Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(101,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.n (of order \(6\), 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: | \(2.59513806569\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 16x^{8} + 84x^{6} + 163x^{4} + 118x^{2} + 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.4 | ||
Root | \(-1.36551i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.101 |
Dual form | 325.2.n.f.251.4 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.18257 | − | 0.682755i | 0.836201 | − | 0.482781i | −0.0197701 | − | 0.999805i | \(-0.506293\pi\) |
0.855971 | + | 0.517024i | \(0.172960\pi\) | |||||||
\(3\) | −0.199959 | − | 0.346339i | −0.115446 | − | 0.199959i | 0.802512 | − | 0.596636i | \(-0.203496\pi\) |
−0.917958 | + | 0.396677i | \(0.870163\pi\) | |||||||
\(4\) | −0.0676905 | + | 0.117243i | −0.0338452 | + | 0.0586217i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.472929 | − | 0.273046i | −0.193073 | − | 0.111471i | ||||
\(7\) | 3.15550 | + | 1.82183i | 1.19267 | + | 0.688586i | 0.958910 | − | 0.283710i | \(-0.0915652\pi\) |
0.233755 | + | 0.972295i | \(0.424899\pi\) | |||||||
\(8\) | 2.91589i | 1.03092i | ||||||||
\(9\) | 1.42003 | − | 2.45957i | 0.473344 | − | 0.819856i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.83806 | − | 1.63856i | 0.855708 | − | 0.494043i | −0.00686453 | − | 0.999976i | \(-0.502185\pi\) |
0.862573 | + | 0.505933i | \(0.168852\pi\) | |||||||
\(12\) | 0.0541412 | 0.0156292 | ||||||||
\(13\) | −3.53491 | + | 0.710223i | −0.980407 | + | 0.196980i | ||||
\(14\) | 4.97545 | 1.32974 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85546 | + | 3.21374i | 0.463864 | + | 0.803436i | ||||
\(17\) | 1.08781 | − | 1.88413i | 0.263832 | − | 0.456970i | −0.703425 | − | 0.710769i | \(-0.748347\pi\) |
0.967257 | + | 0.253799i | \(0.0816803\pi\) | |||||||
\(18\) | − | 3.87814i | − | 0.914086i | ||||||
\(19\) | −0.742787 | − | 0.428848i | −0.170407 | − | 0.0983846i | 0.412371 | − | 0.911016i | \(-0.364701\pi\) |
−0.582778 | + | 0.812632i | \(0.698034\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.45716i | − | 0.317979i | ||||||
\(22\) | 2.23747 | − | 3.87540i | 0.477029 | − | 0.826239i | ||||
\(23\) | 0.382526 | + | 0.662554i | 0.0797621 | + | 0.138152i | 0.903147 | − | 0.429331i | \(-0.141251\pi\) |
−0.823385 | + | 0.567483i | \(0.807917\pi\) | |||||||
\(24\) | 1.00988 | − | 0.583057i | 0.206142 | − | 0.119016i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.69536 | + | 3.25336i | −0.724719 | + | 0.638037i | ||||
\(27\) | −2.33555 | −0.449476 | ||||||||
\(28\) | −0.427194 | + | 0.246641i | −0.0807321 | + | 0.0466107i | ||||
\(29\) | 1.53219 | + | 2.65382i | 0.284520 | + | 0.492803i | 0.972493 | − | 0.232934i | \(-0.0748325\pi\) |
−0.687973 | + | 0.725736i | \(0.741499\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.41833i | − | 1.51198i | −0.654585 | − | 0.755988i | \(-0.727157\pi\) | ||
0.654585 | − | 0.755988i | \(-0.272843\pi\) | |||||||
\(32\) | −0.662062 | − | 0.382242i | −0.117037 | − | 0.0675714i | ||||
\(33\) | −1.13499 | − | 0.655288i | −0.197577 | − | 0.114071i | ||||
\(34\) | − | 2.97082i | − | 0.509491i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.192245 | + | 0.332979i | 0.0320409 | + | 0.0554965i | ||||
\(37\) | −9.40295 | + | 5.42880i | −1.54584 | + | 0.892488i | −0.547383 | + | 0.836882i | \(0.684376\pi\) |
−0.998453 | + | 0.0556060i | \(0.982291\pi\) | |||||||
\(38\) | −1.17119 | −0.189993 | ||||||||
\(39\) | 0.952814 | + | 1.08226i | 0.152572 | + | 0.173300i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.59344 | + | 3.80672i | −1.02972 | + | 0.594510i | −0.916905 | − | 0.399106i | \(-0.869321\pi\) |
−0.112817 | + | 0.993616i | \(0.535987\pi\) | |||||||
\(42\) | −0.994885 | − | 1.72319i | −0.153514 | − | 0.265894i | ||||
\(43\) | −1.91803 | + | 3.32213i | −0.292497 | + | 0.506619i | −0.974399 | − | 0.224824i | \(-0.927819\pi\) |
0.681903 | + | 0.731443i | \(0.261153\pi\) | |||||||
\(44\) | 0.443659i | 0.0668841i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.904724 | + | 0.522343i | 0.133394 | + | 0.0770152i | ||||
\(47\) | 4.68303i | 0.683090i | 0.939865 | + | 0.341545i | \(0.110950\pi\) | ||||
−0.939865 | + | 0.341545i | \(0.889050\pi\) | |||||||
\(48\) | 0.742029 | − | 1.28523i | 0.107103 | − | 0.185507i | ||||
\(49\) | 3.13810 | + | 5.43536i | 0.448301 | + | 0.776479i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.870065 | −0.121834 | ||||||||
\(52\) | 0.156011 | − | 0.462520i | 0.0216348 | − | 0.0641400i | ||||
\(53\) | 3.04646 | 0.418463 | 0.209231 | − | 0.977866i | \(-0.432904\pi\) | ||||
0.209231 | + | 0.977866i | \(0.432904\pi\) | |||||||
\(54\) | −2.76194 | + | 1.59461i | −0.375852 | + | 0.216998i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.31224 | + | 9.20106i | −0.709878 | + | 1.22954i | ||||
\(57\) | 0.343008i | 0.0454325i | ||||||||
\(58\) | 3.62382 | + | 2.09222i | 0.475832 | + | 0.274721i | ||||
\(59\) | −11.5378 | − | 6.66136i | −1.50210 | − | 0.867235i | −0.999997 | − | 0.00242501i | \(-0.999228\pi\) |
−0.502099 | − | 0.864810i | \(-0.667439\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.51531 | − | 11.2848i | 0.834200 | − | 1.44488i | −0.0604805 | − | 0.998169i | \(-0.519263\pi\) |
0.894680 | − | 0.446707i | \(-0.147403\pi\) | |||||||
\(62\) | −5.74766 | − | 9.95524i | −0.729953 | − | 1.26432i | ||||
\(63\) | 8.96182 | − | 5.17411i | 1.12908 | − | 0.651876i | ||||
\(64\) | −8.46573 | −1.05822 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.78960 | −0.220285 | ||||||||
\(67\) | −4.02523 | + | 2.32397i | −0.491760 | + | 0.283918i | −0.725304 | − | 0.688428i | \(-0.758301\pi\) |
0.233544 | + | 0.972346i | \(0.424968\pi\) | |||||||
\(68\) | 0.147268 | + | 0.255076i | 0.0178589 | + | 0.0309325i | ||||
\(69\) | 0.152979 | − | 0.264967i | 0.0184165 | − | 0.0318983i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.38392 | + | 5.41781i | 1.11367 | + | 0.642976i | 0.939777 | − | 0.341789i | \(-0.111033\pi\) |
0.173890 | + | 0.984765i | \(0.444366\pi\) | |||||||
\(72\) | 7.17182 | + | 4.14065i | 0.845207 | + | 0.487981i | ||||
\(73\) | − | 7.68313i | − | 0.899242i | −0.893219 | − | 0.449621i | \(-0.851559\pi\) | ||
0.893219 | − | 0.449621i | \(-0.148441\pi\) | |||||||
\(74\) | −7.41308 | + | 12.8398i | −0.861753 | + | 1.49260i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.100559 | − | 0.0580579i | 0.0115349 | − | 0.00665970i | ||||
\(77\) | 11.9407 | 1.36076 | ||||||||
\(78\) | 1.86569 | + | 0.629307i | 0.211247 | + | 0.0712550i | ||||
\(79\) | −10.2106 | −1.14879 | −0.574394 | − | 0.818579i | \(-0.694762\pi\) | ||||
−0.574394 | + | 0.818579i | \(0.694762\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.79309 | − | 6.56982i | −0.421454 | − | 0.729980i | ||||
\(82\) | −5.19812 | + | 9.00341i | −0.574036 | + | 0.994260i | ||||
\(83\) | − | 1.18065i | − | 0.129593i | −0.997899 | − | 0.0647964i | \(-0.979360\pi\) | ||
0.997899 | − | 0.0647964i | \(-0.0206398\pi\) | |||||||
\(84\) | 0.170842 | + | 0.0986359i | 0.0186404 | + | 0.0107621i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.23818i | 0.564848i | ||||||||
\(87\) | 0.612748 | − | 1.06131i | 0.0656935 | − | 0.113785i | ||||
\(88\) | 4.77784 | + | 8.27547i | 0.509320 | + | 0.882168i | ||||
\(89\) | 2.82548 | − | 1.63129i | 0.299500 | − | 0.172916i | −0.342718 | − | 0.939438i | \(-0.611348\pi\) |
0.642218 | + | 0.766522i | \(0.278014\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.4483 | − | 4.19889i | −1.30494 | − | 0.440163i | ||||
\(92\) | −0.103573 | −0.0107983 | ||||||||
\(93\) | −2.91559 | + | 1.68332i | −0.302333 | + | 0.174552i | ||||
\(94\) | 3.19736 | + | 5.53799i | 0.329783 | + | 0.571200i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.305731i | 0.0312035i | ||||||||
\(97\) | 4.54898 | + | 2.62636i | 0.461879 | + | 0.266666i | 0.712834 | − | 0.701333i | \(-0.247411\pi\) |
−0.250955 | + | 0.967999i | \(0.580745\pi\) | |||||||
\(98\) | 7.42204 | + | 4.28511i | 0.749739 | + | 0.432862i | ||||
\(99\) | − | 9.30722i | − | 0.935410i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.53815 | + | 14.7885i | 0.849577 | + | 1.47151i | 0.881586 | + | 0.472024i | \(0.156476\pi\) |
−0.0320085 | + | 0.999488i | \(0.510190\pi\) | |||||||
\(102\) | −1.02891 | + | 0.594042i | −0.101877 | + | 0.0588189i | ||||
\(103\) | −0.810478 | −0.0798588 | −0.0399294 | − | 0.999203i | \(-0.512713\pi\) | ||||
−0.0399294 | + | 0.999203i | \(0.512713\pi\) | |||||||
\(104\) | −2.07093 | − | 10.3074i | −0.203071 | − | 1.01072i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.60264 | − | 2.07998i | 0.349919 | − | 0.202026i | ||||
\(107\) | −6.69352 | − | 11.5935i | −0.647087 | − | 1.12079i | −0.983815 | − | 0.179185i | \(-0.942654\pi\) |
0.336728 | − | 0.941602i | \(-0.390680\pi\) | |||||||
\(108\) | 0.158094 | − | 0.273827i | 0.0152126 | − | 0.0263490i | ||||
\(109\) | 5.61232i | 0.537562i | 0.963201 | + | 0.268781i | \(0.0866208\pi\) | ||||
−0.963201 | + | 0.268781i | \(0.913379\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.76041 | + | 2.17107i | 0.356922 | + | 0.206069i | ||||
\(112\) | 13.5213i | 1.27764i | ||||||||
\(113\) | 9.11615 | − | 15.7896i | 0.857575 | − | 1.48536i | −0.0166601 | − | 0.999861i | \(-0.505303\pi\) |
0.874235 | − | 0.485503i | \(-0.161363\pi\) | |||||||
\(114\) | 0.234191 | + | 0.405630i | 0.0219340 | + | 0.0379907i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.414858 | −0.0385186 | ||||||||
\(117\) | −3.27285 | + | 9.70289i | −0.302575 | + | 0.897033i | ||||
\(118\) | −18.1923 | −1.67474 | ||||||||
\(119\) | 6.86513 | − | 3.96359i | 0.629326 | − | 0.363341i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.130266 | + | 0.225627i | −0.0118423 | + | 0.0205115i | ||||
\(122\) | − | 17.7934i | − | 1.61094i | ||||||
\(123\) | 2.63683 | + | 1.52238i | 0.237755 | + | 0.137268i | ||||
\(124\) | 0.986993 | + | 0.569841i | 0.0886346 | + | 0.0511732i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.06530 | − | 12.2375i | 0.629427 | − | 1.09020i | ||||
\(127\) | −8.48513 | − | 14.6967i | −0.752933 | − | 1.30412i | −0.946395 | − | 0.323011i | \(-0.895305\pi\) |
0.193462 | − | 0.981108i | \(-0.438028\pi\) | |||||||
\(128\) | −8.68717 | + | 5.01554i | −0.767844 | + | 0.443315i | ||||
\(129\) | 1.53411 | 0.135071 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.7226 | −1.54843 | −0.774215 | − | 0.632923i | \(-0.781855\pi\) | ||||
−0.774215 | + | 0.632923i | \(0.781855\pi\) | |||||||
\(132\) | 0.153656 | − | 0.0887135i | 0.0133741 | − | 0.00772152i | ||||
\(133\) | −1.56258 | − | 2.70646i | −0.135492 | − | 0.234680i | ||||
\(134\) | −3.17340 | + | 5.49649i | −0.274140 | + | 0.474825i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.49392 | + | 3.17192i | 0.471100 | + | 0.271990i | ||||
\(137\) | 13.9505 | + | 8.05434i | 1.19187 | + | 0.688129i | 0.958731 | − | 0.284314i | \(-0.0917658\pi\) |
0.233143 | + | 0.972443i | \(0.425099\pi\) | |||||||
\(138\) | − | 0.417788i | − | 0.0355645i | ||||||
\(139\) | 1.71547 | − | 2.97129i | 0.145505 | − | 0.252021i | −0.784057 | − | 0.620689i | \(-0.786853\pi\) |
0.929561 | + | 0.368668i | \(0.120186\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.62191 | − | 0.936412i | 0.136590 | − | 0.0788602i | ||||
\(142\) | 14.7962 | 1.24167 | ||||||||
\(143\) | −8.86856 | + | 7.80781i | −0.741626 | + | 0.652922i | ||||
\(144\) | 10.5392 | 0.878269 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.24569 | − | 9.08581i | −0.434137 | − | 0.751947i | ||||
\(147\) | 1.25498 | − | 2.17369i | 0.103509 | − | 0.179283i | ||||
\(148\) | − | 1.46991i | − | 0.120826i | ||||||
\(149\) | 16.1603 | + | 9.33018i | 1.32391 | + | 0.764358i | 0.984350 | − | 0.176227i | \(-0.0563893\pi\) |
0.339558 | + | 0.940585i | \(0.389723\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.63134i | − | 0.539651i | −0.962909 | − | 0.269826i | \(-0.913034\pi\) | ||
0.962909 | − | 0.269826i | \(-0.0869660\pi\) | |||||||
\(152\) | 1.25047 | − | 2.16588i | 0.101427 | − | 0.175676i | ||||
\(153\) | −3.08944 | − | 5.35107i | −0.249766 | − | 0.432608i | ||||
\(154\) | 14.1206 | − | 8.15255i | 1.13787 | − | 0.656951i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.191384 | + | 0.0384523i | −0.0153230 | + | 0.00307865i | ||||
\(157\) | −4.61502 | −0.368319 | −0.184159 | − | 0.982896i | \(-0.558956\pi\) | ||||
−0.184159 | + | 0.982896i | \(0.558956\pi\) | |||||||
\(158\) | −12.0748 | + | 6.97137i | −0.960617 | + | 0.554613i | ||||
\(159\) | −0.609166 | − | 1.05511i | −0.0483100 | − | 0.0836754i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.78758i | 0.219692i | ||||||||
\(162\) | −8.97115 | − | 5.17950i | −0.704840 | − | 0.406940i | ||||
\(163\) | 8.44402 | + | 4.87516i | 0.661387 | + | 0.381852i | 0.792805 | − | 0.609475i | \(-0.208620\pi\) |
−0.131418 | + | 0.991327i | \(0.541953\pi\) | |||||||
\(164\) | − | 1.03072i | − | 0.0804853i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.806093 | − | 1.39619i | −0.0625649 | − | 0.108366i | ||||
\(167\) | −8.99356 | + | 5.19243i | −0.695943 | + | 0.401803i | −0.805834 | − | 0.592141i | \(-0.798283\pi\) |
0.109892 | + | 0.993944i | \(0.464950\pi\) | |||||||
\(168\) | 4.24892 | 0.327811 | ||||||||
\(169\) | 11.9912 | − | 5.02115i | 0.922397 | − | 0.386242i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.10956 | + | 1.21796i | −0.161322 | + | 0.0931396i | ||||
\(172\) | −0.259665 | − | 0.449753i | −0.0197993 | − | 0.0342933i | ||||
\(173\) | −7.64543 | + | 13.2423i | −0.581271 | + | 1.00679i | 0.414058 | + | 0.910251i | \(0.364111\pi\) |
−0.995329 | + | 0.0965406i | \(0.969222\pi\) | |||||||
\(174\) | − | 1.67343i | − | 0.126862i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.5318 | + | 6.08054i | 0.793864 | + | 0.458338i | ||||
\(177\) | 5.32799i | 0.400476i | ||||||||
\(178\) | 2.22754 | − | 3.85822i | 0.166961 | − | 0.289186i | ||||
\(179\) | 5.80307 | + | 10.0512i | 0.433742 | + | 0.751263i | 0.997192 | − | 0.0748869i | \(-0.0238596\pi\) |
−0.563450 | + | 0.826150i | \(0.690526\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.01543 | 0.298464 | 0.149232 | − | 0.988802i | \(-0.452320\pi\) | ||||
0.149232 | + | 0.988802i | \(0.452320\pi\) | |||||||
\(182\) | −17.5878 | + | 3.53368i | −1.30369 | + | 0.261933i | ||||
\(183\) | −5.21117 | −0.385221 | ||||||||
\(184\) | −1.93193 | + | 1.11540i | −0.142424 | + | 0.0822284i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.29859 | + | 3.98128i | −0.168541 | + | 0.291921i | ||||
\(187\) | − | 7.12972i | − | 0.521377i | ||||||
\(188\) | −0.549054 | − | 0.316996i | −0.0400439 | − | 0.0231193i | ||||
\(189\) | −7.36981 | − | 4.25496i | −0.536074 | − | 0.309503i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.964496 | − | 1.67056i | 0.0697884 | − | 0.120877i | −0.829020 | − | 0.559219i | \(-0.811101\pi\) |
0.898808 | + | 0.438342i | \(0.144434\pi\) | |||||||
\(192\) | 1.69280 | + | 2.93201i | 0.122167 | + | 0.211600i | ||||
\(193\) | −4.60933 | + | 2.66120i | −0.331787 | + | 0.191557i | −0.656634 | − | 0.754209i | \(-0.728020\pi\) |
0.324847 | + | 0.945766i | \(0.394687\pi\) | |||||||
\(194\) | 7.17263 | 0.514965 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.849679 | −0.0606914 | ||||||||
\(197\) | 13.2873 | − | 7.67142i | 0.946681 | − | 0.546566i | 0.0546323 | − | 0.998507i | \(-0.482601\pi\) |
0.892048 | + | 0.451940i | \(0.149268\pi\) | |||||||
\(198\) | −6.35455 | − | 11.0064i | −0.451598 | − | 0.782191i | ||||
\(199\) | 10.6435 | − | 18.4351i | 0.754500 | − | 1.30683i | −0.191123 | − | 0.981566i | \(-0.561213\pi\) |
0.945623 | − | 0.325266i | \(-0.105454\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.60976 | + | 0.929396i | 0.113544 | + | 0.0655545i | ||||
\(202\) | 20.1939 | + | 11.6589i | 1.42083 | + | 0.820319i | ||||
\(203\) | 11.1655i | 0.783665i | ||||||||
\(204\) | 0.0588951 | − | 0.102009i | 0.00412349 | − | 0.00714209i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.958444 | + | 0.553358i | −0.0667780 | + | 0.0385543i | ||||
\(207\) | 2.17280 | 0.151020 | ||||||||
\(208\) | −8.84134 | − | 10.0425i | −0.613037 | − | 0.696322i | ||||
\(209\) | −2.81077 | −0.194425 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.82083 | + | 11.8140i | 0.469566 | + | 0.813311i | 0.999395 | − | 0.0347931i | \(-0.0110772\pi\) |
−0.529829 | + | 0.848105i | \(0.677744\pi\) | |||||||
\(212\) | −0.206216 | + | 0.357177i | −0.0141630 | + | 0.0245310i | ||||
\(213\) | − | 4.33336i | − | 0.296917i | ||||||
\(214\) | −15.8311 | − | 9.14007i | −1.08219 | − | 0.624802i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 6.81018i | − | 0.463374i | ||||||
\(217\) | 15.3367 | − | 26.5640i | 1.04113 | − | 1.80328i | ||||
\(218\) | 3.83184 | + | 6.63694i | 0.259525 | + | 0.449510i | ||||
\(219\) | −2.66096 | + | 1.53631i | −0.179811 | + | 0.103814i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.50714 | + | 7.43283i | −0.168648 | + | 0.499986i | ||||
\(222\) | 5.92924 | 0.397945 | ||||||||
\(223\) | 21.4013 | − | 12.3560i | 1.43314 | − | 0.827422i | 0.435778 | − | 0.900054i | \(-0.356473\pi\) |
0.997359 | + | 0.0726324i | \(0.0231400\pi\) | |||||||
\(224\) | −1.39276 | − | 2.41233i | −0.0930575 | − | 0.161180i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 24.8964i | − | 1.65608i | ||||||
\(227\) | 10.2349 | + | 5.90911i | 0.679313 | + | 0.392201i | 0.799596 | − | 0.600538i | \(-0.205047\pi\) |
−0.120283 | + | 0.992740i | \(0.538380\pi\) | |||||||
\(228\) | −0.0402154 | − | 0.0232184i | −0.00266333 | − | 0.00153768i | ||||
\(229\) | 2.98379i | 0.197174i | 0.995128 | + | 0.0985872i | \(0.0314323\pi\) | ||||
−0.995128 | + | 0.0985872i | \(0.968568\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.38764 | − | 4.13552i | −0.157095 | − | 0.272097i | ||||
\(232\) | −7.73825 | + | 4.46768i | −0.508041 | + | 0.293317i | ||||
\(233\) | −6.88071 | −0.450770 | −0.225385 | − | 0.974270i | \(-0.572364\pi\) | ||||
−0.225385 | + | 0.974270i | \(0.572364\pi\) | |||||||
\(234\) | 2.75434 | + | 13.7089i | 0.180057 | + | 0.896177i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.56200 | − | 0.901821i | 0.101678 | − | 0.0587036i | ||||
\(237\) | 2.04171 | + | 3.53634i | 0.132623 | + | 0.229710i | ||||
\(238\) | 5.41232 | − | 9.37441i | 0.350829 | − | 0.607653i | ||||
\(239\) | 18.3427i | 1.18649i | 0.805021 | + | 0.593246i | \(0.202154\pi\) | ||||
−0.805021 | + | 0.593246i | \(0.797846\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4077 | + | 8.31828i | 0.928080 | + | 0.535827i | 0.886204 | − | 0.463296i | \(-0.153333\pi\) |
0.0418762 | + | 0.999123i | \(0.486667\pi\) | |||||||
\(242\) | 0.355758i | 0.0228690i | ||||||||
\(243\) | −5.02024 | + | 8.69531i | −0.322049 | + | 0.557804i | ||||
\(244\) | 0.882049 | + | 1.52775i | 0.0564674 | + | 0.0978044i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.15764 | 0.265081 | ||||||||
\(247\) | 2.93026 | + | 0.988396i | 0.186448 | + | 0.0628901i | ||||
\(248\) | 24.5469 | 1.55873 | ||||||||
\(249\) | −0.408904 | + | 0.236081i | −0.0259132 | + | 0.0149610i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.40485 | + | 2.43327i | −0.0886733 | + | 0.153587i | −0.906951 | − | 0.421237i | \(-0.861596\pi\) |
0.818277 | + | 0.574824i | \(0.194929\pi\) | |||||||
\(252\) | 1.40095i | 0.0882516i | ||||||||
\(253\) | 2.17126 | + | 1.25358i | 0.136506 | + | 0.0788119i | ||||
\(254\) | −20.0685 | − | 11.5865i | −1.25921 | − | 0.727003i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.61696 | − | 2.80066i | 0.101060 | − | 0.175041i | ||||
\(257\) | 1.65946 | + | 2.87428i | 0.103515 | + | 0.179292i | 0.913130 | − | 0.407668i | \(-0.133658\pi\) |
−0.809616 | + | 0.586960i | \(0.800325\pi\) | |||||||
\(258\) | 1.81419 | − | 1.04742i | 0.112946 | − | 0.0652096i | ||||
\(259\) | −39.5613 | −2.45822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.70302 | 0.538703 | ||||||||
\(262\) | −20.9581 | + | 12.1002i | −1.29480 | + | 0.747552i | ||||
\(263\) | 12.4809 | + | 21.6176i | 0.769606 | + | 1.33300i | 0.937777 | + | 0.347239i | \(0.112881\pi\) |
−0.168171 | + | 0.985758i | \(0.553786\pi\) | |||||||
\(264\) | 1.91074 | − | 3.30951i | 0.117598 | − | 0.203686i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.69570 | − | 2.13371i | −0.226598 | − | 0.130826i | ||||
\(267\) | −1.12996 | − | 0.652382i | −0.0691523 | − | 0.0399251i | ||||
\(268\) | − | 0.629242i | − | 0.0384371i | ||||||
\(269\) | −5.76837 | + | 9.99111i | −0.351704 | + | 0.609169i | −0.986548 | − | 0.163471i | \(-0.947731\pi\) |
0.634844 | + | 0.772640i | \(0.281064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.3047 | + | 9.99086i | −1.05118 | + | 0.606902i | −0.922981 | − | 0.384846i | \(-0.874254\pi\) |
−0.128204 | + | 0.991748i | \(0.540921\pi\) | |||||||
\(272\) | 8.07350 | 0.489528 | ||||||||
\(273\) | 1.03491 | + | 5.15093i | 0.0626356 | + | 0.311749i | ||||
\(274\) | 21.9966 | 1.32886 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.0207104 | + | 0.0358715i | 0.00124662 | + | 0.00215921i | ||||
\(277\) | −3.06053 | + | 5.30099i | −0.183889 | + | 0.318506i | −0.943202 | − | 0.332221i | \(-0.892202\pi\) |
0.759312 | + | 0.650726i | \(0.225535\pi\) | |||||||
\(278\) | − | 4.68499i | − | 0.280987i | ||||||
\(279\) | −20.7055 | − | 11.9543i | −1.23960 | − | 0.715686i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.6283i | 1.52885i | 0.644711 | + | 0.764427i | \(0.276978\pi\) | ||||
−0.644711 | + | 0.764427i | \(0.723022\pi\) | |||||||
\(282\) | 1.27868 | − | 2.21474i | 0.0761444 | − | 0.131886i | ||||
\(283\) | −8.84118 | − | 15.3134i | −0.525553 | − | 0.910285i | −0.999557 | − | 0.0297622i | \(-0.990525\pi\) |
0.474004 | − | 0.880523i | \(-0.342808\pi\) | |||||||
\(284\) | −1.27040 | + | 0.733468i | −0.0753846 | + | 0.0435233i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.15684 | + | 15.2883i | −0.304930 | + | 0.904016i | ||||
\(287\) | −27.7407 | −1.63748 | ||||||||
\(288\) | −1.88030 | + | 1.08559i | −0.110798 | + | 0.0639691i | ||||
\(289\) | 6.13336 | + | 10.6233i | 0.360786 | + | 0.624899i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 2.10065i | − | 0.123142i | ||||||
\(292\) | 0.900795 | + | 0.520074i | 0.0527151 | + | 0.0304351i | ||||
\(293\) | −19.0564 | − | 11.0022i | −1.11329 | − | 0.642757i | −0.173609 | − | 0.984815i | \(-0.555543\pi\) |
−0.939679 | + | 0.342058i | \(0.888876\pi\) | |||||||
\(294\) | − | 3.42739i | − | 0.199889i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −15.8297 | − | 27.4179i | −0.920085 | − | 1.59363i | ||||
\(297\) | −6.62843 | + | 3.82692i | −0.384620 | + | 0.222061i | ||||
\(298\) | 25.4809 | 1.47607 | ||||||||
\(299\) | −1.82275 | − | 2.07039i | −0.105413 | − | 0.119734i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.1047 | + | 6.98864i | −0.697702 | + | 0.402818i | ||||
\(302\) | −4.52759 | − | 7.84201i | −0.260533 | − | 0.451257i | ||||
\(303\) | 3.41456 | − | 5.91418i | 0.196161 | − | 0.339761i | ||||
\(304\) | − | 3.18284i | − | 0.182548i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.30694 | − | 4.21866i | −0.417710 | − | 0.241165i | ||||
\(307\) | 1.63084i | 0.0930769i | 0.998917 | + | 0.0465384i | \(0.0148190\pi\) | ||||
−0.998917 | + | 0.0465384i | \(0.985181\pi\) | |||||||
\(308\) | −0.808269 | + | 1.39996i | −0.0460554 | + | 0.0797703i | ||||
\(309\) | 0.162062 | + | 0.280700i | 0.00921940 | + | 0.0159685i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.0053 | 1.07769 | 0.538845 | − | 0.842405i | \(-0.318861\pi\) | ||||
0.538845 | + | 0.842405i | \(0.318861\pi\) | |||||||
\(312\) | −3.15575 | + | 2.77830i | −0.178659 | + | 0.157290i | ||||
\(313\) | 11.1004 | 0.627434 | 0.313717 | − | 0.949517i | \(-0.398426\pi\) | ||||
0.313717 | + | 0.949517i | \(0.398426\pi\) | |||||||
\(314\) | −5.45757 | + | 3.15093i | −0.307989 | + | 0.177817i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.691164 | − | 1.19713i | 0.0388810 | − | 0.0673438i | ||||
\(317\) | 5.22062i | 0.293219i | 0.989194 | + | 0.146610i | \(0.0468361\pi\) | ||||
−0.989194 | + | 0.146610i | \(0.953164\pi\) | |||||||
\(318\) | −1.44076 | − | 0.831822i | −0.0807937 | − | 0.0466463i | ||||
\(319\) | 8.69688 | + | 5.02115i | 0.486932 | + | 0.281130i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.67686 | + | 4.63645i | −0.149408 | + | 0.258781i | ||||
\(322\) | 1.90324 | + | 3.29650i | 0.106063 | + | 0.183707i | ||||
\(323\) | −1.61602 | + | 0.933008i | −0.0899176 | + | 0.0519139i | ||||
\(324\) | 1.02702 | 0.0570568 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.3142 | 0.737403 | ||||||||
\(327\) | 1.94376 | − | 1.12223i | 0.107490 | − | 0.0620596i | ||||
\(328\) | −11.1000 | − | 19.2257i | −0.612893 | − | 1.06156i | ||||
\(329\) | −8.53166 | + | 14.7773i | −0.470366 | + | 0.814697i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.2027 | − | 12.8187i | −1.22037 | − | 0.704582i | −0.255374 | − | 0.966842i | \(-0.582199\pi\) |
−0.964997 | + | 0.262261i | \(0.915532\pi\) | |||||||
\(332\) | 0.138423 | + | 0.0799185i | 0.00759695 | + | 0.00438610i | ||||
\(333\) | 30.8363i | 1.68982i | ||||||||
\(334\) | −7.09032 | + | 12.2808i | −0.387965 | + | 0.671975i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.68294 | − | 2.70370i | 0.255475 | − | 0.147499i | ||||
\(337\) | −36.1447 | −1.96892 | −0.984462 | − | 0.175596i | \(-0.943815\pi\) | ||||
−0.984462 | + | 0.175596i | \(0.943815\pi\) | |||||||
\(338\) | 10.7521 | − | 14.1249i | 0.584839 | − | 0.768292i | ||||
\(339\) | −7.29142 | −0.396015 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.7939 | − | 23.8918i | −0.746982 | − | 1.29381i | ||||
\(342\) | −1.66313 | + | 2.88063i | −0.0899320 | + | 0.155767i | ||||
\(343\) | − | 2.63725i | − | 0.142398i | ||||||
\(344\) | −9.68694 | − | 5.59276i | −0.522285 | − | 0.301541i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.8798i | 1.12251i | ||||||||
\(347\) | 7.20541 | − | 12.4801i | 0.386806 | − | 0.669968i | −0.605212 | − | 0.796065i | \(-0.706911\pi\) |
0.992018 | + | 0.126096i | \(0.0402448\pi\) | |||||||
\(348\) | 0.0829545 | + | 0.143681i | 0.00444683 | + | 0.00770213i | ||||
\(349\) | −2.89197 | + | 1.66968i | −0.154803 | + | 0.0893758i | −0.575401 | − | 0.817872i | \(-0.695154\pi\) |
0.420597 | + | 0.907247i | \(0.361821\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.25594 | − | 1.65876i | 0.440670 | − | 0.0885379i | ||||
\(352\) | −2.50530 | −0.133533 | ||||||||
\(353\) | −10.1157 | + | 5.84028i | −0.538403 | + | 0.310847i | −0.744431 | − | 0.667699i | \(-0.767279\pi\) |
0.206029 | + | 0.978546i | \(0.433946\pi\) | |||||||
\(354\) | 3.63771 | + | 6.30071i | 0.193342 | + | 0.334879i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.441691i | 0.0234096i | ||||||||
\(357\) | −2.74549 | − | 1.58511i | −0.145307 | − | 0.0838928i | ||||
\(358\) | 13.7250 | + | 7.92416i | 0.725391 | + | 0.418805i | ||||
\(359\) | − | 6.54679i | − | 0.345526i | −0.984963 | − | 0.172763i | \(-0.944730\pi\) | ||
0.984963 | − | 0.172763i | \(-0.0552695\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.13218 | − | 15.8174i | −0.480641 | − | 0.832495i | ||||
\(362\) | 4.74851 | − | 2.74155i | 0.249576 | − | 0.144093i | ||||
\(363\) | 0.104191 | 0.00546861 | ||||||||
\(364\) | 1.33492 | − | 1.17526i | 0.0699690 | − | 0.0616001i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.16256 | + | 3.55796i | −0.322122 | + | 0.185977i | ||||
\(367\) | −11.3109 | − | 19.5911i | −0.590425 | − | 1.02265i | −0.994175 | − | 0.107777i | \(-0.965627\pi\) |
0.403750 | − | 0.914869i | \(-0.367706\pi\) | |||||||
\(368\) | −1.41952 | + | 2.45868i | −0.0739975 | + | 0.128167i | ||||
\(369\) | 21.6227i | 1.12563i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.61308 | + | 5.55011i | 0.499086 | + | 0.288148i | ||||
\(372\) | − | 0.455779i | − | 0.0236310i | ||||||
\(373\) | −2.12583 | + | 3.68204i | −0.110071 | + | 0.190649i | −0.915799 | − | 0.401637i | \(-0.868441\pi\) |
0.805728 | + | 0.592286i | \(0.201775\pi\) | |||||||
\(374\) | −4.86786 | − | 8.43138i | −0.251711 | − | 0.435976i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.6552 | −0.704211 | ||||||||
\(377\) | −7.30095 | − | 8.29283i | −0.376018 | − | 0.427103i | ||||
\(378\) | −11.6204 | −0.597688 | ||||||||
\(379\) | 9.64880 | − | 5.57074i | 0.495626 | − | 0.286150i | −0.231280 | − | 0.972887i | \(-0.574291\pi\) |
0.726905 | + | 0.686738i | \(0.240958\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.39335 | + | 5.87746i | −0.173847 | + | 0.301111i | ||||
\(382\) | − | 2.63406i | − | 0.134770i | ||||||
\(383\) | 4.75384 | + | 2.74463i | 0.242910 | + | 0.140244i | 0.616513 | − | 0.787344i | \(-0.288545\pi\) |
−0.373604 | + | 0.927588i | \(0.621878\pi\) | |||||||
\(384\) | 3.47415 | + | 2.00580i | 0.177290 | + | 0.102358i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.63389 | + | 6.29409i | −0.184960 | + | 0.320361i | ||||
\(387\) | 5.44733 | + | 9.43506i | 0.276903 | + | 0.479611i | ||||
\(388\) | −0.615846 | + | 0.355559i | −0.0312648 | + | 0.0180508i | ||||
\(389\) | 25.9475 | 1.31559 | 0.657794 | − | 0.753198i | \(-0.271490\pi\) | ||||
0.657794 | + | 0.753198i | \(0.271490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.66445 | 0.0841751 | ||||||||
\(392\) | −15.8489 | + | 9.15035i | −0.800489 | + | 0.462163i | ||||
\(393\) | 3.54379 | + | 6.13802i | 0.178760 | + | 0.309622i | ||||
\(394\) | 10.4754 | − | 18.1439i | 0.527743 | − | 0.914079i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.09121 | + | 0.630010i | 0.0548353 | + | 0.0316592i | ||||
\(397\) | 12.0123 | + | 6.93530i | 0.602880 | + | 0.348073i | 0.770174 | − | 0.637834i | \(-0.220170\pi\) |
−0.167294 | + | 0.985907i | \(0.553503\pi\) | |||||||
\(398\) | − | 29.0677i | − | 1.45703i | ||||||
\(399\) | −0.624901 | + | 1.08236i | −0.0312842 | + | 0.0541858i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.09405 | + | 0.631649i | −0.0546341 | + | 0.0315430i | −0.527068 | − | 0.849823i | \(-0.676709\pi\) |
0.472434 | + | 0.881366i | \(0.343375\pi\) | |||||||
\(402\) | 2.53820 | 0.126594 | ||||||||
\(403\) | 5.97889 | + | 29.7580i | 0.297830 | + | 1.48235i | ||||
\(404\) | −2.31181 | −0.115017 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.62331 | + | 13.2040i | 0.378339 | + | 0.655302i | ||||
\(407\) | −17.7908 | + | 30.8145i | −0.881856 | + | 1.52742i | ||||
\(408\) | − | 2.53701i | − | 0.125601i | ||||||
\(409\) | 19.0947 | + | 11.0243i | 0.944171 | + | 0.545117i | 0.891265 | − | 0.453482i | \(-0.149818\pi\) |
0.0529055 | + | 0.998600i | \(0.483152\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.44215i | − | 0.317768i | ||||||
\(412\) | 0.0548616 | − | 0.0950231i | 0.00270284 | − | 0.00468145i | ||||
\(413\) | −24.2717 | − | 42.0398i | −1.19433 | − | 2.06864i | ||||
\(414\) | 2.56948 | − | 1.48349i | 0.126283 | − | 0.0729095i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.61181 | + | 0.880978i | 0.128054 | + | 0.0431935i | ||||
\(417\) | −1.37210 | −0.0671918 | ||||||||
\(418\) | −3.32392 | + | 1.91907i | −0.162578 | + | 0.0938647i | ||||
\(419\) | −5.84019 | − | 10.1155i | −0.285312 | − | 0.494175i | 0.687373 | − | 0.726305i | \(-0.258764\pi\) |
−0.972685 | + | 0.232130i | \(0.925431\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.9773i | 1.07111i | 0.844501 | + | 0.535555i | \(0.179897\pi\) | ||||
−0.844501 | + | 0.535555i | \(0.820103\pi\) | |||||||
\(422\) | 16.1322 | + | 9.31392i | 0.785302 | + | 0.453395i | ||||
\(423\) | 11.5182 | + | 6.65005i | 0.560035 | + | 0.323337i | ||||
\(424\) | 8.88312i | 0.431402i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.95862 | − | 5.12448i | −0.143346 | − | 0.248282i | ||||
\(427\) | 41.1181 | − | 23.7395i | 1.98984 | − | 1.14884i | ||||
\(428\) | 1.81235 | 0.0876032 | ||||||||
\(429\) | 4.47749 | + | 1.51029i | 0.216175 | + | 0.0729173i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.8856 | − | 12.0583i | 1.00602 | − | 0.580828i | 0.0959983 | − | 0.995382i | \(-0.469396\pi\) |
0.910025 | + | 0.414554i | \(0.136062\pi\) | |||||||
\(432\) | −4.33350 | − | 7.50584i | −0.208496 | − | 0.361125i | ||||
\(433\) | −3.34590 | + | 5.79527i | −0.160794 | + | 0.278503i | −0.935154 | − | 0.354243i | \(-0.884739\pi\) |
0.774360 | + | 0.632746i | \(0.218072\pi\) | |||||||
\(434\) | − | 41.8850i | − | 2.01054i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.658007 | − | 0.379900i | −0.0315128 | − | 0.0181939i | ||||
\(437\) | − | 0.656182i | − | 0.0313894i | ||||||
\(438\) | −2.09785 | + | 3.63358i | −0.100239 | + | 0.173619i | ||||
\(439\) | −13.9887 | − | 24.2292i | −0.667646 | − | 1.15640i | −0.978561 | − | 0.205959i | \(-0.933969\pi\) |
0.310915 | − | 0.950438i | \(-0.399365\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.8248 | 0.848802 | ||||||||
\(442\) | 2.10994 | + | 10.5016i | 0.100360 | + | 0.499509i | ||||
\(443\) | −19.4755 | −0.925309 | −0.462655 | − | 0.886539i | \(-0.653103\pi\) | ||||
−0.462655 | + | 0.886539i | \(0.653103\pi\) | |||||||
\(444\) | −0.509087 | + | 0.293922i | −0.0241602 | + | 0.0139489i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.8723 | − | 29.2237i | 0.798927 | − | 1.38378i | ||||
\(447\) | − | 7.46261i | − | 0.352969i | ||||||
\(448\) | −26.7136 | − | 15.4231i | −1.26210 | − | 0.728673i | ||||
\(449\) | 11.4203 | + | 6.59349i | 0.538955 | + | 0.311166i | 0.744655 | − | 0.667449i | \(-0.232614\pi\) |
−0.205700 | + | 0.978615i | \(0.565947\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.4751 | + | 21.6074i | −0.587428 | + | 1.01745i | ||||
\(452\) | 1.23415 | + | 2.13762i | 0.0580497 | + | 0.100545i | ||||
\(453\) | −2.29669 | + | 1.32600i | −0.107908 | + | 0.0623007i | ||||
\(454\) | 16.1379 | 0.757389 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00017 | −0.0468374 | ||||||||
\(457\) | 12.0014 | − | 6.92898i | 0.561400 | − | 0.324124i | −0.192307 | − | 0.981335i | \(-0.561597\pi\) |
0.753707 | + | 0.657211i | \(0.228264\pi\) | |||||||
\(458\) | 2.03720 | + | 3.52853i | 0.0951920 | + | 0.164877i | ||||
\(459\) | −2.54062 | + | 4.40048i | −0.118586 | + | 0.205397i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.1823 | − | 7.03343i | −0.567384 | − | 0.327580i | 0.188720 | − | 0.982031i | \(-0.439566\pi\) |
−0.756104 | + | 0.654451i | \(0.772900\pi\) | |||||||
\(462\) | −5.64709 | − | 3.26035i | −0.262726 | − | 0.151685i | ||||
\(463\) | 4.86555i | 0.226121i | 0.993588 | + | 0.113061i | \(0.0360655\pi\) | ||||
−0.993588 | + | 0.113061i | \(0.963935\pi\) | |||||||
\(464\) | −5.68580 | + | 9.84810i | −0.263957 | + | 0.457187i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.13690 | + | 4.69784i | −0.376934 | + | 0.217623i | ||||
\(467\) | 26.6409 | 1.23279 | 0.616397 | − | 0.787436i | \(-0.288592\pi\) | ||||
0.616397 | + | 0.787436i | \(0.288592\pi\) | |||||||
\(468\) | −0.916059 | − | 1.04051i | −0.0423449 | − | 0.0480977i | ||||
\(469\) | −16.9355 | −0.782007 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.922815 | + | 1.59836i | 0.0425210 | + | 0.0736486i | ||||
\(472\) | 19.4238 | − | 33.6429i | 0.894051 | − | 1.54854i | ||||
\(473\) | 12.5712i | 0.578024i | ||||||||
\(474\) | 4.82891 | + | 2.78798i | 0.221799 | + | 0.128056i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.07319i | 0.0491895i | ||||||||
\(477\) | 4.32607 | − | 7.49297i | 0.198077 | − | 0.343079i | ||||
\(478\) | 12.5236 | + | 21.6915i | 0.572816 | + | 0.992146i | ||||
\(479\) | −2.61805 | + | 1.51153i | −0.119622 | + | 0.0690637i | −0.558617 | − | 0.829426i | \(-0.688668\pi\) |
0.438995 | + | 0.898489i | \(0.355335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.3829 | − | 25.8685i | 1.33975 | − | 1.17950i | ||||
\(482\) | 22.7174 | 1.03475 | ||||||||
\(483\) | 0.965448 | − | 0.557402i | 0.0439294 | − | 0.0253627i | ||||
\(484\) | −0.0176355 | − | 0.0305455i | −0.000801612 | − | 0.00138843i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13.7104i | 0.621916i | ||||||||
\(487\) | 10.2365 | + | 5.91003i | 0.463859 | + | 0.267809i | 0.713665 | − | 0.700487i | \(-0.247034\pi\) |
−0.249807 | + | 0.968296i | \(0.580367\pi\) | |||||||
\(488\) | 32.9053 | + | 18.9979i | 1.48955 | + | 0.859994i | ||||
\(489\) | − | 3.89932i | − | 0.176333i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.82314 | + | 8.35393i | 0.217665 | + | 0.377008i | 0.954094 | − | 0.299508i | \(-0.0968225\pi\) |
−0.736428 | + | 0.676516i | \(0.763489\pi\) | |||||||
\(492\) | −0.356977 | + | 0.206101i | −0.0160938 | + | 0.00929173i | ||||
\(493\) | 6.66688 | 0.300261 | ||||||||
\(494\) | 4.14007 | − | 0.831809i | 0.186270 | − | 0.0374249i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 27.0543 | − | 15.6198i | 1.21478 | − | 0.701351i | ||||
\(497\) | 19.7406 | + | 34.1918i | 0.885488 | + | 1.53371i | ||||
\(498\) | −0.322371 | + | 0.558362i | −0.0144458 | + | 0.0250208i | ||||
\(499\) | 10.0807i | 0.451274i | 0.974211 | + | 0.225637i | \(0.0724463\pi\) | ||||
−0.974211 | + | 0.225637i | \(0.927554\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.59668 | + | 2.07655i | 0.160688 | + | 0.0927732i | ||||
\(502\) | 3.83667i | 0.171239i | ||||||||
\(503\) | 8.37337 | − | 14.5031i | 0.373350 | − | 0.646661i | −0.616728 | − | 0.787176i | \(-0.711542\pi\) |
0.990079 | + | 0.140515i | \(0.0448757\pi\) | |||||||
\(504\) | 15.0871 | + | 26.1316i | 0.672033 | + | 1.16400i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.42355 | 0.152195 | ||||||||
\(507\) | −4.13676 | − | 3.14898i | −0.183720 | − | 0.139851i | ||||
\(508\) | 2.29745 | 0.101933 | ||||||||
\(509\) | 27.2473 | − | 15.7313i | 1.20772 | − | 0.697276i | 0.245457 | − | 0.969407i | \(-0.421062\pi\) |
0.962260 | + | 0.272132i | \(0.0877286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.9973 | − | 24.2441i | 0.619205 | − | 1.07249i | ||||
\(512\) | − | 24.4781i | − | 1.08179i | ||||||
\(513\) | 1.73481 | + | 1.00160i | 0.0765939 | + | 0.0442215i | ||||
\(514\) | 3.92485 | + | 2.26602i | 0.173118 | + | 0.0999497i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.103845 | + | 0.179864i | −0.00457150 | + | 0.00791807i | ||||
\(517\) | 7.67340 | + | 13.2907i | 0.337476 | + | 0.584525i | ||||
\(518\) | −46.7839 | + | 27.0107i | −2.05557 | + | 1.18678i | ||||
\(519\) | 6.11508 | 0.268422 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.44923 | 0.282546 | 0.141273 | − | 0.989971i | \(-0.454880\pi\) | ||||
0.141273 | + | 0.989971i | \(0.454880\pi\) | |||||||
\(522\) | 10.2919 | − | 5.94203i | 0.450464 | − | 0.260076i | ||||
\(523\) | −5.84076 | − | 10.1165i | −0.255399 | − | 0.442364i | 0.709605 | − | 0.704600i | \(-0.248873\pi\) |
−0.965004 | + | 0.262236i | \(0.915540\pi\) | |||||||
\(524\) | 1.19965 | − | 2.07785i | 0.0524070 | − | 0.0907715i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.5190 | + | 17.0428i | 1.28709 | + | 0.743102i | ||||
\(527\) | −15.8613 | − | 9.15751i | −0.690928 | − | 0.398907i | ||||
\(528\) | − | 4.86343i | − | 0.211654i | ||||||
\(529\) | 11.2073 | − | 19.4117i | 0.487276 | − | 0.843987i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −32.7682 | + | 18.9187i | −1.42202 | + | 0.821002i | ||||
\(532\) | 0.423086 | 0.0183431 | ||||||||
\(533\) | 20.6036 | − | 18.1392i | 0.892440 | − | 0.785697i | ||||
\(534\) | −1.78167 | −0.0771003 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.77642 | − | 11.7371i | −0.292697 | − | 0.506966i | ||||
\(537\) | 2.32075 | − | 4.01966i | 0.100148 | − | 0.173461i | ||||
\(538\) | 15.7535i | 0.679183i | ||||||||
\(539\) | 17.8123 | + | 10.2839i | 0.767229 | + | 0.442960i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5675i | 0.454330i | 0.973856 | + | 0.227165i | \(0.0729457\pi\) | ||||
−0.973856 | + | 0.227165i | \(0.927054\pi\) | |||||||
\(542\) | −13.6426 | + | 23.6297i | −0.586001 | + | 1.01498i | ||||
\(543\) | −0.802920 | − | 1.39070i | −0.0344566 | − | 0.0596806i | ||||
\(544\) | −1.44039 | + | 0.831610i | −0.0617562 | + | 0.0356550i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.74068 | + | 5.38473i | 0.202882 | + | 0.230445i | ||||
\(547\) | −11.1484 | −0.476669 | −0.238335 | − | 0.971183i | \(-0.576601\pi\) | ||||
−0.238335 | + | 0.971183i | \(0.576601\pi\) | |||||||
\(548\) | −1.88864 | + | 1.09040i | −0.0806785 | + | 0.0465798i | ||||
\(549\) | −18.5039 | − | 32.0497i | −0.789727 | − | 1.36785i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.62830i | − | 0.111969i | ||||||
\(552\) | 0.772613 | + | 0.446069i | 0.0328846 | + | 0.0189859i | ||||
\(553\) | −32.2197 | − | 18.6020i | −1.37012 | − | 0.791039i | ||||
\(554\) | 8.35837i | 0.355113i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.232242 | + | 0.402256i | 0.00984927 | + | 0.0170594i | ||||
\(557\) | −10.7694 | + | 6.21770i | −0.456313 | + | 0.263453i | −0.710493 | − | 0.703705i | \(-0.751528\pi\) |
0.254180 | + | 0.967157i | \(0.418195\pi\) | |||||||
\(558\) | −32.6475 | −1.38208 | ||||||||
\(559\) | 4.42061 | − | 13.1056i | 0.186972 | − | 0.554310i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.46930 | + | 1.42565i | −0.104254 | + | 0.0601910i | ||||
\(562\) | 17.4978 | + | 30.3071i | 0.738101 | + | 1.27843i | ||||
\(563\) | 8.77737 | − | 15.2029i | 0.369922 | − | 0.640724i | −0.619631 | − | 0.784893i | \(-0.712718\pi\) |
0.989553 | + | 0.144169i | \(0.0460510\pi\) | |||||||
\(564\) | 0.253545i | 0.0106762i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.9106 | − | 12.0727i | −0.878936 | − | 0.507454i | ||||
\(567\) | − | 27.6414i | − | 1.16083i | ||||||
\(568\) | −15.7977 | + | 27.3624i | −0.662857 | + | 1.14810i | ||||
\(569\) | −15.3084 | − | 26.5150i | −0.641763 | − | 1.11157i | −0.985039 | − | 0.172331i | \(-0.944870\pi\) |
0.343276 | − | 0.939235i | \(-0.388463\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.33906 | −0.223433 | −0.111716 | − | 0.993740i | \(-0.535635\pi\) | ||||
−0.111716 | + | 0.993740i | \(0.535635\pi\) | |||||||
\(572\) | −0.315097 | − | 1.56829i | −0.0131748 | − | 0.0655736i | ||||
\(573\) | −0.771438 | −0.0322273 | ||||||||
\(574\) | −32.8053 | + | 18.9401i | −1.36927 | + | 0.790546i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.0216 | + | 20.8220i | −0.500901 | + | 0.867585i | ||||
\(577\) | − | 2.82977i | − | 0.117805i | −0.998264 | − | 0.0589024i | \(-0.981240\pi\) | ||
0.998264 | − | 0.0589024i | \(-0.0187601\pi\) | |||||||
\(578\) | 14.5062 | + | 8.37516i | 0.603379 | + | 0.348361i | ||||
\(579\) | 1.84335 | + | 1.06426i | 0.0766071 | + | 0.0442291i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.15093 | − | 3.72553i | 0.0892357 | − | 0.154561i | ||||
\(582\) | −1.43423 | − | 2.48416i | −0.0594508 | − | 0.102972i | ||||
\(583\) | 8.64603 | − | 4.99179i | 0.358082 | − | 0.206739i | ||||
\(584\) | 22.4031 | 0.927047 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −30.0473 | −1.24124 | ||||||||
\(587\) | −7.44364 | + | 4.29759i | −0.307232 | + | 0.177380i | −0.645687 | − | 0.763602i | \(-0.723429\pi\) |
0.338455 | + | 0.940982i | \(0.390096\pi\) | |||||||
\(588\) | 0.169901 | + | 0.294277i | 0.00700659 | + | 0.0121358i | ||||
\(589\) | −3.61019 | + | 6.25303i | −0.148755 | + | 0.257652i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.31382 | − | 3.06794i | −0.218582 | − | 0.126198i | ||||
\(592\) | −34.8935 | − | 20.1458i | −1.43411 | − | 0.827986i | ||||
\(593\) | − | 15.6269i | − | 0.641720i | −0.947127 | − | 0.320860i | \(-0.896028\pi\) | ||
0.947127 | − | 0.320860i | \(-0.103972\pi\) | |||||||
\(594\) | −5.22570 | + | 9.05119i | −0.214413 | + | 0.371375i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.18780 | + | 1.26313i | −0.0896159 | + | 0.0517398i | ||||
\(597\) | −8.51307 | −0.348417 | ||||||||
\(598\) | −3.56910 | − | 1.20388i | −0.145951 | − | 0.0492303i | ||||
\(599\) | 5.84438 | 0.238795 | 0.119398 | − | 0.992847i | \(-0.461904\pi\) | ||||
0.119398 | + | 0.992847i | \(0.461904\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.8757 | − | 20.5694i | −0.484421 | − | 0.839042i | 0.515419 | − | 0.856939i | \(-0.327636\pi\) |
−0.999840 | + | 0.0178963i | \(0.994303\pi\) | |||||||
\(602\) | −9.54306 | + | 16.5291i | −0.388946 | + | 0.673674i | ||||
\(603\) | 13.2004i | 0.537564i | ||||||||
\(604\) | 0.777481 | + | 0.448879i | 0.0316353 | + | 0.0182646i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 9.32522i | − | 0.378811i | ||||||
\(607\) | −18.6540 | + | 32.3096i | −0.757141 | + | 1.31141i | 0.187162 | + | 0.982329i | \(0.440071\pi\) |
−0.944303 | + | 0.329078i | \(0.893262\pi\) | |||||||
\(608\) | 0.327848 | + | 0.567849i | 0.0132960 | + | 0.0230293i | ||||
\(609\) | 3.86705 | − | 2.23264i | 0.156701 | − | 0.0904712i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.32599 | − | 16.5541i | −0.134555 | − | 0.669706i | ||||
\(612\) | 0.836503 | 0.0338136 | ||||||||
\(613\) | 35.9007 | − | 20.7273i | 1.45002 | − | 0.837168i | 0.451536 | − | 0.892253i | \(-0.350876\pi\) |
0.998482 | + | 0.0550852i | \(0.0175430\pi\) | |||||||
\(614\) | 1.11346 | + | 1.92858i | 0.0449357 | + | 0.0778310i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 34.8176i | 1.40284i | ||||||||
\(617\) | −7.89098 | − | 4.55586i | −0.317679 | − | 0.183412i | 0.332679 | − | 0.943040i | \(-0.392048\pi\) |
−0.650358 | + | 0.759628i | \(0.725381\pi\) | |||||||
\(618\) | 0.383299 | + | 0.221298i | 0.0154185 | + | 0.00890190i | ||||
\(619\) | 33.6828i | 1.35382i | 0.736064 | + | 0.676912i | \(0.236682\pi\) | ||||
−0.736064 | + | 0.676912i | \(0.763318\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.893406 | − | 1.54742i | −0.0358512 | − | 0.0620960i | ||||
\(622\) | 22.4750 | − | 12.9760i | 0.901166 | − | 0.520289i | ||||
\(623\) | 11.8877 | 0.476271 | ||||||||
\(624\) | −1.71020 | + | 5.07019i | −0.0684630 | + | 0.202970i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.1270 | − | 7.57888i | 0.524661 | − | 0.302913i | ||||
\(627\) | 0.562038 | + | 0.973479i | 0.0224456 | + | 0.0388770i | ||||
\(628\) | 0.312393 | − | 0.541081i | 0.0124658 | − | 0.0215915i | ||||
\(629\) | 23.6219i | 0.941867i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.3619 | + | 12.9106i | 0.890213 | + | 0.513965i | 0.874012 | − | 0.485904i | \(-0.161510\pi\) |
0.0162010 | + | 0.999869i | \(0.494843\pi\) | |||||||
\(632\) | − | 29.7731i | − | 1.18431i | ||||||
\(633\) | 2.72777 | − | 4.72464i | 0.108419 | − | 0.187788i | ||||
\(634\) | 3.56440 | + | 6.17373i | 0.141561 | + | 0.245190i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.164939 | 0.00654025 | ||||||||
\(637\) | −14.9532 | − | 16.9847i | −0.592468 | − | 0.672960i | ||||
\(638\) | 13.7129 | 0.542897 | ||||||||
\(639\) | 26.6510 | − | 15.3869i | 1.05430 | − | 0.608698i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.61778 | − | 11.4623i | 0.261387 | − | 0.452735i | −0.705224 | − | 0.708985i | \(-0.749154\pi\) |
0.966611 | + | 0.256250i | \(0.0824869\pi\) | |||||||
\(642\) | 7.31055i | 0.288524i | ||||||||
\(643\) | −19.8080 | − | 11.4361i | −0.781151 | − | 0.450998i | 0.0556871 | − | 0.998448i | \(-0.482265\pi\) |
−0.836838 | + | 0.547451i | \(0.815598\pi\) | |||||||
\(644\) | −0.326825 | − | 0.188693i | −0.0128787 | − | 0.00743554i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.27403 | + | 2.20669i | −0.0501261 | + | 0.0868210i | ||||
\(647\) | 2.13016 | + | 3.68955i | 0.0837454 | + | 0.145051i | 0.904856 | − | 0.425718i | \(-0.139978\pi\) |
−0.821111 | + | 0.570769i | \(0.806645\pi\) | |||||||
\(648\) | 19.1568 | − | 11.0602i | 0.752551 | − | 0.434486i | ||||
\(649\) | −43.6601 | −1.71381 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.2669 | −0.480776 | ||||||||
\(652\) | −1.14316 | + | 0.660003i | −0.0447696 | + | 0.0258477i | ||||
\(653\) | 6.33210 | + | 10.9675i | 0.247794 | + | 0.429192i | 0.962914 | − | 0.269810i | \(-0.0869610\pi\) |
−0.715119 | + | 0.699002i | \(0.753628\pi\) | |||||||
\(654\) | 1.53242 | − | 2.65423i | 0.0599224 | − | 0.103789i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −24.4676 | − | 14.1264i | −0.955301 | − | 0.551543i | ||||
\(657\) | −18.8972 | − | 10.9103i | −0.737249 | − | 0.425651i | ||||
\(658\) | 23.3001i | 0.908334i | ||||||||
\(659\) | 13.6330 | − | 23.6130i | 0.531066 | − | 0.919833i | −0.468277 | − | 0.883582i | \(-0.655125\pi\) |
0.999343 | − | 0.0362512i | \(-0.0115417\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.94278 | + | 2.27636i | −0.153356 | + | 0.0885403i | −0.574714 | − | 0.818354i | \(-0.694887\pi\) |
0.421358 | + | 0.906894i | \(0.361554\pi\) | |||||||
\(662\) | −35.0082 | −1.36063 | ||||||||
\(663\) | 3.07560 | − | 0.617940i | 0.119447 | − | 0.0239988i | ||||
\(664\) | 3.44263 | 0.133600 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 21.0536 | + | 36.4660i | 0.815812 | + | 1.41303i | ||||
\(667\) | −1.17220 | + | 2.03031i | −0.0453878 | + | 0.0786140i | ||||
\(668\) | − | 1.40591i | − | 0.0543964i | ||||||
\(669\) | −8.55876 | − | 4.94140i | −0.330901 | − | 0.191046i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 42.7028i | − | 1.64852i | ||||||
\(672\) | −0.556988 | + | 0.964731i | −0.0214863 | + | 0.0372153i | ||||
\(673\) | 10.3306 | + | 17.8932i | 0.398217 | + | 0.689732i | 0.993506 | − | 0.113780i | \(-0.0362959\pi\) |
−0.595289 | + | 0.803512i | \(0.702963\pi\) | |||||||
\(674\) | −42.7435 | + | 24.6780i | −1.64642 | + | 0.950559i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.222992 | + | 1.74577i | −0.00857661 | + | 0.0671449i | ||||
\(677\) | 36.1528 | 1.38947 | 0.694733 | − | 0.719268i | \(-0.255523\pi\) | ||||
0.694733 | + | 0.719268i | \(0.255523\pi\) | |||||||
\(678\) | −8.62259 | + | 4.97825i | −0.331149 | + | 0.191189i | ||||
\(679\) | 9.56953 | + | 16.5749i | 0.367245 | + | 0.636087i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.72632i | − | 0.181113i | ||||||
\(682\) | −32.6244 | − | 18.8357i | −1.24925 | − | 0.721257i | ||||
\(683\) | −31.7208 | − | 18.3140i | −1.21376 | − | 0.700765i | −0.250185 | − | 0.968198i | \(-0.580491\pi\) |
−0.963577 | + | 0.267433i | \(0.913825\pi\) | |||||||
\(684\) | − | 0.329777i | − | 0.0126093i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.80059 | − | 3.11872i | −0.0687470 | − | 0.119073i | ||||
\(687\) | 1.03340 | − | 0.596635i | 0.0394268 | − | 0.0227631i | ||||
\(688\) | −14.2353 | −0.542715 | ||||||||
\(689\) | −10.7689 | + | 2.16366i | −0.410264 | + | 0.0824290i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4551 | + | 14.6965i | −0.968359 | + | 0.559082i | −0.898735 | − | 0.438491i | \(-0.855513\pi\) |
−0.0696233 | + | 0.997573i | \(0.522180\pi\) | |||||||
\(692\) | −1.03505 | − | 1.79275i | −0.0393465 | − | 0.0681502i | ||||
\(693\) | 16.9561 | − | 29.3689i | 0.644110 | − | 1.11563i | ||||
\(694\) | − | 19.6781i | − | 0.746971i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.09466 | + | 1.78670i | 0.117303 | + | 0.0677248i | ||||
\(697\) | 16.5639i | 0.627402i | ||||||||
\(698\) | −2.27996 | + | 3.94901i | −0.0862979 | + | 0.149472i | ||||
\(699\) | 1.37586 | + | 2.38306i | 0.0520397 | + | 0.0901355i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.8074 | −0.748116 | −0.374058 | − | 0.927405i | \(-0.622034\pi\) | ||||
−0.374058 | + | 0.927405i | \(0.622034\pi\) | |||||||
\(702\) | 8.63068 | − | 7.59838i | 0.325744 | − | 0.286782i | ||||
\(703\) | 9.31252 | 0.351228 | ||||||||
\(704\) | −24.0263 | + | 13.8716i | −0.905524 | + | 0.522805i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.97497 | + | 13.8131i | −0.300142 | + | 0.519861i | ||||
\(707\) | 62.2201i | 2.34003i | ||||||||
\(708\) | −0.624672 | − | 0.360654i | −0.0234766 | − | 0.0135542i | ||||
\(709\) | 11.6423 | + | 6.72169i | 0.437236 | + | 0.252438i | 0.702424 | − | 0.711758i | \(-0.252101\pi\) |
−0.265189 | + | 0.964197i | \(0.585434\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.4995 | + | 25.1138i | −0.543772 | + | 0.941841i | ||||
\(712\) | 4.75666 | + | 8.23877i | 0.178263 | + | 0.308761i | ||||
\(713\) | 5.57760 | − | 3.22023i | 0.208883 | − | 0.120598i | ||||
\(714\) | −4.32896 | −0.162007 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.57125 | −0.0587204 | ||||||||
\(717\) | 6.35280 | − | 3.66779i | 0.237250 | − | 0.136976i | ||||
\(718\) | −4.46985 | − | 7.74201i | −0.166813 | − | 0.288929i | ||||
\(719\) | −7.11118 | + | 12.3169i | −0.265202 | + | 0.459344i | −0.967617 | − | 0.252425i | \(-0.918772\pi\) |
0.702414 | + | 0.711768i | \(0.252105\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.55746 | − | 1.47655i | −0.0952448 | − | 0.0549896i | ||||
\(722\) | −21.5988 | − | 12.4701i | −0.803825 | − | 0.464089i | ||||
\(723\) | − | 6.65325i | − | 0.247437i | ||||||
\(724\) | −0.271806 | + | 0.470782i | −0.0101016 | + | 0.0174965i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.123213 | − | 0.0711369i | 0.00457286 | − | 0.00264014i | ||||
\(727\) | −47.6220 | −1.76620 | −0.883101 | − | 0.469183i | \(-0.844548\pi\) | ||||
−0.883101 | + | 0.469183i | \(0.844548\pi\) | |||||||
\(728\) | 12.2435 | − | 36.2978i | 0.453773 | − | 1.34529i | ||||
\(729\) | −18.7431 | −0.694191 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.17289 | + | 7.22765i | 0.154340 | + | 0.267324i | ||||
\(732\) | 0.352747 | − | 0.610976i | 0.0130379 | − | 0.0225823i | ||||
\(733\) | 16.0484i | 0.592762i | 0.955070 | + | 0.296381i | \(0.0957799\pi\) | ||||
−0.955070 | + | 0.296381i | \(0.904220\pi\) | |||||||
\(734\) | −26.7518 | − | 15.4452i | −0.987428 | − | 0.570092i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 0.584869i | − | 0.0215586i | ||||||
\(737\) | −7.61591 | + | 13.1911i | −0.280535 | + | 0.485902i | ||||
\(738\) | 14.7630 | + | 25.5703i | 0.543434 | + | 0.941254i | ||||
\(739\) | −7.81546 | + | 4.51226i | −0.287496 | + | 0.165986i | −0.636812 | − | 0.771019i | \(-0.719747\pi\) |
0.349316 | + | 0.937005i | \(0.386414\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.243612 | − | 1.21250i | −0.00894932 | − | 0.0445424i | ||||
\(742\) | 15.1575 | 0.556449 | ||||||||
\(743\) | 31.9885 | − | 18.4686i | 1.17355 | − | 0.677547i | 0.219033 | − | 0.975718i | \(-0.429710\pi\) |
0.954512 | + | 0.298171i | \(0.0963766\pi\) | |||||||
\(744\) | −4.90837 | − | 8.50154i | −0.179949 | − | 0.311682i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.80568i | 0.212561i | ||||||||
\(747\) | −2.90388 | − | 1.67656i | −0.106247 | − | 0.0613420i | ||||
\(748\) | 0.835913 | + | 0.482614i | 0.0305640 | + | 0.0176461i | ||||
\(749\) | − | 48.7777i | − | 1.78230i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.29939 | + | 3.98265i | 0.0839058 | + | 0.145329i | 0.904924 | − | 0.425572i | \(-0.139927\pi\) |
−0.821019 | + | 0.570901i | \(0.806594\pi\) | |||||||
\(752\) | −15.0500 | + | 8.68914i | −0.548818 | + | 0.316861i | ||||
\(753\) | 1.12365 | 0.0409480 | ||||||||
\(754\) | −14.2958 | − | 4.82207i | −0.520623 | − | 0.175609i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.997731 | − | 0.576040i | 0.0362871 | − | 0.0209504i | ||||
\(757\) | −7.84265 | − | 13.5839i | −0.285046 | − | 0.493714i | 0.687574 | − | 0.726114i | \(-0.258676\pi\) |
−0.972620 | + | 0.232400i | \(0.925342\pi\) | |||||||
\(758\) | 7.60690 | − | 13.1755i | 0.276295 | − | 0.478557i | ||||
\(759\) | − | 1.00266i | − | 0.0363942i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.2736 | − | 11.7049i | −0.734916 | − | 0.424304i | 0.0853021 | − | 0.996355i | \(-0.472814\pi\) |
−0.820218 | + | 0.572051i | \(0.806148\pi\) | |||||||
\(762\) | 9.26731i | 0.335719i | ||||||||
\(763\) | −10.2247 | + | 17.7096i | −0.370158 | + | 0.641132i | ||||
\(764\) | 0.130574 | + | 0.226161i | 0.00472401 | + | 0.00818223i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.49564 | 0.270829 | ||||||||
\(767\) | 45.5162 | + | 15.3529i | 1.64349 | + | 0.554361i | ||||
\(768\) | −1.29330 | −0.0466680 | ||||||||
\(769\) | −24.8331 | + | 14.3374i | −0.895504 | + | 0.517020i | −0.875739 | − | 0.482785i | \(-0.839625\pi\) |
−0.0197654 | + | 0.999805i | \(0.506292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.663649 | − | 1.14947i | 0.0239007 | − | 0.0413973i | ||||
\(772\) | − | 0.720551i | − | 0.0259332i | ||||||
\(773\) | 24.7267 | + | 14.2759i | 0.889356 | + | 0.513470i | 0.873732 | − | 0.486408i | \(-0.161693\pi\) |
0.0156243 | + | 0.999878i | \(0.495026\pi\) | |||||||
\(774\) | 12.8837 | + | 7.43839i | 0.463094 | + | 0.267367i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.65815 | + | 13.2643i | −0.274912 | + | 0.476161i | ||||
\(777\) | 7.91063 | + | 13.7016i | 0.283792 | + | 0.491543i | ||||
\(778\) | 30.6846 | − | 17.7158i | 1.10010 | − | 0.635141i | ||||
\(779\) | 6.53003 | 0.233963 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.5096 | 1.27063 | ||||||||
\(782\) | 1.96833 | − | 1.13642i | 0.0703873 | − | 0.0406381i | ||||
\(783\) | −3.57849 | − | 6.19813i | −0.127885 | − | 0.221503i | ||||
\(784\) | −11.6452 | + | 20.1701i | −0.415901 | + | 0.720361i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.38153 | + | 4.83908i | 0.298959 | + | 0.172604i | ||||
\(787\) | 6.70528 | + | 3.87129i | 0.239017 | + | 0.137997i | 0.614725 | − | 0.788742i | \(-0.289267\pi\) |
−0.375708 | + | 0.926738i | \(0.622600\pi\) | |||||||
\(788\) | 2.07713i | 0.0739947i | ||||||||
\(789\) | 4.99134 | − | 8.64525i | 0.177696 | − | 0.307779i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 57.5319 | − | 33.2161i | 2.04560 | − | 1.18103i | ||||
\(792\) | 27.1388 | 0.964334 | ||||||||
\(793\) | −15.0163 | + | 44.5182i | −0.533243 | + | 1.58089i | ||||
\(794\) | 18.9404 | 0.672171 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.44093 | + | 2.49577i | 0.0510724 | + | 0.0884601i | ||||
\(797\) | 16.4245 | − | 28.4481i | 0.581787 | − | 1.00768i | −0.413480 | − | 0.910513i | \(-0.635687\pi\) |
0.995268 | − | 0.0971719i | \(-0.0309797\pi\) | |||||||
\(798\) | 1.70662i | 0.0604137i | ||||||||
\(799\) | 8.82345 | + | 5.09422i | 0.312151 | + | 0.180221i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 9.26594i | − | 0.327396i | ||||||
\(802\) | −0.862523 | + | 1.49393i | −0.0304567 | + | 0.0527526i | ||||
\(803\) | −12.5892 | − | 21.8052i | −0.444264 | − | 0.769489i | ||||
\(804\) | −0.217931 | + | 0.125823i | −0.00768583 | + | 0.00443742i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 27.3879 | + | 31.1087i | 0.964697 | + | 1.09576i | ||||
\(807\) | 4.61375 | 0.162412 | ||||||||
\(808\) | −43.1216 | + | 24.8963i | −1.51701 | + | 0.875847i | ||||
\(809\) | 12.7521 | + | 22.0873i | 0.448341 | + | 0.776549i | 0.998278 | − | 0.0586568i | \(-0.0186818\pi\) |
−0.549937 | + | 0.835206i | \(0.685348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.12653i | − | 0.0746726i | −0.999303 | − | 0.0373363i | \(-0.988113\pi\) | ||
0.999303 | − | 0.0373363i | \(-0.0118873\pi\) | |||||||
\(812\) | −1.30908 | − | 0.755799i | −0.0459398 | − | 0.0265233i | ||||
\(813\) | 6.92045 | + | 3.99552i | 0.242711 | + | 0.140129i | ||||
\(814\) | 48.5870i | 1.70297i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.61437 | − | 2.79617i | −0.0565142 | − | 0.0978854i | ||||
\(817\) | 2.84938 | − | 1.64509i | 0.0996871 | − | 0.0575544i | ||||
\(818\) | 30.1076 | 1.05269 | ||||||||
\(819\) | −28.0044 | + | 24.6549i | −0.978554 | + | 0.861511i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5719 | + | 7.83574i | −0.473662 | + | 0.273469i | −0.717772 | − | 0.696279i | \(-0.754838\pi\) |
0.244109 | + | 0.969748i | \(0.421504\pi\) | |||||||
\(822\) | −4.39841 | − | 7.61827i | −0.153412 | − | 0.265718i | ||||
\(823\) | −17.2139 | + | 29.8154i | −0.600040 | + | 1.03930i | 0.392775 | + | 0.919635i | \(0.371515\pi\) |
−0.992814 | + | 0.119664i | \(0.961818\pi\) | |||||||
\(824\) | − | 2.36326i | − | 0.0823281i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −57.4058 | − | 33.1432i | −1.99740 | − | 1.15320i | ||||
\(827\) | − | 37.6478i | − | 1.30914i | −0.756000 | − | 0.654572i | \(-0.772849\pi\) | ||
0.756000 | − | 0.654572i | \(-0.227151\pi\) | |||||||
\(828\) | −0.147078 | + | 0.254746i | −0.00511130 | + | 0.00885303i | ||||
\(829\) | −16.6669 | − | 28.8679i | −0.578865 | − | 1.00262i | −0.995610 | − | 0.0936002i | \(-0.970162\pi\) |
0.416745 | − | 0.909024i | \(-0.363171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.44792 | 0.0849174 | ||||||||
\(832\) | 29.9256 | − | 6.01256i | 1.03748 | − | 0.208448i | ||||
\(833\) | 13.6546 | 0.473104 | ||||||||
\(834\) | −1.62260 | + | 0.936806i | −0.0561859 | + | 0.0324389i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.190262 | − | 0.329544i | 0.00658036 | − | 0.0113975i | ||||
\(837\) | 19.6614i | 0.679597i | ||||||||
\(838\) | −13.8128 | − | 7.97484i | −0.477156 | − | 0.275486i | ||||
\(839\) | −3.77053 | − | 2.17692i | −0.130173 | − | 0.0751556i | 0.433499 | − | 0.901154i | \(-0.357279\pi\) |
−0.563673 | + | 0.825998i | \(0.690612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.80481 | − | 16.9824i | 0.338097 | − | 0.585601i | ||||
\(842\) | 15.0051 | + | 25.9897i | 0.517111 | + | 0.895663i | ||||
\(843\) | 8.87606 | − | 5.12460i | 0.305708 | − | 0.176500i | ||||
\(844\) | −1.84682 | −0.0635702 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.1614 | 0.624403 | ||||||||
\(847\) | −0.822105 | + | 0.474642i | −0.0282479 | + | 0.0163089i | ||||
\(848\) | 5.65256 | + | 9.79052i | 0.194110 | + | 0.336208i | ||||
\(849\) | −3.53574 | + | 6.12409i | −0.121346 | + | 0.210178i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.19374 | − | 4.15331i | −0.246598 | − | 0.142374i | ||||
\(852\) | 0.508057 | + | 0.293327i | 0.0174058 | + | 0.0100492i | ||||
\(853\) | 11.2955i | 0.386751i | 0.981125 | + | 0.193375i | \(0.0619435\pi\) | ||||
−0.981125 | + | 0.193375i | \(0.938056\pi\) | |||||||
\(854\) | 32.4166 | − | 56.1471i | 1.10927 | − | 1.92132i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33.8054 | − | 19.5175i | 1.15544 | − | 0.667095i | ||||
\(857\) | 9.88043 | 0.337509 | 0.168754 | − | 0.985658i | \(-0.446026\pi\) | ||||
0.168754 | + | 0.985658i | \(0.446026\pi\) | |||||||
\(858\) | 6.32609 | − | 1.27102i | 0.215969 | − | 0.0433918i | ||||
\(859\) | 0.0855154 | 0.00291775 | 0.00145887 | − | 0.999999i | \(-0.499536\pi\) | ||||
0.00145887 | + | 0.999999i | \(0.499536\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.54701 | + | 9.60770i | 0.189042 | + | 0.327430i | ||||
\(862\) | 16.4657 | − | 28.5195i | 0.560825 | − | 0.971377i | ||||
\(863\) | − | 43.5513i | − | 1.48250i | −0.671227 | − | 0.741252i | \(-0.734233\pi\) | ||
0.671227 | − | 0.741252i | \(-0.265767\pi\) | |||||||
\(864\) | 1.54628 | + | 0.892743i | 0.0526054 | + | 0.0303717i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.13773i | 0.310513i | ||||||||
\(867\) | 2.45284 | − | 4.24844i | 0.0833027 | − | 0.144285i | ||||
\(868\) | 2.07630 | + | 3.59626i | 0.0704743 | + | 0.122065i | ||||
\(869\) | −28.9785 | + | 16.7307i | −0.983027 | + | 0.567551i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.5783 | − | 11.0738i | 0.426199 | − | 0.375222i | ||||
\(872\) | −16.3649 | −0.554184 | ||||||||
\(873\) | 12.9194 | − | 7.45903i | 0.437256 | − | 0.252450i | ||||
\(874\) | −0.448012 | − | 0.775979i | −0.0151542 | − | 0.0262479i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 0.415974i | − | 0.0140545i | ||||||
\(877\) | 10.6901 | + | 6.17191i | 0.360978 | + | 0.208411i | 0.669510 | − | 0.742803i | \(-0.266504\pi\) |
−0.308532 | + | 0.951214i | \(0.599838\pi\) | |||||||
\(878\) | −33.0852 | − | 19.1018i | −1.11657 | − | 0.644653i | ||||
\(879\) | 8.79997i | 0.296816i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.2655 | + | 43.7612i | 0.851217 | + | 1.47435i | 0.880111 | + | 0.474769i | \(0.157468\pi\) |
−0.0288935 | + | 0.999582i | \(0.509198\pi\) | |||||||
\(882\) | 21.0791 | − | 12.1700i | 0.709769 | − | 0.409785i | ||||
\(883\) | −23.8742 | −0.803432 | −0.401716 | − | 0.915764i | \(-0.631586\pi\) | ||||
−0.401716 | + | 0.915764i | \(0.631586\pi\) | |||||||
\(884\) | −0.701740 | − | 0.797077i | −0.0236021 | − | 0.0268086i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.0311 | + | 13.2970i | −0.773745 | + | 0.446722i | ||||
\(887\) | 18.1599 | + | 31.4538i | 0.609748 | + | 1.05611i | 0.991282 | + | 0.131760i | \(0.0420628\pi\) |
−0.381533 | + | 0.924355i | \(0.624604\pi\) | |||||||
\(888\) | −6.33059 | + | 10.9649i | −0.212441 | + | 0.367958i | ||||
\(889\) | − | 61.8337i | − | 2.07384i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.5300 | − | 12.4304i | −0.721283 | − | 0.416433i | ||||
\(892\) | 3.34555i | 0.112017i | ||||||||
\(893\) | 2.00831 | − | 3.47849i | 0.0672055 | − | 0.116403i | ||||
\(894\) | −5.09514 | − | 8.82503i | −0.170407 | − | 0.295153i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −36.5498 | −1.22104 | ||||||||
\(897\) | −0.352580 | + | 1.04528i | −0.0117723 | + | 0.0349010i | ||||
\(898\) | 18.0070 | 0.600900 | ||||||||
\(899\) | 22.3408 | − | 12.8984i | 0.745106 | − | 0.430187i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.31395 | − | 5.73993i | 0.110404 | − | 0.191225i | ||||
\(902\) | 34.0696i | 1.13440i | ||||||||
\(903\) | 4.84087 | + | 2.79488i | 0.161094 | + | 0.0930078i | ||||
\(904\) | 46.0408 | + | 26.5816i | 1.53129 | + | 0.884092i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.81066 | + | 3.13616i | −0.0601552 | + | 0.104192i | ||||
\(907\) | −15.2261 | − | 26.3724i | −0.505575 | − | 0.875681i | −0.999979 | − | 0.00644938i | \(-0.997947\pi\) |
0.494404 | − | 0.869232i | \(-0.335386\pi\) | |||||||
\(908\) | −1.38561 | + | 0.799981i | −0.0459830 | + | 0.0265483i | ||||
\(909\) | 48.4978 | 1.60857 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.8054 | 0.987498 | 0.493749 | − | 0.869604i | \(-0.335626\pi\) | ||||
0.493749 | + | 0.869604i | \(0.335626\pi\) | |||||||
\(912\) | −1.10234 | + | 0.636436i | −0.0365021 | + | 0.0210745i | ||||
\(913\) | −1.93456 | − | 3.35075i | −0.0640245 | − | 0.110894i | ||||
\(914\) | 9.46160 | − | 16.3880i | 0.312962 | − | 0.542066i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.349830 | − | 0.201974i | −0.0115587 | − | 0.00667341i | ||||
\(917\) | −55.9235 | − | 32.2875i | −1.84676 | − | 1.06623i | ||||
\(918\) | 6.93849i | 0.229004i | ||||||||
\(919\) | 4.86112 | − | 8.41970i | 0.160353 | − | 0.277740i | −0.774642 | − | 0.632400i | \(-0.782070\pi\) |
0.934995 | + | 0.354660i | \(0.115403\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.564823 | − | 0.326101i | 0.0186115 | − | 0.0107454i | ||||
\(922\) | −19.2084 | −0.632597 | ||||||||
\(923\) | −37.0192 | − | 12.4868i | −1.21850 | − | 0.411008i | ||||
\(924\) | 0.646482 | 0.0212677 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.32198 | + | 5.75384i | 0.109167 | + | 0.189083i | ||||
\(927\) | −1.15091 | + | 1.99343i | −0.0378007 | + | 0.0654727i | ||||
\(928\) | − | 2.34266i | − | 0.0769017i | ||||||
\(929\) | 3.71589 | + | 2.14537i | 0.121914 | + | 0.0703874i | 0.559717 | − | 0.828684i | \(-0.310910\pi\) |
−0.437803 | + | 0.899071i | \(0.644243\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 5.38308i | − | 0.176423i | ||||||
\(932\) | 0.465758 | − | 0.806717i | 0.0152564 | − | 0.0264249i | ||||
\(933\) | −3.80027 | − | 6.58227i | −0.124415 | − | 0.215494i | ||||
\(934\) | 31.5046 | − | 18.1892i | 1.03086 | − | 0.595169i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −28.2925 | − | 9.54324i | −0.924770 | − | 0.311931i | ||||
\(937\) | −8.43750 | −0.275641 | −0.137821 | − | 0.990457i | \(-0.544010\pi\) | ||||
−0.137821 | + | 0.990457i | \(0.544010\pi\) | |||||||
\(938\) | −20.0273 | + | 11.5628i | −0.653915 | + | 0.377538i | ||||
\(939\) | −2.21963 | − | 3.84451i | −0.0724349 | − | 0.125461i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 22.1898i | − | 0.723368i | −0.932301 | − | 0.361684i | \(-0.882202\pi\) | ||
0.932301 | − | 0.361684i | \(-0.117798\pi\) | |||||||
\(942\) | 2.18258 | + | 1.26011i | 0.0711123 | + | 0.0410567i | ||||
\(943\) | −5.04432 | − | 2.91234i | −0.164266 | − | 0.0948388i | ||||
\(944\) | − | 49.4394i | − | 1.60912i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.58305 | + | 14.8663i | 0.279059 | + | 0.483345i | ||||
\(947\) | −10.5323 | + | 6.08080i | −0.342252 | + | 0.197599i | −0.661268 | − | 0.750150i | \(-0.729981\pi\) |
0.319015 | + | 0.947750i | \(0.396648\pi\) | |||||||
\(948\) | −0.552817 | −0.0179547 | ||||||||
\(949\) | 5.45673 | + | 27.1591i | 0.177133 | + | 0.881623i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.80810 | − | 1.04391i | 0.0586317 | − | 0.0338511i | ||||
\(952\) | 11.5574 | + | 20.0179i | 0.374576 | + | 0.648785i | ||||
\(953\) | −27.8920 | + | 48.3104i | −0.903512 | + | 1.56493i | −0.0806088 | + | 0.996746i | \(0.525686\pi\) |
−0.822903 | + | 0.568182i | \(0.807647\pi\) | |||||||
\(954\) | − | 11.8146i | − | 0.382511i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.15056 | − | 1.24163i | −0.0695542 | − | 0.0401571i | ||||
\(957\) | − | 4.01609i | − | 0.129822i | ||||||
\(958\) | −2.06401 | + | 3.57498i | −0.0666853 | + | 0.115502i | ||||
\(959\) | 29.3472 | + | 50.8309i | 0.947671 | + | 1.64141i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −39.8683 | −1.28607 | ||||||||
\(962\) | 17.0854 | − | 50.6526i | 0.550856 | − | 1.63310i | ||||
\(963\) | −38.0201 | −1.22518 | ||||||||
\(964\) | −1.95052 | + | 1.12614i | −0.0628222 | + | 0.0362704i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.761138 | − | 1.31833i | 0.0244892 | − | 0.0424165i | ||||
\(967\) | 12.5378i | 0.403190i | 0.979469 | + | 0.201595i | \(0.0646124\pi\) | ||||
−0.979469 | + | 0.201595i | \(0.935388\pi\) | |||||||
\(968\) | −0.657901 | − | 0.379839i | −0.0211457 | − | 0.0122085i | ||||
\(969\) | 0.646274 | + | 0.373126i | 0.0207613 | + | 0.0119865i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.3267 | + | 17.8864i | −0.331400 | + | 0.574001i | −0.982787 | − | 0.184745i | \(-0.940854\pi\) |
0.651387 | + | 0.758746i | \(0.274187\pi\) | |||||||
\(972\) | −0.679645 | − | 1.17718i | −0.0217996 | − | 0.0377581i | ||||
\(973\) | 10.8263 | − | 6.25059i | 0.347076 | − | 0.200385i | ||||
\(974\) | 16.1404 | 0.517172 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 48.3554 | 1.54782 | ||||||||
\(977\) | 16.6632 | − | 9.62051i | 0.533103 | − | 0.307787i | −0.209176 | − | 0.977878i | \(-0.567078\pi\) |
0.742279 | + | 0.670091i | \(0.233745\pi\) | |||||||
\(978\) | −2.66228 | − | 4.61121i | −0.0851304 | − | 0.147450i | ||||
\(979\) | 5.34592 | − | 9.25941i | 0.170856 | − | 0.295932i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.8039 | + | 7.96967i | 0.440724 | + | 0.254452i | ||||
\(982\) | 11.4074 | + | 6.58605i | 0.364024 | + | 0.210169i | ||||
\(983\) | − | 28.9070i | − | 0.921990i | −0.887403 | − | 0.460995i | \(-0.847493\pi\) | ||
0.887403 | − | 0.460995i | \(-0.152507\pi\) | |||||||
\(984\) | −4.43907 | + | 7.68870i | −0.141512 | + | 0.245107i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.88403 | − | 4.55185i | 0.251079 | − | 0.144960i | ||||
\(987\) | 6.82392 | 0.217208 | ||||||||
\(988\) | −0.314234 | + | 0.276649i | −0.00999711 | + | 0.00880138i | ||||
\(989\) | −2.93478 | −0.0933207 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.2004 | + | 33.2561i | 0.609922 | + | 1.05642i | 0.991253 | + | 0.131977i | \(0.0421324\pi\) |
−0.381331 | + | 0.924438i | \(0.624534\pi\) | |||||||
\(992\) | −3.21784 | + | 5.57346i | −0.102166 | + | 0.176957i | ||||
\(993\) | 10.2529i | 0.325365i | ||||||||
\(994\) | 46.6892 | + | 26.9560i | 1.48089 | + | 0.854993i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 0.0639217i | − | 0.00202544i | ||||||
\(997\) | −26.4900 | + | 45.8820i | −0.838947 | + | 1.45310i | 0.0518287 | + | 0.998656i | \(0.483495\pi\) |
−0.890776 | + | 0.454443i | \(0.849838\pi\) | |||||||
\(998\) | 6.88265 | + | 11.9211i | 0.217867 | + | 0.377356i | ||||
\(999\) | 21.9610 | − | 12.6792i | 0.694816 | − | 0.401152i |
(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 | 325.2.n.f.101.4 | yes | 10 | |
5.2 | odd | 4 | 325.2.m.d.49.8 | 20 | |||
5.3 | odd | 4 | 325.2.m.d.49.3 | 20 | |||
5.4 | even | 2 | 325.2.n.e.101.2 | ✓ | 10 | ||
13.2 | odd | 12 | 4225.2.a.bu.1.8 | 10 | |||
13.4 | even | 6 | inner | 325.2.n.f.251.4 | yes | 10 | |
13.11 | odd | 12 | 4225.2.a.bu.1.3 | 10 | |||
65.4 | even | 6 | 325.2.n.e.251.2 | yes | 10 | ||
65.17 | odd | 12 | 325.2.m.d.199.3 | 20 | |||
65.24 | odd | 12 | 4225.2.a.bv.1.8 | 10 | |||
65.43 | odd | 12 | 325.2.m.d.199.8 | 20 | |||
65.54 | odd | 12 | 4225.2.a.bv.1.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.2.m.d.49.3 | 20 | 5.3 | odd | 4 | |||
325.2.m.d.49.8 | 20 | 5.2 | odd | 4 | |||
325.2.m.d.199.3 | 20 | 65.17 | odd | 12 | |||
325.2.m.d.199.8 | 20 | 65.43 | odd | 12 | |||
325.2.n.e.101.2 | ✓ | 10 | 5.4 | even | 2 | ||
325.2.n.e.251.2 | yes | 10 | 65.4 | even | 6 | ||
325.2.n.f.101.4 | yes | 10 | 1.1 | even | 1 | trivial | |
325.2.n.f.251.4 | yes | 10 | 13.4 | even | 6 | inner | |
4225.2.a.bu.1.3 | 10 | 13.11 | odd | 12 | |||
4225.2.a.bu.1.8 | 10 | 13.2 | odd | 12 | |||
4225.2.a.bv.1.3 | 10 | 65.54 | odd | 12 | |||
4225.2.a.bv.1.8 | 10 | 65.24 | odd | 12 |