Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(149,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.q (of order \(4\), degree \(2\), 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: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 149.2 | ||
Root | \(0.719139 + 1.21772i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.149 |
Dual form | 400.2.q.e.349.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.21772 | − | 0.719139i | −0.861057 | − | 0.508508i | ||||
\(3\) | −1.66783 | − | 1.66783i | −0.962922 | − | 0.962922i | 0.0364144 | − | 0.999337i | \(-0.488406\pi\) |
−0.999337 | + | 0.0364144i | \(0.988406\pi\) | |||||||
\(4\) | 0.965679 | + | 1.75142i | 0.482839 | + | 0.875709i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.831547 | + | 3.23035i | 0.339478 | + | 1.31879i | ||||
\(7\) | 1.87372 | 0.708198 | 0.354099 | − | 0.935208i | \(-0.384788\pi\) | ||||
0.354099 | + | 0.935208i | \(0.384788\pi\) | |||||||
\(8\) | 0.0835873 | − | 2.82719i | 0.0295526 | − | 0.999563i | ||||
\(9\) | 2.56332i | 0.854439i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.29695 | − | 3.29695i | −0.994068 | − | 0.994068i | 0.00591443 | − | 0.999983i | \(-0.498117\pi\) |
−0.999983 | + | 0.00591443i | \(0.998117\pi\) | |||||||
\(12\) | 1.31048 | − | 4.53166i | 0.378303 | − | 1.30818i | ||||
\(13\) | −1.90022 | − | 1.90022i | −0.527027 | − | 0.527027i | 0.392658 | − | 0.919685i | \(-0.371556\pi\) |
−0.919685 | + | 0.392658i | \(0.871556\pi\) | |||||||
\(14\) | −2.28166 | − | 1.34746i | −0.609799 | − | 0.360124i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.13493 | + | 3.38261i | −0.533732 | + | 0.845653i | ||||
\(17\) | 2.57148i | 0.623675i | 0.950135 | + | 0.311838i | \(0.100944\pi\) | ||||
−0.950135 | + | 0.311838i | \(0.899056\pi\) | |||||||
\(18\) | 1.84338 | − | 3.12140i | 0.434489 | − | 0.735721i | ||||
\(19\) | 5.76636 | − | 5.76636i | 1.32289 | − | 1.32289i | 0.411472 | − | 0.911422i | \(-0.365015\pi\) |
0.911422 | − | 0.411472i | \(-0.134985\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.12504 | − | 3.12504i | −0.681940 | − | 0.681940i | ||||
\(22\) | 1.64379 | + | 6.38572i | 0.350458 | + | 1.36144i | ||||
\(23\) | −7.58574 | −1.58174 | −0.790868 | − | 0.611987i | \(-0.790371\pi\) | ||||
−0.790868 | + | 0.611987i | \(0.790371\pi\) | |||||||
\(24\) | −4.85469 | + | 4.57587i | −0.990959 | + | 0.934045i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.947414 | + | 3.68046i | 0.185803 | + | 0.721798i | ||||
\(27\) | −0.728312 | + | 0.728312i | −0.140164 | + | 0.140164i | ||||
\(28\) | 1.80941 | + | 3.28166i | 0.341946 | + | 0.620175i | ||||
\(29\) | −6.45786 | + | 6.45786i | −1.19919 | + | 1.19919i | −0.224787 | + | 0.974408i | \(0.572169\pi\) |
−0.974408 | + | 0.224787i | \(0.927831\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.799135 | −0.143529 | −0.0717644 | − | 0.997422i | \(-0.522863\pi\) | ||||
−0.0717644 | + | 0.997422i | \(0.522863\pi\) | |||||||
\(32\) | 5.03231 | − | 2.58376i | 0.889596 | − | 0.456749i | ||||
\(33\) | 10.9975i | 1.91442i | ||||||||
\(34\) | 1.84925 | − | 3.13134i | 0.317144 | − | 0.537020i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.48944 | + | 2.47534i | −0.748240 | + | 0.412557i | ||||
\(37\) | −2.69652 | + | 2.69652i | −0.443305 | + | 0.443305i | −0.893121 | − | 0.449816i | \(-0.851489\pi\) |
0.449816 | + | 0.893121i | \(0.351489\pi\) | |||||||
\(38\) | −11.1686 | + | 2.87499i | −1.81179 | + | 0.466386i | ||||
\(39\) | 6.33850i | 1.01497i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.946984i | 0.147894i | 0.997262 | + | 0.0739471i | \(0.0235596\pi\) | ||||
−0.997262 | + | 0.0739471i | \(0.976440\pi\) | |||||||
\(42\) | 1.55808 | + | 6.05276i | 0.240417 | + | 0.933961i | ||||
\(43\) | 0.829986 | − | 0.829986i | 0.126572 | − | 0.126572i | −0.640983 | − | 0.767555i | \(-0.721473\pi\) |
0.767555 | + | 0.640983i | \(0.221473\pi\) | |||||||
\(44\) | 2.59054 | − | 8.95813i | 0.390539 | − | 1.35049i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.23730 | + | 5.45520i | 1.36197 | + | 0.804325i | ||||
\(47\) | 1.52421i | 0.222329i | 0.993802 | + | 0.111165i | \(0.0354581\pi\) | ||||
−0.993802 | + | 0.111165i | \(0.964542\pi\) | |||||||
\(48\) | 9.20233 | − | 2.08093i | 1.32824 | − | 0.300356i | ||||
\(49\) | −3.48919 | −0.498456 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.28879 | − | 4.28879i | 0.600551 | − | 0.600551i | ||||
\(52\) | 1.49308 | − | 5.16309i | 0.207053 | − | 0.715992i | ||||
\(53\) | 6.97225 | − | 6.97225i | 0.957712 | − | 0.957712i | −0.0414296 | − | 0.999141i | \(-0.513191\pi\) |
0.999141 | + | 0.0414296i | \(0.0131912\pi\) | |||||||
\(54\) | 1.41064 | − | 0.363122i | 0.191963 | − | 0.0494147i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.156619 | − | 5.29735i | 0.0209291 | − | 0.707889i | ||||
\(57\) | −19.2346 | −2.54769 | ||||||||
\(58\) | 12.5080 | − | 3.21976i | 1.64238 | − | 0.422775i | ||||
\(59\) | −6.84418 | − | 6.84418i | −0.891036 | − | 0.891036i | 0.103585 | − | 0.994621i | \(-0.466969\pi\) |
−0.994621 | + | 0.103585i | \(0.966969\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.87247 | + | 6.87247i | −0.879930 | + | 0.879930i | −0.993527 | − | 0.113597i | \(-0.963763\pi\) |
0.113597 | + | 0.993527i | \(0.463763\pi\) | |||||||
\(62\) | 0.973121 | + | 0.574689i | 0.123587 | + | 0.0729856i | ||||
\(63\) | 4.80293i | 0.605112i | ||||||||
\(64\) | −7.98603 | − | 0.472635i | −0.998253 | − | 0.0590793i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.90874 | − | 13.3919i | 0.973498 | − | 1.64843i | ||||
\(67\) | −3.73647 | − | 3.73647i | −0.456483 | − | 0.456483i | 0.441016 | − | 0.897499i | \(-0.354618\pi\) |
−0.897499 | + | 0.441016i | \(0.854618\pi\) | |||||||
\(68\) | −4.50373 | + | 2.48322i | −0.546158 | + | 0.301135i | ||||
\(69\) | 12.6517 | + | 12.6517i | 1.52309 | + | 1.52309i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.34417i | − | 1.10895i | −0.832201 | − | 0.554475i | \(-0.812919\pi\) | ||
0.832201 | − | 0.554475i | \(-0.187081\pi\) | |||||||
\(72\) | 7.24699 | + | 0.214261i | 0.854066 | + | 0.0252509i | ||||
\(73\) | −0.886316 | −0.103735 | −0.0518677 | − | 0.998654i | \(-0.516517\pi\) | ||||
−0.0518677 | + | 0.998654i | \(0.516517\pi\) | |||||||
\(74\) | 5.22277 | − | 1.34443i | 0.607135 | − | 0.156287i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15.6678 | + | 4.53086i | 1.79722 | + | 0.519725i | ||||
\(77\) | −6.17755 | − | 6.17755i | −0.703997 | − | 0.703997i | ||||
\(78\) | 4.55826 | − | 7.71851i | 0.516122 | − | 0.873949i | ||||
\(79\) | −3.07575 | −0.346049 | −0.173024 | − | 0.984918i | \(-0.555354\pi\) | ||||
−0.173024 | + | 0.984918i | \(0.555354\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.1194 | 1.12437 | ||||||||
\(82\) | 0.681013 | − | 1.15316i | 0.0752053 | − | 0.127345i | ||||
\(83\) | 0.989393 | + | 0.989393i | 0.108600 | + | 0.108600i | 0.759319 | − | 0.650719i | \(-0.225532\pi\) |
−0.650719 | + | 0.759319i | \(0.725532\pi\) | |||||||
\(84\) | 2.45547 | − | 8.49104i | 0.267913 | − | 0.926448i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.60756 | + | 0.413814i | −0.173348 | + | 0.0446227i | ||||
\(87\) | 21.5412 | 2.30946 | ||||||||
\(88\) | −9.59670 | + | 9.04553i | −1.02301 | + | 0.964257i | ||||
\(89\) | − | 10.0942i | − | 1.06998i | −0.844859 | − | 0.534990i | \(-0.820316\pi\) | ||
0.844859 | − | 0.534990i | \(-0.179684\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.56048 | − | 3.56048i | −0.373239 | − | 0.373239i | ||||
\(92\) | −7.32539 | − | 13.2858i | −0.763725 | − | 1.38514i | ||||
\(93\) | 1.33282 | + | 1.33282i | 0.138207 | + | 0.138207i | ||||
\(94\) | 1.09612 | − | 1.85606i | 0.113056 | − | 0.191438i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −12.7023 | − | 4.08377i | −1.29643 | − | 0.416798i | ||||
\(97\) | − | 7.16829i | − | 0.727830i | −0.931432 | − | 0.363915i | \(-0.881440\pi\) | ||
0.931432 | − | 0.363915i | \(-0.118560\pi\) | |||||||
\(98\) | 4.24885 | + | 2.50921i | 0.429199 | + | 0.253469i | ||||
\(99\) | 8.45113 | − | 8.45113i | 0.849371 | − | 0.849371i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.05091 | − | 1.05091i | −0.104570 | − | 0.104570i | 0.652886 | − | 0.757456i | \(-0.273558\pi\) |
−0.757456 | + | 0.652886i | \(0.773558\pi\) | |||||||
\(102\) | −8.30678 | + | 2.13831i | −0.822493 | + | 0.211724i | ||||
\(103\) | 8.20690 | 0.808649 | 0.404325 | − | 0.914616i | \(-0.367507\pi\) | ||||
0.404325 | + | 0.914616i | \(0.367507\pi\) | |||||||
\(104\) | −5.53113 | + | 5.21346i | −0.542372 | + | 0.511222i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.5043 | + | 3.47622i | −1.31165 | + | 0.337641i | ||||
\(107\) | 2.85743 | − | 2.85743i | 0.276238 | − | 0.276238i | −0.555367 | − | 0.831605i | \(-0.687422\pi\) |
0.831605 | + | 0.555367i | \(0.187422\pi\) | |||||||
\(108\) | −1.97889 | − | 0.572264i | −0.190419 | − | 0.0550661i | ||||
\(109\) | 11.3735 | − | 11.3735i | 1.08939 | − | 1.08939i | 0.0937940 | − | 0.995592i | \(-0.470100\pi\) |
0.995592 | − | 0.0937940i | \(-0.0298995\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.99467 | 0.853736 | ||||||||
\(112\) | −4.00025 | + | 6.33806i | −0.377988 | + | 0.598890i | ||||
\(113\) | 3.54221i | 0.333223i | 0.986023 | + | 0.166611i | \(0.0532825\pi\) | ||||
−0.986023 | + | 0.166611i | \(0.946717\pi\) | |||||||
\(114\) | 23.4224 | + | 13.8324i | 2.19371 | + | 1.29552i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −17.5466 | − | 5.07419i | −1.62916 | − | 0.471127i | ||||
\(117\) | 4.87088 | − | 4.87088i | 0.450313 | − | 0.450313i | ||||
\(118\) | 3.41237 | + | 13.2562i | 0.314134 | + | 1.22033i | ||||
\(119\) | 4.81822i | 0.441685i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7398i | 0.976343i | ||||||||
\(122\) | 13.3110 | − | 3.42648i | 1.20512 | − | 0.310219i | ||||
\(123\) | 1.57941 | − | 1.57941i | 0.142411 | − | 0.142411i | ||||
\(124\) | −0.771707 | − | 1.39962i | −0.0693014 | − | 0.125689i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.45397 | − | 5.84862i | 0.307704 | − | 0.521036i | ||||
\(127\) | 18.0693i | 1.60339i | 0.597735 | + | 0.801693i | \(0.296067\pi\) | ||||
−0.597735 | + | 0.801693i | \(0.703933\pi\) | |||||||
\(128\) | 9.38485 | + | 6.31860i | 0.829511 | + | 0.558490i | ||||
\(129\) | −2.76855 | −0.243757 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.39614 | + | 6.39614i | −0.558834 | + | 0.558834i | −0.928975 | − | 0.370142i | \(-0.879309\pi\) |
0.370142 | + | 0.928975i | \(0.379309\pi\) | |||||||
\(132\) | −19.2612 | + | 10.6201i | −1.67648 | + | 0.924358i | ||||
\(133\) | 10.8045 | − | 10.8045i | 0.936871 | − | 0.936871i | ||||
\(134\) | 1.86293 | + | 7.23702i | 0.160933 | + | 0.625183i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.27006 | + | 0.214943i | 0.623403 | + | 0.0184312i | ||||
\(137\) | 10.7357 | 0.917212 | 0.458606 | − | 0.888640i | \(-0.348349\pi\) | ||||
0.458606 | + | 0.888640i | \(0.348349\pi\) | |||||||
\(138\) | −6.30790 | − | 24.5046i | −0.536964 | − | 2.08597i | ||||
\(139\) | 2.31086 | + | 2.31086i | 0.196005 | + | 0.196005i | 0.798285 | − | 0.602280i | \(-0.205741\pi\) |
−0.602280 | + | 0.798285i | \(0.705741\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.54213 | − | 2.54213i | 0.214086 | − | 0.214086i | ||||
\(142\) | −6.71976 | + | 11.3786i | −0.563909 | + | 0.954869i | ||||
\(143\) | 12.5299i | 1.04780i | ||||||||
\(144\) | −8.67071 | − | 5.47250i | −0.722559 | − | 0.456042i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.07928 | + | 0.637384i | 0.0893221 | + | 0.0527503i | ||||
\(147\) | 5.81938 | + | 5.81938i | 0.479974 | + | 0.479974i | ||||
\(148\) | −7.32670 | − | 2.11876i | −0.602251 | − | 0.174161i | ||||
\(149\) | −1.38743 | − | 1.38743i | −0.113663 | − | 0.113663i | 0.647988 | − | 0.761651i | \(-0.275611\pi\) |
−0.761651 | + | 0.647988i | \(0.775611\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.68590i | − | 0.462712i | −0.972869 | − | 0.231356i | \(-0.925684\pi\) | ||
0.972869 | − | 0.231356i | \(-0.0743163\pi\) | |||||||
\(152\) | −15.8206 | − | 16.7846i | −1.28322 | − | 1.36141i | ||||
\(153\) | −6.59152 | −0.532892 | ||||||||
\(154\) | 3.08000 | + | 11.9650i | 0.248194 | + | 0.964170i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11.1014 | + | 6.12096i | −0.888820 | + | 0.490069i | ||||
\(157\) | −2.48874 | − | 2.48874i | −0.198623 | − | 0.198623i | 0.600787 | − | 0.799409i | \(-0.294854\pi\) |
−0.799409 | + | 0.600787i | \(0.794854\pi\) | |||||||
\(158\) | 3.74540 | + | 2.21189i | 0.297968 | + | 0.175969i | ||||
\(159\) | −23.2571 | −1.84440 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.2135 | −1.12018 | ||||||||
\(162\) | −12.3225 | − | 7.27722i | −0.968149 | − | 0.571753i | ||||
\(163\) | −12.7091 | − | 12.7091i | −0.995451 | − | 0.995451i | 0.00453842 | − | 0.999990i | \(-0.498555\pi\) |
−0.999990 | + | 0.00453842i | \(0.998555\pi\) | |||||||
\(164\) | −1.65857 | + | 0.914483i | −0.129512 | + | 0.0714091i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.493292 | − | 1.91631i | −0.0382868 | − | 0.148735i | ||||
\(167\) | 5.00982 | 0.387672 | 0.193836 | − | 0.981034i | \(-0.437907\pi\) | ||||
0.193836 | + | 0.981034i | \(0.437907\pi\) | |||||||
\(168\) | −9.09630 | + | 8.57387i | −0.701795 | + | 0.661489i | ||||
\(169\) | − | 5.77830i | − | 0.444485i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.7810 | + | 14.7810i | 1.13033 | + | 1.13033i | ||||
\(172\) | 2.25515 | + | 0.652152i | 0.171954 | + | 0.0497261i | ||||
\(173\) | −6.19546 | − | 6.19546i | −0.471032 | − | 0.471032i | 0.431216 | − | 0.902249i | \(-0.358085\pi\) |
−0.902249 | + | 0.431216i | \(0.858085\pi\) | |||||||
\(174\) | −26.2312 | − | 15.4911i | −1.98858 | − | 1.17438i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 18.1911 | − | 4.11356i | 1.37120 | − | 0.310071i | ||||
\(177\) | 22.8299i | 1.71600i | ||||||||
\(178\) | −7.25911 | + | 12.2919i | −0.544093 | + | 0.921313i | ||||
\(179\) | 5.51628 | − | 5.51628i | 0.412306 | − | 0.412306i | −0.470235 | − | 0.882541i | \(-0.655831\pi\) |
0.882541 | + | 0.470235i | \(0.155831\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.8993 | + | 11.8993i | 0.884470 | + | 0.884470i | 0.993985 | − | 0.109515i | \(-0.0349298\pi\) |
−0.109515 | + | 0.993985i | \(0.534930\pi\) | |||||||
\(182\) | 1.77518 | + | 6.89614i | 0.131585 | + | 0.511176i | ||||
\(183\) | 22.9242 | 1.69461 | ||||||||
\(184\) | −0.634072 | + | 21.4463i | −0.0467444 | + | 1.58105i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.664518 | − | 2.58149i | −0.0487248 | − | 0.189284i | ||||
\(187\) | 8.47804 | − | 8.47804i | 0.619976 | − | 0.619976i | ||||
\(188\) | −2.66954 | + | 1.47190i | −0.194696 | + | 0.107349i | ||||
\(189\) | −1.36465 | + | 1.36465i | −0.0992637 | + | 0.0992637i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.1278 | 0.805180 | 0.402590 | − | 0.915380i | \(-0.368110\pi\) | ||||
0.402590 | + | 0.915380i | \(0.368110\pi\) | |||||||
\(192\) | 12.5311 | + | 14.1076i | 0.904352 | + | 1.01813i | ||||
\(193\) | − | 20.7821i | − | 1.49593i | −0.663738 | − | 0.747965i | \(-0.731031\pi\) | ||
0.663738 | − | 0.747965i | \(-0.268969\pi\) | |||||||
\(194\) | −5.15500 | + | 8.72896i | −0.370107 | + | 0.626703i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.36944 | − | 6.11103i | −0.240674 | − | 0.436502i | ||||
\(197\) | 14.0309 | − | 14.0309i | 0.999663 | − | 0.999663i | −0.000337236 | − | 1.00000i | \(-0.500107\pi\) |
1.00000 | 0.000337236i | \(0.000107346\pi\) | ||||||||
\(198\) | −16.3686 | + | 4.21357i | −1.16327 | + | 0.299445i | ||||
\(199\) | 3.24727i | 0.230193i | 0.993354 | + | 0.115096i | \(0.0367177\pi\) | ||||
−0.993354 | + | 0.115096i | \(0.963282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.4636i | 0.879115i | ||||||||
\(202\) | 0.523964 | + | 2.03547i | 0.0368660 | + | 0.143215i | ||||
\(203\) | −12.1002 | + | 12.1002i | −0.849267 | + | 0.849267i | ||||
\(204\) | 11.6531 | + | 3.36987i | 0.815877 | + | 0.235938i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.99369 | − | 5.90190i | −0.696294 | − | 0.411205i | ||||
\(207\) | − | 19.4447i | − | 1.35150i | ||||||
\(208\) | 10.4846 | − | 2.37088i | 0.726974 | − | 0.164391i | ||||
\(209\) | −38.0228 | −2.63009 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1821 | + | 10.1821i | −0.700964 | + | 0.700964i | −0.964617 | − | 0.263654i | \(-0.915072\pi\) |
0.263654 | + | 0.964617i | \(0.415072\pi\) | |||||||
\(212\) | 18.9443 | + | 5.47837i | 1.30110 | + | 0.376256i | ||||
\(213\) | −15.5845 | + | 15.5845i | −1.06783 | + | 1.06783i | ||||
\(214\) | −5.53443 | + | 1.42466i | −0.378326 | + | 0.0973876i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.99820 | + | 2.11996i | 0.135960 | + | 0.144245i | ||||
\(217\) | −1.49735 | −0.101647 | ||||||||
\(218\) | −22.0289 | + | 5.67061i | −1.49198 | + | 0.384062i | ||||
\(219\) | 1.47822 | + | 1.47822i | 0.0998892 | + | 0.0998892i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.88638 | − | 4.88638i | 0.328694 | − | 0.328694i | ||||
\(222\) | −10.9530 | − | 6.46842i | −0.735116 | − | 0.434132i | ||||
\(223\) | − | 24.0469i | − | 1.61030i | −0.593070 | − | 0.805151i | \(-0.702084\pi\) | ||
0.593070 | − | 0.805151i | \(-0.297916\pi\) | |||||||
\(224\) | 9.42912 | − | 4.84124i | 0.630010 | − | 0.323469i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.54734 | − | 4.31341i | 0.169446 | − | 0.286924i | ||||
\(227\) | −11.9863 | − | 11.9863i | −0.795562 | − | 0.795562i | 0.186830 | − | 0.982392i | \(-0.440179\pi\) |
−0.982392 | + | 0.186830i | \(0.940179\pi\) | |||||||
\(228\) | −18.5745 | − | 33.6879i | −1.23012 | − | 2.23103i | ||||
\(229\) | 20.1972 | + | 20.1972i | 1.33467 | + | 1.33467i | 0.901140 | + | 0.433529i | \(0.142732\pi\) |
0.433529 | + | 0.901140i | \(0.357268\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.6062i | 1.35579i | ||||||||
\(232\) | 17.7178 | + | 18.7974i | 1.16323 | + | 1.23411i | ||||
\(233\) | 10.0655 | 0.659410 | 0.329705 | − | 0.944084i | \(-0.393051\pi\) | ||||
0.329705 | + | 0.944084i | \(0.393051\pi\) | |||||||
\(234\) | −9.43419 | + | 2.42852i | −0.616733 | + | 0.158757i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.37774 | − | 18.5963i | 0.350061 | − | 1.21052i | ||||
\(237\) | 5.12983 | + | 5.12983i | 0.333218 | + | 0.333218i | ||||
\(238\) | 3.46497 | − | 5.86724i | 0.224601 | − | 0.380316i | ||||
\(239\) | −0.992801 | −0.0642189 | −0.0321095 | − | 0.999484i | \(-0.510223\pi\) | ||||
−0.0321095 | + | 0.999484i | \(0.510223\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1229 | 0.909738 | 0.454869 | − | 0.890558i | \(-0.349686\pi\) | ||||
0.454869 | + | 0.890558i | \(0.349686\pi\) | |||||||
\(242\) | 7.72339 | − | 13.0780i | 0.496478 | − | 0.840687i | ||||
\(243\) | −14.6924 | − | 14.6924i | −0.942520 | − | 0.942520i | ||||
\(244\) | −18.6732 | − | 5.39997i | −1.19543 | − | 0.345698i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.05909 | + | 0.787462i | −0.195041 | + | 0.0502068i | ||||
\(247\) | −21.9148 | −1.39440 | ||||||||
\(248\) | −0.0667975 | + | 2.25931i | −0.00424165 | + | 0.143466i | ||||
\(249\) | − | 3.30028i | − | 0.209147i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.56681 | + | 1.56681i | 0.0988961 | + | 0.0988961i | 0.754824 | − | 0.655928i | \(-0.227722\pi\) |
−0.655928 | + | 0.754824i | \(0.727722\pi\) | |||||||
\(252\) | −8.41193 | + | 4.63809i | −0.529902 | + | 0.292172i | ||||
\(253\) | 25.0098 | + | 25.0098i | 1.57235 | + | 1.57235i | ||||
\(254\) | 12.9943 | − | 22.0033i | 0.815335 | − | 1.38061i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.88415 | − | 14.4433i | −0.430260 | − | 0.902705i | ||||
\(257\) | 10.2593i | 0.639960i | 0.947424 | + | 0.319980i | \(0.103676\pi\) | ||||
−0.947424 | + | 0.319980i | \(0.896324\pi\) | |||||||
\(258\) | 3.37132 | + | 1.99097i | 0.209889 | + | 0.123953i | ||||
\(259\) | −5.05251 | + | 5.05251i | −0.313948 | + | 0.313948i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.5535 | − | 16.5535i | −1.02464 | − | 1.02464i | ||||
\(262\) | 12.3884 | − | 3.18899i | 0.765359 | − | 0.197016i | ||||
\(263\) | 19.0630 | 1.17548 | 0.587739 | − | 0.809051i | \(-0.300018\pi\) | ||||
0.587739 | + | 0.809051i | \(0.300018\pi\) | |||||||
\(264\) | 31.0921 | + | 0.919252i | 1.91358 | + | 0.0565761i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −20.9268 | + | 5.38692i | −1.28311 | + | 0.330293i | ||||
\(267\) | −16.8354 | + | 16.8354i | −1.03031 | + | 1.03031i | ||||
\(268\) | 2.93589 | − | 10.1524i | 0.179338 | − | 0.620154i | ||||
\(269\) | −3.48459 | + | 3.48459i | −0.212459 | + | 0.212459i | −0.805311 | − | 0.592852i | \(-0.798002\pi\) |
0.592852 | + | 0.805311i | \(0.298002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.0045 | −1.82264 | −0.911322 | − | 0.411695i | \(-0.864937\pi\) | ||||
−0.911322 | + | 0.411695i | \(0.864937\pi\) | |||||||
\(272\) | −8.69832 | − | 5.48992i | −0.527413 | − | 0.332876i | ||||
\(273\) | 11.8765i | 0.718801i | ||||||||
\(274\) | −13.0731 | − | 7.72045i | −0.789772 | − | 0.466409i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.94096 | + | 34.3760i | −0.598375 | + | 2.06919i | ||||
\(277\) | 8.43732 | − | 8.43732i | 0.506949 | − | 0.506949i | −0.406639 | − | 0.913589i | \(-0.633299\pi\) |
0.913589 | + | 0.406639i | \(0.133299\pi\) | |||||||
\(278\) | −1.15215 | − | 4.47581i | −0.0691014 | − | 0.268441i | ||||
\(279\) | − | 2.04844i | − | 0.122637i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.44714i | − | 0.384604i | −0.981336 | − | 0.192302i | \(-0.938405\pi\) | ||
0.981336 | − | 0.192302i | \(-0.0615954\pi\) | |||||||
\(282\) | −4.92375 | + | 1.26746i | −0.293205 | + | 0.0754759i | ||||
\(283\) | −2.61000 | + | 2.61000i | −0.155148 | + | 0.155148i | −0.780413 | − | 0.625264i | \(-0.784991\pi\) |
0.625264 | + | 0.780413i | \(0.284991\pi\) | |||||||
\(284\) | 16.3656 | − | 9.02347i | 0.971117 | − | 0.535444i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.01073 | − | 15.2579i | 0.532815 | − | 0.902217i | ||||
\(287\) | 1.77438i | 0.104738i | ||||||||
\(288\) | 6.62300 | + | 12.8994i | 0.390264 | + | 0.760105i | ||||
\(289\) | 10.3875 | 0.611029 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.9555 | + | 11.9555i | −0.700844 | + | 0.700844i | ||||
\(292\) | −0.855896 | − | 1.55231i | −0.0500875 | − | 0.0908420i | ||||
\(293\) | 7.52428 | − | 7.52428i | 0.439573 | − | 0.439573i | −0.452295 | − | 0.891868i | \(-0.649395\pi\) |
0.891868 | + | 0.452295i | \(0.149395\pi\) | |||||||
\(294\) | −2.90143 | − | 11.2713i | −0.169215 | − | 0.657356i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.39818 | + | 7.84897i | 0.430010 | + | 0.456212i | ||||
\(297\) | 4.80242 | 0.278665 | ||||||||
\(298\) | 0.691746 | + | 2.68726i | 0.0400718 | + | 0.155669i | ||||
\(299\) | 14.4146 | + | 14.4146i | 0.833618 | + | 0.833618i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.55516 | − | 1.55516i | 0.0896377 | − | 0.0896377i | ||||
\(302\) | −4.08895 | + | 6.92383i | −0.235293 | + | 0.398422i | ||||
\(303\) | 3.50549i | 0.201385i | ||||||||
\(304\) | 7.19460 | + | 31.8162i | 0.412639 | + | 1.82478i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.02661 | + | 4.74021i | 0.458851 | + | 0.270980i | ||||
\(307\) | −12.7130 | − | 12.7130i | −0.725571 | − | 0.725571i | 0.244163 | − | 0.969734i | \(-0.421487\pi\) |
−0.969734 | + | 0.244163i | \(0.921487\pi\) | |||||||
\(308\) | 4.85394 | − | 16.7850i | 0.276579 | − | 0.956414i | ||||
\(309\) | −13.6877 | − | 13.6877i | −0.778667 | − | 0.778667i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.9313i | − | 0.676563i | −0.941045 | − | 0.338281i | \(-0.890154\pi\) | ||
0.941045 | − | 0.338281i | \(-0.109846\pi\) | |||||||
\(312\) | 17.9202 | + | 0.529818i | 1.01453 | + | 0.0299951i | ||||
\(313\) | −34.3458 | −1.94134 | −0.970670 | − | 0.240414i | \(-0.922717\pi\) | ||||
−0.970670 | + | 0.240414i | \(0.922717\pi\) | |||||||
\(314\) | 1.24083 | + | 4.82033i | 0.0700244 | + | 0.272027i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.97019 | − | 5.38692i | −0.167086 | − | 0.303038i | ||||
\(317\) | 17.1112 | + | 17.1112i | 0.961060 | + | 0.961060i | 0.999270 | − | 0.0382097i | \(-0.0121655\pi\) |
−0.0382097 | + | 0.999270i | \(0.512165\pi\) | |||||||
\(318\) | 28.3206 | + | 16.7251i | 1.58814 | + | 0.937894i | ||||
\(319\) | 42.5825 | 2.38416 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.53141 | −0.531992 | ||||||||
\(322\) | 17.3081 | + | 10.2215i | 0.964541 | + | 0.569622i | ||||
\(323\) | 14.8281 | + | 14.8281i | 0.825056 | + | 0.825056i | ||||
\(324\) | 9.77205 | + | 17.7232i | 0.542891 | + | 0.984623i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.33649 | + | 24.6157i | 0.350946 | + | 1.36334i | ||||
\(327\) | −37.9382 | −2.09799 | ||||||||
\(328\) | 2.67731 | + | 0.0791559i | 0.147830 | + | 0.00437065i | ||||
\(329\) | 2.85594i | 0.157453i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.80246 | + | 9.80246i | 0.538792 | + | 0.538792i | 0.923174 | − | 0.384382i | \(-0.125585\pi\) |
−0.384382 | + | 0.923174i | \(0.625585\pi\) | |||||||
\(332\) | −0.777405 | + | 2.68828i | −0.0426656 | + | 0.147538i | ||||
\(333\) | −6.91203 | − | 6.91203i | −0.378777 | − | 0.378777i | ||||
\(334\) | −6.10056 | − | 3.60276i | −0.333808 | − | 0.197134i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 17.2425 | − | 3.89906i | 0.940658 | − | 0.212711i | ||||
\(337\) | − | 6.07501i | − | 0.330927i | −0.986216 | − | 0.165463i | \(-0.947088\pi\) | ||
0.986216 | − | 0.165463i | \(-0.0529120\pi\) | |||||||
\(338\) | −4.15540 | + | 7.03635i | −0.226024 | + | 0.382727i | ||||
\(339\) | 5.90780 | − | 5.90780i | 0.320868 | − | 0.320868i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.63471 | + | 2.63471i | 0.142677 | + | 0.142677i | ||||
\(342\) | −7.36952 | − | 28.6287i | −0.398498 | − | 1.54806i | ||||
\(343\) | −19.6538 | −1.06120 | ||||||||
\(344\) | −2.27715 | − | 2.41590i | −0.122776 | − | 0.130257i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.08894 | + | 11.9997i | 0.166062 | + | 0.645110i | ||||
\(347\) | 5.77231 | − | 5.77231i | 0.309874 | − | 0.309874i | −0.534987 | − | 0.844860i | \(-0.679683\pi\) |
0.844860 | + | 0.534987i | \(0.179683\pi\) | |||||||
\(348\) | 20.8019 | + | 37.7277i | 1.11510 | + | 2.02242i | ||||
\(349\) | 7.58851 | − | 7.58851i | 0.406203 | − | 0.406203i | −0.474209 | − | 0.880412i | \(-0.657266\pi\) |
0.880412 | + | 0.474209i | \(0.157266\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.76791 | 0.147740 | ||||||||
\(352\) | −25.1098 | − | 8.07275i | −1.33836 | − | 0.430279i | ||||
\(353\) | − | 16.2285i | − | 0.863753i | −0.901933 | − | 0.431877i | \(-0.857852\pi\) | ||
0.901933 | − | 0.431877i | \(-0.142148\pi\) | |||||||
\(354\) | 16.4178 | − | 27.8003i | 0.872598 | − | 1.47757i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 17.6791 | − | 9.74772i | 0.936990 | − | 0.516628i | ||||
\(357\) | 8.03597 | − | 8.03597i | 0.425309 | − | 0.425309i | ||||
\(358\) | −10.6843 | + | 2.75031i | −0.564680 | + | 0.145358i | ||||
\(359\) | 6.77298i | 0.357464i | 0.983898 | + | 0.178732i | \(0.0571996\pi\) | ||||
−0.983898 | + | 0.178732i | \(0.942800\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 47.5019i | − | 2.50010i | ||||||
\(362\) | −5.93277 | − | 23.0473i | −0.311819 | − | 1.21134i | ||||
\(363\) | 17.9121 | − | 17.9121i | 0.940142 | − | 0.940142i | ||||
\(364\) | 2.79761 | − | 9.67416i | 0.146634 | − | 0.507064i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −27.9153 | − | 16.4857i | −1.45915 | − | 0.861722i | ||||
\(367\) | 6.35705i | 0.331835i | 0.986140 | + | 0.165918i | \(0.0530586\pi\) | ||||
−0.986140 | + | 0.165918i | \(0.946941\pi\) | |||||||
\(368\) | 16.1950 | − | 25.6596i | 0.844224 | − | 1.33760i | ||||
\(369\) | −2.42742 | −0.126367 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0640 | − | 13.0640i | 0.678250 | − | 0.678250i | ||||
\(372\) | −1.04725 | + | 3.62140i | −0.0542974 | + | 0.187761i | ||||
\(373\) | −9.20937 | + | 9.20937i | −0.476843 | + | 0.476843i | −0.904121 | − | 0.427278i | \(-0.859473\pi\) |
0.427278 | + | 0.904121i | \(0.359473\pi\) | |||||||
\(374\) | −16.4208 | + | 4.22698i | −0.849097 | + | 0.218572i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.30925 | + | 0.127405i | 0.222232 | + | 0.00657041i | ||||
\(377\) | 24.5428 | 1.26402 | ||||||||
\(378\) | 2.64313 | − | 0.680387i | 0.135948 | − | 0.0349954i | ||||
\(379\) | −5.41600 | − | 5.41600i | −0.278201 | − | 0.278201i | 0.554189 | − | 0.832391i | \(-0.313028\pi\) |
−0.832391 | + | 0.554189i | \(0.813028\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.1365 | − | 30.1365i | 1.54394 | − | 1.54394i | ||||
\(382\) | −13.5505 | − | 8.00244i | −0.693306 | − | 0.409440i | ||||
\(383\) | 28.1626i | 1.43904i | 0.694472 | + | 0.719520i | \(0.255638\pi\) | ||||
−0.694472 | + | 0.719520i | \(0.744362\pi\) | |||||||
\(384\) | −5.11398 | − | 26.1907i | −0.260972 | − | 1.33654i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.9452 | + | 25.3068i | −0.760693 | + | 1.28808i | ||||
\(387\) | 2.12752 | + | 2.12752i | 0.108148 | + | 0.108148i | ||||
\(388\) | 12.5547 | − | 6.92227i | 0.637367 | − | 0.351425i | ||||
\(389\) | −9.59783 | − | 9.59783i | −0.486629 | − | 0.486629i | 0.420611 | − | 0.907241i | \(-0.361816\pi\) |
−0.907241 | + | 0.420611i | \(0.861816\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.5066i | − | 0.986490i | ||||||
\(392\) | −0.291652 | + | 9.86461i | −0.0147307 | + | 0.498238i | ||||
\(393\) | 21.3354 | 1.07623 | ||||||||
\(394\) | −27.1759 | + | 6.99554i | −1.36910 | + | 0.352430i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 22.9625 | + | 6.64039i | 1.15391 | + | 0.333692i | ||||
\(397\) | −10.4884 | − | 10.4884i | −0.526399 | − | 0.526399i | 0.393098 | − | 0.919497i | \(-0.371403\pi\) |
−0.919497 | + | 0.393098i | \(0.871403\pi\) | |||||||
\(398\) | 2.33524 | − | 3.95426i | 0.117055 | − | 0.198209i | ||||
\(399\) | −36.0402 | −1.80427 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.44221 | −0.121958 | −0.0609791 | − | 0.998139i | \(-0.519422\pi\) | ||||
−0.0609791 | + | 0.998139i | \(0.519422\pi\) | |||||||
\(402\) | 8.96306 | − | 15.1772i | 0.447037 | − | 0.756969i | ||||
\(403\) | 1.51853 | + | 1.51853i | 0.0756436 | + | 0.0756436i | ||||
\(404\) | 0.825743 | − | 2.85543i | 0.0410823 | − | 0.142063i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.4364 | − | 6.03292i | 1.16313 | − | 0.299409i | ||||
\(407\) | 17.7806 | 0.881350 | ||||||||
\(408\) | −11.7667 | − | 12.4837i | −0.582541 | − | 0.618036i | ||||
\(409\) | − | 24.6628i | − | 1.21950i | −0.792596 | − | 0.609748i | \(-0.791271\pi\) | ||
0.792596 | − | 0.609748i | \(-0.208729\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.9053 | − | 17.9053i | −0.883204 | − | 0.883204i | ||||
\(412\) | 7.92522 | + | 14.3737i | 0.390448 | + | 0.708142i | ||||
\(413\) | −12.8240 | − | 12.8240i | −0.631030 | − | 0.631030i | ||||
\(414\) | −13.9834 | + | 23.6781i | −0.687247 | + | 1.16372i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −14.4722 | − | 4.65279i | −0.709560 | − | 0.228122i | ||||
\(417\) | − | 7.70826i | − | 0.377475i | ||||||
\(418\) | 46.3011 | + | 27.3437i | 2.26466 | + | 1.33742i | ||||
\(419\) | −19.1661 | + | 19.1661i | −0.936326 | + | 0.936326i | −0.998091 | − | 0.0617649i | \(-0.980327\pi\) |
0.0617649 | + | 0.998091i | \(0.480327\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.43469 | − | 7.43469i | −0.362345 | − | 0.362345i | 0.502331 | − | 0.864676i | \(-0.332476\pi\) |
−0.864676 | + | 0.502331i | \(0.832476\pi\) | |||||||
\(422\) | 19.7213 | − | 5.07659i | 0.960016 | − | 0.247124i | ||||
\(423\) | −3.90704 | −0.189967 | ||||||||
\(424\) | −19.1291 | − | 20.2947i | −0.928991 | − | 0.985596i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 30.1850 | − | 7.77012i | 1.46247 | − | 0.376464i | ||||
\(427\) | −12.8771 | + | 12.8771i | −0.623164 | + | 0.623164i | ||||
\(428\) | 7.76391 | + | 2.24519i | 0.375283 | + | 0.108526i | ||||
\(429\) | 20.8977 | − | 20.8977i | 1.00895 | − | 1.00895i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.5647 | 1.08690 | 0.543451 | − | 0.839441i | \(-0.317117\pi\) | ||||
0.543451 | + | 0.839441i | \(0.317117\pi\) | |||||||
\(432\) | −0.908704 | − | 4.01849i | −0.0437201 | − | 0.193340i | ||||
\(433\) | 26.4811i | 1.27260i | 0.771441 | + | 0.636301i | \(0.219536\pi\) | ||||
−0.771441 | + | 0.636301i | \(0.780464\pi\) | |||||||
\(434\) | 1.82335 | + | 1.07680i | 0.0875237 | + | 0.0516882i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 30.9030 | + | 8.93662i | 1.47998 | + | 0.427986i | ||||
\(437\) | −43.7421 | + | 43.7421i | −2.09247 | + | 2.09247i | ||||
\(438\) | −0.737013 | − | 2.86311i | −0.0352159 | − | 0.136805i | ||||
\(439\) | − | 0.765288i | − | 0.0365252i | −0.999833 | − | 0.0182626i | \(-0.994187\pi\) | ||
0.999833 | − | 0.0182626i | \(-0.00581349\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 8.94390i | − | 0.425900i | ||||||
\(442\) | −9.46423 | + | 2.43625i | −0.450167 | + | 0.115881i | ||||
\(443\) | −20.2685 | + | 20.2685i | −0.962985 | + | 0.962985i | −0.999339 | − | 0.0363537i | \(-0.988426\pi\) |
0.0363537 | + | 0.999339i | \(0.488426\pi\) | |||||||
\(444\) | 8.68596 | + | 15.7534i | 0.412218 | + | 0.747625i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −17.2931 | + | 29.2824i | −0.818851 | + | 1.38656i | ||||
\(447\) | 4.62800i | 0.218897i | ||||||||
\(448\) | −14.9635 | − | 0.885583i | −0.706961 | − | 0.0418399i | ||||
\(449\) | 35.2717 | 1.66457 | 0.832287 | − | 0.554345i | \(-0.187031\pi\) | ||||
0.832287 | + | 0.554345i | \(0.187031\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.12216 | − | 3.12216i | 0.147017 | − | 0.147017i | ||||
\(452\) | −6.20388 | + | 3.42063i | −0.291806 | + | 0.160893i | ||||
\(453\) | −9.48312 | + | 9.48312i | −0.445556 | + | 0.445556i | ||||
\(454\) | 5.97615 | + | 23.2158i | 0.280475 | + | 1.08957i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.60777 | + | 54.3800i | −0.0752908 | + | 2.54658i | ||||
\(457\) | 9.01188 | 0.421558 | 0.210779 | − | 0.977534i | \(-0.432400\pi\) | ||||
0.210779 | + | 0.977534i | \(0.432400\pi\) | |||||||
\(458\) | −10.0699 | − | 39.1191i | −0.470537 | − | 1.82792i | ||||
\(459\) | −1.87284 | − | 1.87284i | −0.0874167 | − | 0.0874167i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.8247 | + | 22.8247i | −1.06305 | + | 1.06305i | −0.0651807 | + | 0.997873i | \(0.520762\pi\) |
−0.997873 | + | 0.0651807i | \(0.979238\pi\) | |||||||
\(462\) | 14.8187 | − | 25.0926i | 0.689429 | − | 1.16741i | ||||
\(463\) | 3.72721i | 0.173218i | 0.996242 | + | 0.0866090i | \(0.0276031\pi\) | ||||
−0.996242 | + | 0.0866090i | \(0.972397\pi\) | |||||||
\(464\) | −8.05738 | − | 35.6315i | −0.374054 | − | 1.65415i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.2569 | − | 7.23846i | −0.567790 | − | 0.335315i | ||||
\(467\) | 3.23477 | + | 3.23477i | 0.149687 | + | 0.149687i | 0.777978 | − | 0.628291i | \(-0.216245\pi\) |
−0.628291 | + | 0.777978i | \(0.716245\pi\) | |||||||
\(468\) | 13.2346 | + | 3.82724i | 0.611771 | + | 0.176914i | ||||
\(469\) | −7.00109 | − | 7.00109i | −0.323280 | − | 0.323280i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.30158i | 0.382517i | ||||||||
\(472\) | −19.9219 | + | 18.7777i | −0.916979 | + | 0.864314i | ||||
\(473\) | −5.47284 | −0.251642 | ||||||||
\(474\) | −2.55763 | − | 9.93575i | −0.117476 | − | 0.456364i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.43871 | + | 4.65285i | −0.386788 | + | 0.213263i | ||||
\(477\) | 17.8721 | + | 17.8721i | 0.818307 | + | 0.818307i | ||||
\(478\) | 1.20895 | + | 0.713961i | 0.0552962 | + | 0.0326558i | ||||
\(479\) | 11.0636 | 0.505508 | 0.252754 | − | 0.967531i | \(-0.418664\pi\) | ||||
0.252754 | + | 0.967531i | \(0.418664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.2480 | 0.467267 | ||||||||
\(482\) | −17.1978 | − | 10.1563i | −0.783336 | − | 0.462609i | ||||
\(483\) | 23.7057 | + | 23.7057i | 1.07865 | + | 1.07865i | ||||
\(484\) | −18.8098 | + | 10.3712i | −0.854992 | + | 0.471417i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.32536 | + | 28.4572i | 0.332285 | + | 1.29084i | ||||
\(487\) | −6.68176 | −0.302779 | −0.151390 | − | 0.988474i | \(-0.548375\pi\) | ||||
−0.151390 | + | 0.988474i | \(0.548375\pi\) | |||||||
\(488\) | 18.8553 | + | 20.0042i | 0.853541 | + | 0.905550i | ||||
\(489\) | 42.3932i | 1.91708i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.4274 | − | 18.4274i | −0.831618 | − | 0.831618i | 0.156120 | − | 0.987738i | \(-0.450101\pi\) |
−0.987738 | + | 0.156120i | \(0.950101\pi\) | |||||||
\(492\) | 4.29141 | + | 1.24100i | 0.193472 | + | 0.0559488i | ||||
\(493\) | −16.6063 | − | 16.6063i | −0.747908 | − | 0.747908i | ||||
\(494\) | 26.6860 | + | 15.7597i | 1.20066 | + | 0.709065i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.70610 | − | 2.70316i | 0.0766060 | − | 0.121376i | ||||
\(497\) | − | 17.5083i | − | 0.785356i | ||||||
\(498\) | −2.37336 | + | 4.01881i | −0.106353 | + | 0.180087i | ||||
\(499\) | −8.84615 | + | 8.84615i | −0.396008 | + | 0.396008i | −0.876822 | − | 0.480814i | \(-0.840341\pi\) |
0.480814 | + | 0.876822i | \(0.340341\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.35554 | − | 8.35554i | −0.373298 | − | 0.373298i | ||||
\(502\) | −0.781180 | − | 3.03469i | −0.0348658 | − | 0.135445i | ||||
\(503\) | −16.8746 | −0.752401 | −0.376201 | − | 0.926538i | \(-0.622770\pi\) | ||||
−0.376201 | + | 0.926538i | \(0.622770\pi\) | |||||||
\(504\) | 13.5788 | + | 0.401464i | 0.604848 | + | 0.0178826i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.4694 | − | 48.4405i | −0.554332 | − | 2.15344i | ||||
\(507\) | −9.63723 | + | 9.63723i | −0.428004 | + | 0.428004i | ||||
\(508\) | −31.6468 | + | 17.4491i | −1.40410 | + | 0.774178i | ||||
\(509\) | −20.5691 | + | 20.5691i | −0.911707 | + | 0.911707i | −0.996407 | − | 0.0846994i | \(-0.973007\pi\) |
0.0846994 | + | 0.996407i | \(0.473007\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.66070 | −0.0734652 | ||||||||
\(512\) | −2.00376 | + | 22.5385i | −0.0885545 | + | 0.996071i | ||||
\(513\) | 8.39943i | 0.370844i | ||||||||
\(514\) | 7.37788 | − | 12.4930i | 0.325425 | − | 0.551042i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.67353 | − | 4.84889i | −0.117696 | − | 0.213460i | ||||
\(517\) | 5.02526 | − | 5.02526i | 0.221011 | − | 0.221011i | ||||
\(518\) | 9.78599 | − | 2.51908i | 0.429972 | − | 0.110682i | ||||
\(519\) | 20.6660i | 0.907135i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6708i | 0.555118i | 0.960709 | + | 0.277559i | \(0.0895253\pi\) | ||||
−0.960709 | + | 0.277559i | \(0.910475\pi\) | |||||||
\(522\) | 8.25327 | + | 32.0619i | 0.361236 | + | 1.40331i | ||||
\(523\) | 27.8509 | − | 27.8509i | 1.21784 | − | 1.21784i | 0.249448 | − | 0.968388i | \(-0.419751\pi\) |
0.968388 | − | 0.249448i | \(-0.0802491\pi\) | |||||||
\(524\) | −17.3789 | − | 5.02570i | −0.759202 | − | 0.219549i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.2134 | − | 13.7090i | −1.01215 | − | 0.597740i | ||||
\(527\) | − | 2.05496i | − | 0.0895154i | ||||||
\(528\) | −37.2003 | − | 23.4789i | −1.61894 | − | 1.02179i | ||||
\(529\) | 34.5435 | 1.50189 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.5438 | − | 17.5438i | 0.761336 | − | 0.761336i | ||||
\(532\) | 29.3569 | + | 8.48954i | 1.27278 | + | 0.368068i | ||||
\(533\) | 1.79948 | − | 1.79948i | 0.0779442 | − | 0.0779442i | ||||
\(534\) | 32.6077 | − | 8.39377i | 1.41107 | − | 0.363234i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.8760 | + | 10.2514i | −0.469774 | + | 0.442793i | ||||
\(537\) | −18.4005 | −0.794038 | ||||||||
\(538\) | 6.74915 | − | 1.73734i | 0.290976 | − | 0.0749023i | ||||
\(539\) | 11.5037 | + | 11.5037i | 0.495499 | + | 0.495499i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.4122 | + | 23.4122i | −1.00657 | + | 1.00657i | −0.00659048 | + | 0.999978i | \(0.502098\pi\) |
−0.999978 | + | 0.00659048i | \(0.997902\pi\) | |||||||
\(542\) | 36.5370 | + | 21.5774i | 1.56940 | + | 0.926829i | ||||
\(543\) | − | 39.6921i | − | 1.70335i | ||||||
\(544\) | 6.64409 | + | 12.9405i | 0.284863 | + | 0.554819i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.54089 | − | 14.4623i | 0.365516 | − | 0.618929i | ||||
\(547\) | −17.3745 | − | 17.3745i | −0.742878 | − | 0.742878i | 0.230253 | − | 0.973131i | \(-0.426045\pi\) |
−0.973131 | + | 0.230253i | \(0.926045\pi\) | |||||||
\(548\) | 10.3672 | + | 18.8027i | 0.442866 | + | 0.803211i | ||||
\(549\) | −17.6163 | − | 17.6163i | −0.751846 | − | 0.751846i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 74.4767i | 3.17282i | ||||||||
\(552\) | 36.8264 | − | 34.7113i | 1.56744 | − | 1.47741i | ||||
\(553\) | −5.76308 | −0.245071 | ||||||||
\(554\) | −16.3419 | + | 4.20668i | −0.694300 | + | 0.178725i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.81574 | + | 6.27884i | −0.0770043 | + | 0.266282i | ||||
\(557\) | −22.8889 | − | 22.8889i | −0.969832 | − | 0.969832i | 0.0297261 | − | 0.999558i | \(-0.490536\pi\) |
−0.999558 | + | 0.0297261i | \(0.990536\pi\) | |||||||
\(558\) | −1.47311 | + | 2.49442i | −0.0623617 | + | 0.105597i | ||||
\(559\) | −3.15432 | −0.133413 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.2799 | −1.19398 | ||||||||
\(562\) | −4.63639 | + | 7.85081i | −0.195574 | + | 0.331166i | ||||
\(563\) | 19.2489 | + | 19.2489i | 0.811246 | + | 0.811246i | 0.984821 | − | 0.173574i | \(-0.0555317\pi\) |
−0.173574 | + | 0.984821i | \(0.555532\pi\) | |||||||
\(564\) | 6.90721 | + | 1.99745i | 0.290846 | + | 0.0841079i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.05520 | − | 1.30129i | 0.212486 | − | 0.0546975i | ||||
\(567\) | 18.9608 | 0.796278 | ||||||||
\(568\) | −26.4178 | − | 0.781054i | −1.10846 | − | 0.0327723i | ||||
\(569\) | − | 34.4274i | − | 1.44327i | −0.692273 | − | 0.721635i | \(-0.743391\pi\) | ||
0.692273 | − | 0.721635i | \(-0.256609\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.85059 | + | 5.85059i | 0.244840 | + | 0.244840i | 0.818849 | − | 0.574009i | \(-0.194613\pi\) |
−0.574009 | + | 0.818849i | \(0.694613\pi\) | |||||||
\(572\) | −21.9451 | + | 12.0998i | −0.917569 | + | 0.505920i | ||||
\(573\) | −18.5593 | − | 18.5593i | −0.775326 | − | 0.775326i | ||||
\(574\) | 1.27603 | − | 2.16070i | 0.0532603 | − | 0.0901857i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.21151 | − | 20.4707i | 0.0504797 | − | 0.852947i | ||||
\(577\) | − | 32.5042i | − | 1.35317i | −0.736365 | − | 0.676585i | \(-0.763459\pi\) | ||
0.736365 | − | 0.676585i | \(-0.236541\pi\) | |||||||
\(578\) | −12.6491 | − | 7.47005i | −0.526131 | − | 0.310713i | ||||
\(579\) | −34.6611 | + | 34.6611i | −1.44047 | + | 1.44047i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.85384 | + | 1.85384i | 0.0769103 | + | 0.0769103i | ||||
\(582\) | 23.1561 | − | 5.96077i | 0.959851 | − | 0.247082i | ||||
\(583\) | −45.9743 | −1.90406 | ||||||||
\(584\) | −0.0740848 | + | 2.50578i | −0.00306565 | + | 0.103690i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.5735 | + | 3.75146i | −0.602024 | + | 0.154971i | ||||
\(587\) | −14.7519 | + | 14.7519i | −0.608875 | + | 0.608875i | −0.942652 | − | 0.333777i | \(-0.891677\pi\) |
0.333777 | + | 0.942652i | \(0.391677\pi\) | |||||||
\(588\) | −4.57251 | + | 15.8118i | −0.188567 | + | 0.652068i | ||||
\(589\) | −4.60810 | + | 4.60810i | −0.189873 | + | 0.189873i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −46.8024 | −1.92520 | ||||||||
\(592\) | −3.36440 | − | 14.8782i | −0.138276 | − | 0.611488i | ||||
\(593\) | − | 20.5310i | − | 0.843108i | −0.906803 | − | 0.421554i | \(-0.861485\pi\) | ||
0.906803 | − | 0.421554i | \(-0.138515\pi\) | |||||||
\(594\) | −5.84800 | − | 3.45361i | −0.239946 | − | 0.141703i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.09016 | − | 3.76979i | 0.0446547 | − | 0.154416i | ||||
\(597\) | 5.41590 | − | 5.41590i | 0.221658 | − | 0.221658i | ||||
\(598\) | −7.18683 | − | 27.9190i | −0.293891 | − | 1.14169i | ||||
\(599\) | − | 12.3998i | − | 0.506644i | −0.967382 | − | 0.253322i | \(-0.918477\pi\) | ||
0.967382 | − | 0.253322i | \(-0.0815232\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3980i | 0.505723i | 0.967502 | + | 0.252862i | \(0.0813718\pi\) | ||||
−0.967502 | + | 0.252862i | \(0.918628\pi\) | |||||||
\(602\) | −3.01212 | + | 0.775370i | −0.122765 | + | 0.0316017i | ||||
\(603\) | 9.57777 | − | 9.57777i | 0.390037 | − | 0.390037i | ||||
\(604\) | 9.95839 | − | 5.49076i | 0.405201 | − | 0.223416i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.52093 | − | 4.26870i | 0.102406 | − | 0.173404i | ||||
\(607\) | − | 4.90398i | − | 0.199046i | −0.995035 | − | 0.0995232i | \(-0.968268\pi\) | ||
0.995035 | − | 0.0995232i | \(-0.0317318\pi\) | |||||||
\(608\) | 14.1192 | − | 43.9171i | 0.572610 | − | 1.78107i | ||||
\(609\) | 40.3621 | 1.63556 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.89635 | − | 2.89635i | 0.117174 | − | 0.117174i | ||||
\(612\) | −6.36529 | − | 11.5445i | −0.257301 | − | 0.466659i | ||||
\(613\) | 0.408547 | − | 0.408547i | 0.0165011 | − | 0.0165011i | −0.698808 | − | 0.715309i | \(-0.746286\pi\) |
0.715309 | + | 0.698808i | \(0.246286\pi\) | |||||||
\(614\) | 6.33846 | + | 24.6233i | 0.255800 | + | 0.993717i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −17.9815 | + | 16.9487i | −0.724494 | + | 0.682884i | ||||
\(617\) | −6.17186 | −0.248470 | −0.124235 | − | 0.992253i | \(-0.539648\pi\) | ||||
−0.124235 | + | 0.992253i | \(0.539648\pi\) | |||||||
\(618\) | 6.82442 | + | 26.5111i | 0.274518 | + | 1.06643i | ||||
\(619\) | −18.5138 | − | 18.5138i | −0.744132 | − | 0.744132i | 0.229238 | − | 0.973370i | \(-0.426377\pi\) |
−0.973370 | + | 0.229238i | \(0.926377\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.52479 | − | 5.52479i | 0.221702 | − | 0.221702i | ||||
\(622\) | −8.58027 | + | 14.5290i | −0.344037 | + | 0.582559i | ||||
\(623\) | − | 18.9136i | − | 0.757757i | ||||||
\(624\) | −21.4407 | − | 13.5323i | −0.858315 | − | 0.541724i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 41.8236 | + | 24.6994i | 1.67161 | + | 0.987187i | ||||
\(627\) | 63.4156 | + | 63.4156i | 2.53258 | + | 2.53258i | ||||
\(628\) | 1.95550 | − | 6.76214i | 0.0780329 | − | 0.269839i | ||||
\(629\) | −6.93404 | − | 6.93404i | −0.276478 | − | 0.276478i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 20.7940i | − | 0.827795i | −0.910323 | − | 0.413897i | \(-0.864167\pi\) | ||
0.910323 | − | 0.413897i | \(-0.135833\pi\) | |||||||
\(632\) | −0.257094 | + | 8.69574i | −0.0102266 | + | 0.345898i | ||||
\(633\) | 33.9640 | 1.34995 | ||||||||
\(634\) | −8.53130 | − | 33.1419i | −0.338821 | − | 1.31623i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −22.4588 | − | 40.7328i | −0.890551 | − | 1.61516i | ||||
\(637\) | 6.63024 | + | 6.63024i | 0.262700 | + | 0.262700i | ||||
\(638\) | −51.8535 | − | 30.6227i | −2.05290 | − | 1.21237i | ||||
\(639\) | 23.9521 | 0.947530 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.1179 | 0.636620 | 0.318310 | − | 0.947987i | \(-0.396885\pi\) | ||||
0.318310 | + | 0.947987i | \(0.396885\pi\) | |||||||
\(642\) | 11.6066 | + | 6.85441i | 0.458075 | + | 0.270522i | ||||
\(643\) | 10.3733 | + | 10.3733i | 0.409082 | + | 0.409082i | 0.881419 | − | 0.472336i | \(-0.156589\pi\) |
−0.472336 | + | 0.881419i | \(0.656589\pi\) | |||||||
\(644\) | −13.7257 | − | 24.8938i | −0.540868 | − | 0.980954i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.39298 | − | 28.7199i | −0.290873 | − | 1.12997i | ||||
\(647\) | −32.5724 | −1.28055 | −0.640276 | − | 0.768145i | \(-0.721180\pi\) | ||||
−0.640276 | + | 0.768145i | \(0.721180\pi\) | |||||||
\(648\) | 0.845850 | − | 28.6094i | 0.0332281 | − | 1.12388i | ||||
\(649\) | 45.1298i | 1.77150i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.49733 | + | 2.49733i | 0.0978780 | + | 0.0978780i | ||||
\(652\) | 9.98601 | − | 34.5318i | 0.391083 | − | 1.35237i | ||||
\(653\) | 4.31962 | + | 4.31962i | 0.169040 | + | 0.169040i | 0.786557 | − | 0.617517i | \(-0.211861\pi\) |
−0.617517 | + | 0.786557i | \(0.711861\pi\) | |||||||
\(654\) | 46.1981 | + | 27.2828i | 1.80649 | + | 1.06684i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.20328 | − | 2.02174i | −0.125067 | − | 0.0789359i | ||||
\(657\) | − | 2.27191i | − | 0.0886356i | ||||||
\(658\) | 2.05382 | − | 3.47774i | 0.0800662 | − | 0.135576i | ||||
\(659\) | 4.19711 | − | 4.19711i | 0.163496 | − | 0.163496i | −0.620617 | − | 0.784114i | \(-0.713118\pi\) |
0.784114 | + | 0.620617i | \(0.213118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.2310 | + | 21.2310i | 0.825790 | + | 0.825790i | 0.986931 | − | 0.161141i | \(-0.0515175\pi\) |
−0.161141 | + | 0.986931i | \(0.551518\pi\) | |||||||
\(662\) | −4.88731 | − | 18.9860i | −0.189951 | − | 0.737911i | ||||
\(663\) | −16.2993 | −0.633013 | ||||||||
\(664\) | 2.87990 | − | 2.71450i | 0.111762 | − | 0.105343i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.44620 | + | 13.3876i | 0.133538 | + | 0.518760i | ||||
\(667\) | 48.9877 | − | 48.9877i | 1.89681 | − | 1.89681i | ||||
\(668\) | 4.83788 | + | 8.77429i | 0.187183 | + | 0.339488i | ||||
\(669\) | −40.1062 | + | 40.1062i | −1.55060 | + | 1.55060i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 45.3164 | 1.74942 | ||||||||
\(672\) | −23.8005 | − | 7.65182i | −0.918126 | − | 0.295175i | ||||
\(673\) | − | 6.08317i | − | 0.234489i | −0.993103 | − | 0.117244i | \(-0.962594\pi\) | ||
0.993103 | − | 0.117244i | \(-0.0374061\pi\) | |||||||
\(674\) | −4.36877 | + | 7.39765i | −0.168279 | + | 0.284947i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.1202 | − | 5.57998i | 0.389239 | − | 0.214615i | ||||
\(677\) | −8.42443 | + | 8.42443i | −0.323777 | + | 0.323777i | −0.850214 | − | 0.526437i | \(-0.823528\pi\) |
0.526437 | + | 0.850214i | \(0.323528\pi\) | |||||||
\(678\) | −11.4426 | + | 2.94551i | −0.439449 | + | 0.113122i | ||||
\(679\) | − | 13.4313i | − | 0.515447i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 39.9824i | 1.53213i | ||||||||
\(682\) | −1.31361 | − | 5.10305i | −0.0503008 | − | 0.195406i | ||||
\(683\) | −14.7609 | + | 14.7609i | −0.564812 | + | 0.564812i | −0.930670 | − | 0.365859i | \(-0.880775\pi\) |
0.365859 | + | 0.930670i | \(0.380775\pi\) | |||||||
\(684\) | −11.6140 | + | 40.1615i | −0.444073 | + | 1.53561i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 23.9328 | + | 14.1338i | 0.913757 | + | 0.539630i | ||||
\(687\) | − | 67.3710i | − | 2.57036i | ||||||
\(688\) | 1.03556 | + | 4.57948i | 0.0394804 | + | 0.174591i | ||||
\(689\) | −26.4977 | −1.00948 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.06268 | + | 4.06268i | −0.154552 | + | 0.154552i | −0.780147 | − | 0.625596i | \(-0.784856\pi\) |
0.625596 | + | 0.780147i | \(0.284856\pi\) | |||||||
\(692\) | 4.86802 | − | 16.8337i | 0.185054 | − | 0.639920i | ||||
\(693\) | 15.8350 | − | 15.8350i | 0.601523 | − | 0.601523i | ||||
\(694\) | −11.1801 | + | 2.87796i | −0.424392 | + | 0.109246i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.80057 | − | 60.9012i | 0.0682506 | − | 2.30845i | ||||
\(697\) | −2.43515 | −0.0922379 | ||||||||
\(698\) | −14.6979 | + | 3.78348i | −0.556322 | + | 0.143207i | ||||
\(699\) | −16.7875 | − | 16.7875i | −0.634961 | − | 0.634961i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.1049 | − | 11.1049i | 0.419428 | − | 0.419428i | −0.465578 | − | 0.885007i | \(-0.654154\pi\) |
0.885007 | + | 0.465578i | \(0.154154\pi\) | |||||||
\(702\) | −3.37054 | − | 1.99051i | −0.127213 | − | 0.0751271i | ||||
\(703\) | 31.0982i | 1.17289i | ||||||||
\(704\) | 24.7713 | + | 27.8878i | 0.933603 | + | 1.05106i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.6705 | + | 19.7617i | −0.439225 | + | 0.743741i | ||||
\(707\) | −1.96911 | − | 1.96911i | −0.0740561 | − | 0.0740561i | ||||
\(708\) | −39.9846 | + | 22.0463i | −1.50271 | + | 0.828551i | ||||
\(709\) | −13.0114 | − | 13.0114i | −0.488652 | − | 0.488652i | 0.419229 | − | 0.907881i | \(-0.362300\pi\) |
−0.907881 | + | 0.419229i | \(0.862300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 7.88412i | − | 0.295678i | ||||||
\(712\) | −28.5381 | − | 0.843744i | −1.06951 | − | 0.0316206i | ||||
\(713\) | 6.06203 | 0.227025 | ||||||||
\(714\) | −15.5645 | + | 4.00658i | −0.582488 | + | 0.149942i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.9883 | + | 4.33436i | 0.560138 | + | 0.161983i | ||||
\(717\) | 1.65582 | + | 1.65582i | 0.0618378 | + | 0.0618378i | ||||
\(718\) | 4.87071 | − | 8.24759i | 0.181773 | − | 0.307797i | ||||
\(719\) | 50.0570 | 1.86681 | 0.933406 | − | 0.358821i | \(-0.116821\pi\) | ||||
0.933406 | + | 0.358821i | \(0.116821\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3774 | 0.572684 | ||||||||
\(722\) | −34.1604 | + | 57.8439i | −1.27132 | + | 2.15273i | ||||
\(723\) | −23.5547 | − | 23.5547i | −0.876007 | − | 0.876007i | ||||
\(724\) | −9.34977 | + | 32.3316i | −0.347481 | + | 1.20160i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −34.6932 | + | 8.93062i | −1.28759 | + | 0.331447i | ||||
\(727\) | 27.7141 | 1.02786 | 0.513930 | − | 0.857832i | \(-0.328189\pi\) | ||||
0.513930 | + | 0.857832i | \(0.328189\pi\) | |||||||
\(728\) | −10.3638 | + | 9.76854i | −0.384107 | + | 0.362046i | ||||
\(729\) | 18.6509i | 0.690775i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.13429 | + | 2.13429i | 0.0789396 | + | 0.0789396i | ||||
\(732\) | 22.1374 | + | 40.1499i | 0.818224 | + | 1.48398i | ||||
\(733\) | 16.8860 | + | 16.8860i | 0.623698 | + | 0.623698i | 0.946475 | − | 0.322777i | \(-0.104616\pi\) |
−0.322777 | + | 0.946475i | \(0.604616\pi\) | |||||||
\(734\) | 4.57160 | − | 7.74110i | 0.168741 | − | 0.285729i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.1738 | + | 19.5998i | −1.40711 | + | 0.722457i | ||||
\(737\) | 24.6379i | 0.907550i | ||||||||
\(738\) | 2.95592 | + | 1.74565i | 0.108809 | + | 0.0642584i | ||||
\(739\) | 23.6286 | − | 23.6286i | 0.869193 | − | 0.869193i | −0.123190 | − | 0.992383i | \(-0.539312\pi\) |
0.992383 | + | 0.123190i | \(0.0393124\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.5501 | + | 36.5501i | 1.34270 | + | 1.34270i | ||||
\(742\) | −25.3031 | + | 6.51345i | −0.928907 | + | 0.239116i | ||||
\(743\) | 6.53356 | 0.239693 | 0.119846 | − | 0.992792i | \(-0.461760\pi\) | ||||
0.119846 | + | 0.992792i | \(0.461760\pi\) | |||||||
\(744\) | 3.87955 | − | 3.65673i | 0.142231 | − | 0.134062i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.8372 | − | 4.59161i | 0.653068 | − | 0.168111i | ||||
\(747\) | −2.53613 | + | 2.53613i | −0.0927921 | + | 0.0927921i | ||||
\(748\) | 23.0356 | + | 6.66153i | 0.842267 | + | 0.243570i | ||||
\(749\) | 5.35401 | − | 5.35401i | 0.195631 | − | 0.195631i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.8483 | −0.833746 | −0.416873 | − | 0.908965i | \(-0.636874\pi\) | ||||
−0.416873 | + | 0.908965i | \(0.636874\pi\) | |||||||
\(752\) | −5.15583 | − | 3.25409i | −0.188014 | − | 0.118664i | ||||
\(753\) | − | 5.22634i | − | 0.190459i | ||||||
\(754\) | −29.8862 | − | 17.6496i | −1.08839 | − | 0.642762i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.70789 | − | 1.07226i | −0.134855 | − | 0.0389977i | ||||
\(757\) | −24.0190 | + | 24.0190i | −0.872985 | + | 0.872985i | −0.992797 | − | 0.119811i | \(-0.961771\pi\) |
0.119811 | + | 0.992797i | \(0.461771\pi\) | |||||||
\(758\) | 2.70031 | + | 10.4900i | 0.0980797 | + | 0.381015i | ||||
\(759\) | − | 83.4243i | − | 3.02811i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 5.51772i | − | 0.200017i | −0.994987 | − | 0.100009i | \(-0.968113\pi\) | ||
0.994987 | − | 0.100009i | \(-0.0318871\pi\) | |||||||
\(762\) | −58.3700 | + | 15.0254i | −2.11452 | + | 0.544314i | ||||
\(763\) | 21.3107 | − | 21.3107i | 0.771501 | − | 0.771501i | ||||
\(764\) | 10.7459 | + | 19.4894i | 0.388772 | + | 0.705103i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.2528 | − | 34.2941i | 0.731763 | − | 1.23910i | ||||
\(767\) | 26.0109i | 0.939200i | ||||||||
\(768\) | −12.6073 | + | 35.5706i | −0.454928 | + | 1.28354i | ||||
\(769\) | −14.0124 | −0.505299 | −0.252649 | − | 0.967558i | \(-0.581302\pi\) | ||||
−0.252649 | + | 0.967558i | \(0.581302\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.1108 | − | 17.1108i | 0.616231 | − | 0.616231i | ||||
\(772\) | 36.3982 | − | 20.0689i | 1.31000 | − | 0.722294i | ||||
\(773\) | −0.753043 | + | 0.753043i | −0.0270851 | + | 0.0270851i | −0.720520 | − | 0.693435i | \(-0.756097\pi\) |
0.693435 | + | 0.720520i | \(0.256097\pi\) | |||||||
\(774\) | −1.06074 | − | 4.12070i | −0.0381274 | − | 0.148115i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −20.2661 | − | 0.599178i | −0.727512 | − | 0.0215092i | ||||
\(777\) | 16.8535 | 0.604614 | ||||||||
\(778\) | 4.78529 | + | 18.5896i | 0.171561 | + | 0.666471i | ||||
\(779\) | 5.46066 | + | 5.46066i | 0.195648 | + | 0.195648i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.8073 | + | 30.8073i | −1.10237 | + | 1.10237i | ||||
\(782\) | −14.0279 | + | 23.7535i | −0.501638 | + | 0.849424i | ||||
\(783\) | − | 9.40668i | − | 0.336167i | ||||||
\(784\) | 7.44917 | − | 11.8026i | 0.266042 | − | 0.421521i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −25.9805 | − | 15.3431i | −0.926693 | − | 0.547270i | ||||
\(787\) | 29.2752 | + | 29.2752i | 1.04355 | + | 1.04355i | 0.999008 | + | 0.0445395i | \(0.0141821\pi\) |
0.0445395 | + | 0.999008i | \(0.485818\pi\) | |||||||
\(788\) | 38.1234 | + | 11.0247i | 1.35809 | + | 0.392737i | ||||
\(789\) | −31.7939 | − | 31.7939i | −1.13189 | − | 1.13189i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.63709i | 0.235988i | ||||||||
\(792\) | −23.1866 | − | 24.5994i | −0.823899 | − | 0.874101i | ||||
\(793\) | 26.1185 | 0.927494 | ||||||||
\(794\) | 5.22932 | + | 20.3146i | 0.185581 | + | 0.720937i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.68733 | + | 3.13582i | −0.201582 | + | 0.111146i | ||||
\(797\) | 6.09658 | + | 6.09658i | 0.215952 | + | 0.215952i | 0.806790 | − | 0.590838i | \(-0.201203\pi\) |
−0.590838 | + | 0.806790i | \(0.701203\pi\) | |||||||
\(798\) | 43.8869 | + | 25.9179i | 1.55358 | + | 0.917485i | ||||
\(799\) | −3.91948 | −0.138661 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.8745 | 0.914232 | ||||||||
\(802\) | 2.97393 | + | 1.75629i | 0.105013 | + | 0.0620167i | ||||
\(803\) | 2.92214 | + | 2.92214i | 0.103120 | + | 0.103120i | ||||
\(804\) | −21.8290 | + | 12.0358i | −0.769849 | + | 0.424471i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.757111 | − | 2.94119i | −0.0266681 | − | 0.103599i | ||||
\(807\) | 11.6234 | 0.409163 | ||||||||
\(808\) | −3.05897 | + | 2.88329i | −0.107614 | + | 0.101434i | ||||
\(809\) | 31.5083i | 1.10777i | 0.832592 | + | 0.553886i | \(0.186856\pi\) | ||||
−0.832592 | + | 0.553886i | \(0.813144\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.2317 | + | 20.2317i | 0.710431 | + | 0.710431i | 0.966625 | − | 0.256194i | \(-0.0824686\pi\) |
−0.256194 | + | 0.966625i | \(0.582469\pi\) | |||||||
\(812\) | −32.8774 | − | 9.50760i | −1.15377 | − | 0.333651i | ||||
\(813\) | 50.0424 | + | 50.0424i | 1.75506 | + | 1.75506i | ||||
\(814\) | −21.6517 | − | 12.7867i | −0.758893 | − | 0.448174i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.35106 | + | 23.6636i | 0.187325 | + | 0.828391i | ||||
\(817\) | − | 9.57200i | − | 0.334882i | ||||||
\(818\) | −17.7359 | + | 30.0323i | −0.620123 | + | 1.05006i | ||||
\(819\) | 9.12664 | − | 9.12664i | 0.318910 | − | 0.318910i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.1821 | − | 19.1821i | −0.669459 | − | 0.669459i | 0.288132 | − | 0.957591i | \(-0.406966\pi\) |
−0.957591 | + | 0.288132i | \(0.906966\pi\) | |||||||
\(822\) | 8.92723 | + | 34.6800i | 0.311373 | + | 1.20961i | ||||
\(823\) | 11.4746 | 0.399979 | 0.199989 | − | 0.979798i | \(-0.435909\pi\) | ||||
0.199989 | + | 0.979798i | \(0.435909\pi\) | |||||||
\(824\) | 0.685992 | − | 23.2025i | 0.0238977 | − | 0.808296i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.39381 | + | 24.8383i | 0.222469 | + | 0.864236i | ||||
\(827\) | 17.7573 | − | 17.7573i | 0.617482 | − | 0.617482i | −0.327403 | − | 0.944885i | \(-0.606173\pi\) |
0.944885 | + | 0.327403i | \(0.106173\pi\) | |||||||
\(828\) | 34.0557 | − | 18.7773i | 1.18352 | − | 0.652556i | ||||
\(829\) | 20.0071 | − | 20.0071i | 0.694876 | − | 0.694876i | −0.268424 | − | 0.963301i | \(-0.586503\pi\) |
0.963301 | + | 0.268424i | \(0.0865030\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.1440 | −0.976306 | ||||||||
\(832\) | 14.2771 | + | 16.0733i | 0.494970 | + | 0.557243i | ||||
\(833\) | − | 8.97238i | − | 0.310874i | ||||||
\(834\) | −5.54331 | + | 9.38649i | −0.191949 | + | 0.325028i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −36.7178 | − | 66.5939i | −1.26991 | − | 2.30320i | ||||
\(837\) | 0.582020 | − | 0.582020i | 0.0201175 | − | 0.0201175i | ||||
\(838\) | 37.1220 | − | 9.55584i | 1.28236 | − | 0.330101i | ||||
\(839\) | − | 20.3936i | − | 0.704065i | −0.935988 | − | 0.352033i | \(-0.885491\pi\) | ||
0.935988 | − | 0.352033i | \(-0.114509\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 54.4079i | − | 1.87614i | ||||||
\(842\) | 3.70679 | + | 14.3999i | 0.127744 | + | 0.496255i | ||||
\(843\) | −10.7527 | + | 10.7527i | −0.370344 | + | 0.370344i | ||||
\(844\) | −27.6657 | − | 8.00047i | −0.952293 | − | 0.275387i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.75768 | + | 2.80971i | 0.163572 | + | 0.0965997i | ||||
\(847\) | 20.1233i | 0.691444i | ||||||||
\(848\) | 8.69917 | + | 38.4697i | 0.298731 | + | 1.32105i | ||||
\(849\) | 8.70608 | 0.298792 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.4551 | − | 20.4551i | 0.701191 | − | 0.701191i | ||||
\(852\) | −42.3446 | − | 12.2453i | −1.45070 | − | 0.419519i | ||||
\(853\) | −37.4481 | + | 37.4481i | −1.28220 | + | 1.28220i | −0.342784 | + | 0.939414i | \(0.611370\pi\) |
−0.939414 | + | 0.342784i | \(0.888630\pi\) | |||||||
\(854\) | 24.9410 | − | 6.42024i | 0.853464 | − | 0.219696i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.83965 | − | 8.31734i | −0.267954 | − | 0.284281i | ||||
\(857\) | 12.7258 | 0.434706 | 0.217353 | − | 0.976093i | \(-0.430258\pi\) | ||||
0.217353 | + | 0.976093i | \(0.430258\pi\) | |||||||
\(858\) | −40.4759 | + | 10.4192i | −1.38183 | + | 0.355705i | ||||
\(859\) | −17.4318 | − | 17.4318i | −0.594766 | − | 0.594766i | 0.344149 | − | 0.938915i | \(-0.388167\pi\) |
−0.938915 | + | 0.344149i | \(0.888167\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.95936 | − | 2.95936i | 0.100855 | − | 0.100855i | ||||
\(862\) | −27.4774 | − | 16.2271i | −0.935885 | − | 0.552699i | ||||
\(863\) | − | 33.6976i | − | 1.14708i | −0.819178 | − | 0.573540i | \(-0.805570\pi\) | ||
0.819178 | − | 0.573540i | \(-0.194430\pi\) | |||||||
\(864\) | −1.78331 | + | 5.54688i | −0.0606694 | + | 0.188709i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.0436 | − | 32.2466i | 0.647128 | − | 1.09578i | ||||
\(867\) | −17.3246 | − | 17.3246i | −0.588374 | − | 0.588374i | ||||
\(868\) | −1.44596 | − | 2.62249i | −0.0490791 | − | 0.0890130i | ||||
\(869\) | 10.1406 | + | 10.1406i | 0.343996 | + | 0.343996i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.2003i | 0.481158i | ||||||||
\(872\) | −31.2044 | − | 33.1058i | −1.05672 | − | 1.12110i | ||||
\(873\) | 18.3746 | 0.621886 | ||||||||
\(874\) | 84.7223 | − | 21.8090i | 2.86577 | − | 0.737699i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.16150 | + | 4.01648i | −0.0392434 | + | 0.135704i | ||||
\(877\) | 21.8386 | + | 21.8386i | 0.737436 | + | 0.737436i | 0.972081 | − | 0.234645i | \(-0.0753927\pi\) |
−0.234645 | + | 0.972081i | \(0.575393\pi\) | |||||||
\(878\) | −0.550349 | + | 0.931906i | −0.0185734 | + | 0.0314503i | ||||
\(879\) | −25.0985 | −0.846550 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.3274 | −1.32497 | −0.662487 | − | 0.749073i | \(-0.730499\pi\) | ||||
−0.662487 | + | 0.749073i | \(0.730499\pi\) | |||||||
\(882\) | −6.43191 | + | 10.8912i | −0.216574 | + | 0.366724i | ||||
\(883\) | −6.80206 | − | 6.80206i | −0.228907 | − | 0.228907i | 0.583329 | − | 0.812236i | \(-0.301750\pi\) |
−0.812236 | + | 0.583329i | \(0.801750\pi\) | |||||||
\(884\) | 13.2768 | + | 3.83942i | 0.446546 | + | 0.129134i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.2572 | − | 10.1055i | 1.31887 | − | 0.339500i | ||||
\(887\) | 29.4190 | 0.987793 | 0.493897 | − | 0.869521i | \(-0.335572\pi\) | ||||
0.493897 | + | 0.869521i | \(0.335572\pi\) | |||||||
\(888\) | 0.751840 | − | 25.4297i | 0.0252301 | − | 0.853363i | ||||
\(889\) | 33.8566i | 1.13552i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.3630 | − | 33.3630i | −1.11770 | − | 1.11770i | ||||
\(892\) | 42.1162 | − | 23.2216i | 1.41016 | − | 0.777517i | ||||
\(893\) | 8.78917 | + | 8.78917i | 0.294118 | + | 0.294118i | ||||
\(894\) | 3.32818 | − | 5.63561i | 0.111311 | − | 0.188483i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 17.5845 | + | 11.8393i | 0.587458 | + | 0.395522i | ||||
\(897\) | − | 48.0822i | − | 1.60542i | ||||||
\(898\) | −42.9510 | − | 25.3652i | −1.43329 | − | 0.846449i | ||||
\(899\) | 5.16070 | − | 5.16070i | 0.172119 | − | 0.172119i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.9290 | + | 17.9290i | 0.597301 | + | 0.597301i | ||||
\(902\) | −6.04718 | + | 1.55665i | −0.201349 | + | 0.0518307i | ||||
\(903\) | −5.18748 | −0.172628 | ||||||||
\(904\) | 10.0145 | + | 0.296084i | 0.333077 | + | 0.00984759i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 18.3675 | − | 4.72810i | 0.610218 | − | 0.157081i | ||||
\(907\) | 16.6137 | − | 16.6137i | 0.551649 | − | 0.551649i | −0.375267 | − | 0.926917i | \(-0.622449\pi\) |
0.926917 | + | 0.375267i | \(0.122449\pi\) | |||||||
\(908\) | 9.41814 | − | 32.5681i | 0.312552 | − | 1.08081i | ||||
\(909\) | 2.69382 | − | 2.69382i | 0.0893485 | − | 0.0893485i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.7299 | 1.34944 | 0.674721 | − | 0.738073i | \(-0.264264\pi\) | ||||
0.674721 | + | 0.738073i | \(0.264264\pi\) | |||||||
\(912\) | 41.0646 | − | 65.0633i | 1.35978 | − | 2.15446i | ||||
\(913\) | − | 6.52396i | − | 0.215912i | ||||||
\(914\) | −10.9739 | − | 6.48079i | −0.362985 | − | 0.214365i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.8697 | + | 54.8777i | −0.524351 | + | 1.81321i | ||||
\(917\) | −11.9846 | + | 11.9846i | −0.395765 | + | 0.395765i | ||||
\(918\) | 0.933760 | + | 3.62742i | 0.0308187 | + | 0.119723i | ||||
\(919\) | − | 35.6125i | − | 1.17475i | −0.809316 | − | 0.587373i | \(-0.800162\pi\) | ||
0.809316 | − | 0.587373i | \(-0.199838\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.4064i | 1.39734i | ||||||||
\(922\) | 44.2083 | − | 11.3800i | 1.45592 | − | 0.374779i | ||||
\(923\) | −17.7560 | + | 17.7560i | −0.584446 | + | 0.584446i | ||||
\(924\) | −36.0901 | + | 19.8990i | −1.18728 | + | 0.654628i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.68038 | − | 4.53869i | 0.0880828 | − | 0.149151i | ||||
\(927\) | 21.0369i | 0.690942i | ||||||||
\(928\) | −15.8124 | + | 49.1836i | −0.519067 | + | 1.61453i | ||||
\(929\) | 0.570971 | 0.0187329 | 0.00936647 | − | 0.999956i | \(-0.497019\pi\) | ||||
0.00936647 | + | 0.999956i | \(0.497019\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.1199 | + | 20.1199i | −0.659404 | + | 0.659404i | ||||
\(932\) | 9.72000 | + | 17.6288i | 0.318389 | + | 0.577451i | ||||
\(933\) | −19.8994 | + | 19.8994i | −0.651477 | + | 0.651477i | ||||
\(934\) | −1.61279 | − | 6.26529i | −0.0527722 | − | 0.205007i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.3638 | − | 14.1780i | −0.436808 | − | 0.463424i | ||||
\(937\) | −21.3585 | −0.697750 | −0.348875 | − | 0.937169i | \(-0.613436\pi\) | ||||
−0.348875 | + | 0.937169i | \(0.613436\pi\) | |||||||
\(938\) | 3.49060 | + | 13.5601i | 0.113972 | + | 0.442753i | ||||
\(939\) | 57.2830 | + | 57.2830i | 1.86936 | + | 1.86936i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.6914 | − | 33.6914i | 1.09831 | − | 1.09831i | 0.103700 | − | 0.994609i | \(-0.466932\pi\) |
0.994609 | − | 0.103700i | \(-0.0330681\pi\) | |||||||
\(942\) | 5.96999 | − | 10.1090i | 0.194513 | − | 0.329369i | ||||
\(943\) | − | 7.18358i | − | 0.233929i | ||||||
\(944\) | 37.7630 | − | 8.53937i | 1.22908 | − | 0.277933i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.66438 | + | 3.93573i | 0.216678 | + | 0.127962i | ||||
\(947\) | −0.421834 | − | 0.421834i | −0.0137078 | − | 0.0137078i | 0.700220 | − | 0.713927i | \(-0.253085\pi\) |
−0.713927 | + | 0.700220i | \(0.753085\pi\) | |||||||
\(948\) | −4.03071 | + | 13.9382i | −0.130911 | + | 0.452693i | ||||
\(949\) | 1.68420 | + | 1.68420i | 0.0546714 | + | 0.0546714i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 57.0771i | − | 1.85085i | ||||||
\(952\) | 13.6220 | + | 0.402742i | 0.441492 | + | 0.0130529i | ||||
\(953\) | 27.7261 | 0.898137 | 0.449069 | − | 0.893497i | \(-0.351756\pi\) | ||||
0.449069 | + | 0.893497i | \(0.351756\pi\) | |||||||
\(954\) | −8.91067 | − | 34.6157i | −0.288493 | − | 1.12072i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.958726 | − | 1.73881i | −0.0310074 | − | 0.0562371i | ||||
\(957\) | −71.0204 | − | 71.0204i | −2.29576 | − | 2.29576i | ||||
\(958\) | −13.4723 | − | 7.95625i | −0.435271 | − | 0.257055i | ||||
\(959\) | 20.1156 | 0.649567 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3614 | −0.979399 | ||||||||
\(962\) | −12.4792 | − | 7.36972i | −0.402344 | − | 0.237609i | ||||
\(963\) | 7.32450 | + | 7.32450i | 0.236029 | + | 0.236029i | ||||
\(964\) | 13.6382 | + | 24.7352i | 0.439257 | + | 0.796666i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11.8192 | − | 45.9147i | −0.380277 | − | 1.47728i | ||||
\(967\) | −41.9640 | −1.34947 | −0.674735 | − | 0.738060i | \(-0.735742\pi\) | ||||
−0.674735 | + | 0.738060i | \(0.735742\pi\) | |||||||
\(968\) | 30.3634 | + | 0.897709i | 0.975916 | + | 0.0288534i | ||||
\(969\) | − | 49.4614i | − | 1.58893i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.0549 | + | 30.0549i | 0.964508 | + | 0.964508i | 0.999391 | − | 0.0348833i | \(-0.0111059\pi\) |
−0.0348833 | + | 0.999391i | \(0.511106\pi\) | |||||||
\(972\) | 11.5444 | − | 39.9208i | 0.370287 | − | 1.28046i | ||||
\(973\) | 4.32990 | + | 4.32990i | 0.138810 | + | 0.138810i | ||||
\(974\) | 8.13651 | + | 4.80511i | 0.260710 | + | 0.153966i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.57468 | − | 37.9192i | −0.274469 | − | 1.21376i | ||||
\(977\) | 44.3389i | 1.41853i | 0.704944 | + | 0.709263i | \(0.250972\pi\) | ||||
−0.704944 | + | 0.709263i | \(0.749028\pi\) | |||||||
\(978\) | 30.4866 | − | 51.6229i | 0.974853 | − | 1.65072i | ||||
\(979\) | −33.2800 | + | 33.2800i | −1.06363 | + | 1.06363i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.1539 | + | 29.1539i | 0.930814 | + | 0.930814i | ||||
\(982\) | 9.18755 | + | 35.6913i | 0.293186 | + | 1.13896i | ||||
\(983\) | 27.0764 | 0.863604 | 0.431802 | − | 0.901968i | \(-0.357878\pi\) | ||||
0.431802 | + | 0.901968i | \(0.357878\pi\) | |||||||
\(984\) | −4.33327 | − | 4.59731i | −0.138140 | − | 0.146557i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.27955 | + | 32.1639i | 0.263674 | + | 1.02431i | ||||
\(987\) | 4.76323 | − | 4.76323i | 0.151615 | − | 0.151615i | ||||
\(988\) | −21.1626 | − | 38.3819i | −0.673272 | − | 1.22109i | ||||
\(989\) | −6.29606 | + | 6.29606i | −0.200203 | + | 0.200203i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.3780 | 0.615564 | 0.307782 | − | 0.951457i | \(-0.400413\pi\) | ||||
0.307782 | + | 0.951457i | \(0.400413\pi\) | |||||||
\(992\) | −4.02150 | + | 2.06477i | −0.127683 | + | 0.0655567i | ||||
\(993\) | − | 32.6977i | − | 1.03763i | ||||||
\(994\) | −12.5909 | + | 21.3202i | −0.399360 | + | 0.676236i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.78017 | − | 3.18701i | 0.183152 | − | 0.100984i | ||||
\(997\) | −8.69453 | + | 8.69453i | −0.275359 | + | 0.275359i | −0.831253 | − | 0.555894i | \(-0.812376\pi\) |
0.555894 | + | 0.831253i | \(0.312376\pi\) | |||||||
\(998\) | 17.1337 | − | 4.41051i | 0.542359 | − | 0.139612i | ||||
\(999\) | − | 3.92782i | − | 0.124271i |
(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 | 400.2.q.e.149.2 | 12 | ||
4.3 | odd | 2 | 1600.2.q.e.49.6 | 12 | |||
5.2 | odd | 4 | 400.2.l.g.101.4 | yes | 12 | ||
5.3 | odd | 4 | 400.2.l.f.101.3 | ✓ | 12 | ||
5.4 | even | 2 | 400.2.q.f.149.5 | 12 | |||
16.3 | odd | 4 | 1600.2.q.f.849.1 | 12 | |||
16.13 | even | 4 | 400.2.q.f.349.5 | 12 | |||
20.3 | even | 4 | 1600.2.l.g.1201.1 | 12 | |||
20.7 | even | 4 | 1600.2.l.f.1201.6 | 12 | |||
20.19 | odd | 2 | 1600.2.q.f.49.1 | 12 | |||
80.3 | even | 4 | 1600.2.l.g.401.1 | 12 | |||
80.13 | odd | 4 | 400.2.l.f.301.3 | yes | 12 | ||
80.19 | odd | 4 | 1600.2.q.e.849.6 | 12 | |||
80.29 | even | 4 | inner | 400.2.q.e.349.2 | 12 | ||
80.67 | even | 4 | 1600.2.l.f.401.6 | 12 | |||
80.77 | odd | 4 | 400.2.l.g.301.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.3 | ✓ | 12 | 5.3 | odd | 4 | ||
400.2.l.f.301.3 | yes | 12 | 80.13 | odd | 4 | ||
400.2.l.g.101.4 | yes | 12 | 5.2 | odd | 4 | ||
400.2.l.g.301.4 | yes | 12 | 80.77 | odd | 4 | ||
400.2.q.e.149.2 | 12 | 1.1 | even | 1 | trivial | ||
400.2.q.e.349.2 | 12 | 80.29 | even | 4 | inner | ||
400.2.q.f.149.5 | 12 | 5.4 | even | 2 | |||
400.2.q.f.349.5 | 12 | 16.13 | even | 4 | |||
1600.2.l.f.401.6 | 12 | 80.67 | even | 4 | |||
1600.2.l.f.1201.6 | 12 | 20.7 | even | 4 | |||
1600.2.l.g.401.1 | 12 | 80.3 | even | 4 | |||
1600.2.l.g.1201.1 | 12 | 20.3 | even | 4 | |||
1600.2.q.e.49.6 | 12 | 4.3 | odd | 2 | |||
1600.2.q.e.849.6 | 12 | 80.19 | odd | 4 | |||
1600.2.q.f.49.1 | 12 | 20.19 | odd | 2 | |||
1600.2.q.f.849.1 | 12 | 16.3 | odd | 4 |