Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(49,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, 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("1600.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.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: | \(12.7760643234\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 849.1 | ||
Root | \(0.719139 - 1.21772i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.849 |
Dual form | 1600.2.q.f.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.66783 | + | 1.66783i | −0.962922 | + | 0.962922i | −0.999337 | − | 0.0364144i | \(-0.988406\pi\) |
0.0364144 | + | 0.999337i | \(0.488406\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.87372 | 0.708198 | 0.354099 | − | 0.935208i | \(-0.384788\pi\) | ||||
0.354099 | + | 0.935208i | \(0.384788\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.56332i | − | 0.854439i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.29695 | − | 3.29695i | 0.994068 | − | 0.994068i | −0.00591443 | − | 0.999983i | \(-0.501883\pi\) |
0.999983 | + | 0.00591443i | \(0.00188263\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.90022 | − | 1.90022i | 0.527027 | − | 0.527027i | −0.392658 | − | 0.919685i | \(-0.628444\pi\) |
0.919685 | + | 0.392658i | \(0.128444\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.57148i | 0.623675i | 0.950135 | + | 0.311838i | \(0.100944\pi\) | ||||
−0.950135 | + | 0.311838i | \(0.899056\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.76636 | − | 5.76636i | −1.32289 | − | 1.32289i | −0.911422 | − | 0.411472i | \(-0.865015\pi\) |
−0.411472 | − | 0.911422i | \(-0.634985\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.12504 | + | 3.12504i | −0.681940 | + | 0.681940i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.58574 | −1.58174 | −0.790868 | − | 0.611987i | \(-0.790371\pi\) | ||||
−0.790868 | + | 0.611987i | \(0.790371\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.728312 | − | 0.728312i | −0.140164 | − | 0.140164i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.45786 | − | 6.45786i | −1.19919 | − | 1.19919i | −0.974408 | − | 0.224787i | \(-0.927831\pi\) |
−0.224787 | − | 0.974408i | \(-0.572169\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.799135 | 0.143529 | 0.0717644 | − | 0.997422i | \(-0.477137\pi\) | ||||
0.0717644 | + | 0.997422i | \(0.477137\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.9975i | 1.91442i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.69652 | + | 2.69652i | 0.443305 | + | 0.443305i | 0.893121 | − | 0.449816i | \(-0.148511\pi\) |
−0.449816 | + | 0.893121i | \(0.648511\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.33850i | 1.01497i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.946984i | − | 0.147894i | −0.997262 | − | 0.0739471i | \(-0.976440\pi\) | ||
0.997262 | − | 0.0739471i | \(-0.0235596\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.829986 | + | 0.829986i | 0.126572 | + | 0.126572i | 0.767555 | − | 0.640983i | \(-0.221473\pi\) |
−0.640983 | + | 0.767555i | \(0.721473\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.52421i | − | 0.222329i | −0.993802 | − | 0.111165i | \(-0.964542\pi\) | ||
0.993802 | − | 0.111165i | \(-0.0354581\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.48919 | −0.498456 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.28879 | − | 4.28879i | −0.600551 | − | 0.600551i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.97225 | − | 6.97225i | −0.957712 | − | 0.957712i | 0.0414296 | − | 0.999141i | \(-0.486809\pi\) |
−0.999141 | + | 0.0414296i | \(0.986809\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19.2346 | 2.54769 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.84418 | − | 6.84418i | 0.891036 | − | 0.891036i | −0.103585 | − | 0.994621i | \(-0.533031\pi\) |
0.994621 | + | 0.103585i | \(0.0330313\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.87247 | − | 6.87247i | −0.879930 | − | 0.879930i | 0.113597 | − | 0.993527i | \(-0.463763\pi\) |
−0.993527 | + | 0.113597i | \(0.963763\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 4.80293i | − | 0.605112i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.73647 | + | 3.73647i | −0.456483 | + | 0.456483i | −0.897499 | − | 0.441016i | \(-0.854618\pi\) |
0.441016 | + | 0.897499i | \(0.354618\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 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 | \(-0.187081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.886316 | 0.103735 | 0.0518677 | − | 0.998654i | \(-0.483483\pi\) | ||||
0.0518677 | + | 0.998654i | \(0.483483\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.17755 | − | 6.17755i | 0.703997 | − | 0.703997i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.07575 | 0.346049 | 0.173024 | − | 0.984918i | \(-0.444646\pi\) | ||||
0.173024 | + | 0.984918i | \(0.444646\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.1194 | 1.12437 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.989393 | − | 0.989393i | 0.108600 | − | 0.108600i | −0.650719 | − | 0.759319i | \(-0.725532\pi\) |
0.759319 | + | 0.650719i | \(0.225532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.5412 | 2.30946 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0942i | 1.06998i | 0.844859 | + | 0.534990i | \(0.179684\pi\) | ||||
−0.844859 | + | 0.534990i | \(0.820316\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.56048 | − | 3.56048i | 0.373239 | − | 0.373239i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.33282 | + | 1.33282i | −0.138207 | + | 0.138207i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.16829i | − | 0.727830i | −0.931432 | − | 0.363915i | \(-0.881440\pi\) | ||
0.931432 | − | 0.363915i | \(-0.118560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.45113 | − | 8.45113i | −0.849371 | − | 0.849371i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.05091 | + | 1.05091i | −0.104570 | + | 0.104570i | −0.757456 | − | 0.652886i | \(-0.773558\pi\) |
0.652886 | + | 0.757456i | \(0.273558\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.20690 | 0.808649 | 0.404325 | − | 0.914616i | \(-0.367507\pi\) | ||||
0.404325 | + | 0.914616i | \(0.367507\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.85743 | + | 2.85743i | 0.276238 | + | 0.276238i | 0.831605 | − | 0.555367i | \(-0.187422\pi\) |
−0.555367 | + | 0.831605i | \(0.687422\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.3735 | + | 11.3735i | 1.08939 | + | 1.08939i | 0.995592 | + | 0.0937940i | \(0.0298995\pi\) |
0.0937940 | + | 0.995592i | \(0.470100\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.99467 | −0.853736 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.54221i | 0.333223i | 0.986023 | + | 0.166611i | \(0.0532825\pi\) | ||||
−0.986023 | + | 0.166611i | \(0.946717\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.87088 | − | 4.87088i | −0.450313 | − | 0.450313i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.81822i | 0.441685i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.7398i | − | 0.976343i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.57941 | + | 1.57941i | 0.142411 | + | 0.142411i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 18.0693i | − | 1.60339i | −0.597735 | − | 0.801693i | \(-0.703933\pi\) | ||
0.597735 | − | 0.801693i | \(-0.296067\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.76855 | −0.243757 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.39614 | + | 6.39614i | 0.558834 | + | 0.558834i | 0.928975 | − | 0.370142i | \(-0.120691\pi\) |
−0.370142 | + | 0.928975i | \(0.620691\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.8045 | − | 10.8045i | −0.936871 | − | 0.936871i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.7357 | −0.917212 | −0.458606 | − | 0.888640i | \(-0.651651\pi\) | ||||
−0.458606 | + | 0.888640i | \(0.651651\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.31086 | + | 2.31086i | −0.196005 | + | 0.196005i | −0.798285 | − | 0.602280i | \(-0.794259\pi\) |
0.602280 | + | 0.798285i | \(0.294259\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.54213 | + | 2.54213i | 0.214086 | + | 0.214086i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 12.5299i | − | 1.04780i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.81938 | − | 5.81938i | 0.479974 | − | 0.479974i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.38743 | + | 1.38743i | −0.113663 | + | 0.113663i | −0.761651 | − | 0.647988i | \(-0.775611\pi\) |
0.647988 | + | 0.761651i | \(0.275611\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.68590i | − | 0.462712i | −0.972869 | − | 0.231356i | \(-0.925684\pi\) | ||
0.972869 | − | 0.231356i | \(-0.0743163\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.59152 | 0.532892 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.48874 | − | 2.48874i | 0.198623 | − | 0.198623i | −0.600787 | − | 0.799409i | \(-0.705146\pi\) |
0.799409 | + | 0.600787i | \(0.205146\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.2571 | 1.84440 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.2135 | −1.12018 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.7091 | + | 12.7091i | −0.995451 | + | 0.995451i | −0.999990 | − | 0.00453842i | \(-0.998555\pi\) |
0.00453842 | + | 0.999990i | \(0.498555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.00982 | 0.387672 | 0.193836 | − | 0.981034i | \(-0.437907\pi\) | ||||
0.193836 | + | 0.981034i | \(0.437907\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.77830i | 0.444485i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.7810 | + | 14.7810i | −1.13033 | + | 1.13033i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.19546 | − | 6.19546i | 0.471032 | − | 0.471032i | −0.431216 | − | 0.902249i | \(-0.641915\pi\) |
0.902249 | + | 0.431216i | \(0.141915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.8299i | 1.71600i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.51628 | − | 5.51628i | −0.412306 | − | 0.412306i | 0.470235 | − | 0.882541i | \(-0.344169\pi\) |
−0.882541 | + | 0.470235i | \(0.844169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.8993 | − | 11.8993i | 0.884470 | − | 0.884470i | −0.109515 | − | 0.993985i | \(-0.534930\pi\) |
0.993985 | + | 0.109515i | \(0.0349298\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.9242 | 1.69461 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.47804 | + | 8.47804i | 0.619976 | + | 0.619976i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.36465 | − | 1.36465i | −0.0992637 | − | 0.0992637i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.1278 | −0.805180 | −0.402590 | − | 0.915380i | \(-0.631890\pi\) | ||||
−0.402590 | + | 0.915380i | \(0.631890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 20.7821i | − | 1.49593i | −0.663738 | − | 0.747965i | \(-0.731031\pi\) | ||
0.663738 | − | 0.747965i | \(-0.268969\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.0309 | − | 14.0309i | −0.999663 | − | 0.999663i | 0.000337236 | − | 1.00000i | \(-0.499893\pi\) |
−1.00000 | 0.000337236i | \(0.999893\pi\) | ||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 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 | 0 | ||||||||
\(203\) | −12.1002 | − | 12.1002i | −0.849267 | − | 0.849267i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.4447i | 1.35150i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −38.0228 | −2.63009 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1821 | + | 10.1821i | 0.700964 | + | 0.700964i | 0.964617 | − | 0.263654i | \(-0.0849276\pi\) |
−0.263654 | + | 0.964617i | \(0.584928\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.5845 | + | 15.5845i | 1.06783 | + | 1.06783i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.49735 | 0.101647 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.47822 | + | 1.47822i | −0.0998892 | + | 0.0998892i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.88638 | + | 4.88638i | 0.328694 | + | 0.328694i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0469i | 1.61030i | 0.593070 | + | 0.805151i | \(0.297916\pi\) | ||||
−0.593070 | + | 0.805151i | \(0.702084\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.9863 | + | 11.9863i | −0.795562 | + | 0.795562i | −0.982392 | − | 0.186830i | \(-0.940179\pi\) |
0.186830 | + | 0.982392i | \(0.440179\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.1972 | − | 20.1972i | 1.33467 | − | 1.33467i | 0.433529 | − | 0.901140i | \(-0.357268\pi\) |
0.901140 | − | 0.433529i | \(-0.142732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.6062i | 1.35579i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0655 | −0.659410 | −0.329705 | − | 0.944084i | \(-0.606949\pi\) | ||||
−0.329705 | + | 0.944084i | \(0.606949\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.12983 | + | 5.12983i | −0.333218 | + | 0.333218i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.992801 | 0.0642189 | 0.0321095 | − | 0.999484i | \(-0.489777\pi\) | ||||
0.0321095 | + | 0.999484i | \(0.489777\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1229 | 0.909738 | 0.454869 | − | 0.890558i | \(-0.349686\pi\) | ||||
0.454869 | + | 0.890558i | \(0.349686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.6924 | + | 14.6924i | −0.942520 | + | 0.942520i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.9148 | −1.39440 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.30028i | 0.209147i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.56681 | + | 1.56681i | −0.0988961 | + | 0.0988961i | −0.754824 | − | 0.655928i | \(-0.772278\pi\) |
0.655928 | + | 0.754824i | \(0.272278\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.0098 | + | 25.0098i | −1.57235 | + | 1.57235i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.2593i | 0.639960i | 0.947424 | + | 0.319980i | \(0.103676\pi\) | ||||
−0.947424 | + | 0.319980i | \(0.896324\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.05251 | + | 5.05251i | 0.313948 | + | 0.313948i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.5535 | + | 16.5535i | −1.02464 | + | 1.02464i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.0630 | 1.17548 | 0.587739 | − | 0.809051i | \(-0.300018\pi\) | ||||
0.587739 | + | 0.809051i | \(0.300018\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.8354 | − | 16.8354i | −1.03031 | − | 1.03031i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.48459 | − | 3.48459i | −0.212459 | − | 0.212459i | 0.592852 | − | 0.805311i | \(-0.298002\pi\) |
−0.805311 | + | 0.592852i | \(0.798002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.0045 | 1.82264 | 0.911322 | − | 0.411695i | \(-0.135063\pi\) | ||||
0.911322 | + | 0.411695i | \(0.135063\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.8765i | 0.718801i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.43732 | − | 8.43732i | −0.506949 | − | 0.506949i | 0.406639 | − | 0.913589i | \(-0.366701\pi\) |
−0.913589 | + | 0.406639i | \(0.866701\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.04844i | − | 0.122637i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.44714i | 0.384604i | 0.981336 | + | 0.192302i | \(0.0615954\pi\) | ||||
−0.981336 | + | 0.192302i | \(0.938405\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.61000 | − | 2.61000i | −0.155148 | − | 0.155148i | 0.625264 | − | 0.780413i | \(-0.284991\pi\) |
−0.780413 | + | 0.625264i | \(0.784991\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.77438i | − | 0.104738i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.3875 | 0.611029 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.9555 | + | 11.9555i | 0.700844 | + | 0.700844i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.52428 | − | 7.52428i | −0.439573 | − | 0.439573i | 0.452295 | − | 0.891868i | \(-0.350605\pi\) |
−0.891868 | + | 0.452295i | \(0.850605\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.80242 | −0.278665 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.4146 | + | 14.4146i | −0.833618 | + | 0.833618i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.55516 | + | 1.55516i | 0.0896377 | + | 0.0896377i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.50549i | − | 0.201385i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.7130 | + | 12.7130i | −0.725571 | + | 0.725571i | −0.969734 | − | 0.244163i | \(-0.921487\pi\) |
0.244163 | + | 0.969734i | \(0.421487\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −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 | \(-0.109846\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.3458 | 1.94134 | 0.970670 | − | 0.240414i | \(-0.0772832\pi\) | ||||
0.970670 | + | 0.240414i | \(0.0772832\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.1112 | + | 17.1112i | −0.961060 | + | 0.961060i | −0.999270 | − | 0.0382097i | \(-0.987835\pi\) |
0.0382097 | + | 0.999270i | \(0.487835\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42.5825 | −2.38416 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.53141 | −0.531992 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.8281 | − | 14.8281i | 0.825056 | − | 0.825056i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −37.9382 | −2.09799 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.85594i | − | 0.157453i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.80246 | + | 9.80246i | −0.538792 | + | 0.538792i | −0.923174 | − | 0.384382i | \(-0.874415\pi\) |
0.384382 | + | 0.923174i | \(0.374415\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.91203 | − | 6.91203i | 0.378777 | − | 0.378777i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6.07501i | − | 0.330927i | −0.986216 | − | 0.165463i | \(-0.947088\pi\) | ||
0.986216 | − | 0.165463i | \(-0.0529120\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.90780 | − | 5.90780i | −0.320868 | − | 0.320868i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.63471 | − | 2.63471i | 0.142677 | − | 0.142677i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.6538 | −1.06120 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.77231 | + | 5.77231i | 0.309874 | + | 0.309874i | 0.844860 | − | 0.534987i | \(-0.179683\pi\) |
−0.534987 | + | 0.844860i | \(0.679683\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.58851 | + | 7.58851i | 0.406203 | + | 0.406203i | 0.880412 | − | 0.474209i | \(-0.157266\pi\) |
−0.474209 | + | 0.880412i | \(0.657266\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.76791 | −0.147740 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 16.2285i | − | 0.863753i | −0.901933 | − | 0.431877i | \(-0.857852\pi\) | ||
0.901933 | − | 0.431877i | \(-0.142148\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.03597 | − | 8.03597i | −0.425309 | − | 0.425309i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.9121 | + | 17.9121i | 0.940142 | + | 0.940142i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6.35705i | − | 0.331835i | −0.986140 | − | 0.165918i | \(-0.946941\pi\) | ||
0.986140 | − | 0.165918i | \(-0.0530586\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.42742 | −0.126367 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.0640 | − | 13.0640i | −0.678250 | − | 0.678250i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.20937 | + | 9.20937i | 0.476843 | + | 0.476843i | 0.904121 | − | 0.427278i | \(-0.140527\pi\) |
−0.427278 | + | 0.904121i | \(0.640527\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.5428 | −1.26402 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.41600 | − | 5.41600i | 0.278201 | − | 0.278201i | −0.554189 | − | 0.832391i | \(-0.686972\pi\) |
0.832391 | + | 0.554189i | \(0.186972\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.1365 | + | 30.1365i | 1.54394 | + | 1.54394i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 28.1626i | − | 1.43904i | −0.694472 | − | 0.719520i | \(-0.744362\pi\) | ||
0.694472 | − | 0.719520i | \(-0.255638\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.12752 | − | 2.12752i | 0.108148 | − | 0.108148i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.59783 | + | 9.59783i | −0.486629 | + | 0.486629i | −0.907241 | − | 0.420611i | \(-0.861816\pi\) |
0.420611 | + | 0.907241i | \(0.361816\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.5066i | − | 0.986490i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.3354 | −1.07623 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.4884 | − | 10.4884i | 0.526399 | − | 0.526399i | −0.393098 | − | 0.919497i | \(-0.628597\pi\) |
0.919497 | + | 0.393098i | \(0.128597\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 36.0402 | 1.80427 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.44221 | −0.121958 | −0.0609791 | − | 0.998139i | \(-0.519422\pi\) | ||||
−0.0609791 | + | 0.998139i | \(0.519422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.51853 | − | 1.51853i | 0.0756436 | − | 0.0756436i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.7806 | 0.881350 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.6628i | 1.21950i | 0.792596 | + | 0.609748i | \(0.208729\pi\) | ||||
−0.792596 | + | 0.609748i | \(0.791271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.9053 | − | 17.9053i | 0.883204 | − | 0.883204i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.8240 | − | 12.8240i | 0.631030 | − | 0.631030i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 7.70826i | − | 0.377475i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.1661 | + | 19.1661i | 0.936326 | + | 0.936326i | 0.998091 | − | 0.0617649i | \(-0.0196729\pi\) |
−0.0617649 | + | 0.998091i | \(0.519673\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.43469 | + | 7.43469i | −0.362345 | + | 0.362345i | −0.864676 | − | 0.502331i | \(-0.832476\pi\) |
0.502331 | + | 0.864676i | \(0.332476\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.90704 | −0.189967 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.8771 | − | 12.8771i | −0.623164 | − | 0.623164i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.8977 | + | 20.8977i | 1.00895 | + | 1.00895i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.5647 | −1.08690 | −0.543451 | − | 0.839441i | \(-0.682883\pi\) | ||||
−0.543451 | + | 0.839441i | \(0.682883\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.4811i | 1.27260i | 0.771441 | + | 0.636301i | \(0.219536\pi\) | ||||
−0.771441 | + | 0.636301i | \(0.780464\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 43.7421 | + | 43.7421i | 2.09247 | + | 2.09247i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 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 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.2685 | − | 20.2685i | −0.962985 | − | 0.962985i | 0.0363537 | − | 0.999339i | \(-0.488426\pi\) |
−0.999339 | + | 0.0363537i | \(0.988426\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 4.62800i | − | 0.218897i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 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 | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.48312 | + | 9.48312i | 0.445556 | + | 0.445556i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.01188 | −0.421558 | −0.210779 | − | 0.977534i | \(-0.567600\pi\) | ||||
−0.210779 | + | 0.977534i | \(0.567600\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.87284 | − | 1.87284i | 0.0874167 | − | 0.0874167i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.8247 | − | 22.8247i | −1.06305 | − | 1.06305i | −0.997873 | − | 0.0651807i | \(-0.979238\pi\) |
−0.0651807 | − | 0.997873i | \(-0.520762\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.72721i | − | 0.173218i | −0.996242 | − | 0.0866090i | \(-0.972397\pi\) | ||
0.996242 | − | 0.0866090i | \(-0.0276031\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.23477 | − | 3.23477i | 0.149687 | − | 0.149687i | −0.628291 | − | 0.777978i | \(-0.716245\pi\) |
0.777978 | + | 0.628291i | \(0.216245\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.00109 | + | 7.00109i | −0.323280 | + | 0.323280i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.30158i | 0.382517i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.47284 | 0.251642 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.8721 | + | 17.8721i | −0.818307 | + | 0.818307i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.0636 | −0.505508 | −0.252754 | − | 0.967531i | \(-0.581336\pi\) | ||||
−0.252754 | + | 0.967531i | \(0.581336\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.2480 | 0.467267 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 23.7057 | − | 23.7057i | 1.07865 | − | 1.07865i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.68176 | −0.302779 | −0.151390 | − | 0.988474i | \(-0.548375\pi\) | ||||
−0.151390 | + | 0.988474i | \(0.548375\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 42.3932i | − | 1.91708i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.4274 | − | 18.4274i | 0.831618 | − | 0.831618i | −0.156120 | − | 0.987738i | \(-0.549899\pi\) |
0.987738 | + | 0.156120i | \(0.0498986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.6063 | − | 16.6063i | 0.747908 | − | 0.747908i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 17.5083i | − | 0.785356i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.84615 | + | 8.84615i | 0.396008 | + | 0.396008i | 0.876822 | − | 0.480814i | \(-0.159659\pi\) |
−0.480814 | + | 0.876822i | \(0.659659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.35554 | + | 8.35554i | −0.373298 | + | 0.373298i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.8746 | −0.752401 | −0.376201 | − | 0.926538i | \(-0.622770\pi\) | ||||
−0.376201 | + | 0.926538i | \(0.622770\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.63723 | − | 9.63723i | −0.428004 | − | 0.428004i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.5691 | − | 20.5691i | −0.911707 | − | 0.911707i | 0.0846994 | − | 0.996407i | \(-0.473007\pi\) |
−0.996407 | + | 0.0846994i | \(0.973007\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.66070 | 0.0734652 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.39943i | 0.370844i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.02526 | − | 5.02526i | −0.221011 | − | 0.221011i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.6660i | 0.907135i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12.6708i | − | 0.555118i | −0.960709 | − | 0.277559i | \(-0.910475\pi\) | ||
0.960709 | − | 0.277559i | \(-0.0895253\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.8509 | + | 27.8509i | 1.21784 | + | 1.21784i | 0.968388 | + | 0.249448i | \(0.0802491\pi\) |
0.249448 | + | 0.968388i | \(0.419751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.05496i | 0.0895154i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 34.5435 | 1.50189 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.5438 | − | 17.5438i | −0.761336 | − | 0.761336i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.79948 | − | 1.79948i | −0.0779442 | − | 0.0779442i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.4005 | 0.794038 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.5037 | + | 11.5037i | −0.495499 | + | 0.495499i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.4122 | − | 23.4122i | −1.00657 | − | 1.00657i | −0.999978 | − | 0.00659048i | \(-0.997902\pi\) |
−0.00659048 | − | 0.999978i | \(-0.502098\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 39.6921i | 1.70335i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.3745 | + | 17.3745i | −0.742878 | + | 0.742878i | −0.973131 | − | 0.230253i | \(-0.926045\pi\) |
0.230253 | + | 0.973131i | \(0.426045\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.6163 | + | 17.6163i | −0.751846 | + | 0.751846i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 74.4767i | 3.17282i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.76308 | 0.245071 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.8889 | − | 22.8889i | 0.969832 | − | 0.969832i | −0.0297261 | − | 0.999558i | \(-0.509464\pi\) |
0.999558 | + | 0.0297261i | \(0.00946351\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.15432 | 0.133413 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.2799 | −1.19398 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.2489 | − | 19.2489i | 0.811246 | − | 0.811246i | −0.173574 | − | 0.984821i | \(-0.555532\pi\) |
0.984821 | + | 0.173574i | \(0.0555317\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.9608 | 0.796278 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.4274i | 1.44327i | 0.692273 | + | 0.721635i | \(0.256609\pi\) | ||||
−0.692273 | + | 0.721635i | \(0.743391\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.85059 | + | 5.85059i | −0.244840 | + | 0.244840i | −0.818849 | − | 0.574009i | \(-0.805387\pi\) |
0.574009 | + | 0.818849i | \(0.305387\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.5593 | − | 18.5593i | 0.775326 | − | 0.775326i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 32.5042i | − | 1.35317i | −0.736365 | − | 0.676585i | \(-0.763459\pi\) | ||
0.736365 | − | 0.676585i | \(-0.236541\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34.6611 | + | 34.6611i | 1.44047 | + | 1.44047i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.85384 | − | 1.85384i | 0.0769103 | − | 0.0769103i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −45.9743 | −1.90406 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.7519 | − | 14.7519i | −0.608875 | − | 0.608875i | 0.333777 | − | 0.942652i | \(-0.391677\pi\) |
−0.942652 | + | 0.333777i | \(0.891677\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.60810 | − | 4.60810i | −0.189873 | − | 0.189873i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 46.8024 | 1.92520 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 20.5310i | − | 0.843108i | −0.906803 | − | 0.421554i | \(-0.861485\pi\) | ||
0.906803 | − | 0.421554i | \(-0.138515\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.41590 | − | 5.41590i | −0.221658 | − | 0.221658i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 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 | \(-0.918628\pi\) | ||
0.967502 | − | 0.252862i | \(-0.0813718\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.57777 | + | 9.57777i | 0.390037 | + | 0.390037i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.90398i | 0.199046i | 0.995035 | + | 0.0995232i | \(0.0317318\pi\) | ||||
−0.995035 | + | 0.0995232i | \(0.968268\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 40.3621 | 1.63556 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.89635 | − | 2.89635i | −0.117174 | − | 0.117174i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.408547 | − | 0.408547i | −0.0165011 | − | 0.0165011i | 0.698808 | − | 0.715309i | \(-0.253714\pi\) |
−0.715309 | + | 0.698808i | \(0.753714\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.17186 | 0.248470 | 0.124235 | − | 0.992253i | \(-0.460352\pi\) | ||||
0.124235 | + | 0.992253i | \(0.460352\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.5138 | − | 18.5138i | 0.744132 | − | 0.744132i | −0.229238 | − | 0.973370i | \(-0.573623\pi\) |
0.973370 | + | 0.229238i | \(0.0736234\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.52479 | + | 5.52479i | 0.221702 | + | 0.221702i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.9136i | 0.757757i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 63.4156 | − | 63.4156i | 2.53258 | − | 2.53258i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −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 | 0 | ||||||||
\(633\) | −33.9640 | −1.34995 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.63024 | + | 6.63024i | −0.262700 | + | 0.262700i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.9521 | −0.947530 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.1179 | 0.636620 | 0.318310 | − | 0.947987i | \(-0.396885\pi\) | ||||
0.318310 | + | 0.947987i | \(0.396885\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.3733 | − | 10.3733i | 0.409082 | − | 0.409082i | −0.472336 | − | 0.881419i | \(-0.656589\pi\) |
0.881419 | + | 0.472336i | \(0.156589\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.5724 | −1.28055 | −0.640276 | − | 0.768145i | \(-0.721180\pi\) | ||||
−0.640276 | + | 0.768145i | \(0.721180\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 45.1298i | − | 1.77150i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.49733 | + | 2.49733i | −0.0978780 | + | 0.0978780i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.31962 | + | 4.31962i | −0.169040 | + | 0.169040i | −0.786557 | − | 0.617517i | \(-0.788139\pi\) |
0.617517 | + | 0.786557i | \(0.288139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2.27191i | − | 0.0886356i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.19711 | − | 4.19711i | −0.163496 | − | 0.163496i | 0.620617 | − | 0.784114i | \(-0.286882\pi\) |
−0.784114 | + | 0.620617i | \(0.786882\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.2310 | − | 21.2310i | 0.825790 | − | 0.825790i | −0.161141 | − | 0.986931i | \(-0.551518\pi\) |
0.986931 | + | 0.161141i | \(0.0515175\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.2993 | −0.633013 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.9877 | + | 48.9877i | 1.89681 | + | 1.89681i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −40.1062 | − | 40.1062i | −1.55060 | − | 1.55060i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −45.3164 | −1.74942 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 6.08317i | − | 0.234489i | −0.993103 | − | 0.117244i | \(-0.962594\pi\) | ||
0.993103 | − | 0.117244i | \(-0.0374061\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.42443 | + | 8.42443i | 0.323777 | + | 0.323777i | 0.850214 | − | 0.526437i | \(-0.176472\pi\) |
−0.526437 | + | 0.850214i | \(0.676472\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.4313i | − | 0.515447i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 39.9824i | − | 1.53213i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.7609 | − | 14.7609i | −0.564812 | − | 0.564812i | 0.365859 | − | 0.930670i | \(-0.380775\pi\) |
−0.930670 | + | 0.365859i | \(0.880775\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 67.3710i | 2.57036i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.4977 | −1.00948 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.06268 | + | 4.06268i | 0.154552 | + | 0.154552i | 0.780147 | − | 0.625596i | \(-0.215144\pi\) |
−0.625596 | + | 0.780147i | \(0.715144\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.8350 | − | 15.8350i | −0.601523 | − | 0.601523i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.43515 | 0.0922379 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.7875 | − | 16.7875i | 0.634961 | − | 0.634961i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.1049 | + | 11.1049i | 0.419428 | + | 0.419428i | 0.885007 | − | 0.465578i | \(-0.154154\pi\) |
−0.465578 | + | 0.885007i | \(0.654154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 31.0982i | − | 1.17289i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.96911 | + | 1.96911i | −0.0740561 | + | 0.0740561i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0114 | + | 13.0114i | −0.488652 | + | 0.488652i | −0.907881 | − | 0.419229i | \(-0.862300\pi\) |
0.419229 | + | 0.907881i | \(0.362300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 7.88412i | − | 0.295678i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.06203 | −0.227025 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.65582 | + | 1.65582i | −0.0618378 | + | 0.0618378i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.0570 | −1.86681 | −0.933406 | − | 0.358821i | \(-0.883179\pi\) | ||||
−0.933406 | + | 0.358821i | \(0.883179\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3774 | 0.572684 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.5547 | + | 23.5547i | −0.876007 | + | 0.876007i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.7141 | 1.02786 | 0.513930 | − | 0.857832i | \(-0.328189\pi\) | ||||
0.513930 | + | 0.857832i | \(0.328189\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 18.6509i | − | 0.690775i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.13429 | + | 2.13429i | −0.0789396 | + | 0.0789396i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.8860 | + | 16.8860i | −0.623698 | + | 0.623698i | −0.946475 | − | 0.322777i | \(-0.895384\pi\) |
0.322777 | + | 0.946475i | \(0.395384\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.6379i | 0.907550i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.6286 | − | 23.6286i | −0.869193 | − | 0.869193i | 0.123190 | − | 0.992383i | \(-0.460688\pi\) |
−0.992383 | + | 0.123190i | \(0.960688\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.5501 | − | 36.5501i | 1.34270 | − | 1.34270i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.53356 | 0.239693 | 0.119846 | − | 0.992792i | \(-0.461760\pi\) | ||||
0.119846 | + | 0.992792i | \(0.461760\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.53613 | − | 2.53613i | −0.0927921 | − | 0.0927921i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.35401 | + | 5.35401i | 0.195631 | + | 0.195631i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.8483 | 0.833746 | 0.416873 | − | 0.908965i | \(-0.363126\pi\) | ||||
0.416873 | + | 0.908965i | \(0.363126\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 5.22634i | − | 0.190459i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.0190 | + | 24.0190i | 0.872985 | + | 0.872985i | 0.992797 | − | 0.119811i | \(-0.0382290\pi\) |
−0.119811 | + | 0.992797i | \(0.538229\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 83.4243i | − | 3.02811i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.51772i | 0.200017i | 0.994987 | + | 0.100009i | \(0.0318871\pi\) | ||||
−0.994987 | + | 0.100009i | \(0.968113\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.3107 | + | 21.3107i | 0.771501 | + | 0.771501i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 26.0109i | − | 0.939200i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −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 | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.753043 | + | 0.753043i | 0.0270851 | + | 0.0270851i | 0.720520 | − | 0.693435i | \(-0.243903\pi\) |
−0.693435 | + | 0.720520i | \(0.743903\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.8535 | −0.604614 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.46066 | + | 5.46066i | −0.195648 | + | 0.195648i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.8073 | − | 30.8073i | −1.10237 | − | 1.10237i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.40668i | 0.336167i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.2752 | − | 29.2752i | 1.04355 | − | 1.04355i | 0.0445395 | − | 0.999008i | \(-0.485818\pi\) |
0.999008 | − | 0.0445395i | \(-0.0141821\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31.7939 | + | 31.7939i | −1.13189 | + | 1.13189i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.63709i | 0.235988i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.1185 | −0.927494 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.09658 | + | 6.09658i | −0.215952 | + | 0.215952i | −0.806790 | − | 0.590838i | \(-0.798797\pi\) |
0.590838 | + | 0.806790i | \(0.298797\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.91948 | 0.138661 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.8745 | 0.914232 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.92214 | − | 2.92214i | 0.103120 | − | 0.103120i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.6234 | 0.409163 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 31.5083i | − | 1.10777i | −0.832592 | − | 0.553886i | \(-0.813144\pi\) | ||
0.832592 | − | 0.553886i | \(-0.186856\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.2317 | + | 20.2317i | −0.710431 | + | 0.710431i | −0.966625 | − | 0.256194i | \(-0.917531\pi\) |
0.256194 | + | 0.966625i | \(0.417531\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −50.0424 | + | 50.0424i | −1.75506 | + | 1.75506i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 9.57200i | − | 0.334882i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.12664 | − | 9.12664i | −0.318910 | − | 0.318910i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.1821 | + | 19.1821i | −0.669459 | + | 0.669459i | −0.957591 | − | 0.288132i | \(-0.906966\pi\) |
0.288132 | + | 0.957591i | \(0.406966\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.4746 | 0.399979 | 0.199989 | − | 0.979798i | \(-0.435909\pi\) | ||||
0.199989 | + | 0.979798i | \(0.435909\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.7573 | + | 17.7573i | 0.617482 | + | 0.617482i | 0.944885 | − | 0.327403i | \(-0.106173\pi\) |
−0.327403 | + | 0.944885i | \(0.606173\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.0071 | + | 20.0071i | 0.694876 | + | 0.694876i | 0.963301 | − | 0.268424i | \(-0.0865030\pi\) |
−0.268424 | + | 0.963301i | \(0.586503\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.1440 | 0.976306 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 8.97238i | − | 0.310874i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.582020 | − | 0.582020i | −0.0201175 | − | 0.0201175i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.7527 | − | 10.7527i | −0.370344 | − | 0.370344i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20.1233i | − | 0.691444i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.70608 | 0.298792 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.4551 | − | 20.4551i | −0.701191 | − | 0.701191i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.4481 | + | 37.4481i | 1.28220 | + | 1.28220i | 0.939414 | + | 0.342784i | \(0.111370\pi\) |
0.342784 | + | 0.939414i | \(0.388630\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.7258 | −0.434706 | −0.217353 | − | 0.976093i | \(-0.569742\pi\) | ||||
−0.217353 | + | 0.976093i | \(0.569742\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.4318 | − | 17.4318i | 0.594766 | − | 0.594766i | −0.344149 | − | 0.938915i | \(-0.611833\pi\) |
0.938915 | + | 0.344149i | \(0.111833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.95936 | + | 2.95936i | 0.100855 | + | 0.100855i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.6976i | 1.14708i | 0.819178 | + | 0.573540i | \(0.194430\pi\) | ||||
−0.819178 | + | 0.573540i | \(0.805570\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.3246 | + | 17.3246i | −0.588374 | + | 0.588374i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.1406 | − | 10.1406i | 0.343996 | − | 0.343996i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.2003i | 0.481158i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.3746 | −0.621886 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.8386 | + | 21.8386i | −0.737436 | + | 0.737436i | −0.972081 | − | 0.234645i | \(-0.924607\pi\) |
0.234645 | + | 0.972081i | \(0.424607\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.0985 | 0.846550 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.3274 | −1.32497 | −0.662487 | − | 0.749073i | \(-0.730499\pi\) | ||||
−0.662487 | + | 0.749073i | \(0.730499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.80206 | + | 6.80206i | −0.228907 | + | 0.228907i | −0.812236 | − | 0.583329i | \(-0.801750\pi\) |
0.583329 | + | 0.812236i | \(0.301750\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.4190 | 0.987793 | 0.493897 | − | 0.869521i | \(-0.335572\pi\) | ||||
0.493897 | + | 0.869521i | \(0.335572\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 33.8566i | − | 1.13552i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.3630 | − | 33.3630i | 1.11770 | − | 1.11770i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.78917 | + | 8.78917i | −0.294118 | + | 0.294118i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 48.0822i | − | 1.60542i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.16070 | − | 5.16070i | −0.172119 | − | 0.172119i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.9290 | − | 17.9290i | 0.597301 | − | 0.597301i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.18748 | −0.172628 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.6137 | + | 16.6137i | 0.551649 | + | 0.551649i | 0.926917 | − | 0.375267i | \(-0.122449\pi\) |
−0.375267 | + | 0.926917i | \(0.622449\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.69382 | + | 2.69382i | 0.0893485 | + | 0.0893485i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.7299 | −1.34944 | −0.674721 | − | 0.738073i | \(-0.735736\pi\) | ||||
−0.674721 | + | 0.738073i | \(0.735736\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 6.52396i | − | 0.215912i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.9846 | + | 11.9846i | 0.395765 | + | 0.395765i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 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 | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.7560 | − | 17.7560i | −0.584446 | − | 0.584446i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 21.0369i | − | 0.690942i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 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 | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.8994 | + | 19.8994i | 0.651477 | + | 0.651477i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.3585 | 0.697750 | 0.348875 | − | 0.937169i | \(-0.386564\pi\) | ||||
0.348875 | + | 0.937169i | \(0.386564\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −57.2830 | + | 57.2830i | −1.86936 | + | 1.86936i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.6914 | + | 33.6914i | 1.09831 | + | 1.09831i | 0.994609 | + | 0.103700i | \(0.0330681\pi\) |
0.103700 | + | 0.994609i | \(0.466932\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.18358i | 0.233929i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.421834 | + | 0.421834i | −0.0137078 | + | 0.0137078i | −0.713927 | − | 0.700220i | \(-0.753085\pi\) |
0.700220 | + | 0.713927i | \(0.253085\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.68420 | − | 1.68420i | 0.0546714 | − | 0.0546714i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 57.0771i | − | 1.85085i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.7261 | −0.898137 | −0.449069 | − | 0.893497i | \(-0.648244\pi\) | ||||
−0.449069 | + | 0.893497i | \(0.648244\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 71.0204 | − | 71.0204i | 2.29576 | − | 2.29576i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.1156 | −0.649567 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3614 | −0.979399 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.32450 | − | 7.32450i | 0.236029 | − | 0.236029i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.9640 | −1.34947 | −0.674735 | − | 0.738060i | \(-0.735742\pi\) | ||||
−0.674735 | + | 0.738060i | \(0.735742\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.4614i | 1.58893i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.0549 | + | 30.0549i | −0.964508 | + | 0.964508i | −0.999391 | − | 0.0348833i | \(-0.988894\pi\) |
0.0348833 | + | 0.999391i | \(0.488894\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.32990 | + | 4.32990i | −0.138810 | + | 0.138810i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.3389i | 1.41853i | 0.704944 | + | 0.709263i | \(0.250972\pi\) | ||||
−0.704944 | + | 0.709263i | \(0.749028\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.2800 | + | 33.2800i | 1.06363 | + | 1.06363i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.1539 | − | 29.1539i | 0.930814 | − | 0.930814i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.0764 | 0.863604 | 0.431802 | − | 0.901968i | \(-0.357878\pi\) | ||||
0.431802 | + | 0.901968i | \(0.357878\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.76323 | + | 4.76323i | 0.151615 | + | 0.151615i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.29606 | − | 6.29606i | −0.200203 | − | 0.200203i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.3780 | −0.615564 | −0.307782 | − | 0.951457i | \(-0.599587\pi\) | ||||
−0.307782 | + | 0.951457i | \(0.599587\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 32.6977i | − | 1.03763i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.69453 | + | 8.69453i | 0.275359 | + | 0.275359i | 0.831253 | − | 0.555894i | \(-0.187624\pi\) |
−0.555894 | + | 0.831253i | \(0.687624\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 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 | 1600.2.q.f.849.1 | 12 | ||
4.3 | odd | 2 | 400.2.q.f.349.5 | 12 | |||
5.2 | odd | 4 | 1600.2.l.f.401.6 | 12 | |||
5.3 | odd | 4 | 1600.2.l.g.401.1 | 12 | |||
5.4 | even | 2 | 1600.2.q.e.849.6 | 12 | |||
16.5 | even | 4 | 1600.2.q.e.49.6 | 12 | |||
16.11 | odd | 4 | 400.2.q.e.149.2 | 12 | |||
20.3 | even | 4 | 400.2.l.f.301.3 | yes | 12 | ||
20.7 | even | 4 | 400.2.l.g.301.4 | yes | 12 | ||
20.19 | odd | 2 | 400.2.q.e.349.2 | 12 | |||
80.27 | even | 4 | 400.2.l.g.101.4 | yes | 12 | ||
80.37 | odd | 4 | 1600.2.l.f.1201.6 | 12 | |||
80.43 | even | 4 | 400.2.l.f.101.3 | ✓ | 12 | ||
80.53 | odd | 4 | 1600.2.l.g.1201.1 | 12 | |||
80.59 | odd | 4 | 400.2.q.f.149.5 | 12 | |||
80.69 | even | 4 | inner | 1600.2.q.f.49.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.3 | ✓ | 12 | 80.43 | even | 4 | ||
400.2.l.f.301.3 | yes | 12 | 20.3 | even | 4 | ||
400.2.l.g.101.4 | yes | 12 | 80.27 | even | 4 | ||
400.2.l.g.301.4 | yes | 12 | 20.7 | even | 4 | ||
400.2.q.e.149.2 | 12 | 16.11 | odd | 4 | |||
400.2.q.e.349.2 | 12 | 20.19 | odd | 2 | |||
400.2.q.f.149.5 | 12 | 80.59 | odd | 4 | |||
400.2.q.f.349.5 | 12 | 4.3 | odd | 2 | |||
1600.2.l.f.401.6 | 12 | 5.2 | odd | 4 | |||
1600.2.l.f.1201.6 | 12 | 80.37 | odd | 4 | |||
1600.2.l.g.401.1 | 12 | 5.3 | odd | 4 | |||
1600.2.l.g.1201.1 | 12 | 80.53 | odd | 4 | |||
1600.2.q.e.49.6 | 12 | 16.5 | even | 4 | |||
1600.2.q.e.849.6 | 12 | 5.4 | even | 2 | |||
1600.2.q.f.49.1 | 12 | 80.69 | even | 4 | inner | ||
1600.2.q.f.849.1 | 12 | 1.1 | even | 1 | trivial |