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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': -2, 'A4': 1, 'A5': 0, 'A6': -2, 'A7': 0, 'A8': 1, 'A9': -3, 'Lhash': '1018315636625861018,1395852588552426471', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.8164965809277259, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.93524110486274, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [79, [1, 0, -1]]], 'bad_primes': [2, 79], 'central_character': '798848.1', 'coefficient_field': '1.1.1.1', 'conductor': 798848, 'conductor_radical': 158, 'degree': 4, 'euler_factors': [[1, -1], [1, 2, 7, 6, 9], [1, 0, 9, 0, 25], [1, 0, 5, 0, 49], [1, -4, 26, -44, 121], [1, 0, 25, 0, 169], [1, 4, 38, 68, 289], [1, 0, 38, 0, 361], [1, 0, 10, 0, 529], [1, 0, -42, 0, 841], [1, 0, 58, 0, 961], [1, 0, 70, 0, 1369], [1, -4, 86, -164, 1681], [1, -8, 102, -344, 1849], [1, 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-0.059521045598887136, 0.12068237190388545, 0.42591506518252364, 0.8455785467880855, 1.347748554592933], 'positive_zeros': ['1.06485830879781620251017267814401', '2.06983106012671431074676520674577', '2.60362431459742126306839445745997', '3.28231565080656425004767856192800', '4.08090613362146692342747948186706', '4.13073034219794476961344305330145', '4.95996492835075275892547561988136', '5.34006059048988750874758197538799', '5.84304457304729519676851015132475', '6.11586748167354289065343430906297', '6.48988831247255432885204202585695', '6.87081593462957102969561941234565', '7.50453196645377754362608030446459', '7.900574670861696081136405729725328'], 'prelabel': '4-798848-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6714963894350543, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 108325215964593538, 'z1': {'__RealLiteral__': 0, 'data': '1.06485830879781620251017267814401', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.06983106012671431074676520674577', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.60362431459742126306839445745997', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 50.93524110486274, 'bad_primes': [2, 79], 'central_character': '1.1', 'conductor': 798848, 'conductor_radical': 158, 'degree': 4, 'dirichlet_coefficients': [1, 1, -2, 1, 0, -2, 0, 1, -3, 0, 4, -2, 0, 0, 0, 1, -4, -3, 0, 0, 0, 4, 0, -2, -9, 0, 14, 0, 0, 0, 0, 1, -8, -4, 0, -3, 0, 0, 0, 0, 4, 0, 8, 4, 0, 0, 0, -2, -5, -9, 8, 0, 0, 14, 0, 0, 0, 0, 10, 0, 0, 0, 0, 1, 0, -8, 16, -4, 0, 0, 0, -3, -12, 0, 18, 0, 0, 0, 0, 0, -4, 4, -12, 0, 0, 8, 0, 4, -30, 0, 0, 0, 0, 0, 0, -2, 26, -5, -12, -9], 'euler11': [1, -4, 26, -44, 121], 'euler13': [1, 0, 25, 0, 169], 'euler17': [1, 4, 38, 68, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, 0, -42, 0, 841], 'euler3': [1, 2, 7, 6, 9], 'euler31': [1, 0, 58, 0, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 85, 0, 2209], 'euler5': [1, 0, 9, 0, 25], 'euler53': [1, 0, 90, 0, 2809], 'euler59': [1, -10, 143, -590, 3481], 'euler61': [1, 0, -22, 0, 3721], 'euler67': [1, -16, 198, -1072, 4489], 'euler7': [1, 0, 5, 0, 49], 'euler71': [1, 0, -27, 0, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, 0, -1, 0, 0], 'euler83': [1, 12, 202, 996, 6889], 'euler89': [1, 30, 403, 2670, 7921], 'euler97': [1, -26, 363, -2522, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 2, 7, 6, 9], [1, 0, 9, 0, 25], [1, 0, 5, 0, 49], [1, -4, 26, -44, 121], [1, 0, 25, 0, 169], [1, 4, 38, 68, 289], [1, 0, 38, 0, 361], [1, 0, 10, 0, 529], [1, 0, -42, 0, 841], [1, 0, 58, 0, 961], [1, 0, 70, 0, 1369], [1, -4, 86, -164, 1681], [1, -8, 102, -344, 1849], [1, 0, 85, 0, 2209], [1, 0, 90, 0, 2809], [1, -10, 143, -590, 3481], [1, 0, -22, 0, 3721], [1, -16, 198, -1072, 4489], [1, 0, -27, 0, 5041], [1, 12, 182, 876, 5329], [1, 0, -1, 0, 0], [1, 12, 202, 996, 6889], [1, 30, 403, 2670, 7921], [1, -26, 363, -2522, 9409]], 'index': 2, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/12482.1/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/12482.1/d'], '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': '4-798848-1.1-c1e2-0-2', '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': '4-798848-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6714963894350543, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 108325215964593538, 'z1': {'__RealLiteral__': 0, 'data': '1.06485830879781620251017267814401', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9818328
{'Lhash': '1018315636625861018,1395852588552426471', 'Lhash_array': ['1018315636625861018', '1395852588552426471'], 'label': '4-798848-1.1-c1e2-0-2', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/12482.1/d'}
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id: 9818218
{'Lhash': '1018315636625861018,1395852588552426471', 'Lhash_array': ['1018315636625861018', '1395852588552426471'], 'label': '4-798848-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/12482.1/d'}