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lfunc_lfunctions • Show schema
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{'Lhash': '1785469501102764319848334691912', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [43.840620433565945, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 119.0821974725887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.449', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '574692095672082530494024325008', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-43.840620433565945, 0], [625.0, 0]], [[1.0, 0], [0, 0], [2401.0, 0]], [[1.0, 0], [0, 0], [14641.0, 0]], [[1.0, 0], [0, 238.0], [-28561.0, 0]], [[1.0, 0], [0, 111.72287142747452], [-83521.0, 0]], [[1.0, 0], [0, 0], [-130321.0, 0]], [[1.0, 0], [0, 0], [-279841.0, 0]], [[1.0, 0], [1129.956636336103, 0], [707281.0, 0]], [[1.0, 0], [0, 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'7.86542254953108736696644672543824', '8.928291921379824980494037922974993', '9.529783657856649961702318071474732'], 'prelabel': '2-1152-24.5-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.912478979250714, 'root_angle': 0.2770433619923482, 'root_number': '-0.1691019787257627481429347680509755569866105044940151880 + 0.9855985596534887808753627929529393543085929980462385641*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2770433619923482', 'prec': 60}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40848708688443499730356699667', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97131160794564611997223165310', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10363804760620292875707558210', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 119.0821974725887, 'bad_primes': [2, 3], 'central_character': '24.5', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 60, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/5/h/b/449/3'], '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': '2-1152-24.5-c4-0-60', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-1152-24.5-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.912478979250714, 'root_angle': 0.2770433619923482, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40848708688443499730356699667', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1785469501102764319848334691912', 'Lhash_array': ['1785469501102764319848334691912'], 'factors': ['2-1152-24.5-c4-0-60'], 'label': '2-1152-24.5-c4-0-60', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/5/h/b/449/3'}