Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,3,Mod(31,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.g (of order \(4\), 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: | \(1.06267303101\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1579585536.10 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 4x^{6} + 28x^{5} - 38x^{4} + 8x^{3} + 200x^{2} - 352x + 484 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.4 | ||
Root | \(2.22833 - 1.32913i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.31 |
Dual form | 39.3.g.a.34.4 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.26523 | − | 2.26523i | 1.13261 | − | 1.13261i | 0.142872 | − | 0.989741i | \(-0.454366\pi\) |
0.989741 | − | 0.142872i | \(-0.0456338\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | − | 6.26250i | − | 1.56563i | ||||||
\(5\) | −2.07379 | + | 2.07379i | −0.414758 | + | 0.414758i | −0.883392 | − | 0.468634i | \(-0.844746\pi\) |
0.468634 | + | 0.883392i | \(0.344746\pi\) | |||||||
\(6\) | −3.92349 | + | 3.92349i | −0.653915 | + | 0.653915i | ||||
\(7\) | 7.04857 | + | 7.04857i | 1.00694 | + | 1.00694i | 0.999976 | + | 0.00696323i | \(0.00221648\pi\) |
0.00696323 | + | 0.999976i | \(0.497784\pi\) | |||||||
\(8\) | −5.12509 | − | 5.12509i | −0.640636 | − | 0.640636i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 9.39521i | 0.939521i | ||||||||
\(11\) | −10.8395 | − | 10.8395i | −0.985413 | − | 0.985413i | 0.0144826 | − | 0.999895i | \(-0.495390\pi\) |
−0.999895 | + | 0.0144826i | \(0.995390\pi\) | |||||||
\(12\) | 10.8470i | 0.903915i | ||||||||
\(13\) | −12.9619 | + | 0.994555i | −0.997069 | + | 0.0765042i | ||||
\(14\) | 31.9332 | 2.28095 | ||||||||
\(15\) | 3.59191 | − | 3.59191i | 0.239461 | − | 0.239461i | ||||
\(16\) | 1.83106 | 0.114441 | ||||||||
\(17\) | 5.74438i | 0.337905i | 0.985624 | + | 0.168952i | \(0.0540384\pi\) | ||||
−0.985624 | + | 0.168952i | \(0.945962\pi\) | |||||||
\(18\) | 6.79568 | − | 6.79568i | 0.377538 | − | 0.377538i | ||||
\(19\) | −7.54533 | + | 7.54533i | −0.397123 | + | 0.397123i | −0.877217 | − | 0.480094i | \(-0.840602\pi\) |
0.480094 | + | 0.877217i | \(0.340602\pi\) | |||||||
\(20\) | 12.9871 | + | 12.9871i | 0.649356 | + | 0.649356i | ||||
\(21\) | −12.2085 | − | 12.2085i | −0.581356 | − | 0.581356i | ||||
\(22\) | −49.1080 | −2.23218 | ||||||||
\(23\) | − | 35.8702i | − | 1.55957i | −0.626045 | − | 0.779787i | \(-0.715328\pi\) | ||
0.626045 | − | 0.779787i | \(-0.284672\pi\) | |||||||
\(24\) | 8.87691 | + | 8.87691i | 0.369871 | + | 0.369871i | ||||
\(25\) | 16.3988i | 0.655952i | ||||||||
\(26\) | −27.1088 | + | 31.6145i | −1.04264 | + | 1.21594i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 44.1417 | − | 44.1417i | 1.57649 | − | 1.57649i | ||||
\(29\) | −7.97423 | −0.274974 | −0.137487 | − | 0.990504i | \(-0.543902\pi\) | ||||
−0.137487 | + | 0.990504i | \(0.543902\pi\) | |||||||
\(30\) | − | 16.2730i | − | 0.542433i | ||||||
\(31\) | 37.2527 | − | 37.2527i | 1.20170 | − | 1.20170i | 0.228049 | − | 0.973650i | \(-0.426765\pi\) |
0.973650 | − | 0.228049i | \(-0.0732346\pi\) | |||||||
\(32\) | 24.6481 | − | 24.6481i | 0.770253 | − | 0.770253i | ||||
\(33\) | 18.7746 | + | 18.7746i | 0.568928 | + | 0.568928i | ||||
\(34\) | 13.0123 | + | 13.0123i | 0.382716 | + | 0.382716i | ||||
\(35\) | −29.2345 | −0.835272 | ||||||||
\(36\) | − | 18.7875i | − | 0.521875i | ||||||
\(37\) | 23.0620 | + | 23.0620i | 0.623297 | + | 0.623297i | 0.946373 | − | 0.323076i | \(-0.104717\pi\) |
−0.323076 | + | 0.946373i | \(0.604717\pi\) | |||||||
\(38\) | 34.1838i | 0.899573i | ||||||||
\(39\) | 22.4507 | − | 1.72262i | 0.575658 | − | 0.0441697i | ||||
\(40\) | 21.2567 | 0.531417 | ||||||||
\(41\) | −23.2376 | + | 23.2376i | −0.566772 | + | 0.566772i | −0.931223 | − | 0.364451i | \(-0.881257\pi\) |
0.364451 | + | 0.931223i | \(0.381257\pi\) | |||||||
\(42\) | −55.3100 | −1.31690 | ||||||||
\(43\) | − | 16.3140i | − | 0.379396i | −0.981843 | − | 0.189698i | \(-0.939249\pi\) | ||
0.981843 | − | 0.189698i | \(-0.0607509\pi\) | |||||||
\(44\) | −67.8827 | + | 67.8827i | −1.54279 | + | 1.54279i | ||||
\(45\) | −6.22137 | + | 6.22137i | −0.138253 | + | 0.138253i | ||||
\(46\) | −81.2541 | − | 81.2541i | −1.76639 | − | 1.76639i | ||||
\(47\) | 18.9476 | + | 18.9476i | 0.403140 | + | 0.403140i | 0.879338 | − | 0.476198i | \(-0.157985\pi\) |
−0.476198 | + | 0.879338i | \(0.657985\pi\) | |||||||
\(48\) | −3.17148 | −0.0660726 | ||||||||
\(49\) | 50.3648i | 1.02785i | ||||||||
\(50\) | 37.1470 | + | 37.1470i | 0.742940 | + | 0.742940i | ||||
\(51\) | − | 9.94957i | − | 0.195090i | ||||||
\(52\) | 6.22841 | + | 81.1740i | 0.119777 | + | 1.56104i | ||||
\(53\) | 5.50653 | 0.103897 | 0.0519484 | − | 0.998650i | \(-0.483457\pi\) | ||||
0.0519484 | + | 0.998650i | \(0.483457\pi\) | |||||||
\(54\) | −11.7705 | + | 11.7705i | −0.217972 | + | 0.217972i | ||||
\(55\) | 44.9578 | 0.817415 | ||||||||
\(56\) | − | 72.2491i | − | 1.29016i | ||||||
\(57\) | 13.0689 | − | 13.0689i | 0.229279 | − | 0.229279i | ||||
\(58\) | −18.0634 | + | 18.0634i | −0.311439 | + | 0.311439i | ||||
\(59\) | 43.2576 | + | 43.2576i | 0.733180 | + | 0.733180i | 0.971248 | − | 0.238069i | \(-0.0765143\pi\) |
−0.238069 | + | 0.971248i | \(0.576514\pi\) | |||||||
\(60\) | −22.4943 | − | 22.4943i | −0.374906 | − | 0.374906i | ||||
\(61\) | −52.1029 | −0.854146 | −0.427073 | − | 0.904217i | \(-0.640455\pi\) | ||||
−0.427073 | + | 0.904217i | \(0.640455\pi\) | |||||||
\(62\) | − | 168.771i | − | 2.72212i | ||||||
\(63\) | 21.1457 | + | 21.1457i | 0.335646 | + | 0.335646i | ||||
\(64\) | − | 104.343i | − | 1.63036i | ||||||
\(65\) | 24.8178 | − | 28.9428i | 0.381812 | − | 0.445273i | ||||
\(66\) | 85.0576 | 1.28875 | ||||||||
\(67\) | 45.3282 | − | 45.3282i | 0.676540 | − | 0.676540i | −0.282676 | − | 0.959216i | \(-0.591222\pi\) |
0.959216 | + | 0.282676i | \(0.0912221\pi\) | |||||||
\(68\) | 35.9742 | 0.529033 | ||||||||
\(69\) | 62.1290i | 0.900420i | ||||||||
\(70\) | −66.2228 | + | 66.2228i | −0.946040 | + | 0.946040i | ||||
\(71\) | −76.4801 | + | 76.4801i | −1.07719 | + | 1.07719i | −0.0804243 | + | 0.996761i | \(0.525628\pi\) |
−0.996761 | + | 0.0804243i | \(0.974372\pi\) | |||||||
\(72\) | −15.3753 | − | 15.3753i | −0.213545 | − | 0.213545i | ||||
\(73\) | 2.46881 | + | 2.46881i | 0.0338193 | + | 0.0338193i | 0.723814 | − | 0.689995i | \(-0.242387\pi\) |
−0.689995 | + | 0.723814i | \(0.742387\pi\) | |||||||
\(74\) | 104.481 | 1.41191 | ||||||||
\(75\) | − | 28.4035i | − | 0.378714i | ||||||
\(76\) | 47.2527 | + | 47.2527i | 0.621745 | + | 0.621745i | ||||
\(77\) | − | 152.807i | − | 1.98450i | ||||||
\(78\) | 46.9537 | − | 54.7580i | 0.601971 | − | 0.702025i | ||||
\(79\) | −98.6735 | −1.24903 | −0.624516 | − | 0.781012i | \(-0.714704\pi\) | ||||
−0.624516 | + | 0.781012i | \(0.714704\pi\) | |||||||
\(80\) | −3.79723 | + | 3.79723i | −0.0474654 | + | 0.0474654i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 105.277i | 1.28387i | ||||||||
\(83\) | 28.1778 | − | 28.1778i | 0.339492 | − | 0.339492i | −0.516684 | − | 0.856176i | \(-0.672834\pi\) |
0.856176 | + | 0.516684i | \(0.172834\pi\) | |||||||
\(84\) | −76.4557 | + | 76.4557i | −0.910187 | + | 0.910187i | ||||
\(85\) | −11.9126 | − | 11.9126i | −0.140149 | − | 0.140149i | ||||
\(86\) | −36.9550 | − | 36.9550i | −0.429709 | − | 0.429709i | ||||
\(87\) | 13.8118 | 0.158756 | ||||||||
\(88\) | 111.107i | 1.26258i | ||||||||
\(89\) | 18.8536 | + | 18.8536i | 0.211838 | + | 0.211838i | 0.805048 | − | 0.593210i | \(-0.202140\pi\) |
−0.593210 | + | 0.805048i | \(0.702140\pi\) | |||||||
\(90\) | 28.1856i | 0.313174i | ||||||||
\(91\) | −98.3731 | − | 84.3527i | −1.08102 | − | 0.926953i | ||||
\(92\) | −224.637 | −2.44171 | ||||||||
\(93\) | −64.5235 | + | 64.5235i | −0.693801 | + | 0.693801i | ||||
\(94\) | 85.8411 | 0.913203 | ||||||||
\(95\) | − | 31.2949i | − | 0.329420i | ||||||
\(96\) | −42.6918 | + | 42.6918i | −0.444706 | + | 0.444706i | ||||
\(97\) | 34.6799 | − | 34.6799i | 0.357525 | − | 0.357525i | −0.505375 | − | 0.862900i | \(-0.668646\pi\) |
0.862900 | + | 0.505375i | \(0.168646\pi\) | |||||||
\(98\) | 114.088 | + | 114.088i | 1.16416 | + | 1.16416i | ||||
\(99\) | −32.5186 | − | 32.5186i | −0.328471 | − | 0.328471i | ||||
\(100\) | 102.698 | 1.02698 | ||||||||
\(101\) | 126.405i | 1.25154i | 0.780008 | + | 0.625769i | \(0.215215\pi\) | ||||
−0.780008 | + | 0.625769i | \(0.784785\pi\) | |||||||
\(102\) | −22.5380 | − | 22.5380i | −0.220961 | − | 0.220961i | ||||
\(103\) | − | 89.7003i | − | 0.870877i | −0.900219 | − | 0.435438i | \(-0.856593\pi\) | ||
0.900219 | − | 0.435438i | \(-0.143407\pi\) | |||||||
\(104\) | 71.5280 | + | 61.3337i | 0.687769 | + | 0.589747i | ||||
\(105\) | 50.6357 | 0.482244 | ||||||||
\(106\) | 12.4735 | − | 12.4735i | 0.117675 | − | 0.117675i | ||||
\(107\) | 48.7860 | 0.455944 | 0.227972 | − | 0.973668i | \(-0.426791\pi\) | ||||
0.227972 | + | 0.973668i | \(0.426791\pi\) | |||||||
\(108\) | 32.5409i | 0.301305i | ||||||||
\(109\) | 29.6606 | − | 29.6606i | 0.272115 | − | 0.272115i | −0.557836 | − | 0.829951i | \(-0.688368\pi\) |
0.829951 | + | 0.557836i | \(0.188368\pi\) | |||||||
\(110\) | 101.840 | − | 101.840i | 0.925816 | − | 0.925816i | ||||
\(111\) | −39.9445 | − | 39.9445i | −0.359861 | − | 0.359861i | ||||
\(112\) | 12.9063 | + | 12.9063i | 0.115235 | + | 0.115235i | ||||
\(113\) | −81.1492 | −0.718135 | −0.359067 | − | 0.933312i | \(-0.616905\pi\) | ||||
−0.359067 | + | 0.933312i | \(0.616905\pi\) | |||||||
\(114\) | − | 59.2080i | − | 0.519369i | ||||||
\(115\) | 74.3872 | + | 74.3872i | 0.646845 | + | 0.646845i | ||||
\(116\) | 49.9387i | 0.430506i | ||||||||
\(117\) | −38.8857 | + | 2.98367i | −0.332356 | + | 0.0255014i | ||||
\(118\) | 195.977 | 1.66082 | ||||||||
\(119\) | −40.4897 | + | 40.4897i | −0.340250 | + | 0.340250i | ||||
\(120\) | −36.8177 | −0.306814 | ||||||||
\(121\) | 113.991i | 0.942076i | ||||||||
\(122\) | −118.025 | + | 118.025i | −0.967417 | + | 0.967417i | ||||
\(123\) | 40.2488 | − | 40.2488i | 0.327226 | − | 0.327226i | ||||
\(124\) | −233.295 | − | 233.295i | −1.88141 | − | 1.88141i | ||||
\(125\) | −85.8524 | − | 85.8524i | −0.686819 | − | 0.686819i | ||||
\(126\) | 95.7997 | 0.760315 | ||||||||
\(127\) | − | 14.5872i | − | 0.114860i | −0.998350 | − | 0.0574301i | \(-0.981709\pi\) | ||
0.998350 | − | 0.0574301i | \(-0.0182906\pi\) | |||||||
\(128\) | −137.768 | − | 137.768i | −1.07631 | − | 1.07631i | ||||
\(129\) | 28.2567i | 0.219044i | ||||||||
\(130\) | −9.34405 | − | 121.780i | −0.0718773 | − | 0.936767i | ||||
\(131\) | −88.9240 | −0.678809 | −0.339405 | − | 0.940640i | \(-0.610226\pi\) | ||||
−0.339405 | + | 0.940640i | \(0.610226\pi\) | |||||||
\(132\) | 117.576 | − | 117.576i | 0.890729 | − | 0.890729i | ||||
\(133\) | −106.368 | −0.799756 | ||||||||
\(134\) | − | 205.357i | − | 1.53252i | ||||||
\(135\) | 10.7757 | − | 10.7757i | 0.0798202 | − | 0.0798202i | ||||
\(136\) | 29.4405 | − | 29.4405i | 0.216474 | − | 0.216474i | ||||
\(137\) | 98.5465 | + | 98.5465i | 0.719317 | + | 0.719317i | 0.968465 | − | 0.249148i | \(-0.0801506\pi\) |
−0.249148 | + | 0.968465i | \(0.580151\pi\) | |||||||
\(138\) | 140.736 | + | 140.736i | 1.01983 | + | 1.01983i | ||||
\(139\) | −113.610 | −0.817341 | −0.408670 | − | 0.912682i | \(-0.634007\pi\) | ||||
−0.408670 | + | 0.912682i | \(0.634007\pi\) | |||||||
\(140\) | 183.081i | 1.30772i | ||||||||
\(141\) | −32.8182 | − | 32.8182i | −0.232753 | − | 0.232753i | ||||
\(142\) | 346.490i | 2.44007i | ||||||||
\(143\) | 151.282 | + | 129.720i | 1.05791 | + | 0.907136i | ||||
\(144\) | 5.49317 | 0.0381470 | ||||||||
\(145\) | 16.5369 | − | 16.5369i | 0.114047 | − | 0.114047i | ||||
\(146\) | 11.1848 | 0.0766084 | ||||||||
\(147\) | − | 87.2343i | − | 0.593431i | ||||||
\(148\) | 144.426 | − | 144.426i | 0.975850 | − | 0.975850i | ||||
\(149\) | 146.466 | − | 146.466i | 0.982990 | − | 0.982990i | −0.0168674 | − | 0.999858i | \(-0.505369\pi\) |
0.999858 | + | 0.0168674i | \(0.00536932\pi\) | |||||||
\(150\) | −64.3405 | − | 64.3405i | −0.428936 | − | 0.428936i | ||||
\(151\) | 117.662 | + | 117.662i | 0.779216 | + | 0.779216i | 0.979698 | − | 0.200481i | \(-0.0642506\pi\) |
−0.200481 | + | 0.979698i | \(0.564251\pi\) | |||||||
\(152\) | 77.3409 | 0.508822 | ||||||||
\(153\) | 17.2332i | 0.112635i | ||||||||
\(154\) | −346.141 | − | 346.141i | −2.24767 | − | 2.24767i | ||||
\(155\) | 154.508i | 0.996828i | ||||||||
\(156\) | −10.7879 | − | 140.597i | −0.0691533 | − | 0.901265i | ||||
\(157\) | −168.697 | −1.07450 | −0.537251 | − | 0.843423i | \(-0.680537\pi\) | ||||
−0.537251 | + | 0.843423i | \(0.680537\pi\) | |||||||
\(158\) | −223.518 | + | 223.518i | −1.41467 | + | 1.41467i | ||||
\(159\) | −9.53760 | −0.0599849 | ||||||||
\(160\) | 102.230i | 0.638937i | ||||||||
\(161\) | 252.834 | − | 252.834i | 1.57040 | − | 1.57040i | ||||
\(162\) | 20.3870 | − | 20.3870i | 0.125846 | − | 0.125846i | ||||
\(163\) | 195.823 | + | 195.823i | 1.20137 | + | 1.20137i | 0.973751 | + | 0.227616i | \(0.0730931\pi\) |
0.227616 | + | 0.973751i | \(0.426907\pi\) | |||||||
\(164\) | 145.526 | + | 145.526i | 0.887353 | + | 0.887353i | ||||
\(165\) | −77.8693 | −0.471935 | ||||||||
\(166\) | − | 127.658i | − | 0.769026i | ||||||
\(167\) | −23.0045 | − | 23.0045i | −0.137751 | − | 0.137751i | 0.634869 | − | 0.772620i | \(-0.281054\pi\) |
−0.772620 | + | 0.634869i | \(0.781054\pi\) | |||||||
\(168\) | 125.139i | 0.744875i | ||||||||
\(169\) | 167.022 | − | 25.7826i | 0.988294 | − | 0.152560i | ||||
\(170\) | −53.9697 | −0.317469 | ||||||||
\(171\) | −22.6360 | + | 22.6360i | −0.132374 | + | 0.132374i | ||||
\(172\) | −102.167 | −0.593992 | ||||||||
\(173\) | − | 7.01149i | − | 0.0405288i | −0.999795 | − | 0.0202644i | \(-0.993549\pi\) | ||
0.999795 | − | 0.0202644i | \(-0.00645081\pi\) | |||||||
\(174\) | 31.2868 | − | 31.2868i | 0.179809 | − | 0.179809i | ||||
\(175\) | −115.588 | + | 115.588i | −0.660503 | + | 0.660503i | ||||
\(176\) | −19.8478 | − | 19.8478i | −0.112772 | − | 0.112772i | ||||
\(177\) | −74.9244 | − | 74.9244i | −0.423302 | − | 0.423302i | ||||
\(178\) | 85.4153 | 0.479861 | ||||||||
\(179\) | 96.9928i | 0.541859i | 0.962599 | + | 0.270930i | \(0.0873311\pi\) | ||||
−0.962599 | + | 0.270930i | \(0.912669\pi\) | |||||||
\(180\) | 38.9614 | + | 38.9614i | 0.216452 | + | 0.216452i | ||||
\(181\) | 173.824i | 0.960355i | 0.877171 | + | 0.480177i | \(0.159428\pi\) | ||||
−0.877171 | + | 0.480177i | \(0.840572\pi\) | |||||||
\(182\) | −413.915 | + | 31.7594i | −2.27426 | + | 0.174502i | ||||
\(183\) | 90.2449 | 0.493142 | ||||||||
\(184\) | −183.838 | + | 183.838i | −0.999118 | + | 0.999118i | ||||
\(185\) | −95.6514 | −0.517035 | ||||||||
\(186\) | 292.321i | 1.57162i | ||||||||
\(187\) | 62.2665 | − | 62.2665i | 0.332976 | − | 0.332976i | ||||
\(188\) | 118.659 | − | 118.659i | 0.631166 | − | 0.631166i | ||||
\(189\) | −36.6255 | − | 36.6255i | −0.193785 | − | 0.193785i | ||||
\(190\) | −70.8899 | − | 70.8899i | −0.373105 | − | 0.373105i | ||||
\(191\) | −134.906 | −0.706314 | −0.353157 | − | 0.935564i | \(-0.614892\pi\) | ||||
−0.353157 | + | 0.935564i | \(0.614892\pi\) | |||||||
\(192\) | 180.727i | 0.941287i | ||||||||
\(193\) | 4.47074 | + | 4.47074i | 0.0231645 | + | 0.0231645i | 0.718594 | − | 0.695430i | \(-0.244786\pi\) |
−0.695430 | + | 0.718594i | \(0.744786\pi\) | |||||||
\(194\) | − | 157.116i | − | 0.809874i | ||||||
\(195\) | −42.9856 | + | 50.1303i | −0.220439 | + | 0.257079i | ||||
\(196\) | 315.410 | 1.60923 | ||||||||
\(197\) | 56.6892 | − | 56.6892i | 0.287763 | − | 0.287763i | −0.548432 | − | 0.836195i | \(-0.684775\pi\) |
0.836195 | + | 0.548432i | \(0.184775\pi\) | |||||||
\(198\) | −147.324 | −0.744061 | ||||||||
\(199\) | − | 360.006i | − | 1.80908i | −0.426392 | − | 0.904539i | \(-0.640216\pi\) | ||
0.426392 | − | 0.904539i | \(-0.359784\pi\) | |||||||
\(200\) | 84.0452 | − | 84.0452i | 0.420226 | − | 0.420226i | ||||
\(201\) | −78.5107 | + | 78.5107i | −0.390600 | + | 0.390600i | ||||
\(202\) | 286.337 | + | 286.337i | 1.41751 | + | 1.41751i | ||||
\(203\) | −56.2070 | − | 56.2070i | −0.276882 | − | 0.276882i | ||||
\(204\) | −62.3092 | −0.305437 | ||||||||
\(205\) | − | 96.3800i | − | 0.470146i | ||||||
\(206\) | −203.191 | − | 203.191i | −0.986366 | − | 0.986366i | ||||
\(207\) | − | 107.611i | − | 0.519858i | ||||||
\(208\) | −23.7340 | + | 1.82109i | −0.114106 | + | 0.00875523i | ||||
\(209\) | 163.576 | 0.782659 | ||||||||
\(210\) | 114.701 | − | 114.701i | 0.546197 | − | 0.546197i | ||||
\(211\) | −212.166 | −1.00553 | −0.502763 | − | 0.864424i | \(-0.667683\pi\) | ||||
−0.502763 | + | 0.864424i | \(0.667683\pi\) | |||||||
\(212\) | − | 34.4847i | − | 0.162664i | ||||||
\(213\) | 132.467 | − | 132.467i | 0.621913 | − | 0.621913i | ||||
\(214\) | 110.511 | − | 110.511i | 0.516408 | − | 0.516408i | ||||
\(215\) | 33.8318 | + | 33.8318i | 0.157357 | + | 0.157357i | ||||
\(216\) | 26.6307 | + | 26.6307i | 0.123290 | + | 0.123290i | ||||
\(217\) | 525.156 | 2.42007 | ||||||||
\(218\) | − | 134.376i | − | 0.616403i | ||||||
\(219\) | −4.27610 | − | 4.27610i | −0.0195256 | − | 0.0195256i | ||||
\(220\) | − | 281.549i | − | 1.27977i | ||||||
\(221\) | −5.71311 | − | 74.4581i | −0.0258512 | − | 0.336915i | ||||
\(222\) | −180.967 | −0.815166 | ||||||||
\(223\) | −42.6102 | + | 42.6102i | −0.191077 | + | 0.191077i | −0.796162 | − | 0.605084i | \(-0.793139\pi\) |
0.605084 | + | 0.796162i | \(0.293139\pi\) | |||||||
\(224\) | 347.468 | 1.55120 | ||||||||
\(225\) | 49.1964i | 0.218651i | ||||||||
\(226\) | −183.821 | + | 183.821i | −0.813369 | + | 0.813369i | ||||
\(227\) | 53.0656 | − | 53.0656i | 0.233769 | − | 0.233769i | −0.580495 | − | 0.814264i | \(-0.697141\pi\) |
0.814264 | + | 0.580495i | \(0.197141\pi\) | |||||||
\(228\) | −81.8440 | − | 81.8440i | −0.358965 | − | 0.358965i | ||||
\(229\) | −135.376 | − | 135.376i | −0.591162 | − | 0.591162i | 0.346783 | − | 0.937945i | \(-0.387274\pi\) |
−0.937945 | + | 0.346783i | \(0.887274\pi\) | |||||||
\(230\) | 337.008 | 1.46525 | ||||||||
\(231\) | 264.669i | 1.14575i | ||||||||
\(232\) | 40.8686 | + | 40.8686i | 0.176158 | + | 0.176158i | ||||
\(233\) | − | 31.3244i | − | 0.134440i | −0.997738 | − | 0.0672198i | \(-0.978587\pi\) | ||
0.997738 | − | 0.0672198i | \(-0.0214129\pi\) | |||||||
\(234\) | −81.3263 | + | 94.8436i | −0.347548 | + | 0.405315i | ||||
\(235\) | −78.5866 | −0.334411 | ||||||||
\(236\) | 270.901 | − | 270.901i | 1.14789 | − | 1.14789i | ||||
\(237\) | 170.908 | 0.721129 | ||||||||
\(238\) | 183.437i | 0.770743i | ||||||||
\(239\) | −333.688 | + | 333.688i | −1.39618 | + | 1.39618i | −0.585544 | + | 0.810641i | \(0.699119\pi\) |
−0.810641 | + | 0.585544i | \(0.800881\pi\) | |||||||
\(240\) | 6.57699 | − | 6.57699i | 0.0274041 | − | 0.0274041i | ||||
\(241\) | −246.650 | − | 246.650i | −1.02345 | − | 1.02345i | −0.999718 | − | 0.0237276i | \(-0.992447\pi\) |
−0.0237276 | − | 0.999718i | \(-0.507553\pi\) | |||||||
\(242\) | 258.216 | + | 258.216i | 1.06701 | + | 1.06701i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 326.295i | 1.33727i | ||||||||
\(245\) | −104.446 | − | 104.446i | −0.426310 | − | 0.426310i | ||||
\(246\) | − | 182.345i | − | 0.741241i | ||||||
\(247\) | 90.2976 | − | 105.306i | 0.365577 | − | 0.426340i | ||||
\(248\) | −381.846 | −1.53970 | ||||||||
\(249\) | −48.8054 | + | 48.8054i | −0.196006 | + | 0.196006i | ||||
\(250\) | −388.950 | −1.55580 | ||||||||
\(251\) | 331.076i | 1.31903i | 0.751693 | + | 0.659513i | \(0.229237\pi\) | ||||
−0.751693 | + | 0.659513i | \(0.770763\pi\) | |||||||
\(252\) | 132.425 | − | 132.425i | 0.525497 | − | 0.525497i | ||||
\(253\) | −388.816 | + | 388.816i | −1.53682 | + | 1.53682i | ||||
\(254\) | −33.0434 | − | 33.0434i | −0.130092 | − | 0.130092i | ||||
\(255\) | 20.6333 | + | 20.6333i | 0.0809149 | + | 0.0809149i | ||||
\(256\) | −206.779 | −0.807731 | ||||||||
\(257\) | − | 82.8095i | − | 0.322216i | −0.986937 | − | 0.161108i | \(-0.948493\pi\) | ||
0.986937 | − | 0.161108i | \(-0.0515068\pi\) | |||||||
\(258\) | 64.0079 | + | 64.0079i | 0.248092 | + | 0.248092i | ||||
\(259\) | 325.108i | 1.25524i | ||||||||
\(260\) | −181.254 | − | 155.421i | −0.697131 | − | 0.597774i | ||||
\(261\) | −23.9227 | −0.0916579 | ||||||||
\(262\) | −201.433 | + | 201.433i | −0.768828 | + | 0.768828i | ||||
\(263\) | 98.6102 | 0.374944 | 0.187472 | − | 0.982270i | \(-0.439971\pi\) | ||||
0.187472 | + | 0.982270i | \(0.439971\pi\) | |||||||
\(264\) | − | 192.443i | − | 0.728951i | ||||||
\(265\) | −11.4194 | + | 11.4194i | −0.0430920 | + | 0.0430920i | ||||
\(266\) | −240.947 | + | 240.947i | −0.905815 | + | 0.905815i | ||||
\(267\) | −32.6554 | − | 32.6554i | −0.122305 | − | 0.122305i | ||||
\(268\) | −283.868 | − | 283.868i | −1.05921 | − | 1.05921i | ||||
\(269\) | 92.5439 | 0.344029 | 0.172015 | − | 0.985094i | \(-0.444972\pi\) | ||||
0.172015 | + | 0.985094i | \(0.444972\pi\) | |||||||
\(270\) | − | 48.8189i | − | 0.180811i | ||||||
\(271\) | 197.527 | + | 197.527i | 0.728881 | + | 0.728881i | 0.970397 | − | 0.241516i | \(-0.0776446\pi\) |
−0.241516 | + | 0.970397i | \(0.577645\pi\) | |||||||
\(272\) | 10.5183i | 0.0386702i | ||||||||
\(273\) | 170.387 | + | 146.103i | 0.624129 | + | 0.535176i | ||||
\(274\) | 446.460 | 1.62942 | ||||||||
\(275\) | 177.755 | − | 177.755i | 0.646383 | − | 0.646383i | ||||
\(276\) | 389.083 | 1.40972 | ||||||||
\(277\) | − | 389.761i | − | 1.40708i | −0.710656 | − | 0.703539i | \(-0.751602\pi\) | ||
0.710656 | − | 0.703539i | \(-0.248398\pi\) | |||||||
\(278\) | −257.353 | + | 257.353i | −0.925731 | + | 0.925731i | ||||
\(279\) | 111.758 | − | 111.758i | 0.400566 | − | 0.400566i | ||||
\(280\) | 149.829 | + | 149.829i | 0.535105 | + | 0.535105i | ||||
\(281\) | 125.522 | + | 125.522i | 0.446699 | + | 0.446699i | 0.894256 | − | 0.447557i | \(-0.147706\pi\) |
−0.447557 | + | 0.894256i | \(0.647706\pi\) | |||||||
\(282\) | −148.681 | −0.527238 | ||||||||
\(283\) | − | 277.295i | − | 0.979841i | −0.871767 | − | 0.489921i | \(-0.837026\pi\) | ||
0.871767 | − | 0.489921i | \(-0.162974\pi\) | |||||||
\(284\) | 478.957 | + | 478.957i | 1.68647 | + | 1.68647i | ||||
\(285\) | 54.2043i | 0.190190i | ||||||||
\(286\) | 636.533 | − | 48.8406i | 2.22564 | − | 0.170771i | ||||
\(287\) | −327.585 | −1.14141 | ||||||||
\(288\) | 73.9443 | − | 73.9443i | 0.256751 | − | 0.256751i | ||||
\(289\) | 256.002 | 0.885820 | ||||||||
\(290\) | − | 74.9196i | − | 0.258343i | ||||||
\(291\) | −60.0673 | + | 60.0673i | −0.206417 | + | 0.206417i | ||||
\(292\) | 15.4609 | − | 15.4609i | 0.0529484 | − | 0.0529484i | ||||
\(293\) | −327.997 | − | 327.997i | −1.11944 | − | 1.11944i | −0.991823 | − | 0.127620i | \(-0.959266\pi\) |
−0.127620 | − | 0.991823i | \(-0.540734\pi\) | |||||||
\(294\) | −197.606 | − | 197.606i | −0.672128 | − | 0.672128i | ||||
\(295\) | −179.414 | −0.608184 | ||||||||
\(296\) | − | 236.389i | − | 0.798613i | ||||||
\(297\) | 56.3239 | + | 56.3239i | 0.189643 | + | 0.189643i | ||||
\(298\) | − | 663.555i | − | 2.22670i | ||||||
\(299\) | 35.6749 | + | 464.946i | 0.119314 | + | 1.55500i | ||||
\(300\) | −177.877 | −0.592924 | ||||||||
\(301\) | 114.991 | − | 114.991i | 0.382028 | − | 0.382028i | ||||
\(302\) | 533.061 | 1.76510 | ||||||||
\(303\) | − | 218.940i | − | 0.722576i | ||||||
\(304\) | −13.8159 | + | 13.8159i | −0.0454471 | + | 0.0454471i | ||||
\(305\) | 108.051 | − | 108.051i | 0.354264 | − | 0.354264i | ||||
\(306\) | 39.0370 | + | 39.0370i | 0.127572 | + | 0.127572i | ||||
\(307\) | −88.7474 | − | 88.7474i | −0.289080 | − | 0.289080i | 0.547637 | − | 0.836716i | \(-0.315528\pi\) |
−0.836716 | + | 0.547637i | \(0.815528\pi\) | |||||||
\(308\) | −956.952 | −3.10699 | ||||||||
\(309\) | 155.365i | 0.502801i | ||||||||
\(310\) | 349.996 | + | 349.996i | 1.12902 | + | 1.12902i | ||||
\(311\) | − | 511.900i | − | 1.64598i | −0.568054 | − | 0.822991i | \(-0.692304\pi\) | ||
0.568054 | − | 0.822991i | \(-0.307696\pi\) | |||||||
\(312\) | −123.890 | − | 106.233i | −0.397084 | − | 0.340490i | ||||
\(313\) | −402.205 | −1.28500 | −0.642500 | − | 0.766285i | \(-0.722103\pi\) | ||||
−0.642500 | + | 0.766285i | \(0.722103\pi\) | |||||||
\(314\) | −382.136 | + | 382.136i | −1.21699 | + | 1.21699i | ||||
\(315\) | −87.7035 | −0.278424 | ||||||||
\(316\) | 617.943i | 1.95552i | ||||||||
\(317\) | −159.843 | + | 159.843i | −0.504238 | + | 0.504238i | −0.912752 | − | 0.408514i | \(-0.866047\pi\) |
0.408514 | + | 0.912752i | \(0.366047\pi\) | |||||||
\(318\) | −21.6048 | + | 21.6048i | −0.0679397 | + | 0.0679397i | ||||
\(319\) | 86.4370 | + | 86.4370i | 0.270962 | + | 0.270962i | ||||
\(320\) | 216.385 | + | 216.385i | 0.676203 | + | 0.676203i | ||||
\(321\) | −84.4998 | −0.263239 | ||||||||
\(322\) | − | 1145.45i | − | 3.55730i | ||||||
\(323\) | −43.3433 | − | 43.3433i | −0.134190 | − | 0.134190i | ||||
\(324\) | − | 56.3625i | − | 0.173958i | ||||||
\(325\) | −16.3095 | − | 212.560i | −0.0501831 | − | 0.654029i | ||||
\(326\) | 887.166 | 2.72137 | ||||||||
\(327\) | −51.3736 | + | 51.3736i | −0.157106 | + | 0.157106i | ||||
\(328\) | 238.190 | 0.726189 | ||||||||
\(329\) | 267.107i | 0.811874i | ||||||||
\(330\) | −176.392 | + | 176.392i | −0.534520 | + | 0.534520i | ||||
\(331\) | 355.451 | − | 355.451i | 1.07387 | − | 1.07387i | 0.0768261 | − | 0.997045i | \(-0.475521\pi\) |
0.997045 | − | 0.0768261i | \(-0.0244786\pi\) | |||||||
\(332\) | −176.464 | − | 176.464i | −0.531517 | − | 0.531517i | ||||
\(333\) | 69.1860 | + | 69.1860i | 0.207766 | + | 0.207766i | ||||
\(334\) | −104.221 | −0.312038 | ||||||||
\(335\) | 188.002i | 0.561200i | ||||||||
\(336\) | −22.3544 | − | 22.3544i | −0.0665311 | − | 0.0665311i | ||||
\(337\) | 436.012i | 1.29381i | 0.762573 | + | 0.646903i | \(0.223936\pi\) | ||||
−0.762573 | + | 0.646903i | \(0.776064\pi\) | |||||||
\(338\) | 319.939 | − | 436.746i | 0.946564 | − | 1.29215i | ||||
\(339\) | 140.555 | 0.414615 | ||||||||
\(340\) | −74.6030 | + | 74.6030i | −0.219421 | + | 0.219421i | ||||
\(341\) | −807.603 | −2.36834 | ||||||||
\(342\) | 102.551i | 0.299858i | ||||||||
\(343\) | −9.61961 | + | 9.61961i | −0.0280455 | + | 0.0280455i | ||||
\(344\) | −83.6107 | + | 83.6107i | −0.243054 | + | 0.243054i | ||||
\(345\) | −128.842 | − | 128.842i | −0.373456 | − | 0.373456i | ||||
\(346\) | −15.8826 | − | 15.8826i | −0.0459035 | − | 0.0459035i | ||||
\(347\) | 327.281 | 0.943174 | 0.471587 | − | 0.881820i | \(-0.343681\pi\) | ||||
0.471587 | + | 0.881820i | \(0.343681\pi\) | |||||||
\(348\) | − | 86.4963i | − | 0.248553i | ||||||
\(349\) | 156.300 | + | 156.300i | 0.447851 | + | 0.447851i | 0.894640 | − | 0.446788i | \(-0.147432\pi\) |
−0.446788 | + | 0.894640i | \(0.647432\pi\) | |||||||
\(350\) | 523.666i | 1.49619i | ||||||||
\(351\) | 67.3520 | − | 5.16786i | 0.191886 | − | 0.0147232i | ||||
\(352\) | −534.348 | −1.51803 | ||||||||
\(353\) | 301.930 | − | 301.930i | 0.855327 | − | 0.855327i | −0.135457 | − | 0.990783i | \(-0.543250\pi\) |
0.990783 | + | 0.135457i | \(0.0432501\pi\) | |||||||
\(354\) | −339.441 | −0.958874 | ||||||||
\(355\) | − | 317.207i | − | 0.893542i | ||||||
\(356\) | 118.071 | − | 118.071i | 0.331659 | − | 0.331659i | ||||
\(357\) | 70.1302 | − | 70.1302i | 0.196443 | − | 0.196443i | ||||
\(358\) | 219.711 | + | 219.711i | 0.613717 | + | 0.613717i | ||||
\(359\) | −459.938 | − | 459.938i | −1.28117 | − | 1.28117i | −0.940005 | − | 0.341160i | \(-0.889180\pi\) |
−0.341160 | − | 0.940005i | \(-0.610820\pi\) | |||||||
\(360\) | 63.7701 | 0.177139 | ||||||||
\(361\) | 247.136i | 0.684587i | ||||||||
\(362\) | 393.751 | + | 393.751i | 1.08771 | + | 1.08771i | ||||
\(363\) | − | 197.438i | − | 0.543908i | ||||||
\(364\) | −528.259 | + | 616.062i | −1.45126 | + | 1.69248i | ||||
\(365\) | −10.2396 | −0.0280537 | ||||||||
\(366\) | 204.425 | − | 204.425i | 0.558539 | − | 0.558539i | ||||
\(367\) | 189.697 | 0.516885 | 0.258443 | − | 0.966027i | \(-0.416791\pi\) | ||||
0.258443 | + | 0.966027i | \(0.416791\pi\) | |||||||
\(368\) | − | 65.6804i | − | 0.178479i | ||||||
\(369\) | −69.7129 | + | 69.7129i | −0.188924 | + | 0.188924i | ||||
\(370\) | −216.672 | + | 216.672i | −0.585601 | + | 0.585601i | ||||
\(371\) | 38.8132 | + | 38.8132i | 0.104618 | + | 0.104618i | ||||
\(372\) | 404.079 | + | 404.079i | 1.08623 | + | 1.08623i | ||||
\(373\) | 204.386 | 0.547951 | 0.273975 | − | 0.961737i | \(-0.411661\pi\) | ||||
0.273975 | + | 0.961737i | \(0.411661\pi\) | |||||||
\(374\) | − | 282.095i | − | 0.754266i | ||||||
\(375\) | 148.701 | + | 148.701i | 0.396535 | + | 0.396535i | ||||
\(376\) | − | 194.216i | − | 0.516532i | ||||||
\(377\) | 103.361 | − | 7.93082i | 0.274168 | − | 0.0210366i | ||||
\(378\) | −165.930 | −0.438968 | ||||||||
\(379\) | 18.5656 | − | 18.5656i | 0.0489858 | − | 0.0489858i | −0.682190 | − | 0.731175i | \(-0.738972\pi\) |
0.731175 | + | 0.682190i | \(0.238972\pi\) | |||||||
\(380\) | −195.984 | −0.515748 | ||||||||
\(381\) | 25.2658i | 0.0663145i | ||||||||
\(382\) | −305.593 | + | 305.593i | −0.799981 | + | 0.799981i | ||||
\(383\) | −60.2763 | + | 60.2763i | −0.157379 | + | 0.157379i | −0.781404 | − | 0.624025i | \(-0.785496\pi\) |
0.624025 | + | 0.781404i | \(0.285496\pi\) | |||||||
\(384\) | 238.621 | + | 238.621i | 0.621408 | + | 0.621408i | ||||
\(385\) | 316.889 | + | 316.889i | 0.823087 | + | 0.823087i | ||||
\(386\) | 20.2545 | 0.0524728 | ||||||||
\(387\) | − | 48.9421i | − | 0.126465i | ||||||
\(388\) | −217.183 | − | 217.183i | −0.559750 | − | 0.559750i | ||||
\(389\) | − | 6.81993i | − | 0.0175320i | −0.999962 | − | 0.00876598i | \(-0.997210\pi\) | ||
0.999962 | − | 0.00876598i | \(-0.00279033\pi\) | |||||||
\(390\) | 16.1844 | + | 210.929i | 0.0414984 | + | 0.540843i | ||||
\(391\) | 206.052 | 0.526988 | ||||||||
\(392\) | 258.124 | − | 258.124i | 0.658479 | − | 0.658479i | ||||
\(393\) | 154.021 | 0.391911 | ||||||||
\(394\) | − | 256.828i | − | 0.651847i | ||||||
\(395\) | 204.628 | − | 204.628i | 0.518046 | − | 0.518046i | ||||
\(396\) | −203.648 | + | 203.648i | −0.514263 | + | 0.514263i | ||||
\(397\) | 105.682 | + | 105.682i | 0.266200 | + | 0.266200i | 0.827567 | − | 0.561367i | \(-0.189724\pi\) |
−0.561367 | + | 0.827567i | \(0.689724\pi\) | |||||||
\(398\) | −815.496 | − | 815.496i | −2.04898 | − | 2.04898i | ||||
\(399\) | 184.234 | 0.461740 | ||||||||
\(400\) | 30.0271i | 0.0750678i | ||||||||
\(401\) | 124.906 | + | 124.906i | 0.311487 | + | 0.311487i | 0.845486 | − | 0.533998i | \(-0.179311\pi\) |
−0.533998 | + | 0.845486i | \(0.679311\pi\) | |||||||
\(402\) | 355.689i | 0.884798i | ||||||||
\(403\) | −445.815 | + | 519.915i | −1.10624 | + | 1.29011i | ||||
\(404\) | 791.614 | 1.95944 | ||||||||
\(405\) | −18.6641 | + | 18.6641i | −0.0460842 | + | 0.0460842i | ||||
\(406\) | −254.643 | −0.627200 | ||||||||
\(407\) | − | 499.963i | − | 1.22841i | ||||||
\(408\) | −50.9924 | + | 50.9924i | −0.124981 | + | 0.124981i | ||||
\(409\) | −341.744 | + | 341.744i | −0.835559 | + | 0.835559i | −0.988271 | − | 0.152712i | \(-0.951199\pi\) |
0.152712 | + | 0.988271i | \(0.451199\pi\) | |||||||
\(410\) | −218.323 | − | 218.323i | −0.532494 | − | 0.532494i | ||||
\(411\) | −170.687 | − | 170.687i | −0.415298 | − | 0.415298i | ||||
\(412\) | −561.748 | −1.36347 | ||||||||
\(413\) | 609.809i | 1.47653i | ||||||||
\(414\) | −243.762 | − | 243.762i | −0.588798 | − | 0.588798i | ||||
\(415\) | 116.870i | 0.281614i | ||||||||
\(416\) | −294.972 | + | 344.000i | −0.709068 | + | 0.826923i | ||||
\(417\) | 196.779 | 0.471892 | ||||||||
\(418\) | 370.536 | − | 370.536i | 0.886450 | − | 0.886450i | ||||
\(419\) | 347.010 | 0.828187 | 0.414093 | − | 0.910234i | \(-0.364099\pi\) | ||||
0.414093 | + | 0.910234i | \(0.364099\pi\) | |||||||
\(420\) | − | 317.106i | − | 0.755014i | ||||||
\(421\) | −52.0656 | + | 52.0656i | −0.123671 | + | 0.123671i | −0.766233 | − | 0.642562i | \(-0.777871\pi\) |
0.642562 | + | 0.766233i | \(0.277871\pi\) | |||||||
\(422\) | −480.604 | + | 480.604i | −1.13887 | + | 1.13887i | ||||
\(423\) | 56.8427 | + | 56.8427i | 0.134380 | + | 0.134380i | ||||
\(424\) | −28.2215 | − | 28.2215i | −0.0665600 | − | 0.0665600i | ||||
\(425\) | −94.2010 | −0.221649 | ||||||||
\(426\) | − | 600.138i | − | 1.40877i | ||||||
\(427\) | −367.251 | − | 367.251i | −0.860073 | − | 0.860073i | ||||
\(428\) | − | 305.523i | − | 0.713838i | ||||||
\(429\) | −262.027 | − | 224.682i | −0.610786 | − | 0.523735i | ||||
\(430\) | 153.274 | 0.356450 | ||||||||
\(431\) | −26.1543 | + | 26.1543i | −0.0606829 | + | 0.0606829i | −0.736797 | − | 0.676114i | \(-0.763663\pi\) |
0.676114 | + | 0.736797i | \(0.263663\pi\) | |||||||
\(432\) | −9.51445 | −0.0220242 | ||||||||
\(433\) | 298.973i | 0.690469i | 0.938517 | + | 0.345234i | \(0.112201\pi\) | ||||
−0.938517 | + | 0.345234i | \(0.887799\pi\) | |||||||
\(434\) | 1189.60 | − | 1189.60i | 2.74101 | − | 2.74101i | ||||
\(435\) | −28.6427 | + | 28.6427i | −0.0658453 | + | 0.0658453i | ||||
\(436\) | −185.749 | − | 185.749i | −0.426031 | − | 0.426031i | ||||
\(437\) | 270.652 | + | 270.652i | 0.619342 | + | 0.619342i | ||||
\(438\) | −19.3727 | −0.0442299 | ||||||||
\(439\) | 176.942i | 0.403057i | 0.979483 | + | 0.201528i | \(0.0645909\pi\) | ||||
−0.979483 | + | 0.201528i | \(0.935409\pi\) | |||||||
\(440\) | −230.413 | − | 230.413i | −0.523665 | − | 0.523665i | ||||
\(441\) | 151.094i | 0.342617i | ||||||||
\(442\) | −181.606 | − | 155.723i | −0.410873 | − | 0.352315i | ||||
\(443\) | 488.694 | 1.10315 | 0.551574 | − | 0.834126i | \(-0.314027\pi\) | ||||
0.551574 | + | 0.834126i | \(0.314027\pi\) | |||||||
\(444\) | −250.153 | + | 250.153i | −0.563407 | + | 0.563407i | ||||
\(445\) | −78.1967 | −0.175723 | ||||||||
\(446\) | 193.044i | 0.432834i | ||||||||
\(447\) | −253.686 | + | 253.686i | −0.567530 | + | 0.567530i | ||||
\(448\) | 735.468 | − | 735.468i | 1.64167 | − | 1.64167i | ||||
\(449\) | 291.469 | + | 291.469i | 0.649151 | + | 0.649151i | 0.952788 | − | 0.303637i | \(-0.0982010\pi\) |
−0.303637 | + | 0.952788i | \(0.598201\pi\) | |||||||
\(450\) | 111.441 | + | 111.441i | 0.247647 | + | 0.247647i | ||||
\(451\) | 503.771 | 1.11701 | ||||||||
\(452\) | 508.198i | 1.12433i | ||||||||
\(453\) | −203.796 | − | 203.796i | −0.449881 | − | 0.449881i | ||||
\(454\) | − | 240.411i | − | 0.529541i | ||||||
\(455\) | 378.935 | − | 29.0753i | 0.832824 | − | 0.0639018i | ||||
\(456\) | −133.958 | −0.293768 | ||||||||
\(457\) | 420.955 | − | 420.955i | 0.921126 | − | 0.921126i | −0.0759832 | − | 0.997109i | \(-0.524210\pi\) |
0.997109 | + | 0.0759832i | \(0.0242096\pi\) | |||||||
\(458\) | −613.315 | −1.33912 | ||||||||
\(459\) | − | 29.8487i | − | 0.0650298i | ||||||
\(460\) | 465.850 | − | 465.850i | 1.01272 | − | 1.01272i | ||||
\(461\) | −209.193 | + | 209.193i | −0.453782 | + | 0.453782i | −0.896608 | − | 0.442826i | \(-0.853976\pi\) |
0.442826 | + | 0.896608i | \(0.353976\pi\) | |||||||
\(462\) | 599.535 | + | 599.535i | 1.29769 | + | 1.29769i | ||||
\(463\) | 203.453 | + | 203.453i | 0.439422 | + | 0.439422i | 0.891818 | − | 0.452395i | \(-0.149430\pi\) |
−0.452395 | + | 0.891818i | \(0.649430\pi\) | |||||||
\(464\) | −14.6013 | −0.0314683 | ||||||||
\(465\) | − | 267.616i | − | 0.575519i | ||||||
\(466\) | −70.9569 | − | 70.9569i | −0.152268 | − | 0.152268i | ||||
\(467\) | − | 110.726i | − | 0.237101i | −0.992948 | − | 0.118551i | \(-0.962175\pi\) | ||
0.992948 | − | 0.118551i | \(-0.0378248\pi\) | |||||||
\(468\) | 18.6852 | + | 243.522i | 0.0399257 | + | 0.520346i | ||||
\(469\) | 638.998 | 1.36247 | ||||||||
\(470\) | −178.016 | + | 178.016i | −0.378758 | + | 0.378758i | ||||
\(471\) | 292.191 | 0.620363 | ||||||||
\(472\) | − | 443.398i | − | 0.939402i | ||||||
\(473\) | −176.836 | + | 176.836i | −0.373861 | + | 0.373861i | ||||
\(474\) | 387.144 | − | 387.144i | 0.816760 | − | 0.816760i | ||||
\(475\) | −123.734 | − | 123.734i | −0.260493 | − | 0.260493i | ||||
\(476\) | 253.567 | + | 253.567i | 0.532704 | + | 0.532704i | ||||
\(477\) | 16.5196 | 0.0346323 | ||||||||
\(478\) | 1511.76i | 3.16267i | ||||||||
\(479\) | −652.131 | − | 652.131i | −1.36144 | − | 1.36144i | −0.872081 | − | 0.489361i | \(-0.837230\pi\) |
−0.489361 | − | 0.872081i | \(-0.662770\pi\) | |||||||
\(480\) | − | 177.067i | − | 0.368891i | ||||||
\(481\) | −321.864 | − | 275.991i | −0.669155 | − | 0.573785i | ||||
\(482\) | −1117.44 | −2.31834 | ||||||||
\(483\) | −437.921 | + | 437.921i | −0.906668 | + | 0.906668i | ||||
\(484\) | 713.870 | 1.47494 | ||||||||
\(485\) | 143.838i | 0.296572i | ||||||||
\(486\) | −35.3114 | + | 35.3114i | −0.0726572 | + | 0.0726572i | ||||
\(487\) | 106.252 | − | 106.252i | 0.218176 | − | 0.218176i | −0.589553 | − | 0.807729i | \(-0.700696\pi\) |
0.807729 | + | 0.589553i | \(0.200696\pi\) | |||||||
\(488\) | 267.032 | + | 267.032i | 0.547197 | + | 0.547197i | ||||
\(489\) | −339.175 | − | 339.175i | −0.693610 | − | 0.693610i | ||||
\(490\) | −473.187 | −0.965689 | ||||||||
\(491\) | − | 742.581i | − | 1.51238i | −0.654350 | − | 0.756192i | \(-0.727058\pi\) | ||
0.654350 | − | 0.756192i | \(-0.272942\pi\) | |||||||
\(492\) | −252.058 | − | 252.058i | −0.512313 | − | 0.512313i | ||||
\(493\) | − | 45.8071i | − | 0.0929150i | ||||||
\(494\) | −33.9976 | − | 443.087i | −0.0688211 | − | 0.896936i | ||||
\(495\) | 134.874 | 0.272472 | ||||||||
\(496\) | 68.2118 | − | 68.2118i | 0.137524 | − | 0.137524i | ||||
\(497\) | −1078.15 | −2.16932 | ||||||||
\(498\) | 221.111i | 0.443997i | ||||||||
\(499\) | −346.438 | + | 346.438i | −0.694265 | + | 0.694265i | −0.963167 | − | 0.268903i | \(-0.913339\pi\) |
0.268903 | + | 0.963167i | \(0.413339\pi\) | |||||||
\(500\) | −537.651 | + | 537.651i | −1.07530 | + | 1.07530i | ||||
\(501\) | 39.8449 | + | 39.8449i | 0.0795307 | + | 0.0795307i | ||||
\(502\) | 749.961 | + | 749.961i | 1.49395 | + | 1.49395i | ||||
\(503\) | −545.549 | −1.08459 | −0.542295 | − | 0.840188i | \(-0.682444\pi\) | ||||
−0.542295 | + | 0.840188i | \(0.682444\pi\) | |||||||
\(504\) | − | 216.747i | − | 0.430054i | ||||||
\(505\) | −262.138 | − | 262.138i | −0.519085 | − | 0.519085i | ||||
\(506\) | 1761.51i | 3.48125i | ||||||||
\(507\) | −289.290 | + | 44.6569i | −0.570592 | + | 0.0880806i | ||||
\(508\) | −91.3526 | −0.179828 | ||||||||
\(509\) | −352.500 | + | 352.500i | −0.692534 | + | 0.692534i | −0.962789 | − | 0.270255i | \(-0.912892\pi\) |
0.270255 | + | 0.962789i | \(0.412892\pi\) | |||||||
\(510\) | 93.4782 | 0.183291 | ||||||||
\(511\) | 34.8032i | 0.0681080i | ||||||||
\(512\) | 82.6694 | − | 82.6694i | 0.161464 | − | 0.161464i | ||||
\(513\) | 39.2067 | − | 39.2067i | 0.0764263 | − | 0.0764263i | ||||
\(514\) | −187.582 | − | 187.582i | −0.364946 | − | 0.364946i | ||||
\(515\) | 186.020 | + | 186.020i | 0.361203 | + | 0.361203i | ||||
\(516\) | 176.958 | 0.342941 | ||||||||
\(517\) | − | 410.766i | − | 0.794518i | ||||||
\(518\) | 736.444 | + | 736.444i | 1.42171 | + | 1.42171i | ||||
\(519\) | 12.1443i | 0.0233993i | ||||||||
\(520\) | −275.527 | + | 21.1410i | −0.529860 | + | 0.0406557i | ||||
\(521\) | 604.304 | 1.15989 | 0.579947 | − | 0.814654i | \(-0.303073\pi\) | ||||
0.579947 | + | 0.814654i | \(0.303073\pi\) | |||||||
\(522\) | −54.1903 | + | 54.1903i | −0.103813 | + | 0.103813i | ||||
\(523\) | −6.78648 | −0.0129761 | −0.00648803 | − | 0.999979i | \(-0.502065\pi\) | ||||
−0.00648803 | + | 0.999979i | \(0.502065\pi\) | |||||||
\(524\) | 556.887i | 1.06276i | ||||||||
\(525\) | 200.204 | − | 200.204i | 0.381342 | − | 0.381342i | ||||
\(526\) | 223.375 | − | 223.375i | 0.424666 | − | 0.424666i | ||||
\(527\) | 213.994 | + | 213.994i | 0.406060 | + | 0.406060i | ||||
\(528\) | 34.3774 | + | 34.3774i | 0.0651088 | + | 0.0651088i | ||||
\(529\) | −757.670 | −1.43227 | ||||||||
\(530\) | 51.7350i | 0.0976133i | ||||||||
\(531\) | 129.773 | + | 129.773i | 0.244393 | + | 0.244393i | ||||
\(532\) | 666.128i | 1.25212i | ||||||||
\(533\) | 278.093 | − | 324.315i | 0.521750 | − | 0.608471i | ||||
\(534\) | −147.944 | −0.277048 | ||||||||
\(535\) | −101.172 | + | 101.172i | −0.189106 | + | 0.189106i | ||||
\(536\) | −464.621 | −0.866831 | ||||||||
\(537\) | − | 167.996i | − | 0.312843i | ||||||
\(538\) | 209.633 | − | 209.633i | 0.389652 | − | 0.389652i | ||||
\(539\) | 545.931 | − | 545.931i | 1.01286 | − | 1.01286i | ||||
\(540\) | −67.4830 | − | 67.4830i | −0.124969 | − | 0.124969i | ||||
\(541\) | −197.678 | − | 197.678i | −0.365393 | − | 0.365393i | 0.500401 | − | 0.865794i | \(-0.333186\pi\) |
−0.865794 | + | 0.500401i | \(0.833186\pi\) | |||||||
\(542\) | 894.886 | 1.65108 | ||||||||
\(543\) | − | 301.072i | − | 0.554461i | ||||||
\(544\) | 141.588 | + | 141.588i | 0.260272 | + | 0.260272i | ||||
\(545\) | 123.020i | 0.225724i | ||||||||
\(546\) | 716.922 | − | 55.0088i | 1.31304 | − | 0.100749i | ||||
\(547\) | −873.392 | −1.59669 | −0.798347 | − | 0.602197i | \(-0.794292\pi\) | ||||
−0.798347 | + | 0.602197i | \(0.794292\pi\) | |||||||
\(548\) | 617.148 | − | 617.148i | 1.12618 | − | 1.12618i | ||||
\(549\) | −156.309 | −0.284715 | ||||||||
\(550\) | − | 805.312i | − | 1.46420i | ||||||
\(551\) | 60.1682 | − | 60.1682i | 0.109198 | − | 0.109198i | ||||
\(552\) | 318.416 | − | 318.416i | 0.576841 | − | 0.576841i | ||||
\(553\) | −695.508 | − | 695.508i | −1.25770 | − | 1.25770i | ||||
\(554\) | −882.897 | − | 882.897i | −1.59368 | − | 1.59368i | ||||
\(555\) | 165.673 | 0.298510 | ||||||||
\(556\) | 711.485i | 1.27965i | ||||||||
\(557\) | 403.156 | + | 403.156i | 0.723799 | + | 0.723799i | 0.969377 | − | 0.245578i | \(-0.0789778\pi\) |
−0.245578 | + | 0.969377i | \(0.578978\pi\) | |||||||
\(558\) | − | 506.314i | − | 0.907373i | ||||||
\(559\) | 16.2252 | + | 211.461i | 0.0290254 | + | 0.378284i | ||||
\(560\) | −53.5301 | −0.0955894 | ||||||||
\(561\) | −107.849 | + | 107.849i | −0.192244 | + | 0.192244i | ||||
\(562\) | 568.674 | 1.01187 | ||||||||
\(563\) | 956.142i | 1.69830i | 0.528153 | + | 0.849149i | \(0.322885\pi\) | ||||
−0.528153 | + | 0.849149i | \(0.677115\pi\) | |||||||
\(564\) | −205.524 | + | 205.524i | −0.364404 | + | 0.364404i | ||||
\(565\) | 168.286 | − | 168.286i | 0.297852 | − | 0.297852i | ||||
\(566\) | −628.136 | − | 628.136i | −1.10978 | − | 1.10978i | ||||
\(567\) | 63.4372 | + | 63.4372i | 0.111882 | + | 0.111882i | ||||
\(568\) | 783.934 | 1.38017 | ||||||||
\(569\) | − | 183.113i | − | 0.321816i | −0.986969 | − | 0.160908i | \(-0.948558\pi\) | ||
0.986969 | − | 0.160908i | \(-0.0514422\pi\) | |||||||
\(570\) | 122.785 | + | 122.785i | 0.215412 | + | 0.215412i | ||||
\(571\) | − | 526.076i | − | 0.921324i | −0.887576 | − | 0.460662i | \(-0.847612\pi\) | ||
0.887576 | − | 0.460662i | \(-0.152388\pi\) | |||||||
\(572\) | 812.375 | − | 947.401i | 1.42024 | − | 1.65630i | ||||
\(573\) | 233.664 | 0.407791 | ||||||||
\(574\) | −742.053 | + | 742.053i | −1.29278 | + | 1.29278i | ||||
\(575\) | 588.228 | 1.02300 | ||||||||
\(576\) | − | 313.029i | − | 0.543452i | ||||||
\(577\) | 277.438 | − | 277.438i | 0.480829 | − | 0.480829i | −0.424568 | − | 0.905396i | \(-0.639574\pi\) |
0.905396 | + | 0.424568i | \(0.139574\pi\) | |||||||
\(578\) | 579.903 | − | 579.903i | 1.00329 | − | 1.00329i | ||||
\(579\) | −7.74355 | − | 7.74355i | −0.0133740 | − | 0.0133740i | ||||
\(580\) | −103.562 | − | 103.562i | −0.178556 | − | 0.178556i | ||||
\(581\) | 397.227 | 0.683695 | ||||||||
\(582\) | 272.132i | 0.467581i | ||||||||
\(583\) | −59.6883 | − | 59.6883i | −0.102381 | − | 0.102381i | ||||
\(584\) | − | 25.3057i | − | 0.0433317i | ||||||
\(585\) | 74.4533 | − | 86.8283i | 0.127271 | − | 0.148424i | ||||
\(586\) | −1485.97 | −2.53579 | ||||||||
\(587\) | 197.192 | − | 197.192i | 0.335932 | − | 0.335932i | −0.518902 | − | 0.854834i | \(-0.673659\pi\) |
0.854834 | + | 0.518902i | \(0.173659\pi\) | |||||||
\(588\) | −546.305 | −0.929091 | ||||||||
\(589\) | 562.167i | 0.954443i | ||||||||
\(590\) | −406.414 | + | 406.414i | −0.688838 | + | 0.688838i | ||||
\(591\) | −98.1886 | + | 98.1886i | −0.166140 | + | 0.166140i | ||||
\(592\) | 42.2278 | + | 42.2278i | 0.0713308 | + | 0.0713308i | ||||
\(593\) | 318.917 | + | 318.917i | 0.537803 | + | 0.537803i | 0.922883 | − | 0.385080i | \(-0.125826\pi\) |
−0.385080 | + | 0.922883i | \(0.625826\pi\) | |||||||
\(594\) | 255.173 | 0.429584 | ||||||||
\(595\) | − | 167.934i | − | 0.282243i | ||||||
\(596\) | −917.241 | − | 917.241i | −1.53900 | − | 1.53900i | ||||
\(597\) | 623.549i | 1.04447i | ||||||||
\(598\) | 1134.02 | + | 972.396i | 1.89635 | + | 1.62608i | ||||
\(599\) | −587.889 | −0.981451 | −0.490725 | − | 0.871314i | \(-0.663268\pi\) | ||||
−0.490725 | + | 0.871314i | \(0.663268\pi\) | |||||||
\(600\) | −145.571 | + | 145.571i | −0.242618 | + | 0.242618i | ||||
\(601\) | 848.887 | 1.41246 | 0.706229 | − | 0.707984i | \(-0.250395\pi\) | ||||
0.706229 | + | 0.707984i | \(0.250395\pi\) | |||||||
\(602\) | − | 520.959i | − | 0.865381i | ||||||
\(603\) | 135.984 | − | 135.984i | 0.225513 | − | 0.225513i | ||||
\(604\) | 736.856 | − | 736.856i | 1.21996 | − | 1.21996i | ||||
\(605\) | −236.394 | − | 236.394i | −0.390733 | − | 0.390733i | ||||
\(606\) | −495.950 | − | 495.950i | −0.818399 | − | 0.818399i | ||||
\(607\) | 147.750 | 0.243411 | 0.121705 | − | 0.992566i | \(-0.461164\pi\) | ||||
0.121705 | + | 0.992566i | \(0.461164\pi\) | |||||||
\(608\) | 371.956i | 0.611770i | ||||||||
\(609\) | 97.3533 | + | 97.3533i | 0.159858 | + | 0.159858i | ||||
\(610\) | − | 489.518i | − | 0.802488i | ||||||
\(611\) | −264.441 | − | 226.752i | −0.432800 | − | 0.371116i | ||||
\(612\) | 107.923 | 0.176344 | ||||||||
\(613\) | −505.998 | + | 505.998i | −0.825446 | + | 0.825446i | −0.986883 | − | 0.161437i | \(-0.948387\pi\) |
0.161437 | + | 0.986883i | \(0.448387\pi\) | |||||||
\(614\) | −402.066 | −0.654831 | ||||||||
\(615\) | 166.935i | 0.271439i | ||||||||
\(616\) | −783.147 | + | 783.147i | −1.27134 | + | 1.27134i | ||||
\(617\) | −803.096 | + | 803.096i | −1.30161 | + | 1.30161i | −0.374311 | + | 0.927303i | \(0.622121\pi\) |
−0.927303 | + | 0.374311i | \(0.877879\pi\) | |||||||
\(618\) | 351.938 | + | 351.938i | 0.569479 | + | 0.569479i | ||||
\(619\) | −67.6340 | − | 67.6340i | −0.109263 | − | 0.109263i | 0.650362 | − | 0.759625i | \(-0.274617\pi\) |
−0.759625 | + | 0.650362i | \(0.774617\pi\) | |||||||
\(620\) | 967.609 | 1.56066 | ||||||||
\(621\) | 186.387i | 0.300140i | ||||||||
\(622\) | −1159.57 | − | 1159.57i | −1.86426 | − | 1.86426i | ||||
\(623\) | 265.782i | 0.426616i | ||||||||
\(624\) | 41.1085 | − | 3.15422i | 0.0658790 | − | 0.00505483i | ||||
\(625\) | −53.8902 | −0.0862243 | ||||||||
\(626\) | −911.086 | + | 911.086i | −1.45541 | + | 1.45541i | ||||
\(627\) | −283.322 | −0.451868 | ||||||||
\(628\) | 1056.46i | 1.68227i | ||||||||
\(629\) | −132.477 | + | 132.477i | −0.210615 | + | 0.210615i | ||||
\(630\) | −198.668 | + | 198.668i | −0.315347 | + | 0.315347i | ||||
\(631\) | 494.414 | + | 494.414i | 0.783540 | + | 0.783540i | 0.980426 | − | 0.196886i | \(-0.0630829\pi\) |
−0.196886 | + | 0.980426i | \(0.563083\pi\) | |||||||
\(632\) | 505.710 | + | 505.710i | 0.800175 | + | 0.800175i | ||||
\(633\) | 367.482 | 0.580541 | ||||||||
\(634\) | 724.163i | 1.14221i | ||||||||
\(635\) | 30.2509 | + | 30.2509i | 0.0476392 | + | 0.0476392i | ||||
\(636\) | 59.7292i | 0.0939139i | ||||||||
\(637\) | −50.0905 | − | 652.823i | −0.0786351 | − | 1.02484i | ||||
\(638\) | 391.599 | 0.613791 | ||||||||
\(639\) | −229.440 | + | 229.440i | −0.359062 | + | 0.359062i | ||||
\(640\) | 571.403 | 0.892817 | ||||||||
\(641\) | 340.781i | 0.531640i | 0.964023 | + | 0.265820i | \(0.0856427\pi\) | ||||
−0.964023 | + | 0.265820i | \(0.914357\pi\) | |||||||
\(642\) | −191.411 | + | 191.411i | −0.298148 | + | 0.298148i | ||||
\(643\) | −3.63964 | + | 3.63964i | −0.00566040 | + | 0.00566040i | −0.709931 | − | 0.704271i | \(-0.751274\pi\) |
0.704271 | + | 0.709931i | \(0.251274\pi\) | |||||||
\(644\) | −1583.37 | − | 1583.37i | −2.45865 | − | 2.45865i | ||||
\(645\) | −58.5985 | − | 58.5985i | −0.0908504 | − | 0.0908504i | ||||
\(646\) | −196.365 | −0.303970 | ||||||||
\(647\) | − | 643.861i | − | 0.995149i | −0.867421 | − | 0.497574i | \(-0.834224\pi\) | ||
0.867421 | − | 0.497574i | \(-0.165776\pi\) | |||||||
\(648\) | −46.1258 | − | 46.1258i | −0.0711817 | − | 0.0711817i | ||||
\(649\) | − | 937.785i | − | 1.44497i | ||||||
\(650\) | −518.440 | − | 444.551i | −0.797600 | − | 0.683924i | ||||
\(651\) | −909.597 | −1.39723 | ||||||||
\(652\) | 1226.34 | − | 1226.34i | 1.88089 | − | 1.88089i | ||||
\(653\) | 1033.33 | 1.58243 | 0.791215 | − | 0.611538i | \(-0.209449\pi\) | ||||
0.791215 | + | 0.611538i | \(0.209449\pi\) | |||||||
\(654\) | 232.746i | 0.355880i | ||||||||
\(655\) | 184.410 | − | 184.410i | 0.281542 | − | 0.281542i | ||||
\(656\) | −42.5495 | + | 42.5495i | −0.0648620 | + | 0.0648620i | ||||
\(657\) | 7.40643 | + | 7.40643i | 0.0112731 | + | 0.0112731i | ||||
\(658\) | 605.057 | + | 605.057i | 0.919540 | + | 0.919540i | ||||
\(659\) | 52.9124 | 0.0802919 | 0.0401460 | − | 0.999194i | \(-0.487218\pi\) | ||||
0.0401460 | + | 0.999194i | \(0.487218\pi\) | |||||||
\(660\) | 487.657i | 0.738874i | ||||||||
\(661\) | 866.525 | + | 866.525i | 1.31093 | + | 1.31093i | 0.920730 | + | 0.390201i | \(0.127594\pi\) |
0.390201 | + | 0.920730i | \(0.372406\pi\) | |||||||
\(662\) | − | 1610.35i | − | 2.43256i | ||||||
\(663\) | 9.89539 | + | 128.965i | 0.0149252 | + | 0.194518i | ||||
\(664\) | −288.827 | −0.434981 | ||||||||
\(665\) | 220.584 | − | 220.584i | 0.331705 | − | 0.331705i | ||||
\(666\) | 313.444 | 0.470636 | ||||||||
\(667\) | 286.037i | 0.428841i | ||||||||
\(668\) | −144.065 | + | 144.065i | −0.215667 | + | 0.215667i | ||||
\(669\) | 73.8031 | − | 73.8031i | 0.110319 | − | 0.110319i | ||||
\(670\) | 425.867 | + | 425.867i | 0.635623 | + | 0.635623i | ||||
\(671\) | 564.772 | + | 564.772i | 0.841686 | + | 0.841686i | ||||
\(672\) | −601.832 | −0.895583 | ||||||||
\(673\) | 230.740i | 0.342852i | 0.985197 | + | 0.171426i | \(0.0548375\pi\) | ||||
−0.985197 | + | 0.171426i | \(0.945162\pi\) | |||||||
\(674\) | 987.667 | + | 987.667i | 1.46538 | + | 1.46538i | ||||
\(675\) | − | 85.2106i | − | 0.126238i | ||||||
\(676\) | −161.464 | − | 1045.97i | −0.238852 | − | 1.54730i | ||||
\(677\) | 799.458 | 1.18088 | 0.590441 | − | 0.807080i | \(-0.298954\pi\) | ||||
0.590441 | + | 0.807080i | \(0.298954\pi\) | |||||||
\(678\) | 318.388 | − | 318.388i | 0.469599 | − | 0.469599i | ||||
\(679\) | 488.887 | 0.720011 | ||||||||
\(680\) | 122.107i | 0.179569i | ||||||||
\(681\) | −91.9124 | + | 91.9124i | −0.134967 | + | 0.134967i | ||||
\(682\) | −1829.40 | + | 1829.40i | −2.68241 | + | 2.68241i | ||||
\(683\) | 750.113 | + | 750.113i | 1.09826 | + | 1.09826i | 0.994614 | + | 0.103648i | \(0.0330517\pi\) |
0.103648 | + | 0.994614i | \(0.466948\pi\) | |||||||
\(684\) | 141.758 | + | 141.758i | 0.207248 | + | 0.207248i | ||||
\(685\) | −408.729 | −0.596685 | ||||||||
\(686\) | 43.5812i | 0.0635295i | ||||||||
\(687\) | 234.478 | + | 234.478i | 0.341308 | + | 0.341308i | ||||
\(688\) | − | 29.8719i | − | 0.0434185i | ||||||
\(689\) | −71.3751 | + | 5.47655i | −0.103592 | + | 0.00794855i | ||||
\(690\) | −583.715 | −0.845963 | ||||||||
\(691\) | −408.357 | + | 408.357i | −0.590965 | + | 0.590965i | −0.937892 | − | 0.346927i | \(-0.887225\pi\) |
0.346927 | + | 0.937892i | \(0.387225\pi\) | |||||||
\(692\) | −43.9095 | −0.0634530 | ||||||||
\(693\) | − | 458.420i | − | 0.661500i | ||||||
\(694\) | 741.366 | − | 741.366i | 1.06825 | − | 1.06825i | ||||
\(695\) | 235.604 | − | 235.604i | 0.338998 | − | 0.338998i | ||||
\(696\) | −70.7865 | − | 70.7865i | −0.101705 | − | 0.101705i | ||||
\(697\) | −133.486 | − | 133.486i | −0.191515 | − | 0.191515i | ||||
\(698\) | 708.110 | 1.01448 | ||||||||
\(699\) | 54.2555i | 0.0776187i | ||||||||
\(700\) | 723.871 | + | 723.871i | 1.03410 | + | 1.03410i | ||||
\(701\) | − | 1057.89i | − | 1.50911i | −0.656236 | − | 0.754556i | \(-0.727852\pi\) | ||
0.656236 | − | 0.754556i | \(-0.272148\pi\) | |||||||
\(702\) | 140.861 | − | 164.274i | 0.200657 | − | 0.234008i | ||||
\(703\) | −348.021 | −0.495051 | ||||||||
\(704\) | −1131.03 | + | 1131.03i | −1.60657 | + | 1.60657i | ||||
\(705\) | 136.116 | 0.193072 | ||||||||
\(706\) | − | 1367.88i | − | 1.93751i | ||||||
\(707\) | −890.977 | + | 890.977i | −1.26022 | + | 1.26022i | ||||
\(708\) | −469.214 | + | 469.214i | −0.662732 | + | 0.662732i | ||||
\(709\) | −154.683 | − | 154.683i | −0.218170 | − | 0.218170i | 0.589557 | − | 0.807727i | \(-0.299302\pi\) |
−0.807727 | + | 0.589557i | \(0.799302\pi\) | |||||||
\(710\) | −718.547 | − | 718.547i | −1.01204 | − | 1.01204i | ||||
\(711\) | −296.021 | −0.416344 | ||||||||
\(712\) | − | 193.252i | − | 0.271422i | ||||||
\(713\) | −1336.26 | − | 1336.26i | −1.87414 | − | 1.87414i | ||||
\(714\) | − | 317.722i | − | 0.444989i | ||||||
\(715\) | −582.739 | + | 44.7131i | −0.815020 | + | 0.0625357i | ||||
\(716\) | 607.418 | 0.848349 | ||||||||
\(717\) | 577.965 | − | 577.965i | 0.806088 | − | 0.806088i | ||||
\(718\) | −2083.73 | −2.90213 | ||||||||
\(719\) | 101.626i | 0.141344i | 0.997500 | + | 0.0706720i | \(0.0225144\pi\) | ||||
−0.997500 | + | 0.0706720i | \(0.977486\pi\) | |||||||
\(720\) | −11.3917 | + | 11.3917i | −0.0158218 | + | 0.0158218i | ||||
\(721\) | 632.259 | − | 632.259i | 0.876920 | − | 0.876920i | ||||
\(722\) | 559.819 | + | 559.819i | 0.775373 | + | 0.775373i | ||||
\(723\) | 427.211 | + | 427.211i | 0.590887 | + | 0.590887i | ||||
\(724\) | 1088.57 | 1.50356 | ||||||||
\(725\) | − | 130.768i | − | 0.180369i | ||||||
\(726\) | −447.243 | − | 447.243i | −0.616037 | − | 0.616037i | ||||
\(727\) | 147.112i | 0.202355i | 0.994868 | + | 0.101177i | \(0.0322610\pi\) | ||||
−0.994868 | + | 0.101177i | \(0.967739\pi\) | |||||||
\(728\) | 71.8557 | + | 936.485i | 0.0987029 | + | 1.28638i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −23.1950 | + | 23.1950i | −0.0317740 | + | 0.0317740i | ||||
\(731\) | 93.7140 | 0.128200 | ||||||||
\(732\) | − | 565.159i | − | 0.772075i | ||||||
\(733\) | 187.854 | − | 187.854i | 0.256281 | − | 0.256281i | −0.567259 | − | 0.823539i | \(-0.691996\pi\) |
0.823539 | + | 0.567259i | \(0.191996\pi\) | |||||||
\(734\) | 429.706 | − | 429.706i | 0.585431 | − | 0.585431i | ||||
\(735\) | 180.906 | + | 180.906i | 0.246130 | + | 0.246130i | ||||
\(736\) | −884.132 | − | 884.132i | −1.20127 | − | 1.20127i | ||||
\(737\) | −982.673 | −1.33334 | ||||||||
\(738\) | 315.831i | 0.427956i | ||||||||
\(739\) | 109.296 | + | 109.296i | 0.147898 | + | 0.147898i | 0.777178 | − | 0.629281i | \(-0.216650\pi\) |
−0.629281 | + | 0.777178i | \(0.716650\pi\) | |||||||
\(740\) | 599.018i | 0.809483i | ||||||||
\(741\) | −156.400 | + | 182.395i | −0.211066 | + | 0.246148i | ||||
\(742\) | 175.841 | 0.236983 | ||||||||
\(743\) | 358.323 | − | 358.323i | 0.482265 | − | 0.482265i | −0.423589 | − | 0.905854i | \(-0.639230\pi\) |
0.905854 | + | 0.423589i | \(0.139230\pi\) | |||||||
\(744\) | 661.377 | 0.888947 | ||||||||
\(745\) | 607.478i | 0.815406i | ||||||||
\(746\) | 462.980 | − | 462.980i | 0.620617 | − | 0.620617i | ||||
\(747\) | 84.5334 | − | 84.5334i | 0.113164 | − | 0.113164i | ||||
\(748\) | −389.944 | − | 389.944i | −0.521316 | − | 0.521316i | ||||
\(749\) | 343.872 | + | 343.872i | 0.459108 | + | 0.459108i | ||||
\(750\) | 673.682 | 0.898242 | ||||||||
\(751\) | 185.270i | 0.246698i | 0.992363 | + | 0.123349i | \(0.0393634\pi\) | ||||
−0.992363 | + | 0.123349i | \(0.960637\pi\) | |||||||
\(752\) | 34.6941 | + | 34.6941i | 0.0461358 | + | 0.0461358i | ||||
\(753\) | − | 573.440i | − | 0.761540i | ||||||
\(754\) | 216.172 | − | 252.102i | 0.286700 | − | 0.334352i | ||||
\(755\) | −488.011 | −0.646372 | ||||||||
\(756\) | −229.367 | + | 229.367i | −0.303396 | + | 0.303396i | ||||
\(757\) | −324.887 | −0.429177 | −0.214588 | − | 0.976705i | \(-0.568841\pi\) | ||||
−0.214588 | + | 0.976705i | \(0.568841\pi\) | |||||||
\(758\) | − | 84.1107i | − | 0.110964i | ||||||
\(759\) | 673.449 | − | 673.449i | 0.887285 | − | 0.887285i | ||||
\(760\) | −160.389 | + | 160.389i | −0.211038 | + | 0.211038i | ||||
\(761\) | −431.075 | − | 431.075i | −0.566459 | − | 0.566459i | 0.364676 | − | 0.931135i | \(-0.381180\pi\) |
−0.931135 | + | 0.364676i | \(0.881180\pi\) | |||||||
\(762\) | 57.2329 | + | 57.2329i | 0.0751087 | + | 0.0751087i | ||||
\(763\) | 418.129 | 0.548007 | ||||||||
\(764\) | 844.850i | 1.10582i | ||||||||
\(765\) | −35.7379 | − | 35.7379i | −0.0467163 | − | 0.0467163i | ||||
\(766\) | 273.079i | 0.356500i | ||||||||
\(767\) | −603.723 | − | 517.679i | −0.787122 | − | 0.674940i | ||||
\(768\) | 358.152 | 0.466344 | ||||||||
\(769\) | −482.446 | + | 482.446i | −0.627368 | + | 0.627368i | −0.947405 | − | 0.320037i | \(-0.896305\pi\) |
0.320037 | + | 0.947405i | \(0.396305\pi\) | |||||||
\(770\) | 1435.65 | 1.86448 | ||||||||
\(771\) | 143.430i | 0.186032i | ||||||||
\(772\) | 27.9980 | − | 27.9980i | 0.0362669 | − | 0.0362669i | ||||
\(773\) | −34.4442 | + | 34.4442i | −0.0445591 | + | 0.0445591i | −0.729035 | − | 0.684476i | \(-0.760031\pi\) |
0.684476 | + | 0.729035i | \(0.260031\pi\) | |||||||
\(774\) | −110.865 | − | 110.865i | −0.143236 | − | 0.143236i | ||||
\(775\) | 610.899 | + | 610.899i | 0.788256 | + | 0.788256i | ||||
\(776\) | −355.475 | −0.458086 | ||||||||
\(777\) | − | 563.104i | − | 0.724716i | ||||||
\(778\) | −15.4487 | − | 15.4487i | −0.0198569 | − | 0.0198569i | ||||
\(779\) | − | 350.671i | − | 0.450156i | ||||||
\(780\) | 313.941 | + | 269.198i | 0.402489 | + | 0.345125i | ||||
\(781\) | 1658.02 | 2.12294 | ||||||||
\(782\) | 466.755 | − | 466.755i | 0.596873 | − | 0.596873i | ||||
\(783\) | 41.4353 | 0.0529187 | ||||||||
\(784\) | 92.2208i | 0.117629i | ||||||||
\(785\) | 349.841 | − | 349.841i | 0.445658 | − | 0.445658i | ||||
\(786\) | 348.892 | − | 348.892i | 0.443883 | − | 0.443883i | ||||
\(787\) | −181.342 | − | 181.342i | −0.230422 | − | 0.230422i | 0.582447 | − | 0.812869i | \(-0.302095\pi\) |
−0.812869 | + | 0.582447i | \(0.802095\pi\) | |||||||
\(788\) | −355.017 | − | 355.017i | −0.450529 | − | 0.450529i | ||||
\(789\) | −170.798 | −0.216474 | ||||||||
\(790\) | − | 927.058i | − | 1.17349i | ||||||
\(791\) | −571.986 | − | 571.986i | −0.723118 | − | 0.723118i | ||||
\(792\) | 333.321i | 0.420860i | ||||||||
\(793\) | 675.353 | − | 51.8192i | 0.851643 | − | 0.0653458i | ||||
\(794\) | 478.785 | 0.603004 | ||||||||
\(795\) | 19.7790 | − | 19.7790i | 0.0248792 | − | 0.0248792i | ||||
\(796\) | −2254.54 | −2.83234 | ||||||||
\(797\) | 1091.56i | 1.36959i | 0.728736 | + | 0.684795i | \(0.240108\pi\) | ||||
−0.728736 | + | 0.684795i | \(0.759892\pi\) | |||||||
\(798\) | 417.332 | − | 417.332i | 0.522972 | − | 0.522972i | ||||
\(799\) | −108.842 | + | 108.842i | −0.136223 | + | 0.136223i | ||||
\(800\) | 404.199 | + | 404.199i | 0.505249 | + | 0.505249i | ||||
\(801\) | 56.5607 | + | 56.5607i | 0.0706127 | + | 0.0706127i | ||||
\(802\) | 565.882 | 0.705589 | ||||||||
\(803\) | − | 53.5215i | − | 0.0666520i | ||||||
\(804\) | 491.673 | + | 491.673i | 0.611534 | + | 0.611534i | ||||
\(805\) | 1048.65i | 1.30267i | ||||||||
\(806\) | 167.852 | + | 2187.60i | 0.208254 | + | 2.71414i | ||||
\(807\) | −160.291 | −0.198625 | ||||||||
\(808\) | 647.838 | − | 647.838i | 0.801780 | − | 0.801780i | ||||
\(809\) | −1040.75 | −1.28646 | −0.643230 | − | 0.765673i | \(-0.722406\pi\) | ||||
−0.643230 | + | 0.765673i | \(0.722406\pi\) | |||||||
\(810\) | 84.5569i | 0.104391i | ||||||||
\(811\) | −621.215 | + | 621.215i | −0.765987 | + | 0.765987i | −0.977397 | − | 0.211411i | \(-0.932194\pi\) |
0.211411 | + | 0.977397i | \(0.432194\pi\) | |||||||
\(812\) | −351.996 | + | 351.996i | −0.433493 | + | 0.433493i | ||||
\(813\) | −342.126 | − | 342.126i | −0.420820 | − | 0.420820i | ||||
\(814\) | −1132.53 | − | 1132.53i | −1.39131 | − | 1.39131i | ||||
\(815\) | −812.191 | −0.996553 | ||||||||
\(816\) | − | 18.2182i | − | 0.0223263i | ||||||
\(817\) | 123.095 | + | 123.095i | 0.150667 | + | 0.150667i | ||||
\(818\) | 1548.25i | 1.89273i | ||||||||
\(819\) | −295.119 | − | 253.058i | −0.360341 | − | 0.308984i | ||||
\(820\) | −603.580 | −0.736073 | ||||||||
\(821\) | 589.552 | − | 589.552i | 0.718090 | − | 0.718090i | −0.250124 | − | 0.968214i | \(-0.580471\pi\) |
0.968214 | + | 0.250124i | \(0.0804713\pi\) | |||||||
\(822\) | −773.292 | −0.940744 | ||||||||
\(823\) | − | 1259.69i | − | 1.53061i | −0.643668 | − | 0.765305i | \(-0.722588\pi\) | ||
0.643668 | − | 0.765305i | \(-0.277412\pi\) | |||||||
\(824\) | −459.722 | + | 459.722i | −0.557915 | + | 0.557915i | ||||
\(825\) | −307.881 | + | 307.881i | −0.373189 | + | 0.373189i | ||||
\(826\) | 1381.36 | + | 1381.36i | 1.67234 | + | 1.67234i | ||||
\(827\) | 425.074 | + | 425.074i | 0.513995 | + | 0.513995i | 0.915748 | − | 0.401753i | \(-0.131599\pi\) |
−0.401753 | + | 0.915748i | \(0.631599\pi\) | |||||||
\(828\) | −673.912 | −0.813903 | ||||||||
\(829\) | − | 1094.86i | − | 1.32069i | −0.750960 | − | 0.660347i | \(-0.770409\pi\) | ||
0.750960 | − | 0.660347i | \(-0.229591\pi\) | |||||||
\(830\) | 264.736 | + | 264.736i | 0.318959 | + | 0.318959i | ||||
\(831\) | 675.086i | 0.812377i | ||||||||
\(832\) | 103.775 | + | 1352.48i | 0.124729 | + | 1.62558i | ||||
\(833\) | −289.315 | −0.347316 | ||||||||
\(834\) | 445.749 | − | 445.749i | 0.534471 | − | 0.534471i | ||||
\(835\) | 95.4128 | 0.114267 | ||||||||
\(836\) | − | 1024.39i | − | 1.22535i | ||||||
\(837\) | −193.570 | + | 193.570i | −0.231267 | + | 0.231267i | ||||
\(838\) | 786.057 | − | 786.057i | 0.938015 | − | 0.938015i | ||||
\(839\) | 185.015 | + | 185.015i | 0.220519 | + | 0.220519i | 0.808717 | − | 0.588198i | \(-0.200162\pi\) |
−0.588198 | + | 0.808717i | \(0.700162\pi\) | |||||||
\(840\) | −259.512 | − | 259.512i | −0.308943 | − | 0.308943i | ||||
\(841\) | −777.412 | −0.924390 | ||||||||
\(842\) | 235.881i | 0.280143i | ||||||||
\(843\) | −217.411 | − | 217.411i | −0.257902 | − | 0.257902i | ||||
\(844\) | 1328.69i | 1.57428i | ||||||||
\(845\) | −292.900 | + | 399.836i | −0.346627 | + | 0.473178i | ||||
\(846\) | 257.523 | 0.304401 | ||||||||
\(847\) | −803.475 | + | 803.475i | −0.948613 | + | 0.948613i | ||||
\(848\) | 10.0828 | 0.0118901 | ||||||||
\(849\) | 480.289i | 0.565712i | ||||||||
\(850\) | −213.387 | + | 213.387i | −0.251043 | + | 0.251043i | ||||
\(851\) | 827.238 | − | 827.238i | 0.972077 | − | 0.972077i | ||||
\(852\) | −829.578 | − | 829.578i | −0.973683 | − | 0.973683i | ||||
\(853\) | −441.207 | − | 441.207i | −0.517242 | − | 0.517242i | 0.399494 | − | 0.916736i | \(-0.369186\pi\) |
−0.916736 | + | 0.399494i | \(0.869186\pi\) | |||||||
\(854\) | −1663.81 | −1.94826 | ||||||||
\(855\) | − | 93.8846i | − | 0.109807i | ||||||
\(856\) | −250.032 | − | 250.032i | −0.292094 | − | 0.292094i | ||||
\(857\) | 1315.33i | 1.53481i | 0.641163 | + | 0.767404i | \(0.278452\pi\) | ||||
−0.641163 | + | 0.767404i | \(0.721548\pi\) | |||||||
\(858\) | −1102.51 | + | 84.5945i | −1.28497 | + | 0.0985949i | ||||
\(859\) | 1595.61 | 1.85752 | 0.928758 | − | 0.370687i | \(-0.120878\pi\) | ||||
0.928758 | + | 0.370687i | \(0.120878\pi\) | |||||||
\(860\) | 211.872 | − | 211.872i | 0.246363 | − | 0.246363i | ||||
\(861\) | 567.393 | 0.658993 | ||||||||
\(862\) | 118.491i | 0.137461i | ||||||||
\(863\) | −162.354 | + | 162.354i | −0.188127 | + | 0.188127i | −0.794886 | − | 0.606759i | \(-0.792469\pi\) |
0.606759 | + | 0.794886i | \(0.292469\pi\) | |||||||
\(864\) | −128.075 | + | 128.075i | −0.148235 | + | 0.148235i | ||||
\(865\) | 14.5404 | + | 14.5404i | 0.0168097 | + | 0.0168097i | ||||
\(866\) | 677.242 | + | 677.242i | 0.782034 | + | 0.782034i | ||||
\(867\) | −443.409 | −0.511429 | ||||||||
\(868\) | − | 3288.79i | − | 3.78893i | ||||||
\(869\) | 1069.58 | + | 1069.58i | 1.23081 | + | 1.23081i | ||||
\(870\) | 129.765i | 0.149155i | ||||||||
\(871\) | −542.458 | + | 632.620i | −0.622799 | + | 0.726315i | ||||
\(872\) | −304.026 | −0.348654 | ||||||||
\(873\) | 104.040 | − | 104.040i | 0.119175 | − | 0.119175i | ||||
\(874\) | 1226.18 | 1.40295 | ||||||||
\(875\) | − | 1210.27i | − | 1.38317i | ||||||
\(876\) | −26.7791 | + | 26.7791i | −0.0305698 | + | 0.0305698i | ||||
\(877\) | 161.563 | − | 161.563i | 0.184222 | − | 0.184222i | −0.608971 | − | 0.793193i | \(-0.708417\pi\) |
0.793193 | + | 0.608971i | \(0.208417\pi\) | |||||||
\(878\) | 400.814 | + | 400.814i | 0.456508 | + | 0.456508i | ||||
\(879\) | 568.107 | + | 568.107i | 0.646311 | + | 0.646311i | ||||
\(880\) | 82.3204 | 0.0935459 | ||||||||
\(881\) | − | 801.723i | − | 0.910015i | −0.890488 | − | 0.455008i | \(-0.849637\pi\) | ||
0.890488 | − | 0.455008i | \(-0.150363\pi\) | |||||||
\(882\) | 342.263 | + | 342.263i | 0.388053 | + | 0.388053i | ||||
\(883\) | 608.168i | 0.688753i | 0.938832 | + | 0.344376i | \(0.111910\pi\) | ||||
−0.938832 | + | 0.344376i | \(0.888090\pi\) | |||||||
\(884\) | −466.294 | + | 35.7784i | −0.527482 | + | 0.0404733i | ||||
\(885\) | 310.755 | 0.351135 | ||||||||
\(886\) | 1107.00 | − | 1107.00i | 1.24944 | − | 1.24944i | ||||
\(887\) | −1169.09 | −1.31802 | −0.659011 | − | 0.752133i | \(-0.729025\pi\) | ||||
−0.659011 | + | 0.752133i | \(0.729025\pi\) | |||||||
\(888\) | 409.438i | 0.461079i | ||||||||
\(889\) | 102.819 | − | 102.819i | 0.115657 | − | 0.115657i | ||||
\(890\) | −177.133 | + | 177.133i | −0.199026 | + | 0.199026i | ||||
\(891\) | −97.5558 | − | 97.5558i | −0.109490 | − | 0.109490i | ||||
\(892\) | 266.847 | + | 266.847i | 0.299156 | + | 0.299156i | ||||
\(893\) | −285.931 | −0.320192 | ||||||||
\(894\) | 1149.31i | 1.28558i | ||||||||
\(895\) | −201.143 | − | 201.143i | −0.224740 | − | 0.224740i | ||||
\(896\) | − | 1942.13i | − | 2.16756i | ||||||
\(897\) | −61.7907 | − | 805.310i | −0.0688859 | − | 0.897781i | ||||
\(898\) | 1320.49 | 1.47047 | ||||||||
\(899\) | −297.061 | + | 297.061i | −0.330435 | + | 0.330435i | ||||
\(900\) | 308.093 | 0.342325 | ||||||||
\(901\) | 31.6316i | 0.0351073i | ||||||||
\(902\) | 1141.15 | − | 1141.15i | 1.26514 | − | 1.26514i | ||||
\(903\) | −199.170 | + | 199.170i | −0.220564 | + | 0.220564i | ||||
\(904\) | 415.897 | + | 415.897i | 0.460063 | + | 0.460063i | ||||
\(905\) | −360.475 | − | 360.475i | −0.398315 | − | 0.398315i | ||||
\(906\) | −923.288 | −1.01908 | ||||||||
\(907\) | 420.272i | 0.463364i | 0.972792 | + | 0.231682i | \(0.0744230\pi\) | ||||
−0.972792 | + | 0.231682i | \(0.925577\pi\) | |||||||
\(908\) | −332.324 | − | 332.324i | −0.365995 | − | 0.365995i | ||||
\(909\) | 379.216i | 0.417179i | ||||||||
\(910\) | 792.511 | − | 924.236i | 0.870891 | − | 1.01564i | ||||
\(911\) | −1503.63 | −1.65053 | −0.825264 | − | 0.564747i | \(-0.808974\pi\) | ||||
−0.825264 | + | 0.564747i | \(0.808974\pi\) | |||||||
\(912\) | 23.9299 | − | 23.9299i | 0.0262389 | − | 0.0262389i | ||||
\(913\) | −610.869 | −0.669079 | ||||||||
\(914\) | − | 1907.11i | − | 2.08656i | ||||||
\(915\) | −187.149 | + | 187.149i | −0.204534 | + | 0.204534i | ||||
\(916\) | −847.794 | + | 847.794i | −0.925539 | + | 0.925539i | ||||
\(917\) | −626.787 | − | 626.787i | −0.683519 | − | 0.683519i | ||||
\(918\) | −67.6141 | − | 67.6141i | −0.0736537 | − | 0.0736537i | ||||
\(919\) | 99.7403 | 0.108531 | 0.0542657 | − | 0.998527i | \(-0.482718\pi\) | ||||
0.0542657 | + | 0.998527i | \(0.482718\pi\) | |||||||
\(920\) | − | 762.482i | − | 0.828784i | ||||||
\(921\) | 153.715 | + | 153.715i | 0.166900 | + | 0.166900i | ||||
\(922\) | 947.740i | 1.02792i | ||||||||
\(923\) | 915.264 | − | 1067.39i | 0.991619 | − | 1.15644i | ||||
\(924\) | 1657.49 | 1.79382 | ||||||||
\(925\) | −378.189 | + | 378.189i | −0.408853 | + | 0.408853i | ||||
\(926\) | 921.732 | 0.995391 | ||||||||
\(927\) | − | 269.101i | − | 0.290292i | ||||||
\(928\) | −196.550 | + | 196.550i | −0.211799 | + | 0.211799i | ||||
\(929\) | −122.462 | + | 122.462i | −0.131821 | + | 0.131821i | −0.769939 | − | 0.638118i | \(-0.779713\pi\) |
0.638118 | + | 0.769939i | \(0.279713\pi\) | |||||||
\(930\) | −606.212 | − | 606.212i | −0.651840 | − | 0.651840i | ||||
\(931\) | −380.019 | − | 380.019i | −0.408183 | − | 0.408183i | ||||
\(932\) | −196.169 | −0.210482 | ||||||||
\(933\) | 886.638i | 0.950308i | ||||||||
\(934\) | −250.820 | − | 250.820i | −0.268544 | − | 0.268544i | ||||
\(935\) | 258.255i | 0.276209i | ||||||||
\(936\) | 214.584 | + | 184.001i | 0.229256 | + | 0.196582i | ||||
\(937\) | 975.263 | 1.04084 | 0.520418 | − | 0.853912i | \(-0.325776\pi\) | ||||
0.520418 | + | 0.853912i | \(0.325776\pi\) | |||||||
\(938\) | 1447.47 | − | 1447.47i | 1.54315 | − | 1.54315i | ||||
\(939\) | 696.640 | 0.741895 | ||||||||
\(940\) | 492.149i | 0.523562i | ||||||||
\(941\) | 1188.28 | − | 1188.28i | 1.26279 | − | 1.26279i | 0.313052 | − | 0.949736i | \(-0.398649\pi\) |
0.949736 | − | 0.313052i | \(-0.101351\pi\) | |||||||
\(942\) | 661.879 | − | 661.879i | 0.702632 | − | 0.702632i | ||||
\(943\) | 833.539 | + | 833.539i | 0.883922 | + | 0.883922i | ||||
\(944\) | 79.2072 | + | 79.2072i | 0.0839059 | + | 0.0839059i | ||||
\(945\) | 151.907 | 0.160748 | ||||||||
\(946\) | 801.149i | 0.846881i | ||||||||
\(947\) | 957.995 | + | 957.995i | 1.01161 | + | 1.01161i | 0.999932 | + | 0.0116790i | \(0.00371764\pi\) |
0.0116790 | + | 0.999932i | \(0.496282\pi\) | |||||||
\(948\) | − | 1070.31i | − | 1.12902i | ||||||
\(949\) | −34.4558 | − | 29.5451i | −0.0363075 | − | 0.0311329i | ||||
\(950\) | −560.572 | −0.590076 | ||||||||
\(951\) | 276.857 | − | 276.857i | 0.291122 | − | 0.291122i | ||||
\(952\) | 415.026 | 0.435952 | ||||||||
\(953\) | 777.339i | 0.815676i | 0.913054 | + | 0.407838i | \(0.133717\pi\) | ||||
−0.913054 | + | 0.407838i | \(0.866283\pi\) | |||||||
\(954\) | 37.4206 | − | 37.4206i | 0.0392250 | − | 0.0392250i | ||||
\(955\) | 279.767 | − | 279.767i | 0.292950 | − | 0.292950i | ||||
\(956\) | 2089.72 | + | 2089.72i | 2.18590 | + | 2.18590i | ||||
\(957\) | −149.713 | − | 149.713i | −0.156440 | − | 0.156440i | ||||
\(958\) | −2954.45 | −3.08398 | ||||||||
\(959\) | 1389.22i | 1.44862i | ||||||||
\(960\) | −374.790 | − | 374.790i | −0.390406 | − | 0.390406i | ||||
\(961\) | − | 1814.52i | − | 1.88816i | ||||||
\(962\) | −1354.28 | + | 103.912i | −1.40777 | + | 0.108017i | ||||
\(963\) | 146.358 | 0.151981 | ||||||||
\(964\) | −1544.65 | + | 1544.65i | −1.60233 | + | 1.60233i | ||||
\(965\) | −18.5428 | −0.0192153 | ||||||||
\(966\) | 1983.98i | 2.05381i | ||||||||
\(967\) | 427.468 | − | 427.468i | 0.442056 | − | 0.442056i | −0.450647 | − | 0.892702i | \(-0.648807\pi\) |
0.892702 | + | 0.450647i | \(0.148807\pi\) | |||||||
\(968\) | 584.214 | − | 584.214i | 0.603527 | − | 0.603527i | ||||
\(969\) | 75.0728 | + | 75.0728i | 0.0774745 | + | 0.0774745i | ||||
\(970\) | 325.825 | + | 325.825i | 0.335902 | + | 0.335902i | ||||
\(971\) | 287.153 | 0.295729 | 0.147865 | − | 0.989008i | \(-0.452760\pi\) | ||||
0.147865 | + | 0.989008i | \(0.452760\pi\) | |||||||
\(972\) | 97.6228i | 0.100435i | ||||||||
\(973\) | −800.791 | − | 800.791i | −0.823012 | − | 0.823012i | ||||
\(974\) | − | 481.369i | − | 0.494218i | ||||||
\(975\) | 28.2489 | + | 368.164i | 0.0289732 | + | 0.377604i | ||||
\(976\) | −95.4034 | −0.0977494 | ||||||||
\(977\) | 478.694 | − | 478.694i | 0.489963 | − | 0.489963i | −0.418332 | − | 0.908294i | \(-0.637385\pi\) |
0.908294 | + | 0.418332i | \(0.137385\pi\) | |||||||
\(978\) | −1536.62 | −1.57118 | ||||||||
\(979\) | − | 408.728i | − | 0.417496i | ||||||
\(980\) | −654.093 | + | 654.093i | −0.667442 | + | 0.667442i | ||||
\(981\) | 88.9817 | − | 88.9817i | 0.0907051 | − | 0.0907051i | ||||
\(982\) | −1682.11 | − | 1682.11i | −1.71295 | − | 1.71295i | ||||
\(983\) | −1192.12 | − | 1192.12i | −1.21273 | − | 1.21273i | −0.970124 | − | 0.242609i | \(-0.921997\pi\) |
−0.242609 | − | 0.970124i | \(-0.578003\pi\) | |||||||
\(984\) | −412.557 | −0.419265 | ||||||||
\(985\) | 235.123i | 0.238704i | ||||||||
\(986\) | −103.763 | − | 103.763i | −0.105237 | − | 0.105237i | ||||
\(987\) | − | 462.642i | − | 0.468736i | ||||||
\(988\) | −659.480 | − | 565.489i | −0.667489 | − | 0.572357i | ||||
\(989\) | −585.187 | −0.591696 | ||||||||
\(990\) | 305.519 | − | 305.519i | 0.308605 | − | 0.308605i | ||||
\(991\) | −1428.83 | −1.44180 | −0.720901 | − | 0.693038i | \(-0.756272\pi\) | ||||
−0.720901 | + | 0.693038i | \(0.756272\pi\) | |||||||
\(992\) | − | 1836.41i | − | 1.85122i | ||||||
\(993\) | −615.659 | + | 615.659i | −0.619999 | + | 0.619999i | ||||
\(994\) | −2442.26 | + | 2442.26i | −2.45700 | + | 2.45700i | ||||
\(995\) | 746.577 | + | 746.577i | 0.750329 | + | 0.750329i | ||||
\(996\) | 305.644 | + | 305.644i | 0.306872 | + | 0.306872i | ||||
\(997\) | 648.361 | 0.650312 | 0.325156 | − | 0.945660i | \(-0.394583\pi\) | ||||
0.325156 | + | 0.945660i | \(0.394583\pi\) | |||||||
\(998\) | 1569.52i | 1.57267i | ||||||||
\(999\) | −119.834 | − | 119.834i | −0.119954 | − | 0.119954i |
(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 | 39.3.g.a.31.4 | ✓ | 8 | |
3.2 | odd | 2 | 117.3.j.b.109.1 | 8 | |||
4.3 | odd | 2 | 624.3.ba.b.577.4 | 8 | |||
13.8 | odd | 4 | inner | 39.3.g.a.34.4 | yes | 8 | |
39.8 | even | 4 | 117.3.j.b.73.1 | 8 | |||
52.47 | even | 4 | 624.3.ba.b.385.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.3.g.a.31.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
39.3.g.a.34.4 | yes | 8 | 13.8 | odd | 4 | inner | |
117.3.j.b.73.1 | 8 | 39.8 | even | 4 | |||
117.3.j.b.109.1 | 8 | 3.2 | odd | 2 | |||
624.3.ba.b.385.4 | 8 | 52.47 | even | 4 | |||
624.3.ba.b.577.4 | 8 | 4.3 | odd | 2 |