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lfunc_lfunctions • Show schema
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{'Lhash': '261358251219670811219218329919', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [2.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.5, 4.330127018922194], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.419972322510946, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [67, [[1.0, 0], [-8.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 67], 'central_character': '804.37', 'coefficient_field': 'CDF', 'conductor': 804, 'conductor_radical': 402, 'conjugate': '2804275509915100694271073526267', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.0, 0], [5.0, 0]], [[1.0, 0], [2.5, -4.330127018922194], [-3.5, -6.06217782649107]], [[1.0, 0], [2.5, -4.330127018922194], [-5.5, -9.526279441628825]], [[1.0, 0], [1.5, 2.598076211353316], [-6.5, 11.258330249197702]], [[1.0, 0], [1.5, 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4.986614057066327, 3.1292119683802215, 1.2071288825738526, -0.22016350860075143, -0.813836107967081], 'positive_zeros': ['0.20617530664413012890178828042536', '1.84417672452927925837383579502910', '3.49342363351217763007779990537848', '4.28799819643648618928183552791039', '5.77039090377263434220253935698662', '6.15836565015958488463690392087610', '7.14709394731671295485955705970939', '8.028178539005413540804408531273617', '9.277037451098849523596741938200782', '10.07222222908808503930706382521843'], 'prelabel': '2-804-67.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.533766430141292, 'root_angle': -0.9341346253323232, 'root_number': '-0.9786678839110743 - 0.2054487113637369*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.467067312666', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20617530664413012890178828043', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84417672452927925837383579503', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49342363351217763007779990538', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.419972322510946, 'bad_primes': [2, 3, 67], 'central_character': '67.37', 'conductor': 804, 'conductor_radical': 402, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/804/2/i/b/37/1'], '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': '2-804-67.37-c1-0-0', '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': '2-804-67.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.533766430141292, 'root_angle': -0.4670673126661616, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.20617530664413012890178828043', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '261358251219670811219218329919', 'Lhash_array': ['261358251219670811219218329919'], 'label': '2-804-67.37-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/804/2/i/b/37/1'}