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lfunc_lfunctions • Show schema
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{'Lhash': '1247180641918667466962340947777', 'a10': [0.0, 0.0], 'a2': [0.539168909802257, -0.9338679456390303], 'a3': [0.06132777053597539, 1.7309647323273478], 'a4': [0.41859377340529136, 0.7250256832699385], 'a5': [0.0, 0.0], 'a6': [1.6495585057326392, 0.8760103285540385], 'a7': [0.9292266361801694, 2.4772036368884347], 'a8': [3.0594466330368038, 0.0], 'a9': [-2.9924778091221733, 0.2123124158200753], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.192146106117222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.06132777053597539, -1.7309647323273478]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.9292266361801694, -2.4772036368884347]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.299', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': '2947637534599512960079421953004', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.539168909802257, 0.9338679456390303], [-1.0, 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[5.0567783722887825, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-525-105.89-c1-0-11', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/525/2/q/e/299/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8325618507142898, 1.662489516091933, 1.487737024741832, 1.3000664031919802, 1.0910431037737571, 0.853813140674371, 0.5845903529967685, 0.2837562493652626, -0.04343601600356449, -0.38655063534452966, -0.7300730786520785, -1.053972483814311, -1.3347648450200091, -1.5470917661843449, -1.6657797226920164, -1.6682800717969286, -1.5373194383186461, -1.2635236792604663, -0.847727204554394, -0.3026536898347514, 0.34633651982679364, 1.0616863278932753, 1.7954290608091819, 2.4923491535457347, 3.0943795844106146, 3.5459235803787545, 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'8.382872653932286352842586194774238', '9.988981773981466722607515024999646', '10.84230969923254484444014819749045'], 'prelabel': '2-525-105.89-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0474731026602577, 'root_angle': -0.39940858572909516, 'root_number': '0.31078350656097226 - 0.9504807268165232*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.199704292865', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.983852050158082599726973137396', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.43539800790345027602272224546', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09481250314475125513329232891', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.192146106117222, 'bad_primes': [3, 5, 7], 'central_character': '105.89', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/2/q/e/299/6'], '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': '2-525-105.89-c1-0-11', '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': '2-525-105.89-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0474731026602577, 'root_angle': -0.19970429286454758, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.983852050158082599726973137396', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1247180641918667466962340947777', 'Lhash_array': ['1247180641918667466962340947777'], 'label': '2-525-105.89-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/2/q/e/299/6'}