Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(251,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.e (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: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.4521217600.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} - 2x^{4} + 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.2 | ||
Root | \(1.29437 + 0.569745i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.251 |
Dual form | 300.2.e.d.251.1 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.29437 | + | 0.569745i | −0.915257 | + | 0.402871i | ||||
\(3\) | −0.908080 | − | 1.47492i | −0.524280 | − | 0.851546i | ||||
\(4\) | 1.35078 | − | 1.47492i | 0.675391 | − | 0.737460i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.01572 | + | 1.39172i | 0.822914 | + | 0.568166i | ||||
\(7\) | 2.50967i | 0.948566i | 0.880373 | + | 0.474283i | \(0.157293\pi\) | ||||
−0.880373 | + | 0.474283i | \(0.842707\pi\) | |||||||
\(8\) | −0.908080 | + | 2.67869i | −0.321055 | + | 0.947061i | ||||
\(9\) | −1.35078 | + | 2.67869i | −0.450260 | + | 0.892897i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.36131 | 1.01347 | 0.506737 | − | 0.862101i | \(-0.330851\pi\) | ||||
0.506737 | + | 0.862101i | \(0.330851\pi\) | |||||||
\(12\) | −3.40201 | − | 0.652949i | −0.982075 | − | 0.188490i | ||||
\(13\) | 3.70156 | 1.02663 | 0.513314 | − | 0.858201i | \(-0.328418\pi\) | ||||
0.513314 | + | 0.858201i | \(0.328418\pi\) | |||||||
\(14\) | −1.42987 | − | 3.24844i | −0.382149 | − | 0.868181i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.350781 | − | 3.98459i | −0.0876953 | − | 0.996147i | ||||
\(17\) | − | 7.63636i | − | 1.85209i | −0.377413 | − | 0.926045i | \(-0.623186\pi\) | ||
0.377413 | − | 0.926045i | \(-0.376814\pi\) | |||||||
\(18\) | 0.222237 | − | 4.23682i | 0.0523818 | − | 0.998627i | ||||
\(19\) | 0.440172i | 0.100982i | 0.998725 | + | 0.0504912i | \(0.0160787\pi\) | ||||
−0.998725 | + | 0.0504912i | \(0.983921\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.70156 | − | 2.27898i | 0.807747 | − | 0.497314i | ||||
\(22\) | −4.35078 | + | 1.91509i | −0.927590 | + | 0.408299i | ||||
\(23\) | 5.17748 | 1.07958 | 0.539789 | − | 0.841800i | \(-0.318504\pi\) | ||||
0.539789 | + | 0.841800i | \(0.318504\pi\) | |||||||
\(24\) | 4.77547 | − | 1.09312i | 0.974788 | − | 0.223132i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.79119 | + | 2.10895i | −0.939629 | + | 0.413599i | ||||
\(27\) | 5.17748 | − | 0.440172i | 0.996406 | − | 0.0847112i | ||||
\(28\) | 3.70156 | + | 3.39001i | 0.699529 | + | 0.640652i | ||||
\(29\) | 2.27898i | 0.423196i | 0.977357 | + | 0.211598i | \(0.0678668\pi\) | ||||
−0.977357 | + | 0.211598i | \(0.932133\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.39001i | − | 0.608864i | −0.952534 | − | 0.304432i | \(-0.901533\pi\) | ||
0.952534 | − | 0.304432i | \(-0.0984667\pi\) | |||||||
\(32\) | 2.72424 | + | 4.95767i | 0.481582 | + | 0.876401i | ||||
\(33\) | −3.05234 | − | 4.95767i | −0.531345 | − | 0.863020i | ||||
\(34\) | 4.35078 | + | 9.88427i | 0.746153 | + | 1.69514i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.12625 | + | 5.61062i | 0.354375 | + | 0.935104i | ||||
\(37\) | 7.40312 | 1.21707 | 0.608533 | − | 0.793529i | \(-0.291758\pi\) | ||||
0.608533 | + | 0.793529i | \(0.291758\pi\) | |||||||
\(38\) | −0.250786 | − | 0.569745i | −0.0406828 | − | 0.0924249i | ||||
\(39\) | −3.36131 | − | 5.45951i | −0.538241 | − | 0.874221i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.07840i | − | 0.480766i | −0.970678 | − | 0.240383i | \(-0.922727\pi\) | ||
0.970678 | − | 0.240383i | \(-0.0772730\pi\) | |||||||
\(42\) | −3.49275 | + | 5.05879i | −0.538943 | + | 0.780588i | ||||
\(43\) | 8.40935i | 1.28241i | 0.767368 | + | 0.641207i | \(0.221566\pi\) | ||||
−0.767368 | + | 0.641207i | \(0.778434\pi\) | |||||||
\(44\) | 4.54040 | − | 4.95767i | 0.684491 | − | 0.747397i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.70156 | + | 2.94984i | −0.988091 | + | 0.434930i | ||||
\(47\) | −3.63232 | −0.529828 | −0.264914 | − | 0.964272i | \(-0.585344\pi\) | ||||
−0.264914 | + | 0.964272i | \(0.585344\pi\) | |||||||
\(48\) | −5.55842 | + | 4.13570i | −0.802288 | + | 0.596937i | ||||
\(49\) | 0.701562 | 0.100223 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.2630 | + | 6.93443i | −1.57714 | + | 0.971014i | ||||
\(52\) | 5.00000 | − | 5.45951i | 0.693375 | − | 0.757098i | ||||
\(53\) | 2.27898i | 0.313042i | 0.987675 | + | 0.156521i | \(0.0500279\pi\) | ||||
−0.987675 | + | 0.156521i | \(0.949972\pi\) | |||||||
\(54\) | −6.45078 | + | 3.51959i | −0.877839 | + | 0.478955i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.72263 | − | 2.27898i | −0.898349 | − | 0.304542i | ||||
\(57\) | 0.649219 | − | 0.399712i | 0.0859911 | − | 0.0529431i | ||||
\(58\) | −1.29844 | − | 2.94984i | −0.170493 | − | 0.387333i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.70156 | −0.730010 | −0.365005 | − | 0.931006i | \(-0.618933\pi\) | ||||
−0.365005 | + | 0.931006i | \(0.618933\pi\) | |||||||
\(62\) | 1.93144 | + | 4.38793i | 0.245294 | + | 0.557267i | ||||
\(63\) | −6.72263 | − | 3.39001i | −0.846972 | − | 0.427102i | ||||
\(64\) | −6.35078 | − | 4.86493i | −0.793848 | − | 0.608117i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.77547 | + | 4.67800i | 0.834002 | + | 0.575822i | ||||
\(67\) | − | 5.45951i | − | 0.666985i | −0.942753 | − | 0.333493i | \(-0.891773\pi\) | ||
0.942753 | − | 0.333493i | \(-0.108227\pi\) | |||||||
\(68\) | −11.2630 | − | 10.3151i | −1.36584 | − | 1.25088i | ||||
\(69\) | −4.70156 | − | 7.63636i | −0.566002 | − | 0.919310i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4421 | 1.47661 | 0.738304 | − | 0.674468i | \(-0.235627\pi\) | ||||
0.738304 | + | 0.674468i | \(0.235627\pi\) | |||||||
\(72\) | −5.94877 | − | 6.05079i | −0.701070 | − | 0.713093i | ||||
\(73\) | −1.29844 | −0.151971 | −0.0759853 | − | 0.997109i | \(-0.524210\pi\) | ||||
−0.0759853 | + | 0.997109i | \(0.524210\pi\) | |||||||
\(74\) | −9.58237 | + | 4.21789i | −1.11393 | + | 0.490320i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.649219 | + | 0.594576i | 0.0744705 | + | 0.0682026i | ||||
\(77\) | 8.43579i | 0.961347i | ||||||||
\(78\) | 7.46131 | + | 5.15153i | 0.844827 | + | 0.583296i | ||||
\(79\) | 5.01934i | 0.564720i | 0.959309 | + | 0.282360i | \(0.0911172\pi\) | ||||
−0.959309 | + | 0.282360i | \(0.908883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.35078 | − | 7.23665i | −0.594531 | − | 0.804073i | ||||
\(82\) | 1.75391 | + | 3.98459i | 0.193686 | + | 0.440024i | ||||
\(83\) | −1.81616 | −0.199349 | −0.0996747 | − | 0.995020i | \(-0.531780\pi\) | ||||
−0.0996747 | + | 0.995020i | \(0.531780\pi\) | |||||||
\(84\) | 1.63869 | − | 8.53791i | 0.178795 | − | 0.931563i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.79119 | − | 10.8848i | −0.516647 | − | 1.17374i | ||||
\(87\) | 3.36131 | − | 2.06950i | 0.360371 | − | 0.221873i | ||||
\(88\) | −3.05234 | + | 9.00393i | −0.325381 | + | 0.959822i | ||||
\(89\) | 5.35738i | 0.567882i | 0.958842 | + | 0.283941i | \(0.0916419\pi\) | ||||
−0.958842 | + | 0.283941i | \(0.908358\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.28970i | 0.973825i | ||||||||
\(92\) | 6.99364 | − | 7.63636i | 0.729137 | − | 0.796146i | ||||
\(93\) | −5.00000 | + | 3.07840i | −0.518476 | + | 0.319216i | ||||
\(94\) | 4.70156 | − | 2.06950i | 0.484929 | − | 0.213452i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.83834 | − | 8.52000i | 0.493811 | − | 0.869569i | ||||
\(97\) | −11.1047 | −1.12751 | −0.563755 | − | 0.825942i | \(-0.690644\pi\) | ||||
−0.563755 | + | 0.825942i | \(0.690644\pi\) | |||||||
\(98\) | −0.908080 | + | 0.399712i | −0.0917299 | + | 0.0403770i | ||||
\(99\) | −4.54040 | + | 9.00393i | −0.456327 | + | 0.904929i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.5517i | 1.74646i | 0.487308 | + | 0.873230i | \(0.337979\pi\) | ||||
−0.487308 | + | 0.873230i | \(0.662021\pi\) | |||||||
\(102\) | 10.6277 | − | 15.3928i | 1.05229 | − | 1.52411i | ||||
\(103\) | − | 10.9190i | − | 1.07588i | −0.842982 | − | 0.537941i | \(-0.819202\pi\) | ||
0.842982 | − | 0.537941i | \(-0.180798\pi\) | |||||||
\(104\) | −3.36131 | + | 9.91534i | −0.329604 | + | 0.972280i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.29844 | − | 2.94984i | −0.126115 | − | 0.286514i | ||||
\(107\) | −6.45162 | −0.623702 | −0.311851 | − | 0.950131i | \(-0.600949\pi\) | ||||
−0.311851 | + | 0.950131i | \(0.600949\pi\) | |||||||
\(108\) | 6.34442 | − | 8.23094i | 0.610492 | − | 0.792023i | ||||
\(109\) | 2.29844 | 0.220150 | 0.110075 | − | 0.993923i | \(-0.464891\pi\) | ||||
0.110075 | + | 0.993923i | \(0.464891\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.72263 | − | 10.9190i | −0.638084 | − | 1.03639i | ||||
\(112\) | 10.0000 | − | 0.880344i | 0.944911 | − | 0.0831847i | ||||
\(113\) | − | 0.799423i | − | 0.0752034i | −0.999293 | − | 0.0376017i | \(-0.988028\pi\) | ||
0.999293 | − | 0.0376017i | \(-0.0119718\pi\) | |||||||
\(114\) | −0.612595 | + | 0.887263i | −0.0573748 | + | 0.0830998i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.36131 | + | 3.07840i | 0.312090 | + | 0.285823i | ||||
\(117\) | −5.00000 | + | 9.91534i | −0.462250 | + | 0.916674i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.1647 | 1.75683 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.298438 | 0.0271307 | ||||||||
\(122\) | 7.37992 | − | 3.24844i | 0.668147 | − | 0.294100i | ||||
\(123\) | −4.54040 | + | 2.79544i | −0.409394 | + | 0.252056i | ||||
\(124\) | −5.00000 | − | 4.57917i | −0.449013 | − | 0.411221i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 10.6330 | + | 0.557742i | 0.947263 | + | 0.0496876i | ||||
\(127\) | 12.6797i | 1.12514i | 0.826749 | + | 0.562571i | \(0.190188\pi\) | ||||
−0.826749 | + | 0.562571i | \(0.809812\pi\) | |||||||
\(128\) | 10.9920 | + | 2.67869i | 0.971567 | + | 0.236765i | ||||
\(129\) | 12.4031 | − | 7.63636i | 1.09203 | − | 0.672344i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.71949 | −0.499714 | −0.249857 | − | 0.968283i | \(-0.580384\pi\) | ||||
−0.249857 | + | 0.968283i | \(0.580384\pi\) | |||||||
\(132\) | −11.4352 | − | 2.19477i | −0.995308 | − | 0.191030i | ||||
\(133\) | −1.10469 | −0.0957885 | ||||||||
\(134\) | 3.11053 | + | 7.06662i | 0.268709 | + | 0.610463i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.4555 | + | 6.93443i | 1.75404 | + | 0.594623i | ||||
\(137\) | 9.91534i | 0.847125i | 0.905867 | + | 0.423563i | \(0.139221\pi\) | ||||
−0.905867 | + | 0.423563i | \(0.860779\pi\) | |||||||
\(138\) | 10.4363 | + | 7.20558i | 0.888400 | + | 0.613380i | ||||
\(139\) | − | 2.94984i | − | 0.250202i | −0.992144 | − | 0.125101i | \(-0.960074\pi\) | ||
0.992144 | − | 0.125101i | \(-0.0399255\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.29844 | + | 5.35738i | 0.277779 | + | 0.451173i | ||||
\(142\) | −16.1047 | + | 7.08883i | −1.35148 | + | 0.594882i | ||||
\(143\) | 12.4421 | 1.04046 | ||||||||
\(144\) | 11.1473 | + | 4.44267i | 0.928943 | + | 0.370223i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.68066 | − | 0.739779i | 0.139092 | − | 0.0612245i | ||||
\(147\) | −0.637075 | − | 1.03475i | −0.0525450 | − | 0.0853446i | ||||
\(148\) | 10.0000 | − | 10.9190i | 0.821995 | − | 0.897538i | ||||
\(149\) | − | 15.2727i | − | 1.25119i | −0.780148 | − | 0.625595i | \(-0.784856\pi\) | ||
0.780148 | − | 0.625595i | \(-0.215144\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 19.3284i | − | 1.57292i | −0.617641 | − | 0.786460i | \(-0.711911\pi\) | ||
0.617641 | − | 0.786460i | \(-0.288089\pi\) | |||||||
\(152\) | −1.17909 | − | 0.399712i | −0.0956365 | − | 0.0324209i | ||||
\(153\) | 20.4555 | + | 10.3151i | 1.65373 | + | 0.833923i | ||||
\(154\) | −4.80625 | − | 10.9190i | −0.387299 | − | 0.879880i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −12.5927 | − | 2.41693i | −1.00823 | − | 0.193509i | ||||
\(157\) | −11.1047 | −0.886250 | −0.443125 | − | 0.896460i | \(-0.646130\pi\) | ||||
−0.443125 | + | 0.896460i | \(0.646130\pi\) | |||||||
\(158\) | −2.85974 | − | 6.49687i | −0.227509 | − | 0.516864i | ||||
\(159\) | 3.36131 | − | 2.06950i | 0.266570 | − | 0.164122i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.9937i | 1.02405i | ||||||||
\(162\) | 11.0489 | + | 6.31832i | 0.868086 | + | 0.496414i | ||||
\(163\) | 0.440172i | 0.0344769i | 0.999851 | + | 0.0172385i | \(0.00548745\pi\) | ||||
−0.999851 | + | 0.0172385i | \(0.994513\pi\) | |||||||
\(164\) | −4.54040 | − | 4.15825i | −0.354546 | − | 0.324705i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.35078 | − | 1.03475i | 0.182456 | − | 0.0803120i | ||||
\(167\) | −15.5324 | −1.20194 | −0.600968 | − | 0.799273i | \(-0.705218\pi\) | ||||
−0.600968 | + | 0.799273i | \(0.705218\pi\) | |||||||
\(168\) | 2.74337 | + | 11.9848i | 0.211656 | + | 0.924651i | ||||
\(169\) | 0.701562 | 0.0539663 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.17909 | − | 0.594576i | −0.0901669 | − | 0.0454684i | ||||
\(172\) | 12.4031 | + | 11.3592i | 0.945729 | + | 0.866130i | ||||
\(173\) | 8.43579i | 0.641361i | 0.947187 | + | 0.320681i | \(0.103912\pi\) | ||||
−0.947187 | + | 0.320681i | \(0.896088\pi\) | |||||||
\(174\) | −3.17170 | + | 4.59378i | −0.240446 | + | 0.348254i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.17909 | − | 13.3935i | −0.0888769 | − | 1.00957i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.05234 | − | 6.93443i | −0.228783 | − | 0.519758i | ||||
\(179\) | −9.08080 | −0.678731 | −0.339365 | − | 0.940655i | \(-0.610212\pi\) | ||||
−0.339365 | + | 0.940655i | \(0.610212\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5078 | 0.781039 | 0.390520 | − | 0.920595i | \(-0.372295\pi\) | ||||
0.390520 | + | 0.920595i | \(0.372295\pi\) | |||||||
\(182\) | −5.29276 | − | 12.0243i | −0.392325 | − | 0.891300i | ||||
\(183\) | 5.17748 | + | 8.40935i | 0.382730 | + | 0.621637i | ||||
\(184\) | −4.70156 | + | 13.8689i | −0.346604 | + | 1.02243i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.71794 | − | 6.83331i | 0.345936 | − | 0.501043i | ||||
\(187\) | − | 25.6682i | − | 1.87705i | ||||||
\(188\) | −4.90647 | + | 5.35738i | −0.357841 | + | 0.390727i | ||||
\(189\) | 1.10469 | + | 12.9937i | 0.0803541 | + | 0.945156i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.4421 | 0.900280 | 0.450140 | − | 0.892958i | \(-0.351374\pi\) | ||||
0.450140 | + | 0.892958i | \(0.351374\pi\) | |||||||
\(192\) | −1.40837 | + | 13.7846i | −0.101641 | + | 0.994821i | ||||
\(193\) | −19.8062 | −1.42568 | −0.712842 | − | 0.701324i | \(-0.752593\pi\) | ||||
−0.712842 | + | 0.701324i | \(0.752593\pi\) | |||||||
\(194\) | 14.3736 | − | 6.32684i | 1.03196 | − | 0.454241i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.947657 | − | 1.03475i | 0.0676898 | − | 0.0739106i | ||||
\(197\) | − | 10.7148i | − | 0.763396i | −0.924287 | − | 0.381698i | \(-0.875340\pi\) | ||
0.924287 | − | 0.381698i | \(-0.124660\pi\) | |||||||
\(198\) | 0.747009 | − | 14.2413i | 0.0530876 | − | 1.01208i | ||||
\(199\) | − | 21.0891i | − | 1.49496i | −0.664282 | − | 0.747482i | \(-0.731263\pi\) | ||
0.664282 | − | 0.747482i | \(-0.268737\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.05234 | + | 4.95767i | −0.567968 | + | 0.349687i | ||||
\(202\) | −10.0000 | − | 22.7184i | −0.703598 | − | 1.59846i | ||||
\(203\) | −5.71949 | −0.401429 | ||||||||
\(204\) | −4.98615 | + | 25.9790i | −0.349101 | + | 1.81889i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.22106 | + | 14.1332i | 0.433442 | + | 0.984709i | ||||
\(207\) | −6.99364 | + | 13.8689i | −0.486091 | + | 0.963952i | ||||
\(208\) | −1.29844 | − | 14.7492i | −0.0900305 | − | 1.02267i | ||||
\(209\) | 1.47956i | 0.102343i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1392i | 1.24876i | 0.781123 | + | 0.624378i | \(0.214647\pi\) | ||||
−0.781123 | + | 0.624378i | \(0.785353\pi\) | |||||||
\(212\) | 3.36131 | + | 3.07840i | 0.230856 | + | 0.211426i | ||||
\(213\) | −11.2984 | − | 18.3511i | −0.774156 | − | 1.25740i | ||||
\(214\) | 8.35078 | − | 3.67578i | 0.570848 | − | 0.251271i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.52248 | + | 14.2686i | −0.239674 | + | 0.970853i | ||||
\(217\) | 8.50781 | 0.577548 | ||||||||
\(218\) | −2.97503 | + | 1.30952i | −0.201494 | + | 0.0886921i | ||||
\(219\) | 1.17909 | + | 1.91509i | 0.0796752 | + | 0.129410i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 28.2665i | − | 1.90141i | ||||||
\(222\) | 14.9226 | + | 10.3031i | 1.00154 | + | 0.691496i | ||||
\(223\) | − | 21.0891i | − | 1.41223i | −0.708098 | − | 0.706114i | \(-0.750447\pi\) | ||
0.708098 | − | 0.706114i | \(-0.249553\pi\) | |||||||
\(224\) | −12.4421 | + | 6.83694i | −0.831324 | + | 0.456812i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.455467 | + | 1.03475i | 0.0302972 | + | 0.0688304i | ||||
\(227\) | 22.2551 | 1.47712 | 0.738560 | − | 0.674188i | \(-0.235506\pi\) | ||||
0.738560 | + | 0.674188i | \(0.235506\pi\) | |||||||
\(228\) | 0.287410 | − | 1.49747i | 0.0190342 | − | 0.0991723i | ||||
\(229\) | 2.29844 | 0.151885 | 0.0759425 | − | 0.997112i | \(-0.475803\pi\) | ||||
0.0759425 | + | 0.997112i | \(0.475803\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.4421 | − | 7.66037i | 0.818631 | − | 0.504015i | ||||
\(232\) | −6.10469 | − | 2.06950i | −0.400792 | − | 0.135869i | ||||
\(233\) | 8.43579i | 0.552647i | 0.961065 | + | 0.276323i | \(0.0891161\pi\) | ||||
−0.961065 | + | 0.276323i | \(0.910884\pi\) | |||||||
\(234\) | 0.822625 | − | 15.6828i | 0.0537767 | − | 1.02522i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.40312 | − | 4.55796i | 0.480885 | − | 0.296071i | ||||
\(238\) | −24.8062 | + | 10.9190i | −1.60795 | + | 0.707775i | ||||
\(239\) | −25.8874 | −1.67452 | −0.837258 | − | 0.546809i | \(-0.815842\pi\) | ||||
−0.837258 | + | 0.546809i | \(0.815842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | 0.450910 | 0.225455 | − | 0.974254i | \(-0.427613\pi\) | ||||
0.225455 | + | 0.974254i | \(0.427613\pi\) | |||||||
\(242\) | −0.386289 | + | 0.170034i | −0.0248316 | + | 0.0109302i | ||||
\(243\) | −5.81455 | + | 14.4634i | −0.373004 | + | 0.927830i | ||||
\(244\) | −7.70156 | + | 8.40935i | −0.493042 | + | 0.538354i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.28427 | − | 6.20520i | 0.273155 | − | 0.395629i | ||||
\(247\) | 1.62932i | 0.103671i | ||||||||
\(248\) | 9.08080 | + | 3.07840i | 0.576631 | + | 0.195479i | ||||
\(249\) | 1.64922 | + | 2.67869i | 0.104515 | + | 0.169755i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.5261 | −1.42183 | −0.710916 | − | 0.703277i | \(-0.751719\pi\) | ||||
−0.710916 | + | 0.703277i | \(0.751719\pi\) | |||||||
\(252\) | −14.0808 | + | 5.33618i | −0.887007 | + | 0.336148i | ||||
\(253\) | 17.4031 | 1.09413 | ||||||||
\(254\) | −7.22420 | − | 16.4122i | −0.453287 | − | 1.02979i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.7539 | + | 2.79544i | −0.984619 | + | 0.174715i | ||||
\(257\) | − | 4.55796i | − | 0.284318i | −0.989844 | − | 0.142159i | \(-0.954596\pi\) | ||
0.989844 | − | 0.142159i | \(-0.0454044\pi\) | |||||||
\(258\) | −11.7034 | + | 16.9509i | −0.728624 | + | 1.05532i | ||||
\(259\) | 18.5794i | 1.15447i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.10469 | − | 3.07840i | −0.377871 | − | 0.190548i | ||||
\(262\) | 7.40312 | − | 3.25865i | 0.457367 | − | 0.201320i | ||||
\(263\) | −18.6227 | −1.14833 | −0.574164 | − | 0.818741i | \(-0.694673\pi\) | ||||
−0.574164 | + | 0.818741i | \(0.694673\pi\) | |||||||
\(264\) | 16.0518 | − | 3.67432i | 0.987923 | − | 0.226139i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.42987 | − | 0.629390i | 0.0876710 | − | 0.0385904i | ||||
\(267\) | 7.90172 | − | 4.86493i | 0.483577 | − | 0.297729i | ||||
\(268\) | −8.05234 | − | 7.37460i | −0.491875 | − | 0.450476i | ||||
\(269\) | 8.43579i | 0.514339i | 0.966366 | + | 0.257170i | \(0.0827899\pi\) | ||||
−0.966366 | + | 0.257170i | \(0.917210\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.15833i | 0.556329i | 0.960533 | + | 0.278165i | \(0.0897260\pi\) | ||||
−0.960533 | + | 0.278165i | \(0.910274\pi\) | |||||||
\(272\) | −30.4278 | + | 2.67869i | −1.84495 | + | 0.162420i | ||||
\(273\) | 13.7016 | − | 8.43579i | 0.829256 | − | 0.510557i | ||||
\(274\) | −5.64922 | − | 12.8341i | −0.341282 | − | 0.775337i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −17.6138 | − | 3.38063i | −1.06023 | − | 0.203490i | ||||
\(277\) | 8.89531 | 0.534468 | 0.267234 | − | 0.963632i | \(-0.413890\pi\) | ||||
0.267234 | + | 0.963632i | \(0.413890\pi\) | |||||||
\(278\) | 1.68066 | + | 3.81818i | 0.100799 | + | 0.228999i | ||||
\(279\) | 9.08080 | + | 4.57917i | 0.543653 | + | 0.274147i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.5517i | − | 1.04705i | −0.852011 | − | 0.523524i | \(-0.824617\pi\) | ||
0.852011 | − | 0.523524i | \(-0.175383\pi\) | |||||||
\(282\) | −7.32174 | − | 5.05516i | −0.436003 | − | 0.301030i | ||||
\(283\) | 16.3785i | 0.973603i | 0.873513 | + | 0.486801i | \(0.161836\pi\) | ||||
−0.873513 | + | 0.486801i | \(0.838164\pi\) | |||||||
\(284\) | 16.8066 | − | 18.3511i | 0.997287 | − | 1.08894i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.1047 | + | 7.08883i | −0.952290 | + | 0.419172i | ||||
\(287\) | 7.72577 | 0.456038 | ||||||||
\(288\) | −16.9599 | + | 0.600671i | −0.999373 | + | 0.0353949i | ||||
\(289\) | −41.3141 | −2.43024 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.0839 | + | 16.3785i | 0.591131 | + | 0.960126i | ||||
\(292\) | −1.75391 | + | 1.91509i | −0.102640 | + | 0.112072i | ||||
\(293\) | − | 21.4295i | − | 1.25193i | −0.779852 | − | 0.625963i | \(-0.784706\pi\) | ||
0.779852 | − | 0.625963i | \(-0.215294\pi\) | |||||||
\(294\) | 1.41415 | + | 0.976376i | 0.0824750 | + | 0.0569434i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.72263 | + | 19.8307i | −0.390745 | + | 1.15264i | ||||
\(297\) | 17.4031 | − | 1.47956i | 1.00983 | − | 0.0858526i | ||||
\(298\) | 8.70156 | + | 19.7685i | 0.504068 | + | 1.14516i | ||||
\(299\) | 19.1647 | 1.10833 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.1047 | −1.21645 | ||||||||
\(302\) | 11.0122 | + | 25.0180i | 0.633683 | + | 1.43963i | ||||
\(303\) | 25.8874 | − | 15.9384i | 1.48719 | − | 0.915635i | ||||
\(304\) | 1.75391 | − | 0.154404i | 0.100593 | − | 0.00885568i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −32.3539 | − | 1.69708i | −1.84955 | − | 0.0970159i | ||||
\(307\) | 26.4172i | 1.50771i | 0.657041 | + | 0.753855i | \(0.271808\pi\) | ||||
−0.657041 | + | 0.753855i | \(0.728192\pi\) | |||||||
\(308\) | 12.4421 | + | 11.3949i | 0.708955 | + | 0.649285i | ||||
\(309\) | −16.1047 | + | 9.91534i | −0.916164 | + | 0.564064i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.4453 | −0.762411 | −0.381205 | − | 0.924490i | \(-0.624491\pi\) | ||||
−0.381205 | + | 0.924490i | \(0.624491\pi\) | |||||||
\(312\) | 17.6767 | − | 4.04625i | 1.00075 | − | 0.229074i | ||||
\(313\) | −16.2984 | −0.921242 | −0.460621 | − | 0.887597i | \(-0.652373\pi\) | ||||
−0.460621 | + | 0.887597i | \(0.652373\pi\) | |||||||
\(314\) | 14.3736 | − | 6.32684i | 0.811147 | − | 0.357044i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.40312 | + | 6.78003i | 0.416458 | + | 0.381406i | ||||
\(317\) | − | 16.8716i | − | 0.947602i | −0.880632 | − | 0.473801i | \(-0.842882\pi\) | ||
0.880632 | − | 0.473801i | \(-0.157118\pi\) | |||||||
\(318\) | −3.17170 | + | 4.59378i | −0.177860 | + | 0.257607i | ||||
\(319\) | 7.66037i | 0.428898i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.85859 | + | 9.51563i | 0.326995 | + | 0.531111i | ||||
\(322\) | −7.40312 | − | 16.8187i | −0.412560 | − | 0.937270i | ||||
\(323\) | 3.36131 | 0.187029 | ||||||||
\(324\) | −17.9012 | − | 1.88316i | −0.994512 | − | 0.104620i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.250786 | − | 0.569745i | −0.0138897 | − | 0.0315553i | ||||
\(327\) | −2.08717 | − | 3.39001i | −0.115421 | − | 0.187468i | ||||
\(328\) | 8.24609 | + | 2.79544i | 0.455314 | + | 0.154352i | ||||
\(329\) | − | 9.11592i | − | 0.502577i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1275i | 0.941413i | 0.882290 | + | 0.470707i | \(0.156001\pi\) | ||||
−0.882290 | + | 0.470707i | \(0.843999\pi\) | |||||||
\(332\) | −2.45323 | + | 2.67869i | −0.134639 | + | 0.147012i | ||||
\(333\) | −10.0000 | + | 19.8307i | −0.547997 | + | 1.08672i | ||||
\(334\) | 20.1047 | − | 8.84952i | 1.10008 | − | 0.484224i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −10.3792 | − | 13.9498i | −0.566234 | − | 0.761023i | ||||
\(337\) | 12.4031 | 0.675641 | 0.337821 | − | 0.941211i | \(-0.390310\pi\) | ||||
0.337821 | + | 0.941211i | \(0.390310\pi\) | |||||||
\(338\) | −0.908080 | + | 0.399712i | −0.0493930 | + | 0.0217414i | ||||
\(339\) | −1.17909 | + | 0.725940i | −0.0640391 | + | 0.0394277i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 11.3949i | − | 0.617069i | ||||||
\(342\) | 1.86493 | + | 0.0978226i | 0.100844 | + | 0.00528964i | ||||
\(343\) | 19.3284i | 1.04363i | ||||||||
\(344\) | −22.5261 | − | 7.63636i | −1.21452 | − | 0.411725i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.80625 | − | 10.9190i | −0.258386 | − | 0.587010i | ||||
\(347\) | 19.4358 | 1.04337 | 0.521683 | − | 0.853139i | \(-0.325304\pi\) | ||||
0.521683 | + | 0.853139i | \(0.325304\pi\) | |||||||
\(348\) | 1.48806 | − | 7.75311i | 0.0797682 | − | 0.415610i | ||||
\(349\) | 26.2094 | 1.40296 | 0.701478 | − | 0.712691i | \(-0.252524\pi\) | ||||
0.701478 | + | 0.712691i | \(0.252524\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.1647 | − | 1.62932i | 1.02294 | − | 0.0869669i | ||||
\(352\) | 9.15703 | + | 16.6643i | 0.488071 | + | 0.888210i | ||||
\(353\) | − | 26.6676i | − | 1.41937i | −0.704517 | − | 0.709687i | \(-0.748836\pi\) | ||
0.704517 | − | 0.709687i | \(-0.251164\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.90172 | + | 7.23665i | 0.418790 | + | 0.383542i | ||||
\(357\) | −17.4031 | − | 28.2665i | −0.921071 | − | 1.49602i | ||||
\(358\) | 11.7539 | − | 5.17374i | 0.621213 | − | 0.273441i | ||||
\(359\) | −7.72577 | −0.407751 | −0.203875 | − | 0.978997i | \(-0.565354\pi\) | ||||
−0.203875 | + | 0.978997i | \(0.565354\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8062 | 0.989803 | ||||||||
\(362\) | −13.6010 | + | 5.98677i | −0.714852 | + | 0.314658i | ||||
\(363\) | −0.271006 | − | 0.440172i | −0.0142241 | − | 0.0231030i | ||||
\(364\) | 13.7016 | + | 12.5483i | 0.718157 | + | 0.657712i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −11.4927 | − | 7.93496i | −0.600736 | − | 0.414767i | ||||
\(367\) | 2.50967i | 0.131004i | 0.997852 | + | 0.0655018i | \(0.0208648\pi\) | ||||
−0.997852 | + | 0.0655018i | \(0.979135\pi\) | |||||||
\(368\) | −1.81616 | − | 20.6301i | −0.0946739 | − | 1.07542i | ||||
\(369\) | 8.24609 | + | 4.15825i | 0.429275 | + | 0.216470i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.71949 | −0.296941 | ||||||||
\(372\) | −2.21350 | + | 11.5329i | −0.114765 | + | 0.597951i | ||||
\(373\) | 23.7016 | 1.22722 | 0.613610 | − | 0.789609i | \(-0.289717\pi\) | ||||
0.613610 | + | 0.789609i | \(0.289717\pi\) | |||||||
\(374\) | 14.6243 | + | 33.2241i | 0.756207 | + | 1.71798i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.29844 | − | 9.72987i | 0.170104 | − | 0.501780i | ||||
\(377\) | 8.43579i | 0.434465i | ||||||||
\(378\) | −8.83300 | − | 16.1893i | −0.454320 | − | 0.832688i | ||||
\(379\) | − | 13.1199i | − | 0.673923i | −0.941518 | − | 0.336961i | \(-0.890601\pi\) | ||
0.941518 | − | 0.336961i | \(-0.109399\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.7016 | − | 11.5142i | 0.958110 | − | 0.589890i | ||||
\(382\) | −16.1047 | + | 7.08883i | −0.823987 | + | 0.362696i | ||||
\(383\) | 7.26464 | 0.371206 | 0.185603 | − | 0.982625i | \(-0.440576\pi\) | ||||
0.185603 | + | 0.982625i | \(0.440576\pi\) | |||||||
\(384\) | −6.03078 | − | 18.6448i | −0.307757 | − | 0.951465i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.6366 | − | 11.2845i | 1.30487 | − | 0.574367i | ||||
\(387\) | −22.5261 | − | 11.3592i | −1.14506 | − | 0.577420i | ||||
\(388\) | −15.0000 | + | 16.3785i | −0.761510 | + | 0.831494i | ||||
\(389\) | 37.3824i | 1.89536i | 0.319218 | + | 0.947681i | \(0.396580\pi\) | ||||
−0.319218 | + | 0.947681i | \(0.603420\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 39.5371i | − | 1.99948i | ||||||
\(392\) | −0.637075 | + | 1.87927i | −0.0321771 | + | 0.0949174i | ||||
\(393\) | 5.19375 | + | 8.43579i | 0.261990 | + | 0.425529i | ||||
\(394\) | 6.10469 | + | 13.8689i | 0.307550 | + | 0.698703i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.14699 | + | 18.8591i | 0.359150 | + | 0.947704i | ||||
\(397\) | 15.9109 | 0.798547 | 0.399273 | − | 0.916832i | \(-0.369262\pi\) | ||||
0.399273 | + | 0.916832i | \(0.369262\pi\) | |||||||
\(398\) | 12.0154 | + | 27.2970i | 0.602277 | + | 1.36828i | ||||
\(399\) | 1.00314 | + | 1.62932i | 0.0502200 | + | 0.0815683i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.23521i | 0.461184i | 0.973050 | + | 0.230592i | \(0.0740663\pi\) | ||||
−0.973050 | + | 0.230592i | \(0.925934\pi\) | |||||||
\(402\) | 7.59809 | − | 11.0048i | 0.378958 | − | 0.548871i | ||||
\(403\) | − | 12.5483i | − | 0.625078i | ||||||
\(404\) | 25.8874 | + | 23.7085i | 1.28795 | + | 1.17954i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.40312 | − | 3.25865i | 0.367411 | − | 0.161724i | ||||
\(407\) | 24.8842 | 1.23347 | ||||||||
\(408\) | −8.34747 | − | 36.4672i | −0.413261 | − | 1.80540i | ||||
\(409\) | 11.2094 | 0.554268 | 0.277134 | − | 0.960831i | \(-0.410615\pi\) | ||||
0.277134 | + | 0.960831i | \(0.410615\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.6243 | − | 9.00393i | 0.721366 | − | 0.444131i | ||||
\(412\) | −16.1047 | − | 14.7492i | −0.793421 | − | 0.726641i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.15063 | − | 21.9360i | 0.0565503 | − | 1.07810i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.0839 | + | 18.3511i | 0.494406 | + | 0.899738i | ||||
\(417\) | −4.35078 | + | 2.67869i | −0.213059 | + | 0.131176i | ||||
\(418\) | −0.842970 | − | 1.91509i | −0.0412310 | − | 0.0936702i | ||||
\(419\) | −34.9682 | −1.70831 | −0.854154 | − | 0.520021i | \(-0.825924\pi\) | ||||
−0.854154 | + | 0.520021i | \(0.825924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.2094 | −0.692522 | −0.346261 | − | 0.938138i | \(-0.612549\pi\) | ||||
−0.346261 | + | 0.938138i | \(0.612549\pi\) | |||||||
\(422\) | −10.3347 | − | 23.4788i | −0.503087 | − | 1.14293i | ||||
\(423\) | 4.90647 | − | 9.72987i | 0.238561 | − | 0.473082i | ||||
\(424\) | −6.10469 | − | 2.06950i | −0.296470 | − | 0.100504i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 25.0798 | + | 17.3159i | 1.21512 | + | 0.838958i | ||||
\(427\) | − | 14.3090i | − | 0.692463i | ||||||
\(428\) | −8.71473 | + | 9.51563i | −0.421242 | + | 0.459955i | ||||
\(429\) | −11.2984 | − | 18.3511i | −0.545494 | − | 0.886001i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.71949 | −0.275498 | −0.137749 | − | 0.990467i | \(-0.543987\pi\) | ||||
−0.137749 | + | 0.990467i | \(0.543987\pi\) | |||||||
\(432\) | −3.57007 | − | 20.4757i | −0.171765 | − | 0.985138i | ||||
\(433\) | 7.20937 | 0.346460 | 0.173230 | − | 0.984881i | \(-0.444580\pi\) | ||||
0.173230 | + | 0.984881i | \(0.444580\pi\) | |||||||
\(434\) | −11.0122 | + | 4.84728i | −0.528605 | + | 0.232677i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.10469 | − | 3.39001i | 0.148688 | − | 0.162352i | ||||
\(437\) | 2.27898i | 0.109018i | ||||||||
\(438\) | −2.61729 | − | 1.80706i | −0.125059 | − | 0.0863446i | ||||
\(439\) | − | 23.4674i | − | 1.12004i | −0.828480 | − | 0.560018i | \(-0.810794\pi\) | ||
0.828480 | − | 0.560018i | \(-0.189206\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.947657 | + | 1.87927i | −0.0451265 | + | 0.0894890i | ||||
\(442\) | 16.1047 | + | 36.5872i | 0.766022 | + | 1.74028i | ||||
\(443\) | −29.7907 | −1.41540 | −0.707699 | − | 0.706514i | \(-0.750267\pi\) | ||||
−0.707699 | + | 0.706514i | \(0.750267\pi\) | |||||||
\(444\) | −25.1855 | − | 4.83386i | −1.19525 | − | 0.229405i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.0154 | + | 27.2970i | 0.568945 | + | 1.29255i | ||||
\(447\) | −22.5261 | + | 13.8689i | −1.06545 | + | 0.655975i | ||||
\(448\) | 12.2094 | − | 15.9384i | 0.576839 | − | 0.753017i | ||||
\(449\) | − | 29.7460i | − | 1.40380i | −0.712274 | − | 0.701901i | \(-0.752335\pi\) | ||
0.712274 | − | 0.701901i | \(-0.247665\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 10.3475i | − | 0.487244i | ||||||
\(452\) | −1.17909 | − | 1.07985i | −0.0554595 | − | 0.0507917i | ||||
\(453\) | −28.5078 | + | 17.5517i | −1.33941 | + | 0.824651i | ||||
\(454\) | −28.8062 | + | 12.6797i | −1.35194 | + | 0.595088i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.481161 | + | 2.10203i | 0.0225324 | + | 0.0984365i | ||||
\(457\) | −36.1047 | −1.68891 | −0.844453 | − | 0.535630i | \(-0.820074\pi\) | ||||
−0.844453 | + | 0.535630i | \(0.820074\pi\) | |||||||
\(458\) | −2.97503 | + | 1.30952i | −0.139014 | + | 0.0611900i | ||||
\(459\) | −3.36131 | − | 39.5371i | −0.156893 | − | 1.84543i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.5517i | 0.817465i | 0.912654 | + | 0.408732i | \(0.134029\pi\) | ||||
−0.912654 | + | 0.408732i | \(0.865971\pi\) | |||||||
\(462\) | −11.7402 | + | 17.0042i | −0.546205 | + | 0.791106i | ||||
\(463\) | 5.01934i | 0.233268i | 0.993175 | + | 0.116634i | \(0.0372105\pi\) | ||||
−0.993175 | + | 0.116634i | \(0.962789\pi\) | |||||||
\(464\) | 9.08080 | − | 0.799423i | 0.421566 | − | 0.0371123i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.80625 | − | 10.9190i | −0.222645 | − | 0.505814i | ||||
\(467\) | −29.5197 | −1.36601 | −0.683004 | − | 0.730414i | \(-0.739327\pi\) | ||||
−0.683004 | + | 0.730414i | \(0.739327\pi\) | |||||||
\(468\) | 7.87044 | + | 20.7681i | 0.363811 | + | 0.960004i | ||||
\(469\) | 13.7016 | 0.632679 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.0839 | + | 16.3785i | 0.464644 | + | 0.754683i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28.2665i | 1.29969i | ||||||||
\(474\) | −6.98550 | + | 10.1176i | −0.320855 | + | 0.464716i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 25.8874 | − | 28.2665i | 1.18655 | − | 1.29559i | ||||
\(477\) | −6.10469 | − | 3.07840i | −0.279514 | − | 0.140950i | ||||
\(478\) | 33.5078 | − | 14.7492i | 1.53261 | − | 0.674613i | ||||
\(479\) | 33.6131 | 1.53582 | 0.767912 | − | 0.640555i | \(-0.221296\pi\) | ||||
0.767912 | + | 0.640555i | \(0.221296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.4031 | 1.24947 | ||||||||
\(482\) | −9.06058 | + | 3.98822i | −0.412698 | + | 0.181658i | ||||
\(483\) | 19.1647 | − | 11.7994i | 0.872026 | − | 0.536890i | ||||
\(484\) | 0.403124 | − | 0.440172i | 0.0183238 | − | 0.0200078i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.714301 | − | 22.0338i | −0.0324013 | − | 0.999475i | ||||
\(487\) | 0.131364i | 0.00595267i | 0.999996 | + | 0.00297634i | \(0.000947399\pi\) | ||||
−0.999996 | + | 0.00297634i | \(0.999053\pi\) | |||||||
\(488\) | 5.17748 | − | 15.2727i | 0.234373 | − | 0.691364i | ||||
\(489\) | 0.649219 | − | 0.399712i | 0.0293587 | − | 0.0180756i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4453 | −0.606776 | −0.303388 | − | 0.952867i | \(-0.598118\pi\) | ||||
−0.303388 | + | 0.952867i | \(0.598118\pi\) | |||||||
\(492\) | −2.01004 | + | 10.4728i | −0.0906196 | + | 0.472148i | ||||
\(493\) | 17.4031 | 0.783797 | ||||||||
\(494\) | −0.928300 | − | 2.10895i | −0.0417662 | − | 0.0948860i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.5078 | + | 1.18915i | −0.606519 | + | 0.0533945i | ||||
\(497\) | 31.2256i | 1.40066i | ||||||||
\(498\) | −3.66087 | − | 2.52758i | −0.164047 | − | 0.113264i | ||||
\(499\) | 40.2861i | 1.80345i | 0.432308 | + | 0.901726i | \(0.357699\pi\) | ||||
−0.432308 | + | 0.901726i | \(0.642301\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.1047 | + | 22.9091i | 0.630151 | + | 1.02350i | ||||
\(502\) | 29.1570 | − | 12.8341i | 1.30134 | − | 0.572814i | ||||
\(503\) | −12.9841 | −0.578934 | −0.289467 | − | 0.957188i | \(-0.593478\pi\) | ||||
−0.289467 | + | 0.957188i | \(0.593478\pi\) | |||||||
\(504\) | 15.1855 | − | 14.9295i | 0.676415 | − | 0.665011i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.5261 | + | 9.91534i | −1.00141 | + | 0.440791i | ||||
\(507\) | −0.637075 | − | 1.03475i | −0.0282935 | − | 0.0459548i | ||||
\(508\) | 18.7016 | + | 17.1275i | 0.829748 | + | 0.759910i | ||||
\(509\) | − | 2.95911i | − | 0.131160i | −0.997847 | − | 0.0655802i | \(-0.979110\pi\) | ||
0.997847 | − | 0.0655802i | \(-0.0208898\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 3.25865i | − | 0.144154i | ||||||
\(512\) | 18.7987 | − | 12.5940i | 0.830792 | − | 0.556583i | ||||
\(513\) | 0.193752 | + | 2.27898i | 0.00855434 | + | 0.100619i | ||||
\(514\) | 2.59688 | + | 5.89968i | 0.114543 | + | 0.260224i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.49087 | − | 28.6087i | 0.241722 | − | 1.25943i | ||||
\(517\) | −12.2094 | −0.536968 | ||||||||
\(518\) | −10.5855 | − | 24.0486i | −0.465101 | − | 1.05663i | ||||
\(519\) | 12.4421 | − | 7.66037i | 0.546148 | − | 0.336253i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.07840i | 0.134867i | 0.997724 | + | 0.0674337i | \(0.0214811\pi\) | ||||
−0.997724 | + | 0.0674337i | \(0.978519\pi\) | |||||||
\(522\) | 9.65562 | + | 0.506474i | 0.422615 | + | 0.0221678i | ||||
\(523\) | 14.0002i | 0.612187i | 0.952001 | + | 0.306094i | \(0.0990220\pi\) | ||||
−0.952001 | + | 0.306094i | \(0.900978\pi\) | |||||||
\(524\) | −7.72577 | + | 8.43579i | −0.337502 | + | 0.368519i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.1047 | − | 10.6102i | 1.05101 | − | 0.462627i | ||||
\(527\) | −25.8874 | −1.12767 | ||||||||
\(528\) | −18.6836 | + | 13.9014i | −0.813099 | + | 0.604980i | ||||
\(529\) | 3.80625 | 0.165489 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.49219 | + | 1.62932i | −0.0646946 | + | 0.0706402i | ||||
\(533\) | − | 11.3949i | − | 0.493568i | ||||||
\(534\) | −7.45596 | + | 10.7990i | −0.322651 | + | 0.467318i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 14.6243 | + | 4.95767i | 0.631676 | + | 0.214139i | ||||
\(537\) | 8.24609 | + | 13.3935i | 0.355845 | + | 0.577970i | ||||
\(538\) | −4.80625 | − | 10.9190i | −0.207212 | − | 0.470752i | ||||
\(539\) | 2.35817 | 0.101574 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.7016 | −1.10500 | −0.552498 | − | 0.833514i | \(-0.686325\pi\) | ||||
−0.552498 | + | 0.833514i | \(0.686325\pi\) | |||||||
\(542\) | −5.21791 | − | 11.8543i | −0.224129 | − | 0.509184i | ||||
\(543\) | −9.54193 | − | 15.4982i | −0.409484 | − | 0.665091i | ||||
\(544\) | 37.8586 | − | 20.8033i | 1.62317 | − | 0.891934i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.9286 | + | 18.7254i | −0.553294 | + | 0.801374i | ||||
\(547\) | 4.71053i | 0.201408i | 0.994916 | + | 0.100704i | \(0.0321095\pi\) | ||||
−0.994916 | + | 0.100704i | \(0.967891\pi\) | |||||||
\(548\) | 14.6243 | + | 13.3935i | 0.624721 | + | 0.572140i | ||||
\(549\) | 7.70156 | − | 15.2727i | 0.328695 | − | 0.651824i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.00314 | −0.0427354 | ||||||||
\(552\) | 24.7249 | − | 5.65961i | 1.05236 | − | 0.240889i | ||||
\(553\) | −12.5969 | −0.535674 | ||||||||
\(554\) | −11.5138 | + | 5.06806i | −0.489175 | + | 0.215321i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.35078 | − | 3.98459i | −0.184514 | − | 0.168984i | ||||
\(557\) | 36.7023i | 1.55512i | 0.628806 | + | 0.777562i | \(0.283544\pi\) | ||||
−0.628806 | + | 0.777562i | \(0.716456\pi\) | |||||||
\(558\) | −14.3629 | − | 0.753387i | −0.608028 | − | 0.0318934i | ||||
\(559\) | 31.1277i | 1.31656i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.8586 | + | 23.3088i | −1.59839 | + | 0.984098i | ||||
\(562\) | 10.0000 | + | 22.7184i | 0.421825 | + | 0.958317i | ||||
\(563\) | 23.3391 | 0.983625 | 0.491812 | − | 0.870701i | \(-0.336335\pi\) | ||||
0.491812 | + | 0.870701i | \(0.336335\pi\) | |||||||
\(564\) | 12.3572 | + | 2.37172i | 0.520331 | + | 0.0998674i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.33159 | − | 21.1999i | −0.392236 | − | 0.891096i | ||||
\(567\) | 18.1616 | − | 13.4287i | 0.762716 | − | 0.563952i | ||||
\(568\) | −11.2984 | + | 33.3286i | −0.474072 | + | 1.39844i | ||||
\(569\) | 10.5955i | 0.444186i | 0.975026 | + | 0.222093i | \(0.0712888\pi\) | ||||
−0.975026 | + | 0.222093i | \(0.928711\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16.9501i | − | 0.709338i | −0.934992 | − | 0.354669i | \(-0.884594\pi\) | ||
0.934992 | − | 0.354669i | \(-0.115406\pi\) | |||||||
\(572\) | 16.8066 | − | 18.3511i | 0.702718 | − | 0.767299i | ||||
\(573\) | −11.2984 | − | 18.3511i | −0.471999 | − | 0.766630i | ||||
\(574\) | −10.0000 | + | 4.40172i | −0.417392 | + | 0.183724i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 21.6102 | − | 10.4403i | 0.900424 | − | 0.435014i | ||||
\(577\) | 12.4031 | 0.516349 | 0.258174 | − | 0.966098i | \(-0.416879\pi\) | ||||
0.258174 | + | 0.966098i | \(0.416879\pi\) | |||||||
\(578\) | 53.4756 | − | 23.5385i | 2.22429 | − | 0.979072i | ||||
\(579\) | 17.9857 | + | 29.2126i | 0.747459 | + | 1.21404i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 4.55796i | − | 0.189096i | ||||||
\(582\) | −22.3839 | − | 15.4546i | −0.927844 | − | 0.640613i | ||||
\(583\) | 7.66037i | 0.317260i | ||||||||
\(584\) | 1.17909 | − | 3.47812i | 0.0487909 | − | 0.143925i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.2094 | + | 27.7377i | 0.504365 | + | 1.14583i | ||||
\(587\) | 31.3359 | 1.29337 | 0.646685 | − | 0.762758i | \(-0.276155\pi\) | ||||
0.646685 | + | 0.762758i | \(0.276155\pi\) | |||||||
\(588\) | −2.38672 | − | 0.458084i | −0.0984267 | − | 0.0188911i | ||||
\(589\) | 1.49219 | 0.0614846 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.8034 | + | 9.72987i | −0.650066 | + | 0.400233i | ||||
\(592\) | −2.59688 | − | 29.4984i | −0.106731 | − | 1.21238i | ||||
\(593\) | 10.5955i | 0.435104i | 0.976049 | + | 0.217552i | \(0.0698072\pi\) | ||||
−0.976049 | + | 0.217552i | \(0.930193\pi\) | |||||||
\(594\) | −21.6831 | + | 11.8304i | −0.889668 | + | 0.485409i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.5261 | − | 20.6301i | −0.922703 | − | 0.845042i | ||||
\(597\) | −31.1047 | + | 19.1506i | −1.27303 | + | 0.783780i | ||||
\(598\) | −24.8062 | + | 10.9190i | −1.01440 | + | 0.446512i | ||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.0156 | −1.63227 | −0.816136 | − | 0.577860i | \(-0.803888\pi\) | ||||
−0.816136 | + | 0.577860i | \(0.803888\pi\) | |||||||
\(602\) | 27.3172 | − | 12.0243i | 1.11337 | − | 0.490074i | ||||
\(603\) | 14.6243 | + | 7.37460i | 0.595549 | + | 0.300317i | ||||
\(604\) | −28.5078 | − | 26.1084i | −1.15997 | − | 1.06234i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −24.4270 | + | 35.3793i | −0.992279 | + | 1.43719i | ||||
\(607\) | − | 3.25865i | − | 0.132264i | −0.997811 | − | 0.0661322i | \(-0.978934\pi\) | ||
0.997811 | − | 0.0661322i | \(-0.0210659\pi\) | |||||||
\(608\) | −2.18223 | + | 1.19913i | −0.0885011 | + | 0.0486313i | ||||
\(609\) | 5.19375 | + | 8.43579i | 0.210461 | + | 0.341835i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.4453 | −0.543937 | ||||||||
\(612\) | 42.8447 | − | 16.2368i | 1.73190 | − | 0.656334i | ||||
\(613\) | −4.80625 | −0.194123 | −0.0970613 | − | 0.995278i | \(-0.530944\pi\) | ||||
−0.0970613 | + | 0.995278i | \(0.530944\pi\) | |||||||
\(614\) | −15.0511 | − | 34.1936i | −0.607412 | − | 1.37994i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.5969 | − | 7.66037i | −0.910454 | − | 0.308645i | ||||
\(617\) | − | 22.1097i | − | 0.890102i | −0.895505 | − | 0.445051i | \(-0.853186\pi\) | ||
0.895505 | − | 0.445051i | \(-0.146814\pi\) | |||||||
\(618\) | 15.1962 | − | 22.0097i | 0.611280 | − | 0.885359i | ||||
\(619\) | − | 5.15070i | − | 0.207024i | −0.994628 | − | 0.103512i | \(-0.966992\pi\) | ||
0.994628 | − | 0.103512i | \(-0.0330080\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.8062 | − | 2.27898i | 1.07570 | − | 0.0914523i | ||||
\(622\) | 17.4031 | − | 7.66037i | 0.697802 | − | 0.307153i | ||||
\(623\) | −13.4453 | −0.538673 | ||||||||
\(624\) | −20.5748 | + | 15.3086i | −0.823652 | + | 0.612833i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.0962 | − | 9.28595i | 0.843173 | − | 0.371141i | ||||
\(627\) | 2.18223 | − | 1.34356i | 0.0871498 | − | 0.0536565i | ||||
\(628\) | −15.0000 | + | 16.3785i | −0.598565 | + | 0.653574i | ||||
\(629\) | − | 56.5330i | − | 2.25412i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.0468i | 1.67385i | 0.547314 | + | 0.836927i | \(0.315650\pi\) | ||||
−0.547314 | + | 0.836927i | \(0.684350\pi\) | |||||||
\(632\) | −13.4453 | − | 4.55796i | −0.534824 | − | 0.181306i | ||||
\(633\) | 26.7539 | − | 16.4719i | 1.06337 | − | 0.654698i | ||||
\(634\) | 9.61250 | + | 21.8380i | 0.381761 | + | 0.867299i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.48806 | − | 7.75311i | 0.0590053 | − | 0.307431i | ||||
\(637\) | 2.59688 | 0.102892 | ||||||||
\(638\) | −4.36446 | − | 9.91534i | −0.172791 | − | 0.392552i | ||||
\(639\) | −16.8066 | + | 33.3286i | −0.664858 | + | 1.31846i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.3136i | − | 0.486359i | −0.969981 | − | 0.243179i | \(-0.921810\pi\) | ||
0.969981 | − | 0.243179i | \(-0.0781903\pi\) | |||||||
\(642\) | −13.0047 | − | 8.97883i | −0.513253 | − | 0.354366i | ||||
\(643\) | − | 24.4791i | − | 0.965360i | −0.875797 | − | 0.482680i | \(-0.839663\pi\) | ||
0.875797 | − | 0.482680i | \(-0.160337\pi\) | |||||||
\(644\) | 19.1647 | + | 17.5517i | 0.755197 | + | 0.691634i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.35078 | + | 1.91509i | −0.171179 | + | 0.0753483i | ||||
\(647\) | 10.3550 | 0.407095 | 0.203548 | − | 0.979065i | \(-0.434753\pi\) | ||||
0.203548 | + | 0.979065i | \(0.434753\pi\) | |||||||
\(648\) | 24.2437 | − | 7.76163i | 0.952383 | − | 0.304906i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.72577 | − | 12.5483i | −0.302797 | − | 0.491808i | ||||
\(652\) | 0.649219 | + | 0.594576i | 0.0254254 | + | 0.0232854i | ||||
\(653\) | 25.9875i | 1.01697i | 0.861071 | + | 0.508485i | \(0.169794\pi\) | ||||
−0.861071 | + | 0.508485i | \(0.830206\pi\) | |||||||
\(654\) | 4.63301 | + | 3.19877i | 0.181165 | + | 0.125082i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12.2662 | + | 1.07985i | −0.478914 | + | 0.0421609i | ||||
\(657\) | 1.75391 | − | 3.47812i | 0.0684264 | − | 0.135694i | ||||
\(658\) | 5.19375 | + | 11.7994i | 0.202474 | + | 0.459987i | ||||
\(659\) | 16.8066 | 0.654691 | 0.327346 | − | 0.944905i | \(-0.393846\pi\) | ||||
0.327346 | + | 0.944905i | \(0.393846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0000 | −0.700119 | −0.350059 | − | 0.936727i | \(-0.613839\pi\) | ||||
−0.350059 | + | 0.936727i | \(0.613839\pi\) | |||||||
\(662\) | −9.75831 | − | 22.1693i | −0.379268 | − | 0.861635i | ||||
\(663\) | −41.6908 | + | 25.6682i | −1.61914 | + | 0.996871i | ||||
\(664\) | 1.64922 | − | 4.86493i | 0.0640021 | − | 0.188796i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.64525 | − | 31.3657i | 0.0637521 | − | 1.21540i | ||||
\(667\) | 11.7994i | 0.456873i | ||||||||
\(668\) | −20.9809 | + | 22.9091i | −0.811776 | + | 0.886379i | ||||
\(669\) | −31.1047 | + | 19.1506i | −1.20258 | + | 0.740403i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.1647 | −0.739847 | ||||||||
\(672\) | 21.3824 | + | 12.1426i | 0.824843 | + | 0.468413i | ||||
\(673\) | −24.8062 | −0.956211 | −0.478105 | − | 0.878303i | \(-0.658676\pi\) | ||||
−0.478105 | + | 0.878303i | \(0.658676\pi\) | |||||||
\(674\) | −16.0542 | + | 7.06662i | −0.618385 | + | 0.272196i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.947657 | − | 1.03475i | 0.0364483 | − | 0.0397980i | ||||
\(677\) | 12.9937i | 0.499390i | 0.968324 | + | 0.249695i | \(0.0803304\pi\) | ||||
−0.968324 | + | 0.249695i | \(0.919670\pi\) | |||||||
\(678\) | 1.11257 | − | 1.61141i | 0.0427280 | − | 0.0618859i | ||||
\(679\) | − | 27.8691i | − | 1.06952i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.2094 | − | 32.8244i | −0.774425 | − | 1.25784i | ||||
\(682\) | 6.49219 | + | 14.7492i | 0.248599 | + | 0.564776i | ||||
\(683\) | −11.6291 | −0.444975 | −0.222488 | − | 0.974936i | \(-0.571418\pi\) | ||||
−0.222488 | + | 0.974936i | \(0.571418\pi\) | |||||||
\(684\) | −2.46964 | + | 0.935915i | −0.0944290 | + | 0.0357856i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.0122 | − | 25.0180i | −0.420449 | − | 0.955193i | ||||
\(687\) | −2.08717 | − | 3.39001i | −0.0796303 | − | 0.129337i | ||||
\(688\) | 33.5078 | − | 2.94984i | 1.27747 | − | 0.112462i | ||||
\(689\) | 8.43579i | 0.321378i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.18915i | 0.0452375i | 0.999744 | + | 0.0226187i | \(0.00720038\pi\) | ||||
−0.999744 | + | 0.0226187i | \(0.992800\pi\) | |||||||
\(692\) | 12.4421 | + | 11.3949i | 0.472978 | + | 0.433169i | ||||
\(693\) | −22.5969 | − | 11.3949i | −0.858384 | − | 0.432857i | ||||
\(694\) | −25.1570 | + | 11.0734i | −0.954948 | + | 0.420341i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.49120 | + | 10.8832i | 0.0944287 | + | 0.412526i | ||||
\(697\) | −23.5078 | −0.890422 | ||||||||
\(698\) | −33.9246 | + | 14.9327i | −1.28406 | + | 0.565210i | ||||
\(699\) | 12.4421 | − | 7.66037i | 0.470604 | − | 0.289742i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.3949i | 0.430380i | 0.976572 | + | 0.215190i | \(0.0690370\pi\) | ||||
−0.976572 | + | 0.215190i | \(0.930963\pi\) | |||||||
\(702\) | −23.8779 | + | 13.0280i | −0.901215 | + | 0.491709i | ||||
\(703\) | 3.25865i | 0.122902i | ||||||||
\(704\) | −21.3470 | − | 16.3526i | −0.804544 | − | 0.616311i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.1938 | + | 34.5177i | 0.571824 | + | 1.29909i | ||||
\(707\) | −44.0490 | −1.65663 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.7016 | −0.664796 | −0.332398 | − | 0.943139i | \(-0.607858\pi\) | ||||
−0.332398 | + | 0.943139i | \(0.607858\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.4453 | − | 6.78003i | −0.504237 | − | 0.254271i | ||||
\(712\) | −14.3508 | − | 4.86493i | −0.537818 | − | 0.182321i | ||||
\(713\) | − | 17.5517i | − | 0.657317i | ||||||
\(714\) | 38.6307 | + | 26.6719i | 1.44572 | + | 0.998171i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.2662 | + | 13.3935i | −0.458408 | + | 0.500537i | ||||
\(717\) | 23.5078 | + | 38.1818i | 0.877915 | + | 1.42593i | ||||
\(718\) | 10.0000 | − | 4.40172i | 0.373197 | − | 0.164271i | ||||
\(719\) | −44.0490 | −1.64275 | −0.821375 | − | 0.570389i | \(-0.806793\pi\) | ||||
−0.821375 | + | 0.570389i | \(0.806793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.4031 | 1.02055 | ||||||||
\(722\) | −24.3422 | + | 10.7148i | −0.905924 | + | 0.398762i | ||||
\(723\) | −6.35656 | − | 10.3244i | −0.236403 | − | 0.383970i | ||||
\(724\) | 14.1938 | − | 15.4982i | 0.527507 | − | 0.575986i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.601567 | + | 0.415341i | 0.0223262 | + | 0.0154148i | ||||
\(727\) | − | 40.5488i | − | 1.50387i | −0.659236 | − | 0.751936i | \(-0.729120\pi\) | ||
0.659236 | − | 0.751936i | \(-0.270880\pi\) | |||||||
\(728\) | −24.8842 | − | 8.43579i | −0.922271 | − | 0.312651i | ||||
\(729\) | 26.6125 | − | 4.55796i | 0.985648 | − | 0.168813i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 64.2169 | 2.37515 | ||||||||
\(732\) | 19.3968 | + | 3.72283i | 0.716925 | + | 0.137600i | ||||
\(733\) | −4.80625 | −0.177523 | −0.0887614 | − | 0.996053i | \(-0.528291\pi\) | ||||
−0.0887614 | + | 0.996053i | \(0.528291\pi\) | |||||||
\(734\) | −1.42987 | − | 3.24844i | −0.0527775 | − | 0.119902i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.1047 | + | 25.6682i | 0.519906 | + | 0.946143i | ||||
\(737\) | − | 18.3511i | − | 0.675973i | ||||||
\(738\) | −13.0426 | − | 0.684136i | −0.480106 | − | 0.0251834i | ||||
\(739\) | − | 29.2357i | − | 1.07545i | −0.843120 | − | 0.537726i | \(-0.819283\pi\) | ||
0.843120 | − | 0.537726i | \(-0.180717\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.40312 | − | 1.47956i | 0.0882810 | − | 0.0543529i | ||||
\(742\) | 7.40312 | − | 3.25865i | 0.271777 | − | 0.119629i | ||||
\(743\) | 40.8778 | 1.49966 | 0.749830 | − | 0.661630i | \(-0.230135\pi\) | ||||
0.749830 | + | 0.661630i | \(0.230135\pi\) | |||||||
\(744\) | −3.70569 | − | 16.1889i | −0.135857 | − | 0.593514i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −30.6786 | + | 13.5038i | −1.12322 | + | 0.494411i | ||||
\(747\) | 2.45323 | − | 4.86493i | 0.0897592 | − | 0.177999i | ||||
\(748\) | −37.8586 | − | 34.6722i | −1.38425 | − | 1.26774i | ||||
\(749\) | − | 16.1914i | − | 0.591622i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.2784i | 1.32382i | 0.749584 | + | 0.661909i | \(0.230254\pi\) | ||||
−0.749584 | + | 0.661909i | \(0.769746\pi\) | |||||||
\(752\) | 1.27415 | + | 14.4733i | 0.0464634 | + | 0.527787i | ||||
\(753\) | 20.4555 | + | 33.2241i | 0.745439 | + | 1.21076i | ||||
\(754\) | −4.80625 | − | 10.9190i | −0.175033 | − | 0.397647i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 20.6569 | + | 15.9224i | 0.751285 | + | 0.579092i | ||||
\(757\) | 35.9109 | 1.30521 | 0.652603 | − | 0.757700i | \(-0.273677\pi\) | ||||
0.652603 | + | 0.757700i | \(0.273677\pi\) | |||||||
\(758\) | 7.47499 | + | 16.9820i | 0.271504 | + | 0.616813i | ||||
\(759\) | −15.8034 | − | 25.6682i | −0.573628 | − | 0.931698i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.6301i | 0.747841i | 0.927461 | + | 0.373920i | \(0.121987\pi\) | ||||
−0.927461 | + | 0.373920i | \(0.878013\pi\) | |||||||
\(762\) | −17.6466 | + | 25.5587i | −0.639268 | + | 0.925895i | ||||
\(763\) | 5.76832i | 0.208827i | ||||||||
\(764\) | 16.8066 | − | 18.3511i | 0.608041 | − | 0.663921i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.40312 | + | 4.13899i | −0.339749 | + | 0.149548i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 18.4289 | + | 20.6973i | 0.664994 | + | 0.746849i | ||||
\(769\) | −14.1938 | −0.511840 | −0.255920 | − | 0.966698i | \(-0.582378\pi\) | ||||
−0.255920 | + | 0.966698i | \(0.582378\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.72263 | + | 4.13899i | −0.242110 | + | 0.149062i | ||||
\(772\) | −26.7539 | + | 29.2126i | −0.962894 | + | 1.05139i | ||||
\(773\) | 2.27898i | 0.0819692i | 0.999160 | + | 0.0409846i | \(0.0130495\pi\) | ||||
−0.999160 | + | 0.0409846i | \(0.986951\pi\) | |||||||
\(774\) | 35.6289 | + | 1.86887i | 1.28065 | + | 0.0671752i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.0839 | − | 29.7460i | 0.361993 | − | 1.06782i | ||||
\(777\) | 27.4031 | − | 16.8716i | 0.983082 | − | 0.605264i | ||||
\(778\) | −21.2984 | − | 48.3866i | −0.763586 | − | 1.73474i | ||||
\(779\) | 1.35503 | 0.0485489 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.8219 | 1.49650 | ||||||||
\(782\) | 22.5261 | + | 51.1756i | 0.805530 | + | 1.83003i | ||||
\(783\) | 1.00314 | + | 11.7994i | 0.0358494 | + | 0.421675i | ||||
\(784\) | −0.246095 | − | 2.79544i | −0.00878910 | − | 0.0998370i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11.5289 | − | 7.95991i | −0.411221 | − | 0.283920i | ||||
\(787\) | 18.4480i | 0.657601i | 0.944399 | + | 0.328801i | \(0.106644\pi\) | ||||
−0.944399 | + | 0.328801i | \(0.893356\pi\) | |||||||
\(788\) | −15.8034 | − | 14.4733i | −0.562974 | − | 0.515590i | ||||
\(789\) | 16.9109 | + | 27.4671i | 0.602045 | + | 0.977853i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.00629 | 0.0713354 | ||||||||
\(792\) | −19.9957 | − | 20.3386i | −0.710516 | − | 0.722701i | ||||
\(793\) | −21.1047 | −0.749449 | ||||||||
\(794\) | −20.5946 | + | 9.06518i | −0.730876 | + | 0.321711i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.1047 | − | 28.4867i | −1.10248 | − | 1.00968i | ||||
\(797\) | − | 45.8182i | − | 1.62296i | −0.584378 | − | 0.811482i | \(-0.698661\pi\) | ||
0.584378 | − | 0.811482i | \(-0.301339\pi\) | |||||||
\(798\) | −2.22674 | − | 1.53741i | −0.0788257 | − | 0.0544237i | ||||
\(799\) | 27.7377i | 0.981290i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.3508 | − | 7.23665i | −0.507060 | − | 0.255695i | ||||
\(802\) | −5.26172 | − | 11.9538i | −0.185798 | − | 0.422102i | ||||
\(803\) | −4.36446 | −0.154018 | ||||||||
\(804\) | −3.56478 | + | 18.5733i | −0.125720 | + | 0.655030i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.14936 | + | 16.2422i | 0.251825 | + | 0.572107i | ||||
\(807\) | 12.4421 | − | 7.66037i | 0.437983 | − | 0.269658i | ||||
\(808\) | −47.0156 | − | 15.9384i | −1.65400 | − | 0.560709i | ||||
\(809\) | 43.5392i | 1.53076i | 0.643580 | + | 0.765378i | \(0.277448\pi\) | ||||
−0.643580 | + | 0.765378i | \(0.722552\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35.2667i | − | 1.23838i | −0.785240 | − | 0.619191i | \(-0.787461\pi\) | ||
0.785240 | − | 0.619191i | \(-0.212539\pi\) | |||||||
\(812\) | −7.72577 | + | 8.43579i | −0.271121 | + | 0.296038i | ||||
\(813\) | 13.5078 | − | 8.31650i | 0.473740 | − | 0.291672i | ||||
\(814\) | −32.2094 | + | 14.1777i | −1.12894 | + | 0.496927i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 31.5817 | + | 42.4461i | 1.10558 | + | 1.48591i | ||||
\(817\) | −3.70156 | −0.129501 | ||||||||
\(818\) | −14.5091 | + | 6.38649i | −0.507297 | + | 0.223298i | ||||
\(819\) | −24.8842 | − | 12.5483i | −0.869525 | − | 0.438475i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.15681i | − | 0.214874i | −0.994212 | − | 0.107437i | \(-0.965736\pi\) | ||
0.994212 | − | 0.107437i | \(-0.0342644\pi\) | |||||||
\(822\) | −13.7994 | + | 19.9866i | −0.481308 | + | 0.697111i | ||||
\(823\) | 6.03105i | 0.210229i | 0.994460 | + | 0.105115i | \(0.0335209\pi\) | ||||
−0.994460 | + | 0.105115i | \(0.966479\pi\) | |||||||
\(824\) | 29.2487 | + | 9.91534i | 1.01893 | + | 0.345417i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.4389 | −0.710730 | −0.355365 | − | 0.934728i | \(-0.615643\pi\) | ||||
−0.355365 | + | 0.934728i | \(0.615643\pi\) | |||||||
\(828\) | 11.0086 | + | 29.0489i | 0.382575 | + | 1.00952i | ||||
\(829\) | 19.1938 | 0.666627 | 0.333313 | − | 0.942816i | \(-0.391833\pi\) | ||||
0.333313 | + | 0.942816i | \(0.391833\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.07766 | − | 13.1199i | −0.280211 | − | 0.455124i | ||||
\(832\) | −23.5078 | − | 18.0079i | −0.814987 | − | 0.624310i | ||||
\(833\) | − | 5.35738i | − | 0.185622i | ||||||
\(834\) | 4.10534 | − | 5.94605i | 0.142156 | − | 0.205895i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.18223 | + | 1.99856i | 0.0754740 | + | 0.0691216i | ||||
\(837\) | −1.49219 | − | 17.5517i | −0.0515776 | − | 0.606676i | ||||
\(838\) | 45.2617 | − | 19.9229i | 1.56354 | − | 0.688227i | ||||
\(839\) | 44.0490 | 1.52074 | 0.760370 | − | 0.649490i | \(-0.225018\pi\) | ||||
0.760370 | + | 0.649490i | \(0.225018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.8062 | 0.820905 | ||||||||
\(842\) | 18.3922 | − | 8.09572i | 0.633836 | − | 0.278997i | ||||
\(843\) | −25.8874 | + | 15.9384i | −0.891609 | + | 0.548946i | ||||
\(844\) | 26.7539 | + | 24.5021i | 0.920907 | + | 0.843397i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.807237 | + | 15.3895i | −0.0277534 | + | 0.529101i | ||||
\(847\) | 0.748980i | 0.0257353i | ||||||||
\(848\) | 9.08080 | − | 0.799423i | 0.311836 | − | 0.0274523i | ||||
\(849\) | 24.1570 | − | 14.8730i | 0.829067 | − | 0.510441i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.3295 | 1.31392 | ||||||||
\(852\) | −42.3282 | − | 8.12406i | −1.45014 | − | 0.278326i | ||||
\(853\) | 43.7016 | 1.49631 | 0.748156 | − | 0.663522i | \(-0.230939\pi\) | ||||
0.748156 | + | 0.663522i | \(0.230939\pi\) | |||||||
\(854\) | 8.15250 | + | 18.5212i | 0.278973 | + | 0.633781i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.85859 | − | 17.2819i | 0.200243 | − | 0.590684i | ||||
\(857\) | − | 31.3449i | − | 1.07072i | −0.844624 | − | 0.535360i | \(-0.820176\pi\) | ||
0.844624 | − | 0.535360i | \(-0.179824\pi\) | |||||||
\(858\) | 25.0798 | + | 17.3159i | 0.856211 | + | 0.591155i | ||||
\(859\) | − | 50.7649i | − | 1.73208i | −0.499978 | − | 0.866038i | \(-0.666658\pi\) | ||
0.499978 | − | 0.866038i | \(-0.333342\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.01562 | − | 11.3949i | −0.239092 | − | 0.388337i | ||||
\(862\) | 7.40312 | − | 3.25865i | 0.252151 | − | 0.110990i | ||||
\(863\) | 40.8778 | 1.39150 | 0.695748 | − | 0.718286i | \(-0.255073\pi\) | ||||
0.695748 | + | 0.718286i | \(0.255073\pi\) | |||||||
\(864\) | 16.2869 | + | 24.4691i | 0.554092 | + | 0.832455i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.33159 | + | 4.10750i | −0.317100 | + | 0.139579i | ||||
\(867\) | 37.5165 | + | 60.9350i | 1.27413 | + | 2.06946i | ||||
\(868\) | 11.4922 | − | 12.5483i | 0.390070 | − | 0.425919i | ||||
\(869\) | 16.8716i | 0.572329i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 20.2087i | − | 0.684746i | ||||||
\(872\) | −2.08717 | + | 6.15681i | −0.0706803 | + | 0.208496i | ||||
\(873\) | 15.0000 | − | 29.7460i | 0.507673 | − | 1.00675i | ||||
\(874\) | −1.29844 | − | 2.94984i | −0.0439203 | − | 0.0997799i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.41730 | + | 0.847813i | 0.149247 | + | 0.0286450i | ||||
\(877\) | −4.08907 | −0.138078 | −0.0690390 | − | 0.997614i | \(-0.521993\pi\) | ||||
−0.0690390 | + | 0.997614i | \(0.521993\pi\) | |||||||
\(878\) | 13.3704 | + | 30.3754i | 0.451230 | + | 1.02512i | ||||
\(879\) | −31.6069 | + | 19.4597i | −1.06607 | + | 0.656361i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 47.4170i | − | 1.59752i | −0.601650 | − | 0.798760i | \(-0.705490\pi\) | ||
0.601650 | − | 0.798760i | \(-0.294510\pi\) | |||||||
\(882\) | 0.155913 | − | 2.97239i | 0.00524987 | − | 0.100086i | ||||
\(883\) | − | 58.5566i | − | 1.97059i | −0.170867 | − | 0.985294i | \(-0.554657\pi\) | ||
0.170867 | − | 0.985294i | \(-0.445343\pi\) | |||||||
\(884\) | −41.6908 | − | 38.1818i | −1.40221 | − | 1.28419i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38.5602 | − | 16.9731i | 1.29545 | − | 0.570223i | ||||
\(887\) | 14.5293 | 0.487846 | 0.243923 | − | 0.969795i | \(-0.421566\pi\) | ||||
0.243923 | + | 0.969795i | \(0.421566\pi\) | |||||||
\(888\) | 35.3534 | − | 8.09251i | 1.18638 | − | 0.271567i | ||||
\(889\) | −31.8219 | −1.06727 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.9857 | − | 24.3247i | −0.602542 | − | 0.814907i | ||||
\(892\) | −31.1047 | − | 28.4867i | −1.04146 | − | 0.953805i | ||||
\(893\) | − | 1.59885i | − | 0.0535034i | ||||||
\(894\) | 21.2553 | − | 30.7855i | 0.710884 | − | 1.02962i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.72263 | + | 27.5863i | −0.224587 | + | 0.921595i | ||||
\(897\) | −17.4031 | − | 28.2665i | −0.581073 | − | 0.943790i | ||||
\(898\) | 16.9477 | + | 38.5023i | 0.565551 | + | 1.28484i | ||||
\(899\) | 7.72577 | 0.257669 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.4031 | 0.579782 | ||||||||
\(902\) | 5.89543 | + | 13.3935i | 0.196296 | + | 0.445953i | ||||
\(903\) | 19.1647 | + | 31.1277i | 0.637763 | + | 1.03587i | ||||
\(904\) | 2.14141 | + | 0.725940i | 0.0712222 | + | 0.0241444i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 26.8996 | − | 38.9606i | 0.893680 | − | 1.29438i | ||||
\(907\) | − | 0.880344i | − | 0.0292314i | −0.999893 | − | 0.0146157i | \(-0.995348\pi\) | ||
0.999893 | − | 0.0146157i | \(-0.00465248\pi\) | |||||||
\(908\) | 30.0617 | − | 32.8244i | 0.997633 | − | 1.08932i | ||||
\(909\) | −47.0156 | − | 23.7085i | −1.55941 | − | 0.786362i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.00629 | 0.0664713 | 0.0332356 | − | 0.999448i | \(-0.489419\pi\) | ||||
0.0332356 | + | 0.999448i | \(0.489419\pi\) | |||||||
\(912\) | −1.82042 | − | 2.44666i | −0.0602801 | − | 0.0810170i | ||||
\(913\) | −6.10469 | −0.202036 | ||||||||
\(914\) | 46.7328 | − | 20.5705i | 1.54578 | − | 0.680411i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.10469 | − | 3.39001i | 0.102582 | − | 0.112009i | ||||
\(917\) | − | 14.3540i | − | 0.474011i | ||||||
\(918\) | 26.8768 | + | 49.2605i | 0.887068 | + | 1.62584i | ||||
\(919\) | 8.40935i | 0.277399i | 0.990335 | + | 0.138699i | \(0.0442922\pi\) | ||||
−0.990335 | + | 0.138699i | \(0.955708\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 38.9633 | − | 23.9889i | 1.28388 | − | 0.790462i | ||||
\(922\) | −10.0000 | − | 22.7184i | −0.329332 | − | 0.748190i | ||||
\(923\) | 46.0553 | 1.51593 | ||||||||
\(924\) | 5.50814 | − | 28.6986i | 0.181204 | − | 0.944115i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.85974 | − | 6.49687i | −0.0939770 | − | 0.213501i | ||||
\(927\) | 29.2487 | + | 14.7492i | 0.960653 | + | 0.484427i | ||||
\(928\) | −11.2984 | + | 6.20849i | −0.370889 | + | 0.203804i | ||||
\(929\) | 43.5392i | 1.42847i | 0.699903 | + | 0.714237i | \(0.253226\pi\) | ||||
−0.699903 | + | 0.714237i | \(0.746774\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.308808i | 0.0101208i | ||||||||
\(932\) | 12.4421 | + | 11.3949i | 0.407555 | + | 0.373252i | ||||
\(933\) | 12.2094 | + | 19.8307i | 0.399717 | + | 0.649228i | ||||
\(934\) | 38.2094 | − | 16.8187i | 1.25025 | − | 0.550325i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −22.0198 | − | 22.3974i | −0.719738 | − | 0.732081i | ||||
\(937\) | −34.6125 | −1.13074 | −0.565370 | − | 0.824837i | \(-0.691267\pi\) | ||||
−0.565370 | + | 0.824837i | \(0.691267\pi\) | |||||||
\(938\) | −17.7349 | + | 7.80640i | −0.579064 | + | 0.254888i | ||||
\(939\) | 14.8003 | + | 24.0389i | 0.482989 | + | 0.784480i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.5738i | 1.74646i | 0.487311 | + | 0.873229i | \(0.337978\pi\) | ||||
−0.487311 | + | 0.873229i | \(0.662022\pi\) | |||||||
\(942\) | −22.3839 | − | 15.4546i | −0.729308 | − | 0.503537i | ||||
\(943\) | − | 15.9384i | − | 0.519024i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.1047 | − | 36.5872i | −0.523609 | − | 1.18955i | ||||
\(947\) | 18.0807 | 0.587545 | 0.293772 | − | 0.955875i | \(-0.405089\pi\) | ||||
0.293772 | + | 0.955875i | \(0.405089\pi\) | |||||||
\(948\) | 3.27737 | − | 17.0758i | 0.106444 | − | 0.554597i | ||||
\(949\) | −4.80625 | −0.156017 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.8842 | + | 15.3207i | −0.806927 | + | 0.496809i | ||||
\(952\) | −17.4031 | + | 51.3364i | −0.564038 | + | 1.66382i | ||||
\(953\) | − | 42.0596i | − | 1.36245i | −0.732076 | − | 0.681223i | \(-0.761448\pi\) | ||
0.732076 | − | 0.681223i | \(-0.238552\pi\) | |||||||
\(954\) | 9.65562 | + | 0.506474i | 0.312612 | + | 0.0163977i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −34.9682 | + | 38.1818i | −1.13095 | + | 1.23489i | ||||
\(957\) | 11.2984 | − | 6.95623i | 0.365227 | − | 0.224863i | ||||
\(958\) | −43.5078 | + | 19.1509i | −1.40567 | + | 0.618738i | ||||
\(959\) | −24.8842 | −0.803554 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.5078 | 0.629284 | ||||||||
\(962\) | −35.4697 | + | 15.6128i | −1.14359 | + | 0.503377i | ||||
\(963\) | 8.71473 | − | 17.2819i | 0.280828 | − | 0.556902i | ||||
\(964\) | 9.45547 | − | 10.3244i | 0.304540 | − | 0.332528i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −18.0836 | + | 26.1917i | −0.581831 | + | 0.842706i | ||||
\(967\) | 1.49796i | 0.0481712i | 0.999710 | + | 0.0240856i | \(0.00766742\pi\) | ||||
−0.999710 | + | 0.0240856i | \(0.992333\pi\) | |||||||
\(968\) | −0.271006 | + | 0.799423i | −0.00871045 | + | 0.0256944i | ||||
\(969\) | −3.05234 | − | 4.95767i | −0.0980554 | − | 0.159263i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.4103 | 1.52147 | 0.760734 | − | 0.649063i | \(-0.224839\pi\) | ||||
0.760734 | + | 0.649063i | \(0.224839\pi\) | |||||||
\(972\) | 13.4782 | + | 28.1129i | 0.432315 | + | 0.901723i | ||||
\(973\) | 7.40312 | 0.237333 | ||||||||
\(974\) | −0.0748440 | − | 0.170034i | −0.00239816 | − | 0.00544823i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | + | 22.7184i | 0.0640184 | + | 0.727198i | ||||
\(977\) | − | 19.0313i | − | 0.608864i | −0.952534 | − | 0.304432i | \(-0.901533\pi\) | ||
0.952534 | − | 0.304432i | \(-0.0984667\pi\) | |||||||
\(978\) | −0.612595 | + | 0.887263i | −0.0195886 | + | 0.0283716i | ||||
\(979\) | 18.0079i | 0.575534i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.10469 | + | 6.15681i | −0.0991250 | + | 0.196572i | ||||
\(982\) | 17.4031 | − | 7.66037i | 0.555356 | − | 0.244452i | ||||
\(983\) | −57.0331 | −1.81907 | −0.909537 | − | 0.415623i | \(-0.863563\pi\) | ||||
−0.909537 | + | 0.415623i | \(0.863563\pi\) | |||||||
\(984\) | −3.36507 | − | 14.7008i | −0.107274 | − | 0.468645i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −22.5261 | + | 9.91534i | −0.717376 | + | 0.315769i | ||||
\(987\) | −13.4453 | + | 8.27799i | −0.427967 | + | 0.263491i | ||||
\(988\) | 2.40312 | + | 2.20086i | 0.0764536 | + | 0.0700187i | ||||
\(989\) | 43.5392i | 1.38447i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.4251i | 1.41121i | 0.708606 | + | 0.705604i | \(0.249324\pi\) | ||||
−0.708606 | + | 0.705604i | \(0.750676\pi\) | |||||||
\(992\) | 16.8066 | − | 9.23521i | 0.533609 | − | 0.293218i | ||||
\(993\) | 25.2617 | − | 15.5532i | 0.801656 | − | 0.493564i | ||||
\(994\) | −17.7906 | − | 40.4174i | −0.564284 | − | 1.28196i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.17859 | + | 1.18586i | 0.195776 | + | 0.0375754i | ||||
\(997\) | 47.4031 | 1.50127 | 0.750636 | − | 0.660716i | \(-0.229747\pi\) | ||||
0.750636 | + | 0.660716i | \(0.229747\pi\) | |||||||
\(998\) | −22.9528 | − | 52.1450i | −0.726558 | − | 1.65062i | ||||
\(999\) | 38.3295 | − | 3.25865i | 1.21269 | − | 0.103099i |
(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 | 300.2.e.d.251.2 | yes | 8 | |
3.2 | odd | 2 | inner | 300.2.e.d.251.7 | yes | 8 | |
4.3 | odd | 2 | inner | 300.2.e.d.251.8 | yes | 8 | |
5.2 | odd | 4 | 300.2.h.c.299.5 | 16 | |||
5.3 | odd | 4 | 300.2.h.c.299.12 | 16 | |||
5.4 | even | 2 | 300.2.e.e.251.7 | yes | 8 | ||
12.11 | even | 2 | inner | 300.2.e.d.251.1 | ✓ | 8 | |
15.2 | even | 4 | 300.2.h.c.299.11 | 16 | |||
15.8 | even | 4 | 300.2.h.c.299.6 | 16 | |||
15.14 | odd | 2 | 300.2.e.e.251.2 | yes | 8 | ||
20.3 | even | 4 | 300.2.h.c.299.9 | 16 | |||
20.7 | even | 4 | 300.2.h.c.299.8 | 16 | |||
20.19 | odd | 2 | 300.2.e.e.251.1 | yes | 8 | ||
60.23 | odd | 4 | 300.2.h.c.299.7 | 16 | |||
60.47 | odd | 4 | 300.2.h.c.299.10 | 16 | |||
60.59 | even | 2 | 300.2.e.e.251.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.e.d.251.1 | ✓ | 8 | 12.11 | even | 2 | inner | |
300.2.e.d.251.2 | yes | 8 | 1.1 | even | 1 | trivial | |
300.2.e.d.251.7 | yes | 8 | 3.2 | odd | 2 | inner | |
300.2.e.d.251.8 | yes | 8 | 4.3 | odd | 2 | inner | |
300.2.e.e.251.1 | yes | 8 | 20.19 | odd | 2 | ||
300.2.e.e.251.2 | yes | 8 | 15.14 | odd | 2 | ||
300.2.e.e.251.7 | yes | 8 | 5.4 | even | 2 | ||
300.2.e.e.251.8 | yes | 8 | 60.59 | even | 2 | ||
300.2.h.c.299.5 | 16 | 5.2 | odd | 4 | |||
300.2.h.c.299.6 | 16 | 15.8 | even | 4 | |||
300.2.h.c.299.7 | 16 | 60.23 | odd | 4 | |||
300.2.h.c.299.8 | 16 | 20.7 | even | 4 | |||
300.2.h.c.299.9 | 16 | 20.3 | even | 4 | |||
300.2.h.c.299.10 | 16 | 60.47 | odd | 4 | |||
300.2.h.c.299.11 | 16 | 15.2 | even | 4 | |||
300.2.h.c.299.12 | 16 | 5.3 | odd | 4 |