Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(136,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.et (of order \(12\), degree \(4\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 136.5 | ||
Character | \(\chi\) | \(=\) | 819.136 |
Dual form | 819.2.et.c.271.5 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.374685 | + | 0.374685i | −0.264942 | + | 0.264942i | −0.827058 | − | 0.562116i | \(-0.809987\pi\) |
0.562116 | + | 0.827058i | \(0.309987\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.71922i | 0.859611i | ||||||||
\(5\) | 0.545981 | − | 2.03763i | 0.244170 | − | 0.911255i | −0.729629 | − | 0.683844i | \(-0.760307\pi\) |
0.973799 | − | 0.227412i | \(-0.0730263\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.03549 | + | 1.69021i | −0.769341 | + | 0.638838i | ||||
\(8\) | −1.39354 | − | 1.39354i | −0.492690 | − | 0.492690i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.558898 | + | 0.968040i | 0.176739 | + | 0.306121i | ||||
\(11\) | 0.745933 | − | 2.78386i | 0.224907 | − | 0.839366i | −0.757534 | − | 0.652795i | \(-0.773596\pi\) |
0.982442 | − | 0.186570i | \(-0.0597372\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.80107 | − | 2.27024i | 0.776877 | − | 0.629652i | ||||
\(14\) | 0.129371 | − | 1.39596i | 0.0345758 | − | 0.373086i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.39417 | −0.598543 | ||||||||
\(17\) | 3.29760 | 0.799786 | 0.399893 | − | 0.916562i | \(-0.369047\pi\) | ||||
0.399893 | + | 0.916562i | \(0.369047\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.53354 | − | 1.75066i | 1.49890 | − | 0.401628i | 0.586166 | − | 0.810191i | \(-0.300637\pi\) |
0.912730 | + | 0.408563i | \(0.133970\pi\) | |||||||
\(20\) | 3.50314 | + | 0.938663i | 0.783325 | + | 0.209891i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.763581 | + | 1.32256i | 0.162796 | + | 0.281971i | ||||
\(23\) | 7.84515i | 1.63583i | 0.575341 | + | 0.817914i | \(0.304870\pi\) | ||||
−0.575341 | + | 0.817914i | \(0.695130\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.476290 | + | 0.274986i | 0.0952579 | + | 0.0549972i | ||||
\(26\) | −0.198893 | + | 1.90015i | −0.0390061 | + | 0.372649i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.90584 | − | 3.49945i | −0.549152 | − | 0.661334i | ||||
\(29\) | −0.677462 | + | 1.17340i | −0.125802 | + | 0.217895i | −0.922046 | − | 0.387080i | \(-0.873484\pi\) |
0.796244 | + | 0.604975i | \(0.206817\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.38499 | − | 1.71085i | 1.14678 | − | 0.307278i | 0.365105 | − | 0.930966i | \(-0.381033\pi\) |
0.781673 | + | 0.623688i | \(0.214366\pi\) | |||||||
\(32\) | 3.68413 | − | 3.68413i | 0.651269 | − | 0.651269i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.23556 | + | 1.23556i | −0.211897 | + | 0.211897i | ||||
\(35\) | 2.33268 | + | 5.07039i | 0.394294 | + | 0.857052i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.87856 | + | 2.87856i | 0.473232 | + | 0.473232i | 0.902959 | − | 0.429727i | \(-0.141390\pi\) |
−0.429727 | + | 0.902959i | \(0.641390\pi\) | |||||||
\(38\) | −1.79207 | + | 3.10396i | −0.290713 | + | 0.503529i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.60036 | + | 2.07867i | −0.569266 | + | 0.328666i | ||||
\(41\) | −6.61712 | + | 1.77305i | −1.03342 | + | 0.276904i | −0.735384 | − | 0.677651i | \(-0.762998\pi\) |
−0.298036 | + | 0.954555i | \(0.596332\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.36301 | + | 2.51899i | −0.665353 | + | 0.384142i | −0.794314 | − | 0.607508i | \(-0.792169\pi\) |
0.128961 | + | 0.991650i | \(0.458836\pi\) | |||||||
\(44\) | 4.78608 | + | 1.28243i | 0.721528 | + | 0.193333i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.93946 | − | 2.93946i | −0.433400 | − | 0.433400i | ||||
\(47\) | 3.53471 | + | 0.947124i | 0.515591 | + | 0.138152i | 0.507226 | − | 0.861813i | \(-0.330671\pi\) |
0.00836456 | + | 0.999965i | \(0.497337\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.28640 | − | 6.88078i | 0.183772 | − | 0.982969i | ||||
\(50\) | −0.281492 | + | 0.0754255i | −0.0398089 | + | 0.0106668i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.90305 | + | 4.81566i | 0.541256 | + | 0.667812i | ||||
\(53\) | 3.87961 | − | 6.71968i | 0.532905 | − | 0.923019i | −0.466356 | − | 0.884597i | \(-0.654433\pi\) |
0.999262 | − | 0.0384223i | \(-0.0122332\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.26521 | − | 3.03987i | −0.709961 | − | 0.409896i | ||||
\(56\) | 5.19189 | + | 0.481159i | 0.693795 | + | 0.0642976i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.185820 | − | 0.693490i | −0.0243994 | − | 0.0910597i | ||||
\(59\) | 2.01369 | − | 2.01369i | 0.262160 | − | 0.262160i | −0.563771 | − | 0.825931i | \(-0.690650\pi\) |
0.825931 | + | 0.563771i | \(0.190650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.14962 | − | 1.81843i | −0.403267 | − | 0.232827i | 0.284625 | − | 0.958639i | \(-0.408131\pi\) |
−0.687893 | + | 0.725812i | \(0.741464\pi\) | |||||||
\(62\) | −1.75133 | + | 3.03339i | −0.222419 | + | 0.385241i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 2.02756i | − | 0.253445i | ||||||
\(65\) | −3.09658 | − | 6.94705i | −0.384084 | − | 0.861676i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.82619 | + | 0.489326i | 0.223104 | + | 0.0597807i | 0.368640 | − | 0.929572i | \(-0.379824\pi\) |
−0.145535 | + | 0.989353i | \(0.546490\pi\) | |||||||
\(68\) | 5.66931i | 0.687505i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.77382 | − | 1.02578i | −0.331534 | − | 0.122604i | ||||
\(71\) | 9.87427 | + | 2.64580i | 1.17186 | + | 0.313999i | 0.791693 | − | 0.610919i | \(-0.209200\pi\) |
0.380167 | + | 0.924918i | \(0.375866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.82296 | + | 6.80337i | 0.213361 | + | 0.796274i | 0.986737 | + | 0.162326i | \(0.0518997\pi\) |
−0.773376 | + | 0.633947i | \(0.781434\pi\) | |||||||
\(74\) | −2.15710 | −0.250758 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.00977 | + | 11.2326i | 0.345244 | + | 1.28847i | ||||
\(77\) | 3.18696 | + | 6.92729i | 0.363188 | + | 0.789438i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.13108 | − | 1.95909i | −0.127256 | − | 0.220414i | 0.795356 | − | 0.606142i | \(-0.207284\pi\) |
−0.922613 | + | 0.385728i | \(0.873950\pi\) | |||||||
\(80\) | −1.30717 | + | 4.87843i | −0.146146 | + | 0.545425i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.81500 | − | 3.14367i | 0.200433 | − | 0.347160i | ||||
\(83\) | 3.97225 | + | 3.97225i | 0.436011 | + | 0.436011i | 0.890667 | − | 0.454656i | \(-0.150238\pi\) |
−0.454656 | + | 0.890667i | \(0.650238\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.80043 | − | 6.71929i | 0.195284 | − | 0.728810i | ||||
\(86\) | 0.690929 | − | 2.57858i | 0.0745048 | − | 0.278056i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.91890 | + | 2.83993i | −0.524356 | + | 0.302737i | ||||
\(89\) | −8.73455 | + | 8.73455i | −0.925861 | + | 0.925861i | −0.997435 | − | 0.0715743i | \(-0.977198\pi\) |
0.0715743 | + | 0.997435i | \(0.477198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.86436 | + | 9.35543i | −0.195438 | + | 0.980716i | ||||
\(92\) | −13.4876 | −1.40618 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.67928 | + | 0.969531i | −0.173204 | + | 0.0999995i | ||||
\(95\) | − | 14.2688i | − | 1.46394i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.94107 | − | 14.7083i | 0.400155 | − | 1.49340i | −0.412664 | − | 0.910883i | \(-0.635402\pi\) |
0.812819 | − | 0.582516i | \(-0.197932\pi\) | |||||||
\(98\) | 2.09613 | + | 3.06012i | 0.211741 | + | 0.309119i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.472762 | + | 0.818848i | −0.0472762 | + | 0.0818848i | ||||
\(101\) | −4.18736 | − | 7.25272i | −0.416658 | − | 0.721673i | 0.578943 | − | 0.815368i | \(-0.303465\pi\) |
−0.995601 | + | 0.0936951i | \(0.970132\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.94643 | + | 6.83541i | 0.388853 | + | 0.673513i | 0.992296 | − | 0.123893i | \(-0.0395380\pi\) |
−0.603442 | + | 0.797407i | \(0.706205\pi\) | |||||||
\(104\) | −7.06706 | − | 0.739728i | −0.692982 | − | 0.0725363i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.06413 | + | 3.97140i | 0.103358 | + | 0.385736i | ||||
\(107\) | 20.0157 | 1.93499 | 0.967497 | − | 0.252883i | \(-0.0813786\pi\) | ||||
0.967497 | + | 0.252883i | \(0.0813786\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.81100 | − | 6.75874i | −0.173462 | − | 0.647370i | −0.996808 | − | 0.0798304i | \(-0.974562\pi\) |
0.823346 | − | 0.567539i | \(-0.192105\pi\) | |||||||
\(110\) | 3.11179 | − | 0.833802i | 0.296698 | − | 0.0794999i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.87330 | − | 4.04664i | 0.460483 | − | 0.382372i | ||||
\(113\) | −2.05899 | − | 3.56627i | −0.193693 | − | 0.335486i | 0.752778 | − | 0.658274i | \(-0.228713\pi\) |
−0.946471 | + | 0.322788i | \(0.895380\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.9855 | + | 4.28331i | 1.49066 | + | 0.399420i | ||||
\(116\) | −2.01733 | − | 1.16471i | −0.187305 | − | 0.108140i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.50900i | 0.138914i | ||||||||
\(119\) | −6.71223 | + | 5.57363i | −0.615309 | + | 0.510934i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.33281 | + | 1.34685i | 0.212074 | + | 0.122441i | ||||
\(122\) | 1.86145 | − | 0.498775i | 0.168528 | − | 0.0451570i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.94134 | + | 10.9772i | 0.264140 | + | 0.985783i | ||||
\(125\) | 8.27861 | − | 8.27861i | 0.740461 | − | 0.740461i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.0417 | − | 8.68434i | −1.33474 | − | 0.770611i | −0.348716 | − | 0.937229i | \(-0.613382\pi\) |
−0.986022 | + | 0.166618i | \(0.946715\pi\) | |||||||
\(128\) | 8.12796 | + | 8.12796i | 0.718417 | + | 0.718417i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.76320 | + | 1.44271i | 0.330054 | + | 0.126534i | ||||
\(131\) | −6.59348 | + | 3.80675i | −0.576075 | + | 0.332597i | −0.759572 | − | 0.650423i | \(-0.774592\pi\) |
0.183497 | + | 0.983020i | \(0.441258\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.3400 | + | 14.6065i | −0.896588 | + | 1.26654i | ||||
\(134\) | −0.867588 | + | 0.500902i | −0.0749482 | + | 0.0432714i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.59533 | − | 4.59533i | −0.394046 | − | 0.394046i | ||||
\(137\) | −11.1157 | − | 11.1157i | −0.949677 | − | 0.949677i | 0.0491165 | − | 0.998793i | \(-0.484359\pi\) |
−0.998793 | + | 0.0491165i | \(0.984359\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0562 | − | 9.27005i | 1.36187 | − | 0.786275i | 0.371996 | − | 0.928234i | \(-0.378674\pi\) |
0.989873 | + | 0.141959i | \(0.0453402\pi\) | |||||||
\(140\) | −8.71712 | + | 4.01039i | −0.736731 | + | 0.338940i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.69109 | + | 2.70840i | −0.393667 | + | 0.227284i | ||||
\(143\) | −4.23063 | − | 9.49124i | −0.353783 | − | 0.793698i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.02107 | + | 2.02107i | 0.167841 | + | 0.167841i | ||||
\(146\) | −3.23215 | − | 1.86608i | −0.267495 | − | 0.154438i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.94888 | + | 4.94888i | −0.406795 | + | 0.406795i | ||||
\(149\) | −5.71487 | − | 21.3282i | −0.468181 | − | 1.74727i | −0.646124 | − | 0.763233i | \(-0.723611\pi\) |
0.177943 | − | 0.984041i | \(-0.443056\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.2088 | + | 4.61110i | −1.40044 | + | 0.375246i | −0.878501 | − | 0.477740i | \(-0.841456\pi\) |
−0.521935 | + | 0.852986i | \(0.674789\pi\) | |||||||
\(152\) | −11.5443 | − | 6.66512i | −0.936369 | − | 0.540613i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.78966 | − | 1.40144i | −0.305379 | − | 0.112932i | ||||
\(155\) | − | 13.9443i | − | 1.12004i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.29871 | + | 1.90451i | 0.263265 | + | 0.151996i | 0.625823 | − | 0.779965i | \(-0.284763\pi\) |
−0.362558 | + | 0.931961i | \(0.618096\pi\) | |||||||
\(158\) | 1.15784 | + | 0.310242i | 0.0921127 | + | 0.0246815i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.49543 | − | 9.51836i | −0.434452 | − | 0.752493i | ||||
\(161\) | −13.2599 | − | 15.9687i | −1.04503 | − | 1.25851i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.66571 | − | 2.05402i | 0.600425 | − | 0.160883i | 0.0542114 | − | 0.998529i | \(-0.482736\pi\) |
0.546213 | + | 0.837646i | \(0.316069\pi\) | |||||||
\(164\) | −3.04827 | − | 11.3763i | −0.238030 | − | 0.888339i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.97668 | −0.231035 | ||||||||
\(167\) | 2.98897 | + | 11.1550i | 0.231294 | + | 0.863200i | 0.979785 | + | 0.200055i | \(0.0641120\pi\) |
−0.748491 | + | 0.663145i | \(0.769221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.69199 | − | 12.7182i | 0.207076 | − | 0.978325i | ||||
\(170\) | 1.84302 | + | 3.19221i | 0.141354 | + | 0.244832i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.33070 | − | 7.50099i | −0.330213 | − | 0.571945i | ||||
\(173\) | −9.52913 | + | 16.5049i | −0.724486 | + | 1.25485i | 0.234699 | + | 0.972068i | \(0.424589\pi\) |
−0.959185 | + | 0.282779i | \(0.908744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.43426 | + | 0.245298i | −0.108420 | + | 0.0185428i | ||||
\(176\) | −1.78589 | + | 6.66504i | −0.134617 | + | 0.502396i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 6.54541i | − | 0.490599i | ||||||
\(179\) | −9.39442 | + | 5.42387i | −0.702172 | + | 0.405399i | −0.808156 | − | 0.588969i | \(-0.799534\pi\) |
0.105984 | + | 0.994368i | \(0.466201\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.71631 | −0.424890 | −0.212445 | − | 0.977173i | \(-0.568143\pi\) | ||||
−0.212445 | + | 0.977173i | \(0.568143\pi\) | |||||||
\(182\) | −2.80679 | − | 4.20389i | −0.208053 | − | 0.311613i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.9325 | − | 10.9325i | 0.805955 | − | 0.805955i | ||||
\(185\) | 7.43707 | − | 4.29379i | 0.546784 | − | 0.315686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.45979 | − | 9.18007i | 0.179878 | − | 0.671313i | ||||
\(188\) | −1.62832 | + | 6.07696i | −0.118757 | + | 0.443208i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.34629 | + | 5.34629i | 0.387860 | + | 0.387860i | ||||
\(191\) | −11.5025 | + | 19.9230i | −0.832294 | + | 1.44157i | 0.0639213 | + | 0.997955i | \(0.479639\pi\) |
−0.896215 | + | 0.443620i | \(0.853694\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.29072 | + | 4.81703i | −0.0929080 | + | 0.346737i | −0.996694 | − | 0.0812474i | \(-0.974110\pi\) |
0.903786 | + | 0.427985i | \(0.140776\pi\) | |||||||
\(194\) | 4.03431 | + | 6.98763i | 0.289647 | + | 0.501683i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.8296 | + | 2.21161i | 0.844971 | + | 0.157972i | ||||
\(197\) | −1.17127 | − | 4.37125i | −0.0834496 | − | 0.311438i | 0.911566 | − | 0.411153i | \(-0.134874\pi\) |
−0.995016 | + | 0.0997145i | \(0.968207\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.8071 | −1.54587 | −0.772934 | − | 0.634487i | \(-0.781211\pi\) | ||||
−0.772934 | + | 0.634487i | \(0.781211\pi\) | |||||||
\(200\) | −0.280524 | − | 1.04693i | −0.0198361 | − | 0.0740292i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.28643 | + | 1.14855i | 0.301592 | + | 0.0808114i | ||||
\(203\) | −0.604322 | − | 3.53349i | −0.0424151 | − | 0.248002i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.4513i | 1.00932i | ||||||||
\(206\) | −4.03979 | − | 1.08246i | −0.281466 | − | 0.0754185i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.70624 | + | 5.43535i | −0.464994 | + | 0.376874i | ||||
\(209\) | − | 19.4943i | − | 1.34845i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.12257 | − | 8.87255i | 0.352652 | − | 0.610811i | −0.634061 | − | 0.773283i | \(-0.718613\pi\) |
0.986713 | + | 0.162472i | \(0.0519466\pi\) | |||||||
\(212\) | 11.5526 | + | 6.66991i | 0.793438 | + | 0.458091i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.49959 | + | 7.49959i | −0.512662 | + | 0.512662i | ||||
\(215\) | 2.75064 | + | 10.2655i | 0.187592 | + | 0.700103i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.1049 | + | 14.2744i | −0.685963 | + | 0.969007i | ||||
\(218\) | 3.21095 | + | 1.85384i | 0.217473 | + | 0.125558i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.22621 | − | 9.05207i | 0.352351 | − | 0.610290i | ||||
\(221\) | 9.23682 | − | 7.48636i | 0.621336 | − | 0.503587i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.9821 | + | 5.62213i | −1.40506 | + | 0.376486i | −0.880161 | − | 0.474675i | \(-0.842565\pi\) |
−0.524904 | + | 0.851161i | \(0.675899\pi\) | |||||||
\(224\) | −1.27205 | + | 13.7259i | −0.0849927 | + | 0.917103i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.10770 | + | 0.564756i | 0.140202 | + | 0.0375670i | ||||
\(227\) | 8.25938 | + | 8.25938i | 0.548194 | + | 0.548194i | 0.925918 | − | 0.377724i | \(-0.123293\pi\) |
−0.377724 | + | 0.925918i | \(0.623293\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.69053 | − | 1.25682i | −0.309959 | − | 0.0830532i | 0.100487 | − | 0.994938i | \(-0.467960\pi\) |
−0.410445 | + | 0.911885i | \(0.634627\pi\) | |||||||
\(230\) | −7.59442 | + | 4.38464i | −0.500761 | + | 0.289115i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.57924 | − | 0.691106i | 0.169336 | − | 0.0453733i | ||||
\(233\) | −1.91696 | + | 1.10676i | −0.125584 | + | 0.0725060i | −0.561476 | − | 0.827493i | \(-0.689766\pi\) |
0.435892 | + | 0.899999i | \(0.356433\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.85977 | − | 6.68532i | 0.251784 | − | 0.436102i | ||||
\(236\) | 3.46198 | + | 3.46198i | 0.225355 | + | 0.225355i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.426614 | − | 4.60333i | 0.0276533 | − | 0.298389i | ||||
\(239\) | 5.82013 | − | 5.82013i | 0.376473 | − | 0.376473i | −0.493355 | − | 0.869828i | \(-0.664230\pi\) |
0.869828 | + | 0.493355i | \(0.164230\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.2858 | + | 10.2858i | −0.662564 | + | 0.662564i | −0.955984 | − | 0.293420i | \(-0.905207\pi\) |
0.293420 | + | 0.955984i | \(0.405207\pi\) | |||||||
\(242\) | −1.37871 | + | 0.369425i | −0.0886271 | + | 0.0237476i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.12629 | − | 5.41490i | 0.200140 | − | 0.346653i | ||||
\(245\) | −13.3181 | − | 6.37799i | −0.850864 | − | 0.407475i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.3265 | − | 19.7364i | 0.911572 | − | 1.25580i | ||||
\(248\) | −11.2819 | − | 6.51358i | −0.716399 | − | 0.413613i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.20374i | 0.392359i | ||||||||
\(251\) | −10.7479 | − | 18.6160i | −0.678403 | − | 1.17503i | −0.975462 | − | 0.220169i | \(-0.929339\pi\) |
0.297058 | − | 0.954859i | \(-0.403994\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.8398 | + | 5.85196i | 1.37306 | + | 0.367910i | ||||
\(254\) | 8.88980 | − | 2.38201i | 0.557796 | − | 0.149461i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.03573 | −0.127233 | ||||||||
\(257\) | 7.54278 | 0.470506 | 0.235253 | − | 0.971934i | \(-0.424408\pi\) | ||||
0.235253 | + | 0.971934i | \(0.424408\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.7246 | − | 0.993906i | −0.666395 | − | 0.0617583i | ||||
\(260\) | 11.9435 | − | 5.32371i | 0.740706 | − | 0.330163i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.04415 | − | 3.89681i | 0.0645076 | − | 0.240746i | ||||
\(263\) | 11.9190 | + | 20.6443i | 0.734955 | + | 1.27298i | 0.954743 | + | 0.297432i | \(0.0961303\pi\) |
−0.219787 | + | 0.975548i | \(0.570536\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.5740 | − | 11.5740i | −0.710987 | − | 0.710987i | ||||
\(266\) | −1.59860 | − | 9.34705i | −0.0980163 | − | 0.573104i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.841260 | + | 3.13962i | −0.0513881 | + | 0.191783i | ||||
\(269\) | 27.6300i | 1.68463i | 0.538985 | + | 0.842316i | \(0.318808\pi\) | ||||
−0.538985 | + | 0.842316i | \(0.681192\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.6246 | + | 14.6246i | −0.888382 | + | 0.888382i | −0.994368 | − | 0.105986i | \(-0.966200\pi\) |
0.105986 | + | 0.994368i | \(0.466200\pi\) | |||||||
\(272\) | −7.89502 | −0.478706 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.32976 | 0.503219 | ||||||||
\(275\) | 1.12080 | − | 1.12080i | 0.0675870 | − | 0.0675870i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 8.98397i | − | 0.539795i | −0.962889 | − | 0.269897i | \(-0.913010\pi\) | ||
0.962889 | − | 0.269897i | \(-0.0869898\pi\) | |||||||
\(278\) | −2.54267 | + | 9.48936i | −0.152499 | + | 0.569134i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.81510 | − | 10.3164i | 0.227996 | − | 0.616525i | ||||
\(281\) | −13.3221 | − | 13.3221i | −0.794731 | − | 0.794731i | 0.187528 | − | 0.982259i | \(-0.439952\pi\) |
−0.982259 | + | 0.187528i | \(0.939952\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.69865 | − | 16.7985i | −0.576525 | − | 0.998570i | −0.995874 | − | 0.0907452i | \(-0.971075\pi\) |
0.419349 | − | 0.907825i | \(-0.362258\pi\) | |||||||
\(284\) | −4.54873 | + | 16.9761i | −0.269917 | + | 1.00734i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.14138 | + | 1.97107i | 0.304016 | + | 0.116552i | ||||
\(287\) | 10.4722 | − | 14.7933i | 0.618156 | − | 0.873222i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.12581 | −0.360342 | ||||||||
\(290\) | −1.51453 | −0.0889362 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.6965 | + | 3.13407i | −0.684486 | + | 0.183407i | ||||
\(293\) | 25.2467 | + | 6.76482i | 1.47493 | + | 0.395205i | 0.904617 | − | 0.426225i | \(-0.140157\pi\) |
0.570309 | + | 0.821431i | \(0.306824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.00371 | − | 5.20258i | −0.174883 | − | 0.302906i | ||||
\(296\) | − | 8.02275i | − | 0.466313i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.1326 | + | 5.85008i | 0.586967 | + | 0.338886i | ||||
\(299\) | 17.8104 | + | 21.9748i | 1.03000 | + | 1.27084i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.62324 | − | 12.5018i | 0.266479 | − | 0.720589i | ||||
\(302\) | 4.72019 | − | 8.17560i | 0.271616 | − | 0.470453i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −15.6424 | + | 4.19137i | −0.897153 | + | 0.240391i | ||||
\(305\) | −5.42493 | + | 5.42493i | −0.310630 | + | 0.310630i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.58354 | − | 1.58354i | 0.0903771 | − | 0.0903771i | −0.660473 | − | 0.750850i | \(-0.729644\pi\) |
0.750850 | + | 0.660473i | \(0.229644\pi\) | |||||||
\(308\) | −11.9096 | + | 5.47910i | −0.678610 | + | 0.312201i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.22473 | + | 5.22473i | 0.296745 | + | 0.296745i | ||||
\(311\) | 7.59574 | − | 13.1562i | 0.430715 | − | 0.746020i | −0.566220 | − | 0.824254i | \(-0.691595\pi\) |
0.996935 | + | 0.0782342i | \(0.0249282\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.66705 | + | 1.53982i | −0.150750 | + | 0.0870358i | −0.573478 | − | 0.819221i | \(-0.694406\pi\) |
0.422727 | + | 0.906257i | \(0.361073\pi\) | |||||||
\(314\) | −1.94957 | + | 0.522385i | −0.110020 | + | 0.0294799i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.36810 | − | 1.94458i | 0.189471 | − | 0.109391i | ||||
\(317\) | 7.94761 | + | 2.12956i | 0.446382 | + | 0.119608i | 0.475006 | − | 0.879982i | \(-0.342446\pi\) |
−0.0286238 | + | 0.999590i | \(0.509112\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.76124 | + | 2.76124i | 0.154600 | + | 0.154600i | ||||
\(320\) | −4.13142 | − | 1.10701i | −0.230953 | − | 0.0618838i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.9515 | + | 1.01494i | 0.610305 | + | 0.0565601i | ||||
\(323\) | 21.5450 | − | 5.77297i | 1.19880 | − | 0.321217i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.95841 | − | 0.311038i | 0.108633 | − | 0.0172533i | ||||
\(326\) | −2.10261 | + | 3.64184i | −0.116453 | + | 0.201703i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.6920 | + | 6.75038i | 0.645583 | + | 0.372728i | ||||
\(329\) | −8.79569 | + | 4.04654i | −0.484922 | + | 0.223093i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.70505 | + | 21.2915i | 0.313578 | + | 1.17029i | 0.925306 | + | 0.379221i | \(0.123808\pi\) |
−0.611728 | + | 0.791068i | \(0.709525\pi\) | |||||||
\(332\) | −6.82918 | + | 6.82918i | −0.374800 | + | 0.374800i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.29953 | − | 3.05969i | −0.289978 | − | 0.167419i | ||||
\(335\) | 1.99413 | − | 3.45393i | 0.108951 | − | 0.188709i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6.60942i | − | 0.360038i | −0.983663 | − | 0.180019i | \(-0.942384\pi\) | ||
0.983663 | − | 0.180019i | \(-0.0576159\pi\) | |||||||
\(338\) | 3.75668 | + | 5.77398i | 0.204336 | + | 0.314063i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.5520 | + | 3.09534i | 0.626493 | + | 0.167868i | ||||
\(341\) | − | 19.0511i | − | 1.03168i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.01149 | + | 16.1800i | 0.486574 | + | 0.873639i | ||||
\(344\) | 9.59032 | + | 2.56972i | 0.517075 | + | 0.138550i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.61373 | − | 9.75457i | −0.140515 | − | 0.524409i | ||||
\(347\) | −15.4106 | −0.827285 | −0.413642 | − | 0.910439i | \(-0.635744\pi\) | ||||
−0.413642 | + | 0.910439i | \(0.635744\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.658426 | + | 2.45728i | 0.0352447 | + | 0.131535i | 0.981307 | − | 0.192451i | \(-0.0616436\pi\) |
−0.946062 | + | 0.323986i | \(0.894977\pi\) | |||||||
\(350\) | 0.445488 | − | 0.629307i | 0.0238123 | − | 0.0336379i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.50800 | − | 13.0042i | −0.400178 | − | 0.693128i | ||||
\(353\) | 1.30540 | − | 4.87182i | 0.0694794 | − | 0.259301i | −0.922445 | − | 0.386127i | \(-0.873813\pi\) |
0.991925 | + | 0.126827i | \(0.0404792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.7823 | − | 18.6756i | 0.572267 | − | 0.991195i | ||||
\(356\) | −15.0166 | − | 15.0166i | −0.795880 | − | 0.795880i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.48771 | − | 5.55219i | 0.0786277 | − | 0.293443i | ||||
\(359\) | 2.50899 | − | 9.36366i | 0.132419 | − | 0.494195i | −0.867576 | − | 0.497305i | \(-0.834323\pi\) |
0.999995 | + | 0.00310948i | \(0.000989781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.1678 | − | 13.3760i | 1.21936 | − | 0.703998i | ||||
\(362\) | 2.14181 | − | 2.14181i | 0.112571 | − | 0.112571i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.0841 | − | 3.20525i | −0.843034 | − | 0.168001i | ||||
\(365\) | 14.8580 | 0.777705 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.48275 | + | 3.74282i | −0.338397 | + | 0.195373i | −0.659563 | − | 0.751649i | \(-0.729259\pi\) |
0.321166 | + | 0.947023i | \(0.395925\pi\) | |||||||
\(368\) | − | 18.7826i | − | 0.979113i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.17774 | + | 4.39538i | −0.0612277 | + | 0.228505i | ||||
\(371\) | 3.46076 | + | 20.2352i | 0.179674 | + | 1.05056i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.46898 | + | 16.4008i | −0.490285 | + | 0.849199i | −0.999937 | − | 0.0111813i | \(-0.996441\pi\) |
0.509652 | + | 0.860381i | \(0.329774\pi\) | |||||||
\(374\) | 2.51799 | + | 4.36128i | 0.130202 | + | 0.225517i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.60590 | − | 6.24561i | −0.185960 | − | 0.322092i | ||||
\(377\) | 0.766281 | + | 4.82478i | 0.0394655 | + | 0.248489i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.61698 | + | 24.6949i | 0.339891 | + | 1.26849i | 0.898468 | + | 0.439039i | \(0.144681\pi\) |
−0.558577 | + | 0.829453i | \(0.688652\pi\) | |||||||
\(380\) | 24.5312 | 1.25842 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.15501 | − | 11.7747i | −0.161424 | − | 0.602444i | ||||
\(383\) | −8.70527 | + | 2.33257i | −0.444819 | + | 0.119189i | −0.474274 | − | 0.880377i | \(-0.657289\pi\) |
0.0294554 | + | 0.999566i | \(0.490623\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.8553 | − | 2.71168i | 0.808060 | − | 0.138200i | ||||
\(386\) | −1.32126 | − | 2.28848i | −0.0672501 | − | 0.116481i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 25.2868 | + | 6.77558i | 1.28374 | + | 0.343978i | ||||
\(389\) | −24.4866 | − | 14.1373i | −1.24152 | − | 0.716792i | −0.272116 | − | 0.962264i | \(-0.587724\pi\) |
−0.969404 | + | 0.245472i | \(0.921057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.8702i | 1.30831i | ||||||||
\(392\) | −11.3813 | + | 7.79597i | −0.574841 | + | 0.393756i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.07670 | + | 1.19898i | 0.104623 | + | 0.0604038i | ||||
\(395\) | −4.60944 | + | 1.23510i | −0.231926 | + | 0.0621444i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.40344 | + | 16.4338i | 0.221002 | + | 0.824791i | 0.983967 | + | 0.178351i | \(0.0570763\pi\) |
−0.762965 | + | 0.646440i | \(0.776257\pi\) | |||||||
\(398\) | 8.17081 | − | 8.17081i | 0.409566 | − | 0.409566i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.14032 | − | 0.658363i | −0.0570159 | − | 0.0329182i | ||||
\(401\) | −4.03016 | − | 4.03016i | −0.201256 | − | 0.201256i | 0.599282 | − | 0.800538i | \(-0.295453\pi\) |
−0.800538 | + | 0.599282i | \(0.795453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.0008 | − | 19.2877i | 0.697427 | − | 0.960789i | ||||
\(404\) | 12.4690 | − | 7.19901i | 0.620358 | − | 0.358164i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.55038 | + | 1.09751i | 0.0769438 | + | 0.0544687i | ||||
\(407\) | 10.1607 | − | 5.86629i | 0.503648 | − | 0.290781i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.37498 | − | 8.37498i | −0.414116 | − | 0.414116i | 0.469054 | − | 0.883170i | \(-0.344595\pi\) |
−0.883170 | + | 0.469054i | \(0.844595\pi\) | |||||||
\(410\) | −5.41468 | − | 5.41468i | −0.267412 | − | 0.267412i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.7516 | + | 6.78479i | −0.578960 | + | 0.334262i | ||||
\(413\) | −0.695284 | + | 7.50238i | −0.0342127 | + | 0.369168i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.2627 | − | 5.92519i | 0.503778 | − | 0.290856i | ||||
\(416\) | 1.95564 | − | 18.6834i | 0.0958831 | − | 0.916029i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.30424 | + | 7.30424i | 0.357262 | + | 0.357262i | ||||
\(419\) | 9.24123 | + | 5.33542i | 0.451463 | + | 0.260653i | 0.708448 | − | 0.705763i | \(-0.249396\pi\) |
−0.256985 | + | 0.966415i | \(0.582729\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.86566 | + | 7.86566i | −0.383349 | + | 0.383349i | −0.872307 | − | 0.488958i | \(-0.837377\pi\) |
0.488958 | + | 0.872307i | \(0.337377\pi\) | |||||||
\(422\) | 1.40506 | + | 5.24376i | 0.0683973 | + | 0.255262i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.7705 | + | 3.95774i | −0.717319 | + | 0.192205i | ||||
\(425\) | 1.57061 | + | 0.906795i | 0.0761860 | + | 0.0439860i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.48453 | − | 1.62211i | 0.458989 | − | 0.0784995i | ||||
\(428\) | 34.4115i | 1.66334i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.87696 | − | 2.81571i | −0.235188 | − | 0.135786i | ||||
\(431\) | −6.29747 | − | 1.68740i | −0.303338 | − | 0.0812793i | 0.103939 | − | 0.994584i | \(-0.466855\pi\) |
−0.407278 | + | 0.913304i | \(0.633522\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.6587 | + | 20.1934i | 0.560281 | + | 0.970435i | 0.997472 | + | 0.0710664i | \(0.0226402\pi\) |
−0.437191 | + | 0.899369i | \(0.644026\pi\) | |||||||
\(434\) | −1.56225 | − | 9.13453i | −0.0749905 | − | 0.438472i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.6198 | − | 3.11351i | 0.556486 | − | 0.149110i | ||||
\(437\) | 13.7342 | + | 51.2566i | 0.656994 | + | 2.45194i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.87248 | 0.280278 | 0.140139 | − | 0.990132i | \(-0.455245\pi\) | ||||
0.140139 | + | 0.990132i | \(0.455245\pi\) | |||||||
\(440\) | 3.10109 | + | 11.5734i | 0.147839 | + | 0.551742i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.655871 | + | 6.26593i | −0.0311966 | + | 0.298040i | ||||
\(443\) | 11.2685 | + | 19.5176i | 0.535381 | + | 0.927308i | 0.999145 | + | 0.0413488i | \(0.0131655\pi\) |
−0.463763 | + | 0.885959i | \(0.653501\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.0289 | + | 22.5667i | 0.617628 | + | 1.06976i | ||||
\(446\) | 5.75515 | − | 9.96820i | 0.272514 | − | 0.472008i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.42700 | + | 4.12707i | 0.161910 | + | 0.194986i | ||||
\(449\) | 1.20603 | − | 4.50095i | 0.0569159 | − | 0.212413i | −0.931611 | − | 0.363456i | \(-0.881597\pi\) |
0.988527 | + | 0.151043i | \(0.0482632\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.7437i | 0.929695i | ||||||||
\(452\) | 6.13121 | − | 3.53986i | 0.288388 | − | 0.166501i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.18933 | −0.290480 | ||||||||
\(455\) | 18.0450 | + | 8.90676i | 0.845963 | + | 0.417556i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.2757 | + | 19.2757i | −0.901678 | + | 0.901678i | −0.995581 | − | 0.0939032i | \(-0.970066\pi\) |
0.0939032 | + | 0.995581i | \(0.470066\pi\) | |||||||
\(458\) | 2.22838 | − | 1.28656i | 0.104125 | − | 0.0601169i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.36396 | + | 27.4827i | −0.343346 | + | 1.28139i | ||||
\(461\) | 5.21155 | − | 19.4498i | 0.242726 | − | 0.905866i | −0.731787 | − | 0.681534i | \(-0.761313\pi\) |
0.974513 | − | 0.224332i | \(-0.0720200\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.95272 | + | 6.95272i | 0.323120 | + | 0.323120i | 0.849963 | − | 0.526843i | \(-0.176624\pi\) |
−0.526843 | + | 0.849963i | \(0.676624\pi\) | |||||||
\(464\) | 1.62196 | − | 2.80932i | 0.0752976 | − | 0.130419i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.303570 | − | 1.13294i | 0.0140626 | − | 0.0524824i | ||||
\(467\) | −7.90161 | − | 13.6860i | −0.365643 | − | 0.633312i | 0.623236 | − | 0.782034i | \(-0.285817\pi\) |
−0.988879 | + | 0.148722i | \(0.952484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.54424 | + | 2.09062i | −0.209834 | + | 0.0965359i | ||||
\(470\) | 1.05869 | + | 3.95109i | 0.0488338 | + | 0.182250i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.61229 | −0.258327 | ||||||||
\(473\) | 3.75799 | + | 14.0250i | 0.172793 | + | 0.644871i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.59326 | + | 0.962812i | 0.164870 | + | 0.0441768i | ||||
\(476\) | −9.58231 | − | 11.5398i | −0.439205 | − | 0.528926i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.36143i | 0.199487i | ||||||||
\(479\) | 31.8547 | + | 8.53543i | 1.45548 | + | 0.389994i | 0.897925 | − | 0.440148i | \(-0.145074\pi\) |
0.557552 | + | 0.830142i | \(0.311741\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.5981 | + | 1.52802i | 0.665615 | + | 0.0696716i | ||||
\(482\) | − | 7.70784i | − | 0.351082i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.31553 | + | 4.01062i | −0.105252 | + | 0.182301i | ||||
\(485\) | −27.8183 | − | 16.0609i | −1.26316 | − | 0.729287i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.1464 | − | 19.1464i | 0.867606 | − | 0.867606i | −0.124601 | − | 0.992207i | \(-0.539765\pi\) |
0.992207 | + | 0.124601i | \(0.0397651\pi\) | |||||||
\(488\) | 1.85506 | + | 6.92316i | 0.0839745 | + | 0.313397i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.37984 | − | 2.60037i | 0.333387 | − | 0.117473i | ||||
\(491\) | 10.9028 | + | 6.29476i | 0.492038 | + | 0.284078i | 0.725420 | − | 0.688307i | \(-0.241646\pi\) |
−0.233381 | + | 0.972385i | \(0.574979\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.23400 | + | 3.86941i | −0.100614 | + | 0.174269i | ||||
\(494\) | 2.02703 | + | 12.7629i | 0.0912002 | + | 0.574228i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.2868 | + | 4.09607i | −0.686396 | + | 0.183919i | ||||
\(497\) | −24.5709 | + | 11.3041i | −1.10216 | + | 0.507057i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.0438 | + | 6.44253i | 1.07635 | + | 0.288407i | 0.753100 | − | 0.657906i | \(-0.228558\pi\) |
0.323251 | + | 0.946313i | \(0.395224\pi\) | |||||||
\(500\) | 14.2328 | + | 14.2328i | 0.636509 | + | 0.636509i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.0022 | + | 2.94803i | 0.491052 | + | 0.131577i | ||||
\(503\) | −22.2573 | + | 12.8503i | −0.992404 | + | 0.572965i | −0.905992 | − | 0.423295i | \(-0.860873\pi\) |
−0.0864120 | + | 0.996259i | \(0.527540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.0646 | + | 4.57244i | −0.759364 | + | 0.203471i | ||||
\(506\) | −10.3757 | + | 5.99041i | −0.461256 | + | 0.266306i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.9303 | − | 25.8601i | 0.662426 | − | 1.14735i | ||||
\(509\) | −6.37261 | − | 6.37261i | −0.282461 | − | 0.282461i | 0.551629 | − | 0.834090i | \(-0.314007\pi\) |
−0.834090 | + | 0.551629i | \(0.814007\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.2097 | − | 10.7670i | −0.672837 | − | 0.476303i | ||||
\(512\) | −15.4932 | + | 15.4932i | −0.684708 | + | 0.684708i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.82617 | + | 2.82617i | −0.124657 | + | 0.124657i | ||||
\(515\) | 16.0827 | − | 4.30935i | 0.708689 | − | 0.189893i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.27332 | − | 9.13366i | 0.231920 | − | 0.401698i | ||||
\(518\) | 4.39076 | − | 3.64595i | 0.192919 | − | 0.160194i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.36577 | + | 13.9962i | −0.235305 | + | 0.613773i | ||||
\(521\) | 10.2174 | + | 5.89904i | 0.447634 | + | 0.258442i | 0.706831 | − | 0.707383i | \(-0.250124\pi\) |
−0.259196 | + | 0.965825i | \(0.583458\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 28.6286i | − | 1.25184i | −0.779888 | − | 0.625920i | \(-0.784724\pi\) | ||
0.779888 | − | 0.625920i | \(-0.215276\pi\) | |||||||
\(524\) | −6.54464 | − | 11.3357i | −0.285904 | − | 0.495200i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.2010 | − | 3.26924i | −0.531987 | − | 0.142545i | ||||
\(527\) | 21.0552 | − | 5.64172i | 0.917178 | − | 0.245757i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −38.5465 | −1.67593 | ||||||||
\(530\) | 8.67323 | 0.376741 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −25.1118 | − | 17.7767i | −1.08873 | − | 0.770717i | ||||
\(533\) | −14.5098 | + | 19.9889i | −0.628487 | + | 0.865815i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.9282 | − | 40.7846i | 0.472468 | − | 1.76327i | ||||
\(536\) | −1.86297 | − | 3.22675i | −0.0804679 | − | 0.139375i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.3525 | − | 10.3525i | −0.446330 | − | 0.446330i | ||||
\(539\) | −18.1956 | − | 8.71378i | −0.783739 | − | 0.375329i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.54336 | − | 20.6881i | 0.238328 | − | 0.889451i | −0.738293 | − | 0.674480i | \(-0.764368\pi\) |
0.976621 | − | 0.214971i | \(-0.0689655\pi\) | |||||||
\(542\) | − | 10.9592i | − | 0.470740i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.1488 | − | 12.1488i | 0.520876 | − | 0.520876i | ||||
\(545\) | −14.7606 | −0.632273 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.1223 | −1.11691 | −0.558455 | − | 0.829535i | \(-0.688606\pi\) | ||||
−0.558455 | + | 0.829535i | \(0.688606\pi\) | |||||||
\(548\) | 19.1103 | − | 19.1103i | 0.816353 | − | 0.816353i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.839896i | 0.0358133i | ||||||||
\(551\) | −2.37201 | + | 8.85245i | −0.101051 | + | 0.377127i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.61355 | + | 2.07593i | 0.238713 | + | 0.0882777i | ||||
\(554\) | 3.36616 | + | 3.36616i | 0.143014 | + | 0.143014i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.9373 | + | 27.6042i | 0.675891 | + | 1.17068i | ||||
\(557\) | −8.92401 | + | 33.3049i | −0.378123 | + | 1.41117i | 0.470606 | + | 0.882344i | \(0.344035\pi\) |
−0.848728 | + | 0.528829i | \(0.822631\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.50239 | + | 16.9610i | −0.275022 | + | 0.717372i | ||||
\(560\) | −5.58483 | − | 12.1394i | −0.236002 | − | 0.512982i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.98320 | 0.421116 | ||||||||
\(563\) | −16.0219 | −0.675243 | −0.337622 | − | 0.941282i | \(-0.609622\pi\) | ||||
−0.337622 | + | 0.941282i | \(0.609622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.39090 | + | 2.24834i | −0.353008 | + | 0.0945882i | ||||
\(566\) | 9.92810 | + | 2.66023i | 0.417309 | + | 0.111818i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.0731 | − | 17.4472i | −0.422660 | − | 0.732068i | ||||
\(569\) | 26.4737i | 1.10983i | 0.831906 | + | 0.554917i | \(0.187250\pi\) | ||||
−0.831906 | + | 0.554917i | \(0.812750\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.5784 | − | 7.83948i | −0.568237 | − | 0.328072i | 0.188208 | − | 0.982129i | \(-0.439732\pi\) |
−0.756445 | + | 0.654057i | \(0.773065\pi\) | |||||||
\(572\) | 16.3176 | − | 7.27339i | 0.682271 | − | 0.304116i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.61905 | + | 9.46662i | 0.0675777 | + | 0.395129i | ||||
\(575\) | −2.15731 | + | 3.73657i | −0.0899660 | + | 0.155826i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.1675 | − | 7.54746i | 1.17263 | − | 0.314205i | 0.380630 | − | 0.924728i | \(-0.375707\pi\) |
0.791999 | + | 0.610523i | \(0.209041\pi\) | |||||||
\(578\) | 2.29525 | − | 2.29525i | 0.0954698 | − | 0.0954698i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.47467 | + | 3.47467i | −0.144278 | + | 0.144278i | ||||
\(581\) | −14.7994 | − | 1.37153i | −0.613981 | − | 0.0569008i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.8127 | − | 15.8127i | −0.654896 | − | 0.654896i | ||||
\(584\) | 6.94038 | − | 12.0211i | 0.287195 | − | 0.497436i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.9942 | + | 6.92487i | −0.495477 | + | 0.286064i | ||||
\(587\) | −7.40030 | + | 1.98290i | −0.305443 | + | 0.0818432i | −0.408285 | − | 0.912854i | \(-0.633873\pi\) |
0.102842 | + | 0.994698i | \(0.467206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 38.7215 | − | 22.3558i | 1.59549 | − | 0.921157i | ||||
\(590\) | 3.07478 | + | 0.823884i | 0.126587 | + | 0.0339188i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.89176 | − | 6.89176i | −0.283249 | − | 0.283249i | ||||
\(593\) | 17.5955 | + | 4.71470i | 0.722561 | + | 0.193610i | 0.601314 | − | 0.799013i | \(-0.294644\pi\) |
0.121247 | + | 0.992622i | \(0.461311\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.69225 | + | 16.7201i | 0.315351 | + | 0.685458i | ||||
\(596\) | 36.6679 | − | 9.82514i | 1.50198 | − | 0.402453i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14.9069 | − | 1.56035i | −0.609590 | − | 0.0638073i | ||||
\(599\) | 7.09934 | − | 12.2964i | 0.290071 | − | 0.502418i | −0.683755 | − | 0.729712i | \(-0.739654\pi\) |
0.973826 | + | 0.227293i | \(0.0729876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.4194 | + | 6.59300i | 0.465807 | + | 0.268934i | 0.714483 | − | 0.699653i | \(-0.246662\pi\) |
−0.248676 | + | 0.968587i | \(0.579995\pi\) | |||||||
\(602\) | 2.95196 | + | 6.41648i | 0.120313 | + | 0.261516i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.92750 | − | 29.5858i | −0.322565 | − | 1.20383i | ||||
\(605\) | 4.01805 | − | 4.01805i | 0.163357 | − | 0.163357i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.77151 | + | 5.64158i | 0.396613 | + | 0.228985i | 0.685022 | − | 0.728523i | \(-0.259793\pi\) |
−0.288408 | + | 0.957508i | \(0.593126\pi\) | |||||||
\(608\) | 17.6208 | − | 30.5201i | 0.714617 | − | 1.23775i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 4.06528i | − | 0.164598i | ||||||
\(611\) | 12.0512 | − | 5.37170i | 0.487539 | − | 0.217316i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.62690 | − | 2.57952i | −0.388827 | − | 0.104186i | 0.0591091 | − | 0.998252i | \(-0.481174\pi\) |
−0.447936 | + | 0.894066i | \(0.647841\pi\) | |||||||
\(614\) | 1.18665i | 0.0478894i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.21228 | − | 14.0946i | 0.210009 | − | 0.567887i | ||||
\(617\) | −37.7991 | − | 10.1282i | −1.52173 | − | 0.407747i | −0.601422 | − | 0.798932i | \(-0.705399\pi\) |
−0.920312 | + | 0.391184i | \(0.872065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.02957 | − | 18.7706i | −0.202156 | − | 0.754455i | −0.990298 | − | 0.138962i | \(-0.955624\pi\) |
0.788142 | − | 0.615493i | \(-0.211043\pi\) | |||||||
\(620\) | 23.9734 | 0.962795 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.08342 | + | 7.77544i | 0.0835376 | + | 0.311767i | ||||
\(623\) | 3.01586 | − | 32.5423i | 0.120828 | − | 1.30378i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.9738 | − | 19.0072i | −0.438953 | − | 0.760290i | ||||
\(626\) | 0.422355 | − | 1.57625i | 0.0168807 | − | 0.0629996i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.27427 | + | 5.67121i | −0.130658 | + | 0.226306i | ||||
\(629\) | 9.49234 | + | 9.49234i | 0.378484 | + | 0.378484i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.13268 | + | 7.95928i | −0.0849008 | + | 0.316854i | −0.995295 | − | 0.0968871i | \(-0.969111\pi\) |
0.910395 | + | 0.413741i | \(0.135778\pi\) | |||||||
\(632\) | −1.15386 | + | 4.30626i | −0.0458980 | + | 0.171294i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.77576 | + | 2.17994i | −0.149955 | + | 0.0865764i | ||||
\(635\) | −25.9080 | + | 25.9080i | −1.02813 | + | 1.02813i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0177 | − | 22.1940i | −0.476160 | − | 0.879359i | ||||
\(638\) | −2.06919 | −0.0819200 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.9995 | − | 12.1241i | 0.830078 | − | 0.479246i | ||||
\(641\) | − | 39.9291i | − | 1.57710i | −0.614968 | − | 0.788552i | \(-0.710831\pi\) | ||
0.614968 | − | 0.788552i | \(-0.289169\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.71724 | − | 13.8729i | 0.146594 | − | 0.547095i | −0.853086 | − | 0.521771i | \(-0.825272\pi\) |
0.999679 | − | 0.0253239i | \(-0.00806170\pi\) | |||||||
\(644\) | 27.4537 | − | 22.7968i | 1.08183 | − | 0.898319i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.90955 | + | 10.2356i | −0.232508 | + | 0.402716i | ||||
\(647\) | −4.52657 | − | 7.84025i | −0.177958 | − | 0.308232i | 0.763223 | − | 0.646135i | \(-0.223616\pi\) |
−0.941181 | + | 0.337903i | \(0.890282\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.10375 | − | 7.10790i | −0.161086 | − | 0.279010i | ||||
\(650\) | −0.617244 | + | 0.850327i | −0.0242103 | + | 0.0333526i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.53132 | + | 13.1791i | 0.138297 | + | 0.516132i | ||||
\(653\) | −33.8493 | −1.32462 | −0.662312 | − | 0.749228i | \(-0.730425\pi\) | ||||
−0.662312 | + | 0.749228i | \(0.730425\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.15682 | + | 15.5135i | 0.162420 | + | 0.606161i | ||||
\(656\) | 15.8425 | − | 4.24499i | 0.618546 | − | 0.165739i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.77944 | − | 4.81179i | 0.0693697 | − | 0.187583i | ||||
\(659\) | −14.7702 | − | 25.5827i | −0.575365 | − | 0.996561i | −0.996002 | − | 0.0893323i | \(-0.971527\pi\) |
0.420637 | − | 0.907229i | \(-0.361807\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.8758 | − | 5.59365i | −0.811973 | − | 0.217568i | −0.171139 | − | 0.985247i | \(-0.554745\pi\) |
−0.640834 | + | 0.767679i | \(0.721411\pi\) | |||||||
\(662\) | −10.1152 | − | 5.84002i | −0.393139 | − | 0.226979i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 11.0709i | − | 0.429636i | ||||||
\(665\) | 24.1171 | + | 29.0438i | 0.935223 | + | 1.12627i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.20550 | − | 5.31480i | −0.356438 | − | 0.205790i | ||||
\(668\) | −19.1779 | + | 5.13871i | −0.742016 | + | 0.198823i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.546967 | + | 2.04131i | 0.0211312 | + | 0.0788626i | ||||
\(671\) | −7.41167 | + | 7.41167i | −0.286124 | + | 0.286124i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0862 | − | 23.1438i | −1.54521 | − | 0.892126i | −0.998497 | − | 0.0548050i | \(-0.982546\pi\) |
−0.546711 | − | 0.837321i | \(-0.684120\pi\) | |||||||
\(674\) | 2.47645 | + | 2.47645i | 0.0953893 | + | 0.0953893i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.8655 | + | 4.62813i | 0.840979 | + | 0.178005i | ||||
\(677\) | −3.29683 | + | 1.90343i | −0.126707 | + | 0.0731546i | −0.562014 | − | 0.827128i | \(-0.689973\pi\) |
0.435307 | + | 0.900282i | \(0.356640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.8380 | + | 36.5997i | 0.646184 | + | 1.40457i | ||||
\(680\) | −11.8725 | + | 6.85462i | −0.455291 | + | 0.262863i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.13816 | + | 7.13816i | 0.273334 | + | 0.273334i | ||||
\(683\) | 7.72051 | + | 7.72051i | 0.295417 | + | 0.295417i | 0.839216 | − | 0.543799i | \(-0.183015\pi\) |
−0.543799 | + | 0.839216i | \(0.683015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.7186 | + | 16.5807i | −1.09728 | + | 0.633515i | ||||
\(686\) | −9.43888 | − | 2.68594i | −0.360378 | − | 0.102550i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.4458 | − | 6.03088i | 0.398242 | − | 0.229925i | ||||
\(689\) | −4.38825 | − | 27.6300i | −0.167179 | − | 1.05262i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.3121 | − | 16.3121i | −0.620541 | − | 0.620541i | 0.325129 | − | 0.945670i | \(-0.394592\pi\) |
−0.945670 | + | 0.325129i | \(0.894592\pi\) | |||||||
\(692\) | −28.3756 | − | 16.3827i | −1.07868 | − | 0.622776i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.77412 | − | 5.77412i | 0.219183 | − | 0.219183i | ||||
\(695\) | −10.1225 | − | 37.7778i | −0.383970 | − | 1.43300i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.8206 | + | 5.84682i | −0.826515 | + | 0.221464i | ||||
\(698\) | −1.16741 | − | 0.674003i | −0.0441870 | − | 0.0255114i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.421722 | − | 2.46582i | −0.0159396 | − | 0.0931992i | ||||
\(701\) | 12.3895i | 0.467945i | 0.972243 | + | 0.233973i | \(0.0751726\pi\) | ||||
−0.972243 | + | 0.233973i | \(0.924827\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.8465 | + | 13.7678i | 0.899389 | + | 0.519262i | ||||
\(704\) | −5.64445 | − | 1.51243i | −0.212733 | − | 0.0570017i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.33628 | + | 2.31451i | 0.0502917 | + | 0.0871077i | ||||
\(707\) | 20.7819 | + | 7.68531i | 0.781584 | + | 0.289036i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.0444 | − | 6.17472i | 0.865449 | − | 0.231896i | 0.201330 | − | 0.979523i | \(-0.435474\pi\) |
0.664119 | + | 0.747627i | \(0.268807\pi\) | |||||||
\(710\) | 2.95747 | + | 11.0374i | 0.110992 | + | 0.414227i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 24.3438 | 0.912324 | ||||||||
\(713\) | 13.4219 | + | 50.0912i | 0.502654 | + | 1.87593i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.6495 | + | 3.43842i | −0.809645 | + | 0.128589i | ||||
\(716\) | −9.32484 | − | 16.1511i | −0.348486 | − | 0.603595i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.56834 | + | 4.44850i | 0.0958498 | + | 0.166017i | ||||
\(719\) | −20.8277 | + | 36.0747i | −0.776744 | + | 1.34536i | 0.157065 | + | 0.987588i | \(0.449797\pi\) |
−0.933809 | + | 0.357771i | \(0.883537\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.5862 | − | 7.24311i | −0.729427 | − | 0.269747i | ||||
\(722\) | −3.66887 | + | 13.6924i | −0.136541 | + | 0.509579i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 9.82760i | − | 0.365240i | ||||||
\(725\) | −0.645337 | + | 0.372585i | −0.0239672 | + | 0.0138375i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.5386 | 1.16970 | 0.584851 | − | 0.811141i | \(-0.301153\pi\) | ||||
0.584851 | + | 0.811141i | \(0.301153\pi\) | |||||||
\(728\) | 15.6352 | − | 10.4391i | 0.579479 | − | 0.386898i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.56708 | + | 5.56708i | −0.206047 | + | 0.206047i | ||||
\(731\) | −14.3875 | + | 8.30662i | −0.532140 | + | 0.307231i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.44436 | + | 31.5148i | −0.311899 | + | 1.16402i | 0.614942 | + | 0.788572i | \(0.289179\pi\) |
−0.926842 | + | 0.375452i | \(0.877487\pi\) | |||||||
\(734\) | 1.02661 | − | 3.83137i | 0.0378929 | − | 0.141418i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.9026 | + | 28.9026i | 1.06536 | + | 1.06536i | ||||
\(737\) | 2.72443 | − | 4.71885i | 0.100356 | − | 0.173821i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.60509 | − | 32.1146i | 0.316543 | − | 1.18136i | −0.606001 | − | 0.795464i | \(-0.707227\pi\) |
0.922544 | − | 0.385892i | \(-0.126106\pi\) | |||||||
\(740\) | 7.38199 | + | 12.7860i | 0.271367 | + | 0.470022i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.87850 | − | 6.28512i | −0.325940 | − | 0.230734i | ||||
\(743\) | −8.41303 | − | 31.3979i | −0.308644 | − | 1.15188i | −0.929763 | − | 0.368159i | \(-0.879988\pi\) |
0.621118 | − | 0.783717i | \(-0.286679\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −46.5792 | −1.70653 | ||||||||
\(746\) | −2.59723 | − | 9.69301i | −0.0950915 | − | 0.354886i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.7826 | + | 4.22893i | 0.577068 | + | 0.154625i | ||||
\(749\) | −40.7417 | + | 33.8307i | −1.48867 | + | 1.23615i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.9234i | 1.56630i | 0.621835 | + | 0.783148i | \(0.286387\pi\) | ||||
−0.621835 | + | 0.783148i | \(0.713613\pi\) | |||||||
\(752\) | −8.46271 | − | 2.26758i | −0.308603 | − | 0.0826900i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.09489 | − | 1.52066i | −0.0762912 | − | 0.0553791i | ||||
\(755\) | 37.5828i | 1.36778i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.45620 | − | 11.1825i | 0.234654 | − | 0.406433i | −0.724518 | − | 0.689256i | \(-0.757937\pi\) |
0.959172 | + | 0.282823i | \(0.0912708\pi\) | |||||||
\(758\) | −11.7321 | − | 6.77353i | −0.426129 | − | 0.246026i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.8840 | + | 19.8840i | −0.721270 | + | 0.721270i | ||||
\(761\) | −9.87024 | − | 36.8362i | −0.357796 | − | 1.33531i | −0.876929 | − | 0.480619i | \(-0.840412\pi\) |
0.519134 | − | 0.854693i | \(-0.326255\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.1099 | + | 10.6964i | 0.547016 | + | 0.387234i | ||||
\(764\) | −34.2520 | − | 19.7754i | −1.23919 | − | 0.715449i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.38776 | − | 4.13571i | 0.0862731 | − | 0.149429i | ||||
\(767\) | 1.06892 | − | 10.2120i | 0.0385965 | − | 0.368735i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.0137463 | − | 0.00368331i | 0.000495704 | − | 0.000132824i | −0.258571 | − | 0.965992i | \(-0.583252\pi\) |
0.259067 | + | 0.965859i | \(0.416585\pi\) | |||||||
\(770\) | −4.92471 | + | 6.95676i | −0.177474 | + | 0.250704i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.28154 | − | 2.21903i | −0.298059 | − | 0.0798647i | ||||
\(773\) | −12.1599 | − | 12.1599i | −0.437360 | − | 0.437360i | 0.453763 | − | 0.891123i | \(-0.350081\pi\) |
−0.891123 | + | 0.453763i | \(0.850081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.51157 | + | 0.940921i | 0.126139 | + | 0.0337989i | ||||
\(776\) | −25.9886 | + | 15.0045i | −0.932935 | + | 0.538630i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.4718 | − | 3.87771i | 0.518840 | − | 0.139023i | ||||
\(779\) | −40.1292 | + | 23.1686i | −1.43778 | + | 0.830101i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.7311 | − | 25.5150i | 0.527120 | − | 0.912999i | ||||
\(782\) | −9.69318 | − | 9.69318i | −0.346627 | − | 0.346627i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.07987 | + | 16.4738i | −0.109995 | + | 0.588349i | ||||
\(785\) | 5.68171 | − | 5.68171i | 0.202789 | − | 0.202789i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.9249 | + | 23.9249i | −0.852829 | + | 0.852829i | −0.990481 | − | 0.137652i | \(-0.956045\pi\) |
0.137652 | + | 0.990481i | \(0.456045\pi\) | |||||||
\(788\) | 7.51514 | − | 2.01368i | 0.267716 | − | 0.0717343i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.26432 | − | 2.18986i | 0.0449823 | − | 0.0779117i | ||||
\(791\) | 10.2188 | + | 3.77898i | 0.363338 | + | 0.134365i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.9506 | + | 2.05684i | −0.459889 | + | 0.0730406i | ||||
\(794\) | −7.80742 | − | 4.50761i | −0.277075 | − | 0.159969i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 37.4913i | − | 1.32884i | ||||||
\(797\) | 10.7585 | + | 18.6343i | 0.381087 | + | 0.660062i | 0.991218 | − | 0.132239i | \(-0.0422166\pi\) |
−0.610131 | + | 0.792300i | \(0.708883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.6561 | + | 3.12324i | 0.412363 | + | 0.110492i | ||||
\(800\) | 2.76780 | − | 0.741630i | 0.0978565 | − | 0.0262206i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.02008 | 0.106643 | ||||||||
\(803\) | 20.2994 | 0.716351 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −39.7780 | + | 18.3002i | −1.40199 | + | 0.644998i | ||||
\(806\) | 1.98094 | + | 12.4727i | 0.0697756 | + | 0.439332i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.27169 | + | 15.9422i | −0.150278 | + | 0.560844i | ||||
\(809\) | −1.69452 | − | 2.93499i | −0.0595761 | − | 0.103189i | 0.834699 | − | 0.550706i | \(-0.185642\pi\) |
−0.894275 | + | 0.447518i | \(0.852308\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.1944 | − | 10.1944i | −0.357974 | − | 0.357974i | 0.505092 | − | 0.863066i | \(-0.331459\pi\) |
−0.863066 | + | 0.505092i | \(0.831459\pi\) | |||||||
\(812\) | 6.07485 | − | 1.03896i | 0.213186 | − | 0.0364605i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.60906 | + | 6.00508i | −0.0563974 | + | 0.210478i | ||||
\(815\) | − | 16.7413i | − | 0.586423i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.0960 | + | 24.0960i | −0.843013 | + | 0.843013i | ||||
\(818\) | 6.27596 | 0.219434 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.8450 | −0.867624 | ||||||||
\(821\) | −2.93440 | + | 2.93440i | −0.102411 | + | 0.102411i | −0.756456 | − | 0.654045i | \(-0.773071\pi\) |
0.654045 | + | 0.756456i | \(0.273071\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.1952i | 1.74969i | 0.484399 | + | 0.874847i | \(0.339038\pi\) | ||||
−0.484399 | + | 0.874847i | \(0.660962\pi\) | |||||||
\(824\) | 4.02591 | − | 15.0249i | 0.140249 | − | 0.523417i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.55052 | − | 3.07154i | −0.0887438 | − | 0.106873i | ||||
\(827\) | −17.6628 | − | 17.6628i | −0.614195 | − | 0.614195i | 0.329842 | − | 0.944036i | \(-0.393005\pi\) |
−0.944036 | + | 0.329842i | \(0.893005\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.4016 | + | 28.4085i | 0.569652 | + | 0.986667i | 0.996600 | + | 0.0823905i | \(0.0262555\pi\) |
−0.426948 | + | 0.904276i | \(0.640411\pi\) | |||||||
\(830\) | −1.62521 | + | 6.06538i | −0.0564119 | + | 0.210532i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.60306 | − | 5.67934i | −0.159582 | − | 0.196896i | ||||
\(833\) | 4.24205 | − | 22.6901i | 0.146978 | − | 0.786165i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.3617 | 0.843071 | ||||||||
\(836\) | 33.5151 | 1.15914 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.46165 | + | 1.46345i | −0.188670 | + | 0.0505539i | ||||
\(839\) | 12.9458 | + | 3.46880i | 0.446937 | + | 0.119756i | 0.475266 | − | 0.879842i | \(-0.342352\pi\) |
−0.0283288 | + | 0.999599i | \(0.509019\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5821 | + | 23.5249i | 0.468348 | + | 0.811202i | ||||
\(842\) | − | 5.89429i | − | 0.203131i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.2539 | + | 8.80683i | 0.525060 | + | 0.303144i | ||||
\(845\) | −24.4452 | − | 12.4292i | −0.840942 | − | 0.427577i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.02486 | + | 1.20144i | −0.241377 | + | 0.0412820i | ||||
\(848\) | −9.28845 | + | 16.0881i | −0.318967 | + | 0.552466i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.928248 | + | 0.248723i | −0.0318387 | + | 0.00853114i | ||||
\(851\) | −22.5827 | + | 22.5827i | −0.774126 | + | 0.774126i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.6788 | − | 26.6788i | 0.913466 | − | 0.913466i | −0.0830772 | − | 0.996543i | \(-0.526475\pi\) |
0.996543 | + | 0.0830772i | \(0.0264748\pi\) | |||||||
\(854\) | −2.94593 | + | 4.16149i | −0.100808 | + | 0.142403i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −27.8927 | − | 27.8927i | −0.953351 | − | 0.953351i | ||||
\(857\) | 23.1022 | − | 40.0142i | 0.789156 | − | 1.36686i | −0.137328 | − | 0.990526i | \(-0.543852\pi\) |
0.926484 | − | 0.376333i | \(-0.122815\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.6394 | − | 13.6482i | 0.806565 | − | 0.465671i | −0.0391966 | − | 0.999232i | \(-0.512480\pi\) |
0.845762 | + | 0.533561i | \(0.179147\pi\) | |||||||
\(860\) | −17.6487 | + | 4.72896i | −0.601816 | + | 0.161256i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.99181 | − | 1.72732i | 0.101902 | − | 0.0588329i | ||||
\(863\) | 17.4947 | + | 4.68768i | 0.595525 | + | 0.159570i | 0.543977 | − | 0.839100i | \(-0.316918\pi\) |
0.0515479 | + | 0.998671i | \(0.483585\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.4282 | + | 28.4282i | 0.966588 | + | 0.966588i | ||||
\(866\) | −11.9345 | − | 3.19784i | −0.405551 | − | 0.108667i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −24.5408 | − | 17.3725i | −0.832970 | − | 0.589661i | ||||
\(869\) | −6.29753 | + | 1.68742i | −0.213629 | + | 0.0572418i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.22617 | − | 2.77526i | 0.210966 | − | 0.0940360i | ||||
\(872\) | −6.89486 | + | 11.9422i | −0.233489 | + | 0.404415i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.3511 | − | 14.0591i | −0.823687 | − | 0.475556i | ||||
\(875\) | −2.85843 | + | 30.8435i | −0.0966326 | + | 1.04270i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.86898 | − | 10.7072i | −0.0968786 | − | 0.361556i | 0.900419 | − | 0.435024i | \(-0.143260\pi\) |
−0.997298 | + | 0.0734680i | \(0.976593\pi\) | |||||||
\(878\) | −2.20033 | + | 2.20033i | −0.0742576 | + | 0.0742576i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12.6058 | + | 7.27797i | 0.424942 | + | 0.245340i | ||||
\(881\) | 5.59477 | − | 9.69042i | 0.188492 | − | 0.326479i | −0.756255 | − | 0.654277i | \(-0.772973\pi\) |
0.944748 | + | 0.327798i | \(0.106307\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.3449i | 1.52598i | 0.646411 | + | 0.762989i | \(0.276269\pi\) | ||||
−0.646411 | + | 0.762989i | \(0.723731\pi\) | |||||||
\(884\) | 12.8707 | + | 15.8801i | 0.432889 | + | 0.534107i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.5351 | − | 3.09081i | −0.387528 | − | 0.103838i | ||||
\(887\) | − | 37.1402i | − | 1.24704i | −0.781805 | − | 0.623522i | \(-0.785701\pi\) | ||
0.781805 | − | 0.623522i | \(-0.214299\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.2955 | − | 7.74676i | 1.51916 | − | 0.259818i | ||||
\(890\) | −13.3371 | − | 3.57367i | −0.447061 | − | 0.119790i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.66570 | − | 36.0729i | −0.323632 | − | 1.20781i | ||||
\(893\) | 24.7523 | 0.828303 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.92266 | + | 22.1037i | 0.197973 | + | 0.738845i | ||||
\(896\) | −30.2823 | − | 2.80642i | −1.01166 | − | 0.0937558i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.23456 | + | 2.13832i | 0.0411978 | + | 0.0713567i | ||||
\(899\) | −2.31808 | + | 8.65118i | −0.0773122 | + | 0.288533i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.7934 | − | 22.1588i | 0.426211 | − | 0.738218i | ||||
\(902\) | −7.39767 | − | 7.39767i | −0.246316 | − | 0.246316i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.10045 | + | 7.83900i | −0.0698601 | + | 0.260721i | ||||
\(905\) | −3.12100 | + | 11.6477i | −0.103745 | + | 0.387183i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.5915 | + | 23.4355i | −1.34782 | + | 0.778163i | −0.987940 | − | 0.154837i | \(-0.950515\pi\) |
−0.359877 | + | 0.933000i | \(0.617181\pi\) | |||||||
\(908\) | −14.1997 | + | 14.1997i | −0.471234 | + | 0.471234i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.0984 | + | 3.42396i | −0.334759 | + | 0.113503i | ||||
\(911\) | 29.2953 | 0.970596 | 0.485298 | − | 0.874349i | \(-0.338711\pi\) | ||||
0.485298 | + | 0.874349i | \(0.338711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.0212 | − | 8.09515i | 0.464035 | − | 0.267910i | ||||
\(914\) | − | 14.4446i | − | 0.477785i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.16076 | − | 8.06406i | 0.0713934 | − | 0.266444i | ||||
\(917\) | 6.98674 | − | 18.8929i | 0.230723 | − | 0.623899i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.4671 | − | 19.8616i | 0.378265 | − | 0.655173i | −0.612545 | − | 0.790435i | \(-0.709854\pi\) |
0.990810 | + | 0.135262i | \(0.0431876\pi\) | |||||||
\(920\) | −16.3075 | − | 28.2453i | −0.537641 | − | 0.931222i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.33484 | + | 9.24022i | 0.175694 | + | 0.304311i | ||||
\(923\) | 33.6652 | − | 15.0059i | 1.10810 | − | 0.493926i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.579464 | + | 2.16259i | 0.0190527 | + | 0.0711055i | ||||
\(926\) | −5.21016 | −0.171217 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.82710 | + | 6.81882i | 0.0599774 | + | 0.223839i | ||||
\(929\) | 16.2916 | − | 4.36533i | 0.534511 | − | 0.143222i | 0.0185406 | − | 0.999828i | \(-0.494098\pi\) |
0.515971 | + | 0.856606i | \(0.327431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.64111 | − | 47.2079i | −0.119333 | − | 1.54718i | ||||
\(932\) | −1.90276 | − | 3.29568i | −0.0623270 | − | 0.107953i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.08855 | + | 2.16732i | 0.264665 | + | 0.0709169i | ||||
\(935\) | −17.3626 | − | 10.0243i | −0.567817 | − | 0.327829i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 42.9957i | − | 1.40461i | −0.711877 | − | 0.702304i | \(-0.752155\pi\) | ||
0.711877 | − | 0.702304i | \(-0.247845\pi\) | |||||||
\(938\) | 0.919335 | − | 2.48598i | 0.0300174 | − | 0.0811702i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.4936 | + | 6.63581i | 0.374879 | + | 0.216436i | ||||
\(941\) | −53.4286 | + | 14.3161i | −1.74172 | + | 0.466693i | −0.982828 | − | 0.184522i | \(-0.940926\pi\) |
−0.758893 | + | 0.651215i | \(0.774260\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.9099 | − | 51.9123i | −0.452967 | − | 1.69050i | ||||
\(944\) | −4.82111 | + | 4.82111i | −0.156914 | + | 0.156914i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.66303 | − | 3.84690i | −0.216634 | − | 0.125074i | ||||
\(947\) | −20.1687 | − | 20.1687i | −0.655394 | − | 0.655394i | 0.298893 | − | 0.954287i | \(-0.403383\pi\) |
−0.954287 | + | 0.298893i | \(0.903383\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.5515 | + | 14.9182i | 0.667131 | + | 0.484264i | ||||
\(950\) | −1.70709 | + | 0.985590i | −0.0553854 | + | 0.0319768i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 17.1208 | + | 1.58667i | 0.554888 | + | 0.0514244i | ||||
\(953\) | −15.2652 | + | 8.81337i | −0.494488 | + | 0.285493i | −0.726435 | − | 0.687236i | \(-0.758824\pi\) |
0.231946 | + | 0.972729i | \(0.425491\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.3154 | + | 34.3154i | 1.11042 | + | 1.11042i | ||||
\(956\) | 10.0061 | + | 10.0061i | 0.323620 | + | 0.323620i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.1336 | + | 8.73737i | −0.488943 | + | 0.282292i | ||||
\(959\) | 41.4136 | + | 3.83801i | 1.33731 | + | 0.123936i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.9943 | − | 6.34756i | 0.354655 | − | 0.204760i | ||||
\(962\) | −6.04220 | + | 4.89715i | −0.194808 | + | 0.157891i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17.6835 | − | 17.6835i | −0.569547 | − | 0.569547i | ||||
\(965\) | 9.11061 | + | 5.26001i | 0.293281 | + | 0.169326i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.451783 | + | 0.451783i | −0.0145284 | + | 0.0145284i | −0.714334 | − | 0.699805i | \(-0.753270\pi\) |
0.699805 | + | 0.714334i | \(0.253270\pi\) | |||||||
\(968\) | −1.37397 | − | 5.12774i | −0.0441612 | − | 0.164812i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.4409 | − | 4.40531i | 0.527884 | − | 0.141446i | ||||
\(971\) | −41.6003 | − | 24.0179i | −1.33502 | − | 0.770772i | −0.348953 | − | 0.937140i | \(-0.613463\pi\) |
−0.986064 | + | 0.166368i | \(0.946796\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.0139 | + | 46.0073i | −0.545439 | + | 1.47493i | ||||
\(974\) | 14.3477i | 0.459731i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.54072 | + | 4.35364i | 0.241373 | + | 0.139357i | ||||
\(977\) | 52.7381 | + | 14.1311i | 1.68724 | + | 0.452095i | 0.969675 | − | 0.244397i | \(-0.0785899\pi\) |
0.717565 | + | 0.696491i | \(0.245257\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.8004 | + | 30.8312i | 0.568903 | + | 0.985369i | ||||
\(980\) | 10.9652 | − | 22.8968i | 0.350270 | − | 0.731412i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.44368 | + | 1.72658i | −0.205626 | + | 0.0550974i | ||||
\(983\) | 11.7532 | + | 43.8637i | 0.374870 | + | 1.39903i | 0.853534 | + | 0.521036i | \(0.174454\pi\) |
−0.478664 | + | 0.877998i | \(0.658879\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.54647 | −0.304176 | ||||||||
\(986\) | −0.612761 | − | 2.28686i | −0.0195143 | − | 0.0728283i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 33.9313 | + | 24.6304i | 1.07950 | + | 0.783598i | ||||
\(989\) | −19.7618 | − | 34.2285i | −0.628390 | − | 1.08840i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.3076 | − | 36.9058i | −0.676858 | − | 1.17235i | −0.975922 | − | 0.218119i | \(-0.930008\pi\) |
0.299064 | − | 0.954233i | \(-0.403325\pi\) | |||||||
\(992\) | 17.2201 | − | 29.8262i | 0.546740 | − | 0.946982i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.97088 | − | 13.4418i | 0.157667 | − | 0.426348i | ||||
\(995\) | −11.9063 | + | 44.4349i | −0.377455 | + | 1.40868i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 30.0295i | − | 0.951045i | −0.879704 | − | 0.475523i | \(-0.842259\pi\) | ||
0.879704 | − | 0.475523i | \(-0.157741\pi\) | |||||||
\(998\) | −11.4228 | + | 6.59495i | −0.361582 | + | 0.208759i | ||||
\(999\) | 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 | 819.2.et.c.136.5 | 36 | ||
3.2 | odd | 2 | 273.2.bt.a.136.5 | ✓ | 36 | ||
7.5 | odd | 6 | 819.2.gh.c.19.5 | 36 | |||
13.11 | odd | 12 | 819.2.gh.c.388.5 | 36 | |||
21.5 | even | 6 | 273.2.cg.a.19.5 | yes | 36 | ||
39.11 | even | 12 | 273.2.cg.a.115.5 | yes | 36 | ||
91.89 | even | 12 | inner | 819.2.et.c.271.5 | 36 | ||
273.89 | odd | 12 | 273.2.bt.a.271.5 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bt.a.136.5 | ✓ | 36 | 3.2 | odd | 2 | ||
273.2.bt.a.271.5 | yes | 36 | 273.89 | odd | 12 | ||
273.2.cg.a.19.5 | yes | 36 | 21.5 | even | 6 | ||
273.2.cg.a.115.5 | yes | 36 | 39.11 | even | 12 | ||
819.2.et.c.136.5 | 36 | 1.1 | even | 1 | trivial | ||
819.2.et.c.271.5 | 36 | 91.89 | even | 12 | inner | ||
819.2.gh.c.19.5 | 36 | 7.5 | odd | 6 | |||
819.2.gh.c.388.5 | 36 | 13.11 | odd | 12 |