Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,3,Mod(37,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.ca (of order \(12\), degree \(4\), 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: | \(8.58312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 37.15 | ||
Character | \(\chi\) | \(=\) | 315.37 |
Dual form | 315.3.ca.b.298.15 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.18498 | − | 0.853412i | 1.59249 | − | 0.426706i | 0.649726 | − | 0.760169i | \(-0.274884\pi\) |
0.942763 | + | 0.333463i | \(0.108217\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.95167 | − | 3.43620i | 1.48792 | − | 0.859049i | ||||
\(5\) | 4.91224 | − | 0.932701i | 0.982447 | − | 0.186540i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.00478 | + | 4.89410i | 0.714968 | + | 0.699157i | ||||
\(8\) | 6.69718 | − | 6.69718i | 0.837147 | − | 0.837147i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 14.8494 | − | 7.16279i | 1.48494 | − | 0.716279i | ||||
\(11\) | 0.581984 | + | 1.00803i | 0.0529076 | + | 0.0916387i | 0.891266 | − | 0.453480i | \(-0.149818\pi\) |
−0.838359 | + | 0.545119i | \(0.816484\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14.6930 | + | 14.6930i | −1.13023 | + | 1.13023i | −0.140089 | + | 0.990139i | \(0.544739\pi\) |
−0.990139 | + | 0.140089i | \(0.955261\pi\) | |||||||
\(14\) | 20.1168 | + | 11.3165i | 1.43691 | + | 0.808318i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.87012 | − | 3.23914i | 0.116882 | − | 0.202446i | ||||
\(17\) | 6.97229 | − | 26.0209i | 0.410135 | − | 1.53064i | −0.384251 | − | 0.923229i | \(-0.625540\pi\) |
0.794385 | − | 0.607414i | \(-0.207793\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −24.9464 | − | 14.4028i | −1.31297 | − | 0.758042i | −0.330381 | − | 0.943848i | \(-0.607177\pi\) |
−0.982586 | + | 0.185806i | \(0.940510\pi\) | |||||||
\(20\) | 26.0311 | − | 22.4305i | 1.30155 | − | 1.12153i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.71387 | + | 2.71387i | 0.123358 | + | 0.123358i | ||||
\(23\) | −3.19577 | − | 11.9268i | −0.138946 | − | 0.518555i | −0.999950 | − | 0.00995696i | \(-0.996831\pi\) |
0.861004 | − | 0.508598i | \(-0.169836\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.2601 | − | 9.16329i | 0.930406 | − | 0.366532i | ||||
\(26\) | −34.2576 | + | 59.3359i | −1.31760 | + | 2.28215i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 46.6039 | + | 11.9307i | 1.66442 | + | 0.426095i | ||||
\(29\) | − | 12.5542i | − | 0.432905i | −0.976293 | − | 0.216452i | \(-0.930551\pi\) | ||
0.976293 | − | 0.216452i | \(-0.0694486\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.24013 | + | 14.2723i | 0.265811 | + | 0.460398i | 0.967776 | − | 0.251814i | \(-0.0810271\pi\) |
−0.701965 | + | 0.712211i | \(0.747694\pi\) | |||||||
\(32\) | −6.61339 | + | 24.6815i | −0.206668 | + | 0.771297i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 88.8263i | − | 2.61254i | ||||||
\(35\) | 29.1494 | + | 19.3730i | 0.832839 | + | 0.553515i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.6641 | − | 3.66129i | 0.369300 | − | 0.0989538i | −0.0693957 | − | 0.997589i | \(-0.522107\pi\) |
0.438696 | + | 0.898635i | \(0.355440\pi\) | |||||||
\(38\) | −91.7452 | − | 24.5830i | −2.41435 | − | 0.646922i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 26.6517 | − | 39.1446i | 0.666292 | − | 0.978615i | ||||
\(41\) | −48.3009 | −1.17807 | −0.589036 | − | 0.808107i | \(-0.700492\pi\) | ||||
−0.589036 | + | 0.808107i | \(0.700492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.357576 | + | 0.357576i | −0.00831573 | + | 0.00831573i | −0.711252 | − | 0.702937i | \(-0.751872\pi\) |
0.702937 | + | 0.711252i | \(0.251872\pi\) | |||||||
\(44\) | 6.92755 | + | 3.99962i | 0.157444 | + | 0.0909005i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −20.3569 | − | 35.2592i | −0.442541 | − | 0.766504i | ||||
\(47\) | −27.3656 | + | 7.33258i | −0.582246 | + | 0.156012i | −0.537907 | − | 0.843004i | \(-0.680785\pi\) |
−0.0443391 | + | 0.999017i | \(0.514118\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.09559 | + | 48.9878i | 0.0223590 | + | 0.999750i | ||||
\(50\) | 66.2630 | − | 49.0354i | 1.32526 | − | 0.980707i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −36.9597 | + | 137.936i | −0.710764 | + | 2.65261i | ||||
\(53\) | 45.5418 | + | 12.2029i | 0.859280 | + | 0.230243i | 0.661447 | − | 0.749992i | \(-0.269943\pi\) |
0.197834 | + | 0.980236i | \(0.436609\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.79903 | + | 4.40884i | 0.0690732 | + | 0.0801608i | ||||
\(56\) | 66.2945 | − | 0.741234i | 1.18383 | − | 0.0132363i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.7139 | − | 39.9849i | −0.184723 | − | 0.689396i | ||||
\(59\) | −49.5210 | + | 28.5910i | −0.839340 | + | 0.484593i | −0.857040 | − | 0.515250i | \(-0.827699\pi\) |
0.0177000 | + | 0.999843i | \(0.494366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.30786 | − | 10.9255i | 0.103408 | − | 0.179107i | −0.809679 | − | 0.586873i | \(-0.800359\pi\) |
0.913086 | + | 0.407766i | \(0.133692\pi\) | |||||||
\(62\) | 38.4248 | + | 38.4248i | 0.619755 | + | 0.619755i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 99.2149i | 1.55023i | ||||||||
\(65\) | −58.4712 | + | 85.8794i | −0.899556 | + | 1.32122i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0537 | − | 44.9851i | 0.179906 | − | 0.671419i | −0.815758 | − | 0.578394i | \(-0.803680\pi\) |
0.995664 | − | 0.0930251i | \(-0.0296537\pi\) | |||||||
\(68\) | −47.9163 | − | 178.826i | −0.704652 | − | 2.62980i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 109.373 | + | 36.8262i | 1.56248 | + | 0.526088i | ||||
\(71\) | −19.0442 | −0.268228 | −0.134114 | − | 0.990966i | \(-0.542819\pi\) | ||||
−0.134114 | + | 0.990966i | \(0.542819\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −118.629 | − | 31.7865i | −1.62505 | − | 0.435432i | −0.672573 | − | 0.740031i | \(-0.734811\pi\) |
−0.952481 | + | 0.304599i | \(0.901477\pi\) | |||||||
\(74\) | 40.3953 | − | 23.3222i | 0.545883 | − | 0.315165i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −197.963 | −2.60478 | ||||||||
\(77\) | −2.02068 | + | 7.89323i | −0.0262426 | + | 0.102509i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74.1583 | + | 42.8153i | 0.938712 | + | 0.541966i | 0.889556 | − | 0.456825i | \(-0.151014\pi\) |
0.0491557 | + | 0.998791i | \(0.484347\pi\) | |||||||
\(80\) | 6.16532 | − | 17.6557i | 0.0770665 | − | 0.220696i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −153.837 | + | 41.2206i | −1.87607 | + | 0.502690i | ||||
\(83\) | −18.0900 | + | 18.0900i | −0.217952 | + | 0.217952i | −0.807635 | − | 0.589683i | \(-0.799253\pi\) |
0.589683 | + | 0.807635i | \(0.299253\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.97979 | − | 134.324i | 0.117409 | − | 1.58028i | ||||
\(86\) | −0.833713 | + | 1.44403i | −0.00969433 | + | 0.0167911i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.6486 | + | 2.85328i | 0.121007 | + | 0.0324236i | ||||
\(89\) | 78.1616 | + | 45.1266i | 0.878220 | + | 0.507041i | 0.870071 | − | 0.492926i | \(-0.164073\pi\) |
0.00814896 | + | 0.999967i | \(0.497406\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −145.444 | + | 1.62620i | −1.59828 | + | 0.0178703i | ||||
\(92\) | −60.0029 | − | 60.0029i | −0.652205 | − | 0.652205i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −80.9010 | + | 46.7082i | −0.860649 | + | 0.496896i | ||||
\(95\) | −135.976 | − | 47.4824i | −1.43133 | − | 0.499815i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 84.2362 | + | 84.2362i | 0.868414 | + | 0.868414i | 0.992297 | − | 0.123883i | \(-0.0395347\pi\) |
−0.123883 | + | 0.992297i | \(0.539535\pi\) | |||||||
\(98\) | 45.2962 | + | 155.090i | 0.462206 | + | 1.58255i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 106.950 | − | 134.463i | 1.06950 | − | 1.34463i | ||||
\(101\) | −37.0883 | − | 64.2388i | −0.367211 | − | 0.636028i | 0.621917 | − | 0.783083i | \(-0.286354\pi\) |
−0.989128 | + | 0.147055i | \(0.953021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 24.8309 | + | 92.6702i | 0.241077 | + | 0.899711i | 0.975315 | + | 0.220819i | \(0.0708729\pi\) |
−0.734238 | + | 0.678892i | \(0.762460\pi\) | |||||||
\(104\) | 196.803i | 1.89233i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 155.464 | 1.46664 | ||||||||
\(107\) | 42.6823 | − | 11.4367i | 0.398900 | − | 0.106885i | −0.0537912 | − | 0.998552i | \(-0.517131\pi\) |
0.452692 | + | 0.891667i | \(0.350464\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 117.615 | − | 67.9052i | 1.07904 | − | 0.622984i | 0.148403 | − | 0.988927i | \(-0.452587\pi\) |
0.930637 | + | 0.365943i | \(0.119254\pi\) | |||||||
\(110\) | 15.8624 | + | 10.7999i | 0.144203 | + | 0.0981812i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 25.2122 | − | 7.05863i | 0.225109 | − | 0.0630235i | ||||
\(113\) | 4.59841 | − | 4.59841i | 0.0406939 | − | 0.0406939i | −0.686467 | − | 0.727161i | \(-0.740839\pi\) |
0.727161 | + | 0.686467i | \(0.240839\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26.8225 | − | 55.6064i | −0.233239 | − | 0.483534i | ||||
\(116\) | −43.1388 | − | 74.7186i | −0.371886 | − | 0.644126i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −133.324 | + | 133.324i | −1.12986 | + | 1.12986i | ||||
\(119\) | 162.244 | − | 96.1059i | 1.36339 | − | 0.807613i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 59.8226 | − | 103.616i | 0.494402 | − | 0.856329i | ||||
\(122\) | 10.7664 | − | 40.1808i | 0.0882492 | − | 0.329351i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 98.0851 | + | 56.6294i | 0.791009 | + | 0.456689i | ||||
\(125\) | 105.713 | − | 66.7070i | 0.845702 | − | 0.533656i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.6949 | + | 16.6949i | 0.131456 | + | 0.131456i | 0.769773 | − | 0.638317i | \(-0.220369\pi\) |
−0.638317 | + | 0.769773i | \(0.720369\pi\) | |||||||
\(128\) | 58.2177 | + | 217.271i | 0.454825 | + | 1.69743i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −112.939 | + | 323.424i | −0.868760 | + | 2.48788i | ||||
\(131\) | 63.4004 | − | 109.813i | 0.483973 | − | 0.838266i | −0.515858 | − | 0.856674i | \(-0.672527\pi\) |
0.999831 | + | 0.0184088i | \(0.00586002\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −54.3623 | − | 194.173i | −0.408739 | − | 1.45995i | ||||
\(134\) | − | 153.563i | − | 1.14599i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −127.572 | − | 220.961i | −0.938031 | − | 1.62472i | ||||
\(137\) | −41.8269 | + | 156.100i | −0.305306 | + | 1.13942i | 0.627377 | + | 0.778716i | \(0.284129\pi\) |
−0.932682 | + | 0.360700i | \(0.882538\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 92.5186i | 0.665601i | 0.942997 | + | 0.332801i | \(0.107994\pi\) | ||||
−0.942997 | + | 0.332801i | \(0.892006\pi\) | |||||||
\(140\) | 240.057 | + | 15.1387i | 1.71469 | + | 0.108134i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −60.6552 | + | 16.2525i | −0.427149 | + | 0.114454i | ||||
\(143\) | −23.3619 | − | 6.25981i | −0.163370 | − | 0.0437749i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.7093 | − | 61.6694i | −0.0807541 | − | 0.425306i | ||||
\(146\) | −404.957 | −2.77368 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 68.7434 | − | 68.7434i | 0.464482 | − | 0.464482i | ||||
\(149\) | 140.299 | + | 81.0014i | 0.941601 | + | 0.543634i | 0.890462 | − | 0.455058i | \(-0.150381\pi\) |
0.0511394 | + | 0.998692i | \(0.483715\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 143.434 | + | 248.435i | 0.949893 | + | 1.64526i | 0.745645 | + | 0.666344i | \(0.232142\pi\) |
0.204248 | + | 0.978919i | \(0.434525\pi\) | |||||||
\(152\) | −263.528 | + | 70.6122i | −1.73374 | + | 0.464554i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.300367 | + | 26.8642i | 0.00195043 | + | 0.174443i | ||||
\(155\) | 53.7893 | + | 62.4235i | 0.347028 | + | 0.402732i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 74.0497 | − | 276.357i | 0.471654 | − | 1.76024i | −0.162174 | − | 0.986762i | \(-0.551851\pi\) |
0.633828 | − | 0.773474i | \(-0.281483\pi\) | |||||||
\(158\) | 272.731 | + | 73.0782i | 1.72615 | + | 0.462520i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.46607 | + | 127.410i | −0.0591630 | + | 0.796310i | ||||
\(161\) | 42.3767 | − | 75.3312i | 0.263209 | − | 0.467896i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.63680 | − | 9.84068i | −0.0161767 | − | 0.0603722i | 0.957366 | − | 0.288879i | \(-0.0932824\pi\) |
−0.973542 | + | 0.228507i | \(0.926616\pi\) | |||||||
\(164\) | −287.471 | + | 165.972i | −1.75287 | + | 1.01202i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −42.1781 | + | 73.0547i | −0.254085 | + | 0.440088i | ||||
\(167\) | 71.1342 | + | 71.1342i | 0.425954 | + | 0.425954i | 0.887247 | − | 0.461294i | \(-0.152615\pi\) |
−0.461294 | + | 0.887247i | \(0.652615\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 262.766i | − | 1.55483i | ||||||
\(170\) | −82.8484 | − | 436.336i | −0.487343 | − | 2.56668i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.899473 | + | 3.35688i | −0.00522949 | + | 0.0195167i | ||||
\(173\) | −77.4717 | − | 289.128i | −0.447813 | − | 1.67126i | −0.708401 | − | 0.705811i | \(-0.750583\pi\) |
0.260588 | − | 0.965450i | \(-0.416084\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 161.258 | + | 67.9772i | 0.921474 | + | 0.388441i | ||||
\(176\) | 4.35351 | 0.0247359 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 287.455 | + | 77.0232i | 1.61491 | + | 0.432715i | ||||
\(179\) | −280.191 | + | 161.768i | −1.56531 | + | 0.903733i | −0.568608 | + | 0.822609i | \(0.692518\pi\) |
−0.996704 | + | 0.0811241i | \(0.974149\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 43.2716 | 0.239069 | 0.119535 | − | 0.992830i | \(-0.461860\pi\) | ||||
0.119535 | + | 0.992830i | \(0.461860\pi\) | |||||||
\(182\) | −461.847 | + | 129.303i | −2.53762 | + | 0.710456i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −101.278 | − | 58.4731i | −0.550426 | − | 0.317788i | ||||
\(185\) | 63.7065 | − | 30.7296i | 0.344359 | − | 0.166106i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.2875 | − | 8.11552i | 0.161965 | − | 0.0433985i | ||||
\(188\) | −137.675 | + | 137.675i | −0.732312 | + | 0.732312i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −473.603 | − | 35.1870i | −2.49265 | − | 0.185195i | ||||
\(191\) | 19.2949 | − | 33.4198i | 0.101021 | − | 0.174973i | −0.811085 | − | 0.584929i | \(-0.801123\pi\) |
0.912105 | + | 0.409956i | \(0.134456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −233.231 | − | 62.4940i | −1.20845 | − | 0.323803i | −0.402296 | − | 0.915509i | \(-0.631788\pi\) |
−0.806154 | + | 0.591706i | \(0.798455\pi\) | |||||||
\(194\) | 340.178 | + | 196.402i | 1.75350 | + | 1.01238i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 174.852 | + | 287.794i | 0.892103 | + | 1.46834i | ||||
\(197\) | −217.403 | − | 217.403i | −1.10357 | − | 1.10357i | −0.993976 | − | 0.109594i | \(-0.965045\pi\) |
−0.109594 | − | 0.993976i | \(-0.534955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −168.448 | + | 97.2533i | −0.846470 | + | 0.488710i | −0.859458 | − | 0.511206i | \(-0.829199\pi\) |
0.0129880 | + | 0.999916i | \(0.495866\pi\) | |||||||
\(200\) | 94.4091 | − | 217.145i | 0.472045 | − | 1.08573i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −172.948 | − | 172.948i | −0.856177 | − | 0.856177i | ||||
\(203\) | 61.4416 | − | 62.8311i | 0.302668 | − | 0.309513i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −237.266 | + | 45.0503i | −1.15739 | + | 0.219758i | ||||
\(206\) | 158.172 | + | 273.962i | 0.767824 | + | 1.32991i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.1150 | + | 75.0701i | 0.0967066 | + | 0.360914i | ||||
\(209\) | − | 33.5288i | − | 0.160425i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −67.4406 | −0.319624 | −0.159812 | − | 0.987147i | \(-0.551089\pi\) | ||||
−0.159812 | + | 0.987147i | \(0.551089\pi\) | |||||||
\(212\) | 312.982 | − | 83.8632i | 1.47633 | − | 0.395581i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 126.182 | − | 72.8513i | 0.589636 | − | 0.340426i | ||||
\(215\) | −1.42299 | + | 2.09001i | −0.00661855 | + | 0.00972098i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −28.6101 | + | 111.758i | −0.131844 | + | 0.515013i | ||||
\(218\) | 316.651 | − | 316.651i | 1.45253 | − | 1.45253i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 37.7602 | + | 13.1858i | 0.171637 | + | 0.0599353i | ||||
\(221\) | 279.881 | + | 484.768i | 1.26643 | + | 2.19352i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.6765 | − | 17.6765i | 0.0792670 | − | 0.0792670i | −0.666362 | − | 0.745629i | \(-0.732149\pi\) |
0.745629 | + | 0.666362i | \(0.232149\pi\) | |||||||
\(224\) | −153.892 | + | 91.1588i | −0.687019 | + | 0.406959i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.7215 | − | 18.5702i | 0.0474402 | − | 0.0821689i | ||||
\(227\) | 83.0011 | − | 309.764i | 0.365644 | − | 1.36460i | −0.500903 | − | 0.865504i | \(-0.666999\pi\) |
0.866546 | − | 0.499097i | \(-0.166335\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 290.289 | + | 167.598i | 1.26764 | + | 0.731870i | 0.974540 | − | 0.224213i | \(-0.0719813\pi\) |
0.293096 | + | 0.956083i | \(0.405315\pi\) | |||||||
\(230\) | −132.884 | − | 154.215i | −0.577757 | − | 0.670498i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −84.0779 | − | 84.0779i | −0.362405 | − | 0.362405i | ||||
\(233\) | −71.7786 | − | 267.882i | −0.308063 | − | 1.14971i | −0.930277 | − | 0.366859i | \(-0.880433\pi\) |
0.622214 | − | 0.782847i | \(-0.286233\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −127.587 | + | 61.5433i | −0.542924 | + | 0.261886i | ||||
\(236\) | −196.489 | + | 340.328i | −0.832579 | + | 1.44207i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 434.725 | − | 444.556i | 1.82657 | − | 1.86788i | ||||
\(239\) | − | 57.1966i | − | 0.239316i | −0.992815 | − | 0.119658i | \(-0.961820\pi\) | ||
0.992815 | − | 0.119658i | \(-0.0381799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.95051 | − | 8.57453i | −0.0205415 | − | 0.0355790i | 0.855572 | − | 0.517684i | \(-0.173206\pi\) |
−0.876113 | + | 0.482105i | \(0.839872\pi\) | |||||||
\(242\) | 102.107 | − | 381.067i | 0.421928 | − | 1.57466i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 86.7002i | − | 0.355329i | ||||||
\(245\) | 51.0727 | + | 239.618i | 0.208460 | + | 0.978031i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 578.156 | − | 154.916i | 2.34071 | − | 0.627192i | ||||
\(248\) | 150.770 | + | 40.3987i | 0.607943 | + | 0.162898i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 279.764 | − | 302.677i | 1.11906 | − | 1.21071i | ||||
\(251\) | 187.727 | 0.747915 | 0.373957 | − | 0.927446i | \(-0.378001\pi\) | ||||
0.373957 | + | 0.927446i | \(0.378001\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.1626 | − | 10.1626i | 0.0401684 | − | 0.0401684i | ||||
\(254\) | 67.4206 | + | 38.9253i | 0.265436 | + | 0.153249i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 172.414 | + | 298.630i | 0.673493 | + | 1.16652i | ||||
\(257\) | 119.767 | − | 32.0914i | 0.466018 | − | 0.124869i | −0.0181666 | − | 0.999835i | \(-0.505783\pi\) |
0.484185 | + | 0.874966i | \(0.339116\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 86.3046 | + | 48.5496i | 0.333222 | + | 0.187450i | ||||
\(260\) | −52.9023 | + | 712.044i | −0.203470 | + | 2.73863i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 108.213 | − | 403.858i | 0.413028 | − | 1.54144i | ||||
\(263\) | −11.8632 | − | 3.17875i | −0.0451074 | − | 0.0120865i | 0.236195 | − | 0.971706i | \(-0.424100\pi\) |
−0.281302 | + | 0.959619i | \(0.590766\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 235.094 | + | 17.4666i | 0.887147 | + | 0.0659118i | ||||
\(266\) | −338.852 | − | 572.043i | −1.27388 | − | 2.15054i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −82.8379 | − | 309.155i | −0.309097 | − | 1.15356i | ||||
\(269\) | −16.4548 | + | 9.50018i | −0.0611703 | + | 0.0353167i | −0.530273 | − | 0.847827i | \(-0.677911\pi\) |
0.469103 | + | 0.883143i | \(0.344577\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 49.9304 | − | 86.4820i | 0.184245 | − | 0.319122i | −0.759077 | − | 0.651001i | \(-0.774349\pi\) |
0.943322 | + | 0.331879i | \(0.107683\pi\) | |||||||
\(272\) | −71.2465 | − | 71.2465i | −0.261935 | − | 0.261935i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 532.870i | 1.94478i | ||||||||
\(275\) | 22.7739 | + | 18.1139i | 0.0828140 | + | 0.0658688i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.4218 | − | 68.7510i | 0.0665046 | − | 0.248199i | −0.924668 | − | 0.380773i | \(-0.875658\pi\) |
0.991173 | + | 0.132575i | \(0.0423245\pi\) | |||||||
\(278\) | 78.9565 | + | 294.670i | 0.284016 | + | 1.05996i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 324.963 | − | 65.4741i | 1.16058 | − | 0.233836i | ||||
\(281\) | 121.502 | 0.432393 | 0.216196 | − | 0.976350i | \(-0.430635\pi\) | ||||
0.216196 | + | 0.976350i | \(0.430635\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 255.612 | + | 68.4910i | 0.903223 | + | 0.242018i | 0.680400 | − | 0.732841i | \(-0.261806\pi\) |
0.222823 | + | 0.974859i | \(0.428473\pi\) | |||||||
\(284\) | −113.345 | + | 65.4395i | −0.399100 | + | 0.230421i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −79.7495 | −0.278844 | ||||||||
\(287\) | −241.735 | − | 236.390i | −0.842284 | − | 0.823657i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −378.195 | − | 218.351i | −1.30863 | − | 0.755539i | ||||
\(290\) | −89.9234 | − | 186.423i | −0.310081 | − | 0.642837i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −815.265 | + | 218.449i | −2.79200 | + | 0.748115i | ||||
\(293\) | −59.1809 | + | 59.1809i | −0.201983 | + | 0.201983i | −0.800849 | − | 0.598866i | \(-0.795618\pi\) |
0.598866 | + | 0.800849i | \(0.295618\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −216.592 | + | 186.634i | −0.734211 | + | 0.632658i | ||||
\(296\) | 66.9907 | − | 116.031i | 0.226320 | − | 0.391998i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 515.976 | + | 138.255i | 1.73146 | + | 0.463944i | ||||
\(299\) | 222.195 | + | 128.284i | 0.743127 | + | 0.429044i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.53960 | + | 0.0395760i | −0.0117595 | + | 0.000131482i | ||||
\(302\) | 668.851 | + | 668.851i | 2.21474 | + | 2.21474i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −93.3054 | + | 53.8699i | −0.306926 | + | 0.177204i | ||||
\(305\) | 20.7954 | − | 59.5521i | 0.0681818 | − | 0.195253i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −100.076 | − | 100.076i | −0.325979 | − | 0.325979i | 0.525076 | − | 0.851055i | \(-0.324037\pi\) |
−0.851055 | + | 0.525076i | \(0.824037\pi\) | |||||||
\(308\) | 15.0963 | + | 53.9213i | 0.0490139 | + | 0.175069i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 224.591 | + | 152.913i | 0.724486 | + | 0.493267i | ||||
\(311\) | 141.092 | + | 244.378i | 0.453671 | + | 0.785781i | 0.998611 | − | 0.0526944i | \(-0.0167809\pi\) |
−0.544940 | + | 0.838475i | \(0.683448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −51.1230 | − | 190.794i | −0.163332 | − | 0.609564i | −0.998247 | − | 0.0591850i | \(-0.981150\pi\) |
0.834915 | − | 0.550379i | \(-0.185517\pi\) | |||||||
\(314\) | − | 943.386i | − | 3.00441i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 588.487 | 1.86230 | ||||||||
\(317\) | −151.390 | + | 40.5648i | −0.477571 | + | 0.127965i | −0.489571 | − | 0.871963i | \(-0.662847\pi\) |
0.0120003 | + | 0.999928i | \(0.496180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.6550 | − | 7.30636i | 0.0396708 | − | 0.0229039i | ||||
\(320\) | 92.5378 | + | 487.367i | 0.289181 | + | 1.52302i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 70.6802 | − | 276.093i | 0.219504 | − | 0.857432i | ||||
\(323\) | −548.708 | + | 548.708i | −1.69878 | + | 1.69878i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −207.124 | + | 476.396i | −0.637306 | + | 1.46583i | ||||
\(326\) | −16.7963 | − | 29.0921i | −0.0515224 | − | 0.0892394i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −323.480 | + | 323.480i | −0.986219 | + | 0.986219i | ||||
\(329\) | −172.845 | − | 97.2319i | −0.525365 | − | 0.295538i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −245.598 | + | 425.389i | −0.741989 | + | 1.28516i | 0.209599 | + | 0.977787i | \(0.432784\pi\) |
−0.951588 | + | 0.307375i | \(0.900549\pi\) | |||||||
\(332\) | −45.5050 | + | 169.827i | −0.137063 | + | 0.511527i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 287.268 | + | 165.854i | 0.860083 | + | 0.496569i | ||||
\(335\) | 17.2531 | − | 232.220i | 0.0515018 | − | 0.693194i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −250.219 | − | 250.219i | −0.742489 | − | 0.742489i | 0.230567 | − | 0.973056i | \(-0.425942\pi\) |
−0.973056 | + | 0.230567i | \(0.925942\pi\) | |||||||
\(338\) | −224.248 | − | 836.904i | −0.663455 | − | 2.47605i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −402.168 | − | 833.745i | −1.18285 | − | 2.45219i | ||||
\(341\) | −9.59124 | + | 16.6125i | −0.0281268 | + | 0.0487171i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −234.268 | + | 250.535i | −0.682996 | + | 0.730422i | ||||
\(344\) | 4.78951i | 0.0139230i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −493.491 | − | 854.751i | −1.42627 | − | 2.47038i | ||||
\(347\) | 160.644 | − | 599.530i | 0.462950 | − | 1.72775i | −0.200649 | − | 0.979663i | \(-0.564305\pi\) |
0.663598 | − | 0.748089i | \(-0.269028\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 69.6374i | 0.199534i | 0.995011 | + | 0.0997671i | \(0.0318098\pi\) | ||||
−0.995011 | + | 0.0997671i | \(0.968190\pi\) | |||||||
\(350\) | 571.615 | + | 78.8864i | 1.63319 | + | 0.225390i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −28.7285 | + | 7.69777i | −0.0816149 | + | 0.0218687i | ||||
\(353\) | 55.0131 | + | 14.7407i | 0.155845 | + | 0.0417584i | 0.335898 | − | 0.941898i | \(-0.390960\pi\) |
−0.180053 | + | 0.983657i | \(0.557627\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −93.5494 | + | 17.7625i | −0.263519 | + | 0.0500352i | ||||
\(356\) | 620.256 | 1.74229 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −754.346 | + | 754.346i | −2.10711 | + | 2.10711i | ||||
\(359\) | −52.7945 | − | 30.4809i | −0.147060 | − | 0.0849051i | 0.424665 | − | 0.905351i | \(-0.360392\pi\) |
−0.571725 | + | 0.820446i | \(0.693725\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 234.381 | + | 405.960i | 0.649255 | + | 1.12454i | ||||
\(362\) | 137.819 | − | 36.9285i | 0.380715 | − | 0.102012i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −860.045 | + | 509.452i | −2.36276 | + | 1.39959i | ||||
\(365\) | −612.380 | − | 45.4976i | −1.67775 | − | 0.124651i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −93.2748 | + | 348.106i | −0.254155 | + | 0.948519i | 0.714404 | + | 0.699734i | \(0.246698\pi\) |
−0.968559 | + | 0.248785i | \(0.919969\pi\) | |||||||
\(368\) | −44.6089 | − | 11.9529i | −0.121220 | − | 0.0324808i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 176.679 | − | 152.241i | 0.477510 | − | 0.411463i | ||||
\(371\) | 168.205 | + | 283.959i | 0.453382 | + | 0.765388i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.66229 | − | 17.3999i | −0.0124994 | − | 0.0466485i | 0.959394 | − | 0.282068i | \(-0.0910203\pi\) |
−0.971894 | + | 0.235419i | \(0.924354\pi\) | |||||||
\(374\) | 89.5392 | − | 51.6955i | 0.239410 | − | 0.138223i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −134.164 | + | 232.380i | −0.356820 | + | 0.618031i | ||||
\(377\) | 184.459 | + | 184.459i | 0.489281 | + | 0.489281i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 93.7813i | − | 0.247444i | −0.992317 | − | 0.123722i | \(-0.960517\pi\) | ||
0.992317 | − | 0.123722i | \(-0.0394831\pi\) | |||||||
\(380\) | −972.443 | + | 184.641i | −2.55906 | + | 0.485896i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 32.9330 | − | 122.908i | 0.0862122 | − | 0.321748i | ||||
\(383\) | −107.167 | − | 399.952i | −0.279809 | − | 1.04426i | −0.952550 | − | 0.304382i | \(-0.901550\pi\) |
0.672741 | − | 0.739878i | \(-0.265117\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.56402 | + | 40.6581i | −0.00665980 | + | 0.105605i | ||||
\(386\) | −796.168 | −2.06261 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 790.798 | + | 211.894i | 2.03814 | + | 0.546118i | ||||
\(389\) | −142.385 | + | 82.2062i | −0.366029 | + | 0.211327i | −0.671722 | − | 0.740803i | \(-0.734445\pi\) |
0.305693 | + | 0.952130i | \(0.401112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −332.627 | −0.850710 | ||||||||
\(392\) | 335.417 | + | 320.742i | 0.855656 | + | 0.818220i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −877.960 | − | 506.890i | −2.22832 | − | 1.28652i | ||||
\(395\) | 404.217 | + | 141.151i | 1.02333 | + | 0.357345i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −564.572 | + | 151.277i | −1.42210 | + | 0.381050i | −0.886227 | − | 0.463251i | \(-0.846683\pi\) |
−0.535870 | + | 0.844301i | \(0.680016\pi\) | |||||||
\(398\) | −453.505 | + | 453.505i | −1.13946 | + | 1.13946i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.8180 | − | 92.4793i | 0.0345451 | − | 0.231198i | ||||
\(401\) | 80.2339 | − | 138.969i | 0.200084 | − | 0.346556i | −0.748471 | − | 0.663168i | \(-0.769212\pi\) |
0.948555 | + | 0.316611i | \(0.102545\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −330.775 | − | 88.6308i | −0.820781 | − | 0.219928i | ||||
\(404\) | −441.475 | − | 254.886i | −1.09276 | − | 0.630905i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 142.069 | − | 252.551i | 0.349925 | − | 0.622046i | ||||
\(407\) | 11.6430 | + | 11.6430i | 0.0286068 | + | 0.0286068i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −143.273 | + | 82.7185i | −0.350300 | + | 0.202246i | −0.664817 | − | 0.747006i | \(-0.731491\pi\) |
0.314518 | + | 0.949252i | \(0.398157\pi\) | |||||||
\(410\) | −717.239 | + | 345.970i | −1.74936 | + | 0.843828i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 466.219 | + | 466.219i | 1.13160 | + | 1.13160i | ||||
\(413\) | −387.769 | − | 99.2694i | −0.938908 | − | 0.240362i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −71.9900 | + | 105.735i | −0.173470 | + | 0.254784i | ||||
\(416\) | −265.474 | − | 459.814i | −0.638159 | − | 1.10532i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −28.6139 | − | 106.788i | −0.0684542 | − | 0.255475i | ||||
\(419\) | 572.116i | 1.36543i | 0.730684 | + | 0.682716i | \(0.239201\pi\) | ||||
−0.730684 | + | 0.682716i | \(0.760799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 259.398 | 0.616148 | 0.308074 | − | 0.951362i | \(-0.400316\pi\) | ||||
0.308074 | + | 0.951362i | \(0.400316\pi\) | |||||||
\(422\) | −214.797 | + | 57.5546i | −0.508997 | + | 0.136385i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 386.727 | − | 223.277i | 0.912092 | − | 0.526596i | ||||
\(425\) | −76.2610 | − | 669.140i | −0.179438 | − | 1.57445i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 85.0401 | − | 23.8086i | 0.199157 | − | 0.0557578i | ||||
\(428\) | 214.732 | − | 214.732i | 0.501711 | − | 0.501711i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.74854 | + | 7.87104i | −0.00639196 | + | 0.0183047i | ||||
\(431\) | 310.336 | + | 537.517i | 0.720036 | + | 1.24714i | 0.960985 | + | 0.276602i | \(0.0892082\pi\) |
−0.240948 | + | 0.970538i | \(0.577458\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 334.651 | − | 334.651i | 0.772865 | − | 0.772865i | −0.205741 | − | 0.978606i | \(-0.565961\pi\) |
0.978606 | + | 0.205741i | \(0.0659605\pi\) | |||||||
\(434\) | 4.25280 | + | 380.362i | 0.00979908 | + | 0.876411i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 466.672 | − | 808.299i | 1.07035 | − | 1.85390i | ||||
\(437\) | −92.0560 | + | 343.558i | −0.210654 | + | 0.786173i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 568.777 | + | 328.383i | 1.29562 | + | 0.748026i | 0.979644 | − | 0.200741i | \(-0.0643351\pi\) |
0.315975 | + | 0.948768i | \(0.397668\pi\) | |||||||
\(440\) | 54.9696 | + | 4.08404i | 0.124931 | + | 0.00928191i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1305.12 | + | 1305.12i | 2.95276 | + | 2.95276i | ||||
\(443\) | 154.454 | + | 576.431i | 0.348655 | + | 1.30120i | 0.888283 | + | 0.459296i | \(0.151898\pi\) |
−0.539628 | + | 0.841904i | \(0.681435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 426.038 | + | 148.771i | 0.957388 | + | 0.334317i | ||||
\(446\) | 41.2140 | − | 71.3847i | 0.0924081 | − | 0.160055i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −485.567 | + | 496.548i | −1.08386 | + | 1.10837i | ||||
\(449\) | 162.638i | 0.362223i | 0.983463 | + | 0.181111i | \(0.0579694\pi\) | ||||
−0.983463 | + | 0.181111i | \(0.942031\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.1104 | − | 48.6886i | −0.0623290 | − | 0.107957i | ||||
\(452\) | 11.5672 | − | 43.1693i | 0.0255911 | − | 0.0955072i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 1057.43i | − | 2.32913i | ||||||
\(455\) | −712.938 | + | 143.644i | −1.56690 | + | 0.315701i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 486.828 | − | 130.445i | 1.06527 | − | 0.285438i | 0.316721 | − | 0.948519i | \(-0.397418\pi\) |
0.748548 | + | 0.663081i | \(0.230751\pi\) | |||||||
\(458\) | 1067.59 | + | 286.061i | 2.33099 | + | 0.624587i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −350.713 | − | 238.784i | −0.762420 | − | 0.519095i | ||||
\(461\) | −323.423 | −0.701568 | −0.350784 | − | 0.936456i | \(-0.614085\pi\) | ||||
−0.350784 | + | 0.936456i | \(0.614085\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 108.492 | − | 108.492i | 0.234324 | − | 0.234324i | −0.580171 | − | 0.814495i | \(-0.697014\pi\) |
0.814495 | + | 0.580171i | \(0.197014\pi\) | |||||||
\(464\) | −40.6649 | − | 23.4779i | −0.0876399 | − | 0.0505989i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −457.227 | − | 791.940i | −0.981173 | − | 1.69944i | ||||
\(467\) | −454.466 | + | 121.774i | −0.973161 | + | 0.260758i | −0.710162 | − | 0.704038i | \(-0.751378\pi\) |
−0.262999 | + | 0.964796i | \(0.584712\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 280.488 | − | 166.148i | 0.598055 | − | 0.354261i | ||||
\(470\) | −353.840 | + | 304.898i | −0.752851 | + | 0.648720i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −140.172 | + | 523.130i | −0.296975 | + | 1.10833i | ||||
\(473\) | −0.568550 | − | 0.152342i | −0.00120201 | − | 0.000322077i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −712.233 | − | 106.420i | −1.49944 | − | 0.224042i | ||||
\(476\) | 635.382 | − | 1129.49i | 1.33484 | − | 2.37288i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −48.8123 | − | 182.170i | −0.102118 | − | 0.381109i | ||||
\(479\) | 79.9576 | − | 46.1636i | 0.166926 | − | 0.0963749i | −0.414209 | − | 0.910182i | \(-0.635942\pi\) |
0.581136 | + | 0.813807i | \(0.302609\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −146.971 | + | 254.561i | −0.305553 | + | 0.529234i | ||||
\(482\) | −23.0849 | − | 23.0849i | −0.0478939 | − | 0.0478939i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 822.249i | − | 1.69886i | ||||||
\(485\) | 492.355 | + | 335.221i | 1.01517 | + | 0.691177i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −206.367 | + | 770.171i | −0.423751 | + | 1.58146i | 0.342884 | + | 0.939378i | \(0.388596\pi\) |
−0.766635 | + | 0.642083i | \(0.778071\pi\) | |||||||
\(488\) | −30.9254 | − | 115.415i | −0.0633717 | − | 0.236506i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 367.158 | + | 719.591i | 0.749302 | + | 1.46855i | ||||
\(491\) | −442.461 | −0.901143 | −0.450572 | − | 0.892740i | \(-0.648780\pi\) | ||||
−0.450572 | + | 0.892740i | \(0.648780\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −326.673 | − | 87.5317i | −0.662622 | − | 0.177549i | ||||
\(494\) | 1709.21 | − | 986.810i | 3.45993 | − | 1.99759i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 61.6401 | 0.124274 | ||||||||
\(497\) | −95.3118 | − | 93.2040i | −0.191774 | − | 0.187533i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 59.9751 | + | 34.6267i | 0.120191 | + | 0.0693921i | 0.558890 | − | 0.829242i | \(-0.311227\pi\) |
−0.438699 | + | 0.898634i | \(0.644561\pi\) | |||||||
\(500\) | 399.949 | − | 760.268i | 0.799897 | − | 1.52054i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 597.905 | − | 160.208i | 1.19105 | − | 0.319140i | ||||
\(503\) | −570.214 | + | 570.214i | −1.13363 | + | 1.13363i | −0.144057 | + | 0.989569i | \(0.546015\pi\) |
−0.989569 | + | 0.144057i | \(0.953985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −242.102 | − | 280.964i | −0.479410 | − | 0.556365i | ||||
\(506\) | 23.6948 | − | 41.0405i | 0.0468276 | − | 0.0811078i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 156.730 | + | 41.9956i | 0.308523 | + | 0.0826685i | ||||
\(509\) | 252.827 | + | 145.970i | 0.496713 | + | 0.286778i | 0.727355 | − | 0.686261i | \(-0.240749\pi\) |
−0.230642 | + | 0.973039i | \(0.574083\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −438.145 | − | 739.666i | −0.857426 | − | 1.44749i | ||||
\(512\) | 167.775 | + | 167.775i | 0.327686 | + | 0.327686i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 354.067 | − | 204.421i | 0.688846 | − | 0.397706i | ||||
\(515\) | 208.409 | + | 432.058i | 0.404677 | + | 0.838948i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.3177 | − | 23.3177i | −0.0451020 | − | 0.0451020i | ||||
\(518\) | 316.311 | + | 80.9760i | 0.610639 | + | 0.156324i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 183.558 | + | 966.742i | 0.352996 | + | 1.85912i | ||||
\(521\) | −204.719 | − | 354.584i | −0.392935 | − | 0.680583i | 0.599900 | − | 0.800075i | \(-0.295207\pi\) |
−0.992835 | + | 0.119491i | \(0.961874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.0443 | − | 138.251i | −0.0708305 | − | 0.264343i | 0.921425 | − | 0.388556i | \(-0.127026\pi\) |
−0.992256 | + | 0.124213i | \(0.960359\pi\) | |||||||
\(524\) | − | 871.426i | − | 1.66303i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −40.4970 | −0.0769904 | ||||||||
\(527\) | 428.832 | − | 114.905i | 0.813723 | − | 0.218036i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 326.093 | − | 188.270i | 0.616432 | − | 0.355897i | ||||
\(530\) | 763.675 | − | 145.001i | 1.44090 | − | 0.273587i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −990.763 | − | 968.853i | −1.86234 | − | 1.82115i | ||||
\(533\) | 709.684 | − | 709.684i | 1.33149 | − | 1.33149i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 198.999 | − | 95.9896i | 0.371960 | − | 0.179420i | ||||
\(536\) | −220.547 | − | 381.999i | −0.411469 | − | 0.712685i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −44.3006 | + | 44.3006i | −0.0823431 | + | 0.0823431i | ||||
\(539\) | −48.7433 | + | 29.6145i | −0.0904328 | + | 0.0549433i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −97.2826 | + | 168.498i | −0.179820 | + | 0.311457i | −0.941819 | − | 0.336121i | \(-0.890885\pi\) |
0.761999 | + | 0.647578i | \(0.224218\pi\) | |||||||
\(542\) | 85.2224 | − | 318.054i | 0.157237 | − | 0.586816i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 596.125 | + | 344.173i | 1.09582 | + | 0.632671i | ||||
\(545\) | 514.419 | − | 443.267i | 0.943888 | − | 0.813333i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −170.750 | − | 170.750i | −0.312158 | − | 0.312158i | 0.533587 | − | 0.845745i | \(-0.320844\pi\) |
−0.845745 | + | 0.533587i | \(0.820844\pi\) | |||||||
\(548\) | 287.451 | + | 1072.78i | 0.524545 | + | 1.95763i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 87.9929 | + | 38.2570i | 0.159987 | + | 0.0695581i | ||||
\(551\) | −180.816 | + | 313.183i | −0.328160 | + | 0.568389i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 161.603 | + | 577.219i | 0.292230 | + | 1.04380i | ||||
\(554\) | − | 234.692i | − | 0.423631i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 317.912 | + | 550.640i | 0.571785 | + | 0.990360i | ||||
\(557\) | −150.676 | + | 562.331i | −0.270514 | + | 1.00957i | 0.688275 | + | 0.725450i | \(0.258368\pi\) |
−0.958789 | + | 0.284121i | \(0.908298\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 10.5077i | − | 0.0187973i | ||||||
\(560\) | 117.265 | − | 58.1891i | 0.209401 | − | 0.103909i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 386.982 | − | 103.692i | 0.688581 | − | 0.184505i | ||||
\(563\) | −403.835 | − | 108.207i | −0.717291 | − | 0.192197i | −0.118328 | − | 0.992975i | \(-0.537754\pi\) |
−0.598963 | + | 0.800777i | \(0.704420\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.2995 | − | 26.8774i | 0.0323886 | − | 0.0475706i | ||||
\(566\) | 872.570 | 1.54164 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −127.542 | + | 127.542i | −0.224546 | + | 0.224546i | ||||
\(569\) | −424.932 | − | 245.335i | −0.746806 | − | 0.431168i | 0.0777329 | − | 0.996974i | \(-0.475232\pi\) |
−0.824539 | + | 0.565806i | \(0.808565\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 105.483 | + | 182.702i | 0.184734 | + | 0.319969i | 0.943487 | − | 0.331410i | \(-0.107524\pi\) |
−0.758753 | + | 0.651379i | \(0.774191\pi\) | |||||||
\(572\) | −160.553 | + | 43.0199i | −0.280686 | + | 0.0752096i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −971.660 | − | 546.595i | −1.69279 | − | 0.952257i | ||||
\(575\) | −183.622 | − | 248.135i | −0.319343 | − | 0.431538i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.3165 | − | 68.3580i | 0.0317443 | − | 0.118471i | −0.948236 | − | 0.317568i | \(-0.897134\pi\) |
0.979980 | + | 0.199096i | \(0.0638006\pi\) | |||||||
\(578\) | −1390.89 | − | 372.687i | −2.40638 | − | 0.644787i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −281.598 | − | 326.800i | −0.485514 | − | 0.563448i | ||||
\(581\) | −179.071 | + | 2.00218i | −0.308212 | + | 0.00344609i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.2038 | + | 53.0092i | 0.0243633 | + | 0.0909249i | ||||
\(584\) | −1007.36 | + | 581.599i | −1.72493 | + | 0.995888i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −137.984 | + | 238.996i | −0.235468 | + | 0.407842i | ||||
\(587\) | 716.384 | + | 716.384i | 1.22042 | + | 1.22042i | 0.967484 | + | 0.252932i | \(0.0813949\pi\) |
0.252932 | + | 0.967484i | \(0.418605\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 474.724i | − | 0.805982i | ||||||
\(590\) | −530.566 | + | 779.268i | −0.899264 | + | 1.32079i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.6941 | − | 51.1070i | 0.0231319 | − | 0.0863294i | ||||
\(593\) | 181.380 | + | 676.921i | 0.305869 | + | 1.14152i | 0.932194 | + | 0.361958i | \(0.117892\pi\) |
−0.626325 | + | 0.779562i | \(0.715442\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 707.342 | − | 623.420i | 1.18881 | − | 1.04776i | ||||
\(596\) | 1113.35 | 1.86803 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 817.165 | + | 218.959i | 1.36650 | + | 0.366152i | ||||
\(599\) | −39.4905 | + | 22.7998i | −0.0659273 | + | 0.0380632i | −0.532601 | − | 0.846366i | \(-0.678785\pi\) |
0.466674 | + | 0.884429i | \(0.345452\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1084.31 | 1.80418 | 0.902092 | − | 0.431544i | \(-0.142031\pi\) | ||||
0.902092 | + | 0.431544i | \(0.142031\pi\) | |||||||
\(602\) | −11.2398 | + | 3.14679i | −0.0186707 | + | 0.00522723i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1707.34 | + | 985.734i | 2.82672 | + | 1.63201i | ||||
\(605\) | 197.220 | − | 564.782i | 0.325984 | − | 0.933524i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 409.938 | − | 109.843i | 0.675351 | − | 0.180960i | 0.0951869 | − | 0.995459i | \(-0.469655\pi\) |
0.580164 | + | 0.814500i | \(0.302988\pi\) | |||||||
\(608\) | 520.462 | − | 520.462i | 0.856024 | − | 0.856024i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.4105 | − | 207.419i | 0.0252631 | − | 0.340032i | ||||
\(611\) | 294.344 | − | 509.819i | 0.481741 | − | 0.834400i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −558.097 | − | 149.542i | −0.910435 | − | 0.243950i | −0.226943 | − | 0.973908i | \(-0.572873\pi\) |
−0.683492 | + | 0.729958i | \(0.739540\pi\) | |||||||
\(614\) | −404.144 | − | 233.333i | −0.658215 | − | 0.380021i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 39.3295 | + | 66.3952i | 0.0638466 | + | 0.107784i | ||||
\(617\) | −23.3244 | − | 23.3244i | −0.0378030 | − | 0.0378030i | 0.687953 | − | 0.725756i | \(-0.258510\pi\) |
−0.725756 | + | 0.687953i | \(0.758510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −534.066 | + | 308.343i | −0.862788 | + | 0.498131i | −0.864945 | − | 0.501867i | \(-0.832647\pi\) |
0.00215709 | + | 0.999998i | \(0.499313\pi\) | |||||||
\(620\) | 534.635 | + | 186.693i | 0.862315 | + | 0.301118i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 657.928 | + | 657.928i | 1.05776 | + | 1.05776i | ||||
\(623\) | 170.327 | + | 608.379i | 0.273398 | + | 0.976532i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 457.068 | − | 426.279i | 0.731309 | − | 0.682046i | ||||
\(626\) | −325.651 | − | 564.044i | −0.520210 | − | 0.901029i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −508.899 | − | 1899.24i | −0.810348 | − | 3.02426i | ||||
\(629\) | − | 381.081i | − | 0.605852i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 524.168 | 0.830695 | 0.415347 | − | 0.909663i | \(-0.363660\pi\) | ||||
0.415347 | + | 0.909663i | \(0.363660\pi\) | |||||||
\(632\) | 783.393 | − | 209.909i | 1.23955 | − | 0.332135i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −447.555 | + | 258.396i | −0.705923 | + | 0.407565i | ||||
\(635\) | 97.5808 | + | 66.4381i | 0.153671 | + | 0.104627i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −735.873 | − | 703.678i | −1.15522 | − | 1.10467i | ||||
\(638\) | 34.0705 | − | 34.0705i | 0.0534020 | − | 0.0534020i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 488.628 | + | 1012.99i | 0.763481 | + | 1.58279i | ||||
\(641\) | −29.7943 | − | 51.6052i | −0.0464809 | − | 0.0805074i | 0.841849 | − | 0.539713i | \(-0.181467\pi\) |
−0.888330 | + | 0.459206i | \(0.848134\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −282.054 | + | 282.054i | −0.438653 | + | 0.438653i | −0.891558 | − | 0.452906i | \(-0.850387\pi\) |
0.452906 | + | 0.891558i | \(0.350387\pi\) | |||||||
\(644\) | −6.64103 | − | 593.961i | −0.0103122 | − | 0.922300i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1279.35 | + | 2215.89i | −1.98041 | + | 3.43018i | ||||
\(647\) | −113.319 | + | 422.913i | −0.175145 | + | 0.653652i | 0.821381 | + | 0.570379i | \(0.193204\pi\) |
−0.996527 | + | 0.0832724i | \(0.973463\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −57.6409 | − | 33.2790i | −0.0888149 | − | 0.0512773i | ||||
\(650\) | −253.124 | + | 1694.07i | −0.389422 | + | 2.60627i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −49.5079 | − | 49.5079i | −0.0759323 | − | 0.0759323i | ||||
\(653\) | −121.826 | − | 454.660i | −0.186563 | − | 0.696263i | −0.994291 | − | 0.106707i | \(-0.965969\pi\) |
0.807727 | − | 0.589556i | \(-0.200697\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 209.016 | − | 598.560i | 0.319108 | − | 0.913832i | ||||
\(656\) | −90.3285 | + | 156.454i | −0.137696 | + | 0.238496i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −633.486 | − | 162.173i | −0.962745 | − | 0.246464i | ||||
\(659\) | − | 1076.98i | − | 1.63426i | −0.576454 | − | 0.817129i | \(-0.695564\pi\) | ||
0.576454 | − | 0.817129i | \(-0.304436\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.2193 | − | 62.7337i | −0.0547948 | − | 0.0949073i | 0.837327 | − | 0.546702i | \(-0.184117\pi\) |
−0.892122 | + | 0.451795i | \(0.850784\pi\) | |||||||
\(662\) | −419.193 | + | 1564.45i | −0.633222 | + | 2.36322i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 242.305i | 0.364916i | ||||||||
\(665\) | −448.146 | − | 903.119i | −0.673904 | − | 1.35807i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −149.731 | + | 40.1204i | −0.224485 | + | 0.0601505i | ||||
\(668\) | 667.799 | + | 178.936i | 0.999699 | + | 0.267868i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −143.229 | − | 754.339i | −0.213774 | − | 1.12588i | ||||
\(671\) | 14.6843 | 0.0218842 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −217.067 | + | 217.067i | −0.322537 | + | 0.322537i | −0.849740 | − | 0.527203i | \(-0.823241\pi\) |
0.527203 | + | 0.849740i | \(0.323241\pi\) | |||||||
\(674\) | −1010.48 | − | 583.402i | −1.49923 | − | 0.865581i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −902.916 | − | 1563.90i | −1.33568 | − | 2.31346i | ||||
\(677\) | 712.265 | − | 190.851i | 1.05209 | − | 0.281907i | 0.308975 | − | 0.951070i | \(-0.400014\pi\) |
0.743115 | + | 0.669164i | \(0.233348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.32314 | + | 833.843i | 0.0137307 | + | 1.22805i | ||||
\(680\) | −832.756 | − | 966.428i | −1.22464 | − | 1.42122i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.3706 | + | 61.0958i | −0.0240038 | + | 0.0895833i | ||||
\(683\) | −447.760 | − | 119.977i | −0.655579 | − | 0.175662i | −0.0843288 | − | 0.996438i | \(-0.526875\pi\) |
−0.571250 | + | 0.820776i | \(0.693541\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −59.8689 | + | 805.812i | −0.0873998 | + | 1.17637i | ||||
\(686\) | −532.328 | + | 997.874i | −0.775988 | + | 1.45463i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.489530 | + | 1.82695i | 0.000711526 | + | 0.00265545i | ||||
\(689\) | −848.441 | + | 489.848i | −1.23141 | + | 0.710955i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 206.290 | − | 357.305i | 0.298538 | − | 0.517084i | −0.677263 | − | 0.735741i | \(-0.736834\pi\) |
0.975802 | + | 0.218657i | \(0.0701676\pi\) | |||||||
\(692\) | −1454.59 | − | 1454.59i | −2.10200 | − | 2.10200i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 2046.58i | − | 2.94897i | ||||||
\(695\) | 86.2922 | + | 454.473i | 0.124161 | + | 0.653918i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −336.768 | + | 1256.84i | −0.483168 | + | 1.80321i | ||||
\(698\) | 59.4294 | + | 221.794i | 0.0851424 | + | 0.317756i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1193.34 | − | 149.536i | 1.70477 | − | 0.213623i | ||||
\(701\) | 946.008 | 1.34951 | 0.674756 | − | 0.738041i | \(-0.264249\pi\) | ||||
0.674756 | + | 0.738041i | \(0.264249\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −393.603 | − | 105.466i | −0.559890 | − | 0.150022i | ||||
\(704\) | −100.011 | + | 57.7415i | −0.142061 | + | 0.0820191i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 187.795 | 0.265999 | ||||||||
\(707\) | 128.772 | − | 503.015i | 0.182139 | − | 0.711478i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −66.1749 | − | 38.2061i | −0.0933355 | − | 0.0538873i | 0.452606 | − | 0.891711i | \(-0.350495\pi\) |
−0.545941 | + | 0.837823i | \(0.683828\pi\) | |||||||
\(710\) | −282.794 | + | 136.409i | −0.398301 | + | 0.192126i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 825.683 | − | 221.241i | 1.15967 | − | 0.310732i | ||||
\(713\) | 143.889 | − | 143.889i | 0.201808 | − | 0.201808i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −120.598 | − | 8.95999i | −0.168668 | − | 0.0125315i | ||||
\(716\) | −1111.74 | + | 1925.58i | −1.55270 | + | 2.68936i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −194.162 | − | 52.0256i | −0.270421 | − | 0.0724591i | ||||
\(719\) | −726.346 | − | 419.356i | −1.01022 | − | 0.583249i | −0.0989618 | − | 0.995091i | \(-0.531552\pi\) |
−0.911255 | + | 0.411842i | \(0.864886\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −329.264 | + | 585.319i | −0.456677 | + | 0.811815i | ||||
\(722\) | 1092.95 | + | 1092.95i | 1.51378 | + | 1.51378i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 257.538 | − | 148.690i | 0.355715 | − | 0.205372i | ||||
\(725\) | −115.038 | − | 292.013i | −0.158673 | − | 0.402777i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 325.814 | + | 325.814i | 0.448162 | + | 0.448162i | 0.894743 | − | 0.446581i | \(-0.147359\pi\) |
−0.446581 | + | 0.894743i | \(0.647359\pi\) | |||||||
\(728\) | −963.172 | + | 984.954i | −1.32304 | + | 1.35296i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1989.25 | + | 377.704i | −2.72500 | + | 0.517403i | ||||
\(731\) | 6.81135 | + | 11.7976i | 0.00931785 | + | 0.0161390i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −176.158 | − | 657.430i | −0.240324 | − | 0.896903i | −0.975676 | − | 0.219217i | \(-0.929650\pi\) |
0.735352 | − | 0.677686i | \(-0.237017\pi\) | |||||||
\(734\) | 1188.31i | 1.61896i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 315.505 | 0.428676 | ||||||||
\(737\) | 52.3612 | − | 14.0301i | 0.0710464 | − | 0.0190368i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1219.14 | + | 703.869i | −1.64971 | + | 0.952461i | −0.672526 | + | 0.740074i | \(0.734791\pi\) |
−0.977185 | + | 0.212388i | \(0.931876\pi\) | |||||||
\(740\) | 273.567 | − | 401.801i | 0.369685 | − | 0.542974i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 778.062 | + | 760.856i | 1.04860 | + | 1.02541i | ||||
\(743\) | 431.433 | − | 431.433i | 0.580664 | − | 0.580664i | −0.354422 | − | 0.935086i | \(-0.615322\pi\) |
0.935086 | + | 0.354422i | \(0.115322\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 764.730 | + | 267.042i | 1.02648 | + | 0.358445i | ||||
\(746\) | −29.6986 | − | 51.4394i | −0.0398104 | − | 0.0689537i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 152.375 | − | 152.375i | 0.203710 | − | 0.203710i | ||||
\(749\) | 269.588 | + | 151.653i | 0.359931 | + | 0.202475i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 98.6211 | − | 170.817i | 0.131320 | − | 0.227452i | −0.792866 | − | 0.609396i | \(-0.791412\pi\) |
0.924186 | + | 0.381944i | \(0.124745\pi\) | |||||||
\(752\) | −27.4256 | + | 102.354i | −0.0364702 | + | 0.136109i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 744.917 | + | 430.078i | 0.987953 | + | 0.570395i | ||||
\(755\) | 936.296 | + | 1086.59i | 1.24013 | + | 1.43919i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −925.874 | − | 925.874i | −1.22308 | − | 1.22308i | −0.966530 | − | 0.256553i | \(-0.917413\pi\) |
−0.256553 | − | 0.966530i | \(-0.582587\pi\) | |||||||
\(758\) | −80.0341 | − | 298.691i | −0.105586 | − | 0.394052i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1228.65 | + | 592.657i | −1.61665 | + | 0.779812i | ||||
\(761\) | −148.294 | + | 256.852i | −0.194867 | + | 0.337519i | −0.946857 | − | 0.321655i | \(-0.895761\pi\) |
0.751990 | + | 0.659174i | \(0.229094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 920.973 | + | 235.770i | 1.20704 | + | 0.309004i | ||||
\(764\) | − | 265.205i | − | 0.347127i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −682.647 | − | 1182.38i | −0.891184 | − | 1.54358i | ||||
\(767\) | 307.524 | − | 1147.70i | 0.400945 | − | 1.49635i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 483.085i | − | 0.628199i | −0.949390 | − | 0.314099i | \(-0.898297\pi\) | ||
0.949390 | − | 0.314099i | \(-0.101703\pi\) | |||||||
\(770\) | 26.5318 | + | 131.683i | 0.0344568 | + | 0.171017i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1602.85 | + | 429.484i | −2.07624 | + | 0.556326i | ||||
\(773\) | −309.472 | − | 82.9229i | −0.400353 | − | 0.107274i | 0.0530240 | − | 0.998593i | \(-0.483114\pi\) |
−0.453376 | + | 0.891319i | \(0.649781\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 322.448 | + | 256.470i | 0.416062 | + | 0.330928i | ||||
\(776\) | 1128.29 | 1.45398 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −383.338 | + | 383.338i | −0.492723 | + | 0.492723i | ||||
\(779\) | 1204.93 | + | 695.669i | 1.54677 | + | 0.893028i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.0834 | − | 19.1970i | −0.0141913 | − | 0.0245800i | ||||
\(782\) | −1059.41 | + | 283.868i | −1.35475 | + | 0.363003i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 160.727 | + | 88.0641i | 0.205009 | + | 0.112327i | ||||
\(785\) | 105.991 | − | 1426.60i | 0.135020 | − | 1.81732i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 219.064 | − | 817.557i | 0.278353 | − | 1.03883i | −0.675208 | − | 0.737627i | \(-0.735946\pi\) |
0.953561 | − | 0.301200i | \(-0.0973870\pi\) | |||||||
\(788\) | −2040.95 | − | 546.872i | −2.59004 | − | 0.694000i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1407.88 | + | 104.600i | 1.78213 | + | 0.132406i | ||||
\(791\) | 45.5191 | − | 0.508945i | 0.0575463 | − | 0.000643420i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 67.8473 | + | 253.209i | 0.0855577 | + | 0.319306i | ||||
\(794\) | −1669.05 | + | 963.626i | −2.10208 | + | 1.21363i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −668.363 | + | 1157.64i | −0.839652 | + | 1.45432i | ||||
\(797\) | −1003.28 | − | 1003.28i | −1.25882 | − | 1.25882i | −0.951658 | − | 0.307160i | \(-0.900621\pi\) |
−0.307160 | − | 0.951658i | \(-0.599379\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 763.203i | 0.955197i | ||||||||
\(800\) | 72.3355 | + | 634.695i | 0.0904193 | + | 0.793369i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 136.945 | − | 511.086i | 0.170755 | − | 0.637265i | ||||
\(803\) | −36.9985 | − | 138.080i | −0.0460753 | − | 0.171955i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 137.903 | − | 409.570i | 0.171308 | − | 0.508782i | ||||
\(806\) | −1129.15 | −1.40093 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −678.606 | − | 181.832i | −0.839859 | − | 0.225040i | ||||
\(809\) | −331.791 | + | 191.559i | −0.410124 | + | 0.236785i | −0.690843 | − | 0.723005i | \(-0.742760\pi\) |
0.280719 | + | 0.959790i | \(0.409427\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 537.982 | 0.663357 | 0.331678 | − | 0.943393i | \(-0.392385\pi\) | ||||
0.331678 | + | 0.943393i | \(0.392385\pi\) | |||||||
\(812\) | 149.780 | − | 585.076i | 0.184458 | − | 0.720537i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 47.0188 | + | 27.1463i | 0.0577627 | + | 0.0333493i | ||||
\(815\) | −22.1310 | − | 45.8804i | −0.0271546 | − | 0.0562950i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.0703 | − | 3.77013i | 0.0172220 | − | 0.00461461i | ||||
\(818\) | −385.727 | + | 385.727i | −0.471549 | + | 0.471549i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1257.32 | + | 1083.42i | −1.53332 | + | 1.32124i | ||||
\(821\) | 192.500 | − | 333.419i | 0.234470 | − | 0.406114i | −0.724649 | − | 0.689119i | \(-0.757998\pi\) |
0.959118 | + | 0.283005i | \(0.0913312\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 214.992 | + | 57.6069i | 0.261230 | + | 0.0699963i | 0.387057 | − | 0.922056i | \(-0.373492\pi\) |
−0.125827 | + | 0.992052i | \(0.540158\pi\) | |||||||
\(824\) | 786.926 | + | 454.332i | 0.955007 | + | 0.551374i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1319.75 | + | 14.7561i | −1.59776 | + | 0.0178645i | ||||
\(827\) | 542.598 | + | 542.598i | 0.656104 | + | 0.656104i | 0.954456 | − | 0.298352i | \(-0.0964370\pi\) |
−0.298352 | + | 0.954456i | \(0.596437\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −968.472 | + | 559.148i | −1.16824 | + | 0.674485i | −0.953265 | − | 0.302135i | \(-0.902301\pi\) |
−0.214976 | + | 0.976619i | \(0.568967\pi\) | |||||||
\(830\) | −139.051 | + | 398.201i | −0.167531 | + | 0.479761i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1457.76 | − | 1457.76i | −1.75212 | − | 1.75212i | ||||
\(833\) | 1282.35 | + | 313.048i | 1.53943 | + | 0.375808i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 415.775 | + | 283.081i | 0.497934 | + | 0.339019i | ||||
\(836\) | −115.212 | − | 199.552i | −0.137813 | − | 0.238699i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 488.251 | + | 1822.18i | 0.582638 | + | 2.17444i | ||||
\(839\) | − | 866.690i | − | 1.03300i | −0.856286 | − | 0.516502i | \(-0.827234\pi\) | ||
0.856286 | − | 0.516502i | \(-0.172766\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 683.391 | 0.812594 | ||||||||
\(842\) | 826.177 | − | 221.374i | 0.981208 | − | 0.262914i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −401.384 | + | 231.739i | −0.475574 | + | 0.274573i | ||||
\(845\) | −245.082 | − | 1290.77i | −0.290038 | − | 1.52754i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 806.505 | − | 225.796i | 0.952190 | − | 0.266583i | ||||
\(848\) | 124.696 | − | 124.696i | 0.147047 | − | 0.147047i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −813.942 | − | 2066.11i | −0.957578 | − | 2.43072i | ||||
\(851\) | −87.3347 | − | 151.268i | −0.102626 | − | 0.177753i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 846.282 | − | 846.282i | 0.992124 | − | 0.992124i | −0.00784512 | − | 0.999969i | \(-0.502497\pi\) |
0.999969 | + | 0.00784512i | \(0.00249721\pi\) | |||||||
\(854\) | 250.532 | − | 148.404i | 0.293363 | − | 0.173775i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 209.258 | − | 362.445i | 0.244460 | − | 0.423417i | ||||
\(857\) | −251.985 | + | 940.421i | −0.294032 | + | 1.09734i | 0.647952 | + | 0.761681i | \(0.275626\pi\) |
−0.941983 | + | 0.335659i | \(0.891041\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1270.34 | − | 733.431i | −1.47886 | − | 0.853819i | −0.479144 | − | 0.877736i | \(-0.659053\pi\) |
−0.999714 | + | 0.0239168i | \(0.992386\pi\) | |||||||
\(860\) | −1.28746 | + | 17.3287i | −0.00149705 | + | 0.0201497i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1447.14 | + | 1447.14i | 1.67881 | + | 1.67881i | ||||
\(863\) | −215.966 | − | 805.996i | −0.250250 | − | 0.933946i | −0.970672 | − | 0.240410i | \(-0.922718\pi\) |
0.720421 | − | 0.693537i | \(-0.243948\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −650.229 | − | 1348.01i | −0.751710 | − | 1.55839i | ||||
\(866\) | 780.260 | − | 1351.45i | 0.900993 | − | 1.56057i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 213.744 | + | 763.456i | 0.246249 | + | 0.879557i | ||||
\(869\) | 99.6712i | 0.114696i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 483.859 | + | 838.069i | 0.555521 | + | 0.962191i | ||||
\(872\) | 332.917 | − | 1242.46i | 0.381786 | − | 1.42484i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1172.79i | 1.34186i | ||||||||
\(875\) | 855.539 | + | 183.515i | 0.977759 | + | 0.209731i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1454.90 | − | 389.839i | 1.65895 | − | 0.444514i | 0.696852 | − | 0.717215i | \(-0.254584\pi\) |
0.962099 | + | 0.272701i | \(0.0879170\pi\) | |||||||
\(878\) | 2091.79 | + | 560.493i | 2.38245 | + | 0.638375i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 21.3855 | − | 4.06053i | 0.0243017 | − | 0.00461423i | ||||
\(881\) | −381.409 | −0.432928 | −0.216464 | − | 0.976291i | \(-0.569452\pi\) | ||||
−0.216464 | + | 0.976291i | \(0.569452\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 523.721 | − | 523.721i | 0.593115 | − | 0.593115i | −0.345356 | − | 0.938472i | \(-0.612242\pi\) |
0.938472 | + | 0.345356i | \(0.112242\pi\) | |||||||
\(884\) | 3331.52 | + | 1923.45i | 3.76869 | + | 2.17585i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 983.867 | + | 1704.11i | 1.11046 | + | 1.92337i | ||||
\(887\) | 1068.20 | − | 286.223i | 1.20428 | − | 0.322686i | 0.399766 | − | 0.916617i | \(-0.369091\pi\) |
0.804516 | + | 0.593931i | \(0.202425\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.84777 | + | 165.261i | 0.00207848 | + | 0.185895i | ||||
\(890\) | 1483.88 | + | 110.247i | 1.66729 | + | 0.123873i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 44.4648 | − | 165.945i | 0.0498485 | − | 0.186037i | ||||
\(893\) | 788.281 | + | 211.219i | 0.882734 | + | 0.236528i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1225.48 | + | 1055.98i | −1.36925 | + | 1.17986i | ||||
\(896\) | −771.981 | + | 1372.32i | −0.861585 | + | 1.53160i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 138.797 | + | 517.998i | 0.154563 | + | 0.576835i | ||||
\(899\) | 179.178 | − | 103.448i | 0.199308 | − | 0.115071i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 635.062 | − | 1099.96i | 0.704841 | − | 1.22082i | ||||
\(902\) | −131.082 | − | 131.082i | −0.145324 | − | 0.145324i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 61.5927i | − | 0.0681336i | ||||||
\(905\) | 212.560 | − | 40.3594i | 0.234873 | − | 0.0445960i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 236.171 | − | 881.400i | 0.260386 | − | 0.971776i | −0.704628 | − | 0.709577i | \(-0.748886\pi\) |
0.965014 | − | 0.262198i | \(-0.0844474\pi\) | |||||||
\(908\) | −570.416 | − | 2128.82i | −0.628212 | − | 2.34452i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2148.10 | + | 1065.93i | −2.36055 | + | 1.17135i | ||||
\(911\) | −269.276 | −0.295583 | −0.147791 | − | 0.989019i | \(-0.547216\pi\) | ||||
−0.147791 | + | 0.989019i | \(0.547216\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.7633 | − | 7.70711i | −0.0315042 | − | 0.00844153i | ||||
\(914\) | 1439.21 | − | 830.930i | 1.57463 | − | 0.909113i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2303.60 | 2.51485 | ||||||||
\(917\) | 854.740 | − | 239.301i | 0.932104 | − | 0.260960i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 723.603 | + | 417.773i | 0.787381 | + | 0.454595i | 0.839040 | − | 0.544070i | \(-0.183117\pi\) |
−0.0516585 | + | 0.998665i | \(0.516451\pi\) | |||||||
\(920\) | −552.041 | − | 192.771i | −0.600045 | − | 0.209534i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1030.09 | + | 276.013i | −1.11724 | + | 0.299363i | ||||
\(923\) | 279.815 | − | 279.815i | 0.303158 | − | 0.303158i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 284.280 | − | 210.370i | 0.307329 | − | 0.227427i | ||||
\(926\) | 252.956 | − | 438.132i | 0.273170 | − | 0.473145i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 309.857 | + | 83.0260i | 0.333898 | + | 0.0894676i | ||||
\(929\) | 1433.61 | + | 827.695i | 1.54318 | + | 0.890953i | 0.998636 | + | 0.0522181i | \(0.0166291\pi\) |
0.544540 | + | 0.838735i | \(0.316704\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 678.230 | − | 1237.85i | 0.728496 | − | 1.32959i | ||||
\(932\) | −1347.70 | − | 1347.70i | −1.44603 | − | 1.44603i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1343.54 | + | 775.694i | −1.43848 | + | 0.830507i | ||||
\(935\) | 141.210 | − | 68.1145i | 0.151027 | − | 0.0728498i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −260.635 | − | 260.635i | −0.278159 | − | 0.278159i | 0.554215 | − | 0.832374i | \(-0.313019\pi\) |
−0.832374 | + | 0.554215i | \(0.813019\pi\) | |||||||
\(938\) | 751.554 | − | 768.550i | 0.801230 | − | 0.819350i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −547.881 | + | 804.699i | −0.582852 | + | 0.856063i | ||||
\(941\) | 398.010 | + | 689.374i | 0.422965 | + | 0.732597i | 0.996228 | − | 0.0867746i | \(-0.0276560\pi\) |
−0.573263 | + | 0.819371i | \(0.694323\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 154.359 | + | 576.074i | 0.163689 | + | 0.610895i | ||||
\(944\) | 213.874i | 0.226562i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.94083 | −0.00205162 | ||||||||
\(947\) | −1564.71 | + | 419.263i | −1.65228 | + | 0.442727i | −0.960250 | − | 0.279142i | \(-0.909950\pi\) |
−0.692030 | + | 0.721869i | \(0.743283\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2210.05 | − | 1275.97i | 2.32882 | − | 1.34454i | ||||
\(950\) | −2359.27 | + | 268.883i | −2.48344 | + | 0.283035i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 442.937 | − | 1730.21i | 0.465270 | − | 1.81745i | ||||
\(953\) | −935.909 | + | 935.909i | −0.982066 | + | 0.982066i | −0.999842 | − | 0.0177757i | \(-0.994342\pi\) |
0.0177757 | + | 0.999842i | \(0.494342\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 63.6106 | − | 182.162i | 0.0666079 | − | 0.190746i | ||||
\(956\) | −196.539 | − | 340.415i | −0.205585 | − | 0.356083i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 215.267 | − | 215.267i | 0.224704 | − | 0.224704i | ||||
\(959\) | −973.303 | + | 576.541i | −1.01491 | + | 0.601190i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 344.701 | − | 597.039i | 0.358689 | − | 0.621268i | ||||
\(962\) | −250.854 | + | 936.200i | −0.260763 | + | 0.973180i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −58.9276 | − | 34.0218i | −0.0611282 | − | 0.0352924i | ||||
\(965\) | −1203.97 | − | 89.4509i | −1.24764 | − | 0.0926952i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −469.949 | − | 469.949i | −0.485987 | − | 0.485987i | 0.421050 | − | 0.907037i | \(-0.361662\pi\) |
−0.907037 | + | 0.421050i | \(0.861662\pi\) | |||||||
\(968\) | −293.291 | − | 1094.58i | −0.302986 | − | 1.13076i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1854.22 | + | 647.489i | 1.91157 | + | 0.667515i | ||||
\(971\) | −313.617 | + | 543.200i | −0.322983 | + | 0.559424i | −0.981102 | − | 0.193490i | \(-0.938019\pi\) |
0.658119 | + | 0.752914i | \(0.271352\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −452.795 | + | 463.035i | −0.465360 | + | 0.475884i | ||||
\(974\) | 2629.09i | 2.69928i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −23.5929 | − | 40.8641i | −0.0241730 | − | 0.0418689i | ||||
\(977\) | −246.004 | + | 918.098i | −0.251795 | + | 0.939712i | 0.718050 | + | 0.695991i | \(0.245035\pi\) |
−0.969845 | + | 0.243721i | \(0.921632\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 105.052i | 0.107305i | ||||||||
\(980\) | 1127.34 | + | 1250.63i | 1.15035 | + | 1.27615i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1409.23 | + | 377.602i | −1.43506 | + | 0.384523i | ||||
\(983\) | −1103.69 | − | 295.733i | −1.12278 | − | 0.300847i | −0.350770 | − | 0.936462i | \(-0.614080\pi\) |
−0.772007 | + | 0.635614i | \(0.780747\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1270.71 | − | 865.165i | −1.29006 | − | 0.878340i | ||||
\(986\) | −1115.15 | −1.13098 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2908.67 | − | 2908.67i | 2.94400 | − | 2.94400i | ||||
\(989\) | 5.40746 | + | 3.12200i | 0.00546761 | + | 0.00315672i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −430.389 | − | 745.456i | −0.434298 | − | 0.752226i | 0.562940 | − | 0.826498i | \(-0.309670\pi\) |
−0.997238 | + | 0.0742715i | \(0.976337\pi\) | |||||||
\(992\) | −406.757 | + | 108.990i | −0.410038 | + | 0.109869i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −383.107 | − | 215.512i | −0.385420 | − | 0.216813i | ||||
\(995\) | −736.746 | + | 634.842i | −0.740449 | + | 0.638032i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 92.4269 | − | 344.942i | 0.0927050 | − | 0.345980i | −0.903957 | − | 0.427624i | \(-0.859351\pi\) |
0.996661 | + | 0.0816447i | \(0.0260173\pi\) | |||||||
\(998\) | 220.570 | + | 59.1016i | 0.221012 | + | 0.0592201i | ||||
\(999\) | 0 | 0 |
(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 | 315.3.ca.b.37.15 | 64 | ||
3.2 | odd | 2 | 105.3.v.a.37.2 | ✓ | 64 | ||
5.3 | odd | 4 | inner | 315.3.ca.b.163.2 | 64 | ||
7.4 | even | 3 | inner | 315.3.ca.b.172.2 | 64 | ||
15.8 | even | 4 | 105.3.v.a.58.15 | yes | 64 | ||
21.11 | odd | 6 | 105.3.v.a.67.15 | yes | 64 | ||
35.18 | odd | 12 | inner | 315.3.ca.b.298.15 | 64 | ||
105.53 | even | 12 | 105.3.v.a.88.2 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.v.a.37.2 | ✓ | 64 | 3.2 | odd | 2 | ||
105.3.v.a.58.15 | yes | 64 | 15.8 | even | 4 | ||
105.3.v.a.67.15 | yes | 64 | 21.11 | odd | 6 | ||
105.3.v.a.88.2 | yes | 64 | 105.53 | even | 12 | ||
315.3.ca.b.37.15 | 64 | 1.1 | even | 1 | trivial | ||
315.3.ca.b.163.2 | 64 | 5.3 | odd | 4 | inner | ||
315.3.ca.b.172.2 | 64 | 7.4 | even | 3 | inner | ||
315.3.ca.b.298.15 | 64 | 35.18 | odd | 12 | inner |