Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(201,950)]
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([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.e (of order \(3\), degree \(2\), 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: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.2 | ||
Root | \(-0.895644 + 1.09445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.201 |
Dual form | 950.2.e.j.501.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.895644 | − | 1.55130i | 0.517100 | − | 0.895644i | −0.482703 | − | 0.875784i | \(-0.660345\pi\) |
0.999803 | − | 0.0198595i | \(-0.00632191\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.895644 | − | 1.55130i | −0.365645 | − | 0.633316i | ||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.104356 | − | 0.180750i | −0.0347854 | − | 0.0602500i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.791288 | 0.238582 | 0.119291 | − | 0.992859i | \(-0.461938\pi\) | ||||
0.119291 | + | 0.992859i | \(0.461938\pi\) | |||||||
\(12\) | −1.79129 | −0.517100 | ||||||||
\(13\) | −2.39564 | − | 4.14938i | −0.664432 | − | 1.15083i | −0.979439 | − | 0.201741i | \(-0.935340\pi\) |
0.315007 | − | 0.949089i | \(-0.397993\pi\) | |||||||
\(14\) | 0.500000 | − | 0.866025i | 0.133631 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.89564 | − | 3.28335i | 0.459761 | − | 0.796330i | −0.539187 | − | 0.842186i | \(-0.681268\pi\) |
0.998948 | + | 0.0458564i | \(0.0146017\pi\) | |||||||
\(18\) | −0.208712 | −0.0491939 | ||||||||
\(19\) | −3.50000 | − | 2.59808i | −0.802955 | − | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.895644 | − | 1.55130i | 0.195446 | − | 0.338522i | ||||
\(22\) | 0.395644 | − | 0.685275i | 0.0843516 | − | 0.146101i | ||||
\(23\) | −2.29129 | − | 3.96863i | −0.477767 | − | 0.827516i | 0.521909 | − | 0.853001i | \(-0.325220\pi\) |
−0.999675 | + | 0.0254855i | \(0.991887\pi\) | |||||||
\(24\) | −0.895644 | + | 1.55130i | −0.182823 | + | 0.316658i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.79129 | −0.939649 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | −0.500000 | − | 0.866025i | −0.0944911 | − | 0.163663i | ||||
\(29\) | −1.10436 | − | 1.91280i | −0.205074 | − | 0.355198i | 0.745082 | − | 0.666972i | \(-0.232410\pi\) |
−0.950156 | + | 0.311774i | \(0.899077\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.208712 | −0.0374858 | −0.0187429 | − | 0.999824i | \(-0.505966\pi\) | ||||
−0.0187429 | + | 0.999824i | \(0.505966\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0.708712 | − | 1.22753i | 0.123371 | − | 0.213685i | ||||
\(34\) | −1.89564 | − | 3.28335i | −0.325100 | − | 0.563090i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.104356 | + | 0.180750i | −0.0173927 | + | 0.0301250i | ||||
\(37\) | 5.58258 | 0.917770 | 0.458885 | − | 0.888496i | \(-0.348249\pi\) | ||||
0.458885 | + | 0.888496i | \(0.348249\pi\) | |||||||
\(38\) | −4.00000 | + | 1.73205i | −0.648886 | + | 0.280976i | ||||
\(39\) | −8.58258 | −1.37431 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.18693 | + | 2.05583i | −0.185368 | + | 0.321066i | −0.943700 | − | 0.330802i | \(-0.892681\pi\) |
0.758333 | + | 0.651868i | \(0.226014\pi\) | |||||||
\(42\) | −0.895644 | − | 1.55130i | −0.138201 | − | 0.239371i | ||||
\(43\) | 0.604356 | − | 1.04678i | 0.0921634 | − | 0.159632i | −0.816258 | − | 0.577688i | \(-0.803955\pi\) |
0.908421 | + | 0.418056i | \(0.137288\pi\) | |||||||
\(44\) | −0.395644 | − | 0.685275i | −0.0596456 | − | 0.103309i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.58258 | −0.675664 | ||||||||
\(47\) | 3.08258 | + | 5.33918i | 0.449640 | + | 0.778799i | 0.998362 | − | 0.0572054i | \(-0.0182190\pi\) |
−0.548723 | + | 0.836005i | \(0.684886\pi\) | |||||||
\(48\) | 0.895644 | + | 1.55130i | 0.129275 | + | 0.223911i | ||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.39564 | − | 5.88143i | −0.475485 | − | 0.823565i | ||||
\(52\) | −2.39564 | + | 4.14938i | −0.332216 | + | 0.575415i | ||||
\(53\) | 2.29129 | + | 3.96863i | 0.314733 | + | 0.545133i | 0.979381 | − | 0.202024i | \(-0.0647518\pi\) |
−0.664648 | + | 0.747157i | \(0.731418\pi\) | |||||||
\(54\) | 2.50000 | − | 4.33013i | 0.340207 | − | 0.589256i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −7.16515 | + | 3.10260i | −0.949047 | + | 0.410950i | ||||
\(58\) | −2.20871 | −0.290018 | ||||||||
\(59\) | 2.29129 | − | 3.96863i | 0.298300 | − | 0.516671i | −0.677447 | − | 0.735572i | \(-0.736914\pi\) |
0.975747 | + | 0.218900i | \(0.0702470\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.18693 | + | 10.7161i | 0.792155 | + | 1.37205i | 0.924630 | + | 0.380867i | \(0.124374\pi\) |
−0.132474 | + | 0.991186i | \(0.542292\pi\) | |||||||
\(62\) | −0.104356 | + | 0.180750i | −0.0132532 | + | 0.0229553i | ||||
\(63\) | −0.104356 | − | 0.180750i | −0.0131476 | − | 0.0227724i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.708712 | − | 1.22753i | −0.0872364 | − | 0.151098i | ||||
\(67\) | 3.20871 | + | 5.55765i | 0.392007 | + | 0.678975i | 0.992714 | − | 0.120494i | \(-0.0384477\pi\) |
−0.600708 | + | 0.799469i | \(0.705114\pi\) | |||||||
\(68\) | −3.79129 | −0.459761 | ||||||||
\(69\) | −8.20871 | −0.988213 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.29129 | + | 3.96863i | −0.271926 | + | 0.470989i | −0.969355 | − | 0.245664i | \(-0.920994\pi\) |
0.697429 | + | 0.716654i | \(0.254327\pi\) | |||||||
\(72\) | 0.104356 | + | 0.180750i | 0.0122985 | + | 0.0213016i | ||||
\(73\) | −0.895644 | + | 1.55130i | −0.104827 | + | 0.181566i | −0.913668 | − | 0.406462i | \(-0.866762\pi\) |
0.808840 | + | 0.588028i | \(0.200096\pi\) | |||||||
\(74\) | 2.79129 | − | 4.83465i | 0.324481 | − | 0.562017i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.500000 | + | 4.33013i | −0.0573539 | + | 0.496700i | ||||
\(77\) | 0.791288 | 0.0901756 | ||||||||
\(78\) | −4.29129 | + | 7.43273i | −0.485893 | + | 0.841591i | ||||
\(79\) | 3.97822 | − | 6.89048i | 0.447585 | − | 0.775239i | −0.550644 | − | 0.834740i | \(-0.685618\pi\) |
0.998228 | + | 0.0595011i | \(0.0189510\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.79129 | − | 8.29875i | 0.532365 | − | 0.922084i | ||||
\(82\) | 1.18693 | + | 2.05583i | 0.131075 | + | 0.227028i | ||||
\(83\) | 0.791288 | 0.0868551 | 0.0434276 | − | 0.999057i | \(-0.486172\pi\) | ||||
0.0434276 | + | 0.999057i | \(0.486172\pi\) | |||||||
\(84\) | −1.79129 | −0.195446 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.604356 | − | 1.04678i | −0.0651694 | − | 0.112877i | ||||
\(87\) | −3.95644 | −0.424175 | ||||||||
\(88\) | −0.791288 | −0.0843516 | ||||||||
\(89\) | 2.29129 | + | 3.96863i | 0.242876 | + | 0.420674i | 0.961532 | − | 0.274692i | \(-0.0885758\pi\) |
−0.718656 | + | 0.695365i | \(0.755243\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.39564 | − | 4.14938i | −0.251132 | − | 0.434973i | ||||
\(92\) | −2.29129 | + | 3.96863i | −0.238883 | + | 0.413758i | ||||
\(93\) | −0.186932 | + | 0.323775i | −0.0193839 | + | 0.0335739i | ||||
\(94\) | 6.16515 | 0.635887 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.79129 | 0.182823 | ||||||||
\(97\) | 0.686932 | − | 1.18980i | 0.0697474 | − | 0.120806i | −0.829043 | − | 0.559185i | \(-0.811114\pi\) |
0.898790 | + | 0.438379i | \(0.144447\pi\) | |||||||
\(98\) | −3.00000 | + | 5.19615i | −0.303046 | + | 0.524891i | ||||
\(99\) | −0.0825757 | − | 0.143025i | −0.00829917 | − | 0.0143746i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | −6.79129 | −0.672438 | ||||||||
\(103\) | 13.1652 | 1.29720 | 0.648600 | − | 0.761129i | \(-0.275355\pi\) | ||||
0.648600 | + | 0.761129i | \(0.275355\pi\) | |||||||
\(104\) | 2.39564 | + | 4.14938i | 0.234912 | + | 0.406880i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.58258 | 0.445099 | ||||||||
\(107\) | 3.95644 | 0.382483 | 0.191242 | − | 0.981543i | \(-0.438749\pi\) | ||||
0.191242 | + | 0.981543i | \(0.438749\pi\) | |||||||
\(108\) | −2.50000 | − | 4.33013i | −0.240563 | − | 0.416667i | ||||
\(109\) | −7.87386 | + | 13.6379i | −0.754179 | + | 1.30628i | 0.191602 | + | 0.981473i | \(0.438632\pi\) |
−0.945781 | + | 0.324804i | \(0.894702\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.00000 | − | 8.66025i | 0.474579 | − | 0.821995i | ||||
\(112\) | −0.500000 | + | 0.866025i | −0.0472456 | + | 0.0818317i | ||||
\(113\) | 8.37386 | 0.787747 | 0.393873 | − | 0.919165i | \(-0.371135\pi\) | ||||
0.393873 | + | 0.919165i | \(0.371135\pi\) | |||||||
\(114\) | −0.895644 | + | 7.75650i | −0.0838847 | + | 0.726463i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.10436 | + | 1.91280i | −0.102537 | + | 0.177599i | ||||
\(117\) | −0.500000 | + | 0.866025i | −0.0462250 | + | 0.0800641i | ||||
\(118\) | −2.29129 | − | 3.96863i | −0.210930 | − | 0.365342i | ||||
\(119\) | 1.89564 | − | 3.28335i | 0.173773 | − | 0.300984i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3739 | −0.943079 | ||||||||
\(122\) | 12.3739 | 1.12028 | ||||||||
\(123\) | 2.12614 | + | 3.68258i | 0.191707 | + | 0.332047i | ||||
\(124\) | 0.104356 | + | 0.180750i | 0.00937145 | + | 0.0162318i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.208712 | −0.0185936 | ||||||||
\(127\) | 8.18693 | + | 14.1802i | 0.726473 | + | 1.25829i | 0.958365 | + | 0.285546i | \(0.0921750\pi\) |
−0.231892 | + | 0.972741i | \(0.574492\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −1.08258 | − | 1.87508i | −0.0953155 | − | 0.165091i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2695 | − | 17.7873i | 0.897251 | − | 1.55408i | 0.0662573 | − | 0.997803i | \(-0.478894\pi\) |
0.830994 | − | 0.556282i | \(-0.187772\pi\) | |||||||
\(132\) | −1.41742 | −0.123371 | ||||||||
\(133\) | −3.50000 | − | 2.59808i | −0.303488 | − | 0.225282i | ||||
\(134\) | 6.41742 | 0.554381 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.89564 | + | 3.28335i | −0.162550 | + | 0.281545i | ||||
\(137\) | −10.6652 | − | 18.4726i | −0.911185 | − | 1.57822i | −0.812392 | − | 0.583111i | \(-0.801835\pi\) |
−0.0987932 | − | 0.995108i | \(-0.531498\pi\) | |||||||
\(138\) | −4.10436 | + | 7.10895i | −0.349386 | + | 0.605154i | ||||
\(139\) | 8.39564 | + | 14.5417i | 0.712109 | + | 1.23341i | 0.964064 | + | 0.265670i | \(0.0855933\pi\) |
−0.251955 | + | 0.967739i | \(0.581073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.0436 | 0.930036 | ||||||||
\(142\) | 2.29129 | + | 3.96863i | 0.192281 | + | 0.333040i | ||||
\(143\) | −1.89564 | − | 3.28335i | −0.158522 | − | 0.274568i | ||||
\(144\) | 0.208712 | 0.0173927 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.895644 | + | 1.55130i | 0.0741240 | + | 0.128387i | ||||
\(147\) | −5.37386 | + | 9.30780i | −0.443229 | + | 0.767695i | ||||
\(148\) | −2.79129 | − | 4.83465i | −0.229442 | − | 0.397406i | ||||
\(149\) | −2.37386 | + | 4.11165i | −0.194474 | + | 0.336840i | −0.946728 | − | 0.322034i | \(-0.895633\pi\) |
0.752254 | + | 0.658874i | \(0.228967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.7477 | −0.956016 | −0.478008 | − | 0.878355i | \(-0.658641\pi\) | ||||
−0.478008 | + | 0.878355i | \(0.658641\pi\) | |||||||
\(152\) | 3.50000 | + | 2.59808i | 0.283887 | + | 0.210732i | ||||
\(153\) | −0.791288 | −0.0639718 | ||||||||
\(154\) | 0.395644 | − | 0.685275i | 0.0318819 | − | 0.0552211i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.29129 | + | 7.43273i | 0.343578 | + | 0.595095i | ||||
\(157\) | 7.47822 | − | 12.9527i | 0.596827 | − | 1.03373i | −0.396459 | − | 0.918052i | \(-0.629761\pi\) |
0.993286 | − | 0.115682i | \(-0.0369054\pi\) | |||||||
\(158\) | −3.97822 | − | 6.89048i | −0.316490 | − | 0.548177i | ||||
\(159\) | 8.20871 | 0.650993 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.29129 | − | 3.96863i | −0.180579 | − | 0.312772i | ||||
\(162\) | −4.79129 | − | 8.29875i | −0.376439 | − | 0.652012i | ||||
\(163\) | 5.41742 | 0.424325 | 0.212163 | − | 0.977234i | \(-0.431949\pi\) | ||||
0.212163 | + | 0.977234i | \(0.431949\pi\) | |||||||
\(164\) | 2.37386 | 0.185368 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.395644 | − | 0.685275i | 0.0307079 | − | 0.0531877i | ||||
\(167\) | −10.2695 | − | 17.7873i | −0.794678 | − | 1.37642i | −0.923043 | − | 0.384696i | \(-0.874306\pi\) |
0.128365 | − | 0.991727i | \(-0.459027\pi\) | |||||||
\(168\) | −0.895644 | + | 1.55130i | −0.0691004 | + | 0.119685i | ||||
\(169\) | −4.97822 | + | 8.62253i | −0.382940 | + | 0.663271i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.104356 | + | 0.903750i | −0.00798031 | + | 0.0691115i | ||||
\(172\) | −1.20871 | −0.0921634 | ||||||||
\(173\) | −10.5000 | + | 18.1865i | −0.798300 | + | 1.38270i | 0.122422 | + | 0.992478i | \(0.460934\pi\) |
−0.920722 | + | 0.390218i | \(0.872399\pi\) | |||||||
\(174\) | −1.97822 | + | 3.42638i | −0.149968 | + | 0.259753i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.395644 | + | 0.685275i | −0.0298228 | + | 0.0516546i | ||||
\(177\) | −4.10436 | − | 7.10895i | −0.308502 | − | 0.534342i | ||||
\(178\) | 4.58258 | 0.343479 | ||||||||
\(179\) | 10.7477 | 0.803323 | 0.401661 | − | 0.915788i | \(-0.368433\pi\) | ||||
0.401661 | + | 0.915788i | \(0.368433\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.6869 | + | 18.5103i | 0.794353 | + | 1.37586i | 0.923249 | + | 0.384202i | \(0.125523\pi\) |
−0.128896 | + | 0.991658i | \(0.541143\pi\) | |||||||
\(182\) | −4.79129 | −0.355154 | ||||||||
\(183\) | 22.1652 | 1.63850 | ||||||||
\(184\) | 2.29129 | + | 3.96863i | 0.168916 | + | 0.292571i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.186932 | + | 0.323775i | 0.0137065 | + | 0.0237404i | ||||
\(187\) | 1.50000 | − | 2.59808i | 0.109691 | − | 0.189990i | ||||
\(188\) | 3.08258 | − | 5.33918i | 0.224820 | − | 0.389400i | ||||
\(189\) | 5.00000 | 0.363696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.95644 | −0.503350 | −0.251675 | − | 0.967812i | \(-0.580981\pi\) | ||||
−0.251675 | + | 0.967812i | \(0.580981\pi\) | |||||||
\(192\) | 0.895644 | − | 1.55130i | 0.0646375 | − | 0.111955i | ||||
\(193\) | 12.3739 | − | 21.4322i | 0.890690 | − | 1.54272i | 0.0516406 | − | 0.998666i | \(-0.483555\pi\) |
0.839050 | − | 0.544055i | \(-0.183112\pi\) | |||||||
\(194\) | −0.686932 | − | 1.18980i | −0.0493188 | − | 0.0854227i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | + | 5.19615i | 0.214286 | + | 0.371154i | ||||
\(197\) | −24.7913 | −1.76631 | −0.883153 | − | 0.469085i | \(-0.844584\pi\) | ||||
−0.883153 | + | 0.469085i | \(0.844584\pi\) | |||||||
\(198\) | −0.165151 | −0.0117368 | ||||||||
\(199\) | 2.79129 | + | 4.83465i | 0.197869 | + | 0.342719i | 0.947837 | − | 0.318755i | \(-0.103265\pi\) |
−0.749968 | + | 0.661474i | \(0.769931\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.4955 | 0.810827 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.10436 | − | 1.91280i | −0.0775106 | − | 0.134252i | ||||
\(204\) | −3.39564 | + | 5.88143i | −0.237743 | + | 0.411782i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.58258 | − | 11.4014i | 0.458630 | − | 0.794370i | ||||
\(207\) | −0.478220 | + | 0.828301i | −0.0332386 | + | 0.0575709i | ||||
\(208\) | 4.79129 | 0.332216 | ||||||||
\(209\) | −2.76951 | − | 2.05583i | −0.191571 | − | 0.142204i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.521780 | + | 0.903750i | −0.0359208 | + | 0.0622167i | −0.883427 | − | 0.468569i | \(-0.844770\pi\) |
0.847506 | + | 0.530786i | \(0.178103\pi\) | |||||||
\(212\) | 2.29129 | − | 3.96863i | 0.157366 | − | 0.272566i | ||||
\(213\) | 4.10436 | + | 7.10895i | 0.281226 | + | 0.487097i | ||||
\(214\) | 1.97822 | − | 3.42638i | 0.135228 | − | 0.234222i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | −0.208712 | −0.0141683 | ||||||||
\(218\) | 7.87386 | + | 13.6379i | 0.533285 | + | 0.923677i | ||||
\(219\) | 1.60436 | + | 2.77883i | 0.108412 | + | 0.187776i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.1652 | −1.22192 | ||||||||
\(222\) | −5.00000 | − | 8.66025i | −0.335578 | − | 0.581238i | ||||
\(223\) | 11.8956 | − | 20.6039i | 0.796591 | − | 1.37974i | −0.125233 | − | 0.992127i | \(-0.539968\pi\) |
0.921824 | − | 0.387609i | \(-0.126699\pi\) | |||||||
\(224\) | 0.500000 | + | 0.866025i | 0.0334077 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.18693 | − | 7.25198i | 0.278511 | − | 0.482394i | ||||
\(227\) | 19.7477 | 1.31070 | 0.655351 | − | 0.755324i | \(-0.272521\pi\) | ||||
0.655351 | + | 0.755324i | \(0.272521\pi\) | |||||||
\(228\) | 6.26951 | + | 4.65390i | 0.415208 | + | 0.308212i | ||||
\(229\) | 11.3303 | 0.748727 | 0.374364 | − | 0.927282i | \(-0.377861\pi\) | ||||
0.374364 | + | 0.927282i | \(0.377861\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.708712 | − | 1.22753i | 0.0466298 | − | 0.0807652i | ||||
\(232\) | 1.10436 | + | 1.91280i | 0.0725045 | + | 0.125582i | ||||
\(233\) | −4.58258 | + | 7.93725i | −0.300215 | + | 0.519987i | −0.976184 | − | 0.216942i | \(-0.930392\pi\) |
0.675970 | + | 0.736929i | \(0.263725\pi\) | |||||||
\(234\) | 0.500000 | + | 0.866025i | 0.0326860 | + | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.58258 | −0.298300 | ||||||||
\(237\) | −7.12614 | − | 12.3428i | −0.462892 | − | 0.801753i | ||||
\(238\) | −1.89564 | − | 3.28335i | −0.122876 | − | 0.212828i | ||||
\(239\) | 7.41742 | 0.479793 | 0.239897 | − | 0.970798i | \(-0.422886\pi\) | ||||
0.239897 | + | 0.970798i | \(0.422886\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.10436 | + | 10.5731i | 0.393216 | + | 0.681070i | 0.992872 | − | 0.119188i | \(-0.0380291\pi\) |
−0.599656 | + | 0.800258i | \(0.704696\pi\) | |||||||
\(242\) | −5.18693 | + | 8.98403i | −0.333429 | + | 0.577515i | ||||
\(243\) | −1.08258 | − | 1.87508i | −0.0694473 | − | 0.120286i | ||||
\(244\) | 6.18693 | − | 10.7161i | 0.396078 | − | 0.686027i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.25227 | 0.271115 | ||||||||
\(247\) | −2.39564 | + | 20.7469i | −0.152431 | + | 1.32009i | ||||
\(248\) | 0.208712 | 0.0132532 | ||||||||
\(249\) | 0.708712 | − | 1.22753i | 0.0449128 | − | 0.0777913i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.0608 | + | 24.3540i | 0.887510 | + | 1.53721i | 0.842810 | + | 0.538211i | \(0.180900\pi\) |
0.0446995 | + | 0.999000i | \(0.485767\pi\) | |||||||
\(252\) | −0.104356 | + | 0.180750i | −0.00657381 | + | 0.0113862i | ||||
\(253\) | −1.81307 | − | 3.14033i | −0.113987 | − | 0.197431i | ||||
\(254\) | 16.3739 | 1.02739 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −7.89564 | − | 13.6757i | −0.492517 | − | 0.853064i | 0.507446 | − | 0.861683i | \(-0.330590\pi\) |
−0.999963 | + | 0.00861948i | \(0.997256\pi\) | |||||||
\(258\) | −2.16515 | −0.134796 | ||||||||
\(259\) | 5.58258 | 0.346884 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.230493 | + | 0.399225i | −0.0142671 | + | 0.0247114i | ||||
\(262\) | −10.2695 | − | 17.7873i | −0.634452 | − | 1.09890i | ||||
\(263\) | −14.2913 | + | 24.7532i | −0.881239 | + | 1.52635i | −0.0312735 | + | 0.999511i | \(0.509956\pi\) |
−0.849965 | + | 0.526839i | \(0.823377\pi\) | |||||||
\(264\) | −0.708712 | + | 1.22753i | −0.0436182 | + | 0.0755490i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.00000 | + | 1.73205i | −0.245256 | + | 0.106199i | ||||
\(267\) | 8.20871 | 0.502365 | ||||||||
\(268\) | 3.20871 | − | 5.55765i | 0.196003 | − | 0.339488i | ||||
\(269\) | 14.0608 | − | 24.3540i | 0.857302 | − | 1.48489i | −0.0171912 | − | 0.999852i | \(-0.505472\pi\) |
0.874493 | − | 0.485038i | \(-0.161194\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0608 | + | 20.8899i | −0.732641 | + | 1.26897i | 0.223109 | + | 0.974793i | \(0.428379\pi\) |
−0.955751 | + | 0.294178i | \(0.904954\pi\) | |||||||
\(272\) | 1.89564 | + | 3.28335i | 0.114940 | + | 0.199082i | ||||
\(273\) | −8.58258 | −0.519441 | ||||||||
\(274\) | −21.3303 | −1.28861 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.10436 | + | 7.10895i | 0.247053 | + | 0.427909i | ||||
\(277\) | −18.7477 | −1.12644 | −0.563221 | − | 0.826306i | \(-0.690438\pi\) | ||||
−0.563221 | + | 0.826306i | \(0.690438\pi\) | |||||||
\(278\) | 16.7913 | 1.00707 | ||||||||
\(279\) | 0.0217804 | + | 0.0377247i | 0.00130396 | + | 0.00225852i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.708712 | − | 1.22753i | −0.0422782 | − | 0.0732280i | 0.844112 | − | 0.536167i | \(-0.180128\pi\) |
−0.886390 | + | 0.462939i | \(0.846795\pi\) | |||||||
\(282\) | 5.52178 | − | 9.56400i | 0.328817 | − | 0.569528i | ||||
\(283\) | −10.0608 | + | 17.4258i | −0.598052 | + | 1.03586i | 0.395056 | + | 0.918657i | \(0.370725\pi\) |
−0.993108 | + | 0.117200i | \(0.962608\pi\) | |||||||
\(284\) | 4.58258 | 0.271926 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.79129 | −0.224184 | ||||||||
\(287\) | −1.18693 | + | 2.05583i | −0.0700624 | + | 0.121352i | ||||
\(288\) | 0.104356 | − | 0.180750i | 0.00614924 | − | 0.0106508i | ||||
\(289\) | 1.31307 | + | 2.27430i | 0.0772393 | + | 0.133782i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.23049 | − | 2.13128i | −0.0721327 | − | 0.124938i | ||||
\(292\) | 1.79129 | 0.104827 | ||||||||
\(293\) | −2.04356 | −0.119386 | −0.0596930 | − | 0.998217i | \(-0.519012\pi\) | ||||
−0.0596930 | + | 0.998217i | \(0.519012\pi\) | |||||||
\(294\) | 5.37386 | + | 9.30780i | 0.313410 | + | 0.542842i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.58258 | −0.324481 | ||||||||
\(297\) | 3.95644 | 0.229576 | ||||||||
\(298\) | 2.37386 | + | 4.11165i | 0.137514 | + | 0.238182i | ||||
\(299\) | −10.9782 | + | 19.0148i | −0.634887 | + | 1.09966i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.604356 | − | 1.04678i | 0.0348345 | − | 0.0603351i | ||||
\(302\) | −5.87386 | + | 10.1738i | −0.338003 | + | 0.585438i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.00000 | − | 1.73205i | 0.229416 | − | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.395644 | + | 0.685275i | −0.0226175 | + | 0.0391746i | ||||
\(307\) | 10.2477 | − | 17.7496i | 0.584869 | − | 1.01302i | −0.410023 | − | 0.912075i | \(-0.634479\pi\) |
0.994892 | − | 0.100947i | \(-0.0321873\pi\) | |||||||
\(308\) | −0.395644 | − | 0.685275i | −0.0225439 | − | 0.0390472i | ||||
\(309\) | 11.7913 | − | 20.4231i | 0.670783 | − | 1.16183i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0000 | −0.850572 | −0.425286 | − | 0.905059i | \(-0.639826\pi\) | ||||
−0.425286 | + | 0.905059i | \(0.639826\pi\) | |||||||
\(312\) | 8.58258 | 0.485893 | ||||||||
\(313\) | 7.87386 | + | 13.6379i | 0.445057 | + | 0.770861i | 0.998056 | − | 0.0623204i | \(-0.0198501\pi\) |
−0.552999 | + | 0.833182i | \(0.686517\pi\) | |||||||
\(314\) | −7.47822 | − | 12.9527i | −0.422020 | − | 0.730961i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.95644 | −0.447585 | ||||||||
\(317\) | 4.58258 | + | 7.93725i | 0.257383 | + | 0.445801i | 0.965540 | − | 0.260254i | \(-0.0838064\pi\) |
−0.708157 | + | 0.706055i | \(0.750473\pi\) | |||||||
\(318\) | 4.10436 | − | 7.10895i | 0.230161 | − | 0.398650i | ||||
\(319\) | −0.873864 | − | 1.51358i | −0.0489270 | − | 0.0847440i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.54356 | − | 6.13763i | 0.197782 | − | 0.342569i | ||||
\(322\) | −4.58258 | −0.255377 | ||||||||
\(323\) | −15.1652 | + | 6.56670i | −0.843812 | + | 0.365381i | ||||
\(324\) | −9.58258 | −0.532365 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.70871 | − | 4.69163i | 0.150022 | − | 0.259845i | ||||
\(327\) | 14.1044 | + | 24.4295i | 0.779973 | + | 1.35095i | ||||
\(328\) | 1.18693 | − | 2.05583i | 0.0655373 | − | 0.113514i | ||||
\(329\) | 3.08258 | + | 5.33918i | 0.169948 | + | 0.294358i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.9129 | 1.53423 | 0.767115 | − | 0.641509i | \(-0.221691\pi\) | ||||
0.767115 | + | 0.641509i | \(0.221691\pi\) | |||||||
\(332\) | −0.395644 | − | 0.685275i | −0.0217138 | − | 0.0376094i | ||||
\(333\) | −0.582576 | − | 1.00905i | −0.0319250 | − | 0.0552956i | ||||
\(334\) | −20.5390 | −1.12384 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.895644 | + | 1.55130i | 0.0488614 | + | 0.0846304i | ||||
\(337\) | −6.66515 | + | 11.5444i | −0.363074 | + | 0.628862i | −0.988465 | − | 0.151449i | \(-0.951606\pi\) |
0.625391 | + | 0.780311i | \(0.284939\pi\) | |||||||
\(338\) | 4.97822 | + | 8.62253i | 0.270779 | + | 0.469004i | ||||
\(339\) | 7.50000 | − | 12.9904i | 0.407344 | − | 0.705541i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.165151 | −0.00894345 | ||||||||
\(342\) | 0.730493 | + | 0.542250i | 0.0395005 | + | 0.0293215i | ||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −0.604356 | + | 1.04678i | −0.0325847 | + | 0.0564383i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5000 | + | 18.1865i | 0.564483 | + | 0.977714i | ||||
\(347\) | 8.68693 | − | 15.0462i | 0.466339 | − | 0.807723i | −0.532922 | − | 0.846164i | \(-0.678906\pi\) |
0.999261 | + | 0.0384417i | \(0.0122394\pi\) | |||||||
\(348\) | 1.97822 | + | 3.42638i | 0.106044 | + | 0.183673i | ||||
\(349\) | −14.5826 | −0.780587 | −0.390294 | − | 0.920690i | \(-0.627627\pi\) | ||||
−0.390294 | + | 0.920690i | \(0.627627\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.9782 | − | 20.7469i | −0.639350 | − | 1.10739i | ||||
\(352\) | 0.395644 | + | 0.685275i | 0.0210879 | + | 0.0365253i | ||||
\(353\) | −13.7477 | −0.731718 | −0.365859 | − | 0.930670i | \(-0.619225\pi\) | ||||
−0.365859 | + | 0.930670i | \(0.619225\pi\) | |||||||
\(354\) | −8.20871 | −0.436288 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.29129 | − | 3.96863i | 0.121438 | − | 0.210337i | ||||
\(357\) | −3.39564 | − | 5.88143i | −0.179717 | − | 0.311278i | ||||
\(358\) | 5.37386 | − | 9.30780i | 0.284018 | − | 0.491933i | ||||
\(359\) | −7.35208 | + | 12.7342i | −0.388028 | + | 0.672084i | −0.992184 | − | 0.124782i | \(-0.960177\pi\) |
0.604156 | + | 0.796866i | \(0.293510\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | + | 18.1865i | 0.289474 | + | 0.957186i | ||||
\(362\) | 21.3739 | 1.12339 | ||||||||
\(363\) | −9.29129 | + | 16.0930i | −0.487666 | + | 0.844663i | ||||
\(364\) | −2.39564 | + | 4.14938i | −0.125566 | + | 0.217486i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.0826 | − | 19.1956i | 0.579296 | − | 1.00337i | ||||
\(367\) | 2.10436 | + | 3.64485i | 0.109846 | + | 0.190260i | 0.915708 | − | 0.401844i | \(-0.131631\pi\) |
−0.805861 | + | 0.592104i | \(0.798297\pi\) | |||||||
\(368\) | 4.58258 | 0.238883 | ||||||||
\(369\) | 0.495454 | 0.0257923 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.29129 | + | 3.96863i | 0.118958 | + | 0.206041i | ||||
\(372\) | 0.373864 | 0.0193839 | ||||||||
\(373\) | 7.62614 | 0.394866 | 0.197433 | − | 0.980316i | \(-0.436739\pi\) | ||||
0.197433 | + | 0.980316i | \(0.436739\pi\) | |||||||
\(374\) | −1.50000 | − | 2.59808i | −0.0775632 | − | 0.134343i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.08258 | − | 5.33918i | −0.158972 | − | 0.275347i | ||||
\(377\) | −5.29129 | + | 9.16478i | −0.272515 | + | 0.472010i | ||||
\(378\) | 2.50000 | − | 4.33013i | 0.128586 | − | 0.222718i | ||||
\(379\) | 23.1652 | 1.18991 | 0.594957 | − | 0.803758i | \(-0.297169\pi\) | ||||
0.594957 | + | 0.803758i | \(0.297169\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.3303 | 1.50264 | ||||||||
\(382\) | −3.47822 | + | 6.02445i | −0.177961 | + | 0.308238i | ||||
\(383\) | −2.29129 | + | 3.96863i | −0.117079 | + | 0.202787i | −0.918609 | − | 0.395168i | \(-0.870687\pi\) |
0.801530 | + | 0.597955i | \(0.204020\pi\) | |||||||
\(384\) | −0.895644 | − | 1.55130i | −0.0457056 | − | 0.0791645i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.3739 | − | 21.4322i | −0.629813 | − | 1.09087i | ||||
\(387\) | −0.252273 | −0.0128238 | ||||||||
\(388\) | −1.37386 | −0.0697474 | ||||||||
\(389\) | −16.1869 | − | 28.0366i | −0.820710 | − | 1.42151i | −0.905154 | − | 0.425083i | \(-0.860245\pi\) |
0.0844442 | − | 0.996428i | \(-0.473089\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.3739 | −0.878634 | ||||||||
\(392\) | 6.00000 | 0.303046 | ||||||||
\(393\) | −18.3956 | − | 31.8622i | −0.927937 | − | 1.60723i | ||||
\(394\) | −12.3956 | + | 21.4699i | −0.624484 | + | 1.08164i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.0825757 | + | 0.143025i | −0.00414958 | + | 0.00718729i | ||||
\(397\) | −10.2913 | + | 17.8250i | −0.516505 | + | 0.894613i | 0.483311 | + | 0.875448i | \(0.339434\pi\) |
−0.999816 | + | 0.0191643i | \(0.993899\pi\) | |||||||
\(398\) | 5.58258 | 0.279829 | ||||||||
\(399\) | −7.16515 | + | 3.10260i | −0.358706 | + | 0.155324i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | − | 10.3923i | 0.299626 | − | 0.518967i | −0.676425 | − | 0.736512i | \(-0.736472\pi\) |
0.976050 | + | 0.217545i | \(0.0698049\pi\) | |||||||
\(402\) | 5.74773 | − | 9.95536i | 0.286671 | − | 0.496528i | ||||
\(403\) | 0.500000 | + | 0.866025i | 0.0249068 | + | 0.0431398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.20871 | −0.109617 | ||||||||
\(407\) | 4.41742 | 0.218964 | ||||||||
\(408\) | 3.39564 | + | 5.88143i | 0.168109 | + | 0.291174i | ||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −38.2087 | −1.88470 | ||||||||
\(412\) | −6.58258 | − | 11.4014i | −0.324300 | − | 0.561704i | ||||
\(413\) | 2.29129 | − | 3.96863i | 0.112747 | − | 0.195283i | ||||
\(414\) | 0.478220 | + | 0.828301i | 0.0235032 | + | 0.0407088i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.39564 | − | 4.14938i | 0.117456 | − | 0.203440i | ||||
\(417\) | 30.0780 | 1.47293 | ||||||||
\(418\) | −3.16515 | + | 1.37055i | −0.154813 | + | 0.0670358i | ||||
\(419\) | 4.74773 | 0.231942 | 0.115971 | − | 0.993253i | \(-0.463002\pi\) | ||||
0.115971 | + | 0.993253i | \(0.463002\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | + | 17.3205i | −0.487370 | + | 0.844150i | −0.999895 | − | 0.0145228i | \(-0.995377\pi\) |
0.512524 | + | 0.858673i | \(0.328710\pi\) | |||||||
\(422\) | 0.521780 | + | 0.903750i | 0.0253999 | + | 0.0439939i | ||||
\(423\) | 0.643371 | − | 1.11435i | 0.0312818 | − | 0.0541816i | ||||
\(424\) | −2.29129 | − | 3.96863i | −0.111275 | − | 0.192734i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.20871 | 0.397713 | ||||||||
\(427\) | 6.18693 | + | 10.7161i | 0.299407 | + | 0.518587i | ||||
\(428\) | −1.97822 | − | 3.42638i | −0.0956209 | − | 0.165620i | ||||
\(429\) | −6.79129 | −0.327886 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.39564 | − | 11.0776i | −0.308067 | − | 0.533588i | 0.669872 | − | 0.742476i | \(-0.266349\pi\) |
−0.977940 | + | 0.208888i | \(0.933016\pi\) | |||||||
\(432\) | −2.50000 | + | 4.33013i | −0.120281 | + | 0.208333i | ||||
\(433\) | −19.4564 | − | 33.6995i | −0.935017 | − | 1.61950i | −0.774604 | − | 0.632447i | \(-0.782051\pi\) |
−0.160413 | − | 0.987050i | \(-0.551283\pi\) | |||||||
\(434\) | −0.104356 | + | 0.180750i | −0.00500925 | + | 0.00867628i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.7477 | 0.754179 | ||||||||
\(437\) | −2.29129 | + | 19.8431i | −0.109607 | + | 0.949226i | ||||
\(438\) | 3.20871 | 0.153318 | ||||||||
\(439\) | −5.66515 | + | 9.81233i | −0.270383 | + | 0.468317i | −0.968960 | − | 0.247218i | \(-0.920484\pi\) |
0.698577 | + | 0.715535i | \(0.253817\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.626136 | + | 1.08450i | 0.0298160 | + | 0.0516429i | ||||
\(442\) | −9.08258 | + | 15.7315i | −0.432014 | + | 0.748270i | ||||
\(443\) | −12.0000 | − | 20.7846i | −0.570137 | − | 0.987507i | −0.996551 | − | 0.0829786i | \(-0.973557\pi\) |
0.426414 | − | 0.904528i | \(-0.359777\pi\) | |||||||
\(444\) | −10.0000 | −0.474579 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.8956 | − | 20.6039i | −0.563275 | − | 0.975621i | ||||
\(447\) | 4.25227 | + | 7.36515i | 0.201126 | + | 0.348360i | ||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −33.3303 | −1.57295 | −0.786477 | − | 0.617619i | \(-0.788097\pi\) | ||||
−0.786477 | + | 0.617619i | \(0.788097\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.939205 | + | 1.62675i | −0.0442254 | + | 0.0766007i | ||||
\(452\) | −4.18693 | − | 7.25198i | −0.196937 | − | 0.341104i | ||||
\(453\) | −10.5218 | + | 18.2243i | −0.494356 | + | 0.856250i | ||||
\(454\) | 9.87386 | − | 17.1020i | 0.463403 | − | 0.802638i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.16515 | − | 3.10260i | 0.335539 | − | 0.145293i | ||||
\(457\) | −6.74773 | −0.315645 | −0.157823 | − | 0.987467i | \(-0.550447\pi\) | ||||
−0.157823 | + | 0.987467i | \(0.550447\pi\) | |||||||
\(458\) | 5.66515 | − | 9.81233i | 0.264715 | − | 0.458500i | ||||
\(459\) | 9.47822 | − | 16.4168i | 0.442405 | − | 0.766269i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.10436 | + | 7.10895i | −0.191159 | + | 0.331097i | −0.945635 | − | 0.325231i | \(-0.894558\pi\) |
0.754476 | + | 0.656328i | \(0.227891\pi\) | |||||||
\(462\) | −0.708712 | − | 1.22753i | −0.0329723 | − | 0.0571097i | ||||
\(463\) | 4.95644 | 0.230345 | 0.115173 | − | 0.993345i | \(-0.463258\pi\) | ||||
0.115173 | + | 0.993345i | \(0.463258\pi\) | |||||||
\(464\) | 2.20871 | 0.102537 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.58258 | + | 7.93725i | 0.212284 | + | 0.367686i | ||||
\(467\) | −24.3303 | −1.12587 | −0.562936 | − | 0.826500i | \(-0.690328\pi\) | ||||
−0.562936 | + | 0.826500i | \(0.690328\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 3.20871 | + | 5.55765i | 0.148165 | + | 0.256629i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.3956 | − | 23.2019i | −0.617239 | − | 1.06909i | ||||
\(472\) | −2.29129 | + | 3.96863i | −0.105465 | + | 0.182671i | ||||
\(473\) | 0.478220 | − | 0.828301i | 0.0219886 | − | 0.0380853i | ||||
\(474\) | −14.2523 | −0.654629 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.79129 | −0.173773 | ||||||||
\(477\) | 0.478220 | − | 0.828301i | 0.0218962 | − | 0.0379253i | ||||
\(478\) | 3.70871 | − | 6.42368i | 0.169633 | − | 0.293812i | ||||
\(479\) | −2.12614 | − | 3.68258i | −0.0971457 | − | 0.168261i | 0.813356 | − | 0.581766i | \(-0.197638\pi\) |
−0.910502 | + | 0.413504i | \(0.864305\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.3739 | − | 23.1642i | −0.609796 | − | 1.05620i | ||||
\(482\) | 12.2087 | 0.556092 | ||||||||
\(483\) | −8.20871 | −0.373509 | ||||||||
\(484\) | 5.18693 | + | 8.98403i | 0.235770 | + | 0.408365i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.16515 | −0.0982133 | ||||||||
\(487\) | −23.0000 | −1.04223 | −0.521115 | − | 0.853487i | \(-0.674484\pi\) | ||||
−0.521115 | + | 0.853487i | \(0.674484\pi\) | |||||||
\(488\) | −6.18693 | − | 10.7161i | −0.280069 | − | 0.485094i | ||||
\(489\) | 4.85208 | − | 8.40405i | 0.219419 | − | 0.380044i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.2913 | − | 35.1455i | 0.915733 | − | 1.58610i | 0.109908 | − | 0.993942i | \(-0.464944\pi\) |
0.805825 | − | 0.592154i | \(-0.201722\pi\) | |||||||
\(492\) | 2.12614 | − | 3.68258i | 0.0958536 | − | 0.166023i | ||||
\(493\) | −8.37386 | −0.377140 | ||||||||
\(494\) | 16.7695 | + | 12.4481i | 0.754496 | + | 0.560068i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.104356 | − | 0.180750i | 0.00468573 | − | 0.00811592i | ||||
\(497\) | −2.29129 | + | 3.96863i | −0.102778 | + | 0.178017i | ||||
\(498\) | −0.708712 | − | 1.22753i | −0.0317582 | − | 0.0550067i | ||||
\(499\) | −8.66515 | + | 15.0085i | −0.387905 | + | 0.671872i | −0.992168 | − | 0.124914i | \(-0.960135\pi\) |
0.604262 | + | 0.796786i | \(0.293468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −36.7913 | −1.64371 | ||||||||
\(502\) | 28.1216 | 1.25513 | ||||||||
\(503\) | 2.29129 | + | 3.96863i | 0.102163 | + | 0.176952i | 0.912576 | − | 0.408908i | \(-0.134090\pi\) |
−0.810412 | + | 0.585860i | \(0.800757\pi\) | |||||||
\(504\) | 0.104356 | + | 0.180750i | 0.00464839 | + | 0.00805125i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.62614 | −0.161201 | ||||||||
\(507\) | 8.91742 | + | 15.4454i | 0.396037 | + | 0.685956i | ||||
\(508\) | 8.18693 | − | 14.1802i | 0.363236 | − | 0.629144i | ||||
\(509\) | −15.7913 | − | 27.3513i | −0.699937 | − | 1.21233i | −0.968488 | − | 0.249060i | \(-0.919878\pi\) |
0.268551 | − | 0.963265i | \(-0.413455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.895644 | + | 1.55130i | −0.0396210 | + | 0.0686255i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −17.5000 | − | 12.9904i | −0.772644 | − | 0.573539i | ||||
\(514\) | −15.7913 | −0.696524 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.08258 | + | 1.87508i | −0.0476577 | + | 0.0825456i | ||||
\(517\) | 2.43920 | + | 4.22483i | 0.107276 | + | 0.185808i | ||||
\(518\) | 2.79129 | − | 4.83465i | 0.122642 | − | 0.212422i | ||||
\(519\) | 18.8085 | + | 32.5773i | 0.825603 | + | 1.42999i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.7477 | 1.78519 | 0.892595 | − | 0.450859i | \(-0.148882\pi\) | ||||
0.892595 | + | 0.450859i | \(0.148882\pi\) | |||||||
\(522\) | 0.230493 | + | 0.399225i | 0.0100884 | + | 0.0174736i | ||||
\(523\) | 4.87386 | + | 8.44178i | 0.213119 | + | 0.369133i | 0.952689 | − | 0.303946i | \(-0.0983044\pi\) |
−0.739570 | + | 0.673080i | \(0.764971\pi\) | |||||||
\(524\) | −20.5390 | −0.897251 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.2913 | + | 24.7532i | 0.623130 | + | 1.07929i | ||||
\(527\) | −0.395644 | + | 0.685275i | −0.0172345 | + | 0.0298511i | ||||
\(528\) | 0.708712 | + | 1.22753i | 0.0308427 | + | 0.0534212i | ||||
\(529\) | 1.00000 | − | 1.73205i | 0.0434783 | − | 0.0753066i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.956439 | −0.0415059 | ||||||||
\(532\) | −0.500000 | + | 4.33013i | −0.0216777 | + | 0.187735i | ||||
\(533\) | 11.3739 | 0.492657 | ||||||||
\(534\) | 4.10436 | − | 7.10895i | 0.177613 | − | 0.307634i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.20871 | − | 5.55765i | −0.138595 | − | 0.240054i | ||||
\(537\) | 9.62614 | − | 16.6730i | 0.415398 | − | 0.719491i | ||||
\(538\) | −14.0608 | − | 24.3540i | −0.606204 | − | 1.04998i | ||||
\(539\) | −4.74773 | −0.204499 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.0608 | − | 20.8899i | −0.518534 | − | 0.898127i | −0.999768 | − | 0.0215352i | \(-0.993145\pi\) |
0.481234 | − | 0.876592i | \(-0.340189\pi\) | |||||||
\(542\) | 12.0608 | + | 20.8899i | 0.518056 | + | 0.897298i | ||||
\(543\) | 38.2867 | 1.64304 | ||||||||
\(544\) | 3.79129 | 0.162550 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.29129 | + | 7.43273i | −0.183650 | + | 0.318091i | ||||
\(547\) | 17.5826 | + | 30.4539i | 0.751777 | + | 1.30212i | 0.946961 | + | 0.321349i | \(0.104136\pi\) |
−0.195184 | + | 0.980767i | \(0.562530\pi\) | |||||||
\(548\) | −10.6652 | + | 18.4726i | −0.455593 | + | 0.789110i | ||||
\(549\) | 1.29129 | − | 2.23658i | 0.0551108 | − | 0.0954547i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.10436 | + | 9.56400i | −0.0470472 | + | 0.407440i | ||||
\(552\) | 8.20871 | 0.349386 | ||||||||
\(553\) | 3.97822 | − | 6.89048i | 0.169171 | − | 0.293013i | ||||
\(554\) | −9.37386 | + | 16.2360i | −0.398257 | + | 0.689802i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.39564 | − | 14.5417i | 0.356055 | − | 0.616705i | ||||
\(557\) | −6.47822 | − | 11.2206i | −0.274491 | − | 0.475432i | 0.695516 | − | 0.718511i | \(-0.255176\pi\) |
−0.970007 | + | 0.243079i | \(0.921843\pi\) | |||||||
\(558\) | 0.0435608 | 0.00184407 | ||||||||
\(559\) | −5.79129 | −0.244945 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.68693 | − | 4.65390i | −0.113442 | − | 0.196488i | ||||
\(562\) | −1.41742 | −0.0597904 | ||||||||
\(563\) | 0.626136 | 0.0263885 | 0.0131943 | − | 0.999913i | \(-0.495800\pi\) | ||||
0.0131943 | + | 0.999913i | \(0.495800\pi\) | |||||||
\(564\) | −5.52178 | − | 9.56400i | −0.232509 | − | 0.402717i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.0608 | + | 17.4258i | 0.422887 | + | 0.732461i | ||||
\(567\) | 4.79129 | − | 8.29875i | 0.201215 | − | 0.348515i | ||||
\(568\) | 2.29129 | − | 3.96863i | 0.0961403 | − | 0.166520i | ||||
\(569\) | −27.1652 | −1.13882 | −0.569411 | − | 0.822053i | \(-0.692829\pi\) | ||||
−0.569411 | + | 0.822053i | \(0.692829\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0000 | −0.920671 | −0.460336 | − | 0.887745i | \(-0.652271\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | −1.89564 | + | 3.28335i | −0.0792609 | + | 0.137284i | ||||
\(573\) | −6.23049 | + | 10.7915i | −0.260283 | + | 0.450823i | ||||
\(574\) | 1.18693 | + | 2.05583i | 0.0495416 | + | 0.0858085i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.104356 | − | 0.180750i | −0.00434817 | − | 0.00753125i | ||||
\(577\) | −14.0000 | −0.582828 | −0.291414 | − | 0.956597i | \(-0.594126\pi\) | ||||
−0.291414 | + | 0.956597i | \(0.594126\pi\) | |||||||
\(578\) | 2.62614 | 0.109233 | ||||||||
\(579\) | −22.1652 | − | 38.3912i | −0.921152 | − | 1.59548i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.791288 | 0.0328282 | ||||||||
\(582\) | −2.46099 | −0.102011 | ||||||||
\(583\) | 1.81307 | + | 3.14033i | 0.0750896 | + | 0.130059i | ||||
\(584\) | 0.895644 | − | 1.55130i | 0.0370620 | − | 0.0641933i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.02178 | + | 1.76978i | −0.0422094 | + | 0.0731088i | ||||
\(587\) | 22.7477 | − | 39.4002i | 0.938899 | − | 1.62622i | 0.171370 | − | 0.985207i | \(-0.445181\pi\) |
0.767529 | − | 0.641014i | \(-0.221486\pi\) | |||||||
\(588\) | 10.7477 | 0.443229 | ||||||||
\(589\) | 0.730493 | + | 0.542250i | 0.0300994 | + | 0.0223430i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.2042 | + | 38.4587i | −0.913357 | + | 1.58198i | ||||
\(592\) | −2.79129 | + | 4.83465i | −0.114721 | + | 0.198703i | ||||
\(593\) | −15.0826 | − | 26.1238i | −0.619367 | − | 1.07278i | −0.989601 | − | 0.143837i | \(-0.954056\pi\) |
0.370234 | − | 0.928938i | \(-0.379277\pi\) | |||||||
\(594\) | 1.97822 | − | 3.42638i | 0.0811673 | − | 0.140586i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.74773 | 0.194474 | ||||||||
\(597\) | 10.0000 | 0.409273 | ||||||||
\(598\) | 10.9782 | + | 19.0148i | 0.448933 | + | 0.777574i | ||||
\(599\) | −2.06080 | − | 3.56940i | −0.0842018 | − | 0.145842i | 0.820849 | − | 0.571145i | \(-0.193501\pi\) |
−0.905051 | + | 0.425303i | \(0.860167\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.9129 | −1.46492 | −0.732458 | − | 0.680812i | \(-0.761627\pi\) | ||||
−0.732458 | + | 0.680812i | \(0.761627\pi\) | |||||||
\(602\) | −0.604356 | − | 1.04678i | −0.0246317 | − | 0.0426634i | ||||
\(603\) | 0.669697 | − | 1.15995i | 0.0272722 | − | 0.0472368i | ||||
\(604\) | 5.87386 | + | 10.1738i | 0.239004 | + | 0.413967i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.7913 | 0.925070 | 0.462535 | − | 0.886601i | \(-0.346940\pi\) | ||||
0.462535 | + | 0.886601i | \(0.346940\pi\) | |||||||
\(608\) | 0.500000 | − | 4.33013i | 0.0202777 | − | 0.175610i | ||||
\(609\) | −3.95644 | −0.160323 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.7695 | − | 25.5815i | 0.597510 | − | 1.03492i | ||||
\(612\) | 0.395644 | + | 0.685275i | 0.0159930 | + | 0.0277006i | ||||
\(613\) | −20.2477 | + | 35.0701i | −0.817798 | + | 1.41647i | 0.0895033 | + | 0.995987i | \(0.471472\pi\) |
−0.907301 | + | 0.420481i | \(0.861861\pi\) | |||||||
\(614\) | −10.2477 | − | 17.7496i | −0.413565 | − | 0.716315i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.791288 | −0.0318819 | ||||||||
\(617\) | −16.5000 | − | 28.5788i | −0.664265 | − | 1.15054i | −0.979484 | − | 0.201522i | \(-0.935411\pi\) |
0.315219 | − | 0.949019i | \(-0.397922\pi\) | |||||||
\(618\) | −11.7913 | − | 20.4231i | −0.474315 | − | 0.821538i | ||||
\(619\) | −10.6261 | −0.427100 | −0.213550 | − | 0.976932i | \(-0.568503\pi\) | ||||
−0.213550 | + | 0.976932i | \(0.568503\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.4564 | − | 19.8431i | −0.459731 | − | 0.796278i | ||||
\(622\) | −7.50000 | + | 12.9904i | −0.300723 | + | 0.520867i | ||||
\(623\) | 2.29129 | + | 3.96863i | 0.0917985 | + | 0.159000i | ||||
\(624\) | 4.29129 | − | 7.43273i | 0.171789 | − | 0.297547i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15.7477 | 0.629406 | ||||||||
\(627\) | −5.66970 | + | 2.45505i | −0.226426 | + | 0.0980453i | ||||
\(628\) | −14.9564 | −0.596827 | ||||||||
\(629\) | 10.5826 | − | 18.3296i | 0.421955 | − | 0.730847i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.3956 | + | 35.3263i | 0.811938 | + | 1.40632i | 0.911506 | + | 0.411287i | \(0.134921\pi\) |
−0.0995683 | + | 0.995031i | \(0.531746\pi\) | |||||||
\(632\) | −3.97822 | + | 6.89048i | −0.158245 | + | 0.274089i | ||||
\(633\) | 0.934659 | + | 1.61888i | 0.0371494 | + | 0.0643446i | ||||
\(634\) | 9.16515 | 0.363995 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.10436 | − | 7.10895i | −0.162748 | − | 0.281888i | ||||
\(637\) | 14.3739 | + | 24.8963i | 0.569513 | + | 0.986426i | ||||
\(638\) | −1.74773 | −0.0691932 | ||||||||
\(639\) | 0.956439 | 0.0378362 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.9782 | + | 34.6033i | −0.789092 | + | 1.36675i | 0.137431 | + | 0.990511i | \(0.456115\pi\) |
−0.926524 | + | 0.376237i | \(0.877218\pi\) | |||||||
\(642\) | −3.54356 | − | 6.13763i | −0.139853 | − | 0.242233i | ||||
\(643\) | −12.7477 | + | 22.0797i | −0.502721 | + | 0.870739i | 0.497274 | + | 0.867594i | \(0.334334\pi\) |
−0.999995 | + | 0.00314512i | \(0.998999\pi\) | |||||||
\(644\) | −2.29129 | + | 3.96863i | −0.0902894 | + | 0.156386i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.89564 | + | 16.4168i | −0.0745831 | + | 0.645909i | ||||
\(647\) | −14.2087 | −0.558602 | −0.279301 | − | 0.960204i | \(-0.590103\pi\) | ||||
−0.279301 | + | 0.960204i | \(0.590103\pi\) | |||||||
\(648\) | −4.79129 | + | 8.29875i | −0.188220 | + | 0.326006i | ||||
\(649\) | 1.81307 | − | 3.14033i | 0.0711692 | − | 0.123269i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.186932 | + | 0.323775i | −0.00732643 | + | 0.0126898i | ||||
\(652\) | −2.70871 | − | 4.69163i | −0.106081 | − | 0.183738i | ||||
\(653\) | −9.33030 | −0.365123 | −0.182561 | − | 0.983194i | \(-0.558439\pi\) | ||||
−0.182561 | + | 0.983194i | \(0.558439\pi\) | |||||||
\(654\) | 28.2087 | 1.10305 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.18693 | − | 2.05583i | −0.0463419 | − | 0.0802665i | ||||
\(657\) | 0.373864 | 0.0145858 | ||||||||
\(658\) | 6.16515 | 0.240343 | ||||||||
\(659\) | 12.8739 | + | 22.2982i | 0.501495 | + | 0.868614i | 0.999999 | + | 0.00172659i | \(0.000549590\pi\) |
−0.498504 | + | 0.866887i | \(0.666117\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.9347 | + | 18.9394i | 0.425309 | + | 0.736657i | 0.996449 | − | 0.0841958i | \(-0.0268321\pi\) |
−0.571140 | + | 0.820852i | \(0.693499\pi\) | |||||||
\(662\) | 13.9564 | − | 24.1733i | 0.542432 | − | 0.939521i | ||||
\(663\) | −16.2695 | + | 28.1796i | −0.631855 | + | 1.09441i | ||||
\(664\) | −0.791288 | −0.0307079 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.16515 | −0.0451487 | ||||||||
\(667\) | −5.06080 | + | 8.76555i | −0.195955 | + | 0.339404i | ||||
\(668\) | −10.2695 | + | 17.7873i | −0.397339 | + | 0.688212i | ||||
\(669\) | −21.3085 | − | 36.9074i | −0.823835 | − | 1.42692i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.89564 | + | 8.47950i | 0.188994 | + | 0.327348i | ||||
\(672\) | 1.79129 | 0.0691004 | ||||||||
\(673\) | 1.79129 | 0.0690491 | 0.0345245 | − | 0.999404i | \(-0.489008\pi\) | ||||
0.0345245 | + | 0.999404i | \(0.489008\pi\) | |||||||
\(674\) | 6.66515 | + | 11.5444i | 0.256732 | + | 0.444673i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.95644 | 0.382940 | ||||||||
\(677\) | −47.2432 | −1.81570 | −0.907851 | − | 0.419292i | \(-0.862278\pi\) | ||||
−0.907851 | + | 0.419292i | \(0.862278\pi\) | |||||||
\(678\) | −7.50000 | − | 12.9904i | −0.288036 | − | 0.498893i | ||||
\(679\) | 0.686932 | − | 1.18980i | 0.0263620 | − | 0.0456604i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.6869 | − | 30.6347i | 0.677765 | − | 1.17392i | ||||
\(682\) | −0.0825757 | + | 0.143025i | −0.00316199 | + | 0.00547672i | ||||
\(683\) | 17.8348 | 0.682432 | 0.341216 | − | 0.939985i | \(-0.389161\pi\) | ||||
0.341216 | + | 0.939985i | \(0.389161\pi\) | |||||||
\(684\) | 0.834849 | − | 0.361500i | 0.0319212 | − | 0.0138223i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.50000 | + | 11.2583i | −0.248171 | + | 0.429845i | ||||
\(687\) | 10.1479 | − | 17.5767i | 0.387167 | − | 0.670593i | ||||
\(688\) | 0.604356 | + | 1.04678i | 0.0230409 | + | 0.0399079i | ||||
\(689\) | 10.9782 | − | 19.0148i | 0.418237 | − | 0.724407i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.12159 | 0.347002 | 0.173501 | − | 0.984834i | \(-0.444492\pi\) | ||||
0.173501 | + | 0.984834i | \(0.444492\pi\) | |||||||
\(692\) | 21.0000 | 0.798300 | ||||||||
\(693\) | −0.0825757 | − | 0.143025i | −0.00313679 | − | 0.00543308i | ||||
\(694\) | −8.68693 | − | 15.0462i | −0.329751 | − | 0.571146i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.95644 | 0.149968 | ||||||||
\(697\) | 4.50000 | + | 7.79423i | 0.170450 | + | 0.295227i | ||||
\(698\) | −7.29129 | + | 12.6289i | −0.275979 | + | 0.478010i | ||||
\(699\) | 8.20871 | + | 14.2179i | 0.310482 | + | 0.537771i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.97822 | + | 8.62253i | −0.188025 | + | 0.325668i | −0.944592 | − | 0.328248i | \(-0.893542\pi\) |
0.756567 | + | 0.653916i | \(0.226875\pi\) | |||||||
\(702\) | −23.9564 | −0.904178 | ||||||||
\(703\) | −19.5390 | − | 14.5040i | −0.736928 | − | 0.547027i | ||||
\(704\) | 0.791288 | 0.0298228 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.87386 | + | 11.9059i | −0.258701 | + | 0.448084i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.10436 | + | 7.10895i | −0.154251 | + | 0.267171i | ||||
\(709\) | −0.373864 | − | 0.647551i | −0.0140407 | − | 0.0243193i | 0.858920 | − | 0.512110i | \(-0.171136\pi\) |
−0.872960 | + | 0.487791i | \(0.837803\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.66061 | −0.0622776 | ||||||||
\(712\) | −2.29129 | − | 3.96863i | −0.0858696 | − | 0.148731i | ||||
\(713\) | 0.478220 | + | 0.828301i | 0.0179095 | + | 0.0310201i | ||||
\(714\) | −6.79129 | −0.254158 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.37386 | − | 9.30780i | −0.200831 | − | 0.347849i | ||||
\(717\) | 6.64337 | − | 11.5067i | 0.248101 | − | 0.429724i | ||||
\(718\) | 7.35208 | + | 12.7342i | 0.274377 | + | 0.475235i | ||||
\(719\) | −3.08258 | + | 5.33918i | −0.114961 | + | 0.199118i | −0.917764 | − | 0.397126i | \(-0.870008\pi\) |
0.802803 | + | 0.596244i | \(0.203341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.1652 | 0.490296 | ||||||||
\(722\) | 18.5000 | + | 4.33013i | 0.688499 | + | 0.161151i | ||||
\(723\) | 21.8693 | 0.813329 | ||||||||
\(724\) | 10.6869 | − | 18.5103i | 0.397177 | − | 0.687930i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.29129 | + | 16.0930i | 0.344832 | + | 0.597267i | ||||
\(727\) | 7.08258 | − | 12.2674i | 0.262678 | − | 0.454972i | −0.704275 | − | 0.709928i | \(-0.748728\pi\) |
0.966953 | + | 0.254956i | \(0.0820609\pi\) | |||||||
\(728\) | 2.39564 | + | 4.14938i | 0.0887885 | + | 0.153786i | ||||
\(729\) | 24.8693 | 0.921086 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.29129 | − | 3.96863i | −0.0847463 | − | 0.146785i | ||||
\(732\) | −11.0826 | − | 19.1956i | −0.409624 | − | 0.709489i | ||||
\(733\) | 14.7477 | 0.544720 | 0.272360 | − | 0.962195i | \(-0.412196\pi\) | ||||
0.272360 | + | 0.962195i | \(0.412196\pi\) | |||||||
\(734\) | 4.20871 | 0.155346 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.29129 | − | 3.96863i | 0.0844580 | − | 0.146286i | ||||
\(737\) | 2.53901 | + | 4.39770i | 0.0935258 | + | 0.161991i | ||||
\(738\) | 0.247727 | − | 0.429076i | 0.00911896 | − | 0.0157945i | ||||
\(739\) | 4.12614 | − | 7.14668i | 0.151782 | − | 0.262895i | −0.780100 | − | 0.625654i | \(-0.784832\pi\) |
0.931883 | + | 0.362760i | \(0.118165\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.0390 | + | 22.2982i | 1.10351 | + | 0.819144i | ||||
\(742\) | 4.58258 | 0.168232 | ||||||||
\(743\) | 14.2913 | − | 24.7532i | 0.524297 | − | 0.908108i | −0.475303 | − | 0.879822i | \(-0.657662\pi\) |
0.999600 | − | 0.0282862i | \(-0.00900498\pi\) | |||||||
\(744\) | 0.186932 | − | 0.323775i | 0.00685325 | − | 0.0118702i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.81307 | − | 6.60443i | 0.139606 | − | 0.241805i | ||||
\(747\) | −0.0825757 | − | 0.143025i | −0.00302129 | − | 0.00523302i | ||||
\(748\) | −3.00000 | −0.109691 | ||||||||
\(749\) | 3.95644 | 0.144565 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.20871 | − | 10.7538i | −0.226559 | − | 0.392412i | 0.730227 | − | 0.683205i | \(-0.239414\pi\) |
−0.956786 | + | 0.290793i | \(0.906081\pi\) | |||||||
\(752\) | −6.16515 | −0.224820 | ||||||||
\(753\) | 50.3739 | 1.83573 | ||||||||
\(754\) | 5.29129 | + | 9.16478i | 0.192697 | + | 0.333762i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.50000 | − | 4.33013i | −0.0909241 | − | 0.157485i | ||||
\(757\) | 9.12614 | − | 15.8069i | 0.331695 | − | 0.574513i | −0.651149 | − | 0.758950i | \(-0.725713\pi\) |
0.982844 | + | 0.184437i | \(0.0590462\pi\) | |||||||
\(758\) | 11.5826 | − | 20.0616i | 0.420698 | − | 0.728670i | ||||
\(759\) | −6.49545 | −0.235770 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.7477 | 1.91210 | 0.956052 | − | 0.293198i | \(-0.0947194\pi\) | ||||
0.956052 | + | 0.293198i | \(0.0947194\pi\) | |||||||
\(762\) | 14.6652 | − | 25.4008i | 0.531262 | − | 0.920173i | ||||
\(763\) | −7.87386 | + | 13.6379i | −0.285053 | + | 0.493726i | ||||
\(764\) | 3.47822 | + | 6.02445i | 0.125838 | + | 0.217957i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.29129 | + | 3.96863i | 0.0827876 | + | 0.143392i | ||||
\(767\) | −21.9564 | −0.792801 | ||||||||
\(768\) | −1.79129 | −0.0646375 | ||||||||
\(769\) | −7.16515 | − | 12.4104i | −0.258382 | − | 0.447531i | 0.707427 | − | 0.706787i | \(-0.249856\pi\) |
−0.965809 | + | 0.259256i | \(0.916523\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.2867 | −1.01872 | ||||||||
\(772\) | −24.7477 | −0.890690 | ||||||||
\(773\) | 7.66515 | + | 13.2764i | 0.275696 | + | 0.477520i | 0.970311 | − | 0.241862i | \(-0.0777582\pi\) |
−0.694614 | + | 0.719382i | \(0.744425\pi\) | |||||||
\(774\) | −0.126136 | + | 0.218475i | −0.00453388 | + | 0.00785291i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.686932 | + | 1.18980i | −0.0246594 | + | 0.0427114i | ||||
\(777\) | 5.00000 | − | 8.66025i | 0.179374 | − | 0.310685i | ||||
\(778\) | −32.3739 | −1.16066 | ||||||||
\(779\) | 9.49545 | − | 4.11165i | 0.340210 | − | 0.147315i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.81307 | + | 3.14033i | −0.0648767 | + | 0.112370i | ||||
\(782\) | −8.68693 | + | 15.0462i | −0.310644 | + | 0.538051i | ||||
\(783\) | −5.52178 | − | 9.56400i | −0.197332 | − | 0.341790i | ||||
\(784\) | 3.00000 | − | 5.19615i | 0.107143 | − | 0.185577i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −36.7913 | −1.31230 | ||||||||
\(787\) | −3.74773 | −0.133592 | −0.0667960 | − | 0.997767i | \(-0.521278\pi\) | ||||
−0.0667960 | + | 0.997767i | \(0.521278\pi\) | |||||||
\(788\) | 12.3956 | + | 21.4699i | 0.441577 | + | 0.764833i | ||||
\(789\) | 25.5998 | + | 44.3402i | 0.911377 | + | 1.57855i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.37386 | 0.297740 | ||||||||
\(792\) | 0.0825757 | + | 0.143025i | 0.00293420 | + | 0.00508218i | ||||
\(793\) | 29.6434 | − | 51.3438i | 1.05267 | − | 1.82327i | ||||
\(794\) | 10.2913 | + | 17.8250i | 0.365224 | + | 0.632587i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.79129 | − | 4.83465i | 0.0989346 | − | 0.171360i | ||||
\(797\) | 6.46099 | 0.228860 | 0.114430 | − | 0.993431i | \(-0.463496\pi\) | ||||
0.114430 | + | 0.993431i | \(0.463496\pi\) | |||||||
\(798\) | −0.895644 | + | 7.75650i | −0.0317055 | + | 0.274577i | ||||
\(799\) | 23.3739 | 0.826908 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.478220 | − | 0.828301i | 0.0168971 | − | 0.0292666i | ||||
\(802\) | −6.00000 | − | 10.3923i | −0.211867 | − | 0.366965i | ||||
\(803\) | −0.708712 | + | 1.22753i | −0.0250099 | + | 0.0433184i | ||||
\(804\) | −5.74773 | − | 9.95536i | −0.202707 | − | 0.351098i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.00000 | 0.0352235 | ||||||||
\(807\) | −25.1869 | − | 43.6250i | −0.886622 | − | 1.53567i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.5390 | 1.03854 | 0.519268 | − | 0.854611i | \(-0.326205\pi\) | ||||
0.519268 | + | 0.854611i | \(0.326205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.4347 | + | 37.1259i | 0.752673 | + | 1.30367i | 0.946523 | + | 0.322636i | \(0.104569\pi\) |
−0.193850 | + | 0.981031i | \(0.562098\pi\) | |||||||
\(812\) | −1.10436 | + | 1.91280i | −0.0387553 | + | 0.0671261i | ||||
\(813\) | 21.6044 | + | 37.4198i | 0.757698 | + | 1.31237i | ||||
\(814\) | 2.20871 | − | 3.82560i | 0.0774153 | − | 0.134087i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.79129 | 0.237743 | ||||||||
\(817\) | −4.83485 | + | 2.09355i | −0.169150 | + | 0.0732441i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | −0.500000 | + | 0.866025i | −0.0174714 | + | 0.0302614i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.165151 | − | 0.286051i | −0.00576382 | − | 0.00998323i | 0.863129 | − | 0.504983i | \(-0.168501\pi\) |
−0.868893 | + | 0.495000i | \(0.835168\pi\) | |||||||
\(822\) | −19.1044 | + | 33.0897i | −0.666341 | + | 1.15414i | ||||
\(823\) | 4.62614 | + | 8.01270i | 0.161257 | + | 0.279305i | 0.935320 | − | 0.353804i | \(-0.115112\pi\) |
−0.774063 | + | 0.633109i | \(0.781779\pi\) | |||||||
\(824\) | −13.1652 | −0.458630 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.29129 | − | 3.96863i | −0.0797241 | − | 0.138086i | ||||
\(827\) | 8.45644 | + | 14.6470i | 0.294059 | + | 0.509325i | 0.974766 | − | 0.223231i | \(-0.0716604\pi\) |
−0.680706 | + | 0.732556i | \(0.738327\pi\) | |||||||
\(828\) | 0.956439 | 0.0332386 | ||||||||
\(829\) | −0.539015 | −0.0187208 | −0.00936038 | − | 0.999956i | \(-0.502980\pi\) | ||||
−0.00936038 | + | 0.999956i | \(0.502980\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.7913 | + | 29.0834i | −0.582483 | + | 1.00889i | ||||
\(832\) | −2.39564 | − | 4.14938i | −0.0830540 | − | 0.143854i | ||||
\(833\) | −11.3739 | + | 19.7001i | −0.394081 | + | 0.682568i | ||||
\(834\) | 15.0390 | − | 26.0483i | 0.520758 | − | 0.901980i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.395644 | + | 3.42638i | −0.0136836 | + | 0.118504i | ||||
\(837\) | −1.04356 | −0.0360707 | ||||||||
\(838\) | 2.37386 | − | 4.11165i | 0.0820038 | − | 0.142035i | ||||
\(839\) | −14.5218 | + | 25.1525i | −0.501348 | + | 0.868359i | 0.498651 | + | 0.866803i | \(0.333829\pi\) |
−0.999999 | + | 0.00155670i | \(0.999504\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.0608 | − | 20.8899i | 0.415889 | − | 0.720342i | ||||
\(842\) | 10.0000 | + | 17.3205i | 0.344623 | + | 0.596904i | ||||
\(843\) | −2.53901 | −0.0874483 | ||||||||
\(844\) | 1.04356 | 0.0359208 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.643371 | − | 1.11435i | −0.0221196 | − | 0.0383122i | ||||
\(847\) | −10.3739 | −0.356450 | ||||||||
\(848\) | −4.58258 | −0.157366 | ||||||||
\(849\) | 18.0218 | + | 31.2146i | 0.618506 | + | 1.07128i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.7913 | − | 22.1552i | −0.438480 | − | 0.759469i | ||||
\(852\) | 4.10436 | − | 7.10895i | 0.140613 | − | 0.243549i | ||||
\(853\) | 17.5172 | − | 30.3407i | 0.599779 | − | 1.03885i | −0.393075 | − | 0.919507i | \(-0.628589\pi\) |
0.992853 | − | 0.119341i | \(-0.0380780\pi\) | |||||||
\(854\) | 12.3739 | 0.423425 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.95644 | −0.135228 | ||||||||
\(857\) | 1.50000 | − | 2.59808i | 0.0512390 | − | 0.0887486i | −0.839268 | − | 0.543718i | \(-0.817016\pi\) |
0.890507 | + | 0.454969i | \(0.150350\pi\) | |||||||
\(858\) | −3.39564 | + | 5.88143i | −0.115925 | + | 0.200789i | ||||
\(859\) | 16.8521 | + | 29.1887i | 0.574986 | + | 0.995904i | 0.996043 | + | 0.0888704i | \(0.0283257\pi\) |
−0.421058 | + | 0.907034i | \(0.638341\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.12614 | + | 3.68258i | 0.0724585 | + | 0.125502i | ||||
\(862\) | −12.7913 | −0.435673 | ||||||||
\(863\) | 13.5826 | 0.462356 | 0.231178 | − | 0.972911i | \(-0.425742\pi\) | ||||
0.231178 | + | 0.972911i | \(0.425742\pi\) | |||||||
\(864\) | 2.50000 | + | 4.33013i | 0.0850517 | + | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −38.9129 | −1.32231 | ||||||||
\(867\) | 4.70417 | 0.159762 | ||||||||
\(868\) | 0.104356 | + | 0.180750i | 0.00354208 | + | 0.00613506i | ||||
\(869\) | 3.14792 | − | 5.45235i | 0.106786 | − | 0.184958i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.3739 | − | 26.6283i | 0.520923 | − | 0.902266i | ||||
\(872\) | 7.87386 | − | 13.6379i | 0.266643 | − | 0.461839i | ||||
\(873\) | −0.286742 | −0.00970475 | ||||||||
\(874\) | 16.0390 | + | 11.9059i | 0.542528 | + | 0.402722i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.60436 | − | 2.77883i | 0.0542062 | − | 0.0938878i | ||||
\(877\) | −14.2477 | + | 24.6778i | −0.481112 | + | 0.833310i | −0.999765 | − | 0.0216749i | \(-0.993100\pi\) |
0.518654 | + | 0.854985i | \(0.326433\pi\) | |||||||
\(878\) | 5.66515 | + | 9.81233i | 0.191190 | + | 0.331150i | ||||
\(879\) | −1.83030 | + | 3.17018i | −0.0617346 | + | 0.106927i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.79129 | 0.127732 | 0.0638659 | − | 0.997958i | \(-0.479657\pi\) | ||||
0.0638659 | + | 0.997958i | \(0.479657\pi\) | |||||||
\(882\) | 1.25227 | 0.0421662 | ||||||||
\(883\) | −1.37386 | − | 2.37960i | −0.0462342 | − | 0.0800800i | 0.841982 | − | 0.539505i | \(-0.181389\pi\) |
−0.888216 | + | 0.459425i | \(0.848055\pi\) | |||||||
\(884\) | 9.08258 | + | 15.7315i | 0.305480 | + | 0.529107i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.0000 | −0.806296 | ||||||||
\(887\) | 3.56080 | + | 6.16748i | 0.119560 | + | 0.207084i | 0.919593 | − | 0.392872i | \(-0.128518\pi\) |
−0.800034 | + | 0.599955i | \(0.795185\pi\) | |||||||
\(888\) | −5.00000 | + | 8.66025i | −0.167789 | + | 0.290619i | ||||
\(889\) | 8.18693 | + | 14.1802i | 0.274581 | + | 0.475588i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.79129 | − | 6.56670i | 0.127013 | − | 0.219993i | ||||
\(892\) | −23.7913 | −0.796591 | ||||||||
\(893\) | 3.08258 | − | 26.6959i | 0.103154 | − | 0.893344i | ||||
\(894\) | 8.50455 | 0.284435 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.500000 | − | 0.866025i | 0.0167038 | − | 0.0289319i | ||||
\(897\) | 19.6652 | + | 34.0610i | 0.656600 | + | 1.13727i | ||||
\(898\) | −16.6652 | + | 28.8649i | −0.556123 | + | 0.963234i | ||||
\(899\) | 0.230493 | + | 0.399225i | 0.00768736 | + | 0.0133149i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.3739 | 0.578807 | ||||||||
\(902\) | 0.939205 | + | 1.62675i | 0.0312721 | + | 0.0541649i | ||||
\(903\) | −1.08258 | − | 1.87508i | −0.0360259 | − | 0.0623986i | ||||
\(904\) | −8.37386 | −0.278511 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.5218 | + | 18.2243i | 0.349563 | + | 0.605460i | ||||
\(907\) | 17.4347 | − | 30.1977i | 0.578908 | − | 1.00270i | −0.416697 | − | 0.909046i | \(-0.636812\pi\) |
0.995605 | − | 0.0936530i | \(-0.0298544\pi\) | |||||||
\(908\) | −9.87386 | − | 17.1020i | −0.327676 | − | 0.567551i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.6606 | 0.817042 | 0.408521 | − | 0.912749i | \(-0.366045\pi\) | ||||
0.408521 | + | 0.912749i | \(0.366045\pi\) | |||||||
\(912\) | 0.895644 | − | 7.75650i | 0.0296577 | − | 0.256844i | ||||
\(913\) | 0.626136 | 0.0207221 | ||||||||
\(914\) | −3.37386 | + | 5.84370i | −0.111597 | + | 0.193293i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.66515 | − | 9.81233i | −0.187182 | − | 0.324209i | ||||
\(917\) | 10.2695 | − | 17.7873i | 0.339129 | − | 0.587389i | ||||
\(918\) | −9.47822 | − | 16.4168i | −0.312828 | − | 0.541834i | ||||
\(919\) | −42.2087 | −1.39234 | −0.696168 | − | 0.717878i | \(-0.745113\pi\) | ||||
−0.696168 | + | 0.717878i | \(0.745113\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.3566 | − | 31.7946i | −0.604871 | − | 1.04767i | ||||
\(922\) | 4.10436 | + | 7.10895i | 0.135170 | + | 0.234121i | ||||
\(923\) | 21.9564 | 0.722705 | ||||||||
\(924\) | −1.41742 | −0.0466298 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.47822 | − | 4.29240i | 0.0814393 | − | 0.141057i | ||||
\(927\) | −1.37386 | − | 2.37960i | −0.0451236 | − | 0.0781564i | ||||
\(928\) | 1.10436 | − | 1.91280i | 0.0362523 | − | 0.0627908i | ||||
\(929\) | −26.0608 | + | 45.1386i | −0.855027 | + | 1.48095i | 0.0215930 | + | 0.999767i | \(0.493126\pi\) |
−0.876620 | + | 0.481183i | \(0.840207\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.0000 | + | 15.5885i | 0.688247 | + | 0.510891i | ||||
\(932\) | 9.16515 | 0.300215 | ||||||||
\(933\) | −13.4347 | + | 23.2695i | −0.439831 | + | 0.761810i | ||||
\(934\) | −12.1652 | + | 21.0707i | −0.398056 | + | 0.689453i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | − | 0.866025i | 0.0163430 | − | 0.0283069i | ||||
\(937\) | −17.5608 | − | 30.4162i | −0.573686 | − | 0.993654i | −0.996183 | − | 0.0872892i | \(-0.972180\pi\) |
0.422497 | − | 0.906364i | \(-0.361154\pi\) | |||||||
\(938\) | 6.41742 | 0.209536 | ||||||||
\(939\) | 28.2087 | 0.920557 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.7087 | + | 27.2083i | 0.512089 | + | 0.886965i | 0.999902 | + | 0.0140163i | \(0.00446168\pi\) |
−0.487812 | + | 0.872948i | \(0.662205\pi\) | |||||||
\(942\) | −26.7913 | −0.872907 | ||||||||
\(943\) | 10.8784 | 0.354250 | ||||||||
\(944\) | 2.29129 | + | 3.96863i | 0.0745751 | + | 0.129168i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.478220 | − | 0.828301i | −0.0155483 | − | 0.0269304i | ||||
\(947\) | −9.70871 | + | 16.8160i | −0.315491 | + | 0.546446i | −0.979542 | − | 0.201241i | \(-0.935502\pi\) |
0.664051 | + | 0.747687i | \(0.268836\pi\) | |||||||
\(948\) | −7.12614 | + | 12.3428i | −0.231446 | + | 0.400876i | ||||
\(949\) | 8.58258 | 0.278602 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.4174 | 0.532371 | ||||||||
\(952\) | −1.89564 | + | 3.28335i | −0.0614382 | + | 0.106414i | ||||
\(953\) | 12.5608 | − | 21.7559i | 0.406884 | − | 0.704744i | −0.587655 | − | 0.809112i | \(-0.699949\pi\) |
0.994539 | + | 0.104368i | \(0.0332820\pi\) | |||||||
\(954\) | −0.478220 | − | 0.828301i | −0.0154829 | − | 0.0268172i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.70871 | − | 6.42368i | −0.119948 | − | 0.207757i | ||||
\(957\) | −3.13068 | −0.101201 | ||||||||
\(958\) | −4.25227 | −0.137385 | ||||||||
\(959\) | −10.6652 | − | 18.4726i | −0.344396 | − | 0.596511i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9564 | −0.998595 | ||||||||
\(962\) | −26.7477 | −0.862381 | ||||||||
\(963\) | −0.412878 | − | 0.715126i | −0.0133048 | − | 0.0230446i | ||||
\(964\) | 6.10436 | − | 10.5731i | 0.196608 | − | 0.340535i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.10436 | + | 7.10895i | −0.132055 | + | 0.228727i | ||||
\(967\) | 6.53901 | − | 11.3259i | 0.210281 | − | 0.364217i | −0.741522 | − | 0.670929i | \(-0.765896\pi\) |
0.951802 | + | 0.306712i | \(0.0992289\pi\) | |||||||
\(968\) | 10.3739 | 0.333429 | ||||||||
\(969\) | −3.39564 | + | 29.4071i | −0.109084 | + | 0.944693i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.4564 | − | 40.6277i | 0.752753 | − | 1.30381i | −0.193731 | − | 0.981055i | \(-0.562059\pi\) |
0.946484 | − | 0.322752i | \(-0.104608\pi\) | |||||||
\(972\) | −1.08258 | + | 1.87508i | −0.0347236 | + | 0.0601431i | ||||
\(973\) | 8.39564 | + | 14.5417i | 0.269152 | + | 0.466185i | ||||
\(974\) | −11.5000 | + | 19.9186i | −0.368484 | + | 0.638233i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.3739 | −0.396078 | ||||||||
\(977\) | −18.6261 | −0.595903 | −0.297951 | − | 0.954581i | \(-0.596303\pi\) | ||||
−0.297951 | + | 0.954581i | \(0.596303\pi\) | |||||||
\(978\) | −4.85208 | − | 8.40405i | −0.155153 | − | 0.268732i | ||||
\(979\) | 1.81307 | + | 3.14033i | 0.0579459 | + | 0.100365i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.28674 | 0.104938 | ||||||||
\(982\) | −20.2913 | − | 35.1455i | −0.647521 | − | 1.12154i | ||||
\(983\) | 20.2087 | − | 35.0025i | 0.644558 | − | 1.11641i | −0.339846 | − | 0.940481i | \(-0.610375\pi\) |
0.984403 | − | 0.175926i | \(-0.0562918\pi\) | |||||||
\(984\) | −2.12614 | − | 3.68258i | −0.0677788 | − | 0.117396i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.18693 | + | 7.25198i | −0.133339 | + | 0.230950i | ||||
\(987\) | 11.0436 | 0.351520 | ||||||||
\(988\) | 19.1652 | − | 8.29875i | 0.609725 | − | 0.264019i | ||||
\(989\) | −5.53901 | −0.176130 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.56080 | − | 14.8277i | 0.271943 | − | 0.471018i | −0.697417 | − | 0.716666i | \(-0.745667\pi\) |
0.969359 | + | 0.245648i | \(0.0790006\pi\) | |||||||
\(992\) | −0.104356 | − | 0.180750i | −0.00331331 | − | 0.00573882i | ||||
\(993\) | 25.0000 | − | 43.3013i | 0.793351 | − | 1.37412i | ||||
\(994\) | 2.29129 | + | 3.96863i | 0.0726752 | + | 0.125877i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.41742 | −0.0449128 | ||||||||
\(997\) | −0.500000 | − | 0.866025i | −0.0158352 | − | 0.0274273i | 0.857999 | − | 0.513651i | \(-0.171707\pi\) |
−0.873834 | + | 0.486224i | \(0.838374\pi\) | |||||||
\(998\) | 8.66515 | + | 15.0085i | 0.274291 | + | 0.475085i | ||||
\(999\) | 27.9129 | 0.883124 |
(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.e.j.201.2 | yes | 4 | |
5.2 | odd | 4 | 950.2.j.h.49.3 | 8 | |||
5.3 | odd | 4 | 950.2.j.h.49.2 | 8 | |||
5.4 | even | 2 | 950.2.e.i.201.1 | ✓ | 4 | ||
19.7 | even | 3 | inner | 950.2.e.j.501.2 | yes | 4 | |
95.7 | odd | 12 | 950.2.j.h.349.2 | 8 | |||
95.64 | even | 6 | 950.2.e.i.501.1 | yes | 4 | ||
95.83 | odd | 12 | 950.2.j.h.349.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.e.i.201.1 | ✓ | 4 | 5.4 | even | 2 | ||
950.2.e.i.501.1 | yes | 4 | 95.64 | even | 6 | ||
950.2.e.j.201.2 | yes | 4 | 1.1 | even | 1 | trivial | |
950.2.e.j.501.2 | yes | 4 | 19.7 | even | 3 | inner | |
950.2.j.h.49.2 | 8 | 5.3 | odd | 4 | |||
950.2.j.h.49.3 | 8 | 5.2 | odd | 4 | |||
950.2.j.h.349.2 | 8 | 95.7 | odd | 12 | |||
950.2.j.h.349.3 | 8 | 95.83 | odd | 12 |