Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(337,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.k (of order \(4\), degree \(2\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 729.17 | ||
Character | \(\chi\) | \(=\) | 1148.729 |
Dual form | 1148.2.k.b.337.17 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 1.86437 | − | 1.86437i | 1.07640 | − | 1.07640i | 0.0795665 | − | 0.996830i | \(-0.474646\pi\) |
0.996830 | − | 0.0795665i | \(-0.0253536\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.96253i | 1.32488i | 0.749114 | + | 0.662441i | \(0.230480\pi\) | ||||
−0.749114 | + | 0.662441i | \(0.769520\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.95177i | − | 1.31726i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.99130 | − | 2.99130i | 0.901912 | − | 0.901912i | −0.0936893 | − | 0.995601i | \(-0.529866\pi\) |
0.995601 | + | 0.0936893i | \(0.0298660\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.619012 | − | 0.619012i | 0.171683 | − | 0.171683i | −0.616035 | − | 0.787718i | \(-0.711262\pi\) |
0.787718 | + | 0.616035i | \(0.211262\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.52326 | + | 5.52326i | 1.42610 | + | 1.42610i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.08301 | + | 1.08301i | 0.262668 | + | 0.262668i | 0.826137 | − | 0.563469i | \(-0.190534\pi\) |
−0.563469 | + | 0.826137i | \(0.690534\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.93662 | − | 1.93662i | −0.444292 | − | 0.444292i | 0.449160 | − | 0.893452i | \(-0.351723\pi\) |
−0.893452 | + | 0.449160i | \(0.851723\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.63662i | − | 0.575358i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.66835 | −0.347875 | −0.173938 | − | 0.984757i | \(-0.555649\pi\) | ||||
−0.173938 | + | 0.984757i | \(0.555649\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.77657 | −0.755314 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.77446 | − | 1.77446i | −0.341494 | − | 0.341494i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.85131 | + | 2.85131i | −0.529475 | + | 0.529475i | −0.920416 | − | 0.390941i | \(-0.872150\pi\) |
0.390941 | + | 0.920416i | \(0.372150\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.4509 | 1.87703 | 0.938515 | − | 0.345238i | \(-0.112202\pi\) | ||||
0.938515 | + | 0.345238i | \(0.112202\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 11.1538i | − | 1.94163i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.09482 | + | 2.09482i | 0.354090 | + | 0.354090i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.67577 | 0.933090 | 0.466545 | − | 0.884497i | \(-0.345499\pi\) | ||||
0.466545 | + | 0.884497i | \(0.345499\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.30814i | − | 0.369598i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.65185 | − | 5.82818i | −0.414150 | − | 0.910209i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.246878i | − | 0.0376486i | −0.999823 | − | 0.0188243i | \(-0.994008\pi\) | ||
0.999823 | − | 0.0188243i | \(-0.00599231\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.7072 | 1.74521 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.86462 | + | 1.86462i | 0.271983 | + | 0.271983i | 0.829898 | − | 0.557915i | \(-0.188399\pi\) |
−0.557915 | + | 0.829898i | \(0.688399\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.03826 | 0.565470 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.37754 | + | 2.37754i | −0.326581 | + | 0.326581i | −0.851285 | − | 0.524704i | \(-0.824176\pi\) |
0.524704 | + | 0.851285i | \(0.324176\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.86182 | + | 8.86182i | 1.19493 | + | 1.19493i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.22118 | −0.956468 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.0601 | 1.57010 | 0.785048 | − | 0.619436i | \(-0.212638\pi\) | ||||
0.785048 | + | 0.619436i | \(0.212638\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.07952i | − | 0.266255i | −0.991099 | − | 0.133128i | \(-0.957498\pi\) | ||
0.991099 | − | 0.133128i | \(-0.0425020\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.79432 | − | 2.79432i | −0.352052 | − | 0.352052i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.83384 | + | 1.83384i | 0.227460 | + | 0.227460i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.35588 | − | 3.35588i | −0.409986 | − | 0.409986i | 0.471748 | − | 0.881734i | \(-0.343623\pi\) |
−0.881734 | + | 0.471748i | \(0.843623\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.11043 | + | 3.11043i | −0.374452 | + | 0.374452i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.87049 | + | 7.87049i | −0.934055 | + | 0.934055i | −0.997956 | − | 0.0639014i | \(-0.979646\pi\) |
0.0639014 | + | 0.997956i | \(0.479646\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.12655i | − | 0.248894i | −0.992226 | − | 0.124447i | \(-0.960284\pi\) | ||
0.992226 | − | 0.124447i | \(-0.0397156\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.04094 | + | 7.04094i | −0.813017 | + | 0.813017i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.23034i | − | 0.482092i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.02140 | + | 3.02140i | −0.339934 | + | 0.339934i | −0.856342 | − | 0.516408i | \(-0.827269\pi\) |
0.516408 | + | 0.856342i | \(0.327269\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.23882 | 0.582091 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.75282 | −0.302162 | −0.151081 | − | 0.988521i | \(-0.548275\pi\) | ||||
−0.151081 | + | 0.988521i | \(0.548275\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.20844 | + | 3.20844i | −0.348004 | + | 0.348004i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.6318i | 1.13985i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.71983 | + | 9.71983i | −1.03030 | + | 1.03030i | −0.0307731 | + | 0.999526i | \(0.509797\pi\) |
−0.999526 | + | 0.0307731i | \(0.990203\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.875415i | − | 0.0917684i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.4843 | − | 19.4843i | 2.02043 | − | 2.02043i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.73730 | − | 5.73730i | 0.588635 | − | 0.588635i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.1964 | − | 11.1964i | −1.13682 | − | 1.13682i | −0.989016 | − | 0.147806i | \(-0.952779\pi\) |
−0.147806 | − | 0.989016i | \(-0.547221\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.8210 | − | 11.8210i | −1.18805 | − | 1.18805i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.9754 | − | 11.9754i | −1.19160 | − | 1.19160i | −0.976619 | − | 0.214977i | \(-0.931032\pi\) |
−0.214977 | − | 0.976619i | \(-0.568968\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.53596i | 0.446941i | 0.974711 | + | 0.223470i | \(0.0717386\pi\) | ||||
−0.974711 | + | 0.223470i | \(0.928261\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.81106 | 0.762282 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.03676 | −0.486922 | −0.243461 | − | 0.969911i | \(-0.578283\pi\) | ||||
−0.243461 | + | 0.969911i | \(0.578283\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.55793 | − | 7.55793i | −0.723918 | − | 0.723918i | 0.245483 | − | 0.969401i | \(-0.421054\pi\) |
−0.969401 | + | 0.245483i | \(0.921054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.5817 | − | 10.5817i | 1.00437 | − | 1.00437i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.4571 | −1.45408 | −0.727041 | − | 0.686594i | \(-0.759105\pi\) | ||||
−0.727041 | + | 0.686594i | \(0.759105\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.94254i | − | 0.460894i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.44619 | − | 2.44619i | −0.226151 | − | 0.226151i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.53160 | 0.140402 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 6.89580i | − | 0.626891i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.8099 | − | 5.92185i | −1.42553 | − | 0.533956i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.62444i | 0.324180i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.48488 | 0.309233 | 0.154616 | − | 0.987975i | \(-0.450586\pi\) | ||||
0.154616 | + | 0.987975i | \(0.450586\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.460273 | − | 0.460273i | −0.0405248 | − | 0.0405248i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.94915i | 0.781891i | 0.920414 | + | 0.390946i | \(0.127852\pi\) | ||||
−0.920414 | + | 0.390946i | \(0.872148\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.73880 | −0.237484 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.25688 | − | 5.25688i | 0.452440 | − | 0.452440i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.10060 | + | 9.10060i | 0.777517 | + | 0.777517i | 0.979408 | − | 0.201891i | \(-0.0647088\pi\) |
−0.201891 | + | 0.979408i | \(0.564709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.6023 | −1.91710 | −0.958552 | − | 0.284919i | \(-0.908033\pi\) | ||||
−0.958552 | + | 0.284919i | \(0.908033\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.95269 | 0.585522 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3.70330i | − | 0.309686i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.44708 | − | 8.44708i | −0.701492 | − | 0.701492i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.86437 | − | 1.86437i | −0.153771 | − | 0.153771i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.0991 | + | 17.0991i | 1.40081 | + | 1.40081i | 0.797520 | + | 0.603292i | \(0.206145\pi\) |
0.603292 | + | 0.797520i | \(0.293855\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.55269 | − | 3.55269i | 0.289114 | − | 0.289114i | −0.547616 | − | 0.836730i | \(-0.684464\pi\) |
0.836730 | + | 0.547616i | \(0.184464\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.27980 | − | 4.27980i | 0.346001 | − | 0.346001i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 30.9610i | 2.48684i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.45235 | + | 3.45235i | −0.275527 | + | 0.275527i | −0.831321 | − | 0.555793i | \(-0.812415\pi\) |
0.555793 | + | 0.831321i | \(0.312415\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.86526i | 0.703061i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.17970 | + | 1.17970i | −0.0929736 | + | 0.0929736i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.9288 | −1.01266 | −0.506332 | − | 0.862339i | \(-0.668999\pi\) | ||||
−0.506332 | + | 0.862339i | \(0.668999\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 33.0435 | 2.57243 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.02429 | − | 6.02429i | 0.466173 | − | 0.466173i | −0.434499 | − | 0.900672i | \(-0.643075\pi\) |
0.900672 | + | 0.434499i | \(0.143075\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2336i | 0.941050i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.65309 | + | 7.65309i | −0.585247 | + | 0.585247i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.8343i | 0.823714i | 0.911249 | + | 0.411857i | \(0.135120\pi\) | ||||
−0.911249 | + | 0.411857i | \(0.864880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.67044 | + | 2.67044i | −0.201866 | + | 0.201866i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.4846 | − | 22.4846i | 1.69004 | − | 1.69004i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.4482 | + | 11.4482i | 0.855679 | + | 0.855679i | 0.990826 | − | 0.135147i | \(-0.0431506\pi\) |
−0.135147 | + | 0.990826i | \(0.543151\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7929 | + | 13.7929i | 1.02521 | + | 1.02521i | 0.999674 | + | 0.0255409i | \(0.00813081\pi\) |
0.0255409 | + | 0.999674i | \(0.491869\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.87700 | − | 3.87700i | −0.286596 | − | 0.286596i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.8146i | 1.23623i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.47921 | 0.473807 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.50946 | −0.182536 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.9361 | − | 11.9361i | −0.863665 | − | 0.863665i | 0.128097 | − | 0.991762i | \(-0.459113\pi\) |
−0.991762 | + | 0.128097i | \(0.959113\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.740264 | − | 0.740264i | 0.0532854 | − | 0.0532854i | −0.679962 | − | 0.733247i | \(-0.738004\pi\) |
0.733247 | + | 0.679962i | \(0.238004\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.83792 | 0.489674 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.4556i | 0.744933i | 0.928046 | + | 0.372466i | \(0.121488\pi\) | ||||
−0.928046 | + | 0.372466i | \(0.878512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.72768 | + | 4.72768i | 0.335137 | + | 0.335137i | 0.854533 | − | 0.519397i | \(-0.173843\pi\) |
−0.519397 | + | 0.854533i | \(0.673843\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.5132 | −0.882615 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.03236i | 0.283016i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.2661 | − | 7.85619i | 1.20592 | − | 0.548700i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.59295i | 0.458241i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.5861 | −0.801424 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.37936 | − | 1.37936i | −0.0949588 | − | 0.0949588i | 0.658032 | − | 0.752990i | \(-0.271389\pi\) |
−0.752990 | + | 0.658032i | \(0.771389\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 29.3470i | 2.01083i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.731384 | 0.0498800 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.38987 | − | 7.38987i | 0.501657 | − | 0.501657i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.96468 | − | 3.96468i | −0.267908 | − | 0.267908i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.34079 | 0.0901912 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.79309 | −0.254004 | −0.127002 | − | 0.991902i | \(-0.540535\pi\) | ||||
−0.127002 | + | 0.991902i | \(0.540535\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.9241i | 0.994943i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.0020 | − | 13.0020i | −0.862975 | − | 0.862975i | 0.128707 | − | 0.991683i | \(-0.458917\pi\) |
−0.991683 | + | 0.128707i | \(0.958917\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.9076 | − | 10.9076i | −0.720797 | − | 0.720797i | 0.247970 | − | 0.968768i | \(-0.420236\pi\) |
−0.968768 | + | 0.247970i | \(0.920236\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.88694 | − | 7.88694i | −0.518922 | − | 0.518922i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.61461 | + | 8.61461i | −0.564362 | + | 0.564362i | −0.930543 | − | 0.366181i | \(-0.880665\pi\) |
0.366181 | + | 0.930543i | \(0.380665\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.52399 | + | 5.52399i | −0.360345 | + | 0.360345i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.2660i | 0.731807i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.44216 | − | 4.44216i | 0.287340 | − | 0.287340i | −0.548688 | − | 0.836027i | \(-0.684872\pi\) |
0.836027 | + | 0.548688i | \(0.184872\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 8.60928i | − | 0.554573i | −0.960787 | − | 0.277286i | \(-0.910565\pi\) | ||
0.960787 | − | 0.277286i | \(-0.0894350\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.0905 | − | 15.0905i | 0.968055 | − | 0.968055i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.96253 | 0.189269 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.39759 | −0.152555 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.13229 | + | 5.13229i | −0.325246 | + | 0.325246i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.75004i | − | 0.426059i | −0.977046 | − | 0.213029i | \(-0.931667\pi\) | ||
0.977046 | − | 0.213029i | \(-0.0683330\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.99055 | + | 4.99055i | −0.313753 | + | 0.313753i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.9635i | 0.749181i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.70135 | − | 9.70135i | 0.605154 | − | 0.605154i | −0.336522 | − | 0.941676i | \(-0.609251\pi\) |
0.941676 | + | 0.336522i | \(0.109251\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.01337 | − | 4.01337i | 0.249379 | − | 0.249379i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.2677 | + | 11.2677i | 0.697454 | + | 0.697454i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.8681 | + | 17.8681i | 1.10179 | + | 1.10179i | 0.994194 | + | 0.107601i | \(0.0343168\pi\) |
0.107601 | + | 0.994194i | \(0.465683\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.04354 | − | 7.04354i | −0.432681 | − | 0.432681i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 36.2428i | 2.21802i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.55438 | 0.399628 | 0.199814 | − | 0.979834i | \(-0.435966\pi\) | ||||
0.199814 | + | 0.979834i | \(0.435966\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8236 | −0.839724 | −0.419862 | − | 0.907588i | \(-0.637922\pi\) | ||||
−0.419862 | + | 0.907588i | \(0.637922\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.63210 | − | 1.63210i | −0.0987792 | − | 0.0987792i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.2969 | + | 11.2969i | −0.681227 | + | 0.681227i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.2742 | 0.677403 | 0.338701 | − | 0.940894i | \(-0.390012\pi\) | ||||
0.338701 | + | 0.940894i | \(0.390012\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 41.2994i | − | 2.47253i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.9759 | + | 15.9759i | 0.953043 | + | 0.953043i | 0.998946 | − | 0.0459031i | \(-0.0146165\pi\) |
−0.0459031 | + | 0.998946i | \(0.514617\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.9982 | −0.772663 | −0.386332 | − | 0.922360i | \(-0.626258\pi\) | ||||
−0.386332 | + | 0.922360i | \(0.626258\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 21.3929i | − | 1.26721i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.99629 | − | 2.24600i | −0.353950 | − | 0.132577i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 14.6542i | − | 0.862011i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −41.7485 | −2.44734 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.9236 | − | 14.9236i | −0.871843 | − | 0.871843i | 0.120830 | − | 0.992673i | \(-0.461444\pi\) |
−0.992673 | + | 0.120830i | \(0.961444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 35.7285i | 2.08019i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.6159 | −0.615996 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.03273 | + | 1.03273i | −0.0597243 | + | 0.0597243i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.174569 | − | 0.174569i | −0.0100620 | − | 0.0100620i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −44.6532 | −2.56526 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.16064 | 0.352757 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.2534i | 1.32714i | 0.748113 | + | 0.663571i | \(0.230960\pi\) | ||||
−0.748113 | + | 0.663571i | \(0.769040\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.45671 | + | 8.45671i | 0.481085 | + | 0.481085i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.99104 | − | 9.99104i | −0.566540 | − | 0.566540i | 0.364618 | − | 0.931157i | \(-0.381200\pi\) |
−0.931157 | + | 0.364618i | \(0.881200\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.24374 | + | 6.24374i | 0.352917 | + | 0.352917i | 0.861194 | − | 0.508277i | \(-0.169717\pi\) |
−0.508277 | + | 0.861194i | \(0.669717\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.27826 | − | 8.27826i | 0.466427 | − | 0.466427i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.18228 | + | 6.18228i | −0.347231 | + | 0.347231i | −0.859077 | − | 0.511846i | \(-0.828962\pi\) |
0.511846 | + | 0.859077i | \(0.328962\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.0583i | 0.955079i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.39040 | + | 9.39040i | −0.524121 | + | 0.524121i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.19476i | − | 0.233402i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.33774 | + | 2.33774i | −0.129675 | + | 0.129675i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −28.1816 | −1.55845 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.63697 | 0.145381 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.41693 | − | 1.41693i | 0.0778817 | − | 0.0778817i | −0.667093 | − | 0.744975i | \(-0.732462\pi\) |
0.744975 | + | 0.667093i | \(0.232462\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 22.4293i | − | 1.22912i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.94189 | − | 9.94189i | 0.543183 | − | 0.543183i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.9764i | − | 1.14266i | −0.820721 | − | 0.571329i | \(-0.806428\pi\) | ||
0.820721 | − | 0.571329i | \(-0.193572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.8178 | + | 28.8178i | −1.56517 | + | 1.56517i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.2617 | − | 31.2617i | 1.69292 | − | 1.69292i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.21474 | − | 9.21474i | −0.496105 | − | 0.496105i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.4052 | + | 10.4052i | 0.558578 | + | 0.558578i | 0.928902 | − | 0.370325i | \(-0.120754\pi\) |
−0.370325 | + | 0.928902i | \(0.620754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.66785i | 0.249864i | 0.992165 | + | 0.124932i | \(0.0398713\pi\) | ||||
−0.992165 | + | 0.124932i | \(0.960129\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.19682 | −0.117258 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.537690 | −0.0286184 | −0.0143092 | − | 0.999898i | \(-0.504555\pi\) | ||||
−0.0143092 | + | 0.999898i | \(0.504555\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.3165 | − | 23.3165i | −1.23751 | − | 1.23751i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.85548 | − | 2.85548i | 0.151128 | − | 0.151128i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.2692 | −1.12255 | −0.561273 | − | 0.827631i | \(-0.689688\pi\) | ||||
−0.561273 | + | 0.827631i | \(0.689688\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 11.4990i | − | 0.605209i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.8563 | − | 12.8563i | −0.674783 | − | 0.674783i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.29996 | 0.329755 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.93875i | − | 0.257801i | −0.991658 | − | 0.128900i | \(-0.958855\pi\) | ||
0.991658 | − | 0.128900i | \(-0.0411447\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.0316 | + | 10.4795i | −1.19898 | + | 0.545542i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.36236i | 0.174565i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.1009 | −1.45501 | −0.727506 | − | 0.686102i | \(-0.759320\pi\) | ||||
−0.727506 | + | 0.686102i | \(0.759320\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.75731 | + | 6.75731i | 0.348946 | + | 0.348946i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.52999i | 0.181804i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.0435824 | −0.00223868 | −0.00111934 | − | 0.999999i | \(-0.500356\pi\) | ||||
−0.00111934 | + | 0.999999i | \(0.500356\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.49711 | − | 6.49711i | 0.332857 | − | 0.332857i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.20923 | + | 2.20923i | 0.112886 | + | 0.112886i | 0.761294 | − | 0.648407i | \(-0.224565\pi\) |
−0.648407 | + | 0.761294i | \(0.724565\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.5325 | 0.638716 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.975607 | −0.0495929 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 12.5762i | − | 0.637638i | −0.947816 | − | 0.318819i | \(-0.896714\pi\) | ||
0.947816 | − | 0.318819i | \(-0.103286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.80684 | − | 1.80684i | −0.0913757 | − | 0.0913757i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.6846 | + | 16.6846i | 0.841625 | + | 0.841625i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.95098 | − | 8.95098i | −0.450373 | − | 0.450373i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.83348 | − | 6.83348i | 0.342962 | − | 0.342962i | −0.514517 | − | 0.857480i | \(-0.672029\pi\) |
0.857480 | + | 0.514517i | \(0.172029\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.10614 | + | 5.10614i | −0.255627 | + | 0.255627i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.3776i | 0.917732i | 0.888505 | + | 0.458866i | \(0.151744\pi\) | ||||
−0.888505 | + | 0.458866i | \(0.848256\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.46921 | − | 6.46921i | 0.322254 | − | 0.322254i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.5201i | 0.771202i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.9779 | − | 16.9779i | 0.841565 | − | 0.841565i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.3286 | −1.59855 | −0.799273 | − | 0.600968i | \(-0.794782\pi\) | ||||
−0.799273 | + | 0.600968i | \(0.794782\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 33.9338 | 1.67383 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.52780 | − | 8.52780i | 0.419626 | − | 0.419626i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.15532i | − | 0.400329i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −42.1391 | + | 42.1391i | −2.06356 | + | 2.06356i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 30.0922i | − | 1.47010i | −0.678014 | − | 0.735049i | \(-0.737159\pi\) | ||
0.678014 | − | 0.735049i | \(-0.262841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.865599 | − | 0.865599i | 0.0421867 | − | 0.0421867i | −0.685699 | − | 0.727885i | \(-0.740503\pi\) |
0.727885 | + | 0.685699i | \(0.240503\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.36855 | − | 7.36855i | 0.358271 | − | 0.358271i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.09006 | − | 4.09006i | −0.198397 | − | 0.198397i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.47044 | − | 1.47044i | −0.0711598 | − | 0.0711598i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.90434 | − | 6.90434i | −0.333345 | − | 0.333345i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.4284i | 0.550488i | 0.961374 | + | 0.275244i | \(0.0887586\pi\) | ||||
−0.961374 | + | 0.275244i | \(0.911241\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.5678 | 1.32482 | 0.662412 | − | 0.749140i | \(-0.269533\pi\) | ||||
0.662412 | + | 0.749140i | \(0.269533\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −31.4970 | −1.51017 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.23097 | + | 3.23097i | 0.154558 | + | 0.154558i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.3450 | + | 17.3450i | −0.827829 | + | 0.827829i | −0.987216 | − | 0.159387i | \(-0.949048\pi\) |
0.159387 | + | 0.987216i | \(0.449048\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.95177 | −0.188180 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.3005i | 1.67718i | 0.544763 | + | 0.838590i | \(0.316619\pi\) | ||||
−0.544763 | + | 0.838590i | \(0.683381\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.7953 | − | 28.7953i | −1.36503 | − | 1.36503i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 63.7582 | 3.01566 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.647504i | 0.0305576i | 0.999883 | + | 0.0152788i | \(0.00486358\pi\) | ||||
−0.999883 | + | 0.0152788i | \(0.995136\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.3664 | − | 9.50136i | −1.19446 | − | 0.447401i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 13.2471i | − | 0.622402i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.59344 | 0.121582 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.1129 | − | 12.1129i | −0.566616 | − | 0.566616i | 0.364563 | − | 0.931179i | \(-0.381218\pi\) |
−0.931179 | + | 0.364563i | \(0.881218\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 3.84350i | − | 0.179399i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.3612 | 1.13462 | 0.567308 | − | 0.823506i | \(-0.307985\pi\) | ||||
0.567308 | + | 0.823506i | \(0.307985\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.63968 | + | 5.63968i | −0.262098 | + | 0.262098i | −0.825906 | − | 0.563808i | \(-0.809336\pi\) |
0.563808 | + | 0.825906i | \(0.309336\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 57.7228 | + | 57.7228i | 2.67683 | + | 2.67683i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.0389 | 1.52886 | 0.764430 | − | 0.644707i | \(-0.223021\pi\) | ||||
0.764430 | + | 0.644707i | \(0.223021\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.74593 | −0.219147 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.8729i | 0.593153i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.738488 | − | 0.738488i | −0.0339557 | − | 0.0339557i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.31380 | + | 7.31380i | 0.335580 | + | 0.335580i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.39551 | + | 9.39551i | 0.430191 | + | 0.430191i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.6584 | − | 10.6584i | 0.486993 | − | 0.486993i | −0.420363 | − | 0.907356i | \(-0.638097\pi\) |
0.907356 | + | 0.420363i | \(0.138097\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.51337 | − | 3.51337i | 0.160196 | − | 0.160196i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.39881i | 0.200153i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33.1696 | − | 33.1696i | 1.50616 | − | 1.50616i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.6853i | 1.39048i | 0.718776 | + | 0.695242i | \(0.244703\pi\) | ||||
−0.718776 | + | 0.695242i | \(0.755297\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.1041 | + | 24.1041i | −1.09003 | + | 1.09003i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.89308 | −0.175692 | −0.0878461 | − | 0.996134i | \(-0.527998\pi\) | ||||
−0.0878461 | + | 0.996134i | \(0.527998\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.17598 | −0.278152 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 35.0199 | − | 35.0199i | 1.57403 | − | 1.57403i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.1305i | 0.499273i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.34648 | − | 3.34648i | 0.149809 | − | 0.149809i | −0.628224 | − | 0.778033i | \(-0.716218\pi\) |
0.778033 | + | 0.628224i | \(0.216218\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 22.4630i | − | 1.00357i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.0237 | + | 16.0237i | −0.714460 | + | 0.714460i | −0.967465 | − | 0.253005i | \(-0.918581\pi\) |
0.253005 | + | 0.967465i | \(0.418581\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 35.4774 | − | 35.4774i | 1.57873 | − | 1.57873i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.8081 | + | 22.8081i | 1.01294 | + | 1.01294i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.4686 | − | 20.4686i | −0.907257 | − | 0.907257i | 0.0887935 | − | 0.996050i | \(-0.471699\pi\) |
−0.996050 | + | 0.0887935i | \(0.971699\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.50370 | − | 1.50370i | −0.0665196 | − | 0.0665196i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.87291i | 0.303446i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.4379 | −0.592144 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.1553 | 0.490609 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.1991 | + | 20.1991i | 0.886642 | + | 0.886642i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.70892 | + | 3.70892i | −0.162491 | + | 0.162491i | −0.783669 | − | 0.621179i | \(-0.786654\pi\) |
0.621179 | + | 0.783669i | \(0.286654\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.5018 | 1.37748 | 0.688738 | − | 0.725010i | \(-0.258165\pi\) | ||||
0.688738 | + | 0.725010i | \(0.258165\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.95739i | 0.434576i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.3184 | + | 11.3184i | 0.493036 | + | 0.493036i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.2166 | −0.878983 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 47.6589i | − | 2.06822i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.24924 | − | 1.96618i | −0.227370 | − | 0.0851648i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 14.9215i | − | 0.645114i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 42.6874 | 1.84210 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.99130 | − | 2.99130i | −0.128845 | − | 0.128845i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 19.6275i | − | 0.843852i | −0.906630 | − | 0.421926i | \(-0.861354\pi\) | ||
0.906630 | − | 0.421926i | \(-0.138646\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 51.4300 | 2.20707 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.3906 | − | 22.3906i | 0.959107 | − | 0.959107i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.7488 | − | 13.7488i | −0.587858 | − | 0.587858i | 0.349193 | − | 0.937051i | \(-0.386456\pi\) |
−0.937051 | + | 0.349193i | \(0.886456\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.21779 | −0.350727 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.0438 | 0.470483 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.27290i | 0.181702i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 31.3487 | + | 31.3487i | 1.33068 | + | 1.33068i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.950248 | − | 0.950248i | −0.0402633 | − | 0.0402633i | 0.686688 | − | 0.726952i | \(-0.259064\pi\) |
−0.726952 | + | 0.686688i | \(0.759064\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.152821 | − | 0.152821i | −0.00646362 | − | 0.00646362i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0797 | − | 12.0797i | 0.510004 | − | 0.510004i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.8627 | − | 29.8627i | 1.25856 | − | 1.25856i | 0.306781 | − | 0.951780i | \(-0.400748\pi\) |
0.951780 | − | 0.306781i | \(-0.0992520\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 45.7921i | − | 1.92649i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.70440 | − | 3.70440i | 0.155570 | − | 0.155570i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 30.1543i | − | 1.26413i | −0.774914 | − | 0.632067i | \(-0.782207\pi\) | ||
0.774914 | − | 0.632067i | \(-0.217793\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.0634064 | + | 0.0634064i | −0.00265348 | + | 0.00265348i | −0.708432 | − | 0.705779i | \(-0.750597\pi\) |
0.705779 | + | 0.708432i | \(0.250597\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −44.5066 | −1.85929 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.30065 | 0.262755 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.1147 | + | 25.1147i | −1.04554 | + | 1.04554i | −0.0466249 | + | 0.998912i | \(0.514847\pi\) |
−0.998912 | + | 0.0466249i | \(0.985153\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 2.76026i | − | 0.114712i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.94654 | + | 1.94654i | −0.0807561 | + | 0.0807561i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.2239i | 0.589094i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.24691 | − | 7.24691i | 0.299623 | − | 0.299623i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.8322 | − | 27.8322i | 1.14876 | − | 1.14876i | 0.161961 | − | 0.986797i | \(-0.448218\pi\) |
0.986797 | − | 0.161961i | \(-0.0517817\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.2394 | − | 20.2394i | −0.833949 | − | 0.833949i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.4932 | + | 19.4932i | 0.801842 | + | 0.801842i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.79150 | + | 8.79150i | 0.361023 | + | 0.361023i | 0.864190 | − | 0.503166i | \(-0.167832\pi\) |
−0.503166 | + | 0.864190i | \(0.667832\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.53742i | 0.186016i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.6283 | 0.721480 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.6899 | −1.33567 | −0.667837 | − | 0.744308i | \(-0.732780\pi\) | ||||
−0.667837 | + | 0.744308i | \(0.732780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.8995 | + | 28.8995i | 1.17883 | + | 1.17883i | 0.980042 | + | 0.198792i | \(0.0637020\pi\) |
0.198792 | + | 0.980042i | \(0.436298\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.2617 | + | 13.2617i | −0.540057 | + | 0.540057i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.4290 | 0.830557 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.35383i | − | 0.0549502i | −0.999622 | − | 0.0274751i | \(-0.991253\pi\) | ||
0.999622 | − | 0.0274751i | \(-0.00874670\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.51782 | + | 7.51782i | 0.304637 | + | 0.304637i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.30844 | 0.0933896 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.1444i | 1.74259i | 0.490764 | + | 0.871293i | \(0.336718\pi\) | ||||
−0.490764 | + | 0.871293i | \(0.663282\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.5437 | − | 46.8374i | 0.707429 | − | 1.88867i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.3454i | 1.58399i | 0.610529 | + | 0.791994i | \(0.290957\pi\) | ||||
−0.610529 | + | 0.791994i | \(0.709043\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.3816 | −1.50249 | −0.751246 | − | 0.660022i | \(-0.770547\pi\) | ||||
−0.751246 | + | 0.660022i | \(0.770547\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.96042 | + | 2.96042i | 0.118798 | + | 0.118798i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.7459i | 0.550718i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.6204 | −1.18481 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.6007 | + | 21.6007i | −0.862650 | + | 0.862650i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.14690 | + | 6.14690i | 0.245093 | + | 0.245093i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.9832 | 1.11399 | 0.556997 | − | 0.830515i | \(-0.311954\pi\) | ||||
0.556997 | + | 0.830515i | \(0.311954\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.14327 | −0.204426 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.3240i | 0.409697i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.619012 | − | 0.619012i | −0.0245261 | − | 0.0245261i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 31.1024 | + | 31.1024i | 1.23039 | + | 1.23039i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.77628 | + | 4.77628i | 0.188652 | + | 0.188652i | 0.795113 | − | 0.606461i | \(-0.207411\pi\) |
−0.606461 | + | 0.795113i | \(0.707411\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.3684 | − | 35.3684i | 1.39480 | − | 1.39480i | 0.580622 | − | 0.814173i | \(-0.302809\pi\) |
0.814173 | − | 0.580622i | \(-0.197191\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.36357 | − | 1.36357i | 0.0536906 | − | 0.0536906i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.9182i | 0.507868i | 0.967221 | + | 0.253934i | \(0.0817247\pi\) | ||||
−0.967221 | + | 0.253934i | \(0.918275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.0755 | − | 36.0755i | 1.41609 | − | 1.41609i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 27.5550i | − | 1.07996i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.7030 | + | 12.7030i | −0.497109 | + | 0.497109i | −0.910537 | − | 0.413428i | \(-0.864331\pi\) |
0.413428 | + | 0.910537i | \(0.364331\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.5121 | −1.03591 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.40363 | −0.327857 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.0826 | − | 22.0826i | 0.860216 | − | 0.860216i | −0.131147 | − | 0.991363i | \(-0.541866\pi\) |
0.991363 | + | 0.131147i | \(0.0418659\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 43.6695i | − | 1.69855i | −0.527953 | − | 0.849274i | \(-0.677040\pi\) | ||
0.527953 | − | 0.849274i | \(-0.322960\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.49973 | − | 2.49973i | 0.0970815 | − | 0.0970815i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 8.11377i | − | 0.314638i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.75699 | − | 4.75699i | 0.184191 | − | 0.184191i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.07174 | + | 7.07174i | −0.273409 | + | 0.273409i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.22048 | − | 6.22048i | −0.240139 | − | 0.240139i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6853 | + | 11.6853i | 0.450437 | + | 0.450437i | 0.895499 | − | 0.445063i | \(-0.146819\pi\) |
−0.445063 | + | 0.895499i | \(0.646819\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.70136 | + | 6.70136i | 0.257936 | + | 0.257936i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 10.4067i | − | 0.399963i | −0.979800 | − | 0.199981i | \(-0.935912\pi\) | ||
0.979800 | − | 0.199981i | \(-0.0640882\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.8341 | −0.607657 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −48.4813 | −1.85781 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.00945 | − | 5.00945i | −0.191681 | − | 0.191681i | 0.604741 | − | 0.796422i | \(-0.293277\pi\) |
−0.796422 | + | 0.604741i | \(0.793277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.9608 | + | 26.9608i | −1.03012 | + | 1.03012i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −40.6718 | −1.55173 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.94346i | 0.112137i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.29478 | − | 9.29478i | −0.353590 | − | 0.353590i | 0.507853 | − | 0.861444i | \(-0.330439\pi\) |
−0.861444 | + | 0.507853i | \(0.830439\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.7173 | −0.635040 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 66.9600i | − | 2.53994i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.43998 | − | 9.18394i | 0.130299 | − | 0.347867i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 32.1217i | 1.21495i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.6512 | 0.817755 | 0.408878 | − | 0.912589i | \(-0.365920\pi\) | ||||
0.408878 | + | 0.912589i | \(0.365920\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.9918 | − | 10.9918i | −0.414564 | − | 0.414564i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.5975i | 0.775748i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.9358 | −0.636935 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.2112 | − | 23.2112i | 0.871717 | − | 0.871717i | −0.120943 | − | 0.992659i | \(-0.538592\pi\) |
0.992659 | + | 0.120943i | \(0.0385918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.9399 | + | 11.9399i | 0.447780 | + | 0.447780i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.4357 | −0.652973 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.9711 | 0.410297 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 16.5637i | − | 0.618582i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.30997 | + | 1.30997i | 0.0488537 | + | 0.0488537i | 0.731112 | − | 0.682258i | \(-0.239002\pi\) |
−0.682258 | + | 0.731112i | \(0.739002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.20740 | + | 3.20740i | 0.119450 | + | 0.119450i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.0509 | − | 16.0509i | −0.596940 | − | 0.596940i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.7682 | − | 10.7682i | 0.399920 | − | 0.399920i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.9337 | − | 25.9337i | 0.961828 | − | 0.961828i | −0.0374696 | − | 0.999298i | \(-0.511930\pi\) |
0.999298 | + | 0.0374696i | \(0.0119297\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 40.5521i | − | 1.50193i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.267371 | − | 0.267371i | 0.00988908 | − | 0.00988908i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 34.9903i | − | 1.29240i | −0.763170 | − | 0.646198i | \(-0.776358\pi\) | ||
0.763170 | − | 0.646198i | \(-0.223642\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.52326 | − | 5.52326i | 0.203728 | − | 0.203728i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.0769 | −0.739543 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.9176 | 1.90982 | 0.954910 | − | 0.296895i | \(-0.0959511\pi\) | ||||
0.954910 | + | 0.296895i | \(0.0959511\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.46999 | + | 4.46999i | −0.164209 | + | 0.164209i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.7958i | 1.79015i | 0.445920 | + | 0.895073i | \(0.352877\pi\) | ||||
−0.445920 | + | 0.895073i | \(0.647123\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −50.6565 | + | 50.6565i | −1.85591 | + | 1.85591i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.8785i | 0.398025i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.56153 | + | 3.56153i | −0.130135 | + | 0.130135i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.3074 | − | 25.3074i | 0.923478 | − | 0.923478i | −0.0737950 | − | 0.997273i | \(-0.523511\pi\) |
0.997273 | + | 0.0737950i | \(0.0235110\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.5846 | − | 12.5846i | −0.458608 | − | 0.458608i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.5249 | + | 10.5249i | 0.383042 | + | 0.383042i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.7127 | + | 10.7127i | 0.389360 | + | 0.389360i | 0.874459 | − | 0.485099i | \(-0.161217\pi\) |
−0.485099 | + | 0.874459i | \(0.661217\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.6085i | 0.675445i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.3994 | −1.35573 | −0.677864 | − | 0.735187i | \(-0.737094\pi\) | ||||
−0.677864 | + | 0.735187i | \(0.737094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.6885 | −0.386951 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.6790 | + | 12.6790i | 0.458411 | + | 0.458411i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.46536 | − | 7.46536i | 0.269559 | − | 0.269559i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.7162 | −1.64857 | −0.824283 | − | 0.566178i | \(-0.808422\pi\) | ||||
−0.824283 | + | 0.566178i | \(0.808422\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 36.1739i | − | 1.30277i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.26643 | − | 4.26643i | −0.153453 | − | 0.153453i | 0.626205 | − | 0.779658i | \(-0.284607\pi\) |
−0.779658 | + | 0.626205i | \(0.784607\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −39.4684 | −1.41775 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 14.9648i | − | 0.536861i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.15135 | + | 16.4226i | −0.220395 | + | 0.588402i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47.0860i | 1.68487i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.1190 | 0.361625 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.2277 | − | 10.2277i | −0.365041 | − | 0.365041i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 13.7853i | − | 0.491394i | −0.969347 | − | 0.245697i | \(-0.920983\pi\) | ||
0.969347 | − | 0.245697i | \(-0.0790168\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 66.6256 | 2.37194 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9298 | + | 10.9298i | −0.388620 | + | 0.388620i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.28725 | − | 1.28725i | −0.0457115 | − | 0.0457115i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26.2636 | −0.931473 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.6666 | −1.44049 | −0.720243 | − | 0.693722i | \(-0.755970\pi\) | ||||
−0.720243 | + | 0.693722i | \(0.755970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.03879i | 0.142882i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 38.4105 | + | 38.4105i | 1.35717 | + | 1.35717i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.36115 | − | 6.36115i | −0.224480 | − | 0.224480i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.49490 | − | 3.49490i | −0.123179 | − | 0.123179i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.2198 | − | 12.2198i | 0.430158 | − | 0.430158i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5316 | − | 19.5316i | 0.686694 | − | 0.686694i | −0.274806 | − | 0.961500i | \(-0.588614\pi\) |
0.961500 | + | 0.274806i | \(0.0886136\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 42.8058i | − | 1.50311i | −0.659668 | − | 0.751557i | \(-0.729303\pi\) | ||
0.659668 | − | 0.751557i | \(-0.270697\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.7724 | + | 25.7724i | −0.903876 | + | 0.903876i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 38.3020i | − | 1.34166i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.478110 | + | 0.478110i | −0.0167270 | + | 0.0167270i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.45944 | −0.120883 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.0891 | 0.910517 | 0.455259 | − | 0.890359i | \(-0.349547\pi\) | ||||
0.455259 | + | 0.890359i | \(0.349547\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.6628 | − | 19.6628i | 0.685403 | − | 0.685403i | −0.275810 | − | 0.961212i | \(-0.588946\pi\) |
0.961212 | + | 0.275810i | \(0.0889459\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 42.1232i | 1.46654i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.9153 | + | 12.9153i | −0.449110 | + | 0.449110i | −0.895058 | − | 0.445949i | \(-0.852866\pi\) |
0.445949 | + | 0.895058i | \(0.352866\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 30.6211i | − | 1.06351i | −0.846897 | − | 0.531757i | \(-0.821532\pi\) | ||
0.846897 | − | 0.531757i | \(-0.178468\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.0194 | − | 21.0194i | 0.729154 | − | 0.729154i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.08301 | − | 1.08301i | 0.0375240 | − | 0.0375240i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.8471 | + | 17.8471i | 0.617625 | + | 0.617625i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.5446 | − | 18.5446i | −0.640995 | − | 0.640995i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.0032 | − | 13.0032i | −0.448920 | − | 0.448920i | 0.446076 | − | 0.894995i | \(-0.352821\pi\) |
−0.894995 | + | 0.446076i | \(0.852821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7401i | 0.439313i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 59.5701 | 2.05170 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −36.2425 | −1.24678 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.87607 | − | 4.87607i | −0.167544 | − | 0.167544i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24.2335 | + | 24.2335i | −0.831692 | + | 0.831692i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.46918 | −0.324599 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 42.5303i | − | 1.45621i | −0.685466 | − | 0.728105i | \(-0.740401\pi\) | ||
0.685466 | − | 0.728105i | \(-0.259599\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.6725 | − | 22.6725i | −0.775383 | − | 0.775383i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.0333 | −0.650165 | −0.325082 | − | 0.945686i | \(-0.605392\pi\) | ||||
−0.325082 | + | 0.945686i | \(0.605392\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.584577i | 0.0199455i | 0.999950 | + | 0.00997276i | \(0.00317448\pi\) | ||||
−0.999950 | + | 0.00997276i | \(0.996826\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.3667 | + | 6.99193i | −0.523696 | + | 0.238284i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.6794i | 0.874137i | 0.899428 | + | 0.437069i | \(0.143983\pi\) | ||||
−0.899428 | + | 0.437069i | \(0.856017\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.0968 | −1.09132 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −27.3209 | − | 27.3209i | −0.927865 | − | 0.927865i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.0758i | 0.613181i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.15466 | −0.140775 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −44.2456 | + | 44.2456i | −1.49749 | + | 1.49749i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.56287 | + | 2.56287i | 0.0866407 | + | 0.0866407i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.0559 | 1.11622 | 0.558109 | − | 0.829768i | \(-0.311527\pi\) | ||||
0.558109 | + | 0.829768i | \(0.311527\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −55.6461 | −1.87690 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 22.5032i | − | 0.758152i | −0.925365 | − | 0.379076i | \(-0.876242\pi\) | ||
0.925365 | − | 0.379076i | \(-0.123758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.25723 | + | 8.25723i | 0.277878 | + | 0.277878i | 0.832261 | − | 0.554383i | \(-0.187046\pi\) |
−0.554383 | + | 0.832261i | \(0.687046\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 66.6112 | + | 66.6112i | 2.23911 | + | 2.23911i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.3633 | + | 40.3633i | 1.35527 | + | 1.35527i | 0.879654 | + | 0.475614i | \(0.157774\pi\) |
0.475614 | + | 0.879654i | \(0.342226\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.46418 | − | 2.46418i | 0.0826459 | − | 0.0826459i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.6709 | − | 15.6709i | 0.524995 | − | 0.524995i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 7.22213i | − | 0.241679i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.9156 | + | 33.9156i | −1.13367 | + | 1.13367i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.85079i | 0.128574i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.7986 | + | 29.7986i | −0.993840 | + | 0.993840i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.14980 | −0.171565 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.650925 | −0.0216614 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.8617 | + | 40.8617i | −1.35829 | + | 1.35829i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.08994i | − | 0.0693952i | −0.999398 | − | 0.0346976i | \(-0.988953\pi\) | ||
0.999398 | − | 0.0346976i | \(-0.0110468\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −47.3240 | + | 47.3240i | −1.56964 | + | 1.56964i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.5975i | 0.516770i | 0.966042 | + | 0.258385i | \(0.0831903\pi\) | ||||
−0.966042 | + | 0.258385i | \(0.916810\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.23453 | + | 8.23453i | −0.272523 | + | 0.272523i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.4857 | − | 11.4857i | 0.379706 | − | 0.379706i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.32801 | + | 6.32801i | 0.208969 | + | 0.208969i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.0984 | − | 37.0984i | −1.22376 | − | 1.22376i | −0.966284 | − | 0.257480i | \(-0.917108\pi\) |
−0.257480 | − | 0.966284i | \(-0.582892\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 43.3530 | + | 43.3530i | 1.42853 | + | 1.42853i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.74385i | 0.320723i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.4349 | −0.704776 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.9251 | 0.588736 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.8169 | + | 16.8169i | 0.551744 | + | 0.551744i | 0.926944 | − | 0.375200i | \(-0.122426\pi\) |
−0.375200 | + | 0.926944i | \(0.622426\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.93662 | + | 1.93662i | −0.0634703 | + | 0.0634703i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −37.2540 | −1.21964 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.1948i | 0.627738i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.3030 | − | 39.3030i | −1.28397 | − | 1.28397i | −0.938386 | − | 0.345588i | \(-0.887680\pi\) |
−0.345588 | − | 0.938386i | \(-0.612320\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.2813 | 0.759757 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.1124i | 0.916438i | 0.888839 | + | 0.458219i | \(0.151512\pi\) | ||||
−0.888839 | + | 0.458219i | \(0.848488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.42423 | + | 9.72346i | 0.144073 | + | 0.316639i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 7.43435i | − | 0.241839i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.13257 | 0.296769 | 0.148384 | − | 0.988930i | \(-0.452593\pi\) | ||||
0.148384 | + | 0.988930i | \(0.452593\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.31636 | − | 1.31636i | −0.0427308 | − | 0.0427308i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.0521i | 0.747517i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.0482 | −0.455067 | −0.227533 | − | 0.973770i | \(-0.573066\pi\) | ||||
−0.227533 | + | 0.973770i | \(0.573066\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35.3610 | − | 35.3610i | 1.14425 | − | 1.14425i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 31.8030 | + | 31.8030i | 1.02804 | + | 1.02804i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.8702 | 0.415600 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.2205 | 2.52324 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.9041i | 0.641401i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.19305 | + | 2.19305i | 0.0705969 | + | 0.0705969i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.5838 | − | 13.5838i | −0.436824 | − | 0.436824i | 0.454118 | − | 0.890942i | \(-0.349955\pi\) |
−0.890942 | + | 0.454118i | \(0.849955\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.82059 | − | 7.82059i | −0.251234 | − | 0.251234i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.00491 | + | 2.00491i | −0.0643406 | + | 0.0643406i | −0.738545 | − | 0.674204i | \(-0.764487\pi\) |
0.674204 | + | 0.738545i | \(0.264487\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.9822 | + | 15.9822i | −0.512367 | + | 0.512367i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.71684i | 0.279162i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.22498 | − | 2.22498i | 0.0711835 | − | 0.0711835i | −0.670619 | − | 0.741802i | \(-0.733971\pi\) |
0.741802 | + | 0.670619i | \(0.233971\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.1499i | 1.85848i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.8672 | + | 29.8672i | −0.953586 | + | 0.953586i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.38864 | −0.0761859 | −0.0380929 | − | 0.999274i | \(-0.512128\pi\) | ||||
−0.0380929 | + | 0.999274i | \(0.512128\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.9751 | −0.986948 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.91629 | − | 4.91629i | 0.156487 | − | 0.156487i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.411880i | 0.0130970i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.56538 | − | 6.56538i | 0.208556 | − | 0.208556i | −0.595097 | − | 0.803654i | \(-0.702887\pi\) |
0.803654 | + | 0.595097i | \(0.202887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 5.28339i | − | 0.167663i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.0059 | + | 14.0059i | −0.444017 | + | 0.444017i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.2458 | − | 22.2458i | 0.704533 | − | 0.704533i | −0.260847 | − | 0.965380i | \(-0.584002\pi\) |
0.965380 | + | 0.260847i | \(0.0840019\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.0714 | − | 10.0714i | −0.318645 | − | 0.318645i |
(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 | 1148.2.k.b.729.17 | yes | 36 | |
41.9 | even | 4 | inner | 1148.2.k.b.337.17 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.k.b.337.17 | ✓ | 36 | 41.9 | even | 4 | inner | |
1148.2.k.b.729.17 | yes | 36 | 1.1 | even | 1 | trivial |