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lfunc_lfunctions • Show schema
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{'Lhash': '863382948208765423426759855411', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.124885419764574, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.28331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': 'CDF', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.124885419764574, 0], [7.0, 0]], [[1.0, 0], [-3.155161514020715, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.5151380471280705, 0], [17.0, 0]], [[1.0, 0], [-6.734632792401078, 0], [19.0, 0]], [[1.0, 0], [4.249770839529148, 0], [23.0, 0]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-7800-1.1-c1-0-28', 'leading_term': '1.5859071541571966802028681671918', '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/7800/2/a/bm/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.5859071541571967, 1.5777178867431838, 1.5531575097424672, 1.5122540646013862, 1.455073096776593, 1.3817444752469894, 1.292497279092966, 1.1877003706112896, 1.0679059445547998, 0.93389320203678, 0.7867093276555219, 0.6277051185132014, 0.45856288798533834, 0.2813146110698369, 0.09834866383518305, -0.08759608315446189, -0.2734496408788704, -0.45584415111601295, -0.631160992476194, -0.7955913070321444, -0.9452090931917433, -1.0760555964832215, -1.184233324919, -1.2660076267448481, -1.3179134050832575, 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'5.15778848764940520258695333935187', '5.84555850954056567130427870280842', '6.52235762616392691878129591882538', '6.91287890109926689397638981891265', '7.84765365525870759820662349900159'], 'prelabel': '2-7800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68108905407635264500246216637', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.56821581285309629810272338961', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81491138345144566489680797618', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.28331357659873, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7800/2/a/bm/1/1'], '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': '2-7800-1.1-c1-0-28', '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': '2-7800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68108905407635264500246216637', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '863382948208765423426759855411', 'Lhash_array': ['863382948208765423426759855411'], 'label': '2-7800-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/bm/1/1'}