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lfunc_lfunctions • Show schema
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{'Lhash': '1010180539158612932552594565777', 'a10': [0, 0], 'a2': [0, -16.0], 'a3': [0, 174.0], 'a4': [-256.0, 0], 'a5': [0, 0], 'a6': [2784.0, 0], 'a7': [0, -4658.0], 'a8': [0, 4096.0], 'a9': [-10593.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.751791808193662, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 16.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '50.49', 'coefficient_field': 'CDF', 'conductor': 50, 'conductor_radical': 10, 'conjugate': '1410671714095955465063621791725', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 16.0]], [[1.0, 0], [0, -174.0], [-19683.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4658.0], [-40353607.0, 0]], [[1.0, 0], [-28992.0, 0], [2357947691.0, 0]], [[1.0, 0], [0, 164446.0], [-10604499373.0, 0]], [[1.0, 0], [0, -594822.0], [-118587876497.0, 0]], [[1.0, 0], [-295780.0, 0], [322687697779.0, 0]], [[1.0, 0], [0, -2544534.0], [-1801152661463.0, 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'4.67871740542370016467871817678416', '6.39716814557642448131544843936065', '7.03244260041193770465922104639005', '8.445057283056486400140726836586631', '9.503795441435983635435565942511027', '11.67632425103022843162697652038217', '12.36236405542627047038927028266448', '13.76121509391862612632516365354845'], 'prelabel': '2-50-5.4-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.0746223315822885, 'root_angle': -0.14758361765043326, 'root_number': '0.894427190999916 - 0.44721359549995787*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07379180882521663', 'prec': 67}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.796891934557313161269382118841086', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.38886327994890721359874780356364', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.67871740542370016467871817678416', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.751791808193662, 'bad_primes': [2, 5], 'central_character': '5.4', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/10/b/d/49/1'], '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': '2-50-5.4-c9-0-5', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-50-5.4-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.0746223315822885, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.796891934557313161269382118841086', 'prec': 117}}
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lfunc_instances • Show schema
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{'Lhash': '1010180539158612932552594565777', 'Lhash_array': ['1010180539158612932552594565777'], 'label': '2-50-5.4-c9-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/10/b/d/49/1'}