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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 1, 'A9': -6, 'Lhash': '1412392933954114716,2155445548887636735', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [-2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.388887119168594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [7, [1, 0, -1]], [11, [1, 2, 1]]], 'bad_primes': [2, 7, 11], 'central_character': '758912.1', 'coefficient_field': '1.1.1.1', 'conductor': 758912, 'conductor_radical': 154, 'degree': 4, 'euler_factors': [[1, -1], [1, 0, 6, 0, 9], [1, 0, 6, 0, 25], [1, 0, -1], [1, 2, 1], [1, 0, 22, 0, 169], [1, -4, 38, -68, 289], [1, 0, 38, 0, 361], [1, 0, -18, 0, 529], [1, 0, 54, 0, 841], [1, 0, -2, 0, 961], [1, 0, 70, 0, 1369], [1, -20, 182, -820, 1681], [1, -8, 102, -344, 1849], [1, 0, 30, 0, 2209], [1, 0, 70, 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0.30785415831386737, -0.1691237496114191, -0.5223574444408169, -0.7071256648961357, -0.7065982285351036], 'positive_zeros': ['1.21399850656019313589842252972977', '2.30984363521644281586554494695849', '2.72854508523448958533903853213924', '3.08172507755908328232950357792725', '3.78476385235783926950251020605742', '4.30916127979318708251021123276503', '4.82761578982425423372007838462338', '5.60617960823028323278478834582860', '5.69715804540238922198121355930202', '6.02643591301064267650899026350154', '6.42169131751856764457567127082322', '7.52779608421941576346985997734362', '7.58187479426412561326624344047563', '7.72024110024881070821541339163291'], 'prelabel': '4-758912-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6374631986750883, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1261995473628057500, 'z1': {'__RealLiteral__': 0, 'data': '1.21399850656019313589842252972977', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.30984363521644281586554494695849', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.72854508523448958533903853213924', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.388887119168594, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 758912, 'conductor_radical': 154, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 0, 1, -6, 0, -2, 0, 0, 0, 0, 1, 4, -6, 0, 0, 0, -2, 0, 0, -6, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, -6, 0, 0, 0, 0, 20, 0, 8, -2, 0, 0, 0, 0, 1, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -24, 4, 0, 0, 0, -6, -28, 0, 0, 0, 0, 0, 0, 0, 27, 20, 0, 0, 0, 8, 0, -2, -12, 0, 0, 0, 0, 0, 0, 0, 20, 1, 12, -6], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, -18, 0, 529], 'euler29': [1, 0, 54, 0, 841], 'euler3': [1, 0, 6, 0, 9], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, -20, 182, -820, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 0, 22, 0, 3721], 'euler67': [1, 24, 278, 1608, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, -114, 0, 5041], 'euler73': [1, 28, 342, 2044, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, -20, 294, -1940, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 0, 6, 0, 9], [1, 0, 6, 0, 25], [1, 0, -1, 0, 0], [1, 2, 1, 0, 0], [1, 0, 22, 0, 169], [1, -4, 38, -68, 289], [1, 0, 38, 0, 361], [1, 0, -18, 0, 529], [1, 0, 54, 0, 841], [1, 0, -2, 0, 961], [1, 0, 70, 0, 1369], [1, -20, 182, -820, 1681], [1, -8, 102, -344, 1849], [1, 0, 30, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, 118, 0, 3481], [1, 0, 22, 0, 3721], [1, 24, 278, 1608, 4489], [1, 0, -114, 0, 5041], [1, 28, 342, 2044, 5329], [1, 0, 158, 0, 6241], [1, 0, 166, 0, 6889], [1, 12, 214, 1068, 7921], [1, -20, 294, -1940, 9409]], 'index': 43, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/11858.2/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/11858.2/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': '4-758912-1.1-c1e2-0-43', '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': '4-758912-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6374631986750883, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1261995473628057500, 'z1': {'__RealLiteral__': 0, 'data': '1.21399850656019313589842252972977', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9816749
{'Lhash': '1412392933954114716,2155445548887636735', 'Lhash_array': ['1412392933954114716', '2155445548887636735'], 'label': '4-758912-1.1-c1e2-0-43', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/11858.2/c'}
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id: 9816590
{'Lhash': '1412392933954114716,2155445548887636735', 'Lhash_array': ['1412392933954114716', '2155445548887636735'], 'label': '4-758912-1.1-c1e2-0-43', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/11858.2/c'}