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 | 97.2 | ||
Root | \(2.16053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.97 |
Dual form | 210.2.m.a.13.2 |
$q$-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 | ||||||||
\(7\) | 0.781409 | + | 2.52773i | 0.295345 | + | 0.955391i | ||||
\(8\) | 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 | 0.0517287 | − | 0.998661i | \(-0.483527\pi\) |
−0.998661 | + | 0.0517287i | \(0.983527\pi\) | |||||||
\(14\) | 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 | −0.290726 | − | 0.956806i | \(-0.593897\pi\) |
0.956806 | + | 0.290726i | \(0.0938969\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | 1.26561 | 0.290351 | 0.145175 | − | 0.989406i | \(-0.453625\pi\) | ||||
0.145175 | + | 0.989406i | \(0.453625\pi\) | |||||||
\(20\) | 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 | ||||
\(28\) | −2.52773 | + | 0.781409i | −0.477695 | + | 0.147672i | ||||
\(29\) | − | 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 | \(0.218423\pi\) | ||||
−0.773662 | + | 0.633598i | \(0.781577\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −3.46967 | − | 3.46967i | −0.603991 | − | 0.603991i | ||||
\(34\) | −3.88388 | −0.666080 | ||||||||
\(35\) | 1.93413 | + | 5.59099i | 0.326928 | + | 0.945049i | ||||
\(36\) | −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 | \(0.139837\pi\) | ||||
−0.905045 | + | 0.425316i | \(0.860163\pi\) | |||||||
\(42\) | −2.52773 | + | 0.781409i | −0.390037 | + | 0.120574i | ||||
\(43\) | −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 | −0.651514 | − | 0.758636i | \(-0.725866\pi\) |
0.758636 | + | 0.651514i | \(0.225866\pi\) | |||||||
\(48\) | 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 | \(-0.471007\pi\) | ||||
0.0909594 | + | 0.995855i | \(0.471007\pi\) | |||||||
\(60\) | 1.52773 | − | 1.63280i | 0.197229 | − | 0.210794i | ||||
\(61\) | 2.29721i | 0.294127i | 0.989127 | + | 0.147064i | \(0.0469822\pi\) | ||||
−0.989127 | + | 0.147064i | \(0.953018\pi\) | |||||||
\(62\) | 4.98896 | − | 4.98896i | 0.633598 | − | 0.633598i | ||||
\(63\) | −2.52773 | + | 0.781409i | −0.318464 | + | 0.0984482i | ||||
\(64\) | − | 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 | ||||||||
\(70\) | 2.58579 | − | 5.32106i | 0.309061 | − | 0.635989i | ||||
\(71\) | −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 | 0.937740 | − | 0.347337i | \(-0.112914\pi\) |
−0.347337 | + | 0.937740i | \(0.612914\pi\) | |||||||
\(74\) | 6.71231i | 0.780290i | ||||||||
\(75\) | −3.76256 | − | 3.29289i | −0.434463 | − | 0.380231i | ||||
\(76\) | 1.26561i | 0.145175i | ||||||||
\(77\) | 3.83425 | + | 12.4032i | 0.436954 | + | 1.41347i | ||||
\(78\) | 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 | \(-0.993374\pi\) |
−0.0208150 | − | 0.999783i | \(-0.506626\pi\) | |||||||
\(84\) | 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 | \(-0.802747\pi\) | ||||
−0.814060 | + | 0.580781i | \(0.802747\pi\) | |||||||
\(90\) | 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 | −0.990810 | − | 0.135264i | \(-0.956812\pi\) |
0.135264 | + | 0.990810i | \(0.456812\pi\) | |||||||
\(98\) | 6.87957 | + | 1.29289i | 0.694941 | + | 0.130602i | ||||
\(99\) | 4.90685i | 0.493157i | ||||||||
\(100\) | 0.332104 | + | 4.98896i | 0.0332104 | + | 0.498896i | ||||
\(101\) | − | 18.1504i | − | 1.80603i | −0.429609 | − | 0.903015i | \(-0.641349\pi\) | ||
0.429609 | − | 0.903015i | \(-0.358651\pi\) | |||||||
\(102\) | 2.74632 | + | 2.74632i | 0.271926 | + | 0.271926i | ||||
\(103\) | 8.36459 | + | 8.36459i | 0.824187 | + | 0.824187i | 0.986706 | − | 0.162518i | \(-0.0519616\pi\) |
−0.162518 | + | 0.986706i | \(0.551962\pi\) | |||||||
\(104\) | −4.82843 | −0.473466 | ||||||||
\(105\) | 2.58579 | − | 5.32106i | 0.252347 | − | 0.519283i | ||||
\(106\) | −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 | ||||||||
\(112\) | −0.781409 | − | 2.52773i | −0.0738362 | − | 0.238848i | ||||
\(113\) | 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 | \(0.189496\pi\) | ||||
−0.827970 | + | 0.560772i | \(0.810504\pi\) | |||||||
\(132\) | 3.46967 | − | 3.46967i | 0.301996 | − | 0.301996i | ||||
\(133\) | 0.988958 | + | 3.19912i | 0.0857536 | + | 0.277399i | ||||
\(134\) | − | 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 | \(-0.447028\pi\) | ||||
0.165650 | + | 0.986185i | \(0.447028\pi\) | |||||||
\(140\) | −5.59099 | + | 1.93413i | −0.472525 | + | 0.163464i | ||||
\(141\) | −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 | ||||||
\(147\) | 6.87957 | + | 1.29289i | 0.567417 | + | 0.106636i | ||||
\(148\) | 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 | \(0.531687\pi\) |
−0.995049 | + | 0.0993827i | \(0.968313\pi\) | |||||||
\(158\) | −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 | −0.917910 | − | 0.396788i | \(-0.870125\pi\) |
0.396788 | + | 0.917910i | \(0.370125\pi\) | |||||||
\(168\) | −0.781409 | − | 2.52773i | −0.0602870 | − | 0.195018i | ||||
\(169\) | 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 | \(0.0254262\pi\) |
0.0797939 | + | 0.996811i | \(0.474574\pi\) | |||||||
\(174\) | 4.76687 | 0.361376 | ||||||||
\(175\) | 4.73788 | + | 12.3512i | 0.358150 | + | 0.933664i | ||||
\(176\) | −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 | \(-0.743798\pi\) | ||
0.693196 | − | 0.720749i | \(-0.256202\pi\) | |||||||
\(182\) | −12.2049 | + | 3.77297i | −0.904691 | + | 0.279671i | ||||
\(183\) | 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 | \(-0.363257\pi\) | ||||
0.416499 | + | 0.909136i | \(0.363257\pi\) | |||||||
\(200\) | 3.29289 | − | 3.76256i | 0.232843 | − | 0.266053i | ||||
\(201\) | − | 4.32106i | − | 0.304784i | ||||||
\(202\) | −12.8343 | + | 12.8343i | −0.903015 | + | 0.903015i | ||||
\(203\) | 12.0494 | − | 3.72488i | 0.845699 | − | 0.261435i | ||||
\(204\) | − | 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 | ||||||||
\(210\) | −5.59099 | + | 1.93413i | −0.385815 | + | 0.133468i | ||||
\(211\) | 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 | ||||||
\(217\) | −17.8343 | + | 5.51319i | −1.21067 | + | 0.374260i | ||||
\(218\) | 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 | 0.374181 | − | 0.927356i | \(-0.377924\pi\) |
−0.927356 | + | 0.374181i | \(0.877924\pi\) | |||||||
\(224\) | −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 | −0.483106 | − | 0.875562i | \(-0.660491\pi\) |
0.875562 | + | 0.483106i | \(0.160491\pi\) | |||||||
\(228\) | 0.894921 | − | 0.894921i | 0.0592676 | − | 0.0592676i | ||||
\(229\) | −9.31371 | −0.615467 | −0.307734 | − | 0.951473i | \(-0.599571\pi\) | ||||
−0.307734 | + | 0.951473i | \(0.599571\pi\) | |||||||
\(230\) | 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 | ||||
\(238\) | −3.03490 | − | 9.81739i | −0.196723 | − | 0.636367i | ||||
\(239\) | − | 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 | \(0.0371532\pi\) | ||||
−0.993196 | + | 0.116455i | \(0.962847\pi\) | |||||||
\(242\) | −9.24695 | − | 9.24695i | −0.594417 | − | 0.594417i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | −2.29721 | −0.147064 | ||||||||
\(245\) | −12.6211 | + | 9.25780i | −0.806335 | + | 0.591459i | ||||
\(246\) | −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 | \(-0.951706\pi\) | ||
0.988513 | − | 0.151138i | \(-0.0482938\pi\) | |||||||
\(252\) | −0.781409 | − | 2.52773i | −0.0492241 | − | 0.159232i | ||||
\(253\) | −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 | \(-0.379846\pi\) |
0.929599 | − | 0.368574i | \(-0.120154\pi\) | |||||||
\(258\) | −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 | \(-0.369029\pi\) | ||||
0.399945 | + | 0.916539i | \(0.369029\pi\) | |||||||
\(270\) | −2.23483 | + | 0.0743018i | −0.136008 | + | 0.00452186i | ||||
\(271\) | − | 18.0836i | − | 1.09850i | −0.835658 | − | 0.549250i | \(-0.814913\pi\) | ||
0.835658 | − | 0.549250i | \(-0.185087\pi\) | |||||||
\(272\) | −2.74632 | + | 2.74632i | −0.166520 | + | 0.166520i | ||||
\(273\) | −12.2049 | + | 3.77297i | −0.738677 | + | 0.228351i | ||||
\(274\) | 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 | ||||||||
\(280\) | 5.32106 | + | 2.58579i | 0.317994 | + | 0.154530i | ||||
\(281\) | 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 | 0.950682 | − | 0.310168i | \(-0.100385\pi\) |
−0.310168 | + | 0.950682i | \(0.600385\pi\) | |||||||
\(284\) | − | 13.0334i | − | 0.773388i | ||||||
\(285\) | −2.06649 | − | 1.93351i | −0.122409 | − | 0.114531i | ||||
\(286\) | 23.6924i | 1.40096i | ||||||||
\(287\) | −13.7678 | + | 4.25610i | −0.812685 | + | 0.251229i | ||||
\(288\) | −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 | 0.608763 | − | 0.793352i | \(-0.291666\pi\) |
−0.793352 | + | 0.608763i | \(0.791666\pi\) | |||||||
\(294\) | −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 | \(-0.432868\pi\) |
0.977843 | − | 0.209340i | \(-0.0671316\pi\) | |||||||
\(308\) | −12.4032 | + | 3.83425i | −0.706736 | + | 0.218477i | ||||
\(309\) | − | 11.8293i | − | 0.672946i | ||||||
\(310\) | 10.7788 | − | 11.5202i | 0.612195 | − | 0.654302i | ||||
\(311\) | 11.4706i | 0.650435i | 0.945639 | + | 0.325218i | \(0.105438\pi\) | ||||
−0.945639 | + | 0.325218i | \(0.894562\pi\) | |||||||
\(312\) | 3.41421 | + | 3.41421i | 0.193292 | + | 0.193292i | ||||
\(313\) | 0.612443 | + | 0.612443i | 0.0346173 | + | 0.0346173i | 0.724204 | − | 0.689586i | \(-0.242208\pi\) |
−0.689586 | + | 0.724204i | \(0.742208\pi\) | |||||||
\(314\) | 19.3934 | 1.09443 | ||||||||
\(315\) | −5.59099 | + | 1.93413i | −0.315016 | + | 0.108976i | ||||
\(316\) | 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 | ||||||
\(322\) | 1.16636 | + | 3.77297i | 0.0649986 | + | 0.210260i | ||||
\(323\) | 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 | ||||
\(343\) | −14.5011 | − | 11.5204i | −0.782984 | − | 0.622042i | ||||
\(344\) | 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 | \(-0.543657\pi\) | ||||
−0.136723 | + | 0.990609i | \(0.543657\pi\) | |||||||
\(350\) | 5.38344 | − | 12.0838i | 0.287757 | − | 0.645907i | ||||
\(351\) | −4.82843 | −0.257722 | ||||||||
\(352\) | 3.46967 | + | 3.46967i | 0.184934 | + | 0.184934i | ||||
\(353\) | 12.0821 | + | 12.0821i | 0.643066 | + | 0.643066i | 0.951308 | − | 0.308242i | \(-0.0997407\pi\) |
−0.308242 | + | 0.951308i | \(0.599741\pi\) | |||||||
\(354\) | 1.39735i | 0.0742681i | ||||||||
\(355\) | −29.1274 | + | 0.968403i | −1.54592 | + | 0.0513975i | ||||
\(356\) | − | 15.3596i | − | 0.814060i | ||||||
\(357\) | −3.03490 | − | 9.81739i | −0.160624 | − | 0.519591i | ||||
\(358\) | 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 | −0.803328 | − | 0.595536i | \(-0.796940\pi\) |
0.595536 | + | 0.803328i | \(0.296940\pi\) | |||||||
\(368\) | 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 | ||||
\(378\) | −0.781409 | − | 2.52773i | −0.0401913 | − | 0.130012i | ||||
\(379\) | 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 | 0.863138 | − | 0.504968i | \(-0.168496\pi\) |
−0.504968 | + | 0.863138i | \(0.668496\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 9.49050 | + | 27.4341i | 0.483680 | + | 1.39817i | ||||
\(386\) | 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 | ||||||||
\(392\) | −1.29289 | + | 6.87957i | −0.0653010 | + | 0.347471i | ||||
\(393\) | 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 | −0.0275544 | − | 0.999620i | \(-0.508772\pi\) |
0.999620 | + | 0.0275544i | \(0.00877196\pi\) | |||||||
\(398\) | −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 | \(-0.649632\pi\) | ||||
−0.452959 | + | 0.891531i | \(0.649632\pi\) | |||||||
\(410\) | 8.32106 | − | 8.89339i | 0.410948 | − | 0.439213i | ||||
\(411\) | 5.12563i | 0.252829i | ||||||||
\(412\) | −8.36459 | + | 8.36459i | −0.412094 | + | 0.412094i | ||||
\(413\) | 1.09190 | + | 3.53211i | 0.0537288 | + | 0.173804i | ||||
\(414\) | 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 | \(-0.542862\pi\) | ||||
−0.134250 | + | 0.990948i | \(0.542862\pi\) | |||||||
\(420\) | 5.32106 | + | 2.58579i | 0.259641 | + | 0.126173i | ||||
\(421\) | 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 | ||||||
\(427\) | −5.80671 | + | 1.79506i | −0.281006 | + | 0.0868689i | ||||
\(428\) | −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 | 0.986510 | − | 0.163700i | \(-0.0523428\pi\) |
−0.163700 | + | 0.986510i | \(0.552343\pi\) | |||||||
\(434\) | 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 | \(-0.826500\pi\) | ||||
−0.855092 | + | 0.518476i | \(0.826500\pi\) | |||||||
\(440\) | 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 | ||||
\(448\) | 2.52773 | − | 0.781409i | 0.119424 | − | 0.0369181i | ||||
\(449\) | 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 | ||||||||
\(455\) | 12.4853 | − | 25.6924i | 0.585319 | − | 1.20448i | ||||
\(456\) | −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 | \(0.00636599\pi\) | ||||
−0.999800 | + | 0.0199980i | \(0.993634\pi\) | |||||||
\(462\) | −12.4032 | + | 3.83425i | −0.577048 | + | 0.178386i | ||||
\(463\) | −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 | −0.474181 | − | 0.880428i | \(-0.657256\pi\) |
0.880428 | + | 0.474181i | \(0.157256\pi\) | |||||||
\(468\) | 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 | \(-0.508521\pi\) | ||||
−0.0267653 | + | 0.999642i | \(0.508521\pi\) | |||||||
\(480\) | −0.0743018 | − | 2.23483i | −0.00339140 | − | 0.102006i | ||||
\(481\) | 32.4099i | 1.47776i | ||||||||
\(482\) | 2.55672 | − | 2.55672i | 0.116455 | − | 0.116455i | ||||
\(483\) | 1.16636 | + | 3.77297i | 0.0530711 | + | 0.171676i | ||||
\(484\) | 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 | ||||||||
\(490\) | 15.4707 | + | 2.37824i | 0.698897 | + | 0.107438i | ||||
\(491\) | −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 | ||||||
\(497\) | −10.1844 | − | 32.9448i | −0.456832 | − | 1.47778i | ||||
\(498\) | 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 | 0.593025 | − | 0.805184i | \(-0.297934\pi\) |
−0.805184 | + | 0.593025i | \(0.797934\pi\) | |||||||
\(504\) | −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 | \(-0.852286\pi\) | ||||
−0.894243 | + | 0.447581i | \(0.852286\pi\) | |||||||
\(510\) | 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 | ||||
\(518\) | −16.9669 | + | 5.24505i | −0.745482 | + | 0.230454i | ||||
\(519\) | − | 20.0260i | − | 0.879045i | ||||||
\(520\) | −10.7907 | + | 0.358761i | −0.473205 | + | 0.0157327i | ||||
\(521\) | 8.96879i | 0.392930i | 0.980511 | + | 0.196465i | \(0.0629462\pi\) | ||||
−0.980511 | + | 0.196465i | \(0.937054\pi\) | |||||||
\(522\) | −3.37069 | − | 3.37069i | −0.147531 | − | 0.147531i | ||||
\(523\) | −8.40290 | − | 8.40290i | −0.367433 | − | 0.367433i | 0.499107 | − | 0.866540i | \(-0.333661\pi\) |
−0.866540 | + | 0.499107i | \(0.833661\pi\) | |||||||
\(524\) | −12.8367 | −0.560772 | ||||||||
\(525\) | 5.38344 | − | 12.0838i | 0.234952 | − | 0.527381i | ||||
\(526\) | −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 | ||||||||
\(532\) | −3.19912 | + | 0.988958i | −0.138699 | + | 0.0428768i | ||||
\(533\) | 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 | ||||
\(553\) | 37.4264 | − | 11.5698i | 1.59153 | − | 0.491998i | ||||
\(554\) | − | 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 | ||||||||
\(560\) | −1.93413 | − | 5.59099i | −0.0817320 | − | 0.236262i | ||||
\(561\) | −19.0576 | −0.804613 | ||||||||
\(562\) | −14.4645 | − | 14.4645i | −0.610146 | − | 0.610146i | ||||
\(563\) | −7.84316 | − | 7.84316i | −0.330550 | − | 0.330550i | 0.522246 | − | 0.852795i | \(-0.325094\pi\) |
−0.852795 | + | 0.522246i | \(0.825094\pi\) | |||||||
\(564\) | − | 1.03858i | − | 0.0437323i | ||||||
\(565\) | 4.39124 | − | 4.69328i | 0.184741 | − | 0.197448i | ||||
\(566\) | − | 15.2383i | − | 0.640514i | ||||||
\(567\) | −0.781409 | − | 2.52773i | −0.0328161 | − | 0.106155i | ||||
\(568\) | −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 | −0.905323 | − | 0.424723i | \(-0.860371\pi\) |
0.424723 | + | 0.905323i | \(0.360371\pi\) | |||||||
\(578\) | 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 | −0.840632 | − | 0.541607i | \(-0.817816\pi\) |
0.541607 | + | 0.840632i | \(0.317816\pi\) | |||||||
\(588\) | −1.29289 | + | 6.87957i | −0.0533180 | + | 0.283709i | ||||
\(589\) | 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 | 0.556605 | − | 0.830777i | \(-0.312104\pi\) |
−0.830777 | + | 0.556605i | \(0.812104\pi\) | |||||||
\(594\) | −4.90685 | −0.201330 | ||||||||
\(595\) | 20.6664 | + | 10.0429i | 0.847239 | + | 0.411718i | ||||
\(596\) | 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 | \(-0.923301\pi\) | ||
0.971110 | − | 0.238632i | \(-0.0766991\pi\) | |||||||
\(602\) | 8.38387 | + | 27.1204i | 0.341701 | + | 1.10535i | ||||
\(603\) | −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 | −0.0538519 | − | 0.998549i | \(-0.517150\pi\) |
0.998549 | + | 0.0538519i | \(0.0171499\pi\) | |||||||
\(608\) | 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 | \(-0.210984\pi\) | ||||
0.788257 | + | 0.615346i | \(0.210984\pi\) | |||||||
\(620\) | −15.7678 | + | 0.524233i | −0.633248 | + | 0.0210537i | ||||
\(621\) | 1.49264i | 0.0598974i | ||||||||
\(622\) | 8.11091 | − | 8.11091i | 0.325218 | − | 0.325218i | ||||
\(623\) | −12.0022 | − | 38.8250i | −0.480856 | − | 1.55549i | ||||
\(624\) | − | 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 | ||||||||
\(630\) | 5.32106 | + | 2.58579i | 0.211996 | + | 0.103020i | ||||
\(631\) | −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 | ||||||
\(637\) | 33.2175 | + | 6.24264i | 1.31612 | + | 0.247342i | ||||
\(638\) | −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 | 0.375089 | − | 0.926989i | \(-0.377612\pi\) |
−0.926989 | + | 0.375089i | \(0.877612\pi\) | |||||||
\(644\) | 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 | −0.596797 | − | 0.802392i | \(-0.703560\pi\) |
0.802392 | + | 0.596797i | \(0.203560\pi\) | |||||||
\(648\) | −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 | ||||
\(658\) | −0.811559 | − | 2.62526i | −0.0316379 | − | 0.102343i | ||||
\(659\) | − | 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 | \(0.0986892\pi\) | ||||
−0.952321 | + | 0.305098i | \(0.901311\pi\) | |||||||
\(662\) | −7.19543 | − | 7.19543i | −0.279658 | − | 0.279658i | ||||
\(663\) | 13.2604 | + | 13.2604i | 0.514991 | + | 0.514991i | ||||
\(664\) | −13.1495 | −0.510299 | ||||||||
\(665\) | 2.44786 | + | 7.07601i | 0.0949238 | + | 0.274396i | ||||
\(666\) | −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 | ||||||||
\(672\) | 2.52773 | − | 0.781409i | 0.0975092 | − | 0.0301435i | ||||
\(673\) | 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 | −0.779637 | − | 0.626232i | \(-0.784596\pi\) |
0.626232 | + | 0.779637i | \(0.284596\pi\) | |||||||
\(678\) | 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 | \(0.0148612\pi\) | ||||
−0.998910 | + | 0.0466709i | \(0.985139\pi\) | |||||||
\(692\) | −14.1605 | + | 14.1605i | −0.538303 | + | 0.538303i | ||||
\(693\) | −12.4032 | + | 3.83425i | −0.471158 | + | 0.145651i | ||||
\(694\) | 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 | ||||||||
\(700\) | −12.3512 | + | 4.73788i | −0.466832 | + | 0.179075i | ||||
\(701\) | −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 | ||||||
\(707\) | 45.8792 | − | 14.1829i | 1.72546 | − | 0.533401i | ||||
\(708\) | 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 | \(-0.339543\pi\) | ||||
0.483011 | + | 0.875614i | \(0.339543\pi\) | |||||||
\(720\) | −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 | \(0.651970\pi\) |
−0.888180 | + | 0.459495i | \(0.848030\pi\) | |||||||
\(728\) | −3.77297 | − | 12.2049i | −0.139836 | − | 0.452345i | ||||
\(729\) | − | 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 | 0.959525 | − | 0.281622i | \(-0.0908723\pi\) |
−0.281622 | + | 0.959525i | \(0.590872\pi\) | |||||||
\(734\) | 5.62959 | 0.207792 | ||||||||
\(735\) | 15.4707 | + | 2.37824i | 0.570647 | + | 0.0877226i | ||||
\(736\) | −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 | ||||||||
\(742\) | −1.39860 | − | 4.52423i | −0.0513442 | − | 0.166090i | ||||
\(743\) | −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 | \(-0.671663\pi\) | ||
0.513532 | − | 0.858070i | \(-0.328337\pi\) | |||||||
\(762\) | 11.1761 | − | 11.1761i | 0.404869 | − | 0.404869i | ||||
\(763\) | −0.220039 | + | 0.0680216i | −0.00796593 | + | 0.00246255i | ||||
\(764\) | − | 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 | \(-0.207849\pi\) | ||||
0.794278 | + | 0.607554i | \(0.207849\pi\) | |||||||
\(770\) | 12.6881 | − | 26.1097i | 0.457246 | − | 0.940927i | ||||
\(771\) | −29.4316 | −1.05995 | ||||||||
\(772\) | −4.81370 | − | 4.81370i | −0.173249 | − | 0.173249i | ||||
\(773\) | 11.1336 | + | 11.1336i | 0.400448 | + | 0.400448i | 0.878391 | − | 0.477943i | \(-0.158617\pi\) |
−0.477943 | + | 0.878391i | \(0.658617\pi\) | |||||||
\(774\) | 10.7292i | 0.385652i | ||||||||
\(775\) | 2.34315 | + | 35.1994i | 0.0841683 | + | 1.26440i | ||||
\(776\) | 11.9164i | 0.427773i | ||||||||
\(777\) | −16.9669 | + | 5.24505i | −0.608683 | + | 0.188165i | ||||
\(778\) | −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 | −0.466901 | − | 0.884310i | \(-0.654630\pi\) |
0.884310 | + | 0.466901i | \(0.154630\pi\) | |||||||
\(788\) | −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 | −0.444847 | − | 0.895607i | \(-0.646742\pi\) |
0.895607 | + | 0.444847i | \(0.146742\pi\) | |||||||
\(798\) | −3.19912 | + | 0.988958i | −0.113247 | + | 0.0350088i | ||||
\(799\) | − | 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 | ||||||||
\(805\) | −7.94241 | − | 3.85964i | −0.279933 | − | 0.136034i | ||||
\(806\) | −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 | \(-0.995964\pi\) | ||
0.999920 | − | 0.0126797i | \(-0.00403619\pi\) | |||||||
\(812\) | 3.72488 | + | 12.0494i | 0.130718 | + | 0.422849i | ||||
\(813\) | −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 | \(-0.618858\pi\) | ||||
−0.364786 | + | 0.931092i | \(0.618858\pi\) | |||||||
\(830\) | 0.977031 | + | 29.3869i | 0.0339132 | + | 1.02003i | ||||
\(831\) | − | 3.72704i | − | 0.129289i | ||||||
\(832\) | −3.41421 | + | 3.41421i | −0.118367 | + | 0.118367i | ||||
\(833\) | −5.02144 | + | 26.7194i | −0.173983 | + | 0.925773i | ||||
\(834\) | 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 | \(-0.165356\pi\) | ||||
0.868077 | + | 0.496430i | \(0.165356\pi\) | |||||||
\(840\) | −1.93413 | − | 5.59099i | −0.0667339 | − | 0.192907i | ||||
\(841\) | 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 | ||||||
\(847\) | 10.2186 | + | 33.0555i | 0.351116 | + | 1.13580i | ||||
\(848\) | −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 | 0.444853 | − | 0.895604i | \(-0.353256\pi\) |
−0.895604 | + | 0.444853i | \(0.853256\pi\) | |||||||
\(854\) | 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 | −0.957478 | − | 0.288505i | \(-0.906842\pi\) |
0.288505 | + | 0.957478i | \(0.406842\pi\) | |||||||
\(858\) | 16.7530 | − | 16.7530i | 0.571939 | − | 0.571939i | ||||
\(859\) | 7.58185 | 0.258689 | 0.129345 | − | 0.991600i | \(-0.458713\pi\) | ||||
0.129345 | + | 0.991600i | \(0.458713\pi\) | |||||||
\(860\) | −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 | ||||
\(868\) | −5.51319 | − | 17.8343i | −0.187130 | − | 0.605334i | ||||
\(869\) | − | 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 | ||||||||
\(875\) | 11.5061 | + | 27.2509i | 0.388977 | + | 0.921247i | ||||
\(876\) | 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 | \(-0.820033\pi\) | ||
0.844383 | − | 0.535740i | \(-0.179967\pi\) | |||||||
\(882\) | −1.29289 | + | 6.87957i | −0.0435340 | + | 0.231647i | ||||
\(883\) | −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 | −0.824570 | − | 0.565760i | \(-0.808583\pi\) |
0.565760 | + | 0.824570i | \(0.308583\pi\) | |||||||
\(888\) | 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 | ||||
\(903\) | 8.38387 | + | 27.1204i | 0.278998 | + | 0.902511i | ||||
\(904\) | − | 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 | ||||||||
\(910\) | −26.9957 | + | 9.33882i | −0.894898 | + | 0.309579i | ||||
\(911\) | −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 | ||||||
\(917\) | −32.4476 | + | 10.0307i | −1.07151 | + | 0.331242i | ||||
\(918\) | −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 | \(-0.556727\pi\) | ||||
−0.177272 | + | 0.984162i | \(0.556727\pi\) | |||||||
\(930\) | −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 | −0.762233 | − | 0.647303i | \(-0.775897\pi\) |
0.647303 | + | 0.762233i | \(0.275897\pi\) | |||||||
\(938\) | 10.9225 | − | 3.37652i | 0.356631 | − | 0.110247i | ||||
\(939\) | − | 0.866125i | − | 0.0282649i | ||||||
\(940\) | 1.69581 | + | 1.58667i | 0.0553111 | + | 0.0517516i | ||||
\(941\) | 54.9021i | 1.78976i | 0.446309 | + | 0.894879i | \(0.352738\pi\) | ||||
−0.446309 | + | 0.894879i | \(0.647262\pi\) | |||||||
\(942\) | −13.7132 | − | 13.7132i | −0.446800 | − | 0.446800i | ||||
\(943\) | −5.74873 | − | 5.74873i | −0.187204 | − | 0.187204i | ||||
\(944\) | −1.39735 | −0.0454797 | ||||||||
\(945\) | 5.32106 | + | 2.58579i | 0.173094 | + | 0.0841156i | ||||
\(946\) | 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 | ||||||
\(952\) | 9.81739 | − | 3.03490i | 0.318183 | − | 0.0983616i | ||||
\(953\) | 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 | \(-0.731721\pi\) | ||
0.665357 | − | 0.746525i | \(-0.268279\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 3.05215 | + | 9.87321i | 0.0978475 | + | 0.316520i | ||||
\(974\) | − | 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 | ||||||||
\(980\) | −9.25780 | − | 12.6211i | −0.295730 | − | 0.403167i | ||||
\(981\) | −0.0870500 | −0.00277929 | ||||||||
\(982\) | 11.9770 | + | 11.9770i | 0.382202 | + | 0.382202i | ||||
\(983\) | 1.34529 | + | 1.34529i | 0.0429079 | + | 0.0429079i | 0.728235 | − | 0.685327i | \(-0.240341\pi\) |
−0.685327 | + | 0.728235i | \(0.740341\pi\) | |||||||
\(984\) | − | 5.44670i | − | 0.173634i | ||||||
\(985\) | 30.0958 | + | 28.1590i | 0.958932 | + | 0.897220i | ||||
\(986\) | 18.5140i | 0.589605i | ||||||||
\(987\) | −0.811559 | − | 2.62526i | −0.0258322 | − | 0.0835629i | ||||
\(988\) | 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 | −0.00121964 | − | 0.999999i | \(-0.500388\pi\) |
0.999999 | + | 0.00121964i | \(0.000388223\pi\) | |||||||
\(998\) | 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.a.97.2 | yes | 8 | |
3.2 | odd | 2 | 630.2.p.b.307.3 | 8 | |||
4.3 | odd | 2 | 1680.2.cz.b.97.4 | 8 | |||
5.2 | odd | 4 | 1050.2.m.a.643.3 | 8 | |||
5.3 | odd | 4 | 210.2.m.b.13.1 | yes | 8 | ||
5.4 | even | 2 | 1050.2.m.b.307.4 | 8 | |||
7.6 | odd | 2 | 210.2.m.b.97.1 | yes | 8 | ||
15.8 | even | 4 | 630.2.p.c.433.4 | 8 | |||
20.3 | even | 4 | 1680.2.cz.a.433.1 | 8 | |||
21.20 | even | 2 | 630.2.p.c.307.4 | 8 | |||
28.27 | even | 2 | 1680.2.cz.a.97.1 | 8 | |||
35.13 | even | 4 | inner | 210.2.m.a.13.2 | ✓ | 8 | |
35.27 | even | 4 | 1050.2.m.b.643.4 | 8 | |||
35.34 | odd | 2 | 1050.2.m.a.307.3 | 8 | |||
105.83 | odd | 4 | 630.2.p.b.433.3 | 8 | |||
140.83 | odd | 4 | 1680.2.cz.b.433.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.m.a.13.2 | ✓ | 8 | 35.13 | even | 4 | inner | |
210.2.m.a.97.2 | yes | 8 | 1.1 | even | 1 | trivial | |
210.2.m.b.13.1 | yes | 8 | 5.3 | odd | 4 | ||
210.2.m.b.97.1 | yes | 8 | 7.6 | odd | 2 | ||
630.2.p.b.307.3 | 8 | 3.2 | odd | 2 | |||
630.2.p.b.433.3 | 8 | 105.83 | odd | 4 | |||
630.2.p.c.307.4 | 8 | 21.20 | even | 2 | |||
630.2.p.c.433.4 | 8 | 15.8 | even | 4 | |||
1050.2.m.a.307.3 | 8 | 35.34 | odd | 2 | |||
1050.2.m.a.643.3 | 8 | 5.2 | odd | 4 | |||
1050.2.m.b.307.4 | 8 | 5.4 | even | 2 | |||
1050.2.m.b.643.4 | 8 | 35.27 | even | 4 | |||
1680.2.cz.a.97.1 | 8 | 28.27 | even | 2 | |||
1680.2.cz.a.433.1 | 8 | 20.3 | even | 4 | |||
1680.2.cz.b.97.4 | 8 | 4.3 | odd | 2 | |||
1680.2.cz.b.433.4 | 8 | 140.83 | odd | 4 |