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lfunc_lfunctions • Show schema
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{'Lhash': '1279130433947786642270442014687', 'a10': [-4.349107724585149, 0.26411195327769976], 'a2': [1.2653548587172025, 0.6315671631115477], 'a3': [-1.6927283552396108, 0.36697508821145], 'a4': [1.2022458369584634, 1.5983131568988738], 'a5': [-2.6681800766564447, 1.5404744855039947], 'a6': [-2.373671464185136, -0.604717934340625], 'a7': [-1.463066402379498, 2.204413006273623], 'a8': [0.5118255049014375, 2.7817323114441455], 'a9': [2.730658569264397, -1.2423782749641579], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.2653548587172025, -0.6315671631115477]]], [3, [[1.0, 0], [1.6927283552396108, -0.36697508821145]]], [7, [[1.0, 0], [1.463066402379498, -2.204413006273623]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'4.43897338832240604633388142857577', '5.93215886714571118066612173783977', '6.87622732268785573608822717597190', '8.126304074720731508485898975932011', '9.895099341995364885230130682160721', '10.92032230535651300735214414158578', '11.55975016547637150357212857421785', '12.55484004340723346050653828620450'], 'prelabel': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.6463765037826366, 'root_number': '-0.4438184873793336 - 0.8961167057143395*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.323188251891', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00905599201979661993226028240', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.80681228782733170981325195499', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.43897338832240604633388142858', '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': '168.101', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/20'], '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': '2-168-168.101-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': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.3231882518913183, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00905599201979661993226028240', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1279130433947786642270442014687', 'Lhash_array': ['1279130433947786642270442014687'], 'label': '2-168-168.101-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/20'}