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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_19.11', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.5, -0.8660254037844386], 'a6': [-0.5, 0.8660254037844386], 'a7': [1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.11', 'coeff_info': ['x^3 - 1', '-0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{3}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.7', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^2', 'a^1', 'a^2', 'a^1', 'a^0', 'a^0', 'a^1', 'a^1', 'a^0', 'a^0', 'a^1', 'a^2', 'a^1', 'a^2', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^2', 'a^1', 'a^2', 'a^1', 'a^0', 'a^0', 'a^1', 'a^1', 'a^0', 'a^0', 'a^1', 'a^2', 'a^1', 'a^2', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^2', 'a^1', 'a^2', 'a^1', 'a^0', 'a^0', 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'180.32662014895363784839578069048', '181.85383039282618105113133332120', '182.614112455309346201436201788358', '183.54778008788171313009394186108', '184.35041420643929035798495683950', '185.04811645283199710692704676109', '186.009397097975860527541002017688', '187.917277398523622656259485438453', '188.70257773979588825612391934347', '189.51608680983691948120279484170', '190.54134736551517918903514793476', '191.40867725975580042728459563704', '192.29488950405995213221437463337', '193.17234019486261768482432425465', '194.4841230892649139182328290464', '195.58113063802111414485010438942', '195.63401827802546195222472147363', '197.51705910360244093291478902822', '198.579463987526744438130796301391', '199.703414236943928285103441882852'], 'prelabel': '1-19-19.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.08823562904964981, 'root_angle': -0.5989133786043899, 'root_number': '-0.305768557761552452011664520618-0.952105870733092455999549975738*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.299456689302', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(3)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.499203515292847917722790398520-0.402214131376183779474163237453*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.57320808455', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.63964563055', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.49842260072', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'bad_primes': [19], 'central_character': '19.11', 'conductor': 19, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/19/11'], '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': '1-19-19.11-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': '1-19-19.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.08823562904964981, 'root_angle': -0.29945668930219493, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57320808455', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_19.11', 'Lhash_array': ['dirichlet_L_19.11'], 'label': '1-19-19.11-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/19/11'}
Lfunction data - 1-19-19.11-r0-0-0