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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_197.23', 'a10': [0.8014136218679566, 0.598110530491216], 'a2': [-0.7614459583691344, -0.6482283953077884], 'a3': [0.40478334312239383, -0.9144126230158125], 'a4': [0.15959989503337924, 0.9871817834144502], 'a5': [-0.9979453927503363, 0.06407021998071293], 'a6': [-0.9009688679024191, 0.4338837391175581], 'a7': [-0.7614459583691344, 0.6482283953077884], 'a8': [0.518392568310525, -0.8551427630053462], 'a9': [-0.6723008902613168, -0.7402779970753155], 'algebraic': True, 'analytic_conductor': 0.9148641538305795, 'analytic_normalization': 0, 'bad_lfactors': [[197, [1]]], 'bad_primes': [197], 'central_character': '197.23', 'coeff_info': ['x^49 - 1', '0.991790013823246 + 0.127877161684506*I', '\\\\zeta_{49}'], 'conductor': 197, 'conductor_radical': 197, 'conjugate': 'dirichlet_L_197.60', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^30', 'a^40', 'a^11', 'a^24', 'a^21', 'a^19', 'a^41', 'a^31', 'a^5', 'a^37', 'a^2', 'a^15', 'a^0', 'a^15', 'a^22', 'a^17', 'a^12', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-197-197.23-r0-0-0', 'leading_term': '0.134029116144790674359496031300+0.114506880519872197947310867053*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/197/23', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.17628281158679665, 0.5118787548007355, 0.870551483466246, 1.058492595534516, 0.8824431591927482, 0.31933311247907614, -0.4306923756584343, -1.0085820951679976, -1.073788456257926, -0.5262746645943228, 0.3498914833080244, 0.9375360108267232, 0.5610315646065612, -1.1212239693643204, -3.818187003460747, -6.609558099707206, -8.318591672111797, -8.103398638155085, -5.948417447029091, -2.745069459376486, 0.1373988526947968, 1.5795766432619294, 1.3130989279495269, 0.014309839931975234, -1.1850721487665608, -1.4601572206214728, 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'184.69925575432689393537500066224', '185.94694935982207545463499682666', '186.19595647450528181310961085489', '187.39270679445217378838620907627', '188.04820312937698964136695962670', '189.07492121099118384386719700299', '189.723834251006581968239459178279', '190.369733060989088088791497960763', '190.79771320811300483759924280924', '191.49652654884663531151367878529', '192.15984428385642657316059367794', '192.77419752117921476607193125711', '193.78784293648669481979772045219', '194.49933841710812724169151688704', '195.163337042832126530336857254641', '195.91995137679614949609872587602', '196.78877375108424743574838612965', '197.43773056301672680511284161728', '198.102036072333568102196530518894', '199.031960475307234377447440504693', '199.66213888580063641381306294495'], 'prelabel': '1-197-197.23-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9148641538305795, 'root_angle': 0.4500966656748483, 'root_number': '0.156134512513487913717796685763+0.987735801721379078859312200103*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.225048332837', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(49)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.456184243217670458571287553530-0.159251947370923561327542008800*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.69723413645', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.00196685389', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.88378118763', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.9148641538305795, 'bad_primes': [197], 'central_character': '197.23', 'conductor': 197, 'conductor_radical': 197, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/197/23'], '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': '1-197-197.23-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': '1-197-197.23-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9148641538305795, 'root_angle': 0.22504833283742415, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.69723413645', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_197.23', 'Lhash_array': ['dirichlet_L_197.23'], 'label': '1-197-197.23-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/197/23'}
Lfunction data - 1-197-197.23-r0-0-0