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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 2, 'Lhash': '1648707306886089994114441720488', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.394856848540837, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 1]]], 'bad_primes': [2, 7], 'central_character': '351232.1', 'coefficient_field': '1.1.1.1', 'conductor': 351232, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, -2, 0, 9], [1, 0, 2, 0, 25], [1, 1], [1, 4, 22, 44, 121], [1, 0, -22, 0, 169], [1, 0, -26, 0, 289], [1, 0, 14, 0, 361], [1, 4, 46, 92, 529], [1, 4, 46, 116, 841], [1, 0, -2, 0, 961], [1, -4, 14, -148, 1369], [1, 0, -58, 0, 1681], [1, 4, 86, 172, 1849], [1, 0, 46, 0, 2209], [1, -16, 166, -848, 2809], [1, 0, 46, 0, 3481], 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-1.1026000086834649, -1.5905266802844114], 'positive_zeros': ['1.30060073855465746315896674222105', '2.32663258305922464642586414326868', '2.61053992400072698195409707231070', '3.69118644749220381828651256017055', '3.86124321267387660659658432736837', '4.60272102909805621149187123784847', '5.27807460637331501227023990458566', '5.50672974501345464733363955727456', '6.18075263653323740699097579634754', '6.66604112797957105579502813908285', '7.10806684701676873333766594299779', '7.71100304878316816193426157991308', '7.954825299153241619049294570284269', '8.347573294462718521585261464100803'], 'prelabel': '4-351232-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.175389723875967, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1159286921233162959, 'z1': {'__RealLiteral__': 0, 'data': '1.30060073855465746315896674222105', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.32663258305922464642586414326868', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.61053992400072698195409707231070', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.394856848540837, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 351232, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -1, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -8, 0, 0, 0, 16, 0, 0, 0, 0, 0, 4, 0, 16, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0], 'euler11': [1, 4, 22, 44, 121], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, 0, -26, 0, 289], 'euler19': [1, 0, 14, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 4, 46, 92, 529], 'euler29': [1, 4, 46, 116, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, -4, 14, -148, 1369], 'euler41': [1, 0, -58, 0, 1681], 'euler43': [1, 4, 86, 172, 1849], 'euler47': [1, 0, 46, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, -16, 166, -848, 2809], 'euler59': [1, 0, 46, 0, 3481], 'euler61': [1, 0, 66, 0, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 1, 0, 0, 0], 'euler71': [1, -16, 142, -1136, 5041], 'euler73': [1, 0, 14, 0, 5329], 'euler79': [1, -16, 158, -1264, 6241], 'euler83': [1, 0, 110, 0, 6889], 'euler89': [1, 0, 78, 0, 7921], 'euler97': [1, 0, 22, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -2, 0, 9], [1, 0, 2, 0, 25], [1, 1, 0, 0, 0], [1, 4, 22, 44, 121], [1, 0, -22, 0, 169], [1, 0, -26, 0, 289], [1, 0, 14, 0, 361], [1, 4, 46, 92, 529], [1, 4, 46, 116, 841], [1, 0, -2, 0, 961], [1, -4, 14, -148, 1369], [1, 0, -58, 0, 1681], [1, 4, 86, 172, 1849], [1, 0, 46, 0, 2209], [1, -16, 166, -848, 2809], [1, 0, 46, 0, 3481], [1, 0, 66, 0, 3721], [1, 8, 150, 536, 4489], [1, -16, 142, -1136, 5041], [1, 0, 14, 0, 5329], [1, -16, 158, -1264, 6241], [1, 0, 110, 0, 6889], [1, 0, 78, 0, 7921], [1, 0, 22, 0, 9409]], 'index': 17, 'instance_types': ['BMF', 'ECNF', 'ECNF', 'BMF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/7168.5/c', 'EllipticCurve/2.0.7.1/7168.5/c', 'EllipticCurve/2.0.7.1/7168.7/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/7168.7/c'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, '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': '4-351232-1.1-c1e2-0-17', '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': '4-351232-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.175389723875967, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1159286921233162959, 'z1': {'__RealLiteral__': 0, 'data': '1.30060073855465746315896674222105', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9644510
{'Lhash': '1648707306886089994114441720488', 'Lhash_array': ['1648707306886089994114441720488'], 'label': '4-351232-1.1-c1e2-0-17', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/7168.7/c'}
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id: 9644376
{'Lhash': '1648707306886089994114441720488', 'Lhash_array': ['1648707306886089994114441720488'], 'label': '4-351232-1.1-c1e2-0-17', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/7168.7/c'}
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id: 9644276
{'Lhash': '1648707306886089994114441720488', 'Lhash_array': ['1648707306886089994114441720488'], 'label': '4-351232-1.1-c1e2-0-17', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/7168.5/c'}
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id: 9643782
{'Lhash': '1648707306886089994114441720488', 'Lhash_array': ['1648707306886089994114441720488'], 'label': '4-351232-1.1-c1e2-0-17', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/7168.5/c'}