Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(337,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.c (of order \(2\), degree \(1\), 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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 16x^{10} + 96x^{8} + 266x^{6} + 332x^{4} + 141x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.3 | ||
Root | \(1.54570i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.337 |
Dual form | 1183.2.c.h.337.10 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.93488i | − 1.36817i | −0.729404 | − | 0.684083i | \(-0.760202\pi\) | ||||
0.729404 | − | 0.684083i | \(-0.239798\pi\) | |||||||
\(3\) | −2.54570 | −1.46976 | −0.734880 | − | 0.678198i | \(-0.762761\pi\) | ||||
−0.734880 | + | 0.678198i | \(0.762761\pi\) | |||||||
\(4\) | −1.74376 | −0.871880 | ||||||||
\(5\) | − 0.312100i | − 0.139575i | −0.997562 | − | 0.0697876i | \(-0.977768\pi\) | ||||
0.997562 | − | 0.0697876i | \(-0.0222322\pi\) | |||||||
\(6\) | 4.92562i | 2.01088i | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | − 0.495793i | − 0.175289i | ||||||||
\(9\) | 3.48058 | 1.16019 | ||||||||
\(10\) | −0.603875 | −0.190962 | ||||||||
\(11\) | 4.16701i | 1.25640i | 0.778052 | + | 0.628200i | \(0.216208\pi\) | ||||
−0.778052 | + | 0.628200i | \(0.783792\pi\) | |||||||
\(12\) | 4.43909 | 1.28145 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.93488 | −0.517118 | ||||||||
\(15\) | 0.794512i | 0.205142i | ||||||||
\(16\) | −4.44682 | −1.11171 | ||||||||
\(17\) | 5.20672 | 1.26281 | 0.631407 | − | 0.775451i | \(-0.282478\pi\) | ||||
0.631407 | + | 0.775451i | \(0.282478\pi\) | |||||||
\(18\) | − 6.73450i | − 1.58734i | ||||||||
\(19\) | 4.87572i | 1.11857i | 0.828977 | + | 0.559283i | \(0.188923\pi\) | ||||
−0.828977 | + | 0.559283i | \(0.811077\pi\) | |||||||
\(20\) | 0.544227i | 0.121693i | ||||||||
\(21\) | 2.54570i | 0.555517i | ||||||||
\(22\) | 8.06266 | 1.71896 | ||||||||
\(23\) | −3.39655 | −0.708230 | −0.354115 | − | 0.935202i | \(-0.615218\pi\) | ||||
−0.354115 | + | 0.935202i | \(0.615218\pi\) | |||||||
\(24\) | 1.26214i | 0.257633i | ||||||||
\(25\) | 4.90259 | 0.980519 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.22341 | −0.235445 | ||||||||
\(28\) | 1.74376i | 0.329540i | ||||||||
\(29\) | 3.54362 | 0.658034 | 0.329017 | − | 0.944324i | \(-0.393283\pi\) | ||||
0.329017 | + | 0.944324i | \(0.393283\pi\) | |||||||
\(30\) | 1.53728 | 0.280668 | ||||||||
\(31\) | 9.52510i | 1.71076i | 0.518002 | + | 0.855380i | \(0.326676\pi\) | ||||
−0.518002 | + | 0.855380i | \(0.673324\pi\) | |||||||
\(32\) | 7.61248i | 1.34571i | ||||||||
\(33\) | − 10.6079i | − 1.84661i | ||||||||
\(34\) | − 10.0744i | − 1.72774i | ||||||||
\(35\) | −0.312100 | −0.0527545 | ||||||||
\(36\) | −6.06929 | −1.01155 | ||||||||
\(37\) | − 11.7368i | − 1.92951i | −0.263146 | − | 0.964756i | \(-0.584760\pi\) | ||||
0.263146 | − | 0.964756i | \(-0.415240\pi\) | |||||||
\(38\) | 9.43392 | 1.53038 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.154737 | −0.0244661 | ||||||||
\(41\) | 0.433763i | 0.0677424i | 0.999426 | + | 0.0338712i | \(0.0107836\pi\) | ||||
−0.999426 | + | 0.0338712i | \(0.989216\pi\) | |||||||
\(42\) | 4.92562 | 0.760040 | ||||||||
\(43\) | 8.96489 | 1.36713 | 0.683567 | − | 0.729888i | \(-0.260428\pi\) | ||||
0.683567 | + | 0.729888i | \(0.260428\pi\) | |||||||
\(44\) | − 7.26626i | − 1.09543i | ||||||||
\(45\) | − 1.08629i | − 0.161934i | ||||||||
\(46\) | 6.57192i | 0.968977i | ||||||||
\(47\) | 8.62354i | 1.25787i | 0.777457 | + | 0.628936i | \(0.216509\pi\) | ||||
−0.777457 | + | 0.628936i | \(0.783491\pi\) | |||||||
\(48\) | 11.3203 | 1.63394 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | − 9.48593i | − 1.34151i | ||||||||
\(51\) | −13.2547 | −1.85603 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.14124 | −0.156761 | −0.0783807 | − | 0.996924i | \(-0.524975\pi\) | ||||
−0.0783807 | + | 0.996924i | \(0.524975\pi\) | |||||||
\(54\) | 2.36714i | 0.322127i | ||||||||
\(55\) | 1.30052 | 0.175362 | ||||||||
\(56\) | −0.495793 | −0.0662532 | ||||||||
\(57\) | − 12.4121i | − 1.64402i | ||||||||
\(58\) | − 6.85649i | − 0.900301i | ||||||||
\(59\) | − 11.7192i | − 1.52571i | −0.646569 | − | 0.762855i | \(-0.723797\pi\) | ||||
0.646569 | − | 0.762855i | \(-0.276203\pi\) | |||||||
\(60\) | − 1.38544i | − 0.178859i | ||||||||
\(61\) | −4.87971 | −0.624783 | −0.312392 | − | 0.949953i | \(-0.601130\pi\) | ||||
−0.312392 | + | 0.949953i | \(0.601130\pi\) | |||||||
\(62\) | 18.4299 | 2.34060 | ||||||||
\(63\) | − 3.48058i | − 0.438512i | ||||||||
\(64\) | 5.83559 | 0.729448 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −20.5251 | −2.52646 | ||||||||
\(67\) | − 8.71761i | − 1.06503i | −0.846422 | − | 0.532513i | \(-0.821248\pi\) | ||||
0.846422 | − | 0.532513i | \(-0.178752\pi\) | |||||||
\(68\) | −9.07927 | −1.10102 | ||||||||
\(69\) | 8.64660 | 1.04093 | ||||||||
\(70\) | 0.603875i | 0.0721769i | ||||||||
\(71\) | − 6.09160i | − 0.722939i | −0.932384 | − | 0.361470i | \(-0.882275\pi\) | ||||
0.932384 | − | 0.361470i | \(-0.117725\pi\) | |||||||
\(72\) | − 1.72565i | − 0.203369i | ||||||||
\(73\) | − 3.59203i | − 0.420415i | −0.977657 | − | 0.210208i | \(-0.932586\pi\) | ||||
0.977657 | − | 0.210208i | \(-0.0674140\pi\) | |||||||
\(74\) | −22.7092 | −2.63989 | ||||||||
\(75\) | −12.4805 | −1.44113 | ||||||||
\(76\) | − 8.50208i | − 0.975255i | ||||||||
\(77\) | 4.16701 | 0.474875 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.90686 | 1.11461 | 0.557304 | − | 0.830308i | \(-0.311836\pi\) | ||||
0.557304 | + | 0.830308i | \(0.311836\pi\) | |||||||
\(80\) | 1.38785i | 0.155167i | ||||||||
\(81\) | −7.32731 | −0.814146 | ||||||||
\(82\) | 0.839279 | 0.0926829 | ||||||||
\(83\) | 0.500966i | 0.0549882i | 0.999622 | + | 0.0274941i | \(0.00875274\pi\) | ||||
−0.999622 | + | 0.0274941i | \(0.991247\pi\) | |||||||
\(84\) | − 4.43909i | − 0.484344i | ||||||||
\(85\) | − 1.62502i | − 0.176258i | ||||||||
\(86\) | − 17.3460i | − 1.87047i | ||||||||
\(87\) | −9.02100 | −0.967152 | ||||||||
\(88\) | 2.06597 | 0.220234 | ||||||||
\(89\) | 10.5068i | 1.11372i | 0.830606 | + | 0.556861i | \(0.187994\pi\) | ||||
−0.830606 | + | 0.556861i | \(0.812006\pi\) | |||||||
\(90\) | −2.10184 | −0.221553 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.92277 | 0.617492 | ||||||||
\(93\) | − 24.2480i | − 2.51440i | ||||||||
\(94\) | 16.6855 | 1.72098 | ||||||||
\(95\) | 1.52171 | 0.156124 | ||||||||
\(96\) | − 19.3791i | − 1.97787i | ||||||||
\(97\) | 2.35258i | 0.238868i | 0.992842 | + | 0.119434i | \(0.0381080\pi\) | ||||
−0.992842 | + | 0.119434i | \(0.961892\pi\) | |||||||
\(98\) | 1.93488i | 0.195452i | ||||||||
\(99\) | 14.5036i | 1.45767i | ||||||||
\(100\) | −8.54895 | −0.854895 | ||||||||
\(101\) | 6.26932 | 0.623821 | 0.311910 | − | 0.950112i | \(-0.399031\pi\) | ||||
0.311910 | + | 0.950112i | \(0.399031\pi\) | |||||||
\(102\) | 25.6463i | 2.53936i | ||||||||
\(103\) | 3.76722 | 0.371195 | 0.185598 | − | 0.982626i | \(-0.440578\pi\) | ||||
0.185598 | + | 0.982626i | \(0.440578\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.794512 | 0.0775364 | ||||||||
\(106\) | 2.20816i | 0.214476i | ||||||||
\(107\) | 4.01657 | 0.388296 | 0.194148 | − | 0.980972i | \(-0.437806\pi\) | ||||
0.194148 | + | 0.980972i | \(0.437806\pi\) | |||||||
\(108\) | 2.13333 | 0.205279 | ||||||||
\(109\) | − 4.97360i | − 0.476384i | −0.971218 | − | 0.238192i | \(-0.923445\pi\) | ||||
0.971218 | − | 0.238192i | \(-0.0765548\pi\) | |||||||
\(110\) | − 2.51635i | − 0.239925i | ||||||||
\(111\) | 29.8783i | 2.83592i | ||||||||
\(112\) | 4.44682i | 0.420185i | ||||||||
\(113\) | −13.0735 | −1.22985 | −0.614925 | − | 0.788586i | \(-0.710814\pi\) | ||||
−0.614925 | + | 0.788586i | \(0.710814\pi\) | |||||||
\(114\) | −24.0159 | −2.24930 | ||||||||
\(115\) | 1.06006i | 0.0988514i | ||||||||
\(116\) | −6.17923 | −0.573727 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −22.6753 | −2.08743 | ||||||||
\(119\) | − 5.20672i | − 0.477299i | ||||||||
\(120\) | 0.393914 | 0.0359592 | ||||||||
\(121\) | −6.36395 | −0.578541 | ||||||||
\(122\) | 9.44166i | 0.854807i | ||||||||
\(123\) | − 1.10423i | − 0.0995650i | ||||||||
\(124\) | − 16.6095i | − 1.49158i | ||||||||
\(125\) | − 3.09060i | − 0.276431i | ||||||||
\(126\) | −6.73450 | −0.599957 | ||||||||
\(127\) | 10.8005 | 0.958389 | 0.479194 | − | 0.877709i | \(-0.340929\pi\) | ||||
0.479194 | + | 0.877709i | \(0.340929\pi\) | |||||||
\(128\) | 3.93379i | 0.347701i | ||||||||
\(129\) | −22.8219 | −2.00936 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.6661 | 1.10664 | 0.553320 | − | 0.832969i | \(-0.313361\pi\) | ||||
0.553320 | + | 0.832969i | \(0.313361\pi\) | |||||||
\(132\) | 18.4977i | 1.61002i | ||||||||
\(133\) | 4.87572 | 0.422778 | ||||||||
\(134\) | −16.8675 | −1.45713 | ||||||||
\(135\) | 0.381825i | 0.0328622i | ||||||||
\(136\) | − 2.58146i | − 0.221358i | ||||||||
\(137\) | 14.7249i | 1.25803i | 0.777391 | + | 0.629017i | \(0.216543\pi\) | ||||
−0.777391 | + | 0.629017i | \(0.783457\pi\) | |||||||
\(138\) | − 16.7301i | − 1.42416i | ||||||||
\(139\) | 22.7805 | 1.93222 | 0.966111 | − | 0.258129i | \(-0.0831059\pi\) | ||||
0.966111 | + | 0.258129i | \(0.0831059\pi\) | |||||||
\(140\) | 0.544227 | 0.0459956 | ||||||||
\(141\) | − 21.9529i | − 1.84877i | ||||||||
\(142\) | −11.7865 | −0.989102 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −15.4775 | −1.28979 | ||||||||
\(145\) | − 1.10596i | − 0.0918453i | ||||||||
\(146\) | −6.95014 | −0.575198 | ||||||||
\(147\) | 2.54570 | 0.209966 | ||||||||
\(148\) | 20.4661i | 1.68230i | ||||||||
\(149\) | − 7.21670i | − 0.591215i | −0.955309 | − | 0.295608i | \(-0.904478\pi\) | ||||
0.955309 | − | 0.295608i | \(-0.0955221\pi\) | |||||||
\(150\) | 24.1483i | 1.97170i | ||||||||
\(151\) | − 0.657085i | − 0.0534728i | −0.999643 | − | 0.0267364i | \(-0.991489\pi\) | ||||
0.999643 | − | 0.0267364i | \(-0.00851148\pi\) | |||||||
\(152\) | 2.41735 | 0.196073 | ||||||||
\(153\) | 18.1224 | 1.46511 | ||||||||
\(154\) | − 8.06266i | − 0.649708i | ||||||||
\(155\) | 2.97278 | 0.238780 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.62702 | −0.688511 | −0.344255 | − | 0.938876i | \(-0.611869\pi\) | ||||
−0.344255 | + | 0.938876i | \(0.611869\pi\) | |||||||
\(158\) | − 19.1686i | − 1.52497i | ||||||||
\(159\) | 2.90525 | 0.230401 | ||||||||
\(160\) | 2.37585 | 0.187828 | ||||||||
\(161\) | 3.39655i | 0.267686i | ||||||||
\(162\) | 14.1775i | 1.11389i | ||||||||
\(163\) | 11.5337i | 0.903386i | 0.892173 | + | 0.451693i | \(0.149180\pi\) | ||||
−0.892173 | + | 0.451693i | \(0.850820\pi\) | |||||||
\(164\) | − 0.756378i | − 0.0590632i | ||||||||
\(165\) | −3.31074 | −0.257740 | ||||||||
\(166\) | 0.969309 | 0.0752330 | ||||||||
\(167\) | 10.7650i | 0.833020i | 0.909131 | + | 0.416510i | \(0.136747\pi\) | ||||
−0.909131 | + | 0.416510i | \(0.863253\pi\) | |||||||
\(168\) | 1.26214 | 0.0973762 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −3.14421 | −0.241150 | ||||||||
\(171\) | 16.9703i | 1.29775i | ||||||||
\(172\) | −15.6326 | −1.19198 | ||||||||
\(173\) | 10.1547 | 0.772045 | 0.386022 | − | 0.922489i | \(-0.373849\pi\) | ||||
0.386022 | + | 0.922489i | \(0.373849\pi\) | |||||||
\(174\) | 17.4545i | 1.32323i | ||||||||
\(175\) | − 4.90259i | − 0.370601i | ||||||||
\(176\) | − 18.5299i | − 1.39675i | ||||||||
\(177\) | 29.8336i | 2.24243i | ||||||||
\(178\) | 20.3295 | 1.52376 | ||||||||
\(179\) | 7.03271 | 0.525650 | 0.262825 | − | 0.964844i | \(-0.415346\pi\) | ||||
0.262825 | + | 0.964844i | \(0.415346\pi\) | |||||||
\(180\) | 1.89422i | 0.141187i | ||||||||
\(181\) | 21.0737 | 1.56640 | 0.783198 | − | 0.621773i | \(-0.213587\pi\) | ||||
0.783198 | + | 0.621773i | \(0.213587\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.4223 | 0.918281 | ||||||||
\(184\) | 1.68399i | 0.124145i | ||||||||
\(185\) | −3.66304 | −0.269312 | ||||||||
\(186\) | −46.9170 | −3.44012 | ||||||||
\(187\) | 21.6964i | 1.58660i | ||||||||
\(188\) | − 15.0374i | − 1.09671i | ||||||||
\(189\) | 1.22341i | 0.0889897i | ||||||||
\(190\) | − 2.94432i | − 0.213604i | ||||||||
\(191\) | −18.1189 | −1.31104 | −0.655520 | − | 0.755178i | \(-0.727550\pi\) | ||||
−0.655520 | + | 0.755178i | \(0.727550\pi\) | |||||||
\(192\) | −14.8556 | −1.07211 | ||||||||
\(193\) | − 1.53602i | − 0.110565i | −0.998471 | − | 0.0552827i | \(-0.982394\pi\) | ||||
0.998471 | − | 0.0552827i | \(-0.0176060\pi\) | |||||||
\(194\) | 4.55195 | 0.326811 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.74376 | 0.124554 | ||||||||
\(197\) | − 6.72807i | − 0.479355i | −0.970853 | − | 0.239677i | \(-0.922958\pi\) | ||||
0.970853 | − | 0.239677i | \(-0.0770417\pi\) | |||||||
\(198\) | 28.0627 | 1.99433 | ||||||||
\(199\) | −0.640433 | −0.0453991 | −0.0226995 | − | 0.999742i | \(-0.507226\pi\) | ||||
−0.0226995 | + | 0.999742i | \(0.507226\pi\) | |||||||
\(200\) | − 2.43067i | − 0.171875i | ||||||||
\(201\) | 22.1924i | 1.56533i | ||||||||
\(202\) | − 12.1304i | − 0.853491i | ||||||||
\(203\) | − 3.54362i | − 0.248714i | ||||||||
\(204\) | 23.1131 | 1.61824 | ||||||||
\(205\) | 0.135377 | 0.00945516 | ||||||||
\(206\) | − 7.28911i | − 0.507857i | ||||||||
\(207\) | −11.8220 | −0.821683 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.3171 | −1.40537 | ||||||||
\(210\) | − 1.53728i | − 0.106083i | ||||||||
\(211\) | 17.5658 | 1.20928 | 0.604638 | − | 0.796500i | \(-0.293318\pi\) | ||||
0.604638 | + | 0.796500i | \(0.293318\pi\) | |||||||
\(212\) | 1.99005 | 0.136677 | ||||||||
\(213\) | 15.5074i | 1.06255i | ||||||||
\(214\) | − 7.77157i | − 0.531254i | ||||||||
\(215\) | − 2.79794i | − 0.190818i | ||||||||
\(216\) | 0.606556i | 0.0412709i | ||||||||
\(217\) | 9.52510 | 0.646606 | ||||||||
\(218\) | −9.62331 | −0.651773 | ||||||||
\(219\) | 9.14422i | 0.617909i | ||||||||
\(220\) | −2.26780 | −0.152895 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 57.8108 | 3.88001 | ||||||||
\(223\) | 18.3241i | 1.22707i | 0.789667 | + | 0.613535i | \(0.210253\pi\) | ||||
−0.789667 | + | 0.613535i | \(0.789747\pi\) | |||||||
\(224\) | 7.61248 | 0.508630 | ||||||||
\(225\) | 17.0639 | 1.13759 | ||||||||
\(226\) | 25.2956i | 1.68264i | ||||||||
\(227\) | − 0.673988i | − 0.0447342i | −0.999750 | − | 0.0223671i | \(-0.992880\pi\) | ||||
0.999750 | − | 0.0223671i | \(-0.00712026\pi\) | |||||||
\(228\) | 21.6437i | 1.43339i | ||||||||
\(229\) | 19.4805i | 1.28730i | 0.765318 | + | 0.643652i | \(0.222582\pi\) | ||||
−0.765318 | + | 0.643652i | \(0.777418\pi\) | |||||||
\(230\) | 2.05110 | 0.135245 | ||||||||
\(231\) | −10.6079 | −0.697951 | ||||||||
\(232\) | − 1.75691i | − 0.115346i | ||||||||
\(233\) | 30.1222 | 1.97337 | 0.986686 | − | 0.162637i | \(-0.0520001\pi\) | ||||
0.986686 | + | 0.162637i | \(0.0520001\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.69140 | 0.175568 | ||||||||
\(236\) | 20.4355i | 1.33024i | ||||||||
\(237\) | −25.2199 | −1.63821 | ||||||||
\(238\) | −10.0744 | −0.653025 | ||||||||
\(239\) | − 13.2375i | − 0.856266i | −0.903716 | − | 0.428133i | \(-0.859172\pi\) | ||||
0.903716 | − | 0.428133i | \(-0.140828\pi\) | |||||||
\(240\) | − 3.53305i | − 0.228057i | ||||||||
\(241\) | 13.3135i | 0.857596i | 0.903400 | + | 0.428798i | \(0.141063\pi\) | ||||
−0.903400 | + | 0.428798i | \(0.858937\pi\) | |||||||
\(242\) | 12.3135i | 0.791540i | ||||||||
\(243\) | 22.3233 | 1.43204 | ||||||||
\(244\) | 8.50905 | 0.544736 | ||||||||
\(245\) | 0.312100i | 0.0199393i | ||||||||
\(246\) | −2.13655 | −0.136222 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.72248 | 0.299878 | ||||||||
\(249\) | − 1.27531i | − 0.0808194i | ||||||||
\(250\) | −5.97993 | −0.378204 | ||||||||
\(251\) | −25.5724 | −1.61411 | −0.807056 | − | 0.590474i | \(-0.798941\pi\) | ||||
−0.807056 | + | 0.590474i | \(0.798941\pi\) | |||||||
\(252\) | 6.06929i | 0.382330i | ||||||||
\(253\) | − 14.1535i | − 0.889820i | ||||||||
\(254\) | − 20.8977i | − 1.31124i | ||||||||
\(255\) | 4.13680i | 0.259056i | ||||||||
\(256\) | 19.2826 | 1.20516 | ||||||||
\(257\) | −0.589113 | −0.0367478 | −0.0183739 | − | 0.999831i | \(-0.505849\pi\) | ||||
−0.0183739 | + | 0.999831i | \(0.505849\pi\) | |||||||
\(258\) | 44.1577i | 2.74914i | ||||||||
\(259\) | −11.7368 | −0.729287 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.3339 | 0.763447 | ||||||||
\(262\) | − 24.5073i | − 1.51407i | ||||||||
\(263\) | −18.5016 | −1.14085 | −0.570427 | − | 0.821348i | \(-0.693222\pi\) | ||||
−0.570427 | + | 0.821348i | \(0.693222\pi\) | |||||||
\(264\) | −5.25935 | −0.323690 | ||||||||
\(265\) | 0.356181i | 0.0218800i | ||||||||
\(266\) | − 9.43392i | − 0.578431i | ||||||||
\(267\) | − 26.7472i | − 1.63690i | ||||||||
\(268\) | 15.2014i | 0.928575i | ||||||||
\(269\) | −2.70804 | −0.165112 | −0.0825560 | − | 0.996586i | \(-0.526308\pi\) | ||||
−0.0825560 | + | 0.996586i | \(0.526308\pi\) | |||||||
\(270\) | 0.738785 | 0.0449610 | ||||||||
\(271\) | − 11.7872i | − 0.716018i | −0.933718 | − | 0.358009i | \(-0.883456\pi\) | ||||
0.933718 | − | 0.358009i | \(-0.116544\pi\) | |||||||
\(272\) | −23.1533 | −1.40388 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 28.4910 | 1.72120 | ||||||||
\(275\) | 20.4291i | 1.23192i | ||||||||
\(276\) | −15.0776 | −0.907564 | ||||||||
\(277\) | 24.0504 | 1.44505 | 0.722523 | − | 0.691347i | \(-0.242982\pi\) | ||||
0.722523 | + | 0.691347i | \(0.242982\pi\) | |||||||
\(278\) | − 44.0776i | − 2.64360i | ||||||||
\(279\) | 33.1529i | 1.98481i | ||||||||
\(280\) | 0.154737i | 0.00924730i | ||||||||
\(281\) | − 19.1899i | − 1.14477i | −0.819983 | − | 0.572387i | \(-0.806017\pi\) | ||||
0.819983 | − | 0.572387i | \(-0.193983\pi\) | |||||||
\(282\) | −42.4763 | −2.52943 | ||||||||
\(283\) | 12.2120 | 0.725930 | 0.362965 | − | 0.931803i | \(-0.381765\pi\) | ||||
0.362965 | + | 0.931803i | \(0.381765\pi\) | |||||||
\(284\) | 10.6223i | 0.630316i | ||||||||
\(285\) | −3.87381 | −0.229465 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.433763 | 0.0256042 | ||||||||
\(288\) | 26.4958i | 1.56128i | ||||||||
\(289\) | 10.1099 | 0.594702 | ||||||||
\(290\) | −2.13991 | −0.125660 | ||||||||
\(291\) | − 5.98895i | − 0.351078i | ||||||||
\(292\) | 6.26364i | 0.366552i | ||||||||
\(293\) | − 11.3644i | − 0.663914i | −0.943295 | − | 0.331957i | \(-0.892291\pi\) | ||||
0.943295 | − | 0.331957i | \(-0.107709\pi\) | |||||||
\(294\) | − 4.92562i | − 0.287268i | ||||||||
\(295\) | −3.65756 | −0.212951 | ||||||||
\(296\) | −5.81901 | −0.338223 | ||||||||
\(297\) | − 5.09794i | − 0.295813i | ||||||||
\(298\) | −13.9635 | −0.808881 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 21.7630 | 1.25649 | ||||||||
\(301\) | − 8.96489i | − 0.516728i | ||||||||
\(302\) | −1.27138 | −0.0731597 | ||||||||
\(303\) | −15.9598 | −0.916867 | ||||||||
\(304\) | − 21.6814i | − 1.24352i | ||||||||
\(305\) | 1.52296i | 0.0872043i | ||||||||
\(306\) | − 35.0647i | − 2.00451i | ||||||||
\(307\) | 8.19392i | 0.467652i | 0.972278 | + | 0.233826i | \(0.0751246\pi\) | ||||
−0.972278 | + | 0.233826i | \(0.924875\pi\) | |||||||
\(308\) | −7.26626 | −0.414034 | ||||||||
\(309\) | −9.59020 | −0.545567 | ||||||||
\(310\) | − 5.75198i | − 0.326690i | ||||||||
\(311\) | −28.5674 | −1.61991 | −0.809954 | − | 0.586493i | \(-0.800508\pi\) | ||||
−0.809954 | + | 0.586493i | \(0.800508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.40971 | 0.531869 | 0.265934 | − | 0.963991i | \(-0.414320\pi\) | ||||
0.265934 | + | 0.963991i | \(0.414320\pi\) | |||||||
\(314\) | 16.6922i | 0.941998i | ||||||||
\(315\) | −1.08629 | −0.0612054 | ||||||||
\(316\) | −17.2752 | −0.971805 | ||||||||
\(317\) | 1.95188i | 0.109628i | 0.998497 | + | 0.0548142i | \(0.0174567\pi\) | ||||
−0.998497 | + | 0.0548142i | \(0.982543\pi\) | |||||||
\(318\) | − 5.62131i | − 0.315228i | ||||||||
\(319\) | 14.7663i | 0.826754i | ||||||||
\(320\) | − 1.82129i | − 0.101813i | ||||||||
\(321\) | −10.2250 | −0.570702 | ||||||||
\(322\) | 6.57192 | 0.366239 | ||||||||
\(323\) | 25.3865i | 1.41254i | ||||||||
\(324\) | 12.7771 | 0.709837 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.3162 | 1.23598 | ||||||||
\(327\) | 12.6613i | 0.700170i | ||||||||
\(328\) | 0.215057 | 0.0118745 | ||||||||
\(329\) | 8.62354 | 0.475431 | ||||||||
\(330\) | 6.40588i | 0.352632i | ||||||||
\(331\) | 7.34325i | 0.403622i | 0.979425 | + | 0.201811i | \(0.0646826\pi\) | ||||
−0.979425 | + | 0.201811i | \(0.935317\pi\) | |||||||
\(332\) | − 0.873565i | − 0.0479431i | ||||||||
\(333\) | − 40.8507i | − 2.23861i | ||||||||
\(334\) | 20.8290 | 1.13971 | ||||||||
\(335\) | −2.72076 | −0.148651 | ||||||||
\(336\) | − 11.3203i | − 0.617571i | ||||||||
\(337\) | 23.0416 | 1.25516 | 0.627579 | − | 0.778553i | \(-0.284046\pi\) | ||||
0.627579 | + | 0.778553i | \(0.284046\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 33.2811 | 1.80758 | ||||||||
\(340\) | 2.83364i | 0.153676i | ||||||||
\(341\) | −39.6912 | −2.14940 | ||||||||
\(342\) | 32.8355 | 1.77554 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | − 4.44473i | − 0.239644i | ||||||||
\(345\) | − 2.69860i | − 0.145288i | ||||||||
\(346\) | − 19.6480i | − 1.05629i | ||||||||
\(347\) | −25.2471 | −1.35533 | −0.677667 | − | 0.735369i | \(-0.737009\pi\) | ||||
−0.677667 | + | 0.735369i | \(0.737009\pi\) | |||||||
\(348\) | 15.7305 | 0.843241 | ||||||||
\(349\) | − 2.03258i | − 0.108802i | −0.998519 | − | 0.0544008i | \(-0.982675\pi\) | ||||
0.998519 | − | 0.0544008i | \(-0.0173249\pi\) | |||||||
\(350\) | −9.48593 | −0.507044 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −31.7212 | −1.69075 | ||||||||
\(353\) | 9.68813i | 0.515647i | 0.966192 | + | 0.257824i | \(0.0830053\pi\) | ||||
−0.966192 | + | 0.257824i | \(0.916995\pi\) | |||||||
\(354\) | 57.7243 | 3.06801 | ||||||||
\(355\) | −1.90119 | −0.100904 | ||||||||
\(356\) | − 18.3214i | − 0.971032i | ||||||||
\(357\) | 13.2547i | 0.701515i | ||||||||
\(358\) | − 13.6075i | − 0.719176i | ||||||||
\(359\) | 26.9664i | 1.42323i | 0.702569 | + | 0.711616i | \(0.252036\pi\) | ||||
−0.702569 | + | 0.711616i | \(0.747964\pi\) | |||||||
\(360\) | −0.538574 | −0.0283853 | ||||||||
\(361\) | −4.77260 | −0.251189 | ||||||||
\(362\) | − 40.7751i | − 2.14309i | ||||||||
\(363\) | 16.2007 | 0.850316 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.12107 | −0.0586796 | ||||||||
\(366\) | − 24.0356i | − 1.25636i | ||||||||
\(367\) | −6.58796 | −0.343888 | −0.171944 | − | 0.985107i | \(-0.555005\pi\) | ||||
−0.171944 | + | 0.985107i | \(0.555005\pi\) | |||||||
\(368\) | 15.1039 | 0.787343 | ||||||||
\(369\) | 1.50975i | 0.0785942i | ||||||||
\(370\) | 7.08754i | 0.368464i | ||||||||
\(371\) | 1.14124i | 0.0592502i | ||||||||
\(372\) | 42.2828i | 2.19226i | ||||||||
\(373\) | 16.5944 | 0.859225 | 0.429613 | − | 0.903013i | \(-0.358650\pi\) | ||||
0.429613 | + | 0.903013i | \(0.358650\pi\) | |||||||
\(374\) | 41.9800 | 2.17073 | ||||||||
\(375\) | 7.86773i | 0.406288i | ||||||||
\(376\) | 4.27549 | 0.220492 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.36714 | 0.121753 | ||||||||
\(379\) | 30.7940i | 1.58178i | 0.611959 | + | 0.790890i | \(0.290382\pi\) | ||||
−0.611959 | + | 0.790890i | \(0.709618\pi\) | |||||||
\(380\) | −2.65350 | −0.136121 | ||||||||
\(381\) | −27.4948 | −1.40860 | ||||||||
\(382\) | 35.0579i | 1.79372i | ||||||||
\(383\) | − 28.2978i | − 1.44595i | −0.690875 | − | 0.722974i | \(-0.742774\pi\) | ||||
0.690875 | − | 0.722974i | \(-0.257226\pi\) | |||||||
\(384\) | − 10.0142i | − 0.511038i | ||||||||
\(385\) | − 1.30052i | − 0.0662807i | ||||||||
\(386\) | −2.97202 | −0.151272 | ||||||||
\(387\) | 31.2030 | 1.58614 | ||||||||
\(388\) | − 4.10233i | − 0.208264i | ||||||||
\(389\) | −12.9393 | −0.656047 | −0.328024 | − | 0.944670i | \(-0.606383\pi\) | ||||
−0.328024 | + | 0.944670i | \(0.606383\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.6849 | −0.894364 | ||||||||
\(392\) | 0.495793i | 0.0250413i | ||||||||
\(393\) | −32.2440 | −1.62650 | ||||||||
\(394\) | −13.0180 | −0.655837 | ||||||||
\(395\) | − 3.09193i | − 0.155572i | ||||||||
\(396\) | − 25.2908i | − 1.27091i | ||||||||
\(397\) | − 18.3110i | − 0.919004i | −0.888177 | − | 0.459502i | \(-0.848028\pi\) | ||||
0.888177 | − | 0.459502i | \(-0.151972\pi\) | |||||||
\(398\) | 1.23916i | 0.0621135i | ||||||||
\(399\) | −12.4121 | −0.621382 | ||||||||
\(400\) | −21.8010 | −1.09005 | ||||||||
\(401\) | − 1.31244i | − 0.0655402i | −0.999463 | − | 0.0327701i | \(-0.989567\pi\) | ||||
0.999463 | − | 0.0327701i | \(-0.0104329\pi\) | |||||||
\(402\) | 42.9397 | 2.14164 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −10.9322 | −0.543897 | ||||||||
\(405\) | 2.28685i | 0.113635i | ||||||||
\(406\) | −6.85649 | −0.340282 | ||||||||
\(407\) | 48.9072 | 2.42424 | ||||||||
\(408\) | 6.57161i | 0.325343i | ||||||||
\(409\) | − 29.3018i | − 1.44888i | −0.689338 | − | 0.724440i | \(-0.742099\pi\) | ||||
0.689338 | − | 0.724440i | \(-0.257901\pi\) | |||||||
\(410\) | − 0.261939i | − 0.0129362i | ||||||||
\(411\) | − 37.4852i | − 1.84901i | ||||||||
\(412\) | −6.56912 | −0.323638 | ||||||||
\(413\) | −11.7192 | −0.576664 | ||||||||
\(414\) | 22.8741i | 1.12420i | ||||||||
\(415\) | 0.156351 | 0.00767499 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −57.9924 | −2.83990 | ||||||||
\(418\) | 39.3112i | 1.92277i | ||||||||
\(419\) | −0.303569 | −0.0148303 | −0.00741516 | − | 0.999973i | \(-0.502360\pi\) | ||||
−0.00741516 | + | 0.999973i | \(0.502360\pi\) | |||||||
\(420\) | −1.38544 | −0.0676024 | ||||||||
\(421\) | 1.19312i | 0.0581492i | 0.999577 | + | 0.0290746i | \(0.00925604\pi\) | ||||
−0.999577 | + | 0.0290746i | \(0.990744\pi\) | |||||||
\(422\) | − 33.9876i | − 1.65449i | ||||||||
\(423\) | 30.0149i | 1.45937i | ||||||||
\(424\) | 0.565819i | 0.0274786i | ||||||||
\(425\) | 25.5264 | 1.23821 | ||||||||
\(426\) | 30.0049 | 1.45374 | ||||||||
\(427\) | 4.87971i | 0.236146i | ||||||||
\(428\) | −7.00393 | −0.338548 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.41368 | −0.261071 | ||||||||
\(431\) | 22.7978i | 1.09813i | 0.835780 | + | 0.549065i | \(0.185016\pi\) | ||||
−0.835780 | + | 0.549065i | \(0.814984\pi\) | |||||||
\(432\) | 5.44027 | 0.261745 | ||||||||
\(433\) | 4.00964 | 0.192691 | 0.0963455 | − | 0.995348i | \(-0.469285\pi\) | ||||
0.0963455 | + | 0.995348i | \(0.469285\pi\) | |||||||
\(434\) | − 18.4299i | − 0.884665i | ||||||||
\(435\) | 2.81545i | 0.134991i | ||||||||
\(436\) | 8.67276i | 0.415350i | ||||||||
\(437\) | − 16.5606i | − 0.792202i | ||||||||
\(438\) | 17.6930 | 0.845403 | ||||||||
\(439\) | 2.55835 | 0.122103 | 0.0610516 | − | 0.998135i | \(-0.480555\pi\) | ||||
0.0610516 | + | 0.998135i | \(0.480555\pi\) | |||||||
\(440\) | − 0.644790i | − 0.0307392i | ||||||||
\(441\) | −3.48058 | −0.165742 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.363292 | 0.0172605 | 0.00863026 | − | 0.999963i | \(-0.497253\pi\) | ||||
0.00863026 | + | 0.999963i | \(0.497253\pi\) | |||||||
\(444\) | − 52.1005i | − 2.47258i | ||||||||
\(445\) | 3.27918 | 0.155448 | ||||||||
\(446\) | 35.4549 | 1.67884 | ||||||||
\(447\) | 18.3715i | 0.868944i | ||||||||
\(448\) | − 5.83559i | − 0.275706i | ||||||||
\(449\) | 15.3032i | 0.722202i | 0.932527 | + | 0.361101i | \(0.117599\pi\) | ||||
−0.932527 | + | 0.361101i | \(0.882401\pi\) | |||||||
\(450\) | − 33.0165i | − 1.55641i | ||||||||
\(451\) | −1.80749 | −0.0851115 | ||||||||
\(452\) | 22.7970 | 1.07228 | ||||||||
\(453\) | 1.67274i | 0.0785922i | ||||||||
\(454\) | −1.30409 | −0.0612038 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.15383 | −0.288180 | ||||||||
\(457\) | 8.91104i | 0.416841i | 0.978039 | + | 0.208420i | \(0.0668322\pi\) | ||||
−0.978039 | + | 0.208420i | \(0.933168\pi\) | |||||||
\(458\) | 37.6923 | 1.76125 | ||||||||
\(459\) | −6.36993 | −0.297323 | ||||||||
\(460\) | − 1.84850i | − 0.0861866i | ||||||||
\(461\) | 21.4636i | 0.999657i | 0.866124 | + | 0.499829i | \(0.166604\pi\) | ||||
−0.866124 | + | 0.499829i | \(0.833396\pi\) | |||||||
\(462\) | 20.5251i | 0.954914i | ||||||||
\(463\) | − 3.09472i | − 0.143824i | −0.997411 | − | 0.0719119i | \(-0.977090\pi\) | ||||
0.997411 | − | 0.0719119i | \(-0.0229101\pi\) | |||||||
\(464\) | −15.7579 | −0.731540 | ||||||||
\(465\) | −7.56781 | −0.350949 | ||||||||
\(466\) | − 58.2829i | − 2.69990i | ||||||||
\(467\) | −20.9079 | −0.967503 | −0.483751 | − | 0.875205i | \(-0.660726\pi\) | ||||
−0.483751 | + | 0.875205i | \(0.660726\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.71761 | −0.402542 | ||||||||
\(470\) | − 5.20755i | − 0.240206i | ||||||||
\(471\) | 21.9618 | 1.01195 | ||||||||
\(472\) | −5.81030 | −0.267441 | ||||||||
\(473\) | 37.3568i | 1.71767i | ||||||||
\(474\) | 48.7974i | 2.24134i | ||||||||
\(475\) | 23.9037i | 1.09677i | ||||||||
\(476\) | 9.07927i | 0.416148i | ||||||||
\(477\) | −3.97217 | −0.181873 | ||||||||
\(478\) | −25.6131 | −1.17151 | ||||||||
\(479\) | 18.3562i | 0.838715i | 0.907821 | + | 0.419357i | \(0.137745\pi\) | ||||
−0.907821 | + | 0.419357i | \(0.862255\pi\) | |||||||
\(480\) | −6.04820 | −0.276061 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 25.7600 | 1.17333 | ||||||||
\(483\) | − 8.64660i | − 0.393434i | ||||||||
\(484\) | 11.0972 | 0.504418 | ||||||||
\(485\) | 0.734238 | 0.0333400 | ||||||||
\(486\) | − 43.1930i | − 1.95927i | ||||||||
\(487\) | 13.3086i | 0.603070i | 0.953455 | + | 0.301535i | \(0.0974990\pi\) | ||||
−0.953455 | + | 0.301535i | \(0.902501\pi\) | |||||||
\(488\) | 2.41933i | 0.109518i | ||||||||
\(489\) | − 29.3612i | − 1.32776i | ||||||||
\(490\) | 0.603875 | 0.0272803 | ||||||||
\(491\) | 14.5460 | 0.656452 | 0.328226 | − | 0.944599i | \(-0.393549\pi\) | ||||
0.328226 | + | 0.944599i | \(0.393549\pi\) | |||||||
\(492\) | 1.92551i | 0.0868087i | ||||||||
\(493\) | 18.4507 | 0.830976 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.52657 | 0.203454 | ||||||||
\(496\) | − 42.3564i | − 1.90186i | ||||||||
\(497\) | −6.09160 | −0.273245 | ||||||||
\(498\) | −2.46757 | −0.110574 | ||||||||
\(499\) | − 31.7570i | − 1.42164i | −0.703375 | − | 0.710819i | \(-0.748325\pi\) | ||||
0.703375 | − | 0.710819i | \(-0.251675\pi\) | |||||||
\(500\) | 5.38926i | 0.241015i | ||||||||
\(501\) | − 27.4044i | − 1.22434i | ||||||||
\(502\) | 49.4794i | 2.20838i | ||||||||
\(503\) | −16.6463 | −0.742224 | −0.371112 | − | 0.928588i | \(-0.621023\pi\) | ||||
−0.371112 | + | 0.928588i | \(0.621023\pi\) | |||||||
\(504\) | −1.72565 | −0.0768664 | ||||||||
\(505\) | − 1.95665i | − 0.0870699i | ||||||||
\(506\) | −27.3852 | −1.21742 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.8335 | −0.835600 | ||||||||
\(509\) | − 25.1990i | − 1.11693i | −0.829529 | − | 0.558463i | \(-0.811391\pi\) | ||||
0.829529 | − | 0.558463i | \(-0.188609\pi\) | |||||||
\(510\) | 8.00421 | 0.354432 | ||||||||
\(511\) | −3.59203 | −0.158902 | ||||||||
\(512\) | − 29.4419i | − 1.30116i | ||||||||
\(513\) | − 5.96498i | − 0.263360i | ||||||||
\(514\) | 1.13986i | 0.0502772i | ||||||||
\(515\) | − 1.17575i | − 0.0518096i | ||||||||
\(516\) | 39.7959 | 1.75192 | ||||||||
\(517\) | −35.9344 | −1.58039 | ||||||||
\(518\) | 22.7092i | 0.997786i | ||||||||
\(519\) | −25.8507 | −1.13472 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.9887 | −1.05096 | −0.525481 | − | 0.850805i | \(-0.676115\pi\) | ||||
−0.525481 | + | 0.850805i | \(0.676115\pi\) | |||||||
\(522\) | − 23.8645i | − 1.04452i | ||||||||
\(523\) | 12.9042 | 0.564259 | 0.282130 | − | 0.959376i | \(-0.408959\pi\) | ||||
0.282130 | + | 0.959376i | \(0.408959\pi\) | |||||||
\(524\) | −22.0866 | −0.964858 | ||||||||
\(525\) | 12.4805i | 0.544695i | ||||||||
\(526\) | 35.7983i | 1.56088i | ||||||||
\(527\) | 49.5945i | 2.16037i | ||||||||
\(528\) | 47.1716i | 2.05288i | ||||||||
\(529\) | −11.4634 | −0.498410 | ||||||||
\(530\) | 0.689167 | 0.0299355 | ||||||||
\(531\) | − 40.7896i | − 1.77012i | ||||||||
\(532\) | −8.50208 | −0.368612 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −51.7526 | −2.23956 | ||||||||
\(535\) | − 1.25357i | − 0.0541965i | ||||||||
\(536\) | −4.32213 | −0.186688 | ||||||||
\(537\) | −17.9032 | −0.772579 | ||||||||
\(538\) | 5.23973i | 0.225901i | ||||||||
\(539\) | − 4.16701i | − 0.179486i | ||||||||
\(540\) | − 0.665811i | − 0.0286519i | ||||||||
\(541\) | 11.5539i | 0.496739i | 0.968665 | + | 0.248370i | \(0.0798948\pi\) | ||||
−0.968665 | + | 0.248370i | \(0.920105\pi\) | |||||||
\(542\) | −22.8067 | −0.979633 | ||||||||
\(543\) | −53.6473 | −2.30222 | ||||||||
\(544\) | 39.6360i | 1.69938i | ||||||||
\(545\) | −1.55226 | −0.0664914 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.4142 | −1.34318 | −0.671588 | − | 0.740925i | \(-0.734387\pi\) | ||||
−0.671588 | + | 0.740925i | \(0.734387\pi\) | |||||||
\(548\) | − 25.6767i | − 1.09686i | ||||||||
\(549\) | −16.9842 | −0.724869 | ||||||||
\(550\) | 39.5279 | 1.68548 | ||||||||
\(551\) | 17.2777i | 0.736055i | ||||||||
\(552\) | − 4.28693i | − 0.182464i | ||||||||
\(553\) | − 9.90686i | − 0.421283i | ||||||||
\(554\) | − 46.5345i | − 1.97706i | ||||||||
\(555\) | 9.32499 | 0.395824 | ||||||||
\(556\) | −39.7238 | −1.68467 | ||||||||
\(557\) | − 37.9319i | − 1.60723i | −0.595151 | − | 0.803614i | \(-0.702908\pi\) | ||||
0.595151 | − | 0.803614i | \(-0.297092\pi\) | |||||||
\(558\) | 64.1468 | 2.71555 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.38785 | 0.0586474 | ||||||||
\(561\) | − 55.2326i | − 2.33192i | ||||||||
\(562\) | −37.1302 | −1.56624 | ||||||||
\(563\) | −22.3144 | −0.940438 | −0.470219 | − | 0.882550i | \(-0.655825\pi\) | ||||
−0.470219 | + | 0.882550i | \(0.655825\pi\) | |||||||
\(564\) | 38.2806i | 1.61191i | ||||||||
\(565\) | 4.08023i | 0.171657i | ||||||||
\(566\) | − 23.6288i | − 0.993193i | ||||||||
\(567\) | 7.32731i | 0.307718i | ||||||||
\(568\) | −3.02017 | −0.126724 | ||||||||
\(569\) | 4.83382 | 0.202644 | 0.101322 | − | 0.994854i | \(-0.467693\pi\) | ||||
0.101322 | + | 0.994854i | \(0.467693\pi\) | |||||||
\(570\) | 7.49536i | 0.313946i | ||||||||
\(571\) | 8.46200 | 0.354124 | 0.177062 | − | 0.984200i | \(-0.443341\pi\) | ||||
0.177062 | + | 0.984200i | \(0.443341\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 46.1253 | 1.92691 | ||||||||
\(574\) | − 0.839279i | − 0.0350308i | ||||||||
\(575\) | −16.6519 | −0.694433 | ||||||||
\(576\) | 20.3112 | 0.846301 | ||||||||
\(577\) | 9.70860i | 0.404174i | 0.979368 | + | 0.202087i | \(0.0647724\pi\) | ||||
−0.979368 | + | 0.202087i | \(0.935228\pi\) | |||||||
\(578\) | − 19.5615i | − 0.813651i | ||||||||
\(579\) | 3.91026i | 0.162505i | ||||||||
\(580\) | 1.92854i | 0.0800781i | ||||||||
\(581\) | 0.500966 | 0.0207836 | ||||||||
\(582\) | −11.5879 | −0.480333 | ||||||||
\(583\) | − 4.75555i | − 0.196955i | ||||||||
\(584\) | −1.78090 | −0.0736943 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.9887 | −0.908344 | ||||||||
\(587\) | − 5.01204i | − 0.206869i | −0.994636 | − | 0.103434i | \(-0.967017\pi\) | ||||
0.994636 | − | 0.103434i | \(-0.0329832\pi\) | |||||||
\(588\) | −4.43909 | −0.183065 | ||||||||
\(589\) | −46.4417 | −1.91360 | ||||||||
\(590\) | 7.07694i | 0.291353i | ||||||||
\(591\) | 17.1276i | 0.704536i | ||||||||
\(592\) | 52.1913i | 2.14505i | ||||||||
\(593\) | − 7.85096i | − 0.322400i | −0.986922 | − | 0.161200i | \(-0.948464\pi\) | ||||
0.986922 | − | 0.161200i | \(-0.0515365\pi\) | |||||||
\(594\) | −9.86390 | −0.404721 | ||||||||
\(595\) | −1.62502 | −0.0666191 | ||||||||
\(596\) | 12.5842i | 0.515469i | ||||||||
\(597\) | 1.63035 | 0.0667257 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.9758 | −1.18392 | −0.591960 | − | 0.805967i | \(-0.701646\pi\) | ||||
−0.591960 | + | 0.805967i | \(0.701646\pi\) | |||||||
\(600\) | 6.18776i | 0.252614i | ||||||||
\(601\) | 7.84625 | 0.320055 | 0.160028 | − | 0.987113i | \(-0.448842\pi\) | ||||
0.160028 | + | 0.987113i | \(0.448842\pi\) | |||||||
\(602\) | −17.3460 | −0.706970 | ||||||||
\(603\) | − 30.3423i | − 1.23564i | ||||||||
\(604\) | 1.14580i | 0.0466219i | ||||||||
\(605\) | 1.98619i | 0.0807500i | ||||||||
\(606\) | 30.8803i | 1.25443i | ||||||||
\(607\) | −41.8833 | −1.69999 | −0.849995 | − | 0.526791i | \(-0.823395\pi\) | ||||
−0.849995 | + | 0.526791i | \(0.823395\pi\) | |||||||
\(608\) | −37.1163 | −1.50526 | ||||||||
\(609\) | 9.02100i | 0.365549i | ||||||||
\(610\) | 2.94674 | 0.119310 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −31.6011 | −1.27740 | ||||||||
\(613\) | − 19.3299i | − 0.780725i | −0.920661 | − | 0.390363i | \(-0.872350\pi\) | ||||
0.920661 | − | 0.390363i | \(-0.127650\pi\) | |||||||
\(614\) | 15.8543 | 0.639826 | ||||||||
\(615\) | −0.344630 | −0.0138968 | ||||||||
\(616\) | − 2.06597i | − 0.0832405i | ||||||||
\(617\) | 39.7821i | 1.60157i | 0.598955 | + | 0.800783i | \(0.295583\pi\) | ||||
−0.598955 | + | 0.800783i | \(0.704417\pi\) | |||||||
\(618\) | 18.5559i | 0.746427i | ||||||||
\(619\) | 14.2327i | 0.572059i | 0.958221 | + | 0.286029i | \(0.0923355\pi\) | ||||
−0.958221 | + | 0.286029i | \(0.907665\pi\) | |||||||
\(620\) | −5.18382 | −0.208187 | ||||||||
\(621\) | 4.15536 | 0.166749 | ||||||||
\(622\) | 55.2745i | 2.21630i | ||||||||
\(623\) | 10.5068 | 0.420947 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.5484 | 0.941936 | ||||||||
\(626\) | − 18.2067i | − 0.727685i | ||||||||
\(627\) | 51.7213 | 2.06555 | ||||||||
\(628\) | 15.0434 | 0.600299 | ||||||||
\(629\) | − 61.1100i | − 2.43662i | ||||||||
\(630\) | 2.10184i | 0.0837391i | ||||||||
\(631\) | − 22.2652i | − 0.886364i | −0.896432 | − | 0.443182i | \(-0.853850\pi\) | ||||
0.896432 | − | 0.443182i | \(-0.146150\pi\) | |||||||
\(632\) | − 4.91175i | − 0.195379i | ||||||||
\(633\) | −44.7171 | −1.77735 | ||||||||
\(634\) | 3.77665 | 0.149990 | ||||||||
\(635\) | − 3.37083i | − 0.133767i | ||||||||
\(636\) | −5.06606 | −0.200882 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 28.5710 | 1.13114 | ||||||||
\(639\) | − 21.2023i | − 0.838749i | ||||||||
\(640\) | 1.22774 | 0.0485305 | ||||||||
\(641\) | −4.25054 | −0.167886 | −0.0839430 | − | 0.996471i | \(-0.526751\pi\) | ||||
−0.0839430 | + | 0.996471i | \(0.526751\pi\) | |||||||
\(642\) | 19.7841i | 0.780815i | ||||||||
\(643\) | − 26.5252i | − 1.04605i | −0.852317 | − | 0.523026i | \(-0.824803\pi\) | ||||
0.852317 | − | 0.523026i | \(-0.175197\pi\) | |||||||
\(644\) | − 5.92277i | − 0.233390i | ||||||||
\(645\) | 7.12271i | 0.280456i | ||||||||
\(646\) | 49.1198 | 1.93259 | ||||||||
\(647\) | −15.4298 | −0.606607 | −0.303304 | − | 0.952894i | \(-0.598090\pi\) | ||||
−0.303304 | + | 0.952894i | \(0.598090\pi\) | |||||||
\(648\) | 3.63283i | 0.142711i | ||||||||
\(649\) | 48.8340 | 1.91690 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.2480 | −0.950355 | ||||||||
\(652\) | − 20.1119i | − 0.787644i | ||||||||
\(653\) | 15.8223 | 0.619176 | 0.309588 | − | 0.950871i | \(-0.399809\pi\) | ||||
0.309588 | + | 0.950871i | \(0.399809\pi\) | |||||||
\(654\) | 24.4980 | 0.957949 | ||||||||
\(655\) | − 3.95308i | − 0.154460i | ||||||||
\(656\) | − 1.92887i | − 0.0753096i | ||||||||
\(657\) | − 12.5023i | − 0.487763i | ||||||||
\(658\) | − 16.6855i | − 0.650469i | ||||||||
\(659\) | 32.7593 | 1.27612 | 0.638061 | − | 0.769986i | \(-0.279737\pi\) | ||||
0.638061 | + | 0.769986i | \(0.279737\pi\) | |||||||
\(660\) | 5.77313 | 0.224719 | ||||||||
\(661\) | 14.4345i | 0.561436i | 0.959790 | + | 0.280718i | \(0.0905725\pi\) | ||||
−0.959790 | + | 0.280718i | \(0.909427\pi\) | |||||||
\(662\) | 14.2083 | 0.552222 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.248376 | 0.00963884 | ||||||||
\(665\) | − 1.52171i | − 0.0590094i | ||||||||
\(666\) | −79.0412 | −3.06279 | ||||||||
\(667\) | −12.0361 | −0.466040 | ||||||||
\(668\) | − 18.7716i | − 0.726294i | ||||||||
\(669\) | − 46.6475i | − 1.80350i | ||||||||
\(670\) | 5.26435i | 0.203380i | ||||||||
\(671\) | − 20.3338i | − 0.784978i | ||||||||
\(672\) | −19.3791 | −0.747564 | ||||||||
\(673\) | 17.6481 | 0.680284 | 0.340142 | − | 0.940374i | \(-0.389525\pi\) | ||||
0.340142 | + | 0.940374i | \(0.389525\pi\) | |||||||
\(674\) | − 44.5828i | − 1.71726i | ||||||||
\(675\) | −5.99786 | −0.230858 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.0522 | 0.386338 | 0.193169 | − | 0.981165i | \(-0.438123\pi\) | ||||
0.193169 | + | 0.981165i | \(0.438123\pi\) | |||||||
\(678\) | − 64.3950i | − 2.47307i | ||||||||
\(679\) | 2.35258 | 0.0902835 | ||||||||
\(680\) | −0.805672 | −0.0308961 | ||||||||
\(681\) | 1.71577i | 0.0657485i | ||||||||
\(682\) | 76.7977i | 2.94073i | ||||||||
\(683\) | − 28.7118i | − 1.09863i | −0.835616 | − | 0.549313i | \(-0.814889\pi\) | ||||
0.835616 | − | 0.549313i | \(-0.185111\pi\) | |||||||
\(684\) | − 29.5921i | − 1.13148i | ||||||||
\(685\) | 4.59564 | 0.175591 | ||||||||
\(686\) | 1.93488 | 0.0738741 | ||||||||
\(687\) | − 49.5914i | − 1.89203i | ||||||||
\(688\) | −39.8653 | −1.51985 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −5.22147 | −0.198778 | ||||||||
\(691\) | 39.7668i | 1.51280i | 0.654109 | + | 0.756400i | \(0.273044\pi\) | ||||
−0.654109 | + | 0.756400i | \(0.726956\pi\) | |||||||
\(692\) | −17.7073 | −0.673130 | ||||||||
\(693\) | 14.5036 | 0.550946 | ||||||||
\(694\) | 48.8501i | 1.85432i | ||||||||
\(695\) | − 7.10980i | − 0.269690i | ||||||||
\(696\) | 4.47255i | 0.169532i | ||||||||
\(697\) | 2.25848i | 0.0855461i | ||||||||
\(698\) | −3.93280 | −0.148859 | ||||||||
\(699\) | −76.6821 | −2.90038 | ||||||||
\(700\) | 8.54895i | 0.323120i | ||||||||
\(701\) | −10.4132 | −0.393301 | −0.196651 | − | 0.980474i | \(-0.563006\pi\) | ||||
−0.196651 | + | 0.980474i | \(0.563006\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 57.2251 | 2.15829 | ||||||||
\(704\) | 24.3169i | 0.916479i | ||||||||
\(705\) | −6.85150 | −0.258043 | ||||||||
\(706\) | 18.7454 | 0.705491 | ||||||||
\(707\) | − 6.26932i | − 0.235782i | ||||||||
\(708\) | − 52.0226i | − 1.95513i | ||||||||
\(709\) | 33.7060i | 1.26586i | 0.774210 | + | 0.632928i | \(0.218147\pi\) | ||||
−0.774210 | + | 0.632928i | \(0.781853\pi\) | |||||||
\(710\) | 3.67857i | 0.138054i | ||||||||
\(711\) | 34.4816 | 1.29316 | ||||||||
\(712\) | 5.20922 | 0.195224 | ||||||||
\(713\) | − 32.3525i | − 1.21161i | ||||||||
\(714\) | 25.6463 | 0.959789 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.2634 | −0.458304 | ||||||||
\(717\) | 33.6988i | 1.25850i | ||||||||
\(718\) | 52.1767 | 1.94722 | ||||||||
\(719\) | 42.0927 | 1.56979 | 0.784896 | − | 0.619628i | \(-0.212716\pi\) | ||||
0.784896 | + | 0.619628i | \(0.212716\pi\) | |||||||
\(720\) | 4.83053i | 0.180023i | ||||||||
\(721\) | − 3.76722i | − 0.140299i | ||||||||
\(722\) | 9.23440i | 0.343669i | ||||||||
\(723\) | − 33.8921i | − 1.26046i | ||||||||
\(724\) | −36.7475 | −1.36571 | ||||||||
\(725\) | 17.3729 | 0.645215 | ||||||||
\(726\) | − 31.3464i | − 1.16337i | ||||||||
\(727\) | 19.9921 | 0.741465 | 0.370733 | − | 0.928740i | \(-0.379107\pi\) | ||||
0.370733 | + | 0.928740i | \(0.379107\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.8465 | −1.29061 | ||||||||
\(730\) | 2.16914i | 0.0802834i | ||||||||
\(731\) | 46.6777 | 1.72644 | ||||||||
\(732\) | −21.6615 | −0.800631 | ||||||||
\(733\) | − 20.7416i | − 0.766108i | −0.923726 | − | 0.383054i | \(-0.874872\pi\) | ||||
0.923726 | − | 0.383054i | \(-0.125128\pi\) | |||||||
\(734\) | 12.7469i | 0.470497i | ||||||||
\(735\) | − 0.794512i | − 0.0293060i | ||||||||
\(736\) | − 25.8562i | − 0.953072i | ||||||||
\(737\) | 36.3264 | 1.33810 | ||||||||
\(738\) | 2.92118 | 0.107530 | ||||||||
\(739\) | − 22.5049i | − 0.827855i | −0.910310 | − | 0.413927i | \(-0.864157\pi\) | ||||
0.910310 | − | 0.413927i | \(-0.135843\pi\) | |||||||
\(740\) | 6.38746 | 0.234808 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.20816 | 0.0810642 | ||||||||
\(743\) | 3.81492i | 0.139956i | 0.997549 | + | 0.0699780i | \(0.0222929\pi\) | ||||
−0.997549 | + | 0.0699780i | \(0.977707\pi\) | |||||||
\(744\) | −12.0220 | −0.440748 | ||||||||
\(745\) | −2.25233 | −0.0825190 | ||||||||
\(746\) | − 32.1082i | − 1.17556i | ||||||||
\(747\) | 1.74365i | 0.0637969i | ||||||||
\(748\) | − 37.8334i | − 1.38333i | ||||||||
\(749\) | − 4.01657i | − 0.146762i | ||||||||
\(750\) | 15.2231 | 0.555869 | ||||||||
\(751\) | 30.1283 | 1.09940 | 0.549699 | − | 0.835363i | \(-0.314742\pi\) | ||||
0.549699 | + | 0.835363i | \(0.314742\pi\) | |||||||
\(752\) | − 38.3473i | − 1.39838i | ||||||||
\(753\) | 65.0995 | 2.37236 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.205076 | −0.00746348 | ||||||||
\(756\) | − 2.13333i | − 0.0775883i | ||||||||
\(757\) | 34.9608 | 1.27067 | 0.635335 | − | 0.772237i | \(-0.280862\pi\) | ||||
0.635335 | + | 0.772237i | \(0.280862\pi\) | |||||||
\(758\) | 59.5826 | 2.16414 | ||||||||
\(759\) | 36.0304i | 1.30782i | ||||||||
\(760\) | − 0.754453i | − 0.0273669i | ||||||||
\(761\) | − 14.6724i | − 0.531875i | −0.963990 | − | 0.265938i | \(-0.914318\pi\) | ||||
0.963990 | − | 0.265938i | \(-0.0856815\pi\) | |||||||
\(762\) | 53.1991i | 1.92720i | ||||||||
\(763\) | −4.97360 | −0.180056 | ||||||||
\(764\) | 31.5951 | 1.14307 | ||||||||
\(765\) | − 5.65599i | − 0.204493i | ||||||||
\(766\) | −54.7528 | −1.97830 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −49.0877 | −1.77130 | ||||||||
\(769\) | 8.21482i | 0.296234i | 0.988970 | + | 0.148117i | \(0.0473212\pi\) | ||||
−0.988970 | + | 0.148117i | \(0.952679\pi\) | |||||||
\(770\) | −2.51635 | −0.0906831 | ||||||||
\(771\) | 1.49970 | 0.0540105 | ||||||||
\(772\) | 2.67846i | 0.0963998i | ||||||||
\(773\) | − 46.8567i | − 1.68532i | −0.538448 | − | 0.842659i | \(-0.680989\pi\) | ||||
0.538448 | − | 0.842659i | \(-0.319011\pi\) | |||||||
\(774\) | − 60.3741i | − 2.17010i | ||||||||
\(775\) | 46.6977i | 1.67743i | ||||||||
\(776\) | 1.16639 | 0.0418710 | ||||||||
\(777\) | 29.8783 | 1.07188 | ||||||||
\(778\) | 25.0359i | 0.897582i | ||||||||
\(779\) | −2.11490 | −0.0757743 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.3837 | 0.908301 | ||||||||
\(782\) | 34.2182i | 1.22364i | ||||||||
\(783\) | −4.33529 | −0.154931 | ||||||||
\(784\) | 4.44682 | 0.158815 | ||||||||
\(785\) | 2.69249i | 0.0960991i | ||||||||
\(786\) | 62.3883i | 2.22532i | ||||||||
\(787\) | − 39.4146i | − 1.40498i | −0.711693 | − | 0.702490i | \(-0.752071\pi\) | ||||
0.711693 | − | 0.702490i | \(-0.247929\pi\) | |||||||
\(788\) | 11.7321i | 0.417940i | ||||||||
\(789\) | 47.0994 | 1.67678 | ||||||||
\(790\) | −5.98251 | −0.212848 | ||||||||
\(791\) | 13.0735i | 0.464839i | ||||||||
\(792\) | 7.19078 | 0.255513 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −35.4296 | −1.25735 | ||||||||
\(795\) | − 0.906728i | − 0.0321583i | ||||||||
\(796\) | 1.11676 | 0.0395826 | ||||||||
\(797\) | −19.5718 | −0.693267 | −0.346634 | − | 0.938001i | \(-0.612675\pi\) | ||||
−0.346634 | + | 0.938001i | \(0.612675\pi\) | |||||||
\(798\) | 24.0159i | 0.850154i | ||||||||
\(799\) | 44.9004i | 1.58846i | ||||||||
\(800\) | 37.3209i | 1.31949i | ||||||||
\(801\) | 36.5698i | 1.29213i | ||||||||
\(802\) | −2.53942 | −0.0896699 | ||||||||
\(803\) | 14.9680 | 0.528210 | ||||||||
\(804\) | − 38.6982i | − 1.36478i | ||||||||
\(805\) | 1.06006 | 0.0373623 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.89385 | 0.242675 | ||||||||
\(808\) | − 3.10829i | − 0.109349i | ||||||||
\(809\) | 0.917176 | 0.0322462 | 0.0161231 | − | 0.999870i | \(-0.494868\pi\) | ||||
0.0161231 | + | 0.999870i | \(0.494868\pi\) | |||||||
\(810\) | 4.42478 | 0.155471 | ||||||||
\(811\) | − 55.0717i | − 1.93383i | −0.255098 | − | 0.966915i | \(-0.582108\pi\) | ||||
0.255098 | − | 0.966915i | \(-0.417892\pi\) | |||||||
\(812\) | 6.17923i | 0.216848i | ||||||||
\(813\) | 30.0065i | 1.05237i | ||||||||
\(814\) | − 94.6295i | − 3.31676i | ||||||||
\(815\) | 3.59965 | 0.126090 | ||||||||
\(816\) | 58.9414 | 2.06336 | ||||||||
\(817\) | 43.7103i | 1.52923i | ||||||||
\(818\) | −56.6954 | −1.98231 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.236066 | −0.00824377 | ||||||||
\(821\) | 19.9874i | 0.697564i | 0.937204 | + | 0.348782i | \(0.113405\pi\) | ||||
−0.937204 | + | 0.348782i | \(0.886595\pi\) | |||||||
\(822\) | −72.5294 | −2.52975 | ||||||||
\(823\) | −4.78565 | −0.166817 | −0.0834087 | − | 0.996515i | \(-0.526581\pi\) | ||||
−0.0834087 | + | 0.996515i | \(0.526581\pi\) | |||||||
\(824\) | − 1.86776i | − 0.0650666i | ||||||||
\(825\) | − 52.0064i | − 1.81063i | ||||||||
\(826\) | 22.6753i | 0.788973i | ||||||||
\(827\) | − 19.7389i | − 0.686390i | −0.939264 | − | 0.343195i | \(-0.888491\pi\) | ||||
0.939264 | − | 0.343195i | \(-0.111509\pi\) | |||||||
\(828\) | 20.6147 | 0.716409 | ||||||||
\(829\) | −15.5467 | −0.539959 | −0.269980 | − | 0.962866i | \(-0.587017\pi\) | ||||
−0.269980 | + | 0.962866i | \(0.587017\pi\) | |||||||
\(830\) | − 0.302521i | − 0.0105007i | ||||||||
\(831\) | −61.2249 | −2.12387 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.20672 | −0.180402 | ||||||||
\(834\) | 112.208i | 3.88546i | ||||||||
\(835\) | 3.35975 | 0.116269 | ||||||||
\(836\) | 35.4282 | 1.22531 | ||||||||
\(837\) | − 11.6531i | − 0.402789i | ||||||||
\(838\) | 0.587369i | 0.0202903i | ||||||||
\(839\) | − 28.9070i | − 0.997982i | −0.866607 | − | 0.498991i | \(-0.833704\pi\) | ||||
0.866607 | − | 0.498991i | \(-0.166296\pi\) | |||||||
\(840\) | − 0.393914i | − 0.0135913i | ||||||||
\(841\) | −16.4427 | −0.566991 | ||||||||
\(842\) | 2.30855 | 0.0795579 | ||||||||
\(843\) | 48.8517i | 1.68254i | ||||||||
\(844\) | −30.6305 | −1.05434 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 58.0752 | 1.99667 | ||||||||
\(847\) | 6.36395i | 0.218668i | ||||||||
\(848\) | 5.07489 | 0.174272 | ||||||||
\(849\) | −31.0881 | −1.06694 | ||||||||
\(850\) | − 49.3906i | − 1.69408i | ||||||||
\(851\) | 39.8645i | 1.36654i | ||||||||
\(852\) | − 27.0411i | − 0.926413i | ||||||||
\(853\) | 0.564390i | 0.0193244i | 0.999953 | + | 0.00966218i | \(0.00307562\pi\) | ||||
−0.999953 | + | 0.00966218i | \(0.996924\pi\) | |||||||
\(854\) | 9.44166 | 0.323087 | ||||||||
\(855\) | 5.29643 | 0.181134 | ||||||||
\(856\) | − 1.99139i | − 0.0680642i | ||||||||
\(857\) | 39.8324 | 1.36065 | 0.680325 | − | 0.732911i | \(-0.261839\pi\) | ||||
0.680325 | + | 0.732911i | \(0.261839\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.3937 | −1.65117 | −0.825585 | − | 0.564278i | \(-0.809155\pi\) | ||||
−0.825585 | + | 0.564278i | \(0.809155\pi\) | |||||||
\(860\) | 4.87894i | 0.166370i | ||||||||
\(861\) | −1.10423 | −0.0376320 | ||||||||
\(862\) | 44.1110 | 1.50243 | ||||||||
\(863\) | 3.81608i | 0.129901i | 0.997888 | + | 0.0649505i | \(0.0206889\pi\) | ||||
−0.997888 | + | 0.0649505i | \(0.979311\pi\) | |||||||
\(864\) | − 9.31315i | − 0.316840i | ||||||||
\(865\) | − 3.16927i | − 0.107758i | ||||||||
\(866\) | − 7.75817i | − 0.263633i | ||||||||
\(867\) | −25.7368 | −0.874068 | ||||||||
\(868\) | −16.6095 | −0.563763 | ||||||||
\(869\) | 41.2820i | 1.40039i | ||||||||
\(870\) | 5.44756 | 0.184690 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −2.46588 | −0.0835051 | ||||||||
\(873\) | 8.18832i | 0.277133i | ||||||||
\(874\) | −32.0428 | −1.08386 | ||||||||
\(875\) | −3.09060 | −0.104481 | ||||||||
\(876\) | − 15.9453i | − 0.538743i | ||||||||
\(877\) | − 3.07809i | − 0.103940i | −0.998649 | − | 0.0519699i | \(-0.983450\pi\) | ||||
0.998649 | − | 0.0519699i | \(-0.0165500\pi\) | |||||||
\(878\) | − 4.95009i | − 0.167058i | ||||||||
\(879\) | 28.9303i | 0.975793i | ||||||||
\(880\) | −5.78319 | −0.194951 | ||||||||
\(881\) | 34.7729 | 1.17153 | 0.585764 | − | 0.810482i | \(-0.300795\pi\) | ||||
0.585764 | + | 0.810482i | \(0.300795\pi\) | |||||||
\(882\) | 6.73450i | 0.226762i | ||||||||
\(883\) | 17.6873 | 0.595224 | 0.297612 | − | 0.954687i | \(-0.403810\pi\) | ||||
0.297612 | + | 0.954687i | \(0.403810\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.31104 | 0.312987 | ||||||||
\(886\) | − 0.702926i | − 0.0236153i | ||||||||
\(887\) | 39.2893 | 1.31921 | 0.659603 | − | 0.751614i | \(-0.270725\pi\) | ||||
0.659603 | + | 0.751614i | \(0.270725\pi\) | |||||||
\(888\) | 14.8134 | 0.497106 | ||||||||
\(889\) | − 10.8005i | − 0.362237i | ||||||||
\(890\) | − 6.34482i | − 0.212679i | ||||||||
\(891\) | − 30.5330i | − 1.02289i | ||||||||
\(892\) | − 31.9528i | − 1.06986i | ||||||||
\(893\) | −42.0459 | −1.40701 | ||||||||
\(894\) | 35.5467 | 1.18886 | ||||||||
\(895\) | − 2.19491i | − 0.0733677i | ||||||||
\(896\) | 3.93379 | 0.131419 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.6098 | 0.988093 | ||||||||
\(899\) | 33.7534i | 1.12574i | ||||||||
\(900\) | −29.7553 | −0.991843 | ||||||||
\(901\) | −5.94211 | −0.197961 | ||||||||
\(902\) | 3.49728i | 0.116447i | ||||||||
\(903\) | 22.8219i | 0.759466i | ||||||||
\(904\) | 6.48174i | 0.215580i | ||||||||
\(905\) | − 6.57709i | − 0.218630i | ||||||||
\(906\) | 3.23655 | 0.107527 | ||||||||
\(907\) | −42.6219 | −1.41524 | −0.707618 | − | 0.706595i | \(-0.750230\pi\) | ||||
−0.707618 | + | 0.706595i | \(0.750230\pi\) | |||||||
\(908\) | 1.17527i | 0.0390028i | ||||||||
\(909\) | 21.8209 | 0.723752 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56.5310 | 1.87296 | 0.936478 | − | 0.350727i | \(-0.114065\pi\) | ||||
0.936478 | + | 0.350727i | \(0.114065\pi\) | |||||||
\(912\) | 55.1944i | 1.82767i | ||||||||
\(913\) | −2.08753 | −0.0690871 | ||||||||
\(914\) | 17.2418 | 0.570308 | ||||||||
\(915\) | − 3.87699i | − 0.128169i | ||||||||
\(916\) | − 33.9692i | − 1.12238i | ||||||||
\(917\) | − 12.6661i | − 0.418271i | ||||||||
\(918\) | 12.3251i | 0.406787i | ||||||||
\(919\) | −35.2658 | −1.16331 | −0.581655 | − | 0.813435i | \(-0.697595\pi\) | ||||
−0.581655 | + | 0.813435i | \(0.697595\pi\) | |||||||
\(920\) | 0.525572 | 0.0173276 | ||||||||
\(921\) | − 20.8593i | − 0.687336i | ||||||||
\(922\) | 41.5294 | 1.36770 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 18.4977 | 0.608530 | ||||||||
\(925\) | − 57.5406i | − 1.89192i | ||||||||
\(926\) | −5.98791 | −0.196775 | ||||||||
\(927\) | 13.1121 | 0.430658 | ||||||||
\(928\) | 26.9758i | 0.885523i | ||||||||
\(929\) | 5.51296i | 0.180874i | 0.995902 | + | 0.0904372i | \(0.0288264\pi\) | ||||
−0.995902 | + | 0.0904372i | \(0.971174\pi\) | |||||||
\(930\) | 14.6428i | 0.480156i | ||||||||
\(931\) | − 4.87572i | − 0.159795i | ||||||||
\(932\) | −52.5259 | −1.72054 | ||||||||
\(933\) | 72.7239 | 2.38088 | ||||||||
\(934\) | 40.4543i | 1.32371i | ||||||||
\(935\) | 6.77145 | 0.221450 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.2496 | 1.44557 | 0.722785 | − | 0.691073i | \(-0.242861\pi\) | ||||
0.722785 | + | 0.691073i | \(0.242861\pi\) | |||||||
\(938\) | 16.8675i | 0.550745i | ||||||||
\(939\) | −23.9543 | −0.781719 | ||||||||
\(940\) | −4.69316 | −0.153074 | ||||||||
\(941\) | 46.2818i | 1.50874i | 0.656448 | + | 0.754372i | \(0.272058\pi\) | ||||
−0.656448 | + | 0.754372i | \(0.727942\pi\) | |||||||
\(942\) | − 42.4934i | − 1.38451i | ||||||||
\(943\) | − 1.47330i | − 0.0479772i | ||||||||
\(944\) | 52.1132i | 1.69614i | ||||||||
\(945\) | 0.381825 | 0.0124208 | ||||||||
\(946\) | 72.2809 | 2.35005 | ||||||||
\(947\) | 55.7472i | 1.81154i | 0.423769 | + | 0.905770i | \(0.360707\pi\) | ||||
−0.423769 | + | 0.905770i | \(0.639293\pi\) | |||||||
\(948\) | 43.9774 | 1.42832 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 46.2507 | 1.50057 | ||||||||
\(951\) | − 4.96889i | − 0.161127i | ||||||||
\(952\) | −2.58146 | −0.0836655 | ||||||||
\(953\) | 4.03648 | 0.130754 | 0.0653772 | − | 0.997861i | \(-0.479175\pi\) | ||||
0.0653772 | + | 0.997861i | \(0.479175\pi\) | |||||||
\(954\) | 7.68568i | 0.248833i | ||||||||
\(955\) | 5.65491i | 0.182989i | ||||||||
\(956\) | 23.0831i | 0.746561i | ||||||||
\(957\) | − 37.5906i | − 1.21513i | ||||||||
\(958\) | 35.5170 | 1.14750 | ||||||||
\(959\) | 14.7249 | 0.475492 | ||||||||
\(960\) | 4.63644i | 0.149641i | ||||||||
\(961\) | −59.7276 | −1.92670 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.9800 | 0.450498 | ||||||||
\(964\) | − 23.2155i | − 0.747721i | ||||||||
\(965\) | −0.479393 | −0.0154322 | ||||||||
\(966\) | −16.7301 | −0.538283 | ||||||||
\(967\) | − 52.0755i | − 1.67463i | −0.546717 | − | 0.837317i | \(-0.684123\pi\) | ||||
0.546717 | − | 0.837317i | \(-0.315877\pi\) | |||||||
\(968\) | 3.15520i | 0.101412i | ||||||||
\(969\) | − 64.6263i | − 2.07610i | ||||||||
\(970\) | − 1.42066i | − 0.0456147i | ||||||||
\(971\) | 16.0432 | 0.514851 | 0.257426 | − | 0.966298i | \(-0.417126\pi\) | ||||
0.257426 | + | 0.966298i | \(0.417126\pi\) | |||||||
\(972\) | −38.9265 | −1.24857 | ||||||||
\(973\) | − 22.7805i | − 0.730311i | ||||||||
\(974\) | 25.7505 | 0.825101 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.6992 | 0.694575 | ||||||||
\(977\) | 10.0736i | 0.322284i | 0.986931 | + | 0.161142i | \(0.0515177\pi\) | ||||
−0.986931 | + | 0.161142i | \(0.948482\pi\) | |||||||
\(978\) | −56.8104 | −1.81660 | ||||||||
\(979\) | −43.7820 | −1.39928 | ||||||||
\(980\) | − 0.544227i | − 0.0173847i | ||||||||
\(981\) | − 17.3110i | − 0.552697i | ||||||||
\(982\) | − 28.1448i | − 0.898136i | ||||||||
\(983\) | − 52.7163i | − 1.68139i | −0.541509 | − | 0.840695i | \(-0.682147\pi\) | ||||
0.541509 | − | 0.840695i | \(-0.317853\pi\) | |||||||
\(984\) | −0.547470 | −0.0174527 | ||||||||
\(985\) | −2.09983 | −0.0669061 | ||||||||
\(986\) | − 35.6998i | − 1.13691i | ||||||||
\(987\) | −21.9529 | −0.698769 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.4497 | −0.968245 | ||||||||
\(990\) | − 8.75836i | − 0.278359i | ||||||||
\(991\) | −62.8727 | −1.99722 | −0.998609 | − | 0.0527258i | \(-0.983209\pi\) | ||||
−0.998609 | + | 0.0527258i | \(0.983209\pi\) | |||||||
\(992\) | −72.5096 | −2.30218 | ||||||||
\(993\) | − 18.6937i | − 0.593227i | ||||||||
\(994\) | 11.7865i | 0.373845i | ||||||||
\(995\) | 0.199879i | 0.00633659i | ||||||||
\(996\) | 2.22383i | 0.0704648i | ||||||||
\(997\) | 33.1634 | 1.05030 | 0.525148 | − | 0.851011i | \(-0.324010\pi\) | ||||
0.525148 | + | 0.851011i | \(0.324010\pi\) | |||||||
\(998\) | −61.4460 | −1.94504 | ||||||||
\(999\) | 14.3588i | 0.454293i |
(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 | 1183.2.c.h.337.3 | 12 | ||
13.5 | odd | 4 | 1183.2.a.n.1.2 | ✓ | 6 | ||
13.8 | odd | 4 | 1183.2.a.o.1.5 | yes | 6 | ||
13.12 | even | 2 | inner | 1183.2.c.h.337.10 | 12 | ||
91.34 | even | 4 | 8281.2.a.cg.1.5 | 6 | |||
91.83 | even | 4 | 8281.2.a.cb.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.a.n.1.2 | ✓ | 6 | 13.5 | odd | 4 | ||
1183.2.a.o.1.5 | yes | 6 | 13.8 | odd | 4 | ||
1183.2.c.h.337.3 | 12 | 1.1 | even | 1 | trivial | ||
1183.2.c.h.337.10 | 12 | 13.12 | even | 2 | inner | ||
8281.2.a.cb.1.2 | 6 | 91.83 | even | 4 | |||
8281.2.a.cg.1.5 | 6 | 91.34 | even | 4 |