Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(22,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.f (of order \(3\), 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: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 29.2 | ||
Root | \(-0.309017 - 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.29 |
Dual form | 91.2.f.a.22.2 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.190983 | − | 0.330792i | −0.135045 | − | 0.233905i | 0.790569 | − | 0.612372i | \(-0.209785\pi\) |
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | 0.190983 | + | 0.330792i | 0.110264 | + | 0.190983i | 0.915877 | − | 0.401460i | \(-0.131497\pi\) |
−0.805613 | + | 0.592443i | \(0.798164\pi\) | |||||||
\(4\) | 0.927051 | − | 1.60570i | 0.463525 | − | 0.802850i | ||||
\(5\) | 0.381966 | 0.170820 | 0.0854102 | − | 0.996346i | \(-0.472780\pi\) | ||||
0.0854102 | + | 0.996346i | \(0.472780\pi\) | |||||||
\(6\) | 0.0729490 | − | 0.126351i | 0.0297813 | − | 0.0515827i | ||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | −1.47214 | −0.520479 | ||||||||
\(9\) | 1.42705 | − | 2.47172i | 0.475684 | − | 0.823908i | ||||
\(10\) | −0.0729490 | − | 0.126351i | −0.0230685 | − | 0.0399558i | ||||
\(11\) | 2.42705 | + | 4.20378i | 0.731783 | + | 1.26749i | 0.956120 | + | 0.292974i | \(0.0946451\pi\) |
−0.224337 | + | 0.974512i | \(0.572022\pi\) | |||||||
\(12\) | 0.708204 | 0.204441 | ||||||||
\(13\) | −2.50000 | − | 2.59808i | −0.693375 | − | 0.720577i | ||||
\(14\) | 0.381966 | 0.102085 | ||||||||
\(15\) | 0.0729490 | + | 0.126351i | 0.0188354 | + | 0.0326238i | ||||
\(16\) | −1.57295 | − | 2.72443i | −0.393237 | − | 0.681107i | ||||
\(17\) | −3.73607 | + | 6.47106i | −0.906130 | + | 1.56946i | −0.0867359 | + | 0.996231i | \(0.527644\pi\) |
−0.819394 | + | 0.573231i | \(0.805690\pi\) | |||||||
\(18\) | −1.09017 | −0.256956 | ||||||||
\(19\) | −2.42705 | + | 4.20378i | −0.556804 | + | 0.964412i | 0.440957 | + | 0.897528i | \(0.354639\pi\) |
−0.997761 | + | 0.0668841i | \(0.978694\pi\) | |||||||
\(20\) | 0.354102 | − | 0.613323i | 0.0791796 | − | 0.137143i | ||||
\(21\) | −0.381966 | −0.0833518 | ||||||||
\(22\) | 0.927051 | − | 1.60570i | 0.197648 | − | 0.342336i | ||||
\(23\) | −2.23607 | − | 3.87298i | −0.466252 | − | 0.807573i | 0.533005 | − | 0.846112i | \(-0.321063\pi\) |
−0.999257 | + | 0.0385394i | \(0.987729\pi\) | |||||||
\(24\) | −0.281153 | − | 0.486971i | −0.0573901 | − | 0.0994026i | ||||
\(25\) | −4.85410 | −0.970820 | ||||||||
\(26\) | −0.381966 | + | 1.32317i | −0.0749097 | + | 0.259495i | ||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 0.927051 | + | 1.60570i | 0.175196 | + | 0.303449i | ||||
\(29\) | 2.04508 | + | 3.54219i | 0.379763 | + | 0.657768i | 0.991028 | − | 0.133658i | \(-0.0426723\pi\) |
−0.611265 | + | 0.791426i | \(0.709339\pi\) | |||||||
\(30\) | 0.0278640 | − | 0.0482619i | 0.00508726 | − | 0.00881138i | ||||
\(31\) | 8.70820 | 1.56404 | 0.782020 | − | 0.623254i | \(-0.214190\pi\) | ||||
0.782020 | + | 0.623254i | \(0.214190\pi\) | |||||||
\(32\) | −2.07295 | + | 3.59045i | −0.366449 | + | 0.634708i | ||||
\(33\) | −0.927051 | + | 1.60570i | −0.161379 | + | 0.279516i | ||||
\(34\) | 2.85410 | 0.489474 | ||||||||
\(35\) | −0.190983 | + | 0.330792i | −0.0322820 | + | 0.0559141i | ||||
\(36\) | −2.64590 | − | 4.58283i | −0.440983 | − | 0.763805i | ||||
\(37\) | −2.00000 | − | 3.46410i | −0.328798 | − | 0.569495i | 0.653476 | − | 0.756948i | \(-0.273310\pi\) |
−0.982274 | + | 0.187453i | \(0.939977\pi\) | |||||||
\(38\) | 1.85410 | 0.300775 | ||||||||
\(39\) | 0.381966 | − | 1.32317i | 0.0611635 | − | 0.211877i | ||||
\(40\) | −0.562306 | −0.0889084 | ||||||||
\(41\) | −2.61803 | − | 4.53457i | −0.408868 | − | 0.708181i | 0.585895 | − | 0.810387i | \(-0.300743\pi\) |
−0.994763 | + | 0.102206i | \(0.967410\pi\) | |||||||
\(42\) | 0.0729490 | + | 0.126351i | 0.0112563 | + | 0.0194964i | ||||
\(43\) | 3.78115 | − | 6.54915i | 0.576620 | − | 0.998736i | −0.419243 | − | 0.907874i | \(-0.637704\pi\) |
0.995864 | − | 0.0908618i | \(-0.0289622\pi\) | |||||||
\(44\) | 9.00000 | 1.35680 | ||||||||
\(45\) | 0.545085 | − | 0.944115i | 0.0812565 | − | 0.140740i | ||||
\(46\) | −0.854102 | + | 1.47935i | −0.125930 | + | 0.218118i | ||||
\(47\) | 2.23607 | 0.326164 | 0.163082 | − | 0.986613i | \(-0.447856\pi\) | ||||
0.163082 | + | 0.986613i | \(0.447856\pi\) | |||||||
\(48\) | 0.600813 | − | 1.04064i | 0.0867199 | − | 0.150203i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0.927051 | + | 1.60570i | 0.131105 | + | 0.227080i | ||||
\(51\) | −2.85410 | −0.399654 | ||||||||
\(52\) | −6.48936 | + | 1.60570i | −0.899912 | + | 0.222670i | ||||
\(53\) | 8.23607 | 1.13131 | 0.565655 | − | 0.824642i | \(-0.308623\pi\) | ||||
0.565655 | + | 0.824642i | \(0.308623\pi\) | |||||||
\(54\) | −0.427051 | − | 0.739674i | −0.0581143 | − | 0.100657i | ||||
\(55\) | 0.927051 | + | 1.60570i | 0.125004 | + | 0.216512i | ||||
\(56\) | 0.736068 | − | 1.27491i | 0.0983612 | − | 0.170367i | ||||
\(57\) | −1.85410 | −0.245582 | ||||||||
\(58\) | 0.781153 | − | 1.35300i | 0.102570 | − | 0.177657i | ||||
\(59\) | −1.11803 | + | 1.93649i | −0.145556 | + | 0.252110i | −0.929580 | − | 0.368620i | \(-0.879830\pi\) |
0.784024 | + | 0.620730i | \(0.213164\pi\) | |||||||
\(60\) | 0.270510 | 0.0349227 | ||||||||
\(61\) | 3.00000 | − | 5.19615i | 0.384111 | − | 0.665299i | −0.607535 | − | 0.794293i | \(-0.707841\pi\) |
0.991645 | + | 0.128994i | \(0.0411748\pi\) | |||||||
\(62\) | −1.66312 | − | 2.88061i | −0.211216 | − | 0.365837i | ||||
\(63\) | 1.42705 | + | 2.47172i | 0.179792 | + | 0.311408i | ||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | −0.954915 | − | 0.992377i | −0.118443 | − | 0.123089i | ||||
\(66\) | 0.708204 | 0.0871739 | ||||||||
\(67\) | −0.354102 | − | 0.613323i | −0.0432604 | − | 0.0749293i | 0.843584 | − | 0.536997i | \(-0.180441\pi\) |
−0.886845 | + | 0.462067i | \(0.847108\pi\) | |||||||
\(68\) | 6.92705 | + | 11.9980i | 0.840028 | + | 1.45497i | ||||
\(69\) | 0.854102 | − | 1.47935i | 0.102822 | − | 0.178093i | ||||
\(70\) | 0.145898 | 0.0174382 | ||||||||
\(71\) | −4.09017 | + | 7.08438i | −0.485414 | + | 0.840761i | −0.999860 | − | 0.0167615i | \(-0.994664\pi\) |
0.514446 | + | 0.857523i | \(0.327998\pi\) | |||||||
\(72\) | −2.10081 | + | 3.63871i | −0.247583 | + | 0.428827i | ||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | −0.763932 | + | 1.32317i | −0.0888053 | + | 0.153815i | ||||
\(75\) | −0.927051 | − | 1.60570i | −0.107047 | − | 0.185410i | ||||
\(76\) | 4.50000 | + | 7.79423i | 0.516185 | + | 0.894059i | ||||
\(77\) | −4.85410 | −0.553176 | ||||||||
\(78\) | −0.510643 | + | 0.126351i | −0.0578189 | + | 0.0143065i | ||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | −0.600813 | − | 1.04064i | −0.0671729 | − | 0.116347i | ||||
\(81\) | −3.85410 | − | 6.67550i | −0.428234 | − | 0.741722i | ||||
\(82\) | −1.00000 | + | 1.73205i | −0.110432 | + | 0.191273i | ||||
\(83\) | −6.70820 | −0.736321 | −0.368161 | − | 0.929762i | \(-0.620012\pi\) | ||||
−0.368161 | + | 0.929762i | \(0.620012\pi\) | |||||||
\(84\) | −0.354102 | + | 0.613323i | −0.0386357 | + | 0.0669190i | ||||
\(85\) | −1.42705 | + | 2.47172i | −0.154785 | + | 0.268096i | ||||
\(86\) | −2.88854 | −0.311480 | ||||||||
\(87\) | −0.781153 | + | 1.35300i | −0.0837484 | + | 0.145056i | ||||
\(88\) | −3.57295 | − | 6.18853i | −0.380878 | − | 0.659699i | ||||
\(89\) | −8.04508 | − | 13.9345i | −0.852777 | − | 1.47705i | −0.878692 | − | 0.477389i | \(-0.841583\pi\) |
0.0259145 | − | 0.999664i | \(-0.491750\pi\) | |||||||
\(90\) | −0.416408 | −0.0438932 | ||||||||
\(91\) | 3.50000 | − | 0.866025i | 0.366900 | − | 0.0907841i | ||||
\(92\) | −8.29180 | −0.864479 | ||||||||
\(93\) | 1.66312 | + | 2.88061i | 0.172457 | + | 0.298705i | ||||
\(94\) | −0.427051 | − | 0.739674i | −0.0440469 | − | 0.0762915i | ||||
\(95\) | −0.927051 | + | 1.60570i | −0.0951134 | + | 0.164741i | ||||
\(96\) | −1.58359 | −0.161625 | ||||||||
\(97\) | −6.07295 | + | 10.5187i | −0.616615 | + | 1.06801i | 0.373484 | + | 0.927636i | \(0.378163\pi\) |
−0.990099 | + | 0.140371i | \(0.955170\pi\) | |||||||
\(98\) | −0.190983 | + | 0.330792i | −0.0192922 | + | 0.0334151i | ||||
\(99\) | 13.8541 | 1.39239 | ||||||||
\(100\) | −4.50000 | + | 7.79423i | −0.450000 | + | 0.779423i | ||||
\(101\) | −4.28115 | − | 7.41517i | −0.425991 | − | 0.737837i | 0.570522 | − | 0.821283i | \(-0.306741\pi\) |
−0.996512 | + | 0.0834451i | \(0.973408\pi\) | |||||||
\(102\) | 0.545085 | + | 0.944115i | 0.0539715 | + | 0.0934813i | ||||
\(103\) | 4.70820 | 0.463913 | 0.231957 | − | 0.972726i | \(-0.425487\pi\) | ||||
0.231957 | + | 0.972726i | \(0.425487\pi\) | |||||||
\(104\) | 3.68034 | + | 3.82472i | 0.360887 | + | 0.375045i | ||||
\(105\) | −0.145898 | −0.0142382 | ||||||||
\(106\) | −1.57295 | − | 2.72443i | −0.152778 | − | 0.264620i | ||||
\(107\) | 2.80902 | + | 4.86536i | 0.271558 | + | 0.470352i | 0.969261 | − | 0.246035i | \(-0.0791278\pi\) |
−0.697703 | + | 0.716387i | \(0.745794\pi\) | |||||||
\(108\) | 2.07295 | − | 3.59045i | 0.199470 | − | 0.345492i | ||||
\(109\) | 10.7082 | 1.02566 | 0.512830 | − | 0.858490i | \(-0.328597\pi\) | ||||
0.512830 | + | 0.858490i | \(0.328597\pi\) | |||||||
\(110\) | 0.354102 | − | 0.613323i | 0.0337623 | − | 0.0584780i | ||||
\(111\) | 0.763932 | − | 1.32317i | 0.0725092 | − | 0.125590i | ||||
\(112\) | 3.14590 | 0.297259 | ||||||||
\(113\) | 3.73607 | − | 6.47106i | 0.351460 | − | 0.608746i | −0.635046 | − | 0.772475i | \(-0.719019\pi\) |
0.986505 | + | 0.163728i | \(0.0523521\pi\) | |||||||
\(114\) | 0.354102 | + | 0.613323i | 0.0331647 | + | 0.0574429i | ||||
\(115\) | −0.854102 | − | 1.47935i | −0.0796454 | − | 0.137950i | ||||
\(116\) | 7.58359 | 0.704119 | ||||||||
\(117\) | −9.98936 | + | 2.47172i | −0.923516 | + | 0.228511i | ||||
\(118\) | 0.854102 | 0.0786265 | ||||||||
\(119\) | −3.73607 | − | 6.47106i | −0.342485 | − | 0.593201i | ||||
\(120\) | −0.107391 | − | 0.186006i | −0.00980340 | − | 0.0169800i | ||||
\(121\) | −6.28115 | + | 10.8793i | −0.571014 | + | 0.989025i | ||||
\(122\) | −2.29180 | −0.207489 | ||||||||
\(123\) | 1.00000 | − | 1.73205i | 0.0901670 | − | 0.156174i | ||||
\(124\) | 8.07295 | − | 13.9828i | 0.724972 | − | 1.25569i | ||||
\(125\) | −3.76393 | −0.336656 | ||||||||
\(126\) | 0.545085 | − | 0.944115i | 0.0485600 | − | 0.0841084i | ||||
\(127\) | 7.07295 | + | 12.2507i | 0.627623 | + | 1.08707i | 0.988027 | + | 0.154278i | \(0.0493053\pi\) |
−0.360405 | + | 0.932796i | \(0.617361\pi\) | |||||||
\(128\) | 5.04508 | + | 8.73834i | 0.445927 | + | 0.772368i | ||||
\(129\) | 2.88854 | 0.254322 | ||||||||
\(130\) | −0.145898 | + | 0.505406i | −0.0127961 | + | 0.0443270i | ||||
\(131\) | 0.326238 | 0.0285035 | 0.0142518 | − | 0.999898i | \(-0.495463\pi\) | ||||
0.0142518 | + | 0.999898i | \(0.495463\pi\) | |||||||
\(132\) | 1.71885 | + | 2.97713i | 0.149606 | + | 0.259126i | ||||
\(133\) | −2.42705 | − | 4.20378i | −0.210452 | − | 0.364514i | ||||
\(134\) | −0.135255 | + | 0.234268i | −0.0116842 | + | 0.0202377i | ||||
\(135\) | 0.854102 | 0.0735094 | ||||||||
\(136\) | 5.50000 | − | 9.52628i | 0.471621 | − | 0.816872i | ||||
\(137\) | 0.190983 | − | 0.330792i | 0.0163168 | − | 0.0282615i | −0.857752 | − | 0.514064i | \(-0.828139\pi\) |
0.874069 | + | 0.485803i | \(0.161473\pi\) | |||||||
\(138\) | −0.652476 | −0.0555424 | ||||||||
\(139\) | 7.78115 | − | 13.4774i | 0.659989 | − | 1.14313i | −0.320629 | − | 0.947205i | \(-0.603894\pi\) |
0.980618 | − | 0.195929i | \(-0.0627723\pi\) | |||||||
\(140\) | 0.354102 | + | 0.613323i | 0.0299271 | + | 0.0518352i | ||||
\(141\) | 0.427051 | + | 0.739674i | 0.0359642 | + | 0.0622918i | ||||
\(142\) | 3.12461 | 0.262212 | ||||||||
\(143\) | 4.85410 | − | 16.8151i | 0.405920 | − | 1.40615i | ||||
\(144\) | −8.97871 | −0.748226 | ||||||||
\(145\) | 0.781153 | + | 1.35300i | 0.0648712 | + | 0.112360i | ||||
\(146\) | 0.381966 | + | 0.661585i | 0.0316117 | + | 0.0547531i | ||||
\(147\) | 0.190983 | − | 0.330792i | 0.0157520 | − | 0.0272833i | ||||
\(148\) | −7.41641 | −0.609625 | ||||||||
\(149\) | 2.42705 | − | 4.20378i | 0.198832 | − | 0.344387i | −0.749318 | − | 0.662210i | \(-0.769619\pi\) |
0.948150 | + | 0.317823i | \(0.102952\pi\) | |||||||
\(150\) | −0.354102 | + | 0.613323i | −0.0289123 | + | 0.0500776i | ||||
\(151\) | −14.7082 | −1.19694 | −0.598468 | − | 0.801146i | \(-0.704224\pi\) | ||||
−0.598468 | + | 0.801146i | \(0.704224\pi\) | |||||||
\(152\) | 3.57295 | − | 6.18853i | 0.289804 | − | 0.501956i | ||||
\(153\) | 10.6631 | + | 18.4691i | 0.862062 | + | 1.49314i | ||||
\(154\) | 0.927051 | + | 1.60570i | 0.0747039 | + | 0.129391i | ||||
\(155\) | 3.32624 | 0.267170 | ||||||||
\(156\) | −1.77051 | − | 1.83997i | −0.141754 | − | 0.147315i | ||||
\(157\) | 8.14590 | 0.650113 | 0.325057 | − | 0.945695i | \(-0.394617\pi\) | ||||
0.325057 | + | 0.945695i | \(0.394617\pi\) | |||||||
\(158\) | −0.763932 | − | 1.32317i | −0.0607752 | − | 0.105266i | ||||
\(159\) | 1.57295 | + | 2.72443i | 0.124743 | + | 0.216061i | ||||
\(160\) | −0.791796 | + | 1.37143i | −0.0625970 | + | 0.108421i | ||||
\(161\) | 4.47214 | 0.352454 | ||||||||
\(162\) | −1.47214 | + | 2.54981i | −0.115662 | + | 0.200332i | ||||
\(163\) | −4.85410 | + | 8.40755i | −0.380203 | + | 0.658530i | −0.991091 | − | 0.133186i | \(-0.957479\pi\) |
0.610888 | + | 0.791717i | \(0.290812\pi\) | |||||||
\(164\) | −9.70820 | −0.758083 | ||||||||
\(165\) | −0.354102 | + | 0.613323i | −0.0275668 | + | 0.0477471i | ||||
\(166\) | 1.28115 | + | 2.21902i | 0.0994368 | + | 0.172230i | ||||
\(167\) | −4.88197 | − | 8.45581i | −0.377778 | − | 0.654330i | 0.612961 | − | 0.790113i | \(-0.289978\pi\) |
−0.990739 | + | 0.135783i | \(0.956645\pi\) | |||||||
\(168\) | 0.562306 | 0.0433828 | ||||||||
\(169\) | −0.500000 | + | 12.9904i | −0.0384615 | + | 0.999260i | ||||
\(170\) | 1.09017 | 0.0836122 | ||||||||
\(171\) | 6.92705 | + | 11.9980i | 0.529725 | + | 0.917510i | ||||
\(172\) | −7.01064 | − | 12.1428i | −0.534557 | − | 0.925879i | ||||
\(173\) | 4.50000 | − | 7.79423i | 0.342129 | − | 0.592584i | −0.642699 | − | 0.766119i | \(-0.722185\pi\) |
0.984828 | + | 0.173534i | \(0.0555188\pi\) | |||||||
\(174\) | 0.596748 | 0.0452393 | ||||||||
\(175\) | 2.42705 | − | 4.20378i | 0.183468 | − | 0.317776i | ||||
\(176\) | 7.63525 | − | 13.2246i | 0.575529 | − | 0.996845i | ||||
\(177\) | −0.854102 | −0.0641982 | ||||||||
\(178\) | −3.07295 | + | 5.32250i | −0.230327 | + | 0.398939i | ||||
\(179\) | 4.50000 | + | 7.79423i | 0.336346 | + | 0.582568i | 0.983742 | − | 0.179585i | \(-0.0574756\pi\) |
−0.647397 | + | 0.762153i | \(0.724142\pi\) | |||||||
\(180\) | −1.01064 | − | 1.75049i | −0.0753289 | − | 0.130473i | ||||
\(181\) | −3.70820 | −0.275629 | −0.137814 | − | 0.990458i | \(-0.544008\pi\) | ||||
−0.137814 | + | 0.990458i | \(0.544008\pi\) | |||||||
\(182\) | −0.954915 | − | 0.992377i | −0.0707830 | − | 0.0735599i | ||||
\(183\) | 2.29180 | 0.169414 | ||||||||
\(184\) | 3.29180 | + | 5.70156i | 0.242674 | + | 0.420324i | ||||
\(185\) | −0.763932 | − | 1.32317i | −0.0561654 | − | 0.0972813i | ||||
\(186\) | 0.635255 | − | 1.10029i | 0.0465792 | − | 0.0806775i | ||||
\(187\) | −36.2705 | −2.65236 | ||||||||
\(188\) | 2.07295 | − | 3.59045i | 0.151185 | − | 0.261861i | ||||
\(189\) | −1.11803 | + | 1.93649i | −0.0813250 | + | 0.140859i | ||||
\(190\) | 0.708204 | 0.0513785 | ||||||||
\(191\) | −11.8090 | + | 20.4538i | −0.854470 | + | 1.47999i | 0.0226649 | + | 0.999743i | \(0.492785\pi\) |
−0.877135 | + | 0.480243i | \(0.840548\pi\) | |||||||
\(192\) | −0.899187 | − | 1.55744i | −0.0648932 | − | 0.112398i | ||||
\(193\) | 3.00000 | + | 5.19615i | 0.215945 | + | 0.374027i | 0.953564 | − | 0.301189i | \(-0.0973836\pi\) |
−0.737620 | + | 0.675216i | \(0.764050\pi\) | |||||||
\(194\) | 4.63932 | 0.333084 | ||||||||
\(195\) | 0.145898 | − | 0.505406i | 0.0104480 | − | 0.0361928i | ||||
\(196\) | −1.85410 | −0.132436 | ||||||||
\(197\) | −3.89919 | − | 6.75359i | −0.277806 | − | 0.481173i | 0.693034 | − | 0.720905i | \(-0.256274\pi\) |
−0.970839 | + | 0.239732i | \(0.922940\pi\) | |||||||
\(198\) | −2.64590 | − | 4.58283i | −0.188036 | − | 0.325688i | ||||
\(199\) | −1.20820 | + | 2.09267i | −0.0856473 | + | 0.148345i | −0.905667 | − | 0.423990i | \(-0.860629\pi\) |
0.820020 | + | 0.572336i | \(0.193962\pi\) | |||||||
\(200\) | 7.14590 | 0.505291 | ||||||||
\(201\) | 0.135255 | − | 0.234268i | 0.00954015 | − | 0.0165240i | ||||
\(202\) | −1.63525 | + | 2.83234i | −0.115056 | + | 0.199283i | ||||
\(203\) | −4.09017 | −0.287074 | ||||||||
\(204\) | −2.64590 | + | 4.58283i | −0.185250 | + | 0.320862i | ||||
\(205\) | −1.00000 | − | 1.73205i | −0.0698430 | − | 0.120972i | ||||
\(206\) | −0.899187 | − | 1.55744i | −0.0626493 | − | 0.108512i | ||||
\(207\) | −12.7639 | −0.887155 | ||||||||
\(208\) | −3.14590 | + | 10.8977i | −0.218129 | + | 0.755620i | ||||
\(209\) | −23.5623 | −1.62984 | ||||||||
\(210\) | 0.0278640 | + | 0.0482619i | 0.00192280 | + | 0.00333039i | ||||
\(211\) | 4.35410 | + | 7.54153i | 0.299749 | + | 0.519180i | 0.976078 | − | 0.217419i | \(-0.0697638\pi\) |
−0.676330 | + | 0.736599i | \(0.736430\pi\) | |||||||
\(212\) | 7.63525 | − | 13.2246i | 0.524391 | − | 0.908273i | ||||
\(213\) | −3.12461 | −0.214095 | ||||||||
\(214\) | 1.07295 | − | 1.85840i | 0.0733453 | − | 0.127038i | ||||
\(215\) | 1.44427 | − | 2.50155i | 0.0984985 | − | 0.170604i | ||||
\(216\) | −3.29180 | −0.223978 | ||||||||
\(217\) | −4.35410 | + | 7.54153i | −0.295576 | + | 0.511952i | ||||
\(218\) | −2.04508 | − | 3.54219i | −0.138511 | − | 0.239907i | ||||
\(219\) | −0.381966 | − | 0.661585i | −0.0258109 | − | 0.0447057i | ||||
\(220\) | 3.43769 | 0.231769 | ||||||||
\(221\) | 26.1525 | − | 6.47106i | 1.75921 | − | 0.435291i | ||||
\(222\) | −0.583592 | −0.0391681 | ||||||||
\(223\) | 6.63525 | + | 11.4926i | 0.444330 | + | 0.769601i | 0.998005 | − | 0.0631310i | \(-0.0201086\pi\) |
−0.553676 | + | 0.832732i | \(0.686775\pi\) | |||||||
\(224\) | −2.07295 | − | 3.59045i | −0.138505 | − | 0.239897i | ||||
\(225\) | −6.92705 | + | 11.9980i | −0.461803 | + | 0.799867i | ||||
\(226\) | −2.85410 | −0.189852 | ||||||||
\(227\) | 3.73607 | − | 6.47106i | 0.247972 | − | 0.429499i | −0.714991 | − | 0.699133i | \(-0.753569\pi\) |
0.962963 | + | 0.269634i | \(0.0869027\pi\) | |||||||
\(228\) | −1.71885 | + | 2.97713i | −0.113833 | + | 0.197165i | ||||
\(229\) | 27.1246 | 1.79244 | 0.896222 | − | 0.443605i | \(-0.146301\pi\) | ||||
0.896222 | + | 0.443605i | \(0.146301\pi\) | |||||||
\(230\) | −0.326238 | + | 0.565061i | −0.0215115 | + | 0.0372590i | ||||
\(231\) | −0.927051 | − | 1.60570i | −0.0609955 | − | 0.105647i | ||||
\(232\) | −3.01064 | − | 5.21459i | −0.197658 | − | 0.342354i | ||||
\(233\) | 0.381966 | 0.0250234 | 0.0125117 | − | 0.999922i | \(-0.496017\pi\) | ||||
0.0125117 | + | 0.999922i | \(0.496017\pi\) | |||||||
\(234\) | 2.72542 | + | 2.83234i | 0.178167 | + | 0.185156i | ||||
\(235\) | 0.854102 | 0.0557155 | ||||||||
\(236\) | 2.07295 | + | 3.59045i | 0.134937 | + | 0.233719i | ||||
\(237\) | 0.763932 | + | 1.32317i | 0.0496227 | + | 0.0859491i | ||||
\(238\) | −1.42705 | + | 2.47172i | −0.0925020 | + | 0.160218i | ||||
\(239\) | −11.2918 | −0.730406 | −0.365203 | − | 0.930928i | \(-0.619000\pi\) | ||||
−0.365203 | + | 0.930928i | \(0.619000\pi\) | |||||||
\(240\) | 0.229490 | − | 0.397489i | 0.0148135 | − | 0.0256578i | ||||
\(241\) | −2.21885 | + | 3.84316i | −0.142929 | + | 0.247559i | −0.928598 | − | 0.371087i | \(-0.878985\pi\) |
0.785670 | + | 0.618646i | \(0.212319\pi\) | |||||||
\(242\) | 4.79837 | 0.308451 | ||||||||
\(243\) | 4.82624 | − | 8.35929i | 0.309603 | − | 0.536249i | ||||
\(244\) | −5.56231 | − | 9.63420i | −0.356090 | − | 0.616766i | ||||
\(245\) | −0.190983 | − | 0.330792i | −0.0122015 | − | 0.0211335i | ||||
\(246\) | −0.763932 | −0.0487065 | ||||||||
\(247\) | 16.9894 | − | 4.20378i | 1.08101 | − | 0.267480i | ||||
\(248\) | −12.8197 | −0.814049 | ||||||||
\(249\) | −1.28115 | − | 2.21902i | −0.0811898 | − | 0.140625i | ||||
\(250\) | 0.718847 | + | 1.24508i | 0.0454639 | + | 0.0787457i | ||||
\(251\) | −2.61803 | + | 4.53457i | −0.165249 | + | 0.286219i | −0.936744 | − | 0.350016i | \(-0.886176\pi\) |
0.771495 | + | 0.636236i | \(0.219509\pi\) | |||||||
\(252\) | 5.29180 | 0.333352 | ||||||||
\(253\) | 10.8541 | − | 18.7999i | 0.682392 | − | 1.18194i | ||||
\(254\) | 2.70163 | − | 4.67935i | 0.169515 | − | 0.293609i | ||||
\(255\) | −1.09017 | −0.0682691 | ||||||||
\(256\) | −2.78115 | + | 4.81710i | −0.173822 | + | 0.301069i | ||||
\(257\) | 12.8713 | + | 22.2938i | 0.802891 | + | 1.39065i | 0.917706 | + | 0.397261i | \(0.130039\pi\) |
−0.114815 | + | 0.993387i | \(0.536627\pi\) | |||||||
\(258\) | −0.551663 | − | 0.955508i | −0.0343450 | − | 0.0594873i | ||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | −2.47871 | + | 0.613323i | −0.153723 | + | 0.0380367i | ||||
\(261\) | 11.6738 | 0.722588 | ||||||||
\(262\) | −0.0623059 | − | 0.107917i | −0.00384927 | − | 0.00666713i | ||||
\(263\) | −4.50000 | − | 7.79423i | −0.277482 | − | 0.480613i | 0.693276 | − | 0.720672i | \(-0.256167\pi\) |
−0.970758 | + | 0.240059i | \(0.922833\pi\) | |||||||
\(264\) | 1.36475 | − | 2.36381i | 0.0839943 | − | 0.145482i | ||||
\(265\) | 3.14590 | 0.193251 | ||||||||
\(266\) | −0.927051 | + | 1.60570i | −0.0568411 | + | 0.0984517i | ||||
\(267\) | 3.07295 | − | 5.32250i | 0.188061 | − | 0.325732i | ||||
\(268\) | −1.31308 | −0.0802093 | ||||||||
\(269\) | −6.87132 | + | 11.9015i | −0.418952 | + | 0.725646i | −0.995834 | − | 0.0911812i | \(-0.970936\pi\) |
0.576882 | + | 0.816827i | \(0.304269\pi\) | |||||||
\(270\) | −0.163119 | − | 0.282530i | −0.00992710 | − | 0.0171942i | ||||
\(271\) | −9.20820 | − | 15.9491i | −0.559359 | − | 0.968837i | −0.997550 | − | 0.0699558i | \(-0.977714\pi\) |
0.438192 | − | 0.898882i | \(-0.355619\pi\) | |||||||
\(272\) | 23.5066 | 1.42530 | ||||||||
\(273\) | 0.954915 | + | 0.992377i | 0.0577941 | + | 0.0600614i | ||||
\(274\) | −0.145898 | −0.00881402 | ||||||||
\(275\) | −11.7812 | − | 20.4056i | −0.710430 | − | 1.23050i | ||||
\(276\) | −1.58359 | − | 2.74286i | −0.0953210 | − | 0.165101i | ||||
\(277\) | 2.50000 | − | 4.33013i | 0.150210 | − | 0.260172i | −0.781094 | − | 0.624413i | \(-0.785338\pi\) |
0.931305 | + | 0.364241i | \(0.118672\pi\) | |||||||
\(278\) | −5.94427 | −0.356514 | ||||||||
\(279\) | 12.4271 | − | 21.5243i | 0.743988 | − | 1.28863i | ||||
\(280\) | 0.281153 | − | 0.486971i | 0.0168021 | − | 0.0291021i | ||||
\(281\) | −2.18034 | −0.130068 | −0.0650341 | − | 0.997883i | \(-0.520716\pi\) | ||||
−0.0650341 | + | 0.997883i | \(0.520716\pi\) | |||||||
\(282\) | 0.163119 | − | 0.282530i | 0.00971359 | − | 0.0168244i | ||||
\(283\) | 6.70820 | + | 11.6190i | 0.398761 | + | 0.690675i | 0.993573 | − | 0.113190i | \(-0.0361069\pi\) |
−0.594812 | + | 0.803865i | \(0.702774\pi\) | |||||||
\(284\) | 7.58359 | + | 13.1352i | 0.450003 | + | 0.779429i | ||||
\(285\) | −0.708204 | −0.0419504 | ||||||||
\(286\) | −6.48936 | + | 1.60570i | −0.383724 | + | 0.0949470i | ||||
\(287\) | 5.23607 | 0.309075 | ||||||||
\(288\) | 5.91641 | + | 10.2475i | 0.348628 | + | 0.603841i | ||||
\(289\) | −19.4164 | − | 33.6302i | −1.14214 | − | 1.97825i | ||||
\(290\) | 0.298374 | − | 0.516799i | 0.0175211 | − | 0.0303475i | ||||
\(291\) | −4.63932 | −0.271962 | ||||||||
\(292\) | −1.85410 | + | 3.21140i | −0.108503 | + | 0.187933i | ||||
\(293\) | 5.61803 | − | 9.73072i | 0.328209 | − | 0.568475i | −0.653947 | − | 0.756540i | \(-0.726888\pi\) |
0.982157 | + | 0.188065i | \(0.0602216\pi\) | |||||||
\(294\) | −0.145898 | −0.00850895 | ||||||||
\(295\) | −0.427051 | + | 0.739674i | −0.0248639 | + | 0.0430655i | ||||
\(296\) | 2.94427 | + | 5.09963i | 0.171132 | + | 0.296410i | ||||
\(297\) | 5.42705 | + | 9.39993i | 0.314909 | + | 0.545439i | ||||
\(298\) | −1.85410 | −0.107405 | ||||||||
\(299\) | −4.47214 | + | 15.4919i | −0.258630 | + | 0.895922i | ||||
\(300\) | −3.43769 | −0.198475 | ||||||||
\(301\) | 3.78115 | + | 6.54915i | 0.217942 | + | 0.377487i | ||||
\(302\) | 2.80902 | + | 4.86536i | 0.161641 | + | 0.279970i | ||||
\(303\) | 1.63525 | − | 2.83234i | 0.0939429 | − | 0.162714i | ||||
\(304\) | 15.2705 | 0.875824 | ||||||||
\(305\) | 1.14590 | − | 1.98475i | 0.0656139 | − | 0.113647i | ||||
\(306\) | 4.07295 | − | 7.05455i | 0.232835 | − | 0.403282i | ||||
\(307\) | 1.85410 | 0.105819 | 0.0529096 | − | 0.998599i | \(-0.483150\pi\) | ||||
0.0529096 | + | 0.998599i | \(0.483150\pi\) | |||||||
\(308\) | −4.50000 | + | 7.79423i | −0.256411 | + | 0.444117i | ||||
\(309\) | 0.899187 | + | 1.55744i | 0.0511530 | + | 0.0885995i | ||||
\(310\) | −0.635255 | − | 1.10029i | −0.0360801 | − | 0.0624925i | ||||
\(311\) | −12.3262 | −0.698957 | −0.349478 | − | 0.936944i | \(-0.613641\pi\) | ||||
−0.349478 | + | 0.936944i | \(0.613641\pi\) | |||||||
\(312\) | −0.562306 | + | 1.94788i | −0.0318343 | + | 0.110277i | ||||
\(313\) | −15.1246 | −0.854894 | −0.427447 | − | 0.904041i | \(-0.640587\pi\) | ||||
−0.427447 | + | 0.904041i | \(0.640587\pi\) | |||||||
\(314\) | −1.55573 | − | 2.69460i | −0.0877948 | − | 0.152065i | ||||
\(315\) | 0.545085 | + | 0.944115i | 0.0307121 | + | 0.0531948i | ||||
\(316\) | 3.70820 | − | 6.42280i | 0.208603 | − | 0.361311i | ||||
\(317\) | 21.7639 | 1.22238 | 0.611192 | − | 0.791482i | \(-0.290690\pi\) | ||||
0.611192 | + | 0.791482i | \(0.290690\pi\) | |||||||
\(318\) | 0.600813 | − | 1.04064i | 0.0336919 | − | 0.0583561i | ||||
\(319\) | −9.92705 | + | 17.1942i | −0.555808 | + | 0.962688i | ||||
\(320\) | −1.79837 | −0.100532 | ||||||||
\(321\) | −1.07295 | + | 1.85840i | −0.0598862 | + | 0.103726i | ||||
\(322\) | −0.854102 | − | 1.47935i | −0.0475972 | − | 0.0824408i | ||||
\(323\) | −18.1353 | − | 31.4112i | −1.00907 | − | 1.74776i | ||||
\(324\) | −14.2918 | −0.793989 | ||||||||
\(325\) | 12.1353 | + | 12.6113i | 0.673143 | + | 0.699551i | ||||
\(326\) | 3.70820 | 0.205378 | ||||||||
\(327\) | 2.04508 | + | 3.54219i | 0.113093 | + | 0.195884i | ||||
\(328\) | 3.85410 | + | 6.67550i | 0.212807 | + | 0.368593i | ||||
\(329\) | −1.11803 | + | 1.93649i | −0.0616392 | + | 0.106762i | ||||
\(330\) | 0.270510 | 0.0148911 | ||||||||
\(331\) | 8.42705 | − | 14.5961i | 0.463193 | − | 0.802273i | −0.535925 | − | 0.844265i | \(-0.680037\pi\) |
0.999118 | + | 0.0419923i | \(0.0133705\pi\) | |||||||
\(332\) | −6.21885 | + | 10.7714i | −0.341304 | + | 0.591155i | ||||
\(333\) | −11.4164 | −0.625615 | ||||||||
\(334\) | −1.86475 | + | 3.22983i | −0.102034 | + | 0.176729i | ||||
\(335\) | −0.135255 | − | 0.234268i | −0.00738977 | − | 0.0127994i | ||||
\(336\) | 0.600813 | + | 1.04064i | 0.0327770 | + | 0.0567715i | ||||
\(337\) | 8.56231 | 0.466419 | 0.233209 | − | 0.972427i | \(-0.425077\pi\) | ||||
0.233209 | + | 0.972427i | \(0.425077\pi\) | |||||||
\(338\) | 4.39261 | − | 2.31555i | 0.238926 | − | 0.125949i | ||||
\(339\) | 2.85410 | 0.155014 | ||||||||
\(340\) | 2.64590 | + | 4.58283i | 0.143494 | + | 0.248539i | ||||
\(341\) | 21.1353 | + | 36.6073i | 1.14454 | + | 1.98240i | ||||
\(342\) | 2.64590 | − | 4.58283i | 0.143074 | − | 0.247811i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −5.56637 | + | 9.64124i | −0.300119 | + | 0.519821i | ||||
\(345\) | 0.326238 | − | 0.565061i | 0.0175641 | − | 0.0304218i | ||||
\(346\) | −3.43769 | −0.184812 | ||||||||
\(347\) | −17.6180 | + | 30.5153i | −0.945786 | + | 1.63815i | −0.191615 | + | 0.981470i | \(0.561373\pi\) |
−0.754171 | + | 0.656679i | \(0.771961\pi\) | |||||||
\(348\) | 1.44834 | + | 2.50859i | 0.0776390 | + | 0.134475i | ||||
\(349\) | −3.64590 | − | 6.31488i | −0.195160 | − | 0.338028i | 0.751793 | − | 0.659400i | \(-0.229189\pi\) |
−0.946953 | + | 0.321372i | \(0.895856\pi\) | |||||||
\(350\) | −1.85410 | −0.0991059 | ||||||||
\(351\) | −5.59017 | − | 5.80948i | −0.298381 | − | 0.310087i | ||||
\(352\) | −20.1246 | −1.07265 | ||||||||
\(353\) | −14.4271 | − | 24.9884i | −0.767874 | − | 1.33000i | −0.938713 | − | 0.344699i | \(-0.887981\pi\) |
0.170839 | − | 0.985299i | \(-0.445352\pi\) | |||||||
\(354\) | 0.163119 | + | 0.282530i | 0.00866967 | + | 0.0150163i | ||||
\(355\) | −1.56231 | + | 2.70599i | −0.0829186 | + | 0.143619i | ||||
\(356\) | −29.8328 | −1.58114 | ||||||||
\(357\) | 1.42705 | − | 2.47172i | 0.0755275 | − | 0.130818i | ||||
\(358\) | 1.71885 | − | 2.97713i | 0.0908439 | − | 0.157346i | ||||
\(359\) | −10.9098 | −0.575799 | −0.287899 | − | 0.957661i | \(-0.592957\pi\) | ||||
−0.287899 | + | 0.957661i | \(0.592957\pi\) | |||||||
\(360\) | −0.802439 | + | 1.38987i | −0.0422923 | + | 0.0732523i | ||||
\(361\) | −2.28115 | − | 3.95107i | −0.120061 | − | 0.207951i | ||||
\(362\) | 0.708204 | + | 1.22665i | 0.0372224 | + | 0.0644710i | ||||
\(363\) | −4.79837 | −0.251849 | ||||||||
\(364\) | 1.85410 | − | 6.42280i | 0.0971813 | − | 0.336646i | ||||
\(365\) | −0.763932 | −0.0399860 | ||||||||
\(366\) | −0.437694 | − | 0.758108i | −0.0228786 | − | 0.0396270i | ||||
\(367\) | −12.7082 | − | 22.0113i | −0.663363 | − | 1.14898i | −0.979726 | − | 0.200340i | \(-0.935795\pi\) |
0.316364 | − | 0.948638i | \(-0.397538\pi\) | |||||||
\(368\) | −7.03444 | + | 12.1840i | −0.366696 | + | 0.635135i | ||||
\(369\) | −14.9443 | −0.777968 | ||||||||
\(370\) | −0.291796 | + | 0.505406i | −0.0151698 | + | 0.0262748i | ||||
\(371\) | −4.11803 | + | 7.13264i | −0.213798 | + | 0.370308i | ||||
\(372\) | 6.16718 | 0.319754 | ||||||||
\(373\) | 0.218847 | − | 0.379054i | 0.0113315 | − | 0.0196267i | −0.860304 | − | 0.509781i | \(-0.829726\pi\) |
0.871636 | + | 0.490155i | \(0.163060\pi\) | |||||||
\(374\) | 6.92705 | + | 11.9980i | 0.358189 | + | 0.620402i | ||||
\(375\) | −0.718847 | − | 1.24508i | −0.0371211 | − | 0.0642956i | ||||
\(376\) | −3.29180 | −0.169761 | ||||||||
\(377\) | 4.09017 | − | 14.1688i | 0.210654 | − | 0.729728i | ||||
\(378\) | 0.854102 | 0.0439303 | ||||||||
\(379\) | 6.42705 | + | 11.1320i | 0.330135 | + | 0.571811i | 0.982538 | − | 0.186061i | \(-0.0595722\pi\) |
−0.652403 | + | 0.757872i | \(0.726239\pi\) | |||||||
\(380\) | 1.71885 | + | 2.97713i | 0.0881750 | + | 0.152724i | ||||
\(381\) | −2.70163 | + | 4.67935i | −0.138408 | + | 0.239731i | ||||
\(382\) | 9.02129 | 0.461569 | ||||||||
\(383\) | −12.4894 | + | 21.6322i | −0.638176 | + | 1.10535i | 0.347656 | + | 0.937622i | \(0.386978\pi\) |
−0.985833 | + | 0.167732i | \(0.946356\pi\) | |||||||
\(384\) | −1.92705 | + | 3.33775i | −0.0983394 | + | 0.170329i | ||||
\(385\) | −1.85410 | −0.0944938 | ||||||||
\(386\) | 1.14590 | − | 1.98475i | 0.0583247 | − | 0.101021i | ||||
\(387\) | −10.7918 | − | 18.6919i | −0.548578 | − | 0.950165i | ||||
\(388\) | 11.2599 | + | 19.5027i | 0.571633 | + | 0.990098i | ||||
\(389\) | 23.8885 | 1.21120 | 0.605599 | − | 0.795770i | \(-0.292934\pi\) | ||||
0.605599 | + | 0.795770i | \(0.292934\pi\) | |||||||
\(390\) | −0.195048 | + | 0.0482619i | −0.00987666 | + | 0.00244384i | ||||
\(391\) | 33.4164 | 1.68994 | ||||||||
\(392\) | 0.736068 | + | 1.27491i | 0.0371770 | + | 0.0643925i | ||||
\(393\) | 0.0623059 | + | 0.107917i | 0.00314292 | + | 0.00544369i | ||||
\(394\) | −1.48936 | + | 2.57964i | −0.0750327 | + | 0.129960i | ||||
\(395\) | 1.52786 | 0.0768752 | ||||||||
\(396\) | 12.8435 | − | 22.2455i | 0.645408 | − | 1.11788i | ||||
\(397\) | 12.7082 | − | 22.0113i | 0.637806 | − | 1.10471i | −0.348107 | − | 0.937455i | \(-0.613175\pi\) |
0.985913 | − | 0.167258i | \(-0.0534914\pi\) | |||||||
\(398\) | 0.922986 | 0.0462651 | ||||||||
\(399\) | 0.927051 | − | 1.60570i | 0.0464106 | − | 0.0803855i | ||||
\(400\) | 7.63525 | + | 13.2246i | 0.381763 | + | 0.661232i | ||||
\(401\) | 10.2254 | + | 17.7110i | 0.510633 | + | 0.884443i | 0.999924 | + | 0.0123222i | \(0.00392237\pi\) |
−0.489291 | + | 0.872121i | \(0.662744\pi\) | |||||||
\(402\) | −0.103326 | −0.00515341 | ||||||||
\(403\) | −21.7705 | − | 22.6246i | −1.08447 | − | 1.12701i | ||||
\(404\) | −15.8754 | −0.789830 | ||||||||
\(405\) | −1.47214 | − | 2.54981i | −0.0731510 | − | 0.126701i | ||||
\(406\) | 0.781153 | + | 1.35300i | 0.0387680 | + | 0.0671481i | ||||
\(407\) | 9.70820 | − | 16.8151i | 0.481218 | − | 0.833494i | ||||
\(408\) | 4.20163 | 0.208011 | ||||||||
\(409\) | −17.2812 | + | 29.9318i | −0.854498 | + | 1.48003i | 0.0226119 | + | 0.999744i | \(0.492802\pi\) |
−0.877110 | + | 0.480290i | \(0.840532\pi\) | |||||||
\(410\) | −0.381966 | + | 0.661585i | −0.0188640 | + | 0.0326733i | ||||
\(411\) | 0.145898 | 0.00719662 | ||||||||
\(412\) | 4.36475 | − | 7.55996i | 0.215036 | − | 0.372453i | ||||
\(413\) | −1.11803 | − | 1.93649i | −0.0550149 | − | 0.0952885i | ||||
\(414\) | 2.43769 | + | 4.22221i | 0.119806 | + | 0.207510i | ||||
\(415\) | −2.56231 | −0.125779 | ||||||||
\(416\) | 14.5106 | − | 3.59045i | 0.711443 | − | 0.176036i | ||||
\(417\) | 5.94427 | 0.291092 | ||||||||
\(418\) | 4.50000 | + | 7.79423i | 0.220102 | + | 0.381228i | ||||
\(419\) | −2.97214 | − | 5.14789i | −0.145198 | − | 0.251491i | 0.784249 | − | 0.620447i | \(-0.213049\pi\) |
−0.929447 | + | 0.368956i | \(0.879715\pi\) | |||||||
\(420\) | −0.135255 | + | 0.234268i | −0.00659976 | + | 0.0114311i | ||||
\(421\) | −25.4164 | −1.23872 | −0.619360 | − | 0.785107i | \(-0.712608\pi\) | ||||
−0.619360 | + | 0.785107i | \(0.712608\pi\) | |||||||
\(422\) | 1.66312 | − | 2.88061i | 0.0809594 | − | 0.140226i | ||||
\(423\) | 3.19098 | − | 5.52694i | 0.155151 | − | 0.268729i | ||||
\(424\) | −12.1246 | −0.588823 | ||||||||
\(425\) | 18.1353 | − | 31.4112i | 0.879689 | − | 1.52367i | ||||
\(426\) | 0.596748 | + | 1.03360i | 0.0289125 | + | 0.0500780i | ||||
\(427\) | 3.00000 | + | 5.19615i | 0.145180 | + | 0.251459i | ||||
\(428\) | 10.4164 | 0.503496 | ||||||||
\(429\) | 6.48936 | − | 1.60570i | 0.313309 | − | 0.0775239i | ||||
\(430\) | −1.10333 | −0.0532071 | ||||||||
\(431\) | 8.39919 | + | 14.5478i | 0.404575 | + | 0.700744i | 0.994272 | − | 0.106881i | \(-0.0340863\pi\) |
−0.589697 | + | 0.807624i | \(0.700753\pi\) | |||||||
\(432\) | −3.51722 | − | 6.09201i | −0.169222 | − | 0.293102i | ||||
\(433\) | −0.500000 | + | 0.866025i | −0.0240285 | + | 0.0416185i | −0.877790 | − | 0.479046i | \(-0.840983\pi\) |
0.853761 | + | 0.520665i | \(0.174316\pi\) | |||||||
\(434\) | 3.32624 | 0.159665 | ||||||||
\(435\) | −0.298374 | + | 0.516799i | −0.0143059 | + | 0.0247786i | ||||
\(436\) | 9.92705 | − | 17.1942i | 0.475420 | − | 0.823451i | ||||
\(437\) | 21.7082 | 1.03844 | ||||||||
\(438\) | −0.145898 | + | 0.252703i | −0.00697128 | + | 0.0120746i | ||||
\(439\) | −4.07295 | − | 7.05455i | −0.194391 | − | 0.336696i | 0.752310 | − | 0.658810i | \(-0.228940\pi\) |
−0.946701 | + | 0.322114i | \(0.895606\pi\) | |||||||
\(440\) | −1.36475 | − | 2.36381i | −0.0650617 | − | 0.112690i | ||||
\(441\) | −2.85410 | −0.135910 | ||||||||
\(442\) | −7.13525 | − | 7.41517i | −0.339389 | − | 0.352704i | ||||
\(443\) | −0.763932 | −0.0362955 | −0.0181478 | − | 0.999835i | \(-0.505777\pi\) | ||||
−0.0181478 | + | 0.999835i | \(0.505777\pi\) | |||||||
\(444\) | −1.41641 | − | 2.45329i | −0.0672197 | − | 0.116428i | ||||
\(445\) | −3.07295 | − | 5.32250i | −0.145672 | − | 0.252311i | ||||
\(446\) | 2.53444 | − | 4.38978i | 0.120009 | − | 0.207862i | ||||
\(447\) | 1.85410 | 0.0876960 | ||||||||
\(448\) | 2.35410 | − | 4.07742i | 0.111221 | − | 0.192640i | ||||
\(449\) | −14.2361 | + | 24.6576i | −0.671842 | + | 1.16366i | 0.305540 | + | 0.952179i | \(0.401163\pi\) |
−0.977381 | + | 0.211484i | \(0.932170\pi\) | |||||||
\(450\) | 5.29180 | 0.249458 | ||||||||
\(451\) | 12.7082 | − | 22.0113i | 0.598406 | − | 1.03647i | ||||
\(452\) | −6.92705 | − | 11.9980i | −0.325821 | − | 0.564339i | ||||
\(453\) | −2.80902 | − | 4.86536i | −0.131979 | − | 0.228595i | ||||
\(454\) | −2.85410 | −0.133950 | ||||||||
\(455\) | 1.33688 | − | 0.330792i | 0.0626739 | − | 0.0155078i | ||||
\(456\) | 2.72949 | 0.127820 | ||||||||
\(457\) | 5.70820 | + | 9.88690i | 0.267019 | + | 0.462490i | 0.968090 | − | 0.250601i | \(-0.0806282\pi\) |
−0.701072 | + | 0.713091i | \(0.747295\pi\) | |||||||
\(458\) | −5.18034 | − | 8.97261i | −0.242061 | − | 0.419263i | ||||
\(459\) | −8.35410 | + | 14.4697i | −0.389936 | + | 0.675389i | ||||
\(460\) | −3.16718 | −0.147671 | ||||||||
\(461\) | −19.6074 | + | 33.9610i | −0.913207 | + | 1.58172i | −0.103702 | + | 0.994608i | \(0.533069\pi\) |
−0.809505 | + | 0.587113i | \(0.800264\pi\) | |||||||
\(462\) | −0.354102 | + | 0.613323i | −0.0164743 | + | 0.0285343i | ||||
\(463\) | −6.70820 | −0.311757 | −0.155878 | − | 0.987776i | \(-0.549821\pi\) | ||||
−0.155878 | + | 0.987776i | \(0.549821\pi\) | |||||||
\(464\) | 6.43363 | − | 11.1434i | 0.298674 | − | 0.517318i | ||||
\(465\) | 0.635255 | + | 1.10029i | 0.0294592 | + | 0.0510249i | ||||
\(466\) | −0.0729490 | − | 0.126351i | −0.00337930 | − | 0.00585312i | ||||
\(467\) | 33.6525 | 1.55725 | 0.778625 | − | 0.627489i | \(-0.215917\pi\) | ||||
0.778625 | + | 0.627489i | \(0.215917\pi\) | |||||||
\(468\) | −5.29180 | + | 18.3313i | −0.244613 | + | 0.847366i | ||||
\(469\) | 0.708204 | 0.0327018 | ||||||||
\(470\) | −0.163119 | − | 0.282530i | −0.00752412 | − | 0.0130322i | ||||
\(471\) | 1.55573 | + | 2.69460i | 0.0716842 | + | 0.124161i | ||||
\(472\) | 1.64590 | − | 2.85078i | 0.0757586 | − | 0.131218i | ||||
\(473\) | 36.7082 | 1.68785 | ||||||||
\(474\) | 0.291796 | − | 0.505406i | 0.0134026 | − | 0.0232140i | ||||
\(475\) | 11.7812 | − | 20.4056i | 0.540556 | − | 0.936271i | ||||
\(476\) | −13.8541 | −0.635002 | ||||||||
\(477\) | 11.7533 | − | 20.3573i | 0.538146 | − | 0.932096i | ||||
\(478\) | 2.15654 | + | 3.73524i | 0.0986379 | + | 0.170846i | ||||
\(479\) | 10.9894 | + | 19.0341i | 0.502117 | + | 0.869691i | 0.999997 | + | 0.00244569i | \(0.000778487\pi\) |
−0.497880 | + | 0.867246i | \(0.665888\pi\) | |||||||
\(480\) | −0.604878 | −0.0276088 | ||||||||
\(481\) | −4.00000 | + | 13.8564i | −0.182384 | + | 0.631798i | ||||
\(482\) | 1.69505 | 0.0772073 | ||||||||
\(483\) | 0.854102 | + | 1.47935i | 0.0388630 | + | 0.0673127i | ||||
\(484\) | 11.6459 | + | 20.1713i | 0.529359 | + | 0.916877i | ||||
\(485\) | −2.31966 | + | 4.01777i | −0.105330 | + | 0.182438i | ||||
\(486\) | −3.68692 | −0.167242 | ||||||||
\(487\) | 8.48936 | − | 14.7040i | 0.384689 | − | 0.666302i | −0.607037 | − | 0.794674i | \(-0.707642\pi\) |
0.991726 | + | 0.128372i | \(0.0409752\pi\) | |||||||
\(488\) | −4.41641 | + | 7.64944i | −0.199921 | + | 0.346274i | ||||
\(489\) | −3.70820 | −0.167691 | ||||||||
\(490\) | −0.0729490 | + | 0.126351i | −0.00329550 | + | 0.00570797i | ||||
\(491\) | −7.30902 | − | 12.6596i | −0.329851 | − | 0.571319i | 0.652631 | − | 0.757676i | \(-0.273665\pi\) |
−0.982482 | + | 0.186357i | \(0.940332\pi\) | |||||||
\(492\) | −1.85410 | − | 3.21140i | −0.0835894 | − | 0.144781i | ||||
\(493\) | −30.5623 | −1.37646 | ||||||||
\(494\) | −4.63525 | − | 4.81710i | −0.208550 | − | 0.216731i | ||||
\(495\) | 5.29180 | 0.237849 | ||||||||
\(496\) | −13.6976 | − | 23.7249i | −0.615039 | − | 1.06528i | ||||
\(497\) | −4.09017 | − | 7.08438i | −0.183469 | − | 0.317778i | ||||
\(498\) | −0.489357 | + | 0.847591i | −0.0219286 | + | 0.0379815i | ||||
\(499\) | 8.14590 | 0.364660 | 0.182330 | − | 0.983237i | \(-0.441636\pi\) | ||||
0.182330 | + | 0.983237i | \(0.441636\pi\) | |||||||
\(500\) | −3.48936 | + | 6.04374i | −0.156049 | + | 0.270284i | ||||
\(501\) | 1.86475 | − | 3.22983i | 0.0833107 | − | 0.144298i | ||||
\(502\) | 2.00000 | 0.0892644 | ||||||||
\(503\) | −12.1910 | + | 21.1154i | −0.543569 | + | 0.941489i | 0.455126 | + | 0.890427i | \(0.349594\pi\) |
−0.998695 | + | 0.0510624i | \(0.983739\pi\) | |||||||
\(504\) | −2.10081 | − | 3.63871i | −0.0935777 | − | 0.162081i | ||||
\(505\) | −1.63525 | − | 2.83234i | −0.0727679 | − | 0.126038i | ||||
\(506\) | −8.29180 | −0.368615 | ||||||||
\(507\) | −4.39261 | + | 2.31555i | −0.195083 | + | 0.102837i | ||||
\(508\) | 26.2279 | 1.16368 | ||||||||
\(509\) | −15.2984 | − | 26.4976i | −0.678089 | − | 1.17448i | −0.975556 | − | 0.219752i | \(-0.929475\pi\) |
0.297467 | − | 0.954732i | \(-0.403858\pi\) | |||||||
\(510\) | 0.208204 | + | 0.360620i | 0.00921943 | + | 0.0159685i | ||||
\(511\) | 1.00000 | − | 1.73205i | 0.0442374 | − | 0.0766214i | ||||
\(512\) | 22.3050 | 0.985749 | ||||||||
\(513\) | −5.42705 | + | 9.39993i | −0.239610 | + | 0.415017i | ||||
\(514\) | 4.91641 | − | 8.51547i | 0.216853 | − | 0.375601i | ||||
\(515\) | 1.79837 | 0.0792458 | ||||||||
\(516\) | 2.67783 | − | 4.63813i | 0.117885 | − | 0.204182i | ||||
\(517\) | 5.42705 | + | 9.39993i | 0.238681 | + | 0.413408i | ||||
\(518\) | −0.763932 | − | 1.32317i | −0.0335652 | − | 0.0581367i | ||||
\(519\) | 3.43769 | 0.150898 | ||||||||
\(520\) | 1.40576 | + | 1.46091i | 0.0616469 | + | 0.0640653i | ||||
\(521\) | −12.6525 | −0.554315 | −0.277158 | − | 0.960824i | \(-0.589392\pi\) | ||||
−0.277158 | + | 0.960824i | \(0.589392\pi\) | |||||||
\(522\) | −2.22949 | − | 3.86159i | −0.0975821 | − | 0.169017i | ||||
\(523\) | 19.5623 | + | 33.8829i | 0.855400 | + | 1.48160i | 0.876274 | + | 0.481814i | \(0.160022\pi\) |
−0.0208736 | + | 0.999782i | \(0.506645\pi\) | |||||||
\(524\) | 0.302439 | − | 0.523840i | 0.0132121 | − | 0.0228841i | ||||
\(525\) | 1.85410 | 0.0809196 | ||||||||
\(526\) | −1.71885 | + | 2.97713i | −0.0749453 | + | 0.129809i | ||||
\(527\) | −32.5344 | + | 56.3513i | −1.41722 | + | 2.45470i | ||||
\(528\) | 5.83282 | 0.253841 | ||||||||
\(529\) | 1.50000 | − | 2.59808i | 0.0652174 | − | 0.112960i | ||||
\(530\) | −0.600813 | − | 1.04064i | −0.0260977 | − | 0.0452025i | ||||
\(531\) | 3.19098 | + | 5.52694i | 0.138477 | + | 0.239849i | ||||
\(532\) | −9.00000 | −0.390199 | ||||||||
\(533\) | −5.23607 | + | 18.1383i | −0.226799 | + | 0.785656i | ||||
\(534\) | −2.34752 | −0.101587 | ||||||||
\(535\) | 1.07295 | + | 1.85840i | 0.0463876 | + | 0.0803457i | ||||
\(536\) | 0.521286 | + | 0.902894i | 0.0225161 | + | 0.0389991i | ||||
\(537\) | −1.71885 | + | 2.97713i | −0.0741737 | + | 0.128473i | ||||
\(538\) | 5.24922 | 0.226310 | ||||||||
\(539\) | 2.42705 | − | 4.20378i | 0.104540 | − | 0.181069i | ||||
\(540\) | 0.791796 | − | 1.37143i | 0.0340735 | − | 0.0590170i | ||||
\(541\) | 1.72949 | 0.0743566 | 0.0371783 | − | 0.999309i | \(-0.488163\pi\) | ||||
0.0371783 | + | 0.999309i | \(0.488163\pi\) | |||||||
\(542\) | −3.51722 | + | 6.09201i | −0.151078 | + | 0.261674i | ||||
\(543\) | −0.708204 | − | 1.22665i | −0.0303919 | − | 0.0526404i | ||||
\(544\) | −15.4894 | − | 26.8284i | −0.664101 | − | 1.15026i | ||||
\(545\) | 4.09017 | 0.175204 | ||||||||
\(546\) | 0.145898 | − | 0.505406i | 0.00624386 | − | 0.0216294i | ||||
\(547\) | −3.00000 | −0.128271 | −0.0641354 | − | 0.997941i | \(-0.520429\pi\) | ||||
−0.0641354 | + | 0.997941i | \(0.520429\pi\) | |||||||
\(548\) | −0.354102 | − | 0.613323i | −0.0151265 | − | 0.0261998i | ||||
\(549\) | −8.56231 | − | 14.8303i | −0.365430 | − | 0.632944i | ||||
\(550\) | −4.50000 | + | 7.79423i | −0.191881 | + | 0.332347i | ||||
\(551\) | −19.8541 | −0.845813 | ||||||||
\(552\) | −1.25735 | + | 2.17780i | −0.0535165 | + | 0.0926934i | ||||
\(553\) | −2.00000 | + | 3.46410i | −0.0850487 | + | 0.147309i | ||||
\(554\) | −1.90983 | −0.0811409 | ||||||||
\(555\) | 0.291796 | − | 0.505406i | 0.0123861 | − | 0.0214533i | ||||
\(556\) | −14.4271 | − | 24.9884i | −0.611843 | − | 1.05974i | ||||
\(557\) | −9.48936 | − | 16.4360i | −0.402077 | − | 0.696418i | 0.591899 | − | 0.806012i | \(-0.298378\pi\) |
−0.993976 | + | 0.109594i | \(0.965045\pi\) | |||||||
\(558\) | −9.49342 | −0.401889 | ||||||||
\(559\) | −26.4681 | + | 6.54915i | −1.11948 | + | 0.276999i | ||||
\(560\) | 1.20163 | 0.0507780 | ||||||||
\(561\) | −6.92705 | − | 11.9980i | −0.292460 | − | 0.506556i | ||||
\(562\) | 0.416408 | + | 0.721240i | 0.0175651 | + | 0.0304237i | ||||
\(563\) | 19.4721 | − | 33.7267i | 0.820653 | − | 1.42141i | −0.0845442 | − | 0.996420i | \(-0.526943\pi\) |
0.905197 | − | 0.424992i | \(-0.139723\pi\) | |||||||
\(564\) | 1.58359 | 0.0666813 | ||||||||
\(565\) | 1.42705 | − | 2.47172i | 0.0600365 | − | 0.103986i | ||||
\(566\) | 2.56231 | − | 4.43804i | 0.107702 | − | 0.186545i | ||||
\(567\) | 7.70820 | 0.323714 | ||||||||
\(568\) | 6.02129 | − | 10.4292i | 0.252648 | − | 0.437598i | ||||
\(569\) | 1.47214 | + | 2.54981i | 0.0617151 | + | 0.106894i | 0.895232 | − | 0.445600i | \(-0.147010\pi\) |
−0.833517 | + | 0.552494i | \(0.813676\pi\) | |||||||
\(570\) | 0.135255 | + | 0.234268i | 0.00566521 | + | 0.00981242i | ||||
\(571\) | −35.6869 | −1.49345 | −0.746726 | − | 0.665132i | \(-0.768375\pi\) | ||||
−0.746726 | + | 0.665132i | \(0.768375\pi\) | |||||||
\(572\) | −22.5000 | − | 23.3827i | −0.940772 | − | 0.977679i | ||||
\(573\) | −9.02129 | −0.376870 | ||||||||
\(574\) | −1.00000 | − | 1.73205i | −0.0417392 | − | 0.0722944i | ||||
\(575\) | 10.8541 | + | 18.7999i | 0.452647 | + | 0.784008i | ||||
\(576\) | −6.71885 | + | 11.6374i | −0.279952 | + | 0.484891i | ||||
\(577\) | 9.83282 | 0.409345 | 0.204673 | − | 0.978830i | \(-0.434387\pi\) | ||||
0.204673 | + | 0.978830i | \(0.434387\pi\) | |||||||
\(578\) | −7.41641 | + | 12.8456i | −0.308482 | + | 0.534306i | ||||
\(579\) | −1.14590 | + | 1.98475i | −0.0476219 | + | 0.0824835i | ||||
\(580\) | 2.89667 | 0.120278 | ||||||||
\(581\) | 3.35410 | − | 5.80948i | 0.139152 | − | 0.241018i | ||||
\(582\) | 0.886031 | + | 1.53465i | 0.0367272 | + | 0.0636133i | ||||
\(583\) | 19.9894 | + | 34.6226i | 0.827875 | + | 1.43392i | ||||
\(584\) | 2.94427 | 0.121835 | ||||||||
\(585\) | −3.81559 | + | 0.944115i | −0.157755 | + | 0.0390343i | ||||
\(586\) | −4.29180 | −0.177292 | ||||||||
\(587\) | 15.5451 | + | 26.9249i | 0.641614 | + | 1.11131i | 0.985072 | + | 0.172141i | \(0.0550683\pi\) |
−0.343458 | + | 0.939168i | \(0.611598\pi\) | |||||||
\(588\) | −0.354102 | − | 0.613323i | −0.0146029 | − | 0.0252930i | ||||
\(589\) | −21.1353 | + | 36.6073i | −0.870863 | + | 1.50838i | ||||
\(590\) | 0.326238 | 0.0134310 | ||||||||
\(591\) | 1.48936 | − | 2.57964i | 0.0612640 | − | 0.106112i | ||||
\(592\) | −6.29180 | + | 10.8977i | −0.258591 | + | 0.447893i | ||||
\(593\) | 19.2016 | 0.788516 | 0.394258 | − | 0.919000i | \(-0.371002\pi\) | ||||
0.394258 | + | 0.919000i | \(0.371002\pi\) | |||||||
\(594\) | 2.07295 | − | 3.59045i | 0.0850541 | − | 0.147318i | ||||
\(595\) | −1.42705 | − | 2.47172i | −0.0585034 | − | 0.101331i | ||||
\(596\) | −4.50000 | − | 7.79423i | −0.184327 | − | 0.319264i | ||||
\(597\) | −0.922986 | −0.0377753 | ||||||||
\(598\) | 5.97871 | − | 1.47935i | 0.244488 | − | 0.0604950i | ||||
\(599\) | −8.50658 | −0.347569 | −0.173785 | − | 0.984784i | \(-0.555600\pi\) | ||||
−0.173785 | + | 0.984784i | \(0.555600\pi\) | |||||||
\(600\) | 1.36475 | + | 2.36381i | 0.0557155 | + | 0.0965021i | ||||
\(601\) | 16.6976 | + | 28.9210i | 0.681108 | + | 1.17971i | 0.974643 | + | 0.223765i | \(0.0718348\pi\) |
−0.293535 | + | 0.955948i | \(0.594832\pi\) | |||||||
\(602\) | 1.44427 | − | 2.50155i | 0.0588641 | − | 0.101956i | ||||
\(603\) | −2.02129 | −0.0823131 | ||||||||
\(604\) | −13.6353 | + | 23.6170i | −0.554811 | + | 0.960960i | ||||
\(605\) | −2.39919 | + | 4.15551i | −0.0975408 | + | 0.168946i | ||||
\(606\) | −1.24922 | −0.0507462 | ||||||||
\(607\) | 11.5000 | − | 19.9186i | 0.466771 | − | 0.808470i | −0.532509 | − | 0.846424i | \(-0.678751\pi\) |
0.999279 | + | 0.0379540i | \(0.0120840\pi\) | |||||||
\(608\) | −10.0623 | − | 17.4284i | −0.408080 | − | 0.706816i | ||||
\(609\) | −0.781153 | − | 1.35300i | −0.0316539 | − | 0.0548262i | ||||
\(610\) | −0.875388 | −0.0354434 | ||||||||
\(611\) | −5.59017 | − | 5.80948i | −0.226154 | − | 0.235026i | ||||
\(612\) | 39.5410 | 1.59835 | ||||||||
\(613\) | −7.21885 | − | 12.5034i | −0.291566 | − | 0.505008i | 0.682614 | − | 0.730779i | \(-0.260843\pi\) |
−0.974180 | + | 0.225771i | \(0.927510\pi\) | |||||||
\(614\) | −0.354102 | − | 0.613323i | −0.0142904 | − | 0.0247517i | ||||
\(615\) | 0.381966 | − | 0.661585i | 0.0154024 | − | 0.0266777i | ||||
\(616\) | 7.14590 | 0.287916 | ||||||||
\(617\) | −8.97214 | + | 15.5402i | −0.361205 | + | 0.625625i | −0.988159 | − | 0.153431i | \(-0.950968\pi\) |
0.626955 | + | 0.779056i | \(0.284301\pi\) | |||||||
\(618\) | 0.343459 | − | 0.594888i | 0.0138159 | − | 0.0239299i | ||||
\(619\) | −17.4164 | −0.700025 | −0.350012 | − | 0.936745i | \(-0.613823\pi\) | ||||
−0.350012 | + | 0.936745i | \(0.613823\pi\) | |||||||
\(620\) | 3.08359 | − | 5.34094i | 0.123840 | − | 0.214497i | ||||
\(621\) | −5.00000 | − | 8.66025i | −0.200643 | − | 0.347524i | ||||
\(622\) | 2.35410 | + | 4.07742i | 0.0943909 | + | 0.163490i | ||||
\(623\) | 16.0902 | 0.644639 | ||||||||
\(624\) | −4.20569 | + | 1.04064i | −0.168362 | + | 0.0416589i | ||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | 2.88854 | + | 5.00310i | 0.115449 | + | 0.199964i | ||||
\(627\) | −4.50000 | − | 7.79423i | −0.179713 | − | 0.311272i | ||||
\(628\) | 7.55166 | − | 13.0799i | 0.301344 | − | 0.521943i | ||||
\(629\) | 29.8885 | 1.19173 | ||||||||
\(630\) | 0.208204 | − | 0.360620i | 0.00829504 | − | 0.0143674i | ||||
\(631\) | 19.6976 | − | 34.1172i | 0.784148 | − | 1.35818i | −0.145360 | − | 0.989379i | \(-0.546434\pi\) |
0.929507 | − | 0.368804i | \(-0.120233\pi\) | |||||||
\(632\) | −5.88854 | −0.234234 | ||||||||
\(633\) | −1.66312 | + | 2.88061i | −0.0661030 | + | 0.114494i | ||||
\(634\) | −4.15654 | − | 7.19934i | −0.165077 | − | 0.285922i | ||||
\(635\) | 2.70163 | + | 4.67935i | 0.107211 | + | 0.185694i | ||||
\(636\) | 5.83282 | 0.231286 | ||||||||
\(637\) | −1.00000 | + | 3.46410i | −0.0396214 | + | 0.137253i | ||||
\(638\) | 7.58359 | 0.300237 | ||||||||
\(639\) | 11.6738 | + | 20.2195i | 0.461807 | + | 0.799873i | ||||
\(640\) | 1.92705 | + | 3.33775i | 0.0761734 | + | 0.131936i | ||||
\(641\) | 4.74671 | − | 8.22154i | 0.187484 | − | 0.324731i | −0.756927 | − | 0.653500i | \(-0.773300\pi\) |
0.944411 | + | 0.328768i | \(0.106633\pi\) | |||||||
\(642\) | 0.819660 | 0.0323494 | ||||||||
\(643\) | 3.50000 | − | 6.06218i | 0.138027 | − | 0.239069i | −0.788723 | − | 0.614749i | \(-0.789257\pi\) |
0.926750 | + | 0.375680i | \(0.122591\pi\) | |||||||
\(644\) | 4.14590 | − | 7.18091i | 0.163371 | − | 0.282967i | ||||
\(645\) | 1.10333 | 0.0434434 | ||||||||
\(646\) | −6.92705 | + | 11.9980i | −0.272541 | + | 0.472055i | ||||
\(647\) | −14.6180 | − | 25.3192i | −0.574694 | − | 0.995400i | −0.996075 | − | 0.0885157i | \(-0.971788\pi\) |
0.421381 | − | 0.906884i | \(-0.361546\pi\) | |||||||
\(648\) | 5.67376 | + | 9.82724i | 0.222886 | + | 0.386051i | ||||
\(649\) | −10.8541 | −0.426061 | ||||||||
\(650\) | 1.85410 | − | 6.42280i | 0.0727239 | − | 0.251923i | ||||
\(651\) | −3.32624 | −0.130366 | ||||||||
\(652\) | 9.00000 | + | 15.5885i | 0.352467 | + | 0.610491i | ||||
\(653\) | 1.30902 | + | 2.26728i | 0.0512258 | + | 0.0887257i | 0.890501 | − | 0.454981i | \(-0.150354\pi\) |
−0.839275 | + | 0.543706i | \(0.817021\pi\) | |||||||
\(654\) | 0.781153 | − | 1.35300i | 0.0305455 | − | 0.0529064i | ||||
\(655\) | 0.124612 | 0.00486899 | ||||||||
\(656\) | −8.23607 | + | 14.2653i | −0.321564 | + | 0.556966i | ||||
\(657\) | −2.85410 | + | 4.94345i | −0.111349 | + | 0.192862i | ||||
\(658\) | 0.854102 | 0.0332964 | ||||||||
\(659\) | −5.94427 | + | 10.2958i | −0.231556 | + | 0.401067i | −0.958266 | − | 0.285877i | \(-0.907715\pi\) |
0.726710 | + | 0.686944i | \(0.241048\pi\) | |||||||
\(660\) | 0.656541 | + | 1.13716i | 0.0255558 | + | 0.0442640i | ||||
\(661\) | −9.27051 | − | 16.0570i | −0.360581 | − | 0.624545i | 0.627476 | − | 0.778636i | \(-0.284088\pi\) |
−0.988057 | + | 0.154092i | \(0.950755\pi\) | |||||||
\(662\) | −6.43769 | −0.250208 | ||||||||
\(663\) | 7.13525 | + | 7.41517i | 0.277110 | + | 0.287982i | ||||
\(664\) | 9.87539 | 0.383239 | ||||||||
\(665\) | −0.927051 | − | 1.60570i | −0.0359495 | − | 0.0622664i | ||||
\(666\) | 2.18034 | + | 3.77646i | 0.0844865 | + | 0.146335i | ||||
\(667\) | 9.14590 | − | 15.8412i | 0.354131 | − | 0.613372i | ||||
\(668\) | −18.1033 | −0.700439 | ||||||||
\(669\) | −2.53444 | + | 4.38978i | −0.0979872 | + | 0.169719i | ||||
\(670\) | −0.0516628 | + | 0.0894826i | −0.00199591 | + | 0.00345701i | ||||
\(671\) | 29.1246 | 1.12434 | ||||||||
\(672\) | 0.791796 | − | 1.37143i | 0.0305442 | − | 0.0529041i | ||||
\(673\) | −20.6246 | − | 35.7229i | −0.795020 | − | 1.37702i | −0.922826 | − | 0.385216i | \(-0.874127\pi\) |
0.127806 | − | 0.991799i | \(-0.459207\pi\) | |||||||
\(674\) | −1.63525 | − | 2.83234i | −0.0629877 | − | 0.109098i | ||||
\(675\) | −10.8541 | −0.417775 | ||||||||
\(676\) | 20.3951 | + | 12.8456i | 0.784428 | + | 0.494061i | ||||
\(677\) | 1.25735 | 0.0483240 | 0.0241620 | − | 0.999708i | \(-0.492308\pi\) | ||||
0.0241620 | + | 0.999708i | \(0.492308\pi\) | |||||||
\(678\) | −0.545085 | − | 0.944115i | −0.0209339 | − | 0.0362585i | ||||
\(679\) | −6.07295 | − | 10.5187i | −0.233058 | − | 0.403669i | ||||
\(680\) | 2.10081 | − | 3.63871i | 0.0805625 | − | 0.139538i | ||||
\(681\) | 2.85410 | 0.109369 | ||||||||
\(682\) | 8.07295 | − | 13.9828i | 0.309129 | − | 0.535427i | ||||
\(683\) | 3.73607 | − | 6.47106i | 0.142957 | − | 0.247608i | −0.785652 | − | 0.618669i | \(-0.787672\pi\) |
0.928609 | + | 0.371060i | \(0.121006\pi\) | |||||||
\(684\) | 25.6869 | 0.982164 | ||||||||
\(685\) | 0.0729490 | − | 0.126351i | 0.00278724 | − | 0.00482764i | ||||
\(686\) | −0.190983 | − | 0.330792i | −0.00729177 | − | 0.0126297i | ||||
\(687\) | 5.18034 | + | 8.97261i | 0.197642 | + | 0.342326i | ||||
\(688\) | −23.7902 | −0.906995 | ||||||||
\(689\) | −20.5902 | − | 21.3979i | −0.784423 | − | 0.815196i | ||||
\(690\) | −0.249224 | −0.00948778 | ||||||||
\(691\) | −0.427051 | − | 0.739674i | −0.0162458 | − | 0.0281385i | 0.857788 | − | 0.514003i | \(-0.171838\pi\) |
−0.874034 | + | 0.485865i | \(0.838505\pi\) | |||||||
\(692\) | −8.34346 | − | 14.4513i | −0.317171 | − | 0.549356i | ||||
\(693\) | −6.92705 | + | 11.9980i | −0.263137 | + | 0.455766i | ||||
\(694\) | 13.4590 | 0.510896 | ||||||||
\(695\) | 2.97214 | − | 5.14789i | 0.112740 | − | 0.195271i | ||||
\(696\) | 1.14996 | − | 1.99179i | 0.0435892 | − | 0.0754988i | ||||
\(697\) | 39.1246 | 1.48195 | ||||||||
\(698\) | −1.39261 | + | 2.41207i | −0.0527110 | + | 0.0912982i | ||||
\(699\) | 0.0729490 | + | 0.126351i | 0.00275919 | + | 0.00477905i | ||||
\(700\) | −4.50000 | − | 7.79423i | −0.170084 | − | 0.294594i | ||||
\(701\) | 6.76393 | 0.255470 | 0.127735 | − | 0.991808i | \(-0.459229\pi\) | ||||
0.127735 | + | 0.991808i | \(0.459229\pi\) | |||||||
\(702\) | −0.854102 | + | 2.95870i | −0.0322360 | + | 0.111669i | ||||
\(703\) | 19.4164 | 0.732304 | ||||||||
\(704\) | −11.4271 | − | 19.7922i | −0.430673 | − | 0.745948i | ||||
\(705\) | 0.163119 | + | 0.282530i | 0.00614342 | + | 0.0106407i | ||||
\(706\) | −5.51064 | + | 9.54471i | −0.207396 | + | 0.359220i | ||||
\(707\) | 8.56231 | 0.322019 | ||||||||
\(708\) | −0.791796 | + | 1.37143i | −0.0297575 | + | 0.0515415i | ||||
\(709\) | −1.71885 | + | 2.97713i | −0.0645527 | + | 0.111808i | −0.896495 | − | 0.443053i | \(-0.853895\pi\) |
0.831943 | + | 0.554861i | \(0.187229\pi\) | |||||||
\(710\) | 1.19350 | 0.0447911 | ||||||||
\(711\) | 5.70820 | − | 9.88690i | 0.214074 | − | 0.370788i | ||||
\(712\) | 11.8435 | + | 20.5135i | 0.443852 | + | 0.768775i | ||||
\(713\) | −19.4721 | − | 33.7267i | −0.729237 | − | 1.26308i | ||||
\(714\) | −1.09017 | −0.0407986 | ||||||||
\(715\) | 1.85410 | − | 6.42280i | 0.0693395 | − | 0.240199i | ||||
\(716\) | 16.6869 | 0.623619 | ||||||||
\(717\) | −2.15654 | − | 3.73524i | −0.0805375 | − | 0.139495i | ||||
\(718\) | 2.08359 | + | 3.60889i | 0.0777590 | + | 0.134682i | ||||
\(719\) | 16.0623 | − | 27.8207i | 0.599023 | − | 1.03754i | −0.393943 | − | 0.919135i | \(-0.628889\pi\) |
0.992966 | − | 0.118403i | \(-0.0377775\pi\) | |||||||
\(720\) | −3.42956 | −0.127812 | ||||||||
\(721\) | −2.35410 | + | 4.07742i | −0.0876713 | + | 0.151851i | ||||
\(722\) | −0.871323 | + | 1.50918i | −0.0324273 | + | 0.0561657i | ||||
\(723\) | −1.69505 | −0.0630395 | ||||||||
\(724\) | −3.43769 | + | 5.95426i | −0.127761 | + | 0.221288i | ||||
\(725\) | −9.92705 | − | 17.1942i | −0.368681 | − | 0.638575i | ||||
\(726\) | 0.916408 | + | 1.58726i | 0.0340111 | + | 0.0589089i | ||||
\(727\) | −17.2918 | −0.641317 | −0.320659 | − | 0.947195i | \(-0.603904\pi\) | ||||
−0.320659 | + | 0.947195i | \(0.603904\pi\) | |||||||
\(728\) | −5.15248 | + | 1.27491i | −0.190963 | + | 0.0472512i | ||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | 0.145898 | + | 0.252703i | 0.00539993 | + | 0.00935295i | ||||
\(731\) | 28.2533 | + | 48.9361i | 1.04499 | + | 1.80997i | ||||
\(732\) | 2.12461 | − | 3.67994i | 0.0785279 | − | 0.136014i | ||||
\(733\) | 1.27051 | 0.0469274 | 0.0234637 | − | 0.999725i | \(-0.492531\pi\) | ||||
0.0234637 | + | 0.999725i | \(0.492531\pi\) | |||||||
\(734\) | −4.85410 | + | 8.40755i | −0.179168 | + | 0.310328i | ||||
\(735\) | 0.0729490 | − | 0.126351i | 0.00269077 | − | 0.00466054i | ||||
\(736\) | 18.5410 | 0.683431 | ||||||||
\(737\) | 1.71885 | − | 2.97713i | 0.0633145 | − | 0.109664i | ||||
\(738\) | 2.85410 | + | 4.94345i | 0.105061 | + | 0.181971i | ||||
\(739\) | 23.5623 | + | 40.8111i | 0.866753 | + | 1.50126i | 0.865296 | + | 0.501262i | \(0.167131\pi\) |
0.00145790 | + | 0.999999i | \(0.499536\pi\) | |||||||
\(740\) | −2.83282 | −0.104136 | ||||||||
\(741\) | 4.63525 | + | 4.81710i | 0.170280 | + | 0.176961i | ||||
\(742\) | 3.14590 | 0.115490 | ||||||||
\(743\) | −11.8369 | − | 20.5021i | −0.434253 | − | 0.752148i | 0.562981 | − | 0.826470i | \(-0.309654\pi\) |
−0.997234 | + | 0.0743213i | \(0.976321\pi\) | |||||||
\(744\) | −2.44834 | − | 4.24064i | −0.0897604 | − | 0.155470i | ||||
\(745\) | 0.927051 | − | 1.60570i | 0.0339645 | − | 0.0588283i | ||||
\(746\) | −0.167184 | −0.00612105 | ||||||||
\(747\) | −9.57295 | + | 16.5808i | −0.350256 | + | 0.606661i | ||||
\(748\) | −33.6246 | + | 58.2395i | −1.22944 | + | 2.12945i | ||||
\(749\) | −5.61803 | −0.205278 | ||||||||
\(750\) | −0.274575 | + | 0.475578i | −0.0100261 | + | 0.0173657i | ||||
\(751\) | −4.64590 | − | 8.04693i | −0.169531 | − | 0.293637i | 0.768724 | − | 0.639581i | \(-0.220892\pi\) |
−0.938255 | + | 0.345944i | \(0.887559\pi\) | |||||||
\(752\) | −3.51722 | − | 6.09201i | −0.128260 | − | 0.222153i | ||||
\(753\) | −2.00000 | −0.0728841 | ||||||||
\(754\) | −5.46807 | + | 1.35300i | −0.199135 | + | 0.0492732i | ||||
\(755\) | −5.61803 | −0.204461 | ||||||||
\(756\) | 2.07295 | + | 3.59045i | 0.0753924 | + | 0.130584i | ||||
\(757\) | −14.0000 | − | 24.2487i | −0.508839 | − | 0.881334i | −0.999948 | − | 0.0102362i | \(-0.996742\pi\) |
0.491109 | − | 0.871098i | \(-0.336592\pi\) | |||||||
\(758\) | 2.45492 | − | 4.25204i | 0.0891665 | − | 0.154441i | ||||
\(759\) | 8.29180 | 0.300973 | ||||||||
\(760\) | 1.36475 | − | 2.36381i | 0.0495045 | − | 0.0857443i | ||||
\(761\) | 11.0729 | − | 19.1789i | 0.401394 | − | 0.695235i | −0.592500 | − | 0.805570i | \(-0.701859\pi\) |
0.993894 | + | 0.110335i | \(0.0351925\pi\) | |||||||
\(762\) | 2.06386 | 0.0747657 | ||||||||
\(763\) | −5.35410 | + | 9.27358i | −0.193832 | + | 0.335726i | ||||
\(764\) | 21.8951 | + | 37.9235i | 0.792138 | + | 1.37202i | ||||
\(765\) | 4.07295 | + | 7.05455i | 0.147258 | + | 0.255058i | ||||
\(766\) | 9.54102 | 0.344731 | ||||||||
\(767\) | 7.82624 | − | 1.93649i | 0.282589 | − | 0.0699227i | ||||
\(768\) | −2.12461 | −0.0766653 | ||||||||
\(769\) | −4.20820 | − | 7.28882i | −0.151752 | − | 0.262842i | 0.780120 | − | 0.625630i | \(-0.215158\pi\) |
−0.931872 | + | 0.362788i | \(0.881825\pi\) | |||||||
\(770\) | 0.354102 | + | 0.613323i | 0.0127609 | + | 0.0221026i | ||||
\(771\) | −4.91641 | + | 8.51547i | −0.177060 | + | 0.306677i | ||||
\(772\) | 11.1246 | 0.400384 | ||||||||
\(773\) | 9.68034 | − | 16.7668i | 0.348178 | − | 0.603061i | −0.637748 | − | 0.770245i | \(-0.720134\pi\) |
0.985926 | + | 0.167184i | \(0.0534673\pi\) | |||||||
\(774\) | −4.12210 | + | 7.13969i | −0.148166 | + | 0.256631i | ||||
\(775\) | −42.2705 | −1.51840 | ||||||||
\(776\) | 8.94021 | − | 15.4849i | 0.320935 | − | 0.555875i | ||||
\(777\) | 0.763932 | + | 1.32317i | 0.0274059 | + | 0.0474684i | ||||
\(778\) | −4.56231 | − | 7.90215i | −0.163567 | − | 0.283306i | ||||
\(779\) | 25.4164 | 0.910637 | ||||||||
\(780\) | −0.676275 | − | 0.702805i | −0.0242145 | − | 0.0251645i | ||||
\(781\) | −39.7082 | −1.42087 | ||||||||
\(782\) | −6.38197 | − | 11.0539i | −0.228219 | − | 0.395286i | ||||
\(783\) | 4.57295 | + | 7.92058i | 0.163424 | + | 0.283058i | ||||
\(784\) | −1.57295 | + | 2.72443i | −0.0561768 | + | 0.0973010i | ||||
\(785\) | 3.11146 | 0.111053 | ||||||||
\(786\) | 0.0237987 | − | 0.0412206i | 0.000848873 | − | 0.00147029i | ||||
\(787\) | −14.7082 | + | 25.4754i | −0.524291 | + | 0.908098i | 0.475309 | + | 0.879819i | \(0.342336\pi\) |
−0.999600 | + | 0.0282796i | \(0.990997\pi\) | |||||||
\(788\) | −14.4590 | −0.515080 | ||||||||
\(789\) | 1.71885 | − | 2.97713i | 0.0611926 | − | 0.105989i | ||||
\(790\) | −0.291796 | − | 0.505406i | −0.0103816 | − | 0.0179815i | ||||
\(791\) | 3.73607 | + | 6.47106i | 0.132839 | + | 0.230084i | ||||
\(792\) | −20.3951 | −0.724709 | ||||||||
\(793\) | −21.0000 | + | 5.19615i | −0.745732 | + | 0.184521i | ||||
\(794\) | −9.70820 | −0.344531 | ||||||||
\(795\) | 0.600813 | + | 1.04064i | 0.0213086 | + | 0.0369077i | ||||
\(796\) | 2.24013 | + | 3.88002i | 0.0793994 | + | 0.137524i | ||||
\(797\) | −7.09017 | + | 12.2805i | −0.251147 | + | 0.434999i | −0.963842 | − | 0.266475i | \(-0.914141\pi\) |
0.712695 | + | 0.701474i | \(0.247474\pi\) | |||||||
\(798\) | −0.708204 | −0.0250701 | ||||||||
\(799\) | −8.35410 | + | 14.4697i | −0.295547 | + | 0.511902i | ||||
\(800\) | 10.0623 | − | 17.4284i | 0.355756 | − | 0.616188i | ||||
\(801\) | −45.9230 | −1.62261 | ||||||||
\(802\) | 3.90576 | − | 6.76498i | 0.137917 | − | 0.238880i | ||||
\(803\) | −4.85410 | − | 8.40755i | −0.171298 | − | 0.296696i | ||||
\(804\) | −0.250776 | − | 0.434357i | −0.00884420 | − | 0.0153186i | ||||
\(805\) | 1.70820 | 0.0602063 | ||||||||
\(806\) | −3.32624 | + | 11.5224i | −0.117162 | + | 0.405860i | ||||
\(807\) | −5.24922 | −0.184781 | ||||||||
\(808\) | 6.30244 | + | 10.9161i | 0.221719 | + | 0.384029i | ||||
\(809\) | −11.2082 | − | 19.4132i | −0.394059 | − | 0.682531i | 0.598921 | − | 0.800808i | \(-0.295596\pi\) |
−0.992981 | + | 0.118277i | \(0.962263\pi\) | |||||||
\(810\) | −0.562306 | + | 0.973942i | −0.0197574 | + | 0.0342208i | ||||
\(811\) | 5.72949 | 0.201190 | 0.100595 | − | 0.994927i | \(-0.467925\pi\) | ||||
0.100595 | + | 0.994927i | \(0.467925\pi\) | |||||||
\(812\) | −3.79180 | + | 6.56758i | −0.133066 | + | 0.230477i | ||||
\(813\) | 3.51722 | − | 6.09201i | 0.123354 | − | 0.213656i | ||||
\(814\) | −7.41641 | −0.259945 | ||||||||
\(815\) | −1.85410 | + | 3.21140i | −0.0649464 | + | 0.112490i | ||||
\(816\) | 4.48936 | + | 7.77579i | 0.157159 | + | 0.272207i | ||||
\(817\) | 18.3541 | + | 31.7902i | 0.642129 | + | 1.11220i | ||||
\(818\) | 13.2016 | 0.461584 | ||||||||
\(819\) | 2.85410 | − | 9.88690i | 0.0997304 | − | 0.345476i | ||||
\(820\) | −3.70820 | −0.129496 | ||||||||
\(821\) | −18.6803 | − | 32.3553i | −0.651948 | − | 1.12921i | −0.982650 | − | 0.185472i | \(-0.940619\pi\) |
0.330701 | − | 0.943736i | \(-0.392715\pi\) | |||||||
\(822\) | −0.0278640 | − | 0.0482619i | −0.000971870 | − | 0.00168333i | ||||
\(823\) | 5.79180 | − | 10.0317i | 0.201889 | − | 0.349683i | −0.747248 | − | 0.664545i | \(-0.768625\pi\) |
0.949137 | + | 0.314863i | \(0.101959\pi\) | |||||||
\(824\) | −6.93112 | −0.241457 | ||||||||
\(825\) | 4.50000 | − | 7.79423i | 0.156670 | − | 0.271360i | ||||
\(826\) | −0.427051 | + | 0.739674i | −0.0148590 | + | 0.0257366i | ||||
\(827\) | −30.9787 | −1.07724 | −0.538618 | − | 0.842550i | \(-0.681053\pi\) | ||||
−0.538618 | + | 0.842550i | \(0.681053\pi\) | |||||||
\(828\) | −11.8328 | + | 20.4950i | −0.411219 | + | 0.712252i | ||||
\(829\) | 6.28115 | + | 10.8793i | 0.218153 | + | 0.377853i | 0.954243 | − | 0.299031i | \(-0.0966633\pi\) |
−0.736090 | + | 0.676884i | \(0.763330\pi\) | |||||||
\(830\) | 0.489357 | + | 0.847591i | 0.0169858 | + | 0.0294203i | ||||
\(831\) | 1.90983 | 0.0662513 | ||||||||
\(832\) | 11.7705 | + | 12.2323i | 0.408069 | + | 0.424078i | ||||
\(833\) | 7.47214 | 0.258894 | ||||||||
\(834\) | −1.13525 | − | 1.96632i | −0.0393107 | − | 0.0680881i | ||||
\(835\) | −1.86475 | − | 3.22983i | −0.0645322 | − | 0.111773i | ||||
\(836\) | −21.8435 | + | 37.8340i | −0.755472 | + | 1.30852i | ||||
\(837\) | 19.4721 | 0.673055 | ||||||||
\(838\) | −1.13525 | + | 1.96632i | −0.0392167 | + | 0.0679254i | ||||
\(839\) | 14.3713 | − | 24.8919i | 0.496153 | − | 0.859362i | −0.503837 | − | 0.863799i | \(-0.668079\pi\) |
0.999990 | + | 0.00443626i | \(0.00141211\pi\) | |||||||
\(840\) | 0.214782 | 0.00741067 | ||||||||
\(841\) | 6.13525 | − | 10.6266i | 0.211561 | − | 0.366434i | ||||
\(842\) | 4.85410 | + | 8.40755i | 0.167283 | + | 0.289743i | ||||
\(843\) | −0.416408 | − | 0.721240i | −0.0143418 | − | 0.0248408i | ||||
\(844\) | 16.1459 | 0.555765 | ||||||||
\(845\) | −0.190983 | + | 4.96188i | −0.00657002 | + | 0.170694i | ||||
\(846\) | −2.43769 | −0.0838096 | ||||||||
\(847\) | −6.28115 | − | 10.8793i | −0.215823 | − | 0.373816i | ||||
\(848\) | −12.9549 | − | 22.4386i | −0.444874 | − | 0.770544i | ||||
\(849\) | −2.56231 | + | 4.43804i | −0.0879381 | + | 0.152313i | ||||
\(850\) | −13.8541 | −0.475192 | ||||||||
\(851\) | −8.94427 | + | 15.4919i | −0.306606 | + | 0.531057i | ||||
\(852\) | −2.89667 | + | 5.01719i | −0.0992384 | + | 0.171886i | ||||
\(853\) | −26.1246 | −0.894490 | −0.447245 | − | 0.894412i | \(-0.647595\pi\) | ||||
−0.447245 | + | 0.894412i | \(0.647595\pi\) | |||||||
\(854\) | 1.14590 | − | 1.98475i | 0.0392118 | − | 0.0679169i | ||||
\(855\) | 2.64590 | + | 4.58283i | 0.0904878 | + | 0.156729i | ||||
\(856\) | −4.13525 | − | 7.16247i | −0.141340 | − | 0.244808i | ||||
\(857\) | 29.4508 | 1.00602 | 0.503011 | − | 0.864280i | \(-0.332226\pi\) | ||||
0.503011 | + | 0.864280i | \(0.332226\pi\) | |||||||
\(858\) | −1.77051 | − | 1.83997i | −0.0604442 | − | 0.0628155i | ||||
\(859\) | 36.2492 | 1.23681 | 0.618404 | − | 0.785861i | \(-0.287780\pi\) | ||||
0.618404 | + | 0.785861i | \(0.287780\pi\) | |||||||
\(860\) | −2.67783 | − | 4.63813i | −0.0913132 | − | 0.158159i | ||||
\(861\) | 1.00000 | + | 1.73205i | 0.0340799 | + | 0.0590281i | ||||
\(862\) | 3.20820 | − | 5.55677i | 0.109272 | − | 0.189264i | ||||
\(863\) | −23.8885 | −0.813175 | −0.406588 | − | 0.913612i | \(-0.633281\pi\) | ||||
−0.406588 | + | 0.913612i | \(0.633281\pi\) | |||||||
\(864\) | −4.63525 | + | 8.02850i | −0.157695 | + | 0.273135i | ||||
\(865\) | 1.71885 | − | 2.97713i | 0.0584426 | − | 0.101225i | ||||
\(866\) | 0.381966 | 0.0129797 | ||||||||
\(867\) | 7.41641 | − | 12.8456i | 0.251874 | − | 0.436259i | ||||
\(868\) | 8.07295 | + | 13.9828i | 0.274014 | + | 0.474606i | ||||
\(869\) | 9.70820 | + | 16.8151i | 0.329328 | + | 0.570413i | ||||
\(870\) | 0.227937 | 0.00772780 | ||||||||
\(871\) | −0.708204 | + | 2.45329i | −0.0239966 | + | 0.0831266i | ||||
\(872\) | −15.7639 | −0.533834 | ||||||||
\(873\) | 17.3328 | + | 30.0213i | 0.586627 | + | 1.01607i | ||||
\(874\) | −4.14590 | − | 7.18091i | −0.140237 | − | 0.242898i | ||||
\(875\) | 1.88197 | − | 3.25966i | 0.0636221 | − | 0.110197i | ||||
\(876\) | −1.41641 | −0.0478560 | ||||||||
\(877\) | 6.35410 | − | 11.0056i | 0.214563 | − | 0.371634i | −0.738574 | − | 0.674172i | \(-0.764501\pi\) |
0.953137 | + | 0.302538i | \(0.0978340\pi\) | |||||||
\(878\) | −1.55573 | + | 2.69460i | −0.0525033 | + | 0.0909383i | ||||
\(879\) | 4.29180 | 0.144759 | ||||||||
\(880\) | 2.91641 | − | 5.05137i | 0.0983121 | − | 0.170282i | ||||
\(881\) | −6.29837 | − | 10.9091i | −0.212198 | − | 0.367537i | 0.740204 | − | 0.672382i | \(-0.234729\pi\) |
−0.952402 | + | 0.304845i | \(0.901395\pi\) | |||||||
\(882\) | 0.545085 | + | 0.944115i | 0.0183540 | + | 0.0317900i | ||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | 13.8541 | − | 47.9920i | 0.465964 | − | 1.61415i | ||||
\(885\) | −0.326238 | −0.0109664 | ||||||||
\(886\) | 0.145898 | + | 0.252703i | 0.00490154 | + | 0.00848972i | ||||
\(887\) | −11.6738 | − | 20.2195i | −0.391967 | − | 0.678906i | 0.600742 | − | 0.799443i | \(-0.294872\pi\) |
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(888\) | −1.12461 | + | 1.94788i | −0.0377395 | + | 0.0653667i | ||||
\(889\) | −14.1459 | −0.474438 | ||||||||
\(890\) | −1.17376 | + | 2.03302i | −0.0393446 | + | 0.0681468i | ||||
\(891\) | 18.7082 | − | 32.4036i | 0.626748 | − | 1.08556i | ||||
\(892\) | 24.6049 | 0.823832 | ||||||||
\(893\) | −5.42705 | + | 9.39993i | −0.181609 | + | 0.314557i | ||||
\(894\) | −0.354102 | − | 0.613323i | −0.0118429 | − | 0.0205126i | ||||
\(895\) | 1.71885 | + | 2.97713i | 0.0574547 | + | 0.0995145i | ||||
\(896\) | −10.0902 | −0.337089 | ||||||||
\(897\) | −5.97871 | + | 1.47935i | −0.199623 | + | 0.0493940i | ||||
\(898\) | 10.8754 | 0.362916 | ||||||||
\(899\) | 17.8090 | + | 30.8461i | 0.593964 | + | 1.02878i | ||||
\(900\) | 12.8435 | + | 22.2455i | 0.428115 | + | 0.741517i | ||||
\(901\) | −30.7705 | + | 53.2961i | −1.02511 | + | 1.77555i | ||||
\(902\) | −9.70820 | −0.323248 | ||||||||
\(903\) | −1.44427 | + | 2.50155i | −0.0480624 | + | 0.0832464i | ||||
\(904\) | −5.50000 | + | 9.52628i | −0.182927 | + | 0.316839i | ||||
\(905\) | −1.41641 | −0.0470830 | ||||||||
\(906\) | −1.07295 | + | 1.85840i | −0.0356463 | + | 0.0617413i | ||||
\(907\) | 12.0000 | + | 20.7846i | 0.398453 | + | 0.690142i | 0.993535 | − | 0.113523i | \(-0.0362137\pi\) |
−0.595082 | + | 0.803665i | \(0.702880\pi\) | |||||||
\(908\) | −6.92705 | − | 11.9980i | −0.229882 | − | 0.398168i | ||||
\(909\) | −24.4377 | −0.810547 | ||||||||
\(910\) | −0.364745 | − | 0.379054i | −0.0120912 | − | 0.0125655i | ||||
\(911\) | 37.6869 | 1.24862 | 0.624312 | − | 0.781175i | \(-0.285380\pi\) | ||||
0.624312 | + | 0.781175i | \(0.285380\pi\) | |||||||
\(912\) | 2.91641 | + | 5.05137i | 0.0965719 | + | 0.167267i | ||||
\(913\) | −16.2812 | − | 28.1998i | −0.538828 | − | 0.933277i | ||||
\(914\) | 2.18034 | − | 3.77646i | 0.0721192 | − | 0.124914i | ||||
\(915\) | 0.875388 | 0.0289394 | ||||||||
\(916\) | 25.1459 | − | 43.5540i | 0.830844 | − | 1.43906i | ||||
\(917\) | −0.163119 | + | 0.282530i | −0.00538666 | + | 0.00932997i | ||||
\(918\) | 6.38197 | 0.210636 | ||||||||
\(919\) | 15.0000 | − | 25.9808i | 0.494804 | − | 0.857026i | −0.505178 | − | 0.863015i | \(-0.668573\pi\) |
0.999982 | + | 0.00598907i | \(0.00190639\pi\) | |||||||
\(920\) | 1.25735 | + | 2.17780i | 0.0414537 | + | 0.0718000i | ||||
\(921\) | 0.354102 | + | 0.613323i | 0.0116681 | + | 0.0202097i | ||||
\(922\) | 14.9787 | 0.493298 | ||||||||
\(923\) | 28.6312 | − | 7.08438i | 0.942407 | − | 0.233185i | ||||
\(924\) | −3.43769 | −0.113092 | ||||||||
\(925\) | 9.70820 | + | 16.8151i | 0.319204 | + | 0.552877i | ||||
\(926\) | 1.28115 | + | 2.21902i | 0.0421013 | + | 0.0729216i | ||||
\(927\) | 6.71885 | − | 11.6374i | 0.220676 | − | 0.382222i | ||||
\(928\) | −16.9574 | −0.556655 | ||||||||
\(929\) | 23.5344 | − | 40.7628i | 0.772140 | − | 1.33739i | −0.164248 | − | 0.986419i | \(-0.552520\pi\) |
0.936388 | − | 0.350967i | \(-0.114147\pi\) | |||||||
\(930\) | 0.242646 | − | 0.420275i | 0.00795667 | − | 0.0137814i | ||||
\(931\) | 4.85410 | 0.159087 | ||||||||
\(932\) | 0.354102 | − | 0.613323i | 0.0115990 | − | 0.0200900i | ||||
\(933\) | −2.35410 | − | 4.07742i | −0.0770698 | − | 0.133489i | ||||
\(934\) | −6.42705 | − | 11.1320i | −0.210300 | − | 0.364249i | ||||
\(935\) | −13.8541 | −0.453078 | ||||||||
\(936\) | 14.7057 | − | 3.63871i | 0.480671 | − | 0.118935i | ||||
\(937\) | −56.1246 | −1.83351 | −0.916756 | − | 0.399449i | \(-0.869202\pi\) | ||||
−0.916756 | + | 0.399449i | \(0.869202\pi\) | |||||||
\(938\) | −0.135255 | − | 0.234268i | −0.00441623 | − | 0.00764913i | ||||
\(939\) | −2.88854 | − | 5.00310i | −0.0942641 | − | 0.163270i | ||||
\(940\) | 0.791796 | − | 1.37143i | 0.0258255 | − | 0.0447311i | ||||
\(941\) | 51.6525 | 1.68382 | 0.841911 | − | 0.539616i | \(-0.181431\pi\) | ||||
0.841911 | + | 0.539616i | \(0.181431\pi\) | |||||||
\(942\) | 0.594235 | − | 1.02925i | 0.0193612 | − | 0.0335346i | ||||
\(943\) | −11.7082 | + | 20.2792i | −0.381272 | + | 0.660382i | ||||
\(944\) | 7.03444 | 0.228952 | ||||||||
\(945\) | −0.427051 | + | 0.739674i | −0.0138920 | + | 0.0240616i | ||||
\(946\) | −7.01064 | − | 12.1428i | −0.227936 | − | 0.394796i | ||||
\(947\) | −22.9336 | − | 39.7222i | −0.745243 | − | 1.29080i | −0.950081 | − | 0.312003i | \(-0.899000\pi\) |
0.204838 | − | 0.978796i | \(-0.434333\pi\) | |||||||
\(948\) | 2.83282 | 0.0920056 | ||||||||
\(949\) | 5.00000 | + | 5.19615i | 0.162307 | + | 0.168674i | ||||
\(950\) | −9.00000 | −0.291999 | ||||||||
\(951\) | 4.15654 | + | 7.19934i | 0.134785 | + | 0.233455i | ||||
\(952\) | 5.50000 | + | 9.52628i | 0.178256 | + | 0.308748i | ||||
\(953\) | 22.3885 | − | 38.7781i | 0.725236 | − | 1.25615i | −0.233641 | − | 0.972323i | \(-0.575064\pi\) |
0.958877 | − | 0.283823i | \(-0.0916027\pi\) | |||||||
\(954\) | −8.97871 | −0.290697 | ||||||||
\(955\) | −4.51064 | + | 7.81266i | −0.145961 | + | 0.252812i | ||||
\(956\) | −10.4681 | + | 18.1312i | −0.338562 | + | 0.586406i | ||||
\(957\) | −7.58359 | −0.245143 | ||||||||
\(958\) | 4.19756 | − | 7.27039i | 0.135617 | − | 0.234896i | ||||
\(959\) | 0.190983 | + | 0.330792i | 0.00616716 | + | 0.0106818i | ||||
\(960\) | −0.343459 | − | 0.594888i | −0.0110851 | − | 0.0191999i | ||||
\(961\) | 44.8328 | 1.44622 | ||||||||
\(962\) | 5.34752 | − | 1.32317i | 0.172411 | − | 0.0426607i | ||||
\(963\) | 16.0344 | 0.516703 | ||||||||
\(964\) | 4.11397 | + | 7.12560i | 0.132502 | + | 0.229500i | ||||
\(965\) | 1.14590 | + | 1.98475i | 0.0368878 | + | 0.0638915i | ||||
\(966\) | 0.326238 | − | 0.565061i | 0.0104965 | − | 0.0181805i | ||||
\(967\) | −39.0000 | −1.25416 | −0.627078 | − | 0.778957i | \(-0.715749\pi\) | ||||
−0.627078 | + | 0.778957i | \(0.715749\pi\) | |||||||
\(968\) | 9.24671 | − | 16.0158i | 0.297201 | − | 0.514766i | ||||
\(969\) | 6.92705 | − | 11.9980i | 0.222529 | − | 0.385431i | ||||
\(970\) | 1.77206 | 0.0568975 | ||||||||
\(971\) | −29.2082 | + | 50.5901i | −0.937336 | + | 1.62351i | −0.166921 | + | 0.985970i | \(0.553383\pi\) |
−0.770415 | + | 0.637543i | \(0.779951\pi\) | |||||||
\(972\) | −8.94834 | − | 15.4990i | −0.287018 | − | 0.497130i | ||||
\(973\) | 7.78115 | + | 13.4774i | 0.249452 | + | 0.432064i | ||||
\(974\) | −6.48529 | −0.207802 | ||||||||
\(975\) | −1.85410 | + | 6.42280i | −0.0593788 | + | 0.205694i | ||||
\(976\) | −18.8754 | −0.604186 | ||||||||
\(977\) | 15.7361 | + | 27.2557i | 0.503441 | + | 0.871986i | 0.999992 | + | 0.00397838i | \(0.00126636\pi\) |
−0.496551 | + | 0.868008i | \(0.665400\pi\) | |||||||
\(978\) | 0.708204 | + | 1.22665i | 0.0226459 | + | 0.0392238i | ||||
\(979\) | 39.0517 | − | 67.6395i | 1.24810 | − | 2.16177i | ||||
\(980\) | −0.708204 | −0.0226227 | ||||||||
\(981\) | 15.2812 | − | 26.4677i | 0.487890 | − | 0.845050i | ||||
\(982\) | −2.79180 | + | 4.83553i | −0.0890898 | + | 0.154308i | ||||
\(983\) | 20.6180 | 0.657613 | 0.328807 | − | 0.944397i | \(-0.393354\pi\) | ||||
0.328807 | + | 0.944397i | \(0.393354\pi\) | |||||||
\(984\) | −1.47214 | + | 2.54981i | −0.0469300 | + | 0.0812851i | ||||
\(985\) | −1.48936 | − | 2.57964i | −0.0474549 | − | 0.0821942i | ||||
\(986\) | 5.83688 | + | 10.1098i | 0.185884 | + | 0.321961i | ||||
\(987\) | −0.854102 | −0.0271864 | ||||||||
\(988\) | 9.00000 | − | 31.1769i | 0.286328 | − | 0.991870i | ||||
\(989\) | −33.8197 | −1.07540 | ||||||||
\(990\) | −1.01064 | − | 1.75049i | −0.0321203 | − | 0.0556341i | ||||
\(991\) | 11.4271 | + | 19.7922i | 0.362992 | + | 0.628721i | 0.988452 | − | 0.151536i | \(-0.0484218\pi\) |
−0.625460 | + | 0.780257i | \(0.715088\pi\) | |||||||
\(992\) | −18.0517 | + | 31.2664i | −0.573141 | + | 0.992709i | ||||
\(993\) | 6.43769 | 0.204294 | ||||||||
\(994\) | −1.56231 | + | 2.70599i | −0.0495533 | + | 0.0858289i | ||||
\(995\) | −0.461493 | + | 0.799329i | −0.0146303 | + | 0.0253404i | ||||
\(996\) | −4.75078 | −0.150534 | ||||||||
\(997\) | −24.5000 | + | 42.4352i | −0.775923 | + | 1.34394i | 0.158352 | + | 0.987383i | \(0.449382\pi\) |
−0.934274 | + | 0.356555i | \(0.883951\pi\) | |||||||
\(998\) | −1.55573 | − | 2.69460i | −0.0492457 | − | 0.0852961i | ||||
\(999\) | −4.47214 | − | 7.74597i | −0.141492 | − | 0.245072i |
(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 | 91.2.f.a.29.2 | yes | 4 | |
3.2 | odd | 2 | 819.2.o.c.757.1 | 4 | |||
4.3 | odd | 2 | 1456.2.s.h.1121.2 | 4 | |||
7.2 | even | 3 | 637.2.g.b.263.2 | 4 | |||
7.3 | odd | 6 | 637.2.h.f.471.1 | 4 | |||
7.4 | even | 3 | 637.2.h.g.471.1 | 4 | |||
7.5 | odd | 6 | 637.2.g.c.263.2 | 4 | |||
7.6 | odd | 2 | 637.2.f.c.393.2 | 4 | |||
13.2 | odd | 12 | 1183.2.c.c.337.2 | 4 | |||
13.3 | even | 3 | 1183.2.a.g.1.1 | 2 | |||
13.9 | even | 3 | inner | 91.2.f.a.22.2 | ✓ | 4 | |
13.10 | even | 6 | 1183.2.a.c.1.2 | 2 | |||
13.11 | odd | 12 | 1183.2.c.c.337.3 | 4 | |||
39.35 | odd | 6 | 819.2.o.c.568.1 | 4 | |||
52.35 | odd | 6 | 1456.2.s.h.113.2 | 4 | |||
91.9 | even | 3 | 637.2.h.g.165.1 | 4 | |||
91.48 | odd | 6 | 637.2.f.c.295.2 | 4 | |||
91.55 | odd | 6 | 8281.2.a.bb.1.1 | 2 | |||
91.61 | odd | 6 | 637.2.h.f.165.1 | 4 | |||
91.62 | odd | 6 | 8281.2.a.n.1.2 | 2 | |||
91.74 | even | 3 | 637.2.g.b.373.2 | 4 | |||
91.87 | odd | 6 | 637.2.g.c.373.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.a.22.2 | ✓ | 4 | 13.9 | even | 3 | inner | |
91.2.f.a.29.2 | yes | 4 | 1.1 | even | 1 | trivial | |
637.2.f.c.295.2 | 4 | 91.48 | odd | 6 | |||
637.2.f.c.393.2 | 4 | 7.6 | odd | 2 | |||
637.2.g.b.263.2 | 4 | 7.2 | even | 3 | |||
637.2.g.b.373.2 | 4 | 91.74 | even | 3 | |||
637.2.g.c.263.2 | 4 | 7.5 | odd | 6 | |||
637.2.g.c.373.2 | 4 | 91.87 | odd | 6 | |||
637.2.h.f.165.1 | 4 | 91.61 | odd | 6 | |||
637.2.h.f.471.1 | 4 | 7.3 | odd | 6 | |||
637.2.h.g.165.1 | 4 | 91.9 | even | 3 | |||
637.2.h.g.471.1 | 4 | 7.4 | even | 3 | |||
819.2.o.c.568.1 | 4 | 39.35 | odd | 6 | |||
819.2.o.c.757.1 | 4 | 3.2 | odd | 2 | |||
1183.2.a.c.1.2 | 2 | 13.10 | even | 6 | |||
1183.2.a.g.1.1 | 2 | 13.3 | even | 3 | |||
1183.2.c.c.337.2 | 4 | 13.2 | odd | 12 | |||
1183.2.c.c.337.3 | 4 | 13.11 | odd | 12 | |||
1456.2.s.h.113.2 | 4 | 52.35 | odd | 6 | |||
1456.2.s.h.1121.2 | 4 | 4.3 | odd | 2 | |||
8281.2.a.n.1.2 | 2 | 91.62 | odd | 6 | |||
8281.2.a.bb.1.1 | 2 | 91.55 | odd | 6 |