Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(49,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-1.41485 + 0.816862i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.49 |
Dual form | 225.2.k.c.124.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41485 | + | 0.816862i | −1.00045 | + | 0.577608i | −0.908381 | − | 0.418144i | \(-0.862681\pi\) |
−0.0920666 | + | 0.995753i | \(0.529347\pi\) | |||||||
\(3\) | −1.36657 | − | 1.06419i | −0.788988 | − | 0.614409i | ||||
\(4\) | 0.334526 | − | 0.579416i | 0.167263 | − | 0.289708i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.80278 | + | 0.389365i | 1.14423 | + | 0.158958i | ||||
\(7\) | −0.437645 | + | 0.252674i | −0.165414 | + | 0.0955019i | −0.580422 | − | 0.814316i | \(-0.697112\pi\) |
0.415008 | + | 0.909818i | \(0.363779\pi\) | |||||||
\(8\) | − | 2.17440i | − | 0.768767i | ||||||
\(9\) | 0.735010 | + | 2.90857i | 0.245003 | + | 0.969522i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.55010 | − | 2.68485i | −0.467373 | − | 0.809514i | 0.531932 | − | 0.846787i | \(-0.321466\pi\) |
−0.999305 | + | 0.0372730i | \(0.988133\pi\) | |||||||
\(12\) | −1.07376 | + | 0.435812i | −0.309968 | + | 0.125808i | ||||
\(13\) | 5.40337 | + | 3.11964i | 1.49863 | + | 0.865232i | 0.999999 | − | 0.00158518i | \(-0.000504579\pi\) |
0.498627 | + | 0.866817i | \(0.333838\pi\) | |||||||
\(14\) | 0.412800 | − | 0.714990i | 0.110325 | − | 0.191089i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.44524 | + | 4.23527i | 0.611309 | + | 1.05882i | ||||
\(17\) | 6.10020i | 1.47952i | 0.672873 | + | 0.739758i | \(0.265060\pi\) | ||||
−0.672873 | + | 0.739758i | \(0.734940\pi\) | |||||||
\(18\) | −3.41582 | − | 3.51477i | −0.805117 | − | 0.828440i | ||||
\(19\) | 5.57022 | 1.27790 | 0.638948 | − | 0.769250i | \(-0.279370\pi\) | ||||
0.638948 | + | 0.769250i | \(0.279370\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.866963 | + | 0.120440i | 0.189187 | + | 0.0262821i | ||||
\(22\) | 4.38631 | + | 2.53244i | 0.935164 | + | 0.539917i | ||||
\(23\) | 3.31307 | + | 1.91280i | 0.690822 | + | 0.398846i | 0.803920 | − | 0.594738i | \(-0.202744\pi\) |
−0.113098 | + | 0.993584i | \(0.536077\pi\) | |||||||
\(24\) | −2.31397 | + | 2.97146i | −0.472337 | + | 0.606547i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −10.1932 | −1.99906 | ||||||||
\(27\) | 2.09082 | − | 4.75694i | 0.402379 | − | 0.915473i | ||||
\(28\) | 0.338104i | 0.0638957i | ||||||||
\(29\) | 1.22966 | + | 2.12984i | 0.228342 | + | 0.395501i | 0.957317 | − | 0.289040i | \(-0.0933361\pi\) |
−0.728975 | + | 0.684541i | \(0.760003\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.11429 | + | 3.66206i | −0.379738 | + | 0.657725i | −0.991024 | − | 0.133685i | \(-0.957319\pi\) |
0.611286 | + | 0.791409i | \(0.290652\pi\) | |||||||
\(32\) | −3.15309 | − | 1.82044i | −0.557394 | − | 0.321811i | ||||
\(33\) | −0.738871 | + | 5.31863i | −0.128621 | + | 0.925855i | ||||
\(34\) | −4.98302 | − | 8.63085i | −0.854581 | − | 1.48018i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.93115 | + | 0.547115i | 0.321858 | + | 0.0911858i | ||||
\(37\) | − | 6.72677i | − | 1.10587i | −0.833223 | − | 0.552937i | \(-0.813507\pi\) | ||
0.833223 | − | 0.552937i | \(-0.186493\pi\) | |||||||
\(38\) | −7.88101 | + | 4.55010i | −1.27847 | + | 0.738124i | ||||
\(39\) | −4.06419 | − | 10.0134i | −0.650791 | − | 1.60343i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.72092 | − | 4.71278i | 0.424937 | − | 0.736012i | −0.571478 | − | 0.820618i | \(-0.693630\pi\) |
0.996415 | + | 0.0846053i | \(0.0269630\pi\) | |||||||
\(42\) | −1.32500 | + | 0.537785i | −0.204452 | + | 0.0829821i | ||||
\(43\) | 1.14957 | − | 0.663704i | 0.175308 | − | 0.101214i | −0.409779 | − | 0.912185i | \(-0.634394\pi\) |
0.585086 | + | 0.810971i | \(0.301061\pi\) | |||||||
\(44\) | −2.07420 | −0.312697 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.24997 | −0.921508 | ||||||||
\(47\) | 3.21115 | − | 1.85396i | 0.468395 | − | 0.270428i | −0.247173 | − | 0.968971i | \(-0.579501\pi\) |
0.715568 | + | 0.698544i | \(0.246168\pi\) | |||||||
\(48\) | 1.16555 | − | 8.38998i | 0.168232 | − | 1.21099i | ||||
\(49\) | −3.37231 | + | 5.84101i | −0.481759 | + | 0.834431i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.49176 | − | 8.33633i | 0.909028 | − | 1.16732i | ||||
\(52\) | 3.61514 | − | 2.08720i | 0.501329 | − | 0.289443i | ||||
\(53\) | 2.54205i | 0.349177i | 0.984641 | + | 0.174589i | \(0.0558596\pi\) | ||||
−0.984641 | + | 0.174589i | \(0.944140\pi\) | |||||||
\(54\) | 0.927572 | + | 8.43825i | 0.126227 | + | 1.14830i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.549415 | + | 0.951614i | 0.0734187 | + | 0.127165i | ||||
\(57\) | −7.61208 | − | 5.92776i | −1.00824 | − | 0.785151i | ||||
\(58\) | −3.47956 | − | 2.00893i | −0.456889 | − | 0.263785i | ||||
\(59\) | 1.44116 | − | 2.49616i | 0.187623 | − | 0.324973i | −0.756834 | − | 0.653607i | \(-0.773255\pi\) |
0.944457 | + | 0.328634i | \(0.106588\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.42173 | + | 2.46250i | 0.182033 | + | 0.315291i | 0.942573 | − | 0.334001i | \(-0.108399\pi\) |
−0.760539 | + | 0.649292i | \(0.775065\pi\) | |||||||
\(62\) | − | 6.90833i | − | 0.877358i | ||||||
\(63\) | −1.05659 | − | 1.08720i | −0.133118 | − | 0.136974i | ||||
\(64\) | −3.83276 | −0.479095 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.29920 | − | 8.12860i | −0.406103 | − | 1.00056i | ||||
\(67\) | 2.08411 | + | 1.20326i | 0.254614 | + | 0.147002i | 0.621875 | − | 0.783116i | \(-0.286371\pi\) |
−0.367261 | + | 0.930118i | \(0.619704\pi\) | |||||||
\(68\) | 3.53456 | + | 2.04068i | 0.428628 | + | 0.247468i | ||||
\(69\) | −2.49195 | − | 6.13969i | −0.299995 | − | 0.739132i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.54205 | 0.657720 | 0.328860 | − | 0.944379i | \(-0.393336\pi\) | ||||
0.328860 | + | 0.944379i | \(0.393336\pi\) | |||||||
\(72\) | 6.32439 | − | 1.59821i | 0.745336 | − | 0.188350i | ||||
\(73\) | − | 11.7988i | − | 1.38095i | −0.723359 | − | 0.690473i | \(-0.757403\pi\) | ||
0.723359 | − | 0.690473i | \(-0.242597\pi\) | |||||||
\(74\) | 5.49484 | + | 9.51734i | 0.638762 | + | 1.10637i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.86338 | − | 3.22748i | 0.213745 | − | 0.370217i | ||||
\(77\) | 1.35679 | + | 0.783341i | 0.154620 | + | 0.0892700i | ||||
\(78\) | 13.9298 | + | 10.8475i | 1.57723 | + | 1.22824i | ||||
\(79\) | 1.70149 | + | 2.94707i | 0.191433 | + | 0.331571i | 0.945725 | − | 0.324967i | \(-0.105353\pi\) |
−0.754293 | + | 0.656538i | \(0.772020\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.91952 | + | 4.27565i | −0.879947 | + | 0.475072i | ||||
\(82\) | 8.89047i | 0.981789i | ||||||||
\(83\) | −12.0388 | + | 6.95059i | −1.32143 | + | 0.762926i | −0.983956 | − | 0.178410i | \(-0.942905\pi\) |
−0.337470 | + | 0.941336i | \(0.609571\pi\) | |||||||
\(84\) | 0.359807 | − | 0.462042i | 0.0392581 | − | 0.0504129i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.08431 | + | 1.87808i | −0.116924 | + | 0.202518i | ||||
\(87\) | 0.586130 | − | 4.21915i | 0.0628398 | − | 0.452341i | ||||
\(88\) | −5.83795 | + | 3.37054i | −0.622327 | + | 0.359301i | ||||
\(89\) | −3.38513 | −0.358823 | −0.179411 | − | 0.983774i | \(-0.557419\pi\) | ||||
−0.179411 | + | 0.983774i | \(0.557419\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.15301 | −0.330525 | ||||||||
\(92\) | 2.21661 | − | 1.27976i | 0.231098 | − | 0.133425i | ||||
\(93\) | 6.78643 | − | 2.75444i | 0.703720 | − | 0.285623i | ||||
\(94\) | −3.02886 | + | 5.24614i | −0.312403 | + | 0.541098i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.37162 | + | 5.84324i | 0.242053 | + | 0.596373i | ||||
\(97\) | −9.59173 | + | 5.53779i | −0.973892 | + | 0.562277i | −0.900421 | − | 0.435020i | \(-0.856741\pi\) |
−0.0734716 | + | 0.997297i | \(0.523408\pi\) | |||||||
\(98\) | − | 11.0188i | − | 1.11307i | ||||||
\(99\) | 6.66974 | − | 6.48197i | 0.670334 | − | 0.651462i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.68451 | + | 15.0420i | 0.864141 | + | 1.49674i | 0.867897 | + | 0.496744i | \(0.165471\pi\) |
−0.00375621 | + | 0.999993i | \(0.501196\pi\) | |||||||
\(102\) | −2.37521 | + | 17.0975i | −0.235181 | + | 1.69290i | ||||
\(103\) | −0.721188 | − | 0.416378i | −0.0710608 | − | 0.0410269i | 0.464049 | − | 0.885810i | \(-0.346396\pi\) |
−0.535109 | + | 0.844783i | \(0.679730\pi\) | |||||||
\(104\) | 6.78334 | − | 11.7491i | 0.665161 | − | 1.15209i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.07650 | − | 3.59661i | −0.201688 | − | 0.349334i | ||||
\(107\) | 11.0684i | 1.07002i | 0.844844 | + | 0.535012i | \(0.179693\pi\) | ||||
−0.844844 | + | 0.535012i | \(0.820307\pi\) | |||||||
\(108\) | −2.05681 | − | 2.80278i | −0.197917 | − | 0.269697i | ||||
\(109\) | 4.65836 | 0.446190 | 0.223095 | − | 0.974797i | \(-0.428384\pi\) | ||||
0.223095 | + | 0.974797i | \(0.428384\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.15854 | + | 9.19258i | −0.679459 | + | 0.872521i | ||||
\(112\) | −2.14029 | − | 1.23570i | −0.202238 | − | 0.116762i | ||||
\(113\) | 10.3873 | + | 5.99711i | 0.977155 | + | 0.564160i | 0.901410 | − | 0.432967i | \(-0.142533\pi\) |
0.0757447 | + | 0.997127i | \(0.475867\pi\) | |||||||
\(114\) | 15.6121 | + | 2.16885i | 1.46221 | + | 0.203132i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.64542 | 0.152773 | ||||||||
\(117\) | −5.10214 | + | 18.0090i | −0.471693 | + | 1.66494i | ||||
\(118\) | 4.70892i | 0.433491i | ||||||||
\(119\) | −1.54136 | − | 2.66972i | −0.141297 | − | 0.244733i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.694371 | − | 1.20269i | 0.0631246 | − | 0.109335i | ||||
\(122\) | −4.02305 | − | 2.32271i | −0.364230 | − | 0.210288i | ||||
\(123\) | −8.73360 | + | 3.54475i | −0.787483 | + | 0.319620i | ||||
\(124\) | 1.41457 | + | 2.45011i | 0.127032 | + | 0.220026i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.38301 | + | 0.675131i | 0.212295 | + | 0.0601454i | ||||
\(127\) | − | 3.22858i | − | 0.286490i | −0.989687 | − | 0.143245i | \(-0.954246\pi\) | ||
0.989687 | − | 0.143245i | \(-0.0457537\pi\) | |||||||
\(128\) | 11.7289 | − | 6.77171i | 1.03670 | − | 0.598540i | ||||
\(129\) | −2.27727 | − | 0.316361i | −0.200502 | − | 0.0278540i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.69256 | − | 8.12776i | 0.409991 | − | 0.710125i | −0.584897 | − | 0.811107i | \(-0.698865\pi\) |
0.994888 | + | 0.100982i | \(0.0321985\pi\) | |||||||
\(132\) | 2.83453 | + | 2.20734i | 0.246714 | + | 0.192124i | ||||
\(133\) | −2.43778 | + | 1.40745i | −0.211382 | + | 0.122042i | ||||
\(134\) | −3.93159 | −0.339637 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.2643 | 1.13740 | ||||||||
\(137\) | 2.00013 | − | 1.15478i | 0.170883 | − | 0.0986593i | −0.412119 | − | 0.911130i | \(-0.635211\pi\) |
0.583002 | + | 0.812471i | \(0.301878\pi\) | |||||||
\(138\) | 8.54100 | + | 6.65114i | 0.727059 | + | 0.566183i | ||||
\(139\) | 5.44701 | − | 9.43449i | 0.462009 | − | 0.800223i | −0.537052 | − | 0.843549i | \(-0.680462\pi\) |
0.999061 | + | 0.0433260i | \(0.0137954\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.36122 | − | 0.883709i | −0.535711 | − | 0.0744217i | ||||
\(142\) | −7.84115 | + | 4.52709i | −0.658014 | + | 0.379905i | ||||
\(143\) | − | 19.3430i | − | 1.61754i | ||||||
\(144\) | −10.5213 | + | 10.2251i | −0.876775 | + | 0.852092i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.63799 | + | 16.6935i | 0.797646 | + | 1.38156i | ||||
\(147\) | 10.8244 | − | 4.39337i | 0.892783 | − | 0.362359i | ||||
\(148\) | −3.89760 | − | 2.25028i | −0.320381 | − | 0.184972i | ||||
\(149\) | −8.17151 | + | 14.1535i | −0.669436 | + | 1.15950i | 0.308626 | + | 0.951183i | \(0.400131\pi\) |
−0.978062 | + | 0.208314i | \(0.933202\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.3913 | − | 19.7304i | −0.927015 | − | 1.60564i | −0.788288 | − | 0.615306i | \(-0.789032\pi\) |
−0.138727 | − | 0.990331i | \(-0.544301\pi\) | |||||||
\(152\) | − | 12.1119i | − | 0.982404i | ||||||
\(153\) | −17.7428 | + | 4.48371i | −1.43442 | + | 0.362486i | ||||
\(154\) | −2.55953 | −0.206252 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.16150 | − | 0.994885i | −0.573379 | − | 0.0796545i | ||||
\(157\) | −10.7913 | − | 6.23035i | −0.861238 | − | 0.497236i | 0.00318877 | − | 0.999995i | \(-0.498985\pi\) |
−0.864427 | + | 0.502759i | \(0.832318\pi\) | |||||||
\(158\) | −4.81469 | − | 2.77976i | −0.383036 | − | 0.221146i | ||||
\(159\) | 2.70522 | − | 3.47388i | 0.214538 | − | 0.275497i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.93326 | −0.152362 | ||||||||
\(162\) | 7.71229 | − | 12.5185i | 0.605935 | − | 0.983549i | ||||
\(163\) | 7.57384i | 0.593229i | 0.954997 | + | 0.296614i | \(0.0958576\pi\) | ||||
−0.954997 | + | 0.296614i | \(0.904142\pi\) | |||||||
\(164\) | −1.82044 | − | 3.15309i | −0.142152 | − | 0.246215i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.3553 | − | 19.6680i | 0.881345 | − | 1.52653i | ||||
\(167\) | 2.57793 | + | 1.48837i | 0.199486 | + | 0.115174i | 0.596416 | − | 0.802676i | \(-0.296591\pi\) |
−0.396929 | + | 0.917849i | \(0.629924\pi\) | |||||||
\(168\) | 0.261884 | − | 1.88513i | 0.0202048 | − | 0.145441i | ||||
\(169\) | 12.9643 | + | 22.4548i | 0.997252 | + | 1.72729i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.09417 | + | 16.2014i | 0.313089 | + | 1.23895i | ||||
\(172\) | − | 0.888105i | − | 0.0677174i | ||||||
\(173\) | 13.7291 | − | 7.92649i | 1.04380 | − | 0.602640i | 0.122895 | − | 0.992420i | \(-0.460782\pi\) |
0.920908 | + | 0.389780i | \(0.127449\pi\) | |||||||
\(174\) | 2.61718 | + | 6.44824i | 0.198408 | + | 0.488840i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.58073 | − | 13.1302i | 0.571419 | − | 0.989727i | ||||
\(177\) | −4.62583 | + | 1.87751i | −0.347699 | + | 0.141122i | ||||
\(178\) | 4.78943 | − | 2.76518i | 0.358983 | − | 0.207259i | ||||
\(179\) | −17.0841 | −1.27693 | −0.638463 | − | 0.769653i | \(-0.720429\pi\) | ||||
−0.638463 | + | 0.769653i | \(0.720429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3690 | 0.993712 | 0.496856 | − | 0.867833i | \(-0.334488\pi\) | ||||
0.496856 | + | 0.867833i | \(0.334488\pi\) | |||||||
\(182\) | 4.46102 | − | 2.57557i | 0.330673 | − | 0.190914i | ||||
\(183\) | 0.677680 | − | 4.87816i | 0.0500956 | − | 0.360604i | ||||
\(184\) | 4.15919 | − | 7.20393i | 0.306620 | − | 0.531081i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.35176 | + | 9.44069i | −0.539057 | + | 0.692225i | ||||
\(187\) | 16.3782 | − | 9.45593i | 1.19769 | − | 0.691486i | ||||
\(188\) | − | 2.48079i | − | 0.180930i | ||||||
\(189\) | 0.286920 | + | 2.61014i | 0.0208703 | + | 0.189860i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.6686 | − | 21.9427i | −0.916669 | − | 1.58772i | −0.804439 | − | 0.594035i | \(-0.797534\pi\) |
−0.112230 | − | 0.993682i | \(-0.535799\pi\) | |||||||
\(192\) | 5.23772 | + | 4.07877i | 0.378000 | + | 0.294360i | ||||
\(193\) | −8.27879 | − | 4.77976i | −0.595921 | − | 0.344055i | 0.171515 | − | 0.985182i | \(-0.445134\pi\) |
−0.767435 | + | 0.641127i | \(0.778467\pi\) | |||||||
\(194\) | 9.04721 | − | 15.6702i | 0.649552 | − | 1.12506i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.25625 | + | 3.90794i | 0.161161 | + | 0.279139i | ||||
\(197\) | − | 2.06841i | − | 0.147368i | −0.997282 | − | 0.0736842i | \(-0.976524\pi\) | ||
0.997282 | − | 0.0736842i | \(-0.0234757\pi\) | |||||||
\(198\) | −4.14178 | + | 14.6192i | −0.294344 | + | 1.03894i | ||||
\(199\) | −13.0970 | −0.928419 | −0.464210 | − | 0.885725i | \(-0.653662\pi\) | ||||
−0.464210 | + | 0.885725i | \(0.653662\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.56758 | − | 3.86221i | −0.110568 | − | 0.272420i | ||||
\(202\) | −24.5745 | − | 14.1881i | −1.72906 | − | 0.998271i | ||||
\(203\) | −1.07631 | − | 0.621407i | −0.0755421 | − | 0.0436142i | ||||
\(204\) | −2.65854 | − | 6.55015i | −0.186135 | − | 0.458602i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.36049 | 0.0947900 | ||||||||
\(207\) | −3.12837 | + | 11.0422i | −0.217437 | + | 0.767486i | ||||
\(208\) | 30.5130i | 2.11570i | ||||||||
\(209\) | −8.63441 | − | 14.9552i | −0.597255 | − | 1.03448i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.55595 | + | 9.62318i | −0.382487 | + | 0.662487i | −0.991417 | − | 0.130737i | \(-0.958266\pi\) |
0.608930 | + | 0.793224i | \(0.291599\pi\) | |||||||
\(212\) | 1.47291 | + | 0.850382i | 0.101160 | + | 0.0584045i | ||||
\(213\) | −7.57358 | − | 5.89778i | −0.518933 | − | 0.404109i | ||||
\(214\) | −9.04136 | − | 15.6601i | −0.618055 | − | 1.07050i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.3435 | − | 4.54628i | −0.703785 | − | 0.309335i | ||||
\(217\) | − | 2.13690i | − | 0.145063i | ||||||
\(218\) | −6.59086 | + | 3.80523i | −0.446389 | + | 0.257723i | ||||
\(219\) | −12.5561 | + | 16.1238i | −0.848465 | + | 1.08955i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.0304 | + | 32.9617i | −1.28012 | + | 2.21724i | ||||
\(222\) | 2.61917 | − | 18.8536i | 0.175787 | − | 1.26537i | ||||
\(223\) | 3.37231 | − | 1.94701i | 0.225827 | − | 0.130381i | −0.382819 | − | 0.923824i | \(-0.625047\pi\) |
0.608645 | + | 0.793442i | \(0.291713\pi\) | |||||||
\(224\) | 1.83991 | 0.122934 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.5952 | −1.30346 | ||||||||
\(227\) | 11.0922 | − | 6.40406i | 0.736213 | − | 0.425053i | −0.0844781 | − | 0.996425i | \(-0.526922\pi\) |
0.820691 | + | 0.571373i | \(0.193589\pi\) | |||||||
\(228\) | −5.98108 | + | 2.42757i | −0.396107 | + | 0.160770i | ||||
\(229\) | 3.32647 | − | 5.76162i | 0.219820 | − | 0.380739i | −0.734933 | − | 0.678140i | \(-0.762786\pi\) |
0.954753 | + | 0.297401i | \(0.0961198\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.02052 | − | 2.51436i | −0.0671451 | − | 0.165433i | ||||
\(232\) | 4.63112 | − | 2.67378i | 0.304048 | − | 0.175542i | ||||
\(233\) | 3.65836i | 0.239667i | 0.992794 | + | 0.119833i | \(0.0382360\pi\) | ||||
−0.992794 | + | 0.119833i | \(0.961764\pi\) | |||||||
\(234\) | −7.49214 | − | 29.6477i | −0.489776 | − | 1.93813i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.964212 | − | 1.67006i | −0.0627648 | − | 0.108712i | ||||
\(237\) | 0.811032 | − | 5.83807i | 0.0526822 | − | 0.379223i | ||||
\(238\) | 4.36158 | + | 2.51816i | 0.282720 | + | 0.163228i | ||||
\(239\) | −7.84576 | + | 13.5893i | −0.507500 | + | 0.879016i | 0.492462 | + | 0.870334i | \(0.336097\pi\) |
−0.999962 | + | 0.00868195i | \(0.997236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.61248 | − | 9.72110i | −0.361532 | − | 0.626191i | 0.626681 | − | 0.779276i | \(-0.284413\pi\) |
−0.988213 | + | 0.153084i | \(0.951079\pi\) | |||||||
\(242\) | 2.26882i | 0.145845i | ||||||||
\(243\) | 15.3726 | + | 2.58489i | 0.986156 | + | 0.165821i | ||||
\(244\) | 1.90242 | 0.121790 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.46113 | − | 12.1494i | 0.603220 | − | 0.774619i | ||||
\(247\) | 30.0980 | + | 17.3771i | 1.91509 | + | 1.10568i | ||||
\(248\) | 7.96278 | + | 4.59731i | 0.505637 | + | 0.291930i | ||||
\(249\) | 23.8485 | + | 3.31307i | 1.51134 | + | 0.209957i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.94042 | 0.438075 | 0.219038 | − | 0.975716i | \(-0.429708\pi\) | ||||
0.219038 | + | 0.975716i | \(0.429708\pi\) | |||||||
\(252\) | −0.983399 | + | 0.248510i | −0.0619483 | + | 0.0156547i | ||||
\(253\) | − | 11.8601i | − | 0.745640i | ||||||
\(254\) | 2.63730 | + | 4.56794i | 0.165479 | + | 0.286618i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.23035 | + | 12.5233i | −0.451897 | + | 0.782708i | ||||
\(257\) | −15.8766 | − | 9.16635i | −0.990354 | − | 0.571781i | −0.0849739 | − | 0.996383i | \(-0.527081\pi\) |
−0.905380 | + | 0.424602i | \(0.860414\pi\) | |||||||
\(258\) | 3.48041 | − | 1.41261i | 0.216681 | − | 0.0879453i | ||||
\(259\) | 1.69968 | + | 2.94393i | 0.105613 | + | 0.182927i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.29096 | + | 5.14200i | −0.327502 | + | 0.318282i | ||||
\(262\) | 15.3327i | 0.947257i | ||||||||
\(263\) | −13.9228 | + | 8.03832i | −0.858515 | + | 0.495664i | −0.863515 | − | 0.504323i | \(-0.831742\pi\) |
0.00499942 | + | 0.999988i | \(0.498409\pi\) | |||||||
\(264\) | 11.5648 | + | 1.60660i | 0.711766 | + | 0.0988795i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.29939 | − | 3.98265i | 0.140984 | − | 0.244192i | ||||
\(267\) | 4.62600 | + | 3.60241i | 0.283107 | + | 0.220464i | ||||
\(268\) | 1.39438 | − | 0.805043i | 0.0851751 | − | 0.0491758i | ||||
\(269\) | 18.2004 | 1.10970 | 0.554849 | − | 0.831951i | \(-0.312776\pi\) | ||||
0.554849 | + | 0.831951i | \(0.312776\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.48571 | −0.150996 | −0.0754979 | − | 0.997146i | \(-0.524055\pi\) | ||||
−0.0754979 | + | 0.997146i | \(0.524055\pi\) | |||||||
\(272\) | −25.8360 | + | 14.9164i | −1.56654 | + | 0.904442i | ||||
\(273\) | 4.30879 | + | 3.35539i | 0.260780 | + | 0.203077i | ||||
\(274\) | −1.88659 | + | 3.26766i | −0.113973 | + | 0.197407i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.39106 | − | 0.610012i | −0.264311 | − | 0.0367184i | ||||
\(277\) | 6.64004 | − | 3.83363i | 0.398962 | − | 0.230341i | −0.287074 | − | 0.957908i | \(-0.592683\pi\) |
0.686036 | + | 0.727568i | \(0.259349\pi\) | |||||||
\(278\) | 17.7978i | 1.06744i | ||||||||
\(279\) | −12.2054 | − | 3.45790i | −0.730716 | − | 0.207019i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.136615 | − | 0.236624i | −0.00814978 | − | 0.0141158i | 0.861922 | − | 0.507041i | \(-0.169261\pi\) |
−0.870072 | + | 0.492925i | \(0.835928\pi\) | |||||||
\(282\) | 9.72201 | − | 3.94592i | 0.578937 | − | 0.234976i | ||||
\(283\) | 2.91928 | + | 1.68544i | 0.173533 | + | 0.100189i | 0.584251 | − | 0.811573i | \(-0.301389\pi\) |
−0.410718 | + | 0.911763i | \(0.634722\pi\) | |||||||
\(284\) | 1.85396 | − | 3.21115i | 0.110012 | − | 0.190547i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.8006 | + | 27.3674i | 0.934307 | + | 1.61827i | ||||
\(287\) | 2.75003i | 0.162329i | ||||||||
\(288\) | 2.97732 | − | 10.5090i | 0.175440 | − | 0.619250i | ||||
\(289\) | −20.2125 | −1.18897 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.0010 | + | 2.63964i | 1.11386 | + | 0.154739i | ||||
\(292\) | −6.83642 | − | 3.94701i | −0.400071 | − | 0.230981i | ||||
\(293\) | −4.88788 | − | 2.82202i | −0.285553 | − | 0.164864i | 0.350382 | − | 0.936607i | \(-0.386052\pi\) |
−0.635935 | + | 0.771743i | \(0.719385\pi\) | |||||||
\(294\) | −11.7261 | + | 15.0580i | −0.683881 | + | 0.878200i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −14.6267 | −0.850159 | ||||||||
\(297\) | −16.0127 | + | 1.76019i | −0.929150 | + | 0.102137i | ||||
\(298\) | − | 26.7000i | − | 1.54669i | ||||||
\(299\) | 11.9345 | + | 20.6711i | 0.690189 | + | 1.19544i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.335402 | + | 0.580933i | −0.0193322 | + | 0.0334844i | ||||
\(302\) | 32.2340 | + | 18.6103i | 1.85486 | + | 1.07090i | ||||
\(303\) | 4.13956 | − | 29.7979i | 0.237811 | − | 1.71184i | ||||
\(304\) | 13.6205 | + | 23.5914i | 0.781190 | + | 1.35306i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 21.4408 | − | 20.8372i | 1.22569 | − | 1.19118i | ||||
\(307\) | 5.44105i | 0.310537i | 0.987872 | + | 0.155269i | \(0.0496243\pi\) | ||||
−0.987872 | + | 0.155269i | \(0.950376\pi\) | |||||||
\(308\) | 0.907761 | − | 0.524096i | 0.0517245 | − | 0.0298632i | ||||
\(309\) | 0.542447 | + | 1.33649i | 0.0308587 | + | 0.0760301i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.53985 | − | 16.5235i | 0.540955 | − | 0.936962i | −0.457895 | − | 0.889007i | \(-0.651396\pi\) |
0.998849 | − | 0.0479550i | \(-0.0152704\pi\) | |||||||
\(312\) | −21.7731 | + | 8.83717i | −1.23266 | + | 0.500306i | ||||
\(313\) | 7.91747 | − | 4.57116i | 0.447522 | − | 0.258377i | −0.259261 | − | 0.965807i | \(-0.583479\pi\) |
0.706783 | + | 0.707430i | \(0.250146\pi\) | |||||||
\(314\) | 20.3573 | 1.14883 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.27677 | 0.128078 | ||||||||
\(317\) | 12.3294 | − | 7.11836i | 0.692486 | − | 0.399807i | −0.112056 | − | 0.993702i | \(-0.535744\pi\) |
0.804543 | + | 0.593895i | \(0.202410\pi\) | |||||||
\(318\) | −0.989786 | + | 7.12480i | −0.0555045 | + | 0.399539i | ||||
\(319\) | 3.81220 | − | 6.60292i | 0.213442 | − | 0.369693i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.7789 | − | 15.1257i | 0.657432 | − | 0.844236i | ||||
\(322\) | 2.73527 | − | 1.57921i | 0.152430 | − | 0.0880057i | ||||
\(323\) | 33.9795i | 1.89067i | ||||||||
\(324\) | −0.171906 | + | 6.01902i | −0.00955032 | + | 0.334390i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.18678 | − | 10.7158i | −0.342654 | − | 0.593494i | ||||
\(327\) | −6.36595 | − | 4.95736i | −0.352038 | − | 0.274143i | ||||
\(328\) | −10.2475 | − | 5.91638i | −0.565822 | − | 0.326677i | ||||
\(329\) | −0.936896 | + | 1.62275i | −0.0516527 | + | 0.0894652i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.10001 | + | 10.5655i | 0.335287 | + | 0.580734i | 0.983540 | − | 0.180691i | \(-0.0578334\pi\) |
−0.648253 | + | 0.761425i | \(0.724500\pi\) | |||||||
\(332\) | 9.30061i | 0.510437i | ||||||||
\(333\) | 19.5653 | − | 4.94424i | 1.07217 | − | 0.270943i | ||||
\(334\) | −4.86317 | −0.266101 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.60984 | + | 3.96633i | 0.0878237 | + | 0.216381i | ||||
\(337\) | −3.97494 | − | 2.29493i | −0.216529 | − | 0.125013i | 0.387813 | − | 0.921738i | \(-0.373231\pi\) |
−0.604342 | + | 0.796725i | \(0.706564\pi\) | |||||||
\(338\) | −36.6849 | − | 21.1800i | −1.99540 | − | 1.15204i | ||||
\(339\) | −7.81289 | − | 19.2495i | −0.424338 | − | 1.04549i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.1094 | 0.709917 | ||||||||
\(342\) | −19.0269 | − | 19.5781i | −1.02886 | − | 1.05866i | ||||
\(343\) | − | 6.94582i | − | 0.375039i | ||||||
\(344\) | −1.44316 | − | 2.49962i | −0.0778099 | − | 0.134771i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.9497 | + | 22.4295i | −0.696180 | + | 1.20582i | ||||
\(347\) | −28.9775 | − | 16.7301i | −1.55559 | − | 0.898121i | −0.997670 | − | 0.0682272i | \(-0.978266\pi\) |
−0.557921 | − | 0.829894i | \(-0.688401\pi\) | |||||||
\(348\) | −2.24857 | − | 1.75103i | −0.120536 | − | 0.0938651i | ||||
\(349\) | −14.0408 | − | 24.3193i | −0.751586 | − | 1.30178i | −0.947054 | − | 0.321074i | \(-0.895956\pi\) |
0.195468 | − | 0.980710i | \(-0.437377\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 26.1374 | − | 19.1809i | 1.39511 | − | 1.02380i | ||||
\(352\) | 11.2875i | 0.601624i | ||||||||
\(353\) | 1.59496 | − | 0.920851i | 0.0848912 | − | 0.0490119i | −0.456954 | − | 0.889491i | \(-0.651059\pi\) |
0.541845 | + | 0.840479i | \(0.317726\pi\) | |||||||
\(354\) | 5.01117 | − | 6.43505i | 0.266341 | − | 0.342019i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.13241 | + | 1.96140i | −0.0600178 | + | 0.103954i | ||||
\(357\) | −0.734707 | + | 5.28865i | −0.0388848 | + | 0.279905i | ||||
\(358\) | 24.1714 | − | 13.9553i | 1.27750 | − | 0.737563i | ||||
\(359\) | 12.1119 | 0.639241 | 0.319621 | − | 0.947546i | \(-0.396445\pi\) | ||||
0.319621 | + | 0.947546i | \(0.396445\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.0274 | 0.633020 | ||||||||
\(362\) | −18.9151 | + | 10.9206i | −0.994156 | + | 0.573976i | ||||
\(363\) | −2.22879 | + | 0.904610i | −0.116981 | + | 0.0474797i | ||||
\(364\) | −1.05476 | + | 1.82690i | −0.0552846 | + | 0.0957558i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.02597 | + | 7.45541i | 0.158170 | + | 0.389701i | ||||
\(367\) | −12.6212 | + | 7.28688i | −0.658824 | + | 0.380372i | −0.791829 | − | 0.610743i | \(-0.790871\pi\) |
0.133005 | + | 0.991115i | \(0.457537\pi\) | |||||||
\(368\) | 18.7090i | 0.975274i | ||||||||
\(369\) | 15.7073 | + | 4.45005i | 0.817691 | + | 0.231660i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.642310 | − | 1.11251i | −0.0333471 | − | 0.0577589i | ||||
\(372\) | 0.674269 | − | 4.85360i | 0.0349592 | − | 0.251648i | ||||
\(373\) | −8.18087 | − | 4.72323i | −0.423590 | − | 0.244560i | 0.273022 | − | 0.962008i | \(-0.411977\pi\) |
−0.696612 | + | 0.717448i | \(0.745310\pi\) | |||||||
\(374\) | −15.4484 | + | 26.7574i | −0.798817 | + | 1.38359i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.03125 | − | 6.98233i | −0.207896 | − | 0.360086i | ||||
\(377\) | 15.3444i | 0.790276i | ||||||||
\(378\) | −2.53807 | − | 3.45858i | −0.130544 | − | 0.177890i | ||||
\(379\) | 28.5541 | 1.46673 | 0.733363 | − | 0.679837i | \(-0.237949\pi\) | ||||
0.733363 | + | 0.679837i | \(0.237949\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.43581 | + | 4.41207i | −0.176022 | + | 0.226037i | ||||
\(382\) | 35.8483 | + | 20.6970i | 1.83416 | + | 1.05895i | ||||
\(383\) | 1.26908 | + | 0.732704i | 0.0648470 | + | 0.0374394i | 0.532073 | − | 0.846699i | \(-0.321413\pi\) |
−0.467226 | + | 0.884138i | \(0.654747\pi\) | |||||||
\(384\) | −23.2348 | − | 3.22780i | −1.18569 | − | 0.164718i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.6176 | 0.794916 | ||||||||
\(387\) | 2.77537 | + | 2.85577i | 0.141080 | + | 0.145167i | ||||
\(388\) | 7.41014i | 0.376193i | ||||||||
\(389\) | −6.45506 | − | 11.1805i | −0.327284 | − | 0.566873i | 0.654688 | − | 0.755900i | \(-0.272800\pi\) |
−0.981972 | + | 0.189026i | \(0.939467\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.6685 | + | 20.2104i | −0.590100 | + | 1.02208i | ||||
\(392\) | 12.7007 | + | 7.33276i | 0.641483 | + | 0.370360i | ||||
\(393\) | −15.0622 | + | 6.11336i | −0.759785 | + | 0.308378i | ||||
\(394\) | 1.68961 | + | 2.92649i | 0.0851212 | + | 0.147434i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.52456 | − | 6.03294i | −0.0766118 | − | 0.303167i | ||||
\(397\) | − | 0.868386i | − | 0.0435831i | −0.999763 | − | 0.0217915i | \(-0.993063\pi\) | ||
0.999763 | − | 0.0217915i | \(-0.00693701\pi\) | |||||||
\(398\) | 18.5302 | − | 10.6984i | 0.928834 | − | 0.536263i | ||||
\(399\) | 4.82918 | + | 0.670876i | 0.241761 | + | 0.0335858i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.7063 | + | 28.9361i | −0.834270 | + | 1.44500i | 0.0603527 | + | 0.998177i | \(0.480777\pi\) |
−0.894623 | + | 0.446822i | \(0.852556\pi\) | |||||||
\(402\) | 5.37277 | + | 4.18394i | 0.267970 | + | 0.208676i | ||||
\(403\) | −22.8486 | + | 13.1916i | −1.13817 | + | 0.657122i | ||||
\(404\) | 11.6208 | 0.578156 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.03042 | 0.100768 | ||||||||
\(407\) | −18.0604 | + | 10.4272i | −0.895221 | + | 0.516856i | ||||
\(408\) | −18.1265 | − | 14.1157i | −0.897397 | − | 0.698831i | ||||
\(409\) | 2.52767 | − | 4.37806i | 0.124985 | − | 0.216481i | −0.796742 | − | 0.604320i | \(-0.793445\pi\) |
0.921727 | + | 0.387839i | \(0.126778\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.96221 | − | 0.550436i | −0.195442 | − | 0.0271510i | ||||
\(412\) | −0.482512 | + | 0.278579i | −0.0237717 | + | 0.0137246i | ||||
\(413\) | 1.45658i | 0.0716734i | ||||||||
\(414\) | −4.59379 | − | 18.1785i | −0.225772 | − | 0.893423i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11.3582 | − | 19.6730i | −0.556883 | − | 0.964549i | ||||
\(417\) | −17.4838 | + | 7.09623i | −0.856184 | + | 0.347504i | ||||
\(418\) | 24.4327 | + | 14.1062i | 1.19504 | + | 0.689959i | ||||
\(419\) | 5.47880 | − | 9.48955i | 0.267657 | − | 0.463595i | −0.700600 | − | 0.713555i | \(-0.747084\pi\) |
0.968256 | + | 0.249960i | \(0.0804174\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.31932 | + | 9.21333i | 0.259248 | + | 0.449030i | 0.966041 | − | 0.258390i | \(-0.0831921\pi\) |
−0.706793 | + | 0.707421i | \(0.749859\pi\) | |||||||
\(422\) | − | 18.1538i | − | 0.883711i | ||||||
\(423\) | 7.75260 | + | 7.97718i | 0.376944 | + | 0.387864i | ||||
\(424\) | 5.52744 | 0.268436 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 15.5331 | + | 2.15788i | 0.752582 | + | 0.104550i | ||||
\(427\) | −1.24442 | − | 0.718467i | −0.0602218 | − | 0.0347691i | ||||
\(428\) | 6.41322 | + | 3.70267i | 0.309995 | + | 0.178975i | ||||
\(429\) | −20.5846 | + | 26.4335i | −0.993834 | + | 1.27622i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.3529 | −1.79923 | −0.899613 | − | 0.436687i | \(-0.856152\pi\) | ||||
−0.899613 | + | 0.436687i | \(0.856152\pi\) | |||||||
\(432\) | 25.2595 | − | 2.77664i | 1.21530 | − | 0.133591i | ||||
\(433\) | 17.2125i | 0.827179i | 0.910464 | + | 0.413589i | \(0.135725\pi\) | ||||
−0.910464 | + | 0.413589i | \(0.864275\pi\) | |||||||
\(434\) | 1.74556 | + | 3.02339i | 0.0837894 | + | 0.145127i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.55834 | − | 2.69913i | 0.0746310 | − | 0.129265i | ||||
\(437\) | 18.4545 | + | 10.6547i | 0.882799 | + | 0.509684i | ||||
\(438\) | 4.59404 | − | 33.0694i | 0.219512 | − | 1.58012i | ||||
\(439\) | −15.8744 | − | 27.4952i | −0.757642 | − | 1.31228i | −0.944050 | − | 0.329803i | \(-0.893018\pi\) |
0.186408 | − | 0.982473i | \(-0.440316\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.4677 | − | 5.51539i | −0.927032 | − | 0.262638i | ||||
\(442\) | − | 62.1809i | − | 2.95764i | ||||||
\(443\) | 0.308268 | − | 0.177979i | 0.0146463 | − | 0.00845603i | −0.492659 | − | 0.870222i | \(-0.663975\pi\) |
0.507305 | + | 0.861766i | \(0.330642\pi\) | |||||||
\(444\) | 2.93161 | + | 7.22293i | 0.139128 | + | 0.342785i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.18087 | + | 5.50943i | −0.150619 | + | 0.260879i | ||||
\(447\) | 26.2289 | − | 10.6456i | 1.24058 | − | 0.503522i | ||||
\(448\) | 1.67738 | − | 0.968438i | 0.0792490 | − | 0.0457544i | ||||
\(449\) | 7.85632 | 0.370762 | 0.185381 | − | 0.982667i | \(-0.440648\pi\) | ||||
0.185381 | + | 0.982667i | \(0.440648\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.8708 | −0.794416 | ||||||||
\(452\) | 6.94964 | − | 4.01238i | 0.326884 | − | 0.188726i | ||||
\(453\) | −5.42980 | + | 39.0854i | −0.255114 | + | 1.83639i | ||||
\(454\) | −10.4625 | + | 18.1215i | −0.491028 | + | 0.850485i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.8893 | + | 16.5517i | −0.603598 | + | 0.775105i | ||||
\(457\) | 18.6118 | − | 10.7455i | 0.870622 | − | 0.502654i | 0.00306742 | − | 0.999995i | \(-0.499024\pi\) |
0.867555 | + | 0.497341i | \(0.165690\pi\) | |||||||
\(458\) | 10.8691i | 0.507879i | ||||||||
\(459\) | 29.0183 | + | 12.7544i | 1.35446 | + | 0.595326i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.4964 | − | 35.5007i | −0.954611 | − | 1.65343i | −0.735256 | − | 0.677789i | \(-0.762938\pi\) |
−0.219355 | − | 0.975645i | \(-0.570395\pi\) | |||||||
\(462\) | 3.49776 | + | 2.72382i | 0.162731 | + | 0.126723i | ||||
\(463\) | 36.4890 | + | 21.0669i | 1.69579 | + | 0.979063i | 0.949671 | + | 0.313248i | \(0.101417\pi\) |
0.746116 | + | 0.665816i | \(0.231916\pi\) | |||||||
\(464\) | −6.01363 | + | 10.4159i | −0.279176 | + | 0.483546i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.98837 | − | 5.17601i | −0.138434 | − | 0.239774i | ||||
\(467\) | − | 22.5376i | − | 1.04292i | −0.853276 | − | 0.521459i | \(-0.825388\pi\) | ||
0.853276 | − | 0.521459i | \(-0.174612\pi\) | |||||||
\(468\) | 8.72792 | + | 8.98075i | 0.403448 | + | 0.415136i | ||||
\(469\) | −1.21613 | −0.0561557 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.11675 | + | 19.9981i | 0.374000 | + | 0.921465i | ||||
\(472\) | −5.42766 | − | 3.13366i | −0.249828 | − | 0.144238i | ||||
\(473\) | −3.56390 | − | 2.05762i | −0.163868 | − | 0.0946093i | ||||
\(474\) | 3.62141 | + | 8.92247i | 0.166337 | + | 0.409822i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.06251 | −0.0945348 | ||||||||
\(477\) | −7.39372 | + | 1.86843i | −0.338535 | + | 0.0855496i | ||||
\(478\) | − | 25.6356i | − | 1.17255i | ||||||
\(479\) | −16.6440 | − | 28.8282i | −0.760483 | − | 1.31720i | −0.942602 | − | 0.333919i | \(-0.891629\pi\) |
0.182119 | − | 0.983277i | \(-0.441704\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.9851 | − | 36.3472i | 0.956837 | − | 1.65729i | ||||
\(482\) | 15.8816 | + | 9.16924i | 0.723387 | + | 0.417647i | ||||
\(483\) | 2.64193 | + | 2.05735i | 0.120212 | + | 0.0936127i | ||||
\(484\) | −0.464570 | − | 0.804660i | −0.0211168 | − | 0.0365754i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −23.8614 | + | 8.90010i | −1.08238 | + | 0.403717i | ||||
\(487\) | 23.7703i | 1.07713i | 0.842583 | + | 0.538566i | \(0.181034\pi\) | ||||
−0.842583 | + | 0.538566i | \(0.818966\pi\) | |||||||
\(488\) | 5.35447 | − | 3.09140i | 0.242385 | − | 0.139941i | ||||
\(489\) | 8.05999 | − | 10.3502i | 0.364485 | − | 0.468050i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.30281 | − | 3.98859i | 0.103925 | − | 0.180003i | −0.809374 | − | 0.587294i | \(-0.800193\pi\) |
0.913298 | + | 0.407291i | \(0.133527\pi\) | |||||||
\(492\) | −0.867731 | + | 6.24620i | −0.0391203 | + | 0.281601i | ||||
\(493\) | −12.9924 | + | 7.50118i | −0.585150 | + | 0.337836i | ||||
\(494\) | −56.7787 | −2.55459 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.6797 | −0.928548 | ||||||||
\(497\) | −2.42545 | + | 1.40033i | −0.108796 | + | 0.0628135i | ||||
\(498\) | −36.4483 | + | 14.7935i | −1.63329 | + | 0.662910i | ||||
\(499\) | −9.44878 | + | 16.3658i | −0.422985 | + | 0.732632i | −0.996230 | − | 0.0867522i | \(-0.972351\pi\) |
0.573245 | + | 0.819384i | \(0.305684\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.93901 | − | 4.77736i | −0.0866287 | − | 0.213437i | ||||
\(502\) | −9.81962 | + | 5.66936i | −0.438271 | + | 0.253036i | ||||
\(503\) | − | 35.7581i | − | 1.59438i | −0.603731 | − | 0.797188i | \(-0.706320\pi\) | ||
0.603731 | − | 0.797188i | \(-0.293680\pi\) | |||||||
\(504\) | −2.36401 | + | 2.29746i | −0.105301 | + | 0.102337i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.68809 | + | 16.7803i | 0.430688 | + | 0.745974i | ||||
\(507\) | 6.17955 | − | 44.4824i | 0.274444 | − | 1.97553i | ||||
\(508\) | −1.87069 | − | 1.08004i | −0.0829985 | − | 0.0479192i | ||||
\(509\) | 12.2034 | − | 21.1368i | 0.540904 | − | 0.936874i | −0.457948 | − | 0.888979i | \(-0.651415\pi\) |
0.998852 | − | 0.0478949i | \(-0.0152513\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.98125 | + | 5.16368i | 0.131883 | + | 0.228428i | ||||
\(512\) | 3.46207i | 0.153003i | ||||||||
\(513\) | 11.6463 | − | 26.4972i | 0.514198 | − | 1.16988i | ||||
\(514\) | 29.9506 | 1.32106 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.945110 | + | 1.21365i | −0.0416062 | + | 0.0534282i | ||||
\(517\) | −9.95523 | − | 5.74765i | −0.437830 | − | 0.252782i | ||||
\(518\) | −4.80957 | − | 2.77681i | −0.211321 | − | 0.122006i | ||||
\(519\) | −27.1970 | − | 3.77824i | −1.19381 | − | 0.165846i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.3968 | 1.46314 | 0.731571 | − | 0.681766i | \(-0.238788\pi\) | ||||
0.731571 | + | 0.681766i | \(0.238788\pi\) | |||||||
\(522\) | 3.28558 | − | 11.5971i | 0.143806 | − | 0.507592i | ||||
\(523\) | 37.3654i | 1.63388i | 0.576726 | + | 0.816938i | \(0.304330\pi\) | ||||
−0.576726 | + | 0.816938i | \(0.695670\pi\) | |||||||
\(524\) | −3.13957 | − | 5.43789i | −0.137153 | − | 0.237555i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.1324 | − | 22.7460i | 0.572600 | − | 0.991772i | ||||
\(527\) | −22.3393 | − | 12.8976i | −0.973115 | − | 0.561828i | ||||
\(528\) | −24.3326 | + | 9.87599i | −1.05894 | + | 0.429797i | ||||
\(529\) | −4.18239 | − | 7.24412i | −0.181843 | − | 0.314962i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.31953 | + | 2.35701i | 0.361037 | + | 0.102285i | ||||
\(532\) | 1.88332i | 0.0816521i | ||||||||
\(533\) | 29.4043 | − | 16.9766i | 1.27364 | − | 0.735338i | ||||
\(534\) | −9.48775 | − | 1.31805i | −0.410575 | − | 0.0570376i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.61637 | − | 4.53168i | 0.113010 | − | 0.195739i | ||||
\(537\) | 23.3466 | + | 18.1807i | 1.00748 | + | 0.784555i | ||||
\(538\) | −25.7508 | + | 14.8672i | −1.11019 | + | 0.640971i | ||||
\(539\) | 20.9097 | 0.900645 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.2560 | 1.21482 | 0.607409 | − | 0.794389i | \(-0.292209\pi\) | ||||
0.607409 | + | 0.794389i | \(0.292209\pi\) | |||||||
\(542\) | 3.51689 | − | 2.03048i | 0.151063 | − | 0.0872165i | ||||
\(543\) | −18.2697 | − | 14.2271i | −0.784026 | − | 0.610545i | ||||
\(544\) | 11.1051 | − | 19.2345i | 0.476125 | − | 0.824673i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.83717 | − | 1.22767i | −0.378196 | − | 0.0525395i | ||||
\(547\) | −33.3811 | + | 19.2726i | −1.42727 | + | 0.824036i | −0.996905 | − | 0.0786172i | \(-0.974950\pi\) |
−0.430368 | + | 0.902654i | \(0.641616\pi\) | |||||||
\(548\) | − | 1.54521i | − | 0.0660082i | ||||||
\(549\) | −6.11737 | + | 5.94515i | −0.261083 | + | 0.253733i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.84949 | + | 11.8637i | 0.291798 | + | 0.505409i | ||||
\(552\) | −13.3502 | + | 5.41850i | −0.568220 | + | 0.230626i | ||||
\(553\) | −1.48929 | − | 0.859845i | −0.0633313 | − | 0.0365643i | ||||
\(554\) | −6.26309 | + | 10.8480i | −0.266093 | + | 0.460887i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.64433 | − | 6.31217i | −0.154554 | − | 0.267696i | ||||
\(557\) | − | 27.4125i | − | 1.16151i | −0.814080 | − | 0.580753i | \(-0.802758\pi\) | ||
0.814080 | − | 0.580753i | \(-0.197242\pi\) | |||||||
\(558\) | 20.0933 | − | 5.07769i | 0.850618 | − | 0.214956i | ||||
\(559\) | 8.28206 | 0.350294 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.4447 | − | 4.50727i | −1.36982 | − | 0.190297i | ||||
\(562\) | 0.386579 | + | 0.223191i | 0.0163068 | + | 0.00941476i | ||||
\(563\) | −23.9363 | − | 13.8196i | −1.00879 | − | 0.582427i | −0.0979551 | − | 0.995191i | \(-0.531230\pi\) |
−0.910838 | + | 0.412764i | \(0.864563\pi\) | |||||||
\(564\) | −2.64003 | + | 3.39017i | −0.111165 | + | 0.142752i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.50710 | −0.231481 | ||||||||
\(567\) | 2.38559 | − | 3.87227i | 0.100185 | − | 0.162620i | ||||
\(568\) | − | 12.0506i | − | 0.505634i | ||||||
\(569\) | −7.35807 | − | 12.7446i | −0.308467 | − | 0.534280i | 0.669561 | − | 0.742757i | \(-0.266482\pi\) |
−0.978027 | + | 0.208478i | \(0.933149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.1503 | − | 24.5090i | 0.592172 | − | 1.02567i | −0.401768 | − | 0.915742i | \(-0.631604\pi\) |
0.993939 | − | 0.109930i | \(-0.0350627\pi\) | |||||||
\(572\) | −11.2077 | − | 6.47074i | −0.468616 | − | 0.270555i | ||||
\(573\) | −6.03862 | + | 43.4679i | −0.252267 | + | 1.81590i | ||||
\(574\) | −2.24639 | − | 3.89087i | −0.0937626 | − | 0.162402i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.81711 | − | 11.1478i | −0.117380 | − | 0.464493i | ||||
\(577\) | − | 40.7976i | − | 1.69843i | −0.528049 | − | 0.849214i | \(-0.677076\pi\) | ||
0.528049 | − | 0.849214i | \(-0.322924\pi\) | |||||||
\(578\) | 28.5975 | − | 16.5108i | 1.18950 | − | 0.686759i | ||||
\(579\) | 6.22696 | + | 15.3421i | 0.258784 | + | 0.637594i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.51247 | − | 6.08377i | 0.145722 | − | 0.252397i | ||||
\(582\) | −29.0397 | + | 11.7865i | −1.20373 | + | 0.488565i | ||||
\(583\) | 6.82504 | − | 3.94044i | 0.282664 | − | 0.163196i | ||||
\(584\) | −25.6553 | −1.06162 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.22080 | 0.380908 | ||||||||
\(587\) | 2.40784 | − | 1.39016i | 0.0993820 | − | 0.0573782i | −0.449485 | − | 0.893288i | \(-0.648393\pi\) |
0.548867 | + | 0.835910i | \(0.315059\pi\) | |||||||
\(588\) | 1.07547 | − | 7.74154i | 0.0443514 | − | 0.319256i | ||||
\(589\) | −11.7771 | + | 20.3985i | −0.485265 | + | 0.840504i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.20118 | + | 2.82663i | −0.0905445 | + | 0.116272i | ||||
\(592\) | 28.4897 | − | 16.4485i | 1.17092 | − | 0.676031i | ||||
\(593\) | 14.8084i | 0.608109i | 0.952655 | + | 0.304055i | \(0.0983405\pi\) | ||||
−0.952655 | + | 0.304055i | \(0.901659\pi\) | |||||||
\(594\) | 21.2176 | − | 15.5705i | 0.870570 | − | 0.638867i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.46717 | + | 9.46941i | 0.223944 | + | 0.387882i | ||||
\(597\) | 17.8979 | + | 13.9376i | 0.732511 | + | 0.570429i | ||||
\(598\) | −33.7709 | − | 19.4976i | −1.38100 | − | 0.797318i | ||||
\(599\) | −8.17151 | + | 14.1535i | −0.333879 | + | 0.578295i | −0.983269 | − | 0.182160i | \(-0.941691\pi\) |
0.649390 | + | 0.760456i | \(0.275024\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.31185 | + | 5.73630i | 0.135093 | + | 0.233988i | 0.925633 | − | 0.378422i | \(-0.123533\pi\) |
−0.790540 | + | 0.612411i | \(0.790200\pi\) | |||||||
\(602\) | − | 1.09591i | − | 0.0446658i | ||||||
\(603\) | −1.96792 | + | 6.94617i | −0.0801400 | + | 0.282870i | ||||
\(604\) | −15.2428 | −0.620221 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.4839 | + | 45.5408i | 0.750857 | + | 1.84997i | ||||
\(607\) | −26.2487 | − | 15.1547i | −1.06540 | − | 0.615110i | −0.138480 | − | 0.990365i | \(-0.544222\pi\) |
−0.926921 | + | 0.375256i | \(0.877555\pi\) | |||||||
\(608\) | −17.5634 | − | 10.1403i | −0.712291 | − | 0.411242i | ||||
\(609\) | 0.809554 | + | 1.99459i | 0.0328048 | + | 0.0808248i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.1347 | 0.935931 | ||||||||
\(612\) | −3.33751 | + | 11.7804i | −0.134911 | + | 0.476195i | ||||
\(613\) | − | 14.7803i | − | 0.596969i | −0.954415 | − | 0.298484i | \(-0.903519\pi\) | ||
0.954415 | − | 0.298484i | \(-0.0964811\pi\) | |||||||
\(614\) | −4.44459 | − | 7.69825i | −0.179369 | − | 0.310676i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.70330 | − | 2.95020i | 0.0686278 | − | 0.118867i | ||||
\(617\) | 29.3160 | + | 16.9256i | 1.18022 | + | 0.681399i | 0.956065 | − | 0.293155i | \(-0.0947053\pi\) |
0.224152 | + | 0.974554i | \(0.428039\pi\) | |||||||
\(618\) | −1.85920 | − | 1.44782i | −0.0747882 | − | 0.0582399i | ||||
\(619\) | 5.84433 | + | 10.1227i | 0.234903 | + | 0.406865i | 0.959245 | − | 0.282577i | \(-0.0911893\pi\) |
−0.724341 | + | 0.689442i | \(0.757856\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.0261 | − | 11.7607i | 0.643105 | − | 0.471942i | ||||
\(622\) | 31.1709i | 1.24984i | ||||||||
\(623\) | 1.48148 | − | 0.855334i | 0.0593543 | − | 0.0342682i | ||||
\(624\) | 32.4716 | − | 41.6981i | 1.29990 | − | 1.66926i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.46800 | + | 12.9350i | −0.298481 | + | 0.516985i | ||||
\(627\) | −4.11568 | + | 29.6260i | −0.164364 | + | 1.18315i | ||||
\(628\) | −7.21993 | + | 4.16843i | −0.288107 | + | 0.166338i | ||||
\(629\) | 41.0347 | 1.63616 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.1357 | −1.51816 | −0.759078 | − | 0.650999i | \(-0.774350\pi\) | ||||
−0.759078 | + | 0.650999i | \(0.774350\pi\) | |||||||
\(632\) | 6.40810 | − | 3.69972i | 0.254901 | − | 0.147167i | ||||
\(633\) | 17.8334 | − | 7.23815i | 0.708816 | − | 0.287691i | ||||
\(634\) | −11.6294 | + | 20.1428i | −0.461864 | + | 0.799972i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.10786 | − | 2.72955i | −0.0439294 | − | 0.108234i | ||||
\(637\) | −36.4437 | + | 21.0408i | −1.44395 | + | 0.833666i | ||||
\(638\) | 12.4562i | 0.493144i | ||||||||
\(639\) | 4.07346 | + | 16.1194i | 0.161144 | + | 0.637675i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.3827 | + | 30.1077i | 0.686576 | + | 1.18918i | 0.972939 | + | 0.231063i | \(0.0742204\pi\) |
−0.286363 | + | 0.958121i | \(0.592446\pi\) | |||||||
\(642\) | −4.30966 | + | 31.0223i | −0.170089 | + | 1.22435i | ||||
\(643\) | 2.32541 | + | 1.34258i | 0.0917053 | + | 0.0529461i | 0.545151 | − | 0.838338i | \(-0.316472\pi\) |
−0.453446 | + | 0.891284i | \(0.649806\pi\) | |||||||
\(644\) | −0.646726 | + | 1.12016i | −0.0254846 | + | 0.0441406i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.7565 | − | 48.0757i | −1.09207 | − | 1.89151i | ||||
\(647\) | 40.5103i | 1.59262i | 0.604887 | + | 0.796311i | \(0.293218\pi\) | ||||
−0.604887 | + | 0.796311i | \(0.706782\pi\) | |||||||
\(648\) | 9.29698 | + | 17.2202i | 0.365220 | + | 0.676474i | ||||
\(649\) | −8.93578 | −0.350760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.27407 | + | 2.92022i | −0.0891277 | + | 0.114453i | ||||
\(652\) | 4.38841 | + | 2.53365i | 0.171863 | + | 0.0992253i | ||||
\(653\) | 11.5488 | + | 6.66772i | 0.451941 | + | 0.260928i | 0.708650 | − | 0.705561i | \(-0.249305\pi\) |
−0.256709 | + | 0.966489i | \(0.582638\pi\) | |||||||
\(654\) | 13.0563 | + | 1.81380i | 0.510543 | + | 0.0709253i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 26.6132 | 1.03907 | ||||||||
\(657\) | 34.3176 | − | 8.67223i | 1.33886 | − | 0.338336i | ||||
\(658\) | − | 3.06126i | − | 0.119340i | ||||||
\(659\) | 15.5772 | + | 26.9804i | 0.606800 | + | 1.05101i | 0.991764 | + | 0.128077i | \(0.0408803\pi\) |
−0.384965 | + | 0.922931i | \(0.625786\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.15894 | + | 5.47145i | −0.122869 | + | 0.212815i | −0.920898 | − | 0.389804i | \(-0.872543\pi\) |
0.798029 | + | 0.602619i | \(0.205876\pi\) | |||||||
\(662\) | −17.2612 | − | 9.96574i | −0.670874 | − | 0.387329i | ||||
\(663\) | 61.0837 | − | 24.7924i | 2.37230 | − | 0.962856i | ||||
\(664\) | 15.1134 | + | 26.1771i | 0.586512 | + | 1.01587i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −23.6431 | + | 22.9775i | −0.916150 | + | 0.890358i | ||||
\(667\) | 9.40838i | 0.364294i | ||||||||
\(668\) | 1.72477 | − | 0.995798i | 0.0667334 | − | 0.0385286i | ||||
\(669\) | −6.68047 | − | 0.928060i | −0.258282 | − | 0.0358809i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.40764 | − | 7.63426i | 0.170155 | − | 0.294717i | ||||
\(672\) | −2.51436 | − | 1.95801i | −0.0969937 | − | 0.0755320i | ||||
\(673\) | 5.70901 | − | 3.29610i | 0.220066 | − | 0.127055i | −0.385915 | − | 0.922534i | \(-0.626114\pi\) |
0.605981 | + | 0.795479i | \(0.292781\pi\) | |||||||
\(674\) | 7.49857 | 0.288834 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.3476 | 0.667214 | ||||||||
\(677\) | 30.2197 | − | 17.4473i | 1.16144 | − | 0.670556i | 0.209788 | − | 0.977747i | \(-0.432722\pi\) |
0.951648 | + | 0.307191i | \(0.0993891\pi\) | |||||||
\(678\) | 26.7782 | + | 20.8530i | 1.02841 | + | 0.800855i | ||||
\(679\) | 2.79851 | − | 4.84716i | 0.107397 | − | 0.186017i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.9733 | − | 3.05256i | −0.842019 | − | 0.116974i | ||||
\(682\) | −18.5479 | + | 10.7086i | −0.710234 | + | 0.410054i | ||||
\(683\) | − | 26.0958i | − | 0.998528i | −0.866450 | − | 0.499264i | \(-0.833604\pi\) | ||
0.866450 | − | 0.499264i | \(-0.166396\pi\) | |||||||
\(684\) | 10.7569 | + | 3.04755i | 0.411302 | + | 0.116526i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.67378 | + | 9.82727i | 0.216626 | + | 0.375207i | ||||
\(687\) | −10.6773 | + | 4.33365i | −0.407364 | + | 0.165339i | ||||
\(688\) | 5.62194 | + | 3.24583i | 0.214334 | + | 0.123746i | ||||
\(689\) | −7.93028 | + | 13.7356i | −0.302119 | + | 0.523286i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.6529 | + | 25.3796i | 0.557423 | + | 0.965485i | 0.997711 | + | 0.0676282i | \(0.0215432\pi\) |
−0.440288 | + | 0.897857i | \(0.645124\pi\) | |||||||
\(692\) | − | 10.6065i | − | 0.403197i | ||||||
\(693\) | −1.28115 | + | 4.52207i | −0.0486668 | + | 0.171779i | ||||
\(694\) | 54.6648 | 2.07505 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.17413 | − | 1.27448i | −0.347745 | − | 0.0483091i | ||||
\(697\) | 28.7489 | + | 16.5982i | 1.08894 | + | 0.628701i | ||||
\(698\) | 39.7311 | + | 22.9387i | 1.50384 | + | 0.868244i | ||||
\(699\) | 3.89318 | − | 4.99939i | 0.147253 | − | 0.189094i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.3891 | 0.581239 | 0.290620 | − | 0.956839i | \(-0.406139\pi\) | ||||
0.290620 | + | 0.956839i | \(0.406139\pi\) | |||||||
\(702\) | −21.3123 | + | 48.4887i | −0.804379 | + | 1.83009i | ||||
\(703\) | − | 37.4696i | − | 1.41319i | ||||||
\(704\) | 5.94116 | + | 10.2904i | 0.223916 | + | 0.387834i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.50442 | + | 2.60572i | −0.0566194 | + | 0.0980677i | ||||
\(707\) | −7.60146 | − | 4.38870i | −0.285882 | − | 0.165054i | ||||
\(708\) | −0.459601 | + | 3.30836i | −0.0172729 | + | 0.124336i | ||||
\(709\) | −3.86996 | − | 6.70296i | −0.145339 | − | 0.251735i | 0.784160 | − | 0.620558i | \(-0.213094\pi\) |
−0.929499 | + | 0.368823i | \(0.879761\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.32113 | + | 7.11502i | −0.274564 | + | 0.266834i | ||||
\(712\) | 7.36062i | 0.275851i | ||||||||
\(713\) | −14.0096 | + | 8.08842i | −0.524662 | + | 0.302914i | ||||
\(714\) | −3.28060 | − | 8.08278i | −0.122773 | − | 0.302490i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.71508 | + | 9.89880i | −0.213582 | + | 0.369936i | ||||
\(717\) | 25.1833 | − | 10.2213i | 0.940486 | − | 0.381720i | ||||
\(718\) | −17.1365 | + | 9.89374i | −0.639527 | + | 0.369231i | ||||
\(719\) | 15.1316 | 0.564313 | 0.282156 | − | 0.959368i | \(-0.408950\pi\) | ||||
0.282156 | + | 0.959368i | \(0.408950\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.420832 | 0.0156726 | ||||||||
\(722\) | −17.0169 | + | 9.82470i | −0.633303 | + | 0.365638i | ||||
\(723\) | −2.67525 | + | 19.2573i | −0.0994934 | + | 0.716185i | ||||
\(724\) | 4.47229 | − | 7.74623i | 0.166211 | − | 0.287886i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.41445 | − | 3.10049i | 0.0896086 | − | 0.115070i | ||||
\(727\) | 0.140189 | − | 0.0809381i | 0.00519932 | − | 0.00300183i | −0.497398 | − | 0.867522i | \(-0.665711\pi\) |
0.502597 | + | 0.864521i | \(0.332378\pi\) | |||||||
\(728\) | 6.85590i | 0.254097i | ||||||||
\(729\) | −18.2569 | − | 19.8918i | −0.676183 | − | 0.736734i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.04873 | + | 7.01260i | 0.149748 | + | 0.259370i | ||||
\(732\) | −2.59978 | − | 2.02453i | −0.0960907 | − | 0.0748288i | ||||
\(733\) | −43.3300 | − | 25.0166i | −1.60043 | − | 0.924009i | −0.991401 | − | 0.130861i | \(-0.958226\pi\) |
−0.609029 | − | 0.793148i | \(-0.708441\pi\) | |||||||
\(734\) | 11.9047 | − | 20.6196i | 0.439412 | − | 0.761084i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.96427 | − | 12.0625i | −0.256707 | − | 0.444629i | ||||
\(737\) | − | 7.46070i | − | 0.274818i | ||||||
\(738\) | −25.8585 | + | 6.53458i | −0.951866 | + | 0.240541i | ||||
\(739\) | −30.5505 | −1.12382 | −0.561909 | − | 0.827199i | \(-0.689933\pi\) | ||||
−0.561909 | + | 0.827199i | \(0.689933\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.6384 | − | 55.7768i | −0.831643 | − | 2.04901i | ||||
\(742\) | 1.81754 | + | 1.04936i | 0.0667240 | + | 0.0385231i | ||||
\(743\) | 5.16743 | + | 2.98342i | 0.189575 | + | 0.109451i | 0.591783 | − | 0.806097i | \(-0.298424\pi\) |
−0.402209 | + | 0.915548i | \(0.631757\pi\) | |||||||
\(744\) | −5.98927 | − | 14.7564i | −0.219577 | − | 0.540997i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.4329 | 0.565039 | ||||||||
\(747\) | −29.0649 | − | 29.9068i | −1.06343 | − | 1.09423i | ||||
\(748\) | − | 12.6530i | − | 0.462640i | ||||||
\(749\) | −2.79670 | − | 4.84403i | −0.102189 | − | 0.176997i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.1988 | + | 29.7892i | −0.627593 | + | 1.08702i | 0.360441 | + | 0.932782i | \(0.382626\pi\) |
−0.988033 | + | 0.154240i | \(0.950707\pi\) | |||||||
\(752\) | 15.7041 | + | 9.06674i | 0.572668 | + | 0.330630i | ||||
\(753\) | −9.48454 | − | 7.38591i | −0.345636 | − | 0.269157i | ||||
\(754\) | −12.5342 | − | 21.7099i | −0.456470 | − | 0.790630i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.60834 | + | 0.706916i | 0.0584948 | + | 0.0257103i | ||||
\(757\) | 40.6873i | 1.47881i | 0.673263 | + | 0.739403i | \(0.264892\pi\) | ||||
−0.673263 | + | 0.739403i | \(0.735108\pi\) | |||||||
\(758\) | −40.3997 | + | 23.3248i | −1.46738 | + | 0.847194i | ||||
\(759\) | −12.6214 | + | 16.2077i | −0.458128 | + | 0.588301i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.1298 | + | 24.4735i | −0.512204 | + | 0.887164i | 0.487696 | + | 0.873014i | \(0.337838\pi\) |
−0.999900 | + | 0.0141502i | \(0.995496\pi\) | |||||||
\(762\) | 1.25710 | − | 9.04898i | 0.0455398 | − | 0.327810i | ||||
\(763\) | −2.03870 | + | 1.17705i | −0.0738060 | + | 0.0426119i | ||||
\(764\) | −16.9519 | −0.613299 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.39407 | −0.0865013 | ||||||||
\(767\) | 15.5743 | − | 8.99180i | 0.562354 | − | 0.324675i | ||||
\(768\) | 23.2079 | − | 9.41952i | 0.837444 | − | 0.339898i | ||||
\(769\) | −23.4518 | + | 40.6197i | −0.845694 | + | 1.46478i | 0.0393235 | + | 0.999227i | \(0.487480\pi\) |
−0.885017 | + | 0.465558i | \(0.845854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.9417 | + | 29.4221i | 0.430070 | + | 1.05961i | ||||
\(772\) | −5.53894 | + | 3.19791i | −0.199351 | + | 0.115095i | ||||
\(773\) | − | 9.19641i | − | 0.330772i | −0.986229 | − | 0.165386i | \(-0.947113\pi\) | ||
0.986229 | − | 0.165386i | \(-0.0528870\pi\) | |||||||
\(774\) | −6.25949 | − | 1.77338i | −0.224993 | − | 0.0637428i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12.0414 | + | 20.8563i | 0.432260 | + | 0.748696i | ||||
\(777\) | 0.810170 | − | 5.83186i | 0.0290647 | − | 0.209217i | ||||
\(778\) | 18.2658 | + | 10.5458i | 0.654862 | + | 0.378085i | ||||
\(779\) | 15.1562 | − | 26.2512i | 0.543025 | − | 0.940548i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.59074 | − | 14.8796i | −0.307401 | − | 0.532434i | ||||
\(782\) | − | 38.1261i | − | 1.36339i | ||||||
\(783\) | 12.7025 | − | 1.39632i | 0.453950 | − | 0.0499004i | ||||
\(784\) | −32.9844 | −1.17801 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 16.3169 | − | 20.9532i | 0.582003 | − | 0.747374i | ||||
\(787\) | −4.97651 | − | 2.87319i | −0.177393 | − | 0.102418i | 0.408674 | − | 0.912680i | \(-0.365991\pi\) |
−0.586067 | + | 0.810262i | \(0.699325\pi\) | |||||||
\(788\) | −1.19847 | − | 0.691939i | −0.0426938 | − | 0.0246493i | ||||
\(789\) | 27.5807 | + | 3.83155i | 0.981899 | + | 0.136407i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.06126 | −0.215514 | ||||||||
\(792\) | −14.0944 | − | 14.5027i | −0.500823 | − | 0.515330i | ||||
\(793\) | 17.7411i | 0.630004i | ||||||||
\(794\) | 0.709351 | + | 1.22863i | 0.0251739 | + | 0.0436025i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.38128 | + | 7.58859i | −0.155290 | + | 0.268971i | ||||
\(797\) | 6.12670 | + | 3.53725i | 0.217019 | + | 0.125296i | 0.604569 | − | 0.796553i | \(-0.293345\pi\) |
−0.387550 | + | 0.921849i | \(0.626679\pi\) | |||||||
\(798\) | −7.38056 | + | 2.99558i | −0.261269 | + | 0.106043i | ||||
\(799\) | 11.3095 | + | 19.5887i | 0.400103 | + | 0.692998i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.48810 | − | 9.84586i | −0.0879127 | − | 0.347886i | ||||
\(802\) | − | 54.5868i | − | 1.92753i | ||||||
\(803\) | −31.6781 | + | 18.2893i | −1.11789 | + | 0.645417i | ||||
\(804\) | −2.76222 | − | 0.383732i | −0.0974162 | − | 0.0135332i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.5515 | − | 37.3282i | 0.759118 | − | 1.31483i | ||||
\(807\) | −24.8721 | − | 19.3686i | −0.875538 | − | 0.681809i | ||||
\(808\) | 32.7074 | − | 18.8836i | 1.15064 | − | 0.664323i | ||||
\(809\) | −38.1075 | −1.33979 | −0.669894 | − | 0.742457i | \(-0.733660\pi\) | ||||
−0.669894 | + | 0.742457i | \(0.733660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.44105 | −0.0506022 | −0.0253011 | − | 0.999680i | \(-0.508054\pi\) | ||||
−0.0253011 | + | 0.999680i | \(0.508054\pi\) | |||||||
\(812\) | −0.720107 | + | 0.415754i | −0.0252708 | + | 0.0145901i | ||||
\(813\) | 3.39688 | + | 2.64526i | 0.119134 | + | 0.0927732i | ||||
\(814\) | 17.0351 | − | 29.5057i | 0.597081 | − | 1.03417i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 51.1806 | + | 7.11007i | 1.79168 | + | 0.248902i | ||||
\(817\) | 6.40335 | − | 3.69698i | 0.224025 | − | 0.129341i | ||||
\(818\) | 8.25904i | 0.288771i | ||||||||
\(819\) | −2.31749 | − | 9.17073i | −0.0809797 | − | 0.320451i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.2571 | − | 19.4979i | −0.392876 | − | 0.680482i | 0.599951 | − | 0.800037i | \(-0.295187\pi\) |
−0.992828 | + | 0.119555i | \(0.961853\pi\) | |||||||
\(822\) | 6.05555 | − | 2.45780i | 0.211212 | − | 0.0857256i | ||||
\(823\) | −35.9045 | − | 20.7295i | −1.25155 | − | 0.722583i | −0.280134 | − | 0.959961i | \(-0.590379\pi\) |
−0.971417 | + | 0.237378i | \(0.923712\pi\) | |||||||
\(824\) | −0.905373 | + | 1.56815i | −0.0315402 | + | 0.0546291i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.18982 | − | 2.06083i | −0.0413992 | − | 0.0717055i | ||||
\(827\) | 27.8133i | 0.967164i | 0.875299 | + | 0.483582i | \(0.160664\pi\) | ||||
−0.875299 | + | 0.483582i | \(0.839336\pi\) | |||||||
\(828\) | 5.35151 | + | 5.50653i | 0.185978 | + | 0.191365i | ||||
\(829\) | −20.7232 | −0.719745 | −0.359872 | − | 0.933002i | \(-0.617180\pi\) | ||||
−0.359872 | + | 0.933002i | \(0.617180\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.1538 | − | 1.82734i | −0.456299 | − | 0.0633897i | ||||
\(832\) | −20.7098 | − | 11.9568i | −0.717983 | − | 0.414528i | ||||
\(833\) | −35.6314 | − | 20.5718i | −1.23455 | − | 0.712770i | ||||
\(834\) | 18.9402 | − | 24.3219i | 0.655846 | − | 0.842198i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −11.5537 | −0.399595 | ||||||||
\(837\) | 12.9996 | + | 17.7142i | 0.449331 | + | 0.612294i | ||||
\(838\) | 17.9017i | 0.618403i | ||||||||
\(839\) | 9.07253 | + | 15.7141i | 0.313218 | + | 0.542510i | 0.979057 | − | 0.203585i | \(-0.0652595\pi\) |
−0.665839 | + | 0.746096i | \(0.731926\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.4759 | − | 19.8768i | 0.395720 | − | 0.685406i | ||||
\(842\) | −15.0520 | − | 8.69029i | −0.518727 | − | 0.299487i | ||||
\(843\) | −0.0651190 | + | 0.468747i | −0.00224282 | + | 0.0161445i | ||||
\(844\) | 3.71722 | + | 6.43841i | 0.127952 | + | 0.221619i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −17.4850 | − | 4.95368i | −0.601146 | − | 0.170311i | ||||
\(847\) | 0.701798i | 0.0241141i | ||||||||
\(848\) | −10.7663 | + | 6.21591i | −0.369716 | + | 0.213455i | ||||
\(849\) | −2.19576 | − | 5.40993i | −0.0753581 | − | 0.185668i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.8670 | − | 22.2862i | 0.441074 | − | 0.763962i | ||||
\(852\) | −5.95083 | + | 2.41529i | −0.203872 | + | 0.0827466i | ||||
\(853\) | 3.47023 | − | 2.00354i | 0.118819 | − | 0.0685999i | −0.439413 | − | 0.898285i | \(-0.644813\pi\) |
0.558231 | + | 0.829685i | \(0.311480\pi\) | |||||||
\(854\) | 2.34755 | 0.0803316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.0672 | 0.822599 | ||||||||
\(857\) | −7.87192 | + | 4.54485i | −0.268900 | + | 0.155249i | −0.628387 | − | 0.777901i | \(-0.716285\pi\) |
0.359488 | + | 0.933150i | \(0.382951\pi\) | |||||||
\(858\) | 7.53150 | − | 54.2141i | 0.257121 | − | 1.85084i | ||||
\(859\) | 8.19348 | − | 14.1915i | 0.279558 | − | 0.484208i | −0.691717 | − | 0.722169i | \(-0.743145\pi\) |
0.971275 | + | 0.237960i | \(0.0764788\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.92655 | − | 3.75810i | 0.0997364 | − | 0.128076i | ||||
\(862\) | 52.8486 | − | 30.5122i | 1.80003 | − | 1.03925i | ||||
\(863\) | − | 23.7967i | − | 0.810050i | −0.914306 | − | 0.405025i | \(-0.867263\pi\) | ||
0.914306 | − | 0.405025i | \(-0.132737\pi\) | |||||||
\(864\) | −15.2523 | + | 11.1929i | −0.518893 | + | 0.380789i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.0602 | − | 24.3530i | −0.477785 | − | 0.827549i | ||||
\(867\) | 27.6217 | + | 21.5099i | 0.938082 | + | 0.730513i | ||||
\(868\) | −1.23816 | − | 0.714850i | −0.0420258 | − | 0.0242636i | ||||
\(869\) | 5.27496 | − | 9.13650i | 0.178941 | − | 0.309935i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.50747 | + | 13.0033i | 0.254381 | + | 0.440600i | ||||
\(872\) | − | 10.1291i | − | 0.343016i | ||||||
\(873\) | −23.1570 | − | 23.8278i | −0.783747 | − | 0.806450i | ||||
\(874\) | −34.8137 | −1.17759 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.14206 | + | 12.6691i | 0.173734 | + | 0.428048i | ||||
\(877\) | −31.2413 | − | 18.0372i | −1.05495 | − | 0.609073i | −0.130916 | − | 0.991394i | \(-0.541792\pi\) |
−0.924030 | + | 0.382321i | \(0.875125\pi\) | |||||||
\(878\) | 44.9196 | + | 25.9343i | 1.51596 | + | 0.875241i | ||||
\(879\) | 3.67646 | + | 9.05811i | 0.124004 | + | 0.305522i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.4575 | −1.19459 | −0.597297 | − | 0.802020i | \(-0.703759\pi\) | ||||
−0.597297 | + | 0.802020i | \(0.703759\pi\) | |||||||
\(882\) | 32.0491 | − | 8.09896i | 1.07915 | − | 0.272706i | ||||
\(883\) | 39.1320i | 1.31690i | 0.752626 | + | 0.658448i | \(0.228787\pi\) | ||||
−0.752626 | + | 0.658448i | \(0.771213\pi\) | |||||||
\(884\) | 12.7323 | + | 22.0531i | 0.428235 | + | 0.741725i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.290768 | + | 0.503625i | −0.00976855 | + | 0.0169196i | ||||
\(887\) | −44.4126 | − | 25.6416i | −1.49123 | − | 0.860962i | −0.491280 | − | 0.871002i | \(-0.663471\pi\) |
−0.999950 | + | 0.0100402i | \(0.996804\pi\) | |||||||
\(888\) | 19.9884 | + | 15.5655i | 0.670765 | + | 0.522345i | ||||
\(889\) | 0.815778 | + | 1.41297i | 0.0273603 | + | 0.0473895i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.7556 | + | 14.6351i | 0.795841 | + | 0.490293i | ||||
\(892\) | − | 2.60530i | − | 0.0872318i | ||||||
\(893\) | 17.8868 | − | 10.3270i | 0.598560 | − | 0.345579i | ||||
\(894\) | −28.4138 | + | 36.4873i | −0.950299 | + | 1.22032i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.42207 | + | 5.92720i | −0.114323 | + | 0.198014i | ||||
\(897\) | 5.68869 | − | 40.9490i | 0.189940 | − | 1.36725i | ||||
\(898\) | −11.1155 | + | 6.41752i | −0.370928 | + | 0.214156i | ||||
\(899\) | −10.3994 | −0.346841 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.5070 | −0.516614 | ||||||||
\(902\) | 23.8696 | − | 13.7811i | 0.794772 | − | 0.458862i | ||||
\(903\) | 1.07657 | − | 0.436953i | 0.0358260 | − | 0.0145409i | ||||
\(904\) | 13.0401 | − | 22.5861i | 0.433708 | − | 0.751204i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −24.2451 | − | 59.7353i | −0.805488 | − | 1.98457i | ||||
\(907\) | 41.4470 | − | 23.9294i | 1.37622 | − | 0.794563i | 0.384522 | − | 0.923116i | \(-0.374366\pi\) |
0.991703 | + | 0.128552i | \(0.0410331\pi\) | |||||||
\(908\) | − | 8.56930i | − | 0.284382i | ||||||
\(909\) | −37.3675 | + | 36.3155i | −1.23940 | + | 1.20451i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.02153 | − | 15.6258i | −0.298897 | − | 0.517704i | 0.676987 | − | 0.735995i | \(-0.263285\pi\) |
−0.975884 | + | 0.218291i | \(0.929952\pi\) | |||||||
\(912\) | 6.49235 | − | 46.7340i | 0.214983 | − | 1.54752i | ||||
\(913\) | 37.3226 | + | 21.5482i | 1.23520 | + | 0.713142i | ||||
\(914\) | −17.5552 | + | 30.4065i | −0.580675 | + | 1.00576i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.22559 | − | 3.85483i | −0.0735354 | − | 0.127367i | ||||
\(917\) | 4.74276i | 0.156620i | ||||||||
\(918\) | −51.4750 | + | 5.65838i | −1.69893 | + | 0.186754i | ||||
\(919\) | −10.3976 | −0.342984 | −0.171492 | − | 0.985185i | \(-0.554859\pi\) | ||||
−0.171492 | + | 0.985185i | \(0.554859\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.79030 | − | 7.43556i | 0.190797 | − | 0.245010i | ||||
\(922\) | 57.9984 | + | 33.4854i | 1.91008 | + | 1.10278i | ||||
\(923\) | 29.9458 | + | 17.2892i | 0.985676 | + | 0.569081i | ||||
\(924\) | −1.79825 | − | 0.249816i | −0.0591582 | − | 0.00821833i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −68.8351 | −2.26206 | ||||||||
\(927\) | 0.680983 | − | 2.40367i | 0.0223664 | − | 0.0789467i | ||||
\(928\) | − | 8.95410i | − | 0.293933i | ||||||
\(929\) | −18.0108 | − | 31.1956i | −0.590915 | − | 1.02349i | −0.994109 | − | 0.108381i | \(-0.965433\pi\) |
0.403194 | − | 0.915114i | \(-0.367900\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.7845 | + | 32.5358i | −0.615638 | + | 1.06632i | ||||
\(932\) | 2.11971 | + | 1.22382i | 0.0694334 | + | 0.0400874i | ||||
\(933\) | −30.6209 | + | 12.4283i | −1.00248 | + | 0.406884i | ||||
\(934\) | 18.4101 | + | 31.8873i | 0.602398 | + | 1.04338i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 39.1588 | + | 11.0941i | 1.27995 | + | 0.362622i | ||||
\(937\) | 24.0326i | 0.785111i | 0.919728 | + | 0.392555i | \(0.128409\pi\) | ||||
−0.919728 | + | 0.392555i | \(0.871591\pi\) | |||||||
\(938\) | 1.72064 | − | 0.993410i | 0.0561808 | − | 0.0324360i | ||||
\(939\) | −15.6843 | − | 2.17889i | −0.511839 | − | 0.0711053i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.33380 | + | 14.4346i | −0.271674 | + | 0.470553i | −0.969291 | − | 0.245918i | \(-0.920911\pi\) |
0.697616 | + | 0.716471i | \(0.254244\pi\) | |||||||
\(942\) | −27.8197 | − | 21.6640i | −0.906413 | − | 0.705852i | ||||
\(943\) | 18.0292 | − | 10.4092i | 0.587112 | − | 0.338969i | ||||
\(944\) | 14.0959 | 0.458783 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.72315 | 0.218589 | ||||||||
\(947\) | −23.8503 | + | 13.7700i | −0.775031 | + | 0.447464i | −0.834666 | − | 0.550756i | \(-0.814339\pi\) |
0.0596355 | + | 0.998220i | \(0.481006\pi\) | |||||||
\(948\) | −3.11136 | − | 2.42291i | −0.101052 | − | 0.0786925i | ||||
\(949\) | 36.8080 | − | 63.7533i | 1.19484 | − | 2.06952i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.4242 | − | 3.39304i | −0.792008 | − | 0.110027i | ||||
\(952\) | −5.80504 | + | 3.35154i | −0.188142 | + | 0.108624i | ||||
\(953\) | 18.1344i | 0.587432i | 0.955893 | + | 0.293716i | \(0.0948920\pi\) | ||||
−0.955893 | + | 0.293716i | \(0.905108\pi\) | |||||||
\(954\) | 8.93473 | − | 8.68319i | 0.289273 | − | 0.281129i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.24922 | + | 9.09192i | 0.169772 | + | 0.294054i | ||||
\(957\) | −12.2364 | + | 4.96644i | −0.395546 | + | 0.160542i | ||||
\(958\) | 47.0974 | + | 27.1917i | 1.52165 | + | 0.878523i | ||||
\(959\) | −0.583565 | + | 1.01076i | −0.0188443 | + | 0.0326393i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.55956 | + | 11.3615i | 0.211599 | + | 0.366500i | ||||
\(962\) | 68.5676i | 2.21071i | ||||||||
\(963\) | −32.1932 | + | 8.13539i | −1.03741 | + | 0.262159i | ||||
\(964\) | −7.51009 | −0.241884 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.41850 | − | 0.752745i | −0.174337 | − | 0.0242192i | ||||
\(967\) | −31.3393 | − | 18.0937i | −1.00780 | − | 0.581855i | −0.0972552 | − | 0.995259i | \(-0.531006\pi\) |
−0.910548 | + | 0.413404i | \(0.864340\pi\) | |||||||
\(968\) | −2.61512 | − | 1.50984i | −0.0840532 | − | 0.0485281i | ||||
\(969\) | 36.1605 | − | 46.4352i | 1.16164 | − | 1.49171i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.6173 | −1.11092 | −0.555461 | − | 0.831542i | \(-0.687458\pi\) | ||||
−0.555461 | + | 0.831542i | \(0.687458\pi\) | |||||||
\(972\) | 6.64028 | − | 8.04245i | 0.212987 | − | 0.257962i | ||||
\(973\) | 5.50527i | 0.176491i | ||||||||
\(974\) | −19.4170 | − | 33.6312i | −0.622161 | − | 1.07761i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.95292 | + | 12.0428i | −0.222557 | + | 0.385481i | ||||
\(977\) | 25.4898 | + | 14.7166i | 0.815492 | + | 0.470825i | 0.848860 | − | 0.528618i | \(-0.177290\pi\) |
−0.0333671 | + | 0.999443i | \(0.510623\pi\) | |||||||
\(978\) | −2.94899 | + | 21.2278i | −0.0942983 | + | 0.678789i | ||||
\(979\) | 5.24729 | + | 9.08857i | 0.167704 | + | 0.290472i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.42394 | + | 13.5491i | 0.109318 | + | 0.432591i | ||||
\(982\) | 7.52432i | 0.240111i | ||||||||
\(983\) | −21.2099 | + | 12.2456i | −0.676492 | + | 0.390573i | −0.798532 | − | 0.601953i | \(-0.794390\pi\) |
0.122040 | + | 0.992525i | \(0.461056\pi\) | |||||||
\(984\) | 7.70771 | + | 18.9904i | 0.245713 | + | 0.605390i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12.2549 | − | 21.2260i | 0.390274 | − | 0.675975i | ||||
\(987\) | 3.00724 | − | 1.22057i | 0.0957216 | − | 0.0388510i | ||||
\(988\) | 20.1371 | − | 11.6262i | 0.640647 | − | 0.369878i | ||||
\(989\) | 5.07813 | 0.161475 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.2821 | −0.421919 | −0.210959 | − | 0.977495i | \(-0.567659\pi\) | ||||
−0.210959 | + | 0.977495i | \(0.567659\pi\) | |||||||
\(992\) | 13.3331 | − | 7.69787i | 0.423327 | − | 0.244408i | ||||
\(993\) | 2.90763 | − | 20.9301i | 0.0922709 | − | 0.664196i | ||||
\(994\) | 2.28776 | − | 3.96251i | 0.0725632 | − | 0.125683i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9.89759 | − | 12.7099i | 0.313617 | − | 0.402729i | ||||
\(997\) | 33.9075 | − | 19.5765i | 1.07386 | − | 0.619994i | 0.144627 | − | 0.989486i | \(-0.453802\pi\) |
0.929234 | + | 0.369492i | \(0.120468\pi\) | |||||||
\(998\) | − | 30.8734i | − | 0.977280i | ||||||
\(999\) | −31.9988 | − | 14.0645i | −1.01240 | − | 0.444980i |
(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 | 225.2.k.c.49.2 | 16 | ||
3.2 | odd | 2 | 675.2.k.c.199.7 | 16 | |||
5.2 | odd | 4 | 225.2.e.e.76.1 | yes | 8 | ||
5.3 | odd | 4 | 225.2.e.c.76.4 | ✓ | 8 | ||
5.4 | even | 2 | inner | 225.2.k.c.49.7 | 16 | ||
9.2 | odd | 6 | 675.2.k.c.424.2 | 16 | |||
9.4 | even | 3 | 2025.2.b.n.649.2 | 8 | |||
9.5 | odd | 6 | 2025.2.b.o.649.7 | 8 | |||
9.7 | even | 3 | inner | 225.2.k.c.124.7 | 16 | ||
15.2 | even | 4 | 675.2.e.c.226.4 | 8 | |||
15.8 | even | 4 | 675.2.e.e.226.1 | 8 | |||
15.14 | odd | 2 | 675.2.k.c.199.2 | 16 | |||
45.2 | even | 12 | 675.2.e.c.451.4 | 8 | |||
45.4 | even | 6 | 2025.2.b.n.649.7 | 8 | |||
45.7 | odd | 12 | 225.2.e.e.151.1 | yes | 8 | ||
45.13 | odd | 12 | 2025.2.a.y.1.1 | 4 | |||
45.14 | odd | 6 | 2025.2.b.o.649.2 | 8 | |||
45.22 | odd | 12 | 2025.2.a.q.1.4 | 4 | |||
45.23 | even | 12 | 2025.2.a.p.1.4 | 4 | |||
45.29 | odd | 6 | 675.2.k.c.424.7 | 16 | |||
45.32 | even | 12 | 2025.2.a.z.1.1 | 4 | |||
45.34 | even | 6 | inner | 225.2.k.c.124.2 | 16 | ||
45.38 | even | 12 | 675.2.e.e.451.1 | 8 | |||
45.43 | odd | 12 | 225.2.e.c.151.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.e.c.76.4 | ✓ | 8 | 5.3 | odd | 4 | ||
225.2.e.c.151.4 | yes | 8 | 45.43 | odd | 12 | ||
225.2.e.e.76.1 | yes | 8 | 5.2 | odd | 4 | ||
225.2.e.e.151.1 | yes | 8 | 45.7 | odd | 12 | ||
225.2.k.c.49.2 | 16 | 1.1 | even | 1 | trivial | ||
225.2.k.c.49.7 | 16 | 5.4 | even | 2 | inner | ||
225.2.k.c.124.2 | 16 | 45.34 | even | 6 | inner | ||
225.2.k.c.124.7 | 16 | 9.7 | even | 3 | inner | ||
675.2.e.c.226.4 | 8 | 15.2 | even | 4 | |||
675.2.e.c.451.4 | 8 | 45.2 | even | 12 | |||
675.2.e.e.226.1 | 8 | 15.8 | even | 4 | |||
675.2.e.e.451.1 | 8 | 45.38 | even | 12 | |||
675.2.k.c.199.2 | 16 | 15.14 | odd | 2 | |||
675.2.k.c.199.7 | 16 | 3.2 | odd | 2 | |||
675.2.k.c.424.2 | 16 | 9.2 | odd | 6 | |||
675.2.k.c.424.7 | 16 | 45.29 | odd | 6 | |||
2025.2.a.p.1.4 | 4 | 45.23 | even | 12 | |||
2025.2.a.q.1.4 | 4 | 45.22 | odd | 12 | |||
2025.2.a.y.1.1 | 4 | 45.13 | odd | 12 | |||
2025.2.a.z.1.1 | 4 | 45.32 | even | 12 | |||
2025.2.b.n.649.2 | 8 | 9.4 | even | 3 | |||
2025.2.b.n.649.7 | 8 | 45.4 | even | 6 | |||
2025.2.b.o.649.2 | 8 | 45.14 | odd | 6 | |||
2025.2.b.o.649.7 | 8 | 9.5 | odd | 6 |