Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(13,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.i (of order \(11\), degree \(10\), 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: | \(2.20387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{11})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 18 x^{18} - 58 x^{17} + 169 x^{16} - 363 x^{15} + 800 x^{14} - 1682 x^{13} + \cdots + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 133.2 | ||
Root | \(-0.908456 - 1.98924i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 276.133 |
Dual form | 276.2.i.b.193.2 |
$q$-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 \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(139\) | \(185\) |
\(\chi(n)\) | \(e\left(\frac{6}{11}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.654861 | − | 0.755750i | 0.378084 | − | 0.436332i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.355980 | − | 2.47589i | 0.159199 | − | 1.10725i | −0.740915 | − | 0.671599i | \(-0.765608\pi\) |
0.900114 | − | 0.435654i | \(-0.143483\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.671250 | − | 1.46983i | −0.253709 | − | 0.555544i | 0.739329 | − | 0.673345i | \(-0.235143\pi\) |
−0.993037 | + | 0.117800i | \(0.962416\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.142315 | − | 0.989821i | −0.0474383 | − | 0.329940i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.90865 | + | 0.854058i | −0.876992 | + | 0.257508i | −0.689087 | − | 0.724679i | \(-0.741988\pi\) |
−0.187905 | + | 0.982187i | \(0.560170\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.814407 | − | 1.78330i | 0.225876 | − | 0.494599i | −0.762432 | − | 0.647068i | \(-0.775995\pi\) |
0.988308 | + | 0.152469i | \(0.0487223\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.63804 | − | 1.89040i | −0.422939 | − | 0.488098i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.513691 | + | 0.330129i | −0.124588 | + | 0.0800681i | −0.601451 | − | 0.798910i | \(-0.705410\pi\) |
0.476862 | + | 0.878978i | \(0.341774\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.77936 | + | 3.07151i | 1.09646 | + | 0.704652i | 0.958302 | − | 0.285758i | \(-0.0922455\pi\) |
0.138158 | + | 0.990410i | \(0.455882\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.55040 | − | 0.455239i | −0.338325 | − | 0.0993412i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.13430 | − | 4.65976i | −0.236518 | − | 0.971627i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.20586 | − | 0.354071i | −0.241171 | − | 0.0708143i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.841254 | − | 0.540641i | −0.161899 | − | 0.104046i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.08975 | − | 3.27098i | 0.945143 | − | 0.607406i | 0.0252942 | − | 0.999680i | \(-0.491948\pi\) |
0.919849 | + | 0.392274i | \(0.128311\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.59855 | + | 7.61514i | 1.18514 | + | 1.36772i | 0.914272 | + | 0.405101i | \(0.132764\pi\) |
0.270864 | + | 0.962618i | \(0.412691\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.25931 | + | 2.75750i | −0.219218 | + | 0.480019i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.87810 | + | 1.13871i | −0.655518 | + | 0.192477i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.255743 | + | 1.77873i | 0.0420439 | + | 0.292422i | 0.999985 | + | 0.00545711i | \(0.00173706\pi\) |
−0.957941 | + | 0.286964i | \(0.907354\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.814407 | − | 1.78330i | −0.130409 | − | 0.285557i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.781353 | − | 5.43443i | 0.122027 | − | 0.848716i | −0.833228 | − | 0.552930i | \(-0.813510\pi\) |
0.955254 | − | 0.295785i | \(-0.0955813\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.13145 | + | 7.07607i | −0.935037 | + | 1.07909i | 0.0616774 | + | 0.998096i | \(0.480355\pi\) |
−0.996715 | + | 0.0809942i | \(0.974190\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.50135 | −0.372880 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.60979 | −0.234812 | −0.117406 | − | 0.993084i | \(-0.537458\pi\) | ||||
−0.117406 | + | 0.993084i | \(0.537458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.87420 | − | 3.31700i | 0.410599 | − | 0.473857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0869011 | + | 0.604411i | −0.0121686 | + | 0.0846344i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.13986 | + | 6.87534i | 0.431293 | + | 0.944400i | 0.993115 | + | 0.117142i | \(0.0373733\pi\) |
−0.561822 | + | 0.827258i | \(0.689899\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.07913 | + | 7.50554i | 0.145510 | + | 1.01205i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.45110 | − | 1.60059i | 0.722016 | − | 0.212003i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.62648 | + | 7.94087i | −0.472127 | + | 1.03381i | 0.512427 | + | 0.858731i | \(0.328747\pi\) |
−0.984554 | + | 0.175083i | \(0.943981\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.65940 | + | 1.91505i | 0.212465 | + | 0.245197i | 0.851972 | − | 0.523588i | \(-0.175407\pi\) |
−0.639507 | + | 0.768785i | \(0.720861\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.35934 | + | 0.873596i | −0.171261 | + | 0.110063i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.12535 | − | 2.65120i | −0.511687 | − | 0.328841i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.507772 | + | 0.149095i | 0.0620343 | + | 0.0182149i | 0.312602 | − | 0.949884i | \(-0.398799\pi\) |
−0.250568 | + | 0.968099i | \(0.580617\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.26442 | − | 2.19425i | −0.513376 | − | 0.264156i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.986827 | − | 0.289758i | −0.117115 | − | 0.0343880i | 0.222650 | − | 0.974898i | \(-0.428529\pi\) |
−0.339765 | + | 0.940510i | \(0.610347\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.40469 | + | 1.54540i | 0.281447 | + | 0.180875i | 0.673747 | − | 0.738962i | \(-0.264684\pi\) |
−0.392299 | + | 0.919838i | \(0.628320\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.05726 | + | 0.679458i | −0.122082 | + | 0.0784570i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.20775 | + | 3.70195i | 0.365557 | + | 0.421876i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.69594 | + | 3.71359i | −0.190808 | + | 0.417811i | −0.980723 | − | 0.195406i | \(-0.937398\pi\) |
0.789914 | + | 0.613217i | \(0.210125\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.959493 | + | 0.281733i | −0.106610 | + | 0.0313036i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.25332 | + | 8.71701i | 0.137569 | + | 0.956816i | 0.935314 | + | 0.353820i | \(0.115117\pi\) |
−0.797744 | + | 0.602996i | \(0.793974\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.634501 | + | 1.38936i | 0.0688213 | + | 0.150698i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.861033 | − | 5.98861i | 0.0923124 | − | 0.642047i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.26229 | + | 10.6892i | −0.981800 | + | 1.13306i | 0.00930212 | + | 0.999957i | \(0.497039\pi\) |
−0.991102 | + | 0.133101i | \(0.957506\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.16782 | −0.332078 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.0763 | 1.04486 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.30607 | − | 10.7398i | 0.954783 | − | 1.10188i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.48478 | − | 17.2820i | 0.252291 | − | 1.75472i | −0.332095 | − | 0.943246i | \(-0.607755\pi\) |
0.584386 | − | 0.811476i | \(-0.301336\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.25931 | + | 2.75750i | 0.126565 | + | 0.277139i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.479387 | + | 3.33421i | 0.0477008 | + | 0.331767i | 0.999673 | + | 0.0255812i | \(0.00814365\pi\) |
−0.951972 | + | 0.306185i | \(0.900947\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.21481 | + | 1.82483i | −0.612363 | + | 0.179806i | −0.573185 | − | 0.819426i | \(-0.694292\pi\) |
−0.0391785 | + | 0.999232i | \(0.512474\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.67903 | + | 3.67657i | −0.163857 | + | 0.358796i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.07731 | − | 10.4758i | −0.877537 | − | 1.01273i | −0.999795 | − | 0.0202334i | \(-0.993559\pi\) |
0.122258 | − | 0.992498i | \(-0.460986\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.10123 | − | 4.56368i | 0.680174 | − | 0.437121i | −0.154406 | − | 0.988007i | \(-0.549346\pi\) |
0.834580 | + | 0.550886i | \(0.185710\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.51175 | + | 0.971543i | 0.143489 | + | 0.0922148i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.85561 | − | 1.13211i | −0.362705 | − | 0.106500i | 0.0953017 | − | 0.995448i | \(-0.469618\pi\) |
−0.458007 | + | 0.888949i | \(0.651437\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.9409 | + | 1.14963i | −1.11349 | + | 0.107203i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.88105 | − | 0.552327i | −0.173903 | − | 0.0510626i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.830050 | + | 0.533440i | 0.0760905 | + | 0.0489004i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.52294 | + | 0.978735i | −0.138449 | + | 0.0889759i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.59539 | − | 4.14930i | −0.324186 | − | 0.374130i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.88959 | − | 8.51702i | 0.347896 | − | 0.761786i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.6937 | − | 4.60810i | 1.39259 | − | 0.408903i | 0.502460 | − | 0.864601i | \(-0.332429\pi\) |
0.890134 | + | 0.455698i | \(0.150610\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.33249 | + | 9.26768i | 0.117319 | + | 0.815974i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.48164 | − | 5.43403i | −0.216822 | − | 0.474774i | 0.769699 | − | 0.638406i | \(-0.220406\pi\) |
−0.986521 | + | 0.163633i | \(0.947679\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.30646 | − | 9.08660i | 0.113284 | − | 0.787908i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.63804 | + | 1.89040i | −0.140980 | + | 0.162699i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.20400 | 0.786350 | 0.393175 | − | 0.919464i | \(-0.371377\pi\) | ||||
0.393175 | + | 0.919464i | \(0.371377\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.62219 | −0.646506 | −0.323253 | − | 0.946313i | \(-0.604776\pi\) | ||||
−0.323253 | + | 0.946313i | \(0.604776\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.05419 | + | 1.21660i | −0.0887787 | + | 0.102456i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.845784 | + | 5.88256i | −0.0707280 | + | 0.491924i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.28676 | − | 13.7661i | −0.522087 | − | 1.14321i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.624622 | − | 4.34434i | −0.0515180 | − | 0.358315i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5125 | − | 3.08675i | 0.861219 | − | 0.252877i | 0.178843 | − | 0.983878i | \(-0.442765\pi\) |
0.682377 | + | 0.731001i | \(0.260946\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.45242 | − | 16.3185i | 0.606470 | − | 1.32798i | −0.318493 | − | 0.947925i | \(-0.603177\pi\) |
0.924963 | − | 0.380058i | \(-0.124096\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.399875 | + | 0.461480i | 0.0323280 | + | 0.0373085i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.2032 | − | 13.6265i | 1.70308 | − | 1.09450i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.4538 | − | 9.28890i | −1.15354 | − | 0.741335i | −0.183199 | − | 0.983076i | \(-0.558645\pi\) |
−0.970341 | + | 0.241741i | \(0.922282\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.25221 | + | 2.12944i | 0.575137 | + | 0.168876i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.08766 | + | 4.79510i | −0.479775 | + | 0.377906i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.3595 | − | 4.80359i | −1.28138 | − | 0.376246i | −0.430967 | − | 0.902368i | \(-0.641828\pi\) |
−0.850409 | + | 0.526121i | \(0.823646\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.37899 | + | 4.09953i | 0.496604 | + | 0.319148i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.3476 | − | 12.4339i | 1.49716 | − | 0.962166i | 0.501898 | − | 0.864927i | \(-0.332635\pi\) |
0.995261 | − | 0.0972393i | \(-0.0310012\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.99628 | + | 6.92008i | 0.461252 | + | 0.532314i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.36007 | − | 5.16783i | 0.180479 | − | 0.395194i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.98436 | + | 2.05079i | −0.531011 | + | 0.155919i | −0.536237 | − | 0.844067i | \(-0.680155\pi\) |
0.00522586 | + | 0.999986i | \(0.498337\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.289005 | + | 2.01008i | 0.0218467 | + | 0.151947i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.62648 | + | 7.94087i | 0.272583 | + | 0.596873i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.90103 | + | 13.2219i | −0.142089 | + | 0.988253i | 0.786618 | + | 0.617440i | \(0.211830\pi\) |
−0.928707 | + | 0.370813i | \(0.879079\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.1977 | + | 19.8472i | −1.27829 | + | 1.47523i | −0.474581 | + | 0.880212i | \(0.657400\pi\) |
−0.803713 | + | 0.595017i | \(0.797145\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.53398 | 0.187317 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.49498 | 0.330478 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.21220 | − | 1.39895i | 0.0886448 | − | 0.102302i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.229960 | + | 1.59941i | −0.0167271 | + | 0.116340i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.12174 | − | 2.45628i | −0.0811665 | − | 0.177730i | 0.864698 | − | 0.502293i | \(-0.167510\pi\) |
−0.945864 | + | 0.324563i | \(0.894783\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.20061 | − | 15.3056i | −0.158403 | − | 1.10172i | −0.901576 | − | 0.432621i | \(-0.857589\pi\) |
0.743173 | − | 0.669100i | \(-0.233320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.70518 | + | 1.38156i | −0.336945 | + | 0.0989359i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.28776 | + | 20.3374i | −0.661725 | + | 1.44898i | 0.219180 | + | 0.975684i | \(0.429662\pi\) |
−0.880906 | + | 0.473292i | \(0.843066\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.29918 | − | 3.80746i | −0.233873 | − | 0.269904i | 0.626667 | − | 0.779287i | \(-0.284419\pi\) |
−0.860539 | + | 0.509384i | \(0.829873\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.445199 | − | 0.286112i | 0.0314019 | − | 0.0201808i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.22429 | − | 5.28543i | −0.577232 | − | 0.370964i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.1769 | − | 3.86909i | −0.920316 | − | 0.270229i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.45090 | + | 1.78591i | −0.309359 | + | 0.124129i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.5247 | − | 4.85210i | −1.14304 | − | 0.335627i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4314 | + | 11.8451i | 1.26887 | + | 0.815453i | 0.989472 | − | 0.144722i | \(-0.0462288\pi\) |
0.279398 | + | 0.960175i | \(0.409865\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.865219 | + | 0.556042i | −0.0592838 | + | 0.0380994i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.3369 | + | 17.6997i | 1.04597 | + | 1.20711i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.76369 | − | 14.8104i | 0.459149 | − | 1.00540i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.74267 | − | 0.805320i | 0.185332 | − | 0.0544185i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.170367 | + | 1.18493i | 0.0114601 | + | 0.0797067i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.42932 | + | 14.0782i | 0.430539 | + | 0.942749i | 0.993239 | + | 0.116088i | \(0.0370354\pi\) |
−0.562700 | + | 0.826661i | \(0.690237\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.178856 | + | 1.24397i | −0.0119237 | + | 0.0829315i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.89546 | − | 6.80372i | 0.391295 | − | 0.451579i | −0.525585 | − | 0.850741i | \(-0.676154\pi\) |
0.916880 | + | 0.399162i | \(0.130699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.7181 | −1.89775 | −0.948874 | − | 0.315656i | \(-0.897775\pi\) | ||||
−0.948874 | + | 0.315656i | \(0.897775\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.89838 | 0.322289 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.8636 | + | 15.9995i | −0.908236 | + | 1.04816i | 0.0903974 | + | 0.995906i | \(0.471186\pi\) |
−0.998634 | + | 0.0522548i | \(0.983359\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.573053 | + | 3.98567i | −0.0373818 | + | 0.259996i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.69594 | + | 3.71359i | 0.110163 | + | 0.241224i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.05689 | + | 7.35085i | 0.0683647 | + | 0.475487i | 0.995028 | + | 0.0995946i | \(0.0317546\pi\) |
−0.926663 | + | 0.375892i | \(0.877336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.31515 | + | 2.14792i | −0.471210 | + | 0.138360i | −0.508712 | − | 0.860937i | \(-0.669878\pi\) |
0.0375017 | + | 0.999297i | \(0.488060\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.415415 | + | 0.909632i | −0.0266489 | + | 0.0583529i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.18938 | − | 8.29698i | −0.459312 | − | 0.530075i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.36976 | − | 6.02158i | 0.596184 | − | 0.383144i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.40862 | + | 4.76123i | 0.469502 | + | 0.301731i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.0357 | − | 5.88303i | −1.26465 | − | 0.371333i | −0.420424 | − | 0.907328i | \(-0.638119\pi\) |
−0.844221 | + | 0.535994i | \(0.819937\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.27899 | + | 12.5849i | 0.457626 | + | 0.791204i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.46552 | + | 0.430316i | 0.0917744 | + | 0.0269474i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.2321 | + | 11.0744i | 1.07491 | + | 0.690803i | 0.953376 | − | 0.301785i | \(-0.0975824\pi\) |
0.121534 | + | 0.992587i | \(0.461219\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.44277 | − | 1.56987i | 0.151786 | − | 0.0975471i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.96204 | − | 4.57243i | −0.245244 | − | 0.283027i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.76803 | + | 3.87144i | −0.109021 | + | 0.238723i | −0.956277 | − | 0.292461i | \(-0.905526\pi\) |
0.847256 | + | 0.531185i | \(0.178253\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.1403 | − | 5.32648i | 1.11435 | − | 0.327203i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.01289 | + | 13.9999i | 0.123187 | + | 0.856782i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.4807 | + | 25.1393i | 0.699993 | + | 1.53277i | 0.839980 | + | 0.542617i | \(0.182567\pi\) |
−0.139987 | + | 0.990153i | \(0.544706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.72634 | − | 18.9621i | 0.165613 | − | 1.15187i | −0.722207 | − | 0.691677i | \(-0.756872\pi\) |
0.887820 | − | 0.460190i | \(-0.152219\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.07448 | + | 2.39408i | −0.125553 | + | 0.144896i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.80981 | 0.229740 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.797542 | −0.0479197 | −0.0239598 | − | 0.999713i | \(-0.507627\pi\) | ||||
−0.0239598 | + | 0.999713i | \(0.507627\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.59855 | − | 7.61514i | 0.395045 | − | 0.455906i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.52989 | + | 24.5509i | −0.210576 | + | 1.46459i | 0.560665 | + | 0.828043i | \(0.310546\pi\) |
−0.771241 | + | 0.636544i | \(0.780363\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.38329 | + | 5.21867i | 0.141672 | + | 0.310218i | 0.967146 | − | 0.254222i | \(-0.0818195\pi\) |
−0.825474 | + | 0.564440i | \(0.809092\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.02240 | − | 14.0661i | −0.119797 | − | 0.833205i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.51218 | + | 2.49940i | −0.502458 | + | 0.147535i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.90716 | + | 15.1246i | −0.406304 | + | 0.889681i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.4337 | − | 13.1952i | −0.670255 | − | 0.773515i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.6240 | − | 10.6836i | 0.971182 | − | 0.624141i | 0.0441110 | − | 0.999027i | \(-0.485954\pi\) |
0.927071 | + | 0.374886i | \(0.122318\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.3698 | + | 11.8055i | 1.06953 | + | 0.687346i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.90865 | + | 0.854058i | 0.168777 | + | 0.0495574i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.23354 | − | 1.77214i | −0.533990 | − | 0.102485i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.5164 | + | 4.26239i | 0.836709 | + | 0.245680i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.83376 | + | 1.82115i | 0.162795 | + | 0.104622i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.33217 | − | 3.42678i | 0.305319 | − | 0.196217i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.7426 | − | 23.9382i | −1.18384 | − | 1.36623i | −0.915207 | − | 0.402985i | \(-0.867973\pi\) |
−0.268636 | − | 0.963242i | \(-0.586573\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.69072 | + | 5.89185i | −0.153070 | + | 0.335176i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.7275 | − | 4.03076i | 0.778415 | − | 0.228563i | 0.131695 | − | 0.991290i | \(-0.457958\pi\) |
0.646721 | + | 0.762727i | \(0.276140\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.07729 | + | 21.4031i | 0.173939 | + | 1.20977i | 0.870461 | + | 0.492237i | \(0.163821\pi\) |
−0.696522 | + | 0.717535i | \(0.745270\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.67903 | + | 3.67657i | 0.0946027 | + | 0.207151i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.98125 | − | 27.6902i | 0.223609 | − | 1.55524i | −0.500614 | − | 0.865671i | \(-0.666892\pi\) |
0.724223 | − | 0.689566i | \(-0.242199\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0107 | + | 13.8611i | −0.672470 | + | 0.776072i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.8614 | −0.773670 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.46911 | −0.193026 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.61347 | + | 1.86205i | −0.0894994 | + | 0.103288i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.20131 | − | 8.35532i | 0.0664328 | − | 0.462050i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.08057 | + | 2.36612i | 0.0595739 | + | 0.130449i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.08444 | + | 21.4527i | 0.169536 | + | 1.17915i | 0.879846 | + | 0.475260i | \(0.157646\pi\) |
−0.710309 | + | 0.703890i | \(0.751445\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.72423 | − | 0.506280i | 0.0944872 | − | 0.0277439i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.549901 | − | 1.20411i | 0.0300443 | − | 0.0657878i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.9749 | − | 12.6657i | −0.597841 | − | 0.689945i | 0.373501 | − | 0.927630i | \(-0.378157\pi\) |
−0.971342 | + | 0.237684i | \(0.923612\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.38048 | + | 2.17250i | −0.183602 | + | 0.117994i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.6967 | − | 16.5142i | −1.39155 | − | 0.894297i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.6575 | − | 5.18472i | −0.953417 | − | 0.279949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.95076 | + | 9.77714i | −0.374216 | + | 0.526384i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.8306 | − | 8.46543i | −1.54771 | − | 0.454448i | −0.607294 | − | 0.794478i | \(-0.707745\pi\) |
−0.940415 | + | 0.340029i | \(0.889563\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.71136 | + | 3.02781i | 0.252193 | + | 0.162075i | 0.660630 | − | 0.750712i | \(-0.270289\pi\) |
−0.408436 | + | 0.912787i | \(0.633926\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.64925 | + | 1.05991i | −0.0880304 | + | 0.0565737i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.9623 | + | 16.1134i | 0.743140 | + | 0.857629i | 0.993885 | − | 0.110424i | \(-0.0352209\pi\) |
−0.250745 | + | 0.968053i | \(0.580675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.06870 | + | 2.34013i | −0.0567207 | + | 0.124201i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.946714 | − | 0.277980i | 0.0501054 | − | 0.0147123i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.62462 | − | 18.2546i | −0.138522 | − | 0.963444i | −0.933952 | − | 0.357398i | \(-0.883664\pi\) |
0.795430 | − | 0.606046i | \(-0.207245\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.51521 | + | 12.0766i | 0.290274 | + | 0.635612i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.257636 | + | 1.79190i | −0.0135224 | + | 0.0940502i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.68226 | − | 5.40361i | 0.245080 | − | 0.282838i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.46516 | 0.389678 | 0.194839 | − | 0.980835i | \(-0.437582\pi\) | ||||
0.194839 | + | 0.980835i | \(0.437582\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.49032 | −0.285814 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.99796 | − | 9.23014i | 0.415233 | − | 0.479205i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.661732 | + | 4.60245i | −0.0342632 | + | 0.238306i | −0.999755 | − | 0.0221271i | \(-0.992956\pi\) |
0.965492 | + | 0.260433i | \(0.0838653\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.88959 | − | 8.51702i | −0.200858 | − | 0.439817i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.68803 | − | 11.7405i | −0.0869377 | − | 0.604665i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.92080 | − | 1.15125i | 0.201398 | − | 0.0591358i | −0.179478 | − | 0.983762i | \(-0.557441\pi\) |
0.380876 | + | 0.924626i | \(0.375623\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.79465 | − | 14.8782i | 0.348100 | − | 0.762233i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.3199 | − | 19.9883i | −0.885008 | − | 1.02135i | −0.999610 | − | 0.0279421i | \(-0.991105\pi\) |
0.114602 | − | 0.993412i | \(-0.463441\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.3075 | − | 6.62424i | 0.525319 | − | 0.337602i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.87664 | + | 5.06201i | 0.400392 | + | 0.257316i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.71837 | + | 2.55994i | 0.442039 | + | 0.129794i | 0.495176 | − | 0.868793i | \(-0.335104\pi\) |
−0.0531368 | + | 0.998587i | \(0.516922\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.12100 | + | 2.01921i | 0.107264 | + | 0.102116i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.73190 | − | 1.68304i | −0.289136 | − | 0.0848979i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.59073 | + | 5.52093i | 0.432246 | + | 0.277788i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.35151 | + | 0.868564i | −0.0678305 | + | 0.0435920i | −0.574117 | − | 0.818774i | \(-0.694654\pi\) |
0.506286 | + | 0.862366i | \(0.331018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.01165 | − | 6.93781i | −0.300959 | − | 0.347325i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.6987 | − | 29.9960i | 0.684081 | − | 1.49793i | −0.174178 | − | 0.984714i | \(-0.555727\pi\) |
0.858260 | − | 0.513215i | \(-0.171546\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.9540 | − | 5.56540i | 0.944166 | − | 0.277232i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.355980 | + | 2.47589i | 0.0176888 | + | 0.123028i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.26301 | − | 4.95529i | −0.112173 | − | 0.245625i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.77104 | − | 26.2281i | 0.186466 | − | 1.29690i | −0.654604 | − | 0.755972i | \(-0.727165\pi\) |
0.841070 | − | 0.540926i | \(-0.181926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.02734 | − | 6.95592i | 0.297307 | − | 0.343110i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.1060 | 0.694112 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.0285 | 1.08134 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.99147 | + | 5.76047i | −0.244434 | + | 0.282091i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.26435 | + | 22.7040i | −0.159474 | + | 1.10916i | 0.740132 | + | 0.672461i | \(0.234763\pi\) |
−0.899606 | + | 0.436703i | \(0.856146\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.15716 | + | 13.4823i | 0.300082 | + | 0.657087i | 0.998268 | − | 0.0588288i | \(-0.0187366\pi\) |
−0.698186 | + | 0.715916i | \(0.746009\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.229097 | + | 1.59341i | 0.0111391 | + | 0.0774740i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.736327 | − | 0.216205i | 0.0357171 | − | 0.0104875i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.70093 | − | 3.72452i | 0.0823138 | − | 0.180242i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.89187 | + | 4.49146i | 0.187901 | + | 0.216850i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.05600 | − | 0.678649i | 0.0508657 | − | 0.0326894i | −0.514961 | − | 0.857214i | \(-0.672194\pi\) |
0.565827 | + | 0.824524i | \(0.308557\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.294500 | + | 0.189264i | 0.0141528 | + | 0.00909544i | 0.547698 | − | 0.836676i | \(-0.315504\pi\) |
−0.533545 | + | 0.845771i | \(0.679141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.5207 | − | 4.26365i | −0.696212 | − | 0.204426i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.89125 | − | 25.7547i | 0.425326 | − | 1.23201i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.2354 | − | 5.06076i | −0.822600 | − | 0.241537i | −0.156765 | − | 0.987636i | \(-0.550106\pi\) |
−0.665835 | + | 0.746099i | \(0.731925\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.69228 | − | 2.37288i | −0.175823 | − | 0.112994i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.7884 | − | 8.86127i | 0.655107 | − | 0.421011i | −0.170422 | − | 0.985371i | \(-0.554513\pi\) |
0.825529 | + | 0.564360i | \(0.190877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.1682 | + | 26.7376i | 1.09828 | + | 1.26748i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.55142 | − | 9.96623i | 0.215275 | − | 0.471386i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.2638 | + | 8.88625i | −1.42824 | + | 0.419368i | −0.902283 | − | 0.431145i | \(-0.858110\pi\) |
−0.525954 | + | 0.850513i | \(0.676292\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.36863 | + | 16.4742i | 0.111535 | + | 0.775740i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.45242 | − | 16.3185i | −0.350145 | − | 0.766712i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.12768 | + | 7.84319i | −0.0528665 | + | 0.367695i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.9113 | − | 18.3627i | 0.744301 | − | 0.858969i | −0.249702 | − | 0.968323i | \(-0.580333\pi\) |
0.994003 | + | 0.109354i | \(0.0348781\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.610626 | 0.0285016 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −40.1961 | −1.87212 | −0.936060 | − | 0.351840i | \(-0.885556\pi\) | ||||
−0.936060 | + | 0.351840i | \(0.885556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.7810 | − | 17.0582i | 0.686933 | − | 0.792763i | −0.299992 | − | 0.953942i | \(-0.596984\pi\) |
0.986925 | + | 0.161178i | \(0.0515295\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.58695 | − | 24.9478i | 0.166341 | − | 1.15692i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.65531 | + | 18.9525i | 0.400520 | + | 0.877016i | 0.997217 | + | 0.0745500i | \(0.0237520\pi\) |
−0.596697 | + | 0.802466i | \(0.703521\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.121697 | − | 0.846420i | −0.00561944 | − | 0.0390840i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.4853 | + | 4.84053i | −0.759603 | + | 0.223040i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.7909 | − | 25.8184i | 0.542146 | − | 1.18713i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.67568 | − | 5.39603i | −0.214535 | − | 0.247587i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.35851 | − | 4.08637i | 0.291136 | − | 0.187102i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2916 | − | 6.61398i | −0.470233 | − | 0.302200i | 0.283980 | − | 0.958830i | \(-0.408345\pi\) |
−0.754213 | + | 0.656630i | \(0.771981\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.38029 | + | 0.992544i | 0.154128 | + | 0.0452561i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.362681 | + | 7.74087i | −0.0165025 | + | 0.352222i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −41.9039 | − | 12.3041i | −1.90276 | − | 0.558700i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.00238 | − | 1.92951i | −0.136051 | − | 0.0874345i | 0.470845 | − | 0.882216i | \(-0.343949\pi\) |
−0.606896 | + | 0.794781i | \(0.707585\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.3435 | + | 9.21802i | −0.648636 | + | 0.416853i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0655 | + | 16.2325i | 0.634769 | + | 0.732563i | 0.978441 | − | 0.206527i | \(-0.0662162\pi\) |
−0.343672 | + | 0.939090i | \(0.611671\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.53471 | + | 3.36055i | −0.0691199 | + | 0.151352i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.27557 | − | 2.13630i | 0.327012 | − | 0.0960195i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.236511 | + | 1.64497i | 0.0106090 | + | 0.0737870i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.35323 | + | 7.34254i | 0.150111 | + | 0.328697i | 0.969717 | − | 0.244230i | \(-0.0785351\pi\) |
−0.819606 | + | 0.572927i | \(0.805808\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.27303 | − | 22.7644i | 0.146228 | − | 1.01704i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.9232 | + | 26.4548i | −1.02210 | + | 1.17956i | −0.0384842 | + | 0.999259i | \(0.512253\pi\) |
−0.983611 | + | 0.180302i | \(0.942293\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.42580 | 0.374943 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.15657 | 0.406658 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.65162 | − | 7.67637i | 0.294828 | − | 0.340249i | −0.588939 | − | 0.808178i | \(-0.700454\pi\) |
0.883766 | + | 0.467928i | \(0.155000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.657330 | − | 4.57183i | 0.0290786 | − | 0.202246i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.36007 | − | 5.16783i | −0.104200 | − | 0.228165i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.30574 | + | 16.0368i | 0.101603 | + | 0.706666i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.68232 | − | 1.37485i | 0.205928 | − | 0.0604660i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.02390 | + | 6.62141i | −0.132734 | + | 0.290648i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.0514 | + | 25.4487i | 0.966090 | + | 1.11493i | 0.993331 | + | 0.115298i | \(0.0367823\pi\) |
−0.0272413 | + | 0.999629i | \(0.508672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.36033 | + | 3.44488i | −0.234391 | + | 0.150634i | −0.652564 | − | 0.757733i | \(-0.726307\pi\) |
0.418173 | + | 0.908367i | \(0.362670\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.70837 | + | 1.09790i | 0.0745595 | + | 0.0479165i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.90360 | − | 1.73345i | −0.257165 | − | 0.0755104i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.4267 | + | 10.5711i | −0.888118 | + | 0.459615i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.37615 | + | 2.45946i | 0.363494 | + | 0.106731i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.05489 | − | 5.81923i | −0.392211 | − | 0.252059i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.1682 | + | 18.7453i | −1.26105 | + | 0.810429i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.74756 | + | 10.0952i | 0.377485 | + | 0.435641i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.52713 | + | 12.1027i | −0.238070 | + | 0.521301i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.87014 | − | 1.13638i | 0.166390 | − | 0.0488566i | −0.197476 | − | 0.980308i | \(-0.563275\pi\) |
0.363867 | + | 0.931451i | \(0.381456\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.73741 | + | 25.9943i | 0.160388 | + | 1.11552i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.77129 | − | 19.2064i | −0.375721 | − | 0.822714i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.33463 | + | 9.28254i | −0.0570645 | + | 0.396893i | 0.941192 | + | 0.337872i | \(0.109707\pi\) |
−0.998257 | + | 0.0590210i | \(0.981202\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.65940 | − | 1.91505i | 0.0708215 | − | 0.0817324i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.3726 | 1.46432 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.59675 | 0.280522 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.94359 | − | 3.39708i | 0.124948 | − | 0.144198i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.40952 | + | 9.80344i | −0.0597234 | + | 0.415385i | 0.937925 | + | 0.346839i | \(0.112745\pi\) |
−0.997648 | + | 0.0685460i | \(0.978164\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.62528 | + | 16.6970i | 0.322515 | + | 0.706209i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.263436 | − | 1.83224i | −0.0111223 | − | 0.0773572i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.7671 | + | 4.04239i | −0.580215 | + | 0.170366i | −0.558654 | − | 0.829401i | \(-0.688682\pi\) |
−0.0215613 | + | 0.999768i | \(0.506864\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.17550 | + | 9.14307i | −0.175665 | + | 0.384652i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.05816 | + | 1.22118i | 0.0444385 | + | 0.0512848i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.6520 | − | 9.41629i | 0.614245 | − | 0.394751i | −0.196202 | − | 0.980564i | \(-0.562861\pi\) |
0.810447 | + | 0.585812i | \(0.199224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.6294 | + | 6.83113i | 0.444828 | + | 0.285874i | 0.743818 | − | 0.668383i | \(-0.233013\pi\) |
−0.298989 | + | 0.954256i | \(0.596650\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.59091 | − | 0.760761i | −0.108237 | − | 0.0317813i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.282083 | + | 6.02062i | −0.0117637 | + | 0.251077i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.7269 | + | 4.03057i | 0.571457 | + | 0.167795i | 0.554679 | − | 0.832064i | \(-0.312841\pi\) |
0.0167776 | + | 0.999859i | \(0.494659\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.0083 | − | 8.35992i | −0.540606 | − | 0.347426i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.9712 | − | 7.69345i | 0.496651 | − | 0.319178i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.0047 | − | 17.3164i | −0.621431 | − | 0.717170i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.03712 | + | 4.46067i | −0.0842245 | + | 0.184426i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.18381 | − | 0.641224i | 0.0901354 | − | 0.0264661i | −0.236354 | − | 0.971667i | \(-0.575952\pi\) |
0.326489 | + | 0.945201i | \(0.394134\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.14690 | + | 56.6630i | 0.335687 | + | 2.33476i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.28776 | + | 20.3374i | 0.382047 | + | 0.836567i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.01280 | + | 20.9545i | −0.123721 | + | 0.860497i | 0.829561 | + | 0.558416i | \(0.188591\pi\) |
−0.953282 | + | 0.302082i | \(0.902319\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.61622 | − | 1.86522i | 0.0662586 | − | 0.0764665i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.03799 | −0.206191 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.2579 | −1.07287 | −0.536434 | − | 0.843942i | \(-0.680229\pi\) | ||||
−0.536434 | + | 0.843942i | \(0.680229\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.58618 | + | 4.13868i | −0.146283 | + | 0.168820i | −0.824163 | − | 0.566353i | \(-0.808354\pi\) |
0.677879 | + | 0.735173i | \(0.262899\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.0753143 | − | 0.523822i | 0.00306703 | − | 0.0213317i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.88111 | + | 4.11905i | 0.0764778 | + | 0.167463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.16397 | − | 42.8713i | −0.250188 | − | 1.74009i | −0.597074 | − | 0.802186i | \(-0.703670\pi\) |
0.346886 | − | 0.937907i | \(-0.387239\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.38022 | + | 2.75428i | −0.380106 | + | 0.111609i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.31102 | + | 2.87074i | −0.0530384 | + | 0.116138i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.5692 | + | 12.1975i | 0.426885 | + | 0.492652i | 0.927922 | − | 0.372774i | \(-0.121593\pi\) |
−0.501037 | + | 0.865426i | \(0.667048\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.5531 | + | 7.42474i | −0.465867 | + | 0.299394i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.9966 | + | 17.3497i | 1.08684 | + | 0.698472i | 0.956128 | − | 0.292948i | \(-0.0946363\pi\) |
0.130715 | + | 0.991420i | \(0.458273\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.217610 | − | 0.0638960i | −0.00874648 | − | 0.00256820i | 0.277356 | − | 0.960767i | \(-0.410542\pi\) |
−0.286103 | + | 0.958199i | \(0.592360\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.56502 | + | 4.53329i | −0.0628021 | + | 0.181915i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.9287 | + | 6.43885i | 0.878555 | + | 0.257967i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9889 | − | 16.0594i | −0.999556 | − | 0.642376i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.4884 | + | 9.31111i | −0.578610 | + | 0.371850i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.718584 | − | 0.829290i | −0.0286518 | − | 0.0330660i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.9417 | + | 30.5281i | −0.555010 | + | 1.21530i | 0.399392 | + | 0.916780i | \(0.369221\pi\) |
−0.954402 | + | 0.298523i | \(0.903506\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.0220 | − | 6.17261i | 0.835548 | − | 0.245339i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.82250 | − | 40.4964i | −0.231059 | − | 1.60705i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.57445 | − | 7.82695i | −0.141625 | − | 0.310115i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.146369 | + | 1.01802i | −0.00579027 | + | 0.0402722i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.4259 | + | 23.5728i | −0.806775 | + | 0.931068i | −0.998732 | − | 0.0503354i | \(-0.983971\pi\) |
0.191958 | + | 0.981403i | \(0.438516\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.46023 | −0.215331 | −0.107665 | − | 0.994187i | \(-0.534337\pi\) | ||||
−0.107665 | + | 0.994187i | \(0.534337\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.4201 | 0.922166 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.6796 | − | 15.7871i | 0.537802 | − | 0.620657i | −0.420195 | − | 0.907434i | \(-0.638038\pi\) |
0.957997 | + | 0.286777i | \(0.0925839\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.76620 | − | 26.1945i | 0.147836 | − | 1.02822i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.76369 | − | 14.8104i | −0.265090 | − | 0.580466i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.13271 | + | 14.8333i | 0.0834594 | + | 0.580473i | 0.988043 | + | 0.154177i | \(0.0492727\pi\) |
−0.904584 | + | 0.426296i | \(0.859818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.3375 | + | 4.20987i | −0.560212 | + | 0.164493i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.18745 | − | 2.60014i | 0.0463266 | − | 0.101441i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.35307 | + | 8.48590i | 0.286435 | + | 0.330564i | 0.880672 | − | 0.473726i | \(-0.157091\pi\) |
−0.594237 | + | 0.804290i | \(0.702546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.3819 | + | 22.7386i | −1.37620 | + | 0.884429i | −0.999128 | − | 0.0417560i | \(-0.986705\pi\) |
−0.377070 | + | 0.926185i | \(0.623068\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.00707 | + | 0.647207i | 0.0391115 | + | 0.0251354i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.0324 | − | 6.46929i | −0.854379 | − | 0.250868i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.0153 | − | 20.0067i | −0.813716 | − | 0.774664i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.8499 | + | 4.36033i | 0.574132 | + | 0.168580i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.46219 | − | 4.15299i | −0.249470 | − | 0.160325i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.7664 | − | 8.20450i | 0.492110 | − | 0.316260i | −0.270943 | − | 0.962595i | \(-0.587336\pi\) |
0.763054 | + | 0.646335i | \(0.223699\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.823005 | + | 0.949799i | 0.0316775 | + | 0.0365578i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.26590 | + | 2.77194i | −0.0486526 | + | 0.106534i | −0.932397 | − | 0.361435i | \(-0.882287\pi\) |
0.883745 | + | 0.467969i | \(0.155014\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.0696 | + | 7.94834i | −1.03883 | + | 0.305029i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.28121 | − | 8.91098i | −0.0490959 | − | 0.341469i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.7116 | + | 30.0241i | 0.524658 | + | 1.14884i | 0.967646 | + | 0.252313i | \(0.0811913\pi\) |
−0.442987 | + | 0.896528i | \(0.646081\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.27643 | − | 22.7881i | 0.125186 | − | 0.870689i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.8064 | + | 21.7037i | −0.717508 | + | 0.828048i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.8179 | 0.564518 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.9216 | 0.871980 | 0.435990 | − | 0.899952i | \(-0.356398\pi\) | ||||
0.435990 | + | 0.899952i | \(0.356398\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.20775 | − | 3.70195i | 0.121852 | − | 0.140625i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.71334 | + | 18.8717i | −0.102923 | + | 0.715845i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.39269 | + | 3.04957i | 0.0527519 | + | 0.115511i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.01285 | + | 20.9549i | 0.113957 | + | 0.792586i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.5411 | − | 13.9593i | 1.79560 | − | 0.527237i | 0.798411 | − | 0.602113i | \(-0.205674\pi\) |
0.997193 | + | 0.0748762i | \(0.0238562\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.24110 | + | 9.28670i | −0.159956 | + | 0.350255i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.63690 | + | 3.04314i | 0.0993113 | + | 0.114611i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.57894 | − | 2.94271i | 0.172209 | − | 0.110672i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.475138 | − | 0.305353i | −0.0178442 | − | 0.0114678i | 0.531688 | − | 0.846940i | \(-0.321558\pi\) |
−0.549532 | + | 0.835472i | \(0.685194\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.91715 | + | 1.15018i | 0.146905 | + | 0.0431351i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.0000 | − | 39.3855i | 1.04861 | − | 1.47500i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.2635 | + | 4.18814i | 0.533425 | + | 0.156628i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.24752 | + | 4.01503i | 0.233318 | + | 0.149944i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.35123 | − | 1.51105i | 0.0876862 | − | 0.0563525i | −0.496063 | − | 0.868287i | \(-0.665222\pi\) |
0.583749 | + | 0.811934i | \(0.301585\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.85389 | + | 7.90981i | 0.255252 | + | 0.294577i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.16712 | + | 6.93501i | −0.117786 | + | 0.257916i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.29567 | + | 2.14220i | −0.270954 | + | 0.0795593i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.27336 | − | 29.7218i | −0.158490 | − | 1.10232i | −0.901418 | − | 0.432950i | \(-0.857473\pi\) |
0.742928 | − | 0.669372i | \(-0.233437\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.415415 | + | 0.909632i | 0.0153857 | + | 0.0336901i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.813653 | − | 5.65908i | 0.0300941 | − | 0.209309i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.8893 | − | 12.5669i | 0.402204 | − | 0.464168i | −0.518130 | − | 0.855302i | \(-0.673372\pi\) |
0.920334 | + | 0.391134i | \(0.127917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.9785 | −0.404947 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.60427 | −0.0590940 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.7465 | − | 22.7886i | 0.726386 | − | 0.838294i | −0.265674 | − | 0.964063i | \(-0.585594\pi\) |
0.992060 | + | 0.125769i | \(0.0401399\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.58508 | − | 11.0245i | 0.0582295 | − | 0.404995i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.1160 | + | 28.7201i | 0.481180 | + | 1.05364i | 0.982137 | + | 0.188165i | \(0.0602541\pi\) |
−0.500957 | + | 0.865472i | \(0.667019\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.90023 | − | 27.1267i | −0.142893 | − | 0.993845i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.44991 | − | 2.48112i | 0.309166 | − | 0.0907794i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.30449 | + | 20.3740i | −0.339979 | + | 0.744449i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.8275 | − | 21.7281i | −0.687024 | − | 0.792868i | 0.299914 | − | 0.953966i | \(-0.403042\pi\) |
−0.986938 | + | 0.161098i | \(0.948497\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.5667 | + | 11.2894i | −0.640167 | + | 0.411410i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.7500 | − | 24.2605i | −1.37386 | − | 0.882929i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.365428 | − | 0.107299i | −0.0132817 | − | 0.00389986i | 0.275085 | − | 0.961420i | \(-0.411294\pi\) |
−0.288367 | + | 0.957520i | \(0.593112\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.2777 | + | 2.74024i | 0.518249 | + | 0.0994643i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.7681 | − | 11.0897i | −1.36909 | − | 0.402002i | −0.487134 | − | 0.873327i | \(-0.661958\pi\) |
−0.881959 | + | 0.471325i | \(0.843776\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.4745 | − | 7.37424i | −0.415406 | − | 0.266965i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.28492 | − | 0.825770i | 0.0464565 | − | 0.0298558i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.2075 | + | 12.9342i | 0.404681 | + | 0.467027i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.1975 | − | 39.8470i | 0.656218 | − | 1.43692i | −0.229786 | − | 0.973241i | \(-0.573803\pi\) |
0.886004 | − | 0.463677i | \(-0.153470\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.6541 | − | 5.77097i | 0.707826 | − | 0.207836i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.11390 | − | 42.5231i | −0.219902 | − | 1.52945i | −0.738395 | − | 0.674369i | \(-0.764416\pi\) |
0.518493 | − | 0.855082i | \(-0.326493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.26061 | − | 11.5191i | −0.188967 | − | 0.413779i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.413243 | − | 2.87417i | 0.0148250 | − | 0.103110i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.4263 | − | 23.5732i | 0.731847 | − | 0.844596i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.11781 | 0.111564 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.05020 | −0.216216 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.1436 | + | 32.4794i | −1.00449 | + | 1.15924i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.74077 | − | 12.1073i | 0.0620519 | − | 0.431580i | −0.934987 | − | 0.354682i | \(-0.884589\pi\) |
0.997039 | − | 0.0768984i | \(-0.0245017\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.76803 | + | 3.87144i | 0.0629435 | + | 0.137827i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.924067 | + | 6.42703i | 0.0328560 | + | 0.228519i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.76654 | − | 1.39958i | 0.169265 | − | 0.0497007i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.85390 | − | 17.1976i | 0.278549 | − | 0.609938i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.9546 | + | 21.8748i | 0.671407 | + | 0.774845i | 0.984596 | − | 0.174846i | \(-0.0559428\pi\) |
−0.313189 | + | 0.949691i | \(0.601397\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.826935 | − | 0.531439i | 0.0292549 | − | 0.0188010i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.8986 | + | 7.64677i | 0.420417 | + | 0.270185i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.31425 | − | 2.44129i | −0.293404 | − | 0.0861511i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.70506 | + | 16.7794i | 0.342058 | + | 0.591395i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.5173 | + | 7.78618i | 0.933453 | + | 0.274087i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.98988 | + | 5.77745i | 0.316067 | + | 0.203124i | 0.689049 | − | 0.724714i | \(-0.258028\pi\) |
−0.372982 | + | 0.927839i | \(0.621665\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.21110 | − | 4.63429i | 0.253216 | − | 0.162732i | −0.407875 | − | 0.913038i | \(-0.633730\pi\) |
0.661091 | + | 0.750306i | \(0.270094\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.5452 | − | 14.4780i | −0.439981 | − | 0.507765i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.7168 | + | 38.7944i | −0.620593 | + | 1.35891i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51.0386 | + | 14.9863i | −1.78561 | + | 0.524303i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.450828 | + | 3.13558i | 0.0157532 | + | 0.109566i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.9219 | − | 34.8641i | −0.555678 | − | 1.21677i | −0.954079 | − | 0.299554i | \(-0.903162\pi\) |
0.398401 | − | 0.917211i | \(-0.369565\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.615787 | + | 4.28289i | −0.0214650 | + | 0.149292i | −0.997735 | − | 0.0672635i | \(-0.978573\pi\) |
0.976270 | + | 0.216556i | \(0.0694823\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.49490 | − | 2.87927i | 0.0868612 | − | 0.100243i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.6700 | 1.20559 | 0.602797 | − | 0.797895i | \(-0.294053\pi\) | ||||
0.602797 | + | 0.797895i | \(0.294053\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.55014 | −0.0538385 | −0.0269192 | − | 0.999638i | \(-0.508570\pi\) | ||||
−0.0269192 | + | 0.999638i | \(0.508570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.522279 | + | 0.602742i | −0.0181177 | + | 0.0209089i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.381411 | + | 2.65277i | −0.0132151 | + | 0.0919130i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.8977 | − | 52.3287i | −0.827015 | − | 1.81091i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.43400 | − | 9.97371i | −0.0495664 | − | 0.344742i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.79245 | + | 1.11356i | −0.130930 | + | 0.0384445i | −0.346541 | − | 0.938035i | \(-0.612644\pi\) |
0.215611 | + | 0.976479i | \(0.430826\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.15918 | − | 6.91764i | 0.108937 | − | 0.238539i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.2428 | + | 18.7452i | 0.559431 | + | 0.645618i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.2679 | − | 12.3827i | 0.662837 | − | 0.425979i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.46085 | + | 1.58149i | 0.0845558 | + | 0.0543407i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.50473 | + | 1.61633i | 0.188922 | + | 0.0554724i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.99837 | − | 3.20932i | 0.274181 | − | 0.110014i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.97214 | − | 0.579072i | −0.0675247 | − | 0.0198270i | 0.247796 | − | 0.968812i | \(-0.420294\pi\) |
−0.315320 | + | 0.948985i | \(0.602112\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.9549 | − | 7.68292i | −0.408847 | − | 0.262750i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.40147 | − | 4.75664i | 0.252829 | − | 0.162484i | −0.408087 | − | 0.912943i | \(-0.633804\pi\) |
0.660917 | + | 0.750459i | \(0.270168\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.3074 | − | 41.9010i | −1.23879 | − | 1.42964i | −0.864728 | − | 0.502240i | \(-0.832509\pi\) |
−0.374064 | − | 0.927403i | \(-0.622036\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.68537 | + | 8.06984i | −0.125597 | + | 0.275019i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.2359 | + | 12.1080i | −1.40369 | + | 0.412159i | −0.893948 | − | 0.448170i | \(-0.852076\pi\) |
−0.509738 | + | 0.860330i | \(0.670258\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.59125 | + | 18.0226i | 0.0881053 | + | 0.612786i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.90716 | + | 15.1246i | 0.234580 | + | 0.513657i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.76128 | − | 12.2500i | 0.0597473 | − | 0.415552i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.679415 | − | 0.784087i | 0.0230211 | − | 0.0265678i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.4597 | −0.590922 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.1295 | −0.511470 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.2257 | + | 27.9579i | −0.818042 | + | 0.944071i | −0.999224 | − | 0.0393786i | \(-0.987462\pi\) |
0.181182 | + | 0.983450i | \(0.442008\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.81227 | − | 19.5598i | 0.0948557 | − | 0.659736i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.6152 | − | 36.3823i | −0.559782 | − | 1.22575i | −0.952062 | − | 0.305905i | \(-0.901041\pi\) |
0.392280 | − | 0.919846i | \(-0.371686\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.53099 | − | 17.6034i | −0.0851747 | − | 0.592403i | −0.987051 | − | 0.160408i | \(-0.948719\pi\) |
0.901876 | − | 0.431995i | \(-0.142190\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.9517 | − | 6.15197i | 0.704284 | − | 0.206796i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.6344 | + | 23.2861i | −0.357068 | + | 0.781870i | 0.642806 | + | 0.766029i | \(0.277770\pi\) |
−0.999875 | + | 0.0158416i | \(0.994957\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.3075 | − | 19.9740i | −0.580477 | − | 0.669906i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.55022 | − | 1.63892i | 0.0854355 | − | 0.0549060i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.69377 | − | 4.94448i | −0.257462 | − | 0.165461i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.0593 | + | 9.41347i | 1.07163 | + | 0.314658i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.38598 | + | 5.81774i | −0.246611 | + | 0.194249i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.4940 | + | 17.1754i | 1.95088 | + | 0.572831i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.88267 | − | 2.49524i | −0.129350 | − | 0.0831285i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.7275 | − | 8.17947i | 0.423545 | − | 0.272196i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 43.0175 | + | 49.6448i | 1.42995 | + | 1.65025i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.35740 | − | 9.54137i | 0.144685 | − | 0.316816i | −0.823390 | − | 0.567476i | \(-0.807920\pi\) |
0.968075 | + | 0.250659i | \(0.0806474\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.23205 | − | 0.949016i | 0.107200 | − | 0.0314769i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.38396 | − | 51.3566i | −0.244642 | − | 1.70152i | −0.628240 | − | 0.778020i | \(-0.716224\pi\) |
0.383598 | − | 0.923500i | \(-0.374685\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.0903 | − | 24.2843i | −0.367035 | − | 0.803694i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.902043 | − | 6.27385i | 0.0298206 | − | 0.207407i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.32131 | + | 7.29518i | −0.208748 | + | 0.240908i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.7901 | 0.454892 | 0.227446 | − | 0.973791i | \(-0.426962\pi\) | ||||
0.227446 | + | 0.973791i | \(0.426962\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.6748 | −1.04372 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.32041 | + | 1.52383i | −0.0434617 | + | 0.0501574i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.321408 | − | 2.23544i | 0.0105678 | − | 0.0735010i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.69072 | + | 5.89185i | 0.0883748 | + | 0.193514i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.468124 | + | 3.25588i | 0.0153587 | + | 0.106822i | 0.996059 | − | 0.0886966i | \(-0.0282701\pi\) |
−0.980700 | + | 0.195518i | \(0.937361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.9250 | − | 7.02501i | 0.784110 | − | 0.230235i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.94336 | − | 13.0141i | 0.194577 | − | 0.426064i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.03214 | − | 3.49927i | −0.0991615 | − | 0.114439i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.2975 | + | 27.8256i | −1.41447 | + | 0.909023i | −0.999999 | − | 0.00104172i | \(-0.999668\pi\) |
−0.414467 | + | 0.910064i | \(0.636032\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.1905 | + | 11.6904i | 0.593626 | + | 0.381500i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.5826 | + | 9.86073i | 1.09476 | + | 0.321451i | 0.778769 | − | 0.627311i | \(-0.215845\pi\) |
0.315992 | + | 0.948762i | \(0.397663\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.2094 | + | 2.52337i | −0.853497 | + | 0.0821721i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.87810 | + | 1.13871i | 0.126154 | + | 0.0370423i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.4594 | + | 18.9324i | 0.957303 | + | 0.615221i | 0.923250 | − | 0.384199i | \(-0.125522\pi\) |
0.0340525 | + | 0.999420i | \(0.489159\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.71430 | − | 3.02970i | 0.153033 | − | 0.0983482i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.3197 | − | 21.1421i | −0.594057 | − | 0.685578i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.44966 | − | 20.6919i | 0.306104 | − | 0.670275i | −0.692591 | − | 0.721330i | \(-0.743531\pi\) |
0.998696 | + | 0.0510549i | \(0.0162584\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.48079 | + | 1.90293i | −0.209713 | + | 0.0615774i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.61018 | + | 18.1542i | 0.0843750 | + | 0.586841i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.17818 | − | 13.5283i | −0.199504 | − | 0.436852i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.0376 | + | 69.8133i | −0.323795 | + | 2.25204i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.07731 | + | 10.4758i | −0.292512 | + | 0.337577i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −38.6784 | −1.24510 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.0114 | 1.28668 | 0.643341 | − | 0.765580i | \(-0.277548\pi\) | ||||
0.643341 | + | 0.765580i | \(0.277548\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.27178 | + | 2.62178i | −0.0729801 | + | 0.0842236i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.26227 | − | 29.6448i | 0.136783 | − | 0.951346i | −0.799642 | − | 0.600477i | \(-0.794977\pi\) |
0.936425 | − | 0.350868i | \(-0.114114\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.11639 | + | 11.2033i | 0.164024 | + | 0.359163i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.350641 | + | 2.43876i | 0.0112295 | + | 0.0781030i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.9792 | + | 10.2708i | −1.11908 | + | 0.328592i | −0.788408 | − | 0.615153i | \(-0.789094\pi\) |
−0.330675 | + | 0.943745i | \(0.607276\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.8115 | − | 39.0018i | 0.569259 | − | 1.24650i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.52784 | − | 6.37947i | −0.176490 | − | 0.203681i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.5494 | − | 8.06499i | 0.400263 | − | 0.257233i | −0.324988 | − | 0.945718i | \(-0.605360\pi\) |
0.725251 | + | 0.688485i | \(0.241724\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 47.0468 | + | 30.2352i | 1.49904 | + | 0.963373i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.49582 | + | 0.732839i | 0.0794428 | + | 0.0233265i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39.9277 | + | 20.5447i | 1.26963 | + | 0.653283i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.3163 | + | 7.72716i | 0.835964 | + | 0.245461i | 0.671577 | − | 0.740935i | \(-0.265617\pi\) |
0.164387 | + | 0.986396i | \(0.447435\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.2328 | + | 11.7175i | 0.578600 | + | 0.371843i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.6013 | + | 6.81304i | −0.336084 | + | 0.215988i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.1351 | − | 32.4696i | −0.891048 | − | 1.02832i | −0.999415 | − | 0.0342127i | \(-0.989108\pi\) |
0.108367 | − | 0.994111i | \(-0.465438\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.746510 | − | 1.63463i | 0.0236185 | − | 0.0517174i |
(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 | 276.2.i.b.133.2 | ✓ | 20 | |
3.2 | odd | 2 | 828.2.q.b.685.1 | 20 | |||
23.3 | even | 11 | 6348.2.a.r.1.2 | 10 | |||
23.9 | even | 11 | inner | 276.2.i.b.193.2 | yes | 20 | |
23.20 | odd | 22 | 6348.2.a.q.1.9 | 10 | |||
69.32 | odd | 22 | 828.2.q.b.469.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.b.133.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
276.2.i.b.193.2 | yes | 20 | 23.9 | even | 11 | inner | |
828.2.q.b.469.1 | 20 | 69.32 | odd | 22 | |||
828.2.q.b.685.1 | 20 | 3.2 | odd | 2 | |||
6348.2.a.q.1.9 | 10 | 23.20 | odd | 22 | |||
6348.2.a.r.1.2 | 10 | 23.3 | even | 11 |