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lfunc_lfunctions • Show schema
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{'Lhash': '2550564540266851040887432316724', 'a10': [0.0045830756932046055, 0.5517356370350801], 'a2': [0.7172555650348209, 1.2188291325803546], 'a3': [1.1114175808150812, -1.3284392952089126], 'a4': [-0.9710889088531597, 1.7484239563396458], 'a5': [0.3378793522235315, 0.19507473495987226], 'a6': [2.4163109587822915, 0.4017976486598739], 'a7': [1.3952565872118234, 2.2479455188776294], 'a8': [-2.8275489781066834, 0.07047536028890983], 'a9': [-0.529501922110305, -2.952901575481562], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7172555650348209, -1.2188291325803546]]], [3, [[1.0, 0], [-1.1114175808150812, 1.3284392952089126]]], [7, [[1.0, 0], [-1.3952565872118234, -2.2479455188776294]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': '3085479328886007410488751329876', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7172555650348209, -1.2188291325803546]], [[1.0, 0], [-1.1114175808150812, 1.3284392952089126]], [[1.0, 0], [-0.3378793522235315, -0.19507473495987226], [2.5, 4.330127018922194]], [[1.0, 0], [-1.3952565872118234, -2.2479455188776294]], [[1.0, 0], [0.7485818614482928, 1.296581817652929], [-5.5, 9.526279441628825]], [[1.0, 0], [-3.2876798044711153, 0], [13.0, 0]], [[1.0, 0], [1.681694330587959, 2.9127800233788768], [-8.5, 14.722431864335457]], [[1.0, 0], [2.562025898155181, -4.437559025912059], [-9.5, -16.454482671904334]], [[1.0, 0], [4.727636213713769, 2.7295020406182675], [11.5, 19.91858428704209]], [[1.0, 0], [4.138013373621486, 0], [29.0, 0]], [[1.0, 0], [3.602371304706329, -2.079830042493182], [15.5, -26.846787517317598]], [[1.0, 0], [-7.465805410367592, -4.310384763393094], [18.5, 32.04293994002423]], [[1.0, 0], [-11.160704639297274, 0], [41.0, 0]], [[1.0, 0], [0, 4.793229105477323], [-43.0, 0]], 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'4.48311518166199324488276551381906', '5.83690754241104142686159390298342', '7.68779094598316587303878462037827', '8.929749721887275897312341524217961', '9.799869400436738809930094962868391', '10.87267836071858866350301473626575', '11.26734029236166023118629178523849', '13.05544679212223144781047519927173'], 'prelabel': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.25597550515754064, 'root_number': '0.6937087335675973 - 0.7202556441792319*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.127987752579', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01204065205952192747816406954', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.73653766108167827150187749057', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48311518166199324488276551382', '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': '168.5', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/16'], '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': '2-168-168.5-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': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.12798775257877032, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.01204065205952192747816406954', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2550564540266851040887432316724', 'Lhash_array': ['2550564540266851040887432316724'], 'label': '2-168-168.5-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/16'}