Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(298,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.298");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.dl (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 298.8 | ||
Root | \(-1.97871 - 1.14241i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.298 |
Dual form | 819.2.dl.e.415.8 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.97871 | − | 1.14241i | 1.39916 | − | 0.807803i | 0.404852 | − | 0.914382i | \(-0.367323\pi\) |
0.994304 | + | 0.106579i | \(0.0339896\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.61019 | − | 2.78892i | 0.805093 | − | 1.39446i | ||||
\(5\) | 1.84030 | − | 1.06250i | 0.823005 | − | 0.475162i | −0.0284464 | − | 0.999595i | \(-0.509056\pi\) |
0.851452 | + | 0.524433i | \(0.175723\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.62488 | + | 0.331665i | 0.992112 | + | 0.125358i | ||||
\(8\) | − | 2.78832i | − | 0.985820i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.42760 | − | 4.20473i | 0.767676 | − | 1.32965i | ||||
\(11\) | 0.267139 | + | 0.154233i | 0.0805454 | + | 0.0465029i | 0.539732 | − | 0.841837i | \(-0.318526\pi\) |
−0.459186 | + | 0.888340i | \(0.651859\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.22037 | + | 1.62148i | −0.893170 | + | 0.449718i | ||||
\(14\) | 5.57276 | − | 2.34241i | 1.48938 | − | 0.626036i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0349749 | + | 0.0605784i | 0.00874373 | + | 0.0151446i | ||||
\(17\) | 0.887368 | − | 1.53697i | 0.215218 | − | 0.372769i | −0.738122 | − | 0.674667i | \(-0.764287\pi\) |
0.953340 | + | 0.301898i | \(0.0976204\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.54266 | + | 0.890653i | −0.353909 | + | 0.204330i | −0.666406 | − | 0.745589i | \(-0.732168\pi\) |
0.312496 | + | 0.949919i | \(0.398835\pi\) | |||||||
\(20\) | − | 6.84326i | − | 1.53020i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.704786 | 0.150261 | ||||||||
\(23\) | −0.575211 | − | 0.996294i | −0.119940 | − | 0.207742i | 0.799804 | − | 0.600261i | \(-0.204937\pi\) |
−0.919744 | + | 0.392520i | \(0.871603\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.242207 | + | 0.419515i | −0.0484414 | + | 0.0839029i | ||||
\(26\) | −4.51978 | + | 6.88741i | −0.886401 | + | 1.35073i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.15153 | − | 6.78655i | 0.973548 | − | 1.28254i | ||||
\(29\) | −2.01052 | −0.373345 | −0.186672 | − | 0.982422i | \(-0.559770\pi\) | ||||
−0.186672 | + | 0.982422i | \(0.559770\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.98791 | − | 2.30242i | −0.716251 | − | 0.413527i | 0.0971205 | − | 0.995273i | \(-0.469037\pi\) |
−0.813371 | + | 0.581745i | \(0.802370\pi\) | |||||||
\(32\) | 4.96792 | + | 2.86823i | 0.878213 | + | 0.507037i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.05494i | − | 0.695416i | ||||||
\(35\) | 5.18295 | − | 2.17856i | 0.876078 | − | 0.368244i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.79901 | + | 2.77071i | −0.788953 | + | 0.455502i | −0.839594 | − | 0.543215i | \(-0.817207\pi\) |
0.0506410 | + | 0.998717i | \(0.483874\pi\) | |||||||
\(38\) | −2.03497 | + | 3.52468i | −0.330117 | + | 0.571779i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.96258 | − | 5.13134i | −0.468425 | − | 0.811336i | ||||
\(41\) | − | 6.72984i | − | 1.05102i | −0.850786 | − | 0.525512i | \(-0.823874\pi\) | ||
0.850786 | − | 0.525512i | \(-0.176126\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.52611 | −0.232729 | −0.116365 | − | 0.993207i | \(-0.537124\pi\) | ||||
−0.116365 | + | 0.993207i | \(0.537124\pi\) | |||||||
\(44\) | 0.860286 | − | 0.496686i | 0.129693 | − | 0.0748783i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.27635 | − | 1.31425i | −0.335629 | − | 0.193776i | ||||
\(47\) | −8.24297 | + | 4.75908i | −1.20236 | + | 0.694183i | −0.961079 | − | 0.276272i | \(-0.910901\pi\) |
−0.241281 | + | 0.970455i | \(0.577568\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.78000 | + | 1.74116i | 0.968571 | + | 0.248738i | ||||
\(50\) | 1.10680i | 0.156524i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.663205 | + | 11.5923i | −0.0919700 | + | 1.60756i | ||||
\(53\) | 3.72037 | − | 6.44387i | 0.511032 | − | 0.885134i | −0.488886 | − | 0.872348i | \(-0.662597\pi\) |
0.999918 | − | 0.0127862i | \(-0.00407010\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.655486 | 0.0883857 | ||||||||
\(56\) | 0.924789 | − | 7.31901i | 0.123580 | − | 0.978044i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.97823 | + | 2.29683i | −0.522368 | + | 0.301589i | ||||
\(59\) | −7.03304 | − | 4.06053i | −0.915624 | − | 0.528636i | −0.0333877 | − | 0.999442i | \(-0.510630\pi\) |
−0.882236 | + | 0.470807i | \(0.843963\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.72037 | + | 2.97977i | 0.220271 | + | 0.381521i | 0.954890 | − | 0.296959i | \(-0.0959725\pi\) |
−0.734619 | + | 0.678480i | \(0.762639\pi\) | |||||||
\(62\) | −10.5212 | −1.33620 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.9669 | 1.62086 | ||||||||
\(65\) | −4.20362 | + | 6.40564i | −0.521395 | + | 0.794522i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9249 | + | 6.30747i | 1.33468 | + | 0.770580i | 0.986014 | − | 0.166665i | \(-0.0532998\pi\) |
0.348671 | + | 0.937245i | \(0.386633\pi\) | |||||||
\(68\) | −2.85765 | − | 4.94960i | −0.346541 | − | 0.600227i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.76673 | − | 10.2318i | 0.928302 | − | 1.22293i | ||||
\(71\) | − | 1.35070i | − | 0.160299i | −0.996783 | − | 0.0801494i | \(-0.974460\pi\) | ||
0.996783 | − | 0.0801494i | \(-0.0255397\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2894 | − | 5.94059i | −1.20428 | − | 0.695293i | −0.242778 | − | 0.970082i | \(-0.578059\pi\) |
−0.961505 | + | 0.274789i | \(0.911392\pi\) | |||||||
\(74\) | −6.33056 | + | 10.9648i | −0.735912 | + | 1.27464i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.73646i | 0.658018i | ||||||||
\(77\) | 0.650054 | + | 0.493443i | 0.0740805 | + | 0.0562330i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.96258 | + | 6.86339i | 0.445825 | + | 0.772191i | 0.998109 | − | 0.0614644i | \(-0.0195771\pi\) |
−0.552284 | + | 0.833656i | \(0.686244\pi\) | |||||||
\(80\) | 0.128728 | + | 0.0743214i | 0.0143923 | + | 0.00830939i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.68821 | − | 13.3164i | −0.849021 | − | 1.47055i | ||||
\(83\) | − | 11.2290i | − | 1.23255i | −0.787533 | − | 0.616273i | \(-0.788642\pi\) | ||
0.787533 | − | 0.616273i | \(-0.211358\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 3.77130i | − | 0.409055i | ||||||
\(86\) | −3.01972 | + | 1.74344i | −0.325625 | + | 0.188000i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.430050 | − | 0.744869i | 0.0458435 | − | 0.0794033i | ||||
\(89\) | 1.43688 | − | 0.829583i | 0.152309 | − | 0.0879357i | −0.421909 | − | 0.906638i | \(-0.638640\pi\) |
0.574218 | + | 0.818703i | \(0.305306\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.99088 | + | 3.18811i | −0.942500 | + | 0.334205i | ||||
\(92\) | −3.70479 | −0.386251 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.8736 | + | 18.8336i | −1.12153 | + | 1.94254i | ||||
\(95\) | −1.89263 | + | 3.27813i | −0.194180 | + | 0.336329i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.66641i | 0.778406i | 0.921152 | + | 0.389203i | \(0.127250\pi\) | ||||
−0.921152 | + | 0.389203i | \(0.872750\pi\) | |||||||
\(98\) | 15.4047 | − | 4.30026i | 1.55611 | − | 0.434392i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.779996 | + | 1.35099i | 0.0779996 | + | 0.135099i | ||||
\(101\) | −4.55864 | + | 7.89579i | −0.453601 | + | 0.785660i | −0.998607 | − | 0.0527721i | \(-0.983194\pi\) |
0.545005 | + | 0.838433i | \(0.316528\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.02085 | + | 5.23226i | 0.297653 | + | 0.515550i | 0.975599 | − | 0.219562i | \(-0.0704629\pi\) |
−0.677946 | + | 0.735112i | \(0.737130\pi\) | |||||||
\(104\) | 4.52122 | + | 8.97943i | 0.443342 | + | 0.880506i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 17.0007i | − | 1.65125i | ||||||
\(107\) | 6.04305 | + | 10.4669i | 0.584204 | + | 1.01187i | 0.994974 | + | 0.100132i | \(0.0319264\pi\) |
−0.410770 | + | 0.911739i | \(0.634740\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.17942 | + | 0.680941i | 0.112968 | + | 0.0652223i | 0.555420 | − | 0.831570i | \(-0.312558\pi\) |
−0.442451 | + | 0.896793i | \(0.645891\pi\) | |||||||
\(110\) | 1.29701 | − | 0.748831i | 0.123665 | − | 0.0713983i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0717133 | + | 0.170611i | 0.00677627 | + | 0.0161212i | ||||
\(113\) | 9.42009 | 0.886168 | 0.443084 | − | 0.896480i | \(-0.353884\pi\) | ||||
0.443084 | + | 0.896480i | \(0.353884\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.11712 | − | 1.22232i | −0.197422 | − | 0.113982i | ||||
\(116\) | −3.23731 | + | 5.60719i | −0.300577 | + | 0.520615i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −18.5551 | −1.70814 | ||||||||
\(119\) | 2.83899 | − | 3.74004i | 0.260250 | − | 0.342849i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.45242 | − | 9.44388i | −0.495675 | − | 0.858534i | ||||
\(122\) | 6.80822 | + | 3.93073i | 0.616387 | + | 0.355871i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.8426 | + | 7.41466i | −1.15330 | + | 0.665856i | ||||
\(125\) | 11.6543i | 1.04239i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.3998 | 1.18904 | 0.594519 | − | 0.804081i | \(-0.297342\pi\) | ||||
0.594519 | + | 0.804081i | \(0.297342\pi\) | |||||||
\(128\) | 15.7217 | − | 9.07695i | 1.38962 | − | 0.802297i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.999884 | + | 17.4771i | −0.0876956 | + | 1.53284i | ||||
\(131\) | 6.69854 | + | 11.6022i | 0.585254 | + | 1.01369i | 0.994844 | + | 0.101420i | \(0.0323385\pi\) |
−0.409590 | + | 0.912270i | \(0.634328\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.34469 | + | 1.82621i | −0.376732 | + | 0.158353i | ||||
\(134\) | 28.8228 | 2.48991 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.28555 | − | 2.47427i | −0.367483 | − | 0.212167i | ||||
\(137\) | 0.433917 | + | 0.250522i | 0.0370720 | + | 0.0214036i | 0.518421 | − | 0.855125i | \(-0.326520\pi\) |
−0.481349 | + | 0.876529i | \(0.659853\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.41936 | 0.120388 | 0.0601941 | − | 0.998187i | \(-0.480828\pi\) | ||||
0.0601941 | + | 0.998187i | \(0.480828\pi\) | |||||||
\(140\) | 2.26967 | − | 17.9627i | 0.191822 | − | 1.51813i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.54305 | − | 2.67264i | −0.129490 | − | 0.224283i | ||||
\(143\) | −1.11037 | − | 0.0635255i | −0.0928539 | − | 0.00531227i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.69996 | + | 2.13617i | −0.307265 | + | 0.177399i | ||||
\(146\) | −27.1463 | −2.24664 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.8454i | 1.46689i | ||||||||
\(149\) | −18.2652 | + | 10.5454i | −1.49635 | + | 0.863916i | −0.999991 | − | 0.00420426i | \(-0.998662\pi\) |
−0.496355 | + | 0.868120i | \(0.665328\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.1591 | + | 8.75211i | 1.23363 | + | 0.712236i | 0.967785 | − | 0.251779i | \(-0.0810157\pi\) |
0.265845 | + | 0.964016i | \(0.414349\pi\) | |||||||
\(152\) | 2.48343 | + | 4.30142i | 0.201432 | + | 0.348891i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.84998 | + | 0.233753i | 0.149075 | + | 0.0188363i | ||||
\(155\) | −9.78526 | −0.785971 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0377894 | + | 0.0654532i | −0.00301593 | + | 0.00522374i | −0.867529 | − | 0.497386i | \(-0.834293\pi\) |
0.864514 | + | 0.502610i | \(0.167627\pi\) | |||||||
\(158\) | 15.6816 | + | 9.05375i | 1.24756 | + | 0.720278i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.1899 | 0.963699 | ||||||||
\(161\) | −1.17942 | − | 2.80593i | −0.0929516 | − | 0.221138i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.73102 | + | 5.04086i | −0.683866 | + | 0.394830i | −0.801310 | − | 0.598249i | \(-0.795863\pi\) |
0.117444 | + | 0.993080i | \(0.462530\pi\) | |||||||
\(164\) | −18.7690 | − | 10.8363i | −1.46561 | − | 0.846172i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.8281 | − | 22.2189i | −0.995655 | − | 1.72452i | ||||
\(167\) | 5.84989i | 0.452678i | 0.974049 | + | 0.226339i | \(0.0726757\pi\) | ||||
−0.974049 | + | 0.226339i | \(0.927324\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.74159 | − | 10.4436i | 0.595507 | − | 0.803350i | ||||
\(170\) | −4.30835 | − | 7.46229i | −0.330436 | − | 0.572331i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.45732 | + | 4.25620i | −0.187369 | + | 0.324532i | ||||
\(173\) | −8.49511 | − | 14.7140i | −0.645871 | − | 1.11868i | −0.984100 | − | 0.177617i | \(-0.943161\pi\) |
0.338229 | − | 0.941064i | \(-0.390172\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.774903 | + | 1.02084i | −0.0585771 | + | 0.0771686i | ||||
\(176\) | 0.0215771i | 0.00162644i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.89544 | − | 3.28300i | 0.142069 | − | 0.246072i | ||||
\(179\) | 7.65079 | − | 13.2516i | 0.571847 | − | 0.990468i | −0.424529 | − | 0.905414i | \(-0.639560\pi\) |
0.996376 | − | 0.0850537i | \(-0.0271062\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.84958 | −0.434796 | −0.217398 | − | 0.976083i | \(-0.569757\pi\) | ||||
−0.217398 | + | 0.976083i | \(0.569757\pi\) | |||||||
\(182\) | −14.1482 | + | 16.5796i | −1.04873 | + | 1.22896i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.77799 | + | 1.60387i | −0.204796 | + | 0.118239i | ||||
\(185\) | −5.88774 | + | 10.1979i | −0.432875 | + | 0.749761i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.474101 | − | 0.273722i | 0.0346697 | − | 0.0200165i | ||||
\(188\) | 30.6520i | 2.23553i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.64861i | 0.627436i | ||||||||
\(191\) | −13.4090 | − | 23.2250i | −0.970238 | − | 1.68050i | −0.694831 | − | 0.719173i | \(-0.744521\pi\) |
−0.275407 | − | 0.961328i | \(-0.588812\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.185315 | + | 0.106992i | 0.0133393 | + | 0.00770145i | 0.506655 | − | 0.862149i | \(-0.330882\pi\) |
−0.493316 | + | 0.869850i | \(0.664215\pi\) | |||||||
\(194\) | 8.75816 | + | 15.1696i | 0.628799 | + | 1.08911i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.7730 | − | 16.1053i | 1.12664 | − | 1.15038i | ||||
\(197\) | 11.2290i | 0.800035i | 0.916508 | + | 0.400017i | \(0.130996\pi\) | ||||
−0.916508 | + | 0.400017i | \(0.869004\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.2100 | − | 17.6843i | 0.723771 | − | 1.25361i | −0.235707 | − | 0.971824i | \(-0.575741\pi\) |
0.959478 | − | 0.281784i | \(-0.0909261\pi\) | |||||||
\(200\) | 1.16974 | + | 0.675351i | 0.0827132 | + | 0.0477545i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.8313i | 1.46568i | ||||||||
\(203\) | −5.27738 | − | 0.666820i | −0.370399 | − | 0.0468016i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.15042 | − | 12.3849i | −0.499407 | − | 0.864999i | ||||
\(206\) | 11.9547 | + | 6.90207i | 0.832926 | + | 0.480890i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.210859 | − | 0.138374i | −0.0146204 | − | 0.00959448i | ||||
\(209\) | −0.549471 | −0.0380077 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.41738 | 0.579476 | 0.289738 | − | 0.957106i | \(-0.406432\pi\) | ||||
0.289738 | + | 0.957106i | \(0.406432\pi\) | |||||||
\(212\) | −11.9810 | − | 20.7517i | −0.822857 | − | 1.42523i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23.9148 | + | 13.8072i | 1.63479 | + | 0.943844i | ||||
\(215\) | −2.80849 | + | 1.62148i | −0.191537 | + | 0.110584i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.70417 | − | 7.36624i | −0.658762 | − | 0.500053i | ||||
\(218\) | 3.11164 | 0.210747 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.05545 | − | 1.82810i | 0.0711587 | − | 0.123250i | ||||
\(221\) | −0.365490 | + | 6.38845i | −0.0245855 | + | 0.429734i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.6091i | − | 0.911333i | −0.890151 | − | 0.455666i | \(-0.849401\pi\) | ||
0.890151 | − | 0.455666i | \(-0.150599\pi\) | |||||||
\(224\) | 12.0889 | + | 9.17646i | 0.807725 | + | 0.613128i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.6396 | − | 10.7616i | 1.23989 | − | 0.715849i | ||||
\(227\) | 3.12008 | + | 1.80138i | 0.207087 | + | 0.119562i | 0.599957 | − | 0.800032i | \(-0.295184\pi\) |
−0.392870 | + | 0.919594i | \(0.628518\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.9212 | + | 9.19208i | −1.05210 | + | 0.607430i | −0.923236 | − | 0.384232i | \(-0.874466\pi\) |
−0.128863 | + | 0.991662i | \(0.541133\pi\) | |||||||
\(230\) | −5.58554 | −0.368299 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.60598i | 0.368051i | ||||||||
\(233\) | −10.1348 | − | 17.5541i | −0.663955 | − | 1.15000i | −0.979567 | − | 0.201116i | \(-0.935543\pi\) |
0.315612 | − | 0.948888i | \(-0.397790\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1130 | + | 17.5162i | −0.659699 | + | 1.14263i | ||||
\(236\) | −22.6490 | + | 13.0764i | −1.47432 | + | 0.851202i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.34488 | − | 10.6437i | 0.0871758 | − | 0.689931i | ||||
\(239\) | − | 20.8097i | − | 1.34607i | −0.739612 | − | 0.673033i | \(-0.764991\pi\) | ||
0.739612 | − | 0.673033i | \(-0.235009\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.0113 | − | 6.35736i | −0.709299 | − | 0.409514i | 0.101503 | − | 0.994835i | \(-0.467635\pi\) |
−0.810801 | + | 0.585322i | \(0.800968\pi\) | |||||||
\(242\) | −21.5775 | − | 12.4578i | −1.38705 | − | 0.800816i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.0805 | 0.709355 | ||||||||
\(245\) | 14.3272 | − | 3.99946i | 0.915330 | − | 0.255516i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.52375 | − | 5.36962i | 0.224211 | − | 0.341661i | ||||
\(248\) | −6.41990 | + | 11.1196i | −0.407664 | + | 0.706094i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.3140 | + | 23.0605i | 0.842050 | + | 1.45847i | ||||
\(251\) | 13.7436 | 0.867486 | 0.433743 | − | 0.901037i | \(-0.357193\pi\) | ||||
0.433743 | + | 0.901037i | \(0.357193\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.354865i | − | 0.0223102i | ||||||
\(254\) | 26.5142 | − | 15.3080i | 1.66365 | − | 0.960510i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.77229 | − | 13.4620i | 0.485768 | − | 0.841375i | ||||
\(257\) | 3.66736 | + | 6.35206i | 0.228764 | + | 0.396231i | 0.957442 | − | 0.288626i | \(-0.0931983\pi\) |
−0.728678 | + | 0.684856i | \(0.759865\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.5158 | + | 5.68112i | −0.839830 | + | 0.353008i | ||||
\(260\) | 11.0962 | + | 22.0378i | 0.688159 | + | 1.36673i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 26.5089 | + | 15.3049i | 1.63772 | + | 0.945540i | ||||
\(263\) | −3.33942 | + | 5.78405i | −0.205918 | + | 0.356660i | −0.950425 | − | 0.310955i | \(-0.899351\pi\) |
0.744507 | + | 0.667615i | \(0.232685\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 15.8115i | − | 0.971293i | ||||||
\(266\) | −6.51058 | + | 8.57693i | −0.399189 | + | 0.525886i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 35.1821 | − | 20.3124i | 2.14909 | − | 1.24078i | ||||
\(269\) | 8.11263 | − | 14.0515i | 0.494636 | − | 0.856735i | −0.505345 | − | 0.862917i | \(-0.668635\pi\) |
0.999981 | + | 0.00618287i | \(0.00196808\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.2277 | − | 9.36904i | 0.985760 | − | 0.569129i | 0.0817555 | − | 0.996652i | \(-0.473947\pi\) |
0.904004 | + | 0.427524i | \(0.140614\pi\) | |||||||
\(272\) | 0.124143 | 0.00752725 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.14479 | 0.0691595 | ||||||||
\(275\) | −0.129406 | + | 0.0747124i | −0.00780346 | + | 0.00450533i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.0163 | − | 26.0090i | 0.902243 | − | 1.56273i | 0.0776679 | − | 0.996979i | \(-0.475253\pi\) |
0.824575 | − | 0.565752i | \(-0.191414\pi\) | |||||||
\(278\) | 2.80849 | − | 1.62148i | 0.168442 | − | 0.0972501i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.07453 | − | 14.4517i | −0.363023 | − | 0.863656i | ||||
\(281\) | 2.23065i | 0.133070i | 0.997784 | + | 0.0665348i | \(0.0211943\pi\) | ||||
−0.997784 | + | 0.0665348i | \(0.978806\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.88774 | − | 11.9299i | 0.409433 | − | 0.709159i | −0.585393 | − | 0.810750i | \(-0.699060\pi\) |
0.994826 | + | 0.101590i | \(0.0323931\pi\) | |||||||
\(284\) | −3.76700 | − | 2.17488i | −0.223531 | − | 0.129055i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.26967 | + | 1.14280i | −0.134208 | + | 0.0675750i | ||||
\(287\) | 2.23205 | − | 17.6650i | 0.131754 | − | 1.04273i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.92516 | + | 11.9947i | 0.407362 | + | 0.705572i | ||||
\(290\) | −4.88075 | + | 8.45371i | −0.286608 | + | 0.496419i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −33.1357 | + | 19.1309i | −1.93912 | + | 1.11955i | ||||
\(293\) | − | 1.01231i | − | 0.0591400i | −0.999563 | − | 0.0295700i | \(-0.990586\pi\) | ||
0.999563 | − | 0.0295700i | \(-0.00941380\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.2572 | −1.00475 | ||||||||
\(296\) | 7.72563 | + | 13.3812i | 0.449043 | + | 0.777766i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.0943 | + | 41.7326i | −1.39575 | + | 2.41751i | ||||
\(299\) | 3.46787 | + | 2.27574i | 0.200552 | + | 0.131610i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00585 | − | 0.506157i | −0.230893 | − | 0.0291744i | ||||
\(302\) | 39.9939 | 2.30139 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.107909 | − | 0.0623010i | −0.00618898 | − | 0.00357321i | ||||
\(305\) | 6.33199 | + | 3.65577i | 0.362568 | + | 0.209329i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.0527i | − | 1.37276i | −0.727244 | − | 0.686379i | \(-0.759199\pi\) | ||
0.727244 | − | 0.686379i | \(-0.240801\pi\) | |||||||
\(308\) | 2.42288 | − | 1.01842i | 0.138057 | − | 0.0580296i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −19.3622 | + | 11.1787i | −1.09970 | + | 0.634910i | ||||
\(311\) | 4.49548 | − | 7.78639i | 0.254915 | − | 0.441526i | −0.709957 | − | 0.704245i | \(-0.751286\pi\) |
0.964872 | + | 0.262719i | \(0.0846192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.61806 | + | 13.1949i | 0.430598 | + | 0.745818i | 0.996925 | − | 0.0783626i | \(-0.0249692\pi\) |
−0.566326 | + | 0.824181i | \(0.691636\pi\) | |||||||
\(314\) | 0.172684i | 0.00974510i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.5220 | 1.43572 | ||||||||
\(317\) | −5.91972 | + | 3.41775i | −0.332484 | + | 0.191960i | −0.656944 | − | 0.753940i | \(-0.728151\pi\) |
0.324459 | + | 0.945900i | \(0.394818\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.537088 | − | 0.310088i | −0.0300712 | − | 0.0173616i | ||||
\(320\) | 23.8628 | − | 13.7772i | 1.33397 | − | 0.770170i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.53925 | − | 4.20473i | −0.308690 | − | 0.234321i | ||||
\(323\) | 3.16135i | 0.175902i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0997604 | − | 1.74373i | 0.00553371 | − | 0.0967246i | ||||
\(326\) | −11.5174 | + | 19.9487i | −0.637890 | + | 1.10486i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −18.7649 | −1.03612 | ||||||||
\(329\) | −23.2152 | + | 9.75811i | −1.27990 | + | 0.537982i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.9637 | − | 6.90727i | 0.657587 | − | 0.379658i | −0.133770 | − | 0.991012i | \(-0.542708\pi\) |
0.791357 | + | 0.611354i | \(0.209375\pi\) | |||||||
\(332\) | −31.3169 | − | 18.0808i | −1.71874 | − | 0.992314i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.68295 | + | 11.5752i | 0.365675 | + | 0.633367i | ||||
\(335\) | 26.8066 | 1.46460 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.0432 | −1.47314 | −0.736568 | − | 0.676364i | \(-0.763555\pi\) | ||||
−0.736568 | + | 0.676364i | \(0.763555\pi\) | |||||||
\(338\) | 3.38754 | − | 29.5088i | 0.184258 | − | 1.60507i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.5179 | − | 6.07249i | −0.570411 | − | 0.329327i | ||||
\(341\) | −0.710218 | − | 1.23013i | −0.0384604 | − | 0.0666154i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2192 | + | 6.81903i | 0.929749 | + | 0.368193i | ||||
\(344\) | 4.25528i | 0.229429i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −33.6186 | − | 19.4097i | −1.80735 | − | 1.04347i | ||||
\(347\) | −9.65568 | + | 16.7241i | −0.518344 | + | 0.897799i | 0.481429 | + | 0.876485i | \(0.340118\pi\) |
−0.999773 | + | 0.0213132i | \(0.993215\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.1573i | 0.757821i | 0.925433 | + | 0.378911i | \(0.123701\pi\) | ||||
−0.925433 | + | 0.378911i | \(0.876299\pi\) | |||||||
\(350\) | −0.367085 | + | 2.90521i | −0.0196215 | + | 0.155290i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.884750 | + | 1.53243i | 0.0471573 | + | 0.0816789i | ||||
\(353\) | −14.6919 | − | 8.48235i | −0.781969 | − | 0.451470i | 0.0551585 | − | 0.998478i | \(-0.482434\pi\) |
−0.837128 | + | 0.547008i | \(0.815767\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.43511 | − | 2.48569i | −0.0761680 | − | 0.131927i | ||||
\(356\) | − | 5.34313i | − | 0.283186i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 34.9613i | − | 1.84776i | ||||||
\(359\) | 19.7136 | − | 11.3816i | 1.04044 | − | 0.600700i | 0.120484 | − | 0.992715i | \(-0.461555\pi\) |
0.919959 | + | 0.392016i | \(0.128222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.91348 | + | 13.7065i | −0.416499 | + | 0.721397i | ||||
\(362\) | −11.5746 | + | 6.68260i | −0.608347 | + | 0.351229i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.58558 | + | 30.2083i | −0.292764 | + | 1.58335i | ||||
\(365\) | −25.2474 | −1.32151 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.29168 | + | 14.3616i | −0.432822 | + | 0.749670i | −0.997115 | − | 0.0759048i | \(-0.975815\pi\) |
0.564293 | + | 0.825575i | \(0.309149\pi\) | |||||||
\(368\) | 0.0402359 | − | 0.0696907i | 0.00209744 | − | 0.00363288i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 26.9048i | 1.39871i | ||||||||
\(371\) | 11.9027 | − | 15.6805i | 0.617959 | − | 0.814090i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.8230 | − | 23.9422i | −0.715730 | − | 1.23968i | −0.962677 | − | 0.270652i | \(-0.912761\pi\) |
0.246947 | − | 0.969029i | \(-0.420573\pi\) | |||||||
\(374\) | 0.625404 | − | 1.08323i | 0.0323389 | − | 0.0560126i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.2698 | + | 22.9840i | 0.684340 | + | 1.18531i | ||||
\(377\) | 6.47463 | − | 3.26003i | 0.333460 | − | 0.167900i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.24228i | 0.474744i | 0.971419 | + | 0.237372i | \(0.0762860\pi\) | ||||
−0.971419 | + | 0.237372i | \(0.923714\pi\) | |||||||
\(380\) | 6.09497 | + | 10.5568i | 0.312665 | + | 0.541552i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −53.0648 | − | 30.6369i | −2.71503 | − | 1.56752i | ||||
\(383\) | 6.62358 | − | 3.82413i | 0.338449 | − | 0.195404i | −0.321137 | − | 0.947033i | \(-0.604065\pi\) |
0.659586 | + | 0.751629i | \(0.270732\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.72057 | + | 0.217402i | 0.0876885 | + | 0.0110798i | ||||
\(386\) | 0.488913 | 0.0248850 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21.3810 | + | 12.3443i | 1.08546 | + | 0.626689i | ||||
\(389\) | −3.26868 | + | 5.66153i | −0.165729 | + | 0.287051i | −0.936914 | − | 0.349560i | \(-0.886331\pi\) |
0.771185 | + | 0.636611i | \(0.219664\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.04169 | −0.103253 | ||||||||
\(392\) | 4.85492 | − | 18.9048i | 0.245211 | − | 0.954837i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.8281 | + | 22.2189i | 0.646271 | + | 1.11937i | ||||
\(395\) | 14.5846 | + | 8.42044i | 0.733833 | + | 0.423678i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.0548 | − | 14.4654i | 1.25746 | − | 0.725996i | 0.284882 | − | 0.958563i | \(-0.408046\pi\) |
0.972581 | + | 0.232566i | \(0.0747123\pi\) | |||||||
\(398\) | − | 46.6561i | − | 2.33866i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.0338847 | −0.00169423 | ||||||||
\(401\) | −23.1603 | + | 13.3716i | −1.15657 | + | 0.667747i | −0.950480 | − | 0.310786i | \(-0.899408\pi\) |
−0.206092 | + | 0.978533i | \(0.566075\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.5759 | + | 0.948324i | 0.825705 | + | 0.0472394i | ||||
\(404\) | 14.6805 | + | 25.4274i | 0.730382 | + | 1.26506i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.2042 | + | 4.70947i | −0.556053 | + | 0.233727i | ||||
\(407\) | −1.70934 | −0.0847287 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.1138 | − | 17.3862i | −1.48903 | − | 0.859694i | −0.489112 | − | 0.872221i | \(-0.662679\pi\) |
−0.999922 | + | 0.0125273i | \(0.996012\pi\) | |||||||
\(410\) | −28.2972 | − | 16.3374i | −1.39750 | − | 0.806846i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 19.4565 | 0.958553 | ||||||||
\(413\) | −17.1142 | − | 12.9910i | −0.842133 | − | 0.639246i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.9308 | − | 20.6647i | −0.585659 | − | 1.01439i | ||||
\(416\) | −20.6494 | − | 1.18137i | −1.01242 | − | 0.0579214i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.08724 | + | 0.627719i | −0.0531787 | + | 0.0307027i | ||||
\(419\) | 4.19246 | 0.204815 | 0.102407 | − | 0.994743i | \(-0.467345\pi\) | ||||
0.102407 | + | 0.994743i | \(0.467345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.9526i | 1.02117i | 0.859828 | + | 0.510584i | \(0.170571\pi\) | ||||
−0.859828 | + | 0.510584i | \(0.829429\pi\) | |||||||
\(422\) | 16.6555 | − | 9.61607i | 0.810778 | − | 0.468103i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.9676 | − | 10.3736i | −0.872583 | − | 0.503786i | ||||
\(425\) | 0.429853 | + | 0.744528i | 0.0208509 | + | 0.0361149i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.52748 | + | 8.39213i | 0.170707 | + | 0.406124i | ||||
\(428\) | 38.9217 | 1.88135 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.70479 | + | 6.41688i | −0.178661 | + | 0.309449i | ||||
\(431\) | −14.6309 | − | 8.44713i | −0.704744 | − | 0.406884i | 0.104368 | − | 0.994539i | \(-0.466718\pi\) |
−0.809112 | + | 0.587655i | \(0.800051\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.42241 | 0.164471 | 0.0822353 | − | 0.996613i | \(-0.473794\pi\) | ||||
0.0822353 | + | 0.996613i | \(0.473794\pi\) | |||||||
\(434\) | −27.6169 | − | 3.48952i | −1.32566 | − | 0.167502i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.79818 | − | 2.19288i | 0.181900 | − | 0.105020i | ||||
\(437\) | 1.77470 | + | 1.02463i | 0.0848956 | + | 0.0490145i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.03253 | + | 15.6448i | 0.431099 | + | 0.746685i | 0.996968 | − | 0.0778096i | \(-0.0247926\pi\) |
−0.565869 | + | 0.824495i | \(0.691459\pi\) | |||||||
\(440\) | − | 1.82771i | − | 0.0871324i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.57501 | + | 13.0584i | 0.312742 | + | 0.621125i | ||||
\(443\) | 3.22173 | + | 5.58020i | 0.153069 | + | 0.265123i | 0.932354 | − | 0.361546i | \(-0.117751\pi\) |
−0.779285 | + | 0.626669i | \(0.784418\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.76286 | − | 3.05336i | 0.0835674 | − | 0.144743i | ||||
\(446\) | −15.5471 | − | 26.9284i | −0.736178 | − | 1.27510i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 34.0364 | + | 4.30065i | 1.60807 | + | 0.203187i | ||||
\(449\) | − | 1.75306i | − | 0.0827322i | −0.999144 | − | 0.0413661i | \(-0.986829\pi\) | ||
0.999144 | − | 0.0413661i | \(-0.0131710\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.03796 | − | 1.79780i | 0.0488757 | − | 0.0846551i | ||||
\(452\) | 15.1681 | − | 26.2719i | 0.713447 | − | 1.23573i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.23163 | 0.386330 | ||||||||
\(455\) | −13.1585 | + | 15.4198i | −0.616881 | + | 0.722893i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.3277 | + | 16.3550i | −1.32511 | + | 0.765054i | −0.984539 | − | 0.175164i | \(-0.943954\pi\) |
−0.340573 | + | 0.940218i | \(0.610621\pi\) | |||||||
\(458\) | −21.0022 | + | 36.3769i | −0.981368 | + | 1.69978i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.81790 | + | 3.93632i | −0.317886 | + | 0.183532i | ||||
\(461\) | 7.66641i | 0.357060i | 0.983934 | + | 0.178530i | \(0.0571342\pi\) | ||||
−0.983934 | + | 0.178530i | \(0.942866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 14.4720i | − | 0.672570i | −0.941760 | − | 0.336285i | \(-0.890829\pi\) | ||
0.941760 | − | 0.336285i | \(-0.109171\pi\) | |||||||
\(464\) | −0.0703179 | − | 0.121794i | −0.00326443 | − | 0.00565415i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −40.1077 | − | 23.1562i | −1.85795 | − | 1.07269i | ||||
\(467\) | 1.68801 | + | 2.92373i | 0.0781120 | + | 0.135294i | 0.902435 | − | 0.430825i | \(-0.141777\pi\) |
−0.824323 | + | 0.566119i | \(0.808444\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.5845 | + | 20.1798i | 1.22756 | + | 0.931815i | ||||
\(470\) | 46.2126i | 2.13163i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.3221 | + | 19.6104i | −0.521140 | + | 0.902641i | ||||
\(473\) | −0.407683 | − | 0.235376i | −0.0187453 | − | 0.0108226i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.862889i | − | 0.0395921i | ||||||
\(476\) | −5.85939 | − | 13.9399i | −0.268565 | − | 0.638934i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −23.7731 | − | 41.1763i | −1.08736 | − | 1.88336i | ||||
\(479\) | 0.125768 | + | 0.0726124i | 0.00574651 | + | 0.00331775i | 0.502871 | − | 0.864362i | \(-0.332277\pi\) |
−0.497124 | + | 0.867680i | \(0.665611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.9619 | − | 16.7042i | 0.499822 | − | 0.761648i | ||||
\(482\) | −29.0508 | −1.32323 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −35.1177 | −1.59626 | ||||||||
\(485\) | 8.14553 | + | 14.1085i | 0.369869 | + | 0.640633i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.2214 | − | 8.21073i | −0.644433 | − | 0.372064i | 0.141887 | − | 0.989883i | \(-0.454683\pi\) |
−0.786320 | + | 0.617819i | \(0.788016\pi\) | |||||||
\(488\) | 8.30856 | − | 4.79695i | 0.376111 | − | 0.217148i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 23.7803 | − | 24.2812i | 1.07428 | − | 1.09691i | ||||
\(491\) | 18.2077 | 0.821701 | 0.410850 | − | 0.911703i | \(-0.365232\pi\) | ||||
0.410850 | + | 0.911703i | \(0.365232\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.78407 | + | 3.09010i | −0.0803506 | + | 0.139171i | ||||
\(494\) | 0.838167 | − | 14.6505i | 0.0377109 | − | 0.659155i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.322108i | − | 0.0144631i | ||||||
\(497\) | 0.447981 | − | 3.54543i | 0.0200947 | − | 0.159034i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.5383 | + | 18.7860i | −1.45661 | + | 0.840976i | −0.998843 | − | 0.0480945i | \(-0.984685\pi\) |
−0.457770 | + | 0.889070i | \(0.651352\pi\) | |||||||
\(500\) | 32.5030 | + | 18.7656i | 1.45358 | + | 0.839225i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 27.1945 | − | 15.7007i | 1.21375 | − | 0.700758i | ||||
\(503\) | 4.20535 | 0.187507 | 0.0937537 | − | 0.995595i | \(-0.470113\pi\) | ||||
0.0937537 | + | 0.995595i | \(0.470113\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.3741i | 0.862137i | ||||||||
\(506\) | −0.405400 | − | 0.702174i | −0.0180222 | − | 0.0312154i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21.5761 | − | 37.3710i | 0.957287 | − | 1.65807i | ||||
\(509\) | −7.30705 | + | 4.21873i | −0.323879 | + | 0.186992i | −0.653120 | − | 0.757254i | \(-0.726540\pi\) |
0.329241 | + | 0.944246i | \(0.393207\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.0382 | − | 19.0060i | −1.10762 | − | 0.840775i | ||||
\(512\) | 0.791350i | 0.0349731i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.5133 | + | 8.37924i | 0.640153 | + | 0.369593i | ||||
\(515\) | 11.1185 | + | 6.41927i | 0.489940 | + | 0.282867i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.93602 | −0.129126 | ||||||||
\(518\) | −20.2536 | + | 26.6818i | −0.889893 | + | 1.17233i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.8610 | + | 11.7210i | 0.783256 | + | 0.514002i | ||||
\(521\) | 12.9140 | − | 22.3677i | 0.565773 | − | 0.979948i | −0.431204 | − | 0.902254i | \(-0.641911\pi\) |
0.996977 | − | 0.0776936i | \(-0.0247556\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.378202 | + | 0.655065i | 0.0165376 | + | 0.0286440i | 0.874176 | − | 0.485610i | \(-0.161402\pi\) |
−0.857638 | + | 0.514254i | \(0.828069\pi\) | |||||||
\(524\) | 43.1436 | 1.88473 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.2599i | 0.665364i | ||||||||
\(527\) | −7.07749 | + | 4.08619i | −0.308300 | + | 0.177997i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.8383 | − | 18.7724i | 0.471229 | − | 0.816192i | ||||
\(530\) | −18.0632 | − | 31.2863i | −0.784614 | − | 1.35899i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.90259 | + | 15.0575i | −0.0824876 | + | 0.652827i | ||||
\(533\) | 10.9123 | + | 21.6726i | 0.472665 | + | 0.938744i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.2420 | + | 12.8414i | 0.961606 | + | 0.555183i | ||||
\(536\) | 17.5873 | − | 30.4620i | 0.759654 | − | 1.31576i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 37.0717i | − | 1.59827i | ||||||
\(539\) | 1.54266 | + | 1.51083i | 0.0664469 | + | 0.0650760i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.4099 | − | 11.2063i | 0.834496 | − | 0.481797i | −0.0208936 | − | 0.999782i | \(-0.506651\pi\) |
0.855390 | + | 0.517985i | \(0.173318\pi\) | |||||||
\(542\) | 21.4065 | − | 37.0772i | 0.919488 | − | 1.59260i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.81675 | − | 5.09035i | 0.378015 | − | 0.218247i | ||||
\(545\) | 2.89398 | 0.123965 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.8059 | −0.504784 | −0.252392 | − | 0.967625i | \(-0.581217\pi\) | ||||
−0.252392 | + | 0.967625i | \(0.581217\pi\) | |||||||
\(548\) | 1.39737 | − | 0.806774i | 0.0596929 | − | 0.0344637i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.170704 | + | 0.295668i | −0.00727884 | + | 0.0126073i | ||||
\(551\) | 3.10154 | − | 1.79068i | 0.132130 | − | 0.0762854i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.12495 | + | 19.3298i | 0.345508 | + | 0.821988i | ||||
\(554\) | − | 68.6190i | − | 2.91534i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.28543 | − | 3.95848i | 0.0969238 | − | 0.167877i | ||||
\(557\) | 7.59273 | + | 4.38366i | 0.321714 | + | 0.185742i | 0.652156 | − | 0.758084i | \(-0.273865\pi\) |
−0.330442 | + | 0.943826i | \(0.607198\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.91464 | − | 2.47456i | 0.207867 | − | 0.104663i | ||||
\(560\) | 0.313247 | + | 0.237780i | 0.0132371 | + | 0.0100480i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.54831 | + | 4.41380i | 0.107494 | + | 0.186185i | ||||
\(563\) | −18.3879 | + | 31.8488i | −0.774958 | + | 1.34227i | 0.159860 | + | 0.987140i | \(0.448896\pi\) |
−0.934818 | + | 0.355127i | \(0.884438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.3358 | − | 10.0088i | 0.729321 | − | 0.421074i | ||||
\(566\) | − | 31.4744i | − | 1.32297i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.76619 | −0.158026 | ||||||||
\(569\) | 17.8918 | + | 30.9896i | 0.750065 | + | 1.29915i | 0.947791 | + | 0.318893i | \(0.103311\pi\) |
−0.197726 | + | 0.980257i | \(0.563356\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.46920 | − | 12.9370i | 0.312576 | − | 0.541398i | −0.666343 | − | 0.745645i | \(-0.732141\pi\) |
0.978919 | + | 0.204248i | \(0.0654747\pi\) | |||||||
\(572\) | −1.96507 | + | 2.99445i | −0.0821638 | + | 0.125204i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.7641 | − | 37.5038i | −0.657979 | − | 1.56538i | ||||
\(575\) | 0.557280 | 0.0232402 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.5892 | + | 8.42309i | 0.607357 | + | 0.350658i | 0.771930 | − | 0.635707i | \(-0.219291\pi\) |
−0.164573 | + | 0.986365i | \(0.552625\pi\) | |||||||
\(578\) | 27.4057 | + | 15.8227i | 1.13993 | + | 0.658137i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.7585i | 0.571292i | ||||||||
\(581\) | 3.72428 | − | 29.4748i | 0.154509 | − | 1.22282i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.98771 | − | 1.14761i | 0.0823226 | − | 0.0475290i | ||||
\(584\) | −16.5643 | + | 28.6901i | −0.685434 | + | 1.18721i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.15647 | − | 2.00307i | −0.0477735 | − | 0.0827461i | ||||
\(587\) | − | 36.8833i | − | 1.52234i | −0.648555 | − | 0.761168i | \(-0.724626\pi\) | ||
0.648555 | − | 0.761168i | \(-0.275374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.20264 | 0.337984 | ||||||||
\(590\) | −34.1469 | + | 19.7147i | −1.40580 | + | 0.811642i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.335690 | − | 0.193811i | −0.0137968 | − | 0.00796558i | ||||
\(593\) | 13.9894 | − | 8.07676i | 0.574474 | − | 0.331673i | −0.184460 | − | 0.982840i | \(-0.559054\pi\) |
0.758934 | + | 0.651167i | \(0.225720\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.25081 | − | 9.89920i | 0.0512781 | − | 0.405828i | ||||
\(596\) | 67.9204i | 2.78213i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.46172 | + | 0.541314i | 0.386918 | + | 0.0221360i | ||||
\(599\) | −1.24238 | + | 2.15186i | −0.0507622 | + | 0.0879227i | −0.890290 | − | 0.455394i | \(-0.849498\pi\) |
0.839528 | + | 0.543317i | \(0.182832\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.55999 | 0.389960 | 0.194980 | − | 0.980807i | \(-0.437536\pi\) | ||||
0.194980 | + | 0.980807i | \(0.437536\pi\) | |||||||
\(602\) | −8.50464 | + | 3.57478i | −0.346623 | + | 0.145697i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 48.8179 | − | 28.1850i | 1.98637 | − | 1.14683i | ||||
\(605\) | −20.0682 | − | 11.5864i | −0.815886 | − | 0.471052i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.74294 | + | 16.8753i | 0.395454 | + | 0.684946i | 0.993159 | − | 0.116770i | \(-0.0372540\pi\) |
−0.597705 | + | 0.801716i | \(0.703921\pi\) | |||||||
\(608\) | −10.2184 | −0.414411 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.7055 | 0.676387 | ||||||||
\(611\) | 18.8287 | − | 28.6918i | 0.761726 | − | 1.16075i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.7896 | + | 7.38409i | 0.516568 | + | 0.298241i | 0.735529 | − | 0.677493i | \(-0.236934\pi\) |
−0.218962 | + | 0.975733i | \(0.570267\pi\) | |||||||
\(614\) | −27.4779 | − | 47.5931i | −1.10892 | − | 1.92070i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.37588 | − | 1.81256i | 0.0554357 | − | 0.0730301i | ||||
\(617\) | − | 30.9478i | − | 1.24591i | −0.782257 | − | 0.622955i | \(-0.785932\pi\) | ||
0.782257 | − | 0.622955i | \(-0.214068\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.3297 | + | 6.54123i | 0.455380 | + | 0.262914i | 0.710100 | − | 0.704101i | \(-0.248650\pi\) |
−0.254719 | + | 0.967015i | \(0.581983\pi\) | |||||||
\(620\) | −15.7561 | + | 27.2903i | −0.632780 | + | 1.09601i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 20.5426i | − | 0.823685i | ||||||
\(623\) | 4.04678 | − | 1.70099i | 0.162131 | − | 0.0681489i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.1716 | + | 19.3498i | 0.446865 | + | 0.773994i | ||||
\(626\) | 30.1478 | + | 17.4059i | 1.20495 | + | 0.695678i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.121696 | + | 0.210784i | 0.00485620 | + | 0.00841119i | ||||
\(629\) | 9.83456i | 0.392130i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 35.3591i | − | 1.40762i | −0.710387 | − | 0.703812i | \(-0.751480\pi\) | ||
0.710387 | − | 0.703812i | \(-0.248520\pi\) | |||||||
\(632\) | 19.1373 | − | 11.0489i | 0.761242 | − | 0.439503i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.80892 | + | 13.5254i | −0.310132 | + | 0.537164i | ||||
\(635\) | 24.6596 | − | 14.2372i | 0.978585 | − | 0.564986i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.6574 | + | 5.38646i | −0.976961 | + | 0.213419i | ||||
\(638\) | −1.41699 | −0.0560990 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 19.2884 | − | 33.4086i | 0.762443 | − | 1.32059i | ||||
\(641\) | 10.6188 | − | 18.3923i | 0.419417 | − | 0.726452i | −0.576464 | − | 0.817123i | \(-0.695568\pi\) |
0.995881 | + | 0.0906706i | \(0.0289010\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 25.4808i | − | 1.00486i | −0.864617 | − | 0.502432i | \(-0.832439\pi\) | ||
0.864617 | − | 0.502432i | \(-0.167561\pi\) | |||||||
\(644\) | −9.72462 | − | 1.22875i | −0.383204 | − | 0.0484195i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.61154 | + | 6.25537i | 0.142094 | + | 0.246114i | ||||
\(647\) | −11.3928 | + | 19.7329i | −0.447897 | + | 0.775781i | −0.998249 | − | 0.0591522i | \(-0.981160\pi\) |
0.550352 | + | 0.834933i | \(0.314494\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.25253 | − | 2.16945i | −0.0491662 | − | 0.0851583i | ||||
\(650\) | −1.79465 | − | 3.56429i | −0.0703919 | − | 0.139803i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.4669i | 1.27150i | ||||||||
\(653\) | 8.13928 | + | 14.0976i | 0.318515 | + | 0.551684i | 0.980178 | − | 0.198117i | \(-0.0634827\pi\) |
−0.661664 | + | 0.749801i | \(0.730149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.6546 | + | 14.2343i | 0.963334 | + | 0.556181i | ||||
\(656\) | 0.407683 | − | 0.235376i | 0.0159173 | − | 0.00918988i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −34.7884 | + | 45.8297i | −1.35619 | + | 1.78663i | ||||
\(659\) | −20.5596 | −0.800888 | −0.400444 | − | 0.916321i | \(-0.631144\pi\) | ||||
−0.400444 | + | 0.916321i | \(0.631144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.0518 | + | 13.8863i | 0.935507 | + | 0.540115i | 0.888549 | − | 0.458782i | \(-0.151714\pi\) |
0.0469576 | + | 0.998897i | \(0.485047\pi\) | |||||||
\(662\) | 15.7818 | − | 27.3349i | 0.613378 | − | 1.06240i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −31.3101 | −1.21507 | ||||||||
\(665\) | −6.05517 | + | 7.97698i | −0.234809 | + | 0.309334i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.15647 | + | 2.00307i | 0.0447789 | + | 0.0775593i | ||||
\(668\) | 16.3149 | + | 9.41941i | 0.631242 | + | 0.364448i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 53.0425 | − | 30.6241i | 2.04921 | − | 1.18311i | ||||
\(671\) | 1.06135i | 0.0409730i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.20337 | 0.200575 | 0.100288 | − | 0.994958i | \(-0.468024\pi\) | ||||
0.100288 | + | 0.994958i | \(0.468024\pi\) | |||||||
\(674\) | −53.5105 | + | 30.8943i | −2.06115 | + | 1.19000i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.6609 | − | 38.4068i | −0.640803 | − | 1.47718i | ||||
\(677\) | 22.4239 | + | 38.8394i | 0.861821 | + | 1.49272i | 0.870169 | + | 0.492753i | \(0.164009\pi\) |
−0.00834820 | + | 0.999965i | \(0.502657\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.54268 | + | 20.1234i | −0.0975792 | + | 0.772266i | ||||
\(680\) | −10.5156 | −0.403254 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.81062 | − | 1.62271i | −0.107624 | − | 0.0621370i | ||||
\(683\) | 16.4318 | + | 9.48691i | 0.628745 | + | 0.363006i | 0.780266 | − | 0.625448i | \(-0.215084\pi\) |
−0.151521 | + | 0.988454i | \(0.548417\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.06471 | 0.0406807 | ||||||||
\(686\) | 41.8618 | − | 6.17846i | 1.59829 | − | 0.235895i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.0533755 | − | 0.0924491i | −0.00203492 | − | 0.00352459i | ||||
\(689\) | −1.53235 | + | 26.7842i | −0.0583779 | + | 1.02040i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.4085 | + | 18.7111i | −1.23288 | + | 0.711803i | −0.967629 | − | 0.252376i | \(-0.918788\pi\) |
−0.265250 | + | 0.964180i | \(0.585455\pi\) | |||||||
\(692\) | −54.7148 | −2.07994 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 44.1229i | 1.67488i | ||||||||
\(695\) | 2.61204 | − | 1.50806i | 0.0990802 | − | 0.0572040i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.3435 | − | 5.97184i | −0.391789 | − | 0.226200i | ||||
\(698\) | 16.1734 | + | 28.0131i | 0.612171 | + | 1.06031i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.59932 | + | 3.80489i | 0.0604486 | + | 0.143811i | ||||
\(701\) | −42.5513 | −1.60714 | −0.803570 | − | 0.595210i | \(-0.797069\pi\) | ||||
−0.803570 | + | 0.595210i | \(0.797069\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.93548 | − | 8.54851i | 0.186145 | − | 0.322413i | ||||
\(704\) | 3.46395 | + | 1.99991i | 0.130552 | + | 0.0753745i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −38.7612 | −1.45880 | ||||||||
\(707\) | −14.5846 | + | 19.2136i | −0.548512 | + | 0.722600i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.5889 | + | 25.1661i | −1.63702 | + | 0.945131i | −0.655163 | + | 0.755488i | \(0.727400\pi\) |
−0.981853 | + | 0.189644i | \(0.939267\pi\) | |||||||
\(710\) | −5.67934 | − | 3.27897i | −0.213142 | − | 0.123057i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.31315 | − | 4.00648i | −0.0866888 | − | 0.150149i | ||||
\(713\) | 5.29752i | 0.198394i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.11091 | + | 1.06286i | −0.0789435 | + | 0.0397487i | ||||
\(716\) | −24.6384 | − | 42.6749i | −0.920780 | − | 1.59484i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.0049 | − | 45.0418i | 0.970495 | − | 1.68095i | ||||
\(719\) | −14.4616 | − | 25.0482i | −0.539326 | − | 0.934141i | −0.998940 | − | 0.0460219i | \(-0.985346\pi\) |
0.459614 | − | 0.888119i | \(-0.347988\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.19400 | + | 14.7360i | 0.230677 | + | 0.548796i | ||||
\(722\) | 36.1616i | 1.34580i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.41891 | + | 16.3140i | −0.350051 | + | 0.606306i | ||||
\(725\) | 0.486962 | − | 0.843444i | 0.0180853 | − | 0.0313247i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.8593 | 0.736539 | 0.368269 | − | 0.929719i | \(-0.379950\pi\) | ||||
0.368269 | + | 0.929719i | \(0.379950\pi\) | |||||||
\(728\) | 8.88949 | + | 25.0695i | 0.329466 | + | 0.929136i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −49.9572 | + | 28.8428i | −1.84900 | + | 1.06752i | ||||
\(731\) | −1.35422 | + | 2.34558i | −0.0500876 | + | 0.0867543i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.6237 | + | 10.1751i | −0.650947 | + | 0.375824i | −0.788819 | − | 0.614626i | \(-0.789307\pi\) |
0.137872 | + | 0.990450i | \(0.455974\pi\) | |||||||
\(734\) | 37.8899i | 1.39854i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.59935i | − | 0.243255i | ||||||
\(737\) | 1.94564 | + | 3.36994i | 0.0716684 | + | 0.124133i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.4554 | − | 9.50055i | −0.605323 | − | 0.349483i | 0.165810 | − | 0.986158i | \(-0.446976\pi\) |
−0.771133 | + | 0.636674i | \(0.780310\pi\) | |||||||
\(740\) | 18.9607 | + | 32.8409i | 0.697009 | + | 1.20726i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.63854 | − | 44.6248i | 0.206997 | − | 1.63823i | ||||
\(743\) | 8.15098i | 0.299030i | 0.988759 | + | 0.149515i | \(0.0477713\pi\) | ||||
−0.988759 | + | 0.149515i | \(0.952229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.4090 | + | 38.8134i | −0.821000 | + | 1.42201i | ||||
\(746\) | −54.7035 | − | 31.5831i | −2.00284 | − | 1.15634i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.76297i | − | 0.0644607i | ||||||
\(749\) | 12.3908 | + | 29.4786i | 0.452750 | + | 1.07712i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.3713 | + | 31.8201i | 0.670379 | + | 1.16113i | 0.977797 | + | 0.209556i | \(0.0672020\pi\) |
−0.307417 | + | 0.951575i | \(0.599465\pi\) | |||||||
\(752\) | −0.576595 | − | 0.332897i | −0.0210262 | − | 0.0121395i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.08711 | − | 13.8473i | 0.330933 | − | 0.504289i | ||||
\(755\) | 37.1963 | 1.35371 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.3971 | 1.39557 | 0.697783 | − | 0.716310i | \(-0.254170\pi\) | ||||
0.697783 | + | 0.716310i | \(0.254170\pi\) | |||||||
\(758\) | 10.5584 | + | 18.2878i | 0.383500 | + | 0.664241i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.14048 | + | 5.27726i | 0.331560 | + | 0.191426i | ||||
\(761\) | −10.7922 | + | 6.23089i | −0.391218 | + | 0.225870i | −0.682688 | − | 0.730710i | \(-0.739189\pi\) |
0.291470 | + | 0.956580i | \(0.405856\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.87000 | + | 2.17856i | 0.103901 | + | 0.0788692i | ||||
\(764\) | −86.3636 | −3.12453 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.73742 | − | 15.1336i | 0.315696 | − | 0.546801i | ||||
\(767\) | 29.2331 | + | 1.67245i | 1.05555 | + | 0.0603888i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4.81390i | − | 0.173594i | −0.996226 | − | 0.0867969i | \(-0.972337\pi\) | ||
0.996226 | − | 0.0867969i | \(-0.0276631\pi\) | |||||||
\(770\) | 3.65287 | − | 1.53542i | 0.131640 | − | 0.0553326i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.596785 | − | 0.344554i | 0.0214787 | − | 0.0124008i | ||||
\(773\) | −24.4863 | − | 14.1372i | −0.880713 | − | 0.508480i | −0.00981931 | − | 0.999952i | \(-0.503126\pi\) |
−0.870893 | + | 0.491472i | \(0.836459\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.93180 | − | 1.11533i | 0.0693923 | − | 0.0400637i | ||||
\(776\) | 21.3764 | 0.767369 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.9367i | 0.535505i | ||||||||
\(779\) | 5.99395 | + | 10.3818i | 0.214755 | + | 0.371967i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.208322 | − | 0.360825i | 0.00745436 | − | 0.0129113i | ||||
\(782\) | −4.03991 | + | 2.33244i | −0.144467 | + | 0.0834081i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.131653 | + | 0.471618i | 0.00470190 | + | 0.0168435i | ||||
\(785\) | 0.160604i | 0.00573222i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.0053 | + | 24.8291i | 1.53297 | + | 0.885062i | 0.999223 | + | 0.0394193i | \(0.0125508\pi\) |
0.533749 | + | 0.845643i | \(0.320783\pi\) | |||||||
\(788\) | 31.3169 | + | 18.0808i | 1.11562 | + | 0.644102i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 38.4783 | 1.36900 | ||||||||
\(791\) | 24.7266 | + | 3.12432i | 0.879177 | + | 0.111088i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.3719 | − | 6.80642i | −0.368316 | − | 0.241703i | ||||
\(794\) | 33.0507 | − | 57.2455i | 1.17292 | − | 2.03157i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −32.8801 | − | 56.9501i | −1.16541 | − | 2.01854i | ||||
\(797\) | 5.37263 | 0.190308 | 0.0951542 | − | 0.995463i | \(-0.469666\pi\) | ||||
0.0951542 | + | 0.995463i | \(0.469666\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.8922i | 0.597604i | ||||||||
\(800\) | −2.40653 | + | 1.38941i | −0.0850837 | + | 0.0491231i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30.5517 | + | 52.9170i | −1.07882 | + | 1.86857i | ||||
\(803\) | −1.83246 | − | 3.17392i | −0.0646663 | − | 0.112005i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.15178 | − | 3.91061i | −0.181576 | − | 0.137831i | ||||
\(806\) | 33.8822 | − | 17.0600i | 1.19345 | − | 0.600912i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22.0160 | + | 12.7109i | 0.774520 | + | 0.447169i | ||||
\(809\) | 20.6184 | − | 35.7122i | 0.724905 | − | 1.25557i | −0.234107 | − | 0.972211i | \(-0.575217\pi\) |
0.959013 | − | 0.283362i | \(-0.0914499\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 19.4366i | − | 0.682512i | −0.939970 | − | 0.341256i | \(-0.889148\pi\) | ||
0.939970 | − | 0.341256i | \(-0.110852\pi\) | |||||||
\(812\) | −10.3573 | + | 13.6445i | −0.363469 | + | 0.478828i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.38227 | + | 1.95276i | −0.118549 | + | 0.0684441i | ||||
\(815\) | −10.7118 | + | 18.5533i | −0.375217 | + | 0.649895i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.35426 | − | 1.35923i | 0.0823651 | − | 0.0475535i | ||||
\(818\) | −79.4486 | −2.77785 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −46.0540 | −1.60828 | ||||||||
\(821\) | −17.4856 | + | 10.0953i | −0.610251 | + | 0.352329i | −0.773064 | − | 0.634328i | \(-0.781277\pi\) |
0.162813 | + | 0.986657i | \(0.447943\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.4049 | + | 37.0743i | −0.746127 | + | 1.29233i | 0.203539 | + | 0.979067i | \(0.434756\pi\) |
−0.949666 | + | 0.313263i | \(0.898578\pi\) | |||||||
\(824\) | 14.5892 | − | 8.42309i | 0.508240 | − | 0.293432i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −48.7049 | − | 6.15408i | −1.69466 | − | 0.214128i | ||||
\(827\) | − | 33.5376i | − | 1.16622i | −0.812394 | − | 0.583109i | \(-0.801836\pi\) | ||
0.812394 | − | 0.583109i | \(-0.198164\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.8949 | + | 34.4590i | −0.690978 | + | 1.19681i | 0.280540 | + | 0.959842i | \(0.409487\pi\) |
−0.971518 | + | 0.236967i | \(0.923847\pi\) | |||||||
\(830\) | −47.2150 | − | 27.2596i | −1.63886 | − | 0.946195i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −41.7581 | + | 21.0255i | −1.44770 | + | 0.728929i | ||||
\(833\) | 8.69246 | − | 8.87557i | 0.301176 | − | 0.307520i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.21548 | + | 10.7655i | 0.215096 | + | 0.372556i | ||||
\(836\) | −0.884750 | + | 1.53243i | −0.0305997 | + | 0.0530003i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.29564 | − | 4.78949i | 0.286568 | − | 0.165450i | ||||
\(839\) | 36.7098i | 1.26736i | 0.773594 | + | 0.633682i | \(0.218457\pi\) | ||||
−0.773594 | + | 0.633682i | \(0.781543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.9578 | −0.860614 | ||||||||
\(842\) | 23.9364 | + | 41.4591i | 0.824903 | + | 1.42877i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.5535 | − | 23.4754i | 0.466532 | − | 0.808058i | ||||
\(845\) | 3.15058 | − | 27.4446i | 0.108383 | − | 0.944124i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.1798 | − | 26.5974i | −0.384141 | − | 0.913898i | ||||
\(848\) | 0.520479 | 0.0178733 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.70111 | + | 0.982134i | 0.0583475 | + | 0.0336869i | ||||
\(851\) | 5.52089 | + | 3.18749i | 0.189254 | + | 0.109266i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.7156i | 0.401136i | 0.979680 | + | 0.200568i | \(0.0642788\pi\) | ||||
−0.979680 | + | 0.200568i | \(0.935721\pi\) | |||||||
\(854\) | 16.5671 | + | 12.5757i | 0.566914 | + | 0.430333i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.1850 | − | 16.8500i | 0.997523 | − | 0.575920i | ||||
\(857\) | 13.8453 | − | 23.9807i | 0.472945 | − | 0.819164i | −0.526576 | − | 0.850128i | \(-0.676524\pi\) |
0.999521 | + | 0.0309639i | \(0.00985769\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.2819 | + | 33.3972i | 0.657890 | + | 1.13950i | 0.981161 | + | 0.193192i | \(0.0618840\pi\) |
−0.323271 | + | 0.946306i | \(0.604783\pi\) | |||||||
\(860\) | 10.4436i | 0.356122i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −38.6002 | −1.31473 | ||||||||
\(863\) | −15.4613 | + | 8.92660i | −0.526310 | + | 0.303865i | −0.739512 | − | 0.673143i | \(-0.764944\pi\) |
0.213203 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.2670 | − | 18.0520i | −1.06311 | − | 0.613787i | ||||
\(866\) | 6.77195 | − | 3.90979i | 0.230120 | − | 0.132860i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −36.1694 | + | 15.2032i | −1.22767 | + | 0.516029i | ||||
\(869\) | 2.44464i | 0.0829286i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.4096 | − | 2.59793i | −1.53864 | − | 0.0880274i | ||||
\(872\) | 1.89868 | − | 3.28861i | 0.0642975 | − | 0.111366i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.68216 | 0.158376 | ||||||||
\(875\) | −3.86534 | + | 30.5912i | −0.130672 | + | 1.03417i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.72524 | + | 4.46017i | −0.260863 | + | 0.150609i | −0.624728 | − | 0.780842i | \(-0.714790\pi\) |
0.363865 | + | 0.931452i | \(0.381457\pi\) | |||||||
\(878\) | 35.7454 | + | 20.6376i | 1.20635 | + | 0.696487i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.0229256 | + | 0.0397083i | 0.000772821 | + | 0.00133857i | ||||
\(881\) | −54.6144 | −1.84001 | −0.920003 | − | 0.391911i | \(-0.871814\pi\) | ||||
−0.920003 | + | 0.391911i | \(0.871814\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.51632 | −0.252944 | −0.126472 | − | 0.991970i | \(-0.540365\pi\) | ||||
−0.126472 | + | 0.991970i | \(0.540365\pi\) | |||||||
\(884\) | 17.2284 | + | 11.3059i | 0.579454 | + | 0.380259i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.7497 | + | 7.36105i | 0.428335 | + | 0.247299i | ||||
\(887\) | 22.5391 | + | 39.0389i | 0.756790 | + | 1.31080i | 0.944479 | + | 0.328571i | \(0.106567\pi\) |
−0.187689 | + | 0.982229i | \(0.560100\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.1728 | + | 4.44424i | 1.17966 | + | 0.149055i | ||||
\(890\) | − | 8.05560i | − | 0.270024i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −37.9547 | − | 21.9132i | −1.27082 | − | 0.733708i | ||||
\(893\) | 8.47737 | − | 14.6832i | 0.283684 | − | 0.491356i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 32.5157i | − | 1.08688i | ||||||
\(896\) | 44.2782 | − | 18.6116i | 1.47923 | − | 0.621769i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.00271 | − | 3.46880i | −0.0668314 | − | 0.115755i | ||||
\(899\) | 8.01779 | + | 4.62907i | 0.267408 | + | 0.154388i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.60268 | − | 11.4362i | −0.219967 | − | 0.380994i | ||||
\(902\) | − | 4.74309i | − | 0.157928i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 26.2662i | − | 0.873602i | ||||||
\(905\) | −10.7650 | + | 6.21515i | −0.357839 | + | 0.206599i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.18295 | − | 5.51303i | 0.105688 | − | 0.183057i | −0.808331 | − | 0.588728i | \(-0.799629\pi\) |
0.914019 | + | 0.405671i | \(0.132962\pi\) | |||||||
\(908\) | 10.0478 | − | 5.80111i | 0.333449 | − | 0.192517i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.42113 | + | 45.5437i | −0.279158 | + | 1.50976i | ||||
\(911\) | −20.9161 | −0.692982 | −0.346491 | − | 0.938053i | \(-0.612627\pi\) | ||||
−0.346491 | + | 0.938053i | \(0.612627\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.73188 | − | 2.99971i | 0.0573169 | − | 0.0992758i | ||||
\(914\) | −37.3681 | + | 64.7234i | −1.23603 | + | 2.14086i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 59.2038i | 1.95615i | ||||||||
\(917\) | 13.7348 | + | 32.6761i | 0.453563 | + | 1.07906i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.44326 | − | 4.23185i | −0.0805957 | − | 0.139596i | 0.822910 | − | 0.568171i | \(-0.192349\pi\) |
−0.903506 | + | 0.428576i | \(0.859016\pi\) | |||||||
\(920\) | −3.40821 | + | 5.90320i | −0.112366 | + | 0.194623i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.75816 | + | 15.1696i | 0.288435 | + | 0.499584i | ||||
\(923\) | 2.19014 | + | 4.34976i | 0.0720893 | + | 0.143174i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.68434i | − | 0.0882606i | ||||||
\(926\) | −16.5329 | − | 28.6358i | −0.543305 | − | 0.941031i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.98812 | − | 5.76664i | −0.327876 | − | 0.189299i | ||||
\(929\) | −44.6306 | + | 25.7675i | −1.46428 | + | 0.845404i | −0.999205 | − | 0.0398663i | \(-0.987307\pi\) |
−0.465077 | + | 0.885270i | \(0.653973\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.0100 | + | 3.35261i | −0.393611 | + | 0.109877i | ||||
\(932\) | −65.2759 | −2.13818 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.68017 | + | 3.85680i | 0.218582 | + | 0.126198i | ||||
\(935\) | 0.581657 | − | 1.00746i | 0.0190222 | − | 0.0329474i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.3565 | 0.665016 | 0.332508 | − | 0.943100i | \(-0.392105\pi\) | ||||
0.332508 | + | 0.943100i | \(0.392105\pi\) | |||||||
\(938\) | 75.6564 | + | 9.55952i | 2.47027 | + | 0.312129i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 32.5676 | + | 56.4088i | 1.06224 | + | 1.83985i | ||||
\(941\) | 29.6730 | + | 17.1317i | 0.967314 | + | 0.558479i | 0.898416 | − | 0.439145i | \(-0.144719\pi\) |
0.0688974 | + | 0.997624i | \(0.478052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.70490 | + | 3.87108i | −0.218342 | + | 0.126060i | ||||
\(944\) | − | 0.568067i | − | 0.0184890i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.07558 | −0.0349701 | ||||||||
\(947\) | 47.9046 | − | 27.6578i | 1.55669 | − | 0.898756i | 0.559122 | − | 0.829086i | \(-0.311138\pi\) |
0.997570 | − | 0.0696707i | \(-0.0221949\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.7682 | + | 2.44681i | 1.38832 | + | 0.0794270i | ||||
\(950\) | −0.985770 | − | 1.70740i | −0.0319826 | − | 0.0553955i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.4284 | − | 7.91602i | −0.337988 | − | 0.256560i | ||||
\(953\) | 14.8378 | 0.480644 | 0.240322 | − | 0.970693i | \(-0.422747\pi\) | ||||
0.240322 | + | 0.970693i | \(0.422747\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −49.3529 | − | 28.4939i | −1.59702 | − | 0.922041i | ||||
\(956\) | −58.0366 | − | 33.5075i | −1.87704 | − | 1.08371i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.331812 | 0.0107203 | ||||||||
\(959\) | 1.05589 | + | 0.801506i | 0.0340965 | + | 0.0258820i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.89769 | − | 8.48305i | −0.157990 | − | 0.273647i | ||||
\(962\) | 2.60744 | − | 45.5758i | 0.0840671 | − | 1.46942i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −35.4604 | + | 20.4731i | −1.14210 | + | 0.659393i | ||||
\(965\) | 0.454714 | 0.0146378 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.09473i | 0.0995199i | 0.998761 | + | 0.0497600i | \(0.0158456\pi\) | ||||
−0.998761 | + | 0.0497600i | \(0.984154\pi\) | |||||||
\(968\) | −26.3326 | + | 15.2031i | −0.846361 | + | 0.488647i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 32.2352 | + | 18.6110i | 1.03501 | + | 0.597564i | ||||
\(971\) | 27.4506 | + | 47.5459i | 0.880933 | + | 1.52582i | 0.850305 | + | 0.526290i | \(0.176417\pi\) |
0.0306280 | + | 0.999531i | \(0.490249\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.72564 | + | 0.470751i | 0.119439 | + | 0.0150916i | ||||
\(974\) | −37.5200 | −1.20222 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.120340 | + | 0.208435i | −0.00385198 | + | 0.00667183i | ||||
\(977\) | −37.4196 | − | 21.6042i | −1.19716 | − | 0.691181i | −0.237239 | − | 0.971451i | \(-0.576243\pi\) |
−0.959921 | + | 0.280270i | \(0.909576\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.511795 | 0.0163570 | ||||||||
\(980\) | 11.9152 | − | 46.3973i | 0.380618 | − | 1.48211i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.0276 | − | 20.8006i | 1.14969 | − | 0.663773i | ||||
\(983\) | −21.5498 | − | 12.4418i | −0.687332 | − | 0.396831i | 0.115280 | − | 0.993333i | \(-0.463224\pi\) |
−0.802612 | + | 0.596502i | \(0.796557\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.9308 | + | 20.6647i | 0.380146 | + | 0.658433i | ||||
\(986\) | 8.15254i | 0.259630i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.30158 | − | 18.4735i | −0.295923 | − | 0.587722i | ||||
\(989\) | 0.877834 | + | 1.52045i | 0.0279135 | + | 0.0483476i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.39164 | + | 4.14244i | −0.0759730 | + | 0.131589i | −0.901509 | − | 0.432760i | \(-0.857540\pi\) |
0.825536 | + | 0.564349i | \(0.190873\pi\) | |||||||
\(992\) | −13.2078 | − | 22.8765i | −0.419347 | − | 0.726331i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.16390 | − | 7.52714i | −0.100353 | − | 0.238746i | ||||
\(995\) | − | 43.3925i | − | 1.37564i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.72037 | + | 2.97977i | −0.0544847 | + | 0.0943703i | −0.891981 | − | 0.452072i | \(-0.850685\pi\) |
0.837497 | + | 0.546442i | \(0.184018\pi\) | |||||||
\(998\) | −42.9225 | + | 74.3439i | −1.35869 | + | 2.35331i | ||||
\(999\) | 0 | 0 |
(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 | 819.2.dl.e.298.8 | 16 | ||
3.2 | odd | 2 | 91.2.r.a.25.1 | ✓ | 16 | ||
7.2 | even | 3 | inner | 819.2.dl.e.415.1 | 16 | ||
13.12 | even | 2 | inner | 819.2.dl.e.298.1 | 16 | ||
21.2 | odd | 6 | 91.2.r.a.51.8 | yes | 16 | ||
21.5 | even | 6 | 637.2.r.f.324.8 | 16 | |||
21.11 | odd | 6 | 637.2.c.f.246.1 | 8 | |||
21.17 | even | 6 | 637.2.c.e.246.1 | 8 | |||
21.20 | even | 2 | 637.2.r.f.116.1 | 16 | |||
39.5 | even | 4 | 1183.2.e.i.508.8 | 16 | |||
39.8 | even | 4 | 1183.2.e.i.508.1 | 16 | |||
39.38 | odd | 2 | 91.2.r.a.25.8 | yes | 16 | ||
91.51 | even | 6 | inner | 819.2.dl.e.415.8 | 16 | ||
273.38 | even | 6 | 637.2.c.e.246.8 | 8 | |||
273.44 | even | 12 | 1183.2.e.i.170.8 | 16 | |||
273.86 | even | 12 | 1183.2.e.i.170.1 | 16 | |||
273.116 | odd | 6 | 637.2.c.f.246.8 | 8 | |||
273.122 | odd | 12 | 8281.2.a.cj.1.1 | 8 | |||
273.164 | odd | 12 | 8281.2.a.cj.1.8 | 8 | |||
273.194 | even | 6 | 637.2.r.f.324.1 | 16 | |||
273.200 | even | 12 | 8281.2.a.ck.1.1 | 8 | |||
273.233 | odd | 6 | 91.2.r.a.51.1 | yes | 16 | ||
273.242 | even | 12 | 8281.2.a.ck.1.8 | 8 | |||
273.272 | even | 2 | 637.2.r.f.116.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.1 | ✓ | 16 | 3.2 | odd | 2 | ||
91.2.r.a.25.8 | yes | 16 | 39.38 | odd | 2 | ||
91.2.r.a.51.1 | yes | 16 | 273.233 | odd | 6 | ||
91.2.r.a.51.8 | yes | 16 | 21.2 | odd | 6 | ||
637.2.c.e.246.1 | 8 | 21.17 | even | 6 | |||
637.2.c.e.246.8 | 8 | 273.38 | even | 6 | |||
637.2.c.f.246.1 | 8 | 21.11 | odd | 6 | |||
637.2.c.f.246.8 | 8 | 273.116 | odd | 6 | |||
637.2.r.f.116.1 | 16 | 21.20 | even | 2 | |||
637.2.r.f.116.8 | 16 | 273.272 | even | 2 | |||
637.2.r.f.324.1 | 16 | 273.194 | even | 6 | |||
637.2.r.f.324.8 | 16 | 21.5 | even | 6 | |||
819.2.dl.e.298.1 | 16 | 13.12 | even | 2 | inner | ||
819.2.dl.e.298.8 | 16 | 1.1 | even | 1 | trivial | ||
819.2.dl.e.415.1 | 16 | 7.2 | even | 3 | inner | ||
819.2.dl.e.415.8 | 16 | 91.51 | even | 6 | inner | ||
1183.2.e.i.170.1 | 16 | 273.86 | even | 12 | |||
1183.2.e.i.170.8 | 16 | 273.44 | even | 12 | |||
1183.2.e.i.508.1 | 16 | 39.8 | even | 4 | |||
1183.2.e.i.508.8 | 16 | 39.5 | even | 4 | |||
8281.2.a.cj.1.1 | 8 | 273.122 | odd | 12 | |||
8281.2.a.cj.1.8 | 8 | 273.164 | odd | 12 | |||
8281.2.a.ck.1.1 | 8 | 273.200 | even | 12 | |||
8281.2.a.ck.1.8 | 8 | 273.242 | even | 12 |