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lfunc_lfunctions • Show schema
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{'Lhash': '2241241661353087129236355270974', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.49230307877208324, 0.15995896680914984], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.630445396272019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '3267.2296', 'coefficient_field': 'CDF', 'conductor': 3267, 'conductor_radical': 33, 'conjugate': '802480990601106978280541897092', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.49230307877208324, -0.15995896680914984], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.1355139110022712, 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[[1.0, 0], [-1.837300102699998, -0.5969749912579709], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-1.1355139110022712, -1.5629008175470391], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.8090169943749475, -0.5877852522924731], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.30901699437494745, 0.9510565162951535], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 1.9318516525781366], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.8090169943749475, 0.5877852522924731]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-3267-11.8-c0-0-2', 'leading_term': '1.12448956235846905520581873373', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 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'root_analytic_conductor': 1.27688895220846, 'root_angle': 0.6040139007302212, 'root_number': '-0.32098496969323065382539254873816 + 0.94708428834557053835530716051681*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3020069503651106', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.76802792579404070325287092040', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51933629844779239433390031452', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56281480999043333341723487878', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.630445396272019, 'bad_primes': [3, 11], 'central_character': '11.8', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/1/l/a/2296/3'], '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': '2-3267-11.8-c0-0-2', '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': '2-3267-11.8-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': 0.3020069503651106, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76802792579404070325287092040', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2241241661353087129236355270974', 'Lhash_array': ['2241241661353087129236355270974'], 'label': '2-3267-11.8-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/1/l/a/2296/3'}