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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': -4, 'Lhash': '2162376935267360956708659190931', 'a10': [0.316227766016838, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [-1.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.01009965548294, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 0, 2]], [89, [1, 1, 89]]], 'bad_primes': [2, 89], 'central_character': '15842.1', 'coefficient_field': '1.1.1.1', 'conductor': 15842, 'conductor_radical': 178, 'degree': 4, 'euler_factors': [[1, -1, 0, 2], [1, 0, 4, 0, 9], [1, -1, 4, -5, 25], [1, 0, 1, 0, 49], [1, -5, 22, -55, 121], [1, 0, 14, 0, 169], [1, -9, 48, -153, 289], [1, 0, 2, 0, 361], [1, 0, 29, 0, 529], [1, 0, -8, 0, 841], [1, 0, 18, 0, 961], [1, 0, 16, 0, 1369], [1, 0, 63, 0, 1681], [1, 0, -36, 0, 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1.5773446436829555, 2.899472943292235, 3.9778691542254228, 4.673433206790658, 4.895577798638764, 4.617240005638469, 3.8803236674110213, 2.7903832093989585, 1.5011240508581396], 'positive_zeros': ['1.70581462658404761171497866648132', '3.13163524465221465375217618832785', '3.34228072249885749569002547896061', '4.43830843924901719623986028675105', '5.33491583183369725841938108131029', '5.86249394904599278160568029052979', '6.24616920554874021767754263929187', '6.87867502477427305358091343102474', '7.75456583606896705833766076179918', '8.296741473353169824858822633472251', '8.945836535217341721093195996342689', '9.572558499423294552564299053641330', '9.809164145641349077396594833303816', '10.68385138209229190917850337843566', '11.36256181879199372961864697868359'], 'prelabel': '4-15842-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.0025154070362237, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 644719490429149523, 'z1': {'__RealLiteral__': 0, 'data': '1.70581462658404761171497866648132', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.13163524465221465375217618832785', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.34228072249885749569002547896061', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.01009965548294, 'bad_primes': [2, 89], 'central_character': '1.1', 'conductor': 15842, 'conductor_radical': 178, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 1, 0, 0, -1, -4, 1, 5, 0, 0, 0, 0, -3, 9, -4, 0, 1, 0, 5, 0, 0, -3, 0, 0, 0, 0, 0, 0, -5, 0, 9, 0, -4, 0, 0, 0, -1, 0, 0, 0, 5, -4, 0, -14, 0, -1, -3, 0, 0, -17, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 6, 9, 0, 0, -16, 4, -2, 0, 0, 0, 0, 0, -3, -3, 7, 0, 0, 0, 9, 0, 0, -5, -1, -4, 0, 0, 0, -14, 0, 0, -4, -1, -20, -3], 'euler11': [1, -5, 22, -55, 121], 'euler13': [1, 0, 14, 0, 169], 'euler17': [1, -9, 48, -153, 289], 'euler19': [1, 0, 2, 0, 361], 'euler2': [1, -1, 0, 2, 0], 'euler23': [1, 0, 29, 0, 529], 'euler29': [1, 0, -8, 0, 841], 'euler3': [1, 0, 4, 0, 9], 'euler31': [1, 0, 18, 0, 961], 'euler37': [1, 0, 16, 0, 1369], 'euler41': [1, 0, 63, 0, 1681], 'euler43': [1, 0, -36, 0, 1849], 'euler47': [1, 14, 143, 658, 2209], 'euler5': [1, -1, 4, -5, 25], 'euler53': [1, 17, 172, 901, 2809], 'euler59': [1, 0, -48, 0, 3481], 'euler61': [1, 0, 68, 0, 3721], 'euler67': [1, -6, 118, -402, 4489], 'euler7': [1, 0, 1, 0, 49], 'euler71': [1, 16, 181, 1136, 5041], 'euler73': [1, 2, 122, 146, 5329], 'euler79': [1, 3, 154, 237, 6241], 'euler83': [1, 0, -146, 0, 6889], 'euler89': [1, 1, 89, 0, 0], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, -1, 0, 2, 0], [1, 0, 4, 0, 9], [1, -1, 4, -5, 25], [1, 0, 1, 0, 49], [1, -5, 22, -55, 121], [1, 0, 14, 0, 169], [1, -9, 48, -153, 289], [1, 0, 2, 0, 361], [1, 0, 29, 0, 529], [1, 0, -8, 0, 841], [1, 0, 18, 0, 961], [1, 0, 16, 0, 1369], [1, 0, 63, 0, 1681], [1, 0, -36, 0, 1849], [1, 14, 143, 658, 2209], [1, 17, 172, 901, 2809], [1, 0, -48, 0, 3481], [1, 0, 68, 0, 3721], [1, -6, 118, -402, 4489], [1, 16, 181, 1136, 5041], [1, 2, 122, 146, 5329], [1, 3, 154, 237, 6241], [1, 0, -146, 0, 6889], [1, 1, 89, 0, 0], [1, 4, 198, 388, 9409]], 'index': 0, 'instance_types': ['ECNF', 'HMF', 'ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.89.1/2.2/a', 'ModularForm/GL2/TotallyReal/2.2.89.1/holomorphic/2.2.89.1-2.2-a', 'EllipticCurve/2.2.89.1/2.1/a', 'ModularForm/GL2/TotallyReal/2.2.89.1/holomorphic/2.2.89.1-2.1-a'], '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': '4-15842-1.1-c1e2-0-0', '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': '4-15842-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.0025154070362237, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 644719490429149523, 'z1': {'__RealLiteral__': 0, 'data': '1.70581462658404761171497866648132', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9472026
{'Lhash': '2162376935267360956708659190931', 'Lhash_array': ['2162376935267360956708659190931'], 'label': '4-15842-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.89.1/holomorphic/2.2.89.1-2.1-a'}
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id: 9472025
{'Lhash': '2162376935267360956708659190931', 'Lhash_array': ['2162376935267360956708659190931'], 'label': '4-15842-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.89.1/2.1/a'}
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id: 9471878
{'Lhash': '2162376935267360956708659190931', 'Lhash_array': ['2162376935267360956708659190931'], 'label': '4-15842-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.89.1/holomorphic/2.2.89.1-2.2-a'}
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id: 9471766
{'Lhash': '2162376935267360956708659190931', 'Lhash_array': ['2162376935267360956708659190931'], 'label': '4-15842-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.89.1/2.2/a'}