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lfunc_lfunctions • Show schema
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{'Lhash': '1348217212422910631933516683588', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8660254037844386, 1.5], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.3887628415618263, 1.1374586088176875], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.589528141489629, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.3887628415618263, -1.1374586088176875]]]], 'bad_primes': [2, 5, 7], 'central_character': '700.501', 'coefficient_field': 'CDF', 'conductor': 700, 'conductor_radical': 70, 'conjugate': '1741991953467272147560786723616', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.8660254037844386, -1.5], [-1.5, -2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.3887628415618263, -1.1374586088176875]], [[1.0, 0], [-2.6374586088176875, 4.568212313332163], [-5.5, -9.526279441628825]], [[1.0, 0], 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-0.33836917909150305, 'root_number': '0.48623697942908767 - 0.8738269850695142*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.169184589546', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06355585062648644404595131153', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.07469347460716453669495629770', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.96224881433107441035677121778', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.589528141489629, 'bad_primes': [2, 5, 7], 'central_character': '7.4', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/700/2/i/f/501/2'], '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': '2-700-7.4-c1-0-5', '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': '2-700-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.364218293958836, 'root_angle': -0.16918458954575152, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06355585062648644404595131153', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1348217212422910631933516683588', 'Lhash_array': ['1348217212422910631933516683588'], 'label': '2-700-7.4-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/2/i/f/501/2'}