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lfunc_lfunctions • Show schema
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{'Lhash': '3412901102354550572070842411670', 'a10': [-1.849814074137659, -3.203971960962407], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.34981407413765897, -1.696357896652476], 'a4': [-0.5, 0.8660254037844386], 'a5': [3.699628148275318, 0.0], 'a6': [-1.2941819953425522, 1.1511268231307836], 'a7': [-1.405446152932766, -2.2415889701741682], 'a8': [1.0, 0.0], 'a9': [-2.755260227070425, 1.1868197340471849], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0061150654681332, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0.34981407413765897, 1.696357896652476]]], [7, [[1.0, 0], [1.405446152932766, 2.2415889701741682]]]], 'bad_primes': [2, 3, 7], 'central_character': '126.79', 'coefficient_field': 'CDF', 'conductor': 126, 'conductor_radical': 42, 'conjugate': '1820500867057671571245040615832', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], 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'8.846352245948556128457438628790500', '9.504701238221960355706801512548652', '10.05968500629716346319034192055547', '11.37350463318408199483191858967866', '12.83101482163249803133184390571552', '13.94766192463054388064119898495553'], 'prelabel': '2-126-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.00305287271815, 'root_angle': 0.5609883281836097, 'root_number': '-0.19043033426658357 + 0.9817007119235054*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.280494164092', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.69230425303319982947513031520', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.08360387653250249905864693145', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.68636237895206756386659361644', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0061150654681332, 'bad_primes': [2, 3, 7], 'central_character': '63.16', 'conductor': 126, 'conductor_radical': 42, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/126/2/h/c/79/1'], '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': '2-126-63.16-c1-0-6', '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': '2-126-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.00305287271815, 'root_angle': 0.28049416409180483, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.69230425303319982947513031520', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3412901102354550572070842411670', 'Lhash_array': ['3412901102354550572070842411670'], 'label': '2-126-63.16-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/126/2/h/c/79/1'}