Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.383");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(22.6567334422\) |
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: | \( x^{12} + 39x^{10} + 549x^{8} + 3500x^{6} + 10236x^{4} + 11952x^{2} + 4624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.3 | ||
Root | \(-4.03251i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.4.c.d.383.4 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.52186 | − | 4.54315i | −0.485332 | − | 0.874330i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.01133i | 0.716555i | 0.933615 | + | 0.358278i | \(0.116636\pi\) | ||||
−0.933615 | + | 0.358278i | \(0.883364\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 12.6015i | − | 0.680418i | −0.940350 | − | 0.340209i | \(-0.889502\pi\) | ||
0.940350 | − | 0.340209i | \(-0.110498\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −14.2805 | + | 22.9144i | −0.528906 | + | 0.848680i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 37.7546 | 1.03486 | 0.517429 | − | 0.855726i | \(-0.326889\pi\) | ||||
0.517429 | + | 0.855726i | \(0.326889\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −60.0661 | −1.28149 | −0.640744 | − | 0.767755i | \(-0.721374\pi\) | ||||
−0.640744 | + | 0.767755i | \(0.721374\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 36.3967 | − | 20.2034i | 0.626506 | − | 0.347767i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 37.0747i | − | 0.528938i | −0.964394 | − | 0.264469i | \(-0.914803\pi\) | ||
0.964394 | − | 0.264469i | \(-0.0851967\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 127.761i | 1.54265i | 0.636441 | + | 0.771325i | \(0.280406\pi\) | ||||
−0.636441 | + | 0.771325i | \(0.719594\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −57.2506 | + | 31.7792i | −0.594910 | + | 0.330228i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −56.9249 | −0.516072 | −0.258036 | − | 0.966135i | \(-0.583075\pi\) | ||||
−0.258036 | + | 0.966135i | \(0.583075\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 60.8186 | 0.486549 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 140.117 | + | 7.09157i | 0.998722 | + | 0.0505471i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 220.677i | 1.41306i | 0.707683 | + | 0.706530i | \(0.249741\pi\) | ||||
−0.707683 | + | 0.706530i | \(0.750259\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.26106i | 0.0130999i | 0.999979 | + | 0.00654997i | \(0.00208493\pi\) | ||||
−0.999979 | + | 0.00654997i | \(0.997915\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −95.2117 | − | 171.525i | −0.502250 | − | 0.904808i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 100.955 | 0.487557 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 166.549 | 0.740015 | 0.370007 | − | 0.929029i | \(-0.379355\pi\) | ||||
0.370007 | + | 0.929029i | \(0.379355\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 151.478 | + | 272.890i | 0.621947 | + | 1.12044i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 154.816i | − | 0.589713i | −0.955542 | − | 0.294857i | \(-0.904728\pi\) | ||
0.955542 | − | 0.294857i | \(-0.0952719\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 53.4029i | 0.189392i | 0.995506 | + | 0.0946961i | \(0.0301879\pi\) | ||||
−0.995506 | + | 0.0946961i | \(0.969812\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −183.575 | − | 114.406i | −0.608126 | − | 0.378990i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 591.855 | 1.83683 | 0.918413 | − | 0.395622i | \(-0.129471\pi\) | ||||
0.918413 | + | 0.395622i | \(0.129471\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 184.202 | 0.537032 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −168.436 | + | 93.4972i | −0.462466 | + | 0.256710i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 538.619i | 1.39594i | 0.716126 | + | 0.697971i | \(0.245914\pi\) | ||||
−0.716126 | + | 0.697971i | \(0.754086\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 302.465i | 0.741533i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 580.437 | − | 322.195i | 1.34879 | − | 0.748697i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 586.798 | 1.29482 | 0.647412 | − | 0.762141i | \(-0.275852\pi\) | ||||
0.647412 | + | 0.762141i | \(0.275852\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −431.489 | −0.905681 | −0.452840 | − | 0.891592i | \(-0.649589\pi\) | ||||
−0.452840 | + | 0.891592i | \(0.649589\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 288.756 | + | 179.956i | 0.577457 | + | 0.359877i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 481.209i | − | 0.918257i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 175.719i | − | 0.320411i | −0.987084 | − | 0.160205i | \(-0.948784\pi\) | ||
0.987084 | − | 0.160205i | \(-0.0512157\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 143.557 | + | 258.619i | 0.250466 | + | 0.451218i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29.5180 | 0.0493400 | 0.0246700 | − | 0.999696i | \(-0.492147\pi\) | ||||
0.0246700 | + | 0.999696i | \(0.492147\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 937.448 | 1.50301 | 0.751506 | − | 0.659726i | \(-0.229328\pi\) | ||||
0.751506 | + | 0.659726i | \(0.229328\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −153.376 | − | 276.308i | −0.236138 | − | 0.425404i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 475.765i | − | 0.704136i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 409.780i | 0.583593i | 0.956480 | + | 0.291796i | \(0.0942530\pi\) | ||||
−0.956480 | + | 0.291796i | \(0.905747\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −321.136 | − | 654.456i | −0.440516 | − | 0.897745i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1299.81 | 1.71895 | 0.859477 | − | 0.511174i | \(-0.170789\pi\) | ||||
0.859477 | + | 0.511174i | \(0.170789\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 297.018 | 0.379013 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1002.57 | − | 556.517i | 1.23548 | − | 0.685803i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 921.475i | 1.09748i | 0.835992 | + | 0.548742i | \(0.184893\pi\) | ||||
−0.835992 | + | 0.548742i | \(0.815107\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 756.924i | 0.871947i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.2723 | − | 5.70207i | 0.0114537 | − | 0.00635781i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1023.53 | −1.10539 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1644.22 | −1.72108 | −0.860542 | − | 0.509379i | \(-0.829875\pi\) | ||||
−0.860542 | + | 0.509379i | \(0.829875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −539.153 | + | 865.123i | −0.547343 | + | 0.878264i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1708.51i | 1.68320i | 0.540105 | + | 0.841598i | \(0.318385\pi\) | ||||
−0.540105 | + | 0.841598i | \(0.681615\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 354.419i | − | 0.339048i | −0.985526 | − | 0.169524i | \(-0.945777\pi\) | ||
0.985526 | − | 0.169524i | \(-0.0542230\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −254.594 | − | 458.653i | −0.236627 | − | 0.426286i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −532.454 | −0.481068 | −0.240534 | − | 0.970641i | \(-0.577323\pi\) | ||||
−0.240534 | + | 0.970641i | \(0.577323\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2099.43 | −1.84485 | −0.922427 | − | 0.386171i | \(-0.873797\pi\) | ||||
−0.922427 | + | 0.386171i | \(0.873797\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −420.014 | − | 756.659i | −0.359153 | − | 0.647017i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 510.544i | 0.425026i | 0.977158 | + | 0.212513i | \(0.0681647\pi\) | ||||
−0.977158 | + | 0.212513i | \(0.931835\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 456.044i | − | 0.369794i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 857.772 | − | 1376.38i | 0.677787 | − | 1.08757i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −467.198 | −0.359899 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 94.4098 | 0.0709315 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −703.354 | + | 390.425i | −0.515604 | + | 0.286207i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1488.65i | 1.06519i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 989.228i | 0.691180i | 0.938386 | + | 0.345590i | \(0.112321\pi\) | ||||
−0.938386 | + | 0.345590i | \(0.887679\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 242.617 | − | 134.674i | 0.165591 | − | 0.0919180i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 519.522 | 0.346495 | 0.173248 | − | 0.984878i | \(-0.444574\pi\) | ||||
0.173248 | + | 0.984878i | \(0.444574\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1609.98 | 1.04965 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −56.8129 | + | 1122.52i | −0.0362198 | + | 0.715639i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2731.83i | 1.70362i | 0.523853 | + | 0.851809i | \(0.324494\pi\) | ||||
−0.523853 | + | 0.851809i | \(0.675506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 182.811i | 0.111553i | 0.998443 | + | 0.0557765i | \(0.0177634\pi\) | ||||
−0.998443 | + | 0.0557765i | \(0.982237\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1492.57 | − | 2688.89i | −0.891470 | − | 1.60599i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2267.77 | −1.32616 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1767.92 | −1.01254 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −464.531 | − | 836.857i | −0.260638 | − | 0.469543i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 935.337i | − | 0.514267i | −0.966376 | − | 0.257134i | \(-0.917222\pi\) | ||
0.966376 | − | 0.257134i | \(-0.0827780\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3637.89i | − | 1.96058i | −0.197572 | − | 0.980288i | \(-0.563306\pi\) | ||
0.197572 | − | 0.980288i | \(-0.436694\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 849.544 | + | 529.445i | 0.448899 | + | 0.279759i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.1141 | −0.00938682 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2194.94 | 1.11577 | 0.557883 | − | 0.829919i | \(-0.311614\pi\) | ||||
0.557883 | + | 0.829919i | \(0.311614\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2447.03 | − | 1358.32i | 1.22051 | − | 0.677495i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 717.340i | 0.351145i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2938.89i | − | 1.41222i | −0.708103 | − | 0.706109i | \(-0.750449\pi\) | ||
0.708103 | − | 0.706109i | \(-0.249551\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1374.14 | − | 762.773i | 0.648345 | − | 0.359889i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3106.90 | −1.43964 | −0.719818 | − | 0.694163i | \(-0.755775\pi\) | ||||
−0.719818 | + | 0.694163i | \(0.755775\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1410.94 | 0.642211 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2927.56 | − | 1824.49i | −1.30922 | − | 0.815918i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2882.13i | − | 1.26662i | −0.773900 | − | 0.633308i | \(-0.781697\pi\) | ||
0.773900 | − | 0.633308i | \(-0.218303\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 766.406i | − | 0.331056i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1479.82 | − | 2665.91i | −0.628419 | − | 1.13210i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2571.39 | −1.07371 | −0.536857 | − | 0.843673i | \(-0.680389\pi\) | ||||
−0.536857 | + | 0.843673i | \(0.680389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 563.098 | 0.231242 | 0.115621 | − | 0.993293i | \(-0.463114\pi\) | ||||
0.115621 | + | 0.993293i | \(0.463114\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1088.15 | + | 1960.32i | 0.439556 | + | 0.791864i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1334.28i | 0.530261i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1399.74i | − | 0.547376i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 89.3645 | − | 1765.68i | 0.0343932 | − | 0.679548i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2637.29 | −0.999098 | −0.499549 | − | 0.866286i | \(-0.666501\pi\) | ||||
−0.499549 | + | 0.866286i | \(0.666501\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1498.22 | 0.558777 | 0.279388 | − | 0.960178i | \(-0.409868\pi\) | ||||
0.279388 | + | 0.960178i | \(0.409868\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2186.21 | + | 1213.54i | −0.802860 | + | 0.445659i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 394.173i | 0.142557i | 0.997456 | + | 0.0712783i | \(0.0227079\pi\) | ||||
−0.997456 | + | 0.0712783i | \(0.977292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3133.05i | 1.11606i | 0.829821 | + | 0.558030i | \(0.188443\pi\) | ||||
−0.829821 | + | 0.558030i | \(0.811557\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −798.320 | + | 443.139i | −0.280145 | + | 0.155506i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2780.87 | 0.961471 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1240.28 | 0.422562 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 812.915 | − | 1304.40i | 0.272954 | − | 0.437981i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4823.56i | 1.59642i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1665.67i | 0.543458i | 0.962374 | + | 0.271729i | \(0.0875955\pi\) | ||||
−0.962374 | + | 0.271729i | \(0.912405\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −74.4401 | − | 134.105i | −0.0239462 | − | 0.0431394i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −427.828 | −0.135710 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.4927 | 0.00891343 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2364.11 | − | 4258.97i | −0.729460 | − | 1.31413i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2226.94i | 0.677828i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2675.69i | 0.803488i | 0.915752 | + | 0.401744i | \(0.131596\pi\) | ||||
−0.915752 | + | 0.401744i | \(0.868404\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −868.518 | + | 1393.62i | −0.257339 | + | 0.412924i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −47.7540 | −0.0139627 | −0.00698137 | − | 0.999976i | \(-0.502222\pi\) | ||||
−0.00698137 | + | 0.999976i | \(0.502222\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1392.28 | 0.401767 | 0.200884 | − | 0.979615i | \(-0.435619\pi\) | ||||
0.200884 | + | 0.979615i | \(0.435619\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2161.47 | + | 1199.81i | −0.615647 | + | 0.341740i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1627.49i | − | 0.457598i | −0.973474 | − | 0.228799i | \(-0.926520\pi\) | ||
0.973474 | − | 0.228799i | \(-0.0734799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4741.54i | 1.31619i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1861.69 | − | 1033.41i | 0.510253 | − | 0.283236i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2858.90 | 0.773752 | 0.386876 | − | 0.922132i | \(-0.373554\pi\) | ||||
0.386876 | + | 0.922132i | \(0.373554\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1021.31 | −0.272982 | −0.136491 | − | 0.990641i | \(-0.543582\pi\) | ||||
−0.136491 | + | 0.990641i | \(0.543582\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2163.43 | + | 3109.42i | −0.571128 | + | 0.820861i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1475.70i | 0.384813i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 7674.10i | − | 1.97689i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3277.95 | − | 5905.26i | −0.834263 | − | 1.50293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3017.49 | 0.758814 | 0.379407 | − | 0.925230i | \(-0.376128\pi\) | ||||
0.379407 | + | 0.925230i | \(0.376128\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2149.18 | −0.534062 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −749.037 | − | 1349.40i | −0.183947 | − | 0.331383i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1097.93i | 0.266486i | 0.991083 | + | 0.133243i | \(0.0425390\pi\) | ||||
−0.991083 | + | 0.133243i | \(0.957461\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2098.77i | − | 0.503519i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5056.68 | − | 3151.37i | −1.19924 | − | 0.747376i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2785.15 | −0.653002 | −0.326501 | − | 0.945197i | \(-0.605870\pi\) | ||||
−0.326501 | + | 0.945197i | \(0.605870\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4315.05 | −1.00027 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4186.40 | − | 2323.83i | 0.959564 | − | 0.532644i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4034.08i | 0.914358i | 0.889375 | + | 0.457179i | \(0.151140\pi\) | ||||
−0.889375 | + | 0.457179i | \(0.848860\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2226.42i | − | 0.499060i | −0.968367 | − | 0.249530i | \(-0.919724\pi\) | ||
0.968367 | − | 0.249530i | \(-0.0802761\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3438.82 | − | 1908.85i | 0.762370 | − | 0.423184i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2296.18 | 0.503509 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6418.65 | −1.39227 | −0.696136 | − | 0.717910i | \(-0.745099\pi\) | ||||
−0.696136 | + | 0.717910i | \(0.745099\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −51.8107 | − | 32.2890i | −0.0111177 | − | 0.00692864i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3917.54i | 0.831675i | 0.909439 | + | 0.415838i | \(0.136512\pi\) | ||||
−0.909439 | + | 0.415838i | \(0.863488\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4219.70i | 0.886343i | 0.896437 | + | 0.443171i | \(0.146147\pi\) | ||||
−0.896437 | + | 0.443171i | \(0.853853\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2581.21 | + | 4650.08i | 0.536483 | + | 0.966480i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1950.92 | −0.401251 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3538.46 | 0.720225 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4146.49 | + | 7469.94i | 0.835297 | + | 1.50480i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 766.953i | 0.152921i | 0.997073 | + | 0.0764605i | \(0.0243619\pi\) | ||||
−0.997073 | + | 0.0764605i | \(0.975638\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4701.03i | 0.927812i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5290.05 | + | 267.739i | 1.03354 | + | 0.0523091i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3419.26 | 0.661341 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 672.957 | 0.128866 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7762.01 | − | 4308.61i | 1.47167 | − | 0.816908i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3456.80i | − | 0.648970i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7296.62i | − | 1.35648i | −0.734839 | − | 0.678242i | \(-0.762742\pi\) | ||
0.734839 | − | 0.678242i | \(-0.237258\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1610.18 | + | 893.794i | −0.296440 | + | 0.164551i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8641.39 | 1.57559 | 0.787795 | − | 0.615938i | \(-0.211223\pi\) | ||||
0.787795 | + | 0.615938i | \(0.211223\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2171.54 | −0.392149 | −0.196075 | − | 0.980589i | \(-0.562819\pi\) | ||||
−0.196075 | + | 0.980589i | \(0.562819\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1441.68 | + | 2313.32i | −0.257872 | + | 0.413780i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1682.16i | 0.298043i | 0.988834 | + | 0.149021i | \(0.0476123\pi\) | ||||
−0.988834 | + | 0.149021i | \(0.952388\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8331.58i | 1.46232i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1342.77 | + | 2419.02i | 0.233478 | + | 0.420613i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4736.70 | 0.815967 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3653.14 | −0.623506 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5294.47 | + | 9538.04i | 0.895366 | + | 1.61301i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 7458.26i | − | 1.24981i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2389.41i | 0.396779i | 0.980123 | + | 0.198389i | \(0.0635711\pi\) | ||||
−0.980123 | + | 0.198389i | \(0.936429\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2378.40 | + | 3816.37i | −0.391398 | + | 0.628036i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1407.75 | 0.229592 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11043.0 | 1.78501 | 0.892505 | − | 0.451037i | \(-0.148946\pi\) | ||||
0.892505 | + | 0.451037i | \(0.148946\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2319.48 | − | 1287.52i | 0.371613 | − | 0.206278i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 85.3653i | 0.0135566i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6643.54i | − | 1.04582i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2071.88 | + | 1150.08i | −0.323322 | + | 0.179473i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8790.06 | −1.35987 | −0.679935 | − | 0.733272i | \(-0.737992\pi\) | ||||
−0.679935 | + | 0.733272i | \(0.737992\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2636.08 | 0.404316 | 0.202158 | − | 0.979353i | \(-0.435205\pi\) | ||||
0.202158 | + | 0.979353i | \(0.435205\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8416.27 | − | 425.963i | −1.27985 | − | 0.0647756i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10828.6i | − | 1.63272i | −0.577544 | − | 0.816359i | \(-0.695989\pi\) | ||
0.577544 | − | 0.816359i | \(-0.304011\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 236.478i | 0.0353548i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1178.21 | + | 2122.55i | 0.174670 | + | 0.314670i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 278.615 | 0.0409603 | 0.0204802 | − | 0.999790i | \(-0.493481\pi\) | ||||
0.0204802 | + | 0.999790i | \(0.493481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9463.85 | −1.37977 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −238.088 | − | 428.918i | −0.0344253 | − | 0.0620176i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7510.20i | 1.07699i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12082.9i | 1.71860i | 0.511476 | + | 0.859298i | \(0.329099\pi\) | ||||
−0.511476 | + | 0.859298i | \(0.670901\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3547.52 | + | 2210.85i | 0.500478 | + | 0.311903i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6787.41 | 0.949824 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2101.82 | −0.291764 | −0.145882 | − | 0.989302i | \(-0.546602\pi\) | ||||
−0.145882 | + | 0.989302i | \(0.546602\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6763.18 | − | 3754.17i | 0.931331 | − | 0.516973i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 13255.2i | − | 1.81082i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2146.64i | 0.290938i | 0.989363 | + | 0.145469i | \(0.0464691\pi\) | ||||
−0.989363 | + | 0.145469i | \(0.953531\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4494.21 | − | 2494.69i | 0.604319 | − | 0.335451i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8881.17 | 1.18487 | 0.592437 | − | 0.805617i | \(-0.298166\pi\) | ||||
0.592437 | + | 0.805617i | \(0.298166\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3811.51 | 0.504552 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1223.69 | − | 762.618i | −0.160733 | − | 0.100171i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3095.15i | − | 0.403420i | −0.979445 | − | 0.201710i | \(-0.935350\pi\) | ||
0.979445 | − | 0.201710i | \(-0.0646498\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2110.48i | 0.272970i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1310.16 | − | 2360.27i | −0.168165 | − | 0.302951i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3282.88 | −0.418176 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10755.4 | 1.35969 | 0.679847 | − | 0.733354i | \(-0.262046\pi\) | ||||
0.679847 | + | 0.733354i | \(0.262046\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4060.14 | − | 7314.39i | −0.509427 | − | 0.917738i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8333.04i | 1.03774i | 0.854854 | + | 0.518868i | \(0.173646\pi\) | ||||
−0.854854 | + | 0.518868i | \(0.826354\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 135.813i | − | 0.0167874i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5243.06 | − | 2572.73i | 0.643283 | − | 0.315654i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6288.00 | 0.765810 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8921.31 | 1.07856 | 0.539279 | − | 0.842127i | \(-0.318697\pi\) | ||||
0.539279 | + | 0.842127i | \(0.318697\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12411.1 | − | 6889.27i | 1.48952 | − | 0.826820i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 7394.54i | − | 0.881021i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10413.2i | 1.23173i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 830.540 | − | 461.024i | 0.0975341 | − | 0.0541402i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6810.32 | −0.794048 | −0.397024 | − | 0.917808i | \(-0.629957\pi\) | ||||
−0.397024 | + | 0.917808i | \(0.629957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8336.91 | −0.965121 | −0.482561 | − | 0.875863i | \(-0.660293\pi\) | ||||
−0.482561 | + | 0.875863i | \(0.660293\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8451.96 | + | 13562.0i | −0.971509 | + | 1.55888i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2254.83i | − | 0.257354i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5437.42i | 0.616241i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5719.00 | + | 10302.8i | 0.643627 | + | 1.15950i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 755.175 | 0.0843979 | 0.0421990 | − | 0.999109i | \(-0.486564\pi\) | ||||
0.0421990 | + | 0.999109i | \(0.486564\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2736.36 | −0.303697 | −0.151849 | − | 0.988404i | \(-0.548523\pi\) | ||||
−0.151849 | + | 0.988404i | \(0.548523\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4458.44 | + | 8031.92i | 0.491416 | + | 0.885290i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 7272.78i | − | 0.796120i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15732.1i | − | 1.71037i | −0.518322 | − | 0.855186i | \(-0.673443\pi\) | ||
0.518322 | − | 0.855186i | \(-0.326557\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2630.49 | + | 4220.87i | −0.284039 | + | 0.455768i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1568.89 | 0.168263 | 0.0841313 | − | 0.996455i | \(-0.473188\pi\) | ||||
0.0841313 | + | 0.996455i | \(0.473188\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7382.24 | −0.786408 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4249.38 | + | 2358.79i | −0.449639 | + | 0.249590i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8882.13i | 0.933571i | 0.884371 | + | 0.466786i | \(0.154588\pi\) | ||||
−0.884371 | + | 0.466786i | \(0.845412\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5845.03i | − | 0.610270i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16527.5 | + | 9174.23i | −1.71419 | + | 0.951530i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6063.97 | −0.624798 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6441.62 | 0.659357 | 0.329679 | − | 0.944093i | \(-0.393060\pi\) | ||||
0.329679 | + | 0.944093i | \(0.393060\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 262.918 | − | 5194.79i | 0.0267363 | − | 0.528262i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4112.54i | 0.415488i | 0.978183 | + | 0.207744i | \(0.0666122\pi\) | ||||
−0.978183 | + | 0.207744i | \(0.933388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16061.5i | − | 1.61219i | −0.591788 | − | 0.806094i | \(-0.701578\pi\) | ||
0.591788 | − | 0.806094i | \(-0.298422\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 45.6811 | + | 82.2950i | 0.00455572 | + | 0.00820718i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12155.4 | −1.20447 | −0.602233 | − | 0.798321i | \(-0.705722\pi\) | ||||
−0.602233 | + | 0.798321i | \(0.705722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2214.33 | −0.218013 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5535.33 | − | 9971.95i | −0.541517 | − | 0.975548i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2016.20i | 0.195994i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7770.24i | 0.750575i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12342.1 | − | 7691.73i | −1.18471 | − | 0.738323i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3121.62 | 0.297767 | 0.148883 | − | 0.988855i | \(-0.452432\pi\) | ||||
0.148883 | + | 0.988855i | \(0.452432\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10004.0 | −0.948320 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3258.99 | − | 1809.03i | 0.307017 | − | 0.170422i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 13172.4i | − | 1.23325i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1582.51i | 0.147249i | 0.997286 | + | 0.0736244i | \(0.0234566\pi\) | ||||
−0.997286 | + | 0.0736244i | \(0.976543\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13351.8 | + | 7411.46i | −1.23474 | + | 0.685394i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12211.6 | −1.12241 | −0.561205 | − | 0.827677i | \(-0.689662\pi\) | ||||
−0.561205 | + | 0.827677i | \(0.689662\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8181.55 | 0.747421 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6930.78 | − | 4319.34i | −0.629324 | − | 0.392201i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 371.971i | − | 0.0335718i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3871.87i | − | 0.347352i | −0.984803 | − | 0.173676i | \(-0.944435\pi\) | ||
0.984803 | − | 0.173676i | \(-0.0555646\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7835.16 | + | 14115.1i | 0.698701 | + | 1.25872i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10985.0 | 0.973753 | 0.486876 | − | 0.873471i | \(-0.338136\pi\) | ||||
0.486876 | + | 0.873471i | \(0.338136\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13687.4 | −1.20610 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3558.19 | − | 6410.11i | −0.311686 | − | 0.561505i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 21191.9i | − | 1.84541i | −0.385509 | − | 0.922704i | \(-0.625974\pi\) | ||
0.385509 | − | 0.922704i | \(-0.374026\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 11813.3i | − | 1.02268i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −906.025 | + | 17901.4i | −0.0779766 | + | 1.54068i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2839.37 | 0.242947 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22345.2 | 1.90086 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13094.0 | + | 7268.33i | −1.10744 | + | 0.614729i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8953.89i | 0.752931i | 0.926431 | + | 0.376465i | \(0.122861\pi\) | ||||
−0.926431 | + | 0.376465i | \(0.877139\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8410.95i | − | 0.703223i | −0.936146 | − | 0.351611i | \(-0.885634\pi\) | ||
0.936146 | − | 0.351611i | \(-0.114366\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3481.90 | + | 1932.77i | −0.289453 | + | 0.160672i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 83.8281 | 0.00692905 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8926.55 | −0.733669 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8379.75 | + | 13446.1i | −0.684840 | + | 1.09889i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9299.21i | 0.755710i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 4265.67i | − | 0.344712i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6484.69 | + | 11682.2i | 0.521108 | + | 0.938781i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6954.47 | 0.555752 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2640.19 | −0.209816 | −0.104908 | − | 0.994482i | \(-0.533455\pi\) | ||||
−0.104908 | + | 0.994482i | \(0.533455\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1420.05 | − | 2558.24i | −0.112229 | − | 0.202182i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 16819.2i | − | 1.32194i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 133.631i | 0.0104455i | 0.999986 | + | 0.00522273i | \(0.00166245\pi\) | ||||
−0.999986 | + | 0.00522273i | \(0.998338\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6161.87 | − | 9887.30i | 0.479020 | − | 0.768633i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28193.9 | −2.17986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5163.85 | 0.397087 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6061.84 | − | 3364.87i | 0.463623 | − | 0.257353i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 15450.3i | − | 1.17531i | −0.809110 | − | 0.587657i | \(-0.800051\pi\) | ||
0.809110 | − | 0.587657i | \(-0.199949\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3207.70i | − | 0.242704i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6359.24 | + | 3529.95i | −0.478587 | + | 0.265659i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11670.9 | −0.873662 | −0.436831 | − | 0.899544i | \(-0.643899\pi\) | ||||
−0.436831 | + | 0.899544i | \(0.643899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4090.13 | −0.304554 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8247.13 | + | 4046.81i | −0.610841 | + | 0.299735i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3730.57i | 0.274857i | 0.990512 | + | 0.137428i | \(0.0438837\pi\) | ||||
−0.990512 | + | 0.137428i | \(0.956116\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1257.89i | 0.0921907i | 0.998937 | + | 0.0460954i | \(0.0146778\pi\) | ||||
−0.998937 | + | 0.0460954i | \(0.985322\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6650.87 | + | 11981.6i | 0.484894 | + | 0.873541i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3462.09 | −0.251094 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3631.50 | 0.262013 | 0.131006 | − | 0.991382i | \(-0.458179\pi\) | ||||
0.131006 | + | 0.991382i | \(0.458179\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3778.29 | − | 6806.62i | −0.271192 | − | 0.488555i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 16379.6i | − | 1.16961i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20335.3i | 1.44460i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11026.6 | + | 6871.90i | 0.779306 | + | 0.485672i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15455.9 | −1.08677 | −0.543383 | − | 0.839485i | \(-0.682857\pi\) | ||||
−0.543383 | + | 0.839485i | \(0.682857\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −288.875 | −0.0202086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1790.79 | − | 994.048i | 0.124642 | − | 0.0691873i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 15871.0i | − | 1.09906i | −0.835474 | − | 0.549530i | \(-0.814807\pi\) | ||
0.835474 | − | 0.549530i | \(-0.185193\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 3742.88i | − | 0.257887i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14233.9 | − | 7901.11i | 0.975805 | − | 0.541660i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4369.74 | 0.298068 | 0.149034 | − | 0.988832i | \(-0.452384\pi\) | ||||
0.149034 | + | 0.988832i | \(0.452384\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 507.273 | 0.0344295 | 0.0172147 | − | 0.999852i | \(-0.494520\pi\) | ||||
0.0172147 | + | 0.999852i | \(0.494520\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4026.50 | + | 2509.35i | 0.271926 | + | 0.169467i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 756.348i | 0.0508263i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14525.6i | 0.971293i | 0.874155 | + | 0.485647i | \(0.161416\pi\) | ||||
−0.874155 | + | 0.485647i | \(0.838584\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7012.95 | − | 12633.9i | −0.466633 | − | 0.840643i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35550.4 | −2.35387 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14948.5 | 0.984932 | 0.492466 | − | 0.870332i | \(-0.336096\pi\) | ||||
0.492466 | + | 0.870332i | \(0.336096\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3127.82 | − | 5634.80i | −0.205083 | − | 0.369459i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3250.68i | − | 0.212103i | −0.994361 | − | 0.106052i | \(-0.966179\pi\) | ||
0.994361 | − | 0.106052i | \(-0.0338209\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 4111.34i | − | 0.266961i | −0.991051 | − | 0.133480i | \(-0.957385\pi\) | ||
0.991051 | − | 0.133480i | \(-0.0426153\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7976.14 | − | 403.687i | −0.515413 | − | 0.0260860i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11612.0 | 0.746748 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4323.78 | −0.276722 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21914.2 | − | 12164.3i | 1.39580 | − | 0.774796i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 6174.77i | − | 0.391422i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 25436.9i | − | 1.60480i | −0.596790 | − | 0.802398i | \(-0.703557\pi\) | ||
0.596790 | − | 0.802398i | \(-0.296443\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7567.41 | − | 4200.59i | 0.475162 | − | 0.263757i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7925.03 | −0.495268 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11064.3 | −0.688199 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −421.530 | + | 676.385i | −0.0260962 | + | 0.0418738i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22085.5i | 1.36088i | 0.732803 | + | 0.680440i | \(0.238211\pi\) | ||||
−0.732803 | + | 0.680440i | \(0.761789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 930.199i | 0.0570505i | 0.999593 | + | 0.0285252i | \(0.00908110\pi\) | ||||
−0.999593 | + | 0.0285252i | \(0.990919\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1078.92 | + | 1943.69i | 0.0658644 | + | 0.118655i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28562.0 | 1.73553 | 0.867764 | − | 0.496977i | \(-0.165557\pi\) | ||||
0.867764 | + | 0.496977i | \(0.165557\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22154.3 | 1.33996 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −71.8547 | − | 129.447i | −0.00432597 | − | 0.00779328i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 9597.11i | − | 0.575136i | −0.957760 | − | 0.287568i | \(-0.907153\pi\) | ||
0.957760 | − | 0.287568i | \(-0.0928467\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4162.07i | 0.248283i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13387.2 | + | 21481.0i | −0.794953 | + | 1.27558i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −477.222 | −0.0282093 | −0.0141046 | − | 0.999901i | \(-0.504490\pi\) | ||||
−0.0141046 | + | 0.999901i | \(0.504490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −584.379 | −0.0343869 | −0.0171934 | − | 0.999852i | \(-0.505473\pi\) | ||||
−0.0171934 | + | 0.999852i | \(0.505473\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10117.3 | − | 5616.02i | 0.592645 | − | 0.328971i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12898.1i | 0.752130i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 12562.0i | − | 0.729241i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12156.1 | − | 6747.72i | 0.702513 | − | 0.389958i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16290.7 | −0.937251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8219.98 | −0.470813 | −0.235406 | − | 0.971897i | \(-0.575642\pi\) | ||||
−0.235406 | + | 0.971897i | \(0.575642\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8521.70 | + | 431.299i | 0.485927 | + | 0.0245936i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23269.5i | 1.32101i | 0.750824 | + | 0.660503i | \(0.229657\pi\) | ||||
−0.750824 | + | 0.660503i | \(0.770343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20719.7i | 1.17106i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 120.429 | + | 216.954i | 0.00677656 | + | 0.0122080i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12757.4 | 0.714713 | 0.357357 | − | 0.933968i | \(-0.383678\pi\) | ||||
0.357357 | + | 0.933968i | \(0.383678\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21885.6 | −1.22074 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3511.14 | − | 6325.36i | −0.194990 | − | 0.351277i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 32352.7i | − | 1.78888i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 13188.1i | − | 0.726049i | −0.931780 | − | 0.363025i | \(-0.881744\pi\) | ||
0.931780 | − | 0.363025i | \(-0.118256\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10901.9 | + | 6794.15i | 0.597586 | + | 0.372422i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1464.56 | −0.0799338 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5739.77 | −0.311922 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7393.93 | + | 4104.30i | −0.400092 | + | 0.222087i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 686.418i | − | 0.0369838i | −0.999829 | − | 0.0184919i | \(-0.994114\pi\) | ||
0.999829 | − | 0.0184919i | \(-0.00588649\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21278.5i | 1.14158i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21541.6 | − | 11957.5i | 1.15078 | − | 0.638788i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21529.8 | 1.14528 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24361.8 | 1.29045 | 0.645224 | − | 0.763993i | \(-0.276764\pi\) | ||||
0.645224 | + | 0.763993i | \(0.276764\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9389.85 | − | 5851.85i | −0.495284 | − | 0.308666i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 128.711i | − | 0.00676051i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 18167.9i | − | 0.950266i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7209.74 | − | 12988.4i | −0.375527 | − | 0.676515i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10763.6 | 0.558293 | 0.279147 | − | 0.960248i | \(-0.409948\pi\) | ||||
0.279147 | + | 0.960248i | \(0.409948\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4466.22 | −0.230694 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2575.61 | + | 4639.98i | 0.132487 | + | 0.238676i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13421.3i | 0.687523i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 13784.5i | − | 0.703217i | −0.936147 | − | 0.351609i | \(-0.885635\pi\) | ||
0.936147 | − | 0.351609i | \(-0.114365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19582.4 | + | 1987.30i | 0.994890 | + | 0.100965i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1979.90 | 0.100177 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26315.5 | −1.32604 | −0.663020 | − | 0.748602i | \(-0.730725\pi\) | ||||
−0.663020 | + | 0.748602i | \(0.730725\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6704.34 | − | 3721.51i | 0.336453 | − | 0.186762i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 6634.21i | − | 0.331580i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37873.7i | 1.88526i | 0.333843 | + | 0.942629i | \(0.391654\pi\) | ||||
−0.333843 | + | 0.942629i | \(0.608346\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −34864.6 | + | 19353.0i | −1.72845 | + | 0.959447i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23306.0 | 1.15076 | 0.575381 | − | 0.817886i | \(-0.304854\pi\) | ||||
0.575381 | + | 0.817886i | \(0.304854\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7493.29 | 0.368501 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18562.0 | + | 29784.4i | −0.909166 | + | 1.45884i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6709.73i | 0.327327i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 18843.1i | − | 0.915572i | −0.889062 | − | 0.457786i | \(-0.848642\pi\) | ||
0.889062 | − | 0.457786i | \(-0.151358\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7609.68 | − | 13708.9i | −0.368277 | − | 0.663454i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29144.3 | 1.40486 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8504.43 | −0.408320 | −0.204160 | − | 0.978937i | \(-0.565446\pi\) | ||||
−0.204160 | + | 0.978937i | \(0.565446\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5419.92 | + | 9764.04i | 0.259197 | + | 0.466946i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 26943.9i | − | 1.28346i | −0.766929 | − | 0.641732i | \(-0.778216\pi\) | ||
0.766929 | − | 0.641732i | \(-0.221784\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26456.0i | 1.25527i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4241.56 | + | 6805.98i | −0.200462 | + | 0.321661i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35246.7 | −1.65930 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20451.5 | −0.959040 | −0.479520 | − | 0.877531i | \(-0.659189\pi\) | ||||
−0.479520 | + | 0.877531i | \(0.659189\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4988.05 | − | 2768.81i | 0.232996 | − | 0.129334i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25810.2i | 1.20094i | 0.799647 | + | 0.600470i | \(0.205020\pi\) | ||||
−0.799647 | + | 0.600470i | \(0.794980\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 137.514i | 0.00637376i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9535.05 | + | 5292.81i | −0.440242 | + | 0.244374i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19779.5 | 0.909722 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1114.44 | 0.0510599 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1564.95 | + | 30920.6i | −0.0714262 | + | 1.41125i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17584.4i | 0.799508i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9016.03i | 0.408370i | 0.978932 | + | 0.204185i | \(0.0654544\pi\) | ||||
−0.978932 | + | 0.204185i | \(0.934546\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7023.74 | + | 12653.3i | 0.316922 | + | 0.570939i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6433.62 | 0.289195 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25917.9 | 1.16062 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10881.9 | + | 19603.9i | 0.485463 | + | 0.874566i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3898.40i | 0.173260i | 0.996241 | + | 0.0866302i | \(0.0276099\pi\) | ||||
−0.996241 | + | 0.0866302i | \(0.972390\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 21942.9i | − | 0.971568i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21115.0 | − | 13159.1i | −0.931413 | − | 0.580466i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35393.0 | 1.55541 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5746.85 | −0.251615 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18327.5 | − | 10173.4i | 0.799451 | − | 0.443767i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5567.95i | 0.241976i | 0.992654 | + | 0.120988i | \(0.0386063\pi\) | ||||
−0.992654 | + | 0.120988i | \(0.961394\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42428.3i | 1.83706i | 0.395346 | + | 0.918532i | \(0.370625\pi\) | ||||
−0.395346 | + | 0.918532i | \(0.629375\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10115.0 | + | 5614.71i | −0.436343 | + | 0.242210i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23544.4 | 1.01193 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6822.80 | −0.292166 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17344.4 | − | 10809.2i | −0.740004 | − | 0.461178i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 18734.2i | − | 0.796379i | −0.917303 | − | 0.398190i | \(-0.869639\pi\) | ||
0.917303 | − | 0.398190i | \(-0.130361\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31710.5i | 1.34309i | 0.740965 | + | 0.671543i | \(0.234368\pi\) | ||||
−0.740965 | + | 0.671543i | \(0.765632\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5790.64 | − | 10431.9i | −0.244369 | − | 0.440233i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5275.05 | −0.221803 | −0.110902 | − | 0.993831i | \(-0.535374\pi\) | ||||
−0.110902 | + | 0.993831i | \(0.535374\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10279.5 | 0.430665 | 0.215332 | − | 0.976541i | \(-0.430917\pi\) | ||||
0.215332 | + | 0.976541i | \(0.430917\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16186.9 | + | 29160.9i | 0.675713 | + | 1.21730i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6829.24i | − | 0.284056i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 24890.4i | − | 1.03158i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.0344 | + | 316.812i | −0.000662164 | + | 0.0130832i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30259.2 | −1.24513 | −0.622564 | − | 0.782569i | \(-0.713909\pi\) | ||||
−0.622564 | + | 0.782569i | \(0.713909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24309.5 | −0.996739 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17798.0 | − | 9879.48i | 0.727159 | − | 0.403638i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11303.5i | 0.460180i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1189.71i | − | 0.0482631i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19170.7 | − | 10641.5i | 0.774956 | − | 0.430170i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9480.81 | −0.381901 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18713.7 | −0.751167 | −0.375584 | − | 0.926789i | \(-0.622558\pi\) | ||||
−0.375584 | + | 0.926789i | \(0.622558\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14616.6 | − | 23453.7i | 0.584650 | − | 0.938126i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10924.0i | 0.435423i | 0.976013 | + | 0.217711i | \(0.0698591\pi\) | ||||
−0.976013 | + | 0.217711i | \(0.930141\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 33510.2i | − | 1.33103i | −0.746385 | − | 0.665514i | \(-0.768212\pi\) | ||
0.746385 | − | 0.665514i | \(-0.231788\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4919.94 | + | 8863.33i | 0.194740 | + | 0.350826i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30253.2 | 1.19331 | 0.596657 | − | 0.802497i | \(-0.296495\pi\) | ||||
0.596657 | + | 0.802497i | \(0.296495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23089.7 | 0.907600 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8923.50 | − | 16075.8i | −0.349548 | − | 0.629714i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15471.1i | 0.603936i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10554.8i | 0.410603i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23480.2 | − | 37676.2i | 0.910292 | − | 1.46065i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18759.3 | 0.724777 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11900.1 | 0.458194 | 0.229097 | − | 0.973404i | \(-0.426423\pi\) | ||||
0.229097 | + | 0.973404i | \(0.426423\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3484.38 | − | 1934.15i | 0.133704 | − | 0.0742175i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8633.31i | 0.330152i | 0.986281 | + | 0.165076i | \(0.0527869\pi\) | ||||
−0.986281 | + | 0.165076i | \(0.947213\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27438.6i | 1.04573i | 0.852414 | + | 0.522867i | \(0.175138\pi\) | ||||
−0.852414 | + | 0.522867i | \(0.824862\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21357.5 | − | 11855.3i | 0.811214 | − | 0.450297i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3124.21 | −0.118264 | −0.0591322 | − | 0.998250i | \(-0.518833\pi\) | ||||
−0.0591322 | + | 0.998250i | \(0.518833\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12465.8 | 0.470291 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12124.4 | − | 24708.7i | −0.455872 | − | 0.929038i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 75615.9i | 2.83358i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 20600.3i | − | 0.769376i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8622.88 | − | 15534.2i | −0.320970 | − | 0.578230i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −498.964 | −0.0185110 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19969.1 | 0.738367 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1697.10 | − | 3057.35i | −0.0625427 | − | 0.112671i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4511.17i | 0.165698i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 21850.0i | − | 0.799909i | −0.916535 | − | 0.399955i | \(-0.869026\pi\) | ||
0.916535 | − | 0.399955i | \(-0.130974\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −39149.3 | − | 24398.3i | −1.42849 | − | 0.890253i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16739.3 | −0.608781 | −0.304390 | − | 0.952547i | \(-0.598453\pi\) | ||||
−0.304390 | + | 0.952547i | \(0.598453\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 49074.0 | 1.77887 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15704.8 | + | 8717.56i | −0.567414 | + | 0.314966i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 6546.77i | − | 0.235762i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36772.7i | 1.31994i | 0.751294 | + | 0.659968i | \(0.229430\pi\) | ||||
−0.751294 | + | 0.659968i | \(0.770570\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33149.7 | + | 18401.0i | −1.18601 | + | 0.658344i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1773.03 | −0.0632286 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10129.3 | 0.360053 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8121.29 | + | 5061.27i | 0.287743 | + | 0.179325i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28060.4i | 0.990991i | 0.868611 | + | 0.495495i | \(0.165013\pi\) | ||||
−0.868611 | + | 0.495495i | \(0.834987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23533.8i | 0.828452i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21792.4 | − | 39259.1i | −0.764683 | − | 1.37758i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11213.8 | 0.392225 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5258.29 | 0.183331 | 0.0916653 | − | 0.995790i | \(-0.470781\pi\) | ||||
0.0916653 | + | 0.995790i | \(0.470781\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5476.32 | + | 9865.64i | 0.190323 | + | 0.342868i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 37769.5i | − | 1.30845i | −0.756300 | − | 0.654224i | \(-0.772995\pi\) | ||
0.756300 | − | 0.654224i | \(-0.227005\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8812.91i | 0.304335i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14145.5 | + | 715.928i | 0.486934 | + | 0.0246446i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9839.83 | 0.337647 | 0.168823 | − | 0.985646i | \(-0.446003\pi\) | ||||
0.168823 | + | 0.985646i | \(0.446003\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −56308.8 | −1.92609 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7642.31 | − | 4242.17i | 0.260588 | − | 0.144650i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 21903.4i | − | 0.744514i | −0.928130 | − | 0.372257i | \(-0.878584\pi\) | ||
0.928130 | − | 0.372257i | \(-0.121416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 21128.2i | − | 0.715909i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37851.7 | − | 21011.1i | 1.27855 | − | 0.709709i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34425.1 | 1.15917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29785.9 | 0.999828 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7603.70 | − | 12200.9i | 0.254440 | − | 0.408273i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12002.7i | 0.400394i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 11943.8i | − | 0.397193i | −0.980081 | − | 0.198597i | \(-0.936362\pi\) | ||
0.980081 | − | 0.198597i | \(-0.0636384\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11945.3 | − | 21519.6i | −0.396015 | − | 0.713424i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15658.6 | 0.517517 | 0.258758 | − | 0.965942i | \(-0.416687\pi\) | ||||
0.258758 | + | 0.965942i | \(0.416687\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2303.70 | 0.0759026 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9212.69 | + | 16596.8i | 0.302607 | + | 0.545150i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 14022.1i | − | 0.459168i | −0.973289 | − | 0.229584i | \(-0.926263\pi\) | ||
0.973289 | − | 0.229584i | \(-0.0737366\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34789.9i | 1.13574i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29980.9 | − | 48107.2i | 0.975755 | − | 1.56569i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24228.1 | −0.786120 | −0.393060 | − | 0.919513i | \(-0.628583\pi\) | ||||
−0.393060 | + | 0.919513i | \(0.628583\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3157.85 | −0.102150 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −33884.0 | + | 18808.7i | −1.09275 | + | 0.606572i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3039.96i | − | 0.0977401i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 17211.8i | − | 0.551715i | −0.961198 | − | 0.275858i | \(-0.911038\pi\) | ||
0.961198 | − | 0.275858i | \(-0.0889618\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10855.4 | − | 6025.75i | 0.346916 | − | 0.192569i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25099.9 | −0.799719 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55019.5 | 1.74773 | 0.873864 | − | 0.486171i | \(-0.161607\pi\) | ||||
0.873864 | + | 0.486171i | \(0.161607\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23336.4 | + | 1181.10i | 0.739069 | + | 0.0374056i |
(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 | 384.4.c.d.383.3 | yes | 12 | |
3.2 | odd | 2 | 384.4.c.a.383.9 | ✓ | 12 | ||
4.3 | odd | 2 | 384.4.c.a.383.10 | yes | 12 | ||
8.3 | odd | 2 | 384.4.c.c.383.3 | yes | 12 | ||
8.5 | even | 2 | 384.4.c.b.383.10 | yes | 12 | ||
12.11 | even | 2 | inner | 384.4.c.d.383.4 | yes | 12 | |
16.3 | odd | 4 | 768.4.f.e.383.2 | 12 | |||
16.5 | even | 4 | 768.4.f.f.383.2 | 12 | |||
16.11 | odd | 4 | 768.4.f.h.383.11 | 12 | |||
16.13 | even | 4 | 768.4.f.g.383.11 | 12 | |||
24.5 | odd | 2 | 384.4.c.c.383.4 | yes | 12 | ||
24.11 | even | 2 | 384.4.c.b.383.9 | yes | 12 | ||
48.5 | odd | 4 | 768.4.f.e.383.1 | 12 | |||
48.11 | even | 4 | 768.4.f.g.383.12 | 12 | |||
48.29 | odd | 4 | 768.4.f.h.383.12 | 12 | |||
48.35 | even | 4 | 768.4.f.f.383.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.c.a.383.9 | ✓ | 12 | 3.2 | odd | 2 | ||
384.4.c.a.383.10 | yes | 12 | 4.3 | odd | 2 | ||
384.4.c.b.383.9 | yes | 12 | 24.11 | even | 2 | ||
384.4.c.b.383.10 | yes | 12 | 8.5 | even | 2 | ||
384.4.c.c.383.3 | yes | 12 | 8.3 | odd | 2 | ||
384.4.c.c.383.4 | yes | 12 | 24.5 | odd | 2 | ||
384.4.c.d.383.3 | yes | 12 | 1.1 | even | 1 | trivial | |
384.4.c.d.383.4 | yes | 12 | 12.11 | even | 2 | inner | |
768.4.f.e.383.1 | 12 | 48.5 | odd | 4 | |||
768.4.f.e.383.2 | 12 | 16.3 | odd | 4 | |||
768.4.f.f.383.1 | 12 | 48.35 | even | 4 | |||
768.4.f.f.383.2 | 12 | 16.5 | even | 4 | |||
768.4.f.g.383.11 | 12 | 16.13 | even | 4 | |||
768.4.f.g.383.12 | 12 | 48.11 | even | 4 | |||
768.4.f.h.383.11 | 12 | 16.11 | odd | 4 | |||
768.4.f.h.383.12 | 12 | 48.29 | odd | 4 |