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lfunc_lfunctions • Show schema
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{'Lhash': '2626972777980422906242896013354', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8660254037844386, 0.5], 'a4': [0.0, -1.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.8660254037844386, -0.5], 'a8': [0.0, 0.0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, -0.5]]], [7, [[1.0, 0], [-0.8660254037844386, 0.5]]], [13, [[1.0, 0], [-0.8660254037844386, -0.5]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.227', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '1904198858438780792019802291321', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], 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2.7434489431991005, 3.473032914484372, 4.145731653017263], 'positive_zeros': ['2.07231612362859248253041835300223', '3.87042298282541794138872455743710', '5.17358557078102877837631555532451', '6.19970708999153305762628923763547', '7.46453818625146142633300934425445', '8.107211141571774721641999490708232', '9.151878976193034306692145014546513', '10.77008989429976638105072027550927', '11.34984707967465724632257761780624', '12.14283645568478792849058137253071'], 'prelabel': '2-273-273.227-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': 0.13861189952350722, 'root_number': '0.90667520108659576545660934379400 + 0.42182944389241148951030267423627*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0693059497617536', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.07231612362859248253041835300', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'bad_primes': [3, 7, 13], 'central_character': '273.227', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/1/bs/a/227/1'], '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': '2-273-273.227-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-273-273.227-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': 0.06930594976175361, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.07231612362859248253041835300', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2626972777980422906242896013354', 'Lhash_array': ['2626972777980422906242896013354'], 'label': '2-273-273.227-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/1/bs/a/227/1'}