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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_199.169', 'a10': [0.8738493770697849, -0.4861967361004687], 'a2': [0.5272254676105024, 0.8497254299495144], 'a3': [-0.07924995685678846, -0.9968547759519424], 'a4': [-0.4440666126057741, 0.8959937742913359], 'a5': [0.0475819158237423, -0.998867339183008], 'a6': [0.8052702575310586, -0.5929079290546405], 'a7': [-0.266473813690035, -0.963842158559942], 'a8': [-0.9954719225730846, 0.09505604330418266], 'a9': [-0.9874388886763943, 0.1580013959733499], 'algebraic': True, 'analytic_conductor': 0.9241521147831743, 'analytic_normalization': 0, 'bad_lfactors': [[199, [1]]], 'bad_primes': [199], 'central_character': '199.169', 'coeff_info': ['x^99 - 1', '0.997986676471884 + 0.0634239196565645*I', '\\\\zeta_{99}'], 'conductor': 199, 'conductor_radical': 199, 'conjugate': 'dirichlet_L_199.126', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^16', 'a^73', 'a^32', 'a^75', 'a^89', 'a^70', 'a^48', 'a^47', 'a^91', 'a^36', 'a^6', 'a^82', 'a^86', 'a^49', 'a^64', 'a^69', 'a^63', 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False, 'root_analytic_conductor': 0.9241521147831743, 'root_angle': -0.4407419353193054, 'root_number': '0.185091235011494778775900514261-0.982721341338387547180577260472*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.22037096766', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(99)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.04286407946219214224492690053-0.211007035316438297876014383395*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.674976670053', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.66125673285', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.30383082625', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9241521147831743, 'bad_primes': [199], 'central_character': '199.169', 'conductor': 199, 'conductor_radical': 199, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/199/169'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-199-199.169-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-199-199.169-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9241521147831743, 'root_angle': -0.2203709676596527, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.674976670053', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_199.169', 'Lhash_array': ['dirichlet_L_199.169'], 'label': '1-199-199.169-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/199/169'}