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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -4, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '735138132754319977,772252924710736021', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-1.788854381999832, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.793387376695364, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]], [7, [1, 0, -1]]], 'bad_primes': [2, 3, 7], 'central_character': '451584.1', 'coefficient_field': '1.1.1.1', 'conductor': 451584, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, 4, 14, 20, 25], [1, 0, -1], [1, 0, 6, 0, 121], [1, 12, 62, 156, 169], [1, 4, 38, 68, 289], [1, 0, 22, 0, 361], [1, 0, 30, 0, 529], [1, 4, 62, 116, 841], [1, 0, -2, 0, 961], [1, 20, 174, 740, 1369], [1, 4, 86, 164, 1681], [1, 0, 22, 0, 1849], [1, 0, 94, 0, 2209], [1, 20, 206, 1060, 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0.8152412327117317], 'positive_zeros': ['1.90612310330978239121510440565516', '2.32898343675991772184414351496222', '3.27099070744047974080065927216430', '3.61417461907435968748262507790591', '4.44304823928958265064368122585693', '4.52969287471330622027217048773280', '5.33934975205348273864801508198948', '5.36857771747617040863256466681062', '6.77473142578757723529467681345810', '6.78044077445841975719051191645491', '7.20214522889553119059062687434598', '7.70276610727881458590413914622849', '8.034900753827151172045193415180565'], 'prelabel': '4-672e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1507391057465055998, 'z1': {'__RealLiteral__': 0, 'data': '1.90612310330978239121510440565516', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.32898343675991772184414351496222', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.27099070744047974080065927216430', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.793387376695364, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 451584, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -4, 0, 0, 0, 1, 0, 0, 0, -12, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 1, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 16, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 12, 62, 156, 169], 'euler17': [1, 4, 38, 68, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 20, 174, 740, 1369], 'euler41': [1, 4, 86, 164, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 4, 14, 20, 25], 'euler53': [1, 20, 206, 1060, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, -20, 222, -1220, 3721], 'euler67': [1, 0, 70, 0, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, -2, 0, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, 4, 14, 20, 25], [1, 0, -1, 0, 0], [1, 0, 6, 0, 121], [1, 12, 62, 156, 169], [1, 4, 38, 68, 289], [1, 0, 22, 0, 361], [1, 0, 30, 0, 529], [1, 4, 62, 116, 841], [1, 0, -2, 0, 961], [1, 20, 174, 740, 1369], [1, 4, 86, 164, 1681], [1, 0, 22, 0, 1849], [1, 0, 94, 0, 2209], [1, 20, 206, 1060, 2809], [1, 0, -26, 0, 3481], [1, -20, 222, -1220, 3721], [1, 0, 70, 0, 4489], [1, 0, -2, 0, 5041], [1, -4, 150, -292, 5329], [1, 0, 158, 0, 6241], [1, 0, 22, 0, 6889], [1, -12, 214, -1068, 7921], [1, -4, 198, -388, 9409]], 'index': 87, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.4.1/28224.1/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/28224.1/b'], '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': '4-672e2-1.1-c1e2-0-87', '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': 2, 'prelabel': '4-672e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1507391057465055998, 'z1': {'__RealLiteral__': 0, 'data': '1.90612310330978239121510440565516', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9663526
{'Lhash': '735138132754319977,772252924710736021', 'Lhash_array': ['735138132754319977', '772252924710736021'], 'label': '4-672e2-1.1-c1e2-0-87', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/28224.1/b'}
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id: 9663525
{'Lhash': '735138132754319977,772252924710736021', 'Lhash_array': ['735138132754319977', '772252924710736021'], 'label': '4-672e2-1.1-c1e2-0-87', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/28224.1/b'}