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lfunc_lfunctions • Show schema
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{'Lhash': '891116482495409276819319384891', 'a10': [0.0, 0.0], 'a2': [1.2511768171302318, 0.0], 'a3': [0.0, 0.0], 'a4': [-6.434556572275863, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [5.670285905157892, 0.0], 'a8': [-18.06018254878638, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.82628925387493, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '675.1', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2511768171302318, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.670285905157892, 0], [343.0, 0]], [[1.0, 0], [21.25371283021977, 0], [1331.0, 0]], [[1.0, 0], [40.947911243970964, 0], [2197.0, 0]], [[1.0, 0], [-59.18525491488007, 0], [4913.0, 0]], [[1.0, 0], [-21.879970860025402, 0], [6859.0, 0]], [[1.0, 0], 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'3.61530032560255252320590118973792', '4.68858555581077858333915699657859', '5.34726847478434689860375454593958', '6.33193236188468574747189429354990', '7.72526378294249314675198601141397', '8.183133899766903843461166459828151', '9.451366789595046859162398839665520', '9.890212196841404743095242827386251'], 'prelabel': '2-675-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.310807337724305, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70296695503869248308554323077', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45231743918533493121436469465', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61530032560255252320590118974', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.82628925387493, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/4/a/bc/1/4'], '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': '2-675-1.1-c3-0-16', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-675-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.310807337724305, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70296695503869248308554323077', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '891116482495409276819319384891', 'Lhash_array': ['891116482495409276819319384891'], 'factors': ['2-675-1.1-c3-0-16'], 'label': '2-675-1.1-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/4/a/bc/1/4'}