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lfunc_lfunctions • Show schema
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{'Lhash': '2671269976158764020329206574529', 'a10': [-2.3795909039765366, -1.533154716335538], 'a2': [0.06892169403862215, -1.412533114688235], 'a3': [0.7281359992228844, 1.5715654509550951], 'a4': [-1.990499600181693, -0.194708350299929], 'a5': [1.000813185271718, -1.7334592857754594], 'a6': [2.270072607930967, -0.9202012577265349], 'a7': [2.5098624972023416, -0.8370126911446595], 'a8': [-0.41222059693268903, 2.798226970684197], 'a9': [-1.9396359332713833, 2.288626759950702], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.06892169403862215, 1.412533114688235]]], [3, [[1.0, 0], [-0.7281359992228844, -1.5715654509550951]]], [7, [[1.0, 0], [-2.5098624972023416, 0.8370126911446595]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.107', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'4.15694190844097891925159393110540', '5.76141948181943555037045259649496', '6.84322998440855193410607557377853', '7.41645216081794887181714616271196', '8.781710458579367965737270817622679', '9.379033878580322788815918580611211', '11.09870775837198768916435107639266', '12.13621982110016406598507203714991', '13.26906879885149665419083379715145'], 'prelabel': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.2858163109605226, 'root_number': '0.623239175830204 + 0.7820312843553563*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.14290815548', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.10726045148231320893132985378', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.15694190844097891925159393111', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.76141948181943555037045259649', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.107', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/v/a/107/15'], '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': '2-168-168.107-c1-0-14', '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': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.1429081554802613, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.10726045148231320893132985378', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2671269976158764020329206574529', 'Lhash_array': ['2671269976158764020329206574529'], 'label': '2-168-168.107-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/v/a/107/15'}