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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2925.644', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.5877852522924731, -0.8090169943749475], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.30901699437494745, 0.9510565162951535], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8660254037844386, -0.5], 'a8': [0.9510565162951535, -0.30901699437494745], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 13.583642893169772, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [13, [1]]], 'bad_primes': [3, 5, 13], 'central_character': '2925.644', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 2925, 'conductor_radical': 195, 'conjugate': 'dirichlet_L_2925.704', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^39', 0, 'a^18', 0, 0, 'a^55', 'a^57', 0, 0, 'a^39', 0, 0, 'a^34', 0, 'a^36', 'a^2', 0, 'a^47', 0, 0, 'a^18', 'a^14', 0, 0, 0, 0, 'a^13', 'a^18', 0, 'a^7', 'a^15', 0, 'a^41', 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'-0.357102183684357482259647158972-0.934065324486389125692708462179*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.773311810644984921226345274315-0.407746513434325346474498692945*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.577357229031', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.40386086571', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.26982380868', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 13.583642893169772, 'bad_primes': [3, 5, 13], 'central_character': '2925.644', 'conductor': 2925, 'conductor_radical': 195, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2925/644'], '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': '1-2925-2925.644-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': '1-2925-2925.644-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.583642893169772, 'root_angle': -0.30811760413242256, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.577357229031', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2925.644', 'Lhash_array': ['dirichlet_L_2925.644'], 'factors': ['1-2925-2925.644-r0-0-0'], 'label': '1-2925-2925.644-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2925/644'}
Lfunction data - 1-2925-2925.644-r0-0-0