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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_367.132', 'a10': [-0.9670277247913204, 0.25467112024122873], 'a2': [0.32854238191083474, -0.9444892287836613], 'a3': [-0.9357168190404936, 0.3527520865490948], 'a4': [-0.7841198065767104, -0.6206094818274228], 'a5': [-0.5582437220268648, -0.8296770135526189], 'a6': [0.025747913654988557, 0.999668467514313], 'a7': [0.9526353808033825, -0.3041148323275179], 'a8': [-0.8437755598231856, 0.5366961939916005], 'a9': [0.7511319308705199, -0.6601521206712317], 'algebraic': True, 'analytic_conductor': 1.7043408348011304, 'analytic_normalization': 0, 'bad_lfactors': [[367, [1]]], 'bad_primes': [367], 'central_character': '367.132', 'coeff_info': ['x^61 - 1', '0.994699875614589 + 0.102820997137360*I', '\\\\zeta_{61}'], 'conductor': 367, 'conductor_radical': 367, 'conjugate': 'dirichlet_L_367.114', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^49', 'a^27', 'a^37', 'a^40', 'a^15', 'a^58', 'a^25', 'a^54', 'a^28', 'a^5', 'a^3', 'a^54', 'a^46', 'a^6', 'a^13', 'a^4', 'a^42', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-367-367.132-r0-0-0', 'leading_term': '0.311672560437018712325149383774-0.955288712030114071523742048190*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/367/132', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.0048464102844374, 0.6597919101512877, 0.1855745234458103, -0.39508820609556344, -0.6978681520051626, -0.3337919618550282, 0.7723865189241732, 2.239854908997028, 3.371895754600921, 3.5442974071109736, 2.6219987238221387, 1.1070327560498678, -0.14423777980317698, -0.49778746043847155, -0.015171136106911813, 0.5696069391863474, 0.4320918878914827, -0.5931208079517158, -1.7054281576711845, -1.627889594408132, 0.364310587324281, 3.6475909282961427, 6.407950773761787, 6.800132405664595, 4.324586986766848, 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'189.11054165753771326921332248434', '190.001066463612289991652374309696', '190.46570139186148648903988822919', '191.63218161452127944884998774711', '192.06419162954348384381945392113', '192.57299263094449714251153602890', '192.995438826171957458629393666536', '194.22416196229967693390128265207', '194.410314707544864676487676453335', '195.09983197483072920864147078933', '195.75460508338358103387727296179', '196.08247117385616819542638102073', '197.16516088704654427789235553087', '198.46793634107976714673575134733', '198.78577657612868451310081837800', '199.35434869810116490255334301999'], 'prelabel': '1-367-367.132-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7043408348011304, 'root_angle': -0.7992284805386504, 'root_number': '-0.807589945542986280182631507292-0.589744419098541749318837967092*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.399614240269', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(61)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.693112929422890730673360749796-0.594891048081750014429587969463*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.723458149879', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.67829724267', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.70166447155', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.7043408348011304, 'bad_primes': [367], 'central_character': '367.132', 'conductor': 367, 'conductor_radical': 367, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/367/132'], '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': '1-367-367.132-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': '1-367-367.132-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7043408348011304, 'root_angle': -0.3996142402693252, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.723458149879', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_367.132', 'Lhash_array': ['dirichlet_L_367.132'], 'label': '1-367-367.132-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/367/132'}
Lfunction data - 1-367-367.132-r0-0-0