Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1320,2,Mod(329,1320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1320.329");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1320.ba (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5402530668\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 329.69 | ||
Character | \(\chi\) | \(=\) | 1320.329 |
Dual form | 1320.2.ba.a.329.71 |
$q$-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 \(\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times\).
\(n\) | \(661\) | \(881\) | \(991\) | \(1057\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.72947 | − | 0.0944935i | 0.998511 | − | 0.0545558i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.89340 | − | 1.18956i | −0.846753 | − | 0.531986i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.85425 | −1.07881 | −0.539403 | − | 0.842048i | \(-0.681350\pi\) | ||||
−0.539403 | + | 0.842048i | \(0.681350\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.98214 | − | 0.326848i | 0.994047 | − | 0.108949i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.833543 | + | 3.21017i | −0.251323 | + | 0.967903i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.11005 | −0.862571 | −0.431286 | − | 0.902215i | \(-0.641940\pi\) | ||||
−0.431286 | + | 0.902215i | \(0.641940\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.38698 | − | 1.87839i | −0.874515 | − | 0.484998i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.53160i | − | 0.371467i | −0.982600 | − | 0.185733i | \(-0.940534\pi\) | ||
0.982600 | − | 0.185733i | \(-0.0594660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.78889i | 1.32806i | 0.747705 | + | 0.664031i | \(0.231156\pi\) | ||||
−0.747705 | + | 0.664031i | \(0.768844\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.93635 | + | 0.269708i | −1.07720 | + | 0.0588551i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.49565 | −0.728894 | −0.364447 | − | 0.931224i | \(-0.618742\pi\) | ||||
−0.364447 | + | 0.931224i | \(0.618742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.16991 | + | 4.50461i | 0.433983 | + | 0.900921i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.12664 | − | 0.847066i | 0.986623 | − | 0.163018i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.02861 | −0.748093 | −0.374047 | − | 0.927410i | \(-0.622030\pi\) | ||||
−0.374047 | + | 0.927410i | \(0.622030\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.83886 | −0.869085 | −0.434543 | − | 0.900651i | \(-0.643090\pi\) | ||||
−0.434543 | + | 0.900651i | \(0.643090\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.13825 | + | 5.63067i | −0.198144 | + | 0.980173i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.40423 | + | 3.39529i | 0.913482 | + | 0.573909i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.57664i | 0.259199i | 0.991566 | + | 0.129599i | \(0.0413691\pi\) | ||||
−0.991566 | + | 0.129599i | \(0.958631\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.37873 | + | 0.293879i | −0.861287 | + | 0.0470583i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.72289 | 0.269069 | 0.134535 | − | 0.990909i | \(-0.457046\pi\) | ||||
0.134535 | + | 0.990909i | \(0.457046\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.34300 | −1.42479 | −0.712397 | − | 0.701777i | \(-0.752390\pi\) | ||||
−0.712397 | + | 0.701777i | \(0.752390\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.03519 | − | 2.92857i | −0.899672 | − | 0.436566i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.91856 | 0.425716 | 0.212858 | − | 0.977083i | \(-0.431723\pi\) | ||||
0.212858 | + | 0.977083i | \(0.431723\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.14675 | 0.163822 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.144726 | − | 2.64885i | −0.0202657 | − | 0.370913i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.08253 | 0.286058 | 0.143029 | − | 0.989719i | \(-0.454316\pi\) | ||||
0.143029 | + | 0.989719i | \(0.454316\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.39691 | − | 5.08659i | 0.727719 | − | 0.685875i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.547012 | + | 10.0117i | 0.0724536 | + | 1.32608i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.46884i | 1.10255i | 0.834324 | + | 0.551274i | \(0.185858\pi\) | ||||
−0.834324 | + | 0.551274i | \(0.814142\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.6324i | 1.61742i | 0.588210 | + | 0.808708i | \(0.299833\pi\) | ||||
−0.588210 | + | 0.808708i | \(0.700167\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.51178 | + | 0.932905i | −1.07238 | + | 0.117535i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.88855 | + | 3.69957i | 0.730385 | + | 0.458876i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.93483i | 0.602885i | 0.953484 | + | 0.301443i | \(0.0974682\pi\) | ||||
−0.953484 | + | 0.301443i | \(0.902532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.04563 | + | 0.330316i | −0.727808 | + | 0.0397654i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.89348i | − | 1.17414i | −0.809536 | − | 0.587070i | \(-0.800281\pi\) | ||
0.809536 | − | 0.587070i | \(-0.199719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.6216 | −1.94541 | −0.972707 | − | 0.232037i | \(-0.925461\pi\) | ||||
−0.972707 | + | 0.232037i | \(0.925461\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.17846 | + | 7.58554i | 0.482487 | + | 0.875903i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.37914 | − | 9.16264i | 0.271128 | − | 1.04418i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6160i | 1.41941i | 0.704498 | + | 0.709706i | \(0.251172\pi\) | ||||
−0.704498 | + | 0.709706i | \(0.748828\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.78634 | − | 1.94941i | 0.976260 | − | 0.216601i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.80377i | − | 0.307754i | −0.988090 | − | 0.153877i | \(-0.950824\pi\) | ||
0.988090 | − | 0.153877i | \(-0.0491759\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.82192 | + | 2.89992i | −0.197615 | + | 0.314541i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.96736 | + | 0.380677i | −0.746979 | + | 0.0408129i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14.9751i | − | 1.58735i | −0.608339 | − | 0.793677i | \(-0.708164\pi\) | ||
0.608339 | − | 0.793677i | \(-0.291836\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.87685 | 0.930547 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.36867 | + | 0.457241i | −0.867791 | + | 0.0474137i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.88621 | − | 10.9607i | 0.706510 | − | 1.12454i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.53318i | − | 0.358740i | −0.983782 | − | 0.179370i | \(-0.942594\pi\) | ||
0.983782 | − | 0.179370i | \(-0.0574060\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.43651 | + | 9.84563i | −0.144374 | + | 0.989523i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.1409 | 1.40708 | 0.703538 | − | 0.710658i | \(-0.251603\pi\) | ||||
0.703538 | + | 0.710658i | \(0.251603\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.04284i | 0.891017i | 0.895278 | + | 0.445509i | \(0.146977\pi\) | ||||
−0.895278 | + | 0.445509i | \(0.853023\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.66730 | + | 5.36140i | 0.943432 | + | 0.523219i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13.8773i | − | 1.34157i | −0.741652 | − | 0.670785i | \(-0.765957\pi\) | ||
0.741652 | − | 0.670785i | \(-0.234043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.1610i | − | 1.16481i | −0.812899 | − | 0.582405i | \(-0.802112\pi\) | ||
0.812899 | − | 0.582405i | \(-0.197888\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.148982 | + | 2.72676i | 0.0141408 | + | 0.258812i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.29497 | −0.404037 | −0.202018 | − | 0.979382i | \(-0.564750\pi\) | ||||
−0.202018 | + | 0.979382i | \(0.564750\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.61866 | + | 4.15827i | 0.617193 | + | 0.387761i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.27460 | + | 1.01651i | −0.857437 | + | 0.0939764i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.37156i | 0.400740i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.61041 | − | 5.35164i | −0.873674 | − | 0.486512i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.97968 | − | 0.162801i | 0.268669 | − | 0.0146793i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.24997 | − | 11.1102i | 0.111801 | − | 0.993731i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.7890 | 1.48978 | 0.744890 | − | 0.667187i | \(-0.232502\pi\) | ||||
0.744890 | + | 0.667187i | \(0.232502\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.1585 | + | 0.882853i | −1.42267 | + | 0.0777308i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.5944 | 1.44986 | 0.724932 | − | 0.688821i | \(-0.241871\pi\) | ||||
0.724932 | + | 0.688821i | \(0.241871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 16.5229i | − | 1.43272i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.7144 | − | 4.49460i | −0.922150 | − | 0.386833i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.8798 | −1.35670 | −0.678352 | − | 0.734737i | \(-0.737305\pi\) | ||||
−0.678352 | + | 0.734737i | \(0.737305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 19.2178i | − | 1.63004i | −0.579436 | − | 0.815018i | \(-0.696727\pi\) | ||
0.579436 | − | 0.815018i | \(-0.303273\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.04756 | − | 0.275785i | 0.425082 | − | 0.0232253i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.59236 | − | 9.98378i | 0.216784 | − | 0.834886i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.62775 | + | 4.79225i | 0.633450 | + | 0.397975i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.98327 | − | 0.108361i | 0.163578 | − | 0.00893743i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.62393 | −0.378807 | −0.189403 | − | 0.981899i | \(-0.560655\pi\) | ||||
−0.189403 | + | 0.981899i | \(0.560655\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.71459i | 0.302289i | 0.988512 | + | 0.151144i | \(0.0482958\pi\) | ||||
−0.988512 | + | 0.151144i | \(0.951704\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.500598 | − | 4.56744i | −0.0404710 | − | 0.369255i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.16189 | + | 5.75610i | 0.735901 | + | 0.462341i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.1138i | − | 0.966787i | −0.875403 | − | 0.483394i | \(-0.839404\pi\) | ||
0.875403 | − | 0.483394i | \(-0.160596\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.60168 | − | 0.196786i | 0.285632 | − | 0.0156061i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.97747 | 0.786335 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.7433i | 1.15479i | 0.816466 | + | 0.577393i | \(0.195930\pi\) | ||||
−0.816466 | + | 0.577393i | \(0.804070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.85315 | − | 9.30708i | 0.689217 | − | 0.724555i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.9065i | 1.23089i | 0.788182 | + | 0.615443i | \(0.211023\pi\) | ||||
−0.788182 | + | 0.615443i | \(0.788977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.32762 | −0.255971 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.89208 | + | 17.2633i | 0.144691 | + | 1.32016i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.73933i | − | 0.512382i | −0.966626 | − | 0.256191i | \(-0.917532\pi\) | ||
0.966626 | − | 0.256191i | \(-0.0824675\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.19348 | − | 12.8573i | −0.468183 | − | 0.971919i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.800250 | + | 14.6466i | 0.0601505 | + | 1.10091i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.5261i | 0.861499i | 0.902472 | + | 0.430749i | \(0.141751\pi\) | ||||
−0.902472 | + | 0.430749i | \(0.858249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.8383 | −1.54890 | −0.774448 | − | 0.632638i | \(-0.781972\pi\) | ||||
−0.774448 | + | 0.632638i | \(0.781972\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.19368 | + | 21.8474i | 0.0882395 | + | 1.61501i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.87551 | − | 2.98521i | 0.137890 | − | 0.219477i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.91669 | + | 1.27665i | 0.359544 | + | 0.0933580i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.6327 | + | 2.41774i | −1.06437 | + | 0.175865i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 5.85510i | − | 0.423660i | −0.977306 | − | 0.211830i | \(-0.932058\pi\) | ||
0.977306 | − | 0.211830i | \(-0.0679424\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.63637 | 0.405715 | 0.202857 | − | 0.979208i | \(-0.434977\pi\) | ||||
0.202857 | + | 0.979208i | \(0.434977\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.5337 | + | 5.84187i | 0.754332 | + | 0.418345i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.09270i | − | 0.505334i | −0.967553 | − | 0.252667i | \(-0.918692\pi\) | ||
0.967553 | − | 0.252667i | \(-0.0813077\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.55075 | 0.109930 | 0.0549650 | − | 0.998488i | \(-0.482495\pi\) | ||||
0.0549650 | + | 0.998488i | \(0.482495\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.466309 | + | 8.53465i | 0.0328909 | + | 0.601988i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.4987 | 0.807047 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.26211 | − | 2.04947i | −0.227836 | − | 0.143141i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.4245 | + | 1.14254i | −0.724555 | + | 0.0794124i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.5833 | − | 4.82529i | −1.28544 | − | 0.333772i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 12.0173i | − | 0.827307i | −0.910434 | − | 0.413653i | \(-0.864253\pi\) | ||
0.910434 | − | 0.413653i | \(-0.135747\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.934870 | − | 17.1105i | −0.0640562 | − | 1.17239i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.6900 | + | 11.1140i | 1.20645 | + | 0.757970i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.8113 | 0.937574 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −28.7466 | + | 1.57064i | −1.94252 | + | 0.106134i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.76333i | 0.320416i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.8792i | 1.73300i | 0.499180 | + | 0.866498i | \(0.333635\pi\) | ||||
−0.499180 | + | 0.866498i | \(0.666365\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.94331 | + | 12.7241i | 0.529554 | + | 0.848276i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.3114i | 0.750765i | 0.926870 | + | 0.375382i | \(0.122489\pi\) | ||||
−0.926870 | + | 0.375382i | \(0.877511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.41353 | −0.291654 | −0.145827 | − | 0.989310i | \(-0.546584\pi\) | ||||
−0.145827 | + | 0.989310i | \(0.546584\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.24885 | − | 16.0713i | 0.213759 | − | 1.05742i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.66292i | 0.370990i | 0.982645 | + | 0.185495i | \(0.0593888\pi\) | ||||
−0.982645 | + | 0.185495i | \(0.940611\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.52599 | − | 3.47179i | −0.360476 | − | 0.226475i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.19213 | + | 21.8190i | 0.0774372 | + | 1.41730i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.1548 | −1.43307 | −0.716536 | − | 0.697550i | \(-0.754273\pi\) | ||||
−0.716536 | + | 0.697550i | \(0.754273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.1130i | − | 0.715854i | −0.933749 | − | 0.357927i | \(-0.883484\pi\) | ||
0.933749 | − | 0.357927i | \(-0.116516\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.0115 | − | 4.20170i | 0.962989 | − | 0.269539i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.17126 | − | 1.36413i | −0.138717 | − | 0.0871508i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 18.0037i | − | 1.14555i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.264938 | − | 4.84904i | −0.0167898 | − | 0.307295i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.01227i | 0.505730i | 0.967502 | + | 0.252865i | \(0.0813729\pi\) | ||||
−0.967502 | + | 0.252865i | \(0.918627\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.91378 | − | 11.2216i | 0.183188 | − | 0.705499i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.87693 | + | 5.18749i | −0.180161 | + | 0.324853i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.5090 | −1.02980 | −0.514902 | − | 0.857249i | \(-0.672172\pi\) | ||||
−0.514902 | + | 0.857249i | \(0.672172\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 4.50014i | − | 0.279625i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.0139 | + | 1.31674i | −0.743640 | + | 0.0815041i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.9046i | − | 1.04238i | −0.853440 | − | 0.521192i | \(-0.825488\pi\) | ||
0.853440 | − | 0.521192i | \(-0.174512\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.94306 | − | 2.47729i | −0.242220 | − | 0.152178i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.41505 | − | 25.8990i | −0.0865995 | − | 1.58499i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.6816i | 0.712237i | 0.934441 | + | 0.356119i | \(0.115900\pi\) | ||||
−0.934441 | + | 0.356119i | \(0.884100\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.450474i | 0.0273644i | 0.999906 | + | 0.0136822i | \(0.00435531\pi\) | ||||
−0.999906 | + | 0.0136822i | \(0.995645\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.3523 | − | 0.838805i | 0.929161 | − | 0.0507668i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.2693 | + | 3.21101i | −0.981074 | + | 0.193631i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.2776 | 1.15828 | 0.579141 | − | 0.815228i | \(-0.303388\pi\) | ||||
0.579141 | + | 0.815228i | \(0.303388\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.4302 | + | 1.58157i | −0.863912 | + | 0.0946861i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.61183 | 0.334774 | 0.167387 | − | 0.985891i | \(-0.446467\pi\) | ||||
0.167387 | + | 0.985891i | \(0.446467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.2333 | 0.905524 | 0.452762 | − | 0.891631i | \(-0.350439\pi\) | ||||
0.452762 | + | 0.891631i | \(0.350439\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.8738 | − | 19.6069i | 0.644108 | − | 1.16141i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.91755 | −0.290274 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.6542 | 0.862013 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.333863 | − | 6.11054i | −0.0195714 | − | 0.358206i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.2814i | 1.76906i | 0.466485 | + | 0.884529i | \(0.345520\pi\) | ||||
−0.466485 | + | 0.884529i | \(0.654480\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.0742 | − | 16.0349i | 0.586540 | − | 0.933587i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.55405 | + | 17.1635i | −0.0901752 | + | 0.995926i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.8716 | 0.628723 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.6673 | 1.53708 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.4563 | − | 1.33623i | 1.40498 | − | 0.0767642i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.0270 | − | 23.9182i | 0.860443 | − | 1.36955i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.95142 | 0.225520 | 0.112760 | − | 0.993622i | \(-0.464031\pi\) | ||||
0.112760 | + | 0.993622i | \(0.464031\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.854489 | + | 15.6393i | 0.0486102 | + | 0.889690i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 25.7829i | − | 1.46201i | −0.682371 | − | 0.731006i | \(-0.739051\pi\) | ||
0.682371 | − | 0.731006i | \(-0.260949\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 22.3603i | − | 1.26388i | −0.775019 | − | 0.631939i | \(-0.782260\pi\) | ||
0.775019 | − | 0.631939i | \(-0.217740\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17.2259 | + | 8.35888i | 0.970572 | + | 0.470970i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.7447 | 0.884311 | 0.442156 | − | 0.896938i | \(-0.354214\pi\) | ||||
0.442156 | + | 0.896938i | \(0.354214\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.35802 | − | 12.9325i | 0.188013 | − | 0.724082i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.31132 | − | 24.0004i | −0.0731905 | − | 1.33957i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.86624 | 0.493331 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.74853 | − | 14.0095i | −0.374341 | − | 0.777109i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.14913 | − | 21.0320i | −0.0635471 | − | 1.16307i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.33030 | −0.459264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.04784 | −0.277455 | −0.138727 | − | 0.990331i | \(-0.544301\pi\) | ||||
−0.138727 | + | 0.990331i | \(0.544301\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.515322 | + | 4.70177i | 0.0282395 | + | 0.257656i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.87026 | − | 9.34360i | 0.320726 | − | 0.510495i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.0466 | 0.819639 | 0.409819 | − | 0.912167i | \(-0.365592\pi\) | ||||
0.409819 | + | 0.912167i | \(0.365592\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.42803 | + | 0.405847i | −0.403435 | + | 0.0220426i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.03340 | − | 15.5336i | 0.218421 | − | 0.841191i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7066 | 0.902074 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.8397 | + | 6.56619i | 0.637429 | + | 0.353512i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 1.80479i | − | 0.0968863i | −0.998826 | − | 0.0484432i | \(-0.984574\pi\) | ||
0.998826 | − | 0.0484432i | \(-0.0154260\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.5453i | 1.31388i | 0.753943 | + | 0.656940i | \(0.228150\pi\) | ||||
−0.753943 | + | 0.656940i | \(0.771850\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.9441 | + | 2.63441i | −0.851033 | + | 0.140615i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.2136 | −0.596839 | −0.298419 | − | 0.954435i | \(-0.596459\pi\) | ||||
−0.298419 | + | 0.954435i | \(0.596459\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.7688 | + | 18.7323i | −0.624626 | + | 0.994207i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.413084 | + | 7.56049i | 0.0218627 | + | 0.400143i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.81900 | −0.201559 | −0.100780 | − | 0.994909i | \(-0.532134\pi\) | ||||
−0.100780 | + | 0.994909i | \(0.532134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5113 | −0.763750 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.1266 | − | 8.34738i | −0.898915 | − | 0.438124i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 31.4714 | + | 19.7724i | 1.64729 | + | 1.03493i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.9646i | 1.30314i | 0.758588 | + | 0.651571i | \(0.225890\pi\) | ||||
−0.758588 | + | 0.651571i | \(0.774110\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.13789 | − | 0.563121i | 0.267468 | − | 0.0293149i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.94406 | −0.308600 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.56378 | 0.184525 | 0.0922627 | − | 0.995735i | \(-0.470590\pi\) | ||||
0.0922627 | + | 0.995735i | \(0.470590\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.11194 | − | 19.3330i | 0.0574205 | − | 0.998350i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.5291 | 0.645284 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.36403 | −0.0700653 | −0.0350326 | − | 0.999386i | \(-0.511154\pi\) | ||||
−0.0350326 | + | 0.999386i | \(0.511154\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.0360 | − | 1.58645i | 1.48756 | − | 0.0812762i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.1317 | −1.69295 | −0.846476 | − | 0.532426i | \(-0.821280\pi\) | ||||
−0.846476 | + | 0.532426i | \(0.821280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.4041 | + | 14.5184i | −0.785067 | + | 0.739926i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.8622 | + | 3.05374i | −1.41631 | + | 0.155230i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.703620i | 0.0356749i | 0.999841 | + | 0.0178375i | \(0.00567814\pi\) | ||||
−0.999841 | + | 0.0178375i | \(0.994322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.35392i | 0.270760i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.6996 | − | 1.56807i | 1.44770 | − | 0.0790985i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.0075 | − | 23.8871i | 0.755107 | − | 1.20189i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.3397i | 0.820067i | 0.912071 | + | 0.410033i | \(0.134483\pi\) | ||||
−0.912071 | + | 0.410033i | \(0.865517\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.56131 | − | 28.5760i | −0.0781633 | − | 1.43059i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.8574i | 1.39113i | 0.718463 | + | 0.695566i | \(0.244846\pi\) | ||||
−0.718463 | + | 0.695566i | \(0.755154\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.0491 | 0.749648 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.9550 | − | 6.76083i | −0.941880 | − | 0.335948i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.06130 | − | 1.31420i | −0.250879 | − | 0.0651425i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.0592i | 0.843525i | 0.906706 | + | 0.421763i | \(0.138588\pi\) | ||||
−0.906706 | + | 0.421763i | \(0.861412\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27.4637 | + | 1.50054i | −1.35468 | + | 0.0740161i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 24.1722i | − | 1.18944i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.33524 | + | 5.30865i | −0.163721 | + | 0.260591i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.81596 | − | 33.2367i | −0.0889280 | − | 1.62761i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.0521i | 1.12617i | 0.826399 | + | 0.563085i | \(0.190386\pi\) | ||||
−0.826399 | + | 0.563085i | \(0.809614\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.43047 | −0.313402 | −0.156701 | − | 0.987646i | \(-0.550086\pi\) | ||||
−0.156701 | + | 0.987646i | \(0.550086\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.70356 | − | 0.953924i | 0.423181 | − | 0.0463814i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.89924 | − | 3.32343i | 0.334662 | − | 0.161210i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 36.0561i | − | 1.74488i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.54001 | − | 17.5116i | 0.170913 | − | 0.845469i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.9821 | 1.49236 | 0.746178 | − | 0.665746i | \(-0.231887\pi\) | ||||
0.746178 | + | 0.665746i | \(0.231887\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 19.6214i | − | 0.942943i | −0.881881 | − | 0.471472i | \(-0.843723\pi\) | ||
0.881881 | − | 0.471472i | \(-0.156277\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.6448 | + | 7.56729i | 0.654219 | + | 0.362824i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 20.2359i | − | 0.968016i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.47009i | − | 0.165618i | −0.996565 | − | 0.0828091i | \(-0.973611\pi\) | ||
0.996565 | − | 0.0828091i | \(-0.0263892\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.41978 | − | 0.374813i | 0.162847 | − | 0.0178482i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.74196 | −0.0827631 | −0.0413815 | − | 0.999143i | \(-0.513176\pi\) | ||||
−0.0413815 | + | 0.999143i | \(0.513176\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.8137 | + | 28.3538i | −0.844450 | + | 1.34410i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.99695 | + | 0.436931i | −0.378243 | + | 0.0206661i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 29.9424i | − | 1.41307i | −0.707679 | − | 0.706534i | \(-0.750258\pi\) | ||
0.707679 | − | 0.706534i | \(-0.249742\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.43610 | + | 5.53076i | −0.0676233 | + | 0.260433i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.351004 | + | 6.42427i | 0.0164916 | + | 0.301839i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.8074 | − | 10.5595i | −0.787944 | − | 0.495038i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3336 | −0.670495 | −0.335248 | − | 0.942130i | \(-0.608820\pi\) | ||||
−0.335248 | + | 0.942130i | \(0.608820\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.29736 | − | 7.85195i | −0.0605557 | − | 0.366497i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.3747 | −0.762646 | −0.381323 | − | 0.924442i | \(-0.624531\pi\) | ||||
−0.381323 | + | 0.924442i | \(0.624531\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.6647i | 0.820950i | 0.911872 | + | 0.410475i | \(0.134637\pi\) | ||||
−0.911872 | + | 0.410475i | \(0.865363\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.3891 | + | 9.08927i | 0.760028 | + | 0.421505i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.6501 | 1.64969 | 0.824845 | − | 0.565358i | \(-0.191262\pi\) | ||||
0.824845 | + | 0.565358i | \(0.191262\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 14.0852i | − | 0.650396i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.14468 | − | 20.9505i | −0.0527439 | − | 0.965347i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.78780 | − | 29.9926i | 0.358083 | − | 1.37906i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.0767 | + | 12.5614i | −1.19648 | + | 0.576356i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.21040 | − | 0.680670i | 0.284355 | − | 0.0311657i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.2573 | −1.56525 | −0.782627 | − | 0.622491i | \(-0.786121\pi\) | ||||
−0.782627 | + | 0.622491i | \(0.786121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 4.90343i | − | 0.223577i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.2557 | − | 0.942806i | 0.785163 | − | 0.0428991i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.20292 | + | 6.68972i | −0.190845 | + | 0.303765i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.65422i | − | 0.120274i | −0.998190 | − | 0.0601371i | \(-0.980846\pi\) | ||
0.998190 | − | 0.0601371i | \(-0.0191538\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.39315 | + | 25.4982i | 0.0630003 | + | 1.15307i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.84041 | 0.0830567 | 0.0415283 | − | 0.999137i | \(-0.486777\pi\) | ||||
0.0415283 | + | 0.999137i | \(0.486777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.17019i | 0.277892i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.4318 | − | 16.9329i | 0.648662 | − | 0.761077i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.2385i | 1.26667i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.8478 | 0.485615 | 0.242807 | − | 0.970075i | \(-0.421932\pi\) | ||||
0.242807 | + | 0.970075i | \(0.421932\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.50306 | + | 27.5099i | 0.0671520 | + | 1.22905i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.36875i | 0.150205i | 0.997176 | + | 0.0751025i | \(0.0239284\pi\) | ||||
−0.997176 | + | 0.0751025i | \(0.976072\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.7744 | − | 16.8214i | −1.19145 | − | 0.748544i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.75502 | + | 0.314438i | −0.255590 | + | 0.0139647i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.5352i | 0.865884i | 0.901422 | + | 0.432942i | \(0.142524\pi\) | ||||
−0.901422 | + | 0.432942i | \(0.857476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 47.4423 | 2.09872 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.90357 | + | 29.6776i | 0.216498 | + | 1.31030i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.7570 | − | 17.1217i | 0.474008 | − | 0.754472i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.43275 | + | 9.36908i | −0.106992 | + | 0.412052i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.636823 | − | 11.6555i | −0.0279534 | − | 0.511619i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.5830i | 1.20843i | 0.796820 | + | 0.604217i | \(0.206514\pi\) | ||||
−0.796820 | + | 0.604217i | \(0.793486\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.8074 | −0.997298 | −0.498649 | − | 0.866804i | \(-0.666170\pi\) | ||||
−0.498649 | + | 0.866804i | \(0.666170\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.9264 | − | 21.6511i | −0.520510 | − | 0.944929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.41118i | 0.322836i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.7804 | −0.468714 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.76802 | + | 25.2553i | 0.120122 | + | 1.09599i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.35825 | −0.232092 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.5078 | + | 26.2753i | −0.713696 | + | 1.13598i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.08914 | + | 19.9340i | 0.0469998 | + | 0.860216i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.955867 | + | 3.68127i | −0.0411721 | + | 0.158564i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.48613i | 0.321854i | 0.986966 | + | 0.160927i | \(0.0514484\pi\) | ||||
−0.986966 | + | 0.160927i | \(0.948552\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −36.0392 | + | 1.96908i | −1.54659 | + | 0.0845013i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.4661 | + | 23.0255i | −0.619662 | + | 0.986306i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.3067 | 0.825495 | 0.412748 | − | 0.910845i | \(-0.364569\pi\) | ||||
0.412748 | + | 0.910845i | \(0.364569\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.12888 | + | 37.6717i | 0.176216 | + | 1.60779i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 23.3212i | − | 0.993515i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 36.0093i | − | 1.53127i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.96155 | − | 5.34006i | 0.125711 | − | 0.226673i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.75354i | 0.0742999i | 0.999310 | + | 0.0371499i | \(0.0118279\pi\) | ||||
−0.999310 | + | 0.0371499i | \(0.988172\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.0572 | 1.22899 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.62390 | + | 1.74334i | 0.364101 | + | 0.0736038i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.8178i | 1.80456i | 0.431156 | + | 0.902278i | \(0.358106\pi\) | ||||
−0.431156 | + | 0.902278i | \(0.641894\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.13209 | + | 5.10911i | 0.342120 | + | 0.214942i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −25.0784 | + | 5.56411i | −1.05319 | + | 0.233671i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.0195 | −1.46810 | −0.734048 | − | 0.679098i | \(-0.762371\pi\) | ||||
−0.734048 | + | 0.679098i | \(0.762371\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.23069i | − | 0.0515027i | −0.999668 | − | 0.0257514i | \(-0.991802\pi\) | ||
0.999668 | − | 0.0257514i | \(-0.00819782\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.553269 | − | 10.1262i | −0.0231131 | − | 0.423029i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.58526 | − | 15.7465i | −0.316327 | − | 0.656676i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 15.4170i | − | 0.641816i | −0.947110 | − | 0.320908i | \(-0.896012\pi\) | ||
0.947110 | − | 0.320908i | \(-0.103988\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.74795 | − | 0.532601i | 0.405111 | − | 0.0221341i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00266i | 0.332006i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.73588 | + | 6.68528i | −0.0718928 | + | 0.276876i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.7697 | + | 9.10799i | 0.776032 | + | 0.376569i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.1973 | 1.24638 | 0.623188 | − | 0.782072i | \(-0.285837\pi\) | ||||
0.623188 | + | 0.782072i | \(0.285837\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 28.0116i | − | 1.15420i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.670214 | − | 12.2666i | −0.0275689 | − | 0.504581i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.2410i | 0.420547i | 0.977643 | + | 0.210273i | \(0.0674354\pi\) | ||||
−0.977643 | + | 0.210273i | \(0.932565\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.20021 | − | 8.27710i | 0.213188 | − | 0.339328i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.68198 | − | 0.146536i | 0.109766 | − | 0.00599732i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 23.8017i | − | 0.972510i | −0.873817 | − | 0.486255i | \(-0.838363\pi\) | ||
0.873817 | − | 0.486255i | \(-0.161637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.9489i | 0.976894i | 0.872594 | + | 0.488447i | \(0.162436\pi\) | ||||
−0.872594 | + | 0.488447i | \(0.837564\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.61294 | + | 14.7164i | 0.0656839 | + | 0.599297i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.8303 | + | 21.5649i | 0.480969 | + | 0.876738i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.2526 | 0.659673 | 0.329836 | − | 0.944038i | \(-0.393006\pi\) | ||||
0.329836 | + | 0.944038i | \(0.393006\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.8866 | − | 1.08655i | 0.805845 | − | 0.0440291i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.07685 | −0.367210 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.3624 | −0.983989 | −0.491995 | − | 0.870598i | \(-0.663732\pi\) | ||||
−0.491995 | + | 0.870598i | \(0.663732\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.83538 | − | 3.23625i | −0.235305 | − | 0.130498i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.6638 | 1.55655 | 0.778273 | − | 0.627926i | \(-0.216096\pi\) | ||||
0.778273 | + | 0.627926i | \(0.216096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.2276 | −1.77766 | −0.888828 | − | 0.458240i | \(-0.848480\pi\) | ||||
−0.888828 | + | 0.458240i | \(0.848480\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.9210 | + | 2.96105i | −0.719143 | + | 0.118823i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 42.7426i | 1.71245i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.5830 | + | 19.5492i | −0.623318 | + | 0.781968i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −32.5953 | − | 6.58920i | −1.30173 | − | 0.263147i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.41478 | 0.0962836 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.4500 | −1.17239 | −0.586193 | − | 0.810171i | \(-0.699374\pi\) | ||||
−0.586193 | + | 0.810171i | \(0.699374\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.13556 | − | 20.7836i | −0.0451344 | − | 0.826075i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31.7882 | − | 19.9714i | −1.26148 | − | 0.792541i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.56645 | −0.141308 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.23366 | − | 29.5038i | −0.127922 | − | 1.16715i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 10.5555i | − | 0.416917i | −0.978031 | − | 0.208459i | \(-0.933155\pi\) | ||
0.978031 | − | 0.208459i | \(-0.0668447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.1520i | 0.834154i | 0.908871 | + | 0.417077i | \(0.136946\pi\) | ||||
−0.908871 | + | 0.417077i | \(0.863054\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.6446 | + | 17.5498i | 1.24600 | + | 0.691022i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.9567 | −1.61017 | −0.805087 | − | 0.593156i | \(-0.797882\pi\) | ||||
−0.805087 | + | 0.593156i | \(0.797882\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.1864 | − | 7.05914i | −1.06716 | − | 0.277096i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.8863 | − | 1.30508i | 0.936178 | − | 0.0511501i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.7908 | 1.75280 | 0.876400 | − | 0.481584i | \(-0.159938\pi\) | ||||
0.876400 | + | 0.481584i | \(0.159938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31.4199 | − | 19.7400i | −1.22768 | − | 0.771307i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −49.5680 | + | 5.43274i | −1.93383 | + | 0.211951i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.1491 | −0.862806 | −0.431403 | − | 0.902159i | \(-0.641981\pi\) | ||||
−0.431403 | + | 0.902159i | \(0.641981\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.6906 | 1.19372 | 0.596862 | − | 0.802344i | \(-0.296414\pi\) | ||||
0.596862 | + | 0.802344i | \(0.296414\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.450104 | + | 8.23805i | 0.0174806 | + | 0.319939i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.6550 | + | 31.2845i | −0.762187 | + | 1.21316i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.0826 | 0.545280 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.44541 | + | 44.7573i | 0.0945451 | + | 1.73042i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40.5523 | − | 10.5297i | −1.56550 | − | 0.406494i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.6146 | −0.948825 | −0.474412 | − | 0.880303i | \(-0.657339\pi\) | ||||
−0.474412 | + | 0.880303i | \(0.657339\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.9401 | + | 21.2555i | 0.575044 | + | 0.818123i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.01530i | 0.346486i | 0.984879 | + | 0.173243i | \(0.0554246\pi\) | ||||
−0.984879 | + | 0.173243i | \(0.944575\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0846i | 0.387011i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.06885 | + | 19.5628i | 0.0409586 | + | 0.749647i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.47492 | −0.209492 | −0.104746 | − | 0.994499i | \(-0.533403\pi\) | ||||
−0.104746 | + | 0.994499i | \(0.533403\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.0668 | + | 18.8899i | 1.14879 | + | 0.721747i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.63308 | + | 0.417050i | −0.291220 | + | 0.0159114i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.47676 | −0.246745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.6040 | 1.54465 | 0.772325 | − | 0.635228i | \(-0.219094\pi\) | ||||
0.772325 | + | 0.635228i | \(0.219094\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.10016 | − | 28.1019i | 0.155752 | − | 1.06750i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.8607 | + | 36.3870i | −0.867156 | + | 1.38024i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.63876i | − | 0.0999503i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.535109 | + | 9.79385i | 0.0202397 | + | 0.370437i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.21074 | 0.0457290 | 0.0228645 | − | 0.999739i | \(-0.492721\pi\) | ||||
0.0228645 | + | 0.999739i | \(0.492721\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.12701 | −0.344232 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.88511 | − | 5.48219i | −0.372295 | − | 0.206471i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −40.3618 | −1.51796 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.8172 | −1.19492 | −0.597461 | − | 0.801898i | \(-0.703824\pi\) | ||||
−0.597461 | + | 0.801898i | \(0.703824\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.12351 | + | 37.6227i | 0.154644 | + | 1.41096i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.9150 | 0.633471 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.7846 | + | 15.8195i | −0.627710 | + | 0.591616i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −38.3160 | + | 2.09348i | −1.43094 | + | 0.0781824i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 8.98425i | − | 0.335056i | −0.985867 | − | 0.167528i | \(-0.946422\pi\) | ||
0.985867 | − | 0.167528i | \(-0.0535785\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 25.8105i | − | 0.961235i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.05011 | − | 19.2197i | −0.0390540 | − | 0.714788i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.74172 | − | 18.1473i | −0.324659 | − | 0.673973i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.4630i | 1.24107i | 0.784177 | + | 0.620537i | \(0.213085\pi\) | ||||
−0.784177 | + | 0.620537i | \(0.786915\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.5650 | − | 8.68522i | 0.946850 | − | 0.321675i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.3097i | 0.529263i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.4593 | 0.497132 | 0.248566 | − | 0.968615i | \(-0.420041\pi\) | ||||
0.248566 | + | 0.968615i | \(0.420041\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.88403 | − | 2.15405i | −0.143265 | − | 0.0794532i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.8417 | − | 4.11339i | −0.583535 | − | 0.151519i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.2072i | 1.62619i | 0.582132 | + | 0.813094i | \(0.302219\pi\) | ||||
−0.582132 | + | 0.813094i | \(0.697781\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.70123 | − | 31.1369i | −0.0624964 | − | 1.14384i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 15.5730i | − | 0.571319i | −0.958331 | − | 0.285659i | \(-0.907787\pi\) | ||
0.958331 | − | 0.285659i | \(-0.0922126\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.75494 | + | 5.50042i | 0.320756 | + | 0.201520i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.916405 | − | 8.36124i | −0.0335295 | − | 0.305922i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 39.6093i | 1.44729i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.8398 | −0.614493 | −0.307247 | − | 0.951630i | \(-0.599408\pi\) | ||||
−0.307247 | + | 0.951630i | \(0.599408\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.757108 | + | 13.8570i | 0.0275905 | + | 0.504977i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.41871 | − | 7.03319i | 0.160813 | − | 0.255964i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.0102i | 1.01805i | 0.860753 | + | 0.509023i | \(0.169993\pi\) | ||||
−0.860753 | + | 0.509023i | \(0.830007\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.97892 | − | 19.6828i | 0.144426 | − | 0.714442i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0535 | 0.654437 | 0.327219 | − | 0.944949i | \(-0.393889\pi\) | ||||
0.327219 | + | 0.944949i | \(0.393889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.7104i | 1.25660i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.48539 | + | 9.24346i | −0.162170 | + | 0.334198i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 26.3385i | − | 0.951027i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.2306i | 1.81136i | 0.423961 | + | 0.905680i | \(0.360639\pi\) | ||||
−0.423961 | + | 0.905680i | \(0.639361\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.5519 | + | 1.56000i | −1.02827 | + | 0.0561818i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.37504 | −0.121392 | −0.0606959 | − | 0.998156i | \(-0.519332\pi\) | ||||
−0.0606959 | + | 0.998156i | \(0.519332\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.4999 | − | 21.7972i | −0.377168 | − | 0.782977i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.425234 | − | 7.78286i | −0.0152552 | − | 0.279208i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.97359i | 0.357341i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.7598 | + | 8.24665i | 1.13645 | + | 0.295088i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.6532 | + | 3.41250i | −0.738086 | + | 0.121953i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.4101 | + | 22.9363i | −0.514317 | + | 0.818630i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.6114 | −1.19812 | −0.599058 | − | 0.800706i | \(-0.704458\pi\) | ||||
−0.599058 | + | 0.800706i | \(0.704458\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.59738 | − | 29.2360i | −0.0568681 | − | 1.04083i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.2589 | 0.435877 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 39.2874i | − | 1.39514i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.05349 | − | 3.91180i | −0.250162 | − | 0.138737i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.5377 | −0.514952 | −0.257476 | − | 0.966285i | \(-0.582891\pi\) | ||||
−0.257476 | + | 0.966285i | \(0.582891\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.47005i | − | 0.158139i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.89457 | − | 44.6578i | −0.172941 | − | 1.57791i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.8548 | − | 53.3583i | 0.488927 | − | 1.88297i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.8913 | − | 11.8688i | −0.665831 | − | 0.418319i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.10383 | + | 20.2029i | 0.0388567 | + | 0.711177i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.5054 | 1.52957 | 0.764785 | − | 0.644286i | \(-0.222845\pi\) | ||||
0.764785 | + | 0.644286i | \(0.222845\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.57717i | 0.125612i | 0.998026 | + | 0.0628058i | \(0.0200049\pi\) | ||||
−0.998026 | + | 0.0628058i | \(0.979995\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0425669 | + | 0.779082i | 0.00149289 | + | 0.0273236i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.5380 | − | 27.9150i | 0.614330 | − | 0.977819i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 54.0856i | − | 1.89222i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 26.4720 | − | 2.90138i | 0.925008 | − | 0.101382i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.4349 | −1.06219 | −0.531093 | − | 0.847314i | \(-0.678218\pi\) | ||||
−0.531093 | + | 0.847314i | \(0.678218\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.8246i | − | 0.935048i | −0.883980 | − | 0.467524i | \(-0.845146\pi\) | ||
0.883980 | − | 0.467524i | \(-0.154854\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.8338 | + | 7.09069i | −0.969050 | + | 0.246866i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.9746i | 0.451171i | 0.974223 | + | 0.225585i | \(0.0724294\pi\) | ||||
−0.974223 | + | 0.225585i | \(0.927571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.4042 | 0.882324 | 0.441162 | − | 0.897428i | \(-0.354566\pi\) | ||||
0.441162 | + | 0.897428i | \(0.354566\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.3401 | − | 1.82161i | 1.15656 | − | 0.0631910i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.75636i | − | 0.0608543i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.9217 | − | 30.1174i | 0.654813 | − | 1.04226i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.8071 | + | 4.09884i | −0.857460 | + | 0.141677i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.8716i | 0.893185i | 0.894737 | + | 0.446593i | \(0.147363\pi\) | ||||
−0.894737 | + | 0.446593i | \(0.852637\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.7703 | −0.440357 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.70550 | − | 0.530281i | 0.334275 | − | 0.0182639i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.30051 | + | 3.95839i | 0.216744 | + | 0.136173i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.4305 | + | 15.2749i | 0.942524 | + | 0.524852i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.3455 | − | 1.43945i | 0.904176 | − | 0.0494016i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 5.51139i | − | 0.188928i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.5474 | −1.38831 | −0.694157 | − | 0.719823i | \(-0.744223\pi\) | ||||
−0.694157 | + | 0.719823i | \(0.744223\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.9532 | − | 34.9370i | 0.579787 | − | 1.19482i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.8235i | 0.779635i | 0.920892 | + | 0.389818i | \(0.127462\pi\) | ||||
−0.920892 | + | 0.389818i | \(0.872538\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.3018 | 0.453851 | 0.226926 | − | 0.973912i | \(-0.427133\pi\) | ||||
0.226926 | + | 0.973912i | \(0.427133\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.50476 | + | 0.464676i | −0.289841 | + | 0.0158361i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.6076 | −0.599370 | −0.299685 | − | 0.954038i | \(-0.596882\pi\) | ||||
−0.299685 | + | 0.954038i | \(0.596882\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.01681 | + | 12.7602i | −0.272580 | + | 0.433861i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.3440 | − | 1.38473i | 0.860729 | − | 0.0470278i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.4996 | − | 10.5160i | −1.37385 | − | 0.356731i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 15.3475i | − | 0.520032i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.15481 | − | 10.5364i | −0.0390845 | − | 0.356605i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.56773 | + | 31.7114i | −0.120611 | + | 1.07204i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.2099 | 1.45909 | 0.729547 | − | 0.683930i | \(-0.239731\pi\) | ||||
0.729547 | + | 0.683930i | \(0.239731\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.86140 | + | 52.3708i | 0.0965125 | + | 1.76642i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.8470i | − | 0.803427i | −0.915765 | − | 0.401714i | \(-0.868415\pi\) | ||
0.915765 | − | 0.401714i | \(-0.131585\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.6588i | 1.63750i | 0.574152 | + | 0.818749i | \(0.305332\pi\) | ||||
−0.574152 | + | 0.818749i | \(0.694668\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.9078 | − | 28.6838i | 0.534734 | − | 0.964196i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.99894i | 0.201425i | 0.994916 | + | 0.100712i | \(0.0321122\pi\) | ||||
−0.994916 | + | 0.100712i | \(0.967888\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −47.9199 | −1.60718 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.06585 | + | 29.8306i | −0.0357073 | + | 0.999362i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.8952i | 0.565377i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.7109 | − | 21.8234i | 0.458305 | − | 0.729477i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.8022 | − | 1.02730i | 0.627786 | − | 0.0343005i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.4939 | 0.650157 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.18959i | − | 0.106261i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 46.1203 | − | 2.51988i | 1.53479 | − | 0.0838565i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 39.4551 | + | 24.7883i | 1.31153 | + | 0.823990i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 43.4114i | − | 1.44145i | −0.693220 | − | 0.720726i | \(-0.743809\pi\) | ||
0.693220 | − | 0.720726i | \(-0.256191\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42.1703 | − | 4.62193i | 1.39870 | − | 0.153300i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.4001i | 1.70296i | 0.524385 | + | 0.851481i | \(0.324295\pi\) | ||||
−0.524385 | + | 0.851481i | \(0.675705\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.00058 | + | 2.33706i | 0.297876 | + | 0.0773455i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23.7286 | − | 42.7858i | 0.784444 | − | 1.41446i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −47.3647 | −1.56412 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 59.0084i | − | 1.94651i | −0.229733 | − | 0.973254i | \(-0.573785\pi\) | ||
0.229733 | − | 0.973254i | \(-0.426215\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.83387 | − | 0.373384i | 0.225184 | − | 0.0123034i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.7692i | 1.01278i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.10216 | + | 3.42118i | −0.233517 | + | 0.112488i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.95563 | + | 26.9670i | 0.0970756 | + | 0.885713i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 55.7545i | − | 1.82925i | −0.404306 | − | 0.914624i | \(-0.632487\pi\) | ||
0.404306 | − | 0.914624i | \(-0.367513\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.63842i | 0.217565i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.43631 | − | 44.5907i | −0.0797613 | − | 1.45983i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.79060 | − | 8.26588i | −0.254780 | − | 0.270323i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.426723 | −0.0139404 | −0.00697022 | − | 0.999976i | \(-0.502219\pi\) | ||||
−0.00697022 | + | 0.999976i | \(0.502219\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.11290 | − | 38.6714i | −0.0689519 | − | 1.26199i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.83536 | −0.190227 | −0.0951136 | − | 0.995466i | \(-0.530321\pi\) | ||||
−0.0951136 | + | 0.995466i | \(0.530321\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.02261 | −0.196123 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 30.5816 | + | 12.8287i | 0.994820 | + | 0.417318i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.0982 | −1.23803 | −0.619013 | − | 0.785381i | \(-0.712467\pi\) | ||||
−0.619013 | + | 0.785381i | \(0.712467\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 51.6940 | 1.67806 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.2300 | − | 1.48777i | 0.882994 | − | 0.0482443i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.9366i | 1.06692i | 0.845825 | + | 0.533461i | \(0.179109\pi\) | ||||
−0.845825 | + | 0.533461i | \(0.820891\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.96497 | + | 11.0860i | −0.225381 | + | 0.358736i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.58556 | − | 22.6837i | 0.148230 | − | 0.733261i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.3250 | 1.46362 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.58541 | −0.244691 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.53577 | − | 41.3841i | −0.146163 | − | 1.33358i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.6719 | − | 6.70478i | −0.343541 | − | 0.215835i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.2073 | 0.874928 | 0.437464 | − | 0.899236i | \(-0.355877\pi\) | ||||
0.437464 | + | 0.899236i | \(0.355877\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.3339 | − | 0.837802i | 0.492596 | − | 0.0269141i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.2003i | 0.680351i | 0.940362 | + | 0.340176i | \(0.110487\pi\) | ||||
−0.940362 | + | 0.340176i | \(0.889513\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 54.8525i | 1.75849i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.9952 | − | 23.5914i | −0.416179 | − | 0.755529i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.4560 | 1.13434 | 0.567169 | − | 0.823601i | \(-0.308039\pi\) | ||||
0.567169 | + | 0.823601i | \(0.308039\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.0726 | + | 12.4824i | 1.53641 | + | 0.398938i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.97478 | − | 36.2657i | −0.126905 | − | 1.15788i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.3822 | −0.777670 | −0.388835 | − | 0.921307i | \(-0.627122\pi\) | ||||
−0.388835 | + | 0.921307i | \(0.627122\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.43716 | + | 13.4293i | −0.268830 | + | 0.427893i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.4070 | + | 0.787159i | −0.458580 | + | 0.0250556i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.6599 | 1.03852 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.2746 | −1.18407 | −0.592034 | − | 0.805913i | \(-0.701675\pi\) | ||||
−0.592034 | + | 0.805913i | \(0.701675\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.73010 | + | 0.476988i | −0.277041 | + | 0.0151368i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.93619 | − | 1.84471i | −0.0930835 | − | 0.0584811i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.9697 | 0.949151 | 0.474575 | − | 0.880215i | \(-0.342602\pi\) | ||||
0.474575 | + | 0.880215i | \(0.342602\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.33552 | + | 8.08289i | 0.0422540 | + | 0.255731i |
(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 | 1320.2.ba.a.329.69 | yes | 72 | |
3.2 | odd | 2 | inner | 1320.2.ba.a.329.1 | ✓ | 72 | |
5.4 | even | 2 | inner | 1320.2.ba.a.329.4 | yes | 72 | |
11.10 | odd | 2 | inner | 1320.2.ba.a.329.70 | yes | 72 | |
15.14 | odd | 2 | inner | 1320.2.ba.a.329.72 | yes | 72 | |
33.32 | even | 2 | inner | 1320.2.ba.a.329.2 | yes | 72 | |
55.54 | odd | 2 | inner | 1320.2.ba.a.329.3 | yes | 72 | |
165.164 | even | 2 | inner | 1320.2.ba.a.329.71 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1320.2.ba.a.329.1 | ✓ | 72 | 3.2 | odd | 2 | inner | |
1320.2.ba.a.329.2 | yes | 72 | 33.32 | even | 2 | inner | |
1320.2.ba.a.329.3 | yes | 72 | 55.54 | odd | 2 | inner | |
1320.2.ba.a.329.4 | yes | 72 | 5.4 | even | 2 | inner | |
1320.2.ba.a.329.69 | yes | 72 | 1.1 | even | 1 | trivial | |
1320.2.ba.a.329.70 | yes | 72 | 11.10 | odd | 2 | inner | |
1320.2.ba.a.329.71 | yes | 72 | 165.164 | even | 2 | inner | |
1320.2.ba.a.329.72 | yes | 72 | 15.14 | odd | 2 | inner |