Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.146");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.2 | ||
Root | \(2.70662 + 1.29391i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.4.c.a.146.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.54551i | − | 1.60708i | −0.595250 | − | 0.803541i | \(-0.702947\pi\) | ||
0.595250 | − | 0.803541i | \(-0.297053\pi\) | |||||||
\(3\) | 2.93937 | − | 4.28487i | 0.565682 | − | 0.824624i | ||||
\(4\) | −12.6617 | −1.58271 | ||||||||
\(5\) | −11.6039 | −1.03788 | −0.518941 | − | 0.854810i | \(-0.673674\pi\) | ||||
−0.518941 | + | 0.854810i | \(0.673674\pi\) | |||||||
\(6\) | −19.4769 | − | 13.3609i | −1.32524 | − | 0.909097i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 21.1897i | 0.936463i | ||||||||
\(9\) | −9.72022 | − | 25.1896i | −0.360008 | − | 0.932949i | ||||
\(10\) | 52.7455i | 1.66796i | ||||||||
\(11\) | − | 17.9160i | − | 0.491080i | −0.969387 | − | 0.245540i | \(-0.921035\pi\) | ||
0.969387 | − | 0.245540i | \(-0.0789652\pi\) | |||||||
\(12\) | −37.2174 | + | 54.2537i | −0.895311 | + | 1.30514i | ||||
\(13\) | 62.4185i | 1.33167i | 0.746097 | + | 0.665837i | \(0.231925\pi\) | ||||
−0.746097 | + | 0.665837i | \(0.768075\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −34.1081 | + | 49.7211i | −0.587111 | + | 0.855862i | ||||
\(16\) | −4.97524 | −0.0777381 | ||||||||
\(17\) | 21.4164 | 0.305544 | 0.152772 | − | 0.988261i | \(-0.451180\pi\) | ||||
0.152772 | + | 0.988261i | \(0.451180\pi\) | |||||||
\(18\) | −114.500 | + | 44.1834i | −1.49933 | + | 0.578562i | ||||
\(19\) | − | 10.9783i | − | 0.132557i | −0.997801 | − | 0.0662787i | \(-0.978887\pi\) | ||
0.997801 | − | 0.0662787i | \(-0.0211126\pi\) | |||||||
\(20\) | 146.925 | 1.64267 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −81.4374 | −0.789205 | ||||||||
\(23\) | − | 69.0934i | − | 0.626390i | −0.949689 | − | 0.313195i | \(-0.898601\pi\) | ||
0.949689 | − | 0.313195i | \(-0.101399\pi\) | |||||||
\(24\) | 90.7953 | + | 62.2845i | 0.772230 | + | 0.529740i | ||||
\(25\) | 9.64979 | 0.0771983 | ||||||||
\(26\) | 283.724 | 2.14011 | ||||||||
\(27\) | −136.506 | − | 32.3918i | −0.972982 | − | 0.230881i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 265.583i | − | 1.70061i | −0.526294 | − | 0.850303i | \(-0.676419\pi\) | ||
0.526294 | − | 0.850303i | \(-0.323581\pi\) | |||||||
\(30\) | 226.008 | + | 155.039i | 1.37544 | + | 0.943535i | ||||
\(31\) | 10.2283i | 0.0592598i | 0.999561 | + | 0.0296299i | \(0.00943286\pi\) | ||||
−0.999561 | + | 0.0296299i | \(0.990567\pi\) | |||||||
\(32\) | 192.133i | 1.06139i | ||||||||
\(33\) | −76.7677 | − | 52.6617i | −0.404956 | − | 0.277795i | ||||
\(34\) | − | 97.3486i | − | 0.491034i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 123.074 | + | 318.943i | 0.569788 | + | 1.47659i | ||||
\(37\) | 41.6514 | 0.185066 | 0.0925331 | − | 0.995710i | \(-0.470504\pi\) | ||||
0.0925331 | + | 0.995710i | \(0.470504\pi\) | |||||||
\(38\) | −49.9019 | −0.213031 | ||||||||
\(39\) | 267.455 | + | 183.471i | 1.09813 | + | 0.753304i | ||||
\(40\) | − | 245.883i | − | 0.971938i | ||||||
\(41\) | 31.0035 | 0.118096 | 0.0590480 | − | 0.998255i | \(-0.481193\pi\) | ||||
0.0590480 | + | 0.998255i | \(0.481193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −224.550 | −0.796363 | −0.398181 | − | 0.917307i | \(-0.630359\pi\) | ||||
−0.398181 | + | 0.917307i | \(0.630359\pi\) | |||||||
\(44\) | 226.847i | 0.777237i | ||||||||
\(45\) | 112.792 | + | 292.297i | 0.373646 | + | 0.968291i | ||||
\(46\) | −314.065 | −1.00666 | ||||||||
\(47\) | −163.719 | −0.508103 | −0.254052 | − | 0.967191i | \(-0.581763\pi\) | ||||
−0.254052 | + | 0.967191i | \(0.581763\pi\) | |||||||
\(48\) | −14.6241 | + | 21.3182i | −0.0439750 | + | 0.0641046i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 43.8633i | − | 0.124064i | ||||||
\(51\) | 62.9508 | − | 91.7665i | 0.172841 | − | 0.251959i | ||||
\(52\) | − | 790.323i | − | 2.10765i | ||||||
\(53\) | − | 527.220i | − | 1.36640i | −0.730231 | − | 0.683200i | \(-0.760588\pi\) | ||
0.730231 | − | 0.683200i | \(-0.239412\pi\) | |||||||
\(54\) | −147.237 | + | 620.488i | −0.371045 | + | 1.56366i | ||||
\(55\) | 207.895i | 0.509682i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −47.0405 | − | 32.2692i | −0.109310 | − | 0.0749853i | ||||
\(58\) | −1207.21 | −2.73301 | ||||||||
\(59\) | −411.956 | −0.909020 | −0.454510 | − | 0.890742i | \(-0.650186\pi\) | ||||
−0.454510 | + | 0.890742i | \(0.650186\pi\) | |||||||
\(60\) | 431.865 | − | 629.552i | 0.929227 | − | 1.35458i | ||||
\(61\) | − | 258.431i | − | 0.542437i | −0.962518 | − | 0.271218i | \(-0.912573\pi\) | ||
0.962518 | − | 0.271218i | \(-0.0874266\pi\) | |||||||
\(62\) | 46.4928 | 0.0952352 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 833.541 | 1.62801 | ||||||||
\(65\) | − | 724.296i | − | 1.38212i | ||||||
\(66\) | −239.375 | + | 348.949i | −0.446439 | + | 0.650797i | ||||
\(67\) | 323.474 | 0.589831 | 0.294915 | − | 0.955523i | \(-0.404709\pi\) | ||||
0.294915 | + | 0.955523i | \(0.404709\pi\) | |||||||
\(68\) | −271.168 | −0.483587 | ||||||||
\(69\) | −296.056 | − | 203.091i | −0.516536 | − | 0.354338i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 45.4199i | 0.0759205i | 0.999279 | + | 0.0379603i | \(0.0120860\pi\) | ||||
−0.999279 | + | 0.0379603i | \(0.987914\pi\) | |||||||
\(72\) | 533.762 | − | 205.969i | 0.873673 | − | 0.337134i | ||||
\(73\) | − | 562.199i | − | 0.901376i | −0.892682 | − | 0.450688i | \(-0.851179\pi\) | ||
0.892682 | − | 0.450688i | \(-0.148821\pi\) | |||||||
\(74\) | − | 189.327i | − | 0.297416i | ||||||
\(75\) | 28.3643 | − | 41.3481i | 0.0436697 | − | 0.0636596i | ||||
\(76\) | 139.004i | 0.209800i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 833.969 | − | 1215.72i | 1.21062 | − | 1.76478i | ||||
\(79\) | 289.221 | 0.411898 | 0.205949 | − | 0.978563i | \(-0.433972\pi\) | ||||
0.205949 | + | 0.978563i | \(0.433972\pi\) | |||||||
\(80\) | 57.7320 | 0.0806829 | ||||||||
\(81\) | −540.035 | + | 489.697i | −0.740789 | + | 0.671738i | ||||
\(82\) | − | 140.927i | − | 0.189790i | ||||||
\(83\) | −448.767 | −0.593477 | −0.296738 | − | 0.954959i | \(-0.595899\pi\) | ||||
−0.296738 | + | 0.954959i | \(0.595899\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −248.513 | −0.317118 | ||||||||
\(86\) | 1020.70i | 1.27982i | ||||||||
\(87\) | −1137.99 | − | 780.647i | −1.40236 | − | 0.962002i | ||||
\(88\) | 379.635 | 0.459878 | ||||||||
\(89\) | −561.628 | −0.668904 | −0.334452 | − | 0.942413i | \(-0.608551\pi\) | ||||
−0.334452 | + | 0.942413i | \(0.608551\pi\) | |||||||
\(90\) | 1328.64 | − | 512.698i | 1.55612 | − | 0.600479i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 874.839i | 0.991394i | ||||||||
\(93\) | 43.8268 | + | 30.0647i | 0.0488670 | + | 0.0335222i | ||||
\(94\) | 744.187i | 0.816564i | ||||||||
\(95\) | 127.391i | 0.137579i | ||||||||
\(96\) | 823.265 | + | 564.750i | 0.875251 | + | 0.600412i | ||||
\(97\) | − | 214.364i | − | 0.224385i | −0.993686 | − | 0.112192i | \(-0.964213\pi\) | ||
0.993686 | − | 0.112192i | \(-0.0357873\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −451.297 | + | 174.147i | −0.458152 | + | 0.176793i | ||||
\(100\) | −122.183 | −0.122183 | ||||||||
\(101\) | 1717.69 | 1.69224 | 0.846122 | − | 0.532990i | \(-0.178932\pi\) | ||||
0.846122 | + | 0.532990i | \(0.178932\pi\) | |||||||
\(102\) | −417.126 | − | 286.143i | −0.404918 | − | 0.277769i | ||||
\(103\) | − | 1157.71i | − | 1.10750i | −0.832683 | − | 0.553750i | \(-0.813196\pi\) | ||
0.832683 | − | 0.553750i | \(-0.186804\pi\) | |||||||
\(104\) | −1322.63 | −1.24706 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2396.48 | −2.19592 | ||||||||
\(107\) | 1217.79i | 1.10027i | 0.835077 | + | 0.550134i | \(0.185423\pi\) | ||||
−0.835077 | + | 0.550134i | \(0.814577\pi\) | |||||||
\(108\) | 1728.39 | + | 410.134i | 1.53995 | + | 0.365418i | ||||
\(109\) | 1298.26 | 1.14084 | 0.570418 | − | 0.821355i | \(-0.306781\pi\) | ||||
0.570418 | + | 0.821355i | \(0.306781\pi\) | |||||||
\(110\) | 944.989 | 0.819101 | ||||||||
\(111\) | 122.429 | − | 178.471i | 0.104689 | − | 0.152610i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1437.86i | 1.19701i | 0.801118 | + | 0.598506i | \(0.204239\pi\) | ||||
−0.801118 | + | 0.598506i | \(0.795761\pi\) | |||||||
\(114\) | −146.680 | + | 213.823i | −0.120508 | + | 0.175670i | ||||
\(115\) | 801.751i | 0.650119i | ||||||||
\(116\) | 3362.73i | 2.69157i | ||||||||
\(117\) | 1572.30 | − | 606.721i | 1.24238 | − | 0.479413i | ||||
\(118\) | 1872.55i | 1.46087i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1053.58 | − | 722.741i | −0.801483 | − | 0.549808i | ||||
\(121\) | 1010.02 | 0.758841 | ||||||||
\(122\) | −1174.70 | −0.871740 | ||||||||
\(123\) | 91.1308 | − | 132.846i | 0.0668048 | − | 0.0973848i | ||||
\(124\) | − | 129.507i | − | 0.0937910i | ||||||
\(125\) | 1338.51 | 0.957759 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2686.32 | 1.87695 | 0.938475 | − | 0.345347i | \(-0.112239\pi\) | ||||
0.938475 | + | 0.345347i | \(0.112239\pi\) | |||||||
\(128\) | − | 2251.81i | − | 1.55495i | ||||||
\(129\) | −660.036 | + | 962.169i | −0.450488 | + | 0.656699i | ||||
\(130\) | −3292.29 | −2.22118 | ||||||||
\(131\) | −1603.27 | −1.06930 | −0.534651 | − | 0.845073i | \(-0.679557\pi\) | ||||
−0.534651 | + | 0.845073i | \(0.679557\pi\) | |||||||
\(132\) | 972.008 | + | 666.786i | 0.640928 | + | 0.439669i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 1470.36i | − | 0.947906i | ||||||
\(135\) | 1583.99 | + | 375.870i | 1.00984 | + | 0.239628i | ||||
\(136\) | 453.808i | 0.286130i | ||||||||
\(137\) | − | 2318.52i | − | 1.44588i | −0.690913 | − | 0.722938i | \(-0.742791\pi\) | ||
0.690913 | − | 0.722938i | \(-0.257209\pi\) | |||||||
\(138\) | −923.153 | + | 1345.73i | −0.569449 | + | 0.830116i | ||||
\(139\) | − | 1841.57i | − | 1.12374i | −0.827225 | − | 0.561871i | \(-0.810082\pi\) | ||
0.827225 | − | 0.561871i | \(-0.189918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −481.230 | + | 701.514i | −0.287425 | + | 0.418994i | ||||
\(142\) | 206.457 | 0.122010 | ||||||||
\(143\) | 1118.29 | 0.653958 | ||||||||
\(144\) | 48.3604 | + | 125.324i | 0.0279863 | + | 0.0725257i | ||||
\(145\) | 3081.79i | 1.76503i | ||||||||
\(146\) | −2555.48 | −1.44858 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −527.377 | −0.292906 | ||||||||
\(149\) | − | 1300.98i | − | 0.715302i | −0.933855 | − | 0.357651i | \(-0.883578\pi\) | ||
0.933855 | − | 0.357651i | \(-0.116422\pi\) | |||||||
\(150\) | −187.948 | − | 128.930i | −0.102306 | − | 0.0701808i | ||||
\(151\) | −2616.49 | −1.41011 | −0.705055 | − | 0.709152i | \(-0.749078\pi\) | ||||
−0.705055 | + | 0.709152i | \(0.749078\pi\) | |||||||
\(152\) | 232.627 | 0.124135 | ||||||||
\(153\) | −208.172 | − | 539.472i | −0.109998 | − | 0.285057i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 118.688i | − | 0.0615046i | ||||||
\(156\) | −3386.43 | − | 2323.05i | −1.73802 | − | 1.19226i | ||||
\(157\) | − | 935.164i | − | 0.475377i | −0.971341 | − | 0.237689i | \(-0.923610\pi\) | ||
0.971341 | − | 0.237689i | \(-0.0763898\pi\) | |||||||
\(158\) | − | 1314.66i | − | 0.661953i | ||||||
\(159\) | −2259.07 | − | 1549.69i | −1.12677 | − | 0.772948i | ||||
\(160\) | − | 2229.49i | − | 1.10160i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2225.92 | + | 2454.74i | 1.07954 | + | 1.19051i | ||||
\(163\) | −518.158 | −0.248989 | −0.124495 | − | 0.992220i | \(-0.539731\pi\) | ||||
−0.124495 | + | 0.992220i | \(0.539731\pi\) | |||||||
\(164\) | −392.557 | −0.186912 | ||||||||
\(165\) | 890.802 | + | 611.080i | 0.420296 | + | 0.288318i | ||||
\(166\) | 2039.88i | 0.953765i | ||||||||
\(167\) | 3767.97 | 1.74595 | 0.872977 | − | 0.487761i | \(-0.162186\pi\) | ||||
0.872977 | + | 0.487761i | \(0.162186\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1699.06 | −0.773356 | ||||||||
\(170\) | 1129.62i | 0.509635i | ||||||||
\(171\) | −276.539 | + | 106.711i | −0.123669 | + | 0.0477217i | ||||
\(172\) | 2843.18 | 1.26041 | ||||||||
\(173\) | 2393.06 | 1.05168 | 0.525841 | − | 0.850583i | \(-0.323751\pi\) | ||||
0.525841 | + | 0.850583i | \(0.323751\pi\) | |||||||
\(174\) | −3548.44 | + | 5172.74i | −1.54602 | + | 2.25371i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 89.1363i | 0.0381756i | ||||||||
\(177\) | −1210.89 | + | 1765.18i | −0.514216 | + | 0.749599i | ||||
\(178\) | 2552.89i | 1.07498i | ||||||||
\(179\) | − | 640.144i | − | 0.267299i | −0.991029 | − | 0.133650i | \(-0.957330\pi\) | ||
0.991029 | − | 0.133650i | \(-0.0426697\pi\) | |||||||
\(180\) | −1428.14 | − | 3700.97i | −0.591373 | − | 1.53252i | ||||
\(181\) | 4204.05i | 1.72643i | 0.504833 | + | 0.863217i | \(0.331554\pi\) | ||||
−0.504833 | + | 0.863217i | \(0.668446\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1107.34 | − | 759.623i | −0.447306 | − | 0.306847i | ||||
\(184\) | 1464.07 | 0.586591 | ||||||||
\(185\) | −483.318 | −0.192077 | ||||||||
\(186\) | 136.659 | − | 199.215i | 0.0538729 | − | 0.0785332i | ||||
\(187\) | − | 383.696i | − | 0.150046i | ||||||
\(188\) | 2072.96 | 0.804181 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 579.056 | 0.221101 | ||||||||
\(191\) | − | 1457.06i | − | 0.551985i | −0.961160 | − | 0.275993i | \(-0.910993\pi\) | ||
0.961160 | − | 0.275993i | \(-0.0890066\pi\) | |||||||
\(192\) | 2450.08 | − | 3571.61i | 0.920935 | − | 1.34249i | ||||
\(193\) | 1829.27 | 0.682246 | 0.341123 | − | 0.940019i | \(-0.389193\pi\) | ||||
0.341123 | + | 0.940019i | \(0.389193\pi\) | |||||||
\(194\) | −974.393 | −0.360605 | ||||||||
\(195\) | −3103.51 | − | 2128.97i | −1.13973 | − | 0.781840i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 661.168i | − | 0.239118i | −0.992827 | − | 0.119559i | \(-0.961852\pi\) | ||
0.992827 | − | 0.119559i | \(-0.0381481\pi\) | |||||||
\(198\) | 791.589 | + | 2051.38i | 0.284120 | + | 0.736288i | ||||
\(199\) | − | 1949.13i | − | 0.694322i | −0.937806 | − | 0.347161i | \(-0.887146\pi\) | ||
0.937806 | − | 0.347161i | \(-0.112854\pi\) | |||||||
\(200\) | 204.477i | 0.0722934i | ||||||||
\(201\) | 950.810 | − | 1386.04i | 0.333657 | − | 0.486388i | ||||
\(202\) | − | 7807.78i | − | 2.71957i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −797.063 | + | 1161.92i | −0.273557 | + | 0.398777i | ||||
\(205\) | −359.761 | −0.122570 | ||||||||
\(206\) | −5262.38 | −1.77984 | ||||||||
\(207\) | −1740.44 | + | 671.603i | −0.584390 | + | 0.225505i | ||||
\(208\) | − | 310.547i | − | 0.103522i | ||||||
\(209\) | −196.687 | −0.0650963 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3341.96 | 1.09038 | 0.545189 | − | 0.838313i | \(-0.316458\pi\) | ||||
0.545189 | + | 0.838313i | \(0.316458\pi\) | |||||||
\(212\) | 6675.49i | 2.16262i | ||||||||
\(213\) | 194.619 | + | 133.506i | 0.0626058 | + | 0.0429469i | ||||
\(214\) | 5535.50 | 1.76822 | ||||||||
\(215\) | 2605.65 | 0.826530 | ||||||||
\(216\) | 686.373 | − | 2892.52i | 0.216212 | − | 0.911162i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 5901.27i | − | 1.83342i | ||||||
\(219\) | −2408.95 | − | 1652.51i | −0.743296 | − | 0.509892i | ||||
\(220\) | − | 2632.30i | − | 0.806680i | ||||||
\(221\) | 1336.78i | 0.406885i | ||||||||
\(222\) | −811.242 | − | 556.502i | −0.245257 | − | 0.168243i | ||||
\(223\) | 2143.28i | 0.643608i | 0.946806 | + | 0.321804i | \(0.104289\pi\) | ||||
−0.946806 | + | 0.321804i | \(0.895711\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −93.7981 | − | 243.075i | −0.0277920 | − | 0.0720221i | ||||
\(226\) | 6535.80 | 1.92370 | ||||||||
\(227\) | 2569.11 | 0.751178 | 0.375589 | − | 0.926786i | \(-0.377440\pi\) | ||||
0.375589 | + | 0.926786i | \(0.377440\pi\) | |||||||
\(228\) | 595.612 | + | 408.583i | 0.173006 | + | 0.118680i | ||||
\(229\) | − | 105.173i | − | 0.0303495i | −0.999885 | − | 0.0151748i | \(-0.995170\pi\) | ||
0.999885 | − | 0.0151748i | \(-0.00483046\pi\) | |||||||
\(230\) | 3644.37 | 1.04479 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5627.64 | 1.59255 | ||||||||
\(233\) | 2625.72i | 0.738270i | 0.929376 | + | 0.369135i | \(0.120346\pi\) | ||||
−0.929376 | + | 0.369135i | \(0.879654\pi\) | |||||||
\(234\) | −2757.86 | − | 7146.90i | −0.770456 | − | 1.99661i | ||||
\(235\) | 1899.77 | 0.527351 | ||||||||
\(236\) | 5216.06 | 1.43872 | ||||||||
\(237\) | 850.127 | − | 1239.27i | 0.233003 | − | 0.339660i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6080.85i | − | 1.64576i | −0.568212 | − | 0.822882i | \(-0.692365\pi\) | ||
0.568212 | − | 0.822882i | \(-0.307635\pi\) | |||||||
\(240\) | 169.696 | − | 247.374i | 0.0456409 | − | 0.0665330i | ||||
\(241\) | 4628.89i | 1.23723i | 0.785693 | + | 0.618616i | \(0.212306\pi\) | ||||
−0.785693 | + | 0.618616i | \(0.787694\pi\) | |||||||
\(242\) | − | 4591.05i | − | 1.21952i | ||||||
\(243\) | 510.927 | + | 3753.38i | 0.134881 | + | 0.990862i | ||||
\(244\) | 3272.17i | 0.858521i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −603.853 | − | 414.236i | −0.156505 | − | 0.107361i | ||||
\(247\) | 685.248 | 0.176523 | ||||||||
\(248\) | −216.735 | −0.0554946 | ||||||||
\(249\) | −1319.09 | + | 1922.91i | −0.335719 | + | 0.489395i | ||||
\(250\) | − | 6084.21i | − | 1.53920i | ||||||
\(251\) | −5967.85 | −1.50075 | −0.750373 | − | 0.661015i | \(-0.770126\pi\) | ||||
−0.750373 | + | 0.661015i | \(0.770126\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1237.88 | −0.307607 | ||||||||
\(254\) | − | 12210.7i | − | 3.01641i | ||||||
\(255\) | −730.472 | + | 1064.85i | −0.179388 | + | 0.261503i | ||||
\(256\) | −3567.29 | −0.870920 | ||||||||
\(257\) | −5639.40 | −1.36878 | −0.684389 | − | 0.729117i | \(-0.739931\pi\) | ||||
−0.684389 | + | 0.729117i | \(0.739931\pi\) | |||||||
\(258\) | 4373.55 | + | 3000.20i | 1.05537 | + | 0.723971i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9170.80i | 2.18750i | ||||||||
\(261\) | −6689.94 | + | 2581.53i | −1.58658 | + | 0.612232i | ||||
\(262\) | 7287.70i | 1.71846i | ||||||||
\(263\) | 3485.62i | 0.817234i | 0.912706 | + | 0.408617i | \(0.133989\pi\) | ||||
−0.912706 | + | 0.408617i | \(0.866011\pi\) | |||||||
\(264\) | 1115.89 | − | 1626.69i | 0.260145 | − | 0.379226i | ||||
\(265\) | 6117.79i | 1.41816i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1650.83 | + | 2406.50i | −0.378387 | + | 0.551594i | ||||
\(268\) | −4095.73 | −0.933531 | ||||||||
\(269\) | −3794.55 | −0.860066 | −0.430033 | − | 0.902813i | \(-0.641498\pi\) | ||||
−0.430033 | + | 0.902813i | \(0.641498\pi\) | |||||||
\(270\) | 1708.52 | − | 7200.06i | 0.385101 | − | 1.62290i | ||||
\(271\) | 7457.62i | 1.67165i | 0.548993 | + | 0.835827i | \(0.315011\pi\) | ||||
−0.548993 | + | 0.835827i | \(0.684989\pi\) | |||||||
\(272\) | −106.552 | −0.0237524 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10538.9 | −2.32364 | ||||||||
\(275\) | − | 172.886i | − | 0.0379105i | ||||||
\(276\) | 3748.57 | + | 2571.48i | 0.817527 | + | 0.560814i | ||||
\(277\) | −3415.49 | −0.740856 | −0.370428 | − | 0.928861i | \(-0.620789\pi\) | ||||
−0.370428 | + | 0.928861i | \(0.620789\pi\) | |||||||
\(278\) | −8370.89 | −1.80595 | ||||||||
\(279\) | 257.646 | − | 99.4210i | 0.0552863 | − | 0.0213340i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2762.14i | 0.586390i | 0.956053 | + | 0.293195i | \(0.0947185\pi\) | ||||
−0.956053 | + | 0.293195i | \(0.905281\pi\) | |||||||
\(282\) | 3188.74 | + | 2187.44i | 0.673358 | + | 0.461915i | ||||
\(283\) | − | 5505.20i | − | 1.15636i | −0.815909 | − | 0.578181i | \(-0.803763\pi\) | ||
0.815909 | − | 0.578181i | \(-0.196237\pi\) | |||||||
\(284\) | − | 575.093i | − | 0.120160i | ||||||
\(285\) | 545.852 | + | 374.448i | 0.113451 | + | 0.0778259i | ||||
\(286\) | − | 5083.19i | − | 1.05096i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4839.76 | − | 1867.57i | 0.990227 | − | 0.382110i | ||||
\(289\) | −4454.34 | −0.906643 | ||||||||
\(290\) | 14008.3 | 2.83654 | ||||||||
\(291\) | −918.520 | − | 630.094i | −0.185033 | − | 0.126930i | ||||
\(292\) | 7118.39i | 1.42662i | ||||||||
\(293\) | −4101.08 | −0.817705 | −0.408853 | − | 0.912600i | \(-0.634071\pi\) | ||||
−0.408853 | + | 0.912600i | \(0.634071\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4780.29 | 0.943455 | ||||||||
\(296\) | 882.583i | 0.173308i | ||||||||
\(297\) | −580.331 | + | 2445.63i | −0.113381 | + | 0.477812i | ||||
\(298\) | −5913.60 | −1.14955 | ||||||||
\(299\) | 4312.70 | 0.834148 | ||||||||
\(300\) | −359.140 | + | 523.537i | −0.0691165 | + | 0.100755i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11893.3i | 2.26616i | ||||||||
\(303\) | 5048.93 | − | 7360.08i | 0.957271 | − | 1.39546i | ||||
\(304\) | 54.6196i | 0.0103048i | ||||||||
\(305\) | 2998.80i | 0.562985i | ||||||||
\(306\) | −2452.17 | + | 946.249i | −0.458109 | + | 0.176776i | ||||
\(307\) | − | 8281.42i | − | 1.53956i | −0.638308 | − | 0.769781i | \(-0.720365\pi\) | ||
0.638308 | − | 0.769781i | \(-0.279635\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4960.63 | − | 3402.94i | −0.913270 | − | 0.626493i | ||||
\(310\) | −539.496 | −0.0988429 | ||||||||
\(311\) | −6871.05 | −1.25280 | −0.626401 | − | 0.779501i | \(-0.715473\pi\) | ||||
−0.626401 | + | 0.779501i | \(0.715473\pi\) | |||||||
\(312\) | −3887.70 | + | 5667.30i | −0.705441 | + | 1.02836i | ||||
\(313\) | 3374.49i | 0.609386i | 0.952451 | + | 0.304693i | \(0.0985538\pi\) | ||||
−0.952451 | + | 0.304693i | \(0.901446\pi\) | |||||||
\(314\) | −4250.80 | −0.763970 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3662.02 | −0.651914 | ||||||||
\(317\) | 2369.77i | 0.419872i | 0.977715 | + | 0.209936i | \(0.0673255\pi\) | ||||
−0.977715 | + | 0.209936i | \(0.932674\pi\) | |||||||
\(318\) | −7044.15 | + | 10268.6i | −1.24219 | + | 1.81080i | ||||
\(319\) | −4758.19 | −0.835133 | ||||||||
\(320\) | −9672.30 | −1.68968 | ||||||||
\(321\) | 5218.09 | + | 3579.55i | 0.907306 | + | 0.622401i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 235.116i | − | 0.0405021i | ||||||
\(324\) | 6837.75 | − | 6200.39i | 1.17245 | − | 1.06317i | ||||
\(325\) | 602.325i | 0.102803i | ||||||||
\(326\) | 2355.29i | 0.400146i | ||||||||
\(327\) | 3816.08 | − | 5562.89i | 0.645350 | − | 0.940760i | ||||
\(328\) | 656.957i | 0.110593i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2777.67 | − | 4049.15i | 0.463351 | − | 0.675450i | ||||
\(331\) | 3803.61 | 0.631617 | 0.315808 | − | 0.948823i | \(-0.397724\pi\) | ||||
0.315808 | + | 0.948823i | \(0.397724\pi\) | |||||||
\(332\) | 5682.14 | 0.939302 | ||||||||
\(333\) | −404.861 | − | 1049.18i | −0.0666253 | − | 0.172657i | ||||
\(334\) | − | 17127.4i | − | 2.80589i | ||||||
\(335\) | −3753.55 | −0.612175 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −592.955 | −0.0958466 | −0.0479233 | − | 0.998851i | \(-0.515260\pi\) | ||||
−0.0479233 | + | 0.998851i | \(0.515260\pi\) | |||||||
\(338\) | 7723.11i | 1.24285i | ||||||||
\(339\) | 6161.04 | + | 4226.40i | 0.987084 | + | 0.677128i | ||||
\(340\) | 3146.60 | 0.501906 | ||||||||
\(341\) | 183.250 | 0.0291013 | ||||||||
\(342\) | 485.058 | + | 1257.01i | 0.0766927 | + | 0.198747i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 4758.16i | − | 0.745764i | ||||||
\(345\) | 3435.40 | + | 2356.64i | 0.536103 | + | 0.367760i | ||||
\(346\) | − | 10877.7i | − | 1.69014i | ||||||
\(347\) | 4777.16i | 0.739054i | 0.929220 | + | 0.369527i | \(0.120480\pi\) | ||||
−0.929220 | + | 0.369527i | \(0.879520\pi\) | |||||||
\(348\) | 14408.9 | + | 9884.31i | 2.21953 | + | 1.52257i | ||||
\(349\) | 7358.26i | 1.12859i | 0.825573 | + | 0.564296i | \(0.190852\pi\) | ||||
−0.825573 | + | 0.564296i | \(0.809148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2021.84 | − | 8520.47i | 0.307459 | − | 1.29569i | ||||
\(352\) | 3442.25 | 0.521229 | ||||||||
\(353\) | 3305.55 | 0.498405 | 0.249202 | − | 0.968451i | \(-0.419832\pi\) | ||||
0.249202 | + | 0.968451i | \(0.419832\pi\) | |||||||
\(354\) | 8023.65 | + | 5504.13i | 1.20467 | + | 0.826387i | ||||
\(355\) | − | 527.047i | − | 0.0787965i | ||||||
\(356\) | 7111.16 | 1.05868 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2909.78 | −0.429572 | ||||||||
\(359\) | − | 414.716i | − | 0.0609689i | −0.999535 | − | 0.0304845i | \(-0.990295\pi\) | ||
0.999535 | − | 0.0304845i | \(-0.00970501\pi\) | |||||||
\(360\) | −6193.70 | + | 2390.04i | −0.906769 | + | 0.349905i | ||||
\(361\) | 6738.48 | 0.982429 | ||||||||
\(362\) | 19109.6 | 2.77452 | ||||||||
\(363\) | 2968.81 | − | 4327.79i | 0.429263 | − | 0.625758i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6523.69i | 0.935522i | ||||||||
\(366\) | −3452.88 | + | 5033.43i | −0.493128 | + | 0.718858i | ||||
\(367\) | − | 76.1227i | − | 0.0108272i | −0.999985 | − | 0.00541359i | \(-0.998277\pi\) | ||
0.999985 | − | 0.00541359i | \(-0.00172321\pi\) | |||||||
\(368\) | 343.756i | 0.0486944i | ||||||||
\(369\) | −301.361 | − | 780.967i | −0.0425155 | − | 0.110178i | ||||
\(370\) | 2196.93i | 0.308683i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −554.921 | − | 380.669i | −0.0773423 | − | 0.0530559i | ||||
\(373\) | −12301.0 | −1.70756 | −0.853781 | − | 0.520632i | \(-0.825696\pi\) | ||||
−0.853781 | + | 0.520632i | \(0.825696\pi\) | |||||||
\(374\) | −1744.10 | −0.241137 | ||||||||
\(375\) | 3934.37 | − | 5735.34i | 0.541787 | − | 0.789791i | ||||
\(376\) | − | 3469.16i | − | 0.475820i | ||||||
\(377\) | 16577.3 | 2.26465 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1429.02 | −0.193678 | −0.0968389 | − | 0.995300i | \(-0.530873\pi\) | ||||
−0.0968389 | + | 0.995300i | \(0.530873\pi\) | |||||||
\(380\) | − | 1612.98i | − | 0.217748i | ||||||
\(381\) | 7896.10 | − | 11510.5i | 1.06176 | − | 1.54778i | ||||
\(382\) | −6623.09 | −0.887086 | ||||||||
\(383\) | 5110.90 | 0.681866 | 0.340933 | − | 0.940088i | \(-0.389257\pi\) | ||||
0.340933 | + | 0.940088i | \(0.389257\pi\) | |||||||
\(384\) | −9648.70 | − | 6618.89i | −1.28225 | − | 0.879606i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 8314.95i | − | 1.09642i | ||||||
\(387\) | 2182.68 | + | 5656.34i | 0.286697 | + | 0.742966i | ||||
\(388\) | 2714.20i | 0.355136i | ||||||||
\(389\) | − | 7320.62i | − | 0.954165i | −0.878858 | − | 0.477083i | \(-0.841694\pi\) | ||
0.878858 | − | 0.477083i | \(-0.158306\pi\) | |||||||
\(390\) | −9677.27 | + | 14107.1i | −1.25648 | + | 1.83164i | ||||
\(391\) | − | 1479.73i | − | 0.191390i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4712.61 | + | 6869.82i | −0.604885 | + | 0.881772i | ||||
\(394\) | −3005.35 | −0.384283 | ||||||||
\(395\) | −3356.08 | −0.427501 | ||||||||
\(396\) | 5714.18 | − | 2205.00i | 0.725122 | − | 0.279811i | ||||
\(397\) | − | 8679.44i | − | 1.09725i | −0.836068 | − | 0.548625i | \(-0.815151\pi\) | ||
0.836068 | − | 0.548625i | \(-0.184849\pi\) | |||||||
\(398\) | −8859.79 | −1.11583 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −48.0100 | −0.00600125 | ||||||||
\(401\) | 9754.54i | 1.21476i | 0.794412 | + | 0.607379i | \(0.207779\pi\) | ||||
−0.794412 | + | 0.607379i | \(0.792221\pi\) | |||||||
\(402\) | −6300.28 | − | 4321.92i | −0.781666 | − | 0.536213i | ||||
\(403\) | −638.433 | −0.0789147 | ||||||||
\(404\) | −21748.9 | −2.67833 | ||||||||
\(405\) | 6266.49 | − | 5682.38i | 0.768851 | − | 0.697185i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 746.226i | − | 0.0908822i | ||||||
\(408\) | 1944.51 | + | 1333.91i | 0.235950 | + | 0.161859i | ||||
\(409\) | 3389.41i | 0.409769i | 0.978786 | + | 0.204885i | \(0.0656819\pi\) | ||||
−0.978786 | + | 0.204885i | \(0.934318\pi\) | |||||||
\(410\) | 1635.30i | 0.196979i | ||||||||
\(411\) | −9934.58 | − | 6815.00i | −1.19230 | − | 0.817906i | ||||
\(412\) | 14658.5i | 1.75285i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3052.78 | + | 7911.18i | 0.362406 | + | 0.939163i | ||||
\(415\) | 5207.43 | 0.615959 | ||||||||
\(416\) | −11992.6 | −1.41343 | ||||||||
\(417\) | −7890.90 | − | 5413.06i | −0.926664 | − | 0.635681i | ||||
\(418\) | 894.043i | 0.104615i | ||||||||
\(419\) | −12777.4 | −1.48977 | −0.744887 | − | 0.667191i | \(-0.767496\pi\) | ||||
−0.744887 | + | 0.667191i | \(0.767496\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11005.4 | 1.27404 | 0.637020 | − | 0.770848i | \(-0.280167\pi\) | ||||
0.637020 | + | 0.770848i | \(0.280167\pi\) | |||||||
\(422\) | − | 15190.9i | − | 1.75233i | ||||||
\(423\) | 1591.38 | + | 4124.02i | 0.182921 | + | 0.474035i | ||||
\(424\) | 11171.6 | 1.27958 | ||||||||
\(425\) | 206.664 | 0.0235875 | ||||||||
\(426\) | 606.853 | − | 884.641i | 0.0690191 | − | 0.100613i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 15419.3i | − | 1.74140i | ||||||
\(429\) | 3287.06 | − | 4791.72i | 0.369932 | − | 0.539269i | ||||
\(430\) | − | 11844.0i | − | 1.32830i | ||||||
\(431\) | − | 3786.41i | − | 0.423167i | −0.977360 | − | 0.211584i | \(-0.932138\pi\) | ||
0.977360 | − | 0.211584i | \(-0.0678621\pi\) | |||||||
\(432\) | 679.147 | + | 161.157i | 0.0756377 | + | 0.0179483i | ||||
\(433\) | − | 3191.67i | − | 0.354230i | −0.984190 | − | 0.177115i | \(-0.943323\pi\) | ||
0.984190 | − | 0.177115i | \(-0.0566765\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13205.1 | + | 9058.53i | 1.45548 | + | 0.998444i | ||||
\(436\) | −16438.2 | −1.80561 | ||||||||
\(437\) | −758.527 | −0.0830327 | ||||||||
\(438\) | −7511.51 | + | 10949.9i | −0.819438 | + | 1.19454i | ||||
\(439\) | 3317.34i | 0.360656i | 0.983607 | + | 0.180328i | \(0.0577159\pi\) | ||||
−0.983607 | + | 0.180328i | \(0.942284\pi\) | |||||||
\(440\) | −4405.24 | −0.477299 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6076.35 | 0.653897 | ||||||||
\(443\) | − | 10700.5i | − | 1.14763i | −0.818986 | − | 0.573813i | \(-0.805464\pi\) | ||
0.818986 | − | 0.573813i | \(-0.194536\pi\) | |||||||
\(444\) | −1550.16 | + | 2259.74i | −0.165692 | + | 0.241537i | ||||
\(445\) | 6517.06 | 0.694243 | ||||||||
\(446\) | 9742.29 | 1.03433 | ||||||||
\(447\) | −5574.51 | − | 3824.05i | −0.589855 | − | 0.404634i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4017.92i | 0.422310i | 0.977453 | + | 0.211155i | \(0.0677225\pi\) | ||||
−0.977453 | + | 0.211155i | \(0.932278\pi\) | |||||||
\(450\) | −1104.90 | + | 426.360i | −0.115745 | + | 0.0446640i | ||||
\(451\) | − | 555.459i | − | 0.0579945i | ||||||
\(452\) | − | 18205.7i | − | 1.89452i | ||||||
\(453\) | −7690.82 | + | 11211.3i | −0.797674 | + | 1.16281i | ||||
\(454\) | − | 11677.9i | − | 1.20720i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 683.777 | − | 996.777i | 0.0702210 | − | 0.102365i | ||||
\(457\) | 9169.65 | 0.938596 | 0.469298 | − | 0.883040i | \(-0.344507\pi\) | ||||
0.469298 | + | 0.883040i | \(0.344507\pi\) | |||||||
\(458\) | −478.066 | −0.0487742 | ||||||||
\(459\) | −2923.46 | − | 693.716i | −0.297289 | − | 0.0705444i | ||||
\(460\) | − | 10151.5i | − | 1.02895i | ||||||
\(461\) | 1289.80 | 0.130308 | 0.0651542 | − | 0.997875i | \(-0.479246\pi\) | ||||
0.0651542 | + | 0.997875i | \(0.479246\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6976.52 | 0.700273 | 0.350137 | − | 0.936699i | \(-0.386135\pi\) | ||||
0.350137 | + | 0.936699i | \(0.386135\pi\) | |||||||
\(464\) | 1321.34i | 0.132202i | ||||||||
\(465\) | −508.561 | − | 348.867i | −0.0507182 | − | 0.0347920i | ||||
\(466\) | 11935.3 | 1.18646 | ||||||||
\(467\) | −7863.66 | −0.779201 | −0.389600 | − | 0.920984i | \(-0.627387\pi\) | ||||
−0.389600 | + | 0.920984i | \(0.627387\pi\) | |||||||
\(468\) | −19907.9 | + | 7682.11i | −1.96633 | + | 0.758772i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 8635.44i | − | 0.847496i | ||||||
\(471\) | −4007.06 | − | 2748.79i | −0.392007 | − | 0.268912i | ||||
\(472\) | − | 8729.25i | − | 0.851263i | ||||||
\(473\) | 4023.04i | 0.391077i | ||||||||
\(474\) | −5633.14 | − | 3864.26i | −0.545862 | − | 0.374455i | ||||
\(475\) | − | 105.938i | − | 0.0102332i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13280.5 | + | 5124.69i | −1.27478 | + | 0.491915i | ||||
\(478\) | −27640.6 | −2.64488 | ||||||||
\(479\) | 3694.27 | 0.352391 | 0.176196 | − | 0.984355i | \(-0.443621\pi\) | ||||
0.176196 | + | 0.984355i | \(0.443621\pi\) | |||||||
\(480\) | −9553.05 | − | 6553.28i | −0.908407 | − | 0.623156i | ||||
\(481\) | 2599.82i | 0.246448i | ||||||||
\(482\) | 21040.7 | 1.98833 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12788.5 | −1.20103 | ||||||||
\(485\) | 2487.45i | 0.232885i | ||||||||
\(486\) | 17061.0 | − | 2322.42i | 1.59240 | − | 0.216764i | ||||
\(487\) | −1052.72 | −0.0979533 | −0.0489766 | − | 0.998800i | \(-0.515596\pi\) | ||||
−0.0489766 | + | 0.998800i | \(0.515596\pi\) | |||||||
\(488\) | 5476.08 | 0.507972 | ||||||||
\(489\) | −1523.06 | + | 2220.24i | −0.140849 | + | 0.205322i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2378.40i | − | 0.218607i | −0.994008 | − | 0.109303i | \(-0.965138\pi\) | ||
0.994008 | − | 0.109303i | \(-0.0348620\pi\) | |||||||
\(492\) | −1153.87 | + | 1682.05i | −0.105733 | + | 0.154132i | ||||
\(493\) | − | 5687.84i | − | 0.519609i | ||||||
\(494\) | − | 3114.80i | − | 0.283687i | ||||||
\(495\) | 5236.79 | − | 2020.78i | 0.475508 | − | 0.183490i | ||||
\(496\) | − | 50.8881i | − | 0.00460674i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8740.60 | + | 5995.95i | 0.786497 | + | 0.539528i | ||||
\(499\) | 18771.5 | 1.68402 | 0.842011 | − | 0.539461i | \(-0.181372\pi\) | ||||
0.842011 | + | 0.539461i | \(0.181372\pi\) | |||||||
\(500\) | −16947.8 | −1.51586 | ||||||||
\(501\) | 11075.5 | − | 16145.3i | 0.987655 | − | 1.43975i | ||||
\(502\) | 27126.9i | 2.41182i | ||||||||
\(503\) | 16095.2 | 1.42674 | 0.713370 | − | 0.700788i | \(-0.247168\pi\) | ||||
0.713370 | + | 0.700788i | \(0.247168\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19931.9 | −1.75635 | ||||||||
\(506\) | 5626.79i | 0.494350i | ||||||||
\(507\) | −4994.17 | + | 7280.26i | −0.437473 | + | 0.637728i | ||||
\(508\) | −34013.4 | −2.97067 | ||||||||
\(509\) | 3150.63 | 0.274360 | 0.137180 | − | 0.990546i | \(-0.456196\pi\) | ||||
0.137180 | + | 0.990546i | \(0.456196\pi\) | |||||||
\(510\) | 4840.28 | + | 3320.37i | 0.420257 | + | 0.288291i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1799.30i | − | 0.155310i | ||||||
\(513\) | −355.606 | + | 1498.60i | −0.0306051 | + | 0.128976i | ||||
\(514\) | 25633.9i | 2.19974i | ||||||||
\(515\) | 13433.9i | 1.14945i | ||||||||
\(516\) | 8357.17 | − | 12182.7i | 0.712992 | − | 1.03937i | ||||
\(517\) | 2933.19i | 0.249519i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7034.08 | − | 10253.9i | 0.594917 | − | 0.867241i | ||||
\(520\) | 15347.6 | 1.29430 | ||||||||
\(521\) | −4979.20 | −0.418700 | −0.209350 | − | 0.977841i | \(-0.567135\pi\) | ||||
−0.209350 | + | 0.977841i | \(0.567135\pi\) | |||||||
\(522\) | 11734.4 | + | 30409.2i | 0.983906 | + | 2.54976i | ||||
\(523\) | − | 13829.8i | − | 1.15628i | −0.815936 | − | 0.578142i | \(-0.803778\pi\) | ||
0.815936 | − | 0.578142i | \(-0.196222\pi\) | |||||||
\(524\) | 20300.1 | 1.69240 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15843.9 | 1.31336 | ||||||||
\(527\) | 219.053i | 0.0181064i | ||||||||
\(528\) | 381.937 | + | 262.005i | 0.0314805 | + | 0.0215952i | ||||
\(529\) | 7393.10 | 0.607635 | ||||||||
\(530\) | 27808.5 | 2.27910 | ||||||||
\(531\) | 4004.31 | + | 10377.0i | 0.327254 | + | 0.848069i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1935.19i | 0.157265i | ||||||||
\(534\) | 10938.8 | + | 7503.88i | 0.886456 | + | 0.608098i | ||||
\(535\) | − | 14131.1i | − | 1.14195i | ||||||
\(536\) | 6854.33i | 0.552355i | ||||||||
\(537\) | −2742.93 | − | 1881.62i | −0.220421 | − | 0.151206i | ||||
\(538\) | 17248.2i | 1.38220i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −20056.0 | − | 4759.15i | −1.59828 | − | 0.379261i | ||||
\(541\) | 5317.95 | 0.422618 | 0.211309 | − | 0.977419i | \(-0.432227\pi\) | ||||
0.211309 | + | 0.977419i | \(0.432227\pi\) | |||||||
\(542\) | 33898.7 | 2.68648 | ||||||||
\(543\) | 18013.8 | + | 12357.3i | 1.42366 | + | 0.976613i | ||||
\(544\) | 4114.80i | 0.324302i | ||||||||
\(545\) | −15064.9 | −1.18405 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9266.96 | −0.724363 | −0.362181 | − | 0.932108i | \(-0.617968\pi\) | ||||
−0.362181 | + | 0.932108i | \(0.617968\pi\) | |||||||
\(548\) | 29356.4i | 2.28840i | ||||||||
\(549\) | −6509.77 | + | 2512.00i | −0.506066 | + | 0.195282i | ||||
\(550\) | −785.854 | −0.0609253 | ||||||||
\(551\) | −2915.65 | −0.225428 | ||||||||
\(552\) | 4303.45 | − | 6273.36i | 0.331824 | − | 0.483717i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15525.2i | 1.19062i | ||||||||
\(555\) | −1420.65 | + | 2070.95i | −0.108654 | + | 0.158391i | ||||
\(556\) | 23317.4i | 1.77856i | ||||||||
\(557\) | 145.400i | 0.0110607i | 0.999985 | + | 0.00553033i | \(0.00176037\pi\) | ||||
−0.999985 | + | 0.00553033i | \(0.998240\pi\) | |||||||
\(558\) | −451.920 | − | 1171.14i | −0.0342854 | − | 0.0888497i | ||||
\(559\) | − | 14016.1i | − | 1.06050i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1644.09 | − | 1127.83i | −0.123732 | − | 0.0848785i | ||||
\(562\) | 12555.4 | 0.942376 | ||||||||
\(563\) | 3916.24 | 0.293161 | 0.146581 | − | 0.989199i | \(-0.453173\pi\) | ||||
0.146581 | + | 0.989199i | \(0.453173\pi\) | |||||||
\(564\) | 6093.19 | − | 8882.35i | 0.454910 | − | 0.663146i | ||||
\(565\) | − | 16684.7i | − | 1.24236i | ||||||
\(566\) | −25024.0 | −1.85837 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −962.437 | −0.0710968 | ||||||||
\(569\) | − | 8550.53i | − | 0.629977i | −0.949096 | − | 0.314988i | \(-0.897999\pi\) | ||
0.949096 | − | 0.314988i | \(-0.102001\pi\) | |||||||
\(570\) | 1702.06 | − | 2481.18i | 0.125073 | − | 0.182325i | ||||
\(571\) | −23913.7 | −1.75264 | −0.876318 | − | 0.481733i | \(-0.840007\pi\) | ||||
−0.876318 | + | 0.481733i | \(0.840007\pi\) | |||||||
\(572\) | −14159.4 | −1.03503 | ||||||||
\(573\) | −6243.32 | − | 4282.84i | −0.455180 | − | 0.312248i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 666.737i | − | 0.0483563i | ||||||
\(576\) | −8102.20 | − | 20996.6i | −0.586096 | − | 1.51885i | ||||
\(577\) | 13103.3i | 0.945405i | 0.881222 | + | 0.472703i | \(0.156721\pi\) | ||||
−0.881222 | + | 0.472703i | \(0.843279\pi\) | |||||||
\(578\) | 20247.2i | 1.45705i | ||||||||
\(579\) | 5376.89 | − | 7838.16i | 0.385934 | − | 0.562596i | ||||
\(580\) | − | 39020.7i | − | 2.79353i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2864.10 | + | 4175.15i | −0.203988 | + | 0.297363i | ||||
\(583\) | −9445.66 | −0.671011 | ||||||||
\(584\) | 11912.9 | 0.844106 | ||||||||
\(585\) | −18244.7 | + | 7040.31i | −1.28945 | + | 0.497574i | ||||
\(586\) | 18641.5i | 1.31412i | ||||||||
\(587\) | −18034.7 | −1.26809 | −0.634047 | − | 0.773294i | \(-0.718608\pi\) | ||||
−0.634047 | + | 0.773294i | \(0.718608\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 112.289 | 0.00785532 | ||||||||
\(590\) | − | 21728.9i | − | 1.51621i | ||||||
\(591\) | −2833.02 | − | 1943.42i | −0.197183 | − | 0.135265i | ||||
\(592\) | −207.226 | −0.0143867 | ||||||||
\(593\) | 22716.2 | 1.57309 | 0.786547 | − | 0.617531i | \(-0.211867\pi\) | ||||
0.786547 | + | 0.617531i | \(0.211867\pi\) | |||||||
\(594\) | 11116.7 | + | 2637.90i | 0.767882 | + | 0.182213i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16472.5i | 1.13212i | ||||||||
\(597\) | −8351.76 | − | 5729.21i | −0.572554 | − | 0.392765i | ||||
\(598\) | − | 19603.5i | − | 1.34054i | ||||||
\(599\) | − | 13533.6i | − | 0.923149i | −0.887101 | − | 0.461575i | \(-0.847285\pi\) | ||
0.887101 | − | 0.461575i | \(-0.152715\pi\) | |||||||
\(600\) | 876.156 | + | 601.032i | 0.0596148 | + | 0.0408951i | ||||
\(601\) | 3667.98i | 0.248952i | 0.992223 | + | 0.124476i | \(0.0397250\pi\) | ||||
−0.992223 | + | 0.124476i | \(0.960275\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3144.24 | − | 8148.20i | −0.212344 | − | 0.550282i | ||||
\(604\) | 33129.1 | 2.23180 | ||||||||
\(605\) | −11720.1 | −0.787587 | ||||||||
\(606\) | −33455.3 | − | 22950.0i | −2.24262 | − | 1.53841i | ||||
\(607\) | 8017.00i | 0.536079i | 0.963408 | + | 0.268039i | \(0.0863758\pi\) | ||||
−0.963408 | + | 0.268039i | \(0.913624\pi\) | |||||||
\(608\) | 2109.29 | 0.140696 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13631.1 | 0.904763 | ||||||||
\(611\) | − | 10219.1i | − | 0.676628i | ||||||
\(612\) | 2635.81 | + | 6830.62i | 0.174095 | + | 0.451162i | ||||
\(613\) | 9396.52 | 0.619122 | 0.309561 | − | 0.950880i | \(-0.399818\pi\) | ||||
0.309561 | + | 0.950880i | \(0.399818\pi\) | |||||||
\(614\) | −37643.3 | −2.47420 | ||||||||
\(615\) | −1057.47 | + | 1541.53i | −0.0693355 | + | 0.101074i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8906.76i | − | 0.581155i | −0.956851 | − | 0.290578i | \(-0.906153\pi\) | ||
0.956851 | − | 0.290578i | \(-0.0938474\pi\) | |||||||
\(618\) | −15468.1 | + | 22548.6i | −1.00682 | + | 1.46770i | ||||
\(619\) | − | 7034.12i | − | 0.456745i | −0.973574 | − | 0.228373i | \(-0.926660\pi\) | ||
0.973574 | − | 0.228373i | \(-0.0733404\pi\) | |||||||
\(620\) | 1502.78i | 0.0973440i | ||||||||
\(621\) | −2238.06 | + | 9431.64i | −0.144622 | + | 0.609466i | ||||
\(622\) | 31232.4i | 2.01335i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1330.65 | − | 912.811i | −0.0853665 | − | 0.0585604i | ||||
\(625\) | −16738.1 | −1.07124 | ||||||||
\(626\) | 15338.8 | 0.979332 | ||||||||
\(627\) | −578.135 | + | 842.778i | −0.0368238 | + | 0.0536799i | ||||
\(628\) | 11840.8i | 0.752385i | ||||||||
\(629\) | 892.024 | 0.0565458 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12628.6 | −0.796728 | −0.398364 | − | 0.917227i | \(-0.630422\pi\) | ||||
−0.398364 | + | 0.917227i | \(0.630422\pi\) | |||||||
\(632\) | 6128.52i | 0.385727i | ||||||||
\(633\) | 9823.25 | − | 14319.9i | 0.616808 | − | 0.899152i | ||||
\(634\) | 10771.8 | 0.674768 | ||||||||
\(635\) | −31171.8 | −1.94805 | ||||||||
\(636\) | 28603.6 | + | 19621.7i | 1.78334 | + | 1.22335i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 21628.4i | 1.34213i | ||||||||
\(639\) | 1144.11 | − | 441.492i | 0.0708300 | − | 0.0273320i | ||||
\(640\) | 26129.7i | 1.61385i | ||||||||
\(641\) | 9923.02i | 0.611444i | 0.952121 | + | 0.305722i | \(0.0988978\pi\) | ||||
−0.952121 | + | 0.305722i | \(0.901102\pi\) | |||||||
\(642\) | 16270.9 | − | 23718.9i | 1.00025 | − | 1.45811i | ||||
\(643\) | − | 294.191i | − | 0.0180432i | −0.999959 | − | 0.00902160i | \(-0.997128\pi\) | ||
0.999959 | − | 0.00902160i | \(-0.00287170\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7658.97 | − | 11164.9i | 0.467553 | − | 0.681576i | ||||
\(646\) | −1068.72 | −0.0650902 | ||||||||
\(647\) | −7718.79 | −0.469021 | −0.234511 | − | 0.972114i | \(-0.575349\pi\) | ||||
−0.234511 | + | 0.972114i | \(0.575349\pi\) | |||||||
\(648\) | −10376.6 | − | 11443.2i | −0.629058 | − | 0.693721i | ||||
\(649\) | 7380.61i | 0.446401i | ||||||||
\(650\) | 2737.88 | 0.165213 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6560.75 | 0.394078 | ||||||||
\(653\) | − | 11370.2i | − | 0.681395i | −0.940173 | − | 0.340697i | \(-0.889337\pi\) | ||
0.940173 | − | 0.340697i | \(-0.110663\pi\) | |||||||
\(654\) | −25286.2 | − | 17346.0i | −1.51188 | − | 1.03713i | ||||
\(655\) | 18604.2 | 1.10981 | ||||||||
\(656\) | −154.250 | −0.00918056 | ||||||||
\(657\) | −14161.6 | + | 5464.70i | −0.840938 | + | 0.324503i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19795.1i | 1.17012i | 0.810990 | + | 0.585060i | \(0.198929\pi\) | ||||
−0.810990 | + | 0.585060i | \(0.801071\pi\) | |||||||
\(660\) | −11279.1 | − | 7737.30i | −0.665207 | − | 0.456324i | ||||
\(661\) | 31057.5i | 1.82753i | 0.406247 | + | 0.913763i | \(0.366837\pi\) | ||||
−0.406247 | + | 0.913763i | \(0.633163\pi\) | |||||||
\(662\) | − | 17289.3i | − | 1.01506i | ||||||
\(663\) | 5727.93 | + | 3929.29i | 0.335527 | + | 0.230167i | ||||
\(664\) | − | 9509.25i | − | 0.555769i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4769.08 | + | 1840.30i | −0.277474 | + | 0.107072i | ||||
\(667\) | −18350.1 | −1.06524 | ||||||||
\(668\) | −47708.9 | −2.76334 | ||||||||
\(669\) | 9183.66 | + | 6299.88i | 0.530734 | + | 0.364077i | ||||
\(670\) | 17061.8i | 0.983814i | ||||||||
\(671\) | −4630.04 | −0.266380 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5340.26 | 0.305872 | 0.152936 | − | 0.988236i | \(-0.451127\pi\) | ||||
0.152936 | + | 0.988236i | \(0.451127\pi\) | |||||||
\(674\) | 2695.28i | 0.154033i | ||||||||
\(675\) | −1317.25 | − | 312.574i | −0.0751126 | − | 0.0178237i | ||||
\(676\) | 21513.0 | 1.22400 | ||||||||
\(677\) | −24956.6 | −1.41678 | −0.708389 | − | 0.705822i | \(-0.750578\pi\) | ||||
−0.708389 | + | 0.705822i | \(0.750578\pi\) | |||||||
\(678\) | 19211.1 | − | 28005.1i | 1.08820 | − | 1.58632i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 5265.93i | − | 0.296970i | ||||||
\(681\) | 7551.55 | − | 11008.3i | 0.424928 | − | 0.619439i | ||||
\(682\) | − | 832.964i | − | 0.0467681i | ||||||
\(683\) | − | 11208.5i | − | 0.627937i | −0.949433 | − | 0.313968i | \(-0.898341\pi\) | ||
0.949433 | − | 0.313968i | \(-0.101659\pi\) | |||||||
\(684\) | 3501.45 | − | 1351.14i | 0.195733 | − | 0.0755297i | ||||
\(685\) | 26903.9i | 1.50065i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −450.654 | − | 309.143i | −0.0250269 | − | 0.0171682i | ||||
\(688\) | 1117.19 | 0.0619077 | ||||||||
\(689\) | 32908.2 | 1.81960 | ||||||||
\(690\) | 10712.1 | − | 15615.6i | 0.591021 | − | 0.861562i | ||||
\(691\) | 10937.8i | 0.602159i | 0.953599 | + | 0.301079i | \(0.0973469\pi\) | ||||
−0.953599 | + | 0.301079i | \(0.902653\pi\) | |||||||
\(692\) | −30300.2 | −1.66451 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21714.7 | 1.18772 | ||||||||
\(695\) | 21369.4i | 1.16631i | ||||||||
\(696\) | 16541.7 | − | 24113.7i | 0.900879 | − | 1.31326i | ||||
\(697\) | 663.984 | 0.0360835 | ||||||||
\(698\) | 33447.1 | 1.81374 | ||||||||
\(699\) | 11250.9 | + | 7717.97i | 0.608795 | + | 0.417626i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27949.3i | − | 1.50589i | −0.658082 | − | 0.752947i | \(-0.728632\pi\) | ||
0.658082 | − | 0.752947i | \(-0.271368\pi\) | |||||||
\(702\) | −38729.9 | − | 9190.32i | −2.08229 | − | 0.494111i | ||||
\(703\) | − | 457.261i | − | 0.0245319i | ||||||
\(704\) | − | 14933.7i | − | 0.799482i | ||||||
\(705\) | 5584.14 | − | 8140.28i | 0.298313 | − | 0.434866i | ||||
\(706\) | − | 15025.4i | − | 0.800977i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 15331.9 | − | 22350.1i | 0.813855 | − | 1.18640i | ||||
\(709\) | 20945.4 | 1.10948 | 0.554741 | − | 0.832023i | \(-0.312817\pi\) | ||||
0.554741 | + | 0.832023i | \(0.312817\pi\) | |||||||
\(710\) | −2395.70 | −0.126632 | ||||||||
\(711\) | −2811.29 | − | 7285.37i | −0.148286 | − | 0.384279i | ||||
\(712\) | − | 11900.8i | − | 0.626404i | ||||||
\(713\) | 706.707 | 0.0371197 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12976.5 | −0.678731 | ||||||||
\(716\) | 8105.30i | 0.423058i | ||||||||
\(717\) | −26055.7 | − | 17873.9i | −1.35714 | − | 0.930979i | ||||
\(718\) | −1885.09 | −0.0979820 | ||||||||
\(719\) | 8300.21 | 0.430522 | 0.215261 | − | 0.976557i | \(-0.430940\pi\) | ||||
0.215261 | + | 0.976557i | \(0.430940\pi\) | |||||||
\(720\) | −561.167 | − | 1454.25i | −0.0290465 | − | 0.0752731i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 30629.8i | − | 1.57884i | ||||||
\(723\) | 19834.2 | + | 13606.0i | 1.02025 | + | 0.699880i | ||||
\(724\) | − | 53230.4i | − | 2.73245i | ||||||
\(725\) | − | 2562.82i | − | 0.131284i | ||||||
\(726\) | −19672.0 | − | 13494.8i | −1.00564 | − | 0.689860i | ||||
\(727\) | − | 20951.5i | − | 1.06884i | −0.845218 | − | 0.534421i | \(-0.820530\pi\) | ||
0.845218 | − | 0.534421i | \(-0.179470\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17584.5 | + | 8843.31i | 0.893388 | + | 0.449287i | ||||
\(730\) | 29653.5 | 1.50346 | ||||||||
\(731\) | −4809.06 | −0.243324 | ||||||||
\(732\) | 14020.8 | + | 9618.11i | 0.707956 | + | 0.485650i | ||||
\(733\) | − | 5641.56i | − | 0.284278i | −0.989847 | − | 0.142139i | \(-0.954602\pi\) | ||
0.989847 | − | 0.142139i | \(-0.0453980\pi\) | |||||||
\(734\) | −346.017 | −0.0174001 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13275.1 | 0.664847 | ||||||||
\(737\) | − | 5795.36i | − | 0.289654i | ||||||
\(738\) | −3549.90 | + | 1369.84i | −0.177064 | + | 0.0683259i | ||||
\(739\) | −11382.2 | −0.566576 | −0.283288 | − | 0.959035i | \(-0.591425\pi\) | ||||
−0.283288 | + | 0.959035i | \(0.591425\pi\) | |||||||
\(740\) | 6119.61 | 0.304002 | ||||||||
\(741\) | 2014.20 | − | 2936.20i | 0.0998560 | − | 0.145565i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4665.46i | 0.230362i | 0.993345 | + | 0.115181i | \(0.0367449\pi\) | ||||
−0.993345 | + | 0.115181i | \(0.963255\pi\) | |||||||
\(744\) | −637.063 | + | 928.679i | −0.0313923 | + | 0.0457621i | ||||
\(745\) | 15096.3i | 0.742399i | ||||||||
\(746\) | 55914.3i | 2.74419i | ||||||||
\(747\) | 4362.11 | + | 11304.3i | 0.213656 | + | 0.553684i | ||||
\(748\) | 4858.24i | 0.237480i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −26070.0 | − | 17883.7i | −1.26926 | − | 0.870696i | ||||
\(751\) | −9560.86 | −0.464555 | −0.232277 | − | 0.972650i | \(-0.574618\pi\) | ||||
−0.232277 | + | 0.972650i | \(0.574618\pi\) | |||||||
\(752\) | 814.540 | 0.0394990 | ||||||||
\(753\) | −17541.7 | + | 25571.5i | −0.848945 | + | 1.23755i | ||||
\(754\) | − | 75352.3i | − | 3.63948i | ||||||
\(755\) | 30361.4 | 1.46353 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31574.1 | 1.51596 | 0.757979 | − | 0.652279i | \(-0.226187\pi\) | ||||
0.757979 | + | 0.652279i | \(0.226187\pi\) | |||||||
\(758\) | 6495.63i | 0.311256i | ||||||||
\(759\) | −3638.58 | + | 5304.14i | −0.174008 | + | 0.253660i | ||||
\(760\) | −2699.37 | −0.128838 | ||||||||
\(761\) | 22429.9 | 1.06844 | 0.534221 | − | 0.845345i | \(-0.320605\pi\) | ||||
0.534221 | + | 0.845345i | \(0.320605\pi\) | |||||||
\(762\) | −52321.3 | − | 35891.8i | −2.48740 | − | 1.70633i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18448.8i | 0.873633i | ||||||||
\(765\) | 2415.60 | + | 6259.96i | 0.114165 | + | 0.295855i | ||||
\(766\) | − | 23231.6i | − | 1.09581i | ||||||
\(767\) | − | 25713.7i | − | 1.21052i | ||||||
\(768\) | −10485.6 | + | 15285.4i | −0.492664 | + | 0.718181i | ||||
\(769\) | − | 26887.4i | − | 1.26084i | −0.776254 | − | 0.630420i | \(-0.782883\pi\) | ||
0.776254 | − | 0.630420i | \(-0.217117\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16576.3 | + | 24164.1i | −0.774293 | + | 1.12873i | ||||
\(772\) | −23161.6 | −1.07980 | ||||||||
\(773\) | 22209.1 | 1.03339 | 0.516693 | − | 0.856171i | \(-0.327163\pi\) | ||||
0.516693 | + | 0.856171i | \(0.327163\pi\) | |||||||
\(774\) | 25711.0 | − | 9921.39i | 1.19401 | − | 0.460745i | ||||
\(775\) | 98.7007i | 0.00457476i | ||||||||
\(776\) | 4542.31 | 0.210128 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −33276.0 | −1.53342 | ||||||||
\(779\) | − | 340.366i | − | 0.0156545i | ||||||
\(780\) | 39295.7 | + | 26956.4i | 1.80386 | + | 1.23743i | ||||
\(781\) | 813.743 | 0.0372830 | ||||||||
\(782\) | −6726.15 | −0.307579 | ||||||||
\(783\) | −8602.71 | + | 36253.6i | −0.392638 | + | 1.65466i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10851.5i | 0.493385i | ||||||||
\(786\) | 31226.8 | + | 21421.2i | 1.41708 | + | 0.972100i | ||||
\(787\) | − | 20095.5i | − | 0.910200i | −0.890440 | − | 0.455100i | \(-0.849603\pi\) | ||
0.890440 | − | 0.455100i | \(-0.150397\pi\) | |||||||
\(788\) | 8371.51i | 0.378455i | ||||||||
\(789\) | 14935.4 | + | 10245.5i | 0.673910 | + | 0.462294i | ||||
\(790\) | 15255.1i | 0.687029i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3690.14 | − | 9562.87i | −0.165560 | − | 0.429043i | ||||
\(793\) | 16130.8 | 0.722349 | ||||||||
\(794\) | −39452.5 | −1.76337 | ||||||||
\(795\) | 26213.9 | + | 17982.4i | 1.16945 | + | 0.802228i | ||||
\(796\) | 24679.2i | 1.09891i | ||||||||
\(797\) | 14300.8 | 0.635583 | 0.317791 | − | 0.948161i | \(-0.397059\pi\) | ||||
0.317791 | + | 0.948161i | \(0.397059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3506.27 | −0.155248 | ||||||||
\(800\) | 1854.04i | 0.0819379i | ||||||||
\(801\) | 5459.15 | + | 14147.2i | 0.240811 | + | 0.624053i | ||||
\(802\) | 44339.4 | 1.95222 | ||||||||
\(803\) | −10072.4 | −0.442647 | ||||||||
\(804\) | −12038.9 | + | 17549.7i | −0.528082 | + | 0.769812i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2902.01i | 0.126822i | ||||||||
\(807\) | −11153.6 | + | 16259.2i | −0.486524 | + | 0.709231i | ||||
\(808\) | 36397.4i | 1.58472i | ||||||||
\(809\) | − | 14748.9i | − | 0.640967i | −0.947254 | − | 0.320483i | \(-0.896155\pi\) | ||
0.947254 | − | 0.320483i | \(-0.103845\pi\) | |||||||
\(810\) | −25829.3 | − | 28484.4i | −1.12043 | − | 1.23561i | ||||
\(811\) | − | 4569.51i | − | 0.197851i | −0.995095 | − | 0.0989255i | \(-0.968459\pi\) | ||
0.995095 | − | 0.0989255i | \(-0.0315405\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31954.9 | + | 21920.7i | 1.37848 | + | 0.945624i | ||||
\(814\) | −3391.98 | −0.146055 | ||||||||
\(815\) | 6012.63 | 0.258421 | ||||||||
\(816\) | −313.195 | + | 456.560i | −0.0134363 | + | 0.0195868i | ||||
\(817\) | 2465.18i | 0.105564i | ||||||||
\(818\) | 15406.6 | 0.658532 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4555.18 | 0.193992 | ||||||||
\(821\) | 46797.8i | 1.98935i | 0.103070 | + | 0.994674i | \(0.467133\pi\) | ||||
−0.103070 | + | 0.994674i | \(0.532867\pi\) | |||||||
\(822\) | −30977.7 | + | 45157.7i | −1.31444 | + | 1.91613i | ||||
\(823\) | −26173.4 | −1.10856 | −0.554281 | − | 0.832330i | \(-0.687007\pi\) | ||||
−0.554281 | + | 0.832330i | \(0.687007\pi\) | |||||||
\(824\) | 24531.6 | 1.03713 | ||||||||
\(825\) | −740.792 | − | 508.175i | −0.0312619 | − | 0.0214453i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 42212.0i | − | 1.77492i | −0.460888 | − | 0.887458i | \(-0.652469\pi\) | ||
0.460888 | − | 0.887458i | \(-0.347531\pi\) | |||||||
\(828\) | 22036.9 | − | 8503.62i | 0.924921 | − | 0.356910i | ||||
\(829\) | − | 22637.9i | − | 0.948430i | −0.880409 | − | 0.474215i | \(-0.842732\pi\) | ||
0.880409 | − | 0.474215i | \(-0.157268\pi\) | |||||||
\(830\) | − | 23670.5i | − | 0.989896i | ||||||
\(831\) | −10039.4 | + | 14634.9i | −0.419089 | + | 0.610927i | ||||
\(832\) | 52028.3i | 2.16798i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −24605.1 | + | 35868.2i | −1.02159 | + | 1.48923i | ||||
\(835\) | −43723.0 | −1.81209 | ||||||||
\(836\) | 2490.39 | 0.103029 | ||||||||
\(837\) | 331.312 | − | 1396.22i | 0.0136820 | − | 0.0576587i | ||||
\(838\) | 58079.7i | 2.39419i | ||||||||
\(839\) | 39480.0 | 1.62455 | 0.812277 | − | 0.583272i | \(-0.198228\pi\) | ||||
0.812277 | + | 0.583272i | \(0.198228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −46145.4 | −1.89206 | ||||||||
\(842\) | − | 50025.2i | − | 2.04748i | ||||||
\(843\) | 11835.4 | + | 8118.96i | 0.483551 | + | 0.331710i | ||||
\(844\) | −42314.8 | −1.72575 | ||||||||
\(845\) | 19715.7 | 0.802652 | ||||||||
\(846\) | 18745.8 | − | 7233.65i | 0.761812 | − | 0.293969i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2623.04i | 0.106221i | ||||||||
\(849\) | −23589.1 | − | 16181.8i | −0.953563 | − | 0.654133i | ||||
\(850\) | − | 939.394i | − | 0.0379070i | ||||||
\(851\) | − | 2877.84i | − | 0.115924i | ||||||
\(852\) | −2464.20 | − | 1690.41i | −0.0990869 | − | 0.0679724i | ||||
\(853\) | − | 44021.1i | − | 1.76700i | −0.468430 | − | 0.883501i | \(-0.655180\pi\) | ||
0.468430 | − | 0.883501i | \(-0.344820\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3208.92 | − | 1238.26i | 0.128354 | − | 0.0495295i | ||||
\(856\) | −25804.7 | −1.03036 | ||||||||
\(857\) | 2014.90 | 0.0803124 | 0.0401562 | − | 0.999193i | \(-0.487214\pi\) | ||||
0.0401562 | + | 0.999193i | \(0.487214\pi\) | |||||||
\(858\) | −21780.8 | − | 14941.4i | −0.866649 | − | 0.594511i | ||||
\(859\) | − | 18295.7i | − | 0.726706i | −0.931652 | − | 0.363353i | \(-0.881632\pi\) | ||
0.931652 | − | 0.363353i | \(-0.118368\pi\) | |||||||
\(860\) | −32991.9 | −1.30816 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17211.2 | −0.680064 | ||||||||
\(863\) | − | 6904.01i | − | 0.272323i | −0.990687 | − | 0.136162i | \(-0.956523\pi\) | ||
0.990687 | − | 0.136162i | \(-0.0434767\pi\) | |||||||
\(864\) | 6223.53 | − | 26227.2i | 0.245056 | − | 1.03272i | ||||
\(865\) | −27768.7 | −1.09152 | ||||||||
\(866\) | −14507.8 | −0.569277 | ||||||||
\(867\) | −13092.9 | + | 19086.3i | −0.512872 | + | 0.747639i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 5181.68i | − | 0.202274i | ||||||
\(870\) | 41175.6 | − | 60023.9i | 1.60458 | − | 2.33908i | ||||
\(871\) | 20190.8i | 0.785462i | ||||||||
\(872\) | 27509.9i | 1.06835i | ||||||||
\(873\) | −5399.74 | + | 2083.66i | −0.209340 | + | 0.0807803i | ||||
\(874\) | 3447.90i | 0.133440i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 30501.4 | + | 20923.6i | 1.17642 | + | 0.807012i | ||||
\(877\) | 417.193 | 0.0160634 | 0.00803171 | − | 0.999968i | \(-0.497443\pi\) | ||||
0.00803171 | + | 0.999968i | \(0.497443\pi\) | |||||||
\(878\) | 15079.0 | 0.579603 | ||||||||
\(879\) | −12054.6 | + | 17572.6i | −0.462561 | + | 0.674299i | ||||
\(880\) | − | 1034.33i | − | 0.0396217i | ||||||
\(881\) | 7244.25 | 0.277032 | 0.138516 | − | 0.990360i | \(-0.455767\pi\) | ||||
0.138516 | + | 0.990360i | \(0.455767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38284.4 | 1.45908 | 0.729542 | − | 0.683936i | \(-0.239733\pi\) | ||||
0.729542 | + | 0.683936i | \(0.239733\pi\) | |||||||
\(884\) | − | 16925.9i | − | 0.643981i | ||||||
\(885\) | 14051.0 | − | 20482.9i | 0.533695 | − | 0.777995i | ||||
\(886\) | −48639.5 | −1.84433 | ||||||||
\(887\) | 17868.0 | 0.676378 | 0.338189 | − | 0.941078i | \(-0.390186\pi\) | ||||
0.338189 | + | 0.941078i | \(0.390186\pi\) | |||||||
\(888\) | 3781.75 | + | 2594.24i | 0.142914 | + | 0.0980370i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 29623.4i | − | 1.11571i | ||||||
\(891\) | 8773.41 | + | 9675.26i | 0.329877 | + | 0.363786i | ||||
\(892\) | − | 27137.5i | − | 1.01864i | ||||||
\(893\) | 1797.35i | 0.0673529i | ||||||||
\(894\) | −17382.3 | + | 25339.0i | −0.650279 | + | 0.947945i | ||||
\(895\) | 7428.15i | 0.277425i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12676.6 | − | 18479.4i | 0.471862 | − | 0.687858i | ||||
\(898\) | 18263.5 | 0.678687 | ||||||||
\(899\) | 2716.46 | 0.100777 | ||||||||
\(900\) | 1187.64 | + | 3077.74i | 0.0439867 | + | 0.113990i | ||||
\(901\) | − | 11291.2i | − | 0.417495i | ||||||
\(902\) | −2524.85 | −0.0932020 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −30467.9 | −1.12096 | ||||||||
\(905\) | − | 48783.3i | − | 1.79183i | ||||||
\(906\) | 50961.1 | + | 34958.7i | 1.86873 | + | 1.28193i | ||||
\(907\) | −6562.99 | −0.240265 | −0.120132 | − | 0.992758i | \(-0.538332\pi\) | ||||
−0.120132 | + | 0.992758i | \(0.538332\pi\) | |||||||
\(908\) | −32529.2 | −1.18890 | ||||||||
\(909\) | −16696.3 | − | 43268.0i | −0.609221 | − | 1.57878i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41084.1i | 1.49416i | 0.664735 | + | 0.747079i | \(0.268544\pi\) | ||||
−0.664735 | + | 0.747079i | \(0.731456\pi\) | |||||||
\(912\) | 234.038 | + | 160.547i | 0.00849755 | + | 0.00582922i | ||||
\(913\) | 8040.11i | 0.291444i | ||||||||
\(914\) | − | 41680.8i | − | 1.50840i | ||||||
\(915\) | 12849.4 | + | 8814.57i | 0.464251 | + | 0.318471i | ||||
\(916\) | 1331.67i | 0.0480345i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3153.29 | + | 13288.6i | −0.113371 | + | 0.477767i | ||||
\(919\) | 5524.67 | 0.198305 | 0.0991524 | − | 0.995072i | \(-0.468387\pi\) | ||||
0.0991524 | + | 0.995072i | \(0.468387\pi\) | |||||||
\(920\) | −16988.9 | −0.608812 | ||||||||
\(921\) | −35484.8 | − | 24342.2i | −1.26956 | − | 0.870903i | ||||
\(922\) | − | 5862.82i | − | 0.209416i | ||||||
\(923\) | −2835.04 | −0.101101 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 401.928 | 0.0142868 | ||||||||
\(926\) | − | 31711.9i | − | 1.12540i | ||||||
\(927\) | −29162.3 | + | 11253.2i | −1.03324 | + | 0.398709i | ||||
\(928\) | 51027.3 | 1.80501 | ||||||||
\(929\) | −25260.3 | −0.892104 | −0.446052 | − | 0.895007i | \(-0.647170\pi\) | ||||
−0.446052 | + | 0.895007i | \(0.647170\pi\) | |||||||
\(930\) | −1585.78 | + | 2311.67i | −0.0559136 | + | 0.0815082i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 33246.1i | − | 1.16847i | ||||||
\(933\) | −20196.5 | + | 29441.5i | −0.708687 | + | 1.03309i | ||||
\(934\) | 35744.4i | 1.25224i | ||||||||
\(935\) | 4452.36i | 0.155730i | ||||||||
\(936\) | 12856.3 | + | 33316.6i | 0.448953 | + | 1.16345i | ||||
\(937\) | 46069.3i | 1.60621i | 0.595838 | + | 0.803105i | \(0.296820\pi\) | ||||
−0.595838 | + | 0.803105i | \(0.703180\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14459.3 | + | 9918.89i | 0.502514 | + | 0.344718i | ||||
\(940\) | −24054.3 | −0.834644 | ||||||||
\(941\) | −48224.7 | −1.67065 | −0.835325 | − | 0.549756i | \(-0.814721\pi\) | ||||
−0.835325 | + | 0.549756i | \(0.814721\pi\) | |||||||
\(942\) | −12494.7 | + | 18214.1i | −0.432164 | + | 0.629988i | ||||
\(943\) | − | 2142.14i | − | 0.0739742i | ||||||
\(944\) | 2049.58 | 0.0706654 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18286.8 | 0.628493 | ||||||||
\(947\) | 24641.6i | 0.845559i | 0.906233 | + | 0.422779i | \(0.138945\pi\) | ||||
−0.906233 | + | 0.422779i | \(0.861055\pi\) | |||||||
\(948\) | −10764.0 | + | 15691.3i | −0.368776 | + | 0.537584i | ||||
\(949\) | 35091.6 | 1.20034 | ||||||||
\(950\) | −481.543 | −0.0164456 | ||||||||
\(951\) | 10154.1 | + | 6965.62i | 0.346236 | + | 0.237514i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13271.1i | 0.451095i | 0.974232 | + | 0.225548i | \(0.0724171\pi\) | ||||
−0.974232 | + | 0.225548i | \(0.927583\pi\) | |||||||
\(954\) | 23294.3 | + | 60366.5i | 0.790547 | + | 2.04868i | ||||
\(955\) | 16907.5i | 0.572896i | ||||||||
\(956\) | 76993.9i | 2.60477i | ||||||||
\(957\) | −13986.1 | + | 20388.2i | −0.472419 | + | 0.688670i | ||||
\(958\) | − | 16792.3i | − | 0.566321i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −28430.5 | + | 41444.5i | −0.955822 | + | 1.39335i | ||||
\(961\) | 29686.4 | 0.996488 | ||||||||
\(962\) | 11817.5 | 0.396062 | ||||||||
\(963\) | 30675.8 | − | 11837.2i | 1.02649 | − | 0.396105i | ||||
\(964\) | − | 58609.5i | − | 1.95818i | ||||||
\(965\) | −21226.6 | −0.708090 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15785.8 | −0.524959 | −0.262480 | − | 0.964938i | \(-0.584540\pi\) | ||||
−0.262480 | + | 0.964938i | \(0.584540\pi\) | |||||||
\(968\) | 21402.0i | 0.710626i | ||||||||
\(969\) | −1007.44 | − | 691.091i | −0.0333990 | − | 0.0229113i | ||||
\(970\) | 11306.7 | 0.374265 | ||||||||
\(971\) | 51785.2 | 1.71150 | 0.855750 | − | 0.517389i | \(-0.173096\pi\) | ||||
0.855750 | + | 0.517389i | \(0.173096\pi\) | |||||||
\(972\) | −6469.20 | − | 47524.1i | −0.213477 | − | 1.56825i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4785.15i | 0.157419i | ||||||||
\(975\) | 2580.88 | + | 1770.46i | 0.0847738 | + | 0.0581538i | ||||
\(976\) | 1285.75i | 0.0421680i | ||||||||
\(977\) | 28631.9i | 0.937581i | 0.883309 | + | 0.468790i | \(0.155310\pi\) | ||||
−0.883309 | + | 0.468790i | \(0.844690\pi\) | |||||||
\(978\) | 10092.1 | + | 6923.07i | 0.329970 | + | 0.226355i | ||||
\(979\) | 10062.1i | 0.328485i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12619.4 | − | 32702.8i | −0.410710 | − | 1.06434i | ||||
\(982\) | −10811.1 | −0.351319 | ||||||||
\(983\) | 43968.6 | 1.42663 | 0.713317 | − | 0.700841i | \(-0.247192\pi\) | ||||
0.713317 | + | 0.700841i | \(0.247192\pi\) | |||||||
\(984\) | 2814.97 | + | 1931.04i | 0.0911972 | + | 0.0625602i | ||||
\(985\) | 7672.11i | 0.248176i | ||||||||
\(986\) | −25854.1 | −0.835055 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8676.39 | −0.279385 | ||||||||
\(989\) | 15514.9i | 0.498834i | ||||||||
\(990\) | −9185.49 | − | 23803.9i | −0.294883 | − | 0.764180i | ||||
\(991\) | −15154.7 | −0.485776 | −0.242888 | − | 0.970054i | \(-0.578095\pi\) | ||||
−0.242888 | + | 0.970054i | \(0.578095\pi\) | |||||||
\(992\) | −1965.19 | −0.0628980 | ||||||||
\(993\) | 11180.2 | − | 16298.0i | 0.357294 | − | 0.520846i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22617.4i | 0.720624i | ||||||||
\(996\) | 16701.9 | − | 24347.2i | 0.531346 | − | 0.774570i | ||||
\(997\) | − | 27611.9i | − | 0.877110i | −0.898704 | − | 0.438555i | \(-0.855490\pi\) | ||
0.898704 | − | 0.438555i | \(-0.144510\pi\) | |||||||
\(998\) | − | 85326.0i | − | 2.70636i | ||||||
\(999\) | −5685.65 | − | 1349.16i | −0.180066 | − | 0.0427284i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 147.4.c.a.146.2 | 12 | ||
3.2 | odd | 2 | inner | 147.4.c.a.146.11 | 12 | ||
7.2 | even | 3 | 147.4.g.d.80.1 | 12 | |||
7.3 | odd | 6 | 147.4.g.d.68.6 | 12 | |||
7.4 | even | 3 | 21.4.g.a.5.6 | yes | 12 | ||
7.5 | odd | 6 | 21.4.g.a.17.1 | yes | 12 | ||
7.6 | odd | 2 | inner | 147.4.c.a.146.1 | 12 | ||
21.2 | odd | 6 | 147.4.g.d.80.6 | 12 | |||
21.5 | even | 6 | 21.4.g.a.17.6 | yes | 12 | ||
21.11 | odd | 6 | 21.4.g.a.5.1 | ✓ | 12 | ||
21.17 | even | 6 | 147.4.g.d.68.1 | 12 | |||
21.20 | even | 2 | inner | 147.4.c.a.146.12 | 12 | ||
28.11 | odd | 6 | 336.4.bc.d.257.6 | 12 | |||
28.19 | even | 6 | 336.4.bc.d.17.4 | 12 | |||
84.11 | even | 6 | 336.4.bc.d.257.4 | 12 | |||
84.47 | odd | 6 | 336.4.bc.d.17.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.g.a.5.1 | ✓ | 12 | 21.11 | odd | 6 | ||
21.4.g.a.5.6 | yes | 12 | 7.4 | even | 3 | ||
21.4.g.a.17.1 | yes | 12 | 7.5 | odd | 6 | ||
21.4.g.a.17.6 | yes | 12 | 21.5 | even | 6 | ||
147.4.c.a.146.1 | 12 | 7.6 | odd | 2 | inner | ||
147.4.c.a.146.2 | 12 | 1.1 | even | 1 | trivial | ||
147.4.c.a.146.11 | 12 | 3.2 | odd | 2 | inner | ||
147.4.c.a.146.12 | 12 | 21.20 | even | 2 | inner | ||
147.4.g.d.68.1 | 12 | 21.17 | even | 6 | |||
147.4.g.d.68.6 | 12 | 7.3 | odd | 6 | |||
147.4.g.d.80.1 | 12 | 7.2 | even | 3 | |||
147.4.g.d.80.6 | 12 | 21.2 | odd | 6 | |||
336.4.bc.d.17.4 | 12 | 28.19 | even | 6 | |||
336.4.bc.d.17.6 | 12 | 84.47 | odd | 6 | |||
336.4.bc.d.257.4 | 12 | 84.11 | even | 6 | |||
336.4.bc.d.257.6 | 12 | 28.11 | odd | 6 |