Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(43,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.bd (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 10 x^{14} - 8 x^{13} - 3 x^{12} + 32 x^{11} - 5 x^{10} - 44 x^{9} + 214 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 127.8 | ||
Root | \(1.31463 - 1.12772i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.127 |
Dual form | 273.2.bd.b.43.8 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.35660 | − | 1.36058i | 1.66636 | − | 0.962076i | 0.696791 | − | 0.717274i | \(-0.254610\pi\) |
0.969573 | − | 0.244802i | \(-0.0787230\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 2.70236 | − | 4.68063i | 1.35118 | − | 2.34031i | ||||
\(5\) | 1.58278i | 0.707839i | 0.935276 | + | 0.353920i | \(0.115151\pi\) | ||||
−0.935276 | + | 0.353920i | \(0.884849\pi\) | |||||||
\(6\) | 2.35660 | + | 1.36058i | 0.962076 | + | 0.555455i | ||||
\(7\) | −0.866025 | − | 0.500000i | −0.327327 | − | 0.188982i | ||||
\(8\) | − | 9.26480i | − | 3.27560i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 2.15350 | + | 3.72996i | 0.680995 | + | 1.17952i | ||||
\(11\) | −4.79969 | + | 2.77110i | −1.44716 | + | 0.835519i | −0.998311 | − | 0.0580877i | \(-0.981500\pi\) |
−0.448850 | + | 0.893607i | \(0.648166\pi\) | |||||||
\(12\) | 5.40472 | 1.56021 | ||||||||
\(13\) | −1.34211 | + | 3.34645i | −0.372235 | + | 0.928139i | ||||
\(14\) | −2.72116 | −0.727261 | ||||||||
\(15\) | −1.37073 | + | 0.791388i | −0.353920 | + | 0.204336i | ||||
\(16\) | −7.20078 | − | 12.4721i | −1.80020 | − | 3.11803i | ||||
\(17\) | 2.40288 | − | 4.16192i | 0.582785 | − | 1.00941i | −0.412363 | − | 0.911020i | \(-0.635296\pi\) |
0.995148 | − | 0.0983932i | \(-0.0313703\pi\) | |||||||
\(18\) | 2.72116i | 0.641384i | ||||||||
\(19\) | 0.772957 | + | 0.446267i | 0.177328 | + | 0.102381i | 0.586037 | − | 0.810284i | \(-0.300687\pi\) |
−0.408708 | + | 0.912665i | \(0.634021\pi\) | |||||||
\(20\) | 7.40839 | + | 4.27723i | 1.65657 | + | 0.956419i | ||||
\(21\) | − | 1.00000i | − | 0.218218i | ||||||
\(22\) | −7.54062 | + | 13.0607i | −1.60767 | + | 2.78456i | ||||
\(23\) | −2.31507 | − | 4.00983i | −0.482726 | − | 0.836107i | 0.517077 | − | 0.855939i | \(-0.327020\pi\) |
−0.999803 | + | 0.0198323i | \(0.993687\pi\) | |||||||
\(24\) | 8.02355 | − | 4.63240i | 1.63780 | − | 0.945584i | ||||
\(25\) | 2.49482 | 0.498963 | ||||||||
\(26\) | 1.39030 | + | 9.71228i | 0.272661 | + | 1.90474i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.68063 | + | 2.70236i | −0.884555 | + | 0.510698i | ||||
\(29\) | 0.941087 | + | 1.63001i | 0.174755 | + | 0.302685i | 0.940077 | − | 0.340963i | \(-0.110753\pi\) |
−0.765321 | + | 0.643649i | \(0.777420\pi\) | |||||||
\(30\) | −2.15350 | + | 3.72996i | −0.393173 | + | 0.680995i | ||||
\(31\) | − | 1.47545i | − | 0.264998i | −0.991183 | − | 0.132499i | \(-0.957700\pi\) | ||
0.991183 | − | 0.132499i | \(-0.0423001\pi\) | |||||||
\(32\) | −17.8916 | − | 10.3297i | −3.16281 | − | 1.82605i | ||||
\(33\) | −4.79969 | − | 2.77110i | −0.835519 | − | 0.482387i | ||||
\(34\) | − | 13.0773i | − | 2.24273i | ||||||
\(35\) | 0.791388 | − | 1.37073i | 0.133769 | − | 0.231695i | ||||
\(36\) | 2.70236 | + | 4.68063i | 0.450393 | + | 0.780104i | ||||
\(37\) | 4.32400 | − | 2.49646i | 0.710862 | − | 0.410416i | −0.100518 | − | 0.994935i | \(-0.532050\pi\) |
0.811380 | + | 0.584519i | \(0.198717\pi\) | |||||||
\(38\) | 2.42873 | 0.393992 | ||||||||
\(39\) | −3.56917 | + | 0.510922i | −0.571524 | + | 0.0818130i | ||||
\(40\) | 14.6641 | 2.31860 | ||||||||
\(41\) | −8.45175 | + | 4.87962i | −1.31994 | + | 0.762069i | −0.983719 | − | 0.179713i | \(-0.942483\pi\) |
−0.336223 | + | 0.941782i | \(0.609150\pi\) | |||||||
\(42\) | −1.36058 | − | 2.35660i | −0.209942 | − | 0.363631i | ||||
\(43\) | 0.506349 | − | 0.877022i | 0.0772174 | − | 0.133745i | −0.824831 | − | 0.565379i | \(-0.808730\pi\) |
0.902048 | + | 0.431635i | \(0.142063\pi\) | |||||||
\(44\) | 29.9541i | 4.51575i | ||||||||
\(45\) | −1.37073 | − | 0.791388i | −0.204336 | − | 0.117973i | ||||
\(46\) | −10.9114 | − | 6.29969i | −1.60880 | − | 0.928839i | ||||
\(47\) | 12.5703i | 1.83357i | 0.399385 | + | 0.916783i | \(0.369224\pi\) | ||||
−0.399385 | + | 0.916783i | \(0.630776\pi\) | |||||||
\(48\) | 7.20078 | − | 12.4721i | 1.03934 | − | 1.80020i | ||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | 5.87927 | − | 3.39440i | 0.831455 | − | 0.480041i | ||||
\(51\) | 4.80577 | 0.672942 | ||||||||
\(52\) | 12.0366 | + | 15.3252i | 1.66918 | + | 2.12523i | ||||
\(53\) | 6.25784 | 0.859581 | 0.429790 | − | 0.902929i | \(-0.358587\pi\) | ||||
0.429790 | + | 0.902929i | \(0.358587\pi\) | |||||||
\(54\) | −2.35660 | + | 1.36058i | −0.320692 | + | 0.185152i | ||||
\(55\) | −4.38604 | − | 7.59684i | −0.591413 | − | 1.02436i | ||||
\(56\) | −4.63240 | + | 8.02355i | −0.619030 | + | 1.07219i | ||||
\(57\) | 0.892533i | 0.118219i | ||||||||
\(58\) | 4.43552 | + | 2.56085i | 0.582413 | + | 0.336256i | ||||
\(59\) | 2.98511 | + | 1.72345i | 0.388628 | + | 0.224374i | 0.681565 | − | 0.731757i | \(-0.261300\pi\) |
−0.292938 | + | 0.956132i | \(0.594633\pi\) | |||||||
\(60\) | 8.55447i | 1.10438i | ||||||||
\(61\) | 1.79275 | − | 3.10513i | 0.229538 | − | 0.397571i | −0.728134 | − | 0.685435i | \(-0.759612\pi\) |
0.957671 | + | 0.287864i | \(0.0929453\pi\) | |||||||
\(62\) | −2.00746 | − | 3.47703i | −0.254948 | − | 0.441583i | ||||
\(63\) | 0.866025 | − | 0.500000i | 0.109109 | − | 0.0629941i | ||||
\(64\) | −27.4144 | −3.42681 | ||||||||
\(65\) | −5.29669 | − | 2.12426i | −0.656973 | − | 0.263483i | ||||
\(66\) | −15.0812 | −1.85637 | ||||||||
\(67\) | 12.7653 | − | 7.37003i | 1.55953 | − | 0.900392i | 0.562223 | − | 0.826986i | \(-0.309946\pi\) |
0.997302 | − | 0.0734069i | \(-0.0233872\pi\) | |||||||
\(68\) | −12.9869 | − | 22.4940i | −1.57489 | − | 2.72780i | ||||
\(69\) | 2.31507 | − | 4.00983i | 0.278702 | − | 0.482726i | ||||
\(70\) | − | 4.30699i | − | 0.514784i | ||||||
\(71\) | −11.3794 | − | 6.56988i | −1.35048 | − | 0.779702i | −0.362166 | − | 0.932114i | \(-0.617963\pi\) |
−0.988317 | + | 0.152412i | \(0.951296\pi\) | |||||||
\(72\) | 8.02355 | + | 4.63240i | 0.945584 | + | 0.545933i | ||||
\(73\) | − | 5.33654i | − | 0.624595i | −0.949984 | − | 0.312298i | \(-0.898901\pi\) | ||
0.949984 | − | 0.312298i | \(-0.101099\pi\) | |||||||
\(74\) | 6.79328 | − | 11.7663i | 0.789703 | − | 1.36781i | ||||
\(75\) | 1.24741 | + | 2.16058i | 0.144038 | + | 0.249482i | ||||
\(76\) | 4.17762 | − | 2.41195i | 0.479205 | − | 0.276669i | ||||
\(77\) | 5.54221 | 0.631593 | ||||||||
\(78\) | −7.71593 | + | 6.06018i | −0.873657 | + | 0.686180i | ||||
\(79\) | 0.779028 | 0.0876475 | 0.0438237 | − | 0.999039i | \(-0.486046\pi\) | ||||
0.0438237 | + | 0.999039i | \(0.486046\pi\) | |||||||
\(80\) | 19.7406 | − | 11.3972i | 2.20707 | − | 1.27425i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −13.2782 | + | 22.9986i | −1.46634 | + | 2.53977i | ||||
\(83\) | − | 1.47136i | − | 0.161503i | −0.996734 | − | 0.0807513i | \(-0.974268\pi\) | ||
0.996734 | − | 0.0807513i | \(-0.0257320\pi\) | |||||||
\(84\) | −4.68063 | − | 2.70236i | −0.510698 | − | 0.294852i | ||||
\(85\) | 6.58738 | + | 3.80323i | 0.714502 | + | 0.412518i | ||||
\(86\) | − | 2.75571i | − | 0.297156i | ||||||
\(87\) | −0.941087 | + | 1.63001i | −0.100895 | + | 0.174755i | ||||
\(88\) | 25.6737 | + | 44.4682i | 2.73683 | + | 4.74032i | ||||
\(89\) | 6.63332 | − | 3.82975i | 0.703130 | − | 0.405953i | −0.105382 | − | 0.994432i | \(-0.533606\pi\) |
0.808512 | + | 0.588479i | \(0.200273\pi\) | |||||||
\(90\) | −4.30699 | −0.453997 | ||||||||
\(91\) | 2.83553 | − | 2.22706i | 0.297244 | − | 0.233459i | ||||
\(92\) | −25.0247 | −2.60900 | ||||||||
\(93\) | 1.27777 | − | 0.737723i | 0.132499 | − | 0.0764983i | ||||
\(94\) | 17.1029 | + | 29.6231i | 1.76403 | + | 3.05539i | ||||
\(95\) | −0.706341 | + | 1.22342i | −0.0724690 | + | 0.125520i | ||||
\(96\) | − | 20.6594i | − | 2.10854i | ||||||
\(97\) | −0.657035 | − | 0.379340i | −0.0667118 | − | 0.0385161i | 0.466273 | − | 0.884641i | \(-0.345596\pi\) |
−0.532985 | + | 0.846125i | \(0.678930\pi\) | |||||||
\(98\) | 2.35660 | + | 1.36058i | 0.238052 | + | 0.137439i | ||||
\(99\) | − | 5.54221i | − | 0.557013i | ||||||
\(100\) | 6.74190 | − | 11.6773i | 0.674190 | − | 1.16773i | ||||
\(101\) | −5.88701 | − | 10.1966i | −0.585779 | − | 1.01460i | −0.994778 | − | 0.102064i | \(-0.967455\pi\) |
0.408998 | − | 0.912535i | \(-0.365878\pi\) | |||||||
\(102\) | 11.3252 | − | 6.53863i | 1.12137 | − | 0.647421i | ||||
\(103\) | −9.61981 | −0.947868 | −0.473934 | − | 0.880560i | \(-0.657167\pi\) | ||||
−0.473934 | + | 0.880560i | \(0.657167\pi\) | |||||||
\(104\) | 31.0042 | + | 12.4344i | 3.04021 | + | 1.21929i | ||||
\(105\) | 1.58278 | 0.154463 | ||||||||
\(106\) | 14.7472 | − | 8.51430i | 1.43237 | − | 0.826982i | ||||
\(107\) | −1.84459 | − | 3.19493i | −0.178323 | − | 0.308865i | 0.762983 | − | 0.646419i | \(-0.223734\pi\) |
−0.941306 | + | 0.337553i | \(0.890401\pi\) | |||||||
\(108\) | −2.70236 | + | 4.68063i | −0.260035 | + | 0.450393i | ||||
\(109\) | 8.92215i | 0.854587i | 0.904113 | + | 0.427293i | \(0.140533\pi\) | ||||
−0.904113 | + | 0.427293i | \(0.859467\pi\) | |||||||
\(110\) | −20.6722 | − | 11.9351i | −1.97102 | − | 1.13797i | ||||
\(111\) | 4.32400 | + | 2.49646i | 0.410416 | + | 0.236954i | ||||
\(112\) | 14.4016i | 1.36082i | ||||||||
\(113\) | −8.06766 | + | 13.9736i | −0.758941 | + | 1.31452i | 0.184450 | + | 0.982842i | \(0.440950\pi\) |
−0.943391 | + | 0.331683i | \(0.892384\pi\) | |||||||
\(114\) | 1.21436 | + | 2.10334i | 0.113736 | + | 0.196996i | ||||
\(115\) | 6.34666 | − | 3.66425i | 0.591829 | − | 0.341693i | ||||
\(116\) | 10.1726 | 0.944504 | ||||||||
\(117\) | −2.22706 | − | 2.83553i | −0.205891 | − | 0.262145i | ||||
\(118\) | 9.37958 | 0.863460 | ||||||||
\(119\) | −4.16192 | + | 2.40288i | −0.381522 | + | 0.220272i | ||||
\(120\) | 7.33205 | + | 12.6995i | 0.669322 | + | 1.15930i | ||||
\(121\) | 9.85803 | − | 17.0746i | 0.896185 | − | 1.55224i | ||||
\(122\) | − | 9.75670i | − | 0.883330i | ||||||
\(123\) | −8.45175 | − | 4.87962i | −0.762069 | − | 0.439981i | ||||
\(124\) | −6.90601 | − | 3.98719i | −0.620178 | − | 0.358060i | ||||
\(125\) | 11.8626i | 1.06103i | ||||||||
\(126\) | 1.36058 | − | 2.35660i | 0.121210 | − | 0.209942i | ||||
\(127\) | −2.31228 | − | 4.00499i | −0.205182 | − | 0.355386i | 0.745009 | − | 0.667055i | \(-0.232445\pi\) |
−0.950191 | + | 0.311669i | \(0.899112\pi\) | |||||||
\(128\) | −28.8216 | + | 16.6402i | −2.54749 | + | 1.47080i | ||||
\(129\) | 1.01270 | 0.0891630 | ||||||||
\(130\) | −15.3724 | + | 2.20054i | −1.34825 | + | 0.193000i | ||||
\(131\) | −7.78183 | −0.679902 | −0.339951 | − | 0.940443i | \(-0.610410\pi\) | ||||
−0.339951 | + | 0.940443i | \(0.610410\pi\) | |||||||
\(132\) | −25.9410 | + | 14.9770i | −2.25787 | + | 1.30358i | ||||
\(133\) | −0.446267 | − | 0.772957i | −0.0386962 | − | 0.0670238i | ||||
\(134\) | 20.0550 | − | 34.7364i | 1.73249 | − | 3.00076i | ||||
\(135\) | − | 1.58278i | − | 0.136224i | ||||||
\(136\) | −38.5593 | − | 22.2622i | −3.30643 | − | 1.90897i | ||||
\(137\) | 0.239328 | + | 0.138176i | 0.0204472 | + | 0.0118052i | 0.510189 | − | 0.860062i | \(-0.329576\pi\) |
−0.489742 | + | 0.871868i | \(0.662909\pi\) | |||||||
\(138\) | − | 12.5994i | − | 1.07253i | ||||||
\(139\) | −1.98032 | + | 3.43002i | −0.167969 | + | 0.290931i | −0.937706 | − | 0.347431i | \(-0.887054\pi\) |
0.769737 | + | 0.638362i | \(0.220387\pi\) | |||||||
\(140\) | −4.27723 | − | 7.40839i | −0.361492 | − | 0.626123i | ||||
\(141\) | −10.8862 | + | 6.28515i | −0.916783 | + | 0.529305i | ||||
\(142\) | −35.7554 | −3.00053 | ||||||||
\(143\) | −2.83164 | − | 19.7811i | −0.236793 | − | 1.65418i | ||||
\(144\) | 14.4016 | 1.20013 | ||||||||
\(145\) | −2.57994 | + | 1.48953i | −0.214253 | + | 0.123699i | ||||
\(146\) | −7.26080 | − | 12.5761i | −0.600908 | − | 1.04080i | ||||
\(147\) | −0.500000 | + | 0.866025i | −0.0412393 | + | 0.0714286i | ||||
\(148\) | − | 26.9854i | − | 2.21818i | ||||||
\(149\) | 18.7838 | + | 10.8449i | 1.53883 | + | 0.888446i | 0.998907 | + | 0.0467327i | \(0.0148809\pi\) |
0.539925 | + | 0.841713i | \(0.318452\pi\) | |||||||
\(150\) | 5.87927 | + | 3.39440i | 0.480041 | + | 0.277152i | ||||
\(151\) | 5.66673i | 0.461152i | 0.973054 | + | 0.230576i | \(0.0740610\pi\) | ||||
−0.973054 | + | 0.230576i | \(0.925939\pi\) | |||||||
\(152\) | 4.13457 | − | 7.16129i | 0.335358 | − | 0.580857i | ||||
\(153\) | 2.40288 | + | 4.16192i | 0.194262 | + | 0.336471i | ||||
\(154\) | 13.0607 | − | 7.54062i | 1.05246 | − | 0.607641i | ||||
\(155\) | 2.33530 | 0.187576 | ||||||||
\(156\) | −7.25374 | + | 18.0866i | −0.580764 | + | 1.44809i | ||||
\(157\) | 1.06406 | 0.0849216 | 0.0424608 | − | 0.999098i | \(-0.486480\pi\) | ||||
0.0424608 | + | 0.999098i | \(0.486480\pi\) | |||||||
\(158\) | 1.83585 | − | 1.05993i | 0.146053 | − | 0.0843235i | ||||
\(159\) | 3.12892 | + | 5.41945i | 0.248140 | + | 0.429790i | ||||
\(160\) | 16.3496 | − | 28.3184i | 1.29255 | − | 2.23876i | ||||
\(161\) | 4.63015i | 0.364907i | ||||||||
\(162\) | −2.35660 | − | 1.36058i | −0.185152 | − | 0.106897i | ||||
\(163\) | −6.24073 | − | 3.60309i | −0.488812 | − | 0.282216i | 0.235269 | − | 0.971930i | \(-0.424403\pi\) |
−0.724082 | + | 0.689714i | \(0.757736\pi\) | |||||||
\(164\) | 52.7460i | 4.11877i | ||||||||
\(165\) | 4.38604 | − | 7.59684i | 0.341453 | − | 0.591413i | ||||
\(166\) | −2.00190 | − | 3.46740i | −0.155378 | − | 0.269122i | ||||
\(167\) | −0.405731 | + | 0.234249i | −0.0313964 | + | 0.0181267i | −0.515616 | − | 0.856820i | \(-0.672437\pi\) |
0.484220 | + | 0.874946i | \(0.339104\pi\) | |||||||
\(168\) | −9.26480 | −0.714795 | ||||||||
\(169\) | −9.39747 | − | 8.98263i | −0.722882 | − | 0.690971i | ||||
\(170\) | 20.6984 | 1.58749 | ||||||||
\(171\) | −0.772957 | + | 0.446267i | −0.0591095 | + | 0.0341269i | ||||
\(172\) | −2.73667 | − | 4.74006i | −0.208669 | − | 0.361426i | ||||
\(173\) | −5.30504 | + | 9.18861i | −0.403335 | + | 0.698597i | −0.994126 | − | 0.108228i | \(-0.965482\pi\) |
0.590791 | + | 0.806825i | \(0.298816\pi\) | |||||||
\(174\) | 5.12170i | 0.388275i | ||||||||
\(175\) | −2.16058 | − | 1.24741i | −0.163324 | − | 0.0942952i | ||||
\(176\) | 69.1231 | + | 39.9082i | 5.21035 | + | 3.00820i | ||||
\(177\) | 3.44690i | 0.259085i | ||||||||
\(178\) | 10.4214 | − | 18.0503i | 0.781114 | − | 1.35293i | ||||
\(179\) | −9.68369 | − | 16.7726i | −0.723793 | − | 1.25365i | −0.959469 | − | 0.281814i | \(-0.909064\pi\) |
0.235676 | − | 0.971832i | \(-0.424270\pi\) | |||||||
\(180\) | −7.40839 | + | 4.27723i | −0.552189 | + | 0.318806i | ||||
\(181\) | 16.0004 | 1.18930 | 0.594649 | − | 0.803986i | \(-0.297291\pi\) | ||||
0.594649 | + | 0.803986i | \(0.297291\pi\) | |||||||
\(182\) | 3.65210 | − | 9.10623i | 0.270712 | − | 0.674999i | ||||
\(183\) | 3.58549 | 0.265047 | ||||||||
\(184\) | −37.1502 | + | 21.4487i | −2.73875 | + | 1.58122i | ||||
\(185\) | 3.95134 | + | 6.84393i | 0.290509 | + | 0.503176i | ||||
\(186\) | 2.00746 | − | 3.47703i | 0.147194 | − | 0.254948i | ||||
\(187\) | 26.6346i | 1.94771i | ||||||||
\(188\) | 58.8369 | + | 33.9695i | 4.29112 | + | 2.47748i | ||||
\(189\) | 0.866025 | + | 0.500000i | 0.0629941 | + | 0.0363696i | ||||
\(190\) | 3.84413i | 0.278883i | ||||||||
\(191\) | −1.57415 | + | 2.72651i | −0.113902 | + | 0.197284i | −0.917340 | − | 0.398104i | \(-0.869668\pi\) |
0.803438 | + | 0.595388i | \(0.203002\pi\) | |||||||
\(192\) | −13.7072 | − | 23.7416i | −0.989234 | − | 1.71340i | ||||
\(193\) | 20.1629 | − | 11.6411i | 1.45136 | − | 0.837942i | 0.452800 | − | 0.891612i | \(-0.350425\pi\) |
0.998559 | + | 0.0536700i | \(0.0170919\pi\) | |||||||
\(194\) | −2.06449 | −0.148222 | ||||||||
\(195\) | −0.808676 | − | 5.64920i | −0.0579105 | − | 0.404547i | ||||
\(196\) | 5.40472 | 0.386052 | ||||||||
\(197\) | −15.2788 | + | 8.82123i | −1.08857 | + | 0.628487i | −0.933196 | − | 0.359369i | \(-0.882992\pi\) |
−0.155376 | + | 0.987855i | \(0.549659\pi\) | |||||||
\(198\) | −7.54062 | − | 13.0607i | −0.535889 | − | 0.928186i | ||||
\(199\) | 5.96255 | − | 10.3274i | 0.422674 | − | 0.732093i | −0.573526 | − | 0.819187i | \(-0.694425\pi\) |
0.996200 | + | 0.0870944i | \(0.0277582\pi\) | |||||||
\(200\) | − | 23.1140i | − | 1.63440i | ||||||
\(201\) | 12.7653 | + | 7.37003i | 0.900392 | + | 0.519842i | ||||
\(202\) | −27.7466 | − | 16.0195i | −1.95224 | − | 1.12713i | ||||
\(203\) | − | 1.88217i | − | 0.132103i | ||||||
\(204\) | 12.9869 | − | 22.4940i | 0.909266 | − | 1.57489i | ||||
\(205\) | −7.72335 | − | 13.3772i | −0.539422 | − | 0.934307i | ||||
\(206\) | −22.6700 | + | 13.0885i | −1.57949 | + | 0.911921i | ||||
\(207\) | 4.63015 | 0.321818 | ||||||||
\(208\) | 51.4016 | − | 7.35808i | 3.56406 | − | 0.510191i | ||||
\(209\) | −4.94661 | −0.342164 | ||||||||
\(210\) | 3.72996 | − | 2.15350i | 0.257392 | − | 0.148605i | ||||
\(211\) | 7.56510 | + | 13.1031i | 0.520803 | + | 0.902057i | 0.999707 | + | 0.0241902i | \(0.00770074\pi\) |
−0.478904 | + | 0.877867i | \(0.658966\pi\) | |||||||
\(212\) | 16.9109 | − | 29.2906i | 1.16145 | − | 2.01169i | ||||
\(213\) | − | 13.1398i | − | 0.900322i | ||||||
\(214\) | −8.69391 | − | 5.01943i | −0.594304 | − | 0.343121i | ||||
\(215\) | 1.38813 | + | 0.801437i | 0.0946696 | + | 0.0546575i | ||||
\(216\) | 9.26480i | 0.630390i | ||||||||
\(217\) | −0.737723 | + | 1.27777i | −0.0500799 | + | 0.0867409i | ||||
\(218\) | 12.1393 | + | 21.0259i | 0.822177 | + | 1.42405i | ||||
\(219\) | 4.62158 | − | 2.66827i | 0.312298 | − | 0.180305i | ||||
\(220\) | −47.4106 | −3.19642 | ||||||||
\(221\) | 10.7027 | + | 13.6269i | 0.719942 | + | 0.916644i | ||||
\(222\) | 13.5866 | 0.911870 | ||||||||
\(223\) | −16.5898 | + | 9.57812i | −1.11093 | + | 0.641398i | −0.939071 | − | 0.343723i | \(-0.888312\pi\) |
−0.171863 | + | 0.985121i | \(0.554979\pi\) | |||||||
\(224\) | 10.3297 | + | 17.8916i | 0.690182 | + | 1.19543i | ||||
\(225\) | −1.24741 | + | 2.16058i | −0.0831606 | + | 0.144038i | ||||
\(226\) | 43.9068i | 2.92064i | ||||||||
\(227\) | −15.1052 | − | 8.72097i | −1.00257 | − | 0.578831i | −0.0935590 | − | 0.995614i | \(-0.529824\pi\) |
−0.909006 | + | 0.416782i | \(0.863158\pi\) | |||||||
\(228\) | 4.17762 | + | 2.41195i | 0.276669 | + | 0.159735i | ||||
\(229\) | − | 10.5075i | − | 0.694354i | −0.937800 | − | 0.347177i | \(-0.887140\pi\) | ||
0.937800 | − | 0.347177i | \(-0.112860\pi\) | |||||||
\(230\) | 9.97101 | − | 17.2703i | 0.657469 | − | 1.13877i | ||||
\(231\) | 2.77110 | + | 4.79969i | 0.182325 | + | 0.315797i | ||||
\(232\) | 15.1017 | − | 8.71898i | 0.991476 | − | 0.572429i | ||||
\(233\) | 9.69049 | 0.634845 | 0.317422 | − | 0.948284i | \(-0.397183\pi\) | ||||
0.317422 | + | 0.948284i | \(0.397183\pi\) | |||||||
\(234\) | −9.10623 | − | 3.65210i | −0.595293 | − | 0.238746i | ||||
\(235\) | −19.8960 | −1.29787 | ||||||||
\(236\) | 16.1337 | − | 9.31478i | 1.05021 | − | 0.606340i | ||||
\(237\) | 0.389514 | + | 0.674658i | 0.0253017 | + | 0.0438237i | ||||
\(238\) | −6.53863 | + | 11.3252i | −0.423837 | + | 0.734107i | ||||
\(239\) | 18.4302i | 1.19215i | 0.802929 | + | 0.596074i | \(0.203274\pi\) | ||||
−0.802929 | + | 0.596074i | \(0.796726\pi\) | |||||||
\(240\) | 19.7406 | + | 11.3972i | 1.27425 | + | 0.735688i | ||||
\(241\) | 13.2961 | + | 7.67652i | 0.856479 | + | 0.494488i | 0.862832 | − | 0.505492i | \(-0.168689\pi\) |
−0.00635271 | + | 0.999980i | \(0.502022\pi\) | |||||||
\(242\) | − | 53.6506i | − | 3.44879i | ||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −9.68929 | − | 16.7823i | −0.620293 | − | 1.07438i | ||||
\(245\) | −1.37073 | + | 0.791388i | −0.0875724 | + | 0.0505600i | ||||
\(246\) | −26.5565 | −1.69318 | ||||||||
\(247\) | −2.53080 | + | 1.98772i | −0.161031 | + | 0.126476i | ||||
\(248\) | −13.6697 | −0.868027 | ||||||||
\(249\) | 1.27423 | − | 0.735679i | 0.0807513 | − | 0.0466218i | ||||
\(250\) | 16.1401 | + | 27.9554i | 1.02079 | + | 1.76805i | ||||
\(251\) | 4.31450 | − | 7.47294i | 0.272329 | − | 0.471688i | −0.697129 | − | 0.716946i | \(-0.745539\pi\) |
0.969458 | + | 0.245258i | \(0.0788728\pi\) | |||||||
\(252\) | − | 5.40472i | − | 0.340465i | ||||||
\(253\) | 22.2233 | + | 12.8306i | 1.39717 | + | 0.806654i | ||||
\(254\) | −10.8982 | − | 6.29210i | −0.683816 | − | 0.394801i | ||||
\(255\) | 7.60646i | 0.476335i | ||||||||
\(256\) | −17.8661 | + | 30.9450i | −1.11663 | + | 1.93407i | ||||
\(257\) | 1.36475 | + | 2.36381i | 0.0851305 | + | 0.147450i | 0.905447 | − | 0.424460i | \(-0.139536\pi\) |
−0.820316 | + | 0.571910i | \(0.806203\pi\) | |||||||
\(258\) | 2.38652 | − | 1.37786i | 0.148578 | − | 0.0857816i | ||||
\(259\) | −4.99293 | −0.310245 | ||||||||
\(260\) | −24.2564 | + | 19.0513i | −1.50432 | + | 1.18151i | ||||
\(261\) | −1.88217 | −0.116504 | ||||||||
\(262\) | −18.3386 | + | 10.5878i | −1.13296 | + | 0.654117i | ||||
\(263\) | 2.80709 | + | 4.86203i | 0.173093 | + | 0.299806i | 0.939500 | − | 0.342550i | \(-0.111291\pi\) |
−0.766407 | + | 0.642356i | \(0.777957\pi\) | |||||||
\(264\) | −25.6737 | + | 44.4682i | −1.58011 | + | 2.73683i | ||||
\(265\) | 9.90477i | 0.608445i | ||||||||
\(266\) | −2.10334 | − | 1.21436i | −0.128964 | − | 0.0744574i | ||||
\(267\) | 6.63332 | + | 3.82975i | 0.405953 | + | 0.234377i | ||||
\(268\) | − | 79.6659i | − | 4.86637i | ||||||
\(269\) | 0.0911180 | − | 0.157821i | 0.00555556 | − | 0.00962252i | −0.863234 | − | 0.504804i | \(-0.831565\pi\) |
0.868790 | + | 0.495181i | \(0.164898\pi\) | |||||||
\(270\) | −2.15350 | − | 3.72996i | −0.131058 | − | 0.226998i | ||||
\(271\) | −25.4028 | + | 14.6663i | −1.54311 | + | 0.890914i | −0.544468 | + | 0.838782i | \(0.683268\pi\) |
−0.998640 | + | 0.0521319i | \(0.983398\pi\) | |||||||
\(272\) | −69.2106 | −4.19651 | ||||||||
\(273\) | 3.34645 | + | 1.34211i | 0.202536 | + | 0.0812283i | ||||
\(274\) | 0.752000 | 0.0454300 | ||||||||
\(275\) | −11.9744 | + | 6.91340i | −0.722081 | + | 0.416894i | ||||
\(276\) | −12.5123 | − | 21.6720i | −0.753154 | − | 1.30450i | ||||
\(277\) | −8.08739 | + | 14.0078i | −0.485924 | + | 0.841646i | −0.999869 | − | 0.0161776i | \(-0.994850\pi\) |
0.513945 | + | 0.857823i | \(0.328184\pi\) | |||||||
\(278\) | 10.7776i | 0.646395i | ||||||||
\(279\) | 1.27777 | + | 0.737723i | 0.0764983 | + | 0.0441663i | ||||
\(280\) | −12.6995 | − | 7.33205i | −0.758940 | − | 0.438174i | ||||
\(281\) | 3.71644i | 0.221704i | 0.993837 | + | 0.110852i | \(0.0353580\pi\) | ||||
−0.993837 | + | 0.110852i | \(0.964642\pi\) | |||||||
\(282\) | −17.1029 | + | 29.6231i | −1.01846 | + | 1.76403i | ||||
\(283\) | 1.88685 | + | 3.26812i | 0.112162 | + | 0.194270i | 0.916642 | − | 0.399710i | \(-0.130889\pi\) |
−0.804480 | + | 0.593980i | \(0.797556\pi\) | |||||||
\(284\) | −61.5023 | + | 35.5084i | −3.64949 | + | 2.10703i | ||||
\(285\) | −1.41268 | −0.0836800 | ||||||||
\(286\) | −33.5868 | − | 42.7633i | −1.98603 | − | 2.52865i | ||||
\(287\) | 9.75924 | 0.576070 | ||||||||
\(288\) | 17.8916 | − | 10.3297i | 1.05427 | − | 0.608684i | ||||
\(289\) | −3.04770 | − | 5.27877i | −0.179276 | − | 0.310516i | ||||
\(290\) | −4.05325 | + | 7.02044i | −0.238015 | + | 0.412254i | ||||
\(291\) | − | 0.758679i | − | 0.0444746i | ||||||
\(292\) | −24.9784 | − | 14.4213i | −1.46175 | − | 0.843941i | ||||
\(293\) | 13.3509 | + | 7.70816i | 0.779970 | + | 0.450316i | 0.836419 | − | 0.548090i | \(-0.184645\pi\) |
−0.0564499 | + | 0.998405i | \(0.517978\pi\) | |||||||
\(294\) | 2.72116i | 0.158701i | ||||||||
\(295\) | −2.72784 | + | 4.72476i | −0.158821 | + | 0.275086i | ||||
\(296\) | −23.1292 | − | 40.0610i | −1.34436 | − | 2.32850i | ||||
\(297\) | 4.79969 | − | 2.77110i | 0.278506 | − | 0.160796i | ||||
\(298\) | 59.0212 | 3.41901 | ||||||||
\(299\) | 16.5258 | − | 2.36565i | 0.955710 | − | 0.136809i | ||||
\(300\) | 13.4838 | 0.778487 | ||||||||
\(301\) | −0.877022 | + | 0.506349i | −0.0505507 | + | 0.0291854i | ||||
\(302\) | 7.71004 | + | 13.3542i | 0.443663 | + | 0.768447i | ||||
\(303\) | 5.88701 | − | 10.1966i | 0.338200 | − | 0.585779i | ||||
\(304\) | − | 12.8539i | − | 0.737221i | ||||||
\(305\) | 4.91472 | + | 2.83752i | 0.281416 | + | 0.162476i | ||||
\(306\) | 11.3252 | + | 6.53863i | 0.647421 | + | 0.373789i | ||||
\(307\) | 33.2617i | 1.89834i | 0.314758 | + | 0.949172i | \(0.398077\pi\) | ||||
−0.314758 | + | 0.949172i | \(0.601923\pi\) | |||||||
\(308\) | 14.9770 | − | 25.9410i | 0.853396 | − | 1.47813i | ||||
\(309\) | −4.80991 | − | 8.33100i | −0.273626 | − | 0.473934i | ||||
\(310\) | 5.50336 | − | 3.17737i | 0.312570 | − | 0.180462i | ||||
\(311\) | 5.28263 | 0.299551 | 0.149775 | − | 0.988720i | \(-0.452145\pi\) | ||||
0.149775 | + | 0.988720i | \(0.452145\pi\) | |||||||
\(312\) | 4.73359 | + | 33.0676i | 0.267987 | + | 1.87209i | ||||
\(313\) | −17.4853 | −0.988329 | −0.494165 | − | 0.869368i | \(-0.664526\pi\) | ||||
−0.494165 | + | 0.869368i | \(0.664526\pi\) | |||||||
\(314\) | 2.50757 | − | 1.44775i | 0.141510 | − | 0.0817010i | ||||
\(315\) | 0.791388 | + | 1.37073i | 0.0445897 | + | 0.0772316i | ||||
\(316\) | 2.10521 | − | 3.64634i | 0.118428 | − | 0.205123i | ||||
\(317\) | 6.89451i | 0.387234i | 0.981077 | + | 0.193617i | \(0.0620219\pi\) | ||||
−0.981077 | + | 0.193617i | \(0.937978\pi\) | |||||||
\(318\) | 14.7472 | + | 8.51430i | 0.826982 | + | 0.477458i | ||||
\(319\) | −9.03386 | − | 5.21570i | −0.505799 | − | 0.292023i | ||||
\(320\) | − | 43.3909i | − | 2.42563i | ||||||
\(321\) | 1.84459 | − | 3.19493i | 0.102955 | − | 0.178323i | ||||
\(322\) | 6.29969 | + | 10.9114i | 0.351068 | + | 0.608068i | ||||
\(323\) | 3.71465 | − | 2.14465i | 0.206689 | − | 0.119332i | ||||
\(324\) | −5.40472 | −0.300262 | ||||||||
\(325\) | −3.34832 | + | 8.34878i | −0.185732 | + | 0.463107i | ||||
\(326\) | −19.6092 | −1.08605 | ||||||||
\(327\) | −7.72680 | + | 4.46107i | −0.427293 | + | 0.246698i | ||||
\(328\) | 45.2087 | + | 78.3038i | 2.49623 | + | 4.32360i | ||||
\(329\) | 6.28515 | − | 10.8862i | 0.346512 | − | 0.600176i | ||||
\(330\) | − | 23.8702i | − | 1.31401i | ||||||
\(331\) | −2.60340 | − | 1.50307i | −0.143096 | − | 0.0826163i | 0.426743 | − | 0.904373i | \(-0.359661\pi\) |
−0.569839 | + | 0.821757i | \(0.692994\pi\) | |||||||
\(332\) | −6.88688 | − | 3.97614i | −0.377967 | − | 0.218219i | ||||
\(333\) | 4.99293i | 0.273611i | ||||||||
\(334\) | −0.637429 | + | 1.10406i | −0.0348785 | + | 0.0604114i | ||||
\(335\) | 11.6651 | + | 20.2046i | 0.637333 | + | 1.10389i | ||||
\(336\) | −12.4721 | + | 7.20078i | −0.680410 | + | 0.392835i | ||||
\(337\) | 7.21913 | 0.393251 | 0.196626 | − | 0.980479i | \(-0.437002\pi\) | ||||
0.196626 | + | 0.980479i | \(0.437002\pi\) | |||||||
\(338\) | −34.3676 | − | 8.38240i | −1.86935 | − | 0.455942i | ||||
\(339\) | −16.1353 | −0.876350 | ||||||||
\(340\) | 35.6030 | − | 20.5554i | 1.93084 | − | 1.11477i | ||||
\(341\) | 4.08861 | + | 7.08169i | 0.221411 | + | 0.383495i | ||||
\(342\) | −1.21436 | + | 2.10334i | −0.0656653 | + | 0.113736i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −8.12543 | − | 4.69122i | −0.438094 | − | 0.252933i | ||||
\(345\) | 6.34666 | + | 3.66425i | 0.341693 | + | 0.197276i | ||||
\(346\) | 28.8718i | 1.55216i | ||||||||
\(347\) | −0.962380 | + | 1.66689i | −0.0516633 | + | 0.0894834i | −0.890701 | − | 0.454591i | \(-0.849786\pi\) |
0.839037 | + | 0.544074i | \(0.183119\pi\) | |||||||
\(348\) | 5.08631 | + | 8.80975i | 0.272655 | + | 0.472252i | ||||
\(349\) | 2.82299 | − | 1.62985i | 0.151111 | − | 0.0872441i | −0.422538 | − | 0.906345i | \(-0.638861\pi\) |
0.573649 | + | 0.819101i | \(0.305527\pi\) | |||||||
\(350\) | −6.78880 | −0.362877 | ||||||||
\(351\) | 1.34211 | − | 3.34645i | 0.0716367 | − | 0.178620i | ||||
\(352\) | 114.499 | 6.10280 | ||||||||
\(353\) | 7.71876 | − | 4.45643i | 0.410828 | − | 0.237192i | −0.280317 | − | 0.959907i | \(-0.590440\pi\) |
0.691145 | + | 0.722716i | \(0.257106\pi\) | |||||||
\(354\) | 4.68979 | + | 8.12296i | 0.249260 | + | 0.431730i | ||||
\(355\) | 10.3987 | − | 18.0110i | 0.551903 | − | 0.955925i | ||||
\(356\) | − | 41.3974i | − | 2.19406i | ||||||
\(357\) | −4.16192 | − | 2.40288i | −0.220272 | − | 0.127174i | ||||
\(358\) | −45.6411 | − | 26.3509i | −2.41221 | − | 1.39269i | ||||
\(359\) | − | 20.1320i | − | 1.06253i | −0.847207 | − | 0.531263i | \(-0.821718\pi\) | ||
0.847207 | − | 0.531263i | \(-0.178282\pi\) | |||||||
\(360\) | −7.33205 | + | 12.6995i | −0.386433 | + | 0.669322i | ||||
\(361\) | −9.10169 | − | 15.7646i | −0.479036 | − | 0.829715i | ||||
\(362\) | 37.7064 | − | 21.7698i | 1.98180 | − | 1.14419i | ||||
\(363\) | 19.7161 | 1.03483 | ||||||||
\(364\) | −2.76139 | − | 19.2904i | −0.144736 | − | 1.01109i | ||||
\(365\) | 8.44656 | 0.442113 | ||||||||
\(366\) | 8.44955 | − | 4.87835i | 0.441665 | − | 0.254996i | ||||
\(367\) | 15.6709 | + | 27.1428i | 0.818013 | + | 1.41684i | 0.907144 | + | 0.420820i | \(0.138258\pi\) |
−0.0891309 | + | 0.996020i | \(0.528409\pi\) | |||||||
\(368\) | −33.3407 | + | 57.7478i | −1.73800 | + | 3.01031i | ||||
\(369\) | − | 9.75924i | − | 0.508046i | ||||||
\(370\) | 18.6234 | + | 10.7522i | 0.968187 | + | 0.558983i | ||||
\(371\) | −5.41945 | − | 3.12892i | −0.281364 | − | 0.162446i | ||||
\(372\) | − | 7.97437i | − | 0.413452i | ||||||
\(373\) | −8.97172 | + | 15.5395i | −0.464538 | + | 0.804604i | −0.999181 | − | 0.0404746i | \(-0.987113\pi\) |
0.534642 | + | 0.845078i | \(0.320446\pi\) | |||||||
\(374\) | 36.2385 | + | 62.7669i | 1.87385 | + | 3.24560i | ||||
\(375\) | −10.2733 | + | 5.93131i | −0.530513 | + | 0.306292i | ||||
\(376\) | 116.461 | 6.00603 | ||||||||
\(377\) | −6.71779 | + | 0.961644i | −0.345984 | + | 0.0495272i | ||||
\(378\) | 2.72116 | 0.139961 | ||||||||
\(379\) | 17.4484 | − | 10.0738i | 0.896263 | − | 0.517458i | 0.0202771 | − | 0.999794i | \(-0.493545\pi\) |
0.875986 | + | 0.482337i | \(0.160212\pi\) | |||||||
\(380\) | 3.81757 | + | 6.61223i | 0.195837 | + | 0.339200i | ||||
\(381\) | 2.31228 | − | 4.00499i | 0.118462 | − | 0.205182i | ||||
\(382\) | 8.56705i | 0.438329i | ||||||||
\(383\) | −32.4871 | − | 18.7565i | −1.66002 | − | 0.958410i | −0.972705 | − | 0.232047i | \(-0.925458\pi\) |
−0.687311 | − | 0.726363i | \(-0.741209\pi\) | |||||||
\(384\) | −28.8216 | − | 16.6402i | −1.47080 | − | 0.849165i | ||||
\(385\) | 8.77208i | 0.447067i | ||||||||
\(386\) | 31.6772 | − | 54.8666i | 1.61233 | − | 2.79263i | ||||
\(387\) | 0.506349 | + | 0.877022i | 0.0257391 | + | 0.0445815i | ||||
\(388\) | −3.55109 | + | 2.05022i | −0.180279 | + | 0.104084i | ||||
\(389\) | 23.1946 | 1.17601 | 0.588006 | − | 0.808857i | \(-0.299913\pi\) | ||||
0.588006 | + | 0.808857i | \(0.299913\pi\) | |||||||
\(390\) | −9.59191 | − | 12.2126i | −0.485705 | − | 0.618409i | ||||
\(391\) | −22.2514 | −1.12530 | ||||||||
\(392\) | 8.02355 | − | 4.63240i | 0.405250 | − | 0.233971i | ||||
\(393\) | −3.89091 | − | 6.73926i | −0.196271 | − | 0.339951i | ||||
\(394\) | −24.0040 | + | 41.5762i | −1.20930 | + | 2.09458i | ||||
\(395\) | 1.23303i | 0.0620403i | ||||||||
\(396\) | −25.9410 | − | 14.9770i | −1.30358 | − | 0.752625i | ||||
\(397\) | −33.0480 | − | 19.0803i | −1.65863 | − | 0.957612i | −0.973347 | − | 0.229339i | \(-0.926344\pi\) |
−0.685286 | − | 0.728274i | \(-0.740323\pi\) | |||||||
\(398\) | − | 32.4501i | − | 1.62658i | ||||||
\(399\) | 0.446267 | − | 0.772957i | 0.0223413 | − | 0.0386962i | ||||
\(400\) | −17.9646 | − | 31.1157i | −0.898232 | − | 1.55578i | ||||
\(401\) | 7.17772 | − | 4.14406i | 0.358438 | − | 0.206944i | −0.309957 | − | 0.950750i | \(-0.600315\pi\) |
0.668395 | + | 0.743806i | \(0.266981\pi\) | |||||||
\(402\) | 40.1101 | 2.00051 | ||||||||
\(403\) | 4.93751 | + | 1.98021i | 0.245955 | + | 0.0986415i | ||||
\(404\) | −63.6353 | −3.16597 | ||||||||
\(405\) | 1.37073 | − | 0.791388i | 0.0681119 | − | 0.0393244i | ||||
\(406\) | −2.56085 | − | 4.43552i | −0.127093 | − | 0.220131i | ||||
\(407\) | −13.8359 | + | 23.9645i | −0.685821 | + | 1.18788i | ||||
\(408\) | − | 44.5245i | − | 2.20429i | ||||||
\(409\) | −33.8724 | − | 19.5562i | −1.67488 | − | 0.966994i | −0.964841 | − | 0.262834i | \(-0.915343\pi\) |
−0.710041 | − | 0.704160i | \(-0.751324\pi\) | |||||||
\(410\) | −36.4016 | − | 21.0165i | −1.79775 | − | 1.03793i | ||||
\(411\) | 0.276352i | 0.0136315i | ||||||||
\(412\) | −25.9962 | + | 45.0267i | −1.28074 | + | 2.21831i | ||||
\(413\) | −1.72345 | − | 2.98511i | −0.0848055 | − | 0.146887i | ||||
\(414\) | 10.9114 | − | 6.29969i | 0.536265 | − | 0.309613i | ||||
\(415\) | 2.32883 | 0.114318 | ||||||||
\(416\) | 58.5803 | − | 46.0096i | 2.87214 | − | 2.25581i | ||||
\(417\) | −3.96065 | −0.193954 | ||||||||
\(418\) | −11.6571 | + | 6.73026i | −0.570170 | + | 0.329188i | ||||
\(419\) | −13.7733 | − | 23.8560i | −0.672869 | − | 1.16544i | −0.977087 | − | 0.212841i | \(-0.931728\pi\) |
0.304218 | − | 0.952602i | \(-0.401605\pi\) | |||||||
\(420\) | 4.27723 | − | 7.40839i | 0.208708 | − | 0.361492i | ||||
\(421\) | 34.1236i | 1.66308i | 0.555465 | + | 0.831540i | \(0.312540\pi\) | ||||
−0.555465 | + | 0.831540i | \(0.687460\pi\) | |||||||
\(422\) | 35.6558 | + | 20.5859i | 1.73570 | + | 1.00210i | ||||
\(423\) | −10.8862 | − | 6.28515i | −0.529305 | − | 0.305594i | ||||
\(424\) | − | 57.9776i | − | 2.81564i | ||||||
\(425\) | 5.99476 | − | 10.3832i | 0.290788 | − | 0.503660i | ||||
\(426\) | −17.8777 | − | 30.9651i | −0.866178 | − | 1.50026i | ||||
\(427\) | −3.10513 | + | 1.79275i | −0.150268 | + | 0.0867571i | ||||
\(428\) | −19.9390 | −0.963788 | ||||||||
\(429\) | 15.7151 | − | 12.3428i | 0.758732 | − | 0.595916i | ||||
\(430\) | 4.36168 | 0.210339 | ||||||||
\(431\) | −4.33090 | + | 2.50044i | −0.208612 | + | 0.120442i | −0.600666 | − | 0.799500i | \(-0.705098\pi\) |
0.392054 | + | 0.919942i | \(0.371765\pi\) | |||||||
\(432\) | 7.20078 | + | 12.4721i | 0.346448 | + | 0.600065i | ||||
\(433\) | 7.45679 | − | 12.9155i | 0.358351 | − | 0.620681i | −0.629335 | − | 0.777134i | \(-0.716673\pi\) |
0.987685 | + | 0.156453i | \(0.0500059\pi\) | |||||||
\(434\) | 4.01493i | 0.192723i | ||||||||
\(435\) | −2.57994 | − | 1.48953i | −0.123699 | − | 0.0714175i | ||||
\(436\) | 41.7612 | + | 24.1109i | 2.00000 | + | 1.15470i | ||||
\(437\) | − | 4.13256i | − | 0.197687i | ||||||
\(438\) | 7.26080 | − | 12.5761i | 0.346934 | − | 0.600908i | ||||
\(439\) | −3.55138 | − | 6.15117i | −0.169498 | − | 0.293579i | 0.768745 | − | 0.639555i | \(-0.220881\pi\) |
−0.938244 | + | 0.345976i | \(0.887548\pi\) | |||||||
\(440\) | −70.3832 | + | 40.6358i | −3.35539 | + | 1.93723i | ||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 43.7624 | + | 17.5512i | 2.08157 | + | 0.834824i | ||||
\(443\) | −4.63166 | −0.220057 | −0.110028 | − | 0.993928i | \(-0.535094\pi\) | ||||
−0.110028 | + | 0.993928i | \(0.535094\pi\) | |||||||
\(444\) | 23.3700 | − | 13.4927i | 1.10909 | − | 0.640335i | ||||
\(445\) | 6.06164 | + | 10.4991i | 0.287349 | + | 0.497703i | ||||
\(446\) | −26.0636 | + | 45.1435i | −1.23415 | + | 2.13761i | ||||
\(447\) | 21.6897i | 1.02589i | ||||||||
\(448\) | 23.7416 | + | 13.7072i | 1.12169 | + | 0.647605i | ||||
\(449\) | −19.5486 | − | 11.2864i | −0.922558 | − | 0.532639i | −0.0381076 | − | 0.999274i | \(-0.512133\pi\) |
−0.884450 | + | 0.466635i | \(0.845466\pi\) | |||||||
\(450\) | 6.78880i | 0.320027i | ||||||||
\(451\) | 27.0439 | − | 46.8414i | 1.27345 | − | 2.20567i | ||||
\(452\) | 43.6034 | + | 75.5234i | 2.05093 | + | 3.55232i | ||||
\(453\) | −4.90753 | + | 2.83336i | −0.230576 | + | 0.133123i | ||||
\(454\) | −47.4624 | −2.22752 | ||||||||
\(455\) | 3.52493 | + | 4.48801i | 0.165251 | + | 0.210401i | ||||
\(456\) | 8.26914 | 0.387238 | ||||||||
\(457\) | 25.8184 | − | 14.9063i | 1.20773 | − | 0.697286i | 0.245471 | − | 0.969404i | \(-0.421057\pi\) |
0.962264 | + | 0.272118i | \(0.0877241\pi\) | |||||||
\(458\) | −14.2963 | − | 24.7619i | −0.668022 | − | 1.15705i | ||||
\(459\) | −2.40288 | + | 4.16192i | −0.112157 | + | 0.194262i | ||||
\(460\) | − | 39.6085i | − | 1.84675i | ||||||
\(461\) | −13.2819 | − | 7.66832i | −0.618601 | − | 0.357149i | 0.157723 | − | 0.987483i | \(-0.449585\pi\) |
−0.776324 | + | 0.630334i | \(0.782918\pi\) | |||||||
\(462\) | 13.0607 | + | 7.54062i | 0.607641 | + | 0.350821i | ||||
\(463\) | 13.7066i | 0.636998i | 0.947923 | + | 0.318499i | \(0.103179\pi\) | ||||
−0.947923 | + | 0.318499i | \(0.896821\pi\) | |||||||
\(464\) | 13.5531 | − | 23.4747i | 0.629188 | − | 1.08979i | ||||
\(465\) | 1.16765 | + | 2.02243i | 0.0541485 | + | 0.0937880i | ||||
\(466\) | 22.8366 | − | 13.1847i | 1.05788 | − | 0.610769i | ||||
\(467\) | 41.2833 | 1.91036 | 0.955182 | − | 0.296020i | \(-0.0956594\pi\) | ||||
0.955182 | + | 0.296020i | \(0.0956594\pi\) | |||||||
\(468\) | −19.2904 | + | 2.76139i | −0.891697 | + | 0.127645i | ||||
\(469\) | −14.7401 | −0.680633 | ||||||||
\(470\) | −46.8868 | + | 27.0701i | −2.16273 | + | 1.24865i | ||||
\(471\) | 0.532032 | + | 0.921507i | 0.0245147 | + | 0.0424608i | ||||
\(472\) | 15.9674 | − | 27.6564i | 0.734961 | − | 1.27299i | ||||
\(473\) | 5.61258i | 0.258067i | ||||||||
\(474\) | 1.83585 | + | 1.05993i | 0.0843235 | + | 0.0486842i | ||||
\(475\) | 1.92839 | + | 1.11335i | 0.0884804 | + | 0.0510842i | ||||
\(476\) | 25.9738i | 1.19051i | ||||||||
\(477\) | −3.12892 | + | 5.41945i | −0.143263 | + | 0.248140i | ||||
\(478\) | 25.0757 | + | 43.4324i | 1.14694 | + | 1.98655i | ||||
\(479\) | −2.65614 | + | 1.53352i | −0.121362 | + | 0.0700685i | −0.559452 | − | 0.828863i | \(-0.688988\pi\) |
0.438090 | + | 0.898931i | \(0.355655\pi\) | |||||||
\(480\) | 32.6992 | 1.49251 | ||||||||
\(481\) | 2.55100 | + | 17.8206i | 0.116315 | + | 0.812549i | ||||
\(482\) | 41.7781 | 1.90294 | ||||||||
\(483\) | −4.00983 | + | 2.31507i | −0.182453 | + | 0.105340i | ||||
\(484\) | −53.2799 | − | 92.2835i | −2.42181 | − | 4.19471i | ||||
\(485\) | 0.600410 | − | 1.03994i | 0.0272632 | − | 0.0472213i | ||||
\(486\) | − | 2.72116i | − | 0.123434i | ||||||
\(487\) | 7.17045 | + | 4.13986i | 0.324924 | + | 0.187595i | 0.653585 | − | 0.756853i | \(-0.273264\pi\) |
−0.328661 | + | 0.944448i | \(0.606597\pi\) | |||||||
\(488\) | −28.7684 | − | 16.6094i | −1.30228 | − | 0.751874i | ||||
\(489\) | − | 7.20618i | − | 0.325875i | ||||||
\(490\) | −2.15350 | + | 3.72996i | −0.0972850 | + | 0.168503i | ||||
\(491\) | −2.48977 | − | 4.31241i | −0.112362 | − | 0.194616i | 0.804360 | − | 0.594142i | \(-0.202508\pi\) |
−0.916722 | + | 0.399526i | \(0.869175\pi\) | |||||||
\(492\) | −45.6794 | + | 26.3730i | −2.05939 | + | 1.18899i | ||||
\(493\) | 9.04529 | 0.407379 | ||||||||
\(494\) | −3.25963 | + | 8.12762i | −0.146657 | + | 0.365679i | ||||
\(495\) | 8.77208 | 0.394276 | ||||||||
\(496\) | −18.4019 | + | 10.6244i | −0.826272 | + | 0.477048i | ||||
\(497\) | 6.56988 | + | 11.3794i | 0.294699 | + | 0.510434i | ||||
\(498\) | 2.00190 | − | 3.46740i | 0.0897074 | − | 0.155378i | ||||
\(499\) | 0.00121934i | 5.45852e-5i | 1.00000 | 2.72926e-5i | \(8.68751e-6\pi\) | |||||
−1.00000 | 2.72926e-5i | \(0.999991\pi\) | ||||||||
\(500\) | 55.5245 | + | 32.0571i | 2.48313 | + | 1.43364i | ||||
\(501\) | −0.405731 | − | 0.234249i | −0.0181267 | − | 0.0104655i | ||||
\(502\) | − | 23.4809i | − | 1.04800i | ||||||
\(503\) | 6.65968 | − | 11.5349i | 0.296941 | − | 0.514316i | −0.678494 | − | 0.734606i | \(-0.737367\pi\) |
0.975434 | + | 0.220290i | \(0.0707004\pi\) | |||||||
\(504\) | −4.63240 | − | 8.02355i | −0.206343 | − | 0.357397i | ||||
\(505\) | 16.1389 | − | 9.31782i | 0.718173 | − | 0.414638i | ||||
\(506\) | 69.8284 | 3.10425 | ||||||||
\(507\) | 3.08045 | − | 12.6298i | 0.136807 | − | 0.560907i | ||||
\(508\) | −24.9945 | −1.10895 | ||||||||
\(509\) | 21.6361 | − | 12.4916i | 0.959005 | − | 0.553682i | 0.0631380 | − | 0.998005i | \(-0.479889\pi\) |
0.895867 | + | 0.444323i | \(0.146556\pi\) | |||||||
\(510\) | 10.3492 | + | 17.9253i | 0.458270 | + | 0.793747i | ||||
\(511\) | −2.66827 | + | 4.62158i | −0.118037 | + | 0.204447i | ||||
\(512\) | 30.6726i | 1.35555i | ||||||||
\(513\) | −0.772957 | − | 0.446267i | −0.0341269 | − | 0.0197032i | ||||
\(514\) | 6.43230 | + | 3.71369i | 0.283717 | + | 0.163804i | ||||
\(515\) | − | 15.2260i | − | 0.670939i | ||||||
\(516\) | 2.73667 | − | 4.74006i | 0.120475 | − | 0.208669i | ||||
\(517\) | −34.8336 | − | 60.3336i | −1.53198 | − | 2.65347i | ||||
\(518\) | −11.7663 | + | 6.79328i | −0.516982 | + | 0.298480i | ||||
\(519\) | −10.6101 | −0.465731 | ||||||||
\(520\) | −19.6809 | + | 49.0727i | −0.863064 | + | 2.15198i | ||||
\(521\) | 29.3265 | 1.28482 | 0.642409 | − | 0.766362i | \(-0.277935\pi\) | ||||
0.642409 | + | 0.766362i | \(0.277935\pi\) | |||||||
\(522\) | −4.43552 | + | 2.56085i | −0.194138 | + | 0.112085i | ||||
\(523\) | −5.72560 | − | 9.91702i | −0.250363 | − | 0.433641i | 0.713263 | − | 0.700897i | \(-0.247217\pi\) |
−0.963626 | + | 0.267255i | \(0.913883\pi\) | |||||||
\(524\) | −21.0293 | + | 36.4238i | −0.918670 | + | 1.59118i | ||||
\(525\) | − | 2.49482i | − | 0.108883i | ||||||
\(526\) | 13.2304 | + | 7.63856i | 0.576872 | + | 0.333057i | ||||
\(527\) | −6.14068 | − | 3.54532i | −0.267492 | − | 0.154437i | ||||
\(528\) | 79.8165i | 3.47357i | ||||||||
\(529\) | 0.780861 | − | 1.35249i | 0.0339505 | − | 0.0588040i | ||||
\(530\) | 13.4762 | + | 23.3415i | 0.585370 | + | 1.01389i | ||||
\(531\) | −2.98511 | + | 1.72345i | −0.129543 | + | 0.0747914i | ||||
\(532\) | −4.82389 | −0.209142 | ||||||||
\(533\) | −4.98621 | − | 34.8324i | −0.215977 | − | 1.50876i | ||||
\(534\) | 20.8427 | 0.901953 | ||||||||
\(535\) | 5.05686 | − | 2.91958i | 0.218627 | − | 0.126224i | ||||
\(536\) | −68.2818 | − | 118.268i | −2.94933 | − | 5.10838i | ||||
\(537\) | 9.68369 | − | 16.7726i | 0.417882 | − | 0.723793i | ||||
\(538\) | − | 0.495894i | − | 0.0213795i | ||||||
\(539\) | −4.79969 | − | 2.77110i | −0.206737 | − | 0.119360i | ||||
\(540\) | −7.40839 | − | 4.27723i | −0.318806 | − | 0.184063i | ||||
\(541\) | 7.24411i | 0.311449i | 0.987801 | + | 0.155724i | \(0.0497712\pi\) | ||||
−0.987801 | + | 0.155724i | \(0.950229\pi\) | |||||||
\(542\) | −39.9094 | + | 69.1250i | −1.71425 | + | 2.96917i | ||||
\(543\) | 8.00018 | + | 13.8567i | 0.343321 | + | 0.594649i | ||||
\(544\) | −85.9827 | + | 49.6421i | −3.68648 | + | 2.12839i | ||||
\(545\) | −14.1218 | −0.604910 | ||||||||
\(546\) | 9.71228 | − | 1.39030i | 0.415647 | − | 0.0594994i | ||||
\(547\) | 24.3579 | 1.04147 | 0.520735 | − | 0.853718i | \(-0.325658\pi\) | ||||
0.520735 | + | 0.853718i | \(0.325658\pi\) | |||||||
\(548\) | 1.29350 | − | 0.746804i | 0.0552557 | − | 0.0319019i | ||||
\(549\) | 1.79275 | + | 3.10513i | 0.0765125 | + | 0.132524i | ||||
\(550\) | −18.8125 | + | 32.5842i | −0.802167 | + | 1.38939i | ||||
\(551\) | 1.67990i | 0.0715663i | ||||||||
\(552\) | −37.1502 | − | 21.4487i | −1.58122 | − | 0.912917i | ||||
\(553\) | −0.674658 | − | 0.389514i | −0.0286894 | − | 0.0165638i | ||||
\(554\) | 44.0142i | 1.86998i | ||||||||
\(555\) | −3.95134 | + | 6.84393i | −0.167725 | + | 0.290509i | ||||
\(556\) | 10.7031 | + | 18.5383i | 0.453913 | + | 0.786200i | ||||
\(557\) | 3.59179 | − | 2.07372i | 0.152189 | − | 0.0878664i | −0.421972 | − | 0.906609i | \(-0.638662\pi\) |
0.574161 | + | 0.818743i | \(0.305328\pi\) | |||||||
\(558\) | 4.01493 | 0.169965 | ||||||||
\(559\) | 2.25533 | + | 2.87153i | 0.0953904 | + | 0.121453i | ||||
\(560\) | −22.7945 | −0.963242 | ||||||||
\(561\) | −23.0662 | + | 13.3173i | −0.973856 | + | 0.562256i | ||||
\(562\) | 5.05652 | + | 8.75814i | 0.213296 | + | 0.369440i | ||||
\(563\) | −0.483932 | + | 0.838195i | −0.0203953 | + | 0.0353257i | −0.876043 | − | 0.482233i | \(-0.839826\pi\) |
0.855648 | + | 0.517559i | \(0.173159\pi\) | |||||||
\(564\) | 67.9390i | 2.86075i | ||||||||
\(565\) | −22.1171 | − | 12.7693i | −0.930472 | − | 0.537209i | ||||
\(566\) | 8.89308 | + | 5.13442i | 0.373804 | + | 0.215816i | ||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | −60.8686 | + | 105.428i | −2.55399 | + | 4.42364i | ||||
\(569\) | −6.08730 | − | 10.5435i | −0.255193 | − | 0.442007i | 0.709755 | − | 0.704449i | \(-0.248806\pi\) |
−0.964948 | + | 0.262442i | \(0.915472\pi\) | |||||||
\(570\) | −3.32912 | + | 1.92207i | −0.139441 | + | 0.0805065i | ||||
\(571\) | −28.8995 | −1.20941 | −0.604703 | − | 0.796451i | \(-0.706708\pi\) | ||||
−0.604703 | + | 0.796451i | \(0.706708\pi\) | |||||||
\(572\) | −100.240 | − | 40.2017i | −4.19124 | − | 1.68092i | ||||
\(573\) | −3.14831 | −0.131522 | ||||||||
\(574\) | 22.9986 | − | 13.2782i | 0.959943 | − | 0.554223i | ||||
\(575\) | −5.77569 | − | 10.0038i | −0.240863 | − | 0.417187i | ||||
\(576\) | 13.7072 | − | 23.7416i | 0.571134 | − | 0.989234i | ||||
\(577\) | 14.5003i | 0.603657i | 0.953362 | + | 0.301828i | \(0.0975970\pi\) | ||||
−0.953362 | + | 0.301828i | \(0.902403\pi\) | |||||||
\(578\) | −14.3644 | − | 8.29328i | −0.597479 | − | 0.344955i | ||||
\(579\) | 20.1629 | + | 11.6411i | 0.837942 | + | 0.483786i | ||||
\(580\) | 16.1010i | 0.668557i | ||||||||
\(581\) | −0.735679 | + | 1.27423i | −0.0305211 | + | 0.0528641i | ||||
\(582\) | −1.03224 | − | 1.78790i | −0.0427879 | − | 0.0741108i | ||||
\(583\) | −30.0357 | + | 17.3411i | −1.24395 | + | 0.718196i | ||||
\(584\) | −49.4420 | −2.04592 | ||||||||
\(585\) | 4.48801 | − | 3.52493i | 0.185556 | − | 0.145738i | ||||
\(586\) | 41.9503 | 1.73295 | ||||||||
\(587\) | 24.0493 | − | 13.8849i | 0.992621 | − | 0.573090i | 0.0865640 | − | 0.996246i | \(-0.472411\pi\) |
0.906057 | + | 0.423157i | \(0.139078\pi\) | |||||||
\(588\) | 2.70236 | + | 4.68063i | 0.111443 | + | 0.193026i | ||||
\(589\) | 0.658442 | − | 1.14046i | 0.0271306 | − | 0.0469917i | ||||
\(590\) | 14.8458i | 0.611191i | ||||||||
\(591\) | −15.2788 | − | 8.82123i | −0.628487 | − | 0.362857i | ||||
\(592\) | −62.2724 | − | 35.9530i | −2.55938 | − | 1.47766i | ||||
\(593\) | − | 8.09800i | − | 0.332545i | −0.986080 | − | 0.166273i | \(-0.946827\pi\) | ||
0.986080 | − | 0.166273i | \(-0.0531731\pi\) | |||||||
\(594\) | 7.54062 | − | 13.0607i | 0.309395 | − | 0.535889i | ||||
\(595\) | −3.80323 | − | 6.58738i | −0.155917 | − | 0.270056i | ||||
\(596\) | 101.521 | − | 58.6134i | 4.15848 | − | 2.40090i | ||||
\(597\) | 11.9251 | 0.488062 | ||||||||
\(598\) | 35.7259 | − | 28.0595i | 1.46094 | − | 1.14744i | ||||
\(599\) | 12.8054 | 0.523216 | 0.261608 | − | 0.965174i | \(-0.415747\pi\) | ||||
0.261608 | + | 0.965174i | \(0.415747\pi\) | |||||||
\(600\) | 20.0173 | − | 11.5570i | 0.817202 | − | 0.471812i | ||||
\(601\) | 8.90245 | + | 15.4195i | 0.363138 | + | 0.628974i | 0.988476 | − | 0.151381i | \(-0.0483719\pi\) |
−0.625337 | + | 0.780355i | \(0.715039\pi\) | |||||||
\(602\) | −1.37786 | + | 2.38652i | −0.0561572 | + | 0.0972672i | ||||
\(603\) | 14.7401i | 0.600262i | ||||||||
\(604\) | 26.5238 | + | 15.3135i | 1.07924 | + | 0.623099i | ||||
\(605\) | 27.0253 | + | 15.6031i | 1.09873 | + | 0.634355i | ||||
\(606\) | − | 32.0390i | − | 1.30150i | ||||||
\(607\) | −3.05078 | + | 5.28410i | −0.123827 | + | 0.214475i | −0.921274 | − | 0.388914i | \(-0.872850\pi\) |
0.797447 | + | 0.603389i | \(0.206184\pi\) | |||||||
\(608\) | −9.21960 | − | 15.9688i | −0.373904 | − | 0.647621i | ||||
\(609\) | 1.63001 | − | 0.941087i | 0.0660513 | − | 0.0381348i | ||||
\(610\) | 15.4427 | 0.625256 | ||||||||
\(611\) | −42.0659 | − | 16.8708i | −1.70180 | − | 0.682518i | ||||
\(612\) | 25.9738 | 1.04993 | ||||||||
\(613\) | −14.7559 | + | 8.51931i | −0.595984 | + | 0.344092i | −0.767460 | − | 0.641097i | \(-0.778480\pi\) |
0.171476 | + | 0.985188i | \(0.445146\pi\) | |||||||
\(614\) | 45.2552 | + | 78.3843i | 1.82635 | + | 3.16333i | ||||
\(615\) | 7.72335 | − | 13.3772i | 0.311436 | − | 0.539422i | ||||
\(616\) | − | 51.3474i | − | 2.06885i | ||||||
\(617\) | −21.9462 | − | 12.6707i | −0.883523 | − | 0.510102i | −0.0117043 | − | 0.999932i | \(-0.503726\pi\) |
−0.871818 | + | 0.489830i | \(0.837059\pi\) | |||||||
\(618\) | −22.6700 | − | 13.0885i | −0.911921 | − | 0.526498i | ||||
\(619\) | − | 45.5457i | − | 1.83064i | −0.402731 | − | 0.915319i | \(-0.631939\pi\) | ||
0.402731 | − | 0.915319i | \(-0.368061\pi\) | |||||||
\(620\) | 6.31083 | − | 10.9307i | 0.253449 | − | 0.438986i | ||||
\(621\) | 2.31507 | + | 4.00983i | 0.0929007 | + | 0.160909i | ||||
\(622\) | 12.4490 | − | 7.18745i | 0.499161 | − | 0.288191i | ||||
\(623\) | −7.65950 | −0.306871 | ||||||||
\(624\) | 32.0731 | + | 40.8361i | 1.28395 | + | 1.63475i | ||||
\(625\) | −6.30180 | −0.252072 | ||||||||
\(626\) | −41.2059 | + | 23.7902i | −1.64692 | + | 0.950848i | ||||
\(627\) | −2.47330 | − | 4.28389i | −0.0987742 | − | 0.171082i | ||||
\(628\) | 2.87549 | − | 4.98049i | 0.114744 | − | 0.198743i | ||||
\(629\) | − | 23.9948i | − | 0.956737i | ||||||
\(630\) | 3.72996 | + | 2.15350i | 0.148605 | + | 0.0857973i | ||||
\(631\) | 1.72180 | + | 0.994084i | 0.0685440 | + | 0.0395739i | 0.533880 | − | 0.845560i | \(-0.320733\pi\) |
−0.465336 | + | 0.885134i | \(0.654067\pi\) | |||||||
\(632\) | − | 7.21754i | − | 0.287098i | ||||||
\(633\) | −7.56510 | + | 13.1031i | −0.300686 | + | 0.520803i | ||||
\(634\) | 9.38054 | + | 16.2476i | 0.372549 | + | 0.645273i | ||||
\(635\) | 6.33901 | − | 3.65983i | 0.251556 | − | 0.145236i | ||||
\(636\) | 33.8219 | 1.34113 | ||||||||
\(637\) | −3.56917 | + | 0.510922i | −0.141416 | + | 0.0202435i | ||||
\(638\) | −28.3855 | −1.12379 | ||||||||
\(639\) | 11.3794 | − | 6.56988i | 0.450161 | − | 0.259901i | ||||
\(640\) | −26.3377 | − | 45.6182i | −1.04109 | − | 1.80322i | ||||
\(641\) | −6.84746 | + | 11.8602i | −0.270459 | + | 0.468448i | −0.968979 | − | 0.247142i | \(-0.920509\pi\) |
0.698521 | + | 0.715590i | \(0.253842\pi\) | |||||||
\(642\) | − | 10.0389i | − | 0.396202i | ||||||
\(643\) | 16.7590 | + | 9.67580i | 0.660909 | + | 0.381576i | 0.792623 | − | 0.609711i | \(-0.208715\pi\) |
−0.131714 | + | 0.991288i | \(0.542048\pi\) | |||||||
\(644\) | 21.6720 | + | 12.5123i | 0.853996 | + | 0.493055i | ||||
\(645\) | 1.60287i | 0.0631131i | ||||||||
\(646\) | 5.83595 | − | 10.1082i | 0.229612 | − | 0.397700i | ||||
\(647\) | −18.3354 | − | 31.7578i | −0.720839 | − | 1.24853i | −0.960664 | − | 0.277713i | \(-0.910423\pi\) |
0.239825 | − | 0.970816i | \(-0.422910\pi\) | |||||||
\(648\) | −8.02355 | + | 4.63240i | −0.315195 | + | 0.181978i | ||||
\(649\) | −19.1035 | −0.749876 | ||||||||
\(650\) | 3.46855 | + | 24.2304i | 0.136048 | + | 0.950393i | ||||
\(651\) | −1.47545 | −0.0578273 | ||||||||
\(652\) | −33.7294 | + | 19.4737i | −1.32095 | + | 0.762649i | ||||
\(653\) | 7.79808 | + | 13.5067i | 0.305163 | + | 0.528557i | 0.977298 | − | 0.211872i | \(-0.0679559\pi\) |
−0.672135 | + | 0.740429i | \(0.734623\pi\) | |||||||
\(654\) | −12.1393 | + | 21.0259i | −0.474684 | + | 0.822177i | ||||
\(655\) | − | 12.3169i | − | 0.481261i | ||||||
\(656\) | 121.719 | + | 70.2742i | 4.75231 | + | 2.74375i | ||||
\(657\) | 4.62158 | + | 2.66827i | 0.180305 | + | 0.104099i | ||||
\(658\) | − | 34.2058i | − | 1.33348i | ||||||
\(659\) | 13.7314 | − | 23.7835i | 0.534900 | − | 0.926474i | −0.464268 | − | 0.885695i | \(-0.653683\pi\) |
0.999168 | − | 0.0407792i | \(-0.0129840\pi\) | |||||||
\(660\) | −23.7053 | − | 41.0588i | −0.922728 | − | 1.59821i | ||||
\(661\) | −13.2412 | + | 7.64481i | −0.515023 | + | 0.297348i | −0.734896 | − | 0.678180i | \(-0.762769\pi\) |
0.219873 | + | 0.975528i | \(0.429436\pi\) | |||||||
\(662\) | −8.18021 | −0.317933 | ||||||||
\(663\) | −6.44988 | + | 16.0823i | −0.250493 | + | 0.624583i | ||||
\(664\) | −13.6318 | −0.529018 | ||||||||
\(665\) | 1.22342 | − | 0.706341i | 0.0474421 | − | 0.0273907i | ||||
\(666\) | 6.79328 | + | 11.7663i | 0.263234 | + | 0.455935i | ||||
\(667\) | 4.35737 | − | 7.54719i | 0.168718 | − | 0.292228i | ||||
\(668\) | 2.53210i | 0.0979698i | ||||||||
\(669\) | −16.5898 | − | 9.57812i | −0.641398 | − | 0.370311i | ||||
\(670\) | 54.9799 | + | 31.7427i | 2.12406 | + | 1.22633i | ||||
\(671\) | 19.8715i | 0.767132i | ||||||||
\(672\) | −10.3297 | + | 17.8916i | −0.398477 | + | 0.690182i | ||||
\(673\) | −12.4288 | − | 21.5273i | −0.479094 | − | 0.829815i | 0.520618 | − | 0.853789i | \(-0.325701\pi\) |
−0.999713 | + | 0.0239740i | \(0.992368\pi\) | |||||||
\(674\) | 17.0126 | − | 9.82222i | 0.655300 | − | 0.378338i | ||||
\(675\) | −2.49482 | −0.0960256 | ||||||||
\(676\) | −67.4397 | + | 19.7117i | −2.59383 | + | 0.758144i | ||||
\(677\) | −4.31671 | −0.165905 | −0.0829523 | − | 0.996554i | \(-0.526435\pi\) | ||||
−0.0829523 | + | 0.996554i | \(0.526435\pi\) | |||||||
\(678\) | −38.0244 | + | 21.9534i | −1.46032 | + | 0.843115i | ||||
\(679\) | 0.379340 | + | 0.657035i | 0.0145577 | + | 0.0252147i | ||||
\(680\) | 35.2361 | − | 61.0308i | 1.35124 | − | 2.34042i | ||||
\(681\) | − | 17.4419i | − | 0.668377i | ||||||
\(682\) | 19.2704 | + | 11.1258i | 0.737902 | + | 0.426028i | ||||
\(683\) | 32.6030 | + | 18.8233i | 1.24752 | + | 0.720255i | 0.970614 | − | 0.240642i | \(-0.0773581\pi\) |
0.276904 | + | 0.960897i | \(0.410691\pi\) | |||||||
\(684\) | 4.82389i | 0.184446i | ||||||||
\(685\) | −0.218702 | + | 0.378803i | −0.00835618 | + | 0.0144733i | ||||
\(686\) | −1.36058 | − | 2.35660i | −0.0519472 | − | 0.0899752i | ||||
\(687\) | 9.09975 | − | 5.25374i | 0.347177 | − | 0.200443i | ||||
\(688\) | −14.5844 | −0.556026 | ||||||||
\(689\) | −8.39873 | + | 20.9416i | −0.319966 | + | 0.797810i | ||||
\(690\) | 19.9420 | 0.759179 | ||||||||
\(691\) | 43.5579 | − | 25.1482i | 1.65702 | − | 0.956682i | 0.682943 | − | 0.730472i | \(-0.260700\pi\) |
0.974078 | − | 0.226210i | \(-0.0726337\pi\) | |||||||
\(692\) | 28.6723 | + | 49.6618i | 1.08996 | + | 1.88786i | ||||
\(693\) | −2.77110 | + | 4.79969i | −0.105266 | + | 0.182325i | ||||
\(694\) | 5.23758i | 0.198816i | ||||||||
\(695\) | −5.42896 | − | 3.13441i | −0.205932 | − | 0.118895i | ||||
\(696\) | 15.1017 | + | 8.71898i | 0.572429 | + | 0.330492i | ||||
\(697\) | 46.9007i | 1.77649i | ||||||||
\(698\) | 4.43510 | − | 7.68182i | 0.167871 | − | 0.290761i | ||||
\(699\) | 4.84524 | + | 8.39221i | 0.183264 | + | 0.317422i | ||||
\(700\) | −11.6773 | + | 6.74190i | −0.441361 | + | 0.254820i | ||||
\(701\) | 12.0336 | 0.454504 | 0.227252 | − | 0.973836i | \(-0.427026\pi\) | ||||
0.227252 | + | 0.973836i | \(0.427026\pi\) | |||||||
\(702\) | −1.39030 | − | 9.71228i | −0.0524736 | − | 0.366566i | ||||
\(703\) | 4.45635 | 0.168075 | ||||||||
\(704\) | 131.581 | − | 75.9683i | 4.95914 | − | 2.86316i | ||||
\(705\) | −9.94799 | − | 17.2304i | −0.374663 | − | 0.648935i | ||||
\(706\) | 12.1267 | − | 21.0040i | 0.456393 | − | 0.790495i | ||||
\(707\) | 11.7740i | 0.442808i | ||||||||
\(708\) | 16.1337 | + | 9.31478i | 0.606340 | + | 0.350071i | ||||
\(709\) | −37.4205 | − | 21.6047i | −1.40536 | − | 0.811383i | −0.410421 | − | 0.911896i | \(-0.634618\pi\) |
−0.994936 | + | 0.100513i | \(0.967951\pi\) | |||||||
\(710\) | − | 56.5929i | − | 2.12389i | ||||||
\(711\) | −0.389514 | + | 0.674658i | −0.0146079 | + | 0.0253017i | ||||
\(712\) | −35.4818 | − | 61.4564i | −1.32974 | − | 2.30317i | ||||
\(713\) | −5.91628 | + | 3.41577i | −0.221567 | + | 0.127921i | ||||
\(714\) | −13.0773 | −0.489404 | ||||||||
\(715\) | 31.3090 | − | 4.48185i | 1.17089 | − | 0.167612i | ||||
\(716\) | −104.675 | −3.91190 | ||||||||
\(717\) | −15.9610 | + | 9.21508i | −0.596074 | + | 0.344143i | ||||
\(718\) | −27.3912 | − | 47.4429i | −1.02223 | − | 1.77055i | ||||
\(719\) | 20.4763 | − | 35.4661i | 0.763639 | − | 1.32266i | −0.177325 | − | 0.984152i | \(-0.556744\pi\) |
0.940963 | − | 0.338508i | \(-0.109922\pi\) | |||||||
\(720\) | 22.7945i | 0.849500i | ||||||||
\(721\) | 8.33100 | + | 4.80991i | 0.310263 | + | 0.179130i | ||||
\(722\) | −42.8980 | − | 24.7672i | −1.59650 | − | 0.921739i | ||||
\(723\) | 15.3530i | 0.570986i | ||||||||
\(724\) | 43.2387 | − | 74.8917i | 1.60695 | − | 2.78333i | ||||
\(725\) | 2.34784 | + | 4.06658i | 0.0871966 | + | 0.151029i | ||||
\(726\) | 46.4628 | − | 26.8253i | 1.72440 | − | 0.995580i | ||||
\(727\) | 24.7078 | 0.916360 | 0.458180 | − | 0.888859i | \(-0.348501\pi\) | ||||
0.458180 | + | 0.888859i | \(0.348501\pi\) | |||||||
\(728\) | −20.6332 | − | 26.2706i | −0.764718 | − | 0.973653i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 19.9051 | − | 11.4922i | 0.736722 | − | 0.425346i | ||||
\(731\) | −2.43339 | − | 4.21476i | −0.0900023 | − | 0.155889i | ||||
\(732\) | 9.68929 | − | 16.7823i | 0.358127 | − | 0.620293i | ||||
\(733\) | 8.10694i | 0.299437i | 0.988729 | + | 0.149718i | \(0.0478367\pi\) | ||||
−0.988729 | + | 0.149718i | \(0.952163\pi\) | |||||||
\(734\) | 73.8598 | + | 42.6430i | 2.72622 | + | 1.57398i | ||||
\(735\) | −1.37073 | − | 0.791388i | −0.0505600 | − | 0.0291908i | ||||
\(736\) | 95.6561i | 3.52593i | ||||||||
\(737\) | −40.8462 | + | 70.7477i | −1.50459 | + | 2.60603i | ||||
\(738\) | −13.2782 | − | 22.9986i | −0.488779 | − | 0.846590i | ||||
\(739\) | −31.9300 | + | 18.4348i | −1.17456 | + | 0.678135i | −0.954751 | − | 0.297408i | \(-0.903878\pi\) |
−0.219813 | + | 0.975542i | \(0.570545\pi\) | |||||||
\(740\) | 42.7118 | 1.57012 | ||||||||
\(741\) | −2.98682 | − | 1.19788i | −0.109724 | − | 0.0440052i | ||||
\(742\) | −17.0286 | −0.625140 | ||||||||
\(743\) | −6.60077 | + | 3.81096i | −0.242159 | + | 0.139810i | −0.616169 | − | 0.787614i | \(-0.711316\pi\) |
0.374010 | + | 0.927425i | \(0.377983\pi\) | |||||||
\(744\) | −6.83485 | − | 11.8383i | −0.250578 | − | 0.434014i | ||||
\(745\) | −17.1650 | + | 29.7306i | −0.628877 | + | 1.08925i | ||||
\(746\) | 48.8270i | 1.78768i | ||||||||
\(747\) | 1.27423 | + | 0.735679i | 0.0466218 | + | 0.0269171i | ||||
\(748\) | 124.666 | + | 71.9762i | 4.55825 | + | 2.63171i | ||||
\(749\) | 3.68918i | 0.134800i | ||||||||
\(750\) | −16.1401 | + | 27.9554i | −0.589352 | + | 1.02079i | ||||
\(751\) | 10.3356 | + | 17.9017i | 0.377150 | + | 0.653243i | 0.990646 | − | 0.136455i | \(-0.0435708\pi\) |
−0.613496 | + | 0.789698i | \(0.710237\pi\) | |||||||
\(752\) | 156.778 | − | 90.5160i | 5.71712 | − | 3.30078i | ||||
\(753\) | 8.62900 | 0.314458 | ||||||||
\(754\) | −14.5227 | + | 11.4063i | −0.528886 | + | 0.415393i | ||||
\(755\) | −8.96916 | −0.326421 | ||||||||
\(756\) | 4.68063 | − | 2.70236i | 0.170233 | − | 0.0982839i | ||||
\(757\) | 1.09408 | + | 1.89500i | 0.0397650 | + | 0.0688749i | 0.885223 | − | 0.465167i | \(-0.154006\pi\) |
−0.845458 | + | 0.534042i | \(0.820672\pi\) | |||||||
\(758\) | 27.4125 | − | 47.4799i | 0.995667 | − | 1.72455i | ||||
\(759\) | 25.6612i | 0.931444i | ||||||||
\(760\) | 11.3347 | + | 6.54410i | 0.411153 | + | 0.237380i | ||||
\(761\) | 27.1726 | + | 15.6881i | 0.985006 | + | 0.568694i | 0.903778 | − | 0.428002i | \(-0.140782\pi\) |
0.0812283 | + | 0.996696i | \(0.474116\pi\) | |||||||
\(762\) | − | 12.5842i | − | 0.455877i | ||||||
\(763\) | 4.46107 | − | 7.72680i | 0.161502 | − | 0.279729i | ||||
\(764\) | 8.50786 | + | 14.7360i | 0.307804 | + | 0.533132i | ||||
\(765\) | −6.58738 | + | 3.80323i | −0.238167 | + | 0.137506i | ||||
\(766\) | −102.079 | −3.68825 | ||||||||
\(767\) | −9.77379 | + | 7.67645i | −0.352911 | + | 0.277180i | ||||
\(768\) | −35.7323 | −1.28938 | ||||||||
\(769\) | 7.71490 | − | 4.45420i | 0.278207 | − | 0.160623i | −0.354405 | − | 0.935092i | \(-0.615316\pi\) |
0.632611 | + | 0.774470i | \(0.281983\pi\) | |||||||
\(770\) | 11.9351 | + | 20.6722i | 0.430112 | + | 0.744976i | ||||
\(771\) | −1.36475 | + | 2.36381i | −0.0491501 | + | 0.0851305i | ||||
\(772\) | − | 125.833i | − | 4.52884i | ||||||
\(773\) | 3.06396 | + | 1.76898i | 0.110203 | + | 0.0636258i | 0.554088 | − | 0.832458i | \(-0.313067\pi\) |
−0.443885 | + | 0.896084i | \(0.646400\pi\) | |||||||
\(774\) | 2.38652 | + | 1.37786i | 0.0857816 | + | 0.0495260i | ||||
\(775\) | − | 3.68097i | − | 0.132224i | ||||||
\(776\) | −3.51450 | + | 6.08730i | −0.126163 | + | 0.218521i | ||||
\(777\) | −2.49646 | − | 4.32400i | −0.0895601 | − | 0.155123i | ||||
\(778\) | 54.6602 | − | 31.5581i | 1.95966 | − | 1.13141i | ||||
\(779\) | −8.71045 | −0.312084 | ||||||||
\(780\) | −28.6271 | − | 11.4811i | −1.02501 | − | 0.411088i | ||||
\(781\) | 72.8233 | 2.60582 | ||||||||
\(782\) | −52.4376 | + | 30.2749i | −1.87516 | + | 1.08263i | ||||
\(783\) | −0.941087 | − | 1.63001i | −0.0336317 | − | 0.0582518i | ||||
\(784\) | 7.20078 | − | 12.4721i | 0.257171 | − | 0.445433i | ||||
\(785\) | 1.68418i | 0.0601108i | ||||||||
\(786\) | −18.3386 | − | 10.5878i | −0.654117 | − | 0.377655i | ||||
\(787\) | −17.7715 | − | 10.2604i | −0.633484 | − | 0.365742i | 0.148616 | − | 0.988895i | \(-0.452518\pi\) |
−0.782100 | + | 0.623153i | \(0.785852\pi\) | |||||||
\(788\) | 95.3526i | 3.39680i | ||||||||
\(789\) | −2.80709 | + | 4.86203i | −0.0999352 | + | 0.173093i | ||||
\(790\) | 1.67763 | + | 2.90575i | 0.0596875 | + | 0.103382i | ||||
\(791\) | 13.9736 | − | 8.06766i | 0.496844 | − | 0.286853i | ||||
\(792\) | −51.3474 | −1.82455 | ||||||||
\(793\) | 7.98509 | + | 10.1668i | 0.283559 | + | 0.361032i | ||||
\(794\) | −103.841 | −3.68518 | ||||||||
\(795\) | −8.57778 | + | 4.95238i | −0.304223 | + | 0.175643i | ||||
\(796\) | −32.2259 | − | 55.8170i | −1.14222 | − | 1.97838i | ||||
\(797\) | −19.9325 | + | 34.5241i | −0.706045 | + | 1.22291i | 0.260269 | + | 0.965536i | \(0.416189\pi\) |
−0.966313 | + | 0.257369i | \(0.917144\pi\) | |||||||
\(798\) | − | 2.42873i | − | 0.0859760i | ||||||
\(799\) | 52.3165 | + | 30.2050i | 1.85083 | + | 1.06857i | ||||
\(800\) | −44.6362 | − | 25.7707i | −1.57813 | − | 0.911133i | ||||
\(801\) | 7.65950i | 0.270635i | ||||||||
\(802\) | 11.2767 | − | 19.5317i | 0.398192 | − | 0.689690i | ||||
\(803\) | 14.7881 | + | 25.6138i | 0.521861 | + | 0.903890i | ||||
\(804\) | 68.9927 | − | 39.8330i | 2.43318 | − | 1.40480i | ||||
\(805\) | −7.32849 | −0.258295 | ||||||||
\(806\) | 14.3299 | − | 2.05132i | 0.504751 | − | 0.0722545i | ||||
\(807\) | 0.182236 | 0.00641501 | ||||||||
\(808\) | −94.4694 | + | 54.5419i | −3.32342 | + | 1.91878i | ||||
\(809\) | −20.8347 | − | 36.0868i | −0.732509 | − | 1.26874i | −0.955808 | − | 0.293993i | \(-0.905016\pi\) |
0.223299 | − | 0.974750i | \(-0.428317\pi\) | |||||||
\(810\) | 2.15350 | − | 3.72996i | 0.0756661 | − | 0.131058i | ||||
\(811\) | − | 20.6446i | − | 0.724931i | −0.931997 | − | 0.362465i | \(-0.881935\pi\) | ||
0.931997 | − | 0.362465i | \(-0.118065\pi\) | |||||||
\(812\) | −8.80975 | − | 5.08631i | −0.309162 | − | 0.178495i | ||||
\(813\) | −25.4028 | − | 14.6663i | −0.890914 | − | 0.514369i | ||||
\(814\) | 75.2995i | 2.63925i | ||||||||
\(815\) | 5.70289 | − | 9.87769i | 0.199763 | − | 0.346000i | ||||
\(816\) | −34.6053 | − | 59.9381i | −1.21143 | − | 2.09825i | ||||
\(817\) | 0.782771 | − | 0.451933i | 0.0273857 | − | 0.0158111i | ||||
\(818\) | −106.431 | −3.72129 | ||||||||
\(819\) | 0.510922 | + | 3.56917i | 0.0178531 | + | 0.124717i | ||||
\(820\) | −83.4851 | −2.91543 | ||||||||
\(821\) | −12.2424 | + | 7.06813i | −0.427261 | + | 0.246679i | −0.698179 | − | 0.715923i | \(-0.746006\pi\) |
0.270918 | + | 0.962602i | \(0.412673\pi\) | |||||||
\(822\) | 0.376000 | + | 0.651251i | 0.0131145 | + | 0.0227150i | ||||
\(823\) | 0.822984 | − | 1.42545i | 0.0286874 | − | 0.0496881i | −0.851325 | − | 0.524638i | \(-0.824201\pi\) |
0.880013 | + | 0.474950i | \(0.157534\pi\) | |||||||
\(824\) | 89.1256i | 3.10484i | ||||||||
\(825\) | −11.9744 | − | 6.91340i | −0.416894 | − | 0.240694i | ||||
\(826\) | −8.12296 | − | 4.68979i | −0.282634 | − | 0.163179i | ||||
\(827\) | 10.1980i | 0.354620i | 0.984155 | + | 0.177310i | \(0.0567396\pi\) | ||||
−0.984155 | + | 0.177310i | \(0.943260\pi\) | |||||||
\(828\) | 12.5123 | − | 21.6720i | 0.434834 | − | 0.753154i | ||||
\(829\) | −0.838869 | − | 1.45296i | −0.0291351 | − | 0.0504635i | 0.851090 | − | 0.525020i | \(-0.175942\pi\) |
−0.880225 | + | 0.474556i | \(0.842609\pi\) | |||||||
\(830\) | 5.48812 | − | 3.16856i | 0.190495 | − | 0.109982i | ||||
\(831\) | −16.1748 | −0.561097 | ||||||||
\(832\) | 36.7933 | − | 91.7411i | 1.27558 | − | 3.18055i | ||||
\(833\) | 4.80577 | 0.166510 | ||||||||
\(834\) | −9.33365 | + | 5.38878i | −0.323198 | + | 0.186598i | ||||
\(835\) | −0.370763 | − | 0.642181i | −0.0128308 | − | 0.0222236i | ||||
\(836\) | −13.3675 | + | 23.1532i | −0.462325 | + | 0.800771i | ||||
\(837\) | 1.47545i | 0.0509989i | ||||||||
\(838\) | −64.9161 | − | 37.4793i | −2.24249 | − | 1.29470i | ||||
\(839\) | −9.28491 | − | 5.36065i | −0.320551 | − | 0.185070i | 0.331087 | − | 0.943600i | \(-0.392585\pi\) |
−0.651638 | + | 0.758530i | \(0.725918\pi\) | |||||||
\(840\) | − | 14.6641i | − | 0.505960i | ||||||
\(841\) | 12.7287 | − | 22.0468i | 0.438921 | − | 0.760234i | ||||
\(842\) | 46.4279 | + | 80.4154i | 1.60001 | + | 2.77130i | ||||
\(843\) | −3.21853 | + | 1.85822i | −0.110852 | + | 0.0640005i | ||||
\(844\) | 81.7745 | 2.81480 | ||||||||
\(845\) | 14.2175 | − | 14.8741i | 0.489097 | − | 0.511685i | ||||
\(846\) | −34.2058 | −1.17602 | ||||||||
\(847\) | −17.0746 | + | 9.85803i | −0.586691 | + | 0.338726i | ||||
\(848\) | −45.0614 | − | 78.0486i | −1.54741 | − | 2.68020i | ||||
\(849\) | −1.88685 | + | 3.26812i | −0.0647565 | + | 0.112162i | ||||
\(850\) | − | 32.6254i | − | 1.11904i | ||||||
\(851\) | −20.0208 | − | 11.5590i | −0.686303 | − | 0.396237i | ||||
\(852\) | −61.5023 | − | 35.5084i | −2.10703 | − | 1.21650i | ||||
\(853\) | 5.01741i | 0.171793i | 0.996304 | + | 0.0858964i | \(0.0273754\pi\) | ||||
−0.996304 | + | 0.0858964i | \(0.972625\pi\) | |||||||
\(854\) | −4.87835 | + | 8.44955i | −0.166934 | + | 0.289138i | ||||
\(855\) | −0.706341 | − | 1.22342i | −0.0241563 | − | 0.0418400i | ||||
\(856\) | −29.6004 | + | 17.0898i | −1.01172 | + | 0.584116i | ||||
\(857\) | −25.0009 | −0.854015 | −0.427008 | − | 0.904248i | \(-0.640432\pi\) | ||||
−0.427008 | + | 0.904248i | \(0.640432\pi\) | |||||||
\(858\) | 20.2407 | − | 50.4686i | 0.691007 | − | 1.72297i | ||||
\(859\) | 17.9200 | 0.611424 | 0.305712 | − | 0.952124i | \(-0.401106\pi\) | ||||
0.305712 | + | 0.952124i | \(0.401106\pi\) | |||||||
\(860\) | 7.50245 | − | 4.33154i | 0.255832 | − | 0.147704i | ||||
\(861\) | 4.87962 | + | 8.45175i | 0.166297 | + | 0.288035i | ||||
\(862\) | −6.80411 | + | 11.7851i | −0.231749 | + | 0.401401i | ||||
\(863\) | 7.10038i | 0.241700i | 0.992671 | + | 0.120850i | \(0.0385620\pi\) | ||||
−0.992671 | + | 0.120850i | \(0.961438\pi\) | |||||||
\(864\) | 17.8916 | + | 10.3297i | 0.608684 | + | 0.351424i | ||||
\(865\) | −14.5435 | − | 8.39670i | −0.494494 | − | 0.285496i | ||||
\(866\) | − | 40.5823i | − | 1.37904i | ||||||
\(867\) | 3.04770 | − | 5.27877i | 0.103505 | − | 0.179276i | ||||
\(868\) | 3.98719 | + | 6.90601i | 0.135334 | + | 0.234405i | ||||
\(869\) | −3.73909 | + | 2.15877i | −0.126840 | + | 0.0732312i | ||||
\(870\) | −8.10651 | −0.274836 | ||||||||
\(871\) | 7.53102 | + | 52.6097i | 0.255179 | + | 1.78261i | ||||
\(872\) | 82.6619 | 2.79928 | ||||||||
\(873\) | 0.657035 | − | 0.379340i | 0.0222373 | − | 0.0128387i | ||||
\(874\) | −5.62269 | − | 9.73878i | −0.190190 | − | 0.329419i | ||||
\(875\) | 5.93131 | − | 10.2733i | 0.200515 | − | 0.347302i | ||||
\(876\) | − | 28.8425i | − | 0.974499i | ||||||
\(877\) | 23.1653 | + | 13.3745i | 0.782236 | + | 0.451624i | 0.837222 | − | 0.546863i | \(-0.184178\pi\) |
−0.0549864 | + | 0.998487i | \(0.517512\pi\) | |||||||
\(878\) | −16.7383 | − | 9.66388i | −0.564891 | − | 0.326140i | ||||
\(879\) | 15.4163i | 0.519980i | ||||||||
\(880\) | −63.1658 | + | 109.406i | −2.12932 | + | 3.68809i | ||||
\(881\) | 5.01467 | + | 8.68567i | 0.168949 | + | 0.292628i | 0.938050 | − | 0.346499i | \(-0.112629\pi\) |
−0.769102 | + | 0.639126i | \(0.779296\pi\) | |||||||
\(882\) | −2.35660 | + | 1.36058i | −0.0793507 | + | 0.0458131i | ||||
\(883\) | 1.88319 | 0.0633743 | 0.0316871 | − | 0.999498i | \(-0.489912\pi\) | ||||
0.0316871 | + | 0.999498i | \(0.489912\pi\) | |||||||
\(884\) | 92.7050 | − | 13.2706i | 3.11801 | − | 0.446339i | ||||
\(885\) | −5.45568 | −0.183391 | ||||||||
\(886\) | −10.9149 | + | 6.30174i | −0.366695 | + | 0.211711i | ||||
\(887\) | 19.2887 | + | 33.4090i | 0.647652 | + | 1.12177i | 0.983682 | + | 0.179915i | \(0.0575822\pi\) |
−0.336030 | + | 0.941851i | \(0.609084\pi\) | |||||||
\(888\) | 23.1292 | − | 40.0610i | 0.776166 | − | 1.34436i | ||||
\(889\) | 4.62457i | 0.155103i | ||||||||
\(890\) | 28.5697 | + | 16.4947i | 0.957657 | + | 0.552903i | ||||
\(891\) | 4.79969 | + | 2.77110i | 0.160796 | + | 0.0928355i | ||||
\(892\) | 103.534i | 3.46658i | ||||||||
\(893\) | −5.60971 | + | 9.71630i | −0.187722 | + | 0.325143i | ||||
\(894\) | 29.5106 | + | 51.1139i | 0.986983 | + | 1.70950i | ||||
\(895\) | 26.5473 | − | 15.3271i | 0.887380 | − | 0.512329i | ||||
\(896\) | 33.2803 | 1.11182 | ||||||||
\(897\) | 10.3116 | + | 13.1289i | 0.344294 | + | 0.438362i | ||||
\(898\) | −61.4243 | −2.04976 | ||||||||
\(899\) | 2.40499 | − | 1.38852i | 0.0802110 | − | 0.0463098i | ||||
\(900\) | 6.74190 | + | 11.6773i | 0.224730 | + | 0.389244i | ||||
\(901\) | 15.0369 | − | 26.0446i | 0.500951 | − | 0.867672i | ||||
\(902\) | − | 147.182i | − | 4.90061i | ||||||
\(903\) | −0.877022 | − | 0.506349i | −0.0291854 | − | 0.0168502i | ||||
\(904\) | 129.462 | + | 74.7452i | 4.30586 | + | 2.48599i | ||||
\(905\) | 25.3250i | 0.841831i | ||||||||
\(906\) | −7.71004 | + | 13.3542i | −0.256149 | + | 0.443663i | ||||
\(907\) | 18.1585 | + | 31.4515i | 0.602944 | + | 1.04433i | 0.992373 | + | 0.123273i | \(0.0393390\pi\) |
−0.389429 | + | 0.921056i | \(0.627328\pi\) | |||||||
\(908\) | −81.6392 | + | 47.1344i | −2.70929 | + | 1.56421i | ||||
\(909\) | 11.7740 | 0.390520 | ||||||||
\(910\) | 14.4131 | + | 5.78047i | 0.477791 | + | 0.191621i | ||||
\(911\) | 5.42183 | 0.179633 | 0.0898167 | − | 0.995958i | \(-0.471372\pi\) | ||||
0.0898167 | + | 0.995958i | \(0.471372\pi\) | |||||||
\(912\) | 11.1318 | − | 6.42694i | 0.368610 | − | 0.212817i | ||||
\(913\) | 4.07729 | + | 7.06207i | 0.134939 | + | 0.233720i | ||||
\(914\) | 40.5624 | − | 70.2561i | 1.34168 | − | 2.32387i | ||||
\(915\) | 5.67503i | 0.187611i | ||||||||
\(916\) | −49.1816 | − | 28.3950i | −1.62501 | − | 0.938198i | ||||
\(917\) | 6.73926 | + | 3.89091i | 0.222550 | + | 0.128489i | ||||
\(918\) | 13.0773i | 0.431614i | ||||||||
\(919\) | −7.91774 | + | 13.7139i | −0.261182 | + | 0.452381i | −0.966556 | − | 0.256454i | \(-0.917446\pi\) |
0.705374 | + | 0.708835i | \(0.250779\pi\) | |||||||
\(920\) | −33.9485 | − | 58.8005i | −1.11925 | − | 1.93860i | ||||
\(921\) | −28.8054 | + | 16.6308i | −0.949172 | + | 0.548005i | ||||
\(922\) | −41.7335 | −1.37442 | ||||||||
\(923\) | 37.2582 | − | 29.2630i | 1.22637 | − | 0.963203i | ||||
\(924\) | 29.9541 | 0.985417 | ||||||||
\(925\) | 10.7876 | − | 6.22822i | 0.354694 | − | 0.204783i | ||||
\(926\) | 18.6489 | + | 32.3008i | 0.612841 | + | 1.06147i | ||||
\(927\) | 4.80991 | − | 8.33100i | 0.157978 | − | 0.273626i | ||||
\(928\) | − | 38.8846i | − | 1.27645i | ||||||
\(929\) | −19.9419 | − | 11.5135i | −0.654272 | − | 0.377744i | 0.135819 | − | 0.990734i | \(-0.456633\pi\) |
−0.790091 | + | 0.612990i | \(0.789967\pi\) | |||||||
\(930\) | 5.50336 | + | 3.17737i | 0.180462 | + | 0.104190i | ||||
\(931\) | 0.892533i | 0.0292516i | ||||||||
\(932\) | 26.1872 | − | 45.3575i | 0.857790 | − | 1.48574i | ||||
\(933\) | 2.64132 | + | 4.57490i | 0.0864728 | + | 0.149775i | ||||
\(934\) | 97.2880 | − | 56.1693i | 3.18336 | − | 1.83792i | ||||
\(935\) | −42.1566 | −1.37867 | ||||||||
\(936\) | −26.2706 | + | 20.6332i | −0.858681 | + | 0.674418i | ||||
\(937\) | −48.9751 | −1.59995 | −0.799974 | − | 0.600035i | \(-0.795153\pi\) | ||||
−0.799974 | + | 0.600035i | \(0.795153\pi\) | |||||||
\(938\) | −34.7364 | + | 20.0550i | −1.13418 | + | 0.654820i | ||||
\(939\) | −8.74267 | − | 15.1427i | −0.285306 | − | 0.494165i | ||||
\(940\) | −53.7661 | + | 93.1256i | −1.75366 | + | 3.03742i | ||||
\(941\) | − | 31.1637i | − | 1.01591i | −0.861384 | − | 0.507954i | \(-0.830402\pi\) | ||
0.861384 | − | 0.507954i | \(-0.169598\pi\) | |||||||
\(942\) | 2.50757 | + | 1.44775i | 0.0817010 | + | 0.0471701i | ||||
\(943\) | 39.1329 | + | 22.5934i | 1.27434 | + | 0.735742i | ||||
\(944\) | − | 49.6408i | − | 1.61567i | ||||||
\(945\) | −0.791388 | + | 1.37073i | −0.0257439 | + | 0.0445897i | ||||
\(946\) | 7.63637 | + | 13.2266i | 0.248280 | + | 0.430033i | ||||
\(947\) | 39.0165 | − | 22.5262i | 1.26787 | − | 0.732003i | 0.293282 | − | 0.956026i | \(-0.405253\pi\) |
0.974584 | + | 0.224023i | \(0.0719192\pi\) | |||||||
\(948\) | 4.21043 | 0.136748 | ||||||||
\(949\) | 17.8585 | + | 7.16224i | 0.579711 | + | 0.232496i | ||||
\(950\) | 6.05923 | 0.196587 | ||||||||
\(951\) | −5.97082 | + | 3.44725i | −0.193617 | + | 0.111785i | ||||
\(952\) | 22.2622 | + | 38.5593i | 0.721523 | + | 1.24971i | ||||
\(953\) | 4.36983 | − | 7.56877i | 0.141553 | − | 0.245176i | −0.786529 | − | 0.617554i | \(-0.788124\pi\) |
0.928081 | + | 0.372377i | \(0.121457\pi\) | |||||||
\(954\) | 17.0286i | 0.551321i | ||||||||
\(955\) | −4.31546 | − | 2.49153i | −0.139645 | − | 0.0806242i | ||||
\(956\) | 86.2647 | + | 49.8049i | 2.79000 | + | 1.61081i | ||||
\(957\) | − | 10.4314i | − | 0.337199i | ||||||
\(958\) | −4.17297 | + | 7.22779i | −0.134822 | + | 0.233519i | ||||
\(959\) | −0.138176 | − | 0.239328i | −0.00446194 | − | 0.00772831i | ||||
\(960\) | 37.5777 | − | 21.6955i | 1.21281 | − | 0.700218i | ||||
\(961\) | 28.8231 | 0.929776 | ||||||||
\(962\) | 30.2580 | + | 38.5251i | 0.975558 | + | 1.24210i | ||||
\(963\) | 3.68918 | 0.118882 | ||||||||
\(964\) | 71.8619 | − | 41.4895i | 2.31451 | − | 1.33629i | ||||
\(965\) | 18.4252 | + | 31.9134i | 0.593128 | + | 1.02733i | ||||
\(966\) | −6.29969 | + | 10.9114i | −0.202689 | + | 0.351068i | ||||
\(967\) | − | 5.92797i | − | 0.190631i | −0.995447 | − | 0.0953154i | \(-0.969614\pi\) | ||
0.995447 | − | 0.0953154i | \(-0.0303860\pi\) | |||||||
\(968\) | −158.193 | − | 91.3327i | −5.08451 | − | 2.93554i | ||||
\(969\) | 3.71465 | + | 2.14465i | 0.119332 | + | 0.0688962i | ||||
\(970\) | − | 3.26762i | − | 0.104917i | ||||||
\(971\) | 15.7086 | − | 27.2081i | 0.504114 | − | 0.873151i | −0.495875 | − | 0.868394i | \(-0.665153\pi\) |
0.999989 | − | 0.00475668i | \(-0.00151410\pi\) | |||||||
\(972\) | −2.70236 | − | 4.68063i | −0.0866783 | − | 0.150131i | ||||
\(973\) | 3.43002 | − | 1.98032i | 0.109961 | − | 0.0634863i | ||||
\(974\) | 22.5305 | 0.721923 | ||||||||
\(975\) | −8.90442 | + | 1.27466i | −0.285170 | + | 0.0408217i | ||||
\(976\) | −51.6367 | −1.65285 | ||||||||
\(977\) | −33.1515 | + | 19.1400i | −1.06061 | + | 0.612344i | −0.925601 | − | 0.378500i | \(-0.876440\pi\) |
−0.135010 | + | 0.990844i | \(0.543107\pi\) | |||||||
\(978\) | −9.80459 | − | 16.9820i | −0.313516 | − | 0.543026i | ||||
\(979\) | −21.2253 | + | 36.7632i | −0.678362 | + | 1.17496i | ||||
\(980\) | 8.55447i | 0.273262i | ||||||||
\(981\) | −7.72680 | − | 4.46107i | −0.246698 | − | 0.142431i | ||||
\(982\) | −11.7348 | − | 6.77507i | −0.374471 | − | 0.216201i | ||||
\(983\) | 30.9632i | 0.987572i | 0.869583 | + | 0.493786i | \(0.164387\pi\) | ||||
−0.869583 | + | 0.493786i | \(0.835613\pi\) | |||||||
\(984\) | −45.2087 | + | 78.3038i | −1.44120 | + | 2.49623i | ||||
\(985\) | −13.9620 | − | 24.1830i | −0.444868 | − | 0.770534i | ||||
\(986\) | 21.3161 | − | 12.3068i | 0.678842 | − | 0.391930i | ||||
\(987\) | 12.5703 | 0.400117 | ||||||||
\(988\) | 2.46463 | + | 17.2173i | 0.0784105 | + | 0.547755i | ||||
\(989\) | −4.68894 | −0.149100 | ||||||||
\(990\) | 20.6722 | − | 11.9351i | 0.657007 | − | 0.379323i | ||||
\(991\) | 5.56474 | + | 9.63842i | 0.176770 | + | 0.306174i | 0.940772 | − | 0.339039i | \(-0.110102\pi\) |
−0.764002 | + | 0.645213i | \(0.776768\pi\) | |||||||
\(992\) | −15.2409 | + | 26.3980i | −0.483900 | + | 0.838139i | ||||
\(993\) | − | 3.00614i | − | 0.0953971i | ||||||
\(994\) | 30.9651 | + | 17.8777i | 0.982153 | + | 0.567047i | ||||
\(995\) | 16.3460 | + | 9.43739i | 0.518204 | + | 0.299185i | ||||
\(996\) | − | 7.95228i | − | 0.251978i | ||||||
\(997\) | −7.14902 | + | 12.3825i | −0.226412 | + | 0.392156i | −0.956742 | − | 0.290938i | \(-0.906033\pi\) |
0.730330 | + | 0.683094i | \(0.239366\pi\) | |||||||
\(998\) | 0.00165901 | + | 0.00287349i | 5.25151e−5 | + | 9.09588e-5i | ||||
\(999\) | −4.32400 | + | 2.49646i | −0.136805 | + | 0.0789846i |
(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 | 273.2.bd.b.127.8 | yes | 16 | |
3.2 | odd | 2 | 819.2.ct.c.127.1 | 16 | |||
13.2 | odd | 12 | 3549.2.a.bc.1.8 | 8 | |||
13.4 | even | 6 | inner | 273.2.bd.b.43.8 | ✓ | 16 | |
13.11 | odd | 12 | 3549.2.a.ba.1.1 | 8 | |||
39.17 | odd | 6 | 819.2.ct.c.316.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bd.b.43.8 | ✓ | 16 | 13.4 | even | 6 | inner | |
273.2.bd.b.127.8 | yes | 16 | 1.1 | even | 1 | trivial | |
819.2.ct.c.127.1 | 16 | 3.2 | odd | 2 | |||
819.2.ct.c.316.1 | 16 | 39.17 | odd | 6 | |||
3549.2.a.ba.1.1 | 8 | 13.11 | odd | 12 | |||
3549.2.a.bc.1.8 | 8 | 13.2 | odd | 12 |