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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1007.329', 'a10': [0.06707764439100236, -0.9977477585156251], 'a2': [0.7830258624176222, -0.6219891468387041], 'a3': [0.897613727639014, 0.44078293518918576], 'a4': [0.22625900242972208, -0.9740671762355546], 'a5': [0.6731118074275702, -0.7395407322802373], 'a6': [0.9770169650018171, -0.21316155867941614], 'a7': [-0.20002569377604443, 0.9797906520422677], 'a8': [-0.4286925614030542, -0.9034504346103823], 'a9': [0.6114208080920122, 0.7913056270696619], 'algebraic': True, 'analytic_conductor': 4.676488339631439, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]], [53, [1]]], 'bad_primes': [19, 53], 'central_character': '1007.329', 'coeff_info': ['x^234 - 1', '0.999639527670885 + 0.0268479928100611*I', '\\\\zeta_{234}'], 'conductor': 1007, 'conductor_radical': 1007, 'conjugate': 'dirichlet_L_1007.453', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^209', 'a^17', 'a^184', 'a^203', 'a^226', 'a^66', 'a^159', 'a^34', 'a^178', 'a^6', 'a^201', 'a^154', 'a^41', 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'a^233'], [1, 'a^39'], [1, 'a^10'], [1, 'a^164'], [1, 'a^73']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1007-1007.329-r0-0-0', 'leading_term': '3.32692815501808392321679060367-1.74384423685601873358820458757*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/1007/329', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.7562539412382625, 3.6266535045586714, 3.1703563826567542, 1.816966698897861, 0.1290760072511644, -0.9066349863483114, -0.7701720798903586, 0.13474569367190195, 0.814071998063398, 0.5754512751264813, -0.3033217239999044, -0.8139151189881468, -0.23250784655754392, 1.0568918690264444, 1.8499177024601607, 1.3727427766891136, 0.23991203618030188, -0.043817301956903046, 1.2450397457710594, 2.9108578100918514, 2.6961832232298013, -0.3878958793936094, 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'root_analytic_conductor': 4.676488339631439, 'root_angle': -0.30735279702793794, 'root_number': '0.568942221492171796643364764075-0.822377497627186129810122889094*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.153676398514', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(234)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.26043455792749726001194561384-0.783957728956115925188499056766*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.2772128212', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.14449908772', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.02216722451', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.676488339631439, 'bad_primes': [19, 53], 'central_character': '1007.329', 'conductor': 1007, 'conductor_radical': 1007, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1007/329'], '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': '1-1007-1007.329-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': '1-1007-1007.329-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.676488339631439, 'root_angle': -0.15367639851396897, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.2772128212', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1007.329', 'Lhash_array': ['dirichlet_L_1007.329'], 'label': '1-1007-1007.329-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1007/329'}
Lfunction data - 1-1007-1007.329-r0-0-0