Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(769,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1155.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.k (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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.18 | ||
Character | \(\chi\) | \(=\) | 1155.769 |
Dual form | 1155.2.k.a.769.17 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.12050 | −0.792311 | −0.396156 | − | 0.918183i | \(-0.629656\pi\) | ||||
−0.396156 | + | 0.918183i | \(0.629656\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.744486 | −0.372243 | ||||||||
\(5\) | −1.27295 | − | 1.83837i | −0.569280 | − | 0.822144i | ||||
\(6\) | 1.12050 | 0.457441 | ||||||||
\(7\) | 2.54893 | + | 0.709189i | 0.963406 | + | 0.268048i | ||||
\(8\) | 3.07519 | 1.08724 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.42634 | + | 2.05989i | 0.451047 | + | 0.651394i | ||||
\(11\) | 2.57061 | − | 2.09571i | 0.775067 | − | 0.631879i | ||||
\(12\) | 0.744486 | 0.214915 | ||||||||
\(13\) | − | 0.476765i | − | 0.132231i | −0.997812 | − | 0.0661154i | \(-0.978939\pi\) | ||
0.997812 | − | 0.0661154i | \(-0.0210605\pi\) | |||||||
\(14\) | −2.85607 | − | 0.794644i | −0.763317 | − | 0.212378i | ||||
\(15\) | 1.27295 | + | 1.83837i | 0.328674 | + | 0.474665i | ||||
\(16\) | −1.95677 | −0.489192 | ||||||||
\(17\) | 4.13710i | 1.00340i | 0.865043 | + | 0.501698i | \(0.167291\pi\) | ||||
−0.865043 | + | 0.501698i | \(0.832709\pi\) | |||||||
\(18\) | −1.12050 | −0.264104 | ||||||||
\(19\) | −3.40984 | −0.782270 | −0.391135 | − | 0.920333i | \(-0.627918\pi\) | ||||
−0.391135 | + | 0.920333i | \(0.627918\pi\) | |||||||
\(20\) | 0.947693 | + | 1.36864i | 0.211911 | + | 0.306037i | ||||
\(21\) | −2.54893 | − | 0.709189i | −0.556222 | − | 0.154758i | ||||
\(22\) | −2.88036 | + | 2.34823i | −0.614094 | + | 0.500645i | ||||
\(23\) | 2.30034i | 0.479654i | 0.970816 | + | 0.239827i | \(0.0770907\pi\) | ||||
−0.970816 | + | 0.239827i | \(0.922909\pi\) | |||||||
\(24\) | −3.07519 | −0.627720 | ||||||||
\(25\) | −1.75920 | + | 4.68030i | −0.351840 | + | 0.936060i | ||||
\(26\) | 0.534214i | 0.104768i | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.89764 | − | 0.527981i | −0.358621 | − | 0.0997791i | ||||
\(29\) | − | 8.78831i | − | 1.63195i | −0.578089 | − | 0.815974i | \(-0.696201\pi\) | ||
0.578089 | − | 0.815974i | \(-0.303799\pi\) | |||||||
\(30\) | −1.42634 | − | 2.05989i | −0.260412 | − | 0.376082i | ||||
\(31\) | 7.12148i | 1.27906i | 0.768768 | + | 0.639528i | \(0.220870\pi\) | ||||
−0.768768 | + | 0.639528i | \(0.779130\pi\) | |||||||
\(32\) | −3.95782 | −0.699651 | ||||||||
\(33\) | −2.57061 | + | 2.09571i | −0.447485 | + | 0.364816i | ||||
\(34\) | − | 4.63561i | − | 0.795001i | ||||||
\(35\) | −1.94091 | − | 5.58864i | −0.328074 | − | 0.944652i | ||||
\(36\) | −0.744486 | −0.124081 | ||||||||
\(37\) | 4.59966i | 0.756179i | 0.925769 | + | 0.378090i | \(0.123419\pi\) | ||||
−0.925769 | + | 0.378090i | \(0.876581\pi\) | |||||||
\(38\) | 3.82071 | 0.619802 | ||||||||
\(39\) | 0.476765i | 0.0763435i | ||||||||
\(40\) | −3.91456 | − | 5.65333i | −0.618946 | − | 0.893870i | ||||
\(41\) | 6.76000 | 1.05573 | 0.527867 | − | 0.849327i | \(-0.322992\pi\) | ||||
0.527867 | + | 0.849327i | \(0.322992\pi\) | |||||||
\(42\) | 2.85607 | + | 0.794644i | 0.440701 | + | 0.122616i | ||||
\(43\) | 4.78259 | 0.729338 | 0.364669 | − | 0.931137i | \(-0.381182\pi\) | ||||
0.364669 | + | 0.931137i | \(0.381182\pi\) | |||||||
\(44\) | −1.91378 | + | 1.56022i | −0.288513 | + | 0.235213i | ||||
\(45\) | −1.27295 | − | 1.83837i | −0.189760 | − | 0.274048i | ||||
\(46\) | − | 2.57752i | − | 0.380035i | ||||||
\(47\) | 9.14037 | 1.33326 | 0.666630 | − | 0.745389i | \(-0.267736\pi\) | ||||
0.666630 | + | 0.745389i | \(0.267736\pi\) | |||||||
\(48\) | 1.95677 | 0.282435 | ||||||||
\(49\) | 5.99410 | + | 3.61535i | 0.856300 | + | 0.516478i | ||||
\(50\) | 1.97118 | − | 5.24426i | 0.278767 | − | 0.741651i | ||||
\(51\) | − | 4.13710i | − | 0.579310i | ||||||
\(52\) | 0.354945i | 0.0492220i | ||||||||
\(53\) | 4.46060i | 0.612710i | 0.951917 | + | 0.306355i | \(0.0991095\pi\) | ||||
−0.951917 | + | 0.306355i | \(0.900891\pi\) | |||||||
\(54\) | 1.12050 | 0.152480 | ||||||||
\(55\) | −7.12493 | − | 2.05799i | −0.960726 | − | 0.277500i | ||||
\(56\) | 7.83845 | + | 2.18089i | 1.04746 | + | 0.291434i | ||||
\(57\) | 3.40984 | 0.451644 | ||||||||
\(58\) | 9.84727i | 1.29301i | ||||||||
\(59\) | − | 10.6711i | − | 1.38926i | −0.719368 | − | 0.694629i | \(-0.755568\pi\) | ||
0.719368 | − | 0.694629i | \(-0.244432\pi\) | |||||||
\(60\) | −0.947693 | − | 1.36864i | −0.122347 | − | 0.176691i | ||||
\(61\) | −2.11783 | −0.271160 | −0.135580 | − | 0.990766i | \(-0.543290\pi\) | ||||
−0.135580 | + | 0.990766i | \(0.543290\pi\) | |||||||
\(62\) | − | 7.97960i | − | 1.01341i | ||||||
\(63\) | 2.54893 | + | 0.709189i | 0.321135 | + | 0.0893494i | ||||
\(64\) | 8.34827 | 1.04353 | ||||||||
\(65\) | −0.876470 | + | 0.606897i | −0.108713 | + | 0.0752763i | ||||
\(66\) | 2.88036 | − | 2.34823i | 0.354547 | − | 0.289048i | ||||
\(67\) | − | 11.4547i | − | 1.39942i | −0.714427 | − | 0.699710i | \(-0.753313\pi\) | ||
0.714427 | − | 0.699710i | \(-0.246687\pi\) | |||||||
\(68\) | − | 3.08002i | − | 0.373507i | ||||||
\(69\) | − | 2.30034i | − | 0.276928i | ||||||
\(70\) | 2.17478 | + | 6.26205i | 0.259936 | + | 0.748458i | ||||
\(71\) | 14.1690 | 1.68155 | 0.840777 | − | 0.541381i | \(-0.182098\pi\) | ||||
0.840777 | + | 0.541381i | \(0.182098\pi\) | |||||||
\(72\) | 3.07519 | 0.362414 | ||||||||
\(73\) | − | 9.29571i | − | 1.08798i | −0.839092 | − | 0.543990i | \(-0.816913\pi\) | ||
0.839092 | − | 0.543990i | \(-0.183087\pi\) | |||||||
\(74\) | − | 5.15390i | − | 0.599129i | ||||||
\(75\) | 1.75920 | − | 4.68030i | 0.203135 | − | 0.540435i | ||||
\(76\) | 2.53858 | 0.291195 | ||||||||
\(77\) | 8.03855 | − | 3.51877i | 0.916078 | − | 0.401001i | ||||
\(78\) | − | 0.534214i | − | 0.0604878i | ||||||
\(79\) | 0.726204i | 0.0817044i | 0.999165 | + | 0.0408522i | \(0.0130073\pi\) | ||||
−0.999165 | + | 0.0408522i | \(0.986993\pi\) | |||||||
\(80\) | 2.49087 | + | 3.59726i | 0.278487 | + | 0.402186i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.57456 | −0.836470 | ||||||||
\(83\) | − | 8.78886i | − | 0.964703i | −0.875978 | − | 0.482352i | \(-0.839783\pi\) | ||
0.875978 | − | 0.482352i | \(-0.160217\pi\) | |||||||
\(84\) | 1.89764 | + | 0.527981i | 0.207050 | + | 0.0576075i | ||||
\(85\) | 7.60552 | − | 5.26632i | 0.824935 | − | 0.571213i | ||||
\(86\) | −5.35887 | −0.577862 | ||||||||
\(87\) | 8.78831i | 0.942205i | ||||||||
\(88\) | 7.90510 | − | 6.44469i | 0.842686 | − | 0.687007i | ||||
\(89\) | 10.2107i | 1.08233i | 0.840915 | + | 0.541167i | \(0.182017\pi\) | ||||
−0.840915 | + | 0.541167i | \(0.817983\pi\) | |||||||
\(90\) | 1.42634 | + | 2.05989i | 0.150349 | + | 0.217131i | ||||
\(91\) | 0.338116 | − | 1.21524i | 0.0354442 | − | 0.127392i | ||||
\(92\) | − | 1.71257i | − | 0.178548i | ||||||
\(93\) | − | 7.12148i | − | 0.738463i | ||||||
\(94\) | −10.2418 | −1.05636 | ||||||||
\(95\) | 4.34055 | + | 6.26854i | 0.445331 | + | 0.643139i | ||||
\(96\) | 3.95782 | 0.403944 | ||||||||
\(97\) | −4.36785 | −0.443488 | −0.221744 | − | 0.975105i | \(-0.571175\pi\) | ||||
−0.221744 | + | 0.975105i | \(0.571175\pi\) | |||||||
\(98\) | −6.71637 | − | 4.05099i | −0.678456 | − | 0.409211i | ||||
\(99\) | 2.57061 | − | 2.09571i | 0.258356 | − | 0.210626i | ||||
\(100\) | 1.30970 | − | 3.48442i | 0.130970 | − | 0.348442i | ||||
\(101\) | 10.2868 | 1.02358 | 0.511788 | − | 0.859112i | \(-0.328983\pi\) | ||||
0.511788 | + | 0.859112i | \(0.328983\pi\) | |||||||
\(102\) | 4.63561i | 0.458994i | ||||||||
\(103\) | −17.2764 | −1.70229 | −0.851145 | − | 0.524931i | \(-0.824091\pi\) | ||||
−0.851145 | + | 0.524931i | \(0.824091\pi\) | |||||||
\(104\) | − | 1.46614i | − | 0.143767i | ||||||
\(105\) | 1.94091 | + | 5.58864i | 0.189413 | + | 0.545395i | ||||
\(106\) | − | 4.99809i | − | 0.485457i | ||||||
\(107\) | −3.72911 | −0.360507 | −0.180254 | − | 0.983620i | \(-0.557692\pi\) | ||||
−0.180254 | + | 0.983620i | \(0.557692\pi\) | |||||||
\(108\) | 0.744486 | 0.0716382 | ||||||||
\(109\) | 11.3168i | 1.08395i | 0.840393 | + | 0.541977i | \(0.182324\pi\) | ||||
−0.840393 | + | 0.541977i | \(0.817676\pi\) | |||||||
\(110\) | 7.98347 | + | 2.30598i | 0.761194 | + | 0.219866i | ||||
\(111\) | − | 4.59966i | − | 0.436580i | ||||||
\(112\) | −4.98767 | − | 1.38772i | −0.471290 | − | 0.131127i | ||||
\(113\) | 6.26655i | 0.589508i | 0.955573 | + | 0.294754i | \(0.0952377\pi\) | ||||
−0.955573 | + | 0.294754i | \(0.904762\pi\) | |||||||
\(114\) | −3.82071 | −0.357843 | ||||||||
\(115\) | 4.22887 | − | 2.92821i | 0.394344 | − | 0.273057i | ||||
\(116\) | 6.54277i | 0.607481i | ||||||||
\(117\) | − | 0.476765i | − | 0.0440769i | ||||||
\(118\) | 11.9569i | 1.10073i | ||||||||
\(119\) | −2.93399 | + | 10.5452i | −0.268958 | + | 0.966676i | ||||
\(120\) | 3.91456 | + | 5.65333i | 0.357349 | + | 0.516076i | ||||
\(121\) | 2.21603 | − | 10.7745i | 0.201457 | − | 0.979497i | ||||
\(122\) | 2.37302 | 0.214843 | ||||||||
\(123\) | −6.76000 | −0.609528 | ||||||||
\(124\) | − | 5.30185i | − | 0.476120i | ||||||
\(125\) | 10.8435 | − | 2.72372i | 0.969871 | − | 0.243617i | ||||
\(126\) | −2.85607 | − | 0.794644i | −0.254439 | − | 0.0707925i | ||||
\(127\) | 8.57420 | 0.760837 | 0.380418 | − | 0.924814i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924814i | \(0.375780\pi\) | |||||||
\(128\) | −1.43856 | −0.127152 | ||||||||
\(129\) | −4.78259 | −0.421083 | ||||||||
\(130\) | 0.982082 | − | 0.680027i | 0.0861343 | − | 0.0596423i | ||||
\(131\) | 14.2168 | 1.24213 | 0.621063 | − | 0.783760i | \(-0.286701\pi\) | ||||
0.621063 | + | 0.783760i | \(0.286701\pi\) | |||||||
\(132\) | 1.91378 | − | 1.56022i | 0.166573 | − | 0.135800i | ||||
\(133\) | −8.69144 | − | 2.41822i | −0.753644 | − | 0.209686i | ||||
\(134\) | 12.8350i | 1.10878i | ||||||||
\(135\) | 1.27295 | + | 1.83837i | 0.109558 | + | 0.158222i | ||||
\(136\) | 12.7224i | 1.09093i | ||||||||
\(137\) | − | 8.16717i | − | 0.697768i | −0.937166 | − | 0.348884i | \(-0.886561\pi\) | ||
0.937166 | − | 0.348884i | \(-0.113439\pi\) | |||||||
\(138\) | 2.57752i | 0.219413i | ||||||||
\(139\) | 5.25987 | 0.446136 | 0.223068 | − | 0.974803i | \(-0.428393\pi\) | ||||
0.223068 | + | 0.974803i | \(0.428393\pi\) | |||||||
\(140\) | 1.44498 | + | 4.16066i | 0.122123 | + | 0.351640i | ||||
\(141\) | −9.14037 | −0.769758 | ||||||||
\(142\) | −15.8764 | −1.33231 | ||||||||
\(143\) | −0.999159 | − | 1.22557i | −0.0835539 | − | 0.102488i | ||||
\(144\) | −1.95677 | −0.163064 | ||||||||
\(145\) | −16.1562 | + | 11.1871i | −1.34170 | + | 0.929035i | ||||
\(146\) | 10.4158i | 0.862019i | ||||||||
\(147\) | −5.99410 | − | 3.61535i | −0.494385 | − | 0.298189i | ||||
\(148\) | − | 3.42438i | − | 0.281482i | ||||||
\(149\) | − | 22.3770i | − | 1.83319i | −0.399812 | − | 0.916597i | \(-0.630925\pi\) | ||
0.399812 | − | 0.916597i | \(-0.369075\pi\) | |||||||
\(150\) | −1.97118 | + | 5.24426i | −0.160946 | + | 0.428192i | ||||
\(151\) | − | 2.40104i | − | 0.195394i | −0.995216 | − | 0.0976969i | \(-0.968852\pi\) | ||
0.995216 | − | 0.0976969i | \(-0.0311476\pi\) | |||||||
\(152\) | −10.4859 | −0.850518 | ||||||||
\(153\) | 4.13710i | 0.334465i | ||||||||
\(154\) | −9.00717 | + | 3.94277i | −0.725819 | + | 0.317717i | ||||
\(155\) | 13.0919 | − | 9.06529i | 1.05157 | − | 0.728141i | ||||
\(156\) | − | 0.354945i | − | 0.0284183i | ||||||
\(157\) | 12.3697 | 0.987211 | 0.493605 | − | 0.869686i | \(-0.335679\pi\) | ||||
0.493605 | + | 0.869686i | \(0.335679\pi\) | |||||||
\(158\) | − | 0.813710i | − | 0.0647353i | ||||||
\(159\) | − | 4.46060i | − | 0.353748i | ||||||
\(160\) | 5.03811 | + | 7.27594i | 0.398298 | + | 0.575214i | ||||
\(161\) | −1.63137 | + | 5.86341i | −0.128570 | + | 0.462101i | ||||
\(162\) | −1.12050 | −0.0880346 | ||||||||
\(163\) | 20.8684i | 1.63454i | 0.576256 | + | 0.817269i | \(0.304513\pi\) | ||||
−0.576256 | + | 0.817269i | \(0.695487\pi\) | |||||||
\(164\) | −5.03272 | −0.392990 | ||||||||
\(165\) | 7.12493 | + | 2.05799i | 0.554675 | + | 0.160215i | ||||
\(166\) | 9.84790i | 0.764345i | ||||||||
\(167\) | − | 11.4710i | − | 0.887654i | −0.896113 | − | 0.443827i | \(-0.853620\pi\) | ||
0.896113 | − | 0.443827i | \(-0.146380\pi\) | |||||||
\(168\) | −7.83845 | − | 2.18089i | −0.604749 | − | 0.168259i | ||||
\(169\) | 12.7727 | 0.982515 | ||||||||
\(170\) | −8.52197 | + | 5.90090i | −0.653605 | + | 0.452578i | ||||
\(171\) | −3.40984 | −0.260757 | ||||||||
\(172\) | −3.56057 | −0.271491 | ||||||||
\(173\) | − | 21.5558i | − | 1.63886i | −0.573183 | − | 0.819428i | \(-0.694291\pi\) | ||
0.573183 | − | 0.819428i | \(-0.305709\pi\) | |||||||
\(174\) | − | 9.84727i | − | 0.746520i | ||||||
\(175\) | −7.80330 | + | 10.6822i | −0.589874 | + | 0.807495i | ||||
\(176\) | −5.03008 | + | 4.10081i | −0.379157 | + | 0.309110i | ||||
\(177\) | 10.6711i | 0.802089i | ||||||||
\(178\) | − | 11.4411i | − | 0.857545i | ||||||
\(179\) | −14.1203 | −1.05540 | −0.527701 | − | 0.849430i | \(-0.676946\pi\) | ||||
−0.527701 | + | 0.849430i | \(0.676946\pi\) | |||||||
\(180\) | 0.947693 | + | 1.36864i | 0.0706369 | + | 0.102012i | ||||
\(181\) | − | 6.42683i | − | 0.477702i | −0.971056 | − | 0.238851i | \(-0.923229\pi\) | ||
0.971056 | − | 0.238851i | \(-0.0767708\pi\) | |||||||
\(182\) | −0.378858 | + | 1.36167i | −0.0280828 | + | 0.100934i | ||||
\(183\) | 2.11783 | 0.156554 | ||||||||
\(184\) | 7.07398i | 0.521501i | ||||||||
\(185\) | 8.45587 | − | 5.85513i | 0.621688 | − | 0.430478i | ||||
\(186\) | 7.97960i | 0.585093i | ||||||||
\(187\) | 8.67016 | + | 10.6349i | 0.634025 | + | 0.777698i | ||||
\(188\) | −6.80488 | −0.496297 | ||||||||
\(189\) | −2.54893 | − | 0.709189i | −0.185407 | − | 0.0515859i | ||||
\(190\) | −4.86357 | − | 7.02388i | −0.352841 | − | 0.509566i | ||||
\(191\) | 1.65973 | 0.120094 | 0.0600469 | − | 0.998196i | \(-0.480875\pi\) | ||||
0.0600469 | + | 0.998196i | \(0.480875\pi\) | |||||||
\(192\) | −8.34827 | −0.602484 | ||||||||
\(193\) | 7.02842 | 0.505916 | 0.252958 | − | 0.967477i | \(-0.418596\pi\) | ||||
0.252958 | + | 0.967477i | \(0.418596\pi\) | |||||||
\(194\) | 4.89416 | 0.351380 | ||||||||
\(195\) | 0.876470 | − | 0.606897i | 0.0627653 | − | 0.0434608i | ||||
\(196\) | −4.46253 | − | 2.69158i | −0.318752 | − | 0.192255i | ||||
\(197\) | 8.04622 | 0.573269 | 0.286635 | − | 0.958040i | \(-0.407463\pi\) | ||||
0.286635 | + | 0.958040i | \(0.407463\pi\) | |||||||
\(198\) | −2.88036 | + | 2.34823i | −0.204698 | + | 0.166882i | ||||
\(199\) | − | 22.3264i | − | 1.58268i | −0.611379 | − | 0.791338i | \(-0.709385\pi\) | ||
0.611379 | − | 0.791338i | \(-0.290615\pi\) | |||||||
\(200\) | −5.40987 | + | 14.3928i | −0.382536 | + | 1.01773i | ||||
\(201\) | 11.4547i | 0.807955i | ||||||||
\(202\) | −11.5263 | −0.810990 | ||||||||
\(203\) | 6.23257 | − | 22.4008i | 0.437441 | − | 1.57223i | ||||
\(204\) | 3.08002i | 0.215644i | ||||||||
\(205\) | −8.60513 | − | 12.4274i | −0.601009 | − | 0.867965i | ||||
\(206\) | 19.3581 | 1.34874 | ||||||||
\(207\) | 2.30034i | 0.159885i | ||||||||
\(208\) | 0.932918i | 0.0646862i | ||||||||
\(209\) | −8.76535 | + | 7.14602i | −0.606312 | + | 0.494300i | ||||
\(210\) | −2.17478 | − | 6.26205i | −0.150074 | − | 0.432123i | ||||
\(211\) | 14.8136i | 1.01981i | 0.860231 | + | 0.509905i | \(0.170320\pi\) | ||||
−0.860231 | + | 0.509905i | \(0.829680\pi\) | |||||||
\(212\) | − | 3.32085i | − | 0.228077i | ||||||
\(213\) | −14.1690 | −0.970846 | ||||||||
\(214\) | 4.17846 | 0.285634 | ||||||||
\(215\) | −6.08799 | − | 8.79216i | −0.415197 | − | 0.599620i | ||||
\(216\) | −3.07519 | −0.209240 | ||||||||
\(217\) | −5.05048 | + | 18.1522i | −0.342849 | + | 1.23225i | ||||
\(218\) | − | 12.6805i | − | 0.858829i | ||||||
\(219\) | 9.29571i | 0.628146i | ||||||||
\(220\) | 5.30441 | + | 1.53215i | 0.357623 | + | 0.103297i | ||||
\(221\) | 1.97243 | 0.132680 | ||||||||
\(222\) | 5.15390i | 0.345907i | ||||||||
\(223\) | 3.11670 | 0.208709 | 0.104355 | − | 0.994540i | \(-0.466722\pi\) | ||||
0.104355 | + | 0.994540i | \(0.466722\pi\) | |||||||
\(224\) | −10.0882 | − | 2.80684i | −0.674048 | − | 0.187540i | ||||
\(225\) | −1.75920 | + | 4.68030i | −0.117280 | + | 0.312020i | ||||
\(226\) | − | 7.02166i | − | 0.467074i | ||||||
\(227\) | − | 13.6688i | − | 0.907232i | −0.891197 | − | 0.453616i | \(-0.850134\pi\) | ||
0.891197 | − | 0.453616i | \(-0.149866\pi\) | |||||||
\(228\) | −2.53858 | −0.168121 | ||||||||
\(229\) | − | 5.12695i | − | 0.338798i | −0.985548 | − | 0.169399i | \(-0.945817\pi\) | ||
0.985548 | − | 0.169399i | \(-0.0541827\pi\) | |||||||
\(230\) | −4.73844 | + | 3.28106i | −0.312443 | + | 0.216346i | ||||
\(231\) | −8.03855 | + | 3.51877i | −0.528898 | + | 0.231518i | ||||
\(232\) | − | 27.0257i | − | 1.77432i | ||||||
\(233\) | −7.14633 | −0.468171 | −0.234086 | − | 0.972216i | \(-0.575210\pi\) | ||||
−0.234086 | + | 0.972216i | \(0.575210\pi\) | |||||||
\(234\) | 0.534214i | 0.0349226i | ||||||||
\(235\) | −11.6352 | − | 16.8034i | −0.758999 | − | 1.09613i | ||||
\(236\) | 7.94449i | 0.517142i | ||||||||
\(237\) | − | 0.726204i | − | 0.0471720i | ||||||
\(238\) | 3.28752 | − | 11.8159i | 0.213099 | − | 0.765908i | ||||
\(239\) | 9.42544i | 0.609681i | 0.952403 | + | 0.304841i | \(0.0986032\pi\) | ||||
−0.952403 | + | 0.304841i | \(0.901397\pi\) | |||||||
\(240\) | −2.49087 | − | 3.59726i | −0.160785 | − | 0.232202i | ||||
\(241\) | 20.5632 | 1.32459 | 0.662297 | − | 0.749242i | \(-0.269582\pi\) | ||||
0.662297 | + | 0.749242i | \(0.269582\pi\) | |||||||
\(242\) | −2.48305 | + | 12.0728i | −0.159617 | + | 0.776067i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.57669 | 0.100937 | ||||||||
\(245\) | −0.983846 | − | 15.6215i | −0.0628556 | − | 0.998023i | ||||
\(246\) | 7.57456 | 0.482936 | ||||||||
\(247\) | 1.62569i | 0.103440i | ||||||||
\(248\) | 21.8999i | 1.39065i | ||||||||
\(249\) | 8.78886i | 0.556972i | ||||||||
\(250\) | −12.1501 | + | 3.05193i | −0.768440 | + | 0.193021i | ||||
\(251\) | 21.5112i | 1.35778i | 0.734242 | + | 0.678888i | \(0.237538\pi\) | ||||
−0.734242 | + | 0.678888i | \(0.762462\pi\) | |||||||
\(252\) | −1.89764 | − | 0.527981i | −0.119540 | − | 0.0332597i | ||||
\(253\) | 4.82084 | + | 5.91326i | 0.303083 | + | 0.371764i | ||||
\(254\) | −9.60736 | −0.602820 | ||||||||
\(255\) | −7.60552 | + | 5.26632i | −0.476276 | + | 0.329790i | ||||
\(256\) | −15.0846 | −0.942789 | ||||||||
\(257\) | 24.5941 | 1.53414 | 0.767068 | − | 0.641566i | \(-0.221715\pi\) | ||||
0.767068 | + | 0.641566i | \(0.221715\pi\) | |||||||
\(258\) | 5.35887 | 0.333629 | ||||||||
\(259\) | −3.26203 | + | 11.7242i | −0.202692 | + | 0.728507i | ||||
\(260\) | 0.652519 | − | 0.451827i | 0.0404675 | − | 0.0280211i | ||||
\(261\) | − | 8.78831i | − | 0.543983i | ||||||
\(262\) | −15.9299 | −0.984151 | ||||||||
\(263\) | −30.0425 | −1.85250 | −0.926250 | − | 0.376910i | \(-0.876987\pi\) | ||||
−0.926250 | + | 0.376910i | \(0.876987\pi\) | |||||||
\(264\) | −7.90510 | + | 6.44469i | −0.486525 | + | 0.396643i | ||||
\(265\) | 8.20022 | − | 5.67811i | 0.503736 | − | 0.348804i | ||||
\(266\) | 9.73874 | + | 2.70961i | 0.597120 | + | 0.166137i | ||||
\(267\) | − | 10.2107i | − | 0.624885i | ||||||
\(268\) | 8.52790i | 0.520924i | ||||||||
\(269\) | 11.3709i | 0.693294i | 0.937996 | + | 0.346647i | \(0.112680\pi\) | ||||
−0.937996 | + | 0.346647i | \(0.887320\pi\) | |||||||
\(270\) | −1.42634 | − | 2.05989i | −0.0868040 | − | 0.125361i | ||||
\(271\) | 9.14710 | 0.555647 | 0.277823 | − | 0.960632i | \(-0.410387\pi\) | ||||
0.277823 | + | 0.960632i | \(0.410387\pi\) | |||||||
\(272\) | − | 8.09535i | − | 0.490853i | ||||||
\(273\) | −0.338116 | + | 1.21524i | −0.0204637 | + | 0.0735497i | ||||
\(274\) | 9.15129i | 0.552850i | ||||||||
\(275\) | 5.28633 | + | 15.7180i | 0.318777 | + | 0.947830i | ||||
\(276\) | 1.71257i | 0.103085i | ||||||||
\(277\) | −10.6798 | −0.641688 | −0.320844 | − | 0.947132i | \(-0.603967\pi\) | ||||
−0.320844 | + | 0.947132i | \(0.603967\pi\) | |||||||
\(278\) | −5.89367 | −0.353479 | ||||||||
\(279\) | 7.12148i | 0.426352i | ||||||||
\(280\) | −5.96866 | − | 17.1861i | −0.356696 | − | 1.02707i | ||||
\(281\) | − | 26.3350i | − | 1.57101i | −0.618854 | − | 0.785506i | \(-0.712403\pi\) | ||
0.618854 | − | 0.785506i | \(-0.287597\pi\) | |||||||
\(282\) | 10.2418 | 0.609888 | ||||||||
\(283\) | − | 0.827641i | − | 0.0491981i | −0.999697 | − | 0.0245991i | \(-0.992169\pi\) | ||
0.999697 | − | 0.0245991i | \(-0.00783092\pi\) | |||||||
\(284\) | −10.5486 | −0.625947 | ||||||||
\(285\) | −4.34055 | − | 6.26854i | −0.257112 | − | 0.371316i | ||||
\(286\) | 1.11955 | + | 1.37325i | 0.0662007 | + | 0.0812021i | ||||
\(287\) | 17.2308 | + | 4.79411i | 1.01710 | + | 0.282988i | ||||
\(288\) | −3.95782 | −0.233217 | ||||||||
\(289\) | −0.115630 | −0.00680177 | ||||||||
\(290\) | 18.1029 | − | 12.5351i | 1.06304 | − | 0.736085i | ||||
\(291\) | 4.36785 | 0.256048 | ||||||||
\(292\) | 6.92052i | 0.404993i | ||||||||
\(293\) | 5.25394i | 0.306938i | 0.988153 | + | 0.153469i | \(0.0490446\pi\) | ||||
−0.988153 | + | 0.153469i | \(0.950955\pi\) | |||||||
\(294\) | 6.71637 | + | 4.05099i | 0.391707 | + | 0.236258i | ||||
\(295\) | −19.6174 | + | 13.5838i | −1.14217 | + | 0.790877i | ||||
\(296\) | 14.1448i | 0.822151i | ||||||||
\(297\) | −2.57061 | + | 2.09571i | −0.149162 | + | 0.121605i | ||||
\(298\) | 25.0733i | 1.45246i | ||||||||
\(299\) | 1.09672 | 0.0634250 | ||||||||
\(300\) | −1.30970 | + | 3.48442i | −0.0756156 | + | 0.201173i | ||||
\(301\) | 12.1905 | + | 3.39176i | 0.702648 | + | 0.195498i | ||||
\(302\) | 2.69036i | 0.154813i | ||||||||
\(303\) | −10.2868 | −0.590962 | ||||||||
\(304\) | 6.67226 | 0.382680 | ||||||||
\(305\) | 2.69589 | + | 3.89335i | 0.154366 | + | 0.222932i | ||||
\(306\) | − | 4.63561i | − | 0.265000i | ||||||
\(307\) | 7.14246i | 0.407642i | 0.979008 | + | 0.203821i | \(0.0653360\pi\) | ||||
−0.979008 | + | 0.203821i | \(0.934664\pi\) | |||||||
\(308\) | −5.98459 | + | 2.61967i | −0.341004 | + | 0.149270i | ||||
\(309\) | 17.2764 | 0.982818 | ||||||||
\(310\) | −14.6695 | + | 10.1576i | −0.833169 | + | 0.576915i | ||||
\(311\) | − | 0.743752i | − | 0.0421743i | −0.999778 | − | 0.0210872i | \(-0.993287\pi\) | ||
0.999778 | − | 0.0210872i | \(-0.00671275\pi\) | |||||||
\(312\) | 1.46614i | 0.0830039i | ||||||||
\(313\) | 7.12227 | 0.402575 | 0.201287 | − | 0.979532i | \(-0.435488\pi\) | ||||
0.201287 | + | 0.979532i | \(0.435488\pi\) | |||||||
\(314\) | −13.8602 | −0.782178 | ||||||||
\(315\) | −1.94091 | − | 5.58864i | −0.109358 | − | 0.314884i | ||||
\(316\) | − | 0.540649i | − | 0.0304139i | ||||||
\(317\) | 33.7483i | 1.89550i | 0.319020 | + | 0.947748i | \(0.396646\pi\) | ||||
−0.319020 | + | 0.947748i | \(0.603354\pi\) | |||||||
\(318\) | 4.99809i | 0.280279i | ||||||||
\(319\) | −18.4177 | − | 22.5913i | −1.03119 | − | 1.26487i | ||||
\(320\) | −10.6269 | − | 15.3472i | −0.594063 | − | 0.857934i | ||||
\(321\) | 3.72911 | 0.208139 | ||||||||
\(322\) | 1.82795 | − | 6.56993i | 0.101868 | − | 0.366128i | ||||
\(323\) | − | 14.1069i | − | 0.784926i | ||||||
\(324\) | −0.744486 | −0.0413603 | ||||||||
\(325\) | 2.23140 | + | 0.838725i | 0.123776 | + | 0.0465241i | ||||
\(326\) | − | 23.3830i | − | 1.29506i | ||||||
\(327\) | − | 11.3168i | − | 0.625821i | ||||||
\(328\) | 20.7883 | 1.14784 | ||||||||
\(329\) | 23.2982 | + | 6.48225i | 1.28447 | + | 0.357378i | ||||
\(330\) | −7.98347 | − | 2.30598i | −0.439475 | − | 0.126940i | ||||
\(331\) | −23.7696 | −1.30650 | −0.653248 | − | 0.757144i | \(-0.726594\pi\) | ||||
−0.653248 | + | 0.757144i | \(0.726594\pi\) | |||||||
\(332\) | 6.54319i | 0.359104i | ||||||||
\(333\) | 4.59966i | 0.252060i | ||||||||
\(334\) | 12.8532i | 0.703298i | ||||||||
\(335\) | −21.0580 | + | 14.5813i | −1.15052 | + | 0.796662i | ||||
\(336\) | 4.98767 | + | 1.38772i | 0.272100 | + | 0.0757062i | ||||
\(337\) | 12.7589 | 0.695022 | 0.347511 | − | 0.937676i | \(-0.387027\pi\) | ||||
0.347511 | + | 0.937676i | \(0.387027\pi\) | |||||||
\(338\) | −14.3118 | −0.778458 | ||||||||
\(339\) | − | 6.26655i | − | 0.340353i | ||||||
\(340\) | −5.66221 | + | 3.92070i | −0.307076 | + | 0.212630i | ||||
\(341\) | 14.9245 | + | 18.3065i | 0.808209 | + | 0.991354i | ||||
\(342\) | 3.82071 | 0.206601 | ||||||||
\(343\) | 12.7146 | + | 13.4662i | 0.686523 | + | 0.727108i | ||||
\(344\) | 14.7074 | 0.792968 | ||||||||
\(345\) | −4.22887 | + | 2.92821i | −0.227675 | + | 0.157650i | ||||
\(346\) | 24.1532i | 1.29848i | ||||||||
\(347\) | −17.6529 | −0.947658 | −0.473829 | − | 0.880617i | \(-0.657129\pi\) | ||||
−0.473829 | + | 0.880617i | \(0.657129\pi\) | |||||||
\(348\) | − | 6.54277i | − | 0.350729i | ||||||
\(349\) | 1.12533 | 0.0602377 | 0.0301189 | − | 0.999546i | \(-0.490411\pi\) | ||||
0.0301189 | + | 0.999546i | \(0.490411\pi\) | |||||||
\(350\) | 8.74357 | − | 11.9693i | 0.467364 | − | 0.639788i | ||||
\(351\) | 0.476765i | 0.0254478i | ||||||||
\(352\) | −10.1740 | + | 8.29444i | −0.542276 | + | 0.442095i | ||||
\(353\) | −26.6713 | −1.41957 | −0.709784 | − | 0.704419i | \(-0.751208\pi\) | ||||
−0.709784 | + | 0.704419i | \(0.751208\pi\) | |||||||
\(354\) | − | 11.9569i | − | 0.635504i | ||||||
\(355\) | −18.0365 | − | 26.0479i | −0.957276 | − | 1.38248i | ||||
\(356\) | − | 7.60173i | − | 0.402891i | ||||||
\(357\) | 2.93399 | − | 10.5452i | 0.155283 | − | 0.558111i | ||||
\(358\) | 15.8218 | 0.836207 | ||||||||
\(359\) | − | 30.0463i | − | 1.58578i | −0.609362 | − | 0.792892i | \(-0.708574\pi\) | ||
0.609362 | − | 0.792892i | \(-0.291426\pi\) | |||||||
\(360\) | −3.91456 | − | 5.65333i | −0.206315 | − | 0.297957i | ||||
\(361\) | −7.37301 | −0.388053 | ||||||||
\(362\) | 7.20124i | 0.378489i | ||||||||
\(363\) | −2.21603 | + | 10.7745i | −0.116311 | + | 0.565513i | ||||
\(364\) | −0.251723 | + | 0.904730i | −0.0131939 | + | 0.0474207i | ||||
\(365\) | −17.0889 | + | 11.8330i | −0.894476 | + | 0.619365i | ||||
\(366\) | −2.37302 | −0.124040 | ||||||||
\(367\) | −1.39804 | −0.0729769 | −0.0364885 | − | 0.999334i | \(-0.511617\pi\) | ||||
−0.0364885 | + | 0.999334i | \(0.511617\pi\) | |||||||
\(368\) | − | 4.50123i | − | 0.234643i | ||||||
\(369\) | 6.76000 | 0.351911 | ||||||||
\(370\) | −9.47478 | + | 6.56066i | −0.492570 | + | 0.341072i | ||||
\(371\) | −3.16341 | + | 11.3698i | −0.164236 | + | 0.590288i | ||||
\(372\) | 5.30185i | 0.274888i | ||||||||
\(373\) | −7.28539 | −0.377223 | −0.188612 | − | 0.982052i | \(-0.560399\pi\) | ||||
−0.188612 | + | 0.982052i | \(0.560399\pi\) | |||||||
\(374\) | −9.71489 | − | 11.9163i | −0.502345 | − | 0.616179i | ||||
\(375\) | −10.8435 | + | 2.72372i | −0.559956 | + | 0.140653i | ||||
\(376\) | 28.1084 | 1.44958 | ||||||||
\(377\) | −4.18995 | −0.215794 | ||||||||
\(378\) | 2.85607 | + | 0.794644i | 0.146900 | + | 0.0408721i | ||||
\(379\) | −6.68357 | −0.343312 | −0.171656 | − | 0.985157i | \(-0.554912\pi\) | ||||
−0.171656 | + | 0.985157i | \(0.554912\pi\) | |||||||
\(380\) | −3.23148 | − | 4.66684i | −0.165771 | − | 0.239404i | ||||
\(381\) | −8.57420 | −0.439269 | ||||||||
\(382\) | −1.85972 | −0.0951517 | ||||||||
\(383\) | 24.6757 | 1.26087 | 0.630435 | − | 0.776242i | \(-0.282877\pi\) | ||||
0.630435 | + | 0.776242i | \(0.282877\pi\) | |||||||
\(384\) | 1.43856 | 0.0734112 | ||||||||
\(385\) | −16.7015 | − | 10.2986i | −0.851185 | − | 0.524866i | ||||
\(386\) | −7.87532 | −0.400843 | ||||||||
\(387\) | 4.78259 | 0.243113 | ||||||||
\(388\) | 3.25180 | 0.165085 | ||||||||
\(389\) | −1.28344 | −0.0650728 | −0.0325364 | − | 0.999471i | \(-0.510358\pi\) | ||||
−0.0325364 | + | 0.999471i | \(0.510358\pi\) | |||||||
\(390\) | −0.982082 | + | 0.680027i | −0.0497296 | + | 0.0344345i | ||||
\(391\) | −9.51674 | −0.481282 | ||||||||
\(392\) | 18.4330 | + | 11.1179i | 0.931007 | + | 0.561537i | ||||
\(393\) | −14.2168 | −0.717142 | ||||||||
\(394\) | −9.01576 | −0.454208 | ||||||||
\(395\) | 1.33503 | − | 0.924421i | 0.0671727 | − | 0.0465127i | ||||
\(396\) | −1.91378 | + | 1.56022i | −0.0961711 | + | 0.0784042i | ||||
\(397\) | 10.4696 | 0.525455 | 0.262728 | − | 0.964870i | \(-0.415378\pi\) | ||||
0.262728 | + | 0.964870i | \(0.415378\pi\) | |||||||
\(398\) | 25.0167i | 1.25397i | ||||||||
\(399\) | 8.69144 | + | 2.41822i | 0.435116 | + | 0.121062i | ||||
\(400\) | 3.44235 | − | 9.15826i | 0.172117 | − | 0.457913i | ||||
\(401\) | 10.6984 | 0.534251 | 0.267125 | − | 0.963662i | \(-0.413926\pi\) | ||||
0.267125 | + | 0.963662i | \(0.413926\pi\) | |||||||
\(402\) | − | 12.8350i | − | 0.640152i | ||||||
\(403\) | 3.39527 | 0.169131 | ||||||||
\(404\) | −7.65839 | −0.381019 | ||||||||
\(405\) | −1.27295 | − | 1.83837i | −0.0632534 | − | 0.0913493i | ||||
\(406\) | −6.98358 | + | 25.1000i | −0.346589 | + | 1.24569i | ||||
\(407\) | 9.63953 | + | 11.8239i | 0.477814 | + | 0.586089i | ||||
\(408\) | − | 12.7224i | − | 0.629851i | ||||||
\(409\) | 8.76079 | 0.433193 | 0.216597 | − | 0.976261i | \(-0.430504\pi\) | ||||
0.216597 | + | 0.976261i | \(0.430504\pi\) | |||||||
\(410\) | 9.64203 | + | 13.9248i | 0.476186 | + | 0.687698i | ||||
\(411\) | 8.16717i | 0.402857i | ||||||||
\(412\) | 12.8620 | 0.633666 | ||||||||
\(413\) | 7.56782 | − | 27.1999i | 0.372388 | − | 1.33842i | ||||
\(414\) | − | 2.57752i | − | 0.126678i | ||||||
\(415\) | −16.1572 | + | 11.1878i | −0.793124 | + | 0.549186i | ||||
\(416\) | 1.88695i | 0.0925154i | ||||||||
\(417\) | −5.25987 | −0.257577 | ||||||||
\(418\) | 9.82155 | − | 8.00709i | 0.480388 | − | 0.391640i | ||||
\(419\) | 27.5310i | 1.34498i | 0.740107 | + | 0.672489i | \(0.234775\pi\) | ||||
−0.740107 | + | 0.672489i | \(0.765225\pi\) | |||||||
\(420\) | −1.44498 | − | 4.16066i | −0.0705078 | − | 0.203020i | ||||
\(421\) | 26.1898 | 1.27641 | 0.638207 | − | 0.769865i | \(-0.279676\pi\) | ||||
0.638207 | + | 0.769865i | \(0.279676\pi\) | |||||||
\(422\) | − | 16.5986i | − | 0.808007i | ||||||
\(423\) | 9.14037 | 0.444420 | ||||||||
\(424\) | 13.7172i | 0.666165i | ||||||||
\(425\) | −19.3629 | − | 7.27800i | −0.939238 | − | 0.353035i | ||||
\(426\) | 15.8764 | 0.769212 | ||||||||
\(427\) | −5.39820 | − | 1.50194i | −0.261237 | − | 0.0726839i | ||||
\(428\) | 2.77627 | 0.134196 | ||||||||
\(429\) | 0.999159 | + | 1.22557i | 0.0482399 | + | 0.0591713i | ||||
\(430\) | 6.82158 | + | 9.85159i | 0.328966 | + | 0.475086i | ||||
\(431\) | 22.3030i | 1.07430i | 0.843488 | + | 0.537149i | \(0.180499\pi\) | ||||
−0.843488 | + | 0.537149i | \(0.819501\pi\) | |||||||
\(432\) | 1.95677 | 0.0941451 | ||||||||
\(433\) | −3.91589 | −0.188186 | −0.0940928 | − | 0.995563i | \(-0.529995\pi\) | ||||
−0.0940928 | + | 0.995563i | \(0.529995\pi\) | |||||||
\(434\) | 5.65904 | − | 20.3395i | 0.271643 | − | 0.976325i | ||||
\(435\) | 16.1562 | − | 11.1871i | 0.774628 | − | 0.536379i | ||||
\(436\) | − | 8.42521i | − | 0.403494i | ||||||
\(437\) | − | 7.84378i | − | 0.375219i | ||||||
\(438\) | − | 10.4158i | − | 0.497687i | ||||||
\(439\) | 7.00412 | 0.334288 | 0.167144 | − | 0.985932i | \(-0.446545\pi\) | ||||
0.167144 | + | 0.985932i | \(0.446545\pi\) | |||||||
\(440\) | −21.9105 | − | 6.32872i | −1.04454 | − | 0.301710i | ||||
\(441\) | 5.99410 | + | 3.61535i | 0.285433 | + | 0.172159i | ||||
\(442\) | −2.21010 | −0.105124 | ||||||||
\(443\) | − | 18.3450i | − | 0.871595i | −0.900045 | − | 0.435798i | \(-0.856466\pi\) | ||
0.900045 | − | 0.435798i | \(-0.143534\pi\) | |||||||
\(444\) | 3.42438i | 0.162514i | ||||||||
\(445\) | 18.7711 | − | 12.9977i | 0.889833 | − | 0.616151i | ||||
\(446\) | −3.49225 | −0.165363 | ||||||||
\(447\) | 22.3770i | 1.05840i | ||||||||
\(448\) | 21.2792 | + | 5.92050i | 1.00535 | + | 0.279717i | ||||
\(449\) | −9.69505 | −0.457538 | −0.228769 | − | 0.973481i | \(-0.573470\pi\) | ||||
−0.228769 | + | 0.973481i | \(0.573470\pi\) | |||||||
\(450\) | 1.97118 | − | 5.24426i | 0.0929223 | − | 0.247217i | ||||
\(451\) | 17.3773 | − | 14.1670i | 0.818265 | − | 0.667097i | ||||
\(452\) | − | 4.66536i | − | 0.219440i | ||||||
\(453\) | 2.40104i | 0.112811i | ||||||||
\(454\) | 15.3159i | 0.718810i | ||||||||
\(455\) | −2.66447 | + | 0.925357i | −0.124912 | + | 0.0433814i | ||||
\(456\) | 10.4859 | 0.491047 | ||||||||
\(457\) | 25.1070 | 1.17446 | 0.587228 | − | 0.809422i | \(-0.300219\pi\) | ||||
0.587228 | + | 0.809422i | \(0.300219\pi\) | |||||||
\(458\) | 5.74473i | 0.268434i | ||||||||
\(459\) | − | 4.13710i | − | 0.193103i | ||||||
\(460\) | −3.14834 | + | 2.18002i | −0.146792 | + | 0.101644i | ||||
\(461\) | −41.2119 | −1.91943 | −0.959716 | − | 0.280973i | \(-0.909343\pi\) | ||||
−0.959716 | + | 0.280973i | \(0.909343\pi\) | |||||||
\(462\) | 9.00717 | − | 3.94277i | 0.419052 | − | 0.183434i | ||||
\(463\) | 0.834251i | 0.0387709i | 0.999812 | + | 0.0193855i | \(0.00617097\pi\) | ||||
−0.999812 | + | 0.0193855i | \(0.993829\pi\) | |||||||
\(464\) | 17.1967i | 0.798336i | ||||||||
\(465\) | −13.0919 | + | 9.06529i | −0.607123 | + | 0.420393i | ||||
\(466\) | 8.00744 | 0.370937 | ||||||||
\(467\) | −15.6729 | −0.725257 | −0.362628 | − | 0.931934i | \(-0.618121\pi\) | ||||
−0.362628 | + | 0.931934i | \(0.618121\pi\) | |||||||
\(468\) | 0.354945i | 0.0164073i | ||||||||
\(469\) | 8.12357 | − | 29.1974i | 0.375112 | − | 1.34821i | ||||
\(470\) | 13.0372 | + | 18.8281i | 0.601363 | + | 0.868477i | ||||
\(471\) | −12.3697 | −0.569966 | ||||||||
\(472\) | − | 32.8156i | − | 1.51046i | ||||||
\(473\) | 12.2941 | − | 10.0229i | 0.565285 | − | 0.460853i | ||||
\(474\) | 0.813710i | 0.0373749i | ||||||||
\(475\) | 5.99859 | − | 15.9591i | 0.275234 | − | 0.732252i | ||||
\(476\) | 2.18431 | − | 7.85075i | 0.100118 | − | 0.359839i | ||||
\(477\) | 4.46060i | 0.204237i | ||||||||
\(478\) | − | 10.5612i | − | 0.483057i | ||||||
\(479\) | −0.782115 | −0.0357358 | −0.0178679 | − | 0.999840i | \(-0.505688\pi\) | ||||
−0.0178679 | + | 0.999840i | \(0.505688\pi\) | |||||||
\(480\) | −5.03811 | − | 7.27594i | −0.229957 | − | 0.332100i | ||||
\(481\) | 2.19295 | 0.0999901 | ||||||||
\(482\) | −23.0410 | −1.04949 | ||||||||
\(483\) | 1.63137 | − | 5.86341i | 0.0742301 | − | 0.266794i | ||||
\(484\) | −1.64980 | + | 8.02144i | −0.0749910 | + | 0.364611i | ||||
\(485\) | 5.56005 | + | 8.02971i | 0.252469 | + | 0.364610i | ||||
\(486\) | 1.12050 | 0.0508268 | ||||||||
\(487\) | − | 2.35861i | − | 0.106879i | −0.998571 | − | 0.0534395i | \(-0.982982\pi\) | ||
0.998571 | − | 0.0534395i | \(-0.0170184\pi\) | |||||||
\(488\) | −6.51272 | −0.294817 | ||||||||
\(489\) | − | 20.8684i | − | 0.943701i | ||||||
\(490\) | 1.10240 | + | 17.5039i | 0.0498012 | + | 0.790744i | ||||
\(491\) | − | 13.8928i | − | 0.626975i | −0.949592 | − | 0.313488i | \(-0.898503\pi\) | ||
0.949592 | − | 0.313488i | \(-0.101497\pi\) | |||||||
\(492\) | 5.03272 | 0.226893 | ||||||||
\(493\) | 36.3581 | 1.63749 | ||||||||
\(494\) | − | 1.82158i | − | 0.0819568i | ||||||
\(495\) | −7.12493 | − | 2.05799i | −0.320242 | − | 0.0924999i | ||||
\(496\) | − | 13.9351i | − | 0.625704i | ||||||
\(497\) | 36.1159 | + | 10.0485i | 1.62002 | + | 0.450738i | ||||
\(498\) | − | 9.84790i | − | 0.441295i | ||||||
\(499\) | 0.751292 | 0.0336325 | 0.0168162 | − | 0.999859i | \(-0.494647\pi\) | ||||
0.0168162 | + | 0.999859i | \(0.494647\pi\) | |||||||
\(500\) | −8.07283 | + | 2.02778i | −0.361028 | + | 0.0906849i | ||||
\(501\) | 11.4710i | 0.512487i | ||||||||
\(502\) | − | 24.1033i | − | 1.07578i | ||||||
\(503\) | − | 8.81058i | − | 0.392844i | −0.980519 | − | 0.196422i | \(-0.937068\pi\) | ||
0.980519 | − | 0.196422i | \(-0.0629323\pi\) | |||||||
\(504\) | 7.83845 | + | 2.18089i | 0.349152 | + | 0.0971445i | ||||
\(505\) | −13.0946 | − | 18.9109i | −0.582701 | − | 0.841526i | ||||
\(506\) | −5.40173 | − | 6.62580i | −0.240136 | − | 0.294553i | ||||
\(507\) | −12.7727 | −0.567255 | ||||||||
\(508\) | −6.38337 | −0.283216 | ||||||||
\(509\) | − | 18.7722i | − | 0.832065i | −0.909350 | − | 0.416033i | \(-0.863420\pi\) | ||
0.909350 | − | 0.416033i | \(-0.136580\pi\) | |||||||
\(510\) | 8.52197 | − | 5.90090i | 0.377359 | − | 0.261296i | ||||
\(511\) | 6.59241 | − | 23.6941i | 0.291631 | − | 1.04817i | ||||
\(512\) | 19.7794 | 0.874135 | ||||||||
\(513\) | 3.40984 | 0.150548 | ||||||||
\(514\) | −27.5576 | −1.21551 | ||||||||
\(515\) | 21.9919 | + | 31.7603i | 0.969080 | + | 1.39953i | ||||
\(516\) | 3.56057 | 0.156745 | ||||||||
\(517\) | 23.4963 | − | 19.1555i | 1.03337 | − | 0.842460i | ||||
\(518\) | 3.65509 | − | 13.1369i | 0.160595 | − | 0.577204i | ||||
\(519\) | 21.5558i | 0.946193i | ||||||||
\(520\) | −2.69531 | + | 1.86632i | −0.118197 | + | 0.0818437i | ||||
\(521\) | − | 25.6661i | − | 1.12445i | −0.826983 | − | 0.562227i | \(-0.809945\pi\) | ||
0.826983 | − | 0.562227i | \(-0.190055\pi\) | |||||||
\(522\) | 9.84727i | 0.431003i | ||||||||
\(523\) | 36.1446i | 1.58049i | 0.612790 | + | 0.790246i | \(0.290047\pi\) | ||||
−0.612790 | + | 0.790246i | \(0.709953\pi\) | |||||||
\(524\) | −10.5842 | −0.462373 | ||||||||
\(525\) | 7.80330 | − | 10.6822i | 0.340564 | − | 0.466208i | ||||
\(526\) | 33.6625 | 1.46776 | ||||||||
\(527\) | −29.4623 | −1.28340 | ||||||||
\(528\) | 5.03008 | − | 4.10081i | 0.218906 | − | 0.178465i | ||||
\(529\) | 17.7084 | 0.769932 | ||||||||
\(530\) | −9.18833 | + | 6.36231i | −0.399115 | + | 0.276361i | ||||
\(531\) | − | 10.6711i | − | 0.463086i | ||||||
\(532\) | 6.47066 | + | 1.80033i | 0.280539 | + | 0.0780542i | ||||
\(533\) | − | 3.22293i | − | 0.139601i | ||||||
\(534\) | 11.4411i | 0.495104i | ||||||||
\(535\) | 4.74697 | + | 6.85549i | 0.205230 | + | 0.296389i | ||||
\(536\) | − | 35.2255i | − | 1.52151i | ||||||
\(537\) | 14.1203 | 0.609336 | ||||||||
\(538\) | − | 12.7410i | − | 0.549304i | ||||||
\(539\) | 22.9852 | − | 3.26825i | 0.990042 | − | 0.140773i | ||||
\(540\) | −0.947693 | − | 1.36864i | −0.0407822 | − | 0.0588969i | ||||
\(541\) | − | 30.0504i | − | 1.29197i | −0.763351 | − | 0.645984i | \(-0.776447\pi\) | ||
0.763351 | − | 0.645984i | \(-0.223553\pi\) | |||||||
\(542\) | −10.2493 | −0.440245 | ||||||||
\(543\) | 6.42683i | 0.275801i | ||||||||
\(544\) | − | 16.3739i | − | 0.702027i | ||||||
\(545\) | 20.8045 | − | 14.4057i | 0.891166 | − | 0.617073i | ||||
\(546\) | 0.378858 | − | 1.36167i | 0.0162136 | − | 0.0582743i | ||||
\(547\) | −28.6466 | −1.22484 | −0.612420 | − | 0.790532i | \(-0.709804\pi\) | ||||
−0.612420 | + | 0.790532i | \(0.709804\pi\) | |||||||
\(548\) | 6.08034i | 0.259739i | ||||||||
\(549\) | −2.11783 | −0.0903867 | ||||||||
\(550\) | −5.92331 | − | 17.6119i | −0.252571 | − | 0.750976i | ||||
\(551\) | 29.9667i | 1.27662i | ||||||||
\(552\) | − | 7.07398i | − | 0.301088i | ||||||
\(553\) | −0.515016 | + | 1.85105i | −0.0219007 | + | 0.0787145i | ||||
\(554\) | 11.9667 | 0.508416 | ||||||||
\(555\) | −8.45587 | + | 5.85513i | −0.358932 | + | 0.248536i | ||||
\(556\) | −3.91590 | −0.166071 | ||||||||
\(557\) | 15.1173 | 0.640540 | 0.320270 | − | 0.947326i | \(-0.396226\pi\) | ||||
0.320270 | + | 0.947326i | \(0.396226\pi\) | |||||||
\(558\) | − | 7.97960i | − | 0.337804i | ||||||
\(559\) | − | 2.28017i | − | 0.0964409i | ||||||
\(560\) | 3.79791 | + | 10.9357i | 0.160491 | + | 0.462116i | ||||
\(561\) | −8.67016 | − | 10.6349i | −0.366054 | − | 0.449004i | ||||
\(562\) | 29.5083i | 1.24473i | ||||||||
\(563\) | 18.8199i | 0.793164i | 0.917999 | + | 0.396582i | \(0.129804\pi\) | ||||
−0.917999 | + | 0.396582i | \(0.870196\pi\) | |||||||
\(564\) | 6.80488 | 0.286537 | ||||||||
\(565\) | 11.5202 | − | 7.97700i | 0.484660 | − | 0.335595i | ||||
\(566\) | 0.927369i | 0.0389802i | ||||||||
\(567\) | 2.54893 | + | 0.709189i | 0.107045 | + | 0.0297831i | ||||
\(568\) | 43.5724 | 1.82826 | ||||||||
\(569\) | 9.67129i | 0.405442i | 0.979237 | + | 0.202721i | \(0.0649784\pi\) | ||||
−0.979237 | + | 0.202721i | \(0.935022\pi\) | |||||||
\(570\) | 4.86357 | + | 7.02388i | 0.203713 | + | 0.294198i | ||||
\(571\) | 23.8505i | 0.998111i | 0.866570 | + | 0.499055i | \(0.166320\pi\) | ||||
−0.866570 | + | 0.499055i | \(0.833680\pi\) | |||||||
\(572\) | 0.743860 | + | 0.912423i | 0.0311024 | + | 0.0381503i | ||||
\(573\) | −1.65973 | −0.0693362 | ||||||||
\(574\) | −19.3070 | − | 5.37179i | −0.805860 | − | 0.224214i | ||||
\(575\) | −10.7663 | − | 4.04676i | −0.448985 | − | 0.168761i | ||||
\(576\) | 8.34827 | 0.347844 | ||||||||
\(577\) | −34.7774 | −1.44780 | −0.723902 | − | 0.689903i | \(-0.757653\pi\) | ||||
−0.723902 | + | 0.689903i | \(0.757653\pi\) | |||||||
\(578\) | 0.129563 | 0.00538912 | ||||||||
\(579\) | −7.02842 | −0.292091 | ||||||||
\(580\) | 12.0280 | − | 8.32862i | 0.499437 | − | 0.345827i | ||||
\(581\) | 6.23296 | − | 22.4022i | 0.258587 | − | 0.929400i | ||||
\(582\) | −4.89416 | −0.202869 | ||||||||
\(583\) | 9.34810 | + | 11.4664i | 0.387159 | + | 0.474891i | ||||
\(584\) | − | 28.5861i | − | 1.18290i | ||||||
\(585\) | −0.876470 | + | 0.606897i | −0.0362376 | + | 0.0250921i | ||||
\(586\) | − | 5.88702i | − | 0.243191i | ||||||
\(587\) | −22.0581 | −0.910436 | −0.455218 | − | 0.890380i | \(-0.650439\pi\) | ||||
−0.455218 | + | 0.890380i | \(0.650439\pi\) | |||||||
\(588\) | 4.46253 | + | 2.69158i | 0.184031 | + | 0.110999i | ||||
\(589\) | − | 24.2831i | − | 1.00057i | ||||||
\(590\) | 21.9813 | − | 15.2206i | 0.904954 | − | 0.626621i | ||||
\(591\) | −8.04622 | −0.330977 | ||||||||
\(592\) | − | 9.00046i | − | 0.369917i | ||||||
\(593\) | 41.1949i | 1.69167i | 0.533444 | + | 0.845836i | \(0.320898\pi\) | ||||
−0.533444 | + | 0.845836i | \(0.679102\pi\) | |||||||
\(594\) | 2.88036 | − | 2.34823i | 0.118182 | − | 0.0963492i | ||||
\(595\) | 23.1208 | − | 8.02974i | 0.947859 | − | 0.329187i | ||||
\(596\) | 16.6594i | 0.682394i | ||||||||
\(597\) | 22.3264i | 0.913759i | ||||||||
\(598\) | −1.22887 | −0.0502523 | ||||||||
\(599\) | −15.1101 | −0.617382 | −0.308691 | − | 0.951162i | \(-0.599891\pi\) | ||||
−0.308691 | + | 0.951162i | \(0.599891\pi\) | |||||||
\(600\) | 5.40987 | − | 14.3928i | 0.220857 | − | 0.587584i | ||||
\(601\) | 15.6214 | 0.637209 | 0.318605 | − | 0.947888i | \(-0.396786\pi\) | ||||
0.318605 | + | 0.947888i | \(0.396786\pi\) | |||||||
\(602\) | −13.6594 | − | 3.80045i | −0.556716 | − | 0.154895i | ||||
\(603\) | − | 11.4547i | − | 0.466473i | ||||||
\(604\) | 1.78754i | 0.0727340i | ||||||||
\(605\) | −22.6283 | + | 9.64148i | −0.919973 | + | 0.391982i | ||||
\(606\) | 11.5263 | 0.468226 | ||||||||
\(607\) | 33.0830i | 1.34280i | 0.741096 | + | 0.671399i | \(0.234306\pi\) | ||||
−0.741096 | + | 0.671399i | \(0.765694\pi\) | |||||||
\(608\) | 13.4955 | 0.547316 | ||||||||
\(609\) | −6.23257 | + | 22.4008i | −0.252556 | + | 0.907726i | ||||
\(610\) | −3.02073 | − | 4.36248i | −0.122306 | − | 0.176632i | ||||
\(611\) | − | 4.35781i | − | 0.176298i | ||||||
\(612\) | − | 3.08002i | − | 0.124502i | ||||||
\(613\) | 41.6396 | 1.68181 | 0.840903 | − | 0.541186i | \(-0.182024\pi\) | ||||
0.840903 | + | 0.541186i | \(0.182024\pi\) | |||||||
\(614\) | − | 8.00311i | − | 0.322979i | ||||||
\(615\) | 8.60513 | + | 12.4274i | 0.346992 | + | 0.501120i | ||||
\(616\) | 24.7201 | − | 10.8209i | 0.995999 | − | 0.435986i | ||||
\(617\) | 0.241842i | 0.00973618i | 0.999988 | + | 0.00486809i | \(0.00154957\pi\) | ||||
−0.999988 | + | 0.00486809i | \(0.998450\pi\) | |||||||
\(618\) | −19.3581 | −0.778697 | ||||||||
\(619\) | 45.8257i | 1.84189i | 0.389692 | + | 0.920945i | \(0.372581\pi\) | ||||
−0.389692 | + | 0.920945i | \(0.627419\pi\) | |||||||
\(620\) | −9.74675 | + | 6.74898i | −0.391439 | + | 0.271046i | ||||
\(621\) | − | 2.30034i | − | 0.0923094i | ||||||
\(622\) | 0.833372i | 0.0334152i | ||||||||
\(623\) | −7.24132 | + | 26.0264i | −0.290117 | + | 1.04273i | ||||
\(624\) | − | 0.932918i | − | 0.0373466i | ||||||
\(625\) | −18.8104 | − | 16.4672i | −0.752417 | − | 0.658687i | ||||
\(626\) | −7.98049 | −0.318964 | ||||||||
\(627\) | 8.76535 | − | 7.14602i | 0.350054 | − | 0.285385i | ||||
\(628\) | −9.20908 | −0.367482 | ||||||||
\(629\) | −19.0293 | −0.758746 | ||||||||
\(630\) | 2.17478 | + | 6.26205i | 0.0866455 | + | 0.249486i | ||||
\(631\) | −5.31291 | −0.211504 | −0.105752 | − | 0.994393i | \(-0.533725\pi\) | ||||
−0.105752 | + | 0.994393i | \(0.533725\pi\) | |||||||
\(632\) | 2.23322i | 0.0888326i | ||||||||
\(633\) | − | 14.8136i | − | 0.588788i | ||||||
\(634\) | − | 37.8149i | − | 1.50182i | ||||||
\(635\) | −10.9145 | − | 15.7625i | −0.433129 | − | 0.625517i | ||||
\(636\) | 3.32085i | 0.131680i | ||||||||
\(637\) | 1.72367 | − | 2.85778i | 0.0682943 | − | 0.113229i | ||||
\(638\) | 20.6370 | + | 25.3135i | 0.817026 | + | 1.00217i | ||||
\(639\) | 14.1690 | 0.560518 | ||||||||
\(640\) | 1.83121 | + | 2.64461i | 0.0723851 | + | 0.104537i | ||||
\(641\) | −3.41919 | −0.135050 | −0.0675249 | − | 0.997718i | \(-0.521510\pi\) | ||||
−0.0675249 | + | 0.997718i | \(0.521510\pi\) | |||||||
\(642\) | −4.17846 | −0.164911 | ||||||||
\(643\) | 46.7632 | 1.84416 | 0.922080 | − | 0.386998i | \(-0.126488\pi\) | ||||
0.922080 | + | 0.386998i | \(0.126488\pi\) | |||||||
\(644\) | 1.21454 | − | 4.36522i | 0.0478594 | − | 0.172014i | ||||
\(645\) | 6.08799 | + | 8.79216i | 0.239714 | + | 0.346191i | ||||
\(646\) | 15.8067i | 0.621906i | ||||||||
\(647\) | −15.6538 | −0.615415 | −0.307708 | − | 0.951481i | \(-0.599562\pi\) | ||||
−0.307708 | + | 0.951481i | \(0.599562\pi\) | |||||||
\(648\) | 3.07519 | 0.120805 | ||||||||
\(649\) | −22.3635 | − | 27.4312i | −0.877844 | − | 1.07677i | ||||
\(650\) | −2.50028 | − | 0.939789i | −0.0980690 | − | 0.0368616i | ||||
\(651\) | 5.05048 | − | 18.1522i | 0.197944 | − | 0.711440i | ||||
\(652\) | − | 15.5362i | − | 0.608445i | ||||||
\(653\) | 34.1748i | 1.33736i | 0.743548 | + | 0.668682i | \(0.233141\pi\) | ||||
−0.743548 | + | 0.668682i | \(0.766859\pi\) | |||||||
\(654\) | 12.6805i | 0.495845i | ||||||||
\(655\) | −18.0972 | − | 26.1357i | −0.707118 | − | 1.02121i | ||||
\(656\) | −13.2277 | −0.516457 | ||||||||
\(657\) | − | 9.29571i | − | 0.362660i | ||||||
\(658\) | −26.1055 | − | 7.26334i | −1.01770 | − | 0.283155i | ||||
\(659\) | 12.0053i | 0.467660i | 0.972277 | + | 0.233830i | \(0.0751260\pi\) | ||||
−0.972277 | + | 0.233830i | \(0.924874\pi\) | |||||||
\(660\) | −5.30441 | − | 1.53215i | −0.206474 | − | 0.0596388i | ||||
\(661\) | 8.58426i | 0.333889i | 0.985966 | + | 0.166944i | \(0.0533900\pi\) | ||||
−0.985966 | + | 0.166944i | \(0.946610\pi\) | |||||||
\(662\) | 26.6338 | 1.03515 | ||||||||
\(663\) | −1.97243 | −0.0766027 | ||||||||
\(664\) | − | 27.0274i | − | 1.04887i | ||||||
\(665\) | 6.61819 | + | 19.0563i | 0.256642 | + | 0.738973i | ||||
\(666\) | − | 5.15390i | − | 0.199710i | ||||||
\(667\) | 20.2161 | 0.782770 | ||||||||
\(668\) | 8.54001i | 0.330423i | ||||||||
\(669\) | −3.11670 | −0.120498 | ||||||||
\(670\) | 23.5955 | − | 16.3383i | 0.911573 | − | 0.631204i | ||||
\(671\) | −5.44410 | + | 4.43834i | −0.210167 | + | 0.171340i | ||||
\(672\) | 10.0882 | + | 2.80684i | 0.389162 | + | 0.108276i | ||||
\(673\) | −32.3671 | −1.24766 | −0.623829 | − | 0.781561i | \(-0.714424\pi\) | ||||
−0.623829 | + | 0.781561i | \(0.714424\pi\) | |||||||
\(674\) | −14.2963 | −0.550674 | ||||||||
\(675\) | 1.75920 | − | 4.68030i | 0.0677117 | − | 0.180145i | ||||
\(676\) | −9.50909 | −0.365734 | ||||||||
\(677\) | − | 11.9557i | − | 0.459497i | −0.973250 | − | 0.229748i | \(-0.926210\pi\) | ||
0.973250 | − | 0.229748i | \(-0.0737903\pi\) | |||||||
\(678\) | 7.02166i | 0.269665i | ||||||||
\(679\) | −11.1333 | − | 3.09763i | −0.427258 | − | 0.118876i | ||||
\(680\) | 23.3884 | − | 16.1949i | 0.896905 | − | 0.621048i | ||||
\(681\) | 13.6688i | 0.523791i | ||||||||
\(682\) | −16.7229 | − | 20.5124i | −0.640353 | − | 0.785461i | ||||
\(683\) | − | 7.34339i | − | 0.280987i | −0.990082 | − | 0.140494i | \(-0.955131\pi\) | ||
0.990082 | − | 0.140494i | \(-0.0448689\pi\) | |||||||
\(684\) | 2.53858 | 0.0970649 | ||||||||
\(685\) | −15.0143 | + | 10.3964i | −0.573666 | + | 0.397226i | ||||
\(686\) | −14.2467 | − | 15.0889i | −0.543940 | − | 0.576095i | ||||
\(687\) | 5.12695i | 0.195605i | ||||||||
\(688\) | −9.35841 | −0.356786 | ||||||||
\(689\) | 2.12666 | 0.0810191 | ||||||||
\(690\) | 4.73844 | − | 3.28106i | 0.180389 | − | 0.124908i | ||||
\(691\) | 7.78297i | 0.296078i | 0.988982 | + | 0.148039i | \(0.0472961\pi\) | ||||
−0.988982 | + | 0.148039i | \(0.952704\pi\) | |||||||
\(692\) | 16.0480i | 0.610052i | ||||||||
\(693\) | 8.03855 | − | 3.51877i | 0.305359 | − | 0.133667i | ||||
\(694\) | 19.7800 | 0.750840 | ||||||||
\(695\) | −6.69554 | − | 9.66958i | −0.253976 | − | 0.366788i | ||||
\(696\) | 27.0257i | 1.02441i | ||||||||
\(697\) | 27.9668i | 1.05932i | ||||||||
\(698\) | −1.26093 | −0.0477270 | ||||||||
\(699\) | 7.14633 | 0.270299 | ||||||||
\(700\) | 5.80945 | − | 7.95272i | 0.219576 | − | 0.300585i | ||||
\(701\) | 14.4847i | 0.547078i | 0.961861 | + | 0.273539i | \(0.0881943\pi\) | ||||
−0.961861 | + | 0.273539i | \(0.911806\pi\) | |||||||
\(702\) | − | 0.534214i | − | 0.0201626i | ||||||
\(703\) | − | 15.6841i | − | 0.591537i | ||||||
\(704\) | 21.4601 | − | 17.4955i | 0.808808 | − | 0.659387i | ||||
\(705\) | 11.6352 | + | 16.8034i | 0.438208 | + | 0.632852i | ||||
\(706\) | 29.8851 | 1.12474 | ||||||||
\(707\) | 26.2204 | + | 7.29529i | 0.986118 | + | 0.274368i | ||||
\(708\) | − | 7.94449i | − | 0.298572i | ||||||
\(709\) | 13.2996 | 0.499476 | 0.249738 | − | 0.968313i | \(-0.419655\pi\) | ||||
0.249738 | + | 0.968313i | \(0.419655\pi\) | |||||||
\(710\) | 20.2098 | + | 29.1866i | 0.758460 | + | 1.09535i | ||||
\(711\) | 0.726204i | 0.0272348i | ||||||||
\(712\) | 31.3999i | 1.17676i | ||||||||
\(713\) | −16.3818 | −0.613504 | ||||||||
\(714\) | −3.28752 | + | 11.8159i | −0.123033 | + | 0.442197i | ||||
\(715\) | −0.981179 | + | 3.39692i | −0.0366940 | + | 0.127037i | ||||
\(716\) | 10.5124 | 0.392866 | ||||||||
\(717\) | − | 9.42544i | − | 0.352000i | ||||||
\(718\) | 33.6668i | 1.25643i | ||||||||
\(719\) | − | 21.8590i | − | 0.815203i | −0.913160 | − | 0.407602i | \(-0.866365\pi\) | ||
0.913160 | − | 0.407602i | \(-0.133635\pi\) | |||||||
\(720\) | 2.49087 | + | 3.59726i | 0.0928291 | + | 0.134062i | ||||
\(721\) | −44.0363 | − | 12.2522i | −1.64000 | − | 0.456296i | ||||
\(722\) | 8.26143 | 0.307459 | ||||||||
\(723\) | −20.5632 | −0.764754 | ||||||||
\(724\) | 4.78468i | 0.177821i | ||||||||
\(725\) | 41.1319 | + | 15.4604i | 1.52760 | + | 0.574185i | ||||
\(726\) | 2.48305 | − | 12.0728i | 0.0921547 | − | 0.448062i | ||||
\(727\) | −6.31100 | −0.234062 | −0.117031 | − | 0.993128i | \(-0.537338\pi\) | ||||
−0.117031 | + | 0.993128i | \(0.537338\pi\) | |||||||
\(728\) | 1.03977 | − | 3.73709i | 0.0385365 | − | 0.138506i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 19.1481 | − | 13.2588i | 0.708703 | − | 0.490730i | ||||
\(731\) | 19.7861i | 0.731814i | ||||||||
\(732\) | −1.57669 | −0.0582762 | ||||||||
\(733\) | − | 6.36583i | − | 0.235127i | −0.993065 | − | 0.117564i | \(-0.962492\pi\) | ||
0.993065 | − | 0.117564i | \(-0.0375084\pi\) | |||||||
\(734\) | 1.56650 | 0.0578204 | ||||||||
\(735\) | 0.983846 | + | 15.6215i | 0.0362897 | + | 0.576209i | ||||
\(736\) | − | 9.10434i | − | 0.335590i | ||||||
\(737\) | −24.0058 | − | 29.4456i | −0.884264 | − | 1.08464i | ||||
\(738\) | −7.57456 | −0.278823 | ||||||||
\(739\) | 42.1815i | 1.55167i | 0.630935 | + | 0.775835i | \(0.282671\pi\) | ||||
−0.630935 | + | 0.775835i | \(0.717329\pi\) | |||||||
\(740\) | −6.29528 | + | 4.35906i | −0.231419 | + | 0.160242i | ||||
\(741\) | − | 1.62569i | − | 0.0597212i | ||||||
\(742\) | 3.54459 | − | 12.7398i | 0.130126 | − | 0.467692i | ||||
\(743\) | 3.62823 | 0.133107 | 0.0665534 | − | 0.997783i | \(-0.478800\pi\) | ||||
0.0665534 | + | 0.997783i | \(0.478800\pi\) | |||||||
\(744\) | − | 21.8999i | − | 0.802890i | ||||||
\(745\) | −41.1372 | + | 28.4848i | −1.50715 | + | 1.04360i | ||||
\(746\) | 8.16326 | 0.298878 | ||||||||
\(747\) | − | 8.78886i | − | 0.321568i | ||||||
\(748\) | −6.45481 | − | 7.91751i | −0.236011 | − | 0.289493i | ||||
\(749\) | −9.50526 | − | 2.64465i | −0.347314 | − | 0.0966333i | ||||
\(750\) | 12.1501 | − | 3.05193i | 0.443659 | − | 0.111441i | ||||
\(751\) | 4.91421 | 0.179322 | 0.0896610 | − | 0.995972i | \(-0.471422\pi\) | ||||
0.0896610 | + | 0.995972i | \(0.471422\pi\) | |||||||
\(752\) | −17.8856 | −0.652220 | ||||||||
\(753\) | − | 21.5112i | − | 0.783912i | ||||||
\(754\) | 4.69483 | 0.170976 | ||||||||
\(755\) | −4.41400 | + | 3.05640i | −0.160642 | + | 0.111234i | ||||
\(756\) | 1.89764 | + | 0.527981i | 0.0690166 | + | 0.0192025i | ||||
\(757\) | 12.5745i | 0.457030i | 0.973540 | + | 0.228515i | \(0.0733869\pi\) | ||||
−0.973540 | + | 0.228515i | \(0.926613\pi\) | |||||||
\(758\) | 7.48893 | 0.272010 | ||||||||
\(759\) | −4.82084 | − | 5.91326i | −0.174985 | − | 0.214638i | ||||
\(760\) | 13.3480 | + | 19.2769i | 0.484183 | + | 0.699248i | ||||
\(761\) | 50.2936 | 1.82314 | 0.911571 | − | 0.411142i | \(-0.134870\pi\) | ||||
0.911571 | + | 0.411142i | \(0.134870\pi\) | |||||||
\(762\) | 9.60736 | 0.348038 | ||||||||
\(763\) | −8.02575 | + | 28.8458i | −0.290552 | + | 1.04429i | ||||
\(764\) | −1.23565 | −0.0447041 | ||||||||
\(765\) | 7.60552 | − | 5.26632i | 0.274978 | − | 0.190404i | ||||
\(766\) | −27.6491 | −0.999001 | ||||||||
\(767\) | −5.08760 | −0.183703 | ||||||||
\(768\) | 15.0846 | 0.544320 | ||||||||
\(769\) | 52.8622 | 1.90626 | 0.953129 | − | 0.302563i | \(-0.0978424\pi\) | ||||
0.953129 | + | 0.302563i | \(0.0978424\pi\) | |||||||
\(770\) | 18.7139 | + | 11.5396i | 0.674403 | + | 0.415857i | ||||
\(771\) | −24.5941 | −0.885734 | ||||||||
\(772\) | −5.23256 | −0.188324 | ||||||||
\(773\) | 50.9018 | 1.83081 | 0.915405 | − | 0.402534i | \(-0.131870\pi\) | ||||
0.915405 | + | 0.402534i | \(0.131870\pi\) | |||||||
\(774\) | −5.35887 | −0.192621 | ||||||||
\(775\) | −33.3307 | − | 12.5281i | −1.19727 | − | 0.450023i | ||||
\(776\) | −13.4320 | −0.482179 | ||||||||
\(777\) | 3.26203 | − | 11.7242i | 0.117025 | − | 0.420604i | ||||
\(778\) | 1.43809 | 0.0515579 | ||||||||
\(779\) | −23.0505 | −0.825870 | ||||||||
\(780\) | −0.652519 | + | 0.451827i | −0.0233639 | + | 0.0161780i | ||||
\(781\) | 36.4230 | − | 29.6941i | 1.30332 | − | 1.06254i | ||||
\(782\) | 10.6635 | 0.381325 | ||||||||
\(783\) | 8.78831i | 0.314068i | ||||||||
\(784\) | −11.7291 | − | 7.07440i | −0.418895 | − | 0.252657i | ||||
\(785\) | −15.7460 | − | 22.7401i | −0.562000 | − | 0.811629i | ||||
\(786\) | 15.9299 | 0.568200 | ||||||||
\(787\) | − | 35.5901i | − | 1.26865i | −0.773067 | − | 0.634324i | \(-0.781278\pi\) | ||
0.773067 | − | 0.634324i | \(-0.218722\pi\) | |||||||
\(788\) | −5.99030 | −0.213395 | ||||||||
\(789\) | 30.0425 | 1.06954 | ||||||||
\(790\) | −1.49590 | + | 1.03581i | −0.0532217 | + | 0.0368525i | ||||
\(791\) | −4.44417 | + | 15.9730i | −0.158016 | + | 0.567935i | ||||
\(792\) | 7.90510 | − | 6.44469i | 0.280895 | − | 0.229002i | ||||
\(793\) | 1.00971i | 0.0358557i | ||||||||
\(794\) | −11.7312 | −0.416324 | ||||||||
\(795\) | −8.20022 | + | 5.67811i | −0.290832 | + | 0.201382i | ||||
\(796\) | 16.6217i | 0.589140i | ||||||||
\(797\) | −10.2007 | −0.361326 | −0.180663 | − | 0.983545i | \(-0.557824\pi\) | ||||
−0.180663 | + | 0.983545i | \(0.557824\pi\) | |||||||
\(798\) | −9.73874 | − | 2.70961i | −0.344748 | − | 0.0959190i | ||||
\(799\) | 37.8147i | 1.33779i | ||||||||
\(800\) | 6.96261 | − | 18.5238i | 0.246165 | − | 0.654916i | ||||
\(801\) | 10.2107i | 0.360778i | ||||||||
\(802\) | −11.9875 | −0.423293 | ||||||||
\(803\) | −19.4811 | − | 23.8956i | −0.687472 | − | 0.843257i | ||||
\(804\) | − | 8.52790i | − | 0.300756i | ||||||
\(805\) | 12.8558 | − | 4.46475i | 0.453106 | − | 0.157362i | ||||
\(806\) | −3.80439 | −0.134004 | ||||||||
\(807\) | − | 11.3709i | − | 0.400273i | ||||||
\(808\) | 31.6339 | 1.11288 | ||||||||
\(809\) | − | 30.0386i | − | 1.05610i | −0.849213 | − | 0.528050i | \(-0.822923\pi\) | ||
0.849213 | − | 0.528050i | \(-0.177077\pi\) | |||||||
\(810\) | 1.42634 | + | 2.05989i | 0.0501163 | + | 0.0723771i | ||||
\(811\) | −23.5708 | −0.827683 | −0.413841 | − | 0.910349i | \(-0.635813\pi\) | ||||
−0.413841 | + | 0.910349i | \(0.635813\pi\) | |||||||
\(812\) | −4.64006 | + | 16.6771i | −0.162834 | + | 0.585251i | ||||
\(813\) | −9.14710 | −0.320803 | ||||||||
\(814\) | −10.8011 | − | 13.2487i | −0.378577 | − | 0.464365i | ||||
\(815\) | 38.3638 | − | 26.5644i | 1.34382 | − | 0.930510i | ||||
\(816\) | 8.09535i | 0.283394i | ||||||||
\(817\) | −16.3078 | −0.570539 | ||||||||
\(818\) | −9.81644 | −0.343224 | ||||||||
\(819\) | 0.338116 | − | 1.21524i | 0.0118147 | − | 0.0424639i | ||||
\(820\) | 6.40640 | + | 9.25200i | 0.223721 | + | 0.323094i | ||||
\(821\) | − | 0.143674i | − | 0.00501425i | −0.999997 | − | 0.00250713i | \(-0.999202\pi\) | ||
0.999997 | − | 0.00250713i | \(-0.000798044\pi\) | |||||||
\(822\) | − | 9.15129i | − | 0.319188i | ||||||
\(823\) | − | 4.96934i | − | 0.173220i | −0.996242 | − | 0.0866102i | \(-0.972397\pi\) | ||
0.996242 | − | 0.0866102i | \(-0.0276035\pi\) | |||||||
\(824\) | −53.1281 | −1.85080 | ||||||||
\(825\) | −5.28633 | − | 15.7180i | −0.184046 | − | 0.547230i | ||||
\(826\) | −8.47972 | + | 30.4774i | −0.295047 | + | 1.06044i | ||||
\(827\) | −28.6141 | −0.995010 | −0.497505 | − | 0.867461i | \(-0.665750\pi\) | ||||
−0.497505 | + | 0.867461i | \(0.665750\pi\) | |||||||
\(828\) | − | 1.71257i | − | 0.0595159i | ||||||
\(829\) | 25.4245i | 0.883029i | 0.897254 | + | 0.441515i | \(0.145559\pi\) | ||||
−0.897254 | + | 0.441515i | \(0.854441\pi\) | |||||||
\(830\) | 18.1041 | − | 12.5359i | 0.628401 | − | 0.435126i | ||||
\(831\) | 10.6798 | 0.370479 | ||||||||
\(832\) | − | 3.98016i | − | 0.137987i | ||||||
\(833\) | −14.9571 | + | 24.7982i | −0.518232 | + | 0.859208i | ||||
\(834\) | 5.89367 | 0.204081 | ||||||||
\(835\) | −21.0880 | + | 14.6020i | −0.729779 | + | 0.505324i | ||||
\(836\) | 6.52568 | − | 5.32011i | 0.225695 | − | 0.184000i | ||||
\(837\) | − | 7.12148i | − | 0.246154i | ||||||
\(838\) | − | 30.8484i | − | 1.06564i | ||||||
\(839\) | − | 6.73515i | − | 0.232523i | −0.993219 | − | 0.116262i | \(-0.962909\pi\) | ||
0.993219 | − | 0.116262i | \(-0.0370911\pi\) | |||||||
\(840\) | 5.96866 | + | 17.1861i | 0.205938 | + | 0.592977i | ||||
\(841\) | −48.2343 | −1.66325 | ||||||||
\(842\) | −29.3456 | −1.01132 | ||||||||
\(843\) | 26.3350i | 0.907024i | ||||||||
\(844\) | − | 11.0285i | − | 0.379617i | ||||||
\(845\) | −16.2590 | − | 23.4809i | −0.559326 | − | 0.807768i | ||||
\(846\) | −10.2418 | −0.352119 | ||||||||
\(847\) | 13.2896 | − | 25.8918i | 0.456637 | − | 0.889653i | ||||
\(848\) | − | 8.72835i | − | 0.299733i | ||||||
\(849\) | 0.827641i | 0.0284046i | ||||||||
\(850\) | 21.6961 | + | 8.15497i | 0.744169 | + | 0.279713i | ||||
\(851\) | −10.5808 | −0.362704 | ||||||||
\(852\) | 10.5486 | 0.361391 | ||||||||
\(853\) | − | 30.4003i | − | 1.04089i | −0.853896 | − | 0.520444i | \(-0.825767\pi\) | ||
0.853896 | − | 0.520444i | \(-0.174233\pi\) | |||||||
\(854\) | 6.04866 | + | 1.68292i | 0.206981 | + | 0.0575883i | ||||
\(855\) | 4.34055 | + | 6.26854i | 0.148444 | + | 0.214380i | ||||
\(856\) | −11.4677 | −0.391959 | ||||||||
\(857\) | − | 2.21267i | − | 0.0755834i | −0.999286 | − | 0.0377917i | \(-0.987968\pi\) | ||
0.999286 | − | 0.0377917i | \(-0.0120323\pi\) | |||||||
\(858\) | −1.11955 | − | 1.37325i | −0.0382210 | − | 0.0468821i | ||||
\(859\) | 26.2514i | 0.895687i | 0.894112 | + | 0.447843i | \(0.147808\pi\) | ||||
−0.894112 | + | 0.447843i | \(0.852192\pi\) | |||||||
\(860\) | 4.53242 | + | 6.54564i | 0.154554 | + | 0.223204i | ||||
\(861\) | −17.2308 | − | 4.79411i | −0.587223 | − | 0.163383i | ||||
\(862\) | − | 24.9904i | − | 0.851178i | ||||||
\(863\) | 31.5519i | 1.07404i | 0.843569 | + | 0.537020i | \(0.180450\pi\) | ||||
−0.843569 | + | 0.537020i | \(0.819550\pi\) | |||||||
\(864\) | 3.95782 | 0.134648 | ||||||||
\(865\) | −39.6275 | + | 27.4394i | −1.34737 | + | 0.932968i | ||||
\(866\) | 4.38774 | 0.149102 | ||||||||
\(867\) | 0.115630 | 0.00392700 | ||||||||
\(868\) | 3.76001 | − | 13.5140i | 0.127623 | − | 0.458696i | ||||
\(869\) | 1.52191 | + | 1.86679i | 0.0516273 | + | 0.0633264i | ||||
\(870\) | −18.1029 | + | 12.5351i | −0.613746 | + | 0.424979i | ||||
\(871\) | −5.46122 | −0.185046 | ||||||||
\(872\) | 34.8013i | 1.17852i | ||||||||
\(873\) | −4.36785 | −0.147829 | ||||||||
\(874\) | 8.78894i | 0.297290i | ||||||||
\(875\) | 29.5710 | + | 0.747496i | 0.999681 | + | 0.0252700i | ||||
\(876\) | − | 6.92052i | − | 0.233823i | ||||||
\(877\) | −15.5996 | −0.526762 | −0.263381 | − | 0.964692i | \(-0.584838\pi\) | ||||
−0.263381 | + | 0.964692i | \(0.584838\pi\) | |||||||
\(878\) | −7.84810 | −0.264860 | ||||||||
\(879\) | − | 5.25394i | − | 0.177211i | ||||||
\(880\) | 13.9418 | + | 4.02702i | 0.469979 | + | 0.135751i | ||||
\(881\) | − | 42.7607i | − | 1.44065i | −0.693639 | − | 0.720323i | \(-0.743994\pi\) | ||
0.693639 | − | 0.720323i | \(-0.256006\pi\) | |||||||
\(882\) | −6.71637 | − | 4.05099i | −0.226152 | − | 0.136404i | ||||
\(883\) | − | 19.1056i | − | 0.642956i | −0.946917 | − | 0.321478i | \(-0.895820\pi\) | ||
0.946917 | − | 0.321478i | \(-0.104180\pi\) | |||||||
\(884\) | −1.46844 | −0.0493891 | ||||||||
\(885\) | 19.6174 | − | 13.5838i | 0.659432 | − | 0.456613i | ||||
\(886\) | 20.5555i | 0.690574i | ||||||||
\(887\) | 51.6117i | 1.73295i | 0.499221 | + | 0.866475i | \(0.333620\pi\) | ||||
−0.499221 | + | 0.866475i | \(0.666380\pi\) | |||||||
\(888\) | − | 14.1448i | − | 0.474669i | ||||||
\(889\) | 21.8550 | + | 6.08072i | 0.732994 | + | 0.203941i | ||||
\(890\) | −21.0329 | + | 14.5639i | −0.705025 | + | 0.488183i | ||||
\(891\) | 2.57061 | − | 2.09571i | 0.0861185 | − | 0.0702088i | ||||
\(892\) | −2.32034 | −0.0776906 | ||||||||
\(893\) | −31.1672 | −1.04297 | ||||||||
\(894\) | − | 25.0733i | − | 0.838578i | ||||||
\(895\) | 17.9744 | + | 25.9583i | 0.600819 | + | 0.867692i | ||||
\(896\) | −3.66679 | − | 1.02021i | −0.122499 | − | 0.0340829i | ||||
\(897\) | −1.09672 | −0.0366184 | ||||||||
\(898\) | 10.8633 | 0.362512 | ||||||||
\(899\) | 62.5858 | 2.08735 | ||||||||
\(900\) | 1.30970 | − | 3.48442i | 0.0436567 | − | 0.116147i | ||||
\(901\) | −18.4540 | −0.614790 | ||||||||
\(902\) | −19.4712 | + | 15.8741i | −0.648320 | + | 0.528548i | ||||
\(903\) | −12.1905 | − | 3.39176i | −0.405674 | − | 0.112871i | ||||
\(904\) | 19.2708i | 0.640939i | ||||||||
\(905\) | −11.8149 | + | 8.18102i | −0.392740 | + | 0.271946i | ||||
\(906\) | − | 2.69036i | − | 0.0893812i | ||||||
\(907\) | − | 6.32362i | − | 0.209972i | −0.994474 | − | 0.104986i | \(-0.966520\pi\) | ||
0.994474 | − | 0.104986i | \(-0.0334798\pi\) | |||||||
\(908\) | 10.1763i | 0.337711i | ||||||||
\(909\) | 10.2868 | 0.341192 | ||||||||
\(910\) | 2.98553 | − | 1.03686i | 0.0989692 | − | 0.0343716i | ||||
\(911\) | −39.5020 | −1.30876 | −0.654379 | − | 0.756167i | \(-0.727070\pi\) | ||||
−0.654379 | + | 0.756167i | \(0.727070\pi\) | |||||||
\(912\) | −6.67226 | −0.220941 | ||||||||
\(913\) | −18.4189 | − | 22.5927i | −0.609576 | − | 0.747709i | ||||
\(914\) | −28.1323 | −0.930534 | ||||||||
\(915\) | −2.69589 | − | 3.89335i | −0.0891232 | − | 0.128710i | ||||
\(916\) | 3.81694i | 0.126115i | ||||||||
\(917\) | 36.2376 | + | 10.0824i | 1.19667 | + | 0.332950i | ||||
\(918\) | 4.63561i | 0.152998i | ||||||||
\(919\) | − | 10.5173i | − | 0.346934i | −0.984840 | − | 0.173467i | \(-0.944503\pi\) | ||
0.984840 | − | 0.173467i | \(-0.0554969\pi\) | |||||||
\(920\) | 13.0046 | − | 9.00481i | 0.428748 | − | 0.296880i | ||||
\(921\) | − | 7.14246i | − | 0.235352i | ||||||
\(922\) | 46.1779 | 1.52079 | ||||||||
\(923\) | − | 6.75529i | − | 0.222353i | ||||||
\(924\) | 5.98459 | − | 2.61967i | 0.196879 | − | 0.0861809i | ||||
\(925\) | −21.5278 | − | 8.09172i | −0.707829 | − | 0.266054i | ||||
\(926\) | − | 0.934776i | − | 0.0307186i | ||||||
\(927\) | −17.2764 | −0.567430 | ||||||||
\(928\) | 34.7826i | 1.14179i | ||||||||
\(929\) | 36.2241i | 1.18847i | 0.804290 | + | 0.594237i | \(0.202546\pi\) | ||||
−0.804290 | + | 0.594237i | \(0.797454\pi\) | |||||||
\(930\) | 14.6695 | − | 10.1576i | 0.481030 | − | 0.333082i | ||||
\(931\) | −20.4389 | − | 12.3277i | −0.669858 | − | 0.404026i | ||||
\(932\) | 5.32034 | 0.174274 | ||||||||
\(933\) | 0.743752i | 0.0243494i | ||||||||
\(934\) | 17.5615 | 0.574629 | ||||||||
\(935\) | 8.51413 | − | 29.4766i | 0.278442 | − | 0.963987i | ||||
\(936\) | − | 1.46614i | − | 0.0479223i | ||||||
\(937\) | 2.65704i | 0.0868018i | 0.999058 | + | 0.0434009i | \(0.0138193\pi\) | ||||
−0.999058 | + | 0.0434009i | \(0.986181\pi\) | |||||||
\(938\) | −9.10244 | + | 32.7155i | −0.297205 | + | 1.06820i | ||||
\(939\) | −7.12227 | −0.232427 | ||||||||
\(940\) | 8.66227 | + | 12.5099i | 0.282532 | + | 0.408027i | ||||
\(941\) | −40.6135 | −1.32396 | −0.661982 | − | 0.749520i | \(-0.730284\pi\) | ||||
−0.661982 | + | 0.749520i | \(0.730284\pi\) | |||||||
\(942\) | 13.8602 | 0.451591 | ||||||||
\(943\) | 15.5503i | 0.506387i | ||||||||
\(944\) | 20.8809i | 0.679614i | ||||||||
\(945\) | 1.94091 | + | 5.58864i | 0.0631378 | + | 0.181798i | ||||
\(946\) | −13.7756 | + | 11.2306i | −0.447882 | + | 0.365139i | ||||
\(947\) | − | 17.3928i | − | 0.565191i | −0.959239 | − | 0.282595i | \(-0.908805\pi\) | ||
0.959239 | − | 0.282595i | \(-0.0911954\pi\) | |||||||
\(948\) | 0.540649i | 0.0175595i | ||||||||
\(949\) | −4.43186 | −0.143864 | ||||||||
\(950\) | −6.72140 | + | 17.8821i | −0.218071 | + | 0.580171i | ||||
\(951\) | − | 33.7483i | − | 1.09437i | ||||||
\(952\) | −9.02257 | + | 32.4285i | −0.292423 | + | 1.05101i | ||||
\(953\) | −18.0925 | −0.586072 | −0.293036 | − | 0.956101i | \(-0.594666\pi\) | ||||
−0.293036 | + | 0.956101i | \(0.594666\pi\) | |||||||
\(954\) | − | 4.99809i | − | 0.161819i | ||||||
\(955\) | −2.11275 | − | 3.05120i | −0.0683670 | − | 0.0987344i | ||||
\(956\) | − | 7.01711i | − | 0.226950i | ||||||
\(957\) | 18.4177 | + | 22.5913i | 0.595360 | + | 0.730272i | ||||
\(958\) | 0.876358 | 0.0283138 | ||||||||
\(959\) | 5.79206 | − | 20.8176i | 0.187036 | − | 0.672234i | ||||
\(960\) | 10.6269 | + | 15.3472i | 0.342982 | + | 0.495329i | ||||
\(961\) | −19.7155 | −0.635985 | ||||||||
\(962\) | −2.45720 | −0.0792233 | ||||||||
\(963\) | −3.72911 | −0.120169 | ||||||||
\(964\) | −15.3090 | −0.493071 | ||||||||
\(965\) | −8.94682 | − | 12.9208i | −0.288008 | − | 0.415936i | ||||
\(966\) | −1.82795 | + | 6.56993i | −0.0588134 | + | 0.211384i | ||||
\(967\) | −50.4552 | −1.62253 | −0.811265 | − | 0.584678i | \(-0.801221\pi\) | ||||
−0.811265 | + | 0.584678i | \(0.801221\pi\) | |||||||
\(968\) | 6.81470 | − | 33.1335i | 0.219033 | − | 1.06495i | ||||
\(969\) | 14.1069i | 0.453177i | ||||||||
\(970\) | −6.23002 | − | 8.99727i | −0.200034 | − | 0.288885i | ||||
\(971\) | − | 51.6403i | − | 1.65722i | −0.559830 | − | 0.828608i | \(-0.689133\pi\) | ||
0.559830 | − | 0.828608i | \(-0.310867\pi\) | |||||||
\(972\) | 0.744486 | 0.0238794 | ||||||||
\(973\) | 13.4070 | + | 3.73024i | 0.429810 | + | 0.119586i | ||||
\(974\) | 2.64282i | 0.0846814i | ||||||||
\(975\) | −2.23140 | − | 0.838725i | −0.0714621 | − | 0.0268607i | ||||
\(976\) | 4.14410 | 0.132649 | ||||||||
\(977\) | − | 46.0339i | − | 1.47275i | −0.676571 | − | 0.736377i | \(-0.736535\pi\) | ||
0.676571 | − | 0.736377i | \(-0.263465\pi\) | |||||||
\(978\) | 23.3830i | 0.747705i | ||||||||
\(979\) | 21.3987 | + | 26.2477i | 0.683904 | + | 0.838881i | ||||
\(980\) | 0.732460 | + | 11.6300i | 0.0233976 | + | 0.371507i | ||||
\(981\) | 11.3168i | 0.361318i | ||||||||
\(982\) | 15.5669i | 0.496760i | ||||||||
\(983\) | 10.1938 | 0.325131 | 0.162566 | − | 0.986698i | \(-0.448023\pi\) | ||||
0.162566 | + | 0.986698i | \(0.448023\pi\) | |||||||
\(984\) | −20.7883 | −0.662706 | ||||||||
\(985\) | −10.2424 | − | 14.7919i | −0.326351 | − | 0.471310i | ||||
\(986\) | −40.7392 | −1.29740 | ||||||||
\(987\) | −23.2982 | − | 6.48225i | −0.741589 | − | 0.206332i | ||||
\(988\) | − | 1.21030i | − | 0.0385049i | ||||||
\(989\) | 11.0016i | 0.349830i | ||||||||
\(990\) | 7.98347 | + | 2.30598i | 0.253731 | + | 0.0732887i | ||||
\(991\) | −26.8543 | −0.853056 | −0.426528 | − | 0.904474i | \(-0.640263\pi\) | ||||
−0.426528 | + | 0.904474i | \(0.640263\pi\) | |||||||
\(992\) | − | 28.1856i | − | 0.894893i | ||||||
\(993\) | 23.7696 | 0.754305 | ||||||||
\(994\) | −40.4678 | − | 11.2593i | −1.28356 | − | 0.357124i | ||||
\(995\) | −41.0442 | + | 28.4204i | −1.30119 | + | 0.900986i | ||||
\(996\) | − | 6.54319i | − | 0.207329i | ||||||
\(997\) | − | 43.7961i | − | 1.38704i | −0.720439 | − | 0.693519i | \(-0.756060\pi\) | ||
0.720439 | − | 0.693519i | \(-0.243940\pi\) | |||||||
\(998\) | −0.841821 | −0.0266474 | ||||||||
\(999\) | − | 4.59966i | − | 0.145527i |
(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 | 1155.2.k.a.769.18 | yes | 48 | |
5.4 | even | 2 | 1155.2.k.b.769.31 | yes | 48 | ||
7.6 | odd | 2 | 1155.2.k.b.769.17 | yes | 48 | ||
11.10 | odd | 2 | inner | 1155.2.k.a.769.31 | yes | 48 | |
35.34 | odd | 2 | inner | 1155.2.k.a.769.32 | yes | 48 | |
55.54 | odd | 2 | 1155.2.k.b.769.18 | yes | 48 | ||
77.76 | even | 2 | 1155.2.k.b.769.32 | yes | 48 | ||
385.384 | even | 2 | inner | 1155.2.k.a.769.17 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.k.a.769.17 | ✓ | 48 | 385.384 | even | 2 | inner | |
1155.2.k.a.769.18 | yes | 48 | 1.1 | even | 1 | trivial | |
1155.2.k.a.769.31 | yes | 48 | 11.10 | odd | 2 | inner | |
1155.2.k.a.769.32 | yes | 48 | 35.34 | odd | 2 | inner | |
1155.2.k.b.769.17 | yes | 48 | 7.6 | odd | 2 | ||
1155.2.k.b.769.18 | yes | 48 | 55.54 | odd | 2 | ||
1155.2.k.b.769.31 | yes | 48 | 5.4 | even | 2 | ||
1155.2.k.b.769.32 | yes | 48 | 77.76 | even | 2 |