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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.48', 'a10': [-0.30901699437494745, 0.9510565162951535], 'a2': [-0.5877852522924731, 0.8090169943749475], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [-0.30901699437494745, -0.9510565162951535], 'a5': [0.9510565162951535, -0.30901699437494745], 'a6': [-0.9876883405951378, 0.15643446504023087], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9510565162951535, 0.30901699437494745], 'a9': [-7.040766286173228e-31, 1.0], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.48', 'coeff_info': ['x^40 - 1', '0.987688340595138 + 0.156434465040231*I', '\\\\zeta_{40}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.6', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^5', 'a^28', 'a^38', 'a^19', 0, 'a^2', 'a^10', 'a^12', 'a^37', 'a^33', 'a^29', 0, 'a^3', 'a^16', 'a^27', 'a^24', 'a^11', 'a^26', 0, 'a^11', 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'195.95252650791398235724531422256', '196.11607232740065520186103985887', '197.09127225006301354198465800532', '197.53498462043149401781936747958', '197.97217232111563847819050097078', '198.66740842693500972906428500737', '199.54018693235275800960672464739'], 'prelabel': '1-287-287.48-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.35528241313780773, 'root_number': '0.439142242459603764220131430830+0.898417548185447333254802960708*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.177641206569', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(40)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.05477804409698412682443856987+0.495240879148957762331641873877*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.35607854808', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.81829200496', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.4223218489', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.48', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/48'], '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': '1-287-287.48-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': '1-287-287.48-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.17764120656890386, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35607854808', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.48', 'Lhash_array': ['dirichlet_L_287.48'], 'label': '1-287-287.48-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/48'}
Lfunction data - 1-287-287.48-r0-0-0