Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(43,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 5, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.w (of order \(8\), degree \(4\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(48\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 99.10 | ||
Character | \(\chi\) | \(=\) | 224.99 |
Dual form | 224.3.w.a.43.10 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70535 | + | 1.04488i | −0.852676 | + | 0.522440i | ||||
\(3\) | 0.502742 | − | 1.21373i | 0.167581 | − | 0.404576i | −0.817671 | − | 0.575685i | \(-0.804735\pi\) |
0.985252 | + | 0.171110i | \(0.0547353\pi\) | |||||||
\(4\) | 1.81645 | − | 3.56377i | 0.454114 | − | 0.890944i | ||||
\(5\) | −0.0438594 | − | 0.105886i | −0.00877188 | − | 0.0211772i | 0.919433 | − | 0.393247i | \(-0.128648\pi\) |
−0.928205 | + | 0.372070i | \(0.878648\pi\) | |||||||
\(6\) | 0.410845 | + | 2.59514i | 0.0684742 | + | 0.432523i | ||||
\(7\) | −1.87083 | − | 1.87083i | −0.267261 | − | 0.267261i | ||||
\(8\) | 0.626019 | + | 7.97547i | 0.0782523 | + | 0.996934i | ||||
\(9\) | 5.14358 | + | 5.14358i | 0.571509 | + | 0.571509i | ||||
\(10\) | 0.185434 | + | 0.134745i | 0.0185434 | + | 0.0134745i | ||||
\(11\) | 1.37483 | + | 3.31914i | 0.124985 | + | 0.301740i | 0.973970 | − | 0.226677i | \(-0.0727860\pi\) |
−0.848985 | + | 0.528416i | \(0.822786\pi\) | |||||||
\(12\) | −3.41224 | − | 3.99634i | −0.284353 | − | 0.333028i | ||||
\(13\) | 5.53835 | − | 13.3708i | 0.426027 | − | 1.02852i | −0.554508 | − | 0.832178i | \(-0.687094\pi\) |
0.980535 | − | 0.196342i | \(-0.0629064\pi\) | |||||||
\(14\) | 5.14521 | + | 1.23563i | 0.367515 | + | 0.0882595i | ||||
\(15\) | −0.150567 | −0.0100378 | ||||||||
\(16\) | −9.40098 | − | 12.9469i | −0.587561 | − | 0.809180i | ||||
\(17\) | − | 25.0349i | − | 1.47264i | −0.676634 | − | 0.736319i | \(-0.736562\pi\) | ||
0.676634 | − | 0.736319i | \(-0.263438\pi\) | |||||||
\(18\) | −14.1460 | − | 3.39720i | −0.785891 | − | 0.188733i | ||||
\(19\) | 4.85961 | + | 2.01292i | 0.255769 | + | 0.105943i | 0.506884 | − | 0.862014i | \(-0.330797\pi\) |
−0.251115 | + | 0.967957i | \(0.580797\pi\) | |||||||
\(20\) | −0.457022 | − | 0.0360320i | −0.0228511 | − | 0.00180160i | ||||
\(21\) | −3.21122 | + | 1.33013i | −0.152915 | + | 0.0633395i | ||||
\(22\) | −5.81267 | − | 4.22377i | −0.264212 | − | 0.191989i | ||||
\(23\) | −1.30671 | + | 1.30671i | −0.0568134 | + | 0.0568134i | −0.734943 | − | 0.678129i | \(-0.762791\pi\) |
0.678129 | + | 0.734943i | \(0.262791\pi\) | |||||||
\(24\) | 9.99477 | + | 3.24979i | 0.416449 | + | 0.135408i | ||||
\(25\) | 17.6684 | − | 17.6684i | 0.706735 | − | 0.706735i | ||||
\(26\) | 4.52599 | + | 28.5888i | 0.174077 | + | 1.09957i | ||||
\(27\) | 19.7523 | − | 8.18168i | 0.731568 | − | 0.303025i | ||||
\(28\) | −10.0655 | + | 3.26894i | −0.359482 | + | 0.116748i | ||||
\(29\) | 15.1031 | + | 6.25590i | 0.520796 | + | 0.215721i | 0.627566 | − | 0.778563i | \(-0.284051\pi\) |
−0.106771 | + | 0.994284i | \(0.534051\pi\) | |||||||
\(30\) | 0.256769 | − | 0.157324i | 0.00855897 | − | 0.00524413i | ||||
\(31\) | − | 41.0028i | − | 1.32267i | −0.750090 | − | 0.661336i | \(-0.769990\pi\) | ||
0.750090 | − | 0.661336i | \(-0.230010\pi\) | |||||||
\(32\) | 29.5599 | + | 12.2561i | 0.923747 | + | 0.383003i | ||||
\(33\) | 4.71971 | 0.143022 | ||||||||
\(34\) | 26.1584 | + | 42.6933i | 0.769365 | + | 1.25568i | ||||
\(35\) | −0.116041 | + | 0.280148i | −0.00331546 | + | 0.00800423i | ||||
\(36\) | 27.6736 | − | 8.98748i | 0.768712 | − | 0.249652i | ||||
\(37\) | −9.38050 | − | 22.6465i | −0.253527 | − | 0.612069i | 0.744957 | − | 0.667113i | \(-0.232470\pi\) |
−0.998484 | + | 0.0550441i | \(0.982470\pi\) | |||||||
\(38\) | −10.3906 | + | 1.64497i | −0.273437 | + | 0.0432888i | ||||
\(39\) | −13.4441 | − | 13.4441i | −0.344720 | − | 0.344720i | ||||
\(40\) | 0.817033 | − | 0.416086i | 0.0204258 | − | 0.0104021i | ||||
\(41\) | 33.4077 | + | 33.4077i | 0.814823 | + | 0.814823i | 0.985353 | − | 0.170530i | \(-0.0545479\pi\) |
−0.170530 | + | 0.985353i | \(0.554548\pi\) | |||||||
\(42\) | 4.08643 | − | 5.62368i | 0.0972961 | − | 0.133897i | ||||
\(43\) | 4.08867 | + | 9.87092i | 0.0950853 | + | 0.229556i | 0.964265 | − | 0.264941i | \(-0.0853523\pi\) |
−0.869179 | + | 0.494497i | \(0.835352\pi\) | |||||||
\(44\) | 14.3260 | + | 1.12947i | 0.325590 | + | 0.0256698i | ||||
\(45\) | 0.319038 | − | 0.770227i | 0.00708974 | − | 0.0171162i | ||||
\(46\) | 0.863046 | − | 3.59375i | 0.0187619 | − | 0.0781250i | ||||
\(47\) | 20.9665 | 0.446097 | 0.223048 | − | 0.974807i | \(-0.428399\pi\) | ||||
0.223048 | + | 0.974807i | \(0.428399\pi\) | |||||||
\(48\) | −20.4402 | + | 4.90129i | −0.425838 | + | 0.102110i | ||||
\(49\) | 7.00000i | 0.142857i | ||||||||
\(50\) | −11.6695 | + | 48.5921i | −0.233390 | + | 0.971843i | ||||
\(51\) | −30.3855 | − | 12.5861i | −0.595794 | − | 0.246786i | ||||
\(52\) | −37.5902 | − | 44.0248i | −0.722889 | − | 0.846631i | ||||
\(53\) | 71.4971 | − | 29.6151i | 1.34900 | − | 0.558775i | 0.412987 | − | 0.910737i | \(-0.364485\pi\) |
0.936014 | + | 0.351962i | \(0.114485\pi\) | |||||||
\(54\) | −25.1358 | + | 34.5915i | −0.465478 | + | 0.640583i | ||||
\(55\) | 0.291151 | − | 0.291151i | 0.00529365 | − | 0.00529365i | ||||
\(56\) | 13.7496 | − | 16.0919i | 0.245528 | − | 0.287356i | ||||
\(57\) | 4.88626 | − | 4.88626i | 0.0857239 | − | 0.0857239i | ||||
\(58\) | −32.2927 | + | 5.11238i | −0.556771 | + | 0.0881445i | ||||
\(59\) | −84.5124 | + | 35.0062i | −1.43241 | + | 0.593325i | −0.957946 | − | 0.286948i | \(-0.907359\pi\) |
−0.474467 | + | 0.880273i | \(0.657359\pi\) | |||||||
\(60\) | −0.273497 | + | 0.536585i | −0.00455829 | + | 0.00894309i | ||||
\(61\) | −35.0338 | − | 14.5115i | −0.574324 | − | 0.237893i | 0.0765663 | − | 0.997064i | \(-0.475604\pi\) |
−0.650891 | + | 0.759172i | \(0.725604\pi\) | |||||||
\(62\) | 42.8430 | + | 69.9243i | 0.691017 | + | 1.12781i | ||||
\(63\) | − | 19.2455i | − | 0.305484i | ||||||
\(64\) | −63.2162 | + | 9.98558i | −0.987753 | + | 0.156025i | ||||
\(65\) | −1.65868 | −0.0255182 | ||||||||
\(66\) | −8.04877 | + | 4.93153i | −0.121951 | + | 0.0747201i | ||||
\(67\) | −34.1693 | + | 82.4920i | −0.509989 | + | 1.23122i | 0.433900 | + | 0.900961i | \(0.357137\pi\) |
−0.943889 | + | 0.330262i | \(0.892863\pi\) | |||||||
\(68\) | −89.2186 | − | 45.4747i | −1.31204 | − | 0.668746i | ||||
\(69\) | 0.929050 | + | 2.24292i | 0.0134645 | + | 0.0325062i | ||||
\(70\) | −0.0948298 | − | 0.599000i | −0.00135471 | − | 0.00855714i | ||||
\(71\) | −26.1620 | − | 26.1620i | −0.368478 | − | 0.368478i | 0.498444 | − | 0.866922i | \(-0.333905\pi\) |
−0.866922 | + | 0.498444i | \(0.833905\pi\) | |||||||
\(72\) | −37.8025 | + | 44.2424i | −0.525034 | + | 0.614478i | ||||
\(73\) | −22.9027 | − | 22.9027i | −0.313735 | − | 0.313735i | 0.532620 | − | 0.846355i | \(-0.321208\pi\) |
−0.846355 | + | 0.532620i | \(0.821208\pi\) | |||||||
\(74\) | 39.6600 | + | 28.8188i | 0.535945 | + | 0.389444i | ||||
\(75\) | −12.5619 | − | 30.3272i | −0.167493 | − | 0.404363i | ||||
\(76\) | 16.0009 | − | 13.6622i | 0.210538 | − | 0.179766i | ||||
\(77\) | 3.63746 | − | 8.78161i | 0.0472398 | − | 0.114047i | ||||
\(78\) | 36.9744 | + | 8.87946i | 0.474030 | + | 0.113839i | ||||
\(79\) | −120.602 | −1.52661 | −0.763305 | − | 0.646038i | \(-0.776425\pi\) | ||||
−0.763305 | + | 0.646038i | \(0.776425\pi\) | |||||||
\(80\) | −0.958570 | + | 1.56327i | −0.0119821 | + | 0.0195409i | ||||
\(81\) | 37.3799i | 0.461480i | ||||||||
\(82\) | −91.8790 | − | 22.0649i | −1.12048 | − | 0.269084i | ||||
\(83\) | −2.08476 | − | 0.863534i | −0.0251175 | − | 0.0104040i | 0.370089 | − | 0.928996i | \(-0.379327\pi\) |
−0.395207 | + | 0.918592i | \(0.629327\pi\) | |||||||
\(84\) | −1.09275 | + | 13.8602i | −0.0130089 | + | 0.165002i | ||||
\(85\) | −2.65084 | + | 1.09801i | −0.0311864 | + | 0.0129178i | ||||
\(86\) | −17.2865 | − | 12.5612i | −0.201006 | − | 0.146061i | ||||
\(87\) | 15.1859 | − | 15.1859i | 0.174551 | − | 0.174551i | ||||
\(88\) | −25.6110 | + | 13.0428i | −0.291034 | + | 0.148213i | ||||
\(89\) | 49.1699 | − | 49.1699i | 0.552470 | − | 0.552470i | −0.374683 | − | 0.927153i | \(-0.622248\pi\) |
0.927153 | + | 0.374683i | \(0.122248\pi\) | |||||||
\(90\) | 0.260721 | + | 1.64686i | 0.00289690 | + | 0.0182985i | ||||
\(91\) | −35.3757 | + | 14.6531i | −0.388744 | + | 0.161023i | ||||
\(92\) | 2.28324 | + | 7.03039i | 0.0248178 | + | 0.0764173i | ||||
\(93\) | −49.7663 | − | 20.6139i | −0.535121 | − | 0.221654i | ||||
\(94\) | −35.7553 | + | 21.9075i | −0.380376 | + | 0.233059i | ||||
\(95\) | − | 0.602850i | − | 0.00634579i | ||||||
\(96\) | 29.7366 | − | 29.7160i | 0.309756 | − | 0.309542i | ||||
\(97\) | 123.684 | 1.27510 | 0.637548 | − | 0.770411i | \(-0.279949\pi\) | ||||
0.637548 | + | 0.770411i | \(0.279949\pi\) | |||||||
\(98\) | −7.31415 | − | 11.9375i | −0.0746342 | − | 0.121811i | ||||
\(99\) | −10.0007 | + | 24.1438i | −0.101017 | + | 0.243877i | ||||
\(100\) | −30.8723 | − | 95.0600i | −0.308723 | − | 0.950600i | ||||
\(101\) | 30.7964 | + | 74.3490i | 0.304915 | + | 0.736129i | 0.999854 | + | 0.0170611i | \(0.00543098\pi\) |
−0.694940 | + | 0.719068i | \(0.744569\pi\) | |||||||
\(102\) | 64.9689 | − | 10.2855i | 0.636950 | − | 0.100838i | ||||
\(103\) | 19.7466 | + | 19.7466i | 0.191715 | + | 0.191715i | 0.796437 | − | 0.604722i | \(-0.206716\pi\) |
−0.604722 | + | 0.796437i | \(0.706716\pi\) | |||||||
\(104\) | 110.105 | + | 35.8006i | 1.05870 | + | 0.344237i | ||||
\(105\) | 0.281684 | + | 0.281684i | 0.00268271 | + | 0.00268271i | ||||
\(106\) | −90.9836 | + | 125.210i | −0.858336 | + | 1.18123i | ||||
\(107\) | 25.0630 | + | 60.5074i | 0.234234 | + | 0.565490i | 0.996667 | − | 0.0815768i | \(-0.0259956\pi\) |
−0.762434 | + | 0.647067i | \(0.775996\pi\) | |||||||
\(108\) | 6.72154 | − | 85.2545i | 0.0622365 | − | 0.789394i | ||||
\(109\) | −63.4258 | + | 153.123i | −0.581888 | + | 1.40480i | 0.309211 | + | 0.950994i | \(0.399935\pi\) |
−0.891099 | + | 0.453809i | \(0.850065\pi\) | |||||||
\(110\) | −0.192297 | + | 0.800732i | −0.00174816 | + | 0.00727938i | ||||
\(111\) | −32.2027 | −0.290114 | ||||||||
\(112\) | −6.63375 | + | 41.8090i | −0.0592299 | + | 0.373295i | ||||
\(113\) | 115.255i | 1.01996i | 0.860188 | + | 0.509978i | \(0.170346\pi\) | ||||
−0.860188 | + | 0.509978i | \(0.829654\pi\) | |||||||
\(114\) | −3.22725 | + | 13.4384i | −0.0283092 | + | 0.117880i | ||||
\(115\) | 0.195674 | + | 0.0810506i | 0.00170151 | + | 0.000704788i | ||||
\(116\) | 49.7287 | − | 42.4604i | 0.428696 | − | 0.366038i | ||||
\(117\) | 97.2605 | − | 40.2866i | 0.831287 | − | 0.344330i | ||||
\(118\) | 107.546 | − | 148.003i | 0.911408 | − | 1.25426i | ||||
\(119\) | −46.8359 | + | 46.8359i | −0.393579 | + | 0.393579i | ||||
\(120\) | −0.0942575 | − | 1.20084i | −0.000785479 | − | 0.0100070i | ||||
\(121\) | 76.4334 | − | 76.4334i | 0.631681 | − | 0.631681i | ||||
\(122\) | 74.9077 | − | 11.8589i | 0.613997 | − | 0.0972041i | ||||
\(123\) | 57.3433 | − | 23.7524i | 0.466206 | − | 0.193109i | ||||
\(124\) | −146.125 | − | 74.4798i | −1.17843 | − | 0.600644i | ||||
\(125\) | −5.29291 | − | 2.19239i | −0.0423433 | − | 0.0175391i | ||||
\(126\) | 20.1092 | + | 32.8204i | 0.159597 | + | 0.260479i | ||||
\(127\) | − | 233.128i | − | 1.83565i | −0.396979 | − | 0.917827i | \(-0.629942\pi\) | ||
0.396979 | − | 0.917827i | \(-0.370058\pi\) | |||||||
\(128\) | 97.3722 | − | 83.0822i | 0.760720 | − | 0.649080i | ||||
\(129\) | 14.0361 | 0.108807 | ||||||||
\(130\) | 2.82864 | − | 1.73313i | 0.0217588 | − | 0.0133317i | ||||
\(131\) | −36.9624 | + | 89.2351i | −0.282156 | + | 0.681184i | −0.999885 | − | 0.0151377i | \(-0.995181\pi\) |
0.717730 | + | 0.696322i | \(0.245181\pi\) | |||||||
\(132\) | 8.57314 | − | 16.8200i | 0.0649481 | − | 0.127424i | ||||
\(133\) | −5.32568 | − | 12.8573i | −0.0400427 | − | 0.0966716i | ||||
\(134\) | −27.9235 | − | 176.381i | −0.208384 | − | 1.31627i | ||||
\(135\) | −1.73265 | − | 1.73265i | −0.0128344 | − | 0.0128344i | ||||
\(136\) | 199.665 | − | 15.6723i | 1.46812 | − | 0.115237i | ||||
\(137\) | 154.978 | + | 154.978i | 1.13123 | + | 1.13123i | 0.989973 | + | 0.141253i | \(0.0451132\pi\) |
0.141253 | + | 0.989973i | \(0.454887\pi\) | |||||||
\(138\) | −3.92794 | − | 2.85423i | −0.0284634 | − | 0.0206828i | ||||
\(139\) | 39.9820 | + | 96.5251i | 0.287640 | + | 0.694425i | 0.999972 | − | 0.00741717i | \(-0.00236098\pi\) |
−0.712332 | + | 0.701843i | \(0.752361\pi\) | |||||||
\(140\) | 0.787601 | + | 0.922420i | 0.00562572 | + | 0.00658872i | ||||
\(141\) | 10.5408 | − | 25.4477i | 0.0747572 | − | 0.180480i | ||||
\(142\) | 71.9515 | + | 17.2793i | 0.506700 | + | 0.121685i | ||||
\(143\) | 51.9937 | 0.363592 | ||||||||
\(144\) | 18.2386 | − | 114.948i | 0.126657 | − | 0.798250i | ||||
\(145\) | − | 1.87358i | − | 0.0129213i | ||||||
\(146\) | 62.9877 | + | 15.1266i | 0.431422 | + | 0.103607i | ||||
\(147\) | 8.49609 | + | 3.51919i | 0.0577965 | + | 0.0239401i | ||||
\(148\) | −97.7464 | − | 7.70641i | −0.660449 | − | 0.0520703i | ||||
\(149\) | −212.248 | + | 87.9158i | −1.42448 | + | 0.590039i | −0.955982 | − | 0.293426i | \(-0.905205\pi\) |
−0.468498 | + | 0.883465i | \(0.655205\pi\) | |||||||
\(150\) | 53.1108 | + | 38.5929i | 0.354072 | + | 0.257286i | ||||
\(151\) | 11.1880 | − | 11.1880i | 0.0740926 | − | 0.0740926i | −0.669089 | − | 0.743182i | \(-0.733316\pi\) |
0.743182 | + | 0.669089i | \(0.233316\pi\) | |||||||
\(152\) | −13.0118 | + | 40.0178i | −0.0856036 | + | 0.263275i | ||||
\(153\) | 128.769 | − | 128.769i | 0.841626 | − | 0.841626i | ||||
\(154\) | 2.97257 | + | 18.7765i | 0.0193024 | + | 0.121925i | ||||
\(155\) | −4.34163 | + | 1.79836i | −0.0280105 | + | 0.0116023i | ||||
\(156\) | −72.3323 | + | 23.4911i | −0.463669 | + | 0.150584i | ||||
\(157\) | −259.059 | − | 107.306i | −1.65006 | − | 0.683477i | −0.652805 | − | 0.757526i | \(-0.726408\pi\) |
−0.997255 | + | 0.0740493i | \(0.976408\pi\) | |||||||
\(158\) | 205.669 | − | 126.015i | 1.30170 | − | 0.797562i | ||||
\(159\) | − | 101.667i | − | 0.639413i | ||||||
\(160\) | 0.00126782 | − | 3.66752i | 7.92390e−6 | − | 0.0229220i | ||||
\(161\) | 4.88926 | 0.0303680 | ||||||||
\(162\) | −39.0574 | − | 63.7458i | −0.241095 | − | 0.393493i | ||||
\(163\) | −66.0630 | + | 159.490i | −0.405295 | + | 0.978468i | 0.581064 | + | 0.813858i | \(0.302637\pi\) |
−0.986359 | + | 0.164610i | \(0.947363\pi\) | |||||||
\(164\) | 179.741 | − | 58.3740i | 1.09598 | − | 0.355939i | ||||
\(165\) | −0.207004 | − | 0.499751i | −0.00125457 | − | 0.00302879i | ||||
\(166\) | 4.45753 | − | 0.705688i | 0.0268526 | − | 0.00425113i | ||||
\(167\) | 97.9708 | + | 97.9708i | 0.586652 | + | 0.586652i | 0.936723 | − | 0.350071i | \(-0.113843\pi\) |
−0.350071 | + | 0.936723i | \(0.613843\pi\) | |||||||
\(168\) | −12.6187 | − | 24.7783i | −0.0751113 | − | 0.147490i | ||||
\(169\) | −28.6030 | − | 28.6030i | −0.169248 | − | 0.169248i | ||||
\(170\) | 3.37333 | − | 4.64231i | 0.0198431 | − | 0.0273077i | ||||
\(171\) | 14.6422 | + | 35.3494i | 0.0856269 | + | 0.206722i | ||||
\(172\) | 42.6046 | + | 3.35898i | 0.247701 | + | 0.0195290i | ||||
\(173\) | 28.5637 | − | 68.9588i | 0.165108 | − | 0.398606i | −0.819572 | − | 0.572976i | \(-0.805789\pi\) |
0.984680 | + | 0.174370i | \(0.0557889\pi\) | |||||||
\(174\) | −10.0299 | + | 41.7648i | −0.0576430 | + | 0.240027i | ||||
\(175\) | −66.1090 | −0.377766 | ||||||||
\(176\) | 30.0477 | − | 49.0029i | 0.170725 | − | 0.278426i | ||||
\(177\) | 120.174i | 0.678949i | ||||||||
\(178\) | −32.4754 | + | 135.229i | −0.182446 | + | 0.759711i | ||||
\(179\) | −147.104 | − | 60.9323i | −0.821808 | − | 0.340404i | −0.0681533 | − | 0.997675i | \(-0.521711\pi\) |
−0.753654 | + | 0.657271i | \(0.771711\pi\) | |||||||
\(180\) | −2.16540 | − | 2.53606i | −0.0120300 | − | 0.0140892i | ||||
\(181\) | 51.6031 | − | 21.3747i | 0.285100 | − | 0.118092i | −0.235551 | − | 0.971862i | \(-0.575689\pi\) |
0.520651 | + | 0.853770i | \(0.325689\pi\) | |||||||
\(182\) | 45.0174 | − | 61.9521i | 0.247348 | − | 0.340396i | ||||
\(183\) | −35.2259 | + | 35.2259i | −0.192491 | + | 0.192491i | ||||
\(184\) | −11.2396 | − | 9.60359i | −0.0610850 | − | 0.0521934i | ||||
\(185\) | −1.98653 | + | 1.98653i | −0.0107380 | + | 0.0107380i | ||||
\(186\) | 106.408 | − | 16.8458i | 0.572086 | − | 0.0905690i | ||||
\(187\) | 83.0942 | − | 34.4187i | 0.444354 | − | 0.184057i | ||||
\(188\) | 38.0848 | − | 74.7200i | 0.202579 | − | 0.397447i | ||||
\(189\) | −52.2598 | − | 21.6467i | −0.276507 | − | 0.114533i | ||||
\(190\) | 0.629905 | + | 1.02807i | 0.00331529 | + | 0.00541090i | ||||
\(191\) | − | 92.5743i | − | 0.484682i | −0.970191 | − | 0.242341i | \(-0.922085\pi\) | ||
0.970191 | − | 0.242341i | \(-0.0779153\pi\) | |||||||
\(192\) | −19.6617 | + | 81.7474i | −0.102405 | + | 0.425768i | ||||
\(193\) | −82.3723 | −0.426800 | −0.213400 | − | 0.976965i | \(-0.568454\pi\) | ||||
−0.213400 | + | 0.976965i | \(0.568454\pi\) | |||||||
\(194\) | −210.925 | + | 129.235i | −1.08724 | + | 0.666160i | ||||
\(195\) | −0.833891 | + | 2.01319i | −0.00427636 | + | 0.0103241i | ||||
\(196\) | 24.9464 | + | 12.7152i | 0.127278 | + | 0.0648734i | ||||
\(197\) | 13.2647 | + | 32.0238i | 0.0673334 | + | 0.162557i | 0.953964 | − | 0.299921i | \(-0.0969603\pi\) |
−0.886631 | + | 0.462478i | \(0.846960\pi\) | |||||||
\(198\) | −8.17265 | − | 51.6232i | −0.0412760 | − | 0.260723i | ||||
\(199\) | 240.256 | + | 240.256i | 1.20732 | + | 1.20732i | 0.971893 | + | 0.235422i | \(0.0756472\pi\) |
0.235422 | + | 0.971893i | \(0.424353\pi\) | |||||||
\(200\) | 151.974 | + | 129.853i | 0.759872 | + | 0.649264i | ||||
\(201\) | 82.9444 | + | 82.9444i | 0.412659 | + | 0.412659i | ||||
\(202\) | −130.204 | − | 94.6128i | −0.644576 | − | 0.468380i | ||||
\(203\) | −16.5516 | − | 39.9590i | −0.0815348 | − | 0.196842i | ||||
\(204\) | −100.048 | + | 85.4250i | −0.490430 | + | 0.418750i | ||||
\(205\) | 2.07217 | − | 5.00265i | 0.0101081 | − | 0.0244032i | ||||
\(206\) | −54.3078 | − | 13.0421i | −0.263630 | − | 0.0633112i | ||||
\(207\) | −13.4423 | −0.0649387 | ||||||||
\(208\) | −225.176 | + | 53.9940i | −1.08257 | + | 0.259587i | ||||
\(209\) | 18.8971i | 0.0904170i | ||||||||
\(210\) | −0.774697 | − | 0.186045i | −0.00368903 | − | 0.000885928i | ||||
\(211\) | −14.5042 | − | 6.00783i | −0.0687402 | − | 0.0284731i | 0.348048 | − | 0.937477i | \(-0.386844\pi\) |
−0.416789 | + | 0.909003i | \(0.636844\pi\) | |||||||
\(212\) | 24.3298 | − | 308.594i | 0.114763 | − | 1.45563i | ||||
\(213\) | −44.9062 | + | 18.6008i | −0.210827 | + | 0.0873275i | ||||
\(214\) | −105.964 | − | 76.9987i | −0.495160 | − | 0.359807i | ||||
\(215\) | 0.865865 | − | 0.865865i | 0.00402728 | − | 0.00402728i | ||||
\(216\) | 77.6181 | + | 152.412i | 0.359343 | + | 0.705612i | ||||
\(217\) | −76.7093 | + | 76.7093i | −0.353499 | + | 0.353499i | ||||
\(218\) | −51.8322 | − | 327.402i | −0.237762 | − | 1.50184i | ||||
\(219\) | −39.3117 | + | 16.2834i | −0.179506 | + | 0.0743536i | ||||
\(220\) | −0.508734 | − | 1.56646i | −0.00231243 | − | 0.00712026i | ||||
\(221\) | −334.735 | − | 138.652i | −1.51464 | − | 0.627384i | ||||
\(222\) | 54.9169 | − | 33.6479i | 0.247374 | − | 0.151567i | ||||
\(223\) | − | 105.709i | − | 0.474030i | −0.971506 | − | 0.237015i | \(-0.923831\pi\) | ||
0.971506 | − | 0.237015i | \(-0.0761690\pi\) | |||||||
\(224\) | −32.3725 | − | 78.2306i | −0.144520 | − | 0.349244i | ||||
\(225\) | 181.757 | 0.807811 | ||||||||
\(226\) | −120.427 | − | 196.550i | −0.532865 | − | 0.869692i | ||||
\(227\) | −78.8701 | + | 190.409i | −0.347445 | + | 0.838807i | 0.649475 | + | 0.760383i | \(0.274989\pi\) |
−0.996920 | + | 0.0784239i | \(0.975011\pi\) | |||||||
\(228\) | −8.53787 | − | 26.2892i | −0.0374468 | − | 0.115304i | ||||
\(229\) | −26.3996 | − | 63.7343i | −0.115282 | − | 0.278316i | 0.855698 | − | 0.517475i | \(-0.173128\pi\) |
−0.970980 | + | 0.239160i | \(0.923128\pi\) | |||||||
\(230\) | −0.418380 | + | 0.0662353i | −0.00181905 | + | 0.000287980i | ||||
\(231\) | −8.82977 | − | 8.82977i | −0.0382241 | − | 0.0382241i | ||||
\(232\) | −40.4389 | + | 124.370i | −0.174306 | + | 0.536080i | ||||
\(233\) | −289.049 | − | 289.049i | −1.24055 | − | 1.24055i | −0.959772 | − | 0.280780i | \(-0.909407\pi\) |
−0.280780 | − | 0.959772i | \(-0.590593\pi\) | |||||||
\(234\) | −123.769 | + | 170.328i | −0.528927 | + | 0.727899i | ||||
\(235\) | −0.919580 | − | 2.22006i | −0.00391311 | − | 0.00944707i | ||||
\(236\) | −28.7588 | + | 364.770i | −0.121859 | + | 1.54564i | ||||
\(237\) | −60.6318 | + | 146.378i | −0.255830 | + | 0.617629i | ||||
\(238\) | 30.9339 | − | 128.810i | 0.129974 | − | 0.541217i | ||||
\(239\) | −125.138 | −0.523592 | −0.261796 | − | 0.965123i | \(-0.584315\pi\) | ||||
−0.261796 | + | 0.965123i | \(0.584315\pi\) | |||||||
\(240\) | 1.41547 | + | 1.94937i | 0.00589781 | + | 0.00812236i | ||||
\(241\) | 11.1031i | 0.0460710i | 0.999735 | + | 0.0230355i | \(0.00733308\pi\) | ||||
−0.999735 | + | 0.0230355i | \(0.992667\pi\) | |||||||
\(242\) | −50.4822 | + | 210.210i | −0.208604 | + | 0.868635i | ||||
\(243\) | 223.140 | + | 92.4276i | 0.918271 | + | 0.380360i | ||||
\(244\) | −115.353 | + | 98.4931i | −0.472758 | + | 0.403660i | ||||
\(245\) | 0.741202 | − | 0.307016i | 0.00302531 | − | 0.00125313i | ||||
\(246\) | −72.9722 | + | 100.423i | −0.296635 | + | 0.408224i | ||||
\(247\) | 53.8285 | − | 53.8285i | 0.217929 | − | 0.217929i | ||||
\(248\) | 327.017 | − | 25.6685i | 1.31862 | − | 0.103502i | ||||
\(249\) | −2.09619 | + | 2.09619i | −0.00841843 | + | 0.00841843i | ||||
\(250\) | 11.3171 | − | 1.79164i | 0.0452682 | − | 0.00716658i | ||||
\(251\) | 212.454 | − | 88.0014i | 0.846431 | − | 0.350603i | 0.0830451 | − | 0.996546i | \(-0.473535\pi\) |
0.763386 | + | 0.645943i | \(0.223535\pi\) | |||||||
\(252\) | −68.5867 | − | 34.9586i | −0.272169 | − | 0.138725i | ||||
\(253\) | −6.13365 | − | 2.54064i | −0.0242437 | − | 0.0100421i | ||||
\(254\) | 243.591 | + | 397.566i | 0.959019 | + | 1.56522i | ||||
\(255\) | 3.76941i | 0.0147820i | ||||||||
\(256\) | −79.2430 | + | 243.427i | −0.309543 | + | 0.950885i | ||||
\(257\) | 11.5021 | 0.0447553 | 0.0223777 | − | 0.999750i | \(-0.492876\pi\) | ||||
0.0223777 | + | 0.999750i | \(0.492876\pi\) | |||||||
\(258\) | −23.9366 | + | 14.6661i | −0.0927774 | + | 0.0568453i | ||||
\(259\) | −24.8185 | + | 59.9171i | −0.0958242 | + | 0.231340i | ||||
\(260\) | −3.01293 | + | 5.91118i | −0.0115882 | + | 0.0227353i | ||||
\(261\) | 45.5062 | + | 109.862i | 0.174353 | + | 0.420926i | ||||
\(262\) | −30.2060 | − | 190.799i | −0.115290 | − | 0.728239i | ||||
\(263\) | −126.388 | − | 126.388i | −0.480563 | − | 0.480563i | 0.424748 | − | 0.905312i | \(-0.360363\pi\) |
−0.905312 | + | 0.424748i | \(0.860363\pi\) | |||||||
\(264\) | 2.95463 | + | 37.6419i | 0.0111918 | + | 0.142583i | ||||
\(265\) | −6.27164 | − | 6.27164i | −0.0236666 | − | 0.0236666i | ||||
\(266\) | 22.5165 | + | 16.3616i | 0.0846486 | + | 0.0615097i | ||||
\(267\) | −34.9590 | − | 84.3985i | −0.130933 | − | 0.316099i | ||||
\(268\) | 231.916 | + | 271.615i | 0.865358 | + | 1.01349i | ||||
\(269\) | −45.8563 | + | 110.707i | −0.170470 | + | 0.411550i | −0.985907 | − | 0.167295i | \(-0.946497\pi\) |
0.815437 | + | 0.578846i | \(0.196497\pi\) | |||||||
\(270\) | 4.76519 | + | 1.14437i | 0.0176489 | + | 0.00423841i | ||||
\(271\) | 318.563 | 1.17551 | 0.587755 | − | 0.809039i | \(-0.300012\pi\) | ||||
0.587755 | + | 0.809039i | \(0.300012\pi\) | |||||||
\(272\) | −324.123 | + | 235.352i | −1.19163 | + | 0.865266i | ||||
\(273\) | 50.3032i | 0.184261i | ||||||||
\(274\) | −426.226 | − | 102.359i | −1.55557 | − | 0.373573i | ||||
\(275\) | 82.9348 | + | 34.3527i | 0.301581 | + | 0.124919i | ||||
\(276\) | 9.68085 | + | 0.763247i | 0.0350756 | + | 0.00276539i | ||||
\(277\) | −66.2492 | + | 27.4413i | −0.239167 | + | 0.0990661i | −0.499048 | − | 0.866575i | \(-0.666317\pi\) |
0.259881 | + | 0.965641i | \(0.416317\pi\) | |||||||
\(278\) | −169.041 | − | 122.833i | −0.608060 | − | 0.441845i | ||||
\(279\) | 210.901 | − | 210.901i | 0.755919 | − | 0.755919i | ||||
\(280\) | −2.30695 | − | 0.750104i | −0.00823912 | − | 0.00267894i | ||||
\(281\) | 119.493 | − | 119.493i | 0.425243 | − | 0.425243i | −0.461761 | − | 0.887004i | \(-0.652782\pi\) |
0.887004 | + | 0.461761i | \(0.152782\pi\) | |||||||
\(282\) | 8.61401 | + | 54.4110i | 0.0305461 | + | 0.192947i | ||||
\(283\) | 479.828 | − | 198.751i | 1.69550 | − | 0.702301i | 0.695633 | − | 0.718397i | \(-0.255124\pi\) |
0.999870 | + | 0.0160962i | \(0.00512379\pi\) | |||||||
\(284\) | −140.757 | + | 45.7133i | −0.495624 | + | 0.160962i | ||||
\(285\) | −0.731695 | − | 0.303078i | −0.00256735 | − | 0.00106343i | ||||
\(286\) | −88.6676 | + | 54.3272i | −0.310027 | + | 0.189955i | ||||
\(287\) | − | 125.000i | − | 0.435541i | ||||||
\(288\) | 89.0036 | + | 215.084i | 0.309040 | + | 0.746819i | ||||
\(289\) | −337.744 | −1.16867 | ||||||||
\(290\) | 1.95767 | + | 3.19512i | 0.00675058 | + | 0.0110177i | ||||
\(291\) | 62.1813 | − | 150.119i | 0.213681 | − | 0.515872i | ||||
\(292\) | −123.222 | + | 40.0183i | −0.421992 | + | 0.137049i | ||||
\(293\) | 68.8973 | + | 166.333i | 0.235144 | + | 0.567688i | 0.996768 | − | 0.0803308i | \(-0.0255977\pi\) |
−0.761624 | + | 0.648019i | \(0.775598\pi\) | |||||||
\(294\) | −18.1660 | + | 2.87592i | −0.0617890 | + | 0.00978203i | ||||
\(295\) | 7.41332 | + | 7.41332i | 0.0251299 | + | 0.0251299i | ||||
\(296\) | 174.744 | − | 88.9911i | 0.590353 | − | 0.300645i | ||||
\(297\) | 54.3123 | + | 54.3123i | 0.182870 | + | 0.182870i | ||||
\(298\) | 270.095 | − | 371.700i | 0.906361 | − | 1.24732i | ||||
\(299\) | 10.2347 | + | 24.7087i | 0.0342297 | + | 0.0826378i | ||||
\(300\) | −130.898 | − | 10.3201i | −0.436325 | − | 0.0344003i | ||||
\(301\) | 10.8176 | − | 26.1160i | 0.0359389 | − | 0.0867641i | ||||
\(302\) | −7.38936 | + | 30.7695i | −0.0244681 | + | 0.101886i | ||||
\(303\) | 105.722 | 0.348918 | ||||||||
\(304\) | −19.6242 | − | 81.8402i | −0.0645531 | − | 0.269211i | ||||
\(305\) | 4.34605i | 0.0142493i | ||||||||
\(306\) | −85.0483 | + | 354.144i | −0.277936 | + | 1.15733i | ||||
\(307\) | −444.545 | − | 184.137i | −1.44803 | − | 0.599793i | −0.486299 | − | 0.873792i | \(-0.661653\pi\) |
−0.961730 | + | 0.273999i | \(0.911653\pi\) | |||||||
\(308\) | −24.6884 | − | 28.9145i | −0.0801572 | − | 0.0938783i | ||||
\(309\) | 33.8945 | − | 14.0395i | 0.109691 | − | 0.0454354i | ||||
\(310\) | 5.52493 | − | 7.60331i | 0.0178224 | − | 0.0245268i | ||||
\(311\) | −54.5820 | + | 54.5820i | −0.175505 | + | 0.175505i | −0.789393 | − | 0.613888i | \(-0.789605\pi\) |
0.613888 | + | 0.789393i | \(0.289605\pi\) | |||||||
\(312\) | 98.8067 | − | 115.639i | 0.316688 | − | 0.370638i | ||||
\(313\) | 285.265 | − | 285.265i | 0.911389 | − | 0.911389i | −0.0849925 | − | 0.996382i | \(-0.527087\pi\) |
0.996382 | + | 0.0849925i | \(0.0270866\pi\) | |||||||
\(314\) | 553.909 | − | 87.6913i | 1.76404 | − | 0.279272i | ||||
\(315\) | −2.03783 | + | 0.844096i | −0.00646930 | + | 0.00267967i | ||||
\(316\) | −219.069 | + | 429.799i | −0.693255 | + | 1.36012i | ||||
\(317\) | −209.082 | − | 86.6048i | −0.659566 | − | 0.273201i | 0.0276898 | − | 0.999617i | \(-0.491185\pi\) |
−0.687256 | + | 0.726415i | \(0.741185\pi\) | |||||||
\(318\) | 106.229 | + | 173.378i | 0.334055 | + | 0.545212i | ||||
\(319\) | 58.7300i | 0.184107i | ||||||||
\(320\) | 3.82996 | + | 6.25575i | 0.0119686 | + | 0.0195492i | ||||
\(321\) | 86.0397 | 0.268036 | ||||||||
\(322\) | −8.33790 | + | 5.10868i | −0.0258941 | + | 0.0158655i | ||||
\(323\) | 50.3931 | − | 121.660i | 0.156016 | − | 0.376656i | ||||
\(324\) | 133.213 | + | 67.8988i | 0.411152 | + | 0.209564i | ||||
\(325\) | −138.386 | − | 334.094i | −0.425803 | − | 1.02798i | ||||
\(326\) | −53.9873 | − | 341.015i | −0.165605 | − | 1.04606i | ||||
\(327\) | 153.963 | + | 153.963i | 0.470836 | + | 0.470836i | ||||
\(328\) | −245.529 | + | 287.356i | −0.748563 | + | 0.876086i | ||||
\(329\) | −39.2248 | − | 39.2248i | −0.119224 | − | 0.119224i | ||||
\(330\) | 0.875194 | + | 0.635958i | 0.00265210 | + | 0.00192715i | ||||
\(331\) | 165.713 | + | 400.066i | 0.500642 | + | 1.20866i | 0.949134 | + | 0.314871i | \(0.101961\pi\) |
−0.448492 | + | 0.893787i | \(0.648039\pi\) | |||||||
\(332\) | −6.86431 | + | 5.86103i | −0.0206756 | + | 0.0176537i | ||||
\(333\) | 68.2349 | − | 164.734i | 0.204910 | − | 0.494695i | ||||
\(334\) | −269.442 | − | 64.7071i | −0.806714 | − | 0.193734i | ||||
\(335\) | 10.2334 | 0.0305474 | ||||||||
\(336\) | 47.4096 | + | 29.0707i | 0.141100 | + | 0.0865200i | ||||
\(337\) | 361.400i | 1.07240i | 0.844090 | + | 0.536202i | \(0.180141\pi\) | ||||
−0.844090 | + | 0.536202i | \(0.819859\pi\) | |||||||
\(338\) | 78.6648 | + | 18.8915i | 0.232736 | + | 0.0558920i | ||||
\(339\) | 139.888 | + | 57.9435i | 0.412649 | + | 0.170925i | ||||
\(340\) | −0.902057 | + | 11.4415i | −0.00265311 | + | 0.0336514i | ||||
\(341\) | 136.094 | − | 56.3720i | 0.399103 | − | 0.165314i | ||||
\(342\) | −61.9060 | − | 44.9839i | −0.181012 | − | 0.131532i | ||||
\(343\) | 13.0958 | − | 13.0958i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | −76.1656 | + | 38.7884i | −0.221412 | + | 0.112757i | ||||
\(345\) | 0.196747 | − | 0.196747i | 0.000570280 | − | 0.000570280i | ||||
\(346\) | 23.3425 | + | 147.445i | 0.0674638 | + | 0.426141i | ||||
\(347\) | −251.891 | + | 104.337i | −0.725911 | + | 0.300682i | −0.714870 | − | 0.699257i | \(-0.753514\pi\) |
−0.0110405 | + | 0.999939i | \(0.503514\pi\) | |||||||
\(348\) | −26.5346 | − | 81.7037i | −0.0762490 | − | 0.234781i | ||||
\(349\) | −163.743 | − | 67.8246i | −0.469178 | − | 0.194340i | 0.135553 | − | 0.990770i | \(-0.456719\pi\) |
−0.604730 | + | 0.796430i | \(0.706719\pi\) | |||||||
\(350\) | 112.739 | − | 69.0760i | 0.322112 | − | 0.197360i | ||||
\(351\) | − | 309.417i | − | 0.881529i | ||||||
\(352\) | −0.0397416 | + | 114.963i | −0.000112902 | + | 0.326601i | ||||
\(353\) | −516.062 | −1.46193 | −0.730965 | − | 0.682414i | \(-0.760930\pi\) | ||||
−0.730965 | + | 0.682414i | \(0.760930\pi\) | |||||||
\(354\) | −125.567 | − | 204.939i | −0.354710 | − | 0.578924i | ||||
\(355\) | −1.62274 | + | 3.91763i | −0.00457109 | + | 0.0110356i | ||||
\(356\) | −85.9155 | − | 264.545i | −0.241336 | − | 0.743104i | ||||
\(357\) | 33.2996 | + | 80.3924i | 0.0932763 | + | 0.225189i | ||||
\(358\) | 314.530 | − | 49.7944i | 0.878576 | − | 0.139091i | ||||
\(359\) | −59.5942 | − | 59.5942i | −0.166000 | − | 0.166000i | 0.619218 | − | 0.785219i | \(-0.287450\pi\) |
−0.785219 | + | 0.619218i | \(0.787450\pi\) | |||||||
\(360\) | 6.34264 | + | 2.06230i | 0.0176185 | + | 0.00572862i | ||||
\(361\) | −235.702 | − | 235.702i | −0.652913 | − | 0.652913i | ||||
\(362\) | −65.6674 | + | 90.3703i | −0.181402 | + | 0.249642i | ||||
\(363\) | −54.3430 | − | 131.196i | −0.149705 | − | 0.361420i | ||||
\(364\) | −12.0380 | + | 152.688i | −0.0330715 | + | 0.419472i | ||||
\(365\) | −1.42057 | + | 3.42957i | −0.00389198 | + | 0.00939608i | ||||
\(366\) | 23.2658 | − | 96.8794i | 0.0635677 | − | 0.264698i | ||||
\(367\) | 112.975 | 0.307834 | 0.153917 | − | 0.988084i | \(-0.450811\pi\) | ||||
0.153917 | + | 0.988084i | \(0.450811\pi\) | |||||||
\(368\) | 29.2021 | + | 4.63344i | 0.0793536 | + | 0.0125909i | ||||
\(369\) | 343.671i | 0.931357i | ||||||||
\(370\) | 1.31205 | − | 5.46341i | 0.00354608 | − | 0.0147660i | ||||
\(371\) | −189.164 | − | 78.3541i | −0.509875 | − | 0.211197i | ||||
\(372\) | −163.861 | + | 139.912i | −0.440487 | + | 0.376106i | ||||
\(373\) | 297.236 | − | 123.119i | 0.796879 | − | 0.330078i | 0.0531735 | − | 0.998585i | \(-0.483066\pi\) |
0.743706 | + | 0.668507i | \(0.233066\pi\) | |||||||
\(374\) | −105.741 | + | 145.519i | −0.282731 | + | 0.389089i | ||||
\(375\) | −5.32193 | + | 5.32193i | −0.0141918 | + | 0.0141918i | ||||
\(376\) | 13.1254 | + | 167.218i | 0.0349081 | + | 0.444729i | ||||
\(377\) | 167.292 | − | 167.292i | 0.443746 | − | 0.443746i | ||||
\(378\) | 111.739 | − | 17.6899i | 0.295607 | − | 0.0467986i | ||||
\(379\) | 547.024 | − | 226.585i | 1.44333 | − | 0.597849i | 0.482730 | − | 0.875769i | \(-0.339645\pi\) |
0.960604 | + | 0.277921i | \(0.0896452\pi\) | |||||||
\(380\) | −2.14842 | − | 1.09505i | −0.00565374 | − | 0.00288171i | ||||
\(381\) | −282.954 | − | 117.203i | −0.742661 | − | 0.307620i | ||||
\(382\) | 96.7289 | + | 157.872i | 0.253217 | + | 0.413277i | ||||
\(383\) | − | 399.124i | − | 1.04210i | −0.853526 | − | 0.521050i | \(-0.825541\pi\) | ||
0.853526 | − | 0.521050i | \(-0.174459\pi\) | |||||||
\(384\) | −51.8860 | − | 159.952i | −0.135120 | − | 0.416542i | ||||
\(385\) | −1.08939 | −0.00282957 | ||||||||
\(386\) | 140.474 | − | 86.0691i | 0.363922 | − | 0.222977i | ||||
\(387\) | −29.7415 | + | 71.8022i | −0.0768513 | + | 0.185535i | ||||
\(388\) | 224.667 | − | 440.783i | 0.579038 | − | 1.13604i | ||||
\(389\) | 235.318 | + | 568.107i | 0.604930 | + | 1.46043i | 0.868450 | + | 0.495776i | \(0.165116\pi\) |
−0.263520 | + | 0.964654i | \(0.584884\pi\) | |||||||
\(390\) | −0.681463 | − | 4.30451i | −0.00174734 | − | 0.0110372i | ||||
\(391\) | 32.7133 | + | 32.7133i | 0.0836656 | + | 0.0836656i | ||||
\(392\) | −55.8283 | + | 4.38213i | −0.142419 | + | 0.0111789i | ||||
\(393\) | 89.7245 | + | 89.7245i | 0.228307 | + | 0.228307i | ||||
\(394\) | −56.0819 | − | 40.7518i | −0.142340 | − | 0.103431i | ||||
\(395\) | 5.28954 | + | 12.7701i | 0.0133912 | + | 0.0323293i | ||||
\(396\) | 67.8773 | + | 79.4963i | 0.171407 | + | 0.200748i | ||||
\(397\) | 192.537 | − | 464.826i | 0.484981 | − | 1.17085i | −0.472236 | − | 0.881472i | \(-0.656553\pi\) |
0.957216 | − | 0.289374i | \(-0.0934472\pi\) | |||||||
\(398\) | −660.759 | − | 158.682i | −1.66020 | − | 0.398700i | ||||
\(399\) | −18.2827 | −0.0458214 | ||||||||
\(400\) | −394.850 | − | 62.6501i | −0.987126 | − | 0.156625i | ||||
\(401\) | 178.008i | 0.443911i | 0.975057 | + | 0.221956i | \(0.0712440\pi\) | ||||
−0.975057 | + | 0.221956i | \(0.928756\pi\) | |||||||
\(402\) | −228.116 | − | 54.7825i | −0.567453 | − | 0.136275i | ||||
\(403\) | −548.239 | − | 227.088i | −1.36040 | − | 0.563494i | ||||
\(404\) | 320.903 | + | 25.3003i | 0.794315 | + | 0.0626245i | ||||
\(405\) | 3.95800 | − | 1.63946i | 0.00977284 | − | 0.00404804i | ||||
\(406\) | 69.9786 | + | 50.8498i | 0.172361 | + | 0.125246i | ||||
\(407\) | 62.2704 | − | 62.2704i | 0.152998 | − | 0.152998i | ||||
\(408\) | 81.3580 | − | 250.218i | 0.199407 | − | 0.613278i | ||||
\(409\) | −128.627 | + | 128.627i | −0.314490 | + | 0.314490i | −0.846646 | − | 0.532156i | \(-0.821382\pi\) |
0.532156 | + | 0.846646i | \(0.321382\pi\) | |||||||
\(410\) | 1.69339 | + | 10.6965i | 0.00413023 | + | 0.0260889i | ||||
\(411\) | 266.015 | − | 110.187i | 0.647239 | − | 0.268095i | ||||
\(412\) | 106.241 | − | 34.5037i | 0.257867 | − | 0.0837468i | ||||
\(413\) | 223.599 | + | 92.6176i | 0.541401 | + | 0.224256i | ||||
\(414\) | 22.9239 | − | 14.0456i | 0.0553717 | − | 0.0339266i | ||||
\(415\) | 0.258621i | 0.000623182i | ||||||||
\(416\) | 327.586 | − | 327.360i | 0.787468 | − | 0.786923i | ||||
\(417\) | 137.256 | 0.329151 | ||||||||
\(418\) | −19.7452 | − | 32.2263i | −0.0472374 | − | 0.0770964i | ||||
\(419\) | −86.1029 | + | 207.871i | −0.205496 | + | 0.496112i | −0.992704 | − | 0.120576i | \(-0.961526\pi\) |
0.787208 | + | 0.616688i | \(0.211526\pi\) | |||||||
\(420\) | 1.51553 | − | 0.492193i | 0.00360840 | − | 0.00117189i | ||||
\(421\) | 105.929 | + | 255.735i | 0.251613 | + | 0.607447i | 0.998335 | − | 0.0576893i | \(-0.0183733\pi\) |
−0.746722 | + | 0.665137i | \(0.768373\pi\) | |||||||
\(422\) | 31.0122 | − | 4.90965i | 0.0734886 | − | 0.0116342i | ||||
\(423\) | 107.843 | + | 107.843i | 0.254948 | + | 0.254948i | ||||
\(424\) | 280.953 | + | 551.683i | 0.662624 | + | 1.30114i | ||||
\(425\) | −442.326 | − | 442.326i | −1.04077 | − | 1.04077i | ||||
\(426\) | 57.1453 | − | 78.6424i | 0.134144 | − | 0.184607i | ||||
\(427\) | 38.3937 | + | 92.6907i | 0.0899151 | + | 0.217074i | ||||
\(428\) | 261.161 | + | 20.5901i | 0.610188 | + | 0.0481077i | ||||
\(429\) | 26.1394 | − | 63.1062i | 0.0609311 | − | 0.147101i | ||||
\(430\) | −0.571881 | + | 2.38133i | −0.00132996 | + | 0.00553798i | ||||
\(431\) | −601.428 | −1.39543 | −0.697713 | − | 0.716378i | \(-0.745799\pi\) | ||||
−0.697713 | + | 0.716378i | \(0.745799\pi\) | |||||||
\(432\) | −291.619 | − | 178.815i | −0.675043 | − | 0.413924i | ||||
\(433\) | − | 307.274i | − | 0.709639i | −0.934935 | − | 0.354819i | \(-0.884542\pi\) | ||
0.934935 | − | 0.354819i | \(-0.115458\pi\) | |||||||
\(434\) | 50.6644 | − | 210.968i | 0.116738 | − | 0.486102i | ||||
\(435\) | −2.27402 | − | 0.941929i | −0.00522763 | − | 0.00216535i | ||||
\(436\) | 430.487 | + | 504.177i | 0.987357 | + | 1.15637i | ||||
\(437\) | −8.98039 | + | 3.71980i | −0.0205501 | + | 0.00851213i | ||||
\(438\) | 50.0261 | − | 68.8450i | 0.114215 | − | 0.157180i | ||||
\(439\) | 93.6494 | − | 93.6494i | 0.213324 | − | 0.213324i | −0.592354 | − | 0.805678i | \(-0.701801\pi\) |
0.805678 | + | 0.592354i | \(0.201801\pi\) | |||||||
\(440\) | 2.50433 | + | 2.13980i | 0.00569166 | + | 0.00486318i | ||||
\(441\) | −36.0050 | + | 36.0050i | −0.0816441 | + | 0.0816441i | ||||
\(442\) | 715.716 | − | 113.308i | 1.61927 | − | 0.256352i | ||||
\(443\) | 486.277 | − | 201.423i | 1.09769 | − | 0.454679i | 0.241009 | − | 0.970523i | \(-0.422522\pi\) |
0.856683 | + | 0.515844i | \(0.172522\pi\) | |||||||
\(444\) | −58.4947 | + | 114.763i | −0.131745 | + | 0.258475i | ||||
\(445\) | −7.36296 | − | 3.04984i | −0.0165460 | − | 0.00685357i | ||||
\(446\) | 110.453 | + | 180.270i | 0.247652 | + | 0.404194i | ||||
\(447\) | 301.809i | 0.675189i | ||||||||
\(448\) | 136.948 | + | 99.5854i | 0.305687 | + | 0.222289i | ||||
\(449\) | 27.5182 | 0.0612877 | 0.0306439 | − | 0.999530i | \(-0.490244\pi\) | ||||
0.0306439 | + | 0.999530i | \(0.490244\pi\) | |||||||
\(450\) | −309.960 | + | 189.915i | −0.688801 | + | 0.422032i | ||||
\(451\) | −64.9549 | + | 156.815i | −0.144024 | + | 0.347705i | ||||
\(452\) | 410.743 | + | 209.355i | 0.908723 | + | 0.463176i | ||||
\(453\) | −7.95448 | − | 19.2038i | −0.0175596 | − | 0.0423925i | ||||
\(454\) | −64.4533 | − | 407.124i | −0.141968 | − | 0.896750i | ||||
\(455\) | 3.10312 | + | 3.10312i | 0.00682003 | + | 0.00682003i | ||||
\(456\) | 42.0291 | + | 35.9114i | 0.0921692 | + | 0.0787530i | ||||
\(457\) | 74.1666 | + | 74.1666i | 0.162290 | + | 0.162290i | 0.783580 | − | 0.621290i | \(-0.213391\pi\) |
−0.621290 | + | 0.783580i | \(0.713391\pi\) | |||||||
\(458\) | 111.615 | + | 81.1051i | 0.243702 | + | 0.177085i | ||||
\(459\) | −204.827 | − | 494.497i | −0.446247 | − | 1.07734i | ||||
\(460\) | 0.644278 | − | 0.550112i | 0.00140060 | − | 0.00119589i | ||||
\(461\) | −270.858 | + | 653.908i | −0.587543 | + | 1.41846i | 0.298300 | + | 0.954472i | \(0.403580\pi\) |
−0.885844 | + | 0.463983i | \(0.846420\pi\) | |||||||
\(462\) | 24.2839 | + | 5.83183i | 0.0525626 | + | 0.0126230i | ||||
\(463\) | 44.7224 | 0.0965927 | 0.0482964 | − | 0.998833i | \(-0.484621\pi\) | ||||
0.0482964 | + | 0.998833i | \(0.484621\pi\) | |||||||
\(464\) | −60.9895 | − | 254.349i | −0.131443 | − | 0.548167i | ||||
\(465\) | 6.17366i | 0.0132767i | ||||||||
\(466\) | 794.951 | + | 190.909i | 1.70590 | + | 0.409676i | ||||
\(467\) | 296.025 | + | 122.618i | 0.633887 | + | 0.262565i | 0.676404 | − | 0.736531i | \(-0.263538\pi\) |
−0.0425167 | + | 0.999096i | \(0.513538\pi\) | |||||||
\(468\) | 33.0969 | − | 419.793i | 0.0707198 | − | 0.896995i | ||||
\(469\) | 218.253 | − | 90.4035i | 0.465359 | − | 0.192758i | ||||
\(470\) | 3.88790 | + | 2.82514i | 0.00827214 | + | 0.00601093i | ||||
\(471\) | −260.480 | + | 260.480i | −0.553036 | + | 0.553036i | ||||
\(472\) | −332.097 | − | 652.111i | −0.703595 | − | 1.38159i | ||||
\(473\) | −27.1417 | + | 27.1417i | −0.0573820 | + | 0.0573820i | ||||
\(474\) | −49.5489 | − | 312.979i | −0.104533 | − | 0.660294i | ||||
\(475\) | 121.426 | − | 50.2965i | 0.255635 | − | 0.105887i | ||||
\(476\) | 81.8374 | + | 251.988i | 0.171927 | + | 0.529387i | ||||
\(477\) | 520.078 | + | 215.423i | 1.09031 | + | 0.451622i | ||||
\(478\) | 213.405 | − | 130.755i | 0.446454 | − | 0.273545i | ||||
\(479\) | 676.370i | 1.41205i | 0.708189 | + | 0.706023i | \(0.249512\pi\) | ||||
−0.708189 | + | 0.706023i | \(0.750488\pi\) | |||||||
\(480\) | −4.45073 | − | 1.84536i | −0.00927236 | − | 0.00384449i | ||||
\(481\) | −354.754 | −0.737534 | ||||||||
\(482\) | −11.6014 | − | 18.9347i | −0.0240693 | − | 0.0392836i | ||||
\(483\) | 2.45803 | − | 5.93422i | 0.00508910 | − | 0.0122862i | ||||
\(484\) | −133.554 | − | 411.229i | −0.275937 | − | 0.849647i | ||||
\(485\) | −5.42472 | − | 13.0964i | −0.0111850 | − | 0.0270029i | ||||
\(486\) | −477.108 | + | 75.5327i | −0.981703 | + | 0.155417i | ||||
\(487\) | 630.190 | + | 630.190i | 1.29402 | + | 1.29402i | 0.932275 | + | 0.361750i | \(0.117820\pi\) |
0.361750 | + | 0.932275i | \(0.382180\pi\) | |||||||
\(488\) | 93.8039 | − | 288.495i | 0.192221 | − | 0.591179i | ||||
\(489\) | 160.365 | + | 160.365i | 0.327945 | + | 0.327945i | ||||
\(490\) | −0.943216 | + | 1.29804i | −0.00192493 | + | 0.00264905i | ||||
\(491\) | −41.5293 | − | 100.261i | −0.0845810 | − | 0.204197i | 0.875930 | − | 0.482438i | \(-0.160249\pi\) |
−0.960511 | + | 0.278241i | \(0.910249\pi\) | |||||||
\(492\) | 19.5134 | − | 247.504i | 0.0396614 | − | 0.503057i | ||||
\(493\) | 156.616 | − | 378.104i | 0.317679 | − | 0.766944i | ||||
\(494\) | −35.5523 | + | 148.041i | −0.0719682 | + | 0.299678i | ||||
\(495\) | 2.99511 | 0.00605073 | ||||||||
\(496\) | −530.859 | + | 385.467i | −1.07028 | + | 0.777151i | ||||
\(497\) | 97.8891i | 0.196960i | ||||||||
\(498\) | 1.38448 | − | 5.76501i | 0.00278008 | − | 0.0115763i | ||||
\(499\) | 627.249 | + | 259.815i | 1.25701 | + | 0.520671i | 0.908991 | − | 0.416815i | \(-0.136854\pi\) |
0.348021 | + | 0.937487i | \(0.386854\pi\) | |||||||
\(500\) | −17.4275 | + | 14.8803i | −0.0348550 | + | 0.0297607i | ||||
\(501\) | 168.164 | − | 69.6558i | 0.335656 | − | 0.139033i | ||||
\(502\) | −270.358 | + | 372.062i | −0.538563 | + | 0.741160i | ||||
\(503\) | −668.772 | + | 668.772i | −1.32957 | + | 1.32957i | −0.423819 | + | 0.905747i | \(0.639311\pi\) |
−0.905747 | + | 0.423819i | \(0.860689\pi\) | |||||||
\(504\) | 153.492 | − | 12.0480i | 0.304547 | − | 0.0239049i | ||||
\(505\) | 6.52181 | − | 6.52181i | 0.0129145 | − | 0.0129145i | ||||
\(506\) | 13.1147 | − | 2.07623i | 0.0259184 | − | 0.00410323i | ||||
\(507\) | −49.0961 | + | 20.3363i | −0.0968365 | + | 0.0401110i | ||||
\(508\) | −830.816 | − | 423.467i | −1.63547 | − | 0.833596i | ||||
\(509\) | 454.172 | + | 188.124i | 0.892283 | + | 0.369596i | 0.781248 | − | 0.624221i | \(-0.214583\pi\) |
0.111035 | + | 0.993816i | \(0.464583\pi\) | |||||||
\(510\) | −3.93858 | − | 6.42818i | −0.00772271 | − | 0.0126043i | ||||
\(511\) | 85.6940i | 0.167699i | ||||||||
\(512\) | −119.214 | − | 497.928i | −0.232840 | − | 0.972515i | ||||
\(513\) | 112.458 | 0.219216 | ||||||||
\(514\) | −19.6152 | + | 12.0183i | −0.0381618 | + | 0.0233819i | ||||
\(515\) | 1.22481 | − | 2.95696i | 0.00237828 | − | 0.00574168i | ||||
\(516\) | 25.4960 | − | 50.0217i | 0.0494109 | − | 0.0969412i | ||||
\(517\) | 28.8255 | + | 69.5908i | 0.0557553 | + | 0.134605i | ||||
\(518\) | −20.2819 | − | 128.112i | −0.0391542 | − | 0.247321i | ||||
\(519\) | −69.3370 | − | 69.3370i | −0.133597 | − | 0.133597i | ||||
\(520\) | −1.03837 | − | 13.2288i | −0.00199686 | − | 0.0254400i | ||||
\(521\) | −665.541 | − | 665.541i | −1.27743 | − | 1.27743i | −0.942101 | − | 0.335329i | \(-0.891153\pi\) |
−0.335329 | − | 0.942101i | \(-0.608847\pi\) | |||||||
\(522\) | −192.396 | − | 139.804i | −0.368575 | − | 0.267824i | ||||
\(523\) | −76.5057 | − | 184.701i | −0.146282 | − | 0.353157i | 0.833707 | − | 0.552207i | \(-0.186214\pi\) |
−0.979989 | + | 0.199050i | \(0.936214\pi\) | |||||||
\(524\) | 250.873 | + | 293.817i | 0.478766 | + | 0.560720i | ||||
\(525\) | −33.2358 | + | 80.2383i | −0.0633063 | + | 0.152835i | ||||
\(526\) | 347.597 | + | 83.4760i | 0.660830 | + | 0.158700i | ||||
\(527\) | −1026.50 | −1.94782 | ||||||||
\(528\) | −44.3699 | − | 61.1055i | −0.0840340 | − | 0.115730i | ||||
\(529\) | 525.585i | 0.993544i | ||||||||
\(530\) | 17.2485 | + | 4.14225i | 0.0325443 | + | 0.00781557i | ||||
\(531\) | −614.753 | − | 254.639i | −1.15773 | − | 0.479546i | ||||
\(532\) | −55.4945 | − | 4.37523i | −0.104313 | − | 0.00822412i | ||||
\(533\) | 631.711 | − | 261.663i | 1.18520 | − | 0.490925i | ||||
\(534\) | 147.804 | + | 107.401i | 0.276786 | + | 0.201126i | ||||
\(535\) | 5.30764 | − | 5.30764i | 0.00992081 | − | 0.00992081i | ||||
\(536\) | −679.303 | − | 220.875i | −1.26736 | − | 0.412080i | ||||
\(537\) | −147.910 | + | 147.910i | −0.275438 | + | 0.275438i | ||||
\(538\) | −37.4742 | − | 236.709i | −0.0696547 | − | 0.439979i | ||||
\(539\) | −23.2340 | + | 9.62382i | −0.0431057 | + | 0.0178550i | ||||
\(540\) | −9.32206 | + | 3.02750i | −0.0172631 | + | 0.00560647i | ||||
\(541\) | −319.044 | − | 132.153i | −0.589731 | − | 0.244275i | 0.0678039 | − | 0.997699i | \(-0.478401\pi\) |
−0.657535 | + | 0.753424i | \(0.728401\pi\) | |||||||
\(542\) | −543.262 | + | 332.860i | −1.00233 | + | 0.614133i | ||||
\(543\) | − | 73.3780i | − | 0.135134i | ||||||
\(544\) | 306.830 | − | 740.028i | 0.564025 | − | 1.36035i | ||||
\(545\) | 18.9954 | 0.0348540 | ||||||||
\(546\) | −52.5608 | − | 85.7847i | −0.0962651 | − | 0.157115i | ||||
\(547\) | −299.065 | + | 722.007i | −0.546737 | + | 1.31994i | 0.373155 | + | 0.927769i | \(0.378276\pi\) |
−0.919892 | + | 0.392171i | \(0.871724\pi\) | |||||||
\(548\) | 833.818 | − | 270.796i | 1.52157 | − | 0.494154i | ||||
\(549\) | −105.558 | − | 254.840i | −0.192273 | − | 0.464189i | ||||
\(550\) | −177.328 | + | 28.0734i | −0.322414 | + | 0.0510425i | ||||
\(551\) | 60.8025 | + | 60.8025i | 0.110349 | + | 0.110349i | ||||
\(552\) | −17.3068 | + | 8.81372i | −0.0313528 | + | 0.0159669i | ||||
\(553\) | 225.626 | + | 225.626i | 0.408004 | + | 0.408004i | ||||
\(554\) | 84.3054 | − | 116.019i | 0.152176 | − | 0.209421i | ||||
\(555\) | 1.41239 | + | 3.40981i | 0.00254485 | + | 0.00614380i | ||||
\(556\) | 416.619 | + | 32.8466i | 0.749315 | + | 0.0590767i | ||||
\(557\) | −101.235 | + | 244.402i | −0.181750 | + | 0.438783i | −0.988327 | − | 0.152346i | \(-0.951317\pi\) |
0.806578 | + | 0.591128i | \(0.201317\pi\) | |||||||
\(558\) | −139.295 | + | 580.028i | −0.249632 | + | 1.03948i | ||||
\(559\) | 154.626 | 0.276612 | ||||||||
\(560\) | 4.71794 | − | 1.13130i | 0.00842489 | − | 0.00202017i | ||||
\(561\) | − | 118.157i | − | 0.210619i | ||||||
\(562\) | −78.9222 | + | 328.634i | −0.140431 | + | 0.584759i | ||||
\(563\) | −888.243 | − | 367.922i | −1.57770 | − | 0.653503i | −0.589650 | − | 0.807659i | \(-0.700734\pi\) |
−0.988047 | + | 0.154155i | \(0.950734\pi\) | |||||||
\(564\) | −71.5429 | − | 83.7894i | −0.126849 | − | 0.148563i | ||||
\(565\) | 12.2039 | − | 5.05501i | 0.0215998 | − | 0.00894692i | ||||
\(566\) | −610.604 | + | 840.303i | −1.07881 | + | 1.48463i | ||||
\(567\) | 69.9313 | − | 69.9313i | 0.123336 | − | 0.123336i | ||||
\(568\) | 192.276 | − | 225.032i | 0.338514 | − | 0.396183i | ||||
\(569\) | −467.459 | + | 467.459i | −0.821546 | + | 0.821546i | −0.986330 | − | 0.164784i | \(-0.947307\pi\) |
0.164784 | + | 0.986330i | \(0.447307\pi\) | |||||||
\(570\) | 1.56448 | − | 0.247678i | 0.00274470 | − | 0.000434523i | ||||
\(571\) | −549.011 | + | 227.408i | −0.961491 | + | 0.398263i | −0.807538 | − | 0.589816i | \(-0.799200\pi\) |
−0.153953 | + | 0.988078i | \(0.549200\pi\) | |||||||
\(572\) | 94.4442 | − | 185.294i | 0.165112 | − | 0.323940i | ||||
\(573\) | −112.360 | − | 46.5410i | −0.196091 | − | 0.0812234i | ||||
\(574\) | 130.610 | + | 213.170i | 0.227544 | + | 0.371376i | ||||
\(575\) | 46.1748i | 0.0803041i | ||||||||
\(576\) | −376.519 | − | 273.796i | −0.653679 | − | 0.475340i | ||||
\(577\) | −141.741 | −0.245652 | −0.122826 | − | 0.992428i | \(-0.539196\pi\) | ||||
−0.122826 | + | 0.992428i | \(0.539196\pi\) | |||||||
\(578\) | 575.973 | − | 352.902i | 0.996493 | − | 0.610557i | ||||
\(579\) | −41.4120 | + | 99.9775i | −0.0715234 | + | 0.172673i | ||||
\(580\) | −6.67703 | − | 3.40328i | −0.0115121 | − | 0.00586772i | ||||
\(581\) | 2.28470 | + | 5.51575i | 0.00393235 | + | 0.00949354i | ||||
\(582\) | 50.8151 | + | 320.978i | 0.0873112 | + | 0.551508i | ||||
\(583\) | 196.593 | + | 196.593i | 0.337209 | + | 0.337209i | ||||
\(584\) | 168.322 | − | 196.997i | 0.288223 | − | 0.337324i | ||||
\(585\) | −8.53158 | − | 8.53158i | −0.0145839 | − | 0.0145839i | ||||
\(586\) | −291.292 | − | 211.667i | −0.497085 | − | 0.361206i | ||||
\(587\) | −446.045 | − | 1076.85i | −0.759873 | − | 1.83450i | −0.490434 | − | 0.871478i | \(-0.663162\pi\) |
−0.269439 | − | 0.963018i | \(-0.586838\pi\) | |||||||
\(588\) | 27.9744 | − | 23.8857i | 0.0475755 | − | 0.0406219i | ||||
\(589\) | 82.5354 | − | 199.258i | 0.140128 | − | 0.338299i | ||||
\(590\) | −20.3884 | − | 4.89630i | −0.0345565 | − | 0.00829882i | ||||
\(591\) | 45.5368 | 0.0770504 | ||||||||
\(592\) | −205.016 | + | 334.348i | −0.346311 | + | 0.564777i | ||||
\(593\) | 881.498i | 1.48651i | 0.669011 | + | 0.743253i | \(0.266718\pi\) | ||||
−0.669011 | + | 0.743253i | \(0.733282\pi\) | |||||||
\(594\) | −149.371 | − | 35.8718i | −0.251467 | − | 0.0603902i | ||||
\(595\) | 7.01346 | + | 2.90507i | 0.0117873 | + | 0.00488247i | ||||
\(596\) | −72.2259 | + | 916.097i | −0.121184 | + | 1.53708i | ||||
\(597\) | 412.391 | − | 170.818i | 0.690773 | − | 0.286128i | ||||
\(598\) | −43.2714 | − | 31.4430i | −0.0723601 | − | 0.0525803i | ||||
\(599\) | −22.3963 | + | 22.3963i | −0.0373895 | + | 0.0373895i | −0.725554 | − | 0.688165i | \(-0.758417\pi\) |
0.688165 | + | 0.725554i | \(0.258417\pi\) | |||||||
\(600\) | 234.010 | − | 119.173i | 0.390016 | − | 0.198621i | ||||
\(601\) | 214.917 | − | 214.917i | 0.357599 | − | 0.357599i | −0.505328 | − | 0.862927i | \(-0.668629\pi\) |
0.862927 | + | 0.505328i | \(0.168629\pi\) | |||||||
\(602\) | 8.84024 | + | 55.8401i | 0.0146848 | + | 0.0927576i | ||||
\(603\) | −600.056 | + | 248.551i | −0.995118 | + | 0.412191i | ||||
\(604\) | −19.5490 | − | 60.1939i | −0.0323659 | − | 0.0996588i | ||||
\(605\) | −11.4455 | − | 4.74090i | −0.0189183 | − | 0.00783620i | ||||
\(606\) | −180.293 | + | 110.467i | −0.297514 | + | 0.182288i | ||||
\(607\) | 544.542i | 0.897103i | 0.893757 | + | 0.448552i | \(0.148060\pi\) | ||||
−0.893757 | + | 0.448552i | \(0.851940\pi\) | |||||||
\(608\) | 118.979 | + | 119.062i | 0.195690 | + | 0.195825i | ||||
\(609\) | −56.8205 | −0.0933012 | ||||||||
\(610\) | −4.54110 | − | 7.41155i | −0.00744442 | − | 0.0121501i | ||||
\(611\) | 116.120 | − | 280.339i | 0.190049 | − | 0.458820i | ||||
\(612\) | −225.000 | − | 692.806i | −0.367648 | − | 1.13204i | ||||
\(613\) | 350.821 | + | 846.957i | 0.572302 | + | 1.38166i | 0.899591 | + | 0.436734i | \(0.143865\pi\) |
−0.327289 | + | 0.944924i | \(0.606135\pi\) | |||||||
\(614\) | 950.506 | − | 150.478i | 1.54806 | − | 0.245078i | ||||
\(615\) | −5.03009 | − | 5.03009i | −0.00817901 | − | 0.00817901i | ||||
\(616\) | 72.3146 | + | 23.5130i | 0.117394 | + | 0.0381705i | ||||
\(617\) | 281.218 | + | 281.218i | 0.455783 | + | 0.455783i | 0.897269 | − | 0.441485i | \(-0.145548\pi\) |
−0.441485 | + | 0.897269i | \(0.645548\pi\) | |||||||
\(618\) | −43.1324 | + | 59.3580i | −0.0697935 | + | 0.0960485i | ||||
\(619\) | 381.822 | + | 921.800i | 0.616837 | + | 1.48918i | 0.855357 | + | 0.518039i | \(0.173338\pi\) |
−0.238520 | + | 0.971138i | \(0.576662\pi\) | |||||||
\(620\) | −1.47742 | + | 18.7392i | −0.00238293 | + | 0.0302245i | ||||
\(621\) | −15.1195 | + | 36.5016i | −0.0243470 | + | 0.0587788i | ||||
\(622\) | 36.0500 | − | 150.113i | 0.0579581 | − | 0.241340i | ||||
\(623\) | −183.977 | −0.295308 | ||||||||
\(624\) | −47.6713 | + | 300.447i | −0.0763962 | + | 0.481485i | ||||
\(625\) | − | 624.015i | − | 0.998424i | ||||||
\(626\) | −188.410 | + | 784.544i | −0.300974 | + | 1.25327i | ||||
\(627\) | 22.9360 | + | 9.50039i | 0.0365805 | + | 0.0151521i | ||||
\(628\) | −852.984 | + | 728.313i | −1.35825 | + | 1.15973i | ||||
\(629\) | −566.953 | + | 234.840i | −0.901356 | + | 0.373354i | ||||
\(630\) | 2.59324 | − | 3.56877i | 0.00411625 | − | 0.00566471i | ||||
\(631\) | −521.466 | + | 521.466i | −0.826413 | + | 0.826413i | −0.987019 | − | 0.160606i | \(-0.948655\pi\) |
0.160606 | + | 0.987019i | \(0.448655\pi\) | |||||||
\(632\) | −75.4992 | − | 961.859i | −0.119461 | − | 1.52193i | ||||
\(633\) | −14.5837 | + | 14.5837i | −0.0230390 | + | 0.0230390i | ||||
\(634\) | 447.051 | − | 70.7742i | 0.705128 | − | 0.111631i | ||||
\(635\) | −24.6850 | + | 10.2249i | −0.0388740 | + | 0.0161021i | ||||
\(636\) | −362.317 | − | 184.673i | −0.569681 | − | 0.290366i | ||||
\(637\) | 93.5954 | + | 38.7685i | 0.146931 | + | 0.0608610i | ||||
\(638\) | −61.3658 | − | 100.155i | −0.0961846 | − | 0.156983i | ||||
\(639\) | − | 269.132i | − | 0.421177i | ||||||
\(640\) | −13.0679 | − | 6.66641i | −0.0204186 | − | 0.0104163i | ||||
\(641\) | 337.238 | 0.526112 | 0.263056 | − | 0.964781i | \(-0.415270\pi\) | ||||
0.263056 | + | 0.964781i | \(0.415270\pi\) | |||||||
\(642\) | −146.728 | + | 89.9011i | −0.228548 | + | 0.140033i | ||||
\(643\) | 316.087 | − | 763.103i | 0.491582 | − | 1.18678i | −0.462332 | − | 0.886707i | \(-0.652987\pi\) |
0.953915 | − | 0.300078i | \(-0.0970127\pi\) | |||||||
\(644\) | 8.88111 | − | 17.4242i | 0.0137905 | − | 0.0270562i | ||||
\(645\) | −0.615617 | − | 1.48623i | −0.000954445 | − | 0.00230423i | ||||
\(646\) | 41.1817 | + | 260.127i | 0.0637488 | + | 0.402674i | ||||
\(647\) | 428.698 | + | 428.698i | 0.662594 | + | 0.662594i | 0.955991 | − | 0.293397i | \(-0.0947858\pi\) |
−0.293397 | + | 0.955991i | \(0.594786\pi\) | |||||||
\(648\) | −298.122 | + | 23.4005i | −0.460065 | + | 0.0361119i | ||||
\(649\) | −232.381 | − | 232.381i | −0.358060 | − | 0.358060i | ||||
\(650\) | 585.084 | + | 425.150i | 0.900130 | + | 0.654078i | ||||
\(651\) | 54.5391 | + | 131.669i | 0.0837775 | + | 0.202257i | ||||
\(652\) | 448.387 | + | 525.141i | 0.687710 | + | 0.805430i | ||||
\(653\) | 201.780 | − | 487.139i | 0.309004 | − | 0.746002i | −0.690734 | − | 0.723109i | \(-0.742712\pi\) |
0.999738 | − | 0.0228926i | \(-0.00728757\pi\) | |||||||
\(654\) | −423.435 | − | 101.689i | −0.647453 | − | 0.155487i | ||||
\(655\) | 11.0699 | 0.0169006 | ||||||||
\(656\) | 118.460 | − | 746.591i | 0.180579 | − | 1.13810i | ||||
\(657\) | − | 235.603i | − | 0.358605i | ||||||
\(658\) | 107.877 | + | 25.9069i | 0.163947 | + | 0.0393723i | ||||
\(659\) | 7.55233 | + | 3.12828i | 0.0114603 | + | 0.00474701i | 0.388406 | − | 0.921488i | \(-0.373026\pi\) |
−0.376946 | + | 0.926235i | \(0.623026\pi\) | |||||||
\(660\) | −2.15701 | − | 0.170061i | −0.00326820 | − | 0.000257668i | ||||
\(661\) | −134.823 | + | 55.8457i | −0.203969 | + | 0.0844867i | −0.482329 | − | 0.875990i | \(-0.660209\pi\) |
0.278360 | + | 0.960477i | \(0.410209\pi\) | |||||||
\(662\) | −700.619 | − | 509.103i | −1.05834 | − | 0.769038i | ||||
\(663\) | −336.571 | + | 336.571i | −0.507649 | + | 0.507649i | ||||
\(664\) | 5.58200 | − | 17.1675i | 0.00840662 | − | 0.0258547i | ||||
\(665\) | −1.12783 | + | 1.12783i | −0.00169598 | + | 0.00169598i | ||||
\(666\) | 55.7622 | + | 352.226i | 0.0837270 | + | 0.528868i | ||||
\(667\) | −27.9100 | + | 11.5607i | −0.0418440 | + | 0.0173324i | ||||
\(668\) | 527.106 | − | 171.186i | 0.789080 | − | 0.256267i | ||||
\(669\) | −128.301 | − | 53.1442i | −0.191781 | − | 0.0794382i | ||||
\(670\) | −17.4515 | + | 10.6927i | −0.0260471 | + | 0.0159592i | ||||
\(671\) | − | 136.233i | − | 0.203029i | ||||||
\(672\) | −111.226 | − | 0.0384495i | −0.165514 | − | 5.72165e-5i | ||||
\(673\) | −652.697 | −0.969832 | −0.484916 | − | 0.874561i | \(-0.661150\pi\) | ||||
−0.484916 | + | 0.874561i | \(0.661150\pi\) | |||||||
\(674\) | −377.619 | − | 616.314i | −0.560266 | − | 0.914413i | ||||
\(675\) | 204.435 | − | 493.549i | 0.302866 | − | 0.731183i | ||||
\(676\) | −153.891 | + | 49.9786i | −0.227649 | + | 0.0739328i | ||||
\(677\) | 100.307 | + | 242.162i | 0.148163 | + | 0.357698i | 0.980485 | − | 0.196595i | \(-0.0629885\pi\) |
−0.832321 | + | 0.554293i | \(0.812989\pi\) | |||||||
\(678\) | −299.102 | + | 47.3520i | −0.441154 | + | 0.0698406i | ||||
\(679\) | −231.392 | − | 231.392i | −0.340784 | − | 0.340784i | ||||
\(680\) | −10.4167 | − | 20.4543i | −0.0153186 | − | 0.0300799i | ||||
\(681\) | 191.453 | + | 191.453i | 0.281136 | + | 0.281136i | ||||
\(682\) | −173.186 | + | 238.336i | −0.253939 | + | 0.349466i | ||||
\(683\) | −91.1509 | − | 220.058i | −0.133457 | − | 0.322193i | 0.842998 | − | 0.537917i | \(-0.180789\pi\) |
−0.976454 | + | 0.215724i | \(0.930789\pi\) | |||||||
\(684\) | 152.574 | + | 12.0291i | 0.223062 | + | 0.0175864i | ||||
\(685\) | 9.61276 | − | 23.2072i | 0.0140332 | − | 0.0338792i | ||||
\(686\) | −8.64943 | + | 36.0165i | −0.0126085 | + | 0.0525022i | ||||
\(687\) | −90.6283 | −0.131919 | ||||||||
\(688\) | 89.3600 | − | 145.732i | 0.129884 | − | 0.211820i | ||||
\(689\) | − | 1119.99i | − | 1.62553i | ||||||
\(690\) | −0.129946 | + | 0.541099i | −0.000188327 | + | 0.000784201i | ||||
\(691\) | 149.012 | + | 61.7227i | 0.215646 | + | 0.0893237i | 0.487892 | − | 0.872904i | \(-0.337766\pi\) |
−0.272245 | + | 0.962228i | \(0.587766\pi\) | |||||||
\(692\) | −193.869 | − | 227.055i | −0.280158 | − | 0.328114i | ||||
\(693\) | 63.8785 | − | 26.4593i | 0.0921767 | − | 0.0381809i | ||||
\(694\) | 320.544 | − | 441.127i | 0.461879 | − | 0.635629i | ||||
\(695\) | 8.46707 | − | 8.46707i | 0.0121828 | − | 0.0121828i | ||||
\(696\) | 130.621 | + | 111.608i | 0.187674 | + | 0.160356i | ||||
\(697\) | 836.358 | − | 836.358i | 1.19994 | − | 1.19994i | ||||
\(698\) | 350.108 | − | 55.4269i | 0.501587 | − | 0.0794081i | ||||
\(699\) | −496.143 | + | 205.509i | −0.709790 | + | 0.294005i | ||||
\(700\) | −120.084 | + | 235.598i | −0.171549 | + | 0.336568i | ||||
\(701\) | 1082.83 | + | 448.521i | 1.54469 | + | 0.639830i | 0.982346 | − | 0.187076i | \(-0.0599009\pi\) |
0.562341 | + | 0.826906i | \(0.309901\pi\) | |||||||
\(702\) | 323.303 | + | 527.665i | 0.460546 | + | 0.751659i | ||||
\(703\) | − | 128.936i | − | 0.183408i | ||||||
\(704\) | −120.055 | − | 196.095i | −0.170533 | − | 0.278544i | ||||
\(705\) | −3.15686 | −0.00447782 | ||||||||
\(706\) | 880.067 | − | 539.222i | 1.24655 | − | 0.763771i | ||||
\(707\) | 81.4795 | − | 196.709i | 0.115247 | − | 0.278231i | ||||
\(708\) | 428.273 | + | 218.291i | 0.604906 | + | 0.308320i | ||||
\(709\) | 77.1824 | + | 186.335i | 0.108861 | + | 0.262813i | 0.968917 | − | 0.247386i | \(-0.0795716\pi\) |
−0.860056 | + | 0.510199i | \(0.829572\pi\) | |||||||
\(710\) | −1.32611 | − | 8.37651i | −0.00186777 | − | 0.0117979i | ||||
\(711\) | −620.327 | − | 620.327i | −0.872471 | − | 0.872471i | ||||
\(712\) | 422.934 | + | 361.371i | 0.594008 | + | 0.507544i | ||||
\(713\) | 53.5788 | + | 53.5788i | 0.0751455 | + | 0.0751455i | ||||
\(714\) | −140.788 | − | 102.303i | −0.197182 | − | 0.143282i | ||||
\(715\) | −2.28041 | − | 5.50540i | −0.00318939 | − | 0.00769987i | ||||
\(716\) | −484.356 | + | 413.563i | −0.676475 | + | 0.577602i | ||||
\(717\) | −62.9123 | + | 151.884i | −0.0877439 | + | 0.211832i | ||||
\(718\) | 163.898 | + | 39.3604i | 0.228270 | + | 0.0548194i | ||||
\(719\) | 151.151 | 0.210224 | 0.105112 | − | 0.994460i | \(-0.466480\pi\) | ||||
0.105112 | + | 0.994460i | \(0.466480\pi\) | |||||||
\(720\) | −12.9713 | + | 3.11034i | −0.0180157 | + | 0.00431992i | ||||
\(721\) | − | 73.8851i | − | 0.102476i | ||||||
\(722\) | 648.234 | + | 155.675i | 0.897831 | + | 0.215616i | ||||
\(723\) | 13.4761 | + | 5.58200i | 0.0186392 | + | 0.00772061i | ||||
\(724\) | 17.5601 | − | 222.728i | 0.0242542 | − | 0.307635i | ||||
\(725\) | 377.379 | − | 156.315i | 0.520522 | − | 0.215607i | ||||
\(726\) | 229.757 | + | 166.953i | 0.316470 | + | 0.229963i | ||||
\(727\) | −164.336 | + | 164.336i | −0.226047 | + | 0.226047i | −0.811039 | − | 0.584992i | \(-0.801098\pi\) |
0.584992 | + | 0.811039i | \(0.301098\pi\) | |||||||
\(728\) | −139.011 | − | 272.965i | −0.190949 | − | 0.374952i | ||||
\(729\) | −13.5203 | + | 13.5203i | −0.0185463 | + | 0.0185463i | ||||
\(730\) | −1.16091 | − | 7.33295i | −0.00159028 | − | 0.0100451i | ||||
\(731\) | 247.117 | − | 102.359i | 0.338053 | − | 0.140026i | ||||
\(732\) | 61.5509 | + | 189.523i | 0.0840860 | + | 0.258912i | ||||
\(733\) | 125.388 | + | 51.9372i | 0.171061 | + | 0.0708557i | 0.466570 | − | 0.884484i | \(-0.345489\pi\) |
−0.295510 | + | 0.955340i | \(0.595489\pi\) | |||||||
\(734\) | −192.662 | + | 118.045i | −0.262483 | + | 0.160825i | ||||
\(735\) | − | 1.05397i | − | 0.00143397i | ||||||
\(736\) | −54.6413 | + | 22.6111i | −0.0742409 | + | 0.0307215i | ||||
\(737\) | −320.779 | −0.435250 | ||||||||
\(738\) | −359.094 | − | 586.080i | −0.486578 | − | 0.794146i | ||||
\(739\) | 498.598 | − | 1203.72i | 0.674693 | − | 1.62885i | −0.0988460 | − | 0.995103i | \(-0.531515\pi\) |
0.773539 | − | 0.633749i | \(-0.218485\pi\) | |||||||
\(740\) | 3.47110 | + | 10.6880i | 0.00469067 | + | 0.0144432i | ||||
\(741\) | −38.2712 | − | 92.3949i | −0.0516481 | − | 0.124690i | ||||
\(742\) | 404.461 | − | 64.0317i | 0.545096 | − | 0.0862961i | ||||
\(743\) | −738.261 | − | 738.261i | −0.993622 | − | 0.993622i | 0.00635773 | − | 0.999980i | \(-0.497976\pi\) |
−0.999980 | + | 0.00635773i | \(0.997976\pi\) | |||||||
\(744\) | 133.251 | − | 409.814i | 0.179100 | − | 0.550825i | ||||
\(745\) | 18.6181 | + | 18.6181i | 0.0249907 | + | 0.0249907i | ||||
\(746\) | −378.247 | + | 520.537i | −0.507034 | + | 0.697771i | ||||
\(747\) | −6.28145 | − | 15.1648i | −0.00840890 | − | 0.0203009i | ||||
\(748\) | 28.2762 | − | 358.649i | 0.0378024 | − | 0.479477i | ||||
\(749\) | 66.3104 | − | 160.088i | 0.0885319 | − | 0.213735i | ||||
\(750\) | 3.51500 | − | 14.6366i | 0.00468666 | − | 0.0195154i | ||||
\(751\) | 1212.63 | 1.61469 | 0.807344 | − | 0.590081i | \(-0.200904\pi\) | ||||
0.807344 | + | 0.590081i | \(0.200904\pi\) | |||||||
\(752\) | −197.106 | − | 271.451i | −0.262109 | − | 0.360972i | ||||
\(753\) | − | 302.103i | − | 0.401200i | ||||||
\(754\) | −110.492 | + | 460.093i | −0.146541 | + | 0.610203i | ||||
\(755\) | −1.67535 | − | 0.693952i | −0.00221900 | − | 0.000919142i | ||||
\(756\) | −172.071 | + | 146.922i | −0.227608 | + | 0.194341i | ||||
\(757\) | 507.696 | − | 210.295i | 0.670669 | − | 0.277800i | −0.0212514 | − | 0.999774i | \(-0.506765\pi\) |
0.691920 | + | 0.721974i | \(0.256765\pi\) | |||||||
\(758\) | −696.115 | + | 957.980i | −0.918357 | + | 1.26383i | ||||
\(759\) | −6.16729 | + | 6.16729i | −0.00812554 | + | 0.00812554i | ||||
\(760\) | 4.80801 | − | 0.377395i | 0.00632633 | − | 0.000496573i | ||||
\(761\) | 150.165 | − | 150.165i | 0.197326 | − | 0.197326i | −0.601527 | − | 0.798853i | \(-0.705441\pi\) |
0.798853 | + | 0.601527i | \(0.205441\pi\) | |||||||
\(762\) | 604.999 | − | 95.7796i | 0.793963 | − | 0.125695i | ||||
\(763\) | 405.127 | − | 167.809i | 0.530965 | − | 0.219933i | ||||
\(764\) | −329.914 | − | 168.157i | −0.431824 | − | 0.220101i | ||||
\(765\) | −19.2825 | − | 7.98708i | −0.0252059 | − | 0.0104406i | ||||
\(766\) | 417.037 | + | 680.647i | 0.544434 | + | 0.888574i | ||||
\(767\) | 1323.87i | 1.72604i | ||||||||
\(768\) | 255.615 | + | 218.560i | 0.332832 | + | 0.284584i | ||||
\(769\) | 830.546 | 1.08003 | 0.540017 | − | 0.841654i | \(-0.318418\pi\) | ||||
0.540017 | + | 0.841654i | \(0.318418\pi\) | |||||||
\(770\) | 1.85779 | − | 1.13828i | 0.00241271 | − | 0.00147828i | ||||
\(771\) | 5.78260 | − | 13.9604i | 0.00750012 | − | 0.0181069i | ||||
\(772\) | −149.626 | + | 293.556i | −0.193816 | + | 0.380254i | ||||
\(773\) | −125.118 | − | 302.062i | −0.161861 | − | 0.390766i | 0.822053 | − | 0.569411i | \(-0.192829\pi\) |
−0.983914 | + | 0.178645i | \(0.942829\pi\) | |||||||
\(774\) | −24.3050 | − | 153.524i | −0.0314018 | − | 0.198352i | ||||
\(775\) | −724.454 | − | 724.454i | −0.934779 | − | 0.934779i | ||||
\(776\) | 77.4286 | + | 986.440i | 0.0997792 | + | 1.27119i | ||||
\(777\) | 60.2457 | + | 60.2457i | 0.0775363 | + | 0.0775363i | ||||
\(778\) | −994.903 | − | 722.945i | −1.27880 | − | 0.929235i | ||||
\(779\) | 95.1017 | + | 229.596i | 0.122082 | + | 0.294731i | ||||
\(780\) | 5.65983 | + | 6.62867i | 0.00725619 | + | 0.00849829i | ||||
\(781\) | 50.8669 | − | 122.803i | 0.0651304 | − | 0.157239i | ||||
\(782\) | −89.9691 | − | 21.6062i | −0.115050 | − | 0.0276295i | ||||
\(783\) | 349.505 | 0.446366 | ||||||||
\(784\) | 90.6281 | − | 65.8069i | 0.115597 | − | 0.0839374i | ||||
\(785\) | 32.1371i | 0.0409390i | ||||||||
\(786\) | −246.763 | − | 59.2606i | −0.313948 | − | 0.0753952i | ||||
\(787\) | 786.823 | + | 325.913i | 0.999775 | + | 0.414121i | 0.821715 | − | 0.569899i | \(-0.193018\pi\) |
0.178061 | + | 0.984020i | \(0.443018\pi\) | |||||||
\(788\) | 138.220 | + | 10.8974i | 0.175406 | + | 0.0138292i | ||||
\(789\) | −216.941 | + | 89.8600i | −0.274957 | + | 0.113891i | ||||
\(790\) | −22.3637 | − | 16.2506i | −0.0283085 | − | 0.0205703i | ||||
\(791\) | 215.622 | − | 215.622i | 0.272594 | − | 0.272594i | ||||
\(792\) | −198.819 | − | 64.6457i | −0.251034 | − | 0.0816234i | ||||
\(793\) | −388.059 | + | 388.059i | −0.489355 | + | 0.489355i | ||||
\(794\) | 157.343 | + | 993.871i | 0.198165 | + | 1.25173i | ||||
\(795\) | −10.7651 | + | 4.45904i | −0.0135410 | + | 0.00560885i | ||||
\(796\) | 1292.63 | − | 419.804i | 1.62391 | − | 0.527392i | ||||
\(797\) | 1076.18 | + | 445.767i | 1.35028 | + | 0.559306i | 0.936372 | − | 0.351010i | \(-0.114162\pi\) |
0.413913 | + | 0.910316i | \(0.364162\pi\) | |||||||
\(798\) | 31.1785 | − | 19.1032i | 0.0390708 | − | 0.0239389i | ||||
\(799\) | − | 524.895i | − | 0.656939i | ||||||
\(800\) | 738.821 | − | 305.731i | 0.923526 | − | 0.382163i | ||||
\(801\) | 505.818 | 0.631483 | ||||||||
\(802\) | −185.997 | − | 303.567i | −0.231917 | − | 0.378513i | ||||
\(803\) | 44.5298 | − | 107.504i | 0.0554543 | − | 0.133879i | ||||
\(804\) | 446.260 | − | 144.930i | 0.555049 | − | 0.180262i | ||||
\(805\) | −0.214440 | − | 0.517703i | −0.000266385 | − | 0.000643110i | ||||
\(806\) | 1172.22 | − | 185.579i | 1.45437 | − | 0.230246i | ||||
\(807\) | 111.314 | + | 111.314i | 0.137936 | + | 0.137936i | ||||
\(808\) | −573.689 | + | 292.159i | −0.710011 | + | 0.361583i | ||||
\(809\) | 547.972 | + | 547.972i | 0.677345 | + | 0.677345i | 0.959399 | − | 0.282054i | \(-0.0910156\pi\) |
−0.282054 | + | 0.959399i | \(0.591016\pi\) | |||||||
\(810\) | −5.03675 | + | 6.93149i | −0.00621821 | + | 0.00855739i | ||||
\(811\) | −497.746 | − | 1201.67i | −0.613744 | − | 1.48171i | −0.858858 | − | 0.512214i | \(-0.828826\pi\) |
0.245114 | − | 0.969494i | \(-0.421174\pi\) | |||||||
\(812\) | −172.470 | − | 13.5977i | −0.212401 | − | 0.0167459i | ||||
\(813\) | 160.155 | − | 386.648i | 0.196993 | − | 0.475582i | ||||
\(814\) | −41.1279 | + | 171.258i | −0.0505257 | + | 0.210391i | ||||
\(815\) | 19.7853 | 0.0242764 | ||||||||
\(816\) | 122.703 | + | 511.718i | 0.150371 | + | 0.627106i | ||||
\(817\) | 56.1990i | 0.0687870i | ||||||||
\(818\) | 84.9544 | − | 353.753i | 0.103856 | − | 0.432461i | ||||
\(819\) | −257.327 | − | 106.588i | −0.314197 | − | 0.130145i | ||||
\(820\) | −14.0643 | − | 16.4718i | −0.0171516 | − | 0.0200876i | ||||
\(821\) | 1109.04 | − | 459.379i | 1.35084 | − | 0.559536i | 0.414314 | − | 0.910134i | \(-0.364022\pi\) |
0.936526 | + | 0.350598i | \(0.114022\pi\) | |||||||
\(822\) | −338.517 | + | 465.861i | −0.411822 | + | 0.566741i | ||||
\(823\) | 865.297 | − | 865.297i | 1.05139 | − | 1.05139i | 0.0527884 | − | 0.998606i | \(-0.483189\pi\) |
0.998606 | − | 0.0527884i | \(-0.0168109\pi\) | |||||||
\(824\) | −145.127 | + | 169.850i | −0.176125 | + | 0.206129i | ||||
\(825\) | 83.3897 | − | 83.3897i | 0.101078 | − | 0.101078i | ||||
\(826\) | −478.089 | + | 75.6880i | −0.578800 | + | 0.0916319i | ||||
\(827\) | 260.547 | − | 107.922i | 0.315051 | − | 0.130498i | −0.219554 | − | 0.975600i | \(-0.570460\pi\) |
0.534605 | + | 0.845102i | \(0.320460\pi\) | |||||||
\(828\) | −24.4174 | + | 47.9054i | −0.0294896 | + | 0.0578567i | ||||
\(829\) | −436.242 | − | 180.698i | −0.526227 | − | 0.217970i | 0.103723 | − | 0.994606i | \(-0.466925\pi\) |
−0.629950 | + | 0.776636i | \(0.716925\pi\) | |||||||
\(830\) | −0.270227 | − | 0.441039i | −0.000325575 | − | 0.000531373i | ||||
\(831\) | 94.2043i | 0.113363i | ||||||||
\(832\) | −216.599 | + | 900.553i | −0.260335 | + | 1.08240i | ||||
\(833\) | 175.244 | 0.210377 | ||||||||
\(834\) | −234.069 | + | 143.416i | −0.280659 | + | 0.171961i | ||||
\(835\) | 6.07679 | − | 14.6707i | 0.00727760 | − | 0.0175697i | ||||
\(836\) | 67.3452 | + | 34.3258i | 0.0805564 | + | 0.0410596i | ||||
\(837\) | −335.472 | − | 809.902i | −0.400803 | − | 0.967625i | ||||
\(838\) | −70.3641 | − | 444.460i | −0.0839667 | − | 0.530382i | ||||
\(839\) | 973.336 | + | 973.336i | 1.16011 | + | 1.16011i | 0.984450 | + | 0.175664i | \(0.0562072\pi\) |
0.175664 | + | 0.984450i | \(0.443793\pi\) | |||||||
\(840\) | −2.07022 | + | 2.42290i | −0.00246455 | + | 0.00288441i | ||||
\(841\) | −405.710 | − | 405.710i | −0.482414 | − | 0.482414i | ||||
\(842\) | −447.859 | − | 325.436i | −0.531899 | − | 0.386503i | ||||
\(843\) | −84.9580 | − | 205.107i | −0.100780 | − | 0.243306i | ||||
\(844\) | −47.7567 | + | 40.7767i | −0.0565838 | + | 0.0483136i | ||||
\(845\) | −1.77414 | + | 4.28316i | −0.00209958 | + | 0.00506883i | ||||
\(846\) | −296.593 | − | 71.2275i | −0.350583 | − | 0.0841932i | ||||
\(847\) | −285.988 | −0.337648 | ||||||||
\(848\) | −1055.57 | − | 647.253i | −1.24477 | − | 0.763270i | ||||
\(849\) | − | 682.300i | − | 0.803651i | ||||||
\(850\) | 1216.50 | + | 292.144i | 1.43117 | + | 0.343699i | ||||
\(851\) | 41.8500 | + | 17.3348i | 0.0491774 | + | 0.0203700i | ||||
\(852\) | −15.2812 | + | 193.823i | −0.0179356 | + | 0.227492i | ||||
\(853\) | −1447.51 | + | 599.580i | −1.69697 | + | 0.702907i | −0.999901 | − | 0.0140978i | \(-0.995512\pi\) |
−0.697068 | + | 0.717005i | \(0.745512\pi\) | |||||||
\(854\) | −162.325 | − | 117.953i | −0.190077 | − | 0.138119i | ||||
\(855\) | 3.10081 | − | 3.10081i | 0.00362667 | − | 0.00362667i | ||||
\(856\) | −466.885 | + | 237.768i | −0.545426 | + | 0.277766i | ||||
\(857\) | −156.450 | + | 156.450i | −0.182555 | + | 0.182555i | −0.792468 | − | 0.609913i | \(-0.791204\pi\) |
0.609913 | + | 0.792468i | \(0.291204\pi\) | |||||||
\(858\) | 21.3614 | + | 134.931i | 0.0248967 | + | 0.157262i | ||||
\(859\) | −495.482 | + | 205.235i | −0.576812 | + | 0.238923i | −0.651966 | − | 0.758249i | \(-0.726055\pi\) |
0.0751535 | + | 0.997172i | \(0.476055\pi\) | |||||||
\(860\) | −1.51294 | − | 4.65855i | −0.00175924 | − | 0.00541692i | ||||
\(861\) | −151.716 | − | 62.8429i | −0.176209 | − | 0.0729883i | ||||
\(862\) | 1025.65 | − | 628.420i | 1.18985 | − | 0.729026i | ||||
\(863\) | − | 190.961i | − | 0.221276i | −0.993861 | − | 0.110638i | \(-0.964711\pi\) | ||
0.993861 | − | 0.110638i | \(-0.0352894\pi\) | |||||||
\(864\) | 684.153 | + | 0.236504i | 0.791843 | + | 0.000273732i | ||||
\(865\) | −8.55455 | −0.00988966 | ||||||||
\(866\) | 321.064 | + | 524.010i | 0.370743 | + | 0.605092i | ||||
\(867\) | −169.798 | + | 409.929i | −0.195846 | + | 0.472814i | ||||
\(868\) | 134.036 | + | 412.714i | 0.154419 | + | 0.475477i | ||||
\(869\) | −165.808 | − | 400.295i | −0.190803 | − | 0.460639i | ||||
\(870\) | 4.86221 | − | 0.769753i | 0.00558874 | − | 0.000884774i | ||||
\(871\) | 913.739 | + | 913.739i | 1.04907 | + | 1.04907i | ||||
\(872\) | −1260.94 | − | 409.992i | −1.44603 | − | 0.470175i | ||||
\(873\) | 636.180 | + | 636.180i | 0.728728 | + | 0.728728i | ||||
\(874\) | 11.4280 | − | 15.7270i | 0.0130755 | − | 0.0179943i | ||||
\(875\) | 5.80053 | + | 14.0037i | 0.00662918 | + | 0.0160042i | ||||
\(876\) | −13.3774 | + | 169.676i | −0.0152710 | + | 0.193694i | ||||
\(877\) | −150.409 | + | 363.119i | −0.171504 | + | 0.414047i | −0.986138 | − | 0.165929i | \(-0.946938\pi\) |
0.814634 | + | 0.579975i | \(0.196938\pi\) | |||||||
\(878\) | −61.8529 | + | 257.557i | −0.0704475 | + | 0.293346i | ||||
\(879\) | 236.520 | 0.269078 | ||||||||
\(880\) | −6.50659 | − | 1.03239i | −0.00739386 | − | 0.00117317i | ||||
\(881\) | 193.624i | 0.219777i | 0.993944 | + | 0.109889i | \(0.0350494\pi\) | ||||
−0.993944 | + | 0.109889i | \(0.964951\pi\) | |||||||
\(882\) | 23.7804 | − | 99.0222i | 0.0269619 | − | 0.112270i | ||||
\(883\) | 40.2949 | + | 16.6907i | 0.0456341 | + | 0.0189023i | 0.405384 | − | 0.914147i | \(-0.367138\pi\) |
−0.359750 | + | 0.933049i | \(0.617138\pi\) | |||||||
\(884\) | −1102.16 | + | 941.066i | −1.24678 | + | 1.06455i | ||||
\(885\) | 12.7247 | − | 5.27076i | 0.0143782 | − | 0.00595566i | ||||
\(886\) | −618.812 | + | 851.598i | −0.698434 | + | 0.961172i | ||||
\(887\) | −613.864 | + | 613.864i | −0.692067 | + | 0.692067i | −0.962686 | − | 0.270619i | \(-0.912772\pi\) |
0.270619 | + | 0.962686i | \(0.412772\pi\) | |||||||
\(888\) | −20.1595 | − | 256.831i | −0.0227021 | − | 0.289225i | ||||
\(889\) | −436.143 | + | 436.143i | −0.490599 | + | 0.490599i | ||||
\(890\) | 15.7432 | − | 2.49235i | 0.0176889 | − | 0.00280040i | ||||
\(891\) | −124.069 | + | 51.3910i | −0.139247 | + | 0.0576779i | ||||
\(892\) | −376.722 | − | 192.015i | −0.422334 | − | 0.215263i | ||||
\(893\) | 101.889 | + | 42.2039i | 0.114098 | + | 0.0472608i | ||||
\(894\) | −315.354 | − | 514.692i | −0.352745 | − | 0.575718i | ||||
\(895\) | 18.2487i | 0.0203896i | ||||||||
\(896\) | −337.599 | − | 26.7340i | −0.376785 | − | 0.0298371i | ||||
\(897\) | 35.1350 | 0.0391695 | ||||||||
\(898\) | −46.9282 | + | 28.7532i | −0.0522586 | + | 0.0320191i | ||||
\(899\) | 256.510 | − | 619.269i | 0.285328 | − | 0.688842i | ||||
\(900\) | 330.154 | − | 647.742i | 0.366838 | − | 0.719714i | ||||
\(901\) | −741.409 | − | 1789.92i | −0.822874 | − | 1.98659i | ||||
\(902\) | −53.0817 | − | 335.295i | −0.0588489 | − | 0.371724i | ||||
\(903\) | −26.2592 | − | 26.2592i | −0.0290800 | − | 0.0290800i | ||||
\(904\) | −919.212 | + | 72.1517i | −1.01683 | + | 0.0798139i | ||||
\(905\) | −4.52656 | − | 4.52656i | −0.00500172 | − | 0.00500172i | ||||
\(906\) | 33.6309 | + | 24.4378i | 0.0371202 | + | 0.0269733i | ||||
\(907\) | 237.293 | + | 572.877i | 0.261624 | + | 0.631617i | 0.999039 | − | 0.0438228i | \(-0.0139537\pi\) |
−0.737415 | + | 0.675440i | \(0.763954\pi\) | |||||||
\(908\) | 535.312 | + | 626.945i | 0.589550 | + | 0.690468i | ||||
\(909\) | −224.016 | + | 540.824i | −0.246443 | + | 0.594965i | ||||
\(910\) | −8.53429 | − | 2.04952i | −0.00937834 | − | 0.00225223i | ||||
\(911\) | −799.807 | −0.877944 | −0.438972 | − | 0.898501i | \(-0.644657\pi\) | ||||
−0.438972 | + | 0.898501i | \(0.644657\pi\) | |||||||
\(912\) | −109.198 | − | 17.3261i | −0.119734 | − | 0.0189980i | ||||
\(913\) | − | 8.10681i | − | 0.00887931i | ||||||
\(914\) | −203.975 | − | 48.9851i | −0.223168 | − | 0.0535942i | ||||
\(915\) | 5.27492 | + | 2.18494i | 0.00576493 | + | 0.00238791i | ||||
\(916\) | −275.089 | − | 21.6882i | −0.300315 | − | 0.0236771i | ||||
\(917\) | 236.094 | − | 97.7933i | 0.257463 | − | 0.106645i | ||||
\(918\) | 865.992 | + | 629.272i | 0.943347 | + | 0.685481i | ||||
\(919\) | 1101.16 | − | 1101.16i | 1.19821 | − | 1.19821i | 0.223510 | − | 0.974702i | \(-0.428248\pi\) |
0.974702 | − | 0.223510i | \(-0.0717517\pi\) | |||||||
\(920\) | −0.523921 | + | 1.61133i | −0.000569480 | + | 0.00175144i | ||||
\(921\) | −446.983 | + | 446.983i | −0.485323 | + | 0.485323i | ||||
\(922\) | −221.347 | − | 1398.16i | −0.240073 | − | 1.51644i | ||||
\(923\) | −494.700 | + | 204.911i | −0.535969 | + | 0.222006i | ||||
\(924\) | −47.5062 | + | 15.4284i | −0.0514136 | + | 0.0166974i | ||||
\(925\) | −565.866 | − | 234.389i | −0.611747 | − | 0.253394i | ||||
\(926\) | −76.2675 | + | 46.7295i | −0.0823623 | + | 0.0504639i | ||||
\(927\) | 203.137i | 0.219133i | ||||||||
\(928\) | 369.773 | + | 370.029i | 0.398462 | + | 0.398738i | ||||
\(929\) | −1584.16 | −1.70524 | −0.852618 | − | 0.522535i | \(-0.824987\pi\) | ||||
−0.852618 | + | 0.522535i | \(0.824987\pi\) | |||||||
\(930\) | −6.45073 | − | 10.5283i | −0.00693627 | − | 0.0113207i | ||||
\(931\) | −14.0904 | + | 34.0173i | −0.0151347 | + | 0.0365384i | ||||
\(932\) | −1555.15 | + | 505.061i | −1.66861 | + | 0.541911i | ||||
\(933\) | 38.8070 | + | 93.6883i | 0.0415938 | + | 0.100416i | ||||
\(934\) | −632.948 | + | 100.204i | −0.677674 | + | 0.107285i | ||||
\(935\) | −7.28892 | − | 7.28892i | −0.00779564 | − | 0.00779564i | ||||
\(936\) | 382.192 | + | 750.478i | 0.408324 | + | 0.801793i | ||||
\(937\) | −362.033 | − | 362.033i | −0.386375 | − | 0.386375i | 0.487018 | − | 0.873392i | \(-0.338085\pi\) |
−0.873392 | + | 0.487018i | \(0.838085\pi\) | |||||||
\(938\) | −277.738 | + | 382.218i | −0.296096 | + | 0.407482i | ||||
\(939\) | −202.819 | − | 489.648i | −0.215995 | − | 0.521457i | ||||
\(940\) | −9.58218 | − | 0.755467i | −0.0101938 | − | 0.000803688i | ||||
\(941\) | −198.037 | + | 478.103i | −0.210454 | + | 0.508080i | −0.993493 | − | 0.113892i | \(-0.963668\pi\) |
0.783040 | + | 0.621972i | \(0.213668\pi\) | |||||||
\(942\) | 172.040 | − | 716.380i | 0.182633 | − | 0.760489i | ||||
\(943\) | −87.3084 | −0.0925857 | ||||||||
\(944\) | 1247.72 | + | 765.079i | 1.32174 | + | 0.810465i | ||||
\(945\) | 6.48298i | 0.00686030i | ||||||||
\(946\) | 17.9264 | − | 74.6460i | 0.0189497 | − | 0.0789070i | ||||
\(947\) | 741.185 | + | 307.009i | 0.782667 | + | 0.324191i | 0.737991 | − | 0.674810i | \(-0.235775\pi\) |
0.0446755 | + | 0.999002i | \(0.485775\pi\) | |||||||
\(948\) | 411.524 | + | 481.968i | 0.434097 | + | 0.508405i | ||||
\(949\) | −433.069 | + | 179.383i | −0.456343 | + | 0.189023i | ||||
\(950\) | −154.521 | + | 212.649i | −0.162654 | + | 0.223841i | ||||
\(951\) | −210.229 | + | 210.229i | −0.221061 | + | 0.221061i | ||||
\(952\) | −402.859 | − | 344.218i | −0.423171 | − | 0.361574i | ||||
\(953\) | −1098.50 | + | 1098.50i | −1.15268 | + | 1.15268i | −0.166661 | + | 0.986014i | \(0.553299\pi\) |
−0.986014 | + | 0.166661i | \(0.946701\pi\) | |||||||
\(954\) | −1112.01 | + | 176.046i | −1.16563 | + | 0.184535i | ||||
\(955\) | −9.80231 | + | 4.06025i | −0.0102642 | + | 0.00425157i | ||||
\(956\) | −227.308 | + | 445.965i | −0.237770 | + | 0.466491i | ||||
\(957\) | 71.2822 | + | 29.5260i | 0.0744850 | + | 0.0308527i | ||||
\(958\) | −706.725 | − | 1153.45i | −0.737708 | − | 1.20402i | ||||
\(959\) | − | 579.875i | − | 0.604666i | ||||||
\(960\) | 9.51825 | − | 1.50349i | 0.00991484 | − | 0.00156614i | ||||
\(961\) | −720.233 | −0.749463 | ||||||||
\(962\) | 604.981 | − | 370.675i | 0.628878 | − | 0.385317i | ||||
\(963\) | −182.311 | + | 440.138i | −0.189316 | + | 0.457049i | ||||
\(964\) | 39.5690 | + | 20.1683i | 0.0410467 | + | 0.0209215i | ||||
\(965\) | 3.61280 | + | 8.72207i | 0.00374383 | + | 0.00903841i | ||||
\(966\) | 2.00873 | + | 12.6883i | 0.00207943 | + | 0.0131349i | ||||
\(967\) | −448.949 | − | 448.949i | −0.464270 | − | 0.464270i | 0.435782 | − | 0.900052i | \(-0.356472\pi\) |
−0.900052 | + | 0.435782i | \(0.856472\pi\) | |||||||
\(968\) | 657.441 | + | 561.744i | 0.679175 | + | 0.580314i | ||||
\(969\) | −122.327 | − | 122.327i | −0.126240 | − | 0.126240i | ||||
\(970\) | 22.9352 | + | 16.6658i | 0.0236446 | + | 0.0171813i | ||||
\(971\) | −286.432 | − | 691.509i | −0.294987 | − | 0.712161i | −0.999996 | − | 0.00296270i | \(-0.999057\pi\) |
0.705009 | − | 0.709199i | \(-0.250943\pi\) | |||||||
\(972\) | 734.715 | − | 627.330i | 0.755879 | − | 0.645401i | ||||
\(973\) | 105.782 | − | 255.381i | 0.108718 | − | 0.262468i | ||||
\(974\) | −1733.17 | − | 416.224i | −1.77943 | − | 0.427334i | ||||
\(975\) | −475.071 | −0.487252 | ||||||||
\(976\) | 141.474 | + | 590.000i | 0.144953 | + | 0.604508i | ||||
\(977\) | − | 1284.44i | − | 1.31467i | −0.753597 | − | 0.657337i | \(-0.771683\pi\) | ||
0.753597 | − | 0.657337i | \(-0.228317\pi\) | |||||||
\(978\) | −441.041 | − | 105.917i | −0.450962 | − | 0.108299i | ||||
\(979\) | 230.802 | + | 95.6013i | 0.235753 | + | 0.0976520i | ||||
\(980\) | 0.252224 | − | 3.19916i | 0.000257372 | − | 0.00326444i | ||||
\(981\) | −1113.84 | + | 461.367i | −1.13541 | + | 0.470303i | ||||
\(982\) | 175.582 | + | 127.587i | 0.178801 | + | 0.129925i | ||||
\(983\) | 690.418 | − | 690.418i | 0.702358 | − | 0.702358i | −0.262558 | − | 0.964916i | \(-0.584566\pi\) |
0.964916 | + | 0.262558i | \(0.0845662\pi\) | |||||||
\(984\) | 225.334 | + | 442.471i | 0.228998 | + | 0.449665i | ||||
\(985\) | 2.80909 | − | 2.80909i | 0.00285186 | − | 0.00285186i | ||||
\(986\) | 127.988 | + | 808.444i | 0.129805 | + | 0.819923i | ||||
\(987\) | −67.3282 | + | 27.8882i | −0.0682150 | + | 0.0282556i | ||||
\(988\) | −94.0556 | − | 289.610i | −0.0951980 | − | 0.293127i | ||||
\(989\) | −18.2411 | − | 7.55572i | −0.0184440 | − | 0.00763975i | ||||
\(990\) | −5.10772 | + | 3.12953i | −0.00515932 | + | 0.00316114i | ||||
\(991\) | 260.959i | 0.263329i | 0.991294 | + | 0.131664i | \(0.0420321\pi\) | ||||
−0.991294 | + | 0.131664i | \(0.957968\pi\) | |||||||
\(992\) | 502.535 | − | 1212.04i | 0.506587 | − | 1.22181i | ||||
\(993\) | 568.881 | 0.572891 | ||||||||
\(994\) | −102.282 | − | 166.935i | −0.102900 | − | 0.167943i | ||||
\(995\) | 14.9022 | − | 35.9772i | 0.0149771 | − | 0.0361580i | ||||
\(996\) | 3.66271 | + | 11.2780i | 0.00367742 | + | 0.0113233i | ||||
\(997\) | 198.541 | + | 479.321i | 0.199138 | + | 0.480763i | 0.991629 | − | 0.129122i | \(-0.0412158\pi\) |
−0.792490 | + | 0.609885i | \(0.791216\pi\) | |||||||
\(998\) | −1341.16 | + | 212.323i | −1.34384 | + | 0.212749i | ||||
\(999\) | −370.574 | − | 370.574i | −0.370945 | − | 0.370945i |
(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 | 224.3.w.a.99.10 | yes | 192 | |
32.11 | odd | 8 | inner | 224.3.w.a.43.10 | ✓ | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.w.a.43.10 | ✓ | 192 | 32.11 | odd | 8 | inner | |
224.3.w.a.99.10 | yes | 192 | 1.1 | even | 1 | trivial |