Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(17,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 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("560.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.ci (of order \(12\), degree \(4\), not 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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 353.1 | ||
Root | \(-0.144868 + 1.25092i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.353 |
Dual form | 560.2.ci.c.257.1 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.523277 | − | 1.95290i | −0.302114 | − | 1.12751i | −0.935401 | − | 0.353588i | \(-0.884961\pi\) |
0.633287 | − | 0.773917i | \(-0.281705\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.03078 | + | 0.935904i | −0.908194 | + | 0.418549i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.83959 | − | 1.90155i | −0.695300 | − | 0.718719i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.941911 | + | 0.543813i | −0.313970 | + | 0.181271i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.01999 | + | 3.49872i | −0.609049 | + | 1.05490i | 0.382349 | + | 0.924018i | \(0.375115\pi\) |
−0.991397 | + | 0.130886i | \(0.958218\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.204875 | − | 0.204875i | 0.0568221 | − | 0.0568221i | −0.678125 | − | 0.734947i | \(-0.737207\pi\) |
0.734947 | + | 0.678125i | \(0.237207\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.89039 | + | 3.47617i | 0.746295 | + | 0.897544i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.97024 | + | 0.527924i | −0.477853 | + | 0.128040i | −0.489703 | − | 0.871890i | \(-0.662895\pi\) |
0.0118498 | + | 0.999930i | \(0.496228\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.10166 | + | 5.37224i | 0.711571 | + | 1.23248i | 0.964267 | + | 0.264931i | \(0.0853491\pi\) |
−0.252697 | + | 0.967545i | \(0.581318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.75092 | + | 4.58757i | −0.600300 | + | 1.00109i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.17456 | + | 4.38350i | −0.244912 | + | 0.914023i | 0.728516 | + | 0.685029i | \(0.240210\pi\) |
−0.973428 | + | 0.228994i | \(0.926456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.24817 | − | 3.80124i | 0.649633 | − | 0.760248i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.73397 | − | 2.73397i | −0.526152 | − | 0.526152i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.15869i | 1.32934i | 0.747139 | + | 0.664668i | \(0.231427\pi\) | ||||
−0.747139 | + | 0.664668i | \(0.768573\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.33287 | − | 3.65628i | −1.13742 | − | 0.656688i | −0.191627 | − | 0.981468i | \(-0.561376\pi\) |
−0.945790 | + | 0.324780i | \(0.894710\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.88965 | + | 2.11403i | 1.37341 | + | 0.368005i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.51548 | + | 2.13996i | 0.932287 | + | 0.361719i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.46814 | − | 1.19723i | −0.734558 | − | 0.196824i | −0.127900 | − | 0.991787i | \(-0.540824\pi\) |
−0.606658 | + | 0.794963i | \(0.707490\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.507306 | − | 0.292893i | −0.0812340 | − | 0.0469005i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.58745i | − | 0.404093i | −0.979376 | − | 0.202046i | \(-0.935241\pi\) | ||
0.979376 | − | 0.202046i | \(-0.0647591\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.97801 | + | 4.97801i | 0.759140 | + | 0.759140i | 0.976166 | − | 0.217026i | \(-0.0696356\pi\) |
−0.217026 | + | 0.976166i | \(0.569636\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.40386 | − | 1.98590i | 0.209275 | − | 0.296041i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0815604 | − | 0.304388i | 0.0118968 | − | 0.0443995i | −0.959722 | − | 0.280950i | \(-0.909350\pi\) |
0.971619 | + | 0.236551i | \(0.0760170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.231803 | + | 6.99616i | −0.0331148 | + | 0.999452i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.06196 | + | 3.57142i | 0.288732 | + | 0.500099i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.00039 | + | 2.14370i | −1.09894 | + | 0.294460i | −0.762332 | − | 0.647186i | \(-0.775946\pi\) |
−0.336606 | + | 0.941646i | \(0.609279\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.827689 | − | 8.99566i | 0.111606 | − | 1.21297i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.86840 | − | 8.86840i | 1.17465 | − | 1.17465i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.427702 | + | 0.740802i | −0.0556821 | + | 0.0964442i | −0.892523 | − | 0.451002i | \(-0.851067\pi\) |
0.836841 | + | 0.547446i | \(0.184400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.99356 | + | 3.46038i | −0.767397 | + | 0.443057i | −0.831945 | − | 0.554858i | \(-0.812773\pi\) |
0.0645484 | + | 0.997915i | \(0.479439\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.76682 | + | 0.790700i | 0.348587 | + | 0.0996189i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.224313 | + | 0.607800i | −0.0278226 | + | 0.0753883i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.817530 | + | 3.05106i | 0.0998772 | + | 0.372747i | 0.997714 | − | 0.0675822i | \(-0.0215285\pi\) |
−0.897837 | + | 0.440329i | \(0.854862\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.17514 | 1.10456 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.12240 | −0.845273 | −0.422637 | − | 0.906299i | \(-0.638895\pi\) | ||||
−0.422637 | + | 0.906299i | \(0.638895\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.98311 | − | 11.1331i | −0.349147 | − | 1.30303i | −0.887692 | − | 0.460438i | \(-0.847693\pi\) |
0.538545 | − | 0.842597i | \(-0.318974\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.12312 | − | 4.35423i | −1.05345 | − | 0.502783i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.3690 | − | 2.59511i | 1.18165 | − | 0.295740i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.39618 | − | 2.53813i | 0.494609 | − | 0.285562i | −0.231876 | − | 0.972745i | \(-0.574486\pi\) |
0.726484 | + | 0.687183i | \(0.241153\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.53997 | + | 9.59552i | −0.615553 | + | 1.06617i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.85372 | − | 3.85372i | 0.423001 | − | 0.423001i | −0.463235 | − | 0.886236i | \(-0.653311\pi\) |
0.886236 | + | 0.463235i | \(0.153311\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.50704 | − | 2.91605i | 0.380392 | − | 0.316290i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.9802 | − | 3.74598i | 1.49883 | − | 0.401611i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.53615 | − | 2.66069i | −0.162832 | − | 0.282033i | 0.773051 | − | 0.634343i | \(-0.218729\pi\) |
−0.935883 | + | 0.352310i | \(0.885396\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.766467 | − | 0.0126942i | −0.0803475 | − | 0.00133071i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.82650 | + | 14.2807i | −0.396789 | + | 1.48084i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.3267 | − | 8.00700i | −1.16210 | − | 0.821501i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.63103 | − | 6.63103i | −0.673279 | − | 0.673279i | 0.285191 | − | 0.958471i | \(-0.407943\pi\) |
−0.958471 | + | 0.285191i | \(0.907943\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.39398i | − | 0.441611i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.56364 | − | 4.94422i | −0.852114 | − | 0.491968i | 0.00924966 | − | 0.999957i | \(-0.497056\pi\) |
−0.861364 | + | 0.507989i | \(0.830389\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.13612 | − | 1.10827i | −0.407544 | − | 0.109201i | 0.0492221 | − | 0.998788i | \(-0.484326\pi\) |
−0.456766 | + | 0.889587i | \(0.650992\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.29299 | − | 11.8910i | 0.126183 | − | 1.16044i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.3653 | − | 3.84918i | −1.38875 | − | 0.372114i | −0.514457 | − | 0.857516i | \(-0.672007\pi\) |
−0.874291 | + | 0.485402i | \(0.838673\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.4586 | − | 6.61564i | −1.09754 | − | 0.633664i | −0.161964 | − | 0.986797i | \(-0.551783\pi\) |
−0.935573 | + | 0.353133i | \(0.885116\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.35230i | 0.887681i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.75336 | + | 9.75336i | 0.917519 | + | 0.917519i | 0.996848 | − | 0.0793296i | \(-0.0252780\pi\) |
−0.0793296 | + | 0.996848i | \(0.525278\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.71727 | − | 10.0012i | −0.160136 | − | 0.932618i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.0815604 | + | 0.304388i | −0.00754026 | + | 0.0281406i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.62831 | + | 2.77535i | 0.424276 | + | 0.254416i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.66069 | − | 4.60846i | −0.241881 | − | 0.418951i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.05303 | + | 1.35396i | −0.455617 | + | 0.122082i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.03873 | + | 10.7595i | −0.271792 | + | 0.962356i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.19984 | − | 2.19984i | 0.195204 | − | 0.195204i | −0.602736 | − | 0.797940i | \(-0.705923\pi\) |
0.797940 | + | 0.602736i | \(0.205923\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.11667 | − | 12.3264i | 0.626587 | − | 1.08528i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.32091 | − | 3.64938i | 0.552260 | − | 0.318848i | −0.197773 | − | 0.980248i | \(-0.563371\pi\) |
0.750033 | + | 0.661400i | \(0.230037\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.50980 | − | 15.7807i | 0.391049 | − | 1.36836i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.11083 | + | 2.99337i | 0.698069 | + | 0.257628i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.85804 | + | 6.93431i | 0.158743 | + | 0.592438i | 0.998756 | + | 0.0498710i | \(0.0158810\pi\) |
−0.840012 | + | 0.542567i | \(0.817452\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.4172 | −1.05321 | −0.526605 | − | 0.850110i | \(-0.676535\pi\) | ||||
−0.526605 | + | 0.850110i | \(0.676535\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.637116 | −0.0536549 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.302955 | + | 1.13064i | 0.0253344 | + | 0.0945492i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.69985 | − | 14.5378i | −0.556392 | − | 1.20730i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.7841 | − | 3.20824i | 1.13689 | − | 0.264611i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.7399 | − | 11.9742i | 1.69908 | − | 0.980963i | 0.752440 | − | 0.658661i | \(-0.228877\pi\) |
0.946637 | − | 0.322302i | \(-0.104457\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.77167 | + | 3.06862i | −0.144176 | + | 0.249721i | −0.929065 | − | 0.369916i | \(-0.879387\pi\) |
0.784889 | + | 0.619636i | \(0.212720\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.56870 | − | 1.56870i | 0.126822 | − | 0.126822i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.2826 | + | 1.49816i | 1.30785 | + | 0.120335i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.91389 | + | 1.58462i | −0.471980 | + | 0.126467i | −0.486966 | − | 0.873421i | \(-0.661896\pi\) |
0.0149859 | + | 0.999888i | \(0.495230\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.37284 | + | 14.5022i | 0.664010 | + | 1.15010i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.4962 | − | 5.83037i | 0.827213 | − | 0.459498i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.28549 | − | 15.9937i | 0.335666 | − | 1.25272i | −0.567480 | − | 0.823387i | \(-0.692082\pi\) |
0.903146 | − | 0.429334i | \(-0.141252\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18.0007 | + | 3.09083i | −1.40135 | + | 0.240621i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.2873 | + | 10.2873i | 0.796056 | + | 0.796056i | 0.982471 | − | 0.186415i | \(-0.0596869\pi\) |
−0.186415 | + | 0.982471i | \(0.559687\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9161i | 0.993543i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.84298 | − | 3.37345i | −0.446824 | − | 0.257974i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.50720 | + | 2.01155i | 0.570762 | + | 0.152935i | 0.532646 | − | 0.846338i | \(-0.321198\pi\) |
0.0381159 | + | 0.999273i | \(0.487864\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.2036 | + | 0.816171i | −0.998095 | + | 0.0616967i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.67052 | + | 0.447613i | 0.125564 | + | 0.0336447i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.34695 | − | 1.93236i | −0.250163 | − | 0.144431i | 0.369676 | − | 0.929161i | \(-0.379469\pi\) |
−0.619839 | + | 0.784729i | \(0.712802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.99107i | 0.519642i | 0.965657 | + | 0.259821i | \(0.0836636\pi\) | ||||
−0.965657 | + | 0.259821i | \(0.916336\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.89407 | + | 9.89407i | 0.731390 | + | 0.731390i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.1943 | − | 1.75043i | 0.749502 | − | 0.128694i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.13280 | − | 7.95971i | 0.155966 | − | 0.582071i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.169398 | + | 10.2282i | −0.0123219 | + | 0.743990i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.23721 | + | 3.87496i | 0.161879 | + | 0.280383i | 0.935543 | − | 0.353214i | \(-0.114911\pi\) |
−0.773664 | + | 0.633597i | \(0.781578\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.3907 | − | 5.19573i | 1.39577 | − | 0.373997i | 0.518949 | − | 0.854805i | \(-0.326324\pi\) |
0.876825 | + | 0.480809i | \(0.159657\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.30435 | + | 0.120013i | 0.0934064 | + | 0.00859431i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.84901 | + | 7.84901i | −0.559219 | + | 0.559219i | −0.929085 | − | 0.369866i | \(-0.879404\pi\) |
0.369866 | + | 0.929085i | \(0.379404\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.40103 | − | 9.35485i | 0.382869 | − | 0.663148i | −0.608602 | − | 0.793475i | \(-0.708270\pi\) |
0.991471 | + | 0.130327i | \(0.0416028\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.53062 | − | 3.19310i | 0.390100 | − | 0.225224i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.6126 | − | 13.1691i | 0.955419 | − | 0.924288i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.42161 | + | 5.25456i | 0.169133 | + | 0.366995i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.27748 | − | 4.76761i | −0.0887908 | − | 0.331372i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −25.0613 | −1.73353 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.56555 | −0.520834 | −0.260417 | − | 0.965496i | \(-0.583860\pi\) | ||||
−0.260417 | + | 0.965496i | \(0.583860\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.72699 | + | 13.9093i | 0.255369 | + | 0.953050i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.7682 | − | 5.45032i | −1.00718 | − | 0.371709i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.69728 | + | 18.7683i | 0.318872 | + | 1.27408i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.1809 | + | 11.6514i | −1.36370 | + | 0.787330i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.295494 | + | 0.511811i | −0.0198771 | + | 0.0344281i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.35230 | + | 9.35230i | −0.626277 | + | 0.626277i | −0.947129 | − | 0.320853i | \(-0.896031\pi\) |
0.320853 | + | 0.947129i | \(0.396031\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.992322 | + | 5.34682i | −0.0661548 | + | 0.356455i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.6420 | + | 4.19127i | −1.03820 | + | 0.278184i | −0.737367 | − | 0.675493i | \(-0.763931\pi\) |
−0.300832 | + | 0.953677i | \(0.597264\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.88820 | + | 10.1987i | 0.389103 | + | 0.673947i | 0.992329 | − | 0.123624i | \(-0.0394515\pi\) |
−0.603226 | + | 0.797570i | \(0.706118\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.4938 | − | 18.8915i | −0.690442 | − | 1.24297i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.48154 | + | 5.52920i | −0.0970591 | + | 0.362230i | −0.997324 | − | 0.0731138i | \(-0.976706\pi\) |
0.900264 | + | 0.435343i | \(0.143373\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.119246 | + | 0.694478i | 0.00777876 | + | 0.0453028i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.25713 | − | 7.25713i | −0.471402 | − | 0.471402i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.33794i | 0.539337i | 0.962953 | + | 0.269668i | \(0.0869141\pi\) | ||||
−0.962953 | + | 0.269668i | \(0.913086\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.56723 | + | 1.48219i | 0.165370 | + | 0.0954763i | 0.580401 | − | 0.814331i | \(-0.302896\pi\) |
−0.415031 | + | 0.909807i | \(0.636229\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.4340 | + | 2.79578i | 0.669340 | + | 0.179349i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.07700 | − | 14.4246i | −0.388245 | − | 0.921556i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.73609 | + | 0.465184i | 0.110465 | + | 0.0295989i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.54248 | − | 5.50936i | −0.604730 | − | 0.349141i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.1800i | 1.02127i | 0.859796 | + | 0.510637i | \(0.170590\pi\) | ||||
−0.859796 | + | 0.510637i | \(0.829410\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.9641 | − | 12.9641i | −0.815043 | − | 0.815043i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.52990 | − | 5.32298i | −0.471541 | − | 0.333338i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.50754 | + | 5.62621i | −0.0940377 | + | 0.350954i | −0.996872 | − | 0.0790355i | \(-0.974816\pi\) |
0.902834 | + | 0.429989i | \(0.141483\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.94295 | + | 10.6988i | 0.369277 | + | 0.664793i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.89299 | − | 6.74285i | −0.240970 | − | 0.417372i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.67793 | − | 0.449601i | 0.103466 | − | 0.0277236i | −0.206715 | − | 0.978401i | \(-0.566277\pi\) |
0.310180 | + | 0.950678i | \(0.399611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.2408 | − | 11.8410i | 0.874803 | − | 0.727386i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.39223 | + | 4.39223i | −0.268800 | + | 0.268800i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.89169 | + | 3.27650i | −0.115338 | + | 0.199772i | −0.917915 | − | 0.396777i | \(-0.870128\pi\) |
0.802577 | + | 0.596549i | \(0.203462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4029 | − | 10.6249i | 1.11789 | − | 0.645416i | 0.177032 | − | 0.984205i | \(-0.443351\pi\) |
0.940862 | + | 0.338789i | \(0.110017\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.376284 | + | 1.50347i | 0.0227737 | + | 0.0909943i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.73822 | + | 19.0429i | 0.406330 | + | 1.14833i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.26567 | − | 4.72353i | −0.0760465 | − | 0.283810i | 0.917422 | − | 0.397916i | \(-0.130266\pi\) |
−0.993469 | + | 0.114106i | \(0.963600\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.95333 | 0.476153 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.4776 | −1.75849 | −0.879243 | − | 0.476373i | \(-0.841951\pi\) | ||||
−0.879243 | + | 0.476373i | \(0.841951\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.92041 | + | 10.8991i | 0.173601 | + | 0.647886i | 0.996786 | + | 0.0801133i | \(0.0255282\pi\) |
−0.823185 | + | 0.567773i | \(0.807805\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.70983 | + | 26.3098i | −0.575161 | + | 1.55846i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.92018 | + | 4.75986i | −0.290429 | + | 0.280966i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.1193 | + | 6.41973i | −0.654076 | + | 0.377631i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.47985 | + | 16.4196i | −0.555719 | + | 0.962533i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.23407 | + | 7.23407i | −0.422619 | + | 0.422619i | −0.886105 | − | 0.463485i | \(-0.846599\pi\) |
0.463485 | + | 0.886105i | \(0.346599\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.175251 | − | 1.90470i | 0.0102035 | − | 0.110896i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.0880 | − | 4.04281i | 0.875493 | − | 0.234588i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.657432 | + | 1.13871i | 0.0380203 | + | 0.0658531i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.308440 | − | 18.6235i | 0.0177782 | − | 1.07344i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.17439 | + | 19.3111i | −0.297261 | + | 1.10939i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.93304 | − | 12.6367i | 0.511504 | − | 0.723575i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.07859 | + | 1.07859i | 0.0615584 | + | 0.0615584i | 0.737216 | − | 0.675657i | \(-0.236140\pi\) |
−0.675657 | + | 0.737216i | \(0.736140\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.65735i | 0.492500i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.33830 | + | 4.81412i | 0.472821 | + | 0.272984i | 0.717420 | − | 0.696641i | \(-0.245323\pi\) |
−0.244599 | + | 0.969624i | \(0.578656\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.92361 | + | 0.783378i | 0.165252 | + | 0.0442791i | 0.340496 | − | 0.940246i | \(-0.389405\pi\) |
−0.175244 | + | 0.984525i | \(0.556072\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.35883 | + | 0.983739i | −0.358280 | + | 0.0554274i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.88227 | − | 0.504353i | −0.105719 | − | 0.0283273i | 0.205572 | − | 0.978642i | \(-0.434095\pi\) |
−0.311291 | + | 0.950315i | \(0.600761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.0463 | − | 14.4605i | −1.40232 | − | 0.809631i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.0682i | 1.67824i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.94715 | − | 8.94715i | −0.497833 | − | 0.497833i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.113311 | − | 1.44425i | −0.00628535 | − | 0.0801124i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.92363 | + | 25.8393i | −0.382878 | + | 1.42892i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.728847 | + | 0.404858i | −0.0401826 | + | 0.0223205i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4468 | − | 25.0225i | −0.794066 | − | 1.37536i | −0.923431 | − | 0.383765i | \(-0.874627\pi\) |
0.129365 | − | 0.991597i | \(-0.458706\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.85966 | − | 1.30214i | 0.266308 | − | 0.0713570i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.51573 | − | 5.43092i | −0.246721 | − | 0.296723i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.823226 | + | 0.823226i | −0.0448440 | + | 0.0448440i | −0.729173 | − | 0.684329i | \(-0.760095\pi\) |
0.684329 | + | 0.729173i | \(0.260095\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.9436 | − | 24.1510i | 0.757312 | − | 1.31170i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.5846 | − | 14.7713i | 1.38548 | − | 0.799910i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.7300 | − | 12.4293i | 0.741350 | − | 0.671119i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.6327 | + | 8.58706i | −1.00315 | + | 0.462312i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.32336 | + | 16.1350i | 0.232090 | + | 0.866172i | 0.979439 | + | 0.201740i | \(0.0646597\pi\) |
−0.747349 | + | 0.664432i | \(0.768674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.7146 | 1.96529 | 0.982644 | − | 0.185503i | \(-0.0593916\pi\) | ||||
0.982644 | + | 0.185503i | \(0.0593916\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.12024 | −0.0597942 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.69356 | − | 13.7845i | −0.196588 | − | 0.733677i | −0.991850 | − | 0.127411i | \(-0.959333\pi\) |
0.795262 | − | 0.606266i | \(-0.207333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.4640 | − | 6.66588i | 0.767672 | − | 0.353788i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.99808 | − | 10.4909i | 0.158675 | − | 0.555236i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.4596 | − | 13.5444i | 1.23815 | − | 0.714847i | 0.269435 | − | 0.963019i | \(-0.413163\pi\) |
0.968716 | + | 0.248172i | \(0.0798298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.74064 | + | 16.8713i | −0.512665 | + | 0.887962i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.60756 | + | 7.60756i | −0.399293 | + | 0.399293i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.4776 | + | 19.8171i | 0.862477 | + | 1.03727i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.8990 | + | 5.86782i | −1.14312 | + | 0.306298i | −0.780204 | − | 0.625525i | \(-0.784885\pi\) |
−0.362914 | + | 0.931823i | \(0.618218\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.40709 | + | 2.43715i | 0.0732502 | + | 0.126873i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.7938 | + | 11.2696i | 0.975726 | + | 0.585090i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.32215 | + | 12.3984i | −0.172014 | + | 0.641966i | 0.825027 | + | 0.565094i | \(0.191160\pi\) |
−0.997041 | + | 0.0768720i | \(0.975507\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 22.6022 | + | 0.304135i | 1.16717 | + | 0.0157055i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.46664 | + | 1.46664i | 0.0755356 | + | 0.0755356i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4739i | 0.743476i | 0.928338 | + | 0.371738i | \(0.121238\pi\) | ||||
−0.928338 | + | 0.371738i | \(0.878762\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.44718 | − | 3.14493i | −0.279068 | − | 0.161120i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.69189 | − | 0.453341i | −0.0864517 | − | 0.0231647i | 0.215334 | − | 0.976540i | \(-0.430916\pi\) |
−0.301786 | + | 0.953376i | \(0.597583\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.6283 | + | 14.9744i | −0.949387 | + | 0.763168i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.39595 | − | 1.98174i | −0.375957 | − | 0.100737i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.40954 | − | 1.39115i | −0.122169 | − | 0.0705341i | 0.437670 | − | 0.899135i | \(-0.355804\pi\) |
−0.559839 | + | 0.828601i | \(0.689137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9.25661i | − | 0.468127i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.4344 | − | 10.4344i | −0.526348 | − | 0.526348i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.55224 | + | 9.26881i | −0.329679 | + | 0.466364i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.2668 | − | 38.3163i | 0.515277 | − | 1.92304i | 0.165486 | − | 0.986212i | \(-0.447081\pi\) |
0.349791 | − | 0.936828i | \(-0.386253\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −33.1780 | − | 0.549491i | −1.66098 | − | 0.0275089i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.98528 | + | 17.2950i | 0.498641 | + | 0.863672i | 0.999999 | − | 0.00156835i | \(-0.000499221\pi\) |
−0.501358 | + | 0.865240i | \(0.667166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.04653 | + | 0.548365i | −0.101945 | + | 0.0273160i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.27000 | − | 24.6713i | 0.112797 | − | 1.22593i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.2144 | − | 13.2144i | 0.655012 | − | 0.655012i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.65280 | + | 13.2550i | −0.378407 | + | 0.655419i | −0.990831 | − | 0.135110i | \(-0.956861\pi\) |
0.612424 | + | 0.790529i | \(0.290195\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.5697 | − | 7.25713i | 0.620019 | − | 0.357968i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.19547 | − | 0.549475i | 0.108032 | − | 0.0270379i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.21936 | + | 11.4328i | −0.207120 | + | 0.561214i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.49762 | + | 24.2495i | 0.318190 | + | 1.18750i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.7027 | 1.35337 | 0.676684 | − | 0.736274i | \(-0.263416\pi\) | ||||
0.676684 | + | 0.736274i | \(0.263416\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.0159 | 1.60910 | 0.804549 | − | 0.593887i | \(-0.202407\pi\) | ||||
0.804549 | + | 0.593887i | \(0.202407\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.0887072 | + | 0.331060i | 0.00431309 | + | 0.0160967i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.39289 | + | 9.20413i | −0.213087 | + | 0.446466i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.6058 | + | 5.03138i | 0.852005 | + | 0.243485i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.04950 | − | 1.18328i | 0.0989509 | − | 0.0571293i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.9586 | − | 20.7129i | 0.576027 | − | 0.997708i | −0.419902 | − | 0.907569i | \(-0.637936\pi\) |
0.995929 | − | 0.0901384i | \(-0.0287309\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.2515 | + | 13.2515i | −0.636829 | + | 0.636829i | −0.949772 | − | 0.312943i | \(-0.898685\pi\) |
0.312943 | + | 0.949772i | \(0.398685\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −24.8849 | + | 20.6914i | −1.19314 | + | 0.992077i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.1923 | + | 7.28615i | −1.30078 | + | 0.348544i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.05383 | + | 12.2176i | 0.336661 | + | 0.583114i | 0.983802 | − | 0.179256i | \(-0.0573690\pi\) |
−0.647141 | + | 0.762370i | \(0.724036\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.58626 | − | 6.71582i | −0.170774 | − | 0.319801i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.45161 | + | 20.3457i | −0.259014 | + | 0.966652i | 0.706800 | + | 0.707414i | \(0.250138\pi\) |
−0.965813 | + | 0.259238i | \(0.916528\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.60975 | + | 3.96560i | 0.265928 | + | 0.187988i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −34.2370 | − | 34.2370i | −1.61936 | − | 1.61936i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 31.3247i | − | 1.47831i | −0.673538 | − | 0.739153i | \(-0.735226\pi\) | ||
0.673538 | − | 0.739153i | \(-0.264774\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.05278 | + | 5.22662i | 0.426279 | + | 0.246112i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.91977 | + | 1.85415i | 0.325119 | + | 0.0871154i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.56841 | − | 0.691560i | 0.0735281 | − | 0.0324209i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.76404 | + | 0.740622i | 0.129296 | + | 0.0346448i | 0.322887 | − | 0.946438i | \(-0.395347\pi\) |
−0.193591 | + | 0.981082i | \(0.562013\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.82989 | + | 3.94324i | 0.318792 | + | 0.184055i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.02674i | 0.140969i | 0.997513 | + | 0.0704846i | \(0.0224546\pi\) | ||||
−0.997513 | + | 0.0704846i | \(0.977545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.2889 | − | 19.2889i | −0.896431 | − | 0.896431i | 0.0986876 | − | 0.995118i | \(-0.468536\pi\) |
−0.995118 | + | 0.0986876i | \(0.968536\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.59457 | − | 32.5822i | −0.259442 | − | 1.51096i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.50385 | − | 24.2727i | 0.300962 | − | 1.12321i | −0.635403 | − | 0.772180i | \(-0.719166\pi\) |
0.936366 | − | 0.351026i | \(-0.114167\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.29784 | − | 7.16729i | 0.198456 | − | 0.330955i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.18921 | + | 10.7200i | 0.285184 | + | 0.493953i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.4722 | + | 7.36115i | −1.26317 | + | 0.338466i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.4959 | + | 5.65976i | 1.39925 | + | 0.259688i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.36989 | − | 6.36989i | 0.291657 | − | 0.291657i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.14346 | − | 7.17668i | 0.189319 | − | 0.327911i | −0.755704 | − | 0.654913i | \(-0.772705\pi\) |
0.945024 | + | 0.327002i | \(0.106039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.16069 | + | 0.670127i | −0.0529231 | + | 0.0305551i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.8785 | − | 17.4470i | −0.767999 | − | 0.793867i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.6722 | + | 7.26018i | 0.893269 | + | 0.329668i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.76375 | − | 10.3144i | −0.125237 | − | 0.467392i | 0.874611 | − | 0.484826i | \(-0.161117\pi\) |
−0.999848 | + | 0.0174340i | \(0.994450\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −33.4765 | −1.51386 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.7259 | −1.16100 | −0.580498 | − | 0.814262i | \(-0.697142\pi\) | ||||
−0.580498 | + | 0.814262i | \(0.697142\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.77924 | − | 14.1043i | −0.170209 | − | 0.635227i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.11234 | + | 8.92322i | 0.184836 | + | 0.401069i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.1023 | + | 13.5436i | 0.587719 | + | 0.607514i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.6429 | − | 7.29940i | 0.565975 | − | 0.326766i | −0.189565 | − | 0.981868i | \(-0.560708\pi\) |
0.755540 | + | 0.655102i | \(0.227374\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.7069 | − | 25.4732i | 0.657058 | − | 1.13806i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.9891 | + | 13.9891i | −0.623744 | + | 0.623744i | −0.946487 | − | 0.322743i | \(-0.895395\pi\) |
0.322743 | + | 0.946487i | \(0.395395\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.0182 | + | 2.02589i | 0.979798 | + | 0.0901510i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.2237 | − | 6.75868i | 1.12022 | − | 0.300163i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.42883 | + | 2.47481i | 0.0633319 | + | 0.109694i | 0.895953 | − | 0.444149i | \(-0.146494\pi\) |
−0.832621 | + | 0.553843i | \(0.813161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.6825 | + | 26.1530i | −0.693754 | + | 1.15694i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.20768 | − | 23.1674i | 0.274076 | − | 1.02287i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.43680 | − | 1.62036i | 0.415835 | − | 0.0714015i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.900216 | + | 0.900216i | 0.0395914 | + | 0.0395914i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 15.7134i | − | 0.689741i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.7917 | + | 14.3135i | 1.08614 | + | 0.627084i | 0.932547 | − | 0.361049i | \(-0.117581\pi\) |
0.153595 | + | 0.988134i | \(0.450915\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.5069 | − | 8.17429i | −1.33397 | − | 0.357437i | −0.479777 | − | 0.877390i | \(-0.659283\pi\) |
−0.854195 | + | 0.519954i | \(0.825949\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.50302 | + | 25.3581i | 0.371102 | + | 1.10672i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.4075 | + | 3.86048i | 0.627600 | + | 0.168165i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.08308 | + | 1.20267i | 0.0905687 | + | 0.0522899i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 0.930359i | − | 0.0403742i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.530105 | − | 0.530105i | −0.0229614 | − | 0.0229614i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.7753 | − | 5.62772i | 1.41700 | − | 0.243308i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.02232 | + | 7.54741i | −0.0872696 | + | 0.325695i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.0094 | − | 14.9432i | −1.03416 | − | 0.643648i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.4994 | − | 32.0420i | −0.795353 | − | 1.37759i | −0.922615 | − | 0.385722i | \(-0.873952\pi\) |
0.127262 | − | 0.991869i | \(-0.459381\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.6528 | − | 3.65827i | 0.585899 | − | 0.156991i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.4616 | + | 2.71076i | 1.26200 | + | 0.116116i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0765 | − | 20.0765i | 0.858409 | − | 0.858409i | −0.132742 | − | 0.991151i | \(-0.542378\pi\) |
0.991151 | + | 0.132742i | \(0.0423781\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.76360 | − | 6.51875i | 0.160627 | − | 0.278213i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.4582 | + | 22.2039i | −1.63838 | + | 0.945916i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9136 | − | 3.69043i | −0.549141 | − | 0.156933i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.75286 | − | 18.9925i | −0.371538 | − | 0.806187i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.65499 | − | 24.8367i | −0.281981 | − | 1.05237i | −0.951017 | − | 0.309137i | \(-0.899960\pi\) |
0.669037 | − | 0.743229i | \(-0.266707\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.03974 | 0.0862718 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.6605 | −0.703408 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.38907 | − | 5.18407i | −0.0585422 | − | 0.218482i | 0.930458 | − | 0.366400i | \(-0.119410\pi\) |
−0.989000 | + | 0.147917i | \(0.952743\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.9352 | − | 10.6788i | −1.21731 | − | 0.449258i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 28.4377 | − | 7.11728i | 1.19427 | − | 0.298898i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.0839 | − | 12.7502i | 0.925806 | − | 0.534514i | 0.0403234 | − | 0.999187i | \(-0.487161\pi\) |
0.885483 | + | 0.464672i | \(0.153828\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.95235 | − | 13.7739i | 0.332795 | − | 0.576419i | −0.650263 | − | 0.759709i | \(-0.725341\pi\) |
0.983059 | + | 0.183290i | \(0.0586748\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.39672 | − | 6.39672i | 0.267227 | − | 0.267227i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.8476 | + | 18.7031i | 0.535781 | + | 0.779973i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.2641 | + | 5.96565i | −0.926867 | + | 0.248353i | −0.690518 | − | 0.723315i | \(-0.742617\pi\) |
−0.236349 | + | 0.971668i | \(0.575951\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.2934 | − | 35.1493i | −0.843366 | − | 1.46075i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.4173 | − | 0.238779i | −0.598132 | − | 0.00990621i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.66048 | − | 32.3214i | 0.358681 | − | 1.33861i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.119246 | − | 0.694478i | −0.00493022 | − | 0.0287131i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.2277 | − | 28.2277i | −1.16508 | − | 1.16508i | −0.983348 | − | 0.181734i | \(-0.941829\pi\) |
−0.181734 | − | 0.983348i | \(-0.558171\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 45.3622i | − | 1.86912i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.4355 | + | 11.2211i | 0.799471 | + | 0.461575i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.2220 | − | 9.16977i | −1.40533 | − | 0.376557i | −0.525075 | − | 0.851056i | \(-0.675963\pi\) |
−0.880256 | + | 0.474499i | \(0.842629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.9965 | − | 1.30447i | −0.491811 | − | 0.0534782i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.0953 | − | 5.65247i | −0.863373 | − | 0.231340i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.5339 | − | 8.39115i | −0.593839 | − | 0.342853i | 0.172775 | − | 0.984961i | \(-0.444727\pi\) |
−0.766614 | + | 0.642108i | \(0.778060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.73528i | 0.0707833i | 0.999374 | + | 0.0353917i | \(0.0112679\pi\) | ||||
−0.999374 | + | 0.0353917i | \(0.988732\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.42925 | − | 2.42925i | −0.0989266 | − | 0.0989266i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.71637 | + | 6.86862i | 0.395027 | + | 0.279249i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.2070 | + | 38.0930i | −0.414288 | + | 1.54615i | 0.371968 | + | 0.928245i | \(0.378683\pi\) |
−0.786257 | + | 0.617900i | \(0.787984\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −32.8410 | − | 19.6930i | −1.33079 | − | 0.798000i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0456517 | − | 0.0790711i | −0.00184687 | − | 0.00319887i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.330293 | + | 0.0885018i | −0.0133404 | + | 0.00357455i | −0.265483 | − | 0.964116i | \(-0.585531\pi\) |
0.252143 | + | 0.967690i | \(0.418865\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.99444 | − | 7.47875i | 0.362691 | − | 0.301572i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.1876 | − | 11.1876i | 0.450397 | − | 0.450397i | −0.445089 | − | 0.895486i | \(-0.646828\pi\) |
0.895486 | + | 0.445089i | \(0.146828\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.2682 | + | 31.6414i | −0.734260 | + | 1.27178i | 0.220787 | + | 0.975322i | \(0.429138\pi\) |
−0.955047 | + | 0.296454i | \(0.904196\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.1956 | − | 8.77316i | 0.609777 | − | 0.352055i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.23356 | + | 7.81566i | −0.0894855 | + | 0.313128i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.89884 | − | 24.6941i | −0.155953 | − | 0.987764i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.1140 | + | 48.9421i | 0.523723 | + | 1.95456i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.43535 | 0.376212 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.8189 | 1.42593 | 0.712964 | − | 0.701201i | \(-0.247352\pi\) | ||||
0.712964 | + | 0.701201i | \(0.247352\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.95888 | + | 14.7747i | 0.157351 | + | 0.587243i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.40856 | + | 6.52623i | −0.0955807 | + | 0.258986i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.38585 | + | 1.48083i | 0.0549093 | + | 0.0586726i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.70867 | − | 3.87325i | 0.265391 | − | 0.153223i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.16573 | − | 12.4114i | 0.283029 | − | 0.490221i | −0.689100 | − | 0.724666i | \(-0.741994\pi\) |
0.972129 | + | 0.234445i | \(0.0753272\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.65201 | + | 7.65201i | −0.301766 | + | 0.301766i | −0.841704 | − | 0.539939i | \(-0.818447\pi\) |
0.539939 | + | 0.841704i | \(0.318447\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.91605 | + | 31.6928i | −0.114819 | + | 1.24790i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.2468 | + | 8.37254i | −1.22844 | + | 0.329159i | −0.813971 | − | 0.580906i | \(-0.802698\pi\) |
−0.414466 | + | 0.910065i | \(0.636032\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.72791 | − | 2.99282i | −0.0678262 | − | 0.117478i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 34.1947 | − | 18.9943i | 1.34019 | − | 0.744447i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.132578 | + | 0.494788i | −0.00518818 | + | 0.0193625i | −0.968471 | − | 0.249125i | \(-0.919857\pi\) |
0.963283 | + | 0.268487i | \(0.0865237\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.42093 | + | 13.3269i | −0.368106 | + | 0.520724i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.86417 | + | 8.86417i | 0.345824 | + | 0.345824i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.5542i | 0.761723i | 0.924632 | + | 0.380862i | \(0.124373\pi\) | ||||
−0.924632 | + | 0.380862i | \(0.875627\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.0324 | + | 19.6486i | 1.32371 | + | 0.764242i | 0.984318 | − | 0.176405i | \(-0.0564468\pi\) |
0.339388 | + | 0.940647i | \(0.389780\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.15414 | + | 0.309250i | 0.0448230 | + | 0.0120103i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.61080 | + | 36.2679i | 0.217578 | + | 1.40641i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.3801 | − | 8.40828i | −1.21504 | − | 0.325570i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.1579 | + | 13.3702i | 0.895337 | + | 0.516923i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 27.9597i | − | 1.07937i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.4813 | + | 18.4813i | 0.712401 | + | 0.712401i | 0.967037 | − | 0.254636i | \(-0.0819556\pi\) |
−0.254636 | + | 0.967037i | \(0.581956\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.2729 | + | 1.51208i | −0.741812 | + | 0.0582002i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.6631 | + | 39.7951i | −0.409815 | + | 1.52945i | 0.385183 | + | 0.922840i | \(0.374138\pi\) |
−0.794999 | + | 0.606611i | \(0.792528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.410862 | + | 24.8076i | −0.0157674 | + | 0.952030i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.3702 | + | 28.3541i | 0.627309 | + | 1.08653i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.81689 | + | 2.36248i | −0.337369 | + | 0.0903978i | −0.423526 | − | 0.905884i | \(-0.639208\pi\) |
0.0861573 | + | 0.996282i | \(0.472541\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.2631 | − | 12.3431i | −0.392134 | − | 0.471607i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.8358 | − | 16.8358i | 0.642325 | − | 0.642325i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.19989 | + | 2.07827i | −0.0457121 | + | 0.0791758i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.9971 | − | 24.2470i | 1.59765 | − | 0.922401i | 0.605706 | − | 0.795689i | \(-0.292891\pi\) |
0.991940 | − | 0.126712i | \(-0.0404424\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.35538 | + | 8.08313i | −0.317395 | + | 0.307053i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.2166 | − | 11.6213i | 0.956520 | − | 0.440821i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.36598 | + | 5.09790i | 0.0517401 | + | 0.193097i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.5732 | 0.437739 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.8898 | −1.16669 | −0.583347 | − | 0.812223i | \(-0.698257\pi\) | ||||
−0.583347 | + | 0.812223i | \(0.698257\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.42684 | − | 27.7173i | −0.280109 | − | 1.04538i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.29385 | − | 0.596280i | 0.0487290 | − | 0.0224572i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.35191 | + | 25.3796i | 0.238888 | + | 0.954496i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.7354 | + | 7.35277i | −0.478287 | + | 0.276139i | −0.719702 | − | 0.694283i | \(-0.755722\pi\) |
0.241416 | + | 0.970422i | \(0.422388\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.76054 | + | 4.78140i | −0.103528 | + | 0.179316i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.4656 | − | 23.4656i | 0.878795 | − | 0.878795i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.67341 | − | 2.01256i | −0.0625821 | − | 0.0752654i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.2831 | − | 4.36306i | 0.608105 | − | 0.162941i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.7360 | − | 20.3273i | −0.437679 | − | 0.758082i | 0.559831 | − | 0.828607i | \(-0.310866\pi\) |
−0.997510 | + | 0.0705247i | \(0.977533\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.50134 | + | 9.90382i | 0.204881 | + | 0.368837i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.55119 | − | 5.78913i | 0.0576895 | − | 0.215300i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27.2119 | + | 23.2526i | 1.01062 | + | 0.863581i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.1380 | + | 14.1380i | 0.524349 | + | 0.524349i | 0.918882 | − | 0.394533i | \(-0.129093\pi\) |
−0.394533 | + | 0.918882i | \(0.629093\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.4004i | 0.422236i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.4359 | − | 7.17986i | −0.459958 | − | 0.265557i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.7908 | − | 7.17859i | −0.989543 | − | 0.265147i | −0.272484 | − | 0.962160i | \(-0.587845\pi\) |
−0.717058 | + | 0.697013i | \(0.754512\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −24.9899 | + | 19.4158i | −0.921765 | + | 0.716164i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.3262 | − | 3.30280i | −0.454042 | − | 0.121660i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.7451 | + | 6.78102i | 0.432050 | + | 0.249444i | 0.700219 | − | 0.713928i | \(-0.253085\pi\) |
−0.268170 | + | 0.963372i | \(0.586419\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 3.63383i | − | 0.133492i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.5961 | − | 13.5961i | −0.498791 | − | 0.498791i | 0.412270 | − | 0.911062i | \(-0.364736\pi\) |
−0.911062 | + | 0.412270i | \(0.864736\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.9115 | + | 43.7275i | −1.13251 | + | 1.60205i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.53416 | + | 5.72557i | −0.0561320 | + | 0.209488i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.1069 | + | 34.3973i | 0.698152 | + | 1.25685i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.8309 | + | 37.8123i | 0.796622 | + | 1.37979i | 0.921804 | + | 0.387656i | \(0.126715\pi\) |
−0.125182 | + | 0.992134i | \(0.539951\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.5979 | − | 8.46663i | 1.15149 | − | 0.308541i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.725941 | − | 7.88981i | 0.0264197 | − | 0.287140i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.88896 | − | 7.88896i | 0.286729 | − | 0.286729i | −0.549056 | − | 0.835785i | \(-0.685013\pi\) |
0.835785 | + | 0.549056i | \(0.185013\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.5337 | + | 32.1013i | −0.672730 | + | 1.16520i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.70923 | + | 0.986825i | −0.0619596 | + | 0.0357724i | −0.530660 | − | 0.847585i | \(-0.678056\pi\) |
0.468700 | + | 0.883357i | \(0.344722\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.49921 | + | 33.9593i | 0.307692 | + | 1.22941i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.71753 | + | 4.65384i | −0.0620976 | + | 0.168260i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.0641463 | + | 0.239397i | 0.00231619 | + | 0.00864413i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.4914 | −0.630756 | −0.315378 | − | 0.948966i | \(-0.602131\pi\) | ||||
−0.315378 | + | 0.948966i | \(0.602131\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.7763 | 0.424112 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.5736 | + | 43.1933i | 0.416274 | + | 1.55355i | 0.782271 | + | 0.622939i | \(0.214061\pi\) |
−0.365997 | + | 0.930616i | \(0.619272\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.4686 | + | 12.1965i | −1.23815 | + | 0.438112i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.7839 | − | 17.2044i | 0.637994 | − | 0.617205i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.9004 | − | 8.02542i | 0.498035 | − | 0.287540i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.3871 | − | 24.9193i | 0.514813 | − | 0.891682i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.5716 | − | 19.5716i | 0.699433 | − | 0.699433i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.5268 | − | 8.75286i | 0.375717 | − | 0.312403i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.0643 | + | 6.71595i | −0.893445 | + | 0.239398i | −0.676199 | − | 0.736719i | \(-0.736374\pi\) |
−0.217246 | + | 0.976117i | \(0.569707\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.75605 | − | 3.04156i | −0.0625170 | − | 0.108283i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.604323 | − | 36.4887i | 0.0214873 | − | 1.29739i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.518984 | + | 1.93688i | −0.0184297 | + | 0.0687805i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −30.5761 | − | 21.6146i | −1.08442 | − | 0.766592i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.3374 | − | 37.3374i | −1.32256 | − | 1.32256i | −0.911698 | − | 0.410861i | \(-0.865228\pi\) |
−0.410861 | − | 0.911698i | \(-0.634772\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.642773i | 0.0227397i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.89384 | + | 1.67076i | 0.102249 | + | 0.0590333i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 44.9776 | + | 12.0517i | 1.58722 | + | 0.425295i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.8588 | + | 21.6636i | −0.558948 | + | 0.763543i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.38854 | + | 1.97975i | 0.260089 | + | 0.0696906i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.9001 | − | 8.02525i | −0.488703 | − | 0.282153i | 0.235333 | − | 0.971915i | \(-0.424382\pi\) |
−0.724036 | + | 0.689762i | \(0.757715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.4040i | 1.24320i | 0.783334 | + | 0.621602i | \(0.213518\pi\) | ||||
−0.783334 | + | 0.621602i | \(0.786482\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.3791 | − | 30.3791i | −1.06544 | − | 1.06544i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.26564 | + | 36.4905i | 0.219476 | + | 1.27821i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.3030 | + | 42.1832i | −0.395440 | + | 1.47580i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.728847 | − | 0.404858i | 0.0254680 | − | 0.0141469i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.4231 | − | 23.2495i | −0.468469 | − | 0.811412i | 0.530881 | − | 0.847446i | \(-0.321861\pi\) |
−0.999351 | + | 0.0360337i | \(0.988528\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.0285 | − | 7.24225i | 0.942153 | − | 0.252449i | 0.245124 | − | 0.969492i | \(-0.421171\pi\) |
0.697029 | + | 0.717043i | \(0.254505\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 33.6628 | − | 23.1237i | 1.17199 | − | 0.805066i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.8901 | + | 16.8901i | −0.587325 | + | 0.587325i | −0.936906 | − | 0.349581i | \(-0.886324\pi\) |
0.349581 | + | 0.936906i | \(0.386324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.08412 | − | 12.2701i | 0.246042 | − | 0.426157i | −0.716382 | − | 0.697708i | \(-0.754203\pi\) |
0.962424 | + | 0.271551i | \(0.0875367\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.56228 | + | 4.94343i | −0.297022 | + | 0.171486i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.23673 | − | 13.9065i | −0.112146 | − | 0.481831i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.5192 | − | 11.2634i | −1.05616 | − | 0.389785i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.31770 | + | 27.3100i | 0.252937 | + | 0.943972i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.1874 | −0.627900 | −0.313950 | − | 0.949439i | \(-0.601652\pi\) | ||||
−0.313950 | + | 0.949439i | \(0.601652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2469 | −0.767134 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.4250 | + | 57.5667i | 0.531264 | + | 1.98270i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.0882 | − | 26.2297i | −0.415846 | − | 0.902329i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.86863 | + | 13.5371i | −0.132928 | + | 0.465141i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.7567 | − | 11.4065i | 0.678048 | − | 0.391471i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.4962 | − | 18.1799i | 0.359804 | − | 0.623198i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.4820 | + | 17.4820i | −0.598574 | + | 0.598574i | −0.939933 | − | 0.341359i | \(-0.889113\pi\) |
0.341359 | + | 0.939933i | \(0.389113\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.0231 | + | 1.38227i | 0.513778 | + | 0.0472726i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.2634 | + | 6.76932i | −0.862982 | + | 0.231235i | −0.663051 | − | 0.748574i | \(-0.730739\pi\) |
−0.199932 | + | 0.979810i | \(0.564072\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.4126 | − | 42.2838i | −0.832946 | − | 1.44271i | −0.895692 | − | 0.444676i | \(-0.853319\pi\) |
0.0627455 | − | 0.998030i | \(-0.480014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.8701 | + | 7.11788i | 0.404533 | + | 0.242577i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.97256 | + | 14.8258i | −0.135228 | + | 0.504676i | 0.864769 | + | 0.502169i | \(0.167465\pi\) |
−0.999997 | + | 0.00250685i | \(0.999202\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.1281 | + | 2.94100i | −0.582373 | + | 0.0999971i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.3555 | + | 18.3555i | 0.623387 | + | 0.623387i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.5080i | 0.695686i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.792578 | + | 0.457595i | 0.0268555 | + | 0.0155050i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.85188 | + | 2.63980i | 0.333436 | + | 0.0893438i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.0497 | − | 14.0147i | 0.880641 | − | 0.473784i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.1169 | + | 10.2134i | 1.28712 | + | 0.344882i | 0.836565 | − | 0.547868i | \(-0.184560\pi\) |
0.450552 | + | 0.892750i | \(0.351227\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.9128 | + | 10.3420i | 0.604185 | + | 0.348826i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 52.5926i | − | 1.77189i | −0.463791 | − | 0.885945i | \(-0.653511\pi\) | ||
0.463791 | − | 0.885945i | \(-0.346489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.0940 | − | 13.0940i | −0.440649 | − | 0.440649i | 0.451581 | − | 0.892230i | \(-0.350860\pi\) |
−0.892230 | + | 0.451581i | \(0.850860\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.81138 | + | 0.654437i | −0.128118 | + | 0.0219987i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.56553 | + | 35.6990i | −0.321179 | + | 1.19866i | 0.596919 | + | 0.802302i | \(0.296391\pi\) |
−0.918098 | + | 0.396354i | \(0.870275\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.22991 | − | 0.136303i | −0.276022 | − | 0.00457146i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.3813 | − | 38.7656i | −0.749803 | − | 1.29870i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.88822 | − | 0.505946i | 0.0631867 | − | 0.0169308i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.60543 | + | 0.791785i | 0.287648 | + | 0.0264664i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.87976 | − | 1.87976i | 0.0627633 | − | 0.0627633i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.1742 | − | 45.3351i | 0.872959 | − | 1.51201i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.6310 | − | 8.44719i | 0.487428 | − | 0.281417i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.5311 | + | 9.14288i | −1.21568 | + | 0.304256i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.54297 | − | 14.1974i | −0.217496 | − | 0.471936i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.28883 | + | 16.0061i | 0.142408 | + | 0.531474i | 0.999857 | + | 0.0169054i | \(0.00538141\pi\) |
−0.857449 | + | 0.514569i | \(0.827952\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.7549 | 0.356718 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.46770 | 0.0486270 | 0.0243135 | − | 0.999704i | \(-0.492260\pi\) | ||||
0.0243135 | + | 0.999704i | \(0.492260\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.69862 | + | 21.2676i | 0.188597 | + | 0.703853i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −29.3526 | − | 10.8328i | −0.970367 | − | 0.358122i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.5674 | − | 5.30617i | −0.613149 | − | 0.175225i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.1523 | + | 13.9443i | −0.796710 | + | 0.459981i | −0.842319 | − | 0.538979i | \(-0.818810\pi\) |
0.0456096 | + | 0.998959i | \(0.485477\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.54197 | − | 2.67078i | 0.0508098 | − | 0.0880051i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.45920 | + | 1.45920i | −0.0480302 | + | 0.0480302i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.0642 | + | 13.0957i | −0.626828 | + | 0.430582i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.49855 | − | 1.20538i | 0.147752 | − | 0.0395900i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.6468 | − | 28.8331i | −0.546164 | − | 0.945984i | −0.998533 | − | 0.0541530i | \(-0.982754\pi\) |
0.452368 | − | 0.891831i | \(-0.350579\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.3040 | + | 20.4544i | −1.25536 | + | 0.670367i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.03824 | − | 18.8030i | 0.164944 | − | 0.615581i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.11828 | + | 18.1605i | 0.101979 | + | 0.593913i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.6651 | + | 25.6651i | 0.838442 | + | 0.838442i | 0.988654 | − | 0.150212i | \(-0.0479957\pi\) |
−0.150212 | + | 0.988654i | \(0.547996\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 6.11942i | − | 0.199700i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.0732 | − | 12.1666i | −0.686967 | − | 0.396621i | 0.115508 | − | 0.993307i | \(-0.463151\pi\) |
−0.802475 | + | 0.596686i | \(0.796484\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.3421 | + | 3.03911i | 0.369350 | + | 0.0989670i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.22858 | − | 20.9297i | −0.300206 | − | 0.680845i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.07680 | − | 0.556477i | −0.0674869 | − | 0.0180831i | 0.224918 | − | 0.974378i | \(-0.427789\pi\) |
−0.292405 | + | 0.956295i | \(0.594455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.89206 | − | 1.66973i | −0.0938804 | − | 0.0542019i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.93980i | 0.127757i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.1863 | − | 13.1863i | −0.427146 | − | 0.427146i | 0.460509 | − | 0.887655i | \(-0.347667\pi\) |
−0.887655 | + | 0.460509i | \(0.847667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.16989 | − | 5.77540i | −0.264371 | − | 0.186887i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.1337 | + | 56.4796i | −0.489202 | + | 1.82573i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.76792 | − | 16.2895i | 0.315423 | − | 0.526015i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.2368 | + | 19.4627i | 0.362477 | + | 0.627829i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.6241 | − | 4.18646i | 0.503479 | − | 0.134907i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34.5156 | + | 28.6993i | −1.11110 | + | 0.923862i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.7931 | − | 27.7931i | 0.893766 | − | 0.893766i | −0.101109 | − | 0.994875i | \(-0.532239\pi\) |
0.994875 | + | 0.101109i | \(0.0322392\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.7910 | + | 22.1547i | −0.410907 | + | 0.711711i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.1029 | + | 6.98760i | −0.388400 | + | 0.224243i | −0.681467 | − | 0.731849i | \(-0.738658\pi\) |
0.293067 | + | 0.956092i | \(0.405324\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.8425 | + | 23.6119i | 0.732298 | + | 0.756963i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.76117 | + | 0.977025i | −0.0884282 | + | 0.0312899i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.16089 | + | 8.06456i | 0.0691331 | + | 0.258008i | 0.991839 | − | 0.127496i | \(-0.0406941\pi\) |
−0.922706 | + | 0.385505i | \(0.874027\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.4120 | 0.396690 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.3907 | 0.459459 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.30383 | + | 23.5262i | 0.201061 | + | 0.750370i | 0.990614 | + | 0.136688i | \(0.0436457\pi\) |
−0.789553 | + | 0.613682i | \(0.789688\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.59372 | − | 23.2856i | 0.273819 | − | 0.741940i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.17203 | + | 1.21151i | 0.0373062 | + | 0.0385628i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.6681 | + | 15.9742i | −0.879794 | + | 0.507949i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.72002 | − | 15.1035i | 0.277000 | − | 0.479779i | −0.693637 | − | 0.720324i | \(-0.743993\pi\) |
0.970638 | + | 0.240545i | \(0.0773263\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −41.3067 | + | 41.3067i | −1.31083 | + | 1.31083i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.21307 | + | 24.0525i | −0.0701590 | + | 0.762516i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.2781 | − | 6.77324i | 0.800565 | − | 0.214511i | 0.164733 | − | 0.986338i | \(-0.447324\pi\) |
0.635832 | + | 0.771827i | \(0.280657\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.94255 | + | 15.4890i | 0.282930 | + | 0.490049i |
(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 | 560.2.ci.c.353.1 | 16 | ||
4.3 | odd | 2 | 70.2.k.a.3.2 | ✓ | 16 | ||
5.2 | odd | 4 | inner | 560.2.ci.c.17.1 | 16 | ||
7.5 | odd | 6 | inner | 560.2.ci.c.33.1 | 16 | ||
12.11 | even | 2 | 630.2.bv.c.73.4 | 16 | |||
20.3 | even | 4 | 350.2.o.c.157.1 | 16 | |||
20.7 | even | 4 | 70.2.k.a.17.4 | yes | 16 | ||
20.19 | odd | 2 | 350.2.o.c.143.3 | 16 | |||
28.3 | even | 6 | 490.2.g.c.293.5 | 16 | |||
28.11 | odd | 6 | 490.2.g.c.293.8 | 16 | |||
28.19 | even | 6 | 70.2.k.a.33.4 | yes | 16 | ||
28.23 | odd | 6 | 490.2.l.c.313.3 | 16 | |||
28.27 | even | 2 | 490.2.l.c.423.1 | 16 | |||
35.12 | even | 12 | inner | 560.2.ci.c.257.1 | 16 | ||
60.47 | odd | 4 | 630.2.bv.c.577.2 | 16 | |||
84.47 | odd | 6 | 630.2.bv.c.523.2 | 16 | |||
140.19 | even | 6 | 350.2.o.c.243.1 | 16 | |||
140.27 | odd | 4 | 490.2.l.c.227.3 | 16 | |||
140.47 | odd | 12 | 70.2.k.a.47.2 | yes | 16 | ||
140.67 | even | 12 | 490.2.g.c.97.5 | 16 | |||
140.87 | odd | 12 | 490.2.g.c.97.8 | 16 | |||
140.103 | odd | 12 | 350.2.o.c.257.3 | 16 | |||
140.107 | even | 12 | 490.2.l.c.117.1 | 16 | |||
420.47 | even | 12 | 630.2.bv.c.397.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.k.a.3.2 | ✓ | 16 | 4.3 | odd | 2 | ||
70.2.k.a.17.4 | yes | 16 | 20.7 | even | 4 | ||
70.2.k.a.33.4 | yes | 16 | 28.19 | even | 6 | ||
70.2.k.a.47.2 | yes | 16 | 140.47 | odd | 12 | ||
350.2.o.c.143.3 | 16 | 20.19 | odd | 2 | |||
350.2.o.c.157.1 | 16 | 20.3 | even | 4 | |||
350.2.o.c.243.1 | 16 | 140.19 | even | 6 | |||
350.2.o.c.257.3 | 16 | 140.103 | odd | 12 | |||
490.2.g.c.97.5 | 16 | 140.67 | even | 12 | |||
490.2.g.c.97.8 | 16 | 140.87 | odd | 12 | |||
490.2.g.c.293.5 | 16 | 28.3 | even | 6 | |||
490.2.g.c.293.8 | 16 | 28.11 | odd | 6 | |||
490.2.l.c.117.1 | 16 | 140.107 | even | 12 | |||
490.2.l.c.227.3 | 16 | 140.27 | odd | 4 | |||
490.2.l.c.313.3 | 16 | 28.23 | odd | 6 | |||
490.2.l.c.423.1 | 16 | 28.27 | even | 2 | |||
560.2.ci.c.17.1 | 16 | 5.2 | odd | 4 | inner | ||
560.2.ci.c.33.1 | 16 | 7.5 | odd | 6 | inner | ||
560.2.ci.c.257.1 | 16 | 35.12 | even | 12 | inner | ||
560.2.ci.c.353.1 | 16 | 1.1 | even | 1 | trivial | ||
630.2.bv.c.73.4 | 16 | 12.11 | even | 2 | |||
630.2.bv.c.397.4 | 16 | 420.47 | even | 12 | |||
630.2.bv.c.523.2 | 16 | 84.47 | odd | 6 | |||
630.2.bv.c.577.2 | 16 | 60.47 | odd | 4 |