Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,3,Mod(39,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.39");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.3542500457\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 39.20 | ||
Character | \(\chi\) | \(=\) | 380.39 |
Dual form | 380.3.h.a.39.19 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.68898 | + | 1.07114i | −0.844490 | + | 0.535571i | ||||
\(3\) | 5.94620 | 1.98207 | 0.991033 | − | 0.133617i | \(-0.0426591\pi\) | ||||
0.991033 | + | 0.133617i | \(0.0426591\pi\) | |||||||
\(4\) | 1.70531 | − | 3.61828i | 0.426327 | − | 0.904569i | ||||
\(5\) | 1.71987 | + | 4.69490i | 0.343974 | + | 0.938979i | ||||
\(6\) | −10.0430 | + | 6.36923i | −1.67384 | + | 1.06154i | ||||
\(7\) | −9.59523 | −1.37075 | −0.685374 | − | 0.728192i | \(-0.740361\pi\) | ||||
−0.685374 | + | 0.728192i | \(0.740361\pi\) | |||||||
\(8\) | 0.995461 | + | 7.93782i | 0.124433 | + | 0.992228i | ||||
\(9\) | 26.3573 | 2.92859 | ||||||||
\(10\) | −7.93373 | − | 6.08736i | −0.793373 | − | 0.608736i | ||||
\(11\) | 5.60839i | 0.509854i | 0.966960 | + | 0.254927i | \(0.0820514\pi\) | ||||
−0.966960 | + | 0.254927i | \(0.917949\pi\) | |||||||
\(12\) | 10.1401 | − | 21.5150i | 0.845008 | − | 1.79292i | ||||
\(13\) | − | 1.46557i | − | 0.112736i | −0.998410 | − | 0.0563682i | \(-0.982048\pi\) | ||
0.998410 | − | 0.0563682i | \(-0.0179521\pi\) | |||||||
\(14\) | 16.2062 | − | 10.2779i | 1.15758 | − | 0.734133i | ||||
\(15\) | 10.2267 | + | 27.9168i | 0.681780 | + | 1.86112i | ||||
\(16\) | −10.1839 | − | 12.3405i | −0.636491 | − | 0.771284i | ||||
\(17\) | 30.4749i | 1.79264i | 0.443404 | + | 0.896322i | \(0.353771\pi\) | ||||
−0.443404 | + | 0.896322i | \(0.646229\pi\) | |||||||
\(18\) | −44.5169 | + | 28.2324i | −2.47316 | + | 1.56847i | ||||
\(19\) | 4.35890i | 0.229416i | ||||||||
\(20\) | 19.9203 | + | 1.78326i | 0.996017 | + | 0.0891632i | ||||
\(21\) | −57.0551 | −2.71691 | ||||||||
\(22\) | −6.00738 | − | 9.47246i | −0.273063 | − | 0.430566i | ||||
\(23\) | 5.38208 | 0.234004 | 0.117002 | − | 0.993132i | \(-0.462672\pi\) | ||||
0.117002 | + | 0.993132i | \(0.462672\pi\) | |||||||
\(24\) | 5.91921 | + | 47.1999i | 0.246634 | + | 1.96666i | ||||
\(25\) | −19.0841 | + | 16.1492i | −0.763363 | + | 0.645970i | ||||
\(26\) | 1.56984 | + | 2.47533i | 0.0603784 | + | 0.0952048i | ||||
\(27\) | 103.210 | 3.82259 | ||||||||
\(28\) | −16.3628 | + | 34.7182i | −0.584386 | + | 1.23994i | ||||
\(29\) | 25.0321 | 0.863177 | 0.431589 | − | 0.902071i | \(-0.357953\pi\) | ||||
0.431589 | + | 0.902071i | \(0.357953\pi\) | |||||||
\(30\) | −47.1755 | − | 36.1966i | −1.57252 | − | 1.20655i | ||||
\(31\) | − | 26.0540i | − | 0.840453i | −0.907419 | − | 0.420226i | \(-0.861951\pi\) | ||
0.907419 | − | 0.420226i | \(-0.138049\pi\) | |||||||
\(32\) | 30.4188 | + | 9.93458i | 0.950588 | + | 0.310456i | ||||
\(33\) | 33.3486i | 1.01056i | ||||||||
\(34\) | −32.6430 | − | 51.4716i | −0.960088 | − | 1.51387i | ||||
\(35\) | −16.5026 | − | 45.0486i | −0.471502 | − | 1.28710i | ||||
\(36\) | 44.9473 | − | 95.3679i | 1.24853 | − | 2.64911i | ||||
\(37\) | − | 35.8792i | − | 0.969708i | −0.874595 | − | 0.484854i | \(-0.838873\pi\) | ||
0.874595 | − | 0.484854i | \(-0.161127\pi\) | |||||||
\(38\) | −4.66900 | − | 7.36209i | −0.122868 | − | 0.193739i | ||||
\(39\) | − | 8.71460i | − | 0.223451i | ||||||
\(40\) | −35.5552 | + | 18.3256i | −0.888880 | + | 0.458141i | ||||
\(41\) | 3.18512 | 0.0776859 | 0.0388430 | − | 0.999245i | \(-0.487633\pi\) | ||||
0.0388430 | + | 0.999245i | \(0.487633\pi\) | |||||||
\(42\) | 96.3650 | − | 61.1142i | 2.29440 | − | 1.45510i | ||||
\(43\) | 57.1393 | 1.32882 | 0.664411 | − | 0.747368i | \(-0.268683\pi\) | ||||
0.664411 | + | 0.747368i | \(0.268683\pi\) | |||||||
\(44\) | 20.2927 | + | 9.56403i | 0.461198 | + | 0.217364i | ||||
\(45\) | 45.3311 | + | 123.745i | 1.00736 | + | 2.74988i | ||||
\(46\) | −9.09023 | + | 5.76498i | −0.197614 | + | 0.125326i | ||||
\(47\) | −30.6020 | −0.651106 | −0.325553 | − | 0.945524i | \(-0.605550\pi\) | ||||
−0.325553 | + | 0.945524i | \(0.605550\pi\) | |||||||
\(48\) | −60.5552 | − | 73.3793i | −1.26157 | − | 1.52874i | ||||
\(49\) | 43.0685 | 0.878948 | ||||||||
\(50\) | 14.9345 | − | 47.7175i | 0.298690 | − | 0.954350i | ||||
\(51\) | 181.210i | 3.55314i | ||||||||
\(52\) | −5.30285 | − | 2.49925i | −0.101978 | − | 0.0480626i | ||||
\(53\) | − | 61.6843i | − | 1.16385i | −0.813241 | − | 0.581927i | \(-0.802299\pi\) | ||
0.813241 | − | 0.581927i | \(-0.197701\pi\) | |||||||
\(54\) | −174.319 | + | 110.552i | −3.22814 | + | 2.04727i | ||||
\(55\) | −26.3308 | + | 9.64571i | −0.478742 | + | 0.175377i | ||||
\(56\) | −9.55168 | − | 76.1653i | −0.170566 | − | 1.36009i | ||||
\(57\) | 25.9189i | 0.454717i | ||||||||
\(58\) | −42.2788 | + | 26.8130i | −0.728944 | + | 0.462293i | ||||
\(59\) | − | 50.5937i | − | 0.857521i | −0.903418 | − | 0.428761i | \(-0.858950\pi\) | ||
0.903418 | − | 0.428761i | \(-0.141050\pi\) | |||||||
\(60\) | 118.450 | + | 10.6036i | 1.97417 | + | 0.176727i | ||||
\(61\) | −31.5158 | −0.516652 | −0.258326 | − | 0.966058i | \(-0.583171\pi\) | ||||
−0.258326 | + | 0.966058i | \(0.583171\pi\) | |||||||
\(62\) | 27.9076 | + | 44.0047i | 0.450122 | + | 0.709754i | ||||
\(63\) | −252.904 | −4.01435 | ||||||||
\(64\) | −62.0181 | + | 15.8036i | −0.969033 | + | 0.246931i | ||||
\(65\) | 6.88072 | − | 2.52060i | 0.105857 | − | 0.0387785i | ||||
\(66\) | −35.7211 | − | 56.3251i | −0.541229 | − | 0.853411i | ||||
\(67\) | −13.4084 | −0.200125 | −0.100062 | − | 0.994981i | \(-0.531904\pi\) | ||||
−0.100062 | + | 0.994981i | \(0.531904\pi\) | |||||||
\(68\) | 110.267 | + | 51.9691i | 1.62157 | + | 0.764252i | ||||
\(69\) | 32.0029 | 0.463811 | ||||||||
\(70\) | 76.1260 | + | 58.4096i | 1.08751 | + | 0.834423i | ||||
\(71\) | 23.8999i | 0.336618i | 0.985734 | + | 0.168309i | \(0.0538306\pi\) | ||||
−0.985734 | + | 0.168309i | \(0.946169\pi\) | |||||||
\(72\) | 26.2376 | + | 209.219i | 0.364412 | + | 2.90583i | ||||
\(73\) | 63.7064i | 0.872690i | 0.899779 | + | 0.436345i | \(0.143727\pi\) | ||||
−0.899779 | + | 0.436345i | \(0.856273\pi\) | |||||||
\(74\) | 38.4317 | + | 60.5992i | 0.519348 | + | 0.818908i | ||||
\(75\) | −113.478 | + | 96.0266i | −1.51304 | + | 1.28035i | ||||
\(76\) | 15.7717 | + | 7.43326i | 0.207522 | + | 0.0978061i | ||||
\(77\) | − | 53.8138i | − | 0.698880i | ||||||
\(78\) | 9.33458 | + | 14.7188i | 0.119674 | + | 0.188702i | ||||
\(79\) | − | 57.1288i | − | 0.723149i | −0.932343 | − | 0.361574i | \(-0.882239\pi\) | ||
0.932343 | − | 0.361574i | \(-0.117761\pi\) | |||||||
\(80\) | 40.4226 | − | 69.0363i | 0.505283 | − | 0.862954i | ||||
\(81\) | 376.491 | 4.64803 | ||||||||
\(82\) | −5.37961 | + | 3.41172i | −0.0656050 | + | 0.0416063i | ||||
\(83\) | −71.3250 | −0.859338 | −0.429669 | − | 0.902987i | \(-0.641370\pi\) | ||||
−0.429669 | + | 0.902987i | \(0.641370\pi\) | |||||||
\(84\) | −97.2965 | + | 206.441i | −1.15829 | + | 2.45763i | ||||
\(85\) | −143.077 | + | 52.4130i | −1.68325 | + | 0.616623i | ||||
\(86\) | −96.5072 | + | 61.2044i | −1.12218 | + | 0.711679i | ||||
\(87\) | 148.846 | 1.71087 | ||||||||
\(88\) | −44.5184 | + | 5.58293i | −0.505891 | + | 0.0634424i | ||||
\(89\) | −7.54874 | −0.0848173 | −0.0424086 | − | 0.999100i | \(-0.513503\pi\) | ||||
−0.0424086 | + | 0.999100i | \(0.513503\pi\) | |||||||
\(90\) | −209.112 | − | 160.446i | −2.32346 | − | 1.78273i | ||||
\(91\) | 14.0625i | 0.154533i | ||||||||
\(92\) | 9.17811 | − | 19.4739i | 0.0997620 | − | 0.211673i | ||||
\(93\) | − | 154.922i | − | 1.66583i | ||||||
\(94\) | 51.6861 | − | 32.7791i | 0.549852 | − | 0.348714i | ||||
\(95\) | −20.4646 | + | 7.49675i | −0.215417 | + | 0.0789131i | ||||
\(96\) | 180.876 | + | 59.0730i | 1.88413 | + | 0.615343i | ||||
\(97\) | − | 118.660i | − | 1.22330i | −0.791128 | − | 0.611650i | \(-0.790506\pi\) | ||
0.791128 | − | 0.611650i | \(-0.209494\pi\) | |||||||
\(98\) | −72.7418 | + | 46.1325i | −0.742263 | + | 0.470739i | ||||
\(99\) | 147.822i | 1.49315i | ||||||||
\(100\) | 25.8882 | + | 96.5909i | 0.258882 | + | 0.965909i | ||||
\(101\) | 73.2975 | 0.725718 | 0.362859 | − | 0.931844i | \(-0.381801\pi\) | ||||
0.362859 | + | 0.931844i | \(0.381801\pi\) | |||||||
\(102\) | −194.102 | − | 306.060i | −1.90296 | − | 3.00059i | ||||
\(103\) | 23.4616 | 0.227782 | 0.113891 | − | 0.993493i | \(-0.463669\pi\) | ||||
0.113891 | + | 0.993493i | \(0.463669\pi\) | |||||||
\(104\) | 11.6335 | − | 1.45892i | 0.111860 | − | 0.0140281i | ||||
\(105\) | −98.1276 | − | 267.868i | −0.934548 | − | 2.55112i | ||||
\(106\) | 66.0727 | + | 104.184i | 0.623327 | + | 0.982863i | ||||
\(107\) | −95.4606 | −0.892155 | −0.446077 | − | 0.894994i | \(-0.647179\pi\) | ||||
−0.446077 | + | 0.894994i | \(0.647179\pi\) | |||||||
\(108\) | 176.004 | − | 373.442i | 1.62967 | − | 3.45779i | ||||
\(109\) | −79.3688 | −0.728154 | −0.364077 | − | 0.931369i | \(-0.618616\pi\) | ||||
−0.364077 | + | 0.931369i | \(0.618616\pi\) | |||||||
\(110\) | 34.1403 | − | 44.4955i | 0.310366 | − | 0.404504i | ||||
\(111\) | − | 213.345i | − | 1.92202i | ||||||
\(112\) | 97.7164 | + | 118.410i | 0.872468 | + | 1.05724i | ||||
\(113\) | 63.7939i | 0.564548i | 0.959334 | + | 0.282274i | \(0.0910887\pi\) | ||||
−0.959334 | + | 0.282274i | \(0.908911\pi\) | |||||||
\(114\) | −27.7628 | − | 43.7765i | −0.243533 | − | 0.384004i | ||||
\(115\) | 9.25650 | + | 25.2683i | 0.0804913 | + | 0.219725i | ||||
\(116\) | 42.6875 | − | 90.5732i | 0.367996 | − | 0.780803i | ||||
\(117\) | − | 38.6286i | − | 0.330159i | ||||||
\(118\) | 54.1931 | + | 85.4518i | 0.459264 | + | 0.724168i | ||||
\(119\) | − | 292.414i | − | 2.45726i | ||||||
\(120\) | −211.418 | + | 108.968i | −1.76182 | + | 0.908065i | ||||
\(121\) | 89.5460 | 0.740049 | ||||||||
\(122\) | 53.2295 | − | 33.7579i | 0.436308 | − | 0.276704i | ||||
\(123\) | 18.9394 | 0.153979 | ||||||||
\(124\) | −94.2707 | − | 44.4301i | −0.760248 | − | 0.358307i | ||||
\(125\) | −108.641 | − | 61.8231i | −0.869129 | − | 0.494585i | ||||
\(126\) | 427.150 | − | 270.896i | 3.39008 | − | 2.14997i | ||||
\(127\) | −24.0747 | −0.189565 | −0.0947823 | − | 0.995498i | \(-0.530216\pi\) | ||||
−0.0947823 | + | 0.995498i | \(0.530216\pi\) | |||||||
\(128\) | 87.8195 | − | 93.1222i | 0.686090 | − | 0.727517i | ||||
\(129\) | 339.762 | 2.63381 | ||||||||
\(130\) | −8.92147 | + | 11.6275i | −0.0686267 | + | 0.0894421i | ||||
\(131\) | − | 122.140i | − | 0.932367i | −0.884688 | − | 0.466184i | \(-0.845629\pi\) | ||
0.884688 | − | 0.466184i | \(-0.154371\pi\) | |||||||
\(132\) | 120.664 | + | 56.8696i | 0.914125 | + | 0.430830i | ||||
\(133\) | − | 41.8246i | − | 0.314471i | ||||||
\(134\) | 22.6464 | − | 14.3623i | 0.169003 | − | 0.107181i | ||||
\(135\) | 177.508 | + | 484.559i | 1.31487 | + | 3.58933i | ||||
\(136\) | −241.905 | + | 30.3366i | −1.77871 | + | 0.223063i | ||||
\(137\) | − | 83.0890i | − | 0.606489i | −0.952913 | − | 0.303245i | \(-0.901930\pi\) | ||
0.952913 | − | 0.303245i | \(-0.0980699\pi\) | |||||||
\(138\) | −54.0523 | + | 34.2797i | −0.391684 | + | 0.248404i | ||||
\(139\) | − | 81.3364i | − | 0.585154i | −0.956242 | − | 0.292577i | \(-0.905487\pi\) | ||
0.956242 | − | 0.292577i | \(-0.0945128\pi\) | |||||||
\(140\) | −191.140 | − | 17.1108i | −1.36529 | − | 0.122220i | ||||
\(141\) | −181.965 | −1.29053 | ||||||||
\(142\) | −25.6002 | − | 40.3664i | −0.180283 | − | 0.284270i | ||||
\(143\) | 8.21951 | 0.0574791 | ||||||||
\(144\) | −268.419 | − | 325.263i | −1.86402 | − | 2.25877i | ||||
\(145\) | 43.0521 | + | 117.523i | 0.296911 | + | 0.810505i | ||||
\(146\) | −68.2386 | − | 107.599i | −0.467388 | − | 0.736978i | ||||
\(147\) | 256.094 | 1.74213 | ||||||||
\(148\) | −129.821 | − | 61.1850i | −0.877168 | − | 0.413412i | ||||
\(149\) | 92.6290 | 0.621671 | 0.310836 | − | 0.950464i | \(-0.399391\pi\) | ||||
0.310836 | + | 0.950464i | \(0.399391\pi\) | |||||||
\(150\) | 88.8035 | − | 283.738i | 0.592023 | − | 1.89159i | ||||
\(151\) | 176.136i | 1.16646i | 0.812307 | + | 0.583231i | \(0.198212\pi\) | ||||
−0.812307 | + | 0.583231i | \(0.801788\pi\) | |||||||
\(152\) | −34.6002 | + | 4.33911i | −0.227633 | + | 0.0285468i | ||||
\(153\) | 803.236i | 5.24991i | ||||||||
\(154\) | 57.6422 | + | 90.8904i | 0.374300 | + | 0.590198i | ||||
\(155\) | 122.321 | − | 44.8096i | 0.789167 | − | 0.289094i | ||||
\(156\) | −31.5318 | − | 14.8611i | −0.202127 | − | 0.0952632i | ||||
\(157\) | 139.701i | 0.889814i | 0.895577 | + | 0.444907i | \(0.146763\pi\) | ||||
−0.895577 | + | 0.444907i | \(0.853237\pi\) | |||||||
\(158\) | 61.1930 | + | 96.4893i | 0.387298 | + | 0.610692i | ||||
\(159\) | − | 366.787i | − | 2.30684i | ||||||
\(160\) | 5.67467 | + | 159.899i | 0.0354667 | + | 0.999371i | ||||
\(161\) | −51.6423 | −0.320760 | ||||||||
\(162\) | −635.885 | + | 403.275i | −3.92522 | + | 2.48935i | ||||
\(163\) | −96.8205 | −0.593991 | −0.296995 | − | 0.954879i | \(-0.595985\pi\) | ||||
−0.296995 | + | 0.954879i | \(0.595985\pi\) | |||||||
\(164\) | 5.43161 | − | 11.5247i | 0.0331196 | − | 0.0702723i | ||||
\(165\) | −156.568 | + | 57.3553i | −0.948898 | + | 0.347608i | ||||
\(166\) | 120.467 | − | 76.3993i | 0.725702 | − | 0.460237i | ||||
\(167\) | 13.2832 | 0.0795399 | 0.0397700 | − | 0.999209i | \(-0.487337\pi\) | ||||
0.0397700 | + | 0.999209i | \(0.487337\pi\) | |||||||
\(168\) | −56.7962 | − | 452.894i | −0.338072 | − | 2.69580i | ||||
\(169\) | 166.852 | 0.987290 | ||||||||
\(170\) | 185.512 | − | 241.780i | 1.09125 | − | 1.42224i | ||||
\(171\) | 114.889i | 0.671864i | ||||||||
\(172\) | 97.4401 | − | 206.746i | 0.566512 | − | 1.20201i | ||||
\(173\) | − | 113.836i | − | 0.658014i | −0.944327 | − | 0.329007i | \(-0.893286\pi\) | ||
0.944327 | − | 0.329007i | \(-0.106714\pi\) | |||||||
\(174\) | −251.398 | + | 159.435i | −1.44482 | + | 0.916295i | ||||
\(175\) | 183.116 | − | 154.956i | 1.04638 | − | 0.885461i | ||||
\(176\) | 69.2106 | − | 57.1150i | 0.393242 | − | 0.324517i | ||||
\(177\) | − | 300.840i | − | 1.69966i | ||||||
\(178\) | 12.7497 | − | 8.08577i | 0.0716273 | − | 0.0454257i | ||||
\(179\) | − | 156.693i | − | 0.875380i | −0.899126 | − | 0.437690i | \(-0.855797\pi\) | ||
0.899126 | − | 0.437690i | \(-0.144203\pi\) | |||||||
\(180\) | 525.046 | + | 47.0020i | 2.91692 | + | 0.261122i | ||||
\(181\) | −86.4748 | −0.477761 | −0.238881 | − | 0.971049i | \(-0.576780\pi\) | ||||
−0.238881 | + | 0.971049i | \(0.576780\pi\) | |||||||
\(182\) | −15.0630 | − | 23.7513i | −0.0827636 | − | 0.130502i | ||||
\(183\) | −187.399 | −1.02404 | ||||||||
\(184\) | 5.35765 | + | 42.7220i | 0.0291177 | + | 0.232185i | ||||
\(185\) | 168.449 | − | 61.7076i | 0.910535 | − | 0.333555i | ||||
\(186\) | 165.944 | + | 261.661i | 0.892172 | + | 1.40678i | ||||
\(187\) | −170.915 | −0.913986 | ||||||||
\(188\) | −52.1858 | + | 110.726i | −0.277584 | + | 0.588970i | ||||
\(189\) | −990.322 | −5.23980 | ||||||||
\(190\) | 26.5342 | − | 34.5823i | 0.139654 | − | 0.182012i | ||||
\(191\) | − | 174.191i | − | 0.911993i | −0.889982 | − | 0.455996i | \(-0.849283\pi\) | ||
0.889982 | − | 0.455996i | \(-0.150717\pi\) | |||||||
\(192\) | −368.772 | + | 93.9713i | −1.92069 | + | 0.489434i | ||||
\(193\) | − | 361.081i | − | 1.87088i | −0.353480 | − | 0.935442i | \(-0.615002\pi\) | ||
0.353480 | − | 0.935442i | \(-0.384998\pi\) | |||||||
\(194\) | 127.102 | + | 200.415i | 0.655165 | + | 1.03307i | ||||
\(195\) | 40.9141 | − | 14.9880i | 0.209816 | − | 0.0768615i | ||||
\(196\) | 73.4449 | − | 155.834i | 0.374719 | − | 0.795069i | ||||
\(197\) | − | 97.7118i | − | 0.495999i | −0.968760 | − | 0.248000i | \(-0.920227\pi\) | ||
0.968760 | − | 0.248000i | \(-0.0797732\pi\) | |||||||
\(198\) | −158.338 | − | 249.668i | −0.799688 | − | 1.26095i | ||||
\(199\) | 305.860i | 1.53698i | 0.639860 | + | 0.768492i | \(0.278992\pi\) | ||||
−0.639860 | + | 0.768492i | \(0.721008\pi\) | |||||||
\(200\) | −147.187 | − | 135.410i | −0.735936 | − | 0.677051i | ||||
\(201\) | −79.7288 | −0.396660 | ||||||||
\(202\) | −123.798 | + | 78.5121i | −0.612862 | + | 0.388674i | ||||
\(203\) | −240.189 | −1.18320 | ||||||||
\(204\) | 655.668 | + | 309.019i | 3.21406 | + | 1.51480i | ||||
\(205\) | 5.47800 | + | 14.9538i | 0.0267220 | + | 0.0729454i | ||||
\(206\) | −39.6261 | + | 25.1307i | −0.192360 | + | 0.121994i | ||||
\(207\) | 141.857 | 0.685300 | ||||||||
\(208\) | −18.0860 | + | 14.9252i | −0.0869519 | + | 0.0717558i | ||||
\(209\) | −24.4464 | −0.116968 | ||||||||
\(210\) | 452.660 | + | 347.315i | 2.15552 | + | 1.65388i | ||||
\(211\) | − | 138.674i | − | 0.657221i | −0.944466 | − | 0.328611i | \(-0.893420\pi\) | ||
0.944466 | − | 0.328611i | \(-0.106580\pi\) | |||||||
\(212\) | −223.191 | − | 105.191i | −1.05279 | − | 0.496182i | ||||
\(213\) | 142.113i | 0.667199i | ||||||||
\(214\) | 161.231 | − | 102.252i | 0.753416 | − | 0.477813i | ||||
\(215\) | 98.2723 | + | 268.263i | 0.457081 | + | 1.24774i | ||||
\(216\) | 102.741 | + | 819.261i | 0.475654 | + | 3.79288i | ||||
\(217\) | 249.994i | 1.15205i | ||||||||
\(218\) | 134.052 | − | 85.0153i | 0.614919 | − | 0.389979i | ||||
\(219\) | 378.811i | 1.72973i | ||||||||
\(220\) | −10.0012 | + | 111.721i | −0.0454602 | + | 0.507823i | ||||
\(221\) | 44.6633 | 0.202096 | ||||||||
\(222\) | 228.523 | + | 360.335i | 1.02938 | + | 1.62313i | ||||
\(223\) | 106.512 | 0.477631 | 0.238815 | − | 0.971065i | \(-0.423241\pi\) | ||||
0.238815 | + | 0.971065i | \(0.423241\pi\) | |||||||
\(224\) | −291.876 | − | 95.3246i | −1.30302 | − | 0.425556i | ||||
\(225\) | −503.004 | + | 425.650i | −2.23558 | + | 1.89178i | ||||
\(226\) | −68.3324 | − | 107.747i | −0.302356 | − | 0.476755i | ||||
\(227\) | −214.157 | −0.943421 | −0.471710 | − | 0.881754i | \(-0.656363\pi\) | ||||
−0.471710 | + | 0.881754i | \(0.656363\pi\) | |||||||
\(228\) | 93.7817 | + | 44.1996i | 0.411323 | + | 0.193858i | ||||
\(229\) | 362.385 | 1.58247 | 0.791234 | − | 0.611513i | \(-0.209439\pi\) | ||||
0.791234 | + | 0.611513i | \(0.209439\pi\) | |||||||
\(230\) | −42.7000 | − | 32.7627i | −0.185652 | − | 0.142446i | ||||
\(231\) | − | 319.987i | − | 1.38523i | ||||||
\(232\) | 24.9185 | + | 198.701i | 0.107407 | + | 0.856469i | ||||
\(233\) | − | 313.374i | − | 1.34495i | −0.740119 | − | 0.672476i | \(-0.765231\pi\) | ||
0.740119 | − | 0.672476i | \(-0.234769\pi\) | |||||||
\(234\) | 41.3767 | + | 65.2429i | 0.176823 | + | 0.278816i | ||||
\(235\) | −52.6315 | − | 143.673i | −0.223964 | − | 0.611375i | ||||
\(236\) | −183.062 | − | 86.2779i | −0.775687 | − | 0.365584i | ||||
\(237\) | − | 339.699i | − | 1.43333i | ||||||
\(238\) | 313.217 | + | 493.882i | 1.31604 | + | 2.07513i | ||||
\(239\) | 234.305i | 0.980357i | 0.871622 | + | 0.490179i | \(0.163068\pi\) | ||||
−0.871622 | + | 0.490179i | \(0.836932\pi\) | |||||||
\(240\) | 240.361 | − | 410.504i | 1.00150 | − | 1.71043i | ||||
\(241\) | −33.4260 | −0.138697 | −0.0693485 | − | 0.997592i | \(-0.522092\pi\) | ||||
−0.0693485 | + | 0.997592i | \(0.522092\pi\) | |||||||
\(242\) | −151.241 | + | 95.9165i | −0.624964 | + | 0.396349i | ||||
\(243\) | 1309.80 | 5.39012 | ||||||||
\(244\) | −53.7441 | + | 114.033i | −0.220263 | + | 0.467348i | ||||
\(245\) | 74.0722 | + | 202.202i | 0.302336 | + | 0.825314i | ||||
\(246\) | −31.9882 | + | 20.2868i | −0.130033 | + | 0.0824665i | ||||
\(247\) | 6.38829 | 0.0258635 | ||||||||
\(248\) | 206.812 | − | 25.9358i | 0.833921 | − | 0.104580i | ||||
\(249\) | −424.113 | −1.70326 | ||||||||
\(250\) | 249.714 | − | 11.9521i | 0.998857 | − | 0.0478085i | ||||
\(251\) | 243.661i | 0.970762i | 0.874303 | + | 0.485381i | \(0.161319\pi\) | ||||
−0.874303 | + | 0.485381i | \(0.838681\pi\) | |||||||
\(252\) | −431.279 | + | 915.077i | −1.71143 | + | 3.63126i | ||||
\(253\) | 30.1848i | 0.119308i | ||||||||
\(254\) | 40.6617 | − | 25.7875i | 0.160085 | − | 0.101525i | ||||
\(255\) | −850.762 | + | 311.658i | −3.33632 | + | 1.22219i | ||||
\(256\) | −48.5782 | + | 251.349i | −0.189759 | + | 0.981831i | ||||
\(257\) | − | 25.5522i | − | 0.0994249i | −0.998764 | − | 0.0497124i | \(-0.984170\pi\) | ||
0.998764 | − | 0.0497124i | \(-0.0158305\pi\) | |||||||
\(258\) | −573.851 | + | 363.933i | −2.22423 | + | 1.41059i | ||||
\(259\) | 344.269i | 1.32922i | ||||||||
\(260\) | 2.61351 | − | 29.1947i | 0.0100520 | − | 0.112287i | ||||
\(261\) | 659.779 | 2.52789 | ||||||||
\(262\) | 130.829 | + | 206.292i | 0.499349 | + | 0.787375i | ||||
\(263\) | 70.2136 | 0.266972 | 0.133486 | − | 0.991051i | \(-0.457383\pi\) | ||||
0.133486 | + | 0.991051i | \(0.457383\pi\) | |||||||
\(264\) | −264.715 | + | 33.1972i | −1.00271 | + | 0.125747i | ||||
\(265\) | 289.601 | − | 106.089i | 1.09283 | − | 0.400336i | ||||
\(266\) | 44.8002 | + | 70.6410i | 0.168422 | + | 0.265568i | ||||
\(267\) | −44.8863 | −0.168113 | ||||||||
\(268\) | −22.8654 | + | 48.5152i | −0.0853185 | + | 0.181027i | ||||
\(269\) | 266.100 | 0.989219 | 0.494609 | − | 0.869115i | \(-0.335311\pi\) | ||||
0.494609 | + | 0.869115i | \(0.335311\pi\) | |||||||
\(270\) | −818.839 | − | 628.275i | −3.03274 | − | 2.32694i | ||||
\(271\) | − | 38.6132i | − | 0.142484i | −0.997459 | − | 0.0712421i | \(-0.977304\pi\) | ||
0.997459 | − | 0.0712421i | \(-0.0226963\pi\) | |||||||
\(272\) | 376.077 | − | 310.352i | 1.38264 | − | 1.14100i | ||||
\(273\) | 83.6186i | 0.306295i | ||||||||
\(274\) | 89.0002 | + | 140.336i | 0.324818 | + | 0.512174i | ||||
\(275\) | −90.5712 | − | 107.031i | −0.329350 | − | 0.389203i | ||||
\(276\) | 54.5748 | − | 115.796i | 0.197735 | − | 0.419549i | ||||
\(277\) | − | 358.921i | − | 1.29574i | −0.761750 | − | 0.647872i | \(-0.775659\pi\) | ||
0.761750 | − | 0.647872i | \(-0.224341\pi\) | |||||||
\(278\) | 87.1229 | + | 137.376i | 0.313392 | + | 0.494157i | ||||
\(279\) | − | 686.713i | − | 2.46134i | ||||||
\(280\) | 341.160 | − | 175.839i | 1.21843 | − | 0.627995i | ||||
\(281\) | 268.327 | 0.954901 | 0.477450 | − | 0.878659i | \(-0.341561\pi\) | ||||
0.477450 | + | 0.878659i | \(0.341561\pi\) | |||||||
\(282\) | 307.336 | − | 194.911i | 1.08984 | − | 0.691173i | ||||
\(283\) | −421.545 | −1.48956 | −0.744779 | − | 0.667311i | \(-0.767445\pi\) | ||||
−0.744779 | + | 0.667311i | \(0.767445\pi\) | |||||||
\(284\) | 86.4763 | + | 40.7566i | 0.304494 | + | 0.143509i | ||||
\(285\) | −121.686 | + | 44.5772i | −0.426970 | + | 0.156411i | ||||
\(286\) | −13.8826 | + | 8.80427i | −0.0485405 | + | 0.0307842i | ||||
\(287\) | −30.5620 | −0.106488 | ||||||||
\(288\) | 801.757 | + | 261.848i | 2.78388 | + | 0.909196i | ||||
\(289\) | −639.722 | −2.21357 | ||||||||
\(290\) | −198.598 | − | 152.380i | −0.684822 | − | 0.525447i | ||||
\(291\) | − | 705.577i | − | 2.42466i | ||||||
\(292\) | 230.507 | + | 108.639i | 0.789409 | + | 0.372051i | ||||
\(293\) | 291.588i | 0.995181i | 0.867412 | + | 0.497591i | \(0.165782\pi\) | ||||
−0.867412 | + | 0.497591i | \(0.834218\pi\) | |||||||
\(294\) | −432.537 | + | 274.313i | −1.47121 | + | 0.933037i | ||||
\(295\) | 237.532 | − | 87.0148i | 0.805194 | − | 0.294965i | ||||
\(296\) | 284.803 | − | 35.7163i | 0.962171 | − | 0.120663i | ||||
\(297\) | 578.841i | 1.94896i | ||||||||
\(298\) | −156.449 | + | 99.2189i | −0.524995 | + | 0.332949i | ||||
\(299\) | − | 7.88784i | − | 0.0263808i | ||||||
\(300\) | 153.936 | + | 574.349i | 0.513121 | + | 1.91450i | ||||
\(301\) | −548.265 | −1.82148 | ||||||||
\(302\) | −188.666 | − | 297.490i | −0.624723 | − | 0.985065i | ||||
\(303\) | 435.842 | 1.43842 | ||||||||
\(304\) | 53.7912 | − | 44.3904i | 0.176945 | − | 0.146021i | ||||
\(305\) | −54.2031 | − | 147.963i | −0.177715 | − | 0.485126i | ||||
\(306\) | −860.381 | − | 1356.65i | −2.81170 | − | 4.43350i | ||||
\(307\) | 320.420 | 1.04371 | 0.521856 | − | 0.853033i | \(-0.325240\pi\) | ||||
0.521856 | + | 0.853033i | \(0.325240\pi\) | |||||||
\(308\) | −194.713 | − | 91.7690i | −0.632186 | − | 0.297951i | ||||
\(309\) | 139.507 | 0.451479 | ||||||||
\(310\) | −158.600 | + | 206.706i | −0.511613 | + | 0.666793i | ||||
\(311\) | 539.671i | 1.73528i | 0.497195 | + | 0.867639i | \(0.334363\pi\) | ||||
−0.497195 | + | 0.867639i | \(0.665637\pi\) | |||||||
\(312\) | 69.1749 | − | 8.67504i | 0.221715 | − | 0.0278046i | ||||
\(313\) | − | 340.685i | − | 1.08845i | −0.838940 | − | 0.544225i | \(-0.816824\pi\) | ||
0.838940 | − | 0.544225i | \(-0.183176\pi\) | |||||||
\(314\) | −149.640 | − | 235.952i | −0.476559 | − | 0.751439i | ||||
\(315\) | −434.963 | − | 1187.36i | −1.38083 | − | 3.76939i | ||||
\(316\) | −206.708 | − | 97.4221i | −0.654138 | − | 0.308298i | ||||
\(317\) | 459.485i | 1.44948i | 0.689022 | + | 0.724740i | \(0.258040\pi\) | ||||
−0.689022 | + | 0.724740i | \(0.741960\pi\) | |||||||
\(318\) | 392.881 | + | 619.496i | 1.23548 | + | 1.94810i | ||||
\(319\) | 140.390i | 0.440094i | ||||||||
\(320\) | −180.859 | − | 263.988i | −0.565186 | − | 0.824964i | ||||
\(321\) | −567.628 | −1.76831 | ||||||||
\(322\) | 87.2229 | − | 55.3163i | 0.270879 | − | 0.171790i | ||||
\(323\) | −132.837 | −0.411261 | ||||||||
\(324\) | 642.032 | − | 1362.25i | 1.98158 | − | 4.20447i | ||||
\(325\) | 23.6679 | + | 27.9691i | 0.0728243 | + | 0.0860589i | ||||
\(326\) | 163.528 | − | 103.709i | 0.501619 | − | 0.318124i | ||||
\(327\) | −471.943 | −1.44325 | ||||||||
\(328\) | 3.17066 | + | 25.2829i | 0.00966666 | + | 0.0770821i | ||||
\(329\) | 293.633 | 0.892501 | ||||||||
\(330\) | 203.005 | − | 264.579i | 0.615166 | − | 0.801754i | ||||
\(331\) | − | 389.319i | − | 1.17619i | −0.808792 | − | 0.588095i | \(-0.799878\pi\) | ||
0.808792 | − | 0.588095i | \(-0.200122\pi\) | |||||||
\(332\) | −121.631 | + | 258.074i | −0.366359 | + | 0.777330i | ||||
\(333\) | − | 945.678i | − | 2.83987i | ||||||
\(334\) | −22.4350 | + | 14.2282i | −0.0671707 | + | 0.0425993i | ||||
\(335\) | −23.0607 | − | 62.9508i | −0.0688378 | − | 0.187913i | ||||
\(336\) | 581.041 | + | 704.092i | 1.72929 | + | 2.09551i | ||||
\(337\) | 81.0640i | 0.240546i | 0.992741 | + | 0.120273i | \(0.0383770\pi\) | ||||
−0.992741 | + | 0.120273i | \(0.961623\pi\) | |||||||
\(338\) | −281.810 | + | 178.722i | −0.833757 | + | 0.528764i | ||||
\(339\) | 379.331i | 1.11897i | ||||||||
\(340\) | −54.3449 | + | 607.071i | −0.159838 | + | 1.78550i | ||||
\(341\) | 146.121 | 0.428508 | ||||||||
\(342\) | −123.062 | − | 194.045i | −0.359831 | − | 0.567382i | ||||
\(343\) | 56.9146 | 0.165932 | ||||||||
\(344\) | 56.8800 | + | 453.562i | 0.165349 | + | 1.31849i | ||||
\(345\) | 55.0410 | + | 150.250i | 0.159539 | + | 0.435509i | ||||
\(346\) | 121.935 | + | 192.268i | 0.352414 | + | 0.555687i | ||||
\(347\) | −387.114 | −1.11560 | −0.557801 | − | 0.829975i | \(-0.688355\pi\) | ||||
−0.557801 | + | 0.829975i | \(0.688355\pi\) | |||||||
\(348\) | 253.828 | − | 538.566i | 0.729391 | − | 1.54760i | ||||
\(349\) | −529.262 | −1.51651 | −0.758255 | − | 0.651959i | \(-0.773948\pi\) | ||||
−0.758255 | + | 0.651959i | \(0.773948\pi\) | |||||||
\(350\) | −143.300 | + | 457.861i | −0.409428 | + | 1.30817i | ||||
\(351\) | − | 151.262i | − | 0.430945i | ||||||
\(352\) | −55.7170 | + | 170.601i | −0.158287 | + | 0.484661i | ||||
\(353\) | 95.5466i | 0.270670i | 0.990800 | + | 0.135335i | \(0.0432111\pi\) | ||||
−0.990800 | + | 0.135335i | \(0.956789\pi\) | |||||||
\(354\) | 322.243 | + | 508.113i | 0.910291 | + | 1.43535i | ||||
\(355\) | −112.207 | + | 41.1047i | −0.316077 | + | 0.115788i | ||||
\(356\) | −12.8729 | + | 27.3134i | −0.0361599 | + | 0.0767231i | ||||
\(357\) | − | 1738.75i | − | 4.87045i | ||||||
\(358\) | 167.841 | + | 264.651i | 0.468828 | + | 0.739249i | ||||
\(359\) | − | 180.861i | − | 0.503790i | −0.967755 | − | 0.251895i | \(-0.918946\pi\) | ||
0.967755 | − | 0.251895i | \(-0.0810538\pi\) | |||||||
\(360\) | −937.138 | + | 483.014i | −2.60316 | + | 1.34170i | ||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | 146.054 | − | 92.6268i | 0.403465 | − | 0.255875i | ||||
\(363\) | 532.458 | 1.46683 | ||||||||
\(364\) | 50.8821 | + | 23.9809i | 0.139786 | + | 0.0658817i | ||||
\(365\) | −299.095 | + | 109.567i | −0.819438 | + | 0.300183i | ||||
\(366\) | 316.513 | − | 200.731i | 0.864791 | − | 0.548446i | ||||
\(367\) | −300.710 | −0.819373 | −0.409686 | − | 0.912226i | \(-0.634362\pi\) | ||||
−0.409686 | + | 0.912226i | \(0.634362\pi\) | |||||||
\(368\) | −54.8104 | − | 66.4179i | −0.148941 | − | 0.180483i | ||||
\(369\) | 83.9512 | 0.227510 | ||||||||
\(370\) | −218.409 | + | 284.656i | −0.590296 | + | 0.769340i | ||||
\(371\) | 591.875i | 1.59535i | ||||||||
\(372\) | −560.552 | − | 264.190i | −1.50686 | − | 0.710189i | ||||
\(373\) | 612.828i | 1.64297i | 0.570229 | + | 0.821486i | \(0.306854\pi\) | ||||
−0.570229 | + | 0.821486i | \(0.693146\pi\) | |||||||
\(374\) | 288.673 | − | 183.075i | 0.771852 | − | 0.489505i | ||||
\(375\) | −646.002 | − | 367.613i | −1.72267 | − | 0.980300i | ||||
\(376\) | −30.4631 | − | 242.913i | −0.0810188 | − | 0.646045i | ||||
\(377\) | − | 36.6865i | − | 0.0973116i | ||||||
\(378\) | 1672.63 | − | 1060.78i | 4.42496 | − | 2.80629i | ||||
\(379\) | 45.3764i | 0.119727i | 0.998207 | + | 0.0598633i | \(0.0190665\pi\) | ||||
−0.998207 | + | 0.0598633i | \(0.980934\pi\) | |||||||
\(380\) | −7.77307 | + | 86.8308i | −0.0204555 | + | 0.228502i | ||||
\(381\) | −143.153 | −0.375730 | ||||||||
\(382\) | 186.583 | + | 294.205i | 0.488437 | + | 0.770169i | ||||
\(383\) | −454.950 | −1.18786 | −0.593930 | − | 0.804517i | \(-0.702424\pi\) | ||||
−0.593930 | + | 0.804517i | \(0.702424\pi\) | |||||||
\(384\) | 522.192 | − | 553.723i | 1.35987 | − | 1.44199i | ||||
\(385\) | 252.650 | − | 92.5528i | 0.656234 | − | 0.240397i | ||||
\(386\) | 386.769 | + | 609.858i | 1.00199 | + | 1.57994i | ||||
\(387\) | 1506.04 | 3.89157 | ||||||||
\(388\) | −429.345 | − | 202.352i | −1.10656 | − | 0.521526i | ||||
\(389\) | 375.923 | 0.966382 | 0.483191 | − | 0.875515i | \(-0.339478\pi\) | ||||
0.483191 | + | 0.875515i | \(0.339478\pi\) | |||||||
\(390\) | −53.0489 | + | 69.1393i | −0.136023 | + | 0.177280i | ||||
\(391\) | 164.019i | 0.419485i | ||||||||
\(392\) | 42.8730 | + | 341.870i | 0.109370 | + | 0.872117i | ||||
\(393\) | − | 726.269i | − | 1.84801i | ||||||
\(394\) | 104.663 | + | 165.033i | 0.265643 | + | 0.418866i | ||||
\(395\) | 268.214 | − | 98.2542i | 0.679022 | − | 0.248745i | ||||
\(396\) | 534.860 | + | 252.082i | 1.35066 | + | 0.636570i | ||||
\(397\) | 234.640i | 0.591033i | 0.955338 | + | 0.295516i | \(0.0954917\pi\) | ||||
−0.955338 | + | 0.295516i | \(0.904508\pi\) | |||||||
\(398\) | −327.619 | − | 516.591i | −0.823164 | − | 1.29797i | ||||
\(399\) | − | 248.698i | − | 0.623302i | ||||||
\(400\) | 393.640 | + | 71.0465i | 0.984100 | + | 0.177616i | ||||
\(401\) | 370.607 | 0.924207 | 0.462103 | − | 0.886826i | \(-0.347095\pi\) | ||||
0.462103 | + | 0.886826i | \(0.347095\pi\) | |||||||
\(402\) | 134.660 | − | 85.4009i | 0.334976 | − | 0.212440i | ||||
\(403\) | −38.1841 | −0.0947497 | ||||||||
\(404\) | 124.995 | − | 265.211i | 0.309393 | − | 0.656462i | ||||
\(405\) | 647.516 | + | 1767.58i | 1.59880 | + | 4.36440i | ||||
\(406\) | 405.675 | − | 257.277i | 0.999199 | − | 0.633687i | ||||
\(407\) | 201.224 | 0.494409 | ||||||||
\(408\) | −1438.41 | + | 180.387i | −3.52552 | + | 0.442126i | ||||
\(409\) | 47.8575 | 0.117011 | 0.0585055 | − | 0.998287i | \(-0.481366\pi\) | ||||
0.0585055 | + | 0.998287i | \(0.481366\pi\) | |||||||
\(410\) | −25.2699 | − | 19.3890i | −0.0616339 | − | 0.0472902i | ||||
\(411\) | − | 494.064i | − | 1.20210i | ||||||
\(412\) | 40.0092 | − | 84.8904i | 0.0971096 | − | 0.206045i | ||||
\(413\) | 485.459i | 1.17544i | ||||||||
\(414\) | −239.594 | + | 151.949i | −0.578729 | + | 0.367027i | ||||
\(415\) | −122.670 | − | 334.864i | −0.295590 | − | 0.806900i | ||||
\(416\) | 14.5599 | − | 44.5810i | 0.0349997 | − | 0.107166i | ||||
\(417\) | − | 483.642i | − | 1.15981i | ||||||
\(418\) | 41.2895 | − | 26.1856i | 0.0987787 | − | 0.0626449i | ||||
\(419\) | 27.2392i | 0.0650101i | 0.999472 | + | 0.0325050i | \(0.0103485\pi\) | ||||
−0.999472 | + | 0.0325050i | \(0.989652\pi\) | |||||||
\(420\) | −1136.56 | − | 101.744i | −2.70609 | − | 0.242249i | ||||
\(421\) | −478.944 | −1.13763 | −0.568817 | − | 0.822464i | \(-0.692599\pi\) | ||||
−0.568817 | + | 0.822464i | \(0.692599\pi\) | |||||||
\(422\) | 148.539 | + | 234.217i | 0.351989 | + | 0.555017i | ||||
\(423\) | −806.585 | −1.90682 | ||||||||
\(424\) | 489.639 | − | 61.4043i | 1.15481 | − | 0.144821i | ||||
\(425\) | −492.147 | − | 581.586i | −1.15799 | − | 1.36844i | ||||
\(426\) | −152.224 | − | 240.027i | −0.357333 | − | 0.563443i | ||||
\(427\) | 302.401 | 0.708200 | ||||||||
\(428\) | −162.790 | + | 345.403i | −0.380350 | + | 0.807016i | ||||
\(429\) | 48.8749 | 0.113927 | ||||||||
\(430\) | −453.328 | − | 347.827i | −1.05425 | − | 0.808901i | ||||
\(431\) | 637.923i | 1.48010i | 0.672552 | + | 0.740050i | \(0.265198\pi\) | ||||
−0.672552 | + | 0.740050i | \(0.734802\pi\) | |||||||
\(432\) | −1051.07 | − | 1273.67i | −2.43304 | − | 2.94830i | ||||
\(433\) | 616.138i | 1.42295i | 0.702711 | + | 0.711476i | \(0.251973\pi\) | ||||
−0.702711 | + | 0.711476i | \(0.748027\pi\) | |||||||
\(434\) | −267.780 | − | 422.236i | −0.617004 | − | 0.972893i | ||||
\(435\) | 255.996 | + | 698.817i | 0.588497 | + | 1.60647i | ||||
\(436\) | −135.348 | + | 287.178i | −0.310432 | + | 0.658666i | ||||
\(437\) | 23.4600i | 0.0536841i | ||||||||
\(438\) | −405.760 | − | 639.804i | −0.926394 | − | 1.46074i | ||||
\(439\) | − | 329.983i | − | 0.751669i | −0.926687 | − | 0.375834i | \(-0.877356\pi\) | ||
0.926687 | − | 0.375834i | \(-0.122644\pi\) | |||||||
\(440\) | −102.777 | − | 199.407i | −0.233585 | − | 0.453199i | ||||
\(441\) | 1135.17 | 2.57408 | ||||||||
\(442\) | −75.4354 | + | 47.8408i | −0.170668 | + | 0.108237i | ||||
\(443\) | −253.518 | −0.572274 | −0.286137 | − | 0.958189i | \(-0.592371\pi\) | ||||
−0.286137 | + | 0.958189i | \(0.592371\pi\) | |||||||
\(444\) | −771.940 | − | 363.818i | −1.73860 | − | 0.819411i | ||||
\(445\) | −12.9829 | − | 35.4405i | −0.0291750 | − | 0.0796416i | ||||
\(446\) | −179.896 | + | 114.089i | −0.403354 | + | 0.255805i | ||||
\(447\) | 550.791 | 1.23219 | ||||||||
\(448\) | 595.078 | − | 151.639i | 1.32830 | − | 0.338480i | ||||
\(449\) | 377.768 | 0.841354 | 0.420677 | − | 0.907210i | \(-0.361793\pi\) | ||||
0.420677 | + | 0.907210i | \(0.361793\pi\) | |||||||
\(450\) | 393.633 | − | 1257.70i | 0.874739 | − | 2.79490i | ||||
\(451\) | 17.8634i | 0.0396084i | ||||||||
\(452\) | 230.824 | + | 108.788i | 0.510673 | + | 0.240682i | ||||
\(453\) | 1047.34i | 2.31200i | ||||||||
\(454\) | 361.706 | − | 229.392i | 0.796709 | − | 0.505269i | ||||
\(455\) | −66.0221 | + | 24.1857i | −0.145103 | + | 0.0531555i | ||||
\(456\) | −205.740 | + | 25.8012i | −0.451183 | + | 0.0565816i | ||||
\(457\) | 439.338i | 0.961353i | 0.876898 | + | 0.480677i | \(0.159609\pi\) | ||||
−0.876898 | + | 0.480677i | \(0.840391\pi\) | |||||||
\(458\) | −612.061 | + | 388.166i | −1.33638 | + | 0.847525i | ||||
\(459\) | 3145.31i | 6.85253i | ||||||||
\(460\) | 107.213 | + | 9.59768i | 0.233072 | + | 0.0208645i | ||||
\(461\) | −384.916 | −0.834958 | −0.417479 | − | 0.908687i | \(-0.637086\pi\) | ||||
−0.417479 | + | 0.908687i | \(0.637086\pi\) | |||||||
\(462\) | 342.752 | + | 540.452i | 0.741888 | + | 1.16981i | ||||
\(463\) | −684.264 | −1.47789 | −0.738946 | − | 0.673764i | \(-0.764676\pi\) | ||||
−0.738946 | + | 0.673764i | \(0.764676\pi\) | |||||||
\(464\) | −254.924 | − | 308.910i | −0.549404 | − | 0.665755i | ||||
\(465\) | 727.345 | − | 266.447i | 1.56418 | − | 0.573004i | ||||
\(466\) | 335.668 | + | 529.282i | 0.720318 | + | 1.13580i | ||||
\(467\) | 871.751 | 1.86670 | 0.933352 | − | 0.358963i | \(-0.116869\pi\) | ||||
0.933352 | + | 0.358963i | \(0.116869\pi\) | |||||||
\(468\) | −139.769 | − | 65.8735i | −0.298651 | − | 0.140755i | ||||
\(469\) | 128.656 | 0.274320 | ||||||||
\(470\) | 242.788 | + | 186.285i | 0.516570 | + | 0.396351i | ||||
\(471\) | 830.689i | 1.76367i | ||||||||
\(472\) | 401.604 | − | 50.3641i | 0.850856 | − | 0.106704i | ||||
\(473\) | 320.460i | 0.677505i | ||||||||
\(474\) | 363.866 | + | 573.745i | 0.767650 | + | 1.21043i | ||||
\(475\) | −70.3929 | − | 83.1856i | −0.148196 | − | 0.175128i | ||||
\(476\) | −1058.04 | − | 498.656i | −2.22276 | − | 1.04760i | ||||
\(477\) | − | 1625.83i | − | 3.40845i | ||||||
\(478\) | −250.974 | − | 395.737i | −0.525051 | − | 0.827902i | ||||
\(479\) | 320.952i | 0.670047i | 0.942210 | + | 0.335023i | \(0.108744\pi\) | ||||
−0.942210 | + | 0.335023i | \(0.891256\pi\) | |||||||
\(480\) | 33.7427 | + | 950.793i | 0.0702974 | + | 1.98082i | ||||
\(481\) | −52.5836 | −0.109321 | ||||||||
\(482\) | 56.4558 | − | 35.8040i | 0.117128 | − | 0.0742822i | ||||
\(483\) | −307.076 | −0.635767 | ||||||||
\(484\) | 152.703 | − | 324.002i | 0.315503 | − | 0.669426i | ||||
\(485\) | 557.097 | − | 204.080i | 1.14865 | − | 0.420784i | ||||
\(486\) | −2212.22 | + | 1402.98i | −4.55190 | + | 2.88679i | ||||
\(487\) | 515.213 | 1.05793 | 0.528966 | − | 0.848643i | \(-0.322580\pi\) | ||||
0.528966 | + | 0.848643i | \(0.322580\pi\) | |||||||
\(488\) | −31.3727 | − | 250.167i | −0.0642884 | − | 0.512637i | ||||
\(489\) | −575.714 | −1.17733 | ||||||||
\(490\) | −341.694 | − | 262.173i | −0.697334 | − | 0.535047i | ||||
\(491\) | 494.567i | 1.00726i | 0.863918 | + | 0.503632i | \(0.168003\pi\) | ||||
−0.863918 | + | 0.503632i | \(0.831997\pi\) | |||||||
\(492\) | 32.2974 | − | 68.5279i | 0.0656452 | − | 0.139284i | ||||
\(493\) | 762.853i | 1.54737i | ||||||||
\(494\) | −10.7897 | + | 6.84277i | −0.0218415 | + | 0.0138518i | ||||
\(495\) | −694.008 | + | 254.235i | −1.40204 | + | 0.513606i | ||||
\(496\) | −321.521 | + | 265.330i | −0.648228 | + | 0.534940i | ||||
\(497\) | − | 229.325i | − | 0.461418i | ||||||
\(498\) | 716.318 | − | 454.285i | 1.43839 | − | 0.912219i | ||||
\(499\) | 443.284i | 0.888345i | 0.895941 | + | 0.444172i | \(0.146502\pi\) | ||||
−0.895941 | + | 0.444172i | \(0.853498\pi\) | |||||||
\(500\) | −408.960 | + | 287.666i | −0.817919 | + | 0.575333i | ||||
\(501\) | 78.9844 | 0.157653 | ||||||||
\(502\) | −260.996 | − | 411.539i | −0.519912 | − | 0.819799i | ||||
\(503\) | −636.079 | −1.26457 | −0.632285 | − | 0.774736i | \(-0.717883\pi\) | ||||
−0.632285 | + | 0.774736i | \(0.717883\pi\) | |||||||
\(504\) | −251.756 | − | 2007.51i | −0.499516 | − | 3.98315i | ||||
\(505\) | 126.062 | + | 344.124i | 0.249628 | + | 0.681434i | ||||
\(506\) | −32.3323 | − | 50.9816i | −0.0638977 | − | 0.100754i | ||||
\(507\) | 992.136 | 1.95688 | ||||||||
\(508\) | −41.0548 | + | 87.1090i | −0.0808165 | + | 0.171474i | ||||
\(509\) | 364.309 | 0.715735 | 0.357868 | − | 0.933772i | \(-0.383504\pi\) | ||||
0.357868 | + | 0.933772i | \(0.383504\pi\) | |||||||
\(510\) | 1103.09 | − | 1437.67i | 2.16292 | − | 2.81896i | ||||
\(511\) | − | 611.277i | − | 1.19624i | ||||||
\(512\) | −187.183 | − | 476.557i | −0.365591 | − | 0.930776i | ||||
\(513\) | 449.881i | 0.876961i | ||||||||
\(514\) | 27.3700 | + | 43.1572i | 0.0532491 | + | 0.0839633i | ||||
\(515\) | 40.3509 | + | 110.150i | 0.0783512 | + | 0.213883i | ||||
\(516\) | 579.398 | − | 1229.35i | 1.12286 | − | 2.38247i | ||||
\(517\) | − | 171.628i | − | 0.331969i | ||||||
\(518\) | −368.761 | − | 581.464i | −0.711894 | − | 1.12252i | ||||
\(519\) | − | 676.894i | − | 1.30423i | ||||||
\(520\) | 26.8576 | + | 52.1088i | 0.0516492 | + | 0.100209i | ||||
\(521\) | 25.4568 | 0.0488615 | 0.0244308 | − | 0.999702i | \(-0.492223\pi\) | ||||
0.0244308 | + | 0.999702i | \(0.492223\pi\) | |||||||
\(522\) | −1114.35 | + | 706.717i | −2.13478 | + | 1.35386i | ||||
\(523\) | 1006.89 | 1.92522 | 0.962610 | − | 0.270890i | \(-0.0873179\pi\) | ||||
0.962610 | + | 0.270890i | \(0.0873179\pi\) | |||||||
\(524\) | −441.937 | − | 208.286i | −0.843391 | − | 0.397493i | ||||
\(525\) | 1088.85 | − | 921.397i | 2.07399 | − | 1.75504i | ||||
\(526\) | −118.589 | + | 75.2088i | −0.225455 | + | 0.142983i | ||||
\(527\) | 793.995 | 1.50663 | ||||||||
\(528\) | 411.540 | − | 339.617i | 0.779432 | − | 0.643215i | ||||
\(529\) | −500.033 | −0.945242 | ||||||||
\(530\) | −375.494 | + | 489.387i | −0.708480 | + | 0.923371i | ||||
\(531\) | − | 1333.51i | − | 2.51132i | ||||||
\(532\) | −151.333 | − | 71.3239i | −0.284461 | − | 0.134067i | ||||
\(533\) | − | 4.66803i | − | 0.00875804i | ||||||
\(534\) | 75.8120 | − | 48.0796i | 0.141970 | − | 0.0900367i | ||||
\(535\) | −164.180 | − | 448.177i | −0.306878 | − | 0.837715i | ||||
\(536\) | −13.3475 | − | 106.433i | −0.0249020 | − | 0.198569i | ||||
\(537\) | − | 931.728i | − | 1.73506i | ||||||
\(538\) | −449.437 | + | 285.031i | −0.835385 | + | 0.529797i | ||||
\(539\) | 241.545i | 0.448135i | ||||||||
\(540\) | 2055.97 | + | 184.050i | 3.80736 | + | 0.340834i | ||||
\(541\) | 473.253 | 0.874774 | 0.437387 | − | 0.899273i | \(-0.355904\pi\) | ||||
0.437387 | + | 0.899273i | \(0.355904\pi\) | |||||||
\(542\) | 41.3603 | + | 65.2170i | 0.0763105 | + | 0.120326i | ||||
\(543\) | −514.196 | −0.946955 | ||||||||
\(544\) | −302.756 | + | 927.011i | −0.556536 | + | 1.70407i | ||||
\(545\) | −136.504 | − | 372.628i | −0.250466 | − | 0.683722i | ||||
\(546\) | −89.5674 | − | 141.230i | −0.164043 | − | 0.258663i | ||||
\(547\) | −470.952 | −0.860972 | −0.430486 | − | 0.902597i | \(-0.641658\pi\) | ||||
−0.430486 | + | 0.902597i | \(0.641658\pi\) | |||||||
\(548\) | −300.639 | − | 141.692i | −0.548611 | − | 0.258563i | ||||
\(549\) | −830.671 | −1.51306 | ||||||||
\(550\) | 267.618 | + | 83.7585i | 0.486579 | + | 0.152288i | ||||
\(551\) | 109.113i | 0.198026i | ||||||||
\(552\) | 31.8577 | + | 254.034i | 0.0577132 | + | 0.460206i | ||||
\(553\) | 548.164i | 0.991254i | ||||||||
\(554\) | 384.455 | + | 606.210i | 0.693963 | + | 1.09424i | ||||
\(555\) | 1001.63 | − | 366.926i | 1.80474 | − | 0.661127i | ||||
\(556\) | −294.298 | − | 138.704i | −0.529312 | − | 0.249467i | ||||
\(557\) | 51.0296i | 0.0916152i | 0.998950 | + | 0.0458076i | \(0.0145861\pi\) | ||||
−0.998950 | + | 0.0458076i | \(0.985414\pi\) | |||||||
\(558\) | 735.568 | + | 1159.84i | 1.31822 | + | 2.07858i | ||||
\(559\) | − | 83.7419i | − | 0.149807i | ||||||
\(560\) | −387.865 | + | 662.419i | −0.692615 | + | 1.18289i | ||||
\(561\) | −1016.30 | −1.81158 | ||||||||
\(562\) | −453.199 | + | 287.417i | −0.806404 | + | 0.511418i | ||||
\(563\) | −107.822 | −0.191514 | −0.0957570 | − | 0.995405i | \(-0.530527\pi\) | ||||
−0.0957570 | + | 0.995405i | \(0.530527\pi\) | |||||||
\(564\) | −310.307 | + | 658.401i | −0.550190 | + | 1.16738i | ||||
\(565\) | −299.506 | + | 109.717i | −0.530099 | + | 0.194190i | ||||
\(566\) | 711.981 | − | 451.535i | 1.25792 | − | 0.797765i | ||||
\(567\) | −3612.51 | −6.37128 | ||||||||
\(568\) | −189.713 | + | 23.7914i | −0.334002 | + | 0.0418862i | ||||
\(569\) | 567.877 | 0.998026 | 0.499013 | − | 0.866595i | \(-0.333696\pi\) | ||||
0.499013 | + | 0.866595i | \(0.333696\pi\) | |||||||
\(570\) | 157.777 | − | 205.633i | 0.276803 | − | 0.360760i | ||||
\(571\) | 342.894i | 0.600515i | 0.953858 | + | 0.300258i | \(0.0970726\pi\) | ||||
−0.953858 | + | 0.300258i | \(0.902927\pi\) | |||||||
\(572\) | 14.0168 | − | 29.7405i | 0.0245049 | − | 0.0519938i | ||||
\(573\) | − | 1035.77i | − | 1.80763i | ||||||
\(574\) | 51.6186 | − | 32.7362i | 0.0899278 | − | 0.0570318i | ||||
\(575\) | −102.712 | + | 86.9166i | −0.178630 | + | 0.151159i | ||||
\(576\) | −1634.63 | + | 416.539i | −2.83790 | + | 0.723159i | ||||
\(577\) | − | 14.6235i | − | 0.0253440i | −0.999920 | − | 0.0126720i | \(-0.995966\pi\) | ||
0.999920 | − | 0.0126720i | \(-0.00403373\pi\) | |||||||
\(578\) | 1080.48 | − | 685.233i | 1.86934 | − | 1.18552i | ||||
\(579\) | − | 2147.06i | − | 3.70822i | ||||||
\(580\) | 498.649 | + | 44.6389i | 0.859739 | + | 0.0769637i | ||||
\(581\) | 684.380 | 1.17793 | ||||||||
\(582\) | 755.774 | + | 1191.71i | 1.29858 | + | 2.04760i | ||||
\(583\) | 345.949 | 0.593395 | ||||||||
\(584\) | −505.690 | + | 63.4172i | −0.865908 | + | 0.108591i | ||||
\(585\) | 181.357 | − | 66.4362i | 0.310012 | − | 0.113566i | ||||
\(586\) | −312.332 | − | 492.486i | −0.532990 | − | 0.840421i | ||||
\(587\) | 633.620 | 1.07942 | 0.539711 | − | 0.841851i | \(-0.318534\pi\) | ||||
0.539711 | + | 0.841851i | \(0.318534\pi\) | |||||||
\(588\) | 436.718 | − | 926.617i | 0.742718 | − | 1.57588i | ||||
\(589\) | 113.567 | 0.192813 | ||||||||
\(590\) | −307.982 | + | 401.397i | −0.522004 | + | 0.680334i | ||||
\(591\) | − | 581.014i | − | 0.983103i | ||||||
\(592\) | −442.769 | + | 365.388i | −0.747920 | + | 0.617210i | ||||
\(593\) | − | 284.861i | − | 0.480373i | −0.970727 | − | 0.240186i | \(-0.922791\pi\) | ||
0.970727 | − | 0.240186i | \(-0.0772085\pi\) | |||||||
\(594\) | −620.021 | − | 977.651i | −1.04381 | − | 1.64588i | ||||
\(595\) | 1372.85 | − | 502.915i | 2.30732 | − | 0.845235i | ||||
\(596\) | 157.961 | − | 335.157i | 0.265035 | − | 0.562345i | ||||
\(597\) | 1818.70i | 3.04640i | ||||||||
\(598\) | 8.44901 | + | 13.3224i | 0.0141288 | + | 0.0222783i | ||||
\(599\) | − | 222.749i | − | 0.371868i | −0.982562 | − | 0.185934i | \(-0.940469\pi\) | ||
0.982562 | − | 0.185934i | \(-0.0595310\pi\) | |||||||
\(600\) | −875.205 | − | 805.176i | −1.45867 | − | 1.34196i | ||||
\(601\) | −908.522 | −1.51168 | −0.755842 | − | 0.654755i | \(-0.772772\pi\) | ||||
−0.755842 | + | 0.654755i | \(0.772772\pi\) | |||||||
\(602\) | 926.009 | − | 587.270i | 1.53822 | − | 0.975532i | ||||
\(603\) | −353.408 | −0.586083 | ||||||||
\(604\) | 637.308 | + | 300.365i | 1.05515 | + | 0.497294i | ||||
\(605\) | 154.008 | + | 420.409i | 0.254558 | + | 0.694891i | ||||
\(606\) | −736.128 | + | 466.848i | −1.21473 | + | 0.770377i | ||||
\(607\) | −853.291 | −1.40575 | −0.702876 | − | 0.711313i | \(-0.748101\pi\) | ||||
−0.702876 | + | 0.711313i | \(0.748101\pi\) | |||||||
\(608\) | −43.3038 | + | 132.593i | −0.0712234 | + | 0.218080i | ||||
\(609\) | −1428.21 | −2.34518 | ||||||||
\(610\) | 250.038 | + | 191.848i | 0.409898 | + | 0.314505i | ||||
\(611\) | 44.8495i | 0.0734034i | ||||||||
\(612\) | 2906.33 | + | 1369.76i | 4.74891 | + | 2.23818i | ||||
\(613\) | 34.7413i | 0.0566742i | 0.999598 | + | 0.0283371i | \(0.00902118\pi\) | ||||
−0.999598 | + | 0.0283371i | \(0.990979\pi\) | |||||||
\(614\) | −541.183 | + | 343.215i | −0.881405 | + | 0.558982i | ||||
\(615\) | 32.5733 | + | 88.9184i | 0.0529647 | + | 0.144583i | ||||
\(616\) | 427.164 | − | 53.5695i | 0.693449 | − | 0.0869635i | ||||
\(617\) | 622.522i | 1.00895i | 0.863427 | + | 0.504475i | \(0.168314\pi\) | ||||
−0.863427 | + | 0.504475i | \(0.831686\pi\) | |||||||
\(618\) | −235.625 | + | 149.432i | −0.381270 | + | 0.241799i | ||||
\(619\) | − | 173.004i | − | 0.279490i | −0.990188 | − | 0.139745i | \(-0.955372\pi\) | ||
0.990188 | − | 0.139745i | \(-0.0446283\pi\) | |||||||
\(620\) | 46.4612 | − | 519.005i | 0.0749375 | − | 0.837105i | ||||
\(621\) | 555.484 | 0.894499 | ||||||||
\(622\) | −578.065 | − | 911.494i | −0.929365 | − | 1.46542i | ||||
\(623\) | 72.4319 | 0.116263 | ||||||||
\(624\) | −107.543 | + | 88.7482i | −0.172344 | + | 0.142225i | ||||
\(625\) | 103.404 | − | 616.387i | 0.165447 | − | 0.986219i | ||||
\(626\) | 364.922 | + | 575.409i | 0.582942 | + | 0.919184i | ||||
\(627\) | −145.363 | −0.231839 | ||||||||
\(628\) | 505.476 | + | 238.233i | 0.804899 | + | 0.379352i | ||||
\(629\) | 1093.42 | 1.73834 | ||||||||
\(630\) | 2006.47 | + | 1539.52i | 3.18488 | + | 2.44368i | ||||
\(631\) | 715.897i | 1.13454i | 0.823530 | + | 0.567272i | \(0.192001\pi\) | ||||
−0.823530 | + | 0.567272i | \(0.807999\pi\) | |||||||
\(632\) | 453.478 | − | 56.8694i | 0.717529 | − | 0.0899833i | ||||
\(633\) | − | 824.581i | − | 1.30266i | ||||||
\(634\) | −492.174 | − | 776.061i | −0.776300 | − | 1.22407i | ||||
\(635\) | −41.4054 | − | 113.028i | −0.0652054 | − | 0.177997i | ||||
\(636\) | −1327.14 | − | 625.484i | −2.08669 | − | 0.983466i | ||||
\(637\) | − | 63.1200i | − | 0.0990895i | ||||||
\(638\) | −150.378 | − | 237.116i | −0.235702 | − | 0.371655i | ||||
\(639\) | 629.935i | 0.985814i | ||||||||
\(640\) | 588.237 | + | 252.145i | 0.919121 | + | 0.393976i | ||||
\(641\) | 194.821 | 0.303933 | 0.151967 | − | 0.988386i | \(-0.451439\pi\) | ||||
0.151967 | + | 0.988386i | \(0.451439\pi\) | |||||||
\(642\) | 958.712 | − | 608.010i | 1.49332 | − | 0.947056i | ||||
\(643\) | −700.497 | −1.08942 | −0.544710 | − | 0.838624i | \(-0.683360\pi\) | ||||
−0.544710 | + | 0.838624i | \(0.683360\pi\) | |||||||
\(644\) | −88.0661 | + | 186.856i | −0.136749 | + | 0.290150i | ||||
\(645\) | 584.347 | + | 1595.15i | 0.905964 | + | 2.47309i | ||||
\(646\) | 224.359 | − | 142.288i | 0.347305 | − | 0.220259i | ||||
\(647\) | −377.524 | −0.583499 | −0.291750 | − | 0.956495i | \(-0.594237\pi\) | ||||
−0.291750 | + | 0.956495i | \(0.594237\pi\) | |||||||
\(648\) | 374.782 | + | 2988.52i | 0.578367 | + | 4.61191i | ||||
\(649\) | 283.749 | 0.437210 | ||||||||
\(650\) | −69.9336 | − | 21.8876i | −0.107590 | − | 0.0336732i | ||||
\(651\) | 1486.52i | 2.28344i | ||||||||
\(652\) | −165.109 | + | 350.323i | −0.253234 | + | 0.537306i | ||||
\(653\) | 212.287i | 0.325095i | 0.986701 | + | 0.162548i | \(0.0519711\pi\) | ||||
−0.986701 | + | 0.162548i | \(0.948029\pi\) | |||||||
\(654\) | 797.102 | − | 505.518i | 1.21881 | − | 0.772963i | ||||
\(655\) | 573.435 | − | 210.065i | 0.875473 | − | 0.320710i | ||||
\(656\) | −32.4368 | − | 39.3062i | −0.0494464 | − | 0.0599179i | ||||
\(657\) | 1679.13i | 2.55575i | ||||||||
\(658\) | −495.940 | + | 314.523i | −0.753709 | + | 0.477998i | ||||
\(659\) | − | 301.196i | − | 0.457051i | −0.973538 | − | 0.228525i | \(-0.926610\pi\) | ||
0.973538 | − | 0.228525i | \(-0.0733904\pi\) | |||||||
\(660\) | −59.4694 | + | 664.315i | −0.0901051 | + | 1.00654i | ||||
\(661\) | 162.779 | 0.246261 | 0.123130 | − | 0.992390i | \(-0.460707\pi\) | ||||
0.123130 | + | 0.992390i | \(0.460707\pi\) | |||||||
\(662\) | 417.016 | + | 657.552i | 0.629934 | + | 0.993281i | ||||
\(663\) | 265.577 | 0.400568 | ||||||||
\(664\) | −71.0013 | − | 566.166i | −0.106930 | − | 0.852659i | ||||
\(665\) | 196.362 | − | 71.9330i | 0.295282 | − | 0.108170i | ||||
\(666\) | 1012.96 | + | 1597.23i | 1.52095 | + | 2.39824i | ||||
\(667\) | 134.725 | 0.201987 | ||||||||
\(668\) | 22.6519 | − | 48.0622i | 0.0339100 | − | 0.0719494i | ||||
\(669\) | 633.339 | 0.946695 | ||||||||
\(670\) | 106.378 | + | 81.6214i | 0.158774 | + | 0.121823i | ||||
\(671\) | − | 176.753i | − | 0.263417i | ||||||
\(672\) | −1735.55 | − | 566.819i | −2.58266 | − | 0.843480i | ||||
\(673\) | − | 398.525i | − | 0.592162i | −0.955163 | − | 0.296081i | \(-0.904320\pi\) | ||
0.955163 | − | 0.296081i | \(-0.0956799\pi\) | |||||||
\(674\) | −86.8311 | − | 136.916i | −0.128830 | − | 0.203139i | ||||
\(675\) | −1969.66 | + | 1666.76i | −2.91802 | + | 2.46927i | ||||
\(676\) | 284.534 | − | 603.717i | 0.420908 | − | 0.893073i | ||||
\(677\) | − | 1257.14i | − | 1.85693i | −0.371422 | − | 0.928464i | \(-0.621130\pi\) | ||
0.371422 | − | 0.928464i | \(-0.378870\pi\) | |||||||
\(678\) | −406.318 | − | 640.683i | −0.599289 | − | 0.944960i | ||||
\(679\) | 1138.57i | 1.67684i | ||||||||
\(680\) | −558.472 | − | 1083.54i | −0.821283 | − | 1.59344i | ||||
\(681\) | −1273.42 | −1.86992 | ||||||||
\(682\) | −246.796 | + | 156.517i | −0.361871 | + | 0.229496i | ||||
\(683\) | −856.254 | −1.25367 | −0.626833 | − | 0.779154i | \(-0.715649\pi\) | ||||
−0.626833 | + | 0.779154i | \(0.715649\pi\) | |||||||
\(684\) | 415.699 | + | 195.921i | 0.607747 | + | 0.286434i | ||||
\(685\) | 390.094 | − | 142.902i | 0.569481 | − | 0.208617i | ||||
\(686\) | −96.1276 | + | 60.9636i | −0.140128 | + | 0.0888682i | ||||
\(687\) | 2154.81 | 3.13656 | ||||||||
\(688\) | −581.899 | − | 705.131i | −0.845783 | − | 1.02490i | ||||
\(689\) | −90.4029 | −0.131209 | ||||||||
\(690\) | −253.903 | − | 194.813i | −0.367975 | − | 0.282338i | ||||
\(691\) | − | 228.113i | − | 0.330120i | −0.986284 | − | 0.165060i | \(-0.947218\pi\) | ||
0.986284 | − | 0.165060i | \(-0.0527818\pi\) | |||||||
\(692\) | −411.892 | − | 194.126i | −0.595219 | − | 0.280529i | ||||
\(693\) | − | 1418.39i | − | 2.04673i | ||||||
\(694\) | 653.828 | − | 414.654i | 0.942115 | − | 0.597484i | ||||
\(695\) | 381.866 | − | 139.888i | 0.549447 | − | 0.201278i | ||||
\(696\) | 148.170 | + | 1181.51i | 0.212888 | + | 1.69758i | ||||
\(697\) | 97.0664i | 0.139263i | ||||||||
\(698\) | 893.912 | − | 566.915i | 1.28068 | − | 0.812199i | ||||
\(699\) | − | 1863.38i | − | 2.66578i | ||||||
\(700\) | −248.403 | − | 926.812i | −0.354862 | − | 1.32402i | ||||
\(701\) | −427.683 | −0.610104 | −0.305052 | − | 0.952336i | \(-0.598674\pi\) | ||||
−0.305052 | + | 0.952336i | \(0.598674\pi\) | |||||||
\(702\) | 162.023 | + | 255.478i | 0.230802 | + | 0.363929i | ||||
\(703\) | 156.394 | 0.222466 | ||||||||
\(704\) | −88.6327 | − | 347.822i | −0.125899 | − | 0.494065i | ||||
\(705\) | −312.957 | − | 854.308i | −0.443911 | − | 1.21179i | ||||
\(706\) | −102.344 | − | 161.376i | −0.144963 | − | 0.228578i | ||||
\(707\) | −703.306 | −0.994776 | ||||||||
\(708\) | −1088.52 | − | 513.025i | −1.53746 | − | 0.724612i | ||||
\(709\) | −482.104 | −0.679977 | −0.339989 | − | 0.940430i | \(-0.610423\pi\) | ||||
−0.339989 | + | 0.940430i | \(0.610423\pi\) | |||||||
\(710\) | 145.487 | − | 189.615i | 0.204911 | − | 0.267064i | ||||
\(711\) | − | 1505.76i | − | 2.11780i | ||||||
\(712\) | −7.51447 | − | 59.9205i | −0.0105540 | − | 0.0841581i | ||||
\(713\) | − | 140.225i | − | 0.196669i | ||||||
\(714\) | 1862.45 | + | 2936.72i | 2.60848 | + | 4.11305i | ||||
\(715\) | 14.1365 | + | 38.5897i | 0.0197713 | + | 0.0539717i | ||||
\(716\) | −566.959 | − | 267.210i | −0.791842 | − | 0.373198i | ||||
\(717\) | 1393.23i | 1.94313i | ||||||||
\(718\) | 193.728 | + | 305.470i | 0.269816 | + | 0.425446i | ||||
\(719\) | 621.374i | 0.864219i | 0.901821 | + | 0.432110i | \(0.142231\pi\) | ||||
−0.901821 | + | 0.432110i | \(0.857769\pi\) | |||||||
\(720\) | 1065.43 | − | 1819.61i | 1.47977 | − | 2.52723i | ||||
\(721\) | −225.119 | −0.312232 | ||||||||
\(722\) | 32.0906 | − | 20.3517i | 0.0444468 | − | 0.0281880i | ||||
\(723\) | −198.758 | −0.274907 | ||||||||
\(724\) | −147.466 | + | 312.890i | −0.203682 | + | 0.432168i | ||||
\(725\) | −477.715 | + | 404.250i | −0.658918 | + | 0.557586i | ||||
\(726\) | −899.311 | + | 570.339i | −1.23872 | + | 0.785590i | ||||
\(727\) | −500.188 | −0.688017 | −0.344009 | − | 0.938967i | \(-0.611785\pi\) | ||||
−0.344009 | + | 0.938967i | \(0.611785\pi\) | |||||||
\(728\) | −111.626 | + | 13.9987i | −0.153332 | + | 0.0192290i | ||||
\(729\) | 4399.91 | 6.03554 | ||||||||
\(730\) | 387.803 | − | 505.429i | 0.531238 | − | 0.692369i | ||||
\(731\) | 1741.32i | 2.38210i | ||||||||
\(732\) | −319.573 | + | 678.062i | −0.436575 | + | 0.926314i | ||||
\(733\) | − | 1128.57i | − | 1.53966i | −0.638251 | − | 0.769828i | \(-0.720342\pi\) | ||
0.638251 | − | 0.769828i | \(-0.279658\pi\) | |||||||
\(734\) | 507.893 | − | 322.103i | 0.691952 | − | 0.438833i | ||||
\(735\) | 440.448 | + | 1202.33i | 0.599249 | + | 1.63583i | ||||
\(736\) | 163.717 | + | 53.4687i | 0.222441 | + | 0.0726477i | ||||
\(737\) | − | 75.1993i | − | 0.102034i | ||||||
\(738\) | −141.792 | + | 89.9237i | −0.192130 | + | 0.121848i | ||||
\(739\) | − | 859.823i | − | 1.16349i | −0.813370 | − | 0.581747i | \(-0.802369\pi\) | ||
0.813370 | − | 0.581747i | \(-0.197631\pi\) | |||||||
\(740\) | 63.9821 | − | 714.726i | 0.0864623 | − | 0.965845i | ||||
\(741\) | 37.9860 | 0.0512632 | ||||||||
\(742\) | −633.982 | − | 999.665i | −0.854424 | − | 1.34726i | ||||
\(743\) | 546.879 | 0.736042 | 0.368021 | − | 0.929817i | \(-0.380035\pi\) | ||||
0.368021 | + | 0.929817i | \(0.380035\pi\) | |||||||
\(744\) | 1229.75 | − | 154.219i | 1.65289 | − | 0.207284i | ||||
\(745\) | 159.310 | + | 434.884i | 0.213839 | + | 0.583736i | ||||
\(746\) | −656.427 | − | 1035.05i | −0.879928 | − | 1.38747i | ||||
\(747\) | −1879.93 | −2.51664 | ||||||||
\(748\) | −291.463 | + | 618.419i | −0.389657 | + | 0.826763i | ||||
\(749\) | 915.966 | 1.22292 | ||||||||
\(750\) | 1484.85 | − | 71.0698i | 1.97980 | − | 0.0947597i | ||||
\(751\) | − | 470.979i | − | 0.627135i | −0.949566 | − | 0.313568i | \(-0.898476\pi\) | ||
0.949566 | − | 0.313568i | \(-0.101524\pi\) | |||||||
\(752\) | 311.646 | + | 377.645i | 0.414423 | + | 0.502188i | ||||
\(753\) | 1448.86i | 1.92411i | ||||||||
\(754\) | 39.2964 | + | 61.9627i | 0.0521173 | + | 0.0821786i | ||||
\(755\) | −826.938 | + | 302.931i | −1.09528 | + | 0.401233i | ||||
\(756\) | −1688.80 | + | 3583.26i | −2.23387 | + | 4.73976i | ||||
\(757\) | − | 1011.74i | − | 1.33651i | −0.743932 | − | 0.668255i | \(-0.767041\pi\) | ||
0.743932 | − | 0.668255i | \(-0.232959\pi\) | |||||||
\(758\) | −48.6046 | − | 76.6399i | −0.0641222 | − | 0.101108i | ||||
\(759\) | 179.485i | 0.236476i | ||||||||
\(760\) | −79.8796 | − | 154.981i | −0.105105 | − | 0.203923i | ||||
\(761\) | −1071.31 | −1.40776 | −0.703881 | − | 0.710318i | \(-0.748551\pi\) | ||||
−0.703881 | + | 0.710318i | \(0.748551\pi\) | |||||||
\(762\) | 241.783 | − | 153.337i | 0.317300 | − | 0.201230i | ||||
\(763\) | 761.562 | 0.998116 | ||||||||
\(764\) | −630.270 | − | 297.049i | −0.824961 | − | 0.388807i | ||||
\(765\) | −3771.11 | + | 1381.46i | −4.92956 | + | 1.80584i | ||||
\(766\) | 768.402 | − | 487.317i | 1.00314 | − | 0.636184i | ||||
\(767\) | −74.1489 | −0.0966739 | ||||||||
\(768\) | −288.856 | + | 1494.57i | −0.376114 | + | 1.94605i | ||||
\(769\) | −1361.48 | −1.77045 | −0.885227 | − | 0.465160i | \(-0.845997\pi\) | ||||
−0.885227 | + | 0.465160i | \(0.845997\pi\) | |||||||
\(770\) | −327.584 | + | 426.944i | −0.425433 | + | 0.554473i | ||||
\(771\) | − | 151.938i | − | 0.197067i | ||||||
\(772\) | −1306.49 | − | 615.753i | −1.69234 | − | 0.797608i | ||||
\(773\) | 85.6518i | 0.110804i | 0.998464 | + | 0.0554022i | \(0.0176441\pi\) | ||||
−0.998464 | + | 0.0554022i | \(0.982356\pi\) | |||||||
\(774\) | −2543.67 | + | 1613.18i | −3.28639 | + | 2.08421i | ||||
\(775\) | 420.753 | + | 497.217i | 0.542907 | + | 0.641571i | ||||
\(776\) | 941.904 | − | 118.122i | 1.21379 | − | 0.152218i | ||||
\(777\) | 2047.09i | 2.63461i | ||||||||
\(778\) | −634.926 | + | 402.667i | −0.816100 | + | 0.517566i | ||||
\(779\) | 13.8836i | 0.0178224i | ||||||||
\(780\) | 15.5404 | − | 173.598i | 0.0199236 | − | 0.222561i | ||||
\(781\) | −134.040 | −0.171626 | ||||||||
\(782\) | −175.687 | − | 277.024i | −0.224664 | − | 0.354251i | ||||
\(783\) | 2583.56 | 3.29957 | ||||||||
\(784\) | −438.603 | − | 531.488i | −0.559442 | − | 0.677919i | ||||
\(785\) | −655.881 | + | 240.268i | −0.835517 | + | 0.306073i | ||||
\(786\) | 777.938 | + | 1226.65i | 0.989743 | + | 1.56063i | ||||
\(787\) | 242.404 | 0.308010 | 0.154005 | − | 0.988070i | \(-0.450783\pi\) | ||||
0.154005 | + | 0.988070i | \(0.450783\pi\) | |||||||
\(788\) | −353.549 | − | 166.629i | −0.448666 | − | 0.211458i | ||||
\(789\) | 417.504 | 0.529156 | ||||||||
\(790\) | −347.763 | + | 453.244i | −0.440206 | + | 0.573727i | ||||
\(791\) | − | 612.117i | − | 0.773853i | ||||||
\(792\) | −1173.38 | + | 147.151i | −1.48155 | + | 0.185797i | ||||
\(793\) | 46.1887i | 0.0582456i | ||||||||
\(794\) | −251.333 | − | 396.302i | −0.316540 | − | 0.499121i | ||||
\(795\) | 1722.03 | − | 630.827i | 2.16607 | − | 0.793493i | ||||
\(796\) | 1106.68 | + | 521.585i | 1.39031 | + | 0.655257i | ||||
\(797\) | 763.446i | 0.957899i | 0.877842 | + | 0.478950i | \(0.158982\pi\) | ||||
−0.877842 | + | 0.478950i | \(0.841018\pi\) | |||||||
\(798\) | 266.391 | + | 420.045i | 0.333823 | + | 0.526373i | ||||
\(799\) | − | 932.593i | − | 1.16720i | ||||||
\(800\) | −740.951 | + | 301.648i | −0.926189 | + | 0.377060i | ||||
\(801\) | −198.964 | −0.248395 | ||||||||
\(802\) | −625.948 | + | 396.973i | −0.780483 | + | 0.494978i | ||||
\(803\) | −357.290 | −0.444944 | ||||||||
\(804\) | −135.962 | + | 288.481i | −0.169107 | + | 0.358807i | ||||
\(805\) | −88.8182 | − | 242.455i | −0.110333 | − | 0.301187i | ||||
\(806\) | 64.4922 | − | 40.9006i | 0.0800152 | − | 0.0507452i | ||||
\(807\) | 1582.28 | 1.96070 | ||||||||
\(808\) | 72.9648 | + | 581.823i | 0.0903030 | + | 0.720078i | ||||
\(809\) | −994.007 | −1.22869 | −0.614343 | − | 0.789039i | \(-0.710579\pi\) | ||||
−0.614343 | + | 0.789039i | \(0.710579\pi\) | |||||||
\(810\) | −2986.98 | − | 2291.83i | −3.68762 | − | 2.82942i | ||||
\(811\) | 722.784i | 0.891226i | 0.895226 | + | 0.445613i | \(0.147014\pi\) | ||||
−0.895226 | + | 0.445613i | \(0.852986\pi\) | |||||||
\(812\) | −409.596 | + | 869.071i | −0.504429 | + | 1.07028i | ||||
\(813\) | − | 229.602i | − | 0.282413i | ||||||
\(814\) | −339.864 | + | 215.540i | −0.417523 | + | 0.264791i | ||||
\(815\) | −166.519 | − | 454.562i | −0.204318 | − | 0.557745i | ||||
\(816\) | 2236.23 | − | 1845.42i | 2.74048 | − | 2.26154i | ||||
\(817\) | 249.065i | 0.304853i | ||||||||
\(818\) | −80.8303 | + | 51.2622i | −0.0988146 | + | 0.0626677i | ||||
\(819\) | 370.650i | 0.452564i | ||||||||
\(820\) | 63.4487 | + | 5.67992i | 0.0773765 | + | 0.00692673i | ||||
\(821\) | 347.379 | 0.423117 | 0.211559 | − | 0.977365i | \(-0.432146\pi\) | ||||
0.211559 | + | 0.977365i | \(0.432146\pi\) | |||||||
\(822\) | 529.213 | + | 834.464i | 0.643811 | + | 1.01516i | ||||
\(823\) | 1156.27 | 1.40495 | 0.702473 | − | 0.711710i | \(-0.252079\pi\) | ||||
0.702473 | + | 0.711710i | \(0.252079\pi\) | |||||||
\(824\) | 23.3551 | + | 186.234i | 0.0283435 | + | 0.226012i | ||||
\(825\) | −538.554 | − | 636.427i | −0.652793 | − | 0.771427i | ||||
\(826\) | −519.995 | − | 819.930i | −0.629534 | − | 0.992651i | ||||
\(827\) | 279.759 | 0.338282 | 0.169141 | − | 0.985592i | \(-0.445901\pi\) | ||||
0.169141 | + | 0.985592i | \(0.445901\pi\) | |||||||
\(828\) | 241.910 | − | 513.278i | 0.292162 | − | 0.619901i | ||||
\(829\) | −1494.76 | −1.80309 | −0.901546 | − | 0.432684i | \(-0.857567\pi\) | ||||
−0.901546 | + | 0.432684i | \(0.857567\pi\) | |||||||
\(830\) | 565.874 | + | 434.181i | 0.681775 | + | 0.523109i | ||||
\(831\) | − | 2134.21i | − | 2.56825i | ||||||
\(832\) | 23.1613 | + | 90.8922i | 0.0278381 | + | 0.109245i | ||||
\(833\) | 1312.51i | 1.57564i | ||||||||
\(834\) | 518.050 | + | 816.862i | 0.621163 | + | 0.979451i | ||||
\(835\) | 22.8454 | + | 62.3631i | 0.0273597 | + | 0.0746863i | ||||
\(836\) | −41.6886 | + | 88.4539i | −0.0498668 | + | 0.105806i | ||||
\(837\) | − | 2689.03i | − | 3.21270i | ||||||
\(838\) | −29.1771 | − | 46.0065i | −0.0348175 | − | 0.0549004i | ||||
\(839\) | − | 947.342i | − | 1.12913i | −0.825388 | − | 0.564566i | \(-0.809043\pi\) | ||
0.825388 | − | 0.564566i | \(-0.190957\pi\) | |||||||
\(840\) | 2028.61 | − | 1045.57i | 2.41501 | − | 1.24473i | ||||
\(841\) | −214.392 | −0.254925 | ||||||||
\(842\) | 808.926 | − | 513.017i | 0.960720 | − | 0.609284i | ||||
\(843\) | 1595.53 | 1.89268 | ||||||||
\(844\) | −501.760 | − | 236.481i | −0.594502 | − | 0.280191i | ||||
\(845\) | 286.964 | + | 783.353i | 0.339603 | + | 0.927045i | ||||
\(846\) | 1362.31 | − | 863.967i | 1.61029 | − | 1.02124i | ||||
\(847\) | −859.214 | −1.01442 | ||||||||
\(848\) | −761.218 | + | 628.184i | −0.897662 | + | 0.740783i | ||||
\(849\) | −2506.59 | −2.95240 | ||||||||
\(850\) | 1454.19 | + | 455.128i | 1.71081 | + | 0.535444i | ||||
\(851\) | − | 193.105i | − | 0.226915i | ||||||
\(852\) | 514.205 | + | 242.347i | 0.603527 | + | 0.284445i | ||||
\(853\) | − | 1113.72i | − | 1.30565i | −0.757508 | − | 0.652826i | \(-0.773583\pi\) | ||
0.757508 | − | 0.652826i | \(-0.226417\pi\) | |||||||
\(854\) | −510.750 | + | 323.915i | −0.598068 | + | 0.379291i | ||||
\(855\) | −539.390 | + | 197.594i | −0.630866 | + | 0.231104i | ||||
\(856\) | −95.0273 | − | 757.749i | −0.111013 | − | 0.885221i | ||||
\(857\) | − | 1294.60i | − | 1.51062i | −0.655367 | − | 0.755311i | \(-0.727486\pi\) | ||
0.655367 | − | 0.755311i | \(-0.272514\pi\) | |||||||
\(858\) | −82.5487 | + | 52.3519i | −0.0962105 | + | 0.0610162i | ||||
\(859\) | − | 790.141i | − | 0.919839i | −0.887961 | − | 0.459919i | \(-0.847878\pi\) | ||
0.887961 | − | 0.459919i | \(-0.152122\pi\) | |||||||
\(860\) | 1138.24 | + | 101.895i | 1.32353 | + | 0.118482i | ||||
\(861\) | −181.728 | −0.211066 | ||||||||
\(862\) | −683.306 | − | 1077.44i | −0.792699 | − | 1.24993i | ||||
\(863\) | −274.774 | −0.318394 | −0.159197 | − | 0.987247i | \(-0.550891\pi\) | ||||
−0.159197 | + | 0.987247i | \(0.550891\pi\) | |||||||
\(864\) | 3139.52 | + | 1025.35i | 3.63370 | + | 1.18674i | ||||
\(865\) | 534.450 | − | 195.784i | 0.617862 | − | 0.226340i | ||||
\(866\) | −659.972 | − | 1040.64i | −0.762092 | − | 1.20167i | ||||
\(867\) | −3803.91 | −4.38744 | ||||||||
\(868\) | 904.549 | + | 426.317i | 1.04211 | + | 0.491149i | ||||
\(869\) | 320.400 | 0.368700 | ||||||||
\(870\) | −1180.90 | − | 906.079i | −1.35736 | − | 1.04147i | ||||
\(871\) | 19.6509i | 0.0225614i | ||||||||
\(872\) | −79.0086 | − | 630.016i | −0.0906061 | − | 0.722495i | ||||
\(873\) | − | 3127.56i | − | 3.58254i | ||||||
\(874\) | −25.1290 | − | 39.6234i | −0.0287517 | − | 0.0453357i | ||||
\(875\) | 1042.44 | + | 593.207i | 1.19136 | + | 0.677951i | ||||
\(876\) | 1370.64 | + | 645.989i | 1.56466 | + | 0.737430i | ||||
\(877\) | − | 713.727i | − | 0.813828i | −0.913467 | − | 0.406914i | \(-0.866605\pi\) | ||
0.913467 | − | 0.406914i | \(-0.133395\pi\) | |||||||
\(878\) | 353.458 | + | 557.334i | 0.402572 | + | 0.634777i | ||||
\(879\) | 1733.84i | 1.97251i | ||||||||
\(880\) | 387.182 | + | 226.706i | 0.439980 | + | 0.257620i | ||||
\(881\) | −1530.65 | −1.73740 | −0.868698 | − | 0.495342i | \(-0.835043\pi\) | ||||
−0.868698 | + | 0.495342i | \(0.835043\pi\) | |||||||
\(882\) | −1917.27 | + | 1215.93i | −2.17378 | + | 1.37860i | ||||
\(883\) | 768.156 | 0.869938 | 0.434969 | − | 0.900445i | \(-0.356759\pi\) | ||||
0.434969 | + | 0.900445i | \(0.356759\pi\) | |||||||
\(884\) | 76.1646 | − | 161.604i | 0.0861591 | − | 0.182810i | ||||
\(885\) | 1412.41 | − | 517.407i | 1.59595 | − | 0.584641i | ||||
\(886\) | 428.186 | − | 271.553i | 0.483280 | − | 0.306494i | ||||
\(887\) | 959.350 | 1.08157 | 0.540784 | − | 0.841162i | \(-0.318128\pi\) | ||||
0.540784 | + | 0.841162i | \(0.318128\pi\) | |||||||
\(888\) | 1693.49 | − | 212.376i | 1.90709 | − | 0.239163i | ||||
\(889\) | 231.002 | 0.259845 | ||||||||
\(890\) | 59.8897 | + | 45.9518i | 0.0672917 | + | 0.0516313i | ||||
\(891\) | 2111.51i | 2.36982i | ||||||||
\(892\) | 181.635 | − | 385.388i | 0.203627 | − | 0.432050i | ||||
\(893\) | − | 133.391i | − | 0.149374i | ||||||
\(894\) | −930.274 | + | 589.975i | −1.04058 | + | 0.659928i | ||||
\(895\) | 735.657 | − | 269.492i | 0.821963 | − | 0.301108i | ||||
\(896\) | −842.648 | + | 893.529i | −0.940455 | + | 0.997242i | ||||
\(897\) | − | 46.9027i | − | 0.0522884i | ||||||
\(898\) | −638.043 | + | 404.643i | −0.710515 | + | 0.450605i | ||||
\(899\) | − | 652.188i | − | 0.725459i | ||||||
\(900\) | 682.342 | + | 2545.87i | 0.758158 | + | 2.82875i | ||||
\(901\) | 1879.82 | 2.08638 | ||||||||
\(902\) | −19.1343 | − | 30.1709i | −0.0212131 | − | 0.0334489i | ||||
\(903\) | −3260.09 | −3.61029 | ||||||||
\(904\) | −506.385 | + | 63.5043i | −0.560160 | + | 0.0702482i | ||||
\(905\) | −148.726 | − | 405.990i | −0.164338 | − | 0.448608i | ||||
\(906\) | −1121.85 | − | 1768.93i | −1.23824 | − | 1.95246i | ||||
\(907\) | 1051.70 | 1.15954 | 0.579769 | − | 0.814781i | \(-0.303143\pi\) | ||||
0.579769 | + | 0.814781i | \(0.303143\pi\) | |||||||
\(908\) | −365.203 | + | 774.878i | −0.402206 | + | 0.853389i | ||||
\(909\) | 1931.92 | 2.12533 | ||||||||
\(910\) | 85.6036 | − | 111.568i | 0.0940699 | − | 0.122603i | ||||
\(911\) | 877.343i | 0.963055i | 0.876431 | + | 0.481528i | \(0.159918\pi\) | ||||
−0.876431 | + | 0.481528i | \(0.840082\pi\) | |||||||
\(912\) | 319.853 | − | 263.954i | 0.350716 | − | 0.289423i | ||||
\(913\) | − | 400.019i | − | 0.438136i | ||||||
\(914\) | −470.594 | − | 742.034i | −0.514873 | − | 0.811853i | ||||
\(915\) | −322.303 | − | 879.819i | −0.352243 | − | 0.961551i | ||||
\(916\) | 617.978 | − | 1311.21i | 0.674649 | − | 1.43145i | ||||
\(917\) | 1171.96i | 1.27804i | ||||||||
\(918\) | −3369.08 | − | 5312.37i | −3.67002 | − | 5.78690i | ||||
\(919\) | − | 650.090i | − | 0.707389i | −0.935361 | − | 0.353694i | \(-0.884925\pi\) | ||
0.935361 | − | 0.353694i | \(-0.115075\pi\) | |||||||
\(920\) | −191.361 | + | 98.6301i | −0.208001 | + | 0.107207i | ||||
\(921\) | 1905.28 | 2.06871 | ||||||||
\(922\) | 650.115 | − | 412.300i | 0.705114 | − | 0.447180i | ||||
\(923\) | 35.0270 | 0.0379491 | ||||||||
\(924\) | −1157.80 | − | 545.677i | −1.25303 | − | 0.590559i | ||||
\(925\) | 579.422 | + | 684.721i | 0.626402 | + | 0.740239i | ||||
\(926\) | 1155.71 | − | 732.945i | 1.24807 | − | 0.791517i | ||||
\(927\) | 618.383 | 0.667080 | ||||||||
\(928\) | 761.448 | + | 248.684i | 0.820526 | + | 0.267978i | ||||
\(929\) | 559.216 | 0.601955 | 0.300977 | − | 0.953631i | \(-0.402687\pi\) | ||||
0.300977 | + | 0.953631i | \(0.402687\pi\) | |||||||
\(930\) | −943.068 | + | 1229.11i | −1.01405 | + | 1.32163i | ||||
\(931\) | 187.731i | 0.201645i | ||||||||
\(932\) | −1133.87 | − | 534.399i | −1.21660 | − | 0.573389i | ||||
\(933\) | 3208.99i | 3.43943i | ||||||||
\(934\) | −1472.37 | + | 933.769i | −1.57641 | + | 0.999753i | ||||
\(935\) | −293.953 | − | 802.430i | −0.314388 | − | 0.858213i | ||||
\(936\) | 306.627 | − | 38.4532i | 0.327593 | − | 0.0410825i | ||||
\(937\) | 1082.01i | 1.15476i | 0.816476 | + | 0.577380i | \(0.195925\pi\) | ||||
−0.816476 | + | 0.577380i | \(0.804075\pi\) | |||||||
\(938\) | −217.298 | + | 137.809i | −0.231661 | + | 0.146918i | ||||
\(939\) | − | 2025.78i | − | 2.15738i | ||||||
\(940\) | −609.602 | − | 54.5714i | −0.648512 | − | 0.0580547i | ||||
\(941\) | −1259.52 | −1.33849 | −0.669244 | − | 0.743042i | \(-0.733382\pi\) | ||||
−0.669244 | + | 0.743042i | \(0.733382\pi\) | |||||||
\(942\) | −889.787 | − | 1403.02i | −0.944572 | − | 1.48940i | ||||
\(943\) | 17.1426 | 0.0181788 | ||||||||
\(944\) | −624.354 | + | 515.239i | −0.661392 | + | 0.545804i | ||||
\(945\) | −1703.23 | − | 4649.46i | −1.80236 | − | 4.92006i | ||||
\(946\) | −343.258 | − | 541.250i | −0.362852 | − | 0.572146i | ||||
\(947\) | 1810.83 | 1.91217 | 0.956085 | − | 0.293089i | \(-0.0946833\pi\) | ||||
0.956085 | + | 0.293089i | \(0.0946833\pi\) | |||||||
\(948\) | −1229.12 | − | 579.291i | −1.29655 | − | 0.611067i | ||||
\(949\) | 93.3664 | 0.0983840 | ||||||||
\(950\) | 207.996 | + | 65.0980i | 0.218943 | + | 0.0685242i | ||||
\(951\) | 2732.19i | 2.87297i | ||||||||
\(952\) | 2321.13 | − | 291.087i | 2.43816 | − | 0.305763i | ||||
\(953\) | 837.455i | 0.878757i | 0.898302 | + | 0.439378i | \(0.144801\pi\) | ||||
−0.898302 | + | 0.439378i | \(0.855199\pi\) | |||||||
\(954\) | 1741.50 | + | 2745.99i | 1.82547 | + | 2.87840i | ||||
\(955\) | 817.807 | − | 299.586i | 0.856342 | − | 0.313702i | ||||
\(956\) | 847.782 | + | 399.563i | 0.886801 | + | 0.417952i | ||||
\(957\) | 834.787i | 0.872295i | ||||||||
\(958\) | −343.786 | − | 542.082i | −0.358858 | − | 0.565848i | ||||
\(959\) | 797.258i | 0.831343i | ||||||||
\(960\) | −1075.43 | − | 1569.73i | −1.12024 | − | 1.63513i | ||||
\(961\) | 282.188 | 0.293640 | ||||||||
\(962\) | 88.8127 | − | 56.3246i | 0.0923209 | − | 0.0585494i | ||||
\(963\) | −2516.08 | −2.61275 | ||||||||
\(964\) | −57.0016 | + | 120.944i | −0.0591303 | + | 0.125461i | ||||
\(965\) | 1695.24 | − | 621.012i | 1.75672 | − | 0.643536i | ||||
\(966\) | 518.645 | − | 328.922i | 0.536899 | − | 0.340499i | ||||
\(967\) | −876.040 | −0.905936 | −0.452968 | − | 0.891527i | \(-0.649635\pi\) | ||||
−0.452968 | + | 0.891527i | \(0.649635\pi\) | |||||||
\(968\) | 89.1395 | + | 710.800i | 0.0920863 | + | 0.734298i | ||||
\(969\) | −789.876 | −0.815146 | ||||||||
\(970\) | −722.327 | + | 941.418i | −0.744667 | + | 0.970534i | ||||
\(971\) | 544.201i | 0.560454i | 0.959934 | + | 0.280227i | \(0.0904098\pi\) | ||||
−0.959934 | + | 0.280227i | \(0.909590\pi\) | |||||||
\(972\) | 2233.61 | − | 4739.22i | 2.29795 | − | 4.87574i | ||||
\(973\) | 780.442i | 0.802098i | ||||||||
\(974\) | −870.184 | + | 551.866i | −0.893412 | + | 0.566598i | ||||
\(975\) | 140.734 | + | 166.310i | 0.144343 | + | 0.170574i | ||||
\(976\) | 320.952 | + | 388.922i | 0.328845 | + | 0.398486i | ||||
\(977\) | 1823.45i | 1.86637i | 0.359394 | + | 0.933186i | \(0.382983\pi\) | ||||
−0.359394 | + | 0.933186i | \(0.617017\pi\) | |||||||
\(978\) | 972.369 | − | 616.672i | 0.994243 | − | 0.630544i | ||||
\(979\) | − | 42.3363i | − | 0.0432444i | ||||||
\(980\) | 857.938 | + | 76.8025i | 0.875447 | + | 0.0783699i | ||||
\(981\) | −2091.95 | −2.13246 | ||||||||
\(982\) | −529.752 | − | 835.314i | −0.539462 | − | 0.850625i | ||||
\(983\) | 521.962 | 0.530989 | 0.265495 | − | 0.964112i | \(-0.414465\pi\) | ||||
0.265495 | + | 0.964112i | \(0.414465\pi\) | |||||||
\(984\) | 18.8534 | + | 150.337i | 0.0191600 | + | 0.152782i | ||||
\(985\) | 458.747 | − | 168.052i | 0.465733 | − | 0.170611i | ||||
\(986\) | −817.124 | − | 1288.44i | −0.828726 | − | 1.30674i | ||||
\(987\) | 1746.00 | 1.76900 | ||||||||
\(988\) | 10.8940 | − | 23.1146i | 0.0110263 | − | 0.0233953i | ||||
\(989\) | 307.529 | 0.310949 | ||||||||
\(990\) | 899.844 | − | 1172.78i | 0.908934 | − | 1.18463i | ||||
\(991\) | 978.158i | 0.987041i | 0.869734 | + | 0.493521i | \(0.164290\pi\) | ||||
−0.869734 | + | 0.493521i | \(0.835710\pi\) | |||||||
\(992\) | 258.836 | − | 792.533i | 0.260923 | − | 0.798924i | ||||
\(993\) | − | 2314.97i | − | 2.33129i | ||||||
\(994\) | 245.639 | + | 387.325i | 0.247122 | + | 0.389663i | ||||
\(995\) | −1435.98 | + | 526.039i | −1.44319 | + | 0.528683i | ||||
\(996\) | −723.243 | + | 1534.56i | −0.726147 | + | 1.54072i | ||||
\(997\) | 41.2743i | 0.0413985i | 0.999786 | + | 0.0206993i | \(0.00658925\pi\) | ||||
−0.999786 | + | 0.0206993i | \(0.993411\pi\) | |||||||
\(998\) | −474.820 | − | 748.698i | −0.475772 | − | 0.750198i | ||||
\(999\) | − | 3703.08i | − | 3.70679i |
(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 | 380.3.h.a.39.20 | yes | 108 | |
4.3 | odd | 2 | inner | 380.3.h.a.39.90 | yes | 108 | |
5.4 | even | 2 | inner | 380.3.h.a.39.89 | yes | 108 | |
20.19 | odd | 2 | inner | 380.3.h.a.39.19 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.3.h.a.39.19 | ✓ | 108 | 20.19 | odd | 2 | inner | |
380.3.h.a.39.20 | yes | 108 | 1.1 | even | 1 | trivial | |
380.3.h.a.39.89 | yes | 108 | 5.4 | even | 2 | inner | |
380.3.h.a.39.90 | yes | 108 | 4.3 | odd | 2 | inner |