Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(244,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.244");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.c (of order \(3\), 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: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 487.6 | ||
Root | \(0.0878222i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 729.487 |
Dual form | 729.2.c.d.244.6 |
$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35253 | − | 2.34265i | 0.956385 | − | 1.65651i | 0.225218 | − | 0.974308i | \(-0.427691\pi\) |
0.731167 | − | 0.682199i | \(-0.238976\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.65869 | − | 4.60498i | −1.32934 | − | 2.30249i | ||||
\(5\) | −0.836192 | − | 1.44833i | −0.373957 | − | 0.647712i | 0.616214 | − | 0.787579i | \(-0.288666\pi\) |
−0.990170 | + | 0.139867i | \(0.955332\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.250296 | + | 0.433525i | −0.0946028 | + | 0.163857i | −0.909443 | − | 0.415829i | \(-0.863491\pi\) |
0.814840 | + | 0.579686i | \(0.196825\pi\) | |||||||
\(8\) | −8.97372 | −3.17269 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.52391 | −1.43059 | ||||||||
\(11\) | −0.958859 | + | 1.66079i | −0.289107 | + | 0.500748i | −0.973597 | − | 0.228275i | \(-0.926692\pi\) |
0.684490 | + | 0.729022i | \(0.260025\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.55622 | − | 2.69545i | −0.431617 | − | 0.747583i | 0.565396 | − | 0.824820i | \(-0.308723\pi\) |
−0.997013 | + | 0.0772371i | \(0.975390\pi\) | |||||||
\(14\) | 0.677066 | + | 1.17271i | 0.180953 | + | 0.313421i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.81987 | + | 11.8124i | −1.70497 | + | 2.95309i | ||||
\(17\) | −2.66467 | −0.646278 | −0.323139 | − | 0.946352i | \(-0.604738\pi\) | ||||
−0.323139 | + | 0.946352i | \(0.604738\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.79664 | 1.32984 | 0.664920 | − | 0.746915i | \(-0.268466\pi\) | ||||
0.664920 | + | 0.746915i | \(0.268466\pi\) | |||||||
\(20\) | −4.44635 | + | 7.70130i | −0.994234 | + | 1.72206i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.59378 | + | 4.49255i | 0.552995 | + | 0.957815i | ||||
\(23\) | −2.32293 | − | 4.02344i | −0.484365 | − | 0.838945i | 0.515473 | − | 0.856906i | \(-0.327616\pi\) |
−0.999839 | + | 0.0179603i | \(0.994283\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.10156 | − | 1.90797i | 0.220313 | − | 0.381593i | ||||
\(26\) | −8.41934 | −1.65117 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.66183 | 0.503039 | ||||||||
\(29\) | −1.30754 | + | 2.26472i | −0.242803 | + | 0.420547i | −0.961512 | − | 0.274764i | \(-0.911400\pi\) |
0.718709 | + | 0.695312i | \(0.244734\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.30730 | + | 3.99636i | 0.414404 | + | 0.717768i | 0.995366 | − | 0.0961626i | \(-0.0306569\pi\) |
−0.580962 | + | 0.813931i | \(0.697324\pi\) | |||||||
\(32\) | 9.47446 | + | 16.4103i | 1.67486 | + | 2.90095i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.60406 | + | 6.24241i | −0.618090 | + | 1.07056i | ||||
\(35\) | 0.837181 | 0.141509 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.85867 | −0.798761 | −0.399381 | − | 0.916785i | \(-0.630775\pi\) | ||||
−0.399381 | + | 0.916785i | \(0.630775\pi\) | |||||||
\(38\) | 7.84014 | − | 13.5795i | 1.27184 | − | 2.20289i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.50375 | + | 12.9969i | 1.18645 | + | 2.05499i | ||||
\(41\) | −5.77408 | − | 10.0010i | −0.901760 | − | 1.56189i | −0.825208 | − | 0.564828i | \(-0.808942\pi\) |
−0.0765514 | − | 0.997066i | \(-0.524391\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.50217 | − | 7.79798i | 0.686574 | − | 1.18918i | −0.286365 | − | 0.958121i | \(-0.592447\pi\) |
0.972939 | − | 0.231061i | \(-0.0742196\pi\) | |||||||
\(44\) | 10.1972 | 1.53729 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.5674 | −1.85296 | ||||||||
\(47\) | 3.41612 | − | 5.91689i | 0.498292 | − | 0.863067i | −0.501706 | − | 0.865038i | \(-0.667294\pi\) |
0.999998 | + | 0.00197091i | \(0.000627360\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.37470 | + | 5.84516i | 0.482101 | + | 0.835023i | ||||
\(50\) | −2.97980 | − | 5.16117i | −0.421408 | − | 0.729900i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.27499 | + | 14.3327i | −1.14754 | + | 1.98759i | ||||
\(53\) | 5.43322 | 0.746309 | 0.373155 | − | 0.927769i | \(-0.378276\pi\) | ||||
0.373155 | + | 0.927769i | \(0.378276\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.20716 | 0.432454 | ||||||||
\(56\) | 2.24608 | − | 3.89033i | 0.300145 | − | 0.519867i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.53697 | + | 6.12621i | 0.464427 | + | 0.804410i | ||||
\(59\) | −1.09566 | − | 1.89773i | −0.142642 | − | 0.247064i | 0.785849 | − | 0.618419i | \(-0.212227\pi\) |
−0.928491 | + | 0.371355i | \(0.878893\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.42017 | + | 5.92391i | −0.437908 | + | 0.758478i | −0.997528 | − | 0.0702708i | \(-0.977614\pi\) |
0.559620 | + | 0.828749i | \(0.310947\pi\) | |||||||
\(62\) | 12.4828 | 1.58532 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 23.9786 | 2.99733 | ||||||||
\(65\) | −2.60259 | + | 4.50783i | −0.322812 | + | 0.559127i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.24180 | − | 10.8111i | −0.762557 | − | 1.32079i | −0.941529 | − | 0.336933i | \(-0.890610\pi\) |
0.178971 | − | 0.983854i | \(-0.442723\pi\) | |||||||
\(68\) | 7.08453 | + | 12.2708i | 0.859126 | + | 1.48805i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.13231 | − | 1.96123i | 0.135337 | − | 0.234411i | ||||
\(71\) | 2.83568 | 0.336534 | 0.168267 | − | 0.985741i | \(-0.446183\pi\) | ||||
0.168267 | + | 0.985741i | \(0.446183\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.93497 | 1.16280 | 0.581400 | − | 0.813618i | \(-0.302505\pi\) | ||||
0.581400 | + | 0.813618i | \(0.302505\pi\) | |||||||
\(74\) | −6.57151 | + | 11.3822i | −0.763923 | + | 1.32315i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −15.4114 | − | 26.6934i | −1.76781 | − | 3.06194i | ||||
\(77\) | −0.479996 | − | 0.831378i | −0.0547007 | − | 0.0947443i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.65561 | + | 4.59964i | −0.298779 | + | 0.517500i | −0.975857 | − | 0.218411i | \(-0.929913\pi\) |
0.677078 | + | 0.735911i | \(0.263246\pi\) | |||||||
\(80\) | 22.8109 | 2.55033 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −31.2385 | −3.44972 | ||||||||
\(83\) | −1.36408 | + | 2.36265i | −0.149727 | + | 0.259334i | −0.931126 | − | 0.364697i | \(-0.881173\pi\) |
0.781400 | + | 0.624031i | \(0.214506\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.22818 | + | 3.85932i | 0.241680 | + | 0.418602i | ||||
\(86\) | −12.1787 | − | 21.0941i | −1.31326 | − | 2.27463i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.60453 | − | 14.9035i | 0.917246 | − | 1.58872i | ||||
\(89\) | −11.2189 | −1.18920 | −0.594600 | − | 0.804021i | \(-0.702690\pi\) | ||||
−0.594600 | + | 0.804021i | \(0.702690\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.55806 | 0.163329 | ||||||||
\(92\) | −12.3519 | + | 21.3941i | −1.28778 | + | 2.23049i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.24082 | − | 16.0056i | −0.953118 | − | 1.65085i | ||||
\(95\) | −4.84710 | − | 8.39543i | −0.497302 | − | 0.861353i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.44457 | − | 5.96617i | 0.349743 | − | 0.605773i | −0.636461 | − | 0.771309i | \(-0.719602\pi\) |
0.986204 | + | 0.165536i | \(0.0529355\pi\) | |||||||
\(98\) | 18.2576 | 1.84429 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.7149 | −1.17149 | ||||||||
\(101\) | 1.86482 | − | 3.22997i | 0.185557 | − | 0.321394i | −0.758207 | − | 0.652014i | \(-0.773924\pi\) |
0.943764 | + | 0.330620i | \(0.107258\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.84040 | − | 6.65177i | −0.378406 | − | 0.655418i | 0.612425 | − | 0.790529i | \(-0.290194\pi\) |
−0.990830 | + | 0.135111i | \(0.956861\pi\) | |||||||
\(104\) | 13.9651 | + | 24.1882i | 1.36939 | + | 2.37185i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.34860 | − | 12.7281i | 0.713759 | − | 1.23627i | ||||
\(107\) | 10.7658 | 1.04077 | 0.520383 | − | 0.853933i | \(-0.325789\pi\) | ||||
0.520383 | + | 0.853933i | \(0.325789\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2298 | 1.17141 | 0.585703 | − | 0.810526i | \(-0.300819\pi\) | ||||
0.585703 | + | 0.810526i | \(0.300819\pi\) | |||||||
\(110\) | 4.33779 | − | 7.51328i | 0.413592 | − | 0.716363i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.41396 | − | 5.91316i | −0.322589 | − | 0.558741i | ||||
\(113\) | −0.971975 | − | 1.68351i | −0.0914357 | − | 0.158371i | 0.816680 | − | 0.577091i | \(-0.195812\pi\) |
−0.908115 | + | 0.418720i | \(0.862479\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.88484 | + | 6.72874i | −0.362263 | + | 0.627458i | ||||
\(116\) | 13.9053 | 1.29108 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.92764 | −0.545684 | ||||||||
\(119\) | 0.666956 | − | 1.15520i | 0.0611397 | − | 0.105897i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.66118 | + | 6.34135i | 0.332834 | + | 0.576486i | ||||
\(122\) | 9.25178 | + | 16.0245i | 0.837617 | + | 1.45079i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.2688 | − | 21.2502i | 1.10177 | − | 1.90832i | ||||
\(125\) | −12.0464 | −1.07746 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.34433 | 0.208026 | 0.104013 | − | 0.994576i | \(-0.466832\pi\) | ||||
0.104013 | + | 0.994576i | \(0.466832\pi\) | |||||||
\(128\) | 13.4829 | − | 23.3531i | 1.19173 | − | 2.06414i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.04019 | + | 12.1940i | 0.617465 | + | 1.06948i | ||||
\(131\) | −8.55119 | − | 14.8111i | −0.747121 | − | 1.29405i | −0.949197 | − | 0.314682i | \(-0.898102\pi\) |
0.202076 | − | 0.979370i | \(-0.435231\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.45087 | + | 2.51298i | −0.125807 | + | 0.217903i | ||||
\(134\) | −33.7689 | −2.91719 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 23.9120 | 2.05044 | ||||||||
\(137\) | 6.96358 | − | 12.0613i | 0.594939 | − | 1.03046i | −0.398617 | − | 0.917118i | \(-0.630510\pi\) |
0.993556 | − | 0.113347i | \(-0.0361570\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.95832 | − | 6.85601i | −0.335740 | − | 0.581519i | 0.647887 | − | 0.761737i | \(-0.275653\pi\) |
−0.983627 | + | 0.180218i | \(0.942320\pi\) | |||||||
\(140\) | −2.22580 | − | 3.85520i | −0.188115 | − | 0.325824i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.83536 | − | 6.64303i | 0.321856 | − | 0.557471i | ||||
\(143\) | 5.96877 | 0.499134 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.37340 | 0.363191 | ||||||||
\(146\) | 13.4374 | − | 23.2742i | 1.11208 | − | 1.92619i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.9177 | + | 22.3741i | 1.06183 | + | 1.83914i | ||||
\(149\) | 0.364067 | + | 0.630583i | 0.0298255 | + | 0.0516594i | 0.880553 | − | 0.473948i | \(-0.157171\pi\) |
−0.850727 | + | 0.525607i | \(0.823838\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.17105 | + | 3.76036i | −0.176677 | + | 0.306014i | −0.940740 | − | 0.339128i | \(-0.889868\pi\) |
0.764063 | + | 0.645141i | \(0.223202\pi\) | |||||||
\(152\) | −52.0174 | −4.21917 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.59684 | −0.209260 | ||||||||
\(155\) | 3.85870 | − | 6.68346i | 0.309938 | − | 0.536828i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.76163 | + | 13.4435i | 0.619446 | + | 1.07291i | 0.989587 | + | 0.143936i | \(0.0459759\pi\) |
−0.370141 | + | 0.928975i | \(0.620691\pi\) | |||||||
\(158\) | 7.18359 | + | 12.4423i | 0.571495 | + | 0.989859i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 15.8449 | − | 27.4443i | 1.25265 | − | 2.16966i | ||||
\(161\) | 2.32568 | 0.183289 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.49738 | 0.665566 | 0.332783 | − | 0.943003i | \(-0.392012\pi\) | ||||
0.332783 | + | 0.943003i | \(0.392012\pi\) | |||||||
\(164\) | −30.7030 | + | 53.1791i | −2.39750 | + | 4.15259i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.68991 | + | 6.39111i | 0.286393 | + | 0.496047i | ||||
\(167\) | 11.5710 | + | 20.0415i | 0.895389 | + | 1.55086i | 0.833323 | + | 0.552787i | \(0.186436\pi\) |
0.0620658 | + | 0.998072i | \(0.480231\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.65637 | − | 2.86892i | 0.127413 | − | 0.220686i | ||||
\(170\) | 12.0547 | 0.924556 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −47.8794 | −3.65077 | ||||||||
\(173\) | −1.28924 | + | 2.23303i | −0.0980190 | + | 0.169774i | −0.910865 | − | 0.412705i | \(-0.864584\pi\) |
0.812846 | + | 0.582479i | \(0.197917\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.551433 | + | 0.955111i | 0.0416845 | + | 0.0721996i | ||||
\(176\) | −13.0786 | − | 22.6528i | −0.985835 | − | 1.70752i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.1739 | + | 26.2820i | −1.13733 | + | 1.96992i | ||||
\(179\) | 8.89613 | 0.664928 | 0.332464 | − | 0.943116i | \(-0.392120\pi\) | ||||
0.332464 | + | 0.943116i | \(0.392120\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.91183 | 0.588082 | 0.294041 | − | 0.955793i | \(-0.405000\pi\) | ||||
0.294041 | + | 0.955793i | \(0.405000\pi\) | |||||||
\(182\) | 2.10732 | − | 3.64999i | 0.156205 | − | 0.270555i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 20.8454 | + | 36.1052i | 1.53674 | + | 2.66171i | ||||
\(185\) | 4.06279 | + | 7.03695i | 0.298702 | + | 0.517367i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.55504 | − | 4.42547i | 0.186843 | − | 0.323622i | ||||
\(188\) | −36.3296 | −2.64961 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −26.2235 | −1.90245 | ||||||||
\(191\) | −7.94867 | + | 13.7675i | −0.575146 | + | 0.996182i | 0.420880 | + | 0.907116i | \(0.361721\pi\) |
−0.996026 | + | 0.0890656i | \(0.971612\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.29239 | + | 3.97054i | 0.165010 | + | 0.285805i | 0.936659 | − | 0.350243i | \(-0.113901\pi\) |
−0.771649 | + | 0.636049i | \(0.780568\pi\) | |||||||
\(194\) | −9.31779 | − | 16.1389i | −0.668978 | − | 1.15870i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 17.9446 | − | 31.0809i | 1.28176 | − | 2.22006i | ||||
\(197\) | −2.99417 | −0.213326 | −0.106663 | − | 0.994295i | \(-0.534017\pi\) | ||||
−0.106663 | + | 0.994295i | \(0.534017\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.8885 | 1.05542 | 0.527709 | − | 0.849425i | \(-0.323051\pi\) | ||||
0.527709 | + | 0.849425i | \(0.323051\pi\) | |||||||
\(200\) | −9.88513 | + | 17.1215i | −0.698984 | + | 1.21068i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.04447 | − | 8.73727i | −0.354928 | − | 0.614753i | ||||
\(203\) | −0.654541 | − | 1.13370i | −0.0459397 | − | 0.0795700i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.65648 | + | 16.7255i | −0.674438 | + | 1.16816i | ||||
\(206\) | −20.7771 | −1.44761 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 42.4528 | 2.94357 | ||||||||
\(209\) | −5.55816 | + | 9.62701i | −0.384466 | + | 0.665914i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.93948 | − | 12.0195i | −0.477733 | − | 0.827459i | 0.521941 | − | 0.852982i | \(-0.325208\pi\) |
−0.999674 | + | 0.0255232i | \(0.991875\pi\) | |||||||
\(212\) | −14.4452 | − | 25.0199i | −0.992102 | − | 1.71837i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.5610 | − | 25.2205i | 0.995372 | − | 1.72403i | ||||
\(215\) | −15.0587 | −1.02700 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.31003 | −0.156815 | ||||||||
\(218\) | 16.5412 | − | 28.6503i | 1.12031 | − | 1.94044i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.52684 | − | 14.7689i | −0.574880 | − | 0.995721i | ||||
\(221\) | 4.14681 | + | 7.18248i | 0.278945 | + | 0.483146i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.40599 | − | 5.89935i | 0.228082 | − | 0.395050i | −0.729158 | − | 0.684346i | \(-0.760088\pi\) |
0.957240 | + | 0.289296i | \(0.0934213\pi\) | |||||||
\(224\) | −9.48567 | −0.633788 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.25851 | −0.349791 | ||||||||
\(227\) | −4.87042 | + | 8.43582i | −0.323261 | + | 0.559905i | −0.981159 | − | 0.193202i | \(-0.938113\pi\) |
0.657898 | + | 0.753107i | \(0.271446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.02242 | + | 12.1632i | 0.464055 | + | 0.803766i | 0.999158 | − | 0.0410201i | \(-0.0130608\pi\) |
−0.535104 | + | 0.844786i | \(0.679727\pi\) | |||||||
\(230\) | 10.5087 | + | 18.2017i | 0.692926 | + | 1.20018i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.7334 | − | 20.3229i | 0.770339 | − | 1.33427i | ||||
\(233\) | −5.32333 | −0.348743 | −0.174372 | − | 0.984680i | \(-0.555789\pi\) | ||||
−0.174372 | + | 0.984680i | \(0.555789\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.4261 | −0.745359 | ||||||||
\(236\) | −5.82602 | + | 10.0910i | −0.379241 | + | 0.656865i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.80416 | − | 3.12489i | −0.116946 | − | 0.202557i | ||||
\(239\) | 8.88675 | + | 15.3923i | 0.574836 | + | 0.995646i | 0.996059 | + | 0.0886886i | \(0.0282676\pi\) |
−0.421223 | + | 0.906957i | \(0.638399\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00340 | − | 1.73793i | 0.0646344 | − | 0.111950i | −0.831897 | − | 0.554930i | \(-0.812745\pi\) |
0.896532 | + | 0.442979i | \(0.146079\pi\) | |||||||
\(242\) | 19.8075 | 1.27327 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 36.3726 | 2.32852 | ||||||||
\(245\) | 5.64380 | − | 9.77536i | 0.360569 | − | 0.624525i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.02083 | − | 15.6245i | −0.573981 | − | 0.994165i | ||||
\(248\) | −20.7051 | − | 35.8622i | −1.31477 | − | 2.27725i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −16.2932 | + | 28.2206i | −1.03047 | + | 1.78483i | ||||
\(251\) | −23.5643 | −1.48737 | −0.743683 | − | 0.668533i | \(-0.766923\pi\) | ||||
−0.743683 | + | 0.668533i | \(0.766923\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.90947 | 0.560133 | ||||||||
\(254\) | 3.17079 | − | 5.49196i | 0.198953 | − | 0.344596i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.4936 | − | 21.6395i | −0.780848 | − | 1.35247i | ||||
\(257\) | 2.93728 | + | 5.08752i | 0.183223 | + | 0.317351i | 0.942976 | − | 0.332860i | \(-0.108014\pi\) |
−0.759754 | + | 0.650211i | \(0.774680\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.21610 | − | 2.10635i | 0.0755651 | − | 0.130883i | ||||
\(260\) | 27.6779 | 1.71651 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −46.2631 | −2.85814 | ||||||||
\(263\) | 10.9891 | − | 19.0336i | 0.677615 | − | 1.17366i | −0.298082 | − | 0.954540i | \(-0.596347\pi\) |
0.975697 | − | 0.219123i | \(-0.0703197\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.54321 | − | 7.86908i | −0.279087 | − | 0.483393i | ||||
\(266\) | 3.92470 | + | 6.79779i | 0.240639 | + | 0.416799i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −33.1900 | + | 57.4867i | −2.02740 | + | 3.51156i | ||||
\(269\) | 30.6026 | 1.86587 | 0.932937 | − | 0.360041i | \(-0.117237\pi\) | ||||
0.932937 | + | 0.360041i | \(0.117237\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0823 | −0.976928 | −0.488464 | − | 0.872584i | \(-0.662443\pi\) | ||||
−0.488464 | + | 0.872584i | \(0.662443\pi\) | |||||||
\(272\) | 18.1727 | − | 31.4761i | 1.10188 | − | 1.90852i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.8369 | − | 32.6265i | −1.13798 | − | 1.97104i | ||||
\(275\) | 2.11249 | + | 3.65894i | 0.127388 | + | 0.220642i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4068 | − | 18.0251i | 0.625283 | − | 1.08302i | −0.363203 | − | 0.931710i | \(-0.618317\pi\) |
0.988486 | − | 0.151312i | \(-0.0483499\pi\) | |||||||
\(278\) | −21.4150 | −1.28439 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.51263 | −0.448965 | ||||||||
\(281\) | 6.13014 | − | 10.6177i | 0.365693 | − | 0.633400i | −0.623194 | − | 0.782067i | \(-0.714165\pi\) |
0.988887 | + | 0.148668i | \(0.0474985\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.28629 | − | 3.95997i | −0.135906 | − | 0.235396i | 0.790037 | − | 0.613059i | \(-0.210061\pi\) |
−0.925943 | + | 0.377663i | \(0.876728\pi\) | |||||||
\(284\) | −7.53920 | − | 13.0583i | −0.447369 | − | 0.774866i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.07296 | − | 13.9828i | 0.477364 | − | 0.826819i | ||||
\(287\) | 5.78091 | 0.341236 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.89952 | −0.582325 | ||||||||
\(290\) | 5.91517 | − | 10.2454i | 0.347351 | − | 0.601629i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −26.4140 | − | 45.7504i | −1.54576 | − | 2.67734i | ||||
\(293\) | 13.0617 | + | 22.6235i | 0.763073 | + | 1.32168i | 0.941259 | + | 0.337685i | \(0.109644\pi\) |
−0.178186 | + | 0.983997i | \(0.557023\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.83236 | + | 3.17374i | −0.106684 | + | 0.184782i | ||||
\(296\) | 43.6004 | 2.53422 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.96965 | 0.114099 | ||||||||
\(299\) | −7.22998 | + | 12.5227i | −0.418121 | + | 0.724206i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.25375 | + | 3.90360i | 0.129904 | + | 0.225000i | ||||
\(302\) | 5.87282 | + | 10.1720i | 0.337943 | + | 0.585334i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −39.5323 | + | 68.4719i | −2.26733 | + | 3.92713i | ||||
\(305\) | 11.4397 | 0.655034 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.29277 | 0.187928 | 0.0939641 | − | 0.995576i | \(-0.470046\pi\) | ||||
0.0939641 | + | 0.995576i | \(0.470046\pi\) | |||||||
\(308\) | −2.55232 | + | 4.42075i | −0.145432 | + | 0.251896i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.4380 | − | 18.0792i | −0.592840 | − | 1.02683i | ||||
\(311\) | 17.3963 | + | 30.1313i | 0.986455 | + | 1.70859i | 0.635285 | + | 0.772278i | \(0.280883\pi\) |
0.351170 | + | 0.936312i | \(0.385784\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.31392 | + | 9.20398i | −0.300360 | + | 0.520239i | −0.976218 | − | 0.216793i | \(-0.930440\pi\) |
0.675857 | + | 0.737033i | \(0.263774\pi\) | |||||||
\(314\) | 41.9914 | 2.36971 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 28.2417 | 1.58872 | ||||||||
\(317\) | −7.75011 | + | 13.4236i | −0.435290 | + | 0.753944i | −0.997319 | − | 0.0731733i | \(-0.976687\pi\) |
0.562030 | + | 0.827117i | \(0.310021\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.50748 | − | 4.34309i | −0.140392 | − | 0.243166i | ||||
\(320\) | −20.0507 | − | 34.7289i | −1.12087 | − | 1.94140i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.14556 | − | 5.44827i | 0.175295 | − | 0.303620i | ||||
\(323\) | −15.4461 | −0.859446 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.85710 | −0.380363 | ||||||||
\(326\) | 11.4930 | − | 19.9064i | 0.636538 | − | 1.10252i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 51.8150 | + | 89.7461i | 2.86100 | + | 4.95540i | ||||
\(329\) | 1.71008 | + | 2.96194i | 0.0942797 | + | 0.163297i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.28514 | − | 12.6182i | 0.400427 | − | 0.693561i | −0.593350 | − | 0.804945i | \(-0.702195\pi\) |
0.993777 | + | 0.111384i | \(0.0355283\pi\) | |||||||
\(332\) | 14.5066 | 0.796153 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 62.6005 | 3.42534 | ||||||||
\(335\) | −10.4387 | + | 18.0803i | −0.570327 | + | 0.987834i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.3074 | + | 17.8529i | 0.561479 | + | 0.972511i | 0.997368 | + | 0.0725099i | \(0.0231009\pi\) |
−0.435888 | + | 0.900001i | \(0.643566\pi\) | |||||||
\(338\) | −4.48060 | − | 7.76062i | −0.243712 | − | 0.422122i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.8481 | − | 20.5214i | 0.642551 | − | 1.11293i | ||||
\(341\) | −8.84951 | −0.479228 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.88283 | −0.371638 | ||||||||
\(344\) | −40.4012 | + | 69.9769i | −2.17829 | + | 3.77290i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.48748 | + | 6.04048i | 0.187488 | + | 0.324738i | ||||
\(347\) | −10.5918 | − | 18.3455i | −0.568596 | − | 0.984838i | −0.996705 | − | 0.0811104i | \(-0.974153\pi\) |
0.428109 | − | 0.903727i | \(-0.359180\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.31299 | − | 4.00621i | 0.123811 | − | 0.214447i | −0.797456 | − | 0.603377i | \(-0.793822\pi\) |
0.921268 | + | 0.388929i | \(0.127155\pi\) | |||||||
\(350\) | 2.98333 | 0.159466 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −36.3387 | −1.93686 | ||||||||
\(353\) | −6.82171 | + | 11.8155i | −0.363083 | + | 0.628878i | −0.988467 | − | 0.151440i | \(-0.951609\pi\) |
0.625384 | + | 0.780317i | \(0.284942\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.37118 | − | 4.10700i | −0.125849 | − | 0.217977i | ||||
\(356\) | 29.8275 | + | 51.6628i | 1.58086 | + | 2.73812i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0323 | − | 20.8406i | 0.635927 | − | 1.10146i | ||||
\(359\) | 28.2447 | 1.49070 | 0.745349 | − | 0.666675i | \(-0.232283\pi\) | ||||
0.745349 | + | 0.666675i | \(0.232283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.6010 | 0.768473 | ||||||||
\(362\) | 10.7010 | − | 18.5347i | 0.562432 | − | 0.974162i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.14239 | − | 7.17483i | −0.217120 | − | 0.376063i | ||||
\(365\) | −8.30755 | − | 14.3891i | −0.434837 | − | 0.753160i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.4401 | + | 30.2071i | −0.910366 | + | 1.57680i | −0.0968183 | + | 0.995302i | \(0.530867\pi\) |
−0.813548 | + | 0.581498i | \(0.802467\pi\) | |||||||
\(368\) | 63.3684 | 3.30331 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.9802 | 1.14270 | ||||||||
\(371\) | −1.35991 | + | 2.35543i | −0.0706030 | + | 0.122288i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.52972 | − | 2.64955i | −0.0792059 | − | 0.137189i | 0.823702 | − | 0.567023i | \(-0.191905\pi\) |
−0.902908 | + | 0.429835i | \(0.858572\pi\) | |||||||
\(374\) | −6.91156 | − | 11.9712i | −0.357388 | − | 0.619015i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −30.6553 | + | 53.0965i | −1.58093 | + | 2.73824i | ||||
\(377\) | 8.13924 | 0.419192 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.67705 | −0.394344 | −0.197172 | − | 0.980369i | \(-0.563176\pi\) | ||||
−0.197172 | + | 0.980369i | \(0.563176\pi\) | |||||||
\(380\) | −25.7739 | + | 44.6417i | −1.32217 | + | 2.29007i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.5017 | + | 37.2420i | 1.10012 | + | 1.90547i | ||||
\(383\) | 5.18097 | + | 8.97370i | 0.264735 | + | 0.458535i | 0.967494 | − | 0.252893i | \(-0.0813821\pi\) |
−0.702759 | + | 0.711428i | \(0.748049\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.802739 | + | 1.39038i | −0.0409113 | + | 0.0708605i | ||||
\(386\) | 12.4021 | 0.631252 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −36.6322 | −1.85972 | ||||||||
\(389\) | −0.213476 | + | 0.369751i | −0.0108236 | + | 0.0187471i | −0.871386 | − | 0.490597i | \(-0.836779\pi\) |
0.860563 | + | 0.509344i | \(0.170112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.18986 | + | 10.7211i | 0.313035 | + | 0.542192i | ||||
\(392\) | −30.2836 | − | 52.4528i | −1.52955 | − | 2.64927i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.04971 | + | 7.01430i | −0.204021 | + | 0.353376i | ||||
\(395\) | 8.88239 | 0.446922 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.0891 | −1.35956 | −0.679781 | − | 0.733416i | \(-0.737925\pi\) | ||||
−0.679781 | + | 0.733416i | \(0.737925\pi\) | |||||||
\(398\) | 20.1372 | − | 34.8786i | 1.00939 | − | 1.74831i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.0250 | + | 26.0241i | 0.751252 | + | 1.30121i | ||||
\(401\) | 14.6802 | + | 25.4269i | 0.733096 | + | 1.26976i | 0.955554 | + | 0.294817i | \(0.0952588\pi\) |
−0.222458 | + | 0.974942i | \(0.571408\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.18133 | − | 12.4384i | 0.357727 | − | 0.619602i | ||||
\(404\) | −19.8319 | −0.986675 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.54115 | −0.175744 | ||||||||
\(407\) | 4.65878 | − | 8.06925i | 0.230927 | − | 0.399978i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0920 | + | 17.4798i | 0.499015 | + | 0.864320i | 0.999999 | − | 0.00113651i | \(-0.000361762\pi\) |
−0.500984 | + | 0.865457i | \(0.667028\pi\) | |||||||
\(410\) | 26.1214 | + | 45.2436i | 1.29004 | + | 2.23442i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.4208 | + | 35.3699i | −1.00606 | + | 1.74255i | ||||
\(413\) | 1.09695 | 0.0539775 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.56252 | 0.223965 | ||||||||
\(416\) | 29.4887 | − | 51.0758i | 1.44580 | − | 2.50420i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.0352 | + | 26.0417i | 0.735395 | + | 1.27374i | ||||
\(419\) | 12.1852 | + | 21.1053i | 0.595284 | + | 1.03106i | 0.993507 | + | 0.113774i | \(0.0362938\pi\) |
−0.398223 | + | 0.917289i | \(0.630373\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0873 | − | 22.6678i | 0.637835 | − | 1.10476i | −0.348072 | − | 0.937468i | \(-0.613164\pi\) |
0.985907 | − | 0.167294i | \(-0.0535030\pi\) | |||||||
\(422\) | −37.5435 | −1.82759 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −48.7561 | −2.36781 | ||||||||
\(425\) | −2.93531 | + | 5.08410i | −0.142383 | + | 0.246615i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.71211 | − | 2.96545i | −0.0828546 | − | 0.143508i | ||||
\(428\) | −28.6228 | − | 49.5761i | −1.38353 | − | 2.39635i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20.3674 | + | 35.2774i | −0.982203 | + | 1.70123i | ||||
\(431\) | −31.9185 | −1.53746 | −0.768731 | − | 0.639572i | \(-0.779111\pi\) | ||||
−0.768731 | + | 0.639572i | \(0.779111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.0123080 | 0.000591484 | 0.000295742 | − | 1.00000i | \(-0.499906\pi\) | ||||
0.000295742 | 1.00000i | \(0.499906\pi\) | ||||||||
\(434\) | −3.12439 | + | 5.41160i | −0.149976 | + | 0.259765i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32.5153 | − | 56.3182i | −1.55720 | − | 2.69715i | ||||
\(437\) | −13.4652 | − | 23.3224i | −0.644128 | − | 1.11566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.65240 | + | 4.59410i | −0.126592 | + | 0.219264i | −0.922354 | − | 0.386345i | \(-0.873737\pi\) |
0.795762 | + | 0.605610i | \(0.207071\pi\) | |||||||
\(440\) | −28.7802 | −1.37204 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.4348 | 1.06711 | ||||||||
\(443\) | 20.3482 | − | 35.2441i | 0.966771 | − | 1.67450i | 0.261990 | − | 0.965071i | \(-0.415621\pi\) |
0.704781 | − | 0.709425i | \(-0.251045\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.38116 | + | 16.2486i | 0.444709 | + | 0.770259i | ||||
\(446\) | −9.21342 | − | 15.9581i | −0.436268 | − | 0.755639i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.00174 | + | 10.3953i | −0.283556 | + | 0.491133i | ||||
\(449\) | −15.4280 | −0.728093 | −0.364047 | − | 0.931381i | \(-0.618605\pi\) | ||||
−0.364047 | + | 0.931381i | \(0.618605\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.1461 | 1.04282 | ||||||||
\(452\) | −5.16835 | + | 8.95185i | −0.243099 | + | 0.421060i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.1748 | + | 22.8194i | 0.618324 | + | 1.07097i | ||||
\(455\) | −1.30284 | − | 2.25658i | −0.0610779 | − | 0.105790i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.19437 | + | 2.06872i | −0.0558704 | + | 0.0967704i | −0.892608 | − | 0.450834i | \(-0.851127\pi\) |
0.836737 | + | 0.547604i | \(0.184460\pi\) | |||||||
\(458\) | 37.9922 | 1.77526 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 41.3143 | 1.92629 | ||||||||
\(461\) | 16.2419 | − | 28.1319i | 0.756462 | − | 1.31023i | −0.188182 | − | 0.982134i | \(-0.560259\pi\) |
0.944644 | − | 0.328097i | \(-0.106407\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.9393 | − | 29.3397i | −0.787234 | − | 1.36353i | −0.927655 | − | 0.373438i | \(-0.878179\pi\) |
0.140421 | − | 0.990092i | \(-0.455155\pi\) | |||||||
\(464\) | −17.8344 | − | 30.8901i | −0.827943 | − | 1.43404i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.19998 | + | 12.4707i | −0.333533 | + | 0.577696i | ||||
\(467\) | 13.8027 | 0.638711 | 0.319356 | − | 0.947635i | \(-0.396534\pi\) | ||||
0.319356 | + | 0.947635i | \(0.396534\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.24918 | 0.288560 | ||||||||
\(470\) | −15.4542 | + | 26.7675i | −0.712850 | + | 1.23469i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.83211 | + | 17.0297i | 0.452559 | + | 0.783856i | ||||
\(473\) | 8.63389 | + | 14.9543i | 0.396987 | + | 0.687601i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.38537 | − | 11.0598i | 0.292981 | − | 0.507458i | ||||
\(476\) | −7.09291 | −0.325103 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 48.0785 | 2.19906 | ||||||||
\(479\) | 2.94556 | − | 5.10186i | 0.134586 | − | 0.233110i | −0.790853 | − | 0.612006i | \(-0.790363\pi\) |
0.925439 | + | 0.378896i | \(0.123696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.56115 | + | 13.0963i | 0.344759 | + | 0.597140i | ||||
\(482\) | −2.71425 | − | 4.70122i | −0.123631 | − | 0.214135i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.4679 | − | 33.7193i | 0.884903 | − | 1.53270i | ||||
\(485\) | −11.5213 | −0.523155 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.0299 | 1.31547 | 0.657736 | − | 0.753249i | \(-0.271514\pi\) | ||||
0.657736 | + | 0.753249i | \(0.271514\pi\) | |||||||
\(488\) | 30.6916 | − | 53.1594i | 1.38934 | − | 2.40642i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −15.2669 | − | 26.4430i | −0.689686 | − | 1.19457i | ||||
\(491\) | 2.19175 | + | 3.79623i | 0.0989125 | + | 0.171321i | 0.911235 | − | 0.411887i | \(-0.135130\pi\) |
−0.812322 | + | 0.583209i | \(0.801797\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.48415 | − | 6.03473i | 0.156918 | − | 0.271791i | ||||
\(494\) | −48.8038 | −2.19579 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −62.9420 | −2.82618 | ||||||||
\(497\) | −0.709759 | + | 1.22934i | −0.0318371 | + | 0.0551434i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.6718 | − | 30.6084i | −0.791096 | − | 1.37022i | −0.925289 | − | 0.379264i | \(-0.876177\pi\) |
0.134192 | − | 0.990955i | \(-0.457156\pi\) | |||||||
\(500\) | 32.0276 | + | 55.4735i | 1.43232 | + | 2.48085i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −31.8715 | + | 55.2030i | −1.42249 | + | 2.46383i | ||||
\(503\) | 8.37659 | 0.373494 | 0.186747 | − | 0.982408i | \(-0.440206\pi\) | ||||
0.186747 | + | 0.982408i | \(0.440206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.23740 | −0.277561 | ||||||||
\(506\) | 12.0503 | − | 20.8718i | 0.535703 | − | 0.927865i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.23285 | − | 10.7956i | −0.276538 | − | 0.478978i | ||||
\(509\) | −1.92148 | − | 3.32811i | −0.0851683 | − | 0.147516i | 0.820295 | − | 0.571941i | \(-0.193809\pi\) |
−0.905463 | + | 0.424425i | \(0.860476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.48668 | + | 4.30706i | −0.110004 | + | 0.190533i | ||||
\(512\) | −13.6601 | −0.603699 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.8911 | 0.700925 | ||||||||
\(515\) | −6.42262 | + | 11.1243i | −0.283015 | + | 0.490196i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.55115 | + | 11.3469i | 0.288119 | + | 0.499037i | ||||
\(518\) | −3.28964 | − | 5.69783i | −0.144539 | − | 0.250348i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 23.3549 | − | 40.4520i | 1.02418 | − | 1.77394i | ||||
\(521\) | −19.6523 | −0.860983 | −0.430491 | − | 0.902595i | \(-0.641660\pi\) | ||||
−0.430491 | + | 0.902595i | \(0.641660\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.6103 | −1.73204 | −0.866018 | − | 0.500012i | \(-0.833329\pi\) | ||||
−0.866018 | + | 0.500012i | \(0.833329\pi\) | |||||||
\(524\) | −45.4699 | + | 78.7562i | −1.98636 | + | 3.44048i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.7261 | − | 51.4872i | −1.29612 | − | 2.24495i | ||||
\(527\) | −6.14820 | − | 10.6490i | −0.267820 | − | 0.463878i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.707953 | − | 1.22621i | 0.0307806 | − | 0.0533135i | ||||
\(530\) | −24.5794 | −1.06766 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.4297 | 0.668961 | ||||||||
\(533\) | −17.9715 | + | 31.1275i | −0.778430 | + | 1.34828i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00224 | − | 15.5923i | −0.389201 | − | 0.674116i | ||||
\(536\) | 56.0121 | + | 97.0159i | 2.41936 | + | 4.19045i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 41.3910 | − | 71.6913i | 1.78449 | − | 3.09083i | ||||
\(539\) | −12.9435 | −0.557514 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.8257 | −1.79823 | −0.899115 | − | 0.437713i | \(-0.855788\pi\) | ||||
−0.899115 | + | 0.437713i | \(0.855788\pi\) | |||||||
\(542\) | −21.7518 | + | 37.6752i | −0.934319 | + | 1.61829i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −25.2463 | − | 43.7279i | −1.08243 | − | 1.87482i | ||||
\(545\) | −10.2265 | − | 17.7128i | −0.438055 | − | 0.758733i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.51716 | − | 14.7522i | 0.364168 | − | 0.630757i | −0.624475 | − | 0.781045i | \(-0.714687\pi\) |
0.988642 | + | 0.150288i | \(0.0480202\pi\) | |||||||
\(548\) | −74.0559 | −3.16351 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.4288 | 0.487328 | ||||||||
\(551\) | −7.57931 | + | 13.1277i | −0.322889 | + | 0.559261i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.32937 | − | 2.30254i | −0.0565307 | − | 0.0979140i | ||||
\(554\) | −28.1510 | − | 48.7590i | −1.19602 | − | 2.07157i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.0479 | + | 36.4560i | −0.892628 | + | 1.54608i | ||||
\(557\) | 33.7680 | 1.43080 | 0.715398 | − | 0.698717i | \(-0.246245\pi\) | ||||
0.715398 | + | 0.698717i | \(0.246245\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.0254 | −1.18535 | ||||||||
\(560\) | −5.70946 | + | 9.88908i | −0.241269 | + | 0.417890i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.5824 | − | 28.7216i | −0.699487 | − | 1.21155i | ||||
\(563\) | −11.3556 | − | 19.6685i | −0.478583 | − | 0.828930i | 0.521115 | − | 0.853486i | \(-0.325516\pi\) |
−0.999698 | + | 0.0245561i | \(0.992183\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.62552 | + | 2.81548i | −0.0683860 | + | 0.118448i | ||||
\(566\) | −12.3691 | −0.519913 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −25.4466 | −1.06772 | ||||||||
\(569\) | 5.43572 | − | 9.41495i | 0.227877 | − | 0.394695i | −0.729301 | − | 0.684193i | \(-0.760155\pi\) |
0.957179 | + | 0.289497i | \(0.0934881\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.44185 | − | 12.8897i | −0.311432 | − | 0.539416i | 0.667241 | − | 0.744842i | \(-0.267475\pi\) |
−0.978673 | + | 0.205426i | \(0.934142\pi\) | |||||||
\(572\) | −15.8691 | − | 27.4861i | −0.663521 | − | 1.14925i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.81886 | − | 13.5427i | 0.326353 | − | 0.565260i | ||||
\(575\) | −10.2354 | −0.426848 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.1163 | −1.54517 | −0.772586 | − | 0.634910i | \(-0.781037\pi\) | ||||
−0.772586 | + | 0.634910i | \(0.781037\pi\) | |||||||
\(578\) | −13.3894 | + | 23.1912i | −0.556927 | + | 0.964625i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.6275 | − | 20.1394i | −0.482806 | − | 0.836245i | ||||
\(581\) | −0.682844 | − | 1.18272i | −0.0283291 | − | 0.0490675i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.20969 | + | 9.02344i | −0.215763 | + | 0.373713i | ||||
\(584\) | −89.1536 | −3.68920 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 70.6655 | 2.91917 | ||||||||
\(587\) | 7.32161 | − | 12.6814i | 0.302195 | − | 0.523417i | −0.674438 | − | 0.738332i | \(-0.735614\pi\) |
0.976633 | + | 0.214914i | \(0.0689472\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.3746 | + | 23.1655i | 0.551090 | + | 0.954516i | ||||
\(590\) | 4.95665 | + | 8.58517i | 0.204062 | + | 0.353446i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 33.1355 | − | 57.3924i | 1.36186 | − | 2.35881i | ||||
\(593\) | 36.4392 | 1.49638 | 0.748189 | − | 0.663485i | \(-0.230924\pi\) | ||||
0.748189 | + | 0.663485i | \(0.230924\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.23081 | −0.0914544 | ||||||||
\(596\) | 1.93588 | − | 3.35305i | 0.0792968 | − | 0.137346i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 19.5576 | + | 33.8747i | 0.799769 | + | 1.38524i | ||||
\(599\) | −13.7474 | − | 23.8113i | −0.561705 | − | 0.972902i | −0.997348 | − | 0.0727826i | \(-0.976812\pi\) |
0.435642 | − | 0.900120i | \(-0.356521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.5885 | + | 39.1244i | −0.921404 | + | 1.59592i | −0.124159 | + | 0.992262i | \(0.539623\pi\) |
−0.797245 | + | 0.603656i | \(0.793710\pi\) | |||||||
\(602\) | 12.1931 | 0.496952 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.0885 | 0.939459 | ||||||||
\(605\) | 6.12290 | − | 10.6052i | 0.248931 | − | 0.431162i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.56858 | − | 14.8412i | −0.347788 | − | 0.602387i | 0.638068 | − | 0.769980i | \(-0.279734\pi\) |
−0.985856 | + | 0.167593i | \(0.946400\pi\) | |||||||
\(608\) | 54.9200 | + | 95.1243i | 2.22730 | + | 3.85780i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.4725 | − | 26.7992i | 0.626464 | − | 1.08507i | ||||
\(611\) | −21.2649 | −0.860286 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.468761 | −0.0189331 | −0.00946653 | − | 0.999955i | \(-0.503013\pi\) | ||||
−0.00946653 | + | 0.999955i | \(0.503013\pi\) | |||||||
\(614\) | 4.45358 | − | 7.71382i | 0.179732 | − | 0.311304i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.30735 | + | 7.46055i | 0.173548 | + | 0.300594i | ||||
\(617\) | 1.06742 | + | 1.84883i | 0.0429729 | + | 0.0744312i | 0.886712 | − | 0.462323i | \(-0.152984\pi\) |
−0.843739 | + | 0.536754i | \(0.819650\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.26880 | + | 7.39378i | −0.171578 | + | 0.297181i | −0.938972 | − | 0.343995i | \(-0.888220\pi\) |
0.767394 | + | 0.641176i | \(0.221553\pi\) | |||||||
\(620\) | −41.0363 | −1.64806 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 94.1163 | 3.77372 | ||||||||
\(623\) | 2.80804 | − | 4.86367i | 0.112502 | − | 0.194859i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.56529 | + | 7.90731i | 0.182612 | + | 0.316292i | ||||
\(626\) | 14.3745 | + | 24.8974i | 0.574520 | + | 0.995098i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 41.2715 | − | 71.4844i | 1.64691 | − | 2.85254i | ||||
\(629\) | 12.9468 | 0.516222 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.8708 | −0.472569 | −0.236284 | − | 0.971684i | \(-0.575930\pi\) | ||||
−0.236284 | + | 0.971684i | \(0.575930\pi\) | |||||||
\(632\) | 23.8307 | − | 41.2759i | 0.947933 | − | 1.64187i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.9646 | + | 36.3117i | 0.832609 | + | 1.44212i | ||||
\(635\) | −1.96031 | − | 3.39536i | −0.0777926 | − | 0.134741i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.5035 | − | 18.1927i | 0.416166 | − | 0.720820i | ||||
\(638\) | −13.5658 | −0.537076 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −45.0973 | −1.78263 | ||||||||
\(641\) | −2.65183 | + | 4.59310i | −0.104741 | + | 0.181417i | −0.913632 | − | 0.406541i | \(-0.866735\pi\) |
0.808891 | + | 0.587958i | \(0.200068\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.411934 | + | 0.713491i | 0.0162451 | + | 0.0281374i | 0.874034 | − | 0.485865i | \(-0.161495\pi\) |
−0.857789 | + | 0.514003i | \(0.828162\pi\) | |||||||
\(644\) | −6.18326 | − | 10.7097i | −0.243655 | − | 0.422022i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.8914 | + | 36.1850i | −0.821961 | + | 1.42368i | ||||
\(647\) | −40.8373 | −1.60548 | −0.802740 | − | 0.596329i | \(-0.796626\pi\) | ||||
−0.802740 | + | 0.596329i | \(0.796626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.20232 | 0.164955 | ||||||||
\(650\) | −9.27445 | + | 16.0638i | −0.363774 | + | 0.630074i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −22.5919 | − | 39.1303i | −0.884767 | − | 1.53246i | ||||
\(653\) | −0.534678 | − | 0.926090i | −0.0209236 | − | 0.0362407i | 0.855374 | − | 0.518011i | \(-0.173327\pi\) |
−0.876298 | + | 0.481770i | \(0.839994\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.3009 | + | 24.7699i | −0.558782 | + | 0.967838i | ||||
\(656\) | 157.514 | 6.14988 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.25175 | 0.360671 | ||||||||
\(659\) | 14.3321 | − | 24.8240i | 0.558301 | − | 0.967006i | −0.439337 | − | 0.898322i | \(-0.644787\pi\) |
0.997638 | − | 0.0686837i | \(-0.0218799\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.24786 | + | 3.89341i | 0.0874316 | + | 0.151436i | 0.906425 | − | 0.422367i | \(-0.138801\pi\) |
−0.818993 | + | 0.573803i | \(0.805467\pi\) | |||||||
\(662\) | −19.7068 | − | 34.1331i | −0.765925 | − | 1.32662i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.2408 | − | 21.2017i | 0.475036 | − | 0.822787i | ||||
\(665\) | 4.85283 | 0.188185 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.1493 | 0.470422 | ||||||||
\(668\) | 61.5272 | − | 106.568i | 2.38056 | − | 4.12325i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 28.2373 | + | 48.9085i | 1.09090 | + | 1.88950i | ||||
\(671\) | −6.55892 | − | 11.3604i | −0.253204 | − | 0.438563i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.02929 | + | 15.6392i | −0.348054 | + | 0.602846i | −0.985904 | − | 0.167314i | \(-0.946491\pi\) |
0.637850 | + | 0.770161i | \(0.279824\pi\) | |||||||
\(674\) | 55.7643 | 2.14796 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.6151 | −0.677505 | ||||||||
\(677\) | −7.86959 | + | 13.6305i | −0.302453 | + | 0.523864i | −0.976691 | − | 0.214650i | \(-0.931139\pi\) |
0.674238 | + | 0.738514i | \(0.264472\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.72432 | + | 2.98661i | 0.0661734 | + | 0.114616i | ||||
\(680\) | −19.9950 | − | 34.6324i | −0.766775 | − | 1.32809i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.9692 | + | 20.7313i | −0.458326 | + | 0.793844i | ||||
\(683\) | −2.76118 | −0.105654 | −0.0528268 | − | 0.998604i | \(-0.516823\pi\) | ||||
−0.0528268 | + | 0.998604i | \(0.516823\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.2916 | −0.889925 | ||||||||
\(686\) | −9.30925 | + | 16.1241i | −0.355429 | + | 0.615621i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 61.4084 | + | 106.362i | 2.34117 | + | 4.05503i | ||||
\(689\) | −8.45526 | − | 14.6449i | −0.322120 | − | 0.557928i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.2628 | − | 29.9000i | 0.656707 | − | 1.13745i | −0.324756 | − | 0.945798i | \(-0.605282\pi\) |
0.981463 | − | 0.191652i | \(-0.0613844\pi\) | |||||||
\(692\) | 13.7107 | 0.521204 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −57.3029 | −2.17519 | ||||||||
\(695\) | −6.61983 | + | 11.4659i | −0.251104 | + | 0.434926i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.3860 | + | 26.6494i | 0.582787 | + | 1.00942i | ||||
\(698\) | −6.25678 | − | 10.8371i | −0.236822 | − | 0.410189i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.93218 | − | 5.07868i | 0.110826 | − | 0.191956i | ||||
\(701\) | −20.7410 | −0.783378 | −0.391689 | − | 0.920098i | \(-0.628109\pi\) | ||||
−0.391689 | + | 0.920098i | \(0.628109\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.1640 | −1.06222 | ||||||||
\(704\) | −22.9921 | + | 39.8235i | −0.866548 | + | 1.50090i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.4532 | + | 31.9618i | 0.694494 | + | 1.20290i | ||||
\(707\) | 0.933514 | + | 1.61689i | 0.0351084 | + | 0.0608095i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.8536 | + | 23.9951i | −0.520281 | + | 0.901154i | 0.479441 | + | 0.877574i | \(0.340840\pi\) |
−0.999722 | + | 0.0235795i | \(0.992494\pi\) | |||||||
\(710\) | −12.8284 | −0.481441 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 100.675 | 3.77296 | ||||||||
\(713\) | 10.7194 | − | 18.5666i | 0.401445 | − | 0.695324i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.99104 | − | 8.64474i | −0.186654 | − | 0.323295i | ||||
\(716\) | −23.6520 | − | 40.9665i | −0.883918 | − | 1.53099i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 38.2018 | − | 66.1675i | 1.42568 | − | 2.46935i | ||||
\(719\) | 33.1314 | 1.23559 | 0.617797 | − | 0.786337i | \(-0.288025\pi\) | ||||
0.617797 | + | 0.786337i | \(0.288025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.84494 | 0.143193 | ||||||||
\(722\) | 19.7483 | − | 34.2051i | 0.734956 | − | 1.27298i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21.0351 | − | 36.4338i | −0.781763 | − | 1.35405i | ||||
\(725\) | 2.88067 | + | 4.98946i | 0.106985 | + | 0.185304i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.0413027 | − | 0.0715384i | 0.00153183 | − | 0.00265321i | −0.865258 | − | 0.501326i | \(-0.832846\pi\) |
0.866790 | + | 0.498673i | \(0.166179\pi\) | |||||||
\(728\) | −13.9816 | −0.518191 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −44.9449 | −1.66349 | ||||||||
\(731\) | −11.9968 | + | 20.7791i | −0.443718 | + | 0.768542i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.9587 | + | 27.6414i | 0.589450 | + | 1.02096i | 0.994305 | + | 0.106576i | \(0.0339887\pi\) |
−0.404855 | + | 0.914381i | \(0.632678\pi\) | |||||||
\(734\) | 47.1766 | + | 81.7123i | 1.74132 | + | 3.01606i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 44.0171 | − | 76.2399i | 1.62249 | − | 2.81024i | ||||
\(737\) | 23.9400 | 0.881842 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.7919 | −1.31663 | −0.658314 | − | 0.752744i | \(-0.728730\pi\) | ||||
−0.658314 | + | 0.752744i | \(0.728730\pi\) | |||||||
\(740\) | 21.6034 | − | 37.4181i | 0.794155 | − | 1.37552i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.67864 | + | 6.37160i | 0.135047 | + | 0.233909i | ||||
\(743\) | −9.88944 | − | 17.1290i | −0.362808 | − | 0.628402i | 0.625614 | − | 0.780133i | \(-0.284849\pi\) |
−0.988422 | + | 0.151731i | \(0.951515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.608860 | − | 1.05458i | 0.0223069 | − | 0.0386367i | ||||
\(746\) | −8.27598 | −0.303005 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −27.1723 | −0.993517 | ||||||||
\(749\) | −2.69462 | + | 4.66722i | −0.0984593 | + | 0.170537i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.2903 | − | 26.4835i | −0.557950 | − | 0.966398i | −0.997667 | − | 0.0682617i | \(-0.978255\pi\) |
0.439717 | − | 0.898136i | \(-0.355079\pi\) | |||||||
\(752\) | 46.5950 | + | 80.7048i | 1.69914 | + | 2.94300i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.0086 | − | 19.0674i | 0.400909 | − | 0.694395i | ||||
\(755\) | 7.26165 | 0.264278 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.4129 | 0.923647 | 0.461824 | − | 0.886972i | \(-0.347195\pi\) | ||||
0.461824 | + | 0.886972i | \(0.347195\pi\) | |||||||
\(758\) | −10.3835 | + | 17.9847i | −0.377144 | + | 0.653233i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 43.4965 | + | 75.3382i | 1.57778 | + | 2.73280i | ||||
\(761\) | −23.4090 | − | 40.5456i | −0.848575 | − | 1.46978i | −0.882480 | − | 0.470350i | \(-0.844128\pi\) |
0.0339049 | − | 0.999425i | \(-0.489206\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.06107 | + | 5.30194i | −0.110818 | + | 0.191943i | ||||
\(764\) | 84.5322 | 3.05827 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.0297 | 1.01275 | ||||||||
\(767\) | −3.41016 | + | 5.90657i | −0.123134 | + | 0.213274i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.28271 | − | 12.6140i | −0.262621 | − | 0.454873i | 0.704316 | − | 0.709886i | \(-0.251254\pi\) |
−0.966938 | + | 0.255013i | \(0.917920\pi\) | |||||||
\(770\) | 2.17146 | + | 3.76108i | 0.0782540 | + | 0.135540i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.1895 | − | 21.1128i | 0.438710 | − | 0.759867i | ||||
\(773\) | −24.3533 | −0.875929 | −0.437964 | − | 0.898992i | \(-0.644300\pi\) | ||||
−0.437964 | + | 0.898992i | \(0.644300\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.1666 | 0.365194 | ||||||||
\(776\) | −30.9106 | + | 53.5387i | −1.10963 | + | 1.92193i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.577465 | + | 1.00020i | 0.0207031 | + | 0.0358589i | ||||
\(779\) | −33.4702 | − | 57.9722i | −1.19920 | − | 2.07707i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.71902 | + | 4.70948i | −0.0972943 | + | 0.168519i | ||||
\(782\) | 33.4879 | 1.19753 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −92.0601 | −3.28786 | ||||||||
\(785\) | 12.9804 | − | 22.4828i | 0.463292 | − | 0.802445i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.7836 | + | 23.8739i | 0.491332 | + | 0.851012i | 0.999950 | − | 0.00998024i | \(-0.00317686\pi\) |
−0.508618 | + | 0.860992i | \(0.669844\pi\) | |||||||
\(788\) | 7.96056 | + | 13.7881i | 0.283583 | + | 0.491181i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.0137 | − | 20.8084i | 0.427429 | − | 0.740329i | ||||
\(791\) | 0.973124 | 0.0346003 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.2901 | 0.756034 | ||||||||
\(794\) | −36.6388 | + | 63.4603i | −1.30026 | + | 2.25212i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −39.5839 | − | 68.5613i | −1.40301 | − | 2.43009i | ||||
\(797\) | −3.30846 | − | 5.73042i | −0.117192 | − | 0.202982i | 0.801462 | − | 0.598046i | \(-0.204056\pi\) |
−0.918654 | + | 0.395064i | \(0.870722\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.10284 | + | 15.7666i | −0.322035 | + | 0.557781i | ||||
\(800\) | 41.7469 | 1.47598 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 79.4220 | 2.80449 | ||||||||
\(803\) | −9.52624 | + | 16.4999i | −0.336174 | + | 0.582270i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.94472 | − | 3.36835i | −0.0685422 | − | 0.118719i | ||||
\(806\) | −19.4260 | − | 33.6467i | −0.684250 | − | 1.18516i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.7344 | + | 28.9848i | −0.588714 | + | 1.01968i | ||||
\(809\) | 8.61362 | 0.302839 | 0.151419 | − | 0.988470i | \(-0.451616\pi\) | ||||
0.151419 | + | 0.988470i | \(0.451616\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.58716 | −0.336651 | −0.168325 | − | 0.985732i | \(-0.553836\pi\) | ||||
−0.168325 | + | 0.985732i | \(0.553836\pi\) | |||||||
\(812\) | −3.48044 | + | 6.02830i | −0.122139 | + | 0.211552i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.6023 | − | 21.8278i | −0.441711 | − | 0.765065i | ||||
\(815\) | −7.10545 | − | 12.3070i | −0.248893 | − | 0.431095i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.0974 | − | 45.2021i | 0.913034 | − | 1.58142i | ||||
\(818\) | 54.5988 | 1.90900 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 102.694 | 3.58624 | ||||||||
\(821\) | −6.93174 | + | 12.0061i | −0.241919 | + | 0.419016i | −0.961261 | − | 0.275640i | \(-0.911110\pi\) |
0.719342 | + | 0.694656i | \(0.244444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.9129 | − | 41.4183i | −0.833550 | − | 1.44375i | −0.895205 | − | 0.445654i | \(-0.852971\pi\) |
0.0616554 | − | 0.998097i | \(-0.480362\pi\) | |||||||
\(824\) | 34.4626 | + | 59.6911i | 1.20056 | + | 2.07944i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.48366 | − | 2.56978i | 0.0516232 | − | 0.0894141i | ||||
\(827\) | 42.4417 | 1.47584 | 0.737921 | − | 0.674887i | \(-0.235808\pi\) | ||||
0.737921 | + | 0.674887i | \(0.235808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.0037 | 0.903146 | 0.451573 | − | 0.892234i | \(-0.350863\pi\) | ||||
0.451573 | + | 0.892234i | \(0.350863\pi\) | |||||||
\(830\) | 6.17095 | − | 10.6884i | 0.214197 | − | 0.371000i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −37.3159 | − | 64.6331i | −1.29370 | − | 2.24075i | ||||
\(833\) | −8.99248 | − | 15.5754i | −0.311571 | − | 0.539657i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.3511 | − | 33.5171i | 0.669673 | − | 1.15991i | ||||
\(836\) | 59.1096 | 2.04435 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 65.9233 | 2.27728 | ||||||||
\(839\) | 0.628138 | − | 1.08797i | 0.0216857 | − | 0.0375608i | −0.854979 | − | 0.518663i | \(-0.826430\pi\) |
0.876665 | + | 0.481102i | \(0.159763\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0807 | + | 19.1923i | 0.382093 | + | 0.661805i | ||||
\(842\) | −35.4019 | − | 61.3179i | −1.22003 | − | 2.11315i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −36.8998 | + | 63.9124i | −1.27014 | + | 2.19995i | ||||
\(845\) | −5.54019 | −0.190588 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.66551 | −0.125948 | ||||||||
\(848\) | −37.0538 | + | 64.1791i | −1.27243 | + | 2.20392i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.94020 | + | 13.7528i | 0.272347 | + | 0.471718i | ||||
\(851\) | 11.2864 | + | 19.5486i | 0.386892 | + | 0.670117i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.727173 | + | 1.25950i | −0.0248979 | + | 0.0431245i | −0.878206 | − | 0.478283i | \(-0.841259\pi\) |
0.853308 | + | 0.521407i | \(0.174593\pi\) | |||||||
\(854\) | −9.26272 | −0.316964 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −96.6089 | −3.30202 | ||||||||
\(857\) | −26.1548 | + | 45.3015i | −0.893432 | + | 1.54747i | −0.0576998 | + | 0.998334i | \(0.518377\pi\) |
−0.835733 | + | 0.549136i | \(0.814957\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.5022 | + | 18.1903i | 0.358329 | + | 0.620645i | 0.987682 | − | 0.156475i | \(-0.0500132\pi\) |
−0.629353 | + | 0.777120i | \(0.716680\pi\) | |||||||
\(860\) | 40.0364 | + | 69.3451i | 1.36523 | + | 2.36465i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −43.1708 | + | 74.7741i | −1.47040 | + | 2.54682i | ||||
\(863\) | −12.9813 | −0.441890 | −0.220945 | − | 0.975286i | \(-0.570914\pi\) | ||||
−0.220945 | + | 0.975286i | \(0.570914\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.31221 | 0.146619 | ||||||||
\(866\) | 0.0166469 | − | 0.0288334i | 0.000565686 | − | 0.000979797i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.14165 | + | 10.6376i | 0.208461 | + | 0.361065i | ||||
\(869\) | −5.09270 | − | 8.82082i | −0.172758 | − | 0.299226i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.4272 | + | 33.6489i | −0.658265 | + | 1.14015i | ||||
\(872\) | −109.747 | −3.71650 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −72.8485 | −2.46414 | ||||||||
\(875\) | 3.01516 | − | 5.22241i | 0.101931 | − | 0.176550i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.5228 | − | 26.8863i | −0.524169 | − | 0.907887i | −0.999604 | − | 0.0281364i | \(-0.991043\pi\) |
0.475435 | − | 0.879751i | \(-0.342291\pi\) | |||||||
\(878\) | 7.17492 | + | 12.4273i | 0.242142 | + | 0.419402i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −21.8724 | + | 37.8841i | −0.737319 | + | 1.27707i | ||||
\(881\) | −19.2957 | −0.650087 | −0.325044 | − | 0.945699i | \(-0.605379\pi\) | ||||
−0.325044 | + | 0.945699i | \(0.605379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.82388 | −0.330600 | −0.165300 | − | 0.986243i | \(-0.552859\pi\) | ||||
−0.165300 | + | 0.986243i | \(0.552859\pi\) | |||||||
\(884\) | 22.0501 | − | 38.1920i | 0.741627 | − | 1.28453i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −55.0431 | − | 95.3375i | −1.84921 | − | 3.20293i | ||||
\(887\) | 22.0566 | + | 38.2032i | 0.740590 | + | 1.28274i | 0.952227 | + | 0.305391i | \(0.0987870\pi\) |
−0.211638 | + | 0.977348i | \(0.567880\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.586776 | + | 1.01633i | −0.0196798 | + | 0.0340865i | ||||
\(890\) | 50.7533 | 1.70125 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −36.2219 | −1.21280 | ||||||||
\(893\) | 19.8020 | − | 34.2981i | 0.662649 | − | 1.14774i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.43888 | − | 12.8845i | −0.248654 | − | 0.430682i | ||||
\(896\) | 6.74943 | + | 11.6904i | 0.225483 | + | 0.390548i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.8669 | + | 36.1425i | −0.696338 | + | 1.20609i | ||||
\(899\) | −12.0675 | −0.402474 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.4777 | −0.482323 | ||||||||
\(902\) | 29.9533 | − | 51.8807i | 0.997337 | − | 1.72744i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.72222 | + | 15.1073i | 0.290097 | + | 0.502463i | ||||
\(905\) | −6.61581 | − | 11.4589i | −0.219917 | − | 0.380908i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.2062 | − | 36.7302i | 0.704140 | − | 1.21961i | −0.262861 | − | 0.964834i | \(-0.584666\pi\) |
0.967001 | − | 0.254773i | \(-0.0820006\pi\) | |||||||
\(908\) | 51.7957 | 1.71890 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.04851 | −0.233656 | ||||||||
\(911\) | 18.3552 | − | 31.7921i | 0.608134 | − | 1.05332i | −0.383414 | − | 0.923577i | \(-0.625252\pi\) |
0.991548 | − | 0.129743i | \(-0.0414151\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.61591 | − | 4.53089i | −0.0865740 | − | 0.149951i | ||||
\(914\) | 3.23086 | + | 5.59601i | 0.106867 | + | 0.185100i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 37.3409 | − | 64.6763i | 1.23378 | − | 2.13696i | ||||
\(917\) | 8.56130 | 0.282719 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.0589 | −0.463761 | −0.231881 | − | 0.972744i | \(-0.574488\pi\) | ||||
−0.231881 | + | 0.972744i | \(0.574488\pi\) | |||||||
\(920\) | 34.8615 | − | 60.3818i | 1.14935 | − | 1.99073i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −43.9355 | − | 76.0985i | −1.44694 | − | 2.50617i | ||||
\(923\) | −4.41294 | − | 7.64344i | −0.145254 | − | 0.251587i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.35214 | + | 9.27018i | −0.175977 | + | 0.304802i | ||||
\(926\) | −91.6436 | −3.01160 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −49.5528 | −1.62665 | ||||||||
\(929\) | −9.25875 | + | 16.0366i | −0.303770 | + | 0.526144i | −0.976987 | − | 0.213301i | \(-0.931579\pi\) |
0.673217 | + | 0.739445i | \(0.264912\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.5619 | + | 33.8823i | 0.641116 | + | 1.11045i | ||||
\(932\) | 14.1531 | + | 24.5139i | 0.463600 | + | 0.802978i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.6686 | − | 32.3349i | 0.610854 | − | 1.05803i | ||||
\(935\) | −8.54604 | −0.279485 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.46818 | 0.145969 | 0.0729845 | − | 0.997333i | \(-0.476748\pi\) | ||||
0.0729845 | + | 0.997333i | \(0.476748\pi\) | |||||||
\(938\) | 8.45222 | − | 14.6397i | 0.275975 | − | 0.478002i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 30.3785 | + | 52.6171i | 0.990838 | + | 1.71618i | ||||
\(941\) | −1.00193 | − | 1.73539i | −0.0326620 | − | 0.0565722i | 0.849232 | − | 0.528019i | \(-0.177065\pi\) |
−0.881894 | + | 0.471447i | \(0.843732\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.8256 | + | 46.4633i | −0.873562 | + | 1.51305i | ||||
\(944\) | 29.8889 | 0.972801 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 46.7105 | 1.51869 | ||||||||
\(947\) | −6.29191 | + | 10.8979i | −0.204460 | + | 0.354134i | −0.949960 | − | 0.312370i | \(-0.898877\pi\) |
0.745501 | + | 0.666505i | \(0.232210\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.4610 | − | 26.7792i | −0.501885 | − | 0.869290i | ||||
\(950\) | −17.2728 | − | 29.9174i | −0.560405 | − | 0.970650i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.98507 | + | 10.3664i | −0.193977 | + | 0.335978i | ||||
\(953\) | 19.9641 | 0.646700 | 0.323350 | − | 0.946279i | \(-0.395191\pi\) | ||||
0.323350 | + | 0.946279i | \(0.395191\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.5865 | 0.860318 | ||||||||
\(956\) | 47.2542 | − | 81.8467i | 1.52831 | − | 2.64711i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.96793 | − | 13.8009i | −0.257432 | − | 0.445885i | ||||
\(959\) | 3.48591 | + | 6.03777i | 0.112566 | + | 0.194970i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.85272 | − | 8.40515i | 0.156539 | − | 0.271134i | ||||
\(962\) | 40.9068 | 1.31889 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.6709 | −0.343686 | ||||||||
\(965\) | 3.83376 | − | 6.64026i | 0.123413 | − | 0.213758i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.1043 | + | 27.8934i | 0.517879 | + | 0.896993i | 0.999784 | + | 0.0207695i | \(0.00661162\pi\) |
−0.481905 | + | 0.876223i | \(0.660055\pi\) | |||||||
\(968\) | −32.8544 | − | 56.9055i | −1.05598 | − | 1.82901i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.5829 | + | 26.9904i | −0.500338 | + | 0.866610i | ||||
\(971\) | 6.62934 | 0.212746 | 0.106373 | − | 0.994326i | \(-0.466076\pi\) | ||||
0.106373 | + | 0.994326i | \(0.466076\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.96300 | 0.127048 | ||||||||
\(974\) | 39.2639 | − | 68.0071i | 1.25810 | − | 2.17909i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46.6502 | − | 80.8005i | −1.49324 | − | 2.58636i | ||||
\(977\) | 5.92832 | + | 10.2682i | 0.189664 | + | 0.328507i | 0.945138 | − | 0.326671i | \(-0.105927\pi\) |
−0.755474 | + | 0.655178i | \(0.772594\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.7573 | − | 18.6323i | 0.343806 | − | 0.595490i | ||||
\(980\) | −60.0205 | −1.91728 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.8577 | 0.378394 | ||||||||
\(983\) | −26.0325 | + | 45.0896i | −0.830308 | + | 1.43814i | 0.0674866 | + | 0.997720i | \(0.478502\pi\) |
−0.897794 | + | 0.440415i | \(0.854831\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.50370 | + | 4.33654i | 0.0797746 | + | 0.138174i | ||||
\(986\) | −9.42486 | − | 16.3243i | −0.300149 | − | 0.519873i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −47.9671 | + | 83.0815i | −1.52604 | + | 2.64317i | ||||
\(989\) | −41.8330 | −1.33021 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.47115 | 0.0467326 | 0.0233663 | − | 0.999727i | \(-0.492562\pi\) | ||||
0.0233663 | + | 0.999727i | \(0.492562\pi\) | |||||||
\(992\) | −43.7209 | + | 75.7268i | −1.38814 | + | 2.40433i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.91995 | + | 3.32544i | 0.0608970 | + | 0.105477i | ||||
\(995\) | −12.4496 | − | 21.5634i | −0.394680 | − | 0.683606i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.2106 | − | 22.8815i | 0.418385 | − | 0.724665i | −0.577392 | − | 0.816467i | \(-0.695930\pi\) |
0.995777 | + | 0.0918025i | \(0.0292628\pi\) | |||||||
\(998\) | −95.6065 | −3.02637 | ||||||||
\(999\) | 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 | 729.2.c.d.487.6 | 12 | ||
3.2 | odd | 2 | 729.2.c.a.487.1 | 12 | |||
9.2 | odd | 6 | 729.2.a.e.1.6 | yes | 6 | ||
9.4 | even | 3 | inner | 729.2.c.d.244.6 | 12 | ||
9.5 | odd | 6 | 729.2.c.a.244.1 | 12 | |||
9.7 | even | 3 | 729.2.a.b.1.1 | ✓ | 6 | ||
27.2 | odd | 18 | 729.2.e.u.325.2 | 12 | |||
27.4 | even | 9 | 729.2.e.t.163.2 | 12 | |||
27.5 | odd | 18 | 729.2.e.u.406.2 | 12 | |||
27.7 | even | 9 | 729.2.e.s.82.1 | 12 | |||
27.11 | odd | 18 | 729.2.e.k.568.1 | 12 | |||
27.13 | even | 9 | 729.2.e.s.649.1 | 12 | |||
27.14 | odd | 18 | 729.2.e.l.649.2 | 12 | |||
27.16 | even | 9 | 729.2.e.t.568.2 | 12 | |||
27.20 | odd | 18 | 729.2.e.l.82.2 | 12 | |||
27.22 | even | 9 | 729.2.e.j.406.1 | 12 | |||
27.23 | odd | 18 | 729.2.e.k.163.1 | 12 | |||
27.25 | even | 9 | 729.2.e.j.325.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
729.2.a.b.1.1 | ✓ | 6 | 9.7 | even | 3 | ||
729.2.a.e.1.6 | yes | 6 | 9.2 | odd | 6 | ||
729.2.c.a.244.1 | 12 | 9.5 | odd | 6 | |||
729.2.c.a.487.1 | 12 | 3.2 | odd | 2 | |||
729.2.c.d.244.6 | 12 | 9.4 | even | 3 | inner | ||
729.2.c.d.487.6 | 12 | 1.1 | even | 1 | trivial | ||
729.2.e.j.325.1 | 12 | 27.25 | even | 9 | |||
729.2.e.j.406.1 | 12 | 27.22 | even | 9 | |||
729.2.e.k.163.1 | 12 | 27.23 | odd | 18 | |||
729.2.e.k.568.1 | 12 | 27.11 | odd | 18 | |||
729.2.e.l.82.2 | 12 | 27.20 | odd | 18 | |||
729.2.e.l.649.2 | 12 | 27.14 | odd | 18 | |||
729.2.e.s.82.1 | 12 | 27.7 | even | 9 | |||
729.2.e.s.649.1 | 12 | 27.13 | even | 9 | |||
729.2.e.t.163.2 | 12 | 27.4 | even | 9 | |||
729.2.e.t.568.2 | 12 | 27.16 | even | 9 | |||
729.2.e.u.325.2 | 12 | 27.2 | odd | 18 | |||
729.2.e.u.406.2 | 12 | 27.5 | odd | 18 |