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lfunc_lfunctions • Show schema
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{'Lhash': '2585494604108464890743183526313', 'a10': [2.2094632885487315, -0.34390693007763823], 'a2': [0.15643446504023087, -0.9876883405951378], 'a3': [2.925048397996867, -0.46328215343891527], 'a4': [-0.9510565162951535, -0.30901699437494745], 'a5': [0.6853090726577006, 2.128462232442249], 'a6': [-1.6636767197131263e-60, -2.961509494213894], 'a7': [0.07320771959611308, 0.1436782395634068], 'a8': [-0.4539904997395468, 0.8910065241883679], 'a9': [5.488108228043577, -1.7831944583492332], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.4753624626596933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.15643446504023087, 0.9876883405951378]]], [5, [[1.0, 0], [-0.6853090726577006, -2.128462232442249]]], [31, [[1.0, 0], [3.0011447035872854, 4.6896834080916365]]]], 'bad_primes': [2, 5, 31], 'central_character': '310.263', 'coefficient_field': 'CDF', 'conductor': 310, 'conductor_radical': 310, 'conjugate': 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[-78.93769085249775, -25.648410533120636]], [[1.0, 0], [-4.874815721174054, 15.003140091820494], [-72.00251249937033, -52.31288745403011]], [[1.0, 0], [-4.634267556237403, -9.095262191193209], [-57.01516947236989, 78.4746484543699]], [[1.0, 0], [0.9645467768289538, 2.9685697358819243], [-81.71071643186968, 59.366310481539784]], [[1.0, 0], [-11.278070745173366, -1.7862709229148097], [97.95882117840081, 31.828750420619585]], [[1.0, 0], [-7.8621517948103525, -4.005966427244175], [62.893021995294625, 86.56481839811937]], [[1.0, 0], [-1.6711245636316536, 2.3001056362378876], [-33.68285238686927, -103.66516027617173]], [[1.0, 0], [0.6179442628280845, -0.3148583282799832], [66.41973350904946, -91.41892036436906]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-310-155.108-c1-0-9', '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, 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'0.7320650421328043 + 0.6812347422783834*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.119278349081', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03959561384104516220868810433', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.57050335140696539114795568533', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.62035192164635323102883198650', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4753624626596933, 'bad_primes': [2, 5, 31], 'central_character': '155.108', 'conductor': 310, 'conductor_radical': 310, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/310/2/s/a/263/16'], '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': '2-310-155.108-c1-0-9', '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': '2-310-155.108-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5733284662331937, 'root_angle': 0.11927834908115445, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03959561384104516220868810433', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2585494604108464890743183526313', 'Lhash_array': ['2585494604108464890743183526313'], 'label': '2-310-155.108-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/310/2/s/a/263/16'}