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lfunc_lfunctions • Show schema
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{'Lhash': '3448137530978033345249315372245', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [4.898979485566356, -1.7320508075688772], 'a4': [0.0, 0.0], 'a5': [0.0, -16.97056274847714], 'a6': [0.0, 0.0], 'a7': [0.0, 17.320508075688775], 'a8': [0.0, 0.0], 'a9': [21.0, -16.97056274847714], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8320916802755507, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-4.898979485566356, 1.7320508075688772]]]], 'bad_primes': [2, 3], 'central_character': '48.47', 'coefficient_field': 'CDF', 'conductor': 48, 'conductor_radical': 6, 'conjugate': '2224658153385608977820392182848', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-4.898979485566356, 1.7320508075688772]], [[1.0, 0], [0, 16.97056274847714], [-125.0, 0]], [[1.0, 0], [0, -17.320508075688775], [-343.0, 0]], [[1.0, 0], [-29.393876913398138, 0], [1331.0, 0]], [[1.0, 0], [26.0, 0], [2197.0, 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'6.77038550770534651089334425736548', '7.65139944315157107934638018103673', '9.462328934448477676119150971923829', '10.38761988252446993438826674431084', '11.54188170785379744056233105645004', '13.51402010216281726835148161662899', '14.23585388024235261656112629711115', '14.99546401687598441522008309311116'], 'prelabel': '2-48-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6828819567264814, 'root_angle': 0.2251598853639406, 'root_number': '0.7600796553858445 + 0.6498299142610594*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.112579942682', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.72010089401387602088294765869', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.17134027108114254946896496833', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.77038550770534651089334425737', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8320916802755507, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/4/c/b/47/3'], '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': '2-48-12.11-c3-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-48-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6828819567264814, 'root_angle': 0.1125799426819703, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.72010089401387602088294765869', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3448137530978033345249315372245', 'Lhash_array': ['3448137530978033345249315372245'], 'label': '2-48-12.11-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/4/c/b/47/3'}