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lfunc_lfunctions • Show schema
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{'Lhash': '1623543885865308567999312536335', 'a10': [6.897410811994094, 0.0], 'a2': [1.6118077997186302, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.5979243832338123, 0.0], 'a5': [4.2793010514021335, 0.0], 'a6': [-1.6118077997186302, 0.0], 'a7': [1.9879911572483133, 0.0], 'a8': [-2.2598764148990504, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.07388592688375, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [61, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 11, 61], 'central_character': '2013.1', 'coefficient_field': 'CDF', 'conductor': 2013, 'conductor_radical': 2013, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.6118077997186302, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.2793010514021335, 0], [5.0, 0]], [[1.0, 0], [-1.9879911572483133, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.25074579134223146, 0], [13.0, 0]], [[1.0, 0], 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'2.29138802434919553474741042214968', '3.36978610695397873972395898322259', '4.65771167804981718879506660644520', '5.13334687574432185745942462931485', '5.79423895609877617742206660194390', '6.38112711559247772533187782230622', '7.17295189082387233857344486495558', '8.620722289465538675293143708420640', '9.186610930281698015579817370905053'], 'prelabel': '2-2013-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.009225103044695, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28075029946974639043645695509', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29138802434919553474741042215', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36978610695397873972395898322', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.07388592688375, 'bad_primes': [3, 11, 61], 'central_character': '1.1', 'conductor': 2013, 'conductor_radical': 2013, 'degree': 2, 'index': 49, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2013/2/a/e/1/10'], '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': '2-2013-1.1-c1-0-49', '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': '2-2013-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.009225103044695, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28075029946974639043645695509', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1623543885865308567999312536335', 'Lhash_array': ['1623543885865308567999312536335'], 'label': '2-2013-1.1-c1-0-49', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2013/2/a/e/1/10'}