-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_763.149', 'a10': [-0.9983081582712682, -0.05814482891047583], 'a2': [0.984807753012208, 0.17364817766693036], 'a3': [-0.05814482891047583, 0.9983081582712682], 'a4': [0.9396926207859084, 0.3420201433256687], 'a5': [-0.993238357741943, 0.11609291412523023], 'a6': [-0.23061587074244017, 0.9730448705798238], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.8660254037844386, 0.5], 'a9': [-0.993238357741943, -0.11609291412523023], 'algebraic': True, 'analytic_conductor': 81.99573761829889, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [109, [1]]], 'bad_primes': [7, 109], 'central_character': '763.149', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 763, 'conductor_radical': 763, 'conjugate': 'dirichlet_L_763.466', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^28', 'a^6', 'a^52', 'a^31', 0, 'a^9', 'a^56', 'a^55', 'a^17', 'a^34', 'a^25', 0, 'a^80', 'a^12', 'a^3', 'a^59', 'a^21', 'a^58', 0, 'a^20', 'a^15', 'a^37', 'a^104', 'a^28', 'a^84', 0, 'a^82', 'a^83', 'a^38', 'a^15', 'a^45', 'a^6', 0, 'a^62', 'a^11', 'a^24', 'a^53', 'a^61', 'a^99', 0, 'a^66', 'a^23', 'a^0', 'a^18', 'a^59', 'a^40', 0, 'a^107', 'a^31', 'a^31', 'a^43', 'a^87', 'a^69', 0, 'a^49', 'a^85', 'a^89', 'a^86', 'a^58', 'a^41', 0, 'a^18', 'a^77', 'a^48', 'a^65', 'a^9', 'a^43', 0, 'a^42', 'a^65', 'a^44', 'a^14', 'a^24', 'a^27', 0, 'a^56', 'a^29', 'a^64', 'a^4', 'a^102', 'a^10', 0, 'a^55', 'a^69', 'a^2', 'a^26', 'a^76', 'a^3', 0, 'a^21', 'a^66', 'a^62', 'a^73', 'a^43', 'a^16', 0, 'a^73', 'a^2'], 'euler_factors': [[1, 'a^3'], [1, 'a^28'], [1, 'a^52'], [0], [1, 'a^17'], [1, 'a^25'], [1, 'a^3'], [1, 'a^21'], [1, 'a^15'], [1, 'a^82'], [1, 'a^38'], [1, 'a^11'], [1, 'a^99'], [1, 'a^66'], [1, 'a^59'], [1, 'a^43'], [1, 'a^89'], [1, 'a^58'], [1, 'a^65'], [1, 'a^42'], [1, 'a^44'], [1, 'a^29'], [1, 'a^10'], [1, 'a^76'], [1, 'a^16'], [1, 'a^99']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-763-763.149-r1-0-0', 'leading_term': '0.0393626248408146050542006279380+3.17504418712615254210146305931*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/763/149', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.1752881769121246, 4.982060085073206, 5.84837908839128, 5.201254485190986, 2.9824265582341223, -0.09062840031715612, -2.731522151071138, -3.7889716923934684, -3.0029991864011074, -1.2062055138148144, 0.2772261345469558, 0.6247581393251075, 0.09033008632646428, -0.3620056997629766, -0.06378362342606131, 0.6574161208896057, 0.8132433067992217, -0.13437202294532619, -1.5058420552028118, -1.8936507712837922, -0.5903274025129228, 1.4616854430747028, 2.3488427742611067, 1.0608534810142292, -1.2648259323370474, -2.186182228436467, -0.323124628875321, 3.0432864896127194, 4.927848330639129, 3.4501870333384703, -0.2370279413371607, -2.946598195736539, -2.503518145857284, 0.22169802273913447, 2.378131827074118, 2.135444525421422, 0.3984582402313963, -0.5454830120699841, 0.19394915067350474, 1.1209878068613914, 0.27055692328730974, -2.2623700247253176, -4.218465498761818, -3.6778151521049907, -1.234961946431586, 0.7282288123260802, 0.7713129869534459, -0.1722882253163351, -0.30858266443738597, 0.6056548255103411, 1.1036261691163087, 0.2722203797746599, -0.7014888064191386, -0.07337926541543888, 1.6005090321676523, 1.2817674420471405, -3.071880239144748, -9.252786726005091, -12.13523458245425, -8.803617542325822, -1.8631628876187531, 3.044022216196795, 2.9182310166683036, -0.0494001285068274, -1.6634878959693564, -0.5442164787729642, 1.0652295688158322, 0.8534722180395447, -0.581397950040026, -0.9785655446548169, 0.2691043736555663, 1.404078649222126, 0.9720988803781399, -0.11107146112137084, -0.09008391032144984, 0.7778687962863378, 0.3746474638214691, -2.0534081988410238, -4.196987107790262, -3.3644202960139173, -0.2405192658309569, 1.5685829868225811, 0.056436604786086336, -2.4929084864902595, -2.460355691522428, 0.2547035604983141, 2.04556026224284, 0.4943927541746525, -2.2358964393481555, -2.2676608637003266, 0.6190009610076687, 2.4735894656933466, 0.42561307036576385, -3.302283684285888, -4.095853653174903, -0.8282397785634894, 2.853116454329103, 3.3174317213884135, 1.2317750840528903, -0.11302221716897601, 0.49994182700839573, 1.1590977006376197, 0.3139399119317091, -0.8078034851819303, -0.3653468999815599, 1.0040989224296097, 1.133451985294629, -0.15805262396340075, -0.6570700307783602, 0.6084297656042137, 1.3764945536851694, -0.5211533745645117, -3.137284840757999, -2.3313810401716015, 2.0737789717143644, 4.649508244308161, 0.6690336160959531, -7.38511383832445, -12.053612407645561, -9.479546882694601, -3.419389761216994, 0.06136291351586969, -0.33270633990180687, -1.2813808080733415, -0.5907433134286055, 0.26866373780677216, -0.3406238486901577, -1.08660307784576, 0.040028236816344064, 2.0054210352313446, 1.9430652637530819, -0.3004490936747818, -1.504480196894307, 0.2712451125699935, 2.669310127608683, 2.388499419124304, -0.060058370506001324, -1.3702068376843026, -0.5047651872303448, 0.17554105052368393, -0.6111964760780874, -0.4403695910657913, 2.830547394113929, 6.501283887434656, 5.785312563775705, 0.7806808326956352, -2.7751481644764344, -0.9893834211768462, 2.813077463882256, 2.7403769236417492, -1.447978390711253, -4.2310110931504665, -2.2177723445108657, 1.4558591940193688, 2.0927270735921994, -0.10334743224011136, -1.288213810537708, -0.07064941885847068, 1.0678580453046158, 0.332179406529121, -0.7335861807417198, -0.3534558646921192, 0.46150448107233555, 0.12295772035177663, -0.33790040784995645, 0.8265922527434154, 2.099584255542843, 0.1907308500996226, -4.195856750506925, -5.755245616268841, -1.675542275698523, 3.5769837331778414, 3.726515318130121, -0.758403099646938, -3.4868017191593914, -1.2818683216470215, 1.744548830694691, 0.8337418349336058, -2.4392584198196525, -3.1362346441044733, -0.6171408786693662, 1.0434530488878204, -0.15262524848861067, -1.2810520015154607, 0.2638134425317024, 2.410474561329219, 1.9677773091719355, -0.0636941060071938, -0.24132535327349397, 1.5762027972536166, 2.100496526081605, 0.21701996987955147, -1.1153396943174538, 0.18245865325298136, 1.8649007774549897, 1.1843069346409476, -0.5836333307861796, -0.6314964648941808, 0.2871395076392974, -0.7034741299673163, -2.8344532798099564, -2.145649462111968, 1.2264449777458164, 1.0042183534935563, -6.669277445908145, -15.988938131669796, -17.485308654407014, -9.932413788054774, -1.485954011957343, 1.165243868446154, -0.06566873623772855, -0.04350031382918815, 1.6747062114159916, 2.020574717437097, 0.5612411631779579, -0.21896027488437575, 0.19969553753388583, -0.29200482072458395, -1.9096988367784746, -1.9486855807545242, 0.4058636728021577, 2.0087175609428893, 0.709808594715806, -0.9320276336536064, -0.00031538992013005105, 1.4763510845685932, -0.22271163342091452, -3.6330386793914844, -3.608393760063946, 0.278396546886361, 2.2016798737102796, -1.157062252272798, -5.1682834390230985, -4.143997011328005, 0.08559265012076037, 1.3612371102624592, -1.2543624029245546, -2.8141130446806475, -1.0234374459197835, 0.4666843380249118, -1.0173799981465794, -2.260751471730775, 0.3412822434422821, 4.28760301400773, 4.509760356762304, 1.1124748358602163, -1.2225645151247309, -0.559576847811275, 0.39913652738034033, -0.16670627049695255, -0.5790383275076777, 0.19188106102098015, 0.23685277446958425, -1.1954721817198535, -1.3393747925212407, 1.238756182737457, 3.0764380824690334, 1.3235723467299336, -0.1700364642530271, 4.0738835191300975, 11.389168742615379, 12.811742274887875, 5.593671658729572, -2.3791542093393856, -3.4602184037564334, -0.0625275205127352, 0.781809112788498, -1.671699765979545, -2.4056544615623308, 0.1869925228787501, 2.2036145434561134, 1.2959207026338357, -0.09017287233736711, 0.0742226082581595, 0.12354473166763305, -1.073934664371107, -1.2018878065673206, 1.0252411731165383, 2.3903402620211054, 0.12029849092187486, -2.8454025011530417, -2.124659656522142, 0.9008771664088067, 1.3622596461559078, -0.9895628982177177, -1.748264623197437, 0.23978716095937172, 1.146744376312273, -0.3162613457517317, 0.02627943083929928, 4.0490774683627535, 6.432463706433511, 2.584300864834552, -2.9633273612984725, -2.4561038385478327, 3.372549850707423, 6.470411044532938, 3.5742631151435766, 0.016388056467058796, 0.3532586535418451, 2.0043461805731524, 1.1785158770719857, -0.6194928820179583, -0.2743598174462154, 1.0581999858613997, 0.56253485575491, -0.7925782406077888, -0.3097338206299429, 1.1531506224213397, 0.8912864479442589, -0.3444348474034725, 0.05653172725627928, 0.940588936870134, -0.7744559233897538, -3.143541822161771, -0.8731756774521388, 4.92338657144799, 5.867274741810241, -1.4611915880980564, -8.95457747727647, -7.7967251873765715, -0.6727806857385814, 3.195299070851549, 1.4255060122441088, -0.5288155798340802, 0.2384453375593577, 0.7560069973584731, -0.49575011990151435, -0.5202669910731953, 1.8232196830027536, 2.877363421745713, 0.7022787243073682, -1.022778560477948, 0.6908587111530445, 2.8147201431315882, 1.6043228497840525, -0.9917134827560621, -1.1326258626828887, 0.2120619430335866, -0.21118163619741048, -1.4992138990227635, -0.6015878402765331, 1.2585501896573594, 0.5880393099205526, -1.1753563151041064, 0.5213114757755571, 4.489907778472636, 4.388281851189163, -0.4616715168771598, -2.74256013948084, 1.100202791494992, 4.350566974019096, 0.6020987393812087, -5.5724458486290995, -5.575154680287824, 0.11076254808811103, 3.640084814810458, 2.0654005289542376, -0.14657357498747592, -0.034637343693563145, 0.17678257786165852, -0.9271145155188458, -1.1945857432929485, 0.14088799314542808, 0.6703610565459672, -0.19222020721242924, -0.00466910215726812, 1.0460911013846927, -0.7634891594630324, -5.366663476019622, -6.884518072061735, -2.6667769871070406, 1.647903446472737, 0.9196255339373386, -1.4052136837578677, -0.15535483027005303, 1.8175242050364888, -1.3330448871391858, -7.224887932420833, -8.034455288539746, -3.099283700098648, 0.2676861512262478, -1.170441587861632, -2.5064133962411312, -0.4457112781240984, 1.3091959203195451, -0.20189062478237563, -1.5940141786854696, 0.20293912820365212, 2.058045893372184, 0.5686614725164002, -1.517821010592509, -0.3757954655409811, 1.9411646851617121, 1.4483243622610373, -0.6446973327717544, -0.7221315500341032, 0.5229430332873726, 0.20489665884968117, -0.7763039691966468, -0.07674294698925935, 0.5976599635845016, -0.7988931589425943, -0.22330916753244173, 6.825568249089782, 14.898328530927856, 13.497355243655763, 2.928437836924502, -4.532878979951211, -1.8026616748009077, 4.056491936668609, 4.167053813868204, 0.27400076111741006, -1.1991863133260428, -0.10485782855911446, -0.14059509298790826, -0.8042487787422709, 0.5931262000390761, 2.488871064773357, 1.6766173147629595, -0.4187756974348968, -0.48968581511027065, 0.2884566751570163, -1.0139439641266734, -2.6516397636917963, -1.2625628104909121, 1.047823463465563, -0.0454539350317115, -2.7355849253322098, -1.8612313380767602, 1.34326056325055, 0.8665358830178971, -3.123732713534671, -4.099239401419427, -0.7729611943329007, 0.5666795741421596, -2.4730173883005437, -4.072633317780344, -1.0652513971996072, 1.062445014600094, -1.705824464534707, -4.2141976777108265, -1.216510065375317, 3.0608236719113533, 2.092273638067529, -1.9708628082669937, -2.5919326758723726, 0.25018016232369444, 1.538444705696384, 0.3756606424761093, -0.13361052938525722, 0.22139711824129926, -0.6881124591053115, -1.8257790939753114, -0.9047163560166711, 0.1736092932703147, -1.4894821178350925, -3.4831336281592744, -2.0934280580916584, 0.04138458861410698, -1.518186573886587, -3.316384418521144, 1.344687446374059, 9.308759822345191, 10.106043940453624, 2.3875499242876788, -3.2939388979766853, -0.7861571436268986, 3.3359037780647602, 2.0806656206226464, -1.3559294190416855, -1.2793841343422008, 0.7475267548160299, 0.675532949416339, -0.34525859544494863, 0.24935289145957576, 0.7505933263027473, -0.4754942098450543, -0.3941984785593273, 2.849285862753504, 4.820137009312737, 1.7818455008368335, -2.331787069343471, -2.3142538227242655, -0.027369378700575913, 0.2537203878835022, -0.23365859346879103, 1.4116040815708508, 2.877564048548381, 1.2184840966140873, -0.4207466073785178, 1.2356307007366627, 1.743891100961389, -3.6817864783237293, -9.33210717442283, -6.243014653663703, 2.697647177778757, 6.275105447715721, 2.1310099555828645, -1.1845731362924976, 0.6919003990763735, 2.496145421774594, 0.7168482891394852, -0.6153483216572884, 1.22124647832284, 2.5489883540195013, 0.8242549228376707, -0.8718398899899811, -0.32291113294881674, 0.17687454456252816, -0.4857445725062075, -0.029816970875831135, 1.4424629548306895, 0.7633101199420701, -1.4023925755931341, -0.9651163269282669, 0.7008653567361607, -2.4555260026454886, -9.166494471469413, -9.986650038539649, -2.329224173918495, 4.126355135698308, 2.3846593052807, -1.7322560942931247, -0.9743980668649687, 1.6349080515469838, 0.5080837146844427, -1.795133075482553, -0.545377729416359, 1.6286640263151548, 0.2304037368604036, -2.1210703053860924, -0.9495192183103368, 1.2199546113498827, -0.20647415373059738, -2.9949117668564376, -2.43784462522405, -0.08949465089828999, -0.09780108363560495, -1.1269532241375029, 0.21536300926835167, 2.110203112756796, 1.310982917624728, -0.09746444186581701, 0.8889539438422903, 1.7033662336668765, -0.46021206336164966, -2.100899786794897, -0.009309338392519798, 1.573201581304768, -0.7905420818660531, -0.8401114676042678, 7.314175506939364, 16.05891759204826, 13.62200621993176, 2.5622350883680873, -3.8878640214127804, -1.5058049993517668, 1.6618583525025497, 0.5660229075947254, -0.9611606312039664, -0.14058929722404703, 0.34768562916569884, -0.5716111292962914, -0.43487992397809283, 0.5515156374554552, -0.2808181305430715, -1.6555321898774715, -0.2643722895831217, 1.8938253261496396, 0.5339056695483828, -2.186956590282291, -1.0251845525926928, 2.21877956832903, 1.6931597545730799, -1.4320170485719559, -1.3987087221591894, 0.64049761457985, -0.9793675491275927, -4.094087360955977, -1.1892613912110845, 6.241642043161161, 8.53942494046052, 3.695416018461875, -0.1507700038348952, 0.7968602196341819, 1.4727373763395843, -0.21605185005847094, 0.5209301835843533, 4.51367059283678, 5.54372235538999, 1.598785812407305, -1.3726476544199424, -0.2711437261731022, 0.5680409639742567, -1.3437918598833414, -2.360000832699197, -0.6198943793158452, 0.6462599354038007, 0.07846397467485547, 0.11110645163544015, 0.7496667206691523, -0.1376619739544821, -0.4245813621929489, 3.017600094593841, 5.7325468395706904, 1.3321367481479724, -5.358757103516048, -3.512291372917873, 5.489493828508617, 8.865422762599788, 2.715150162033402, -2.7495351941179704, -0.9889915037734036, 1.9452870988884743, 0.5280107851752325, -1.3637206120548246, -0.028449273215140607, 1.1245473375406174, -0.41965003433243875, -1.3264795062176604, 0.043861249372346055, 0.28355873724584163, -1.4922187384421202, -1.6227772229435398, 0.24103885475212083, 0.33821432995353135, -0.7646919173652238, 1.4019338311811729, 5.4721356185262415, 5.1783220091528674, 0.7106377457992931, -1.4027111750963117, -0.06987617545375308, -0.2946892419263817, -2.197310032458627, -1.1626933984518346, 1.2144835168039538, -1.1407878179416207, -6.112958389143972, -5.6127435872163485], 'positive_zeros': ['1.553350135404322043973961239555', '3.04744509373185153720781840036', '3.79313254864431004618962873309', '4.40468799212377934186417115042', '5.28130409684260099773142048069', '6.33941456654215066275808090455', '7.328490863619163268694199618236', '8.157263173988343384090699616565', '9.35543229914247708657164515372', '10.2890585013496221059302706369', '11.330586981881937569403285877516', '11.82413184905637517628451737904', '12.54102363611425203112577289907', '13.91405527775603096887162483319', '14.6246203694809804978914146550', '15.1273260393805025031188911440', '16.00537875466744687834970567160', '16.57731024063525964686558389379', '17.31314313831160959308205991715', '18.84077028252966936544175196773', '19.68216210844977989458051946362', '20.40112273080898485478367066195', '21.12306971492477095570309779910', '21.82160008497050082864093523839', '22.76967453948113001961853869320', '23.16117772742956723089489765753', '23.81509295517630993977183554844', '25.02470773863653635642242433481', '25.631490594319547166146904952229', '26.53588449803233289273632396013', '27.24021088801096126148899802242', '28.0652072350745851178623577455', '28.78540178266433829367320674051', '29.74768226758684680721650950180', '30.867280405274609954255708589821', '31.082908927832983700752416782301', '31.94556046644096069995219955017', '32.583316226796879096212792508401', '33.40100970632650620850173217981', '33.94175128524223369968602242982', '34.6301305574675629635728562141', '35.49038044179895661770341980456', '36.27866381481566182821988681092', '37.797977299496114277864968300642', '38.03972295718266748234942049412', '38.91429917188816615706796778260', '39.271426355261066778995987218355', '39.99376056026911043126396686174', '40.89850969058042059546848968471', '41.53129697329068488177621071790', '42.49222876410487374141781480392', '43.270628988438540168437312525053', '43.55009409255928675815232899116', '44.128408689264893734065767277413', '45.358996957809862463786927633820', '46.01329451954372164303920039177', '46.77806289085428398581706576432', '47.67495184222330560954679801676', '48.42367975018925117453492833935', '49.07536773947662312083493927805', '49.76404013344625056160871309366', '50.42286279610410762256460137062', '50.98577927207373600552520179583', '51.39626084405046316429132901190', '52.20292133979017849337328418291', '53.21247656330566899578086172158', '54.01373894284733821234337209344', '54.79559799250174734221465101452', '55.39399024085396583352501326557', '56.32215143343369604342764393282', '56.84953225606329959988609277724', '57.46663399563314792942243282671', '58.425057225533968859754988629984', '58.80329464493927405947708597104', '59.71818204516996848274128383453', '60.28539783446763678723761502907', '61.13084585307094990735915747430', '61.74577979885722680040097042213', '62.062012713923329666799697152890', '63.009837931166868959755244857774', '63.501344236404553308860011166427', '65.094198122001724377287164187296', '65.60873706709855232821067795944', '65.947694762796971892104654746317', '67.01672866489539537068537623559', '67.368590395507072706978179417782', '67.733744022429674674177020410557', '68.703030865679009155399079607134', '69.477569796436474943082287935074', '70.00005058753014299681481802504', '70.60377261020964035573407128777', '71.541285825186283773405820293572', '72.1116154021711071893301668977', '73.117655566488296018004247424829', '73.62360369982720988503550655327', '74.52082283863740652479885828393', '74.84631286580351931010291444925', '75.59914652011495164245134963873', '76.66680262467607495026051581455', '77.318641720015072424629166674114', '77.7551977902756197507526563537', '78.37021635048494945350829624396', '78.8169182560342956609305843204', '79.5605660468138798987274728512', '80.48827424130578156101227571862', '80.66459495666241877330742219840', '82.07181045740338669268841470544', '82.819052023054201311610137606050', '83.24380317156275034102570470257', '84.04376720513345844036338169172', '84.96116239596185957382913861561', '85.2706981659273666229585737822', '85.67145521124121665572183549397', '86.44003037985760277099879058388', '87.1981082544339285318327408627', '88.02447158411289424113164885240', '88.62788923149054094141364363487', '89.341428910738368391461958403321', '89.93743270662545215649209514113', '90.30922216921437817355609439904', '91.37793946419637704230120464081', '92.018246842103361713413463994553', '93.127944199493400816081734077207', '93.371509269414044414349261628448', '94.242605871821203240298506037968', '94.74505092451996657207229858431', '95.42554762120501004969808464727', '95.99919441049294536532089250470', '96.765410479495399669284270244049', '97.172995490617821467210117699994', '97.72304468998474495193760901649', '98.48795369573863830727281713404', '99.32604488341660446376719605866', '100.344399877732814835136640717655', '101.11204038694707416144414302417', '101.50628924238972778959713428649', '102.07820447474888747935165385988', '102.58811587010102754284045414224', '103.51899843638871869137754349658', '103.981861881082508657785240178896', '104.86389162135246517632421013827', '105.5588842651791509418341303911', '105.88772956122541826421838991300', '106.6501471334948682943108414128', '107.27358333836912085021622806794', '107.76618718026177966711246850236', '108.72160091968062896634392925695', '109.308601356458990347341993198247', '110.028104449794272010188644591831', '110.93163399127163388602253344548', '111.83653763167973469831140594532', '112.20262468596993099070121228991', '112.57105440592888448597563617103', '113.406537198574307090151299084624', '113.99266317433483808828319974147', '114.376313514220888192756776046527', '114.93093550391442704601650485115', '116.0959617707042629870468933556', '116.6633943550146469412759820157', '117.20481789006408692590901735848', '117.73352341840100819501529567298', '118.996438842235916887338045038654', '119.2102094153316422428508901344', '120.05007263788759468976850187365', '120.59812167430778207532157240167', '121.2266161068235247614519080368', '121.94066684966589888687614717014', '122.54469440560711132135994022581', '123.32769345644736275424064525323', '123.91634731844944628431268100833', '124.42755545176385885744704880426', '125.01844423306215958311983253089', '125.47961497615963059616516217635', '125.95534852281744557046747573577', '127.27381441148996508314495596182', '127.898490882360447428708715572262', '128.77604526503420314214534176386', '129.413930987585596427981656848821', '129.63156769007545794596020141207', '130.226745506186444078394112420766', '131.171433292937029468899424827258', '131.70749826931871530644752144233', '132.01274959512098331349658341416', '132.95471671317745186992090585292', '133.432428677894830021341550618672', '134.23252404465583680312682622167', '134.763668541632112882223521096', '135.70238910027157190337439320031', '136.025503044852220655541118373502', '136.9680387804882809197924648444', '137.35847519108584992640363378724', '138.19920317712351542518435332592', '138.90527523745982230640694268744', '139.66030826549523642970560745975', '140.42409046503003713698617098955', '140.72432192275149956566431285399', '141.08143881786420678842552545742', '142.066113739069220892409306069424', '142.27369769632617173046316539362', '143.41862328933006565098093221451', '143.52943696884442031786098986673', '144.31902841945490495045951665308', '145.40366523099892646968292139704', '145.98532900729023357535416570055', '146.73272235651910407789431843117', '147.36947918803754170598448502440', '147.98242548522520578676218340328', '148.36600173971920577022172635177', '148.95999578467831516576528511416', '149.4299933185414264321790744308', '150.42868503199921563069591265661', '151.255276222334209782201764173424', '151.65574137904162036719923177310', '151.96167764114563583475902449285', '152.97754791467007325250627797182', '153.264755487408204184040062333558', '153.88850750513508347821462185698', '154.90299167970829408326522173132', '155.76627871482485990931997206198', '156.178222835476434706861824197817', '156.97135649935640951105585990326', '157.33806160178422706797171059083', '158.23575537425495978816176789868', '158.8554770682919441602088926829', '159.16746597455793354652338154336', '159.69400040194000667400463311945', '160.415959388963076029700102831637', '161.07624491495506610342022431137', '161.40002251944372024892410293936', '162.58309440182183558772257880531', '163.28014330449828182624157032460', '163.84752084611432722720771297035', '164.43031187039770481746001686844', '165.06082521617858530581668529029', '165.64964827586081197217994237454', '166.358142485306791704456790353000', '166.85355457451554771062350992063', '167.83195454293807896768476943890', '168.09917107833438723420846952277', '168.7210414991676009864219256094', '169.6327498285987684474830873839', '169.80247581171903226296254973828', '170.57524277106693722071339173314', '171.250976830397192337153847392166', '171.79345514396386559248719640181', '172.24130613446992242617038079004', '173.51815775980484761624332475498', '174.17266315797798697892042401972', '174.76678284690579080469134504951', '175.34900488164404931393958470115', '175.75938435350620504283832136395', '176.36799615754860558501617172644', '176.82259361453930412064598490650', '177.53082561259295613732565180498', '178.17788993647037826625928329318', '178.84124161868307848257768256810', '179.535758656189925604149981008625', '180.18631193326779980952360841413', '180.52899117237000205643175731975', '181.30333524898568807174610441758', '182.46669323289475316466539468690', '182.67071272610256143101091037120', '183.39379480989208287656485344557', '183.68781647735238867803759552427', '184.80584517533033072206640377954', '185.357745915970231793992598616486', '185.75191602749761693213913005147', '186.66046192634228791723671612582', '187.2279269382374673414345999249', '187.44607229601571460582572532650', '188.09394523569484619357414515823', '188.503186397998063895848978553', '189.429383487549433893615612853566', '190.128735112717673013517013913898', '191.05195804332169166147597888650', '191.64074766711770081273346798552', '192.2471277444820667722790361898', '192.81666857010725809364543807051', '193.3729067133099551771390275725', '194.05327221263120200682109024898', '194.43748645502708282439247248036', '195.26714163581363207169189221598', '195.70202380348823817898874972769', '196.12241953021845148073775082834', '197.24322920421061232347293995207', '197.82998818792476839001234455010', '198.06493654312420054915234848386', '198.87377558434012207425639310722', '199.295435857261112994897091507406'], 'prelabel': '1-763-763.149-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 81.99573761829889, 'root_angle': 0.49605395388759554, 'root_number': '-0.999692650999509669139668362274+0.0247911987925666740086928864981*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.496053953888', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(108)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.28374550436459632466863898788+1.13925164818298491140472211431*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.5533501354', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.04744509373', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.79313254864', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 81.99573761829889, 'bad_primes': [7, 109], 'central_character': '763.149', 'conductor': 763, 'conductor_radical': 763, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/763/149'], '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': '1-763-763.149-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': '1-763-763.149-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 81.99573761829889, 'root_angle': 0.49605395388759554, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.5533501354', 'prec': 40}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_763.149', 'Lhash_array': ['dirichlet_L_763.149'], 'factors': ['1-763-763.149-r1-0-0'], 'label': '1-763-763.149-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/763/149'}