, 278, -1780, 7921], [1, -26, 338, -2522, 9409]], 'index': 5, 'instance_types': ['ECNF', 'ECNF', 'CMF'], 'instance_urls': ['EllipticCurve/2.0.4.1/4225.3/CMb', 'EllipticCurve/2.0.4.1/4225.7/CMb', 'ModularForm/GL2/Q/holomorphic/260/2/p/b'], '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': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-260e2-1.1-c1e2-0-5', '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': '4-260e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 706228385348195489, 'z1': {'__RealLiteral__': 0, 'data': '1.05784920675631122175991650457', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10124049
{'Lhash': '1340983181895594265382446367884,3529273562380180225651125552466', 'Lhash_array': ['1340983181895594265382446367884', '3529273562380180225651125552466'], 'label': '4-260e2-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/p/b'}
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id: 9682013
{'Lhash': '_1340983181895594265382446367884', 'Lhash_array': ['_1340983181895594265382446367884'], 'label': '4-260e2-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/4225.7/CMb'}
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id: 9681667
{'Lhash': '_1340983181895594265382446367884', 'Lhash_array': ['_1340983181895594265382446367884'], 'label': '4-260e2-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/4225.3/CMb'}