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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.658', 'a10': [-0.5326077245747999, 0.8463622225284244], 'a2': [-0.6548607339452851, 0.7557495743542583], 'a3': [-0.10452846326765347, -0.9945218953682733], 'a4': [-0.14231483827328514, -0.9898214418809327], 'a5': [0.9884217748453624, -0.15173132508333165], 'a6': [0.8200610852841911, 0.5722759967030896], 'a7': [0.7237340381050702, -0.690079011482112], 'a8': [0.8412535328311812, 0.5406408174555976], 'a9': [-0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.658', 'coeff_info': ['x^165 - 1', '0.999275047800474 + 0.0380707084693900*I', '\\\\zeta_{165}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.2799', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^60', 'a^121', 'a^120', 'a^161', 'a^16', 'a^145', 'a^15', 'a^77', 'a^56', 0, 'a^76', 'a^98', 'a^40', 'a^117', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-3751-3751.658-r0-0-0', 'leading_term': '0.534178142704607309158032019698-1.22167663936072852647984661885*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/3751/658', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.3333567037005014, 0.5647212162478938, -0.14478196043434705, -0.1590188414511631, 0.8697010751785024, 1.971070135737539, 1.7426248067036096, 0.3855274430241559, 0.3264062951784334, 3.8944976005829237, 10.055716284215016, 14.227607477945465, 12.391354134195044, 5.486543374736536, -1.1270982022746125, -3.0540292742428043, -1.0811529260581798, 0.6285456037179239, -0.15170282215985612, -1.6547821239057734, -1.449883701859092, -0.017654749955172244, 0.4106233013859204, -0.4875510789866356, -0.7907923420974676, 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'194.70760358437428561974963818861', '195.31210261674649754628029603810', '195.87332716701095390741585224527', '196.33234624044629442053448035418', '196.68681502761496156498706032160', '197.35814669736330996385775989581', '197.675692310547657129633118701092', '198.363836701626215662025905840001', '198.73213358246680123262432833745', '199.45369947194230564841508809090'], 'prelabel': '1-3751-3751.658-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.368792471268696, 'root_number': '-0.678996678885572828464449686322-0.734141342019615659995432892503*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(165)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.837453380801068481403982383833-0.337146911282244096185927263501*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.547250133806', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.00992681493', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.3482579319', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.658', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/658'], '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': '1-3751-3751.658-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': '1-3751-3751.658-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.368792471268696, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.547250133806', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.658', 'Lhash_array': ['dirichlet_L_3751.658'], 'factors': ['1-3751-3751.658-r0-0-0'], 'label': '1-3751-3751.658-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/658'}
Lfunction data - 1-3751-3751.658-r0-0-0