Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(299,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.299");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.h (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.342102016.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 299.7 | ||
Root | \(0.599676 - 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.299 |
Dual form | 300.2.h.b.299.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28078 | + | 0.599676i | 0.905646 | + | 0.424035i | ||||
\(3\) | −1.66757 | − | 0.468213i | −0.962770 | − | 0.270323i | ||||
\(4\) | 1.28078 | + | 1.53610i | 0.640388 | + | 0.768051i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.85500 | − | 1.59968i | −0.757302 | − | 0.653065i | ||||
\(7\) | 0.936426 | 0.353936 | 0.176968 | − | 0.984217i | \(-0.443371\pi\) | ||||
0.176968 | + | 0.984217i | \(0.443371\pi\) | |||||||
\(8\) | 0.719224 | + | 2.73546i | 0.254284 | + | 0.967130i | ||||
\(9\) | 2.56155 | + | 1.56155i | 0.853851 | + | 0.520518i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.27156 | 1.28792 | 0.643962 | − | 0.765058i | \(-0.277290\pi\) | ||||
0.643962 | + | 0.765058i | \(0.277290\pi\) | |||||||
\(12\) | −1.41656 | − | 3.16123i | −0.408924 | − | 0.912568i | ||||
\(13\) | 3.12311i | 0.866194i | 0.901347 | + | 0.433097i | \(0.142579\pi\) | ||||
−0.901347 | + | 0.433097i | \(0.857421\pi\) | |||||||
\(14\) | 1.19935 | + | 0.561553i | 0.320541 | + | 0.150081i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.719224 | + | 3.93481i | −0.179806 | + | 0.983702i | ||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 2.34435 | + | 3.53610i | 0.552569 | + | 0.833467i | ||||
\(19\) | 4.27156i | 0.979963i | 0.871733 | + | 0.489981i | \(0.162996\pi\) | ||||
−0.871733 | + | 0.489981i | \(0.837004\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.56155 | − | 0.438447i | −0.340759 | − | 0.0956770i | ||||
\(22\) | 5.47091 | + | 2.56155i | 1.16640 | + | 0.546125i | ||||
\(23\) | − | 7.60669i | − | 1.58610i | −0.609154 | − | 0.793052i | \(-0.708491\pi\) | ||
0.609154 | − | 0.793052i | \(-0.291509\pi\) | |||||||
\(24\) | 0.0814236 | − | 4.89830i | 0.0166205 | − | 0.999862i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.87285 | + | 4.00000i | −0.367297 | + | 0.784465i | ||||
\(27\) | −3.54042 | − | 3.80335i | −0.681354 | − | 0.731954i | ||||
\(28\) | 1.19935 | + | 1.43845i | 0.226656 | + | 0.271841i | ||||
\(29\) | − | 5.12311i | − | 0.951337i | −0.879625 | − | 0.475668i | \(-0.842206\pi\) | ||
0.879625 | − | 0.475668i | \(-0.157794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.39871i | − | 0.430820i | −0.976524 | − | 0.215410i | \(-0.930891\pi\) | ||
0.976524 | − | 0.215410i | \(-0.0691088\pi\) | |||||||
\(32\) | −3.28078 | + | 4.60831i | −0.579965 | + | 0.814642i | ||||
\(33\) | −7.12311 | − | 2.00000i | −1.23997 | − | 0.348155i | ||||
\(34\) | −2.56155 | − | 1.19935i | −0.439303 | − | 0.205687i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.882071 | + | 5.93481i | 0.147012 | + | 0.989135i | ||||
\(37\) | 3.12311i | 0.513435i | 0.966486 | + | 0.256718i | \(0.0826411\pi\) | ||||
−0.966486 | + | 0.256718i | \(0.917359\pi\) | |||||||
\(38\) | −2.56155 | + | 5.47091i | −0.415539 | + | 0.887499i | ||||
\(39\) | 1.46228 | − | 5.20798i | 0.234152 | − | 0.833945i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.12311i | − | 1.11244i | −0.831034 | − | 0.556221i | \(-0.812251\pi\) | ||
0.831034 | − | 0.556221i | \(-0.187749\pi\) | |||||||
\(42\) | −1.73707 | − | 1.49798i | −0.268036 | − | 0.231143i | ||||
\(43\) | −1.46228 | −0.222995 | −0.111498 | − | 0.993765i | \(-0.535565\pi\) | ||||
−0.111498 | + | 0.993765i | \(0.535565\pi\) | |||||||
\(44\) | 5.47091 | + | 6.56155i | 0.824771 | + | 0.989191i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.56155 | − | 9.74247i | 0.672564 | − | 1.43645i | ||||
\(47\) | − | 0.936426i | − | 0.136592i | −0.997665 | − | 0.0682959i | \(-0.978244\pi\) | ||
0.997665 | − | 0.0682959i | \(-0.0217562\pi\) | |||||||
\(48\) | 3.04168 | − | 6.22480i | 0.439029 | − | 0.898473i | ||||
\(49\) | −6.12311 | −0.874729 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.33513 | + | 0.936426i | 0.467012 | + | 0.131126i | ||||
\(52\) | −4.79741 | + | 4.00000i | −0.665281 | + | 0.554700i | ||||
\(53\) | 4.24621 | 0.583262 | 0.291631 | − | 0.956531i | \(-0.405802\pi\) | ||||
0.291631 | + | 0.956531i | \(0.405802\pi\) | |||||||
\(54\) | −2.25371 | − | 6.99434i | −0.306691 | − | 0.951809i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.673500 | + | 2.56155i | 0.0900002 | + | 0.342302i | ||||
\(57\) | 2.00000 | − | 7.12311i | 0.264906 | − | 0.943478i | ||||
\(58\) | 3.07221 | − | 6.56155i | 0.403400 | − | 0.861574i | ||||
\(59\) | −7.19612 | −0.936855 | −0.468427 | − | 0.883502i | \(-0.655179\pi\) | ||||
−0.468427 | + | 0.883502i | \(0.655179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.12311 | −0.655946 | −0.327973 | − | 0.944687i | \(-0.606366\pi\) | ||||
−0.327973 | + | 0.944687i | \(0.606366\pi\) | |||||||
\(62\) | 1.43845 | − | 3.07221i | 0.182683 | − | 0.390171i | ||||
\(63\) | 2.39871 | + | 1.46228i | 0.302209 | + | 0.184230i | ||||
\(64\) | −6.96543 | + | 3.93481i | −0.870679 | + | 0.491851i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.92375 | − | 6.83311i | −0.975347 | − | 0.841098i | ||||
\(67\) | 5.20798 | 0.636257 | 0.318128 | − | 0.948048i | \(-0.396946\pi\) | ||||
0.318128 | + | 0.948048i | \(0.396946\pi\) | |||||||
\(68\) | −2.56155 | − | 3.07221i | −0.310634 | − | 0.372560i | ||||
\(69\) | −3.56155 | + | 12.6847i | −0.428761 | + | 1.52705i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.67026 | −0.791615 | −0.395807 | − | 0.918334i | \(-0.629535\pi\) | ||||
−0.395807 | + | 0.918334i | \(0.629535\pi\) | |||||||
\(72\) | −2.42923 | + | 8.13012i | −0.286287 | + | 0.958144i | ||||
\(73\) | − | 8.24621i | − | 0.965146i | −0.875856 | − | 0.482573i | \(-0.839702\pi\) | ||
0.875856 | − | 0.482573i | \(-0.160298\pi\) | |||||||
\(74\) | −1.87285 | + | 4.00000i | −0.217715 | + | 0.464991i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.56155 | + | 5.47091i | −0.752662 | + | 0.627557i | ||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 4.99596 | − | 5.79337i | 0.565681 | − | 0.655970i | ||||
\(79\) | − | 9.06897i | − | 1.02034i | −0.860074 | − | 0.510169i | \(-0.829583\pi\) | ||
0.860074 | − | 0.510169i | \(-0.170417\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.12311 | + | 8.00000i | 0.458123 | + | 0.888889i | ||||
\(82\) | 4.27156 | − | 9.12311i | 0.471715 | − | 1.00748i | ||||
\(83\) | 4.68213i | 0.513931i | 0.966421 | + | 0.256965i | \(0.0827226\pi\) | ||||
−0.966421 | + | 0.256965i | \(0.917277\pi\) | |||||||
\(84\) | −1.32650 | − | 2.96026i | −0.144733 | − | 0.322991i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.87285 | − | 0.876894i | −0.201955 | − | 0.0945580i | ||||
\(87\) | −2.39871 | + | 8.54312i | −0.257168 | + | 0.915918i | ||||
\(88\) | 3.07221 | + | 11.6847i | 0.327498 | + | 1.24559i | ||||
\(89\) | − | 6.24621i | − | 0.662097i | −0.943614 | − | 0.331049i | \(-0.892598\pi\) | ||
0.943614 | − | 0.331049i | \(-0.107402\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.92456i | 0.306577i | ||||||||
\(92\) | 11.6847 | − | 9.74247i | 1.21821 | − | 1.01572i | ||||
\(93\) | −1.12311 | + | 4.00000i | −0.116461 | + | 0.414781i | ||||
\(94\) | 0.561553 | − | 1.19935i | 0.0579198 | − | 0.123704i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.62858 | − | 6.14856i | 0.778589 | − | 0.627534i | ||||
\(97\) | 6.00000i | 0.609208i | 0.952479 | + | 0.304604i | \(0.0985241\pi\) | ||||
−0.952479 | + | 0.304604i | \(0.901476\pi\) | |||||||
\(98\) | −7.84233 | − | 3.67188i | −0.792195 | − | 0.370916i | ||||
\(99\) | 10.9418 | + | 6.67026i | 1.09969 | + | 0.670387i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.12311i | 0.907783i | 0.891057 | + | 0.453891i | \(0.149965\pi\) | ||||
−0.891057 | + | 0.453891i | \(0.850035\pi\) | |||||||
\(102\) | 3.71001 | + | 3.19935i | 0.367345 | + | 0.316783i | ||||
\(103\) | 12.4041 | 1.22221 | 0.611106 | − | 0.791549i | \(-0.290725\pi\) | ||||
0.611106 | + | 0.791549i | \(0.290725\pi\) | |||||||
\(104\) | −8.54312 | + | 2.24621i | −0.837722 | + | 0.220259i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.43845 | + | 2.54635i | 0.528229 | + | 0.247324i | ||||
\(107\) | 0.936426i | 0.0905278i | 0.998975 | + | 0.0452639i | \(0.0144129\pi\) | ||||
−0.998975 | + | 0.0452639i | \(0.985587\pi\) | |||||||
\(108\) | 1.30784 | − | 10.3097i | 0.125847 | − | 0.992050i | ||||
\(109\) | 9.12311 | 0.873835 | 0.436918 | − | 0.899502i | \(-0.356070\pi\) | ||||
0.436918 | + | 0.899502i | \(0.356070\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.46228 | − | 5.20798i | 0.138793 | − | 0.494320i | ||||
\(112\) | −0.673500 | + | 3.68466i | −0.0636398 | + | 0.348167i | ||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 6.83311 | − | 7.92375i | 0.639980 | − | 0.742127i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.86962 | − | 6.56155i | 0.730676 | − | 0.609225i | ||||
\(117\) | −4.87689 | + | 8.00000i | −0.450869 | + | 0.739600i | ||||
\(118\) | −9.21662 | − | 4.31534i | −0.848458 | − | 0.397259i | ||||
\(119\) | −1.87285 | −0.171684 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.24621 | 0.658746 | ||||||||
\(122\) | −6.56155 | − | 3.07221i | −0.594055 | − | 0.278144i | ||||
\(123\) | −3.33513 | + | 11.8782i | −0.300719 | + | 1.07103i | ||||
\(124\) | 3.68466 | − | 3.07221i | 0.330892 | − | 0.275892i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.19531 | + | 3.31130i | 0.195574 | + | 0.294994i | ||||
\(127\) | −4.68213 | −0.415472 | −0.207736 | − | 0.978185i | \(-0.566609\pi\) | ||||
−0.207736 | + | 0.978185i | \(0.566609\pi\) | |||||||
\(128\) | −11.2808 | + | 0.862603i | −0.997089 | + | 0.0762440i | ||||
\(129\) | 2.43845 | + | 0.684658i | 0.214693 | + | 0.0602808i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.6121 | −1.53878 | −0.769388 | − | 0.638782i | \(-0.779438\pi\) | ||||
−0.769388 | + | 0.638782i | \(0.779438\pi\) | |||||||
\(132\) | −6.05090 | − | 13.5034i | −0.526663 | − | 1.17532i | ||||
\(133\) | 4.00000i | 0.346844i | ||||||||
\(134\) | 6.67026 | + | 3.12311i | 0.576223 | + | 0.269795i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.43845 | − | 5.47091i | −0.123346 | − | 0.469127i | ||||
\(137\) | −8.24621 | −0.704521 | −0.352261 | − | 0.935902i | \(-0.614587\pi\) | ||||
−0.352261 | + | 0.935902i | \(0.614587\pi\) | |||||||
\(138\) | −12.1682 | + | 14.1104i | −1.03583 | + | 1.20116i | ||||
\(139\) | 13.8664i | 1.17613i | 0.808813 | + | 0.588066i | \(0.200110\pi\) | ||||
−0.808813 | + | 0.588066i | \(0.799890\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.438447 | + | 1.56155i | −0.0369239 | + | 0.131506i | ||||
\(142\) | −8.54312 | − | 4.00000i | −0.716922 | − | 0.335673i | ||||
\(143\) | 13.3405i | 1.11559i | ||||||||
\(144\) | −7.98674 | + | 8.95611i | −0.665562 | + | 0.746343i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.94506 | − | 10.5616i | 0.409256 | − | 0.874080i | ||||
\(147\) | 10.2107 | + | 2.86692i | 0.842163 | + | 0.236459i | ||||
\(148\) | −4.79741 | + | 4.00000i | −0.394345 | + | 0.328798i | ||||
\(149\) | − | 14.0000i | − | 1.14692i | −0.819232 | − | 0.573462i | \(-0.805600\pi\) | ||
0.819232 | − | 0.573462i | \(-0.194400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.14441i | 0.500025i | 0.968243 | + | 0.250013i | \(0.0804347\pi\) | ||||
−0.968243 | + | 0.250013i | \(0.919565\pi\) | |||||||
\(152\) | −11.6847 | + | 3.07221i | −0.947751 | + | 0.249189i | ||||
\(153\) | −5.12311 | − | 3.12311i | −0.414179 | − | 0.252488i | ||||
\(154\) | 5.12311 | + | 2.39871i | 0.412832 | + | 0.193293i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.87285 | − | 4.42405i | 0.790461 | − | 0.354208i | ||||
\(157\) | − | 21.3693i | − | 1.70546i | −0.522354 | − | 0.852729i | \(-0.674946\pi\) | ||
0.522354 | − | 0.852729i | \(-0.325054\pi\) | |||||||
\(158\) | 5.43845 | − | 11.6153i | 0.432660 | − | 0.924065i | ||||
\(159\) | −7.08084 | − | 1.98813i | −0.561547 | − | 0.157669i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.12311i | − | 0.561379i | ||||||
\(162\) | 0.483365 | + | 12.7187i | 0.0379768 | + | 0.999279i | ||||
\(163\) | −24.1671 | −1.89291 | −0.946456 | − | 0.322834i | \(-0.895364\pi\) | ||||
−0.946456 | + | 0.322834i | \(0.895364\pi\) | |||||||
\(164\) | 10.9418 | − | 9.12311i | 0.854413 | − | 0.712395i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.80776 | + | 5.99676i | −0.217925 | + | 0.465439i | ||||
\(167\) | 2.80928i | 0.217389i | 0.994075 | + | 0.108694i | \(0.0346670\pi\) | ||||
−0.994075 | + | 0.108694i | \(0.965333\pi\) | |||||||
\(168\) | 0.0762472 | − | 4.58690i | 0.00588260 | − | 0.353887i | ||||
\(169\) | 3.24621 | 0.249709 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.67026 | + | 10.9418i | −0.510088 | + | 0.836742i | ||||
\(172\) | −1.87285 | − | 2.24621i | −0.142804 | − | 0.171272i | ||||
\(173\) | 2.00000 | 0.152057 | 0.0760286 | − | 0.997106i | \(-0.475776\pi\) | ||||
0.0760286 | + | 0.997106i | \(0.475776\pi\) | |||||||
\(174\) | −8.19531 | + | 9.50338i | −0.621285 | + | 0.720449i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.07221 | + | 16.8078i | −0.231576 | + | 1.26693i | ||||
\(177\) | 12.0000 | + | 3.36932i | 0.901975 | + | 0.253253i | ||||
\(178\) | 3.74571 | − | 8.00000i | 0.280752 | − | 0.599625i | ||||
\(179\) | 14.6875 | 1.09780 | 0.548899 | − | 0.835889i | \(-0.315047\pi\) | ||||
0.548899 | + | 0.835889i | \(0.315047\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.24621 | 0.315618 | 0.157809 | − | 0.987470i | \(-0.449557\pi\) | ||||
0.157809 | + | 0.987470i | \(0.449557\pi\) | |||||||
\(182\) | −1.75379 | + | 3.74571i | −0.129999 | + | 0.277650i | ||||
\(183\) | 8.54312 | + | 2.39871i | 0.631525 | + | 0.177317i | ||||
\(184\) | 20.8078 | − | 5.47091i | 1.53397 | − | 0.403321i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.83715 | + | 4.44961i | −0.281354 | + | 0.326261i | ||||
\(187\) | −8.54312 | −0.624735 | ||||||||
\(188\) | 1.43845 | − | 1.19935i | 0.104910 | − | 0.0874718i | ||||
\(189\) | −3.31534 | − | 3.56155i | −0.241156 | − | 0.259065i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.72197 | 0.558742 | 0.279371 | − | 0.960183i | \(-0.409874\pi\) | ||||
0.279371 | + | 0.960183i | \(0.409874\pi\) | |||||||
\(192\) | 13.4577 | − | 3.30024i | 0.971222 | − | 0.238175i | ||||
\(193\) | 16.2462i | 1.16943i | 0.811240 | + | 0.584714i | \(0.198793\pi\) | ||||
−0.811240 | + | 0.584714i | \(0.801207\pi\) | |||||||
\(194\) | −3.59806 | + | 7.68466i | −0.258326 | + | 0.551726i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.84233 | − | 9.40572i | −0.560166 | − | 0.671837i | ||||
\(197\) | 12.2462 | 0.872506 | 0.436253 | − | 0.899824i | \(-0.356305\pi\) | ||||
0.436253 | + | 0.899824i | \(0.356305\pi\) | |||||||
\(198\) | 10.0140 | + | 15.1047i | 0.711666 | + | 1.07344i | ||||
\(199\) | − | 17.6121i | − | 1.24849i | −0.781230 | − | 0.624244i | \(-0.785407\pi\) | ||
0.781230 | − | 0.624244i | \(-0.214593\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.68466 | − | 2.43845i | −0.612569 | − | 0.171995i | ||||
\(202\) | −5.47091 | + | 11.6847i | −0.384932 | + | 0.822130i | ||||
\(203\) | − | 4.79741i | − | 0.336712i | ||||||
\(204\) | 2.83311 | + | 6.32246i | 0.198357 | + | 0.442661i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.8869 | + | 7.43845i | 1.10689 | + | 0.518261i | ||||
\(207\) | 11.8782 | − | 19.4849i | 0.825595 | − | 1.35430i | ||||
\(208\) | −12.2888 | − | 2.24621i | −0.852077 | − | 0.155747i | ||||
\(209\) | 18.2462i | 1.26212i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.34700i | 0.0927313i | 0.998925 | + | 0.0463656i | \(0.0147639\pi\) | ||||
−0.998925 | + | 0.0463656i | \(0.985236\pi\) | |||||||
\(212\) | 5.43845 | + | 6.52262i | 0.373514 | + | 0.447975i | ||||
\(213\) | 11.1231 | + | 3.12311i | 0.762143 | + | 0.213992i | ||||
\(214\) | −0.561553 | + | 1.19935i | −0.0383870 | + | 0.0819861i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.85753 | − | 12.4201i | 0.534637 | − | 0.845082i | ||||
\(217\) | − | 2.24621i | − | 0.152483i | ||||||
\(218\) | 11.6847 | + | 5.47091i | 0.791385 | + | 0.370537i | ||||
\(219\) | −3.86098 | + | 13.7511i | −0.260901 | + | 0.929213i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.24621i | − | 0.420166i | ||||||
\(222\) | 4.99596 | − | 5.79337i | 0.335307 | − | 0.388826i | ||||
\(223\) | 18.0227 | 1.20689 | 0.603443 | − | 0.797406i | \(-0.293795\pi\) | ||||
0.603443 | + | 0.797406i | \(0.293795\pi\) | |||||||
\(224\) | −3.07221 | + | 4.31534i | −0.205270 | + | 0.288331i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.9309 | + | 8.39547i | 1.19274 | + | 0.558458i | ||||
\(227\) | 8.65840i | 0.574678i | 0.957829 | + | 0.287339i | \(0.0927706\pi\) | ||||
−0.957829 | + | 0.287339i | \(0.907229\pi\) | |||||||
\(228\) | 13.5034 | − | 6.05090i | 0.894283 | − | 0.400731i | ||||
\(229\) | −0.246211 | −0.0162701 | −0.00813505 | − | 0.999967i | \(-0.502589\pi\) | ||||
−0.00813505 | + | 0.999967i | \(0.502589\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.67026 | − | 1.87285i | −0.438871 | − | 0.123225i | ||||
\(232\) | 14.0140 | − | 3.68466i | 0.920066 | − | 0.241910i | ||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | −11.0436 | + | 7.32165i | −0.721944 | + | 0.478631i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.21662 | − | 11.0540i | −0.599951 | − | 0.719553i | ||||
\(237\) | −4.24621 | + | 15.1231i | −0.275821 | + | 0.982351i | ||||
\(238\) | −2.39871 | − | 1.12311i | −0.155485 | − | 0.0728001i | ||||
\(239\) | −20.8319 | −1.34751 | −0.673753 | − | 0.738957i | \(-0.735319\pi\) | ||||
−0.673753 | + | 0.738957i | \(0.735319\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.3693 | −0.732362 | −0.366181 | − | 0.930544i | \(-0.619335\pi\) | ||||
−0.366181 | + | 0.930544i | \(0.619335\pi\) | |||||||
\(242\) | 9.28078 | + | 4.34538i | 0.596591 | + | 0.279332i | ||||
\(243\) | −3.12985 | − | 15.2710i | −0.200780 | − | 0.979636i | ||||
\(244\) | −6.56155 | − | 7.86962i | −0.420060 | − | 0.503801i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.3947 | + | 13.2134i | −0.726497 | + | 0.842454i | ||||
\(247\) | −13.3405 | −0.848837 | ||||||||
\(248\) | 6.56155 | − | 1.72521i | 0.416659 | − | 0.109551i | ||||
\(249\) | 2.19224 | − | 7.80776i | 0.138927 | − | 0.494797i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.1035 | 1.58452 | 0.792259 | − | 0.610184i | \(-0.208905\pi\) | ||||
0.792259 | + | 0.610184i | \(0.208905\pi\) | |||||||
\(252\) | 0.825994 | + | 5.55751i | 0.0520328 | + | 0.350090i | ||||
\(253\) | − | 32.4924i | − | 2.04278i | ||||||
\(254\) | −5.99676 | − | 2.80776i | −0.376270 | − | 0.176175i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.9654 | − | 5.66001i | −0.935340 | − | 0.353751i | ||||
\(257\) | 2.49242 | 0.155473 | 0.0777365 | − | 0.996974i | \(-0.475231\pi\) | ||||
0.0777365 | + | 0.996974i | \(0.475231\pi\) | |||||||
\(258\) | 2.71253 | + | 2.33917i | 0.168875 | + | 0.145631i | ||||
\(259\) | 2.92456i | 0.181723i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | − | 13.1231i | 0.495188 | − | 0.812300i | ||||
\(262\) | −22.5571 | − | 10.5616i | −1.39359 | − | 0.652495i | ||||
\(263\) | − | 15.0981i | − | 0.930989i | −0.885051 | − | 0.465494i | \(-0.845877\pi\) | ||
0.885051 | − | 0.465494i | \(-0.154123\pi\) | |||||||
\(264\) | 0.347806 | − | 20.9234i | 0.0214060 | − | 1.28775i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.39871 | + | 5.12311i | −0.147074 | + | 0.314118i | ||||
\(267\) | −2.92456 | + | 10.4160i | −0.178980 | + | 0.637447i | ||||
\(268\) | 6.67026 | + | 8.00000i | 0.407451 | + | 0.488678i | ||||
\(269\) | 14.0000i | 0.853595i | 0.904347 | + | 0.426798i | \(0.140358\pi\) | ||||
−0.904347 | + | 0.426798i | \(0.859642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 31.7738i | − | 1.93012i | −0.262032 | − | 0.965059i | \(-0.584392\pi\) | ||
0.262032 | − | 0.965059i | \(-0.415608\pi\) | |||||||
\(272\) | 1.43845 | − | 7.86962i | 0.0872187 | − | 0.477166i | ||||
\(273\) | 1.36932 | − | 4.87689i | 0.0828748 | − | 0.295163i | ||||
\(274\) | −10.5616 | − | 4.94506i | −0.638047 | − | 0.298742i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −24.0465 | + | 10.7753i | −1.44743 | + | 0.648597i | ||||
\(277\) | 1.36932i | 0.0822743i | 0.999154 | + | 0.0411371i | \(0.0130981\pi\) | ||||
−0.999154 | + | 0.0411371i | \(0.986902\pi\) | |||||||
\(278\) | −8.31534 | + | 17.7597i | −0.498721 | + | 1.06516i | ||||
\(279\) | 3.74571 | − | 6.14441i | 0.224250 | − | 0.367856i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.6155i | 1.64740i | 0.567023 | + | 0.823702i | \(0.308095\pi\) | ||||
−0.567023 | + | 0.823702i | \(0.691905\pi\) | |||||||
\(282\) | −1.49798 | + | 1.73707i | −0.0892034 | + | 0.103441i | ||||
\(283\) | −4.38684 | −0.260770 | −0.130385 | − | 0.991463i | \(-0.541621\pi\) | ||||
−0.130385 | + | 0.991463i | \(0.541621\pi\) | |||||||
\(284\) | −8.54312 | − | 10.2462i | −0.506941 | − | 0.608001i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.00000 | + | 17.0862i | −0.473050 | + | 1.01033i | ||||
\(287\) | − | 6.67026i | − | 0.393733i | ||||||
\(288\) | −15.6000 | + | 6.68132i | −0.919239 | + | 0.393701i | ||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.80928 | − | 10.0054i | 0.164683 | − | 0.586527i | ||||
\(292\) | 12.6670 | − | 10.5616i | 0.741282 | − | 0.618068i | ||||
\(293\) | −30.4924 | −1.78139 | −0.890693 | − | 0.454605i | \(-0.849780\pi\) | ||||
−0.890693 | + | 0.454605i | \(0.849780\pi\) | |||||||
\(294\) | 11.3584 | + | 9.79499i | 0.662434 | + | 0.571255i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.54312 | + | 2.24621i | −0.496559 | + | 0.130558i | ||||
\(297\) | −15.1231 | − | 16.2462i | −0.877532 | − | 0.942701i | ||||
\(298\) | 8.39547 | − | 17.9309i | 0.486337 | − | 1.03871i | ||||
\(299\) | 23.7565 | 1.37387 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.36932 | −0.0789261 | ||||||||
\(302\) | −3.68466 | + | 7.86962i | −0.212028 | + | 0.452846i | ||||
\(303\) | 4.27156 | − | 15.2134i | 0.245395 | − | 0.873986i | ||||
\(304\) | −16.8078 | − | 3.07221i | −0.963991 | − | 0.176203i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.68870 | − | 7.07221i | −0.268035 | − | 0.404291i | ||||
\(307\) | 8.13254 | 0.464149 | 0.232074 | − | 0.972698i | \(-0.425449\pi\) | ||||
0.232074 | + | 0.972698i | \(0.425449\pi\) | |||||||
\(308\) | 5.12311 | + | 6.14441i | 0.291916 | + | 0.350110i | ||||
\(309\) | −20.6847 | − | 5.80776i | −1.17671 | − | 0.330392i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.1617 | 0.803035 | 0.401517 | − | 0.915851i | \(-0.368483\pi\) | ||||
0.401517 | + | 0.915851i | \(0.368483\pi\) | |||||||
\(312\) | 15.2979 | + | 0.254294i | 0.866074 | + | 0.0143966i | ||||
\(313\) | 10.4924i | 0.593067i | 0.955022 | + | 0.296533i | \(0.0958306\pi\) | ||||
−0.955022 | + | 0.296533i | \(0.904169\pi\) | |||||||
\(314\) | 12.8147 | − | 27.3693i | 0.723174 | − | 1.54454i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.9309 | − | 11.6153i | 0.783673 | − | 0.653413i | ||||
\(317\) | −32.7386 | −1.83878 | −0.919392 | − | 0.393342i | \(-0.871319\pi\) | ||||
−0.919392 | + | 0.393342i | \(0.871319\pi\) | |||||||
\(318\) | −7.87673 | − | 6.79256i | −0.441705 | − | 0.380908i | ||||
\(319\) | − | 21.8836i | − | 1.22525i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.438447 | − | 1.56155i | 0.0244717 | − | 0.0871574i | ||||
\(322\) | 4.27156 | − | 9.12311i | 0.238045 | − | 0.508411i | ||||
\(323\) | − | 8.54312i | − | 0.475352i | ||||||
\(324\) | −7.00805 | + | 16.5797i | −0.389336 | + | 0.921096i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −30.9526 | − | 14.4924i | −1.71431 | − | 0.802661i | ||||
\(327\) | −15.2134 | − | 4.27156i | −0.841302 | − | 0.236218i | ||||
\(328\) | 19.4849 | − | 5.12311i | 1.07588 | − | 0.282876i | ||||
\(329\) | − | 0.876894i | − | 0.0483448i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.0281i | 1.54056i | 0.637705 | + | 0.770281i | \(0.279884\pi\) | ||||
−0.637705 | + | 0.770281i | \(0.720116\pi\) | |||||||
\(332\) | −7.19224 | + | 5.99676i | −0.394725 | + | 0.329115i | ||||
\(333\) | −4.87689 | + | 8.00000i | −0.267252 | + | 0.438397i | ||||
\(334\) | −1.68466 | + | 3.59806i | −0.0921804 | + | 0.196877i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.84831 | − | 5.82907i | 0.155388 | − | 0.318002i | ||||
\(337\) | 34.4924i | 1.87892i | 0.342656 | + | 0.939461i | \(0.388674\pi\) | ||||
−0.342656 | + | 0.939461i | \(0.611326\pi\) | |||||||
\(338\) | 4.15767 | + | 1.94668i | 0.226147 | + | 0.105885i | ||||
\(339\) | −23.3459 | − | 6.55498i | −1.26798 | − | 0.356018i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 10.2462i | − | 0.554863i | ||||||
\(342\) | −15.1047 | + | 10.0140i | −0.816767 | + | 0.541497i | ||||
\(343\) | −12.2888 | −0.663534 | ||||||||
\(344\) | −1.05171 | − | 4.00000i | −0.0567042 | − | 0.215666i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.56155 | + | 1.19935i | 0.137710 | + | 0.0644776i | ||||
\(347\) | − | 23.8718i | − | 1.28150i | −0.767748 | − | 0.640752i | \(-0.778623\pi\) | ||
0.767748 | − | 0.640752i | \(-0.221377\pi\) | |||||||
\(348\) | −16.1953 | + | 7.25716i | −0.868160 | + | 0.389025i | ||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.8782 | − | 11.0571i | 0.634014 | − | 0.590184i | ||||
\(352\) | −14.0140 | + | 19.6847i | −0.746950 | + | 1.04920i | ||||
\(353\) | −3.75379 | −0.199794 | −0.0998970 | − | 0.994998i | \(-0.531851\pi\) | ||||
−0.0998970 | + | 0.994998i | \(0.531851\pi\) | |||||||
\(354\) | 13.3488 | + | 11.5115i | 0.709482 | + | 0.611827i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.59482 | − | 8.00000i | 0.508525 | − | 0.423999i | ||||
\(357\) | 3.12311 | + | 0.876894i | 0.165292 | + | 0.0464102i | ||||
\(358\) | 18.8114 | + | 8.80776i | 0.994215 | + | 0.465505i | ||||
\(359\) | 1.05171 | 0.0555069 | 0.0277535 | − | 0.999615i | \(-0.491165\pi\) | ||||
0.0277535 | + | 0.999615i | \(0.491165\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.753789 | 0.0396731 | ||||||||
\(362\) | 5.43845 | + | 2.54635i | 0.285838 | + | 0.133833i | ||||
\(363\) | −12.0835 | − | 3.39277i | −0.634221 | − | 0.178074i | ||||
\(364\) | −4.49242 | + | 3.74571i | −0.235467 | + | 0.196328i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.50338 | + | 8.19531i | 0.496749 | + | 0.428376i | ||||
\(367\) | 26.5658 | 1.38672 | 0.693361 | − | 0.720590i | \(-0.256129\pi\) | ||||
0.693361 | + | 0.720590i | \(0.256129\pi\) | |||||||
\(368\) | 29.9309 | + | 5.47091i | 1.56025 | + | 0.285191i | ||||
\(369\) | 11.1231 | − | 18.2462i | 0.579046 | − | 0.949860i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.97626 | 0.206437 | ||||||||
\(372\) | −7.58286 | + | 3.39790i | −0.393153 | + | 0.176173i | ||||
\(373\) | − | 0.876894i | − | 0.0454039i | −0.999742 | − | 0.0227019i | \(-0.992773\pi\) | ||
0.999742 | − | 0.0227019i | \(-0.00722687\pi\) | |||||||
\(374\) | −10.9418 | − | 5.12311i | −0.565788 | − | 0.264909i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.56155 | − | 0.673500i | 0.132102 | − | 0.0347331i | ||||
\(377\) | 16.0000 | 0.824042 | ||||||||
\(378\) | −2.11043 | − | 6.54968i | −0.108549 | − | 0.336879i | ||||
\(379\) | 25.1035i | 1.28948i | 0.764402 | + | 0.644740i | \(0.223034\pi\) | ||||
−0.764402 | + | 0.644740i | \(0.776966\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.80776 | + | 2.19224i | 0.400004 | + | 0.112312i | ||||
\(382\) | 9.89012 | + | 4.63068i | 0.506022 | + | 0.236926i | ||||
\(383\) | − | 4.68213i | − | 0.239246i | −0.992819 | − | 0.119623i | \(-0.961831\pi\) | ||
0.992819 | − | 0.119623i | \(-0.0381685\pi\) | |||||||
\(384\) | 19.2153 | + | 3.84336i | 0.980578 | + | 0.196131i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.74247 | + | 20.8078i | −0.495879 | + | 1.05909i | ||||
\(387\) | −3.74571 | − | 2.28343i | −0.190405 | − | 0.116073i | ||||
\(388\) | −9.21662 | + | 7.68466i | −0.467903 | + | 0.390129i | ||||
\(389\) | 28.7386i | 1.45711i | 0.684989 | + | 0.728553i | \(0.259807\pi\) | ||||
−0.684989 | + | 0.728553i | \(0.740193\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.2134i | 0.769374i | ||||||||
\(392\) | −4.40388 | − | 16.7495i | −0.222430 | − | 0.845977i | ||||
\(393\) | 29.3693 | + | 8.24621i | 1.48149 | + | 0.415966i | ||||
\(394\) | 15.6847 | + | 7.34376i | 0.790182 | + | 0.369973i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.76782 | + | 25.3509i | 0.189340 | + | 1.27393i | ||||
\(397\) | − | 23.1231i | − | 1.16052i | −0.814433 | − | 0.580258i | \(-0.802952\pi\) | ||
0.814433 | − | 0.580258i | \(-0.197048\pi\) | |||||||
\(398\) | 10.5616 | − | 22.5571i | 0.529403 | − | 1.13069i | ||||
\(399\) | 1.87285 | − | 6.67026i | 0.0937599 | − | 0.333931i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 24.0000i | − | 1.19850i | −0.800561 | − | 0.599251i | \(-0.795465\pi\) | ||
0.800561 | − | 0.599251i | \(-0.204535\pi\) | |||||||
\(402\) | −9.66083 | − | 8.33109i | −0.481838 | − | 0.415517i | ||||
\(403\) | 7.49141 | 0.373174 | ||||||||
\(404\) | −14.0140 | + | 11.6847i | −0.697224 | + | 0.581333i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.87689 | − | 6.14441i | 0.142778 | − | 0.304942i | ||||
\(407\) | 13.3405i | 0.661265i | ||||||||
\(408\) | −0.162847 | + | 9.79661i | −0.00806214 | + | 0.485004i | ||||
\(409\) | −0.630683 | −0.0311853 | −0.0155926 | − | 0.999878i | \(-0.504963\pi\) | ||||
−0.0155926 | + | 0.999878i | \(0.504963\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.7511 | + | 3.86098i | 0.678292 | + | 0.190448i | ||||
\(412\) | 15.8869 | + | 19.0540i | 0.782690 | + | 0.938722i | ||||
\(413\) | −6.73863 | −0.331586 | ||||||||
\(414\) | 26.8980 | − | 17.8327i | 1.32197 | − | 0.876432i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −14.3922 | − | 10.2462i | −0.705637 | − | 0.502362i | ||||
\(417\) | 6.49242 | − | 23.1231i | 0.317935 | − | 1.13234i | ||||
\(418\) | −10.9418 | + | 23.3693i | −0.535182 | + | 1.14303i | ||||
\(419\) | −6.14441 | −0.300174 | −0.150087 | − | 0.988673i | \(-0.547955\pi\) | ||||
−0.150087 | + | 0.988673i | \(0.547955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.630683 | −0.0307376 | −0.0153688 | − | 0.999882i | \(-0.504892\pi\) | ||||
−0.0153688 | + | 0.999882i | \(0.504892\pi\) | |||||||
\(422\) | −0.807764 | + | 1.72521i | −0.0393213 | + | 0.0839817i | ||||
\(423\) | 1.46228 | − | 2.39871i | 0.0710985 | − | 0.116629i | ||||
\(424\) | 3.05398 | + | 11.6153i | 0.148314 | + | 0.564090i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.3734 | + | 10.6703i | 0.599491 | + | 0.516976i | ||||
\(427\) | −4.79741 | −0.232163 | ||||||||
\(428\) | −1.43845 | + | 1.19935i | −0.0695300 | + | 0.0579729i | ||||
\(429\) | 6.24621 | − | 22.2462i | 0.301570 | − | 1.07406i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.0453 | −1.73624 | −0.868121 | − | 0.496353i | \(-0.834672\pi\) | ||||
−0.868121 | + | 0.496353i | \(0.834672\pi\) | |||||||
\(432\) | 17.5118 | − | 11.1954i | 0.842536 | − | 0.538640i | ||||
\(433\) | 18.0000i | 0.865025i | 0.901628 | + | 0.432512i | \(0.142373\pi\) | ||||
−0.901628 | + | 0.432512i | \(0.857627\pi\) | |||||||
\(434\) | 1.34700 | − | 2.87689i | 0.0646581 | − | 0.138095i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.6847 | + | 14.0140i | 0.559594 | + | 0.671150i | ||||
\(437\) | 32.4924 | 1.55432 | ||||||||
\(438\) | −13.1913 | + | 15.2967i | −0.630303 | + | 0.730907i | ||||
\(439\) | 29.9009i | 1.42709i | 0.700608 | + | 0.713546i | \(0.252912\pi\) | ||||
−0.700608 | + | 0.713546i | \(0.747088\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.6847 | − | 9.56155i | −0.746888 | − | 0.455312i | ||||
\(442\) | 3.74571 | − | 8.00000i | 0.178165 | − | 0.380521i | ||||
\(443\) | 25.7446i | 1.22316i | 0.791181 | + | 0.611582i | \(0.209467\pi\) | ||||
−0.791181 | + | 0.611582i | \(0.790533\pi\) | |||||||
\(444\) | 9.87285 | − | 4.42405i | 0.468545 | − | 0.209956i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 23.0830 | + | 10.8078i | 1.09301 | + | 0.511762i | ||||
\(447\) | −6.55498 | + | 23.3459i | −0.310040 | + | 1.10422i | ||||
\(448\) | −6.52262 | + | 3.68466i | −0.308165 | + | 0.174084i | ||||
\(449\) | − | 2.63068i | − | 0.124150i | −0.998071 | − | 0.0620748i | \(-0.980228\pi\) | ||
0.998071 | − | 0.0620748i | \(-0.0197717\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 30.4268i | − | 1.43274i | ||||||
\(452\) | 17.9309 | + | 21.5054i | 0.843397 | + | 1.01153i | ||||
\(453\) | 2.87689 | − | 10.2462i | 0.135168 | − | 0.481409i | ||||
\(454\) | −5.19224 | + | 11.0895i | −0.243684 | + | 0.520455i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.9234 | + | 0.347806i | 0.979827 | + | 0.0162875i | ||||
\(457\) | 10.0000i | 0.467780i | 0.972263 | + | 0.233890i | \(0.0751456\pi\) | ||||
−0.972263 | + | 0.233890i | \(0.924854\pi\) | |||||||
\(458\) | −0.315342 | − | 0.147647i | −0.0147349 | − | 0.00689909i | ||||
\(459\) | 7.08084 | + | 7.60669i | 0.330505 | + | 0.355050i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.8617i | 0.738755i | 0.929279 | + | 0.369377i | \(0.120429\pi\) | ||||
−0.929279 | + | 0.369377i | \(0.879571\pi\) | |||||||
\(462\) | −7.42001 | − | 6.39871i | −0.345210 | − | 0.297695i | ||||
\(463\) | 0.936426 | 0.0435194 | 0.0217597 | − | 0.999763i | \(-0.493073\pi\) | ||||
0.0217597 | + | 0.999763i | \(0.493073\pi\) | |||||||
\(464\) | 20.1584 | + | 3.68466i | 0.935832 | + | 0.171056i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.8078 | − | 5.99676i | −0.593308 | − | 0.277795i | ||||
\(467\) | − | 16.1498i | − | 0.747324i | −0.927565 | − | 0.373662i | \(-0.878102\pi\) | ||
0.927565 | − | 0.373662i | \(-0.121898\pi\) | |||||||
\(468\) | −18.5350 | + | 2.75480i | −0.856782 | + | 0.127341i | ||||
\(469\) | 4.87689 | 0.225194 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0054 | + | 35.6347i | −0.461024 | + | 1.64196i | ||||
\(472\) | −5.17562 | − | 19.6847i | −0.238227 | − | 0.906060i | ||||
\(473\) | −6.24621 | −0.287201 | ||||||||
\(474\) | −14.5074 | + | 16.8230i | −0.666348 | + | 0.772704i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.39871 | − | 2.87689i | −0.109944 | − | 0.131862i | ||||
\(477\) | 10.8769 | + | 6.63068i | 0.498019 | + | 0.303598i | ||||
\(478\) | −26.6811 | − | 12.4924i | −1.22036 | − | 0.571390i | ||||
\(479\) | 22.9354 | 1.04794 | 0.523971 | − | 0.851736i | \(-0.324450\pi\) | ||||
0.523971 | + | 0.851736i | \(0.324450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.75379 | −0.444734 | ||||||||
\(482\) | −14.5616 | − | 6.81791i | −0.663261 | − | 0.310547i | ||||
\(483\) | −3.33513 | + | 11.8782i | −0.151754 | + | 0.540479i | ||||
\(484\) | 9.28078 | + | 11.1309i | 0.421853 | + | 0.505951i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.14904 | − | 21.4357i | 0.233565 | − | 0.972341i | ||||
\(487\) | −15.3287 | −0.694608 | −0.347304 | − | 0.937753i | \(-0.612903\pi\) | ||||
−0.347304 | + | 0.937753i | \(0.612903\pi\) | |||||||
\(488\) | −3.68466 | − | 14.0140i | −0.166797 | − | 0.634385i | ||||
\(489\) | 40.3002 | + | 11.3153i | 1.82244 | + | 0.511697i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.6638 | −0.842285 | −0.421143 | − | 0.906994i | \(-0.638371\pi\) | ||||
−0.421143 | + | 0.906994i | \(0.638371\pi\) | |||||||
\(492\) | −22.5178 | + | 10.0903i | −1.01518 | + | 0.454905i | ||||
\(493\) | 10.2462i | 0.461466i | ||||||||
\(494\) | −17.0862 | − | 8.00000i | −0.768746 | − | 0.359937i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.43845 | + | 1.72521i | 0.423799 | + | 0.0774640i | ||||
\(497\) | −6.24621 | −0.280181 | ||||||||
\(498\) | 7.48990 | − | 8.68537i | 0.335630 | − | 0.389201i | ||||
\(499\) | − | 1.57756i | − | 0.0706212i | −0.999376 | − | 0.0353106i | \(-0.988758\pi\) | ||
0.999376 | − | 0.0353106i | \(-0.0112421\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.31534 | − | 4.68466i | 0.0587651 | − | 0.209295i | ||||
\(502\) | 32.1520 | + | 15.0540i | 1.43501 | + | 0.671892i | ||||
\(503\) | 19.8955i | 0.887097i | 0.896250 | + | 0.443549i | \(0.146281\pi\) | ||||
−0.896250 | + | 0.443549i | \(0.853719\pi\) | |||||||
\(504\) | −2.27479 | + | 7.61326i | −0.101327 | + | 0.339121i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 19.4849 | − | 41.6155i | 0.866211 | − | 1.85004i | ||||
\(507\) | −5.41327 | − | 1.51992i | −0.240412 | − | 0.0675020i | ||||
\(508\) | −5.99676 | − | 7.19224i | −0.266063 | − | 0.319104i | ||||
\(509\) | 2.87689i | 0.127516i | 0.997965 | + | 0.0637581i | \(0.0203086\pi\) | ||||
−0.997965 | + | 0.0637581i | \(0.979691\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.72197i | − | 0.341600i | ||||||
\(512\) | −15.7732 | − | 16.2236i | −0.697083 | − | 0.716990i | ||||
\(513\) | 16.2462 | − | 15.1231i | 0.717288 | − | 0.667701i | ||||
\(514\) | 3.19224 | + | 1.49465i | 0.140803 | + | 0.0659261i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.07140 | + | 4.62260i | 0.0911883 | + | 0.203499i | ||||
\(517\) | − | 4.00000i | − | 0.175920i | ||||||
\(518\) | −1.75379 | + | 3.74571i | −0.0770571 | + | 0.164577i | ||||
\(519\) | −3.33513 | − | 0.936426i | −0.146396 | − | 0.0411046i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.7538i | 0.953051i | 0.879161 | + | 0.476525i | \(0.158104\pi\) | ||||
−0.879161 | + | 0.476525i | \(0.841896\pi\) | |||||||
\(522\) | 18.1158 | − | 12.0104i | 0.792908 | − | 0.525679i | ||||
\(523\) | 0.641132 | 0.0280348 | 0.0140174 | − | 0.999902i | \(-0.495538\pi\) | ||||
0.0140174 | + | 0.999902i | \(0.495538\pi\) | |||||||
\(524\) | −22.5571 | − | 27.0540i | −0.985413 | − | 1.18186i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.05398 | − | 19.3373i | 0.394772 | − | 0.843146i | ||||
\(527\) | 4.79741i | 0.208979i | ||||||||
\(528\) | 12.9927 | − | 26.5896i | 0.565436 | − | 1.15716i | ||||
\(529\) | −34.8617 | −1.51573 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.4332 | − | 11.2371i | −0.799934 | − | 0.487649i | ||||
\(532\) | −6.14441 | + | 5.12311i | −0.266394 | + | 0.222115i | ||||
\(533\) | 22.2462 | 0.963590 | ||||||||
\(534\) | −9.99192 | + | 11.5867i | −0.432393 | + | 0.501407i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.74571 | + | 14.2462i | 0.161790 | + | 0.615343i | ||||
\(537\) | −24.4924 | − | 6.87689i | −1.05693 | − | 0.296760i | ||||
\(538\) | −8.39547 | + | 17.9309i | −0.361954 | + | 0.773055i | ||||
\(539\) | −26.1552 | −1.12658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.9848 | 1.67609 | 0.838045 | − | 0.545602i | \(-0.183699\pi\) | ||||
0.838045 | + | 0.545602i | \(0.183699\pi\) | |||||||
\(542\) | 19.0540 | − | 40.6951i | 0.818438 | − | 1.74800i | ||||
\(543\) | −7.08084 | − | 1.98813i | −0.303868 | − | 0.0853189i | ||||
\(544\) | 6.56155 | − | 9.21662i | 0.281324 | − | 0.395159i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.67835 | − | 5.42506i | 0.200215 | − | 0.232171i | ||||
\(547\) | 25.2188 | 1.07828 | 0.539139 | − | 0.842217i | \(-0.318750\pi\) | ||||
0.539139 | + | 0.842217i | \(0.318750\pi\) | |||||||
\(548\) | −10.5616 | − | 12.6670i | −0.451167 | − | 0.541109i | ||||
\(549\) | −13.1231 | − | 8.00000i | −0.560080 | − | 0.341432i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.8836 | 0.932275 | ||||||||
\(552\) | −37.2599 | − | 0.619364i | −1.58589 | − | 0.0263619i | ||||
\(553\) | − | 8.49242i | − | 0.361135i | ||||||
\(554\) | −0.821147 | + | 1.75379i | −0.0348872 | + | 0.0745113i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.3002 | + | 17.7597i | −0.903329 | + | 0.753180i | ||||
\(557\) | −19.7538 | −0.836995 | −0.418497 | − | 0.908218i | \(-0.637443\pi\) | ||||
−0.418497 | + | 0.908218i | \(0.637443\pi\) | |||||||
\(558\) | 8.48207 | − | 5.62341i | 0.359075 | − | 0.238058i | ||||
\(559\) | − | 4.56685i | − | 0.193157i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.2462 | + | 4.00000i | 0.601476 | + | 0.168880i | ||||
\(562\) | −16.5604 | + | 35.3693i | −0.698558 | + | 1.49196i | ||||
\(563\) | 36.1606i | 1.52399i | 0.647584 | + | 0.761994i | \(0.275779\pi\) | ||||
−0.647584 | + | 0.761994i | \(0.724221\pi\) | |||||||
\(564\) | −2.96026 | + | 1.32650i | −0.124649 | + | 0.0558557i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.61856 | − | 2.63068i | −0.236166 | − | 0.110576i | ||||
\(567\) | 3.86098 | + | 7.49141i | 0.162146 | + | 0.314610i | ||||
\(568\) | −4.79741 | − | 18.2462i | −0.201295 | − | 0.765594i | ||||
\(569\) | − | 4.87689i | − | 0.204450i | −0.994761 | − | 0.102225i | \(-0.967404\pi\) | ||
0.994761 | − | 0.102225i | \(-0.0325962\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.7909i | 0.702679i | 0.936248 | + | 0.351339i | \(0.114274\pi\) | ||||
−0.936248 | + | 0.351339i | \(0.885726\pi\) | |||||||
\(572\) | −20.4924 | + | 17.0862i | −0.856831 | + | 0.714411i | ||||
\(573\) | −12.8769 | − | 3.61553i | −0.537940 | − | 0.151041i | ||||
\(574\) | 4.00000 | − | 8.54312i | 0.166957 | − | 0.356583i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −23.9867 | − | 0.797675i | −0.999448 | − | 0.0332364i | ||||
\(577\) | 15.7538i | 0.655839i | 0.944706 | + | 0.327919i | \(0.106347\pi\) | ||||
−0.944706 | + | 0.327919i | \(0.893653\pi\) | |||||||
\(578\) | −16.6501 | − | 7.79579i | −0.692553 | − | 0.324262i | ||||
\(579\) | 7.60669 | − | 27.0916i | 0.316123 | − | 1.12589i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.38447i | 0.181899i | ||||||||
\(582\) | 9.59806 | − | 11.1300i | 0.397852 | − | 0.461354i | ||||
\(583\) | 18.1379 | 0.751197 | ||||||||
\(584\) | 22.5571 | − | 5.93087i | 0.933421 | − | 0.245421i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.0540 | − | 18.2856i | −1.61330 | − | 0.755371i | ||||
\(587\) | 38.0335i | 1.56981i | 0.619617 | + | 0.784904i | \(0.287288\pi\) | ||||
−0.619617 | + | 0.784904i | \(0.712712\pi\) | |||||||
\(588\) | 8.67372 | + | 19.3565i | 0.357698 | + | 0.798250i | ||||
\(589\) | 10.2462 | 0.422188 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.4214 | − | 5.73384i | −0.840023 | − | 0.235859i | ||||
\(592\) | −12.2888 | − | 2.24621i | −0.505067 | − | 0.0923187i | ||||
\(593\) | −8.24621 | −0.338631 | −0.169316 | − | 0.985562i | \(-0.554156\pi\) | ||||
−0.169316 | + | 0.985562i | \(0.554156\pi\) | |||||||
\(594\) | −9.62685 | − | 29.8767i | −0.394994 | − | 1.22586i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.5054 | − | 17.9309i | 0.880897 | − | 0.734477i | ||||
\(597\) | −8.24621 | + | 29.3693i | −0.337495 | + | 1.20201i | ||||
\(598\) | 30.4268 | + | 14.2462i | 1.24424 | + | 0.582571i | ||||
\(599\) | 36.8665 | 1.50632 | 0.753162 | − | 0.657836i | \(-0.228528\pi\) | ||||
0.753162 | + | 0.657836i | \(0.228528\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.8769 | 0.606841 | 0.303421 | − | 0.952857i | \(-0.401871\pi\) | ||||
0.303421 | + | 0.952857i | \(0.401871\pi\) | |||||||
\(602\) | −1.75379 | − | 0.821147i | −0.0714791 | − | 0.0334675i | ||||
\(603\) | 13.3405 | + | 8.13254i | 0.543268 | + | 0.331183i | ||||
\(604\) | −9.43845 | + | 7.86962i | −0.384045 | + | 0.320210i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.5940 | − | 16.9234i | 0.592841 | − | 0.687466i | ||||
\(607\) | 29.4903 | 1.19698 | 0.598488 | − | 0.801132i | \(-0.295768\pi\) | ||||
0.598488 | + | 0.801132i | \(0.295768\pi\) | |||||||
\(608\) | −19.6847 | − | 14.0140i | −0.798318 | − | 0.568344i | ||||
\(609\) | −2.24621 | + | 8.00000i | −0.0910211 | + | 0.324176i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.92456 | 0.118315 | ||||||||
\(612\) | −1.76414 | − | 11.8696i | −0.0713112 | − | 0.479801i | ||||
\(613\) | 0.876894i | 0.0354174i | 0.999843 | + | 0.0177087i | \(0.00563715\pi\) | ||||
−0.999843 | + | 0.0177087i | \(0.994363\pi\) | |||||||
\(614\) | 10.4160 | + | 4.87689i | 0.420354 | + | 0.196815i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.87689 | + | 10.9418i | 0.115913 | + | 0.440859i | ||||
\(617\) | 14.0000 | 0.563619 | 0.281809 | − | 0.959470i | \(-0.409065\pi\) | ||||
0.281809 | + | 0.959470i | \(0.409065\pi\) | |||||||
\(618\) | −23.0096 | − | 19.8425i | −0.925584 | − | 0.798184i | ||||
\(619\) | − | 20.3061i | − | 0.816171i | −0.912944 | − | 0.408085i | \(-0.866197\pi\) | ||
0.912944 | − | 0.408085i | \(-0.133803\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.9309 | + | 26.9309i | −1.16096 | + | 1.08070i | ||||
\(622\) | 18.1379 | + | 8.49242i | 0.727265 | + | 0.340515i | ||||
\(623\) | − | 5.84912i | − | 0.234340i | ||||||
\(624\) | 19.4407 | + | 9.49949i | 0.778252 | + | 0.380284i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.29206 | + | 13.4384i | −0.251481 | + | 0.537108i | ||||
\(627\) | 8.54312 | − | 30.4268i | 0.341179 | − | 1.21513i | ||||
\(628\) | 32.8255 | − | 27.3693i | 1.30988 | − | 1.09215i | ||||
\(629\) | − | 6.24621i | − | 0.249053i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.1315i | 1.19951i | 0.800182 | + | 0.599757i | \(0.204736\pi\) | ||||
−0.800182 | + | 0.599757i | \(0.795264\pi\) | |||||||
\(632\) | 24.8078 | − | 6.52262i | 0.986800 | − | 0.259456i | ||||
\(633\) | 0.630683 | − | 2.24621i | 0.0250674 | − | 0.0892789i | ||||
\(634\) | −41.9309 | − | 19.6326i | −1.66529 | − | 0.779710i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.01499 | − | 13.4232i | −0.238510 | − | 0.532266i | ||||
\(637\) | − | 19.1231i | − | 0.757685i | ||||||
\(638\) | 13.1231 | − | 28.0281i | 0.519549 | − | 1.10964i | ||||
\(639\) | −17.0862 | − | 10.4160i | −0.675921 | − | 0.412049i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.6155i | 1.88070i | 0.340208 | + | 0.940350i | \(0.389502\pi\) | ||||
−0.340208 | + | 0.940350i | \(0.610498\pi\) | |||||||
\(642\) | 1.49798 | − | 1.73707i | 0.0591205 | − | 0.0685568i | ||||
\(643\) | 20.4214 | 0.805340 | 0.402670 | − | 0.915345i | \(-0.368082\pi\) | ||||
0.402670 | + | 0.915345i | \(0.368082\pi\) | |||||||
\(644\) | 10.9418 | − | 9.12311i | 0.431168 | − | 0.359501i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.12311 | − | 10.9418i | 0.201566 | − | 0.430500i | ||||
\(647\) | 3.63043i | 0.142727i | 0.997450 | + | 0.0713634i | \(0.0227350\pi\) | ||||
−0.997450 | + | 0.0713634i | \(0.977265\pi\) | |||||||
\(648\) | −18.9182 | + | 17.0324i | −0.743177 | + | 0.669094i | ||||
\(649\) | −30.7386 | −1.20660 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.05171 | + | 3.74571i | −0.0412196 | + | 0.146806i | ||||
\(652\) | −30.9526 | − | 37.1231i | −1.21220 | − | 1.45385i | ||||
\(653\) | 26.9848 | 1.05600 | 0.527999 | − | 0.849245i | \(-0.322942\pi\) | ||||
0.527999 | + | 0.849245i | \(0.322942\pi\) | |||||||
\(654\) | −16.9234 | − | 14.5940i | −0.661757 | − | 0.570671i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 28.0281 | + | 5.12311i | 1.09431 | + | 0.200024i | ||||
\(657\) | 12.8769 | − | 21.1231i | 0.502375 | − | 0.824091i | ||||
\(658\) | 0.525853 | − | 1.12311i | 0.0204999 | − | 0.0437832i | ||||
\(659\) | −26.9764 | −1.05085 | −0.525425 | − | 0.850840i | \(-0.676094\pi\) | ||||
−0.525425 | + | 0.850840i | \(0.676094\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.1080 | −1.79339 | −0.896696 | − | 0.442647i | \(-0.854039\pi\) | ||||
−0.896696 | + | 0.442647i | \(0.854039\pi\) | |||||||
\(662\) | −16.8078 | + | 35.8977i | −0.653252 | + | 1.39520i | ||||
\(663\) | −2.92456 | + | 10.4160i | −0.113580 | + | 0.404523i | ||||
\(664\) | −12.8078 | + | 3.36750i | −0.497038 | + | 0.130684i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11.0436 | + | 7.32165i | −0.427932 | + | 0.283708i | ||||
\(667\) | −38.9699 | −1.50892 | ||||||||
\(668\) | −4.31534 | + | 3.59806i | −0.166966 | + | 0.139213i | ||||
\(669\) | −30.0540 | − | 8.43845i | −1.16195 | − | 0.326249i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.8836 | −0.844809 | ||||||||
\(672\) | 7.14361 | − | 5.75767i | 0.275571 | − | 0.222107i | ||||
\(673\) | − | 10.4924i | − | 0.404453i | −0.979339 | − | 0.202227i | \(-0.935182\pi\) | ||
0.979339 | − | 0.202227i | \(-0.0648177\pi\) | |||||||
\(674\) | −20.6843 | + | 44.1771i | −0.796729 | + | 1.70164i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.15767 | + | 4.98651i | 0.159910 | + | 0.191789i | ||||
\(677\) | −34.4924 | −1.32565 | −0.662826 | − | 0.748774i | \(-0.730643\pi\) | ||||
−0.662826 | + | 0.748774i | \(0.730643\pi\) | |||||||
\(678\) | −25.9700 | − | 22.3955i | −0.997373 | − | 0.860093i | ||||
\(679\) | 5.61856i | 0.215620i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.05398 | − | 14.4384i | 0.155349 | − | 0.553282i | ||||
\(682\) | 6.14441 | − | 13.1231i | 0.235282 | − | 0.502510i | ||||
\(683\) | − | 36.1606i | − | 1.38365i | −0.722067 | − | 0.691823i | \(-0.756808\pi\) | ||
0.722067 | − | 0.691823i | \(-0.243192\pi\) | |||||||
\(684\) | −25.3509 | + | 3.76782i | −0.969315 | + | 0.144066i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.7392 | − | 7.36932i | −0.600927 | − | 0.281362i | ||||
\(687\) | 0.410574 | + | 0.115279i | 0.0156644 | + | 0.00439818i | ||||
\(688\) | 1.05171 | − | 5.75379i | 0.0400959 | − | 0.219361i | ||||
\(689\) | 13.2614i | 0.505218i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 29.0798i | − | 1.10625i | −0.833100 | − | 0.553123i | \(-0.813436\pi\) | ||
0.833100 | − | 0.553123i | \(-0.186564\pi\) | |||||||
\(692\) | 2.56155 | + | 3.07221i | 0.0973756 | + | 0.116788i | ||||
\(693\) | 10.2462 | + | 6.24621i | 0.389221 | + | 0.237274i | ||||
\(694\) | 14.3153 | − | 30.5744i | 0.543403 | − | 1.16059i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −25.0945 | − | 0.417142i | −0.951205 | − | 0.0158117i | ||||
\(697\) | 14.2462i | 0.539614i | ||||||||
\(698\) | 17.9309 | + | 8.39547i | 0.678693 | + | 0.317773i | ||||
\(699\) | 16.6757 | + | 4.68213i | 0.630731 | + | 0.177094i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 50.4924i | − | 1.90707i | −0.301278 | − | 0.953536i | \(-0.597413\pi\) | ||
0.301278 | − | 0.953536i | \(-0.402587\pi\) | |||||||
\(702\) | 21.8441 | − | 7.03857i | 0.824451 | − | 0.265654i | ||||
\(703\) | −13.3405 | −0.503148 | ||||||||
\(704\) | −29.7533 | + | 16.8078i | −1.12137 | + | 0.633466i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.80776 | − | 2.25106i | −0.180943 | − | 0.0847197i | ||||
\(707\) | 8.54312i | 0.321297i | ||||||||
\(708\) | 10.1937 | + | 22.7486i | 0.383103 | + | 0.854944i | ||||
\(709\) | 26.4924 | 0.994944 | 0.497472 | − | 0.867480i | \(-0.334262\pi\) | ||||
0.497472 | + | 0.867480i | \(0.334262\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.1617 | − | 23.2306i | 0.531104 | − | 0.871217i | ||||
\(712\) | 17.0862 | − | 4.49242i | 0.640334 | − | 0.168361i | ||||
\(713\) | −18.2462 | −0.683326 | ||||||||
\(714\) | 3.47415 | + | 2.99596i | 0.130017 | + | 0.112121i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.8114 | + | 22.5616i | 0.703016 | + | 0.843165i | ||||
\(717\) | 34.7386 | + | 9.75379i | 1.29734 | + | 0.364262i | ||||
\(718\) | 1.34700 | + | 0.630683i | 0.0502696 | + | 0.0235369i | ||||
\(719\) | −5.84912 | −0.218135 | −0.109068 | − | 0.994034i | \(-0.534787\pi\) | ||||
−0.109068 | + | 0.994034i | \(0.534787\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.6155 | 0.432585 | ||||||||
\(722\) | 0.965435 | + | 0.452029i | 0.0359298 | + | 0.0168228i | ||||
\(723\) | 18.9591 | + | 5.32326i | 0.705096 | + | 0.197974i | ||||
\(724\) | 5.43845 | + | 6.52262i | 0.202118 | + | 0.242411i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −13.4417 | − | 11.5916i | −0.498870 | − | 0.430204i | ||||
\(727\) | −26.5658 | −0.985270 | −0.492635 | − | 0.870236i | \(-0.663966\pi\) | ||||
−0.492635 | + | 0.870236i | \(0.663966\pi\) | |||||||
\(728\) | −8.00000 | + | 2.10341i | −0.296500 | + | 0.0779576i | ||||
\(729\) | −1.93087 | + | 26.9309i | −0.0715137 | + | 0.997440i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.92456 | 0.108169 | ||||||||
\(732\) | 7.25716 | + | 16.1953i | 0.268233 | + | 0.598596i | ||||
\(733\) | − | 35.1231i | − | 1.29730i | −0.761086 | − | 0.648651i | \(-0.775334\pi\) | ||
0.761086 | − | 0.648651i | \(-0.224666\pi\) | |||||||
\(734\) | 34.0248 | + | 15.9309i | 1.25588 | + | 0.588019i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35.0540 | + | 24.9559i | 1.29211 | + | 0.919885i | ||||
\(737\) | 22.2462 | 0.819450 | ||||||||
\(738\) | 25.1880 | − | 16.6991i | 0.927184 | − | 0.614701i | ||||
\(739\) | − | 18.6638i | − | 0.686559i | −0.939233 | − | 0.343279i | \(-0.888462\pi\) | ||
0.939233 | − | 0.343279i | \(-0.111538\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.2462 | + | 6.24621i | 0.817235 | + | 0.229460i | ||||
\(742\) | 5.09271 | + | 2.38447i | 0.186959 | + | 0.0875367i | ||||
\(743\) | 12.4041i | 0.455062i | 0.973771 | + | 0.227531i | \(0.0730654\pi\) | ||||
−0.973771 | + | 0.227531i | \(0.926935\pi\) | |||||||
\(744\) | −11.7496 | − | 0.195311i | −0.430761 | − | 0.00716046i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.525853 | − | 1.12311i | 0.0192528 | − | 0.0411198i | ||||
\(747\) | −7.31140 | + | 11.9935i | −0.267510 | + | 0.438820i | ||||
\(748\) | −10.9418 | − | 13.1231i | −0.400073 | − | 0.479828i | ||||
\(749\) | 0.876894i | 0.0320410i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 15.7392i | − | 0.574333i | −0.957881 | − | 0.287166i | \(-0.907287\pi\) | ||
0.957881 | − | 0.287166i | \(-0.0927133\pi\) | |||||||
\(752\) | 3.68466 | + | 0.673500i | 0.134366 | + | 0.0245600i | ||||
\(753\) | −41.8617 | − | 11.7538i | −1.52553 | − | 0.428332i | ||||
\(754\) | 20.4924 | + | 9.59482i | 0.746290 | + | 0.349423i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.22470 | − | 9.65426i | 0.0445419 | − | 0.351122i | ||||
\(757\) | − | 19.1231i | − | 0.695041i | −0.937672 | − | 0.347521i | \(-0.887024\pi\) | ||
0.937672 | − | 0.347521i | \(-0.112976\pi\) | |||||||
\(758\) | −15.0540 | + | 32.1520i | −0.546785 | + | 1.16781i | ||||
\(759\) | −15.2134 | + | 54.1833i | −0.552211 | + | 1.96673i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 51.2311i | − | 1.85712i | −0.371177 | − | 0.928562i | \(-0.621046\pi\) | ||
0.371177 | − | 0.928562i | \(-0.378954\pi\) | |||||||
\(762\) | 8.68537 | + | 7.48990i | 0.314638 | + | 0.271330i | ||||
\(763\) | 8.54312 | 0.309282 | ||||||||
\(764\) | 9.89012 | + | 11.8617i | 0.357812 | + | 0.429143i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.80776 | − | 5.99676i | 0.101449 | − | 0.216672i | ||||
\(767\) | − | 22.4742i | − | 0.811498i | ||||||
\(768\) | 22.3058 | + | 16.4455i | 0.804890 | + | 0.593424i | ||||
\(769\) | 26.9848 | 0.973098 | 0.486549 | − | 0.873653i | \(-0.338255\pi\) | ||||
0.486549 | + | 0.873653i | \(0.338255\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.15628 | − | 1.16699i | −0.149685 | − | 0.0420279i | ||||
\(772\) | −24.9559 | + | 20.8078i | −0.898181 | + | 0.748888i | ||||
\(773\) | 16.2462 | 0.584336 | 0.292168 | − | 0.956367i | \(-0.405623\pi\) | ||||
0.292168 | + | 0.956367i | \(0.405623\pi\) | |||||||
\(774\) | −3.42809 | − | 5.17077i | −0.123220 | − | 0.185859i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.4127 | + | 4.31534i | −0.589183 | + | 0.154912i | ||||
\(777\) | 1.36932 | − | 4.87689i | 0.0491240 | − | 0.174958i | ||||
\(778\) | −17.2339 | + | 36.8078i | −0.617865 | + | 1.31962i | ||||
\(779\) | 30.4268 | 1.09015 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.4924 | −1.01954 | ||||||||
\(782\) | −9.12311 | + | 19.4849i | −0.326242 | + | 0.696780i | ||||
\(783\) | −19.4849 | + | 18.1379i | −0.696335 | + | 0.648197i | ||||
\(784\) | 4.40388 | − | 24.0932i | 0.157282 | − | 0.860473i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 32.6705 | + | 28.1736i | 1.16532 | + | 1.00492i | ||||
\(787\) | 13.9817 | 0.498392 | 0.249196 | − | 0.968453i | \(-0.419834\pi\) | ||||
0.249196 | + | 0.968453i | \(0.419834\pi\) | |||||||
\(788\) | 15.6847 | + | 18.8114i | 0.558743 | + | 0.670130i | ||||
\(789\) | −7.06913 | + | 25.1771i | −0.251668 | + | 0.896328i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.1100 | 0.466137 | ||||||||
\(792\) | −10.3766 | + | 34.7283i | −0.368716 | + | 1.23402i | ||||
\(793\) | − | 16.0000i | − | 0.568177i | ||||||
\(794\) | 13.8664 | − | 29.6155i | 0.492099 | − | 1.05102i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27.0540 | − | 22.5571i | 0.958903 | − | 0.799517i | ||||
\(797\) | 36.7386 | 1.30135 | 0.650675 | − | 0.759357i | \(-0.274486\pi\) | ||||
0.650675 | + | 0.759357i | \(0.274486\pi\) | |||||||
\(798\) | 6.39871 | − | 7.42001i | 0.226512 | − | 0.262666i | ||||
\(799\) | 1.87285i | 0.0662568i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.75379 | − | 16.0000i | 0.344633 | − | 0.565332i | ||||
\(802\) | 14.3922 | − | 30.7386i | 0.508207 | − | 1.08542i | ||||
\(803\) | − | 35.2242i | − | 1.24303i | ||||||
\(804\) | −7.37740 | − | 16.4636i | −0.260181 | − | 0.580628i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.59482 | + | 4.49242i | 0.337963 | + | 0.158239i | ||||
\(807\) | 6.55498 | − | 23.3459i | 0.230746 | − | 0.821815i | ||||
\(808\) | −24.9559 | + | 6.56155i | −0.877944 | + | 0.230835i | ||||
\(809\) | − | 46.2462i | − | 1.62593i | −0.582312 | − | 0.812965i | \(-0.697852\pi\) | ||
0.582312 | − | 0.812965i | \(-0.302148\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.9246i | 0.910337i | 0.890405 | + | 0.455169i | \(0.150421\pi\) | ||||
−0.890405 | + | 0.455169i | \(0.849579\pi\) | |||||||
\(812\) | 7.36932 | − | 6.14441i | 0.258612 | − | 0.215627i | ||||
\(813\) | −14.8769 | + | 52.9848i | −0.521755 | + | 1.85826i | ||||
\(814\) | −8.00000 | + | 17.0862i | −0.280400 | + | 0.598872i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.08336 | + | 12.4496i | −0.212960 | + | 0.435823i | ||||
\(817\) | − | 6.24621i | − | 0.218527i | ||||||
\(818\) | −0.807764 | − | 0.378206i | −0.0282428 | − | 0.0132237i | ||||
\(819\) | −4.56685 | + | 7.49141i | −0.159579 | + | 0.261771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.2311i | 1.02017i | 0.860124 | + | 0.510085i | \(0.170386\pi\) | ||||
−0.860124 | + | 0.510085i | \(0.829614\pi\) | |||||||
\(822\) | 15.2967 | + | 13.1913i | 0.533535 | + | 0.460098i | ||||
\(823\) | −46.8071 | −1.63159 | −0.815797 | − | 0.578338i | \(-0.803701\pi\) | ||||
−0.815797 | + | 0.578338i | \(0.803701\pi\) | |||||||
\(824\) | 8.92132 | + | 33.9309i | 0.310789 | + | 1.18204i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.63068 | − | 4.04100i | −0.300300 | − | 0.140604i | ||||
\(827\) | 13.2252i | 0.459887i | 0.973204 | + | 0.229943i | \(0.0738541\pi\) | ||||
−0.973204 | + | 0.229943i | \(0.926146\pi\) | |||||||
\(828\) | 45.1443 | − | 6.70964i | 1.56887 | − | 0.233176i | ||||
\(829\) | 17.1231 | 0.594710 | 0.297355 | − | 0.954767i | \(-0.403896\pi\) | ||||
0.297355 | + | 0.954767i | \(0.403896\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.641132 | − | 2.28343i | 0.0222406 | − | 0.0792112i | ||||
\(832\) | −12.2888 | − | 21.7538i | −0.426038 | − | 0.754177i | ||||
\(833\) | 12.2462 | 0.424306 | ||||||||
\(834\) | 22.1817 | − | 25.7222i | 0.768090 | − | 0.890686i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −28.0281 | + | 23.3693i | −0.969371 | + | 0.808245i | ||||
\(837\) | −9.12311 | + | 8.49242i | −0.315341 | + | 0.293541i | ||||
\(838\) | −7.86962 | − | 3.68466i | −0.271851 | − | 0.127284i | ||||
\(839\) | −48.5647 | −1.67664 | −0.838320 | − | 0.545179i | \(-0.816462\pi\) | ||||
−0.838320 | + | 0.545179i | \(0.816462\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.75379 | 0.0949582 | ||||||||
\(842\) | −0.807764 | − | 0.378206i | −0.0278374 | − | 0.0130338i | ||||
\(843\) | 12.9300 | − | 46.0507i | 0.445331 | − | 1.58607i | ||||
\(844\) | −2.06913 | + | 1.72521i | −0.0712224 | + | 0.0593840i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.31130 | − | 2.19531i | 0.113845 | − | 0.0754764i | ||||
\(847\) | 6.78554 | 0.233154 | ||||||||
\(848\) | −3.05398 | + | 16.7080i | −0.104874 | + | 0.573756i | ||||
\(849\) | 7.31534 | + | 2.05398i | 0.251062 | + | 0.0704923i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.7565 | 0.814362 | ||||||||
\(852\) | 9.44880 | + | 21.0862i | 0.323711 | + | 0.722402i | ||||
\(853\) | 49.8617i | 1.70723i | 0.520902 | + | 0.853617i | \(0.325596\pi\) | ||||
−0.520902 | + | 0.853617i | \(0.674404\pi\) | |||||||
\(854\) | −6.14441 | − | 2.87689i | −0.210257 | − | 0.0984453i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.56155 | + | 0.673500i | −0.0875521 | + | 0.0230198i | ||||
\(857\) | −28.7386 | −0.981693 | −0.490847 | − | 0.871246i | \(-0.663312\pi\) | ||||
−0.490847 | + | 0.871246i | \(0.663312\pi\) | |||||||
\(858\) | 21.3405 | − | 24.7467i | 0.728554 | − | 0.844839i | ||||
\(859\) | − | 37.3923i | − | 1.27581i | −0.770115 | − | 0.637905i | \(-0.779801\pi\) | ||
0.770115 | − | 0.637905i | \(-0.220199\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.12311 | + | 11.1231i | −0.106435 | + | 0.379074i | ||||
\(862\) | −46.1660 | − | 21.6155i | −1.57242 | − | 0.736228i | ||||
\(863\) | − | 27.6175i | − | 0.940110i | −0.882637 | − | 0.470055i | \(-0.844234\pi\) | ||
0.882637 | − | 0.470055i | \(-0.155766\pi\) | |||||||
\(864\) | 29.1423 | − | 3.83742i | 0.991442 | − | 0.130552i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10.7942 | + | 23.0540i | −0.366801 | + | 0.783406i | ||||
\(867\) | 21.6784 | + | 6.08677i | 0.736236 | + | 0.206718i | ||||
\(868\) | 3.45041 | − | 2.87689i | 0.117115 | − | 0.0976482i | ||||
\(869\) | − | 38.7386i | − | 1.31412i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.2651i | 0.551121i | ||||||||
\(872\) | 6.56155 | + | 24.9559i | 0.222202 | + | 0.845112i | ||||
\(873\) | −9.36932 | + | 15.3693i | −0.317103 | + | 0.520173i | ||||
\(874\) | 41.6155 | + | 19.4849i | 1.40767 | + | 0.659088i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −26.0682 | + | 11.6812i | −0.880762 | + | 0.394672i | ||||
\(877\) | 3.61553i | 0.122088i | 0.998135 | + | 0.0610439i | \(0.0194430\pi\) | ||||
−0.998135 | + | 0.0610439i | \(0.980557\pi\) | |||||||
\(878\) | −17.9309 | + | 38.2964i | −0.605138 | + | 1.29244i | ||||
\(879\) | 50.8481 | + | 14.2770i | 1.71506 | + | 0.481550i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 25.3693i | − | 0.854714i | −0.904083 | − | 0.427357i | \(-0.859445\pi\) | ||
0.904083 | − | 0.427357i | \(-0.140555\pi\) | |||||||
\(882\) | −14.3547 | − | 21.6519i | −0.483348 | − | 0.729058i | ||||
\(883\) | −10.8265 | −0.364342 | −0.182171 | − | 0.983267i | \(-0.558312\pi\) | ||||
−0.182171 | + | 0.983267i | \(0.558312\pi\) | |||||||
\(884\) | 9.59482 | − | 8.00000i | 0.322709 | − | 0.269069i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.4384 | + | 32.9731i | −0.518665 | + | 1.10775i | ||||
\(887\) | − | 53.4774i | − | 1.79560i | −0.440408 | − | 0.897798i | \(-0.645166\pi\) | ||
0.440408 | − | 0.897798i | \(-0.354834\pi\) | |||||||
\(888\) | 15.2979 | + | 0.254294i | 0.513364 | + | 0.00853356i | ||||
\(889\) | −4.38447 | −0.147050 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.6121 | + | 34.1725i | 0.590027 | + | 1.14482i | ||||
\(892\) | 23.0830 | + | 27.6847i | 0.772876 | + | 0.926951i | ||||
\(893\) | 4.00000 | 0.133855 | ||||||||
\(894\) | −22.3955 | + | 25.9700i | −0.749017 | + | 0.868568i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.5636 | + | 0.807764i | −0.352906 | + | 0.0269855i | ||||
\(897\) | −39.6155 | − | 11.1231i | −1.32272 | − | 0.371390i | ||||
\(898\) | 1.57756 | − | 3.36932i | 0.0526438 | − | 0.112436i | ||||
\(899\) | −12.2888 | −0.409855 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.49242 | −0.282924 | ||||||||
\(902\) | 18.2462 | − | 38.9699i | 0.607532 | − | 1.29756i | ||||
\(903\) | 2.28343 | + | 0.641132i | 0.0759877 | + | 0.0213355i | ||||
\(904\) | 10.0691 | + | 38.2964i | 0.334894 | + | 1.27372i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.82907 | − | 11.3979i | 0.326549 | − | 0.378670i | ||||
\(907\) | −35.8653 | −1.19089 | −0.595444 | − | 0.803397i | \(-0.703024\pi\) | ||||
−0.595444 | + | 0.803397i | \(0.703024\pi\) | |||||||
\(908\) | −13.3002 | + | 11.0895i | −0.441382 | + | 0.368017i | ||||
\(909\) | −14.2462 | + | 23.3693i | −0.472517 | + | 0.775111i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.8944 | 1.38802 | 0.694012 | − | 0.719963i | \(-0.255841\pi\) | ||||
0.694012 | + | 0.719963i | \(0.255841\pi\) | |||||||
\(912\) | 26.5896 | + | 12.9927i | 0.880470 | + | 0.430232i | ||||
\(913\) | 20.0000i | 0.661903i | ||||||||
\(914\) | −5.99676 | + | 12.8078i | −0.198355 | + | 0.423643i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.315342 | − | 0.378206i | −0.0104192 | − | 0.0124963i | ||||
\(917\) | −16.4924 | −0.544628 | ||||||||
\(918\) | 4.50742 | + | 13.9887i | 0.148767 | + | 0.461695i | ||||
\(919\) | 50.1423i | 1.65404i | 0.562172 | + | 0.827020i | \(0.309966\pi\) | ||||
−0.562172 | + | 0.827020i | \(0.690034\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5616 | − | 3.80776i | −0.446868 | − | 0.125470i | ||||
\(922\) | −9.51191 | + | 20.3153i | −0.313258 | + | 0.669050i | ||||
\(923\) | − | 20.8319i | − | 0.685692i | ||||||
\(924\) | −5.66622 | − | 12.6449i | −0.186405 | − | 0.415987i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.19935 | + | 0.561553i | 0.0394132 | + | 0.0184538i | ||||
\(927\) | 31.7738 | + | 19.3697i | 1.04359 | + | 0.636183i | ||||
\(928\) | 23.6089 | + | 16.8078i | 0.774998 | + | 0.551742i | ||||
\(929\) | − | 24.8769i | − | 0.816184i | −0.912941 | − | 0.408092i | \(-0.866194\pi\) | ||
0.912941 | − | 0.408092i | \(-0.133806\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 26.1552i | − | 0.857202i | ||||||
\(932\) | −12.8078 | − | 15.3610i | −0.419532 | − | 0.503167i | ||||
\(933\) | −23.6155 | − | 6.63068i | −0.773138 | − | 0.217079i | ||||
\(934\) | 9.68466 | − | 20.6843i | 0.316892 | − | 0.676811i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −25.3912 | − | 7.58674i | −0.829938 | − | 0.247980i | ||||
\(937\) | − | 10.4924i | − | 0.342773i | −0.985204 | − | 0.171386i | \(-0.945175\pi\) | ||
0.985204 | − | 0.171386i | \(-0.0548246\pi\) | |||||||
\(938\) | 6.24621 | + | 2.92456i | 0.203946 | + | 0.0954902i | ||||
\(939\) | 4.91269 | − | 17.4968i | 0.160320 | − | 0.570987i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 9.12311i | − | 0.297405i | −0.988882 | − | 0.148702i | \(-0.952490\pi\) | ||
0.988882 | − | 0.148702i | \(-0.0475096\pi\) | |||||||
\(942\) | −34.1840 | + | 39.6401i | −1.11377 | + | 1.29155i | ||||
\(943\) | −54.1833 | −1.76445 | ||||||||
\(944\) | 5.17562 | − | 28.3153i | 0.168452 | − | 0.921586i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.00000 | − | 3.74571i | −0.260102 | − | 0.121783i | ||||
\(947\) | − | 25.5141i | − | 0.829096i | −0.910027 | − | 0.414548i | \(-0.863940\pi\) | ||
0.910027 | − | 0.414548i | \(-0.136060\pi\) | |||||||
\(948\) | −28.6691 | + | 12.8467i | −0.931129 | + | 0.417241i | ||||
\(949\) | 25.7538 | 0.836003 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 54.5938 | + | 15.3287i | 1.77033 | + | 0.497066i | ||||
\(952\) | −1.34700 | − | 5.12311i | −0.0436565 | − | 0.166041i | ||||
\(953\) | 10.4924 | 0.339883 | 0.169941 | − | 0.985454i | \(-0.445642\pi\) | ||||
0.169941 | + | 0.985454i | \(0.445642\pi\) | |||||||
\(954\) | 9.95461 | + | 15.0150i | 0.322292 | + | 0.486130i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −26.6811 | − | 32.0000i | −0.862927 | − | 1.03495i | ||||
\(957\) | −10.2462 | + | 36.4924i | −0.331213 | + | 1.17963i | ||||
\(958\) | 29.3751 | + | 13.7538i | 0.949065 | + | 0.444365i | ||||
\(959\) | −7.72197 | −0.249355 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.2462 | 0.814394 | ||||||||
\(962\) | −12.4924 | − | 5.84912i | −0.402772 | − | 0.188583i | ||||
\(963\) | −1.46228 | + | 2.39871i | −0.0471213 | + | 0.0772972i | ||||
\(964\) | −14.5616 | − | 17.4644i | −0.468996 | − | 0.562492i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11.3947 | + | 13.2134i | −0.366617 | + | 0.425134i | ||||
\(967\) | −23.6412 | −0.760250 | −0.380125 | − | 0.924935i | \(-0.624119\pi\) | ||||
−0.380125 | + | 0.924935i | \(0.624119\pi\) | |||||||
\(968\) | 5.21165 | + | 19.8217i | 0.167509 | + | 0.637093i | ||||
\(969\) | −4.00000 | + | 14.2462i | −0.128499 | + | 0.457654i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.5991 | −1.33498 | −0.667490 | − | 0.744619i | \(-0.732631\pi\) | ||||
−0.667490 | + | 0.744619i | \(0.732631\pi\) | |||||||
\(972\) | 19.4492 | − | 24.3665i | 0.623834 | − | 0.781557i | ||||
\(973\) | 12.9848i | 0.416275i | ||||||||
\(974\) | −19.6326 | − | 9.19224i | −0.629069 | − | 0.294538i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.68466 | − | 20.1584i | 0.117943 | − | 0.645256i | ||||
\(977\) | −48.2462 | −1.54353 | −0.771767 | − | 0.635906i | \(-0.780627\pi\) | ||||
−0.771767 | + | 0.635906i | \(0.780627\pi\) | |||||||
\(978\) | 44.8300 | + | 38.6595i | 1.43350 | + | 1.23619i | ||||
\(979\) | − | 26.6811i | − | 0.852730i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.3693 | + | 14.2462i | 0.746125 | + | 0.454847i | ||||
\(982\) | −23.9041 | − | 11.1922i | −0.762812 | − | 0.357159i | ||||
\(983\) | − | 3.03984i | − | 0.0969558i | −0.998824 | − | 0.0484779i | \(-0.984563\pi\) | ||
0.998824 | − | 0.0484779i | \(-0.0154370\pi\) | |||||||
\(984\) | −34.8911 | − | 0.579989i | −1.11229 | − | 0.0184894i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.14441 | + | 13.1231i | −0.195678 | + | 0.417925i | ||||
\(987\) | −0.410574 | + | 1.46228i | −0.0130687 | + | 0.0465449i | ||||
\(988\) | −17.0862 | − | 20.4924i | −0.543586 | − | 0.651951i | ||||
\(989\) | 11.1231i | 0.353694i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 16.7909i | − | 0.533382i | −0.963782 | − | 0.266691i | \(-0.914070\pi\) | ||
0.963782 | − | 0.266691i | \(-0.0859303\pi\) | |||||||
\(992\) | 11.0540 | + | 7.86962i | 0.350964 | + | 0.249861i | ||||
\(993\) | 13.1231 | − | 46.7386i | 0.416449 | − | 1.48321i | ||||
\(994\) | −8.00000 | − | 3.74571i | −0.253745 | − | 0.118807i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.8013 | − | 6.63250i | 0.468997 | − | 0.210159i | ||||
\(997\) | − | 7.61553i | − | 0.241186i | −0.992702 | − | 0.120593i | \(-0.961520\pi\) | ||
0.992702 | − | 0.120593i | \(-0.0384796\pi\) | |||||||
\(998\) | 0.946025 | − | 2.02050i | 0.0299459 | − | 0.0639578i | ||||
\(999\) | 11.8782 | − | 11.0571i | 0.375811 | − | 0.349831i |
(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 | 300.2.h.b.299.7 | 8 | ||
3.2 | odd | 2 | 300.2.h.a.299.1 | 8 | |||
4.3 | odd | 2 | inner | 300.2.h.b.299.6 | 8 | ||
5.2 | odd | 4 | 60.2.e.a.11.4 | yes | 8 | ||
5.3 | odd | 4 | 300.2.e.c.251.5 | 8 | |||
5.4 | even | 2 | 300.2.h.a.299.2 | 8 | |||
12.11 | even | 2 | 300.2.h.a.299.4 | 8 | |||
15.2 | even | 4 | 60.2.e.a.11.5 | yes | 8 | ||
15.8 | even | 4 | 300.2.e.c.251.4 | 8 | |||
15.14 | odd | 2 | inner | 300.2.h.b.299.8 | 8 | ||
20.3 | even | 4 | 300.2.e.c.251.3 | 8 | |||
20.7 | even | 4 | 60.2.e.a.11.6 | yes | 8 | ||
20.19 | odd | 2 | 300.2.h.a.299.3 | 8 | |||
40.27 | even | 4 | 960.2.h.g.191.4 | 8 | |||
40.37 | odd | 4 | 960.2.h.g.191.5 | 8 | |||
60.23 | odd | 4 | 300.2.e.c.251.6 | 8 | |||
60.47 | odd | 4 | 60.2.e.a.11.3 | ✓ | 8 | ||
60.59 | even | 2 | inner | 300.2.h.b.299.5 | 8 | ||
120.77 | even | 4 | 960.2.h.g.191.3 | 8 | |||
120.107 | odd | 4 | 960.2.h.g.191.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.2.e.a.11.3 | ✓ | 8 | 60.47 | odd | 4 | ||
60.2.e.a.11.4 | yes | 8 | 5.2 | odd | 4 | ||
60.2.e.a.11.5 | yes | 8 | 15.2 | even | 4 | ||
60.2.e.a.11.6 | yes | 8 | 20.7 | even | 4 | ||
300.2.e.c.251.3 | 8 | 20.3 | even | 4 | |||
300.2.e.c.251.4 | 8 | 15.8 | even | 4 | |||
300.2.e.c.251.5 | 8 | 5.3 | odd | 4 | |||
300.2.e.c.251.6 | 8 | 60.23 | odd | 4 | |||
300.2.h.a.299.1 | 8 | 3.2 | odd | 2 | |||
300.2.h.a.299.2 | 8 | 5.4 | even | 2 | |||
300.2.h.a.299.3 | 8 | 20.19 | odd | 2 | |||
300.2.h.a.299.4 | 8 | 12.11 | even | 2 | |||
300.2.h.b.299.5 | 8 | 60.59 | even | 2 | inner | ||
300.2.h.b.299.6 | 8 | 4.3 | odd | 2 | inner | ||
300.2.h.b.299.7 | 8 | 1.1 | even | 1 | trivial | ||
300.2.h.b.299.8 | 8 | 15.14 | odd | 2 | inner | ||
960.2.h.g.191.3 | 8 | 120.77 | even | 4 | |||
960.2.h.g.191.4 | 8 | 40.27 | even | 4 | |||
960.2.h.g.191.5 | 8 | 40.37 | odd | 4 | |||
960.2.h.g.191.6 | 8 | 120.107 | odd | 4 |