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lfunc_lfunctions • Show schema
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{'Lhash': '3137063611814434624004947206706', 'a10': [-0.8090169943749475, -0.5877852522924731], 'a2': [0.8090169943749475, -0.5877852522924731], 'a3': [0.0, 0.0], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [-0.30901699437494745, -0.9510565162951535], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4491585113697022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.30901699437494745, 0.9510565162951535]]]], 'bad_primes': [2, 3, 5], 'central_character': '900.811', 'coefficient_field': 'CDF', 'conductor': 900, 'conductor_radical': 30, 'conjugate': '1561105251504374233644172398602', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0]], [[1.0, 0], 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0, 'label': '2-30e2-100.11-c0-0-0', 'leading_term': '1.42396316189849894471540203578', '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/900/1/x/a/811/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.423963161898499, 1.4921031988572329, 1.582054117421087, 1.6943849463459095, 1.8284484658241387, 1.9826509147515103, 2.1547433849186897, 2.342057182472132, 2.541658544546511, 2.7504333120692244, 2.965124905831811, 3.1823479878656524, 3.3985943203690927, 3.6102413225016106, 3.8135692565166193, 4.004789920182401, 4.180087791985207, 4.335673363749768, 4.467847605693158, 4.573075955570573, 4.6480698010612915, 4.689873079193889, 4.69595132584155, 4.664280267492046, 4.5934308618897575, 4.482647574083869, 4.331916632230285, 4.142021055512887, 3.9145793956623645, 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'8.735601538043212685785742143111785', '9.683651154086042175510409792961865', '10.76486800999752715139386487573296'], 'prelabel': '2-30e2-100.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6701928911661942, 'root_angle': 0.56, 'root_number': '-0.18738131458572463054255073444767 + 0.98228725072868868108564174286545*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.28', 'prec': 14}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.47470684055183168209442359936', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.28030407126397008424340129123', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.37427395437747443119762081843', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4491585113697022, 'bad_primes': [2, 3, 5], 'central_character': '100.11', 'conductor': 900, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/900/1/x/a/811/1'], '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': '2-30e2-100.11-c0-0-0', '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': '2-30e2-100.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6701928911661942, 'root_angle': 0.28, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.47470684055183168209442359936', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3137063611814434624004947206706', 'Lhash_array': ['3137063611814434624004947206706'], 'label': '2-30e2-100.11-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/900/1/x/a/811/1'}