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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1411133521748658178874097088948', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.0, 0], 'a5': [0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.72625940905021, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 3]], [5, [1, -1]]], 'bad_primes': [2, 3, 5], 'central_character': '576000.1', 'coefficient_field': '1.1.1.1', 'conductor': 576000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 2, 3], [1, -1], [1, 0, -6, 0, 49], [1, 0, -10, 0, 121], [1, 0, -2, 0, 169], [1, 0, -10, 0, 289], [1, 0, 38, 0, 361], [1, 4, 34, 92, 529], [1, -4, 62, -116, 841], [1, 0, 14, 0, 961], [1, 0, -50, 0, 1369], [1, 0, 30, 0, 1681], [1, 4, 74, 172, 1849], [1, -4, 98, -188, 2209], [1, 0, 102, 0, 2809], [1, 0, 70, 0, 3481], [1, 0, 6, 0, 3721], [1, 12, 154, 804, 4489], [1, 16, 190, 1136, 5041], [1, 16, 174, 1168, 5329], [1, 0, -34, 0, 6241], [1, 0, 2, 0, 6889], [1, 0, 62, 0, 7921], [1, 16, 222, 1552, 9409], [1, -4, -50, -404, 10201], [1, 0, 170, 0, 10609], [1, 0, -126, 0, 11449], [1, 0, -10, 0, 11881], [1, 0, -106, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 24, 'label': '4-576000-1.1-c1e2-0-24', 'load_key': 'Costa', '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, 'origin': 'EllipticCurve/2.2.24.1/1000.2/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.048828125', 'prec': 37}, 'plot_values': [-6.79740466828967e-75, 0.13851636779625937, 0.27634685649602403, 0.4127246392299414, 0.5467253256773805, 0.6771989536815088, 0.8027147407900752, 0.9215225434385004, 1.031534661360994, 1.1303311828859528, 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1.8211216662645517, 1.8594400668064825, 1.627935013480954], 'positive_zeros': ['1.11318806735436084084095379141838', '1.87248077085664228992419693976709', '2.73950895106643991740122890989921', '3.17306312543156255737439470128770', '4.16977632743161296090171115807804', '4.39400603172446289891117063197285', '5.06358661139685213346031755583515', '5.50821594029589561372147870725551', '5.96339077192636481068384282336368', '6.21392083232497598786968397514710', '6.72952739658898814292199143838409', '7.31810520828115958082961904738245', '7.54776785489074273760473316510417', '8.340550675439908834607126306333183'], 'prelabel': '4-576000-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4617512910967707, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 76414325590159301, 'z1': {'__RealLiteral__': 0, 'data': '1.11318806735436084084095379141838', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.87248077085664228992419693976709', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.73950895106643991740122890989921', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.72625940905021, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 576000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 1, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 1, 0, 4, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 8, 0, -16, 0, -16, 0, -2, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, 0, -2, 0, 169], 'euler17': [1, 0, -10, 0, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 4, 34, 92, 529], 'euler29': [1, -4, 62, -116, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 0, 14, 0, 961], 'euler37': [1, 0, -50, 0, 1369], 'euler41': [1, 0, 30, 0, 1681], 'euler43': [1, 4, 74, 172, 1849], 'euler47': [1, -4, 98, -188, 2209], 'euler5': [1, -1, 0, 0, 0], 'euler53': [1, 0, 102, 0, 2809], 'euler59': [1, 0, 70, 0, 3481], 'euler61': [1, 0, 6, 0, 3721], 'euler67': [1, 12, 154, 804, 4489], 'euler7': [1, 0, -6, 0, 49], 'euler71': [1, 16, 190, 1136, 5041], 'euler73': [1, 16, 174, 1168, 5329], 'euler79': [1, 0, -34, 0, 6241], 'euler83': [1, 0, 2, 0, 6889], 'euler89': [1, 0, 62, 0, 7921], 'euler97': [1, 16, 222, 1552, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 3, 0, 0], [1, -1, 0, 0, 0], [1, 0, -6, 0, 49], [1, 0, -10, 0, 121], [1, 0, -2, 0, 169], [1, 0, -10, 0, 289], [1, 0, 38, 0, 361], [1, 4, 34, 92, 529], [1, -4, 62, -116, 841], [1, 0, 14, 0, 961], [1, 0, -50, 0, 1369], [1, 0, 30, 0, 1681], [1, 4, 74, 172, 1849], [1, -4, 98, -188, 2209], [1, 0, 102, 0, 2809], [1, 0, 70, 0, 3481], [1, 0, 6, 0, 3721], [1, 12, 154, 804, 4489], [1, 16, 190, 1136, 5041], [1, 16, 174, 1168, 5329], [1, 0, -34, 0, 6241], [1, 0, 2, 0, 6889], [1, 0, 62, 0, 7921], [1, 16, 222, 1552, 9409]], 'index': 24, 'instance_types': ['HMF', 'ECNF', 'ECNF', 'HMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-1000.1-o', 'EllipticCurve/2.2.24.1/1000.1/o', 'EllipticCurve/2.2.24.1/1000.2/o', 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-1000.2-o'], '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': '4-576000-1.1-c1e2-0-24', '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': '4-576000-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4617512910967707, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 76414325590159301, 'z1': {'__RealLiteral__': 0, 'data': '1.11318806735436084084095379141838', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9511303
{'Lhash': '1411133521748658178874097088948', 'Lhash_array': ['1411133521748658178874097088948'], 'label': '4-576000-1.1-c1e2-0-24', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-1000.2-o'}
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id: 9510766
{'Lhash': '1411133521748658178874097088948', 'Lhash_array': ['1411133521748658178874097088948'], 'label': '4-576000-1.1-c1e2-0-24', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/1000.2/o'}
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id: 9510556
{'Lhash': '1411133521748658178874097088948', 'Lhash_array': ['1411133521748658178874097088948'], 'label': '4-576000-1.1-c1e2-0-24', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/1000.1/o'}
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id: 9510551
{'Lhash': '1411133521748658178874097088948', 'Lhash_array': ['1411133521748658178874097088948'], 'label': '4-576000-1.1-c1e2-0-24', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-1000.1-o'}