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lfunc_lfunctions • Show schema
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{'Lhash': '1416763667648925928965965763685', 'a10': [-0.888370902561467, 3.9992886385587294], 'a2': [1.7920941398226775, 0.3809213685497042], 'a3': [-1.4969159216711705, 0.8713453525711546], 'a4': [1.2394094016838009, 0.5518206184707181], 'a5': [-0.020445597173549948, 2.2359745028859828], 'a6': [-3.0145283152149958, 0.991325638617667], 'a7': [-2.1592381836659356, 3.739910239752139], 'a8': [-0.9535115043495089, -0.6927666588522868], 'a9': [1.4815145531053002, -2.608661463075882], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.4969159216711705, -0.8713453525711546]]], [5, [[1.0, 0], [0.020445597173549948, -2.2359745028859828]]]], 'bad_primes': [3, 5], 'central_character': '225.106', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '3892048315076733030454100148445', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'root_angle': -0.5608835767735691, 'root_number': '-0.19010725974486667 - 0.9817633267709167*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.280441788387', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11762946934577242663088876464', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.60183300742592881802237602923', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.44980498860464769320313272925', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '225.106', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/q/a/106/23'], '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': '2-15e2-225.106-c1-0-7', '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': '2-15e2-225.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.2804417883867846, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11762946934577242663088876464', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1416763667648925928965965763685', 'Lhash_array': ['1416763667648925928965965763685'], 'label': '2-15e2-225.106-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/q/a/106/23'}