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lfunc_lfunctions • Show schema
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{'Lhash': '2444473152743453867045316359153', 'a10': [-2.3805798488220677, 2.5126421980656612], 'a2': [-1.3556531685204192, 0.40274618145992125], 'a3': [0.0, 0.0], 'a4': [1.6755910266389045, -1.091968274011284], 'a5': [2.1195988328087525, -1.22375095669615], 'a6': [0.0, 0.0], 'a7': [-1.6481444731651576, 2.0696907487774943], 'a8': [-1.8317342317739873, 2.1551681382544983], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.0366903928088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3556531685204192, -0.40274618145992125]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.6481444731651576, -2.0696907487774943]]]], 'bad_primes': [2, 3, 7], 'central_character': '756.703', 'coefficient_field': 'CDF', 'conductor': 756, 'conductor_radical': 42, 'conjugate': '175039589323051342577152436696', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3556531685204192, -0.40274618145992125]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 54, 'label': '2-756-28.3-c1-0-54', '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/756/2/bf/b/703/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.22644126912234816, 0.4261013979123358, 0.6226754231635178, 0.8158655327290202, 1.0021957860880746, 1.1747262112936034, 1.32344756444097, 1.4362339659491574, 1.5002190465871923, 1.5034736651068092, 1.4368586918293285, 1.2958971819270235, 1.0824686788100144, 0.8060920000496687, 0.4845476801644632, 0.14360938267929285, -0.18428767021618062, -0.462512293744787, -0.6537699757102455, -0.724472643388657, -0.649546996331326, -0.41713311910191886, -0.03252183429988369, 0.4793509801188172, 1.0734711432039075, 1.6868237065449887, 2.243161965777939, 2.660299849108021, 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'9.268159246447145550727918124880817', '9.975568434357339266144597033234633', '10.61195804622347654038487205117133'], 'prelabel': '2-756-28.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.8232052636071837, 'root_number': '-0.8496806072737149 + 0.5272977011356783*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.411602631804', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92834930406166167515144880423', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75886368362648249849160450133', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05782157583201904721466017520', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.0366903928088, 'bad_primes': [2, 3, 7], 'central_character': '28.3', 'conductor': 756, 'conductor_radical': 42, 'degree': 2, 'index': 54, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/756/2/bf/b/703/2'], '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': '2-756-28.3-c1-0-54', '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': '2-756-28.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.41160263180359186, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92834930406166167515144880423', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2444473152743453867045316359153', 'Lhash_array': ['2444473152743453867045316359153'], 'label': '2-756-28.3-c1-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/756/2/bf/b/703/2'}