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lfunc_lfunctions • Show schema
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{'Lhash': '1561252456984888504986994898310', 'a10': [-4.188104864667475, 7.254010413030444], 'a2': [-1.0, -1.7320508075688772], 'a3': [1.5, 2.598076211353316], 'a4': [-2.0, 3.4641016151377544], 'a5': [-2.0940524323337373, -3.627005206515222], 'a6': [3.0, -5.196152422706632], 'a7': [3.188104864667475, 0.0], 'a8': [8.0, 0.0], 'a9': [-4.5, 7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.726217740654433, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 1.7320508075688772]]], [3, [[1.0, 0], [-1.5, -2.598076211353316]]], [19, [[1.0, 0], [-42.66557422727189, -70.98344015231406]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.7', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '1739783639111903137735351047350', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.7320508075688772]], [[1.0, 0], [-1.5, -2.598076211353316]], [[1.0, 0], [2.0940524323337373, 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'7.33979911940053856171184913566949', '8.924256945638157890260441164838270', '9.482463430252967589015214696837831', '11.22148550212298954619264545885545', '11.95490428546494127058363217147912', '13.45683425558209076638662135082630'], 'prelabel': '2-114-19.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5934952748471383, 'root_angle': 0.062150224836451114, 'root_number': '0.9809990634357966 + 0.19401246748106135*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0310751124182', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23161102649562794158986510908', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.46670369489069848524575477029', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.29695464713185838189864783887', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.726217740654433, 'bad_primes': [2, 3, 19], 'central_character': '19.7', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/4/e/d/7/2'], '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': '2-114-19.7-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': '2-114-19.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5934952748471383, 'root_angle': 0.031075112418225557, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23161102649562794158986510908', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1561252456984888504986994898310', 'Lhash_array': ['1561252456984888504986994898310'], 'label': '2-114-19.7-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/4/e/d/7/2'}