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lfunc_lfunctions • Show schema
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{'Lhash': '4364543619107143081806623702931', 'a10': [-27.712142642814275, 47.99883904395038], 'a2': [-3.570714214271425, -2.0615528128088303], 'a3': [1.5, -2.598076211353316], 'a4': [4.5, 7.794228634059948], 'a5': [0.0, -13.442363673941953], 'a6': [-10.712142642814275, 6.18465843842649], 'a7': [-27.212142642814275, 15.710937880055315], 'a8': [0.0, -4.123105625617661], 'a9': [-4.5, -7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.301074490223885, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.5, 2.598076211353316]]], [13, [[1.0, 0], [-42.13642792844283, 20.53098734671919]]]], 'bad_primes': [3, 13], 'central_character': '39.4', 'coefficient_field': 'CDF', 'conductor': 39, 'conductor_radical': 39, 'conjugate': '676635591778220295775650879015', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.570714214271425, 2.0615528128088303], [4.0, 6.928203230275509]], [[1.0, 0], [-1.5, 2.598076211353316]], 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'13.01016566552357720410455458100333', '14.35195807109856558262729279908134', '15.77122176988081621379118791477699', '16.09003191765808513741895079111780'], 'prelabel': '2-39-13.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': -0.9817356422774762, 'root_number': '-0.9983542669122372 - 0.05734769165476064*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.490867821139', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.44301783024545184853557167260', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.47291460446494201590771646096', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.29763802444551228660047312993', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.301074490223885, 'bad_primes': [3, 13], 'central_character': '13.4', 'conductor': 39, 'conductor_radical': 39, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/39/4/j/b/4/1'], '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': '2-39-13.4-c3-0-7', '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': '2-39-13.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': -0.4908678211387381, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.44301783024545184853557167260', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4364543619107143081806623702931', 'Lhash_array': ['4364543619107143081806623702931'], 'label': '2-39-13.4-c3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/39/4/j/b/4/1'}