Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(49,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.1 | ||
Root | \(-0.228425 + 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.349 |
Dual form | 950.2.j.h.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −2.41733 | + | 1.39564i | −1.39564 | + | 0.805775i | −0.993933 | − | 0.109991i | \(-0.964918\pi\) |
−0.401711 | + | 0.915766i | \(0.631584\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.39564 | − | 2.41733i | 0.569769 | − | 0.986869i | ||||
\(7\) | 1.00000i | 0.377964i | 0.981981 | + | 0.188982i | \(0.0605189\pi\) | ||||
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.39564 | − | 4.14938i | 0.798548 | − | 1.38313i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.79129 | −1.14312 | −0.571558 | − | 0.820562i | \(-0.693661\pi\) | ||||
−0.571558 | + | 0.820562i | \(0.693661\pi\) | |||||||
\(12\) | 2.79129i | 0.805775i | ||||||||
\(13\) | 0.180750 | + | 0.104356i | 0.0501310 | + | 0.0289432i | 0.524856 | − | 0.851191i | \(-0.324119\pi\) |
−0.474725 | + | 0.880134i | \(0.657452\pi\) | |||||||
\(14\) | −0.500000 | − | 0.866025i | −0.133631 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.685275 | − | 0.395644i | 0.166204 | − | 0.0959577i | −0.414591 | − | 0.910008i | \(-0.636075\pi\) |
0.580795 | + | 0.814050i | \(0.302742\pi\) | |||||||
\(18\) | 4.79129i | 1.12932i | ||||||||
\(19\) | 3.50000 | − | 2.59808i | 0.802955 | − | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.39564 | − | 2.41733i | −0.304554 | − | 0.527504i | ||||
\(22\) | 3.28335 | − | 1.89564i | 0.700013 | − | 0.404153i | ||||
\(23\) | −3.96863 | − | 2.29129i | −0.827516 | − | 0.477767i | 0.0254855 | − | 0.999675i | \(-0.491887\pi\) |
−0.853001 | + | 0.521909i | \(0.825220\pi\) | |||||||
\(24\) | −1.39564 | − | 2.41733i | −0.284885 | − | 0.493435i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.208712 | −0.0409318 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 0.866025 | + | 0.500000i | 0.163663 | + | 0.0944911i | ||||
\(29\) | 3.39564 | − | 5.88143i | 0.630555 | − | 1.09215i | −0.356883 | − | 0.934149i | \(-0.616161\pi\) |
0.987438 | − | 0.158005i | \(-0.0505061\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.79129 | −0.860541 | −0.430270 | − | 0.902700i | \(-0.641582\pi\) | ||||
−0.430270 | + | 0.902700i | \(0.641582\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 9.16478 | − | 5.29129i | 1.59538 | − | 0.921095i | ||||
\(34\) | −0.395644 | + | 0.685275i | −0.0678524 | + | 0.117524i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.39564 | − | 4.14938i | −0.399274 | − | 0.691563i | ||||
\(37\) | − | 3.58258i | − | 0.588972i | −0.955656 | − | 0.294486i | \(-0.904852\pi\) | ||
0.955656 | − | 0.294486i | \(-0.0951484\pi\) | |||||||
\(38\) | −1.73205 | + | 4.00000i | −0.280976 | + | 0.648886i | ||||
\(39\) | −0.582576 | −0.0932868 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.68693 | + | 9.85005i | 0.888150 | + | 1.53832i | 0.842061 | + | 0.539383i | \(0.181342\pi\) |
0.0460888 | + | 0.998937i | \(0.485324\pi\) | |||||||
\(42\) | 2.41733 | + | 1.39564i | 0.373002 | + | 0.215353i | ||||
\(43\) | 5.01540 | − | 2.89564i | 0.764842 | − | 0.441582i | −0.0661897 | − | 0.997807i | \(-0.521084\pi\) |
0.831031 | + | 0.556225i | \(0.187751\pi\) | |||||||
\(44\) | −1.89564 | + | 3.28335i | −0.285779 | + | 0.494984i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.58258 | 0.675664 | ||||||||
\(47\) | −10.5353 | − | 6.08258i | −1.53674 | − | 0.887235i | −0.999027 | − | 0.0441043i | \(-0.985957\pi\) |
−0.537709 | − | 0.843131i | \(-0.680710\pi\) | |||||||
\(48\) | 2.41733 | + | 1.39564i | 0.348911 | + | 0.201444i | ||||
\(49\) | 6.00000 | 0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.10436 | + | 1.91280i | −0.154641 | + | 0.267846i | ||||
\(52\) | 0.180750 | − | 0.104356i | 0.0250655 | − | 0.0144716i | ||||
\(53\) | 3.96863 | + | 2.29129i | 0.545133 | + | 0.314733i | 0.747157 | − | 0.664648i | \(-0.231418\pi\) |
−0.202024 | + | 0.979381i | \(0.564752\pi\) | |||||||
\(54\) | −2.50000 | − | 4.33013i | −0.340207 | − | 0.589256i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −4.83465 | + | 11.1652i | −0.640365 | + | 1.47886i | ||||
\(58\) | 6.79129i | 0.891740i | ||||||||
\(59\) | 2.29129 | + | 3.96863i | 0.298300 | + | 0.516671i | 0.975747 | − | 0.218900i | \(-0.0702470\pi\) |
−0.677447 | + | 0.735572i | \(0.736914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.686932 | + | 1.18980i | −0.0879526 | + | 0.152338i | −0.906646 | − | 0.421893i | \(-0.861366\pi\) |
0.818693 | + | 0.574232i | \(0.194699\pi\) | |||||||
\(62\) | 4.14938 | − | 2.39564i | 0.526971 | − | 0.304247i | ||||
\(63\) | 4.14938 | + | 2.39564i | 0.522772 | + | 0.301823i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.29129 | + | 9.16478i | −0.651313 | + | 1.12811i | ||||
\(67\) | 13.4949 | + | 7.79129i | 1.64867 | + | 0.951857i | 0.977603 | + | 0.210456i | \(0.0674949\pi\) |
0.671062 | + | 0.741401i | \(0.265838\pi\) | |||||||
\(68\) | − | 0.791288i | − | 0.0959577i | ||||||
\(69\) | 12.7913 | 1.53989 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.29129 | + | 3.96863i | 0.271926 | + | 0.470989i | 0.969355 | − | 0.245664i | \(-0.0790061\pi\) |
−0.697429 | + | 0.716654i | \(0.745673\pi\) | |||||||
\(72\) | 4.14938 | + | 2.39564i | 0.489009 | + | 0.282329i | ||||
\(73\) | 2.41733 | − | 1.39564i | 0.282927 | − | 0.163348i | −0.351821 | − | 0.936067i | \(-0.614437\pi\) |
0.634748 | + | 0.772720i | \(0.281104\pi\) | |||||||
\(74\) | 1.79129 | + | 3.10260i | 0.208233 | + | 0.360670i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.500000 | − | 4.33013i | −0.0573539 | − | 0.496700i | ||||
\(77\) | − | 3.79129i | − | 0.432057i | ||||||
\(78\) | 0.504525 | − | 0.291288i | 0.0571262 | − | 0.0329819i | ||||
\(79\) | 7.47822 | + | 12.9527i | 0.841365 | + | 1.45729i | 0.888741 | + | 0.458411i | \(0.151581\pi\) |
−0.0473751 | + | 0.998877i | \(0.515086\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.208712 | + | 0.361500i | 0.0231902 | + | 0.0401667i | ||||
\(82\) | −9.85005 | − | 5.68693i | −1.08776 | − | 0.628017i | ||||
\(83\) | 3.79129i | 0.416148i | 0.978113 | + | 0.208074i | \(0.0667195\pi\) | ||||
−0.978113 | + | 0.208074i | \(0.933281\pi\) | |||||||
\(84\) | −2.79129 | −0.304554 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.89564 | + | 5.01540i | −0.312245 | + | 0.540825i | ||||
\(87\) | 18.9564i | 2.03234i | ||||||||
\(88\) | − | 3.79129i | − | 0.404153i | ||||||
\(89\) | 2.29129 | − | 3.96863i | 0.242876 | − | 0.420674i | −0.718656 | − | 0.695365i | \(-0.755243\pi\) |
0.961532 | + | 0.274692i | \(0.0885758\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.104356 | + | 0.180750i | −0.0109395 | + | 0.0189478i | ||||
\(92\) | −3.96863 | + | 2.29129i | −0.413758 | + | 0.238883i | ||||
\(93\) | 11.5821 | − | 6.68693i | 1.20101 | − | 0.693403i | ||||
\(94\) | 12.1652 | 1.25474 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.79129 | −0.284885 | ||||||||
\(97\) | 10.7161 | − | 6.18693i | 1.08805 | − | 0.628188i | 0.154996 | − | 0.987915i | \(-0.450464\pi\) |
0.933057 | + | 0.359727i | \(0.117130\pi\) | |||||||
\(98\) | −5.19615 | + | 3.00000i | −0.524891 | + | 0.303046i | ||||
\(99\) | −9.08258 | + | 15.7315i | −0.912833 | + | 1.58107i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | − | 2.20871i | − | 0.218695i | ||||||
\(103\) | 5.16515i | 0.508937i | 0.967081 | + | 0.254469i | \(0.0819006\pi\) | ||||
−0.967081 | + | 0.254469i | \(0.918099\pi\) | |||||||
\(104\) | −0.104356 | + | 0.180750i | −0.0102330 | + | 0.0177240i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.58258 | −0.445099 | ||||||||
\(107\) | − | 18.9564i | − | 1.83259i | −0.400506 | − | 0.916294i | \(-0.631166\pi\) | ||
0.400506 | − | 0.916294i | \(-0.368834\pi\) | |||||||
\(108\) | 4.33013 | + | 2.50000i | 0.416667 | + | 0.240563i | ||||
\(109\) | −5.87386 | − | 10.1738i | −0.562614 | − | 0.974476i | −0.997267 | − | 0.0738783i | \(-0.976462\pi\) |
0.434653 | − | 0.900598i | \(-0.356871\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.00000 | + | 8.66025i | 0.474579 | + | 0.821995i | ||||
\(112\) | 0.866025 | − | 0.500000i | 0.0818317 | − | 0.0472456i | ||||
\(113\) | 5.37386i | 0.505531i | 0.967528 | + | 0.252765i | \(0.0813400\pi\) | ||||
−0.967528 | + | 0.252765i | \(0.918660\pi\) | |||||||
\(114\) | −1.39564 | − | 12.0866i | −0.130714 | − | 1.13202i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.39564 | − | 5.88143i | −0.315278 | − | 0.546077i | ||||
\(117\) | 0.866025 | − | 0.500000i | 0.0800641 | − | 0.0462250i | ||||
\(118\) | −3.96863 | − | 2.29129i | −0.365342 | − | 0.210930i | ||||
\(119\) | 0.395644 | + | 0.685275i | 0.0362686 | + | 0.0628191i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.37386 | 0.306715 | ||||||||
\(122\) | − | 1.37386i | − | 0.124384i | ||||||
\(123\) | −27.4943 | − | 15.8739i | −2.47908 | − | 1.43130i | ||||
\(124\) | −2.39564 | + | 4.14938i | −0.215135 | + | 0.372625i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.79129 | −0.426842 | ||||||||
\(127\) | 2.27430 | + | 1.31307i | 0.201812 | + | 0.116516i | 0.597500 | − | 0.801869i | \(-0.296161\pi\) |
−0.395689 | + | 0.918385i | \(0.629494\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −8.08258 | + | 13.9994i | −0.711631 | + | 1.23258i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.76951 | − | 9.99308i | −0.504084 | − | 0.873099i | −0.999989 | − | 0.00472247i | \(-0.998497\pi\) |
0.495905 | − | 0.868377i | \(-0.334837\pi\) | |||||||
\(132\) | − | 10.5826i | − | 0.921095i | ||||||
\(133\) | 2.59808 | + | 3.50000i | 0.225282 | + | 0.303488i | ||||
\(134\) | −15.5826 | −1.34613 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.395644 | + | 0.685275i | 0.0339262 | + | 0.0587619i | ||||
\(137\) | 13.2764 | + | 7.66515i | 1.13428 | + | 0.654878i | 0.945008 | − | 0.327046i | \(-0.106053\pi\) |
0.189274 | + | 0.981924i | \(0.439387\pi\) | |||||||
\(138\) | −11.0776 | + | 6.39564i | −0.942986 | + | 0.544433i | ||||
\(139\) | −6.10436 | + | 10.5731i | −0.517765 | + | 0.896795i | 0.482022 | + | 0.876159i | \(0.339902\pi\) |
−0.999787 | + | 0.0206359i | \(0.993431\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.9564 | 2.85965 | ||||||||
\(142\) | −3.96863 | − | 2.29129i | −0.333040 | − | 0.192281i | ||||
\(143\) | −0.685275 | − | 0.395644i | −0.0573056 | − | 0.0330854i | ||||
\(144\) | −4.79129 | −0.399274 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.39564 | + | 2.41733i | −0.115504 | + | 0.200059i | ||||
\(147\) | −14.5040 | + | 8.37386i | −1.19627 | + | 0.690665i | ||||
\(148\) | −3.10260 | − | 1.79129i | −0.255032 | − | 0.147243i | ||||
\(149\) | −11.3739 | − | 19.7001i | −0.931783 | − | 1.61390i | −0.780272 | − | 0.625440i | \(-0.784919\pi\) |
−0.151511 | − | 0.988456i | \(-0.548414\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.7477 | 1.28153 | 0.640766 | − | 0.767736i | \(-0.278617\pi\) | ||||
0.640766 | + | 0.767736i | \(0.278617\pi\) | |||||||
\(152\) | 2.59808 | + | 3.50000i | 0.210732 | + | 0.283887i | ||||
\(153\) | − | 3.79129i | − | 0.306507i | ||||||
\(154\) | 1.89564 | + | 3.28335i | 0.152755 | + | 0.264580i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.291288 | + | 0.504525i | −0.0233217 | + | 0.0403944i | ||||
\(157\) | 6.89048 | − | 3.97822i | 0.549920 | − | 0.317496i | −0.199170 | − | 0.979965i | \(-0.563824\pi\) |
0.749090 | + | 0.662469i | \(0.230491\pi\) | |||||||
\(158\) | −12.9527 | − | 7.47822i | −1.03046 | − | 0.594935i | ||||
\(159\) | −12.7913 | −1.01442 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.29129 | − | 3.96863i | 0.180579 | − | 0.312772i | ||||
\(162\) | −0.361500 | − | 0.208712i | −0.0284021 | − | 0.0163980i | ||||
\(163\) | − | 14.5826i | − | 1.14220i | −0.820882 | − | 0.571098i | \(-0.806518\pi\) | ||
0.820882 | − | 0.571098i | \(-0.193482\pi\) | |||||||
\(164\) | 11.3739 | 0.888150 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.89564 | − | 3.28335i | −0.147131 | − | 0.254838i | ||||
\(167\) | 9.99308 | + | 5.76951i | 0.773288 | + | 0.446458i | 0.834046 | − | 0.551695i | \(-0.186019\pi\) |
−0.0607584 | + | 0.998152i | \(0.519352\pi\) | |||||||
\(168\) | 2.41733 | − | 1.39564i | 0.186501 | − | 0.107676i | ||||
\(169\) | −6.47822 | − | 11.2206i | −0.498325 | − | 0.863124i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.39564 | − | 20.7469i | −0.183199 | − | 1.58655i | ||||
\(172\) | − | 5.79129i | − | 0.441582i | ||||||
\(173\) | −18.1865 | + | 10.5000i | −1.38270 | + | 0.798300i | −0.992478 | − | 0.122422i | \(-0.960934\pi\) |
−0.390218 | + | 0.920722i | \(0.627601\pi\) | |||||||
\(174\) | −9.47822 | − | 16.4168i | −0.718542 | − | 1.24455i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.89564 | + | 3.28335i | 0.142890 | + | 0.247492i | ||||
\(177\) | −11.0776 | − | 6.39564i | −0.832642 | − | 0.480726i | ||||
\(178\) | 4.58258i | 0.343479i | ||||||||
\(179\) | 16.7477 | 1.25178 | 0.625892 | − | 0.779910i | \(-0.284735\pi\) | ||||
0.625892 | + | 0.779910i | \(0.284735\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.81307 | − | 6.60443i | 0.283423 | − | 0.490903i | −0.688802 | − | 0.724949i | \(-0.741863\pi\) |
0.972226 | + | 0.234046i | \(0.0751966\pi\) | |||||||
\(182\) | − | 0.208712i | − | 0.0154708i | ||||||
\(183\) | − | 3.83485i | − | 0.283480i | ||||||
\(184\) | 2.29129 | − | 3.96863i | 0.168916 | − | 0.292571i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.68693 | + | 11.5821i | −0.490310 | + | 0.849241i | ||||
\(187\) | −2.59808 | + | 1.50000i | −0.189990 | + | 0.109691i | ||||
\(188\) | −10.5353 | + | 6.08258i | −0.768368 | + | 0.443617i | ||||
\(189\) | −5.00000 | −0.363696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.9564 | 1.15457 | 0.577284 | − | 0.816544i | \(-0.304113\pi\) | ||||
0.577284 | + | 0.816544i | \(0.304113\pi\) | |||||||
\(192\) | 2.41733 | − | 1.39564i | 0.174455 | − | 0.100722i | ||||
\(193\) | −2.37960 | + | 1.37386i | −0.171287 | + | 0.0988929i | −0.583193 | − | 0.812334i | \(-0.698197\pi\) |
0.411905 | + | 0.911227i | \(0.364863\pi\) | |||||||
\(194\) | −6.18693 | + | 10.7161i | −0.444196 | + | 0.769370i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | − | 5.19615i | 0.214286 | − | 0.371154i | ||||
\(197\) | − | 20.2087i | − | 1.43981i | −0.694072 | − | 0.719906i | \(-0.744185\pi\) | ||
0.694072 | − | 0.719906i | \(-0.255815\pi\) | |||||||
\(198\) | − | 18.1652i | − | 1.29094i | ||||||
\(199\) | 1.79129 | − | 3.10260i | 0.126981 | − | 0.219938i | −0.795525 | − | 0.605921i | \(-0.792805\pi\) |
0.922506 | + | 0.385984i | \(0.126138\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −43.4955 | −3.06793 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.88143 | + | 3.39564i | 0.412795 | + | 0.238327i | ||||
\(204\) | 1.10436 | + | 1.91280i | 0.0773204 | + | 0.133923i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.58258 | − | 4.47315i | −0.179937 | − | 0.311659i | ||||
\(207\) | −19.0148 | + | 10.9782i | −1.32162 | + | 0.763039i | ||||
\(208\) | − | 0.208712i | − | 0.0144716i | ||||||
\(209\) | −13.2695 | + | 9.85005i | −0.917871 | + | 0.681343i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.9782 | − | 20.7469i | −0.824615 | − | 1.42827i | −0.902213 | − | 0.431290i | \(-0.858059\pi\) |
0.0775988 | − | 0.996985i | \(-0.475275\pi\) | |||||||
\(212\) | 3.96863 | − | 2.29129i | 0.272566 | − | 0.157366i | ||||
\(213\) | −11.0776 | − | 6.39564i | −0.759023 | − | 0.438222i | ||||
\(214\) | 9.47822 | + | 16.4168i | 0.647918 | + | 1.12223i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | − | 4.79129i | − | 0.325254i | ||||||
\(218\) | 10.1738 | + | 5.87386i | 0.689059 | + | 0.397828i | ||||
\(219\) | −3.89564 | + | 6.74745i | −0.263243 | + | 0.455951i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.165151 | 0.0111093 | ||||||||
\(222\) | −8.66025 | − | 5.00000i | −0.581238 | − | 0.335578i | ||||
\(223\) | 16.6352 | − | 9.60436i | 1.11398 | − | 0.643155i | 0.174121 | − | 0.984724i | \(-0.444292\pi\) |
0.939857 | + | 0.341569i | \(0.110958\pi\) | |||||||
\(224\) | −0.500000 | + | 0.866025i | −0.0334077 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.68693 | − | 4.65390i | −0.178732 | − | 0.309573i | ||||
\(227\) | − | 7.74773i | − | 0.514235i | −0.966380 | − | 0.257117i | \(-0.917227\pi\) | ||
0.966380 | − | 0.257117i | \(-0.0827727\pi\) | |||||||
\(228\) | 7.25198 | + | 9.76951i | 0.480274 | + | 0.647001i | ||||
\(229\) | 25.3303 | 1.67387 | 0.836937 | − | 0.547300i | \(-0.184344\pi\) | ||||
0.836937 | + | 0.547300i | \(0.184344\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.29129 | + | 9.16478i | 0.348141 | + | 0.602998i | ||||
\(232\) | 5.88143 | + | 3.39564i | 0.386135 | + | 0.222935i | ||||
\(233\) | 7.93725 | − | 4.58258i | 0.519987 | − | 0.300215i | −0.216942 | − | 0.976184i | \(-0.569608\pi\) |
0.736929 | + | 0.675970i | \(0.236275\pi\) | |||||||
\(234\) | −0.500000 | + | 0.866025i | −0.0326860 | + | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.58258 | 0.298300 | ||||||||
\(237\) | −36.1546 | − | 20.8739i | −2.34849 | − | 1.35590i | ||||
\(238\) | −0.685275 | − | 0.395644i | −0.0444198 | − | 0.0256458i | ||||
\(239\) | −16.5826 | −1.07264 | −0.536319 | − | 0.844015i | \(-0.680186\pi\) | ||||
−0.536319 | + | 0.844015i | \(0.680186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.39564 | − | 14.5417i | 0.540811 | − | 0.936712i | −0.458047 | − | 0.888928i | \(-0.651451\pi\) |
0.998858 | − | 0.0477840i | \(-0.0152159\pi\) | |||||||
\(242\) | −2.92185 | + | 1.68693i | −0.187824 | + | 0.108440i | ||||
\(243\) | −13.9994 | − | 8.08258i | −0.898064 | − | 0.518497i | ||||
\(244\) | 0.686932 | + | 1.18980i | 0.0439763 | + | 0.0761692i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 31.7477 | 2.02416 | ||||||||
\(247\) | 0.903750 | − | 0.104356i | 0.0575042 | − | 0.00664002i | ||||
\(248\) | − | 4.79129i | − | 0.304247i | ||||||
\(249\) | −5.29129 | − | 9.16478i | −0.335322 | − | 0.580794i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.56080 | + | 11.3636i | −0.414114 | + | 0.717266i | −0.995335 | − | 0.0964796i | \(-0.969242\pi\) |
0.581221 | + | 0.813746i | \(0.302575\pi\) | |||||||
\(252\) | 4.14938 | − | 2.39564i | 0.261386 | − | 0.150911i | ||||
\(253\) | 15.0462 | + | 8.68693i | 0.945947 | + | 0.546143i | ||||
\(254\) | −2.62614 | −0.164778 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −9.70703 | − | 5.60436i | −0.605508 | − | 0.349590i | 0.165697 | − | 0.986177i | \(-0.447012\pi\) |
−0.771205 | + | 0.636587i | \(0.780346\pi\) | |||||||
\(258\) | − | 16.1652i | − | 1.00640i | ||||||
\(259\) | 3.58258 | 0.222610 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.2695 | − | 28.1796i | −1.00706 | − | 1.74427i | ||||
\(262\) | 9.99308 | + | 5.76951i | 0.617375 | + | 0.356441i | ||||
\(263\) | −16.8160 | + | 9.70871i | −1.03692 | + | 0.598665i | −0.918959 | − | 0.394354i | \(-0.870969\pi\) |
−0.117959 | + | 0.993018i | \(0.537635\pi\) | |||||||
\(264\) | 5.29129 | + | 9.16478i | 0.325656 | + | 0.564053i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.00000 | − | 1.73205i | −0.245256 | − | 0.106199i | ||||
\(267\) | 12.7913i | 0.782814i | ||||||||
\(268\) | 13.4949 | − | 7.79129i | 0.824333 | − | 0.475929i | ||||
\(269\) | 6.56080 | + | 11.3636i | 0.400019 | + | 0.692853i | 0.993728 | − | 0.111827i | \(-0.0356703\pi\) |
−0.593709 | + | 0.804680i | \(0.702337\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.56080 | + | 14.8277i | 0.520031 | + | 0.900721i | 0.999729 | + | 0.0232867i | \(0.00741305\pi\) |
−0.479698 | + | 0.877434i | \(0.659254\pi\) | |||||||
\(272\) | −0.685275 | − | 0.395644i | −0.0415509 | − | 0.0239894i | ||||
\(273\) | − | 0.582576i | − | 0.0352591i | ||||||
\(274\) | −15.3303 | −0.926137 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.39564 | − | 11.0776i | 0.384973 | − | 0.666792i | ||||
\(277\) | 8.74773i | 0.525600i | 0.964850 | + | 0.262800i | \(0.0846459\pi\) | ||||
−0.964850 | + | 0.262800i | \(0.915354\pi\) | |||||||
\(278\) | − | 12.2087i | − | 0.732230i | ||||||
\(279\) | −11.4782 | + | 19.8809i | −0.687183 | + | 1.19024i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.29129 | + | 9.16478i | −0.315652 | + | 0.546725i | −0.979576 | − | 0.201075i | \(-0.935556\pi\) |
0.663924 | + | 0.747800i | \(0.268890\pi\) | |||||||
\(282\) | −29.4071 | + | 16.9782i | −1.75117 | + | 1.01104i | ||||
\(283\) | 18.2918 | − | 10.5608i | 1.08734 | − | 0.627774i | 0.154471 | − | 0.987997i | \(-0.450633\pi\) |
0.932866 | + | 0.360223i | \(0.117299\pi\) | |||||||
\(284\) | 4.58258 | 0.271926 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.791288 | 0.0467898 | ||||||||
\(287\) | −9.85005 | + | 5.68693i | −0.581430 | + | 0.335689i | ||||
\(288\) | 4.14938 | − | 2.39564i | 0.244504 | − | 0.141165i | ||||
\(289\) | −8.18693 | + | 14.1802i | −0.481584 | + | 0.834128i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.2695 | + | 29.9117i | −1.01236 | + | 1.75345i | ||||
\(292\) | − | 2.79129i | − | 0.163348i | ||||||
\(293\) | 24.9564i | 1.45797i | 0.684529 | + | 0.728985i | \(0.260008\pi\) | ||||
−0.684529 | + | 0.728985i | \(0.739992\pi\) | |||||||
\(294\) | 8.37386 | − | 14.5040i | 0.488374 | − | 0.845888i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.58258 | 0.208233 | ||||||||
\(297\) | − | 18.9564i | − | 1.09996i | ||||||
\(298\) | 19.7001 | + | 11.3739i | 1.14120 | + | 0.658870i | ||||
\(299\) | −0.478220 | − | 0.828301i | −0.0276562 | − | 0.0479019i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.89564 | + | 5.01540i | 0.166902 | + | 0.289083i | ||||
\(302\) | −13.6379 | + | 7.87386i | −0.784775 | + | 0.453090i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.00000 | − | 1.73205i | −0.229416 | − | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.89564 | + | 3.28335i | 0.108367 | + | 0.187697i | ||||
\(307\) | 29.8739 | − | 17.2477i | 1.70500 | − | 0.984380i | 0.764469 | − | 0.644661i | \(-0.223001\pi\) |
0.940527 | − | 0.339719i | \(-0.110332\pi\) | |||||||
\(308\) | −3.28335 | − | 1.89564i | −0.187086 | − | 0.108014i | ||||
\(309\) | −7.20871 | − | 12.4859i | −0.410089 | − | 0.710296i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0000 | −0.850572 | −0.425286 | − | 0.905059i | \(-0.639826\pi\) | ||||
−0.425286 | + | 0.905059i | \(0.639826\pi\) | |||||||
\(312\) | − | 0.582576i | − | 0.0329819i | ||||||
\(313\) | 10.1738 | + | 5.87386i | 0.575059 | + | 0.332010i | 0.759167 | − | 0.650896i | \(-0.225606\pi\) |
−0.184108 | + | 0.982906i | \(0.558940\pi\) | |||||||
\(314\) | −3.97822 | + | 6.89048i | −0.224504 | + | 0.388852i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.9564 | 0.841365 | ||||||||
\(317\) | −7.93725 | − | 4.58258i | −0.445801 | − | 0.257383i | 0.260254 | − | 0.965540i | \(-0.416194\pi\) |
−0.706055 | + | 0.708157i | \(0.749527\pi\) | |||||||
\(318\) | 11.0776 | − | 6.39564i | 0.621200 | − | 0.358650i | ||||
\(319\) | −12.8739 | + | 22.2982i | −0.720798 | + | 1.24846i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.4564 | + | 45.8239i | 1.47665 | + | 2.55764i | ||||
\(322\) | 4.58258i | 0.255377i | ||||||||
\(323\) | 1.37055 | − | 3.16515i | 0.0762595 | − | 0.176114i | ||||
\(324\) | 0.417424 | 0.0231902 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.29129 | + | 12.6289i | 0.403827 | + | 0.699449i | ||||
\(327\) | 28.3981 | + | 16.3956i | 1.57042 | + | 0.906681i | ||||
\(328\) | −9.85005 | + | 5.68693i | −0.543878 | + | 0.314008i | ||||
\(329\) | 6.08258 | − | 10.5353i | 0.335343 | − | 0.580832i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.9129 | −0.984581 | −0.492290 | − | 0.870431i | \(-0.663840\pi\) | ||||
−0.492290 | + | 0.870431i | \(0.663840\pi\) | |||||||
\(332\) | 3.28335 | + | 1.89564i | 0.180197 | + | 0.104037i | ||||
\(333\) | −14.8655 | − | 8.58258i | −0.814622 | − | 0.470322i | ||||
\(334\) | −11.5390 | −0.631387 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.39564 | + | 2.41733i | −0.0761386 | + | 0.131876i | ||||
\(337\) | −20.2046 | + | 11.6652i | −1.10062 | + | 0.635441i | −0.936383 | − | 0.350980i | \(-0.885848\pi\) |
−0.164234 | + | 0.986421i | \(0.552515\pi\) | |||||||
\(338\) | 11.2206 | + | 6.47822i | 0.610320 | + | 0.352369i | ||||
\(339\) | −7.50000 | − | 12.9904i | −0.407344 | − | 0.705541i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.1652 | 0.983698 | ||||||||
\(342\) | 12.4481 | + | 16.7695i | 0.673118 | + | 0.906791i | ||||
\(343\) | 13.0000i | 0.701934i | ||||||||
\(344\) | 2.89564 | + | 5.01540i | 0.156123 | + | 0.270412i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5000 | − | 18.1865i | 0.564483 | − | 0.977714i | ||||
\(347\) | −3.14033 | + | 1.81307i | −0.168582 | + | 0.0973306i | −0.581917 | − | 0.813248i | \(-0.697697\pi\) |
0.413335 | + | 0.910579i | \(0.364364\pi\) | |||||||
\(348\) | 16.4168 | + | 9.47822i | 0.880031 | + | 0.508086i | ||||
\(349\) | 5.41742 | 0.289988 | 0.144994 | − | 0.989433i | \(-0.453684\pi\) | ||||
0.144994 | + | 0.989433i | \(0.453684\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.521780 | + | 0.903750i | −0.0278506 | + | 0.0482386i | ||||
\(352\) | −3.28335 | − | 1.89564i | −0.175003 | − | 0.101038i | ||||
\(353\) | − | 13.7477i | − | 0.731718i | −0.930670 | − | 0.365859i | \(-0.880775\pi\) | ||
0.930670 | − | 0.365859i | \(-0.119225\pi\) | |||||||
\(354\) | 12.7913 | 0.679849 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.29129 | − | 3.96863i | −0.121438 | − | 0.210337i | ||||
\(357\) | −1.91280 | − | 1.10436i | −0.101236 | − | 0.0584487i | ||||
\(358\) | −14.5040 | + | 8.37386i | −0.766558 | + | 0.442572i | ||||
\(359\) | −17.8521 | − | 30.9207i | −0.942197 | − | 1.63193i | −0.761269 | − | 0.648437i | \(-0.775423\pi\) |
−0.180928 | − | 0.983496i | \(-0.557910\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | − | 18.1865i | 0.289474 | − | 0.957186i | ||||
\(362\) | 7.62614i | 0.400821i | ||||||||
\(363\) | −8.15573 | + | 4.70871i | −0.428065 | + | 0.247143i | ||||
\(364\) | 0.104356 | + | 0.180750i | 0.00546974 | + | 0.00947388i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.91742 | + | 3.32108i | 0.100225 | + | 0.173595i | ||||
\(367\) | 7.61348 | + | 4.39564i | 0.397420 | + | 0.229451i | 0.685370 | − | 0.728195i | \(-0.259640\pi\) |
−0.287950 | + | 0.957645i | \(0.592974\pi\) | |||||||
\(368\) | 4.58258i | 0.238883i | ||||||||
\(369\) | 54.4955 | 2.83692 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.29129 | + | 3.96863i | −0.118958 | + | 0.206041i | ||||
\(372\) | − | 13.3739i | − | 0.693403i | ||||||
\(373\) | − | 21.3739i | − | 1.10670i | −0.832950 | − | 0.553348i | \(-0.813350\pi\) | ||
0.832950 | − | 0.553348i | \(-0.186650\pi\) | |||||||
\(374\) | 1.50000 | − | 2.59808i | 0.0775632 | − | 0.134343i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.08258 | − | 10.5353i | 0.313685 | − | 0.543318i | ||||
\(377\) | 1.22753 | − | 0.708712i | 0.0632208 | − | 0.0365005i | ||||
\(378\) | 4.33013 | − | 2.50000i | 0.222718 | − | 0.128586i | ||||
\(379\) | −4.83485 | −0.248349 | −0.124175 | − | 0.992260i | \(-0.539628\pi\) | ||||
−0.124175 | + | 0.992260i | \(0.539628\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.33030 | −0.375543 | ||||||||
\(382\) | −13.8187 | + | 7.97822i | −0.707025 | + | 0.408201i | ||||
\(383\) | 3.96863 | − | 2.29129i | 0.202787 | − | 0.117079i | −0.395168 | − | 0.918609i | \(-0.629313\pi\) |
0.597955 | + | 0.801530i | \(0.295980\pi\) | |||||||
\(384\) | −1.39564 | + | 2.41733i | −0.0712212 | + | 0.123359i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.37386 | − | 2.37960i | 0.0699278 | − | 0.121119i | ||||
\(387\) | − | 27.7477i | − | 1.41050i | ||||||
\(388\) | − | 12.3739i | − | 0.628188i | ||||||
\(389\) | 9.31307 | − | 16.1307i | 0.472191 | − | 0.817859i | −0.527302 | − | 0.849678i | \(-0.676796\pi\) |
0.999494 | + | 0.0318184i | \(0.0101298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.62614 | −0.183382 | ||||||||
\(392\) | 6.00000i | 0.303046i | ||||||||
\(393\) | 27.8936 | + | 16.1044i | 1.40704 | + | 0.812357i | ||||
\(394\) | 10.1044 | + | 17.5013i | 0.509050 | + | 0.881701i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.08258 | + | 15.7315i | 0.456417 | + | 0.790537i | ||||
\(397\) | 9.88778 | − | 5.70871i | 0.496253 | − | 0.286512i | −0.230912 | − | 0.972975i | \(-0.574171\pi\) |
0.727165 | + | 0.686463i | \(0.240837\pi\) | |||||||
\(398\) | 3.58258i | 0.179578i | ||||||||
\(399\) | −11.1652 | − | 4.83465i | −0.558957 | − | 0.242035i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | + | 10.3923i | 0.299626 | + | 0.518967i | 0.976050 | − | 0.217545i | \(-0.0698049\pi\) |
−0.676425 | + | 0.736512i | \(0.736472\pi\) | |||||||
\(402\) | 37.6682 | − | 21.7477i | 1.87872 | − | 1.08468i | ||||
\(403\) | −0.866025 | − | 0.500000i | −0.0431398 | − | 0.0249068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.79129 | −0.337046 | ||||||||
\(407\) | 13.5826i | 0.673263i | ||||||||
\(408\) | −1.91280 | − | 1.10436i | −0.0946978 | − | 0.0546738i | ||||
\(409\) | −5.00000 | + | 8.66025i | −0.247234 | + | 0.428222i | −0.962757 | − | 0.270367i | \(-0.912855\pi\) |
0.715523 | + | 0.698589i | \(0.246188\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −42.7913 | −2.11074 | ||||||||
\(412\) | 4.47315 | + | 2.58258i | 0.220376 | + | 0.127234i | ||||
\(413\) | −3.96863 | + | 2.29129i | −0.195283 | + | 0.112747i | ||||
\(414\) | 10.9782 | − | 19.0148i | 0.539550 | − | 0.934528i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.104356 | + | 0.180750i | 0.00511648 | + | 0.00886200i | ||||
\(417\) | − | 34.0780i | − | 1.66881i | ||||||
\(418\) | 6.56670 | − | 15.1652i | 0.321188 | − | 0.741752i | ||||
\(419\) | 22.7477 | 1.11130 | 0.555650 | − | 0.831417i | \(-0.312470\pi\) | ||||
0.555650 | + | 0.831417i | \(0.312470\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | − | 17.3205i | −0.487370 | − | 0.844150i | 0.512524 | − | 0.858673i | \(-0.328710\pi\) |
−0.999895 | + | 0.0145228i | \(0.995377\pi\) | |||||||
\(422\) | 20.7469 | + | 11.9782i | 1.00994 | + | 0.583091i | ||||
\(423\) | −50.4778 | + | 29.1434i | −2.45431 | + | 1.41700i | ||||
\(424\) | −2.29129 | + | 3.96863i | −0.111275 | + | 0.192734i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.7913 | 0.619740 | ||||||||
\(427\) | −1.18980 | − | 0.686932i | −0.0575785 | − | 0.0332430i | ||||
\(428\) | −16.4168 | − | 9.47822i | −0.793534 | − | 0.458147i | ||||
\(429\) | 2.20871 | 0.106638 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.10436 | + | 7.10895i | −0.197700 | + | 0.342426i | −0.947782 | − | 0.318918i | \(-0.896680\pi\) |
0.750082 | + | 0.661344i | \(0.230014\pi\) | |||||||
\(432\) | 4.33013 | − | 2.50000i | 0.208333 | − | 0.120281i | ||||
\(433\) | −5.98673 | − | 3.45644i | −0.287704 | − | 0.166106i | 0.349202 | − | 0.937047i | \(-0.386453\pi\) |
−0.636906 | + | 0.770942i | \(0.719786\pi\) | |||||||
\(434\) | 2.39564 | + | 4.14938i | 0.114995 | + | 0.199176i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.7477 | −0.562614 | ||||||||
\(437\) | −19.8431 | + | 2.29129i | −0.949226 | + | 0.109607i | ||||
\(438\) | − | 7.79129i | − | 0.372282i | ||||||
\(439\) | −12.6652 | − | 21.9367i | −0.604475 | − | 1.04698i | −0.992134 | − | 0.125178i | \(-0.960050\pi\) |
0.387660 | − | 0.921803i | \(-0.373284\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.3739 | − | 24.8963i | 0.684470 | − | 1.18554i | ||||
\(442\) | −0.143025 | + | 0.0825757i | −0.00680302 | + | 0.00392773i | ||||
\(443\) | 20.7846 | + | 12.0000i | 0.987507 | + | 0.570137i | 0.904528 | − | 0.426414i | \(-0.140223\pi\) |
0.0829786 | + | 0.996551i | \(0.473557\pi\) | |||||||
\(444\) | 10.0000 | 0.474579 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.60436 | + | 16.6352i | −0.454779 | + | 0.787701i | ||||
\(447\) | 54.9887 | + | 31.7477i | 2.60088 | + | 1.50162i | ||||
\(448\) | − | 1.00000i | − | 0.0472456i | ||||||
\(449\) | −3.33030 | −0.157167 | −0.0785834 | − | 0.996908i | \(-0.525040\pi\) | ||||
−0.0785834 | + | 0.996908i | \(0.525040\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.5608 | − | 37.3444i | −1.01526 | − | 1.75848i | ||||
\(452\) | 4.65390 | + | 2.68693i | 0.218901 | + | 0.126383i | ||||
\(453\) | −38.0674 | + | 21.9782i | −1.78856 | + | 1.03263i | ||||
\(454\) | 3.87386 | + | 6.70973i | 0.181809 | + | 0.314903i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.1652 | − | 4.83465i | −0.522856 | − | 0.226403i | ||||
\(457\) | 20.7477i | 0.970538i | 0.874365 | + | 0.485269i | \(0.161278\pi\) | ||||
−0.874365 | + | 0.485269i | \(0.838722\pi\) | |||||||
\(458\) | −21.9367 | + | 12.6652i | −1.02503 | + | 0.591804i | ||||
\(459\) | 1.97822 | + | 3.42638i | 0.0923354 | + | 0.159930i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.39564 | − | 11.0776i | −0.297875 | − | 0.515934i | 0.677775 | − | 0.735270i | \(-0.262944\pi\) |
−0.975650 | + | 0.219335i | \(0.929611\pi\) | |||||||
\(462\) | −9.16478 | − | 5.29129i | −0.426384 | − | 0.246173i | ||||
\(463\) | 17.9564i | 0.834507i | 0.908790 | + | 0.417253i | \(0.137007\pi\) | ||||
−0.908790 | + | 0.417253i | \(0.862993\pi\) | |||||||
\(464\) | −6.79129 | −0.315278 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.58258 | + | 7.93725i | −0.212284 | + | 0.367686i | ||||
\(467\) | 12.3303i | 0.570578i | 0.958441 | + | 0.285289i | \(0.0920896\pi\) | ||||
−0.958441 | + | 0.285289i | \(0.907910\pi\) | |||||||
\(468\) | − | 1.00000i | − | 0.0462250i | ||||||
\(469\) | −7.79129 | + | 13.4949i | −0.359768 | + | 0.623137i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.1044 | + | 19.2333i | −0.511662 | + | 0.886224i | ||||
\(472\) | −3.96863 | + | 2.29129i | −0.182671 | + | 0.105465i | ||||
\(473\) | −19.0148 | + | 10.9782i | −0.874303 | + | 0.504779i | ||||
\(474\) | 41.7477 | 1.91754 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.791288 | 0.0362686 | ||||||||
\(477\) | 19.0148 | − | 10.9782i | 0.870629 | − | 0.502658i | ||||
\(478\) | 14.3609 | − | 8.29129i | 0.656854 | − | 0.379235i | ||||
\(479\) | 15.8739 | − | 27.4943i | 0.725295 | − | 1.25625i | −0.233557 | − | 0.972343i | \(-0.575037\pi\) |
0.958852 | − | 0.283905i | \(-0.0916301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.373864 | − | 0.647551i | 0.0170467 | − | 0.0295258i | ||||
\(482\) | 16.7913i | 0.764822i | ||||||||
\(483\) | 12.7913i | 0.582024i | ||||||||
\(484\) | 1.68693 | − | 2.92185i | 0.0766787 | − | 0.132811i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.1652 | 0.733266 | ||||||||
\(487\) | − | 23.0000i | − | 1.04223i | −0.853487 | − | 0.521115i | \(-0.825516\pi\) | ||
0.853487 | − | 0.521115i | \(-0.174484\pi\) | |||||||
\(488\) | −1.18980 | − | 0.686932i | −0.0538597 | − | 0.0310959i | ||||
\(489\) | 20.3521 | + | 35.2508i | 0.920353 | + | 1.59410i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.7087 | + | 27.2083i | 0.708924 | + | 1.22789i | 0.965257 | + | 0.261304i | \(0.0841525\pi\) |
−0.256332 | + | 0.966589i | \(0.582514\pi\) | |||||||
\(492\) | −27.4943 | + | 15.8739i | −1.23954 | + | 0.715649i | ||||
\(493\) | − | 5.37386i | − | 0.242027i | ||||||
\(494\) | −0.730493 | + | 0.542250i | −0.0328664 | + | 0.0243970i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.39564 | + | 4.14938i | 0.107568 | + | 0.186313i | ||||
\(497\) | −3.96863 | + | 2.29129i | −0.178017 | + | 0.102778i | ||||
\(498\) | 9.16478 | + | 5.29129i | 0.410684 | + | 0.237108i | ||||
\(499\) | −9.66515 | − | 16.7405i | −0.432672 | − | 0.749409i | 0.564431 | − | 0.825480i | \(-0.309096\pi\) |
−0.997102 | + | 0.0760712i | \(0.975762\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.2087 | −1.43898 | ||||||||
\(502\) | − | 13.1216i | − | 0.585645i | ||||||
\(503\) | 3.96863 | + | 2.29129i | 0.176952 | + | 0.102163i | 0.585860 | − | 0.810412i | \(-0.300757\pi\) |
−0.408908 | + | 0.912576i | \(0.634090\pi\) | |||||||
\(504\) | −2.39564 | + | 4.14938i | −0.106710 | + | 0.184828i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −17.3739 | −0.772362 | ||||||||
\(507\) | 31.3199 | + | 18.0826i | 1.39097 | + | 0.803075i | ||||
\(508\) | 2.27430 | − | 1.31307i | 0.100906 | − | 0.0582580i | ||||
\(509\) | 11.2087 | − | 19.4141i | 0.496817 | − | 0.860513i | −0.503176 | − | 0.864184i | \(-0.667835\pi\) |
0.999993 | + | 0.00367102i | \(0.00116853\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.39564 | + | 2.41733i | 0.0617397 | + | 0.106936i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 12.9904 | + | 17.5000i | 0.573539 | + | 0.772644i | ||||
\(514\) | 11.2087 | 0.494395 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.08258 | + | 13.9994i | 0.355816 | + | 0.616291i | ||||
\(517\) | 39.9425 | + | 23.0608i | 1.75667 | + | 1.01421i | ||||
\(518\) | −3.10260 | + | 1.79129i | −0.136320 | + | 0.0787047i | ||||
\(519\) | 29.3085 | − | 50.7638i | 1.28650 | − | 2.22829i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.2523 | 0.580593 | 0.290296 | − | 0.956937i | \(-0.406246\pi\) | ||||
0.290296 | + | 0.956937i | \(0.406246\pi\) | |||||||
\(522\) | 28.1796 | + | 16.2695i | 1.23339 | + | 0.712097i | ||||
\(523\) | 15.3700 | + | 8.87386i | 0.672082 | + | 0.388027i | 0.796865 | − | 0.604157i | \(-0.206490\pi\) |
−0.124783 | + | 0.992184i | \(0.539823\pi\) | |||||||
\(524\) | −11.5390 | −0.504084 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.70871 | − | 16.8160i | 0.423320 | − | 0.733212i | ||||
\(527\) | −3.28335 | + | 1.89564i | −0.143025 | + | 0.0825755i | ||||
\(528\) | −9.16478 | − | 5.29129i | −0.398846 | − | 0.230274i | ||||
\(529\) | −1.00000 | − | 1.73205i | −0.0434783 | − | 0.0753066i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.9564 | 0.952828 | ||||||||
\(532\) | 4.33013 | − | 0.500000i | 0.187735 | − | 0.0216777i | ||||
\(533\) | 2.37386i | 0.102823i | ||||||||
\(534\) | −6.39564 | − | 11.0776i | −0.276767 | − | 0.479374i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.79129 | + | 13.4949i | −0.336532 | + | 0.582891i | ||||
\(537\) | −40.4847 | + | 23.3739i | −1.74704 | + | 1.00866i | ||||
\(538\) | −11.3636 | − | 6.56080i | −0.489921 | − | 0.282856i | ||||
\(539\) | −22.7477 | −0.979814 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.56080 | − | 14.8277i | 0.368057 | − | 0.637494i | −0.621204 | − | 0.783649i | \(-0.713356\pi\) |
0.989262 | + | 0.146155i | \(0.0466897\pi\) | |||||||
\(542\) | −14.8277 | − | 8.56080i | −0.636906 | − | 0.367718i | ||||
\(543\) | 21.2867i | 0.913502i | ||||||||
\(544\) | 0.791288 | 0.0339262 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.291288 | + | 0.504525i | 0.0124660 | + | 0.0215917i | ||||
\(547\) | 14.5794 | + | 8.41742i | 0.623370 | + | 0.359903i | 0.778180 | − | 0.628041i | \(-0.216143\pi\) |
−0.154810 | + | 0.987944i | \(0.549476\pi\) | |||||||
\(548\) | 13.2764 | − | 7.66515i | 0.567141 | − | 0.327439i | ||||
\(549\) | 3.29129 | + | 5.70068i | 0.140469 | + | 0.243299i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.39564 | − | 29.4071i | −0.144659 | − | 1.25279i | ||||
\(552\) | 12.7913i | 0.544433i | ||||||||
\(553\) | −12.9527 | + | 7.47822i | −0.550803 | + | 0.318006i | ||||
\(554\) | −4.37386 | − | 7.57575i | −0.185828 | − | 0.321863i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.10436 | + | 10.5731i | 0.258882 | + | 0.448397i | ||||
\(557\) | 8.62253 | + | 4.97822i | 0.365348 | + | 0.210934i | 0.671424 | − | 0.741073i | \(-0.265683\pi\) |
−0.306076 | + | 0.952007i | \(0.599016\pi\) | |||||||
\(558\) | − | 22.9564i | − | 0.971824i | ||||||
\(559\) | 1.20871 | 0.0511231 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.18693 | − | 7.25198i | 0.176772 | − | 0.306179i | ||||
\(562\) | − | 10.5826i | − | 0.446399i | ||||||
\(563\) | − | 14.3739i | − | 0.605786i | −0.953025 | − | 0.302893i | \(-0.902047\pi\) | ||
0.953025 | − | 0.302893i | \(-0.0979525\pi\) | |||||||
\(564\) | 16.9782 | − | 29.4071i | 0.714912 | − | 1.23826i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.5608 | + | 18.2918i | −0.443903 | + | 0.768863i | ||||
\(567\) | −0.361500 | + | 0.208712i | −0.0151816 | + | 0.00876509i | ||||
\(568\) | −3.96863 | + | 2.29129i | −0.166520 | + | 0.0961403i | ||||
\(569\) | 8.83485 | 0.370376 | 0.185188 | − | 0.982703i | \(-0.440711\pi\) | ||||
0.185188 | + | 0.982703i | \(0.440711\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0000 | −0.920671 | −0.460336 | − | 0.887745i | \(-0.652271\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | −0.685275 | + | 0.395644i | −0.0286528 | + | 0.0165427i | ||||
\(573\) | −38.5719 | + | 22.2695i | −1.61137 | + | 0.930322i | ||||
\(574\) | 5.68693 | − | 9.85005i | 0.237368 | − | 0.411133i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.39564 | + | 4.14938i | −0.0998185 | + | 0.172891i | ||||
\(577\) | − | 14.0000i | − | 0.582828i | −0.956597 | − | 0.291414i | \(-0.905874\pi\) | ||
0.956597 | − | 0.291414i | \(-0.0941257\pi\) | |||||||
\(578\) | − | 16.3739i | − | 0.681063i | ||||||
\(579\) | 3.83485 | − | 6.64215i | 0.159371 | − | 0.276038i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.79129 | −0.157289 | ||||||||
\(582\) | − | 34.5390i | − | 1.43169i | ||||||
\(583\) | −15.0462 | − | 8.68693i | −0.623150 | − | 0.359776i | ||||
\(584\) | 1.39564 | + | 2.41733i | 0.0577522 | + | 0.100030i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.4782 | − | 21.6129i | −0.515471 | − | 0.892821i | ||||
\(587\) | 8.22330 | − | 4.74773i | 0.339412 | − | 0.195960i | −0.320600 | − | 0.947215i | \(-0.603884\pi\) |
0.660012 | + | 0.751255i | \(0.270551\pi\) | |||||||
\(588\) | 16.7477i | 0.690665i | ||||||||
\(589\) | −16.7695 | + | 12.4481i | −0.690976 | + | 0.512916i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.2042 | + | 48.8510i | 1.16016 | + | 2.00946i | ||||
\(592\) | −3.10260 | + | 1.79129i | −0.127516 | + | 0.0736215i | ||||
\(593\) | 10.2493 | + | 5.91742i | 0.420887 | + | 0.242999i | 0.695457 | − | 0.718568i | \(-0.255202\pi\) |
−0.274569 | + | 0.961567i | \(0.588535\pi\) | |||||||
\(594\) | 9.47822 | + | 16.4168i | 0.388896 | + | 0.673588i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.7477 | −0.931783 | ||||||||
\(597\) | 10.0000i | 0.409273i | ||||||||
\(598\) | 0.828301 | + | 0.478220i | 0.0338717 | + | 0.0195559i | ||||
\(599\) | −18.5608 | + | 32.1482i | −0.758374 | + | 1.31354i | 0.185306 | + | 0.982681i | \(0.440672\pi\) |
−0.943680 | + | 0.330861i | \(0.892661\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.91288 | 0.404355 | 0.202177 | − | 0.979349i | \(-0.435198\pi\) | ||||
0.202177 | + | 0.979349i | \(0.435198\pi\) | |||||||
\(602\) | −5.01540 | − | 2.89564i | −0.204413 | − | 0.118018i | ||||
\(603\) | 64.6580 | − | 37.3303i | 2.63308 | − | 1.52021i | ||||
\(604\) | 7.87386 | − | 13.6379i | 0.320383 | − | 0.554920i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.2087i | 0.739069i | 0.929217 | + | 0.369534i | \(0.120483\pi\) | ||||
−0.929217 | + | 0.369534i | \(0.879517\pi\) | |||||||
\(608\) | 4.33013 | − | 0.500000i | 0.175610 | − | 0.0202777i | ||||
\(609\) | −18.9564 | −0.768154 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.26951 | − | 2.19885i | −0.0513588 | − | 0.0889560i | ||||
\(612\) | −3.28335 | − | 1.89564i | −0.132722 | − | 0.0766269i | ||||
\(613\) | 12.5534 | − | 7.24773i | 0.507028 | − | 0.292733i | −0.224583 | − | 0.974455i | \(-0.572102\pi\) |
0.731611 | + | 0.681722i | \(0.238769\pi\) | |||||||
\(614\) | −17.2477 | + | 29.8739i | −0.696062 | + | 1.20561i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.79129 | 0.152755 | ||||||||
\(617\) | −28.5788 | − | 16.5000i | −1.15054 | − | 0.664265i | −0.201522 | − | 0.979484i | \(-0.564589\pi\) |
−0.949019 | + | 0.315219i | \(0.897922\pi\) | |||||||
\(618\) | 12.4859 | + | 7.20871i | 0.502255 | + | 0.289977i | ||||
\(619\) | 24.3739 | 0.979668 | 0.489834 | − | 0.871816i | \(-0.337057\pi\) | ||||
0.489834 | + | 0.871816i | \(0.337057\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.4564 | − | 19.8431i | 0.459731 | − | 0.796278i | ||||
\(622\) | 12.9904 | − | 7.50000i | 0.520867 | − | 0.300723i | ||||
\(623\) | 3.96863 | + | 2.29129i | 0.159000 | + | 0.0917985i | ||||
\(624\) | 0.291288 | + | 0.504525i | 0.0116608 | + | 0.0201972i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.7477 | −0.469534 | ||||||||
\(627\) | 18.3296 | − | 42.3303i | 0.732012 | − | 1.69051i | ||||
\(628\) | − | 7.95644i | − | 0.317496i | ||||||
\(629\) | −1.41742 | − | 2.45505i | −0.0565164 | − | 0.0978893i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.1044 | − | 31.3577i | 0.720723 | − | 1.24833i | −0.239987 | − | 0.970776i | \(-0.577143\pi\) |
0.960710 | − | 0.277553i | \(-0.0895234\pi\) | |||||||
\(632\) | −12.9527 | + | 7.47822i | −0.515229 | + | 0.297468i | ||||
\(633\) | 57.9105 | + | 33.4347i | 2.30174 | + | 1.32891i | ||||
\(634\) | 9.16515 | 0.363995 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.39564 | + | 11.0776i | −0.253604 | + | 0.439255i | ||||
\(637\) | 1.08450 | + | 0.626136i | 0.0429695 | + | 0.0248084i | ||||
\(638\) | − | 25.7477i | − | 1.01936i | ||||||
\(639\) | 21.9564 | 0.868583 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.52178 | − | 14.7602i | −0.336590 | − | 0.582991i | 0.647199 | − | 0.762321i | \(-0.275940\pi\) |
−0.983789 | + | 0.179330i | \(0.942607\pi\) | |||||||
\(642\) | −45.8239 | − | 26.4564i | −1.80852 | − | 1.04415i | ||||
\(643\) | 25.5438 | − | 14.7477i | 1.00735 | − | 0.581594i | 0.0969351 | − | 0.995291i | \(-0.469096\pi\) |
0.910415 | + | 0.413697i | \(0.135763\pi\) | |||||||
\(644\) | −2.29129 | − | 3.96863i | −0.0902894 | − | 0.156386i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.395644 | + | 3.42638i | 0.0155664 | + | 0.134809i | ||||
\(647\) | − | 18.7913i | − | 0.738762i | −0.929278 | − | 0.369381i | \(-0.879570\pi\) | ||
0.929278 | − | 0.369381i | \(-0.120430\pi\) | |||||||
\(648\) | −0.361500 | + | 0.208712i | −0.0142011 | + | 0.00819899i | ||||
\(649\) | −8.68693 | − | 15.0462i | −0.340992 | − | 0.590615i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.68693 | + | 11.5821i | 0.262082 | + | 0.453939i | ||||
\(652\) | −12.6289 | − | 7.29129i | −0.494585 | − | 0.285549i | ||||
\(653\) | − | 27.3303i | − | 1.06952i | −0.845005 | − | 0.534759i | \(-0.820403\pi\) | ||
0.845005 | − | 0.534759i | \(-0.179597\pi\) | |||||||
\(654\) | −32.7913 | −1.28224 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.68693 | − | 9.85005i | 0.222037 | − | 0.384580i | ||||
\(657\) | − | 13.3739i | − | 0.521764i | ||||||
\(658\) | 12.1652i | 0.474247i | ||||||||
\(659\) | 0.873864 | − | 1.51358i | 0.0340409 | − | 0.0589606i | −0.848503 | − | 0.529190i | \(-0.822496\pi\) |
0.882544 | + | 0.470230i | \(0.155829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.4347 | + | 40.5900i | −0.911503 | + | 1.57877i | −0.0995599 | + | 0.995032i | \(0.531744\pi\) |
−0.811943 | + | 0.583737i | \(0.801590\pi\) | |||||||
\(662\) | 15.5130 | − | 8.95644i | 0.602930 | − | 0.348102i | ||||
\(663\) | −0.399225 | + | 0.230493i | −0.0155046 | + | 0.00895159i | ||||
\(664\) | −3.79129 | −0.147131 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.1652 | 0.665136 | ||||||||
\(667\) | −26.9521 | + | 15.5608i | −1.04359 | + | 0.602516i | ||||
\(668\) | 9.99308 | − | 5.76951i | 0.386644 | − | 0.223229i | ||||
\(669\) | −26.8085 | + | 46.4337i | −1.03648 | + | 1.79523i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.60436 | − | 4.51088i | 0.100540 | − | 0.174140i | ||||
\(672\) | − | 2.79129i | − | 0.107676i | ||||||
\(673\) | 2.79129i | 0.107596i | 0.998552 | + | 0.0537981i | \(0.0171327\pi\) | ||||
−0.998552 | + | 0.0537981i | \(0.982867\pi\) | |||||||
\(674\) | 11.6652 | − | 20.2046i | 0.449325 | − | 0.778253i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9564 | −0.498325 | ||||||||
\(677\) | 35.2432i | 1.35451i | 0.735750 | + | 0.677253i | \(0.236830\pi\) | ||||
−0.735750 | + | 0.677253i | \(0.763170\pi\) | |||||||
\(678\) | 12.9904 | + | 7.50000i | 0.498893 | + | 0.288036i | ||||
\(679\) | 6.18693 | + | 10.7161i | 0.237433 | + | 0.411245i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.8131 | + | 18.7288i | 0.414358 | + | 0.717689i | ||||
\(682\) | −15.7315 | + | 9.08258i | −0.602390 | + | 0.347790i | ||||
\(683\) | − | 36.1652i | − | 1.38382i | −0.721983 | − | 0.691911i | \(-0.756769\pi\) | ||
0.721983 | − | 0.691911i | \(-0.243231\pi\) | |||||||
\(684\) | −19.1652 | − | 8.29875i | −0.732798 | − | 0.317311i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.50000 | − | 11.2583i | −0.248171 | − | 0.429845i | ||||
\(687\) | −61.2316 | + | 35.3521i | −2.33613 | + | 1.34877i | ||||
\(688\) | −5.01540 | − | 2.89564i | −0.191210 | − | 0.110395i | ||||
\(689\) | 0.478220 | + | 0.828301i | 0.0182187 | + | 0.0315557i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.1216 | −1.22196 | −0.610981 | − | 0.791645i | \(-0.709225\pi\) | ||||
−0.610981 | + | 0.791645i | \(0.709225\pi\) | |||||||
\(692\) | 21.0000i | 0.798300i | ||||||||
\(693\) | −15.7315 | − | 9.08258i | −0.597590 | − | 0.345019i | ||||
\(694\) | 1.81307 | − | 3.14033i | 0.0688231 | − | 0.119205i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −18.9564 | −0.718542 | ||||||||
\(697\) | 7.79423 | + | 4.50000i | 0.295227 | + | 0.170450i | ||||
\(698\) | −4.69163 | + | 2.70871i | −0.177581 | + | 0.102526i | ||||
\(699\) | −12.7913 | + | 22.1552i | −0.483811 | + | 0.837985i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.47822 | + | 11.2206i | 0.244679 | + | 0.423796i | 0.962041 | − | 0.272904i | \(-0.0879841\pi\) |
−0.717362 | + | 0.696700i | \(0.754651\pi\) | |||||||
\(702\) | − | 1.04356i | − | 0.0393867i | ||||||
\(703\) | −9.30780 | − | 12.5390i | −0.351051 | − | 0.472918i | ||||
\(704\) | 3.79129 | 0.142890 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.87386 | + | 11.9059i | 0.258701 | + | 0.448084i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −11.0776 | + | 6.39564i | −0.416321 | + | 0.240363i | ||||
\(709\) | −13.3739 | + | 23.1642i | −0.502266 | + | 0.869950i | 0.497731 | + | 0.867332i | \(0.334167\pi\) |
−0.999997 | + | 0.00261852i | \(0.999166\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 71.6606 | 2.68748 | ||||||||
\(712\) | 3.96863 | + | 2.29129i | 0.148731 | + | 0.0858696i | ||||
\(713\) | 19.0148 | + | 10.9782i | 0.712111 | + | 0.411138i | ||||
\(714\) | 2.20871 | 0.0826590 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.37386 | − | 14.5040i | 0.312946 | − | 0.542038i | ||||
\(717\) | 40.0855 | − | 23.1434i | 1.49702 | − | 0.864305i | ||||
\(718\) | 30.9207 | + | 17.8521i | 1.15395 | + | 0.666234i | ||||
\(719\) | −6.08258 | − | 10.5353i | −0.226842 | − | 0.392902i | 0.730029 | − | 0.683417i | \(-0.239507\pi\) |
−0.956870 | + | 0.290515i | \(0.906173\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.16515 | −0.192360 | ||||||||
\(722\) | 4.33013 | + | 18.5000i | 0.161151 | + | 0.688499i | ||||
\(723\) | 46.8693i | 1.74309i | ||||||||
\(724\) | −3.81307 | − | 6.60443i | −0.141712 | − | 0.245452i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.70871 | − | 8.15573i | 0.174757 | − | 0.302687i | ||||
\(727\) | 3.60713 | − | 2.08258i | 0.133781 | − | 0.0772385i | −0.431616 | − | 0.902058i | \(-0.642056\pi\) |
0.565397 | + | 0.824819i | \(0.308723\pi\) | |||||||
\(728\) | −0.180750 | − | 0.104356i | −0.00669904 | − | 0.00386769i | ||||
\(729\) | 43.8693 | 1.62479 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.29129 | − | 3.96863i | 0.0847463 | − | 0.146785i | ||||
\(732\) | −3.32108 | − | 1.91742i | −0.122751 | − | 0.0708700i | ||||
\(733\) | 12.7477i | 0.470848i | 0.971893 | + | 0.235424i | \(0.0756479\pi\) | ||||
−0.971893 | + | 0.235424i | \(0.924352\pi\) | |||||||
\(734\) | −8.79129 | −0.324492 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.29129 | − | 3.96863i | −0.0844580 | − | 0.146286i | ||||
\(737\) | −51.1631 | − | 29.5390i | −1.88462 | − | 1.08808i | ||||
\(738\) | −47.1944 | + | 27.2477i | −1.73725 | + | 1.00300i | ||||
\(739\) | −17.8739 | − | 30.9584i | −0.657501 | − | 1.13882i | −0.981261 | − | 0.192685i | \(-0.938280\pi\) |
0.323760 | − | 0.946139i | \(-0.395053\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.03901 | + | 1.51358i | −0.0749051 | + | 0.0556026i | ||||
\(742\) | − | 4.58258i | − | 0.168232i | ||||||
\(743\) | 16.8160 | − | 9.70871i | 0.616919 | − | 0.356178i | −0.158750 | − | 0.987319i | \(-0.550746\pi\) |
0.775668 | + | 0.631141i | \(0.217413\pi\) | |||||||
\(744\) | 6.68693 | + | 11.5821i | 0.245155 | + | 0.424621i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.6869 | + | 18.5103i | 0.391276 | + | 0.677711i | ||||
\(747\) | 15.7315 | + | 9.08258i | 0.575585 | + | 0.332314i | ||||
\(748\) | 3.00000i | 0.109691i | ||||||||
\(749\) | 18.9564 | 0.692653 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.7913 | + | 18.6911i | −0.393780 | + | 0.682046i | −0.992945 | − | 0.118579i | \(-0.962166\pi\) |
0.599165 | + | 0.800626i | \(0.295499\pi\) | |||||||
\(752\) | 12.1652i | 0.443617i | ||||||||
\(753\) | − | 36.6261i | − | 1.33473i | ||||||
\(754\) | −0.708712 | + | 1.22753i | −0.0258098 | + | 0.0447038i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.50000 | + | 4.33013i | −0.0909241 | + | 0.157485i | ||||
\(757\) | −39.6187 | + | 22.8739i | −1.43997 | + | 0.831365i | −0.997847 | − | 0.0655915i | \(-0.979107\pi\) |
−0.442119 | + | 0.896956i | \(0.645773\pi\) | |||||||
\(758\) | 4.18710 | − | 2.41742i | 0.152082 | − | 0.0878048i | ||||
\(759\) | −48.4955 | −1.76027 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.2523 | 0.915394 | 0.457697 | − | 0.889108i | \(-0.348674\pi\) | ||||
0.457697 | + | 0.889108i | \(0.348674\pi\) | |||||||
\(762\) | 6.34823 | − | 3.66515i | 0.229972 | − | 0.132774i | ||||
\(763\) | 10.1738 | − | 5.87386i | 0.368317 | − | 0.212648i | ||||
\(764\) | 7.97822 | − | 13.8187i | 0.288642 | − | 0.499942i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.29129 | + | 3.96863i | −0.0827876 | + | 0.143392i | ||||
\(767\) | 0.956439i | 0.0345350i | ||||||||
\(768\) | − | 2.79129i | − | 0.100722i | ||||||
\(769\) | −11.1652 | + | 19.3386i | −0.402626 | + | 0.697368i | −0.994042 | − | 0.108998i | \(-0.965236\pi\) |
0.591416 | + | 0.806366i | \(0.298569\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.2867 | 1.12676 | ||||||||
\(772\) | 2.74773i | 0.0988929i | ||||||||
\(773\) | 18.4726 | + | 10.6652i | 0.664413 | + | 0.383599i | 0.793956 | − | 0.607975i | \(-0.208018\pi\) |
−0.129544 | + | 0.991574i | \(0.541351\pi\) | |||||||
\(774\) | 13.8739 | + | 24.0302i | 0.498686 | + | 0.863749i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.18693 | + | 10.7161i | 0.222098 | + | 0.384685i | ||||
\(777\) | −8.66025 | + | 5.00000i | −0.310685 | + | 0.179374i | ||||
\(778\) | 18.6261i | 0.667779i | ||||||||
\(779\) | 45.4955 | + | 19.7001i | 1.63004 | + | 0.705830i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.68693 | − | 15.0462i | −0.310843 | − | 0.538396i | ||||
\(782\) | 3.14033 | − | 1.81307i | 0.112298 | − | 0.0648352i | ||||
\(783\) | 29.4071 | + | 16.9782i | 1.05093 | + | 0.606752i | ||||
\(784\) | −3.00000 | − | 5.19615i | −0.107143 | − | 0.185577i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −32.2087 | −1.14885 | ||||||||
\(787\) | 23.7477i | 0.846515i | 0.906009 | + | 0.423258i | \(0.139113\pi\) | ||||
−0.906009 | + | 0.423258i | \(0.860887\pi\) | |||||||
\(788\) | −17.5013 | − | 10.1044i | −0.623457 | − | 0.359953i | ||||
\(789\) | 27.0998 | − | 46.9382i | 0.964779 | − | 1.67105i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.37386 | −0.191073 | ||||||||
\(792\) | −15.7315 | − | 9.08258i | −0.558994 | − | 0.322735i | ||||
\(793\) | −0.248326 | + | 0.143371i | −0.00881831 | + | 0.00509125i | ||||
\(794\) | −5.70871 | + | 9.88778i | −0.202595 | + | 0.350904i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.79129 | − | 3.10260i | −0.0634905 | − | 0.109969i | ||||
\(797\) | 38.5390i | 1.36512i | 0.730829 | + | 0.682561i | \(0.239134\pi\) | ||||
−0.730829 | + | 0.682561i | \(0.760866\pi\) | |||||||
\(798\) | 12.0866 | − | 1.39564i | 0.427862 | − | 0.0494053i | ||||
\(799\) | −9.62614 | −0.340548 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.9782 | − | 19.0148i | −0.387896 | − | 0.671856i | ||||
\(802\) | −10.3923 | − | 6.00000i | −0.366965 | − | 0.211867i | ||||
\(803\) | −9.16478 | + | 5.29129i | −0.323418 | + | 0.186725i | ||||
\(804\) | −21.7477 | + | 37.6682i | −0.766983 | + | 1.32845i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.00000 | 0.0352235 | ||||||||
\(807\) | −31.7192 | − | 18.3131i | −1.11657 | − | 0.644651i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.53901 | 0.0892670 | 0.0446335 | − | 0.999003i | \(-0.485788\pi\) | ||||
0.0446335 | + | 0.999003i | \(0.485788\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.9347 | + | 22.4035i | −0.454197 | + | 0.786693i | −0.998642 | − | 0.0521042i | \(-0.983407\pi\) |
0.544444 | + | 0.838797i | \(0.316741\pi\) | |||||||
\(812\) | 5.88143 | − | 3.39564i | 0.206398 | − | 0.119164i | ||||
\(813\) | −41.3885 | − | 23.8956i | −1.45156 | − | 0.838057i | ||||
\(814\) | −6.79129 | − | 11.7629i | −0.238035 | − | 0.412288i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.20871 | 0.0773204 | ||||||||
\(817\) | 10.0308 | − | 23.1652i | 0.350933 | − | 0.810446i | ||||
\(818\) | − | 10.0000i | − | 0.349642i | ||||||
\(819\) | 0.500000 | + | 0.866025i | 0.0174714 | + | 0.0302614i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.1652 | − | 31.4630i | 0.633968 | − | 1.09807i | −0.352765 | − | 0.935712i | \(-0.614758\pi\) |
0.986733 | − | 0.162353i | \(-0.0519083\pi\) | |||||||
\(822\) | 37.0583 | − | 21.3956i | 1.29256 | − | 0.746259i | ||||
\(823\) | −31.8245 | − | 18.3739i | −1.10933 | − | 0.640473i | −0.170675 | − | 0.985327i | \(-0.554595\pi\) |
−0.938656 | + | 0.344855i | \(0.887928\pi\) | |||||||
\(824\) | −5.16515 | −0.179937 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.29129 | − | 3.96863i | 0.0797241 | − | 0.138086i | ||||
\(827\) | −25.0393 | − | 14.4564i | −0.870701 | − | 0.502700i | −0.00312009 | − | 0.999995i | \(-0.500993\pi\) |
−0.867581 | + | 0.497295i | \(0.834326\pi\) | |||||||
\(828\) | 21.9564i | 0.763039i | ||||||||
\(829\) | −31.5390 | −1.09540 | −0.547698 | − | 0.836676i | \(-0.684496\pi\) | ||||
−0.547698 | + | 0.836676i | \(0.684496\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.2087 | − | 21.1461i | −0.423516 | − | 0.733550i | ||||
\(832\) | −0.180750 | − | 0.104356i | −0.00626638 | − | 0.00361790i | ||||
\(833\) | 4.11165 | − | 2.37386i | 0.142460 | − | 0.0822495i | ||||
\(834\) | 17.0390 | + | 29.5124i | 0.590013 | + | 1.02193i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.89564 | + | 16.4168i | 0.0655622 | + | 0.567785i | ||||
\(837\) | − | 23.9564i | − | 0.828056i | ||||||
\(838\) | −19.7001 | + | 11.3739i | −0.680529 | + | 0.392904i | ||||
\(839\) | 25.9782 | + | 44.9956i | 0.896868 | + | 1.55342i | 0.831476 | + | 0.555561i | \(0.187496\pi\) |
0.0653918 | + | 0.997860i | \(0.479170\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.56080 | − | 14.8277i | −0.295200 | − | 0.511301i | ||||
\(842\) | 17.3205 | + | 10.0000i | 0.596904 | + | 0.344623i | ||||
\(843\) | − | 29.5390i | − | 1.01738i | ||||||
\(844\) | −23.9564 | −0.824615 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 29.1434 | − | 50.4778i | 1.00197 | − | 1.73546i | ||||
\(847\) | 3.37386i | 0.115927i | ||||||||
\(848\) | − | 4.58258i | − | 0.157366i | ||||||
\(849\) | −29.4782 | + | 51.0578i | −1.01169 | + | 1.75230i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.20871 | + | 14.2179i | −0.281391 | + | 0.487384i | ||||
\(852\) | −11.0776 | + | 6.39564i | −0.379512 | + | 0.219111i | ||||
\(853\) | −45.0632 | + | 26.0172i | −1.54293 | + | 0.890813i | −0.544282 | + | 0.838902i | \(0.683198\pi\) |
−0.998652 | + | 0.0519108i | \(0.983469\pi\) | |||||||
\(854\) | 1.37386 | 0.0470126 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.9564 | 0.647918 | ||||||||
\(857\) | −2.59808 | + | 1.50000i | −0.0887486 | + | 0.0512390i | −0.543718 | − | 0.839268i | \(-0.682984\pi\) |
0.454969 | + | 0.890507i | \(0.349650\pi\) | |||||||
\(858\) | −1.91280 | + | 1.10436i | −0.0653019 | + | 0.0377021i | ||||
\(859\) | 8.35208 | − | 14.4662i | 0.284969 | − | 0.493581i | −0.687632 | − | 0.726059i | \(-0.741350\pi\) |
0.972602 | + | 0.232478i | \(0.0746832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.8739 | − | 27.4943i | 0.540980 | − | 0.937005i | ||||
\(862\) | − | 8.20871i | − | 0.279590i | ||||||
\(863\) | − | 4.41742i | − | 0.150371i | −0.997170 | − | 0.0751854i | \(-0.976045\pi\) | ||
0.997170 | − | 0.0751854i | \(-0.0239549\pi\) | |||||||
\(864\) | −2.50000 | + | 4.33013i | −0.0850517 | + | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.91288 | 0.234909 | ||||||||
\(867\) | − | 45.7042i | − | 1.55219i | ||||||
\(868\) | −4.14938 | − | 2.39564i | −0.140839 | − | 0.0813135i | ||||
\(869\) | −28.3521 | − | 49.1072i | −0.961779 | − | 1.66585i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.62614 | + | 2.81655i | 0.0550995 | + | 0.0954352i | ||||
\(872\) | 10.1738 | − | 5.87386i | 0.344529 | − | 0.198914i | ||||
\(873\) | − | 59.2867i | − | 2.00655i | ||||||
\(874\) | 16.0390 | − | 11.9059i | 0.542528 | − | 0.402722i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.89564 | + | 6.74745i | 0.131622 | + | 0.227975i | ||||
\(877\) | −22.9457 | + | 13.2477i | −0.774822 | + | 0.447344i | −0.834592 | − | 0.550868i | \(-0.814297\pi\) |
0.0597698 | + | 0.998212i | \(0.480963\pi\) | |||||||
\(878\) | 21.9367 | + | 12.6652i | 0.740327 | + | 0.427428i | ||||
\(879\) | −34.8303 | − | 60.3279i | −1.17480 | − | 2.03481i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.791288 | −0.0266592 | −0.0133296 | − | 0.999911i | \(-0.504243\pi\) | ||||
−0.0133296 | + | 0.999911i | \(0.504243\pi\) | |||||||
\(882\) | 28.7477i | 0.967986i | ||||||||
\(883\) | −21.4322 | − | 12.3739i | −0.721250 | − | 0.416414i | 0.0939628 | − | 0.995576i | \(-0.470047\pi\) |
−0.815212 | + | 0.579162i | \(0.803380\pi\) | |||||||
\(884\) | 0.0825757 | − | 0.143025i | 0.00277732 | − | 0.00481046i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.0000 | −0.806296 | ||||||||
\(887\) | −29.5502 | − | 17.0608i | −0.992197 | − | 0.572845i | −0.0862670 | − | 0.996272i | \(-0.527494\pi\) |
−0.905930 | + | 0.423427i | \(0.860827\pi\) | |||||||
\(888\) | −8.66025 | + | 5.00000i | −0.290619 | + | 0.167789i | ||||
\(889\) | −1.31307 | + | 2.27430i | −0.0440389 | + | 0.0762776i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.791288 | − | 1.37055i | −0.0265091 | − | 0.0459152i | ||||
\(892\) | − | 19.2087i | − | 0.643155i | ||||||
\(893\) | −52.6767 | + | 6.08258i | −1.76276 | + | 0.203546i | ||||
\(894\) | −63.4955 | −2.12361 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.500000 | + | 0.866025i | 0.0167038 | + | 0.0289319i | ||||
\(897\) | 2.31203 | + | 1.33485i | 0.0771963 | + | 0.0445693i | ||||
\(898\) | 2.88413 | − | 1.66515i | 0.0962446 | − | 0.0555668i | ||||
\(899\) | −16.2695 | + | 28.1796i | −0.542618 | + | 0.939843i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.62614 | 0.120804 | ||||||||
\(902\) | 37.3444 | + | 21.5608i | 1.24343 | + | 0.717896i | ||||
\(903\) | −13.9994 | − | 8.08258i | −0.465872 | − | 0.268971i | ||||
\(904\) | −5.37386 | −0.178732 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 21.9782 | − | 38.0674i | 0.730177 | − | 1.26470i | ||||
\(907\) | 29.3317 | − | 16.9347i | 0.973943 | − | 0.562306i | 0.0735068 | − | 0.997295i | \(-0.476581\pi\) |
0.900436 | + | 0.434989i | \(0.143248\pi\) | |||||||
\(908\) | −6.70973 | − | 3.87386i | −0.222670 | − | 0.128559i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.6606 | −1.61220 | −0.806099 | − | 0.591781i | \(-0.798425\pi\) | ||||
−0.806099 | + | 0.591781i | \(0.798425\pi\) | |||||||
\(912\) | 12.0866 | − | 1.39564i | 0.400228 | − | 0.0462144i | ||||
\(913\) | − | 14.3739i | − | 0.475705i | ||||||
\(914\) | −10.3739 | − | 17.9681i | −0.343137 | − | 0.594331i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.6652 | − | 21.9367i | 0.418468 | − | 0.724808i | ||||
\(917\) | 9.99308 | − | 5.76951i | 0.330001 | − | 0.190526i | ||||
\(918\) | −3.42638 | − | 1.97822i | −0.113087 | − | 0.0652910i | ||||
\(919\) | 46.7913 | 1.54350 | 0.771751 | − | 0.635925i | \(-0.219381\pi\) | ||||
0.771751 | + | 0.635925i | \(0.219381\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −48.1434 | + | 83.3868i | −1.58638 | + | 2.74769i | ||||
\(922\) | 11.0776 | + | 6.39564i | 0.364821 | + | 0.210629i | ||||
\(923\) | 0.956439i | 0.0314816i | ||||||||
\(924\) | 10.5826 | 0.348141 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.97822 | − | 15.5507i | −0.295043 | − | 0.511029i | ||||
\(927\) | 21.4322 | + | 12.3739i | 0.703925 | + | 0.406411i | ||||
\(928\) | 5.88143 | − | 3.39564i | 0.193067 | − | 0.111467i | ||||
\(929\) | 5.43920 | + | 9.42098i | 0.178455 | + | 0.309092i | 0.941351 | − | 0.337428i | \(-0.109557\pi\) |
−0.762897 | + | 0.646520i | \(0.776224\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.0000 | − | 15.5885i | 0.688247 | − | 0.510891i | ||||
\(932\) | − | 9.16515i | − | 0.300215i | ||||||
\(933\) | 36.2599 | − | 20.9347i | 1.18710 | − | 0.685370i | ||||
\(934\) | −6.16515 | − | 10.6784i | −0.201730 | − | 0.349406i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | + | 0.866025i | 0.0163430 | + | 0.0283069i | ||||
\(937\) | 5.30145 | + | 3.06080i | 0.173191 | + | 0.0999918i | 0.584090 | − | 0.811689i | \(-0.301452\pi\) |
−0.410899 | + | 0.911681i | \(0.634785\pi\) | |||||||
\(938\) | − | 15.5826i | − | 0.508789i | ||||||
\(939\) | −32.7913 | −1.07010 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.2913 | − | 35.1455i | 0.661477 | − | 1.14571i | −0.318751 | − | 0.947839i | \(-0.603263\pi\) |
0.980228 | − | 0.197873i | \(-0.0634034\pi\) | |||||||
\(942\) | − | 22.2087i | − | 0.723599i | ||||||
\(943\) | − | 52.1216i | − | 1.69731i | ||||||
\(944\) | 2.29129 | − | 3.96863i | 0.0745751 | − | 0.129168i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.9782 | − | 19.0148i | 0.356933 | − | 0.618226i | ||||
\(947\) | 24.7532 | − | 14.2913i | 0.804372 | − | 0.464404i | −0.0406256 | − | 0.999174i | \(-0.512935\pi\) |
0.844998 | + | 0.534770i | \(0.179602\pi\) | |||||||
\(948\) | −36.1546 | + | 20.8739i | −1.17425 | + | 0.677952i | ||||
\(949\) | 0.582576 | 0.0189112 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.5826 | 0.829572 | ||||||||
\(952\) | −0.685275 | + | 0.395644i | −0.0222099 | + | 0.0128229i | ||||
\(953\) | −13.9617 | + | 8.06080i | −0.452264 | + | 0.261115i | −0.708786 | − | 0.705424i | \(-0.750757\pi\) |
0.256522 | + | 0.966538i | \(0.417423\pi\) | |||||||
\(954\) | −10.9782 | + | 19.0148i | −0.355433 | + | 0.615628i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.29129 | + | 14.3609i | −0.268159 | + | 0.464466i | ||||
\(957\) | − | 71.8693i | − | 2.32321i | ||||||
\(958\) | 31.7477i | 1.02572i | ||||||||
\(959\) | −7.66515 | + | 13.2764i | −0.247521 | + | 0.428718i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.04356 | −0.259470 | ||||||||
\(962\) | 0.747727i | 0.0241077i | ||||||||
\(963\) | −78.6574 | − | 45.4129i | −2.53470 | − | 1.46341i | ||||
\(964\) | −8.39564 | − | 14.5417i | −0.270405 | − | 0.468356i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.39564 | − | 11.0776i | −0.205776 | − | 0.356415i | ||||
\(967\) | 44.2349 | − | 25.5390i | 1.42250 | − | 0.821279i | 0.425986 | − | 0.904730i | \(-0.359927\pi\) |
0.996512 | + | 0.0834506i | \(0.0265941\pi\) | |||||||
\(968\) | 3.37386i | 0.108440i | ||||||||
\(969\) | 1.10436 | + | 9.56400i | 0.0354770 | + | 0.307240i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.543561 | + | 0.941475i | 0.0174437 | + | 0.0302134i | 0.874615 | − | 0.484817i | \(-0.161114\pi\) |
−0.857172 | + | 0.515031i | \(0.827781\pi\) | |||||||
\(972\) | −13.9994 | + | 8.08258i | −0.449032 | + | 0.259249i | ||||
\(973\) | −10.5731 | − | 6.10436i | −0.338957 | − | 0.195697i | ||||
\(974\) | 11.5000 | + | 19.9186i | 0.368484 | + | 0.638233i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.37386 | 0.0439763 | ||||||||
\(977\) | − | 32.3739i | − | 1.03573i | −0.855462 | − | 0.517866i | \(-0.826727\pi\) | ||
0.855462 | − | 0.517866i | \(-0.173273\pi\) | |||||||
\(978\) | −35.2508 | − | 20.3521i | −1.12720 | − | 0.650788i | ||||
\(979\) | −8.68693 | + | 15.0462i | −0.277636 | + | 0.480879i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −56.2867 | −1.79710 | ||||||||
\(982\) | −27.2083 | − | 15.7087i | −0.868251 | − | 0.501285i | ||||
\(983\) | 42.9398 | − | 24.7913i | 1.36957 | − | 0.790719i | 0.378694 | − | 0.925522i | \(-0.376373\pi\) |
0.990872 | + | 0.134803i | \(0.0430401\pi\) | |||||||
\(984\) | 15.8739 | − | 27.4943i | 0.506040 | − | 0.876487i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.68693 | + | 4.65390i | 0.0855693 | + | 0.148210i | ||||
\(987\) | 33.9564i | 1.08085i | ||||||||
\(988\) | 0.361500 | − | 0.834849i | 0.0115008 | − | 0.0265601i | ||||
\(989\) | −26.5390 | −0.843892 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0608 | − | 20.8899i | −0.383124 | − | 0.663590i | 0.608383 | − | 0.793643i | \(-0.291818\pi\) |
−0.991507 | + | 0.130054i | \(0.958485\pi\) | |||||||
\(992\) | −4.14938 | − | 2.39564i | −0.131743 | − | 0.0760618i | ||||
\(993\) | 43.3013 | − | 25.0000i | 1.37412 | − | 0.793351i | ||||
\(994\) | 2.29129 | − | 3.96863i | 0.0726752 | − | 0.125877i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.5826 | −0.335322 | ||||||||
\(997\) | −0.866025 | − | 0.500000i | −0.0274273 | − | 0.0158352i | 0.486224 | − | 0.873834i | \(-0.338374\pi\) |
−0.513651 | + | 0.857999i | \(0.671707\pi\) | |||||||
\(998\) | 16.7405 | + | 9.66515i | 0.529912 | + | 0.305945i | ||||
\(999\) | 17.9129 | 0.566738 |
(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 | 950.2.j.h.349.1 | 8 | ||
5.2 | odd | 4 | 950.2.e.i.501.2 | yes | 4 | ||
5.3 | odd | 4 | 950.2.e.j.501.1 | yes | 4 | ||
5.4 | even | 2 | inner | 950.2.j.h.349.4 | 8 | ||
19.11 | even | 3 | inner | 950.2.j.h.49.4 | 8 | ||
95.49 | even | 6 | inner | 950.2.j.h.49.1 | 8 | ||
95.68 | odd | 12 | 950.2.e.j.201.1 | yes | 4 | ||
95.87 | odd | 12 | 950.2.e.i.201.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.e.i.201.2 | ✓ | 4 | 95.87 | odd | 12 | ||
950.2.e.i.501.2 | yes | 4 | 5.2 | odd | 4 | ||
950.2.e.j.201.1 | yes | 4 | 95.68 | odd | 12 | ||
950.2.e.j.501.1 | yes | 4 | 5.3 | odd | 4 | ||
950.2.j.h.49.1 | 8 | 95.49 | even | 6 | inner | ||
950.2.j.h.49.4 | 8 | 19.11 | even | 3 | inner | ||
950.2.j.h.349.1 | 8 | 1.1 | even | 1 | trivial | ||
950.2.j.h.349.4 | 8 | 5.4 | even | 2 | inner |