Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,2,Mod(37,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.v (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.29969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 37.5 | ||
Character | \(\chi\) | \(=\) | 288.37 |
Dual form | 288.2.v.d.109.5 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.333592 | − | 1.37431i | −0.235885 | − | 0.971781i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.77743 | + | 0.916914i | −0.888717 | + | 0.458457i | ||||
\(5\) | 1.20409 | + | 0.498752i | 0.538487 | + | 0.223048i | 0.635316 | − | 0.772253i | \(-0.280870\pi\) |
−0.0968290 | + | 0.995301i | \(0.530870\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59422 | + | 2.59422i | 0.980524 | + | 0.980524i | 0.999814 | − | 0.0192902i | \(-0.00614065\pi\) |
−0.0192902 | + | 0.999814i | \(0.506141\pi\) | |||||||
\(8\) | 1.85306 | + | 2.13686i | 0.655154 | + | 0.755495i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.283762 | − | 1.82117i | 0.0897334 | − | 0.575905i | ||||
\(11\) | −2.14608 | + | 5.18109i | −0.647066 | + | 1.56216i | 0.169894 | + | 0.985462i | \(0.445658\pi\) |
−0.816960 | + | 0.576694i | \(0.804342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.984096 | + | 0.407626i | −0.272939 | + | 0.113055i | −0.514955 | − | 0.857217i | \(-0.672191\pi\) |
0.242016 | + | 0.970272i | \(0.422191\pi\) | |||||||
\(14\) | 2.69984 | − | 4.43066i | 0.721564 | − | 1.18414i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.31854 | − | 3.25951i | 0.579635 | − | 0.814876i | ||||
\(17\) | − | 0.979053i | − | 0.237455i | −0.992927 | − | 0.118728i | \(-0.962118\pi\) | ||
0.992927 | − | 0.118728i | \(-0.0378815\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.68961 | − | 2.35671i | 1.30529 | − | 0.540667i | 0.381781 | − | 0.924253i | \(-0.375311\pi\) |
0.923505 | + | 0.383586i | \(0.125311\pi\) | |||||||
\(20\) | −2.59751 | + | 0.217551i | −0.580820 | + | 0.0486459i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.83631 | + | 1.22100i | 1.67071 | + | 0.260318i | ||||
\(23\) | 3.70206 | − | 3.70206i | 0.771932 | − | 0.771932i | −0.206512 | − | 0.978444i | \(-0.566211\pi\) |
0.978444 | + | 0.206512i | \(0.0662113\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.33445 | − | 2.33445i | −0.466890 | − | 0.466890i | ||||
\(26\) | 0.888489 | + | 1.21647i | 0.174247 | + | 0.238569i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.98973 | − | 2.23238i | −1.32094 | − | 0.421880i | ||||
\(29\) | 1.17302 | + | 2.83193i | 0.217825 | + | 0.525876i | 0.994586 | − | 0.103920i | \(-0.0331385\pi\) |
−0.776761 | + | 0.629796i | \(0.783139\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.54469 | 0.277434 | 0.138717 | − | 0.990332i | \(-0.455702\pi\) | ||||
0.138717 | + | 0.990332i | \(0.455702\pi\) | |||||||
\(32\) | −5.25300 | − | 2.09904i | −0.928608 | − | 0.371061i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.34552 | + | 0.326604i | −0.230755 | + | 0.0560121i | ||||
\(35\) | 1.82981 | + | 4.41756i | 0.309295 | + | 0.746703i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.23352 | − | 3.41044i | −1.35358 | − | 0.560672i | −0.416295 | − | 0.909229i | \(-0.636672\pi\) |
−0.937288 | + | 0.348557i | \(0.886672\pi\) | |||||||
\(38\) | −5.13685 | − | 7.03308i | −0.833307 | − | 1.14092i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.16549 | + | 3.49720i | 0.184280 | + | 0.552955i | ||||
\(41\) | 1.10862 | − | 1.10862i | 0.173138 | − | 0.173138i | −0.615219 | − | 0.788357i | \(-0.710932\pi\) |
0.788357 | + | 0.615219i | \(0.210932\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.47106 | + | 8.37989i | −0.529332 | + | 1.27792i | 0.402629 | + | 0.915363i | \(0.368097\pi\) |
−0.931961 | + | 0.362558i | \(0.881903\pi\) | |||||||
\(44\) | −0.936101 | − | 11.1768i | −0.141123 | − | 1.68497i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.32273 | − | 3.85278i | −0.932236 | − | 0.568062i | ||||
\(47\) | 3.15582i | 0.460324i | 0.973152 | + | 0.230162i | \(0.0739256\pi\) | ||||
−0.973152 | + | 0.230162i | \(0.926074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.45997i | 0.922853i | ||||||||
\(50\) | −2.42949 | + | 3.98700i | −0.343582 | + | 0.563847i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.37541 | − | 1.62686i | 0.190735 | − | 0.225605i | ||||
\(53\) | 2.55252 | − | 6.16232i | 0.350615 | − | 0.846460i | −0.645929 | − | 0.763397i | \(-0.723530\pi\) |
0.996544 | − | 0.0830627i | \(-0.0264702\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.16815 | + | 5.16815i | −0.696873 | + | 0.696873i | ||||
\(56\) | −0.736256 | + | 10.3507i | −0.0983864 | + | 1.38318i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.50063 | − | 2.55680i | 0.459655 | − | 0.335724i | ||||
\(59\) | 8.95423 | + | 3.70896i | 1.16574 | + | 0.482866i | 0.879783 | − | 0.475376i | \(-0.157688\pi\) |
0.285958 | + | 0.958242i | \(0.407688\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00717 | − | 4.84573i | −0.256991 | − | 0.620432i | 0.741746 | − | 0.670681i | \(-0.233998\pi\) |
−0.998737 | + | 0.0502499i | \(0.983998\pi\) | |||||||
\(62\) | −0.515295 | − | 2.12287i | −0.0654425 | − | 0.269605i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.13236 | + | 7.91945i | −0.141545 | + | 0.989932i | ||||
\(65\) | −1.38825 | −0.172191 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.14380 | + | 2.76138i | 0.139738 | + | 0.337357i | 0.978220 | − | 0.207573i | \(-0.0665564\pi\) |
−0.838482 | + | 0.544930i | \(0.816556\pi\) | |||||||
\(68\) | 0.897707 | + | 1.74020i | 0.108863 | + | 0.211030i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.46066 | − | 3.98838i | 0.652674 | − | 0.476703i | ||||
\(71\) | −10.0373 | − | 10.0373i | −1.19120 | − | 1.19120i | −0.976730 | − | 0.214474i | \(-0.931196\pi\) |
−0.214474 | − | 0.976730i | \(-0.568804\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.11103 | − | 8.11103i | 0.949324 | − | 0.949324i | −0.0494525 | − | 0.998776i | \(-0.515748\pi\) |
0.998776 | + | 0.0494525i | \(0.0157476\pi\) | |||||||
\(74\) | −1.94035 | + | 12.4531i | −0.225561 | + | 1.44764i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.95200 | + | 9.40578i | −0.912157 | + | 1.07892i | ||||
\(77\) | −19.0083 | + | 7.87349i | −2.16620 | + | 0.897268i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 0.155459i | − | 0.0174905i | −0.999962 | − | 0.00874523i | \(-0.997216\pi\) | ||
0.999962 | − | 0.00874523i | \(-0.00278373\pi\) | |||||||
\(80\) | 4.41742 | − | 2.76837i | 0.493883 | − | 0.309513i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.89342 | − | 1.15376i | −0.209093 | − | 0.127412i | ||||
\(83\) | −5.13862 | + | 2.12849i | −0.564037 | + | 0.233632i | −0.646437 | − | 0.762968i | \(-0.723742\pi\) |
0.0823997 | + | 0.996599i | \(0.473742\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.488304 | − | 1.17887i | 0.0529640 | − | 0.127866i | ||||
\(86\) | 12.6745 | + | 1.97484i | 1.36672 | + | 0.212953i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.0481 | + | 5.01498i | −1.60413 | + | 0.534598i | ||||
\(89\) | 6.15303 | + | 6.15303i | 0.652220 | + | 0.652220i | 0.953527 | − | 0.301307i | \(-0.0974230\pi\) |
−0.301307 | + | 0.953527i | \(0.597423\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.61044 | − | 1.49549i | −0.378477 | − | 0.156770i | ||||
\(92\) | −3.18569 | + | 9.97462i | −0.332131 | + | 1.03993i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.33707 | − | 1.05276i | 0.447334 | − | 0.108583i | ||||
\(95\) | 8.02623 | 0.823474 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.3852 | 1.46059 | 0.730296 | − | 0.683131i | \(-0.239382\pi\) | ||||
0.730296 | + | 0.683131i | \(0.239382\pi\) | |||||||
\(98\) | 8.87798 | − | 2.15499i | 0.896811 | − | 0.217687i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.28981 | + | 2.00884i | 0.628981 | + | 0.200884i | ||||
\(101\) | −12.1198 | − | 5.02020i | −1.20597 | − | 0.499528i | −0.313045 | − | 0.949738i | \(-0.601349\pi\) |
−0.892923 | + | 0.450210i | \(0.851349\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3057 | − | 10.3057i | −1.01545 | − | 1.01545i | −0.999879 | − | 0.0155752i | \(-0.995042\pi\) |
−0.0155752 | − | 0.999879i | \(-0.504958\pi\) | |||||||
\(104\) | −2.69463 | − | 1.34752i | −0.264230 | − | 0.132136i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.32041 | − | 1.45224i | −0.905279 | − | 0.141054i | ||||
\(107\) | 0.576841 | − | 1.39262i | 0.0557653 | − | 0.134629i | −0.893541 | − | 0.448981i | \(-0.851787\pi\) |
0.949307 | + | 0.314352i | \(0.101787\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.0738 | + | 4.58693i | −1.06068 | + | 0.439348i | −0.843693 | − | 0.536826i | \(-0.819623\pi\) |
−0.216987 | + | 0.976174i | \(0.569623\pi\) | |||||||
\(110\) | 8.82667 | + | 5.37857i | 0.841590 | + | 0.512826i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 14.4707 | − | 2.44108i | 1.36735 | − | 0.230660i | ||||
\(113\) | − | 9.41139i | − | 0.885349i | −0.896682 | − | 0.442675i | \(-0.854030\pi\) | ||
0.896682 | − | 0.442675i | \(-0.145970\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.30402 | − | 2.61121i | 0.587853 | − | 0.243497i | ||||
\(116\) | −4.68161 | − | 3.95801i | −0.434676 | − | 0.367492i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.11019 | − | 13.5431i | 0.194259 | − | 1.24675i | ||||
\(119\) | 2.53988 | − | 2.53988i | 0.232831 | − | 0.232831i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.4598 | − | 14.4598i | −1.31453 | − | 1.31453i | ||||
\(122\) | −5.98994 | + | 4.37495i | −0.542303 | + | 0.396090i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.74558 | + | 1.41635i | −0.246560 | + | 0.127192i | ||||
\(125\) | −4.14034 | − | 9.99566i | −0.370323 | − | 0.894039i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0219 | 1.42171 | 0.710855 | − | 0.703338i | \(-0.248308\pi\) | ||||
0.710855 | + | 0.703338i | \(0.248308\pi\) | |||||||
\(128\) | 11.2615 | − | 1.08565i | 0.995385 | − | 0.0959586i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.463107 | + | 1.90788i | 0.0406172 | + | 0.167332i | ||||
\(131\) | −2.18619 | − | 5.27794i | −0.191009 | − | 0.461135i | 0.799142 | − | 0.601142i | \(-0.205288\pi\) |
−0.990151 | + | 0.140007i | \(0.955288\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.8739 | + | 8.64627i | 1.81000 | + | 0.749727i | ||||
\(134\) | 3.41342 | − | 2.49311i | 0.294875 | − | 0.215372i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.09210 | − | 1.81424i | 0.179396 | − | 0.155570i | ||||
\(137\) | 8.63573 | − | 8.63573i | 0.737801 | − | 0.737801i | −0.234351 | − | 0.972152i | \(-0.575297\pi\) |
0.972152 | + | 0.234351i | \(0.0752966\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.05369 | + | 9.78647i | −0.343829 | + | 0.830078i | 0.653492 | + | 0.756933i | \(0.273303\pi\) |
−0.997321 | + | 0.0731441i | \(0.976697\pi\) | |||||||
\(140\) | −7.30288 | − | 6.17413i | −0.617206 | − | 0.521809i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.4459 | + | 17.1426i | −0.876602 | + | 1.43858i | ||||
\(143\) | − | 5.97348i | − | 0.499528i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.99495i | 0.331763i | ||||||||
\(146\) | −13.8528 | − | 8.44126i | −1.14647 | − | 0.698604i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.7616 | − | 1.48760i | 1.46000 | − | 0.122280i | ||||
\(149\) | −1.10547 | + | 2.66884i | −0.0905637 | + | 0.218640i | −0.962671 | − | 0.270675i | \(-0.912753\pi\) |
0.872107 | + | 0.489315i | \(0.162753\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.40487 | − | 6.40487i | 0.521221 | − | 0.521221i | −0.396719 | − | 0.917940i | \(-0.629851\pi\) |
0.917940 | + | 0.396719i | \(0.129851\pi\) | |||||||
\(152\) | 15.5791 | + | 7.79079i | 1.26363 | + | 0.631916i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 17.1616 | + | 23.4967i | 1.38292 | + | 1.89342i | ||||
\(155\) | 1.85995 | + | 0.770416i | 0.149395 | + | 0.0618813i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.85724 | − | 6.89798i | −0.228032 | − | 0.550519i | 0.767905 | − | 0.640563i | \(-0.221299\pi\) |
−0.995938 | + | 0.0900446i | \(0.971299\pi\) | |||||||
\(158\) | −0.213648 | + | 0.0518597i | −0.0169969 | + | 0.00412573i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.27820 | − | 5.14738i | −0.417279 | − | 0.406936i | ||||
\(161\) | 19.2079 | 1.51379 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.958379 | + | 2.31373i | 0.0750661 | + | 0.181225i | 0.956958 | − | 0.290226i | \(-0.0937304\pi\) |
−0.881892 | + | 0.471451i | \(0.843730\pi\) | |||||||
\(164\) | −0.953993 | + | 2.98702i | −0.0744943 | + | 0.233247i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.63939 | + | 6.35199i | 0.360087 | + | 0.493010i | ||||
\(167\) | −3.60896 | − | 3.60896i | −0.279270 | − | 0.279270i | 0.553548 | − | 0.832817i | \(-0.313274\pi\) |
−0.832817 | + | 0.553548i | \(0.813274\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.39010 | + | 8.39010i | −0.645392 | + | 0.645392i | ||||
\(170\) | −1.78302 | − | 0.277818i | −0.136752 | − | 0.0213077i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.51405 | − | 18.0774i | −0.115445 | − | 1.37839i | ||||
\(173\) | 2.16959 | − | 0.898673i | 0.164951 | − | 0.0683248i | −0.298680 | − | 0.954353i | \(-0.596546\pi\) |
0.463631 | + | 0.886028i | \(0.346546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 12.1122i | − | 0.915593i | ||||||
\(176\) | 11.9120 | + | 19.0077i | 0.897902 | + | 1.43276i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.40354 | − | 10.5087i | 0.479966 | − | 0.787663i | ||||
\(179\) | 2.66481 | − | 1.10380i | 0.199177 | − | 0.0825020i | −0.280865 | − | 0.959747i | \(-0.590621\pi\) |
0.480042 | + | 0.877245i | \(0.340621\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.10884 | + | 2.67697i | −0.0824191 | + | 0.198977i | −0.959717 | − | 0.280969i | \(-0.909344\pi\) |
0.877298 | + | 0.479947i | \(0.159344\pi\) | |||||||
\(182\) | −0.850852 | + | 5.46073i | −0.0630693 | + | 0.404776i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 14.7709 | + | 1.05067i | 1.08893 | + | 0.0774562i | ||||
\(185\) | −8.21296 | − | 8.21296i | −0.603829 | − | 0.603829i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.07256 | + | 2.10112i | 0.370942 | + | 0.153649i | ||||
\(188\) | −2.89362 | − | 5.60927i | −0.211039 | − | 0.409098i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.67748 | − | 11.0305i | −0.194245 | − | 0.800236i | ||||
\(191\) | −8.35300 | −0.604402 | −0.302201 | − | 0.953244i | \(-0.597721\pi\) | ||||
−0.302201 | + | 0.953244i | \(0.597721\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.3350 | −0.887894 | −0.443947 | − | 0.896053i | \(-0.646422\pi\) | ||||
−0.443947 | + | 0.896053i | \(0.646422\pi\) | |||||||
\(194\) | −4.79877 | − | 19.7696i | −0.344532 | − | 1.41938i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.92324 | − | 11.4822i | −0.423088 | − | 0.820155i | ||||
\(197\) | 21.5154 | + | 8.91197i | 1.53291 | + | 0.634952i | 0.980126 | − | 0.198374i | \(-0.0635661\pi\) |
0.552782 | + | 0.833326i | \(0.313566\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.0334 | − | 17.0334i | −1.20746 | − | 1.20746i | −0.971846 | − | 0.235616i | \(-0.924289\pi\) |
−0.235616 | − | 0.971846i | \(-0.575711\pi\) | |||||||
\(200\) | 0.662531 | − | 9.31426i | 0.0468480 | − | 0.658617i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.85622 | + | 18.3310i | −0.200963 | + | 1.28977i | ||||
\(203\) | −4.30357 | + | 10.3897i | −0.302051 | + | 0.729217i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.88781 | − | 0.781958i | 0.131851 | − | 0.0546143i | ||||
\(206\) | −10.7253 | + | 17.6011i | −0.747269 | + | 1.22633i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.953006 | + | 4.15276i | −0.0660791 | + | 0.287942i | ||||
\(209\) | 34.5360i | 2.38891i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.86549 | + | 3.67221i | −0.610325 | + | 0.252805i | −0.666368 | − | 0.745623i | \(-0.732152\pi\) |
0.0560422 | + | 0.998428i | \(0.482152\pi\) | |||||||
\(212\) | 1.11339 | + | 13.2936i | 0.0764677 | + | 0.913005i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.10631 | − | 0.328191i | −0.143984 | − | 0.0224347i | ||||
\(215\) | −8.35897 | + | 8.35897i | −0.570077 | + | 0.570077i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00726 | + | 4.00726i | 0.272031 | + | 0.272031i | ||||
\(218\) | 9.99798 | + | 13.6887i | 0.677149 | + | 0.927113i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.44730 | − | 13.9248i | 0.299837 | − | 0.938809i | ||||
\(221\) | 0.399087 | + | 0.963482i | 0.0268455 | + | 0.0648108i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.90976 | 0.462712 | 0.231356 | − | 0.972869i | \(-0.425684\pi\) | ||||
0.231356 | + | 0.972869i | \(0.425684\pi\) | |||||||
\(224\) | −8.18208 | − | 19.0728i | −0.546688 | − | 1.27436i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.9341 | + | 3.13956i | −0.860365 | + | 0.208840i | ||||
\(227\) | −1.65113 | − | 3.98617i | −0.109589 | − | 0.264572i | 0.859565 | − | 0.511026i | \(-0.170734\pi\) |
−0.969154 | + | 0.246454i | \(0.920734\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.09073 | + | 2.93708i | 0.468568 | + | 0.194087i | 0.604459 | − | 0.796636i | \(-0.293389\pi\) |
−0.135890 | + | 0.990724i | \(0.543389\pi\) | |||||||
\(230\) | −5.69157 | − | 7.79258i | −0.375291 | − | 0.513827i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.87777 | + | 7.75432i | −0.254588 | + | 0.509096i | ||||
\(233\) | 1.49412 | − | 1.49412i | 0.0978831 | − | 0.0978831i | −0.656470 | − | 0.754353i | \(-0.727951\pi\) |
0.754353 | + | 0.656470i | \(0.227951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.57397 | + | 3.79990i | −0.102675 | + | 0.247878i | ||||
\(236\) | −19.3163 | + | 1.61782i | −1.25739 | + | 0.105311i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.33786 | − | 2.64329i | −0.281181 | − | 0.171339i | ||||
\(239\) | − | 5.41212i | − | 0.350081i | −0.984561 | − | 0.175041i | \(-0.943994\pi\) | ||
0.984561 | − | 0.175041i | \(-0.0560057\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.6684i | 1.26695i | 0.773762 | + | 0.633476i | \(0.218372\pi\) | ||||
−0.773762 | + | 0.633476i | \(0.781628\pi\) | |||||||
\(242\) | −15.0486 | + | 24.6959i | −0.967359 | + | 1.58752i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.01071 | + | 6.77256i | 0.512833 | + | 0.433569i | ||||
\(245\) | −3.22192 | + | 7.77841i | −0.205841 | + | 0.496944i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.63846 | + | 4.63846i | −0.295138 | + | 0.295138i | ||||
\(248\) | 2.86239 | + | 3.30079i | 0.181762 | + | 0.209600i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.3559 | + | 9.02456i | −0.781457 | + | 0.570763i | ||||
\(251\) | −23.6647 | − | 9.80223i | −1.49370 | − | 0.618711i | −0.521582 | − | 0.853201i | \(-0.674658\pi\) |
−0.972119 | + | 0.234490i | \(0.924658\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.2358 | + | 27.1256i | 0.706387 | + | 1.70537i | ||||
\(254\) | −5.34476 | − | 22.0189i | −0.335360 | − | 1.38159i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.24875 | − | 15.1146i | −0.328047 | − | 0.944661i | ||||
\(257\) | 9.44245 | 0.589004 | 0.294502 | − | 0.955651i | \(-0.404846\pi\) | ||||
0.294502 | + | 0.955651i | \(0.404846\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.5122 | − | 30.2070i | −0.777468 | − | 1.87697i | ||||
\(260\) | 2.46752 | − | 1.27290i | 0.153029 | − | 0.0789421i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.52420 | + | 4.76517i | −0.403067 | + | 0.294393i | ||||
\(263\) | 8.38788 | + | 8.38788i | 0.517219 | + | 0.517219i | 0.916729 | − | 0.399510i | \(-0.130820\pi\) |
−0.399510 | + | 0.916729i | \(0.630820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.14694 | − | 6.14694i | 0.377603 | − | 0.377603i | ||||
\(266\) | 4.91925 | − | 31.5715i | 0.301619 | − | 1.93577i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.56498 | − | 3.85941i | −0.278851 | − | 0.235751i | ||||
\(269\) | −0.0655084 | + | 0.0271345i | −0.00399412 | + | 0.00165442i | −0.384680 | − | 0.923050i | \(-0.625688\pi\) |
0.380685 | + | 0.924705i | \(0.375688\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.4877i | 0.880062i | 0.897982 | + | 0.440031i | \(0.145033\pi\) | ||||
−0.897982 | + | 0.440031i | \(0.854967\pi\) | |||||||
\(272\) | −3.19123 | − | 2.26997i | −0.193497 | − | 0.137637i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.7489 | − | 8.98733i | −0.891017 | − | 0.542945i | ||||
\(275\) | 17.1049 | − | 7.08507i | 1.03146 | − | 0.427246i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.16981 | − | 19.7237i | 0.490876 | − | 1.18508i | −0.463398 | − | 0.886150i | \(-0.653370\pi\) |
0.954275 | − | 0.298931i | \(-0.0966299\pi\) | |||||||
\(278\) | 14.8019 | + | 2.30632i | 0.887758 | + | 0.138324i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.04897 | + | 12.0960i | −0.361495 | + | 0.722876i | ||||
\(281\) | −2.76272 | − | 2.76272i | −0.164810 | − | 0.164810i | 0.619884 | − | 0.784694i | \(-0.287180\pi\) |
−0.784694 | + | 0.619884i | \(0.787180\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.86879 | − | 2.43093i | −0.348864 | − | 0.144504i | 0.201369 | − | 0.979515i | \(-0.435461\pi\) |
−0.550233 | + | 0.835011i | \(0.685461\pi\) | |||||||
\(284\) | 27.0439 | + | 8.63726i | 1.60476 | + | 0.512527i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.20940 | + | 1.99270i | −0.485432 | + | 0.117831i | ||||
\(287\) | 5.75203 | 0.339532 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0415 | 0.943615 | ||||||||
\(290\) | 5.49029 | − | 1.33268i | 0.322401 | − | 0.0782578i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.97970 | + | 21.8539i | −0.408456 | + | 1.27890i | ||||
\(293\) | −4.51526 | − | 1.87028i | −0.263784 | − | 0.109263i | 0.246872 | − | 0.969048i | \(-0.420597\pi\) |
−0.510656 | + | 0.859785i | \(0.670597\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.93187 | + | 8.93187i | 0.520034 | + | 0.520034i | ||||
\(296\) | −7.96955 | − | 23.9136i | −0.463221 | − | 1.38995i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.03658 | + | 0.628952i | 0.233833 | + | 0.0364342i | ||||
\(299\) | −2.13412 | + | 5.15223i | −0.123420 | + | 0.297961i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.7440 | + | 12.7346i | −1.77206 | + | 0.734009i | ||||
\(302\) | −10.9389 | − | 6.66564i | −0.629461 | − | 0.383564i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.50986 | − | 24.0094i | 0.316012 | − | 1.37704i | ||||
\(305\) | − | 6.83578i | − | 0.391416i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.44200 | − | 3.49679i | 0.481810 | − | 0.199572i | −0.128539 | − | 0.991704i | \(-0.541029\pi\) |
0.610350 | + | 0.792132i | \(0.291029\pi\) | |||||||
\(308\) | 26.5667 | − | 31.4236i | 1.51378 | − | 1.79052i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.438324 | − | 2.81314i | 0.0248951 | − | 0.159776i | ||||
\(311\) | −20.8439 | + | 20.8439i | −1.18195 | + | 1.18195i | −0.202710 | + | 0.979239i | \(0.564975\pi\) |
−0.979239 | + | 0.202710i | \(0.935025\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.1026 | + | 14.1026i | 0.797124 | + | 0.797124i | 0.982641 | − | 0.185517i | \(-0.0593959\pi\) |
−0.185517 | + | 0.982641i | \(0.559396\pi\) | |||||||
\(314\) | −8.52678 | + | 6.22782i | −0.481194 | + | 0.351456i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.142542 | + | 0.276317i | 0.00801862 | + | 0.0155441i | ||||
\(317\) | −1.07307 | − | 2.59063i | −0.0602698 | − | 0.145504i | 0.890876 | − | 0.454247i | \(-0.150092\pi\) |
−0.951145 | + | 0.308743i | \(0.900092\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.1899 | −0.962448 | ||||||||
\(320\) | −5.31331 | + | 8.97099i | −0.297023 | + | 0.501494i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.40759 | − | 26.3975i | −0.357081 | − | 1.47108i | ||||
\(323\) | −2.30735 | − | 5.57043i | −0.128384 | − | 0.309947i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.24890 | + | 1.34574i | 0.180217 | + | 0.0746482i | ||||
\(326\) | 2.86007 | − | 2.08895i | 0.158405 | − | 0.115696i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.42332 | + | 0.314634i | 0.244237 | + | 0.0173728i | ||||
\(329\) | −8.18691 | + | 8.18691i | −0.451359 | + | 0.451359i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.37795 | + | 3.32667i | −0.0757390 | + | 0.182850i | −0.957214 | − | 0.289380i | \(-0.906551\pi\) |
0.881475 | + | 0.472230i | \(0.156551\pi\) | |||||||
\(332\) | 7.18192 | − | 8.49492i | 0.394159 | − | 0.466219i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.75590 | + | 6.16374i | −0.205514 | + | 0.337265i | ||||
\(335\) | 3.89544i | 0.212830i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 0.473748i | − | 0.0258067i | −0.999917 | − | 0.0129034i | \(-0.995893\pi\) | ||
0.999917 | − | 0.0129034i | \(-0.00410738\pi\) | |||||||
\(338\) | 14.3294 | + | 8.73170i | 0.779418 | + | 0.474942i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.212994 | + | 2.54310i | 0.0115512 | + | 0.137919i | ||||
\(341\) | −3.31502 | + | 8.00317i | −0.179518 | + | 0.433396i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.40095 | − | 1.40095i | 0.0756440 | − | 0.0756440i | ||||
\(344\) | −24.3388 | + | 8.11122i | −1.31226 | + | 0.437328i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.95881 | − | 2.68189i | −0.105306 | − | 0.144179i | ||||
\(347\) | 9.36785 | + | 3.88029i | 0.502893 | + | 0.208305i | 0.619684 | − | 0.784852i | \(-0.287261\pi\) |
−0.116791 | + | 0.993156i | \(0.537261\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.04231 | − | 4.93057i | −0.109322 | − | 0.263928i | 0.859745 | − | 0.510723i | \(-0.170622\pi\) |
−0.969068 | + | 0.246796i | \(0.920622\pi\) | |||||||
\(350\) | −16.6458 | + | 4.04051i | −0.889755 | + | 0.215974i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 22.1486 | − | 22.7116i | 1.18053 | − | 1.21053i | ||||
\(353\) | −34.7185 | −1.84788 | −0.923939 | − | 0.382539i | \(-0.875050\pi\) | ||||
−0.923939 | + | 0.382539i | \(0.875050\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.07969 | − | 17.0919i | −0.375751 | − | 0.907144i | ||||
\(356\) | −16.5784 | − | 5.29480i | −0.878653 | − | 0.280624i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.40592 | − | 3.29405i | −0.127157 | − | 0.174096i | ||||
\(359\) | 4.06394 | + | 4.06394i | 0.214486 | + | 0.214486i | 0.806170 | − | 0.591684i | \(-0.201537\pi\) |
−0.591684 | + | 0.806170i | \(0.701537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.3825 | − | 13.3825i | 0.704343 | − | 0.704343i | ||||
\(362\) | 4.04887 | + | 0.630867i | 0.212804 | + | 0.0331576i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.78855 | − | 0.652321i | 0.408231 | − | 0.0341909i | ||||
\(365\) | 13.8118 | − | 5.72104i | 0.722944 | − | 0.299453i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.2747i | 1.58033i | 0.612896 | + | 0.790164i | \(0.290004\pi\) | ||||
−0.612896 | + | 0.790164i | \(0.709996\pi\) | |||||||
\(368\) | −3.48351 | − | 20.6502i | −0.181591 | − | 1.07647i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.54735 | + | 14.0269i | −0.444356 | + | 0.729224i | ||||
\(371\) | 22.6082 | − | 9.36463i | 1.17376 | − | 0.486188i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.46231 | − | 20.4298i | 0.438162 | − | 1.05782i | −0.538421 | − | 0.842676i | \(-0.680979\pi\) |
0.976583 | − | 0.215141i | \(-0.0690210\pi\) | |||||||
\(374\) | 1.19542 | − | 7.67217i | 0.0618139 | − | 0.396718i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.74356 | + | 5.84792i | −0.347773 | + | 0.301583i | ||||
\(377\) | −2.30874 | − | 2.30874i | −0.118906 | − | 0.118906i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.3128 | + | 8.82807i | 1.09477 | + | 0.453467i | 0.855667 | − | 0.517527i | \(-0.173147\pi\) |
0.239100 | + | 0.970995i | \(0.423147\pi\) | |||||||
\(380\) | −14.2661 | + | 7.35936i | −0.731835 | + | 0.377527i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.78649 | + | 11.4796i | 0.142569 | + | 0.587346i | ||||
\(383\) | 25.5734 | 1.30674 | 0.653370 | − | 0.757039i | \(-0.273355\pi\) | ||||
0.653370 | + | 0.757039i | \(0.273355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.8147 | −1.36660 | ||||||||
\(386\) | 4.11486 | + | 16.9521i | 0.209441 | + | 0.862839i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −25.5687 | + | 13.1900i | −1.29805 | + | 0.669619i | ||||
\(389\) | 1.19642 | + | 0.495572i | 0.0606608 | + | 0.0251265i | 0.412808 | − | 0.910818i | \(-0.364548\pi\) |
−0.352147 | + | 0.935945i | \(0.614548\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.62451 | − | 3.62451i | −0.183299 | − | 0.183299i | ||||
\(392\) | −13.8041 | + | 11.9707i | −0.697211 | + | 0.604611i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.07042 | − | 32.5417i | 0.255444 | − | 1.63943i | ||||
\(395\) | 0.0775352 | − | 0.187187i | 0.00390122 | − | 0.00941838i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.47211 | − | 2.26662i | 0.274637 | − | 0.113758i | −0.241114 | − | 0.970497i | \(-0.577513\pi\) |
0.515751 | + | 0.856738i | \(0.327513\pi\) | |||||||
\(398\) | −17.7269 | + | 29.0912i | −0.888567 | + | 1.45821i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.0217 | + | 2.19664i | −0.651083 | + | 0.109832i | ||||
\(401\) | 33.2794i | 1.66189i | 0.556352 | + | 0.830947i | \(0.312201\pi\) | ||||
−0.556352 | + | 0.830947i | \(0.687799\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.52012 | + | 0.629655i | −0.0757227 | + | 0.0313654i | ||||
\(404\) | 26.1453 | − | 2.18977i | 1.30078 | − | 0.108945i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.7143 | + | 2.44849i | 0.779888 | + | 0.121517i | ||||
\(407\) | 35.3395 | − | 35.3395i | 1.75172 | − | 1.75172i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.40530 | + | 7.40530i | 0.366168 | + | 0.366168i | 0.866078 | − | 0.499909i | \(-0.166633\pi\) |
−0.499909 | + | 0.866078i | \(0.666633\pi\) | |||||||
\(410\) | −1.70441 | − | 2.33358i | −0.0841747 | − | 0.115247i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 27.7672 | + | 8.86829i | 1.36799 | + | 0.436909i | ||||
\(413\) | 13.6074 | + | 32.8511i | 0.669575 | + | 1.61650i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.24896 | −0.355838 | ||||||||
\(416\) | 6.02508 | − | 0.0756046i | 0.295404 | − | 0.00370682i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 47.4631 | − | 11.5209i | 2.32150 | − | 0.563507i | ||||
\(419\) | 6.43037 | + | 15.5243i | 0.314144 | + | 0.758411i | 0.999543 | + | 0.0302425i | \(0.00962796\pi\) |
−0.685399 | + | 0.728168i | \(0.740372\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.60807 | + | 2.32294i | 0.273321 | + | 0.113213i | 0.515134 | − | 0.857110i | \(-0.327742\pi\) |
−0.241813 | + | 0.970323i | \(0.577742\pi\) | |||||||
\(422\) | 8.00419 | + | 10.9589i | 0.389638 | + | 0.533470i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 17.8980 | − | 5.96475i | 0.869204 | − | 0.289674i | ||||
\(425\) | −2.28555 | + | 2.28555i | −0.110865 | + | 0.110865i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.36385 | − | 17.7779i | 0.356362 | − | 0.860334i | ||||
\(428\) | 0.251613 | + | 3.00420i | 0.0121622 | + | 0.145213i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.2763 | + | 8.69930i | 0.688462 | + | 0.419517i | ||||
\(431\) | − | 0.297166i | − | 0.0143140i | −0.999974 | − | 0.00715698i | \(-0.997722\pi\) | ||
0.999974 | − | 0.00715698i | \(-0.00227816\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.4119i | − | 0.740649i | −0.928902 | − | 0.370325i | \(-0.879246\pi\) | ||
0.928902 | − | 0.370325i | \(-0.120754\pi\) | |||||||
\(434\) | 4.17042 | − | 6.84400i | 0.200186 | − | 0.328522i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.4772 | − | 18.3067i | 0.741222 | − | 0.876732i | ||||
\(437\) | 12.3386 | − | 29.7879i | 0.590233 | − | 1.42495i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.15252 | + | 3.15252i | −0.150462 | + | 0.150462i | −0.778324 | − | 0.627863i | \(-0.783930\pi\) |
0.627863 | + | 0.778324i | \(0.283930\pi\) | |||||||
\(440\) | −20.6205 | − | 1.46675i | −0.983044 | − | 0.0699247i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.19099 | − | 0.869878i | 0.0566495 | − | 0.0413759i | ||||
\(443\) | −2.80647 | − | 1.16248i | −0.133339 | − | 0.0552310i | 0.315016 | − | 0.949086i | \(-0.397990\pi\) |
−0.448355 | + | 0.893855i | \(0.647990\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.33998 | + | 10.4776i | 0.205735 | + | 0.496688i | ||||
\(446\) | −2.30504 | − | 9.49612i | −0.109147 | − | 0.449654i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −23.4824 | + | 17.6072i | −1.10944 | + | 0.831863i | ||||
\(449\) | 3.57715 | 0.168816 | 0.0844080 | − | 0.996431i | \(-0.473100\pi\) | ||||
0.0844080 | + | 0.996431i | \(0.473100\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.36469 | + | 8.12307i | 0.158437 | + | 0.382500i | ||||
\(452\) | 8.62943 | + | 16.7281i | 0.405894 | + | 0.786825i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.92742 | + | 3.59891i | −0.231255 | + | 0.168905i | ||||
\(455\) | −3.60142 | − | 3.60142i | −0.168837 | − | 0.168837i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.97857 | + | 8.97857i | −0.420000 | + | 0.420000i | −0.885204 | − | 0.465204i | \(-0.845981\pi\) |
0.465204 | + | 0.885204i | \(0.345981\pi\) | |||||||
\(458\) | 1.67103 | − | 10.7246i | 0.0780823 | − | 0.501128i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.81073 | + | 10.4215i | −0.410802 | + | 0.485905i | ||||
\(461\) | 26.0500 | − | 10.7903i | 1.21327 | − | 0.502553i | 0.318006 | − | 0.948089i | \(-0.396987\pi\) |
0.895264 | + | 0.445536i | \(0.146987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9782i | 0.510199i | 0.966915 | + | 0.255100i | \(0.0821083\pi\) | ||||
−0.966915 | + | 0.255100i | \(0.917892\pi\) | |||||||
\(464\) | 11.9504 | + | 2.74246i | 0.554783 | + | 0.127316i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.55180 | − | 1.55495i | −0.118210 | − | 0.0720318i | ||||
\(467\) | −38.5388 | + | 15.9633i | −1.78336 | + | 0.738694i | −0.791535 | + | 0.611123i | \(0.790718\pi\) |
−0.991829 | + | 0.127571i | \(0.959282\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.19636 | + | 10.1309i | −0.193770 | + | 0.467802i | ||||
\(470\) | 5.74730 | + | 0.895503i | 0.265103 | + | 0.0413065i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.66714 | + | 26.0069i | 0.398938 | + | 1.19706i | ||||
\(473\) | −35.9678 | − | 35.9678i | −1.65380 | − | 1.65380i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.7837 | − | 7.78047i | −0.861856 | − | 0.356992i | ||||
\(476\) | −2.18562 | + | 6.84332i | −0.100178 | + | 0.313663i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.43791 | + | 1.80544i | −0.340202 | + | 0.0825788i | ||||
\(479\) | −20.8426 | −0.952324 | −0.476162 | − | 0.879357i | \(-0.657973\pi\) | ||||
−0.476162 | + | 0.879357i | \(0.657973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.49276 | 0.432833 | ||||||||
\(482\) | 27.0304 | − | 6.56121i | 1.23120 | − | 0.298855i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 38.9599 | + | 12.4430i | 1.77090 | + | 0.565590i | ||||
\(485\) | 17.3211 | + | 7.17462i | 0.786510 | + | 0.325783i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.3086 | − | 16.3086i | −0.739014 | − | 0.739014i | 0.233373 | − | 0.972387i | \(-0.425024\pi\) |
−0.972387 | + | 0.233373i | \(0.925024\pi\) | |||||||
\(488\) | 6.63526 | − | 13.2684i | 0.300364 | − | 0.600634i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.7647 | + | 1.83310i | 0.531476 | + | 0.0828108i | ||||
\(491\) | 2.22643 | − | 5.37508i | 0.100477 | − | 0.242574i | −0.865645 | − | 0.500658i | \(-0.833091\pi\) |
0.966122 | + | 0.258084i | \(0.0830913\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.77261 | − | 1.14845i | 0.124872 | − | 0.0517237i | ||||
\(494\) | 7.92202 | + | 4.82732i | 0.356429 | + | 0.217191i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.58142 | − | 5.03492i | 0.160811 | − | 0.226075i | ||||
\(497\) | − | 52.0778i | − | 2.33601i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.39859 | − | 3.89302i | 0.420739 | − | 0.174276i | −0.162261 | − | 0.986748i | \(-0.551879\pi\) |
0.583000 | + | 0.812472i | \(0.301879\pi\) | |||||||
\(500\) | 16.5243 | + | 13.9703i | 0.738991 | + | 0.624771i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.57693 | + | 35.7924i | −0.248910 | + | 1.59749i | ||||
\(503\) | −21.5760 | + | 21.5760i | −0.962027 | + | 0.962027i | −0.999305 | − | 0.0372777i | \(-0.988131\pi\) |
0.0372777 | + | 0.999305i | \(0.488131\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0896 | − | 12.0896i | −0.537979 | − | 0.537979i | ||||
\(506\) | 33.5307 | − | 24.4903i | 1.49062 | − | 1.08872i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −28.4778 | + | 14.6907i | −1.26350 | + | 0.651793i | ||||
\(509\) | −1.30560 | − | 3.15200i | −0.0578697 | − | 0.139710i | 0.892300 | − | 0.451443i | \(-0.149091\pi\) |
−0.950170 | + | 0.311733i | \(0.899091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.0836 | 1.86167 | ||||||||
\(512\) | −19.0211 | + | 12.2555i | −0.840623 | + | 0.541621i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.14992 | − | 12.9768i | −0.138937 | − | 0.572383i | ||||
\(515\) | −7.26906 | − | 17.5491i | −0.320313 | − | 0.773304i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.3506 | − | 6.77264i | −0.719099 | − | 0.297860i | ||||
\(518\) | −37.3397 | + | 27.2723i | −1.64061 | + | 1.19828i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.57250 | − | 2.96649i | −0.112812 | − | 0.130089i | ||||
\(521\) | −7.58009 | + | 7.58009i | −0.332090 | + | 0.332090i | −0.853380 | − | 0.521290i | \(-0.825451\pi\) |
0.521290 | + | 0.853380i | \(0.325451\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.67736 | + | 13.7064i | −0.248254 | + | 0.599337i | −0.998056 | − | 0.0623246i | \(-0.980149\pi\) |
0.749802 | + | 0.661662i | \(0.230149\pi\) | |||||||
\(524\) | 8.72522 | + | 7.37663i | 0.381163 | + | 0.322250i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.72939 | − | 14.3256i | 0.380619 | − | 0.624628i | ||||
\(527\) | − | 1.51233i | − | 0.0658782i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 4.41042i | − | 0.191758i | ||||||
\(530\) | −10.4983 | − | 6.39720i | −0.456019 | − | 0.277877i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −45.0299 | + | 3.77143i | −1.95229 | + | 0.163512i | ||||
\(533\) | −0.639089 | + | 1.54290i | −0.0276820 | + | 0.0668303i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.38914 | − | 1.38914i | 0.0600578 | − | 0.0600578i | ||||
\(536\) | −3.78117 | + | 7.56115i | −0.163322 | + | 0.326592i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.0591441 | + | 0.0809768i | 0.00254988 | + | 0.00349116i | ||||
\(539\) | −33.4697 | − | 13.8636i | −1.44164 | − | 0.597148i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.0508 | − | 33.9216i | −0.604090 | − | 1.45840i | −0.869336 | − | 0.494221i | \(-0.835453\pi\) |
0.265247 | − | 0.964181i | \(-0.414547\pi\) | |||||||
\(542\) | 19.9105 | − | 4.83296i | 0.855228 | − | 0.207593i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.05507 | + | 5.14297i | −0.0881104 | + | 0.220503i | ||||
\(545\) | −15.6217 | −0.669158 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.85438 | + | 18.9622i | 0.335829 | + | 0.810763i | 0.998107 | + | 0.0615046i | \(0.0195899\pi\) |
−0.662278 | + | 0.749258i | \(0.730410\pi\) | |||||||
\(548\) | −7.43122 | + | 23.2677i | −0.317446 | + | 0.993945i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.4431 | − | 21.1438i | −0.658496 | − | 0.901576i | ||||
\(551\) | 13.3481 | + | 13.3481i | 0.568648 | + | 0.568648i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.403294 | − | 0.403294i | 0.0171498 | − | 0.0171498i | ||||
\(554\) | −29.8317 | − | 4.64817i | −1.26743 | − | 0.197482i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.76819 | − | 21.1117i | −0.0749878 | − | 0.895335i | ||||
\(557\) | 20.1683 | − | 8.35400i | 0.854560 | − | 0.353970i | 0.0879825 | − | 0.996122i | \(-0.471958\pi\) |
0.766578 | + | 0.642152i | \(0.221958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.66152i | − | 0.408639i | ||||||
\(560\) | 18.6415 | + | 4.27799i | 0.787749 | + | 0.180778i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.87520 | + | 4.71843i | −0.121283 | + | 0.199035i | ||||
\(563\) | 21.3521 | − | 8.84433i | 0.899884 | − | 0.372744i | 0.115708 | − | 0.993283i | \(-0.463086\pi\) |
0.784175 | + | 0.620539i | \(0.213086\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.69395 | − | 11.3322i | 0.197476 | − | 0.476749i | ||||
\(566\) | −1.38307 | + | 8.87646i | −0.0581346 | + | 0.373105i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.84864 | − | 40.0479i | 0.119526 | − | 1.68037i | ||||
\(569\) | 7.60582 | + | 7.60582i | 0.318853 | + | 0.318853i | 0.848326 | − | 0.529474i | \(-0.177611\pi\) |
−0.529474 | + | 0.848326i | \(0.677611\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.616329 | + | 0.255292i | 0.0257926 | + | 0.0106836i | 0.395542 | − | 0.918448i | \(-0.370557\pi\) |
−0.369750 | + | 0.929131i | \(0.620557\pi\) | |||||||
\(572\) | 5.47717 | + | 10.6175i | 0.229012 | + | 0.443939i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.91883 | − | 7.90505i | −0.0800904 | − | 0.329950i | ||||
\(575\) | −17.2845 | −0.720814 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.78481 | −0.365716 | −0.182858 | − | 0.983139i | \(-0.558535\pi\) | ||||
−0.182858 | + | 0.983139i | \(0.558535\pi\) | |||||||
\(578\) | −5.35129 | − | 22.0459i | −0.222584 | − | 0.916987i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.66303 | − | 7.10076i | −0.152099 | − | 0.294843i | ||||
\(581\) | −18.8525 | − | 7.80896i | −0.782133 | − | 0.323970i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.4496 | + | 26.4496i | 1.09543 | + | 1.09543i | ||||
\(584\) | 32.3623 | + | 2.30196i | 1.33916 | + | 0.0952558i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.06409 | + | 6.82925i | −0.0439570 | + | 0.282114i | ||||
\(587\) | 10.5345 | − | 25.4324i | 0.434803 | − | 1.04971i | −0.542915 | − | 0.839788i | \(-0.682679\pi\) |
0.977718 | − | 0.209921i | \(-0.0673206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.78867 | − | 3.64039i | 0.362131 | − | 0.150000i | ||||
\(590\) | 9.29552 | − | 15.2547i | 0.382691 | − | 0.628027i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30.2061 | + | 18.9300i | −1.24146 | + | 0.778018i | ||||
\(593\) | − | 12.6478i | − | 0.519384i | −0.965691 | − | 0.259692i | \(-0.916379\pi\) | ||
0.965691 | − | 0.259692i | \(-0.0836211\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.32502 | − | 1.79148i | 0.177309 | − | 0.0734436i | ||||
\(596\) | −0.482197 | − | 5.75731i | −0.0197516 | − | 0.235829i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.79267 | + | 1.21420i | 0.318666 | + | 0.0496523i | ||||
\(599\) | −10.2749 | + | 10.2749i | −0.419820 | + | 0.419820i | −0.885142 | − | 0.465322i | \(-0.845939\pi\) |
0.465322 | + | 0.885142i | \(0.345939\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.4571 | − | 34.4571i | −1.40554 | − | 1.40554i | −0.780983 | − | 0.624552i | \(-0.785281\pi\) |
−0.624552 | − | 0.780983i | \(-0.714719\pi\) | |||||||
\(602\) | 27.7572 | + | 38.0035i | 1.13130 | + | 1.54891i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.51152 | + | 17.2569i | −0.224260 | + | 0.702175i | ||||
\(605\) | −10.1991 | − | 24.6229i | −0.414653 | − | 1.00106i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.97427 | 0.242488 | 0.121244 | − | 0.992623i | \(-0.461312\pi\) | ||||
0.121244 | + | 0.992623i | \(0.461312\pi\) | |||||||
\(608\) | −34.8344 | + | 0.437112i | −1.41272 | + | 0.0177272i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.39445 | + | 2.28036i | −0.380370 | + | 0.0923290i | ||||
\(611\) | −1.28640 | − | 3.10563i | −0.0520420 | − | 0.125641i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.37874 | + | 0.571093i | 0.0556868 | + | 0.0230662i | 0.410353 | − | 0.911927i | \(-0.365405\pi\) |
−0.354666 | + | 0.934993i | \(0.615405\pi\) | |||||||
\(614\) | −7.62184 | − | 10.4354i | −0.307592 | − | 0.421138i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −52.0480 | − | 26.0281i | −2.09707 | − | 1.04870i | ||||
\(617\) | −20.4851 | + | 20.4851i | −0.824698 | + | 0.824698i | −0.986778 | − | 0.162080i | \(-0.948180\pi\) |
0.162080 | + | 0.986778i | \(0.448180\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.2969 | − | 32.1015i | 0.534447 | − | 1.29027i | −0.394105 | − | 0.919065i | \(-0.628945\pi\) |
0.928552 | − | 0.371203i | \(-0.121055\pi\) | |||||||
\(620\) | −4.01234 | + | 0.336049i | −0.161139 | + | 0.0134961i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 35.5992 | + | 21.6925i | 1.42740 | + | 0.869792i | ||||
\(623\) | 31.9246i | 1.27903i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.40633i | 0.0962532i | ||||||||
\(626\) | 14.6767 | − | 24.0857i | 0.586601 | − | 0.962660i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.4034 | + | 9.64086i | 0.455045 | + | 0.384712i | ||||
\(629\) | −3.33900 | + | 8.06106i | −0.133135 | + | 0.321415i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.04327 | − | 2.04327i | 0.0813412 | − | 0.0813412i | −0.665266 | − | 0.746607i | \(-0.731682\pi\) |
0.746607 | + | 0.665266i | \(0.231682\pi\) | |||||||
\(632\) | 0.332194 | − | 0.288074i | 0.0132140 | − | 0.0114590i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.20235 | + | 2.33894i | −0.127181 | + | 0.0928912i | ||||
\(635\) | 19.2918 | + | 7.99093i | 0.765572 | + | 0.317110i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.63325 | − | 6.35724i | −0.104333 | − | 0.251883i | ||||
\(638\) | 5.73440 | + | 23.6242i | 0.227027 | + | 0.935289i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14.1014 | + | 4.30947i | 0.557405 | + | 0.170347i | ||||
\(641\) | 20.3790 | 0.804922 | 0.402461 | − | 0.915437i | \(-0.368155\pi\) | ||||
0.402461 | + | 0.915437i | \(0.368155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.75816 | + | 11.4872i | 0.187644 | + | 0.453012i | 0.989505 | − | 0.144498i | \(-0.0461568\pi\) |
−0.801861 | + | 0.597510i | \(0.796157\pi\) | |||||||
\(644\) | −34.1408 | + | 17.6120i | −1.34533 | + | 0.694010i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.88576 | + | 5.02925i | −0.270917 | + | 0.197873i | ||||
\(647\) | −8.97597 | − | 8.97597i | −0.352882 | − | 0.352882i | 0.508299 | − | 0.861181i | \(-0.330274\pi\) |
−0.861181 | + | 0.508299i | \(0.830274\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −38.4329 | + | 38.4329i | −1.50862 | + | 1.50862i | ||||
\(650\) | 0.765651 | − | 4.91391i | 0.0300313 | − | 0.192740i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.82495 | − | 3.23375i | −0.149797 | − | 0.126644i | ||||
\(653\) | −42.2027 | + | 17.4809i | −1.65152 | + | 0.684082i | −0.997383 | − | 0.0722952i | \(-0.976968\pi\) |
−0.654136 | + | 0.756377i | \(0.726968\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 7.44549i | − | 0.290919i | ||||||
\(656\) | −1.04318 | − | 6.18395i | −0.0407293 | − | 0.241443i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.9824 | + | 8.52023i | 0.545091 | + | 0.332153i | ||||
\(659\) | −5.50356 | + | 2.27965i | −0.214388 | + | 0.0888025i | −0.487293 | − | 0.873239i | \(-0.662016\pi\) |
0.272905 | + | 0.962041i | \(0.412016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5581 | + | 42.3890i | −0.682931 | + | 1.64874i | 0.0756260 | + | 0.997136i | \(0.475905\pi\) |
−0.758557 | + | 0.651606i | \(0.774095\pi\) | |||||||
\(662\) | 5.03153 | + | 0.783978i | 0.195556 | + | 0.0304702i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.0704 | − | 7.03632i | −0.546039 | − | 0.273062i | ||||
\(665\) | 20.8218 | + | 20.8218i | 0.807436 | + | 0.807436i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.8266 | + | 6.14136i | 0.574087 | + | 0.237795i | ||||
\(668\) | 9.72379 | + | 3.10558i | 0.376225 | + | 0.120159i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.35352 | − | 1.29948i | 0.206824 | − | 0.0502034i | ||||
\(671\) | 29.4137 | 1.13550 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.4979 | −0.558853 | −0.279427 | − | 0.960167i | \(-0.590144\pi\) | ||||
−0.279427 | + | 0.960167i | \(0.590144\pi\) | |||||||
\(674\) | −0.651075 | + | 0.158038i | −0.0250785 | + | 0.00608741i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.21985 | − | 22.6058i | 0.277687 | − | 0.869456i | ||||
\(677\) | 11.0022 | + | 4.55726i | 0.422849 | + | 0.175150i | 0.583953 | − | 0.811788i | \(-0.301505\pi\) |
−0.161104 | + | 0.986937i | \(0.551505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.3183 | + | 37.3183i | 1.43215 | + | 1.43215i | ||||
\(680\) | 3.42394 | − | 1.14107i | 0.131302 | − | 0.0437582i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.1047 | + | 1.88606i | 0.463511 | + | 0.0722211i | ||||
\(683\) | 3.03396 | − | 7.32464i | 0.116091 | − | 0.280269i | −0.855144 | − | 0.518390i | \(-0.826531\pi\) |
0.971236 | + | 0.238121i | \(0.0765314\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.7053 | − | 6.09114i | 0.561861 | − | 0.232730i | ||||
\(686\) | −2.39267 | − | 1.45799i | −0.0913527 | − | 0.0556662i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.2665 | + | 30.7431i | 0.734529 | + | 1.17207i | ||||
\(689\) | 7.10479i | 0.270671i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.8871 | + | 9.06592i | −0.832623 | + | 0.344884i | −0.757941 | − | 0.652324i | \(-0.773794\pi\) |
−0.0746825 | + | 0.997207i | \(0.523794\pi\) | |||||||
\(692\) | −3.03229 | + | 3.58666i | −0.115270 | + | 0.136344i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.20767 | − | 14.1687i | 0.0838021 | − | 0.537837i | ||||
\(695\) | −9.76203 | + | 9.76203i | −0.370295 | + | 0.370295i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.08540 | − | 1.08540i | −0.0411125 | − | 0.0411125i | ||||
\(698\) | −6.09482 | + | 4.45156i | −0.230692 | + | 0.168494i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 11.1058 | + | 21.5285i | 0.419760 | + | 0.813702i | ||||
\(701\) | −18.8146 | − | 45.4224i | −0.710617 | − | 1.71558i | −0.698453 | − | 0.715656i | \(-0.746128\pi\) |
−0.0121647 | − | 0.999926i | \(-0.503872\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −54.8829 | −2.06995 | ||||||||
\(704\) | −38.6012 | − | 22.8626i | −1.45484 | − | 0.861668i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.5818 | + | 47.7138i | 0.435886 | + | 1.79573i | ||||
\(707\) | −18.4180 | − | 44.4650i | −0.692681 | − | 1.67228i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.5420 | − | 9.33718i | −0.846581 | − | 0.350665i | −0.0831359 | − | 0.996538i | \(-0.526494\pi\) |
−0.763445 | + | 0.645873i | \(0.776494\pi\) | |||||||
\(710\) | −21.1278 | + | 15.4314i | −0.792911 | + | 0.579129i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.74627 | + | 24.5501i | −0.0654442 | + | 0.920053i | ||||
\(713\) | 5.71852 | − | 5.71852i | 0.214160 | − | 0.214160i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.97928 | − | 7.19263i | 0.111419 | − | 0.268989i | ||||
\(716\) | −3.72444 | + | 4.40534i | −0.139189 | + | 0.164635i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.22940 | − | 6.94078i | 0.157840 | − | 0.259028i | ||||
\(719\) | 38.2799i | 1.42760i | 0.700350 | + | 0.713800i | \(0.253027\pi\) | ||||
−0.700350 | + | 0.713800i | \(0.746973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 53.4707i | − | 1.99135i | ||||||
\(722\) | −22.8560 | − | 13.9274i | −0.850611 | − | 0.518323i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.483665 | − | 5.77484i | −0.0179753 | − | 0.214620i | ||||
\(725\) | 3.87263 | − | 9.34936i | 0.143826 | − | 0.347226i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.75063 | + | 2.75063i | −0.102015 | + | 0.102015i | −0.756272 | − | 0.654257i | \(-0.772981\pi\) |
0.654257 | + | 0.756272i | \(0.272981\pi\) | |||||||
\(728\) | −3.49468 | − | 10.4862i | −0.129522 | − | 0.388646i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.4700 | − | 17.0732i | −0.461534 | − | 0.631906i | ||||
\(731\) | 8.20436 | + | 3.39836i | 0.303449 | + | 0.125693i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.75290 | − | 16.3029i | −0.249424 | − | 0.602163i | 0.748731 | − | 0.662874i | \(-0.230663\pi\) |
−0.998155 | + | 0.0607106i | \(0.980663\pi\) | |||||||
\(734\) | 41.6067 | − | 10.0994i | 1.53573 | − | 0.372775i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −27.2177 | + | 11.6761i | −1.00326 | + | 0.430389i | ||||
\(737\) | −16.7617 | −0.617424 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.62421 | + | 23.2349i | 0.354032 | + | 0.854709i | 0.996114 | + | 0.0880732i | \(0.0280709\pi\) |
−0.642082 | + | 0.766636i | \(0.721929\pi\) | |||||||
\(740\) | 22.1286 | + | 7.06742i | 0.813463 | + | 0.259803i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.4118 | − | 27.9467i | −0.749340 | − | 1.02595i | ||||
\(743\) | 32.2711 | + | 32.2711i | 1.18391 | + | 1.18391i | 0.978722 | + | 0.205192i | \(0.0657817\pi\) |
0.205192 | + | 0.978722i | \(0.434218\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.66218 | + | 2.66218i | −0.0975347 | + | 0.0975347i | ||||
\(746\) | −30.8998 | − | 4.81459i | −1.13132 | − | 0.176275i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.9427 | + | 0.916493i | −0.400104 | + | 0.0335103i | ||||
\(749\) | 5.10921 | − | 2.11630i | 0.186687 | − | 0.0773281i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2.67256i | − | 0.0975231i | −0.998810 | − | 0.0487616i | \(-0.984473\pi\) | ||
0.998810 | − | 0.0487616i | \(-0.0155274\pi\) | |||||||
\(752\) | 10.2864 | + | 7.31690i | 0.375107 | + | 0.266820i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.40274 | + | 3.94309i | −0.0875025 | + | 0.143599i | ||||
\(755\) | 10.9065 | − | 4.51762i | 0.396928 | − | 0.164413i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.38519 | + | 22.6579i | −0.341111 | + | 0.823514i | 0.656493 | + | 0.754332i | \(0.272039\pi\) |
−0.997604 | + | 0.0691822i | \(0.977961\pi\) | |||||||
\(758\) | 5.02268 | − | 32.2353i | 0.182432 | − | 1.17084i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 14.8731 | + | 17.1510i | 0.539502 | + | 0.622130i | ||||
\(761\) | 12.8473 | + | 12.8473i | 0.465714 | + | 0.465714i | 0.900523 | − | 0.434809i | \(-0.143184\pi\) |
−0.434809 | + | 0.900523i | \(0.643184\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40.6275 | − | 16.8285i | −1.47081 | − | 0.609231i | ||||
\(764\) | 14.8469 | − | 7.65898i | 0.537142 | − | 0.277092i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.53106 | − | 35.1457i | −0.308240 | − | 1.26986i | ||||
\(767\) | −10.3237 | −0.372767 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.9481 | 0.575102 | 0.287551 | − | 0.957765i | \(-0.407159\pi\) | ||||
0.287551 | + | 0.957765i | \(0.407159\pi\) | |||||||
\(770\) | 8.94514 | + | 36.8515i | 0.322361 | + | 1.32804i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.9247 | − | 11.3101i | 0.789086 | − | 0.407061i | ||||
\(773\) | −4.77420 | − | 1.97754i | −0.171716 | − | 0.0711271i | 0.295169 | − | 0.955445i | \(-0.404624\pi\) |
−0.466885 | + | 0.884318i | \(0.654624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.60599 | − | 3.60599i | −0.129531 | − | 0.129531i | ||||
\(776\) | 26.6565 | + | 30.7391i | 0.956914 | + | 1.10347i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.281953 | − | 1.80956i | 0.0101085 | − | 0.0648760i | ||||
\(779\) | 3.69493 | − | 8.92034i | 0.132385 | − | 0.319604i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 73.5447 | − | 30.4632i | 2.63164 | − | 1.09006i | ||||
\(782\) | −3.77208 | + | 6.19029i | −0.134889 | + | 0.221364i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21.0563 | + | 14.9777i | 0.752011 | + | 0.534918i | ||||
\(785\) | − | 9.73086i | − | 0.347309i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.1033 | + | 5.84179i | −0.502730 | + | 0.208237i | −0.619612 | − | 0.784908i | \(-0.712710\pi\) |
0.116882 | + | 0.993146i | \(0.462710\pi\) | |||||||
\(788\) | −46.4137 | + | 3.88733i | −1.65342 | + | 0.138480i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.283117 | − | 0.0441133i | −0.0100728 | − | 0.00156948i | ||||
\(791\) | 24.4152 | − | 24.4152i | 0.868106 | − | 0.868106i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.95049 | + | 3.95049i | 0.140286 | + | 0.140286i | ||||
\(794\) | −4.94048 | − | 6.76422i | −0.175331 | − | 0.240053i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45.8938 | + | 14.6575i | 1.62666 | + | 0.519523i | ||||
\(797\) | 15.7714 | + | 38.0755i | 0.558652 | + | 1.34870i | 0.910834 | + | 0.412773i | \(0.135440\pi\) |
−0.352182 | + | 0.935931i | \(0.614560\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.08972 | 0.109306 | ||||||||
\(800\) | 7.36276 | + | 17.1630i | 0.260313 | + | 0.606802i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 45.7361 | − | 11.1017i | 1.61500 | − | 0.392015i | ||||
\(803\) | 24.6171 | + | 59.4308i | 0.868717 | + | 2.09727i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23.1281 | + | 9.57997i | 0.815158 | + | 0.337650i | ||||
\(806\) | 1.37244 | + | 1.87907i | 0.0483421 | + | 0.0661872i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.7313 | − | 35.2011i | −0.412704 | − | 1.23837i | ||||
\(809\) | 22.3087 | − | 22.3087i | 0.784333 | − | 0.784333i | −0.196226 | − | 0.980559i | \(-0.562869\pi\) |
0.980559 | + | 0.196226i | \(0.0628685\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.0179 | + | 41.0848i | −0.597579 | + | 1.44268i | 0.278462 | + | 0.960447i | \(0.410175\pi\) |
−0.876041 | + | 0.482236i | \(0.839825\pi\) | |||||||
\(812\) | −1.87718 | − | 22.4131i | −0.0658762 | − | 0.786545i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −60.3563 | − | 36.7784i | −2.11549 | − | 1.28908i | ||||
\(815\) | 3.26394i | 0.114331i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 55.8586i | 1.95425i | ||||||||
\(818\) | 7.70680 | − | 12.6475i | 0.269462 | − | 0.442209i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.63848 | + | 3.12084i | −0.0921395 | + | 0.108984i | ||||
\(821\) | −4.17316 | + | 10.0749i | −0.145644 | + | 0.351616i | −0.979820 | − | 0.199883i | \(-0.935944\pi\) |
0.834176 | + | 0.551499i | \(0.185944\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.0647 | + | 21.0647i | −0.734269 | + | 0.734269i | −0.971462 | − | 0.237194i | \(-0.923772\pi\) |
0.237194 | + | 0.971462i | \(0.423772\pi\) | |||||||
\(824\) | 2.92483 | − | 41.1190i | 0.101891 | − | 1.43245i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 40.6082 | − | 29.6596i | 1.41294 | − | 1.03199i | ||||
\(827\) | 51.5584 | + | 21.3562i | 1.79286 | + | 0.742627i | 0.989020 | + | 0.147782i | \(0.0472134\pi\) |
0.803840 | + | 0.594845i | \(0.202787\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.1450 | + | 29.3206i | 0.421813 | + | 1.01835i | 0.981812 | + | 0.189853i | \(0.0608013\pi\) |
−0.560000 | + | 0.828493i | \(0.689199\pi\) | |||||||
\(830\) | 2.41819 | + | 9.96229i | 0.0839367 | + | 0.345796i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.11382 | − | 8.25508i | −0.0732835 | − | 0.286194i | ||||
\(833\) | 6.32466 | 0.219136 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.54555 | − | 6.14550i | −0.0880924 | − | 0.212674i | ||||
\(836\) | −31.6666 | − | 61.3855i | −1.09521 | − | 2.12306i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.1900 | − | 14.0161i | 0.662907 | − | 0.484177i | ||||
\(839\) | −21.1653 | − | 21.1653i | −0.730706 | − | 0.730706i | 0.240054 | − | 0.970760i | \(-0.422835\pi\) |
−0.970760 | + | 0.240054i | \(0.922835\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.8623 | − | 13.8623i | 0.478009 | − | 0.478009i | ||||
\(842\) | 1.32162 | − | 8.48212i | 0.0455462 | − | 0.292313i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.3907 | − | 14.6560i | 0.426506 | − | 0.504480i | ||||
\(845\) | −14.2870 | + | 5.91788i | −0.491489 | + | 0.203581i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 75.0241i | − | 2.57786i | ||||||
\(848\) | −14.1680 | − | 22.6075i | −0.486532 | − | 0.776346i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.90348 | + | 2.37860i | 0.133888 | + | 0.0815854i | ||||
\(851\) | −43.1066 | + | 17.8553i | −1.47767 | + | 0.612073i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.84996 | − | 16.5373i | 0.234538 | − | 0.566225i | −0.762163 | − | 0.647385i | \(-0.775863\pi\) |
0.996701 | + | 0.0811601i | \(0.0258625\pi\) | |||||||
\(854\) | −26.8888 | − | 4.18963i | −0.920116 | − | 0.143366i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.04475 | − | 1.34797i | 0.138247 | − | 0.0460726i | ||||
\(857\) | 33.6370 | + | 33.6370i | 1.14902 | + | 1.14902i | 0.986746 | + | 0.162272i | \(0.0518822\pi\) |
0.162272 | + | 0.986746i | \(0.448118\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.7350 | + | 14.8019i | 1.21926 | + | 0.505035i | 0.897175 | − | 0.441674i | \(-0.145615\pi\) |
0.322088 | + | 0.946710i | \(0.395615\pi\) | |||||||
\(860\) | 7.19306 | − | 22.5220i | 0.245281 | − | 0.767992i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.408396 | + | 0.0991319i | −0.0139100 | + | 0.00337645i | ||||
\(863\) | −44.4296 | −1.51240 | −0.756201 | − | 0.654340i | \(-0.772947\pi\) | ||||
−0.756201 | + | 0.654340i | \(0.772947\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.06060 | 0.104064 | ||||||||
\(866\) | −21.1807 | + | 5.14128i | −0.719749 | + | 0.174708i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.7970 | − | 3.44833i | −0.366473 | − | 0.117044i | ||||
\(869\) | 0.805445 | + | 0.333626i | 0.0273228 | + | 0.0113175i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.25122 | − | 2.25122i | −0.0762798 | − | 0.0762798i | ||||
\(872\) | −30.3221 | − | 15.1634i | −1.02683 | − | 0.513498i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −45.0538 | − | 7.01996i | −1.52397 | − | 0.237454i | ||||
\(875\) | 15.1900 | − | 36.6719i | 0.513516 | − | 1.23974i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.7336 | − | 13.1445i | 1.07157 | − | 0.443857i | 0.224023 | − | 0.974584i | \(-0.428081\pi\) |
0.847543 | + | 0.530727i | \(0.178081\pi\) | |||||||
\(878\) | 5.38418 | + | 3.28087i | 0.181707 | + | 0.110724i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.86306 | + | 28.8282i | 0.163934 | + | 0.971798i | ||||
\(881\) | 42.6814i | 1.43797i | 0.695023 | + | 0.718987i | \(0.255394\pi\) | ||||
−0.695023 | + | 0.718987i | \(0.744606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.4520 | − | 9.29994i | 0.755571 | − | 0.312968i | 0.0285587 | − | 0.999592i | \(-0.490908\pi\) |
0.727012 | + | 0.686624i | \(0.240908\pi\) | |||||||
\(884\) | −1.59278 | − | 1.34660i | −0.0535710 | − | 0.0452910i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.661386 | + | 4.24474i | −0.0222197 | + | 0.142605i | ||||
\(887\) | 25.1413 | − | 25.1413i | 0.844161 | − | 0.844161i | −0.145236 | − | 0.989397i | \(-0.546394\pi\) |
0.989397 | + | 0.145236i | \(0.0463941\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41.5643 | + | 41.5643i | 1.39402 | + | 1.39402i | ||||
\(890\) | 12.9517 | − | 9.45972i | 0.434142 | − | 0.317091i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.2816 | + | 6.33565i | −0.411220 | + | 0.212133i | ||||
\(893\) | 7.43737 | + | 17.9554i | 0.248882 | + | 0.600855i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.75920 | 0.125656 | ||||||||
\(896\) | 32.0312 | + | 26.3984i | 1.07009 | + | 0.881909i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.19331 | − | 4.91609i | −0.0398211 | − | 0.164052i | ||||
\(899\) | 1.81196 | + | 4.37445i | 0.0604321 | + | 0.145896i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.03324 | − | 2.49905i | −0.200996 | − | 0.0832554i | ||||
\(902\) | 10.0412 | − | 7.33389i | 0.334334 | − | 0.244192i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.1108 | − | 17.4398i | 0.668877 | − | 0.580040i | ||||
\(905\) | −2.67028 | + | 2.67028i | −0.0887632 | + | 0.0887632i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.9664 | − | 36.1321i | 0.496951 | − | 1.19975i | −0.454167 | − | 0.890917i | \(-0.650063\pi\) |
0.951118 | − | 0.308829i | \(-0.0999371\pi\) | |||||||
\(908\) | 6.58974 | + | 5.57121i | 0.218688 | + | 0.184887i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.74805 | + | 6.15086i | −0.124247 | + | 0.203899i | ||||
\(911\) | − | 23.3974i | − | 0.775190i | −0.921830 | − | 0.387595i | \(-0.873306\pi\) | ||
0.921830 | − | 0.387595i | \(-0.126694\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 31.1915i | − | 1.03229i | ||||||
\(914\) | 15.3345 | + | 9.34413i | 0.507220 | + | 0.309076i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.2963 | + | 1.28113i | −0.505405 | + | 0.0423297i | ||||
\(917\) | 8.02067 | − | 19.3636i | 0.264866 | − | 0.639442i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.8473 | − | 20.8473i | 0.687689 | − | 0.687689i | −0.274032 | − | 0.961721i | \(-0.588357\pi\) |
0.961721 | + | 0.274032i | \(0.0883574\pi\) | |||||||
\(920\) | 17.2615 | + | 8.63211i | 0.569095 | + | 0.284592i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.5192 | − | 32.2011i | −0.774563 | − | 1.06049i | ||||
\(923\) | 13.9691 | + | 5.78618i | 0.459798 | + | 0.190455i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.2592 | + | 27.1822i | 0.370202 | + | 0.893746i | ||||
\(926\) | 15.0874 | − | 3.66223i | 0.495802 | − | 0.120348i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.217567 | − | 17.3384i | −0.00714199 | − | 0.569160i | ||||
\(929\) | −55.9215 | −1.83472 | −0.917362 | − | 0.398055i | \(-0.869685\pi\) | ||||
−0.917362 | + | 0.398055i | \(0.869685\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.2243 | + | 36.7547i | 0.498956 | + | 1.20459i | ||||
\(932\) | −1.28572 | + | 4.02568i | −0.0421152 | + | 0.131865i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34.7947 | + | 47.6389i | 1.13852 | + | 1.55879i | ||||
\(935\) | 5.05989 | + | 5.05989i | 0.165476 | + | 0.165476i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.6178 | − | 31.6178i | 1.03291 | − | 1.03291i | 0.0334692 | − | 0.999440i | \(-0.489344\pi\) |
0.999440 | − | 0.0334692i | \(-0.0106556\pi\) | |||||||
\(938\) | 15.3229 | + | 2.38750i | 0.500309 | + | 0.0779546i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.686554 | − | 8.19727i | −0.0223929 | − | 0.267366i | ||||
\(941\) | −23.4212 | + | 9.70137i | −0.763509 | + | 0.316256i | −0.730240 | − | 0.683191i | \(-0.760592\pi\) |
−0.0332688 | + | 0.999446i | \(0.510592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.20837i | − | 0.267301i | ||||||
\(944\) | 32.8501 | − | 20.5870i | 1.06918 | − | 0.670049i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −37.4322 | + | 61.4293i | −1.21703 | + | 1.99724i | ||||
\(947\) | −30.2016 | + | 12.5099i | −0.981419 | + | 0.406517i | −0.814951 | − | 0.579530i | \(-0.803236\pi\) |
−0.166468 | + | 0.986047i | \(0.553236\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.67577 | + | 11.2883i | −0.151782 | + | 0.366434i | ||||
\(950\) | −4.42666 | + | 28.4101i | −0.143620 | + | 0.921744i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.1339 | + | 0.720834i | 0.328442 | + | 0.0233624i | ||||
\(953\) | 17.7752 | + | 17.7752i | 0.575795 | + | 0.575795i | 0.933742 | − | 0.357947i | \(-0.116523\pi\) |
−0.357947 | + | 0.933742i | \(0.616523\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0578 | − | 4.16607i | −0.325462 | − | 0.134811i | ||||
\(956\) | 4.96245 | + | 9.61969i | 0.160497 | + | 0.311123i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.95293 | + | 28.6442i | 0.224639 | + | 0.925451i | ||||
\(959\) | 44.8060 | 1.44686 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6139 | −0.923030 | ||||||||
\(962\) | −3.16670 | − | 13.0460i | −0.102099 | − | 0.420619i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.0342 | − | 34.9592i | −0.580843 | − | 1.12596i | ||||
\(965\) | −14.8525 | − | 6.15211i | −0.478119 | − | 0.198043i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.23073 | + | 5.23073i | 0.168209 | + | 0.168209i | 0.786192 | − | 0.617983i | \(-0.212050\pi\) |
−0.617983 | + | 0.786192i | \(0.712050\pi\) | |||||||
\(968\) | 4.10380 | − | 57.6936i | 0.131901 | − | 1.85434i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.08197 | − | 26.1979i | 0.131064 | − | 0.841162i | ||||
\(971\) | −6.01158 | + | 14.5132i | −0.192921 | + | 0.465752i | −0.990509 | − | 0.137451i | \(-0.956109\pi\) |
0.797588 | + | 0.603203i | \(0.206109\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.9044 | + | 14.8721i | −1.15104 | + | 0.476778i | ||||
\(974\) | −16.9726 | + | 27.8535i | −0.543838 | + | 0.892482i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.4484 | − | 4.69264i | −0.654536 | − | 0.150208i | ||||
\(977\) | − | 48.6725i | − | 1.55717i | −0.627539 | − | 0.778585i | \(-0.715938\pi\) | ||
0.627539 | − | 0.778585i | \(-0.284062\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −45.0842 | + | 18.6745i | −1.44090 | + | 0.596840i | ||||
\(980\) | −1.40538 | − | 16.7798i | −0.0448931 | − | 0.536012i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.12973 | − | 1.26672i | −0.259430 | − | 0.0404226i | ||||
\(983\) | −7.17484 | + | 7.17484i | −0.228842 | + | 0.228842i | −0.812209 | − | 0.583367i | \(-0.801735\pi\) |
0.583367 | + | 0.812209i | \(0.301735\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.4617 | + | 21.4617i | 0.683826 | + | 0.683826i | ||||
\(986\) | −2.50324 | − | 3.42730i | −0.0797195 | − | 0.109147i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.99149 | − | 12.4976i | 0.126986 | − | 0.397603i | ||||
\(989\) | 18.1727 | + | 43.8729i | 0.577860 | + | 1.39508i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.8957 | −0.663774 | −0.331887 | − | 0.943319i | \(-0.607685\pi\) | ||||
−0.331887 | + | 0.943319i | \(0.607685\pi\) | |||||||
\(992\) | −8.11425 | − | 3.24236i | −0.257628 | − | 0.102945i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −71.5708 | + | 17.3727i | −2.27009 | + | 0.551029i | ||||
\(995\) | −12.0143 | − | 29.0051i | −0.380880 | − | 0.919525i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.3465 | − | 20.0258i | −1.53115 | − | 0.634223i | −0.551363 | − | 0.834266i | \(-0.685892\pi\) |
−0.979787 | + | 0.200042i | \(0.935892\pi\) | |||||||
\(998\) | −8.48550 | − | 11.6179i | −0.268604 | − | 0.367757i | ||||
\(999\) | 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 | 288.2.v.d.37.5 | 32 | ||
3.2 | odd | 2 | 96.2.n.a.37.4 | yes | 32 | ||
4.3 | odd | 2 | 1152.2.v.c.1009.5 | 32 | |||
12.11 | even | 2 | 384.2.n.a.241.2 | 32 | |||
24.5 | odd | 2 | 768.2.n.a.481.3 | 32 | |||
24.11 | even | 2 | 768.2.n.b.481.7 | 32 | |||
32.13 | even | 8 | inner | 288.2.v.d.109.5 | 32 | ||
32.19 | odd | 8 | 1152.2.v.c.145.5 | 32 | |||
96.29 | odd | 8 | 768.2.n.a.289.3 | 32 | |||
96.35 | even | 8 | 768.2.n.b.289.7 | 32 | |||
96.77 | odd | 8 | 96.2.n.a.13.4 | ✓ | 32 | ||
96.83 | even | 8 | 384.2.n.a.145.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.n.a.13.4 | ✓ | 32 | 96.77 | odd | 8 | ||
96.2.n.a.37.4 | yes | 32 | 3.2 | odd | 2 | ||
288.2.v.d.37.5 | 32 | 1.1 | even | 1 | trivial | ||
288.2.v.d.109.5 | 32 | 32.13 | even | 8 | inner | ||
384.2.n.a.145.2 | 32 | 96.83 | even | 8 | |||
384.2.n.a.241.2 | 32 | 12.11 | even | 2 | |||
768.2.n.a.289.3 | 32 | 96.29 | odd | 8 | |||
768.2.n.a.481.3 | 32 | 24.5 | odd | 2 | |||
768.2.n.b.289.7 | 32 | 96.35 | even | 8 | |||
768.2.n.b.481.7 | 32 | 24.11 | even | 2 | |||
1152.2.v.c.145.5 | 32 | 32.19 | odd | 8 | |||
1152.2.v.c.1009.5 | 32 | 4.3 | odd | 2 |