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lfunc_lfunctions • Show schema
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{'Lhash': '1423749530724804239665965517827', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 1.882592860202197], 'a6': [0, 0], 'a7': [10.972555291255997, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.542294840729653, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '864.161', 'coefficient_field': 'CDF', 'conductor': 864, 'conductor_radical': 6, 'conjugate': '1311795706349598865369375469948', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.882592860202197], [-25.0, 0]], [[1.0, 0], [-10.972555291255997, 0], [49.0, 0]], [[1.0, 0], [0, -0.1715728752538099], [-121.0, 0]], [[1.0, 0], [-6.48528137423857, 0], [169.0, 0]], [[1.0, 0], [0, 27.269887293161403], [-289.0, 0]], [[1.0, 0], [-5.324776710649407, 0], [361.0, 0]], [[1.0, 0], [0, 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'4.61857266990813032871486211055169', '5.48885147796703334697955546588848', '6.41639792472371661823336492738115', '7.71956808777231687534372253503317', '8.216056693317977913035395139319717', '8.943032977860955856760532365780674', '10.01738907241699880327335986993669'], 'prelabel': '2-864-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8520402760828, 'root_angle': 0.0, 'root_number': '1', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12314034361555983269032075098', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.10052713670322295955479425390', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73555773505185841239365025369', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.542294840729653, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 864, 'conductor_radical': 6, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/864/3/e/e/161/6'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '2-864-3.2-c2-0-19', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-864-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8520402760828, 'root_angle': 0.0, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12314034361555983269032075098', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1423749530724804239665965517827', 'Lhash_array': ['1423749530724804239665965517827'], 'label': '2-864-3.2-c2-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/864/3/e/e/161/6'}