Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(35,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.v (of order \(12\), degree \(4\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 179.13 | ||
Character | \(\chi\) | \(=\) | 432.179 |
Dual form | 432.2.v.a.251.13 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.354608 | + | 1.36903i | 0.250746 | + | 0.968053i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.74851 | + | 0.970941i | −0.874253 | + | 0.485471i | ||||
\(5\) | −1.76649 | + | 0.473330i | −0.789999 | + | 0.211679i | −0.631188 | − | 0.775630i | \(-0.717432\pi\) |
−0.158810 | + | 0.987309i | \(0.550766\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.40613 | + | 2.43549i | 0.531468 | + | 0.920530i | 0.999325 | + | 0.0367260i | \(0.0116929\pi\) |
−0.467857 | + | 0.883804i | \(0.654974\pi\) | |||||||
\(8\) | −1.94929 | − | 2.04946i | −0.689177 | − | 0.724593i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.27442 | − | 2.25054i | −0.403006 | − | 0.711683i | ||||
\(11\) | −5.79446 | − | 1.55262i | −1.74710 | − | 0.468133i | −0.763093 | − | 0.646288i | \(-0.776320\pi\) |
−0.984002 | + | 0.178156i | \(0.942987\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.10810 | + | 0.296913i | −0.307330 | + | 0.0823489i | −0.409188 | − | 0.912450i | \(-0.634188\pi\) |
0.101858 | + | 0.994799i | \(0.467521\pi\) | |||||||
\(14\) | −2.83565 | + | 2.78869i | −0.757858 | + | 0.745309i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.11455 | − | 3.39539i | 0.528636 | − | 0.848848i | ||||
\(17\) | 0.699378i | 0.169624i | 0.996397 | + | 0.0848120i | \(0.0270290\pi\) | ||||
−0.996397 | + | 0.0848120i | \(0.972971\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.01481 | + | 2.01481i | −0.462228 | + | 0.462228i | −0.899385 | − | 0.437157i | \(-0.855985\pi\) |
0.437157 | + | 0.899385i | \(0.355985\pi\) | |||||||
\(20\) | 2.62914 | − | 2.54278i | 0.587894 | − | 0.568583i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0708264 | − | 8.48338i | 0.0151002 | − | 1.80866i | ||||
\(23\) | 4.91498 | + | 2.83767i | 1.02485 | + | 0.591695i | 0.915504 | − | 0.402310i | \(-0.131792\pi\) |
0.109341 | + | 0.994004i | \(0.465126\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.43368 | + | 0.827735i | −0.286736 | + | 0.165547i | ||||
\(26\) | −0.799424 | − | 1.41173i | −0.156780 | − | 0.276863i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.82335 | − | 2.89320i | −0.911528 | − | 0.546764i | ||||
\(29\) | −5.41802 | − | 1.45175i | −1.00610 | − | 0.269584i | −0.282101 | − | 0.959385i | \(-0.591031\pi\) |
−0.723999 | + | 0.689801i | \(0.757698\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.15522 | − | 2.97637i | −0.925905 | − | 0.534572i | −0.0403909 | − | 0.999184i | \(-0.512860\pi\) |
−0.885514 | + | 0.464612i | \(0.846194\pi\) | |||||||
\(32\) | 5.39824 | + | 1.69085i | 0.954284 | + | 0.298903i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.957472 | + | 0.248005i | −0.164205 | + | 0.0425325i | ||||
\(35\) | −3.63671 | − | 3.63671i | −0.614717 | − | 0.614717i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.48490 | − | 3.48490i | 0.572913 | − | 0.572913i | −0.360028 | − | 0.932941i | \(-0.617233\pi\) |
0.932941 | + | 0.360028i | \(0.117233\pi\) | |||||||
\(38\) | −3.47280 | − | 2.04387i | −0.563363 | − | 0.331559i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.41347 | + | 2.69770i | 0.697830 | + | 0.426543i | ||||
\(41\) | −1.55998 | + | 2.70196i | −0.243628 | + | 0.421975i | −0.961745 | − | 0.273947i | \(-0.911671\pi\) |
0.718117 | + | 0.695922i | \(0.245004\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.90129 | + | 7.09570i | −0.289944 | + | 1.08208i | 0.655207 | + | 0.755450i | \(0.272581\pi\) |
−0.945151 | + | 0.326635i | \(0.894085\pi\) | |||||||
\(44\) | 11.6392 | − | 2.91131i | 1.75467 | − | 0.438897i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.14197 | + | 7.73504i | −0.315816 | + | 1.14047i | ||||
\(47\) | 2.83634 | + | 4.91269i | 0.413723 | + | 0.716589i | 0.995293 | − | 0.0969068i | \(-0.0308949\pi\) |
−0.581570 | + | 0.813496i | \(0.697562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.454420 | + | 0.787079i | −0.0649172 | + | 0.112440i | ||||
\(50\) | −1.64159 | − | 1.66923i | −0.232156 | − | 0.236065i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.64923 | − | 1.59505i | 0.228706 | − | 0.221194i | ||||
\(53\) | 4.45605 | + | 4.45605i | 0.612086 | + | 0.612086i | 0.943489 | − | 0.331403i | \(-0.107522\pi\) |
−0.331403 | + | 0.943489i | \(0.607522\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.9708 | 1.47930 | ||||||||
\(56\) | 2.25049 | − | 7.62929i | 0.300734 | − | 1.01951i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.0662251 | − | 7.93225i | 0.00869578 | − | 1.04156i | ||||
\(59\) | 3.65938 | + | 13.6570i | 0.476411 | + | 1.77799i | 0.615963 | + | 0.787775i | \(0.288767\pi\) |
−0.139552 | + | 0.990215i | \(0.544566\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.54643 | − | 13.2354i | 0.454074 | − | 1.69463i | −0.236724 | − | 0.971577i | \(-0.576074\pi\) |
0.690797 | − | 0.723048i | \(-0.257260\pi\) | |||||||
\(62\) | 2.24666 | − | 8.11312i | 0.285327 | − | 1.03037i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.400567 | + | 7.98997i | −0.0500709 | + | 0.998746i | ||||
\(65\) | 1.81690 | − | 1.04899i | 0.225359 | − | 0.130111i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.45542 | + | 12.8958i | 0.422146 | + | 1.57547i | 0.770077 | + | 0.637952i | \(0.220218\pi\) |
−0.347930 | + | 0.937520i | \(0.613115\pi\) | |||||||
\(68\) | −0.679055 | − | 1.22287i | −0.0823475 | − | 0.148294i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.68917 | − | 6.26839i | 0.440940 | − | 0.749216i | ||||
\(71\) | 7.21910i | 0.856749i | 0.903601 | + | 0.428375i | \(0.140914\pi\) | ||||
−0.903601 | + | 0.428375i | \(0.859086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.75535i | 0.439531i | 0.975553 | + | 0.219765i | \(0.0705292\pi\) | ||||
−0.975553 | + | 0.219765i | \(0.929471\pi\) | |||||||
\(74\) | 6.00671 | + | 3.53517i | 0.698266 | + | 0.410955i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.56664 | − | 5.47916i | 0.179706 | − | 0.628502i | ||||
\(77\) | −4.36638 | − | 16.2956i | −0.497596 | − | 1.85705i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.96345 | + | 1.71095i | −0.333415 | + | 0.192497i | −0.657356 | − | 0.753580i | \(-0.728325\pi\) |
0.323942 | + | 0.946077i | \(0.394992\pi\) | |||||||
\(80\) | −2.12818 | + | 6.99881i | −0.237938 | + | 0.782490i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.25226 | − | 1.17752i | −0.469583 | − | 0.130036i | ||||
\(83\) | −0.308735 | + | 1.15222i | −0.0338881 | + | 0.126472i | −0.980798 | − | 0.195028i | \(-0.937520\pi\) |
0.946910 | + | 0.321500i | \(0.104187\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.331036 | − | 1.23544i | −0.0359059 | − | 0.134003i | ||||
\(86\) | −10.3885 | − | 0.0867317i | −1.12022 | − | 0.00935252i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.11303 | + | 14.9020i | 0.864852 | + | 1.58856i | ||||
\(89\) | −0.391835 | −0.0415344 | −0.0207672 | − | 0.999784i | \(-0.506611\pi\) | ||||
−0.0207672 | + | 0.999784i | \(0.506611\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.28126 | − | 2.28126i | −0.239141 | − | 0.239141i | ||||
\(92\) | −11.3491 | − | 0.189517i | −1.18322 | − | 0.0197585i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.71984 | + | 5.62513i | −0.589957 | + | 0.580188i | ||||
\(95\) | 2.60547 | − | 4.51280i | 0.267315 | − | 0.463004i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.875387 | − | 1.51622i | −0.0888821 | − | 0.153948i | 0.818157 | − | 0.574995i | \(-0.194996\pi\) |
−0.907039 | + | 0.421047i | \(0.861663\pi\) | |||||||
\(98\) | −1.23868 | − | 0.343012i | −0.125125 | − | 0.0346494i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.70311 | − | 2.83932i | 0.170311 | − | 0.283932i | ||||
\(101\) | 0.218761 | − | 0.816427i | 0.0217675 | − | 0.0812375i | −0.954188 | − | 0.299209i | \(-0.903277\pi\) |
0.975955 | + | 0.217971i | \(0.0699439\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.30341 | + | 9.18577i | −0.522560 | + | 0.905101i | 0.477095 | + | 0.878852i | \(0.341690\pi\) |
−0.999655 | + | 0.0262492i | \(0.991644\pi\) | |||||||
\(104\) | 2.76851 | + | 1.69223i | 0.271474 | + | 0.165937i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.52033 | + | 7.68064i | −0.439054 | + | 0.746010i | ||||
\(107\) | 6.39894 | − | 6.39894i | 0.618609 | − | 0.618609i | −0.326566 | − | 0.945174i | \(-0.605891\pi\) |
0.945174 | + | 0.326566i | \(0.105891\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.52592 | + | 1.52592i | 0.146157 | + | 0.146157i | 0.776399 | − | 0.630242i | \(-0.217044\pi\) |
−0.630242 | + | 0.776399i | \(0.717044\pi\) | |||||||
\(110\) | 3.89032 | + | 15.0193i | 0.370928 | + | 1.43204i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.2428 | + | 0.375588i | 1.06234 | + | 0.0354897i | ||||
\(113\) | −5.75213 | − | 3.32099i | −0.541115 | − | 0.312413i | 0.204416 | − | 0.978884i | \(-0.434471\pi\) |
−0.745531 | + | 0.666471i | \(0.767804\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.0254 | − | 2.68630i | −0.934876 | − | 0.250499i | ||||
\(116\) | 10.8830 | − | 2.72218i | 1.01046 | − | 0.252748i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.3992 | + | 9.85270i | −1.60173 | + | 0.907015i | ||||
\(119\) | −1.70333 | + | 0.983418i | −0.156144 | + | 0.0901498i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.6389 | + | 12.4932i | 1.96717 | + | 1.13575i | ||||
\(122\) | 19.3774 | + | 0.161779i | 1.75434 | + | 0.0146467i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.9038 | + | 0.198780i | 1.06899 | + | 0.0178510i | ||||
\(125\) | 8.60659 | − | 8.60659i | 0.769797 | − | 0.769797i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 13.8224i | − | 1.22654i | −0.789874 | − | 0.613270i | \(-0.789854\pi\) | ||
0.789874 | − | 0.613270i | \(-0.210146\pi\) | |||||||
\(128\) | −11.0806 | + | 2.28492i | −0.979394 | + | 0.201960i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.08039 | + | 2.11542i | 0.182462 | + | 0.185535i | ||||
\(131\) | −8.97914 | + | 2.40595i | −0.784511 | + | 0.210209i | −0.628773 | − | 0.777589i | \(-0.716442\pi\) |
−0.155739 | + | 0.987798i | \(0.549776\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.74013 | − | 2.07396i | −0.671154 | − | 0.179835i | ||||
\(134\) | −16.4295 | + | 9.30354i | −1.41929 | + | 0.803703i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.43335 | − | 1.36329i | 0.122908 | − | 0.116901i | ||||
\(137\) | −5.96603 | − | 10.3335i | −0.509712 | − | 0.882848i | −0.999937 | − | 0.0112514i | \(-0.996419\pi\) |
0.490224 | − | 0.871596i | \(-0.336915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.20712 | − | 0.323448i | 0.102387 | − | 0.0274345i | −0.207262 | − | 0.978286i | \(-0.566455\pi\) |
0.309649 | + | 0.950851i | \(0.399789\pi\) | |||||||
\(140\) | 9.88985 | + | 2.82778i | 0.835845 | + | 0.238991i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.88319 | + | 2.55995i | −0.829379 | + | 0.214826i | ||||
\(143\) | 6.88181 | 0.575486 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.2580 | 0.851884 | ||||||||
\(146\) | −5.14120 | + | 1.33168i | −0.425489 | + | 0.110211i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.70973 | + | 9.47699i | −0.222739 | + | 0.779004i | ||||
\(149\) | 3.47417 | − | 0.930902i | 0.284615 | − | 0.0762625i | −0.113687 | − | 0.993517i | \(-0.536266\pi\) |
0.398302 | + | 0.917254i | \(0.369599\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.43126 | − | 9.40721i | −0.441989 | − | 0.765548i | 0.555848 | − | 0.831284i | \(-0.312394\pi\) |
−0.997837 | + | 0.0657361i | \(0.979060\pi\) | |||||||
\(152\) | 8.05669 | + | 0.201830i | 0.653484 | + | 0.0163705i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 20.7608 | − | 11.7563i | 1.67295 | − | 0.947347i | ||||
\(155\) | 10.5155 | + | 2.81761i | 0.844621 | + | 0.226316i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.52986 | + | 2.55352i | −0.760565 | + | 0.203793i | −0.618199 | − | 0.786021i | \(-0.712138\pi\) |
−0.142366 | + | 0.989814i | \(0.545471\pi\) | |||||||
\(158\) | −3.39321 | − | 3.45035i | −0.269950 | − | 0.274495i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.3363 | − | 0.431720i | −0.817154 | − | 0.0341305i | ||||
\(161\) | 15.9606i | 1.25787i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.66703 | + | 3.66703i | −0.287224 | + | 0.287224i | −0.835981 | − | 0.548758i | \(-0.815101\pi\) |
0.548758 | + | 0.835981i | \(0.315101\pi\) | |||||||
\(164\) | 0.104185 | − | 6.23904i | 0.00813547 | − | 0.487187i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.68690 | − | 0.0140837i | −0.130929 | − | 0.00109311i | ||||
\(167\) | 17.4253 | + | 10.0605i | 1.34841 | + | 0.778505i | 0.988024 | − | 0.154299i | \(-0.0493118\pi\) |
0.360385 | + | 0.932803i | \(0.382645\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1186 | + | 5.84198i | −0.778355 | + | 0.449383i | ||||
\(170\) | 1.57398 | − | 0.891299i | 0.120719 | − | 0.0683595i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.56510 | − | 14.2529i | −0.271836 | − | 1.08677i | ||||
\(173\) | 10.1074 | + | 2.70826i | 0.768450 | + | 0.205906i | 0.621687 | − | 0.783266i | \(-0.286448\pi\) |
0.146763 | + | 0.989172i | \(0.453114\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.03189 | − | 2.32781i | −0.304782 | − | 0.175966i | ||||
\(176\) | −17.5244 | + | 16.3914i | −1.32095 | + | 1.23555i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.138948 | − | 0.536435i | −0.0104146 | − | 0.0402075i | ||||
\(179\) | −12.4542 | − | 12.4542i | −0.930872 | − | 0.930872i | 0.0668885 | − | 0.997760i | \(-0.478693\pi\) |
−0.997760 | + | 0.0668885i | \(0.978693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.12083 | + | 9.12083i | −0.677946 | + | 0.677946i | −0.959535 | − | 0.281589i | \(-0.909139\pi\) |
0.281589 | + | 0.959535i | \(0.409139\pi\) | |||||||
\(182\) | 2.31417 | − | 3.93207i | 0.171537 | − | 0.291465i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.76503 | − | 15.6045i | −0.277561 | − | 1.15038i | ||||
\(185\) | −4.50653 | + | 7.80554i | −0.331327 | + | 0.573875i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.08587 | − | 4.05252i | 0.0794066 | − | 0.296349i | ||||
\(188\) | −9.72929 | − | 5.83594i | −0.709582 | − | 0.425630i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.10210 | + | 1.96670i | 0.515240 | + | 0.142679i | ||||
\(191\) | −1.76985 | − | 3.06547i | −0.128062 | − | 0.221810i | 0.794864 | − | 0.606788i | \(-0.207542\pi\) |
−0.922926 | + | 0.384978i | \(0.874209\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.43004 | − | 12.8692i | 0.534826 | − | 0.926346i | −0.464346 | − | 0.885654i | \(-0.653711\pi\) |
0.999172 | − | 0.0406916i | \(-0.0129561\pi\) | |||||||
\(194\) | 1.76533 | − | 1.73610i | 0.126743 | − | 0.124644i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.0303489 | − | 1.81743i | 0.00216778 | − | 0.129816i | ||||
\(197\) | −11.9105 | − | 11.9105i | −0.848589 | − | 0.848589i | 0.141368 | − | 0.989957i | \(-0.454850\pi\) |
−0.989957 | + | 0.141368i | \(0.954850\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.5983 | 1.10574 | 0.552868 | − | 0.833269i | \(-0.313533\pi\) | ||||
0.552868 | + | 0.833269i | \(0.313533\pi\) | |||||||
\(200\) | 4.49106 | + | 1.32478i | 0.317566 | + | 0.0936757i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.19529 | + | 0.00997929i | 0.0841003 | + | 0.000702140i | ||||
\(203\) | −4.08272 | − | 15.2369i | −0.286551 | − | 1.06942i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.47677 | − | 5.51137i | 0.103142 | − | 0.384931i | ||||
\(206\) | −14.4563 | − | 4.00319i | −1.00722 | − | 0.278916i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.33498 | + | 4.39026i | −0.0925643 | + | 0.304409i | ||||
\(209\) | 14.8029 | − | 8.54648i | 1.02394 | − | 0.591172i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.18049 | − | 15.6018i | −0.287797 | − | 1.07407i | −0.946771 | − | 0.321907i | \(-0.895676\pi\) |
0.658975 | − | 0.752165i | \(-0.270990\pi\) | |||||||
\(212\) | −12.1180 | − | 3.46487i | −0.832268 | − | 0.237968i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.0295 | + | 6.49124i | 0.753960 | + | 0.443732i | ||||
\(215\) | − | 13.4344i | − | 0.916220i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.7407i | − | 1.13643i | ||||||
\(218\) | −1.54793 | + | 2.63014i | −0.104839 | + | 0.178136i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −19.1824 | + | 10.6520i | −1.29328 | + | 0.718155i | ||||
\(221\) | −0.207655 | − | 0.774977i | −0.0139684 | − | 0.0521306i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.9254 | − | 8.03982i | 0.932512 | − | 0.538386i | 0.0449068 | − | 0.998991i | \(-0.485701\pi\) |
0.887605 | + | 0.460605i | \(0.152368\pi\) | |||||||
\(224\) | 3.47259 | + | 15.5249i | 0.232023 | + | 1.03730i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.50680 | − | 9.05251i | 0.166750 | − | 0.602164i | ||||
\(227\) | −2.85895 | + | 10.6697i | −0.189755 | + | 0.708176i | 0.803807 | + | 0.594890i | \(0.202804\pi\) |
−0.993562 | + | 0.113286i | \(0.963862\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.104652 | + | 0.390566i | 0.00691559 | + | 0.0258093i | 0.969297 | − | 0.245891i | \(-0.0790806\pi\) |
−0.962382 | + | 0.271701i | \(0.912414\pi\) | |||||||
\(230\) | 0.122542 | − | 14.6777i | 0.00808018 | − | 0.967821i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.58596 | + | 13.9339i | 0.498043 | + | 0.914805i | ||||
\(233\) | −11.6252 | −0.761590 | −0.380795 | − | 0.924659i | \(-0.624350\pi\) | ||||
−0.380795 | + | 0.924659i | \(0.624350\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.33569 | − | 7.33569i | −0.478528 | − | 0.478528i | ||||
\(236\) | −19.6586 | − | 20.3263i | −1.27967 | − | 1.32313i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.95035 | − | 1.98319i | −0.126422 | − | 0.128551i | ||||
\(239\) | 1.55685 | − | 2.69654i | 0.100704 | − | 0.174425i | −0.811271 | − | 0.584671i | \(-0.801224\pi\) |
0.911975 | + | 0.410246i | \(0.134557\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.16669 | − | 12.4131i | −0.461647 | − | 0.799596i | 0.537396 | − | 0.843330i | \(-0.319408\pi\) |
−0.999043 | + | 0.0437337i | \(0.986075\pi\) | |||||||
\(242\) | −9.43029 | + | 34.0545i | −0.606202 | + | 2.18911i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.64989 | + | 26.5856i | 0.425716 | + | 1.70197i | ||||
\(245\) | 0.430181 | − | 1.60546i | 0.0274833 | − | 0.102569i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.63437 | − | 2.83082i | 0.103993 | − | 0.180121i | ||||
\(248\) | 3.94905 | + | 16.3672i | 0.250765 | + | 1.03932i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.8347 | + | 8.73075i | 0.938228 | + | 0.552181i | ||||
\(251\) | −3.06176 | + | 3.06176i | −0.193257 | + | 0.193257i | −0.797102 | − | 0.603845i | \(-0.793635\pi\) |
0.603845 | + | 0.797102i | \(0.293635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.0739 | − | 24.0739i | −1.51351 | − | 1.51351i | ||||
\(254\) | 18.9233 | − | 4.90154i | 1.18735 | − | 0.307550i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.05739 | − | 14.3594i | −0.441087 | − | 0.897464i | ||||
\(257\) | −2.78074 | − | 1.60546i | −0.173458 | − | 0.100146i | 0.410757 | − | 0.911745i | \(-0.365264\pi\) |
−0.584215 | + | 0.811599i | \(0.698598\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.3877 | + | 3.58722i | 0.831870 | + | 0.222899i | ||||
\(260\) | −2.15836 | + | 3.59827i | −0.133856 | + | 0.223155i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.47791 | − | 11.4396i | −0.400207 | − | 0.706739i | ||||
\(263\) | −2.63762 | + | 1.52283i | −0.162643 | + | 0.0939018i | −0.579112 | − | 0.815248i | \(-0.696601\pi\) |
0.416469 | + | 0.909150i | \(0.363267\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.98076 | − | 5.76240i | −0.613113 | − | 0.353981i | ||||
\(266\) | 0.0946086 | − | 11.3319i | 0.00580082 | − | 0.694806i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −18.5629 | − | 19.1934i | −1.13391 | − | 1.17242i | ||||
\(269\) | 1.99648 | − | 1.99648i | 0.121727 | − | 0.121727i | −0.643619 | − | 0.765346i | \(-0.722568\pi\) |
0.765346 | + | 0.643619i | \(0.222568\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.9357i | 0.846534i | 0.906005 | + | 0.423267i | \(0.139117\pi\) | ||||
−0.906005 | + | 0.423267i | \(0.860883\pi\) | |||||||
\(272\) | 2.37466 | + | 1.47887i | 0.143985 | + | 0.0896695i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0313 | − | 11.8320i | 0.726835 | − | 0.714799i | ||||
\(275\) | 9.59256 | − | 2.57032i | 0.578453 | − | 0.154996i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.2253 | + | 8.09885i | 1.81606 | + | 0.486613i | 0.996289 | − | 0.0860738i | \(-0.0274321\pi\) |
0.819774 | + | 0.572686i | \(0.194099\pi\) | |||||||
\(278\) | 0.870867 | + | 1.53790i | 0.0522311 | + | 0.0922368i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.364301 | + | 14.5423i | −0.0217712 | + | 0.869068i | ||||
\(281\) | 11.3745 | + | 19.7012i | 0.678544 | + | 1.17527i | 0.975419 | + | 0.220357i | \(0.0707222\pi\) |
−0.296875 | + | 0.954916i | \(0.595944\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.36412 | + | 0.633463i | −0.140532 | + | 0.0376555i | −0.328399 | − | 0.944539i | \(-0.606509\pi\) |
0.187867 | + | 0.982194i | \(0.439843\pi\) | |||||||
\(284\) | −7.00932 | − | 12.6226i | −0.415927 | − | 0.749016i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.44035 | + | 9.42143i | 0.144301 | + | 0.557101i | ||||
\(287\) | −8.77415 | −0.517921 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5109 | 0.971228 | ||||||||
\(290\) | 3.63759 | + | 14.0436i | 0.213606 | + | 0.824668i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.64623 | − | 6.56626i | −0.213379 | − | 0.384261i | ||||
\(293\) | −7.53030 | + | 2.01774i | −0.439925 | + | 0.117877i | −0.471981 | − | 0.881609i | \(-0.656461\pi\) |
0.0320565 | + | 0.999486i | \(0.489794\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.9285 | − | 22.3929i | −0.752728 | − | 1.30376i | ||||
\(296\) | −13.9352 | − | 0.349094i | −0.809968 | − | 0.0202907i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.50641 | + | 4.42616i | 0.145192 | + | 0.256400i | ||||
\(299\) | −6.28881 | − | 1.68508i | −0.363691 | − | 0.0974508i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.9550 | + | 5.34693i | −1.15019 | + | 0.308192i | ||||
\(302\) | 10.9528 | − | 10.7714i | 0.630264 | − | 0.619827i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.58066 | + | 11.1015i | 0.148011 | + | 0.636712i | ||||
\(305\) | 25.0589i | 1.43487i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.0831 | + | 24.0831i | −1.37450 | + | 1.37450i | −0.520843 | + | 0.853652i | \(0.674382\pi\) |
−0.853652 | + | 0.520843i | \(0.825618\pi\) | |||||||
\(308\) | 23.4567 | + | 24.2534i | 1.33657 | + | 1.38197i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.128532 | + | 15.3952i | −0.00730011 | + | 0.874386i | ||||
\(311\) | −9.09165 | − | 5.24907i | −0.515540 | − | 0.297647i | 0.219568 | − | 0.975597i | \(-0.429535\pi\) |
−0.735108 | + | 0.677950i | \(0.762869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.1380 | + | 11.0493i | −1.08174 | + | 0.624544i | −0.931366 | − | 0.364085i | \(-0.881382\pi\) |
−0.150376 | + | 0.988629i | \(0.548048\pi\) | |||||||
\(314\) | −6.87522 | − | 12.1412i | −0.387991 | − | 0.685167i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.52038 | − | 5.86895i | 0.198037 | − | 0.330154i | ||||
\(317\) | 21.3323 | + | 5.71597i | 1.19814 | + | 0.321041i | 0.802099 | − | 0.597192i | \(-0.203717\pi\) |
0.396042 | + | 0.918232i | \(0.370383\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.1405 | + | 16.8243i | 1.63155 | + | 0.941978i | ||||
\(320\) | −3.07429 | − | 14.3038i | −0.171858 | − | 0.799607i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −21.8505 | + | 5.65974i | −1.21768 | + | 0.315405i | ||||
\(323\) | −1.40911 | − | 1.40911i | −0.0784050 | − | 0.0784050i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.34289 | − | 1.34289i | 0.0744900 | − | 0.0744900i | ||||
\(326\) | −6.32064 | − | 3.71992i | −0.350068 | − | 0.206028i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.57840 | − | 2.06978i | 0.473663 | − | 0.114285i | ||||
\(329\) | −7.97655 | + | 13.8158i | −0.439761 | + | 0.761689i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.848686 | + | 3.16734i | −0.0466480 | + | 0.174093i | −0.985320 | − | 0.170720i | \(-0.945391\pi\) |
0.938672 | + | 0.344812i | \(0.112057\pi\) | |||||||
\(332\) | −0.578908 | − | 2.31442i | −0.0317717 | − | 0.127020i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.59401 | + | 27.4233i | −0.415525 | + | 1.50054i | ||||
\(335\) | −12.2079 | − | 21.1447i | −0.666990 | − | 1.15526i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5710 | + | 20.0416i | −0.630315 | + | 1.09174i | 0.357172 | + | 0.934038i | \(0.383741\pi\) |
−0.987487 | + | 0.157699i | \(0.949593\pi\) | |||||||
\(338\) | −11.5860 | − | 11.7811i | −0.630196 | − | 0.640808i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.77836 | + | 1.83877i | 0.0964453 | + | 0.0997210i | ||||
\(341\) | 25.2506 | + | 25.2506i | 1.36739 | + | 1.36739i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.1300 | 0.924931 | ||||||||
\(344\) | 18.2485 | − | 9.93494i | 0.983894 | − | 0.535656i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.123544 | + | 14.7977i | −0.00664175 | + | 0.795530i | ||||
\(347\) | −2.03374 | − | 7.59002i | −0.109177 | − | 0.407454i | 0.889609 | − | 0.456724i | \(-0.150977\pi\) |
−0.998785 | + | 0.0492700i | \(0.984311\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.62138 | + | 20.9793i | −0.300905 | + | 1.12299i | 0.635508 | + | 0.772095i | \(0.280791\pi\) |
−0.936413 | + | 0.350900i | \(0.885876\pi\) | |||||||
\(350\) | 1.75711 | − | 6.34525i | 0.0939216 | − | 0.339168i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −28.6547 | − | 18.1790i | −1.52730 | − | 0.968943i | ||||
\(353\) | 0.108858 | − | 0.0628489i | 0.00579390 | − | 0.00334511i | −0.497100 | − | 0.867693i | \(-0.665602\pi\) |
0.502894 | + | 0.864348i | \(0.332269\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.41701 | − | 12.7525i | −0.181356 | − | 0.676831i | ||||
\(356\) | 0.685126 | − | 0.380449i | 0.0363116 | − | 0.0201638i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.6339 | − | 21.4666i | 0.667721 | − | 1.13455i | ||||
\(359\) | − | 4.07414i | − | 0.215025i | −0.994204 | − | 0.107512i | \(-0.965711\pi\) | ||
0.994204 | − | 0.107512i | \(-0.0342886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.8811i | 0.572691i | ||||||||
\(362\) | −15.7210 | − | 9.25240i | −0.826280 | − | 0.486295i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.20377 | + | 1.77383i | 0.325166 | + | 0.0929738i | ||||
\(365\) | −1.77752 | − | 6.63379i | −0.0930396 | − | 0.347229i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.96310 | + | 2.86545i | −0.259072 | + | 0.149575i | −0.623911 | − | 0.781495i | \(-0.714457\pi\) |
0.364839 | + | 0.931071i | \(0.381124\pi\) | |||||||
\(368\) | 20.0280 | − | 10.6879i | 1.04403 | − | 0.557147i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.2841 | − | 3.40168i | −0.638620 | − | 0.176845i | ||||
\(371\) | −4.58689 | + | 17.1185i | −0.238139 | + | 0.888748i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.28955 | − | 19.7409i | −0.273882 | − | 1.02214i | −0.956587 | − | 0.291448i | \(-0.905863\pi\) |
0.682704 | − | 0.730695i | \(-0.260804\pi\) | |||||||
\(374\) | 5.93309 | + | 0.0495344i | 0.306793 | + | 0.00256136i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.53951 | − | 15.3892i | 0.234108 | − | 0.793637i | ||||
\(377\) | 6.43473 | 0.331405 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.85273 | − | 2.85273i | −0.146535 | − | 0.146535i | 0.630033 | − | 0.776568i | \(-0.283041\pi\) |
−0.776568 | + | 0.630033i | \(0.783041\pi\) | |||||||
\(380\) | −0.174009 | + | 10.4204i | −0.00892647 | + | 0.534556i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.56913 | − | 3.51003i | 0.182612 | − | 0.179589i | ||||
\(383\) | 7.78731 | − | 13.4880i | 0.397913 | − | 0.689206i | −0.595555 | − | 0.803314i | \(-0.703068\pi\) |
0.993468 | + | 0.114109i | \(0.0364012\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.4263 | + | 26.7192i | 0.786200 | + | 1.36174i | ||||
\(386\) | 20.2531 | + | 5.60845i | 1.03086 | + | 0.285462i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.00278 | + | 1.80116i | 0.152443 | + | 0.0914401i | ||||
\(389\) | 7.22357 | − | 26.9587i | 0.366250 | − | 1.36686i | −0.499469 | − | 0.866332i | \(-0.666471\pi\) |
0.865719 | − | 0.500531i | \(-0.166862\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.98460 | + | 3.43743i | −0.100366 | + | 0.173838i | ||||
\(392\) | 2.49888 | − | 0.602926i | 0.126213 | − | 0.0304524i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0823 | − | 20.5295i | 0.608699 | − | 1.03426i | ||||
\(395\) | 4.42507 | − | 4.42507i | 0.222649 | − | 0.222649i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.4204 | + | 27.4204i | 1.37619 | + | 1.37619i | 0.850961 | + | 0.525230i | \(0.176021\pi\) |
0.525230 | + | 0.850961i | \(0.323979\pi\) | |||||||
\(398\) | 5.53130 | + | 21.3546i | 0.277259 | + | 1.07041i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.221094 | + | 6.61819i | −0.0110547 | + | 0.330910i | ||||
\(401\) | 14.6316 | + | 8.44757i | 0.730669 | + | 0.421852i | 0.818667 | − | 0.574269i | \(-0.194714\pi\) |
−0.0879981 | + | 0.996121i | \(0.528047\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.59620 | + | 1.76745i | 0.328580 | + | 0.0880428i | ||||
\(404\) | 0.410198 | + | 1.63993i | 0.0204081 | + | 0.0815896i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.4121 | − | 10.9925i | 0.963405 | − | 0.545549i | ||||
\(407\) | −25.6038 | + | 14.7824i | −1.26913 | + | 0.732735i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9737 | + | 8.64508i | 0.740402 | + | 0.427471i | 0.822216 | − | 0.569176i | \(-0.192738\pi\) |
−0.0818133 | + | 0.996648i | \(0.526071\pi\) | |||||||
\(410\) | 8.06893 | + | 0.0673662i | 0.398496 | + | 0.00332698i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.354194 | − | 21.2107i | 0.0174499 | − | 1.04497i | ||||
\(413\) | −28.1160 | + | 28.1160i | −1.38350 | + | 1.38350i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.18151i | − | 0.107086i | ||||||
\(416\) | −6.48380 | − | 0.270812i | −0.317895 | − | 0.0132777i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.9497 | + | 17.2351i | 0.829035 | + | 0.842995i | ||||
\(419\) | −2.94162 | + | 0.788205i | −0.143708 | + | 0.0385063i | −0.329956 | − | 0.943996i | \(-0.607034\pi\) |
0.186248 | + | 0.982503i | \(0.440367\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.89561 | + | 2.38357i | 0.433546 | + | 0.116168i | 0.468990 | − | 0.883203i | \(-0.344618\pi\) |
−0.0354445 | + | 0.999372i | \(0.511285\pi\) | |||||||
\(422\) | 19.8769 | − | 11.2558i | 0.967595 | − | 0.547922i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.446378 | − | 17.8186i | 0.0216780 | − | 0.865349i | ||||
\(425\) | −0.578900 | − | 1.00268i | −0.0280808 | − | 0.0486373i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37.2216 | − | 9.97350i | 1.80128 | − | 0.482651i | ||||
\(428\) | −4.97559 | + | 17.4016i | −0.240504 | + | 0.841137i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.3922 | − | 4.76396i | 0.886950 | − | 0.229739i | ||||
\(431\) | 7.28002 | 0.350666 | 0.175333 | − | 0.984509i | \(-0.443900\pi\) | ||||
0.175333 | + | 0.984509i | \(0.443900\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.9763 | −0.960002 | −0.480001 | − | 0.877268i | \(-0.659364\pi\) | ||||
−0.480001 | + | 0.877268i | \(0.659364\pi\) | |||||||
\(434\) | 22.9186 | − | 5.93638i | 1.10013 | − | 0.284956i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.14966 | − | 1.18650i | −0.198733 | − | 0.0568232i | ||||
\(437\) | −15.6201 | + | 4.18539i | −0.747210 | + | 0.200214i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.3133 | + | 26.5235i | 0.730866 | + | 1.26590i | 0.956513 | + | 0.291688i | \(0.0942170\pi\) |
−0.225647 | + | 0.974209i | \(0.572450\pi\) | |||||||
\(440\) | −21.3852 | − | 22.4841i | −1.01950 | − | 1.07189i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.987334 | − | 0.559099i | 0.0469627 | − | 0.0265937i | ||||
\(443\) | −28.7698 | − | 7.70884i | −1.36689 | − | 0.366258i | −0.500550 | − | 0.865708i | \(-0.666869\pi\) |
−0.866343 | + | 0.499450i | \(0.833536\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.692173 | − | 0.185467i | 0.0328121 | − | 0.00879199i | ||||
\(446\) | 15.9448 | + | 16.2133i | 0.755010 | + | 0.767723i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −20.0228 | + | 10.2594i | −0.945987 | + | 0.484710i | ||||
\(449\) | − | 26.8028i | − | 1.26490i | −0.774599 | − | 0.632452i | \(-0.782048\pi\) | ||
0.774599 | − | 0.632452i | \(-0.217952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.2344 | − | 13.2344i | 0.623181 | − | 0.623181i | ||||
\(452\) | 13.2821 | + | 0.221796i | 0.624739 | + | 0.0104324i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.6211 | − | 0.130418i | −0.733132 | − | 0.00612080i | ||||
\(455\) | 5.10961 | + | 2.95004i | 0.239542 | + | 0.138300i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.25342 | − | 1.87837i | 0.152189 | − | 0.0878662i | −0.421972 | − | 0.906609i | \(-0.638662\pi\) |
0.574161 | + | 0.818743i | \(0.305329\pi\) | |||||||
\(458\) | −0.497588 | + | 0.281770i | −0.0232507 | + | 0.0131662i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 20.1378 | − | 5.03708i | 0.938928 | − | 0.234855i | ||||
\(461\) | −3.92641 | − | 1.05208i | −0.182871 | − | 0.0490002i | 0.166221 | − | 0.986088i | \(-0.446843\pi\) |
−0.349092 | + | 0.937088i | \(0.613510\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.2888 | − | 11.7137i | −0.942899 | − | 0.544383i | −0.0520310 | − | 0.998645i | \(-0.516569\pi\) |
−0.890868 | + | 0.454263i | \(0.849903\pi\) | |||||||
\(464\) | −16.3859 | + | 15.3265i | −0.760697 | + | 0.711515i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.12238 | − | 15.9153i | −0.190966 | − | 0.737260i | ||||
\(467\) | 13.2570 | + | 13.2570i | 0.613463 | + | 0.613463i | 0.943847 | − | 0.330384i | \(-0.107178\pi\) |
−0.330384 | + | 0.943847i | \(0.607178\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.5489 | + | 26.5489i | −1.22591 | + | 1.22591i | ||||
\(470\) | 7.44151 | − | 12.6441i | 0.343251 | − | 0.583229i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 20.8563 | − | 34.1211i | 0.959988 | − | 1.57055i | ||||
\(473\) | 22.0339 | − | 38.1638i | 1.01312 | − | 1.75477i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.22086 | − | 4.55631i | 0.0560169 | − | 0.209058i | ||||
\(476\) | 2.02344 | − | 3.37335i | 0.0927443 | − | 0.154617i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.24372 | + | 1.17516i | 0.194103 | + | 0.0537506i | ||||
\(479\) | 17.6429 | + | 30.5584i | 0.806124 | + | 1.39625i | 0.915529 | + | 0.402251i | \(0.131772\pi\) |
−0.109405 | + | 0.993997i | \(0.534895\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.82689 | + | 4.89631i | −0.128895 | + | 0.223252i | ||||
\(482\) | 14.4525 | − | 14.2132i | 0.658295 | − | 0.647394i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −49.9658 | − | 0.834372i | −2.27117 | − | 0.0379260i | ||||
\(485\) | 2.26403 | + | 2.26403i | 0.102804 | + | 0.102804i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.1433 | −0.550266 | −0.275133 | − | 0.961406i | \(-0.588722\pi\) | ||||
−0.275133 | + | 0.961406i | \(0.588722\pi\) | |||||||
\(488\) | −34.0385 | + | 18.5314i | −1.54085 | + | 0.838878i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.35047 | + | 0.0196237i | 0.106183 | + | 0.000886509i | ||||
\(491\) | 0.200028 | + | 0.746514i | 0.00902713 | + | 0.0336897i | 0.970293 | − | 0.241935i | \(-0.0777820\pi\) |
−0.961265 | + | 0.275625i | \(0.911115\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.01532 | − | 3.78924i | 0.0457279 | − | 0.170659i | ||||
\(494\) | 4.45505 | + | 1.23368i | 0.200442 | + | 0.0555059i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.0069 | + | 11.2103i | −0.943237 | + | 0.503359i | ||||
\(497\) | −17.5821 | + | 10.1510i | −0.788664 | + | 0.455335i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.210439 | − | 0.785369i | −0.00942054 | − | 0.0351579i | 0.961056 | − | 0.276355i | \(-0.0891266\pi\) |
−0.970476 | + | 0.241197i | \(0.922460\pi\) | |||||||
\(500\) | −6.69218 | + | 23.4052i | −0.299283 | + | 1.04671i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.27738 | − | 3.10593i | −0.235541 | − | 0.138624i | ||||
\(503\) | − | 5.40486i | − | 0.240991i | −0.992714 | − | 0.120495i | \(-0.961552\pi\) | ||
0.992714 | − | 0.120495i | \(-0.0384483\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.54576i | 0.0687852i | ||||||||
\(506\) | 24.4211 | − | 41.4947i | 1.08565 | − | 1.84467i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.4207 | + | 24.1685i | 0.595449 | + | 1.07231i | ||||
\(509\) | 7.42301 | + | 27.7030i | 0.329019 | + | 1.22792i | 0.910210 | + | 0.414148i | \(0.135920\pi\) |
−0.581191 | + | 0.813768i | \(0.697413\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.14614 | + | 5.28052i | −0.404601 | + | 0.233597i | ||||
\(512\) | 17.1559 | − | 14.7538i | 0.758192 | − | 0.652031i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.21186 | − | 4.37624i | 0.0534528 | − | 0.193028i | ||||
\(515\) | 5.02052 | − | 18.7368i | 0.221231 | − | 0.825644i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.80753 | − | 32.8701i | −0.387355 | − | 1.44563i | ||||
\(518\) | −0.163639 | + | 19.6002i | −0.00718989 | + | 0.861185i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.69152 | − | 1.67889i | −0.249590 | − | 0.0736241i | ||||
\(521\) | −12.8208 | −0.561689 | −0.280845 | − | 0.959753i | \(-0.590615\pi\) | ||||
−0.280845 | + | 0.959753i | \(0.590615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.08204 | − | 2.08204i | −0.0910411 | − | 0.0910411i | 0.660120 | − | 0.751161i | \(-0.270506\pi\) |
−0.751161 | + | 0.660120i | \(0.770506\pi\) | |||||||
\(524\) | 13.3640 | − | 12.9250i | 0.583811 | − | 0.564633i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.02013 | − | 3.07098i | −0.131684 | − | 0.133901i | ||||
\(527\) | 2.08161 | − | 3.60545i | 0.0906762 | − | 0.157056i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.60471 | + | 7.97560i | 0.200205 | + | 0.346765i | ||||
\(530\) | 4.34965 | − | 15.7074i | 0.188937 | − | 0.682285i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.5474 | − | 3.88888i | 0.674063 | − | 0.168604i | ||||
\(533\) | 0.926356 | − | 3.45721i | 0.0401249 | − | 0.149748i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.27485 | + | 14.3325i | −0.357753 | + | 0.619647i | ||||
\(536\) | 19.6938 | − | 32.2193i | 0.850643 | − | 1.39166i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.44121 | + | 2.02528i | 0.148361 | + | 0.0873158i | ||||
\(539\) | 3.85515 | − | 3.85515i | 0.166053 | − | 0.166053i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.7002 | + | 22.7002i | 0.975956 | + | 0.975956i | 0.999718 | − | 0.0237613i | \(-0.00756417\pi\) |
−0.0237613 | + | 0.999718i | \(0.507564\pi\) | |||||||
\(542\) | −19.0785 | + | 4.94172i | −0.819490 | + | 0.212265i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.18254 | + | 3.77541i | −0.0507011 | + | 0.161869i | ||||
\(545\) | −3.41779 | − | 1.97326i | −0.146402 | − | 0.0845253i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.9084 | + | 5.33444i | 0.851222 | + | 0.228084i | 0.657951 | − | 0.753061i | \(-0.271424\pi\) |
0.193271 | + | 0.981145i | \(0.438090\pi\) | |||||||
\(548\) | 20.4648 | + | 12.2755i | 0.874214 | + | 0.524382i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.92045 | + | 12.2211i | 0.295089 | + | 0.521109i | ||||
\(551\) | 13.8413 | − | 7.99125i | 0.589657 | − | 0.340439i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.33402 | − | 4.81165i | −0.354399 | − | 0.204612i | ||||
\(554\) | −0.369448 | + | 44.2514i | −0.0156963 | + | 1.88006i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.79661 | + | 1.73760i | −0.0761934 | + | 0.0736905i | ||||
\(557\) | −10.7551 | + | 10.7551i | −0.455708 | + | 0.455708i | −0.897244 | − | 0.441535i | \(-0.854434\pi\) |
0.441535 | + | 0.897244i | \(0.354434\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.42723i | − | 0.356434i | ||||||
\(560\) | −20.0381 | + | 4.65807i | −0.846763 | + | 0.196840i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −22.9381 | + | 22.5582i | −0.967585 | + | 0.951562i | ||||
\(563\) | 20.7659 | − | 5.56420i | 0.875177 | − | 0.234503i | 0.206852 | − | 0.978372i | \(-0.433678\pi\) |
0.668325 | + | 0.743869i | \(0.267012\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.7330 | + | 3.14385i | 0.493611 | + | 0.132263i | ||||
\(566\) | −1.70557 | − | 3.01192i | −0.0716904 | − | 0.126601i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.7953 | − | 14.0721i | 0.620795 | − | 0.590452i | ||||
\(569\) | 1.88272 | + | 3.26097i | 0.0789277 | + | 0.136707i | 0.902788 | − | 0.430087i | \(-0.141517\pi\) |
−0.823860 | + | 0.566794i | \(0.808184\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.3264 | − | 4.37466i | 0.683241 | − | 0.183074i | 0.0995287 | − | 0.995035i | \(-0.468266\pi\) |
0.583712 | + | 0.811961i | \(0.301600\pi\) | |||||||
\(572\) | −12.0329 | + | 6.68183i | −0.503120 | + | 0.279381i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.11139 | − | 12.0121i | −0.129867 | − | 0.501375i | ||||
\(575\) | −9.39535 | −0.391813 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.76787 | −0.406642 | −0.203321 | − | 0.979112i | \(-0.565173\pi\) | ||||
−0.203321 | + | 0.979112i | \(0.565173\pi\) | |||||||
\(578\) | 5.85489 | + | 22.6039i | 0.243531 | + | 0.940200i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −17.9362 | + | 9.95995i | −0.744762 | + | 0.413565i | ||||
\(581\) | −3.24034 | + | 0.868246i | −0.134432 | + | 0.0360209i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.9019 | − | 32.7390i | −0.782835 | − | 1.35591i | ||||
\(584\) | 7.69644 | − | 7.32026i | 0.318481 | − | 0.302914i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.43266 | − | 9.59372i | −0.224421 | − | 0.396313i | ||||
\(587\) | 22.1733 | + | 5.94132i | 0.915190 | + | 0.245224i | 0.685528 | − | 0.728046i | \(-0.259571\pi\) |
0.229662 | + | 0.973271i | \(0.426238\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.3836 | − | 4.38996i | 0.675073 | − | 0.180885i | ||||
\(590\) | 26.0720 | − | 25.6403i | 1.07337 | − | 1.05559i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.46362 | − | 19.2016i | −0.183454 | − | 0.789180i | ||||
\(593\) | − | 1.37926i | − | 0.0566394i | −0.999599 | − | 0.0283197i | \(-0.990984\pi\) | ||
0.999599 | − | 0.0283197i | \(-0.00901564\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.54344 | − | 2.54344i | 0.104271 | − | 0.104271i | ||||
\(596\) | −5.17076 | + | 5.00091i | −0.211803 | + | 0.204845i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.0768689 | − | 9.20714i | 0.00314340 | − | 0.376508i | ||||
\(599\) | −26.6820 | − | 15.4049i | −1.09020 | − | 0.629425i | −0.156568 | − | 0.987667i | \(-0.550043\pi\) |
−0.933629 | + | 0.358242i | \(0.883376\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.43951 | + | 1.40845i | −0.0995098 | + | 0.0574520i | −0.548929 | − | 0.835869i | \(-0.684964\pi\) |
0.449419 | + | 0.893321i | \(0.351631\pi\) | |||||||
\(602\) | −14.3963 | − | 25.4230i | −0.586751 | − | 1.03616i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.6304 | + | 11.1751i | 0.758062 | + | 0.454710i | ||||
\(605\) | −44.1382 | − | 11.8268i | −1.79447 | − | 0.480828i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.2297 | − | 15.1437i | −1.06463 | − | 0.614666i | −0.137922 | − | 0.990443i | \(-0.544042\pi\) |
−0.926710 | + | 0.375777i | \(0.877376\pi\) | |||||||
\(608\) | −14.2831 | + | 7.46968i | −0.579258 | + | 0.302935i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −34.3065 | + | 8.88610i | −1.38903 | + | 0.359788i | ||||
\(611\) | −4.60158 | − | 4.60158i | −0.186160 | − | 0.186160i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.66344 | − | 3.66344i | 0.147965 | − | 0.147965i | −0.629243 | − | 0.777208i | \(-0.716635\pi\) |
0.777208 | + | 0.629243i | \(0.216635\pi\) | |||||||
\(614\) | −41.5107 | − | 24.4305i | −1.67523 | − | 0.985935i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −24.8858 | + | 40.7134i | −1.00268 | + | 1.64039i | ||||
\(617\) | −13.2053 | + | 22.8722i | −0.531624 | + | 0.920799i | 0.467695 | + | 0.883890i | \(0.345085\pi\) |
−0.999319 | + | 0.0369091i | \(0.988249\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.6542 | + | 47.2262i | −0.508617 | + | 1.89818i | −0.0747583 | + | 0.997202i | \(0.523819\pi\) |
−0.433858 | + | 0.900981i | \(0.642848\pi\) | |||||||
\(620\) | −21.1221 | + | 5.28329i | −0.848282 | + | 0.212182i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.96218 | − | 14.3081i | 0.158869 | − | 0.573704i | ||||
\(623\) | −0.550972 | − | 0.954312i | −0.0220742 | − | 0.0382337i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.99103 | + | 12.1088i | −0.279641 | + | 0.484353i | ||||
\(626\) | −21.9134 | − | 22.2823i | −0.875834 | − | 0.890582i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.1837 | − | 13.7178i | 0.565991 | − | 0.547399i | ||||
\(629\) | 2.43726 | + | 2.43726i | 0.0971799 | + | 0.0971799i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.5500 | −1.45503 | −0.727516 | − | 0.686090i | \(-0.759325\pi\) | ||||
−0.727516 | + | 0.686090i | \(0.759325\pi\) | |||||||
\(632\) | 9.28314 | + | 2.73834i | 0.369264 | + | 0.108926i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.260747 | + | 31.2315i | −0.0103556 | + | 1.24036i | ||||
\(635\) | 6.54255 | + | 24.4171i | 0.259633 | + | 0.968964i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.269847 | − | 1.00708i | 0.0106917 | − | 0.0399020i | ||||
\(638\) | −12.6995 | + | 45.8603i | −0.502779 | + | 1.81563i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.4922 | − | 9.28105i | 0.730969 | − | 0.366866i | ||||
\(641\) | 5.95425 | − | 3.43769i | 0.235179 | − | 0.135780i | −0.377780 | − | 0.925895i | \(-0.623312\pi\) |
0.612959 | + | 0.790115i | \(0.289979\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.59808 | − | 28.3564i | −0.299639 | − | 1.11827i | −0.937463 | − | 0.348086i | \(-0.886832\pi\) |
0.637823 | − | 0.770183i | \(-0.279835\pi\) | |||||||
\(644\) | −15.4968 | − | 27.9071i | −0.610658 | − | 1.09969i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.42944 | − | 2.42880i | 0.0562405 | − | 0.0955599i | ||||
\(647\) | 1.90726i | 0.0749821i | 0.999297 | + | 0.0374911i | \(0.0119366\pi\) | ||||
−0.999297 | + | 0.0374911i | \(0.988063\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 84.8166i | − | 3.32934i | ||||||
\(650\) | 2.31466 | + | 1.36226i | 0.0907884 | + | 0.0534322i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.85135 | − | 9.97229i | 0.111667 | − | 0.390545i | ||||
\(653\) | 5.94070 | + | 22.1710i | 0.232478 | + | 0.867618i | 0.979270 | + | 0.202560i | \(0.0649263\pi\) |
−0.746792 | + | 0.665057i | \(0.768407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.7228 | − | 8.50019i | 0.575266 | − | 0.332130i | ||||
\(656\) | 5.87558 | + | 11.0102i | 0.229403 | + | 0.429874i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −21.7428 | − | 6.02097i | −0.847624 | − | 0.234722i | ||||
\(659\) | 3.86006 | − | 14.4059i | 0.150366 | − | 0.561175i | −0.849091 | − | 0.528246i | \(-0.822850\pi\) |
0.999458 | − | 0.0329291i | \(-0.0104835\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.76236 | + | 36.4336i | 0.379712 | + | 1.41710i | 0.846337 | + | 0.532648i | \(0.178803\pi\) |
−0.466625 | + | 0.884455i | \(0.654530\pi\) | |||||||
\(662\) | −4.63715 | − | 0.0387148i | −0.180228 | − | 0.00150469i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.96323 | − | 1.61326i | 0.114996 | − | 0.0626065i | ||||
\(665\) | 14.6545 | 0.568278 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.5099 | − | 22.5099i | −0.871586 | − | 0.871586i | ||||
\(668\) | −40.2364 | − | 0.671901i | −1.55679 | − | 0.0259966i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.6188 | − | 24.2112i | 0.951109 | − | 0.935359i | ||||
\(671\) | −41.0993 | + | 71.1860i | −1.58662 | + | 2.74811i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.2966 | − | 19.5664i | −0.435454 | − | 0.754228i | 0.561879 | − | 0.827220i | \(-0.310079\pi\) |
−0.997333 | + | 0.0729916i | \(0.976745\pi\) | |||||||
\(674\) | −31.5409 | − | 8.73421i | −1.21491 | − | 0.336429i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.0202 | − | 20.0393i | 0.462317 | − | 0.770743i | ||||
\(677\) | −8.14191 | + | 30.3860i | −0.312919 | + | 1.16783i | 0.612992 | + | 0.790089i | \(0.289966\pi\) |
−0.925911 | + | 0.377741i | \(0.876701\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.46182 | − | 4.26400i | 0.0944760 | − | 0.163637i | ||||
\(680\) | −1.88671 | + | 3.08668i | −0.0723520 | + | 0.118369i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −25.6148 | + | 43.5229i | −0.980841 | + | 1.66658i | ||||
\(683\) | −24.1502 | + | 24.1502i | −0.924081 | + | 0.924081i | −0.997315 | − | 0.0732336i | \(-0.976668\pi\) |
0.0732336 | + | 0.997315i | \(0.476668\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.4301 | + | 15.4301i | 0.589553 | + | 0.589553i | ||||
\(686\) | 6.07443 | + | 23.4515i | 0.231923 | + | 0.895382i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.0723 | + | 21.4598i | 0.765251 | + | 0.818148i | ||||
\(689\) | −6.26079 | − | 3.61467i | −0.238517 | − | 0.137708i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.9843 | + | 10.7138i | 1.52108 | + | 0.407571i | 0.920096 | − | 0.391693i | \(-0.128111\pi\) |
0.600980 | + | 0.799264i | \(0.294777\pi\) | |||||||
\(692\) | −20.3024 | + | 5.07826i | −0.771781 | + | 0.193046i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.66981 | − | 5.47574i | 0.367061 | − | 0.207856i | ||||
\(695\) | −1.97928 | + | 1.14273i | −0.0750782 | + | 0.0433464i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.88969 | − | 1.09101i | −0.0715772 | − | 0.0413251i | ||||
\(698\) | −30.7147 | − | 0.256432i | −1.16257 | − | 0.00970610i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.30995 | + | 0.155465i | 0.351883 | + | 0.00587604i | ||||
\(701\) | 21.1814 | − | 21.1814i | 0.800009 | − | 0.800009i | −0.183088 | − | 0.983097i | \(-0.558609\pi\) |
0.983097 | + | 0.183088i | \(0.0586092\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.0428i | 0.529633i | ||||||||
\(704\) | 14.7265 | − | 45.6756i | 0.555024 | − | 1.72146i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.124644 | + | 0.126743i | 0.00469104 | + | 0.00477003i | ||||
\(707\) | 2.29601 | − | 0.615214i | 0.0863503 | − | 0.0231375i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.8532 | − | 4.24787i | −0.595381 | − | 0.159532i | −0.0514698 | − | 0.998675i | \(-0.516391\pi\) |
−0.543911 | + | 0.839143i | \(0.683057\pi\) | |||||||
\(710\) | 16.2469 | − | 9.20014i | 0.609734 | − | 0.345275i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.763799 | + | 0.803050i | 0.0286246 | + | 0.0300956i | ||||
\(713\) | −16.8919 | − | 29.2576i | −0.632606 | − | 1.09571i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.1566 | + | 3.25736i | −0.454633 | + | 0.121819i | ||||
\(716\) | 33.8686 | + | 9.68396i | 1.26573 | + | 0.361906i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.57764 | − | 1.44472i | 0.208156 | − | 0.0539166i | ||||
\(719\) | 23.3461 | 0.870664 | 0.435332 | − | 0.900270i | \(-0.356631\pi\) | ||||
0.435332 | + | 0.900270i | \(0.356631\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.8292 | −1.11090 | ||||||||
\(722\) | −14.8966 | + | 3.85854i | −0.554395 | + | 0.143600i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.09203 | − | 24.8036i | 0.263573 | − | 0.921819i | ||||
\(725\) | 8.96937 | − | 2.40334i | 0.333114 | − | 0.0892576i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.90255 | − | 5.02736i | −0.107650 | − | 0.186454i | 0.807168 | − | 0.590322i | \(-0.200999\pi\) |
−0.914818 | + | 0.403867i | \(0.867666\pi\) | |||||||
\(728\) | −0.228521 | + | 9.12218i | −0.00846956 | + | 0.338090i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.45156 | − | 4.78588i | 0.312806 | − | 0.177133i | ||||
\(731\) | −4.96258 | − | 1.32972i | −0.183548 | − | 0.0491814i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.898647 | − | 0.240792i | 0.0331923 | − | 0.00889384i | −0.242185 | − | 0.970230i | \(-0.577864\pi\) |
0.275377 | + | 0.961336i | \(0.411197\pi\) | |||||||
\(734\) | −5.68285 | − | 5.77854i | −0.209758 | − | 0.213290i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.7342 | + | 23.6289i | 0.801134 | + | 0.870973i | ||||
\(737\) | − | 80.0891i | − | 2.95012i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.91328 | − | 5.91328i | 0.217523 | − | 0.217523i | −0.589931 | − | 0.807454i | \(-0.700845\pi\) |
0.807454 | + | 0.589931i | \(0.200845\pi\) | |||||||
\(740\) | 0.300974 | − | 18.0236i | 0.0110640 | − | 0.662561i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25.0624 | − | 0.209242i | −0.920068 | − | 0.00768150i | ||||
\(743\) | −20.3899 | − | 11.7721i | −0.748032 | − | 0.431876i | 0.0769504 | − | 0.997035i | \(-0.475482\pi\) |
−0.824982 | + | 0.565158i | \(0.808815\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.69647 | + | 3.28886i | −0.208703 | + | 0.120494i | ||||
\(746\) | 25.1502 | − | 14.2418i | 0.920814 | − | 0.521431i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.03611 | + | 8.14017i | 0.0744475 | + | 0.297634i | ||||
\(749\) | 24.5823 | + | 6.58682i | 0.898219 | + | 0.240677i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0649 | + | 7.54301i | 0.476744 | + | 0.275248i | 0.719059 | − | 0.694949i | \(-0.244573\pi\) |
−0.242315 | + | 0.970198i | \(0.577907\pi\) | |||||||
\(752\) | 22.6781 | + | 0.757607i | 0.826985 | + | 0.0276271i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.28181 | + | 8.80936i | 0.0830985 | + | 0.320818i | ||||
\(755\) | 14.0470 | + | 14.0470i | 0.511222 | + | 0.511222i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.48920 | − | 4.48920i | 0.163163 | − | 0.163163i | −0.620803 | − | 0.783966i | \(-0.713193\pi\) |
0.783966 | + | 0.620803i | \(0.213193\pi\) | |||||||
\(758\) | 2.89388 | − | 4.91709i | 0.105111 | − | 0.178597i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.3276 | + | 3.45694i | −0.519717 | + | 0.125396i | ||||
\(761\) | 19.0628 | − | 33.0177i | 0.691025 | − | 1.19689i | −0.280477 | − | 0.959861i | \(-0.590493\pi\) |
0.971502 | − | 0.237030i | \(-0.0761739\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.57072 | + | 5.86202i | −0.0568640 | + | 0.212219i | ||||
\(764\) | 6.07099 | + | 3.64157i | 0.219641 | + | 0.131747i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.2270 | + | 5.87813i | 0.766963 | + | 0.212385i | ||||
\(767\) | −8.10989 | − | 14.0467i | −0.292831 | − | 0.507198i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.5683 | − | 30.4291i | 0.633528 | − | 1.09730i | −0.353297 | − | 0.935511i | \(-0.614940\pi\) |
0.986825 | − | 0.161791i | \(-0.0517271\pi\) | |||||||
\(770\) | −31.1092 | + | 30.5940i | −1.12110 | + | 1.10253i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.496223 | + | 29.7160i | −0.0178595 | + | 1.06950i | ||||
\(773\) | −23.4773 | − | 23.4773i | −0.844420 | − | 0.844420i | 0.145010 | − | 0.989430i | \(-0.453678\pi\) |
−0.989430 | + | 0.145010i | \(0.953678\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.85458 | 0.353987 | ||||||||
\(776\) | −1.40104 | + | 4.74961i | −0.0502944 | + | 0.170501i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39.4690 | + | 0.329520i | 1.41503 | + | 0.0118139i | ||||
\(779\) | −2.30087 | − | 8.58698i | −0.0824374 | − | 0.307660i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.2085 | − | 41.8308i | 0.401073 | − | 1.49682i | ||||
\(782\) | −5.40972 | − | 1.49805i | −0.193451 | − | 0.0535700i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.71155 | + | 3.20725i | 0.0611268 | + | 0.114545i | ||||
\(785\) | 15.6257 | − | 9.02153i | 0.557707 | − | 0.321992i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.0559379 | + | 0.208763i | 0.00199397 | + | 0.00744160i | 0.966916 | − | 0.255096i | \(-0.0821072\pi\) |
−0.964922 | + | 0.262538i | \(0.915441\pi\) | |||||||
\(788\) | 32.3900 | + | 9.26119i | 1.15385 | + | 0.329916i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.62723 | + | 4.48890i | 0.271365 | + | 0.159708i | ||||
\(791\) | − | 18.6790i | − | 0.664150i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7191i | 0.558202i | ||||||||
\(794\) | −27.8159 | + | 47.2629i | −0.987151 | + | 1.67730i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.2738 | + | 15.1451i | −0.966693 | + | 0.536803i | ||||
\(797\) | 0.791183 | + | 2.95273i | 0.0280251 | + | 0.104591i | 0.978522 | − | 0.206144i | \(-0.0660915\pi\) |
−0.950497 | + | 0.310735i | \(0.899425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.43583 | + | 1.98367i | −0.121551 | + | 0.0701774i | ||||
\(800\) | −9.13893 | + | 2.04418i | −0.323110 | + | 0.0722727i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.37652 | + | 23.0268i | −0.225163 | + | 0.813103i | ||||
\(803\) | 5.83064 | − | 21.7602i | 0.205759 | − | 0.767902i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.55460 | − | 28.1942i | −0.266265 | − | 0.993714i | ||||
\(806\) | −0.0806262 | + | 9.65717i | −0.00283994 | + | 0.340159i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.09966 | + | 1.14311i | −0.0738658 | + | 0.0402144i | ||||
\(809\) | 42.5506 | 1.49600 | 0.748000 | − | 0.663699i | \(-0.231014\pi\) | ||||
0.748000 | + | 0.663699i | \(0.231014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.1448 | + | 15.1448i | 0.531806 | + | 0.531806i | 0.921109 | − | 0.389304i | \(-0.127284\pi\) |
−0.389304 | + | 0.921109i | \(0.627284\pi\) | |||||||
\(812\) | 21.9328 | + | 22.6777i | 0.769690 | + | 0.795833i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29.3169 | − | 29.8105i | −1.02756 | − | 1.04486i | ||||
\(815\) | 4.74206 | − | 8.21348i | 0.166107 | − | 0.287706i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.4657 | − | 18.1272i | −0.366150 | − | 0.634190i | ||||
\(818\) | −6.52560 | + | 23.5651i | −0.228162 | + | 0.823935i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.76908 | + | 11.0705i | 0.0967006 | + | 0.386599i | ||||
\(821\) | −7.15352 | + | 26.6973i | −0.249660 | + | 0.931742i | 0.721324 | + | 0.692598i | \(0.243534\pi\) |
−0.970984 | + | 0.239145i | \(0.923133\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.1921 | + | 17.6532i | −0.355273 | + | 0.615350i | −0.987165 | − | 0.159706i | \(-0.948945\pi\) |
0.631892 | + | 0.775057i | \(0.282279\pi\) | |||||||
\(824\) | 29.1637 | − | 7.03658i | 1.01597 | − | 0.245131i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −48.4618 | − | 28.5215i | −1.68620 | − | 0.992391i | ||||
\(827\) | 8.34698 | − | 8.34698i | 0.290253 | − | 0.290253i | −0.546927 | − | 0.837180i | \(-0.684203\pi\) |
0.837180 | + | 0.546927i | \(0.184203\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.48126 | − | 2.48126i | −0.0861778 | − | 0.0861778i | 0.662704 | − | 0.748882i | \(-0.269409\pi\) |
−0.748882 | + | 0.662704i | \(0.769409\pi\) | |||||||
\(830\) | 2.98656 | − | 0.773582i | 0.103665 | − | 0.0268514i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.92846 | − | 8.97258i | −0.0668573 | − | 0.311068i | ||||
\(833\) | −0.550465 | − | 0.317811i | −0.0190725 | − | 0.0110115i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.5435 | − | 9.52386i | −1.23004 | − | 0.329587i | ||||
\(836\) | −17.5849 | + | 29.3164i | −0.608186 | + | 1.01393i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.12220 | − | 3.74767i | −0.0733103 | − | 0.129461i | ||||
\(839\) | 17.7430 | − | 10.2439i | 0.612558 | − | 0.353660i | −0.161408 | − | 0.986888i | \(-0.551604\pi\) |
0.773966 | + | 0.633227i | \(0.218270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.13260 | + | 1.23126i | 0.0735380 | + | 0.0424572i | ||||
\(842\) | −0.108732 | + | 13.0236i | −0.00374716 | + | 0.448824i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22.4580 | + | 23.2208i | 0.773038 | + | 0.799294i | ||||
\(845\) | 15.1092 | − | 15.1092i | 0.519774 | − | 0.519774i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 70.2684i | 2.41445i | ||||||||
\(848\) | 24.5526 | − | 5.70753i | 0.843139 | − | 0.195997i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.16743 | − | 1.14809i | 0.0400424 | − | 0.0393793i | ||||
\(851\) | 27.0172 | − | 7.23923i | 0.926137 | − | 0.248158i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.1632 | − | 4.06296i | −0.519177 | − | 0.139113i | −0.0102909 | − | 0.999947i | \(-0.503276\pi\) |
−0.508886 | + | 0.860834i | \(0.669942\pi\) | |||||||
\(854\) | 26.8531 | + | 47.4209i | 0.918896 | + | 1.62271i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.5877 | − | 0.641003i | −0.874570 | − | 0.0219090i | ||||
\(857\) | 0.102894 | + | 0.178217i | 0.00351478 | + | 0.00608778i | 0.867777 | − | 0.496953i | \(-0.165548\pi\) |
−0.864263 | + | 0.503041i | \(0.832215\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.73650 | − | 0.733242i | 0.0933681 | − | 0.0250179i | −0.211833 | − | 0.977306i | \(-0.567943\pi\) |
0.305201 | + | 0.952288i | \(0.401276\pi\) | |||||||
\(860\) | 13.0440 | + | 23.4902i | 0.444798 | + | 0.801008i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.58155 | + | 9.96659i | 0.0879281 | + | 0.339463i | ||||
\(863\) | −26.9928 | −0.918846 | −0.459423 | − | 0.888218i | \(-0.651944\pi\) | ||||
−0.459423 | + | 0.888218i | \(0.651944\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.1365 | −0.650660 | ||||||||
\(866\) | −7.08378 | − | 27.3483i | −0.240717 | − | 0.929333i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.2542 | + | 29.2712i | 0.551704 | + | 0.993528i | ||||
\(869\) | 19.8281 | − | 5.31292i | 0.672621 | − | 0.180228i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.65786 | − | 13.2638i | −0.259477 | − | 0.449427i | ||||
\(872\) | 0.152857 | − | 6.10177i | 0.00517638 | − | 0.206632i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.2689 | − | 19.9002i | −0.381178 | − | 0.673136i | ||||
\(875\) | 33.0633 | + | 8.85929i | 1.11774 | + | 0.299499i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.0038 | − | 13.9344i | 1.75604 | − | 0.470531i | 0.770145 | − | 0.637869i | \(-0.220184\pi\) |
0.985900 | + | 0.167338i | \(0.0535171\pi\) | |||||||
\(878\) | −30.8813 | + | 30.3699i | −1.04219 | + | 1.02494i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 23.1982 | − | 37.2500i | 0.782010 | − | 1.25570i | ||||
\(881\) | 27.9049i | 0.940139i | 0.882629 | + | 0.470069i | \(0.155771\pi\) | ||||
−0.882629 | + | 0.470069i | \(0.844229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.83601 | − | 3.83601i | 0.129092 | − | 0.129092i | −0.639609 | − | 0.768701i | \(-0.720904\pi\) |
0.768701 | + | 0.639609i | \(0.220904\pi\) | |||||||
\(884\) | 1.11554 | + | 1.15343i | 0.0375198 | + | 0.0387941i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.351656 | − | 42.1204i | 0.0118141 | − | 1.41506i | ||||
\(887\) | 44.3036 | + | 25.5787i | 1.48757 | + | 0.858849i | 0.999899 | − | 0.0141788i | \(-0.00451340\pi\) |
0.487671 | + | 0.873028i | \(0.337847\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.6644 | − | 19.4361i | 1.12907 | − | 0.651867i | ||||
\(890\) | 0.499361 | + | 0.881840i | 0.0167386 | + | 0.0295593i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.5424 | + | 27.5784i | −0.553881 | + | 0.923393i | ||||
\(893\) | −15.6128 | − | 4.18343i | −0.522462 | − | 0.139993i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.8952 | + | 16.1053i | 0.932434 | + | 0.538341i | ||||
\(896\) | −21.1457 | − | 23.7738i | −0.706427 | − | 0.794226i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36.6940 | − | 9.50451i | 1.22449 | − | 0.317170i | ||||
\(899\) | 23.6101 | + | 23.6101i | 0.787442 | + | 0.787442i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.11647 | + | 3.11647i | −0.103825 | + | 0.103825i | ||||
\(902\) | 22.8113 | + | 13.4253i | 0.759533 | + | 0.447012i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.40631 | + | 18.2623i | 0.146552 | + | 0.607396i | ||||
\(905\) | 11.7947 | − | 20.4290i | 0.392069 | − | 0.679084i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.67896 | − | 9.99802i | 0.0889535 | − | 0.331979i | −0.907080 | − | 0.420958i | \(-0.861694\pi\) |
0.996033 | + | 0.0889794i | \(0.0283605\pi\) | |||||||
\(908\) | −5.36081 | − | 21.4320i | −0.177905 | − | 0.711246i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.22679 | + | 8.04134i | −0.0738173 | + | 0.266568i | ||||
\(911\) | −5.69107 | − | 9.85722i | −0.188553 | − | 0.326584i | 0.756215 | − | 0.654324i | \(-0.227047\pi\) |
−0.944768 | + | 0.327739i | \(0.893713\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.57791 | − | 6.19712i | 0.118411 | − | 0.205095i | ||||
\(914\) | 3.72524 | + | 3.78796i | 0.123220 | + | 0.125295i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.562201 | − | 0.581296i | −0.0185756 | − | 0.0192066i | ||||
\(917\) | −18.4856 | − | 18.4856i | −0.610447 | − | 0.610447i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.8316 | 0.390288 | 0.195144 | − | 0.980775i | \(-0.437483\pi\) | ||||
0.195144 | + | 0.980775i | \(0.437483\pi\) | |||||||
\(920\) | 14.0369 | + | 25.7831i | 0.462785 | + | 0.850043i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.0479930 | − | 5.74846i | 0.00158056 | − | 0.189315i | ||||
\(923\) | −2.14345 | − | 7.99945i | −0.0705524 | − | 0.263305i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.11165 | + | 7.88080i | −0.0694307 | + | 0.259119i | ||||
\(926\) | 8.84192 | − | 31.9298i | 0.290563 | − | 1.04928i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26.7931 | − | 16.9980i | −0.879526 | − | 0.557986i | ||||
\(929\) | −35.7139 | + | 20.6194i | −1.17174 | + | 0.676502i | −0.954088 | − | 0.299525i | \(-0.903172\pi\) |
−0.217647 | + | 0.976027i | \(0.569838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.670242 | − | 2.50138i | −0.0219663 | − | 0.0819794i | ||||
\(932\) | 20.3267 | − | 11.2874i | 0.665823 | − | 0.369730i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.4483 | + | 22.8504i | −0.440041 | + | 0.747688i | ||||
\(935\) | 7.67271i | 0.250924i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.6750i | − | 0.512081i | −0.966666 | − | 0.256041i | \(-0.917582\pi\) | ||
0.966666 | − | 0.256041i | \(-0.0824181\pi\) | |||||||
\(938\) | −45.7607 | − | 26.9318i | −1.49414 | − | 0.879355i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 19.9490 | + | 5.70397i | 0.650666 | + | 0.186043i | ||||
\(941\) | −2.58237 | − | 9.63753i | −0.0841828 | − | 0.314174i | 0.910975 | − | 0.412461i | \(-0.135331\pi\) |
−0.995158 | + | 0.0982863i | \(0.968664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.3345 | + | 8.85340i | −0.499361 | + | 0.288306i | ||||
\(944\) | 54.1088 | + | 16.4533i | 1.76109 | + | 0.535509i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 60.0609 | + | 16.6319i | 1.95275 | + | 0.540750i | ||||
\(947\) | 0.612832 | − | 2.28712i | 0.0199144 | − | 0.0743214i | −0.955254 | − | 0.295788i | \(-0.904418\pi\) |
0.975168 | + | 0.221467i | \(0.0710844\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.11501 | − | 4.16129i | −0.0361949 | − | 0.135081i | ||||
\(950\) | 6.67067 | + | 0.0556924i | 0.216425 | + | 0.00180690i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.33575 | + | 1.57394i | 0.172933 | + | 0.0510118i | ||||
\(953\) | 43.1152 | 1.39664 | 0.698320 | − | 0.715786i | \(-0.253931\pi\) | ||||
0.698320 | + | 0.715786i | \(0.253931\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.57740 | + | 4.57740i | 0.148121 | + | 0.148121i | ||||
\(956\) | −0.103976 | + | 6.22652i | −0.00336282 | + | 0.201380i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −35.5791 | + | 34.9900i | −1.14951 | + | 1.13047i | ||||
\(959\) | 16.7781 | − | 29.0605i | 0.541792 | − | 0.938411i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.21754 | + | 3.84089i | 0.0715334 | + | 0.123900i | ||||
\(962\) | −7.70565 | − | 2.13383i | −0.248440 | − | 0.0687974i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.5834 | + | 14.7459i | 0.791777 | + | 0.474933i | ||||
\(965\) | −7.03372 | + | 26.2502i | −0.226423 | + | 0.845023i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.1271 | + | 36.5932i | −0.679401 | + | 1.17676i | 0.295761 | + | 0.955262i | \(0.404427\pi\) |
−0.975162 | + | 0.221495i | \(0.928906\pi\) | |||||||
\(968\) | −16.5760 | − | 68.7008i | −0.532773 | − | 2.20813i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.29669 | + | 3.90238i | −0.0737423 | + | 0.125298i | ||||
\(971\) | 11.0093 | − | 11.0093i | 0.353305 | − | 0.353305i | −0.508033 | − | 0.861338i | \(-0.669627\pi\) |
0.861338 | + | 0.508033i | \(0.169627\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.48513 | + | 2.48513i | 0.0796697 | + | 0.0796697i | ||||
\(974\) | −4.30612 | − | 16.6246i | −0.137977 | − | 0.532686i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37.4405 | − | 40.0285i | −1.19844 | − | 1.28128i | ||||
\(977\) | −30.5197 | − | 17.6206i | −0.976413 | − | 0.563732i | −0.0752275 | − | 0.997166i | \(-0.523968\pi\) |
−0.901185 | + | 0.433434i | \(0.857302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.27047 | + | 0.608371i | 0.0725646 | + | 0.0194436i | ||||
\(980\) | 0.806631 | + | 3.22483i | 0.0257669 | + | 0.103013i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.951071 | + | 0.538565i | −0.0303499 | + | 0.0171863i | ||||
\(983\) | 33.9109 | − | 19.5785i | 1.08159 | − | 0.624456i | 0.150264 | − | 0.988646i | \(-0.451987\pi\) |
0.931325 | + | 0.364190i | \(0.118654\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.6774 | + | 15.4022i | 0.850013 | + | 0.490755i | ||||
\(986\) | 5.54764 | + | 0.0463164i | 0.176673 | + | 0.00147501i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.109153 | + | 6.53658i | −0.00347263 | + | 0.207956i | ||||
\(989\) | −29.4801 | + | 29.4801i | −0.937411 | + | 0.937411i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15.1164i | − | 0.480188i | −0.970750 | − | 0.240094i | \(-0.922822\pi\) | ||
0.970750 | − | 0.240094i | \(-0.0771783\pi\) | |||||||
\(992\) | −22.7965 | − | 24.7839i | −0.723791 | − | 0.786888i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.1318 | − | 20.4708i | −0.638543 | − | 0.649295i | ||||
\(995\) | −27.5543 | + | 7.38315i | −0.873530 | + | 0.234062i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.7668 | + | 10.3875i | 1.22776 | + | 0.328976i | 0.813706 | − | 0.581277i | \(-0.197447\pi\) |
0.414051 | + | 0.910254i | \(0.364113\pi\) | |||||||
\(998\) | 1.00057 | − | 0.566596i | 0.0316726 | − | 0.0179353i | ||||
\(999\) | 0 | 0 |
(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 | 432.2.v.a.179.13 | 88 | ||
3.2 | odd | 2 | 144.2.u.a.131.10 | yes | 88 | ||
4.3 | odd | 2 | 1728.2.z.a.1583.6 | 88 | |||
9.2 | odd | 6 | inner | 432.2.v.a.35.6 | 88 | ||
9.7 | even | 3 | 144.2.u.a.83.17 | yes | 88 | ||
12.11 | even | 2 | 576.2.y.a.239.16 | 88 | |||
16.5 | even | 4 | 1728.2.z.a.719.6 | 88 | |||
16.11 | odd | 4 | inner | 432.2.v.a.395.6 | 88 | ||
36.7 | odd | 6 | 576.2.y.a.47.18 | 88 | |||
36.11 | even | 6 | 1728.2.z.a.1007.6 | 88 | |||
48.5 | odd | 4 | 576.2.y.a.527.18 | 88 | |||
48.11 | even | 4 | 144.2.u.a.59.17 | yes | 88 | ||
144.11 | even | 12 | inner | 432.2.v.a.251.13 | 88 | ||
144.43 | odd | 12 | 144.2.u.a.11.10 | ✓ | 88 | ||
144.101 | odd | 12 | 1728.2.z.a.143.6 | 88 | |||
144.133 | even | 12 | 576.2.y.a.335.16 | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.u.a.11.10 | ✓ | 88 | 144.43 | odd | 12 | ||
144.2.u.a.59.17 | yes | 88 | 48.11 | even | 4 | ||
144.2.u.a.83.17 | yes | 88 | 9.7 | even | 3 | ||
144.2.u.a.131.10 | yes | 88 | 3.2 | odd | 2 | ||
432.2.v.a.35.6 | 88 | 9.2 | odd | 6 | inner | ||
432.2.v.a.179.13 | 88 | 1.1 | even | 1 | trivial | ||
432.2.v.a.251.13 | 88 | 144.11 | even | 12 | inner | ||
432.2.v.a.395.6 | 88 | 16.11 | odd | 4 | inner | ||
576.2.y.a.47.18 | 88 | 36.7 | odd | 6 | |||
576.2.y.a.239.16 | 88 | 12.11 | even | 2 | |||
576.2.y.a.335.16 | 88 | 144.133 | even | 12 | |||
576.2.y.a.527.18 | 88 | 48.5 | odd | 4 | |||
1728.2.z.a.143.6 | 88 | 144.101 | odd | 12 | |||
1728.2.z.a.719.6 | 88 | 16.5 | even | 4 | |||
1728.2.z.a.1007.6 | 88 | 36.11 | even | 6 | |||
1728.2.z.a.1583.6 | 88 | 4.3 | odd | 2 |