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lfunc_lfunctions • Show schema
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{'Lhash': '4233424263817395233800241025956', 'a10': [-4.0, 5.830951894845301], 'a2': [-1.4142135623730951, 0.0], 'a3': [0.7071067811865476, -2.9154759474226504], 'a4': [2.0, 0.0], 'a5': [2.8284271247461903, -4.123105625617661], 'a6': [-1.0, 4.123105625617661], 'a7': [0.0, 5.830951894845301], 'a8': [-2.8284271247461903, 0.0], 'a9': [-8.0, -4.123105625617661], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8174407930808908, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.4142135623730951, 0]]], [3, [[1.0, 0], [-0.7071067811865476, 2.9154759474226504]]], [5, [[1.0, 0], [-2.8284271247461903, 4.123105625617661]]]], 'bad_primes': [2, 3, 5], 'central_character': '30.29', 'coefficient_field': 'CDF', 'conductor': 30, 'conductor_radical': 30, 'conjugate': '2483700256272169086764646406035', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4142135623730951, 0]], [[1.0, 0], [-0.7071067811865476, 2.9154759474226504]], [[1.0, 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['3.33958289693958589849844513434924', '5.93398024029878593979916958818239', '7.83056174676368537277650251742597', '9.415512359695815759757034805550548', '10.46766624811856074030811447758373', '11.29219669291262299039085179348418', '13.74599833986201094988772516673052', '14.54709733937679654120319157765491', '16.07300409074822374949127640976656', '16.80953955007483652977582841215910'], 'prelabel': '2-30-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9041243239073323, 'root_angle': 0.2671273567406661, 'root_number': '0.6680543520114205 + 0.7441124799105314*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.13356367837', 'prec': 44}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.33958289693958589849844513435', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.93398024029878593979916958818', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.83056174676368537277650251743', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8174407930808908, 'bad_primes': [2, 3, 5], 'central_character': '15.14', 'conductor': 30, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/30/3/b/a/29/1'], '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': '2-30-15.14-c2-0-2', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-30-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9041243239073323, 'root_angle': 0.13356367837033306, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.33958289693958589849844513435', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4233424263817395233800241025956', 'Lhash_array': ['4233424263817395233800241025956'], 'label': '2-30-15.14-c2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/30/3/b/a/29/1'}