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lfunc_lfunctions • Show schema
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{'Lhash': '3297223767764761040216535292207', 'a10': [0.0, 0.0], 'a2': [0.940755497370863, -1.4972037971811802], 'a3': [-0.2947551744109042, -0.9555728057861407], 'a4': [-0.9227145653426867, -1.9160365378630322], 'a5': [0.0, 0.0], 'a6': [-1.70797978401165, -0.45765180381460496], 'a7': [0.0, 0.0], 'a8': [-1.9796334569165135, -0.2230511215154034], 'a9': [-0.8262387743159949, 0.5633200580636221], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9986290902786379, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.2947551744109042, 0.9555728057861407]]], [23, [[1.0, 0], [-0.9749279121818236, -0.2225209339563144]]], [29, [[1.0, 0], [-0.9972037971811801, -0.07473009358642425]]]], 'bad_primes': [3, 23, 29], 'central_character': '2001.206', 'coefficient_field': 'CDF', 'conductor': 2001, 'conductor_radical': 2001, 'conjugate': '863782678189270874477321485324', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.940755497370863, 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[-0.7818314824680298, 0.6234898018587335]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-2001-2001.206-c0-0-5', 'leading_term': '1.274295332053927098060713729826', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2001/1/bf/d/206/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.2742953320539272, 1.4206871245944666, 1.5923547342063296, 1.793242629269369, 2.02623739870636, 2.2931338517962496, 2.5947065115031958, 2.93081887755293, 3.300523026328325, 3.7021288105255485, 4.133241272968639, 4.590774459454068, 5.070952529970919, 5.569308366614135, 6.080687998783929, 6.599267177192932, 7.11858469030131, 7.631595572601811, 8.130746138322289, 8.608071706669966, 9.055316903308055, 9.464077488619093, 9.825961758710955, 10.132768688568717, 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'5.71677452110442095613420402921217', '6.75729660623488769572183637444016', '7.12061764005104217614802553442862', '8.194113789545654045290916818791407', '8.964070658379146163613722135653247', '9.607279155038357484789751008104274'], 'prelabel': '2-2001-2001.206-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9993143100539679, 'root_angle': -0.6746512637002416, 'root_number': '-0.52156410950372506352007289043649 - 0.85321209536526513711764247701927*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3373256318501208', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.60105092615514459905410929078', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.77622980518830526980438694708', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.44589020372508515528893450723', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9986290902786379, 'bad_primes': [3, 23, 29], 'central_character': '2001.206', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2001/1/bf/d/206/2'], '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': '2-2001-2001.206-c0-0-5', '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': '2-2001-2001.206-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9993143100539679, 'root_angle': -0.3373256318501208, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.60105092615514459905410929078', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3297223767764761040216535292207', 'Lhash_array': ['3297223767764761040216535292207'], 'label': '2-2001-2001.206-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2001/1/bf/d/206/2'}