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lfunc_lfunctions • Show schema
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{'Lhash': '1401196278007361108733063596107', 'a10': [4.0870224044822185, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [4.0870224044822185, 0.0], 'a6': [1.0, 0.0], 'a7': [-2.277756139238791, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.05397193640656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [59, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 17, 59], 'central_character': '6018.1', 'coefficient_field': 'CDF', 'conductor': 6018, 'conductor_radical': 6018, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.0870224044822185, 0], [5.0, 0]], [[1.0, 0], [2.277756139238791, 0], [7.0, 0]], [[1.0, 0], [4.977410374327993, 0], [11.0, 0]], [[1.0, 0], [-3.1447046905563036, 0], [13.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.30689393181244, 0], 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[[1.0, 0], [2.602483869052501, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 70, 'label': '2-6018-1.1-c1-0-70', 'leading_term': '5.29045031924203136621686499130', '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/6018/2/a/bb/1/13', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [5.290450319242032, 5.279550830302558, 5.246718453464007, 5.19156460813668, 5.113484556023404, 5.011718580160623, 4.885431676386036, 4.733806585556958, 4.556144466824754, 4.351967446082603, 4.121117583149325, 3.863847371999342, 3.5808976065304834, 3.2735592168269756, 2.9437164446809527, 2.5938694496171726, 2.227135109402283, 1.8472254092420162, 1.4584034160129544, 1.0654174228314588, 0.673414435850315, 0.28783476370636757, -0.08570994245782772, -0.4415722739163661, 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'5.34159630639209008131887201298923', '5.95970081059327542301383211793211', '6.36374744717229756068014374096726', '7.25848321940788643326042929764096', '8.000492771401695323543560827987943'], 'prelabel': '2-6018-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.932097224967821, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10534896426119940003556916700', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26363054015682631634507334793', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.69407542865908233559213115753', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.05397193640656, 'bad_primes': [2, 3, 17, 59], 'central_character': '1.1', 'conductor': 6018, 'conductor_radical': 6018, 'degree': 2, 'index': 70, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6018/2/a/bb/1/13'], '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': '2-6018-1.1-c1-0-70', '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': '2-6018-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.932097224967821, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10534896426119940003556916700', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1401196278007361108733063596107', 'Lhash_array': ['1401196278007361108733063596107'], 'label': '2-6018-1.1-c1-0-70', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6018/2/a/bb/1/13'}