Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,2,Mod(13,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.i (of order \(9\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.862384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 85.3 | ||
Root | \(1.16555 + 1.28120i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.85 |
Dual form | 108.2.i.a.61.3 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.53346 | + | 0.805294i | 0.885344 | + | 0.464937i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.583982 | − | 3.31193i | 0.261165 | − | 1.48114i | −0.518574 | − | 0.855033i | \(-0.673537\pi\) |
0.779738 | − | 0.626105i | \(-0.215352\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.47262 | + | 1.23568i | −0.556600 | + | 0.467043i | −0.877169 | − | 0.480183i | \(-0.840570\pi\) |
0.320569 | + | 0.947225i | \(0.396126\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.70300 | + | 2.46977i | 0.567668 | + | 0.823258i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.352079 | + | 1.99674i | 0.106156 | + | 0.602040i | 0.990752 | + | 0.135683i | \(0.0433227\pi\) |
−0.884597 | + | 0.466357i | \(0.845566\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.53134 | + | 2.01324i | −1.53412 | + | 0.558373i | −0.964626 | − | 0.263623i | \(-0.915083\pi\) |
−0.569493 | + | 0.821996i | \(0.692860\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.56259 | − | 4.60843i | 0.919856 | − | 1.18989i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.69713 | − | 2.93951i | 0.411613 | − | 0.712935i | −0.583453 | − | 0.812147i | \(-0.698299\pi\) |
0.995066 | + | 0.0992115i | \(0.0316320\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0802464 | − | 0.138991i | −0.0184098 | − | 0.0318867i | 0.856674 | − | 0.515859i | \(-0.172527\pi\) |
−0.875084 | + | 0.483972i | \(0.839194\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.25330 | + | 0.708969i | −0.709927 | + | 0.154710i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.29370 | − | 2.76375i | −0.686785 | − | 0.576281i | 0.231195 | − | 0.972907i | \(-0.425736\pi\) |
−0.917980 | + | 0.396626i | \(0.870181\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.92935 | − | 2.15811i | −1.18587 | − | 0.431622i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.622595 | + | 5.15872i | 0.119819 | + | 0.992796i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.79349 | − | 2.83660i | −1.44722 | − | 0.526743i | −0.505403 | − | 0.862883i | \(-0.668656\pi\) |
−0.941812 | + | 0.336140i | \(0.890878\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.07924 | + | 6.77928i | 1.45107 | + | 1.21760i | 0.931792 | + | 0.362992i | \(0.118245\pi\) |
0.519281 | + | 0.854603i | \(0.326200\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.06806 | + | 3.34545i | −0.185926 | + | 0.582368i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.23249 | + | 5.59884i | 0.546390 | + | 0.946376i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.17770 | − | 3.77190i | 0.358012 | − | 0.620096i | −0.629616 | − | 0.776906i | \(-0.716788\pi\) |
0.987629 | + | 0.156810i | \(0.0501212\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.1034 | − | 1.36713i | −1.61783 | − | 0.218915i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.21218 | − | 0.441196i | 0.189310 | − | 0.0689032i | −0.245626 | − | 0.969365i | \(-0.578993\pi\) |
0.434936 | + | 0.900462i | \(0.356771\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.25374 | − | 7.11032i | −0.191194 | − | 1.08431i | −0.917736 | − | 0.397192i | \(-0.869985\pi\) |
0.726542 | − | 0.687122i | \(-0.241126\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.17423 | − | 4.19792i | 1.36761 | − | 0.625789i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0743444 | − | 0.0623824i | 0.0108442 | − | 0.00909940i | −0.637349 | − | 0.770575i | \(-0.719969\pi\) |
0.648194 | + | 0.761476i | \(0.275525\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.573816 | + | 3.25427i | −0.0819738 | + | 0.464896i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.96964 | − | 3.14094i | 0.695889 | − | 0.439819i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.8006 | 1.75830 | 0.879152 | − | 0.476541i | \(-0.158110\pi\) | ||||
0.879152 | + | 0.476541i | \(0.158110\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.81866 | 0.919428 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0111262 | − | 0.277759i | −0.00147370 | − | 0.0367901i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.422649 | + | 2.39696i | −0.0550242 | + | 0.312058i | −0.999881 | − | 0.0154260i | \(-0.995090\pi\) |
0.944857 | + | 0.327484i | \(0.106201\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.41834 | − | 3.70742i | 0.565710 | − | 0.474687i | −0.314509 | − | 0.949254i | \(-0.601840\pi\) |
0.880219 | + | 0.474567i | \(0.157395\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.55973 | − | 1.53268i | −0.700460 | − | 0.193100i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.43751 | + | 19.4951i | 0.426371 | + | 2.41807i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.89658 | − | 1.41824i | 0.476043 | − | 0.173266i | −0.0928447 | − | 0.995681i | \(-0.529596\pi\) |
0.568888 | + | 0.822415i | \(0.307374\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.82514 | − | 6.89050i | −0.340107 | − | 0.829518i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.09944 | + | 5.36839i | −0.367836 | + | 0.637111i | −0.989227 | − | 0.146390i | \(-0.953235\pi\) |
0.621391 | + | 0.783501i | \(0.286568\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.12803 | + | 3.68585i | 0.249067 | + | 0.431396i | 0.963267 | − | 0.268545i | \(-0.0865428\pi\) |
−0.714200 | + | 0.699941i | \(0.753209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.35452 | − | 8.08425i | −0.849227 | − | 0.933489i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.98581 | − | 2.50539i | −0.340264 | − | 0.285516i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.80608 | + | 1.02133i | 0.315708 | + | 0.114908i | 0.495014 | − | 0.868885i | \(-0.335163\pi\) |
−0.179306 | + | 0.983793i | \(0.557385\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.19956 | + | 8.41206i | −0.355507 | + | 0.934674i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.95967 | − | 3.26105i | −0.983451 | − | 0.357947i | −0.200270 | − | 0.979741i | \(-0.564182\pi\) |
−0.783181 | + | 0.621794i | \(0.786404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.74434 | − | 7.33737i | −0.948457 | − | 0.795850i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.66672 | − | 10.6259i | −1.03638 | − | 1.13921i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.821473 | − | 1.42283i | −0.0870760 | − | 0.150820i | 0.819198 | − | 0.573511i | \(-0.194419\pi\) |
−0.906274 | + | 0.422691i | \(0.861086\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.65787 | − | 9.79971i | 0.593106 | − | 1.02729i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.92987 | + | 16.9019i | 0.718595 | + | 1.75265i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.507190 | + | 0.184602i | −0.0520366 | + | 0.0189398i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.484584 | + | 2.74821i | 0.0492021 | + | 0.279039i | 0.999476 | − | 0.0323773i | \(-0.0103078\pi\) |
−0.950274 | + | 0.311416i | \(0.899197\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.33190 | + | 4.27001i | −0.435373 | + | 0.429152i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.69442 | − | 5.61728i | 0.666120 | − | 0.558941i | −0.245794 | − | 0.969322i | \(-0.579049\pi\) |
0.911914 | + | 0.410381i | \(0.134604\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.935204 | + | 5.30381i | −0.0921484 | + | 0.522600i | 0.903436 | + | 0.428724i | \(0.141037\pi\) |
−0.995584 | + | 0.0938756i | \(0.970074\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.448187 | + | 11.1887i | 0.0437386 | + | 1.09191i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.7899 | −1.42979 | −0.714896 | − | 0.699231i | \(-0.753526\pi\) | ||||
−0.714896 | + | 0.699231i | \(0.753526\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.68614 | 0.257286 | 0.128643 | − | 0.991691i | \(-0.458938\pi\) | ||||
0.128643 | + | 0.991691i | \(0.458938\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.37691 | − | 4.03036i | 0.605269 | − | 0.382545i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.31653 | − | 13.1377i | 0.217921 | − | 1.23589i | −0.657844 | − | 0.753154i | \(-0.728531\pi\) |
0.875765 | − | 0.482738i | \(-0.160358\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.0768 | + | 9.29453i | −1.03292 | + | 0.866719i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.3922 | − | 10.2326i | −1.33055 | − | 0.946004i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.13306 | + | 6.42589i | 0.103867 | + | 0.589061i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.47361 | − | 2.35620i | 0.588510 | − | 0.214200i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.21412 | + | 0.299601i | 0.199640 | + | 0.0270141i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.20259 | + | 3.81499i | −0.197005 | + | 0.341223i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.80710 | − | 8.32614i | −0.426561 | − | 0.738826i | 0.570004 | − | 0.821642i | \(-0.306942\pi\) |
−0.996565 | + | 0.0828165i | \(0.973608\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.80334 | − | 11.9130i | 0.334865 | − | 1.04888i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.9408 | + | 11.6977i | 1.21801 | + | 1.02203i | 0.998926 | + | 0.0463275i | \(0.0147518\pi\) |
0.219085 | + | 0.975706i | \(0.429693\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.289921 | + | 0.105523i | 0.0251393 | + | 0.00914996i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 17.4489 | + | 0.950608i | 1.50176 | + | 0.0818153i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.40892 | − | 1.60472i | −0.376679 | − | 0.137100i | 0.146740 | − | 0.989175i | \(-0.453122\pi\) |
−0.523420 | + | 0.852075i | \(0.675344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.70983 | − | 7.30841i | −0.738758 | − | 0.619892i | 0.193746 | − | 0.981052i | \(-0.437936\pi\) |
−0.932504 | + | 0.361160i | \(0.882381\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.164240 | − | 0.0357918i | 0.0138315 | − | 0.00301421i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.96740 | − | 10.3358i | −0.499019 | − | 0.864326i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.9459 | + | 24.1549i | −1.15814 | + | 2.00596i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.50057 | + | 4.52821i | −0.288722 | + | 0.373481i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.18803 | + | 2.61623i | −0.588867 | + | 0.214330i | −0.619231 | − | 0.785209i | \(-0.712555\pi\) |
0.0303643 | + | 0.999539i | \(0.490333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.09815 | + | 11.8992i | 0.170745 | + | 0.968342i | 0.942941 | + | 0.332959i | \(0.108047\pi\) |
−0.772197 | + | 0.635384i | \(0.780842\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.1501 | − | 0.814477i | 0.820589 | − | 0.0658465i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.1706 | − | 22.7989i | 2.18240 | − | 1.83125i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.444027 | + | 2.51820i | −0.0354372 | + | 0.200974i | −0.997386 | − | 0.0722546i | \(-0.976981\pi\) |
0.961949 | + | 0.273229i | \(0.0880917\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.6293 | + | 10.3083i | 1.55670 | + | 0.817500i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.26549 | 0.651412 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.1557 | −1.50039 | −0.750195 | − | 0.661217i | \(-0.770040\pi\) | ||||
−0.750195 | + | 0.661217i | \(0.770040\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.4561 | + | 5.49103i | 0.814010 | + | 0.427476i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.46665 | + | 19.6603i | −0.268257 | + | 1.52136i | 0.491339 | + | 0.870969i | \(0.336508\pi\) |
−0.759596 | + | 0.650395i | \(0.774603\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.5840 | − | 13.9156i | 1.27569 | − | 1.07043i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.206616 | − | 0.434892i | 0.0158003 | − | 0.0332570i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.11783 | − | 12.0108i | −0.161016 | − | 0.913167i | −0.953078 | − | 0.302726i | \(-0.902103\pi\) |
0.792062 | − | 0.610441i | \(-0.209008\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.3984 | − | 4.14869i | 0.861641 | − | 0.313612i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.57837 | + | 3.33529i | −0.193802 | + | 0.250696i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.8419 | − | 18.7786i | 0.810358 | − | 1.40358i | −0.102255 | − | 0.994758i | \(-0.532606\pi\) |
0.912613 | − | 0.408824i | \(-0.134061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.99749 | + | 5.19181i | 0.222802 | + | 0.385904i | 0.955658 | − | 0.294480i | \(-0.0951464\pi\) |
−0.732856 | + | 0.680384i | \(0.761813\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.76091 | − | 2.12713i | 0.721547 | − | 0.157242i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.2205 | − | 9.41512i | −0.824947 | − | 0.692213i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.46696 | + | 2.35378i | 0.472911 | + | 0.172125i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.29137 | − | 6.82753i | −0.530369 | − | 0.496629i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.9956 | − | 6.54987i | −1.30212 | − | 0.473932i | −0.404432 | − | 0.914568i | \(-0.632531\pi\) |
−0.897686 | + | 0.440636i | \(0.854753\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.345033 | − | 0.289517i | −0.0248360 | − | 0.0208399i | 0.630285 | − | 0.776364i | \(-0.282938\pi\) |
−0.655121 | + | 0.755524i | \(0.727382\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.4280 | + | 32.6632i | −0.746764 | + | 2.33906i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.79534 | − | 3.10963i | −0.127913 | − | 0.221552i | 0.794955 | − | 0.606669i | \(-0.207494\pi\) |
−0.922868 | + | 0.385117i | \(0.874161\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.63803 | + | 6.30125i | −0.257893 | + | 0.446684i | −0.965677 | − | 0.259745i | \(-0.916362\pi\) |
0.707784 | + | 0.706429i | \(0.249695\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.11736 | + | 0.963079i | 0.502020 | + | 0.0679303i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.9820 | − | 5.45301i | 1.05153 | − | 0.382726i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.753319 | − | 4.27229i | −0.0526141 | − | 0.298389i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.21664 | − | 12.8414i | 0.0845621 | − | 0.892537i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.249275 | − | 0.209167i | 0.0172427 | − | 0.0144684i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.12702 | − | 6.39162i | 0.0775870 | − | 0.440017i | −0.921124 | − | 0.389268i | \(-0.872728\pi\) |
0.998711 | − | 0.0507493i | \(-0.0161610\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.07601 | + | 5.73626i | −0.621878 | + | 0.393042i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −24.2810 | −1.65595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.2747 | −1.37634 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.295052 | + | 7.36579i | 0.0199378 | + | 0.497734i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.46944 | + | 19.6762i | −0.233380 | + | 1.32356i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3466 | + | 9.52092i | −0.759824 | + | 0.637568i | −0.938081 | − | 0.346416i | \(-0.887399\pi\) |
0.178257 | + | 0.983984i | \(0.442954\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.76767 | − | 18.3194i | −0.317845 | − | 1.22130i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.144137 | + | 0.817444i | 0.00956673 | + | 0.0542556i | 0.989217 | − | 0.146454i | \(-0.0467862\pi\) |
−0.979651 | + | 0.200710i | \(0.935675\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.7280 | + | 5.36054i | −0.973251 | + | 0.354235i | −0.779213 | − | 0.626759i | \(-0.784381\pi\) |
−0.194039 | + | 0.980994i | \(0.562159\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.56104 | − | 6.24637i | −0.168504 | − | 0.410981i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.29551 | + | 12.6362i | −0.477945 | + | 0.827824i | −0.999680 | − | 0.0252828i | \(-0.991951\pi\) |
0.521736 | + | 0.853107i | \(0.325285\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.163190 | − | 0.282653i | −0.0106453 | − | 0.0184383i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.48054 | + | 3.82588i | 0.226085 | + | 0.248518i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.75790 | + | 5.67056i | 0.437133 | + | 0.366798i | 0.834635 | − | 0.550803i | \(-0.185679\pi\) |
−0.397503 | + | 0.917601i | \(0.630123\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.7593 | + | 4.64402i | 0.821901 | + | 0.299147i | 0.718530 | − | 0.695496i | \(-0.244815\pi\) |
0.103370 | + | 0.994643i | \(0.467037\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.6806 | + | 10.3230i | −0.749310 | + | 0.662220i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.4428 | + | 3.80087i | 0.667167 | + | 0.242829i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.723693 | + | 0.607250i | 0.0460475 | + | 0.0386384i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.1132 | − | 12.2159i | −0.704270 | − | 0.774149i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.80404 | + | 10.0529i | 0.366348 | + | 0.634533i | 0.988992 | − | 0.147972i | \(-0.0472746\pi\) |
−0.622643 | + | 0.782506i | \(0.713941\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.35884 | − | 7.54973i | 0.274038 | − | 0.474647i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.50036 | − | 18.2933i | −0.469691 | − | 1.14557i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.13448 | + | 2.96071i | −0.507415 | + | 0.184684i | −0.583026 | − | 0.812454i | \(-0.698131\pi\) |
0.0756113 | + | 0.997137i | \(0.475909\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.45391 | + | 8.24553i | 0.0903415 | + | 0.512352i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.26659 | − | 24.0789i | −0.387892 | − | 1.49045i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0954 | − | 9.31017i | 0.684173 | − | 0.574089i | −0.233049 | − | 0.972465i | \(-0.574870\pi\) |
0.917222 | + | 0.398375i | \(0.130426\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.47535 | − | 42.3948i | 0.459207 | − | 2.60429i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.113898 | − | 2.84339i | −0.00697044 | − | 0.174012i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.3063 | −0.872273 | −0.436137 | − | 0.899880i | \(-0.643654\pi\) | ||||
−0.436137 | + | 0.899880i | \(0.643654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.43403 | 0.573077 | 0.286538 | − | 0.958069i | \(-0.407495\pi\) | ||||
0.286538 | + | 0.958069i | \(0.407495\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.5678 | − | 10.4712i | 1.00273 | − | 0.633748i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.22158 | − | 12.5992i | 0.133966 | − | 0.759761i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.16538 | − | 0.977871i | 0.0700210 | − | 0.0587546i | −0.607105 | − | 0.794621i | \(-0.707669\pi\) |
0.677126 | + | 0.735867i | \(0.263225\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.98433 | + | 31.4990i | −0.178667 | + | 1.88580i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.44941 | + | 25.2338i | 0.265429 | + | 1.50532i | 0.767810 | + | 0.640678i | \(0.221347\pi\) |
−0.502380 | + | 0.864647i | \(0.667542\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.94272 | + | 2.16297i | −0.353258 | + | 0.128575i | −0.512553 | − | 0.858656i | \(-0.671300\pi\) |
0.159295 | + | 0.987231i | \(0.449078\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.926414 | − | 0.125357i | −0.0548761 | − | 0.00742551i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.23990 | + | 2.14757i | −0.0731892 | + | 0.126767i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.73953 | + | 4.74500i | 0.161149 | + | 0.279118i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.47003 | + | 4.60451i | −0.0861746 | + | 0.269921i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.9435 | + | 14.2173i | 0.989851 | + | 0.830583i | 0.985546 | − | 0.169408i | \(-0.0541854\pi\) |
0.00430446 | + | 0.999991i | \(0.498630\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.69174 | + | 2.79956i | 0.447830 | + | 0.162997i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.0814 | + | 3.05944i | −0.584983 | + | 0.177527i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.7827 | + | 8.65620i | 1.37539 | + | 0.500601i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.6324 | + | 8.92161i | 0.612839 | + | 0.514233i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.7892 | − | 3.22291i | 0.849617 | − | 0.185151i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.69849 | − | 16.7983i | −0.555334 | − | 0.961866i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.48009 | − | 6.02769i | 0.198619 | − | 0.344019i | −0.749462 | − | 0.662048i | \(-0.769688\pi\) |
0.948081 | + | 0.318029i | \(0.103021\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.70522 | + | 7.38006i | −0.324559 | + | 0.419837i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.99620 | + | 3.27435i | −0.510128 | + | 0.185671i | −0.584244 | − | 0.811578i | \(-0.698609\pi\) |
0.0741159 | + | 0.997250i | \(0.476387\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.12624 | + | 12.0585i | 0.120182 | + | 0.681588i | 0.984053 | + | 0.177874i | \(0.0569221\pi\) |
−0.863871 | + | 0.503713i | \(0.831967\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.32291 | + | 17.5184i | −0.468943 | + | 0.987047i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.36450 | + | 7.01865i | −0.469797 | + | 0.394207i | −0.846721 | − | 0.532038i | \(-0.821426\pi\) |
0.376923 | + | 0.926244i | \(0.376982\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.92002 | − | 16.5603i | 0.163490 | − | 0.927198i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −22.6797 | − | 11.9102i | −1.26586 | − | 0.664762i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.544753 | −0.0303109 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 37.1421 | 2.06027 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.11909 | + | 2.16313i | 0.227786 | + | 0.119622i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.0323968 | + | 0.183732i | −0.00178610 | + | 0.0101294i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.0932 | − | 13.5038i | 0.884560 | − | 0.742234i | −0.0825512 | − | 0.996587i | \(-0.526307\pi\) |
0.967112 | + | 0.254353i | \(0.0818623\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.0244 | − | 1.04511i | 0.713731 | − | 0.0572719i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.42157 | − | 13.7334i | −0.132305 | − | 0.750337i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.39458 | − | 2.32744i | 0.348335 | − | 0.126784i | −0.161927 | − | 0.986803i | \(-0.551771\pi\) |
0.510262 | + | 0.860019i | \(0.329549\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.1320 | − | 18.2807i | 0.767547 | − | 0.992870i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.6919 | + | 18.5190i | −0.579001 | + | 1.00286i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.90453 | − | 17.1552i | −0.534794 | − | 0.926291i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −24.4706 | + | 5.33272i | −1.31746 | + | 0.287104i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.61225 | + | 3.03104i | 0.193916 | + | 0.162715i | 0.734576 | − | 0.678526i | \(-0.237381\pi\) |
−0.540660 | + | 0.841241i | \(0.681826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.27656 | + | 3.01242i | 0.443034 | + | 0.161251i | 0.553898 | − | 0.832584i | \(-0.313140\pi\) |
−0.110864 | + | 0.993836i | \(0.535362\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.8295 | − | 27.2812i | −0.738167 | − | 1.45616i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.4528 | − | 5.98832i | −0.875692 | − | 0.318726i | −0.135222 | − | 0.990815i | \(-0.543175\pi\) |
−0.740470 | + | 0.672089i | \(0.765397\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.9697 | + | 13.4002i | 0.847584 | + | 0.711207i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.43723 | + | 10.7663i | −0.181918 | + | 0.569813i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.44318 | + | 16.3561i | 0.498392 | + | 0.863240i | 0.999998 | − | 0.00185580i | \(-0.000590721\pi\) |
−0.501606 | + | 0.865096i | \(0.667257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.48712 | − | 16.4322i | 0.499322 | − | 0.864851i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.8245 | + | 1.60002i | 0.620623 | + | 0.0839791i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.4500 | − | 4.89540i | 0.704005 | − | 0.256237i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.38348 | − | 13.5174i | −0.124417 | − | 0.705602i | −0.981653 | − | 0.190678i | \(-0.938931\pi\) |
0.857236 | − | 0.514924i | \(-0.172180\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.15399 | + | 2.24244i | 0.164190 | + | 0.116737i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.8505 | + | 15.8175i | −0.978671 | + | 0.821203i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.38785 | + | 36.2273i | −0.330751 | + | 1.87578i | 0.134973 | + | 0.990849i | \(0.456905\pi\) |
−0.465723 | + | 0.884930i | \(0.654206\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.44977 | + | 4.07641i | −0.333065 | + | 0.210505i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 48.8192 | 2.51432 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.9790 | −1.48855 | −0.744276 | − | 0.667872i | \(-0.767205\pi\) | ||||
−0.744276 | + | 0.667872i | \(0.767205\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.666508 | − | 16.6389i | −0.0341462 | − | 0.852439i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.31770 | − | 7.47305i | 0.0673313 | − | 0.381855i | −0.932457 | − | 0.361281i | \(-0.882340\pi\) |
0.999788 | − | 0.0205739i | \(-0.00654934\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.0413 | + | 8.42567i | −0.511753 | + | 0.429412i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.4258 | − | 15.2054i | 0.784135 | − | 0.772932i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.02208 | − | 5.79648i | −0.0518213 | − | 0.293893i | 0.947872 | − | 0.318651i | \(-0.103230\pi\) |
−0.999693 | + | 0.0247577i | \(0.992119\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.7139 | + | 4.99145i | −0.693541 | + | 0.252428i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.9575 | + | 29.1644i | 0.603179 | + | 1.47115i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.02126 | − | 8.69708i | 0.252647 | − | 0.437597i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.47451 | + | 16.4103i | 0.475512 | + | 0.823611i | 0.999607 | − | 0.0280490i | \(-0.00892943\pi\) |
−0.524094 | + | 0.851660i | \(0.675596\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.359605 | + | 0.395286i | 0.0180028 | + | 0.0197891i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.2592 | − | 13.6431i | −0.811948 | − | 0.681305i | 0.139124 | − | 0.990275i | \(-0.455571\pi\) |
−0.951072 | + | 0.308970i | \(0.900016\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −58.3374 | − | 21.2331i | −2.90599 | − | 1.05769i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 25.9916 | + | 15.5092i | 1.29154 | + | 0.770658i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.29822 | + | 3.02030i | 0.411327 | + | 0.149711i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.81285 | − | 8.23396i | −0.485214 | − | 0.407143i | 0.367093 | − | 0.930184i | \(-0.380353\pi\) |
−0.852308 | + | 0.523041i | \(0.824797\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.46864 | − | 6.01125i | −0.269748 | − | 0.296513i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.33947 | − | 4.05208i | −0.115118 | − | 0.199390i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.0326 | + | 27.7694i | −0.787012 | + | 1.36314i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.47076 | − | 18.2211i | −0.365845 | − | 0.892293i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.6752 | + | 9.34502i | −1.25432 | + | 0.456534i | −0.881858 | − | 0.471515i | \(-0.843707\pi\) |
−0.372459 | + | 0.928049i | \(0.621485\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.95468 | − | 28.0994i | −0.241476 | − | 1.36948i | −0.828535 | − | 0.559937i | \(-0.810825\pi\) |
0.587059 | − | 0.809544i | \(-0.300286\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.280679 | + | 0.0773764i | 0.0136471 | + | 0.00376217i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.4066 | + | 13.7668i | −0.795839 | + | 0.667788i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.92536 | + | 10.9193i | −0.0931749 | + | 0.528421i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.827383 | − | 20.6551i | −0.0399464 | − | 0.997238i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.44020 | 0.165709 | 0.0828544 | − | 0.996562i | \(-0.473596\pi\) | ||||
0.0828544 | + | 0.996562i | \(0.473596\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.84486 | −0.0886584 | −0.0443292 | − | 0.999017i | \(-0.514115\pi\) | ||||
−0.0443292 | + | 0.999017i | \(0.514115\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −40.8373 | + | 25.8101i | −1.95800 | + | 1.23750i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.119827 | + | 0.679575i | −0.00573213 | + | 0.0325085i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.15794 | − | 3.48892i | 0.198447 | − | 0.166517i | −0.538149 | − | 0.842850i | \(-0.680876\pi\) |
0.736596 | + | 0.676333i | \(0.236432\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.01453 | + | 4.12484i | −0.429263 | + | 0.196421i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.68017 | − | 26.5425i | −0.222361 | − | 1.26107i | −0.867666 | − | 0.497148i | \(-0.834381\pi\) |
0.645304 | − | 0.763926i | \(-0.276731\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.19205 | + | 1.88975i | −0.246127 | + | 0.0895827i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.1294 | − | 1.77659i | −0.620999 | − | 0.0840300i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.3097 | − | 19.5890i | 0.533737 | − | 0.924460i | −0.465486 | − | 0.885055i | \(-0.654120\pi\) |
0.999223 | − | 0.0394051i | \(-0.0125463\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.30773 | + | 2.26506i | 0.0615788 | + | 0.106658i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.36492 | + | 19.9366i | −0.299050 | + | 0.936702i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −29.1518 | − | 24.4613i | −1.36666 | − | 1.14676i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.1532 | + | 7.33515i | 0.942725 | + | 0.343124i | 0.767242 | − | 0.641358i | \(-0.221629\pi\) |
0.175484 | + | 0.984482i | \(0.443851\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.2207 | + | 6.92487i | 0.757118 | + | 0.323225i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.02648 | − | 2.92140i | −0.373830 | − | 0.136063i | 0.148271 | − | 0.988947i | \(-0.452629\pi\) |
−0.522101 | + | 0.852884i | \(0.674852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.27248 | + | 2.74593i | 0.152085 | + | 0.127614i | 0.715655 | − | 0.698454i | \(-0.246128\pi\) |
−0.563570 | + | 0.826068i | \(0.690573\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 60.0248 | − | 13.0808i | 2.78359 | − | 0.606608i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.12319 | + | 7.14157i | 0.190798 | + | 0.330472i | 0.945515 | − | 0.325578i | \(-0.105559\pi\) |
−0.754717 | + | 0.656051i | \(0.772226\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.98571 | + | 6.90346i | −0.184043 | + | 0.318772i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.70879 | + | 3.50399i | −0.124815 | + | 0.161455i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.7560 | − | 5.00679i | 0.632504 | − | 0.230213i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.175852 | + | 0.997306i | 0.00806864 | + | 0.0457596i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.7995 | + | 31.6147i | 0.998133 | + | 1.44754i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.0611 | + | 14.3160i | −0.779541 | + | 0.654112i | −0.943133 | − | 0.332416i | \(-0.892136\pi\) |
0.163592 | + | 0.986528i | \(0.447692\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.45189 | + | 25.2479i | −0.202989 | + | 1.15121i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.6748 | + | 6.65615i | 0.576724 | + | 0.302865i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.38487 | 0.426145 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.7759 | 1.66647 | 0.833237 | − | 0.552916i | \(-0.186485\pi\) | ||||
0.833237 | + | 0.552916i | \(0.186485\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.3745 | − | 15.4260i | −1.32836 | − | 0.697586i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.01904 | − | 28.4644i | 0.226506 | − | 1.28458i | −0.633279 | − | 0.773924i | \(-0.718291\pi\) |
0.859785 | − | 0.510656i | \(-0.170597\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.5647 | + | 18.0950i | −0.971227 | + | 0.814956i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.6122 | + | 16.8405i | 0.521930 | + | 0.756926i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.06929 | − | 11.7355i | −0.0928204 | − | 0.526411i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.1940 | − | 4.80222i | 0.590644 | − | 0.214977i | −0.0293684 | − | 0.999569i | \(-0.509350\pi\) |
0.620013 | + | 0.784592i | \(0.287127\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.1483 | + | 27.3567i | −0.944838 | + | 1.22221i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.4453 | − | 18.0917i | 0.465731 | − | 0.806669i | −0.533503 | − | 0.845798i | \(-0.679125\pi\) |
0.999234 | + | 0.0391285i | \(0.0124582\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.6946 | − | 25.4518i | −0.653902 | − | 1.13259i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 36.6371 | − | 7.98409i | 1.62711 | − | 0.354586i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.22308 | − | 4.38269i | −0.231509 | − | 0.194259i | 0.519652 | − | 0.854378i | \(-0.326062\pi\) |
−0.751161 | + | 0.660119i | \(0.770506\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.68831 | − | 2.79832i | −0.340111 | − | 0.123790i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.667054 | − | 0.500504i | 0.0294511 | − | 0.0220978i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.0197 | + | 6.19465i | 0.749976 | + | 0.272969i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.150736 | + | 0.126483i | 0.00662938 | + | 0.00556271i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.42464 | − | 20.1236i | 0.282010 | − | 0.883329i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.17259 | − | 5.49509i | −0.138994 | − | 0.240744i | 0.788122 | − | 0.615519i | \(-0.211053\pi\) |
−0.927116 | + | 0.374774i | \(0.877720\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.3401 | − | 38.6942i | 0.976864 | − | 1.69198i | 0.303224 | − | 0.952919i | \(-0.401937\pi\) |
0.673641 | − | 0.739059i | \(-0.264730\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.8200 | + | 2.81724i | 0.908658 | + | 0.122954i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.6392 | − | 12.2437i | 1.46535 | − | 0.533343i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.783712 | − | 4.44465i | −0.0340744 | − | 0.193246i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.63972 | + | 3.03818i | −0.288139 | + | 0.131846i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.81672 | + | 4.88081i | −0.251950 | + | 0.211411i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.63702 | + | 48.9830i | −0.373411 | + | 2.11772i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 31.7479 | − | 20.0654i | 1.37002 | − | 0.865887i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.69997 | −0.288588 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.3563 | −0.488244 | −0.244122 | − | 0.969745i | \(-0.578500\pi\) | ||||
−0.244122 | + | 0.969745i | \(0.578500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.415604 | + | 10.3753i | 0.0178353 | + | 0.445246i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.56866 | − | 8.89631i | 0.0671940 | − | 0.381076i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.0798430 | − | 0.0669963i | 0.00341384 | − | 0.00286455i | −0.641079 | − | 0.767475i | \(-0.721513\pi\) |
0.644493 | + | 0.764610i | \(0.277069\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.6809 | + | 4.59853i | 0.711925 | + | 0.196261i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.231138 | + | 1.31085i | 0.00984683 | + | 0.0558441i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.39433 | + | 1.96337i | −0.229390 | + | 0.0834912i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.62426 | − | 23.4735i | −0.408527 | − | 0.996395i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.7684 | + | 23.8476i | −0.583385 | + | 1.01045i | 0.411689 | + | 0.911324i | \(0.364939\pi\) |
−0.995075 | + | 0.0991289i | \(0.968394\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.2497 | + | 36.8055i | 0.898766 | + | 1.55671i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.02134 | + | 8.81723i | 0.338661 | + | 0.372264i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.49216 | + | 2.09117i | 0.105032 | + | 0.0881323i | 0.693791 | − | 0.720176i | \(-0.255939\pi\) |
−0.588759 | + | 0.808308i | \(0.700383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −42.1583 | − | 15.3444i | −1.77361 | − | 0.645543i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.68286 | − | 16.3414i | −0.238658 | − | 0.686276i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.6272 | + | 12.9672i | 1.49357 | + | 0.543615i | 0.954387 | − | 0.298573i | \(-0.0965107\pi\) |
0.539183 | + | 0.842188i | \(0.318733\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.5340 | − | 18.9082i | −0.943017 | − | 0.791285i | 0.0350911 | − | 0.999384i | \(-0.488828\pi\) |
−0.978108 | + | 0.208099i | \(0.933272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.3210 | − | 24.5357i | −0.932474 | − | 1.02500i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.5651 | + | 23.4954i | 0.565703 | + | 0.979826i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.3737 | − | 23.1640i | 0.556755 | − | 0.964329i | −0.441009 | − | 0.897503i | \(-0.645379\pi\) |
0.997765 | − | 0.0668261i | \(-0.0212873\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.295948 | − | 0.721815i | −0.0122992 | − | 0.0299976i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.2238 | − | 6.26896i | 0.714565 | − | 0.260080i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.50684 | + | 25.5596i | 0.186654 | + | 1.05857i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −42.2944 | + | 41.6901i | −1.74866 | + | 1.72367i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.3965 | + | 30.5403i | −1.50225 | + | 1.26053i | −0.624872 | + | 0.780727i | \(0.714849\pi\) |
−0.877374 | + | 0.479807i | \(0.840707\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.293929 | − | 1.66695i | 0.0121111 | − | 0.0686856i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.248926 | − | 6.21427i | −0.0102394 | − | 0.255621i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.40677 | 0.386290 | 0.193145 | − | 0.981170i | \(-0.438131\pi\) | ||||
0.193145 | + | 0.981170i | \(0.438131\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.9438 | 0.899607 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.6531 | + | 6.73304i | −0.436004 | + | 0.275565i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.615845 | + | 3.49263i | −0.0251628 | + | 0.142705i | −0.994801 | − | 0.101839i | \(-0.967527\pi\) |
0.969638 | + | 0.244544i | \(0.0786384\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.6268 | + | 27.3772i | −1.33088 | + | 1.11674i | −0.347004 | + | 0.937864i | \(0.612801\pi\) |
−0.983872 | + | 0.178874i | \(0.942755\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.1386 | + | 7.20841i | 0.412877 | + | 0.293549i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.02309 | − | 22.8161i | −0.163562 | − | 0.927606i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.2067 | − | 3.71493i | 0.414277 | − | 0.150784i | −0.126469 | − | 0.991971i | \(-0.540364\pi\) |
0.540746 | + | 0.841186i | \(0.318142\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.3656 | + | 3.70295i | 1.10891 | + | 0.150051i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.285633 | + | 0.494732i | −0.0115555 | + | 0.0200147i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.6149 | − | 21.8496i | −0.509510 | − | 0.882497i | −0.999939 | − | 0.0110162i | \(-0.996493\pi\) |
0.490429 | − | 0.871481i | \(-0.336840\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.28526 | − | 7.15803i | 0.0921506 | − | 0.288639i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.59580 | − | 5.53453i | −0.265537 | − | 0.222812i | 0.500291 | − | 0.865857i | \(-0.333226\pi\) |
−0.765828 | + | 0.643045i | \(0.777671\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.9476 | + | 12.3559i | 1.36447 | + | 0.496626i | 0.917433 | − | 0.397890i | \(-0.130257\pi\) |
0.447036 | + | 0.894516i | \(0.352480\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.2067 | − | 18.7120i | 0.489840 | − | 0.750886i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.96789 | + | 1.08022i | 0.118906 | + | 0.0432782i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.8196 | − | 10.7569i | −0.512783 | − | 0.430276i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.550695 | − | 0.120009i | 0.0219926 | − | 0.00479271i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.39168 | − | 12.8028i | −0.294726 | − | 0.510480i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0668013 | + | 0.115703i | −0.00265932 | + | 0.00460607i | −0.867352 | − | 0.497695i | \(-0.834180\pi\) |
0.864693 | + | 0.502301i | \(0.167513\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.87537 | − | 8.89372i | 0.273271 | − | 0.353494i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.3828 | + | 11.0584i | −1.20571 | + | 0.438841i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.37767 | − | 19.1557i | −0.133828 | − | 0.758978i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18.5371 | + | 1.48747i | −0.733315 | + | 0.0588434i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.35762 | + | 6.17378i | −0.290609 | + | 0.243850i | −0.776423 | − | 0.630213i | \(-0.782968\pi\) |
0.485814 | + | 0.874062i | \(0.338523\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.18840 | − | 12.4110i | 0.0863020 | − | 0.489443i | −0.910766 | − | 0.412923i | \(-0.864508\pi\) |
0.997068 | − | 0.0765200i | \(-0.0243809\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −37.2340 | − | 19.5534i | −1.46609 | − | 0.769913i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.0753 | −0.828556 | −0.414278 | − | 0.910150i | \(-0.635966\pi\) | ||||
−0.414278 | + | 0.910150i | \(0.635966\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.93491 | −0.193712 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31.0904 | − | 16.3271i | −1.21853 | − | 0.639909i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.40708 | − | 30.6650i | 0.211595 | − | 1.20002i | −0.675123 | − | 0.737705i | \(-0.735909\pi\) |
0.886718 | − | 0.462311i | \(-0.152980\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 46.8831 | − | 39.3396i | 1.83187 | − | 1.53712i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.47918 | + | 11.5328i | −0.213763 | + | 0.449936i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.83780 | + | 33.1078i | 0.227409 | + | 1.28970i | 0.858027 | + | 0.513605i | \(0.171690\pi\) |
−0.630618 | + | 0.776093i | \(0.717199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.5713 | − | 12.5829i | 1.34467 | − | 0.489419i | 0.433389 | − | 0.901207i | \(-0.357318\pi\) |
0.911280 | + | 0.411788i | \(0.135095\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.1653 | + | 27.3787i | −0.821994 | + | 1.06330i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.518791 | − | 0.898573i | 0.0201179 | − | 0.0348452i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.8298 | + | 30.8822i | 0.690373 | + | 1.19576i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.0667 | + | 5.46262i | −0.969134 | + | 0.211197i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.95837 | + | 7.51696i | 0.345834 | + | 0.290189i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.08175 | + | 2.21358i | 0.234434 | + | 0.0853271i | 0.456566 | − | 0.889690i | \(-0.349079\pi\) |
−0.222132 | + | 0.975017i | \(0.571301\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.44149 | − | 31.9315i | 0.286423 | − | 1.22904i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.9751 | + | 13.0939i | 1.38263 | + | 0.503238i | 0.922976 | − | 0.384858i | \(-0.125749\pi\) |
0.459659 | + | 0.888096i | \(0.347972\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.10952 | − | 3.44830i | −0.157709 | − | 0.132333i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.437253 | + | 1.36959i | −0.0167556 | + | 0.0524828i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.7010 | + | 23.7309i | 0.524255 | + | 0.908037i | 0.999601 | + | 0.0282377i | \(0.00898954\pi\) |
−0.475346 | + | 0.879799i | \(0.657677\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.88943 | + | 13.6649i | −0.301440 | + | 0.522109i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.9016 | − | 3.64016i | −1.02636 | − | 0.138881i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −70.8048 | + | 25.7708i | −2.69745 | + | 0.981790i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.49952 | − | 19.8468i | −0.133128 | − | 0.755007i | −0.976145 | − | 0.217120i | \(-0.930334\pi\) |
0.843017 | − | 0.537887i | \(-0.180777\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.10291 | − | 11.6410i | 0.0418959 | − | 0.442203i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.2913 | + | 24.5783i | −1.11108 | + | 0.932309i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.760316 | − | 4.31196i | 0.0287990 | − | 0.163327i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.3632 | + | 13.5021i | −0.808031 | + | 0.510695i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.8155 | −0.975036 | −0.487518 | − | 0.873113i | \(-0.662098\pi\) | ||||
−0.487518 | + | 0.873113i | \(0.662098\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.699012 | −0.0263637 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0226264 | − | 0.564854i | −0.000852160 | − | 0.0212736i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.91721 | + | 16.5443i | −0.109713 | + | 0.622212i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.9831 | − | 20.1242i | 0.900704 | − | 0.755780i | −0.0696241 | − | 0.997573i | \(-0.522180\pi\) |
0.970328 | + | 0.241793i | \(0.0777355\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.25631 | + | 8.66970i | 0.0846182 | + | 0.325139i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.87440 | − | 44.6579i | −0.294898 | − | 1.67245i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −37.7164 | + | 13.7276i | −1.41051 | + | 0.513384i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.79652 | + | 14.1377i | 0.216475 | + | 0.527981i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.9508 | − | 32.8237i | 0.706744 | − | 1.22412i | −0.259314 | − | 0.965793i | \(-0.583496\pi\) |
0.966058 | − | 0.258324i | \(-0.0831702\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.17659 | − | 8.96613i | −0.192786 | − | 0.333916i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.8261 | + | 17.3964i | 0.588580 | + | 0.646980i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40.0887 | + | 33.6384i | 1.48886 | + | 1.24930i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.96307 | − | 1.07847i | −0.109894 | − | 0.0399982i | 0.286488 | − | 0.958084i | \(-0.407512\pi\) |
−0.396382 | + | 0.918086i | \(0.629734\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.2247 | + | 6.42359i | −0.971287 | + | 0.237911i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.0286 | − | 8.38173i | −0.851744 | − | 0.310009i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.8260 | + | 25.8661i | 1.13858 | + | 0.955385i | 0.999392 | − | 0.0348799i | \(-0.0111049\pi\) |
0.139193 | + | 0.990265i | \(0.455549\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.9528 | + | 14.2380i | 0.477772 | + | 0.525178i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.20376 | + | 7.28113i | 0.154848 | + | 0.268204i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.71378 | + | 9.89656i | −0.210185 | + | 0.364051i | −0.951772 | − | 0.306805i | \(-0.900740\pi\) |
0.741587 | + | 0.670856i | \(0.234073\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.620739 | + | 1.51398i | 0.0228034 | + | 0.0556174i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.2580 | − | 8.82918i | 0.889939 | − | 0.323911i | 0.143725 | − | 0.989618i | \(-0.454092\pi\) |
0.746214 | + | 0.665706i | \(0.231870\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.46708 | + | 25.3341i | 0.163661 | + | 0.928168i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.20428 | − | 27.6819i | −0.263591 | − | 1.01283i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.7799 | − | 18.2755i | 0.795821 | − | 0.667773i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.82330 | − | 33.0256i | 0.212495 | − | 1.20512i | −0.672706 | − | 0.739910i | \(-0.734868\pi\) |
0.885201 | − | 0.465209i | \(-0.154021\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.804735 | + | 20.0897i | 0.0293262 | + | 0.732109i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40.6345 | 1.47884 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.62121 | −0.313343 | −0.156672 | − | 0.987651i | \(-0.550076\pi\) | ||||
−0.156672 | + | 0.987651i | \(0.550076\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.7639 | − | 8.06707i | 0.463299 | − | 0.292816i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.56504 | + | 37.2322i | −0.237982 | + | 1.34967i | 0.598258 | + | 0.801303i | \(0.295860\pi\) |
−0.836241 | + | 0.548362i | \(0.815251\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.95568 | + | 3.31921i | −0.143205 | + | 0.120163i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.23001 | − | 34.0921i | 0.116781 | − | 1.23260i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.48785 | − | 14.1093i | −0.0898311 | − | 0.509457i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.0932 | − | 9.86114i | 0.977007 | − | 0.355602i | 0.196331 | − | 0.980538i | \(-0.437097\pi\) |
0.780676 | + | 0.624936i | \(0.214875\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.8581 | − | 2.01052i | −0.535103 | − | 0.0724070i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.9144 | + | 32.7607i | −0.680304 | + | 1.17832i | 0.294584 | + | 0.955626i | \(0.404819\pi\) |
−0.974888 | + | 0.222695i | \(0.928514\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.2742 | − | 57.6326i | −1.19525 | − | 2.07023i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.41056 | + | 13.8150i | −0.158228 | + | 0.495611i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.158595 | − | 0.133077i | −0.00568225 | − | 0.00476798i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.8105 | − | 4.29868i | −0.422614 | − | 0.153819i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.78102 | − | 41.9705i | 0.349545 | − | 1.49990i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.08080 | + | 2.94117i | 0.288416 | + | 0.104975i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.9376 | + | 21.7643i | 0.924577 | + | 0.775812i | 0.974836 | − | 0.222924i | \(-0.0715602\pi\) |
−0.0502589 | + | 0.998736i | \(0.516005\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.5118 | − | 5.34170i | 0.872644 | − | 0.190169i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.8226 | + | 22.2094i | 0.455919 | + | 0.789676i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.9754 | + | 29.4022i | −0.602814 | + | 1.04410i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 45.6034 | − | 58.9909i | 1.61739 | − | 2.09219i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.7073 | − | 18.0920i | 1.76072 | − | 0.640850i | 0.760755 | − | 0.649039i | \(-0.224829\pi\) |
0.999966 | + | 0.00818822i | \(0.00260642\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0572017 | − | 0.324407i | −0.00202365 | − | 0.0114767i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.11510 | − | 4.45194i | 0.0747335 | − | 0.157302i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.61045 | + | 5.54683i | −0.233278 | + | 0.195743i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.82690 | − | 27.3747i | 0.170126 | − | 0.964831i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.9382 | − | 11.5208i | −0.772262 | − | 0.405552i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.9680 | 0.385614 | 0.192807 | − | 0.981237i | \(-0.438241\pi\) | ||||
0.192807 | + | 0.981237i | \(0.438241\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.54690 | 0.229893 | 0.114946 | − | 0.993372i | \(-0.463330\pi\) | ||||
0.114946 | + | 0.993372i | \(0.463330\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.4667 | + | 7.59717i | 0.507370 | + | 0.266444i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.1866 | + | 63.4422i | −0.391849 | + | 2.22228i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.887661 | + | 0.744836i | −0.0310553 | + | 0.0260585i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 33.8384 | − | 2.71530i | 1.18241 | − | 0.0948801i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.50955 | − | 42.5888i | −0.262085 | − | 1.48636i | −0.777209 | − | 0.629243i | \(-0.783365\pi\) |
0.515124 | − | 0.857116i | \(-0.327746\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.409020 | − | 0.148871i | 0.0142575 | − | 0.00518931i | −0.334882 | − | 0.942260i | \(-0.608696\pi\) |
0.349139 | + | 0.937071i | \(0.386474\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.5528 | − | 17.5314i | 0.471847 | − | 0.610364i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.70278 | + | 15.0737i | −0.302625 | + | 0.524162i | −0.976730 | − | 0.214474i | \(-0.931196\pi\) |
0.674105 | + | 0.738636i | \(0.264530\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.7891 | + | 22.1513i | 0.444183 | + | 0.769348i | 0.997995 | − | 0.0632941i | \(-0.0201606\pi\) |
−0.553812 | + | 0.832642i | \(0.686827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.57454 | − | 0.561052i | 0.0893098 | − | 0.0194627i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.59213 | + | 7.20965i | 0.297700 | + | 0.249800i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 63.0892 | + | 22.9626i | 2.18329 | + | 0.794653i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.9423 | + | 45.8993i | −1.03496 | + | 1.58651i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.8836 | + | 17.7922i | 1.68765 | + | 0.614254i | 0.994326 | − | 0.106375i | \(-0.0339243\pi\) |
0.693322 | + | 0.720628i | \(0.256147\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.4769 | + | 25.5732i | 1.05093 | + | 0.881834i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.4977 | + | 42.2782i | −0.464884 | + | 1.45614i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −36.4028 | − | 63.0515i | −1.25230 | − | 2.16904i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.62169 | + | 11.4691i | −0.227524 | + | 0.394083i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.8548 | − | 1.46880i | −0.372534 | − | 0.0504091i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.5973 | + | 6.40489i | −0.603227 | + | 0.219557i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.91369 | − | 27.8669i | −0.168242 | − | 0.954146i | −0.945659 | − | 0.325161i | \(-0.894582\pi\) |
0.777417 | − | 0.628985i | \(-0.216529\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.31967 | − | 0.938266i | −0.0451318 | − | 0.0320880i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.5795 | − | 22.3028i | 0.907938 | − | 0.761850i | −0.0637879 | − | 0.997963i | \(-0.520318\pi\) |
0.971726 | + | 0.236113i | \(0.0758737\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.51676 | − | 31.2871i | 0.188229 | − | 1.06750i | −0.733506 | − | 0.679683i | \(-0.762118\pi\) |
0.921736 | − | 0.387819i | \(-0.126771\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.63077 | + | 2.29474i | −0.123736 | + | 0.0782044i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.0932 | −1.05843 | −0.529213 | − | 0.848489i | \(-0.677513\pi\) | ||||
−0.529213 | + | 0.848489i | \(0.677513\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −41.0158 | −1.39458 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.379837 | + | 9.48240i | 0.0129000 | + | 0.322039i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.05137 | + | 5.96259i | −0.0356651 | + | 0.202267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.6981 | + | 15.6895i | −0.633560 | + | 0.531620i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.96222 | + | 5.87703i | −0.201790 | + | 0.198907i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.47052 | − | 8.33974i | −0.0497127 | − | 0.281935i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.1496 | + | 18.2530i | −1.69343 | + | 0.616359i | −0.995051 | − | 0.0993659i | \(-0.968319\pi\) |
−0.698382 | + | 0.715725i | \(0.746096\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.5331 | + | 35.4462i | 0.490190 | + | 1.19557i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.55673 | + | 11.3566i | −0.220902 | + | 0.382613i | −0.955082 | − | 0.296341i | \(-0.904233\pi\) |
0.734180 | + | 0.678955i | \(0.237567\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.0350 | + | 36.4337i | 0.707885 | + | 1.22609i | 0.965640 | + | 0.259882i | \(0.0836837\pi\) |
−0.257756 | + | 0.966210i | \(0.582983\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.54050 | + | 10.4871i | 0.320701 | + | 0.352521i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.7527 | − | 37.5520i | −1.50265 | − | 1.26087i | −0.876728 | − | 0.480986i | \(-0.840279\pi\) |
−0.625921 | − | 0.779887i | \(-0.715277\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.3675 | + | 6.32125i | 0.582487 | + | 0.212008i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.9232 | − | 3.42697i | −0.600450 | − | 0.114808i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0146364 | − | 0.00532723i | −0.000489790 | − | 0.000178269i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −55.8620 | − | 46.8738i | −1.86726 | − | 1.56682i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.4991 | + | 32.4260i | 0.984945 | + | 1.08267i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −43.7354 | − | 75.7519i | −1.45866 | − | 2.52647i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.7243 | − | 37.6276i | 0.723742 | − | 1.25356i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.11979 | + | 22.2431i | 0.303488 | + | 0.740205i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.9454 | − | 6.89555i | 0.629765 | − | 0.229216i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.47053 | + | 48.0388i | 0.281259 | + | 1.59510i | 0.718349 | + | 0.695683i | \(0.244898\pi\) |
−0.437090 | + | 0.899418i | \(0.643991\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25.2740 | + | 6.96744i | 0.838287 | + | 0.231095i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.5369 | − | 15.5543i | 0.614153 | − | 0.515336i | −0.281806 | − | 0.959471i | \(-0.590934\pi\) |
0.895960 | + | 0.444135i | \(0.146489\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.35696 | − | 19.0383i | 0.111099 | − | 0.630075i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.34470 | − | 33.5696i | −0.0444545 | − | 1.10978i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34.9841 | −1.15528 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.7812 | −1.41122 | −0.705610 | − | 0.708600i | \(-0.749327\pi\) | ||||
−0.705610 | + | 0.708600i | \(0.749327\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.1906 | − | 6.44073i | 0.335793 | − | 0.212229i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.33620 | − | 35.9344i | 0.208558 | − | 1.18279i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.0525 | + | 17.6652i | −0.692203 | + | 0.580828i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.6919 | + | 6.72266i | −0.482544 | + | 0.220801i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.529440 | + | 3.00260i | 0.0173704 | + | 0.0985122i | 0.992260 | − | 0.124175i | \(-0.0396283\pi\) |
−0.974890 | + | 0.222687i | \(0.928517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.498361 | − | 0.181389i | 0.0163331 | − | 0.00594477i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.4321 | − | 2.22350i | −0.537964 | − | 0.0727941i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.5721 | − | 20.0435i | 0.378449 | − | 0.655493i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.1594 | − | 27.9888i | −0.527903 | − | 0.914355i | −0.999471 | − | 0.0325254i | \(-0.989645\pi\) |
0.471568 | − | 0.881830i | \(-0.343688\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.45014 | + | 20.2035i | −0.210492 | + | 0.659317i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.1288 | + | 10.1773i | 0.395389 | + | 0.331770i | 0.818708 | − | 0.574210i | \(-0.194691\pi\) |
−0.423319 | + | 0.905981i | \(0.639135\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.21190 | − | 1.89698i | −0.169723 | − | 0.0617741i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −26.8703 | + | 20.1613i | −0.874090 | + | 0.655848i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.9799 | − | 6.54414i | −0.584267 | − | 0.212656i | 0.0329390 | − | 0.999457i | \(-0.489513\pi\) |
−0.617206 | + | 0.786802i | \(0.711736\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.1914 | − | 16.1035i | −0.622978 | − | 0.522741i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.4787 | + | 4.02694i | −0.599213 | + | 0.130583i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.7660 | + | 25.5755i | 0.478319 | + | 0.828472i | 0.999691 | − | 0.0248569i | \(-0.00791302\pi\) |
−0.521372 | + | 0.853329i | \(0.674580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.2018 | + | 55.7752i | −1.04203 | + | 1.80484i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.8136 | − | 23.0431i | 0.575833 | − | 0.744877i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.47560 | − | 3.08486i | 0.273691 | − | 0.0996155i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.9323 | + | 79.0138i | 0.449428 | + | 2.54883i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.1872 | − | 36.5276i | −0.811646 | − | 1.17709i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.16035 | + | 0.973650i | −0.0373530 | + | 0.0313429i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.14971 | − | 40.5480i | 0.229919 | − | 1.30394i | −0.623135 | − | 0.782114i | \(-0.714141\pi\) |
0.853055 | − | 0.521822i | \(-0.174747\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.835357 | − | 0.438686i | −0.0268355 | − | 0.0140926i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.8784 | −1.18348 | −0.591742 | − | 0.806128i | \(-0.701560\pi\) | ||||
−0.591742 | + | 0.806128i | \(0.701560\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.8572 | 0.700708 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 56.9559 | + | 29.9103i | 1.82405 | + | 0.957896i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.880454 | − | 4.99330i | 0.0281682 | − | 0.159750i | −0.967479 | − | 0.252951i | \(-0.918599\pi\) |
0.995647 | + | 0.0932012i | \(0.0297100\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.55180 | − | 2.14122i | 0.0815560 | − | 0.0684336i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.57451 | + | 6.63416i | 0.146053 | + | 0.211813i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.06602 | + | 23.0595i | 0.129686 | + | 0.735485i | 0.978414 | + | 0.206655i | \(0.0662578\pi\) |
−0.848728 | + | 0.528830i | \(0.822631\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.3473 | + | 4.13008i | −0.361555 | + | 0.131595i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.197637 | + | 0.255656i | −0.00629086 | + | 0.00813762i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.5217 | + | 26.8843i | −0.493561 | + | 0.854872i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.92671 | + | 10.2654i | 0.188268 | + | 0.326090i | 0.944673 | − | 0.328014i | \(-0.106379\pi\) |
−0.756405 | + | 0.654104i | \(0.773046\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 35.5527 | − | 7.74777i | 1.12823 | − | 0.245868i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.7447 | + | 15.7287i | 0.594248 | + | 0.498633i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.3789 | − | 13.9688i | −1.21547 | − | 0.442396i | −0.346873 | − | 0.937912i | \(-0.612757\pi\) |
−0.868599 | + | 0.495516i | \(0.834979\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.8140 | + | 8.88580i | 0.658525 | + | 0.281134i |
(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 | 108.2.i.a.85.3 | yes | 18 | |
3.2 | odd | 2 | 324.2.i.a.145.1 | 18 | |||
4.3 | odd | 2 | 432.2.u.d.193.1 | 18 | |||
9.2 | odd | 6 | 972.2.i.d.757.1 | 18 | |||
9.4 | even | 3 | 972.2.i.c.109.1 | 18 | |||
9.5 | odd | 6 | 972.2.i.b.109.3 | 18 | |||
9.7 | even | 3 | 972.2.i.a.757.3 | 18 | |||
27.2 | odd | 18 | 972.2.i.b.865.3 | 18 | |||
27.4 | even | 9 | 2916.2.e.c.973.2 | 18 | |||
27.5 | odd | 18 | 2916.2.e.d.1945.8 | 18 | |||
27.7 | even | 9 | inner | 108.2.i.a.61.3 | ✓ | 18 | |
27.11 | odd | 18 | 972.2.i.d.217.1 | 18 | |||
27.13 | even | 9 | 2916.2.a.d.1.8 | 9 | |||
27.14 | odd | 18 | 2916.2.a.c.1.2 | 9 | |||
27.16 | even | 9 | 972.2.i.a.217.3 | 18 | |||
27.20 | odd | 18 | 324.2.i.a.181.1 | 18 | |||
27.22 | even | 9 | 2916.2.e.c.1945.2 | 18 | |||
27.23 | odd | 18 | 2916.2.e.d.973.8 | 18 | |||
27.25 | even | 9 | 972.2.i.c.865.1 | 18 | |||
108.7 | odd | 18 | 432.2.u.d.385.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.i.a.61.3 | ✓ | 18 | 27.7 | even | 9 | inner | |
108.2.i.a.85.3 | yes | 18 | 1.1 | even | 1 | trivial | |
324.2.i.a.145.1 | 18 | 3.2 | odd | 2 | |||
324.2.i.a.181.1 | 18 | 27.20 | odd | 18 | |||
432.2.u.d.193.1 | 18 | 4.3 | odd | 2 | |||
432.2.u.d.385.1 | 18 | 108.7 | odd | 18 | |||
972.2.i.a.217.3 | 18 | 27.16 | even | 9 | |||
972.2.i.a.757.3 | 18 | 9.7 | even | 3 | |||
972.2.i.b.109.3 | 18 | 9.5 | odd | 6 | |||
972.2.i.b.865.3 | 18 | 27.2 | odd | 18 | |||
972.2.i.c.109.1 | 18 | 9.4 | even | 3 | |||
972.2.i.c.865.1 | 18 | 27.25 | even | 9 | |||
972.2.i.d.217.1 | 18 | 27.11 | odd | 18 | |||
972.2.i.d.757.1 | 18 | 9.2 | odd | 6 | |||
2916.2.a.c.1.2 | 9 | 27.14 | odd | 18 | |||
2916.2.a.d.1.8 | 9 | 27.13 | even | 9 | |||
2916.2.e.c.973.2 | 18 | 27.4 | even | 9 | |||
2916.2.e.c.1945.2 | 18 | 27.22 | even | 9 | |||
2916.2.e.d.973.8 | 18 | 27.23 | odd | 18 | |||
2916.2.e.d.1945.8 | 18 | 27.5 | odd | 18 |