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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 1, 'Lhash': '416167228757762816,2255635231966396014', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792515, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 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, -2, 3]], [7, [1, -2, 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, -2, 3], [1, 0, 10, 0, 25], [1, -2, 1], [1, 0, 6, 0, 121], [1, 8, 42, 104, 169], [1, 0, 30, 0, 289], [1, -12, 74, -228, 361], [1, 0, -18, 0, 529], [1, 0, 54, 0, 841], [1, -8, 78, -248, 961], [1, -20, 174, -740, 1369], [1, 0, -18, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, 78, 0, 2209], 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0.8024023115134375, 1.658147862056414, 2.7433981237687006, 3.954578608362705, 5.15819006684143, 6.207408893845835, 6.961224343990017, 7.3034880004384135], 'positive_zeros': ['0.867770609357001154731944493797039', '2.00516068697428410265218115685489', '2.38160133368819946421648201020586', '3.09009811816266066443914661488430', '3.39651452170084757716747861998631', '4.38921941756740989472338293857274', '4.62285613804853643208241606945662', '5.20704742703837539203927825544746', '5.72643285643591914021095909045367', '6.19321040018157050389604631781926', '7.03619200467257105345639081242013', '7.53632864653844024945923131797675', '7.64230674264070832489473958475569', '8.142737265603496815088661734935513', '8.247827016681358338699106327510077'], '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': 365959451510464879, 'z1': {'__RealLiteral__': 0, 'data': '0.867770609357001154731944493797039', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.00516068697428410265218115685489', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.38160133368819946421648201020586', '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, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, -8, 0, 0, 0, 0, 0, 12, 0, 4, 0, 0, 0, -10, 0, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 20, 0, -16, 0, 0, 0, -8, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, -16, 0, 2, 0, 0, 0, 16, 0, 0, 0, 0, 0, -12, 0, -20, 0, 0, 0, 32, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 16, 0, 0, 0, -4, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 8, 42, 104, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, -12, 74, -228, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -18, 0, 529], 'euler29': [1, 0, 54, 0, 841], 'euler3': [1, -2, 3, 0, 0], 'euler31': [1, -8, 78, -248, 961], 'euler37': [1, -20, 174, -740, 1369], 'euler41': [1, 0, -18, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, 78, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, 102, 0, 2809], 'euler59': [1, 0, 18, 0, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, -16, 198, -1072, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, -32, 414, -2528, 6241], 'euler83': [1, 0, 162, 0, 6889], 'euler89': [1, 0, -146, 0, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 3, 0, 0], [1, 0, 10, 0, 25], [1, -2, 1, 0, 0], [1, 0, 6, 0, 121], [1, 8, 42, 104, 169], [1, 0, 30, 0, 289], [1, -12, 74, -228, 361], [1, 0, -18, 0, 529], [1, 0, 54, 0, 841], [1, -8, 78, -248, 961], [1, -20, 174, -740, 1369], [1, 0, -18, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, 78, 0, 2209], [1, 0, 102, 0, 2809], [1, 0, 18, 0, 3481], [1, 16, 186, 976, 3721], [1, -16, 198, -1072, 4489], [1, 0, 142, 0, 5041], [1, 12, 182, 876, 5329], [1, -32, 414, -2528, 6241], [1, 0, 162, 0, 6889], [1, 0, -146, 0, 7921], [1, 4, 198, 388, 9409]], 'index': 28, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/50176.2/l', 'EllipticCurve/2.0.3.1/50176.2/l'], '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-c1e2-0-28', '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': '4-672e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 365959451510464879, 'z1': {'__RealLiteral__': 0, 'data': '0.867770609357001154731944493797039', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9776186
{'Lhash': '416167228757762816,2255635231966396014', 'Lhash_array': ['416167228757762816', '2255635231966396014'], 'factors': ['2-2016-1.1-c1-0-6', '2-224-1.1-c1-0-2'], 'label': '4-672e2-1.1-c1e2-0-28', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/50176.2/l'}
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id: 9775957
{'Lhash': '416167228757762816,2255635231966396014', 'Lhash_array': ['416167228757762816', '2255635231966396014'], 'factors': ['2-2016-1.1-c1-0-6', '2-224-1.1-c1-0-2'], 'label': '4-672e2-1.1-c1e2-0-28', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/50176.2/l'}