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lfunc_lfunctions • Show schema
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{'Lhash': '746856114856081160259892906670', 'a10': [3.038723280730688, 0.0], 'a2': [0.0, -1.0], 'a3': [0.5, -0.8660254037844386], 'a4': [-1.0, 0.0], 'a5': [0.0, 3.038723280730688], 'a6': [-0.8660254037844386, -0.5], 'a7': [-1.2286617069933872, -2.3431582127052573], 'a8': [0.0, 1.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.372062081298178, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [1.2286617069933872, 2.3431582127052573]]], [19, [[1.0, 0], [4.3243538418137675, 0.5476895569485591]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '798.145', 'coefficient_field': 'CDF', 'conductor': 798, 'conductor_radical': 798, 'conjugate': '2126183095640846923154744208874', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, -3.038723280730688], [-5.0, 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[3.9995368954866923, -6.927401109729246], [-29.5, -51.09549882328188]], [[1.0, 0], [-10.508259317408482, 6.06694634562018], [30.5, -52.827549630850754]], [[1.0, 0], [0, -9.123374534269248], [-67.0, 0]], [[1.0, 0], [-6.643067311022254, 3.8353767002635015], [35.5, -61.48780366869514]], [[1.0, 0], [10.387382641666937, 5.997158164342052], [36.5, 63.21985447626402]], [[1.0, 0], [0, -9.087357363954363], [-79.0, 0]], [[1.0, 0], [0, 15.748595827722035], [-83.0, 0]], [[1.0, 0], [3.768738872687558, 6.527647207954706], [-44.5, 77.07626093681505]], [[1.0, 0], [-2.7007968518700487, -4.677917368360999], [-48.5, 84.00446416709055]], [[1.0, 0], [0, 16.166211317104914], [-101.0, 0]], [[1.0, 0], [-1.6373755834291341, 2.8360177015719934], [-51.5, -89.20061658979718]], [[1.0, 0], [-9.75479539831435, -5.631933749106513], [53.5, 92.66471820493493]], [[1.0, 0], [8.873050351700567, 5.122858009087426], [54.5, 94.39676901250381]], [[1.0, 0], [0, -8.56105814820251], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-798-133.12-c1-0-4', '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/798/2/m/b/145/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2096889517738485, 1.0264519759174888, 0.8114003800103912, 0.5558749238939096, 0.2511607631297128, -0.10924174031231496, -0.5275770013096209, -1.0002224230296535, -1.5166039646961393, -2.0587155828445045, -2.601329920434137, -3.112988229596435, -3.557825127729092, -3.8982143210965066, -4.098121980029174, -4.126938360508893, -3.9634427479477385, -3.5994613595169405, -3.0427224133673367, -2.318414968098064, -1.4690309950430467, -0.5522178341589703, 0.36341576950957943, 1.2043311268966184, 1.8994347473096378, 2.3880391277662376, 2.6274521313283485, 2.5991467666247376, 2.312513263656638, 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'8.533689883944503337636977491414142', '9.079570502755053509809083863274715', '9.825200067235167161898938603443833'], 'prelabel': '2-798-133.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.524294372948246, 'root_angle': -0.20878605059237984, 'root_number': '0.7924867252843464 - 0.6098891622648274*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.104393025296', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58916559083521614716320096266', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69972924779184387761205585758', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94292345703009256270836333916', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.372062081298178, 'bad_primes': [2, 3, 7, 19], 'central_character': '133.12', 'conductor': 798, 'conductor_radical': 798, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/798/2/m/b/145/7'], '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': '2-798-133.12-c1-0-4', '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': '2-798-133.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.524294372948246, 'root_angle': -0.10439302529618992, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58916559083521614716320096266', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '746856114856081160259892906670', 'Lhash_array': ['746856114856081160259892906670'], 'label': '2-798-133.12-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/798/2/m/b/145/7'}