Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(337,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 337.11 | ||
Character | \(\chi\) | \(=\) | 1148.337 |
Dual form | 1148.2.k.b.729.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.178034 | + | 0.178034i | 0.102788 | + | 0.102788i | 0.756631 | − | 0.653842i | \(-0.226844\pi\) |
−0.653842 | + | 0.756631i | \(0.726844\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.542323i | − | 0.242534i | −0.992620 | − | 0.121267i | \(-0.961304\pi\) | ||
0.992620 | − | 0.121267i | \(-0.0386957\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.93661i | − | 0.978869i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.525032 | + | 0.525032i | 0.158303 | + | 0.158303i | 0.781814 | − | 0.623511i | \(-0.214294\pi\) |
−0.623511 | + | 0.781814i | \(0.714294\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.31231 | − | 2.31231i | −0.641319 | − | 0.641319i | 0.309560 | − | 0.950880i | \(-0.399818\pi\) |
−0.950880 | + | 0.309560i | \(0.899818\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0965521 | − | 0.0965521i | 0.0249296 | − | 0.0249296i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.596624 | − | 0.596624i | 0.144703 | − | 0.144703i | −0.631044 | − | 0.775747i | \(-0.717373\pi\) |
0.775747 | + | 0.631044i | \(0.217373\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.07297 | + | 3.07297i | −0.704988 | + | 0.704988i | −0.965477 | − | 0.260489i | \(-0.916116\pi\) |
0.260489 | + | 0.965477i | \(0.416116\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.251779i | − | 0.0549426i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.35862 | −0.700321 | −0.350161 | − | 0.936690i | \(-0.613873\pi\) | ||||
−0.350161 | + | 0.936690i | \(0.613873\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.70589 | 0.941177 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.05692 | − | 1.05692i | 0.203404 | − | 0.203404i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.56855 | − | 6.56855i | −1.21975 | − | 1.21975i | −0.967720 | − | 0.252029i | \(-0.918902\pi\) |
−0.252029 | − | 0.967720i | \(-0.581098\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.61993 | −1.54818 | −0.774092 | − | 0.633073i | \(-0.781793\pi\) | ||||
−0.774092 | + | 0.633073i | \(0.781793\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.186947i | 0.0325434i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.383480 | + | 0.383480i | −0.0648200 | + | 0.0648200i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.51447 | −0.248977 | −0.124488 | − | 0.992221i | \(-0.539729\pi\) | ||||
−0.124488 | + | 0.992221i | \(0.539729\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.823341i | − | 0.131840i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.28597 | + | 6.27266i | −0.200834 | + | 0.979625i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.10884i | − | 1.08409i | −0.840350 | − | 0.542044i | \(-0.817651\pi\) | ||
0.840350 | − | 0.542044i | \(-0.182349\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.59259 | −0.237409 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.92171 | − | 4.92171i | 0.717905 | − | 0.717905i | −0.250271 | − | 0.968176i | \(-0.580520\pi\) |
0.968176 | + | 0.250271i | \(0.0805196\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.212439 | 0.0297475 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.28325 | − | 3.28325i | −0.450989 | − | 0.450989i | 0.444694 | − | 0.895683i | \(-0.353313\pi\) |
−0.895683 | + | 0.444694i | \(0.853313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.284737 | − | 0.284737i | 0.0383939 | − | 0.0383939i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.09419 | −0.144929 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.28001 | 1.20815 | 0.604077 | − | 0.796926i | \(-0.293542\pi\) | ||||
0.604077 | + | 0.796926i | \(0.293542\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.51233i | − | 0.833819i | −0.908948 | − | 0.416909i | \(-0.863113\pi\) | ||
0.908948 | − | 0.416909i | \(-0.136887\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.07650 | + | 2.07650i | −0.261614 | + | 0.261614i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.25402 | + | 1.25402i | −0.155542 | + | 0.155542i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.81360 | − | 1.81360i | 0.221566 | − | 0.221566i | −0.587592 | − | 0.809158i | \(-0.699924\pi\) |
0.809158 | + | 0.587592i | \(0.199924\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.597950 | − | 0.597950i | −0.0719848 | − | 0.0719848i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.46972 | − | 6.46972i | −0.767815 | − | 0.767815i | 0.209907 | − | 0.977721i | \(-0.432684\pi\) |
−0.977721 | + | 0.209907i | \(0.932684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.1427i | − | 1.42120i | −0.703596 | − | 0.710600i | \(-0.748424\pi\) | ||
0.703596 | − | 0.710600i | \(-0.251576\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.837809 | + | 0.837809i | 0.0967419 | + | 0.0967419i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.742507i | − | 0.0846165i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2071 | + | 10.2071i | 1.14839 | + | 1.14839i | 0.986870 | + | 0.161516i | \(0.0516382\pi\) |
0.161516 | + | 0.986870i | \(0.448362\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.43349 | −0.937054 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.06535 | −0.775523 | −0.387761 | − | 0.921760i | \(-0.626752\pi\) | ||||
−0.387761 | + | 0.921760i | \(0.626752\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.323563 | − | 0.323563i | −0.0350953 | − | 0.0350953i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.33885i | − | 0.250751i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.76083 | − | 2.76083i | −0.292647 | − | 0.292647i | 0.545478 | − | 0.838125i | \(-0.316348\pi\) |
−0.838125 | + | 0.545478i | \(0.816348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.27010i | 0.342800i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.53464 | − | 1.53464i | −0.159135 | − | 0.159135i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.66654 | + | 1.66654i | 0.170984 | + | 0.170984i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.05222 | + | 7.05222i | −0.716045 | + | 0.716045i | −0.967793 | − | 0.251748i | \(-0.918995\pi\) |
0.251748 | + | 0.967793i | \(0.418995\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.54181 | − | 1.54181i | 0.154958 | − | 0.154958i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.12741 | − | 4.12741i | 0.410692 | − | 0.410692i | −0.471287 | − | 0.881980i | \(-0.656210\pi\) |
0.881980 | + | 0.471287i | \(0.156210\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.9721i | 1.57377i | 0.617097 | + | 0.786887i | \(0.288309\pi\) | ||||
−0.617097 | + | 0.786887i | \(0.711691\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.136545 | −0.0133255 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.63533 | 0.448114 | 0.224057 | − | 0.974576i | \(-0.428070\pi\) | ||||
0.224057 | + | 0.974576i | \(0.428070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0759 | − | 10.0759i | 0.965099 | − | 0.965099i | −0.0343125 | − | 0.999411i | \(-0.510924\pi\) |
0.999411 | + | 0.0343125i | \(0.0109242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.269627 | − | 0.269627i | −0.0255919 | − | 0.0255919i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.73727 | 0.257501 | 0.128750 | − | 0.991677i | \(-0.458903\pi\) | ||||
0.128750 | + | 0.991677i | \(0.458903\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.82146i | 0.169852i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.79035 | + | 6.79035i | −0.627768 | + | 0.627768i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.843754 | −0.0773468 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.4487i | − | 0.949880i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.34570 | + | 0.887804i | −0.121337 | + | 0.0800505i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.26372i | − | 0.470802i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.9542 | 1.14950 | 0.574749 | − | 0.818330i | \(-0.305100\pi\) | ||||
0.574749 | + | 0.818330i | \(0.305100\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.26562 | − | 1.26562i | 0.111432 | − | 0.111432i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 0.793872i | − | 0.0693609i | −0.999398 | − | 0.0346805i | \(-0.988959\pi\) | ||
0.999398 | − | 0.0346805i | \(-0.0110413\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.34583 | 0.376832 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.573192 | − | 0.573192i | −0.0493325 | − | 0.0493325i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.86929 | + | 7.86929i | −0.672318 | + | 0.672318i | −0.958250 | − | 0.285932i | \(-0.907697\pi\) |
0.285932 | + | 0.958250i | \(0.407697\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.697026 | −0.0591210 | −0.0295605 | − | 0.999563i | \(-0.509411\pi\) | ||||
−0.0295605 | + | 0.999563i | \(0.509411\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.75247 | 0.147584 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.42807i | − | 0.203046i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.56227 | + | 3.56227i | −0.295831 | + | 0.295831i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.178034 | + | 0.178034i | −0.0146840 | + | 0.0146840i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.4542 | + | 11.4542i | −0.938368 | + | 0.938368i | −0.998208 | − | 0.0598400i | \(-0.980941\pi\) |
0.0598400 | + | 0.998208i | \(0.480941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.4949 | − | 13.4949i | −1.09820 | − | 1.09820i | −0.994621 | − | 0.103581i | \(-0.966970\pi\) |
−0.103581 | − | 0.994621i | \(-0.533030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.75205 | − | 1.75205i | −0.141645 | − | 0.141645i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.67478i | 0.375488i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.08910 | − | 1.08910i | −0.0869198 | − | 0.0869198i | 0.662310 | − | 0.749230i | \(-0.269576\pi\) |
−0.749230 | + | 0.662310i | \(0.769576\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 1.16906i | − | 0.0927127i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.37491 | + | 2.37491i | 0.187169 | + | 0.187169i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.02927 | 0.550575 | 0.275287 | − | 0.961362i | \(-0.411227\pi\) | ||||
0.275287 | + | 0.961362i | \(0.411227\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.101386 | 0.00789287 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.8750 | + | 14.8750i | 1.15106 | + | 1.15106i | 0.986341 | + | 0.164718i | \(0.0526714\pi\) |
0.164718 | + | 0.986341i | \(0.447329\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2.30644i | − | 0.177419i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.02410 | + | 9.02410i | 0.690091 | + | 0.690091i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.5019i | 1.33065i | 0.746555 | + | 0.665324i | \(0.231707\pi\) | ||||
−0.746555 | + | 0.665324i | \(0.768293\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.32756 | − | 3.32756i | −0.251540 | − | 0.251540i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.65216 | + | 1.65216i | 0.124184 | + | 0.124184i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.55909 | − | 2.55909i | 0.191275 | − | 0.191275i | −0.604972 | − | 0.796247i | \(-0.706816\pi\) |
0.796247 | + | 0.604972i | \(0.206816\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.22014 | − | 9.22014i | 0.685328 | − | 0.685328i | −0.275868 | − | 0.961196i | \(-0.588965\pi\) |
0.961196 | + | 0.275868i | \(0.0889652\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.15942 | − | 1.15942i | 0.0857067 | − | 0.0857067i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.821330i | 0.0603854i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.626493 | 0.0458137 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.49471 | −0.108724 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.9361 | + | 14.9361i | −1.08074 | + | 1.08074i | −0.0842972 | + | 0.996441i | \(0.526865\pi\) |
−0.996441 | + | 0.0842972i | \(0.973135\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.1364 | + | 11.1364i | 0.801613 | + | 0.801613i | 0.983348 | − | 0.181734i | \(-0.0581711\pi\) |
−0.181734 | + | 0.983348i | \(0.558171\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.446517 | −0.0319757 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 23.9212i | − | 1.70431i | −0.523286 | − | 0.852157i | \(-0.675294\pi\) | ||
0.523286 | − | 0.852157i | \(-0.324706\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.11493 | − | 3.11493i | 0.220812 | − | 0.220812i | −0.588029 | − | 0.808840i | \(-0.700096\pi\) |
0.808840 | + | 0.588029i | \(0.200096\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.645765 | 0.0455488 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.28933i | 0.651983i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.40181 | + | 0.697408i | 0.237593 | + | 0.0487091i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.86296i | 0.685523i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.22681 | −0.223203 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.25001 | − | 9.25001i | 0.636797 | − | 0.636797i | −0.312967 | − | 0.949764i | \(-0.601323\pi\) |
0.949764 | + | 0.312967i | \(0.101323\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 2.30367i | − | 0.157845i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.85529 | −0.262928 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.09521 | + | 6.09521i | 0.413770 | + | 0.413770i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.16182 | − | 2.16182i | 0.146083 | − | 0.146083i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.75916 | −0.185601 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.7508 | 0.987788 | 0.493894 | − | 0.869522i | \(-0.335573\pi\) | ||||
0.493894 | + | 0.869522i | \(0.335573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 13.8193i | − | 0.921289i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.8150 | + | 16.8150i | −1.11605 | + | 1.11605i | −0.123738 | + | 0.992315i | \(0.539488\pi\) |
−0.992315 | + | 0.123738i | \(0.960512\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.08954 | + | 3.08954i | −0.204162 | + | 0.204162i | −0.801781 | − | 0.597618i | \(-0.796114\pi\) |
0.597618 | + | 0.801781i | \(0.296114\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.132192 | − | 0.132192i | 0.00869758 | − | 0.00869758i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.5638 | + | 12.5638i | 0.823084 | + | 0.823084i | 0.986549 | − | 0.163465i | \(-0.0522671\pi\) |
−0.163465 | + | 0.986549i | \(0.552267\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.66916 | − | 2.66916i | −0.174116 | − | 0.174116i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.63442i | 0.236081i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.469822 | + | 0.469822i | 0.0303903 | + | 0.0303903i | 0.722139 | − | 0.691748i | \(-0.243159\pi\) |
−0.691748 | + | 0.722139i | \(0.743159\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 19.9067i | − | 1.28230i | −0.767414 | − | 0.641152i | \(-0.778457\pi\) | ||
0.767414 | − | 0.641152i | \(-0.221543\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.67221 | − | 4.67221i | −0.299722 | − | 0.299722i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.542323 | 0.0346477 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.2113 | 0.904244 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.25787 | − | 1.25787i | −0.0797146 | − | 0.0797146i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.1954i | 1.90591i | 0.303106 | + | 0.952957i | \(0.401976\pi\) | ||||
−0.303106 | + | 0.952957i | \(0.598024\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.76338 | − | 1.76338i | −0.110863 | − | 0.110863i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 0.115211i | − | 0.00721477i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.5388 | + | 14.5388i | 0.906906 | + | 0.906906i | 0.996021 | − | 0.0891155i | \(-0.0284040\pi\) |
−0.0891155 | + | 0.996021i | \(0.528404\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.07089 | + | 1.07089i | 0.0665419 | + | 0.0665419i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.2892 | + | 19.2892i | −1.19397 | + | 1.19397i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.607933 | − | 0.607933i | 0.0374867 | − | 0.0374867i | −0.688115 | − | 0.725602i | \(-0.741562\pi\) |
0.725602 | + | 0.688115i | \(0.241562\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.78058 | + | 1.78058i | −0.109380 | + | 0.109380i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 0.983044i | − | 0.0601613i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.24006 | 0.319492 | 0.159746 | − | 0.987158i | \(-0.448932\pi\) | ||||
0.159746 | + | 0.987158i | \(0.448932\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.57926 | 0.217425 | 0.108712 | − | 0.994073i | \(-0.465327\pi\) | ||||
0.108712 | + | 0.994073i | \(0.465327\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.582190 | + | 0.582190i | −0.0352358 | + | 0.0352358i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.47074 | + | 2.47074i | 0.148991 | + | 0.148991i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.44984 | 0.447618 | 0.223809 | − | 0.974633i | \(-0.428151\pi\) | ||||
0.223809 | + | 0.974633i | \(0.428151\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 25.3133i | 1.51547i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.6123 | − | 18.6123i | 1.11031 | − | 1.11031i | 0.117207 | − | 0.993108i | \(-0.462606\pi\) |
0.993108 | − | 0.117207i | \(-0.0373941\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.0100 | 1.24891 | 0.624457 | − | 0.781059i | \(-0.285320\pi\) | ||||
0.624457 | + | 0.781059i | \(0.285320\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.593403i | 0.0351502i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.34476 | − | 3.52613i | 0.315491 | − | 0.208141i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.2881i | 0.958122i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.51108 | −0.147202 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.02331 | + | 3.02331i | −0.176624 | + | 0.176624i | −0.789882 | − | 0.613259i | \(-0.789858\pi\) |
0.613259 | + | 0.789882i | \(0.289858\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.03276i | − | 0.293019i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.10983 | 0.0643990 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.76618 | + | 7.76618i | 0.449130 | + | 0.449130i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.02671 | + | 5.02671i | −0.289735 | + | 0.289735i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.46964 | 0.0844287 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.53179 | −0.202230 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.1611i | 1.55017i | 0.631858 | + | 0.775084i | \(0.282292\pi\) | ||||
−0.631858 | + | 0.775084i | \(0.717708\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.84358 | + | 2.84358i | −0.161765 | + | 0.161765i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.52300 | − | 4.52300i | 0.256476 | − | 0.256476i | −0.567143 | − | 0.823619i | \(-0.691951\pi\) |
0.823619 | + | 0.567143i | \(0.191951\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7717 | + | 12.7717i | −0.721899 | + | 0.721899i | −0.968992 | − | 0.247093i | \(-0.920525\pi\) |
0.247093 | + | 0.968992i | \(0.420525\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.12613 | + | 1.12613i | 0.0634503 | + | 0.0634503i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.3262 | − | 23.3262i | −1.31013 | − | 1.31013i | −0.921315 | − | 0.388816i | \(-0.872884\pi\) |
−0.388816 | − | 0.921315i | \(-0.627116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.89739i | − | 0.386180i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.825248 | + | 0.825248i | 0.0460609 | + | 0.0460609i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.66682i | 0.204027i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.8815 | − | 10.8815i | −0.603595 | − | 0.603595i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.58772 | 0.198401 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.96035 | −0.383736 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.71859 | − | 5.71859i | −0.314322 | − | 0.314322i | 0.532259 | − | 0.846581i | \(-0.321343\pi\) |
−0.846581 | + | 0.532259i | \(0.821343\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.44740i | 0.243716i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.983555 | − | 0.983555i | −0.0537373 | − | 0.0537373i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.5107i | − | 0.735973i | −0.929831 | − | 0.367987i | \(-0.880047\pi\) | ||
0.929831 | − | 0.367987i | \(-0.119953\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.487328 | + | 0.487328i | 0.0264681 | + | 0.0264681i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.52573 | − | 4.52573i | −0.245082 | − | 0.245082i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.324282 | + | 0.324282i | −0.0174588 | + | 0.0174588i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.7234 | − | 23.7234i | 1.27354 | − | 1.27354i | 0.329323 | − | 0.944217i | \(-0.393180\pi\) |
0.944217 | − | 0.329323i | \(-0.106820\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 32.5406i | − | 1.74186i | −0.491406 | − | 0.870930i | \(-0.663517\pi\) | ||
0.491406 | − | 0.870930i | \(-0.336483\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.88785 | −0.260894 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.1907 | −1.28754 | −0.643772 | − | 0.765218i | \(-0.722631\pi\) | ||||
−0.643772 | + | 0.765218i | \(0.722631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.50868 | + | 3.50868i | −0.186221 | + | 0.186221i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.150217 | − | 0.150217i | −0.00795034 | − | 0.00795034i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.4843 | 0.764451 | 0.382225 | − | 0.924069i | \(-0.375158\pi\) | ||||
0.382225 | + | 0.924069i | \(0.375158\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.113719i | 0.00598523i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.86022 | − | 1.86022i | 0.0976365 | − | 0.0976365i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.58528 | −0.344689 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.24383i | 0.0649276i | 0.999473 | + | 0.0324638i | \(0.0103354\pi\) | ||||
−0.999473 | + | 0.0324638i | \(0.989665\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.4203 | + | 3.77637i | 0.958925 | + | 0.196590i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.64322i | 0.241064i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.8916 | 1.54773 | 0.773865 | − | 0.633350i | \(-0.218321\pi\) | ||||
0.773865 | + | 0.633350i | \(0.218321\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.937124 | − | 0.937124i | 0.0483929 | − | 0.0483929i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.3770i | 1.56450i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.9846 | 1.02654 | 0.513270 | − | 0.858227i | \(-0.328434\pi\) | ||||
0.513270 | + | 0.858227i | \(0.328434\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.30629 | + | 2.30629i | 0.118155 | + | 0.118155i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.8655 | + | 13.8655i | −0.708493 | + | 0.708493i | −0.966218 | − | 0.257725i | \(-0.917027\pi\) |
0.257725 | + | 0.966218i | \(0.417027\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.402678 | −0.0205224 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.8759 | −1.06118 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.77902i | 0.140902i | 0.997515 | + | 0.0704510i | \(0.0224439\pi\) | ||||
−0.997515 | + | 0.0704510i | \(0.977556\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.00384 | + | 2.00384i | −0.101338 | + | 0.101338i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.141337 | − | 0.141337i | 0.00712949 | − | 0.00712949i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.53553 | − | 5.53553i | 0.278523 | − | 0.278523i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.847681 | − | 0.847681i | −0.0425439 | − | 0.0425439i | 0.685515 | − | 0.728059i | \(-0.259577\pi\) |
−0.728059 | + | 0.685515i | \(0.759577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.773708 | + | 0.773708i | 0.0387338 | + | 0.0387338i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10.4156i | − | 0.520132i | −0.965591 | − | 0.260066i | \(-0.916256\pi\) | ||
0.965591 | − | 0.260066i | \(-0.0837443\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.9319 | + | 19.9319i | 0.992881 | + | 0.992881i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.57367i | 0.227268i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.795143 | − | 0.795143i | −0.0394138 | − | 0.0394138i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.0820 | 1.63580 | 0.817901 | − | 0.575359i | \(-0.195138\pi\) | ||||
0.817901 | + | 0.575359i | \(0.195138\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.80201 | −0.138213 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.56196 | − | 6.56196i | −0.322893 | − | 0.322893i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.83170i | 0.188091i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.124095 | − | 0.124095i | −0.00607694 | − | 0.00607694i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 22.3241i | − | 1.09060i | −0.838240 | − | 0.545301i | \(-0.816415\pi\) | ||
0.838240 | − | 0.545301i | \(-0.183585\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0024 | − | 20.0024i | −0.974855 | − | 0.974855i | 0.0248364 | − | 0.999692i | \(-0.492094\pi\) |
−0.999692 | + | 0.0248364i | \(0.992094\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.4531 | − | 14.4531i | −0.702735 | − | 0.702735i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.80765 | − | 2.80765i | 0.136191 | − | 0.136191i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.60492 | + | 4.60492i | −0.222847 | + | 0.222847i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.432280 | − | 0.432280i | 0.0208707 | − | 0.0208707i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.47963i | 0.167608i | 0.996482 | + | 0.0838039i | \(0.0267069\pi\) | ||||
−0.996482 | + | 0.0838039i | \(0.973293\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.1883 | 0.681848 | 0.340924 | − | 0.940091i | \(-0.389260\pi\) | ||||
0.340924 | + | 0.940091i | \(0.389260\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.26841 | −0.0608158 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.3209 | − | 10.3209i | 0.493718 | − | 0.493718i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.7765 | + | 19.7765i | 0.943881 | + | 0.943881i | 0.998507 | − | 0.0546263i | \(-0.0173968\pi\) |
−0.0546263 | + | 0.998507i | \(0.517397\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.93661 | 0.139838 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 11.7065i | − | 0.556193i | −0.960553 | − | 0.278096i | \(-0.910296\pi\) | ||
0.960553 | − | 0.278096i | \(-0.0897035\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.49726 | + | 1.49726i | −0.0709768 | + | 0.0709768i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.07850 | −0.192906 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.26429i | − | 0.248437i | −0.992255 | − | 0.124219i | \(-0.960358\pi\) | ||
0.992255 | − | 0.124219i | \(-0.0396424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.96852 | + | 2.61817i | −0.186870 | + | 0.123285i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 4.80512i | − | 0.225764i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.77345 | 0.0831406 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.6685 | + | 12.6685i | −0.592608 | + | 0.592608i | −0.938335 | − | 0.345727i | \(-0.887632\pi\) |
0.345727 | + | 0.938335i | \(0.387632\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 1.26117i | − | 0.0588663i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.5860 | −1.56425 | −0.782127 | − | 0.623119i | \(-0.785865\pi\) | ||||
−0.782127 | + | 0.623119i | \(0.785865\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.9326 | − | 11.9326i | −0.554555 | − | 0.554555i | 0.373197 | − | 0.927752i | \(-0.378262\pi\) |
−0.927752 | + | 0.373197i | \(0.878262\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.832272 | + | 0.832272i | −0.0385957 | + | 0.0385957i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.5318 | −0.811277 | −0.405638 | − | 0.914034i | \(-0.632951\pi\) | ||||
−0.405638 | + | 0.914034i | \(0.632951\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.56481 | −0.118432 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 0.387795i | − | 0.0178687i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.73237 | − | 3.73237i | 0.171614 | − | 0.171614i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.4610 | + | 14.4610i | −0.663518 | + | 0.663518i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.64162 | + | 9.64162i | −0.441459 | + | 0.441459i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.6065 | − | 16.6065i | −0.758772 | − | 0.758772i | 0.217327 | − | 0.976099i | \(-0.430266\pi\) |
−0.976099 | + | 0.217327i | \(0.930266\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.50192 | + | 3.50192i | 0.159674 | + | 0.159674i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.845630i | 0.0384775i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.82458 | + | 3.82458i | 0.173665 | + | 0.173665i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 42.1727i | − | 1.91103i | −0.294947 | − | 0.955514i | \(-0.595302\pi\) | ||
0.294947 | − | 0.955514i | \(-0.404698\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.25145 | + | 1.25145i | 0.0565926 | + | 0.0565926i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.47451 | −0.0665436 | −0.0332718 | − | 0.999446i | \(-0.510593\pi\) | ||||
−0.0332718 | + | 0.999446i | \(0.510593\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.83791 | −0.353002 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.836159 | − | 0.836159i | −0.0375826 | − | 0.0375826i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.14957i | 0.410414i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.702287 | + | 0.702287i | 0.0314387 | + | 0.0314387i | 0.722651 | − | 0.691213i | \(-0.242923\pi\) |
−0.691213 | + | 0.722651i | \(0.742923\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.29651i | 0.236630i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.729439 | + | 0.729439i | 0.0325241 | + | 0.0325241i | 0.723182 | − | 0.690658i | \(-0.242679\pi\) |
−0.690658 | + | 0.723182i | \(0.742679\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.23839 | − | 2.23839i | −0.0996069 | − | 0.0996069i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.410626 | − | 0.410626i | 0.0182366 | − | 0.0182366i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.6468 | + | 14.6468i | −0.649209 | + | 0.649209i | −0.952802 | − | 0.303593i | \(-0.901814\pi\) |
0.303593 | + | 0.952802i | \(0.401814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.58621 | + | 8.58621i | −0.379832 | + | 0.379832i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.49577i | 0.286795i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.66201 | 0.381694 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.16811 | 0.227293 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.11595 | + | 3.11595i | −0.136775 | + | 0.136775i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.48443 | + | 3.48443i | 0.152656 | + | 0.152656i | 0.779303 | − | 0.626647i | \(-0.215573\pi\) |
−0.626647 | + | 0.779303i | \(0.715573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.6067 | −0.901066 | −0.450533 | − | 0.892760i | \(-0.648766\pi\) | ||||
−0.450533 | + | 0.892760i | \(0.648766\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.18484i | − | 0.0517107i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.14286 | + | 5.14286i | −0.224026 | + | 0.224026i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7196 | −0.509550 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 27.2517i | − | 1.18263i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.4779 | − | 11.5308i | 0.757051 | − | 0.499454i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.51385i | − | 0.108683i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.911212 | 0.0393217 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.525032 | + | 0.525032i | −0.0226147 | + | 0.0226147i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 29.0500i | − | 1.24896i | −0.781041 | − | 0.624479i | \(-0.785311\pi\) | ||
0.781041 | − | 0.624479i | \(-0.214689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.28300 | 0.140887 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.46440 | − | 5.46440i | −0.234069 | − | 0.234069i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.2391 | − | 28.2391i | 1.20742 | − | 1.20742i | 0.235558 | − | 0.971860i | \(-0.424308\pi\) |
0.971860 | − | 0.235558i | \(-0.0756918\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.1242 | −0.816200 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40.3699 | 1.71981 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 14.4350i | − | 0.613838i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.146225 | + | 0.146225i | −0.00620691 | + | 0.00620691i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.4820 | + | 28.4820i | −1.20682 | + | 1.20682i | −0.234769 | + | 0.972051i | \(0.575433\pi\) |
−0.972051 | + | 0.234769i | \(0.924567\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.4379 | + | 16.4379i | −0.695247 | + | 0.695247i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.111537 | + | 0.111537i | 0.00470911 | + | 0.00470911i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.2705 | − | 30.2705i | −1.27575 | − | 1.27575i | −0.943023 | − | 0.332726i | \(-0.892032\pi\) |
−0.332726 | − | 0.943023i | \(-0.607968\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1.48448i | − | 0.0624527i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.96338 | + | 5.96338i | 0.250438 | + | 0.250438i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.7654i | 0.828609i | 0.910138 | + | 0.414304i | \(0.135975\pi\) | ||||
−0.910138 | + | 0.414304i | \(0.864025\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.0922 | − | 15.0922i | −0.631587 | − | 0.631587i | 0.316879 | − | 0.948466i | \(-0.397365\pi\) |
−0.948466 | + | 0.316879i | \(0.897365\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.31828 | −0.222174 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.8053 | −0.659127 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.39982 | + | 2.39982i | 0.0999058 | + | 0.0999058i | 0.755293 | − | 0.655387i | \(-0.227495\pi\) |
−0.655387 | + | 0.755293i | \(0.727495\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.96531i | 0.164793i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.99596 | + | 4.99596i | 0.207267 | + | 0.207267i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.44762i | − | 0.142786i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.68256 | + | 3.68256i | 0.152255 | + | 0.152255i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.8590 | − | 18.8590i | −0.778392 | − | 0.778392i | 0.201165 | − | 0.979557i | \(-0.435527\pi\) |
−0.979557 | + | 0.201165i | \(0.935527\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.4888 | − | 26.4888i | 1.09145 | − | 1.09145i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.25879 | − | 4.25879i | 0.175183 | − | 0.175183i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.60759 | + | 8.60759i | −0.353471 | + | 0.353471i | −0.861399 | − | 0.507928i | \(-0.830412\pi\) |
0.507928 | + | 0.861399i | \(0.330412\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.457587i | 0.0187592i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.10913 | 0.0453937 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.60470 | 0.106425 | 0.0532125 | − | 0.998583i | \(-0.483054\pi\) | ||||
0.0532125 | + | 0.998583i | \(0.483054\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1861 | − | 18.1861i | 0.741827 | − | 0.741827i | −0.231102 | − | 0.972930i | \(-0.574233\pi\) |
0.972930 | + | 0.231102i | \(0.0742331\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.32582 | − | 5.32582i | −0.216884 | − | 0.216884i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.66656 | −0.230378 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 15.3043i | − | 0.621182i | −0.950544 | − | 0.310591i | \(-0.899473\pi\) | ||
0.950544 | − | 0.310591i | \(-0.100527\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.65382 | + | 1.65382i | −0.0670161 | + | 0.0670161i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.7610 | −0.920813 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23.9660i | − | 0.967979i | −0.875074 | − | 0.483990i | \(-0.839187\pi\) | ||
0.875074 | − | 0.483990i | \(-0.160813\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.481476 | + | 0.729801i | 0.0194150 | + | 0.0294284i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 15.5475i | − | 0.625917i | −0.949767 | − | 0.312959i | \(-0.898680\pi\) | ||
0.949767 | − | 0.312959i | \(-0.101320\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.03135 | −0.282614 | −0.141307 | − | 0.989966i | \(-0.545130\pi\) | ||||
−0.141307 | + | 0.989966i | \(0.545130\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.54980 | + | 3.54980i | −0.142448 | + | 0.142448i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.90440i | 0.156426i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.6748 | 0.826992 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.574483 | − | 0.574483i | −0.0229427 | − | 0.0229427i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.903568 | + | 0.903568i | −0.0360276 | + | 0.0360276i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1914 | −0.485332 | −0.242666 | − | 0.970110i | \(-0.578022\pi\) | ||||
−0.242666 | + | 0.970110i | \(0.578022\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.29364 | 0.130910 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 7.02534i | − | 0.278792i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.31231 | − | 2.31231i | 0.0916171 | − | 0.0916171i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18.9990 | + | 18.9990i | −0.751590 | + | 0.751590i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.18625 | − | 6.18625i | 0.244342 | − | 0.244342i | −0.574302 | − | 0.818644i | \(-0.694726\pi\) |
0.818644 | + | 0.574302i | \(0.194726\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.79421 | + | 4.79421i | 0.189065 | + | 0.189065i | 0.795292 | − | 0.606227i | \(-0.207318\pi\) |
−0.606227 | + | 0.795292i | \(0.707318\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.686374 | − | 0.686374i | −0.0270259 | − | 0.0270259i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.8812i | 1.05681i | 0.848993 | + | 0.528404i | \(0.177209\pi\) | ||||
−0.848993 | + | 0.528404i | \(0.822791\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.87230 | + | 4.87230i | 0.191254 | + | 0.191254i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.17031i | 0.0850613i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.53665 | + | 9.53665i | 0.373198 | + | 0.373198i | 0.868641 | − | 0.495443i | \(-0.164994\pi\) |
−0.495443 | + | 0.868641i | \(0.664994\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.430535 | −0.0168224 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −35.6585 | −1.39117 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.3554 | − | 33.3554i | −1.29934 | − | 1.29934i | −0.928826 | − | 0.370516i | \(-0.879181\pi\) |
−0.370516 | − | 0.928826i | \(-0.620819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 41.2348i | − | 1.60385i | −0.597425 | − | 0.801925i | \(-0.703809\pi\) | ||
0.597425 | − | 0.801925i | \(-0.296191\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.491226 | − | 0.491226i | −0.0190776 | − | 0.0190776i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.35684i | − | 0.0913945i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.0613 | + | 22.0613i | 0.854216 | + | 0.854216i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.62615 | + | 2.62615i | 0.101533 | + | 0.101533i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.41918 | − | 3.41918i | 0.131996 | − | 0.131996i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.5127 | − | 10.5127i | 0.405235 | − | 0.405235i | −0.474838 | − | 0.880073i | \(-0.657493\pi\) |
0.880073 | + | 0.474838i | \(0.157493\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.97375 | − | 4.97375i | 0.191440 | − | 0.191440i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.7826i | 0.645007i | 0.946568 | + | 0.322504i | \(0.104524\pi\) | ||||
−0.946568 | + | 0.322504i | \(0.895476\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.97335 | 0.382742 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.98731 | −0.229434 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.85566 | − | 3.85566i | 0.147533 | − | 0.147533i | −0.629482 | − | 0.777015i | \(-0.716733\pi\) |
0.777015 | + | 0.629482i | \(0.216733\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.26769 | + | 4.26769i | 0.163060 | + | 0.163060i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.10009 | −0.0419710 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.1838i | 0.578456i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.4058 | − | 14.4058i | 0.548021 | − | 0.548021i | −0.377847 | − | 0.925868i | \(-0.623335\pi\) |
0.925868 | + | 0.377847i | \(0.123335\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.18045 | −0.0828285 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.378013i | 0.0143389i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.97519 | + | 4.50966i | 0.112693 | + | 0.170816i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.47359i | 0.169207i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.8055 | 0.483656 | 0.241828 | − | 0.970319i | \(-0.422253\pi\) | ||||
0.241828 | + | 0.970319i | \(0.422253\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.65391 | − | 4.65391i | 0.175526 | − | 0.175526i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 0.950403i | − | 0.0357942i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.83704 | −0.219524 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.9790 | + | 15.9790i | 0.600106 | + | 0.600106i | 0.940341 | − | 0.340235i | \(-0.110507\pi\) |
−0.340235 | + | 0.940341i | \(0.610507\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.9742 | − | 29.9742i | 1.12412 | − | 1.12412i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.9511 | 1.08423 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.31680 | −0.0492455 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.167289i | 0.00624752i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.84421 | − | 9.84421i | 0.367127 | − | 0.367127i | −0.499301 | − | 0.866428i | \(-0.666410\pi\) |
0.866428 | + | 0.499301i | \(0.166410\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.2940 | − | 11.2940i | 0.420609 | − | 0.420609i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.54408 | − | 3.54408i | 0.131806 | − | 0.131806i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −30.9108 | − | 30.9108i | −1.14800 | − | 1.14800i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.7199 | + | 28.7199i | 1.06516 | + | 1.06516i | 0.997723 | + | 0.0674405i | \(0.0214833\pi\) |
0.0674405 | + | 0.997723i | \(0.478517\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.6368i | 0.875438i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.24131 | − | 4.24131i | −0.156871 | − | 0.156871i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 31.5061i | − | 1.16370i | −0.813295 | − | 0.581851i | \(-0.802329\pi\) | ||
0.813295 | − | 0.581851i | \(-0.197671\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0965521 | + | 0.0965521i | 0.00356138 | + | 0.00356138i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.90439 | 0.0701491 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.1899 | −1.69912 | −0.849562 | − | 0.527489i | \(-0.823134\pi\) | ||||
−0.849562 | + | 0.527489i | \(0.823134\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.53010 | + | 2.53010i | 0.0929456 | + | 0.0929456i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.0119i | 0.770851i | 0.922739 | + | 0.385425i | \(0.125945\pi\) | ||||
−0.922739 | + | 0.385425i | \(0.874055\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.21189 | + | 6.21189i | 0.227586 | + | 0.227586i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.7482i | 0.759135i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.27767 | − | 3.27767i | −0.119764 | − | 0.119764i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.4416 | − | 36.4416i | −1.32977 | − | 1.32977i | −0.905566 | − | 0.424205i | \(-0.860553\pi\) |
−0.424205 | − | 0.905566i | \(-0.639447\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.37581 | + | 5.37581i | −0.195905 | + | 0.195905i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.31861 | + | 7.31861i | −0.266351 | + | 0.266351i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.6038 | + | 14.6038i | −0.530785 | + | 0.530785i | −0.920806 | − | 0.390021i | \(-0.872468\pi\) |
0.390021 | + | 0.920806i | \(0.372468\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 0.627886i | − | 0.0227908i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −51.3546 | −1.86160 | −0.930801 | − | 0.365525i | \(-0.880889\pi\) | ||||
−0.930801 | + | 0.365525i | \(0.880889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.2495 | −0.515867 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.950177 | + | 0.950177i | −0.0343537 | + | 0.0343537i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.4583 | − | 21.4583i | −0.774813 | − | 0.774813i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.6372 | 0.888442 | 0.444221 | − | 0.895917i | \(-0.353481\pi\) | ||||
0.444221 | + | 0.895917i | \(0.353481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.17681i | 0.186438i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.4553 | − | 13.4553i | 0.483954 | − | 0.483954i | −0.422438 | − | 0.906392i | \(-0.638826\pi\) |
0.906392 | + | 0.422438i | \(0.138826\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.5644 | −1.45712 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.381311i | 0.0136794i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.3240 | − | 23.2274i | −0.549038 | − | 0.832209i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.79362i | − | 0.243095i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.8849 | −0.496204 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.590645 | + | 0.590645i | −0.0210810 | + | 0.0210810i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.6923i | 0.630663i | 0.948982 | + | 0.315332i | \(0.102116\pi\) | ||||
−0.948982 | + | 0.315332i | \(0.897884\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.216466 | 0.00770639 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.93554 | − | 1.93554i | −0.0688200 | − | 0.0688200i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.0585 | + | 15.0585i | −0.534744 | + | 0.534744i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.634009 | −0.0224860 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.6888 | 0.484883 | 0.242442 | − | 0.970166i | \(-0.422052\pi\) | ||||
0.242442 | + | 0.970166i | \(0.422052\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.87282i | − | 0.207766i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.10746 | + | 8.10746i | −0.286463 | + | 0.286463i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.37532 | − | 6.37532i | 0.224980 | − | 0.224980i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.28797 | − | 1.28797i | 0.0453948 | − | 0.0453948i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.932911 | + | 0.932911i | 0.0328400 | + | 0.0328400i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.8342 | + | 23.8342i | 0.837965 | + | 0.837965i | 0.988591 | − | 0.150625i | \(-0.0481288\pi\) |
−0.150625 | + | 0.988591i | \(0.548129\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.77742i | − | 0.167758i | −0.996476 | − | 0.0838789i | \(-0.973269\pi\) | ||
0.996476 | − | 0.0838789i | \(-0.0267309\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.637232 | + | 0.637232i | 0.0223487 | + | 0.0223487i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 3.81213i | − | 0.133533i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.8453 | + | 21.8453i | 0.764269 | + | 0.764269i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.60300 | 0.335556 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.7523 | −0.410157 | −0.205079 | − | 0.978746i | \(-0.565745\pi\) | ||||
−0.205079 | + | 0.978746i | \(0.565745\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.554263 | + | 0.554263i | 0.0193204 | + | 0.0193204i | 0.716701 | − | 0.697381i | \(-0.245651\pi\) |
−0.697381 | + | 0.716701i | \(0.745651\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.879753i | 0.0306291i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.5740 | + | 36.5740i | 1.27180 | + | 1.27180i | 0.945142 | + | 0.326659i | \(0.105923\pi\) |
0.326659 | + | 0.945142i | \(0.394077\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 13.5767i | − | 0.471537i | −0.971809 | − | 0.235769i | \(-0.924239\pi\) | ||
0.971809 | − | 0.235769i | \(-0.0757608\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.32633 | + | 1.32633i | 0.0460098 | + | 0.0460098i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.596624 | + | 0.596624i | 0.0206718 | + | 0.0206718i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.06703 | − | 8.06703i | 0.279171 | − | 0.279171i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.11058 | + | 9.11058i | −0.314908 | + | 0.314908i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.4934 | + | 16.4934i | −0.569415 | + | 0.569415i | −0.931964 | − | 0.362550i | \(-0.881906\pi\) |
0.362550 | + | 0.931964i | \(0.381906\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.2916i | 1.97557i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.62724 | 0.228254 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.25084 | −0.0430301 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.38834 | + | 7.38834i | −0.253866 | + | 0.253866i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.74050 | + | 3.74050i | 0.128374 | + | 0.128374i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.08653 | 0.174364 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.6224i | 0.363706i | 0.983326 | + | 0.181853i | \(0.0582094\pi\) | ||||
−0.983326 | + | 0.181853i | \(0.941791\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.89398 | − | 4.89398i | 0.167370 | − | 0.167370i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.2056 | 1.44172 | 0.720858 | − | 0.693082i | \(-0.243748\pi\) | ||||
0.720858 | + | 0.693082i | \(0.243748\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 7.70762i | − | 0.262981i | −0.991317 | − | 0.131490i | \(-0.958024\pi\) | ||
0.991317 | − | 0.131490i | \(-0.0419762\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.57932 | + | 0.323779i | 0.0538232 | + | 0.0110343i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 48.2138i | − | 1.64122i | −0.571490 | − | 0.820609i | \(-0.693634\pi\) | ||
0.571490 | − | 0.820609i | \(-0.306366\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.49170 | 0.322728 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.89984 | + | 2.89984i | −0.0984837 | + | 0.0984837i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.7181i | 0.363586i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.38720 | −0.284189 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.7096 | + | 20.7096i | 0.700914 | + | 0.700914i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.72201 | + | 3.72201i | −0.125827 | + | 0.125827i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.6970 | 0.901495 | 0.450748 | − | 0.892651i | \(-0.351157\pi\) | ||||
0.450748 | + | 0.892651i | \(0.351157\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.07651 | −0.0363097 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16.2789i | − | 0.548451i | −0.961665 | − | 0.274225i | \(-0.911579\pi\) | ||
0.961665 | − | 0.274225i | \(-0.0884214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.58579 | − | 5.58579i | 0.187977 | − | 0.187977i | −0.606844 | − | 0.794821i | \(-0.707565\pi\) |
0.794821 | + | 0.606844i | \(0.207565\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.896004 | − | 0.896004i | 0.0301189 | − | 0.0301189i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9344 | − | 16.9344i | 0.568600 | − | 0.568600i | −0.363136 | − | 0.931736i | \(-0.618294\pi\) |
0.931736 | + | 0.363136i | \(0.118294\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.15999 | − | 9.15999i | −0.307216 | − | 0.307216i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.42785 | − | 4.42785i | −0.148338 | − | 0.148338i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.2485i | 1.01223i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.38785 | − | 1.38785i | −0.0463908 | − | 0.0463908i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.76529i | 0.0923305i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 56.6204 | + | 56.6204i | 1.88840 | + | 1.88840i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.91774 | −0.130519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.78985 | −0.0595626 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.00029 | − | 5.00029i | −0.166215 | − | 0.166215i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.5793i | 0.849346i | 0.905347 | + | 0.424673i | \(0.139611\pi\) | ||||
−0.905347 | + | 0.424673i | \(0.860389\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.1206 | − | 12.1206i | −0.402014 | − | 0.402014i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 54.4068i | − | 1.80258i | −0.433219 | − | 0.901288i | \(-0.642622\pi\) | ||
0.433219 | − | 0.901288i | \(-0.357378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.70953 | − | 3.70953i | −0.122768 | − | 0.122768i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.628779 | − | 0.628779i | −0.0207868 | − | 0.0207868i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.561352 | + | 0.561352i | −0.0185375 | + | 0.0185375i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.08399 | + | 3.08399i | −0.101731 | + | 0.101731i | −0.756141 | − | 0.654409i | \(-0.772917\pi\) |
0.654409 | + | 0.756141i | \(0.272917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.83562 | + | 4.83562i | −0.159339 | + | 0.159339i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.9200i | 0.984829i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.12691 | −0.234331 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 46.9037 | 1.54052 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.7154 | + | 22.7154i | −0.745268 | + | 0.745268i | −0.973586 | − | 0.228319i | \(-0.926677\pi\) |
0.228319 | + | 0.973586i | \(0.426677\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.07297 | − | 3.07297i | −0.100713 | − | 0.100713i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.61050 | 0.0527254 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 0.339762i | − | 0.0111114i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.3019 | − | 24.3019i | 0.793908 | − | 0.793908i | −0.188219 | − | 0.982127i | \(-0.560272\pi\) |
0.982127 | + | 0.188219i | \(0.0602715\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.54760 | −0.148405 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 8.12421i | − | 0.264842i | −0.991194 | − | 0.132421i | \(-0.957725\pi\) | ||
0.991194 | − | 0.132421i | \(-0.0422751\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.31907 | − | 21.0675i | 0.140648 | − | 0.686053i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.810616i | 0.0263693i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.2327 | 0.332519 | 0.166259 | − | 0.986082i | \(-0.446831\pi\) | ||||
0.166259 | + | 0.986082i | \(0.446831\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.0778 | + | 28.0778i | −0.911443 | + | 0.911443i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 8.30574i | − | 0.269332i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.5556 | 0.892614 | 0.446307 | − | 0.894880i | \(-0.352739\pi\) | ||||
0.446307 | + | 0.894880i | \(0.352739\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.10018 | + | 8.10018i | 0.262116 | + | 0.262116i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.22797 | − | 1.22797i | 0.0396947 | − | 0.0396947i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.1289 | 0.359369 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.3032 | 1.39688 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 13.6121i | − | 0.438645i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.03951 | − | 6.03951i | 0.194419 | − | 0.194419i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.0649 | + | 24.0649i | −0.773874 | + | 0.773874i | −0.978781 | − | 0.204907i | \(-0.934311\pi\) |
0.204907 | + | 0.978781i | \(0.434311\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.652819 | + | 0.652819i | −0.0209716 | + | 0.0209716i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.21133 | + | 1.21133i | 0.0388733 | + | 0.0388733i | 0.726276 | − | 0.687403i | \(-0.241249\pi\) |
−0.687403 | + | 0.726276i | \(0.741249\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.492872 | + | 0.492872i | 0.0158008 | + | 0.0158008i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 3.87455i | − | 0.124085i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.8227 | + | 31.8227i | 1.01810 | + | 1.01810i | 0.999833 | + | 0.0182646i | \(0.00581412\pi\) |
0.0182646 | + | 0.999833i | \(0.494186\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.89904i | − | 0.0926537i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.5890 | − | 29.5890i | −0.944705 | − | 0.944705i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.75279 | −0.183486 | −0.0917428 | − | 0.995783i | \(-0.529244\pi\) | ||||
−0.0917428 | + | 0.995783i | \(0.529244\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.9730 | −0.413354 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.23918 | − | 1.23918i | −0.0394436 | − | 0.0394436i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.8759i | 0.759210i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.7351 | − | 15.7351i | −0.499841 | − | 0.499841i | 0.411547 | − | 0.911388i | \(-0.364988\pi\) |
−0.911388 | + | 0.411547i | \(0.864988\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.03621i | − | 0.0646172i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.68930 | − | 1.68930i | −0.0535544 | − | 0.0535544i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.2780 | − | 18.2780i | −0.578872 | − | 0.578872i | 0.355721 | − | 0.934592i | \(-0.384235\pi\) |
−0.934592 | + | 0.355721i | \(0.884235\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.60067 | + | 1.60067i | −0.0506430 | + | 0.0506430i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1148.2.k.b.337.11 | ✓ | 36 | |
41.32 | even | 4 | inner | 1148.2.k.b.729.11 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.k.b.337.11 | ✓ | 36 | 1.1 | even | 1 | trivial | |
1148.2.k.b.729.11 | yes | 36 | 41.32 | even | 4 | inner |