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lfunc_lfunctions • Show schema
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{'Lhash': '683771068571038905501269842885', 'a10': [0.8268713252670413, 2.0775668007193238], 'a2': [0, -1.0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [-2.0775668007193238, 0.8268713252670413], 'a6': [0, 0], 'a7': [0, 4.672110227958349], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.59018387308638, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.0775668007193238, -0.8268713252670413]]], [37, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5, 37], 'central_character': '3330.1999', 'coefficient_field': 'CDF', 'conductor': 3330, 'conductor_radical': 1110, 'conjugate': '1089950495920028589816581295576', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0775668007193238, -0.8268713252670413]], [[1.0, 0], [0, -4.672110227958349], [-7.0, 0]], [[1.0, 0], [0.04513195707278844, 0], [11.0, 0]], [[1.0, 0], 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'1.62344997431544734599408318250681', '3.63398472270167328905437470923461', '3.84865184716299926590080838945360', '4.65803506329269988787531628204504', '5.49789391307077471892364960445541', '6.64988435139270175694502076849357', '7.22041709880022152244581660732787', '7.61794498378735648076081707490478', '8.379327814305137717946749053789642'], 'prelabel': '2-3330-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.156567062793461, 'root_angle': -0.12056971866038427, 'root_number': '0.9291161188410334270115528375618756168715440032514659089 - 0.3697880983884887683909699877746219242437157177359043710*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.060284859330192134', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53940026411688828613713336718', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.62344997431544734599408318251', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63398472270167328905437470923', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.59018387308638, 'bad_primes': [2, 3, 5, 37], 'central_character': '5.4', 'conductor': 3330, 'conductor_radical': 1110, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3330/2/d/p/1999/1'], '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': '2-3330-5.4-c1-0-22', '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': '2-3330-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.156567062793461, 'root_angle': -0.060284859330192134, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53940026411688828613713336718', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '683771068571038905501269842885', 'Lhash_array': ['683771068571038905501269842885'], 'label': '2-3330-5.4-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3330/2/d/p/1999/1'}