Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [152,2,Mod(77,152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("152.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 152.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.21372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 77.5 | ||
Root | \(1.14052 + 0.836196i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 152.77 |
Dual form | 152.2.c.b.77.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).
\(n\) | \(39\) | \(77\) | \(97\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.836196 | − | 1.14052i | −0.591280 | − | 0.806467i | ||||
\(3\) | 3.13611i | 1.81063i | 0.424735 | + | 0.905317i | \(0.360367\pi\) | ||||
−0.424735 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(4\) | −0.601554 | + | 1.90739i | −0.300777 | + | 0.953695i | ||||
\(5\) | − | 0.594041i | − | 0.265663i | −0.991139 | − | 0.132832i | \(-0.957593\pi\) | ||
0.991139 | − | 0.132832i | \(-0.0424069\pi\) | |||||||
\(6\) | 3.57679 | − | 2.62240i | 1.46022 | − | 1.07059i | ||||
\(7\) | −3.48756 | −1.31818 | −0.659088 | − | 0.752066i | \(-0.729057\pi\) | ||||
−0.659088 | + | 0.752066i | \(0.729057\pi\) | |||||||
\(8\) | 2.67842 | − | 0.908869i | 0.946966 | − | 0.321334i | ||||
\(9\) | −6.83520 | −2.27840 | ||||||||
\(10\) | −0.677513 | + | 0.496734i | −0.214248 | + | 0.157081i | ||||
\(11\) | 4.83520i | 1.45787i | 0.684585 | + | 0.728933i | \(0.259984\pi\) | ||||
−0.684585 | + | 0.728933i | \(0.740016\pi\) | |||||||
\(12\) | −5.98179 | − | 1.88654i | −1.72679 | − | 0.544597i | ||||
\(13\) | 0.215597i | 0.0597957i | 0.999553 | + | 0.0298979i | \(0.00951821\pi\) | ||||
−0.999553 | + | 0.0298979i | \(0.990482\pi\) | |||||||
\(14\) | 2.91629 | + | 3.97762i | 0.779410 | + | 1.06306i | ||||
\(15\) | 1.86298 | 0.481019 | ||||||||
\(16\) | −3.27627 | − | 2.29479i | −0.819067 | − | 0.573699i | ||||
\(17\) | 1.29720 | 0.314618 | 0.157309 | − | 0.987549i | \(-0.449718\pi\) | ||||
0.157309 | + | 0.987549i | \(0.449718\pi\) | |||||||
\(18\) | 5.71556 | + | 7.79565i | 1.34717 | + | 1.83745i | ||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 1.13307 | + | 0.357348i | 0.253362 | + | 0.0799053i | ||||
\(21\) | − | 10.9374i | − | 2.38673i | ||||||
\(22\) | 5.51462 | − | 4.04317i | 1.17572 | − | 0.862007i | ||||
\(23\) | 4.52815 | 0.944184 | 0.472092 | − | 0.881549i | \(-0.343499\pi\) | ||||
0.472092 | + | 0.881549i | \(0.343499\pi\) | |||||||
\(24\) | 2.85031 | + | 8.39984i | 0.581818 | + | 1.71461i | ||||
\(25\) | 4.64712 | 0.929423 | ||||||||
\(26\) | 0.245891 | − | 0.180281i | 0.0482233 | − | 0.0353560i | ||||
\(27\) | − | 12.0276i | − | 2.31471i | ||||||
\(28\) | 2.09796 | − | 6.65214i | 0.396477 | − | 1.25714i | ||||
\(29\) | 9.41093i | 1.74757i | 0.486316 | + | 0.873783i | \(0.338340\pi\) | ||||
−0.486316 | + | 0.873783i | \(0.661660\pi\) | |||||||
\(30\) | −1.55781 | − | 2.12476i | −0.284417 | − | 0.387926i | ||||
\(31\) | −1.22031 | −0.219174 | −0.109587 | − | 0.993977i | \(-0.534953\pi\) | ||||
−0.109587 | + | 0.993977i | \(0.534953\pi\) | |||||||
\(32\) | 0.122350 | + | 5.65553i | 0.0216286 | + | 0.999766i | ||||
\(33\) | −15.1637 | −2.63966 | ||||||||
\(34\) | −1.08471 | − | 1.47948i | −0.186027 | − | 0.253729i | ||||
\(35\) | 2.07176i | 0.350191i | ||||||||
\(36\) | 4.11174 | − | 13.0374i | 0.685290 | − | 2.17290i | ||||
\(37\) | − | 5.62653i | − | 0.924995i | −0.886621 | − | 0.462498i | \(-0.846953\pi\) | ||
0.886621 | − | 0.462498i | \(-0.153047\pi\) | |||||||
\(38\) | 1.14052 | − | 0.836196i | 0.185016 | − | 0.135649i | ||||
\(39\) | −0.676135 | −0.108268 | ||||||||
\(40\) | −0.539905 | − | 1.59109i | −0.0853665 | − | 0.251574i | ||||
\(41\) | −0.450021 | −0.0702815 | −0.0351407 | − | 0.999382i | \(-0.511188\pi\) | ||||
−0.0351407 | + | 0.999382i | \(0.511188\pi\) | |||||||
\(42\) | −12.4743 | + | 9.14580i | −1.92482 | + | 1.41123i | ||||
\(43\) | − | 0.794359i | − | 0.121139i | −0.998164 | − | 0.0605693i | \(-0.980708\pi\) | ||
0.998164 | − | 0.0605693i | \(-0.0192916\pi\) | |||||||
\(44\) | −9.22260 | − | 2.90863i | −1.39036 | − | 0.438493i | ||||
\(45\) | 4.06039i | 0.605287i | ||||||||
\(46\) | −3.78642 | − | 5.16442i | −0.558277 | − | 0.761453i | ||||
\(47\) | 12.1986 | 1.77935 | 0.889676 | − | 0.456593i | \(-0.150930\pi\) | ||||
0.889676 | + | 0.456593i | \(0.150930\pi\) | |||||||
\(48\) | 7.19673 | − | 10.2747i | 1.03876 | − | 1.48303i | ||||
\(49\) | 5.16310 | 0.737586 | ||||||||
\(50\) | −3.88590 | − | 5.30011i | −0.549549 | − | 0.749549i | ||||
\(51\) | 4.06817i | 0.569658i | ||||||||
\(52\) | −0.411227 | − | 0.129693i | −0.0570269 | − | 0.0179852i | ||||
\(53\) | − | 2.56409i | − | 0.352205i | −0.984372 | − | 0.176103i | \(-0.943651\pi\) | ||
0.984372 | − | 0.176103i | \(-0.0563490\pi\) | |||||||
\(54\) | −13.7177 | + | 10.0574i | −1.86674 | + | 1.36864i | ||||
\(55\) | 2.87231 | 0.387302 | ||||||||
\(56\) | −9.34118 | + | 3.16974i | −1.24827 | + | 0.423574i | ||||
\(57\) | −3.13611 | −0.415388 | ||||||||
\(58\) | 10.7333 | − | 7.86938i | 1.40935 | − | 1.03330i | ||||
\(59\) | − | 2.75191i | − | 0.358268i | −0.983825 | − | 0.179134i | \(-0.942670\pi\) | ||
0.983825 | − | 0.179134i | \(-0.0573295\pi\) | |||||||
\(60\) | −1.12068 | + | 3.55343i | −0.144679 | + | 0.458745i | ||||
\(61\) | 7.76665i | 0.994417i | 0.867631 | + | 0.497209i | \(0.165642\pi\) | ||||
−0.867631 | + | 0.497209i | \(0.834358\pi\) | |||||||
\(62\) | 1.02042 | + | 1.39178i | 0.129593 | + | 0.176757i | ||||
\(63\) | 23.8382 | 3.00333 | ||||||||
\(64\) | 6.34792 | − | 4.86867i | 0.793489 | − | 0.608584i | ||||
\(65\) | 0.128073 | 0.0158855 | ||||||||
\(66\) | 12.6798 | + | 17.2945i | 1.56078 | + | 2.12880i | ||||
\(67\) | − | 4.11631i | − | 0.502887i | −0.967872 | − | 0.251443i | \(-0.919095\pi\) | ||
0.967872 | − | 0.251443i | \(-0.0809053\pi\) | |||||||
\(68\) | −0.780337 | + | 2.47427i | −0.0946297 | + | 0.300049i | ||||
\(69\) | 14.2008i | 1.70957i | ||||||||
\(70\) | 2.36287 | − | 1.73239i | 0.282417 | − | 0.207061i | ||||
\(71\) | −7.82788 | −0.928999 | −0.464499 | − | 0.885573i | \(-0.653766\pi\) | ||||
−0.464499 | + | 0.885573i | \(0.653766\pi\) | |||||||
\(72\) | −18.3076 | + | 6.21230i | −2.15757 | + | 0.732126i | ||||
\(73\) | 3.08931 | 0.361577 | 0.180788 | − | 0.983522i | \(-0.442135\pi\) | ||||
0.180788 | + | 0.983522i | \(0.442135\pi\) | |||||||
\(74\) | −6.41714 | + | 4.70488i | −0.745978 | + | 0.546931i | ||||
\(75\) | 14.5739i | 1.68285i | ||||||||
\(76\) | −1.90739 | − | 0.601554i | −0.218793 | − | 0.0690030i | ||||
\(77\) | − | 16.8631i | − | 1.92172i | ||||||
\(78\) | 0.565381 | + | 0.771143i | 0.0640168 | + | 0.0873147i | ||||
\(79\) | −10.0731 | −1.13331 | −0.566654 | − | 0.823956i | \(-0.691763\pi\) | ||||
−0.566654 | + | 0.823956i | \(0.691763\pi\) | |||||||
\(80\) | −1.36320 | + | 1.94624i | −0.152411 | + | 0.217596i | ||||
\(81\) | 17.2143 | 1.91270 | ||||||||
\(82\) | 0.376306 | + | 0.513256i | 0.0415560 | + | 0.0566797i | ||||
\(83\) | 11.6296i | 1.27651i | 0.769825 | + | 0.638255i | \(0.220343\pi\) | ||||
−0.769825 | + | 0.638255i | \(0.779657\pi\) | |||||||
\(84\) | 20.8619 | + | 6.57943i | 2.27622 | + | 0.717875i | ||||
\(85\) | − | 0.770591i | − | 0.0835823i | ||||||
\(86\) | −0.905979 | + | 0.664240i | −0.0976943 | + | 0.0716268i | ||||
\(87\) | −29.5137 | −3.16420 | ||||||||
\(88\) | 4.39456 | + | 12.9507i | 0.468462 | + | 1.38055i | ||||
\(89\) | 13.7091 | 1.45317 | 0.726583 | − | 0.687079i | \(-0.241107\pi\) | ||||
0.726583 | + | 0.687079i | \(0.241107\pi\) | |||||||
\(90\) | 4.63094 | − | 3.39528i | 0.488144 | − | 0.357894i | ||||
\(91\) | − | 0.751907i | − | 0.0788213i | ||||||
\(92\) | −2.72392 | + | 8.63694i | −0.283989 | + | 0.900463i | ||||
\(93\) | − | 3.82703i | − | 0.396845i | ||||||
\(94\) | −10.2004 | − | 13.9127i | −1.05209 | − | 1.43499i | ||||
\(95\) | 0.594041 | 0.0609473 | ||||||||
\(96\) | −17.7364 | + | 0.383702i | −1.81021 | + | 0.0391615i | ||||
\(97\) | 2.08846 | 0.212051 | 0.106026 | − | 0.994363i | \(-0.466187\pi\) | ||||
0.106026 | + | 0.994363i | \(0.466187\pi\) | |||||||
\(98\) | −4.31736 | − | 5.88860i | −0.436120 | − | 0.594839i | ||||
\(99\) | − | 33.0495i | − | 3.32160i | ||||||
\(100\) | −2.79549 | + | 8.86386i | −0.279549 | + | 0.886386i | ||||
\(101\) | − | 2.77074i | − | 0.275699i | −0.990453 | − | 0.137849i | \(-0.955981\pi\) | ||
0.990453 | − | 0.137849i | \(-0.0440190\pi\) | |||||||
\(102\) | 4.63981 | − | 3.40179i | 0.459410 | − | 0.336827i | ||||
\(103\) | −14.3363 | −1.41260 | −0.706301 | − | 0.707912i | \(-0.749637\pi\) | ||||
−0.706301 | + | 0.707912i | \(0.749637\pi\) | |||||||
\(104\) | 0.195949 | + | 0.577459i | 0.0192144 | + | 0.0566245i | ||||
\(105\) | −6.49726 | −0.634067 | ||||||||
\(106\) | −2.92439 | + | 2.14408i | −0.284042 | + | 0.208252i | ||||
\(107\) | − | 2.42388i | − | 0.234325i | −0.993113 | − | 0.117163i | \(-0.962620\pi\) | ||
0.993113 | − | 0.117163i | \(-0.0373799\pi\) | |||||||
\(108\) | 22.9413 | + | 7.23525i | 2.20753 | + | 0.696213i | ||||
\(109\) | 0.00123810i | 0.000118589i | 1.00000 | 5.92945e-5i | \(1.88740e-5\pi\) | |||||
−1.00000 | 5.92945e-5i | \(0.999981\pi\) | ||||||||
\(110\) | −2.40181 | − | 3.27591i | −0.229003 | − | 0.312346i | ||||
\(111\) | 17.6454 | 1.67483 | ||||||||
\(112\) | 11.4262 | + | 8.00324i | 1.07967 | + | 0.756235i | ||||
\(113\) | 1.81614 | 0.170848 | 0.0854242 | − | 0.996345i | \(-0.472775\pi\) | ||||
0.0854242 | + | 0.996345i | \(0.472775\pi\) | |||||||
\(114\) | 2.62240 | + | 3.57679i | 0.245611 | + | 0.334997i | ||||
\(115\) | − | 2.68990i | − | 0.250835i | ||||||
\(116\) | −17.9503 | − | 5.66118i | −1.66664 | − | 0.525627i | ||||
\(117\) | − | 1.47365i | − | 0.136239i | ||||||
\(118\) | −3.13859 | + | 2.30113i | −0.288931 | + | 0.211836i | ||||
\(119\) | −4.52407 | −0.414721 | ||||||||
\(120\) | 4.98985 | − | 1.69320i | 0.455509 | − | 0.154568i | ||||
\(121\) | −12.3791 | −1.12538 | ||||||||
\(122\) | 8.85798 | − | 6.49444i | 0.801964 | − | 0.587979i | ||||
\(123\) | − | 1.41132i | − | 0.127254i | ||||||
\(124\) | 0.734083 | − | 2.32761i | 0.0659226 | − | 0.209025i | ||||
\(125\) | − | 5.73078i | − | 0.512577i | ||||||
\(126\) | −19.9334 | − | 27.1878i | −1.77581 | − | 2.42209i | ||||
\(127\) | −16.1269 | −1.43103 | −0.715517 | − | 0.698596i | \(-0.753809\pi\) | ||||
−0.715517 | + | 0.698596i | \(0.753809\pi\) | |||||||
\(128\) | −10.8609 | − | 3.16874i | −0.959977 | − | 0.280079i | ||||
\(129\) | 2.49120 | 0.219338 | ||||||||
\(130\) | −0.107094 | − | 0.146070i | −0.00939279 | − | 0.0128111i | ||||
\(131\) | 11.1477i | 0.973983i | 0.873407 | + | 0.486992i | \(0.161906\pi\) | ||||
−0.873407 | + | 0.486992i | \(0.838094\pi\) | |||||||
\(132\) | 9.12179 | − | 28.9231i | 0.793950 | − | 2.51743i | ||||
\(133\) | − | 3.48756i | − | 0.302410i | ||||||
\(134\) | −4.69471 | + | 3.44204i | −0.405562 | + | 0.297347i | ||||
\(135\) | −7.14489 | −0.614934 | ||||||||
\(136\) | 3.47446 | − | 1.17899i | 0.297932 | − | 0.101097i | ||||
\(137\) | 11.1666 | 0.954025 | 0.477013 | − | 0.878896i | \(-0.341720\pi\) | ||||
0.477013 | + | 0.878896i | \(0.341720\pi\) | |||||||
\(138\) | 16.1962 | − | 11.8746i | 1.37871 | − | 1.01084i | ||||
\(139\) | 13.0534i | 1.10718i | 0.832790 | + | 0.553589i | \(0.186742\pi\) | ||||
−0.832790 | + | 0.553589i | \(0.813258\pi\) | |||||||
\(140\) | −3.95164 | − | 1.24627i | −0.333975 | − | 0.105329i | ||||
\(141\) | 38.2562i | 3.22176i | ||||||||
\(142\) | 6.54564 | + | 8.92783i | 0.549298 | + | 0.749207i | ||||
\(143\) | −1.04245 | −0.0871742 | ||||||||
\(144\) | 22.3939 | + | 15.6854i | 1.86616 | + | 1.30711i | ||||
\(145\) | 5.59048 | 0.464264 | ||||||||
\(146\) | −2.58327 | − | 3.52341i | −0.213793 | − | 0.291600i | ||||
\(147\) | 16.1921i | 1.33550i | ||||||||
\(148\) | 10.7320 | + | 3.38466i | 0.882163 | + | 0.278217i | ||||
\(149\) | − | 14.3811i | − | 1.17814i | −0.808080 | − | 0.589072i | \(-0.799493\pi\) | ||
0.808080 | − | 0.589072i | \(-0.200507\pi\) | |||||||
\(150\) | 16.6217 | − | 12.1866i | 1.35716 | − | 0.995032i | ||||
\(151\) | 17.3489 | 1.41184 | 0.705918 | − | 0.708293i | \(-0.250535\pi\) | ||||
0.705918 | + | 0.708293i | \(0.250535\pi\) | |||||||
\(152\) | 0.908869 | + | 2.67842i | 0.0737190 | + | 0.217249i | ||||
\(153\) | −8.86663 | −0.716825 | ||||||||
\(154\) | −19.2326 | + | 14.1008i | −1.54981 | + | 1.13628i | ||||
\(155\) | 0.724915i | 0.0582266i | ||||||||
\(156\) | 0.406732 | − | 1.28965i | 0.0325646 | − | 0.103255i | ||||
\(157\) | − | 9.63293i | − | 0.768791i | −0.923168 | − | 0.384396i | \(-0.874410\pi\) | ||
0.923168 | − | 0.384396i | \(-0.125590\pi\) | |||||||
\(158\) | 8.42306 | + | 11.4885i | 0.670102 | + | 0.913976i | ||||
\(159\) | 8.04128 | 0.637715 | ||||||||
\(160\) | 3.35962 | − | 0.0726808i | 0.265601 | − | 0.00574592i | ||||
\(161\) | −15.7922 | −1.24460 | ||||||||
\(162\) | −14.3945 | − | 19.6332i | −1.13094 | − | 1.54253i | ||||
\(163\) | − | 22.5365i | − | 1.76520i | −0.470129 | − | 0.882598i | \(-0.655793\pi\) | ||
0.470129 | − | 0.882598i | \(-0.344207\pi\) | |||||||
\(164\) | 0.270712 | − | 0.858365i | 0.0211390 | − | 0.0670271i | ||||
\(165\) | 9.00787i | 0.701262i | ||||||||
\(166\) | 13.2637 | − | 9.72458i | 1.02946 | − | 0.754774i | ||||
\(167\) | 16.5108 | 1.27765 | 0.638823 | − | 0.769353i | \(-0.279421\pi\) | ||||
0.638823 | + | 0.769353i | \(0.279421\pi\) | |||||||
\(168\) | −9.94065 | − | 29.2950i | −0.766938 | − | 2.26016i | ||||
\(169\) | 12.9535 | 0.996424 | ||||||||
\(170\) | −0.878871 | + | 0.644365i | −0.0674064 | + | 0.0494205i | ||||
\(171\) | − | 6.83520i | − | 0.522701i | ||||||
\(172\) | 1.51515 | + | 0.477850i | 0.115529 | + | 0.0364357i | ||||
\(173\) | 5.14911i | 0.391479i | 0.980656 | + | 0.195740i | \(0.0627108\pi\) | ||||
−0.980656 | + | 0.195740i | \(0.937289\pi\) | |||||||
\(174\) | 24.6793 | + | 33.6609i | 1.87093 | + | 2.55182i | ||||
\(175\) | −16.2071 | −1.22514 | ||||||||
\(176\) | 11.0958 | − | 15.8414i | 0.836376 | − | 1.19409i | ||||
\(177\) | 8.63029 | 0.648692 | ||||||||
\(178\) | −11.4635 | − | 15.6355i | −0.859227 | − | 1.17193i | ||||
\(179\) | − | 9.31580i | − | 0.696295i | −0.937440 | − | 0.348148i | \(-0.886811\pi\) | ||
0.937440 | − | 0.348148i | \(-0.113189\pi\) | |||||||
\(180\) | −7.74474 | − | 2.44254i | −0.577259 | − | 0.182056i | ||||
\(181\) | 5.15517i | 0.383180i | 0.981475 | + | 0.191590i | \(0.0613645\pi\) | ||||
−0.981475 | + | 0.191590i | \(0.938636\pi\) | |||||||
\(182\) | −0.857562 | + | 0.628741i | −0.0635667 | + | 0.0466054i | ||||
\(183\) | −24.3571 | −1.80053 | ||||||||
\(184\) | 12.1283 | − | 4.11549i | 0.894110 | − | 0.303398i | ||||
\(185\) | −3.34239 | −0.245737 | ||||||||
\(186\) | −4.36479 | + | 3.20015i | −0.320042 | + | 0.234646i | ||||
\(187\) | 6.27223i | 0.458671i | ||||||||
\(188\) | −7.33813 | + | 23.2675i | −0.535188 | + | 1.69696i | ||||
\(189\) | 41.9471i | 3.05120i | ||||||||
\(190\) | −0.496734 | − | 0.677513i | −0.0360369 | − | 0.0491520i | ||||
\(191\) | −14.8805 | −1.07672 | −0.538359 | − | 0.842715i | \(-0.680956\pi\) | ||||
−0.538359 | + | 0.842715i | \(0.680956\pi\) | |||||||
\(192\) | 15.2687 | + | 19.9078i | 1.10192 | + | 1.43672i | ||||
\(193\) | −21.2754 | −1.53144 | −0.765719 | − | 0.643175i | \(-0.777617\pi\) | ||||
−0.765719 | + | 0.643175i | \(0.777617\pi\) | |||||||
\(194\) | −1.74636 | − | 2.38193i | −0.125382 | − | 0.171012i | ||||
\(195\) | 0.401652i | 0.0287629i | ||||||||
\(196\) | −3.10588 | + | 9.84805i | −0.221849 | + | 0.703432i | ||||
\(197\) | 3.69169i | 0.263022i | 0.991315 | + | 0.131511i | \(0.0419829\pi\) | ||||
−0.991315 | + | 0.131511i | \(0.958017\pi\) | |||||||
\(198\) | −37.6935 | + | 27.6359i | −2.67876 | + | 1.96400i | ||||
\(199\) | 11.6857 | 0.828377 | 0.414188 | − | 0.910191i | \(-0.364065\pi\) | ||||
0.414188 | + | 0.910191i | \(0.364065\pi\) | |||||||
\(200\) | 12.4469 | − | 4.22362i | 0.880132 | − | 0.298655i | ||||
\(201\) | 12.9092 | 0.910545 | ||||||||
\(202\) | −3.16007 | + | 2.31688i | −0.222342 | + | 0.163015i | ||||
\(203\) | − | 32.8212i | − | 2.30360i | ||||||
\(204\) | −7.75958 | − | 2.44722i | −0.543279 | − | 0.171340i | ||||
\(205\) | 0.267331i | 0.0186712i | ||||||||
\(206\) | 11.9880 | + | 16.3508i | 0.835243 | + | 1.13922i | ||||
\(207\) | −30.9508 | −2.15123 | ||||||||
\(208\) | 0.494750 | − | 0.706352i | 0.0343047 | − | 0.0489767i | ||||
\(209\) | −4.83520 | −0.334458 | ||||||||
\(210\) | 5.43298 | + | 7.41023i | 0.374911 | + | 0.511354i | ||||
\(211\) | − | 7.61611i | − | 0.524315i | −0.965025 | − | 0.262157i | \(-0.915566\pi\) | ||
0.965025 | − | 0.262157i | \(-0.0844340\pi\) | |||||||
\(212\) | 4.89072 | + | 1.54244i | 0.335896 | + | 0.105935i | ||||
\(213\) | − | 24.5491i | − | 1.68208i | ||||||
\(214\) | −2.76447 | + | 2.02684i | −0.188976 | + | 0.138552i | ||||
\(215\) | −0.471882 | −0.0321821 | ||||||||
\(216\) | −10.9315 | − | 32.2150i | −0.743795 | − | 2.19196i | ||||
\(217\) | 4.25591 | 0.288910 | ||||||||
\(218\) | 0.00141208 | − | 0.00103530i | 9.56380e−5 | − | 7.01192e-5i | ||||
\(219\) | 9.68844i | 0.654684i | ||||||||
\(220\) | −1.72785 | + | 5.47860i | −0.116491 | + | 0.369367i | ||||
\(221\) | 0.279672i | 0.0188128i | ||||||||
\(222\) | −14.7550 | − | 20.1249i | −0.990292 | − | 1.35069i | ||||
\(223\) | −1.95477 | −0.130901 | −0.0654505 | − | 0.997856i | \(-0.520848\pi\) | ||||
−0.0654505 | + | 0.997856i | \(0.520848\pi\) | |||||||
\(224\) | −0.426703 | − | 19.7240i | −0.0285103 | − | 1.31787i | ||||
\(225\) | −31.7640 | −2.11760 | ||||||||
\(226\) | −1.51865 | − | 2.07134i | −0.101019 | − | 0.137784i | ||||
\(227\) | − | 13.3709i | − | 0.887461i | −0.896160 | − | 0.443730i | \(-0.853655\pi\) | ||
0.896160 | − | 0.443730i | \(-0.146345\pi\) | |||||||
\(228\) | 1.88654 | − | 5.98179i | 0.124939 | − | 0.396153i | ||||
\(229\) | 11.5800i | 0.765225i | 0.923909 | + | 0.382613i | \(0.124976\pi\) | ||||
−0.923909 | + | 0.382613i | \(0.875024\pi\) | |||||||
\(230\) | −3.06788 | + | 2.24929i | −0.202290 | + | 0.148314i | ||||
\(231\) | 52.8844 | 3.47954 | ||||||||
\(232\) | 8.55330 | + | 25.2065i | 0.561552 | + | 1.65489i | ||||
\(233\) | 1.58872 | 0.104080 | 0.0520401 | − | 0.998645i | \(-0.483428\pi\) | ||||
0.0520401 | + | 0.998645i | \(0.483428\pi\) | |||||||
\(234\) | −1.68072 | + | 1.23226i | −0.109872 | + | 0.0805551i | ||||
\(235\) | − | 7.24648i | − | 0.472708i | ||||||
\(236\) | 5.24896 | + | 1.65542i | 0.341678 | + | 0.107759i | ||||
\(237\) | − | 31.5903i | − | 2.05201i | ||||||
\(238\) | 3.78301 | + | 5.15978i | 0.245216 | + | 0.334459i | ||||
\(239\) | 23.8219 | 1.54091 | 0.770455 | − | 0.637494i | \(-0.220029\pi\) | ||||
0.770455 | + | 0.637494i | \(0.220029\pi\) | |||||||
\(240\) | −6.10361 | − | 4.27515i | −0.393987 | − | 0.275960i | ||||
\(241\) | 22.8554 | 1.47225 | 0.736123 | − | 0.676848i | \(-0.236654\pi\) | ||||
0.736123 | + | 0.676848i | \(0.236654\pi\) | |||||||
\(242\) | 10.3514 | + | 14.1186i | 0.665412 | + | 0.907578i | ||||
\(243\) | 17.9032i | 1.14849i | ||||||||
\(244\) | −14.8140 | − | 4.67206i | −0.948370 | − | 0.299098i | ||||
\(245\) | − | 3.06710i | − | 0.195950i | ||||||
\(246\) | −1.60963 | + | 1.18014i | −0.102626 | + | 0.0752428i | ||||
\(247\) | −0.215597 | −0.0137181 | ||||||||
\(248\) | −3.26851 | + | 1.10910i | −0.207551 | + | 0.0704281i | ||||
\(249\) | −36.4716 | −2.31129 | ||||||||
\(250\) | −6.53605 | + | 4.79205i | −0.413376 | + | 0.303076i | ||||
\(251\) | − | 2.63524i | − | 0.166335i | −0.996536 | − | 0.0831676i | \(-0.973496\pi\) | ||
0.996536 | − | 0.0831676i | \(-0.0265037\pi\) | |||||||
\(252\) | −14.3400 | + | 45.4687i | −0.903332 | + | 2.86426i | ||||
\(253\) | 21.8945i | 1.37649i | ||||||||
\(254\) | 13.4853 | + | 18.3930i | 0.846141 | + | 1.15408i | ||||
\(255\) | 2.41666 | 0.151337 | ||||||||
\(256\) | 5.46784 | + | 15.0367i | 0.341740 | + | 0.939795i | ||||
\(257\) | 20.0579 | 1.25118 | 0.625588 | − | 0.780153i | \(-0.284859\pi\) | ||||
0.625588 | + | 0.780153i | \(0.284859\pi\) | |||||||
\(258\) | −2.08313 | − | 2.84125i | −0.129690 | − | 0.176889i | ||||
\(259\) | 19.6229i | 1.21931i | ||||||||
\(260\) | −0.0770429 | + | 0.244285i | −0.00477800 | + | 0.0151499i | ||||
\(261\) | − | 64.3256i | − | 3.98165i | ||||||
\(262\) | 12.7142 | − | 9.32170i | 0.785485 | − | 0.575896i | ||||
\(263\) | 4.03667 | 0.248912 | 0.124456 | − | 0.992225i | \(-0.460282\pi\) | ||||
0.124456 | + | 0.992225i | \(0.460282\pi\) | |||||||
\(264\) | −40.6149 | + | 13.7818i | −2.49967 | + | 0.848213i | ||||
\(265\) | −1.52318 | −0.0935679 | ||||||||
\(266\) | −3.97762 | + | 2.91629i | −0.243884 | + | 0.178809i | ||||
\(267\) | 42.9934i | 2.63115i | ||||||||
\(268\) | 7.85140 | + | 2.47618i | 0.479601 | + | 0.151257i | ||||
\(269\) | 14.3095i | 0.872467i | 0.899834 | + | 0.436233i | \(0.143688\pi\) | ||||
−0.899834 | + | 0.436233i | \(0.856312\pi\) | |||||||
\(270\) | 5.97453 | + | 8.14886i | 0.363598 | + | 0.495924i | ||||
\(271\) | 9.85034 | 0.598366 | 0.299183 | − | 0.954196i | \(-0.403286\pi\) | ||||
0.299183 | + | 0.954196i | \(0.403286\pi\) | |||||||
\(272\) | −4.24998 | − | 2.97681i | −0.257693 | − | 0.180496i | ||||
\(273\) | 2.35806 | 0.142717 | ||||||||
\(274\) | −9.33745 | − | 12.7357i | −0.564096 | − | 0.769390i | ||||
\(275\) | 22.4697i | 1.35498i | ||||||||
\(276\) | −27.0864 | − | 8.54253i | −1.63041 | − | 0.514200i | ||||
\(277\) | 16.9641i | 1.01928i | 0.860389 | + | 0.509638i | \(0.170221\pi\) | ||||
−0.860389 | + | 0.509638i | \(0.829779\pi\) | |||||||
\(278\) | 14.8877 | − | 10.9152i | 0.892902 | − | 0.654652i | ||||
\(279\) | 8.34107 | 0.499367 | ||||||||
\(280\) | 1.88295 | + | 5.54904i | 0.112528 | + | 0.331619i | ||||
\(281\) | −10.2078 | −0.608944 | −0.304472 | − | 0.952521i | \(-0.598480\pi\) | ||||
−0.304472 | + | 0.952521i | \(0.598480\pi\) | |||||||
\(282\) | 43.6318 | − | 31.9897i | 2.59824 | − | 1.90496i | ||||
\(283\) | 18.7709i | 1.11581i | 0.829903 | + | 0.557907i | \(0.188396\pi\) | ||||
−0.829903 | + | 0.557907i | \(0.811604\pi\) | |||||||
\(284\) | 4.70889 | − | 14.9308i | 0.279421 | − | 0.885981i | ||||
\(285\) | 1.86298i | 0.110353i | ||||||||
\(286\) | 0.871694 | + | 1.18893i | 0.0515443 | + | 0.0703031i | ||||
\(287\) | 1.56948 | 0.0926433 | ||||||||
\(288\) | −0.836285 | − | 38.6567i | −0.0492785 | − | 2.27787i | ||||
\(289\) | −15.3173 | −0.901016 | ||||||||
\(290\) | −4.67473 | − | 6.37603i | −0.274510 | − | 0.374413i | ||||
\(291\) | 6.54966i | 0.383948i | ||||||||
\(292\) | −1.85839 | + | 5.89253i | −0.108754 | + | 0.344834i | ||||
\(293\) | − | 19.8271i | − | 1.15831i | −0.815217 | − | 0.579155i | \(-0.803382\pi\) | ||
0.815217 | − | 0.579155i | \(-0.196618\pi\) | |||||||
\(294\) | 18.4673 | − | 13.5397i | 1.07704 | − | 0.789654i | ||||
\(295\) | −1.63475 | −0.0951786 | ||||||||
\(296\) | −5.11377 | − | 15.0702i | −0.297232 | − | 0.875939i | ||||
\(297\) | 58.1559 | 3.37454 | ||||||||
\(298\) | −16.4019 | + | 12.0254i | −0.950134 | + | 0.696613i | ||||
\(299\) | 0.976253i | 0.0564582i | ||||||||
\(300\) | −27.7980 | − | 8.76697i | −1.60492 | − | 0.506161i | ||||
\(301\) | 2.77038i | 0.159682i | ||||||||
\(302\) | −14.5071 | − | 19.7867i | −0.834790 | − | 1.13860i | ||||
\(303\) | 8.68935 | 0.499190 | ||||||||
\(304\) | 2.29479 | − | 3.27627i | 0.131615 | − | 0.187907i | ||||
\(305\) | 4.61371 | 0.264180 | ||||||||
\(306\) | 7.41424 | + | 10.1125i | 0.423844 | + | 0.578095i | ||||
\(307\) | − | 18.3935i | − | 1.04977i | −0.851173 | − | 0.524886i | \(-0.824108\pi\) | ||
0.851173 | − | 0.524886i | \(-0.175892\pi\) | |||||||
\(308\) | 32.1644 | + | 10.1440i | 1.83274 | + | 0.578010i | ||||
\(309\) | − | 44.9604i | − | 2.55771i | ||||||
\(310\) | 0.826777 | − | 0.606171i | 0.0469578 | − | 0.0344282i | ||||
\(311\) | 19.1747 | 1.08730 | 0.543648 | − | 0.839313i | \(-0.317043\pi\) | ||||
0.543648 | + | 0.839313i | \(0.317043\pi\) | |||||||
\(312\) | −1.81098 | + | 0.614518i | −0.102526 | + | 0.0347902i | ||||
\(313\) | 14.2274 | 0.804183 | 0.402091 | − | 0.915600i | \(-0.368283\pi\) | ||||
0.402091 | + | 0.915600i | \(0.368283\pi\) | |||||||
\(314\) | −10.9865 | + | 8.05501i | −0.620004 | + | 0.454571i | ||||
\(315\) | − | 14.1609i | − | 0.797874i | ||||||
\(316\) | 6.05949 | − | 19.2133i | 0.340873 | − | 1.08083i | ||||
\(317\) | 0.777938i | 0.0436934i | 0.999761 | + | 0.0218467i | \(0.00695457\pi\) | ||||
−0.999761 | + | 0.0218467i | \(0.993045\pi\) | |||||||
\(318\) | −6.72408 | − | 9.17121i | −0.377068 | − | 0.514296i | ||||
\(319\) | −45.5037 | −2.54772 | ||||||||
\(320\) | −2.89219 | − | 3.77092i | −0.161678 | − | 0.210801i | ||||
\(321\) | 7.60156 | 0.424278 | ||||||||
\(322\) | 13.2054 | + | 18.0113i | 0.735906 | + | 1.00373i | ||||
\(323\) | 1.29720i | 0.0721782i | ||||||||
\(324\) | −10.3553 | + | 32.8344i | −0.575297 | + | 1.82413i | ||||
\(325\) | 1.00190i | 0.0555755i | ||||||||
\(326\) | −25.7033 | + | 18.8449i | −1.42357 | + | 1.04372i | ||||
\(327\) | −0.00388283 | −0.000214721 | ||||||||
\(328\) | −1.20535 | + | 0.409010i | −0.0665542 | + | 0.0225838i | ||||
\(329\) | −42.5435 | −2.34550 | ||||||||
\(330\) | 10.2736 | − | 7.53234i | 0.565544 | − | 0.414642i | ||||
\(331\) | − | 16.3988i | − | 0.901359i | −0.892686 | − | 0.450680i | \(-0.851182\pi\) | ||
0.892686 | − | 0.450680i | \(-0.148818\pi\) | |||||||
\(332\) | −22.1821 | − | 6.99580i | −1.21740 | − | 0.383945i | ||||
\(333\) | 38.4584i | 2.10751i | ||||||||
\(334\) | −13.8063 | − | 18.8309i | −0.755446 | − | 1.03038i | ||||
\(335\) | −2.44525 | −0.133599 | ||||||||
\(336\) | −25.0991 | + | 35.8338i | −1.36927 | + | 1.95489i | ||||
\(337\) | 24.6109 | 1.34064 | 0.670320 | − | 0.742072i | \(-0.266157\pi\) | ||||
0.670320 | + | 0.742072i | \(0.266157\pi\) | |||||||
\(338\) | −10.8317 | − | 14.7737i | −0.589165 | − | 0.803583i | ||||
\(339\) | 5.69563i | 0.309344i | ||||||||
\(340\) | 1.46982 | + | 0.463552i | 0.0797120 | + | 0.0251396i | ||||
\(341\) | − | 5.90045i | − | 0.319527i | ||||||
\(342\) | −7.79565 | + | 5.71556i | −0.421541 | + | 0.309062i | ||||
\(343\) | 6.40629 | 0.345907 | ||||||||
\(344\) | −0.721968 | − | 2.12763i | −0.0389259 | − | 0.114714i | ||||
\(345\) | 8.43584 | 0.454170 | ||||||||
\(346\) | 5.87264 | − | 4.30566i | 0.315715 | − | 0.231474i | ||||
\(347\) | 13.4635i | 0.722760i | 0.932419 | + | 0.361380i | \(0.117694\pi\) | ||||
−0.932419 | + | 0.361380i | \(0.882306\pi\) | |||||||
\(348\) | 17.7541 | − | 56.2942i | 0.951719 | − | 3.01768i | ||||
\(349\) | − | 2.83422i | − | 0.151712i | −0.997119 | − | 0.0758560i | \(-0.975831\pi\) | ||
0.997119 | − | 0.0758560i | \(-0.0241689\pi\) | |||||||
\(350\) | 13.5523 | + | 18.4845i | 0.724402 | + | 0.988037i | ||||
\(351\) | 2.59311 | 0.138410 | ||||||||
\(352\) | −27.3456 | + | 0.591585i | −1.45753 | + | 0.0315316i | ||||
\(353\) | −5.02227 | −0.267308 | −0.133654 | − | 0.991028i | \(-0.542671\pi\) | ||||
−0.133654 | + | 0.991028i | \(0.542671\pi\) | |||||||
\(354\) | −7.21661 | − | 9.84298i | −0.383558 | − | 0.523149i | ||||
\(355\) | 4.65008i | 0.246801i | ||||||||
\(356\) | −8.24678 | + | 26.1487i | −0.437079 | + | 1.38588i | ||||
\(357\) | − | 14.1880i | − | 0.750909i | ||||||
\(358\) | −10.6248 | + | 7.78983i | −0.561539 | + | 0.411705i | ||||
\(359\) | 23.6898 | 1.25030 | 0.625149 | − | 0.780505i | \(-0.285038\pi\) | ||||
0.625149 | + | 0.780505i | \(0.285038\pi\) | |||||||
\(360\) | 3.69036 | + | 10.8754i | 0.194499 | + | 0.573186i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 5.87955 | − | 4.31073i | 0.309022 | − | 0.226567i | ||||
\(363\) | − | 38.8223i | − | 2.03764i | ||||||
\(364\) | 1.43418 | + | 0.452312i | 0.0751714 | + | 0.0237076i | ||||
\(365\) | − | 1.83518i | − | 0.0960577i | ||||||
\(366\) | 20.3673 | + | 27.7796i | 1.06461 | + | 1.45206i | ||||
\(367\) | −16.9338 | −0.883938 | −0.441969 | − | 0.897030i | \(-0.645720\pi\) | ||||
−0.441969 | + | 0.897030i | \(0.645720\pi\) | |||||||
\(368\) | −14.8354 | − | 10.3912i | −0.773349 | − | 0.541677i | ||||
\(369\) | 3.07598 | 0.160129 | ||||||||
\(370\) | 2.79489 | + | 3.81205i | 0.145299 | + | 0.198179i | ||||
\(371\) | 8.94244i | 0.464268i | ||||||||
\(372\) | 7.29964 | + | 2.30217i | 0.378469 | + | 0.119362i | ||||
\(373\) | 12.8599i | 0.665860i | 0.942952 | + | 0.332930i | \(0.108037\pi\) | ||||
−0.942952 | + | 0.332930i | \(0.891963\pi\) | |||||||
\(374\) | 7.15357 | − | 5.24481i | 0.369903 | − | 0.271203i | ||||
\(375\) | 17.9724 | 0.928089 | ||||||||
\(376\) | 32.6731 | − | 11.0869i | 1.68499 | − | 0.571765i | ||||
\(377\) | −2.02896 | −0.104497 | ||||||||
\(378\) | 47.8413 | − | 35.0759i | 2.46069 | − | 1.80411i | ||||
\(379\) | − | 20.7810i | − | 1.06745i | −0.845659 | − | 0.533723i | \(-0.820793\pi\) | ||
0.845659 | − | 0.533723i | \(-0.179207\pi\) | |||||||
\(380\) | −0.357348 | + | 1.13307i | −0.0183315 | + | 0.0581251i | ||||
\(381\) | − | 50.5758i | − | 2.59108i | ||||||
\(382\) | 12.4430 | + | 16.9715i | 0.636642 | + | 0.868338i | ||||
\(383\) | −15.6170 | −0.797993 | −0.398996 | − | 0.916953i | \(-0.630641\pi\) | ||||
−0.398996 | + | 0.916953i | \(0.630641\pi\) | |||||||
\(384\) | 9.93751 | − | 34.0610i | 0.507122 | − | 1.73817i | ||||
\(385\) | −10.0173 | −0.510531 | ||||||||
\(386\) | 17.7904 | + | 24.2650i | 0.905508 | + | 1.23505i | ||||
\(387\) | 5.42960i | 0.276002i | ||||||||
\(388\) | −1.25632 | + | 3.98351i | −0.0637801 | + | 0.202232i | ||||
\(389\) | 10.1133i | 0.512764i | 0.966576 | + | 0.256382i | \(0.0825304\pi\) | ||||
−0.966576 | + | 0.256382i | \(0.917470\pi\) | |||||||
\(390\) | 0.458090 | − | 0.335860i | 0.0231963 | − | 0.0170069i | ||||
\(391\) | 5.87392 | 0.297057 | ||||||||
\(392\) | 13.8290 | − | 4.69258i | 0.698469 | − | 0.237011i | ||||
\(393\) | −34.9606 | −1.76353 | ||||||||
\(394\) | 4.21043 | − | 3.08698i | 0.212119 | − | 0.155520i | ||||
\(395\) | 5.98381i | 0.301078i | ||||||||
\(396\) | 63.0383 | + | 19.8811i | 3.16779 | + | 0.999061i | ||||
\(397\) | 4.60677i | 0.231207i | 0.993295 | + | 0.115604i | \(0.0368802\pi\) | ||||
−0.993295 | + | 0.115604i | \(0.963120\pi\) | |||||||
\(398\) | −9.77153 | − | 13.3277i | −0.489802 | − | 0.668058i | ||||
\(399\) | 10.9374 | 0.547554 | ||||||||
\(400\) | −15.2252 | − | 10.6642i | −0.761259 | − | 0.533209i | ||||
\(401\) | −4.00112 | −0.199806 | −0.0999032 | − | 0.994997i | \(-0.531853\pi\) | ||||
−0.0999032 | + | 0.994997i | \(0.531853\pi\) | |||||||
\(402\) | −10.7946 | − | 14.7231i | −0.538386 | − | 0.734324i | ||||
\(403\) | − | 0.263095i | − | 0.0131057i | ||||||
\(404\) | 5.28488 | + | 1.66675i | 0.262933 | + | 0.0829239i | ||||
\(405\) | − | 10.2260i | − | 0.508135i | ||||||
\(406\) | −37.4331 | + | 27.4450i | −1.85778 | + | 1.36207i | ||||
\(407\) | 27.2054 | 1.34852 | ||||||||
\(408\) | 3.69743 | + | 10.8963i | 0.183050 | + | 0.539446i | ||||
\(409\) | −14.5111 | −0.717529 | −0.358765 | − | 0.933428i | \(-0.616802\pi\) | ||||
−0.358765 | + | 0.933428i | \(0.616802\pi\) | |||||||
\(410\) | 0.304895 | − | 0.223541i | 0.0150577 | − | 0.0110399i | ||||
\(411\) | 35.0196i | 1.72739i | ||||||||
\(412\) | 8.62408 | − | 27.3450i | 0.424878 | − | 1.34719i | ||||
\(413\) | 9.59745i | 0.472260i | ||||||||
\(414\) | 25.8809 | + | 35.2999i | 1.27198 | + | 1.73489i | ||||
\(415\) | 6.90843 | 0.339122 | ||||||||
\(416\) | −1.21931 | + | 0.0263782i | −0.0597817 | + | 0.00129330i | ||||
\(417\) | −40.9370 | −2.00470 | ||||||||
\(418\) | 4.04317 | + | 5.51462i | 0.197758 | + | 0.269729i | ||||
\(419\) | − | 5.02078i | − | 0.245281i | −0.992451 | − | 0.122641i | \(-0.960864\pi\) | ||
0.992451 | − | 0.122641i | \(-0.0391362\pi\) | |||||||
\(420\) | 3.90845 | − | 12.3928i | 0.190713 | − | 0.604707i | ||||
\(421\) | 4.10152i | 0.199896i | 0.994993 | + | 0.0999479i | \(0.0318676\pi\) | ||||
−0.994993 | + | 0.0999479i | \(0.968132\pi\) | |||||||
\(422\) | −8.68630 | + | 6.36856i | −0.422842 | + | 0.310017i | ||||
\(423\) | −83.3800 | −4.05407 | ||||||||
\(424\) | −2.33042 | − | 6.86773i | −0.113175 | − | 0.333526i | ||||
\(425\) | 6.02825 | 0.292413 | ||||||||
\(426\) | −27.9987 | + | 20.5279i | −1.35654 | + | 0.994578i | ||||
\(427\) | − | 27.0867i | − | 1.31082i | ||||||
\(428\) | 4.62328 | + | 1.45809i | 0.223475 | + | 0.0704797i | ||||
\(429\) | − | 3.26925i | − | 0.157841i | ||||||
\(430\) | 0.394585 | + | 0.538189i | 0.0190286 | + | 0.0259538i | ||||
\(431\) | −16.2920 | −0.784760 | −0.392380 | − | 0.919803i | \(-0.628348\pi\) | ||||
−0.392380 | + | 0.919803i | \(0.628348\pi\) | |||||||
\(432\) | −27.6009 | + | 39.4056i | −1.32795 | + | 1.89590i | ||||
\(433\) | 7.44858 | 0.357956 | 0.178978 | − | 0.983853i | \(-0.442721\pi\) | ||||
0.178978 | + | 0.983853i | \(0.442721\pi\) | |||||||
\(434\) | −3.55878 | − | 4.85394i | −0.170827 | − | 0.232997i | ||||
\(435\) | 17.5324i | 0.840612i | ||||||||
\(436\) | −0.00236155 | 0.000744786i | −0.000113098 | 3.56688e-5i | ||||||
\(437\) | 4.52815i | 0.216611i | ||||||||
\(438\) | 11.0498 | − | 8.10143i | 0.527981 | − | 0.387101i | ||||
\(439\) | 15.8898 | 0.758379 | 0.379189 | − | 0.925319i | \(-0.376203\pi\) | ||||
0.379189 | + | 0.925319i | \(0.376203\pi\) | |||||||
\(440\) | 7.69325 | − | 2.61055i | 0.366761 | − | 0.124453i | ||||
\(441\) | −35.2908 | −1.68052 | ||||||||
\(442\) | 0.318971 | − | 0.233861i | 0.0151719 | − | 0.0111236i | ||||
\(443\) | 15.1742i | 0.720949i | 0.932769 | + | 0.360474i | \(0.117385\pi\) | ||||
−0.932769 | + | 0.360474i | \(0.882615\pi\) | |||||||
\(444\) | −10.6147 | + | 33.6567i | −0.503750 | + | 1.59728i | ||||
\(445\) | − | 8.14379i | − | 0.386053i | ||||||
\(446\) | 1.63457 | + | 2.22945i | 0.0773991 | + | 0.105567i | ||||
\(447\) | 45.1007 | 2.13319 | ||||||||
\(448\) | −22.1388 | + | 16.9798i | −1.04596 | + | 0.802220i | ||||
\(449\) | −24.3909 | −1.15108 | −0.575538 | − | 0.817775i | \(-0.695207\pi\) | ||||
−0.575538 | + | 0.817775i | \(0.695207\pi\) | |||||||
\(450\) | 26.5609 | + | 36.2273i | 1.25209 | + | 1.70777i | ||||
\(451\) | − | 2.17594i | − | 0.102461i | ||||||
\(452\) | −1.09251 | + | 3.46409i | −0.0513872 | + | 0.162937i | ||||
\(453\) | 54.4082i | 2.55632i | ||||||||
\(454\) | −15.2498 | + | 11.1807i | −0.715708 | + | 0.524738i | ||||
\(455\) | −0.446664 | −0.0209399 | ||||||||
\(456\) | −8.39984 | + | 2.85031i | −0.393358 | + | 0.133478i | ||||
\(457\) | −10.6860 | −0.499869 | −0.249934 | − | 0.968263i | \(-0.580409\pi\) | ||||
−0.249934 | + | 0.968263i | \(0.580409\pi\) | |||||||
\(458\) | 13.2071 | − | 9.68311i | 0.617129 | − | 0.452462i | ||||
\(459\) | − | 15.6022i | − | 0.728250i | ||||||
\(460\) | 5.13069 | + | 1.61812i | 0.239220 | + | 0.0754453i | ||||
\(461\) | 21.8232i | 1.01641i | 0.861236 | + | 0.508205i | \(0.169691\pi\) | ||||
−0.861236 | + | 0.508205i | \(0.830309\pi\) | |||||||
\(462\) | −44.2217 | − | 60.3156i | −2.05738 | − | 2.80613i | ||||
\(463\) | 0.0258442 | 0.00120108 | 0.000600541 | − | 1.00000i | \(-0.499809\pi\) | ||||
0.000600541 | 1.00000i | \(0.499809\pi\) | ||||||||
\(464\) | 21.5961 | − | 30.8327i | 1.00258 | − | 1.43137i | ||||
\(465\) | −2.27341 | −0.105427 | ||||||||
\(466\) | −1.32848 | − | 1.81196i | −0.0615405 | − | 0.0839372i | ||||
\(467\) | 4.66985i | 0.216095i | 0.994146 | + | 0.108047i | \(0.0344598\pi\) | ||||
−0.994146 | + | 0.108047i | \(0.965540\pi\) | |||||||
\(468\) | 2.81081 | + | 0.886477i | 0.129930 | + | 0.0409774i | ||||
\(469\) | 14.3559i | 0.662893i | ||||||||
\(470\) | −8.26473 | + | 6.05947i | −0.381223 | + | 0.279503i | ||||
\(471\) | 30.2099 | 1.39200 | ||||||||
\(472\) | −2.50112 | − | 7.37078i | −0.115123 | − | 0.339267i | ||||
\(473\) | 3.84088 | 0.176604 | ||||||||
\(474\) | −36.0292 | + | 26.4156i | −1.65488 | + | 1.21331i | ||||
\(475\) | 4.64712i | 0.213224i | ||||||||
\(476\) | 2.72147 | − | 8.62917i | 0.124739 | − | 0.395517i | ||||
\(477\) | 17.5261i | 0.802464i | ||||||||
\(478\) | −19.9198 | − | 27.1692i | −0.911109 | − | 1.24269i | ||||
\(479\) | −30.5428 | −1.39554 | −0.697768 | − | 0.716324i | \(-0.745823\pi\) | ||||
−0.697768 | + | 0.716324i | \(0.745823\pi\) | |||||||
\(480\) | 0.227935 | + | 10.5361i | 0.0104038 | + | 0.480907i | ||||
\(481\) | 1.21306 | 0.0553108 | ||||||||
\(482\) | −19.1116 | − | 26.0670i | −0.870509 | − | 1.18732i | ||||
\(483\) | − | 49.5261i | − | 2.25352i | ||||||
\(484\) | 7.44671 | − | 23.6118i | 0.338487 | − | 1.07326i | ||||
\(485\) | − | 1.24063i | − | 0.0563342i | ||||||
\(486\) | 20.4189 | − | 14.9706i | 0.926222 | − | 0.679081i | ||||
\(487\) | −2.37133 | −0.107455 | −0.0537277 | − | 0.998556i | \(-0.517110\pi\) | ||||
−0.0537277 | + | 0.998556i | \(0.517110\pi\) | |||||||
\(488\) | 7.05886 | + | 20.8024i | 0.319540 | + | 0.941679i | ||||
\(489\) | 70.6770 | 3.19613 | ||||||||
\(490\) | −3.49807 | + | 2.56469i | −0.158027 | + | 0.115861i | ||||
\(491\) | − | 41.3206i | − | 1.86477i | −0.361466 | − | 0.932385i | \(-0.617724\pi\) | ||
0.361466 | − | 0.932385i | \(-0.382276\pi\) | |||||||
\(492\) | 2.69193 | + | 0.848983i | 0.121362 | + | 0.0382751i | ||||
\(493\) | 12.2079i | 0.549815i | ||||||||
\(494\) | 0.180281 | + | 0.245891i | 0.00811122 | + | 0.0110632i | ||||
\(495\) | −19.6328 | −0.882427 | ||||||||
\(496\) | 3.99807 | + | 2.80036i | 0.179518 | + | 0.125740i | ||||
\(497\) | 27.3002 | 1.22458 | ||||||||
\(498\) | 30.4974 | + | 41.5964i | 1.36662 | + | 1.86398i | ||||
\(499\) | 15.8610i | 0.710035i | 0.934860 | + | 0.355018i | \(0.115525\pi\) | ||||
−0.934860 | + | 0.355018i | \(0.884475\pi\) | |||||||
\(500\) | 10.9308 | + | 3.44737i | 0.488842 | + | 0.154171i | ||||
\(501\) | 51.7798i | 2.31335i | ||||||||
\(502\) | −3.00554 | + | 2.20358i | −0.134144 | + | 0.0983506i | ||||
\(503\) | −18.6879 | −0.833254 | −0.416627 | − | 0.909078i | \(-0.636788\pi\) | ||||
−0.416627 | + | 0.909078i | \(0.636788\pi\) | |||||||
\(504\) | 63.8488 | − | 21.6658i | 2.84405 | − | 0.965071i | ||||
\(505\) | −1.64593 | −0.0732431 | ||||||||
\(506\) | 24.9710 | − | 18.3081i | 1.11010 | − | 0.813893i | ||||
\(507\) | 40.6237i | 1.80416i | ||||||||
\(508\) | 9.70121 | − | 30.7603i | 0.430422 | − | 1.36477i | ||||
\(509\) | 33.2172i | 1.47233i | 0.676804 | + | 0.736163i | \(0.263364\pi\) | ||||
−0.676804 | + | 0.736163i | \(0.736636\pi\) | |||||||
\(510\) | −2.02080 | − | 2.75624i | −0.0894825 | − | 0.122048i | ||||
\(511\) | −10.7742 | −0.476622 | ||||||||
\(512\) | 12.5774 | − | 18.8098i | 0.555849 | − | 0.831283i | ||||
\(513\) | 12.0276 | 0.531032 | ||||||||
\(514\) | −16.7723 | − | 22.8763i | −0.739795 | − | 1.00903i | ||||
\(515\) | 8.51637i | 0.375276i | ||||||||
\(516\) | −1.49859 | + | 4.75169i | −0.0659717 | + | 0.209181i | ||||
\(517\) | 58.9827i | 2.59406i | ||||||||
\(518\) | 22.3802 | − | 16.4086i | 0.983330 | − | 0.720951i | ||||
\(519\) | −16.1482 | −0.708826 | ||||||||
\(520\) | 0.343034 | − | 0.116402i | 0.0150431 | − | 0.00510455i | ||||
\(521\) | −10.9831 | −0.481178 | −0.240589 | − | 0.970627i | \(-0.577341\pi\) | ||||
−0.240589 | + | 0.970627i | \(0.577341\pi\) | |||||||
\(522\) | −73.3643 | + | 53.7888i | −3.21107 | + | 2.35427i | ||||
\(523\) | − | 8.00433i | − | 0.350005i | −0.984568 | − | 0.175002i | \(-0.944007\pi\) | ||
0.984568 | − | 0.175002i | \(-0.0559933\pi\) | |||||||
\(524\) | −21.2631 | − | 6.70597i | −0.928882 | − | 0.292952i | ||||
\(525\) | − | 50.8273i | − | 2.21829i | ||||||
\(526\) | −3.37544 | − | 4.60388i | −0.147176 | − | 0.200739i | ||||
\(527\) | −1.58299 | −0.0689561 | ||||||||
\(528\) | 49.6804 | + | 34.7976i | 2.16206 | + | 1.51437i | ||||
\(529\) | −2.49589 | −0.108517 | ||||||||
\(530\) | 1.27367 | + | 1.73721i | 0.0553248 | + | 0.0754594i | ||||
\(531\) | 18.8098i | 0.816277i | ||||||||
\(532\) | 6.65214 | + | 2.09796i | 0.288407 | + | 0.0909580i | ||||
\(533\) | − | 0.0970230i | − | 0.00420253i | ||||||
\(534\) | 49.0346 | − | 35.9509i | 2.12194 | − | 1.55575i | ||||
\(535\) | −1.43988 | −0.0622516 | ||||||||
\(536\) | −3.74118 | − | 11.0252i | −0.161594 | − | 0.476217i | ||||
\(537\) | 29.2154 | 1.26074 | ||||||||
\(538\) | 16.3202 | − | 11.9656i | 0.703615 | − | 0.515872i | ||||
\(539\) | 24.9646i | 1.07530i | ||||||||
\(540\) | 4.29804 | − | 13.6281i | 0.184958 | − | 0.586460i | ||||
\(541\) | − | 24.4359i | − | 1.05058i | −0.850923 | − | 0.525291i | \(-0.823956\pi\) | ||
0.850923 | − | 0.525291i | \(-0.176044\pi\) | |||||||
\(542\) | −8.23681 | − | 11.2345i | −0.353801 | − | 0.482562i | ||||
\(543\) | −16.1672 | −0.693800 | ||||||||
\(544\) | 0.158712 | + | 7.33636i | 0.00680473 | + | 0.314544i | ||||
\(545\) | 0.000735485 | 0 | 3.15047e−5 | 0 | ||||||
\(546\) | −1.97180 | − | 2.68941i | −0.0843854 | − | 0.115096i | ||||
\(547\) | 5.25284i | 0.224595i | 0.993675 | + | 0.112298i | \(0.0358210\pi\) | ||||
−0.993675 | + | 0.112298i | \(0.964179\pi\) | |||||||
\(548\) | −6.71730 | + | 21.2990i | −0.286949 | + | 0.909849i | ||||
\(549\) | − | 53.0866i | − | 2.26568i | ||||||
\(550\) | 25.6271 | − | 18.7891i | 1.09274 | − | 0.801169i | ||||
\(551\) | −9.41093 | −0.400919 | ||||||||
\(552\) | 12.9066 | + | 38.0357i | 0.549343 | + | 1.61891i | ||||
\(553\) | 35.1305 | 1.49390 | ||||||||
\(554\) | 19.3479 | − | 14.1853i | 0.822012 | − | 0.602677i | ||||
\(555\) | − | 10.4821i | − | 0.444940i | ||||||
\(556\) | −24.8980 | − | 7.85234i | −1.05591 | − | 0.333014i | ||||
\(557\) | − | 3.56791i | − | 0.151177i | −0.997139 | − | 0.0755886i | \(-0.975916\pi\) | ||
0.997139 | − | 0.0755886i | \(-0.0240836\pi\) | |||||||
\(558\) | −6.97477 | − | 9.51312i | −0.295265 | − | 0.402723i | ||||
\(559\) | 0.171261 | 0.00724357 | ||||||||
\(560\) | 4.75425 | − | 6.78762i | 0.200904 | − | 0.286829i | ||||
\(561\) | −19.6704 | −0.830485 | ||||||||
\(562\) | 8.53568 | + | 11.6421i | 0.360056 | + | 0.491093i | ||||
\(563\) | 17.0555i | 0.718805i | 0.933183 | + | 0.359403i | \(0.117020\pi\) | ||||
−0.933183 | + | 0.359403i | \(0.882980\pi\) | |||||||
\(564\) | −72.9695 | − | 23.0132i | −3.07257 | − | 0.969030i | ||||
\(565\) | − | 1.07886i | − | 0.0453881i | ||||||
\(566\) | 21.4085 | − | 15.6961i | 0.899867 | − | 0.659758i | ||||
\(567\) | −60.0361 | −2.52128 | ||||||||
\(568\) | −20.9664 | + | 7.11452i | −0.879731 | + | 0.298519i | ||||
\(569\) | −0.858816 | −0.0360034 | −0.0180017 | − | 0.999838i | \(-0.505730\pi\) | ||||
−0.0180017 | + | 0.999838i | \(0.505730\pi\) | |||||||
\(570\) | 2.12476 | − | 1.55781i | 0.0889963 | − | 0.0652497i | ||||
\(571\) | − | 40.5440i | − | 1.69671i | −0.529426 | − | 0.848356i | \(-0.677593\pi\) | ||
0.529426 | − | 0.848356i | \(-0.322407\pi\) | |||||||
\(572\) | 0.627091 | − | 1.98836i | 0.0262200 | − | 0.0831376i | ||||
\(573\) | − | 46.6671i | − | 1.94954i | ||||||
\(574\) | −1.31239 | − | 1.79001i | −0.0547781 | − | 0.0747138i | ||||
\(575\) | 21.0428 | 0.877546 | ||||||||
\(576\) | −43.3893 | + | 33.2783i | −1.80789 | + | 1.38660i | ||||
\(577\) | 36.5405 | 1.52120 | 0.760600 | − | 0.649220i | \(-0.224905\pi\) | ||||
0.760600 | + | 0.649220i | \(0.224905\pi\) | |||||||
\(578\) | 12.8082 | + | 17.4696i | 0.532752 | + | 0.726639i | ||||
\(579\) | − | 66.7221i | − | 2.77288i | ||||||
\(580\) | −3.36297 | + | 10.6632i | −0.139640 | + | 0.442766i | ||||
\(581\) | − | 40.5588i | − | 1.68266i | ||||||
\(582\) | 7.46999 | − | 5.47679i | 0.309641 | − | 0.227020i | ||||
\(583\) | 12.3979 | 0.513468 | ||||||||
\(584\) | 8.27450 | − | 2.80778i | 0.342401 | − | 0.116187i | ||||
\(585\) | −0.875406 | −0.0361936 | ||||||||
\(586\) | −22.6131 | + | 16.5793i | −0.934139 | + | 0.684885i | ||||
\(587\) | − | 30.4022i | − | 1.25483i | −0.778684 | − | 0.627416i | \(-0.784113\pi\) | ||
0.778684 | − | 0.627416i | \(-0.215887\pi\) | |||||||
\(588\) | −30.8846 | − | 9.74040i | −1.27366 | − | 0.401687i | ||||
\(589\) | − | 1.22031i | − | 0.0502821i | ||||||
\(590\) | 1.36697 | + | 1.86445i | 0.0562771 | + | 0.0767583i | ||||
\(591\) | −11.5776 | −0.476237 | ||||||||
\(592\) | −12.9117 | + | 18.4340i | −0.530668 | + | 0.757633i | ||||
\(593\) | −16.3814 | −0.672703 | −0.336351 | − | 0.941737i | \(-0.609193\pi\) | ||||
−0.336351 | + | 0.941737i | \(0.609193\pi\) | |||||||
\(594\) | −48.6297 | − | 66.3277i | −1.99530 | − | 2.72146i | ||||
\(595\) | 2.68749i | 0.110176i | ||||||||
\(596\) | 27.4303 | + | 8.65100i | 1.12359 | + | 0.354359i | ||||
\(597\) | 36.6476i | 1.49989i | ||||||||
\(598\) | 1.11343 | − | 0.816338i | 0.0455316 | − | 0.0333826i | ||||
\(599\) | −2.24749 | −0.0918298 | −0.0459149 | − | 0.998945i | \(-0.514620\pi\) | ||||
−0.0459149 | + | 0.998945i | \(0.514620\pi\) | |||||||
\(600\) | 13.2457 | + | 39.0350i | 0.540755 | + | 1.59360i | ||||
\(601\) | −33.1805 | −1.35346 | −0.676730 | − | 0.736231i | \(-0.736604\pi\) | ||||
−0.676730 | + | 0.736231i | \(0.736604\pi\) | |||||||
\(602\) | 3.15966 | − | 2.31658i | 0.128778 | − | 0.0944167i | ||||
\(603\) | 28.1358i | 1.14578i | ||||||||
\(604\) | −10.4363 | + | 33.0912i | −0.424648 | + | 1.34646i | ||||
\(605\) | 7.35371i | 0.298971i | ||||||||
\(606\) | −7.26600 | − | 9.91035i | −0.295161 | − | 0.402580i | ||||
\(607\) | 35.7847 | 1.45246 | 0.726228 | − | 0.687454i | \(-0.241272\pi\) | ||||
0.726228 | + | 0.687454i | \(0.241272\pi\) | |||||||
\(608\) | −5.65553 | + | 0.122350i | −0.229362 | + | 0.00496194i | ||||
\(609\) | 102.931 | 4.17098 | ||||||||
\(610\) | −3.85796 | − | 5.26201i | −0.156204 | − | 0.213052i | ||||
\(611\) | 2.62998i | 0.106398i | ||||||||
\(612\) | 5.33375 | − | 16.9121i | 0.215604 | − | 0.683632i | ||||
\(613\) | − | 42.2856i | − | 1.70790i | −0.520355 | − | 0.853950i | \(-0.674200\pi\) | ||
0.520355 | − | 0.853950i | \(-0.325800\pi\) | |||||||
\(614\) | −20.9781 | + | 15.3806i | −0.846606 | + | 0.620709i | ||||
\(615\) | −0.838380 | −0.0338067 | ||||||||
\(616\) | −15.3263 | − | 45.1664i | −0.617515 | − | 1.81981i | ||||
\(617\) | −26.2079 | −1.05509 | −0.527545 | − | 0.849527i | \(-0.676887\pi\) | ||||
−0.527545 | + | 0.849527i | \(0.676887\pi\) | |||||||
\(618\) | −51.2780 | + | 37.5957i | −2.06270 | + | 1.51232i | ||||
\(619\) | 40.7494i | 1.63786i | 0.573896 | + | 0.818929i | \(0.305432\pi\) | ||||
−0.573896 | + | 0.818929i | \(0.694568\pi\) | |||||||
\(620\) | −1.38269 | − | 0.436075i | −0.0555304 | − | 0.0175132i | ||||
\(621\) | − | 54.4628i | − | 2.18552i | ||||||
\(622\) | −16.0338 | − | 21.8690i | −0.642896 | − | 0.876868i | ||||
\(623\) | −47.8115 | −1.91553 | ||||||||
\(624\) | 2.21520 | + | 1.55159i | 0.0886789 | + | 0.0621133i | ||||
\(625\) | 19.8313 | 0.793250 | ||||||||
\(626\) | −11.8969 | − | 16.2266i | −0.475497 | − | 0.648546i | ||||
\(627\) | − | 15.1637i | − | 0.605581i | ||||||
\(628\) | 18.3737 | + | 5.79472i | 0.733192 | + | 0.231235i | ||||
\(629\) | − | 7.29874i | − | 0.291020i | ||||||
\(630\) | −16.1507 | + | 11.8412i | −0.643459 | + | 0.471767i | ||||
\(631\) | 42.3804 | 1.68714 | 0.843569 | − | 0.537021i | \(-0.180450\pi\) | ||||
0.843569 | + | 0.537021i | \(0.180450\pi\) | |||||||
\(632\) | −26.9800 | + | 9.15510i | −1.07320 | + | 0.364170i | ||||
\(633\) | 23.8850 | 0.949343 | ||||||||
\(634\) | 0.887251 | − | 0.650509i | 0.0352372 | − | 0.0258350i | ||||
\(635\) | 9.58005i | 0.380173i | ||||||||
\(636\) | −4.83726 | + | 15.3378i | −0.191810 | + | 0.608185i | ||||
\(637\) | 1.11315i | 0.0441045i | ||||||||
\(638\) | 38.0500 | + | 51.8977i | 1.50641 | + | 2.05465i | ||||
\(639\) | 53.5051 | 2.11663 | ||||||||
\(640\) | −1.88236 | + | 6.45182i | −0.0744068 | + | 0.255030i | ||||
\(641\) | −40.0356 | −1.58131 | −0.790656 | − | 0.612261i | \(-0.790260\pi\) | ||||
−0.790656 | + | 0.612261i | \(0.790260\pi\) | |||||||
\(642\) | −6.35639 | − | 8.66970i | −0.250867 | − | 0.342166i | ||||
\(643\) | 2.25369i | 0.0888767i | 0.999012 | + | 0.0444384i | \(0.0141498\pi\) | ||||
−0.999012 | + | 0.0444384i | \(0.985850\pi\) | |||||||
\(644\) | 9.49986 | − | 30.1219i | 0.374347 | − | 1.18697i | ||||
\(645\) | − | 1.47987i | − | 0.0582700i | ||||||
\(646\) | 1.47948 | − | 1.08471i | 0.0582093 | − | 0.0426775i | ||||
\(647\) | −6.89272 | −0.270981 | −0.135490 | − | 0.990779i | \(-0.543261\pi\) | ||||
−0.135490 | + | 0.990779i | \(0.543261\pi\) | |||||||
\(648\) | 46.1073 | − | 15.6456i | 1.81127 | − | 0.614616i | ||||
\(649\) | 13.3060 | 0.522307 | ||||||||
\(650\) | 1.14269 | − | 0.837786i | 0.0448198 | − | 0.0328607i | ||||
\(651\) | 13.3470i | 0.523111i | ||||||||
\(652\) | 42.9859 | + | 13.5569i | 1.68346 | + | 0.530930i | ||||
\(653\) | − | 5.75398i | − | 0.225170i | −0.993642 | − | 0.112585i | \(-0.964087\pi\) | ||
0.993642 | − | 0.112585i | \(-0.0359131\pi\) | |||||||
\(654\) | 0.00324681 | + | 0.00442843i | 0.000126960 | + | 0.000173165i | ||||
\(655\) | 6.62222 | 0.258751 | ||||||||
\(656\) | 1.47439 | + | 1.03271i | 0.0575652 | + | 0.0403204i | ||||
\(657\) | −21.1161 | −0.823817 | ||||||||
\(658\) | 35.5747 | + | 48.5215i | 1.38684 | + | 1.89157i | ||||
\(659\) | − | 34.1024i | − | 1.32844i | −0.747537 | − | 0.664220i | \(-0.768764\pi\) | ||
0.747537 | − | 0.664220i | \(-0.231236\pi\) | |||||||
\(660\) | −17.1815 | − | 5.41872i | −0.668789 | − | 0.210923i | ||||
\(661\) | − | 46.3767i | − | 1.80384i | −0.431900 | − | 0.901922i | \(-0.642157\pi\) | ||
0.431900 | − | 0.901922i | \(-0.357843\pi\) | |||||||
\(662\) | −18.7031 | + | 13.7126i | −0.726916 | + | 0.532955i | ||||
\(663\) | −0.877084 | −0.0340631 | ||||||||
\(664\) | 10.5697 | + | 31.1489i | 0.410185 | + | 1.20881i | ||||
\(665\) | −2.07176 | −0.0803392 | ||||||||
\(666\) | 43.8624 | − | 32.1588i | 1.69964 | − | 1.24613i | ||||
\(667\) | 42.6141i | 1.65002i | ||||||||
\(668\) | −9.93215 | + | 31.4926i | −0.384287 | + | 1.21848i | ||||
\(669\) | − | 6.13038i | − | 0.237014i | ||||||
\(670\) | 2.04471 | + | 2.78885i | 0.0789941 | + | 0.107743i | ||||
\(671\) | −37.5533 | −1.44973 | ||||||||
\(672\) | 61.8568 | − | 1.33819i | 2.38618 | − | 0.0516217i | ||||
\(673\) | −29.1579 | −1.12395 | −0.561977 | − | 0.827153i | \(-0.689959\pi\) | ||||
−0.561977 | + | 0.827153i | \(0.689959\pi\) | |||||||
\(674\) | −20.5795 | − | 28.0691i | −0.792693 | − | 1.08118i | ||||
\(675\) | − | 55.8937i | − | 2.15135i | ||||||
\(676\) | −7.79224 | + | 24.7074i | −0.299701 | + | 0.950285i | ||||
\(677\) | 10.0436i | 0.386006i | 0.981198 | + | 0.193003i | \(0.0618228\pi\) | ||||
−0.981198 | + | 0.193003i | \(0.938177\pi\) | |||||||
\(678\) | 6.49595 | − | 4.76266i | 0.249476 | − | 0.182909i | ||||
\(679\) | −7.28365 | −0.279521 | ||||||||
\(680\) | −0.700366 | − | 2.06397i | −0.0268578 | − | 0.0791496i | ||||
\(681\) | 41.9328 | 1.60687 | ||||||||
\(682\) | −6.72955 | + | 4.93393i | −0.257688 | + | 0.188930i | ||||
\(683\) | 25.5866i | 0.979042i | 0.871991 | + | 0.489521i | \(0.162828\pi\) | ||||
−0.871991 | + | 0.489521i | \(0.837172\pi\) | |||||||
\(684\) | 13.0374 | + | 4.11174i | 0.498497 | + | 0.157216i | ||||
\(685\) | − | 6.63341i | − | 0.253449i | ||||||
\(686\) | −5.35691 | − | 7.30648i | −0.204528 | − | 0.278963i | ||||
\(687\) | −36.3161 | −1.38554 | ||||||||
\(688\) | −1.82289 | + | 2.60253i | −0.0694970 | + | 0.0992206i | ||||
\(689\) | 0.552809 | 0.0210604 | ||||||||
\(690\) | −7.05401 | − | 9.62121i | −0.268542 | − | 0.366273i | ||||
\(691\) | − | 42.2386i | − | 1.60683i | −0.595417 | − | 0.803417i | \(-0.703013\pi\) | ||
0.595417 | − | 0.803417i | \(-0.296987\pi\) | |||||||
\(692\) | −9.82135 | − | 3.09746i | −0.373352 | − | 0.117748i | ||||
\(693\) | 115.262i | 4.37845i | ||||||||
\(694\) | 15.3554 | − | 11.2581i | 0.582882 | − | 0.427353i | ||||
\(695\) | 7.75428 | 0.294136 | ||||||||
\(696\) | −79.0503 | + | 26.8241i | −2.99639 | + | 1.01676i | ||||
\(697\) | −0.583768 | −0.0221118 | ||||||||
\(698\) | −3.23247 | + | 2.36996i | −0.122351 | + | 0.0897043i | ||||
\(699\) | 4.98239i | 0.188451i | ||||||||
\(700\) | 9.74945 | − | 30.9133i | 0.368495 | − | 1.16841i | ||||
\(701\) | 43.9811i | 1.66114i | 0.556911 | + | 0.830572i | \(0.311986\pi\) | ||||
−0.556911 | + | 0.830572i | \(0.688014\pi\) | |||||||
\(702\) | −2.16835 | − | 2.95748i | −0.0818390 | − | 0.111623i | ||||
\(703\) | 5.62653 | 0.212208 | ||||||||
\(704\) | 23.5410 | + | 30.6934i | 0.887234 | + | 1.15680i | ||||
\(705\) | 22.7258 | 0.855902 | ||||||||
\(706\) | 4.19960 | + | 5.72798i | 0.158054 | + | 0.215575i | ||||
\(707\) | 9.66314i | 0.363420i | ||||||||
\(708\) | −5.19158 | + | 16.4613i | −0.195112 | + | 0.618654i | ||||
\(709\) | 11.1307i | 0.418023i | 0.977913 | + | 0.209012i | \(0.0670246\pi\) | ||||
−0.977913 | + | 0.209012i | \(0.932975\pi\) | |||||||
\(710\) | 5.30350 | − | 3.88838i | 0.199037 | − | 0.145928i | ||||
\(711\) | 68.8514 | 2.58213 | ||||||||
\(712\) | 36.7189 | − | 12.4598i | 1.37610 | − | 0.466951i | ||||
\(713\) | −5.52575 | −0.206941 | ||||||||
\(714\) | −16.1816 | + | 11.8639i | −0.605583 | + | 0.443997i | ||||
\(715\) | 0.619259i | 0.0231590i | ||||||||
\(716\) | 17.7688 | + | 5.60395i | 0.664053 | + | 0.209430i | ||||
\(717\) | 74.7081i | 2.79003i | ||||||||
\(718\) | −19.8093 | − | 27.0186i | −0.739276 | − | 1.00832i | ||||
\(719\) | 17.8961 | 0.667413 | 0.333706 | − | 0.942677i | \(-0.391701\pi\) | ||||
0.333706 | + | 0.942677i | \(0.391701\pi\) | |||||||
\(720\) | 9.31775 | − | 13.3029i | 0.347252 | − | 0.495770i | ||||
\(721\) | 49.9989 | 1.86206 | ||||||||
\(722\) | 0.836196 | + | 1.14052i | 0.0311200 | + | 0.0424456i | ||||
\(723\) | 71.6771i | 2.66570i | ||||||||
\(724\) | −9.83291 | − | 3.10111i | −0.365437 | − | 0.115252i | ||||
\(725\) | 43.7337i | 1.62423i | ||||||||
\(726\) | −44.2775 | + | 32.4631i | −1.64329 | + | 1.20482i | ||||
\(727\) | −35.8772 | −1.33061 | −0.665306 | − | 0.746571i | \(-0.731699\pi\) | ||||
−0.665306 | + | 0.746571i | \(0.731699\pi\) | |||||||
\(728\) | −0.683385 | − | 2.01393i | −0.0253279 | − | 0.0746411i | ||||
\(729\) | −4.50357 | −0.166799 | ||||||||
\(730\) | −2.09305 | + | 1.53457i | −0.0774673 | + | 0.0567970i | ||||
\(731\) | − | 1.03044i | − | 0.0381123i | ||||||
\(732\) | 14.6521 | − | 46.4584i | 0.541557 | − | 1.71715i | ||||
\(733\) | − | 24.4618i | − | 0.903516i | −0.892141 | − | 0.451758i | \(-0.850797\pi\) | ||
0.892141 | − | 0.451758i | \(-0.149203\pi\) | |||||||
\(734\) | 14.1600 | + | 19.3133i | 0.522655 | + | 0.712867i | ||||
\(735\) | 9.61875 | 0.354793 | ||||||||
\(736\) | 0.554018 | + | 25.6091i | 0.0204214 | + | 0.943963i | ||||
\(737\) | 19.9032 | 0.733142 | ||||||||
\(738\) | −2.57212 | − | 3.50821i | −0.0946812 | − | 0.129139i | ||||
\(739\) | − | 26.7820i | − | 0.985193i | −0.870258 | − | 0.492596i | \(-0.836048\pi\) | ||
0.870258 | − | 0.492596i | \(-0.163952\pi\) | |||||||
\(740\) | 2.01063 | − | 6.37523i | 0.0739121 | − | 0.234358i | ||||
\(741\) | − | 0.676135i | − | 0.0248384i | ||||||
\(742\) | 10.1990 | − | 7.47763i | 0.374417 | − | 0.274512i | ||||
\(743\) | 23.7835 | 0.872534 | 0.436267 | − | 0.899817i | \(-0.356300\pi\) | ||||
0.436267 | + | 0.899817i | \(0.356300\pi\) | |||||||
\(744\) | −3.47827 | − | 10.2504i | −0.127520 | − | 0.375799i | ||||
\(745\) | −8.54295 | −0.312990 | ||||||||
\(746\) | 14.6669 | − | 10.7534i | 0.536994 | − | 0.393710i | ||||
\(747\) | − | 79.4903i | − | 2.90840i | ||||||
\(748\) | −11.9636 | − | 3.77308i | −0.437432 | − | 0.137958i | ||||
\(749\) | 8.45344i | 0.308882i | ||||||||
\(750\) | −15.0284 | − | 20.4978i | −0.548760 | − | 0.748473i | ||||
\(751\) | 22.4303 | 0.818494 | 0.409247 | − | 0.912424i | \(-0.365791\pi\) | ||||
0.409247 | + | 0.912424i | \(0.365791\pi\) | |||||||
\(752\) | −39.9659 | − | 27.9933i | −1.45741 | − | 1.02081i | ||||
\(753\) | 8.26442 | 0.301172 | ||||||||
\(754\) | 1.69661 | + | 2.31407i | 0.0617869 | + | 0.0842733i | ||||
\(755\) | − | 10.3060i | − | 0.375073i | ||||||
\(756\) | −80.0093 | − | 25.2334i | −2.90991 | − | 0.917730i | ||||
\(757\) | − | 32.2421i | − | 1.17186i | −0.810362 | − | 0.585930i | \(-0.800729\pi\) | ||
0.810362 | − | 0.585930i | \(-0.199271\pi\) | |||||||
\(758\) | −23.7010 | + | 17.3769i | −0.860859 | + | 0.631159i | ||||
\(759\) | −68.6635 | −2.49233 | ||||||||
\(760\) | 1.59109 | − | 0.539905i | 0.0577150 | − | 0.0195844i | ||||
\(761\) | 16.3559 | 0.592902 | 0.296451 | − | 0.955048i | \(-0.404197\pi\) | ||||
0.296451 | + | 0.955048i | \(0.404197\pi\) | |||||||
\(762\) | −57.6826 | + | 42.2913i | −2.08962 | + | 1.53205i | ||||
\(763\) | − | 0.00431797i | − | 0.000156321i | ||||||
\(764\) | 8.95145 | − | 28.3830i | 0.323852 | − | 1.02686i | ||||
\(765\) | 5.26714i | 0.190434i | ||||||||
\(766\) | 13.0589 | + | 17.8115i | 0.471837 | + | 0.643554i | ||||
\(767\) | 0.593302 | 0.0214229 | ||||||||
\(768\) | −47.1568 | + | 17.1478i | −1.70162 | + | 0.618766i | ||||
\(769\) | −19.6832 | −0.709794 | −0.354897 | − | 0.934905i | \(-0.615484\pi\) | ||||
−0.354897 | + | 0.934905i | \(0.615484\pi\) | |||||||
\(770\) | 8.37646 | + | 11.4249i | 0.301867 | + | 0.411727i | ||||
\(771\) | 62.9038i | 2.26542i | ||||||||
\(772\) | 12.7983 | − | 40.5805i | 0.460621 | − | 1.46052i | ||||
\(773\) | − | 33.0819i | − | 1.18987i | −0.803773 | − | 0.594936i | \(-0.797177\pi\) | ||
0.803773 | − | 0.594936i | \(-0.202823\pi\) | |||||||
\(774\) | 6.19255 | − | 4.54021i | 0.222586 | − | 0.163194i | ||||
\(775\) | −5.67093 | −0.203706 | ||||||||
\(776\) | 5.59379 | − | 1.89814i | 0.200805 | − | 0.0681392i | ||||
\(777\) | −61.5395 | −2.20772 | ||||||||
\(778\) | 11.5344 | − | 8.45668i | 0.413527 | − | 0.303187i | ||||
\(779\) | − | 0.450021i | − | 0.0161237i | ||||||
\(780\) | −0.766106 | − | 0.241615i | −0.0274310 | − | 0.00865121i | ||||
\(781\) | − | 37.8494i | − | 1.35436i | ||||||
\(782\) | −4.91175 | − | 6.69930i | −0.175644 | − | 0.239566i | ||||
\(783\) | 113.191 | 4.04512 | ||||||||
\(784\) | −16.9157 | − | 11.8483i | −0.604132 | − | 0.423152i | ||||
\(785\) | −5.72235 | −0.204240 | ||||||||
\(786\) | 29.2339 | + | 39.8731i | 1.04274 | + | 1.42223i | ||||
\(787\) | 35.1617i | 1.25338i | 0.779269 | + | 0.626690i | \(0.215591\pi\) | ||||
−0.779269 | + | 0.626690i | \(0.784409\pi\) | |||||||
\(788\) | −7.04149 | − | 2.22075i | −0.250843 | − | 0.0791110i | ||||
\(789\) | 12.6594i | 0.450688i | ||||||||
\(790\) | 6.82464 | − | 5.00364i | 0.242810 | − | 0.178022i | ||||
\(791\) | −6.33392 | −0.225208 | ||||||||
\(792\) | −30.0377 | − | 88.5207i | −1.06734 | − | 3.14544i | ||||
\(793\) | −1.67446 | −0.0594619 | ||||||||
\(794\) | 5.25410 | − | 3.85216i | 0.186461 | − | 0.136708i | ||||
\(795\) | − | 4.77685i | − | 0.169417i | ||||||
\(796\) | −7.02957 | + | 22.2892i | −0.249157 | + | 0.790019i | ||||
\(797\) | 3.75101i | 0.132868i | 0.997791 | + | 0.0664338i | \(0.0211621\pi\) | ||||
−0.997791 | + | 0.0664338i | \(0.978838\pi\) | |||||||
\(798\) | −9.14580 | − | 12.4743i | −0.323758 | − | 0.441584i | ||||
\(799\) | 15.8241 | 0.559815 | ||||||||
\(800\) | 0.568573 | + | 26.2819i | 0.0201021 | + | 0.929206i | ||||
\(801\) | −93.7046 | −3.31089 | ||||||||
\(802\) | 3.34572 | + | 4.56334i | 0.118141 | + | 0.161137i | ||||
\(803\) | 14.9374i | 0.527131i | ||||||||
\(804\) | −7.76558 | + | 24.6229i | −0.273871 | + | 0.868381i | ||||
\(805\) | 9.38121i | 0.330644i | ||||||||
\(806\) | −0.300064 | + | 0.219999i | −0.0105693 | + | 0.00774913i | ||||
\(807\) | −44.8763 | −1.57972 | ||||||||
\(808\) | −2.51824 | − | 7.42122i | −0.0885913 | − | 0.261078i | ||||
\(809\) | 23.9158 | 0.840836 | 0.420418 | − | 0.907331i | \(-0.361883\pi\) | ||||
0.420418 | + | 0.907331i | \(0.361883\pi\) | |||||||
\(810\) | −11.6629 | + | 8.55095i | −0.409794 | + | 0.300450i | ||||
\(811\) | 52.0538i | 1.82785i | 0.405878 | + | 0.913927i | \(0.366966\pi\) | ||||
−0.405878 | + | 0.913927i | \(0.633034\pi\) | |||||||
\(812\) | 62.6028 | + | 19.7437i | 2.19693 | + | 0.692869i | ||||
\(813\) | 30.8918i | 1.08342i | ||||||||
\(814\) | −22.7490 | − | 31.0282i | −0.797352 | − | 1.08754i | ||||
\(815\) | −13.3876 | −0.468947 | ||||||||
\(816\) | 9.33561 | − | 13.3284i | 0.326812 | − | 0.466588i | ||||
\(817\) | 0.794359 | 0.0277911 | ||||||||
\(818\) | 12.1341 | + | 16.5502i | 0.424260 | + | 0.578663i | ||||
\(819\) | 5.13943i | 0.179586i | ||||||||
\(820\) | −0.509904 | − | 0.160814i | −0.0178066 | − | 0.00561587i | ||||
\(821\) | 0.703590i | 0.0245555i | 0.999925 | + | 0.0122777i | \(0.00390822\pi\) | ||||
−0.999925 | + | 0.0122777i | \(0.996092\pi\) | |||||||
\(822\) | 39.9405 | − | 29.2833i | 1.39308 | − | 1.02137i | ||||
\(823\) | 23.4559 | 0.817622 | 0.408811 | − | 0.912619i | \(-0.365943\pi\) | ||||
0.408811 | + | 0.912619i | \(0.365943\pi\) | |||||||
\(824\) | −38.3988 | + | 13.0299i | −1.33769 | + | 0.453916i | ||||
\(825\) | −70.4676 | −2.45337 | ||||||||
\(826\) | 10.9460 | − | 8.02535i | 0.380862 | − | 0.279238i | ||||
\(827\) | − | 29.5282i | − | 1.02680i | −0.858150 | − | 0.513399i | \(-0.828386\pi\) | ||
0.858150 | − | 0.513399i | \(-0.171614\pi\) | |||||||
\(828\) | 18.6186 | − | 59.0352i | 0.647039 | − | 2.05161i | ||||
\(829\) | − | 4.42946i | − | 0.153841i | −0.997037 | − | 0.0769207i | \(-0.975491\pi\) | ||
0.997037 | − | 0.0769207i | \(-0.0245088\pi\) | |||||||
\(830\) | −5.77680 | − | 7.87918i | −0.200516 | − | 0.273490i | ||||
\(831\) | −53.2014 | −1.84554 | ||||||||
\(832\) | 1.04967 | + | 1.36859i | 0.0363907 | + | 0.0474473i | ||||
\(833\) | 6.69759 | 0.232058 | ||||||||
\(834\) | 34.2314 | + | 46.6893i | 1.18534 | + | 1.61672i | ||||
\(835\) | − | 9.80811i | − | 0.339424i | ||||||
\(836\) | 2.90863 | − | 9.22260i | 0.100597 | − | 0.318970i | ||||
\(837\) | 14.6774i | 0.507326i | ||||||||
\(838\) | −5.72628 | + | 4.19835i | −0.197811 | + | 0.145030i | ||||
\(839\) | −36.4506 | −1.25841 | −0.629207 | − | 0.777237i | \(-0.716620\pi\) | ||||
−0.629207 | + | 0.777237i | \(0.716620\pi\) | |||||||
\(840\) | −17.4024 | + | 5.90515i | −0.600440 | + | 0.203747i | ||||
\(841\) | −59.5656 | −2.05399 | ||||||||
\(842\) | 4.67785 | − | 3.42967i | 0.161209 | − | 0.118194i | ||||
\(843\) | − | 32.0127i | − | 1.10257i | ||||||
\(844\) | 14.5269 | + | 4.58150i | 0.500036 | + | 0.157702i | ||||
\(845\) | − | 7.69492i | − | 0.264713i | ||||||
\(846\) | 69.7220 | + | 95.0962i | 2.39709 | + | 3.26947i | ||||
\(847\) | 43.1730 | 1.48344 | ||||||||
\(848\) | −5.88406 | + | 8.40065i | −0.202060 | + | 0.288479i | ||||
\(849\) | −58.8677 | −2.02033 | ||||||||
\(850\) | −5.04079 | − | 6.87531i | −0.172898 | − | 0.235821i | ||||
\(851\) | − | 25.4777i | − | 0.873366i | ||||||
\(852\) | 46.8247 | + | 14.7676i | 1.60419 | + | 0.505930i | ||||
\(853\) | − | 52.7043i | − | 1.80456i | −0.431149 | − | 0.902281i | \(-0.641892\pi\) | ||
0.431149 | − | 0.902281i | \(-0.358108\pi\) | |||||||
\(854\) | −30.8928 | + | 22.6498i | −1.05713 | + | 0.775059i | ||||
\(855\) | −4.06039 | −0.138862 | ||||||||
\(856\) | −2.20299 | − | 6.49218i | −0.0752966 | − | 0.221898i | ||||
\(857\) | 13.7199 | 0.468662 | 0.234331 | − | 0.972157i | \(-0.424710\pi\) | ||||
0.234331 | + | 0.972157i | \(0.424710\pi\) | |||||||
\(858\) | −3.72863 | + | 2.73373i | −0.127293 | + | 0.0933280i | ||||
\(859\) | − | 55.0757i | − | 1.87916i | −0.342330 | − | 0.939580i | \(-0.611216\pi\) | ||
0.342330 | − | 0.939580i | \(-0.388784\pi\) | |||||||
\(860\) | 0.283862 | − | 0.900062i | 0.00967962 | − | 0.0306919i | ||||
\(861\) | 4.92206i | 0.167743i | ||||||||
\(862\) | 13.6233 | + | 18.5813i | 0.464013 | + | 0.632883i | ||||
\(863\) | 38.3384 | 1.30505 | 0.652527 | − | 0.757766i | \(-0.273709\pi\) | ||||
0.652527 | + | 0.757766i | \(0.273709\pi\) | |||||||
\(864\) | 68.0225 | − | 1.47157i | 2.31417 | − | 0.0500640i | ||||
\(865\) | 3.05878 | 0.104002 | ||||||||
\(866\) | −6.22847 | − | 8.49523i | −0.211652 | − | 0.288680i | ||||
\(867\) | − | 48.0367i | − | 1.63141i | ||||||
\(868\) | −2.56016 | + | 8.11768i | −0.0868975 | + | 0.275532i | ||||
\(869\) | − | 48.7053i | − | 1.65221i | ||||||
\(870\) | 19.9959 | − | 14.6605i | 0.677926 | − | 0.497037i | ||||
\(871\) | 0.887462 | 0.0300705 | ||||||||
\(872\) | 0.00112527 | + | 0.00331617i | 3.81066e−5 | + | 0.000112300i | ||||
\(873\) | −14.2751 | −0.483138 | ||||||||
\(874\) | 5.16442 | − | 3.78642i | 0.174689 | − | 0.128077i | ||||
\(875\) | 19.9865i | 0.675666i | ||||||||
\(876\) | −18.4796 | − | 5.82812i | −0.624368 | − | 0.196914i | ||||
\(877\) | 21.4788i | 0.725288i | 0.931928 | + | 0.362644i | \(0.118126\pi\) | ||||
−0.931928 | + | 0.362644i | \(0.881874\pi\) | |||||||
\(878\) | −13.2870 | − | 18.1226i | −0.448414 | − | 0.611607i | ||||
\(879\) | 62.1800 | 2.09728 | ||||||||
\(880\) | −9.41044 | − | 6.59135i | −0.317226 | − | 0.222194i | ||||
\(881\) | −11.2383 | −0.378629 | −0.189314 | − | 0.981917i | \(-0.560627\pi\) | ||||
−0.189314 | + | 0.981917i | \(0.560627\pi\) | |||||||
\(882\) | 29.5100 | + | 40.2498i | 0.993655 | + | 1.35528i | ||||
\(883\) | 15.7137i | 0.528809i | 0.964412 | + | 0.264405i | \(0.0851755\pi\) | ||||
−0.964412 | + | 0.264405i | \(0.914825\pi\) | |||||||
\(884\) | −0.533444 | − | 0.168238i | −0.0179417 | − | 0.00565845i | ||||
\(885\) | − | 5.12674i | − | 0.172334i | ||||||
\(886\) | 17.3064 | − | 12.6886i | 0.581421 | − | 0.426282i | ||||
\(887\) | 4.48008 | 0.150426 | 0.0752131 | − | 0.997167i | \(-0.476036\pi\) | ||||
0.0752131 | + | 0.997167i | \(0.476036\pi\) | |||||||
\(888\) | 47.2619 | − | 16.0374i | 1.58601 | − | 0.538179i | ||||
\(889\) | 56.2437 | 1.88635 | ||||||||
\(890\) | −9.28812 | + | 6.80980i | −0.311338 | + | 0.228265i | ||||
\(891\) | 83.2347i | 2.78847i | ||||||||
\(892\) | 1.17590 | − | 3.72851i | 0.0393720 | − | 0.124840i | ||||
\(893\) | 12.1986i | 0.408211i | ||||||||
\(894\) | −37.7130 | − | 51.4381i | −1.26131 | − | 1.72035i | ||||
\(895\) | −5.53396 | −0.184980 | ||||||||
\(896\) | 37.8781 | + | 11.0512i | 1.26542 | + | 0.369194i | ||||
\(897\) | −3.06164 | −0.102225 | ||||||||
\(898\) | 20.3955 | + | 27.8182i | 0.680608 | + | 0.928305i | ||||
\(899\) | − | 11.4843i | − | 0.383022i | ||||||
\(900\) | 19.1077 | − | 60.5862i | 0.636924 | − | 2.01954i | ||||
\(901\) | − | 3.32614i | − | 0.110810i | ||||||
\(902\) | −2.48170 | + | 1.81951i | −0.0826314 | + | 0.0605831i | ||||
\(903\) | −8.68822 | −0.289126 | ||||||||
\(904\) | 4.86440 | − | 1.65064i | 0.161788 | − | 0.0548993i | ||||
\(905\) | 3.06238 | 0.101797 | ||||||||
\(906\) | 62.0534 | − | 45.4959i | 2.06159 | − | 1.51150i | ||||
\(907\) | − | 6.37021i | − | 0.211519i | −0.994392 | − | 0.105760i | \(-0.966273\pi\) | ||
0.994392 | − | 0.105760i | \(-0.0337274\pi\) | |||||||
\(908\) | 25.5036 | + | 8.04334i | 0.846367 | + | 0.266928i | ||||
\(909\) | 18.9386i | 0.628152i | ||||||||
\(910\) | 0.373498 | + | 0.509427i | 0.0123813 | + | 0.0168873i | ||||
\(911\) | −30.5275 | −1.01142 | −0.505711 | − | 0.862703i | \(-0.668770\pi\) | ||||
−0.505711 | + | 0.862703i | \(0.668770\pi\) | |||||||
\(912\) | 10.2747 | + | 7.19673i | 0.340231 | + | 0.238308i | ||||
\(913\) | −56.2312 | −1.86098 | ||||||||
\(914\) | 8.93556 | + | 12.1875i | 0.295562 | + | 0.403127i | ||||
\(915\) | 14.4691i | 0.478334i | ||||||||
\(916\) | −22.0875 | − | 6.96597i | −0.729791 | − | 0.230162i | ||||
\(917\) | − | 38.8785i | − | 1.28388i | ||||||
\(918\) | −17.7946 | + | 13.0465i | −0.587309 | + | 0.430599i | ||||
\(919\) | −48.0650 | −1.58552 | −0.792758 | − | 0.609536i | \(-0.791356\pi\) | ||||
−0.792758 | + | 0.609536i | \(0.791356\pi\) | |||||||
\(920\) | −2.44477 | − | 7.20471i | −0.0806017 | − | 0.237532i | ||||
\(921\) | 57.6840 | 1.90075 | ||||||||
\(922\) | 24.8898 | − | 18.2485i | 0.819700 | − | 0.600982i | ||||
\(923\) | − | 1.68767i | − | 0.0555502i | ||||||
\(924\) | −31.8128 | + | 100.871i | −1.04657 | + | 3.31842i | ||||
\(925\) | − | 26.1471i | − | 0.859712i | ||||||
\(926\) | −0.0216108 | − | 0.0294757i | −0.000710175 | − | 0.000968632i | ||||
\(927\) | 97.9917 | 3.21847 | ||||||||
\(928\) | −53.2238 | + | 1.15142i | −1.74716 | + | 0.0377974i | ||||
\(929\) | 47.2953 | 1.55171 | 0.775854 | − | 0.630912i | \(-0.217319\pi\) | ||||
0.775854 | + | 0.630912i | \(0.217319\pi\) | |||||||
\(930\) | 1.90102 | + | 2.59287i | 0.0623369 | + | 0.0850234i | ||||
\(931\) | 5.16310i | 0.169214i | ||||||||
\(932\) | −0.955698 | + | 3.03030i | −0.0313049 | + | 0.0992607i | ||||
\(933\) | 60.1339i | 1.96870i | ||||||||
\(934\) | 5.32604 | − | 3.90491i | 0.174273 | − | 0.127773i | ||||
\(935\) | 3.72596 | 0.121852 | ||||||||
\(936\) | −1.33935 | − | 3.94705i | −0.0437780 | − | 0.129013i | ||||
\(937\) | −8.30237 | −0.271227 | −0.135613 | − | 0.990762i | \(-0.543301\pi\) | ||||
−0.135613 | + | 0.990762i | \(0.543301\pi\) | |||||||
\(938\) | 16.3731 | − | 12.0043i | 0.534601 | − | 0.391955i | ||||
\(939\) | 44.6189i | 1.45608i | ||||||||
\(940\) | 13.8219 | + | 4.35915i | 0.450819 | + | 0.142180i | ||||
\(941\) | − | 31.3955i | − | 1.02347i | −0.859145 | − | 0.511733i | \(-0.829004\pi\) | ||
0.859145 | − | 0.511733i | \(-0.170996\pi\) | |||||||
\(942\) | −25.2614 | − | 34.4549i | −0.823061 | − | 1.12260i | ||||
\(943\) | −2.03776 | −0.0663586 | ||||||||
\(944\) | −6.31506 | + | 9.01598i | −0.205538 | + | 0.293445i | ||||
\(945\) | 24.9183 | 0.810591 | ||||||||
\(946\) | −3.21173 | − | 4.38059i | −0.104422 | − | 0.142425i | ||||
\(947\) | 2.14805i | 0.0698024i | 0.999391 | + | 0.0349012i | \(0.0111117\pi\) | ||||
−0.999391 | + | 0.0349012i | \(0.988888\pi\) | |||||||
\(948\) | 60.2549 | + | 19.0032i | 1.95699 | + | 0.617197i | ||||
\(949\) | 0.666046i | 0.0216208i | ||||||||
\(950\) | 5.30011 | − | 3.88590i | 0.171958 | − | 0.126075i | ||||
\(951\) | −2.43970 | −0.0791127 | ||||||||
\(952\) | −12.1174 | + | 4.11179i | −0.392727 | + | 0.133264i | ||||
\(953\) | 25.3661 | 0.821689 | 0.410844 | − | 0.911705i | \(-0.365234\pi\) | ||||
0.410844 | + | 0.911705i | \(0.365234\pi\) | |||||||
\(954\) | 19.9888 | − | 14.6552i | 0.647160 | − | 0.474480i | ||||
\(955\) | 8.83965i | 0.286044i | ||||||||
\(956\) | −14.3301 | + | 45.4376i | −0.463470 | + | 1.46956i | ||||
\(957\) | − | 142.705i | − | 4.61299i | ||||||
\(958\) | 25.5398 | + | 34.8346i | 0.825152 | + | 1.12545i | ||||
\(959\) | −38.9442 | −1.25757 | ||||||||
\(960\) | 11.8260 | − | 9.07023i | 0.381684 | − | 0.292741i | ||||
\(961\) | −29.5108 | −0.951963 | ||||||||
\(962\) | −1.01436 | − | 1.38351i | −0.0327041 | − | 0.0446063i | ||||
\(963\) | 16.5677i | 0.533887i | ||||||||
\(964\) | −13.7488 | + | 43.5942i | −0.442818 | + | 1.40407i | ||||
\(965\) | 12.6385i | 0.406847i | ||||||||
\(966\) | −56.4853 | + | 41.4135i | −1.81739 | + | 1.33246i | ||||
\(967\) | −12.8395 | −0.412892 | −0.206446 | − | 0.978458i | \(-0.566190\pi\) | ||||
−0.206446 | + | 0.978458i | \(0.566190\pi\) | |||||||
\(968\) | −33.1566 | + | 11.2510i | −1.06569 | + | 0.361621i | ||||
\(969\) | −4.06817 | −0.130688 | ||||||||
\(970\) | −1.41496 | + | 1.03741i | −0.0454317 | + | 0.0333093i | ||||
\(971\) | 8.77909i | 0.281734i | 0.990028 | + | 0.140867i | \(0.0449891\pi\) | ||||
−0.990028 | + | 0.140867i | \(0.955011\pi\) | |||||||
\(972\) | −34.1484 | − | 10.7698i | −1.09531 | − | 0.345440i | ||||
\(973\) | − | 45.5247i | − | 1.45945i | ||||||
\(974\) | 1.98290 | + | 2.70454i | 0.0635362 | + | 0.0866592i | ||||
\(975\) | −3.14208 | −0.100627 | ||||||||
\(976\) | 17.8229 | − | 25.4456i | 0.570496 | − | 0.814494i | ||||
\(977\) | −45.9701 | −1.47071 | −0.735357 | − | 0.677680i | \(-0.762986\pi\) | ||||
−0.735357 | + | 0.677680i | \(0.762986\pi\) | |||||||
\(978\) | −59.0998 | − | 80.6083i | −1.88980 | − | 2.57757i | ||||
\(979\) | 66.2864i | 2.11852i | ||||||||
\(980\) | 5.85014 | + | 1.84502i | 0.186876 | + | 0.0589371i | ||||
\(981\) | − | 0.00846269i | − | 0.000270193i | ||||||
\(982\) | −47.1268 | + | 34.5521i | −1.50388 | + | 1.10260i | ||||
\(983\) | −51.4992 | −1.64257 | −0.821284 | − | 0.570519i | \(-0.806742\pi\) | ||||
−0.821284 | + | 0.570519i | \(0.806742\pi\) | |||||||
\(984\) | −1.28270 | − | 3.78011i | −0.0408910 | − | 0.120505i | ||||
\(985\) | 2.19302 | 0.0698753 | ||||||||
\(986\) | 13.9233 | − | 10.2082i | 0.443407 | − | 0.325094i | ||||
\(987\) | − | 133.421i | − | 4.24684i | ||||||
\(988\) | 0.129693 | − | 0.411227i | 0.00412608 | − | 0.0130829i | ||||
\(989\) | − | 3.59697i | − | 0.114377i | ||||||
\(990\) | 16.4168 | + | 22.3915i | 0.521761 | + | 0.711648i | ||||
\(991\) | −29.4762 | −0.936343 | −0.468171 | − | 0.883638i | \(-0.655087\pi\) | ||||
−0.468171 | + | 0.883638i | \(0.655087\pi\) | |||||||
\(992\) | −0.149305 | − | 6.90151i | −0.00474043 | − | 0.219123i | ||||
\(993\) | 51.4284 | 1.63203 | ||||||||
\(994\) | −22.8283 | − | 31.1364i | −0.724071 | − | 0.987586i | ||||
\(995\) | − | 6.94178i | − | 0.220069i | ||||||
\(996\) | 21.9396 | − | 69.5655i | 0.695184 | − | 2.20427i | ||||
\(997\) | 54.3591i | 1.72157i | 0.508968 | + | 0.860786i | \(0.330027\pi\) | ||||
−0.508968 | + | 0.860786i | \(0.669973\pi\) | |||||||
\(998\) | 18.0897 | − | 13.2629i | 0.572620 | − | 0.419829i | ||||
\(999\) | −67.6737 | −2.14110 |
(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 | 152.2.c.b.77.5 | ✓ | 16 | |
3.2 | odd | 2 | 1368.2.g.b.685.12 | 16 | |||
4.3 | odd | 2 | 608.2.c.b.305.1 | 16 | |||
8.3 | odd | 2 | 608.2.c.b.305.16 | 16 | |||
8.5 | even | 2 | inner | 152.2.c.b.77.6 | yes | 16 | |
12.11 | even | 2 | 5472.2.g.b.2737.9 | 16 | |||
16.3 | odd | 4 | 4864.2.a.bn.1.8 | 8 | |||
16.5 | even | 4 | 4864.2.a.bq.1.8 | 8 | |||
16.11 | odd | 4 | 4864.2.a.bp.1.1 | 8 | |||
16.13 | even | 4 | 4864.2.a.bo.1.1 | 8 | |||
24.5 | odd | 2 | 1368.2.g.b.685.11 | 16 | |||
24.11 | even | 2 | 5472.2.g.b.2737.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
152.2.c.b.77.6 | yes | 16 | 8.5 | even | 2 | inner | |
608.2.c.b.305.1 | 16 | 4.3 | odd | 2 | |||
608.2.c.b.305.16 | 16 | 8.3 | odd | 2 | |||
1368.2.g.b.685.11 | 16 | 24.5 | odd | 2 | |||
1368.2.g.b.685.12 | 16 | 3.2 | odd | 2 | |||
4864.2.a.bn.1.8 | 8 | 16.3 | odd | 4 | |||
4864.2.a.bo.1.1 | 8 | 16.13 | even | 4 | |||
4864.2.a.bp.1.1 | 8 | 16.11 | odd | 4 | |||
4864.2.a.bq.1.8 | 8 | 16.5 | even | 4 | |||
5472.2.g.b.2737.8 | 16 | 24.11 | even | 2 | |||
5472.2.g.b.2737.9 | 16 | 12.11 | even | 2 |