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lfunc_lfunctions • Show schema
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{'Lhash': '1885563330878576049854724300637', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.3662782858272624, 1.064557957875905], 'a4': [0.0, 0.0], 'a5': [1.830170883527768, 0.32270850607299506], 'a6': [0.0, 0.0], 'a7': [-0.44154521773503674, -0.5262130995285227], 'a8': [0.0, 0.0], 'a9': [0.7334327086461653, 2.9089648437009252], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.3662782858272624, -1.064557957875905]]]], 'bad_primes': [2, 3], 'central_character': '432.239', 'coefficient_field': 'CDF', 'conductor': 432, 'conductor_radical': 6, 'conjugate': '2400027706911762919476403443861', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.3662782858272624, -1.064557957875905]], [[1.0, 0], [-1.830170883527768, -0.32270850607299506], [4.698463103929542, 1.7101007166283437]], [[1.0, 0], [0.44154521773503674, 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-0.8373996981804813, 0.0017438200214835516], 'positive_zeros': ['1.48744719604841970377534954390663', '2.67657291448391039879149907849403', '3.93811116776297122424617237577545', '5.50479788393819084527326161566798', '6.41407637723119247003069568711439', '7.36407609628887263835308761539806', '8.428874302253583256117660150691276', '9.197730627202892989665314928138639', '9.891686924022204665038186922127623', '11.04505100854439910501362642012821'], 'prelabel': '2-432-108.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': -0.21977653372075442, 'root_number': '0.7709605500126644 - 0.6368829015793798*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.10988826686', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48744719604841970377534954391', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67657291448391039879149907849', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93811116776297122424617237578', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'bad_primes': [2, 3], 'central_character': '108.23', 'conductor': 432, 'conductor_radical': 6, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/2/be/b/239/5'], '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': '2-432-108.23-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-432-108.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': -0.10988826686037721, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48744719604841970377534954391', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1885563330878576049854724300637', 'Lhash_array': ['1885563330878576049854724300637'], 'label': '2-432-108.23-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/2/be/b/239/5'}