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 | 257.3 | ||
Root | \(1.01089 + 0.750919i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.257 |
Dual form | 560.2.ci.c.353.3 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.0749894 | − | 0.279864i | 0.0432952 | − | 0.161580i | −0.940894 | − | 0.338702i | \(-0.890012\pi\) |
0.984189 | + | 0.177122i | \(0.0566788\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.20382 | − | 0.378409i | 0.985577 | − | 0.169230i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.126334 | − | 2.64273i | −0.0477497 | − | 0.998859i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.52538 | + | 1.45803i | 0.841792 | + | 0.486009i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.81288 | + | 4.87205i | 0.848115 | + | 1.46898i | 0.882888 | + | 0.469583i | \(0.155596\pi\) |
−0.0347729 | + | 0.999395i | \(0.511071\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.42962 | − | 1.42962i | −0.396505 | − | 0.396505i | 0.480493 | − | 0.876998i | \(-0.340458\pi\) |
−0.876998 | + | 0.480493i | \(0.840458\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0593598 | − | 0.645146i | 0.0153266 | − | 0.166576i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.12784 | − | 1.37400i | −1.24368 | − | 0.333244i | −0.423790 | − | 0.905760i | \(-0.639301\pi\) |
−0.819893 | + | 0.572516i | \(0.805967\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.94590 | − | 3.37040i | 0.446420 | − | 0.773223i | −0.551729 | − | 0.834023i | \(-0.686032\pi\) |
0.998150 | + | 0.0608002i | \(0.0193652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.749081 | − | 0.162821i | −0.163463 | − | 0.0355304i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.290892 | + | 1.08562i | 0.0606552 | + | 0.226368i | 0.989599 | − | 0.143852i | \(-0.0459489\pi\) |
−0.928944 | + | 0.370220i | \(0.879282\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.71361 | − | 1.66789i | 0.942723 | − | 0.333577i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.21205 | − | 1.21205i | 0.233259 | − | 0.233259i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.15502i | − | 0.585872i | −0.956132 | − | 0.292936i | \(-0.905368\pi\) | ||
0.956132 | − | 0.292936i | \(-0.0946322\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.33287 | − | 1.92423i | 0.598601 | − | 0.345602i | −0.169890 | − | 0.985463i | \(-0.554341\pi\) |
0.768491 | + | 0.639861i | \(0.221008\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.57445 | − | 0.421872i | 0.274076 | − | 0.0734386i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.27845 | − | 5.77629i | −0.216098 | − | 0.976372i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.86824 | − | 1.30444i | 0.800334 | − | 0.214449i | 0.164603 | − | 0.986360i | \(-0.447366\pi\) |
0.635731 | + | 0.771911i | \(0.280699\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.507306 | + | 0.292893i | −0.0812340 | + | 0.0469005i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.21050i | 1.12609i | 0.826426 | + | 0.563046i | \(0.190371\pi\) | ||||
−0.826426 | + | 0.563046i | \(0.809629\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.85669 | + | 1.85669i | −0.283143 | + | 0.283143i | −0.834361 | − | 0.551218i | \(-0.814163\pi\) |
0.551218 | + | 0.834361i | \(0.314163\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.11719 | + | 2.25760i | 0.911897 | + | 0.336543i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.52590 | + | 5.69475i | 0.222576 | + | 0.830665i | 0.983361 | + | 0.181661i | \(0.0581474\pi\) |
−0.760785 | + | 0.649004i | \(0.775186\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.96808 | + | 0.667734i | −0.995440 | + | 0.0953905i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.769067 | + | 1.33206i | −0.107691 | + | 0.186526i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.33599 | + | 0.357978i | 0.183512 | + | 0.0491720i | 0.349405 | − | 0.936972i | \(-0.386384\pi\) |
−0.165892 | + | 0.986144i | \(0.553050\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.04270 | + | 9.67269i | 1.08448 | + | 1.30426i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.797333 | − | 0.797333i | −0.105609 | − | 0.105609i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.73923 | − | 4.74448i | −0.356617 | − | 0.617679i | 0.630776 | − | 0.775965i | \(-0.282737\pi\) |
−0.987393 | + | 0.158286i | \(0.949403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.99172 | − | 2.30462i | −0.511088 | − | 0.295077i | 0.222193 | − | 0.975003i | \(-0.428678\pi\) |
−0.733281 | + | 0.679926i | \(0.762012\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.53413 | − | 6.85809i | 0.445259 | − | 0.864038i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.69160 | − | 2.60964i | −0.457887 | − | 0.323686i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.218698 | + | 0.816193i | −0.0267182 | + | 0.0997138i | −0.977997 | − | 0.208617i | \(-0.933104\pi\) |
0.951279 | + | 0.308331i | \(0.0997704\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.325641 | 0.0392026 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.77710 | −0.566937 | −0.283469 | − | 0.958982i | \(-0.591485\pi\) | ||||
−0.283469 | + | 0.958982i | \(0.591485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.45256 | − | 5.42104i | 0.170010 | − | 0.634485i | −0.827338 | − | 0.561704i | \(-0.810146\pi\) |
0.997348 | − | 0.0727807i | \(-0.0231873\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.113311 | − | 1.44425i | −0.0130840 | − | 0.166767i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.5202 | − | 8.04920i | 1.42681 | − | 0.917291i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.41079 | − | 3.12392i | −0.608761 | − | 0.351469i | 0.163719 | − | 0.986507i | \(-0.447651\pi\) |
−0.772481 | + | 0.635038i | \(0.780984\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.12576 | + | 7.14603i | 0.458418 | + | 0.794003i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.67281 | − | 5.67281i | −0.622672 | − | 0.622672i | 0.323542 | − | 0.946214i | \(-0.395126\pi\) |
−0.946214 | + | 0.323542i | \(0.895126\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.8207 | − | 1.08763i | −1.28214 | − | 0.117970i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.882976 | − | 0.236593i | −0.0946650 | − | 0.0253654i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.96090 | + | 10.3246i | −0.631855 | + | 1.09440i | 0.355318 | + | 0.934746i | \(0.384373\pi\) |
−0.987172 | + | 0.159659i | \(0.948961\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.59749 | + | 3.95871i | −0.377120 | + | 0.414986i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.288594 | − | 1.07705i | −0.0299258 | − | 0.111685i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.01302 | − | 8.16409i | 0.309129 | − | 0.837618i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.63103 | + | 6.63103i | −0.673279 | + | 0.673279i | −0.958471 | − | 0.285191i | \(-0.907943\pi\) |
0.285191 | + | 0.958471i | \(0.407943\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.4050i | 1.64877i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.9423 | − | 8.04960i | 1.38731 | − | 0.800965i | 0.394301 | − | 0.918981i | \(-0.370987\pi\) |
0.993012 | + | 0.118016i | \(0.0376535\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.9993 | + | 5.09084i | −1.87206 | + | 0.501616i | −0.872132 | + | 0.489271i | \(0.837263\pi\) |
−0.999924 | + | 0.0123445i | \(0.996071\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.71245 | − | 0.0753683i | −0.167118 | − | 0.00735519i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.70557 | − | 0.724955i | 0.261557 | − | 0.0700840i | −0.125657 | − | 0.992074i | \(-0.540104\pi\) |
0.387214 | + | 0.921990i | \(0.373437\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.11895 | + | 2.95543i | −0.490306 | + | 0.283078i | −0.724701 | − | 0.689063i | \(-0.758022\pi\) |
0.234395 | + | 0.972141i | \(0.424689\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.46027i | − | 0.138602i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.5818 | + | 13.5818i | −1.27767 | + | 1.27767i | −0.335697 | + | 0.941970i | \(0.608972\pi\) |
−0.941970 | + | 0.335697i | \(0.891028\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.05188 | + | 2.28244i | 0.0980886 | + | 0.212839i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.52590 | − | 5.69475i | −0.141070 | − | 0.526480i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.98330 | + | 13.7251i | −0.273478 | + | 1.25818i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3246 | + | 17.8827i | −0.938599 | + | 1.62570i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.01796 | + | 0.540712i | 0.181954 | + | 0.0487543i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.75680 | − | 5.45939i | 0.872674 | − | 0.488303i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.63487 | − | 4.63487i | −0.411278 | − | 0.411278i | 0.470906 | − | 0.882184i | \(-0.343927\pi\) |
−0.882184 | + | 0.470906i | \(0.843927\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.380390 | + | 0.658854i | 0.0334915 | + | 0.0580089i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.66437 | + | 3.84768i | 0.582269 | + | 0.336173i | 0.762035 | − | 0.647536i | \(-0.224201\pi\) |
−0.179766 | + | 0.983709i | \(0.557534\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.15290 | − | 4.71670i | −0.793657 | − | 0.408990i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.21249 | − | 3.12979i | 0.190421 | − | 0.269369i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.28687 | + | 8.53471i | −0.195380 | + | 0.729170i | 0.796788 | + | 0.604259i | \(0.206531\pi\) |
−0.992168 | + | 0.124910i | \(0.960136\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0631 | −0.938361 | −0.469180 | − | 0.883102i | \(-0.655451\pi\) | ||||
−0.469180 | + | 0.883102i | \(0.655451\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.70818 | 0.143855 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.94383 | − | 10.9865i | 0.246176 | − | 0.918740i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.19389 | − | 6.95307i | −0.0991468 | − | 0.577421i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.335657 | + | 2.00019i | −0.0276846 | + | 0.164973i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.37243 | − | 2.52443i | −0.358204 | − | 0.206809i | 0.310089 | − | 0.950708i | \(-0.399641\pi\) |
−0.668293 | + | 0.743899i | \(0.732975\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.72142 | + | 11.6418i | 0.546981 | + | 0.947399i | 0.998479 | + | 0.0551270i | \(0.0175564\pi\) |
−0.451498 | + | 0.892272i | \(0.649110\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.9464 | − | 10.9464i | −0.884963 | − | 0.884963i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.61688 | − | 5.50184i | 0.531481 | − | 0.441918i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.06529 | − | 0.285443i | −0.0850191 | − | 0.0227808i | 0.216059 | − | 0.976380i | \(-0.430680\pi\) |
−0.301078 | + | 0.953600i | \(0.597346\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.200370 | − | 0.347052i | 0.0158904 | − | 0.0275230i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.83227 | − | 0.905902i | 0.223214 | − | 0.0713951i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.42705 | + | 12.7899i | 0.268428 | + | 1.00179i | 0.960119 | + | 0.279592i | \(0.0901992\pi\) |
−0.691691 | + | 0.722193i | \(0.743134\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.31016 | − | 1.52551i | 0.257695 | − | 0.118761i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.70680 | − | 4.70680i | 0.364223 | − | 0.364223i | −0.501142 | − | 0.865365i | \(-0.667087\pi\) |
0.865365 | + | 0.501142i | \(0.167087\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 8.91237i | − | 0.685567i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.82827 | − | 5.67435i | 0.751586 | − | 0.433929i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.81421 | + | 1.82586i | −0.518075 | + | 0.138818i | −0.508376 | − | 0.861135i | \(-0.669754\pi\) |
−0.00969875 | + | 0.999953i | \(0.503087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.00327 | − | 12.2461i | −0.378212 | − | 0.925719i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.53322 | + | 0.410826i | −0.115244 | + | 0.0308796i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.91075 | + | 1.10317i | −0.142816 | + | 0.0824550i | −0.569706 | − | 0.821849i | \(-0.692943\pi\) |
0.426889 | + | 0.904304i | \(0.359609\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.11867i | − | 0.306139i | −0.988215 | − | 0.153069i | \(-0.951084\pi\) | ||
0.988215 | − | 0.153069i | \(-0.0489158\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.944318 | + | 0.944318i | −0.0698060 | + | 0.0698060i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.2351 | − | 4.71693i | 0.752499 | − | 0.346796i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.72980 | − | 28.8480i | −0.565259 | − | 2.10957i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.35625 | − | 3.05000i | −0.244131 | − | 0.221855i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.60117 | + | 14.8977i | −0.622359 | + | 1.07796i | 0.366686 | + | 0.930345i | \(0.380492\pi\) |
−0.989045 | + | 0.147613i | \(0.952841\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.6562 | + | 3.12327i | 0.839032 | + | 0.224818i | 0.652650 | − | 0.757659i | \(-0.273657\pi\) |
0.186382 | + | 0.982477i | \(0.440324\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00718 | + | 0.837452i | −0.0721254 | + | 0.0599712i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.3135 | + | 14.3135i | 1.01979 | + | 1.01979i | 0.999800 | + | 0.0199932i | \(0.00636444\pi\) |
0.0199932 | + | 0.999800i | \(0.493636\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.76653 | + | 6.52383i | 0.267002 | + | 0.462462i | 0.968086 | − | 0.250617i | \(-0.0806335\pi\) |
−0.701084 | + | 0.713079i | \(0.747300\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.212023 | + | 0.122412i | 0.0149550 | + | 0.00863425i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.33786 | + | 0.398585i | −0.585203 | + | 0.0279752i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.72852 | + | 15.8906i | 0.190568 | + | 1.10985i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.848257 | + | 3.16574i | −0.0589579 | + | 0.220034i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.8944 | 1.51446 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.5766 | −1.34771 | −0.673854 | − | 0.738865i | \(-0.735362\pi\) | ||||
−0.673854 | + | 0.738865i | \(0.735362\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.358232 | + | 1.33694i | −0.0245456 | + | 0.0916056i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.38922 | + | 4.79440i | −0.231143 | + | 0.326975i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.50629 | − | 8.56478i | −0.373791 | − | 0.581415i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.40823 | − | 0.813041i | −0.0951593 | − | 0.0549402i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.36656 | + | 9.29516i | 0.360994 | + | 0.625260i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.46027 | − | 1.46027i | −0.0977867 | − | 0.0977867i | 0.656521 | − | 0.754308i | \(-0.272027\pi\) |
−0.754308 | + | 0.656521i | \(0.772027\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.3355 | + | 2.66053i | 0.955698 | + | 0.177369i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.0081 | + | 4.82525i | 1.19524 | + | 0.320263i | 0.800954 | − | 0.598726i | \(-0.204326\pi\) |
0.394283 | + | 0.918989i | \(0.370993\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.00384 | + | 3.47074i | −0.132417 | + | 0.229353i | −0.924608 | − | 0.380920i | \(-0.875607\pi\) |
0.792191 | + | 0.610274i | \(0.208941\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.31380 | − | 4.10755i | −0.0864419 | − | 0.270257i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.55400 | − | 13.2637i | −0.232830 | − | 0.868934i | −0.979115 | − | 0.203307i | \(-0.934831\pi\) |
0.746285 | − | 0.665627i | \(-0.231836\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.51775 | + | 11.9728i | 0.359939 | + | 0.781017i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.28003 | + | 1.28003i | −0.0831466 | + | 0.0831466i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.6621i | − | 1.27183i | −0.771758 | − | 0.635916i | \(-0.780622\pi\) | ||
0.771758 | − | 0.635916i | \(-0.219378\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.09667 | + | 2.94256i | −0.328305 | + | 0.189547i | −0.655088 | − | 0.755552i | \(-0.727369\pi\) |
0.326783 | + | 0.945099i | \(0.394035\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.27638 | − | 1.94970i | 0.466780 | − | 0.125073i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.1037 | + | 4.10834i | −0.964939 | + | 0.262473i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.60029 | + | 2.03649i | −0.483595 | + | 0.129579i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.01302 | + | 1.16222i | −0.127570 | + | 0.0736525i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.09950i | 0.448116i | 0.974576 | + | 0.224058i | \(0.0719306\pi\) | ||||
−0.974576 | + | 0.224058i | \(0.928069\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.47097 | + | 4.47097i | −0.281088 | + | 0.281088i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.19082 | + | 3.22665i | −0.0745720 | + | 0.202060i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.55891 | − | 9.54998i | −0.159620 | − | 0.595711i | −0.998665 | − | 0.0516491i | \(-0.983552\pi\) |
0.839045 | − | 0.544062i | \(-0.183114\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.06231 | − | 12.7007i | −0.252420 | − | 0.789181i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.60010 | − | 7.96760i | 0.284739 | − | 0.493182i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.2797 | + | 3.55829i | 0.818861 | + | 0.219413i | 0.643849 | − | 0.765153i | \(-0.277337\pi\) |
0.175013 | + | 0.984566i | \(0.444003\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.07974 | + | 0.283366i | 0.189187 | + | 0.0174071i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.44248 | + | 2.44248i | 0.149477 | + | 0.149477i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.2510 | − | 22.9514i | −0.807928 | − | 1.39937i | −0.914296 | − | 0.405046i | \(-0.867255\pi\) |
0.106368 | − | 0.994327i | \(-0.466078\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0824 | + | 6.39844i | 0.673209 | + | 0.388678i | 0.797292 | − | 0.603594i | \(-0.206265\pi\) |
−0.124082 | + | 0.992272i | \(0.539599\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.838129 | + | 1.30367i | 0.0507259 | + | 0.0789018i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.3849 | + | 18.2734i | 1.28956 | + | 1.10193i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.20313 | − | 19.4184i | 0.312626 | − | 1.16674i | −0.613554 | − | 0.789653i | \(-0.710261\pi\) |
0.926180 | − | 0.377083i | \(-0.123073\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.2223 | 0.671863 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.1498 | −0.844107 | −0.422054 | − | 0.906571i | \(-0.638691\pi\) | ||||
−0.422054 | + | 0.906571i | \(0.638691\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.00563 | − | 26.1454i | 0.416442 | − | 1.55418i | −0.365489 | − | 0.930816i | \(-0.619098\pi\) |
0.781930 | − | 0.623366i | \(-0.214235\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.05889 | − | 1.45546i | −0.121958 | − | 0.0862139i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.0554 | − | 0.910931i | 1.12481 | − | 0.0537706i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.68442 | + | 5.59130i | 0.569672 | + | 0.328900i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.35853 | + | 2.35305i | 0.0796385 | + | 0.137938i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.1191 | + | 17.1191i | 1.00011 | + | 1.00011i | 1.00000 | 0.000106876i | \(3.40197e-5\pi\) | |
0.000106876 | 1.00000i | \(0.499966\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.83211 | − | 9.41941i | −0.456003 | − | 0.548420i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.31453 | + | 2.49582i | 0.540484 | + | 0.144822i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.13616 | − | 1.96790i | 0.0657061 | − | 0.113806i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.14131 | + | 4.67218i | 0.296340 | + | 0.269300i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.20727 | − | 4.50559i | −0.0693558 | − | 0.258840i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.66911 | − | 3.56846i | −0.553652 | − | 0.204329i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.2974 | + | 17.2974i | −0.987217 | + | 0.987217i | −0.999919 | − | 0.0127019i | \(-0.995957\pi\) |
0.0127019 | + | 0.999919i | \(0.495957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.69898i | 0.324204i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.51095 | − | 5.49115i | 0.539316 | − | 0.311374i | −0.205486 | − | 0.978660i | \(-0.565877\pi\) |
0.744802 | + | 0.667286i | \(0.232544\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.4088 | − | 7.61212i | 1.60576 | − | 0.430262i | 0.658985 | − | 0.752156i | \(-0.270986\pi\) |
0.946776 | + | 0.321893i | \(0.104319\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.19342 | − | 16.4513i | 0.292616 | − | 0.926927i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.14766 | + | 1.11136i | −0.232956 | + | 0.0624203i | −0.373408 | − | 0.927667i | \(-0.621811\pi\) |
0.140453 | + | 0.990087i | \(0.455144\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.3714 | − | 8.87468i | 0.860633 | − | 0.496887i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 0.811556i | − | 0.0452966i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.6092 | + | 14.6092i | −0.812878 | + | 0.812878i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.12312 | − | 4.35423i | −0.506060 | − | 0.241529i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.443251 | + | 1.65424i | 0.0245119 | + | 0.0914795i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.8569 | − | 4.75200i | 0.819089 | − | 0.261986i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.7249 | − | 30.7005i | 0.974250 | − | 1.68745i | 0.291863 | − | 0.956460i | \(-0.405725\pi\) |
0.682387 | − | 0.730991i | \(-0.260942\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.1960 | + | 3.80382i | 0.777939 | + | 0.208448i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.173116 | + | 1.88150i | −0.00945835 | + | 0.102797i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.1473 | − | 12.1473i | −0.661708 | − | 0.661708i | 0.294075 | − | 0.955782i | \(-0.404989\pi\) |
−0.955782 | + | 0.294075i | \(0.904989\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.78257 | + | 4.81955i | 0.151128 | + | 0.261762i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.7499 | + | 10.8253i | 1.01536 | + | 0.586221i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.64495 | + | 18.3304i | 0.142814 | + | 0.989750i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.717654 | − | 0.123226i | 0.0386372 | − | 0.00663424i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.32323 | + | 8.67040i | −0.124717 | + | 0.465452i | −0.999829 | − | 0.0184687i | \(-0.994121\pi\) |
0.875112 | + | 0.483920i | \(0.160788\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0251 | −1.39309 | −0.696546 | − | 0.717512i | \(-0.745281\pi\) | ||||
−0.696546 | + | 0.717512i | \(0.745281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.46554 | −0.184977 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.57944 | − | 9.62659i | 0.137290 | − | 0.512372i | −0.862688 | − | 0.505736i | \(-0.831221\pi\) |
0.999978 | − | 0.00663577i | \(-0.00211225\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.5278 | + | 1.80770i | −0.558760 | + | 0.0959425i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.61745 | + | 1.86416i | 0.191456 | + | 0.0986615i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0235 | − | 5.78705i | −0.529019 | − | 0.305429i | 0.211598 | − | 0.977357i | \(-0.432133\pi\) |
−0.740617 | + | 0.671928i | \(0.765467\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.92693 | + | 3.33754i | 0.101417 | + | 0.175660i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.23050 | + | 4.23050i | 0.222044 | + | 0.222044i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.14981 | − | 12.4966i | 0.0601840 | − | 0.654104i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.1256 | − | 4.32083i | −0.841747 | − | 0.225545i | −0.187915 | − | 0.982185i | \(-0.560173\pi\) |
−0.653832 | + | 0.756640i | \(0.726840\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.5131 | + | 18.2092i | −0.547290 | + | 0.947935i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.777258 | − | 3.57589i | 0.0403532 | − | 0.185651i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.822767 | + | 3.07061i | 0.0426013 | + | 0.158990i | 0.983950 | − | 0.178446i | \(-0.0571070\pi\) |
−0.941348 | + | 0.337436i | \(0.890440\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.796232 | − | 3.13998i | −0.0411172 | − | 0.162148i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.51047 | + | 4.51047i | −0.232301 | + | 0.232301i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.15349i | − | 0.367450i | −0.982978 | − | 0.183725i | \(-0.941184\pi\) | ||
0.982978 | − | 0.183725i | \(-0.0588156\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.64470 | + | 0.949568i | −0.0842605 | + | 0.0486478i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.0961 | − | 3.77704i | 0.720278 | − | 0.192998i | 0.119982 | − | 0.992776i | \(-0.461716\pi\) |
0.600296 | + | 0.799778i | \(0.295050\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 24.5463 | − | 22.4767i | 1.25099 | − | 1.14552i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.39595 | + | 1.98174i | −0.375957 | + | 0.100737i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.36634 | − | 3.09826i | 0.272084 | − | 0.157088i | −0.357750 | − | 0.933817i | \(-0.616456\pi\) |
0.629834 | + | 0.776729i | \(0.283123\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.96659i | − | 0.301744i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.57658 | − | 1.57658i | 0.0795282 | − | 0.0795282i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.1065 | − | 4.83706i | −0.659460 | − | 0.243379i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.754685 | + | 2.81652i | 0.0378766 | + | 0.141357i | 0.982275 | − | 0.187447i | \(-0.0600212\pi\) |
−0.944398 | + | 0.328804i | \(0.893354\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.00641 | + | 2.20787i | −0.100446 | + | 0.110532i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.98528 | − | 17.2950i | 0.498641 | − | 0.863672i | −0.501358 | − | 0.865240i | \(-0.667166\pi\) |
0.999999 | + | 0.00156835i | \(0.000499221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.51565 | − | 2.01381i | −0.374381 | − | 0.100315i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.7965 | + | 14.1873i | 0.586175 | + | 0.704973i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.0491 | + | 20.0491i | 0.993796 | + | 0.993796i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.1791 | + | 29.7550i | 0.849451 | + | 1.47129i | 0.881699 | + | 0.471812i | \(0.156400\pi\) |
−0.0322484 | + | 0.999480i | \(0.510267\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.21707 | + | 1.28003i | 0.109360 | + | 0.0631390i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.1923 | + | 7.83843i | −0.599946 | + | 0.385704i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.6485 | − | 10.3552i | −0.719065 | − | 0.508317i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.829616 | + | 3.09617i | −0.0406265 | + | 0.151620i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.1360 | 1.52109 | 0.760547 | − | 0.649283i | \(-0.224931\pi\) | ||||
0.760547 | + | 0.649283i | \(0.224931\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.6728 | −1.64111 | −0.820555 | − | 0.571567i | \(-0.806336\pi\) | ||||
−0.820555 | + | 0.571567i | \(0.806336\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.44962 | + | 16.6062i | −0.216348 | + | 0.807421i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.4623 | + | 2.07615i | −1.28361 | + | 0.100708i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.58621 | + | 10.8402i | −0.270336 | + | 0.524594i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.85398 | − | 1.64775i | −0.137792 | − | 0.0795540i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.37284 | − | 12.7701i | −0.355137 | − | 0.615116i | 0.632004 | − | 0.774965i | \(-0.282233\pi\) |
−0.987141 | + | 0.159849i | \(0.948899\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.98256 | − | 9.98256i | −0.479731 | − | 0.479731i | 0.425315 | − | 0.905046i | \(-0.360163\pi\) |
−0.905046 | + | 0.425315i | \(0.860163\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.03545 | − | 0.187281i | −0.0975922 | − | 0.00897944i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.22504 | + | 1.13210i | 0.202111 | + | 0.0541555i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.2142 | + | 33.2800i | −0.917046 | + | 1.58837i | −0.113167 | + | 0.993576i | \(0.536100\pi\) |
−0.803878 | + | 0.594794i | \(0.797234\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.5706 | − | 8.47336i | −0.884314 | − | 0.403494i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.48448 | − | 5.54016i | −0.0705299 | − | 0.263221i | 0.921653 | − | 0.388016i | \(-0.126839\pi\) |
−0.992183 | + | 0.124795i | \(0.960173\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.22982 | + | 25.0092i | −0.437536 | + | 1.18555i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.03438 | + | 1.03438i | −0.0489247 | + | 0.0489247i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.30267i | 0.344635i | 0.985042 | + | 0.172317i | \(0.0551254\pi\) | ||||
−0.985042 | + | 0.172317i | \(0.944875\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −35.1299 | + | 20.2823i | −1.65420 | + | 0.955055i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.76217 | − | 1.00807i | 0.176762 | − | 0.0473633i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.43021 | + | 10.0856i | −0.301453 | + | 0.472820i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.97047 | + | 1.33183i | −0.232509 | + | 0.0623006i | −0.373192 | − | 0.927754i | \(-0.621737\pi\) |
0.140683 | + | 0.990055i | \(0.455070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.88056 | + | 4.54984i | −0.367833 | + | 0.212368i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 29.4110i | − | 1.36981i | −0.728634 | − | 0.684903i | \(-0.759845\pi\) | ||
0.728634 | − | 0.684903i | \(-0.240155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.04625 | − | 4.04625i | 0.188045 | − | 0.188045i | −0.606805 | − | 0.794851i | \(-0.707549\pi\) |
0.794851 | + | 0.606805i | \(0.207549\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.04357 | − | 2.26441i | −0.0483945 | − | 0.105009i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.30747 | − | 16.0757i | −0.199326 | − | 0.743894i | −0.991105 | − | 0.133086i | \(-0.957511\pi\) |
0.791779 | − | 0.610808i | \(-0.209155\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.18461 | + | 0.474848i | 0.100876 | + | 0.0219264i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.159770 | + | 0.276731i | −0.00736184 | + | 0.0127511i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.2686 | − | 3.82325i | −0.656069 | − | 0.175793i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.55078 | − | 19.1323i | 0.162921 | − | 0.877851i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.85194 | + | 2.85194i | 0.130581 | + | 0.130581i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.69460 | − | 13.3274i | −0.351575 | − | 0.608946i | 0.634950 | − | 0.772553i | \(-0.281021\pi\) |
−0.986526 | + | 0.163607i | \(0.947687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.82459 | − | 5.09488i | −0.402367 | − | 0.232306i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0411396 | − | 0.860583i | −0.00187191 | − | 0.0391579i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.1043 | + | 17.1228i | −0.549629 | + | 0.777507i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.31541 | − | 34.7656i | 0.422122 | − | 1.57538i | −0.348007 | − | 0.937492i | \(-0.613142\pi\) |
0.770129 | − | 0.637888i | \(-0.220192\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.83644 | 0.173490 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.2823 | 0.689680 | 0.344840 | − | 0.938661i | \(-0.387933\pi\) | ||||
0.344840 | + | 0.938661i | \(0.387933\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.33499 | + | 16.1784i | −0.195238 | + | 0.728639i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.20780 | + | 36.1536i | 0.279020 | + | 1.62499i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.603509 | + | 12.6246i | 0.0270711 | + | 0.566290i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.3534 | + | 15.7925i | 1.22451 | + | 0.706969i | 0.965875 | − | 0.259008i | \(-0.0833955\pi\) |
0.258630 | + | 0.965976i | \(0.416729\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.964305 | − | 1.67023i | −0.0430820 | − | 0.0746202i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.9777 | − | 16.9777i | −0.756997 | − | 0.756997i | 0.218778 | − | 0.975775i | \(-0.429793\pi\) |
−0.975775 | + | 0.218778i | \(0.929793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.6803 | − | 23.0157i | 1.23176 | − | 1.02419i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.49426 | − | 0.668334i | −0.110774 | − | 0.0296817i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.7571 | − | 18.6318i | 0.476799 | − | 0.825840i | −0.522848 | − | 0.852426i | \(-0.675130\pi\) |
0.999647 | + | 0.0265865i | \(0.00846373\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.5099 | − | 3.15388i | −0.641879 | − | 0.139519i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.72657 | − | 6.44363i | −0.0762297 | − | 0.284493i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −39.9445 | + | 18.4088i | −1.76017 | + | 0.811188i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.4529 | + | 23.4529i | −1.03146 | + | 1.03146i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.04397i | 0.0897205i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.4657 | − | 6.61973i | 0.502322 | − | 0.290016i | −0.227350 | − | 0.973813i | \(-0.573006\pi\) |
0.729672 | + | 0.683798i | \(0.239673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.0126 | − | 6.97006i | 1.13745 | − | 0.304779i | 0.359526 | − | 0.933135i | \(-0.382938\pi\) |
0.777926 | + | 0.628356i | \(0.216272\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.80244 | + | 0.481908i | −0.165952 | + | 0.0210322i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.7343 | + | 5.28779i | −0.859640 | + | 0.230340i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8246 | − | 10.8684i | 0.818462 | − | 0.472539i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 15.9755i | − | 0.693276i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3083 | − | 10.3083i | 0.446501 | − | 0.446501i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.68825 | − | 2.62148i | 0.245924 | − | 0.113336i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.165453 | + | 0.617477i | 0.00713980 | + | 0.0266461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.8536 | − | 32.0706i | −0.984374 | − | 1.38138i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.66491 | − | 9.81190i | 0.243553 | − | 0.421847i | −0.718171 | − | 0.695867i | \(-0.755020\pi\) |
0.961724 | + | 0.274020i | \(0.0883536\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.15267 | − | 0.308857i | −0.0494658 | − | 0.0132543i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.1629 | + | 8.45027i | −0.435329 | + | 0.361970i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.9149 | + | 30.9149i | 1.32182 | + | 1.32182i | 0.912298 | + | 0.409527i | \(0.134306\pi\) |
0.409527 | + | 0.912298i | \(0.365694\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.72040 | − | 11.6401i | −0.286820 | − | 0.496786i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.6337 | − | 6.13935i | −0.453009 | − | 0.261545i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.57212 | + | 14.6939i | −0.321999 | + | 0.624850i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.552577 | − | 3.21816i | −0.0234556 | − | 0.136603i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.83277 | + | 25.5003i | −0.289514 | + | 1.08048i | 0.655963 | + | 0.754793i | \(0.272263\pi\) |
−0.945477 | + | 0.325688i | \(0.894404\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.30873 | 0.224535 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.65318 | −0.365337 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.22648 | + | 19.5055i | −0.220270 | + | 0.822058i | 0.763975 | + | 0.645246i | \(0.223245\pi\) |
−0.984245 | + | 0.176812i | \(0.943422\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.7923 | + | 35.0712i | −1.04302 | + | 1.47546i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.3638 | − | 11.8061i | 0.771208 | − | 0.495808i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.4890 | + | 12.4067i | 0.900867 | + | 0.520116i | 0.877481 | − | 0.479611i | \(-0.159222\pi\) |
0.0233856 | + | 0.999727i | \(0.492555\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.29029 | + | 3.96690i | 0.0958458 | + | 0.166010i | 0.909961 | − | 0.414693i | \(-0.136111\pi\) |
−0.814116 | + | 0.580703i | \(0.802778\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.52433 | + | 3.52433i | 0.147231 | + | 0.147231i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.18185 | + | 4.63204i | 0.132692 | + | 0.193169i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.1065 | − | 5.11957i | −0.795414 | − | 0.213131i | −0.161845 | − | 0.986816i | \(-0.551744\pi\) |
−0.633570 | + | 0.773686i | \(0.718411\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.74818 | − | 3.02794i | 0.0726520 | − | 0.125837i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.2751 | + | 15.7084i | −0.592229 | + | 0.651694i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.01390 | + | 7.51596i | 0.0834071 | + | 0.311279i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.51775 | − | 11.9728i | −0.228131 | − | 0.495013i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.3782 | + | 19.3782i | −0.799824 | + | 0.799824i | −0.983068 | − | 0.183244i | \(-0.941340\pi\) |
0.183244 | + | 0.983068i | \(0.441340\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 14.9775i | − | 0.617136i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.07919 | − | 2.93247i | 0.208930 | − | 0.120626i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.12741 | − | 0.837988i | 0.128428 | − | 0.0344121i | −0.194033 | − | 0.980995i | \(-0.562157\pi\) |
0.322460 | + | 0.946583i | \(0.395490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.38094 | + | 31.3765i | −0.0566131 | + | 1.28631i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.10824 | − | 0.564900i | 0.0862844 | − | 0.0231198i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.75802 | + | 3.90174i | −0.276125 | + | 0.159421i | −0.631668 | − | 0.775239i | \(-0.717629\pi\) |
0.355543 | + | 0.934660i | \(0.384296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 31.7170i | − | 1.29377i | −0.762590 | − | 0.646883i | \(-0.776072\pi\) | ||
0.762590 | − | 0.646883i | \(-0.223928\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.74233 | + | 1.74233i | −0.0709530 | + | 0.0709530i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.9865 | + | 43.3171i | −0.649945 | + | 1.76109i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.199219 | − | 0.743495i | −0.00808604 | − | 0.0301775i | 0.961765 | − | 0.273876i | \(-0.0883059\pi\) |
−0.969851 | + | 0.243699i | \(0.921639\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.513702 | + | 2.36336i | −0.0208162 | + | 0.0957682i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.95987 | − | 10.3228i | 0.241110 | − | 0.417615i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.8086 | − | 9.05898i | −1.36552 | − | 0.365889i | −0.499676 | − | 0.866212i | \(-0.666548\pi\) |
−0.865839 | + | 0.500323i | \(0.833214\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.65183 | + | 0.428014i | 0.187580 | + | 0.0172592i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.5403 | + | 21.5403i | 0.867179 | + | 0.867179i | 0.992159 | − | 0.124980i | \(-0.0398866\pi\) |
−0.124980 | + | 0.992159i | \(0.539887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.6707 | + | 37.5348i | 0.871021 | + | 1.50865i | 0.860942 | + | 0.508703i | \(0.169875\pi\) |
0.0100783 | + | 0.999949i | \(0.496792\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.66841 | + | 0.963256i | 0.0669509 | + | 0.0386541i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.0382 | + | 14.4487i | 1.12333 | + | 0.578876i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.4363 | − | 15.7235i | 0.777452 | − | 0.628942i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.64184 | − | 6.12745i | 0.0655690 | − | 0.244707i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.7559 | −1.06683 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.53463 | −0.299949 | −0.149974 | − | 0.988690i | \(-0.547919\pi\) | ||||
−0.149974 | + | 0.988690i | \(0.547919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.46804 | + | 5.47879i | −0.0583492 | + | 0.217762i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.9683 | − | 8.46052i | −0.474946 | − | 0.335746i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.9163 | + | 9.00710i | 0.432520 | + | 0.356874i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0640 | − | 6.96513i | −0.477243 | − | 0.275536i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.1657 | − | 21.0717i | −0.480518 | − | 0.832281i | 0.519233 | − | 0.854633i | \(-0.326218\pi\) |
−0.999750 | + | 0.0223521i | \(0.992885\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.21713 | + | 6.21713i | 0.245180 | + | 0.245180i | 0.818989 | − | 0.573809i | \(-0.194535\pi\) |
−0.573809 | + | 0.818989i | \(0.694535\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.08763 | + | 1.30805i | 0.0428252 | + | 0.0515045i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.9243 | − | 5.33869i | −0.783304 | − | 0.209886i | −0.155063 | − | 0.987905i | \(-0.549558\pi\) |
−0.628241 | + | 0.778019i | \(0.716225\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.4102 | − | 26.6913i | 0.604905 | − | 1.04773i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.80989 | + | 0.898745i | −0.110128 | + | 0.0352246i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.76544 | + | 25.2490i | 0.264752 | + | 0.988069i | 0.962402 | + | 0.271630i | \(0.0875625\pi\) |
−0.697650 | + | 0.716439i | \(0.745771\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.1430 | + | 5.95772i | 0.630761 | + | 0.232787i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.5723 | − | 11.5723i | 0.451478 | − | 0.451478i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 24.2448i | − | 0.944443i | −0.881480 | − | 0.472222i | \(-0.843452\pi\) | ||
0.881480 | − | 0.472222i | \(-0.156548\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.5301 | − | 8.96630i | 0.604050 | − | 0.348749i | −0.166583 | − | 0.986027i | \(-0.553273\pi\) |
0.770633 | + | 0.637279i | \(0.219940\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.00382 | − | 0.804871i | 0.116659 | − | 0.0312586i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21.9562 | − | 6.93121i | −0.851423 | − | 0.268781i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.42516 | − | 0.917769i | 0.132623 | − | 0.0355362i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.518181 | + | 0.299172i | −0.0200340 | + | 0.0115667i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 25.9305i | − | 1.00104i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.85386 | + | 4.85386i | −0.187103 | + | 0.187103i | −0.794442 | − | 0.607340i | \(-0.792237\pi\) |
0.607340 | + | 0.794442i | \(0.292237\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.69158 | − | 7.73470i | 0.142089 | − | 0.297709i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.78306 | − | 17.8506i | −0.183828 | − | 0.686055i | −0.994878 | − | 0.101079i | \(-0.967771\pi\) |
0.811051 | − | 0.584976i | \(-0.198896\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.3618 | + | 16.6863i | 0.704660 | + | 0.640362i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.70083 | − | 4.67797i | 0.103496 | − | 0.179260i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.8878 | − | 6.93661i | −0.990569 | − | 0.265422i | −0.273079 | − | 0.961992i | \(-0.588042\pi\) |
−0.717489 | + | 0.696569i | \(0.754709\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.81023 | + | 19.6743i | −0.0691653 | + | 0.751717i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.821071 | + | 0.821071i | 0.0313258 | + | 0.0313258i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.39819 | − | 2.42173i | −0.0532667 | − | 0.0922606i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.1773 | − | 14.5361i | −0.957790 | − | 0.552980i | −0.0622976 | − | 0.998058i | \(-0.519843\pi\) |
−0.895492 | + | 0.445077i | \(0.853176\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 43.3541 | − | 2.07251i | 1.64689 | − | 0.0787281i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.3811 | + | 4.18638i | −0.924827 | + | 0.158798i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.90723 | − | 36.9743i | 0.375263 | − | 1.40050i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.97855 | −0.150483 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.4462 | 0.961089 | 0.480545 | − | 0.876970i | \(-0.340439\pi\) | ||||
0.480545 | + | 0.876970i | \(0.340439\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.07663 | − | 18.9462i | 0.191469 | − | 0.714571i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.76452 | − | 0.646392i | 0.141780 | − | 0.0243445i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.0343 | − | 35.8289i | −0.866295 | − | 1.34748i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.1994 | − | 15.7036i | −1.02150 | − | 0.589760i | −0.106958 | − | 0.994263i | \(-0.534111\pi\) |
−0.914537 | + | 0.404503i | \(0.867445\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.10952 | − | 15.7781i | −0.341634 | − | 0.591727i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.05850 | + | 3.05850i | 0.114542 | + | 0.114542i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.33027 | − | 25.3263i | 0.0871470 | − | 0.947149i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.50271 | − | 1.47445i | −0.205502 | − | 0.0550642i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.40214 | − | 9.35678i | 0.201466 | − | 0.348949i | −0.747535 | − | 0.664222i | \(-0.768763\pi\) |
0.949001 | + | 0.315273i | \(0.102096\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.8540 | + | 49.5669i | 0.590434 | + | 1.84597i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.441322 | + | 1.64704i | 0.0164129 | + | 0.0612539i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.26221 | − | 14.8715i | −0.195433 | − | 0.552315i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.6108 | + | 33.6108i | −1.24656 | + | 1.24656i | −0.289326 | + | 0.957231i | \(0.593431\pi\) |
−0.957231 | + | 0.289326i | \(0.906569\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.5720i | 0.835998i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0719 | − | 6.96972i | 0.446496 | − | 0.257785i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.8800 | − | 6.66658i | 0.918964 | − | 0.246236i | 0.231822 | − | 0.972758i | \(-0.425531\pi\) |
0.687143 | + | 0.726523i | \(0.258865\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0171620 | + | 4.53507i | 0.000633031 | + | 0.167278i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.59170 | + | 1.23034i | −0.169138 | + | 0.0453203i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.4948 | + | 6.05920i | −0.386059 | + | 0.222891i | −0.680451 | − | 0.732793i | \(-0.738216\pi\) |
0.294392 | + | 0.955685i | \(0.404883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.27977i | 0.0837493i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.2618 | + | 23.2618i | −0.853393 | + | 0.853393i | −0.990549 | − | 0.137157i | \(-0.956204\pi\) |
0.137157 | + | 0.990549i | \(0.456204\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.5913 | − | 3.90881i | −0.388036 | − | 0.143208i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.05487 | − | 22.5971i | −0.221536 | − | 0.826784i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.25767 | − | 7.05851i | −0.0824934 | − | 0.257912i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.98887 | − | 12.1051i | 0.255028 | − | 0.441721i | −0.709875 | − | 0.704327i | \(-0.751249\pi\) |
0.964903 | + | 0.262607i | \(0.0845821\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.98690 | + | 0.532387i | 0.0724065 | + | 0.0194013i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.2181 | + | 23.1130i | 0.699420 | + | 0.841169i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.5547 | + | 17.5547i | 0.638036 | + | 0.638036i | 0.950071 | − | 0.312035i | \(-0.101010\pi\) |
−0.312035 | + | 0.950071i | \(0.601010\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.915990 | + | 1.58654i | 0.0332483 | + | 0.0575878i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.9372 | + | 10.9334i | 0.686471 | + | 0.396334i | 0.802289 | − | 0.596936i | \(-0.203615\pi\) |
−0.115817 | + | 0.993271i | \(0.536949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.45710 | + | 13.1546i | 0.306168 | + | 0.476230i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −28.2660 | − | 19.9816i | −1.02196 | − | 0.722437i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.86675 | + | 10.6989i | −0.103512 | + | 0.386313i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.0506 | 1.11971 | 0.559857 | − | 0.828589i | \(-0.310856\pi\) | ||||
0.559857 | + | 0.828589i | \(0.310856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.86459 | −0.103166 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.57065 | + | 5.86173i | −0.0564922 | + | 0.210832i | −0.988402 | − | 0.151857i | \(-0.951475\pi\) |
0.931910 | + | 0.362689i | \(0.118141\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.5004 | − | 14.6289i | 0.449029 | − | 0.525487i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.85909 | + | 0.184481i | −0.138444 | + | 0.00661822i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.3023 | + | 14.0309i | 0.870720 | + | 0.502710i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.4374 | − | 23.2743i | −0.480828 | − | 0.832819i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.82404 | − | 3.82404i | −0.136660 | − | 0.136660i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.45571 | − | 0.225950i | −0.0876481 | − | 0.00806449i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.5993 | + | 5.78752i | 0.769932 | + | 0.206303i | 0.622342 | − | 0.782746i | \(-0.286182\pi\) |
0.147591 | + | 0.989049i | \(0.452848\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.99167 | − | 3.44968i | 0.0709055 | − | 0.122812i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.6089 | + | 34.1772i | 1.33722 | + | 1.21520i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.41191 | + | 9.00138i | 0.0856495 | + | 0.319648i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.310252 | − | 0.840660i | 0.0110035 | − | 0.0298151i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.5528 | − | 16.5528i | 0.586330 | − | 0.586330i | −0.350305 | − | 0.936636i | \(-0.613922\pi\) |
0.936636 | + | 0.350305i | \(0.113922\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 31.2984i | − | 1.10726i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.1070 | + | 17.3823i | −1.06378 | + | 0.614174i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.4975 | − | 8.17177i | 1.07623 | − | 0.288376i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.89899 | − | 3.06820i | 0.207912 | − | 0.108140i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.41697 | + | 1.98737i | −0.261090 | + | 0.0699588i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.84139 | − | 1.64048i | 0.0998980 | − | 0.0576762i | −0.449219 | − | 0.893422i | \(-0.648298\pi\) |
0.549117 | + | 0.835746i | \(0.314964\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17.8693i | − | 0.627476i | −0.949510 | − | 0.313738i | \(-0.898419\pi\) | ||
0.949510 | − | 0.313738i | \(-0.101581\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.62176 | − | 2.62176i | 0.0919491 | − | 0.0919491i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.3924 | + | 26.8898i | 0.434088 | + | 0.941910i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.64486 | + | 9.87074i | 0.0925318 | + | 0.345333i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.8569 | + | 4.75200i | −0.519143 | + | 0.166048i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.90837 | − | 10.2336i | 0.206204 | − | 0.357155i | −0.744312 | − | 0.667832i | \(-0.767222\pi\) |
0.950516 | + | 0.310677i | \(0.100556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.0995 | + | 9.13692i | 1.18863 | + | 0.318493i | 0.798345 | − | 0.602200i | \(-0.205709\pi\) |
0.390287 | + | 0.920693i | \(0.372376\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.71771 | − | 4.61455i | 0.233881 | − | 0.160658i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.2835 | + | 17.2835i | 0.601005 | + | 0.601005i | 0.940579 | − | 0.339574i | \(-0.110283\pi\) |
−0.339574 | + | 0.940579i | \(0.610283\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.2877 | + | 29.9431i | 0.600426 | + | 1.03997i | 0.992756 | + | 0.120144i | \(0.0383357\pi\) |
−0.392330 | + | 0.919824i | \(0.628331\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.04433 | − | 2.91234i | −0.174986 | − | 0.101028i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.6487 | + | 6.15011i | 1.26980 | + | 0.213089i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.59183 | − | 12.1540i | 0.297332 | − | 0.420607i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.70734 | − | 6.37187i | 0.0590142 | − | 0.220244i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 50.1328 | 1.73078 | 0.865388 | − | 0.501102i | \(-0.167072\pi\) | ||||
0.865388 | + | 0.501102i | \(0.167072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0459 | 0.656754 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.06109 | + | 3.96003i | −0.0365458 | + | 0.136391i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.37252 | − | 19.6412i | −0.116018 | − | 0.675679i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.5636 | + | 25.0259i | 1.66866 | + | 0.859901i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.79181 | − | 3.92125i | −0.233094 | − | 0.134577i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.83227 | + | 4.90563i | 0.0970888 | + | 0.168163i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.37500 | − | 2.37500i | −0.0813183 | − | 0.0813183i | 0.665278 | − | 0.746596i | \(-0.268313\pi\) |
−0.746596 | + | 0.665278i | \(0.768313\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.5125 | − | 16.2243i | 0.667312 | − | 0.554860i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.5097 | − | 10.8545i | −1.38378 | − | 0.370784i | −0.511290 | − | 0.859408i | \(-0.670832\pi\) |
−0.872494 | + | 0.488624i | \(0.837499\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.17847 | − | 2.04117i | 0.0402090 | − | 0.0696440i | −0.845221 | − | 0.534418i | \(-0.820531\pi\) |
0.885430 | + | 0.464774i | \(0.153864\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.17402 | − | 5.40125i | 0.0400105 | − | 0.184074i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.5138 | − | 46.7022i | −0.425975 | − | 1.58976i | −0.761784 | − | 0.647831i | \(-0.775676\pi\) |
0.335808 | − | 0.941930i | \(-0.390991\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.3263 | + | 6.60242i | −0.487110 | + | 0.224489i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.29104 | − | 2.29104i | 0.0778076 | − | 0.0778076i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 35.1489i | − | 1.19234i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.47950 | − | 0.854190i | 0.0501310 | − | 0.0289431i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −26.4141 | + | 7.07763i | −0.893980 | + | 0.239541i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.6603 | − | 25.0949i | −0.529416 | − | 0.848363i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.3115 | − | 3.56681i | 0.449498 | − | 0.120443i | −0.0269665 | − | 0.999636i | \(-0.508585\pi\) |
0.476465 | + | 0.879194i | \(0.341918\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.07477 | − | 3.50727i | 0.204897 | − | 0.118297i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.32542i | 0.112036i | 0.998430 | + | 0.0560181i | \(0.0178405\pi\) | ||||
−0.998430 | + | 0.0560181i | \(0.982160\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.8930 | − | 36.8930i | 1.24155 | − | 1.24155i | 0.282191 | − | 0.959358i | \(-0.408939\pi\) |
0.959358 | − | 0.282191i | \(-0.0910610\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.22348 | + | 1.48557i | −0.108356 | + | 0.0499369i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.27107 | + | 34.6001i | 0.311292 | + | 1.16176i | 0.927392 | + | 0.374090i | \(0.122045\pi\) |
−0.616101 | + | 0.787668i | \(0.711289\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.6632 | + | 12.8343i | −0.391170 | + | 0.430447i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.2105 | + | 40.2018i | −0.777582 | + | 1.34681i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.1628 | + | 5.93852i | 0.741651 | + | 0.198725i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.79349 | + | 3.15423i | −0.126803 | + | 0.105434i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.465543 | − | 0.465543i | −0.0155440 | − | 0.0155440i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.07098 | − | 10.5152i | −0.202479 | − | 0.350703i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.35888 | − | 3.67130i | −0.211845 | − | 0.122309i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.69312 | − | 1.08850i | 0.0563435 | − | 0.0362232i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.55854 | − | 9.07680i | −0.0518077 | − | 0.301723i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.46661 | − | 16.6696i | 0.148312 | − | 0.553506i | −0.851274 | − | 0.524721i | \(-0.824170\pi\) |
0.999586 | − | 0.0287849i | \(-0.00916377\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 46.9461 | 1.55710 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.56820 | −0.184483 | −0.0922414 | − | 0.995737i | \(-0.529403\pi\) | ||||
−0.0922414 | + | 0.995737i | \(0.529403\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.6813 | − | 43.5952i | 0.386594 | − | 1.44279i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.72377 | + | 2.43844i | −0.0569859 | + | 0.0806124i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.32645 | − | 18.0982i | 0.307986 | − | 0.597657i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.37964 | − | 3.10593i | −0.177458 | − | 0.102455i | 0.408640 | − | 0.912696i | \(-0.366003\pi\) |
−0.586098 | + | 0.810240i | \(0.699337\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.54381 | + | 6.13806i | 0.116773 | + | 0.202256i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.82943 | + | 6.82943i | 0.224794 | + | 0.224794i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.7713 | − | 14.2683i | 0.682958 | − | 0.469139i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −55.4029 | − | 14.8452i | −1.81967 | − | 0.487579i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.0947297 | − | 0.164077i | 0.00310798 | − | 0.00538318i | −0.864467 | − | 0.502689i | \(-0.832344\pi\) |
0.867575 | + | 0.497306i | \(0.165677\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.3087 | + | 24.7846i | −0.370627 | + | 0.812281i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.823556 | − | 3.07355i | −0.0269620 | − | 0.100624i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −27.9514 | − | 60.6507i | −0.914108 | − | 1.98349i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.2022 | + | 34.2022i | −1.11734 | + | 1.11734i | −0.125208 | + | 0.992131i | \(0.539960\pi\) |
−0.992131 | + | 0.125208i | \(0.960040\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 8.52144i | − | 0.278087i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.3826 | + | 9.45851i | −0.534058 | + | 0.308339i | −0.742667 | − | 0.669660i | \(-0.766440\pi\) |
0.208609 | + | 0.977999i | \(0.433106\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.82790 | + | 2.09748i | −0.254911 | + | 0.0683033i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.55071 | − | 5.45161i | −0.278155 | − | 0.177341i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.5435 | − | 12.2033i | 1.47996 | − | 0.396555i | 0.573629 | − | 0.819115i | \(-0.305535\pi\) |
0.906335 | + | 0.422560i | \(0.138869\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.82664 | + | 5.67341i | −0.318986 | + | 0.184167i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.24412i | 0.0403434i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.8431 | − | 18.8431i | 0.610389 | − | 0.610389i | −0.332658 | − | 0.943047i | \(-0.607946\pi\) |
0.943047 | + | 0.332658i | \(0.107946\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.3180 | + | 36.0865i | −0.430960 | + | 1.16773i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.33101 | − | 4.96741i | −0.0430256 | − | 0.160574i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.8439 | + | 4.96536i | 0.737667 | + | 0.160340i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.09467 | + | 14.0204i | −0.261118 | + | 0.452270i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.88958 | + | 2.11401i | 0.254238 | + | 0.0681229i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.8700 | + | 2.47231i | 0.864976 | + | 0.0795863i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.3703 | − | 27.3703i | −0.880169 | − | 0.880169i | 0.113383 | − | 0.993551i | \(-0.463831\pi\) |
−0.993551 | + | 0.113383i | \(0.963831\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.99306 | + | 5.18413i | 0.0961509 | + | 0.166538i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.8750 | + | 16.0936i | 0.894550 | + | 0.516469i | 0.875428 | − | 0.483348i | \(-0.160580\pi\) |
0.0191221 | + | 0.999817i | \(0.493913\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.39765 | + | 29.2369i | 0.0448065 | + | 0.937291i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.90273 | + | 2.22671i | −0.0609362 | + | 0.0713119i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.02479 | + | 22.4848i | −0.192750 | + | 0.719353i | 0.800088 | + | 0.599883i | \(0.204786\pi\) |
−0.992838 | + | 0.119470i | \(0.961881\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −67.0692 | −2.14354 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.2364 | −0.550314 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.7630 | + | 55.0964i | −0.470868 | + | 1.75730i | 0.165793 | + | 0.986160i | \(0.446981\pi\) |
−0.636662 | + | 0.771143i | \(0.719685\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.9606 | + | 26.1279i | 1.17766 | + | 0.832505i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.215802 | − | 4.51427i | −0.00686904 | − | 0.143691i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.55577 | − | 1.47557i | −0.0812687 | − | 0.0469205i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.7703 | − | 49.8316i | −0.913918 | − | 1.58295i | −0.808478 | − | 0.588526i | \(-0.799708\pi\) |
−0.105440 | − | 0.994426i | \(-0.533625\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.26279 | − | 7.26279i | −0.230478 | − | 0.230478i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.7694 | + | 12.9520i | 0.341414 | + | 0.410607i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.4284 | + | 6.27762i | 0.741985 | + | 0.198814i | 0.609960 | − | 0.792432i | \(-0.291185\pi\) |
0.132025 | + | 0.991246i | \(0.457852\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.31951 | − | 7.48160i | 0.136663 | − | 0.236707i |
(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.257.3 | 16 | ||
4.3 | odd | 2 | 70.2.k.a.47.1 | yes | 16 | ||
5.3 | odd | 4 | inner | 560.2.ci.c.33.3 | 16 | ||
7.3 | odd | 6 | inner | 560.2.ci.c.17.3 | 16 | ||
12.11 | even | 2 | 630.2.bv.c.397.3 | 16 | |||
20.3 | even | 4 | 70.2.k.a.33.3 | yes | 16 | ||
20.7 | even | 4 | 350.2.o.c.243.2 | 16 | |||
20.19 | odd | 2 | 350.2.o.c.257.4 | 16 | |||
28.3 | even | 6 | 70.2.k.a.17.3 | yes | 16 | ||
28.11 | odd | 6 | 490.2.l.c.227.4 | 16 | |||
28.19 | even | 6 | 490.2.g.c.97.7 | 16 | |||
28.23 | odd | 6 | 490.2.g.c.97.6 | 16 | |||
28.27 | even | 2 | 490.2.l.c.117.2 | 16 | |||
35.3 | even | 12 | inner | 560.2.ci.c.353.3 | 16 | ||
60.23 | odd | 4 | 630.2.bv.c.523.1 | 16 | |||
84.59 | odd | 6 | 630.2.bv.c.577.1 | 16 | |||
140.3 | odd | 12 | 70.2.k.a.3.1 | ✓ | 16 | ||
140.23 | even | 12 | 490.2.g.c.293.7 | 16 | |||
140.59 | even | 6 | 350.2.o.c.157.2 | 16 | |||
140.83 | odd | 4 | 490.2.l.c.313.4 | 16 | |||
140.87 | odd | 12 | 350.2.o.c.143.4 | 16 | |||
140.103 | odd | 12 | 490.2.g.c.293.6 | 16 | |||
140.123 | even | 12 | 490.2.l.c.423.2 | 16 | |||
420.143 | even | 12 | 630.2.bv.c.73.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.k.a.3.1 | ✓ | 16 | 140.3 | odd | 12 | ||
70.2.k.a.17.3 | yes | 16 | 28.3 | even | 6 | ||
70.2.k.a.33.3 | yes | 16 | 20.3 | even | 4 | ||
70.2.k.a.47.1 | yes | 16 | 4.3 | odd | 2 | ||
350.2.o.c.143.4 | 16 | 140.87 | odd | 12 | |||
350.2.o.c.157.2 | 16 | 140.59 | even | 6 | |||
350.2.o.c.243.2 | 16 | 20.7 | even | 4 | |||
350.2.o.c.257.4 | 16 | 20.19 | odd | 2 | |||
490.2.g.c.97.6 | 16 | 28.23 | odd | 6 | |||
490.2.g.c.97.7 | 16 | 28.19 | even | 6 | |||
490.2.g.c.293.6 | 16 | 140.103 | odd | 12 | |||
490.2.g.c.293.7 | 16 | 140.23 | even | 12 | |||
490.2.l.c.117.2 | 16 | 28.27 | even | 2 | |||
490.2.l.c.227.4 | 16 | 28.11 | odd | 6 | |||
490.2.l.c.313.4 | 16 | 140.83 | odd | 4 | |||
490.2.l.c.423.2 | 16 | 140.123 | even | 12 | |||
560.2.ci.c.17.3 | 16 | 7.3 | odd | 6 | inner | ||
560.2.ci.c.33.3 | 16 | 5.3 | odd | 4 | inner | ||
560.2.ci.c.257.3 | 16 | 1.1 | even | 1 | trivial | ||
560.2.ci.c.353.3 | 16 | 35.3 | even | 12 | inner | ||
630.2.bv.c.73.3 | 16 | 420.143 | even | 12 | |||
630.2.bv.c.397.3 | 16 | 12.11 | even | 2 | |||
630.2.bv.c.523.1 | 16 | 60.23 | odd | 4 | |||
630.2.bv.c.577.1 | 16 | 84.59 | odd | 6 |