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lfunc_lfunctions • Show schema
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{'Lhash': '3450167051897802388215486058848', 'a10': [-1.986001710627919, -1.1466186222420864], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [1.41274731801723, -1.0020703645129534], 'a4': [0.0, -1.0], 'a5': [-0.5935334738109295, -2.2150970802552408], 'a6': [0.2903924586999066, -1.7075339586462763], 'a7': [1.0784448198990648, 4.024810861022777], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.9917099691297535, -2.831344439860446], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.868499407297962, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [-1.41274731801723, 1.0020703645129534]]], [13, [[1.0, 0], [3.5971175881579063, -0.24646512322243044]]]], 'bad_primes': [2, 3, 13], 'central_character': '234.59', 'coefficient_field': 'CDF', 'conductor': 234, 'conductor_radical': 78, 'conjugate': '2159011780724822603776689695522', 'degree': 2, 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'3.95196693487184408392351247532162', '4.68440177160583202012543887228904', '6.57077034630417523960793008405896', '7.38600691011094675346125955196112', '8.169966456570918081575598800057963', '9.483655394906781142931688644604445', '10.69935048432052968543005219944306', '11.03136736850717133934967308789751', '12.67267811402474282257818962056939'], 'prelabel': '2-234-117.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710362, 'root_angle': 0.4383671181002852, 'root_number': '0.1924178130248116 + 0.9813130923567405*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21918355905', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.72170190372381000859082397901', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.95196693487184408392351247532', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.68440177160583202012543887229', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.868499407297962, 'bad_primes': [2, 3, 13], 'central_character': '117.59', 'conductor': 234, 'conductor_radical': 78, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/234/2/y/a/59/13'], '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': '2-234-117.59-c1-0-12', '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': '2-234-117.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710362, 'root_angle': 0.2191835590501426, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.72170190372381000859082397901', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3450167051897802388215486058848', 'Lhash_array': ['3450167051897802388215486058848'], 'label': '2-234-117.59-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/234/2/y/a/59/13'}