Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(43,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.k (of order \(4\), degree \(2\), 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: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.18 | ||
Character | \(\chi\) | \(=\) | 700.43 |
Dual form | 700.2.k.b.407.18 |
$q$-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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38250 | + | 0.297828i | 0.977573 | + | 0.210596i | ||||
\(3\) | 0.137886 | − | 0.137886i | 0.0796083 | − | 0.0796083i | −0.666181 | − | 0.745790i | \(-0.732072\pi\) |
0.745790 | + | 0.666181i | \(0.232072\pi\) | |||||||
\(4\) | 1.82260 | + | 0.823494i | 0.911298 | + | 0.411747i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.231693 | − | 0.149560i | 0.0945882 | − | 0.0610577i | ||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | 2.27447 | + | 1.68130i | 0.804148 | + | 0.594429i | ||||
\(9\) | 2.96198i | 0.987325i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.12749i | 0.942974i | 0.881873 | + | 0.471487i | \(0.156283\pi\) | ||||
−0.881873 | + | 0.471487i | \(0.843717\pi\) | |||||||
\(12\) | 0.364858 | − | 0.137762i | 0.105325 | − | 0.0397684i | ||||
\(13\) | −2.50519 | − | 2.50519i | −0.694816 | − | 0.694816i | 0.268472 | − | 0.963288i | \(-0.413481\pi\) |
−0.963288 | + | 0.268472i | \(0.913481\pi\) | |||||||
\(14\) | 0.766977 | + | 1.18817i | 0.204983 | + | 0.317552i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.64372 | + | 3.00179i | 0.660929 | + | 0.750449i | ||||
\(17\) | −2.85846 | + | 2.85846i | −0.693278 | + | 0.693278i | −0.962952 | − | 0.269674i | \(-0.913084\pi\) |
0.269674 | + | 0.962952i | \(0.413084\pi\) | |||||||
\(18\) | −0.882160 | + | 4.09492i | −0.207927 | + | 0.965182i | ||||
\(19\) | 3.29172 | 0.755173 | 0.377587 | − | 0.925974i | \(-0.376754\pi\) | ||||
0.377587 | + | 0.925974i | \(0.376754\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.195000 | 0.0425524 | ||||||||
\(22\) | −0.931456 | + | 4.32375i | −0.198587 | + | 0.921826i | ||||
\(23\) | 6.43733 | − | 6.43733i | 1.34228 | − | 1.34228i | 0.448486 | − | 0.893790i | \(-0.351964\pi\) |
0.893790 | − | 0.448486i | \(-0.148036\pi\) | |||||||
\(24\) | 0.545444 | − | 0.0817904i | 0.111338 | − | 0.0166954i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.71731 | − | 4.20954i | −0.532908 | − | 0.825559i | ||||
\(27\) | 0.822071 | + | 0.822071i | 0.158208 | + | 0.158208i | ||||
\(28\) | 0.706472 | + | 1.87107i | 0.133511 | + | 0.353599i | ||||
\(29\) | − | 3.55957i | − | 0.660996i | −0.943807 | − | 0.330498i | \(-0.892783\pi\) | ||
0.943807 | − | 0.330498i | \(-0.107217\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.67099i | − | 1.55735i | −0.627424 | − | 0.778677i | \(-0.715891\pi\) | ||
0.627424 | − | 0.778677i | \(-0.284109\pi\) | |||||||
\(32\) | 2.76091 | + | 4.93735i | 0.488064 | + | 0.872808i | ||||
\(33\) | 0.431236 | + | 0.431236i | 0.0750686 | + | 0.0750686i | ||||
\(34\) | −4.80314 | + | 3.10048i | −0.823732 | + | 0.531728i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.43917 | + | 5.39849i | −0.406528 | + | 0.899748i | ||||
\(37\) | −3.64472 | + | 3.64472i | −0.599189 | + | 0.599189i | −0.940097 | − | 0.340908i | \(-0.889266\pi\) |
0.340908 | + | 0.940097i | \(0.389266\pi\) | |||||||
\(38\) | 4.55080 | + | 0.980369i | 0.738237 | + | 0.159037i | ||||
\(39\) | −0.690861 | −0.110626 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.66648 | 0.260260 | 0.130130 | − | 0.991497i | \(-0.458461\pi\) | ||||
0.130130 | + | 0.991497i | \(0.458461\pi\) | |||||||
\(42\) | 0.269587 | + | 0.0580765i | 0.0415981 | + | 0.00896139i | ||||
\(43\) | −1.17838 | + | 1.17838i | −0.179701 | + | 0.179701i | −0.791225 | − | 0.611525i | \(-0.790557\pi\) |
0.611525 | + | 0.791225i | \(0.290557\pi\) | |||||||
\(44\) | −2.57547 | + | 5.70015i | −0.388267 | + | 0.859331i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.8168 | − | 6.98237i | 1.59485 | − | 1.02949i | ||||
\(47\) | −0.598252 | − | 0.598252i | −0.0872640 | − | 0.0872640i | 0.662127 | − | 0.749391i | \(-0.269654\pi\) |
−0.749391 | + | 0.662127i | \(0.769654\pi\) | |||||||
\(48\) | 0.778435 | + | 0.0493739i | 0.112357 | + | 0.00712650i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.788281i | 0.110381i | ||||||||
\(52\) | −2.50295 | − | 6.62897i | −0.347096 | − | 0.919273i | ||||
\(53\) | 1.12536 | + | 1.12536i | 0.154580 | + | 0.154580i | 0.780160 | − | 0.625580i | \(-0.215138\pi\) |
−0.625580 | + | 0.780160i | \(0.715138\pi\) | |||||||
\(54\) | 0.891674 | + | 1.38135i | 0.121342 | + | 0.187977i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.419438 | + | 2.79715i | 0.0560498 | + | 0.373785i | ||||
\(57\) | 0.453882 | − | 0.453882i | 0.0601181 | − | 0.0601181i | ||||
\(58\) | 1.06014 | − | 4.92110i | 0.139203 | − | 0.646172i | ||||
\(59\) | 10.4032 | 1.35438 | 0.677189 | − | 0.735810i | \(-0.263198\pi\) | ||||
0.677189 | + | 0.735810i | \(0.263198\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.81629 | −0.872736 | −0.436368 | − | 0.899768i | \(-0.643735\pi\) | ||||
−0.436368 | + | 0.899768i | \(0.643735\pi\) | |||||||
\(62\) | 2.58247 | − | 11.9876i | 0.327973 | − | 1.52243i | ||||
\(63\) | −2.09443 | + | 2.09443i | −0.263874 | + | 0.263874i | ||||
\(64\) | 2.34647 | + | 7.64814i | 0.293308 | + | 0.956018i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.467748 | + | 0.724617i | 0.0575758 | + | 0.0891942i | ||||
\(67\) | −6.83728 | − | 6.83728i | −0.835307 | − | 0.835307i | 0.152930 | − | 0.988237i | \(-0.451129\pi\) |
−0.988237 | + | 0.152930i | \(0.951129\pi\) | |||||||
\(68\) | −7.56374 | + | 2.85589i | −0.917238 | + | 0.346328i | ||||
\(69\) | − | 1.77523i | − | 0.213713i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.15952i | − | 0.374966i | −0.982268 | − | 0.187483i | \(-0.939967\pi\) | ||
0.982268 | − | 0.187483i | \(-0.0600329\pi\) | |||||||
\(72\) | −4.97997 | + | 6.73694i | −0.586895 | + | 0.793956i | ||||
\(73\) | −6.00943 | − | 6.00943i | −0.703351 | − | 0.703351i | 0.261778 | − | 0.965128i | \(-0.415691\pi\) |
−0.965128 | + | 0.261778i | \(0.915691\pi\) | |||||||
\(74\) | −6.12432 | + | 3.95332i | −0.711938 | + | 0.459564i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.99949 | + | 2.71072i | 0.688188 | + | 0.310940i | ||||
\(77\) | −2.21147 | + | 2.21147i | −0.252020 | + | 0.252020i | ||||
\(78\) | −0.955113 | − | 0.205758i | −0.108145 | − | 0.0232975i | ||||
\(79\) | 0.153472 | 0.0172670 | 0.00863348 | − | 0.999963i | \(-0.497252\pi\) | ||||
0.00863348 | + | 0.999963i | \(0.497252\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.65922 | −0.962136 | ||||||||
\(82\) | 2.30390 | + | 0.496324i | 0.254423 | + | 0.0548098i | ||||
\(83\) | −8.57229 | + | 8.57229i | −0.940931 | + | 0.940931i | −0.998350 | − | 0.0574191i | \(-0.981713\pi\) |
0.0574191 | + | 0.998350i | \(0.481713\pi\) | |||||||
\(84\) | 0.355406 | + | 0.160581i | 0.0387780 | + | 0.0175208i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.98006 | + | 1.27815i | −0.213515 | + | 0.137826i | ||||
\(87\) | −0.490814 | − | 0.490814i | −0.0526208 | − | 0.0526208i | ||||
\(88\) | −5.25825 | + | 7.11340i | −0.560531 | + | 0.758291i | ||||
\(89\) | − | 17.4053i | − | 1.84496i | −0.386047 | − | 0.922479i | \(-0.626160\pi\) | ||
0.386047 | − | 0.922479i | \(-0.373840\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.54288i | − | 0.371395i | ||||||
\(92\) | 17.0338 | − | 6.43155i | 1.77589 | − | 0.670536i | ||||
\(93\) | −1.19560 | − | 1.19560i | −0.123978 | − | 0.123978i | ||||
\(94\) | −0.648905 | − | 1.00526i | −0.0669295 | − | 0.103684i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.06148 | + | 0.300099i | 0.108337 | + | 0.0306287i | ||||
\(97\) | −2.28422 | + | 2.28422i | −0.231927 | + | 0.231927i | −0.813497 | − | 0.581569i | \(-0.802439\pi\) |
0.581569 | + | 0.813497i | \(0.302439\pi\) | |||||||
\(98\) | −0.297828 | + | 1.38250i | −0.0300852 | + | 0.139653i | ||||
\(99\) | −9.26355 | −0.931022 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.41332 | 0.538645 | 0.269323 | − | 0.963050i | \(-0.413200\pi\) | ||||
0.269323 | + | 0.963050i | \(0.413200\pi\) | |||||||
\(102\) | −0.234772 | + | 1.08980i | −0.0232459 | + | 0.107906i | ||||
\(103\) | 10.1362 | − | 10.1362i | 0.998747 | − | 0.998747i | −0.00125245 | − | 0.999999i | \(-0.500399\pi\) |
0.999999 | + | 0.00125245i | \(0.000398668\pi\) | |||||||
\(104\) | −1.48602 | − | 9.90998i | −0.145716 | − | 0.971754i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.22064 | + | 1.89097i | 0.118559 | + | 0.183668i | ||||
\(107\) | −6.05492 | − | 6.05492i | −0.585352 | − | 0.585352i | 0.351017 | − | 0.936369i | \(-0.385836\pi\) |
−0.936369 | + | 0.351017i | \(0.885836\pi\) | |||||||
\(108\) | 0.821333 | + | 2.17527i | 0.0790328 | + | 0.209316i | ||||
\(109\) | 8.01732i | 0.767920i | 0.923350 | + | 0.383960i | \(0.125440\pi\) | ||||
−0.923350 | + | 0.383960i | \(0.874560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.00511i | 0.0954009i | ||||||||
\(112\) | −0.253200 | + | 3.99198i | −0.0239251 | + | 0.377206i | ||||
\(113\) | −2.96906 | − | 2.96906i | −0.279306 | − | 0.279306i | 0.553526 | − | 0.832832i | \(-0.313282\pi\) |
−0.832832 | + | 0.553526i | \(0.813282\pi\) | |||||||
\(114\) | 0.762669 | − | 0.492311i | 0.0714305 | − | 0.0461092i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.93129 | − | 6.48766i | 0.272163 | − | 0.602364i | ||||
\(117\) | 7.42032 | − | 7.42032i | 0.686009 | − | 0.686009i | ||||
\(118\) | 14.3823 | + | 3.09836i | 1.32400 | + | 0.285227i | ||||
\(119\) | −4.04247 | −0.370573 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.21880 | 0.110800 | ||||||||
\(122\) | −9.42350 | − | 2.03008i | −0.853163 | − | 0.183795i | ||||
\(123\) | 0.229783 | − | 0.229783i | 0.0207188 | − | 0.0207188i | ||||
\(124\) | 7.14050 | − | 15.8037i | 0.641236 | − | 1.41921i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.51933 | + | 2.27177i | −0.313527 | + | 0.202385i | ||||
\(127\) | 5.46545 | + | 5.46545i | 0.484981 | + | 0.484981i | 0.906718 | − | 0.421737i | \(-0.138580\pi\) |
−0.421737 | + | 0.906718i | \(0.638580\pi\) | |||||||
\(128\) | 0.966151 | + | 11.2724i | 0.0853965 | + | 0.996347i | ||||
\(129\) | 0.324962i | 0.0286113i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.22936i | 0.107410i | 0.998557 | + | 0.0537051i | \(0.0171031\pi\) | ||||
−0.998557 | + | 0.0537051i | \(0.982897\pi\) | |||||||
\(132\) | 0.430849 | + | 1.14109i | 0.0375006 | + | 0.0993191i | ||||
\(133\) | 2.32760 | + | 2.32760i | 0.201829 | + | 0.201829i | ||||
\(134\) | −7.41619 | − | 11.4889i | −0.640661 | − | 0.992486i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.3074 | + | 1.69557i | −0.969603 | + | 0.145394i | ||||
\(137\) | 3.17885 | − | 3.17885i | 0.271587 | − | 0.271587i | −0.558152 | − | 0.829739i | \(-0.688489\pi\) |
0.829739 | + | 0.558152i | \(0.188489\pi\) | |||||||
\(138\) | 0.528714 | − | 2.45425i | 0.0450071 | − | 0.208920i | ||||
\(139\) | 1.28774 | 0.109225 | 0.0546125 | − | 0.998508i | \(-0.482608\pi\) | ||||
0.0546125 | + | 0.998508i | \(0.482608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.164981 | −0.0138939 | ||||||||
\(142\) | 0.940994 | − | 4.36802i | 0.0789665 | − | 0.366556i | ||||
\(143\) | 7.83498 | − | 7.83498i | 0.655194 | − | 0.655194i | ||||
\(144\) | −8.89124 | + | 7.83062i | −0.740937 | + | 0.652552i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.51824 | − | 10.0978i | −0.539454 | − | 0.835700i | ||||
\(147\) | 0.137886 | + | 0.137886i | 0.0113726 | + | 0.0113726i | ||||
\(148\) | −9.64427 | + | 3.64145i | −0.792754 | + | 0.299326i | ||||
\(149\) | − | 9.87336i | − | 0.808857i | −0.914570 | − | 0.404429i | \(-0.867470\pi\) | ||
0.914570 | − | 0.404429i | \(-0.132530\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.1711i | 1.88564i | 0.333308 | + | 0.942818i | \(0.391835\pi\) | ||||
−0.333308 | + | 0.942818i | \(0.608165\pi\) | |||||||
\(152\) | 7.48694 | + | 5.53437i | 0.607271 | + | 0.448897i | ||||
\(153\) | −8.46668 | − | 8.46668i | −0.684491 | − | 0.684491i | ||||
\(154\) | −3.71599 | + | 2.39871i | −0.299443 | + | 0.193294i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.25916 | − | 0.568920i | −0.100814 | − | 0.0455500i | ||||
\(157\) | −3.47358 | + | 3.47358i | −0.277222 | + | 0.277222i | −0.831999 | − | 0.554777i | \(-0.812804\pi\) |
0.554777 | + | 0.831999i | \(0.312804\pi\) | |||||||
\(158\) | 0.212175 | + | 0.0457084i | 0.0168797 | + | 0.00363636i | ||||
\(159\) | 0.310342 | 0.0246117 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.10376 | 0.717477 | ||||||||
\(162\) | −11.9713 | − | 2.57896i | −0.940558 | − | 0.202622i | ||||
\(163\) | −1.51463 | + | 1.51463i | −0.118635 | + | 0.118635i | −0.763932 | − | 0.645297i | \(-0.776734\pi\) |
0.645297 | + | 0.763932i | \(0.276734\pi\) | |||||||
\(164\) | 3.03731 | + | 1.37233i | 0.237174 | + | 0.107161i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4042 | + | 9.29809i | −1.11799 | + | 0.721672i | ||||
\(167\) | 9.86696 | + | 9.86696i | 0.763528 | + | 0.763528i | 0.976958 | − | 0.213430i | \(-0.0684636\pi\) |
−0.213430 | + | 0.976958i | \(0.568464\pi\) | |||||||
\(168\) | 0.443522 | + | 0.327853i | 0.0342185 | + | 0.0252944i | ||||
\(169\) | − | 0.447999i | − | 0.0344614i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.75001i | 0.745602i | ||||||||
\(172\) | −3.11809 | + | 1.17732i | −0.237752 | + | 0.0897697i | ||||
\(173\) | −9.97554 | − | 9.97554i | −0.758426 | − | 0.758426i | 0.217610 | − | 0.976036i | \(-0.430174\pi\) |
−0.976036 | + | 0.217610i | \(0.930174\pi\) | |||||||
\(174\) | −0.532370 | − | 0.824727i | −0.0403589 | − | 0.0625224i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.38808 | + | 8.26820i | −0.707654 | + | 0.623239i | ||||
\(177\) | 1.43445 | − | 1.43445i | 0.107820 | − | 0.107820i | ||||
\(178\) | 5.18379 | − | 24.0628i | 0.388542 | − | 1.80358i | ||||
\(179\) | −4.67593 | −0.349495 | −0.174748 | − | 0.984613i | \(-0.555911\pi\) | ||||
−0.174748 | + | 0.984613i | \(0.555911\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.2503 | −1.35654 | −0.678268 | − | 0.734815i | \(-0.737269\pi\) | ||||
−0.678268 | + | 0.734815i | \(0.737269\pi\) | |||||||
\(182\) | 1.05517 | − | 4.89802i | 0.0782144 | − | 0.363066i | ||||
\(183\) | −0.939868 | + | 0.939868i | −0.0694770 | + | 0.0694770i | ||||
\(184\) | 25.4646 | − | 3.81847i | 1.87728 | − | 0.281501i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.29683 | − | 2.00900i | −0.0950885 | − | 0.147307i | ||||
\(187\) | −8.93980 | − | 8.93980i | −0.653743 | − | 0.653743i | ||||
\(188\) | −0.597715 | − | 1.58303i | −0.0435929 | − | 0.115454i | ||||
\(189\) | 1.16258i | 0.0845655i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 18.6406i | − | 1.34879i | −0.738371 | − | 0.674395i | \(-0.764405\pi\) | ||
0.738371 | − | 0.674395i | \(-0.235595\pi\) | |||||||
\(192\) | 1.37811 | + | 0.731025i | 0.0994568 | + | 0.0527572i | ||||
\(193\) | 7.81768 | + | 7.81768i | 0.562729 | + | 0.562729i | 0.930082 | − | 0.367353i | \(-0.119736\pi\) |
−0.367353 | + | 0.930082i | \(0.619736\pi\) | |||||||
\(194\) | −3.83823 | + | 2.47762i | −0.275569 | + | 0.177883i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.823494 | + | 1.82260i | −0.0588210 | + | 0.130185i | ||||
\(197\) | 5.27851 | − | 5.27851i | 0.376078 | − | 0.376078i | −0.493607 | − | 0.869685i | \(-0.664322\pi\) |
0.869685 | + | 0.493607i | \(0.164322\pi\) | |||||||
\(198\) | −12.8068 | − | 2.75895i | −0.910142 | − | 0.196070i | ||||
\(199\) | −0.716716 | −0.0508067 | −0.0254033 | − | 0.999677i | \(-0.508087\pi\) | ||||
−0.0254033 | + | 0.999677i | \(0.508087\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.88553 | −0.132995 | ||||||||
\(202\) | 7.48390 | + | 1.61224i | 0.526565 | + | 0.113437i | ||||
\(203\) | 2.51700 | − | 2.51700i | 0.176659 | − | 0.176659i | ||||
\(204\) | −0.649144 | + | 1.43672i | −0.0454492 | + | 0.100590i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.0321 | − | 10.9944i | 1.18668 | − | 0.766015i | ||||
\(207\) | 19.0672 | + | 19.0672i | 1.32526 | + | 1.32526i | ||||
\(208\) | 0.897056 | − | 14.1431i | 0.0621996 | − | 0.980648i | ||||
\(209\) | 10.2948i | 0.712109i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 9.81937i | − | 0.675994i | −0.941147 | − | 0.337997i | \(-0.890251\pi\) | ||
0.941147 | − | 0.337997i | \(-0.109749\pi\) | |||||||
\(212\) | 1.12435 | + | 2.97781i | 0.0772208 | + | 0.204517i | ||||
\(213\) | −0.435652 | − | 0.435652i | −0.0298504 | − | 0.0298504i | ||||
\(214\) | −6.56759 | − | 10.1742i | −0.448951 | − | 0.695497i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.487632 | + | 3.25193i | 0.0331792 | + | 0.221265i | ||||
\(217\) | 6.13131 | − | 6.13131i | 0.416221 | − | 0.416221i | ||||
\(218\) | −2.38779 | + | 11.0839i | −0.161721 | + | 0.750698i | ||||
\(219\) | −1.65723 | −0.111985 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.3220 | 0.963401 | ||||||||
\(222\) | −0.299350 | + | 1.38956i | −0.0200911 | + | 0.0932613i | ||||
\(223\) | −13.7246 | + | 13.7246i | −0.919066 | + | 0.919066i | −0.996962 | − | 0.0778955i | \(-0.975180\pi\) |
0.0778955 | + | 0.996962i | \(0.475180\pi\) | |||||||
\(224\) | −1.53897 | + | 5.44349i | −0.102827 | + | 0.363708i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.22045 | − | 4.98899i | −0.214221 | − | 0.331862i | ||||
\(227\) | −8.05232 | − | 8.05232i | −0.534451 | − | 0.534451i | 0.387443 | − | 0.921894i | \(-0.373359\pi\) |
−0.921894 | + | 0.387443i | \(0.873359\pi\) | |||||||
\(228\) | 1.20101 | − | 0.453474i | 0.0795389 | − | 0.0300321i | ||||
\(229\) | 12.7874i | 0.845017i | 0.906359 | + | 0.422508i | \(0.138850\pi\) | ||||
−0.906359 | + | 0.422508i | \(0.861150\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.609860i | 0.0401258i | ||||||||
\(232\) | 5.98470 | − | 8.09616i | 0.392915 | − | 0.531539i | ||||
\(233\) | 15.5244 | + | 15.5244i | 1.01704 | + | 1.01704i | 0.999852 | + | 0.0171872i | \(0.00547113\pi\) |
0.0171872 | + | 0.999852i | \(0.494529\pi\) | |||||||
\(234\) | 12.4686 | − | 8.04859i | 0.815095 | − | 0.526153i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 18.9608 | + | 8.56694i | 1.23424 | + | 0.557661i | ||||
\(237\) | 0.0211616 | − | 0.0211616i | 0.00137459 | − | 0.00137459i | ||||
\(238\) | −5.58870 | − | 1.20396i | −0.362262 | − | 0.0780413i | ||||
\(239\) | 2.29513 | 0.148459 | 0.0742297 | − | 0.997241i | \(-0.476350\pi\) | ||||
0.0742297 | + | 0.997241i | \(0.476350\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.7343 | −1.14236 | −0.571182 | − | 0.820823i | \(-0.693515\pi\) | ||||
−0.571182 | + | 0.820823i | \(0.693515\pi\) | |||||||
\(242\) | 1.68498 | + | 0.362993i | 0.108315 | + | 0.0233340i | ||||
\(243\) | −3.66019 | + | 3.66019i | −0.234802 | + | 0.234802i | ||||
\(244\) | −12.4233 | − | 5.61317i | −0.795323 | − | 0.359346i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.386110 | − | 0.249238i | 0.0246175 | − | 0.0158909i | ||||
\(247\) | −8.24641 | − | 8.24641i | −0.524707 | − | 0.524707i | ||||
\(248\) | 14.5785 | − | 19.7219i | 0.925737 | − | 1.25234i | ||||
\(249\) | 2.36399i | 0.149812i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.4484i | 1.79565i | 0.440354 | + | 0.897824i | \(0.354853\pi\) | ||||
−0.440354 | + | 0.897824i | \(0.645147\pi\) | |||||||
\(252\) | −5.54206 | + | 2.09255i | −0.349117 | + | 0.131818i | ||||
\(253\) | 20.1327 | + | 20.1327i | 1.26573 | + | 1.26573i | ||||
\(254\) | 5.92821 | + | 9.18374i | 0.371969 | + | 0.576239i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.02153 | + | 15.8718i | −0.126346 | + | 0.991986i | ||||
\(257\) | 2.62467 | − | 2.62467i | 0.163722 | − | 0.163722i | −0.620491 | − | 0.784214i | \(-0.713067\pi\) |
0.784214 | + | 0.620491i | \(0.213067\pi\) | |||||||
\(258\) | −0.0967830 | + | 0.449259i | −0.00602545 | + | 0.0279697i | ||||
\(259\) | −5.15442 | −0.320280 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.5434 | 0.652618 | ||||||||
\(262\) | −0.366140 | + | 1.69959i | −0.0226202 | + | 0.105001i | ||||
\(263\) | −14.6752 | + | 14.6752i | −0.904912 | + | 0.904912i | −0.995856 | − | 0.0909438i | \(-0.971012\pi\) |
0.0909438 | + | 0.995856i | \(0.471012\pi\) | |||||||
\(264\) | 0.255799 | + | 1.70587i | 0.0157433 | + | 0.104989i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.52468 | + | 3.91113i | 0.154798 | + | 0.239807i | ||||
\(267\) | −2.39994 | − | 2.39994i | −0.146874 | − | 0.146874i | ||||
\(268\) | −6.83115 | − | 18.0921i | −0.417279 | − | 1.10515i | ||||
\(269\) | − | 11.7355i | − | 0.715529i | −0.933812 | − | 0.357764i | \(-0.883539\pi\) | ||
0.933812 | − | 0.357764i | \(-0.116461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 21.0504i | − | 1.27872i | −0.768907 | − | 0.639361i | \(-0.779199\pi\) | ||
0.768907 | − | 0.639361i | \(-0.220801\pi\) | |||||||
\(272\) | −16.1375 | − | 1.02355i | −0.978477 | − | 0.0620619i | ||||
\(273\) | −0.488512 | − | 0.488512i | −0.0295661 | − | 0.0295661i | ||||
\(274\) | 5.34150 | − | 3.44800i | 0.322692 | − | 0.208301i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.46189 | − | 3.23553i | 0.0879955 | − | 0.194756i | ||||
\(277\) | −9.30733 | + | 9.30733i | −0.559223 | + | 0.559223i | −0.929086 | − | 0.369863i | \(-0.879405\pi\) |
0.369863 | + | 0.929086i | \(0.379405\pi\) | |||||||
\(278\) | 1.78030 | + | 0.383527i | 0.106775 | + | 0.0230024i | ||||
\(279\) | 25.6832 | 1.53762 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.2003 | 0.966427 | 0.483214 | − | 0.875502i | \(-0.339469\pi\) | ||||
0.483214 | + | 0.875502i | \(0.339469\pi\) | |||||||
\(282\) | −0.228085 | − | 0.0491360i | −0.0135823 | − | 0.00292600i | ||||
\(283\) | 8.04576 | − | 8.04576i | 0.478271 | − | 0.478271i | −0.426307 | − | 0.904578i | \(-0.640186\pi\) |
0.904578 | + | 0.426307i | \(0.140186\pi\) | |||||||
\(284\) | 2.60184 | − | 5.75852i | 0.154391 | − | 0.341706i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.1653 | − | 8.49835i | 0.778481 | − | 0.502518i | ||||
\(287\) | 1.17838 | + | 1.17838i | 0.0695573 | + | 0.0695573i | ||||
\(288\) | −14.6243 | + | 8.17775i | −0.861745 | + | 0.481878i | ||||
\(289\) | 0.658435i | 0.0387314i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.629922i | 0.0369267i | ||||||||
\(292\) | −6.00404 | − | 15.9015i | −0.351360 | − | 0.930565i | ||||
\(293\) | 18.5783 | + | 18.5783i | 1.08536 | + | 1.08536i | 0.996000 | + | 0.0893564i | \(0.0284810\pi\) |
0.0893564 | + | 0.996000i | \(0.471519\pi\) | |||||||
\(294\) | 0.149560 | + | 0.231693i | 0.00872253 | + | 0.0135126i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −14.4177 | + | 2.16196i | −0.838012 | + | 0.125661i | ||||
\(297\) | −2.57102 | + | 2.57102i | −0.149186 | + | 0.149186i | ||||
\(298\) | 2.94057 | − | 13.6499i | 0.170343 | − | 0.790717i | ||||
\(299\) | −32.2535 | −1.86527 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.66648 | −0.0960540 | ||||||||
\(302\) | −6.90101 | + | 32.0340i | −0.397108 | + | 1.84335i | ||||
\(303\) | 0.746419 | − | 0.746419i | 0.0428807 | − | 0.0428807i | ||||
\(304\) | 8.70238 | + | 9.88108i | 0.499116 | + | 0.566719i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.18354 | − | 14.2268i | −0.524988 | − | 0.813291i | ||||
\(307\) | 11.1792 | + | 11.1792i | 0.638033 | + | 0.638033i | 0.950070 | − | 0.312037i | \(-0.101011\pi\) |
−0.312037 | + | 0.950070i | \(0.601011\pi\) | |||||||
\(308\) | −5.85175 | + | 2.20949i | −0.333434 | + | 0.125897i | ||||
\(309\) | − | 2.79527i | − | 0.159017i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.61486i | 0.204980i | 0.994734 | + | 0.102490i | \(0.0326810\pi\) | ||||
−0.994734 | + | 0.102490i | \(0.967319\pi\) | |||||||
\(312\) | −1.57135 | − | 1.16154i | −0.0889599 | − | 0.0657594i | ||||
\(313\) | 15.5668 | + | 15.5668i | 0.879888 | + | 0.879888i | 0.993523 | − | 0.113635i | \(-0.0362494\pi\) |
−0.113635 | + | 0.993523i | \(0.536249\pi\) | |||||||
\(314\) | −5.83674 | + | 3.76768i | −0.329387 | + | 0.212623i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.279718 | + | 0.126383i | 0.0157353 | + | 0.00710962i | ||||
\(317\) | 14.4642 | − | 14.4642i | 0.812389 | − | 0.812389i | −0.172602 | − | 0.984992i | \(-0.555218\pi\) |
0.984992 | + | 0.172602i | \(0.0552175\pi\) | |||||||
\(318\) | 0.429047 | + | 0.0924287i | 0.0240598 | + | 0.00518315i | ||||
\(319\) | 11.1325 | 0.623302 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.66977 | −0.0931977 | ||||||||
\(322\) | 12.5859 | + | 2.71136i | 0.701386 | + | 0.151098i | ||||
\(323\) | −9.40926 | + | 9.40926i | −0.523545 | + | 0.523545i | ||||
\(324\) | −15.7823 | − | 7.13082i | −0.876793 | − | 0.396156i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.54507 | + | 1.64287i | −0.140958 | + | 0.0909902i | ||||
\(327\) | 1.10547 | + | 1.10547i | 0.0611328 | + | 0.0611328i | ||||
\(328\) | 3.79036 | + | 2.80184i | 0.209287 | + | 0.154706i | ||||
\(329\) | − | 0.846056i | − | 0.0466446i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20.9381i | − | 1.15086i | −0.817851 | − | 0.575430i | \(-0.804835\pi\) | ||
0.817851 | − | 0.575430i | \(-0.195165\pi\) | |||||||
\(332\) | −22.6831 | + | 8.56460i | −1.24489 | + | 0.470043i | ||||
\(333\) | −10.7956 | − | 10.7956i | −0.591594 | − | 0.591594i | ||||
\(334\) | 10.7024 | + | 16.5797i | 0.585608 | + | 0.907201i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.515524 | + | 0.585349i | 0.0281241 | + | 0.0319334i | ||||
\(337\) | 6.60024 | − | 6.60024i | 0.359538 | − | 0.359538i | −0.504104 | − | 0.863643i | \(-0.668177\pi\) |
0.863643 | + | 0.504104i | \(0.168177\pi\) | |||||||
\(338\) | 0.133427 | − | 0.619357i | 0.00725746 | − | 0.0336886i | ||||
\(339\) | −0.818781 | −0.0444701 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.1184 | 1.46855 | ||||||||
\(342\) | −2.90383 | + | 13.4794i | −0.157021 | + | 0.728880i | ||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | −4.66139 | + | 0.698984i | −0.251325 | + | 0.0376867i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.8202 | − | 16.7622i | −0.581695 | − | 0.901139i | ||||
\(347\) | 9.72907 | + | 9.72907i | 0.522284 | + | 0.522284i | 0.918261 | − | 0.395977i | \(-0.129594\pi\) |
−0.395977 | + | 0.918261i | \(0.629594\pi\) | |||||||
\(348\) | −0.490373 | − | 1.29874i | −0.0262868 | − | 0.0696197i | ||||
\(349\) | 26.2310i | 1.40411i | 0.712121 | + | 0.702057i | \(0.247735\pi\) | ||||
−0.712121 | + | 0.702057i | \(0.752265\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.11889i | − | 0.219850i | ||||||
\(352\) | −15.4415 | + | 8.63472i | −0.823035 | + | 0.460232i | ||||
\(353\) | −6.56094 | − | 6.56094i | −0.349203 | − | 0.349203i | 0.510609 | − | 0.859813i | \(-0.329420\pi\) |
−0.859813 | + | 0.510609i | \(0.829420\pi\) | |||||||
\(354\) | 2.41034 | − | 1.55590i | 0.128108 | − | 0.0826952i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.3332 | − | 31.7228i | 0.759656 | − | 1.68131i | ||||
\(357\) | −0.557399 | + | 0.557399i | −0.0295007 | + | 0.0295007i | ||||
\(358\) | −6.46445 | − | 1.39262i | −0.341657 | − | 0.0736024i | ||||
\(359\) | −1.22428 | −0.0646151 | −0.0323076 | − | 0.999478i | \(-0.510286\pi\) | ||||
−0.0323076 | + | 0.999478i | \(0.510286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.16455 | −0.429713 | ||||||||
\(362\) | −25.2310 | − | 5.43546i | −1.32611 | − | 0.285682i | ||||
\(363\) | 0.168055 | − | 0.168055i | 0.00882058 | − | 0.00882058i | ||||
\(364\) | 2.91754 | − | 6.45724i | 0.152921 | − | 0.338451i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.57928 | + | 1.01945i | −0.0825505 | + | 0.0532873i | ||||
\(367\) | −2.79961 | − | 2.79961i | −0.146138 | − | 0.146138i | 0.630252 | − | 0.776391i | \(-0.282952\pi\) |
−0.776391 | + | 0.630252i | \(0.782952\pi\) | |||||||
\(368\) | 36.3420 | + | 2.30507i | 1.89446 | + | 0.120160i | ||||
\(369\) | 4.93606i | 0.256961i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.59150i | 0.0826266i | ||||||||
\(372\) | −1.19453 | − | 3.16368i | −0.0619336 | − | 0.164029i | ||||
\(373\) | −14.2337 | − | 14.2337i | −0.736993 | − | 0.736993i | 0.235002 | − | 0.971995i | \(-0.424490\pi\) |
−0.971995 | + | 0.235002i | \(0.924490\pi\) | |||||||
\(374\) | −9.69672 | − | 15.0218i | −0.501406 | − | 0.776758i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.354869 | − | 2.36655i | −0.0183009 | − | 0.122045i | ||||
\(377\) | −8.91742 | + | 8.91742i | −0.459271 | + | 0.459271i | ||||
\(378\) | −0.346250 | + | 1.60727i | −0.0178092 | + | 0.0826690i | ||||
\(379\) | −30.5331 | −1.56838 | −0.784190 | − | 0.620521i | \(-0.786921\pi\) | ||||
−0.784190 | + | 0.620521i | \(0.786921\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.50722 | 0.0772170 | ||||||||
\(382\) | 5.55171 | − | 25.7706i | 0.284050 | − | 1.31854i | ||||
\(383\) | 5.16784 | − | 5.16784i | 0.264064 | − | 0.264064i | −0.562639 | − | 0.826703i | \(-0.690214\pi\) |
0.826703 | + | 0.562639i | \(0.190214\pi\) | |||||||
\(384\) | 1.68752 | + | 1.42108i | 0.0861158 | + | 0.0725192i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.47959 | + | 13.1363i | 0.431600 | + | 0.668618i | ||||
\(387\) | −3.49032 | − | 3.49032i | −0.177423 | − | 0.177423i | ||||
\(388\) | −6.04425 | + | 2.28217i | −0.306850 | + | 0.115860i | ||||
\(389\) | 31.5845i | 1.60140i | 0.599067 | + | 0.800699i | \(0.295538\pi\) | ||||
−0.599067 | + | 0.800699i | \(0.704462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.8017i | 1.86114i | ||||||||
\(392\) | −1.68130 | + | 2.27447i | −0.0849184 | + | 0.114878i | ||||
\(393\) | 0.169512 | + | 0.169512i | 0.00855074 | + | 0.00855074i | ||||
\(394\) | 8.86961 | − | 5.72543i | 0.446845 | − | 0.288443i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −16.8837 | − | 7.62848i | −0.848439 | − | 0.383345i | ||||
\(397\) | −16.7022 | + | 16.7022i | −0.838260 | + | 0.838260i | −0.988630 | − | 0.150370i | \(-0.951954\pi\) |
0.150370 | + | 0.988630i | \(0.451954\pi\) | |||||||
\(398\) | −0.990858 | − | 0.213459i | −0.0496672 | − | 0.0106997i | ||||
\(399\) | 0.641885 | 0.0321345 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.6522 | 0.831573 | 0.415787 | − | 0.909462i | \(-0.363506\pi\) | ||||
0.415787 | + | 0.909462i | \(0.363506\pi\) | |||||||
\(402\) | −2.60673 | − | 0.561563i | −0.130012 | − | 0.0280082i | ||||
\(403\) | −21.7225 | + | 21.7225i | −1.08208 | + | 1.08208i | ||||
\(404\) | 9.86630 | + | 4.45784i | 0.490867 | + | 0.221786i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.22938 | − | 2.73011i | 0.209900 | − | 0.135493i | ||||
\(407\) | −11.3988 | − | 11.3988i | −0.565020 | − | 0.565020i | ||||
\(408\) | −1.32534 | + | 1.79292i | −0.0656139 | + | 0.0887630i | ||||
\(409\) | 24.1043i | 1.19188i | 0.803029 | + | 0.595940i | \(0.203220\pi\) | ||||
−0.803029 | + | 0.595940i | \(0.796780\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 0.876636i | − | 0.0432412i | ||||||
\(412\) | 26.8212 | − | 10.1271i | 1.32139 | − | 0.498925i | ||||
\(413\) | 7.35615 | + | 7.35615i | 0.361973 | + | 0.361973i | ||||
\(414\) | 20.6816 | + | 32.0391i | 1.01645 | + | 1.57464i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.45239 | − | 19.2856i | 0.267326 | − | 0.945556i | ||||
\(417\) | 0.177561 | − | 0.177561i | 0.00869522 | − | 0.00869522i | ||||
\(418\) | −3.06610 | + | 14.2326i | −0.149968 | + | 0.696139i | ||||
\(419\) | −10.7316 | −0.524272 | −0.262136 | − | 0.965031i | \(-0.584427\pi\) | ||||
−0.262136 | + | 0.965031i | \(0.584427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.45571 | 0.460843 | 0.230422 | − | 0.973091i | \(-0.425989\pi\) | ||||
0.230422 | + | 0.973091i | \(0.425989\pi\) | |||||||
\(422\) | 2.92449 | − | 13.5753i | 0.142362 | − | 0.660833i | ||||
\(423\) | 1.77201 | − | 1.77201i | 0.0861580 | − | 0.0861580i | ||||
\(424\) | 0.667537 | + | 4.45167i | 0.0324184 | + | 0.216192i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.472538 | − | 0.732037i | −0.0228945 | − | 0.0354673i | ||||
\(427\) | −4.81984 | − | 4.81984i | −0.233249 | − | 0.233249i | ||||
\(428\) | −6.04949 | − | 16.0219i | −0.292413 | − | 0.774447i | ||||
\(429\) | − | 2.16066i | − | 0.104318i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 33.1577i | − | 1.59715i | −0.601894 | − | 0.798576i | \(-0.705587\pi\) | ||
0.601894 | − | 0.798576i | \(-0.294413\pi\) | |||||||
\(432\) | −0.294366 | + | 4.64101i | −0.0141627 | + | 0.223291i | ||||
\(433\) | −10.1337 | − | 10.1337i | −0.486995 | − | 0.486995i | 0.420362 | − | 0.907357i | \(-0.361903\pi\) |
−0.907357 | + | 0.420362i | \(0.861903\pi\) | |||||||
\(434\) | 10.3026 | − | 6.65044i | 0.494541 | − | 0.319231i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.60222 | + | 14.6123i | −0.316189 | + | 0.699805i | ||||
\(437\) | 21.1899 | − | 21.1899i | 1.01365 | − | 1.01365i | ||||
\(438\) | −2.29111 | − | 0.493570i | −0.109474 | − | 0.0235837i | ||||
\(439\) | 39.0061 | 1.86166 | 0.930829 | − | 0.365454i | \(-0.119086\pi\) | ||||
0.930829 | + | 0.365454i | \(0.119086\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.96198 | −0.141046 | ||||||||
\(442\) | 19.8001 | + | 4.26550i | 0.941795 | + | 0.202889i | ||||
\(443\) | 28.9618 | − | 28.9618i | 1.37601 | − | 1.37601i | 0.524772 | − | 0.851243i | \(-0.324151\pi\) |
0.851243 | − | 0.524772i | \(-0.175849\pi\) | |||||||
\(444\) | −0.827702 | + | 1.83191i | −0.0392810 | + | 0.0869386i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −23.0618 | + | 14.8866i | −1.09201 | + | 0.704902i | ||||
\(447\) | −1.36140 | − | 1.36140i | −0.0643918 | − | 0.0643918i | ||||
\(448\) | −3.74885 | + | 7.06726i | −0.177117 | + | 0.333897i | ||||
\(449\) | 30.0275i | 1.41709i | 0.705667 | + | 0.708544i | \(0.250648\pi\) | ||||
−0.705667 | + | 0.708544i | \(0.749352\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.21189i | 0.245418i | ||||||||
\(452\) | −2.96639 | − | 7.85640i | −0.139527 | − | 0.369534i | ||||
\(453\) | 3.19496 | + | 3.19496i | 0.150112 | + | 0.150112i | ||||
\(454\) | −8.73410 | − | 13.5305i | −0.409912 | − | 0.635019i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.79545 | − | 0.269231i | 0.0840798 | − | 0.0126079i | ||||
\(457\) | −13.4226 | + | 13.4226i | −0.627883 | + | 0.627883i | −0.947535 | − | 0.319652i | \(-0.896434\pi\) |
0.319652 | + | 0.947535i | \(0.396434\pi\) | |||||||
\(458\) | −3.80846 | + | 17.6786i | −0.177958 | + | 0.826066i | ||||
\(459\) | −4.69971 | −0.219364 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0109 | −1.11830 | −0.559150 | − | 0.829067i | \(-0.688872\pi\) | ||||
−0.559150 | + | 0.829067i | \(0.688872\pi\) | |||||||
\(462\) | −0.181634 | + | 0.843130i | −0.00845036 | + | 0.0392259i | ||||
\(463\) | 14.2733 | − | 14.2733i | 0.663337 | − | 0.663337i | −0.292828 | − | 0.956165i | \(-0.594596\pi\) |
0.956165 | + | 0.292828i | \(0.0945964\pi\) | |||||||
\(464\) | 10.6851 | − | 9.41050i | 0.496043 | − | 0.436871i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.8389 | + | 26.0861i | 0.780045 | + | 1.20842i | ||||
\(467\) | 21.3140 | + | 21.3140i | 0.986296 | + | 0.986296i | 0.999907 | − | 0.0136114i | \(-0.00433278\pi\) |
−0.0136114 | + | 0.999907i | \(0.504333\pi\) | |||||||
\(468\) | 19.6348 | − | 7.41367i | 0.907621 | − | 0.342697i | ||||
\(469\) | − | 9.66938i | − | 0.446490i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.957913i | 0.0441383i | ||||||||
\(472\) | 23.6617 | + | 17.4908i | 1.08912 | + | 0.805081i | ||||
\(473\) | −3.68536 | − | 3.68536i | −0.169453 | − | 0.169453i | ||||
\(474\) | 0.0355584 | − | 0.0229533i | 0.00163325 | − | 0.00105428i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.36779 | − | 3.32895i | −0.337702 | − | 0.152582i | ||||
\(477\) | −3.33329 | + | 3.33329i | −0.152621 | + | 0.152621i | ||||
\(478\) | 3.17301 | + | 0.683554i | 0.145130 | + | 0.0312650i | ||||
\(479\) | 41.3956 | 1.89142 | 0.945708 | − | 0.325019i | \(-0.105371\pi\) | ||||
0.945708 | + | 0.325019i | \(0.105371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.2615 | 0.832652 | ||||||||
\(482\) | −24.5176 | − | 5.28177i | −1.11674 | − | 0.240578i | ||||
\(483\) | 1.25528 | − | 1.25528i | 0.0571171 | − | 0.0571171i | ||||
\(484\) | 2.22138 | + | 1.00367i | 0.100972 | + | 0.0456215i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.15032 | + | 3.97010i | −0.278984 | + | 0.180087i | ||||
\(487\) | 1.60723 | + | 1.60723i | 0.0728304 | + | 0.0728304i | 0.742584 | − | 0.669753i | \(-0.233600\pi\) |
−0.669753 | + | 0.742584i | \(0.733600\pi\) | |||||||
\(488\) | −15.5035 | − | 11.4602i | −0.701809 | − | 0.518780i | ||||
\(489\) | 0.417691i | 0.0188887i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.1931i | 0.911303i | 0.890158 | + | 0.455652i | \(0.150594\pi\) | ||||
−0.890158 | + | 0.455652i | \(0.849406\pi\) | |||||||
\(492\) | 0.608027 | − | 0.229577i | 0.0274120 | − | 0.0103501i | ||||
\(493\) | 10.1749 | + | 10.1749i | 0.458254 | + | 0.458254i | ||||
\(494\) | −8.94462 | − | 13.8567i | −0.402438 | − | 0.623440i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.0285 | − | 22.9236i | 1.16871 | − | 1.02930i | ||||
\(497\) | 2.23412 | − | 2.23412i | 0.100214 | − | 0.100214i | ||||
\(498\) | −0.704064 | + | 3.26821i | −0.0315499 | + | 0.146452i | ||||
\(499\) | −27.6768 | −1.23898 | −0.619492 | − | 0.785003i | \(-0.712661\pi\) | ||||
−0.619492 | + | 0.785003i | \(0.712661\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.72102 | 0.121566 | ||||||||
\(502\) | −8.47275 | + | 39.3299i | −0.378157 | + | 1.75538i | ||||
\(503\) | 1.13993 | − | 1.13993i | 0.0508271 | − | 0.0508271i | −0.681236 | − | 0.732063i | \(-0.738557\pi\) |
0.732063 | + | 0.681236i | \(0.238557\pi\) | |||||||
\(504\) | −8.28510 | + | 1.24237i | −0.369048 | + | 0.0553394i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 21.8373 | + | 33.8295i | 0.970786 | + | 1.50390i | ||||
\(507\) | −0.0617726 | − | 0.0617726i | −0.00274342 | − | 0.00274342i | ||||
\(508\) | 5.46055 | + | 14.4621i | 0.242273 | + | 0.641651i | ||||
\(509\) | − | 11.8542i | − | 0.525429i | −0.964874 | − | 0.262714i | \(-0.915382\pi\) | ||
0.964874 | − | 0.262714i | \(-0.0846177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 8.49862i | − | 0.375957i | ||||||
\(512\) | −7.52183 | + | 21.3406i | −0.332421 | + | 0.943131i | ||||
\(513\) | 2.70603 | + | 2.70603i | 0.119474 | + | 0.119474i | ||||
\(514\) | 4.41030 | − | 2.84690i | 0.194530 | − | 0.125571i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.267604 | + | 0.592275i | −0.0117806 | + | 0.0260735i | ||||
\(517\) | 1.87103 | − | 1.87103i | 0.0822877 | − | 0.0822877i | ||||
\(518\) | −7.12597 | − | 1.53513i | −0.313097 | − | 0.0674499i | ||||
\(519\) | −2.75097 | −0.120754 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.91845 | −0.259292 | −0.129646 | − | 0.991560i | \(-0.541384\pi\) | ||||
−0.129646 | + | 0.991560i | \(0.541384\pi\) | |||||||
\(522\) | 14.5762 | + | 3.14011i | 0.637982 | + | 0.137439i | ||||
\(523\) | −12.7321 | + | 12.7321i | −0.556737 | + | 0.556737i | −0.928377 | − | 0.371640i | \(-0.878796\pi\) |
0.371640 | + | 0.928377i | \(0.378796\pi\) | |||||||
\(524\) | −1.01237 | + | 2.24064i | −0.0442258 | + | 0.0978827i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.6591 | + | 15.9177i | −1.07519 | + | 0.694047i | ||||
\(527\) | 24.7856 | + | 24.7856i | 1.07968 | + | 1.07968i | ||||
\(528\) | −0.154416 | + | 2.43455i | −0.00672011 | + | 0.105950i | ||||
\(529\) | − | 59.8784i | − | 2.60341i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.8139i | 1.33721i | ||||||||
\(532\) | 2.32551 | + | 6.15904i | 0.100824 | + | 0.267028i | ||||
\(533\) | −4.17485 | − | 4.17485i | −0.180833 | − | 0.180833i | ||||
\(534\) | −2.60314 | − | 4.03268i | −0.112649 | − | 0.174511i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.05571 | − | 27.0467i | −0.175180 | − | 1.16824i | ||||
\(537\) | −0.644743 | + | 0.644743i | −0.0278227 | + | 0.0278227i | ||||
\(538\) | 3.49518 | − | 16.2244i | 0.150688 | − | 0.699482i | ||||
\(539\) | −3.12749 | −0.134711 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.3293 | −0.745043 | −0.372521 | − | 0.928024i | \(-0.621507\pi\) | ||||
−0.372521 | + | 0.928024i | \(0.621507\pi\) | |||||||
\(542\) | 6.26941 | − | 29.1021i | 0.269294 | − | 1.25004i | ||||
\(543\) | −2.51646 | + | 2.51646i | −0.107991 | + | 0.107991i | ||||
\(544\) | −22.0051 | − | 6.22125i | −0.943463 | − | 0.266734i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.529874 | − | 0.820860i | −0.0226765 | − | 0.0351296i | ||||
\(547\) | 0.00989653 | + | 0.00989653i | 0.000423145 | + | 0.000423145i | 0.707318 | − | 0.706895i | \(-0.249905\pi\) |
−0.706895 | + | 0.707318i | \(0.749905\pi\) | |||||||
\(548\) | 8.41152 | − | 3.17600i | 0.359323 | − | 0.135672i | ||||
\(549\) | − | 20.1897i | − | 0.861674i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11.7171i | − | 0.499167i | ||||||
\(552\) | 2.98469 | − | 4.03772i | 0.127037 | − | 0.171857i | ||||
\(553\) | 0.108521 | + | 0.108521i | 0.00461479 | + | 0.00461479i | ||||
\(554\) | −15.6394 | + | 10.0954i | −0.664452 | + | 0.428911i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.34704 | + | 1.06045i | 0.0995366 | + | 0.0449731i | ||||
\(557\) | 7.03769 | − | 7.03769i | 0.298196 | − | 0.298196i | −0.542111 | − | 0.840307i | \(-0.682375\pi\) |
0.840307 | + | 0.542111i | \(0.182375\pi\) | |||||||
\(558\) | 35.5070 | + | 7.64920i | 1.50313 | + | 0.323816i | ||||
\(559\) | 5.90412 | 0.249718 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.46534 | −0.104087 | ||||||||
\(562\) | 22.3968 | + | 4.82490i | 0.944753 | + | 0.203526i | ||||
\(563\) | −10.2569 | + | 10.2569i | −0.432276 | + | 0.432276i | −0.889402 | − | 0.457126i | \(-0.848879\pi\) |
0.457126 | + | 0.889402i | \(0.348879\pi\) | |||||||
\(564\) | −0.300693 | − | 0.135861i | −0.0126615 | − | 0.00572076i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 13.5195 | − | 8.72699i | 0.568267 | − | 0.366823i | ||||
\(567\) | −6.12299 | − | 6.12299i | −0.257142 | − | 0.257142i | ||||
\(568\) | 5.31209 | − | 7.18624i | 0.222890 | − | 0.301528i | ||||
\(569\) | − | 20.3219i | − | 0.851939i | −0.904738 | − | 0.425969i | \(-0.859933\pi\) | ||
0.904738 | − | 0.425969i | \(-0.140067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.32953i | 0.390429i | 0.980761 | + | 0.195214i | \(0.0625403\pi\) | ||||
−0.980761 | + | 0.195214i | \(0.937460\pi\) | |||||||
\(572\) | 20.7321 | − | 7.82794i | 0.866851 | − | 0.327303i | ||||
\(573\) | −2.57028 | − | 2.57028i | −0.107375 | − | 0.107375i | ||||
\(574\) | 1.27815 | + | 1.98006i | 0.0533488 | + | 0.0826459i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −22.6536 | + | 6.95018i | −0.943900 | + | 0.289591i | ||||
\(577\) | −22.8297 | + | 22.8297i | −0.950412 | + | 0.950412i | −0.998827 | − | 0.0484150i | \(-0.984583\pi\) |
0.0484150 | + | 0.998827i | \(0.484583\pi\) | |||||||
\(578\) | −0.196101 | + | 0.910284i | −0.00815671 | + | 0.0378628i | ||||
\(579\) | 2.15589 | 0.0895958 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.1230 | −0.502949 | ||||||||
\(582\) | −0.187609 | + | 0.870866i | −0.00777663 | + | 0.0360985i | ||||
\(583\) | −3.51956 | + | 3.51956i | −0.145765 | + | 0.145765i | ||||
\(584\) | −3.56465 | − | 23.7719i | −0.147506 | − | 0.983690i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.1513 | + | 31.2176i | 0.832443 | + | 1.28959i | ||||
\(587\) | −19.2388 | − | 19.2388i | −0.794070 | − | 0.794070i | 0.188083 | − | 0.982153i | \(-0.439773\pi\) |
−0.982153 | + | 0.188083i | \(0.939773\pi\) | |||||||
\(588\) | 0.137762 | + | 0.364858i | 0.00568120 | + | 0.0150465i | ||||
\(589\) | − | 28.5425i | − | 1.17607i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 1.45566i | − | 0.0598779i | ||||||
\(592\) | −20.5763 | − | 1.30510i | −0.845682 | − | 0.0536392i | ||||
\(593\) | 16.3324 | + | 16.3324i | 0.670691 | + | 0.670691i | 0.957875 | − | 0.287184i | \(-0.0927192\pi\) |
−0.287184 | + | 0.957875i | \(0.592719\pi\) | |||||||
\(594\) | −4.32015 | + | 2.78870i | −0.177258 | + | 0.114422i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.13065 | − | 17.9952i | 0.333045 | − | 0.737110i | ||||
\(597\) | −0.0988249 | + | 0.0988249i | −0.00404463 | + | 0.00404463i | ||||
\(598\) | −44.5904 | − | 9.60602i | −1.82344 | − | 0.392819i | ||||
\(599\) | 13.2232 | 0.540283 | 0.270142 | − | 0.962821i | \(-0.412929\pi\) | ||||
0.270142 | + | 0.962821i | \(0.412929\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.28661 | 0.134064 | 0.0670318 | − | 0.997751i | \(-0.478647\pi\) | ||||
0.0670318 | + | 0.997751i | \(0.478647\pi\) | |||||||
\(602\) | −2.30390 | − | 0.496324i | −0.0938998 | − | 0.0202286i | ||||
\(603\) | 20.2519 | − | 20.2519i | 0.824720 | − | 0.824720i | ||||
\(604\) | −19.0812 | + | 42.2315i | −0.776405 | + | 1.71838i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.25423 | − | 0.809617i | 0.0509495 | − | 0.0328885i | ||||
\(607\) | −16.4028 | − | 16.4028i | −0.665770 | − | 0.665770i | 0.290964 | − | 0.956734i | \(-0.406024\pi\) |
−0.956734 | + | 0.290964i | \(0.906024\pi\) | |||||||
\(608\) | 9.08816 | + | 16.2524i | 0.368573 | + | 0.659121i | ||||
\(609\) | − | 0.694116i | − | 0.0281270i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.99748i | 0.121265i | ||||||||
\(612\) | −8.45908 | − | 22.4036i | −0.341938 | − | 0.905612i | ||||
\(613\) | −25.4438 | − | 25.4438i | −1.02767 | − | 1.02767i | −0.999606 | − | 0.0280588i | \(-0.991067\pi\) |
−0.0280588 | − | 0.999606i | \(-0.508933\pi\) | |||||||
\(614\) | 12.1258 | + | 18.7848i | 0.489356 | + | 0.758091i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.74808 | + | 1.31179i | −0.352470 | + | 0.0528535i | ||||
\(617\) | 11.2348 | − | 11.2348i | 0.452295 | − | 0.452295i | −0.443820 | − | 0.896116i | \(-0.646377\pi\) |
0.896116 | + | 0.443820i | \(0.146377\pi\) | |||||||
\(618\) | 0.832509 | − | 3.86445i | 0.0334884 | − | 0.155451i | ||||
\(619\) | −23.1057 | −0.928696 | −0.464348 | − | 0.885653i | \(-0.653711\pi\) | ||||
−0.464348 | + | 0.885653i | \(0.653711\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.5839 | 0.424716 | ||||||||
\(622\) | −1.07661 | + | 4.99753i | −0.0431681 | + | 0.200383i | ||||
\(623\) | 12.3074 | − | 12.3074i | 0.493086 | − | 0.493086i | ||||
\(624\) | −1.82644 | − | 2.07382i | −0.0731161 | − | 0.0830193i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.8848 | + | 26.1573i | 0.674853 | + | 1.04546i | ||||
\(627\) | 1.41951 | + | 1.41951i | 0.0566898 | + | 0.0566898i | ||||
\(628\) | −9.19140 | + | 3.47046i | −0.366777 | + | 0.138487i | ||||
\(629\) | − | 20.8366i | − | 0.830809i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 24.2657i | − | 0.966003i | −0.875619 | − | 0.483002i | \(-0.839546\pi\) | ||
0.875619 | − | 0.483002i | \(-0.160454\pi\) | |||||||
\(632\) | 0.349068 | + | 0.258032i | 0.0138852 | + | 0.0102640i | ||||
\(633\) | −1.35395 | − | 1.35395i | −0.0538147 | − | 0.0538147i | ||||
\(634\) | 24.3045 | − | 15.6888i | 0.965256 | − | 0.623084i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.565629 | + | 0.255565i | 0.0224286 | + | 0.0101338i | ||||
\(637\) | 2.50519 | − | 2.50519i | 0.0992594 | − | 0.0992594i | ||||
\(638\) | 15.3907 | + | 3.31558i | 0.609323 | + | 0.131265i | ||||
\(639\) | 9.35841 | 0.370213 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.6994 | −1.44954 | −0.724770 | − | 0.688991i | \(-0.758054\pi\) | ||||
−0.724770 | + | 0.688991i | \(0.758054\pi\) | |||||||
\(642\) | −2.30846 | − | 0.497306i | −0.0911076 | − | 0.0196271i | ||||
\(643\) | −16.3697 | + | 16.3697i | −0.645558 | + | 0.645558i | −0.951916 | − | 0.306358i | \(-0.900889\pi\) |
0.306358 | + | 0.951916i | \(0.400889\pi\) | |||||||
\(644\) | 16.5925 | + | 7.49689i | 0.653835 | + | 0.295419i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.8106 | + | 10.2059i | −0.622060 | + | 0.401547i | ||||
\(647\) | 6.53001 | + | 6.53001i | 0.256721 | + | 0.256721i | 0.823719 | − | 0.566998i | \(-0.191895\pi\) |
−0.566998 | + | 0.823719i | \(0.691895\pi\) | |||||||
\(648\) | −19.6952 | − | 14.5587i | −0.773700 | − | 0.571921i | ||||
\(649\) | 32.5358i | 1.27714i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.69084i | − | 0.0662692i | ||||||
\(652\) | −4.00785 | + | 1.51327i | −0.156959 | + | 0.0592643i | ||||
\(653\) | −8.77757 | − | 8.77757i | −0.343493 | − | 0.343493i | 0.514186 | − | 0.857679i | \(-0.328094\pi\) |
−0.857679 | + | 0.514186i | \(0.828094\pi\) | |||||||
\(654\) | 1.19907 | + | 1.85756i | 0.0468875 | + | 0.0726362i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.40569 | + | 5.00242i | 0.172013 | + | 0.195312i | ||||
\(657\) | 17.7998 | − | 17.7998i | 0.694436 | − | 0.694436i | ||||
\(658\) | 0.251980 | − | 1.16967i | 0.00982319 | − | 0.0455985i | ||||
\(659\) | 16.8433 | 0.656122 | 0.328061 | − | 0.944657i | \(-0.393605\pi\) | ||||
0.328061 | + | 0.944657i | \(0.393605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.5785 | −1.73390 | −0.866952 | − | 0.498392i | \(-0.833924\pi\) | ||||
−0.866952 | + | 0.498392i | \(0.833924\pi\) | |||||||
\(662\) | 6.23595 | − | 28.9468i | 0.242367 | − | 1.12505i | ||||
\(663\) | 1.97480 | − | 1.97480i | 0.0766947 | − | 0.0766947i | ||||
\(664\) | −33.9100 | + | 5.08487i | −1.31596 | + | 0.197331i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11.7096 | − | 18.1401i | −0.453739 | − | 0.702914i | ||||
\(667\) | −22.9141 | − | 22.9141i | −0.887239 | − | 0.887239i | ||||
\(668\) | 9.85810 | + | 26.1089i | 0.381421 | + | 1.01018i | ||||
\(669\) | 3.78485i | 0.146331i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 21.3179i | − | 0.822967i | ||||||
\(672\) | 0.538377 | + | 0.962781i | 0.0207683 | + | 0.0371401i | ||||
\(673\) | 7.02160 | + | 7.02160i | 0.270663 | + | 0.270663i | 0.829367 | − | 0.558704i | \(-0.188701\pi\) |
−0.558704 | + | 0.829367i | \(0.688701\pi\) | |||||||
\(674\) | 11.0906 | − | 7.15908i | 0.427192 | − | 0.275757i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.368924 | − | 0.816521i | 0.0141894 | − | 0.0314046i | ||||
\(677\) | −3.51482 | + | 3.51482i | −0.135085 | + | 0.135085i | −0.771416 | − | 0.636331i | \(-0.780451\pi\) |
0.636331 | + | 0.771416i | \(0.280451\pi\) | |||||||
\(678\) | −1.13196 | − | 0.243856i | −0.0434728 | − | 0.00936525i | ||||
\(679\) | −3.23037 | −0.123970 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.22060 | −0.0850935 | ||||||||
\(682\) | 37.4912 | + | 8.07664i | 1.43561 | + | 0.309271i | ||||
\(683\) | 9.24465 | − | 9.24465i | 0.353737 | − | 0.353737i | −0.507761 | − | 0.861498i | \(-0.669527\pi\) |
0.861498 | + | 0.507761i | \(0.169527\pi\) | |||||||
\(684\) | −8.02907 | + | 17.7703i | −0.306999 | + | 0.679465i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.18817 | + | 0.766977i | −0.0453645 | + | 0.0292833i | ||||
\(687\) | 1.76320 | + | 1.76320i | 0.0672704 | + | 0.0672704i | ||||
\(688\) | −6.65253 | − | 0.421951i | −0.253625 | − | 0.0160867i | ||||
\(689\) | − | 5.63850i | − | 0.214810i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8.40931i | − | 0.319905i | −0.987125 | − | 0.159953i | \(-0.948866\pi\) | ||
0.987125 | − | 0.159953i | \(-0.0511342\pi\) | |||||||
\(692\) | −9.96659 | − | 26.3962i | −0.378873 | − | 1.00343i | ||||
\(693\) | −6.55032 | − | 6.55032i | −0.248826 | − | 0.248826i | ||||
\(694\) | 10.5528 | + | 16.3480i | 0.400579 | + | 0.620562i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.291139 | − | 1.94155i | −0.0110356 | − | 0.0735942i | ||||
\(697\) | −4.76355 | + | 4.76355i | −0.180432 | + | 0.180432i | ||||
\(698\) | −7.81234 | + | 36.2643i | −0.295701 | + | 1.37262i | ||||
\(699\) | 4.28119 | 0.161930 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.1276 | −0.495822 | −0.247911 | − | 0.968783i | \(-0.579744\pi\) | ||||
−0.247911 | + | 0.968783i | \(0.579744\pi\) | |||||||
\(702\) | 1.22672 | − | 5.69436i | 0.0462997 | − | 0.214920i | ||||
\(703\) | −11.9974 | + | 11.9974i | −0.452492 | + | 0.452492i | ||||
\(704\) | −23.9195 | + | 7.33856i | −0.901500 | + | 0.276582i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.11644 | − | 11.0245i | −0.267831 | − | 0.414913i | ||||
\(707\) | 3.82779 | + | 3.82779i | 0.143959 | + | 0.143959i | ||||
\(708\) | 3.79568 | − | 1.43316i | 0.142650 | − | 0.0538615i | ||||
\(709\) | − | 7.84217i | − | 0.294519i | −0.989098 | − | 0.147259i | \(-0.952955\pi\) | ||
0.989098 | − | 0.147259i | \(-0.0470452\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.454581i | 0.0170481i | ||||||||
\(712\) | 29.2635 | − | 39.5879i | 1.09670 | − | 1.48362i | ||||
\(713\) | −55.8180 | − | 55.8180i | −2.09040 | − | 2.09040i | ||||
\(714\) | −0.936611 | + | 0.604593i | −0.0350518 | + | 0.0226263i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.52233 | − | 3.85060i | −0.318494 | − | 0.143904i | ||||
\(717\) | 0.316465 | − | 0.316465i | 0.0118186 | − | 0.0118186i | ||||
\(718\) | −1.69257 | − | 0.364626i | −0.0631660 | − | 0.0136077i | ||||
\(719\) | −34.9463 | −1.30328 | −0.651639 | − | 0.758529i | \(-0.725918\pi\) | ||||
−0.651639 | + | 0.758529i | \(0.725918\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3347 | 0.533853 | ||||||||
\(722\) | −11.2875 | − | 2.43163i | −0.420076 | − | 0.0904961i | ||||
\(723\) | −2.44530 | + | 2.44530i | −0.0909417 | + | 0.0909417i | ||||
\(724\) | −33.2630 | − | 15.0290i | −1.23621 | − | 0.558549i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.282387 | − | 0.182284i | 0.0104803 | − | 0.00676518i | ||||
\(727\) | 8.74837 | + | 8.74837i | 0.324459 | + | 0.324459i | 0.850475 | − | 0.526016i | \(-0.176315\pi\) |
−0.526016 | + | 0.850475i | \(0.676315\pi\) | |||||||
\(728\) | 5.95664 | − | 8.05819i | 0.220768 | − | 0.298656i | ||||
\(729\) | − | 24.9683i | − | 0.924751i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 6.73668i | − | 0.249165i | ||||||
\(732\) | −2.48698 | + | 0.939024i | −0.0919213 | + | 0.0347073i | ||||
\(733\) | −22.6984 | − | 22.6984i | −0.838385 | − | 0.838385i | 0.150261 | − | 0.988646i | \(-0.451989\pi\) |
−0.988646 | + | 0.150261i | \(0.951989\pi\) | |||||||
\(734\) | −3.03665 | − | 4.70426i | −0.112085 | − | 0.173637i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 49.5562 | + | 14.0104i | 1.82667 | + | 0.516431i | ||||
\(737\) | 21.3835 | − | 21.3835i | 0.787673 | − | 0.787673i | ||||
\(738\) | −1.47010 | + | 6.82409i | −0.0541151 | + | 0.251198i | ||||
\(739\) | 0.138193 | 0.00508353 | 0.00254176 | − | 0.999997i | \(-0.499191\pi\) | ||||
0.00254176 | + | 0.999997i | \(0.499191\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.27412 | −0.0835420 | ||||||||
\(742\) | −0.473994 | + | 2.20025i | −0.0174009 | + | 0.0807735i | ||||
\(743\) | 6.26844 | − | 6.26844i | 0.229967 | − | 0.229967i | −0.582712 | − | 0.812679i | \(-0.698008\pi\) |
0.812679 | + | 0.582712i | \(0.198008\pi\) | |||||||
\(744\) | −0.709203 | − | 4.72954i | −0.0260007 | − | 0.173393i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.4388 | − | 23.9172i | −0.565256 | − | 0.875673i | ||||
\(747\) | −25.3909 | − | 25.3909i | −0.929005 | − | 0.929005i | ||||
\(748\) | −8.93178 | − | 23.6555i | −0.326578 | − | 0.864932i | ||||
\(749\) | − | 8.56296i | − | 0.312884i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.0302132i | 0.00110249i | 1.00000 | 0.000551247i | \(0.000175468\pi\) | |||||
−1.00000 | 0.000551247i | \(0.999825\pi\) | ||||||||
\(752\) | 0.214221 | − | 3.37744i | 0.00781184 | − | 0.123163i | ||||
\(753\) | 3.92263 | + | 3.92263i | 0.142948 | + | 0.142948i | ||||
\(754\) | −14.9842 | + | 9.67245i | −0.545691 | + | 0.352250i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.957380 | + | 2.11892i | −0.0348196 | + | 0.0770644i | ||||
\(757\) | −37.2066 | + | 37.2066i | −1.35230 | + | 1.35230i | −0.469213 | + | 0.883085i | \(0.655462\pi\) |
−0.883085 | + | 0.469213i | \(0.844538\pi\) | |||||||
\(758\) | −42.2119 | − | 9.09362i | −1.53321 | − | 0.330295i | ||||
\(759\) | 5.55202 | 0.201525 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.6576 | −1.36509 | −0.682543 | − | 0.730846i | \(-0.739126\pi\) | ||||
−0.682543 | + | 0.730846i | \(0.739126\pi\) | |||||||
\(762\) | 2.08372 | + | 0.448892i | 0.0754852 | + | 0.0162616i | ||||
\(763\) | −5.66910 | + | 5.66910i | −0.205235 | + | 0.205235i | ||||
\(764\) | 15.3505 | − | 33.9744i | 0.555360 | − | 1.22915i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.68366 | − | 5.60540i | 0.313753 | − | 0.202531i | ||||
\(767\) | −26.0620 | − | 26.0620i | −0.941043 | − | 0.941043i | ||||
\(768\) | 1.90975 | + | 2.46723i | 0.0689122 | + | 0.0890285i | ||||
\(769\) | 1.80452i | 0.0650727i | 0.999471 | + | 0.0325364i | \(0.0103585\pi\) | ||||
−0.999471 | + | 0.0325364i | \(0.989642\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 0.723809i | − | 0.0260673i | ||||||
\(772\) | 7.81067 | + | 20.6863i | 0.281112 | + | 0.744516i | ||||
\(773\) | −0.171122 | − | 0.171122i | −0.00615481 | − | 0.00615481i | 0.704023 | − | 0.710177i | \(-0.251385\pi\) |
−0.710177 | + | 0.704023i | \(0.751385\pi\) | |||||||
\(774\) | −3.78584 | − | 5.86487i | −0.136079 | − | 0.210809i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.03586 | + | 1.35494i | −0.324368 | + | 0.0486396i | ||||
\(777\) | −0.710720 | + | 0.710720i | −0.0254970 | + | 0.0254970i | ||||
\(778\) | −9.40676 | + | 43.6655i | −0.337249 | + | 1.56548i | ||||
\(779\) | 5.48558 | 0.196541 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.88136 | 0.353583 | ||||||||
\(782\) | −10.9606 | + | 50.8782i | −0.391950 | + | 1.81940i | ||||
\(783\) | 2.92622 | − | 2.92622i | 0.104575 | − | 0.104575i | ||||
\(784\) | −3.00179 | + | 2.64372i | −0.107207 | + | 0.0944184i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.183864 | + | 0.284835i | 0.00655822 | + | 0.0101597i | ||||
\(787\) | 5.77212 | + | 5.77212i | 0.205754 | + | 0.205754i | 0.802460 | − | 0.596706i | \(-0.203524\pi\) |
−0.596706 | + | 0.802460i | \(0.703524\pi\) | |||||||
\(788\) | 13.9674 | − | 5.27377i | 0.497568 | − | 0.187870i | ||||
\(789\) | 4.04700i | 0.144077i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 4.19888i | − | 0.149295i | ||||||
\(792\) | −21.0697 | − | 15.5748i | −0.748680 | − | 0.553426i | ||||
\(793\) | 17.0761 | + | 17.0761i | 0.606391 | + | 0.606391i | ||||
\(794\) | −28.0652 | + | 18.1164i | −0.995995 | + | 0.642926i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.30628 | − | 0.590212i | −0.0463000 | − | 0.0209195i | ||||
\(797\) | −18.3814 | + | 18.3814i | −0.651103 | + | 0.651103i | −0.953259 | − | 0.302156i | \(-0.902294\pi\) |
0.302156 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(798\) | 0.887405 | + | 0.191172i | 0.0314138 | + | 0.00676741i | ||||
\(799\) | 3.42016 | 0.120996 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 51.5541 | 1.82157 | ||||||||
\(802\) | 23.0217 | + | 4.95951i | 0.812923 | + | 0.175126i | ||||
\(803\) | 18.7944 | − | 18.7944i | 0.663242 | − | 0.663242i | ||||
\(804\) | −3.43655 | − | 1.55272i | −0.121198 | − | 0.0547602i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.5009 | + | 23.5617i | −1.28569 | + | 0.829926i | ||||
\(807\) | −1.61816 | − | 1.61816i | −0.0569620 | − | 0.0569620i | ||||
\(808\) | 12.3125 | + | 9.10141i | 0.433151 | + | 0.320186i | ||||
\(809\) | − | 5.64567i | − | 0.198491i | −0.995063 | − | 0.0992456i | \(-0.968357\pi\) | ||
0.995063 | − | 0.0992456i | \(-0.0316429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24.0723i | − | 0.845294i | −0.906294 | − | 0.422647i | \(-0.861101\pi\) | ||
0.906294 | − | 0.422647i | \(-0.138899\pi\) | |||||||
\(812\) | 6.66020 | − | 2.51474i | 0.233727 | − | 0.0882500i | ||||
\(813\) | −2.90255 | − | 2.90255i | −0.101797 | − | 0.101797i | ||||
\(814\) | −12.3640 | − | 19.1538i | −0.433357 | − | 0.671339i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.36626 | + | 2.08399i | −0.0828355 | + | 0.0729542i | ||||
\(817\) | −3.87889 | + | 3.87889i | −0.135705 | + | 0.135705i | ||||
\(818\) | −7.17894 | + | 33.3241i | −0.251006 | + | 1.16515i | ||||
\(819\) | 10.4939 | 0.366687 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.7779 | 1.42316 | 0.711579 | − | 0.702606i | \(-0.247980\pi\) | ||||
0.711579 | + | 0.702606i | \(0.247980\pi\) | |||||||
\(822\) | 0.261087 | − | 1.21195i | 0.00910645 | − | 0.0422715i | ||||
\(823\) | 18.8337 | − | 18.8337i | 0.656501 | − | 0.656501i | −0.298049 | − | 0.954551i | \(-0.596336\pi\) |
0.954551 | + | 0.298049i | \(0.0963359\pi\) | |||||||
\(824\) | 40.0964 | − | 6.01253i | 1.39682 | − | 0.209456i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.97899 | + | 12.3607i | 0.277624 | + | 0.430085i | ||||
\(827\) | −15.8664 | − | 15.8664i | −0.551730 | − | 0.551730i | 0.375210 | − | 0.926940i | \(-0.377571\pi\) |
−0.926940 | + | 0.375210i | \(0.877571\pi\) | |||||||
\(828\) | 19.0501 | + | 50.4535i | 0.662037 | + | 1.75338i | ||||
\(829\) | 3.75621i | 0.130459i | 0.997870 | + | 0.0652293i | \(0.0207779\pi\) | ||||
−0.997870 | + | 0.0652293i | \(0.979222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.56670i | 0.0890377i | ||||||||
\(832\) | 13.2817 | − | 25.0384i | 0.460461 | − | 0.868052i | ||||
\(833\) | −2.85846 | − | 2.85846i | −0.0990397 | − | 0.0990397i | ||||
\(834\) | 0.298361 | − | 0.192595i | 0.0103314 | − | 0.00666903i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.47774 | + | 18.7633i | −0.293209 | + | 0.648944i | ||||
\(837\) | 7.12816 | − | 7.12816i | 0.246385 | − | 0.246385i | ||||
\(838\) | −14.8364 | − | 3.19617i | −0.512514 | − | 0.110410i | ||||
\(839\) | 12.2357 | 0.422424 | 0.211212 | − | 0.977440i | \(-0.432259\pi\) | ||||
0.211212 | + | 0.977440i | \(0.432259\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.3294 | 0.563084 | ||||||||
\(842\) | 13.0725 | + | 2.81618i | 0.450508 | + | 0.0970520i | ||||
\(843\) | 2.23378 | − | 2.23378i | 0.0769356 | − | 0.0769356i | ||||
\(844\) | 8.08619 | − | 17.8968i | 0.278338 | − | 0.616032i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.97755 | − | 1.92204i | 0.102370 | − | 0.0660811i | ||||
\(847\) | 0.861820 | + | 0.861820i | 0.0296125 | + | 0.0296125i | ||||
\(848\) | −0.402967 | + | 6.35324i | −0.0138380 | + | 0.218171i | ||||
\(849\) | − | 2.21879i | − | 0.0761487i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46.9246i | 1.60855i | ||||||||
\(852\) | −0.435261 | − | 1.15277i | −0.0149118 | − | 0.0394934i | ||||
\(853\) | 30.8929 | + | 30.8929i | 1.05775 | + | 1.05775i | 0.998227 | + | 0.0595275i | \(0.0189594\pi\) |
0.0595275 | + | 0.998227i | \(0.481041\pi\) | |||||||
\(854\) | −5.22793 | − | 8.09890i | −0.178896 | − | 0.277139i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.59163 | − | 23.9519i | −0.122759 | − | 0.818659i | ||||
\(857\) | 13.2977 | − | 13.2977i | 0.454242 | − | 0.454242i | −0.442517 | − | 0.896760i | \(-0.645915\pi\) |
0.896760 | + | 0.442517i | \(0.145915\pi\) | |||||||
\(858\) | 0.643506 | − | 2.98711i | 0.0219689 | − | 0.101978i | ||||
\(859\) | −20.8029 | −0.709785 | −0.354892 | − | 0.934907i | \(-0.615483\pi\) | ||||
−0.354892 | + | 0.934907i | \(0.615483\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.324962 | 0.0110747 | ||||||||
\(862\) | 9.87532 | − | 45.8405i | 0.336355 | − | 1.56133i | ||||
\(863\) | 1.63985 | − | 1.63985i | 0.0558210 | − | 0.0558210i | −0.678645 | − | 0.734466i | \(-0.737433\pi\) |
0.734466 | + | 0.678645i | \(0.237433\pi\) | |||||||
\(864\) | −1.78918 | + | 6.32851i | −0.0608693 | + | 0.215300i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10.9917 | − | 17.0279i | −0.373514 | − | 0.578632i | ||||
\(867\) | 0.0907887 | + | 0.0907887i | 0.00308334 | + | 0.00308334i | ||||
\(868\) | 16.2240 | − | 6.12581i | 0.550679 | − | 0.207924i | ||||
\(869\) | 0.479983i | 0.0162823i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.2575i | 1.16077i | ||||||||
\(872\) | −13.4795 | + | 18.2352i | −0.456474 | + | 0.617522i | ||||
\(873\) | −6.76580 | − | 6.76580i | −0.228988 | − | 0.228988i | ||||
\(874\) | 35.6060 | − | 22.9840i | 1.20439 | − | 0.777447i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.02046 | − | 1.36472i | −0.102052 | − | 0.0461095i | ||||
\(877\) | −1.43888 | + | 1.43888i | −0.0485874 | + | 0.0485874i | −0.730983 | − | 0.682396i | \(-0.760938\pi\) |
0.682396 | + | 0.730983i | \(0.260938\pi\) | |||||||
\(878\) | 53.9258 | + | 11.6171i | 1.81991 | + | 0.392059i | ||||
\(879\) | 5.12336 | 0.172807 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.5420 | −0.692078 | −0.346039 | − | 0.938220i | \(-0.612474\pi\) | ||||
−0.346039 | + | 0.938220i | \(0.612474\pi\) | |||||||
\(882\) | −4.09492 | − | 0.882160i | −0.137883 | − | 0.0297039i | ||||
\(883\) | 1.94396 | − | 1.94396i | 0.0654196 | − | 0.0654196i | −0.673640 | − | 0.739060i | \(-0.735270\pi\) |
0.739060 | + | 0.673640i | \(0.235270\pi\) | |||||||
\(884\) | 26.1032 | + | 11.7941i | 0.877946 | + | 0.396677i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 48.6652 | − | 31.4139i | 1.63494 | − | 1.05537i | ||||
\(887\) | 18.7634 | + | 18.7634i | 0.630015 | + | 0.630015i | 0.948072 | − | 0.318057i | \(-0.103030\pi\) |
−0.318057 | + | 0.948072i | \(0.603030\pi\) | |||||||
\(888\) | −1.68989 | + | 2.28610i | −0.0567090 | + | 0.0767164i | ||||
\(889\) | 7.72932i | 0.259233i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 27.0816i | − | 0.907269i | ||||||
\(892\) | −36.3165 | + | 13.7123i | −1.21597 | + | 0.459121i | ||||
\(893\) | −1.96928 | − | 1.96928i | −0.0658995 | − | 0.0658995i | ||||
\(894\) | −1.47666 | − | 2.28759i | −0.0493870 | − | 0.0765083i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.28760 | + | 8.65395i | −0.243462 | + | 0.289108i | ||||
\(897\) | −4.44730 | + | 4.44730i | −0.148491 | + | 0.148491i | ||||
\(898\) | −8.94306 | + | 41.5130i | −0.298434 | + | 1.38531i | ||||
\(899\) | −30.8650 | −1.02941 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.43359 | −0.214334 | ||||||||
\(902\) | −1.55225 | + | 7.20542i | −0.0516842 | + | 0.239914i | ||||
\(903\) | −0.229783 | + | 0.229783i | −0.00764670 | + | 0.00764670i | ||||
\(904\) | −1.76117 | − | 11.7449i | −0.0585758 | − | 0.390630i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.46547 | + | 5.36857i | 0.115133 | + | 0.178359i | ||||
\(907\) | −5.74477 | − | 5.74477i | −0.190752 | − | 0.190752i | 0.605269 | − | 0.796021i | \(-0.293066\pi\) |
−0.796021 | + | 0.605269i | \(0.793066\pi\) | |||||||
\(908\) | −8.04509 | − | 21.3072i | −0.266986 | − | 0.707103i | ||||
\(909\) | 16.0341i | 0.531818i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 23.4232i | − | 0.776045i | −0.921650 | − | 0.388023i | \(-0.873158\pi\) | ||
0.921650 | − | 0.388023i | \(-0.126842\pi\) | |||||||
\(912\) | 2.56239 | + | 0.162525i | 0.0848493 | + | 0.00538175i | ||||
\(913\) | −26.8098 | − | 26.8098i | −0.887274 | − | 0.887274i | ||||
\(914\) | −22.5543 | + | 14.5591i | −0.746031 | + | 0.481571i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.5304 | + | 23.3063i | −0.347933 | + | 0.770062i | ||||
\(917\) | −0.869292 | + | 0.869292i | −0.0287066 | + | 0.0287066i | ||||
\(918\) | −6.49733 | − | 1.39971i | −0.214444 | − | 0.0461972i | ||||
\(919\) | 6.14477 | 0.202697 | 0.101349 | − | 0.994851i | \(-0.467684\pi\) | ||||
0.101349 | + | 0.994851i | \(0.467684\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.08291 | 0.101585 | ||||||||
\(922\) | −33.1950 | − | 7.15113i | −1.09322 | − | 0.235510i | ||||
\(923\) | −7.91521 | + | 7.91521i | −0.260532 | + | 0.260532i | ||||
\(924\) | −0.502216 | + | 1.11153i | −0.0165217 | + | 0.0365666i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23.9838 | − | 15.4818i | 0.788157 | − | 0.508764i | ||||
\(927\) | 30.0231 | + | 30.0231i | 0.986088 | + | 0.986088i | ||||
\(928\) | 17.5748 | − | 9.82766i | 0.576922 | − | 0.322609i | ||||
\(929\) | − | 29.7457i | − | 0.975926i | −0.872864 | − | 0.487963i | \(-0.837740\pi\) | ||
0.872864 | − | 0.487963i | \(-0.162260\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.29172i | 0.107882i | ||||||||
\(932\) | 15.5105 | + | 41.0791i | 0.508063 | + | 1.34559i | ||||
\(933\) | 0.498437 | + | 0.498437i | 0.0163181 | + | 0.0163181i | ||||
\(934\) | 23.1187 | + | 35.8145i | 0.756466 | + | 1.17189i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 29.3531 | − | 4.40155i | 0.959437 | − | 0.143869i | ||||
\(937\) | −19.4310 | + | 19.4310i | −0.634784 | + | 0.634784i | −0.949264 | − | 0.314480i | \(-0.898170\pi\) |
0.314480 | + | 0.949264i | \(0.398170\pi\) | |||||||
\(938\) | 2.87982 | − | 13.3679i | 0.0940293 | − | 0.436477i | ||||
\(939\) | 4.29288 | 0.140093 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.1110 | 0.981591 | 0.490796 | − | 0.871275i | \(-0.336706\pi\) | ||||
0.490796 | + | 0.871275i | \(0.336706\pi\) | |||||||
\(942\) | −0.285294 | + | 1.32431i | −0.00929538 | + | 0.0431484i | ||||
\(943\) | 10.7276 | − | 10.7276i | 0.349340 | − | 0.349340i | ||||
\(944\) | 27.5030 | + | 31.2282i | 0.895147 | + | 1.01639i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.99740 | − | 6.19261i | −0.129967 | − | 0.201339i | ||||
\(947\) | 20.1763 | + | 20.1763i | 0.655643 | + | 0.655643i | 0.954346 | − | 0.298703i | \(-0.0965541\pi\) |
−0.298703 | + | 0.954346i | \(0.596554\pi\) | |||||||
\(948\) | 0.0559955 | − | 0.0211426i | 0.00181865 | − | 0.000686680i | ||||
\(949\) | 30.1096i | 0.977399i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 3.98881i | − | 0.129346i | ||||||
\(952\) | −9.19450 | − | 6.79660i | −0.297995 | − | 0.220279i | ||||
\(953\) | −19.5573 | − | 19.5573i | −0.633523 | − | 0.633523i | 0.315427 | − | 0.948950i | \(-0.397852\pi\) |
−0.948950 | + | 0.315427i | \(0.897852\pi\) | |||||||
\(954\) | −5.60101 | + | 3.61552i | −0.181340 | + | 0.117057i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.18309 | + | 1.89002i | 0.135291 | + | 0.0611277i | ||||
\(957\) | 1.53502 | − | 1.53502i | 0.0496200 | − | 0.0496200i | ||||
\(958\) | 57.2294 | + | 12.3288i | 1.84900 | + | 0.398325i | ||||
\(959\) | 4.49557 | 0.145170 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44.1860 | −1.42535 | ||||||||
\(962\) | 25.2465 | + | 5.43879i | 0.813979 | + | 0.175354i | ||||
\(963\) | 17.9345 | − | 17.9345i | 0.577932 | − | 0.577932i | ||||
\(964\) | −32.3224 | − | 14.6041i | −1.04103 | − | 0.470365i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.10927 | − | 1.36156i | 0.0678648 | − | 0.0438075i | ||||
\(967\) | 7.95857 | + | 7.95857i | 0.255930 | + | 0.255930i | 0.823397 | − | 0.567466i | \(-0.192076\pi\) |
−0.567466 | + | 0.823397i | \(0.692076\pi\) | |||||||
\(968\) | 2.77212 | + | 2.04916i | 0.0890994 | + | 0.0658626i | ||||
\(969\) | 2.59480i | 0.0833571i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.0681i | 1.06121i | 0.847620 | + | 0.530603i | \(0.178035\pi\) | ||||
−0.847620 | + | 0.530603i | \(0.821965\pi\) | |||||||
\(972\) | −9.68521 | + | 3.65691i | −0.310653 | + | 0.117295i | ||||
\(973\) | 0.910573 | + | 0.910573i | 0.0291916 | + | 0.0291916i | ||||
\(974\) | 1.74331 | + | 2.70067i | 0.0558592 | + | 0.0865349i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.0203 | − | 20.4611i | −0.576816 | − | 0.654943i | ||||
\(977\) | −20.5925 | + | 20.5925i | −0.658813 | + | 0.658813i | −0.955099 | − | 0.296286i | \(-0.904252\pi\) |
0.296286 | + | 0.955099i | \(0.404252\pi\) | |||||||
\(978\) | −0.124400 | + | 0.577457i | −0.00397789 | + | 0.0184650i | ||||
\(979\) | 54.4349 | 1.73975 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.7471 | −0.758187 | ||||||||
\(982\) | −6.01409 | + | 27.9170i | −0.191917 | + | 0.890866i | ||||
\(983\) | −26.6037 | + | 26.6037i | −0.848528 | + | 0.848528i | −0.989949 | − | 0.141422i | \(-0.954833\pi\) |
0.141422 | + | 0.989949i | \(0.454833\pi\) | |||||||
\(984\) | 0.908969 | − | 0.136302i | 0.0289769 | − | 0.00434514i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.0364 | + | 17.0971i | 0.351470 | + | 0.544483i | ||||
\(987\) | −0.116659 | − | 0.116659i | −0.00371330 | − | 0.00371330i | ||||
\(988\) | −8.23901 | − | 21.8208i | −0.262118 | − | 0.694211i | ||||
\(989\) | 15.1712i | 0.482416i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.3981i | 0.457370i | 0.973500 | + | 0.228685i | \(0.0734426\pi\) | ||||
−0.973500 | + | 0.228685i | \(0.926557\pi\) | |||||||
\(992\) | 42.8116 | − | 23.9398i | 1.35927 | − | 0.760090i | ||||
\(993\) | −2.88706 | − | 2.88706i | −0.0916180 | − | 0.0916180i | ||||
\(994\) | 3.75404 | − | 2.42328i | 0.119071 | − | 0.0768616i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.94673 | + | 4.30860i | −0.0616846 | + | 0.136523i | ||||
\(997\) | 5.81745 | − | 5.81745i | 0.184241 | − | 0.184241i | −0.608960 | − | 0.793201i | \(-0.708413\pi\) |
0.793201 | + | 0.608960i | \(0.208413\pi\) | |||||||
\(998\) | −38.2631 | − | 8.24294i | −1.21120 | − | 0.260926i | ||||
\(999\) | −5.99244 | −0.189593 |
(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 | 700.2.k.b.43.18 | 36 | ||
4.3 | odd | 2 | inner | 700.2.k.b.43.9 | 36 | ||
5.2 | odd | 4 | inner | 700.2.k.b.407.9 | 36 | ||
5.3 | odd | 4 | 140.2.k.a.127.10 | yes | 36 | ||
5.4 | even | 2 | 140.2.k.a.43.1 | ✓ | 36 | ||
20.3 | even | 4 | 140.2.k.a.127.1 | yes | 36 | ||
20.7 | even | 4 | inner | 700.2.k.b.407.18 | 36 | ||
20.19 | odd | 2 | 140.2.k.a.43.10 | yes | 36 | ||
35.3 | even | 12 | 980.2.x.l.667.15 | 72 | |||
35.4 | even | 6 | 980.2.x.k.863.14 | 72 | |||
35.9 | even | 6 | 980.2.x.k.263.11 | 72 | |||
35.13 | even | 4 | 980.2.k.l.687.10 | 36 | |||
35.18 | odd | 12 | 980.2.x.k.667.15 | 72 | |||
35.19 | odd | 6 | 980.2.x.l.263.11 | 72 | |||
35.23 | odd | 12 | 980.2.x.k.67.3 | 72 | |||
35.24 | odd | 6 | 980.2.x.l.863.14 | 72 | |||
35.33 | even | 12 | 980.2.x.l.67.3 | 72 | |||
35.34 | odd | 2 | 980.2.k.l.883.1 | 36 | |||
140.3 | odd | 12 | 980.2.x.l.667.11 | 72 | |||
140.19 | even | 6 | 980.2.x.l.263.15 | 72 | |||
140.23 | even | 12 | 980.2.x.k.67.14 | 72 | |||
140.39 | odd | 6 | 980.2.x.k.863.3 | 72 | |||
140.59 | even | 6 | 980.2.x.l.863.3 | 72 | |||
140.79 | odd | 6 | 980.2.x.k.263.15 | 72 | |||
140.83 | odd | 4 | 980.2.k.l.687.1 | 36 | |||
140.103 | odd | 12 | 980.2.x.l.67.14 | 72 | |||
140.123 | even | 12 | 980.2.x.k.667.11 | 72 | |||
140.139 | even | 2 | 980.2.k.l.883.10 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.k.a.43.1 | ✓ | 36 | 5.4 | even | 2 | ||
140.2.k.a.43.10 | yes | 36 | 20.19 | odd | 2 | ||
140.2.k.a.127.1 | yes | 36 | 20.3 | even | 4 | ||
140.2.k.a.127.10 | yes | 36 | 5.3 | odd | 4 | ||
700.2.k.b.43.9 | 36 | 4.3 | odd | 2 | inner | ||
700.2.k.b.43.18 | 36 | 1.1 | even | 1 | trivial | ||
700.2.k.b.407.9 | 36 | 5.2 | odd | 4 | inner | ||
700.2.k.b.407.18 | 36 | 20.7 | even | 4 | inner | ||
980.2.k.l.687.1 | 36 | 140.83 | odd | 4 | |||
980.2.k.l.687.10 | 36 | 35.13 | even | 4 | |||
980.2.k.l.883.1 | 36 | 35.34 | odd | 2 | |||
980.2.k.l.883.10 | 36 | 140.139 | even | 2 | |||
980.2.x.k.67.3 | 72 | 35.23 | odd | 12 | |||
980.2.x.k.67.14 | 72 | 140.23 | even | 12 | |||
980.2.x.k.263.11 | 72 | 35.9 | even | 6 | |||
980.2.x.k.263.15 | 72 | 140.79 | odd | 6 | |||
980.2.x.k.667.11 | 72 | 140.123 | even | 12 | |||
980.2.x.k.667.15 | 72 | 35.18 | odd | 12 | |||
980.2.x.k.863.3 | 72 | 140.39 | odd | 6 | |||
980.2.x.k.863.14 | 72 | 35.4 | even | 6 | |||
980.2.x.l.67.3 | 72 | 35.33 | even | 12 | |||
980.2.x.l.67.14 | 72 | 140.103 | odd | 12 | |||
980.2.x.l.263.11 | 72 | 35.19 | odd | 6 | |||
980.2.x.l.263.15 | 72 | 140.19 | even | 6 | |||
980.2.x.l.667.11 | 72 | 140.3 | odd | 12 | |||
980.2.x.l.667.15 | 72 | 35.3 | even | 12 | |||
980.2.x.l.863.3 | 72 | 140.59 | even | 6 | |||
980.2.x.l.863.14 | 72 | 35.24 | odd | 6 |