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lfunc_lfunctions • Show schema
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{'Lhash': '2323101238434681551502861823180', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.5739439343559716, 0.0], 'a4': [0.0, 0.0], 'a5': [0.16339850203845604, 0.0], 'a6': [0.0, 0.0], 'a7': [27.81112300513362, 0.0], 'a8': [0.0, 0.0], 'a9': [-20.374812622792103, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.009359924087335, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [89, [[1.0, 0], [89.0, 0]]]], 'bad_primes': [2, 89], 'central_character': '712.1', 'coefficient_field': 'CDF', 'conductor': 712, 'conductor_radical': 178, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.5739439343559716, 0], [27.0, 0]], [[1.0, 0], [-0.16339850203845604, 0], [125.0, 0]], [[1.0, 0], [-27.81112300513362, 0], [343.0, 0]], [[1.0, 0], [24.522228753559894, 0], [1331.0, 0]], [[1.0, 0], [48.634332074745586, 0], [2197.0, 0]], [[1.0, 0], [40.45282258623662, 0], [4913.0, 0]], [[1.0, 0], [6.500739822107637, 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'5.09669817414743533771269253307699', '5.75721155488625001308535549376503', '7.45280375033827964908914315644831', '7.69815235025392319273861713068518', '8.787818598915212164920657719281819', '9.346607484870311424002127123379376'], 'prelabel': '2-712-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.481462792000532, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83260374587163647096602317213', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64359757601414269169048798386', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04525985957906341188294025911', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.009359924087335, 'bad_primes': [2, 89], 'central_character': '1.1', 'conductor': 712, 'conductor_radical': 178, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/712/4/a/c/1/11'], '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': '2-712-1.1-c3-0-57', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-712-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.481462792000532, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83260374587163647096602317213', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2323101238434681551502861823180', 'Lhash_array': ['2323101238434681551502861823180'], 'label': '2-712-1.1-c3-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/712/4/a/c/1/11'}