Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(43,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.t (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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(72\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.15 | ||
Character | \(\chi\) | \(=\) | 560.43 |
Dual form | 560.2.t.a.547.15 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.11562 | + | 0.869134i | −0.788862 | + | 0.614571i | ||||
\(3\) | − | 2.40982i | − | 1.39131i | −0.718376 | − | 0.695655i | \(-0.755114\pi\) | ||
0.718376 | − | 0.695655i | \(-0.244886\pi\) | |||||||
\(4\) | 0.489211 | − | 1.93925i | 0.244606 | − | 0.969623i | ||||
\(5\) | −2.07668 | + | 0.829085i | −0.928722 | + | 0.370778i | ||||
\(6\) | 2.09446 | + | 2.68844i | 0.855058 | + | 1.09755i | ||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | 1.13969 | + | 2.58865i | 0.402942 | + | 0.915226i | ||||
\(9\) | −2.80723 | −0.935742 | ||||||||
\(10\) | 1.59620 | − | 2.72986i | 0.504764 | − | 0.863258i | ||||
\(11\) | −2.34682 | + | 2.34682i | −0.707593 | + | 0.707593i | −0.966029 | − | 0.258435i | \(-0.916793\pi\) |
0.258435 | + | 0.966029i | \(0.416793\pi\) | |||||||
\(12\) | −4.67323 | − | 1.17891i | −1.34905 | − | 0.340322i | ||||
\(13\) | 4.48941 | 1.24514 | 0.622570 | − | 0.782564i | \(-0.286089\pi\) | ||||
0.622570 | + | 0.782564i | \(0.286089\pi\) | |||||||
\(14\) | 0.174291 | − | 1.40343i | 0.0465812 | − | 0.375083i | ||||
\(15\) | 1.99794 | + | 5.00443i | 0.515867 | + | 1.29214i | ||||
\(16\) | −3.52135 | − | 1.89740i | −0.880336 | − | 0.474350i | ||||
\(17\) | −2.44324 | + | 2.44324i | −0.592574 | + | 0.592574i | −0.938326 | − | 0.345752i | \(-0.887624\pi\) |
0.345752 | + | 0.938326i | \(0.387624\pi\) | |||||||
\(18\) | 3.13179 | − | 2.43986i | 0.738171 | − | 0.575080i | ||||
\(19\) | −2.49650 | + | 2.49650i | −0.572736 | + | 0.572736i | −0.932892 | − | 0.360156i | \(-0.882724\pi\) |
0.360156 | + | 0.932892i | \(0.382724\pi\) | |||||||
\(20\) | 0.591861 | + | 4.43280i | 0.132344 | + | 0.991204i | ||||
\(21\) | 1.70400 | + | 1.70400i | 0.371843 | + | 0.371843i | ||||
\(22\) | 0.578455 | − | 4.65786i | 0.123327 | − | 0.993059i | ||||
\(23\) | −2.43246 | − | 2.43246i | −0.507204 | − | 0.507204i | 0.406463 | − | 0.913667i | \(-0.366762\pi\) |
−0.913667 | + | 0.406463i | \(0.866762\pi\) | |||||||
\(24\) | 6.23817 | − | 2.74645i | 1.27336 | − | 0.560617i | ||||
\(25\) | 3.62524 | − | 3.44349i | 0.725048 | − | 0.688699i | ||||
\(26\) | −5.00847 | + | 3.90190i | −0.982243 | + | 0.765226i | ||||
\(27\) | − | 0.464550i | − | 0.0894026i | ||||||
\(28\) | 1.02533 | + | 1.71718i | 0.193769 | + | 0.324516i | ||||
\(29\) | 3.09156 | + | 3.09156i | 0.574089 | + | 0.574089i | 0.933268 | − | 0.359180i | \(-0.116944\pi\) |
−0.359180 | + | 0.933268i | \(0.616944\pi\) | |||||||
\(30\) | −6.57847 | − | 3.84656i | −1.20106 | − | 0.702282i | ||||
\(31\) | 10.1502i | 1.82303i | 0.411265 | + | 0.911516i | \(0.365087\pi\) | ||||
−0.411265 | + | 0.911516i | \(0.634913\pi\) | |||||||
\(32\) | 5.57758 | − | 0.943746i | 0.985985 | − | 0.166832i | ||||
\(33\) | 5.65541 | + | 5.65541i | 0.984481 | + | 0.984481i | ||||
\(34\) | 0.602222 | − | 4.84924i | 0.103280 | − | 0.831637i | ||||
\(35\) | 0.882186 | − | 2.05469i | 0.149117 | − | 0.347306i | ||||
\(36\) | −1.37333 | + | 5.44390i | −0.228888 | + | 0.907317i | ||||
\(37\) | 11.7133 | 1.92565 | 0.962824 | − | 0.270128i | \(-0.0870661\pi\) | ||||
0.962824 | + | 0.270128i | \(0.0870661\pi\) | |||||||
\(38\) | 0.615349 | − | 4.95494i | 0.0998228 | − | 0.803797i | ||||
\(39\) | − | 10.8187i | − | 1.73237i | ||||||
\(40\) | −4.51299 | − | 4.43091i | −0.713566 | − | 0.700588i | ||||
\(41\) | 12.2006i | 1.90542i | 0.303886 | + | 0.952708i | \(0.401716\pi\) | ||||
−0.303886 | + | 0.952708i | \(0.598284\pi\) | |||||||
\(42\) | −3.38202 | − | 0.420010i | −0.521857 | − | 0.0648089i | ||||
\(43\) | 1.81456 | 0.276718 | 0.138359 | − | 0.990382i | \(-0.455817\pi\) | ||||
0.138359 | + | 0.990382i | \(0.455817\pi\) | |||||||
\(44\) | 3.40297 | + | 5.69915i | 0.513017 | + | 0.859179i | ||||
\(45\) | 5.82972 | − | 2.32743i | 0.869044 | − | 0.346952i | ||||
\(46\) | 4.82784 | + | 0.599565i | 0.711826 | + | 0.0884010i | ||||
\(47\) | 2.14045 | + | 2.14045i | 0.312216 | + | 0.312216i | 0.845768 | − | 0.533551i | \(-0.179143\pi\) |
−0.533551 | + | 0.845768i | \(0.679143\pi\) | |||||||
\(48\) | −4.57239 | + | 8.48580i | −0.659968 | + | 1.22482i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −1.05152 | + | 6.99245i | −0.148708 | + | 0.988881i | ||||
\(51\) | 5.88778 | + | 5.88778i | 0.824454 | + | 0.824454i | ||||
\(52\) | 2.19627 | − | 8.70607i | 0.304568 | − | 1.20732i | ||||
\(53\) | − | 4.30788i | − | 0.591732i | −0.955229 | − | 0.295866i | \(-0.904392\pi\) | ||
0.955229 | − | 0.295866i | \(-0.0956082\pi\) | |||||||
\(54\) | 0.403756 | + | 0.518260i | 0.0549442 | + | 0.0705263i | ||||
\(55\) | 2.92789 | − | 6.81932i | 0.394797 | − | 0.919517i | ||||
\(56\) | −2.63633 | − | 1.02457i | −0.352295 | − | 0.136914i | ||||
\(57\) | 6.01611 | + | 6.01611i | 0.796854 | + | 0.796854i | ||||
\(58\) | −6.13599 | − | 0.762022i | −0.805695 | − | 0.100058i | ||||
\(59\) | 4.71152 | + | 4.71152i | 0.613388 | + | 0.613388i | 0.943827 | − | 0.330439i | \(-0.107197\pi\) |
−0.330439 | + | 0.943827i | \(0.607197\pi\) | |||||||
\(60\) | 10.6822 | − | 1.42628i | 1.37907 | − | 0.184132i | ||||
\(61\) | 2.97080 | − | 2.97080i | 0.380372 | − | 0.380372i | −0.490864 | − | 0.871236i | \(-0.663319\pi\) |
0.871236 | + | 0.490864i | \(0.163319\pi\) | |||||||
\(62\) | −8.82190 | − | 11.3238i | −1.12038 | − | 1.43812i | ||||
\(63\) | 1.98501 | − | 1.98501i | 0.250088 | − | 0.250088i | ||||
\(64\) | −5.40221 | + | 5.90052i | −0.675276 | + | 0.737565i | ||||
\(65\) | −9.32309 | + | 3.72210i | −1.15639 | + | 0.461670i | ||||
\(66\) | −11.2246 | − | 1.39397i | −1.38165 | − | 0.171586i | ||||
\(67\) | −8.05320 | −0.983855 | −0.491928 | − | 0.870636i | \(-0.663708\pi\) | ||||
−0.491928 | + | 0.870636i | \(0.663708\pi\) | |||||||
\(68\) | 3.54279 | + | 5.93331i | 0.429626 | + | 0.719520i | ||||
\(69\) | −5.86180 | + | 5.86180i | −0.705677 | + | 0.705677i | ||||
\(70\) | 0.801617 | + | 3.05899i | 0.0958115 | + | 0.365619i | ||||
\(71\) | −11.9106 | −1.41353 | −0.706765 | − | 0.707449i | \(-0.749846\pi\) | ||||
−0.706765 | + | 0.707449i | \(0.749846\pi\) | |||||||
\(72\) | −3.19937 | − | 7.26692i | −0.377050 | − | 0.856415i | ||||
\(73\) | −8.55814 | + | 8.55814i | −1.00165 | + | 1.00165i | −0.00165608 | + | 0.999999i | \(0.500527\pi\) |
−0.999999 | + | 0.00165608i | \(0.999473\pi\) | |||||||
\(74\) | −13.0675 | + | 10.1804i | −1.51907 | + | 1.18345i | ||||
\(75\) | −8.29820 | − | 8.73617i | −0.958193 | − | 1.00877i | ||||
\(76\) | 3.62001 | + | 6.06264i | 0.415244 | + | 0.695433i | ||||
\(77\) | − | 3.31891i | − | 0.378224i | ||||||
\(78\) | 9.40288 | + | 12.0695i | 1.06467 | + | 1.36660i | ||||
\(79\) | 1.48361 | 0.166919 | 0.0834593 | − | 0.996511i | \(-0.473403\pi\) | ||||
0.0834593 | + | 0.996511i | \(0.473403\pi\) | |||||||
\(80\) | 8.88583 | + | 1.02081i | 0.993466 | + | 0.114130i | ||||
\(81\) | −9.54116 | −1.06013 | ||||||||
\(82\) | −10.6040 | − | 13.6112i | −1.17101 | − | 1.50311i | ||||
\(83\) | − | 9.70769i | − | 1.06556i | −0.846254 | − | 0.532779i | \(-0.821148\pi\) | ||
0.846254 | − | 0.532779i | \(-0.178852\pi\) | |||||||
\(84\) | 4.13809 | − | 2.47086i | 0.451502 | − | 0.269593i | ||||
\(85\) | 3.04819 | − | 7.09950i | 0.330623 | − | 0.770049i | ||||
\(86\) | −2.02436 | + | 1.57710i | −0.218292 | + | 0.170063i | ||||
\(87\) | 7.45010 | − | 7.45010i | 0.798735 | − | 0.798735i | ||||
\(88\) | −8.74975 | − | 3.40044i | −0.932726 | − | 0.362488i | ||||
\(89\) | −4.91472 | −0.520959 | −0.260479 | − | 0.965479i | \(-0.583881\pi\) | ||||
−0.260479 | + | 0.965479i | \(0.583881\pi\) | |||||||
\(90\) | −4.48090 | + | 7.66334i | −0.472329 | + | 0.807786i | ||||
\(91\) | −3.17449 | + | 3.17449i | −0.332777 | + | 0.332777i | ||||
\(92\) | −5.90713 | + | 3.52715i | −0.615861 | + | 0.367731i | ||||
\(93\) | 24.4602 | 2.53640 | ||||||||
\(94\) | −4.24826 | − | 0.527587i | −0.438174 | − | 0.0544164i | ||||
\(95\) | 3.11463 | − | 7.25425i | 0.319555 | − | 0.744271i | ||||
\(96\) | −2.27426 | − | 13.4409i | −0.232115 | − | 1.37181i | ||||
\(97\) | −9.69326 | + | 9.69326i | −0.984201 | + | 0.984201i | −0.999877 | − | 0.0156756i | \(-0.995010\pi\) |
0.0156756 | + | 0.999877i | \(0.495010\pi\) | |||||||
\(98\) | 0.869134 | + | 1.11562i | 0.0877958 | + | 0.112695i | ||||
\(99\) | 6.58806 | − | 6.58806i | 0.662125 | − | 0.662125i | ||||
\(100\) | −4.90427 | − | 8.71482i | −0.490427 | − | 0.871482i | ||||
\(101\) | 2.76235 | + | 2.76235i | 0.274864 | + | 0.274864i | 0.831055 | − | 0.556191i | \(-0.187738\pi\) |
−0.556191 | + | 0.831055i | \(0.687738\pi\) | |||||||
\(102\) | −11.6858 | − | 1.45125i | −1.15706 | − | 0.143695i | ||||
\(103\) | −2.54232 | − | 2.54232i | −0.250503 | − | 0.250503i | 0.570674 | − | 0.821177i | \(-0.306682\pi\) |
−0.821177 | + | 0.570674i | \(0.806682\pi\) | |||||||
\(104\) | 5.11655 | + | 11.6215i | 0.501719 | + | 1.13958i | ||||
\(105\) | −4.95143 | − | 2.12591i | −0.483210 | − | 0.207468i | ||||
\(106\) | 3.74412 | + | 4.80595i | 0.363661 | + | 0.466795i | ||||
\(107\) | 5.98004i | 0.578112i | 0.957312 | + | 0.289056i | \(0.0933415\pi\) | ||||
−0.957312 | + | 0.289056i | \(0.906659\pi\) | |||||||
\(108\) | −0.900876 | − | 0.227263i | −0.0866868 | − | 0.0218684i | ||||
\(109\) | −7.04035 | − | 7.04035i | −0.674344 | − | 0.674344i | 0.284371 | − | 0.958714i | \(-0.408215\pi\) |
−0.958714 | + | 0.284371i | \(0.908215\pi\) | |||||||
\(110\) | 2.66049 | + | 10.1525i | 0.253668 | + | 0.968002i | ||||
\(111\) | − | 28.2268i | − | 2.67917i | ||||||
\(112\) | 3.83163 | − | 1.14830i | 0.362055 | − | 0.108504i | ||||
\(113\) | 6.03615 | + | 6.03615i | 0.567833 | + | 0.567833i | 0.931521 | − | 0.363688i | \(-0.118483\pi\) |
−0.363688 | + | 0.931521i | \(0.618483\pi\) | |||||||
\(114\) | −11.9405 | − | 1.48288i | −1.11833 | − | 0.138884i | ||||
\(115\) | 7.06818 | + | 3.03474i | 0.659111 | + | 0.282991i | ||||
\(116\) | 7.50772 | − | 4.48287i | 0.697075 | − | 0.416224i | ||||
\(117\) | −12.6028 | −1.16513 | ||||||||
\(118\) | −9.35120 | − | 1.16132i | −0.860848 | − | 0.106908i | ||||
\(119\) | − | 3.45527i | − | 0.316744i | ||||||
\(120\) | −10.6777 | + | 10.8755i | −0.974735 | + | 0.992791i | ||||
\(121\) | − | 0.0151342i | − | 0.00137584i | ||||||
\(122\) | −0.732257 | + | 5.89631i | −0.0662955 | + | 0.533827i | ||||
\(123\) | 29.4013 | 2.65102 | ||||||||
\(124\) | 19.6838 | + | 4.96560i | 1.76765 | + | 0.445924i | ||||
\(125\) | −4.67353 | + | 10.1567i | −0.418013 | + | 0.908441i | ||||
\(126\) | −0.489274 | + | 3.93975i | −0.0435880 | + | 0.350981i | ||||
\(127\) | 8.74399 | + | 8.74399i | 0.775904 | + | 0.775904i | 0.979131 | − | 0.203228i | \(-0.0651432\pi\) |
−0.203228 | + | 0.979131i | \(0.565143\pi\) | |||||||
\(128\) | 0.898457 | − | 11.2780i | 0.0794131 | − | 0.996842i | ||||
\(129\) | − | 4.37276i | − | 0.385000i | ||||||
\(130\) | 7.16601 | − | 12.2555i | 0.628501 | − | 1.07488i | ||||
\(131\) | 1.34402 | + | 1.34402i | 0.117428 | + | 0.117428i | 0.763379 | − | 0.645951i | \(-0.223539\pi\) |
−0.645951 | + | 0.763379i | \(0.723539\pi\) | |||||||
\(132\) | 13.7339 | − | 8.20054i | 1.19538 | − | 0.713766i | ||||
\(133\) | − | 3.53058i | − | 0.306141i | ||||||
\(134\) | 8.98430 | − | 6.99931i | 0.776126 | − | 0.604649i | ||||
\(135\) | 0.385151 | + | 0.964723i | 0.0331485 | + | 0.0830302i | ||||
\(136\) | −9.10925 | − | 3.54016i | −0.781111 | − | 0.303566i | ||||
\(137\) | 0.585584 | + | 0.585584i | 0.0500299 | + | 0.0500299i | 0.731679 | − | 0.681649i | \(-0.238737\pi\) |
−0.681649 | + | 0.731679i | \(0.738737\pi\) | |||||||
\(138\) | 1.44484 | − | 11.6342i | 0.122993 | − | 0.990370i | ||||
\(139\) | −6.23701 | − | 6.23701i | −0.529016 | − | 0.529016i | 0.391263 | − | 0.920279i | \(-0.372038\pi\) |
−0.920279 | + | 0.391263i | \(0.872038\pi\) | |||||||
\(140\) | −3.55297 | − | 2.71595i | −0.300281 | − | 0.229540i | ||||
\(141\) | 5.15809 | − | 5.15809i | 0.434389 | − | 0.434389i | ||||
\(142\) | 13.2877 | − | 10.3519i | 1.11508 | − | 0.868714i | ||||
\(143\) | −10.5358 | + | 10.5358i | −0.881052 | + | 0.881052i | ||||
\(144\) | 9.88521 | + | 5.32643i | 0.823768 | + | 0.443869i | ||||
\(145\) | −8.98336 | − | 3.85703i | −0.746028 | − | 0.320309i | ||||
\(146\) | 2.10945 | − | 16.9858i | 0.174579 | − | 1.40575i | ||||
\(147\) | −2.40982 | −0.198758 | ||||||||
\(148\) | 5.73026 | − | 22.7149i | 0.471024 | − | 1.86715i | ||||
\(149\) | −1.92918 | + | 1.92918i | −0.158044 | + | 0.158044i | −0.781700 | − | 0.623655i | \(-0.785647\pi\) |
0.623655 | + | 0.781700i | \(0.285647\pi\) | |||||||
\(150\) | 16.8505 | + | 2.53398i | 1.37584 | + | 0.206899i | ||||
\(151\) | 8.05786 | 0.655739 | 0.327870 | − | 0.944723i | \(-0.393669\pi\) | ||||
0.327870 | + | 0.944723i | \(0.393669\pi\) | |||||||
\(152\) | −9.30780 | − | 3.61732i | −0.754963 | − | 0.293404i | ||||
\(153\) | 6.85874 | − | 6.85874i | 0.554496 | − | 0.554496i | ||||
\(154\) | 2.88457 | + | 3.70263i | 0.232446 | + | 0.298367i | ||||
\(155\) | −8.41538 | − | 21.0788i | −0.675940 | − | 1.69309i | ||||
\(156\) | −20.9801 | − | 5.29261i | −1.67975 | − | 0.423748i | ||||
\(157\) | 10.1484i | 0.809928i | 0.914333 | + | 0.404964i | \(0.132716\pi\) | ||||
−0.914333 | + | 0.404964i | \(0.867284\pi\) | |||||||
\(158\) | −1.65514 | + | 1.28945i | −0.131676 | + | 0.102583i | ||||
\(159\) | −10.3812 | −0.823283 | ||||||||
\(160\) | −10.8004 | + | 6.58414i | −0.853848 | + | 0.520522i | ||||
\(161\) | 3.44002 | 0.271112 | ||||||||
\(162\) | 10.6443 | − | 8.29255i | 0.836295 | − | 0.651524i | ||||
\(163\) | − | 15.4065i | − | 1.20673i | −0.797464 | − | 0.603367i | \(-0.793825\pi\) | ||
0.797464 | − | 0.603367i | \(-0.206175\pi\) | |||||||
\(164\) | 23.6600 | + | 5.96868i | 1.84754 | + | 0.466075i | ||||
\(165\) | −16.4333 | − | 7.05569i | −1.27933 | − | 0.549285i | ||||
\(166\) | 8.43729 | + | 10.8301i | 0.654861 | + | 0.840578i | ||||
\(167\) | −8.60232 | + | 8.60232i | −0.665667 | + | 0.665667i | −0.956710 | − | 0.291043i | \(-0.905998\pi\) |
0.291043 | + | 0.956710i | \(0.405998\pi\) | |||||||
\(168\) | −2.46902 | + | 6.35309i | −0.190489 | + | 0.490151i | ||||
\(169\) | 7.15483 | 0.550371 | ||||||||
\(170\) | 2.76980 | + | 10.5696i | 0.212434 | + | 0.810654i | ||||
\(171\) | 7.00824 | − | 7.00824i | 0.535934 | − | 0.535934i | ||||
\(172\) | 0.887703 | − | 3.51888i | 0.0676867 | − | 0.268312i | ||||
\(173\) | 8.07360 | 0.613825 | 0.306912 | − | 0.951738i | \(-0.400704\pi\) | ||||
0.306912 | + | 0.951738i | \(0.400704\pi\) | |||||||
\(174\) | −1.83634 | + | 14.7866i | −0.139212 | + | 1.12097i | ||||
\(175\) | −0.128512 | + | 4.99835i | −0.00971461 | + | 0.377840i | ||||
\(176\) | 12.7168 | − | 3.81111i | 0.958567 | − | 0.287273i | ||||
\(177\) | 11.3539 | − | 11.3539i | 0.853412 | − | 0.853412i | ||||
\(178\) | 5.48295 | − | 4.27155i | 0.410964 | − | 0.320166i | ||||
\(179\) | −10.8927 | + | 10.8927i | −0.814158 | + | 0.814158i | −0.985254 | − | 0.171096i | \(-0.945269\pi\) |
0.171096 | + | 0.985254i | \(0.445269\pi\) | |||||||
\(180\) | −1.66149 | − | 12.4439i | −0.123840 | − | 0.927511i | ||||
\(181\) | −12.5519 | − | 12.5519i | −0.932974 | − | 0.932974i | 0.0649164 | − | 0.997891i | \(-0.479322\pi\) |
−0.997891 | + | 0.0649164i | \(0.979322\pi\) | |||||||
\(182\) | 0.782464 | − | 6.30059i | 0.0580001 | − | 0.467031i | ||||
\(183\) | −7.15910 | − | 7.15910i | −0.529216 | − | 0.529216i | ||||
\(184\) | 3.52454 | − | 9.06905i | 0.259832 | − | 0.668579i | ||||
\(185\) | −24.3248 | + | 9.71129i | −1.78839 | + | 0.713988i | ||||
\(186\) | −27.2882 | + | 21.2592i | −2.00087 | + | 1.55880i | ||||
\(187\) | − | 11.4677i | − | 0.838602i | ||||||
\(188\) | 5.19798 | − | 3.10372i | 0.379102 | − | 0.226362i | ||||
\(189\) | 0.328486 | + | 0.328486i | 0.0238939 | + | 0.0238939i | ||||
\(190\) | 2.83018 | + | 10.8000i | 0.205323 | + | 0.783516i | ||||
\(191\) | − | 9.83980i | − | 0.711983i | −0.934489 | − | 0.355991i | \(-0.884143\pi\) | ||
0.934489 | − | 0.355991i | \(-0.115857\pi\) | |||||||
\(192\) | 14.2192 | + | 13.0183i | 1.02618 | + | 0.939518i | ||||
\(193\) | −6.74831 | − | 6.74831i | −0.485754 | − | 0.485754i | 0.421210 | − | 0.906963i | \(-0.361606\pi\) |
−0.906963 | + | 0.421210i | \(0.861606\pi\) | |||||||
\(194\) | 2.38924 | − | 19.2387i | 0.171537 | − | 1.38126i | ||||
\(195\) | 8.96959 | + | 22.4670i | 0.642326 | + | 1.60889i | ||||
\(196\) | −1.93925 | − | 0.489211i | −0.138518 | − | 0.0349436i | ||||
\(197\) | 11.8523 | 0.844443 | 0.422221 | − | 0.906493i | \(-0.361251\pi\) | ||||
0.422221 | + | 0.906493i | \(0.361251\pi\) | |||||||
\(198\) | −1.62385 | + | 13.0757i | −0.115402 | + | 0.929247i | ||||
\(199\) | 10.3205i | 0.731602i | 0.930693 | + | 0.365801i | \(0.119205\pi\) | ||||
−0.930693 | + | 0.365801i | \(0.880795\pi\) | |||||||
\(200\) | 13.0456 | + | 5.45995i | 0.922467 | + | 0.386077i | ||||
\(201\) | 19.4068i | 1.36885i | ||||||||
\(202\) | −5.48258 | − | 0.680877i | −0.385753 | − | 0.0479063i | ||||
\(203\) | −4.37213 | −0.306863 | ||||||||
\(204\) | 14.2982 | − | 8.53748i | 1.00107 | − | 0.597743i | ||||
\(205\) | −10.1153 | − | 25.3368i | −0.706486 | − | 1.76960i | ||||
\(206\) | 5.04589 | + | 0.626644i | 0.351564 | + | 0.0436603i | ||||
\(207\) | 6.82847 | + | 6.82847i | 0.474612 | + | 0.474612i | ||||
\(208\) | −15.8088 | − | 8.51821i | −1.09614 | − | 0.590632i | ||||
\(209\) | − | 11.7177i | − | 0.810529i | ||||||
\(210\) | 7.37161 | − | 1.93175i | 0.508689 | − | 0.133304i | ||||
\(211\) | 4.12123 | + | 4.12123i | 0.283717 | + | 0.283717i | 0.834590 | − | 0.550872i | \(-0.185705\pi\) |
−0.550872 | + | 0.834590i | \(0.685705\pi\) | |||||||
\(212\) | −8.35403 | − | 2.10746i | −0.573757 | − | 0.144741i | ||||
\(213\) | 28.7024i | 1.96666i | ||||||||
\(214\) | −5.19746 | − | 6.67145i | −0.355291 | − | 0.456051i | ||||
\(215\) | −3.76827 | + | 1.50442i | −0.256994 | + | 0.102601i | ||||
\(216\) | 1.20256 | − | 0.529443i | 0.0818236 | − | 0.0360241i | ||||
\(217\) | −7.17728 | − | 7.17728i | −0.487226 | − | 0.487226i | ||||
\(218\) | 13.9734 | + | 1.73534i | 0.946396 | + | 0.117532i | ||||
\(219\) | 20.6236 | + | 20.6236i | 1.39361 | + | 1.39361i | ||||
\(220\) | −11.7920 | − | 9.01399i | −0.795015 | − | 0.607723i | ||||
\(221\) | −10.9687 | + | 10.9687i | −0.737837 | + | 0.737837i | ||||
\(222\) | 24.5329 | + | 31.4904i | 1.64654 | + | 2.11350i | ||||
\(223\) | −2.97066 | + | 2.97066i | −0.198930 | + | 0.198930i | −0.799541 | − | 0.600611i | \(-0.794924\pi\) |
0.600611 | + | 0.799541i | \(0.294924\pi\) | |||||||
\(224\) | −3.27661 | + | 4.61127i | −0.218928 | + | 0.308103i | ||||
\(225\) | −10.1769 | + | 9.66667i | −0.678458 | + | 0.644444i | ||||
\(226\) | −11.9803 | − | 1.48782i | −0.796915 | − | 0.0989681i | ||||
\(227\) | −14.9111 | −0.989682 | −0.494841 | − | 0.868983i | \(-0.664774\pi\) | ||||
−0.494841 | + | 0.868983i | \(0.664774\pi\) | |||||||
\(228\) | 14.6099 | − | 8.72357i | 0.967562 | − | 0.577733i | ||||
\(229\) | −17.6004 | + | 17.6004i | −1.16307 | + | 1.16307i | −0.179267 | + | 0.983800i | \(0.557373\pi\) |
−0.983800 | + | 0.179267i | \(0.942627\pi\) | |||||||
\(230\) | −10.5230 | + | 2.75758i | −0.693865 | + | 0.181829i | ||||
\(231\) | −7.99796 | −0.526227 | ||||||||
\(232\) | −4.47954 | + | 11.5264i | −0.294096 | + | 0.756745i | ||||
\(233\) | −2.93845 | + | 2.93845i | −0.192505 | + | 0.192505i | −0.796777 | − | 0.604273i | \(-0.793464\pi\) |
0.604273 | + | 0.796777i | \(0.293464\pi\) | |||||||
\(234\) | 14.0599 | − | 10.9535i | 0.919126 | − | 0.716054i | ||||
\(235\) | −6.21964 | − | 2.67042i | −0.405725 | − | 0.174199i | ||||
\(236\) | 11.4417 | − | 6.83187i | 0.744793 | − | 0.444717i | ||||
\(237\) | − | 3.57522i | − | 0.232236i | ||||||
\(238\) | 3.00309 | + | 3.85476i | 0.194662 | + | 0.249867i | ||||
\(239\) | 28.6850 | 1.85548 | 0.927741 | − | 0.373225i | \(-0.121748\pi\) | ||||
0.927741 | + | 0.373225i | \(0.121748\pi\) | |||||||
\(240\) | 2.45997 | − | 21.4132i | 0.158790 | − | 1.38222i | ||||
\(241\) | 23.0840 | 1.48697 | 0.743486 | − | 0.668752i | \(-0.233171\pi\) | ||||
0.743486 | + | 0.668752i | \(0.233171\pi\) | |||||||
\(242\) | 0.0131537 | + | 0.0168840i | 0.000845550 | + | 0.00108535i | ||||
\(243\) | 21.5988i | 1.38556i | ||||||||
\(244\) | −4.30777 | − | 7.21447i | −0.275777 | − | 0.461859i | ||||
\(245\) | 0.829085 | + | 2.07668i | 0.0529683 | + | 0.132675i | ||||
\(246\) | −32.8006 | + | 25.5537i | −2.09129 | + | 1.62924i | ||||
\(247\) | −11.2078 | + | 11.2078i | −0.713137 | + | 0.713137i | ||||
\(248\) | −26.2753 | + | 11.5681i | −1.66849 | + | 0.734576i | ||||
\(249\) | −23.3938 | −1.48252 | ||||||||
\(250\) | −3.61364 | − | 15.3929i | −0.228547 | − | 0.973533i | ||||
\(251\) | 12.7284 | − | 12.7284i | 0.803411 | − | 0.803411i | −0.180216 | − | 0.983627i | \(-0.557680\pi\) |
0.983627 | + | 0.180216i | \(0.0576798\pi\) | |||||||
\(252\) | −2.87833 | − | 4.82051i | −0.181318 | − | 0.303663i | ||||
\(253\) | 11.4171 | 0.717788 | ||||||||
\(254\) | −17.3547 | − | 2.15526i | −1.08893 | − | 0.135233i | ||||
\(255\) | −17.1085 | − | 7.34559i | −1.07138 | − | 0.459999i | ||||
\(256\) | 8.79974 | + | 13.3628i | 0.549984 | + | 0.835175i | ||||
\(257\) | 10.3240 | − | 10.3240i | 0.643995 | − | 0.643995i | −0.307540 | − | 0.951535i | \(-0.599506\pi\) |
0.951535 | + | 0.307540i | \(0.0995057\pi\) | |||||||
\(258\) | 3.80052 | + | 4.87834i | 0.236610 | + | 0.303712i | ||||
\(259\) | −8.28253 | + | 8.28253i | −0.514651 | + | 0.514651i | ||||
\(260\) | 2.65711 | + | 19.9007i | 0.164787 | + | 1.23419i | ||||
\(261\) | −8.67871 | − | 8.67871i | −0.537199 | − | 0.537199i | ||||
\(262\) | −2.66755 | − | 0.331280i | −0.164802 | − | 0.0204665i | ||||
\(263\) | −3.99183 | − | 3.99183i | −0.246147 | − | 0.246147i | 0.573240 | − | 0.819387i | \(-0.305686\pi\) |
−0.819387 | + | 0.573240i | \(0.805686\pi\) | |||||||
\(264\) | −8.19445 | + | 21.0853i | −0.504334 | + | 1.29771i | ||||
\(265\) | 3.57159 | + | 8.94610i | 0.219401 | + | 0.549554i | ||||
\(266\) | 3.06855 | + | 3.93879i | 0.188145 | + | 0.241503i | ||||
\(267\) | 11.8436i | 0.724815i | ||||||||
\(268\) | −3.93971 | + | 15.6171i | −0.240656 | + | 0.953968i | ||||
\(269\) | 14.3428 | + | 14.3428i | 0.874494 | + | 0.874494i | 0.992958 | − | 0.118464i | \(-0.0377971\pi\) |
−0.118464 | + | 0.992958i | \(0.537797\pi\) | |||||||
\(270\) | −1.26816 | − | 0.741516i | −0.0771775 | − | 0.0451272i | ||||
\(271\) | − | 15.2118i | − | 0.924050i | −0.886867 | − | 0.462025i | \(-0.847123\pi\) | ||
0.886867 | − | 0.462025i | \(-0.152877\pi\) | |||||||
\(272\) | 13.2393 | − | 3.96769i | 0.802752 | − | 0.240577i | ||||
\(273\) | 7.64996 | + | 7.64996i | 0.462996 | + | 0.462996i | ||||
\(274\) | −1.16224 | − | 0.144338i | −0.0702135 | − | 0.00871975i | ||||
\(275\) | −0.426520 | + | 16.5890i | −0.0257201 | + | 1.00036i | ||||
\(276\) | 8.49980 | + | 14.2351i | 0.511628 | + | 0.856853i | ||||
\(277\) | 23.7444 | 1.42666 | 0.713331 | − | 0.700827i | \(-0.247186\pi\) | ||||
0.713331 | + | 0.700827i | \(0.247186\pi\) | |||||||
\(278\) | 12.3789 | + | 1.53733i | 0.742439 | + | 0.0922028i | ||||
\(279\) | − | 28.4939i | − | 1.70589i | ||||||
\(280\) | 6.32429 | − | 0.0580407i | 0.377949 | − | 0.00346860i | ||||
\(281\) | − | 7.83055i | − | 0.467131i | −0.972341 | − | 0.233566i | \(-0.924961\pi\) | ||
0.972341 | − | 0.233566i | \(-0.0750394\pi\) | |||||||
\(282\) | −1.27139 | + | 10.2375i | −0.0757101 | + | 0.609636i | ||||
\(283\) | −16.5930 | −0.986353 | −0.493177 | − | 0.869929i | \(-0.664164\pi\) | ||||
−0.493177 | + | 0.869929i | \(0.664164\pi\) | |||||||
\(284\) | −5.82680 | + | 23.0976i | −0.345757 | + | 1.37059i | ||||
\(285\) | −17.4814 | − | 7.50570i | −1.03551 | − | 0.444600i | ||||
\(286\) | 2.59692 | − | 20.9111i | 0.153559 | − | 1.23650i | ||||
\(287\) | −8.62714 | − | 8.62714i | −0.509244 | − | 0.509244i | ||||
\(288\) | −15.6575 | + | 2.64931i | −0.922628 | + | 0.156112i | ||||
\(289\) | 5.06111i | 0.297713i | ||||||||
\(290\) | 13.3743 | − | 3.50477i | 0.785365 | − | 0.205807i | ||||
\(291\) | 23.3590 | + | 23.3590i | 1.36933 | + | 1.36933i | ||||
\(292\) | 12.4096 | + | 20.7831i | 0.726217 | + | 1.21624i | ||||
\(293\) | − | 6.83604i | − | 0.399366i | −0.979861 | − | 0.199683i | \(-0.936009\pi\) | ||
0.979861 | − | 0.199683i | \(-0.0639912\pi\) | |||||||
\(294\) | 2.68844 | − | 2.09446i | 0.156793 | − | 0.122151i | ||||
\(295\) | −13.6906 | − | 5.87809i | −0.797097 | − | 0.342236i | ||||
\(296\) | 13.3495 | + | 30.3215i | 0.775924 | + | 1.76240i | ||||
\(297\) | 1.09021 | + | 1.09021i | 0.0632607 | + | 0.0632607i | ||||
\(298\) | 0.475513 | − | 3.82894i | 0.0275457 | − | 0.221805i | ||||
\(299\) | −10.9203 | − | 10.9203i | −0.631539 | − | 0.631539i | ||||
\(300\) | −21.0011 | + | 11.8184i | −1.21250 | + | 0.682336i | ||||
\(301\) | −1.28309 | + | 1.28309i | −0.0739560 | + | 0.0739560i | ||||
\(302\) | −8.98950 | + | 7.00336i | −0.517287 | + | 0.402998i | ||||
\(303\) | 6.65676 | − | 6.65676i | 0.382421 | − | 0.382421i | ||||
\(304\) | 13.5279 | − | 4.05418i | 0.775878 | − | 0.232523i | ||||
\(305\) | −3.70638 | + | 8.63247i | −0.212226 | + | 0.494294i | ||||
\(306\) | −1.69057 | + | 13.6129i | −0.0966437 | + | 0.778198i | ||||
\(307\) | 0.277015 | 0.0158101 | 0.00790504 | − | 0.999969i | \(-0.497484\pi\) | ||||
0.00790504 | + | 0.999969i | \(0.497484\pi\) | |||||||
\(308\) | −6.43617 | − | 1.62365i | −0.366735 | − | 0.0925158i | ||||
\(309\) | −6.12654 | + | 6.12654i | −0.348527 | + | 0.348527i | ||||
\(310\) | 27.7087 | + | 16.2018i | 1.57375 | + | 0.920200i | ||||
\(311\) | −15.6551 | −0.887718 | −0.443859 | − | 0.896097i | \(-0.646391\pi\) | ||||
−0.443859 | + | 0.896097i | \(0.646391\pi\) | |||||||
\(312\) | 28.0057 | − | 12.3299i | 1.58551 | − | 0.698046i | ||||
\(313\) | 19.7759 | − | 19.7759i | 1.11780 | − | 1.11780i | 0.125734 | − | 0.992064i | \(-0.459871\pi\) |
0.992064 | − | 0.125734i | \(-0.0401287\pi\) | |||||||
\(314\) | −8.82029 | − | 11.3217i | −0.497758 | − | 0.638921i | ||||
\(315\) | −2.47650 | + | 5.76798i | −0.139535 | + | 0.324989i | ||||
\(316\) | 0.725796 | − | 2.87708i | 0.0408292 | − | 0.161848i | ||||
\(317\) | 18.0255i | 1.01241i | 0.862412 | + | 0.506207i | \(0.168953\pi\) | ||||
−0.862412 | + | 0.506207i | \(0.831047\pi\) | |||||||
\(318\) | 11.5815 | − | 9.02266i | 0.649456 | − | 0.505965i | ||||
\(319\) | −14.5107 | −0.812442 | ||||||||
\(320\) | 6.32665 | − | 16.7324i | 0.353670 | − | 0.935370i | ||||
\(321\) | 14.4108 | 0.804333 | ||||||||
\(322\) | −3.83775 | + | 2.98984i | −0.213870 | + | 0.166617i | ||||
\(323\) | − | 12.1991i | − | 0.678777i | ||||||
\(324\) | −4.66764 | + | 18.5026i | −0.259313 | + | 1.02792i | ||||
\(325\) | 16.2752 | − | 15.4593i | 0.902785 | − | 0.857526i | ||||
\(326\) | 13.3904 | + | 17.1878i | 0.741623 | + | 0.951946i | ||||
\(327\) | −16.9660 | + | 16.9660i | −0.938221 | + | 0.938221i | ||||
\(328\) | −31.5831 | + | 13.9049i | −1.74389 | + | 0.767772i | ||||
\(329\) | −3.02705 | −0.166887 | ||||||||
\(330\) | 24.4657 | − | 6.41130i | 1.34679 | − | 0.352930i | ||||
\(331\) | −14.5382 | + | 14.5382i | −0.799093 | + | 0.799093i | −0.982953 | − | 0.183859i | \(-0.941141\pi\) |
0.183859 | + | 0.982953i | \(0.441141\pi\) | |||||||
\(332\) | −18.8256 | − | 4.74911i | −1.03319 | − | 0.260641i | ||||
\(333\) | −32.8818 | −1.80191 | ||||||||
\(334\) | 2.12034 | − | 17.0735i | 0.116020 | − | 0.934219i | ||||
\(335\) | 16.7240 | − | 6.67678i | 0.913727 | − | 0.364792i | ||||
\(336\) | −2.76720 | − | 9.23354i | −0.150963 | − | 0.503731i | ||||
\(337\) | 10.1367 | − | 10.1367i | 0.552183 | − | 0.552183i | −0.374887 | − | 0.927070i | \(-0.622319\pi\) |
0.927070 | + | 0.374887i | \(0.122319\pi\) | |||||||
\(338\) | −7.98206 | + | 6.21851i | −0.434167 | + | 0.338242i | ||||
\(339\) | 14.5460 | − | 14.5460i | 0.790031 | − | 0.790031i | ||||
\(340\) | −12.2765 | − | 9.38435i | −0.665785 | − | 0.508938i | ||||
\(341\) | −23.8207 | − | 23.8207i | −1.28996 | − | 1.28996i | ||||
\(342\) | −1.72742 | + | 13.9096i | −0.0934084 | + | 0.752147i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 2.06804 | + | 4.69726i | 0.111501 | + | 0.253259i | ||||
\(345\) | 7.31318 | − | 17.0330i | 0.393728 | − | 0.917027i | ||||
\(346\) | −9.00706 | + | 7.01704i | −0.484223 | + | 0.377239i | ||||
\(347\) | 8.11318i | 0.435538i | 0.976000 | + | 0.217769i | \(0.0698780\pi\) | ||||
−0.976000 | + | 0.217769i | \(0.930122\pi\) | |||||||
\(348\) | −10.8029 | − | 18.0923i | −0.579097 | − | 0.969846i | ||||
\(349\) | 14.5875 | + | 14.5875i | 0.780851 | + | 0.780851i | 0.979974 | − | 0.199123i | \(-0.0638094\pi\) |
−0.199123 | + | 0.979974i | \(0.563809\pi\) | |||||||
\(350\) | −4.20087 | − | 5.68795i | −0.224546 | − | 0.304034i | ||||
\(351\) | − | 2.08556i | − | 0.111319i | ||||||
\(352\) | −10.8748 | + | 15.3044i | −0.579627 | + | 0.815726i | ||||
\(353\) | −17.1513 | − | 17.1513i | −0.912870 | − | 0.912870i | 0.0836275 | − | 0.996497i | \(-0.473349\pi\) |
−0.996497 | + | 0.0836275i | \(0.973349\pi\) | |||||||
\(354\) | −2.79856 | + | 22.5347i | −0.148742 | + | 1.19771i | ||||
\(355\) | 24.7346 | − | 9.87490i | 1.31278 | − | 0.524106i | ||||
\(356\) | −2.40433 | + | 9.53084i | −0.127429 | + | 0.505133i | ||||
\(357\) | −8.32657 | −0.440689 | ||||||||
\(358\) | 2.68488 | − | 21.6193i | 0.141900 | − | 1.14262i | ||||
\(359\) | − | 25.3205i | − | 1.33637i | −0.743997 | − | 0.668183i | \(-0.767073\pi\) | ||
0.743997 | − | 0.668183i | \(-0.232927\pi\) | |||||||
\(360\) | 12.6690 | + | 12.4386i | 0.667714 | + | 0.655570i | ||||
\(361\) | 6.53497i | 0.343946i | ||||||||
\(362\) | 24.9124 | + | 3.09385i | 1.30937 | + | 0.162609i | ||||
\(363\) | −0.0364707 | −0.00191422 | ||||||||
\(364\) | 4.60313 | + | 7.70912i | 0.241269 | + | 0.404068i | ||||
\(365\) | 10.6771 | − | 24.8680i | 0.558867 | − | 1.30165i | ||||
\(366\) | 14.2090 | + | 1.76461i | 0.742719 | + | 0.0922375i | ||||
\(367\) | −12.5089 | − | 12.5089i | −0.652958 | − | 0.652958i | 0.300746 | − | 0.953704i | \(-0.402764\pi\) |
−0.953704 | + | 0.300746i | \(0.902764\pi\) | |||||||
\(368\) | 3.95019 | + | 13.1809i | 0.205918 | + | 0.687102i | ||||
\(369\) | − | 34.2499i | − | 1.78298i | ||||||
\(370\) | 18.6967 | − | 31.9756i | 0.971997 | − | 1.66233i | ||||
\(371\) | 3.04613 | + | 3.04613i | 0.158147 | + | 0.158147i | ||||
\(372\) | 11.9662 | − | 47.4343i | 0.620418 | − | 2.45935i | ||||
\(373\) | − | 19.4218i | − | 1.00562i | −0.864396 | − | 0.502811i | \(-0.832299\pi\) | ||
0.864396 | − | 0.502811i | \(-0.167701\pi\) | |||||||
\(374\) | 9.96698 | + | 12.7936i | 0.515380 | + | 0.661541i | ||||
\(375\) | 24.4758 | + | 11.2624i | 1.26392 | + | 0.581586i | ||||
\(376\) | −3.10141 | + | 7.98031i | −0.159943 | + | 0.411553i | ||||
\(377\) | 13.8793 | + | 13.8793i | 0.714820 | + | 0.714820i | ||||
\(378\) | −0.651964 | − | 0.0809668i | −0.0335334 | − | 0.00416448i | ||||
\(379\) | 5.54332 | + | 5.54332i | 0.284741 | + | 0.284741i | 0.834997 | − | 0.550255i | \(-0.185470\pi\) |
−0.550255 | + | 0.834997i | \(0.685470\pi\) | |||||||
\(380\) | −12.5441 | − | 9.58890i | −0.643497 | − | 0.491900i | ||||
\(381\) | 21.0714 | − | 21.0714i | 1.07952 | − | 1.07952i | ||||
\(382\) | 8.55211 | + | 10.9775i | 0.437564 | + | 0.561656i | ||||
\(383\) | −8.84593 | + | 8.84593i | −0.452006 | + | 0.452006i | −0.896020 | − | 0.444014i | \(-0.853554\pi\) |
0.444014 | + | 0.896020i | \(0.353554\pi\) | |||||||
\(384\) | −27.1779 | − | 2.16512i | −1.38692 | − | 0.110488i | ||||
\(385\) | 2.75165 | + | 6.89232i | 0.140237 | + | 0.351265i | ||||
\(386\) | 13.3937 | + | 1.66335i | 0.681723 | + | 0.0846625i | ||||
\(387\) | −5.09388 | −0.258937 | ||||||||
\(388\) | 14.0556 | + | 23.5397i | 0.713563 | + | 1.19505i | ||||
\(389\) | 19.8381 | − | 19.8381i | 1.00583 | − | 1.00583i | 0.00584880 | − | 0.999983i | \(-0.498138\pi\) |
0.999983 | − | 0.00584880i | \(-0.00186174\pi\) | |||||||
\(390\) | −29.5335 | − | 17.2688i | −1.49548 | − | 0.874439i | ||||
\(391\) | 11.8862 | 0.601111 | ||||||||
\(392\) | 2.58865 | − | 1.13969i | 0.130747 | − | 0.0575631i | ||||
\(393\) | 3.23884 | − | 3.23884i | 0.163378 | − | 0.163378i | ||||
\(394\) | −13.2227 | + | 10.3013i | −0.666148 | + | 0.518970i | ||||
\(395\) | −3.08098 | + | 1.23003i | −0.155021 | + | 0.0618897i | ||||
\(396\) | −9.55291 | − | 15.9988i | −0.480052 | − | 0.803970i | ||||
\(397\) | 3.92255i | 0.196867i | 0.995144 | + | 0.0984336i | \(0.0313832\pi\) | ||||
−0.995144 | + | 0.0984336i | \(0.968617\pi\) | |||||||
\(398\) | −8.96992 | − | 11.5138i | −0.449621 | − | 0.577133i | ||||
\(399\) | −8.50807 | −0.425936 | ||||||||
\(400\) | −19.2994 | + | 5.24720i | −0.964970 | + | 0.262360i | ||||
\(401\) | 3.65238 | 0.182391 | 0.0911957 | − | 0.995833i | \(-0.470931\pi\) | ||||
0.0911957 | + | 0.995833i | \(0.470931\pi\) | |||||||
\(402\) | −16.8671 | − | 21.6505i | −0.841253 | − | 1.07983i | ||||
\(403\) | 45.5685i | 2.26993i | ||||||||
\(404\) | 6.70825 | − | 4.00550i | 0.333748 | − | 0.199281i | ||||
\(405\) | 19.8140 | − | 7.91043i | 0.984565 | − | 0.393072i | ||||
\(406\) | 4.87763 | − | 3.79997i | 0.242073 | − | 0.188589i | ||||
\(407\) | −27.4889 | + | 27.4889i | −1.36258 | + | 1.36258i | ||||
\(408\) | −8.53114 | + | 21.9516i | −0.422354 | + | 1.08677i | ||||
\(409\) | −5.26435 | −0.260305 | −0.130153 | − | 0.991494i | \(-0.541547\pi\) | ||||
−0.130153 | + | 0.991494i | \(0.541547\pi\) | |||||||
\(410\) | 33.3060 | + | 19.4747i | 1.64487 | + | 0.961785i | ||||
\(411\) | 1.41115 | − | 1.41115i | 0.0696070 | − | 0.0696070i | ||||
\(412\) | −6.17393 | + | 3.68646i | −0.304167 | + | 0.181619i | ||||
\(413\) | −6.66310 | −0.327870 | ||||||||
\(414\) | −13.5528 | − | 1.68311i | −0.666086 | − | 0.0827205i | ||||
\(415\) | 8.04850 | + | 20.1598i | 0.395085 | + | 0.989607i | ||||
\(416\) | 25.0400 | − | 4.23686i | 1.22769 | − | 0.207729i | ||||
\(417\) | −15.0301 | + | 15.0301i | −0.736026 | + | 0.736026i | ||||
\(418\) | 10.1842 | + | 13.0725i | 0.498127 | + | 0.639395i | ||||
\(419\) | 16.3169 | − | 16.3169i | 0.797135 | − | 0.797135i | −0.185508 | − | 0.982643i | \(-0.559393\pi\) |
0.982643 | + | 0.185508i | \(0.0593931\pi\) | |||||||
\(420\) | −6.54495 | + | 8.56202i | −0.319361 | + | 0.417784i | ||||
\(421\) | 4.04552 | + | 4.04552i | 0.197167 | + | 0.197167i | 0.798784 | − | 0.601618i | \(-0.205477\pi\) |
−0.601618 | + | 0.798784i | \(0.705477\pi\) | |||||||
\(422\) | −8.17963 | − | 1.01582i | −0.398178 | − | 0.0494494i | ||||
\(423\) | −6.00872 | − | 6.00872i | −0.292154 | − | 0.292154i | ||||
\(424\) | 11.1516 | − | 4.90965i | 0.541568 | − | 0.238434i | ||||
\(425\) | −0.444044 | + | 17.2706i | −0.0215393 | + | 0.837749i | ||||
\(426\) | −24.9463 | − | 32.0210i | −1.20865 | − | 1.55142i | ||||
\(427\) | 4.20135i | 0.203318i | ||||||||
\(428\) | 11.5968 | + | 2.92550i | 0.560551 | + | 0.141410i | ||||
\(429\) | 25.3895 | + | 25.3895i | 1.22582 | + | 1.22582i | ||||
\(430\) | 2.89641 | − | 4.95350i | 0.139677 | − | 0.238879i | ||||
\(431\) | − | 31.0821i | − | 1.49717i | −0.663037 | − | 0.748587i | \(-0.730733\pi\) | ||
0.663037 | − | 0.748587i | \(-0.269267\pi\) | |||||||
\(432\) | −0.881437 | + | 1.63584i | −0.0424082 | + | 0.0787044i | ||||
\(433\) | 19.1212 | + | 19.1212i | 0.918905 | + | 0.918905i | 0.996950 | − | 0.0780449i | \(-0.0248677\pi\) |
−0.0780449 | + | 0.996950i | \(0.524868\pi\) | |||||||
\(434\) | 14.2451 | + | 1.76909i | 0.683789 | + | 0.0849190i | ||||
\(435\) | −9.29475 | + | 21.6483i | −0.445649 | + | 1.03796i | ||||
\(436\) | −17.0972 | + | 10.2088i | −0.818807 | + | 0.488911i | ||||
\(437\) | 12.1453 | 0.580988 | ||||||||
\(438\) | −40.9327 | − | 5.08339i | −1.95584 | − | 0.242894i | ||||
\(439\) | 29.7712i | 1.42090i | 0.703747 | + | 0.710451i | \(0.251509\pi\) | ||||
−0.703747 | + | 0.710451i | \(0.748491\pi\) | |||||||
\(440\) | 20.9897 | − | 0.192632i | 1.00065 | − | 0.00918335i | ||||
\(441\) | 2.80723i | 0.133677i | ||||||||
\(442\) | 2.70362 | − | 21.7702i | 0.128598 | − | 1.03550i | ||||
\(443\) | 4.41389 | 0.209710 | 0.104855 | − | 0.994487i | \(-0.466562\pi\) | ||||
0.104855 | + | 0.994487i | \(0.466562\pi\) | |||||||
\(444\) | −54.7388 | − | 13.8089i | −2.59779 | − | 0.655341i | ||||
\(445\) | 10.2063 | − | 4.07471i | 0.483826 | − | 0.193160i | ||||
\(446\) | 0.732223 | − | 5.89603i | 0.0346718 | − | 0.279185i | ||||
\(447\) | 4.64897 | + | 4.64897i | 0.219889 | + | 0.219889i | ||||
\(448\) | −0.352363 | − | 7.99224i | −0.0166476 | − | 0.377598i | ||||
\(449\) | − | 5.13263i | − | 0.242224i | −0.992639 | − | 0.121112i | \(-0.961354\pi\) | ||
0.992639 | − | 0.121112i | \(-0.0386460\pi\) | |||||||
\(450\) | 2.95187 | − | 19.6294i | 0.139152 | − | 0.925338i | ||||
\(451\) | −28.6327 | − | 28.6327i | −1.34826 | − | 1.34826i | ||||
\(452\) | 14.6585 | − | 8.75262i | 0.689479 | − | 0.411689i | ||||
\(453\) | − | 19.4180i | − | 0.912336i | ||||||
\(454\) | 16.6351 | − | 12.9597i | 0.780723 | − | 0.608230i | ||||
\(455\) | 3.96050 | − | 9.22435i | 0.185671 | − | 0.432444i | ||||
\(456\) | −8.71709 | + | 22.4301i | −0.408215 | + | 1.05039i | ||||
\(457\) | −22.9695 | − | 22.9695i | −1.07447 | − | 1.07447i | −0.996994 | − | 0.0774759i | \(-0.975314\pi\) |
−0.0774759 | − | 0.996994i | \(-0.524686\pi\) | |||||||
\(458\) | 4.33823 | − | 34.9325i | 0.202712 | − | 1.63229i | ||||
\(459\) | 1.13501 | + | 1.13501i | 0.0529777 | + | 0.0529777i | ||||
\(460\) | 9.34294 | − | 12.2223i | 0.435617 | − | 0.569868i | ||||
\(461\) | −4.69983 | + | 4.69983i | −0.218893 | + | 0.218893i | −0.808032 | − | 0.589139i | \(-0.799467\pi\) |
0.589139 | + | 0.808032i | \(0.299467\pi\) | |||||||
\(462\) | 8.92268 | − | 6.95130i | 0.415120 | − | 0.323404i | ||||
\(463\) | −14.0202 | + | 14.0202i | −0.651575 | + | 0.651575i | −0.953372 | − | 0.301797i | \(-0.902413\pi\) |
0.301797 | + | 0.953372i | \(0.402413\pi\) | |||||||
\(464\) | −5.02052 | − | 16.7524i | −0.233072 | − | 0.777710i | ||||
\(465\) | −50.7961 | + | 20.2796i | −2.35561 | + | 0.940442i | ||||
\(466\) | 0.724284 | − | 5.83211i | 0.0335518 | − | 0.270167i | ||||
\(467\) | −8.90065 | −0.411873 | −0.205937 | − | 0.978565i | \(-0.566024\pi\) | ||||
−0.205937 | + | 0.978565i | \(0.566024\pi\) | |||||||
\(468\) | −6.16543 | + | 24.4399i | −0.284997 | + | 1.12974i | ||||
\(469\) | 5.69447 | − | 5.69447i | 0.262946 | − | 0.262946i | ||||
\(470\) | 9.25970 | − | 2.42653i | 0.427118 | − | 0.111928i | ||||
\(471\) | 24.4557 | 1.12686 | ||||||||
\(472\) | −6.82679 | + | 17.5662i | −0.314229 | + | 0.808548i | ||||
\(473\) | −4.25845 | + | 4.25845i | −0.195804 | + | 0.195804i | ||||
\(474\) | 3.10735 | + | 3.98858i | 0.142725 | + | 0.183202i | ||||
\(475\) | −0.453723 | + | 17.6471i | −0.0208183 | + | 0.809704i | ||||
\(476\) | −6.70062 | − | 1.69036i | −0.307122 | − | 0.0774773i | ||||
\(477\) | 12.0932i | 0.553709i | ||||||||
\(478\) | −32.0016 | + | 24.9312i | −1.46372 | + | 1.14032i | ||||
\(479\) | 27.9791 | 1.27840 | 0.639198 | − | 0.769042i | \(-0.279266\pi\) | ||||
0.639198 | + | 0.769042i | \(0.279266\pi\) | |||||||
\(480\) | 15.8666 | + | 26.0271i | 0.724208 | + | 1.18797i | ||||
\(481\) | 52.5857 | 2.39770 | ||||||||
\(482\) | −25.7530 | + | 20.0631i | −1.17301 | + | 0.913849i | ||||
\(483\) | − | 8.28983i | − | 0.377200i | ||||||
\(484\) | −0.0293490 | − | 0.00740383i | −0.00133404 | − | 0.000336538i | ||||
\(485\) | 12.0933 | − | 28.1664i | 0.549129 | − | 1.27897i | ||||
\(486\) | −18.7723 | − | 24.0960i | −0.851528 | − | 1.09302i | ||||
\(487\) | 27.6242 | − | 27.6242i | 1.25177 | − | 1.25177i | 0.296845 | − | 0.954926i | \(-0.404066\pi\) |
0.954926 | − | 0.296845i | \(-0.0959344\pi\) | |||||||
\(488\) | 11.0762 | + | 4.30457i | 0.501395 | + | 0.194859i | ||||
\(489\) | −37.1270 | −1.67894 | ||||||||
\(490\) | −2.72986 | − | 1.59620i | −0.123323 | − | 0.0721091i | ||||
\(491\) | 2.27238 | − | 2.27238i | 0.102551 | − | 0.102551i | −0.653970 | − | 0.756521i | \(-0.726898\pi\) |
0.756521 | + | 0.653970i | \(0.226898\pi\) | |||||||
\(492\) | 14.3834 | − | 57.0163i | 0.648455 | − | 2.57049i | ||||
\(493\) | −15.1069 | −0.680380 | ||||||||
\(494\) | 2.76256 | − | 22.2448i | 0.124293 | − | 1.00084i | ||||
\(495\) | −8.21926 | + | 19.1434i | −0.369428 | + | 0.860431i | ||||
\(496\) | 19.2590 | − | 35.7424i | 0.864756 | − | 1.60488i | ||||
\(497\) | 8.42208 | − | 8.42208i | 0.377782 | − | 0.377782i | ||||
\(498\) | 26.0985 | − | 20.3323i | 1.16950 | − | 0.911114i | ||||
\(499\) | 5.32226 | − | 5.32226i | 0.238257 | − | 0.238257i | −0.577871 | − | 0.816128i | \(-0.696116\pi\) |
0.816128 | + | 0.577871i | \(0.196116\pi\) | |||||||
\(500\) | 17.4100 | + | 14.0319i | 0.778597 | + | 0.627525i | ||||
\(501\) | 20.7300 | + | 20.7300i | 0.926149 | + | 0.926149i | ||||
\(502\) | −3.13736 | + | 25.2628i | −0.140027 | + | 1.12753i | ||||
\(503\) | 18.3430 | + | 18.3430i | 0.817873 | + | 0.817873i | 0.985800 | − | 0.167927i | \(-0.0537072\pi\) |
−0.167927 | + | 0.985800i | \(0.553707\pi\) | |||||||
\(504\) | 7.40079 | + | 2.87619i | 0.329657 | + | 0.128116i | ||||
\(505\) | −8.02675 | − | 3.44631i | −0.357186 | − | 0.153359i | ||||
\(506\) | −12.7371 | + | 9.92300i | −0.566235 | + | 0.441131i | ||||
\(507\) | − | 17.2418i | − | 0.765737i | ||||||
\(508\) | 21.2344 | − | 12.6791i | 0.942124 | − | 0.562543i | ||||
\(509\) | −17.9583 | − | 17.9583i | −0.795988 | − | 0.795988i | 0.186472 | − | 0.982460i | \(-0.440295\pi\) |
−0.982460 | + | 0.186472i | \(0.940295\pi\) | |||||||
\(510\) | 25.4709 | − | 6.67472i | 1.12787 | − | 0.295562i | ||||
\(511\) | − | 12.1030i | − | 0.535407i | ||||||
\(512\) | −21.4312 | − | 7.25964i | −0.947136 | − | 0.320834i | ||||
\(513\) | 1.15975 | + | 1.15975i | 0.0512042 | + | 0.0512042i | ||||
\(514\) | −2.54471 | + | 20.4907i | −0.112243 | + | 0.903804i | ||||
\(515\) | 7.38741 | + | 3.17180i | 0.325528 | + | 0.139766i | ||||
\(516\) | −8.47986 | − | 2.13920i | −0.373305 | − | 0.0941732i | ||||
\(517\) | −10.0465 | −0.441844 | ||||||||
\(518\) | 2.04152 | − | 16.4388i | 0.0896990 | − | 0.722278i | ||||
\(519\) | − | 19.4559i | − | 0.854020i | ||||||
\(520\) | −20.2607 | − | 19.8922i | −0.888489 | − | 0.872329i | ||||
\(521\) | − | 35.5533i | − | 1.55762i | −0.627262 | − | 0.778809i | \(-0.715824\pi\) | ||
0.627262 | − | 0.778809i | \(-0.284176\pi\) | |||||||
\(522\) | 17.2251 | + | 2.13917i | 0.753922 | + | 0.0936289i | ||||
\(523\) | 34.4599 | 1.50683 | 0.753414 | − | 0.657546i | \(-0.228406\pi\) | ||||
0.753414 | + | 0.657546i | \(0.228406\pi\) | |||||||
\(524\) | 3.26389 | − | 1.94887i | 0.142584 | − | 0.0851370i | ||||
\(525\) | 12.0451 | + | 0.309691i | 0.525692 | + | 0.0135160i | ||||
\(526\) | 7.92280 | + | 0.983925i | 0.345450 | + | 0.0429012i | ||||
\(527\) | −24.7995 | − | 24.7995i | −1.08028 | − | 1.08028i | ||||
\(528\) | −9.18408 | − | 30.6452i | −0.399686 | − | 1.33366i | ||||
\(529\) | − | 11.1662i | − | 0.485489i | ||||||
\(530\) | −11.7599 | − | 6.87624i | −0.510817 | − | 0.298685i | ||||
\(531\) | −13.2263 | − | 13.2263i | −0.573973 | − | 0.573973i | ||||
\(532\) | −6.84667 | − | 1.72720i | −0.296841 | − | 0.0748837i | ||||
\(533\) | 54.7736i | 2.37251i | ||||||||
\(534\) | −10.2937 | − | 13.2129i | −0.445450 | − | 0.571779i | ||||
\(535\) | −4.95796 | − | 12.4187i | −0.214351 | − | 0.536906i | ||||
\(536\) | −9.17816 | − | 20.8469i | −0.396436 | − | 0.900449i | ||||
\(537\) | 26.2494 | + | 26.2494i | 1.13275 | + | 1.13275i | ||||
\(538\) | −28.4669 | − | 3.53527i | −1.22729 | − | 0.152416i | ||||
\(539\) | 2.34682 | + | 2.34682i | 0.101085 | + | 0.101085i | ||||
\(540\) | 2.05926 | − | 0.274949i | 0.0886162 | − | 0.0118319i | ||||
\(541\) | −8.37193 | + | 8.37193i | −0.359938 | + | 0.359938i | −0.863790 | − | 0.503852i | \(-0.831916\pi\) |
0.503852 | + | 0.863790i | \(0.331916\pi\) | |||||||
\(542\) | 13.2211 | + | 16.9706i | 0.567894 | + | 0.728948i | ||||
\(543\) | −30.2478 | + | 30.2478i | −1.29806 | + | 1.29806i | ||||
\(544\) | −11.3216 | + | 15.9332i | −0.485409 | + | 0.683130i | ||||
\(545\) | 20.4576 | + | 8.78355i | 0.876309 | + | 0.376246i | ||||
\(546\) | −15.1833 | − | 1.88560i | −0.649784 | − | 0.0806961i | ||||
\(547\) | −26.3514 | −1.12670 | −0.563352 | − | 0.826217i | \(-0.690488\pi\) | ||||
−0.563352 | + | 0.826217i | \(0.690488\pi\) | |||||||
\(548\) | 1.42207 | − | 0.849118i | 0.0607477 | − | 0.0362725i | ||||
\(549\) | −8.33972 | + | 8.33972i | −0.355931 | + | 0.355931i | ||||
\(550\) | −13.9423 | − | 18.8778i | −0.594501 | − | 0.804950i | ||||
\(551\) | −15.4362 | −0.657603 | ||||||||
\(552\) | −21.8548 | − | 8.49349i | −0.930201 | − | 0.361507i | ||||
\(553\) | −1.04907 | + | 1.04907i | −0.0446109 | + | 0.0446109i | ||||
\(554\) | −26.4897 | + | 20.6371i | −1.12544 | + | 0.876785i | ||||
\(555\) | 23.4024 | + | 58.6182i | 0.993378 | + | 2.48821i | ||||
\(556\) | −15.1463 | + | 9.04388i | −0.642347 | + | 0.383546i | ||||
\(557\) | 31.2312i | 1.32331i | 0.749809 | + | 0.661655i | \(0.230146\pi\) | ||||
−0.749809 | + | 0.661655i | \(0.769854\pi\) | |||||||
\(558\) | 24.7651 | + | 31.7884i | 1.04839 | + | 1.34571i | ||||
\(559\) | 8.14631 | 0.344552 | ||||||||
\(560\) | −7.00505 | + | 5.56141i | −0.296017 | + | 0.235012i | ||||
\(561\) | −27.6351 | −1.16676 | ||||||||
\(562\) | 6.80580 | + | 8.73591i | 0.287085 | + | 0.368502i | ||||
\(563\) | 2.59760i | 0.109476i | 0.998501 | + | 0.0547380i | \(0.0174324\pi\) | ||||
−0.998501 | + | 0.0547380i | \(0.982568\pi\) | |||||||
\(564\) | −7.47940 | − | 12.5262i | −0.314940 | − | 0.527448i | ||||
\(565\) | −17.5397 | − | 7.53070i | −0.737899 | − | 0.316819i | ||||
\(566\) | 18.5115 | − | 14.4216i | 0.778096 | − | 0.606184i | ||||
\(567\) | 6.74662 | − | 6.74662i | 0.283331 | − | 0.283331i | ||||
\(568\) | −13.5744 | − | 30.8324i | −0.569570 | − | 1.29370i | ||||
\(569\) | 32.1881 | 1.34940 | 0.674698 | − | 0.738094i | \(-0.264274\pi\) | ||||
0.674698 | + | 0.738094i | \(0.264274\pi\) | |||||||
\(570\) | 26.0261 | − | 6.82021i | 1.09011 | − | 0.285667i | ||||
\(571\) | −3.12862 | + | 3.12862i | −0.130929 | + | 0.130929i | −0.769534 | − | 0.638606i | \(-0.779512\pi\) |
0.638606 | + | 0.769534i | \(0.279512\pi\) | |||||||
\(572\) | 15.2773 | + | 25.5858i | 0.638778 | + | 1.06980i | ||||
\(573\) | −23.7121 | −0.990588 | ||||||||
\(574\) | 17.1227 | + | 2.12646i | 0.714690 | + | 0.0887566i | ||||
\(575\) | −17.1944 | − | 0.442085i | −0.717057 | − | 0.0184362i | ||||
\(576\) | 15.1652 | − | 16.5641i | 0.631884 | − | 0.690171i | ||||
\(577\) | −19.6591 | + | 19.6591i | −0.818419 | + | 0.818419i | −0.985879 | − | 0.167460i | \(-0.946444\pi\) |
0.167460 | + | 0.985879i | \(0.446444\pi\) | |||||||
\(578\) | −4.39879 | − | 5.64627i | −0.182965 | − | 0.234854i | ||||
\(579\) | −16.2622 | + | 16.2622i | −0.675834 | + | 0.675834i | ||||
\(580\) | −11.8745 | + | 15.5340i | −0.493062 | + | 0.645016i | ||||
\(581\) | 6.86438 | + | 6.86438i | 0.284782 | + | 0.284782i | ||||
\(582\) | −46.3619 | − | 5.75763i | −1.92176 | − | 0.238662i | ||||
\(583\) | 10.1098 | + | 10.1098i | 0.418706 | + | 0.418706i | ||||
\(584\) | −31.9077 | − | 12.4004i | −1.32035 | − | 0.513131i | ||||
\(585\) | 26.1720 | − | 10.4488i | 1.08208 | − | 0.432004i | ||||
\(586\) | 5.94144 | + | 7.62642i | 0.245439 | + | 0.315044i | ||||
\(587\) | − | 23.2725i | − | 0.960559i | −0.877115 | − | 0.480280i | \(-0.840535\pi\) | ||
0.877115 | − | 0.480280i | \(-0.159465\pi\) | |||||||
\(588\) | −1.17891 | + | 4.67323i | −0.0486174 | + | 0.192721i | ||||
\(589\) | −25.3400 | − | 25.3400i | −1.04412 | − | 1.04412i | ||||
\(590\) | 20.3823 | − | 5.34125i | 0.839127 | − | 0.219896i | ||||
\(591\) | − | 28.5619i | − | 1.17488i | ||||||
\(592\) | −41.2464 | − | 22.2248i | −1.69522 | − | 0.913432i | ||||
\(593\) | −32.5472 | − | 32.5472i | −1.33655 | − | 1.33655i | −0.899376 | − | 0.437176i | \(-0.855979\pi\) |
−0.437176 | − | 0.899376i | \(-0.644021\pi\) | |||||||
\(594\) | −2.16381 | − | 0.268721i | −0.0887821 | − | 0.0110258i | ||||
\(595\) | 2.86471 | + | 7.17550i | 0.117442 | + | 0.294167i | ||||
\(596\) | 2.79737 | + | 4.68493i | 0.114585 | + | 0.191902i | ||||
\(597\) | 24.8706 | 1.01789 | ||||||||
\(598\) | 21.6742 | + | 2.69169i | 0.886322 | + | 0.110072i | ||||
\(599\) | 40.6659i | 1.66156i | 0.556599 | + | 0.830781i | \(0.312106\pi\) | ||||
−0.556599 | + | 0.830781i | \(0.687894\pi\) | |||||||
\(600\) | 13.1575 | − | 31.4377i | 0.537152 | − | 1.28344i | ||||
\(601\) | − | 1.52717i | − | 0.0622944i | −0.999515 | − | 0.0311472i | \(-0.990084\pi\) | ||
0.999515 | − | 0.0311472i | \(-0.00991607\pi\) | |||||||
\(602\) | 0.316261 | − | 2.54661i | 0.0128899 | − | 0.103792i | ||||
\(603\) | 22.6072 | 0.920635 | ||||||||
\(604\) | 3.94199 | − | 15.6262i | 0.160397 | − | 0.635819i | ||||
\(605\) | 0.0125475 | + | 0.0314290i | 0.000510130 | + | 0.00127777i | ||||
\(606\) | −1.64079 | + | 13.2120i | −0.0666525 | + | 0.536702i | ||||
\(607\) | 21.9476 | + | 21.9476i | 0.890825 | + | 0.890825i | 0.994601 | − | 0.103776i | \(-0.0330924\pi\) |
−0.103776 | + | 0.994601i | \(0.533092\pi\) | |||||||
\(608\) | −11.5684 | + | 16.2805i | −0.469159 | + | 0.660261i | ||||
\(609\) | 10.5360i | 0.426942i | ||||||||
\(610\) | −3.36787 | − | 12.8519i | −0.136361 | − | 0.520358i | ||||
\(611\) | 9.60935 | + | 9.60935i | 0.388753 | + | 0.388753i | ||||
\(612\) | −9.94541 | − | 16.6562i | −0.402019 | − | 0.673285i | ||||
\(613\) | − | 42.3381i | − | 1.71002i | −0.518612 | − | 0.855010i | \(-0.673551\pi\) | ||
0.518612 | − | 0.855010i | \(-0.326449\pi\) | |||||||
\(614\) | −0.309043 | + | 0.240763i | −0.0124720 | + | 0.00971642i | ||||
\(615\) | −61.0572 | + | 24.3761i | −2.46206 | + | 0.982941i | ||||
\(616\) | 8.59148 | − | 3.78253i | 0.346161 | − | 0.152402i | ||||
\(617\) | 14.4092 | + | 14.4092i | 0.580093 | + | 0.580093i | 0.934929 | − | 0.354836i | \(-0.115463\pi\) |
−0.354836 | + | 0.934929i | \(0.615463\pi\) | |||||||
\(618\) | 1.51010 | − | 12.1597i | 0.0607451 | − | 0.489134i | ||||
\(619\) | 14.6752 | + | 14.6752i | 0.589846 | + | 0.589846i | 0.937590 | − | 0.347744i | \(-0.113052\pi\) |
−0.347744 | + | 0.937590i | \(0.613052\pi\) | |||||||
\(620\) | −44.9938 | + | 6.00752i | −1.80700 | + | 0.241268i | ||||
\(621\) | −1.13000 | + | 1.13000i | −0.0453453 | + | 0.0453453i | ||||
\(622\) | 17.4651 | − | 13.6064i | 0.700287 | − | 0.545566i | ||||
\(623\) | 3.47523 | − | 3.47523i | 0.139232 | − | 0.139232i | ||||
\(624\) | −20.5274 | + | 38.0963i | −0.821752 | + | 1.52507i | ||||
\(625\) | 1.28470 | − | 24.9670i | 0.0513879 | − | 0.998679i | ||||
\(626\) | −4.87445 | + | 39.2502i | −0.194822 | + | 1.56875i | ||||
\(627\) | −28.2375 | −1.12770 | ||||||||
\(628\) | 19.6802 | + | 4.96469i | 0.785324 | + | 0.198113i | ||||
\(629\) | −28.6184 | + | 28.6184i | −1.14109 | + | 1.14109i | ||||
\(630\) | −2.25032 | − | 8.58727i | −0.0896549 | − | 0.342125i | ||||
\(631\) | 19.0148 | 0.756969 | 0.378485 | − | 0.925608i | \(-0.376445\pi\) | ||||
0.378485 | + | 0.925608i | \(0.376445\pi\) | |||||||
\(632\) | 1.69085 | + | 3.84053i | 0.0672585 | + | 0.152768i | ||||
\(633\) | 9.93142 | − | 9.93142i | 0.394739 | − | 0.394739i | ||||
\(634\) | −15.6666 | − | 20.1096i | −0.622200 | − | 0.798655i | ||||
\(635\) | −25.4080 | − | 10.9090i | −1.00829 | − | 0.432911i | ||||
\(636\) | −5.07860 | + | 20.1317i | −0.201379 | + | 0.798273i | ||||
\(637\) | − | 4.48941i | − | 0.177877i | ||||||
\(638\) | 16.1884 | − | 12.6117i | 0.640905 | − | 0.499303i | ||||
\(639\) | 33.4358 | 1.32270 | ||||||||
\(640\) | 7.48459 | + | 24.1657i | 0.295854 | + | 0.955233i | ||||
\(641\) | −34.9937 | −1.38217 | −0.691084 | − | 0.722774i | \(-0.742867\pi\) | ||||
−0.691084 | + | 0.722774i | \(0.742867\pi\) | |||||||
\(642\) | −16.0770 | + | 12.5249i | −0.634508 | + | 0.494320i | ||||
\(643\) | − | 7.16531i | − | 0.282572i | −0.989969 | − | 0.141286i | \(-0.954876\pi\) | ||
0.989969 | − | 0.141286i | \(-0.0451237\pi\) | |||||||
\(644\) | 1.68290 | − | 6.67105i | 0.0663154 | − | 0.262876i | ||||
\(645\) | 3.62539 | + | 9.08085i | 0.142750 | + | 0.357558i | ||||
\(646\) | 10.6027 | + | 13.6096i | 0.417157 | + | 0.535461i | ||||
\(647\) | 12.7344 | − | 12.7344i | 0.500639 | − | 0.500639i | −0.410997 | − | 0.911637i | \(-0.634819\pi\) |
0.911637 | + | 0.410997i | \(0.134819\pi\) | |||||||
\(648\) | −10.8740 | − | 24.6987i | −0.427170 | − | 0.970257i | ||||
\(649\) | −22.1142 | −0.868058 | ||||||||
\(650\) | −4.72073 | + | 31.3920i | −0.185162 | + | 1.23129i | ||||
\(651\) | −17.2960 | + | 17.2960i | −0.677882 | + | 0.677882i | ||||
\(652\) | −29.8771 | − | 7.53705i | −1.17008 | − | 0.295174i | ||||
\(653\) | −24.1866 | −0.946497 | −0.473248 | − | 0.880929i | \(-0.656919\pi\) | ||||
−0.473248 | + | 0.880929i | \(0.656919\pi\) | |||||||
\(654\) | 4.18185 | − | 33.6733i | 0.163523 | − | 1.31673i | ||||
\(655\) | −3.90541 | − | 1.67680i | −0.152597 | − | 0.0655179i | ||||
\(656\) | 23.1495 | − | 42.9626i | 0.903835 | − | 1.67741i | ||||
\(657\) | 24.0246 | − | 24.0246i | 0.937290 | − | 0.937290i | ||||
\(658\) | 3.37703 | − | 2.63091i | 0.131650 | − | 0.102564i | ||||
\(659\) | 0.529989 | − | 0.529989i | 0.0206454 | − | 0.0206454i | −0.696709 | − | 0.717354i | \(-0.745353\pi\) |
0.717354 | + | 0.696709i | \(0.245353\pi\) | |||||||
\(660\) | −21.7221 | + | 28.4165i | −0.845531 | + | 1.10611i | ||||
\(661\) | 21.1546 | + | 21.1546i | 0.822818 | + | 0.822818i | 0.986511 | − | 0.163693i | \(-0.0523408\pi\) |
−0.163693 | + | 0.986511i | \(0.552341\pi\) | |||||||
\(662\) | 3.58345 | − | 28.8548i | 0.139275 | − | 1.12147i | ||||
\(663\) | 26.4327 | + | 26.4327i | 1.02656 | + | 1.02656i | ||||
\(664\) | 25.1298 | − | 11.0638i | 0.975226 | − | 0.429358i | ||||
\(665\) | 2.92715 | + | 7.33191i | 0.113510 | + | 0.284319i | ||||
\(666\) | 36.6835 | − | 28.5787i | 1.42146 | − | 1.10740i | ||||
\(667\) | − | 15.0402i | − | 0.582360i | ||||||
\(668\) | 12.4737 | + | 20.8904i | 0.482620 | + | 0.808272i | ||||
\(669\) | 7.15876 | + | 7.15876i | 0.276774 | + | 0.276774i | ||||
\(670\) | −12.8545 | + | 21.9841i | −0.496614 | + | 0.849320i | ||||
\(671\) | 13.9439i | 0.538298i | ||||||||
\(672\) | 11.1123 | + | 7.89604i | 0.428667 | + | 0.304596i | ||||
\(673\) | 2.40011 | + | 2.40011i | 0.0925176 | + | 0.0925176i | 0.751851 | − | 0.659333i | \(-0.229161\pi\) |
−0.659333 | + | 0.751851i | \(0.729161\pi\) | |||||||
\(674\) | −2.49855 | + | 20.1189i | −0.0962405 | + | 0.774952i | ||||
\(675\) | −1.59967 | − | 1.68410i | −0.0615715 | − | 0.0648212i | ||||
\(676\) | 3.50022 | − | 13.8750i | 0.134624 | − | 0.533653i | ||||
\(677\) | −31.1344 | −1.19659 | −0.598296 | − | 0.801275i | \(-0.704155\pi\) | ||||
−0.598296 | + | 0.801275i | \(0.704155\pi\) | |||||||
\(678\) | −3.58537 | + | 28.8703i | −0.137695 | + | 1.10876i | ||||
\(679\) | − | 13.7083i | − | 0.526078i | ||||||
\(680\) | 21.8521 | − | 0.200546i | 0.837991 | − | 0.00769060i | ||||
\(681\) | 35.9330i | 1.37695i | ||||||||
\(682\) | 47.2783 | + | 5.87144i | 1.81038 | + | 0.224829i | ||||
\(683\) | 5.20104 | 0.199012 | 0.0995061 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995061 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(684\) | −10.1622 | − | 17.0192i | −0.388561 | − | 0.650746i | ||||
\(685\) | −1.70157 | − | 0.730575i | −0.0650138 | − | 0.0279138i | ||||
\(686\) | −1.40343 | − | 0.174291i | −0.0535833 | − | 0.00665446i | ||||
\(687\) | 42.4138 | + | 42.4138i | 1.61819 | + | 1.61819i | ||||
\(688\) | −6.38969 | − | 3.44295i | −0.243605 | − | 0.131261i | ||||
\(689\) | − | 19.3398i | − | 0.736789i | ||||||
\(690\) | 6.64527 | + | 25.3585i | 0.252981 | + | 0.965381i | ||||
\(691\) | 29.4509 | + | 29.4509i | 1.12036 | + | 1.12036i | 0.991687 | + | 0.128677i | \(0.0410730\pi\) |
0.128677 | + | 0.991687i | \(0.458927\pi\) | |||||||
\(692\) | 3.94970 | − | 15.6567i | 0.150145 | − | 0.595178i | ||||
\(693\) | 9.31692i | 0.353920i | ||||||||
\(694\) | −7.05144 | − | 9.05122i | −0.267669 | − | 0.343580i | ||||
\(695\) | 18.1233 | + | 7.78130i | 0.687457 | + | 0.295161i | ||||
\(696\) | 27.7765 | + | 10.7949i | 1.05287 | + | 0.409179i | ||||
\(697\) | −29.8091 | − | 29.8091i | −1.12910 | − | 1.12910i | ||||
\(698\) | −28.9526 | − | 3.59559i | −1.09587 | − | 0.136095i | ||||
\(699\) | 7.08114 | + | 7.08114i | 0.267833 | + | 0.267833i | ||||
\(700\) | 9.63015 | + | 2.69446i | 0.363986 | + | 0.101841i | ||||
\(701\) | 16.8941 | − | 16.8941i | 0.638082 | − | 0.638082i | −0.312000 | − | 0.950082i | \(-0.600999\pi\) |
0.950082 | + | 0.312000i | \(0.100999\pi\) | |||||||
\(702\) | 1.81263 | + | 2.32669i | 0.0684132 | + | 0.0878151i | ||||
\(703\) | −29.2422 | + | 29.2422i | −1.10289 | + | 1.10289i | ||||
\(704\) | −1.16946 | − | 26.5255i | −0.0440757 | − | 0.999717i | ||||
\(705\) | −6.43523 | + | 14.9882i | −0.242365 | + | 0.564489i | ||||
\(706\) | 34.0410 | + | 4.22752i | 1.28115 | + | 0.159105i | ||||
\(707\) | −3.90655 | −0.146921 | ||||||||
\(708\) | −16.4636 | − | 27.5725i | −0.618738 | − | 1.03624i | ||||
\(709\) | 5.13449 | − | 5.13449i | 0.192830 | − | 0.192830i | −0.604088 | − | 0.796918i | \(-0.706462\pi\) |
0.796918 | + | 0.604088i | \(0.206462\pi\) | |||||||
\(710\) | −19.0118 | + | 32.5143i | −0.713498 | + | 1.22024i | ||||
\(711\) | −4.16482 | −0.156193 | ||||||||
\(712\) | −5.60126 | − | 12.7225i | −0.209916 | − | 0.476795i | ||||
\(713\) | 24.6900 | − | 24.6900i | 0.924648 | − | 0.924648i | ||||
\(714\) | 9.28928 | − | 7.23691i | 0.347643 | − | 0.270835i | ||||
\(715\) | 13.1445 | − | 30.6147i | 0.491577 | − | 1.14493i | ||||
\(716\) | 15.7948 | + | 26.4524i | 0.590278 | + | 0.988574i | ||||
\(717\) | − | 69.1258i | − | 2.58155i | ||||||
\(718\) | 22.0069 | + | 28.2480i | 0.821291 | + | 1.05421i | ||||
\(719\) | 21.5817 | 0.804860 | 0.402430 | − | 0.915451i | \(-0.368166\pi\) | ||||
0.402430 | + | 0.915451i | \(0.368166\pi\) | |||||||
\(720\) | −24.9445 | − | 2.86564i | −0.929628 | − | 0.106796i | ||||
\(721\) | 3.59539 | 0.133899 | ||||||||
\(722\) | −5.67977 | − | 7.29054i | −0.211379 | − | 0.271326i | ||||
\(723\) | − | 55.6283i | − | 2.06884i | ||||||
\(724\) | −30.4817 | + | 18.2007i | −1.13284 | + | 0.676422i | ||||
\(725\) | 21.8534 | + | 0.561872i | 0.811616 | + | 0.0208674i | ||||
\(726\) | 0.0406874 | − | 0.0316980i | 0.00151005 | − | 0.00117642i | ||||
\(727\) | −24.6504 | + | 24.6504i | −0.914233 | + | 0.914233i | −0.996602 | − | 0.0823689i | \(-0.973751\pi\) |
0.0823689 | + | 0.996602i | \(0.473751\pi\) | |||||||
\(728\) | −11.8356 | − | 4.59971i | −0.438656 | − | 0.170476i | ||||
\(729\) | 23.4258 | 0.867620 | ||||||||
\(730\) | 9.70200 | + | 37.0231i | 0.359087 | + | 1.37028i | ||||
\(731\) | −4.43341 | + | 4.43341i | −0.163976 | + | 0.163976i | ||||
\(732\) | −17.3856 | + | 10.3809i | −0.642589 | + | 0.383691i | ||||
\(733\) | −8.49140 | −0.313637 | −0.156819 | − | 0.987627i | \(-0.550124\pi\) | ||||
−0.156819 | + | 0.987627i | \(0.550124\pi\) | |||||||
\(734\) | 24.8270 | + | 3.08324i | 0.916382 | + | 0.113805i | ||||
\(735\) | 5.00443 | − | 1.99794i | 0.184591 | − | 0.0736953i | ||||
\(736\) | −15.8629 | − | 11.2716i | −0.584713 | − | 0.415477i | ||||
\(737\) | 18.8994 | − | 18.8994i | 0.696169 | − | 0.696169i | ||||
\(738\) | 29.7678 | + | 38.2098i | 1.09577 | + | 1.40652i | ||||
\(739\) | 20.8443 | − | 20.8443i | 0.766770 | − | 0.766770i | −0.210766 | − | 0.977537i | \(-0.567596\pi\) |
0.977537 | + | 0.210766i | \(0.0675958\pi\) | |||||||
\(740\) | 6.93263 | + | 51.9225i | 0.254848 | + | 1.90871i | ||||
\(741\) | 27.0088 | + | 27.0088i | 0.992194 | + | 0.992194i | ||||
\(742\) | −6.04581 | − | 0.750824i | −0.221949 | − | 0.0275636i | ||||
\(743\) | 29.0367 | + | 29.0367i | 1.06525 | + | 1.06525i | 0.997717 | + | 0.0675365i | \(0.0215139\pi\) |
0.0675365 | + | 0.997717i | \(0.478486\pi\) | |||||||
\(744\) | 27.8771 | + | 63.3188i | 1.02202 | + | 2.32138i | ||||
\(745\) | 2.40684 | − | 5.60575i | 0.0881799 | − | 0.205379i | ||||
\(746\) | 16.8801 | + | 21.6673i | 0.618026 | + | 0.793297i | ||||
\(747\) | 27.2517i | 0.997087i | ||||||||
\(748\) | −22.2387 | − | 5.61013i | −0.813128 | − | 0.205127i | ||||
\(749\) | −4.22853 | − | 4.22853i | −0.154507 | − | 0.154507i | ||||
\(750\) | −37.0941 | + | 8.70822i | −1.35449 | + | 0.317979i | ||||
\(751\) | 25.2691i | 0.922081i | 0.887379 | + | 0.461041i | \(0.152524\pi\) | ||||
−0.887379 | + | 0.461041i | \(0.847476\pi\) | |||||||
\(752\) | −3.47597 | − | 11.5985i | −0.126755 | − | 0.422955i | ||||
\(753\) | −30.6732 | − | 30.6732i | −1.11779 | − | 1.11779i | ||||
\(754\) | −27.5470 | − | 3.42103i | −1.00320 | − | 0.124587i | ||||
\(755\) | −16.7336 | + | 6.68064i | −0.608999 | + | 0.243134i | ||||
\(756\) | 0.797715 | − | 0.476316i | 0.0290126 | − | 0.0173235i | ||||
\(757\) | 6.06652 | 0.220491 | 0.110246 | − | 0.993904i | \(-0.464836\pi\) | ||||
0.110246 | + | 0.993904i | \(0.464836\pi\) | |||||||
\(758\) | −11.0021 | − | 1.36634i | −0.399615 | − | 0.0496278i | ||||
\(759\) | − | 27.5132i | − | 0.998665i | ||||||
\(760\) | 22.3284 | − | 0.204918i | 0.809938 | − | 0.00743314i | ||||
\(761\) | 42.5121i | 1.54106i | 0.637402 | + | 0.770532i | \(0.280009\pi\) | ||||
−0.637402 | + | 0.770532i | \(0.719991\pi\) | |||||||
\(762\) | −5.19378 | + | 41.8216i | −0.188151 | + | 1.51504i | ||||
\(763\) | 9.95656 | 0.360452 | ||||||||
\(764\) | −19.0818 | − | 4.81374i | −0.690355 | − | 0.174155i | ||||
\(765\) | −8.55696 | + | 19.9299i | −0.309378 | + | 0.720568i | ||||
\(766\) | 2.18039 | − | 17.5570i | 0.0787806 | − | 0.634360i | ||||
\(767\) | 21.1520 | + | 21.1520i | 0.763753 | + | 0.763753i | ||||
\(768\) | 32.2019 | − | 21.2058i | 1.16199 | − | 0.765198i | ||||
\(769\) | 14.1317i | 0.509603i | 0.966993 | + | 0.254802i | \(0.0820102\pi\) | ||||
−0.966993 | + | 0.254802i | \(0.917990\pi\) | |||||||
\(770\) | −9.06015 | − | 5.29765i | −0.326505 | − | 0.190914i | ||||
\(771\) | −24.8790 | − | 24.8790i | −0.895997 | − | 0.895997i | ||||
\(772\) | −16.3880 | + | 9.78528i | −0.589816 | + | 0.352180i | ||||
\(773\) | − | 35.8287i | − | 1.28867i | −0.764744 | − | 0.644334i | \(-0.777135\pi\) | ||
0.764744 | − | 0.644334i | \(-0.222865\pi\) | |||||||
\(774\) | 5.68283 | − | 4.42727i | 0.204265 | − | 0.159135i | ||||
\(775\) | 34.9522 | + | 36.7969i | 1.25552 | + | 1.32178i | ||||
\(776\) | −36.1398 | − | 14.0451i | −1.29734 | − | 0.504190i | ||||
\(777\) | 19.9594 | + | 19.9594i | 0.716039 | + | 0.716039i | ||||
\(778\) | −4.88979 | + | 39.3737i | −0.175307 | + | 1.41162i | ||||
\(779\) | −30.4589 | − | 30.4589i | −1.09130 | − | 1.09130i | ||||
\(780\) | 47.9570 | − | 6.40315i | 1.71714 | − | 0.229270i | ||||
\(781\) | 27.9521 | − | 27.9521i | 1.00020 | − | 1.00020i | ||||
\(782\) | −13.2605 | + | 10.3307i | −0.474194 | + | 0.369425i | ||||
\(783\) | 1.43618 | − | 1.43618i | 0.0513250 | − | 0.0513250i | ||||
\(784\) | −1.89740 | + | 3.52135i | −0.0677643 | + | 0.125762i | ||||
\(785\) | −8.41385 | − | 21.0749i | −0.300303 | − | 0.752197i | ||||
\(786\) | −0.798325 | + | 6.42830i | −0.0284753 | + | 0.229290i | ||||
\(787\) | 16.0687 | 0.572789 | 0.286394 | − | 0.958112i | \(-0.407543\pi\) | ||||
0.286394 | + | 0.958112i | \(0.407543\pi\) | |||||||
\(788\) | 5.79828 | − | 22.9845i | 0.206555 | − | 0.818791i | ||||
\(789\) | −9.61959 | + | 9.61959i | −0.342466 | + | 0.342466i | ||||
\(790\) | 2.36814 | − | 4.05004i | 0.0842545 | − | 0.144094i | ||||
\(791\) | −8.53640 | −0.303520 | ||||||||
\(792\) | 24.5625 | + | 9.54581i | 0.872791 | + | 0.339196i | ||||
\(793\) | 13.3372 | − | 13.3372i | 0.473617 | − | 0.473617i | ||||
\(794\) | −3.40922 | − | 4.37607i | −0.120989 | − | 0.155301i | ||||
\(795\) | 21.5585 | − | 8.60689i | 0.764600 | − | 0.305255i | ||||
\(796\) | 20.0140 | + | 5.04891i | 0.709378 | + | 0.178954i | ||||
\(797\) | 0.960275i | 0.0340147i | 0.999855 | + | 0.0170073i | \(0.00541387\pi\) | ||||
−0.999855 | + | 0.0170073i | \(0.994586\pi\) | |||||||
\(798\) | 9.49176 | − | 7.39465i | 0.336005 | − | 0.261768i | ||||
\(799\) | −10.4593 | −0.370022 | ||||||||
\(800\) | 16.9703 | − | 22.6276i | 0.599989 | − | 0.800008i | ||||
\(801\) | 13.7967 | 0.487483 | ||||||||
\(802\) | −4.07467 | + | 3.17441i | −0.143882 | + | 0.112092i | ||||
\(803\) | − | 40.1688i | − | 1.41753i | ||||||
\(804\) | 37.6345 | + | 9.49400i | 1.32726 | + | 0.334828i | ||||
\(805\) | −7.14384 | + | 2.85207i | −0.251787 | + | 0.100522i | ||||
\(806\) | −39.6051 | − | 50.8371i | −1.39503 | − | 1.79066i | ||||
\(807\) | 34.5635 | − | 34.5635i | 1.21669 | − | 1.21669i | ||||
\(808\) | −4.00253 | + | 10.2990i | −0.140808 | + | 0.362317i | ||||
\(809\) | −36.4907 | −1.28295 | −0.641473 | − | 0.767146i | \(-0.721676\pi\) | ||||
−0.641473 | + | 0.767146i | \(0.721676\pi\) | |||||||
\(810\) | −15.2296 | + | 26.0460i | −0.535114 | + | 0.915164i | ||||
\(811\) | −38.9206 | + | 38.9206i | −1.36669 | + | 1.36669i | −0.501571 | + | 0.865117i | \(0.667244\pi\) |
−0.865117 | + | 0.501571i | \(0.832756\pi\) | |||||||
\(812\) | −2.13889 | + | 8.47863i | −0.0750605 | + | 0.297542i | ||||
\(813\) | −36.6577 | −1.28564 | ||||||||
\(814\) | 6.77560 | − | 54.5587i | 0.237485 | − | 1.91228i | ||||
\(815\) | 12.7733 | + | 31.9945i | 0.447430 | + | 1.12072i | ||||
\(816\) | −9.56142 | − | 31.9044i | −0.334717 | − | 1.11688i | ||||
\(817\) | −4.53005 | + | 4.53005i | −0.158486 | + | 0.158486i | ||||
\(818\) | 5.87300 | − | 4.57542i | 0.205345 | − | 0.159976i | ||||
\(819\) | 8.91152 | − | 8.91152i | 0.311394 | − | 0.311394i | ||||
\(820\) | −54.0829 | + | 7.22107i | −1.88866 | + | 0.252171i | ||||
\(821\) | −26.5392 | − | 26.5392i | −0.926224 | − | 0.926224i | 0.0712358 | − | 0.997460i | \(-0.477306\pi\) |
−0.997460 | + | 0.0712358i | \(0.977306\pi\) | |||||||
\(822\) | −0.347827 | + | 2.80079i | −0.0121319 | + | 0.0976887i | ||||
\(823\) | 33.6422 | + | 33.6422i | 1.17269 | + | 1.17269i | 0.981565 | + | 0.191129i | \(0.0612149\pi\) |
0.191129 | + | 0.981565i | \(0.438785\pi\) | |||||||
\(824\) | 3.68372 | − | 9.47865i | 0.128328 | − | 0.330205i | ||||
\(825\) | 39.9766 | + | 1.02784i | 1.39181 | + | 0.0357846i | ||||
\(826\) | 7.43348 | − | 5.79113i | 0.258644 | − | 0.201499i | ||||
\(827\) | − | 55.9964i | − | 1.94719i | −0.228291 | − | 0.973593i | \(-0.573314\pi\) | ||
0.228291 | − | 0.973593i | \(-0.426686\pi\) | |||||||
\(828\) | 16.5827 | − | 9.90152i | 0.576287 | − | 0.344102i | ||||
\(829\) | 26.6012 | + | 26.6012i | 0.923897 | + | 0.923897i | 0.997302 | − | 0.0734049i | \(-0.0233865\pi\) |
−0.0734049 | + | 0.997302i | \(0.523387\pi\) | |||||||
\(830\) | −26.5006 | − | 15.4954i | −0.919851 | − | 0.537855i | ||||
\(831\) | − | 57.2197i | − | 1.98493i | ||||||
\(832\) | −24.2527 | + | 26.4899i | −0.840812 | + | 0.918371i | ||||
\(833\) | 2.44324 | + | 2.44324i | 0.0846534 | + | 0.0846534i | ||||
\(834\) | 3.70468 | − | 29.8310i | 0.128283 | − | 1.03296i | ||||
\(835\) | 10.7323 | − | 24.9964i | 0.371405 | − | 0.865035i | ||||
\(836\) | −22.7235 | − | 5.73242i | −0.785907 | − | 0.198260i | ||||
\(837\) | 4.71528 | 0.162984 | ||||||||
\(838\) | −4.02187 | + | 32.3851i | −0.138933 | + | 1.11872i | ||||
\(839\) | − | 39.9065i | − | 1.37773i | −0.724892 | − | 0.688863i | \(-0.758110\pi\) | ||
0.724892 | − | 0.688863i | \(-0.241890\pi\) | |||||||
\(840\) | −0.139868 | − | 15.2404i | −0.00482589 | − | 0.525843i | ||||
\(841\) | − | 9.88449i | − | 0.340845i | ||||||
\(842\) | −8.02937 | − | 0.997159i | −0.276710 | − | 0.0343644i | ||||
\(843\) | −18.8702 | −0.649924 | ||||||||
\(844\) | 10.0082 | − | 5.97593i | 0.344498 | − | 0.205700i | ||||
\(845\) | −14.8583 | + | 5.93196i | −0.511142 | + | 0.204066i | ||||
\(846\) | 11.9258 | + | 1.48106i | 0.410018 | + | 0.0509198i | ||||
\(847\) | 0.0107015 | + | 0.0107015i | 0.000367708 | + | 0.000367708i | ||||
\(848\) | −8.17377 | + | 15.1695i | −0.280688 | + | 0.520923i | ||||
\(849\) | 39.9862i | 1.37232i | ||||||||
\(850\) | −14.5151 | − | 19.6534i | −0.497865 | − | 0.674106i | ||||
\(851\) | −28.4921 | − | 28.4921i | −0.976696 | − | 0.976696i | ||||
\(852\) | 55.6610 | + | 14.0415i | 1.90692 | + | 0.481055i | ||||
\(853\) | − | 27.3120i | − | 0.935146i | −0.883954 | − | 0.467573i | \(-0.845128\pi\) | ||
0.883954 | − | 0.467573i | \(-0.154872\pi\) | |||||||
\(854\) | −3.65154 | − | 4.68711i | −0.124953 | − | 0.160389i | ||||
\(855\) | −8.74348 | + | 20.3643i | −0.299021 | + | 0.696445i | ||||
\(856\) | −15.4802 | + | 6.81540i | −0.529103 | + | 0.232946i | ||||
\(857\) | 13.3155 | + | 13.3155i | 0.454850 | + | 0.454850i | 0.896960 | − | 0.442111i | \(-0.145770\pi\) |
−0.442111 | + | 0.896960i | \(0.645770\pi\) | |||||||
\(858\) | −50.3919 | − | 6.25812i | −1.72035 | − | 0.213649i | ||||
\(859\) | −0.152620 | − | 0.152620i | −0.00520732 | − | 0.00520732i | 0.704498 | − | 0.709706i | \(-0.251172\pi\) |
−0.709706 | + | 0.704498i | \(0.751172\pi\) | |||||||
\(860\) | 1.07397 | + | 8.04358i | 0.0366220 | + | 0.274284i | ||||
\(861\) | −20.7898 | + | 20.7898i | −0.708516 | + | 0.708516i | ||||
\(862\) | 27.0145 | + | 34.6758i | 0.920119 | + | 1.18106i | ||||
\(863\) | −3.13243 | + | 3.13243i | −0.106629 | + | 0.106629i | −0.758409 | − | 0.651779i | \(-0.774023\pi\) |
0.651779 | + | 0.758409i | \(0.274023\pi\) | |||||||
\(864\) | −0.438417 | − | 2.59106i | −0.0149152 | − | 0.0881497i | ||||
\(865\) | −16.7663 | + | 6.69370i | −0.570072 | + | 0.227593i | ||||
\(866\) | −37.9508 | − | 4.71307i | −1.28962 | − | 0.160157i | ||||
\(867\) | 12.1964 | 0.414210 | ||||||||
\(868\) | −17.4297 | + | 10.4073i | −0.591603 | + | 0.353247i | ||||
\(869\) | −3.48176 | + | 3.48176i | −0.118110 | + | 0.118110i | ||||
\(870\) | −8.44586 | − | 32.2296i | −0.286342 | − | 1.09269i | ||||
\(871\) | −36.1541 | −1.22504 | ||||||||
\(872\) | 10.2012 | − | 26.2488i | 0.345455 | − | 0.888898i | ||||
\(873\) | 27.2112 | − | 27.2112i | 0.920959 | − | 0.920959i | ||||
\(874\) | −13.5495 | + | 10.5559i | −0.458319 | + | 0.357058i | ||||
\(875\) | −3.87717 | − | 10.4865i | −0.131072 | − | 0.354510i | ||||
\(876\) | 50.0834 | − | 29.9049i | 1.69216 | − | 1.01039i | ||||
\(877\) | 26.9004i | 0.908362i | 0.890909 | + | 0.454181i | \(0.150068\pi\) | ||||
−0.890909 | + | 0.454181i | \(0.849932\pi\) | |||||||
\(878\) | −25.8752 | − | 33.2133i | −0.873244 | − | 1.12089i | ||||
\(879\) | −16.4736 | −0.555642 | ||||||||
\(880\) | −23.2491 | + | 18.4578i | −0.783727 | + | 0.622212i | ||||
\(881\) | 7.85863 | 0.264764 | 0.132382 | − | 0.991199i | \(-0.457737\pi\) | ||||
0.132382 | + | 0.991199i | \(0.457737\pi\) | |||||||
\(882\) | −2.43986 | − | 3.13179i | −0.0821542 | − | 0.105453i | ||||
\(883\) | − | 23.2291i | − | 0.781721i | −0.920450 | − | 0.390860i | \(-0.872178\pi\) | ||
0.920450 | − | 0.390860i | \(-0.127822\pi\) | |||||||
\(884\) | 15.9050 | + | 26.6371i | 0.534944 | + | 0.895902i | ||||
\(885\) | −14.1651 | + | 32.9918i | −0.476156 | + | 1.10901i | ||||
\(886\) | −4.92422 | + | 3.83627i | −0.165433 | + | 0.128882i | ||||
\(887\) | 20.2207 | − | 20.2207i | 0.678945 | − | 0.678945i | −0.280816 | − | 0.959762i | \(-0.590605\pi\) |
0.959762 | + | 0.280816i | \(0.0906051\pi\) | |||||||
\(888\) | 73.0694 | − | 32.1699i | 2.45205 | − | 1.07955i | ||||
\(889\) | −12.3659 | −0.414738 | ||||||||
\(890\) | −7.84488 | + | 13.4165i | −0.262961 | + | 0.449722i | ||||
\(891\) | 22.3914 | − | 22.3914i | 0.750140 | − | 0.750140i | ||||
\(892\) | 4.30756 | + | 7.21413i | 0.144228 | + | 0.241547i | ||||
\(893\) | −10.6872 | −0.357635 | ||||||||
\(894\) | −9.22706 | − | 1.14590i | −0.308599 | − | 0.0383246i | ||||
\(895\) | 13.5897 | − | 31.6516i | 0.454254 | − | 1.05800i | ||||
\(896\) | 7.33943 | + | 8.61004i | 0.245193 | + | 0.287641i | ||||
\(897\) | −26.3160 | + | 26.3160i | −0.878666 | + | 0.878666i | ||||
\(898\) | 4.46094 | + | 5.72606i | 0.148864 | + | 0.191081i | ||||
\(899\) | −31.3800 | + | 31.3800i | −1.04658 | + | 1.04658i | ||||
\(900\) | 13.7674 | + | 24.4645i | 0.458914 | + | 0.815482i | ||||
\(901\) | 10.5252 | + | 10.5252i | 0.350645 | + | 0.350645i | ||||
\(902\) | 56.8288 | + | 7.05751i | 1.89219 | + | 0.234989i | ||||
\(903\) | 3.09201 | + | 3.09201i | 0.102896 | + | 0.102896i | ||||
\(904\) | −8.74612 | + | 22.5048i | −0.290892 | + | 0.748499i | ||||
\(905\) | 36.4729 | + | 15.6597i | 1.21240 | + | 0.520547i | ||||
\(906\) | 16.8768 | + | 21.6631i | 0.560695 | + | 0.719707i | ||||
\(907\) | − | 1.14534i | − | 0.0380305i | −0.999819 | − | 0.0190152i | \(-0.993947\pi\) | ||
0.999819 | − | 0.0190152i | \(-0.00605310\pi\) | |||||||
\(908\) | −7.29466 | + | 28.9162i | −0.242082 | + | 0.959618i | ||||
\(909\) | −7.75454 | − | 7.75454i | −0.257202 | − | 0.257202i | ||||
\(910\) | 3.59879 | + | 13.7331i | 0.119299 | + | 0.455247i | ||||
\(911\) | 11.9795i | 0.396899i | 0.980111 | + | 0.198449i | \(0.0635905\pi\) | ||||
−0.980111 | + | 0.198449i | \(0.936409\pi\) | |||||||
\(912\) | −9.76983 | − | 32.5998i | −0.323512 | − | 1.07949i | ||||
\(913\) | 22.7822 | + | 22.7822i | 0.753981 | + | 0.753981i | ||||
\(914\) | 45.5889 | + | 5.66164i | 1.50795 | + | 0.187270i | ||||
\(915\) | 20.8027 | + | 8.93169i | 0.687716 | + | 0.295273i | ||||
\(916\) | 25.5212 | + | 42.7418i | 0.843244 | + | 1.41223i | ||||
\(917\) | −1.90073 | −0.0627676 | ||||||||
\(918\) | −2.25271 | − | 0.279762i | −0.0743506 | − | 0.00923353i | ||||
\(919\) | 5.36067i | 0.176832i | 0.996084 | + | 0.0884160i | \(0.0281805\pi\) | ||||
−0.996084 | + | 0.0884160i | \(0.971820\pi\) | |||||||
\(920\) | 0.199661 | + | 21.7557i | 0.00658264 | + | 0.717264i | ||||
\(921\) | − | 0.667556i | − | 0.0219967i | ||||||
\(922\) | 1.15843 | − | 9.32800i | 0.0381510 | − | 0.307201i | ||||
\(923\) | −53.4717 | −1.76004 | ||||||||
\(924\) | −3.91269 | + | 15.5100i | −0.128718 | + | 0.510242i | ||||
\(925\) | 42.4634 | − | 40.3346i | 1.39619 | − | 1.32619i | ||||
\(926\) | 3.45577 | − | 27.8267i | 0.113564 | − | 0.914441i | ||||
\(927\) | 7.13688 | + | 7.13688i | 0.234406 | + | 0.234406i | ||||
\(928\) | 20.1611 | + | 14.3258i | 0.661819 | + | 0.470266i | ||||
\(929\) | − | 20.1129i | − | 0.659882i | −0.944002 | − | 0.329941i | \(-0.892971\pi\) | ||
0.944002 | − | 0.329941i | \(-0.107029\pi\) | |||||||
\(930\) | 39.0434 | − | 66.7729i | 1.28028 | − | 2.18957i | ||||
\(931\) | 2.49650 | + | 2.49650i | 0.0818195 | + | 0.0818195i | ||||
\(932\) | 4.26086 | + | 7.13591i | 0.139569 | + | 0.233744i | ||||
\(933\) | 37.7259i | 1.23509i | ||||||||
\(934\) | 9.92974 | − | 7.73586i | 0.324911 | − | 0.253125i | ||||
\(935\) | 9.50770 | + | 23.8148i | 0.310935 | + | 0.778828i | ||||
\(936\) | −14.3633 | − | 32.6242i | −0.469479 | − | 1.06636i | ||||
\(937\) | 11.2798 | + | 11.2798i | 0.368495 | + | 0.368495i | 0.866928 | − | 0.498433i | \(-0.166091\pi\) |
−0.498433 | + | 0.866928i | \(0.666091\pi\) | |||||||
\(938\) | −1.40360 | + | 11.3021i | −0.0458292 | + | 0.369027i | ||||
\(939\) | −47.6563 | − | 47.6563i | −1.55520 | − | 1.55520i | ||||
\(940\) | −8.22132 | + | 10.7550i | −0.268150 | + | 0.350790i | ||||
\(941\) | −13.4391 | + | 13.4391i | −0.438102 | + | 0.438102i | −0.891373 | − | 0.453271i | \(-0.850257\pi\) |
0.453271 | + | 0.891373i | \(0.350257\pi\) | |||||||
\(942\) | −27.2833 | + | 21.2553i | −0.888937 | + | 0.692535i | ||||
\(943\) | 29.6776 | − | 29.6776i | 0.966434 | − | 0.966434i | ||||
\(944\) | −7.65125 | − | 25.5305i | −0.249027 | − | 0.830948i | ||||
\(945\) | −0.954505 | − | 0.409819i | −0.0310501 | − | 0.0133314i | ||||
\(946\) | 1.04964 | − | 8.45197i | 0.0341268 | − | 0.274797i | ||||
\(947\) | −16.7848 | −0.545434 | −0.272717 | − | 0.962094i | \(-0.587922\pi\) | ||||
−0.272717 | + | 0.962094i | \(0.587922\pi\) | |||||||
\(948\) | −6.93323 | − | 1.74904i | −0.225181 | − | 0.0568061i | ||||
\(949\) | −38.4210 | + | 38.4210i | −1.24720 | + | 1.24720i | ||||
\(950\) | −14.8315 | − | 20.0818i | −0.481198 | − | 0.651539i | ||||
\(951\) | 43.4382 | 1.40858 | ||||||||
\(952\) | 8.94448 | − | 3.93794i | 0.289892 | − | 0.127629i | ||||
\(953\) | −14.6385 | + | 14.6385i | −0.474188 | + | 0.474188i | −0.903267 | − | 0.429079i | \(-0.858838\pi\) |
0.429079 | + | 0.903267i | \(0.358838\pi\) | |||||||
\(954\) | −10.5106 | − | 13.4914i | −0.340293 | − | 0.436800i | ||||
\(955\) | 8.15802 | + | 20.4342i | 0.263987 | + | 0.661234i | ||||
\(956\) | 14.0330 | − | 55.6273i | 0.453861 | − | 1.79912i | ||||
\(957\) | 34.9681i | 1.13036i | ||||||||
\(958\) | −31.2140 | + | 24.3176i | −1.00848 | + | 0.785665i | ||||
\(959\) | −0.828141 | −0.0267421 | ||||||||
\(960\) | −40.3221 | − | 15.2461i | −1.30139 | − | 0.492065i | ||||
\(961\) | −72.0268 | −2.32345 | ||||||||
\(962\) | −58.6656 | + | 45.7040i | −1.89145 | + | 1.47356i | ||||
\(963\) | − | 16.7873i | − | 0.540964i | ||||||
\(964\) | 11.2929 | − | 44.7655i | 0.363721 | − | 1.44180i | ||||
\(965\) | 19.6090 | + | 8.41919i | 0.631237 | + | 0.271023i | ||||
\(966\) | 7.20498 | + | 9.24829i | 0.231816 | + | 0.297559i | ||||
\(967\) | −18.3696 | + | 18.3696i | −0.590727 | + | 0.590727i | −0.937828 | − | 0.347101i | \(-0.887166\pi\) |
0.347101 | + | 0.937828i | \(0.387166\pi\) | |||||||
\(968\) | 0.0391772 | − | 0.0172483i | 0.00125920 | − | 0.000554383i | ||||
\(969\) | −29.3977 | −0.944389 | ||||||||
\(970\) | 10.9888 | + | 41.9337i | 0.352830 | + | 1.34641i | ||||
\(971\) | −24.3279 | + | 24.3279i | −0.780718 | + | 0.780718i | −0.979952 | − | 0.199234i | \(-0.936155\pi\) |
0.199234 | + | 0.979952i | \(0.436155\pi\) | |||||||
\(972\) | 41.8854 | + | 10.5664i | 1.34347 | + | 0.338917i | ||||
\(973\) | 8.82047 | 0.282771 | ||||||||
\(974\) | −6.80893 | + | 54.8272i | −0.218172 | + | 1.75678i | ||||
\(975\) | −37.2540 | − | 39.2203i | −1.19308 | − | 1.25605i | ||||
\(976\) | −16.0980 | + | 4.82442i | −0.515285 | + | 0.154426i | ||||
\(977\) | 14.1661 | − | 14.1661i | 0.453213 | − | 0.453213i | −0.443207 | − | 0.896419i | \(-0.646159\pi\) |
0.896419 | + | 0.443207i | \(0.146159\pi\) | |||||||
\(978\) | 41.4196 | − | 32.2683i | 1.32445 | − | 1.03183i | ||||
\(979\) | 11.5340 | − | 11.5340i | 0.368627 | − | 0.368627i | ||||
\(980\) | 4.43280 | − | 0.591861i | 0.141601 | − | 0.0189063i | ||||
\(981\) | 19.7639 | + | 19.7639i | 0.631012 | + | 0.631012i | ||||
\(982\) | −0.560105 | + | 4.51010i | −0.0178737 | + | 0.143923i | ||||
\(983\) | 22.5767 | + | 22.5767i | 0.720086 | + | 0.720086i | 0.968623 | − | 0.248536i | \(-0.0799495\pi\) |
−0.248536 | + | 0.968623i | \(0.579950\pi\) | |||||||
\(984\) | 33.5084 | + | 76.1096i | 1.06821 | + | 2.42629i | ||||
\(985\) | −24.6135 | + | 9.82657i | −0.784252 | + | 0.313101i | ||||
\(986\) | 16.8535 | − | 13.1299i | 0.536726 | − | 0.418142i | ||||
\(987\) | 7.29464i | 0.232191i | ||||||||
\(988\) | 16.2517 | + | 27.2177i | 0.517036 | + | 0.865911i | ||||
\(989\) | −4.41385 | − | 4.41385i | −0.140352 | − | 0.140352i | ||||
\(990\) | −7.46860 | − | 28.5003i | −0.237368 | − | 0.905801i | ||||
\(991\) | 49.6002i | 1.57560i | 0.615930 | + | 0.787801i | \(0.288781\pi\) | ||||
−0.615930 | + | 0.787801i | \(0.711219\pi\) | |||||||
\(992\) | 9.57922 | + | 56.6136i | 0.304141 | + | 1.79748i | ||||
\(993\) | 35.0345 | + | 35.0345i | 1.11179 | + | 1.11179i | ||||
\(994\) | −2.07591 | + | 16.7157i | −0.0658439 | + | 0.530191i | ||||
\(995\) | −8.55658 | − | 21.4325i | −0.271262 | − | 0.679455i | ||||
\(996\) | −11.4445 | + | 45.3663i | −0.362633 | + | 1.43749i | ||||
\(997\) | −0.659673 | −0.0208920 | −0.0104460 | − | 0.999945i | \(-0.503325\pi\) | ||||
−0.0104460 | + | 0.999945i | \(0.503325\pi\) | |||||||
\(998\) | −1.31185 | + | 10.5634i | −0.0415260 | + | 0.334378i | ||||
\(999\) | − | 5.44139i | − | 0.172158i |
(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 | 560.2.t.a.43.15 | ✓ | 144 | |
5.2 | odd | 4 | 560.2.bl.a.267.22 | yes | 144 | ||
16.3 | odd | 4 | 560.2.bl.a.323.22 | yes | 144 | ||
80.67 | even | 4 | inner | 560.2.t.a.547.15 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.t.a.43.15 | ✓ | 144 | 1.1 | even | 1 | trivial | |
560.2.t.a.547.15 | yes | 144 | 80.67 | even | 4 | inner | |
560.2.bl.a.267.22 | yes | 144 | 5.2 | odd | 4 | ||
560.2.bl.a.323.22 | yes | 144 | 16.3 | odd | 4 |