Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(13,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.67685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Root | \(2.16053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.97 |
Dual form | 210.2.m.b.13.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −2.23483 | + | 0.0743018i | −0.999448 | + | 0.0332288i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 2.52773 | + | 0.781409i | 0.955391 | + | 0.295345i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 1.63280 | + | 1.52773i | 0.516338 | + | 0.483109i | ||||
\(11\) | 4.90685 | 1.47947 | 0.739735 | − | 0.672898i | \(-0.234951\pi\) | ||||
0.739735 | + | 0.672898i | \(0.234951\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | 3.41421 | + | 3.41421i | 0.946932 | + | 0.946932i | 0.998661 | − | 0.0517287i | \(-0.0164731\pi\) |
−0.0517287 | + | 0.998661i | \(0.516473\pi\) | |||||||
\(14\) | −1.23483 | − | 2.33991i | −0.330023 | − | 0.625368i | ||||
\(15\) | −1.63280 | − | 1.52773i | −0.421588 | − | 0.394457i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.74632 | + | 2.74632i | −0.666080 | + | 0.666080i | −0.956806 | − | 0.290726i | \(-0.906103\pi\) |
0.290726 | + | 0.956806i | \(0.406103\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | −1.26561 | −0.290351 | −0.145175 | − | 0.989406i | \(-0.546375\pi\) | ||||
−0.145175 | + | 0.989406i | \(0.546375\pi\) | |||||||
\(20\) | −0.0743018 | − | 2.23483i | −0.0166144 | − | 0.499724i | ||||
\(21\) | 1.23483 | + | 2.33991i | 0.269463 | + | 0.510611i | ||||
\(22\) | −3.46967 | − | 3.46967i | −0.739735 | − | 0.739735i | ||||
\(23\) | −1.05545 | + | 1.05545i | −0.220077 | + | 0.220077i | −0.808531 | − | 0.588454i | \(-0.799737\pi\) |
0.588454 | + | 0.808531i | \(0.299737\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 4.98896 | − | 0.332104i | 0.997792 | − | 0.0664208i | ||||
\(26\) | − | 4.82843i | − | 0.946932i | ||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −0.781409 | + | 2.52773i | −0.147672 | + | 0.477695i | ||||
\(29\) | − | 4.76687i | − | 0.885186i | −0.896723 | − | 0.442593i | \(-0.854059\pi\) | ||
0.896723 | − | 0.442593i | \(-0.145941\pi\) | |||||||
\(30\) | 0.0743018 | + | 2.23483i | 0.0135656 | + | 0.408023i | ||||
\(31\) | − | 7.05545i | − | 1.26720i | −0.773662 | − | 0.633598i | \(-0.781577\pi\) | ||
0.773662 | − | 0.633598i | \(-0.218423\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 3.46967 | + | 3.46967i | 0.603991 | + | 0.603991i | ||||
\(34\) | 3.88388 | 0.666080 | ||||||||
\(35\) | −5.70711 | − | 1.55850i | −0.964677 | − | 0.263435i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −4.74632 | − | 4.74632i | −0.780290 | − | 0.780290i | 0.199590 | − | 0.979880i | \(-0.436039\pi\) |
−0.979880 | + | 0.199590i | \(0.936039\pi\) | |||||||
\(38\) | 0.894921 | + | 0.894921i | 0.145175 | + | 0.145175i | ||||
\(39\) | 4.82843i | 0.773167i | ||||||||
\(40\) | −1.52773 | + | 1.63280i | −0.241555 | + | 0.258169i | ||||
\(41\) | − | 5.44670i | − | 0.850631i | −0.905045 | − | 0.425316i | \(-0.860163\pi\) | ||
0.905045 | − | 0.425316i | \(-0.139837\pi\) | |||||||
\(42\) | 0.781409 | − | 2.52773i | 0.120574 | − | 0.390037i | ||||
\(43\) | −7.58667 | + | 7.58667i | −1.15696 | + | 1.15696i | −0.171830 | + | 0.985127i | \(0.554968\pi\) |
−0.985127 | + | 0.171830i | \(0.945032\pi\) | |||||||
\(44\) | 4.90685i | 0.739735i | ||||||||
\(45\) | −0.0743018 | − | 2.23483i | −0.0110763 | − | 0.333149i | ||||
\(46\) | 1.49264 | 0.220077 | ||||||||
\(47\) | −0.734390 | + | 0.734390i | −0.107122 | + | 0.107122i | −0.758636 | − | 0.651514i | \(-0.774134\pi\) |
0.651514 | + | 0.758636i | \(0.274134\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | 5.77880 | + | 3.95037i | 0.825543 | + | 0.564339i | ||||
\(50\) | −3.76256 | − | 3.29289i | −0.532106 | − | 0.465685i | ||||
\(51\) | −3.88388 | −0.543852 | ||||||||
\(52\) | −3.41421 | + | 3.41421i | −0.473466 | + | 0.473466i | ||||
\(53\) | 1.26561 | − | 1.26561i | 0.173845 | − | 0.173845i | −0.614821 | − | 0.788666i | \(-0.710772\pi\) |
0.788666 | + | 0.614821i | \(0.210772\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −10.9660 | + | 0.364588i | −1.47865 | + | 0.0491610i | ||||
\(56\) | 2.33991 | − | 1.23483i | 0.312684 | − | 0.165012i | ||||
\(57\) | −0.894921 | − | 0.894921i | −0.118535 | − | 0.118535i | ||||
\(58\) | −3.37069 | + | 3.37069i | −0.442593 | + | 0.442593i | ||||
\(59\) | −1.39735 | −0.181919 | −0.0909594 | − | 0.995855i | \(-0.528993\pi\) | ||||
−0.0909594 | + | 0.995855i | \(0.528993\pi\) | |||||||
\(60\) | 1.52773 | − | 1.63280i | 0.197229 | − | 0.210794i | ||||
\(61\) | − | 2.29721i | − | 0.294127i | −0.989127 | − | 0.147064i | \(-0.953018\pi\) | ||
0.989127 | − | 0.147064i | \(-0.0469822\pi\) | |||||||
\(62\) | −4.98896 | + | 4.98896i | −0.633598 | + | 0.633598i | ||||
\(63\) | −0.781409 | + | 2.52773i | −0.0984482 | + | 0.318464i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −7.88388 | − | 7.37652i | −0.977875 | − | 0.914944i | ||||
\(66\) | − | 4.90685i | − | 0.603991i | ||||||
\(67\) | 3.05545 | + | 3.05545i | 0.373283 | + | 0.373283i | 0.868672 | − | 0.495389i | \(-0.164974\pi\) |
−0.495389 | + | 0.868672i | \(0.664974\pi\) | |||||||
\(68\) | −2.74632 | − | 2.74632i | −0.333040 | − | 0.333040i | ||||
\(69\) | −1.49264 | −0.179692 | ||||||||
\(70\) | 2.93351 | + | 5.13756i | 0.350621 | + | 0.614056i | ||||
\(71\) | −13.0334 | −1.54678 | −0.773388 | − | 0.633933i | \(-0.781440\pi\) | ||||
−0.773388 | + | 0.633933i | \(0.781440\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | −5.04441 | − | 5.04441i | −0.590404 | − | 0.590404i | 0.347337 | − | 0.937740i | \(-0.387086\pi\) |
−0.937740 | + | 0.347337i | \(0.887086\pi\) | |||||||
\(74\) | 6.71231i | 0.780290i | ||||||||
\(75\) | 3.76256 | + | 3.29289i | 0.434463 | + | 0.380231i | ||||
\(76\) | − | 1.26561i | − | 0.145175i | ||||||
\(77\) | 12.4032 | + | 3.83425i | 1.41347 | + | 0.436954i | ||||
\(78\) | 3.41421 | − | 3.41421i | 0.386584 | − | 0.386584i | ||||
\(79\) | − | 14.8063i | − | 1.66584i | −0.553391 | − | 0.832922i | \(-0.686666\pi\) | ||
0.553391 | − | 0.832922i | \(-0.313334\pi\) | |||||||
\(80\) | 2.23483 | − | 0.0743018i | 0.249862 | − | 0.00830719i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −3.85140 | + | 3.85140i | −0.425316 | + | 0.425316i | ||||
\(83\) | 9.29809 | + | 9.29809i | 1.02060 | + | 1.02060i | 0.999783 | + | 0.0208150i | \(0.00662610\pi\) |
0.0208150 | + | 0.999783i | \(0.493374\pi\) | |||||||
\(84\) | −2.33991 | + | 1.23483i | −0.255305 | + | 0.134731i | ||||
\(85\) | 5.93351 | − | 6.34162i | 0.643579 | − | 0.687845i | ||||
\(86\) | 10.7292 | 1.15696 | ||||||||
\(87\) | 3.37069 | − | 3.37069i | 0.361376 | − | 0.361376i | ||||
\(88\) | 3.46967 | − | 3.46967i | 0.369868 | − | 0.369868i | ||||
\(89\) | 15.3596 | 1.62812 | 0.814060 | − | 0.580781i | \(-0.197253\pi\) | ||||
0.814060 | + | 0.580781i | \(0.197253\pi\) | |||||||
\(90\) | −1.52773 | + | 1.63280i | −0.161036 | + | 0.172113i | ||||
\(91\) | 5.96230 | + | 11.2981i | 0.625019 | + | 1.18436i | ||||
\(92\) | −1.05545 | − | 1.05545i | −0.110039 | − | 0.110039i | ||||
\(93\) | 4.98896 | − | 4.98896i | 0.517331 | − | 0.517331i | ||||
\(94\) | 1.03858 | 0.107122 | ||||||||
\(95\) | 2.82843 | − | 0.0940371i | 0.290191 | − | 0.00964800i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 8.42614 | − | 8.42614i | 0.855545 | − | 0.855545i | −0.135264 | − | 0.990810i | \(-0.543188\pi\) |
0.990810 | + | 0.135264i | \(0.0431884\pi\) | |||||||
\(98\) | −1.29289 | − | 6.87957i | −0.130602 | − | 0.694941i | ||||
\(99\) | 4.90685i | 0.493157i | ||||||||
\(100\) | 0.332104 | + | 4.98896i | 0.0332104 | + | 0.498896i | ||||
\(101\) | 18.1504i | 1.80603i | 0.429609 | + | 0.903015i | \(0.358651\pi\) | ||||
−0.429609 | + | 0.903015i | \(0.641349\pi\) | |||||||
\(102\) | 2.74632 | + | 2.74632i | 0.271926 | + | 0.271926i | ||||
\(103\) | −8.36459 | − | 8.36459i | −0.824187 | − | 0.824187i | 0.162518 | − | 0.986706i | \(-0.448038\pi\) |
−0.986706 | + | 0.162518i | \(0.948038\pi\) | |||||||
\(104\) | 4.82843 | 0.473466 | ||||||||
\(105\) | −2.93351 | − | 5.13756i | −0.286281 | − | 0.501375i | ||||
\(106\) | −1.78984 | −0.173845 | ||||||||
\(107\) | 3.77297 | + | 3.77297i | 0.364747 | + | 0.364747i | 0.865557 | − | 0.500810i | \(-0.166964\pi\) |
−0.500810 | + | 0.865557i | \(0.666964\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | 0.0870500i | 0.00833787i | 0.999991 | + | 0.00416894i | \(0.00132702\pi\) | ||||
−0.999991 | + | 0.00416894i | \(0.998673\pi\) | |||||||
\(110\) | 8.01193 | + | 7.49632i | 0.763907 | + | 0.714746i | ||||
\(111\) | − | 6.71231i | − | 0.637104i | ||||||
\(112\) | −2.52773 | − | 0.781409i | −0.238848 | − | 0.0738362i | ||||
\(113\) | 2.03248 | − | 2.03248i | 0.191200 | − | 0.191200i | −0.605014 | − | 0.796214i | \(-0.706833\pi\) |
0.796214 | + | 0.605014i | \(0.206833\pi\) | |||||||
\(114\) | 1.26561i | 0.118535i | ||||||||
\(115\) | 2.28034 | − | 2.43718i | 0.212643 | − | 0.227268i | ||||
\(116\) | 4.76687 | 0.442593 | ||||||||
\(117\) | −3.41421 | + | 3.41421i | −0.315644 | + | 0.315644i | ||||
\(118\) | 0.988072 | + | 0.988072i | 0.0909594 | + | 0.0909594i | ||||
\(119\) | −9.08794 | + | 4.79594i | −0.833090 | + | 0.439643i | ||||
\(120\) | −2.23483 | + | 0.0743018i | −0.204011 | + | 0.00678279i | ||||
\(121\) | 13.0772 | 1.18883 | ||||||||
\(122\) | −1.62437 | + | 1.62437i | −0.147064 | + | 0.147064i | ||||
\(123\) | 3.85140 | − | 3.85140i | 0.347269 | − | 0.347269i | ||||
\(124\) | 7.05545 | 0.633598 | ||||||||
\(125\) | −11.1248 | + | 1.11289i | −0.995034 | + | 0.0995396i | ||||
\(126\) | 2.33991 | − | 1.23483i | 0.208456 | − | 0.110008i | ||||
\(127\) | −11.1761 | − | 11.1761i | −0.991723 | − | 0.991723i | 0.00824340 | − | 0.999966i | \(-0.497376\pi\) |
−0.999966 | + | 0.00824340i | \(0.997376\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −10.7292 | −0.944651 | ||||||||
\(130\) | 0.358761 | + | 10.7907i | 0.0314654 | + | 0.946410i | ||||
\(131\) | − | 12.8367i | − | 1.12154i | −0.827970 | − | 0.560772i | \(-0.810504\pi\) | ||
0.827970 | − | 0.560772i | \(-0.189496\pi\) | |||||||
\(132\) | −3.46967 | + | 3.46967i | −0.301996 | + | 0.301996i | ||||
\(133\) | −3.19912 | − | 0.988958i | −0.277399 | − | 0.0857536i | ||||
\(134\) | − | 4.32106i | − | 0.373283i | ||||||
\(135\) | 1.52773 | − | 1.63280i | 0.131486 | − | 0.140529i | ||||
\(136\) | 3.88388i | 0.333040i | ||||||||
\(137\) | −3.62437 | − | 3.62437i | −0.309651 | − | 0.309651i | 0.535123 | − | 0.844774i | \(-0.320265\pi\) |
−0.844774 | + | 0.535123i | \(0.820265\pi\) | |||||||
\(138\) | 1.05545 | + | 1.05545i | 0.0898461 | + | 0.0898461i | ||||
\(139\) | −3.90596 | −0.331299 | −0.165650 | − | 0.986185i | \(-0.552972\pi\) | ||||
−0.165650 | + | 0.986185i | \(0.552972\pi\) | |||||||
\(140\) | 1.55850 | − | 5.70711i | 0.131718 | − | 0.482339i | ||||
\(141\) | −1.03858 | −0.0874646 | ||||||||
\(142\) | 9.21598 | + | 9.21598i | 0.773388 | + | 0.773388i | ||||
\(143\) | 16.7530 | + | 16.7530i | 1.40096 | + | 1.40096i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 0.354187 | + | 10.6532i | 0.0294137 | + | 0.884697i | ||||
\(146\) | 7.13387i | 0.590404i | ||||||||
\(147\) | 1.29289 | + | 6.87957i | 0.106636 | + | 0.567417i | ||||
\(148\) | 4.74632 | − | 4.74632i | 0.390145 | − | 0.390145i | ||||
\(149\) | − | 5.64124i | − | 0.462148i | −0.972936 | − | 0.231074i | \(-0.925776\pi\) | ||
0.972936 | − | 0.231074i | \(-0.0742240\pi\) | |||||||
\(150\) | −0.332104 | − | 4.98896i | −0.0271162 | − | 0.407347i | ||||
\(151\) | −11.7678 | −0.957647 | −0.478823 | − | 0.877911i | \(-0.658937\pi\) | ||||
−0.478823 | + | 0.877911i | \(0.658937\pi\) | |||||||
\(152\) | −0.894921 | + | 0.894921i | −0.0725877 | + | 0.0725877i | ||||
\(153\) | −2.74632 | − | 2.74632i | −0.222027 | − | 0.222027i | ||||
\(154\) | −6.05914 | − | 11.4816i | −0.488259 | − | 0.925213i | ||||
\(155\) | 0.524233 | + | 15.7678i | 0.0421074 | + | 1.26650i | ||||
\(156\) | −4.82843 | −0.386584 | ||||||||
\(157\) | 13.7132 | − | 13.7132i | 1.09443 | − | 1.09443i | 0.0993827 | − | 0.995049i | \(-0.468313\pi\) |
0.995049 | − | 0.0993827i | \(-0.0316868\pi\) | |||||||
\(158\) | −10.4697 | + | 10.4697i | −0.832922 | + | 0.832922i | ||||
\(159\) | 1.78984 | 0.141944 | ||||||||
\(160\) | −1.63280 | − | 1.52773i | −0.129085 | − | 0.120777i | ||||
\(161\) | −3.49264 | + | 1.84316i | −0.275258 | + | 0.145261i | ||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | −7.21967 | + | 7.21967i | −0.565488 | + | 0.565488i | −0.930861 | − | 0.365373i | \(-0.880941\pi\) |
0.365373 | + | 0.930861i | \(0.380941\pi\) | |||||||
\(164\) | 5.44670 | 0.425316 | ||||||||
\(165\) | −8.01193 | − | 7.49632i | −0.623728 | − | 0.583588i | ||||
\(166\) | − | 13.1495i | − | 1.02060i | ||||||
\(167\) | 6.73439 | − | 6.73439i | 0.521123 | − | 0.521123i | −0.396788 | − | 0.917910i | \(-0.629875\pi\) |
0.917910 | + | 0.396788i | \(0.129875\pi\) | |||||||
\(168\) | 2.52773 | + | 0.781409i | 0.195018 | + | 0.0602870i | ||||
\(169\) | 10.3137i | 0.793362i | ||||||||
\(170\) | −8.67982 | + | 0.288579i | −0.665712 | + | 0.0221330i | ||||
\(171\) | − | 1.26561i | − | 0.0967836i | ||||||
\(172\) | −7.58667 | − | 7.58667i | −0.578478 | − | 0.578478i | ||||
\(173\) | −14.1605 | − | 14.1605i | −1.07661 | − | 1.07661i | −0.996811 | − | 0.0797939i | \(-0.974574\pi\) |
−0.0797939 | − | 0.996811i | \(-0.525426\pi\) | |||||||
\(174\) | −4.76687 | −0.361376 | ||||||||
\(175\) | 12.8702 | + | 3.05895i | 0.972898 | + | 0.231235i | ||||
\(176\) | −4.90685 | −0.369868 | ||||||||
\(177\) | −0.988072 | − | 0.988072i | −0.0742681 | − | 0.0742681i | ||||
\(178\) | −10.8609 | − | 10.8609i | −0.814060 | − | 0.814060i | ||||
\(179\) | 3.28123i | 0.245250i | 0.992453 | + | 0.122625i | \(0.0391313\pi\) | ||||
−0.992453 | + | 0.122625i | \(0.960869\pi\) | |||||||
\(180\) | 2.23483 | − | 0.0743018i | 0.166575 | − | 0.00553813i | ||||
\(181\) | 19.3934i | 1.44150i | 0.693196 | + | 0.720749i | \(0.256202\pi\) | ||||
−0.693196 | + | 0.720749i | \(0.743798\pi\) | |||||||
\(182\) | 3.77297 | − | 12.2049i | 0.279671 | − | 0.904691i | ||||
\(183\) | 1.62437 | − | 1.62437i | 0.120077 | − | 0.120077i | ||||
\(184\) | 1.49264i | 0.110039i | ||||||||
\(185\) | 10.9599 | + | 10.2546i | 0.805787 | + | 0.753931i | ||||
\(186\) | −7.05545 | −0.517331 | ||||||||
\(187\) | −13.4758 | + | 13.4758i | −0.985446 | + | 0.985446i | ||||
\(188\) | −0.734390 | − | 0.734390i | −0.0535609 | − | 0.0535609i | ||||
\(189\) | −2.33991 | + | 1.23483i | −0.170204 | + | 0.0898209i | ||||
\(190\) | −2.06649 | − | 1.93351i | −0.149919 | − | 0.140271i | ||||
\(191\) | −16.8453 | −1.21888 | −0.609441 | − | 0.792831i | \(-0.708606\pi\) | ||||
−0.609441 | + | 0.792831i | \(0.708606\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −4.81370 | + | 4.81370i | −0.346498 | + | 0.346498i | −0.858803 | − | 0.512306i | \(-0.828792\pi\) |
0.512306 | + | 0.858803i | \(0.328792\pi\) | |||||||
\(194\) | −11.9164 | −0.855545 | ||||||||
\(195\) | −0.358761 | − | 10.7907i | −0.0256914 | − | 0.772740i | ||||
\(196\) | −3.95037 | + | 5.77880i | −0.282170 | + | 0.412772i | ||||
\(197\) | 13.0334 | + | 13.0334i | 0.928589 | + | 0.928589i | 0.997615 | − | 0.0690257i | \(-0.0219891\pi\) |
−0.0690257 | + | 0.997615i | \(0.521989\pi\) | |||||||
\(198\) | 3.46967 | − | 3.46967i | 0.246578 | − | 0.246578i | ||||
\(199\) | −11.7509 | −0.832999 | −0.416499 | − | 0.909136i | \(-0.636743\pi\) | ||||
−0.416499 | + | 0.909136i | \(0.636743\pi\) | |||||||
\(200\) | 3.29289 | − | 3.76256i | 0.232843 | − | 0.266053i | ||||
\(201\) | 4.32106i | 0.304784i | ||||||||
\(202\) | 12.8343 | − | 12.8343i | 0.903015 | − | 0.903015i | ||||
\(203\) | 3.72488 | − | 12.0494i | 0.261435 | − | 0.845699i | ||||
\(204\) | − | 3.88388i | − | 0.271926i | ||||||
\(205\) | 0.404699 | + | 12.1725i | 0.0282654 | + | 0.850161i | ||||
\(206\) | 11.8293i | 0.824187i | ||||||||
\(207\) | −1.05545 | − | 1.05545i | −0.0733590 | − | 0.0733590i | ||||
\(208\) | −3.41421 | − | 3.41421i | −0.236733 | − | 0.236733i | ||||
\(209\) | −6.21016 | −0.429566 | ||||||||
\(210\) | −1.55850 | + | 5.70711i | −0.107547 | + | 0.393828i | ||||
\(211\) | 16.5502 | 1.13937 | 0.569683 | − | 0.821864i | \(-0.307066\pi\) | ||||
0.569683 | + | 0.821864i | \(0.307066\pi\) | |||||||
\(212\) | 1.26561 | + | 1.26561i | 0.0869224 | + | 0.0869224i | ||||
\(213\) | −9.21598 | − | 9.21598i | −0.631469 | − | 0.631469i | ||||
\(214\) | − | 5.33579i | − | 0.364747i | ||||||
\(215\) | 16.3912 | − | 17.5187i | 1.11787 | − | 1.19476i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 5.51319 | − | 17.8343i | 0.374260 | − | 1.21067i | ||||
\(218\) | 0.0615536 | − | 0.0615536i | 0.00416894 | − | 0.00416894i | ||||
\(219\) | − | 7.13387i | − | 0.482063i | ||||||
\(220\) | −0.364588 | − | 10.9660i | −0.0245805 | − | 0.739327i | ||||
\(221\) | −18.7530 | −1.26147 | ||||||||
\(222\) | −4.74632 | + | 4.74632i | −0.318552 | + | 0.318552i | ||||
\(223\) | 8.26067 | + | 8.26067i | 0.553175 | + | 0.553175i | 0.927356 | − | 0.374181i | \(-0.122076\pi\) |
−0.374181 | + | 0.927356i | \(0.622076\pi\) | |||||||
\(224\) | 1.23483 | + | 2.33991i | 0.0825058 | + | 0.156342i | ||||
\(225\) | 0.332104 | + | 4.98896i | 0.0221403 | + | 0.332597i | ||||
\(226\) | −2.87437 | −0.191200 | ||||||||
\(227\) | −5.91295 | + | 5.91295i | −0.392456 | + | 0.392456i | −0.875562 | − | 0.483106i | \(-0.839509\pi\) |
0.483106 | + | 0.875562i | \(0.339509\pi\) | |||||||
\(228\) | 0.894921 | − | 0.894921i | 0.0592676 | − | 0.0592676i | ||||
\(229\) | 9.31371 | 0.615467 | 0.307734 | − | 0.951473i | \(-0.400429\pi\) | ||||
0.307734 | + | 0.951473i | \(0.400429\pi\) | |||||||
\(230\) | −3.33579 | + | 0.110906i | −0.219956 | + | 0.00731289i | ||||
\(231\) | 6.05914 | + | 11.4816i | 0.398662 | + | 0.755433i | ||||
\(232\) | −3.37069 | − | 3.37069i | −0.221297 | − | 0.221297i | ||||
\(233\) | 16.0563 | − | 16.0563i | 1.05189 | − | 1.05189i | 0.0533076 | − | 0.998578i | \(-0.483024\pi\) |
0.998578 | − | 0.0533076i | \(-0.0169764\pi\) | |||||||
\(234\) | 4.82843 | 0.315644 | ||||||||
\(235\) | 1.58667 | − | 1.69581i | 0.103503 | − | 0.110622i | ||||
\(236\) | − | 1.39735i | − | 0.0909594i | ||||||
\(237\) | 10.4697 | − | 10.4697i | 0.680078 | − | 0.680078i | ||||
\(238\) | 9.81739 | + | 3.03490i | 0.636367 | + | 0.196723i | ||||
\(239\) | − | 1.68592i | − | 0.109053i | −0.998512 | − | 0.0545267i | \(-0.982635\pi\) | ||
0.998512 | − | 0.0545267i | \(-0.0173650\pi\) | |||||||
\(240\) | 1.63280 | + | 1.52773i | 0.105397 | + | 0.0986143i | ||||
\(241\) | − | 3.61574i | − | 0.232910i | −0.993196 | − | 0.116455i | \(-0.962847\pi\) | ||
0.993196 | − | 0.116455i | \(-0.0371532\pi\) | |||||||
\(242\) | −9.24695 | − | 9.24695i | −0.594417 | − | 0.594417i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 2.29721 | 0.147064 | ||||||||
\(245\) | −13.2082 | − | 8.39905i | −0.843839 | − | 0.536596i | ||||
\(246\) | −5.44670 | −0.347269 | ||||||||
\(247\) | −4.32106 | − | 4.32106i | −0.274943 | − | 0.274943i | ||||
\(248\) | −4.98896 | − | 4.98896i | −0.316799 | − | 0.316799i | ||||
\(249\) | 13.1495i | 0.833315i | ||||||||
\(250\) | 8.65336 | + | 7.07950i | 0.547287 | + | 0.447747i | ||||
\(251\) | 4.78896i | 0.302276i | 0.988513 | + | 0.151138i | \(0.0482938\pi\) | ||||
−0.988513 | + | 0.151138i | \(0.951706\pi\) | |||||||
\(252\) | −2.52773 | − | 0.781409i | −0.159232 | − | 0.0492241i | ||||
\(253\) | −5.17895 | + | 5.17895i | −0.325598 | + | 0.325598i | ||||
\(254\) | 15.8055i | 0.991723i | ||||||||
\(255\) | 8.67982 | − | 0.288579i | 0.543552 | − | 0.0180715i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.8113 | + | 20.8113i | −1.29817 | + | 1.29817i | −0.368574 | + | 0.929599i | \(0.620154\pi\) |
−0.929599 | + | 0.368574i | \(0.879846\pi\) | |||||||
\(258\) | 7.58667 | + | 7.58667i | 0.472326 | + | 0.472326i | ||||
\(259\) | −8.28858 | − | 15.7062i | −0.515027 | − | 0.975936i | ||||
\(260\) | 7.37652 | − | 7.88388i | 0.457472 | − | 0.488937i | ||||
\(261\) | 4.76687 | 0.295062 | ||||||||
\(262\) | −9.07689 | + | 9.07689i | −0.560772 | + | 0.560772i | ||||
\(263\) | 6.61827 | − | 6.61827i | 0.408100 | − | 0.408100i | −0.472976 | − | 0.881076i | \(-0.656820\pi\) |
0.881076 | + | 0.472976i | \(0.156820\pi\) | |||||||
\(264\) | 4.90685 | 0.301996 | ||||||||
\(265\) | −2.73439 | + | 2.92246i | −0.167972 | + | 0.179526i | ||||
\(266\) | 1.56282 | + | 2.96142i | 0.0958225 | + | 0.181576i | ||||
\(267\) | 10.8609 | + | 10.8609i | 0.664677 | + | 0.664677i | ||||
\(268\) | −3.05545 | + | 3.05545i | −0.186641 | + | 0.186641i | ||||
\(269\) | −13.1192 | −0.799890 | −0.399945 | − | 0.916539i | \(-0.630971\pi\) | ||||
−0.399945 | + | 0.916539i | \(0.630971\pi\) | |||||||
\(270\) | −2.23483 | + | 0.0743018i | −0.136008 | + | 0.00452186i | ||||
\(271\) | 18.0836i | 1.09850i | 0.835658 | + | 0.549250i | \(0.185087\pi\) | ||||
−0.835658 | + | 0.549250i | \(0.814913\pi\) | |||||||
\(272\) | 2.74632 | − | 2.74632i | 0.166520 | − | 0.166520i | ||||
\(273\) | −3.77297 | + | 12.2049i | −0.228351 | + | 0.738677i | ||||
\(274\) | 5.12563i | 0.309651i | ||||||||
\(275\) | 24.4801 | − | 1.62959i | 1.47620 | − | 0.0982677i | ||||
\(276\) | − | 1.49264i | − | 0.0898461i | ||||||
\(277\) | 2.63541 | + | 2.63541i | 0.158347 | + | 0.158347i | 0.781834 | − | 0.623487i | \(-0.214285\pi\) |
−0.623487 | + | 0.781834i | \(0.714285\pi\) | |||||||
\(278\) | 2.76193 | + | 2.76193i | 0.165650 | + | 0.165650i | ||||
\(279\) | 7.05545 | 0.422399 | ||||||||
\(280\) | −5.13756 | + | 2.93351i | −0.307028 | + | 0.175310i | ||||
\(281\) | 20.4558 | 1.22029 | 0.610146 | − | 0.792289i | \(-0.291111\pi\) | ||||
0.610146 | + | 0.792289i | \(0.291111\pi\) | |||||||
\(282\) | 0.734390 | + | 0.734390i | 0.0437323 | + | 0.0437323i | ||||
\(283\) | −10.7751 | − | 10.7751i | −0.640514 | − | 0.640514i | 0.310168 | − | 0.950682i | \(-0.399615\pi\) |
−0.950682 | + | 0.310168i | \(0.899615\pi\) | |||||||
\(284\) | − | 13.0334i | − | 0.773388i | ||||||
\(285\) | 2.06649 | + | 1.93351i | 0.122409 | + | 0.114531i | ||||
\(286\) | − | 23.6924i | − | 1.40096i | ||||||
\(287\) | 4.25610 | − | 13.7678i | 0.251229 | − | 0.812685i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 1.91548i | 0.112675i | ||||||||
\(290\) | 7.28248 | − | 7.78337i | 0.427642 | − | 0.457056i | ||||
\(291\) | 11.9164 | 0.698550 | ||||||||
\(292\) | 5.04441 | − | 5.04441i | 0.295202 | − | 0.295202i | ||||
\(293\) | 3.15965 | + | 3.15965i | 0.184588 | + | 0.184588i | 0.793352 | − | 0.608763i | \(-0.208334\pi\) |
−0.608763 | + | 0.793352i | \(0.708334\pi\) | |||||||
\(294\) | 3.95037 | − | 5.77880i | 0.230390 | − | 0.337027i | ||||
\(295\) | 3.12283 | − | 0.103825i | 0.181818 | − | 0.00604494i | ||||
\(296\) | −6.71231 | −0.390145 | ||||||||
\(297\) | −3.46967 | + | 3.46967i | −0.201330 | + | 0.201330i | ||||
\(298\) | −3.98896 | + | 3.98896i | −0.231074 | + | 0.231074i | ||||
\(299\) | −7.20708 | −0.416796 | ||||||||
\(300\) | −3.29289 | + | 3.76256i | −0.190115 | + | 0.217231i | ||||
\(301\) | −25.1053 | + | 13.2487i | −1.44705 | + | 0.763645i | ||||
\(302\) | 8.32106 | + | 8.32106i | 0.478823 | + | 0.478823i | ||||
\(303\) | −12.8343 | + | 12.8343i | −0.737309 | + | 0.737309i | ||||
\(304\) | 1.26561 | 0.0725877 | ||||||||
\(305\) | 0.170687 | + | 5.13387i | 0.00977349 | + | 0.293965i | ||||
\(306\) | 3.88388i | 0.222027i | ||||||||
\(307\) | −20.8011 | + | 20.8011i | −1.18718 | + | 1.18718i | −0.209340 | + | 0.977843i | \(0.567132\pi\) |
−0.977843 | + | 0.209340i | \(0.932868\pi\) | |||||||
\(308\) | −3.83425 | + | 12.4032i | −0.218477 | + | 0.706736i | ||||
\(309\) | − | 11.8293i | − | 0.672946i | ||||||
\(310\) | 10.7788 | − | 11.5202i | 0.612195 | − | 0.654302i | ||||
\(311\) | − | 11.4706i | − | 0.650435i | −0.945639 | − | 0.325218i | \(-0.894562\pi\) | ||
0.945639 | − | 0.325218i | \(-0.105438\pi\) | |||||||
\(312\) | 3.41421 | + | 3.41421i | 0.193292 | + | 0.193292i | ||||
\(313\) | −0.612443 | − | 0.612443i | −0.0346173 | − | 0.0346173i | 0.689586 | − | 0.724204i | \(-0.257792\pi\) |
−0.724204 | + | 0.689586i | \(0.757792\pi\) | |||||||
\(314\) | −19.3934 | −1.09443 | ||||||||
\(315\) | 1.55850 | − | 5.70711i | 0.0878117 | − | 0.321559i | ||||
\(316\) | 14.8063 | 0.832922 | ||||||||
\(317\) | 7.03984 | + | 7.03984i | 0.395397 | + | 0.395397i | 0.876606 | − | 0.481209i | \(-0.159802\pi\) |
−0.481209 | + | 0.876606i | \(0.659802\pi\) | |||||||
\(318\) | −1.26561 | − | 1.26561i | −0.0709719 | − | 0.0709719i | ||||
\(319\) | − | 23.3903i | − | 1.30961i | ||||||
\(320\) | 0.0743018 | + | 2.23483i | 0.00415360 | + | 0.124931i | ||||
\(321\) | 5.33579i | 0.297815i | ||||||||
\(322\) | 3.77297 | + | 1.16636i | 0.210260 | + | 0.0649986i | ||||
\(323\) | 3.47577 | − | 3.47577i | 0.193397 | − | 0.193397i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | 18.1672 | + | 15.8995i | 1.00774 | + | 0.881945i | ||||
\(326\) | 10.2102 | 0.565488 | ||||||||
\(327\) | −0.0615536 | + | 0.0615536i | −0.00340392 | + | 0.00340392i | ||||
\(328\) | −3.85140 | − | 3.85140i | −0.212658 | − | 0.212658i | ||||
\(329\) | −2.43020 | + | 1.28248i | −0.133981 | + | 0.0707053i | ||||
\(330\) | 0.364588 | + | 10.9660i | 0.0200699 | + | 0.603658i | ||||
\(331\) | 10.1759 | 0.559317 | 0.279658 | − | 0.960100i | \(-0.409779\pi\) | ||||
0.279658 | + | 0.960100i | \(0.409779\pi\) | |||||||
\(332\) | −9.29809 | + | 9.29809i | −0.510299 | + | 0.510299i | ||||
\(333\) | 4.74632 | − | 4.74632i | 0.260097 | − | 0.260097i | ||||
\(334\) | −9.52387 | −0.521123 | ||||||||
\(335\) | −7.05545 | − | 6.60140i | −0.385481 | − | 0.360673i | ||||
\(336\) | −1.23483 | − | 2.33991i | −0.0673657 | − | 0.127653i | ||||
\(337\) | 16.8137 | + | 16.8137i | 0.915901 | + | 0.915901i | 0.996728 | − | 0.0808276i | \(-0.0257563\pi\) |
−0.0808276 | + | 0.996728i | \(0.525756\pi\) | |||||||
\(338\) | 7.29289 | − | 7.29289i | 0.396681 | − | 0.396681i | ||||
\(339\) | 2.87437 | 0.156114 | ||||||||
\(340\) | 6.34162 | + | 5.93351i | 0.343923 | + | 0.321790i | ||||
\(341\) | − | 34.6200i | − | 1.87478i | ||||||
\(342\) | −0.894921 | + | 0.894921i | −0.0483918 | + | 0.0483918i | ||||
\(343\) | 11.5204 | + | 14.5011i | 0.622042 | + | 0.782984i | ||||
\(344\) | 10.7292i | 0.578478i | ||||||||
\(345\) | 3.33579 | − | 0.110906i | 0.179593 | − | 0.00597095i | ||||
\(346\) | 20.0260i | 1.07661i | ||||||||
\(347\) | −7.83919 | − | 7.83919i | −0.420830 | − | 0.420830i | 0.464659 | − | 0.885489i | \(-0.346177\pi\) |
−0.885489 | + | 0.464659i | \(0.846177\pi\) | |||||||
\(348\) | 3.37069 | + | 3.37069i | 0.180688 | + | 0.180688i | ||||
\(349\) | 5.10838 | 0.273445 | 0.136723 | − | 0.990609i | \(-0.456343\pi\) | ||||
0.136723 | + | 0.990609i | \(0.456343\pi\) | |||||||
\(350\) | −6.93763 | − | 11.2636i | −0.370832 | − | 0.602066i | ||||
\(351\) | −4.82843 | −0.257722 | ||||||||
\(352\) | 3.46967 | + | 3.46967i | 0.184934 | + | 0.184934i | ||||
\(353\) | −12.0821 | − | 12.0821i | −0.643066 | − | 0.643066i | 0.308242 | − | 0.951308i | \(-0.400259\pi\) |
−0.951308 | + | 0.308242i | \(0.900259\pi\) | |||||||
\(354\) | 1.39735i | 0.0742681i | ||||||||
\(355\) | 29.1274 | − | 0.968403i | 1.54592 | − | 0.0513975i | ||||
\(356\) | 15.3596i | 0.814060i | ||||||||
\(357\) | −9.81739 | − | 3.03490i | −0.519591 | − | 0.160624i | ||||
\(358\) | 2.32018 | − | 2.32018i | 0.122625 | − | 0.122625i | ||||
\(359\) | 3.90596i | 0.206149i | 0.994674 | + | 0.103074i | \(0.0328680\pi\) | ||||
−0.994674 | + | 0.103074i | \(0.967132\pi\) | |||||||
\(360\) | −1.63280 | − | 1.52773i | −0.0860564 | − | 0.0805182i | ||||
\(361\) | −17.3982 | −0.915696 | ||||||||
\(362\) | 13.7132 | − | 13.7132i | 0.720749 | − | 0.720749i | ||||
\(363\) | 9.24695 | + | 9.24695i | 0.485339 | + | 0.485339i | ||||
\(364\) | −11.2981 | + | 5.96230i | −0.592181 | + | 0.312510i | ||||
\(365\) | 11.6482 | + | 10.8986i | 0.609696 | + | 0.570459i | ||||
\(366\) | −2.29721 | −0.120077 | ||||||||
\(367\) | 3.98072 | − | 3.98072i | 0.207792 | − | 0.207792i | −0.595536 | − | 0.803328i | \(-0.703060\pi\) |
0.803328 | + | 0.595536i | \(0.203060\pi\) | |||||||
\(368\) | 1.05545 | − | 1.05545i | 0.0550193 | − | 0.0550193i | ||||
\(369\) | 5.44670 | 0.283544 | ||||||||
\(370\) | −0.498736 | − | 15.0009i | −0.0259281 | − | 0.779859i | ||||
\(371\) | 4.18807 | − | 2.21016i | 0.217434 | − | 0.114746i | ||||
\(372\) | 4.98896 | + | 4.98896i | 0.258665 | + | 0.258665i | ||||
\(373\) | −8.95648 | + | 8.95648i | −0.463749 | + | 0.463749i | −0.899882 | − | 0.436133i | \(-0.856348\pi\) |
0.436133 | + | 0.899882i | \(0.356348\pi\) | |||||||
\(374\) | 19.0576 | 0.985446 | ||||||||
\(375\) | −8.65336 | − | 7.07950i | −0.446858 | − | 0.365584i | ||||
\(376\) | 1.03858i | 0.0535609i | ||||||||
\(377\) | 16.2751 | − | 16.2751i | 0.838212 | − | 0.838212i | ||||
\(378\) | 2.52773 | + | 0.781409i | 0.130012 | + | 0.0401913i | ||||
\(379\) | 14.0190i | 0.720109i | 0.932931 | + | 0.360055i | \(0.117242\pi\) | ||||
−0.932931 | + | 0.360055i | \(0.882758\pi\) | |||||||
\(380\) | 0.0940371 | + | 2.82843i | 0.00482400 | + | 0.145095i | ||||
\(381\) | − | 15.8055i | − | 0.809738i | ||||||
\(382\) | 11.9114 | + | 11.9114i | 0.609441 | + | 0.609441i | ||||
\(383\) | −7.00951 | − | 7.00951i | −0.358169 | − | 0.358169i | 0.504968 | − | 0.863138i | \(-0.331504\pi\) |
−0.863138 | + | 0.504968i | \(0.831504\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −28.0039 | − | 7.64734i | −1.42721 | − | 0.389745i | ||||
\(386\) | 6.80760 | 0.346498 | ||||||||
\(387\) | −7.58667 | − | 7.58667i | −0.385652 | − | 0.385652i | ||||
\(388\) | 8.42614 | + | 8.42614i | 0.427773 | + | 0.427773i | ||||
\(389\) | − | 18.6560i | − | 0.945895i | −0.881091 | − | 0.472948i | \(-0.843190\pi\) | ||
0.881091 | − | 0.472948i | \(-0.156810\pi\) | |||||||
\(390\) | −7.37652 | + | 7.88388i | −0.373524 | + | 0.399216i | ||||
\(391\) | − | 5.79722i | − | 0.293178i | ||||||
\(392\) | 6.87957 | − | 1.29289i | 0.347471 | − | 0.0653010i | ||||
\(393\) | 9.07689 | − | 9.07689i | 0.457869 | − | 0.457869i | ||||
\(394\) | − | 18.4320i | − | 0.928589i | ||||||
\(395\) | 1.10014 | + | 33.0897i | 0.0553539 | + | 1.66492i | ||||
\(396\) | −4.90685 | −0.246578 | ||||||||
\(397\) | −19.3683 | + | 19.3683i | −0.972066 | + | 0.972066i | −0.999620 | − | 0.0275544i | \(-0.991228\pi\) |
0.0275544 | + | 0.999620i | \(0.491228\pi\) | |||||||
\(398\) | 8.30913 | + | 8.30913i | 0.416499 | + | 0.416499i | ||||
\(399\) | −1.56282 | − | 2.96142i | −0.0782387 | − | 0.148256i | ||||
\(400\) | −4.98896 | + | 0.332104i | −0.249448 | + | 0.0166052i | ||||
\(401\) | −27.9099 | −1.39375 | −0.696877 | − | 0.717191i | \(-0.745428\pi\) | ||||
−0.696877 | + | 0.717191i | \(0.745428\pi\) | |||||||
\(402\) | 3.05545 | − | 3.05545i | 0.152392 | − | 0.152392i | ||||
\(403\) | 24.0888 | − | 24.0888i | 1.19995 | − | 1.19995i | ||||
\(404\) | −18.1504 | −0.903015 | ||||||||
\(405\) | 2.23483 | − | 0.0743018i | 0.111050 | − | 0.00369209i | ||||
\(406\) | −11.1541 | + | 5.88629i | −0.553567 | + | 0.292132i | ||||
\(407\) | −23.2895 | − | 23.2895i | −1.15442 | − | 1.15442i | ||||
\(408\) | −2.74632 | + | 2.74632i | −0.135963 | + | 0.135963i | ||||
\(409\) | 18.3211 | 0.905918 | 0.452959 | − | 0.891531i | \(-0.350368\pi\) | ||||
0.452959 | + | 0.891531i | \(0.350368\pi\) | |||||||
\(410\) | 8.32106 | − | 8.89339i | 0.410948 | − | 0.439213i | ||||
\(411\) | − | 5.12563i | − | 0.252829i | ||||||
\(412\) | 8.36459 | − | 8.36459i | 0.412094 | − | 0.412094i | ||||
\(413\) | −3.53211 | − | 1.09190i | −0.173804 | − | 0.0537288i | ||||
\(414\) | 1.49264i | 0.0733590i | ||||||||
\(415\) | −21.4706 | − | 20.0888i | −1.05395 | − | 0.986122i | ||||
\(416\) | 4.82843i | 0.236733i | ||||||||
\(417\) | −2.76193 | − | 2.76193i | −0.135252 | − | 0.135252i | ||||
\(418\) | 4.39124 | + | 4.39124i | 0.214783 | + | 0.214783i | ||||
\(419\) | 5.49605 | 0.268500 | 0.134250 | − | 0.990948i | \(-0.457138\pi\) | ||||
0.134250 | + | 0.990948i | \(0.457138\pi\) | |||||||
\(420\) | 5.13756 | − | 2.93351i | 0.250687 | − | 0.143140i | ||||
\(421\) | 24.5863 | 1.19826 | 0.599132 | − | 0.800651i | \(-0.295513\pi\) | ||||
0.599132 | + | 0.800651i | \(0.295513\pi\) | |||||||
\(422\) | −11.7028 | − | 11.7028i | −0.569683 | − | 0.569683i | ||||
\(423\) | −0.734390 | − | 0.734390i | −0.0357073 | − | 0.0357073i | ||||
\(424\) | − | 1.78984i | − | 0.0869224i | ||||||
\(425\) | −12.7892 | + | 14.6133i | −0.620367 | + | 0.708851i | ||||
\(426\) | 13.0334i | 0.631469i | ||||||||
\(427\) | 1.79506 | − | 5.80671i | 0.0868689 | − | 0.281006i | ||||
\(428\) | −3.77297 | + | 3.77297i | −0.182374 | + | 0.182374i | ||||
\(429\) | 23.6924i | 1.14388i | ||||||||
\(430\) | −23.9779 | + | 0.797197i | −1.15632 | + | 0.0384443i | ||||
\(431\) | 22.8133 | 1.09888 | 0.549440 | − | 0.835533i | \(-0.314841\pi\) | ||||
0.549440 | + | 0.835533i | \(0.314841\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −17.1216 | − | 17.1216i | −0.822811 | − | 0.822811i | 0.163700 | − | 0.986510i | \(-0.447657\pi\) |
−0.986510 | + | 0.163700i | \(0.947657\pi\) | |||||||
\(434\) | −16.5091 | + | 8.71231i | −0.792464 | + | 0.418204i | ||||
\(435\) | −7.28248 | + | 7.78337i | −0.349168 | + | 0.373184i | ||||
\(436\) | −0.0870500 | −0.00416894 | ||||||||
\(437\) | 1.33579 | − | 1.33579i | 0.0638996 | − | 0.0638996i | ||||
\(438\) | −5.04441 | + | 5.04441i | −0.241031 | + | 0.241031i | ||||
\(439\) | 35.8323 | 1.71018 | 0.855092 | − | 0.518476i | \(-0.173500\pi\) | ||||
0.855092 | + | 0.518476i | \(0.173500\pi\) | |||||||
\(440\) | −7.49632 | + | 8.01193i | −0.357373 | + | 0.381954i | ||||
\(441\) | −3.95037 | + | 5.77880i | −0.188113 | + | 0.275181i | ||||
\(442\) | 13.2604 | + | 13.2604i | 0.630733 | + | 0.630733i | ||||
\(443\) | 2.93109 | − | 2.93109i | 0.139260 | − | 0.139260i | −0.634040 | − | 0.773300i | \(-0.718605\pi\) |
0.773300 | + | 0.634040i | \(0.218605\pi\) | |||||||
\(444\) | 6.71231 | 0.318552 | ||||||||
\(445\) | −34.3262 | + | 1.14125i | −1.62722 | + | 0.0541004i | ||||
\(446\) | − | 11.6824i | − | 0.553175i | ||||||
\(447\) | 3.98896 | − | 3.98896i | 0.188671 | − | 0.188671i | ||||
\(448\) | 0.781409 | − | 2.52773i | 0.0369181 | − | 0.119424i | ||||
\(449\) | 1.70279i | 0.0803598i | 0.999192 | + | 0.0401799i | \(0.0127931\pi\) | ||||
−0.999192 | + | 0.0401799i | \(0.987207\pi\) | |||||||
\(450\) | 3.29289 | − | 3.76256i | 0.155228 | − | 0.177369i | ||||
\(451\) | − | 26.7261i | − | 1.25848i | ||||||
\(452\) | 2.03248 | + | 2.03248i | 0.0956000 | + | 0.0956000i | ||||
\(453\) | −8.32106 | − | 8.32106i | −0.390958 | − | 0.390958i | ||||
\(454\) | 8.36217 | 0.392456 | ||||||||
\(455\) | −14.1642 | − | 24.8063i | −0.664029 | − | 1.16294i | ||||
\(456\) | −1.26561 | −0.0592676 | ||||||||
\(457\) | −5.34315 | − | 5.34315i | −0.249942 | − | 0.249942i | 0.571005 | − | 0.820947i | \(-0.306554\pi\) |
−0.820947 | + | 0.571005i | \(0.806554\pi\) | |||||||
\(458\) | −6.58579 | − | 6.58579i | −0.307734 | − | 0.307734i | ||||
\(459\) | − | 3.88388i | − | 0.181284i | ||||||
\(460\) | 2.43718 | + | 2.28034i | 0.113634 | + | 0.106321i | ||||
\(461\) | − | 0.858751i | − | 0.0399960i | −0.999800 | − | 0.0199980i | \(-0.993634\pi\) | ||
0.999800 | − | 0.0199980i | \(-0.00636599\pi\) | |||||||
\(462\) | 3.83425 | − | 12.4032i | 0.178386 | − | 0.577048i | ||||
\(463\) | −20.3594 | + | 20.3594i | −0.946180 | + | 0.946180i | −0.998624 | − | 0.0524436i | \(-0.983299\pi\) |
0.0524436 | + | 0.998624i | \(0.483299\pi\) | |||||||
\(464\) | 4.76687i | 0.221297i | ||||||||
\(465\) | −10.7788 | + | 11.5202i | −0.499855 | + | 0.534235i | ||||
\(466\) | −22.7071 | −1.05189 | ||||||||
\(467\) | −8.77908 | + | 8.77908i | −0.406247 | + | 0.406247i | −0.880428 | − | 0.474181i | \(-0.842744\pi\) |
0.474181 | + | 0.880428i | \(0.342744\pi\) | |||||||
\(468\) | −3.41421 | − | 3.41421i | −0.157822 | − | 0.157822i | ||||
\(469\) | 5.33579 | + | 10.1109i | 0.246384 | + | 0.466878i | ||||
\(470\) | −2.32106 | + | 0.0771687i | −0.107063 | + | 0.00355953i | ||||
\(471\) | 19.3934 | 0.893600 | ||||||||
\(472\) | −0.988072 | + | 0.988072i | −0.0454797 | + | 0.0454797i | ||||
\(473\) | −37.2267 | + | 37.2267i | −1.71168 | + | 1.71168i | ||||
\(474\) | −14.8063 | −0.680078 | ||||||||
\(475\) | −6.31408 | + | 0.420314i | −0.289710 | + | 0.0192853i | ||||
\(476\) | −4.79594 | − | 9.08794i | −0.219822 | − | 0.416545i | ||||
\(477\) | 1.26561 | + | 1.26561i | 0.0579483 | + | 0.0579483i | ||||
\(478\) | −1.19213 | + | 1.19213i | −0.0545267 | + | 0.0545267i | ||||
\(479\) | 1.17157 | 0.0535305 | 0.0267653 | − | 0.999642i | \(-0.491479\pi\) | ||||
0.0267653 | + | 0.999642i | \(0.491479\pi\) | |||||||
\(480\) | −0.0743018 | − | 2.23483i | −0.00339140 | − | 0.102006i | ||||
\(481\) | − | 32.4099i | − | 1.47776i | ||||||
\(482\) | −2.55672 | + | 2.55672i | −0.116455 | + | 0.116455i | ||||
\(483\) | −3.77297 | − | 1.16636i | −0.171676 | − | 0.0530711i | ||||
\(484\) | 13.0772i | 0.594417i | ||||||||
\(485\) | −18.2049 | + | 19.4571i | −0.826644 | + | 0.883501i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 9.70737 | + | 9.70737i | 0.439883 | + | 0.439883i | 0.891972 | − | 0.452090i | \(-0.149321\pi\) |
−0.452090 | + | 0.891972i | \(0.649321\pi\) | |||||||
\(488\) | −1.62437 | − | 1.62437i | −0.0735318 | − | 0.0735318i | ||||
\(489\) | −10.2102 | −0.461719 | ||||||||
\(490\) | 3.40056 | + | 15.2786i | 0.153622 | + | 0.690218i | ||||
\(491\) | −16.9381 | −0.764405 | −0.382202 | − | 0.924079i | \(-0.624834\pi\) | ||||
−0.382202 | + | 0.924079i | \(0.624834\pi\) | |||||||
\(492\) | 3.85140 | + | 3.85140i | 0.173634 | + | 0.173634i | ||||
\(493\) | 13.0913 | + | 13.0913i | 0.589605 | + | 0.589605i | ||||
\(494\) | 6.11091i | 0.274943i | ||||||||
\(495\) | −0.364588 | − | 10.9660i | −0.0163870 | − | 0.492885i | ||||
\(496\) | 7.05545i | 0.316799i | ||||||||
\(497\) | −32.9448 | − | 10.1844i | −1.47778 | − | 0.456832i | ||||
\(498\) | 9.29809 | − | 9.29809i | 0.416658 | − | 0.416658i | ||||
\(499\) | 30.4117i | 1.36141i | 0.732556 | + | 0.680706i | \(0.238327\pi\) | ||||
−0.732556 | + | 0.680706i | \(0.761673\pi\) | |||||||
\(500\) | −1.11289 | − | 11.1248i | −0.0497698 | − | 0.497517i | ||||
\(501\) | 9.52387 | 0.425495 | ||||||||
\(502\) | 3.38630 | − | 3.38630i | 0.151138 | − | 0.151138i | ||||
\(503\) | 4.75825 | + | 4.75825i | 0.212160 | + | 0.212160i | 0.805184 | − | 0.593025i | \(-0.202066\pi\) |
−0.593025 | + | 0.805184i | \(0.702066\pi\) | |||||||
\(504\) | 1.23483 | + | 2.33991i | 0.0550038 | + | 0.104228i | ||||
\(505\) | −1.34861 | − | 40.5631i | −0.0600122 | − | 1.80503i | ||||
\(506\) | 7.32414 | 0.325598 | ||||||||
\(507\) | −7.29289 | + | 7.29289i | −0.323889 | + | 0.323889i | ||||
\(508\) | 11.1761 | − | 11.1761i | 0.495861 | − | 0.495861i | ||||
\(509\) | 40.3501 | 1.78849 | 0.894243 | − | 0.447581i | \(-0.147714\pi\) | ||||
0.894243 | + | 0.447581i | \(0.147714\pi\) | |||||||
\(510\) | −6.34162 | − | 5.93351i | −0.280812 | − | 0.262740i | ||||
\(511\) | −8.80915 | − | 16.6926i | −0.389694 | − | 0.738439i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0.894921 | − | 0.894921i | 0.0395117 | − | 0.0395117i | ||||
\(514\) | 29.4316 | 1.29817 | ||||||||
\(515\) | 19.3150 | + | 18.0720i | 0.851119 | + | 0.796345i | ||||
\(516\) | − | 10.7292i | − | 0.472326i | ||||||
\(517\) | −3.60354 | + | 3.60354i | −0.158484 | + | 0.158484i | ||||
\(518\) | −5.24505 | + | 16.9669i | −0.230454 | + | 0.745482i | ||||
\(519\) | − | 20.0260i | − | 0.879045i | ||||||
\(520\) | −10.7907 | + | 0.358761i | −0.473205 | + | 0.0157327i | ||||
\(521\) | − | 8.96879i | − | 0.392930i | −0.980511 | − | 0.196465i | \(-0.937054\pi\) | ||
0.980511 | − | 0.196465i | \(-0.0629462\pi\) | |||||||
\(522\) | −3.37069 | − | 3.37069i | −0.147531 | − | 0.147531i | ||||
\(523\) | 8.40290 | + | 8.40290i | 0.367433 | + | 0.367433i | 0.866540 | − | 0.499107i | \(-0.166339\pi\) |
−0.499107 | + | 0.866540i | \(0.666339\pi\) | |||||||
\(524\) | 12.8367 | 0.560772 | ||||||||
\(525\) | 6.93763 | + | 11.2636i | 0.302783 | + | 0.491585i | ||||
\(526\) | −9.35965 | −0.408100 | ||||||||
\(527\) | 19.3765 | + | 19.3765i | 0.844054 | + | 0.844054i | ||||
\(528\) | −3.46967 | − | 3.46967i | −0.150998 | − | 0.150998i | ||||
\(529\) | 20.7720i | 0.903132i | ||||||||
\(530\) | 4.00000 | − | 0.132989i | 0.173749 | − | 0.00577665i | ||||
\(531\) | − | 1.39735i | − | 0.0606396i | ||||||
\(532\) | 0.988958 | − | 3.19912i | 0.0428768 | − | 0.138699i | ||||
\(533\) | 18.5962 | − | 18.5962i | 0.805490 | − | 0.805490i | ||||
\(534\) | − | 15.3596i | − | 0.664677i | ||||||
\(535\) | −8.71231 | − | 8.15163i | −0.376666 | − | 0.352426i | ||||
\(536\) | 4.32106 | 0.186641 | ||||||||
\(537\) | −2.32018 | + | 2.32018i | −0.100123 | + | 0.100123i | ||||
\(538\) | 9.27665 | + | 9.27665i | 0.399945 | + | 0.399945i | ||||
\(539\) | 28.3557 | + | 19.3839i | 1.22137 | + | 0.834923i | ||||
\(540\) | 1.63280 | + | 1.52773i | 0.0702647 | + | 0.0657429i | ||||
\(541\) | 27.1611 | 1.16775 | 0.583874 | − | 0.811844i | \(-0.301536\pi\) | ||||
0.583874 | + | 0.811844i | \(0.301536\pi\) | |||||||
\(542\) | 12.7870 | − | 12.7870i | 0.549250 | − | 0.549250i | ||||
\(543\) | −13.7132 | + | 13.7132i | −0.588489 | + | 0.588489i | ||||
\(544\) | −3.88388 | −0.166520 | ||||||||
\(545\) | −0.00646797 | − | 0.194542i | −0.000277057 | − | 0.00833327i | ||||
\(546\) | 11.2981 | − | 5.96230i | 0.483514 | − | 0.255163i | ||||
\(547\) | −16.8471 | − | 16.8471i | −0.720329 | − | 0.720329i | 0.248343 | − | 0.968672i | \(-0.420114\pi\) |
−0.968672 | + | 0.248343i | \(0.920114\pi\) | |||||||
\(548\) | 3.62437 | − | 3.62437i | 0.154825 | − | 0.154825i | ||||
\(549\) | 2.29721 | 0.0980424 | ||||||||
\(550\) | −18.4623 | − | 16.1577i | −0.787236 | − | 0.688968i | ||||
\(551\) | 6.03300i | 0.257015i | ||||||||
\(552\) | −1.05545 | + | 1.05545i | −0.0449231 | + | 0.0449231i | ||||
\(553\) | 11.5698 | − | 37.4264i | 0.491998 | − | 1.59153i | ||||
\(554\) | − | 3.72704i | − | 0.158347i | ||||||
\(555\) | 0.498736 | + | 15.0009i | 0.0211702 | + | 0.636752i | ||||
\(556\) | − | 3.90596i | − | 0.165650i | ||||||
\(557\) | −0.0529257 | − | 0.0529257i | −0.00224253 | − | 0.00224253i | 0.705985 | − | 0.708227i | \(-0.250505\pi\) |
−0.708227 | + | 0.705985i | \(0.750505\pi\) | |||||||
\(558\) | −4.98896 | − | 4.98896i | −0.211199 | − | 0.211199i | ||||
\(559\) | −51.8050 | −2.19112 | ||||||||
\(560\) | 5.70711 | + | 1.55850i | 0.241169 | + | 0.0658588i | ||||
\(561\) | −19.0576 | −0.804613 | ||||||||
\(562\) | −14.4645 | − | 14.4645i | −0.610146 | − | 0.610146i | ||||
\(563\) | 7.84316 | + | 7.84316i | 0.330550 | + | 0.330550i | 0.852795 | − | 0.522246i | \(-0.174906\pi\) |
−0.522246 | + | 0.852795i | \(0.674906\pi\) | |||||||
\(564\) | − | 1.03858i | − | 0.0437323i | ||||||
\(565\) | −4.39124 | + | 4.69328i | −0.184741 | + | 0.197448i | ||||
\(566\) | 15.2383i | 0.640514i | ||||||||
\(567\) | −2.52773 | − | 0.781409i | −0.106155 | − | 0.0328161i | ||||
\(568\) | −9.21598 | + | 9.21598i | −0.386694 | + | 0.386694i | ||||
\(569\) | 6.12311i | 0.256694i | 0.991729 | + | 0.128347i | \(0.0409671\pi\) | ||||
−0.991729 | + | 0.128347i | \(0.959033\pi\) | |||||||
\(570\) | −0.0940371 | − | 2.82843i | −0.00393878 | − | 0.118470i | ||||
\(571\) | 30.4896 | 1.27595 | 0.637974 | − | 0.770058i | \(-0.279773\pi\) | ||||
0.637974 | + | 0.770058i | \(0.279773\pi\) | |||||||
\(572\) | −16.7530 | + | 16.7530i | −0.700479 | + | 0.700479i | ||||
\(573\) | −11.9114 | − | 11.9114i | −0.497607 | − | 0.497607i | ||||
\(574\) | −12.7448 | + | 6.72576i | −0.531957 | + | 0.280728i | ||||
\(575\) | −4.91509 | + | 5.61613i | −0.204973 | + | 0.234209i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 11.5444 | − | 11.5444i | 0.480600 | − | 0.480600i | −0.424723 | − | 0.905323i | \(-0.639629\pi\) |
0.905323 | + | 0.424723i | \(0.139629\pi\) | |||||||
\(578\) | 1.35445 | − | 1.35445i | 0.0563376 | − | 0.0563376i | ||||
\(579\) | −6.80760 | −0.282914 | ||||||||
\(580\) | −10.6532 | + | 0.354187i | −0.442349 | + | 0.0147068i | ||||
\(581\) | 16.2374 | + | 30.7686i | 0.673642 | + | 1.27650i | ||||
\(582\) | −8.42614 | − | 8.42614i | −0.349275 | − | 0.349275i | ||||
\(583\) | 6.21016 | − | 6.21016i | 0.257198 | − | 0.257198i | ||||
\(584\) | −7.13387 | −0.295202 | ||||||||
\(585\) | 7.37652 | − | 7.88388i | 0.304981 | − | 0.325958i | ||||
\(586\) | − | 4.46841i | − | 0.184588i | ||||||
\(587\) | 7.24478 | − | 7.24478i | 0.299024 | − | 0.299024i | −0.541607 | − | 0.840632i | \(-0.682184\pi\) |
0.840632 | + | 0.541607i | \(0.182184\pi\) | |||||||
\(588\) | −6.87957 | + | 1.29289i | −0.283709 | + | 0.0533180i | ||||
\(589\) | 8.92945i | 0.367932i | ||||||||
\(590\) | −2.28159 | − | 2.13476i | −0.0939317 | − | 0.0878867i | ||||
\(591\) | 18.4320i | 0.758190i | ||||||||
\(592\) | 4.74632 | + | 4.74632i | 0.195072 | + | 0.195072i | ||||
\(593\) | 6.67652 | + | 6.67652i | 0.274172 | + | 0.274172i | 0.830777 | − | 0.556605i | \(-0.187896\pi\) |
−0.556605 | + | 0.830777i | \(0.687896\pi\) | |||||||
\(594\) | 4.90685 | 0.201330 | ||||||||
\(595\) | 19.9537 | − | 11.3934i | 0.818021 | − | 0.467083i | ||||
\(596\) | 5.64124 | 0.231074 | ||||||||
\(597\) | −8.30913 | − | 8.30913i | −0.340070 | − | 0.340070i | ||||
\(598\) | 5.09618 | + | 5.09618i | 0.208398 | + | 0.208398i | ||||
\(599\) | − | 2.62526i | − | 0.107265i | −0.998561 | − | 0.0536325i | \(-0.982920\pi\) | ||
0.998561 | − | 0.0536325i | \(-0.0170800\pi\) | |||||||
\(600\) | 4.98896 | − | 0.332104i | 0.203673 | − | 0.0135581i | ||||
\(601\) | 11.7003i | 0.477265i | 0.971110 | + | 0.238632i | \(0.0766991\pi\) | ||||
−0.971110 | + | 0.238632i | \(0.923301\pi\) | |||||||
\(602\) | 27.1204 | + | 8.38387i | 1.10535 | + | 0.341701i | ||||
\(603\) | −3.05545 | + | 3.05545i | −0.124428 | + | 0.124428i | ||||
\(604\) | − | 11.7678i | − | 0.478823i | ||||||
\(605\) | −29.2253 | + | 0.971657i | −1.18818 | + | 0.0395035i | ||||
\(606\) | 18.1504 | 0.737309 | ||||||||
\(607\) | −23.2749 | + | 23.2749i | −0.944697 | + | 0.944697i | −0.998549 | − | 0.0538519i | \(-0.982850\pi\) |
0.0538519 | + | 0.998549i | \(0.482850\pi\) | |||||||
\(608\) | −0.894921 | − | 0.894921i | −0.0362939 | − | 0.0362939i | ||||
\(609\) | 11.1541 | − | 5.88629i | 0.451985 | − | 0.238525i | ||||
\(610\) | 3.50950 | − | 3.75089i | 0.142096 | − | 0.151869i | ||||
\(611\) | −5.01473 | −0.202874 | ||||||||
\(612\) | 2.74632 | − | 2.74632i | 0.111013 | − | 0.111013i | ||||
\(613\) | 18.1372 | − | 18.1372i | 0.732554 | − | 0.732554i | −0.238571 | − | 0.971125i | \(-0.576679\pi\) |
0.971125 | + | 0.238571i | \(0.0766789\pi\) | |||||||
\(614\) | 29.4172 | 1.18718 | ||||||||
\(615\) | −8.32106 | + | 8.89339i | −0.335538 | + | 0.358616i | ||||
\(616\) | 11.4816 | − | 6.05914i | 0.462607 | − | 0.244130i | ||||
\(617\) | 1.59063 | + | 1.59063i | 0.0640365 | + | 0.0640365i | 0.738400 | − | 0.674363i | \(-0.235582\pi\) |
−0.674363 | + | 0.738400i | \(0.735582\pi\) | |||||||
\(618\) | −8.36459 | + | 8.36459i | −0.336473 | + | 0.336473i | ||||
\(619\) | −39.2232 | −1.57651 | −0.788257 | − | 0.615346i | \(-0.789016\pi\) | ||||
−0.788257 | + | 0.615346i | \(0.789016\pi\) | |||||||
\(620\) | −15.7678 | + | 0.524233i | −0.633248 | + | 0.0210537i | ||||
\(621\) | − | 1.49264i | − | 0.0598974i | ||||||
\(622\) | −8.11091 | + | 8.11091i | −0.325218 | + | 0.325218i | ||||
\(623\) | 38.8250 | + | 12.0022i | 1.55549 | + | 0.480856i | ||||
\(624\) | − | 4.82843i | − | 0.193292i | ||||||
\(625\) | 24.7794 | − | 3.31371i | 0.991177 | − | 0.132548i | ||||
\(626\) | 0.866125i | 0.0346173i | ||||||||
\(627\) | −4.39124 | − | 4.39124i | −0.175369 | − | 0.175369i | ||||
\(628\) | 13.7132 | + | 13.7132i | 0.547216 | + | 0.547216i | ||||
\(629\) | 26.0698 | 1.03947 | ||||||||
\(630\) | −5.13756 | + | 2.93351i | −0.204685 | + | 0.116874i | ||||
\(631\) | −1.69542 | −0.0674935 | −0.0337468 | − | 0.999430i | \(-0.510744\pi\) | ||||
−0.0337468 | + | 0.999430i | \(0.510744\pi\) | |||||||
\(632\) | −10.4697 | − | 10.4697i | −0.416461 | − | 0.416461i | ||||
\(633\) | 11.7028 | + | 11.7028i | 0.465144 | + | 0.465144i | ||||
\(634\) | − | 9.95583i | − | 0.395397i | ||||||
\(635\) | 25.8072 | + | 24.1464i | 1.02413 | + | 0.958221i | ||||
\(636\) | 1.78984i | 0.0709719i | ||||||||
\(637\) | 6.24264 | + | 33.2175i | 0.247342 | + | 1.31612i | ||||
\(638\) | −16.5395 | + | 16.5395i | −0.654804 | + | 0.654804i | ||||
\(639\) | − | 13.0334i | − | 0.515592i | ||||||
\(640\) | 1.52773 | − | 1.63280i | 0.0603887 | − | 0.0645423i | ||||
\(641\) | 23.0043 | 0.908615 | 0.454308 | − | 0.890845i | \(-0.349887\pi\) | ||||
0.454308 | + | 0.890845i | \(0.349887\pi\) | |||||||
\(642\) | 3.77297 | − | 3.77297i | 0.148907 | − | 0.148907i | ||||
\(643\) | 13.9948 | + | 13.9948i | 0.551900 | + | 0.551900i | 0.926989 | − | 0.375089i | \(-0.122388\pi\) |
−0.375089 | + | 0.926989i | \(0.622388\pi\) | |||||||
\(644\) | −1.84316 | − | 3.49264i | −0.0726305 | − | 0.137629i | ||||
\(645\) | 23.9779 | − | 0.797197i | 0.944130 | − | 0.0313896i | ||||
\(646\) | −4.91548 | −0.193397 | ||||||||
\(647\) | −5.22955 | + | 5.22955i | −0.205595 | + | 0.205595i | −0.802392 | − | 0.596797i | \(-0.796440\pi\) |
0.596797 | + | 0.802392i | \(0.296440\pi\) | |||||||
\(648\) | −0.707107 | + | 0.707107i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | −6.85656 | −0.269144 | ||||||||
\(650\) | −1.60354 | − | 24.0888i | −0.0628961 | − | 0.944841i | ||||
\(651\) | 16.5091 | − | 8.71231i | 0.647044 | − | 0.341462i | ||||
\(652\) | −7.21967 | − | 7.21967i | −0.282744 | − | 0.282744i | ||||
\(653\) | 1.74516 | − | 1.74516i | 0.0682933 | − | 0.0682933i | −0.672135 | − | 0.740428i | \(-0.734623\pi\) |
0.740428 | + | 0.672135i | \(0.234623\pi\) | |||||||
\(654\) | 0.0870500 | 0.00340392 | ||||||||
\(655\) | 0.953787 | + | 28.6878i | 0.0372676 | + | 1.12093i | ||||
\(656\) | 5.44670i | 0.212658i | ||||||||
\(657\) | 5.04441 | − | 5.04441i | 0.196801 | − | 0.196801i | ||||
\(658\) | 2.62526 | + | 0.811559i | 0.102343 | + | 0.0316379i | ||||
\(659\) | − | 21.4234i | − | 0.834536i | −0.908784 | − | 0.417268i | \(-0.862988\pi\) | ||
0.908784 | − | 0.417268i | \(-0.137012\pi\) | |||||||
\(660\) | 7.49632 | − | 8.01193i | 0.291794 | − | 0.311864i | ||||
\(661\) | − | 15.6881i | − | 0.610196i | −0.952321 | − | 0.305098i | \(-0.901311\pi\) | ||
0.952321 | − | 0.305098i | \(-0.0986892\pi\) | |||||||
\(662\) | −7.19543 | − | 7.19543i | −0.279658 | − | 0.279658i | ||||
\(663\) | −13.2604 | − | 13.2604i | −0.514991 | − | 0.514991i | ||||
\(664\) | 13.1495 | 0.510299 | ||||||||
\(665\) | 7.22297 | + | 1.97246i | 0.280095 | + | 0.0764886i | ||||
\(666\) | −6.71231 | −0.260097 | ||||||||
\(667\) | 5.03121 | + | 5.03121i | 0.194809 | + | 0.194809i | ||||
\(668\) | 6.73439 | + | 6.73439i | 0.260561 | + | 0.260561i | ||||
\(669\) | 11.6824i | 0.451666i | ||||||||
\(670\) | 0.321063 | + | 9.65685i | 0.0124037 | + | 0.373077i | ||||
\(671\) | − | 11.2720i | − | 0.435153i | ||||||
\(672\) | −0.781409 | + | 2.52773i | −0.0301435 | + | 0.0975092i | ||||
\(673\) | 26.0502 | − | 26.0502i | 1.00416 | − | 1.00416i | 0.00417159 | − | 0.999991i | \(-0.498672\pi\) |
0.999991 | − | 0.00417159i | \(-0.00132786\pi\) | |||||||
\(674\) | − | 23.7782i | − | 0.915901i | ||||||
\(675\) | −3.29289 | + | 3.76256i | −0.126744 | + | 0.144821i | ||||
\(676\) | −10.3137 | −0.396681 | ||||||||
\(677\) | 3.99149 | − | 3.99149i | 0.153405 | − | 0.153405i | −0.626232 | − | 0.779637i | \(-0.715404\pi\) |
0.779637 | + | 0.626232i | \(0.215404\pi\) | |||||||
\(678\) | −2.03248 | − | 2.03248i | −0.0780571 | − | 0.0780571i | ||||
\(679\) | 27.8832 | − | 14.7147i | 1.07006 | − | 0.564699i | ||||
\(680\) | −0.288579 | − | 8.67982i | −0.0110665 | − | 0.332856i | ||||
\(681\) | −8.36217 | −0.320439 | ||||||||
\(682\) | −24.4801 | + | 24.4801i | −0.937390 | + | 0.937390i | ||||
\(683\) | −28.2530 | + | 28.2530i | −1.08107 | + | 1.08107i | −0.0846629 | + | 0.996410i | \(0.526981\pi\) |
−0.996410 | + | 0.0846629i | \(0.973019\pi\) | |||||||
\(684\) | 1.26561 | 0.0483918 | ||||||||
\(685\) | 8.36916 | + | 7.83057i | 0.319769 | + | 0.299191i | ||||
\(686\) | 2.10767 | − | 18.3999i | 0.0804713 | − | 0.702513i | ||||
\(687\) | 6.58579 | + | 6.58579i | 0.251263 | + | 0.251263i | ||||
\(688\) | 7.58667 | − | 7.58667i | 0.289239 | − | 0.289239i | ||||
\(689\) | 8.64213 | 0.329239 | ||||||||
\(690\) | −2.43718 | − | 2.28034i | −0.0927820 | − | 0.0868110i | ||||
\(691\) | − | 2.45366i | − | 0.0933418i | −0.998910 | − | 0.0466709i | \(-0.985139\pi\) | ||
0.998910 | − | 0.0466709i | \(-0.0148612\pi\) | |||||||
\(692\) | 14.1605 | − | 14.1605i | 0.538303 | − | 0.538303i | ||||
\(693\) | −3.83425 | + | 12.4032i | −0.145651 | + | 0.471158i | ||||
\(694\) | 11.0863i | 0.420830i | ||||||||
\(695\) | 8.72918 | − | 0.290220i | 0.331116 | − | 0.0110087i | ||||
\(696\) | − | 4.76687i | − | 0.180688i | ||||||
\(697\) | 14.9584 | + | 14.9584i | 0.566588 | + | 0.566588i | ||||
\(698\) | −3.61217 | − | 3.61217i | −0.136723 | − | 0.136723i | ||||
\(699\) | 22.7071 | 0.858861 | ||||||||
\(700\) | −3.05895 | + | 12.8702i | −0.115617 | + | 0.486449i | ||||
\(701\) | −6.34833 | −0.239773 | −0.119887 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119887 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(702\) | 3.41421 | + | 3.41421i | 0.128861 | + | 0.128861i | ||||
\(703\) | 6.00699 | + | 6.00699i | 0.226558 | + | 0.226558i | ||||
\(704\) | − | 4.90685i | − | 0.184934i | ||||||
\(705\) | 2.32106 | − | 0.0771687i | 0.0874163 | − | 0.00290634i | ||||
\(706\) | 17.0867i | 0.643066i | ||||||||
\(707\) | −14.1829 | + | 45.8792i | −0.533401 | + | 1.72546i | ||||
\(708\) | 0.988072 | − | 0.988072i | 0.0371340 | − | 0.0371340i | ||||
\(709\) | 20.3645i | 0.764805i | 0.923996 | + | 0.382402i | \(0.124903\pi\) | ||||
−0.923996 | + | 0.382402i | \(0.875097\pi\) | |||||||
\(710\) | −21.2810 | − | 19.9114i | −0.798660 | − | 0.747262i | ||||
\(711\) | 14.8063 | 0.555281 | ||||||||
\(712\) | 10.8609 | − | 10.8609i | 0.407030 | − | 0.407030i | ||||
\(713\) | 7.44670 | + | 7.44670i | 0.278881 | + | 0.278881i | ||||
\(714\) | 4.79594 | + | 9.08794i | 0.179484 | + | 0.340107i | ||||
\(715\) | −38.6850 | − | 36.1954i | −1.44674 | − | 1.35363i | ||||
\(716\) | −3.28123 | −0.122625 | ||||||||
\(717\) | 1.19213 | − | 1.19213i | 0.0445209 | − | 0.0445209i | ||||
\(718\) | 2.76193 | − | 2.76193i | 0.103074 | − | 0.103074i | ||||
\(719\) | −25.9031 | −0.966021 | −0.483011 | − | 0.875614i | \(-0.660457\pi\) | ||||
−0.483011 | + | 0.875614i | \(0.660457\pi\) | |||||||
\(720\) | 0.0743018 | + | 2.23483i | 0.00276906 | + | 0.0832873i | ||||
\(721\) | −14.6072 | − | 27.6795i | −0.544002 | − | 1.03084i | ||||
\(722\) | 12.3024 | + | 12.3024i | 0.457848 | + | 0.457848i | ||||
\(723\) | 2.55672 | − | 2.55672i | 0.0950853 | − | 0.0950853i | ||||
\(724\) | −19.3934 | −0.720749 | ||||||||
\(725\) | −1.58310 | − | 23.7817i | −0.0587948 | − | 0.883231i | ||||
\(726\) | − | 13.0772i | − | 0.485339i | ||||||
\(727\) | 36.3373 | − | 36.3373i | 1.34768 | − | 1.34768i | 0.459495 | − | 0.888180i | \(-0.348030\pi\) |
0.888180 | − | 0.459495i | \(-0.151970\pi\) | |||||||
\(728\) | 12.2049 | + | 3.77297i | 0.452345 | + | 0.139836i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −0.530060 | − | 15.9430i | −0.0196184 | − | 0.590078i | ||||
\(731\) | − | 41.6708i | − | 1.54125i | ||||||
\(732\) | 1.62437 | + | 1.62437i | 0.0600385 | + | 0.0600385i | ||||
\(733\) | −18.3535 | − | 18.3535i | −0.677904 | − | 0.677904i | 0.281622 | − | 0.959525i | \(-0.409128\pi\) |
−0.959525 | + | 0.281622i | \(0.909128\pi\) | |||||||
\(734\) | −5.62959 | −0.207792 | ||||||||
\(735\) | −3.40056 | − | 15.2786i | −0.125432 | − | 0.563560i | ||||
\(736\) | −1.49264 | −0.0550193 | ||||||||
\(737\) | 14.9926 | + | 14.9926i | 0.552261 | + | 0.552261i | ||||
\(738\) | −3.85140 | − | 3.85140i | −0.141772 | − | 0.141772i | ||||
\(739\) | 21.3934i | 0.786968i | 0.919331 | + | 0.393484i | \(0.128730\pi\) | ||||
−0.919331 | + | 0.393484i | \(0.871270\pi\) | |||||||
\(740\) | −10.2546 | + | 10.9599i | −0.376965 | + | 0.402894i | ||||
\(741\) | − | 6.11091i | − | 0.224490i | ||||||
\(742\) | −4.52423 | − | 1.39860i | −0.166090 | − | 0.0513442i | ||||
\(743\) | −29.9264 | + | 29.9264i | −1.09789 | + | 1.09789i | −0.103235 | + | 0.994657i | \(0.532919\pi\) |
−0.994657 | + | 0.103235i | \(0.967081\pi\) | |||||||
\(744\) | − | 7.05545i | − | 0.258665i | ||||||
\(745\) | 0.419154 | + | 12.6072i | 0.0153566 | + | 0.461893i | ||||
\(746\) | 12.6664 | 0.463749 | ||||||||
\(747\) | −9.29809 | + | 9.29809i | −0.340199 | + | 0.340199i | ||||
\(748\) | −13.4758 | − | 13.4758i | −0.492723 | − | 0.492723i | ||||
\(749\) | 6.58881 | + | 12.4853i | 0.240750 | + | 0.456202i | ||||
\(750\) | 1.11289 | + | 11.1248i | 0.0406369 | + | 0.406221i | ||||
\(751\) | −19.3081 | −0.704563 | −0.352281 | − | 0.935894i | \(-0.614594\pi\) | ||||
−0.352281 | + | 0.935894i | \(0.614594\pi\) | |||||||
\(752\) | 0.734390 | − | 0.734390i | 0.0267804 | − | 0.0267804i | ||||
\(753\) | −3.38630 | + | 3.38630i | −0.123404 | + | 0.123404i | ||||
\(754\) | −23.0165 | −0.838212 | ||||||||
\(755\) | 26.2990 | − | 0.874366i | 0.957118 | − | 0.0318214i | ||||
\(756\) | −1.23483 | − | 2.33991i | −0.0449104 | − | 0.0851018i | ||||
\(757\) | −30.9872 | − | 30.9872i | −1.12625 | − | 1.12625i | −0.990782 | − | 0.135465i | \(-0.956747\pi\) |
−0.135465 | − | 0.990782i | \(-0.543253\pi\) | |||||||
\(758\) | 9.91295 | − | 9.91295i | 0.360055 | − | 0.360055i | ||||
\(759\) | −7.32414 | −0.265849 | ||||||||
\(760\) | 1.93351 | − | 2.06649i | 0.0701356 | − | 0.0749596i | ||||
\(761\) | 47.3418i | 1.71614i | 0.513532 | + | 0.858070i | \(0.328337\pi\) | ||||
−0.513532 | + | 0.858070i | \(0.671663\pi\) | |||||||
\(762\) | −11.1761 | + | 11.1761i | −0.404869 | + | 0.404869i | ||||
\(763\) | −0.0680216 | + | 0.220039i | −0.00246255 | + | 0.00796593i | ||||
\(764\) | − | 16.8453i | − | 0.609441i | ||||||
\(765\) | 6.34162 | + | 5.93351i | 0.229282 | + | 0.214526i | ||||
\(766\) | 9.91295i | 0.358169i | ||||||||
\(767\) | −4.77083 | − | 4.77083i | −0.172265 | − | 0.172265i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −44.0520 | −1.58856 | −0.794278 | − | 0.607554i | \(-0.792151\pi\) | ||||
−0.794278 | + | 0.607554i | \(0.792151\pi\) | |||||||
\(770\) | 14.3943 | + | 25.2092i | 0.518733 | + | 0.908478i | ||||
\(771\) | −29.4316 | −1.05995 | ||||||||
\(772\) | −4.81370 | − | 4.81370i | −0.173249 | − | 0.173249i | ||||
\(773\) | −11.1336 | − | 11.1336i | −0.400448 | − | 0.400448i | 0.477943 | − | 0.878391i | \(-0.341383\pi\) |
−0.878391 | + | 0.477943i | \(0.841383\pi\) | |||||||
\(774\) | 10.7292i | 0.385652i | ||||||||
\(775\) | −2.34315 | − | 35.1994i | −0.0841683 | − | 1.26440i | ||||
\(776\) | − | 11.9164i | − | 0.427773i | ||||||
\(777\) | 5.24505 | − | 16.9669i | 0.188165 | − | 0.608683i | ||||
\(778\) | −13.1918 | + | 13.1918i | −0.472948 | + | 0.472948i | ||||
\(779\) | 6.89339i | 0.246981i | ||||||||
\(780\) | 10.7907 | − | 0.358761i | 0.386370 | − | 0.0128457i | ||||
\(781\) | −63.9528 | −2.28841 | ||||||||
\(782\) | −4.09925 | + | 4.09925i | −0.146589 | + | 0.146589i | ||||
\(783\) | 3.37069 | + | 3.37069i | 0.120459 | + | 0.120459i | ||||
\(784\) | −5.77880 | − | 3.95037i | −0.206386 | − | 0.141085i | ||||
\(785\) | −29.6278 | + | 31.6656i | −1.05746 | + | 1.13019i | ||||
\(786\) | −12.8367 | −0.457869 | ||||||||
\(787\) | −11.7098 | + | 11.7098i | −0.417409 | + | 0.417409i | −0.884310 | − | 0.466901i | \(-0.845370\pi\) |
0.466901 | + | 0.884310i | \(0.345370\pi\) | |||||||
\(788\) | −13.0334 | + | 13.0334i | −0.464295 | + | 0.464295i | ||||
\(789\) | 9.35965 | 0.333212 | ||||||||
\(790\) | 22.6200 | − | 24.1759i | 0.804785 | − | 0.860139i | ||||
\(791\) | 6.72576 | − | 3.54936i | 0.239141 | − | 0.126201i | ||||
\(792\) | 3.46967 | + | 3.46967i | 0.123289 | + | 0.123289i | ||||
\(793\) | 7.84316 | − | 7.84316i | 0.278519 | − | 0.278519i | ||||
\(794\) | 27.3909 | 0.972066 | ||||||||
\(795\) | −4.00000 | + | 0.132989i | −0.141865 | + | 0.00471662i | ||||
\(796\) | − | 11.7509i | − | 0.416499i | ||||||
\(797\) | −12.7255 | + | 12.7255i | −0.450760 | + | 0.450760i | −0.895607 | − | 0.444847i | \(-0.853258\pi\) |
0.444847 | + | 0.895607i | \(0.353258\pi\) | |||||||
\(798\) | −0.988958 | + | 3.19912i | −0.0350088 | + | 0.113247i | ||||
\(799\) | − | 4.03374i | − | 0.142703i | ||||||
\(800\) | 3.76256 | + | 3.29289i | 0.133027 | + | 0.116421i | ||||
\(801\) | 15.3596i | 0.542706i | ||||||||
\(802\) | 19.7353 | + | 19.7353i | 0.696877 | + | 0.696877i | ||||
\(803\) | −24.7522 | − | 24.7522i | −0.873485 | − | 0.873485i | ||||
\(804\) | −4.32106 | −0.152392 | ||||||||
\(805\) | 7.66851 | − | 4.37866i | 0.270279 | − | 0.154327i | ||||
\(806\) | −34.0667 | −1.19995 | ||||||||
\(807\) | −9.27665 | − | 9.27665i | −0.326554 | − | 0.326554i | ||||
\(808\) | 12.8343 | + | 12.8343i | 0.451507 | + | 0.451507i | ||||
\(809\) | − | 22.8744i | − | 0.804220i | −0.915591 | − | 0.402110i | \(-0.868277\pi\) | ||
0.915591 | − | 0.402110i | \(-0.131723\pi\) | |||||||
\(810\) | −1.63280 | − | 1.52773i | −0.0573709 | − | 0.0536788i | ||||
\(811\) | 0.722188i | 0.0253595i | 0.999920 | + | 0.0126797i | \(0.00403619\pi\) | ||||
−0.999920 | + | 0.0126797i | \(0.995964\pi\) | |||||||
\(812\) | 12.0494 | + | 3.72488i | 0.422849 | + | 0.130718i | ||||
\(813\) | −12.7870 | + | 12.7870i | −0.448461 | + | 0.448461i | ||||
\(814\) | 32.9363i | 1.15442i | ||||||||
\(815\) | 15.5983 | − | 16.6712i | 0.546386 | − | 0.583967i | ||||
\(816\) | 3.88388 | 0.135963 | ||||||||
\(817\) | 9.60177 | − | 9.60177i | 0.335923 | − | 0.335923i | ||||
\(818\) | −12.9549 | − | 12.9549i | −0.452959 | − | 0.452959i | ||||
\(819\) | −11.2981 | + | 5.96230i | −0.394787 | + | 0.208340i | ||||
\(820\) | −12.1725 | + | 0.404699i | −0.425081 | + | 0.0141327i | ||||
\(821\) | 21.2417 | 0.741341 | 0.370671 | − | 0.928764i | \(-0.379128\pi\) | ||||
0.370671 | + | 0.928764i | \(0.379128\pi\) | |||||||
\(822\) | −3.62437 | + | 3.62437i | −0.126414 | + | 0.126414i | ||||
\(823\) | 10.3066 | − | 10.3066i | 0.359266 | − | 0.359266i | −0.504276 | − | 0.863542i | \(-0.668241\pi\) |
0.863542 | + | 0.504276i | \(0.168241\pi\) | |||||||
\(824\) | −11.8293 | −0.412094 | ||||||||
\(825\) | 18.4623 | + | 16.1577i | 0.642775 | + | 0.562540i | ||||
\(826\) | 1.72549 | + | 3.26966i | 0.0600374 | + | 0.113766i | ||||
\(827\) | −26.1746 | − | 26.1746i | −0.910181 | − | 0.910181i | 0.0861054 | − | 0.996286i | \(-0.472558\pi\) |
−0.996286 | + | 0.0861054i | \(0.972558\pi\) | |||||||
\(828\) | 1.05545 | − | 1.05545i | 0.0366795 | − | 0.0366795i | ||||
\(829\) | 21.0061 | 0.729571 | 0.364786 | − | 0.931092i | \(-0.381142\pi\) | ||||
0.364786 | + | 0.931092i | \(0.381142\pi\) | |||||||
\(830\) | 0.977031 | + | 29.3869i | 0.0339132 | + | 1.02003i | ||||
\(831\) | 3.72704i | 0.129289i | ||||||||
\(832\) | 3.41421 | − | 3.41421i | 0.118367 | − | 0.118367i | ||||
\(833\) | −26.7194 | + | 5.02144i | −0.925773 | + | 0.173983i | ||||
\(834\) | 3.90596i | 0.135252i | ||||||||
\(835\) | −14.5499 | + | 15.5506i | −0.503519 | + | 0.538151i | ||||
\(836\) | − | 6.21016i | − | 0.214783i | ||||||
\(837\) | 4.98896 | + | 4.98896i | 0.172444 | + | 0.172444i | ||||
\(838\) | −3.88629 | − | 3.88629i | −0.134250 | − | 0.134250i | ||||
\(839\) | −50.2886 | −1.73615 | −0.868077 | − | 0.496430i | \(-0.834644\pi\) | ||||
−0.868077 | + | 0.496430i | \(0.834644\pi\) | |||||||
\(840\) | −5.70711 | − | 1.55850i | −0.196914 | − | 0.0537735i | ||||
\(841\) | 6.27692 | 0.216445 | ||||||||
\(842\) | −17.3851 | − | 17.3851i | −0.599132 | − | 0.599132i | ||||
\(843\) | 14.4645 | + | 14.4645i | 0.498182 | + | 0.498182i | ||||
\(844\) | 16.5502i | 0.569683i | ||||||||
\(845\) | −0.766327 | − | 23.0494i | −0.0263625 | − | 0.792924i | ||||
\(846\) | 1.03858i | 0.0357073i | ||||||||
\(847\) | 33.0555 | + | 10.2186i | 1.13580 | + | 0.351116i | ||||
\(848\) | −1.26561 | + | 1.26561i | −0.0434612 | + | 0.0434612i | ||||
\(849\) | − | 15.2383i | − | 0.522978i | ||||||
\(850\) | 19.3765 | − | 1.28985i | 0.664609 | − | 0.0442416i | ||||
\(851\) | 10.0190 | 0.343448 | ||||||||
\(852\) | 9.21598 | − | 9.21598i | 0.315734 | − | 0.315734i | ||||
\(853\) | 13.1647 | + | 13.1647i | 0.450751 | + | 0.450751i | 0.895604 | − | 0.444853i | \(-0.146744\pi\) |
−0.444853 | + | 0.895604i | \(0.646744\pi\) | |||||||
\(854\) | −5.37526 | + | 2.83667i | −0.183938 | + | 0.0970688i | ||||
\(855\) | 0.0940371 | + | 2.82843i | 0.00321600 | + | 0.0967302i | ||||
\(856\) | 5.33579 | 0.182374 | ||||||||
\(857\) | 19.5839 | − | 19.5839i | 0.668973 | − | 0.668973i | −0.288505 | − | 0.957478i | \(-0.593158\pi\) |
0.957478 | + | 0.288505i | \(0.0931583\pi\) | |||||||
\(858\) | 16.7530 | − | 16.7530i | 0.571939 | − | 0.571939i | ||||
\(859\) | −7.58185 | −0.258689 | −0.129345 | − | 0.991600i | \(-0.541287\pi\) | ||||
−0.129345 | + | 0.991600i | \(0.541287\pi\) | |||||||
\(860\) | 17.5187 | + | 16.3912i | 0.597381 | + | 0.558937i | ||||
\(861\) | 12.7448 | − | 6.72576i | 0.434341 | − | 0.229213i | ||||
\(862\) | −16.1315 | − | 16.1315i | −0.549440 | − | 0.549440i | ||||
\(863\) | −22.1829 | + | 22.1829i | −0.755113 | + | 0.755113i | −0.975429 | − | 0.220315i | \(-0.929291\pi\) |
0.220315 | + | 0.975429i | \(0.429291\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 32.6986 | + | 30.5943i | 1.11179 | + | 1.04024i | ||||
\(866\) | 24.2136i | 0.822811i | ||||||||
\(867\) | −1.35445 | + | 1.35445i | −0.0459994 | + | 0.0459994i | ||||
\(868\) | 17.8343 | + | 5.51319i | 0.605334 | + | 0.187130i | ||||
\(869\) | − | 72.6525i | − | 2.46457i | ||||||
\(870\) | 10.6532 | − | 0.354187i | 0.361176 | − | 0.0120081i | ||||
\(871\) | 20.8639i | 0.706948i | ||||||||
\(872\) | 0.0615536 | + | 0.0615536i | 0.00208447 | + | 0.00208447i | ||||
\(873\) | 8.42614 | + | 8.42614i | 0.285182 | + | 0.285182i | ||||
\(874\) | −1.88909 | −0.0638996 | ||||||||
\(875\) | −28.9901 | − | 5.87995i | −0.980044 | − | 0.198779i | ||||
\(876\) | 7.13387 | 0.241031 | ||||||||
\(877\) | −5.71511 | − | 5.71511i | −0.192985 | − | 0.192985i | 0.603999 | − | 0.796985i | \(-0.293573\pi\) |
−0.796985 | + | 0.603999i | \(0.793573\pi\) | |||||||
\(878\) | −25.3373 | − | 25.3373i | −0.855092 | − | 0.855092i | ||||
\(879\) | 4.46841i | 0.150716i | ||||||||
\(880\) | 10.9660 | − | 0.364588i | 0.369663 | − | 0.0122902i | ||||
\(881\) | 31.8033i | 1.07148i | 0.844383 | + | 0.535740i | \(0.179967\pi\) | ||||
−0.844383 | + | 0.535740i | \(0.820033\pi\) | |||||||
\(882\) | 6.87957 | − | 1.29289i | 0.231647 | − | 0.0435340i | ||||
\(883\) | −16.9653 | + | 16.9653i | −0.570929 | + | 0.570929i | −0.932388 | − | 0.361459i | \(-0.882279\pi\) |
0.361459 | + | 0.932388i | \(0.382279\pi\) | |||||||
\(884\) | − | 18.7530i | − | 0.630733i | ||||||
\(885\) | 2.28159 | + | 2.13476i | 0.0766949 | + | 0.0717592i | ||||
\(886\) | −4.14519 | −0.139260 | ||||||||
\(887\) | 7.70801 | − | 7.70801i | 0.258810 | − | 0.258810i | −0.565760 | − | 0.824570i | \(-0.691417\pi\) |
0.824570 | + | 0.565760i | \(0.191417\pi\) | |||||||
\(888\) | −4.74632 | − | 4.74632i | −0.159276 | − | 0.159276i | ||||
\(889\) | −19.5171 | − | 36.9834i | −0.654583 | − | 1.24038i | ||||
\(890\) | 25.0793 | + | 23.4653i | 0.840660 | + | 0.786560i | ||||
\(891\) | −4.90685 | −0.164386 | ||||||||
\(892\) | −8.26067 | + | 8.26067i | −0.276588 | + | 0.276588i | ||||
\(893\) | 0.929451 | − | 0.929451i | 0.0311029 | − | 0.0311029i | ||||
\(894\) | −5.64124 | −0.188671 | ||||||||
\(895\) | −0.243801 | − | 7.33299i | −0.00814937 | − | 0.245115i | ||||
\(896\) | −2.33991 | + | 1.23483i | −0.0781710 | + | 0.0412529i | ||||
\(897\) | −5.09618 | − | 5.09618i | −0.170156 | − | 0.170156i | ||||
\(898\) | 1.20406 | − | 1.20406i | 0.0401799 | − | 0.0401799i | ||||
\(899\) | −33.6325 | −1.12171 | ||||||||
\(900\) | −4.98896 | + | 0.332104i | −0.166299 | + | 0.0110701i | ||||
\(901\) | 6.95153i | 0.231589i | ||||||||
\(902\) | −18.8982 | + | 18.8982i | −0.629242 | + | 0.629242i | ||||
\(903\) | −27.1204 | − | 8.38387i | −0.902511 | − | 0.278998i | ||||
\(904\) | − | 2.87437i | − | 0.0956000i | ||||||
\(905\) | −1.44096 | − | 43.3410i | −0.0478992 | − | 1.44070i | ||||
\(906\) | 11.7678i | 0.390958i | ||||||||
\(907\) | 0.997860 | + | 0.997860i | 0.0331334 | + | 0.0331334i | 0.723479 | − | 0.690346i | \(-0.242542\pi\) |
−0.690346 | + | 0.723479i | \(0.742542\pi\) | |||||||
\(908\) | −5.91295 | − | 5.91295i | −0.196228 | − | 0.196228i | ||||
\(909\) | −18.1504 | −0.602010 | ||||||||
\(910\) | −7.52512 | + | 27.5563i | −0.249455 | + | 0.913484i | ||||
\(911\) | −21.9623 | −0.727643 | −0.363821 | − | 0.931469i | \(-0.618528\pi\) | ||||
−0.363821 | + | 0.931469i | \(0.618528\pi\) | |||||||
\(912\) | 0.894921 | + | 0.894921i | 0.0296338 | + | 0.0296338i | ||||
\(913\) | 45.6243 | + | 45.6243i | 1.50995 | + | 1.50995i | ||||
\(914\) | 7.55635i | 0.249942i | ||||||||
\(915\) | −3.50950 | + | 3.75089i | −0.116021 | + | 0.124001i | ||||
\(916\) | 9.31371i | 0.307734i | ||||||||
\(917\) | 10.0307 | − | 32.4476i | 0.331242 | − | 1.07151i | ||||
\(918\) | −2.74632 | + | 2.74632i | −0.0906420 | + | 0.0906420i | ||||
\(919\) | 32.6954i | 1.07852i | 0.842138 | + | 0.539262i | \(0.181297\pi\) | ||||
−0.842138 | + | 0.539262i | \(0.818703\pi\) | |||||||
\(920\) | −0.110906 | − | 3.33579i | −0.00365645 | − | 0.109978i | ||||
\(921\) | −29.4172 | −0.969331 | ||||||||
\(922\) | −0.607228 | + | 0.607228i | −0.0199980 | + | 0.0199980i | ||||
\(923\) | −44.4987 | − | 44.4987i | −1.46469 | − | 1.46469i | ||||
\(924\) | −11.4816 | + | 6.05914i | −0.377717 | + | 0.199331i | ||||
\(925\) | −25.2555 | − | 22.1029i | −0.830394 | − | 0.726739i | ||||
\(926\) | 28.7925 | 0.946180 | ||||||||
\(927\) | 8.36459 | − | 8.36459i | 0.274729 | − | 0.274729i | ||||
\(928\) | 3.37069 | − | 3.37069i | 0.110648 | − | 0.110648i | ||||
\(929\) | 10.8063 | 0.354545 | 0.177272 | − | 0.984162i | \(-0.443273\pi\) | ||||
0.177272 | + | 0.984162i | \(0.443273\pi\) | |||||||
\(930\) | 15.7678 | − | 0.524233i | 0.517045 | − | 0.0171903i | ||||
\(931\) | −7.31371 | − | 4.99963i | −0.239697 | − | 0.163856i | ||||
\(932\) | 16.0563 | + | 16.0563i | 0.525943 | + | 0.525943i | ||||
\(933\) | 8.11091 | − | 8.11091i | 0.265539 | − | 0.265539i | ||||
\(934\) | 12.4155 | 0.406247 | ||||||||
\(935\) | 29.1148 | − | 31.1174i | 0.952156 | − | 1.01765i | ||||
\(936\) | 4.82843i | 0.157822i | ||||||||
\(937\) | 3.51804 | − | 3.51804i | 0.114929 | − | 0.114929i | −0.647303 | − | 0.762233i | \(-0.724103\pi\) |
0.762233 | + | 0.647303i | \(0.224103\pi\) | |||||||
\(938\) | 3.37652 | − | 10.9225i | 0.110247 | − | 0.356631i | ||||
\(939\) | − | 0.866125i | − | 0.0282649i | ||||||
\(940\) | 1.69581 | + | 1.58667i | 0.0553111 | + | 0.0517516i | ||||
\(941\) | − | 54.9021i | − | 1.78976i | −0.446309 | − | 0.894879i | \(-0.647262\pi\) | ||
0.446309 | − | 0.894879i | \(-0.352738\pi\) | |||||||
\(942\) | −13.7132 | − | 13.7132i | −0.446800 | − | 0.446800i | ||||
\(943\) | 5.74873 | + | 5.74873i | 0.187204 | + | 0.187204i | ||||
\(944\) | 1.39735 | 0.0454797 | ||||||||
\(945\) | 5.13756 | − | 2.93351i | 0.167125 | − | 0.0954269i | ||||
\(946\) | 52.6464 | 1.71168 | ||||||||
\(947\) | −30.4494 | − | 30.4494i | −0.989471 | − | 0.989471i | 0.0104740 | − | 0.999945i | \(-0.496666\pi\) |
−0.999945 | + | 0.0104740i | \(0.996666\pi\) | |||||||
\(948\) | 10.4697 | + | 10.4697i | 0.340039 | + | 0.340039i | ||||
\(949\) | − | 34.4454i | − | 1.11814i | ||||||
\(950\) | 4.76193 | + | 4.16752i | 0.154498 | + | 0.135212i | ||||
\(951\) | 9.95583i | 0.322840i | ||||||||
\(952\) | −3.03490 | + | 9.81739i | −0.0983616 | + | 0.318183i | ||||
\(953\) | 40.3553 | − | 40.3553i | 1.30724 | − | 1.30724i | 0.383836 | − | 0.923401i | \(-0.374603\pi\) |
0.923401 | − | 0.383836i | \(-0.125397\pi\) | |||||||
\(954\) | − | 1.78984i | − | 0.0579483i | ||||||
\(955\) | 37.6464 | − | 1.25164i | 1.21821 | − | 0.0405020i | ||||
\(956\) | 1.68592 | 0.0545267 | ||||||||
\(957\) | 16.5395 | − | 16.5395i | 0.534645 | − | 0.534645i | ||||
\(958\) | −0.828427 | − | 0.828427i | −0.0267653 | − | 0.0267653i | ||||
\(959\) | −6.32930 | − | 11.9935i | −0.204384 | − | 0.387291i | ||||
\(960\) | −1.52773 | + | 1.63280i | −0.0493072 | + | 0.0526986i | ||||
\(961\) | −18.7794 | −0.605788 | ||||||||
\(962\) | −22.9172 | + | 22.9172i | −0.738882 | + | 0.738882i | ||||
\(963\) | −3.77297 | + | 3.77297i | −0.121582 | + | 0.121582i | ||||
\(964\) | 3.61574 | 0.116455 | ||||||||
\(965\) | 10.4001 | − | 11.1155i | 0.334793 | − | 0.357820i | ||||
\(966\) | 1.84316 | + | 3.49264i | 0.0593026 | + | 0.112374i | ||||
\(967\) | 30.6566 | + | 30.6566i | 0.985849 | + | 0.985849i | 0.999901 | − | 0.0140521i | \(-0.00447307\pi\) |
−0.0140521 | + | 0.999901i | \(0.504473\pi\) | |||||||
\(968\) | 9.24695 | − | 9.24695i | 0.297208 | − | 0.297208i | ||||
\(969\) | 4.91548 | 0.157908 | ||||||||
\(970\) | 26.6311 | − | 0.885407i | 0.855073 | − | 0.0284287i | ||||
\(971\) | 46.5248i | 1.49305i | 0.665357 | + | 0.746525i | \(0.268279\pi\) | ||||
−0.665357 | + | 0.746525i | \(0.731721\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −9.87321 | − | 3.05215i | −0.316520 | − | 0.0978475i | ||||
\(974\) | − | 13.7283i | − | 0.439883i | ||||||
\(975\) | 1.60354 | + | 24.0888i | 0.0513544 | + | 0.771460i | ||||
\(976\) | 2.29721i | 0.0735318i | ||||||||
\(977\) | 42.6690 | + | 42.6690i | 1.36510 | + | 1.36510i | 0.867278 | + | 0.497825i | \(0.165868\pi\) |
0.497825 | + | 0.867278i | \(0.334132\pi\) | |||||||
\(978\) | 7.21967 | + | 7.21967i | 0.230860 | + | 0.230860i | ||||
\(979\) | 75.3675 | 2.40875 | ||||||||
\(980\) | 8.39905 | − | 13.2082i | 0.268298 | − | 0.421920i | ||||
\(981\) | −0.0870500 | −0.00277929 | ||||||||
\(982\) | 11.9770 | + | 11.9770i | 0.382202 | + | 0.382202i | ||||
\(983\) | −1.34529 | − | 1.34529i | −0.0429079 | − | 0.0429079i | 0.685327 | − | 0.728235i | \(-0.259659\pi\) |
−0.728235 | + | 0.685327i | \(0.759659\pi\) | |||||||
\(984\) | − | 5.44670i | − | 0.173634i | ||||||
\(985\) | −30.0958 | − | 28.1590i | −0.958932 | − | 0.897220i | ||||
\(986\) | − | 18.5140i | − | 0.589605i | ||||||
\(987\) | −2.62526 | − | 0.811559i | −0.0835629 | − | 0.0258322i | ||||
\(988\) | 4.32106 | − | 4.32106i | 0.137471 | − | 0.137471i | ||||
\(989\) | − | 16.0147i | − | 0.509239i | ||||||
\(990\) | −7.49632 | + | 8.01193i | −0.238249 | + | 0.254636i | ||||
\(991\) | 3.44975 | 0.109585 | 0.0547925 | − | 0.998498i | \(-0.482550\pi\) | ||||
0.0547925 | + | 0.998498i | \(0.482550\pi\) | |||||||
\(992\) | 4.98896 | − | 4.98896i | 0.158400 | − | 0.158400i | ||||
\(993\) | 7.19543 | + | 7.19543i | 0.228340 | + | 0.228340i | ||||
\(994\) | 16.0940 | + | 30.4969i | 0.510472 | + | 0.967304i | ||||
\(995\) | 26.2613 | − | 0.873112i | 0.832539 | − | 0.0276795i | ||||
\(996\) | −13.1495 | −0.416658 | ||||||||
\(997\) | −31.5368 | + | 31.5368i | −0.998780 | + | 0.998780i | −0.999999 | − | 0.00121964i | \(-0.999612\pi\) |
0.00121964 | + | 0.999999i | \(0.499612\pi\) | |||||||
\(998\) | 21.5043 | − | 21.5043i | 0.680706 | − | 0.680706i | ||||
\(999\) | 6.71231 | 0.212368 |
(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 | 210.2.m.b.97.1 | yes | 8 | |
3.2 | odd | 2 | 630.2.p.c.307.4 | 8 | |||
4.3 | odd | 2 | 1680.2.cz.a.97.1 | 8 | |||
5.2 | odd | 4 | 1050.2.m.b.643.4 | 8 | |||
5.3 | odd | 4 | 210.2.m.a.13.2 | ✓ | 8 | ||
5.4 | even | 2 | 1050.2.m.a.307.3 | 8 | |||
7.6 | odd | 2 | 210.2.m.a.97.2 | yes | 8 | ||
15.8 | even | 4 | 630.2.p.b.433.3 | 8 | |||
20.3 | even | 4 | 1680.2.cz.b.433.4 | 8 | |||
21.20 | even | 2 | 630.2.p.b.307.3 | 8 | |||
28.27 | even | 2 | 1680.2.cz.b.97.4 | 8 | |||
35.13 | even | 4 | inner | 210.2.m.b.13.1 | yes | 8 | |
35.27 | even | 4 | 1050.2.m.a.643.3 | 8 | |||
35.34 | odd | 2 | 1050.2.m.b.307.4 | 8 | |||
105.83 | odd | 4 | 630.2.p.c.433.4 | 8 | |||
140.83 | odd | 4 | 1680.2.cz.a.433.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.m.a.13.2 | ✓ | 8 | 5.3 | odd | 4 | ||
210.2.m.a.97.2 | yes | 8 | 7.6 | odd | 2 | ||
210.2.m.b.13.1 | yes | 8 | 35.13 | even | 4 | inner | |
210.2.m.b.97.1 | yes | 8 | 1.1 | even | 1 | trivial | |
630.2.p.b.307.3 | 8 | 21.20 | even | 2 | |||
630.2.p.b.433.3 | 8 | 15.8 | even | 4 | |||
630.2.p.c.307.4 | 8 | 3.2 | odd | 2 | |||
630.2.p.c.433.4 | 8 | 105.83 | odd | 4 | |||
1050.2.m.a.307.3 | 8 | 5.4 | even | 2 | |||
1050.2.m.a.643.3 | 8 | 35.27 | even | 4 | |||
1050.2.m.b.307.4 | 8 | 35.34 | odd | 2 | |||
1050.2.m.b.643.4 | 8 | 5.2 | odd | 4 | |||
1680.2.cz.a.97.1 | 8 | 4.3 | odd | 2 | |||
1680.2.cz.a.433.1 | 8 | 140.83 | odd | 4 | |||
1680.2.cz.b.97.4 | 8 | 28.27 | even | 2 | |||
1680.2.cz.b.433.4 | 8 | 20.3 | even | 4 |