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lfunc_lfunctions • Show schema
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{'Lhash': '1602152632679195359605803629735', 'a10': [-1.7320508075688772, 0], 'a2': [0, -1.0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [0, -1.7320508075688772], 'a6': [0, 0], 'a7': [0, 4.732050807568878], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.290492294873506, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '3042.1351', 'coefficient_field': 'CDF', 'conductor': 3042, 'conductor_radical': 78, 'conjugate': '384100516209247344710816588336', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-5.0, 0]], [[1.0, 0], [0, -4.732050807568878], [-7.0, 0]], [[1.0, 0], [0, 4.732050807568878], [-11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.196152422706632, 0], [17.0, 0]], [[1.0, 0], [0, 1.2679491924311228], [-19.0, 0]], 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 53, 'label': '2-3042-13.12-c1-0-53', 'leading_term': '0.926160661871921801450317390682794278444226492299483366', '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/3042/2/b/l/1351/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.9261606618719218, 1.0709111610287323, 1.2110318037097627, 1.3457422991760906, 1.4741096432996452, 1.5950228651996041, 1.7071786643922864, 1.8090789327233359, 1.8990404918742825, 1.9752167873539133, 2.0356307999284993, 2.078218075559541, 2.1008785243747368, 2.1015354747680504, 2.078200363139827, 2.029041368298221, 1.952454243799094, 1.8471335509388898, 1.7121424465303532, 1.546979135691619, 1.351638067459384, 1.1266639392040292, 0.8731965944938913, 0.5930049577787075, 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'6.43710574658513813850490025564904', '7.00841506986143513427241358296365', '7.18958337044036658506612967422587', '8.081654031349349833089996492157481', '8.990815706107538061250050632790061'], 'prelabel': '2-3042-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.928538555684992, 'root_angle': 0.9105438124889667, 'root_number': '-0.9607689228305228008995220186061222247804553812294855860 + 0.2773500981126145610091708667284996881731766595265574010*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4552719062444833', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26387557611753727194401765180', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61812365475114739270998892494', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82078439526043869015774741772', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.290492294873506, 'bad_primes': [2, 3, 13], 'central_character': '13.12', 'conductor': 3042, 'conductor_radical': 78, 'degree': 2, 'index': 53, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3042/2/b/l/1351/1'], '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': '2-3042-13.12-c1-0-53', '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': '2-3042-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.928538555684992, 'root_angle': 0.4552719062444833, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26387557611753727194401765180', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1602152632679195359605803629735', 'Lhash_array': ['1602152632679195359605803629735'], 'label': '2-3042-13.12-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3042/2/b/l/1351/1'}