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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1225.204', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.753071466003611, 0.6579387259397126], 'a3': [-0.9362348706397372, -0.3513748240813427], 'a4': [0.1342332658176555, -0.9909497617679347], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9362348706397372, -0.3513748240813427], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.5508969814521025, 0.8345732537213026], 'a9': [0.753071466003611, 0.6579387259397126], 'algebraic': True, 'analytic_conductor': 5.6888760834642635, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '1225.204', 'coeff_info': ['x^70 - 1', '0.995974293995239 + 0.0896393089034335*I', '\\\\zeta_{70}'], 'conductor': 1225, 'conductor_radical': 35, 'conjugate': 'dirichlet_L_1225.1219', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^27', 'a^39', 'a^54', 0, 'a^66', 0, 'a^11', 'a^8', 0, 'a^62', 'a^23', 'a^13', 0, 0, 'a^38', 'a^51', 'a^35', 'a^56', 0, 0, 'a^19', 'a^47', 'a^50', 0, 'a^40', 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'187.00872914190273793460593660361', '187.39300978163379376147202224951', '188.11383344936155604381552383648', '188.6016260817317633791421092164', '189.18872683273304567299020312732', '189.52051546264217418095859746934', '190.34929735253037045199762499440', '190.68606099956584485257067756091', '191.125178867117879865765866921637', '192.20533233235124851821069577116', '192.693344896131259724609783802103', '193.02243514056652330151852522986', '194.17748950440113334137185828610', '194.593888789905237579272080603104', '195.29372090424432885231559752846', '195.53960912210202736354570134229', '196.37701438618346034153253778443', '196.81755592155302684556633359189', '197.60257718344397260865649007015', '198.044288634113244931683708494883', '198.657073043696156369636759647525', '199.520433298718007469546965719533', '199.76053332502582875562706710288'], 'prelabel': '1-35e2-1225.204-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6888760834642635, 'root_angle': -0.22530612244897963, 'root_number': '0.154534433310790505569967988430-0.987987403219956464735892855016*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.225306122449', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(70)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.569614420355686605978692637769+0.0247780971911774413801769562927*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.406743599457', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.36516858671', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.45153397416', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.6888760834642635, 'bad_primes': [5, 7], 'central_character': '1225.204', 'conductor': 1225, 'conductor_radical': 35, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1225/204'], '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': '1-35e2-1225.204-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': '1-35e2-1225.204-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6888760834642635, 'root_angle': -0.22530612244897963, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.406743599457', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1225.204', 'Lhash_array': ['dirichlet_L_1225.204'], 'factors': ['1-35e2-1225.204-r0-0-0'], 'label': '1-35e2-1225.204-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1225/204'}
Lfunction data - 1-35e2-1225.204-r0-0-0