Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(161,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.f (of order \(10\), 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: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.64000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 233.2 | ||
Root | \(0.831254 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.233 |
Dual form | 363.2.f.f.215.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | + | 0.951057i | −0.218508 | + | 0.672499i | 0.780378 | + | 0.625308i | \(0.215027\pi\) |
−0.998886 | + | 0.0471903i | \(0.984973\pi\) | |||||||
\(3\) | 0.0222369 | + | 1.73191i | 0.0128385 | + | 0.999918i | ||||
\(4\) | 0.809017 | + | 0.587785i | 0.404508 | + | 0.293893i | ||||
\(5\) | 2.68999 | − | 0.874032i | 1.20300 | − | 0.390879i | 0.362137 | − | 0.932125i | \(-0.382047\pi\) |
0.840864 | + | 0.541246i | \(0.182047\pi\) | |||||||
\(6\) | −1.65401 | − | 0.514040i | −0.675248 | − | 0.209856i | ||||
\(7\) | −0.831254 | + | 1.14412i | −0.314184 | + | 0.432438i | −0.936680 | − | 0.350185i | \(-0.886119\pi\) |
0.622496 | + | 0.782623i | \(0.286119\pi\) | |||||||
\(8\) | −2.42705 | + | 1.76336i | −0.858092 | + | 0.623440i | ||||
\(9\) | −2.99901 | + | 0.0770245i | −0.999670 | + | 0.0256748i | ||||
\(10\) | 2.82843i | 0.894427i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | + | 1.41421i | −0.288675 | + | 0.408248i | ||||
\(13\) | 4.03499 | + | 1.31105i | 1.11911 | + | 0.363619i | 0.809426 | − | 0.587222i | \(-0.199778\pi\) |
0.309679 | + | 0.950841i | \(0.399778\pi\) | |||||||
\(14\) | −0.831254 | − | 1.14412i | −0.222162 | − | 0.305780i | ||||
\(15\) | 1.57356 | + | 4.63939i | 0.406292 | + | 1.19788i | ||||
\(16\) | −0.309017 | − | 0.951057i | −0.0772542 | − | 0.237764i | ||||
\(17\) | −1.85410 | − | 5.70634i | −0.449686 | − | 1.38399i | −0.877262 | − | 0.480011i | \(-0.840633\pi\) |
0.427576 | − | 0.903979i | \(-0.359367\pi\) | |||||||
\(18\) | 0.853491 | − | 2.87603i | 0.201170 | − | 0.677887i | ||||
\(19\) | 2.49376 | + | 3.43237i | 0.572108 | + | 0.787439i | 0.992802 | − | 0.119763i | \(-0.0382135\pi\) |
−0.420694 | + | 0.907202i | \(0.638214\pi\) | |||||||
\(20\) | 2.68999 | + | 0.874032i | 0.601501 | + | 0.195440i | ||||
\(21\) | −2.00000 | − | 1.41421i | −0.436436 | − | 0.308607i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | −3.10794 | − | 4.16422i | −0.634406 | − | 0.850017i | ||||
\(25\) | 2.42705 | − | 1.76336i | 0.485410 | − | 0.352671i | ||||
\(26\) | −2.49376 | + | 3.43237i | −0.489067 | + | 0.673143i | ||||
\(27\) | −0.200088 | − | 5.19230i | −0.0385069 | − | 0.999258i | ||||
\(28\) | −1.34500 | + | 0.437016i | −0.254181 | + | 0.0825883i | ||||
\(29\) | −1.61803 | − | 1.17557i | −0.300461 | − | 0.218298i | 0.427331 | − | 0.904095i | \(-0.359454\pi\) |
−0.727793 | + | 0.685797i | \(0.759454\pi\) | |||||||
\(30\) | −4.89858 | + | 0.0628954i | −0.894353 | + | 0.0114831i | ||||
\(31\) | −0.618034 | + | 1.90211i | −0.111002 | + | 0.341630i | −0.991092 | − | 0.133177i | \(-0.957482\pi\) |
0.880090 | + | 0.474807i | \(0.157482\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | −1.23607 | + | 3.80423i | −0.208934 | + | 0.643032i | ||||
\(36\) | −2.47152 | − | 1.70046i | −0.411921 | − | 0.283410i | ||||
\(37\) | −6.47214 | − | 4.70228i | −1.06401 | − | 0.773050i | −0.0891861 | − | 0.996015i | \(-0.528427\pi\) |
−0.974827 | + | 0.222965i | \(0.928427\pi\) | |||||||
\(38\) | −4.03499 | + | 1.31105i | −0.654562 | + | 0.212680i | ||||
\(39\) | −2.18089 | + | 7.01739i | −0.349222 | + | 1.12368i | ||||
\(40\) | −4.98752 | + | 6.86474i | −0.788597 | + | 1.08541i | ||||
\(41\) | 4.85410 | − | 3.52671i | 0.758083 | − | 0.550780i | −0.140238 | − | 0.990118i | \(-0.544787\pi\) |
0.898322 | + | 0.439338i | \(0.144787\pi\) | |||||||
\(42\) | 1.96303 | − | 1.46510i | 0.302902 | − | 0.226069i | ||||
\(43\) | − | 4.24264i | − | 0.646997i | −0.946229 | − | 0.323498i | \(-0.895141\pi\) | ||
0.946229 | − | 0.323498i | \(-0.104859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.00000 | + | 2.82843i | −1.19257 | + | 0.421637i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.66251 | + | 2.28825i | 0.242502 | + | 0.333775i | 0.912868 | − | 0.408256i | \(-0.133863\pi\) |
−0.670366 | + | 0.742031i | \(0.733863\pi\) | |||||||
\(48\) | 1.64027 | − | 0.556338i | 0.236753 | − | 0.0803004i | ||||
\(49\) | 1.54508 | + | 4.75528i | 0.220726 | + | 0.679326i | ||||
\(50\) | 0.927051 | + | 2.85317i | 0.131105 | + | 0.403499i | ||||
\(51\) | 9.84163 | − | 3.33803i | 1.37810 | − | 0.467417i | ||||
\(52\) | 2.49376 | + | 3.43237i | 0.345823 | + | 0.475984i | ||||
\(53\) | −5.37999 | − | 1.74806i | −0.738998 | − | 0.240115i | −0.0847577 | − | 0.996402i | \(-0.527012\pi\) |
−0.654241 | + | 0.756287i | \(0.727012\pi\) | |||||||
\(54\) | 5.00000 | + | 1.41421i | 0.680414 | + | 0.192450i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 4.24264i | − | 0.566947i | ||||||
\(57\) | −5.88909 | + | 4.39529i | −0.780029 | + | 0.582171i | ||||
\(58\) | 1.61803 | − | 1.17557i | 0.212458 | − | 0.154360i | ||||
\(59\) | 6.65003 | − | 9.15298i | 0.865760 | − | 1.19162i | −0.114405 | − | 0.993434i | \(-0.536496\pi\) |
0.980165 | − | 0.198183i | \(-0.0635039\pi\) | |||||||
\(60\) | −1.45393 | + | 4.67826i | −0.187701 | + | 0.603961i | ||||
\(61\) | 9.41498 | − | 3.05911i | 1.20546 | − | 0.391679i | 0.363696 | − | 0.931518i | \(-0.381515\pi\) |
0.841769 | + | 0.539839i | \(0.181515\pi\) | |||||||
\(62\) | −1.61803 | − | 1.17557i | −0.205491 | − | 0.149298i | ||||
\(63\) | 2.40481 | − | 3.49526i | 0.302978 | − | 0.440362i | ||||
\(64\) | 2.16312 | − | 6.65740i | 0.270390 | − | 0.832174i | ||||
\(65\) | 12.0000 | 1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | 1.85410 | − | 5.70634i | 0.224843 | − | 0.691995i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.23607 | − | 2.35114i | −0.386784 | − | 0.281015i | ||||
\(71\) | 2.68999 | − | 0.874032i | 0.319244 | − | 0.103729i | −0.145012 | − | 0.989430i | \(-0.546322\pi\) |
0.464255 | + | 0.885701i | \(0.346322\pi\) | |||||||
\(72\) | 7.14293 | − | 5.47527i | 0.841803 | − | 0.645266i | ||||
\(73\) | −0.831254 | + | 1.14412i | −0.0972909 | + | 0.133909i | −0.854887 | − | 0.518814i | \(-0.826374\pi\) |
0.757596 | + | 0.652724i | \(0.226374\pi\) | |||||||
\(74\) | 6.47214 | − | 4.70228i | 0.752371 | − | 0.546629i | ||||
\(75\) | 3.10794 | + | 4.16422i | 0.358874 | + | 0.480842i | ||||
\(76\) | 4.24264i | 0.486664i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.00000 | − | 4.24264i | −0.679366 | − | 0.480384i | ||||
\(79\) | 4.03499 | + | 1.31105i | 0.453972 | + | 0.147504i | 0.527073 | − | 0.849820i | \(-0.323290\pi\) |
−0.0731009 | + | 0.997325i | \(0.523290\pi\) | |||||||
\(80\) | −1.66251 | − | 2.28825i | −0.185874 | − | 0.255834i | ||||
\(81\) | 8.98813 | − | 0.461994i | 0.998682 | − | 0.0513327i | ||||
\(82\) | 1.85410 | + | 5.70634i | 0.204751 | + | 0.630160i | ||||
\(83\) | 4.94427 | + | 15.2169i | 0.542704 | + | 1.67027i | 0.726386 | + | 0.687287i | \(0.241198\pi\) |
−0.183682 | + | 0.982986i | \(0.558802\pi\) | |||||||
\(84\) | −0.786780 | − | 2.31969i | −0.0858447 | − | 0.253099i | ||||
\(85\) | −9.97505 | − | 13.7295i | −1.08195 | − | 1.48917i | ||||
\(86\) | 4.03499 | + | 1.31105i | 0.435104 | + | 0.141374i | ||||
\(87\) | 2.00000 | − | 2.82843i | 0.214423 | − | 0.303239i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | −0.217858 | − | 8.48248i | −0.0229643 | − | 0.894132i | ||||
\(91\) | −4.85410 | + | 3.52671i | −0.508848 | + | 0.369700i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.30803 | − | 1.02808i | −0.343027 | − | 0.106607i | ||||
\(94\) | −2.68999 | + | 0.874032i | −0.277452 | + | 0.0901495i | ||||
\(95\) | 9.70820 | + | 7.05342i | 0.996041 | + | 0.723666i | ||||
\(96\) | −0.111184 | − | 8.65954i | −0.0113477 | − | 0.883811i | ||||
\(97\) | −0.618034 | + | 1.90211i | −0.0627518 | + | 0.193130i | −0.977517 | − | 0.210855i | \(-0.932375\pi\) |
0.914766 | + | 0.403985i | \(0.132375\pi\) | |||||||
\(98\) | −5.00000 | −0.505076 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | 0.300000 | ||||||||
\(101\) | 3.09017 | − | 9.51057i | 0.307483 | − | 0.946337i | −0.671255 | − | 0.741226i | \(-0.734245\pi\) |
0.978739 | − | 0.205110i | \(-0.0657554\pi\) | |||||||
\(102\) | 0.133421 | + | 10.3914i | 0.0132107 | + | 1.02891i | ||||
\(103\) | −6.47214 | − | 4.70228i | −0.637719 | − | 0.463330i | 0.221347 | − | 0.975195i | \(-0.428955\pi\) |
−0.859066 | + | 0.511865i | \(0.828955\pi\) | |||||||
\(104\) | −12.1050 | + | 3.93314i | −1.18699 | + | 0.385677i | ||||
\(105\) | −6.61606 | − | 2.05616i | −0.645661 | − | 0.200661i | ||||
\(106\) | 3.32502 | − | 4.57649i | 0.322954 | − | 0.444508i | ||||
\(107\) | −12.9443 | + | 9.40456i | −1.25137 | + | 0.909174i | −0.998301 | − | 0.0582746i | \(-0.981440\pi\) |
−0.253069 | + | 0.967448i | \(0.581440\pi\) | |||||||
\(108\) | 2.89008 | − | 4.31827i | 0.278098 | − | 0.415525i | ||||
\(109\) | − | 4.24264i | − | 0.406371i | −0.979140 | − | 0.203186i | \(-0.934871\pi\) | ||
0.979140 | − | 0.203186i | \(-0.0651295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | − | 11.3137i | 0.759326 | − | 1.07385i | ||||
\(112\) | 1.34500 | + | 0.437016i | 0.127090 | + | 0.0412941i | ||||
\(113\) | 1.66251 | + | 2.28825i | 0.156396 | + | 0.215260i | 0.880023 | − | 0.474930i | \(-0.157527\pi\) |
−0.723628 | + | 0.690190i | \(0.757527\pi\) | |||||||
\(114\) | −2.36034 | − | 6.95908i | −0.221066 | − | 0.651778i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.618034 | − | 1.90211i | −0.0573830 | − | 0.176607i | ||||
\(117\) | −12.2020 | − | 3.62105i | −1.12807 | − | 0.334767i | ||||
\(118\) | 6.65003 | + | 9.15298i | 0.612185 | + | 0.842600i | ||||
\(119\) | 8.06998 | + | 2.62210i | 0.739774 | + | 0.240367i | ||||
\(120\) | −12.0000 | − | 8.48528i | −1.09545 | − | 0.774597i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 9.89949i | 0.896258i | ||||||||
\(123\) | 6.21588 | + | 8.32844i | 0.560467 | + | 0.750950i | ||||
\(124\) | −1.61803 | + | 1.17557i | −0.145304 | + | 0.105569i | ||||
\(125\) | −3.32502 | + | 4.57649i | −0.297398 | + | 0.409334i | ||||
\(126\) | 2.58107 | + | 3.36721i | 0.229940 | + | 0.299975i | ||||
\(127\) | 9.41498 | − | 3.05911i | 0.835444 | − | 0.271452i | 0.140107 | − | 0.990136i | \(-0.455255\pi\) |
0.695337 | + | 0.718684i | \(0.255255\pi\) | |||||||
\(128\) | −2.42705 | − | 1.76336i | −0.214523 | − | 0.155860i | ||||
\(129\) | 7.34786 | − | 0.0943431i | 0.646943 | − | 0.00830645i | ||||
\(130\) | −3.70820 | + | 11.4127i | −0.325231 | + | 1.00096i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | −0.520266 | ||||||||
\(134\) | −0.618034 | + | 1.90211i | −0.0533900 | + | 0.164318i | ||||
\(135\) | −5.07647 | − | 13.7924i | −0.436913 | − | 1.18706i | ||||
\(136\) | 14.5623 | + | 10.5801i | 1.24871 | + | 0.907239i | ||||
\(137\) | 2.68999 | − | 0.874032i | 0.229822 | − | 0.0746736i | −0.191842 | − | 0.981426i | \(-0.561446\pi\) |
0.421664 | + | 0.906752i | \(0.361446\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.831254 | + | 1.14412i | −0.0705060 | + | 0.0970432i | −0.842814 | − | 0.538206i | \(-0.819102\pi\) |
0.772308 | + | 0.635249i | \(0.219102\pi\) | |||||||
\(140\) | −3.23607 | + | 2.35114i | −0.273498 | + | 0.198708i | ||||
\(141\) | −3.92606 | + | 2.93019i | −0.330634 | + | 0.246767i | ||||
\(142\) | 2.82843i | 0.237356i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | + | 2.82843i | 0.0833333 | + | 0.235702i | ||||
\(145\) | −5.37999 | − | 1.74806i | −0.446784 | − | 0.145169i | ||||
\(146\) | −0.831254 | − | 1.14412i | −0.0687951 | − | 0.0946883i | ||||
\(147\) | −8.20135 | + | 2.78169i | −0.676436 | + | 0.229430i | ||||
\(148\) | −2.47214 | − | 7.60845i | −0.203208 | − | 0.625411i | ||||
\(149\) | −1.85410 | − | 5.70634i | −0.151894 | − | 0.467482i | 0.845939 | − | 0.533280i | \(-0.179041\pi\) |
−0.997833 | + | 0.0657982i | \(0.979041\pi\) | |||||||
\(150\) | −4.92081 | + | 1.66901i | −0.401783 | + | 0.136274i | ||||
\(151\) | 2.49376 | + | 3.43237i | 0.202939 | + | 0.279322i | 0.898341 | − | 0.439300i | \(-0.144773\pi\) |
−0.695401 | + | 0.718622i | \(0.744773\pi\) | |||||||
\(152\) | −12.1050 | − | 3.93314i | −0.981843 | − | 0.319020i | ||||
\(153\) | 6.00000 | + | 16.9706i | 0.485071 | + | 1.37199i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.65685i | 0.454369i | ||||||||
\(156\) | −5.88909 | + | 4.39529i | −0.471505 | + | 0.351905i | ||||
\(157\) | 16.1803 | − | 11.7557i | 1.29133 | − | 0.938207i | 0.291500 | − | 0.956571i | \(-0.405846\pi\) |
0.999831 | + | 0.0183633i | \(0.00584556\pi\) | |||||||
\(158\) | −2.49376 | + | 3.43237i | −0.198393 | + | 0.273065i | ||||
\(159\) | 2.90785 | − | 9.35652i | 0.230608 | − | 0.742020i | ||||
\(160\) | −13.4500 | + | 4.37016i | −1.06331 | + | 0.345492i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.33810 | + | 8.69099i | −0.183699 | + | 0.682829i | ||||
\(163\) | 6.18034 | − | 19.0211i | 0.484082 | − | 1.48985i | −0.349225 | − | 0.937039i | \(-0.613555\pi\) |
0.833307 | − | 0.552811i | \(-0.186445\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.0000 | −1.24184 | ||||||||
\(167\) | −3.70820 | + | 11.4127i | −0.286949 | + | 0.883140i | 0.698858 | + | 0.715260i | \(0.253692\pi\) |
−0.985808 | + | 0.167879i | \(0.946308\pi\) | |||||||
\(168\) | 7.34786 | − | 0.0943431i | 0.566900 | − | 0.00727873i | ||||
\(169\) | 4.04508 | + | 2.93893i | 0.311160 | + | 0.226071i | ||||
\(170\) | 16.1400 | − | 5.24419i | 1.23788 | − | 0.402211i | ||||
\(171\) | −7.74320 | − | 10.1016i | −0.592137 | − | 0.772491i | ||||
\(172\) | 2.49376 | − | 3.43237i | 0.190148 | − | 0.261716i | ||||
\(173\) | 4.85410 | − | 3.52671i | 0.369051 | − | 0.268131i | −0.387767 | − | 0.921758i | \(-0.626753\pi\) |
0.756817 | + | 0.653627i | \(0.226753\pi\) | |||||||
\(174\) | 2.07196 | + | 2.77615i | 0.157075 | + | 0.210459i | ||||
\(175\) | 4.24264i | 0.320713i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.0000 | + | 11.3137i | 1.20263 | + | 0.850390i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.66251 | + | 2.28825i | 0.124262 | + | 0.171032i | 0.866615 | − | 0.498977i | \(-0.166291\pi\) |
−0.742354 | + | 0.670008i | \(0.766291\pi\) | |||||||
\(180\) | −8.13464 | − | 2.41404i | −0.606321 | − | 0.179932i | ||||
\(181\) | −3.09017 | − | 9.51057i | −0.229691 | − | 0.706915i | −0.997781 | − | 0.0665740i | \(-0.978793\pi\) |
0.768091 | − | 0.640341i | \(-0.221207\pi\) | |||||||
\(182\) | −1.85410 | − | 5.70634i | −0.137435 | − | 0.422982i | ||||
\(183\) | 5.50746 | + | 16.2379i | 0.407123 | + | 1.20034i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.5200 | − | 6.99226i | −1.58218 | − | 0.514081i | ||||
\(186\) | 2.00000 | − | 2.82843i | 0.146647 | − | 0.207390i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.82843i | 0.206284i | ||||||||
\(189\) | 6.10695 | + | 4.08719i | 0.444215 | + | 0.297300i | ||||
\(190\) | −9.70820 | + | 7.05342i | −0.704307 | + | 0.511709i | ||||
\(191\) | −11.6376 | + | 16.0177i | −0.842064 | + | 1.15900i | 0.143492 | + | 0.989651i | \(0.454167\pi\) |
−0.985556 | + | 0.169350i | \(0.945833\pi\) | |||||||
\(192\) | 11.5781 | + | 3.59828i | 0.835577 | + | 0.259684i | ||||
\(193\) | −20.1750 | + | 6.55524i | −1.45223 | + | 0.471857i | −0.925685 | − | 0.378294i | \(-0.876511\pi\) |
−0.526540 | + | 0.850151i | \(0.676511\pi\) | |||||||
\(194\) | −1.61803 | − | 1.17557i | −0.116168 | − | 0.0844010i | ||||
\(195\) | 0.266843 | + | 20.7829i | 0.0191090 | + | 1.48829i | ||||
\(196\) | −1.54508 | + | 4.75528i | −0.110363 | + | 0.339663i | ||||
\(197\) | −22.0000 | −1.56744 | −0.783718 | − | 0.621117i | \(-0.786679\pi\) | ||||
−0.783718 | + | 0.621117i | \(0.786679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | −2.78115 | + | 8.55951i | −0.196657 | + | 0.605249i | ||||
\(201\) | 0.0444738 | + | 3.46382i | 0.00313694 | + | 0.244319i | ||||
\(202\) | 8.09017 | + | 5.87785i | 0.569222 | + | 0.413564i | ||||
\(203\) | 2.68999 | − | 0.874032i | 0.188801 | − | 0.0613450i | ||||
\(204\) | 9.92408 | + | 3.08424i | 0.694825 | + | 0.215940i | ||||
\(205\) | 9.97505 | − | 13.7295i | 0.696687 | − | 0.958908i | ||||
\(206\) | 6.47214 | − | 4.70228i | 0.450935 | − | 0.327624i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 4.24264i | − | 0.294174i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.00000 | − | 5.65685i | 0.276026 | − | 0.390360i | ||||
\(211\) | −25.5549 | − | 8.30330i | −1.75927 | − | 0.571623i | −0.762150 | − | 0.647400i | \(-0.775856\pi\) |
−0.997125 | + | 0.0757773i | \(0.975856\pi\) | |||||||
\(212\) | −3.32502 | − | 4.57649i | −0.228363 | − | 0.314315i | ||||
\(213\) | 1.57356 | + | 4.63939i | 0.107819 | + | 0.317886i | ||||
\(214\) | −4.94427 | − | 15.2169i | −0.337983 | − | 1.04021i | ||||
\(215\) | −3.70820 | − | 11.4127i | −0.252897 | − | 0.778338i | ||||
\(216\) | 9.64149 | + | 12.2491i | 0.656021 | + | 0.833449i | ||||
\(217\) | −1.66251 | − | 2.28825i | −0.112858 | − | 0.155336i | ||||
\(218\) | 4.03499 | + | 1.31105i | 0.273284 | + | 0.0887954i | ||||
\(219\) | −2.00000 | − | 1.41421i | −0.135147 | − | 0.0955637i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 25.4558i | − | 1.71235i | ||||||
\(222\) | 8.28784 | + | 11.1046i | 0.556243 | + | 0.745291i | ||||
\(223\) | −19.4164 | + | 14.1068i | −1.30022 | + | 0.944664i | −0.999958 | − | 0.00919277i | \(-0.997074\pi\) |
−0.300261 | + | 0.953857i | \(0.597074\pi\) | |||||||
\(224\) | 4.15627 | − | 5.72061i | 0.277702 | − | 0.382225i | ||||
\(225\) | −7.14293 | + | 5.47527i | −0.476195 | + | 0.365018i | ||||
\(226\) | −2.68999 | + | 0.874032i | −0.178936 | + | 0.0581397i | ||||
\(227\) | −19.4164 | − | 14.1068i | −1.28871 | − | 0.936304i | −0.288934 | − | 0.957349i | \(-0.593301\pi\) |
−0.999779 | + | 0.0210448i | \(0.993301\pi\) | |||||||
\(228\) | −7.34786 | + | 0.0943431i | −0.486624 | + | 0.00624802i | ||||
\(229\) | −7.41641 | + | 22.8254i | −0.490090 | + | 1.50834i | 0.334381 | + | 0.942438i | \(0.391473\pi\) |
−0.824471 | + | 0.565904i | \(0.808527\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | 3.09017 | − | 9.51057i | 0.202444 | − | 0.623058i | −0.797365 | − | 0.603497i | \(-0.793773\pi\) |
0.999809 | − | 0.0195604i | \(-0.00622666\pi\) | |||||||
\(234\) | 7.21444 | − | 10.4858i | 0.471623 | − | 0.685478i | ||||
\(235\) | 6.47214 | + | 4.70228i | 0.422196 | + | 0.306743i | ||||
\(236\) | 10.7600 | − | 3.49613i | 0.700415 | − | 0.227579i | ||||
\(237\) | −2.18089 | + | 7.01739i | −0.141664 | + | 0.455828i | ||||
\(238\) | −4.98752 | + | 6.86474i | −0.323293 | + | 0.444975i | ||||
\(239\) | −12.9443 | + | 9.40456i | −0.837295 | + | 0.608331i | −0.921614 | − | 0.388108i | \(-0.873129\pi\) |
0.0843185 | + | 0.996439i | \(0.473129\pi\) | |||||||
\(240\) | 3.92606 | − | 2.93019i | 0.253426 | − | 0.189143i | ||||
\(241\) | − | 4.24264i | − | 0.273293i | −0.990620 | − | 0.136646i | \(-0.956368\pi\) | ||
0.990620 | − | 0.136646i | \(-0.0436324\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | + | 15.5563i | 0.0641500 | + | 0.997940i | ||||
\(244\) | 9.41498 | + | 3.05911i | 0.602732 | + | 0.195840i | ||||
\(245\) | 8.31254 | + | 11.4412i | 0.531069 | + | 0.730953i | ||||
\(246\) | −9.84163 | + | 3.33803i | −0.627479 | + | 0.212825i | ||||
\(247\) | 5.56231 | + | 17.1190i | 0.353921 | + | 1.08926i | ||||
\(248\) | −1.85410 | − | 5.70634i | −0.117736 | − | 0.362353i | ||||
\(249\) | −26.2443 | + | 8.90140i | −1.66317 | + | 0.564103i | ||||
\(250\) | −3.32502 | − | 4.57649i | −0.210292 | − | 0.289443i | ||||
\(251\) | 24.2099 | + | 7.86629i | 1.52812 | + | 0.496516i | 0.948069 | − | 0.318065i | \(-0.103033\pi\) |
0.580050 | + | 0.814581i | \(0.303033\pi\) | |||||||
\(252\) | 4.00000 | − | 1.41421i | 0.251976 | − | 0.0890871i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 9.89949i | 0.621150i | ||||||||
\(255\) | 23.5564 | − | 17.5812i | 1.47516 | − | 1.10098i | ||||
\(256\) | 13.7533 | − | 9.99235i | 0.859581 | − | 0.624522i | ||||
\(257\) | 6.65003 | − | 9.15298i | 0.414818 | − | 0.570947i | −0.549568 | − | 0.835449i | \(-0.685208\pi\) |
0.964385 | + | 0.264502i | \(0.0852075\pi\) | |||||||
\(258\) | −2.18089 | + | 7.01739i | −0.135776 | + | 0.436883i | ||||
\(259\) | 10.7600 | − | 3.49613i | 0.668592 | − | 0.217239i | ||||
\(260\) | 9.70820 | + | 7.05342i | 0.602077 | + | 0.437435i | ||||
\(261\) | 4.94305 | + | 3.40092i | 0.305967 | + | 0.210512i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.0000 | −0.982872 | ||||||||
\(266\) | 1.85410 | − | 5.70634i | 0.113682 | − | 0.349878i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.61803 | + | 1.17557i | 0.0988372 | + | 0.0718094i | ||||
\(269\) | −26.8999 | + | 8.74032i | −1.64012 | + | 0.532907i | −0.976565 | − | 0.215222i | \(-0.930952\pi\) |
−0.663553 | + | 0.748129i | \(0.730952\pi\) | |||||||
\(270\) | 14.6860 | − | 0.565934i | 0.893764 | − | 0.0344417i | ||||
\(271\) | 17.4563 | − | 24.0266i | 1.06040 | − | 1.45951i | 0.180963 | − | 0.983490i | \(-0.442079\pi\) |
0.879434 | − | 0.476021i | \(-0.157921\pi\) | |||||||
\(272\) | −4.85410 | + | 3.52671i | −0.294323 | + | 0.213838i | ||||
\(273\) | −6.21588 | − | 8.32844i | −0.376202 | − | 0.504060i | ||||
\(274\) | 2.82843i | 0.170872i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.03499 | + | 1.31105i | 0.242439 | + | 0.0787732i | 0.427716 | − | 0.903913i | \(-0.359318\pi\) |
−0.185277 | + | 0.982686i | \(0.559318\pi\) | |||||||
\(278\) | −0.831254 | − | 1.14412i | −0.0498553 | − | 0.0686199i | ||||
\(279\) | 1.70698 | − | 5.75206i | 0.102194 | − | 0.344367i | ||||
\(280\) | −3.70820 | − | 11.4127i | −0.221608 | − | 0.682038i | ||||
\(281\) | −1.85410 | − | 5.70634i | −0.110606 | − | 0.340412i | 0.880399 | − | 0.474234i | \(-0.157275\pi\) |
−0.991005 | + | 0.133822i | \(0.957275\pi\) | |||||||
\(282\) | −1.57356 | − | 4.63939i | −0.0937041 | − | 0.276271i | ||||
\(283\) | −15.7938 | − | 21.7383i | −0.938845 | − | 1.29221i | −0.956308 | − | 0.292362i | \(-0.905559\pi\) |
0.0174623 | − | 0.999848i | \(-0.494441\pi\) | |||||||
\(284\) | 2.68999 | + | 0.874032i | 0.159622 | + | 0.0518643i | ||||
\(285\) | −12.0000 | + | 16.9706i | −0.710819 | + | 1.00525i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.48528i | 0.500870i | ||||||||
\(288\) | 14.9951 | − | 0.385122i | 0.883592 | − | 0.0226936i | ||||
\(289\) | −15.3713 | + | 11.1679i | −0.904195 | + | 0.656936i | ||||
\(290\) | 3.32502 | − | 4.57649i | 0.195252 | − | 0.268741i | ||||
\(291\) | −3.30803 | − | 1.02808i | −0.193920 | − | 0.0602672i | ||||
\(292\) | −1.34500 | + | 0.437016i | −0.0787100 | + | 0.0255744i | ||||
\(293\) | −1.61803 | − | 1.17557i | −0.0945266 | − | 0.0686776i | 0.539518 | − | 0.841974i | \(-0.318606\pi\) |
−0.634045 | + | 0.773296i | \(0.718606\pi\) | |||||||
\(294\) | −0.111184 | − | 8.65954i | −0.00648441 | − | 0.505035i | ||||
\(295\) | 9.88854 | − | 30.4338i | 0.575733 | − | 1.77192i | ||||
\(296\) | 24.0000 | 1.39497 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.0667106 | + | 5.19572i | 0.00385154 | + | 0.299975i | ||||
\(301\) | 4.85410 | + | 3.52671i | 0.279786 | + | 0.203276i | ||||
\(302\) | −4.03499 | + | 1.31105i | −0.232188 | + | 0.0754423i | ||||
\(303\) | 16.5401 | + | 5.14040i | 0.950206 | + | 0.295309i | ||||
\(304\) | 2.49376 | − | 3.43237i | 0.143027 | − | 0.196860i | ||||
\(305\) | 22.6525 | − | 16.4580i | 1.29708 | − | 0.942382i | ||||
\(306\) | −17.9941 | + | 0.462147i | −1.02865 | + | 0.0264192i | ||||
\(307\) | − | 4.24264i | − | 0.242140i | −0.992644 | − | 0.121070i | \(-0.961367\pi\) | ||
0.992644 | − | 0.121070i | \(-0.0386326\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | − | 11.3137i | 0.455104 | − | 0.643614i | ||||
\(310\) | −5.37999 | − | 1.74806i | −0.305563 | − | 0.0992834i | ||||
\(311\) | −16.6251 | − | 22.8825i | −0.942722 | − | 1.29755i | −0.954685 | − | 0.297617i | \(-0.903808\pi\) |
0.0119638 | − | 0.999928i | \(-0.496192\pi\) | |||||||
\(312\) | −7.08102 | − | 20.8772i | −0.400884 | − | 1.18194i | ||||
\(313\) | 3.70820 | + | 11.4127i | 0.209600 | + | 0.645083i | 0.999493 | + | 0.0318380i | \(0.0101361\pi\) |
−0.789893 | + | 0.613245i | \(0.789864\pi\) | |||||||
\(314\) | 6.18034 | + | 19.0211i | 0.348777 | + | 1.07342i | ||||
\(315\) | 3.41396 | − | 11.5041i | 0.192355 | − | 0.648184i | ||||
\(316\) | 2.49376 | + | 3.43237i | 0.140285 | + | 0.193086i | ||||
\(317\) | 24.2099 | + | 7.86629i | 1.35977 | + | 0.441815i | 0.895965 | − | 0.444125i | \(-0.146485\pi\) |
0.463801 | + | 0.885939i | \(0.346485\pi\) | |||||||
\(318\) | 8.00000 | + | 5.65685i | 0.448618 | + | 0.317221i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 19.7990i | − | 1.10680i | ||||||
\(321\) | −16.5757 | − | 22.2092i | −0.925164 | − | 1.23959i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.9626 | − | 20.5942i | 0.832540 | − | 1.14589i | ||||
\(324\) | 7.54311 | + | 4.90933i | 0.419062 | + | 0.272741i | ||||
\(325\) | 12.1050 | − | 3.93314i | 0.671463 | − | 0.218172i | ||||
\(326\) | 16.1803 | + | 11.7557i | 0.896146 | + | 0.651088i | ||||
\(327\) | 7.34786 | − | 0.0943431i | 0.406338 | − | 0.00521719i | ||||
\(328\) | −5.56231 | + | 17.1190i | −0.307127 | + | 0.945240i | ||||
\(329\) | −4.00000 | −0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | −4.94427 | + | 15.2169i | −0.271352 | + | 0.835136i | ||||
\(333\) | 19.7722 | + | 13.6037i | 1.08351 | + | 0.745477i | ||||
\(334\) | −9.70820 | − | 7.05342i | −0.531209 | − | 0.385946i | ||||
\(335\) | 5.37999 | − | 1.74806i | 0.293940 | − | 0.0955069i | ||||
\(336\) | −0.726963 | + | 2.33913i | −0.0396591 | + | 0.127610i | ||||
\(337\) | −19.1188 | + | 26.3148i | −1.04147 | + | 1.43346i | −0.145493 | + | 0.989359i | \(0.546477\pi\) |
−0.895977 | + | 0.444100i | \(0.853523\pi\) | |||||||
\(338\) | −4.04508 | + | 2.93893i | −0.220024 | + | 0.159857i | ||||
\(339\) | −3.92606 | + | 2.93019i | −0.213234 | + | 0.159146i | ||||
\(340\) | − | 16.9706i | − | 0.920358i | ||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 12.0000 | − | 4.24264i | 0.648886 | − | 0.229416i | ||||
\(343\) | −16.1400 | − | 5.24419i | −0.871476 | − | 0.283160i | ||||
\(344\) | 7.48128 | + | 10.2971i | 0.403364 | + | 0.555183i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.85410 | + | 5.70634i | 0.0996771 | + | 0.306775i | ||||
\(347\) | 4.94427 | + | 15.2169i | 0.265422 | + | 0.816886i | 0.991596 | + | 0.129375i | \(0.0412970\pi\) |
−0.726173 | + | 0.687512i | \(0.758703\pi\) | |||||||
\(348\) | 3.28054 | − | 1.11268i | 0.175855 | − | 0.0596456i | ||||
\(349\) | 2.49376 | + | 3.43237i | 0.133488 | + | 0.183730i | 0.870528 | − | 0.492118i | \(-0.163777\pi\) |
−0.737040 | + | 0.675849i | \(0.763777\pi\) | |||||||
\(350\) | −4.03499 | − | 1.31105i | −0.215679 | − | 0.0700785i | ||||
\(351\) | 6.00000 | − | 21.2132i | 0.320256 | − | 1.13228i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | −15.7042 | + | 11.7208i | −0.834671 | + | 0.622952i | ||||
\(355\) | 6.47214 | − | 4.70228i | 0.343505 | − | 0.249571i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.36178 | + | 14.0348i | −0.230850 | + | 0.742799i | ||||
\(358\) | −2.68999 | + | 0.874032i | −0.142171 | + | 0.0461940i | ||||
\(359\) | 16.1803 | + | 11.7557i | 0.853966 | + | 0.620442i | 0.926237 | − | 0.376943i | \(-0.123025\pi\) |
−0.0722709 | + | 0.997385i | \(0.523025\pi\) | |||||||
\(360\) | 14.4289 | − | 20.9716i | 0.760469 | − | 1.10530i | ||||
\(361\) | 0.309017 | − | 0.951057i | 0.0162641 | − | 0.0500556i | ||||
\(362\) | 10.0000 | 0.525588 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.00000 | −0.314485 | ||||||||
\(365\) | −1.23607 | + | 3.80423i | −0.0646988 | + | 0.199122i | ||||
\(366\) | −17.1450 | + | 0.220134i | −0.896184 | + | 0.0115066i | ||||
\(367\) | −6.47214 | − | 4.70228i | −0.337843 | − | 0.245457i | 0.405908 | − | 0.913914i | \(-0.366955\pi\) |
−0.743751 | + | 0.668457i | \(0.766955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.2859 | + | 10.9505i | −0.743692 | + | 0.570062i | ||||
\(370\) | 13.3001 | − | 18.3060i | 0.691437 | − | 0.951682i | ||||
\(371\) | 6.47214 | − | 4.70228i | 0.336017 | − | 0.244130i | ||||
\(372\) | −2.07196 | − | 2.77615i | −0.107426 | − | 0.143936i | ||||
\(373\) | − | 4.24264i | − | 0.219676i | −0.993950 | − | 0.109838i | \(-0.964967\pi\) | ||
0.993950 | − | 0.109838i | \(-0.0350331\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.00000 | − | 5.65685i | −0.413118 | − | 0.292119i | ||||
\(376\) | −8.06998 | − | 2.62210i | −0.416178 | − | 0.135224i | ||||
\(377\) | −4.98752 | − | 6.86474i | −0.256871 | − | 0.353552i | ||||
\(378\) | −5.77430 | + | 4.54504i | −0.296998 | + | 0.233772i | ||||
\(379\) | 3.70820 | + | 11.4127i | 0.190478 | + | 0.586230i | 1.00000 | 0.000859657i | \(-0.000273637\pi\) | |
−0.809522 | + | 0.587090i | \(0.800274\pi\) | |||||||
\(380\) | 3.70820 | + | 11.4127i | 0.190227 | + | 0.585458i | ||||
\(381\) | 5.50746 | + | 16.2379i | 0.282156 | + | 0.831890i | ||||
\(382\) | −11.6376 | − | 16.0177i | −0.595429 | − | 0.819538i | ||||
\(383\) | −5.37999 | − | 1.74806i | −0.274905 | − | 0.0893219i | 0.168320 | − | 0.985732i | \(-0.446166\pi\) |
−0.443225 | + | 0.896410i | \(0.646166\pi\) | |||||||
\(384\) | 3.00000 | − | 4.24264i | 0.153093 | − | 0.216506i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 21.2132i | − | 1.07972i | ||||||
\(387\) | 0.326787 | + | 12.7237i | 0.0166115 | + | 0.646783i | ||||
\(388\) | −1.61803 | + | 1.17557i | −0.0821432 | + | 0.0596806i | ||||
\(389\) | −11.6376 | + | 16.0177i | −0.590047 | + | 0.812131i | −0.994752 | − | 0.102317i | \(-0.967374\pi\) |
0.404704 | + | 0.914448i | \(0.367374\pi\) | |||||||
\(390\) | −19.8482 | − | 6.16849i | −1.00505 | − | 0.312353i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −12.1353 | − | 8.81678i | −0.612923 | − | 0.445315i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.79837 | − | 20.9232i | 0.342497 | − | 1.05410i | ||||
\(395\) | 12.0000 | 0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | −0.618034 | + | 1.90211i | −0.0309792 | + | 0.0953443i | ||||
\(399\) | −0.133421 | − | 10.3914i | −0.00667942 | − | 0.520223i | ||||
\(400\) | −2.42705 | − | 1.76336i | −0.121353 | − | 0.0881678i | ||||
\(401\) | 2.68999 | − | 0.874032i | 0.134332 | − | 0.0436471i | −0.241079 | − | 0.970505i | \(-0.577501\pi\) |
0.375411 | + | 0.926858i | \(0.377501\pi\) | |||||||
\(402\) | −3.30803 | − | 1.02808i | −0.164989 | − | 0.0512760i | ||||
\(403\) | −4.98752 | + | 6.86474i | −0.248446 | + | 0.341957i | ||||
\(404\) | 8.09017 | − | 5.87785i | 0.402501 | − | 0.292434i | ||||
\(405\) | 23.7742 | − | 9.09868i | 1.18135 | − | 0.452117i | ||||
\(406\) | 2.82843i | 0.140372i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −18.0000 | + | 25.4558i | −0.891133 | + | 1.26025i | ||||
\(409\) | 4.03499 | + | 1.31105i | 0.199517 | + | 0.0648272i | 0.407071 | − | 0.913396i | \(-0.366550\pi\) |
−0.207554 | + | 0.978224i | \(0.566550\pi\) | |||||||
\(410\) | 9.97505 | + | 13.7295i | 0.492632 | + | 0.678050i | ||||
\(411\) | 1.57356 | + | 4.63939i | 0.0776180 | + | 0.228844i | ||||
\(412\) | −2.47214 | − | 7.60845i | −0.121793 | − | 0.374842i | ||||
\(413\) | 4.94427 | + | 15.2169i | 0.243292 | + | 0.748775i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.6001 | + | 36.6119i | 1.30575 | + | 1.79721i | ||||
\(416\) | −20.1750 | − | 6.55524i | −0.989159 | − | 0.321397i | ||||
\(417\) | −2.00000 | − | 1.41421i | −0.0979404 | − | 0.0692543i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.1127i | 1.51995i | 0.649950 | + | 0.759977i | \(0.274790\pi\) | ||||
−0.649950 | + | 0.759977i | \(0.725210\pi\) | |||||||
\(420\) | −4.14392 | − | 5.55229i | −0.202203 | − | 0.270924i | ||||
\(421\) | 16.1803 | − | 11.7557i | 0.788582 | − | 0.572938i | −0.118961 | − | 0.992899i | \(-0.537956\pi\) |
0.907542 | + | 0.419961i | \(0.137956\pi\) | |||||||
\(422\) | 15.7938 | − | 21.7383i | 0.768831 | − | 1.05821i | ||||
\(423\) | −5.16213 | − | 6.73442i | −0.250991 | − | 0.327439i | ||||
\(424\) | 16.1400 | − | 5.24419i | 0.783826 | − | 0.254680i | ||||
\(425\) | −14.5623 | − | 10.5801i | −0.706376 | − | 0.513212i | ||||
\(426\) | −4.89858 | + | 0.0628954i | −0.237337 | + | 0.00304729i | ||||
\(427\) | −4.32624 | + | 13.3148i | −0.209361 | + | 0.644348i | ||||
\(428\) | −16.0000 | −0.773389 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.0000 | 0.578691 | ||||||||
\(431\) | 9.88854 | − | 30.4338i | 0.476314 | − | 1.46594i | −0.367862 | − | 0.929880i | \(-0.619910\pi\) |
0.844177 | − | 0.536065i | \(-0.180090\pi\) | |||||||
\(432\) | −4.87634 | + | 1.79480i | −0.234613 | + | 0.0863525i | ||||
\(433\) | −24.2705 | − | 17.6336i | −1.16637 | − | 0.847415i | −0.175797 | − | 0.984426i | \(-0.556250\pi\) |
−0.990569 | + | 0.137012i | \(0.956250\pi\) | |||||||
\(434\) | 2.68999 | − | 0.874032i | 0.129124 | − | 0.0419549i | ||||
\(435\) | 2.90785 | − | 9.35652i | 0.139421 | − | 0.448611i | ||||
\(436\) | 2.49376 | − | 3.43237i | 0.119430 | − | 0.164381i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 1.96303 | − | 1.46510i | 0.0937972 | − | 0.0700050i | ||||
\(439\) | 26.8701i | 1.28244i | 0.767358 | + | 0.641219i | \(0.221571\pi\) | ||||
−0.767358 | + | 0.641219i | \(0.778429\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | − | 14.1421i | −0.238095 | − | 0.673435i | ||||
\(442\) | 24.2099 | + | 7.86629i | 1.15155 | + | 0.374161i | ||||
\(443\) | −16.6251 | − | 22.8825i | −0.789881 | − | 1.08718i | −0.994123 | − | 0.108258i | \(-0.965473\pi\) |
0.204242 | − | 0.978921i | \(-0.434527\pi\) | |||||||
\(444\) | 13.1222 | − | 4.45070i | 0.622750 | − | 0.211221i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.41641 | − | 22.8254i | −0.351177 | − | 1.08081i | ||||
\(447\) | 9.84163 | − | 3.33803i | 0.465493 | − | 0.157883i | ||||
\(448\) | 5.81878 | + | 8.00886i | 0.274911 | + | 0.378383i | ||||
\(449\) | −5.37999 | − | 1.74806i | −0.253897 | − | 0.0824962i | 0.179303 | − | 0.983794i | \(-0.442616\pi\) |
−0.433200 | + | 0.901298i | \(0.642616\pi\) | |||||||
\(450\) | −3.00000 | − | 8.48528i | −0.141421 | − | 0.400000i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2.82843i | 0.133038i | ||||||||
\(453\) | −5.88909 | + | 4.39529i | −0.276694 | + | 0.206509i | ||||
\(454\) | 19.4164 | − | 14.1068i | 0.911257 | − | 0.662067i | ||||
\(455\) | −9.97505 | + | 13.7295i | −0.467637 | + | 0.643648i | ||||
\(456\) | 6.54267 | − | 21.0522i | 0.306388 | − | 0.985858i | ||||
\(457\) | 9.41498 | − | 3.05911i | 0.440414 | − | 0.143099i | −0.0804125 | − | 0.996762i | \(-0.525624\pi\) |
0.520827 | + | 0.853662i | \(0.325624\pi\) | |||||||
\(458\) | −19.4164 | − | 14.1068i | −0.907269 | − | 0.659170i | ||||
\(459\) | −29.2580 | + | 10.7688i | −1.36565 | + | 0.502646i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.0000 | −1.02464 | −0.512321 | − | 0.858794i | \(-0.671214\pi\) | ||||
−0.512321 | + | 0.858794i | \(0.671214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0000 | 1.11537 | 0.557687 | − | 0.830051i | \(-0.311689\pi\) | ||||
0.557687 | + | 0.830051i | \(0.311689\pi\) | |||||||
\(464\) | −0.618034 | + | 1.90211i | −0.0286915 | + | 0.0883034i | ||||
\(465\) | −9.79715 | + | 0.125791i | −0.454332 | + | 0.00583341i | ||||
\(466\) | 8.09017 | + | 5.87785i | 0.374770 | + | 0.272286i | ||||
\(467\) | −26.8999 | + | 8.74032i | −1.24478 | + | 0.404454i | −0.856048 | − | 0.516897i | \(-0.827087\pi\) |
−0.388733 | + | 0.921350i | \(0.627087\pi\) | |||||||
\(468\) | −7.74320 | − | 10.1016i | −0.357929 | − | 0.466948i | ||||
\(469\) | −1.66251 | + | 2.28825i | −0.0767675 | + | 0.105661i | ||||
\(470\) | −6.47214 | + | 4.70228i | −0.298537 | + | 0.216900i | ||||
\(471\) | 20.7196 | + | 27.7615i | 0.954709 | + | 1.27918i | ||||
\(472\) | 33.9411i | 1.56227i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −6.00000 | − | 4.24264i | −0.275589 | − | 0.194871i | ||||
\(475\) | 12.1050 | + | 3.93314i | 0.555414 | + | 0.180465i | ||||
\(476\) | 4.98752 | + | 6.86474i | 0.228603 | + | 0.314645i | ||||
\(477\) | 16.2693 | + | 4.82807i | 0.744919 | + | 0.221062i | ||||
\(478\) | −4.94427 | − | 15.2169i | −0.226146 | − | 0.696005i | ||||
\(479\) | −8.65248 | − | 26.6296i | −0.395342 | − | 1.21674i | −0.928695 | − | 0.370844i | \(-0.879068\pi\) |
0.533353 | − | 0.845893i | \(-0.320932\pi\) | |||||||
\(480\) | −7.86780 | − | 23.1969i | −0.359114 | − | 1.05879i | ||||
\(481\) | −19.9501 | − | 27.4589i | −0.909646 | − | 1.25202i | ||||
\(482\) | 4.03499 | + | 1.31105i | 0.183789 | + | 0.0597166i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.65685i | 0.256865i | ||||||||
\(486\) | −15.1040 | − | 3.85612i | −0.685131 | − | 0.174917i | ||||
\(487\) | −1.61803 | + | 1.17557i | −0.0733201 | + | 0.0532702i | −0.623842 | − | 0.781551i | \(-0.714429\pi\) |
0.550521 | + | 0.834821i | \(0.314429\pi\) | |||||||
\(488\) | −17.4563 | + | 24.0266i | −0.790211 | + | 1.08763i | ||||
\(489\) | 33.0803 | + | 10.2808i | 1.49594 | + | 0.464914i | ||||
\(490\) | −13.4500 | + | 4.37016i | −0.607608 | + | 0.197424i | ||||
\(491\) | 16.1803 | + | 11.7557i | 0.730209 | + | 0.530528i | 0.889629 | − | 0.456683i | \(-0.150963\pi\) |
−0.159421 | + | 0.987211i | \(0.550963\pi\) | |||||||
\(492\) | 0.133421 | + | 10.3914i | 0.00601510 | + | 0.468483i | ||||
\(493\) | −3.70820 | + | 11.4127i | −0.167009 | + | 0.514001i | ||||
\(494\) | −18.0000 | −0.809858 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −1.23607 | + | 3.80423i | −0.0554452 | + | 0.170643i | ||||
\(498\) | −0.355790 | − | 27.7105i | −0.0159433 | − | 1.24174i | ||||
\(499\) | 11.3262 | + | 8.22899i | 0.507032 | + | 0.368380i | 0.811697 | − | 0.584079i | \(-0.198544\pi\) |
−0.304664 | + | 0.952460i | \(0.598544\pi\) | |||||||
\(500\) | −5.37999 | + | 1.74806i | −0.240600 | + | 0.0781758i | ||||
\(501\) | −19.8482 | − | 6.16849i | −0.886751 | − | 0.275588i | ||||
\(502\) | −14.9626 | + | 20.5942i | −0.667812 | + | 0.919165i | ||||
\(503\) | −12.9443 | + | 9.40456i | −0.577157 | + | 0.419329i | −0.837698 | − | 0.546134i | \(-0.816099\pi\) |
0.260541 | + | 0.965463i | \(0.416099\pi\) | |||||||
\(504\) | 0.326787 | + | 12.7237i | 0.0145563 | + | 0.566760i | ||||
\(505\) | − | 28.2843i | − | 1.25863i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.00000 | + | 7.07107i | −0.222058 | + | 0.314037i | ||||
\(508\) | 9.41498 | + | 3.05911i | 0.417722 | + | 0.135726i | ||||
\(509\) | 19.9501 | + | 27.4589i | 0.884272 | + | 1.21710i | 0.975219 | + | 0.221241i | \(0.0710106\pi\) |
−0.0909469 | + | 0.995856i | \(0.528989\pi\) | |||||||
\(510\) | 9.44136 | + | 27.8363i | 0.418071 | + | 1.23261i | ||||
\(511\) | −0.618034 | − | 1.90211i | −0.0273402 | − | 0.0841445i | ||||
\(512\) | 3.39919 | + | 10.4616i | 0.150224 | + | 0.462343i | ||||
\(513\) | 17.3229 | − | 13.6351i | 0.764825 | − | 0.602006i | ||||
\(514\) | 6.65003 | + | 9.15298i | 0.293320 | + | 0.403721i | ||||
\(515\) | −21.5200 | − | 6.99226i | −0.948282 | − | 0.308116i | ||||
\(516\) | 6.00000 | + | 4.24264i | 0.264135 | + | 0.186772i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11.3137i | 0.497096i | ||||||||
\(519\) | 6.21588 | + | 8.32844i | 0.272847 | + | 0.365578i | ||||
\(520\) | −29.1246 | + | 21.1603i | −1.27720 | + | 0.927939i | ||||
\(521\) | −11.6376 | + | 16.0177i | −0.509851 | + | 0.701749i | −0.983894 | − | 0.178752i | \(-0.942794\pi\) |
0.474044 | + | 0.880501i | \(0.342794\pi\) | |||||||
\(522\) | −4.76195 | + | 3.65018i | −0.208425 | + | 0.159764i | ||||
\(523\) | −20.1750 | + | 6.55524i | −0.882189 | + | 0.286641i | −0.714866 | − | 0.699261i | \(-0.753512\pi\) |
−0.167323 | + | 0.985902i | \(0.553512\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.34786 | + | 0.0943431i | −0.320687 | + | 0.00411747i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0000 | 0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 4.94427 | − | 15.2169i | 0.214765 | − | 0.660980i | ||||
\(531\) | −19.2385 | + | 27.9621i | −0.834880 | + | 1.21345i | ||||
\(532\) | −4.85410 | − | 3.52671i | −0.210452 | − | 0.152902i | ||||
\(533\) | 24.2099 | − | 7.86629i | 1.04865 | − | 0.340727i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.6001 | + | 36.6119i | −1.15002 | + | 1.58287i | ||||
\(536\) | −4.85410 | + | 3.52671i | −0.209665 | + | 0.152331i | ||||
\(537\) | −3.92606 | + | 2.93019i | −0.169422 | + | 0.126447i | ||||
\(538\) | − | 28.2843i | − | 1.21942i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.00000 | − | 14.1421i | 0.172133 | − | 0.608581i | ||||
\(541\) | 33.6249 | + | 10.9254i | 1.44565 | + | 0.469720i | 0.923653 | − | 0.383229i | \(-0.125188\pi\) |
0.521995 | + | 0.852949i | \(0.325188\pi\) | |||||||
\(542\) | 17.4563 | + | 24.0266i | 0.749814 | + | 1.03203i | ||||
\(543\) | 16.4027 | − | 5.56338i | 0.703908 | − | 0.238747i | ||||
\(544\) | 9.27051 | + | 28.5317i | 0.397470 | + | 1.22329i | ||||
\(545\) | −3.70820 | − | 11.4127i | −0.158842 | − | 0.488865i | ||||
\(546\) | 9.84163 | − | 3.33803i | 0.421183 | − | 0.142854i | ||||
\(547\) | 20.7813 | + | 28.6031i | 0.888546 | + | 1.22298i | 0.973980 | + | 0.226635i | \(0.0727725\pi\) |
−0.0854335 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(548\) | 2.68999 | + | 0.874032i | 0.114911 | + | 0.0373368i | ||||
\(549\) | −28.0000 | + | 9.89949i | −1.19501 | + | 0.422500i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.48528i | − | 0.361485i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.85410 | + | 3.52671i | −0.206417 | + | 0.149971i | ||||
\(554\) | −2.49376 | + | 3.43237i | −0.105950 | + | 0.145827i | ||||
\(555\) | 11.6314 | − | 37.4261i | 0.493726 | − | 1.58865i | ||||
\(556\) | −1.34500 | + | 0.437016i | −0.0570406 | + | 0.0185336i | ||||
\(557\) | −1.61803 | − | 1.17557i | −0.0685583 | − | 0.0498105i | 0.552978 | − | 0.833196i | \(-0.313491\pi\) |
−0.621537 | + | 0.783385i | \(0.713491\pi\) | |||||||
\(558\) | 4.94305 | + | 3.40092i | 0.209256 | + | 0.143972i | ||||
\(559\) | 5.56231 | − | 17.1190i | 0.235260 | − | 0.724057i | ||||
\(560\) | 4.00000 | 0.169031 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | −3.70820 | + | 11.4127i | −0.156282 | + | 0.480987i | −0.998289 | − | 0.0584805i | \(-0.981374\pi\) |
0.842006 | + | 0.539468i | \(0.181374\pi\) | |||||||
\(564\) | −4.89858 | + | 0.0628954i | −0.206267 | + | 0.00264837i | ||||
\(565\) | 6.47214 | + | 4.70228i | 0.272285 | + | 0.197826i | ||||
\(566\) | 25.5549 | − | 8.30330i | 1.07415 | − | 0.349014i | ||||
\(567\) | −6.94284 | + | 10.6676i | −0.291572 | + | 0.447996i | ||||
\(568\) | −4.98752 | + | 6.86474i | −0.209272 | + | 0.288038i | ||||
\(569\) | −30.7426 | + | 22.3358i | −1.28880 | + | 0.936367i | −0.999780 | − | 0.0209564i | \(-0.993329\pi\) |
−0.289018 | + | 0.957324i | \(0.593329\pi\) | |||||||
\(570\) | −12.4318 | − | 16.6569i | −0.520709 | − | 0.697680i | ||||
\(571\) | 26.8701i | 1.12448i | 0.826975 | + | 0.562238i | \(0.190060\pi\) | ||||
−0.826975 | + | 0.562238i | \(0.809940\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −28.0000 | − | 19.7990i | −1.16972 | − | 0.827115i | ||||
\(574\) | −8.06998 | − | 2.62210i | −0.336835 | − | 0.109444i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.97444 | + | 20.1322i | −0.248935 | + | 0.838842i | ||||
\(577\) | −9.88854 | − | 30.4338i | −0.411665 | − | 1.26698i | −0.915200 | − | 0.403001i | \(-0.867967\pi\) |
0.503534 | − | 0.863975i | \(-0.332033\pi\) | |||||||
\(578\) | −5.87132 | − | 18.0701i | −0.244215 | − | 0.751616i | ||||
\(579\) | −11.8017 | − | 34.7954i | −0.490462 | − | 1.44605i | ||||
\(580\) | −3.32502 | − | 4.57649i | −0.138064 | − | 0.190028i | ||||
\(581\) | −21.5200 | − | 6.99226i | −0.892798 | − | 0.290088i | ||||
\(582\) | 2.00000 | − | 2.82843i | 0.0829027 | − | 0.117242i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 4.24264i | − | 0.175562i | ||||||
\(585\) | −35.9881 | + | 0.924294i | −1.48793 | + | 0.0382148i | ||||
\(586\) | 1.61803 | − | 1.17557i | 0.0668404 | − | 0.0485624i | ||||
\(587\) | 6.65003 | − | 9.15298i | 0.274476 | − | 0.377784i | −0.649418 | − | 0.760431i | \(-0.724988\pi\) |
0.923894 | + | 0.382647i | \(0.124988\pi\) | |||||||
\(588\) | −8.27007 | − | 2.57020i | −0.341052 | − | 0.105993i | ||||
\(589\) | −8.06998 | + | 2.62210i | −0.332518 | + | 0.108042i | ||||
\(590\) | 25.8885 | + | 18.8091i | 1.06581 | + | 0.774360i | ||||
\(591\) | −0.489211 | − | 38.1020i | −0.0201235 | − | 1.56731i | ||||
\(592\) | −2.47214 | + | 7.60845i | −0.101604 | + | 0.312705i | ||||
\(593\) | 22.0000 | 0.903432 | 0.451716 | − | 0.892162i | \(-0.350812\pi\) | ||||
0.451716 | + | 0.892162i | \(0.350812\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.0000 | 0.983904 | ||||||||
\(596\) | 1.85410 | − | 5.70634i | 0.0759470 | − | 0.233741i | ||||
\(597\) | 0.0444738 | + | 3.46382i | 0.00182019 | + | 0.141765i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.2799 | − | 10.4884i | 1.31892 | − | 0.428544i | 0.436798 | − | 0.899560i | \(-0.356113\pi\) |
0.882125 | + | 0.471016i | \(0.156113\pi\) | |||||||
\(600\) | −14.8861 | − | 4.62636i | −0.607724 | − | 0.188871i | ||||
\(601\) | 17.4563 | − | 24.0266i | 0.712059 | − | 0.980065i | −0.287692 | − | 0.957723i | \(-0.592888\pi\) |
0.999750 | − | 0.0223415i | \(-0.00711213\pi\) | |||||||
\(602\) | −4.85410 | + | 3.52671i | −0.197838 | + | 0.143738i | ||||
\(603\) | −5.99802 | + | 0.154049i | −0.244258 | + | 0.00627336i | ||||
\(604\) | 4.24264i | 0.172631i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.0000 | + | 14.1421i | −0.406222 | + | 0.574485i | ||||
\(607\) | 4.03499 | + | 1.31105i | 0.163775 | + | 0.0532138i | 0.389757 | − | 0.920918i | \(-0.372559\pi\) |
−0.225982 | + | 0.974132i | \(0.572559\pi\) | |||||||
\(608\) | −12.4688 | − | 17.1618i | −0.505677 | − | 0.696005i | ||||
\(609\) | 1.57356 | + | 4.63939i | 0.0637639 | + | 0.187997i | ||||
\(610\) | 8.65248 | + | 26.6296i | 0.350329 | + | 1.07820i | ||||
\(611\) | 3.70820 | + | 11.4127i | 0.150018 | + | 0.461708i | ||||
\(612\) | −5.12094 | + | 17.2562i | −0.207002 | + | 0.697540i | ||||
\(613\) | 2.49376 | + | 3.43237i | 0.100722 | + | 0.138632i | 0.856403 | − | 0.516308i | \(-0.172694\pi\) |
−0.755681 | + | 0.654940i | \(0.772694\pi\) | |||||||
\(614\) | 4.03499 | + | 1.31105i | 0.162839 | + | 0.0529096i | ||||
\(615\) | 24.0000 | + | 16.9706i | 0.967773 | + | 0.684319i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.1127i | 1.25255i | 0.779602 | + | 0.626275i | \(0.215421\pi\) | ||||
−0.779602 | + | 0.626275i | \(0.784579\pi\) | |||||||
\(618\) | 8.28784 | + | 11.1046i | 0.333386 | + | 0.446692i | ||||
\(619\) | 16.1803 | − | 11.7557i | 0.650343 | − | 0.472502i | −0.213045 | − | 0.977042i | \(-0.568338\pi\) |
0.863388 | + | 0.504541i | \(0.168338\pi\) | |||||||
\(620\) | −3.32502 | + | 4.57649i | −0.133536 | + | 0.183796i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.8999 | − | 8.74032i | 1.07859 | − | 0.350455i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.34786 | − | 0.0943431i | 0.294150 | − | 0.00377675i | ||||
\(625\) | −9.57953 | + | 29.4828i | −0.383181 | + | 1.17931i | ||||
\(626\) | −12.0000 | −0.479616 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.0000 | 0.798087 | ||||||||
\(629\) | −14.8328 | + | 45.6507i | −0.591423 | + | 1.82021i | ||||
\(630\) | 9.88610 | + | 6.80184i | 0.393872 | + | 0.270992i | ||||
\(631\) | 11.3262 | + | 8.22899i | 0.450890 | + | 0.327591i | 0.789947 | − | 0.613175i | \(-0.210108\pi\) |
−0.339057 | + | 0.940766i | \(0.610108\pi\) | |||||||
\(632\) | −12.1050 | + | 3.93314i | −0.481510 | + | 0.156452i | ||||
\(633\) | 13.8123 | − | 44.4435i | 0.548990 | − | 1.76647i | ||||
\(634\) | −14.9626 | + | 20.5942i | −0.594240 | + | 0.817901i | ||||
\(635\) | 22.6525 | − | 16.4580i | 0.898936 | − | 0.653115i | ||||
\(636\) | 7.85212 | − | 5.86039i | 0.311357 | − | 0.232380i | ||||
\(637\) | 21.2132i | 0.840498i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | + | 2.82843i | −0.316475 | + | 0.111891i | ||||
\(640\) | −8.06998 | − | 2.62210i | −0.318994 | − | 0.103647i | ||||
\(641\) | −16.6251 | − | 22.8825i | −0.656651 | − | 0.903803i | 0.342714 | − | 0.939440i | \(-0.388654\pi\) |
−0.999365 | + | 0.0356372i | \(0.988654\pi\) | |||||||
\(642\) | 26.2443 | − | 8.90140i | 1.03578 | − | 0.351310i | ||||
\(643\) | 3.70820 | + | 11.4127i | 0.146237 | + | 0.450072i | 0.997168 | − | 0.0752058i | \(-0.0239614\pi\) |
−0.850931 | + | 0.525278i | \(0.823961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.6833 | − | 6.67605i | 0.775027 | − | 0.262869i | ||||
\(646\) | 14.9626 | + | 20.5942i | 0.588694 | + | 0.810268i | ||||
\(647\) | −5.37999 | − | 1.74806i | −0.211509 | − | 0.0687235i | 0.201346 | − | 0.979520i | \(-0.435468\pi\) |
−0.412855 | + | 0.910797i | \(0.635468\pi\) | |||||||
\(648\) | −21.0000 | + | 16.9706i | −0.824958 | + | 0.666667i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 12.7279i | 0.499230i | ||||||||
\(651\) | 3.92606 | − | 2.93019i | 0.153875 | − | 0.114843i | ||||
\(652\) | 16.1803 | − | 11.7557i | 0.633671 | − | 0.460389i | ||||
\(653\) | 6.65003 | − | 9.15298i | 0.260236 | − | 0.358184i | −0.658827 | − | 0.752294i | \(-0.728947\pi\) |
0.919063 | + | 0.394110i | \(0.128947\pi\) | |||||||
\(654\) | −2.18089 | + | 7.01739i | −0.0852795 | + | 0.274402i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.85410 | − | 3.52671i | −0.189521 | − | 0.137695i | ||||
\(657\) | 2.40481 | − | 3.49526i | 0.0938207 | − | 0.136363i | ||||
\(658\) | 1.23607 | − | 3.80423i | 0.0481869 | − | 0.148304i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0000 | −0.777910 | −0.388955 | − | 0.921257i | \(-0.627164\pi\) | ||||
−0.388955 | + | 0.921257i | \(0.627164\pi\) | |||||||
\(662\) | 6.18034 | − | 19.0211i | 0.240206 | − | 0.739277i | ||||
\(663\) | 44.0872 | − | 0.566059i | 1.71220 | − | 0.0219839i | ||||
\(664\) | −38.8328 | − | 28.2137i | −1.50701 | − | 1.09490i | ||||
\(665\) | −16.1400 | + | 5.24419i | −0.625881 | + | 0.203361i | ||||
\(666\) | −19.0478 | + | 14.6007i | −0.738088 | + | 0.565766i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −9.70820 | + | 7.05342i | −0.375622 | + | 0.272905i | ||||
\(669\) | −24.8635 | − | 33.3137i | −0.961279 | − | 1.28798i | ||||
\(670\) | 5.65685i | 0.218543i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 10.0000 | + | 7.07107i | 0.385758 | + | 0.272772i | ||||
\(673\) | 4.03499 | + | 1.31105i | 0.155537 | + | 0.0505372i | 0.385751 | − | 0.922603i | \(-0.373942\pi\) |
−0.230213 | + | 0.973140i | \(0.573942\pi\) | |||||||
\(674\) | −19.1188 | − | 26.3148i | −0.736430 | − | 1.01361i | ||||
\(675\) | −9.64149 | − | 12.2491i | −0.371101 | − | 0.471470i | ||||
\(676\) | 1.54508 | + | 4.75528i | 0.0594263 | + | 0.182895i | ||||
\(677\) | 11.7426 | + | 36.1401i | 0.451307 | + | 1.38898i | 0.875417 | + | 0.483368i | \(0.160587\pi\) |
−0.424111 | + | 0.905610i | \(0.639413\pi\) | |||||||
\(678\) | −1.57356 | − | 4.63939i | −0.0604322 | − | 0.178175i | ||||
\(679\) | −1.66251 | − | 2.28825i | −0.0638012 | − | 0.0878148i | ||||
\(680\) | 48.4199 | + | 15.7326i | 1.85682 | + | 0.603317i | ||||
\(681\) | 24.0000 | − | 33.9411i | 0.919682 | − | 1.30063i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 31.1127i | − | 1.19049i | −0.803543 | − | 0.595247i | \(-0.797054\pi\) | ||
0.803543 | − | 0.595247i | \(-0.202946\pi\) | |||||||
\(684\) | −0.326787 | − | 12.7237i | −0.0124950 | − | 0.486504i | ||||
\(685\) | 6.47214 | − | 4.70228i | 0.247288 | − | 0.179665i | ||||
\(686\) | 9.97505 | − | 13.7295i | 0.380849 | − | 0.524194i | ||||
\(687\) | −39.6963 | − | 12.3370i | −1.51451 | − | 0.470685i | ||||
\(688\) | −4.03499 | + | 1.31105i | −0.153833 | + | 0.0499832i | ||||
\(689\) | −19.4164 | − | 14.1068i | −0.739706 | − | 0.537428i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.18034 | − | 19.0211i | 0.235111 | − | 0.723598i | −0.761995 | − | 0.647582i | \(-0.775780\pi\) |
0.997107 | − | 0.0760155i | \(-0.0242198\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.0000 | −0.607352 | ||||||||
\(695\) | −1.23607 | + | 3.80423i | −0.0468867 | + | 0.144303i | ||||
\(696\) | 0.133421 | + | 10.3914i | 0.00505732 | + | 0.393887i | ||||
\(697\) | −29.1246 | − | 21.1603i | −1.10317 | − | 0.801502i | ||||
\(698\) | −4.03499 | + | 1.31105i | −0.152727 | + | 0.0496239i | ||||
\(699\) | 16.5401 | + | 5.14040i | 0.625606 | + | 0.194428i | ||||
\(700\) | −2.49376 | + | 3.43237i | −0.0942553 | + | 0.129731i | ||||
\(701\) | 4.85410 | − | 3.52671i | 0.183337 | − | 0.133202i | −0.492331 | − | 0.870408i | \(-0.663855\pi\) |
0.675668 | + | 0.737206i | \(0.263855\pi\) | |||||||
\(702\) | 18.3209 | + | 12.2616i | 0.691476 | + | 0.462783i | ||||
\(703\) | − | 33.9411i | − | 1.28011i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.00000 | + | 11.3137i | −0.301297 | + | 0.426099i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.31254 | + | 11.4412i | 0.312625 | + | 0.430292i | ||||
\(708\) | 6.29424 | + | 18.5575i | 0.236552 | + | 0.697435i | ||||
\(709\) | −9.88854 | − | 30.4338i | −0.371372 | − | 1.14297i | −0.945894 | − | 0.324476i | \(-0.894812\pi\) |
0.574522 | − | 0.818489i | \(-0.305188\pi\) | |||||||
\(710\) | 2.47214 | + | 7.60845i | 0.0927776 | + | 0.285540i | ||||
\(711\) | −12.2020 | − | 3.62105i | −0.457609 | − | 0.135800i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −12.0000 | − | 8.48528i | −0.449089 | − | 0.317554i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.82843i | 0.105703i | ||||||||
\(717\) | −16.5757 | − | 22.2092i | −0.619030 | − | 0.829416i | ||||
\(718\) | −16.1803 | + | 11.7557i | −0.603845 | + | 0.438719i | ||||
\(719\) | −11.6376 | + | 16.0177i | −0.434008 | + | 0.597360i | −0.968867 | − | 0.247581i | \(-0.920364\pi\) |
0.534860 | + | 0.844941i | \(0.320364\pi\) | |||||||
\(720\) | 5.16213 | + | 6.73442i | 0.192381 | + | 0.250977i | ||||
\(721\) | 10.7600 | − | 3.49613i | 0.400722 | − | 0.130203i | ||||
\(722\) | 0.809017 | + | 0.587785i | 0.0301085 | + | 0.0218751i | ||||
\(723\) | 7.34786 | − | 0.0943431i | 0.273270 | − | 0.00350866i | ||||
\(724\) | 3.09017 | − | 9.51057i | 0.114845 | − | 0.353457i | ||||
\(725\) | −6.00000 | −0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.00000 | 0.0741759 | 0.0370879 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370879 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(728\) | 5.56231 | − | 17.1190i | 0.206153 | − | 0.634473i | ||||
\(729\) | −26.9199 | + | 2.07783i | −0.997034 | + | 0.0769568i | ||||
\(730\) | −3.23607 | − | 2.35114i | −0.119772 | − | 0.0870196i | ||||
\(731\) | −24.2099 | + | 7.86629i | −0.895437 | + | 0.290945i | ||||
\(732\) | −5.08874 | + | 16.3739i | −0.188085 | + | 0.605197i | ||||
\(733\) | −0.831254 | + | 1.14412i | −0.0307031 | + | 0.0422591i | −0.824093 | − | 0.566455i | \(-0.808314\pi\) |
0.793389 | + | 0.608714i | \(0.208314\pi\) | |||||||
\(734\) | 6.47214 | − | 4.70228i | 0.238891 | − | 0.173564i | ||||
\(735\) | −19.6303 | + | 14.6510i | −0.724075 | + | 0.540409i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.00000 | − | 16.9706i | −0.220863 | − | 0.624695i | ||||
\(739\) | 4.03499 | + | 1.31105i | 0.148430 | + | 0.0482277i | 0.382289 | − | 0.924043i | \(-0.375136\pi\) |
−0.233860 | + | 0.972270i | \(0.575136\pi\) | |||||||
\(740\) | −13.3001 | − | 18.3060i | −0.488920 | − | 0.672941i | ||||
\(741\) | −29.5249 | + | 10.0141i | −1.08462 | + | 0.367876i | ||||
\(742\) | 2.47214 | + | 7.60845i | 0.0907550 | + | 0.279315i | ||||
\(743\) | 4.94427 | + | 15.2169i | 0.181388 | + | 0.558254i | 0.999867 | − | 0.0162814i | \(-0.00518275\pi\) |
−0.818480 | + | 0.574535i | \(0.805183\pi\) | |||||||
\(744\) | 9.84163 | − | 3.33803i | 0.360811 | − | 0.122378i | ||||
\(745\) | −9.97505 | − | 13.7295i | −0.365457 | − | 0.503009i | ||||
\(746\) | 4.03499 | + | 1.31105i | 0.147732 | + | 0.0480009i | ||||
\(747\) | −16.0000 | − | 45.2548i | −0.585409 | − | 1.65579i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 22.6274i | − | 0.826788i | ||||||
\(750\) | 7.85212 | − | 5.86039i | 0.286719 | − | 0.213991i | ||||
\(751\) | −1.61803 | + | 1.17557i | −0.0590429 | + | 0.0428972i | −0.616915 | − | 0.787030i | \(-0.711618\pi\) |
0.557872 | + | 0.829927i | \(0.311618\pi\) | |||||||
\(752\) | 1.66251 | − | 2.28825i | 0.0606254 | − | 0.0834437i | ||||
\(753\) | −13.0853 | + | 42.1043i | −0.476856 | + | 1.53437i | ||||
\(754\) | 8.06998 | − | 2.62210i | 0.293891 | − | 0.0954911i | ||||
\(755\) | 9.70820 | + | 7.05342i | 0.353318 | + | 0.256700i | ||||
\(756\) | 2.53824 | + | 6.89618i | 0.0923147 | + | 0.250812i | ||||
\(757\) | 6.18034 | − | 19.0211i | 0.224628 | − | 0.691335i | −0.773701 | − | 0.633551i | \(-0.781597\pi\) |
0.998329 | − | 0.0577836i | \(-0.0184034\pi\) | |||||||
\(758\) | −12.0000 | −0.435860 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −36.0000 | −1.30586 | ||||||||
\(761\) | 3.09017 | − | 9.51057i | 0.112019 | − | 0.344758i | −0.879295 | − | 0.476278i | \(-0.841986\pi\) |
0.991314 | + | 0.131520i | \(0.0419857\pi\) | |||||||
\(762\) | −17.1450 | + | 0.220134i | −0.621098 | + | 0.00797461i | ||||
\(763\) | 4.85410 | + | 3.52671i | 0.175730 | + | 0.127676i | ||||
\(764\) | −18.8300 | + | 6.11822i | −0.681244 | + | 0.221350i | ||||
\(765\) | 30.9728 | + | 40.4065i | 1.11982 | + | 1.46090i | ||||
\(766\) | 3.32502 | − | 4.57649i | 0.120138 | − | 0.165355i | ||||
\(767\) | 38.8328 | − | 28.2137i | 1.40217 | − | 1.01874i | ||||
\(768\) | 17.6117 | + | 23.5972i | 0.635506 | + | 0.851492i | ||||
\(769\) | − | 35.3553i | − | 1.27495i | −0.770473 | − | 0.637473i | \(-0.779980\pi\) | ||
0.770473 | − | 0.637473i | \(-0.220020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.0000 | + | 11.3137i | 0.576226 | + | 0.407453i | ||||
\(772\) | −20.1750 | − | 6.55524i | −0.726113 | − | 0.235928i | ||||
\(773\) | 19.9501 | + | 27.4589i | 0.717555 | + | 0.987630i | 0.999601 | + | 0.0282290i | \(0.00898675\pi\) |
−0.282047 | + | 0.959401i | \(0.591013\pi\) | |||||||
\(774\) | −12.2020 | − | 3.62105i | −0.438591 | − | 0.130156i | ||||
\(775\) | 1.85410 | + | 5.70634i | 0.0666013 | + | 0.204978i | ||||
\(776\) | −1.85410 | − | 5.70634i | −0.0665584 | − | 0.204846i | ||||
\(777\) | 6.29424 | + | 18.5575i | 0.225805 | + | 0.665748i | ||||
\(778\) | −11.6376 | − | 16.0177i | −0.417227 | − | 0.574263i | ||||
\(779\) | 24.2099 | + | 7.86629i | 0.867411 | + | 0.281839i | ||||
\(780\) | −12.0000 | + | 16.9706i | −0.429669 | + | 0.607644i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.78016 | + | 8.63653i | −0.206566 | + | 0.308645i | ||||
\(784\) | 4.04508 | − | 2.93893i | 0.144467 | − | 0.104962i | ||||
\(785\) | 33.2502 | − | 45.7649i | 1.18675 | − | 1.63342i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.1750 | + | 6.55524i | −0.719159 | + | 0.233669i | −0.645659 | − | 0.763626i | \(-0.723417\pi\) |
−0.0735007 | + | 0.997295i | \(0.523417\pi\) | |||||||
\(788\) | −17.7984 | − | 12.9313i | −0.634041 | − | 0.460658i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.70820 | + | 11.4127i | −0.131932 | + | 0.406045i | ||||
\(791\) | −4.00000 | −0.142224 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.0000 | 1.49146 | ||||||||
\(794\) | −0.618034 | + | 1.90211i | −0.0219332 | + | 0.0675035i | ||||
\(795\) | −0.355790 | − | 27.7105i | −0.0126186 | − | 0.982791i | ||||
\(796\) | 1.61803 | + | 1.17557i | 0.0573497 | + | 0.0416670i | ||||
\(797\) | 2.68999 | − | 0.874032i | 0.0952845 | − | 0.0309598i | −0.260987 | − | 0.965342i | \(-0.584048\pi\) |
0.356271 | + | 0.934383i | \(0.384048\pi\) | |||||||
\(798\) | 9.92408 | + | 3.08424i | 0.351309 | + | 0.109181i | ||||
\(799\) | 9.97505 | − | 13.7295i | 0.352892 | − | 0.485714i | ||||
\(800\) | −12.1353 | + | 8.81678i | −0.429046 | + | 0.311720i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.82843i | 0.0998752i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −2.00000 | + | 2.82843i | −0.0705346 | + | 0.0997509i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.98752 | − | 6.86474i | −0.175678 | − | 0.241800i | ||||
\(807\) | −15.7356 | − | 46.3939i | −0.553919 | − | 1.63314i | ||||
\(808\) | 9.27051 | + | 28.5317i | 0.326135 | + | 1.00374i | ||||
\(809\) | −15.4508 | − | 47.5528i | −0.543223 | − | 1.67187i | −0.725178 | − | 0.688561i | \(-0.758243\pi\) |
0.181955 | − | 0.983307i | \(-0.441757\pi\) | |||||||
\(810\) | 1.30672 | + | 25.4223i | 0.0459134 | + | 0.893248i | ||||
\(811\) | −15.7938 | − | 21.7383i | −0.554596 | − | 0.763336i | 0.436031 | − | 0.899932i | \(-0.356384\pi\) |
−0.990627 | + | 0.136596i | \(0.956384\pi\) | |||||||
\(812\) | 2.68999 | + | 0.874032i | 0.0944003 | + | 0.0306725i | ||||
\(813\) | 42.0000 | + | 29.6985i | 1.47300 | + | 1.04157i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 56.5685i | − | 1.98151i | ||||||
\(816\) | −6.21588 | − | 8.32844i | −0.217599 | − | 0.291554i | ||||
\(817\) | 14.5623 | − | 10.5801i | 0.509471 | − | 0.370152i | ||||
\(818\) | −2.49376 | + | 3.43237i | −0.0871923 | + | 0.120010i | ||||
\(819\) | 14.2859 | − | 10.9505i | 0.499188 | − | 0.382643i | ||||
\(820\) | 16.1400 | − | 5.24419i | 0.563632 | − | 0.183135i | ||||
\(821\) | 33.9787 | + | 24.6870i | 1.18587 | + | 0.861582i | 0.992821 | − | 0.119609i | \(-0.0381639\pi\) |
0.193044 | + | 0.981190i | \(0.438164\pi\) | |||||||
\(822\) | −4.89858 | + | 0.0628954i | −0.170857 | + | 0.00219373i | ||||
\(823\) | −7.41641 | + | 22.8254i | −0.258520 | + | 0.795642i | 0.734596 | + | 0.678505i | \(0.237372\pi\) |
−0.993116 | + | 0.117137i | \(0.962628\pi\) | |||||||
\(824\) | 24.0000 | 0.836080 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.0000 | −0.556711 | ||||||||
\(827\) | −3.70820 | + | 11.4127i | −0.128947 | + | 0.396858i | −0.994600 | − | 0.103787i | \(-0.966904\pi\) |
0.865653 | + | 0.500645i | \(0.166904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.3262 | + | 8.22899i | 0.393377 | + | 0.285805i | 0.766838 | − | 0.641841i | \(-0.221829\pi\) |
−0.373461 | + | 0.927646i | \(0.621829\pi\) | |||||||
\(830\) | −43.0399 | + | 13.9845i | −1.49394 | + | 0.485410i | ||||
\(831\) | −2.18089 | + | 7.01739i | −0.0756542 | + | 0.243430i | ||||
\(832\) | 17.4563 | − | 24.0266i | 0.605189 | − | 0.832972i | ||||
\(833\) | 24.2705 | − | 17.6336i | 0.840923 | − | 0.610967i | ||||
\(834\) | 1.96303 | − | 1.46510i | 0.0679742 | − | 0.0507322i | ||||
\(835\) | 33.9411i | 1.17458i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.0000 | + | 2.82843i | 0.345651 | + | 0.0977647i | ||||
\(838\) | −29.5899 | − | 9.61435i | −1.02217 | − | 0.332122i | ||||
\(839\) | 19.9501 | + | 27.4589i | 0.688754 | + | 0.947988i | 0.999997 | − | 0.00234204i | \(-0.000745495\pi\) |
−0.311244 | + | 0.950330i | \(0.600745\pi\) | |||||||
\(840\) | 19.6833 | − | 6.67605i | 0.679137 | − | 0.230346i | ||||
\(841\) | −7.72542 | − | 23.7764i | −0.266394 | − | 0.819876i | ||||
\(842\) | 6.18034 | + | 19.0211i | 0.212989 | + | 0.655511i | ||||
\(843\) | 9.84163 | − | 3.33803i | 0.338964 | − | 0.114968i | ||||
\(844\) | −15.7938 | − | 21.7383i | −0.543646 | − | 0.748264i | ||||
\(845\) | 13.4500 | + | 4.37016i | 0.462693 | + | 0.150338i | ||||
\(846\) | 8.00000 | − | 2.82843i | 0.275046 | − | 0.0972433i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.65685i | 0.194257i | ||||||||
\(849\) | 37.2976 | − | 27.8368i | 1.28005 | − | 0.955358i | ||||
\(850\) | 14.5623 | − | 10.5801i | 0.499483 | − | 0.362896i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −1.45393 | + | 4.67826i | −0.0498107 | + | 0.160274i | ||||
\(853\) | 39.0049 | − | 12.6735i | 1.33550 | − | 0.433931i | 0.447712 | − | 0.894178i | \(-0.352239\pi\) |
0.887791 | + | 0.460247i | \(0.152239\pi\) | |||||||
\(854\) | −11.3262 | − | 8.22899i | −0.387576 | − | 0.281590i | ||||
\(855\) | −29.6583 | − | 20.4055i | −1.01429 | − | 0.697854i | ||||
\(856\) | 14.8328 | − | 45.6507i | 0.506975 | − | 1.56031i | ||||
\(857\) | 22.0000 | 0.751506 | 0.375753 | − | 0.926720i | \(-0.377384\pi\) | ||||
0.375753 | + | 0.926720i | \(0.377384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.0000 | −0.682391 | −0.341196 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341196 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(860\) | 3.70820 | − | 11.4127i | 0.126449 | − | 0.389169i | ||||
\(861\) | −14.6957 | + | 0.188686i | −0.500829 | + | 0.00643041i | ||||
\(862\) | 25.8885 | + | 18.8091i | 0.881767 | + | 0.640641i | ||||
\(863\) | 32.2799 | − | 10.4884i | 1.09882 | − | 0.357029i | 0.297173 | − | 0.954824i | \(-0.403956\pi\) |
0.801649 | + | 0.597795i | \(0.203956\pi\) | |||||||
\(864\) | 1.00044 | + | 25.9615i | 0.0340357 | + | 0.883228i | ||||
\(865\) | 9.97505 | − | 13.7295i | 0.339162 | − | 0.466816i | ||||
\(866\) | 24.2705 | − | 17.6336i | 0.824745 | − | 0.599213i | ||||
\(867\) | −19.6836 | − | 26.3734i | −0.668491 | − | 0.895687i | ||||
\(868\) | − | 2.82843i | − | 0.0960031i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 8.00000 | + | 5.65685i | 0.271225 | + | 0.191785i | ||||
\(871\) | 8.06998 | + | 2.62210i | 0.273441 | + | 0.0888463i | ||||
\(872\) | 7.48128 | + | 10.2971i | 0.253348 | + | 0.348704i | ||||
\(873\) | 1.70698 | − | 5.75206i | 0.0577726 | − | 0.194678i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.47214 | − | 7.60845i | −0.0835734 | − | 0.257213i | ||||
\(876\) | −0.786780 | − | 2.31969i | −0.0265828 | − | 0.0783752i | ||||
\(877\) | 20.7813 | + | 28.6031i | 0.701736 | + | 0.965857i | 0.999936 | + | 0.0113534i | \(0.00361399\pi\) |
−0.298199 | + | 0.954504i | \(0.596386\pi\) | |||||||
\(878\) | −25.5549 | − | 8.30330i | −0.862438 | − | 0.280223i | ||||
\(879\) | 2.00000 | − | 2.82843i | 0.0674583 | − | 0.0954005i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.1127i | 1.04821i | 0.851653 | + | 0.524107i | \(0.175601\pi\) | ||||
−0.851653 | + | 0.524107i | \(0.824399\pi\) | |||||||
\(882\) | 14.9951 | − | 0.385122i | 0.504910 | − | 0.0129677i | ||||
\(883\) | −37.2148 | + | 27.0381i | −1.25238 | + | 0.909905i | −0.998357 | − | 0.0572938i | \(-0.981753\pi\) |
−0.254020 | + | 0.967199i | \(0.581753\pi\) | |||||||
\(884\) | 14.9626 | − | 20.5942i | 0.503246 | − | 0.692658i | ||||
\(885\) | 52.9284 | + | 16.4493i | 1.77917 | + | 0.552937i | ||||
\(886\) | 26.8999 | − | 8.74032i | 0.903721 | − | 0.293637i | ||||
\(887\) | −19.4164 | − | 14.1068i | −0.651939 | − | 0.473662i | 0.211992 | − | 0.977271i | \(-0.432005\pi\) |
−0.863931 | + | 0.503610i | \(0.832005\pi\) | |||||||
\(888\) | 0.533685 | + | 41.5658i | 0.0179093 | + | 1.39486i | ||||
\(889\) | −4.32624 | + | 13.3148i | −0.145097 | + | 0.446564i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.0000 | −0.803579 | ||||||||
\(893\) | −3.70820 | + | 11.4127i | −0.124090 | + | 0.381911i | ||||
\(894\) | 0.133421 | + | 10.3914i | 0.00446228 | + | 0.347542i | ||||
\(895\) | 6.47214 | + | 4.70228i | 0.216340 | + | 0.157180i | ||||
\(896\) | 4.03499 | − | 1.31105i | 0.134800 | − | 0.0437990i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.32502 | − | 4.57649i | 0.110957 | − | 0.152719i | ||||
\(899\) | 3.23607 | − | 2.35114i | 0.107929 | − | 0.0784149i | ||||
\(900\) | −8.99703 | + | 0.231073i | −0.299901 | + | 0.00770245i | ||||
\(901\) | 33.9411i | 1.13074i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.00000 | + | 8.48528i | −0.199667 | + | 0.282372i | ||||
\(904\) | −8.06998 | − | 2.62210i | −0.268404 | − | 0.0872096i | ||||
\(905\) | −16.6251 | − | 22.8825i | −0.552636 | − | 0.760639i | ||||
\(906\) | −2.36034 | − | 6.95908i | −0.0784171 | − | 0.231200i | ||||
\(907\) | 3.70820 | + | 11.4127i | 0.123129 | + | 0.378952i | 0.993556 | − | 0.113346i | \(-0.0361570\pi\) |
−0.870427 | + | 0.492298i | \(0.836157\pi\) | |||||||
\(908\) | −7.41641 | − | 22.8254i | −0.246122 | − | 0.757486i | ||||
\(909\) | −8.53491 | + | 28.7603i | −0.283085 | + | 0.953919i | ||||
\(910\) | −9.97505 | − | 13.7295i | −0.330670 | − | 0.455128i | ||||
\(911\) | −34.9699 | − | 11.3624i | −1.15861 | − | 0.376454i | −0.334227 | − | 0.942493i | \(-0.608475\pi\) |
−0.824378 | + | 0.566039i | \(0.808475\pi\) | |||||||
\(912\) | 6.00000 | + | 4.24264i | 0.198680 | + | 0.140488i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.89949i | 0.327446i | ||||||||
\(915\) | 29.0074 | + | 38.8660i | 0.958956 | + | 1.28487i | ||||
\(916\) | −19.4164 | + | 14.1068i | −0.641536 | + | 0.466103i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.20053 | − | 31.1538i | −0.0396233 | − | 1.02823i | ||||
\(919\) | −20.1750 | + | 6.55524i | −0.665510 | + | 0.216237i | −0.622241 | − | 0.782826i | \(-0.713777\pi\) |
−0.0432697 | + | 0.999063i | \(0.513777\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.34786 | − | 0.0943431i | 0.242120 | − | 0.00310871i | ||||
\(922\) | 6.79837 | − | 20.9232i | 0.223893 | − | 0.689070i | ||||
\(923\) | 12.0000 | 0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.0000 | −0.789115 | ||||||||
\(926\) | −7.41641 | + | 22.8254i | −0.243718 | + | 0.750088i | ||||
\(927\) | 19.7722 | + | 13.6037i | 0.649404 | + | 0.446804i | ||||
\(928\) | 8.09017 | + | 5.87785i | 0.265573 | + | 0.192950i | ||||
\(929\) | 2.68999 | − | 0.874032i | 0.0882558 | − | 0.0286761i | −0.264556 | − | 0.964370i | \(-0.585225\pi\) |
0.352812 | + | 0.935694i | \(0.385225\pi\) | |||||||
\(930\) | 2.90785 | − | 9.35652i | 0.0953522 | − | 0.306812i | ||||
\(931\) | −12.4688 | + | 17.1618i | −0.408649 | + | 0.562457i | ||||
\(932\) | 8.09017 | − | 5.87785i | 0.265002 | − | 0.192535i | ||||
\(933\) | 39.2606 | − | 29.3019i | 1.28534 | − | 0.959302i | ||||
\(934\) | − | 28.2843i | − | 0.925490i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 36.0000 | − | 12.7279i | 1.17670 | − | 0.416025i | ||||
\(937\) | 33.6249 | + | 10.9254i | 1.09848 | + | 0.356917i | 0.801517 | − | 0.597972i | \(-0.204027\pi\) |
0.296962 | + | 0.954889i | \(0.404027\pi\) | |||||||
\(938\) | −1.66251 | − | 2.28825i | −0.0542828 | − | 0.0747139i | ||||
\(939\) | −19.6833 | + | 6.67605i | −0.642339 | + | 0.217865i | ||||
\(940\) | 2.47214 | + | 7.60845i | 0.0806322 | + | 0.248160i | ||||
\(941\) | 11.7426 | + | 36.1401i | 0.382799 | + | 1.17814i | 0.938064 | + | 0.346462i | \(0.112617\pi\) |
−0.555265 | + | 0.831674i | \(0.687383\pi\) | |||||||
\(942\) | −32.8054 | + | 11.1268i | −1.06886 | + | 0.362529i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −10.7600 | − | 3.49613i | −0.350207 | − | 0.113789i | ||||
\(945\) | 20.0000 | + | 5.65685i | 0.650600 | + | 0.184017i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 31.1127i | − | 1.01103i | −0.862819 | − | 0.505513i | \(-0.831303\pi\) | ||
0.862819 | − | 0.505513i | \(-0.168697\pi\) | |||||||
\(948\) | −5.88909 | + | 4.39529i | −0.191269 | + | 0.142752i | ||||
\(949\) | −4.85410 | + | 3.52671i | −0.157571 | + | 0.114482i | ||||
\(950\) | −7.48128 | + | 10.2971i | −0.242725 | + | 0.334082i | ||||
\(951\) | −13.0853 | + | 42.1043i | −0.424321 | + | 1.36533i | ||||
\(952\) | −24.2099 | + | 7.86629i | −0.784649 | + | 0.254948i | ||||
\(953\) | −1.61803 | − | 1.17557i | −0.0524133 | − | 0.0380805i | 0.561270 | − | 0.827633i | \(-0.310313\pi\) |
−0.613683 | + | 0.789552i | \(0.710313\pi\) | |||||||
\(954\) | −9.61926 | + | 13.9811i | −0.311435 | + | 0.452653i | ||||
\(955\) | −17.3050 | + | 53.2592i | −0.559975 | + | 1.72343i | ||||
\(956\) | −16.0000 | −0.517477 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.0000 | 0.904639 | ||||||||
\(959\) | −1.23607 | + | 3.80423i | −0.0399147 | + | 0.122845i | ||||
\(960\) | 34.2900 | − | 0.440268i | 1.10671 | − | 0.0142096i | ||||
\(961\) | 21.8435 | + | 15.8702i | 0.704628 | + | 0.511942i | ||||
\(962\) | 32.2799 | − | 10.4884i | 1.04075 | − | 0.338159i | ||||
\(963\) | 38.0956 | − | 29.2014i | 1.22761 | − | 0.941003i | ||||
\(964\) | 2.49376 | − | 3.43237i | 0.0803187 | − | 0.110549i | ||||
\(965\) | −48.5410 | + | 35.2671i | −1.56259 | + | 1.13529i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.24264i | − | 0.136434i | −0.997671 | − | 0.0682171i | \(-0.978269\pi\) | ||
0.997671 | − | 0.0682171i | \(-0.0217310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.0000 | + | 25.4558i | 1.15649 | + | 0.817760i | ||||
\(970\) | −5.37999 | − | 1.74806i | −0.172741 | − | 0.0561270i | ||||
\(971\) | 19.9501 | + | 27.4589i | 0.640229 | + | 0.881200i | 0.998628 | − | 0.0523690i | \(-0.0166772\pi\) |
−0.358399 | + | 0.933569i | \(0.616677\pi\) | |||||||
\(972\) | −8.33478 | + | 13.1731i | −0.267338 | + | 0.422529i | ||||
\(973\) | −0.618034 | − | 1.90211i | −0.0198133 | − | 0.0609789i | ||||
\(974\) | −0.618034 | − | 1.90211i | −0.0198031 | − | 0.0609476i | ||||
\(975\) | 7.08102 | + | 20.8772i | 0.226774 | + | 0.668607i | ||||
\(976\) | −5.81878 | − | 8.00886i | −0.186255 | − | 0.256357i | ||||
\(977\) | 24.2099 | + | 7.86629i | 0.774545 | + | 0.251665i | 0.669509 | − | 0.742804i | \(-0.266504\pi\) |
0.105035 | + | 0.994468i | \(0.466504\pi\) | |||||||
\(978\) | −20.0000 | + | 28.2843i | −0.639529 | + | 0.904431i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 14.1421i | 0.451754i | ||||||||
\(981\) | 0.326787 | + | 12.7237i | 0.0104335 | + | 0.406237i | ||||
\(982\) | −16.1803 | + | 11.7557i | −0.516335 | + | 0.375140i | ||||
\(983\) | 6.65003 | − | 9.15298i | 0.212103 | − | 0.291935i | −0.689688 | − | 0.724106i | \(-0.742252\pi\) |
0.901791 | + | 0.432171i | \(0.142252\pi\) | |||||||
\(984\) | −29.7723 | − | 9.25273i | −0.949105 | − | 0.294966i | ||||
\(985\) | −59.1799 | + | 19.2287i | −1.88563 | + | 0.612677i | ||||
\(986\) | −9.70820 | − | 7.05342i | −0.309172 | − | 0.224627i | ||||
\(987\) | −0.0889475 | − | 6.92763i | −0.00283123 | − | 0.220509i | ||||
\(988\) | −5.56231 | + | 17.1190i | −0.176961 | + | 0.544628i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.0000 | −1.33417 | −0.667087 | − | 0.744980i | \(-0.732459\pi\) | ||||
−0.667087 | + | 0.744980i | \(0.732459\pi\) | |||||||
\(992\) | 3.09017 | − | 9.51057i | 0.0981130 | − | 0.301961i | ||||
\(993\) | −0.444738 | − | 34.6382i | −0.0141133 | − | 1.09921i | ||||
\(994\) | −3.23607 | − | 2.35114i | −0.102642 | − | 0.0745737i | ||||
\(995\) | 5.37999 | − | 1.74806i | 0.170557 | − | 0.0554174i | ||||
\(996\) | −26.4642 | − | 8.22465i | −0.838551 | − | 0.260608i | ||||
\(997\) | 17.4563 | − | 24.0266i | 0.552848 | − | 0.760929i | −0.437548 | − | 0.899195i | \(-0.644153\pi\) |
0.990395 | + | 0.138266i | \(0.0441528\pi\) | |||||||
\(998\) | −11.3262 | + | 8.22899i | −0.358526 | + | 0.260484i | ||||
\(999\) | −23.1207 | + | 34.5461i | −0.731505 | + | 1.09299i |
(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 | 363.2.f.f.233.2 | 8 | ||
3.2 | odd | 2 | 363.2.f.a.233.1 | 8 | |||
11.2 | odd | 10 | 363.2.f.a.239.2 | 8 | |||
11.3 | even | 5 | inner | 363.2.f.f.161.1 | 8 | ||
11.4 | even | 5 | 363.2.d.a.362.1 | ✓ | 2 | ||
11.5 | even | 5 | inner | 363.2.f.f.215.1 | 8 | ||
11.6 | odd | 10 | 363.2.f.a.215.1 | 8 | |||
11.7 | odd | 10 | 363.2.d.b.362.1 | yes | 2 | ||
11.8 | odd | 10 | 363.2.f.a.161.1 | 8 | |||
11.9 | even | 5 | inner | 363.2.f.f.239.2 | 8 | ||
11.10 | odd | 2 | 363.2.f.a.233.2 | 8 | |||
33.2 | even | 10 | inner | 363.2.f.f.239.1 | 8 | ||
33.5 | odd | 10 | 363.2.f.a.215.2 | 8 | |||
33.8 | even | 10 | inner | 363.2.f.f.161.2 | 8 | ||
33.14 | odd | 10 | 363.2.f.a.161.2 | 8 | |||
33.17 | even | 10 | inner | 363.2.f.f.215.2 | 8 | ||
33.20 | odd | 10 | 363.2.f.a.239.1 | 8 | |||
33.26 | odd | 10 | 363.2.d.b.362.2 | yes | 2 | ||
33.29 | even | 10 | 363.2.d.a.362.2 | yes | 2 | ||
33.32 | even | 2 | inner | 363.2.f.f.233.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.d.a.362.1 | ✓ | 2 | 11.4 | even | 5 | ||
363.2.d.a.362.2 | yes | 2 | 33.29 | even | 10 | ||
363.2.d.b.362.1 | yes | 2 | 11.7 | odd | 10 | ||
363.2.d.b.362.2 | yes | 2 | 33.26 | odd | 10 | ||
363.2.f.a.161.1 | 8 | 11.8 | odd | 10 | |||
363.2.f.a.161.2 | 8 | 33.14 | odd | 10 | |||
363.2.f.a.215.1 | 8 | 11.6 | odd | 10 | |||
363.2.f.a.215.2 | 8 | 33.5 | odd | 10 | |||
363.2.f.a.233.1 | 8 | 3.2 | odd | 2 | |||
363.2.f.a.233.2 | 8 | 11.10 | odd | 2 | |||
363.2.f.a.239.1 | 8 | 33.20 | odd | 10 | |||
363.2.f.a.239.2 | 8 | 11.2 | odd | 10 | |||
363.2.f.f.161.1 | 8 | 11.3 | even | 5 | inner | ||
363.2.f.f.161.2 | 8 | 33.8 | even | 10 | inner | ||
363.2.f.f.215.1 | 8 | 11.5 | even | 5 | inner | ||
363.2.f.f.215.2 | 8 | 33.17 | even | 10 | inner | ||
363.2.f.f.233.1 | 8 | 33.32 | even | 2 | inner | ||
363.2.f.f.233.2 | 8 | 1.1 | even | 1 | trivial | ||
363.2.f.f.239.1 | 8 | 33.2 | even | 10 | inner | ||
363.2.f.f.239.2 | 8 | 11.9 | even | 5 | inner |