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lfunc_lfunctions • Show schema
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{'Lhash': '1728015590626435584633943975918', 'a10': [2.204071708665971, 0.0], 'a2': [0.8015269230931917, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.3575545915567606, 0.0], 'a5': [2.74984114090664, 0.0], 'a6': [0.0, 0.0], 'a7': [2.3768337693186363, 0.0], 'a8': [-2.6911704008879087, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.1', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1728015590626435584633943975918', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8015269230931917, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.74984114090664, 0], [5.0, 0]], [[1.0, 0], [-2.3768337693186363, 0], [7.0, 0]], [[1.0, 0], [-0.25015885909335994, 0], [11.0, 0]], [[1.0, 0], [-2.611983188423377, 0], [13.0, 0]], [[1.0, 0], [-0.29337681908084856, 0], [17.0, 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'5.02188312889748839748182524499672', '5.74146236624903320690813286505341', '6.56973190170137728147159506156877', '7.931653211445087675152416412464809', '8.893347049563682696967928243675719', '9.348637072378261415799462503324252', '10.47017994605221985339116531381958'], 'prelabel': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36316394305759133768250012775', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76093908222073722224892930864', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.10512819238575549410036105488', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/a/d/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': '2-3e6-1.1-c1-0-12', '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': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36316394305759133768250012775', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1728015590626435584633943975918', 'Lhash_array': ['1728015590626435584633943975918'], 'label': '2-3e6-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/a/d/1/4'}