Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(307,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bi (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 307.15 | ||
Character | \(\chi\) | \(=\) | 756.307 |
Dual form | 756.2.bi.c.559.15 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.325239 | − | 1.37631i | −0.229979 | − | 0.973196i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.78844 | + | 0.895257i | −0.894220 | + | 0.447628i | ||||
\(5\) | −3.45303 | − | 1.99361i | −1.54424 | − | 0.891570i | −0.998564 | − | 0.0535758i | \(-0.982938\pi\) |
−0.545680 | − | 0.837994i | \(-0.683729\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.03435 | + | 1.69157i | 0.768913 | + | 0.639353i | ||||
\(8\) | 1.81382 | + | 2.17027i | 0.641281 | + | 0.767306i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.62076 | + | 5.40083i | −0.512529 | + | 1.70789i | ||||
\(11\) | −1.72816 | + | 0.997755i | −0.521061 | + | 0.300834i | −0.737368 | − | 0.675491i | \(-0.763932\pi\) |
0.216308 | + | 0.976325i | \(0.430598\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.38515 | − | 1.37707i | −0.661521 | − | 0.381929i | 0.131335 | − | 0.991338i | \(-0.458074\pi\) |
−0.792856 | + | 0.609409i | \(0.791407\pi\) | |||||||
\(14\) | 1.66647 | − | 3.35006i | 0.445382 | − | 0.895340i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.39703 | − | 3.20222i | 0.599258 | − | 0.800556i | ||||
\(17\) | 2.88632i | 0.700035i | 0.936743 | + | 0.350018i | \(0.113824\pi\) | ||||
−0.936743 | + | 0.350018i | \(0.886176\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0855521 | −0.0196270 | −0.00981349 | − | 0.999952i | \(-0.503124\pi\) | ||||
−0.00981349 | + | 0.999952i | \(0.503124\pi\) | |||||||
\(20\) | 7.96033 | + | 0.474099i | 1.77998 | + | 0.106012i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.93528 | + | 2.05397i | 0.412604 | + | 0.437908i | ||||
\(23\) | 5.06735 | + | 2.92564i | 1.05662 | + | 0.610037i | 0.924494 | − | 0.381196i | \(-0.124488\pi\) |
0.132122 | + | 0.991234i | \(0.457821\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.44896 | + | 9.43788i | 1.08979 | + | 1.88758i | ||||
\(26\) | −1.11952 | + | 3.73057i | −0.219556 | + | 0.731625i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.15271 | − | 1.20400i | −0.973770 | − | 0.227535i | ||||
\(29\) | 2.39499 | + | 4.14825i | 0.444739 | + | 0.770310i | 0.998034 | − | 0.0626752i | \(-0.0199632\pi\) |
−0.553295 | + | 0.832985i | \(0.686630\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.893108 | + | 1.54691i | −0.160407 | + | 0.277833i | −0.935015 | − | 0.354609i | \(-0.884614\pi\) |
0.774608 | + | 0.632442i | \(0.217947\pi\) | |||||||
\(32\) | −5.18685 | − | 2.25756i | −0.916914 | − | 0.399084i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.97246 | − | 0.938743i | 0.681271 | − | 0.160993i | ||||
\(35\) | −3.65236 | − | 9.89675i | −0.617361 | − | 1.67286i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.22828 | 1.02392 | 0.511961 | − | 0.859009i | \(-0.328919\pi\) | ||||
0.511961 | + | 0.859009i | \(0.328919\pi\) | |||||||
\(38\) | 0.0278249 | + | 0.117746i | 0.00451379 | + | 0.0191009i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.93650 | − | 11.1101i | −0.306188 | − | 1.75665i | ||||
\(41\) | 3.94059 | + | 2.27510i | 0.615417 | + | 0.355311i | 0.775083 | − | 0.631860i | \(-0.217708\pi\) |
−0.159666 | + | 0.987171i | \(0.551042\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.28817 | − | 5.36253i | 1.41643 | − | 0.817777i | 0.420449 | − | 0.907316i | \(-0.361873\pi\) |
0.995983 | + | 0.0895388i | \(0.0285393\pi\) | |||||||
\(44\) | 2.19747 | − | 3.33157i | 0.331281 | − | 0.502254i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.37847 | − | 7.92576i | 0.350687 | − | 1.16859i | ||||
\(47\) | −2.22398 | − | 3.85205i | −0.324401 | − | 0.561879i | 0.656990 | − | 0.753899i | \(-0.271829\pi\) |
−0.981391 | + | 0.192020i | \(0.938496\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.27718 | + | 6.88250i | 0.182454 | + | 0.983214i | ||||
\(50\) | 11.2172 | − | 10.5690i | 1.58635 | − | 1.49468i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.49852 | + | 0.327479i | 0.762508 | + | 0.0454132i | ||||
\(53\) | −2.30892 | −0.317154 | −0.158577 | − | 0.987347i | \(-0.550691\pi\) | ||||
−0.158577 | + | 0.987347i | \(0.550691\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.95654 | 1.07286 | ||||||||
\(56\) | 0.0187828 | + | 7.48329i | 0.00250996 | + | 0.999997i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.93031 | − | 4.64541i | 0.647382 | − | 0.609973i | ||||
\(59\) | 2.41588 | − | 4.18443i | 0.314521 | − | 0.544767i | −0.664814 | − | 0.747009i | \(-0.731489\pi\) |
0.979336 | + | 0.202242i | \(0.0648227\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.08218 | + | 4.08890i | −0.906780 | + | 0.523530i | −0.879394 | − | 0.476095i | \(-0.842052\pi\) |
−0.0273862 | + | 0.999625i | \(0.508718\pi\) | |||||||
\(62\) | 2.41949 | + | 0.726076i | 0.307276 | + | 0.0922117i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.42013 | + | 7.87294i | −0.177516 | + | 0.984118i | ||||
\(65\) | 5.49066 | + | 9.51011i | 0.681033 | + | 1.17958i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.76145 | − | 1.01697i | −0.215195 | − | 0.124243i | 0.388528 | − | 0.921437i | \(-0.372984\pi\) |
−0.603724 | + | 0.797194i | \(0.706317\pi\) | |||||||
\(68\) | −2.58400 | − | 5.16201i | −0.313356 | − | 0.625985i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.4331 | + | 8.24557i | −1.48604 | + | 0.985534i | ||||
\(71\) | − | 3.57003i | − | 0.423685i | −0.977304 | − | 0.211842i | \(-0.932054\pi\) | ||
0.977304 | − | 0.211842i | \(-0.0679464\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.4000i | 1.33426i | 0.744940 | + | 0.667132i | \(0.232478\pi\) | ||||
−0.744940 | + | 0.667132i | \(0.767522\pi\) | |||||||
\(74\) | −2.02568 | − | 8.57202i | −0.235480 | − | 0.996477i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.153005 | − | 0.0765911i | 0.0175508 | − | 0.00878560i | ||||
\(77\) | −5.20346 | − | 0.893522i | −0.592990 | − | 0.101826i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.4989 | + | 6.63892i | −1.29373 | + | 0.746936i | −0.979314 | − | 0.202348i | \(-0.935143\pi\) |
−0.314418 | + | 0.949285i | \(0.601809\pi\) | |||||||
\(80\) | −14.6610 | + | 6.27865i | −1.63915 | + | 0.701974i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.84960 | − | 6.16341i | 0.204255 | − | 0.680635i | ||||
\(83\) | 8.56210 | + | 14.8300i | 0.939812 | + | 1.62780i | 0.765820 | + | 0.643056i | \(0.222334\pi\) |
0.173993 | + | 0.984747i | \(0.444333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.75420 | − | 9.96656i | 0.624130 | − | 1.08103i | ||||
\(86\) | −10.4014 | − | 11.0393i | −1.12161 | − | 1.19039i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.29997 | − | 1.94083i | −0.564978 | − | 0.206893i | ||||
\(89\) | 7.76882i | 0.823493i | 0.911298 | + | 0.411746i | \(0.135081\pi\) | ||||
−0.911298 | + | 0.411746i | \(0.864919\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.52283 | − | 6.83608i | −0.264464 | − | 0.716616i | ||||
\(92\) | −11.6818 | − | 0.695744i | −1.21792 | − | 0.0725363i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.57827 | + | 4.31372i | −0.472213 | + | 0.444926i | ||||
\(95\) | 0.295414 | + | 0.170557i | 0.0303089 | + | 0.0174988i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.07462 | − | 2.35248i | 0.413715 | − | 0.238859i | −0.278670 | − | 0.960387i | \(-0.589893\pi\) |
0.692385 | + | 0.721528i | \(0.256560\pi\) | |||||||
\(98\) | 9.05704 | − | 3.99625i | 0.914899 | − | 0.403682i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.1945 | − | 12.0009i | −1.81945 | − | 1.20009i | ||||
\(101\) | 2.46857 | − | 1.42523i | 0.245631 | − | 0.141815i | −0.372131 | − | 0.928180i | \(-0.621373\pi\) |
0.617762 | + | 0.786365i | \(0.288039\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.02846 | − | 1.78135i | 0.101337 | − | 0.175521i | −0.810899 | − | 0.585187i | \(-0.801021\pi\) |
0.912236 | + | 0.409665i | \(0.134355\pi\) | |||||||
\(104\) | −1.33762 | − | 7.67416i | −0.131164 | − | 0.752513i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.750949 | + | 3.17778i | 0.0729387 | + | 0.308653i | ||||
\(107\) | 15.5534i | 1.50361i | 0.659387 | + | 0.751803i | \(0.270816\pi\) | ||||
−0.659387 | + | 0.751803i | \(0.729184\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.28192 | 0.122786 | 0.0613930 | − | 0.998114i | \(-0.480446\pi\) | ||||
0.0613930 | + | 0.998114i | \(0.480446\pi\) | |||||||
\(110\) | −2.58778 | − | 10.9506i | −0.246735 | − | 1.04410i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.2932 | − | 2.45971i | 0.972615 | − | 0.232421i | ||||
\(113\) | −7.39267 | + | 12.8045i | −0.695444 | + | 1.20454i | 0.274586 | + | 0.961562i | \(0.411459\pi\) |
−0.970031 | + | 0.242982i | \(0.921874\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.6652 | − | 20.2046i | −1.08778 | − | 1.88409i | ||||
\(116\) | −7.99704 | − | 5.27475i | −0.742507 | − | 0.489749i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.54480 | − | 1.96406i | −0.602498 | − | 0.180806i | ||||
\(119\) | −4.88241 | + | 5.87179i | −0.447570 | + | 0.538266i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.50897 | + | 6.07771i | −0.318997 | + | 0.552519i | ||||
\(122\) | 7.93097 | + | 8.41738i | 0.718037 | + | 0.762074i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.212389 | − | 3.56611i | 0.0190731 | − | 0.320246i | ||||
\(125\) | − | 23.5163i | − | 2.10336i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.327377i | − | 0.0290500i | −0.999895 | − | 0.0145250i | \(-0.995376\pi\) | ||
0.999895 | − | 0.0145250i | \(-0.00462361\pi\) | |||||||
\(128\) | 11.2975 | − | 0.606051i | 0.998564 | − | 0.0535678i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.3030 | − | 10.6499i | 0.991343 | − | 0.934058i | ||||
\(131\) | −1.15307 | + | 1.99717i | −0.100744 | + | 0.174494i | −0.911991 | − | 0.410209i | \(-0.865456\pi\) |
0.811247 | + | 0.584703i | \(0.198789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.174043 | − | 0.144717i | −0.0150914 | − | 0.0125486i | ||||
\(134\) | −0.826776 | + | 2.75506i | −0.0714226 | + | 0.238001i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.26409 | + | 5.23526i | −0.537141 | + | 0.448920i | ||||
\(137\) | −6.07413 | − | 10.5207i | −0.518948 | − | 0.898844i | −0.999758 | − | 0.0220190i | \(-0.992991\pi\) |
0.480810 | − | 0.876825i | \(-0.340343\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.45697 | + | 7.71970i | −0.378035 | + | 0.654776i | −0.990776 | − | 0.135507i | \(-0.956734\pi\) |
0.612741 | + | 0.790284i | \(0.290067\pi\) | |||||||
\(140\) | 15.3922 | + | 14.4299i | 1.30087 | + | 1.21955i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.91346 | + | 1.16111i | −0.412328 | + | 0.0974384i | ||||
\(143\) | 5.49590 | 0.459590 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 19.0987i | − | 1.58606i | ||||||
\(146\) | 15.6898 | − | 3.70771i | 1.29850 | − | 0.306852i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.1389 | + | 5.57591i | −0.915612 | + | 0.458337i | ||||
\(149\) | 1.02048 | − | 1.76752i | 0.0836008 | − | 0.144801i | −0.821193 | − | 0.570650i | \(-0.806691\pi\) |
0.904794 | + | 0.425849i | \(0.140025\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.32355 | − | 5.38296i | 0.758740 | − | 0.438059i | −0.0701032 | − | 0.997540i | \(-0.522333\pi\) |
0.828843 | + | 0.559481i | \(0.189000\pi\) | |||||||
\(152\) | −0.155176 | − | 0.185671i | −0.0125864 | − | 0.0150599i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.462608 | + | 7.45217i | 0.0372780 | + | 0.600513i | ||||
\(155\) | 6.16786 | − | 3.56102i | 0.495415 | − | 0.286028i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.83827 | − | 3.94808i | −0.545753 | − | 0.315091i | 0.201654 | − | 0.979457i | \(-0.435368\pi\) |
−0.747407 | + | 0.664366i | \(0.768702\pi\) | |||||||
\(158\) | 12.8771 | + | 13.6668i | 1.02445 | + | 1.08727i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.4097 | + | 18.1360i | 1.06013 | + | 1.43378i | ||||
\(161\) | 5.35986 | + | 14.5236i | 0.422416 | + | 1.14462i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.3844i | 1.04835i | 0.851611 | + | 0.524175i | \(0.175626\pi\) | ||||
−0.851611 | + | 0.524175i | \(0.824374\pi\) | |||||||
\(164\) | −9.08431 | − | 0.541040i | −0.709365 | − | 0.0422481i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.6259 | − | 16.6074i | 1.36803 | − | 1.28898i | ||||
\(167\) | 6.33117 | − | 10.9659i | 0.489921 | − | 0.848568i | −0.510012 | − | 0.860167i | \(-0.670359\pi\) |
0.999933 | + | 0.0115994i | \(0.00369227\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.70738 | − | 4.68932i | −0.208260 | − | 0.360717i | ||||
\(170\) | −15.5885 | − | 4.67803i | −1.19559 | − | 0.358788i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.8105 | + | 17.9058i | −0.900541 | + | 1.36531i | ||||
\(173\) | −6.59908 | + | 3.80998i | −0.501719 | + | 0.289668i | −0.729423 | − | 0.684063i | \(-0.760211\pi\) |
0.227704 | + | 0.973730i | \(0.426878\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.87973 | + | 28.4173i | −0.368873 | + | 2.14814i | ||||
\(176\) | −0.947423 | + | 7.92561i | −0.0714147 | + | 0.597416i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.6923 | − | 2.52672i | 0.801420 | − | 0.189386i | ||||
\(179\) | 8.19202i | 0.612300i | 0.951983 | + | 0.306150i | \(0.0990410\pi\) | ||||
−0.951983 | + | 0.306150i | \(0.900959\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.68997i | − | 0.274274i | −0.990552 | − | 0.137137i | \(-0.956210\pi\) | ||
0.990552 | − | 0.137137i | \(-0.0437900\pi\) | |||||||
\(182\) | −8.58802 | + | 5.69554i | −0.636587 | + | 0.422182i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.84183 | + | 16.3041i | 0.209503 | + | 1.20195i | ||||
\(185\) | −21.5065 | − | 12.4168i | −1.58119 | − | 0.912898i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.87984 | − | 4.98803i | −0.210595 | − | 0.364761i | ||||
\(188\) | 7.42603 | + | 4.89812i | 0.541599 | + | 0.357232i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.138659 | − | 0.462052i | 0.0100594 | − | 0.0335208i | ||||
\(191\) | 8.72331 | − | 5.03641i | 0.631197 | − | 0.364422i | −0.150019 | − | 0.988683i | \(-0.547933\pi\) |
0.781215 | + | 0.624262i | \(0.214600\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.87003 | + | 10.1672i | −0.422534 | + | 0.731851i | −0.996187 | − | 0.0872481i | \(-0.972193\pi\) |
0.573652 | + | 0.819099i | \(0.305526\pi\) | |||||||
\(194\) | −4.56296 | − | 4.84281i | −0.327602 | − | 0.347693i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.44576 | − | 11.1655i | −0.603269 | − | 0.797538i | ||||
\(197\) | −20.3333 | −1.44869 | −0.724343 | − | 0.689440i | \(-0.757857\pi\) | ||||
−0.724343 | + | 0.689440i | \(0.757857\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.7777 | 1.61467 | 0.807335 | − | 0.590093i | \(-0.200909\pi\) | ||||
0.807335 | + | 0.590093i | \(0.200909\pi\) | |||||||
\(200\) | −10.5993 | + | 28.9443i | −0.749484 | + | 2.04667i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.76442 | − | 2.93396i | −0.194504 | − | 0.206433i | ||||
\(203\) | −2.14479 | + | 12.4903i | −0.150535 | + | 0.876646i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.07133 | − | 15.7120i | −0.633569 | − | 1.09737i | ||||
\(206\) | −2.78618 | − | 0.836115i | −0.194122 | − | 0.0582549i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.1269 | + | 4.33691i | −0.702177 | + | 0.300711i | ||||
\(209\) | 0.147848 | − | 0.0853600i | 0.0102269 | − | 0.00590447i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.1250 | − | 11.6191i | −1.38546 | − | 0.799895i | −0.392659 | − | 0.919684i | \(-0.628445\pi\) |
−0.992799 | + | 0.119789i | \(0.961778\pi\) | |||||||
\(212\) | 4.12936 | − | 2.06707i | 0.283605 | − | 0.141967i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 21.4063 | − | 5.05858i | 1.46330 | − | 0.345797i | ||||
\(215\) | −42.7631 | −2.91642 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.43360 | + | 1.63620i | −0.300972 | + | 0.111073i | ||||
\(218\) | −0.416932 | − | 1.76432i | −0.0282382 | − | 0.119495i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −14.2298 | + | 7.12314i | −0.959372 | + | 0.480242i | ||||
\(221\) | 3.97465 | − | 6.88430i | 0.267364 | − | 0.463088i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.17435 | − | 7.23018i | −0.279535 | − | 0.484169i | 0.691734 | − | 0.722152i | \(-0.256847\pi\) |
−0.971269 | + | 0.237984i | \(0.923514\pi\) | |||||||
\(224\) | −6.73306 | − | 13.3666i | −0.449871 | − | 0.893093i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.0273 | + | 6.01007i | 1.33220 | + | 0.399784i | ||||
\(227\) | −3.33734 | − | 5.78045i | −0.221507 | − | 0.383662i | 0.733759 | − | 0.679410i | \(-0.237764\pi\) |
−0.955266 | + | 0.295748i | \(0.904431\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.63009 | + | 4.98258i | 0.570292 | + | 0.329258i | 0.757266 | − | 0.653107i | \(-0.226535\pi\) |
−0.186974 | + | 0.982365i | \(0.559868\pi\) | |||||||
\(230\) | −24.0138 | + | 22.6262i | −1.58342 | + | 1.49193i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.65873 | + | 12.7219i | −0.305861 | + | 0.835236i | ||||
\(233\) | −3.55156 | −0.232670 | −0.116335 | − | 0.993210i | \(-0.537115\pi\) | ||||
−0.116335 | + | 0.993210i | \(0.537115\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.7350i | 1.15690i | ||||||||
\(236\) | −0.574520 | + | 9.64644i | −0.0373981 | + | 0.627930i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.66934 | + | 4.80996i | 0.626770 | + | 0.311784i | ||||
\(239\) | −5.01808 | − | 2.89719i | −0.324592 | − | 0.187403i | 0.328845 | − | 0.944384i | \(-0.393341\pi\) |
−0.653438 | + | 0.756980i | \(0.726674\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.63364 | + | 1.52053i | −0.169648 | + | 0.0979461i | −0.582420 | − | 0.812888i | \(-0.697894\pi\) |
0.412772 | + | 0.910834i | \(0.364561\pi\) | |||||||
\(242\) | 9.50605 | + | 2.85271i | 0.611072 | + | 0.183379i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.00543 | − | 13.6531i | 0.576514 | − | 0.874051i | ||||
\(245\) | 9.31087 | − | 26.3117i | 0.594850 | − | 1.68099i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.204054 | + | 0.117811i | 0.0129837 | + | 0.00749612i | ||||
\(248\) | −4.97714 | + | 0.867525i | −0.316049 | + | 0.0550879i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −32.3657 | + | 7.64842i | −2.04698 | + | 0.483729i | ||||
\(251\) | 15.9355 | 1.00584 | 0.502920 | − | 0.864333i | \(-0.332259\pi\) | ||||
0.502920 | + | 0.864333i | \(0.332259\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.6763 | −0.734081 | ||||||||
\(254\) | −0.450571 | + | 0.106476i | −0.0282713 | + | 0.00668087i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.50849 | − | 15.3517i | −0.281780 | − | 0.959479i | ||||
\(257\) | 17.9529 | + | 10.3651i | 1.11987 | + | 0.646559i | 0.941369 | − | 0.337380i | \(-0.109541\pi\) |
0.178505 | + | 0.983939i | \(0.442874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.6705 | + | 10.5356i | 0.787307 | + | 0.654648i | ||||
\(260\) | −18.3337 | − | 12.0927i | −1.13701 | − | 0.749957i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.12375 | + | 0.937417i | 0.192986 | + | 0.0579138i | ||||
\(263\) | 1.29122 | − | 0.745488i | 0.0796202 | − | 0.0459687i | −0.459661 | − | 0.888094i | \(-0.652029\pi\) |
0.539282 | + | 0.842126i | \(0.318696\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.97277 | + | 4.60308i | 0.489763 | + | 0.282765i | ||||
\(266\) | −0.142570 | + | 0.286604i | −0.00874152 | + | 0.0175728i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.06070 | + | 0.241846i | 0.248047 | + | 0.0147731i | ||||
\(269\) | 18.2450i | 1.11242i | 0.831043 | + | 0.556209i | \(0.187745\pi\) | ||||
−0.831043 | + | 0.556209i | \(0.812255\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.4908 | 0.940998 | 0.470499 | − | 0.882400i | \(-0.344074\pi\) | ||||
0.470499 | + | 0.882400i | \(0.344074\pi\) | |||||||
\(272\) | 9.24264 | + | 6.91860i | 0.560418 | + | 0.419502i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.5042 | + | 11.7816i | −0.755404 | + | 0.711753i | ||||
\(275\) | −18.8334 | − | 10.8735i | −1.13570 | − | 0.655694i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.29870 | − | 16.1058i | −0.558705 | − | 0.967705i | −0.997605 | − | 0.0691691i | \(-0.977965\pi\) |
0.438900 | − | 0.898536i | \(-0.355368\pi\) | |||||||
\(278\) | 12.0743 | + | 3.62341i | 0.724165 | + | 0.217318i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 14.8539 | − | 25.8775i | 0.887691 | − | 1.54648i | ||||
\(281\) | 9.87259 | + | 17.0998i | 0.588950 | + | 1.02009i | 0.994370 | + | 0.105960i | \(0.0337917\pi\) |
−0.405421 | + | 0.914130i | \(0.632875\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.53005 | − | 14.7745i | 0.507059 | − | 0.878252i | −0.492908 | − | 0.870082i | \(-0.664066\pi\) |
0.999967 | − | 0.00817031i | \(-0.00260072\pi\) | |||||||
\(284\) | 3.19609 | + | 6.38479i | 0.189653 | + | 0.378867i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.78748 | − | 7.56404i | −0.105696 | − | 0.447271i | ||||
\(287\) | 4.16806 | + | 11.2941i | 0.246033 | + | 0.666672i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.66916 | 0.509950 | ||||||||
\(290\) | −26.2857 | + | 6.21164i | −1.54355 | + | 0.364760i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.2059 | − | 20.3881i | −0.597254 | − | 1.19312i | ||||
\(293\) | 22.2955 | + | 12.8723i | 1.30252 | + | 0.752009i | 0.980835 | − | 0.194838i | \(-0.0624181\pi\) |
0.321683 | + | 0.946847i | \(0.395751\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.6843 | + | 9.63266i | −0.971395 | + | 0.560835i | ||||
\(296\) | 11.2970 | + | 13.5170i | 0.656622 | + | 0.785662i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.76455 | − | 0.829624i | −0.160146 | − | 0.0480588i | ||||
\(299\) | −8.05759 | − | 13.9562i | −0.465982 | − | 0.807105i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.9665 | + | 4.80232i | 1.61196 | + | 0.276801i | ||||
\(302\) | −10.4410 | − | 11.0813i | −0.600811 | − | 0.637658i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.205071 | + | 0.273957i | −0.0117616 | + | 0.0157125i | ||||
\(305\) | 32.6067 | 1.86705 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.34083 | 0.418963 | 0.209482 | − | 0.977813i | \(-0.432822\pi\) | ||||
0.209482 | + | 0.977813i | \(0.432822\pi\) | |||||||
\(308\) | 10.1060 | − | 3.06043i | 0.575843 | − | 0.174384i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.90708 | − | 7.33069i | −0.392296 | − | 0.416355i | ||||
\(311\) | 14.2106 | − | 24.6135i | 0.805809 | − | 1.39570i | −0.109935 | − | 0.993939i | \(-0.535064\pi\) |
0.915744 | − | 0.401763i | \(-0.131602\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.8704 | + | 7.43074i | −0.727479 | + | 0.420010i | −0.817499 | − | 0.575930i | \(-0.804640\pi\) |
0.0900203 | + | 0.995940i | \(0.471307\pi\) | |||||||
\(314\) | −3.20969 | + | 10.6956i | −0.181133 | + | 0.603589i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.6216 | − | 22.1678i | 0.822530 | − | 1.24704i | ||||
\(317\) | −10.7056 | − | 18.5426i | −0.601284 | − | 1.04145i | −0.992627 | − | 0.121209i | \(-0.961323\pi\) |
0.391343 | − | 0.920245i | \(-0.372010\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.27787 | − | 4.77923i | −0.463472 | − | 0.267585i | ||||
\(320\) | 20.5993 | − | 24.3543i | 1.15154 | − | 1.36145i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.2456 | − | 12.1004i | 1.01679 | − | 0.674331i | ||||
\(323\) | − | 0.246931i | − | 0.0137396i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 30.0143i | − | 1.66489i | ||||||
\(326\) | 18.4211 | − | 4.35314i | 1.02025 | − | 0.241098i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.20993 | + | 12.6788i | 0.122023 | + | 0.700067i | ||||
\(329\) | 1.99165 | − | 11.5984i | 0.109803 | − | 0.639443i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.7097 | − | 8.49262i | 0.808515 | − | 0.466797i | −0.0379246 | − | 0.999281i | \(-0.512075\pi\) |
0.846440 | + | 0.532484i | \(0.178741\pi\) | |||||||
\(332\) | −28.5894 | − | 18.8573i | −1.56905 | − | 1.03493i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.1516 | − | 5.14710i | −0.938494 | − | 0.281637i | ||||
\(335\) | 4.05490 | + | 7.02329i | 0.221543 | + | 0.383723i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.90546 | − | 8.49651i | 0.267217 | − | 0.462834i | −0.700925 | − | 0.713235i | \(-0.747229\pi\) |
0.968142 | + | 0.250401i | \(0.0805625\pi\) | |||||||
\(338\) | −5.57340 | + | 5.25133i | −0.303153 | + | 0.285635i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.36840 | + | 22.9761i | −0.0742120 | + | 1.24605i | ||||
\(341\) | − | 3.56441i | − | 0.193024i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.04400 | + | 16.1619i | −0.488330 | + | 0.872659i | ||||
\(344\) | 28.4852 | + | 10.4312i | 1.53582 | + | 0.562411i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.38998 | + | 7.84321i | 0.397288 | + | 0.421653i | ||||
\(347\) | −3.21012 | − | 1.85336i | −0.172328 | − | 0.0994937i | 0.411355 | − | 0.911475i | \(-0.365056\pi\) |
−0.583683 | + | 0.811982i | \(0.698389\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.31419 | − | 2.49080i | 0.230933 | − | 0.133329i | −0.380069 | − | 0.924958i | \(-0.624100\pi\) |
0.611003 | + | 0.791629i | \(0.290767\pi\) | |||||||
\(350\) | 40.6980 | − | 2.52640i | 2.17540 | − | 0.135042i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.2162 | − | 1.27377i | 0.597826 | − | 0.0678923i | ||||
\(353\) | 10.4059 | − | 6.00788i | 0.553853 | − | 0.319767i | −0.196822 | − | 0.980439i | \(-0.563062\pi\) |
0.750674 | + | 0.660672i | \(0.229729\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.11725 | + | 12.3274i | −0.377744 | + | 0.654273i | ||||
\(356\) | −6.95508 | − | 13.8941i | −0.368619 | − | 0.736384i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.2747 | − | 2.66436i | 0.595888 | − | 0.140816i | ||||
\(359\) | − | 27.6368i | − | 1.45861i | −0.684187 | − | 0.729307i | \(-0.739843\pi\) | ||
0.684187 | − | 0.729307i | \(-0.260157\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9927 | −0.999615 | ||||||||
\(362\) | −5.07853 | + | 1.20012i | −0.266922 | + | 0.0630770i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.6320 | + | 9.96734i | 0.557267 | + | 0.522431i | ||||
\(365\) | 22.7271 | − | 39.3644i | 1.18959 | − | 2.06043i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.7663 | − | 25.5760i | −0.770796 | − | 1.33506i | −0.937127 | − | 0.348988i | \(-0.886525\pi\) |
0.166331 | − | 0.986070i | \(-0.446808\pi\) | |||||||
\(368\) | 21.5151 | − | 9.21395i | 1.12155 | − | 0.480311i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.0945 | + | 33.6379i | −0.524790 | + | 1.74875i | ||||
\(371\) | −4.69715 | − | 3.90570i | −0.243864 | − | 0.202774i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.89959 | + | 11.9504i | −0.357247 | + | 0.618770i | −0.987500 | − | 0.157620i | \(-0.949618\pi\) |
0.630253 | + | 0.776390i | \(0.282951\pi\) | |||||||
\(374\) | −5.92842 | + | 5.58584i | −0.306551 | + | 0.288837i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.32608 | − | 11.8136i | 0.223101 | − | 0.609237i | ||||
\(377\) | − | 13.1922i | − | 0.679435i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.1019i | 0.827099i | 0.910482 | + | 0.413549i | \(0.135711\pi\) | ||||
−0.910482 | + | 0.413549i | \(0.864289\pi\) | |||||||
\(380\) | −0.681023 | − | 0.0405602i | −0.0349357 | − | 0.00208069i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.76880 | − | 10.3679i | −0.499815 | − | 0.530469i | ||||
\(383\) | −8.61022 | + | 14.9133i | −0.439962 | + | 0.762036i | −0.997686 | − | 0.0679904i | \(-0.978341\pi\) |
0.557724 | + | 0.830026i | \(0.311675\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.1864 | + | 13.4590i | 0.824935 | + | 0.685936i | ||||
\(386\) | 15.9023 | + | 4.77220i | 0.809408 | + | 0.242898i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.18114 | + | 7.85511i | −0.263032 | + | 0.398783i | ||||
\(389\) | −2.16557 | − | 3.75088i | −0.109799 | − | 0.190177i | 0.805890 | − | 0.592066i | \(-0.201687\pi\) |
−0.915689 | + | 0.401888i | \(0.868354\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.44432 | + | 14.6260i | −0.427048 | + | 0.739668i | ||||
\(392\) | −12.6203 | + | 15.2554i | −0.637421 | + | 0.770515i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.61317 | + | 27.9848i | 0.333167 | + | 1.40985i | ||||
\(395\) | 52.9416 | 2.66378 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.5958i | 1.43518i | 0.696466 | + | 0.717590i | \(0.254755\pi\) | ||||
−0.696466 | + | 0.717590i | \(0.745245\pi\) | |||||||
\(398\) | −7.40820 | − | 31.3491i | −0.371340 | − | 1.57139i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 43.2835 | + | 5.17409i | 2.16418 | + | 0.258704i | ||||
\(401\) | 6.03293 | − | 10.4493i | 0.301270 | − | 0.521815i | −0.675154 | − | 0.737677i | \(-0.735923\pi\) |
0.976424 | + | 0.215862i | \(0.0692561\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.26039 | − | 2.45974i | 0.212225 | − | 0.122528i | ||||
\(404\) | −3.13894 | + | 4.75893i | −0.156168 | + | 0.236766i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.8880 | − | 1.11043i | 0.887768 | − | 0.0551099i | ||||
\(407\) | −10.7635 | + | 6.21430i | −0.533526 | + | 0.308031i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.8538 | − | 11.4626i | −0.981705 | − | 0.566788i | −0.0789208 | − | 0.996881i | \(-0.525147\pi\) |
−0.902785 | + | 0.430093i | \(0.858481\pi\) | |||||||
\(410\) | −18.6742 | + | 17.5951i | −0.922252 | + | 0.868959i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.244578 | + | 4.10657i | −0.0120495 | + | 0.202316i | ||||
\(413\) | 11.9930 | − | 4.42598i | 0.590138 | − | 0.217788i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 68.2779i | − | 3.35163i | ||||||
\(416\) | 9.26259 | + | 12.5273i | 0.454136 | + | 0.614199i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.165567 | − | 0.175722i | −0.00809817 | − | 0.00859482i | ||||
\(419\) | −5.84657 | + | 10.1266i | −0.285624 | + | 0.494715i | −0.972760 | − | 0.231813i | \(-0.925534\pi\) |
0.687136 | + | 0.726528i | \(0.258867\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.56174 | + | 9.63321i | 0.271063 | + | 0.469494i | 0.969134 | − | 0.246534i | \(-0.0792916\pi\) |
−0.698072 | + | 0.716028i | \(0.745958\pi\) | |||||||
\(422\) | −9.44609 | + | 31.4771i | −0.459828 | + | 1.53228i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.18795 | − | 5.01097i | −0.203385 | − | 0.243354i | ||||
\(425\) | −27.2407 | + | 15.7274i | −1.32137 | + | 0.762893i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.3243 | − | 3.66174i | −1.03196 | − | 0.177204i | ||||
\(428\) | −13.9243 | − | 27.8164i | −0.673057 | − | 1.34455i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.9082 | + | 58.8552i | 0.670715 | + | 2.83825i | ||||
\(431\) | − | 33.5046i | − | 1.61386i | −0.590647 | − | 0.806930i | \(-0.701127\pi\) | ||
0.590647 | − | 0.806930i | \(-0.298873\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.77529i | − | 0.325600i | −0.986659 | − | 0.162800i | \(-0.947948\pi\) | ||
0.986659 | − | 0.162800i | \(-0.0520525\pi\) | |||||||
\(434\) | 3.69389 | + | 5.56984i | 0.177313 | + | 0.267361i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.29264 | + | 1.14765i | −0.109798 | + | 0.0549625i | ||||
\(437\) | −0.433522 | − | 0.250294i | −0.0207382 | − | 0.0119732i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.0179749 | + | 0.0311334i | 0.000857895 | + | 0.00148592i | 0.866454 | − | 0.499257i | \(-0.166394\pi\) |
−0.865596 | + | 0.500743i | \(0.833060\pi\) | |||||||
\(440\) | 14.4317 | + | 17.2678i | 0.688005 | + | 0.823211i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.7676 | − | 3.23130i | −0.512163 | − | 0.153697i | ||||
\(443\) | −13.0209 | + | 7.51761i | −0.618641 | + | 0.357172i | −0.776340 | − | 0.630315i | \(-0.782926\pi\) |
0.157699 | + | 0.987487i | \(0.449592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.4880 | − | 26.8260i | 0.734201 | − | 1.27167i | ||||
\(446\) | −8.59328 | + | 8.09671i | −0.406904 | + | 0.383390i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16.2067 | + | 13.6141i | −0.765694 | + | 0.643205i | ||||
\(449\) | 22.0365 | 1.03997 | 0.519983 | − | 0.854177i | \(-0.325938\pi\) | ||||
0.519983 | + | 0.854177i | \(0.325938\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.07998 | −0.427559 | ||||||||
\(452\) | 1.75805 | − | 29.5184i | 0.0826916 | − | 1.38843i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.87024 | + | 6.47323i | −0.322436 | + | 0.303804i | ||||
\(455\) | −4.91707 | + | 28.6348i | −0.230516 | + | 1.34242i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.88558 | − | 15.3903i | −0.415650 | − | 0.719927i | 0.579846 | − | 0.814726i | \(-0.303113\pi\) |
−0.995496 | + | 0.0947989i | \(0.969779\pi\) | |||||||
\(458\) | 4.05072 | − | 13.4982i | 0.189278 | − | 0.630728i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 38.9508 | + | 25.6915i | 1.81609 | + | 1.19787i | ||||
\(461\) | −29.7074 | + | 17.1515i | −1.38361 | + | 0.798827i | −0.992585 | − | 0.121553i | \(-0.961213\pi\) |
−0.391025 | + | 0.920380i | \(0.627879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.4583 | + | 17.5851i | 1.41552 | + | 0.817248i | 0.995901 | − | 0.0904537i | \(-0.0288317\pi\) |
0.419615 | + | 0.907702i | \(0.362165\pi\) | |||||||
\(464\) | 19.0245 | + | 2.27417i | 0.883189 | + | 0.105576i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.15510 | + | 4.88803i | 0.0535092 | + | 0.226434i | ||||
\(467\) | −2.10775 | −0.0975348 | −0.0487674 | − | 0.998810i | \(-0.515529\pi\) | ||||
−0.0487674 | + | 0.998810i | \(0.515529\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.86313 | − | 5.04850i | −0.0860313 | − | 0.233118i | ||||
\(470\) | 24.4088 | − | 5.76811i | 1.12589 | − | 0.266063i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.4633 | − | 2.34668i | 0.619700 | − | 0.108015i | ||||
\(473\) | −10.7010 | + | 18.5346i | −0.492031 | + | 0.852223i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.466170 | − | 0.807430i | −0.0213893 | − | 0.0370474i | ||||
\(476\) | 3.47514 | − | 14.8724i | 0.159283 | − | 0.681673i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.35534 | + | 7.84869i | −0.107731 | + | 0.358991i | ||||
\(479\) | −0.601718 | − | 1.04221i | −0.0274932 | − | 0.0476196i | 0.851951 | − | 0.523621i | \(-0.175419\pi\) |
−0.879445 | + | 0.476001i | \(0.842086\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.8554 | − | 8.57675i | −0.677346 | − | 0.391066i | ||||
\(482\) | 2.94928 | + | 3.13016i | 0.134336 | + | 0.142575i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.834466 | − | 14.0111i | 0.0379303 | − | 0.636866i | ||||
\(485\) | −18.7597 | −0.851836 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.23920i | 0.192097i | 0.995377 | + | 0.0960483i | \(0.0306203\pi\) | ||||
−0.995377 | + | 0.0960483i | \(0.969380\pi\) | |||||||
\(488\) | −21.7198 | − | 7.95371i | −0.983208 | − | 0.360048i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −39.2412 | − | 4.25703i | −1.77274 | − | 0.192313i | ||||
\(491\) | 14.4458 | + | 8.34027i | 0.651928 | + | 0.376391i | 0.789195 | − | 0.614143i | \(-0.210498\pi\) |
−0.137266 | + | 0.990534i | \(0.543832\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.9732 | + | 6.91271i | −0.539244 | + | 0.311333i | ||||
\(494\) | 0.0957774 | − | 0.319158i | 0.00430923 | − | 0.0143596i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.81274 | + | 6.56792i | 0.126296 | + | 0.294908i | ||||
\(497\) | 6.03896 | − | 7.26270i | 0.270884 | − | 0.325777i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.1648 | + | 15.1063i | 1.17130 | + | 0.676249i | 0.953985 | − | 0.299853i | \(-0.0969378\pi\) |
0.217312 | + | 0.976102i | \(0.430271\pi\) | |||||||
\(500\) | 21.0531 | + | 42.0575i | 0.941525 | + | 1.88087i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.18284 | − | 21.9321i | −0.231322 | − | 0.978879i | ||||
\(503\) | 9.33949 | 0.416427 | 0.208214 | − | 0.978083i | \(-0.433235\pi\) | ||||
0.208214 | + | 0.978083i | \(0.433235\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.3654 | −0.505753 | ||||||||
\(506\) | 3.79758 | + | 16.0701i | 0.168823 | + | 0.714404i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.293086 | + | 0.585493i | 0.0130036 | + | 0.0259771i | ||||
\(509\) | 9.96494 | + | 5.75326i | 0.441688 | + | 0.255009i | 0.704313 | − | 0.709889i | \(-0.251255\pi\) |
−0.262625 | + | 0.964898i | \(0.584588\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.2838 | + | 23.1915i | −0.853066 | + | 1.02593i | ||||
\(512\) | −19.6623 | + | 11.1980i | −0.868957 | + | 0.494887i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.42661 | − | 28.0799i | 0.371682 | − | 1.23855i | ||||
\(515\) | −7.10263 | + | 4.10070i | −0.312979 | + | 0.180699i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.68680 | + | 4.43798i | 0.338065 | + | 0.195182i | ||||
\(518\) | 10.3792 | − | 20.8651i | 0.456037 | − | 0.916759i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.6804 | + | 29.1658i | −0.468368 | + | 1.27901i | ||||
\(521\) | − | 28.7291i | − | 1.25865i | −0.777144 | − | 0.629323i | \(-0.783332\pi\) | ||
0.777144 | − | 0.629323i | \(-0.216668\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.1932 | −0.882986 | −0.441493 | − | 0.897265i | \(-0.645551\pi\) | ||||
−0.441493 | + | 0.897265i | \(0.645551\pi\) | |||||||
\(524\) | 0.274210 | − | 4.60412i | 0.0119789 | − | 0.201132i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.44598 | − | 1.53466i | −0.0630475 | − | 0.0669142i | ||||
\(527\) | −4.46487 | − | 2.57779i | −0.194493 | − | 0.112291i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.61870 | + | 9.73187i | 0.244291 | + | 0.423125i | ||||
\(530\) | 3.74220 | − | 12.4701i | 0.162551 | − | 0.541665i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.440825 | + | 0.103005i | 0.0191122 | + | 0.00446583i | ||||
\(533\) | −6.26593 | − | 10.8529i | −0.271408 | − | 0.470092i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.0075 | − | 53.7065i | 1.34057 | − | 2.32193i | ||||
\(536\) | −0.987843 | − | 5.66743i | −0.0426683 | − | 0.244796i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.1107 | − | 5.93398i | 1.08260 | − | 0.255832i | ||||
\(539\) | −9.07422 | − | 10.6198i | −0.390855 | − | 0.457426i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.7977 | 1.36709 | 0.683545 | − | 0.729908i | \(-0.260437\pi\) | ||||
0.683545 | + | 0.729908i | \(0.260437\pi\) | |||||||
\(542\) | −5.03821 | − | 21.3201i | −0.216409 | − | 0.915775i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.51604 | − | 14.9709i | 0.279373 | − | 0.641872i | ||||
\(545\) | −4.42653 | − | 2.55566i | −0.189612 | − | 0.109472i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.72258 | − | 3.88128i | 0.287437 | − | 0.165952i | −0.349349 | − | 0.936993i | \(-0.613597\pi\) |
0.636785 | + | 0.771041i | \(0.280264\pi\) | |||||||
\(548\) | 20.2819 | + | 13.3777i | 0.866401 | + | 0.571468i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.83986 | + | 29.4570i | −0.376933 | + | 1.25605i | ||||
\(551\) | −0.204896 | − | 0.354891i | −0.00872888 | − | 0.0151189i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −34.6231 | − | 5.94537i | −1.47232 | − | 0.252823i | ||||
\(554\) | −19.1422 | + | 18.0361i | −0.813276 | + | 0.766280i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.05991 | − | 17.7963i | 0.0449501 | − | 0.754733i | ||||
\(557\) | −28.2834 | −1.19841 | −0.599203 | − | 0.800597i | \(-0.704516\pi\) | ||||
−0.599203 | + | 0.800597i | \(0.704516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.5382 | −1.24933 | ||||||||
\(560\) | −40.4464 | − | 12.0272i | −1.70917 | − | 0.508240i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.3237 | − | 19.1492i | 0.857302 | − | 0.807762i | ||||
\(563\) | −12.2242 | + | 21.1729i | −0.515187 | + | 0.892331i | 0.484657 | + | 0.874704i | \(0.338944\pi\) |
−0.999845 | + | 0.0176266i | \(0.994389\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 51.0543 | − | 29.4762i | 2.14787 | − | 1.24007i | ||||
\(566\) | −23.1085 | − | 6.93473i | −0.971324 | − | 0.291488i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.74793 | − | 6.47539i | 0.325096 | − | 0.271701i | ||||
\(569\) | 12.6476 | + | 21.9063i | 0.530215 | + | 0.918360i | 0.999379 | + | 0.0352483i | \(0.0112222\pi\) |
−0.469163 | + | 0.883111i | \(0.655444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.5735 | − | 8.99137i | −0.651731 | − | 0.376277i | 0.137388 | − | 0.990517i | \(-0.456129\pi\) |
−0.789119 | + | 0.614240i | \(0.789463\pi\) | |||||||
\(572\) | −9.82908 | + | 4.92024i | −0.410974 | + | 0.205726i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.1886 | − | 9.40982i | 0.592220 | − | 0.392758i | ||||
\(575\) | 63.7667i | 2.65926i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.5843i | 0.565523i | 0.959190 | + | 0.282762i | \(0.0912505\pi\) | ||||
−0.959190 | + | 0.282762i | \(0.908749\pi\) | |||||||
\(578\) | −2.81955 | − | 11.9314i | −0.117278 | − | 0.496282i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17.0982 | + | 34.1569i | 0.709966 | + | 1.41829i | ||||
\(581\) | −7.66764 | + | 44.6528i | −0.318107 | + | 1.85251i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.99018 | − | 2.30373i | 0.165257 | − | 0.0954109i | ||||
\(584\) | −24.7410 | + | 20.6774i | −1.02379 | + | 0.855638i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.4649 | − | 34.8721i | 0.432301 | − | 1.44055i | ||||
\(587\) | −23.6479 | − | 40.9593i | −0.976052 | − | 1.69057i | −0.676418 | − | 0.736518i | \(-0.736469\pi\) |
−0.299634 | − | 0.954054i | \(-0.596865\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0764072 | − | 0.132341i | 0.00314830 | − | 0.00545302i | ||||
\(590\) | 18.6839 | + | 19.8297i | 0.769203 | + | 0.816378i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.9294 | − | 19.9443i | 0.613593 | − | 0.819707i | ||||
\(593\) | − | 0.875544i | − | 0.0359543i | −0.999838 | − | 0.0179772i | \(-0.994277\pi\) | ||
0.999838 | − | 0.0179772i | \(-0.00572261\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.5652 | − | 10.5419i | 1.17106 | − | 0.432175i | ||||
\(596\) | −0.242679 | + | 4.07469i | −0.00994052 | + | 0.166906i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.5873 | + | 15.6288i | −0.678305 | + | 0.639109i | ||||
\(599\) | 12.3931 | + | 7.15518i | 0.506370 | + | 0.292353i | 0.731340 | − | 0.682013i | \(-0.238895\pi\) |
−0.224970 | + | 0.974366i | \(0.572229\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.3634 | + | 17.5303i | −1.23855 | + | 0.715076i | −0.968797 | − | 0.247854i | \(-0.920275\pi\) |
−0.269751 | + | 0.962930i | \(0.586941\pi\) | |||||||
\(602\) | −2.48633 | − | 40.0524i | −0.101335 | − | 1.63241i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.8555 | + | 17.9741i | −0.482393 | + | 0.731354i | ||||
\(605\) | 24.2332 | − | 13.9910i | 0.985219 | − | 0.568816i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.7611 | + | 32.4951i | −0.761489 | + | 1.31894i | 0.180594 | + | 0.983558i | \(0.442198\pi\) |
−0.942083 | + | 0.335380i | \(0.891135\pi\) | |||||||
\(608\) | 0.443746 | + | 0.193139i | 0.0179963 | + | 0.00783282i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.6050 | − | 44.8768i | −0.429382 | − | 1.81701i | ||||
\(611\) | 12.2503i | 0.495593i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.149504 | −0.00603840 | −0.00301920 | − | 0.999995i | \(-0.500961\pi\) | ||||
−0.00301920 | + | 0.999995i | \(0.500961\pi\) | |||||||
\(614\) | −2.38752 | − | 10.1032i | −0.0963526 | − | 0.407733i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.49895 | − | 12.9136i | −0.302141 | − | 0.520304i | ||||
\(617\) | 3.41249 | − | 5.91061i | 0.137382 | − | 0.237952i | −0.789123 | − | 0.614235i | \(-0.789465\pi\) |
0.926505 | + | 0.376283i | \(0.122798\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.1762 | + | 17.6257i | 0.409016 | + | 0.708436i | 0.994780 | − | 0.102045i | \(-0.0325387\pi\) |
−0.585764 | + | 0.810482i | \(0.699205\pi\) | |||||||
\(620\) | −7.84282 | + | 11.8905i | −0.314975 | + | 0.477533i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −38.4975 | − | 11.5529i | −1.54361 | − | 0.463228i | ||||
\(623\) | −13.1415 | + | 15.8045i | −0.526503 | + | 0.633194i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.6376 | + | 34.0133i | −0.785503 | + | 1.36053i | ||||
\(626\) | 14.4129 | + | 15.2969i | 0.576057 | + | 0.611386i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.7644 | + | 0.938889i | 0.629067 | + | 0.0374658i | ||||
\(629\) | 17.9768i | 0.716782i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.2923i | 0.847634i | 0.905748 | + | 0.423817i | \(0.139310\pi\) | ||||
−0.905748 | + | 0.423817i | \(0.860690\pi\) | |||||||
\(632\) | −35.2652 | − | 12.9140i | −1.40277 | − | 0.513691i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.0384 | + | 20.7649i | −0.875256 | + | 0.824679i | ||||
\(635\) | −0.652661 | + | 1.13044i | −0.0259001 | + | 0.0448603i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.43139 | − | 18.1745i | 0.254821 | − | 0.720102i | ||||
\(638\) | −3.88540 | + | 12.9473i | −0.153824 | + | 0.512587i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −40.2188 | − | 20.4300i | −1.58979 | − | 0.807568i | ||||
\(641\) | 3.95191 | + | 6.84490i | 0.156091 | + | 0.270357i | 0.933456 | − | 0.358693i | \(-0.116777\pi\) |
−0.777365 | + | 0.629050i | \(0.783444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.3837 | − | 35.3055i | 0.803853 | − | 1.39231i | −0.113209 | − | 0.993571i | \(-0.536113\pi\) |
0.917062 | − | 0.398744i | \(-0.130554\pi\) | |||||||
\(644\) | −22.5881 | − | 21.1760i | −0.890096 | − | 0.834453i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.339852 | + | 0.0803114i | −0.0133713 | + | 0.00315981i | ||||
\(647\) | 17.8067 | 0.700054 | 0.350027 | − | 0.936740i | \(-0.386172\pi\) | ||||
0.350027 | + | 0.936740i | \(0.386172\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.64184i | 0.378475i | ||||||||
\(650\) | −41.3089 | + | 9.76182i | −1.62027 | + | 0.382890i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.9825 | − | 23.9372i | −0.469271 | − | 0.937454i | ||||
\(653\) | −6.78123 | + | 11.7454i | −0.265370 | + | 0.459635i | −0.967661 | − | 0.252256i | \(-0.918827\pi\) |
0.702290 | + | 0.711891i | \(0.252161\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.96317 | − | 4.59754i | 0.311147 | − | 0.179641i | ||||
\(656\) | 16.7311 | − | 7.16517i | 0.653240 | − | 0.279753i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.6108 | + | 1.03115i | −0.647556 | + | 0.0401983i | ||||
\(659\) | 37.2494 | − | 21.5060i | 1.45103 | − | 0.837754i | 0.452492 | − | 0.891768i | \(-0.350535\pi\) |
0.998540 | + | 0.0540142i | \(0.0172016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.6797 | + | 21.7544i | 1.46557 | + | 0.846148i | 0.999260 | − | 0.0384716i | \(-0.0122489\pi\) |
0.466312 | + | 0.884620i | \(0.345582\pi\) | |||||||
\(662\) | −16.4726 | − | 17.4829i | −0.640226 | − | 0.679491i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.6550 | + | 45.4809i | −0.646338 | + | 1.76500i | ||||
\(665\) | 0.312467 | + | 0.846688i | 0.0121169 | + | 0.0328331i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.0275i | 1.08523i | ||||||||
\(668\) | −1.50561 | + | 25.2799i | −0.0582539 | + | 0.978109i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.34739 | − | 7.86503i | 0.322488 | − | 0.303853i | ||||
\(671\) | 8.15943 | − | 14.1326i | 0.314991 | − | 0.545581i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.6667 | + | 37.5278i | 0.835189 | + | 1.44659i | 0.893877 | + | 0.448313i | \(0.147975\pi\) |
−0.0586878 | + | 0.998276i | \(0.518692\pi\) | |||||||
\(674\) | −13.2892 | − | 3.98802i | −0.511882 | − | 0.153613i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.04013 | + | 5.96276i | 0.347697 | + | 0.229337i | ||||
\(677\) | 18.0239 | − | 10.4061i | 0.692714 | − | 0.399939i | −0.111914 | − | 0.993718i | \(-0.535698\pi\) |
0.804628 | + | 0.593779i | \(0.202365\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.2686 | + | 2.10673i | 0.470826 | + | 0.0808488i | ||||
\(680\) | 32.0672 | − | 5.58937i | 1.22972 | − | 0.214343i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.90572 | + | 1.15929i | −0.187850 | + | 0.0443913i | ||||
\(683\) | − | 10.0088i | − | 0.382976i | −0.981495 | − | 0.191488i | \(-0.938669\pi\) | ||
0.981495 | − | 0.191488i | \(-0.0613313\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.4378i | 1.85071i | ||||||||
\(686\) | 25.1851 | + | 7.19084i | 0.961573 | + | 0.274548i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.09201 | − | 42.5969i | 0.194131 | − | 1.62399i | ||||
\(689\) | 5.50711 | + | 3.17953i | 0.209804 | + | 0.121130i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.4952 | + | 30.3025i | 0.665548 | + | 1.15276i | 0.979136 | + | 0.203204i | \(0.0651355\pi\) |
−0.313588 | + | 0.949559i | \(0.601531\pi\) | |||||||
\(692\) | 8.39115 | − | 12.7218i | 0.318984 | − | 0.483610i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.50674 | + | 5.02089i | −0.0571950 | + | 0.190590i | ||||
\(695\) | 30.7801 | − | 17.7709i | 1.16756 | − | 0.674089i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.56667 | + | 11.3738i | −0.248730 | + | 0.430814i | ||||
\(698\) | −4.83124 | − | 5.12754i | −0.182865 | − | 0.194080i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −16.7137 | − | 55.1912i | −0.631717 | − | 2.08603i | ||||
\(701\) | −30.2491 | −1.14249 | −0.571246 | − | 0.820779i | \(-0.693540\pi\) | ||||
−0.571246 | + | 0.820779i | \(0.693540\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.532842 | −0.0200965 | ||||||||
\(704\) | −5.40105 | − | 15.0227i | −0.203560 | − | 0.566188i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.6531 | − | 12.3678i | −0.438570 | − | 0.465468i | ||||
\(707\) | 7.43280 | + | 1.27634i | 0.279539 | + | 0.0480016i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.3696 | − | 33.5492i | −0.727441 | − | 1.25997i | −0.957961 | − | 0.286897i | \(-0.907376\pi\) |
0.230520 | − | 0.973068i | \(-0.425957\pi\) | |||||||
\(710\) | 19.2811 | + | 5.78616i | 0.723608 | + | 0.217151i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.8604 | + | 14.0912i | −0.631871 | + | 0.528091i | ||||
\(713\) | −9.05138 | + | 5.22582i | −0.338977 | + | 0.195708i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.9775 | − | 10.9567i | −0.709719 | − | 0.409756i | ||||
\(716\) | −7.33396 | − | 14.6509i | −0.274083 | − | 0.547531i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −38.0367 | + | 8.98855i | −1.41952 | + | 0.335450i | ||||
\(719\) | 12.3006 | 0.458734 | 0.229367 | − | 0.973340i | \(-0.426334\pi\) | ||||
0.229367 | + | 0.973340i | \(0.426334\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.10553 | − | 1.88417i | 0.190140 | − | 0.0701703i | ||||
\(722\) | 6.17716 | + | 26.1398i | 0.229890 | + | 0.972821i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.30347 | + | 6.59929i | 0.122773 | + | 0.245261i | ||||
\(725\) | −26.1004 | + | 45.2073i | −0.969346 | + | 1.67896i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.0761 | + | 17.4523i | 0.373701 | + | 0.647269i | 0.990132 | − | 0.140140i | \(-0.0447552\pi\) |
−0.616431 | + | 0.787409i | \(0.711422\pi\) | |||||||
\(728\) | 10.2602 | − | 17.8746i | 0.380268 | − | 0.662478i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −61.5692 | − | 18.4766i | −2.27878 | − | 0.683848i | ||||
\(731\) | 15.4780 | + | 26.8086i | 0.572473 | + | 0.991553i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.3422 | − | 14.6313i | −0.936034 | − | 0.540419i | −0.0473190 | − | 0.998880i | \(-0.515068\pi\) |
−0.888715 | + | 0.458460i | \(0.848401\pi\) | |||||||
\(734\) | −30.3979 | + | 28.6413i | −1.12201 | + | 1.05717i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.6788 | − | 26.6147i | −0.725370 | − | 0.981031i | ||||
\(737\) | 4.05876 | 0.149506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 11.9818i | − | 0.440757i | −0.975414 | − | 0.220378i | \(-0.929271\pi\) | ||
0.975414 | − | 0.220378i | \(-0.0707292\pi\) | |||||||
\(740\) | 49.5792 | + | 2.95282i | 1.82257 | + | 0.108548i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.84774 | + | 7.73500i | −0.141255 | + | 0.283961i | ||||
\(743\) | −30.9885 | − | 17.8912i | −1.13686 | − | 0.656365i | −0.191207 | − | 0.981550i | \(-0.561240\pi\) |
−0.945651 | + | 0.325184i | \(0.894574\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.04749 | + | 4.06887i | −0.258200 | + | 0.149072i | ||||
\(746\) | 18.6915 | + | 5.60920i | 0.684343 | + | 0.205367i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.61599 | + | 6.34259i | 0.351595 | + | 0.231908i | ||||
\(749\) | −26.3097 | + | 31.6412i | −0.961336 | + | 1.15614i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.11442 | + | 2.95281i | 0.186628 | + | 0.107750i | 0.590403 | − | 0.807109i | \(-0.298969\pi\) |
−0.403775 | + | 0.914858i | \(0.632302\pi\) | |||||||
\(752\) | −17.6661 | − | 2.11179i | −0.644216 | − | 0.0770091i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.1566 | + | 4.29063i | −0.661223 | + | 0.156255i | ||||
\(755\) | −42.9261 | −1.56224 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.4509 | −0.525226 | −0.262613 | − | 0.964901i | \(-0.584584\pi\) | ||||
−0.262613 | + | 0.964901i | \(0.584584\pi\) | |||||||
\(758\) | 22.1611 | − | 5.23696i | 0.804929 | − | 0.190215i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.165672 | + | 0.950488i | 0.00600955 | + | 0.0344778i | ||||
\(761\) | −24.8767 | − | 14.3626i | −0.901781 | − | 0.520643i | −0.0240032 | − | 0.999712i | \(-0.507641\pi\) |
−0.877777 | + | 0.479069i | \(0.840975\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.60789 | + | 2.16846i | 0.0944118 | + | 0.0785037i | ||||
\(764\) | −11.0922 | + | 16.8169i | −0.401303 | + | 0.608415i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.3257 | + | 6.99990i | 0.842792 | + | 0.252917i | ||||
\(767\) | −11.5245 | + | 6.65366i | −0.416125 | + | 0.240250i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.21450 | + | 3.01059i | 0.188040 | + | 0.108565i | 0.591065 | − | 0.806624i | \(-0.298708\pi\) |
−0.403025 | + | 0.915189i | \(0.632041\pi\) | |||||||
\(770\) | 13.2593 | − | 26.6549i | 0.477833 | − | 0.960574i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.39595 | − | 23.4386i | 0.0502413 | − | 0.843574i | ||||
\(773\) | − | 32.8018i | − | 1.17980i | −0.807476 | − | 0.589900i | \(-0.799167\pi\) | ||
0.807476 | − | 0.589900i | \(-0.200833\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.4660 | −0.699241 | ||||||||
\(776\) | 12.4961 | + | 4.57605i | 0.448585 | + | 0.164271i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.45804 | + | 4.20043i | −0.159828 | + | 0.150593i | ||||
\(779\) | −0.337126 | − | 0.194640i | −0.0120788 | − | 0.00697369i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.56202 | + | 6.16959i | 0.127459 | + | 0.220765i | ||||
\(782\) | 22.8763 | + | 6.86503i | 0.818054 | + | 0.245493i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25.1008 | + | 12.4077i | 0.896455 | + | 0.443134i | ||||
\(785\) | 15.7418 | + | 27.2657i | 0.561851 | + | 0.973154i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.916080 | + | 1.58670i | −0.0326547 | + | 0.0565597i | −0.881891 | − | 0.471454i | \(-0.843730\pi\) |
0.849236 | + | 0.528013i | \(0.177063\pi\) | |||||||
\(788\) | 36.3648 | − | 18.2035i | 1.29544 | − | 0.648473i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −17.2187 | − | 72.8639i | −0.612613 | − | 2.59238i | ||||
\(791\) | −36.6990 | + | 13.5436i | −1.30487 | + | 0.481556i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.5227 | 0.799805 | ||||||||
\(794\) | 39.3565 | − | 9.30045i | 1.39671 | − | 0.330061i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −40.7366 | + | 20.3919i | −1.44387 | + | 0.722772i | ||||
\(797\) | −24.2935 | − | 14.0259i | −0.860520 | − | 0.496822i | 0.00366627 | − | 0.999993i | \(-0.498833\pi\) |
−0.864186 | + | 0.503172i | \(0.832166\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.1182 | − | 6.41912i | 0.393335 | − | 0.227092i | ||||
\(800\) | −6.95636 | − | 61.2542i | −0.245944 | − | 2.16566i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.3436 | − | 4.90463i | −0.577114 | − | 0.173188i | ||||
\(803\) | −11.3744 | − | 19.7010i | −0.401392 | − | 0.695232i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.4465 | − | 60.8358i | 0.368192 | − | 2.14418i | ||||
\(806\) | −4.77100 | − | 5.06360i | −0.168051 | − | 0.178358i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.57065 | + | 2.77235i | 0.266335 | + | 0.0975309i | ||||
\(809\) | 21.3196 | 0.749557 | 0.374779 | − | 0.927114i | \(-0.377719\pi\) | ||||
0.374779 | + | 0.927114i | \(0.377719\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.69767 | −0.270302 | −0.135151 | − | 0.990825i | \(-0.543152\pi\) | ||||
−0.135151 | + | 0.990825i | \(0.543152\pi\) | |||||||
\(812\) | −7.34618 | − | 24.2583i | −0.257800 | − | 0.851298i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0535 | + | 12.7927i | 0.422474 | + | 0.448384i | ||||
\(815\) | 26.6833 | − | 46.2169i | 0.934676 | − | 1.61891i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.794622 | + | 0.458775i | −0.0278003 | + | 0.0160505i | ||||
\(818\) | −9.31880 | + | 31.0529i | −0.325824 | + | 1.08574i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30.2898 | + | 19.9788i | 1.05777 | + | 0.697690i | ||||
\(821\) | −9.17336 | − | 15.8887i | −0.320152 | − | 0.554520i | 0.660367 | − | 0.750943i | \(-0.270401\pi\) |
−0.980519 | + | 0.196423i | \(0.937067\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.2067 | − | 5.89282i | −0.355782 | − | 0.205411i | 0.311447 | − | 0.950264i | \(-0.399186\pi\) |
−0.667229 | + | 0.744853i | \(0.732520\pi\) | |||||||
\(824\) | 5.73144 | − | 0.999002i | 0.199664 | − | 0.0348019i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.99210 | − | 15.0666i | −0.347670 | − | 0.524233i | ||||
\(827\) | − | 6.80800i | − | 0.236737i | −0.992970 | − | 0.118369i | \(-0.962234\pi\) | ||
0.992970 | − | 0.118369i | \(-0.0377665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 6.20652i | − | 0.215561i | −0.994175 | − | 0.107781i | \(-0.965626\pi\) | ||
0.994175 | − | 0.107781i | \(-0.0343744\pi\) | |||||||
\(830\) | −93.9714 | + | 22.2066i | −3.26179 | + | 0.770804i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14.2288 | − | 16.8225i | 0.493294 | − | 0.583216i | ||||
\(833\) | −19.8651 | + | 3.68635i | −0.688285 | + | 0.127725i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −43.7235 | + | 25.2438i | −1.51311 | + | 0.873597i | ||||
\(836\) | −0.187998 | + | 0.285023i | −0.00650204 | + | 0.00985773i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.8388 | + | 4.75313i | 0.547142 | + | 0.164194i | ||||
\(839\) | 19.9867 | + | 34.6180i | 0.690017 | + | 1.19514i | 0.971832 | + | 0.235676i | \(0.0757304\pi\) |
−0.281815 | + | 0.959469i | \(0.590936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.02804 | − | 5.24471i | 0.104415 | − | 0.180852i | ||||
\(842\) | 11.4494 | − | 10.7878i | 0.394571 | − | 0.371770i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 46.3944 | + | 2.76314i | 1.59696 | + | 0.0951112i | ||||
\(845\) | 21.5898i | 0.742713i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.4194 | + | 6.42854i | −0.598536 | + | 0.220887i | ||||
\(848\) | −5.53455 | + | 7.39367i | −0.190057 | + | 0.253900i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30.5055 | + | 32.3764i | 1.04633 | + | 1.11050i | ||||
\(851\) | 31.5609 | + | 18.2217i | 1.08189 | + | 0.624631i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.2532 | − | 14.5799i | 0.864652 | − | 0.499207i | −0.000915480 | − | 1.00000i | \(-0.500291\pi\) |
0.865567 | + | 0.500793i | \(0.166958\pi\) | |||||||
\(854\) | 1.89581 | + | 30.5397i | 0.0648733 | + | 1.04505i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −33.7551 | + | 28.2111i | −1.15373 | + | 0.964235i | ||||
\(857\) | −30.8516 | + | 17.8122i | −1.05387 | + | 0.608452i | −0.923730 | − | 0.383044i | \(-0.874876\pi\) |
−0.130139 | + | 0.991496i | \(0.541542\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.414494 | − | 0.717924i | 0.0141423 | − | 0.0244953i | −0.858868 | − | 0.512198i | \(-0.828832\pi\) |
0.873010 | + | 0.487702i | \(0.162165\pi\) | |||||||
\(860\) | 76.4793 | − | 38.2840i | 2.60792 | − | 1.30547i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −46.1126 | + | 10.8970i | −1.57060 | + | 0.371153i | ||||
\(863\) | − | 7.37519i | − | 0.251054i | −0.992090 | − | 0.125527i | \(-0.959938\pi\) | ||
0.992090 | − | 0.125527i | \(-0.0400622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.3825 | 1.03304 | ||||||||
\(866\) | −9.32488 | + | 2.20359i | −0.316872 | + | 0.0748810i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.46440 | − | 6.89546i | 0.219416 | − | 0.234047i | ||||
\(869\) | 13.2480 | − | 22.9462i | 0.449408 | − | 0.778398i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.80088 | + | 4.85127i | 0.0949042 | + | 0.164379i | ||||
\(872\) | 2.32518 | + | 2.78212i | 0.0787404 | + | 0.0942145i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.203483 | + | 0.678065i | −0.00688292 | + | 0.0229359i | ||||
\(875\) | 39.7795 | − | 47.8405i | 1.34479 | − | 1.61730i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.0813 | + | 17.4613i | −0.340420 | + | 0.589625i | −0.984511 | − | 0.175324i | \(-0.943903\pi\) |
0.644091 | + | 0.764949i | \(0.277236\pi\) | |||||||
\(878\) | 0.0370030 | − | 0.0348648i | 0.00124879 | − | 0.00117663i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 19.0721 | − | 25.4786i | 0.642919 | − | 0.858884i | ||||
\(881\) | 15.9543i | 0.537513i | 0.963208 | + | 0.268756i | \(0.0866126\pi\) | ||||
−0.963208 | + | 0.268756i | \(0.913387\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 53.4055i | − | 1.79724i | −0.438731 | − | 0.898619i | \(-0.644572\pi\) | ||
0.438731 | − | 0.898619i | \(-0.355428\pi\) | |||||||
\(884\) | −0.945209 | + | 15.8705i | −0.0317908 | + | 0.533782i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.5814 | + | 15.4757i | 0.489873 | + | 0.519917i | ||||
\(887\) | −18.7836 | + | 32.5342i | −0.630692 | + | 1.09239i | 0.356719 | + | 0.934212i | \(0.383895\pi\) |
−0.987411 | + | 0.158178i | \(0.949438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.553781 | − | 0.666000i | 0.0185732 | − | 0.0223369i | ||||
\(890\) | −41.9581 | − | 12.5914i | −1.40644 | − | 0.422064i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.9384 | + | 9.19362i | 0.466693 | + | 0.307825i | ||||
\(893\) | 0.190266 | + | 0.329551i | 0.00636702 | + | 0.0110280i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.3317 | − | 28.2873i | 0.545908 | − | 0.945541i | ||||
\(896\) | 24.0082 | + | 17.8775i | 0.802058 | + | 0.597246i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.16712 | − | 30.3289i | −0.239170 | − | 1.01209i | ||||
\(899\) | −8.55594 | −0.285357 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 6.66427i | − | 0.222019i | ||||||
\(902\) | 2.95316 | + | 12.4968i | 0.0983295 | + | 0.416099i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −41.1981 | + | 7.18092i | −1.37023 | + | 0.238834i | ||||
\(905\) | −7.35637 | + | 12.7416i | −0.244534 | + | 0.423545i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.9768 | + | 14.4203i | −0.829340 | + | 0.478819i | −0.853627 | − | 0.520886i | \(-0.825602\pi\) |
0.0242869 | + | 0.999705i | \(0.492268\pi\) | |||||||
\(908\) | 11.1436 | + | 7.35020i | 0.369814 | + | 0.243925i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 41.0094 | − | 2.54574i | 1.35945 | − | 0.0843904i | ||||
\(911\) | 3.53596 | − | 2.04149i | 0.117152 | − | 0.0676376i | −0.440279 | − | 0.897861i | \(-0.645121\pi\) |
0.557431 | + | 0.830223i | \(0.311787\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.5934 | − | 17.0857i | −0.979398 | − | 0.565456i | ||||
\(914\) | −18.2918 | + | 17.2348i | −0.605039 | + | 0.570077i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.8951 | − | 1.18490i | −0.657352 | − | 0.0391504i | ||||
\(917\) | −5.72411 | + | 2.11246i | −0.189027 | + | 0.0697595i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.244050i | 0.00805047i | 0.999992 | + | 0.00402523i | \(0.00128128\pi\) | ||||
−0.999992 | + | 0.00402523i | \(0.998719\pi\) | |||||||
\(920\) | 22.6910 | − | 61.9641i | 0.748101 | − | 2.04289i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 33.2678 | + | 35.3081i | 1.09562 | + | 1.16281i | ||||
\(923\) | −4.91617 | + | 8.51505i | −0.161818 | + | 0.280276i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.9376 | + | 58.7817i | 1.11586 | + | 1.93273i | ||||
\(926\) | 14.2963 | − | 47.6393i | 0.469804 | − | 1.56552i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.05754 | − | 26.9232i | −0.100369 | − | 0.883796i | ||||
\(929\) | 18.5771 | − | 10.7255i | 0.609496 | − | 0.351893i | −0.163272 | − | 0.986581i | \(-0.552205\pi\) |
0.772768 | + | 0.634688i | \(0.218871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.109265 | − | 0.588812i | −0.00358103 | − | 0.0192975i | ||||
\(932\) | 6.35174 | − | 3.17956i | 0.208058 | − | 0.104150i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.685521 | + | 2.90090i | 0.0224309 | + | 0.0949205i | ||||
\(935\) | 22.9651i | 0.751040i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 57.2133i | − | 1.86908i | −0.355863 | − | 0.934538i | \(-0.615813\pi\) | ||
0.355863 | − | 0.934538i | \(-0.384187\pi\) | |||||||
\(938\) | −6.34232 | + | 4.20620i | −0.207084 | + | 0.137337i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.8774 | − | 31.7180i | −0.517863 | − | 1.03453i | ||||
\(941\) | −8.14635 | − | 4.70330i | −0.265564 | − | 0.153323i | 0.361306 | − | 0.932447i | \(-0.382331\pi\) |
−0.626870 | + | 0.779124i | \(0.715664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3122 | + | 23.0575i | 0.433506 | + | 0.750855i | ||||
\(944\) | −7.60855 | − | 17.7664i | −0.247637 | − | 0.578248i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.9897 | + | 8.69964i | 0.942537 | + | 0.282850i | ||||
\(947\) | −33.4447 | + | 19.3093i | −1.08681 | + | 0.627469i | −0.932725 | − | 0.360589i | \(-0.882576\pi\) |
−0.154083 | + | 0.988058i | \(0.549242\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.6985 | − | 27.1906i | 0.509594 | − | 0.882643i | ||||
\(950\) | −0.959655 | + | 0.904200i | −0.0311353 | + | 0.0293361i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −21.5992 | + | 0.0542133i | −0.700033 | + | 0.00175706i | ||||
\(953\) | −52.7991 | −1.71033 | −0.855166 | − | 0.518355i | \(-0.826545\pi\) | ||||
−0.855166 | + | 0.518355i | \(0.826545\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.1625 | −1.29963 | ||||||||
\(956\) | 11.5683 | + | 0.688978i | 0.374144 | + | 0.0222831i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.23869 | + | 1.16711i | −0.0400203 | + | 0.0377077i | ||||
\(959\) | 5.43958 | − | 31.6776i | 0.175653 | − | 1.02292i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.9047 | + | 24.0837i | 0.448539 | + | 0.776893i | ||||
\(962\) | −6.97269 | + | 23.2350i | −0.224809 | + | 0.749127i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.34884 | − | 5.07716i | 0.107859 | − | 0.163524i | ||||
\(965\) | 40.5388 | − | 23.4051i | 1.30499 | − | 0.753437i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.22794 | − | 5.32776i | −0.296751 | − | 0.171329i | 0.344232 | − | 0.938885i | \(-0.388139\pi\) |
−0.640982 | + | 0.767556i | \(0.721473\pi\) | |||||||
\(968\) | −19.5549 | + | 3.40846i | −0.628518 | + | 0.109552i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.10140 | + | 25.8192i | 0.195904 | + | 0.829003i | ||||
\(971\) | 9.00425 | 0.288960 | 0.144480 | − | 0.989508i | \(-0.453849\pi\) | ||||
0.144480 | + | 0.989508i | \(0.453849\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.1255 | + | 8.16531i | −0.709310 | + | 0.261768i | ||||
\(974\) | 5.83444 | − | 1.37875i | 0.186948 | − | 0.0441781i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.88263 | + | 32.4799i | −0.124280 | + | 1.03966i | ||||
\(977\) | 4.49955 | − | 7.79345i | 0.143953 | − | 0.249334i | −0.785029 | − | 0.619459i | \(-0.787352\pi\) |
0.928982 | + | 0.370125i | \(0.120685\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.75137 | − | 13.4258i | −0.247735 | − | 0.429090i | ||||
\(980\) | 6.90380 | + | 55.3925i | 0.220534 | + | 1.76945i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.78044 | − | 22.5944i | 0.216373 | − | 0.721016i | ||||
\(983\) | 2.02127 | + | 3.50095i | 0.0644686 | + | 0.111663i | 0.896458 | − | 0.443128i | \(-0.146131\pi\) |
−0.831990 | + | 0.554791i | \(0.812798\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 70.2115 | + | 40.5366i | 2.23712 | + | 1.29160i | ||||
\(986\) | 13.4081 | + | 14.2305i | 0.427002 | + | 0.453190i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.470410 | − | 0.0280165i | −0.0149657 | − | 0.000891324i | ||||
\(989\) | 62.7552 | 1.99550 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 27.3007i | − | 0.867235i | −0.901097 | − | 0.433617i | \(-0.857237\pi\) | ||
0.901097 | − | 0.433617i | \(-0.142763\pi\) | |||||||
\(992\) | 8.12466 | − | 6.00734i | 0.257958 | − | 0.190733i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.9598 | − | 5.94935i | −0.379342 | − | 0.188702i | ||||
\(995\) | −78.6523 | − | 45.4099i | −2.49344 | − | 1.43959i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.4727 | + | 16.4387i | −0.901740 | + | 0.520620i | −0.877764 | − | 0.479093i | \(-0.840966\pi\) |
−0.0239754 | + | 0.999713i | \(0.507632\pi\) | |||||||
\(998\) | 12.2810 | − | 40.9239i | 0.388749 | − | 1.29542i | ||||
\(999\) | 0 | 0 |
(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 | 756.2.bi.c.307.15 | 80 | ||
3.2 | odd | 2 | 252.2.bi.c.139.25 | ✓ | 80 | ||
4.3 | odd | 2 | inner | 756.2.bi.c.307.9 | 80 | ||
7.6 | odd | 2 | inner | 756.2.bi.c.307.16 | 80 | ||
9.2 | odd | 6 | 252.2.bi.c.223.31 | yes | 80 | ||
9.7 | even | 3 | inner | 756.2.bi.c.559.10 | 80 | ||
12.11 | even | 2 | 252.2.bi.c.139.32 | yes | 80 | ||
21.20 | even | 2 | 252.2.bi.c.139.26 | yes | 80 | ||
28.27 | even | 2 | inner | 756.2.bi.c.307.10 | 80 | ||
36.7 | odd | 6 | inner | 756.2.bi.c.559.16 | 80 | ||
36.11 | even | 6 | 252.2.bi.c.223.26 | yes | 80 | ||
63.20 | even | 6 | 252.2.bi.c.223.32 | yes | 80 | ||
63.34 | odd | 6 | inner | 756.2.bi.c.559.9 | 80 | ||
84.83 | odd | 2 | 252.2.bi.c.139.31 | yes | 80 | ||
252.83 | odd | 6 | 252.2.bi.c.223.25 | yes | 80 | ||
252.223 | even | 6 | inner | 756.2.bi.c.559.15 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.bi.c.139.25 | ✓ | 80 | 3.2 | odd | 2 | ||
252.2.bi.c.139.26 | yes | 80 | 21.20 | even | 2 | ||
252.2.bi.c.139.31 | yes | 80 | 84.83 | odd | 2 | ||
252.2.bi.c.139.32 | yes | 80 | 12.11 | even | 2 | ||
252.2.bi.c.223.25 | yes | 80 | 252.83 | odd | 6 | ||
252.2.bi.c.223.26 | yes | 80 | 36.11 | even | 6 | ||
252.2.bi.c.223.31 | yes | 80 | 9.2 | odd | 6 | ||
252.2.bi.c.223.32 | yes | 80 | 63.20 | even | 6 | ||
756.2.bi.c.307.9 | 80 | 4.3 | odd | 2 | inner | ||
756.2.bi.c.307.10 | 80 | 28.27 | even | 2 | inner | ||
756.2.bi.c.307.15 | 80 | 1.1 | even | 1 | trivial | ||
756.2.bi.c.307.16 | 80 | 7.6 | odd | 2 | inner | ||
756.2.bi.c.559.9 | 80 | 63.34 | odd | 6 | inner | ||
756.2.bi.c.559.10 | 80 | 9.7 | even | 3 | inner | ||
756.2.bi.c.559.15 | 80 | 252.223 | even | 6 | inner | ||
756.2.bi.c.559.16 | 80 | 36.7 | odd | 6 | inner |