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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2340.2207', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8660254037844386, -0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 251.46792401942255, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '2340.2207', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 2340, 'conductor_radical': 390, 'conjugate': 'dirichlet_L_2340.563', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^7', 0, 0, 0, 'a^6', 0, 0, 0, 0, 0, 'a^5', 0, 'a^14', 0, 0, 0, 'a^17', 0, 0, 0, 0, 0, 'a^0', 0, 'a^16', 0, 0, 0, 0, 0, 'a^1', 0, 0, 0, 'a^8', 0, 'a^7', 0, 0, 0, 'a^17', 0, 'a^2', 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'195.40206478736258395841599520397', '196.03737518697387065265079979852', '196.618948018708271719243809430310', '197.15629417186283863788367225331', '197.533921506942013610983716361469', '198.16602821412672976505158597794', '198.9128503227474272762091719958', '199.31772577642623437720394650598', '199.96401602016445466119435541526'], 'prelabel': '1-2340-2340.2207-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 251.46792401942255, 'root_angle': -0.27504796691628614, 'root_number': '-0.156732132404902795298097927570-0.987641148733593429917641239506*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.275047966916', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.759679056894041016771994118510+0.0367550181948584036306257404304*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.105143472419', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.29403383753', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.35064952901', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 251.46792401942255, 'bad_primes': [2, 3, 5, 13], 'central_character': '2340.2207', 'conductor': 2340, 'conductor_radical': 390, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2340/2207'], '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': '1-2340-2340.2207-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2340-2340.2207-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 251.46792401942255, 'root_angle': -0.27504796691628614, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.105143472419', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2340.2207', 'Lhash_array': ['dirichlet_L_2340.2207'], 'factors': ['1-2340-2340.2207-r1-0-0'], 'label': '1-2340-2340.2207-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2340/2207'}
Lfunction data - 1-2340-2340.2207-r1-0-0