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 | 251.5 | ||
Root | \(0.599676 + 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.251 |
Dual form | 300.2.e.c.251.6 |
$q$-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 | ||||||||
\(6\) | −1.85500 | − | 1.59968i | −0.757302 | − | 0.653065i | ||||
\(7\) | − | 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 | \(-0.277290\pi\) | ||||
0.643962 | + | 0.765058i | \(0.277290\pi\) | |||||||
\(12\) | −3.16123 | + | 1.41656i | −0.912568 | + | 0.408924i | ||||
\(13\) | −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 | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | −3.53610 | + | 2.34435i | −0.833467 | + | 0.552569i | ||||
\(19\) | − | 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 | \(-0.208491\pi\) | ||||
0.793052 | + | 0.609154i | \(0.208491\pi\) | |||||||
\(24\) | −0.0814236 | + | 4.89830i | −0.0166205 | + | 0.999862i | ||||
\(25\) | 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 | \(0.157794\pi\) | ||||
−0.879625 | + | 0.475668i | \(0.842206\pi\) | |||||||
\(30\) | 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 | ||||||||
\(36\) | 0.882071 | + | 5.93481i | 0.147012 | + | 0.989135i | ||||
\(37\) | 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 | \(-0.812251\pi\) | ||
0.831034 | − | 0.556221i | \(-0.187749\pi\) | |||||||
\(42\) | −1.49798 | + | 1.73707i | −0.231143 | + | 0.268036i | ||||
\(43\) | − | 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 | \(-0.521756\pi\) | ||||
−0.0682959 | + | 0.997665i | \(0.521756\pi\) | |||||||
\(48\) | 6.22480 | + | 3.04168i | 0.898473 | + | 0.439029i | ||||
\(49\) | 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 | \(0.0941979\pi\) | ||||
−0.956531 | + | 0.291631i | \(0.905802\pi\) | |||||||
\(54\) | 2.25371 | + | 6.99434i | 0.306691 | + | 0.951809i | ||||
\(55\) | 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 | \(-0.344821\pi\) | ||||
0.468427 | + | 0.883502i | \(0.344821\pi\) | |||||||
\(60\) | 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 | ||||||||
\(66\) | −7.92375 | − | 6.83311i | −0.975347 | − | 0.841098i | ||||
\(67\) | − | 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 | \(-0.629535\pi\) | ||||
−0.395807 | + | 0.918334i | \(0.629535\pi\) | |||||||
\(72\) | 8.13012 | + | 2.42923i | 0.958144 | + | 0.286287i | ||||
\(73\) | 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 | ||||||
\(78\) | 5.79337 | + | 4.99596i | 0.655970 | + | 0.565681i | ||||
\(79\) | 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 | \(-0.582723\pi\) | ||||
−0.256965 | + | 0.966421i | \(0.582723\pi\) | |||||||
\(84\) | 1.32650 | + | 2.96026i | 0.144733 | + | 0.322991i | ||||
\(85\) | 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 | \(0.107402\pi\) | ||||
−0.943614 | + | 0.331049i | \(0.892598\pi\) | |||||||
\(90\) | 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 | ||||||||
\(96\) | 7.62858 | − | 6.14856i | 0.778589 | − | 0.627534i | ||||
\(97\) | 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 | \(0.149965\pi\) | ||||
−0.891057 | + | 0.453891i | \(0.850035\pi\) | |||||||
\(102\) | 3.19935 | − | 3.71001i | 0.316783 | − | 0.367345i | ||||
\(103\) | 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 | \(-0.485587\pi\) | ||||
0.0452639 | + | 0.998975i | \(0.485587\pi\) | |||||||
\(108\) | 10.3097 | + | 1.30784i | 0.992050 | + | 0.125847i | ||||
\(109\) | −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 | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | −6.83311 | + | 7.92375i | −0.639980 | + | 0.742127i | ||||
\(115\) | 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 | ||||||||
\(126\) | 2.19531 | + | 3.31130i | 0.195574 | + | 0.294994i | ||||
\(127\) | 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 | \(-0.779438\pi\) | ||||
−0.769388 | + | 0.638782i | \(0.779438\pi\) | |||||||
\(132\) | −13.5034 | + | 6.05090i | −1.17532 | + | 0.526663i | ||||
\(133\) | −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 | \(0.114587\pi\) | ||||
−0.935902 | + | 0.352261i | \(0.885413\pi\) | |||||||
\(138\) | −14.1104 | − | 12.1682i | −1.20116 | − | 1.03583i | ||||
\(139\) | − | 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 | ||||||||
\(144\) | 7.98674 | − | 8.95611i | 0.665562 | − | 0.746343i | ||||
\(145\) | 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 | \(0.194400\pi\) | ||||
−0.819232 | + | 0.573462i | \(0.805600\pi\) | |||||||
\(150\) | 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 | ||||||||
\(156\) | 9.87285 | − | 4.42405i | 0.790461 | − | 0.354208i | ||||
\(157\) | −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 | ||||||
\(162\) | 12.7187 | − | 0.483365i | 0.999279 | − | 0.0379768i | ||||
\(163\) | − | 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 | \(-0.465333\pi\) | ||||
0.108694 | + | 0.994075i | \(0.465333\pi\) | |||||||
\(168\) | 4.58690 | + | 0.0762472i | 0.353887 | + | 0.00588260i | ||||
\(169\) | −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 | \(0.0242240\pi\) | ||||
−0.997106 | + | 0.0760286i | \(0.975776\pi\) | |||||||
\(174\) | 8.19531 | − | 9.50338i | 0.621285 | − | 0.720449i | ||||
\(175\) | 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 | \(-0.684953\pi\) | ||||
−0.548899 | + | 0.835889i | \(0.684953\pi\) | |||||||
\(180\) | 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 | ||||||||
\(186\) | −3.83715 | + | 4.44961i | −0.281354 | + | 0.326261i | ||||
\(187\) | 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 | \(-0.409874\pi\) | ||||
0.279371 | + | 0.960183i | \(0.409874\pi\) | |||||||
\(192\) | −3.30024 | − | 13.4577i | −0.238175 | − | 0.971222i | ||||
\(193\) | −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 | \(-0.856305\pi\) | ||
0.899824 | − | 0.436253i | \(-0.143695\pi\) | |||||||
\(198\) | −15.1047 | + | 10.0140i | −1.07344 | + | 0.711666i | ||||
\(199\) | 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 | ||||||||
\(204\) | −2.83311 | − | 6.32246i | −0.198357 | − | 0.442661i | ||||
\(205\) | 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 | ||||||||
\(216\) | 7.85753 | − | 12.4201i | 0.534637 | − | 0.845082i | ||||
\(217\) | −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 | ||||||
\(222\) | −5.79337 | − | 4.99596i | −0.388826 | − | 0.335307i | ||||
\(223\) | 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 | \(-0.407229\pi\) | ||||
0.287339 | + | 0.957829i | \(0.407229\pi\) | |||||||
\(228\) | 6.05090 | + | 13.5034i | 0.400731 | + | 0.894283i | ||||
\(229\) | 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 | \(-0.893773\pi\) | ||
0.944830 | − | 0.327561i | \(-0.106227\pi\) | |||||||
\(234\) | 11.0436 | − | 7.32165i | 0.721944 | − | 0.478631i | ||||
\(235\) | 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 | \(-0.264681\pi\) | ||||
0.673753 | + | 0.738957i | \(0.264681\pi\) | |||||||
\(240\) | 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 | ||||||||
\(246\) | −11.3947 | + | 13.2134i | −0.726497 | + | 0.842454i | ||||
\(247\) | 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 | \(-0.208905\pi\) | ||||
0.792259 | + | 0.610184i | \(0.208905\pi\) | |||||||
\(252\) | 5.55751 | − | 0.825994i | 0.350090 | − | 0.0520328i | ||||
\(253\) | 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 | \(-0.975231\pi\) | ||
0.996974 | − | 0.0777365i | \(-0.0247693\pi\) | |||||||
\(258\) | −2.33917 | + | 2.71253i | −0.145631 | + | 0.168875i | ||||
\(259\) | − | 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 | \(-0.345877\pi\) | ||||
0.465494 | + | 0.885051i | \(0.345877\pi\) | |||||||
\(264\) | −0.347806 | + | 20.9234i | −0.0214060 | + | 1.28775i | ||||
\(265\) | 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 | \(-0.859642\pi\) | ||
0.904347 | − | 0.426798i | \(-0.140358\pi\) | |||||||
\(270\) | 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 | ||||||||
\(276\) | −24.0465 | + | 10.7753i | −1.44743 | + | 0.648597i | ||||
\(277\) | 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 | \(0.308095\pi\) | ||||
−0.567023 | + | 0.823702i | \(0.691905\pi\) | |||||||
\(282\) | 1.73707 | + | 1.49798i | 0.103441 | + | 0.0892034i | ||||
\(283\) | − | 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 | ||||||||
\(288\) | −6.68132 | − | 15.6000i | −0.393701 | − | 0.919239i | ||||
\(289\) | 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 | \(-0.650220\pi\) | ||
0.454605 | − | 0.890693i | \(-0.349780\pi\) | |||||||
\(294\) | −11.3584 | − | 9.79499i | −0.662434 | − | 0.571255i | ||||
\(295\) | 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 | ||||||||
\(306\) | −4.68870 | − | 7.07221i | −0.268035 | − | 0.404291i | ||||
\(307\) | − | 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 | \(-0.368483\pi\) | ||||
0.401517 | + | 0.915851i | \(0.368483\pi\) | |||||||
\(312\) | 0.254294 | − | 15.2979i | 0.0143966 | − | 0.866074i | ||||
\(313\) | −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 | \(0.371319\pi\) | ||||
−0.393342 | + | 0.919392i | \(0.628681\pi\) | |||||||
\(318\) | 6.79256 | − | 7.87673i | 0.380908 | − | 0.441705i | ||||
\(319\) | 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 | ||||||||
\(324\) | 7.00805 | − | 16.5797i | 0.389336 | − | 0.921096i | ||||
\(325\) | 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 | ||||||||
\(336\) | 2.84831 | − | 5.82907i | 0.155388 | − | 0.318002i | ||||
\(337\) | 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 | ||||||
\(342\) | 10.0140 | + | 15.1047i | 0.541497 | + | 0.816767i | ||||
\(343\) | − | 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 | \(-0.721377\pi\) | ||||
−0.640752 | + | 0.767748i | \(0.721377\pi\) | |||||||
\(348\) | −7.25716 | − | 16.1953i | −0.389025 | − | 0.868160i | ||||
\(349\) | −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 | \(-0.968149\pi\) | ||
0.994998 | − | 0.0998970i | \(-0.0318513\pi\) | |||||||
\(354\) | −13.3488 | − | 11.5115i | −0.709482 | − | 0.611827i | ||||
\(355\) | 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 | \(-0.508835\pi\) | ||||
−0.0277535 | + | 0.999615i | \(0.508835\pi\) | |||||||
\(360\) | 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 | ||||||||
\(366\) | 9.50338 | + | 8.19531i | 0.496749 | + | 0.428376i | ||||
\(367\) | − | 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 | ||||||||
\(372\) | 3.39790 | + | 7.58286i | 0.176173 | + | 0.393153i | ||||
\(373\) | 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 | ||||||
\(378\) | 6.54968 | − | 2.11043i | 0.336879 | − | 0.108549i | ||||
\(379\) | − | 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 | \(-0.461831\pi\) | ||||
0.119623 | + | 0.992819i | \(0.461831\pi\) | |||||||
\(384\) | −19.2153 | − | 3.84336i | −0.980578 | − | 0.196131i | ||||
\(385\) | 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 | \(-0.740193\pi\) | ||
0.684989 | − | 0.728553i | \(-0.259807\pi\) | |||||||
\(390\) | 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 | ||||||||
\(396\) | 3.76782 | + | 25.3509i | 0.189340 | + | 1.27393i | ||||
\(397\) | −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 | \(-0.795465\pi\) | ||
0.800561 | − | 0.599251i | \(-0.204535\pi\) | |||||||
\(402\) | −8.33109 | + | 9.66083i | −0.415517 | + | 0.481838i | ||||
\(403\) | 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 | ||||||||
\(408\) | −9.79661 | − | 0.162847i | −0.485004 | − | 0.00806214i | ||||
\(409\) | 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 | ||||||
\(414\) | −26.8980 | + | 17.8327i | −1.32197 | + | 0.876432i | ||||
\(415\) | 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 | \(-0.452045\pi\) | ||||
0.150087 | + | 0.988673i | \(0.452045\pi\) | |||||||
\(420\) | 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 | ||||||||
\(426\) | 12.3734 | + | 10.6703i | 0.599491 | + | 0.516976i | ||||
\(427\) | 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 | \(-0.834672\pi\) | ||||
−0.868121 | + | 0.496353i | \(0.834672\pi\) | |||||||
\(432\) | −11.1954 | − | 17.5118i | −0.538640 | − | 0.842536i | ||||
\(433\) | −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 | ||||||
\(438\) | −15.2967 | − | 13.1913i | −0.730907 | − | 0.630303i | ||||
\(439\) | − | 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 | \(-0.709467\pi\) | ||||
−0.611582 | + | 0.791181i | \(0.709467\pi\) | |||||||
\(444\) | −9.87285 | + | 4.42405i | −0.468545 | + | 0.209956i | ||||
\(445\) | 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 | \(0.0197717\pi\) | ||||
−0.998071 | + | 0.0620748i | \(0.980228\pi\) | |||||||
\(450\) | 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 | ||||||||
\(456\) | 20.9234 | + | 0.347806i | 0.979827 | + | 0.0162875i | ||||
\(457\) | 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 | \(0.120429\pi\) | ||||
−0.929279 | + | 0.369377i | \(0.879571\pi\) | |||||||
\(462\) | −6.39871 | + | 7.42001i | −0.297695 | + | 0.345210i | ||||
\(463\) | 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 | \(-0.621898\pi\) | ||||
−0.373662 | + | 0.927565i | \(0.621898\pi\) | |||||||
\(468\) | −2.75480 | − | 18.5350i | −0.127341 | − | 0.856782i | ||||
\(469\) | −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 | ||||||
\(474\) | 14.5074 | − | 16.8230i | 0.666348 | − | 0.772704i | ||||
\(475\) | 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 | \(-0.675550\pi\) | ||||
−0.523971 | + | 0.851736i | \(0.675550\pi\) | |||||||
\(480\) | 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 | ||||||||
\(486\) | 5.14904 | − | 21.4357i | 0.233565 | − | 0.972341i | ||||
\(487\) | 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 | \(-0.638371\pi\) | ||||
−0.421143 | + | 0.906994i | \(0.638371\pi\) | |||||||
\(492\) | 10.0903 | + | 22.5178i | 0.454905 | + | 1.01518i | ||||
\(493\) | −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 | ||||||||
\(498\) | 8.68537 | + | 7.48990i | 0.389201 | + | 0.335630i | ||||
\(499\) | 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 | \(-0.646281\pi\) | ||||
−0.443549 | + | 0.896250i | \(0.646281\pi\) | |||||||
\(504\) | 2.27479 | − | 7.61326i | 0.101327 | − | 0.339121i | ||||
\(505\) | 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 | \(-0.979691\pi\) | ||
0.997965 | − | 0.0637581i | \(-0.0203086\pi\) | |||||||
\(510\) | 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 | ||||||||
\(516\) | 2.07140 | + | 4.62260i | 0.0911883 | + | 0.203499i | ||||
\(517\) | −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 | \(0.158104\pi\) | ||||
−0.879161 | + | 0.476525i | \(0.841896\pi\) | |||||||
\(522\) | −12.0104 | − | 18.1158i | −0.525679 | − | 0.792908i | ||||
\(523\) | 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 | ||||||||
\(528\) | 26.5896 | + | 12.9927i | 1.15716 | + | 0.565436i | ||||
\(529\) | 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 | ||||||||
\(534\) | 9.99192 | − | 11.5867i | 0.432393 | − | 0.501407i | ||||
\(535\) | 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 | ||||||||
\(546\) | 4.67835 | − | 5.42506i | 0.200215 | − | 0.232171i | ||||
\(547\) | − | 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 | ||||||||
\(552\) | −0.619364 | + | 37.2599i | −0.0263619 | + | 1.58589i | ||||
\(553\) | 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 | \(0.137443\pi\) | ||||
−0.908218 | + | 0.418497i | \(0.862557\pi\) | |||||||
\(558\) | 5.62341 | + | 8.48207i | 0.238058 | + | 0.359075i | ||||
\(559\) | 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 | \(-0.775779\pi\) | ||||
−0.761994 | + | 0.647584i | \(0.775779\pi\) | |||||||
\(564\) | 2.96026 | − | 1.32650i | 0.124649 | − | 0.0558557i | ||||
\(565\) | 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 | \(0.0325962\pi\) | ||||
−0.994761 | + | 0.102225i | \(0.967404\pi\) | |||||||
\(570\) | 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 | ||||||||
\(576\) | −23.9867 | − | 0.797675i | −0.999448 | − | 0.0332364i | ||||
\(577\) | 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 | ||||||||
\(582\) | −11.1300 | − | 9.59806i | −0.461354 | − | 0.397852i | ||||
\(583\) | 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 | \(-0.212712\pi\) | ||||
0.784904 | + | 0.619617i | \(0.212712\pi\) | |||||||
\(588\) | −19.3565 | + | 8.67372i | −0.798250 | + | 0.357698i | ||||
\(589\) | −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 | \(-0.945844\pi\) | ||
0.985562 | − | 0.169316i | \(-0.0541557\pi\) | |||||||
\(594\) | 9.62685 | + | 29.8767i | 0.394994 | + | 1.22586i | ||||
\(595\) | 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 | \(-0.771472\pi\) | ||||
−0.753162 | + | 0.657836i | \(0.771472\pi\) | |||||||
\(600\) | 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 | ||||||||
\(606\) | 14.5940 | − | 16.9234i | 0.592841 | − | 0.687466i | ||||
\(607\) | − | 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 | ||||||||
\(612\) | −11.8696 | + | 1.76414i | −0.479801 | + | 0.0713112i | ||||
\(613\) | −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 | \(-0.909065\pi\) | ||
0.959470 | − | 0.281809i | \(-0.0909346\pi\) | |||||||
\(618\) | 19.8425 | − | 23.0096i | 0.798184 | − | 0.925584i | ||||
\(619\) | 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 | ||||||||
\(624\) | −19.4407 | − | 9.49949i | −0.778252 | − | 0.380284i | ||||
\(625\) | 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 | ||||||||
\(636\) | −6.01499 | − | 13.4232i | −0.238510 | − | 0.532266i | ||||
\(637\) | −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 | \(0.389502\pi\) | ||||
−0.340208 | + | 0.940350i | \(0.610498\pi\) | |||||||
\(642\) | −1.73707 | − | 1.49798i | −0.0685568 | − | 0.0591205i | ||||
\(643\) | 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 | \(-0.477265\pi\) | ||||
0.0713634 | + | 0.997450i | \(0.477265\pi\) | |||||||
\(648\) | −17.0324 | − | 18.9182i | −0.669094 | − | 0.743177i | ||||
\(649\) | 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 | \(0.177058\pi\) | ||||
−0.849245 | + | 0.527999i | \(0.822942\pi\) | |||||||
\(654\) | 16.9234 | + | 14.5940i | 0.661757 | + | 0.570671i | ||||
\(655\) | 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 | \(-0.323906\pi\) | ||||
0.525425 | + | 0.850840i | \(0.323906\pi\) | |||||||
\(660\) | 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 | ||||||||
\(666\) | −11.0436 | + | 7.32165i | −0.427932 | + | 0.283708i | ||||
\(667\) | 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 | ||||||||
\(672\) | −5.75767 | − | 7.14361i | −0.222107 | − | 0.275571i | ||||
\(673\) | 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 | \(0.230643\pi\) | ||||
−0.748774 | + | 0.662826i | \(0.769357\pi\) | |||||||
\(678\) | 22.3955 | − | 25.9700i | 0.860093 | − | 0.997373i | ||||
\(679\) | − | 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 | \(-0.256808\pi\) | ||||
0.691823 | + | 0.722067i | \(0.256808\pi\) | |||||||
\(684\) | 25.3509 | − | 3.76782i | 0.969315 | − | 0.144066i | ||||
\(685\) | 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 | ||||||||
\(696\) | −25.0945 | − | 0.417142i | −0.951205 | − | 0.0158117i | ||||
\(697\) | 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 | \(-0.597413\pi\) | ||
0.301278 | − | 0.953536i | \(-0.402587\pi\) | |||||||
\(702\) | −7.03857 | − | 21.8441i | −0.265654 | − | 0.824451i | ||||
\(703\) | − | 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 | ||||||||
\(708\) | −22.7486 | + | 10.1937i | −0.854944 | + | 0.383103i | ||||
\(709\) | −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 | ||||||
\(714\) | −3.47415 | − | 2.99596i | −0.130017 | − | 0.112121i | ||||
\(715\) | 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 | \(-0.465213\pi\) | ||||
0.109068 | + | 0.994034i | \(0.465213\pi\) | |||||||
\(720\) | 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 | ||||||||
\(726\) | −13.4417 | − | 11.5916i | −0.498870 | − | 0.430204i | ||||
\(727\) | 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 | ||||||||
\(732\) | 16.1953 | − | 7.25716i | 0.598596 | − | 0.268233i | ||||
\(733\) | 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 | ||||||
\(738\) | 16.6991 | + | 25.1880i | 0.614701 | + | 0.927184i | ||||
\(739\) | 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 | \(-0.573065\pi\) | ||||
−0.227531 | + | 0.973771i | \(0.573065\pi\) | |||||||
\(744\) | 11.7496 | + | 0.195311i | 0.430761 | + | 0.00716046i | ||||
\(745\) | 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 | ||||||||
\(756\) | 1.22470 | − | 9.65426i | 0.0445419 | − | 0.351122i | ||||
\(757\) | −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 | \(-0.621046\pi\) | ||
0.371177 | − | 0.928562i | \(-0.378954\pi\) | |||||||
\(762\) | 7.48990 | − | 8.68537i | 0.271330 | − | 0.314638i | ||||
\(763\) | 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 | ||||||||
\(768\) | −16.4455 | + | 22.3058i | −0.593424 | + | 0.804890i | ||||
\(769\) | −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 | \(0.0943766\pi\) | ||||
−0.956367 | + | 0.292168i | \(0.905623\pi\) | |||||||
\(774\) | 3.42809 | + | 5.17077i | 0.123220 | + | 0.185859i | ||||
\(775\) | 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 | ||||||||
\(786\) | 32.6705 | + | 28.1736i | 1.16532 | + | 1.00492i | ||||
\(787\) | − | 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 | ||||||||
\(792\) | 34.7283 | + | 10.3766i | 1.23402 | + | 0.368716i | ||||
\(793\) | 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 | \(-0.774486\pi\) | ||
0.759357 | − | 0.650675i | \(-0.225514\pi\) | |||||||
\(798\) | 7.42001 | + | 6.39871i | 0.262666 | + | 0.226512i | ||||
\(799\) | − | 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 | ||||||||
\(804\) | 7.37740 | + | 16.4636i | 0.260181 | + | 0.580628i | ||||
\(805\) | 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 | \(0.302148\pi\) | ||||
−0.582312 | + | 0.812965i | \(0.697852\pi\) | |||||||
\(810\) | 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 | ||||||||
\(816\) | −6.08336 | + | 12.4496i | −0.212960 | + | 0.435823i | ||||
\(817\) | −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 | \(0.170386\pi\) | ||||
−0.860124 | + | 0.510085i | \(0.829614\pi\) | |||||||
\(822\) | 13.1913 | − | 15.2967i | 0.460098 | − | 0.533535i | ||||
\(823\) | − | 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 | \(-0.426146\pi\) | ||||
0.229943 | + | 0.973204i | \(0.426146\pi\) | |||||||
\(828\) | 6.70964 | + | 45.1443i | 0.233176 | + | 1.56887i | ||||
\(829\) | −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 | ||||||||
\(834\) | −22.1817 | + | 25.7222i | −0.768090 | + | 0.890686i | ||||
\(835\) | 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 | \(-0.183538\pi\) | ||||
0.838320 | + | 0.545179i | \(0.183538\pi\) | |||||||
\(840\) | 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 | ||||||||
\(846\) | 3.31130 | − | 2.19531i | 0.113845 | − | 0.0754764i | ||||
\(847\) | − | 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 | ||||||||
\(852\) | 21.0862 | − | 9.44880i | 0.722402 | − | 0.323711i | ||||
\(853\) | −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 | \(0.163312\pi\) | ||||
−0.871246 | + | 0.490847i | \(0.836688\pi\) | |||||||
\(858\) | 24.7467 | + | 21.3405i | 0.844839 | + | 0.728554i | ||||
\(859\) | 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 | \(-0.344234\pi\) | ||||
0.470055 | + | 0.882637i | \(0.344234\pi\) | |||||||
\(864\) | −29.1423 | + | 3.83742i | −0.991442 | + | 0.130552i | ||||
\(865\) | 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 | ||||||||
\(876\) | −26.0682 | + | 11.6812i | −0.880762 | + | 0.394672i | ||||
\(877\) | 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 | \(-0.859445\pi\) | ||
0.904083 | − | 0.427357i | \(-0.140555\pi\) | |||||||
\(882\) | −21.6519 | + | 14.3547i | −0.729058 | + | 0.483348i | ||||
\(883\) | − | 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 | \(-0.854834\pi\) | ||||
−0.897798 | + | 0.440408i | \(0.854834\pi\) | |||||||
\(888\) | −0.254294 | + | 15.2979i | −0.00853356 | + | 0.513364i | ||||
\(889\) | 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 | ||||||||
\(894\) | 22.3955 | − | 25.9700i | 0.749017 | − | 0.868568i | ||||
\(895\) | 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 | ||||||||
\(906\) | 9.82907 | − | 11.3979i | 0.326549 | − | 0.378670i | ||||
\(907\) | 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 | \(-0.255841\pi\) | ||||
0.694012 | + | 0.719963i | \(0.255841\pi\) | |||||||
\(912\) | 12.9927 | − | 26.5896i | 0.430232 | − | 0.880470i | ||||
\(913\) | −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 | ||||||||
\(918\) | −13.9887 | + | 4.50742i | −0.461695 | + | 0.148767i | ||||
\(919\) | − | 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 | ||||||||
\(924\) | 5.66622 | + | 12.6449i | 0.186405 | + | 0.415987i | ||||
\(925\) | 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 | \(0.133806\pi\) | ||||
−0.912941 | + | 0.408092i | \(0.866194\pi\) | |||||||
\(930\) | 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 | ||||||||
\(936\) | −25.3912 | − | 7.58674i | −0.829938 | − | 0.247980i | ||||
\(937\) | −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 | \(-0.952490\pi\) | ||
0.988882 | − | 0.148702i | \(-0.0475096\pi\) | |||||||
\(942\) | 39.6401 | + | 34.1840i | 1.29155 | + | 1.11377i | ||||
\(943\) | − | 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 | \(-0.636060\pi\) | ||||
−0.414548 | + | 0.910027i | \(0.636060\pi\) | |||||||
\(948\) | −12.8467 | − | 28.6691i | −0.417241 | − | 0.931129i | ||||
\(949\) | −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 | \(0.0543579\pi\) | ||||
−0.985454 | + | 0.169941i | \(0.945642\pi\) | |||||||
\(954\) | −9.95461 | − | 15.0150i | −0.322292 | − | 0.486130i | ||||
\(955\) | 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 | ||||||||
\(966\) | −11.3947 | + | 13.2134i | −0.366617 | + | 0.425134i | ||||
\(967\) | 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 | \(-0.732631\pi\) | ||||
−0.667490 | + | 0.744619i | \(0.732631\pi\) | |||||||
\(972\) | −24.3665 | − | 19.4492i | −0.781557 | − | 0.623834i | ||||
\(973\) | −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 | \(0.280627\pi\) | ||||
−0.635906 | + | 0.771767i | \(0.719373\pi\) | |||||||
\(978\) | −38.6595 | + | 44.8300i | −1.23619 | + | 1.43350i | ||||
\(979\) | 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 | \(-0.484563\pi\) | ||||
0.0484779 | + | 0.998824i | \(0.484563\pi\) | |||||||
\(984\) | 34.8911 | + | 0.579989i | 1.11229 | + | 0.0184894i | ||||
\(985\) | 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 | ||||||||
\(996\) | 14.8013 | − | 6.63250i | 0.468997 | − | 0.210159i | ||||
\(997\) | −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.251.5 | 8 | ||
3.2 | odd | 2 | inner | 300.2.e.c.251.4 | 8 | ||
4.3 | odd | 2 | inner | 300.2.e.c.251.3 | 8 | ||
5.2 | odd | 4 | 300.2.h.b.299.7 | 8 | |||
5.3 | odd | 4 | 300.2.h.a.299.2 | 8 | |||
5.4 | even | 2 | 60.2.e.a.11.4 | yes | 8 | ||
12.11 | even | 2 | inner | 300.2.e.c.251.6 | 8 | ||
15.2 | even | 4 | 300.2.h.a.299.1 | 8 | |||
15.8 | even | 4 | 300.2.h.b.299.8 | 8 | |||
15.14 | odd | 2 | 60.2.e.a.11.5 | yes | 8 | ||
20.3 | even | 4 | 300.2.h.a.299.3 | 8 | |||
20.7 | even | 4 | 300.2.h.b.299.6 | 8 | |||
20.19 | odd | 2 | 60.2.e.a.11.6 | yes | 8 | ||
40.19 | odd | 2 | 960.2.h.g.191.4 | 8 | |||
40.29 | even | 2 | 960.2.h.g.191.5 | 8 | |||
60.23 | odd | 4 | 300.2.h.b.299.5 | 8 | |||
60.47 | odd | 4 | 300.2.h.a.299.4 | 8 | |||
60.59 | even | 2 | 60.2.e.a.11.3 | ✓ | 8 | ||
120.29 | odd | 2 | 960.2.h.g.191.3 | 8 | |||
120.59 | even | 2 | 960.2.h.g.191.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.2.e.a.11.3 | ✓ | 8 | 60.59 | even | 2 | ||
60.2.e.a.11.4 | yes | 8 | 5.4 | even | 2 | ||
60.2.e.a.11.5 | yes | 8 | 15.14 | odd | 2 | ||
60.2.e.a.11.6 | yes | 8 | 20.19 | odd | 2 | ||
300.2.e.c.251.3 | 8 | 4.3 | odd | 2 | inner | ||
300.2.e.c.251.4 | 8 | 3.2 | odd | 2 | inner | ||
300.2.e.c.251.5 | 8 | 1.1 | even | 1 | trivial | ||
300.2.e.c.251.6 | 8 | 12.11 | even | 2 | inner | ||
300.2.h.a.299.1 | 8 | 15.2 | even | 4 | |||
300.2.h.a.299.2 | 8 | 5.3 | odd | 4 | |||
300.2.h.a.299.3 | 8 | 20.3 | even | 4 | |||
300.2.h.a.299.4 | 8 | 60.47 | odd | 4 | |||
300.2.h.b.299.5 | 8 | 60.23 | odd | 4 | |||
300.2.h.b.299.6 | 8 | 20.7 | even | 4 | |||
300.2.h.b.299.7 | 8 | 5.2 | odd | 4 | |||
300.2.h.b.299.8 | 8 | 15.8 | even | 4 | |||
960.2.h.g.191.3 | 8 | 120.29 | odd | 2 | |||
960.2.h.g.191.4 | 8 | 40.19 | odd | 2 | |||
960.2.h.g.191.5 | 8 | 40.29 | even | 2 | |||
960.2.h.g.191.6 | 8 | 120.59 | even | 2 |