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lfunc_lfunctions • Show schema
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{'Lhash': '96226709150567040597656225482', 'a10': [-0.21302555475980883, -2.2258975971547468], 'a2': [0.5, 0.8660254037844386], 'a3': [-0.8660254037844386, 0.5], 'a4': [-0.5, 0.8660254037844386], 'a5': [-2.0341966427386557, -0.928463256500106], 'a6': [-0.8660254037844386, -0.5], 'a7': [-1.4024742778494972, 2.4291567055437997], 'a8': [-1.0, 0.0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0.8660254037844386, -0.5]]], [5, [[1.0, 0], [2.0341966427386557, 0.928463256500106]]], [13, [[1.0, 0], [-1.109751431709994, 3.4305177101740227]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.49', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '3658942265441121408736728144268', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 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'7.85392228109841127281000322811219', '8.955326725788848331113946965856628', '10.34940713307947413694059748470142', '10.80404473878573643224480883519426'], 'prelabel': '2-390-65.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.7399670991249916, 'root_number': '-0.6844717552385141 + 0.7290393791015048*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.369983549562', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.07590948888695533562723495423', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13379120202962665539777427992', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98209037440555618101205201937', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.49', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/x/b/49/1'], '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': '2-390-65.49-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': '2-390-65.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.3699835495624958, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.07590948888695533562723495423', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '96226709150567040597656225482', 'Lhash_array': ['96226709150567040597656225482'], 'label': '2-390-65.49-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/x/b/49/1'}