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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': -4, 'A8': 0, 'A9': -2, 'Lhash': '203926327671425217,702150552534926687', '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': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.632278195957787, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 0, -1]]], 'bad_primes': [2, 5], 'central_character': '25600.1', 'coefficient_field': '1.1.1.1', 'conductor': 25600, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 0, 2, 0, 9], [1, 0, -1], [1, 4, 18, 28, 49], [1, 0, 22, 0, 121], [1, 0, 22, 0, 169], [1, 12, 70, 204, 289], [1, 0, 22, 0, 361], [1, 12, 82, 276, 529], [1, 0, 22, 0, 841], [1, -8, 78, -248, 961], [1, 0, 70, 0, 1369], [1, -12, 118, -492, 1681], [1, 0, -14, 0, 1849], [1, -12, 130, -564, 2209], [1, 0, 70, 0, 2809], [1, 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-0.653502687740227], 'positive_zeros': ['2.32736297473362010207341859713837', '2.76929890617261215013507568310634', '4.12250433368686324236236368170536', '4.13045861856120535222472022668035', '5.32703134203753576211066117066954', '6.26903409609752801893873868553040', '6.27087624192875571051851265257857', '6.87772159023272676690262517557743', '7.71273110823499542846308181543922', '8.404829898294941223649273971532204', '8.740293324354028093320034492248334', '9.511328653906225471558818278712108', '9.683565298540966130897522415203267', '10.35239107507603235483123434521475'], 'prelabel': '4-160e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.130312537460541, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 906076880206351904, 'z1': {'__RealLiteral__': 0, 'data': '2.32736297473362010207341859713837', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.76929890617261215013507568310634', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.12250433368686324236236368170536', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.632278195957787, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 25600, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -12, 0, 1, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 12, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 24, 0, 4, 0, 0, 0, 0, 0, -16, 0, -5, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 12, 70, 204, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 12, 82, 276, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, -8, 78, -248, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, 0, -14, 0, 1849], 'euler47': [1, -12, 130, -564, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, 0, 130, 0, 4489], 'euler7': [1, 4, 18, 28, 49], 'euler71': [1, -24, 286, -1704, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, 0, 130, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 2, 0, 9], [1, 0, -1, 0, 0], [1, 4, 18, 28, 49], [1, 0, 22, 0, 121], [1, 0, 22, 0, 169], [1, 12, 70, 204, 289], [1, 0, 22, 0, 361], [1, 12, 82, 276, 529], [1, 0, 22, 0, 841], [1, -8, 78, -248, 961], [1, 0, 70, 0, 1369], [1, -12, 118, -492, 1681], [1, 0, -14, 0, 1849], [1, -12, 130, -564, 2209], [1, 0, 70, 0, 2809], [1, 0, -26, 0, 3481], [1, 0, 118, 0, 3721], [1, 0, 130, 0, 4489], [1, -24, 286, -1704, 5041], [1, -4, 150, -292, 5329], [1, 16, 222, 1264, 6241], [1, 0, 130, 0, 6889], [1, 12, 214, 1068, 7921], [1, -4, 198, -388, 9409]], 'index': 20, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-400.1-a', 'EllipticCurve/2.2.8.1/400.1/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-160e2-1.1-c1e2-0-20', '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': '4-160e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.130312537460541, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 906076880206351904, 'z1': {'__RealLiteral__': 0, 'data': '2.32736297473362010207341859713837', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9561712
{'Lhash': '203926327671425217,702150552534926687', 'Lhash_array': ['203926327671425217', '702150552534926687'], 'label': '4-160e2-1.1-c1e2-0-20', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/400.1/a'}
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id: 9561548
{'Lhash': '203926327671425217,702150552534926687', 'Lhash_array': ['203926327671425217', '702150552534926687'], 'label': '4-160e2-1.1-c1e2-0-20', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-400.1-a'}