Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(593,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.t (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1025.1 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.1025 |
Dual form | 1134.2.t.f.593.1 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −2.44949 | −1.09545 | −0.547723 | − | 0.836660i | \(-0.684505\pi\) | ||||
−0.547723 | + | 0.836660i | \(0.684505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.62132 | − | 0.358719i | 0.990766 | − | 0.135583i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.12132 | + | 1.22474i | 0.670820 | + | 0.387298i | ||||
\(11\) | − | 4.24264i | − | 1.27920i | −0.768706 | − | 0.639602i | \(-0.779099\pi\) | ||
0.768706 | − | 0.639602i | \(-0.220901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.621320 | + | 0.358719i | 0.172323 | + | 0.0994909i | 0.583681 | − | 0.811983i | \(-0.301612\pi\) |
−0.411358 | + | 0.911474i | \(0.634945\pi\) | |||||||
\(14\) | −2.44949 | − | 1.00000i | −0.654654 | − | 0.267261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.22474 | − | 2.12132i | 0.297044 | − | 0.514496i | −0.678414 | − | 0.734680i | \(-0.737332\pi\) |
0.975458 | + | 0.220184i | \(0.0706658\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.24264 | + | 2.44949i | −0.973329 | + | 0.561951i | −0.900249 | − | 0.435375i | \(-0.856616\pi\) |
−0.0730792 | + | 0.997326i | \(0.523283\pi\) | |||||||
\(20\) | −1.22474 | − | 2.12132i | −0.273861 | − | 0.474342i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.12132 | + | 3.67423i | −0.452267 | + | 0.783349i | ||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.358719 | − | 0.621320i | −0.0703507 | − | 0.121851i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.62132 | + | 2.09077i | 0.306401 | + | 0.395118i | ||||
\(29\) | −1.52192 | + | 0.878680i | −0.282613 | + | 0.163167i | −0.634606 | − | 0.772836i | \(-0.718838\pi\) |
0.351993 | + | 0.936003i | \(0.385504\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.86396 | − | 4.54026i | 1.41241 | − | 0.815455i | 0.416794 | − | 0.909001i | \(-0.363154\pi\) |
0.995615 | + | 0.0935461i | \(0.0298203\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.12132 | + | 1.22474i | −0.363803 | + | 0.210042i | ||||
\(35\) | −6.42090 | + | 0.878680i | −1.08533 | + | 0.148524i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.62132 | − | 4.54026i | −0.430942 | − | 0.746414i | 0.566012 | − | 0.824397i | \(-0.308485\pi\) |
−0.996955 | + | 0.0779826i | \(0.975152\pi\) | |||||||
\(38\) | 4.89898 | 0.794719 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.44949i | 0.387298i | ||||||||
\(41\) | −1.22474 | + | 2.12132i | −0.191273 | + | 0.331295i | −0.945672 | − | 0.325121i | \(-0.894595\pi\) |
0.754399 | + | 0.656416i | \(0.227928\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.50000 | − | 6.06218i | −0.533745 | − | 0.924473i | −0.999223 | − | 0.0394140i | \(-0.987451\pi\) |
0.465478 | − | 0.885059i | \(-0.345882\pi\) | |||||||
\(44\) | 3.67423 | − | 2.12132i | 0.553912 | − | 0.319801i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | − | 5.19615i | 0.442326 | − | 0.766131i | ||||
\(47\) | 6.42090 | − | 11.1213i | 0.936584 | − | 1.62221i | 0.164800 | − | 0.986327i | \(-0.447302\pi\) |
0.771784 | − | 0.635884i | \(-0.219364\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.74264 | − | 1.88064i | 0.963234 | − | 0.268662i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.717439i | 0.0994909i | ||||||||
\(53\) | −12.5446 | − | 7.24264i | −1.72314 | − | 0.994853i | −0.912231 | − | 0.409675i | \(-0.865642\pi\) |
−0.810905 | − | 0.585178i | \(-0.801025\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.3923i | 1.40130i | ||||||||
\(56\) | −0.358719 | − | 2.62132i | −0.0479359 | − | 0.350289i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.75736 | 0.230753 | ||||||||
\(59\) | −1.22474 | − | 2.12132i | −0.159448 | − | 0.276172i | 0.775222 | − | 0.631689i | \(-0.217638\pi\) |
−0.934670 | + | 0.355517i | \(0.884305\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.62132 | − | 2.09077i | −0.463663 | − | 0.267696i | 0.249920 | − | 0.968266i | \(-0.419596\pi\) |
−0.713583 | + | 0.700571i | \(0.752929\pi\) | |||||||
\(62\) | −9.08052 | −1.15323 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.52192 | − | 0.878680i | −0.188771 | − | 0.108987i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.74264 | − | 11.6786i | −0.823745 | − | 1.42677i | −0.902875 | − | 0.429903i | \(-0.858548\pi\) |
0.0791303 | − | 0.996864i | \(-0.474786\pi\) | |||||||
\(68\) | 2.44949 | 0.297044 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.00000 | + | 2.44949i | 0.717137 | + | 0.292770i | ||||
\(71\) | − | 12.7279i | − | 1.51053i | −0.655422 | − | 0.755263i | \(-0.727509\pi\) | ||
0.655422 | − | 0.755263i | \(-0.272491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.75736 | − | 2.74666i | −0.556807 | − | 0.321473i | 0.195056 | − | 0.980792i | \(-0.437511\pi\) |
−0.751863 | + | 0.659320i | \(0.770844\pi\) | |||||||
\(74\) | 5.24264i | 0.609445i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.24264 | − | 2.44949i | −0.486664 | − | 0.280976i | ||||
\(77\) | −1.52192 | − | 11.1213i | −0.173439 | − | 1.26739i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.378680 | + | 0.655892i | −0.0426048 | + | 0.0737937i | −0.886541 | − | 0.462649i | \(-0.846899\pi\) |
0.843937 | + | 0.536443i | \(0.180232\pi\) | |||||||
\(80\) | 1.22474 | − | 2.12132i | 0.136931 | − | 0.237171i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.12132 | − | 1.22474i | 0.234261 | − | 0.135250i | ||||
\(83\) | 7.64564 | + | 13.2426i | 0.839218 | + | 1.45357i | 0.890549 | + | 0.454887i | \(0.150320\pi\) |
−0.0513309 | + | 0.998682i | \(0.516346\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | + | 5.19615i | −0.325396 | + | 0.563602i | ||||
\(86\) | 7.00000i | 0.754829i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.24264 | −0.452267 | ||||||||
\(89\) | 1.52192 | + | 2.63604i | 0.161323 | + | 0.279420i | 0.935343 | − | 0.353741i | \(-0.115091\pi\) |
−0.774020 | + | 0.633161i | \(0.781757\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.75736 | + | 0.717439i | 0.184221 | + | 0.0752080i | ||||
\(92\) | −5.19615 | + | 3.00000i | −0.541736 | + | 0.312772i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −11.1213 | + | 6.42090i | −1.14708 | + | 0.662265i | ||||
\(95\) | 10.3923 | − | 6.00000i | 1.06623 | − | 0.615587i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.74264 | − | 1.58346i | 0.278473 | − | 0.160776i | −0.354259 | − | 0.935147i | \(-0.615267\pi\) |
0.632732 | + | 0.774371i | \(0.281934\pi\) | |||||||
\(98\) | −6.77962 | − | 1.74264i | −0.684845 | − | 0.176033i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −7.34847 | −0.731200 | −0.365600 | − | 0.930772i | \(-0.619136\pi\) | ||||
−0.365600 | + | 0.930772i | \(0.619136\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.1097i | 1.09468i | 0.836912 | + | 0.547338i | \(0.184359\pi\) | ||||
−0.836912 | + | 0.547338i | \(0.815641\pi\) | |||||||
\(104\) | 0.358719 | − | 0.621320i | 0.0351753 | − | 0.0609255i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.24264 | + | 12.5446i | 0.703467 | + | 1.21844i | ||||
\(107\) | −2.15232 | + | 1.24264i | −0.208072 | + | 0.120131i | −0.600415 | − | 0.799688i | \(-0.704998\pi\) |
0.392343 | + | 0.919819i | \(0.371665\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.86396 | − | 15.3528i | 0.849013 | − | 1.47053i | −0.0330761 | − | 0.999453i | \(-0.510530\pi\) |
0.882090 | − | 0.471082i | \(-0.156136\pi\) | |||||||
\(110\) | 5.19615 | − | 9.00000i | 0.495434 | − | 0.858116i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | + | 2.44949i | −0.0944911 | + | 0.231455i | ||||
\(113\) | −8.87039 | − | 5.12132i | −0.834456 | − | 0.481773i | 0.0209200 | − | 0.999781i | \(-0.493340\pi\) |
−0.855376 | + | 0.518008i | \(0.826674\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 14.6969i | − | 1.37050i | ||||||
\(116\) | −1.52192 | − | 0.878680i | −0.141307 | − | 0.0815834i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.44949i | 0.225494i | ||||||||
\(119\) | 2.44949 | − | 6.00000i | 0.224544 | − | 0.550019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 2.09077 | + | 3.62132i | 0.189289 | + | 0.327859i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.86396 | + | 4.54026i | 0.706205 | + | 0.407727i | ||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.72792 | −0.685742 | −0.342871 | − | 0.939382i | \(-0.611399\pi\) | ||||
−0.342871 | + | 0.939382i | \(0.611399\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.878680 | + | 1.52192i | 0.0770653 | + | 0.133481i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.2426 | + | 7.94282i | −0.888150 | + | 0.688729i | ||||
\(134\) | 13.4853i | 1.16495i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.12132 | − | 1.22474i | −0.181902 | − | 0.105021i | ||||
\(137\) | 6.00000i | 0.512615i | 0.966595 | + | 0.256307i | \(0.0825059\pi\) | ||||
−0.966595 | + | 0.256307i | \(0.917494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.98528 | − | 4.03295i | −0.592484 | − | 0.342071i | 0.173595 | − | 0.984817i | \(-0.444462\pi\) |
−0.766079 | + | 0.642746i | \(0.777795\pi\) | |||||||
\(140\) | −3.97141 | − | 5.12132i | −0.335645 | − | 0.432831i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.36396 | + | 11.0227i | −0.534052 | + | 0.925005i | ||||
\(143\) | 1.52192 | − | 2.63604i | 0.127269 | − | 0.220437i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.72792 | − | 2.15232i | 0.309587 | − | 0.178740i | ||||
\(146\) | 2.74666 | + | 4.75736i | 0.227315 | + | 0.393722i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.62132 | − | 4.54026i | 0.215471 | − | 0.373207i | ||||
\(149\) | 16.2426i | 1.33065i | 0.746554 | + | 0.665324i | \(0.231707\pi\) | ||||
−0.746554 | + | 0.665324i | \(0.768293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.75736 | 0.712664 | 0.356332 | − | 0.934359i | \(-0.384027\pi\) | ||||
0.356332 | + | 0.934359i | \(0.384027\pi\) | |||||||
\(152\) | 2.44949 | + | 4.24264i | 0.198680 | + | 0.344124i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.24264 | + | 10.3923i | −0.341882 | + | 0.837436i | ||||
\(155\) | −19.2627 | + | 11.1213i | −1.54722 | + | 0.893286i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | − | 5.19615i | 0.718278 | − | 0.414698i | −0.0958404 | − | 0.995397i | \(-0.530554\pi\) |
0.814119 | + | 0.580699i | \(0.197221\pi\) | |||||||
\(158\) | 0.655892 | − | 0.378680i | 0.0521800 | − | 0.0301261i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.12132 | + | 1.22474i | −0.167705 | + | 0.0968246i | ||||
\(161\) | 2.15232 | + | 15.7279i | 0.169626 | + | 1.23953i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.74264 | + | 8.21449i | 0.371472 | + | 0.643409i | 0.989792 | − | 0.142518i | \(-0.0455197\pi\) |
−0.618320 | + | 0.785926i | \(0.712186\pi\) | |||||||
\(164\) | −2.44949 | −0.191273 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 15.2913i | − | 1.18683i | ||||||
\(167\) | −0.297173 | + | 0.514719i | −0.0229959 | + | 0.0398301i | −0.877294 | − | 0.479953i | \(-0.840654\pi\) |
0.854298 | + | 0.519783i | \(0.173987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.24264 | − | 10.8126i | −0.480203 | − | 0.831736i | ||||
\(170\) | 5.19615 | − | 3.00000i | 0.398527 | − | 0.230089i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.50000 | − | 6.06218i | 0.266872 | − | 0.462237i | ||||
\(173\) | 10.3923 | − | 18.0000i | 0.790112 | − | 1.36851i | −0.135785 | − | 0.990738i | \(-0.543356\pi\) |
0.925897 | − | 0.377776i | \(-0.123311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.62132 | − | 0.358719i | 0.198153 | − | 0.0271166i | ||||
\(176\) | 3.67423 | + | 2.12132i | 0.276956 | + | 0.159901i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 3.04384i | − | 0.228145i | ||||||
\(179\) | 5.82655 | + | 3.36396i | 0.435497 | + | 0.251434i | 0.701686 | − | 0.712487i | \(-0.252431\pi\) |
−0.266189 | + | 0.963921i | \(0.585764\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.79796i | − | 0.728277i | −0.931345 | − | 0.364138i | \(-0.881364\pi\) | ||
0.931345 | − | 0.364138i | \(-0.118636\pi\) | |||||||
\(182\) | −1.16320 | − | 1.50000i | −0.0862220 | − | 0.111187i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | 6.42090 | + | 11.1213i | 0.472074 | + | 0.817656i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | − | 5.19615i | −0.658145 | − | 0.379980i | ||||
\(188\) | 12.8418 | 0.936584 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0000 | −0.870572 | ||||||||
\(191\) | −18.3712 | − | 10.6066i | −1.32929 | − | 0.767467i | −0.344101 | − | 0.938933i | \(-0.611816\pi\) |
−0.985190 | + | 0.171466i | \(0.945150\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.742641 | + | 1.28629i | 0.0534564 | + | 0.0925893i | 0.891515 | − | 0.452990i | \(-0.149643\pi\) |
−0.838059 | + | 0.545580i | \(0.816310\pi\) | |||||||
\(194\) | −3.16693 | −0.227372 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.00000 | + | 4.89898i | 0.357143 | + | 0.349927i | ||||
\(197\) | 16.9706i | 1.20910i | 0.796566 | + | 0.604551i | \(0.206648\pi\) | ||||
−0.796566 | + | 0.604551i | \(0.793352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.1066 | − | 10.4539i | −1.28354 | − | 0.741054i | −0.306049 | − | 0.952016i | \(-0.599007\pi\) |
−0.977494 | + | 0.210962i | \(0.932340\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.36396 | + | 3.67423i | 0.447767 | + | 0.258518i | ||||
\(203\) | −3.67423 | + | 2.84924i | −0.257881 | + | 0.199978i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | − | 5.19615i | 0.209529 | − | 0.362915i | ||||
\(206\) | 5.55487 | − | 9.62132i | 0.387026 | − | 0.670349i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.621320 | + | 0.358719i | −0.0430808 | + | 0.0248727i | ||||
\(209\) | 10.3923 | + | 18.0000i | 0.718851 | + | 1.24509i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.74264 | + | 3.01834i | −0.119968 | + | 0.207791i | −0.919755 | − | 0.392493i | \(-0.871613\pi\) |
0.799787 | + | 0.600284i | \(0.204946\pi\) | |||||||
\(212\) | − | 14.4853i | − | 0.994853i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.48528 | 0.169890 | ||||||||
\(215\) | 8.57321 | + | 14.8492i | 0.584688 | + | 1.01271i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.9853 | − | 14.7224i | 1.28880 | − | 0.999424i | ||||
\(218\) | −15.3528 | + | 8.86396i | −1.03982 | + | 0.600343i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.00000 | + | 5.19615i | −0.606780 | + | 0.350325i | ||||
\(221\) | 1.52192 | − | 0.878680i | 0.102375 | − | 0.0591064i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.00000 | + | 5.19615i | −0.602685 | + | 0.347960i | −0.770097 | − | 0.637927i | \(-0.779792\pi\) |
0.167412 | + | 0.985887i | \(0.446459\pi\) | |||||||
\(224\) | 2.09077 | − | 1.62132i | 0.139695 | − | 0.108329i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.12132 | + | 8.87039i | 0.340665 | + | 0.590049i | ||||
\(227\) | 25.0892 | 1.66523 | 0.832616 | − | 0.553851i | \(-0.186842\pi\) | ||||
0.832616 | + | 0.553851i | \(0.186842\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.61642i | − | 0.371143i | −0.982631 | − | 0.185572i | \(-0.940586\pi\) | ||
0.982631 | − | 0.185572i | \(-0.0594137\pi\) | |||||||
\(230\) | −7.34847 | + | 12.7279i | −0.484544 | + | 0.839254i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.878680 | + | 1.52192i | 0.0576881 | + | 0.0999188i | ||||
\(233\) | 17.7408 | − | 10.2426i | 1.16224 | − | 0.671018i | 0.210398 | − | 0.977616i | \(-0.432524\pi\) |
0.951839 | + | 0.306598i | \(0.0991908\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.7279 | + | 27.2416i | −1.02598 | + | 1.77704i | ||||
\(236\) | 1.22474 | − | 2.12132i | 0.0797241 | − | 0.138086i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.12132 | + | 3.97141i | −0.331966 | + | 0.257428i | ||||
\(239\) | −14.0665 | − | 8.12132i | −0.909889 | − | 0.525325i | −0.0294934 | − | 0.999565i | \(-0.509389\pi\) |
−0.880395 | + | 0.474240i | \(0.842723\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.13770i | 0.0732860i | 0.999328 | + | 0.0366430i | \(0.0116664\pi\) | ||||
−0.999328 | + | 0.0366430i | \(0.988334\pi\) | |||||||
\(242\) | 6.06218 | + | 3.50000i | 0.389692 | + | 0.224989i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 4.18154i | − | 0.267696i | ||||||
\(245\) | −16.5160 | + | 4.60660i | −1.05517 | + | 0.294305i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.51472 | −0.223636 | ||||||||
\(248\) | −4.54026 | − | 7.86396i | −0.288307 | − | 0.499362i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.48528 | − | 4.89898i | −0.536656 | − | 0.309839i | ||||
\(251\) | 15.2913 | 0.965177 | 0.482589 | − | 0.875847i | \(-0.339697\pi\) | ||||
0.482589 | + | 0.875847i | \(0.339697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.4558 | 1.60040 | ||||||||
\(254\) | 6.69258 | + | 3.86396i | 0.419930 | + | 0.242446i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 25.0892 | 1.56502 | 0.782512 | − | 0.622636i | \(-0.213938\pi\) | ||||
0.782512 | + | 0.622636i | \(0.213938\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.50000 | − | 10.9612i | −0.528164 | − | 0.681093i | ||||
\(260\) | − | 1.75736i | − | 0.108987i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.72792i | 0.414861i | 0.978250 | + | 0.207431i | \(0.0665102\pi\) | ||||
−0.978250 | + | 0.207431i | \(0.933490\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.7279 | + | 17.7408i | 1.88760 | + | 1.08981i | ||||
\(266\) | 12.8418 | − | 1.75736i | 0.787381 | − | 0.107751i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.74264 | − | 11.6786i | 0.411872 | − | 0.713384i | ||||
\(269\) | −4.89898 | + | 8.48528i | −0.298696 | + | 0.517357i | −0.975838 | − | 0.218496i | \(-0.929885\pi\) |
0.677142 | + | 0.735853i | \(0.263218\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.3492 | + | 9.43924i | −0.993146 | + | 0.573393i | −0.906213 | − | 0.422821i | \(-0.861040\pi\) |
−0.0869326 | + | 0.996214i | \(0.527706\pi\) | |||||||
\(272\) | 1.22474 | + | 2.12132i | 0.0742611 | + | 0.128624i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.00000 | − | 5.19615i | 0.181237 | − | 0.313911i | ||||
\(275\) | − | 4.24264i | − | 0.255841i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.7279 | 1.42567 | 0.712836 | − | 0.701330i | \(-0.247410\pi\) | ||||
0.712836 | + | 0.701330i | \(0.247410\pi\) | |||||||
\(278\) | 4.03295 | + | 6.98528i | 0.241881 | + | 0.418949i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.878680 | + | 6.42090i | 0.0525112 | + | 0.383722i | ||||
\(281\) | −11.9142 | + | 6.87868i | −0.710743 | + | 0.410348i | −0.811336 | − | 0.584580i | \(-0.801259\pi\) |
0.100593 | + | 0.994928i | \(0.467926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.22792 | + | 3.01834i | −0.310768 | + | 0.179422i | −0.647270 | − | 0.762261i | \(-0.724089\pi\) |
0.336502 | + | 0.941683i | \(0.390756\pi\) | |||||||
\(284\) | 11.0227 | − | 6.36396i | 0.654077 | − | 0.377632i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.63604 | + | 1.52192i | −0.155872 | + | 0.0899929i | ||||
\(287\) | −2.44949 | + | 6.00000i | −0.144589 | + | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.50000 | + | 9.52628i | 0.323529 | + | 0.560369i | ||||
\(290\) | −4.30463 | −0.252777 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 5.49333i | − | 0.321473i | ||||||
\(293\) | −6.42090 | + | 11.1213i | −0.375113 | + | 0.649714i | −0.990344 | − | 0.138632i | \(-0.955729\pi\) |
0.615231 | + | 0.788347i | \(0.289063\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | + | 5.19615i | 0.174667 | + | 0.302532i | ||||
\(296\) | −4.54026 | + | 2.62132i | −0.263897 | + | 0.152361i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.12132 | − | 14.0665i | 0.470455 | − | 0.814853i | ||||
\(299\) | −2.15232 | + | 3.72792i | −0.124472 | + | 0.215591i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.3492 | − | 14.6354i | −0.654159 | − | 0.843570i | ||||
\(302\) | −7.58410 | − | 4.37868i | −0.436416 | − | 0.251965i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 4.89898i | − | 0.280976i | ||||||
\(305\) | 8.87039 | + | 5.12132i | 0.507917 | + | 0.293246i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.8213i | 1.53077i | 0.643571 | + | 0.765386i | \(0.277452\pi\) | ||||
−0.643571 | + | 0.765386i | \(0.722548\pi\) | |||||||
\(308\) | 8.87039 | − | 6.87868i | 0.505437 | − | 0.391949i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 22.2426 | 1.26330 | ||||||||
\(311\) | 8.57321 | + | 14.8492i | 0.486142 | + | 0.842023i | 0.999873 | − | 0.0159282i | \(-0.00507031\pi\) |
−0.513731 | + | 0.857951i | \(0.671737\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.4853 | + | 10.0951i | 0.988327 | + | 0.570611i | 0.904774 | − | 0.425893i | \(-0.140040\pi\) |
0.0835529 | + | 0.996503i | \(0.473373\pi\) | |||||||
\(314\) | −10.3923 | −0.586472 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.757359 | −0.0426048 | ||||||||
\(317\) | 19.2627 | + | 11.1213i | 1.08190 | + | 0.624636i | 0.931408 | − | 0.363976i | \(-0.118581\pi\) |
0.150492 | + | 0.988611i | \(0.451914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.72792 | + | 6.45695i | 0.208724 | + | 0.361520i | ||||
\(320\) | 2.44949 | 0.136931 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.00000 | − | 14.6969i | 0.334367 | − | 0.819028i | ||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.621320 | + | 0.358719i | 0.0344647 | + | 0.0198982i | ||||
\(326\) | − | 9.48528i | − | 0.525341i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.12132 | + | 1.22474i | 0.117130 | + | 0.0676252i | ||||
\(329\) | 12.8418 | − | 31.4558i | 0.707991 | − | 1.73422i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.00000 | + | 8.66025i | −0.274825 | + | 0.476011i | −0.970091 | − | 0.242742i | \(-0.921953\pi\) |
0.695266 | + | 0.718752i | \(0.255287\pi\) | |||||||
\(332\) | −7.64564 | + | 13.2426i | −0.419609 | + | 0.726784i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.514719 | − | 0.297173i | 0.0281642 | − | 0.0162606i | ||||
\(335\) | 16.5160 | + | 28.6066i | 0.902367 | + | 1.56295i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7279 | − | 18.5813i | 0.584387 | − | 1.01219i | −0.410564 | − | 0.911832i | \(-0.634668\pi\) |
0.994952 | − | 0.100357i | \(-0.0319984\pi\) | |||||||
\(338\) | 12.4853i | 0.679110i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.00000 | −0.325396 | ||||||||
\(341\) | −19.2627 | − | 33.3640i | −1.04313 | − | 1.80676i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | −6.06218 | + | 3.50000i | −0.326851 | + | 0.188707i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | + | 10.3923i | −0.967686 | + | 0.558694i | ||||
\(347\) | 4.30463 | − | 2.48528i | 0.231085 | − | 0.133417i | −0.379988 | − | 0.924992i | \(-0.624072\pi\) |
0.611072 | + | 0.791575i | \(0.290738\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.106602 | + | 0.0615465i | −0.00570626 | + | 0.00329451i | −0.502850 | − | 0.864373i | \(-0.667715\pi\) |
0.497144 | + | 0.867668i | \(0.334382\pi\) | |||||||
\(350\) | −2.44949 | − | 1.00000i | −0.130931 | − | 0.0534522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.12132 | − | 3.67423i | −0.113067 | − | 0.195837i | ||||
\(353\) | 10.9867 | 0.584760 | 0.292380 | − | 0.956302i | \(-0.405553\pi\) | ||||
0.292380 | + | 0.956302i | \(0.405553\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.1769i | 1.65470i | ||||||||
\(356\) | −1.52192 | + | 2.63604i | −0.0806615 | + | 0.139710i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.36396 | − | 5.82655i | −0.177791 | − | 0.307943i | ||||
\(359\) | −12.5446 | + | 7.24264i | −0.662080 | + | 0.382252i | −0.793069 | − | 0.609132i | \(-0.791518\pi\) |
0.130989 | + | 0.991384i | \(0.458185\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.50000 | − | 4.33013i | 0.131579 | − | 0.227901i | ||||
\(362\) | −4.89898 | + | 8.48528i | −0.257485 | + | 0.445976i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.257359 | + | 1.88064i | 0.0134893 | + | 0.0985722i | ||||
\(365\) | 11.6531 | + | 6.72792i | 0.609951 | + | 0.352156i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.9882i | 1.56537i | 0.622416 | + | 0.782686i | \(0.286151\pi\) | ||||
−0.622416 | + | 0.782686i | \(0.713849\pi\) | |||||||
\(368\) | −5.19615 | − | 3.00000i | −0.270868 | − | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 12.8418i | − | 0.667613i | ||||||
\(371\) | −35.4815 | − | 14.4853i | −1.84211 | − | 0.752038i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 5.19615 | + | 9.00000i | 0.268687 | + | 0.465379i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.1213 | − | 6.42090i | −0.573538 | − | 0.331132i | ||||
\(377\) | −1.26080 | −0.0649344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.48528 | −0.384493 | −0.192247 | − | 0.981347i | \(-0.561577\pi\) | ||||
−0.192247 | + | 0.981347i | \(0.561577\pi\) | |||||||
\(380\) | 10.3923 | + | 6.00000i | 0.533114 | + | 0.307794i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.6066 | + | 18.3712i | 0.542681 | + | 0.939951i | ||||
\(383\) | 5.49333 | 0.280696 | 0.140348 | − | 0.990102i | \(-0.455178\pi\) | ||||
0.140348 | + | 0.990102i | \(0.455178\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.72792 | + | 27.2416i | 0.189993 | + | 1.38836i | ||||
\(386\) | − | 1.48528i | − | 0.0755988i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.74264 | + | 1.58346i | 0.139236 | + | 0.0803882i | ||||
\(389\) | − | 15.5147i | − | 0.786627i | −0.919404 | − | 0.393314i | \(-0.871329\pi\) | ||
0.919404 | − | 0.393314i | \(-0.128671\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.7279 | + | 7.34847i | 0.643679 | + | 0.371628i | ||||
\(392\) | −1.88064 | − | 6.74264i | −0.0949865 | − | 0.340555i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.48528 | − | 14.6969i | 0.427482 | − | 0.740421i | ||||
\(395\) | 0.927572 | − | 1.60660i | 0.0466712 | − | 0.0808369i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.1360 | + | 7.58410i | −0.659279 | + | 0.380635i | −0.792002 | − | 0.610518i | \(-0.790961\pi\) |
0.132723 | + | 0.991153i | \(0.457628\pi\) | |||||||
\(398\) | 10.4539 | + | 18.1066i | 0.524004 | + | 0.907602i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | − | 19.7574i | − | 0.986635i | −0.869849 | − | 0.493318i | \(-0.835784\pi\) | ||
0.869849 | − | 0.493318i | \(-0.164216\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.51472 | 0.324521 | ||||||||
\(404\) | −3.67423 | − | 6.36396i | −0.182800 | − | 0.316619i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.60660 | − | 0.630399i | 0.228622 | − | 0.0312862i | ||||
\(407\) | −19.2627 | + | 11.1213i | −0.954816 | + | 0.551263i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.25736 | − | 1.88064i | 0.161066 | − | 0.0929915i | −0.417300 | − | 0.908769i | \(-0.637024\pi\) |
0.578366 | + | 0.815777i | \(0.303690\pi\) | |||||||
\(410\) | −5.19615 | + | 3.00000i | −0.256620 | + | 0.148159i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.62132 | + | 5.55487i | −0.474008 | + | 0.273669i | ||||
\(413\) | −3.97141 | − | 5.12132i | −0.195420 | − | 0.252004i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.7279 | − | 32.4377i | −0.919318 | − | 1.59230i | ||||
\(416\) | 0.717439 | 0.0351753 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 20.7846i | − | 1.01661i | ||||||
\(419\) | −3.97141 | + | 6.87868i | −0.194016 | + | 0.336045i | −0.946577 | − | 0.322476i | \(-0.895485\pi\) |
0.752562 | + | 0.658522i | \(0.228818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.7279 | + | 20.3134i | 0.571584 | + | 0.990012i | 0.996404 | + | 0.0847344i | \(0.0270042\pi\) |
−0.424820 | + | 0.905278i | \(0.639662\pi\) | |||||||
\(422\) | 3.01834 | − | 1.74264i | 0.146931 | − | 0.0848304i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.24264 | + | 12.5446i | −0.351734 | + | 0.609221i | ||||
\(425\) | 1.22474 | − | 2.12132i | 0.0594089 | − | 0.102899i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.2426 | − | 4.18154i | −0.495676 | − | 0.202359i | ||||
\(428\) | −2.15232 | − | 1.24264i | −0.104036 | − | 0.0600653i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 17.1464i | − | 0.826874i | ||||||
\(431\) | 1.52192 | + | 0.878680i | 0.0733082 | + | 0.0423245i | 0.536206 | − | 0.844087i | \(-0.319857\pi\) |
−0.462898 | + | 0.886412i | \(0.653190\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.57258i | 0.123630i | 0.998088 | + | 0.0618152i | \(0.0196889\pi\) | ||||
−0.998088 | + | 0.0618152i | \(0.980311\pi\) | |||||||
\(434\) | −23.8030 | + | 3.25736i | −1.14258 | + | 0.156358i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.7279 | 0.849013 | ||||||||
\(437\) | −14.6969 | − | 25.4558i | −0.703050 | − | 1.21772i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.72792 | − | 2.15232i | −0.177924 | − | 0.102724i | 0.408393 | − | 0.912806i | \(-0.366089\pi\) |
−0.586317 | + | 0.810082i | \(0.699423\pi\) | |||||||
\(440\) | 10.3923 | 0.495434 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.75736 | −0.0835891 | ||||||||
\(443\) | 22.0454 | + | 12.7279i | 1.04741 | + | 0.604722i | 0.921923 | − | 0.387374i | \(-0.126618\pi\) |
0.125486 | + | 0.992095i | \(0.459951\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.72792 | − | 6.45695i | −0.176720 | − | 0.306089i | ||||
\(446\) | 10.3923 | 0.492090 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.62132 | + | 0.358719i | −0.123846 | + | 0.0169479i | ||||
\(449\) | 5.27208i | 0.248805i | 0.992232 | + | 0.124402i | \(0.0397014\pi\) | ||||
−0.992232 | + | 0.124402i | \(0.960299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | + | 5.19615i | 0.423793 | + | 0.244677i | ||||
\(452\) | − | 10.2426i | − | 0.481773i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.7279 | − | 12.5446i | −1.01974 | − | 0.588748i | ||||
\(455\) | −4.30463 | − | 1.75736i | −0.201804 | − | 0.0823863i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5000 | − | 19.9186i | 0.537947 | − | 0.931752i | −0.461067 | − | 0.887365i | \(-0.652533\pi\) |
0.999014 | − | 0.0443868i | \(-0.0141334\pi\) | |||||||
\(458\) | −2.80821 | + | 4.86396i | −0.131219 | + | 0.227278i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.7279 | − | 7.34847i | 0.593442 | − | 0.342624i | ||||
\(461\) | −10.7255 | − | 18.5772i | −0.499538 | − | 0.865225i | 0.500462 | − | 0.865758i | \(-0.333163\pi\) |
−1.00000 | 0.000533648i | \(0.999830\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0000 | − | 19.0526i | 0.511213 | − | 0.885448i | −0.488702 | − | 0.872451i | \(-0.662530\pi\) |
0.999916 | − | 0.0129968i | \(-0.00413714\pi\) | |||||||
\(464\) | − | 1.75736i | − | 0.0815834i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.4853 | −0.948962 | ||||||||
\(467\) | −8.87039 | − | 15.3640i | −0.410473 | − | 0.710959i | 0.584469 | − | 0.811416i | \(-0.301303\pi\) |
−0.994941 | + | 0.100457i | \(0.967970\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.8640 | − | 28.1946i | −1.00958 | − | 1.30191i | ||||
\(470\) | 27.2416 | − | 15.7279i | 1.25656 | − | 0.725475i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.12132 | + | 1.22474i | −0.0976417 | + | 0.0563735i | ||||
\(473\) | −25.7196 | + | 14.8492i | −1.18259 | + | 0.682769i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.24264 | + | 2.44949i | −0.194666 | + | 0.112390i | ||||
\(476\) | 6.42090 | − | 0.878680i | 0.294301 | − | 0.0402742i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.12132 | + | 14.0665i | 0.371461 | + | 0.643389i | ||||
\(479\) | 2.44949 | 0.111920 | 0.0559600 | − | 0.998433i | \(-0.482178\pi\) | ||||
0.0559600 | + | 0.998433i | \(0.482178\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 3.76127i | − | 0.171499i | ||||||
\(482\) | 0.568852 | − | 0.985281i | 0.0259105 | − | 0.0448783i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.50000 | − | 6.06218i | −0.159091 | − | 0.275554i | ||||
\(485\) | −6.71807 | + | 3.87868i | −0.305052 | + | 0.176122i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0000 | + | 19.0526i | −0.498458 | + | 0.863354i | −0.999998 | − | 0.00178012i | \(-0.999433\pi\) |
0.501541 | + | 0.865134i | \(0.332767\pi\) | |||||||
\(488\) | −2.09077 | + | 3.62132i | −0.0946447 | + | 0.163929i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 16.6066 | + | 4.26858i | 0.750210 | + | 0.192835i | ||||
\(491\) | −30.2854 | − | 17.4853i | −1.36676 | − | 0.789100i | −0.376248 | − | 0.926519i | \(-0.622786\pi\) |
−0.990513 | + | 0.137419i | \(0.956119\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.30463i | 0.193871i | ||||||||
\(494\) | 3.04384 | + | 1.75736i | 0.136949 | + | 0.0790673i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.08052i | 0.407727i | ||||||||
\(497\) | −4.56575 | − | 33.3640i | −0.204802 | − | 1.49658i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.4558 | −1.09479 | −0.547397 | − | 0.836873i | \(-0.684381\pi\) | ||||
−0.547397 | + | 0.836873i | \(0.684381\pi\) | |||||||
\(500\) | 4.89898 | + | 8.48528i | 0.219089 | + | 0.379473i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.2426 | − | 7.64564i | −0.591048 | − | 0.341242i | ||||
\(503\) | −0.594346 | −0.0265006 | −0.0132503 | − | 0.999912i | \(-0.504218\pi\) | ||||
−0.0132503 | + | 0.999912i | \(0.504218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | −22.0454 | − | 12.7279i | −0.980038 | − | 0.565825i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.86396 | − | 6.69258i | −0.171436 | − | 0.296935i | ||||
\(509\) | −9.20361 | −0.407943 | −0.203971 | − | 0.978977i | \(-0.565385\pi\) | ||||
−0.203971 | + | 0.978977i | \(0.565385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.4558 | − | 5.49333i | −0.595251 | − | 0.243010i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.7279 | − | 12.5446i | −0.958378 | − | 0.553320i | ||||
\(515\) | − | 27.2132i | − | 1.19916i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −47.1838 | − | 27.2416i | −2.07514 | − | 1.19808i | ||||
\(518\) | 1.88064 | + | 13.7426i | 0.0826305 | + | 0.603817i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.878680 | + | 1.52192i | −0.0385327 | + | 0.0667405i | ||||
\(521\) | 14.9941 | − | 25.9706i | 0.656904 | − | 1.13779i | −0.324509 | − | 0.945883i | \(-0.605199\pi\) |
0.981413 | − | 0.191908i | \(-0.0614676\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.7426 | − | 13.7078i | 1.03819 | − | 0.599401i | 0.118872 | − | 0.992910i | \(-0.462072\pi\) |
0.919321 | + | 0.393508i | \(0.128739\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.36396 | − | 5.82655i | 0.146676 | − | 0.254050i | ||||
\(527\) | − | 22.2426i | − | 0.968905i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | −17.7408 | − | 30.7279i | −0.770610 | − | 1.33474i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.0000 | − | 4.89898i | −0.520266 | − | 0.212398i | ||||
\(533\) | −1.52192 | + | 0.878680i | −0.0659216 | + | 0.0380598i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.27208 | − | 3.04384i | 0.227932 | − | 0.131596i | ||||
\(536\) | −11.6786 | + | 6.74264i | −0.504439 | + | 0.291238i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.48528 | − | 4.89898i | 0.365826 | − | 0.211210i | ||||
\(539\) | −7.97887 | − | 28.6066i | −0.343674 | − | 1.23217i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.72792 | + | 4.72490i | 0.117283 | + | 0.203139i | 0.918690 | − | 0.394980i | \(-0.129248\pi\) |
−0.801407 | + | 0.598119i | \(0.795915\pi\) | |||||||
\(542\) | 18.8785 | 0.810900 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 2.44949i | − | 0.105021i | ||||||
\(545\) | −21.7122 | + | 37.6066i | −0.930048 | + | 1.61089i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.9853 | − | 34.6155i | −0.854509 | − | 1.48005i | −0.877100 | − | 0.480308i | \(-0.840525\pi\) |
0.0225909 | − | 0.999745i | \(-0.492808\pi\) | |||||||
\(548\) | −5.19615 | + | 3.00000i | −0.221969 | + | 0.128154i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.12132 | + | 3.67423i | −0.0904534 | + | 0.156670i | ||||
\(551\) | 4.30463 | − | 7.45584i | 0.183384 | − | 0.317630i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.757359 | + | 1.85514i | −0.0322062 | + | 0.0788887i | ||||
\(554\) | −20.5490 | − | 11.8640i | −0.873043 | − | 0.504051i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 8.06591i | − | 0.342071i | ||||||
\(557\) | −18.3712 | − | 10.6066i | −0.778412 | − | 0.449416i | 0.0574555 | − | 0.998348i | \(-0.481701\pi\) |
−0.835867 | + | 0.548932i | \(0.815035\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.02207i | − | 0.212411i | ||||||
\(560\) | 2.44949 | − | 6.00000i | 0.103510 | − | 0.253546i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.7574 | 0.580319 | ||||||||
\(563\) | 22.9369 | + | 39.7279i | 0.966676 | + | 1.67433i | 0.705043 | + | 0.709165i | \(0.250928\pi\) |
0.261634 | + | 0.965167i | \(0.415739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.7279 | + | 12.5446i | 0.914101 | + | 0.527756i | ||||
\(566\) | 6.03668 | 0.253741 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.7279 | −0.534052 | ||||||||
\(569\) | 8.87039 | + | 5.12132i | 0.371866 | + | 0.214697i | 0.674273 | − | 0.738482i | \(-0.264457\pi\) |
−0.302407 | + | 0.953179i | \(0.597790\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0000 | + | 19.0526i | 0.460336 | + | 0.797325i | 0.998978 | − | 0.0452101i | \(-0.0143957\pi\) |
−0.538642 | + | 0.842535i | \(0.681062\pi\) | |||||||
\(572\) | 3.04384 | 0.127269 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.12132 | − | 3.97141i | 0.213760 | − | 0.165763i | ||||
\(575\) | 6.00000i | 0.250217i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.7426 | + | 13.7078i | 0.988419 | + | 0.570664i | 0.904801 | − | 0.425834i | \(-0.140019\pi\) |
0.0836177 | + | 0.996498i | \(0.473353\pi\) | |||||||
\(578\) | − | 11.0000i | − | 0.457540i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.72792 | + | 2.15232i | 0.154794 | + | 0.0893701i | ||||
\(581\) | 24.7921 | + | 31.9706i | 1.02855 | + | 1.32636i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.7279 | + | 53.2223i | −1.27262 | + | 2.20424i | ||||
\(584\) | −2.74666 | + | 4.75736i | −0.113658 | + | 0.196861i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.1213 | − | 6.42090i | 0.459418 | − | 0.265245i | ||||
\(587\) | −16.2189 | − | 28.0919i | −0.669424 | − | 1.15948i | −0.978065 | − | 0.208298i | \(-0.933208\pi\) |
0.308642 | − | 0.951178i | \(-0.400126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.2426 | + | 38.5254i | −0.916492 | + | 1.58741i | ||||
\(590\) | − | 6.00000i | − | 0.247016i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.24264 | 0.215471 | ||||||||
\(593\) | 0.927572 | + | 1.60660i | 0.0380908 | + | 0.0659752i | 0.884442 | − | 0.466650i | \(-0.154539\pi\) |
−0.846352 | + | 0.532625i | \(0.821206\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | + | 14.6969i | −0.245976 | + | 0.602516i | ||||
\(596\) | −14.0665 | + | 8.12132i | −0.576188 | + | 0.332662i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.72792 | − | 2.15232i | 0.152446 | − | 0.0880148i | ||||
\(599\) | −3.04384 | + | 1.75736i | −0.124368 | + | 0.0718038i | −0.560893 | − | 0.827888i | \(-0.689542\pi\) |
0.436526 | + | 0.899692i | \(0.356209\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.9558 | − | 20.7591i | 1.46667 | − | 0.846782i | 0.467365 | − | 0.884065i | \(-0.345204\pi\) |
0.999305 | + | 0.0372826i | \(0.0118702\pi\) | |||||||
\(602\) | 2.51104 | + | 18.3492i | 0.102342 | + | 0.747859i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.37868 | + | 7.58410i | 0.178166 | + | 0.308592i | ||||
\(605\) | 17.1464 | 0.697101 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.0759i | 1.46428i | 0.681157 | + | 0.732138i | \(0.261477\pi\) | ||||
−0.681157 | + | 0.732138i | \(0.738523\pi\) | |||||||
\(608\) | −2.44949 | + | 4.24264i | −0.0993399 | + | 0.172062i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.12132 | − | 8.87039i | −0.207356 | − | 0.359151i | ||||
\(611\) | 7.97887 | − | 4.60660i | 0.322790 | − | 0.186363i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.1066 | − | 24.4334i | 0.569760 | − | 0.986854i | −0.426829 | − | 0.904332i | \(-0.640369\pi\) |
0.996589 | − | 0.0825214i | \(-0.0262973\pi\) | |||||||
\(614\) | 13.4106 | − | 23.2279i | 0.541210 | − | 0.937403i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.1213 | + | 1.52192i | −0.448091 | + | 0.0613198i | ||||
\(617\) | −3.67423 | − | 2.12132i | −0.147919 | − | 0.0854011i | 0.424214 | − | 0.905562i | \(-0.360551\pi\) |
−0.572133 | + | 0.820161i | \(0.693884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.7187i | 0.511208i | 0.966782 | + | 0.255604i | \(0.0822743\pi\) | ||||
−0.966782 | + | 0.255604i | \(0.917726\pi\) | |||||||
\(620\) | −19.2627 | − | 11.1213i | −0.773608 | − | 0.446643i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 17.1464i | − | 0.687509i | ||||||
\(623\) | 4.93503 | + | 6.36396i | 0.197718 | + | 0.254967i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | −10.0951 | − | 17.4853i | −0.403483 | − | 0.698852i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.00000 | + | 5.19615i | 0.359139 | + | 0.207349i | ||||
\(629\) | −12.8418 | −0.512036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.7574 | −0.587481 | −0.293741 | − | 0.955885i | \(-0.594900\pi\) | ||||
−0.293741 | + | 0.955885i | \(0.594900\pi\) | |||||||
\(632\) | 0.655892 | + | 0.378680i | 0.0260900 | + | 0.0150631i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.1213 | − | 19.2627i | −0.441684 | − | 0.765019i | ||||
\(635\) | 18.9295 | 0.751193 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.86396 | + | 1.25024i | 0.192717 | + | 0.0495362i | ||||
\(638\) | − | 7.45584i | − | 0.295180i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.12132 | − | 1.22474i | −0.0838525 | − | 0.0484123i | ||||
\(641\) | − | 33.2132i | − | 1.31184i | −0.754829 | − | 0.655921i | \(-0.772280\pi\) | ||
0.754829 | − | 0.655921i | \(-0.227720\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.50000 | + | 0.866025i | 0.0591542 | + | 0.0341527i | 0.529285 | − | 0.848444i | \(-0.322460\pi\) |
−0.470131 | + | 0.882597i | \(0.655793\pi\) | |||||||
\(644\) | −12.5446 | + | 9.72792i | −0.494327 | + | 0.383334i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00000 | − | 10.3923i | 0.236067 | − | 0.408880i | ||||
\(647\) | −10.3923 | + | 18.0000i | −0.408564 | + | 0.707653i | −0.994729 | − | 0.102538i | \(-0.967304\pi\) |
0.586165 | + | 0.810191i | \(0.300637\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | + | 5.19615i | −0.353281 | + | 0.203967i | ||||
\(650\) | −0.358719 | − | 0.621320i | −0.0140701 | − | 0.0243702i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.74264 | + | 8.21449i | −0.185736 | + | 0.321704i | ||||
\(653\) | − | 2.48528i | − | 0.0972566i | −0.998817 | − | 0.0486283i | \(-0.984515\pi\) | ||
0.998817 | − | 0.0486283i | \(-0.0154850\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.22474 | − | 2.12132i | −0.0478183 | − | 0.0828236i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −26.8492 | + | 20.8207i | −1.04669 | + | 0.811674i | ||||
\(659\) | 19.2627 | − | 11.1213i | 0.750368 | − | 0.433225i | −0.0754589 | − | 0.997149i | \(-0.524042\pi\) |
0.825827 | + | 0.563924i | \(0.190709\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.24264 | − | 2.44949i | 0.165020 | − | 0.0952741i | −0.415216 | − | 0.909723i | \(-0.636294\pi\) |
0.580235 | + | 0.814449i | \(0.302961\pi\) | |||||||
\(662\) | 8.66025 | − | 5.00000i | 0.336590 | − | 0.194331i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.2426 | − | 7.64564i | 0.513914 | − | 0.296708i | ||||
\(665\) | 25.0892 | − | 19.4558i | 0.972919 | − | 0.754465i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.27208 | − | 9.13151i | −0.204136 | − | 0.353573i | ||||
\(668\) | −0.594346 | −0.0229959 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 33.0321i | − | 1.27614i | ||||||
\(671\) | −8.87039 | + | 15.3640i | −0.342437 | + | 0.593119i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.7279 | + | 39.3659i | 0.876097 | + | 1.51744i | 0.855590 | + | 0.517655i | \(0.173195\pi\) |
0.0205075 | + | 0.999790i | \(0.493472\pi\) | |||||||
\(674\) | −18.5813 | + | 10.7279i | −0.715725 | + | 0.413224i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.24264 | − | 10.8126i | 0.240102 | − | 0.415868i | ||||
\(677\) | 7.34847 | − | 12.7279i | 0.282425 | − | 0.489174i | −0.689557 | − | 0.724232i | \(-0.742195\pi\) |
0.971981 | + | 0.235058i | \(0.0755280\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.62132 | − | 5.13461i | 0.254103 | − | 0.197048i | ||||
\(680\) | 5.19615 | + | 3.00000i | 0.199263 | + | 0.115045i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 38.5254i | 1.47521i | ||||||||
\(683\) | 8.87039 | + | 5.12132i | 0.339416 | + | 0.195962i | 0.660014 | − | 0.751254i | \(-0.270550\pi\) |
−0.320598 | + | 0.947215i | \(0.603884\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 14.6969i | − | 0.561541i | ||||||
\(686\) | −18.3967 | − | 2.13604i | −0.702388 | − | 0.0815543i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.00000 | 0.266872 | ||||||||
\(689\) | −5.19615 | − | 9.00000i | −0.197958 | − | 0.342873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.22792 | − | 1.28629i | −0.0847541 | − | 0.0489328i | 0.457024 | − | 0.889454i | \(-0.348915\pi\) |
−0.541778 | + | 0.840522i | \(0.682249\pi\) | |||||||
\(692\) | 20.7846 | 0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.97056 | −0.188680 | ||||||||
\(695\) | 17.1104 | + | 9.87868i | 0.649034 | + | 0.374720i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00000 | + | 5.19615i | 0.113633 | + | 0.196818i | ||||
\(698\) | 0.123093 | 0.00465914 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.62132 | + | 2.09077i | 0.0612801 | + | 0.0790237i | ||||
\(701\) | 20.4853i | 0.773718i | 0.922139 | + | 0.386859i | \(0.126440\pi\) | ||||
−0.922139 | + | 0.386859i | \(0.873560\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.2426 | + | 12.8418i | 0.838897 | + | 0.484337i | ||||
\(704\) | 4.24264i | 0.159901i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.51472 | − | 5.49333i | −0.358091 | − | 0.206744i | ||||
\(707\) | −19.2627 | + | 2.63604i | −0.724448 | + | 0.0991384i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.10660 | + | 14.0410i | −0.304450 | + | 0.527323i | −0.977139 | − | 0.212603i | \(-0.931806\pi\) |
0.672689 | + | 0.739925i | \(0.265139\pi\) | |||||||
\(710\) | 15.5885 | − | 27.0000i | 0.585024 | − | 1.01329i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.63604 | − | 1.52192i | 0.0987897 | − | 0.0570363i | ||||
\(713\) | 27.2416 | + | 47.1838i | 1.02020 | + | 1.76705i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.72792 | + | 6.45695i | −0.139416 | + | 0.241476i | ||||
\(716\) | 6.72792i | 0.251434i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.4853 | 0.540586 | ||||||||
\(719\) | −26.3140 | − | 45.5772i | −0.981346 | − | 1.69974i | −0.657166 | − | 0.753746i | \(-0.728245\pi\) |
−0.324181 | − | 0.945995i | \(-0.605089\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.98528 | + | 29.1222i | 0.148420 | + | 1.08457i | ||||
\(722\) | −4.33013 | + | 2.50000i | −0.161151 | + | 0.0930404i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.48528 | − | 4.89898i | 0.315353 | − | 0.182069i | ||||
\(725\) | −1.52192 | + | 0.878680i | −0.0565226 | + | 0.0326333i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.3198 | + | 14.0410i | −0.901972 | + | 0.520754i | −0.877839 | − | 0.478955i | \(-0.841016\pi\) |
−0.0241323 | + | 0.999709i | \(0.507682\pi\) | |||||||
\(728\) | 0.717439 | − | 1.75736i | 0.0265901 | − | 0.0651321i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.72792 | − | 11.6531i | −0.249012 | − | 0.431301i | ||||
\(731\) | −17.1464 | −0.634184 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.31178i | 0.0484519i | 0.999707 | + | 0.0242259i | \(0.00771211\pi\) | ||||
−0.999707 | + | 0.0242259i | \(0.992288\pi\) | |||||||
\(734\) | 14.9941 | − | 25.9706i | 0.553443 | − | 0.958591i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | −49.5481 | + | 28.6066i | −1.82513 | + | 1.05374i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.22792 | − | 7.32298i | 0.155527 | − | 0.269380i | −0.777724 | − | 0.628606i | \(-0.783626\pi\) |
0.933251 | + | 0.359226i | \(0.116959\pi\) | |||||||
\(740\) | −6.42090 | + | 11.1213i | −0.236037 | + | 0.408828i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 23.4853 | + | 30.2854i | 0.862172 | + | 1.11181i | ||||
\(743\) | −16.2189 | − | 9.36396i | −0.595012 | − | 0.343530i | 0.172065 | − | 0.985086i | \(-0.444956\pi\) |
−0.767077 | + | 0.641555i | \(0.778290\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 39.7862i | − | 1.45765i | ||||||
\(746\) | 19.0526 | + | 11.0000i | 0.697564 | + | 0.402739i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 10.3923i | − | 0.379980i | ||||||
\(749\) | −5.19615 | + | 4.02944i | −0.189863 | + | 0.147232i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 53.4558 | 1.95063 | 0.975316 | − | 0.220815i | \(-0.0708717\pi\) | ||||
0.975316 | + | 0.220815i | \(0.0708717\pi\) | |||||||
\(752\) | 6.42090 | + | 11.1213i | 0.234146 | + | 0.405553i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.09188 | + | 0.630399i | 0.0397640 | + | 0.0229578i | ||||
\(755\) | −21.4511 | −0.780684 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.7574 | 1.19059 | 0.595293 | − | 0.803509i | \(-0.297036\pi\) | ||||
0.595293 | + | 0.803509i | \(0.297036\pi\) | |||||||
\(758\) | 6.48244 | + | 3.74264i | 0.235453 | + | 0.135939i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.00000 | − | 10.3923i | −0.217643 | − | 0.376969i | ||||
\(761\) | 24.4949 | 0.887939 | 0.443970 | − | 0.896042i | \(-0.353570\pi\) | ||||
0.443970 | + | 0.896042i | \(0.353570\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.7279 | − | 43.4244i | 0.641794 | − | 1.57207i | ||||
\(764\) | − | 21.2132i | − | 0.767467i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.75736 | − | 2.74666i | −0.171890 | − | 0.0992410i | ||||
\(767\) | − | 1.75736i | − | 0.0634546i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.9706 | + | 20.1903i | 1.26107 | + | 0.728080i | 0.973282 | − | 0.229614i | \(-0.0737465\pi\) |
0.287789 | + | 0.957694i | \(0.407080\pi\) | |||||||
\(770\) | 10.3923 | − | 25.4558i | 0.374513 | − | 0.917365i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.742641 | + | 1.28629i | −0.0267282 | + | 0.0462946i | ||||
\(773\) | 4.89898 | − | 8.48528i | 0.176204 | − | 0.305194i | −0.764373 | − | 0.644774i | \(-0.776951\pi\) |
0.940577 | + | 0.339580i | \(0.110285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.86396 | − | 4.54026i | 0.282482 | − | 0.163091i | ||||
\(776\) | −1.58346 | − | 2.74264i | −0.0568431 | − | 0.0984551i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.75736 | + | 13.4361i | −0.278115 | + | 0.481709i | ||||
\(779\) | − | 12.0000i | − | 0.429945i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.0000 | −1.93227 | ||||||||
\(782\) | −7.34847 | − | 12.7279i | −0.262781 | − | 0.455150i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.74264 | + | 6.77962i | −0.0622372 | + | 0.242129i | ||||
\(785\) | −22.0454 | + | 12.7279i | −0.786834 | + | 0.454279i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.4706 | − | 14.1281i | 0.872281 | − | 0.503612i | 0.00417567 | − | 0.999991i | \(-0.498671\pi\) |
0.868106 | + | 0.496379i | \(0.165338\pi\) | |||||||
\(788\) | −14.6969 | + | 8.48528i | −0.523557 | + | 0.302276i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.60660 | + | 0.927572i | −0.0571603 | + | 0.0330015i | ||||
\(791\) | −25.0892 | − | 10.2426i | −0.892071 | − | 0.364186i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.50000 | − | 2.59808i | −0.0532666 | − | 0.0922604i | ||||
\(794\) | 15.1682 | 0.538299 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 20.9077i | − | 0.741054i | ||||||
\(797\) | 8.87039 | − | 15.3640i | 0.314205 | − | 0.544219i | −0.665063 | − | 0.746787i | \(-0.731595\pi\) |
0.979268 | + | 0.202568i | \(0.0649287\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.7279 | − | 27.2416i | −0.556414 | − | 0.963737i | ||||
\(800\) | 0.866025 | − | 0.500000i | 0.0306186 | − | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.87868 | + | 17.1104i | −0.348828 | + | 0.604188i | ||||
\(803\) | −11.6531 | + | 20.1838i | −0.411229 | + | 0.712270i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.27208 | − | 38.5254i | −0.185816 | − | 1.35784i | ||||
\(806\) | −5.64191 | − | 3.25736i | −0.198728 | − | 0.114736i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.34847i | 0.258518i | ||||||||
\(809\) | 12.5446 | + | 7.24264i | 0.441045 | + | 0.254638i | 0.704041 | − | 0.710159i | \(-0.251377\pi\) |
−0.262996 | + | 0.964797i | \(0.584710\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | −4.30463 | − | 1.75736i | −0.151063 | − | 0.0616712i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.2426 | 0.779604 | ||||||||
\(815\) | −11.6170 | − | 20.1213i | −0.406928 | − | 0.704819i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.6985 | + | 17.1464i | 1.03902 | + | 0.599878i | ||||
\(818\) | −3.76127 | −0.131510 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | −19.8931 | − | 11.4853i | −0.694274 | − | 0.400839i | 0.110937 | − | 0.993827i | \(-0.464615\pi\) |
−0.805211 | + | 0.592988i | \(0.797948\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.37868 | + | 2.38794i | 0.0480578 | + | 0.0832385i | 0.889054 | − | 0.457803i | \(-0.151364\pi\) |
−0.840996 | + | 0.541042i | \(0.818030\pi\) | |||||||
\(824\) | 11.1097 | 0.387026 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.878680 | + | 6.42090i | 0.0305732 | + | 0.223412i | ||||
\(827\) | − | 3.51472i | − | 0.122219i | −0.998131 | − | 0.0611094i | \(-0.980536\pi\) | ||
0.998131 | − | 0.0611094i | \(-0.0194638\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.48528 | + | 4.89898i | 0.294706 | + | 0.170149i | 0.640062 | − | 0.768323i | \(-0.278909\pi\) |
−0.345356 | + | 0.938472i | \(0.612242\pi\) | |||||||
\(830\) | 37.4558i | 1.30011i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.621320 | − | 0.358719i | −0.0215404 | − | 0.0124364i | ||||
\(833\) | 4.26858 | − | 16.6066i | 0.147898 | − | 0.575385i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.727922 | − | 1.26080i | 0.0251908 | − | 0.0436317i | ||||
\(836\) | −10.3923 | + | 18.0000i | −0.359425 | + | 0.622543i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.87868 | − | 3.97141i | 0.237620 | − | 0.137190i | ||||
\(839\) | −7.64564 | − | 13.2426i | −0.263957 | − | 0.457187i | 0.703333 | − | 0.710861i | \(-0.251694\pi\) |
−0.967290 | + | 0.253674i | \(0.918361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.9558 | + | 22.4402i | −0.446753 | + | 0.773799i | ||||
\(842\) | − | 23.4558i | − | 0.808342i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.48528 | −0.119968 | ||||||||
\(845\) | 15.2913 | + | 26.4853i | 0.526036 | + | 0.911121i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.3492 | + | 2.51104i | −0.630487 | + | 0.0862802i | ||||
\(848\) | 12.5446 | − | 7.24264i | 0.430784 | − | 0.248713i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.12132 | + | 1.22474i | −0.0727607 | + | 0.0420084i | ||||
\(851\) | 27.2416 | − | 15.7279i | 0.933829 | − | 0.539146i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.5147 | − | 15.8856i | 0.942086 | − | 0.543914i | 0.0514724 | − | 0.998674i | \(-0.483609\pi\) |
0.890614 | + | 0.454761i | \(0.150275\pi\) | |||||||
\(854\) | 6.77962 | + | 8.74264i | 0.231994 | + | 0.299167i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.24264 | + | 2.15232i | 0.0424726 | + | 0.0735647i | ||||
\(857\) | −27.5387 | −0.940705 | −0.470353 | − | 0.882479i | \(-0.655873\pi\) | ||||
−0.470353 | + | 0.882479i | \(0.655873\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.2562i | 0.964088i | 0.876147 | + | 0.482044i | \(0.160105\pi\) | ||||
−0.876147 | + | 0.482044i | \(0.839895\pi\) | |||||||
\(860\) | −8.57321 | + | 14.8492i | −0.292344 | + | 0.506355i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.878680 | − | 1.52192i | −0.0299279 | − | 0.0518367i | ||||
\(863\) | 32.4377 | − | 18.7279i | 1.10419 | − | 0.637506i | 0.166874 | − | 0.985978i | \(-0.446633\pi\) |
0.937319 | + | 0.348472i | \(0.113300\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.4558 | + | 44.0908i | −0.865525 | + | 1.49913i | ||||
\(866\) | 1.28629 | − | 2.22792i | 0.0437100 | − | 0.0757079i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 22.2426 | + | 9.08052i | 0.754964 | + | 0.308213i | ||||
\(869\) | 2.78272 | + | 1.60660i | 0.0943972 | + | 0.0545002i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 9.67487i | − | 0.327820i | ||||||
\(872\) | −15.3528 | − | 8.86396i | −0.519912 | − | 0.300172i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.3939i | 0.994263i | ||||||||
\(875\) | 25.6836 | − | 3.51472i | 0.868264 | − | 0.118819i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.2132 | −1.56051 | −0.780254 | − | 0.625462i | \(-0.784910\pi\) | ||||
−0.780254 | + | 0.625462i | \(0.784910\pi\) | |||||||
\(878\) | 2.15232 | + | 3.72792i | 0.0726372 | + | 0.125811i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.00000 | − | 5.19615i | −0.303390 | − | 0.175162i | ||||
\(881\) | −25.0892 | −0.845278 | −0.422639 | − | 0.906298i | \(-0.638896\pi\) | ||||
−0.422639 | + | 0.906298i | \(0.638896\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00000 | −0.0673054 | −0.0336527 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336527 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(884\) | 1.52192 | + | 0.878680i | 0.0511876 | + | 0.0295532i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.7279 | − | 22.0454i | −0.427603 | − | 0.740630i | ||||
\(887\) | 9.20361 | 0.309027 | 0.154514 | − | 0.987991i | \(-0.450619\pi\) | ||||
0.154514 | + | 0.987991i | \(0.450619\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.2574 | + | 2.77216i | −0.679410 | + | 0.0929751i | ||||
\(890\) | 7.45584i | 0.249920i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.00000 | − | 5.19615i | −0.301342 | − | 0.173980i | ||||
\(893\) | 62.9117i | 2.10526i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.2721 | − | 8.23999i | −0.477063 | − | 0.275432i | ||||
\(896\) | 2.44949 | + | 1.00000i | 0.0818317 | + | 0.0334077i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.63604 | − | 4.56575i | 0.0879658 | − | 0.152361i | ||||
\(899\) | −7.97887 | + | 13.8198i | −0.266110 | + | 0.460916i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.7279 | + | 17.7408i | −1.02370 | + | 0.591031i | ||||
\(902\) | −5.19615 | − | 9.00000i | −0.173013 | − | 0.299667i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.12132 | + | 8.87039i | −0.170333 | + | 0.295025i | ||||
\(905\) | 24.0000i | 0.797787i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.4853 | −0.447771 | −0.223886 | − | 0.974615i | \(-0.571874\pi\) | ||||
−0.223886 | + | 0.974615i | \(0.571874\pi\) | |||||||
\(908\) | 12.5446 | + | 21.7279i | 0.416308 | + | 0.721066i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.84924 | + | 3.67423i | 0.0944515 | + | 0.121800i | ||||
\(911\) | −8.87039 | + | 5.12132i | −0.293889 | + | 0.169677i | −0.639694 | − | 0.768629i | \(-0.720939\pi\) |
0.345805 | + | 0.938306i | \(0.387606\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 56.1838 | − | 32.4377i | 1.85941 | − | 1.07353i | ||||
\(914\) | −19.9186 | + | 11.5000i | −0.658848 | + | 0.380386i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.86396 | − | 2.80821i | 0.160710 | − | 0.0927858i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.8640 | − | 22.2810i | −0.424343 | − | 0.734983i | 0.572016 | − | 0.820243i | \(-0.306162\pi\) |
−0.996359 | + | 0.0852590i | \(0.972828\pi\) | |||||||
\(920\) | −14.6969 | −0.484544 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 21.4511i | 0.706453i | ||||||||
\(923\) | 4.56575 | − | 7.90812i | 0.150284 | − | 0.260299i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.62132 | − | 4.54026i | −0.0861885 | − | 0.149283i | ||||
\(926\) | −19.0526 | + | 11.0000i | −0.626106 | + | 0.361482i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.878680 | + | 1.52192i | −0.0288441 | + | 0.0499594i | ||||
\(929\) | −14.3637 | + | 24.8787i | −0.471258 | + | 0.816243i | −0.999459 | − | 0.0328762i | \(-0.989533\pi\) |
0.528201 | + | 0.849119i | \(0.322867\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.0000 | + | 24.4949i | −0.786568 | + | 0.802788i | ||||
\(932\) | 17.7408 | + | 10.2426i | 0.581118 | + | 0.335509i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.7408i | 0.580496i | ||||||||
\(935\) | 22.0454 | + | 12.7279i | 0.720962 | + | 0.416248i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 33.5033i | − | 1.09451i | −0.836967 | − | 0.547253i | \(-0.815674\pi\) | ||
0.836967 | − | 0.547253i | \(-0.184326\pi\) | |||||||
\(938\) | 4.83743 | + | 35.3492i | 0.157948 | + | 1.15419i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −31.4558 | −1.02598 | ||||||||
\(941\) | −21.1178 | − | 36.5772i | −0.688422 | − | 1.19238i | −0.972348 | − | 0.233535i | \(-0.924971\pi\) |
0.283927 | − | 0.958846i | \(-0.408363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.7279 | − | 7.34847i | −0.414478 | − | 0.239299i | ||||
\(944\) | 2.44949 | 0.0797241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.6985 | 0.965581 | ||||||||
\(947\) | 14.0665 | + | 8.12132i | 0.457101 | + | 0.263907i | 0.710825 | − | 0.703369i | \(-0.248322\pi\) |
−0.253723 | + | 0.967277i | \(0.581655\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.97056 | − | 3.41311i | −0.0639672 | − | 0.110794i | ||||
\(950\) | 4.89898 | 0.158944 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.00000 | − | 2.44949i | −0.194461 | − | 0.0793884i | ||||
\(953\) | − | 1.02944i | − | 0.0333467i | −0.999861 | − | 0.0166734i | \(-0.994692\pi\) | ||
0.999861 | − | 0.0166734i | \(-0.00530755\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.0000 | + | 25.9808i | 1.45617 | + | 0.840718i | ||||
\(956\) | − | 16.2426i | − | 0.525325i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.12132 | − | 1.22474i | −0.0685367 | − | 0.0395697i | ||||
\(959\) | 2.15232 | + | 15.7279i | 0.0695019 | + | 0.507881i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.7279 | − | 44.5621i | 0.829933 | − | 1.43749i | ||||
\(962\) | −1.88064 | + | 3.25736i | −0.0606342 | + | 0.105021i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.985281 | + | 0.568852i | −0.0317338 | + | 0.0183215i | ||||
\(965\) | −1.81909 | − | 3.15076i | −0.0585586 | − | 0.101426i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.3492 | − | 36.9780i | 0.686545 | − | 1.18913i | −0.286403 | − | 0.958109i | \(-0.592460\pi\) |
0.972948 | − | 0.231022i | \(-0.0742070\pi\) | |||||||
\(968\) | 7.00000i | 0.224989i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.75736 | 0.249074 | ||||||||
\(971\) | 20.1903 | + | 34.9706i | 0.647936 | + | 1.12226i | 0.983615 | + | 0.180282i | \(0.0577011\pi\) |
−0.335679 | + | 0.941977i | \(0.608966\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.7574 | − | 8.06591i | −0.633392 | − | 0.258581i | ||||
\(974\) | 19.0526 | − | 11.0000i | 0.610483 | − | 0.352463i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.62132 | − | 2.09077i | 0.115916 | − | 0.0669239i | ||||
\(977\) | 5.19615 | − | 3.00000i | 0.166240 | − | 0.0959785i | −0.414572 | − | 0.910017i | \(-0.636069\pi\) |
0.580812 | + | 0.814038i | \(0.302735\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.1838 | − | 6.45695i | 0.357435 | − | 0.206365i | ||||
\(980\) | −12.2474 | − | 12.0000i | −0.391230 | − | 0.383326i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.4853 | + | 30.2854i | 0.557978 | + | 0.966446i | ||||
\(983\) | 23.2341 | 0.741053 | 0.370526 | − | 0.928822i | \(-0.379177\pi\) | ||||
0.370526 | + | 0.928822i | \(0.379177\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 41.5692i | − | 1.32451i | ||||||
\(986\) | 2.15232 | − | 3.72792i | 0.0685437 | − | 0.118721i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.75736 | − | 3.04384i | −0.0559090 | − | 0.0968373i | ||||
\(989\) | 36.3731 | − | 21.0000i | 1.15660 | − | 0.667761i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.1066 | − | 17.5051i | 0.321047 | − | 0.556069i | −0.659658 | − | 0.751566i | \(-0.729299\pi\) |
0.980704 | + | 0.195497i | \(0.0626320\pi\) | |||||||
\(992\) | 4.54026 | − | 7.86396i | 0.144153 | − | 0.249681i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.7279 | + | 31.1769i | −0.403705 | + | 0.988872i | ||||
\(995\) | 44.3519 | + | 25.6066i | 1.40605 | + | 0.811784i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 19.4728i | − | 0.616711i | −0.951271 | − | 0.308355i | \(-0.900221\pi\) | ||
0.951271 | − | 0.308355i | \(-0.0997786\pi\) | |||||||
\(998\) | 21.1794 | + | 12.2279i | 0.670422 | + | 0.387068i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1134.2.t.f.1025.1 | 8 | ||
3.2 | odd | 2 | inner | 1134.2.t.f.1025.4 | 8 | ||
7.5 | odd | 6 | 1134.2.l.e.215.3 | 8 | |||
9.2 | odd | 6 | 1134.2.l.e.269.1 | 8 | |||
9.4 | even | 3 | 378.2.k.d.269.4 | yes | 8 | ||
9.5 | odd | 6 | 378.2.k.d.269.1 | yes | 8 | ||
9.7 | even | 3 | 1134.2.l.e.269.4 | 8 | |||
21.5 | even | 6 | 1134.2.l.e.215.2 | 8 | |||
63.4 | even | 3 | 2646.2.d.d.2645.5 | 8 | |||
63.5 | even | 6 | 378.2.k.d.215.4 | yes | 8 | ||
63.31 | odd | 6 | 2646.2.d.d.2645.7 | 8 | |||
63.32 | odd | 6 | 2646.2.d.d.2645.4 | 8 | |||
63.40 | odd | 6 | 378.2.k.d.215.1 | ✓ | 8 | ||
63.47 | even | 6 | inner | 1134.2.t.f.593.1 | 8 | ||
63.59 | even | 6 | 2646.2.d.d.2645.2 | 8 | |||
63.61 | odd | 6 | inner | 1134.2.t.f.593.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.k.d.215.1 | ✓ | 8 | 63.40 | odd | 6 | ||
378.2.k.d.215.4 | yes | 8 | 63.5 | even | 6 | ||
378.2.k.d.269.1 | yes | 8 | 9.5 | odd | 6 | ||
378.2.k.d.269.4 | yes | 8 | 9.4 | even | 3 | ||
1134.2.l.e.215.2 | 8 | 21.5 | even | 6 | |||
1134.2.l.e.215.3 | 8 | 7.5 | odd | 6 | |||
1134.2.l.e.269.1 | 8 | 9.2 | odd | 6 | |||
1134.2.l.e.269.4 | 8 | 9.7 | even | 3 | |||
1134.2.t.f.593.1 | 8 | 63.47 | even | 6 | inner | ||
1134.2.t.f.593.4 | 8 | 63.61 | odd | 6 | inner | ||
1134.2.t.f.1025.1 | 8 | 1.1 | even | 1 | trivial | ||
1134.2.t.f.1025.4 | 8 | 3.2 | odd | 2 | inner | ||
2646.2.d.d.2645.2 | 8 | 63.59 | even | 6 | |||
2646.2.d.d.2645.4 | 8 | 63.32 | odd | 6 | |||
2646.2.d.d.2645.5 | 8 | 63.4 | even | 3 | |||
2646.2.d.d.2645.7 | 8 | 63.31 | odd | 6 |