Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(251,300)]
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, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.e (of order \(2\), degree \(1\), 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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.4 | ||
Root | \(-0.599676 - 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.251 |
Dual form | 300.2.e.c.251.3 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.599676 | + | 1.28078i | −0.424035 | + | 0.905646i | ||||
\(3\) | −0.468213 | − | 1.66757i | −0.270323 | − | 0.962770i | ||||
\(4\) | −1.28078 | − | 1.53610i | −0.640388 | − | 0.768051i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.41656 | + | 0.400324i | 0.986555 | + | 0.163431i | ||||
\(7\) | − | 0.936426i | − | 0.353936i | −0.984217 | − | 0.176968i | \(-0.943371\pi\) | ||
0.984217 | − | 0.176968i | \(-0.0566289\pi\) | |||||||
\(8\) | 2.73546 | − | 0.719224i | 0.967130 | − | 0.254284i | ||||
\(9\) | −2.56155 | + | 1.56155i | −0.853851 | + | 0.520518i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.27156 | −1.28792 | −0.643962 | − | 0.765058i | \(-0.722710\pi\) | ||||
−0.643962 | + | 0.765058i | \(0.722710\pi\) | |||||||
\(12\) | −1.96188 | + | 2.85500i | −0.566345 | + | 0.824168i | ||||
\(13\) | −3.12311 | −0.866194 | −0.433097 | − | 0.901347i | \(-0.642579\pi\) | ||||
−0.433097 | + | 0.901347i | \(0.642579\pi\) | |||||||
\(14\) | 1.19935 | + | 0.561553i | 0.320541 | + | 0.150081i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.719224 | + | 3.93481i | −0.179806 | + | 0.983702i | ||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | −0.463897 | − | 4.21720i | −0.109342 | − | 0.994004i | ||||
\(19\) | − | 4.27156i | − | 0.979963i | −0.871733 | − | 0.489981i | \(-0.837004\pi\) | ||
0.871733 | − | 0.489981i | \(-0.162996\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.56155 | + | 0.438447i | −0.340759 | + | 0.0956770i | ||||
\(22\) | 2.56155 | − | 5.47091i | 0.546125 | − | 1.16640i | ||||
\(23\) | −7.60669 | −1.58610 | −0.793052 | − | 0.609154i | \(-0.791509\pi\) | ||||
−0.793052 | + | 0.609154i | \(0.791509\pi\) | |||||||
\(24\) | −2.48013 | − | 4.22480i | −0.506254 | − | 0.862384i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.87285 | − | 4.00000i | 0.367297 | − | 0.784465i | ||||
\(27\) | 3.80335 | + | 3.54042i | 0.731954 | + | 0.681354i | ||||
\(28\) | −1.43845 | + | 1.19935i | −0.271841 | + | 0.226656i | ||||
\(29\) | − | 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 | \(-0.0691088\pi\) | |||||||
\(32\) | −4.60831 | − | 3.28078i | −0.814642 | − | 0.579965i | ||||
\(33\) | 2.00000 | + | 7.12311i | 0.348155 | + | 1.23997i | ||||
\(34\) | 2.56155 | + | 1.19935i | 0.439303 | + | 0.205687i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.67948 | + | 1.93481i | 0.946580 | + | 0.322468i | ||||
\(37\) | 3.12311 | 0.513435 | 0.256718 | − | 0.966486i | \(-0.417359\pi\) | ||||
0.256718 | + | 0.966486i | \(0.417359\pi\) | |||||||
\(38\) | 5.47091 | + | 2.56155i | 0.887499 | + | 0.415539i | ||||
\(39\) | 1.46228 | + | 5.20798i | 0.234152 | + | 0.833945i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.12311i | 1.11244i | 0.831034 | + | 0.556221i | \(0.187749\pi\) | ||||
−0.831034 | + | 0.556221i | \(0.812251\pi\) | |||||||
\(42\) | 0.374874 | − | 2.26293i | 0.0578442 | − | 0.349177i | ||||
\(43\) | − | 1.46228i | − | 0.222995i | −0.993765 | − | 0.111498i | \(-0.964435\pi\) | ||
0.993765 | − | 0.111498i | \(-0.0355648\pi\) | |||||||
\(44\) | 5.47091 | + | 6.56155i | 0.824771 | + | 0.989191i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.56155 | − | 9.74247i | 0.672564 | − | 1.43645i | ||||
\(47\) | 0.936426 | 0.136592 | 0.0682959 | − | 0.997665i | \(-0.478244\pi\) | ||||
0.0682959 | + | 0.997665i | \(0.478244\pi\) | |||||||
\(48\) | 6.89830 | − | 0.642976i | 0.995684 | − | 0.0928056i | ||||
\(49\) | 6.12311 | 0.874729 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.33513 | + | 0.936426i | −0.467012 | + | 0.131126i | ||||
\(52\) | 4.00000 | + | 4.79741i | 0.554700 | + | 0.665281i | ||||
\(53\) | − | 4.24621i | − | 0.583262i | −0.956531 | − | 0.291631i | \(-0.905802\pi\) | ||
0.956531 | − | 0.291631i | \(-0.0941979\pi\) | |||||||
\(54\) | −6.81526 | + | 2.74813i | −0.927440 | + | 0.373973i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.673500 | − | 2.56155i | −0.0900002 | − | 0.342302i | ||||
\(57\) | −7.12311 | + | 2.00000i | −0.943478 | + | 0.264906i | ||||
\(58\) | 6.56155 | + | 3.07221i | 0.861574 | + | 0.403400i | ||||
\(59\) | −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 | \(0.606366\pi\) | |||||||
\(62\) | 3.07221 | + | 1.43845i | 0.390171 | + | 0.182683i | ||||
\(63\) | 1.46228 | + | 2.39871i | 0.184230 | + | 0.302209i | ||||
\(64\) | 6.96543 | − | 3.93481i | 0.870679 | − | 0.491851i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −10.3225 | − | 1.71001i | −1.27061 | − | 0.210487i | ||||
\(67\) | − | 5.20798i | − | 0.636257i | −0.948048 | − | 0.318128i | \(-0.896946\pi\) | ||
0.948048 | − | 0.318128i | \(-0.103054\pi\) | |||||||
\(68\) | −3.07221 | + | 2.56155i | −0.372560 | + | 0.310634i | ||||
\(69\) | 3.56155 | + | 12.6847i | 0.428761 | + | 1.52705i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.67026 | 0.791615 | 0.395807 | − | 0.918334i | \(-0.370465\pi\) | ||||
0.395807 | + | 0.918334i | \(0.370465\pi\) | |||||||
\(72\) | −5.88391 | + | 6.11389i | −0.693425 | + | 0.720529i | ||||
\(73\) | 8.24621 | 0.965146 | 0.482573 | − | 0.875856i | \(-0.339702\pi\) | ||||
0.482573 | + | 0.875856i | \(0.339702\pi\) | |||||||
\(74\) | −1.87285 | + | 4.00000i | −0.217715 | + | 0.464991i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.56155 | + | 5.47091i | −0.752662 | + | 0.627557i | ||||
\(77\) | 4.00000i | 0.455842i | ||||||||
\(78\) | −7.54716 | − | 1.25025i | −0.854547 | − | 0.141563i | ||||
\(79\) | 9.06897i | 1.02034i | 0.860074 | + | 0.510169i | \(0.170417\pi\) | ||||
−0.860074 | + | 0.510169i | \(0.829583\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.12311 | − | 8.00000i | 0.458123 | − | 0.888889i | ||||
\(82\) | −9.12311 | − | 4.27156i | −1.00748 | − | 0.471715i | ||||
\(83\) | 4.68213 | 0.513931 | 0.256965 | − | 0.966421i | \(-0.417277\pi\) | ||||
0.256965 | + | 0.966421i | \(0.417277\pi\) | |||||||
\(84\) | 2.67350 | + | 1.83715i | 0.291703 | + | 0.200450i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.87285 | + | 0.876894i | 0.201955 | + | 0.0945580i | ||||
\(87\) | −8.54312 | + | 2.39871i | −0.915918 | + | 0.257168i | ||||
\(88\) | −11.6847 | + | 3.07221i | −1.24559 | + | 0.327498i | ||||
\(89\) | − | 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 | ||||||||
\(92\) | 9.74247 | + | 11.6847i | 1.01572 | + | 1.21821i | ||||
\(93\) | −4.00000 | + | 1.12311i | −0.414781 | + | 0.116461i | ||||
\(94\) | −0.561553 | + | 1.19935i | −0.0579198 | + | 0.123704i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.31324 | + | 9.22076i | −0.338156 | + | 0.941090i | ||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | −3.67188 | + | 7.84233i | −0.370916 | + | 0.792195i | ||||
\(99\) | 10.9418 | − | 6.67026i | 1.09969 | − | 0.670387i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 9.12311i | − | 0.907783i | −0.891057 | − | 0.453891i | \(-0.850035\pi\) | ||
0.891057 | − | 0.453891i | \(-0.149965\pi\) | |||||||
\(102\) | 0.800647 | − | 4.83311i | 0.0792759 | − | 0.478549i | ||||
\(103\) | 12.4041i | 1.22221i | 0.791549 | + | 0.611106i | \(0.209275\pi\) | ||||
−0.791549 | + | 0.611106i | \(0.790725\pi\) | |||||||
\(104\) | −8.54312 | + | 2.24621i | −0.837722 | + | 0.220259i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.43845 | + | 2.54635i | 0.528229 | + | 0.247324i | ||||
\(107\) | −0.936426 | −0.0905278 | −0.0452639 | − | 0.998975i | \(-0.514413\pi\) | ||||
−0.0452639 | + | 0.998975i | \(0.514413\pi\) | |||||||
\(108\) | 0.567212 | − | 10.3768i | 0.0545800 | − | 0.998509i | ||||
\(109\) | −9.12311 | −0.873835 | −0.436918 | − | 0.899502i | \(-0.643930\pi\) | ||||
−0.436918 | + | 0.899502i | \(0.643930\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.46228 | − | 5.20798i | −0.138793 | − | 0.494320i | ||||
\(112\) | 3.68466 | + | 0.673500i | 0.348167 | + | 0.0636398i | ||||
\(113\) | − | 14.0000i | − | 1.31701i | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||
0.752577 | − | 0.658505i | \(-0.228811\pi\) | |||||||
\(114\) | 1.71001 | − | 10.3225i | 0.160157 | − | 0.966787i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.86962 | + | 6.56155i | −0.730676 | + | 0.609225i | ||||
\(117\) | 8.00000 | − | 4.87689i | 0.739600 | − | 0.450869i | ||||
\(118\) | 4.31534 | − | 9.21662i | 0.397259 | − | 0.848458i | ||||
\(119\) | −1.87285 | −0.171684 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.24621 | 0.658746 | ||||||||
\(122\) | 3.07221 | − | 6.56155i | 0.278144 | − | 0.594055i | ||||
\(123\) | 11.8782 | − | 3.33513i | 1.07103 | − | 0.300719i | ||||
\(124\) | −3.68466 | + | 3.07221i | −0.330892 | + | 0.275892i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.94910 | + | 0.434406i | −0.351814 | + | 0.0386999i | ||||
\(127\) | 4.68213i | 0.415472i | 0.978185 | + | 0.207736i | \(0.0666095\pi\) | ||||
−0.978185 | + | 0.207736i | \(0.933391\pi\) | |||||||
\(128\) | 0.862603 | + | 11.2808i | 0.0762440 | + | 0.997089i | ||||
\(129\) | −2.43845 | + | 0.684658i | −0.214693 | + | 0.0602808i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.6121 | 1.53878 | 0.769388 | − | 0.638782i | \(-0.220562\pi\) | ||||
0.769388 | + | 0.638782i | \(0.220562\pi\) | |||||||
\(132\) | 8.38027 | − | 12.1953i | 0.729409 | − | 1.06147i | ||||
\(133\) | −4.00000 | −0.346844 | ||||||||
\(134\) | 6.67026 | + | 3.12311i | 0.576223 | + | 0.269795i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.43845 | − | 5.47091i | −0.123346 | − | 0.469127i | ||||
\(137\) | − | 8.24621i | − | 0.704521i | −0.935902 | − | 0.352261i | \(-0.885413\pi\) | ||
0.935902 | − | 0.352261i | \(-0.114587\pi\) | |||||||
\(138\) | −18.3820 | − | 3.04514i | −1.56478 | − | 0.259219i | ||||
\(139\) | − | 13.8664i | − | 1.17613i | −0.808813 | − | 0.588066i | \(-0.799890\pi\) | ||
0.808813 | − | 0.588066i | \(-0.200110\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.438447 | − | 1.56155i | −0.0369239 | − | 0.131506i | ||||
\(142\) | −4.00000 | + | 8.54312i | −0.335673 | + | 0.716922i | ||||
\(143\) | 13.3405 | 1.11559 | ||||||||
\(144\) | −4.30208 | − | 11.2023i | −0.358507 | − | 0.933527i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.94506 | + | 10.5616i | −0.409256 | + | 0.874080i | ||||
\(147\) | −2.86692 | − | 10.2107i | −0.236459 | − | 0.842163i | ||||
\(148\) | −4.00000 | − | 4.79741i | −0.328798 | − | 0.394345i | ||||
\(149\) | − | 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 | \(0.919565\pi\) | |||||||
\(152\) | −3.07221 | − | 11.6847i | −0.249189 | − | 0.947751i | ||||
\(153\) | 3.12311 | + | 5.12311i | 0.252488 | + | 0.414179i | ||||
\(154\) | −5.12311 | − | 2.39871i | −0.412832 | − | 0.193293i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.12715 | − | 8.91648i | 0.490564 | − | 0.713889i | ||||
\(157\) | −21.3693 | −1.70546 | −0.852729 | − | 0.522354i | \(-0.825054\pi\) | ||||
−0.852729 | + | 0.522354i | \(0.825054\pi\) | |||||||
\(158\) | −11.6153 | − | 5.43845i | −0.924065 | − | 0.432660i | ||||
\(159\) | −7.08084 | + | 1.98813i | −0.561547 | + | 0.157669i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.12311i | 0.561379i | ||||||||
\(162\) | 7.77368 | + | 10.0782i | 0.610758 | + | 0.791817i | ||||
\(163\) | − | 24.1671i | − | 1.89291i | −0.322834 | − | 0.946456i | \(-0.604636\pi\) | ||
0.322834 | − | 0.946456i | \(-0.395364\pi\) | |||||||
\(164\) | 10.9418 | − | 9.12311i | 0.854413 | − | 0.712395i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.80776 | + | 5.99676i | −0.217925 | + | 0.465439i | ||||
\(167\) | −2.80928 | −0.217389 | −0.108694 | − | 0.994075i | \(-0.534667\pi\) | ||||
−0.108694 | + | 0.994075i | \(0.534667\pi\) | |||||||
\(168\) | −3.95622 | + | 2.32246i | −0.305229 | + | 0.179182i | ||||
\(169\) | −3.24621 | −0.249709 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.67026 | + | 10.9418i | 0.510088 | + | 0.836742i | ||||
\(172\) | −2.24621 | + | 1.87285i | −0.171272 | + | 0.142804i | ||||
\(173\) | − | 2.00000i | − | 0.152057i | −0.997106 | − | 0.0760286i | \(-0.975776\pi\) | ||
0.997106 | − | 0.0760286i | \(-0.0242240\pi\) | |||||||
\(174\) | 2.05090 | − | 12.3803i | 0.155478 | − | 0.938546i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.07221 | − | 16.8078i | 0.231576 | − | 1.26693i | ||||
\(177\) | 3.36932 | + | 12.0000i | 0.253253 | + | 0.901975i | ||||
\(178\) | 8.00000 | + | 3.74571i | 0.599625 | + | 0.280752i | ||||
\(179\) | 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 | \(0.449557\pi\) | |||||||
\(182\) | −3.74571 | − | 1.75379i | −0.277650 | − | 0.129999i | ||||
\(183\) | 2.39871 | + | 8.54312i | 0.177317 | + | 0.631525i | ||||
\(184\) | −20.8078 | + | 5.47091i | −1.53397 | + | 0.403321i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.960258 | − | 5.79661i | 0.0704096 | − | 0.425028i | ||||
\(187\) | 8.54312i | 0.624735i | ||||||||
\(188\) | −1.19935 | − | 1.43845i | −0.0874718 | − | 0.104910i | ||||
\(189\) | 3.31534 | − | 3.56155i | 0.241156 | − | 0.259065i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.72197 | −0.558742 | −0.279371 | − | 0.960183i | \(-0.590126\pi\) | ||||
−0.279371 | + | 0.960183i | \(0.590126\pi\) | |||||||
\(192\) | −9.82286 | − | 9.77299i | −0.708904 | − | 0.705305i | ||||
\(193\) | −16.2462 | −1.16943 | −0.584714 | − | 0.811240i | \(-0.698793\pi\) | ||||
−0.584714 | + | 0.811240i | \(0.698793\pi\) | |||||||
\(194\) | −3.59806 | + | 7.68466i | −0.258326 | + | 0.551726i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.84233 | − | 9.40572i | −0.560166 | − | 0.671837i | ||||
\(197\) | 12.2462i | 0.872506i | 0.899824 | + | 0.436253i | \(0.143695\pi\) | ||||
−0.899824 | + | 0.436253i | \(0.856305\pi\) | |||||||
\(198\) | 1.98156 | + | 18.0140i | 0.140824 | + | 1.28020i | ||||
\(199\) | 17.6121i | 1.24849i | 0.781230 | + | 0.624244i | \(0.214593\pi\) | ||||
−0.781230 | + | 0.624244i | \(0.785407\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.68466 | + | 2.43845i | −0.612569 | + | 0.171995i | ||||
\(202\) | 11.6847 | + | 5.47091i | 0.822130 | + | 0.384932i | ||||
\(203\) | −4.79741 | −0.336712 | ||||||||
\(204\) | 5.71001 | + | 3.92375i | 0.399780 | + | 0.274718i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.8869 | − | 7.43845i | −1.10689 | − | 0.518261i | ||||
\(207\) | 19.4849 | − | 11.8782i | 1.35430 | − | 0.825595i | ||||
\(208\) | 2.24621 | − | 12.2888i | 0.155747 | − | 0.852077i | ||||
\(209\) | 18.2462i | 1.26212i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.34700i | 0.0927313i | 0.998925 | + | 0.0463656i | \(0.0147639\pi\) | ||||
−0.998925 | + | 0.0463656i | \(0.985236\pi\) | |||||||
\(212\) | −6.52262 | + | 5.43845i | −0.447975 | + | 0.373514i | ||||
\(213\) | −3.12311 | − | 11.1231i | −0.213992 | − | 0.762143i | ||||
\(214\) | 0.561553 | − | 1.19935i | 0.0383870 | − | 0.0819861i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 12.9502 | + | 6.94920i | 0.881152 | + | 0.472833i | ||||
\(217\) | −2.24621 | −0.152483 | ||||||||
\(218\) | 5.47091 | − | 11.6847i | 0.370537 | − | 0.791385i | ||||
\(219\) | −3.86098 | − | 13.7511i | −0.260901 | − | 0.929213i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.24621i | 0.420166i | ||||||||
\(222\) | 7.54716 | + | 1.25025i | 0.506532 | + | 0.0839115i | ||||
\(223\) | 18.0227i | 1.20689i | 0.797406 | + | 0.603443i | \(0.206205\pi\) | ||||
−0.797406 | + | 0.603443i | \(0.793795\pi\) | |||||||
\(224\) | −3.07221 | + | 4.31534i | −0.205270 | + | 0.288331i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.9309 | + | 8.39547i | 1.19274 | + | 0.558458i | ||||
\(227\) | −8.65840 | −0.574678 | −0.287339 | − | 0.957829i | \(-0.592771\pi\) | ||||
−0.287339 | + | 0.957829i | \(0.592771\pi\) | |||||||
\(228\) | 12.1953 | + | 8.38027i | 0.807654 | + | 0.554997i | ||||
\(229\) | 0.246211 | 0.0162701 | 0.00813505 | − | 0.999967i | \(-0.497411\pi\) | ||||
0.00813505 | + | 0.999967i | \(0.497411\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.67026 | − | 1.87285i | 0.438871 | − | 0.123225i | ||||
\(232\) | −3.68466 | − | 14.0140i | −0.241910 | − | 0.920066i | ||||
\(233\) | 10.0000i | 0.655122i | 0.944830 | + | 0.327561i | \(0.106227\pi\) | ||||
−0.944830 | + | 0.327561i | \(0.893773\pi\) | |||||||
\(234\) | 1.44880 | + | 13.1708i | 0.0947110 | + | 0.861000i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.21662 | + | 11.0540i | 0.599951 | + | 0.719553i | ||||
\(237\) | 15.1231 | − | 4.24621i | 0.982351 | − | 0.275821i | ||||
\(238\) | 1.12311 | − | 2.39871i | 0.0728001 | − | 0.155485i | ||||
\(239\) | −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 | \(0.619335\pi\) | |||||||
\(242\) | −4.34538 | + | 9.28078i | −0.279332 | + | 0.596591i | ||||
\(243\) | −15.2710 | − | 3.12985i | −0.979636 | − | 0.200780i | ||||
\(244\) | 6.56155 | + | 7.86962i | 0.420060 | + | 0.503801i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.85155 | + | 17.2134i | −0.181808 | + | 1.09749i | ||||
\(247\) | 13.3405i | 0.848837i | ||||||||
\(248\) | −1.72521 | − | 6.56155i | −0.109551 | − | 0.416659i | ||||
\(249\) | −2.19224 | − | 7.80776i | −0.138927 | − | 0.494797i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.1035 | −1.58452 | −0.792259 | − | 0.610184i | \(-0.791095\pi\) | ||||
−0.792259 | + | 0.610184i | \(0.791095\pi\) | |||||||
\(252\) | 1.81181 | − | 5.31842i | 0.114133 | − | 0.335029i | ||||
\(253\) | 32.4924 | 2.04278 | ||||||||
\(254\) | −5.99676 | − | 2.80776i | −0.376270 | − | 0.176175i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.9654 | − | 5.66001i | −0.935340 | − | 0.353751i | ||||
\(257\) | 2.49242i | 0.155473i | 0.996974 | + | 0.0777365i | \(0.0247693\pi\) | ||||
−0.996974 | + | 0.0777365i | \(0.975231\pi\) | |||||||
\(258\) | 0.585385 | − | 3.53368i | 0.0364445 | − | 0.219997i | ||||
\(259\) | − | 2.92456i | − | 0.181723i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | + | 13.1231i | 0.495188 | + | 0.812300i | ||||
\(262\) | −10.5616 | + | 22.5571i | −0.652495 | + | 1.39359i | ||||
\(263\) | −15.0981 | −0.930989 | −0.465494 | − | 0.885051i | \(-0.654123\pi\) | ||||
−0.465494 | + | 0.885051i | \(0.654123\pi\) | |||||||
\(264\) | 10.5940 | + | 18.0465i | 0.652017 | + | 1.11068i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.39871 | − | 5.12311i | 0.147074 | − | 0.314118i | ||||
\(267\) | −10.4160 | + | 2.92456i | −0.637447 | + | 0.178980i | ||||
\(268\) | −8.00000 | + | 6.67026i | −0.488678 | + | 0.407451i | ||||
\(269\) | 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 | \(-0.415608\pi\) | |||||||
\(272\) | 7.86962 | + | 1.43845i | 0.477166 | + | 0.0872187i | ||||
\(273\) | 4.87689 | − | 1.36932i | 0.295163 | − | 0.0828748i | ||||
\(274\) | 10.5616 | + | 4.94506i | 0.638047 | + | 0.298742i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 14.9234 | − | 21.7171i | 0.898282 | − | 1.30722i | ||||
\(277\) | 1.36932 | 0.0822743 | 0.0411371 | − | 0.999154i | \(-0.486902\pi\) | ||||
0.0411371 | + | 0.999154i | \(0.486902\pi\) | |||||||
\(278\) | 17.7597 | + | 8.31534i | 1.06516 | + | 0.498721i | ||||
\(279\) | 3.74571 | + | 6.14441i | 0.224250 | + | 0.367856i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.6155i | − | 1.64740i | −0.567023 | − | 0.823702i | \(-0.691905\pi\) | ||
0.567023 | − | 0.823702i | \(-0.308095\pi\) | |||||||
\(282\) | 2.26293 | + | 0.374874i | 0.134755 | + | 0.0223234i | ||||
\(283\) | − | 4.38684i | − | 0.260770i | −0.991463 | − | 0.130385i | \(-0.958379\pi\) | ||
0.991463 | − | 0.130385i | \(-0.0416214\pi\) | |||||||
\(284\) | −8.54312 | − | 10.2462i | −0.506941 | − | 0.608001i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.00000 | + | 17.0862i | −0.473050 | + | 1.01033i | ||||
\(287\) | 6.67026 | 0.393733 | ||||||||
\(288\) | 16.9275 | + | 1.20777i | 0.997464 | + | 0.0711682i | ||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.80928 | − | 10.0054i | −0.164683 | − | 0.586527i | ||||
\(292\) | −10.5616 | − | 12.6670i | −0.618068 | − | 0.741282i | ||||
\(293\) | 30.4924i | 1.78139i | 0.454605 | + | 0.890693i | \(0.349780\pi\) | ||||
−0.454605 | + | 0.890693i | \(0.650220\pi\) | |||||||
\(294\) | 14.7968 | + | 2.45122i | 0.862968 | + | 0.142958i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.54312 | − | 2.24621i | 0.496559 | − | 0.130558i | ||||
\(297\) | −16.2462 | − | 15.1231i | −0.942701 | − | 0.877532i | ||||
\(298\) | 17.9309 | + | 8.39547i | 1.03871 | + | 0.486337i | ||||
\(299\) | 23.7565 | 1.37387 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.36932 | −0.0789261 | ||||||||
\(302\) | −7.86962 | − | 3.68466i | −0.452846 | − | 0.212028i | ||||
\(303\) | −15.2134 | + | 4.27156i | −0.873986 | + | 0.245395i | ||||
\(304\) | 16.8078 | + | 3.07221i | 0.963991 | + | 0.176203i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.43441 | + | 0.927794i | −0.482163 | + | 0.0530385i | ||||
\(307\) | − | 8.13254i | − | 0.464149i | −0.972698 | − | 0.232074i | \(-0.925449\pi\) | ||
0.972698 | − | 0.232074i | \(-0.0745513\pi\) | |||||||
\(308\) | 6.14441 | − | 5.12311i | 0.350110 | − | 0.291916i | ||||
\(309\) | 20.6847 | − | 5.80776i | 1.17671 | − | 0.330392i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.1617 | −0.803035 | −0.401517 | − | 0.915851i | \(-0.631517\pi\) | ||||
−0.401517 | + | 0.915851i | \(0.631517\pi\) | |||||||
\(312\) | 7.74571 | + | 13.1945i | 0.438514 | + | 0.746992i | ||||
\(313\) | −10.4924 | −0.593067 | −0.296533 | − | 0.955022i | \(-0.595831\pi\) | ||||
−0.296533 | + | 0.955022i | \(0.595831\pi\) | |||||||
\(314\) | 12.8147 | − | 27.3693i | 0.723174 | − | 1.54454i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.9309 | − | 11.6153i | 0.783673 | − | 0.653413i | ||||
\(317\) | − | 32.7386i | − | 1.83878i | −0.393342 | − | 0.919392i | \(-0.628681\pi\) | ||
0.393342 | − | 0.919392i | \(-0.371319\pi\) | |||||||
\(318\) | 1.69986 | − | 10.2612i | 0.0953233 | − | 0.575420i | ||||
\(319\) | 21.8836i | 1.22525i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.438447 | + | 1.56155i | 0.0244717 | + | 0.0871574i | ||||
\(322\) | −9.12311 | − | 4.27156i | −0.508411 | − | 0.238045i | ||||
\(323\) | −8.54312 | −0.475352 | ||||||||
\(324\) | −17.5696 | + | 3.91270i | −0.976089 | + | 0.217372i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 30.9526 | + | 14.4924i | 1.71431 | + | 0.802661i | ||||
\(327\) | 4.27156 | + | 15.2134i | 0.236218 | + | 0.841302i | ||||
\(328\) | 5.12311 | + | 19.4849i | 0.282876 | + | 1.07588i | ||||
\(329\) | − | 0.876894i | − | 0.0483448i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.0281i | 1.54056i | 0.637705 | + | 0.770281i | \(0.279884\pi\) | ||||
−0.637705 | + | 0.770281i | \(0.720116\pi\) | |||||||
\(332\) | −5.99676 | − | 7.19224i | −0.329115 | − | 0.394725i | ||||
\(333\) | −8.00000 | + | 4.87689i | −0.438397 | + | 0.267252i | ||||
\(334\) | 1.68466 | − | 3.59806i | 0.0921804 | − | 0.196877i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.602100 | − | 6.45975i | −0.0328473 | − | 0.352408i | ||||
\(337\) | 34.4924 | 1.87892 | 0.939461 | − | 0.342656i | \(-0.111326\pi\) | ||||
0.939461 | + | 0.342656i | \(0.111326\pi\) | |||||||
\(338\) | 1.94668 | − | 4.15767i | 0.105885 | − | 0.226147i | ||||
\(339\) | −23.3459 | + | 6.55498i | −1.26798 | + | 0.356018i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.2462i | 0.554863i | ||||||||
\(342\) | −18.0140 | + | 1.98156i | −0.974087 | + | 0.107151i | ||||
\(343\) | − | 12.2888i | − | 0.663534i | ||||||
\(344\) | −1.05171 | − | 4.00000i | −0.0567042 | − | 0.215666i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.56155 | + | 1.19935i | 0.137710 | + | 0.0644776i | ||||
\(347\) | 23.8718 | 1.28150 | 0.640752 | − | 0.767748i | \(-0.278623\pi\) | ||||
0.640752 | + | 0.767748i | \(0.278623\pi\) | |||||||
\(348\) | 14.6265 | + | 10.0509i | 0.784062 | + | 0.538785i | ||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.8782 | − | 11.0571i | −0.634014 | − | 0.590184i | ||||
\(352\) | 19.6847 | + | 14.0140i | 1.04920 | + | 0.746950i | ||||
\(353\) | 3.75379i | 0.199794i | 0.994998 | + | 0.0998970i | \(0.0318513\pi\) | ||||
−0.994998 | + | 0.0998970i | \(0.968149\pi\) | |||||||
\(354\) | −17.3898 | − | 2.88078i | −0.924258 | − | 0.153111i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.59482 | + | 8.00000i | −0.508525 | + | 0.423999i | ||||
\(357\) | 0.876894 | + | 3.12311i | 0.0464102 | + | 0.165292i | ||||
\(358\) | −8.80776 | + | 18.8114i | −0.465505 | + | 0.994215i | ||||
\(359\) | 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 | ||||||||
\(362\) | −2.54635 | + | 5.43845i | −0.133833 | + | 0.285838i | ||||
\(363\) | −3.39277 | − | 12.0835i | −0.178074 | − | 0.634221i | ||||
\(364\) | 4.49242 | − | 3.74571i | 0.235467 | − | 0.196328i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.3803 | − | 2.05090i | −0.647127 | − | 0.107202i | ||||
\(367\) | − | 26.5658i | − | 1.38672i | −0.720590 | − | 0.693361i | \(-0.756129\pi\) | ||
0.720590 | − | 0.693361i | \(-0.243871\pi\) | |||||||
\(368\) | 5.47091 | − | 29.9309i | 0.285191 | − | 1.56025i | ||||
\(369\) | −11.1231 | − | 18.2462i | −0.579046 | − | 0.949860i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.97626 | −0.206437 | ||||||||
\(372\) | 6.84831 | + | 4.70596i | 0.355068 | + | 0.243993i | ||||
\(373\) | 0.876894 | 0.0454039 | 0.0227019 | − | 0.999742i | \(-0.492773\pi\) | ||||
0.0227019 | + | 0.999742i | \(0.492773\pi\) | |||||||
\(374\) | −10.9418 | − | 5.12311i | −0.565788 | − | 0.264909i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.56155 | − | 0.673500i | 0.132102 | − | 0.0347331i | ||||
\(377\) | 16.0000i | 0.824042i | ||||||||
\(378\) | 2.57342 | + | 6.38199i | 0.132362 | + | 0.328254i | ||||
\(379\) | − | 25.1035i | − | 1.28948i | −0.764402 | − | 0.644740i | \(-0.776966\pi\) | ||
0.764402 | − | 0.644740i | \(-0.223034\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.80776 | − | 2.19224i | 0.400004 | − | 0.112312i | ||||
\(382\) | 4.63068 | − | 9.89012i | 0.236926 | − | 0.506022i | ||||
\(383\) | −4.68213 | −0.239246 | −0.119623 | − | 0.992819i | \(-0.538169\pi\) | ||||
−0.119623 | + | 0.992819i | \(0.538169\pi\) | |||||||
\(384\) | 18.4076 | − | 6.72026i | 0.939357 | − | 0.342942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.74247 | − | 20.8078i | 0.495879 | − | 1.05909i | ||||
\(387\) | 2.28343 | + | 3.74571i | 0.116073 | + | 0.190405i | ||||
\(388\) | −7.68466 | − | 9.21662i | −0.390129 | − | 0.467903i | ||||
\(389\) | 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 | ||||||||
\(392\) | 16.7495 | − | 4.40388i | 0.845977 | − | 0.222430i | ||||
\(393\) | −8.24621 | − | 29.3693i | −0.415966 | − | 1.48149i | ||||
\(394\) | −15.6847 | − | 7.34376i | −0.790182 | − | 0.369973i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −24.2602 | − | 8.26465i | −1.21912 | − | 0.415314i | ||||
\(397\) | −23.1231 | −1.16052 | −0.580258 | − | 0.814433i | \(-0.697048\pi\) | ||||
−0.580258 | + | 0.814433i | \(0.697048\pi\) | |||||||
\(398\) | −22.5571 | − | 10.5616i | −1.13069 | − | 0.529403i | ||||
\(399\) | 1.87285 | + | 6.67026i | 0.0937599 | + | 0.333931i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.0000i | 1.19850i | 0.800561 | + | 0.599251i | \(0.204535\pi\) | ||||
−0.800561 | + | 0.599251i | \(0.795465\pi\) | |||||||
\(402\) | 2.08488 | − | 12.5854i | 0.103984 | − | 0.627702i | ||||
\(403\) | 7.49141i | 0.373174i | ||||||||
\(404\) | −14.0140 | + | 11.6847i | −0.697224 | + | 0.581333i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.87689 | − | 6.14441i | 0.142778 | − | 0.304942i | ||||
\(407\) | −13.3405 | −0.661265 | ||||||||
\(408\) | −8.44961 | + | 4.96026i | −0.418318 | + | 0.245569i | ||||
\(409\) | 0.630683 | 0.0311853 | 0.0155926 | − | 0.999878i | \(-0.495037\pi\) | ||||
0.0155926 | + | 0.999878i | \(0.495037\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.7511 | + | 3.86098i | −0.678292 | + | 0.190448i | ||||
\(412\) | 19.0540 | − | 15.8869i | 0.938722 | − | 0.782690i | ||||
\(413\) | 6.73863i | 0.331586i | ||||||||
\(414\) | 3.52872 | + | 32.0790i | 0.173427 | + | 1.57659i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 14.3922 | + | 10.2462i | 0.705637 | + | 0.502362i | ||||
\(417\) | −23.1231 | + | 6.49242i | −1.13234 | + | 0.317935i | ||||
\(418\) | −23.3693 | − | 10.9418i | −1.14303 | − | 0.535182i | ||||
\(419\) | −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 | \(0.504892\pi\) | |||||||
\(422\) | −1.72521 | − | 0.807764i | −0.0839817 | − | 0.0393213i | ||||
\(423\) | −2.39871 | + | 1.46228i | −0.116629 | + | 0.0710985i | ||||
\(424\) | −3.05398 | − | 11.6153i | −0.148314 | − | 0.564090i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 16.1191 | + | 2.67026i | 0.780971 | + | 0.129375i | ||||
\(427\) | 4.79741i | 0.232163i | ||||||||
\(428\) | 1.19935 | + | 1.43845i | 0.0579729 | + | 0.0695300i | ||||
\(429\) | −6.24621 | − | 22.2462i | −0.301570 | − | 1.07406i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.0453 | 1.73624 | 0.868121 | − | 0.496353i | \(-0.165328\pi\) | ||||
0.868121 | + | 0.496353i | \(0.165328\pi\) | |||||||
\(432\) | −16.6663 | + | 12.4191i | −0.801859 | + | 0.597513i | ||||
\(433\) | −18.0000 | −0.865025 | −0.432512 | − | 0.901628i | \(-0.642373\pi\) | ||||
−0.432512 | + | 0.901628i | \(0.642373\pi\) | |||||||
\(434\) | 1.34700 | − | 2.87689i | 0.0646581 | − | 0.138095i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.6847 | + | 14.0140i | 0.559594 | + | 0.671150i | ||||
\(437\) | 32.4924i | 1.55432i | ||||||||
\(438\) | 19.9274 | + | 3.30115i | 0.952169 | + | 0.157735i | ||||
\(439\) | − | 29.9009i | − | 1.42709i | −0.700608 | − | 0.713546i | \(-0.747088\pi\) | ||
0.700608 | − | 0.713546i | \(-0.252912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.6847 | + | 9.56155i | −0.746888 | + | 0.455312i | ||||
\(442\) | −8.00000 | − | 3.74571i | −0.380521 | − | 0.178165i | ||||
\(443\) | 25.7446 | 1.22316 | 0.611582 | − | 0.791181i | \(-0.290533\pi\) | ||||
0.611582 | + | 0.791181i | \(0.290533\pi\) | |||||||
\(444\) | −6.12715 | + | 8.91648i | −0.290782 | + | 0.423157i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −23.0830 | − | 10.8078i | −1.09301 | − | 0.511762i | ||||
\(447\) | −23.3459 | + | 6.55498i | −1.10422 | + | 0.310040i | ||||
\(448\) | −3.68466 | − | 6.52262i | −0.174084 | − | 0.308165i | ||||
\(449\) | − | 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 | ||||||
\(452\) | −21.5054 | + | 17.9309i | −1.01153 | + | 0.843397i | ||||
\(453\) | 10.2462 | − | 2.87689i | 0.481409 | − | 0.135168i | ||||
\(454\) | 5.19224 | − | 11.0895i | 0.243684 | − | 0.520455i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.0465 | + | 10.5940i | −0.845104 | + | 0.496110i | ||||
\(457\) | 10.0000 | 0.467780 | 0.233890 | − | 0.972263i | \(-0.424854\pi\) | ||||
0.233890 | + | 0.972263i | \(0.424854\pi\) | |||||||
\(458\) | −0.147647 | + | 0.315342i | −0.00689909 | + | 0.0147349i | ||||
\(459\) | 7.08084 | − | 7.60669i | 0.330505 | − | 0.355050i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 15.8617i | − | 0.738755i | −0.929279 | − | 0.369377i | \(-0.879571\pi\) | ||
0.929279 | − | 0.369377i | \(-0.120429\pi\) | |||||||
\(462\) | −1.60129 | + | 9.66622i | −0.0744990 | + | 0.449713i | ||||
\(463\) | 0.936426i | 0.0435194i | 0.999763 | + | 0.0217597i | \(0.00692688\pi\) | ||||
−0.999763 | + | 0.0217597i | \(0.993073\pi\) | |||||||
\(464\) | 20.1584 | + | 3.68466i | 0.935832 | + | 0.171056i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.8078 | − | 5.99676i | −0.593308 | − | 0.277795i | ||||
\(467\) | 16.1498 | 0.747324 | 0.373662 | − | 0.927565i | \(-0.378102\pi\) | ||||
0.373662 | + | 0.927565i | \(0.378102\pi\) | |||||||
\(468\) | −17.7376 | − | 6.04261i | −0.819922 | − | 0.279320i | ||||
\(469\) | −4.87689 | −0.225194 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.0054 | + | 35.6347i | 0.461024 | + | 1.64196i | ||||
\(472\) | −19.6847 | + | 5.17562i | −0.906060 | + | 0.238227i | ||||
\(473\) | 6.24621i | 0.287201i | ||||||||
\(474\) | −3.63052 | + | 21.9157i | −0.166755 | + | 1.00662i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.39871 | + | 2.87689i | 0.109944 | + | 0.131862i | ||||
\(477\) | 6.63068 | + | 10.8769i | 0.303598 | + | 0.498019i | ||||
\(478\) | 12.4924 | − | 26.6811i | 0.571390 | − | 1.22036i | ||||
\(479\) | 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 | ||||||||
\(482\) | 6.81791 | − | 14.5616i | 0.310547 | − | 0.663261i | ||||
\(483\) | 11.8782 | − | 3.33513i | 0.540479 | − | 0.151754i | ||||
\(484\) | −9.28078 | − | 11.1309i | −0.421853 | − | 0.505951i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13.1663 | − | 17.6819i | 0.597236 | − | 0.802066i | ||||
\(487\) | 15.3287i | 0.694608i | 0.937753 | + | 0.347304i | \(0.112903\pi\) | ||||
−0.937753 | + | 0.347304i | \(0.887097\pi\) | |||||||
\(488\) | −14.0140 | + | 3.68466i | −0.634385 | + | 0.166797i | ||||
\(489\) | −40.3002 | + | 11.3153i | −1.82244 | + | 0.511697i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.6638 | 0.842285 | 0.421143 | − | 0.906994i | \(-0.361629\pi\) | ||||
0.421143 | + | 0.906994i | \(0.361629\pi\) | |||||||
\(492\) | −20.3365 | − | 13.9747i | −0.916840 | − | 0.630026i | ||||
\(493\) | −10.2462 | −0.461466 | ||||||||
\(494\) | −17.0862 | − | 8.00000i | −0.768746 | − | 0.359937i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.43845 | + | 1.72521i | 0.423799 | + | 0.0774640i | ||||
\(497\) | − | 6.24621i | − | 0.280181i | ||||||
\(498\) | 11.3146 | + | 1.87437i | 0.507021 | + | 0.0839924i | ||||
\(499\) | 1.57756i | 0.0706212i | 0.999376 | + | 0.0353106i | \(0.0112421\pi\) | ||||
−0.999376 | + | 0.0353106i | \(0.988758\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.31534 | + | 4.68466i | 0.0587651 | + | 0.209295i | ||||
\(502\) | 15.0540 | − | 32.1520i | 0.671892 | − | 1.43501i | ||||
\(503\) | 19.8955 | 0.887097 | 0.443549 | − | 0.896250i | \(-0.353719\pi\) | ||||
0.443549 | + | 0.896250i | \(0.353719\pi\) | |||||||
\(504\) | 5.72521 | + | 5.50985i | 0.255021 | + | 0.245428i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −19.4849 | + | 41.6155i | −0.866211 | + | 1.85004i | ||||
\(507\) | 1.51992 | + | 5.41327i | 0.0675020 | + | 0.240412i | ||||
\(508\) | 7.19224 | − | 5.99676i | 0.319104 | − | 0.266063i | ||||
\(509\) | 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 | ||||||
\(512\) | 16.2236 | − | 15.7732i | 0.716990 | − | 0.697083i | ||||
\(513\) | 15.1231 | − | 16.2462i | 0.667701 | − | 0.717288i | ||||
\(514\) | −3.19224 | − | 1.49465i | −0.140803 | − | 0.0659261i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.17481 | + | 2.86881i | 0.183786 | + | 0.126292i | ||||
\(517\) | −4.00000 | −0.175920 | ||||||||
\(518\) | 3.74571 | + | 1.75379i | 0.164577 | + | 0.0770571i | ||||
\(519\) | −3.33513 | + | 0.936426i | −0.146396 | + | 0.0411046i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 21.7538i | − | 0.953051i | −0.879161 | − | 0.476525i | \(-0.841896\pi\) | ||
0.879161 | − | 0.476525i | \(-0.158104\pi\) | |||||||
\(522\) | −21.6052 | + | 2.37659i | −0.945633 | + | 0.104021i | ||||
\(523\) | 0.641132i | 0.0280348i | 0.999902 | + | 0.0140174i | \(0.00446202\pi\) | ||||
−0.999902 | + | 0.0140174i | \(0.995538\pi\) | |||||||
\(524\) | −22.5571 | − | 27.0540i | −0.985413 | − | 1.18186i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.05398 | − | 19.3373i | 0.394772 | − | 0.843146i | ||||
\(527\) | −4.79741 | −0.208979 | ||||||||
\(528\) | −29.4665 | + | 2.74651i | −1.28236 | + | 0.119527i | ||||
\(529\) | 34.8617 | 1.51573 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.4332 | − | 11.2371i | 0.799934 | − | 0.487649i | ||||
\(532\) | 5.12311 | + | 6.14441i | 0.222115 | + | 0.266394i | ||||
\(533\) | − | 22.2462i | − | 0.963590i | ||||||
\(534\) | 2.50051 | − | 15.0943i | 0.108207 | − | 0.653195i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.74571 | − | 14.2462i | −0.161790 | − | 0.615343i | ||||
\(537\) | −6.87689 | − | 24.4924i | −0.296760 | − | 1.05693i | ||||
\(538\) | −17.9309 | − | 8.39547i | −0.773055 | − | 0.361954i | ||||
\(539\) | −26.1552 | −1.12658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.9848 | 1.67609 | 0.838045 | − | 0.545602i | \(-0.183699\pi\) | ||||
0.838045 | + | 0.545602i | \(0.183699\pi\) | |||||||
\(542\) | 40.6951 | + | 19.0540i | 1.74800 | + | 0.818438i | ||||
\(543\) | −1.98813 | − | 7.08084i | −0.0853189 | − | 0.303868i | ||||
\(544\) | −6.56155 | + | 9.21662i | −0.281324 | + | 0.395159i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.17077 | + | 7.06736i | −0.0501043 | + | 0.302455i | ||||
\(547\) | − | 25.2188i | − | 1.07828i | −0.842217 | − | 0.539139i | \(-0.818750\pi\) | ||
0.842217 | − | 0.539139i | \(-0.181250\pi\) | |||||||
\(548\) | −12.6670 | + | 10.5616i | −0.541109 | + | 0.451167i | ||||
\(549\) | 13.1231 | − | 8.00000i | 0.560080 | − | 0.341432i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.8836 | −0.932275 | ||||||||
\(552\) | 18.8656 | + | 32.1368i | 0.802972 | + | 1.36783i | ||||
\(553\) | 8.49242 | 0.361135 | ||||||||
\(554\) | −0.821147 | + | 1.75379i | −0.0348872 | + | 0.0745113i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.3002 | + | 17.7597i | −0.903329 | + | 0.753180i | ||||
\(557\) | − | 19.7538i | − | 0.836995i | −0.908218 | − | 0.418497i | \(-0.862557\pi\) | ||
0.908218 | − | 0.418497i | \(-0.137443\pi\) | |||||||
\(558\) | −10.1158 | + | 1.11275i | −0.428237 | + | 0.0471066i | ||||
\(559\) | 4.56685i | 0.193157i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.2462 | − | 4.00000i | 0.601476 | − | 0.168880i | ||||
\(562\) | 35.3693 | + | 16.5604i | 1.49196 | + | 0.698558i | ||||
\(563\) | 36.1606 | 1.52399 | 0.761994 | − | 0.647584i | \(-0.224221\pi\) | ||||
0.761994 | + | 0.647584i | \(0.224221\pi\) | |||||||
\(564\) | −1.83715 | + | 2.67350i | −0.0773581 | + | 0.112575i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.61856 | + | 2.63068i | 0.236166 | + | 0.110576i | ||||
\(567\) | −7.49141 | − | 3.86098i | −0.314610 | − | 0.162146i | ||||
\(568\) | 18.2462 | − | 4.79741i | 0.765594 | − | 0.201295i | ||||
\(569\) | − | 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 | \(0.885726\pi\) | |||||||
\(572\) | −17.0862 | − | 20.4924i | −0.714411 | − | 0.856831i | ||||
\(573\) | 3.61553 | + | 12.8769i | 0.151041 | + | 0.537940i | ||||
\(574\) | −4.00000 | + | 8.54312i | −0.166957 | + | 0.356583i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.6979 | + | 20.9561i | −0.487413 | + | 0.873171i | ||||
\(577\) | 15.7538 | 0.655839 | 0.327919 | − | 0.944706i | \(-0.393653\pi\) | ||||
0.327919 | + | 0.944706i | \(0.393653\pi\) | |||||||
\(578\) | −7.79579 | + | 16.6501i | −0.324262 | + | 0.692553i | ||||
\(579\) | 7.60669 | + | 27.0916i | 0.316123 | + | 1.12589i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 4.38447i | − | 0.181899i | ||||||
\(582\) | 14.4993 | + | 2.40194i | 0.601017 | + | 0.0995637i | ||||
\(583\) | 18.1379i | 0.751197i | ||||||||
\(584\) | 22.5571 | − | 5.93087i | 0.933421 | − | 0.245421i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.0540 | − | 18.2856i | −1.61330 | − | 0.755371i | ||||
\(587\) | −38.0335 | −1.56981 | −0.784904 | − | 0.619617i | \(-0.787288\pi\) | ||||
−0.784904 | + | 0.619617i | \(0.787288\pi\) | |||||||
\(588\) | −12.0128 | + | 17.4815i | −0.495399 | + | 0.720924i | ||||
\(589\) | −10.2462 | −0.422188 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.4214 | − | 5.73384i | 0.840023 | − | 0.235859i | ||||
\(592\) | −2.24621 | + | 12.2888i | −0.0923187 | + | 0.505067i | ||||
\(593\) | 8.24621i | 0.338631i | 0.985562 | + | 0.169316i | \(0.0541557\pi\) | ||||
−0.985562 | + | 0.169316i | \(0.945844\pi\) | |||||||
\(594\) | 29.1118 | − | 11.7388i | 1.19447 | − | 0.481649i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.5054 | + | 17.9309i | −0.880897 | + | 0.734477i | ||||
\(597\) | 29.3693 | − | 8.24621i | 1.20201 | − | 0.337495i | ||||
\(598\) | −14.2462 | + | 30.4268i | −0.582571 | + | 1.24424i | ||||
\(599\) | 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 | \(0.401871\pi\) | |||||||
\(602\) | 0.821147 | − | 1.75379i | 0.0334675 | − | 0.0714791i | ||||
\(603\) | 8.13254 | + | 13.3405i | 0.331183 | + | 0.543268i | ||||
\(604\) | 9.43845 | − | 7.86962i | 0.384045 | − | 0.320210i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.65219 | − | 22.0465i | 0.148360 | − | 0.895578i | ||||
\(607\) | − | 29.4903i | − | 1.19698i | −0.801132 | − | 0.598488i | \(-0.795768\pi\) | ||
0.801132 | − | 0.598488i | \(-0.204232\pi\) | |||||||
\(608\) | −14.0140 | + | 19.6847i | −0.568344 | + | 0.798318i | ||||
\(609\) | 2.24621 | + | 8.00000i | 0.0910211 | + | 0.324176i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.92456 | −0.118315 | ||||||||
\(612\) | 3.86962 | − | 11.3590i | 0.156420 | − | 0.459159i | ||||
\(613\) | −0.876894 | −0.0354174 | −0.0177087 | − | 0.999843i | \(-0.505637\pi\) | ||||
−0.0177087 | + | 0.999843i | \(0.505637\pi\) | |||||||
\(614\) | 10.4160 | + | 4.87689i | 0.420354 | + | 0.196815i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.87689 | + | 10.9418i | 0.115913 | + | 0.440859i | ||||
\(617\) | 14.0000i | 0.563619i | 0.959470 | + | 0.281809i | \(0.0909346\pi\) | ||||
−0.959470 | + | 0.281809i | \(0.909065\pi\) | |||||||
\(618\) | −4.96565 | + | 29.9752i | −0.199748 | + | 1.20578i | ||||
\(619\) | 20.3061i | 0.816171i | 0.912944 | + | 0.408085i | \(0.133803\pi\) | ||||
−0.912944 | + | 0.408085i | \(0.866197\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.9309 | − | 26.9309i | −1.16096 | − | 1.08070i | ||||
\(622\) | 8.49242 | − | 18.1379i | 0.340515 | − | 0.727265i | ||||
\(623\) | −5.84912 | −0.234340 | ||||||||
\(624\) | −21.5441 | + | 2.00808i | −0.862455 | + | 0.0803877i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.29206 | − | 13.4384i | 0.251481 | − | 0.537108i | ||||
\(627\) | 30.4268 | − | 8.54312i | 1.21513 | − | 0.341179i | ||||
\(628\) | 27.3693 | + | 32.8255i | 1.09215 | + | 1.30988i | ||||
\(629\) | − | 6.24621i | − | 0.249053i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.1315i | 1.19951i | 0.800182 | + | 0.599757i | \(0.204736\pi\) | ||||
−0.800182 | + | 0.599757i | \(0.795264\pi\) | |||||||
\(632\) | 6.52262 | + | 24.8078i | 0.259456 | + | 0.986800i | ||||
\(633\) | 2.24621 | − | 0.630683i | 0.0892789 | − | 0.0250674i | ||||
\(634\) | 41.9309 | + | 19.6326i | 1.66529 | + | 0.779710i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12.1229 | + | 8.33054i | 0.480706 | + | 0.330327i | ||||
\(637\) | −19.1231 | −0.757685 | ||||||||
\(638\) | −28.0281 | − | 13.1231i | −1.10964 | − | 0.519549i | ||||
\(639\) | −17.0862 | + | 10.4160i | −0.675921 | + | 0.412049i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 47.6155i | − | 1.88070i | −0.340208 | − | 0.940350i | \(-0.610498\pi\) | ||
0.340208 | − | 0.940350i | \(-0.389502\pi\) | |||||||
\(642\) | −2.26293 | − | 0.374874i | −0.0893106 | − | 0.0147951i | ||||
\(643\) | 20.4214i | 0.805340i | 0.915345 | + | 0.402670i | \(0.131918\pi\) | ||||
−0.915345 | + | 0.402670i | \(0.868082\pi\) | |||||||
\(644\) | 10.9418 | − | 9.12311i | 0.431168 | − | 0.359501i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.12311 | − | 10.9418i | 0.201566 | − | 0.430500i | ||||
\(647\) | −3.63043 | −0.142727 | −0.0713634 | − | 0.997450i | \(-0.522735\pi\) | ||||
−0.0713634 | + | 0.997450i | \(0.522735\pi\) | |||||||
\(648\) | 5.52478 | − | 24.8491i | 0.217034 | − | 0.976164i | ||||
\(649\) | 30.7386 | 1.20660 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.05171 | + | 3.74571i | 0.0412196 | + | 0.146806i | ||||
\(652\) | −37.1231 | + | 30.9526i | −1.45385 | + | 1.21220i | ||||
\(653\) | − | 26.9848i | − | 1.05600i | −0.849245 | − | 0.527999i | \(-0.822942\pi\) | ||
0.849245 | − | 0.527999i | \(-0.177058\pi\) | |||||||
\(654\) | −22.0465 | − | 3.65219i | −0.862086 | − | 0.142812i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −28.0281 | − | 5.12311i | −1.09431 | − | 0.200024i | ||||
\(657\) | −21.1231 | + | 12.8769i | −0.824091 | + | 0.502375i | ||||
\(658\) | 1.12311 | + | 0.525853i | 0.0437832 | + | 0.0204999i | ||||
\(659\) | −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 | \(0.854039\pi\) | |||||||
\(662\) | −35.8977 | − | 16.8078i | −1.39520 | − | 0.653252i | ||||
\(663\) | 10.4160 | − | 2.92456i | 0.404523 | − | 0.113580i | ||||
\(664\) | 12.8078 | − | 3.36750i | 0.497038 | − | 0.130684i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.44880 | − | 13.1708i | −0.0561399 | − | 0.510357i | ||||
\(667\) | 38.9699i | 1.50892i | ||||||||
\(668\) | 3.59806 | + | 4.31534i | 0.139213 | + | 0.166966i | ||||
\(669\) | 30.0540 | − | 8.43845i | 1.16195 | − | 0.326249i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.8836 | 0.844809 | ||||||||
\(672\) | 8.63456 | + | 3.10261i | 0.333086 | + | 0.119686i | ||||
\(673\) | 10.4924 | 0.404453 | 0.202227 | − | 0.979339i | \(-0.435182\pi\) | ||||
0.202227 | + | 0.979339i | \(0.435182\pi\) | |||||||
\(674\) | −20.6843 | + | 44.1771i | −0.796729 | + | 1.70164i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.15767 | + | 4.98651i | 0.159910 | + | 0.191789i | ||||
\(677\) | − | 34.4924i | − | 1.32565i | −0.748774 | − | 0.662826i | \(-0.769357\pi\) | ||
0.748774 | − | 0.662826i | \(-0.230643\pi\) | |||||||
\(678\) | 5.60453 | − | 33.8318i | 0.215241 | − | 1.29930i | ||||
\(679\) | − | 5.61856i | − | 0.215620i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.05398 | + | 14.4384i | 0.155349 | + | 0.553282i | ||||
\(682\) | −13.1231 | − | 6.14441i | −0.502510 | − | 0.235282i | ||||
\(683\) | −36.1606 | −1.38365 | −0.691823 | − | 0.722067i | \(-0.743192\pi\) | ||||
−0.691823 | + | 0.722067i | \(0.743192\pi\) | |||||||
\(684\) | 8.26465 | − | 24.2602i | 0.316007 | − | 0.927613i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.7392 | + | 7.36932i | 0.600927 | + | 0.281362i | ||||
\(687\) | −0.115279 | − | 0.410574i | −0.00439818 | − | 0.0156644i | ||||
\(688\) | 5.75379 | + | 1.05171i | 0.219361 | + | 0.0400959i | ||||
\(689\) | 13.2614i | 0.505218i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 29.0798i | − | 1.10625i | −0.833100 | − | 0.553123i | \(-0.813436\pi\) | ||
0.833100 | − | 0.553123i | \(-0.186564\pi\) | |||||||
\(692\) | −3.07221 | + | 2.56155i | −0.116788 | + | 0.0973756i | ||||
\(693\) | −6.24621 | − | 10.2462i | −0.237274 | − | 0.389221i | ||||
\(694\) | −14.3153 | + | 30.5744i | −0.543403 | + | 1.16059i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −21.6441 | + | 12.7060i | −0.820418 | + | 0.481618i | ||||
\(697\) | 14.2462 | 0.539614 | ||||||||
\(698\) | 8.39547 | − | 17.9309i | 0.317773 | − | 0.678693i | ||||
\(699\) | 16.6757 | − | 4.68213i | 0.630731 | − | 0.177094i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.4924i | 1.90707i | 0.301278 | + | 0.953536i | \(0.402587\pi\) | ||||
−0.301278 | + | 0.953536i | \(0.597413\pi\) | |||||||
\(702\) | 21.2848 | − | 8.58270i | 0.803342 | − | 0.323933i | ||||
\(703\) | − | 13.3405i | − | 0.503148i | ||||||
\(704\) | −29.7533 | + | 16.8078i | −1.12137 | + | 0.633466i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.80776 | − | 2.25106i | −0.180943 | − | 0.0847197i | ||||
\(707\) | −8.54312 | −0.321297 | ||||||||
\(708\) | 14.1179 | − | 20.5449i | 0.530583 | − | 0.772126i | ||||
\(709\) | −26.4924 | −0.994944 | −0.497472 | − | 0.867480i | \(-0.665738\pi\) | ||||
−0.497472 | + | 0.867480i | \(0.665738\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.1617 | − | 23.2306i | −0.531104 | − | 0.871217i | ||||
\(712\) | −4.49242 | − | 17.0862i | −0.168361 | − | 0.640334i | ||||
\(713\) | 18.2462i | 0.683326i | ||||||||
\(714\) | −4.52585 | − | 0.749747i | −0.169376 | − | 0.0280586i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.8114 | − | 22.5616i | −0.703016 | − | 0.843165i | ||||
\(717\) | 9.75379 | + | 34.7386i | 0.364262 | + | 1.29734i | ||||
\(718\) | −0.630683 | + | 1.34700i | −0.0235369 | + | 0.0502696i | ||||
\(719\) | −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 | ||||||||
\(722\) | −0.452029 | + | 0.965435i | −0.0168228 | + | 0.0359298i | ||||
\(723\) | 5.32326 | + | 18.9591i | 0.197974 | + | 0.705096i | ||||
\(724\) | −5.43845 | − | 6.52262i | −0.202118 | − | 0.242411i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.5109 | + | 2.90083i | 0.649889 | + | 0.107660i | ||||
\(727\) | 26.5658i | 0.985270i | 0.870236 | + | 0.492635i | \(0.163966\pi\) | ||||
−0.870236 | + | 0.492635i | \(0.836034\pi\) | |||||||
\(728\) | 2.10341 | + | 8.00000i | 0.0779576 | + | 0.296500i | ||||
\(729\) | 1.93087 | + | 26.9309i | 0.0715137 | + | 0.997440i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.92456 | −0.108169 | ||||||||
\(732\) | 10.0509 | − | 14.6265i | 0.371492 | − | 0.540610i | ||||
\(733\) | 35.1231 | 1.29730 | 0.648651 | − | 0.761086i | \(-0.275334\pi\) | ||||
0.648651 | + | 0.761086i | \(0.275334\pi\) | |||||||
\(734\) | 34.0248 | + | 15.9309i | 1.25588 | + | 0.588019i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35.0540 | + | 24.9559i | 1.29211 | + | 0.919885i | ||||
\(737\) | 22.2462i | 0.819450i | ||||||||
\(738\) | 30.0396 | − | 3.30439i | 1.10577 | − | 0.121636i | ||||
\(739\) | 18.6638i | 0.686559i | 0.939233 | + | 0.343279i | \(0.111538\pi\) | ||||
−0.939233 | + | 0.343279i | \(0.888462\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.2462 | − | 6.24621i | 0.817235 | − | 0.229460i | ||||
\(742\) | 2.38447 | − | 5.09271i | 0.0875367 | − | 0.186959i | ||||
\(743\) | 12.4041 | 0.455062 | 0.227531 | − | 0.973771i | \(-0.426935\pi\) | ||||
0.227531 | + | 0.973771i | \(0.426935\pi\) | |||||||
\(744\) | −10.1341 | + | 5.94910i | −0.371533 | + | 0.218105i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.525853 | + | 1.12311i | −0.0192528 | + | 0.0411198i | ||||
\(747\) | −11.9935 | + | 7.31140i | −0.438820 | + | 0.267510i | ||||
\(748\) | 13.1231 | − | 10.9418i | 0.479828 | − | 0.400073i | ||||
\(749\) | 0.876894i | 0.0320410i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 15.7392i | − | 0.574333i | −0.957881 | − | 0.287166i | \(-0.907287\pi\) | ||
0.957881 | − | 0.287166i | \(-0.0927133\pi\) | |||||||
\(752\) | −0.673500 | + | 3.68466i | −0.0245600 | + | 0.134366i | ||||
\(753\) | 11.7538 | + | 41.8617i | 0.428332 | + | 1.52553i | ||||
\(754\) | −20.4924 | − | 9.59482i | −0.746290 | − | 0.349423i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9.71712 | − | 0.531153i | −0.353408 | − | 0.0193178i | ||||
\(757\) | −19.1231 | −0.695041 | −0.347521 | − | 0.937672i | \(-0.612976\pi\) | ||||
−0.347521 | + | 0.937672i | \(0.612976\pi\) | |||||||
\(758\) | 32.1520 | + | 15.0540i | 1.16781 | + | 0.546785i | ||||
\(759\) | −15.2134 | − | 54.1833i | −0.552211 | − | 1.96673i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 51.2311i | 1.85712i | 0.371177 | + | 0.928562i | \(0.378954\pi\) | ||||
−0.371177 | + | 0.928562i | \(0.621046\pi\) | |||||||
\(762\) | −1.87437 | + | 11.3146i | −0.0679012 | + | 0.409886i | ||||
\(763\) | 8.54312i | 0.309282i | ||||||||
\(764\) | 9.89012 | + | 11.8617i | 0.357812 | + | 0.429143i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.80776 | − | 5.99676i | 0.101449 | − | 0.216672i | ||||
\(767\) | 22.4742 | 0.811498 | ||||||||
\(768\) | −2.43143 | + | 27.6059i | −0.0877368 | + | 0.996144i | ||||
\(769\) | −26.9848 | −0.973098 | −0.486549 | − | 0.873653i | \(-0.661745\pi\) | ||||
−0.486549 | + | 0.873653i | \(0.661745\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.15628 | − | 1.16699i | 0.149685 | − | 0.0420279i | ||||
\(772\) | 20.8078 | + | 24.9559i | 0.748888 | + | 0.898181i | ||||
\(773\) | − | 16.2462i | − | 0.584336i | −0.956367 | − | 0.292168i | \(-0.905623\pi\) | ||
0.956367 | − | 0.292168i | \(-0.0943766\pi\) | |||||||
\(774\) | −6.16673 | + | 0.678347i | −0.221658 | + | 0.0243827i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16.4127 | − | 4.31534i | 0.589183 | − | 0.154912i | ||||
\(777\) | −4.87689 | + | 1.36932i | −0.174958 | + | 0.0491240i | ||||
\(778\) | −36.8078 | − | 17.2339i | −1.31962 | − | 0.617865i | ||||
\(779\) | 30.4268 | 1.09015 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.4924 | −1.01954 | ||||||||
\(782\) | −19.4849 | − | 9.12311i | −0.696780 | − | 0.326242i | ||||
\(783\) | 18.1379 | − | 19.4849i | 0.648197 | − | 0.696335i | ||||
\(784\) | −4.40388 | + | 24.0932i | −0.157282 | + | 0.860473i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 42.5606 | + | 7.05053i | 1.51809 | + | 0.251484i | ||||
\(787\) | − | 13.9817i | − | 0.498392i | −0.968453 | − | 0.249196i | \(-0.919834\pi\) | ||
0.968453 | − | 0.249196i | \(-0.0801664\pi\) | |||||||
\(788\) | 18.8114 | − | 15.6847i | 0.670130 | − | 0.558743i | ||||
\(789\) | 7.06913 | + | 25.1771i | 0.251668 | + | 0.896328i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.1100 | −0.466137 | ||||||||
\(792\) | 25.1335 | − | 26.1158i | 0.893079 | − | 0.927986i | ||||
\(793\) | 16.0000 | 0.568177 | ||||||||
\(794\) | 13.8664 | − | 29.6155i | 0.492099 | − | 1.05102i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27.0540 | − | 22.5571i | 0.958903 | − | 0.799517i | ||||
\(797\) | 36.7386i | 1.30135i | 0.759357 | + | 0.650675i | \(0.225514\pi\) | ||||
−0.759357 | + | 0.650675i | \(0.774486\pi\) | |||||||
\(798\) | −9.66622 | − | 1.60129i | −0.342181 | − | 0.0566852i | ||||
\(799\) | − | 1.87285i | − | 0.0662568i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.75379 | + | 16.0000i | 0.344633 | + | 0.565332i | ||||
\(802\) | −30.7386 | − | 14.3922i | −1.08542 | − | 0.508207i | ||||
\(803\) | −35.2242 | −1.24303 | ||||||||
\(804\) | 14.8688 | + | 10.2174i | 0.524383 | + | 0.360341i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.59482 | − | 4.49242i | −0.337963 | − | 0.158239i | ||||
\(807\) | 23.3459 | − | 6.55498i | 0.821815 | − | 0.230746i | ||||
\(808\) | −6.56155 | − | 24.9559i | −0.230835 | − | 0.877944i | ||||
\(809\) | − | 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 | \(0.849579\pi\) | |||||||
\(812\) | 6.14441 | + | 7.36932i | 0.215627 | + | 0.258612i | ||||
\(813\) | −52.9848 | + | 14.8769i | −1.85826 | + | 0.521755i | ||||
\(814\) | 8.00000 | − | 17.0862i | 0.280400 | − | 0.598872i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.28595 | − | 13.7966i | −0.0450174 | − | 0.482978i | ||||
\(817\) | −6.24621 | −0.218527 | ||||||||
\(818\) | −0.378206 | + | 0.807764i | −0.0132237 | + | 0.0282428i | ||||
\(819\) | −4.56685 | − | 7.49141i | −0.159579 | − | 0.261771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 29.2311i | − | 1.02017i | −0.860124 | − | 0.510085i | \(-0.829614\pi\) | ||
0.860124 | − | 0.510085i | \(-0.170386\pi\) | |||||||
\(822\) | 3.30115 | − | 19.9274i | 0.115141 | − | 0.695049i | ||||
\(823\) | − | 46.8071i | − | 1.63159i | −0.578338 | − | 0.815797i | \(-0.696299\pi\) | ||
0.578338 | − | 0.815797i | \(-0.303701\pi\) | |||||||
\(824\) | 8.92132 | + | 33.9309i | 0.310789 | + | 1.18204i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.63068 | − | 4.04100i | −0.300300 | − | 0.140604i | ||||
\(827\) | −13.2252 | −0.459887 | −0.229943 | − | 0.973204i | \(-0.573854\pi\) | ||||
−0.229943 | + | 0.973204i | \(0.573854\pi\) | |||||||
\(828\) | −43.2021 | − | 14.7175i | −1.50138 | − | 0.511468i | ||||
\(829\) | −17.1231 | −0.594710 | −0.297355 | − | 0.954767i | \(-0.596104\pi\) | ||||
−0.297355 | + | 0.954767i | \(0.596104\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.641132 | − | 2.28343i | −0.0222406 | − | 0.0792112i | ||||
\(832\) | −21.7538 | + | 12.2888i | −0.754177 | + | 0.426038i | ||||
\(833\) | − | 12.2462i | − | 0.424306i | ||||||
\(834\) | 5.55104 | − | 33.5089i | 0.192217 | − | 1.16032i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 28.0281 | − | 23.3693i | 0.969371 | − | 0.808245i | ||||
\(837\) | 8.49242 | − | 9.12311i | 0.293541 | − | 0.315341i | ||||
\(838\) | 3.68466 | − | 7.86962i | 0.127284 | − | 0.271851i | ||||
\(839\) | −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 | ||||||||
\(842\) | 0.378206 | − | 0.807764i | 0.0130338 | − | 0.0278374i | ||||
\(843\) | −46.0507 | + | 12.9300i | −1.58607 | + | 0.445331i | ||||
\(844\) | 2.06913 | − | 1.72521i | 0.0712224 | − | 0.0593840i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.434406 | − | 3.94910i | −0.0149352 | − | 0.135773i | ||||
\(847\) | − | 6.78554i | − | 0.233154i | ||||||
\(848\) | 16.7080 | + | 3.05398i | 0.573756 | + | 0.104874i | ||||
\(849\) | −7.31534 | + | 2.05398i | −0.251062 | + | 0.0704923i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.7565 | −0.814362 | ||||||||
\(852\) | −13.0862 | + | 19.0436i | −0.448327 | + | 0.652424i | ||||
\(853\) | −49.8617 | −1.70723 | −0.853617 | − | 0.520902i | \(-0.825596\pi\) | ||||
−0.853617 | + | 0.520902i | \(0.825596\pi\) | |||||||
\(854\) | −6.14441 | − | 2.87689i | −0.210257 | − | 0.0984453i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.56155 | + | 0.673500i | −0.0875521 | + | 0.0230198i | ||||
\(857\) | − | 28.7386i | − | 0.981693i | −0.871246 | − | 0.490847i | \(-0.836688\pi\) | ||
0.871246 | − | 0.490847i | \(-0.163312\pi\) | |||||||
\(858\) | 32.2381 | + | 5.34053i | 1.10059 | + | 0.182323i | ||||
\(859\) | 37.3923i | 1.27581i | 0.770115 | + | 0.637905i | \(0.220199\pi\) | ||||
−0.770115 | + | 0.637905i | \(0.779801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.12311 | − | 11.1231i | −0.106435 | − | 0.379074i | ||||
\(862\) | −21.6155 | + | 46.1660i | −0.736228 | + | 1.57242i | ||||
\(863\) | −27.6175 | −0.940110 | −0.470055 | − | 0.882637i | \(-0.655766\pi\) | ||||
−0.470055 | + | 0.882637i | \(0.655766\pi\) | |||||||
\(864\) | −5.91167 | − | 28.7933i | −0.201119 | − | 0.979567i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.7942 | − | 23.0540i | 0.366801 | − | 0.783406i | ||||
\(867\) | −6.08677 | − | 21.6784i | −0.206718 | − | 0.736236i | ||||
\(868\) | 2.87689 | + | 3.45041i | 0.0976482 | + | 0.117115i | ||||
\(869\) | − | 38.7386i | − | 1.31412i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.2651i | 0.551121i | ||||||||
\(872\) | −24.9559 | + | 6.56155i | −0.845112 | + | 0.222202i | ||||
\(873\) | −15.3693 | + | 9.36932i | −0.520173 | + | 0.317103i | ||||
\(874\) | −41.6155 | − | 19.4849i | −1.40767 | − | 0.659088i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.1780 | + | 23.5430i | −0.546606 | + | 0.795443i | ||||
\(877\) | 3.61553 | 0.122088 | 0.0610439 | − | 0.998135i | \(-0.480557\pi\) | ||||
0.0610439 | + | 0.998135i | \(0.480557\pi\) | |||||||
\(878\) | 38.2964 | + | 17.9309i | 1.29244 | + | 0.605138i | ||||
\(879\) | 50.8481 | − | 14.2770i | 1.71506 | − | 0.481550i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.3693i | 0.854714i | 0.904083 | + | 0.427357i | \(0.140555\pi\) | ||||
−0.904083 | + | 0.427357i | \(0.859445\pi\) | |||||||
\(882\) | −2.84049 | − | 25.8224i | −0.0956443 | − | 0.869485i | ||||
\(883\) | − | 10.8265i | − | 0.364342i | −0.983267 | − | 0.182171i | \(-0.941688\pi\) | ||
0.983267 | − | 0.182171i | \(-0.0583125\pi\) | |||||||
\(884\) | 9.59482 | − | 8.00000i | 0.322709 | − | 0.269069i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.4384 | + | 32.9731i | −0.518665 | + | 1.10775i | ||||
\(887\) | 53.4774 | 1.79560 | 0.897798 | − | 0.440408i | \(-0.145166\pi\) | ||||
0.897798 | + | 0.440408i | \(0.145166\pi\) | |||||||
\(888\) | −7.74571 | − | 13.1945i | −0.259929 | − | 0.442779i | ||||
\(889\) | 4.38447 | 0.147050 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.6121 | + | 34.1725i | −0.590027 | + | 1.14482i | ||||
\(892\) | 27.6847 | − | 23.0830i | 0.926951 | − | 0.772876i | ||||
\(893\) | − | 4.00000i | − | 0.133855i | ||||||
\(894\) | 5.60453 | − | 33.8318i | 0.187444 | − | 1.13150i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 10.5636 | − | 0.807764i | 0.352906 | − | 0.0269855i | ||||
\(897\) | −11.1231 | − | 39.6155i | −0.371390 | − | 1.32272i | ||||
\(898\) | 3.36932 | + | 1.57756i | 0.112436 | + | 0.0526438i | ||||
\(899\) | −12.2888 | −0.409855 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.49242 | −0.282924 | ||||||||
\(902\) | 38.9699 | + | 18.2462i | 1.29756 | + | 0.607532i | ||||
\(903\) | 0.641132 | + | 2.28343i | 0.0213355 | + | 0.0759877i | ||||
\(904\) | −10.0691 | − | 38.2964i | −0.334894 | − | 1.27372i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.45975 | + | 14.8483i | −0.0817198 | + | 0.493302i | ||||
\(907\) | 35.8653i | 1.19089i | 0.803397 | + | 0.595444i | \(0.203024\pi\) | ||||
−0.803397 | + | 0.595444i | \(0.796976\pi\) | |||||||
\(908\) | 11.0895 | + | 13.3002i | 0.368017 | + | 0.441382i | ||||
\(909\) | 14.2462 | + | 23.3693i | 0.472517 | + | 0.775111i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.8944 | −1.38802 | −0.694012 | − | 0.719963i | \(-0.744159\pi\) | ||||
−0.694012 | + | 0.719963i | \(0.744159\pi\) | |||||||
\(912\) | −2.74651 | − | 29.4665i | −0.0909461 | − | 0.975733i | ||||
\(913\) | −20.0000 | −0.661903 | ||||||||
\(914\) | −5.99676 | + | 12.8078i | −0.198355 | + | 0.423643i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.315342 | − | 0.378206i | −0.0104192 | − | 0.0124963i | ||||
\(917\) | − | 16.4924i | − | 0.544628i | ||||||
\(918\) | 5.49626 | + | 13.6305i | 0.181404 | + | 0.449874i | ||||
\(919\) | − | 50.1423i | − | 1.65404i | −0.562172 | − | 0.827020i | \(-0.690034\pi\) | ||
0.562172 | − | 0.827020i | \(-0.309966\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5616 | + | 3.80776i | −0.446868 | + | 0.125470i | ||||
\(922\) | 20.3153 | + | 9.51191i | 0.669050 | + | 0.313258i | ||||
\(923\) | −20.8319 | −0.685692 | ||||||||
\(924\) | −11.4200 | − | 7.84751i | −0.375691 | − | 0.258164i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.19935 | − | 0.561553i | −0.0394132 | − | 0.0184538i | ||||
\(927\) | −19.3697 | − | 31.7738i | −0.636183 | − | 1.04359i | ||||
\(928\) | −16.8078 | + | 23.6089i | −0.551742 | + | 0.774998i | ||||
\(929\) | − | 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 | ||||||
\(932\) | 15.3610 | − | 12.8078i | 0.503167 | − | 0.419532i | ||||
\(933\) | 6.63068 | + | 23.6155i | 0.217079 | + | 0.773138i | ||||
\(934\) | −9.68466 | + | 20.6843i | −0.316892 | + | 0.676811i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 18.3761 | − | 19.0943i | 0.600641 | − | 0.624117i | ||||
\(937\) | −10.4924 | −0.342773 | −0.171386 | − | 0.985204i | \(-0.554825\pi\) | ||||
−0.171386 | + | 0.985204i | \(0.554825\pi\) | |||||||
\(938\) | 2.92456 | − | 6.24621i | 0.0954902 | − | 0.203946i | ||||
\(939\) | 4.91269 | + | 17.4968i | 0.160320 | + | 0.570987i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.12311i | 0.297405i | 0.988882 | + | 0.148702i | \(0.0475096\pi\) | ||||
−0.988882 | + | 0.148702i | \(0.952490\pi\) | |||||||
\(942\) | −51.6401 | − | 8.55464i | −1.68253 | − | 0.278725i | ||||
\(943\) | − | 54.1833i | − | 1.76445i | ||||||
\(944\) | 5.17562 | − | 28.3153i | 0.168452 | − | 0.921586i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.00000 | − | 3.74571i | −0.260102 | − | 0.121783i | ||||
\(947\) | 25.5141 | 0.829096 | 0.414548 | − | 0.910027i | \(-0.363940\pi\) | ||||
0.414548 | + | 0.910027i | \(0.363940\pi\) | |||||||
\(948\) | −25.8919 | − | 17.7922i | −0.840931 | − | 0.577864i | ||||
\(949\) | −25.7538 | −0.836003 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −54.5938 | + | 15.3287i | −1.77033 | + | 0.497066i | ||||
\(952\) | −5.12311 | + | 1.34700i | −0.166041 | + | 0.0436565i | ||||
\(953\) | − | 10.4924i | − | 0.339883i | −0.985454 | − | 0.169941i | \(-0.945642\pi\) | ||
0.985454 | − | 0.169941i | \(-0.0543579\pi\) | |||||||
\(954\) | −17.9071 | + | 1.96981i | −0.579765 | + | 0.0637748i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 26.6811 | + | 32.0000i | 0.862927 | + | 1.03495i | ||||
\(957\) | 36.4924 | − | 10.2462i | 1.17963 | − | 0.331213i | ||||
\(958\) | −13.7538 | + | 29.3751i | −0.444365 | + | 0.949065i | ||||
\(959\) | −7.72197 | −0.249355 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.2462 | 0.814394 | ||||||||
\(962\) | 5.84912 | − | 12.4924i | 0.188583 | − | 0.402772i | ||||
\(963\) | 2.39871 | − | 1.46228i | 0.0772972 | − | 0.0471213i | ||||
\(964\) | 14.5616 | + | 17.4644i | 0.468996 | + | 0.562492i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.85155 | + | 17.2134i | −0.0917470 | + | 0.553831i | ||||
\(967\) | 23.6412i | 0.760250i | 0.924935 | + | 0.380125i | \(0.124119\pi\) | ||||
−0.924935 | + | 0.380125i | \(0.875881\pi\) | |||||||
\(968\) | 19.8217 | − | 5.21165i | 0.637093 | − | 0.167509i | ||||
\(969\) | 4.00000 | + | 14.2462i | 0.128499 | + | 0.457654i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.5991 | 1.33498 | 0.667490 | − | 0.744619i | \(-0.267369\pi\) | ||||
0.667490 | + | 0.744619i | \(0.267369\pi\) | |||||||
\(972\) | 14.7510 | + | 27.4665i | 0.473139 | + | 0.880988i | ||||
\(973\) | −12.9848 | −0.416275 | ||||||||
\(974\) | −19.6326 | − | 9.19224i | −0.629069 | − | 0.294538i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.68466 | − | 20.1584i | 0.117943 | − | 0.645256i | ||||
\(977\) | − | 48.2462i | − | 1.54353i | −0.635906 | − | 0.771767i | \(-0.719373\pi\) | ||
0.635906 | − | 0.771767i | \(-0.280627\pi\) | |||||||
\(978\) | 9.67465 | − | 58.4011i | 0.309361 | − | 1.86746i | ||||
\(979\) | 26.6811i | 0.852730i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.3693 | − | 14.2462i | 0.746125 | − | 0.454847i | ||||
\(982\) | −11.1922 | + | 23.9041i | −0.357159 | + | 0.762812i | ||||
\(983\) | −3.03984 | −0.0969558 | −0.0484779 | − | 0.998824i | \(-0.515437\pi\) | ||||
−0.0484779 | + | 0.998824i | \(0.515437\pi\) | |||||||
\(984\) | 30.0937 | − | 17.6662i | 0.959353 | − | 0.563179i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.14441 | − | 13.1231i | 0.195678 | − | 0.417925i | ||||
\(987\) | −1.46228 | + | 0.410574i | −0.0465449 | + | 0.0130687i | ||||
\(988\) | 20.4924 | − | 17.0862i | 0.651951 | − | 0.543586i | ||||
\(989\) | 11.1231i | 0.353694i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 16.7909i | − | 0.533382i | −0.963782 | − | 0.266691i | \(-0.914070\pi\) | ||
0.963782 | − | 0.266691i | \(-0.0859303\pi\) | |||||||
\(992\) | −7.86962 | + | 11.0540i | −0.249861 | + | 0.350964i | ||||
\(993\) | 46.7386 | − | 13.1231i | 1.48321 | − | 0.416449i | ||||
\(994\) | 8.00000 | + | 3.74571i | 0.253745 | + | 0.118807i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.18576 | + | 13.3675i | −0.291062 | + | 0.423565i | ||||
\(997\) | −7.61553 | −0.241186 | −0.120593 | − | 0.992702i | \(-0.538480\pi\) | ||||
−0.120593 | + | 0.992702i | \(0.538480\pi\) | |||||||
\(998\) | −2.02050 | − | 0.946025i | −0.0639578 | − | 0.0299459i | ||||
\(999\) | 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.e.c.251.4 | 8 | ||
3.2 | odd | 2 | inner | 300.2.e.c.251.5 | 8 | ||
4.3 | odd | 2 | inner | 300.2.e.c.251.6 | 8 | ||
5.2 | odd | 4 | 300.2.h.a.299.1 | 8 | |||
5.3 | odd | 4 | 300.2.h.b.299.8 | 8 | |||
5.4 | even | 2 | 60.2.e.a.11.5 | yes | 8 | ||
12.11 | even | 2 | inner | 300.2.e.c.251.3 | 8 | ||
15.2 | even | 4 | 300.2.h.b.299.7 | 8 | |||
15.8 | even | 4 | 300.2.h.a.299.2 | 8 | |||
15.14 | odd | 2 | 60.2.e.a.11.4 | yes | 8 | ||
20.3 | even | 4 | 300.2.h.b.299.5 | 8 | |||
20.7 | even | 4 | 300.2.h.a.299.4 | 8 | |||
20.19 | odd | 2 | 60.2.e.a.11.3 | ✓ | 8 | ||
40.19 | odd | 2 | 960.2.h.g.191.6 | 8 | |||
40.29 | even | 2 | 960.2.h.g.191.3 | 8 | |||
60.23 | odd | 4 | 300.2.h.a.299.3 | 8 | |||
60.47 | odd | 4 | 300.2.h.b.299.6 | 8 | |||
60.59 | even | 2 | 60.2.e.a.11.6 | yes | 8 | ||
120.29 | odd | 2 | 960.2.h.g.191.5 | 8 | |||
120.59 | even | 2 | 960.2.h.g.191.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.2.e.a.11.3 | ✓ | 8 | 20.19 | odd | 2 | ||
60.2.e.a.11.4 | yes | 8 | 15.14 | odd | 2 | ||
60.2.e.a.11.5 | yes | 8 | 5.4 | even | 2 | ||
60.2.e.a.11.6 | yes | 8 | 60.59 | even | 2 | ||
300.2.e.c.251.3 | 8 | 12.11 | even | 2 | inner | ||
300.2.e.c.251.4 | 8 | 1.1 | even | 1 | trivial | ||
300.2.e.c.251.5 | 8 | 3.2 | odd | 2 | inner | ||
300.2.e.c.251.6 | 8 | 4.3 | odd | 2 | inner | ||
300.2.h.a.299.1 | 8 | 5.2 | odd | 4 | |||
300.2.h.a.299.2 | 8 | 15.8 | even | 4 | |||
300.2.h.a.299.3 | 8 | 60.23 | odd | 4 | |||
300.2.h.a.299.4 | 8 | 20.7 | even | 4 | |||
300.2.h.b.299.5 | 8 | 20.3 | even | 4 | |||
300.2.h.b.299.6 | 8 | 60.47 | odd | 4 | |||
300.2.h.b.299.7 | 8 | 15.2 | even | 4 | |||
300.2.h.b.299.8 | 8 | 5.3 | odd | 4 | |||
960.2.h.g.191.3 | 8 | 40.29 | even | 2 | |||
960.2.h.g.191.4 | 8 | 120.59 | even | 2 | |||
960.2.h.g.191.5 | 8 | 120.29 | odd | 2 | |||
960.2.h.g.191.6 | 8 | 40.19 | odd | 2 |