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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_555.77', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.984807753012208, 0.17364817766693036], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9396926207859084, -0.3420201433256687], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6427876096865394, 0.766044443118978], 'a8': [-0.8660254037844386, 0.5], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.577409164345034, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [37, [1]]], 'bad_primes': [3, 5, 37], 'central_character': '555.77', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 555, 'conductor_radical': 555, 'conjugate': 'dirichlet_L_555.173', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 0, 'a^34', 0, 0, 'a^13', 'a^15', 0, 0, 'a^6', 0, 'a^25', 'a^30', 0, 'a^32', 'a^29', 0, 'a^28', 0, 0, 'a^23', 'a^3', 0, 0, 'a^6', 0, 'a^11', 'a^6', 0, 'a^18', 'a^13', 0, 'a^10', 0, 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'186.72100093132275959727718599023', '187.38886014095529942443775984667', '187.99733955691810787481713795682', '188.67281206166324875714134515277', '189.38643197652500440883719742904', '189.87151579786321439691535648747', '190.469952102259502199416144191235', '191.02631692292107340598282171779', '191.75366521244955973673636883978', '192.290841438899635416225335029820', '193.20136651695813104089296885018', '193.45373248790177075370542601741', '194.10034709520360194380390771410', '195.45484192408289080806975925832', '195.6717032023056295948708900779', '196.554767237466270108914042327873', '196.96463732277413931198631619779', '197.64326591957690793836293750497', '198.42857350129456025466298835358', '198.8904314091470734528674726404', '199.48730384541222309105472141262'], 'prelabel': '1-555-555.77-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.577409164345034, 'root_angle': 0.11105698726482227, 'root_number': '0.766262991701675219779677798066+0.642527063670004808669692486698*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.111056987265', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.691153079519372248371023771144+0.114005470222795550105506333649*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.972625805599', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.42199120807', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.15775414476', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.577409164345034, 'bad_primes': [3, 5, 37], 'central_character': '555.77', 'conductor': 555, 'conductor_radical': 555, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/555/77'], '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': '1-555-555.77-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': '1-555-555.77-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.577409164345034, 'root_angle': 0.11105698726482227, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.972625805599', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_555.77', 'Lhash_array': ['dirichlet_L_555.77'], 'factors': ['1-555-555.77-r0-0-0'], 'label': '1-555-555.77-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/555/77'}
Lfunction data - 1-555-555.77-r0-0-0