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lfunc_lfunctions • Show schema
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{'Lhash': '1444173902299379687382180265439', 'a10': [0.7922869913932613, -2.623208463869533e-62], 'a2': [0.25881904510252074, 0.9659258262890683], 'a3': [0.0, 0.0], 'a4': [-0.8660254037844386, 0.5], 'a5': [0.20505896255955297, -0.7652904668196159], 'a6': [0.0, 0.0], 'a7': [-0.10385650430336936, -0.17988474214993147], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.318036774617276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [3, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [-5.850708976296783, -1.6640926881277534]]]], 'bad_primes': [2, 3, 37], 'central_character': '666.125', 'coefficient_field': 'CDF', 'conductor': 666, 'conductor_radical': 222, 'conjugate': '1642482505748364081896859902123', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.25881904510252074, -0.9659258262890683]], [[1.0, 0], [0, 0]], [[1.0, 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'7.86891023372858099666431816282604', '8.898259300839418803708681134806931', '9.593461981277997341309709174772386', '10.51251576070109077751412253748736'], 'prelabel': '2-666-111.14-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': -0.29491355578157147, 'root_number': '0.6006373755613867 - 0.7995215713654821*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.147456777891', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13925233186444972260261100897', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65940842112393880189001343408', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63280086091979688156531299912', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.318036774617276, 'bad_primes': [2, 3, 37], 'central_character': '111.14', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/666/2/be/d/125/4'], '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': '2-666-111.14-c1-0-4', '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': '2-666-111.14-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': -0.14745677789078573, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13925233186444972260261100897', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1444173902299379687382180265439', 'Lhash_array': ['1444173902299379687382180265439'], 'label': '2-666-111.14-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/be/d/125/4'}