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lfunc_lfunctions • Show schema
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{'Lhash': '2026644245433567977055146709582', 'a10': [-1.7071067811865475, 0.7071067811865476], 'a2': [-1.3065629648763766, 1.3065629648763766], 'a3': [0.0, 0.0], 'a4': [0.0, -2.414213562373095], 'a5': [0.9238795325112867, 0.3826834323650898], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.8477590650225735, 1.8477590650225735], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2919530323903064, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.9238795325112867, -0.3826834323650898]]], [13, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.532', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '1565896808409867287105948761663', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3065629648763766, -1.3065629648763766], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.9238795325112867, 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'7.49277186874296420089037597519426', '8.655214474780048353855139455041163', '9.189510731008228967679438582306305', '10.02986158880638050593872769126586', '10.39916256938488087519610781853773'], 'prelabel': '2-585-65.12-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5403267829659255, 'root_angle': -0.30120819117478337, 'root_number': '0.58471028466376494325476189408372 - 0.81124218517556085398167691672200*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.15060409558739168', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59874041401367885536930546194', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27312621645193045876677843939', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80276706457507418806013034548', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2919530323903064, 'bad_primes': [3, 5, 13], 'central_character': '65.12', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/1/o/a/532/1'], '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': '2-585-65.12-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-585-65.12-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5403267829659255, 'root_angle': -0.15060409558739168, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59874041401367885536930546194', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2026644245433567977055146709582', 'Lhash_array': ['2026644245433567977055146709582'], 'label': '2-585-65.12-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/1/o/a/532/1'}