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lfunc_lfunctions • Show schema
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{'Lhash': '833381501149603572657254087463', 'a10': [0.0, -1.7320508075688772], 'a2': [0.0, 1.0], 'a3': [0.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [-1.7320508075688772, 0.0], 'a6': [0.0, 0.0], 'a7': [2.0, 1.7320508075688772], 'a8': [0.0, -1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.0, -1.7320508075688772]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.377', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '2650707870057564512072092502109', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.7320508075688772, 0], [5.0, 0]], [[1.0, 0], [-2.0, -1.7320508075688772]], [[1.0, 0], [0, -3.0], [-11.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-13.0, 0]], [[1.0, 0], [6.928203230275509, 0], [17.0, 0]], 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'9.135122218821324976242156531872303', '10.49208491166796264591504321121592', '11.05352991001634789015774597396165'], 'prelabel': '2-378-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.7728144741714951, 'root_number': '-0.7559289460184545 - 0.6546536707079771*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.386407237086', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65742208539132196488344514468', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58436935133502546713499710304', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94386026353510527376359751277', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/d/b/377/3'], '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': '2-378-21.20-c1-0-2', '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': '2-378-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.38640723708574753, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65742208539132196488344514468', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '833381501149603572657254087463', 'Lhash_array': ['833381501149603572657254087463'], 'label': '2-378-21.20-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/d/b/377/3'}