Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 251.1 | ||
Root | \(0.418926 + 1.28932i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.251 |
Dual form | 605.2.g.e.511.1 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.418926 | + | 1.28932i | −0.296226 | + | 0.911689i | 0.686581 | + | 0.727053i | \(0.259111\pi\) |
−0.982807 | + | 0.184636i | \(0.940889\pi\) | |||||||
\(3\) | −0.465584 | + | 0.338266i | −0.268805 | + | 0.195298i | −0.714020 | − | 0.700126i | \(-0.753127\pi\) |
0.445215 | + | 0.895424i | \(0.353127\pi\) | |||||||
\(4\) | 0.131180 | + | 0.0953077i | 0.0655899 | + | 0.0476539i | ||||
\(5\) | −0.309017 | − | 0.951057i | −0.138197 | − | 0.425325i | ||||
\(6\) | −0.241089 | − | 0.741996i | −0.0984243 | − | 0.302919i | ||||
\(7\) | −2.95244 | − | 2.14507i | −1.11592 | − | 0.810761i | −0.132331 | − | 0.991206i | \(-0.542246\pi\) |
−0.983585 | + | 0.180445i | \(0.942246\pi\) | |||||||
\(8\) | −2.37136 | + | 1.72290i | −0.838404 | + | 0.609136i | ||||
\(9\) | −0.824707 | + | 2.53819i | −0.274902 | + | 0.846062i | ||||
\(10\) | 1.35567 | 0.428702 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.0933146 | −0.0269376 | ||||||||
\(13\) | 0.874813 | − | 2.69240i | 0.242630 | − | 0.746737i | −0.753388 | − | 0.657577i | \(-0.771582\pi\) |
0.996017 | − | 0.0891604i | \(-0.0284184\pi\) | |||||||
\(14\) | 4.00254 | − | 2.90802i | 1.06972 | − | 0.777201i | ||||
\(15\) | 0.465584 | + | 0.338266i | 0.120213 | + | 0.0873400i | ||||
\(16\) | −1.12773 | − | 3.47080i | −0.281933 | − | 0.867700i | ||||
\(17\) | −1.14088 | − | 3.51126i | −0.276703 | − | 0.851605i | −0.988764 | − | 0.149487i | \(-0.952238\pi\) |
0.712060 | − | 0.702118i | \(-0.247762\pi\) | |||||||
\(18\) | −2.92705 | − | 2.12663i | −0.689913 | − | 0.501251i | ||||
\(19\) | −0.0769572 | + | 0.0559127i | −0.0176552 | + | 0.0128272i | −0.596578 | − | 0.802555i | \(-0.703473\pi\) |
0.578923 | + | 0.815382i | \(0.303473\pi\) | |||||||
\(20\) | 0.0501062 | − | 0.154211i | 0.0112041 | − | 0.0344827i | ||||
\(21\) | 2.10021 | 0.458304 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.16215 | 0.242324 | 0.121162 | − | 0.992633i | \(-0.461338\pi\) | ||||
0.121162 | + | 0.992633i | \(0.461338\pi\) | |||||||
\(24\) | 0.521270 | − | 1.60431i | 0.106404 | − | 0.327477i | ||||
\(25\) | −0.809017 | + | 0.587785i | −0.161803 | + | 0.117557i | ||||
\(26\) | 3.10489 | + | 2.25583i | 0.608919 | + | 0.442405i | ||||
\(27\) | −1.00812 | − | 3.10269i | −0.194014 | − | 0.597113i | ||||
\(28\) | −0.182858 | − | 0.562780i | −0.0345570 | − | 0.106355i | ||||
\(29\) | −5.46401 | − | 3.96984i | −1.01464 | − | 0.737180i | −0.0494639 | − | 0.998776i | \(-0.515751\pi\) |
−0.965178 | + | 0.261596i | \(0.915751\pi\) | |||||||
\(30\) | −0.631180 | + | 0.458579i | −0.115237 | + | 0.0837247i | ||||
\(31\) | 2.09463 | − | 6.44661i | 0.376207 | − | 1.15785i | −0.566454 | − | 0.824094i | \(-0.691685\pi\) |
0.942661 | − | 0.333753i | \(-0.108315\pi\) | |||||||
\(32\) | −0.914918 | −0.161736 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.00509 | 0.858366 | ||||||||
\(35\) | −1.12773 | + | 3.47080i | −0.190621 | + | 0.586672i | ||||
\(36\) | −0.350094 | + | 0.254358i | −0.0583490 | + | 0.0423930i | ||||
\(37\) | −7.96056 | − | 5.78369i | −1.30871 | − | 0.950832i | −0.308708 | − | 0.951157i | \(-0.599897\pi\) |
−1.00000 | 0.000324402i | \(0.999897\pi\) | ||||||||
\(38\) | −0.0398501 | − | 0.122646i | −0.00646454 | − | 0.0198958i | ||||
\(39\) | 0.503449 | + | 1.54946i | 0.0806163 | + | 0.248112i | ||||
\(40\) | 2.37136 | + | 1.72290i | 0.374946 | + | 0.272414i | ||||
\(41\) | −6.72958 | + | 4.88933i | −1.05098 | + | 0.763585i | −0.972399 | − | 0.233323i | \(-0.925040\pi\) |
−0.0785849 | + | 0.996907i | \(0.525040\pi\) | |||||||
\(42\) | −0.879834 | + | 2.70785i | −0.135761 | + | 0.417831i | ||||
\(43\) | 2.96862 | 0.452710 | 0.226355 | − | 0.974045i | \(-0.427319\pi\) | ||||
0.226355 | + | 0.974045i | \(0.427319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.66881 | 0.397842 | ||||||||
\(46\) | −0.486854 | + | 1.49838i | −0.0717827 | + | 0.220925i | ||||
\(47\) | 1.79999 | − | 1.30777i | 0.262555 | − | 0.190757i | −0.448718 | − | 0.893674i | \(-0.648119\pi\) |
0.711273 | + | 0.702916i | \(0.248119\pi\) | |||||||
\(48\) | 1.69911 | + | 1.23447i | 0.245245 | + | 0.178181i | ||||
\(49\) | 1.95244 | + | 6.00899i | 0.278920 | + | 0.858427i | ||||
\(50\) | −0.418926 | − | 1.28932i | −0.0592451 | − | 0.182338i | ||||
\(51\) | 1.71891 | + | 1.24886i | 0.240696 | + | 0.174876i | ||||
\(52\) | 0.371364 | − | 0.269812i | 0.0514990 | − | 0.0374162i | ||||
\(53\) | 0.925174 | − | 2.84739i | 0.127082 | − | 0.391120i | −0.867192 | − | 0.497973i | \(-0.834078\pi\) |
0.994275 | + | 0.106854i | \(0.0340777\pi\) | |||||||
\(54\) | 4.42270 | 0.601853 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.6970 | 1.42945 | ||||||||
\(57\) | 0.0169166 | − | 0.0520641i | 0.00224066 | − | 0.00689605i | ||||
\(58\) | 7.40742 | − | 5.38181i | 0.972642 | − | 0.706666i | ||||
\(59\) | 6.88361 | + | 5.00123i | 0.896169 | + | 0.651105i | 0.937479 | − | 0.348041i | \(-0.113153\pi\) |
−0.0413101 | + | 0.999146i | \(0.513153\pi\) | |||||||
\(60\) | 0.0288358 | + | 0.0887475i | 0.00372269 | + | 0.0114572i | ||||
\(61\) | 2.62058 | + | 8.06531i | 0.335531 | + | 1.03266i | 0.966460 | + | 0.256817i | \(0.0826737\pi\) |
−0.630929 | + | 0.775840i | \(0.717326\pi\) | |||||||
\(62\) | 7.43427 | + | 5.40131i | 0.944153 | + | 0.685968i | ||||
\(63\) | 7.87949 | − | 5.72478i | 0.992722 | − | 0.721255i | ||||
\(64\) | 2.63875 | − | 8.12122i | 0.329843 | − | 1.01515i | ||||
\(65\) | −2.83095 | −0.351137 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.4153 | −1.63894 | −0.819469 | − | 0.573123i | \(-0.805732\pi\) | ||||
−0.819469 | + | 0.573123i | \(0.805732\pi\) | |||||||
\(68\) | 0.184990 | − | 0.569341i | 0.0224333 | − | 0.0690427i | ||||
\(69\) | −0.541077 | + | 0.393115i | −0.0651380 | + | 0.0473255i | ||||
\(70\) | −4.00254 | − | 2.90802i | −0.478396 | − | 0.347575i | ||||
\(71\) | 2.56580 | + | 7.89671i | 0.304504 | + | 0.937167i | 0.979862 | + | 0.199677i | \(0.0639892\pi\) |
−0.675358 | + | 0.737490i | \(0.736011\pi\) | |||||||
\(72\) | −2.41735 | − | 7.43985i | −0.284888 | − | 0.876795i | ||||
\(73\) | −1.06793 | − | 0.775895i | −0.124991 | − | 0.0908116i | 0.523533 | − | 0.852005i | \(-0.324614\pi\) |
−0.648525 | + | 0.761194i | \(0.724614\pi\) | |||||||
\(74\) | 10.7919 | − | 7.84080i | 1.25454 | − | 0.911474i | ||||
\(75\) | 0.177837 | − | 0.547326i | 0.0205349 | − | 0.0631998i | ||||
\(76\) | −0.0154241 | −0.00176927 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.20866 | −0.250081 | ||||||||
\(79\) | 4.28486 | − | 13.1874i | 0.482084 | − | 1.48370i | −0.354076 | − | 0.935217i | \(-0.615205\pi\) |
0.836160 | − | 0.548486i | \(-0.184795\pi\) | |||||||
\(80\) | −2.95244 | + | 2.14507i | −0.330093 | + | 0.239826i | ||||
\(81\) | −4.95843 | − | 3.60251i | −0.550937 | − | 0.400279i | ||||
\(82\) | −3.48472 | − | 10.7249i | −0.384823 | − | 1.18436i | ||||
\(83\) | 3.28932 | + | 10.1235i | 0.361050 | + | 1.11120i | 0.952418 | + | 0.304795i | \(0.0985879\pi\) |
−0.591368 | + | 0.806402i | \(0.701412\pi\) | |||||||
\(84\) | 0.275506 | + | 0.200167i | 0.0300601 | + | 0.0218400i | ||||
\(85\) | −2.98685 | + | 2.17008i | −0.323970 | + | 0.235378i | ||||
\(86\) | −1.24363 | + | 3.82751i | −0.134104 | + | 0.412731i | ||||
\(87\) | 3.88682 | 0.416710 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.1612 | −1.28908 | −0.644540 | − | 0.764570i | \(-0.722951\pi\) | ||||
−0.644540 | + | 0.764570i | \(0.722951\pi\) | |||||||
\(90\) | −1.11803 | + | 3.44095i | −0.117851 | + | 0.362708i | ||||
\(91\) | −8.35822 | + | 6.07260i | −0.876179 | + | 0.636582i | ||||
\(92\) | 0.152450 | + | 0.110762i | 0.0158940 | + | 0.0115477i | ||||
\(93\) | 1.20545 | + | 3.70998i | 0.124999 | + | 0.384707i | ||||
\(94\) | 0.932072 | + | 2.86862i | 0.0961359 | + | 0.295876i | ||||
\(95\) | 0.0769572 | + | 0.0559127i | 0.00789564 | + | 0.00573652i | ||||
\(96\) | 0.425971 | − | 0.309486i | 0.0434755 | − | 0.0315868i | ||||
\(97\) | −1.33845 | + | 4.11934i | −0.135899 | + | 0.418255i | −0.995729 | − | 0.0923261i | \(-0.970570\pi\) |
0.859829 | + | 0.510581i | \(0.170570\pi\) | |||||||
\(98\) | −8.56545 | −0.865241 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.162147 | −0.0162147 | ||||||||
\(101\) | −3.06103 | + | 9.42088i | −0.304584 | + | 0.937413i | 0.675248 | + | 0.737590i | \(0.264036\pi\) |
−0.979832 | + | 0.199822i | \(0.935964\pi\) | |||||||
\(102\) | −2.33029 | + | 1.69305i | −0.230733 | + | 0.167637i | ||||
\(103\) | −3.28939 | − | 2.38988i | −0.324113 | − | 0.235482i | 0.413816 | − | 0.910361i | \(-0.364196\pi\) |
−0.737928 | + | 0.674879i | \(0.764196\pi\) | |||||||
\(104\) | 2.56422 | + | 7.89187i | 0.251443 | + | 0.773861i | ||||
\(105\) | −0.649001 | − | 1.99742i | −0.0633360 | − | 0.194928i | ||||
\(106\) | 3.28363 | + | 2.38570i | 0.318934 | + | 0.231719i | ||||
\(107\) | 1.56834 | − | 1.13947i | 0.151617 | − | 0.110156i | −0.509390 | − | 0.860536i | \(-0.670129\pi\) |
0.661008 | + | 0.750379i | \(0.270129\pi\) | |||||||
\(108\) | 0.163465 | − | 0.503092i | 0.0157294 | − | 0.0484101i | ||||
\(109\) | −6.12664 | −0.586825 | −0.293413 | − | 0.955986i | \(-0.594791\pi\) | ||||
−0.293413 | + | 0.955986i | \(0.594791\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.66273 | 0.537483 | ||||||||
\(112\) | −4.11556 | + | 12.6664i | −0.388884 | + | 1.19686i | ||||
\(113\) | −4.68038 | + | 3.40050i | −0.440293 | + | 0.319892i | −0.785751 | − | 0.618542i | \(-0.787724\pi\) |
0.345458 | + | 0.938434i | \(0.387724\pi\) | |||||||
\(114\) | 0.0600406 | + | 0.0436220i | 0.00562331 | + | 0.00408558i | ||||
\(115\) | −0.359123 | − | 1.10527i | −0.0334884 | − | 0.103067i | ||||
\(116\) | −0.338412 | − | 1.04153i | −0.0314208 | − | 0.0967032i | ||||
\(117\) | 6.11235 | + | 4.44088i | 0.565087 | + | 0.410559i | ||||
\(118\) | −9.33193 | + | 6.78004i | −0.859073 | + | 0.624153i | ||||
\(119\) | −4.16353 | + | 12.8140i | −0.381670 | + | 1.17466i | ||||
\(120\) | −1.68687 | −0.153989 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −11.4966 | −1.04085 | ||||||||
\(123\) | 1.47929 | − | 4.55278i | 0.133383 | − | 0.410511i | ||||
\(124\) | 0.889186 | − | 0.646031i | 0.0798512 | − | 0.0580153i | ||||
\(125\) | 0.809017 | + | 0.587785i | 0.0723607 | + | 0.0525731i | ||||
\(126\) | 4.08017 | + | 12.5575i | 0.363490 | + | 1.11871i | ||||
\(127\) | −0.753330 | − | 2.31851i | −0.0668472 | − | 0.205735i | 0.912053 | − | 0.410071i | \(-0.134496\pi\) |
−0.978901 | + | 0.204337i | \(0.934496\pi\) | |||||||
\(128\) | 7.88507 | + | 5.72884i | 0.696948 | + | 0.506363i | ||||
\(129\) | −1.38214 | + | 1.00418i | −0.121691 | + | 0.0884135i | ||||
\(130\) | 1.18596 | − | 3.65001i | 0.104016 | − | 0.320127i | ||||
\(131\) | −7.04156 | −0.615224 | −0.307612 | − | 0.951512i | \(-0.599530\pi\) | ||||
−0.307612 | + | 0.951512i | \(0.599530\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.347148 | 0.0301016 | ||||||||
\(134\) | 5.62002 | − | 17.2966i | 0.485496 | − | 1.49420i | ||||
\(135\) | −2.63930 | + | 1.91757i | −0.227155 | + | 0.165038i | ||||
\(136\) | 8.75497 | + | 6.36086i | 0.750732 | + | 0.545439i | ||||
\(137\) | −2.95818 | − | 9.10433i | −0.252734 | − | 0.777835i | −0.994268 | − | 0.106920i | \(-0.965901\pi\) |
0.741534 | − | 0.670916i | \(-0.234099\pi\) | |||||||
\(138\) | −0.280181 | − | 0.862309i | −0.0238506 | − | 0.0734046i | ||||
\(139\) | 0.417050 | + | 0.303004i | 0.0353737 | + | 0.0257005i | 0.605332 | − | 0.795973i | \(-0.293041\pi\) |
−0.569958 | + | 0.821674i | \(0.693041\pi\) | |||||||
\(140\) | −0.478730 | + | 0.347817i | −0.0404600 | + | 0.0293959i | ||||
\(141\) | −0.395671 | + | 1.21775i | −0.0333215 | + | 0.102553i | ||||
\(142\) | −11.2563 | −0.944607 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 9.73958 | 0.811632 | ||||||||
\(145\) | −2.08707 | + | 6.42333i | −0.173321 | + | 0.533429i | ||||
\(146\) | 1.44776 | − | 1.05186i | 0.119818 | − | 0.0870526i | ||||
\(147\) | −2.94166 | − | 2.13724i | −0.242624 | − | 0.176277i | ||||
\(148\) | −0.493035 | − | 1.51741i | −0.0405272 | − | 0.124730i | ||||
\(149\) | 2.52153 | + | 7.76046i | 0.206571 | + | 0.635761i | 0.999645 | + | 0.0266359i | \(0.00847946\pi\) |
−0.793074 | + | 0.609126i | \(0.791521\pi\) | |||||||
\(150\) | 0.631180 | + | 0.458579i | 0.0515356 | + | 0.0374428i | ||||
\(151\) | 1.56968 | − | 1.14044i | 0.127738 | − | 0.0928073i | −0.522082 | − | 0.852896i | \(-0.674844\pi\) |
0.649820 | + | 0.760088i | \(0.274844\pi\) | |||||||
\(152\) | 0.0861618 | − | 0.265179i | 0.00698864 | − | 0.0215088i | ||||
\(153\) | 9.85312 | 0.796577 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.77837 | −0.544452 | ||||||||
\(156\) | −0.0816328 | + | 0.251240i | −0.00653586 | + | 0.0201153i | ||||
\(157\) | −17.2114 | + | 12.5048i | −1.37362 | + | 0.997994i | −0.376176 | + | 0.926548i | \(0.622761\pi\) |
−0.997445 | + | 0.0714455i | \(0.977239\pi\) | |||||||
\(158\) | 15.2078 | + | 11.0491i | 1.20987 | + | 0.879021i | ||||
\(159\) | 0.532431 | + | 1.63866i | 0.0422246 | + | 0.129954i | ||||
\(160\) | 0.282725 | + | 0.870139i | 0.0223514 | + | 0.0687905i | ||||
\(161\) | −3.43117 | − | 2.49289i | −0.270414 | − | 0.196467i | ||||
\(162\) | 6.72202 | − | 4.88383i | 0.528132 | − | 0.383710i | ||||
\(163\) | −4.93839 | + | 15.1988i | −0.386804 | + | 1.19046i | 0.548359 | + | 0.836243i | \(0.315253\pi\) |
−0.935163 | + | 0.354218i | \(0.884747\pi\) | |||||||
\(164\) | −1.34878 | −0.105322 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4304 | −1.12002 | ||||||||
\(167\) | −5.47239 | + | 16.8423i | −0.423466 | + | 1.30330i | 0.480989 | + | 0.876727i | \(0.340278\pi\) |
−0.904455 | + | 0.426569i | \(0.859722\pi\) | |||||||
\(168\) | −4.98037 | + | 3.61845i | −0.384244 | + | 0.279169i | ||||
\(169\) | 4.03351 | + | 2.93052i | 0.310270 | + | 0.225424i | ||||
\(170\) | −1.54666 | − | 4.76012i | −0.118623 | − | 0.365085i | ||||
\(171\) | −0.0784497 | − | 0.241443i | −0.00599920 | − | 0.0184636i | ||||
\(172\) | 0.389423 | + | 0.282932i | 0.0296932 | + | 0.0215734i | ||||
\(173\) | 12.8516 | − | 9.33725i | 0.977091 | − | 0.709898i | 0.0200344 | − | 0.999799i | \(-0.493622\pi\) |
0.957057 | + | 0.289901i | \(0.0936224\pi\) | |||||||
\(174\) | −1.62829 | + | 5.01136i | −0.123440 | + | 0.379910i | ||||
\(175\) | 3.64941 | 0.275870 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.89664 | −0.368054 | ||||||||
\(178\) | 5.09463 | − | 15.6797i | 0.381859 | − | 1.17524i | ||||
\(179\) | 13.6570 | − | 9.92242i | 1.02078 | − | 0.741637i | 0.0543338 | − | 0.998523i | \(-0.482696\pi\) |
0.966442 | + | 0.256886i | \(0.0826965\pi\) | |||||||
\(180\) | 0.350094 | + | 0.254358i | 0.0260945 | + | 0.0189587i | ||||
\(181\) | −7.44341 | − | 22.9085i | −0.553264 | − | 1.70277i | −0.700484 | − | 0.713668i | \(-0.747032\pi\) |
0.147220 | − | 0.989104i | \(-0.452968\pi\) | |||||||
\(182\) | −4.32807 | − | 13.3204i | −0.320818 | − | 0.987375i | ||||
\(183\) | −3.94832 | − | 2.86862i | −0.291868 | − | 0.212055i | ||||
\(184\) | −2.75587 | + | 2.00226i | −0.203166 | + | 0.147609i | ||||
\(185\) | −3.04066 | + | 9.35820i | −0.223554 | + | 0.688029i | ||||
\(186\) | −5.28836 | −0.387761 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.360762 | 0.0263113 | ||||||||
\(189\) | −3.67906 | + | 11.3230i | −0.267613 | + | 0.823627i | ||||
\(190\) | −0.104329 | + | 0.0757994i | −0.00756881 | + | 0.00549906i | ||||
\(191\) | −4.35477 | − | 3.16393i | −0.315100 | − | 0.228934i | 0.418982 | − | 0.907995i | \(-0.362387\pi\) |
−0.734082 | + | 0.679061i | \(0.762387\pi\) | |||||||
\(192\) | 1.51858 | + | 4.67371i | 0.109594 | + | 0.337296i | ||||
\(193\) | −5.65008 | − | 17.3892i | −0.406702 | − | 1.25170i | −0.919466 | − | 0.393170i | \(-0.871378\pi\) |
0.512764 | − | 0.858530i | \(-0.328622\pi\) | |||||||
\(194\) | −4.75044 | − | 3.45140i | −0.341062 | − | 0.247796i | ||||
\(195\) | 1.31805 | − | 0.957617i | 0.0943873 | − | 0.0685764i | ||||
\(196\) | −0.316582 | + | 0.974340i | −0.0226130 | + | 0.0695957i | ||||
\(197\) | −2.64566 | −0.188496 | −0.0942478 | − | 0.995549i | \(-0.530045\pi\) | ||||
−0.0942478 | + | 0.995549i | \(0.530045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.52800 | 0.462757 | 0.231379 | − | 0.972864i | \(-0.425676\pi\) | ||||
0.231379 | + | 0.972864i | \(0.425676\pi\) | |||||||
\(200\) | 0.905781 | − | 2.78771i | 0.0640484 | − | 0.197121i | ||||
\(201\) | 6.24594 | − | 4.53794i | 0.440555 | − | 0.320082i | ||||
\(202\) | −10.8642 | − | 7.89331i | −0.764403 | − | 0.555371i | ||||
\(203\) | 7.61657 | + | 23.4414i | 0.534578 | + | 1.64526i | ||||
\(204\) | 0.106460 | + | 0.327652i | 0.00745372 | + | 0.0229402i | ||||
\(205\) | 6.72958 | + | 4.88933i | 0.470014 | + | 0.341485i | ||||
\(206\) | 4.45934 | − | 3.23990i | 0.310697 | − | 0.225734i | ||||
\(207\) | −0.958431 | + | 2.94975i | −0.0666155 | + | 0.205022i | ||||
\(208\) | −10.3313 | −0.716349 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.84720 | 0.196476 | ||||||||
\(211\) | 8.48183 | − | 26.1044i | 0.583913 | − | 1.79710i | −0.0196771 | − | 0.999806i | \(-0.506264\pi\) |
0.603591 | − | 0.797294i | \(-0.293736\pi\) | |||||||
\(212\) | 0.392743 | − | 0.285344i | 0.0269737 | − | 0.0195975i | ||||
\(213\) | −3.86578 | − | 2.80866i | −0.264879 | − | 0.192446i | ||||
\(214\) | 0.812120 | + | 2.49945i | 0.0555154 | + | 0.170859i | ||||
\(215\) | −0.917354 | − | 2.82333i | −0.0625630 | − | 0.192549i | ||||
\(216\) | 7.73624 | + | 5.62071i | 0.526385 | + | 0.382441i | ||||
\(217\) | −20.0127 | + | 14.5401i | −1.35855 | + | 0.987046i | ||||
\(218\) | 2.56661 | − | 7.89921i | 0.173833 | − | 0.535002i | ||||
\(219\) | 0.759669 | 0.0513337 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.4518 | −0.703061 | ||||||||
\(222\) | −2.37227 | + | 7.30109i | −0.159216 | + | 0.490017i | ||||
\(223\) | 4.11137 | − | 2.98709i | 0.275318 | − | 0.200030i | −0.441555 | − | 0.897234i | \(-0.645573\pi\) |
0.716873 | + | 0.697204i | \(0.245573\pi\) | |||||||
\(224\) | 2.70124 | + | 1.96257i | 0.180484 | + | 0.131129i | ||||
\(225\) | −0.824707 | − | 2.53819i | −0.0549805 | − | 0.169212i | ||||
\(226\) | −2.42360 | − | 7.45908i | −0.161216 | − | 0.496171i | ||||
\(227\) | 3.02556 | + | 2.19820i | 0.200814 | + | 0.145900i | 0.683648 | − | 0.729812i | \(-0.260393\pi\) |
−0.482834 | + | 0.875712i | \(0.660393\pi\) | |||||||
\(228\) | 0.00718123 | − | 0.00521747i | 0.000475589 | − | 0.000345535i | ||||
\(229\) | 8.32001 | − | 25.6064i | 0.549802 | − | 1.69212i | −0.159490 | − | 0.987200i | \(-0.550985\pi\) |
0.709291 | − | 0.704916i | \(-0.249015\pi\) | |||||||
\(230\) | 1.57549 | 0.103885 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.7968 | 1.29972 | ||||||||
\(233\) | −5.66017 | + | 17.4202i | −0.370810 | + | 1.14124i | 0.575452 | + | 0.817836i | \(0.304826\pi\) |
−0.946262 | + | 0.323401i | \(0.895174\pi\) | |||||||
\(234\) | −8.28635 | + | 6.02039i | −0.541696 | + | 0.393565i | ||||
\(235\) | −1.79999 | − | 1.30777i | −0.117418 | − | 0.0853093i | ||||
\(236\) | 0.426334 | + | 1.31212i | 0.0277520 | + | 0.0854118i | ||||
\(237\) | 2.46591 | + | 7.58928i | 0.160178 | + | 0.492977i | ||||
\(238\) | −14.7772 | − | 10.7363i | −0.957864 | − | 0.695929i | ||||
\(239\) | −8.86348 | + | 6.43970i | −0.573331 | + | 0.416549i | −0.836314 | − | 0.548251i | \(-0.815294\pi\) |
0.262983 | + | 0.964801i | \(0.415294\pi\) | |||||||
\(240\) | 0.649001 | − | 1.99742i | 0.0418929 | − | 0.128933i | ||||
\(241\) | 9.99444 | 0.643798 | 0.321899 | − | 0.946774i | \(-0.395679\pi\) | ||||
0.321899 | + | 0.946774i | \(0.395679\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.3143 | 0.854110 | ||||||||
\(244\) | −0.424919 | + | 1.30777i | −0.0272027 | + | 0.0837212i | ||||
\(245\) | 5.11155 | − | 3.71376i | 0.326565 | − | 0.237263i | ||||
\(246\) | 5.25029 | + | 3.81456i | 0.334747 | + | 0.243208i | ||||
\(247\) | 0.0832160 | + | 0.256113i | 0.00529491 | + | 0.0162961i | ||||
\(248\) | 6.13972 | + | 18.8961i | 0.389872 | + | 1.19990i | ||||
\(249\) | −4.95589 | − | 3.60066i | −0.314067 | − | 0.228183i | ||||
\(250\) | −1.09676 | + | 0.796845i | −0.0693654 | + | 0.0503969i | ||||
\(251\) | 2.98431 | − | 9.18476i | 0.188368 | − | 0.579737i | −0.811622 | − | 0.584183i | \(-0.801415\pi\) |
0.999990 | + | 0.00444573i | \(0.00141513\pi\) | |||||||
\(252\) | 1.57925 | 0.0994832 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.30490 | 0.207368 | ||||||||
\(255\) | 0.656567 | − | 2.02070i | 0.0411158 | − | 0.126541i | ||||
\(256\) | 3.12706 | − | 2.27194i | 0.195441 | − | 0.141997i | ||||
\(257\) | −8.43608 | − | 6.12917i | −0.526228 | − | 0.382327i | 0.292717 | − | 0.956199i | \(-0.405441\pi\) |
−0.818945 | + | 0.573872i | \(0.805441\pi\) | |||||||
\(258\) | −0.715702 | − | 2.20271i | −0.0445577 | − | 0.137134i | ||||
\(259\) | 11.0966 | + | 34.1520i | 0.689512 | + | 2.12210i | ||||
\(260\) | −0.371364 | − | 0.269812i | −0.0230310 | − | 0.0167330i | ||||
\(261\) | 14.5824 | − | 10.5947i | 0.902628 | − | 0.655797i | ||||
\(262\) | 2.94989 | − | 9.07884i | 0.182245 | − | 0.560893i | ||||
\(263\) | 10.9619 | 0.675937 | 0.337968 | − | 0.941157i | \(-0.390260\pi\) | ||||
0.337968 | + | 0.941157i | \(0.390260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.99393 | −0.183915 | ||||||||
\(266\) | −0.145429 | + | 0.447586i | −0.00891685 | + | 0.0274433i | ||||
\(267\) | 5.66204 | − | 4.11371i | 0.346511 | − | 0.251755i | ||||
\(268\) | −1.75982 | − | 1.27858i | −0.107498 | − | 0.0781018i | ||||
\(269\) | −0.0276091 | − | 0.0849721i | −0.00168336 | − | 0.00518084i | 0.950211 | − | 0.311606i | \(-0.100867\pi\) |
−0.951895 | + | 0.306425i | \(0.900867\pi\) | |||||||
\(270\) | −1.36669 | − | 4.20623i | −0.0831740 | − | 0.255983i | ||||
\(271\) | −10.8405 | − | 7.87606i | −0.658511 | − | 0.478436i | 0.207649 | − | 0.978203i | \(-0.433419\pi\) |
−0.866160 | + | 0.499767i | \(0.833419\pi\) | |||||||
\(272\) | −10.9003 | + | 7.91951i | −0.660926 | + | 0.480191i | ||||
\(273\) | 1.83729 | − | 5.65461i | 0.111198 | − | 0.342232i | ||||
\(274\) | 12.9777 | 0.784010 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.108445 | −0.00652764 | ||||||||
\(277\) | 1.20723 | − | 3.71548i | 0.0725356 | − | 0.223241i | −0.908216 | − | 0.418502i | \(-0.862555\pi\) |
0.980751 | + | 0.195261i | \(0.0625553\pi\) | |||||||
\(278\) | −0.565384 | + | 0.410775i | −0.0339095 | + | 0.0246367i | ||||
\(279\) | 14.6353 | + | 10.6331i | 0.876190 | + | 0.636589i | ||||
\(280\) | −3.30557 | − | 10.1735i | −0.197545 | − | 0.607982i | ||||
\(281\) | 0.475093 | + | 1.46218i | 0.0283416 | + | 0.0872266i | 0.964227 | − | 0.265079i | \(-0.0853979\pi\) |
−0.935885 | + | 0.352305i | \(0.885398\pi\) | |||||||
\(282\) | −1.40432 | − | 1.02030i | −0.0836258 | − | 0.0607577i | ||||
\(283\) | −4.37815 | + | 3.18091i | −0.260254 | + | 0.189086i | −0.710259 | − | 0.703940i | \(-0.751422\pi\) |
0.450005 | + | 0.893026i | \(0.351422\pi\) | |||||||
\(284\) | −0.416037 | + | 1.28043i | −0.0246872 | + | 0.0759795i | ||||
\(285\) | −0.0547434 | −0.00324272 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 30.3566 | 1.79190 | ||||||||
\(288\) | 0.754539 | − | 2.32223i | 0.0444617 | − | 0.136839i | ||||
\(289\) | 2.72596 | − | 1.98052i | 0.160351 | − | 0.116501i | ||||
\(290\) | −7.40742 | − | 5.38181i | −0.434979 | − | 0.316030i | ||||
\(291\) | −0.770271 | − | 2.37065i | −0.0451541 | − | 0.138970i | ||||
\(292\) | −0.0661418 | − | 0.203564i | −0.00387066 | − | 0.0119127i | ||||
\(293\) | 9.23613 | + | 6.71044i | 0.539581 | + | 0.392028i | 0.823929 | − | 0.566693i | \(-0.191777\pi\) |
−0.284349 | + | 0.958721i | \(0.591777\pi\) | |||||||
\(294\) | 3.98793 | − | 2.89740i | 0.232581 | − | 0.168980i | ||||
\(295\) | 2.62930 | − | 8.09216i | 0.153084 | − | 0.471144i | ||||
\(296\) | 28.8421 | 1.67641 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.0621 | −0.640808 | ||||||||
\(299\) | 1.01666 | − | 3.12896i | 0.0587951 | − | 0.180953i | ||||
\(300\) | 0.0754931 | − | 0.0548489i | 0.00435860 | − | 0.00316671i | ||||
\(301\) | −8.76467 | − | 6.36790i | −0.505187 | − | 0.367040i | ||||
\(302\) | 0.812812 | + | 2.50158i | 0.0467720 | + | 0.143950i | ||||
\(303\) | −1.76160 | − | 5.42165i | −0.101201 | − | 0.311466i | ||||
\(304\) | 0.280849 | + | 0.204048i | 0.0161078 | + | 0.0117030i | ||||
\(305\) | 6.86076 | − | 4.98464i | 0.392846 | − | 0.285419i | ||||
\(306\) | −4.12773 | + | 12.7038i | −0.235967 | + | 0.726231i | ||||
\(307\) | 4.25008 | 0.242565 | 0.121282 | − | 0.992618i | \(-0.461299\pi\) | ||||
0.121282 | + | 0.992618i | \(0.461299\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.33990 | 0.133112 | ||||||||
\(310\) | 2.83964 | − | 8.73951i | 0.161281 | − | 0.496371i | ||||
\(311\) | 13.4454 | − | 9.76868i | 0.762420 | − | 0.553931i | −0.137231 | − | 0.990539i | \(-0.543820\pi\) |
0.899652 | + | 0.436608i | \(0.143820\pi\) | |||||||
\(312\) | −3.86341 | − | 2.80694i | −0.218723 | − | 0.158911i | ||||
\(313\) | −8.21273 | − | 25.2762i | −0.464211 | − | 1.42869i | −0.859972 | − | 0.510341i | \(-0.829519\pi\) |
0.395761 | − | 0.918354i | \(-0.370481\pi\) | |||||||
\(314\) | −8.91244 | − | 27.4297i | −0.502958 | − | 1.54795i | ||||
\(315\) | −7.87949 | − | 5.72478i | −0.443959 | − | 0.322555i | ||||
\(316\) | 1.81895 | − | 1.32155i | 0.102324 | − | 0.0743427i | ||||
\(317\) | 1.79135 | − | 5.51322i | 0.100612 | − | 0.309653i | −0.888063 | − | 0.459721i | \(-0.847949\pi\) |
0.988676 | + | 0.150068i | \(0.0479493\pi\) | |||||||
\(318\) | −2.33581 | −0.130985 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −8.53916 | −0.477353 | ||||||||
\(321\) | −0.344751 | + | 1.06103i | −0.0192421 | + | 0.0592211i | ||||
\(322\) | 4.65155 | − | 3.37955i | 0.259220 | − | 0.188335i | ||||
\(323\) | 0.284122 | + | 0.206427i | 0.0158090 | + | 0.0114859i | ||||
\(324\) | −0.307099 | − | 0.945154i | −0.0170611 | − | 0.0525085i | ||||
\(325\) | 0.874813 | + | 2.69240i | 0.0485259 | + | 0.149347i | ||||
\(326\) | −17.5273 | − | 12.7344i | −0.970749 | − | 0.705290i | ||||
\(327\) | 2.85246 | − | 2.07244i | 0.157742 | − | 0.114606i | ||||
\(328\) | 7.53448 | − | 23.1888i | 0.416022 | − | 1.28038i | ||||
\(329\) | −8.11961 | −0.447648 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9230 | −0.710311 | −0.355155 | − | 0.934807i | \(-0.615572\pi\) | ||||
−0.355155 | + | 0.934807i | \(0.615572\pi\) | |||||||
\(332\) | −0.533354 | + | 1.64149i | −0.0292716 | + | 0.0900887i | ||||
\(333\) | 21.2452 | − | 15.4355i | 1.16423 | − | 0.845863i | ||||
\(334\) | −19.4226 | − | 14.1114i | −1.06276 | − | 0.772139i | ||||
\(335\) | 4.14555 | + | 12.7587i | 0.226496 | + | 0.697082i | ||||
\(336\) | −2.36847 | − | 7.28942i | −0.129211 | − | 0.397670i | ||||
\(337\) | 10.8290 | + | 7.86773i | 0.589893 | + | 0.428582i | 0.842277 | − | 0.539045i | \(-0.181215\pi\) |
−0.252384 | + | 0.967627i | \(0.581215\pi\) | |||||||
\(338\) | −5.46813 | + | 3.97283i | −0.297427 | + | 0.216093i | ||||
\(339\) | 1.02884 | − | 3.16643i | 0.0558787 | − | 0.171977i | ||||
\(340\) | −0.598640 | −0.0324658 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.344163 | 0.0186102 | ||||||||
\(343\) | −0.768863 | + | 2.36632i | −0.0415147 | + | 0.127769i | ||||
\(344\) | −7.03968 | + | 5.11463i | −0.379554 | + | 0.275762i | ||||
\(345\) | 0.541077 | + | 0.393115i | 0.0291306 | + | 0.0211646i | ||||
\(346\) | 6.65485 | + | 20.4815i | 0.357767 | + | 1.10109i | ||||
\(347\) | 2.61088 | + | 8.03547i | 0.140159 | + | 0.431366i | 0.996357 | − | 0.0852825i | \(-0.0271793\pi\) |
−0.856197 | + | 0.516649i | \(0.827179\pi\) | |||||||
\(348\) | 0.509872 | + | 0.370444i | 0.0273320 | + | 0.0198579i | ||||
\(349\) | −8.41283 | + | 6.11228i | −0.450328 | + | 0.327183i | −0.789725 | − | 0.613461i | \(-0.789777\pi\) |
0.339397 | + | 0.940643i | \(0.389777\pi\) | |||||||
\(350\) | −1.52884 | + | 4.70527i | −0.0817197 | + | 0.251507i | ||||
\(351\) | −9.23559 | −0.492959 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.1073 | 1.01698 | 0.508489 | − | 0.861069i | \(-0.330204\pi\) | ||||
0.508489 | + | 0.861069i | \(0.330204\pi\) | |||||||
\(354\) | 2.05133 | − | 6.31335i | 0.109027 | − | 0.335551i | ||||
\(355\) | 6.71734 | − | 4.88043i | 0.356519 | − | 0.259027i | ||||
\(356\) | −1.59530 | − | 1.15905i | −0.0845507 | − | 0.0614297i | ||||
\(357\) | −2.39608 | − | 7.37439i | −0.126814 | − | 0.390294i | ||||
\(358\) | 7.07191 | + | 21.7651i | 0.373762 | + | 1.15032i | ||||
\(359\) | −3.57114 | − | 2.59458i | −0.188478 | − | 0.136937i | 0.489545 | − | 0.871978i | \(-0.337163\pi\) |
−0.678023 | + | 0.735041i | \(0.737163\pi\) | |||||||
\(360\) | −6.32872 | + | 4.59808i | −0.333553 | + | 0.242340i | ||||
\(361\) | −5.86853 | + | 18.0615i | −0.308870 | + | 0.950604i | ||||
\(362\) | 32.6546 | 1.71629 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.67520 | −0.0878041 | ||||||||
\(365\) | −0.407912 | + | 1.25542i | −0.0213511 | + | 0.0657119i | ||||
\(366\) | 5.35264 | − | 3.88892i | 0.279787 | − | 0.203277i | ||||
\(367\) | 23.7541 | + | 17.2584i | 1.23996 | + | 0.900880i | 0.997595 | − | 0.0693059i | \(-0.0220785\pi\) |
0.242360 | + | 0.970186i | \(0.422078\pi\) | |||||||
\(368\) | −1.31059 | − | 4.03358i | −0.0683192 | − | 0.210265i | ||||
\(369\) | −6.86009 | − | 21.1132i | −0.357122 | − | 1.09911i | ||||
\(370\) | −10.7919 | − | 7.84080i | −0.561046 | − | 0.407624i | ||||
\(371\) | −8.83938 | + | 6.42219i | −0.458918 | + | 0.333423i | ||||
\(372\) | −0.195460 | + | 0.601563i | −0.0101341 | + | 0.0311896i | ||||
\(373\) | 4.96478 | 0.257067 | 0.128533 | − | 0.991705i | \(-0.458973\pi\) | ||||
0.128533 | + | 0.991705i | \(0.458973\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.575493 | −0.0297183 | ||||||||
\(376\) | −2.01528 | + | 6.20239i | −0.103930 | + | 0.319864i | ||||
\(377\) | −15.4684 | + | 11.2384i | −0.796662 | + | 0.578809i | ||||
\(378\) | −13.0577 | − | 9.48700i | −0.671618 | − | 0.487959i | ||||
\(379\) | 2.44839 | + | 7.53536i | 0.125765 | + | 0.387066i | 0.994040 | − | 0.109018i | \(-0.0347708\pi\) |
−0.868274 | + | 0.496084i | \(0.834771\pi\) | |||||||
\(380\) | 0.00476632 | + | 0.0146692i | 0.000244507 | + | 0.000752516i | ||||
\(381\) | 1.13501 | + | 0.824635i | 0.0581485 | + | 0.0422473i | ||||
\(382\) | 5.90365 | − | 4.28925i | 0.302057 | − | 0.219457i | ||||
\(383\) | −7.57571 | + | 23.3156i | −0.387101 | + | 1.19137i | 0.547844 | + | 0.836580i | \(0.315449\pi\) |
−0.934945 | + | 0.354793i | \(0.884551\pi\) | |||||||
\(384\) | −5.60903 | −0.286235 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.7872 | 1.26164 | ||||||||
\(387\) | −2.44824 | + | 7.53491i | −0.124451 | + | 0.383021i | ||||
\(388\) | −0.568183 | + | 0.412809i | −0.0288451 | + | 0.0209572i | ||||
\(389\) | −4.41799 | − | 3.20986i | −0.224001 | − | 0.162746i | 0.470125 | − | 0.882600i | \(-0.344209\pi\) |
−0.694126 | + | 0.719854i | \(0.744209\pi\) | |||||||
\(390\) | 0.682513 | + | 2.10056i | 0.0345604 | + | 0.106366i | ||||
\(391\) | −1.32587 | − | 4.08060i | −0.0670520 | − | 0.206365i | ||||
\(392\) | −14.9828 | − | 10.8856i | −0.756746 | − | 0.549808i | ||||
\(393\) | 3.27843 | − | 2.38192i | 0.165375 | − | 0.120152i | ||||
\(394\) | 1.10834 | − | 3.41111i | 0.0558372 | − | 0.171849i | ||||
\(395\) | −13.8661 | −0.697679 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.43455 | −0.322941 | −0.161470 | − | 0.986878i | \(-0.551624\pi\) | ||||
−0.161470 | + | 0.986878i | \(0.551624\pi\) | |||||||
\(398\) | −2.73475 | + | 8.41670i | −0.137081 | + | 0.421891i | ||||
\(399\) | −0.161626 | + | 0.117429i | −0.00809144 | + | 0.00587878i | ||||
\(400\) | 2.95244 | + | 2.14507i | 0.147622 | + | 0.107254i | ||||
\(401\) | −4.54336 | − | 13.9830i | −0.226884 | − | 0.698278i | −0.998095 | − | 0.0616980i | \(-0.980348\pi\) |
0.771211 | − | 0.636580i | \(-0.219652\pi\) | |||||||
\(402\) | 3.23428 | + | 9.95410i | 0.161311 | + | 0.496465i | ||||
\(403\) | −15.5244 | − | 11.2792i | −0.773327 | − | 0.561855i | ||||
\(404\) | −1.29943 | + | 0.944090i | −0.0646490 | + | 0.0469702i | ||||
\(405\) | −1.89395 | + | 5.82899i | −0.0941112 | + | 0.289645i | ||||
\(406\) | −33.4143 | −1.65832 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −6.22784 | −0.308324 | ||||||||
\(409\) | −1.35837 | + | 4.18062i | −0.0671668 | + | 0.206718i | −0.979007 | − | 0.203828i | \(-0.934662\pi\) |
0.911840 | + | 0.410546i | \(0.134662\pi\) | |||||||
\(410\) | −9.12312 | + | 6.62834i | −0.450559 | + | 0.327350i | ||||
\(411\) | 4.45697 | + | 3.23818i | 0.219846 | + | 0.159727i | ||||
\(412\) | −0.203727 | − | 0.627008i | −0.0100369 | − | 0.0308905i | ||||
\(413\) | −9.59542 | − | 29.5317i | −0.472160 | − | 1.45316i | ||||
\(414\) | −3.40166 | − | 2.47145i | −0.167183 | − | 0.121465i | ||||
\(415\) | 8.61155 | − | 6.25666i | 0.422724 | − | 0.307127i | ||||
\(416\) | −0.800383 | + | 2.46332i | −0.0392420 | + | 0.120774i | ||||
\(417\) | −0.296668 | −0.0145279 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.8526 | 0.872159 | 0.436079 | − | 0.899908i | \(-0.356367\pi\) | ||||
0.436079 | + | 0.899908i | \(0.356367\pi\) | |||||||
\(420\) | 0.105234 | − | 0.323876i | 0.00513488 | − | 0.0158035i | ||||
\(421\) | 3.90637 | − | 2.83814i | 0.190385 | − | 0.138323i | −0.488510 | − | 0.872558i | \(-0.662459\pi\) |
0.678895 | + | 0.734236i | \(0.262459\pi\) | |||||||
\(422\) | 30.1037 | + | 21.8716i | 1.46543 | + | 1.06469i | ||||
\(423\) | 1.83490 | + | 5.64723i | 0.0892157 | + | 0.274578i | ||||
\(424\) | 2.71184 | + | 8.34619i | 0.131699 | + | 0.405327i | ||||
\(425\) | 2.98685 | + | 2.17008i | 0.144884 | + | 0.105264i | ||||
\(426\) | 5.24074 | − | 3.80762i | 0.253915 | − | 0.184480i | ||||
\(427\) | 9.56357 | − | 29.4337i | 0.462814 | − | 1.42439i | ||||
\(428\) | 0.314335 | 0.0151939 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.02448 | 0.194078 | ||||||||
\(431\) | 7.68647 | − | 23.6565i | 0.370244 | − | 1.13949i | −0.576387 | − | 0.817177i | \(-0.695538\pi\) |
0.946631 | − | 0.322318i | \(-0.104462\pi\) | |||||||
\(432\) | −9.63191 | + | 6.99800i | −0.463416 | + | 0.336691i | ||||
\(433\) | 17.1918 | + | 12.4906i | 0.826186 | + | 0.600259i | 0.918478 | − | 0.395473i | \(-0.129419\pi\) |
−0.0922919 | + | 0.995732i | \(0.529419\pi\) | |||||||
\(434\) | −10.3630 | − | 31.8941i | −0.497441 | − | 1.53097i | ||||
\(435\) | −1.20109 | − | 3.69658i | −0.0575880 | − | 0.177238i | ||||
\(436\) | −0.803691 | − | 0.583916i | −0.0384898 | − | 0.0279645i | ||||
\(437\) | −0.0894356 | + | 0.0649788i | −0.00427828 | + | 0.00310836i | ||||
\(438\) | −0.318245 | + | 0.979458i | −0.0152064 | + | 0.0468003i | ||||
\(439\) | 15.9119 | 0.759434 | 0.379717 | − | 0.925103i | \(-0.376021\pi\) | ||||
0.379717 | + | 0.925103i | \(0.376021\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.8621 | −0.802958 | ||||||||
\(442\) | 4.37852 | − | 13.4757i | 0.208265 | − | 0.640973i | ||||
\(443\) | −21.2671 | + | 15.4515i | −1.01043 | + | 0.734122i | −0.964300 | − | 0.264814i | \(-0.914690\pi\) |
−0.0461323 | + | 0.998935i | \(0.514690\pi\) | |||||||
\(444\) | 0.742837 | + | 0.539702i | 0.0352535 | + | 0.0256131i | ||||
\(445\) | 3.75801 | + | 11.5660i | 0.178147 | + | 0.548279i | ||||
\(446\) | 2.12896 | + | 6.55226i | 0.100809 | + | 0.310258i | ||||
\(447\) | −3.79908 | − | 2.76020i | −0.179690 | − | 0.130553i | ||||
\(448\) | −25.2113 | + | 18.3171i | −1.19112 | + | 0.865402i | ||||
\(449\) | −2.53073 | + | 7.78879i | −0.119433 | + | 0.367576i | −0.992846 | − | 0.119404i | \(-0.961902\pi\) |
0.873413 | + | 0.486980i | \(0.161902\pi\) | |||||||
\(450\) | 3.61803 | 0.170556 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.938065 | −0.0441229 | ||||||||
\(453\) | −0.345044 | + | 1.06194i | −0.0162116 | + | 0.0498941i | ||||
\(454\) | −4.10168 | + | 2.98004i | −0.192501 | + | 0.139860i | ||||
\(455\) | 8.35822 | + | 6.07260i | 0.391839 | + | 0.284688i | ||||
\(456\) | 0.0495855 | + | 0.152608i | 0.00232205 | + | 0.00714655i | ||||
\(457\) | −3.68237 | − | 11.3332i | −0.172254 | − | 0.530143i | 0.827244 | − | 0.561843i | \(-0.189908\pi\) |
−0.999497 | + | 0.0317007i | \(0.989908\pi\) | |||||||
\(458\) | 29.5294 | + | 21.4544i | 1.37982 | + | 1.00250i | ||||
\(459\) | −9.74419 | + | 7.07957i | −0.454820 | + | 0.330446i | ||||
\(460\) | 0.0582308 | − | 0.179216i | 0.00271503 | − | 0.00835599i | ||||
\(461\) | −6.96172 | −0.324240 | −0.162120 | − | 0.986771i | \(-0.551833\pi\) | ||||
−0.162120 | + | 0.986771i | \(0.551833\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.4762 | 0.579817 | 0.289909 | − | 0.957054i | \(-0.406375\pi\) | ||||
0.289909 | + | 0.957054i | \(0.406375\pi\) | |||||||
\(464\) | −7.61657 | + | 23.4414i | −0.353590 | + | 1.08824i | ||||
\(465\) | 3.15590 | − | 2.29290i | 0.146351 | − | 0.106330i | ||||
\(466\) | −20.0891 | − | 14.5956i | −0.930609 | − | 0.676127i | ||||
\(467\) | −1.89927 | − | 5.84535i | −0.0878877 | − | 0.270491i | 0.897447 | − | 0.441122i | \(-0.145419\pi\) |
−0.985335 | + | 0.170631i | \(0.945419\pi\) | |||||||
\(468\) | 0.378566 | + | 1.16511i | 0.0174992 | + | 0.0538571i | ||||
\(469\) | 39.6078 | + | 28.7768i | 1.82892 | + | 1.32879i | ||||
\(470\) | 2.44020 | − | 1.77291i | 0.112558 | − | 0.0817781i | ||||
\(471\) | 3.78339 | − | 11.6441i | 0.174330 | − | 0.536531i | ||||
\(472\) | −24.9401 | −1.14796 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −10.8181 | −0.496890 | ||||||||
\(475\) | 0.0293950 | − | 0.0904686i | 0.00134874 | − | 0.00415098i | ||||
\(476\) | −1.76745 | + | 1.28413i | −0.0810108 | + | 0.0588578i | ||||
\(477\) | 6.46422 | + | 4.69653i | 0.295976 | + | 0.215039i | ||||
\(478\) | −4.58970 | − | 14.1256i | −0.209928 | − | 0.646092i | ||||
\(479\) | −6.85838 | − | 21.1079i | −0.313367 | − | 0.964445i | −0.976421 | − | 0.215874i | \(-0.930740\pi\) |
0.663054 | − | 0.748571i | \(-0.269260\pi\) | |||||||
\(480\) | −0.425971 | − | 0.309486i | −0.0194428 | − | 0.0141260i | ||||
\(481\) | −22.5360 | + | 16.3734i | −1.02755 | + | 0.746561i | ||||
\(482\) | −4.18693 | + | 12.8861i | −0.190710 | + | 0.586944i | ||||
\(483\) | 2.44076 | 0.111058 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.33133 | 0.196675 | ||||||||
\(486\) | −5.57769 | + | 17.1664i | −0.253009 | + | 0.778682i | ||||
\(487\) | 27.6932 | − | 20.1203i | 1.25490 | − | 0.911736i | 0.256402 | − | 0.966570i | \(-0.417463\pi\) |
0.998495 | + | 0.0548341i | \(0.0174630\pi\) | |||||||
\(488\) | −20.1100 | − | 14.6108i | −0.910339 | − | 0.661400i | ||||
\(489\) | −2.84201 | − | 8.74680i | −0.128520 | − | 0.395544i | ||||
\(490\) | 2.64687 | + | 8.14623i | 0.119573 | + | 0.368009i | ||||
\(491\) | −13.7498 | − | 9.98984i | −0.620522 | − | 0.450835i | 0.232582 | − | 0.972577i | \(-0.425283\pi\) |
−0.853104 | + | 0.521741i | \(0.825283\pi\) | |||||||
\(492\) | 0.627968 | − | 0.456246i | 0.0283110 | − | 0.0205691i | ||||
\(493\) | −7.70536 | + | 23.7146i | −0.347032 | + | 1.06805i | ||||
\(494\) | −0.365073 | −0.0164254 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.7371 | −1.11073 | ||||||||
\(497\) | 9.36365 | − | 28.8184i | 0.420017 | − | 1.29268i | ||||
\(498\) | 6.71857 | − | 4.88133i | 0.301066 | − | 0.218737i | ||||
\(499\) | −4.23072 | − | 3.07380i | −0.189393 | − | 0.137602i | 0.489048 | − | 0.872257i | \(-0.337344\pi\) |
−0.678441 | + | 0.734655i | \(0.737344\pi\) | |||||||
\(500\) | 0.0501062 | + | 0.154211i | 0.00224082 | + | 0.00689653i | ||||
\(501\) | −3.14932 | − | 9.69262i | −0.140701 | − | 0.433034i | ||||
\(502\) | 10.5919 | + | 7.69548i | 0.472740 | + | 0.343466i | ||||
\(503\) | 33.9340 | − | 24.6545i | 1.51304 | − | 1.09929i | 0.548240 | − | 0.836321i | \(-0.315298\pi\) |
0.964804 | − | 0.262970i | \(-0.0847020\pi\) | |||||||
\(504\) | −8.82193 | + | 27.1511i | −0.392960 | + | 1.20941i | ||||
\(505\) | 9.90570 | 0.440798 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.86923 | −0.127427 | ||||||||
\(508\) | 0.122150 | − | 0.375940i | 0.00541955 | − | 0.0166797i | ||||
\(509\) | −16.4779 | + | 11.9719i | −0.730370 | + | 0.530645i | −0.889680 | − | 0.456584i | \(-0.849073\pi\) |
0.159311 | + | 0.987228i | \(0.449073\pi\) | |||||||
\(510\) | 2.33029 | + | 1.69305i | 0.103187 | + | 0.0749696i | ||||
\(511\) | 1.48864 | + | 4.58156i | 0.0658536 | + | 0.202676i | ||||
\(512\) | 7.64292 | + | 23.5225i | 0.337772 | + | 1.03956i | ||||
\(513\) | 0.251062 | + | 0.182407i | 0.0110847 | + | 0.00805348i | ||||
\(514\) | 11.4366 | − | 8.30916i | 0.504446 | − | 0.366501i | ||||
\(515\) | −1.25643 | + | 3.86690i | −0.0553651 | + | 0.170396i | ||||
\(516\) | −0.277016 | −0.0121949 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −48.6816 | −2.13895 | ||||||||
\(519\) | −2.82503 | + | 8.69454i | −0.124005 | + | 0.381648i | ||||
\(520\) | 6.71323 | − | 4.87744i | 0.294394 | − | 0.213890i | ||||
\(521\) | −11.7128 | − | 8.50988i | −0.513149 | − | 0.372824i | 0.300868 | − | 0.953666i | \(-0.402724\pi\) |
−0.814017 | + | 0.580841i | \(0.802724\pi\) | |||||||
\(522\) | 7.55108 | + | 23.2398i | 0.330502 | + | 1.01718i | ||||
\(523\) | −3.44867 | − | 10.6139i | −0.150800 | − | 0.464114i | 0.846911 | − | 0.531734i | \(-0.178459\pi\) |
−0.997711 | + | 0.0676203i | \(0.978459\pi\) | |||||||
\(524\) | −0.923710 | − | 0.671115i | −0.0403525 | − | 0.0293178i | ||||
\(525\) | −1.69911 | + | 1.23447i | −0.0741551 | + | 0.0538769i | ||||
\(526\) | −4.59221 | + | 14.1334i | −0.200230 | + | 0.616244i | ||||
\(527\) | −25.0254 | −1.09013 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6494 | −0.941279 | ||||||||
\(530\) | 1.25424 | − | 3.86014i | 0.0544805 | − | 0.167674i | ||||
\(531\) | −18.3710 | + | 13.3473i | −0.797234 | + | 0.579225i | ||||
\(532\) | 0.0455388 | + | 0.0330859i | 0.00197436 | + | 0.00143446i | ||||
\(533\) | 7.27689 | + | 22.3960i | 0.315197 | + | 0.970077i | ||||
\(534\) | 2.93193 | + | 9.02354i | 0.126877 | + | 0.390487i | ||||
\(535\) | −1.56834 | − | 1.13947i | −0.0678053 | − | 0.0492634i | ||||
\(536\) | 31.8125 | − | 23.1132i | 1.37409 | − | 0.998337i | ||||
\(537\) | −3.00208 | + | 9.23944i | −0.129549 | + | 0.398711i | ||||
\(538\) | 0.121123 | 0.00522197 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.528983 | −0.0227638 | ||||||||
\(541\) | −3.30055 | + | 10.1580i | −0.141902 | + | 0.436728i | −0.996600 | − | 0.0823974i | \(-0.973742\pi\) |
0.854698 | + | 0.519126i | \(0.173742\pi\) | |||||||
\(542\) | 14.6961 | − | 10.6774i | 0.631253 | − | 0.458632i | ||||
\(543\) | 11.2147 | + | 8.14795i | 0.481268 | + | 0.349662i | ||||
\(544\) | 1.04381 | + | 3.21251i | 0.0447529 | + | 0.137735i | ||||
\(545\) | 1.89324 | + | 5.82678i | 0.0810973 | + | 0.249592i | ||||
\(546\) | 6.52092 | + | 4.73773i | 0.279070 | + | 0.202756i | ||||
\(547\) | 1.41384 | − | 1.02721i | 0.0604514 | − | 0.0439205i | −0.557149 | − | 0.830412i | \(-0.688105\pi\) |
0.617601 | + | 0.786492i | \(0.288105\pi\) | |||||||
\(548\) | 0.479660 | − | 1.47624i | 0.0204901 | − | 0.0630619i | ||||
\(549\) | −22.6325 | −0.965930 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.642459 | 0.0273697 | ||||||||
\(552\) | 0.605793 | − | 1.86444i | 0.0257843 | − | 0.0793558i | ||||
\(553\) | −40.9388 | + | 29.7438i | −1.74089 | + | 1.26483i | ||||
\(554\) | 4.28471 | + | 3.11302i | 0.182040 | + | 0.132260i | ||||
\(555\) | −1.74988 | − | 5.38558i | −0.0742783 | − | 0.228605i | ||||
\(556\) | 0.0258299 | + | 0.0794961i | 0.00109543 | + | 0.00337139i | ||||
\(557\) | −15.7632 | − | 11.4526i | −0.667908 | − | 0.485263i | 0.201416 | − | 0.979506i | \(-0.435446\pi\) |
−0.869324 | + | 0.494242i | \(0.835446\pi\) | |||||||
\(558\) | −19.8406 | + | 14.4151i | −0.839921 | + | 0.610238i | ||||
\(559\) | 2.59699 | − | 7.99271i | 0.109841 | − | 0.338055i | ||||
\(560\) | 13.3182 | 0.562798 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.08426 | −0.0879191 | ||||||||
\(563\) | 4.53920 | − | 13.9702i | 0.191304 | − | 0.588775i | −0.808695 | − | 0.588228i | \(-0.799826\pi\) |
1.00000 | 0.000546971i | \(-0.000174106\pi\) | ||||||||
\(564\) | −0.167965 | + | 0.122034i | −0.00707261 | + | 0.00513855i | ||||
\(565\) | 4.68038 | + | 3.40050i | 0.196905 | + | 0.143060i | ||||
\(566\) | −2.26710 | − | 6.97742i | −0.0952934 | − | 0.293283i | ||||
\(567\) | 6.91181 | + | 21.2724i | 0.290269 | + | 0.893356i | ||||
\(568\) | −19.6897 | − | 14.3054i | −0.826159 | − | 0.600240i | ||||
\(569\) | 16.1266 | − | 11.7166i | 0.676061 | − | 0.491187i | −0.195987 | − | 0.980606i | \(-0.562791\pi\) |
0.872049 | + | 0.489419i | \(0.162791\pi\) | |||||||
\(570\) | 0.0229335 | − | 0.0705819i | 0.000960577 | − | 0.00295635i | ||||
\(571\) | −5.24422 | −0.219464 | −0.109732 | − | 0.993961i | \(-0.534999\pi\) | ||||
−0.109732 | + | 0.993961i | \(0.534999\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.09776 | 0.129411 | ||||||||
\(574\) | −12.7172 | + | 39.1395i | −0.530805 | + | 1.63365i | ||||
\(575\) | −0.940197 | + | 0.683093i | −0.0392089 | + | 0.0284869i | ||||
\(576\) | 18.4370 | + | 13.3953i | 0.768208 | + | 0.558136i | ||||
\(577\) | 11.6192 | + | 35.7601i | 0.483712 | + | 1.48871i | 0.833838 | + | 0.552010i | \(0.186139\pi\) |
−0.350125 | + | 0.936703i | \(0.613861\pi\) | |||||||
\(578\) | 1.41156 | + | 4.34433i | 0.0587132 | + | 0.180701i | ||||
\(579\) | 8.51275 | + | 6.18488i | 0.353778 | + | 0.257035i | ||||
\(580\) | −0.885974 | + | 0.643698i | −0.0367881 | + | 0.0267281i | ||||
\(581\) | 12.0041 | − | 36.9448i | 0.498013 | − | 1.53273i | ||||
\(582\) | 3.37922 | 0.140073 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.86923 | 0.160110 | ||||||||
\(585\) | 2.33471 | − | 7.18549i | 0.0965283 | − | 0.297084i | ||||
\(586\) | −12.5212 | + | 9.09718i | −0.517246 | + | 0.375801i | ||||
\(587\) | −20.6875 | − | 15.0303i | −0.853863 | − | 0.620368i | 0.0723456 | − | 0.997380i | \(-0.476952\pi\) |
−0.926208 | + | 0.377012i | \(0.876952\pi\) | |||||||
\(588\) | −0.182191 | − | 0.560726i | −0.00751343 | − | 0.0231240i | ||||
\(589\) | 0.199250 | + | 0.613230i | 0.00820997 | + | 0.0252677i | ||||
\(590\) | 9.33193 | + | 6.78004i | 0.384189 | + | 0.279130i | ||||
\(591\) | 1.23178 | − | 0.894938i | 0.0506685 | − | 0.0368128i | ||||
\(592\) | −11.0966 | + | 34.1520i | −0.456069 | + | 1.40364i | ||||
\(593\) | −40.2260 | −1.65188 | −0.825942 | − | 0.563754i | \(-0.809356\pi\) | ||||
−0.825942 | + | 0.563754i | \(0.809356\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.4735 | 0.552358 | ||||||||
\(596\) | −0.408858 | + | 1.25834i | −0.0167475 | + | 0.0515435i | ||||
\(597\) | −3.03933 | + | 2.20820i | −0.124391 | + | 0.0903757i | ||||
\(598\) | 3.60834 | + | 2.62161i | 0.147556 | + | 0.107206i | ||||
\(599\) | 1.52344 | + | 4.68868i | 0.0622462 | + | 0.191574i | 0.977344 | − | 0.211659i | \(-0.0678865\pi\) |
−0.915097 | + | 0.403233i | \(0.867886\pi\) | |||||||
\(600\) | 0.521270 | + | 1.60431i | 0.0212808 | + | 0.0654955i | ||||
\(601\) | 37.2873 | + | 27.0908i | 1.52098 | + | 1.10506i | 0.960999 | + | 0.276551i | \(0.0891914\pi\) |
0.559981 | + | 0.828506i | \(0.310809\pi\) | |||||||
\(602\) | 11.8820 | − | 8.63280i | 0.484276 | − | 0.351847i | ||||
\(603\) | 11.0637 | − | 34.0505i | 0.450548 | − | 1.38664i | ||||
\(604\) | 0.314602 | 0.0128010 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.72824 | 0.313938 | ||||||||
\(607\) | 13.9479 | − | 42.9273i | 0.566129 | − | 1.74237i | −0.0984428 | − | 0.995143i | \(-0.531386\pi\) |
0.664572 | − | 0.747224i | \(-0.268614\pi\) | |||||||
\(608\) | 0.0704095 | − | 0.0511555i | 0.00285548 | − | 0.00207463i | ||||
\(609\) | −11.4756 | − | 8.33750i | −0.465014 | − | 0.337853i | ||||
\(610\) | 3.55265 | + | 10.9339i | 0.143843 | + | 0.442702i | ||||
\(611\) | −1.94638 | − | 5.99034i | −0.0787420 | − | 0.242343i | ||||
\(612\) | 1.29253 | + | 0.939078i | 0.0522474 | + | 0.0379600i | ||||
\(613\) | 3.83003 | − | 2.78268i | 0.154694 | − | 0.112391i | −0.507746 | − | 0.861507i | \(-0.669521\pi\) |
0.662440 | + | 0.749115i | \(0.269521\pi\) | |||||||
\(614\) | −1.78047 | + | 5.47973i | −0.0718540 | + | 0.221144i | ||||
\(615\) | −4.78708 | −0.193034 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.8468 | 0.718486 | 0.359243 | − | 0.933244i | \(-0.383035\pi\) | ||||
0.359243 | + | 0.933244i | \(0.383035\pi\) | |||||||
\(618\) | −0.980246 | + | 3.01689i | −0.0394313 | + | 0.121357i | ||||
\(619\) | −0.288781 | + | 0.209811i | −0.0116071 | + | 0.00843303i | −0.593574 | − | 0.804780i | \(-0.702283\pi\) |
0.581967 | + | 0.813213i | \(0.302283\pi\) | |||||||
\(620\) | −0.889186 | − | 0.646031i | −0.0357106 | − | 0.0259452i | ||||
\(621\) | −1.17159 | − | 3.60578i | −0.0470143 | − | 0.144695i | ||||
\(622\) | 6.96233 | + | 21.4279i | 0.279164 | + | 0.859179i | ||||
\(623\) | 35.9051 | + | 26.0866i | 1.43851 | + | 1.04514i | ||||
\(624\) | 4.81010 | − | 3.49474i | 0.192558 | − | 0.139902i | ||||
\(625\) | 0.309017 | − | 0.951057i | 0.0123607 | − | 0.0380423i | ||||
\(626\) | 36.0297 | 1.44004 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.44960 | −0.137654 | ||||||||
\(629\) | −11.2260 | + | 34.5501i | −0.447610 | + | 1.37760i | ||||
\(630\) | 10.6820 | − | 7.76094i | 0.425582 | − | 0.309203i | ||||
\(631\) | 25.8822 | + | 18.8046i | 1.03036 | + | 0.748597i | 0.968380 | − | 0.249480i | \(-0.0802598\pi\) |
0.0619761 | + | 0.998078i | \(0.480260\pi\) | |||||||
\(632\) | 12.5596 | + | 38.6546i | 0.499595 | + | 1.53760i | ||||
\(633\) | 4.88124 | + | 15.0229i | 0.194012 | + | 0.597107i | ||||
\(634\) | 6.35787 | + | 4.61926i | 0.252503 | + | 0.183454i | ||||
\(635\) | −1.97224 | + | 1.43292i | −0.0782661 | + | 0.0568637i | ||||
\(636\) | −0.0863323 | + | 0.265703i | −0.00342330 | + | 0.0105358i | ||||
\(637\) | 17.8866 | 0.708693 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.1594 | −0.876610 | ||||||||
\(640\) | 3.01183 | − | 9.26945i | 0.119053 | − | 0.366407i | ||||
\(641\) | −0.819410 | + | 0.595336i | −0.0323647 | + | 0.0235144i | −0.603850 | − | 0.797098i | \(-0.706367\pi\) |
0.571485 | + | 0.820612i | \(0.306367\pi\) | |||||||
\(642\) | −1.22359 | − | 0.888990i | −0.0482912 | − | 0.0350856i | ||||
\(643\) | −4.62674 | − | 14.2396i | −0.182461 | − | 0.561556i | 0.817435 | − | 0.576021i | \(-0.195395\pi\) |
−0.999895 | + | 0.0144651i | \(0.995395\pi\) | |||||||
\(644\) | −0.212508 | − | 0.654034i | −0.00837400 | − | 0.0257725i | ||||
\(645\) | 1.38214 | + | 1.00418i | 0.0544218 | + | 0.0395397i | ||||
\(646\) | −0.385178 | + | 0.279848i | −0.0151546 | + | 0.0110105i | ||||
\(647\) | 5.52749 | − | 17.0119i | 0.217308 | − | 0.668806i | −0.781674 | − | 0.623688i | \(-0.785634\pi\) |
0.998982 | − | 0.0451179i | \(-0.0143664\pi\) | |||||||
\(648\) | 17.9650 | 0.705732 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.83785 | −0.150533 | ||||||||
\(651\) | 4.39917 | − | 13.5393i | 0.172417 | − | 0.530645i | ||||
\(652\) | −2.09638 | + | 1.52311i | −0.0821006 | + | 0.0596495i | ||||
\(653\) | −37.0240 | − | 26.8995i | −1.44886 | − | 1.05266i | −0.986095 | − | 0.166181i | \(-0.946856\pi\) |
−0.462767 | − | 0.886480i | \(-0.653144\pi\) | |||||||
\(654\) | 1.47707 | + | 4.54594i | 0.0577579 | + | 0.177760i | ||||
\(655\) | 2.17596 | + | 6.69692i | 0.0850218 | + | 0.261670i | ||||
\(656\) | 24.5590 | + | 17.8432i | 0.958869 | + | 0.696659i | ||||
\(657\) | 2.85009 | − | 2.07071i | 0.111193 | − | 0.0807863i | ||||
\(658\) | 3.40152 | − | 10.4688i | 0.132605 | − | 0.408116i | ||||
\(659\) | 9.54036 | 0.371640 | 0.185820 | − | 0.982584i | \(-0.440506\pi\) | ||||
0.185820 | + | 0.982584i | \(0.440506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.7769 | 0.613651 | 0.306825 | − | 0.951766i | \(-0.400733\pi\) | ||||
0.306825 | + | 0.951766i | \(0.400733\pi\) | |||||||
\(662\) | 5.41377 | − | 16.6619i | 0.210412 | − | 0.647582i | ||||
\(663\) | 4.86617 | − | 3.53548i | 0.188986 | − | 0.137307i | ||||
\(664\) | −25.2419 | − | 18.3393i | −0.979575 | − | 0.711703i | ||||
\(665\) | −0.107275 | − | 0.330157i | −0.00415993 | − | 0.0128030i | ||||
\(666\) | 11.0012 | + | 33.8583i | 0.426289 | + | 1.31198i | ||||
\(667\) | −6.34999 | − | 4.61353i | −0.245872 | − | 0.178637i | ||||
\(668\) | −2.32307 | + | 1.68781i | −0.0898822 | + | 0.0653032i | ||||
\(669\) | −0.903757 | + | 2.78148i | −0.0349413 | + | 0.107538i | ||||
\(670\) | −18.1868 | −0.702616 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.92152 | −0.0741243 | ||||||||
\(673\) | −14.6175 | + | 44.9879i | −0.563462 | + | 1.73416i | 0.109016 | + | 0.994040i | \(0.465230\pi\) |
−0.672478 | + | 0.740117i | \(0.734770\pi\) | |||||||
\(674\) | −14.6806 | + | 10.6661i | −0.565475 | + | 0.410842i | ||||
\(675\) | 2.63930 | + | 1.91757i | 0.101587 | + | 0.0738072i | ||||
\(676\) | 0.249814 | + | 0.768850i | 0.00960825 | + | 0.0295711i | ||||
\(677\) | −8.51129 | − | 26.1950i | −0.327115 | − | 1.00676i | −0.970477 | − | 0.241195i | \(-0.922461\pi\) |
0.643361 | − | 0.765563i | \(-0.277539\pi\) | |||||||
\(678\) | 3.65155 | + | 2.65300i | 0.140237 | + | 0.101888i | ||||
\(679\) | 12.7880 | − | 9.29100i | 0.490757 | − | 0.356556i | ||||
\(680\) | 3.34410 | − | 10.2921i | 0.128240 | − | 0.394683i | ||||
\(681\) | −2.15223 | −0.0824736 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.1617 | −1.03931 | −0.519656 | − | 0.854375i | \(-0.673940\pi\) | ||||
−0.519656 | + | 0.854375i | \(0.673940\pi\) | |||||||
\(684\) | 0.0127204 | − | 0.0391494i | 0.000486377 | − | 0.00149691i | ||||
\(685\) | −7.74461 | + | 5.62678i | −0.295906 | + | 0.214988i | ||||
\(686\) | −2.72885 | − | 1.98262i | −0.104188 | − | 0.0756969i | ||||
\(687\) | 4.78811 | + | 14.7363i | 0.182678 | + | 0.562224i | ||||
\(688\) | −3.34780 | − | 10.3035i | −0.127634 | − | 0.392817i | ||||
\(689\) | −6.85696 | − | 4.98188i | −0.261229 | − | 0.189794i | ||||
\(690\) | −0.733524 | + | 0.532936i | −0.0279248 | + | 0.0202885i | ||||
\(691\) | −2.32591 | + | 7.15841i | −0.0884817 | + | 0.272319i | −0.985500 | − | 0.169674i | \(-0.945728\pi\) |
0.897018 | + | 0.441993i | \(0.145728\pi\) | |||||||
\(692\) | 2.57579 | 0.0979167 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.4541 | −0.434791 | ||||||||
\(695\) | 0.159299 | − | 0.490271i | 0.00604255 | − | 0.0185971i | ||||
\(696\) | −9.21706 | + | 6.69658i | −0.349372 | + | 0.253833i | ||||
\(697\) | 24.8453 | + | 18.0512i | 0.941083 | + | 0.683737i | ||||
\(698\) | −4.35634 | − | 13.4074i | −0.164890 | − | 0.507479i | ||||
\(699\) | −3.25739 | − | 10.0252i | −0.123206 | − | 0.379189i | ||||
\(700\) | 0.478730 | + | 0.347817i | 0.0180943 | + | 0.0131463i | ||||
\(701\) | −25.7435 | + | 18.7038i | −0.972319 | + | 0.706431i | −0.955979 | − | 0.293435i | \(-0.905201\pi\) |
−0.0163401 | + | 0.999866i | \(0.505201\pi\) | |||||||
\(702\) | 3.86903 | − | 11.9077i | 0.146027 | − | 0.449426i | ||||
\(703\) | 0.936004 | 0.0353021 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.28042 | 0.0482234 | ||||||||
\(706\) | −8.00454 | + | 24.6355i | −0.301255 | + | 0.927167i | ||||
\(707\) | 29.2460 | − | 21.2484i | 1.09991 | − | 0.799130i | ||||
\(708\) | −0.642341 | − | 0.466688i | −0.0241406 | − | 0.0175392i | ||||
\(709\) | −4.46162 | − | 13.7315i | −0.167560 | − | 0.515696i | 0.831656 | − | 0.555291i | \(-0.187393\pi\) |
−0.999216 | + | 0.0395951i | \(0.987393\pi\) | |||||||
\(710\) | 3.47838 | + | 10.7054i | 0.130541 | + | 0.401765i | ||||
\(711\) | 29.9384 | + | 21.7515i | 1.12278 | + | 0.815746i | ||||
\(712\) | 28.8385 | − | 20.9524i | 1.08077 | − | 0.785226i | ||||
\(713\) | 2.43427 | − | 7.49191i | 0.0911642 | − | 0.280574i | ||||
\(714\) | 10.5117 | 0.393392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.73721 | 0.102294 | ||||||||
\(717\) | 1.94836 | − | 5.99644i | 0.0727628 | − | 0.223941i | ||||
\(718\) | 4.84130 | − | 3.51741i | 0.180676 | − | 0.131269i | ||||
\(719\) | −4.37682 | − | 3.17994i | −0.163228 | − | 0.118592i | 0.503173 | − | 0.864186i | \(-0.332166\pi\) |
−0.666401 | + | 0.745594i | \(0.732166\pi\) | |||||||
\(720\) | −3.00970 | − | 9.26289i | −0.112165 | − | 0.345208i | ||||
\(721\) | 4.58525 | + | 14.1119i | 0.170763 | + | 0.525556i | ||||
\(722\) | −20.8286 | − | 15.1329i | −0.775160 | − | 0.563186i | ||||
\(723\) | −4.65325 | + | 3.38078i | −0.173056 | + | 0.125733i | ||||
\(724\) | 1.20693 | − | 3.71454i | 0.0448551 | − | 0.138050i | ||||
\(725\) | 6.75389 | 0.250833 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.7753 | −0.622161 | −0.311080 | − | 0.950384i | \(-0.600691\pi\) | ||||
−0.311080 | + | 0.950384i | \(0.600691\pi\) | |||||||
\(728\) | 9.35791 | − | 28.8007i | 0.346827 | − | 1.06742i | ||||
\(729\) | 8.67639 | − | 6.30377i | 0.321348 | − | 0.233473i | ||||
\(730\) | −1.44776 | − | 1.05186i | −0.0535841 | − | 0.0389311i | ||||
\(731\) | −3.38683 | − | 10.4236i | −0.125266 | − | 0.385530i | ||||
\(732\) | −0.244538 | − | 0.752611i | −0.00903839 | − | 0.0278173i | ||||
\(733\) | −11.3950 | − | 8.27899i | −0.420886 | − | 0.305791i | 0.357108 | − | 0.934063i | \(-0.383763\pi\) |
−0.777994 | + | 0.628272i | \(0.783763\pi\) | |||||||
\(734\) | −32.2029 | + | 23.3968i | −1.18863 | + | 0.863590i | ||||
\(735\) | −1.12361 | + | 3.45813i | −0.0414451 | + | 0.127555i | ||||
\(736\) | −1.06327 | −0.0391926 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 30.0956 | 1.10783 | ||||||||
\(739\) | 11.2314 | − | 34.5668i | 0.413155 | − | 1.27156i | −0.500736 | − | 0.865600i | \(-0.666937\pi\) |
0.913891 | − | 0.405960i | \(-0.133063\pi\) | |||||||
\(740\) | −1.29078 | + | 0.937809i | −0.0474501 | + | 0.0344745i | ||||
\(741\) | −0.125378 | − | 0.0910927i | −0.00460589 | − | 0.00334637i | ||||
\(742\) | −4.57722 | − | 14.0872i | −0.168035 | − | 0.517159i | ||||
\(743\) | 0.604796 | + | 1.86137i | 0.0221878 | + | 0.0682870i | 0.961537 | − | 0.274674i | \(-0.0885700\pi\) |
−0.939350 | + | 0.342961i | \(0.888570\pi\) | |||||||
\(744\) | −9.25047 | − | 6.72086i | −0.339139 | − | 0.246399i | ||||
\(745\) | 6.60144 | − | 4.79623i | 0.241858 | − | 0.175720i | ||||
\(746\) | −2.07988 | + | 6.40121i | −0.0761498 | + | 0.234365i | ||||
\(747\) | −28.4080 | −1.03939 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.07466 | −0.258503 | ||||||||
\(750\) | 0.241089 | − | 0.741996i | 0.00880333 | − | 0.0270939i | ||||
\(751\) | −15.1372 | + | 10.9978i | −0.552363 | + | 0.401316i | −0.828656 | − | 0.559758i | \(-0.810894\pi\) |
0.276293 | + | 0.961074i | \(0.410894\pi\) | |||||||
\(752\) | −6.56890 | − | 4.77258i | −0.239543 | − | 0.174038i | ||||
\(753\) | 1.71745 | + | 5.28577i | 0.0625874 | + | 0.192624i | ||||
\(754\) | −8.00985 | − | 24.6518i | −0.291702 | − | 0.897766i | ||||
\(755\) | −1.56968 | − | 1.14044i | −0.0571263 | − | 0.0415047i | ||||
\(756\) | −1.56179 | + | 1.13471i | −0.0568017 | + | 0.0412688i | ||||
\(757\) | −4.49528 | + | 13.8351i | −0.163384 | + | 0.502844i | −0.998914 | − | 0.0466015i | \(-0.985161\pi\) |
0.835530 | + | 0.549445i | \(0.185161\pi\) | |||||||
\(758\) | −10.7412 | −0.390138 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.278825 | −0.0101141 | ||||||||
\(761\) | −4.06066 | + | 12.4974i | −0.147199 | + | 0.453031i | −0.997287 | − | 0.0736088i | \(-0.976548\pi\) |
0.850088 | + | 0.526640i | \(0.176548\pi\) | |||||||
\(762\) | −1.53871 | + | 1.11794i | −0.0557415 | + | 0.0404986i | ||||
\(763\) | 18.0885 | + | 13.1421i | 0.654848 | + | 0.475775i | ||||
\(764\) | −0.269711 | − | 0.830086i | −0.00975782 | − | 0.0300315i | ||||
\(765\) | −3.04478 | − | 9.37087i | −0.110084 | − | 0.338805i | ||||
\(766\) | −26.8877 | − | 19.5351i | −0.971492 | − | 0.705831i | ||||
\(767\) | 19.4872 | − | 14.1583i | 0.703641 | − | 0.511225i | ||||
\(768\) | −0.687387 | + | 2.11556i | −0.0248040 | + | 0.0763387i | ||||
\(769\) | −38.9767 | −1.40554 | −0.702768 | − | 0.711419i | \(-0.748053\pi\) | ||||
−0.702768 | + | 0.711419i | \(0.748053\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.00099 | 0.216121 | ||||||||
\(772\) | 0.916145 | − | 2.81960i | 0.0329728 | − | 0.101480i | ||||
\(773\) | 31.3526 | − | 22.7790i | 1.12767 | − | 0.819303i | 0.142319 | − | 0.989821i | \(-0.454544\pi\) |
0.985355 | + | 0.170518i | \(0.0545442\pi\) | |||||||
\(774\) | −8.68930 | − | 6.31315i | −0.312331 | − | 0.226921i | ||||
\(775\) | 2.09463 | + | 6.44661i | 0.0752414 | + | 0.231569i | ||||
\(776\) | −3.92323 | − | 12.0745i | −0.140836 | − | 0.433448i | ||||
\(777\) | −16.7189 | − | 12.1470i | −0.599786 | − | 0.435770i | ||||
\(778\) | 5.98936 | − | 4.35152i | 0.214729 | − | 0.156010i | ||||
\(779\) | 0.244514 | − | 0.752538i | 0.00876064 | − | 0.0269625i | ||||
\(780\) | 0.264169 | 0.00945878 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 5.81665 | 0.208003 | ||||||||
\(783\) | −6.80876 | + | 20.9552i | −0.243325 | + | 0.748878i | ||||
\(784\) | 18.6542 | − | 13.5530i | 0.666220 | − | 0.484037i | ||||
\(785\) | 17.2114 | + | 12.5048i | 0.614302 | + | 0.446316i | ||||
\(786\) | 1.69764 | + | 5.22481i | 0.0605529 | + | 0.186363i | ||||
\(787\) | 6.60808 | + | 20.3376i | 0.235553 | + | 0.724957i | 0.997048 | + | 0.0767858i | \(0.0244657\pi\) |
−0.761495 | + | 0.648171i | \(0.775534\pi\) | |||||||
\(788\) | −0.347057 | − | 0.252152i | −0.0123634 | − | 0.00898254i | ||||
\(789\) | −5.10366 | + | 3.70803i | −0.181695 | + | 0.132009i | ||||
\(790\) | 5.80887 | − | 17.8779i | 0.206670 | − | 0.636066i | ||||
\(791\) | 21.1128 | 0.750686 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0075 | 0.852533 | ||||||||
\(794\) | 2.69560 | − | 8.29621i | 0.0956634 | − | 0.294422i | ||||
\(795\) | 1.39392 | − | 1.01274i | 0.0494374 | − | 0.0359184i | ||||
\(796\) | 0.856342 | + | 0.622169i | 0.0303522 | + | 0.0220522i | ||||
\(797\) | −0.687426 | − | 2.11568i | −0.0243499 | − | 0.0749412i | 0.938143 | − | 0.346248i | \(-0.112544\pi\) |
−0.962493 | + | 0.271306i | \(0.912544\pi\) | |||||||
\(798\) | −0.0836937 | − | 0.257583i | −0.00296272 | − | 0.00911833i | ||||
\(799\) | −6.64547 | − | 4.82822i | −0.235100 | − | 0.170810i | ||||
\(800\) | 0.740184 | − | 0.537775i | 0.0261695 | − | 0.0190132i | ||||
\(801\) | 10.0294 | − | 30.8673i | 0.354371 | − | 1.09064i | ||||
\(802\) | 19.9319 | 0.703821 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.25184 | 0.0441491 | ||||||||
\(805\) | −1.31059 | + | 4.03358i | −0.0461922 | + | 0.142165i | ||||
\(806\) | 21.0461 | − | 15.2909i | 0.741317 | − | 0.538598i | ||||
\(807\) | 0.0415975 | + | 0.0302224i | 0.00146430 | + | 0.00106388i | ||||
\(808\) | −8.97239 | − | 27.6142i | −0.315648 | − | 0.971463i | ||||
\(809\) | −6.54133 | − | 20.1321i | −0.229981 | − | 0.707809i | −0.997748 | − | 0.0670791i | \(-0.978632\pi\) |
0.767767 | − | 0.640730i | \(-0.221368\pi\) | |||||||
\(810\) | −6.72202 | − | 4.88383i | −0.236188 | − | 0.171600i | ||||
\(811\) | −29.7049 | + | 21.5818i | −1.04308 | + | 0.757841i | −0.970884 | − | 0.239550i | \(-0.923000\pi\) |
−0.0721943 | + | 0.997391i | \(0.523000\pi\) | |||||||
\(812\) | −1.23501 | + | 3.80096i | −0.0433402 | + | 0.133387i | ||||
\(813\) | 7.71135 | 0.270449 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.9810 | 0.559788 | ||||||||
\(816\) | 2.39608 | − | 7.37439i | 0.0838797 | − | 0.258155i | ||||
\(817\) | −0.228457 | + | 0.165983i | −0.00799269 | + | 0.00580703i | ||||
\(818\) | −4.82111 | − | 3.50274i | −0.168566 | − | 0.122471i | ||||
\(819\) | −8.52032 | − | 26.2228i | −0.297724 | − | 0.916300i | ||||
\(820\) | 0.416795 | + | 1.28276i | 0.0145551 | + | 0.0447960i | ||||
\(821\) | −32.0932 | − | 23.3170i | −1.12006 | − | 0.813771i | −0.135841 | − | 0.990731i | \(-0.543374\pi\) |
−0.984218 | + | 0.176960i | \(0.943374\pi\) | |||||||
\(822\) | −6.04220 | + | 4.38991i | −0.210746 | + | 0.153116i | ||||
\(823\) | −14.1926 | + | 43.6804i | −0.494724 | + | 1.52260i | 0.322662 | + | 0.946514i | \(0.395422\pi\) |
−0.817386 | + | 0.576090i | \(0.804578\pi\) | |||||||
\(824\) | 11.9178 | 0.415178 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 42.0956 | 1.46469 | ||||||||
\(827\) | 12.2664 | − | 37.7521i | 0.426545 | − | 1.31277i | −0.474962 | − | 0.880006i | \(-0.657538\pi\) |
0.901507 | − | 0.432764i | \(-0.142462\pi\) | |||||||
\(828\) | −0.406861 | + | 0.295601i | −0.0141394 | + | 0.0102729i | ||||
\(829\) | −6.19370 | − | 4.49999i | −0.215116 | − | 0.156291i | 0.475009 | − | 0.879981i | \(-0.342445\pi\) |
−0.690125 | + | 0.723690i | \(0.742445\pi\) | |||||||
\(830\) | 4.45925 | + | 13.7241i | 0.154783 | + | 0.476372i | ||||
\(831\) | 0.694754 | + | 2.13823i | 0.0241007 | + | 0.0741745i | ||||
\(832\) | −19.5572 | − | 14.2091i | −0.678022 | − | 0.492612i | ||||
\(833\) | 18.8716 | − | 13.7110i | 0.653862 | − | 0.475059i | ||||
\(834\) | 0.124282 | − | 0.382501i | 0.00430353 | − | 0.0132449i | ||||
\(835\) | 17.7090 | 0.612846 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.1135 | −0.764354 | ||||||||
\(838\) | −7.47894 | + | 23.0178i | −0.258356 | + | 0.795137i | ||||
\(839\) | −22.3197 | + | 16.2162i | −0.770561 | + | 0.559845i | −0.902131 | − | 0.431462i | \(-0.857998\pi\) |
0.131571 | + | 0.991307i | \(0.457998\pi\) | |||||||
\(840\) | 4.98037 | + | 3.61845i | 0.171839 | + | 0.124848i | ||||
\(841\) | 5.13432 | + | 15.8018i | 0.177046 | + | 0.544891i | ||||
\(842\) | 2.02280 | + | 6.22554i | 0.0697103 | + | 0.214546i | ||||
\(843\) | −0.715803 | − | 0.520061i | −0.0246536 | − | 0.0179119i | ||||
\(844\) | 3.60060 | − | 2.61599i | 0.123938 | − | 0.0900460i | ||||
\(845\) | 1.54066 | − | 4.74168i | 0.0530005 | − | 0.163119i | ||||
\(846\) | −8.04979 | −0.276757 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.9261 | −0.375203 | ||||||||
\(849\) | 0.962401 | − | 2.96196i | 0.0330295 | − | 0.101654i | ||||
\(850\) | −4.04920 | + | 2.94192i | −0.138886 | + | 0.100907i | ||||
\(851\) | −9.25135 | − | 6.72150i | −0.317132 | − | 0.230410i | ||||
\(852\) | −0.239426 | − | 0.736878i | −0.00820261 | − | 0.0252450i | ||||
\(853\) | −13.0250 | − | 40.0867i | −0.445966 | − | 1.37254i | −0.881421 | − | 0.472331i | \(-0.843413\pi\) |
0.435455 | − | 0.900210i | \(-0.356587\pi\) | |||||||
\(854\) | 33.9430 | + | 24.6611i | 1.16151 | + | 0.843884i | ||||
\(855\) | −0.205384 | + | 0.149220i | −0.00702398 | + | 0.00510322i | ||||
\(856\) | −1.75592 | + | 5.40418i | −0.0600162 | + | 0.184711i | ||||
\(857\) | 45.0850 | 1.54008 | 0.770038 | − | 0.637998i | \(-0.220237\pi\) | ||||
0.770038 | + | 0.637998i | \(0.220237\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.8257 | −0.403488 | −0.201744 | − | 0.979438i | \(-0.564661\pi\) | ||||
−0.201744 | + | 0.979438i | \(0.564661\pi\) | |||||||
\(860\) | 0.148746 | − | 0.457794i | 0.00507221 | − | 0.0156107i | ||||
\(861\) | −14.1336 | + | 10.2686i | −0.481670 | + | 0.349954i | ||||
\(862\) | 27.2808 | + | 19.8207i | 0.929189 | + | 0.675095i | ||||
\(863\) | 8.61271 | + | 26.5072i | 0.293180 | + | 0.902315i | 0.983827 | + | 0.179123i | \(0.0573260\pi\) |
−0.690647 | + | 0.723192i | \(0.742674\pi\) | |||||||
\(864\) | 0.922352 | + | 2.83871i | 0.0313790 | + | 0.0965747i | ||||
\(865\) | −12.8516 | − | 9.33725i | −0.436968 | − | 0.317476i | ||||
\(866\) | −23.3065 | + | 16.9332i | −0.791987 | + | 0.575412i | ||||
\(867\) | −0.599217 | + | 1.84420i | −0.0203505 | + | 0.0626323i | ||||
\(868\) | −4.01105 | −0.136144 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 5.26926 | 0.178645 | ||||||||
\(871\) | −11.7359 | + | 36.1193i | −0.397655 | + | 1.22386i | ||||
\(872\) | 14.5285 | − | 10.5556i | 0.491997 | − | 0.357457i | ||||
\(873\) | −9.35181 | − | 6.79449i | −0.316511 | − | 0.229959i | ||||
\(874\) | −0.0463117 | − | 0.142533i | −0.00156652 | − | 0.00482124i | ||||
\(875\) | −1.12773 | − | 3.47080i | −0.0381243 | − | 0.117334i | ||||
\(876\) | 0.0996532 | + | 0.0724023i | 0.00336697 | + | 0.00244625i | ||||
\(877\) | −9.26093 | + | 6.72846i | −0.312720 | + | 0.227204i | −0.733063 | − | 0.680161i | \(-0.761910\pi\) |
0.420343 | + | 0.907365i | \(0.361910\pi\) | |||||||
\(878\) | −6.66592 | + | 20.5156i | −0.224964 | + | 0.692367i | ||||
\(879\) | −6.57011 | −0.221604 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.0037 | 1.58360 | 0.791798 | − | 0.610783i | \(-0.209145\pi\) | ||||
0.791798 | + | 0.610783i | \(0.209145\pi\) | |||||||
\(882\) | 7.06399 | − | 21.7407i | 0.237857 | − | 0.732048i | ||||
\(883\) | 37.9547 | − | 27.5757i | 1.27728 | − | 0.927997i | 0.277811 | − | 0.960636i | \(-0.410391\pi\) |
0.999467 | + | 0.0326386i | \(0.0103910\pi\) | |||||||
\(884\) | −1.37106 | − | 0.996133i | −0.0461137 | − | 0.0335036i | ||||
\(885\) | 1.51315 | + | 4.65698i | 0.0508638 | + | 0.156543i | ||||
\(886\) | −11.0126 | − | 33.8932i | −0.369975 | − | 1.13867i | ||||
\(887\) | −22.5252 | − | 16.3655i | −0.756322 | − | 0.549500i | 0.141458 | − | 0.989944i | \(-0.454821\pi\) |
−0.897780 | + | 0.440444i | \(0.854821\pi\) | |||||||
\(888\) | −13.4284 | + | 9.75631i | −0.450628 | + | 0.327400i | ||||
\(889\) | −2.74921 | + | 8.46121i | −0.0922057 | + | 0.283780i | ||||
\(890\) | −16.4866 | −0.552631 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.824022 | 0.0275903 | ||||||||
\(893\) | −0.0654012 | + | 0.201284i | −0.00218857 | + | 0.00673572i | ||||
\(894\) | 5.15032 | − | 3.74193i | 0.172252 | − | 0.125149i | ||||
\(895\) | −13.6570 | − | 9.92242i | −0.456505 | − | 0.331670i | ||||
\(896\) | −10.9914 | − | 33.8281i | −0.367197 | − | 1.13012i | ||||
\(897\) | 0.585082 | + | 1.80070i | 0.0195353 | + | 0.0601235i | ||||
\(898\) | −8.98207 | − | 6.52586i | −0.299736 | − | 0.217771i | ||||
\(899\) | −37.0371 | + | 26.9090i | −1.23526 | + | 0.897466i | ||||
\(900\) | 0.133724 | − | 0.411560i | 0.00445746 | − | 0.0137187i | ||||
\(901\) | −11.0534 | −0.368244 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.23473 | 0.207479 | ||||||||
\(904\) | 5.24018 | − | 16.1276i | 0.174286 | − | 0.536397i | ||||
\(905\) | −19.4871 | + | 14.1582i | −0.647773 | + | 0.470635i | ||||
\(906\) | −1.22463 | − | 0.889747i | −0.0406856 | − | 0.0295598i | ||||
\(907\) | −8.84508 | − | 27.2224i | −0.293696 | − | 0.903904i | −0.983656 | − | 0.180056i | \(-0.942372\pi\) |
0.689960 | − | 0.723847i | \(-0.257628\pi\) | |||||||
\(908\) | 0.187387 | + | 0.576719i | 0.00621867 | + | 0.0191391i | ||||
\(909\) | −21.3875 | − | 15.5389i | −0.709379 | − | 0.515394i | ||||
\(910\) | −11.3310 | + | 8.23247i | −0.375620 | + | 0.272904i | ||||
\(911\) | 1.58471 | − | 4.87724i | 0.0525038 | − | 0.161590i | −0.921367 | − | 0.388695i | \(-0.872926\pi\) |
0.973870 | + | 0.227105i | \(0.0729260\pi\) | |||||||
\(912\) | −0.199781 | −0.00661542 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 16.1547 | 0.534351 | ||||||||
\(915\) | −1.50812 | + | 4.64153i | −0.0498571 | + | 0.153444i | ||||
\(916\) | 3.53190 | − | 2.56608i | 0.116697 | − | 0.0847855i | ||||
\(917\) | 20.7898 | + | 15.1046i | 0.686538 | + | 0.498799i | ||||
\(918\) | −5.04575 | − | 15.5292i | −0.166535 | − | 0.512541i | ||||
\(919\) | −10.9024 | − | 33.5542i | −0.359638 | − | 1.10685i | −0.953271 | − | 0.302116i | \(-0.902307\pi\) |
0.593634 | − | 0.804735i | \(-0.297693\pi\) | |||||||
\(920\) | 2.75587 | + | 2.00226i | 0.0908585 | + | 0.0660126i | ||||
\(921\) | −1.97877 | + | 1.43766i | −0.0652026 | + | 0.0473725i | ||||
\(922\) | 2.91645 | − | 8.97591i | 0.0960481 | − | 0.295606i | ||||
\(923\) | 23.5057 | 0.773699 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.83980 | 0.323531 | ||||||||
\(926\) | −5.22660 | + | 16.0858i | −0.171757 | + | 0.528613i | ||||
\(927\) | 8.77874 | − | 6.37813i | 0.288332 | − | 0.209485i | ||||
\(928\) | 4.99912 | + | 3.63208i | 0.164104 | + | 0.119229i | ||||
\(929\) | −18.2761 | − | 56.2480i | −0.599619 | − | 1.84544i | −0.530240 | − | 0.847848i | \(-0.677898\pi\) |
−0.0693793 | − | 0.997590i | \(-0.522102\pi\) | |||||||
\(930\) | 1.63419 | + | 5.02953i | 0.0535873 | + | 0.164925i | ||||
\(931\) | −0.486233 | − | 0.353269i | −0.0159356 | − | 0.0115779i | ||||
\(932\) | −2.40278 | + | 1.74572i | −0.0787058 | + | 0.0571831i | ||||
\(933\) | −2.95556 | + | 9.09627i | −0.0967606 | + | 0.297799i | ||||
\(934\) | 8.33220 | 0.272638 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −22.1458 | −0.723857 | ||||||||
\(937\) | −4.46299 | + | 13.7357i | −0.145800 | + | 0.448725i | −0.997113 | − | 0.0759326i | \(-0.975807\pi\) |
0.851313 | + | 0.524657i | \(0.175807\pi\) | |||||||
\(938\) | −53.6953 | + | 39.0119i | −1.75321 | + | 1.27378i | ||||
\(939\) | 12.3738 | + | 8.99009i | 0.403804 | + | 0.293381i | ||||
\(940\) | −0.111482 | − | 0.343105i | −0.00363613 | − | 0.0111909i | ||||
\(941\) | 5.76598 | + | 17.7459i | 0.187966 | + | 0.578499i | 0.999987 | − | 0.00512923i | \(-0.00163269\pi\) |
−0.812021 | + | 0.583628i | \(0.801633\pi\) | |||||||
\(942\) | 13.4280 | + | 9.75603i | 0.437509 | + | 0.317869i | ||||
\(943\) | −7.82077 | + | 5.68212i | −0.254679 | + | 0.185035i | ||||
\(944\) | 9.59542 | − | 29.5317i | 0.312304 | − | 0.961173i | ||||
\(945\) | 11.9057 | 0.387292 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.991391 | −0.0322159 | −0.0161079 | − | 0.999870i | \(-0.505128\pi\) | ||||
−0.0161079 | + | 0.999870i | \(0.505128\pi\) | |||||||
\(948\) | −0.399840 | + | 1.23058i | −0.0129862 | + | 0.0399674i | ||||
\(949\) | −3.02326 | + | 2.19652i | −0.0981390 | + | 0.0713022i | ||||
\(950\) | 0.104329 | + | 0.0757994i | 0.00338488 | + | 0.00245926i | ||||
\(951\) | 1.03091 | + | 3.17282i | 0.0334296 | + | 0.102886i | ||||
\(952\) | −12.2040 | − | 37.5601i | −0.395534 | − | 1.21733i | ||||
\(953\) | −6.68575 | − | 4.85748i | −0.216573 | − | 0.157349i | 0.474210 | − | 0.880412i | \(-0.342734\pi\) |
−0.690783 | + | 0.723063i | \(0.742734\pi\) | |||||||
\(954\) | −8.76338 | + | 6.36697i | −0.283725 | + | 0.206138i | ||||
\(955\) | −1.66337 | + | 5.11934i | −0.0538255 | + | 0.165658i | ||||
\(956\) | −1.77646 | −0.0574549 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.0881 | 0.972101 | ||||||||
\(959\) | −10.7956 | + | 33.2255i | −0.348608 | + | 1.07291i | ||||
\(960\) | 3.97569 | − | 2.88851i | 0.128315 | − | 0.0932263i | ||||
\(961\) | −12.0918 | − | 8.78523i | −0.390059 | − | 0.283394i | ||||
\(962\) | −11.6696 | − | 35.9154i | −0.376244 | − | 1.15796i | ||||
\(963\) | 1.59876 | + | 4.92047i | 0.0515192 | + | 0.158560i | ||||
\(964\) | 1.31107 | + | 0.952547i | 0.0422267 | + | 0.0306795i | ||||
\(965\) | −14.7921 | + | 10.7471i | −0.476175 | + | 0.345961i | ||||
\(966\) | −1.02250 | + | 3.14692i | −0.0328983 | + | 0.101251i | ||||
\(967\) | −7.36029 | −0.236691 | −0.118345 | − | 0.992972i | \(-0.537759\pi\) | ||||
−0.118345 | + | 0.992972i | \(0.537759\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.202110 | −0.00649271 | ||||||||
\(970\) | −1.81451 | + | 5.58448i | −0.0582603 | + | 0.179307i | ||||
\(971\) | 4.02674 | − | 2.92560i | 0.129224 | − | 0.0938870i | −0.521296 | − | 0.853376i | \(-0.674551\pi\) |
0.650520 | + | 0.759489i | \(0.274551\pi\) | |||||||
\(972\) | 1.74656 | + | 1.26895i | 0.0560210 | + | 0.0407016i | ||||
\(973\) | −0.581347 | − | 1.78920i | −0.0186371 | − | 0.0573592i | ||||
\(974\) | 14.3401 | + | 44.1343i | 0.459487 | + | 1.41416i | ||||
\(975\) | −1.31805 | − | 0.957617i | −0.0422113 | − | 0.0306683i | ||||
\(976\) | 25.0378 | − | 18.1910i | 0.801439 | − | 0.582280i | ||||
\(977\) | 3.19425 | − | 9.83089i | 0.102193 | − | 0.314518i | −0.886868 | − | 0.462022i | \(-0.847124\pi\) |
0.989061 | + | 0.147504i | \(0.0471240\pi\) | |||||||
\(978\) | 12.4680 | 0.398684 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.02448 | 0.0327259 | ||||||||
\(981\) | 5.05268 | − | 15.5506i | 0.161320 | − | 0.496491i | ||||
\(982\) | 18.6403 | − | 13.5430i | 0.594836 | − | 0.432174i | ||||
\(983\) | 23.5111 | + | 17.0818i | 0.749888 | + | 0.544826i | 0.895792 | − | 0.444473i | \(-0.146609\pi\) |
−0.145904 | + | 0.989299i | \(0.546609\pi\) | |||||||
\(984\) | 4.33604 | + | 13.3450i | 0.138228 | + | 0.425422i | ||||
\(985\) | 0.817554 | + | 2.51617i | 0.0260494 | + | 0.0801719i | ||||
\(986\) | −27.3479 | − | 19.8694i | −0.870933 | − | 0.632770i | ||||
\(987\) | 3.78036 | − | 2.74659i | 0.120330 | − | 0.0874249i | ||||
\(988\) | −0.0134932 | + | 0.0415279i | −0.000429277 | + | 0.00132118i | ||||
\(989\) | 3.44997 | 0.109703 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.70381 | 0.244719 | 0.122360 | − | 0.992486i | \(-0.460954\pi\) | ||||
0.122360 | + | 0.992486i | \(0.460954\pi\) | |||||||
\(992\) | −1.91642 | + | 5.89812i | −0.0608463 | + | 0.187266i | ||||
\(993\) | 6.01672 | − | 4.37141i | 0.190935 | − | 0.138722i | ||||
\(994\) | 33.2335 | + | 24.1455i | 1.05410 | + | 0.765850i | ||||
\(995\) | −2.01726 | − | 6.20849i | −0.0639515 | − | 0.196823i | ||||
\(996\) | −0.306941 | − | 0.944669i | −0.00972581 | − | 0.0299330i | ||||
\(997\) | −2.31717 | − | 1.68352i | −0.0733855 | − | 0.0533177i | 0.550488 | − | 0.834843i | \(-0.314442\pi\) |
−0.623873 | + | 0.781526i | \(0.714442\pi\) | |||||||
\(998\) | 5.73548 | − | 4.16707i | 0.181554 | − | 0.131906i | ||||
\(999\) | −9.91974 | + | 30.5298i | −0.313847 | + | 0.965921i |
(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 | 605.2.g.e.251.1 | 8 | ||
11.2 | odd | 10 | 55.2.g.b.36.1 | yes | 8 | ||
11.3 | even | 5 | 605.2.g.k.81.2 | 8 | |||
11.4 | even | 5 | 605.2.a.k.1.1 | 4 | |||
11.5 | even | 5 | inner | 605.2.g.e.511.1 | 8 | ||
11.6 | odd | 10 | 605.2.g.m.511.2 | 8 | |||
11.7 | odd | 10 | 605.2.a.j.1.4 | 4 | |||
11.8 | odd | 10 | 55.2.g.b.26.1 | ✓ | 8 | ||
11.9 | even | 5 | 605.2.g.k.366.2 | 8 | |||
11.10 | odd | 2 | 605.2.g.m.251.2 | 8 | |||
33.2 | even | 10 | 495.2.n.e.91.2 | 8 | |||
33.8 | even | 10 | 495.2.n.e.136.2 | 8 | |||
33.26 | odd | 10 | 5445.2.a.bi.1.4 | 4 | |||
33.29 | even | 10 | 5445.2.a.bp.1.1 | 4 | |||
44.7 | even | 10 | 9680.2.a.cn.1.2 | 4 | |||
44.15 | odd | 10 | 9680.2.a.cm.1.2 | 4 | |||
44.19 | even | 10 | 880.2.bo.h.81.1 | 8 | |||
44.35 | even | 10 | 880.2.bo.h.641.1 | 8 | |||
55.2 | even | 20 | 275.2.z.a.124.1 | 16 | |||
55.4 | even | 10 | 3025.2.a.w.1.4 | 4 | |||
55.8 | even | 20 | 275.2.z.a.224.1 | 16 | |||
55.13 | even | 20 | 275.2.z.a.124.4 | 16 | |||
55.19 | odd | 10 | 275.2.h.a.26.2 | 8 | |||
55.24 | odd | 10 | 275.2.h.a.201.2 | 8 | |||
55.29 | odd | 10 | 3025.2.a.bd.1.1 | 4 | |||
55.52 | even | 20 | 275.2.z.a.224.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.b.26.1 | ✓ | 8 | 11.8 | odd | 10 | ||
55.2.g.b.36.1 | yes | 8 | 11.2 | odd | 10 | ||
275.2.h.a.26.2 | 8 | 55.19 | odd | 10 | |||
275.2.h.a.201.2 | 8 | 55.24 | odd | 10 | |||
275.2.z.a.124.1 | 16 | 55.2 | even | 20 | |||
275.2.z.a.124.4 | 16 | 55.13 | even | 20 | |||
275.2.z.a.224.1 | 16 | 55.8 | even | 20 | |||
275.2.z.a.224.4 | 16 | 55.52 | even | 20 | |||
495.2.n.e.91.2 | 8 | 33.2 | even | 10 | |||
495.2.n.e.136.2 | 8 | 33.8 | even | 10 | |||
605.2.a.j.1.4 | 4 | 11.7 | odd | 10 | |||
605.2.a.k.1.1 | 4 | 11.4 | even | 5 | |||
605.2.g.e.251.1 | 8 | 1.1 | even | 1 | trivial | ||
605.2.g.e.511.1 | 8 | 11.5 | even | 5 | inner | ||
605.2.g.k.81.2 | 8 | 11.3 | even | 5 | |||
605.2.g.k.366.2 | 8 | 11.9 | even | 5 | |||
605.2.g.m.251.2 | 8 | 11.10 | odd | 2 | |||
605.2.g.m.511.2 | 8 | 11.6 | odd | 10 | |||
880.2.bo.h.81.1 | 8 | 44.19 | even | 10 | |||
880.2.bo.h.641.1 | 8 | 44.35 | even | 10 | |||
3025.2.a.w.1.4 | 4 | 55.4 | even | 10 | |||
3025.2.a.bd.1.1 | 4 | 55.29 | odd | 10 | |||
5445.2.a.bi.1.4 | 4 | 33.26 | odd | 10 | |||
5445.2.a.bp.1.1 | 4 | 33.29 | even | 10 | |||
9680.2.a.cm.1.2 | 4 | 44.15 | odd | 10 | |||
9680.2.a.cn.1.2 | 4 | 44.7 | even | 10 |