Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(97,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.97");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.j (of order \(4\), degree \(2\), not 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: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.8 | ||
Character | \(\chi\) | \(=\) | 384.97 |
Dual form | 384.4.j.b.289.8 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 2.12132 | − | 2.12132i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.72414 | + | 3.72414i | 0.333097 | + | 0.333097i | 0.853762 | − | 0.520664i | \(-0.174316\pi\) |
−0.520664 | + | 0.853762i | \(0.674316\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 20.2675i | − | 1.09434i | −0.837020 | − | 0.547172i | \(-0.815704\pi\) | ||
0.837020 | − | 0.547172i | \(-0.184296\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 9.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 47.5467 | + | 47.5467i | 1.30326 | + | 1.30326i | 0.926180 | + | 0.377081i | \(0.123072\pi\) |
0.377081 | + | 0.926180i | \(0.376928\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −27.8636 | + | 27.8636i | −0.594460 | + | 0.594460i | −0.938833 | − | 0.344373i | \(-0.888091\pi\) |
0.344373 | + | 0.938833i | \(0.388091\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 15.8002 | 0.271973 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 56.3788 | 0.804345 | 0.402173 | − | 0.915564i | \(-0.368255\pi\) | ||||
0.402173 | + | 0.915564i | \(0.368255\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 66.1489 | − | 66.1489i | 0.798716 | − | 0.798716i | −0.184177 | − | 0.982893i | \(-0.558962\pi\) |
0.982893 | + | 0.184177i | \(0.0589621\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −42.9939 | − | 42.9939i | −0.446764 | − | 0.446764i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.66579i | 0.0332335i | 0.999862 | + | 0.0166167i | \(0.00528951\pi\) | ||||
−0.999862 | + | 0.0166167i | \(0.994710\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 97.2615i | − | 0.778092i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19.0919 | − | 19.0919i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 86.8428 | − | 86.8428i | 0.556079 | − | 0.556079i | −0.372109 | − | 0.928189i | \(-0.621365\pi\) |
0.928189 | + | 0.372109i | \(0.121365\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −102.846 | −0.595858 | −0.297929 | − | 0.954588i | \(-0.596296\pi\) | ||||
−0.297929 | + | 0.954588i | \(0.596296\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 201.724 | 1.06411 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 75.4791 | − | 75.4791i | 0.364523 | − | 0.364523i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −66.8267 | − | 66.8267i | −0.296925 | − | 0.296925i | 0.542883 | − | 0.839808i | \(-0.317333\pi\) |
−0.839808 | + | 0.542883i | \(0.817333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 118.215i | 0.485374i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 29.5734i | − | 0.112649i | −0.998413 | − | 0.0563243i | \(-0.982062\pi\) | ||
0.998413 | − | 0.0563243i | \(-0.0179381\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 372.929 | + | 372.929i | 1.32258 | + | 1.32258i | 0.911678 | + | 0.410905i | \(0.134787\pi\) |
0.410905 | + | 0.911678i | \(0.365213\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 33.5173 | − | 33.5173i | 0.111032 | − | 0.111032i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 539.082 | 1.67305 | 0.836524 | − | 0.547930i | \(-0.184584\pi\) | ||||
0.836524 | + | 0.547930i | \(0.184584\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −67.7725 | −0.197587 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 119.598 | − | 119.598i | 0.328373 | − | 0.328373i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −385.376 | − | 385.376i | −0.998781 | − | 0.998781i | 0.00121789 | − | 0.999999i | \(-0.499612\pi\) |
−0.999999 | + | 0.00121789i | \(0.999612\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 354.142i | 0.868226i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 280.646i | − | 0.652149i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −71.0380 | − | 71.0380i | −0.156752 | − | 0.156752i | 0.624374 | − | 0.781126i | \(-0.285354\pi\) |
−0.781126 | + | 0.624374i | \(0.785354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 155.133 | − | 155.133i | 0.325619 | − | 0.325619i | −0.525299 | − | 0.850918i | \(-0.676046\pi\) |
0.850918 | + | 0.525299i | \(0.176046\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −182.408 | −0.364781 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −207.536 | −0.396026 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 178.141 | − | 178.141i | 0.324827 | − | 0.324827i | −0.525788 | − | 0.850615i | \(-0.676230\pi\) |
0.850615 | + | 0.525788i | \(0.176230\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.77631 | + | 7.77631i | 0.0135675 | + | 0.0135675i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 483.585i | − | 0.808323i | −0.914688 | − | 0.404162i | \(-0.867563\pi\) | ||
0.914688 | − | 0.404162i | \(-0.132437\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 908.791i | − | 1.45707i | −0.685010 | − | 0.728534i | \(-0.740202\pi\) | ||
0.685010 | − | 0.728534i | \(-0.259798\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −206.323 | − | 206.323i | −0.317655 | − | 0.317655i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 963.654 | − | 963.654i | 1.42622 | − | 1.42622i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1066.46 | 1.51882 | 0.759409 | − | 0.650613i | \(-0.225488\pi\) | ||||
0.759409 | + | 0.650613i | \(0.225488\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −81.0000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −871.541 | + | 871.541i | −1.15258 | + | 1.15258i | −0.166544 | + | 0.986034i | \(0.553261\pi\) |
−0.986034 | + | 0.166544i | \(0.946739\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 209.963 | + | 209.963i | 0.267925 | + | 0.267925i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 368.443i | − | 0.454037i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 185.044i | − | 0.220388i | −0.993910 | − | 0.110194i | \(-0.964853\pi\) | ||
0.993910 | − | 0.110194i | \(-0.0351473\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 564.727 | + | 564.727i | 0.650543 | + | 0.650543i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −218.168 | + | 218.168i | −0.243258 | + | 0.243258i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 492.696 | 0.532100 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −725.140 | −0.759039 | −0.379519 | − | 0.925184i | \(-0.623911\pi\) | ||||
−0.379519 | + | 0.925184i | \(0.623911\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 427.921 | − | 427.921i | 0.434420 | − | 0.434420i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1141.34 | + | 1141.34i | 1.12443 | + | 1.12443i | 0.991068 | + | 0.133359i | \(0.0425765\pi\) |
0.133359 | + | 0.991068i | \(0.457424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1099.46i | 1.05177i | 0.850555 | + | 0.525886i | \(0.176266\pi\) | ||||
−0.850555 | + | 0.525886i | \(0.823734\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 320.231i | − | 0.297632i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −361.438 | − | 361.438i | −0.326556 | − | 0.326556i | 0.524719 | − | 0.851275i | \(-0.324170\pi\) |
−0.851275 | + | 0.524719i | \(0.824170\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1405.61 | + | 1405.61i | −1.23517 | + | 1.23517i | −0.273215 | + | 0.961953i | \(0.588087\pi\) |
−0.961953 | + | 0.273215i | \(0.911913\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −283.522 | −0.242439 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −290.830 | −0.242115 | −0.121058 | − | 0.992645i | \(-0.538629\pi\) | ||||
−0.121058 | + | 0.992645i | \(0.538629\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.6519 | + | 13.6519i | −0.0110700 | + | 0.0110700i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 250.773 | + | 250.773i | 0.198153 | + | 0.198153i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1142.66i | − | 0.880230i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3190.38i | 2.39698i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −62.7347 | − | 62.7347i | −0.0459886 | − | 0.0459886i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 827.734 | − | 827.734i | 0.592278 | − | 0.592278i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 278.588 | 0.194651 | 0.0973256 | − | 0.995253i | \(-0.468971\pi\) | ||||
0.0973256 | + | 0.995253i | \(0.468971\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1582.20 | 1.07988 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 666.234 | − | 666.234i | 0.444345 | − | 0.444345i | −0.449124 | − | 0.893469i | \(-0.648264\pi\) |
0.893469 | + | 0.449124i | \(0.148264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1340.67 | − | 1340.67i | −0.874069 | − | 0.874069i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 142.202i | − | 0.0906576i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 632.580i | 0.394489i | 0.980354 | + | 0.197244i | \(0.0631992\pi\) | ||||
−0.980354 | + | 0.197244i | \(0.936801\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1097.95 | − | 1097.95i | −0.669976 | − | 0.669976i | 0.287734 | − | 0.957710i | \(-0.407098\pi\) |
−0.957710 | + | 0.287734i | \(0.907098\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1143.57 | − | 1143.57i | 0.683019 | − | 0.683019i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2649.65 | −1.54947 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 646.830 | 0.370457 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −143.767 | + | 143.767i | −0.0806647 | + | 0.0806647i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −963.349 | − | 963.349i | −0.529669 | − | 0.529669i | 0.390805 | − | 0.920474i | \(-0.372197\pi\) |
−0.920474 | + | 0.390805i | \(0.872197\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2047.36i | 1.10339i | 0.834046 | + | 0.551694i | \(0.186019\pi\) | ||||
−0.834046 | + | 0.551694i | \(0.813981\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 507.409i | − | 0.268115i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −383.011 | − | 383.011i | −0.198479 | − | 0.198479i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2663.57 | + | 2663.57i | −1.35399 | + | 1.35399i | −0.472843 | + | 0.881147i | \(0.656772\pi\) |
−0.881147 | + | 0.472843i | \(0.843228\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1635.01 | −0.815502 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 74.2964 | 0.0363688 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1003.92 | + | 1003.92i | −0.482410 | + | 0.482410i | −0.905900 | − | 0.423491i | \(-0.860805\pi\) |
0.423491 | + | 0.905900i | \(0.360805\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 751.248 | + | 751.248i | 0.354452 | + | 0.354452i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1282.05i | − | 0.594061i | −0.954868 | − | 0.297031i | \(-0.904004\pi\) | ||
0.954868 | − | 0.297031i | \(-0.0959964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 644.238i | 0.293235i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −595.340 | − | 595.340i | −0.266239 | − | 0.266239i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1974.96 | + | 1974.96i | −0.867937 | + | 0.867937i | −0.992244 | − | 0.124306i | \(-0.960329\pi\) |
0.124306 | + | 0.992244i | \(0.460329\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1971.25 | −0.851500 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −301.389 | −0.127987 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −66.3425 | + | 66.3425i | −0.0277021 | + | 0.0277021i | −0.720822 | − | 0.693120i | \(-0.756236\pi\) |
0.693120 | + | 0.720822i | \(0.256236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 371.784 | + | 371.784i | 0.152677 | + | 0.152677i | 0.779312 | − | 0.626636i | \(-0.215569\pi\) |
−0.626636 | + | 0.779312i | \(0.715569\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 658.174i | − | 0.265867i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 497.744i | − | 0.197810i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2680.63 | + | 2680.63i | 1.04827 | + | 1.04827i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −386.945 | + | 386.945i | −0.148921 | + | 0.148921i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2857.35 | −1.08246 | −0.541232 | − | 0.840873i | \(-0.682042\pi\) | ||||
−0.541232 | + | 0.840873i | \(0.682042\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4318.58 | −1.61066 | −0.805332 | − | 0.592824i | \(-0.798013\pi\) | ||||
−0.805332 | + | 0.592824i | \(0.798013\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −440.251 | + | 440.251i | −0.161677 | + | 0.161677i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1400.78 | + | 1400.78i | 0.506605 | + | 0.506605i | 0.913483 | − | 0.406878i | \(-0.133382\pi\) |
−0.406878 | + | 0.913483i | \(0.633382\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2154.43i | − | 0.767454i | −0.923447 | − | 0.383727i | \(-0.874640\pi\) | ||
0.923447 | − | 0.383727i | \(-0.125360\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 755.789i | − | 0.265220i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1760.09 | − | 1760.09i | −0.608542 | − | 0.608542i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 110.136 | − | 110.136i | 0.0375230 | − | 0.0375230i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 32.9921 | 0.0110778 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6290.33 | 2.08187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −663.531 | + | 663.531i | −0.216490 | + | 0.216490i | −0.807017 | − | 0.590528i | \(-0.798920\pi\) |
0.590528 | + | 0.807017i | \(0.298920\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1025.84 | − | 1025.84i | −0.329997 | − | 0.329997i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2777.68i | 0.881098i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2084.42i | 0.652073i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1927.84 | − | 1927.84i | −0.594846 | − | 0.594846i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1570.92 | + | 1570.92i | −0.478151 | + | 0.478151i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 432.791 | 0.129963 | 0.0649816 | − | 0.997886i | \(-0.479301\pi\) | ||||
0.0649816 | + | 0.997886i | \(0.479301\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −875.354 | −0.259364 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −482.544 | + | 482.544i | −0.141091 | + | 0.141091i | −0.774124 | − | 0.633034i | \(-0.781809\pi\) |
0.633034 | + | 0.774124i | \(0.281809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2717.39 | + | 2717.39i | 0.784150 | + | 0.784150i | 0.980528 | − | 0.196378i | \(-0.0629180\pi\) |
−0.196378 | + | 0.980528i | \(0.562918\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 4088.44i | − | 1.16450i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1214.38i | 0.341445i | 0.985319 | + | 0.170722i | \(0.0546102\pi\) | ||||
−0.985319 | + | 0.170722i | \(0.945390\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2007.62 | + | 2007.62i | 0.557288 | + | 0.557288i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2262.31 | − | 2262.31i | 0.620055 | − | 0.620055i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2676.38 | 0.724353 | 0.362177 | − | 0.932110i | \(-0.382034\pi\) | ||||
0.362177 | + | 0.932110i | \(0.382034\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2415.81 | −0.645708 | −0.322854 | − | 0.946449i | \(-0.604642\pi\) | ||||
−0.322854 | + | 0.946449i | \(0.604642\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −171.827 | + | 171.827i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −252.394 | − | 252.394i | −0.0658158 | − | 0.0658158i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3686.29i | 0.949609i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3697.63i | 0.941076i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1492.39 | − | 1492.39i | −0.375295 | − | 0.375295i | 0.494106 | − | 0.869402i | \(-0.335495\pi\) |
−0.869402 | + | 0.494106i | \(0.835495\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −174.296 | + | 174.296i | −0.0433119 | + | 0.0433119i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 890.797 | 0.218760 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3266.32 | −0.792791 | −0.396395 | − | 0.918080i | \(-0.629739\pi\) | ||||
−0.396395 | + | 0.918080i | \(0.629739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1354.41 | + | 1354.41i | −0.324938 | + | 0.324938i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −781.585 | − | 781.585i | −0.185360 | − | 0.185360i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 893.279i | 0.209437i | 0.994502 | + | 0.104719i | \(0.0333942\pi\) | ||||
−0.994502 | + | 0.104719i | \(0.966606\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2870.39i | − | 0.665383i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −392.537 | − | 392.537i | −0.0899732 | − | 0.0899732i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2619.13 | − | 2619.13i | 0.593647 | − | 0.593647i | −0.344967 | − | 0.938615i | \(-0.612110\pi\) |
0.938615 | + | 0.344967i | \(0.112110\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5424.67 | 1.21596 | 0.607980 | − | 0.793952i | \(-0.291980\pi\) | ||||
0.607980 | + | 0.793952i | \(0.291980\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2395.93 | 0.531166 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4624.47 | − | 4624.47i | 1.01406 | − | 1.01406i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2242.55 | − | 2242.55i | −0.486432 | − | 0.486432i | 0.420746 | − | 0.907178i | \(-0.361768\pi\) |
−0.907178 | + | 0.420746i | \(0.861768\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 925.610i | 0.198619i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3622.87i | − | 0.769119i | −0.923100 | − | 0.384559i | \(-0.874353\pi\) | ||
0.923100 | − | 0.384559i | \(-0.125647\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.00634733 | + | 0.00634733i | 1.33325e−6 | + | 1.33325e-6i | 0.707107 | − | 0.707106i | \(-0.250000\pi\) |
−0.707106 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1045.17 | − | 1045.17i | 0.217229 | − | 0.217229i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −599.380 | −0.123276 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1734.43 | −0.353028 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1538.25 | + | 1538.25i | −0.309876 | + | 0.309876i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.9384 | + | 24.9384i | 0.00497241 | + | 0.00497241i | 0.709589 | − | 0.704616i | \(-0.248881\pi\) |
−0.704616 | + | 0.709589i | \(0.748881\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 529.112i | − | 0.104427i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1815.51i | − | 0.354703i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −102.142 | − | 102.142i | −0.0197560 | − | 0.0197560i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7558.34 | − | 7558.34i | 1.44736 | − | 1.44736i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4842.28 | 0.918091 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1155.48 | 0.216926 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 618.757 | − | 618.757i | 0.115030 | − | 0.115030i | −0.647249 | − | 0.762279i | \(-0.724080\pi\) |
0.762279 | + | 0.647249i | \(0.224080\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2332.30 | + | 2332.30i | 0.429384 | + | 0.429384i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 4183.92i | − | 0.762856i | −0.924399 | − | 0.381428i | \(-0.875432\pi\) | ||
0.924399 | − | 0.381428i | \(-0.124568\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2124.18i | 0.383597i | 0.981434 | + | 0.191799i | \(0.0614321\pi\) | ||||
−0.981434 | + | 0.191799i | \(0.938568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −679.312 | − | 679.312i | −0.121508 | − | 0.121508i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1064.95 | + | 1064.95i | −0.188687 | + | 0.188687i | −0.795128 | − | 0.606442i | \(-0.792596\pi\) |
0.606442 | + | 0.795128i | \(0.292596\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8258.18 | 1.44943 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1533.45 | −0.266632 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3729.40 | − | 3729.40i | 0.642443 | − | 0.642443i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2710.06 | + | 2710.06i | 0.462545 | + | 0.462545i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5963.51i | 1.00851i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 10925.9i | − | 1.83089i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1785.55 | + | 1785.55i | 0.296504 | + | 0.296504i | 0.839643 | − | 0.543139i | \(-0.182764\pi\) |
−0.543139 | + | 0.839643i | \(0.682764\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −601.440 | + | 601.440i | −0.0989751 | + | 0.0989751i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1326.85 | 0.216398 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 549.365 | 0.0888006 | 0.0444003 | − | 0.999014i | \(-0.485862\pi\) | ||||
0.0444003 | + | 0.999014i | \(0.485862\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −616.944 | + | 616.944i | −0.0988430 | + | 0.0988430i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4889.97 | − | 4889.97i | −0.776559 | − | 0.776559i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 5578.18i | − | 0.878115i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 57.9202i | 0.00903860i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6594.28 | + | 6594.28i | 1.02017 | + | 1.02017i | 0.999792 | + | 0.0203788i | \(0.00648721\pi\) |
0.0203788 | + | 0.999792i | \(0.493513\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6550.56 | + | 6550.56i | −1.00471 | + | 1.00471i | −0.00471950 | + | 0.999989i | \(0.501502\pi\) |
−0.999989 | + | 0.00471950i | \(0.998498\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1063.94 | 0.161791 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −939.592 | −0.141670 | −0.0708349 | − | 0.997488i | \(-0.522566\pi\) | ||||
−0.0708349 | + | 0.997488i | \(0.522566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1800.94 | − | 1800.94i | 0.269250 | − | 0.269250i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2423.95 | − | 2423.95i | −0.359352 | − | 0.359352i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11175.4i | 1.64294i | 0.570254 | + | 0.821469i | \(0.306845\pi\) | ||||
−0.570254 | + | 0.821469i | \(0.693155\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1892.35i | − | 0.275893i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6767.82 | + | 6767.82i | 0.978563 | + | 0.978563i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3384.47 | − | 3384.47i | 0.485346 | − | 0.485346i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10474.8 | −1.48986 | −0.744930 | − | 0.667143i | \(-0.767517\pi\) | ||||
−0.744930 | + | 0.667143i | \(0.767517\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −266.161 | −0.0375496 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7810.61 | + | 7810.61i | −1.09301 | + | 1.09301i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7160.10 | − | 7160.10i | −0.993930 | − | 0.993930i | 0.00605119 | − | 0.999982i | \(-0.498074\pi\) |
−0.999982 | + | 0.00605119i | \(0.998074\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 3511.78i | − | 0.483593i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4839.51i | 0.661134i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3707.91 | − | 3707.91i | −0.502540 | − | 0.502540i | 0.409687 | − | 0.912226i | \(-0.365638\pi\) |
−0.912226 | + | 0.409687i | \(0.865638\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 590.975 | − | 590.975i | 0.0794660 | − | 0.0794660i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1619.09 | 0.216010 | 0.108005 | − | 0.994150i | \(-0.465554\pi\) | ||||
0.108005 | + | 0.994150i | \(0.465554\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7177.57 | 0.950137 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3356.36 | − | 3356.36i | 0.440861 | − | 0.440861i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3130.25 | + | 3130.25i | 0.407995 | + | 0.407995i | 0.881039 | − | 0.473044i | \(-0.156845\pi\) |
−0.473044 | + | 0.881039i | \(0.656845\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 206.673i | 0.0267312i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2826.59i | − | 0.362806i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3971.67 | + | 3971.67i | 0.505914 | + | 0.505914i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4797.49 | − | 4797.49i | 0.606497 | − | 0.606497i | −0.335532 | − | 0.942029i | \(-0.608916\pi\) |
0.942029 | + | 0.335532i | \(0.108916\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5688.00 | −0.713674 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10424.9 | 1.29825 | 0.649123 | − | 0.760684i | \(-0.275136\pi\) | ||||
0.649123 | + | 0.760684i | \(0.275136\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2865.65 | − | 2865.65i | 0.354214 | − | 0.354214i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −301.656 | − | 301.656i | −0.0370108 | − | 0.0370108i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6354.78i | − | 0.773943i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12366.0i | − | 1.49501i | −0.664255 | − | 0.747506i | \(-0.731251\pi\) | ||
0.664255 | − | 0.747506i | \(-0.268749\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1341.90 | + | 1341.90i | 0.161049 | + | 0.161049i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1439.77 | + | 1439.77i | −0.171540 | + | 0.171540i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6491.48 | −0.767842 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4658.20 | −0.547034 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1809.65 | − | 1809.65i | 0.210996 | − | 0.210996i | −0.593694 | − | 0.804691i | \(-0.702331\pi\) |
0.804691 | + | 0.593694i | \(0.202331\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2481.06 | − | 2481.06i | −0.287219 | − | 0.287219i | 0.548760 | − | 0.835980i | \(-0.315100\pi\) |
−0.835980 | + | 0.548760i | \(0.815100\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 4851.74i | − | 0.557683i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 5483.49i | − | 0.625855i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3144.17 | − | 3144.17i | −0.356339 | − | 0.356339i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5620.75 | + | 5620.75i | −0.632570 | + | 0.632570i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4925.25 | −0.550443 | −0.275221 | − | 0.961381i | \(-0.588751\pi\) | ||||
−0.275221 | + | 0.961381i | \(0.588751\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13472.5 | 1.49526 | 0.747630 | − | 0.664115i | \(-0.231192\pi\) | ||||
0.747630 | + | 0.664115i | \(0.231192\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1372.13 | − | 1372.13i | 0.151239 | − | 0.151239i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 242.488 | + | 242.488i | 0.0265441 | + | 0.0265441i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.7683i | 0.00149687i | 1.00000 | 0.000748434i | \(0.000238234\pi\) | |||||
−1.00000 | 0.000748434i | \(0.999762\pi\) | ||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 609.952i | 0.0658624i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 112.762 | + | 112.762i | 0.0120936 | + | 0.0120936i | 0.713128 | − | 0.701034i | \(-0.247278\pi\) |
−0.701034 | + | 0.713128i | \(0.747278\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 689.129 | − | 689.129i | 0.0734108 | − | 0.0734108i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4087.14 | −0.432473 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17094.6 | −1.79676 | −0.898380 | − | 0.439218i | \(-0.855255\pi\) | ||||
−0.898380 | + | 0.439218i | \(0.855255\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1406.12 | − | 1406.12i | 0.146811 | − | 0.146811i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4343.10 | + | 4343.10i | 0.450457 | + | 0.450457i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4206.24i | 0.433389i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4074.04i | 0.417015i | 0.978021 | + | 0.208507i | \(0.0668605\pi\) | ||||
−0.978021 | + | 0.208507i | \(0.933140\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1076.38 | − | 1076.38i | −0.109458 | − | 0.109458i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2329.41 | + | 2329.41i | −0.235339 | + | 0.235339i | −0.814917 | − | 0.579578i | \(-0.803217\pi\) |
0.579578 | + | 0.814917i | \(0.303217\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12448.0 | 1.24948 | 0.624738 | − | 0.780834i | \(-0.285206\pi\) | ||||
0.624738 | + | 0.780834i | \(0.285206\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1624.98 | −0.162057 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −366.937 | + | 366.937i | −0.0363594 | + | 0.0363594i | −0.725053 | − | 0.688693i | \(-0.758185\pi\) |
0.688693 | + | 0.725053i | \(0.258185\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3610.48 | − | 3610.48i | −0.355472 | − | 0.355472i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11300.6i | 1.10553i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35463.1i | 3.44734i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6433.74 | − | 6433.74i | −0.621474 | − | 0.621474i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3468.38 | + | 3468.38i | −0.332927 | + | 0.332927i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18458.4 | 1.76072 | 0.880361 | − | 0.474304i | \(-0.157300\pi\) | ||||
0.880361 | + | 0.474304i | \(0.157300\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3724.07 | 0.353020 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 157.607 | − | 157.607i | 0.0148475 | − | 0.0148475i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2700.52 | − | 2700.52i | −0.252834 | − | 0.252834i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3880.55i | 0.361077i | 0.983568 | + | 0.180538i | \(0.0577840\pi\) | ||||
−0.983568 | + | 0.180538i | \(0.942216\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4259.26i | 0.393886i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3893.20 | − | 3893.20i | −0.357836 | − | 0.357836i | 0.505179 | − | 0.863015i | \(-0.331427\pi\) |
−0.863015 | + | 0.505179i | \(0.831427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4896.10 | − | 4896.10i | 0.447280 | − | 0.447280i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3187.27 | 0.289409 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9801.06 | −0.884583 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5061.87 | − | 5061.87i | 0.454110 | − | 0.454110i | −0.442606 | − | 0.896716i | \(-0.645946\pi\) |
0.896716 | + | 0.442606i | \(0.145946\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2719.65 | − | 2719.65i | −0.242525 | − | 0.242525i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 11814.7i | − | 1.04730i | −0.851933 | − | 0.523651i | \(-0.824570\pi\) | ||
0.851933 | − | 0.523651i | \(-0.175430\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8500.99i | 0.749088i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1366.63 | + | 1366.63i | 0.119713 | + | 0.119713i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7553.16 | + | 7553.16i | −0.657737 | + | 0.657737i | −0.954844 | − | 0.297107i | \(-0.903978\pi\) |
0.297107 | + | 0.954844i | \(0.403978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18418.9 | −1.59453 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2525.81 | −0.217383 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4094.53 | + | 4094.53i | −0.350343 | + | 0.350343i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25631.6 | + | 25631.6i | 2.18042 | + | 2.18042i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8379.03i | 0.708668i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1696.39i | − | 0.142649i | −0.997453 | − | 0.0713245i | \(-0.977277\pi\) | ||
0.997453 | − | 0.0713245i | \(-0.0227226\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6684.89 | − | 6684.89i | −0.558910 | − | 0.558910i | 0.370087 | − | 0.928997i | \(-0.379328\pi\) |
−0.928997 | + | 0.370087i | \(0.879328\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4181.65 | + | 4181.65i | −0.347623 | + | 0.347623i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5798.31 | −0.479276 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12153.6 | 0.998896 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −639.342 | + | 639.342i | −0.0522506 | + | 0.0522506i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 824.023 | + | 824.023i | 0.0669651 | + | 0.0669651i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2692.09i | − | 0.217550i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 281.468i | 0.0226187i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3222.36 | − | 3222.36i | −0.257508 | − | 0.257508i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5108.56 | − | 5108.56i | 0.405978 | − | 0.405978i | −0.474355 | − | 0.880333i | \(-0.657319\pi\) |
0.880333 | + | 0.474355i | \(0.157319\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1577.34 | 0.124660 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10469.4 | −0.822863 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13162.0 | + | 13162.0i | −1.02883 | + | 1.02883i | −0.0292549 | + | 0.999572i | \(0.509313\pi\) |
−0.999572 | + | 0.0292549i | \(0.990687\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1396.20 | − | 1396.20i | −0.108540 | − | 0.108540i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11489.1i | − | 0.888299i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 21614.6i | − | 1.66211i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1055.87 | − | 1055.87i | −0.0807557 | − | 0.0807557i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10462.8 | − | 10462.8i | 0.795911 | − | 0.795911i | −0.186537 | − | 0.982448i | \(-0.559726\pi\) |
0.982448 | + | 0.186537i | \(0.0597263\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20782.3 | −1.57245 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11372.9 | 0.855911 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11673.6 | + | 11673.6i | −0.873857 | + | 0.873857i | −0.992890 | − | 0.119033i | \(-0.962020\pi\) |
0.119033 | + | 0.992890i | \(0.462020\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1083.09 | − | 1083.09i | −0.0806479 | − | 0.0806479i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1641.67i | 0.121594i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 238.804i | 0.0175943i | 0.999961 | + | 0.00879717i | \(0.00280026\pi\) | ||||
−0.999961 | + | 0.00879717i | \(0.997200\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14395.8 | − | 14395.8i | −1.05507 | − | 1.05507i | −0.998393 | − | 0.0566747i | \(-0.981950\pi\) |
−0.0566747 | − | 0.998393i | \(-0.518050\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6061.36 | + | 6061.36i | −0.441914 | + | 0.441914i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 356.540 | 0.0258587 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14732.2 | −1.06293 | −0.531463 | − | 0.847081i | \(-0.678358\pi\) | ||||
−0.531463 | + | 0.847081i | \(0.678358\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9161.09 | + | 9161.09i | −0.657551 | + | 0.657551i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17664.0 | + | 17664.0i | 1.26132 | + | 1.26132i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 36646.7i | − | 2.60335i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1867.83i | 0.132009i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4120.47 | + | 4120.47i | 0.289727 | + | 0.289727i | 0.836972 | − | 0.547245i | \(-0.184323\pi\) |
−0.547245 | + | 0.836972i | \(0.684323\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6803.12 | + | 6803.12i | −0.475921 | + | 0.475921i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5942.99 | 0.413641 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18995.5 | −1.31543 | −0.657716 | − | 0.753266i | \(-0.728477\pi\) | ||||
−0.657716 | + | 0.753266i | \(0.728477\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4255.43 | − | 4255.43i | 0.293202 | − | 0.293202i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4570.23 | − | 4570.23i | −0.313312 | − | 0.313312i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19402.7i | 1.32349i | 0.749728 | + | 0.661747i | \(0.230185\pi\) | ||||
−0.749728 | + | 0.661747i | \(0.769815\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14134.5i | 0.959329i | 0.877452 | + | 0.479665i | \(0.159242\pi\) | ||||
−0.877452 | + | 0.479665i | \(0.840758\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1603.27 | − | 1603.27i | −0.108276 | − | 0.108276i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11881.4 | + | 11881.4i | −0.798428 | + | 0.798428i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2098.86 | −0.140346 | −0.0701731 | − | 0.997535i | \(-0.522355\pi\) | ||||
−0.0701731 | + | 0.997535i | \(0.522355\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7467.42 | −0.496872 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15020.8 | + | 15020.8i | −0.994560 | + | 0.994560i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6577.63 | − | 6577.63i | −0.433390 | − | 0.433390i | 0.456390 | − | 0.889780i | \(-0.349142\pi\) |
−0.889780 | + | 0.456390i | \(0.849142\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 467.266i | − | 0.0306374i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8011.43i | 0.522736i | 0.965239 | + | 0.261368i | \(0.0841736\pi\) | ||||
−0.965239 | + | 0.261368i | \(0.915826\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7930.76 | + | 7930.76i | 0.514966 | + | 0.514966i | 0.916044 | − | 0.401078i | \(-0.131364\pi\) |
−0.401078 | + | 0.916044i | \(0.631364\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 69.9868 | − | 69.9868i | 0.00452250 | − | 0.00452250i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3750.37 | −0.241181 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5992.49 | −0.383520 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13343.8 | − | 13343.8i | 0.849920 | − | 0.849920i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3767.61 | − | 3767.61i | −0.238831 | − | 0.238831i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 205.500i | − | 0.0129649i | −0.999979 | − | 0.00648243i | \(-0.997937\pi\) | ||
0.999979 | − | 0.00648243i | \(-0.00206344\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2815.12i | 0.176763i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1037.50 | + | 1037.50i | 0.0648378 | + | 0.0648378i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1888.39 | − | 1888.39i | 0.117458 | − | 0.117458i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4352.26 | −0.269441 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24945.2 | 1.53709 | 0.768545 | − | 0.639795i | \(-0.220981\pi\) | ||||
0.768545 | + | 0.639795i | \(0.220981\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2568.72 | + | 2568.72i | −0.157543 | + | 0.157543i | −0.781477 | − | 0.623934i | \(-0.785533\pi\) |
0.623934 | + | 0.781477i | \(0.285533\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5892.35 | + | 5892.35i | 0.359707 | + | 0.359707i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24443.7i | 1.48529i | 0.669687 | + | 0.742643i | \(0.266428\pi\) | ||||
−0.669687 | + | 0.742643i | \(0.733572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6755.25i | − | 0.408578i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4421.73 | + | 4421.73i | 0.266208 | + | 0.266208i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9074.73 | − | 9074.73i | 0.543831 | − | 0.543831i | −0.380819 | − | 0.924650i | \(-0.624358\pi\) |
0.924650 | + | 0.380819i | \(0.124358\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4962.30 | 0.296020 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8179.12 | −0.485689 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7745.96 | − | 7745.96i | 0.457875 | − | 0.457875i | −0.440082 | − | 0.897957i | \(-0.645051\pi\) |
0.897957 | + | 0.440082i | \(0.145051\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6346.77 | + | 6346.77i | 0.373465 | + | 0.373465i | 0.868738 | − | 0.495272i | \(-0.164932\pi\) |
−0.495272 | + | 0.868738i | \(0.664932\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6664.84i | 0.390409i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 9985.72i | − | 0.582300i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 318.347 | + | 318.347i | 0.0184804 | + | 0.0184804i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 918.088 | − | 918.088i | 0.0530573 | − | 0.0530573i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14752.1 | 0.848734 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10029.4 | −0.574450 | −0.287225 | − | 0.957863i | \(-0.592733\pi\) | ||||
−0.287225 | + | 0.957863i | \(0.592733\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1856.91 | + | 1856.91i | −0.105885 | + | 0.105885i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16757.3 | − | 16757.3i | −0.951309 | − | 0.951309i | 0.0475592 | − | 0.998868i | \(-0.484856\pi\) |
−0.998868 | + | 0.0475592i | \(0.984856\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14696.8i | 0.830649i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2047.26i | 0.115200i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15221.0 | − | 15221.0i | −0.852731 | − | 0.852731i | 0.137738 | − | 0.990469i | \(-0.456017\pi\) |
−0.990469 | + | 0.137738i | \(0.956017\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2355.82 | + | 2355.82i | −0.131403 | + | 0.131403i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11528.9 | 0.640256 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21475.9 | 1.18747 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12184.0 | − | 12184.0i | 0.670769 | − | 0.670769i | −0.287125 | − | 0.957893i | \(-0.592699\pi\) |
0.957893 | + | 0.287125i | \(0.0926994\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8672.89 | − | 8672.89i | −0.475405 | − | 0.475405i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8177.83i | − | 0.446335i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1667.32i | − | 0.0906084i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2576.09 | + | 2576.09i | 0.139394 | + | 0.139394i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 420.818 | − | 420.818i | 0.0226734 | − | 0.0226734i | −0.695679 | − | 0.718353i | \(-0.744896\pi\) |
0.718353 | + | 0.695679i | \(0.244896\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8841.02 | −0.474318 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8517.61 | 0.455024 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23132.0 | − | 23132.0i | 1.23051 | − | 1.23051i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9956.34 | − | 9956.34i | −0.527388 | − | 0.527388i | 0.392405 | − | 0.919793i | \(-0.371643\pi\) |
−0.919793 | + | 0.392405i | \(0.871643\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 9598.18i | − | 0.506273i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 377.010i | − | 0.0198024i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9867.67 | − | 9867.67i | −0.516126 | − | 0.516126i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5677.45 | − | 5677.45i | 0.295716 | − | 0.295716i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20878.5 | −1.08295 | −0.541473 | − | 0.840718i | \(-0.682133\pi\) | ||||
−0.541473 | + | 0.840718i | \(0.682133\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22283.2 | 1.15100 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5124.70 | + | 5124.70i | −0.263609 | + | 0.263609i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8446.46 | − | 8446.46i | −0.432681 | − | 0.432681i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2726.84i | 0.139110i | 0.997578 | + | 0.0695549i | \(0.0221579\pi\) | ||||
−0.997578 | + | 0.0695549i | \(0.977842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21025.3 | + | 21025.3i | 1.06381 | + | 1.06381i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1081.50 | − | 1081.50i | 0.0544967 | − | 0.0544967i | −0.679333 | − | 0.733830i | \(-0.737731\pi\) |
0.733830 | + | 0.679333i | \(0.237731\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1070.82 | −0.0537384 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16940.1 | 0.846669 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15055.3 | − | 15055.3i | 0.749416 | − | 0.749416i | −0.224954 | − | 0.974369i | \(-0.572223\pi\) |
0.974369 | + | 0.224954i | \(0.0722232\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7819.81 | + | 7819.81i | 0.387676 | + | 0.387676i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 21909.2i | − | 1.08179i | −0.841090 | − | 0.540896i | \(-0.818085\pi\) | ||
0.841090 | − | 0.540896i | \(-0.181915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 7175.30i | − | 0.352863i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7843.86 | + | 7843.86i | 0.384193 | + | 0.384193i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7325.45 | + | 7325.45i | −0.357365 | + | 0.357365i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4501.15 | 0.218707 | 0.109354 | − | 0.994003i | \(-0.465122\pi\) | ||||
0.109354 | + | 0.994003i | \(0.465122\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6331.69 | −0.306427 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7624.66 | + | 7624.66i | −0.367536 | + | 0.367536i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3638.27 | + | 3638.27i | 0.174683 | + | 0.174683i | 0.789034 | − | 0.614350i | \(-0.210582\pi\) |
−0.614350 | + | 0.789034i | \(0.710582\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 739.476i | 0.0353640i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 7208.65i | − | 0.343381i | −0.985151 | − | 0.171691i | \(-0.945077\pi\) | ||
0.985151 | − | 0.171691i | \(-0.0549230\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28488.3 | + | 28488.3i | 1.35170 | + | 1.35170i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1889.66 | − | 1889.66i | 0.0893085 | − | 0.0893085i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3958.75 | 0.186365 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6428.86 | −0.301470 | −0.150735 | − | 0.988574i | \(-0.548164\pi\) | ||||
−0.150735 | + | 0.988574i | \(0.548164\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6928.90 | + | 6928.90i | −0.323655 | + | 0.323655i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21187.9 | − | 21187.9i | −0.985867 | − | 0.985867i | 0.0140348 | − | 0.999902i | \(-0.495532\pi\) |
−0.999902 | + | 0.0140348i | \(0.995532\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10002.9i | 0.463633i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5746.28i | 0.265311i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1956.25 | − | 1956.25i | −0.0899742 | − | 0.0899742i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22992.9 | − | 22992.9i | 1.05346 | − | 1.05346i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3315.99 | −0.151346 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19839.1 | −0.902021 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25780.3 | + | 25780.3i | −1.16769 | + | 1.16769i | −0.184935 | + | 0.982751i | \(0.559207\pi\) |
−0.982751 | + | 0.184935i | \(0.940793\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1894.93 | + | 1894.93i | 0.0855024 | + | 0.0855024i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5894.41i | 0.264957i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8645.14i | 0.387135i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6089.01 | − | 6089.01i | −0.271641 | − | 0.271641i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19825.4 | + | 19825.4i | −0.881121 | + | 0.881121i | −0.993649 | − | 0.112528i | \(-0.964105\pi\) |
0.112528 | + | 0.993649i | \(0.464105\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30392.8 | 1.34571 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1665.39 | −0.0734628 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 43210.0 | − | 43210.0i | 1.89894 | − | 1.89894i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 276.691 | + | 276.691i | 0.0121144 | + | 0.0121144i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 11112.0i | − | 0.484711i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 40019.8i | − | 1.73921i | −0.493749 | − | 0.869605i | \(-0.664374\pi\) | ||
0.493749 | − | 0.869605i | \(-0.335626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24193.5 | + | 24193.5i | 1.04753 | + | 1.04753i | 0.998812 | + | 0.0487212i | \(0.0155146\pi\) |
0.0487212 | + | 0.998812i | \(0.484485\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11507.5 | − | 11507.5i | 0.496414 | − | 0.496414i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7477.45 | −0.321379 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49337.6 | 2.11274 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5082.54 | − | 5082.54i | 0.216848 | − | 0.216848i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18924.0 | + | 18924.0i | 0.804450 | + | 0.804450i | 0.983788 | − | 0.179338i | \(-0.0573954\pi\) |
−0.179338 | + | 0.983788i | \(0.557395\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 4894.21i | − | 0.207292i | −0.994614 | − | 0.103646i | \(-0.966949\pi\) | ||
0.994614 | − | 0.103646i | \(-0.0330509\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 19620.0i | − | 0.827975i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19015.3 | + | 19015.3i | 0.799549 | + | 0.799549i | 0.983024 | − | 0.183475i | \(-0.0587348\pi\) |
−0.183475 | + | 0.983024i | \(0.558735\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7608.33 | − | 7608.33i | 0.318755 | − | 0.318755i | −0.529534 | − | 0.848289i | \(-0.677633\pi\) |
0.848289 | + | 0.529534i | \(0.177633\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9514.33 | −0.397170 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3820.93 | −0.158928 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4774.55 | − | 4774.55i | 0.197880 | − | 0.197880i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1963.51 | + | 1963.51i | 0.0810860 | + | 0.0810860i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31098.4i | 1.27966i | 0.768517 | + | 0.639830i | \(0.220995\pi\) | ||||
−0.768517 | + | 0.639830i | \(0.779005\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9305.65i | 0.381551i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7685.27 | − | 7685.27i | −0.313991 | − | 0.313991i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2399.23 | + | 2399.23i | −0.0976759 | + | 0.0976759i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 64661.1 | 2.62312 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.0269294 | 1.08859e−6 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 244.972 | − | 244.972i | 0.00986786 | − | 0.00986786i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28324.9 | − | 28324.9i | −1.13696 | − | 1.13696i | −0.988992 | − | 0.147968i | \(-0.952727\pi\) |
−0.147968 | − | 0.988992i | \(-0.547273\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 4434.26i | − | 0.177367i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 14990.8i | − | 0.597520i | −0.954328 | − | 0.298760i | \(-0.903427\pi\) | ||
0.954328 | − | 0.298760i | \(-0.0965730\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19751.5 | − | 19751.5i | −0.784533 | − | 0.784533i | 0.196059 | − | 0.980592i | \(-0.437185\pi\) |
−0.980592 | + | 0.196059i | \(0.937185\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1271.48 | + | 1271.48i | −0.0503273 | + | 0.0503273i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9084.96 | −0.358349 | −0.179175 | − | 0.983817i | \(-0.557343\pi\) | ||||
−0.179175 | + | 0.983817i | \(0.557343\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14710.0 | −0.578215 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3679.28 | + | 3679.28i | −0.144123 | + | 0.144123i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50706.9 | + | 50706.9i | 1.97942 | + | 1.97942i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9927.32i | 0.386193i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6526.26i | 0.253013i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16776.1 | − | 16776.1i | −0.648155 | − | 0.648155i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18336.8 | + | 18336.8i | −0.706031 | + | 0.706031i | −0.965698 | − | 0.259668i | \(-0.916387\pi\) |
0.259668 | + | 0.965698i | \(0.416387\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 105.805 | 0.00405995 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13402.7 | 0.512543 | 0.256271 | − | 0.966605i | \(-0.417506\pi\) | ||||
0.256271 | + | 0.966605i | \(0.417506\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16285.1 | + | 16285.1i | −0.620656 | + | 0.620656i | −0.945699 | − | 0.325044i | \(-0.894621\pi\) |
0.325044 | + | 0.945699i | \(0.394621\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1122.42 | − | 1122.42i | −0.0426323 | − | 0.0426323i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 35406.7i | − | 1.34029i | −0.742229 | − | 0.670146i | \(-0.766231\pi\) | ||
0.742229 | − | 0.670146i | \(-0.233769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 5646.29i | − | 0.213015i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3851.28 | − | 3851.28i | −0.144807 | − | 0.144807i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35659.7 | − | 35659.7i | 1.33629 | − | 1.33629i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −494.138 | −0.0184550 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −433.352 | −0.0161307 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8931.39 | + | 8931.39i | −0.331344 | + | 0.331344i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21727.0 | − | 21727.0i | −0.803365 | − | 0.803365i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 32067.3i | − | 1.18176i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2769.15i | 0.101712i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8884.93 | + | 8884.93i | 0.325269 | + | 0.325269i | 0.850784 | − | 0.525515i | \(-0.176127\pi\) |
−0.525515 | + | 0.850784i | \(0.676127\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10272.0 | − | 10272.0i | 0.374809 | − | 0.374809i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16668.9 | 0.606219 | 0.303110 | − | 0.952956i | \(-0.401975\pi\) | ||||
0.303110 | + | 0.952956i | \(0.401975\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −82877.8 | −3.00422 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2451.14 | − | 2451.14i | 0.0885596 | − | 0.0885596i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13502.9 | − | 13502.9i | −0.486266 | − | 0.486266i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26028.5i | 0.934276i | 0.884184 | + | 0.467138i | \(0.154715\pi\) | ||||
−0.884184 | + | 0.467138i | \(0.845285\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 2625.16i | − | 0.0939218i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13474.4 | + | 13474.4i | 0.480516 | + | 0.480516i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6499.66 | + | 6499.66i | −0.231035 | + | 0.231035i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9895.10 | 0.350591 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13806.2 | −0.487584 | −0.243792 | − | 0.969828i | \(-0.578391\pi\) | ||||
−0.243792 | + | 0.969828i | \(0.578391\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4483.07 | + | 4483.07i | −0.157816 | + | 0.157816i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8875.43 | − | 8875.43i | −0.311435 | − | 0.311435i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19966.1i | 0.698354i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1798.08i | 0.0626901i | 0.999509 | + | 0.0313451i | \(0.00997908\pi\) | ||||
−0.999509 | + | 0.0313451i | \(0.990021\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4506.08 | + | 4506.08i | 0.156603 | + | 0.156603i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8722.11 | − | 8722.11i | 0.302160 | − | 0.302160i | −0.539698 | − | 0.841858i | \(-0.681462\pi\) |
0.841858 | + | 0.539698i | \(0.181462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 108.410 | 0.00374371 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2882.08 | −0.0992106 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15872.2 | + | 15872.2i | −0.544644 | + | 0.544644i | −0.924887 | − | 0.380243i | \(-0.875840\pi\) |
0.380243 | + | 0.924887i | \(0.375840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25322.2 | + | 25322.2i | 0.866168 | + | 0.866168i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4518.21i | 0.154062i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 34643.6i | − | 1.17756i | −0.808292 | − | 0.588782i | \(-0.799608\pi\) | ||
0.808292 | − | 0.588782i | \(-0.200392\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10641.2 | − | 10641.2i | −0.360566 | − | 0.360566i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17518.2 | − | 17518.2i | 0.591729 | − | 0.591729i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12820.8 | 0.431706 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19213.8 | −0.644953 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3252.94 | + | 3252.94i | −0.108852 | + | 0.108852i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16083.0 | − | 16083.0i | −0.536508 | − | 0.536508i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22531.8i | 0.749301i | 0.927166 | + | 0.374650i | \(0.122237\pi\) | ||||
−0.927166 | + | 0.374650i | \(0.877763\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 15822.5i | − | 0.524553i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5854.80 | − | 5854.80i | −0.193501 | − | 0.193501i | 0.603706 | − | 0.797207i | \(-0.293690\pi\) |
−0.797207 | + | 0.603706i | \(0.793690\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22252.7 | + | 22252.7i | −0.733184 | + | 0.733184i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11497.8 | 0.377666 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50312.5 | 1.64753 | 0.823766 | − | 0.566930i | \(-0.191869\pi\) | ||||
0.823766 | + | 0.566930i | \(0.191869\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8798.21 | − | 8798.21i | 0.287224 | − | 0.287224i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12650.5 | + | 12650.5i | 0.411723 | + | 0.411723i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1796.13i | 0.0582783i | 0.999575 | + | 0.0291391i | \(0.00927659\pi\) | ||||
−0.999575 | + | 0.0291391i | \(0.990723\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10433.4i | 0.337498i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −23177.3 | − | 23177.3i | −0.747457 | − | 0.747457i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1367.08 | + | 1367.08i | −0.0439540 | + | 0.0439540i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32363.5 | −1.03740 | −0.518698 | − | 0.854958i | \(-0.673583\pi\) | ||||
−0.518698 | + | 0.854958i | \(0.673583\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7575.45 | 0.242094 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8023.40 | − | 8023.40i | 0.255637 | − | 0.255637i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −680.434 | − | 680.434i | −0.0216144 | − | 0.0216144i | 0.696217 | − | 0.717831i | \(-0.254865\pi\) |
−0.717831 | + | 0.696217i | \(0.754865\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2551.69i | 0.0808128i |
(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.j.b.97.8 | 24 | ||
4.3 | odd | 2 | 384.4.j.a.97.5 | 24 | |||
8.3 | odd | 2 | 192.4.j.a.49.9 | 24 | |||
8.5 | even | 2 | 48.4.j.a.37.1 | yes | 24 | ||
16.3 | odd | 4 | 384.4.j.a.289.5 | 24 | |||
16.5 | even | 4 | 48.4.j.a.13.1 | ✓ | 24 | ||
16.11 | odd | 4 | 192.4.j.a.145.9 | 24 | |||
16.13 | even | 4 | inner | 384.4.j.b.289.8 | 24 | ||
24.5 | odd | 2 | 144.4.k.b.37.12 | 24 | |||
24.11 | even | 2 | 576.4.k.b.433.8 | 24 | |||
48.5 | odd | 4 | 144.4.k.b.109.12 | 24 | |||
48.11 | even | 4 | 576.4.k.b.145.8 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.4.j.a.13.1 | ✓ | 24 | 16.5 | even | 4 | ||
48.4.j.a.37.1 | yes | 24 | 8.5 | even | 2 | ||
144.4.k.b.37.12 | 24 | 24.5 | odd | 2 | |||
144.4.k.b.109.12 | 24 | 48.5 | odd | 4 | |||
192.4.j.a.49.9 | 24 | 8.3 | odd | 2 | |||
192.4.j.a.145.9 | 24 | 16.11 | odd | 4 | |||
384.4.j.a.97.5 | 24 | 4.3 | odd | 2 | |||
384.4.j.a.289.5 | 24 | 16.3 | odd | 4 | |||
384.4.j.b.97.8 | 24 | 1.1 | even | 1 | trivial | ||
384.4.j.b.289.8 | 24 | 16.13 | even | 4 | inner | ||
576.4.k.b.145.8 | 24 | 48.11 | even | 4 | |||
576.4.k.b.433.8 | 24 | 24.11 | even | 2 |