Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(551,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.551");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 551.6 | ||
Root | \(1.37342 - 1.05533i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.551 |
Dual form | 690.2.e.a.551.14 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.05533 | + | 1.37342i | 0.609294 | + | 0.792944i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.37342 | − | 1.05533i | 0.560696 | − | 0.430836i | ||||
\(7\) | 1.91110i | 0.722326i | 0.932503 | + | 0.361163i | \(0.117620\pi\) | ||||
−0.932503 | + | 0.361163i | \(0.882380\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.772562 | + | 2.89882i | −0.257521 | + | 0.966273i | ||||
\(10\) | 1.00000i | 0.316228i | ||||||||
\(11\) | −2.07465 | −0.625530 | −0.312765 | − | 0.949830i | \(-0.601255\pi\) | ||||
−0.312765 | + | 0.949830i | \(0.601255\pi\) | |||||||
\(12\) | −1.05533 | − | 1.37342i | −0.304647 | − | 0.396472i | ||||
\(13\) | 1.28828 | 0.357305 | 0.178652 | − | 0.983912i | \(-0.442826\pi\) | ||||
0.178652 | + | 0.983912i | \(0.442826\pi\) | |||||||
\(14\) | 1.91110 | 0.510762 | ||||||||
\(15\) | −1.05533 | − | 1.37342i | −0.272485 | − | 0.354615i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.04657 | −0.981438 | −0.490719 | − | 0.871318i | \(-0.663266\pi\) | ||||
−0.490719 | + | 0.871318i | \(0.663266\pi\) | |||||||
\(18\) | 2.89882 | + | 0.772562i | 0.683258 | + | 0.182095i | ||||
\(19\) | 3.79764i | 0.871238i | 0.900131 | + | 0.435619i | \(0.143470\pi\) | ||||
−0.900131 | + | 0.435619i | \(0.856530\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.62474 | + | 2.01683i | −0.572764 | + | 0.440109i | ||||
\(22\) | 2.07465i | 0.442317i | ||||||||
\(23\) | −2.86177 | + | 3.84841i | −0.596721 | + | 0.802449i | ||||
\(24\) | −1.37342 | + | 1.05533i | −0.280348 | + | 0.215418i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | − | 1.28828i | − | 0.252652i | ||||||
\(27\) | −4.79660 | + | 1.99816i | −0.923106 | + | 0.384545i | ||||
\(28\) | − | 1.91110i | − | 0.361163i | ||||||
\(29\) | 2.78403i | 0.516981i | 0.966014 | + | 0.258491i | \(0.0832251\pi\) | ||||
−0.966014 | + | 0.258491i | \(0.916775\pi\) | |||||||
\(30\) | −1.37342 | + | 1.05533i | −0.250751 | + | 0.192676i | ||||
\(31\) | 1.87654 | 0.337036 | 0.168518 | − | 0.985699i | \(-0.446102\pi\) | ||||
0.168518 | + | 0.985699i | \(0.446102\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −2.18944 | − | 2.84936i | −0.381132 | − | 0.496011i | ||||
\(34\) | 4.04657i | 0.693981i | ||||||||
\(35\) | − | 1.91110i | − | 0.323034i | ||||||
\(36\) | 0.772562 | − | 2.89882i | 0.128760 | − | 0.483136i | ||||
\(37\) | 2.18386i | 0.359024i | 0.983756 | + | 0.179512i | \(0.0574519\pi\) | ||||
−0.983756 | + | 0.179512i | \(0.942548\pi\) | |||||||
\(38\) | 3.79764 | 0.616058 | ||||||||
\(39\) | 1.35956 | + | 1.76935i | 0.217704 | + | 0.283323i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | − | 0.590353i | − | 0.0921977i | −0.998937 | − | 0.0460988i | \(-0.985321\pi\) | ||
0.998937 | − | 0.0460988i | \(-0.0146789\pi\) | |||||||
\(42\) | 2.01683 | + | 2.62474i | 0.311204 | + | 0.405005i | ||||
\(43\) | − | 0.332844i | − | 0.0507583i | −0.999678 | − | 0.0253791i | \(-0.991921\pi\) | ||
0.999678 | − | 0.0253791i | \(-0.00807929\pi\) | |||||||
\(44\) | 2.07465 | 0.312765 | ||||||||
\(45\) | 0.772562 | − | 2.89882i | 0.115167 | − | 0.432130i | ||||
\(46\) | 3.84841 | + | 2.86177i | 0.567417 | + | 0.421946i | ||||
\(47\) | 4.11977i | 0.600931i | 0.953793 | + | 0.300465i | \(0.0971419\pi\) | ||||
−0.953793 | + | 0.300465i | \(0.902858\pi\) | |||||||
\(48\) | 1.05533 | + | 1.37342i | 0.152324 | + | 0.198236i | ||||
\(49\) | 3.34771 | 0.478245 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | −4.27046 | − | 5.55764i | −0.597985 | − | 0.778225i | ||||
\(52\) | −1.28828 | −0.178652 | ||||||||
\(53\) | 3.47550 | 0.477397 | 0.238698 | − | 0.971094i | \(-0.423279\pi\) | ||||
0.238698 | + | 0.971094i | \(0.423279\pi\) | |||||||
\(54\) | 1.99816 | + | 4.79660i | 0.271914 | + | 0.652735i | ||||
\(55\) | 2.07465 | 0.279746 | ||||||||
\(56\) | −1.91110 | −0.255381 | ||||||||
\(57\) | −5.21575 | + | 4.00776i | −0.690843 | + | 0.530840i | ||||
\(58\) | 2.78403 | 0.365561 | ||||||||
\(59\) | 2.07202i | 0.269753i | 0.990862 | + | 0.134877i | \(0.0430638\pi\) | ||||
−0.990862 | + | 0.134877i | \(0.956936\pi\) | |||||||
\(60\) | 1.05533 | + | 1.37342i | 0.136242 | + | 0.177308i | ||||
\(61\) | − | 3.23836i | − | 0.414630i | −0.978274 | − | 0.207315i | \(-0.933527\pi\) | ||
0.978274 | − | 0.207315i | \(-0.0664725\pi\) | |||||||
\(62\) | − | 1.87654i | − | 0.238321i | ||||||
\(63\) | −5.53992 | − | 1.47644i | −0.697964 | − | 0.186014i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.28828 | −0.159791 | ||||||||
\(66\) | −2.84936 | + | 2.18944i | −0.350733 | + | 0.269501i | ||||
\(67\) | 6.73067i | 0.822282i | 0.911572 | + | 0.411141i | \(0.134870\pi\) | ||||
−0.911572 | + | 0.411141i | \(0.865130\pi\) | |||||||
\(68\) | 4.04657 | 0.490719 | ||||||||
\(69\) | −8.30559 | + | 0.130920i | −0.999876 | + | 0.0157609i | ||||
\(70\) | −1.91110 | −0.228420 | ||||||||
\(71\) | − | 9.09793i | − | 1.07973i | −0.841753 | − | 0.539863i | \(-0.818476\pi\) | ||
0.841753 | − | 0.539863i | \(-0.181524\pi\) | |||||||
\(72\) | −2.89882 | − | 0.772562i | −0.341629 | − | 0.0910473i | ||||
\(73\) | −3.52030 | −0.412020 | −0.206010 | − | 0.978550i | \(-0.566048\pi\) | ||||
−0.206010 | + | 0.978550i | \(0.566048\pi\) | |||||||
\(74\) | 2.18386 | 0.253868 | ||||||||
\(75\) | 1.05533 | + | 1.37342i | 0.121859 | + | 0.158589i | ||||
\(76\) | − | 3.79764i | − | 0.435619i | ||||||
\(77\) | − | 3.96485i | − | 0.451837i | ||||||
\(78\) | 1.76935 | − | 1.35956i | 0.200339 | − | 0.153940i | ||||
\(79\) | 3.38420i | 0.380753i | 0.981711 | + | 0.190376i | \(0.0609708\pi\) | ||||
−0.981711 | + | 0.190376i | \(0.939029\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −7.80630 | − | 4.47903i | −0.867366 | − | 0.497670i | ||||
\(82\) | −0.590353 | −0.0651936 | ||||||||
\(83\) | 5.68044 | 0.623509 | 0.311754 | − | 0.950163i | \(-0.399083\pi\) | ||||
0.311754 | + | 0.950163i | \(0.399083\pi\) | |||||||
\(84\) | 2.62474 | − | 2.01683i | 0.286382 | − | 0.220055i | ||||
\(85\) | 4.04657 | 0.438912 | ||||||||
\(86\) | −0.332844 | −0.0358915 | ||||||||
\(87\) | −3.82364 | + | 2.93807i | −0.409937 | + | 0.314994i | ||||
\(88\) | − | 2.07465i | − | 0.221158i | ||||||
\(89\) | 10.9473 | 1.16042 | 0.580208 | − | 0.814468i | \(-0.302971\pi\) | ||||
0.580208 | + | 0.814468i | \(0.302971\pi\) | |||||||
\(90\) | −2.89882 | − | 0.772562i | −0.305562 | − | 0.0814352i | ||||
\(91\) | 2.46203i | 0.258090i | ||||||||
\(92\) | 2.86177 | − | 3.84841i | 0.298361 | − | 0.401224i | ||||
\(93\) | 1.98036 | + | 2.57727i | 0.205354 | + | 0.267251i | ||||
\(94\) | 4.11977 | 0.424922 | ||||||||
\(95\) | − | 3.79764i | − | 0.389629i | ||||||
\(96\) | 1.37342 | − | 1.05533i | 0.140174 | − | 0.107709i | ||||
\(97\) | − | 14.3560i | − | 1.45763i | −0.684712 | − | 0.728813i | \(-0.740072\pi\) | ||
0.684712 | − | 0.728813i | \(-0.259928\pi\) | |||||||
\(98\) | − | 3.34771i | − | 0.338170i | ||||||
\(99\) | 1.60280 | − | 6.01403i | 0.161087 | − | 0.604433i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | − | 6.90670i | − | 0.687243i | −0.939108 | − | 0.343621i | \(-0.888346\pi\) | ||
0.939108 | − | 0.343621i | \(-0.111654\pi\) | |||||||
\(102\) | −5.55764 | + | 4.27046i | −0.550289 | + | 0.422839i | ||||
\(103\) | 15.1722i | 1.49496i | 0.664282 | + | 0.747482i | \(0.268738\pi\) | ||||
−0.664282 | + | 0.747482i | \(0.731262\pi\) | |||||||
\(104\) | 1.28828i | 0.126326i | ||||||||
\(105\) | 2.62474 | − | 2.01683i | 0.256148 | − | 0.196823i | ||||
\(106\) | − | 3.47550i | − | 0.337571i | ||||||
\(107\) | 15.9284 | 1.53986 | 0.769930 | − | 0.638129i | \(-0.220291\pi\) | ||||
0.769930 | + | 0.638129i | \(0.220291\pi\) | |||||||
\(108\) | 4.79660 | − | 1.99816i | 0.461553 | − | 0.192273i | ||||
\(109\) | − | 3.31710i | − | 0.317721i | −0.987301 | − | 0.158860i | \(-0.949218\pi\) | ||
0.987301 | − | 0.158860i | \(-0.0507820\pi\) | |||||||
\(110\) | − | 2.07465i | − | 0.197810i | ||||||
\(111\) | −2.99935 | + | 2.30469i | −0.284686 | + | 0.218751i | ||||
\(112\) | 1.91110i | 0.180582i | ||||||||
\(113\) | 16.7721 | 1.57779 | 0.788893 | − | 0.614531i | \(-0.210655\pi\) | ||||
0.788893 | + | 0.614531i | \(0.210655\pi\) | |||||||
\(114\) | 4.00776 | + | 5.21575i | 0.375361 | + | 0.488500i | ||||
\(115\) | 2.86177 | − | 3.84841i | 0.266862 | − | 0.358866i | ||||
\(116\) | − | 2.78403i | − | 0.258491i | ||||||
\(117\) | −0.995276 | + | 3.73449i | −0.0920133 | + | 0.345254i | ||||
\(118\) | 2.07202 | 0.190745 | ||||||||
\(119\) | − | 7.73339i | − | 0.708918i | ||||||
\(120\) | 1.37342 | − | 1.05533i | 0.125375 | − | 0.0963379i | ||||
\(121\) | −6.69583 | −0.608712 | ||||||||
\(122\) | −3.23836 | −0.293188 | ||||||||
\(123\) | 0.810803 | − | 0.623017i | 0.0731076 | − | 0.0561755i | ||||
\(124\) | −1.87654 | −0.168518 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.47644 | + | 5.53992i | −0.131532 | + | 0.493535i | ||||
\(127\) | −0.980016 | −0.0869623 | −0.0434812 | − | 0.999054i | \(-0.513845\pi\) | ||||
−0.0434812 | + | 0.999054i | \(0.513845\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0.457135 | − | 0.351260i | 0.0402485 | − | 0.0309267i | ||||
\(130\) | 1.28828i | 0.112990i | ||||||||
\(131\) | − | 9.96859i | − | 0.870960i | −0.900198 | − | 0.435480i | \(-0.856579\pi\) | ||
0.900198 | − | 0.435480i | \(-0.143421\pi\) | |||||||
\(132\) | 2.18944 | + | 2.84936i | 0.190566 | + | 0.248005i | ||||
\(133\) | −7.25765 | −0.629318 | ||||||||
\(134\) | 6.73067 | 0.581442 | ||||||||
\(135\) | 4.79660 | − | 1.99816i | 0.412826 | − | 0.171974i | ||||
\(136\) | − | 4.04657i | − | 0.346991i | ||||||
\(137\) | 14.3513 | 1.22612 | 0.613058 | − | 0.790038i | \(-0.289939\pi\) | ||||
0.613058 | + | 0.790038i | \(0.289939\pi\) | |||||||
\(138\) | 0.130920 | + | 8.30559i | 0.0111447 | + | 0.707019i | ||||
\(139\) | −4.62609 | −0.392380 | −0.196190 | − | 0.980566i | \(-0.562857\pi\) | ||||
−0.196190 | + | 0.980566i | \(0.562857\pi\) | |||||||
\(140\) | 1.91110i | 0.161517i | ||||||||
\(141\) | −5.65817 | + | 4.34771i | −0.476504 | + | 0.366144i | ||||
\(142\) | −9.09793 | −0.763482 | ||||||||
\(143\) | −2.67273 | −0.223505 | ||||||||
\(144\) | −0.772562 | + | 2.89882i | −0.0643802 | + | 0.241568i | ||||
\(145\) | − | 2.78403i | − | 0.231201i | ||||||
\(146\) | 3.52030i | 0.291342i | ||||||||
\(147\) | 3.53294 | + | 4.59782i | 0.291392 | + | 0.379221i | ||||
\(148\) | − | 2.18386i | − | 0.179512i | ||||||
\(149\) | −21.2559 | −1.74135 | −0.870676 | − | 0.491856i | \(-0.836319\pi\) | ||||
−0.870676 | + | 0.491856i | \(0.836319\pi\) | |||||||
\(150\) | 1.37342 | − | 1.05533i | 0.112139 | − | 0.0861672i | ||||
\(151\) | 13.0135 | 1.05903 | 0.529514 | − | 0.848301i | \(-0.322374\pi\) | ||||
0.529514 | + | 0.848301i | \(0.322374\pi\) | |||||||
\(152\) | −3.79764 | −0.308029 | ||||||||
\(153\) | 3.12623 | − | 11.7303i | 0.252741 | − | 0.948337i | ||||
\(154\) | −3.96485 | −0.319497 | ||||||||
\(155\) | −1.87654 | −0.150727 | ||||||||
\(156\) | −1.35956 | − | 1.76935i | −0.108852 | − | 0.141661i | ||||
\(157\) | − | 10.4319i | − | 0.832557i | −0.909237 | − | 0.416278i | \(-0.863334\pi\) | ||
0.909237 | − | 0.416278i | \(-0.136666\pi\) | |||||||
\(158\) | 3.38420 | 0.269233 | ||||||||
\(159\) | 3.66780 | + | 4.77332i | 0.290875 | + | 0.378549i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | −7.35468 | − | 5.46912i | −0.579630 | − | 0.431027i | ||||
\(162\) | −4.47903 | + | 7.80630i | −0.351906 | + | 0.613321i | ||||
\(163\) | −2.70739 | −0.212059 | −0.106030 | − | 0.994363i | \(-0.533814\pi\) | ||||
−0.106030 | + | 0.994363i | \(0.533814\pi\) | |||||||
\(164\) | 0.590353i | 0.0460988i | ||||||||
\(165\) | 2.18944 | + | 2.84936i | 0.170448 | + | 0.221823i | ||||
\(166\) | − | 5.68044i | − | 0.440887i | ||||||
\(167\) | 16.7966i | 1.29976i | 0.760038 | + | 0.649879i | \(0.225181\pi\) | ||||
−0.760038 | + | 0.649879i | \(0.774819\pi\) | |||||||
\(168\) | −2.01683 | − | 2.62474i | −0.155602 | − | 0.202503i | ||||
\(169\) | −11.3403 | −0.872333 | ||||||||
\(170\) | − | 4.04657i | − | 0.310358i | ||||||
\(171\) | −11.0087 | − | 2.93391i | −0.841853 | − | 0.224362i | ||||
\(172\) | 0.332844i | 0.0253791i | ||||||||
\(173\) | 18.5634i | 1.41135i | 0.708535 | + | 0.705676i | \(0.249356\pi\) | ||||
−0.708535 | + | 0.705676i | \(0.750644\pi\) | |||||||
\(174\) | 2.93807 | + | 3.82364i | 0.222734 | + | 0.289870i | ||||
\(175\) | 1.91110i | 0.144465i | ||||||||
\(176\) | −2.07465 | −0.156383 | ||||||||
\(177\) | −2.84575 | + | 2.18666i | −0.213899 | + | 0.164359i | ||||
\(178\) | − | 10.9473i | − | 0.820538i | ||||||
\(179\) | − | 20.1835i | − | 1.50859i | −0.656538 | − | 0.754293i | \(-0.727980\pi\) | ||
0.656538 | − | 0.754293i | \(-0.272020\pi\) | |||||||
\(180\) | −0.772562 | + | 2.89882i | −0.0575834 | + | 0.216065i | ||||
\(181\) | − | 14.5787i | − | 1.08362i | −0.840500 | − | 0.541811i | \(-0.817739\pi\) | ||
0.840500 | − | 0.541811i | \(-0.182261\pi\) | |||||||
\(182\) | 2.46203 | 0.182498 | ||||||||
\(183\) | 4.44763 | − | 3.41754i | 0.328778 | − | 0.252632i | ||||
\(184\) | −3.84841 | − | 2.86177i | −0.283708 | − | 0.210973i | ||||
\(185\) | − | 2.18386i | − | 0.160560i | ||||||
\(186\) | 2.57727 | − | 1.98036i | 0.188975 | − | 0.145207i | ||||
\(187\) | 8.39522 | 0.613919 | ||||||||
\(188\) | − | 4.11977i | − | 0.300465i | ||||||
\(189\) | −3.81867 | − | 9.16676i | −0.277767 | − | 0.666784i | ||||
\(190\) | −3.79764 | −0.275510 | ||||||||
\(191\) | −5.69209 | −0.411865 | −0.205932 | − | 0.978566i | \(-0.566023\pi\) | ||||
−0.205932 | + | 0.978566i | \(0.566023\pi\) | |||||||
\(192\) | −1.05533 | − | 1.37342i | −0.0761618 | − | 0.0991180i | ||||
\(193\) | −16.8306 | −1.21149 | −0.605746 | − | 0.795658i | \(-0.707125\pi\) | ||||
−0.605746 | + | 0.795658i | \(0.707125\pi\) | |||||||
\(194\) | −14.3560 | −1.03070 | ||||||||
\(195\) | −1.35956 | − | 1.76935i | −0.0973600 | − | 0.126706i | ||||
\(196\) | −3.34771 | −0.239122 | ||||||||
\(197\) | 6.99478i | 0.498358i | 0.968458 | + | 0.249179i | \(0.0801607\pi\) | ||||
−0.968458 | + | 0.249179i | \(0.919839\pi\) | |||||||
\(198\) | −6.01403 | − | 1.60280i | −0.427399 | − | 0.113906i | ||||
\(199\) | − | 4.72003i | − | 0.334594i | −0.985907 | − | 0.167297i | \(-0.946496\pi\) | ||
0.985907 | − | 0.167297i | \(-0.0535038\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −9.24404 | + | 7.10307i | −0.652024 | + | 0.501012i | ||||
\(202\) | −6.90670 | −0.485954 | ||||||||
\(203\) | −5.32055 | −0.373429 | ||||||||
\(204\) | 4.27046 | + | 5.55764i | 0.298992 | + | 0.389113i | ||||
\(205\) | 0.590353i | 0.0412321i | ||||||||
\(206\) | 15.1722 | 1.05710 | ||||||||
\(207\) | −8.94494 | − | 11.2689i | −0.621716 | − | 0.783243i | ||||
\(208\) | 1.28828 | 0.0893261 | ||||||||
\(209\) | − | 7.87877i | − | 0.544986i | ||||||
\(210\) | −2.01683 | − | 2.62474i | −0.139175 | − | 0.181124i | ||||
\(211\) | 22.6122 | 1.55669 | 0.778344 | − | 0.627838i | \(-0.216060\pi\) | ||||
0.778344 | + | 0.627838i | \(0.216060\pi\) | |||||||
\(212\) | −3.47550 | −0.238698 | ||||||||
\(213\) | 12.4953 | − | 9.60131i | 0.856162 | − | 0.657871i | ||||
\(214\) | − | 15.9284i | − | 1.08885i | ||||||
\(215\) | 0.332844i | 0.0226998i | ||||||||
\(216\) | −1.99816 | − | 4.79660i | −0.135957 | − | 0.326367i | ||||
\(217\) | 3.58624i | 0.243450i | ||||||||
\(218\) | −3.31710 | −0.224662 | ||||||||
\(219\) | −3.71508 | − | 4.83485i | −0.251042 | − | 0.326709i | ||||
\(220\) | −2.07465 | −0.139873 | ||||||||
\(221\) | −5.21312 | −0.350672 | ||||||||
\(222\) | 2.30469 | + | 2.99935i | 0.154680 | + | 0.201303i | ||||
\(223\) | −23.3059 | −1.56068 | −0.780340 | − | 0.625355i | \(-0.784954\pi\) | ||||
−0.780340 | + | 0.625355i | \(0.784954\pi\) | |||||||
\(224\) | 1.91110 | 0.127690 | ||||||||
\(225\) | −0.772562 | + | 2.89882i | −0.0515041 | + | 0.193255i | ||||
\(226\) | − | 16.7721i | − | 1.11566i | ||||||
\(227\) | 27.6254 | 1.83356 | 0.916780 | − | 0.399394i | \(-0.130779\pi\) | ||||
0.916780 | + | 0.399394i | \(0.130779\pi\) | |||||||
\(228\) | 5.21575 | − | 4.00776i | 0.345421 | − | 0.265420i | ||||
\(229\) | 24.2738i | 1.60406i | 0.597286 | + | 0.802028i | \(0.296246\pi\) | ||||
−0.597286 | + | 0.802028i | \(0.703754\pi\) | |||||||
\(230\) | −3.84841 | − | 2.86177i | −0.253757 | − | 0.188700i | ||||
\(231\) | 5.44541 | − | 4.18422i | 0.358282 | − | 0.275302i | ||||
\(232\) | −2.78403 | −0.182781 | ||||||||
\(233\) | 0.568005i | 0.0372112i | 0.999827 | + | 0.0186056i | \(0.00592269\pi\) | ||||
−0.999827 | + | 0.0186056i | \(0.994077\pi\) | |||||||
\(234\) | 3.73449 | + | 0.995276i | 0.244131 | + | 0.0650632i | ||||
\(235\) | − | 4.11977i | − | 0.268744i | ||||||
\(236\) | − | 2.07202i | − | 0.134877i | ||||||
\(237\) | −4.64793 | + | 3.57145i | −0.301916 | + | 0.231990i | ||||
\(238\) | −7.73339 | −0.501281 | ||||||||
\(239\) | − | 1.41185i | − | 0.0913250i | −0.998957 | − | 0.0456625i | \(-0.985460\pi\) | ||
0.998957 | − | 0.0456625i | \(-0.0145399\pi\) | |||||||
\(240\) | −1.05533 | − | 1.37342i | −0.0681212 | − | 0.0886538i | ||||
\(241\) | − | 0.433010i | − | 0.0278926i | −0.999903 | − | 0.0139463i | \(-0.995561\pi\) | ||
0.999903 | − | 0.0139463i | \(-0.00443939\pi\) | |||||||
\(242\) | 6.69583i | 0.430424i | ||||||||
\(243\) | −2.08662 | − | 15.4482i | −0.133857 | − | 0.991001i | ||||
\(244\) | 3.23836i | 0.207315i | ||||||||
\(245\) | −3.34771 | −0.213878 | ||||||||
\(246\) | −0.623017 | − | 0.810803i | −0.0397221 | − | 0.0516949i | ||||
\(247\) | 4.89242i | 0.311297i | ||||||||
\(248\) | 1.87654i | 0.119160i | ||||||||
\(249\) | 5.99473 | + | 7.80162i | 0.379900 | + | 0.494408i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | 22.4064 | 1.41428 | 0.707140 | − | 0.707074i | \(-0.249985\pi\) | ||||
0.707140 | + | 0.707074i | \(0.249985\pi\) | |||||||
\(252\) | 5.53992 | + | 1.47644i | 0.348982 | + | 0.0930070i | ||||
\(253\) | 5.93718 | − | 7.98410i | 0.373267 | − | 0.501956i | ||||
\(254\) | 0.980016i | 0.0614917i | ||||||||
\(255\) | 4.27046 | + | 5.55764i | 0.267427 | + | 0.348033i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.6632i | 1.28894i | 0.764632 | + | 0.644468i | \(0.222921\pi\) | ||||
−0.764632 | + | 0.644468i | \(0.777079\pi\) | |||||||
\(258\) | −0.351260 | − | 0.457135i | −0.0218685 | − | 0.0284600i | ||||
\(259\) | −4.17356 | −0.259332 | ||||||||
\(260\) | 1.28828 | 0.0798957 | ||||||||
\(261\) | −8.07040 | − | 2.15084i | −0.499545 | − | 0.133133i | ||||
\(262\) | −9.96859 | −0.615862 | ||||||||
\(263\) | −2.57099 | −0.158534 | −0.0792669 | − | 0.996853i | \(-0.525258\pi\) | ||||
−0.0792669 | + | 0.996853i | \(0.525258\pi\) | |||||||
\(264\) | 2.84936 | − | 2.18944i | 0.175366 | − | 0.134751i | ||||
\(265\) | −3.47550 | −0.213498 | ||||||||
\(266\) | 7.25765i | 0.444995i | ||||||||
\(267\) | 11.5530 | + | 15.0353i | 0.707035 | + | 0.920145i | ||||
\(268\) | − | 6.73067i | − | 0.411141i | ||||||
\(269\) | − | 2.88848i | − | 0.176113i | −0.996115 | − | 0.0880567i | \(-0.971934\pi\) | ||
0.996115 | − | 0.0880567i | \(-0.0280657\pi\) | |||||||
\(270\) | −1.99816 | − | 4.79660i | −0.121604 | − | 0.291912i | ||||
\(271\) | 15.1639 | 0.921141 | 0.460571 | − | 0.887623i | \(-0.347645\pi\) | ||||
0.460571 | + | 0.887623i | \(0.347645\pi\) | |||||||
\(272\) | −4.04657 | −0.245360 | ||||||||
\(273\) | −3.38139 | + | 2.59825i | −0.204651 | + | 0.157253i | ||||
\(274\) | − | 14.3513i | − | 0.866994i | ||||||
\(275\) | −2.07465 | −0.125106 | ||||||||
\(276\) | 8.30559 | − | 0.130920i | 0.499938 | − | 0.00788047i | ||||
\(277\) | 3.10829 | 0.186759 | 0.0933796 | − | 0.995631i | \(-0.470233\pi\) | ||||
0.0933796 | + | 0.995631i | \(0.470233\pi\) | |||||||
\(278\) | 4.62609i | 0.277455i | ||||||||
\(279\) | −1.44974 | + | 5.43974i | −0.0867938 | + | 0.325669i | ||||
\(280\) | 1.91110 | 0.114210 | ||||||||
\(281\) | −12.8651 | −0.767468 | −0.383734 | − | 0.923444i | \(-0.625362\pi\) | ||||
−0.383734 | + | 0.923444i | \(0.625362\pi\) | |||||||
\(282\) | 4.34771 | + | 5.65817i | 0.258903 | + | 0.336939i | ||||
\(283\) | 24.2159i | 1.43948i | 0.694242 | + | 0.719742i | \(0.255740\pi\) | ||||
−0.694242 | + | 0.719742i | \(0.744260\pi\) | |||||||
\(284\) | 9.09793i | 0.539863i | ||||||||
\(285\) | 5.21575 | − | 4.00776i | 0.308954 | − | 0.237399i | ||||
\(286\) | 2.67273i | 0.158042i | ||||||||
\(287\) | 1.12822 | 0.0665968 | ||||||||
\(288\) | 2.89882 | + | 0.772562i | 0.170815 | + | 0.0455237i | ||||
\(289\) | −0.625250 | −0.0367794 | ||||||||
\(290\) | −2.78403 | −0.163484 | ||||||||
\(291\) | 19.7168 | − | 15.1503i | 1.15582 | − | 0.888124i | ||||
\(292\) | 3.52030 | 0.206010 | ||||||||
\(293\) | −27.3847 | −1.59983 | −0.799916 | − | 0.600112i | \(-0.795123\pi\) | ||||
−0.799916 | + | 0.600112i | \(0.795123\pi\) | |||||||
\(294\) | 4.59782 | − | 3.53294i | 0.268150 | − | 0.206045i | ||||
\(295\) | − | 2.07202i | − | 0.120637i | ||||||
\(296\) | −2.18386 | −0.126934 | ||||||||
\(297\) | 9.95127 | − | 4.14547i | 0.577431 | − | 0.240545i | ||||
\(298\) | 21.2559i | 1.23132i | ||||||||
\(299\) | −3.68677 | + | 4.95783i | −0.213211 | + | 0.286719i | ||||
\(300\) | −1.05533 | − | 1.37342i | −0.0609294 | − | 0.0792944i | ||||
\(301\) | 0.636097 | 0.0366640 | ||||||||
\(302\) | − | 13.0135i | − | 0.748845i | ||||||
\(303\) | 9.48580 | − | 7.28884i | 0.544945 | − | 0.418733i | ||||
\(304\) | 3.79764i | 0.217809i | ||||||||
\(305\) | 3.23836i | 0.185428i | ||||||||
\(306\) | −11.7303 | − | 3.12623i | −0.670575 | − | 0.178715i | ||||
\(307\) | 27.5618 | 1.57304 | 0.786518 | − | 0.617567i | \(-0.211882\pi\) | ||||
0.786518 | + | 0.617567i | \(0.211882\pi\) | |||||||
\(308\) | 3.96485i | 0.225919i | ||||||||
\(309\) | −20.8378 | + | 16.0117i | −1.18542 | + | 0.910874i | ||||
\(310\) | 1.87654i | 0.106580i | ||||||||
\(311\) | − | 13.2819i | − | 0.753148i | −0.926387 | − | 0.376574i | \(-0.877102\pi\) | ||
0.926387 | − | 0.376574i | \(-0.122898\pi\) | |||||||
\(312\) | −1.76935 | + | 1.35956i | −0.100170 | + | 0.0769699i | ||||
\(313\) | 23.2441i | 1.31383i | 0.753963 | + | 0.656917i | \(0.228140\pi\) | ||||
−0.753963 | + | 0.656917i | \(0.771860\pi\) | |||||||
\(314\) | −10.4319 | −0.588706 | ||||||||
\(315\) | 5.53992 | + | 1.47644i | 0.312139 | + | 0.0831879i | ||||
\(316\) | − | 3.38420i | − | 0.190376i | ||||||
\(317\) | 17.6217i | 0.989733i | 0.868969 | + | 0.494867i | \(0.164783\pi\) | ||||
−0.868969 | + | 0.494867i | \(0.835217\pi\) | |||||||
\(318\) | 4.77332 | − | 3.66780i | 0.267675 | − | 0.205680i | ||||
\(319\) | − | 5.77589i | − | 0.323388i | ||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 16.8097 | + | 21.8764i | 0.938228 | + | 1.22102i | ||||
\(322\) | −5.46912 | + | 7.35468i | −0.304782 | + | 0.409860i | ||||
\(323\) | − | 15.3674i | − | 0.855066i | ||||||
\(324\) | 7.80630 | + | 4.47903i | 0.433683 | + | 0.248835i | ||||
\(325\) | 1.28828 | 0.0714609 | ||||||||
\(326\) | 2.70739i | 0.149948i | ||||||||
\(327\) | 4.55577 | − | 3.50063i | 0.251935 | − | 0.193585i | ||||
\(328\) | 0.590353 | 0.0325968 | ||||||||
\(329\) | −7.87328 | −0.434068 | ||||||||
\(330\) | 2.84936 | − | 2.18944i | 0.156852 | − | 0.120525i | ||||
\(331\) | 20.7361 | 1.13976 | 0.569879 | − | 0.821729i | \(-0.306990\pi\) | ||||
0.569879 | + | 0.821729i | \(0.306990\pi\) | |||||||
\(332\) | −5.68044 | −0.311754 | ||||||||
\(333\) | −6.33060 | − | 1.68716i | −0.346915 | − | 0.0924561i | ||||
\(334\) | 16.7966 | 0.919068 | ||||||||
\(335\) | − | 6.73067i | − | 0.367736i | ||||||
\(336\) | −2.62474 | + | 2.01683i | −0.143191 | + | 0.110027i | ||||
\(337\) | − | 9.08954i | − | 0.495139i | −0.968870 | − | 0.247569i | \(-0.920368\pi\) | ||
0.968870 | − | 0.247569i | \(-0.0796318\pi\) | |||||||
\(338\) | 11.3403i | 0.616833i | ||||||||
\(339\) | 17.7001 | + | 23.0351i | 0.961336 | + | 1.25110i | ||||
\(340\) | −4.04657 | −0.219456 | ||||||||
\(341\) | −3.89316 | −0.210826 | ||||||||
\(342\) | −2.93391 | + | 11.0087i | −0.158648 | + | 0.595280i | ||||
\(343\) | 19.7755i | 1.06777i | ||||||||
\(344\) | 0.332844 | 0.0179458 | ||||||||
\(345\) | 8.30559 | − | 0.130920i | 0.447158 | − | 0.00704850i | ||||
\(346\) | 18.5634 | 0.997976 | ||||||||
\(347\) | 28.2337i | 1.51567i | 0.652449 | + | 0.757833i | \(0.273742\pi\) | ||||
−0.652449 | + | 0.757833i | \(0.726258\pi\) | |||||||
\(348\) | 3.82364 | − | 2.93807i | 0.204969 | − | 0.157497i | ||||
\(349\) | −9.07266 | −0.485648 | −0.242824 | − | 0.970070i | \(-0.578074\pi\) | ||||
−0.242824 | + | 0.970070i | \(0.578074\pi\) | |||||||
\(350\) | 1.91110 | 0.102152 | ||||||||
\(351\) | −6.17936 | + | 2.57418i | −0.329830 | + | 0.137400i | ||||
\(352\) | 2.07465i | 0.110579i | ||||||||
\(353\) | 1.12881i | 0.0600806i | 0.999549 | + | 0.0300403i | \(0.00956357\pi\) | ||||
−0.999549 | + | 0.0300403i | \(0.990436\pi\) | |||||||
\(354\) | 2.18666 | + | 2.84575i | 0.116220 | + | 0.151250i | ||||
\(355\) | 9.09793i | 0.482868i | ||||||||
\(356\) | −10.9473 | −0.580208 | ||||||||
\(357\) | 10.6212 | − | 8.16127i | 0.562133 | − | 0.431940i | ||||
\(358\) | −20.1835 | −1.06673 | ||||||||
\(359\) | 14.4991 | 0.765233 | 0.382617 | − | 0.923907i | \(-0.375023\pi\) | ||||
0.382617 | + | 0.923907i | \(0.375023\pi\) | |||||||
\(360\) | 2.89882 | + | 0.772562i | 0.152781 | + | 0.0407176i | ||||
\(361\) | 4.57796 | 0.240945 | ||||||||
\(362\) | −14.5787 | −0.766237 | ||||||||
\(363\) | −7.06630 | − | 9.19618i | −0.370885 | − | 0.482674i | ||||
\(364\) | − | 2.46203i | − | 0.129045i | ||||||
\(365\) | 3.52030 | 0.184261 | ||||||||
\(366\) | −3.41754 | − | 4.44763i | −0.178638 | − | 0.232481i | ||||
\(367\) | 22.1178i | 1.15454i | 0.816553 | + | 0.577270i | \(0.195882\pi\) | ||||
−0.816553 | + | 0.577270i | \(0.804118\pi\) | |||||||
\(368\) | −2.86177 | + | 3.84841i | −0.149180 | + | 0.200612i | ||||
\(369\) | 1.71133 | + | 0.456085i | 0.0890881 | + | 0.0237428i | ||||
\(370\) | −2.18386 | −0.113533 | ||||||||
\(371\) | 6.64202i | 0.344836i | ||||||||
\(372\) | −1.98036 | − | 2.57727i | −0.102677 | − | 0.133625i | ||||
\(373\) | 19.6820i | 1.01910i | 0.860442 | + | 0.509548i | \(0.170187\pi\) | ||||
−0.860442 | + | 0.509548i | \(0.829813\pi\) | |||||||
\(374\) | − | 8.39522i | − | 0.434107i | ||||||
\(375\) | −1.05533 | − | 1.37342i | −0.0544969 | − | 0.0709231i | ||||
\(376\) | −4.11977 | −0.212461 | ||||||||
\(377\) | 3.58661i | 0.184720i | ||||||||
\(378\) | −9.16676 | + | 3.81867i | −0.471487 | + | 0.196411i | ||||
\(379\) | 17.0269i | 0.874613i | 0.899312 | + | 0.437307i | \(0.144068\pi\) | ||||
−0.899312 | + | 0.437307i | \(0.855932\pi\) | |||||||
\(380\) | 3.79764i | 0.194815i | ||||||||
\(381\) | −1.03424 | − | 1.34597i | −0.0529857 | − | 0.0689563i | ||||
\(382\) | 5.69209i | 0.291232i | ||||||||
\(383\) | 1.29893 | 0.0663722 | 0.0331861 | − | 0.999449i | \(-0.489435\pi\) | ||||
0.0331861 | + | 0.999449i | \(0.489435\pi\) | |||||||
\(384\) | −1.37342 | + | 1.05533i | −0.0700870 | + | 0.0538545i | ||||
\(385\) | 3.96485i | 0.202068i | ||||||||
\(386\) | 16.8306i | 0.856654i | ||||||||
\(387\) | 0.964855 | + | 0.257143i | 0.0490463 | + | 0.0130713i | ||||
\(388\) | 14.3560i | 0.728813i | ||||||||
\(389\) | 14.9186 | 0.756404 | 0.378202 | − | 0.925723i | \(-0.376542\pi\) | ||||
0.378202 | + | 0.925723i | \(0.376542\pi\) | |||||||
\(390\) | −1.76935 | + | 1.35956i | −0.0895945 | + | 0.0688440i | ||||
\(391\) | 11.5804 | − | 15.5729i | 0.585645 | − | 0.787554i | ||||
\(392\) | 3.34771i | 0.169085i | ||||||||
\(393\) | 13.6911 | − | 10.5201i | 0.690622 | − | 0.530671i | ||||
\(394\) | 6.99478 | 0.352392 | ||||||||
\(395\) | − | 3.38420i | − | 0.170278i | ||||||
\(396\) | −1.60280 | + | 6.01403i | −0.0805435 | + | 0.302217i | ||||
\(397\) | 31.5845 | 1.58518 | 0.792591 | − | 0.609754i | \(-0.208732\pi\) | ||||
0.792591 | + | 0.609754i | \(0.208732\pi\) | |||||||
\(398\) | −4.72003 | −0.236594 | ||||||||
\(399\) | −7.65920 | − | 9.96779i | −0.383440 | − | 0.499014i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −29.5255 | −1.47443 | −0.737216 | − | 0.675657i | \(-0.763860\pi\) | ||||
−0.737216 | + | 0.675657i | \(0.763860\pi\) | |||||||
\(402\) | 7.10307 | + | 9.24404i | 0.354269 | + | 0.461051i | ||||
\(403\) | 2.41751 | 0.120425 | ||||||||
\(404\) | 6.90670i | 0.343621i | ||||||||
\(405\) | 7.80630 | + | 4.47903i | 0.387898 | + | 0.222565i | ||||
\(406\) | 5.32055i | 0.264054i | ||||||||
\(407\) | − | 4.53074i | − | 0.224580i | ||||||
\(408\) | 5.55764 | − | 4.27046i | 0.275144 | − | 0.211420i | ||||
\(409\) | 32.5691 | 1.61044 | 0.805219 | − | 0.592978i | \(-0.202048\pi\) | ||||
0.805219 | + | 0.592978i | \(0.202048\pi\) | |||||||
\(410\) | 0.590353 | 0.0291555 | ||||||||
\(411\) | 15.1454 | + | 19.7104i | 0.747065 | + | 0.972241i | ||||
\(412\) | − | 15.1722i | − | 0.747482i | ||||||
\(413\) | −3.95982 | −0.194850 | ||||||||
\(414\) | −11.2689 | + | 8.94494i | −0.553836 | + | 0.439620i | ||||
\(415\) | −5.68044 | −0.278842 | ||||||||
\(416\) | − | 1.28828i | − | 0.0631631i | ||||||
\(417\) | −4.88205 | − | 6.35357i | −0.239075 | − | 0.311136i | ||||
\(418\) | −7.87877 | −0.385363 | ||||||||
\(419\) | −1.54122 | −0.0752934 | −0.0376467 | − | 0.999291i | \(-0.511986\pi\) | ||||
−0.0376467 | + | 0.999291i | \(0.511986\pi\) | |||||||
\(420\) | −2.62474 | + | 2.01683i | −0.128074 | + | 0.0984114i | ||||
\(421\) | 7.43732i | 0.362473i | 0.983440 | + | 0.181236i | \(0.0580099\pi\) | ||||
−0.983440 | + | 0.181236i | \(0.941990\pi\) | |||||||
\(422\) | − | 22.6122i | − | 1.10075i | ||||||
\(423\) | −11.9425 | − | 3.18278i | −0.580663 | − | 0.154752i | ||||
\(424\) | 3.47550i | 0.168785i | ||||||||
\(425\) | −4.04657 | −0.196288 | ||||||||
\(426\) | −9.60131 | − | 12.4953i | −0.465185 | − | 0.605398i | ||||
\(427\) | 6.18882 | 0.299498 | ||||||||
\(428\) | −15.9284 | −0.769930 | ||||||||
\(429\) | −2.82061 | − | 3.67078i | −0.136180 | − | 0.177227i | ||||
\(430\) | 0.332844 | 0.0160512 | ||||||||
\(431\) | 1.28640 | 0.0619637 | 0.0309819 | − | 0.999520i | \(-0.490137\pi\) | ||||
0.0309819 | + | 0.999520i | \(0.490137\pi\) | |||||||
\(432\) | −4.79660 | + | 1.99816i | −0.230777 | + | 0.0961363i | ||||
\(433\) | − | 37.5477i | − | 1.80443i | −0.431291 | − | 0.902213i | \(-0.641942\pi\) | ||
0.431291 | − | 0.902213i | \(-0.358058\pi\) | |||||||
\(434\) | 3.58624 | 0.172145 | ||||||||
\(435\) | 3.82364 | − | 2.93807i | 0.183330 | − | 0.140870i | ||||
\(436\) | 3.31710i | 0.158860i | ||||||||
\(437\) | −14.6149 | − | 10.8680i | −0.699123 | − | 0.519886i | ||||
\(438\) | −4.83485 | + | 3.71508i | −0.231018 | + | 0.177513i | ||||
\(439\) | −14.9511 | −0.713576 | −0.356788 | − | 0.934185i | \(-0.616128\pi\) | ||||
−0.356788 | + | 0.934185i | \(0.616128\pi\) | |||||||
\(440\) | 2.07465i | 0.0989051i | ||||||||
\(441\) | −2.58632 | + | 9.70442i | −0.123158 | + | 0.462115i | ||||
\(442\) | 5.21312i | 0.247963i | ||||||||
\(443\) | − | 26.4573i | − | 1.25702i | −0.777800 | − | 0.628512i | \(-0.783664\pi\) | ||
0.777800 | − | 0.628512i | \(-0.216336\pi\) | |||||||
\(444\) | 2.99935 | − | 2.30469i | 0.142343 | − | 0.109376i | ||||
\(445\) | −10.9473 | −0.518954 | ||||||||
\(446\) | 23.3059i | 1.10357i | ||||||||
\(447\) | −22.4320 | − | 29.1933i | −1.06100 | − | 1.38080i | ||||
\(448\) | − | 1.91110i | − | 0.0902908i | ||||||
\(449\) | − | 5.06155i | − | 0.238869i | −0.992842 | − | 0.119435i | \(-0.961892\pi\) | ||
0.992842 | − | 0.119435i | \(-0.0381082\pi\) | |||||||
\(450\) | 2.89882 | + | 0.772562i | 0.136652 | + | 0.0364189i | ||||
\(451\) | 1.22478i | 0.0576725i | ||||||||
\(452\) | −16.7721 | −0.788893 | ||||||||
\(453\) | 13.7336 | + | 17.8731i | 0.645259 | + | 0.839749i | ||||
\(454\) | − | 27.6254i | − | 1.29652i | ||||||
\(455\) | − | 2.46203i | − | 0.115422i | ||||||
\(456\) | −4.00776 | − | 5.21575i | −0.187680 | − | 0.244250i | ||||
\(457\) | − | 32.8030i | − | 1.53446i | −0.641373 | − | 0.767229i | \(-0.721635\pi\) | ||
0.641373 | − | 0.767229i | \(-0.278365\pi\) | |||||||
\(458\) | 24.2738 | 1.13424 | ||||||||
\(459\) | 19.4098 | − | 8.08568i | 0.905972 | − | 0.377407i | ||||
\(460\) | −2.86177 | + | 3.84841i | −0.133431 | + | 0.179433i | ||||
\(461\) | − | 0.398299i | − | 0.0185506i | −0.999957 | − | 0.00927532i | \(-0.997048\pi\) | ||
0.999957 | − | 0.00927532i | \(-0.00295247\pi\) | |||||||
\(462\) | −4.18422 | − | 5.44541i | −0.194668 | − | 0.253343i | ||||
\(463\) | −1.18031 | −0.0548535 | −0.0274267 | − | 0.999624i | \(-0.508731\pi\) | ||||
−0.0274267 | + | 0.999624i | \(0.508731\pi\) | |||||||
\(464\) | 2.78403i | 0.129245i | ||||||||
\(465\) | −1.98036 | − | 2.57727i | −0.0918372 | − | 0.119518i | ||||
\(466\) | 0.568005 | 0.0263123 | ||||||||
\(467\) | −3.01078 | −0.139322 | −0.0696610 | − | 0.997571i | \(-0.522192\pi\) | ||||
−0.0696610 | + | 0.997571i | \(0.522192\pi\) | |||||||
\(468\) | 0.995276 | − | 3.73449i | 0.0460067 | − | 0.172627i | ||||
\(469\) | −12.8630 | −0.593956 | ||||||||
\(470\) | −4.11977 | −0.190031 | ||||||||
\(471\) | 14.3274 | − | 11.0091i | 0.660171 | − | 0.507272i | ||||
\(472\) | −2.07202 | −0.0953723 | ||||||||
\(473\) | 0.690535i | 0.0317508i | ||||||||
\(474\) | 3.57145 | + | 4.64793i | 0.164042 | + | 0.213487i | ||||
\(475\) | 3.79764i | 0.174248i | ||||||||
\(476\) | 7.73339i | 0.354459i | ||||||||
\(477\) | −2.68504 | + | 10.0748i | −0.122940 | + | 0.461296i | ||||
\(478\) | −1.41185 | −0.0645765 | ||||||||
\(479\) | −42.0364 | −1.92069 | −0.960347 | − | 0.278807i | \(-0.910061\pi\) | ||||
−0.960347 | + | 0.278807i | \(0.910061\pi\) | |||||||
\(480\) | −1.37342 | + | 1.05533i | −0.0626877 | + | 0.0481690i | ||||
\(481\) | 2.81342i | 0.128281i | ||||||||
\(482\) | −0.433010 | −0.0197231 | ||||||||
\(483\) | −0.250201 | − | 15.8728i | −0.0113845 | − | 0.722236i | ||||
\(484\) | 6.69583 | 0.304356 | ||||||||
\(485\) | 14.3560i | 0.651870i | ||||||||
\(486\) | −15.4482 | + | 2.08662i | −0.700743 | + | 0.0946509i | ||||
\(487\) | −19.4738 | −0.882440 | −0.441220 | − | 0.897399i | \(-0.645454\pi\) | ||||
−0.441220 | + | 0.897399i | \(0.645454\pi\) | |||||||
\(488\) | 3.23836 | 0.146594 | ||||||||
\(489\) | −2.85719 | − | 3.71838i | −0.129206 | − | 0.168151i | ||||
\(490\) | 3.34771i | 0.151234i | ||||||||
\(491\) | 32.6143i | 1.47186i | 0.677056 | + | 0.735931i | \(0.263255\pi\) | ||||
−0.677056 | + | 0.735931i | \(0.736745\pi\) | |||||||
\(492\) | −0.810803 | + | 0.623017i | −0.0365538 | + | 0.0280878i | ||||
\(493\) | − | 11.2658i | − | 0.507385i | ||||||
\(494\) | 4.89242 | 0.220120 | ||||||||
\(495\) | −1.60280 | + | 6.01403i | −0.0720403 | + | 0.270311i | ||||
\(496\) | 1.87654 | 0.0842591 | ||||||||
\(497\) | 17.3870 | 0.779914 | ||||||||
\(498\) | 7.80162 | − | 5.99473i | 0.349599 | − | 0.268630i | ||||
\(499\) | −6.60178 | −0.295536 | −0.147768 | − | 0.989022i | \(-0.547209\pi\) | ||||
−0.147768 | + | 0.989022i | \(0.547209\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −23.0687 | + | 17.7259i | −1.03064 | + | 0.791935i | ||||
\(502\) | − | 22.4064i | − | 1.00005i | ||||||
\(503\) | 14.7686 | 0.658501 | 0.329251 | − | 0.944243i | \(-0.393204\pi\) | ||||
0.329251 | + | 0.944243i | \(0.393204\pi\) | |||||||
\(504\) | 1.47644 | − | 5.53992i | 0.0657658 | − | 0.246768i | ||||
\(505\) | 6.90670i | 0.307344i | ||||||||
\(506\) | −7.98410 | − | 5.93718i | −0.354937 | − | 0.263940i | ||||
\(507\) | −11.9678 | − | 15.5750i | −0.531508 | − | 0.691712i | ||||
\(508\) | 0.980016 | 0.0434812 | ||||||||
\(509\) | 29.6739i | 1.31527i | 0.753336 | + | 0.657636i | \(0.228443\pi\) | ||||
−0.753336 | + | 0.657636i | \(0.771557\pi\) | |||||||
\(510\) | 5.55764 | − | 4.27046i | 0.246097 | − | 0.189099i | ||||
\(511\) | − | 6.72764i | − | 0.297613i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −7.58827 | − | 18.2157i | −0.335030 | − | 0.804245i | ||||
\(514\) | 20.6632 | 0.911415 | ||||||||
\(515\) | − | 15.1722i | − | 0.668569i | ||||||
\(516\) | −0.457135 | + | 0.351260i | −0.0201242 | + | 0.0154634i | ||||
\(517\) | − | 8.54708i | − | 0.375900i | ||||||
\(518\) | 4.17356i | 0.183376i | ||||||||
\(519\) | −25.4954 | + | 19.5905i | −1.11912 | + | 0.859928i | ||||
\(520\) | − | 1.28828i | − | 0.0564948i | ||||||
\(521\) | 20.0886 | 0.880099 | 0.440049 | − | 0.897974i | \(-0.354961\pi\) | ||||
0.440049 | + | 0.897974i | \(0.354961\pi\) | |||||||
\(522\) | −2.15084 | + | 8.07040i | −0.0941395 | + | 0.353232i | ||||
\(523\) | 31.7144i | 1.38677i | 0.720565 | + | 0.693387i | \(0.243883\pi\) | ||||
−0.720565 | + | 0.693387i | \(0.756117\pi\) | |||||||
\(524\) | 9.96859i | 0.435480i | ||||||||
\(525\) | −2.62474 | + | 2.01683i | −0.114553 | + | 0.0880219i | ||||
\(526\) | 2.57099i | 0.112100i | ||||||||
\(527\) | −7.59355 | −0.330780 | ||||||||
\(528\) | −2.18944 | − | 2.84936i | −0.0952831 | − | 0.124003i | ||||
\(529\) | −6.62050 | − | 22.0266i | −0.287848 | − | 0.957676i | ||||
\(530\) | 3.47550i | 0.150966i | ||||||||
\(531\) | −6.00640 | − | 1.60076i | −0.260655 | − | 0.0694671i | ||||
\(532\) | 7.25765 | 0.314659 | ||||||||
\(533\) | − | 0.760540i | − | 0.0329427i | ||||||
\(534\) | 15.0353 | − | 11.5530i | 0.650641 | − | 0.499949i | ||||
\(535\) | −15.9284 | −0.688646 | ||||||||
\(536\) | −6.73067 | −0.290721 | ||||||||
\(537\) | 27.7204 | − | 21.3002i | 1.19622 | − | 0.919173i | ||||
\(538\) | −2.88848 | −0.124531 | ||||||||
\(539\) | −6.94534 | −0.299157 | ||||||||
\(540\) | −4.79660 | + | 1.99816i | −0.206413 | + | 0.0859869i | ||||
\(541\) | −26.2050 | −1.12664 | −0.563321 | − | 0.826238i | \(-0.690476\pi\) | ||||
−0.563321 | + | 0.826238i | \(0.690476\pi\) | |||||||
\(542\) | − | 15.1639i | − | 0.651345i | ||||||
\(543\) | 20.0226 | − | 15.3853i | 0.859252 | − | 0.660245i | ||||
\(544\) | 4.04657i | 0.173495i | ||||||||
\(545\) | 3.31710i | 0.142089i | ||||||||
\(546\) | 2.59825 | + | 3.38139i | 0.111195 | + | 0.144710i | ||||
\(547\) | 16.0293 | 0.685363 | 0.342681 | − | 0.939452i | \(-0.388665\pi\) | ||||
0.342681 | + | 0.939452i | \(0.388665\pi\) | |||||||
\(548\) | −14.3513 | −0.613058 | ||||||||
\(549\) | 9.38743 | + | 2.50184i | 0.400646 | + | 0.106776i | ||||
\(550\) | 2.07465i | 0.0884634i | ||||||||
\(551\) | −10.5727 | −0.450414 | ||||||||
\(552\) | −0.130920 | − | 8.30559i | −0.00557233 | − | 0.353509i | ||||
\(553\) | −6.46754 | −0.275028 | ||||||||
\(554\) | − | 3.10829i | − | 0.132059i | ||||||
\(555\) | 2.99935 | − | 2.30469i | 0.127315 | − | 0.0978285i | ||||
\(556\) | 4.62609 | 0.196190 | ||||||||
\(557\) | −25.4592 | −1.07874 | −0.539370 | − | 0.842069i | \(-0.681338\pi\) | ||||
−0.539370 | + | 0.842069i | \(0.681338\pi\) | |||||||
\(558\) | 5.43974 | + | 1.44974i | 0.230283 | + | 0.0613725i | ||||
\(559\) | − | 0.428796i | − | 0.0181362i | ||||||
\(560\) | − | 1.91110i | − | 0.0807585i | ||||||
\(561\) | 8.85972 | + | 11.5302i | 0.374058 | + | 0.486804i | ||||
\(562\) | 12.8651i | 0.542681i | ||||||||
\(563\) | 14.8803 | 0.627130 | 0.313565 | − | 0.949567i | \(-0.398477\pi\) | ||||
0.313565 | + | 0.949567i | \(0.398477\pi\) | |||||||
\(564\) | 5.65817 | − | 4.34771i | 0.238252 | − | 0.183072i | ||||
\(565\) | −16.7721 | −0.705607 | ||||||||
\(566\) | 24.2159 | 1.01787 | ||||||||
\(567\) | 8.55986 | − | 14.9186i | 0.359480 | − | 0.626521i | ||||
\(568\) | 9.09793 | 0.381741 | ||||||||
\(569\) | −2.00209 | −0.0839320 | −0.0419660 | − | 0.999119i | \(-0.513362\pi\) | ||||
−0.0419660 | + | 0.999119i | \(0.513362\pi\) | |||||||
\(570\) | −4.00776 | − | 5.21575i | −0.167866 | − | 0.218464i | ||||
\(571\) | − | 20.4145i | − | 0.854319i | −0.904176 | − | 0.427159i | \(-0.859514\pi\) | ||
0.904176 | − | 0.427159i | \(-0.140486\pi\) | |||||||
\(572\) | 2.67273 | 0.111752 | ||||||||
\(573\) | −6.00702 | − | 7.81762i | −0.250947 | − | 0.326586i | ||||
\(574\) | − | 1.12822i | − | 0.0470911i | ||||||
\(575\) | −2.86177 | + | 3.84841i | −0.119344 | + | 0.160490i | ||||
\(576\) | 0.772562 | − | 2.89882i | 0.0321901 | − | 0.120784i | ||||
\(577\) | −16.5287 | −0.688098 | −0.344049 | − | 0.938952i | \(-0.611799\pi\) | ||||
−0.344049 | + | 0.938952i | \(0.611799\pi\) | |||||||
\(578\) | 0.625250i | 0.0260070i | ||||||||
\(579\) | −17.7618 | − | 23.1154i | −0.738155 | − | 0.960645i | ||||
\(580\) | 2.78403i | 0.115601i | ||||||||
\(581\) | 10.8559i | 0.450377i | ||||||||
\(582\) | −15.1503 | − | 19.7168i | −0.627998 | − | 0.817286i | ||||
\(583\) | −7.21045 | −0.298626 | ||||||||
\(584\) | − | 3.52030i | − | 0.145671i | ||||||
\(585\) | 0.995276 | − | 3.73449i | 0.0411496 | − | 0.154402i | ||||
\(586\) | 27.3847i | 1.13125i | ||||||||
\(587\) | − | 23.8478i | − | 0.984305i | −0.870509 | − | 0.492153i | \(-0.836210\pi\) | ||
0.870509 | − | 0.492153i | \(-0.163790\pi\) | |||||||
\(588\) | −3.53294 | − | 4.59782i | −0.145696 | − | 0.189611i | ||||
\(589\) | 7.12641i | 0.293639i | ||||||||
\(590\) | −2.07202 | −0.0853035 | ||||||||
\(591\) | −9.60677 | + | 7.38179i | −0.395170 | + | 0.303646i | ||||
\(592\) | 2.18386i | 0.0897560i | ||||||||
\(593\) | − | 14.2410i | − | 0.584810i | −0.956295 | − | 0.292405i | \(-0.905545\pi\) | ||
0.956295 | − | 0.292405i | \(-0.0944555\pi\) | |||||||
\(594\) | −4.14547 | − | 9.95127i | −0.170091 | − | 0.408305i | ||||
\(595\) | 7.73339i | 0.317038i | ||||||||
\(596\) | 21.2559 | 0.870676 | ||||||||
\(597\) | 6.48258 | − | 4.98118i | 0.265314 | − | 0.203866i | ||||
\(598\) | 4.95783 | + | 3.68677i | 0.202741 | + | 0.150763i | ||||
\(599\) | 30.5083i | 1.24653i | 0.782009 | + | 0.623267i | \(0.214195\pi\) | ||||
−0.782009 | + | 0.623267i | \(0.785805\pi\) | |||||||
\(600\) | −1.37342 | + | 1.05533i | −0.0560696 | + | 0.0430836i | ||||
\(601\) | −40.3133 | −1.64441 | −0.822207 | − | 0.569189i | \(-0.807257\pi\) | ||||
−0.822207 | + | 0.569189i | \(0.807257\pi\) | |||||||
\(602\) | − | 0.636097i | − | 0.0259254i | ||||||
\(603\) | −19.5110 | − | 5.19986i | −0.794549 | − | 0.211755i | ||||
\(604\) | −13.0135 | −0.529514 | ||||||||
\(605\) | 6.69583 | 0.272224 | ||||||||
\(606\) | −7.28884 | − | 9.48580i | −0.296089 | − | 0.385334i | ||||
\(607\) | 15.6385 | 0.634747 | 0.317373 | − | 0.948301i | \(-0.397199\pi\) | ||||
0.317373 | + | 0.948301i | \(0.397199\pi\) | |||||||
\(608\) | 3.79764 | 0.154015 | ||||||||
\(609\) | −5.61493 | − | 7.30734i | −0.227528 | − | 0.296109i | ||||
\(610\) | 3.23836 | 0.131118 | ||||||||
\(611\) | 5.30742i | 0.214715i | ||||||||
\(612\) | −3.12623 | + | 11.7303i | −0.126370 | + | 0.474168i | ||||
\(613\) | − | 19.8409i | − | 0.801367i | −0.916217 | − | 0.400684i | \(-0.868773\pi\) | ||
0.916217 | − | 0.400684i | \(-0.131227\pi\) | |||||||
\(614\) | − | 27.5618i | − | 1.11230i | ||||||
\(615\) | −0.810803 | + | 0.623017i | −0.0326947 | + | 0.0251225i | ||||
\(616\) | 3.96485 | 0.159749 | ||||||||
\(617\) | −46.2270 | −1.86103 | −0.930515 | − | 0.366255i | \(-0.880640\pi\) | ||||
−0.930515 | + | 0.366255i | \(0.880640\pi\) | |||||||
\(618\) | 16.0117 | + | 20.8378i | 0.644085 | + | 0.838221i | ||||
\(619\) | 33.1341i | 1.33177i | 0.746053 | + | 0.665886i | \(0.231946\pi\) | ||||
−0.746053 | + | 0.665886i | \(0.768054\pi\) | |||||||
\(620\) | 1.87654 | 0.0753636 | ||||||||
\(621\) | 6.03707 | − | 24.1775i | 0.242259 | − | 0.970212i | ||||
\(622\) | −13.2819 | −0.532556 | ||||||||
\(623\) | 20.9214i | 0.838199i | ||||||||
\(624\) | 1.35956 | + | 1.76935i | 0.0544259 | + | 0.0708306i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.2441 | 0.929021 | ||||||||
\(627\) | 10.8209 | − | 8.31469i | 0.432143 | − | 0.332057i | ||||
\(628\) | 10.4319i | 0.416278i | ||||||||
\(629\) | − | 8.83714i | − | 0.352360i | ||||||
\(630\) | 1.47644 | − | 5.53992i | 0.0588228 | − | 0.220716i | ||||
\(631\) | − | 42.5630i | − | 1.69440i | −0.531271 | − | 0.847202i | \(-0.678285\pi\) | ||
0.531271 | − | 0.847202i | \(-0.321715\pi\) | |||||||
\(632\) | −3.38420 | −0.134616 | ||||||||
\(633\) | 23.8633 | + | 31.0560i | 0.948482 | + | 1.23437i | ||||
\(634\) | 17.6217 | 0.699847 | ||||||||
\(635\) | 0.980016 | 0.0388907 | ||||||||
\(636\) | −3.66780 | − | 4.77332i | −0.145438 | − | 0.189275i | ||||
\(637\) | 4.31279 | 0.170879 | ||||||||
\(638\) | −5.77589 | −0.228670 | ||||||||
\(639\) | 26.3733 | + | 7.02872i | 1.04331 | + | 0.278052i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | 15.4390 | 0.609803 | 0.304901 | − | 0.952384i | \(-0.401376\pi\) | ||||
0.304901 | + | 0.952384i | \(0.401376\pi\) | |||||||
\(642\) | 21.8764 | − | 16.8097i | 0.863393 | − | 0.663427i | ||||
\(643\) | 4.85712i | 0.191546i | 0.995403 | + | 0.0957730i | \(0.0305323\pi\) | ||||
−0.995403 | + | 0.0957730i | \(0.969468\pi\) | |||||||
\(644\) | 7.35468 | + | 5.46912i | 0.289815 | + | 0.215514i | ||||
\(645\) | −0.457135 | + | 0.351260i | −0.0179997 | + | 0.0138309i | ||||
\(646\) | −15.3674 | −0.604623 | ||||||||
\(647\) | − | 31.5461i | − | 1.24021i | −0.784521 | − | 0.620103i | \(-0.787091\pi\) | ||
0.784521 | − | 0.620103i | \(-0.212909\pi\) | |||||||
\(648\) | 4.47903 | − | 7.80630i | 0.175953 | − | 0.306660i | ||||
\(649\) | − | 4.29871i | − | 0.168739i | ||||||
\(650\) | − | 1.28828i | − | 0.0505305i | ||||||
\(651\) | −4.92542 | + | 3.78467i | −0.193042 | + | 0.148333i | ||||
\(652\) | 2.70739 | 0.106030 | ||||||||
\(653\) | 7.16896i | 0.280543i | 0.990113 | + | 0.140272i | \(0.0447975\pi\) | ||||
−0.990113 | + | 0.140272i | \(0.955202\pi\) | |||||||
\(654\) | −3.50063 | − | 4.55577i | −0.136886 | − | 0.178145i | ||||
\(655\) | 9.96859i | 0.389505i | ||||||||
\(656\) | − | 0.590353i | − | 0.0230494i | ||||||
\(657\) | 2.71965 | − | 10.2047i | 0.106104 | − | 0.398124i | ||||
\(658\) | 7.87328i | 0.306932i | ||||||||
\(659\) | 12.5890 | 0.490399 | 0.245199 | − | 0.969473i | \(-0.421147\pi\) | ||||
0.245199 | + | 0.969473i | \(0.421147\pi\) | |||||||
\(660\) | −2.18944 | − | 2.84936i | −0.0852238 | − | 0.110911i | ||||
\(661\) | 24.6283i | 0.957931i | 0.877834 | + | 0.478966i | \(0.158988\pi\) | ||||
−0.877834 | + | 0.478966i | \(0.841012\pi\) | |||||||
\(662\) | − | 20.7361i | − | 0.805930i | ||||||
\(663\) | −5.50155 | − | 7.15980i | −0.213663 | − | 0.278064i | ||||
\(664\) | 5.68044i | 0.220444i | ||||||||
\(665\) | 7.25765 | 0.281439 | ||||||||
\(666\) | −1.68716 | + | 6.33060i | −0.0653763 | + | 0.245306i | ||||
\(667\) | −10.7141 | − | 7.96727i | −0.414851 | − | 0.308494i | ||||
\(668\) | − | 16.7966i | − | 0.649879i | ||||||
\(669\) | −24.5954 | − | 32.0088i | −0.950914 | − | 1.23753i | ||||
\(670\) | −6.73067 | −0.260029 | ||||||||
\(671\) | 6.71847i | 0.259364i | ||||||||
\(672\) | 2.01683 | + | 2.62474i | 0.0778011 | + | 0.101251i | ||||
\(673\) | −6.41377 | −0.247233 | −0.123616 | − | 0.992330i | \(-0.539449\pi\) | ||||
−0.123616 | + | 0.992330i | \(0.539449\pi\) | |||||||
\(674\) | −9.08954 | −0.350116 | ||||||||
\(675\) | −4.79660 | + | 1.99816i | −0.184621 | + | 0.0769090i | ||||
\(676\) | 11.3403 | 0.436167 | ||||||||
\(677\) | 8.85737 | 0.340416 | 0.170208 | − | 0.985408i | \(-0.445556\pi\) | ||||
0.170208 | + | 0.985408i | \(0.445556\pi\) | |||||||
\(678\) | 23.0351 | − | 17.7001i | 0.884658 | − | 0.679767i | ||||
\(679\) | 27.4356 | 1.05288 | ||||||||
\(680\) | 4.04657i | 0.155179i | ||||||||
\(681\) | 29.1538 | + | 37.9412i | 1.11718 | + | 1.45391i | ||||
\(682\) | 3.89316i | 0.149077i | ||||||||
\(683\) | 4.92339i | 0.188388i | 0.995554 | + | 0.0941941i | \(0.0300274\pi\) | ||||
−0.995554 | + | 0.0941941i | \(0.969973\pi\) | |||||||
\(684\) | 11.0087 | + | 2.93391i | 0.420927 | + | 0.112181i | ||||
\(685\) | −14.3513 | −0.548335 | ||||||||
\(686\) | 19.7755 | 0.755031 | ||||||||
\(687\) | −33.3381 | + | 25.6168i | −1.27193 | + | 0.977342i | ||||
\(688\) | − | 0.332844i | − | 0.0126896i | ||||||
\(689\) | 4.47742 | 0.170576 | ||||||||
\(690\) | −0.130920 | − | 8.30559i | −0.00498404 | − | 0.316188i | ||||
\(691\) | 48.6905 | 1.85227 | 0.926137 | − | 0.377187i | \(-0.123109\pi\) | ||||
0.926137 | + | 0.377187i | \(0.123109\pi\) | |||||||
\(692\) | − | 18.5634i | − | 0.705676i | ||||||
\(693\) | 11.4934 | + | 3.06310i | 0.436598 | + | 0.116357i | ||||
\(694\) | 28.2337 | 1.07174 | ||||||||
\(695\) | 4.62609 | 0.175478 | ||||||||
\(696\) | −2.93807 | − | 3.82364i | −0.111367 | − | 0.144935i | ||||
\(697\) | 2.38891i | 0.0904863i | ||||||||
\(698\) | 9.07266i | 0.343405i | ||||||||
\(699\) | −0.780109 | + | 0.599432i | −0.0295064 | + | 0.0226726i | ||||
\(700\) | − | 1.91110i | − | 0.0722326i | ||||||
\(701\) | 5.73622 | 0.216654 | 0.108327 | − | 0.994115i | \(-0.465451\pi\) | ||||
0.108327 | + | 0.994115i | \(0.465451\pi\) | |||||||
\(702\) | 2.57418 | + | 6.17936i | 0.0971563 | + | 0.233225i | ||||
\(703\) | −8.29350 | −0.312795 | ||||||||
\(704\) | 2.07465 | 0.0781913 | ||||||||
\(705\) | 5.65817 | − | 4.34771i | 0.213099 | − | 0.163744i | ||||
\(706\) | 1.12881 | 0.0424834 | ||||||||
\(707\) | 13.1994 | 0.496413 | ||||||||
\(708\) | 2.84575 | − | 2.18666i | 0.106950 | − | 0.0821796i | ||||
\(709\) | − | 28.6828i | − | 1.07720i | −0.842560 | − | 0.538602i | \(-0.818953\pi\) | ||
0.842560 | − | 0.538602i | \(-0.181047\pi\) | |||||||
\(710\) | 9.09793 | 0.341439 | ||||||||
\(711\) | −9.81019 | − | 2.61451i | −0.367911 | − | 0.0980517i | ||||
\(712\) | 10.9473i | 0.410269i | ||||||||
\(713\) | −5.37023 | + | 7.22169i | −0.201117 | + | 0.270454i | ||||
\(714\) | −8.16127 | − | 10.6212i | −0.305428 | − | 0.397488i | ||||
\(715\) | 2.67273 | 0.0999544 | ||||||||
\(716\) | 20.1835i | 0.754293i | ||||||||
\(717\) | 1.93906 | − | 1.48997i | 0.0724156 | − | 0.0556438i | ||||
\(718\) | − | 14.4991i | − | 0.541102i | ||||||
\(719\) | − | 7.25724i | − | 0.270650i | −0.990801 | − | 0.135325i | \(-0.956792\pi\) | ||
0.990801 | − | 0.135325i | \(-0.0432078\pi\) | |||||||
\(720\) | 0.772562 | − | 2.89882i | 0.0287917 | − | 0.108033i | ||||
\(721\) | −28.9956 | −1.07985 | ||||||||
\(722\) | − | 4.57796i | − | 0.170374i | ||||||
\(723\) | 0.594704 | − | 0.456968i | 0.0221173 | − | 0.0169948i | ||||
\(724\) | 14.5787i | 0.541811i | ||||||||
\(725\) | 2.78403i | 0.103396i | ||||||||
\(726\) | −9.19618 | + | 7.06630i | −0.341302 | + | 0.262255i | ||||
\(727\) | − | 31.5613i | − | 1.17054i | −0.810837 | − | 0.585272i | \(-0.800988\pi\) | ||
0.810837 | − | 0.585272i | \(-0.199012\pi\) | |||||||
\(728\) | −2.46203 | −0.0912488 | ||||||||
\(729\) | 19.0148 | − | 19.1687i | 0.704250 | − | 0.709952i | ||||
\(730\) | − | 3.52030i | − | 0.130292i | ||||||
\(731\) | 1.34688i | 0.0498161i | ||||||||
\(732\) | −4.44763 | + | 3.41754i | −0.164389 | + | 0.126316i | ||||
\(733\) | − | 36.4315i | − | 1.34563i | −0.739811 | − | 0.672815i | \(-0.765085\pi\) | ||
0.739811 | − | 0.672815i | \(-0.234915\pi\) | |||||||
\(734\) | 22.1178 | 0.816383 | ||||||||
\(735\) | −3.53294 | − | 4.59782i | −0.130314 | − | 0.169593i | ||||
\(736\) | 3.84841 | + | 2.86177i | 0.141854 | + | 0.105486i | ||||
\(737\) | − | 13.9638i | − | 0.514363i | ||||||
\(738\) | 0.456085 | − | 1.71133i | 0.0167887 | − | 0.0629948i | ||||
\(739\) | 7.94486 | 0.292257 | 0.146128 | − | 0.989266i | \(-0.453319\pi\) | ||||
0.146128 | + | 0.989266i | \(0.453319\pi\) | |||||||
\(740\) | 2.18386i | 0.0802802i | ||||||||
\(741\) | −6.71934 | + | 5.16311i | −0.246841 | + | 0.189672i | ||||
\(742\) | 6.64202 | 0.243836 | ||||||||
\(743\) | −53.0693 | −1.94692 | −0.973461 | − | 0.228851i | \(-0.926503\pi\) | ||||
−0.973461 | + | 0.228851i | \(0.926503\pi\) | |||||||
\(744\) | −2.57727 | + | 1.98036i | −0.0944875 | + | 0.0726037i | ||||
\(745\) | 21.2559 | 0.778757 | ||||||||
\(746\) | 19.6820 | 0.720609 | ||||||||
\(747\) | −4.38849 | + | 16.4666i | −0.160566 | + | 0.602480i | ||||
\(748\) | −8.39522 | −0.306960 | ||||||||
\(749\) | 30.4408i | 1.11228i | ||||||||
\(750\) | −1.37342 | + | 1.05533i | −0.0501502 | + | 0.0385352i | ||||
\(751\) | − | 1.56981i | − | 0.0572830i | −0.999590 | − | 0.0286415i | \(-0.990882\pi\) | ||
0.999590 | − | 0.0286415i | \(-0.00911812\pi\) | |||||||
\(752\) | 4.11977i | 0.150233i | ||||||||
\(753\) | 23.6461 | + | 30.7734i | 0.861713 | + | 1.12144i | ||||
\(754\) | 3.58661 | 0.130617 | ||||||||
\(755\) | −13.0135 | −0.473611 | ||||||||
\(756\) | 3.81867 | + | 9.16676i | 0.138884 | + | 0.333392i | ||||
\(757\) | 36.3159i | 1.31992i | 0.751299 | + | 0.659962i | \(0.229427\pi\) | ||||
−0.751299 | + | 0.659962i | \(0.770573\pi\) | |||||||
\(758\) | 17.0269 | 0.618445 | ||||||||
\(759\) | 17.2312 | − | 0.271613i | 0.625453 | − | 0.00985894i | ||||
\(760\) | 3.79764 | 0.137755 | ||||||||
\(761\) | − | 38.7002i | − | 1.40288i | −0.712728 | − | 0.701440i | \(-0.752541\pi\) | ||
0.712728 | − | 0.701440i | \(-0.247459\pi\) | |||||||
\(762\) | −1.34597 | + | 1.03424i | −0.0487594 | + | 0.0374665i | ||||
\(763\) | 6.33930 | 0.229498 | ||||||||
\(764\) | 5.69209 | 0.205932 | ||||||||
\(765\) | −3.12623 | + | 11.7303i | −0.113029 | + | 0.424109i | ||||
\(766\) | − | 1.29893i | − | 0.0469322i | ||||||
\(767\) | 2.66934i | 0.0963842i | ||||||||
\(768\) | 1.05533 | + | 1.37342i | 0.0380809 | + | 0.0495590i | ||||
\(769\) | − | 36.0369i | − | 1.29952i | −0.760137 | − | 0.649762i | \(-0.774868\pi\) | ||
0.760137 | − | 0.649762i | \(-0.225132\pi\) | |||||||
\(770\) | 3.96485 | 0.142883 | ||||||||
\(771\) | −28.3792 | + | 21.8065i | −1.02205 | + | 0.785341i | ||||
\(772\) | 16.8306 | 0.605746 | ||||||||
\(773\) | 52.6097 | 1.89224 | 0.946119 | − | 0.323819i | \(-0.104967\pi\) | ||||
0.946119 | + | 0.323819i | \(0.104967\pi\) | |||||||
\(774\) | 0.257143 | − | 0.964855i | 0.00924280 | − | 0.0346810i | ||||
\(775\) | 1.87654 | 0.0674072 | ||||||||
\(776\) | 14.3560 | 0.515349 | ||||||||
\(777\) | −4.40448 | − | 5.73205i | −0.158010 | − | 0.205636i | ||||
\(778\) | − | 14.9186i | − | 0.534858i | ||||||
\(779\) | 2.24195 | 0.0803261 | ||||||||
\(780\) | 1.35956 | + | 1.76935i | 0.0486800 | + | 0.0633529i | ||||
\(781\) | 18.8750i | 0.675401i | ||||||||
\(782\) | −15.5729 | − | 11.5804i | −0.556885 | − | 0.414113i | ||||
\(783\) | −5.56292 | − | 13.3539i | −0.198803 | − | 0.477229i | ||||
\(784\) | 3.34771 | 0.119561 | ||||||||
\(785\) | 10.4319i | 0.372331i | ||||||||
\(786\) | −10.5201 | − | 13.6911i | −0.375241 | − | 0.488344i | ||||
\(787\) | − | 11.4505i | − | 0.408165i | −0.978954 | − | 0.204082i | \(-0.934579\pi\) | ||
0.978954 | − | 0.204082i | \(-0.0654210\pi\) | |||||||
\(788\) | − | 6.99478i | − | 0.249179i | ||||||
\(789\) | −2.71324 | − | 3.53104i | −0.0965938 | − | 0.125708i | ||||
\(790\) | −3.38420 | −0.120405 | ||||||||
\(791\) | 32.0531i | 1.13968i | ||||||||
\(792\) | 6.01403 | + | 1.60280i | 0.213699 | + | 0.0569529i | ||||
\(793\) | − | 4.17192i | − | 0.148149i | ||||||
\(794\) | − | 31.5845i | − | 1.12089i | ||||||
\(795\) | −3.66780 | − | 4.77332i | −0.130083 | − | 0.169292i | ||||
\(796\) | 4.72003i | 0.167297i | ||||||||
\(797\) | −3.35423 | −0.118813 | −0.0594065 | − | 0.998234i | \(-0.518921\pi\) | ||||
−0.0594065 | + | 0.998234i | \(0.518921\pi\) | |||||||
\(798\) | −9.96779 | + | 7.65920i | −0.352856 | + | 0.271133i | ||||
\(799\) | − | 16.6710i | − | 0.589776i | ||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | −8.45750 | + | 31.7344i | −0.298831 | + | 1.12128i | ||||
\(802\) | 29.5255i | 1.04258i | ||||||||
\(803\) | 7.30340 | 0.257731 | ||||||||
\(804\) | 9.24404 | − | 7.10307i | 0.326012 | − | 0.250506i | ||||
\(805\) | 7.35468 | + | 5.46912i | 0.259218 | + | 0.192761i | ||||
\(806\) | − | 2.41751i | − | 0.0851530i | ||||||
\(807\) | 3.96709 | − | 3.04829i | 0.139648 | − | 0.107305i | ||||
\(808\) | 6.90670 | 0.242977 | ||||||||
\(809\) | − | 17.2475i | − | 0.606391i | −0.952928 | − | 0.303195i | \(-0.901947\pi\) | ||
0.952928 | − | 0.303195i | \(-0.0980535\pi\) | |||||||
\(810\) | 4.47903 | − | 7.80630i | 0.157377 | − | 0.274285i | ||||
\(811\) | −45.3598 | −1.59280 | −0.796399 | − | 0.604772i | \(-0.793264\pi\) | ||||
−0.796399 | + | 0.604772i | \(0.793264\pi\) | |||||||
\(812\) | 5.32055 | 0.186715 | ||||||||
\(813\) | 16.0029 | + | 20.8264i | 0.561246 | + | 0.730413i | ||||
\(814\) | −4.53074 | −0.158802 | ||||||||
\(815\) | 2.70739 | 0.0948357 | ||||||||
\(816\) | −4.27046 | − | 5.55764i | −0.149496 | − | 0.194556i | ||||
\(817\) | 1.26402 | 0.0442225 | ||||||||
\(818\) | − | 32.5691i | − | 1.13875i | ||||||
\(819\) | −7.13697 | − | 1.90207i | −0.249386 | − | 0.0664636i | ||||
\(820\) | − | 0.590353i | − | 0.0206160i | ||||||
\(821\) | − | 19.7496i | − | 0.689266i | −0.938738 | − | 0.344633i | \(-0.888003\pi\) | ||
0.938738 | − | 0.344633i | \(-0.111997\pi\) | |||||||
\(822\) | 19.7104 | − | 15.1454i | 0.687478 | − | 0.528255i | ||||
\(823\) | −49.0137 | −1.70851 | −0.854255 | − | 0.519854i | \(-0.825986\pi\) | ||||
−0.854255 | + | 0.519854i | \(0.825986\pi\) | |||||||
\(824\) | −15.1722 | −0.528550 | ||||||||
\(825\) | −2.18944 | − | 2.84936i | −0.0762264 | − | 0.0992021i | ||||
\(826\) | 3.95982i | 0.137780i | ||||||||
\(827\) | −12.7598 | −0.443703 | −0.221851 | − | 0.975080i | \(-0.571210\pi\) | ||||
−0.221851 | + | 0.975080i | \(0.571210\pi\) | |||||||
\(828\) | 8.94494 | + | 11.2689i | 0.310858 | + | 0.391621i | ||||
\(829\) | −12.3057 | −0.427395 | −0.213698 | − | 0.976900i | \(-0.568551\pi\) | ||||
−0.213698 | + | 0.976900i | \(0.568551\pi\) | |||||||
\(830\) | 5.68044i | 0.197171i | ||||||||
\(831\) | 3.28027 | + | 4.26899i | 0.113791 | + | 0.148090i | ||||
\(832\) | −1.28828 | −0.0446631 | ||||||||
\(833\) | −13.5468 | −0.469368 | ||||||||
\(834\) | −6.35357 | + | 4.88205i | −0.220006 | + | 0.169052i | ||||
\(835\) | − | 16.7966i | − | 0.581270i | ||||||
\(836\) | 7.87877i | 0.272493i | ||||||||
\(837\) | −9.00100 | + | 3.74961i | −0.311120 | + | 0.129606i | ||||
\(838\) | 1.54122i | 0.0532405i | ||||||||
\(839\) | 20.5015 | 0.707791 | 0.353896 | − | 0.935285i | \(-0.384857\pi\) | ||||
0.353896 | + | 0.935285i | \(0.384857\pi\) | |||||||
\(840\) | 2.01683 | + | 2.62474i | 0.0695874 | + | 0.0905620i | ||||
\(841\) | 21.2492 | 0.732730 | ||||||||
\(842\) | 7.43732 | 0.256307 | ||||||||
\(843\) | −13.5769 | − | 17.6692i | −0.467614 | − | 0.608559i | ||||
\(844\) | −22.6122 | −0.778344 | ||||||||
\(845\) | 11.3403 | 0.390119 | ||||||||
\(846\) | −3.18278 | + | 11.9425i | −0.109426 | + | 0.410591i | ||||
\(847\) | − | 12.7964i | − | 0.439688i | ||||||
\(848\) | 3.47550 | 0.119349 | ||||||||
\(849\) | −33.2585 | + | 25.5557i | −1.14143 | + | 0.877069i | ||||
\(850\) | 4.04657i | 0.138796i | ||||||||
\(851\) | −8.40437 | − | 6.24971i | −0.288098 | − | 0.214237i | ||||
\(852\) | −12.4953 | + | 9.60131i | −0.428081 | + | 0.328935i | ||||
\(853\) | 27.4688 | 0.940514 | 0.470257 | − | 0.882529i | \(-0.344161\pi\) | ||||
0.470257 | + | 0.882529i | \(0.344161\pi\) | |||||||
\(854\) | − | 6.18882i | − | 0.211777i | ||||||
\(855\) | 11.0087 | + | 2.93391i | 0.376488 | + | 0.100338i | ||||
\(856\) | 15.9284i | 0.544423i | ||||||||
\(857\) | − | 27.2616i | − | 0.931238i | −0.884985 | − | 0.465619i | \(-0.845832\pi\) | ||
0.884985 | − | 0.465619i | \(-0.154168\pi\) | |||||||
\(858\) | −3.67078 | + | 2.82061i | −0.125318 | + | 0.0962940i | ||||
\(859\) | 26.2463 | 0.895513 | 0.447756 | − | 0.894156i | \(-0.352223\pi\) | ||||
0.447756 | + | 0.894156i | \(0.352223\pi\) | |||||||
\(860\) | − | 0.332844i | − | 0.0113499i | ||||||
\(861\) | 1.19064 | + | 1.54952i | 0.0405771 | + | 0.0528075i | ||||
\(862\) | − | 1.28640i | − | 0.0438150i | ||||||
\(863\) | 56.1744i | 1.91220i | 0.293043 | + | 0.956099i | \(0.405332\pi\) | ||||
−0.293043 | + | 0.956099i | \(0.594668\pi\) | |||||||
\(864\) | 1.99816 | + | 4.79660i | 0.0679786 | + | 0.163184i | ||||
\(865\) | − | 18.5634i | − | 0.631175i | ||||||
\(866\) | −37.5477 | −1.27592 | ||||||||
\(867\) | −0.659844 | − | 0.858730i | −0.0224095 | − | 0.0291640i | ||||
\(868\) | − | 3.58624i | − | 0.121725i | ||||||
\(869\) | − | 7.02104i | − | 0.238172i | ||||||
\(870\) | −2.93807 | − | 3.82364i | −0.0996098 | − | 0.129634i | ||||
\(871\) | 8.67099i | 0.293805i | ||||||||
\(872\) | 3.31710 | 0.112331 | ||||||||
\(873\) | 41.6153 | + | 11.0909i | 1.40846 | + | 0.375369i | ||||
\(874\) | −10.8680 | + | 14.6149i | −0.367615 | + | 0.494355i | ||||
\(875\) | − | 1.91110i | − | 0.0646068i | ||||||
\(876\) | 3.71508 | + | 4.83485i | 0.125521 | + | 0.163355i | ||||
\(877\) | −19.3519 | −0.653467 | −0.326733 | − | 0.945117i | \(-0.605948\pi\) | ||||
−0.326733 | + | 0.945117i | \(0.605948\pi\) | |||||||
\(878\) | 14.9511i | 0.504574i | ||||||||
\(879\) | −28.8999 | − | 37.6107i | −0.974768 | − | 1.26858i | ||||
\(880\) | 2.07465 | 0.0699364 | ||||||||
\(881\) | −20.0985 | −0.677137 | −0.338568 | − | 0.940942i | \(-0.609943\pi\) | ||||
−0.338568 | + | 0.940942i | \(0.609943\pi\) | |||||||
\(882\) | 9.70442 | + | 2.58632i | 0.326765 | + | 0.0870858i | ||||
\(883\) | −24.3604 | −0.819791 | −0.409896 | − | 0.912132i | \(-0.634435\pi\) | ||||
−0.409896 | + | 0.912132i | \(0.634435\pi\) | |||||||
\(884\) | 5.21312 | 0.175336 | ||||||||
\(885\) | 2.84575 | − | 2.18666i | 0.0956587 | − | 0.0735037i | ||||
\(886\) | −26.4573 | −0.888850 | ||||||||
\(887\) | − | 2.78228i | − | 0.0934200i | −0.998908 | − | 0.0467100i | \(-0.985126\pi\) | ||
0.998908 | − | 0.0467100i | \(-0.0148737\pi\) | |||||||
\(888\) | −2.30469 | − | 2.99935i | −0.0773402 | − | 0.100652i | ||||
\(889\) | − | 1.87290i | − | 0.0628152i | ||||||
\(890\) | 10.9473i | 0.366956i | ||||||||
\(891\) | 16.1953 | + | 9.29243i | 0.542564 | + | 0.311308i | ||||
\(892\) | 23.3059 | 0.780340 | ||||||||
\(893\) | −15.6454 | −0.523553 | ||||||||
\(894\) | −29.1933 | + | 22.4320i | −0.976370 | + | 0.750238i | ||||
\(895\) | 20.1835i | 0.674660i | ||||||||
\(896\) | −1.91110 | −0.0638452 | ||||||||
\(897\) | −10.6999 | + | 0.168662i | −0.357260 | + | 0.00563145i | ||||
\(898\) | −5.06155 | −0.168906 | ||||||||
\(899\) | 5.22434i | 0.174241i | ||||||||
\(900\) | 0.772562 | − | 2.89882i | 0.0257521 | − | 0.0966273i | ||||
\(901\) | −14.0639 | −0.468535 | ||||||||
\(902\) | 1.22478 | 0.0407806 | ||||||||
\(903\) | 0.671291 | + | 0.873628i | 0.0223392 | + | 0.0290725i | ||||
\(904\) | 16.7721i | 0.557831i | ||||||||
\(905\) | 14.5787i | 0.484611i | ||||||||
\(906\) | 17.8731 | − | 13.7336i | 0.593792 | − | 0.456267i | ||||
\(907\) | − | 39.5902i | − | 1.31457i | −0.753641 | − | 0.657286i | \(-0.771704\pi\) | ||
0.753641 | − | 0.657286i | \(-0.228296\pi\) | |||||||
\(908\) | −27.6254 | −0.916780 | ||||||||
\(909\) | 20.0213 | + | 5.33586i | 0.664064 | + | 0.176979i | ||||
\(910\) | −2.46203 | −0.0816154 | ||||||||
\(911\) | 7.13408 | 0.236363 | 0.118181 | − | 0.992992i | \(-0.462294\pi\) | ||||
0.118181 | + | 0.992992i | \(0.462294\pi\) | |||||||
\(912\) | −5.21575 | + | 4.00776i | −0.172711 | + | 0.132710i | ||||
\(913\) | −11.7849 | −0.390024 | ||||||||
\(914\) | −32.8030 | −1.08503 | ||||||||
\(915\) | −4.44763 | + | 3.41754i | −0.147034 | + | 0.112980i | ||||
\(916\) | − | 24.2738i | − | 0.802028i | ||||||
\(917\) | 19.0509 | 0.629117 | ||||||||
\(918\) | −8.08568 | − | 19.4098i | −0.266867 | − | 0.640619i | ||||
\(919\) | 1.89956i | 0.0626607i | 0.999509 | + | 0.0313304i | \(0.00997440\pi\) | ||||
−0.999509 | + | 0.0313304i | \(0.990026\pi\) | |||||||
\(920\) | 3.84841 | + | 2.86177i | 0.126878 | + | 0.0943499i | ||||
\(921\) | 29.0868 | + | 37.8539i | 0.958442 | + | 1.24733i | ||||
\(922\) | −0.398299 | −0.0131173 | ||||||||
\(923\) | − | 11.7207i | − | 0.385791i | ||||||
\(924\) | −5.44541 | + | 4.18422i | −0.179141 | + | 0.137651i | ||||
\(925\) | 2.18386i | 0.0718048i | ||||||||
\(926\) | 1.18031i | 0.0387873i | ||||||||
\(927\) | −43.9816 | − | 11.7215i | −1.44454 | − | 0.384984i | ||||
\(928\) | 2.78403 | 0.0913903 | ||||||||
\(929\) | − | 54.6440i | − | 1.79281i | −0.443233 | − | 0.896406i | \(-0.646169\pi\) | ||
0.443233 | − | 0.896406i | \(-0.353831\pi\) | |||||||
\(930\) | −2.57727 | + | 1.98036i | −0.0845121 | + | 0.0649387i | ||||
\(931\) | 12.7134i | 0.416665i | ||||||||
\(932\) | − | 0.568005i | − | 0.0186056i | ||||||
\(933\) | 18.2416 | − | 14.0168i | 0.597204 | − | 0.458889i | ||||
\(934\) | 3.01078i | 0.0985156i | ||||||||
\(935\) | −8.39522 | −0.274553 | ||||||||
\(936\) | −3.73449 | − | 0.995276i | −0.122066 | − | 0.0325316i | ||||
\(937\) | − | 22.5511i | − | 0.736713i | −0.929685 | − | 0.368356i | \(-0.879921\pi\) | ||
0.929685 | − | 0.368356i | \(-0.120079\pi\) | |||||||
\(938\) | 12.8630i | 0.419990i | ||||||||
\(939\) | −31.9239 | + | 24.5302i | −1.04180 | + | 0.800512i | ||||
\(940\) | 4.11977i | 0.134372i | ||||||||
\(941\) | 0.592934 | 0.0193291 | 0.00966455 | − | 0.999953i | \(-0.496924\pi\) | ||||
0.00966455 | + | 0.999953i | \(0.496924\pi\) | |||||||
\(942\) | −11.0091 | − | 14.3274i | −0.358696 | − | 0.466811i | ||||
\(943\) | 2.27192 | + | 1.68946i | 0.0739839 | + | 0.0550163i | ||||
\(944\) | 2.07202i | 0.0674384i | ||||||||
\(945\) | 3.81867 | + | 9.16676i | 0.124221 | + | 0.298195i | ||||
\(946\) | 0.690535 | 0.0224512 | ||||||||
\(947\) | 17.6575i | 0.573791i | 0.957962 | + | 0.286895i | \(0.0926232\pi\) | ||||
−0.957962 | + | 0.286895i | \(0.907377\pi\) | |||||||
\(948\) | 4.64793 | − | 3.57145i | 0.150958 | − | 0.115995i | ||||
\(949\) | −4.53514 | −0.147217 | ||||||||
\(950\) | 3.79764 | 0.123212 | ||||||||
\(951\) | −24.2020 | + | 18.5967i | −0.784803 | + | 0.603039i | ||||
\(952\) | 7.73339 | 0.250640 | ||||||||
\(953\) | 14.8606 | 0.481382 | 0.240691 | − | 0.970602i | \(-0.422626\pi\) | ||||
0.240691 | + | 0.970602i | \(0.422626\pi\) | |||||||
\(954\) | 10.0748 | + | 2.68504i | 0.326185 | + | 0.0869314i | ||||
\(955\) | 5.69209 | 0.184192 | ||||||||
\(956\) | 1.41185i | 0.0456625i | ||||||||
\(957\) | 7.93272 | − | 6.09546i | 0.256428 | − | 0.197038i | ||||
\(958\) | 42.0364i | 1.35814i | ||||||||
\(959\) | 27.4267i | 0.885655i | ||||||||
\(960\) | 1.05533 | + | 1.37342i | 0.0340606 | + | 0.0443269i | ||||
\(961\) | −27.4786 | −0.886407 | ||||||||
\(962\) | 2.81342 | 0.0907083 | ||||||||
\(963\) | −12.3057 | + | 46.1736i | −0.396546 | + | 1.48792i | ||||
\(964\) | 0.433010i | 0.0139463i | ||||||||
\(965\) | 16.8306 | 0.541795 | ||||||||
\(966\) | −15.8728 | + | 0.250201i | −0.510698 | + | 0.00805008i | ||||
\(967\) | −51.8296 | −1.66673 | −0.833364 | − | 0.552724i | \(-0.813588\pi\) | ||||
−0.833364 | + | 0.552724i | \(0.813588\pi\) | |||||||
\(968\) | − | 6.69583i | − | 0.215212i | ||||||
\(969\) | 21.1059 | − | 16.2177i | 0.678019 | − | 0.520987i | ||||
\(970\) | 14.3560 | 0.460942 | ||||||||
\(971\) | 5.91874 | 0.189941 | 0.0949707 | − | 0.995480i | \(-0.469724\pi\) | ||||
0.0949707 | + | 0.995480i | \(0.469724\pi\) | |||||||
\(972\) | 2.08662 | + | 15.4482i | 0.0669283 | + | 0.495500i | ||||
\(973\) | − | 8.84091i | − | 0.283426i | ||||||
\(974\) | 19.4738i | 0.623979i | ||||||||
\(975\) | 1.35956 | + | 1.76935i | 0.0435407 | + | 0.0566645i | ||||
\(976\) | − | 3.23836i | − | 0.103658i | ||||||
\(977\) | 16.1823 | 0.517717 | 0.258859 | − | 0.965915i | \(-0.416654\pi\) | ||||
0.258859 | + | 0.965915i | \(0.416654\pi\) | |||||||
\(978\) | −3.71838 | + | 2.85719i | −0.118901 | + | 0.0913627i | ||||
\(979\) | −22.7119 | −0.725876 | ||||||||
\(980\) | 3.34771 | 0.106939 | ||||||||
\(981\) | 9.61568 | + | 2.56267i | 0.307005 | + | 0.0818197i | ||||
\(982\) | 32.6143 | 1.04076 | ||||||||
\(983\) | 29.8451 | 0.951910 | 0.475955 | − | 0.879470i | \(-0.342103\pi\) | ||||
0.475955 | + | 0.879470i | \(0.342103\pi\) | |||||||
\(984\) | 0.623017 | + | 0.810803i | 0.0198611 | + | 0.0258474i | ||||
\(985\) | − | 6.99478i | − | 0.222872i | ||||||
\(986\) | −11.2658 | −0.358776 | ||||||||
\(987\) | −8.30890 | − | 10.8133i | −0.264475 | − | 0.344192i | ||||
\(988\) | − | 4.89242i | − | 0.155649i | ||||||
\(989\) | 1.28092 | + | 0.952525i | 0.0407309 | + | 0.0302885i | ||||
\(990\) | 6.01403 | + | 1.60280i | 0.191139 | + | 0.0509402i | ||||
\(991\) | 17.3339 | 0.550628 | 0.275314 | − | 0.961354i | \(-0.411218\pi\) | ||||
0.275314 | + | 0.961354i | \(0.411218\pi\) | |||||||
\(992\) | − | 1.87654i | − | 0.0595801i | ||||||
\(993\) | 21.8834 | + | 28.4793i | 0.694448 | + | 0.903764i | ||||
\(994\) | − | 17.3870i | − | 0.551483i | ||||||
\(995\) | 4.72003i | 0.149635i | ||||||||
\(996\) | −5.99473 | − | 7.80162i | −0.189950 | − | 0.247204i | ||||
\(997\) | 22.6619 | 0.717711 | 0.358855 | − | 0.933393i | \(-0.383167\pi\) | ||||
0.358855 | + | 0.933393i | \(0.383167\pi\) | |||||||
\(998\) | 6.60178i | 0.208976i | ||||||||
\(999\) | −4.36369 | − | 10.4751i | −0.138061 | − | 0.331417i |
(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 | 690.2.e.a.551.6 | ✓ | 16 | |
3.2 | odd | 2 | 690.2.e.b.551.14 | yes | 16 | ||
23.22 | odd | 2 | 690.2.e.b.551.6 | yes | 16 | ||
69.68 | even | 2 | inner | 690.2.e.a.551.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.e.a.551.6 | ✓ | 16 | 1.1 | even | 1 | trivial | |
690.2.e.a.551.14 | yes | 16 | 69.68 | even | 2 | inner | |
690.2.e.b.551.6 | yes | 16 | 23.22 | odd | 2 | ||
690.2.e.b.551.14 | yes | 16 | 3.2 | odd | 2 |