Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(117,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.117");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.h (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 117.7 | ||
Root | \(1.28931 - 1.28931i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.117 |
Dual form | 370.2.h.e.253.7 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.28931 | + | 1.28931i | 0.744384 | + | 0.744384i | 0.973418 | − | 0.229034i | \(-0.0735568\pi\) |
−0.229034 | + | 0.973418i | \(0.573557\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.69364 | + | 1.45999i | 0.757420 | + | 0.652928i | ||||
\(6\) | −1.28931 | − | 1.28931i | −0.526359 | − | 0.526359i | ||||
\(7\) | 0.579841 | + | 0.579841i | 0.219159 | + | 0.219159i | 0.808144 | − | 0.588985i | \(-0.200472\pi\) |
−0.588985 | + | 0.808144i | \(0.700472\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.324646i | 0.108215i | ||||||||
\(10\) | −1.69364 | − | 1.45999i | −0.535577 | − | 0.461690i | ||||
\(11\) | 3.64633i | 1.09941i | 0.835359 | + | 0.549705i | \(0.185260\pi\) | ||||
−0.835359 | + | 0.549705i | \(0.814740\pi\) | |||||||
\(12\) | 1.28931 | + | 1.28931i | 0.372192 | + | 0.372192i | ||||
\(13\) | 3.10704 | 0.861737 | 0.430868 | − | 0.902415i | \(-0.358207\pi\) | ||||
0.430868 | + | 0.902415i | \(0.358207\pi\) | |||||||
\(14\) | −0.579841 | − | 0.579841i | −0.154969 | − | 0.154969i | ||||
\(15\) | 0.301249 | + | 4.06602i | 0.0777820 | + | 1.04984i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 8.09027i | − | 1.96218i | −0.193558 | − | 0.981089i | \(-0.562003\pi\) | ||
0.193558 | − | 0.981089i | \(-0.437997\pi\) | |||||||
\(18\) | − | 0.324646i | − | 0.0765198i | ||||||
\(19\) | −3.05234 | + | 3.05234i | −0.700255 | + | 0.700255i | −0.964465 | − | 0.264210i | \(-0.914889\pi\) |
0.264210 | + | 0.964465i | \(0.414889\pi\) | |||||||
\(20\) | 1.69364 | + | 1.45999i | 0.378710 | + | 0.326464i | ||||
\(21\) | 1.49519i | 0.326278i | ||||||||
\(22\) | − | 3.64633i | − | 0.777401i | ||||||
\(23\) | −7.79067 | −1.62447 | −0.812233 | − | 0.583333i | \(-0.801748\pi\) | ||||
−0.812233 | + | 0.583333i | \(0.801748\pi\) | |||||||
\(24\) | −1.28931 | − | 1.28931i | −0.263180 | − | 0.263180i | ||||
\(25\) | 0.736849 | + | 4.94541i | 0.147370 | + | 0.989081i | ||||
\(26\) | −3.10704 | −0.609340 | ||||||||
\(27\) | 3.44936 | − | 3.44936i | 0.663830 | − | 0.663830i | ||||
\(28\) | 0.579841 | + | 0.579841i | 0.109580 | + | 0.109580i | ||||
\(29\) | 1.37472 | + | 1.37472i | 0.255279 | + | 0.255279i | 0.823131 | − | 0.567852i | \(-0.192225\pi\) |
−0.567852 | + | 0.823131i | \(0.692225\pi\) | |||||||
\(30\) | −0.301249 | − | 4.06602i | −0.0550002 | − | 0.742349i | ||||
\(31\) | 3.23904 | − | 3.23904i | 0.581749 | − | 0.581749i | −0.353635 | − | 0.935384i | \(-0.615054\pi\) |
0.935384 | + | 0.353635i | \(0.115054\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.70126 | + | 4.70126i | −0.818384 | + | 0.818384i | ||||
\(34\) | 8.09027i | 1.38747i | ||||||||
\(35\) | 0.135480 | + | 1.82861i | 0.0229004 | + | 0.309091i | ||||
\(36\) | 0.324646i | 0.0541076i | ||||||||
\(37\) | −4.87870 | + | 3.63294i | −0.802054 | + | 0.597252i | ||||
\(38\) | 3.05234 | − | 3.05234i | 0.495155 | − | 0.495155i | ||||
\(39\) | 4.00594 | + | 4.00594i | 0.641463 | + | 0.641463i | ||||
\(40\) | −1.69364 | − | 1.45999i | −0.267788 | − | 0.230845i | ||||
\(41\) | 9.31106i | 1.45414i | 0.686562 | + | 0.727072i | \(0.259119\pi\) | ||||
−0.686562 | + | 0.727072i | \(0.740881\pi\) | |||||||
\(42\) | − | 1.49519i | − | 0.230713i | ||||||
\(43\) | 10.9160 | 1.66467 | 0.832334 | − | 0.554275i | \(-0.187004\pi\) | ||||
0.832334 | + | 0.554275i | \(0.187004\pi\) | |||||||
\(44\) | 3.64633i | 0.549705i | ||||||||
\(45\) | −0.473980 | + | 0.549834i | −0.0706568 | + | 0.0819644i | ||||
\(46\) | 7.79067 | 1.14867 | ||||||||
\(47\) | −4.11794 | − | 4.11794i | −0.600663 | − | 0.600663i | 0.339825 | − | 0.940489i | \(-0.389632\pi\) |
−0.940489 | + | 0.339825i | \(0.889632\pi\) | |||||||
\(48\) | 1.28931 | + | 1.28931i | 0.186096 | + | 0.186096i | ||||
\(49\) | − | 6.32757i | − | 0.903938i | ||||||
\(50\) | −0.736849 | − | 4.94541i | −0.104206 | − | 0.699386i | ||||
\(51\) | 10.4309 | − | 10.4309i | 1.46061 | − | 1.46061i | ||||
\(52\) | 3.10704 | 0.430868 | ||||||||
\(53\) | 0.446555 | − | 0.446555i | 0.0613390 | − | 0.0613390i | −0.675772 | − | 0.737111i | \(-0.736190\pi\) |
0.737111 | + | 0.675772i | \(0.236190\pi\) | |||||||
\(54\) | −3.44936 | + | 3.44936i | −0.469399 | + | 0.469399i | ||||
\(55\) | −5.32361 | + | 6.17558i | −0.717836 | + | 0.832715i | ||||
\(56\) | −0.579841 | − | 0.579841i | −0.0774846 | − | 0.0774846i | ||||
\(57\) | −7.87084 | −1.04252 | ||||||||
\(58\) | −1.37472 | − | 1.37472i | −0.180509 | − | 0.180509i | ||||
\(59\) | −6.16388 | + | 6.16388i | −0.802468 | + | 0.802468i | −0.983481 | − | 0.181012i | \(-0.942063\pi\) |
0.181012 | + | 0.983481i | \(0.442063\pi\) | |||||||
\(60\) | 0.301249 | + | 4.06602i | 0.0388910 | + | 0.524920i | ||||
\(61\) | 8.71382 | − | 8.71382i | 1.11569 | − | 1.11569i | 0.123324 | − | 0.992366i | \(-0.460644\pi\) |
0.992366 | − | 0.123324i | \(-0.0393555\pi\) | |||||||
\(62\) | −3.23904 | + | 3.23904i | −0.411359 | + | 0.411359i | ||||
\(63\) | −0.188243 | + | 0.188243i | −0.0237164 | + | 0.0237164i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.26221 | + | 4.53625i | 0.652697 | + | 0.562652i | ||||
\(66\) | 4.70126 | − | 4.70126i | 0.578685 | − | 0.578685i | ||||
\(67\) | −2.01024 | + | 2.01024i | −0.245590 | + | 0.245590i | −0.819158 | − | 0.573568i | \(-0.805559\pi\) |
0.573568 | + | 0.819158i | \(0.305559\pi\) | |||||||
\(68\) | − | 8.09027i | − | 0.981089i | ||||||
\(69\) | −10.0446 | − | 10.0446i | −1.20923 | − | 1.20923i | ||||
\(70\) | −0.135480 | − | 1.82861i | −0.0161930 | − | 0.218560i | ||||
\(71\) | 0.00151598 | 0.000179913 | 8.99567e−5 | − | 1.00000i | \(-0.499971\pi\) | ||||
8.99567e−5 | 1.00000i | \(0.499971\pi\) | ||||||||
\(72\) | − | 0.324646i | − | 0.0382599i | ||||||
\(73\) | −9.32759 | − | 9.32759i | −1.09171 | − | 1.09171i | −0.995346 | − | 0.0963663i | \(-0.969278\pi\) |
−0.0963663 | − | 0.995346i | \(-0.530722\pi\) | |||||||
\(74\) | 4.87870 | − | 3.63294i | 0.567138 | − | 0.422321i | ||||
\(75\) | −5.42614 | + | 7.32620i | −0.626557 | + | 0.845956i | ||||
\(76\) | −3.05234 | + | 3.05234i | −0.350128 | + | 0.350128i | ||||
\(77\) | −2.11429 | + | 2.11429i | −0.240946 | + | 0.240946i | ||||
\(78\) | −4.00594 | − | 4.00594i | −0.453583 | − | 0.453583i | ||||
\(79\) | 0.760897 | − | 0.760897i | 0.0856076 | − | 0.0856076i | −0.663006 | − | 0.748614i | \(-0.730720\pi\) |
0.748614 | + | 0.663006i | \(0.230720\pi\) | |||||||
\(80\) | 1.69364 | + | 1.45999i | 0.189355 | + | 0.163232i | ||||
\(81\) | 9.86854 | 1.09650 | ||||||||
\(82\) | − | 9.31106i | − | 1.02823i | ||||||
\(83\) | 3.16981 | − | 3.16981i | 0.347932 | − | 0.347932i | −0.511407 | − | 0.859339i | \(-0.670875\pi\) |
0.859339 | + | 0.511407i | \(0.170875\pi\) | |||||||
\(84\) | 1.49519i | 0.163139i | ||||||||
\(85\) | 11.8117 | − | 13.7020i | 1.28116 | − | 1.48619i | ||||
\(86\) | −10.9160 | −1.17710 | ||||||||
\(87\) | 3.54488i | 0.380051i | ||||||||
\(88\) | − | 3.64633i | − | 0.388700i | ||||||
\(89\) | −5.80016 | − | 5.80016i | −0.614816 | − | 0.614816i | 0.329381 | − | 0.944197i | \(-0.393160\pi\) |
−0.944197 | + | 0.329381i | \(0.893160\pi\) | |||||||
\(90\) | 0.473980 | − | 0.549834i | 0.0499619 | − | 0.0579576i | ||||
\(91\) | 1.80159 | + | 1.80159i | 0.188858 | + | 0.188858i | ||||
\(92\) | −7.79067 | −0.812233 | ||||||||
\(93\) | 8.35226 | 0.866089 | ||||||||
\(94\) | 4.11794 | + | 4.11794i | 0.424733 | + | 0.424733i | ||||
\(95\) | −9.62597 | + | 0.713182i | −0.987604 | + | 0.0731710i | ||||
\(96\) | −1.28931 | − | 1.28931i | −0.131590 | − | 0.131590i | ||||
\(97\) | − | 14.6206i | − | 1.48449i | −0.670127 | − | 0.742246i | \(-0.733760\pi\) | ||
0.670127 | − | 0.742246i | \(-0.266240\pi\) | |||||||
\(98\) | 6.32757i | 0.639181i | ||||||||
\(99\) | −1.18377 | −0.118973 | ||||||||
\(100\) | 0.736849 | + | 4.94541i | 0.0736849 | + | 0.494541i | ||||
\(101\) | 3.68870i | 0.367039i | 0.983016 | + | 0.183520i | \(0.0587491\pi\) | ||||
−0.983016 | + | 0.183520i | \(0.941251\pi\) | |||||||
\(102\) | −10.4309 | + | 10.4309i | −1.03281 | + | 1.03281i | ||||
\(103\) | − | 11.1543i | − | 1.09907i | −0.835471 | − | 0.549535i | \(-0.814805\pi\) | ||
0.835471 | − | 0.549535i | \(-0.185195\pi\) | |||||||
\(104\) | −3.10704 | −0.304670 | ||||||||
\(105\) | −2.18297 | + | 2.53232i | −0.213036 | + | 0.247129i | ||||
\(106\) | −0.446555 | + | 0.446555i | −0.0433732 | + | 0.0433732i | ||||
\(107\) | −3.88311 | − | 3.88311i | −0.375394 | − | 0.375394i | 0.494043 | − | 0.869437i | \(-0.335519\pi\) |
−0.869437 | + | 0.494043i | \(0.835519\pi\) | |||||||
\(108\) | 3.44936 | − | 3.44936i | 0.331915 | − | 0.331915i | ||||
\(109\) | 2.01583 | − | 2.01583i | 0.193081 | − | 0.193081i | −0.603945 | − | 0.797026i | \(-0.706405\pi\) |
0.797026 | + | 0.603945i | \(0.206405\pi\) | |||||||
\(110\) | 5.32361 | − | 6.17558i | 0.507587 | − | 0.588819i | ||||
\(111\) | −10.9742 | − | 1.60617i | −1.04162 | − | 0.152451i | ||||
\(112\) | 0.579841 | + | 0.579841i | 0.0547899 | + | 0.0547899i | ||||
\(113\) | − | 11.8892i | − | 1.11844i | −0.829019 | − | 0.559220i | \(-0.811101\pi\) | ||
0.829019 | − | 0.559220i | \(-0.188899\pi\) | |||||||
\(114\) | 7.87084 | 0.737171 | ||||||||
\(115\) | −13.1946 | − | 11.3743i | −1.23040 | − | 1.06066i | ||||
\(116\) | 1.37472 | + | 1.37472i | 0.127639 | + | 0.127639i | ||||
\(117\) | 1.00869i | 0.0932531i | ||||||||
\(118\) | 6.16388 | − | 6.16388i | 0.567431 | − | 0.567431i | ||||
\(119\) | 4.69107 | − | 4.69107i | 0.430030 | − | 0.430030i | ||||
\(120\) | −0.301249 | − | 4.06602i | −0.0275001 | − | 0.371175i | ||||
\(121\) | −2.29574 | −0.208704 | ||||||||
\(122\) | −8.71382 | + | 8.71382i | −0.788912 | + | 0.788912i | ||||
\(123\) | −12.0049 | + | 12.0049i | −1.08244 | + | 1.08244i | ||||
\(124\) | 3.23904 | − | 3.23904i | 0.290875 | − | 0.290875i | ||||
\(125\) | −5.97229 | + | 9.45154i | −0.534178 | + | 0.845372i | ||||
\(126\) | 0.188243 | − | 0.188243i | 0.0167700 | − | 0.0167700i | ||||
\(127\) | 13.9019 | + | 13.9019i | 1.23359 | + | 1.23359i | 0.962575 | + | 0.271015i | \(0.0873593\pi\) |
0.271015 | + | 0.962575i | \(0.412641\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 14.0741 | + | 14.0741i | 1.23915 | + | 1.23915i | ||||
\(130\) | −5.26221 | − | 4.53625i | −0.461526 | − | 0.397855i | ||||
\(131\) | 2.71250 | − | 2.71250i | 0.236992 | − | 0.236992i | −0.578611 | − | 0.815603i | \(-0.696405\pi\) |
0.815603 | + | 0.578611i | \(0.196405\pi\) | |||||||
\(132\) | −4.70126 | + | 4.70126i | −0.409192 | + | 0.409192i | ||||
\(133\) | −3.53975 | −0.306935 | ||||||||
\(134\) | 2.01024 | − | 2.01024i | 0.173658 | − | 0.173658i | ||||
\(135\) | 10.8780 | − | 0.805947i | 0.936232 | − | 0.0693648i | ||||
\(136\) | 8.09027i | 0.693735i | ||||||||
\(137\) | −11.4519 | − | 11.4519i | −0.978406 | − | 0.978406i | 0.0213660 | − | 0.999772i | \(-0.493198\pi\) |
−0.999772 | + | 0.0213660i | \(0.993198\pi\) | |||||||
\(138\) | 10.0446 | + | 10.0446i | 0.855053 | + | 0.855053i | ||||
\(139\) | −2.41427 | −0.204775 | −0.102388 | − | 0.994745i | \(-0.532648\pi\) | ||||
−0.102388 | + | 0.994745i | \(0.532648\pi\) | |||||||
\(140\) | 0.135480 | + | 1.82861i | 0.0114502 | + | 0.154546i | ||||
\(141\) | − | 10.6186i | − | 0.894248i | ||||||
\(142\) | −0.00151598 | −0.000127218 | ||||||||
\(143\) | 11.3293i | 0.947403i | ||||||||
\(144\) | 0.324646i | 0.0270538i | ||||||||
\(145\) | 0.321204 | + | 4.33536i | 0.0266746 | + | 0.360032i | ||||
\(146\) | 9.32759 | + | 9.32759i | 0.771957 | + | 0.771957i | ||||
\(147\) | 8.15820 | − | 8.15820i | 0.672877 | − | 0.672877i | ||||
\(148\) | −4.87870 | + | 3.63294i | −0.401027 | + | 0.298626i | ||||
\(149\) | 4.02923i | 0.330088i | 0.986286 | + | 0.165044i | \(0.0527765\pi\) | ||||
−0.986286 | + | 0.165044i | \(0.947223\pi\) | |||||||
\(150\) | 5.42614 | − | 7.32620i | 0.443043 | − | 0.598181i | ||||
\(151\) | 8.86568i | 0.721479i | 0.932667 | + | 0.360739i | \(0.117476\pi\) | ||||
−0.932667 | + | 0.360739i | \(0.882524\pi\) | |||||||
\(152\) | 3.05234 | − | 3.05234i | 0.247578 | − | 0.247578i | ||||
\(153\) | 2.62647 | 0.212338 | ||||||||
\(154\) | 2.11429 | − | 2.11429i | 0.170375 | − | 0.170375i | ||||
\(155\) | 10.2148 | − | 0.756805i | 0.820469 | − | 0.0607880i | ||||
\(156\) | 4.00594 | + | 4.00594i | 0.320732 | + | 0.320732i | ||||
\(157\) | 6.87897 | + | 6.87897i | 0.549001 | + | 0.549001i | 0.926152 | − | 0.377151i | \(-0.123096\pi\) |
−0.377151 | + | 0.926152i | \(0.623096\pi\) | |||||||
\(158\) | −0.760897 | + | 0.760897i | −0.0605337 | + | 0.0605337i | ||||
\(159\) | 1.15150 | 0.0913196 | ||||||||
\(160\) | −1.69364 | − | 1.45999i | −0.133894 | − | 0.115422i | ||||
\(161\) | −4.51735 | − | 4.51735i | −0.356017 | − | 0.356017i | ||||
\(162\) | −9.86854 | −0.775346 | ||||||||
\(163\) | 10.6733i | 0.835995i | 0.908448 | + | 0.417997i | \(0.137268\pi\) | ||||
−0.908448 | + | 0.417997i | \(0.862732\pi\) | |||||||
\(164\) | 9.31106i | 0.727072i | ||||||||
\(165\) | −14.8260 | + | 1.09845i | −1.15421 | + | 0.0855144i | ||||
\(166\) | −3.16981 | + | 3.16981i | −0.246025 | + | 0.246025i | ||||
\(167\) | − | 0.864796i | − | 0.0669199i | −0.999440 | − | 0.0334600i | \(-0.989347\pi\) | ||
0.999440 | − | 0.0334600i | \(-0.0106526\pi\) | |||||||
\(168\) | − | 1.49519i | − | 0.115357i | ||||||
\(169\) | −3.34633 | −0.257410 | ||||||||
\(170\) | −11.8117 | + | 13.7020i | −0.905918 | + | 1.05090i | ||||
\(171\) | −0.990930 | − | 0.990930i | −0.0757783 | − | 0.0757783i | ||||
\(172\) | 10.9160 | 0.832334 | ||||||||
\(173\) | −2.14973 | − | 2.14973i | −0.163441 | − | 0.163441i | 0.620648 | − | 0.784089i | \(-0.286870\pi\) |
−0.784089 | + | 0.620648i | \(0.786870\pi\) | |||||||
\(174\) | − | 3.54488i | − | 0.268737i | ||||||
\(175\) | −2.44030 | + | 3.29481i | −0.184469 | + | 0.249064i | ||||
\(176\) | 3.64633i | 0.274853i | ||||||||
\(177\) | −15.8943 | −1.19469 | ||||||||
\(178\) | 5.80016 | + | 5.80016i | 0.434741 | + | 0.434741i | ||||
\(179\) | −0.313292 | − | 0.313292i | −0.0234165 | − | 0.0234165i | 0.695302 | − | 0.718718i | \(-0.255271\pi\) |
−0.718718 | + | 0.695302i | \(0.755271\pi\) | |||||||
\(180\) | −0.473980 | + | 0.549834i | −0.0353284 | + | 0.0409822i | ||||
\(181\) | 16.2161 | 1.20533 | 0.602667 | − | 0.797993i | \(-0.294105\pi\) | ||||
0.602667 | + | 0.797993i | \(0.294105\pi\) | |||||||
\(182\) | −1.80159 | − | 1.80159i | −0.133543 | − | 0.133543i | ||||
\(183\) | 22.4697 | 1.66100 | ||||||||
\(184\) | 7.79067 | 0.574336 | ||||||||
\(185\) | −13.5668 | − | 0.969960i | −0.997454 | − | 0.0713129i | ||||
\(186\) | −8.35226 | −0.612418 | ||||||||
\(187\) | 29.4998 | 2.15724 | ||||||||
\(188\) | −4.11794 | − | 4.11794i | −0.300332 | − | 0.300332i | ||||
\(189\) | 4.00017 | 0.290969 | ||||||||
\(190\) | 9.62597 | − | 0.713182i | 0.698341 | − | 0.0517397i | ||||
\(191\) | 0.276686 | + | 0.276686i | 0.0200203 | + | 0.0200203i | 0.717046 | − | 0.697026i | \(-0.245494\pi\) |
−0.697026 | + | 0.717046i | \(0.745494\pi\) | |||||||
\(192\) | 1.28931 | + | 1.28931i | 0.0930480 | + | 0.0930480i | ||||
\(193\) | 8.78779 | 0.632559 | 0.316279 | − | 0.948666i | \(-0.397566\pi\) | ||||
0.316279 | + | 0.948666i | \(0.397566\pi\) | |||||||
\(194\) | 14.6206i | 1.04969i | ||||||||
\(195\) | 0.935990 | + | 12.6333i | 0.0670276 | + | 0.904686i | ||||
\(196\) | − | 6.32757i | − | 0.451969i | ||||||
\(197\) | 8.41487 | + | 8.41487i | 0.599535 | + | 0.599535i | 0.940189 | − | 0.340654i | \(-0.110649\pi\) |
−0.340654 | + | 0.940189i | \(0.610649\pi\) | |||||||
\(198\) | 1.18377 | 0.0841266 | ||||||||
\(199\) | 4.20114 | + | 4.20114i | 0.297811 | + | 0.297811i | 0.840156 | − | 0.542345i | \(-0.182463\pi\) |
−0.542345 | + | 0.840156i | \(0.682463\pi\) | |||||||
\(200\) | −0.736849 | − | 4.94541i | −0.0521031 | − | 0.349693i | ||||
\(201\) | −5.18365 | −0.365627 | ||||||||
\(202\) | − | 3.68870i | − | 0.259536i | ||||||
\(203\) | 1.59424i | 0.111894i | ||||||||
\(204\) | 10.4309 | − | 10.4309i | 0.730307 | − | 0.730307i | ||||
\(205\) | −13.5941 | + | 15.7696i | −0.949451 | + | 1.10140i | ||||
\(206\) | 11.1543i | 0.777160i | ||||||||
\(207\) | − | 2.52921i | − | 0.175792i | ||||||
\(208\) | 3.10704 | 0.215434 | ||||||||
\(209\) | −11.1299 | − | 11.1299i | −0.769868 | − | 0.769868i | ||||
\(210\) | 2.18297 | − | 2.53232i | 0.150639 | − | 0.174747i | ||||
\(211\) | −27.4901 | −1.89250 | −0.946248 | − | 0.323442i | \(-0.895160\pi\) | ||||
−0.946248 | + | 0.323442i | \(0.895160\pi\) | |||||||
\(212\) | 0.446555 | − | 0.446555i | 0.0306695 | − | 0.0306695i | ||||
\(213\) | 0.00195457 | + | 0.00195457i | 0.000133925 | + | 0.000133925i | ||||
\(214\) | 3.88311 | + | 3.88311i | 0.265444 | + | 0.265444i | ||||
\(215\) | 18.4877 | + | 15.9372i | 1.26085 | + | 1.08691i | ||||
\(216\) | −3.44936 | + | 3.44936i | −0.234699 | + | 0.234699i | ||||
\(217\) | 3.75626 | 0.254992 | ||||||||
\(218\) | −2.01583 | + | 2.01583i | −0.136529 | + | 0.136529i | ||||
\(219\) | − | 24.0523i | − | 1.62531i | ||||||
\(220\) | −5.32361 | + | 6.17558i | −0.358918 | + | 0.416358i | ||||
\(221\) | − | 25.1367i | − | 1.69088i | ||||||
\(222\) | 10.9742 | + | 1.60617i | 0.736537 | + | 0.107799i | ||||
\(223\) | −9.42660 | + | 9.42660i | −0.631252 | + | 0.631252i | −0.948382 | − | 0.317130i | \(-0.897281\pi\) |
0.317130 | + | 0.948382i | \(0.397281\pi\) | |||||||
\(224\) | −0.579841 | − | 0.579841i | −0.0387423 | − | 0.0387423i | ||||
\(225\) | −1.60551 | + | 0.239215i | −0.107034 | + | 0.0159477i | ||||
\(226\) | 11.8892i | 0.790856i | ||||||||
\(227\) | 17.9587i | 1.19196i | 0.802999 | + | 0.595981i | \(0.203237\pi\) | ||||
−0.802999 | + | 0.595981i | \(0.796763\pi\) | |||||||
\(228\) | −7.87084 | −0.521259 | ||||||||
\(229\) | 18.1673i | 1.20053i | 0.799802 | + | 0.600264i | \(0.204938\pi\) | ||||
−0.799802 | + | 0.600264i | \(0.795062\pi\) | |||||||
\(230\) | 13.1946 | + | 11.3743i | 0.870027 | + | 0.750000i | ||||
\(231\) | −5.45197 | −0.358713 | ||||||||
\(232\) | −1.37472 | − | 1.37472i | −0.0902547 | − | 0.0902547i | ||||
\(233\) | 2.23686 | + | 2.23686i | 0.146541 | + | 0.146541i | 0.776571 | − | 0.630030i | \(-0.216957\pi\) |
−0.630030 | + | 0.776571i | \(0.716957\pi\) | |||||||
\(234\) | − | 1.00869i | − | 0.0659399i | ||||||
\(235\) | −0.962160 | − | 12.9865i | −0.0627644 | − | 0.847144i | ||||
\(236\) | −6.16388 | + | 6.16388i | −0.401234 | + | 0.401234i | ||||
\(237\) | 1.96207 | 0.127450 | ||||||||
\(238\) | −4.69107 | + | 4.69107i | −0.304077 | + | 0.304077i | ||||
\(239\) | 4.53542 | − | 4.53542i | 0.293372 | − | 0.293372i | −0.545039 | − | 0.838411i | \(-0.683485\pi\) |
0.838411 | + | 0.545039i | \(0.183485\pi\) | |||||||
\(240\) | 0.301249 | + | 4.06602i | 0.0194455 | + | 0.262460i | ||||
\(241\) | 2.95256 | + | 2.95256i | 0.190191 | + | 0.190191i | 0.795779 | − | 0.605587i | \(-0.207062\pi\) |
−0.605587 | + | 0.795779i | \(0.707062\pi\) | |||||||
\(242\) | 2.29574 | 0.147576 | ||||||||
\(243\) | 2.37553 | + | 2.37553i | 0.152390 | + | 0.152390i | ||||
\(244\) | 8.71382 | − | 8.71382i | 0.557845 | − | 0.557845i | ||||
\(245\) | 9.23820 | − | 10.7166i | 0.590207 | − | 0.684661i | ||||
\(246\) | 12.0049 | − | 12.0049i | 0.765402 | − | 0.765402i | ||||
\(247\) | −9.48374 | + | 9.48374i | −0.603436 | + | 0.603436i | ||||
\(248\) | −3.23904 | + | 3.23904i | −0.205679 | + | 0.205679i | ||||
\(249\) | 8.17374 | 0.517990 | ||||||||
\(250\) | 5.97229 | − | 9.45154i | 0.377721 | − | 0.597768i | ||||
\(251\) | −9.93109 | + | 9.93109i | −0.626845 | + | 0.626845i | −0.947273 | − | 0.320428i | \(-0.896173\pi\) |
0.320428 | + | 0.947273i | \(0.396173\pi\) | |||||||
\(252\) | −0.188243 | + | 0.188243i | −0.0118582 | + | 0.0118582i | ||||
\(253\) | − | 28.4074i | − | 1.78596i | ||||||
\(254\) | −13.9019 | − | 13.9019i | −0.872280 | − | 0.872280i | ||||
\(255\) | 32.8951 | − | 2.43718i | 2.05997 | − | 0.152622i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 15.1135i | − | 0.942757i | −0.881931 | − | 0.471378i | \(-0.843757\pi\) | ||
0.881931 | − | 0.471378i | \(-0.156243\pi\) | |||||||
\(258\) | −14.0741 | − | 14.0741i | −0.876213 | − | 0.876213i | ||||
\(259\) | −4.93540 | − | 0.722344i | −0.306671 | − | 0.0448842i | ||||
\(260\) | 5.26221 | + | 4.53625i | 0.326348 | + | 0.281326i | ||||
\(261\) | −0.446297 | + | 0.446297i | −0.0276251 | + | 0.0276251i | ||||
\(262\) | −2.71250 | + | 2.71250i | −0.167579 | + | 0.167579i | ||||
\(263\) | 9.74250 | + | 9.74250i | 0.600749 | + | 0.600749i | 0.940511 | − | 0.339763i | \(-0.110347\pi\) |
−0.339763 | + | 0.940511i | \(0.610347\pi\) | |||||||
\(264\) | 4.70126 | − | 4.70126i | 0.289342 | − | 0.289342i | ||||
\(265\) | 1.40827 | − | 0.104338i | 0.0865094 | − | 0.00640942i | ||||
\(266\) | 3.53975 | 0.217036 | ||||||||
\(267\) | − | 14.9564i | − | 0.915319i | ||||||
\(268\) | −2.01024 | + | 2.01024i | −0.122795 | + | 0.122795i | ||||
\(269\) | 6.43418i | 0.392299i | 0.980574 | + | 0.196150i | \(0.0628438\pi\) | ||||
−0.980574 | + | 0.196150i | \(0.937156\pi\) | |||||||
\(270\) | −10.8780 | + | 0.805947i | −0.662016 | + | 0.0490483i | ||||
\(271\) | −25.6662 | −1.55911 | −0.779556 | − | 0.626332i | \(-0.784555\pi\) | ||||
−0.779556 | + | 0.626332i | \(0.784555\pi\) | |||||||
\(272\) | − | 8.09027i | − | 0.490544i | ||||||
\(273\) | 4.64561i | 0.281165i | ||||||||
\(274\) | 11.4519 | + | 11.4519i | 0.691837 | + | 0.691837i | ||||
\(275\) | −18.0326 | + | 2.68680i | −1.08741 | + | 0.162020i | ||||
\(276\) | −10.0446 | − | 10.0446i | −0.604614 | − | 0.604614i | ||||
\(277\) | −17.2625 | −1.03720 | −0.518602 | − | 0.855016i | \(-0.673548\pi\) | ||||
−0.518602 | + | 0.855016i | \(0.673548\pi\) | |||||||
\(278\) | 2.41427 | 0.144798 | ||||||||
\(279\) | 1.05154 | + | 1.05154i | 0.0629541 | + | 0.0629541i | ||||
\(280\) | −0.135480 | − | 1.82861i | −0.00809650 | − | 0.109280i | ||||
\(281\) | −3.84098 | − | 3.84098i | −0.229134 | − | 0.229134i | 0.583197 | − | 0.812331i | \(-0.301802\pi\) |
−0.812331 | + | 0.583197i | \(0.801802\pi\) | |||||||
\(282\) | 10.6186i | 0.632329i | ||||||||
\(283\) | − | 20.5564i | − | 1.22195i | −0.791650 | − | 0.610975i | \(-0.790778\pi\) | ||
0.791650 | − | 0.610975i | \(-0.209222\pi\) | |||||||
\(284\) | 0.00151598 | 8.99567e−5 | ||||||||
\(285\) | −13.3304 | − | 11.4914i | −0.789624 | − | 0.680689i | ||||
\(286\) | − | 11.3293i | − | 0.669915i | ||||||
\(287\) | −5.39894 | + | 5.39894i | −0.318689 | + | 0.318689i | ||||
\(288\) | − | 0.324646i | − | 0.0191299i | ||||||
\(289\) | −48.4524 | −2.85014 | ||||||||
\(290\) | −0.321204 | − | 4.33536i | −0.0188618 | − | 0.254581i | ||||
\(291\) | 18.8504 | − | 18.8504i | 1.10503 | − | 1.10503i | ||||
\(292\) | −9.32759 | − | 9.32759i | −0.545856 | − | 0.545856i | ||||
\(293\) | −11.2671 | + | 11.2671i | −0.658232 | + | 0.658232i | −0.954962 | − | 0.296729i | \(-0.904104\pi\) |
0.296729 | + | 0.954962i | \(0.404104\pi\) | |||||||
\(294\) | −8.15820 | + | 8.15820i | −0.475796 | + | 0.475796i | ||||
\(295\) | −19.4386 | + | 1.44019i | −1.13176 | + | 0.0838514i | ||||
\(296\) | 4.87870 | − | 3.63294i | 0.283569 | − | 0.211160i | ||||
\(297\) | 12.5775 | + | 12.5775i | 0.729822 | + | 0.729822i | ||||
\(298\) | − | 4.02923i | − | 0.233407i | ||||||
\(299\) | −24.2059 | −1.39986 | ||||||||
\(300\) | −5.42614 | + | 7.32620i | −0.313278 | + | 0.422978i | ||||
\(301\) | 6.32952 | + | 6.32952i | 0.364828 | + | 0.364828i | ||||
\(302\) | − | 8.86568i | − | 0.510163i | ||||||
\(303\) | −4.75588 | + | 4.75588i | −0.273218 | + | 0.273218i | ||||
\(304\) | −3.05234 | + | 3.05234i | −0.175064 | + | 0.175064i | ||||
\(305\) | 27.4802 | − | 2.03599i | 1.57351 | − | 0.116581i | ||||
\(306\) | −2.62647 | −0.150145 | ||||||||
\(307\) | 9.43686 | − | 9.43686i | 0.538590 | − | 0.538590i | −0.384525 | − | 0.923115i | \(-0.625635\pi\) |
0.923115 | + | 0.384525i | \(0.125635\pi\) | |||||||
\(308\) | −2.11429 | + | 2.11429i | −0.120473 | + | 0.120473i | ||||
\(309\) | 14.3814 | − | 14.3814i | 0.818131 | − | 0.818131i | ||||
\(310\) | −10.2148 | + | 0.756805i | −0.580159 | + | 0.0429836i | ||||
\(311\) | 6.70368 | − | 6.70368i | 0.380131 | − | 0.380131i | −0.491019 | − | 0.871149i | \(-0.663375\pi\) |
0.871149 | + | 0.491019i | \(0.163375\pi\) | |||||||
\(312\) | −4.00594 | − | 4.00594i | −0.226791 | − | 0.226791i | ||||
\(313\) | −23.2157 | −1.31223 | −0.656114 | − | 0.754662i | \(-0.727801\pi\) | ||||
−0.656114 | + | 0.754662i | \(0.727801\pi\) | |||||||
\(314\) | −6.87897 | − | 6.87897i | −0.388203 | − | 0.388203i | ||||
\(315\) | −0.593650 | + | 0.0439832i | −0.0334484 | + | 0.00247817i | ||||
\(316\) | 0.760897 | − | 0.760897i | 0.0428038 | − | 0.0428038i | ||||
\(317\) | −15.3696 | + | 15.3696i | −0.863245 | + | 0.863245i | −0.991714 | − | 0.128469i | \(-0.958994\pi\) |
0.128469 | + | 0.991714i | \(0.458994\pi\) | |||||||
\(318\) | −1.15150 | −0.0645727 | ||||||||
\(319\) | −5.01268 | + | 5.01268i | −0.280656 | + | 0.280656i | ||||
\(320\) | 1.69364 | + | 1.45999i | 0.0946775 | + | 0.0816160i | ||||
\(321\) | − | 10.0131i | − | 0.558875i | ||||||
\(322\) | 4.51735 | + | 4.51735i | 0.251742 | + | 0.251742i | ||||
\(323\) | 24.6943 | + | 24.6943i | 1.37403 | + | 1.37403i | ||||
\(324\) | 9.86854 | 0.548252 | ||||||||
\(325\) | 2.28942 | + | 15.3656i | 0.126994 | + | 0.852328i | ||||
\(326\) | − | 10.6733i | − | 0.591137i | ||||||
\(327\) | 5.19806 | 0.287454 | ||||||||
\(328\) | − | 9.31106i | − | 0.514117i | ||||||
\(329\) | − | 4.77550i | − | 0.263282i | ||||||
\(330\) | 14.8260 | − | 1.09845i | 0.816147 | − | 0.0604678i | ||||
\(331\) | −5.72839 | − | 5.72839i | −0.314861 | − | 0.314861i | 0.531929 | − | 0.846789i | \(-0.321467\pi\) |
−0.846789 | + | 0.531929i | \(0.821467\pi\) | |||||||
\(332\) | 3.16981 | − | 3.16981i | 0.173966 | − | 0.173966i | ||||
\(333\) | −1.17942 | − | 1.58385i | −0.0646318 | − | 0.0867945i | ||||
\(334\) | 0.864796i | 0.0473195i | ||||||||
\(335\) | −6.33957 | + | 0.469695i | −0.346368 | + | 0.0256622i | ||||
\(336\) | 1.49519i | 0.0815694i | ||||||||
\(337\) | 5.31333 | − | 5.31333i | 0.289436 | − | 0.289436i | −0.547421 | − | 0.836857i | \(-0.684391\pi\) |
0.836857 | + | 0.547421i | \(0.184391\pi\) | |||||||
\(338\) | 3.34633 | 0.182016 | ||||||||
\(339\) | 15.3288 | − | 15.3288i | 0.832549 | − | 0.832549i | ||||
\(340\) | 11.8117 | − | 13.7020i | 0.640580 | − | 0.743096i | ||||
\(341\) | 11.8106 | + | 11.8106i | 0.639581 | + | 0.639581i | ||||
\(342\) | 0.990930 | + | 0.990930i | 0.0535834 | + | 0.0535834i | ||||
\(343\) | 7.72788 | − | 7.72788i | 0.417266 | − | 0.417266i | ||||
\(344\) | −10.9160 | −0.588549 | ||||||||
\(345\) | −2.34693 | − | 31.6770i | −0.126354 | − | 1.70543i | ||||
\(346\) | 2.14973 | + | 2.14973i | 0.115570 | + | 0.115570i | ||||
\(347\) | 32.7620 | 1.75876 | 0.879379 | − | 0.476123i | \(-0.157958\pi\) | ||||
0.879379 | + | 0.476123i | \(0.157958\pi\) | |||||||
\(348\) | 3.54488i | 0.190026i | ||||||||
\(349\) | − | 14.0604i | − | 0.752637i | −0.926490 | − | 0.376318i | \(-0.877190\pi\) | ||
0.926490 | − | 0.376318i | \(-0.122810\pi\) | |||||||
\(350\) | 2.44030 | − | 3.29481i | 0.130439 | − | 0.176115i | ||||
\(351\) | 10.7173 | − | 10.7173i | 0.572047 | − | 0.572047i | ||||
\(352\) | − | 3.64633i | − | 0.194350i | ||||||
\(353\) | − | 6.79098i | − | 0.361447i | −0.983534 | − | 0.180724i | \(-0.942156\pi\) | ||
0.983534 | − | 0.180724i | \(-0.0578440\pi\) | |||||||
\(354\) | 15.8943 | 0.844773 | ||||||||
\(355\) | 0.00256752 | + | 0.00221331i | 0.000136270 | + | 0.000117471i | ||||
\(356\) | −5.80016 | − | 5.80016i | −0.307408 | − | 0.307408i | ||||
\(357\) | 12.0965 | 0.640215 | ||||||||
\(358\) | 0.313292 | + | 0.313292i | 0.0165580 | + | 0.0165580i | ||||
\(359\) | 4.91904i | 0.259617i | 0.991539 | + | 0.129808i | \(0.0414362\pi\) | ||||
−0.991539 | + | 0.129808i | \(0.958564\pi\) | |||||||
\(360\) | 0.473980 | − | 0.549834i | 0.0249810 | − | 0.0289788i | ||||
\(361\) | 0.366413i | 0.0192849i | ||||||||
\(362\) | −16.2161 | −0.852300 | ||||||||
\(363\) | −2.95992 | − | 2.95992i | −0.155356 | − | 0.155356i | ||||
\(364\) | 1.80159 | + | 1.80159i | 0.0944289 | + | 0.0944289i | ||||
\(365\) | −2.17940 | − | 29.4158i | −0.114075 | − | 1.53969i | ||||
\(366\) | −22.4697 | −1.17451 | ||||||||
\(367\) | 21.4924 | + | 21.4924i | 1.12189 | + | 1.12189i | 0.991457 | + | 0.130436i | \(0.0416378\pi\) |
0.130436 | + | 0.991457i | \(0.458362\pi\) | |||||||
\(368\) | −7.79067 | −0.406117 | ||||||||
\(369\) | −3.02280 | −0.157361 | ||||||||
\(370\) | 13.5668 | + | 0.969960i | 0.705306 | + | 0.0504258i | ||||
\(371\) | 0.517862 | 0.0268860 | ||||||||
\(372\) | 8.35226 | 0.433045 | ||||||||
\(373\) | 19.5734 | + | 19.5734i | 1.01347 | + | 1.01347i | 0.999908 | + | 0.0135632i | \(0.00431743\pi\) |
0.0135632 | + | 0.999908i | \(0.495683\pi\) | |||||||
\(374\) | −29.4998 | −1.52540 | ||||||||
\(375\) | −19.8861 | + | 4.48584i | −1.02692 | + | 0.231648i | ||||
\(376\) | 4.11794 | + | 4.11794i | 0.212367 | + | 0.212367i | ||||
\(377\) | 4.27130 | + | 4.27130i | 0.219983 | + | 0.219983i | ||||
\(378\) | −4.00017 | −0.205746 | ||||||||
\(379\) | 1.90775i | 0.0979943i | 0.998799 | + | 0.0489972i | \(0.0156025\pi\) | ||||
−0.998799 | + | 0.0489972i | \(0.984397\pi\) | |||||||
\(380\) | −9.62597 | + | 0.713182i | −0.493802 | + | 0.0365855i | ||||
\(381\) | 35.8476i | 1.83653i | ||||||||
\(382\) | −0.276686 | − | 0.276686i | −0.0141565 | − | 0.0141565i | ||||
\(383\) | 12.0669 | 0.616591 | 0.308295 | − | 0.951291i | \(-0.400241\pi\) | ||||
0.308295 | + | 0.951291i | \(0.400241\pi\) | |||||||
\(384\) | −1.28931 | − | 1.28931i | −0.0657949 | − | 0.0657949i | ||||
\(385\) | −6.66771 | + | 0.494007i | −0.339818 | + | 0.0251769i | ||||
\(386\) | −8.78779 | −0.447287 | ||||||||
\(387\) | 3.54382i | 0.180142i | ||||||||
\(388\) | − | 14.6206i | − | 0.742246i | ||||||
\(389\) | −16.8015 | + | 16.8015i | −0.851868 | + | 0.851868i | −0.990363 | − | 0.138495i | \(-0.955773\pi\) |
0.138495 | + | 0.990363i | \(0.455773\pi\) | |||||||
\(390\) | −0.935990 | − | 12.6333i | −0.0473957 | − | 0.639710i | ||||
\(391\) | 63.0286i | 3.18749i | ||||||||
\(392\) | 6.32757i | 0.319590i | ||||||||
\(393\) | 6.99450 | 0.352826 | ||||||||
\(394\) | −8.41487 | − | 8.41487i | −0.423935 | − | 0.423935i | ||||
\(395\) | 2.39959 | − | 0.177784i | 0.120737 | − | 0.00894529i | ||||
\(396\) | −1.18377 | −0.0594865 | ||||||||
\(397\) | −6.99419 | + | 6.99419i | −0.351028 | + | 0.351028i | −0.860492 | − | 0.509464i | \(-0.829844\pi\) |
0.509464 | + | 0.860492i | \(0.329844\pi\) | |||||||
\(398\) | −4.20114 | − | 4.20114i | −0.210584 | − | 0.210584i | ||||
\(399\) | −4.56384 | − | 4.56384i | −0.228478 | − | 0.228478i | ||||
\(400\) | 0.736849 | + | 4.94541i | 0.0368425 | + | 0.247270i | ||||
\(401\) | 0.759591 | − | 0.759591i | 0.0379322 | − | 0.0379322i | −0.687886 | − | 0.725818i | \(-0.741461\pi\) |
0.725818 | + | 0.687886i | \(0.241461\pi\) | |||||||
\(402\) | 5.18365 | 0.258537 | ||||||||
\(403\) | 10.0638 | − | 10.0638i | 0.501315 | − | 0.501315i | ||||
\(404\) | 3.68870i | 0.183520i | ||||||||
\(405\) | 16.7138 | + | 14.4080i | 0.830515 | + | 0.715939i | ||||
\(406\) | − | 1.59424i | − | 0.0791207i | ||||||
\(407\) | −13.2469 | − | 17.7894i | −0.656625 | − | 0.881786i | ||||
\(408\) | −10.4309 | + | 10.4309i | −0.516405 | + | 0.516405i | ||||
\(409\) | 22.0320 | + | 22.0320i | 1.08941 | + | 1.08941i | 0.995589 | + | 0.0938237i | \(0.0299090\pi\) |
0.0938237 | + | 0.995589i | \(0.470091\pi\) | |||||||
\(410\) | 13.5941 | − | 15.7696i | 0.671363 | − | 0.778805i | ||||
\(411\) | − | 29.5302i | − | 1.45662i | ||||||
\(412\) | − | 11.1543i | − | 0.549535i | ||||||
\(413\) | −7.14814 | −0.351737 | ||||||||
\(414\) | 2.52921i | 0.124304i | ||||||||
\(415\) | 9.99642 | − | 0.740629i | 0.490705 | − | 0.0363560i | ||||
\(416\) | −3.10704 | −0.152335 | ||||||||
\(417\) | −3.11274 | − | 3.11274i | −0.152432 | − | 0.152432i | ||||
\(418\) | 11.1299 | + | 11.1299i | 0.544379 | + | 0.544379i | ||||
\(419\) | 13.7527i | 0.671863i | 0.941886 | + | 0.335931i | \(0.109051\pi\) | ||||
−0.941886 | + | 0.335931i | \(0.890949\pi\) | |||||||
\(420\) | −2.18297 | + | 2.53232i | −0.106518 | + | 0.123565i | ||||
\(421\) | 4.62725 | − | 4.62725i | 0.225519 | − | 0.225519i | −0.585299 | − | 0.810818i | \(-0.699023\pi\) |
0.810818 | + | 0.585299i | \(0.199023\pi\) | |||||||
\(422\) | 27.4901 | 1.33820 | ||||||||
\(423\) | 1.33687 | − | 1.33687i | 0.0650010 | − | 0.0650010i | ||||
\(424\) | −0.446555 | + | 0.446555i | −0.0216866 | + | 0.0216866i | ||||
\(425\) | 40.0097 | − | 5.96131i | 1.94075 | − | 0.289166i | ||||
\(426\) | −0.00195457 | − | 0.00195457i | −9.46990e−5 | − | 9.46990e-5i | ||||
\(427\) | 10.1053 | 0.489028 | ||||||||
\(428\) | −3.88311 | − | 3.88311i | −0.187697 | − | 0.187697i | ||||
\(429\) | −14.6070 | + | 14.6070i | −0.705231 | + | 0.705231i | ||||
\(430\) | −18.4877 | − | 15.9372i | −0.891557 | − | 0.768560i | ||||
\(431\) | 2.01292 | − | 2.01292i | 0.0969591 | − | 0.0969591i | −0.656963 | − | 0.753922i | \(-0.728159\pi\) |
0.753922 | + | 0.656963i | \(0.228159\pi\) | |||||||
\(432\) | 3.44936 | − | 3.44936i | 0.165958 | − | 0.165958i | ||||
\(433\) | −23.2986 | + | 23.2986i | −1.11966 | + | 1.11966i | −0.127870 | + | 0.991791i | \(0.540814\pi\) |
−0.991791 | + | 0.127870i | \(0.959186\pi\) | |||||||
\(434\) | −3.75626 | −0.180306 | ||||||||
\(435\) | −5.17549 | + | 6.00376i | −0.248146 | + | 0.287858i | ||||
\(436\) | 2.01583 | − | 2.01583i | 0.0965407 | − | 0.0965407i | ||||
\(437\) | 23.7798 | − | 23.7798i | 1.13754 | − | 1.13754i | ||||
\(438\) | 24.0523i | 1.14927i | ||||||||
\(439\) | −6.59762 | − | 6.59762i | −0.314887 | − | 0.314887i | 0.531912 | − | 0.846800i | \(-0.321474\pi\) |
−0.846800 | + | 0.531912i | \(0.821474\pi\) | |||||||
\(440\) | 5.32361 | − | 6.17558i | 0.253793 | − | 0.294409i | ||||
\(441\) | 2.05422 | 0.0978199 | ||||||||
\(442\) | 25.1367i | 1.19563i | ||||||||
\(443\) | −28.2758 | − | 28.2758i | −1.34343 | − | 1.34343i | −0.892625 | − | 0.450801i | \(-0.851138\pi\) |
−0.450801 | − | 0.892625i | \(-0.648862\pi\) | |||||||
\(444\) | −10.9742 | − | 1.60617i | −0.520810 | − | 0.0762256i | ||||
\(445\) | −1.35521 | − | 18.2916i | −0.0642432 | − | 0.867105i | ||||
\(446\) | 9.42660 | − | 9.42660i | 0.446363 | − | 0.446363i | ||||
\(447\) | −5.19493 | + | 5.19493i | −0.245712 | + | 0.245712i | ||||
\(448\) | 0.579841 | + | 0.579841i | 0.0273949 | + | 0.0273949i | ||||
\(449\) | 11.7576 | − | 11.7576i | 0.554876 | − | 0.554876i | −0.372968 | − | 0.927844i | \(-0.621660\pi\) |
0.927844 | + | 0.372968i | \(0.121660\pi\) | |||||||
\(450\) | 1.60551 | − | 0.239215i | 0.0756843 | − | 0.0112767i | ||||
\(451\) | −33.9512 | −1.59870 | ||||||||
\(452\) | − | 11.8892i | − | 0.559220i | ||||||
\(453\) | −11.4306 | + | 11.4306i | −0.537057 | + | 0.537057i | ||||
\(454\) | − | 17.9587i | − | 0.842844i | ||||||
\(455\) | 0.420942 | + | 5.68155i | 0.0197341 | + | 0.266355i | ||||
\(456\) | 7.87084 | 0.368586 | ||||||||
\(457\) | 31.9954i | 1.49668i | 0.663314 | + | 0.748341i | \(0.269149\pi\) | ||||
−0.663314 | + | 0.748341i | \(0.730851\pi\) | |||||||
\(458\) | − | 18.1673i | − | 0.848901i | ||||||
\(459\) | −27.9063 | − | 27.9063i | −1.30255 | − | 1.30255i | ||||
\(460\) | −13.1946 | − | 11.3743i | −0.615202 | − | 0.530330i | ||||
\(461\) | −17.2203 | − | 17.2203i | −0.802031 | − | 0.802031i | 0.181382 | − | 0.983413i | \(-0.441943\pi\) |
−0.983413 | + | 0.181382i | \(0.941943\pi\) | |||||||
\(462\) | 5.45197 | 0.253648 | ||||||||
\(463\) | −13.3316 | −0.619570 | −0.309785 | − | 0.950807i | \(-0.600257\pi\) | ||||
−0.309785 | + | 0.950807i | \(0.600257\pi\) | |||||||
\(464\) | 1.37472 | + | 1.37472i | 0.0638197 | + | 0.0638197i | ||||
\(465\) | 14.1457 | + | 12.1942i | 0.655993 | + | 0.565494i | ||||
\(466\) | −2.23686 | − | 2.23686i | −0.103620 | − | 0.103620i | ||||
\(467\) | 32.1997i | 1.49003i | 0.667050 | + | 0.745013i | \(0.267557\pi\) | ||||
−0.667050 | + | 0.745013i | \(0.732443\pi\) | |||||||
\(468\) | 1.00869i | 0.0466265i | ||||||||
\(469\) | −2.33124 | −0.107647 | ||||||||
\(470\) | 0.962160 | + | 12.9865i | 0.0443811 | + | 0.599022i | ||||
\(471\) | 17.7383i | 0.817336i | ||||||||
\(472\) | 6.16388 | − | 6.16388i | 0.283715 | − | 0.283715i | ||||
\(473\) | 39.8032i | 1.83015i | ||||||||
\(474\) | −1.96207 | −0.0901207 | ||||||||
\(475\) | −17.3442 | − | 12.8460i | −0.795806 | − | 0.589413i | ||||
\(476\) | 4.69107 | − | 4.69107i | 0.215015 | − | 0.215015i | ||||
\(477\) | 0.144972 | + | 0.144972i | 0.00663782 | + | 0.00663782i | ||||
\(478\) | −4.53542 | + | 4.53542i | −0.207445 | + | 0.207445i | ||||
\(479\) | 10.6512 | − | 10.6512i | 0.486664 | − | 0.486664i | −0.420588 | − | 0.907252i | \(-0.638176\pi\) |
0.907252 | + | 0.420588i | \(0.138176\pi\) | |||||||
\(480\) | −0.301249 | − | 4.06602i | −0.0137501 | − | 0.185587i | ||||
\(481\) | −15.1583 | + | 11.2877i | −0.691159 | + | 0.514674i | ||||
\(482\) | −2.95256 | − | 2.95256i | −0.134486 | − | 0.134486i | ||||
\(483\) | − | 11.6485i | − | 0.530027i | ||||||
\(484\) | −2.29574 | −0.104352 | ||||||||
\(485\) | 21.3459 | − | 24.7620i | 0.969267 | − | 1.12438i | ||||
\(486\) | −2.37553 | − | 2.37553i | −0.107756 | − | 0.107756i | ||||
\(487\) | 17.1695i | 0.778022i | 0.921233 | + | 0.389011i | \(0.127183\pi\) | ||||
−0.921233 | + | 0.389011i | \(0.872817\pi\) | |||||||
\(488\) | −8.71382 | + | 8.71382i | −0.394456 | + | 0.394456i | ||||
\(489\) | −13.7612 | + | 13.7612i | −0.622301 | + | 0.622301i | ||||
\(490\) | −9.23820 | + | 10.7166i | −0.417339 | + | 0.484128i | ||||
\(491\) | −9.04897 | −0.408374 | −0.204187 | − | 0.978932i | \(-0.565455\pi\) | ||||
−0.204187 | + | 0.978932i | \(0.565455\pi\) | |||||||
\(492\) | −12.0049 | + | 12.0049i | −0.541221 | + | 0.541221i | ||||
\(493\) | 11.1218 | − | 11.1218i | 0.500902 | − | 0.500902i | ||||
\(494\) | 9.48374 | − | 9.48374i | 0.426694 | − | 0.426694i | ||||
\(495\) | −2.00488 | − | 1.72829i | −0.0901125 | − | 0.0776808i | ||||
\(496\) | 3.23904 | − | 3.23904i | 0.145437 | − | 0.145437i | ||||
\(497\) | 0.000879026 | 0 | 0.000879026i | 3.94297e−5 | 0 | 3.94297e-5i | ||||
\(498\) | −8.17374 | −0.366274 | ||||||||
\(499\) | −8.81194 | − | 8.81194i | −0.394477 | − | 0.394477i | 0.481803 | − | 0.876280i | \(-0.339982\pi\) |
−0.876280 | + | 0.481803i | \(0.839982\pi\) | |||||||
\(500\) | −5.97229 | + | 9.45154i | −0.267089 | + | 0.422686i | ||||
\(501\) | 1.11499 | − | 1.11499i | 0.0498141 | − | 0.0498141i | ||||
\(502\) | 9.93109 | − | 9.93109i | 0.443246 | − | 0.443246i | ||||
\(503\) | 13.2027 | 0.588678 | 0.294339 | − | 0.955701i | \(-0.404900\pi\) | ||||
0.294339 | + | 0.955701i | \(0.404900\pi\) | |||||||
\(504\) | 0.188243 | − | 0.188243i | 0.00838501 | − | 0.00838501i | ||||
\(505\) | −5.38547 | + | 6.24734i | −0.239650 | + | 0.278003i | ||||
\(506\) | 28.4074i | 1.26286i | ||||||||
\(507\) | −4.31446 | − | 4.31446i | −0.191612 | − | 0.191612i | ||||
\(508\) | 13.9019 | + | 13.9019i | 0.616795 | + | 0.616795i | ||||
\(509\) | 25.2057 | 1.11722 | 0.558612 | − | 0.829429i | \(-0.311334\pi\) | ||||
0.558612 | + | 0.829429i | \(0.311334\pi\) | |||||||
\(510\) | −32.8951 | + | 2.43718i | −1.45662 | + | 0.107920i | ||||
\(511\) | − | 10.8170i | − | 0.478518i | ||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 21.0573i | 0.929701i | ||||||||
\(514\) | 15.1135i | 0.666630i | ||||||||
\(515\) | 16.2853 | − | 18.8915i | 0.717614 | − | 0.832458i | ||||
\(516\) | 14.0741 | + | 14.0741i | 0.619576 | + | 0.619576i | ||||
\(517\) | 15.0154 | − | 15.0154i | 0.660376 | − | 0.660376i | ||||
\(518\) | 4.93540 | + | 0.722344i | 0.216849 | + | 0.0317380i | ||||
\(519\) | − | 5.54335i | − | 0.243326i | ||||||
\(520\) | −5.26221 | − | 4.53625i | −0.230763 | − | 0.198928i | ||||
\(521\) | − | 8.65279i | − | 0.379086i | −0.981872 | − | 0.189543i | \(-0.939299\pi\) | ||
0.981872 | − | 0.189543i | \(-0.0607006\pi\) | |||||||
\(522\) | 0.446297 | − | 0.446297i | 0.0195339 | − | 0.0195339i | ||||
\(523\) | −28.4569 | −1.24433 | −0.622167 | − | 0.782884i | \(-0.713748\pi\) | ||||
−0.622167 | + | 0.782884i | \(0.713748\pi\) | |||||||
\(524\) | 2.71250 | − | 2.71250i | 0.118496 | − | 0.118496i | ||||
\(525\) | −7.39433 | + | 1.10173i | −0.322715 | + | 0.0480835i | ||||
\(526\) | −9.74250 | − | 9.74250i | −0.424793 | − | 0.424793i | ||||
\(527\) | −26.2047 | − | 26.2047i | −1.14149 | − | 1.14149i | ||||
\(528\) | −4.70126 | + | 4.70126i | −0.204596 | + | 0.204596i | ||||
\(529\) | 37.6945 | 1.63889 | ||||||||
\(530\) | −1.40827 | + | 0.104338i | −0.0611713 | + | 0.00453215i | ||||
\(531\) | −2.00108 | − | 2.00108i | −0.0868393 | − | 0.0868393i | ||||
\(532\) | −3.53975 | −0.153468 | ||||||||
\(533\) | 28.9298i | 1.25309i | ||||||||
\(534\) | 14.9564i | 0.647228i | ||||||||
\(535\) | −0.907292 | − | 12.2459i | −0.0392256 | − | 0.529437i | ||||
\(536\) | 2.01024 | − | 2.01024i | 0.0868292 | − | 0.0868292i | ||||
\(537\) | − | 0.807861i | − | 0.0348618i | ||||||
\(538\) | − | 6.43418i | − | 0.277397i | ||||||
\(539\) | 23.0724 | 0.993799 | ||||||||
\(540\) | 10.8780 | − | 0.805947i | 0.468116 | − | 0.0346824i | ||||
\(541\) | 22.0757 | + | 22.0757i | 0.949106 | + | 0.949106i | 0.998766 | − | 0.0496598i | \(-0.0158137\pi\) |
−0.0496598 | + | 0.998766i | \(0.515814\pi\) | |||||||
\(542\) | 25.6662 | 1.10246 | ||||||||
\(543\) | 20.9076 | + | 20.9076i | 0.897231 | + | 0.897231i | ||||
\(544\) | 8.09027i | 0.346867i | ||||||||
\(545\) | 6.35719 | − | 0.471000i | 0.272312 | − | 0.0201754i | ||||
\(546\) | − | 4.64561i | − | 0.198814i | ||||||
\(547\) | −24.7795 | −1.05949 | −0.529747 | − | 0.848155i | \(-0.677713\pi\) | ||||
−0.529747 | + | 0.848155i | \(0.677713\pi\) | |||||||
\(548\) | −11.4519 | − | 11.4519i | −0.489203 | − | 0.489203i | ||||
\(549\) | 2.82891 | + | 2.82891i | 0.120735 | + | 0.120735i | ||||
\(550\) | 18.0326 | − | 2.68680i | 0.768913 | − | 0.114565i | ||||
\(551\) | −8.39222 | −0.357521 | ||||||||
\(552\) | 10.0446 | + | 10.0446i | 0.427526 | + | 0.427526i | ||||
\(553\) | 0.882399 | 0.0375234 | ||||||||
\(554\) | 17.2625 | 0.733415 | ||||||||
\(555\) | −16.2413 | − | 18.7425i | −0.689405 | − | 0.795573i | ||||
\(556\) | −2.41427 | −0.102388 | ||||||||
\(557\) | −28.3582 | −1.20157 | −0.600787 | − | 0.799409i | \(-0.705146\pi\) | ||||
−0.600787 | + | 0.799409i | \(0.705146\pi\) | |||||||
\(558\) | −1.05154 | − | 1.05154i | −0.0445153 | − | 0.0445153i | ||||
\(559\) | 33.9163 | 1.43451 | ||||||||
\(560\) | 0.135480 | + | 1.82861i | 0.00572509 | + | 0.0772728i | ||||
\(561\) | 38.0344 | + | 38.0344i | 1.60581 | + | 1.60581i | ||||
\(562\) | 3.84098 | + | 3.84098i | 0.162022 | + | 0.162022i | ||||
\(563\) | −16.8486 | −0.710085 | −0.355043 | − | 0.934850i | \(-0.615534\pi\) | ||||
−0.355043 | + | 0.934850i | \(0.615534\pi\) | |||||||
\(564\) | − | 10.6186i | − | 0.447124i | ||||||
\(565\) | 17.3581 | − | 20.1360i | 0.730261 | − | 0.847128i | ||||
\(566\) | 20.5564i | 0.864049i | ||||||||
\(567\) | 5.72219 | + | 5.72219i | 0.240309 | + | 0.240309i | ||||
\(568\) | −0.00151598 | −6.36090e−5 | ||||||||
\(569\) | 4.89447 | + | 4.89447i | 0.205187 | + | 0.205187i | 0.802218 | − | 0.597031i | \(-0.203653\pi\) |
−0.597031 | + | 0.802218i | \(0.703653\pi\) | |||||||
\(570\) | 13.3304 | + | 11.4914i | 0.558348 | + | 0.481320i | ||||
\(571\) | −38.8520 | −1.62590 | −0.812952 | − | 0.582330i | \(-0.802141\pi\) | ||||
−0.812952 | + | 0.582330i | \(0.802141\pi\) | |||||||
\(572\) | 11.3293i | 0.473701i | ||||||||
\(573\) | 0.713470i | 0.0298056i | ||||||||
\(574\) | 5.39894 | − | 5.39894i | 0.225347 | − | 0.225347i | ||||
\(575\) | −5.74055 | − | 38.5280i | −0.239397 | − | 1.60673i | ||||
\(576\) | 0.324646i | 0.0135269i | ||||||||
\(577\) | − | 18.6556i | − | 0.776642i | −0.921524 | − | 0.388321i | \(-0.873055\pi\) | ||
0.921524 | − | 0.388321i | \(-0.126945\pi\) | |||||||
\(578\) | 48.4524 | 2.01535 | ||||||||
\(579\) | 11.3302 | + | 11.3302i | 0.470867 | + | 0.470867i | ||||
\(580\) | 0.321204 | + | 4.33536i | 0.0133373 | + | 0.180016i | ||||
\(581\) | 3.67597 | 0.152505 | ||||||||
\(582\) | −18.8504 | + | 18.8504i | −0.781376 | + | 0.781376i | ||||
\(583\) | 1.62829 | + | 1.62829i | 0.0674368 | + | 0.0674368i | ||||
\(584\) | 9.32759 | + | 9.32759i | 0.385979 | + | 0.385979i | ||||
\(585\) | −1.47267 | + | 1.70835i | −0.0608876 | + | 0.0706317i | ||||
\(586\) | 11.2671 | − | 11.2671i | 0.465441 | − | 0.465441i | ||||
\(587\) | −5.75904 | −0.237701 | −0.118851 | − | 0.992912i | \(-0.537921\pi\) | ||||
−0.118851 | + | 0.992912i | \(0.537921\pi\) | |||||||
\(588\) | 8.15820 | − | 8.15820i | 0.336439 | − | 0.336439i | ||||
\(589\) | 19.7733i | 0.814746i | ||||||||
\(590\) | 19.4386 | − | 1.44019i | 0.800275 | − | 0.0592919i | ||||
\(591\) | 21.6988i | 0.892568i | ||||||||
\(592\) | −4.87870 | + | 3.63294i | −0.200513 | + | 0.149313i | ||||
\(593\) | −16.3572 | + | 16.3572i | −0.671709 | + | 0.671709i | −0.958110 | − | 0.286401i | \(-0.907541\pi\) |
0.286401 | + | 0.958110i | \(0.407541\pi\) | |||||||
\(594\) | −12.5775 | − | 12.5775i | −0.516062 | − | 0.516062i | ||||
\(595\) | 14.7939 | − | 1.09607i | 0.606492 | − | 0.0449346i | ||||
\(596\) | 4.02923i | 0.165044i | ||||||||
\(597\) | 10.8332i | 0.443372i | ||||||||
\(598\) | 24.2059 | 0.989852 | ||||||||
\(599\) | − | 23.6157i | − | 0.964910i | −0.875921 | − | 0.482455i | \(-0.839745\pi\) | ||
0.875921 | − | 0.482455i | \(-0.160255\pi\) | |||||||
\(600\) | 5.42614 | − | 7.32620i | 0.221521 | − | 0.299091i | ||||
\(601\) | 30.4617 | 1.24256 | 0.621279 | − | 0.783589i | \(-0.286613\pi\) | ||||
0.621279 | + | 0.783589i | \(0.286613\pi\) | |||||||
\(602\) | −6.32952 | − | 6.32952i | −0.257972 | − | 0.257972i | ||||
\(603\) | −0.652617 | − | 0.652617i | −0.0265766 | − | 0.0265766i | ||||
\(604\) | 8.86568i | 0.360739i | ||||||||
\(605\) | −3.88816 | − | 3.35176i | −0.158076 | − | 0.136268i | ||||
\(606\) | 4.75588 | − | 4.75588i | 0.193195 | − | 0.193195i | ||||
\(607\) | −17.6781 | −0.717530 | −0.358765 | − | 0.933428i | \(-0.616802\pi\) | ||||
−0.358765 | + | 0.933428i | \(0.616802\pi\) | |||||||
\(608\) | 3.05234 | − | 3.05234i | 0.123789 | − | 0.123789i | ||||
\(609\) | −2.05547 | + | 2.05547i | −0.0832918 | + | 0.0832918i | ||||
\(610\) | −27.4802 | + | 2.03599i | −1.11264 | + | 0.0824349i | ||||
\(611\) | −12.7946 | − | 12.7946i | −0.517614 | − | 0.517614i | ||||
\(612\) | 2.62647 | 0.106169 | ||||||||
\(613\) | −24.9613 | − | 24.9613i | −1.00818 | − | 1.00818i | −0.999966 | − | 0.00821132i | \(-0.997386\pi\) |
−0.00821132 | − | 0.999966i | \(-0.502614\pi\) | |||||||
\(614\) | −9.43686 | + | 9.43686i | −0.380841 | + | 0.380841i | ||||
\(615\) | −37.8589 | + | 2.80494i | −1.52662 | + | 0.113106i | ||||
\(616\) | 2.11429 | − | 2.11429i | 0.0851873 | − | 0.0851873i | ||||
\(617\) | −6.37297 | + | 6.37297i | −0.256566 | + | 0.256566i | −0.823656 | − | 0.567090i | \(-0.808069\pi\) |
0.567090 | + | 0.823656i | \(0.308069\pi\) | |||||||
\(618\) | −14.3814 | + | 14.3814i | −0.578506 | + | 0.578506i | ||||
\(619\) | −2.43520 | −0.0978789 | −0.0489394 | − | 0.998802i | \(-0.515584\pi\) | ||||
−0.0489394 | + | 0.998802i | \(0.515584\pi\) | |||||||
\(620\) | 10.2148 | − | 0.756805i | 0.410234 | − | 0.0303940i | ||||
\(621\) | −26.8729 | + | 26.8729i | −1.07837 | + | 1.07837i | ||||
\(622\) | −6.70368 | + | 6.70368i | −0.268793 | + | 0.268793i | ||||
\(623\) | − | 6.72635i | − | 0.269485i | ||||||
\(624\) | 4.00594 | + | 4.00594i | 0.160366 | + | 0.160366i | ||||
\(625\) | −23.9141 | + | 7.28804i | −0.956564 | + | 0.291522i | ||||
\(626\) | 23.2157 | 0.927885 | ||||||||
\(627\) | − | 28.6997i | − | 1.14616i | ||||||
\(628\) | 6.87897 | + | 6.87897i | 0.274501 | + | 0.274501i | ||||
\(629\) | 29.3915 | + | 39.4700i | 1.17191 | + | 1.57377i | ||||
\(630\) | 0.593650 | − | 0.0439832i | 0.0236516 | − | 0.00175233i | ||||
\(631\) | 8.01035 | − | 8.01035i | 0.318887 | − | 0.318887i | −0.529453 | − | 0.848340i | \(-0.677603\pi\) |
0.848340 | + | 0.529453i | \(0.177603\pi\) | |||||||
\(632\) | −0.760897 | + | 0.760897i | −0.0302669 | + | 0.0302669i | ||||
\(633\) | −35.4433 | − | 35.4433i | −1.40874 | − | 1.40874i | ||||
\(634\) | 15.3696 | − | 15.3696i | 0.610406 | − | 0.610406i | ||||
\(635\) | 3.24818 | + | 43.8414i | 0.128900 | + | 1.73979i | ||||
\(636\) | 1.15150 | 0.0456598 | ||||||||
\(637\) | − | 19.6600i | − | 0.778957i | ||||||
\(638\) | 5.01268 | − | 5.01268i | 0.198454 | − | 0.198454i | ||||
\(639\) | 0 | 0.000492156i | 0 | 1.94694e-5i | ||||||
\(640\) | −1.69364 | − | 1.45999i | −0.0669471 | − | 0.0577112i | ||||
\(641\) | 20.0552 | 0.792134 | 0.396067 | − | 0.918222i | \(-0.370375\pi\) | ||||
0.396067 | + | 0.918222i | \(0.370375\pi\) | |||||||
\(642\) | 10.0131i | 0.395184i | ||||||||
\(643\) | 2.02458i | 0.0798417i | 0.999203 | + | 0.0399208i | \(0.0127106\pi\) | ||||
−0.999203 | + | 0.0399208i | \(0.987289\pi\) | |||||||
\(644\) | −4.51735 | − | 4.51735i | −0.178009 | − | 0.178009i | ||||
\(645\) | 3.28842 | + | 44.3844i | 0.129481 | + | 1.74764i | ||||
\(646\) | −24.6943 | − | 24.6943i | −0.971583 | − | 0.971583i | ||||
\(647\) | 37.8245 | 1.48703 | 0.743517 | − | 0.668717i | \(-0.233156\pi\) | ||||
0.743517 | + | 0.668717i | \(0.233156\pi\) | |||||||
\(648\) | −9.86854 | −0.387673 | ||||||||
\(649\) | −22.4755 | − | 22.4755i | −0.882242 | − | 0.882242i | ||||
\(650\) | −2.28942 | − | 15.3656i | −0.0897983 | − | 0.602687i | ||||
\(651\) | 4.84299 | + | 4.84299i | 0.189812 | + | 0.189812i | ||||
\(652\) | 10.6733i | 0.417997i | ||||||||
\(653\) | − | 24.2252i | − | 0.948006i | −0.880523 | − | 0.474003i | \(-0.842808\pi\) | ||
0.880523 | − | 0.474003i | \(-0.157192\pi\) | |||||||
\(654\) | −5.19806 | −0.203260 | ||||||||
\(655\) | 8.55422 | − | 0.633777i | 0.334241 | − | 0.0247637i | ||||
\(656\) | 9.31106i | 0.363536i | ||||||||
\(657\) | 3.02816 | − | 3.02816i | 0.118140 | − | 0.118140i | ||||
\(658\) | 4.77550i | 0.186169i | ||||||||
\(659\) | 16.7841 | 0.653814 | 0.326907 | − | 0.945056i | \(-0.393994\pi\) | ||||
0.326907 | + | 0.945056i | \(0.393994\pi\) | |||||||
\(660\) | −14.8260 | + | 1.09845i | −0.577103 | + | 0.0427572i | ||||
\(661\) | 2.96671 | − | 2.96671i | 0.115392 | − | 0.115392i | −0.647053 | − | 0.762445i | \(-0.723999\pi\) |
0.762445 | + | 0.647053i | \(0.223999\pi\) | |||||||
\(662\) | 5.72839 | + | 5.72839i | 0.222640 | + | 0.222640i | ||||
\(663\) | 32.4091 | − | 32.4091i | 1.25866 | − | 1.25866i | ||||
\(664\) | −3.16981 | + | 3.16981i | −0.123012 | + | 0.123012i | ||||
\(665\) | −5.99507 | − | 5.16800i | −0.232479 | − | 0.200407i | ||||
\(666\) | 1.17942 | + | 1.58385i | 0.0457016 | + | 0.0613730i | ||||
\(667\) | −10.7100 | − | 10.7100i | −0.414692 | − | 0.414692i | ||||
\(668\) | − | 0.864796i | − | 0.0334600i | ||||||
\(669\) | −24.3077 | −0.939788 | ||||||||
\(670\) | 6.33957 | − | 0.469695i | 0.244919 | − | 0.0181459i | ||||
\(671\) | 31.7735 | + | 31.7735i | 1.22660 | + | 1.22660i | ||||
\(672\) | − | 1.49519i | − | 0.0576783i | ||||||
\(673\) | 23.2071 | − | 23.2071i | 0.894567 | − | 0.894567i | −0.100382 | − | 0.994949i | \(-0.532007\pi\) |
0.994949 | + | 0.100382i | \(0.0320066\pi\) | |||||||
\(674\) | −5.31333 | + | 5.31333i | −0.204662 | + | 0.204662i | ||||
\(675\) | 19.6002 | + | 14.5168i | 0.754411 | + | 0.558754i | ||||
\(676\) | −3.34633 | −0.128705 | ||||||||
\(677\) | 4.70869 | − | 4.70869i | 0.180970 | − | 0.180970i | −0.610809 | − | 0.791778i | \(-0.709156\pi\) |
0.791778 | + | 0.610809i | \(0.209156\pi\) | |||||||
\(678\) | −15.3288 | + | 15.3288i | −0.588701 | + | 0.588701i | ||||
\(679\) | 8.47761 | − | 8.47761i | 0.325341 | − | 0.325341i | ||||
\(680\) | −11.8117 | + | 13.7020i | −0.452959 | + | 0.525448i | ||||
\(681\) | −23.1544 | + | 23.1544i | −0.887277 | + | 0.887277i | ||||
\(682\) | −11.8106 | − | 11.8106i | −0.452252 | − | 0.452252i | ||||
\(683\) | −46.0160 | −1.76075 | −0.880376 | − | 0.474277i | \(-0.842710\pi\) | ||||
−0.880376 | + | 0.474277i | \(0.842710\pi\) | |||||||
\(684\) | −0.990930 | − | 0.990930i | −0.0378892 | − | 0.0378892i | ||||
\(685\) | −2.67576 | − | 36.1152i | −0.102235 | − | 1.37989i | ||||
\(686\) | −7.72788 | + | 7.72788i | −0.295052 | + | 0.295052i | ||||
\(687\) | −23.4233 | + | 23.4233i | −0.893653 | + | 0.893653i | ||||
\(688\) | 10.9160 | 0.416167 | ||||||||
\(689\) | 1.38746 | − | 1.38746i | 0.0528581 | − | 0.0528581i | ||||
\(690\) | 2.34693 | + | 31.6770i | 0.0893460 | + | 1.20592i | ||||
\(691\) | − | 37.9434i | − | 1.44344i | −0.692187 | − | 0.721718i | \(-0.743353\pi\) | ||
0.692187 | − | 0.721718i | \(-0.256647\pi\) | |||||||
\(692\) | −2.14973 | − | 2.14973i | −0.0817206 | − | 0.0817206i | ||||
\(693\) | −0.686397 | − | 0.686397i | −0.0260741 | − | 0.0260741i | ||||
\(694\) | −32.7620 | −1.24363 | ||||||||
\(695\) | −4.08890 | − | 3.52481i | −0.155101 | − | 0.133704i | ||||
\(696\) | − | 3.54488i | − | 0.134368i | ||||||
\(697\) | 75.3290 | 2.85329 | ||||||||
\(698\) | 14.0604i | 0.532194i | ||||||||
\(699\) | 5.76801i | 0.218166i | ||||||||
\(700\) | −2.44030 | + | 3.29481i | −0.0922345 | + | 0.124532i | ||||
\(701\) | 11.9143 | + | 11.9143i | 0.449995 | + | 0.449995i | 0.895353 | − | 0.445358i | \(-0.146923\pi\) |
−0.445358 | + | 0.895353i | \(0.646923\pi\) | |||||||
\(702\) | −10.7173 | + | 10.7173i | −0.404498 | + | 0.404498i | ||||
\(703\) | 3.80249 | − | 25.9805i | 0.143414 | − | 0.979871i | ||||
\(704\) | 3.64633i | 0.137426i | ||||||||
\(705\) | 15.5031 | − | 17.9841i | 0.583880 | − | 0.677322i | ||||
\(706\) | 6.79098i | 0.255582i | ||||||||
\(707\) | −2.13886 | + | 2.13886i | −0.0804402 | + | 0.0804402i | ||||
\(708\) | −15.8943 | −0.597345 | ||||||||
\(709\) | −13.4491 | + | 13.4491i | −0.505093 | + | 0.505093i | −0.913016 | − | 0.407923i | \(-0.866253\pi\) |
0.407923 | + | 0.913016i | \(0.366253\pi\) | |||||||
\(710\) | −0.00256752 | − | 0.00221331i | −9.63574e−5 | − | 8.30642e-5i | ||||
\(711\) | 0.247022 | + | 0.247022i | 0.00926405 | + | 0.00926405i | ||||
\(712\) | 5.80016 | + | 5.80016i | 0.217370 | + | 0.217370i | ||||
\(713\) | −25.2343 | + | 25.2343i | −0.945032 | + | 0.945032i | ||||
\(714\) | −12.0965 | −0.452700 | ||||||||
\(715\) | −16.5407 | + | 19.1878i | −0.618586 | + | 0.717582i | ||||
\(716\) | −0.313292 | − | 0.313292i | −0.0117083 | − | 0.0117083i | ||||
\(717\) | 11.6951 | 0.436763 | ||||||||
\(718\) | − | 4.91904i | − | 0.183577i | ||||||
\(719\) | 15.0482i | 0.561204i | 0.959824 | + | 0.280602i | \(0.0905342\pi\) | ||||
−0.959824 | + | 0.280602i | \(0.909466\pi\) | |||||||
\(720\) | −0.473980 | + | 0.549834i | −0.0176642 | + | 0.0204911i | ||||
\(721\) | 6.46775 | − | 6.46775i | 0.240872 | − | 0.240872i | ||||
\(722\) | − | 0.366413i | − | 0.0136365i | ||||||
\(723\) | 7.61354i | 0.283151i | ||||||||
\(724\) | 16.2161 | 0.602667 | ||||||||
\(725\) | −5.78558 | + | 7.81150i | −0.214871 | + | 0.290112i | ||||
\(726\) | 2.95992 | + | 2.95992i | 0.109853 | + | 0.109853i | ||||
\(727\) | −48.0498 | −1.78207 | −0.891033 | − | 0.453938i | \(-0.850019\pi\) | ||||
−0.891033 | + | 0.453938i | \(0.850019\pi\) | |||||||
\(728\) | −1.80159 | − | 1.80159i | −0.0667713 | − | 0.0667713i | ||||
\(729\) | − | 23.4800i | − | 0.869631i | ||||||
\(730\) | 2.17940 | + | 29.4158i | 0.0806632 | + | 1.08873i | ||||
\(731\) | − | 88.3130i | − | 3.26637i | ||||||
\(732\) | 22.4697 | 0.830502 | ||||||||
\(733\) | 17.9391 | + | 17.9391i | 0.662596 | + | 0.662596i | 0.955991 | − | 0.293395i | \(-0.0947851\pi\) |
−0.293395 | + | 0.955991i | \(0.594785\pi\) | |||||||
\(734\) | −21.4924 | − | 21.4924i | −0.793298 | − | 0.793298i | ||||
\(735\) | 25.7280 | − | 1.90617i | 0.948991 | − | 0.0703102i | ||||
\(736\) | 7.79067 | 0.287168 | ||||||||
\(737\) | −7.33001 | − | 7.33001i | −0.270004 | − | 0.270004i | ||||
\(738\) | 3.02280 | 0.111271 | ||||||||
\(739\) | 27.0049 | 0.993391 | 0.496696 | − | 0.867925i | \(-0.334547\pi\) | ||||
0.496696 | + | 0.867925i | \(0.334547\pi\) | |||||||
\(740\) | −13.5668 | − | 0.969960i | −0.498727 | − | 0.0356564i | ||||
\(741\) | −24.4550 | −0.898376 | ||||||||
\(742\) | −0.517862 | −0.0190113 | ||||||||
\(743\) | 21.8683 | + | 21.8683i | 0.802270 | + | 0.802270i | 0.983450 | − | 0.181180i | \(-0.0579917\pi\) |
−0.181180 | + | 0.983450i | \(0.557992\pi\) | |||||||
\(744\) | −8.35226 | −0.306209 | ||||||||
\(745\) | −5.88265 | + | 6.82408i | −0.215523 | + | 0.250015i | ||||
\(746\) | −19.5734 | − | 19.5734i | −0.716632 | − | 0.716632i | ||||
\(747\) | 1.02907 | + | 1.02907i | 0.0376515 | + | 0.0376515i | ||||
\(748\) | 29.4998 | 1.07862 | ||||||||
\(749\) | − | 4.50318i | − | 0.164542i | ||||||
\(750\) | 19.8861 | − | 4.48584i | 0.726139 | − | 0.163800i | ||||
\(751\) | 17.0169i | 0.620957i | 0.950580 | + | 0.310479i | \(0.100489\pi\) | ||||
−0.950580 | + | 0.310479i | \(0.899511\pi\) | |||||||
\(752\) | −4.11794 | − | 4.11794i | −0.150166 | − | 0.150166i | ||||
\(753\) | −25.6085 | −0.933227 | ||||||||
\(754\) | −4.27130 | − | 4.27130i | −0.155552 | − | 0.155552i | ||||
\(755\) | −12.9438 | + | 15.0153i | −0.471074 | + | 0.546462i | ||||
\(756\) | 4.00017 | 0.145485 | ||||||||
\(757\) | 31.0722i | 1.12934i | 0.825317 | + | 0.564669i | \(0.190996\pi\) | ||||
−0.825317 | + | 0.564669i | \(0.809004\pi\) | |||||||
\(758\) | − | 1.90775i | − | 0.0692925i | ||||||
\(759\) | 36.6259 | − | 36.6259i | 1.32944 | − | 1.32944i | ||||
\(760\) | 9.62597 | − | 0.713182i | 0.349171 | − | 0.0258698i | ||||
\(761\) | − | 14.8739i | − | 0.539180i | −0.962975 | − | 0.269590i | \(-0.913112\pi\) | ||
0.962975 | − | 0.269590i | \(-0.0868882\pi\) | |||||||
\(762\) | − | 35.8476i | − | 1.29862i | ||||||
\(763\) | 2.33772 | 0.0846312 | ||||||||
\(764\) | 0.276686 | + | 0.276686i | 0.0100102 | + | 0.0100102i | ||||
\(765\) | 4.44830 | + | 3.83463i | 0.160829 | + | 0.138641i | ||||
\(766\) | −12.0669 | −0.435996 | ||||||||
\(767\) | −19.1514 | + | 19.1514i | −0.691516 | + | 0.691516i | ||||
\(768\) | 1.28931 | + | 1.28931i | 0.0465240 | + | 0.0465240i | ||||
\(769\) | 21.6211 | + | 21.6211i | 0.779677 | + | 0.779677i | 0.979776 | − | 0.200099i | \(-0.0641264\pi\) |
−0.200099 | + | 0.979776i | \(0.564126\pi\) | |||||||
\(770\) | 6.66771 | − | 0.494007i | 0.240288 | − | 0.0178028i | ||||
\(771\) | 19.4861 | − | 19.4861i | 0.701773 | − | 0.701773i | ||||
\(772\) | 8.78779 | 0.316279 | ||||||||
\(773\) | 8.11195 | − | 8.11195i | 0.291766 | − | 0.291766i | −0.546011 | − | 0.837778i | \(-0.683854\pi\) |
0.837778 | + | 0.546011i | \(0.183854\pi\) | |||||||
\(774\) | − | 3.54382i | − | 0.127380i | ||||||
\(775\) | 18.4051 | + | 13.6317i | 0.661129 | + | 0.489665i | ||||
\(776\) | 14.6206i | 0.524847i | ||||||||
\(777\) | −5.43194 | − | 7.29460i | −0.194870 | − | 0.261692i | ||||
\(778\) | 16.8015 | − | 16.8015i | 0.602361 | − | 0.602361i | ||||
\(779\) | −28.4205 | − | 28.4205i | −1.01827 | − | 1.01827i | ||||
\(780\) | 0.935990 | + | 12.6333i | 0.0335138 | + | 0.452343i | ||||
\(781\) | 0.00552776i | 0.000197799i | ||||||||
\(782\) | − | 63.0286i | − | 2.25390i | ||||||
\(783\) | 9.48381 | 0.338924 | ||||||||
\(784\) | − | 6.32757i | − | 0.225985i | ||||||
\(785\) | 1.60728 | + | 21.6937i | 0.0573662 | + | 0.774283i | ||||
\(786\) | −6.99450 | −0.249486 | ||||||||
\(787\) | −25.9363 | − | 25.9363i | −0.924530 | − | 0.924530i | 0.0728158 | − | 0.997345i | \(-0.476801\pi\) |
−0.997345 | + | 0.0728158i | \(0.976801\pi\) | |||||||
\(788\) | 8.41487 | + | 8.41487i | 0.299767 | + | 0.299767i | ||||
\(789\) | 25.1222i | 0.894375i | ||||||||
\(790\) | −2.39959 | + | 0.177784i | −0.0853736 | + | 0.00632528i | ||||
\(791\) | 6.89384 | − | 6.89384i | 0.245117 | − | 0.245117i | ||||
\(792\) | 1.18377 | 0.0420633 | ||||||||
\(793\) | 27.0742 | − | 27.0742i | 0.961432 | − | 0.961432i | ||||
\(794\) | 6.99419 | − | 6.99419i | 0.248214 | − | 0.248214i | ||||
\(795\) | 1.95022 | + | 1.68117i | 0.0691673 | + | 0.0596251i | ||||
\(796\) | 4.20114 | + | 4.20114i | 0.148906 | + | 0.148906i | ||||
\(797\) | 7.46766 | 0.264518 | 0.132259 | − | 0.991215i | \(-0.457777\pi\) | ||||
0.132259 | + | 0.991215i | \(0.457777\pi\) | |||||||
\(798\) | 4.56384 | + | 4.56384i | 0.161558 | + | 0.161558i | ||||
\(799\) | −33.3152 | + | 33.3152i | −1.17861 | + | 1.17861i | ||||
\(800\) | −0.736849 | − | 4.94541i | −0.0260516 | − | 0.174847i | ||||
\(801\) | 1.88300 | − | 1.88300i | 0.0665325 | − | 0.0665325i | ||||
\(802\) | −0.759591 | + | 0.759591i | −0.0268221 | + | 0.0268221i | ||||
\(803\) | 34.0115 | − | 34.0115i | 1.20024 | − | 1.20024i | ||||
\(804\) | −5.18365 | −0.182813 | ||||||||
\(805\) | −1.05548 | − | 14.2461i | −0.0372009 | − | 0.502108i | ||||
\(806\) | −10.0638 | + | 10.0638i | −0.354483 | + | 0.354483i | ||||
\(807\) | −8.29566 | + | 8.29566i | −0.292021 | + | 0.292021i | ||||
\(808\) | − | 3.68870i | − | 0.129768i | ||||||
\(809\) | 13.5592 | + | 13.5592i | 0.476716 | + | 0.476716i | 0.904080 | − | 0.427364i | \(-0.140558\pi\) |
−0.427364 | + | 0.904080i | \(0.640558\pi\) | |||||||
\(810\) | −16.7138 | − | 14.4080i | −0.587262 | − | 0.506245i | ||||
\(811\) | −19.5616 | −0.686901 | −0.343450 | − | 0.939171i | \(-0.611596\pi\) | ||||
−0.343450 | + | 0.939171i | \(0.611596\pi\) | |||||||
\(812\) | 1.59424i | 0.0559468i | ||||||||
\(813\) | −33.0918 | − | 33.0918i | −1.16058 | − | 1.16058i | ||||
\(814\) | 13.2469 | + | 17.7894i | 0.464304 | + | 0.623517i | ||||
\(815\) | −15.5829 | + | 18.0767i | −0.545844 | + | 0.633199i | ||||
\(816\) | 10.4309 | − | 10.4309i | 0.365153 | − | 0.365153i | ||||
\(817\) | −33.3192 | + | 33.3192i | −1.16569 | + | 1.16569i | ||||
\(818\) | −22.0320 | − | 22.0320i | −0.770331 | − | 0.770331i | ||||
\(819\) | −0.584878 | + | 0.584878i | −0.0204373 | + | 0.0204373i | ||||
\(820\) | −13.5941 | + | 15.7696i | −0.474726 | + | 0.550699i | ||||
\(821\) | −3.12570 | −0.109088 | −0.0545438 | − | 0.998511i | \(-0.517370\pi\) | ||||
−0.0545438 | + | 0.998511i | \(0.517370\pi\) | |||||||
\(822\) | 29.5302i | 1.02999i | ||||||||
\(823\) | −19.9647 | + | 19.9647i | −0.695926 | + | 0.695926i | −0.963529 | − | 0.267603i | \(-0.913768\pi\) |
0.267603 | + | 0.963529i | \(0.413768\pi\) | |||||||
\(824\) | 11.1543i | 0.388580i | ||||||||
\(825\) | −26.7137 | − | 19.7855i | −0.930053 | − | 0.688843i | ||||
\(826\) | 7.14814 | 0.248716 | ||||||||
\(827\) | 18.4817i | 0.642673i | 0.946965 | + | 0.321336i | \(0.104132\pi\) | ||||
−0.946965 | + | 0.321336i | \(0.895868\pi\) | |||||||
\(828\) | − | 2.52921i | − | 0.0878961i | ||||||
\(829\) | −21.6955 | − | 21.6955i | −0.753515 | − | 0.753515i | 0.221618 | − | 0.975134i | \(-0.428866\pi\) |
−0.975134 | + | 0.221618i | \(0.928866\pi\) | |||||||
\(830\) | −9.99642 | + | 0.740629i | −0.346981 | + | 0.0257076i | ||||
\(831\) | −22.2568 | − | 22.2568i | −0.772079 | − | 0.772079i | ||||
\(832\) | 3.10704 | 0.107717 | ||||||||
\(833\) | −51.1917 | −1.77369 | ||||||||
\(834\) | 3.11274 | + | 3.11274i | 0.107785 | + | 0.107785i | ||||
\(835\) | 1.26260 | − | 1.46466i | 0.0436939 | − | 0.0506865i | ||||
\(836\) | −11.1299 | − | 11.1299i | −0.384934 | − | 0.384934i | ||||
\(837\) | − | 22.3453i | − | 0.772365i | ||||||
\(838\) | − | 13.7527i | − | 0.475079i | ||||||
\(839\) | 35.7782 | 1.23520 | 0.617600 | − | 0.786492i | \(-0.288105\pi\) | ||||
0.617600 | + | 0.786492i | \(0.288105\pi\) | |||||||
\(840\) | 2.18297 | − | 2.53232i | 0.0753195 | − | 0.0873733i | ||||
\(841\) | − | 25.2203i | − | 0.869665i | ||||||
\(842\) | −4.62725 | + | 4.62725i | −0.159466 | + | 0.159466i | ||||
\(843\) | − | 9.90444i | − | 0.341127i | ||||||
\(844\) | −27.4901 | −0.946248 | ||||||||
\(845\) | −5.66748 | − | 4.88561i | −0.194967 | − | 0.168070i | ||||
\(846\) | −1.33687 | + | 1.33687i | −0.0459626 | + | 0.0459626i | ||||
\(847\) | −1.33117 | − | 1.33117i | −0.0457394 | − | 0.0457394i | ||||
\(848\) | 0.446555 | − | 0.446555i | 0.0153348 | − | 0.0153348i | ||||
\(849\) | 26.5036 | − | 26.5036i | 0.909600 | − | 0.909600i | ||||
\(850\) | −40.0097 | + | 5.96131i | −1.37232 | + | 0.204471i | ||||
\(851\) | 38.0084 | − | 28.3030i | 1.30291 | − | 0.970216i | ||||
\(852\) | 0.00195457 | + | 0.00195457i | 6.69623e−5 | + | 6.69623e-5i | ||||
\(853\) | − | 37.5829i | − | 1.28681i | −0.765524 | − | 0.643407i | \(-0.777520\pi\) | ||
0.765524 | − | 0.643407i | \(-0.222480\pi\) | |||||||
\(854\) | −10.1053 | −0.345795 | ||||||||
\(855\) | −0.231532 | − | 3.12503i | −0.00791822 | − | 0.106874i | ||||
\(856\) | 3.88311 | + | 3.88311i | 0.132722 | + | 0.132722i | ||||
\(857\) | − | 24.8711i | − | 0.849581i | −0.905292 | − | 0.424791i | \(-0.860348\pi\) | ||
0.905292 | − | 0.424791i | \(-0.139652\pi\) | |||||||
\(858\) | 14.6070 | − | 14.6070i | 0.498674 | − | 0.498674i | ||||
\(859\) | −15.0119 | + | 15.0119i | −0.512199 | + | 0.512199i | −0.915200 | − | 0.403000i | \(-0.867967\pi\) |
0.403000 | + | 0.915200i | \(0.367967\pi\) | |||||||
\(860\) | 18.4877 | + | 15.9372i | 0.630426 | + | 0.543454i | ||||
\(861\) | −13.9218 | −0.474454 | ||||||||
\(862\) | −2.01292 | + | 2.01292i | −0.0685605 | + | 0.0685605i | ||||
\(863\) | 28.2484 | − | 28.2484i | 0.961586 | − | 0.961586i | −0.0377026 | − | 0.999289i | \(-0.512004\pi\) |
0.999289 | + | 0.0377026i | \(0.0120039\pi\) | |||||||
\(864\) | −3.44936 | + | 3.44936i | −0.117350 | + | 0.117350i | ||||
\(865\) | −0.502287 | − | 6.77948i | −0.0170783 | − | 0.230509i | ||||
\(866\) | 23.2986 | − | 23.2986i | 0.791720 | − | 0.791720i | ||||
\(867\) | −62.4702 | − | 62.4702i | −2.12160 | − | 2.12160i | ||||
\(868\) | 3.75626 | 0.127496 | ||||||||
\(869\) | 2.77448 | + | 2.77448i | 0.0941179 | + | 0.0941179i | ||||
\(870\) | 5.17549 | − | 6.00376i | 0.175466 | − | 0.203546i | ||||
\(871\) | −6.24589 | + | 6.24589i | −0.211634 | + | 0.211634i | ||||
\(872\) | −2.01583 | + | 2.01583i | −0.0682646 | + | 0.0682646i | ||||
\(873\) | 4.74650 | 0.160645 | ||||||||
\(874\) | −23.7798 | + | 23.7798i | −0.804363 | + | 0.804363i | ||||
\(875\) | −8.94338 | + | 2.01741i | −0.302341 | + | 0.0682010i | ||||
\(876\) | − | 24.0523i | − | 0.812653i | ||||||
\(877\) | 20.7098 | + | 20.7098i | 0.699322 | + | 0.699322i | 0.964264 | − | 0.264943i | \(-0.0853530\pi\) |
−0.264943 | + | 0.964264i | \(0.585353\pi\) | |||||||
\(878\) | 6.59762 | + | 6.59762i | 0.222659 | + | 0.222659i | ||||
\(879\) | −29.0537 | −0.979955 | ||||||||
\(880\) | −5.32361 | + | 6.17558i | −0.179459 | + | 0.208179i | ||||
\(881\) | − | 2.51776i | − | 0.0848254i | −0.999100 | − | 0.0424127i | \(-0.986496\pi\) | ||
0.999100 | − | 0.0424127i | \(-0.0135044\pi\) | |||||||
\(882\) | −2.05422 | −0.0691691 | ||||||||
\(883\) | − | 8.49437i | − | 0.285858i | −0.989733 | − | 0.142929i | \(-0.954348\pi\) | ||
0.989733 | − | 0.142929i | \(-0.0456521\pi\) | |||||||
\(884\) | − | 25.1367i | − | 0.845440i | ||||||
\(885\) | −26.9193 | − | 23.2056i | −0.904881 | − | 0.780046i | ||||
\(886\) | 28.2758 | + | 28.2758i | 0.949945 | + | 0.949945i | ||||
\(887\) | 13.0043 | − | 13.0043i | 0.436643 | − | 0.436643i | −0.454238 | − | 0.890881i | \(-0.650088\pi\) |
0.890881 | + | 0.454238i | \(0.150088\pi\) | |||||||
\(888\) | 10.9742 | + | 1.60617i | 0.368269 | + | 0.0538996i | ||||
\(889\) | 16.1217i | 0.540706i | ||||||||
\(890\) | 1.35521 | + | 18.2916i | 0.0454268 | + | 0.613136i | ||||
\(891\) | 35.9840i | 1.20551i | ||||||||
\(892\) | −9.42660 | + | 9.42660i | −0.315626 | + | 0.315626i | ||||
\(893\) | 25.1387 | 0.841235 | ||||||||
\(894\) | 5.19493 | − | 5.19493i | 0.173745 | − | 0.173745i | ||||
\(895\) | −0.0732008 | − | 0.988007i | −0.00244683 | − | 0.0330254i | ||||
\(896\) | −0.579841 | − | 0.579841i | −0.0193711 | − | 0.0193711i | ||||
\(897\) | −31.2089 | − | 31.2089i | −1.04204 | − | 1.04204i | ||||
\(898\) | −11.7576 | + | 11.7576i | −0.392357 | + | 0.392357i | ||||
\(899\) | 8.90554 | 0.297016 | ||||||||
\(900\) | −1.60551 | + | 0.239215i | −0.0535169 | + | 0.00797383i | ||||
\(901\) | −3.61275 | − | 3.61275i | −0.120358 | − | 0.120358i | ||||
\(902\) | 33.9512 | 1.13045 | ||||||||
\(903\) | 16.3214i | 0.543144i | ||||||||
\(904\) | 11.8892i | 0.395428i | ||||||||
\(905\) | 27.4643 | + | 23.6754i | 0.912944 | + | 0.786996i | ||||
\(906\) | 11.4306 | − | 11.4306i | 0.379757 | − | 0.379757i | ||||
\(907\) | 39.4216i | 1.30897i | 0.756074 | + | 0.654487i | \(0.227115\pi\) | ||||
−0.756074 | + | 0.654487i | \(0.772885\pi\) | |||||||
\(908\) | 17.9587i | 0.595981i | ||||||||
\(909\) | −1.19752 | −0.0397193 | ||||||||
\(910\) | −0.420942 | − | 5.68155i | −0.0139541 | − | 0.188342i | ||||
\(911\) | −10.3558 | − | 10.3558i | −0.343105 | − | 0.343105i | 0.514429 | − | 0.857533i | \(-0.328004\pi\) |
−0.857533 | + | 0.514429i | \(0.828004\pi\) | |||||||
\(912\) | −7.87084 | −0.260629 | ||||||||
\(913\) | 11.5582 | + | 11.5582i | 0.382520 | + | 0.382520i | ||||
\(914\) | − | 31.9954i | − | 1.05831i | ||||||
\(915\) | 38.0556 | + | 32.8055i | 1.25808 | + | 1.08452i | ||||
\(916\) | 18.1673i | 0.600264i | ||||||||
\(917\) | 3.14564 | 0.103878 | ||||||||
\(918\) | 27.9063 | + | 27.9063i | 0.921044 | + | 0.921044i | ||||
\(919\) | 21.8092 | + | 21.8092i | 0.719419 | + | 0.719419i | 0.968486 | − | 0.249068i | \(-0.0801241\pi\) |
−0.249068 | + | 0.968486i | \(0.580124\pi\) | |||||||
\(920\) | 13.1946 | + | 11.3743i | 0.435013 | + | 0.375000i | ||||
\(921\) | 24.3341 | 0.801836 | ||||||||
\(922\) | 17.2203 | + | 17.2203i | 0.567122 | + | 0.567122i | ||||
\(923\) | 0.00471020 | 0.000155038 | ||||||||
\(924\) | −5.45197 | −0.179357 | ||||||||
\(925\) | −21.5612 | − | 21.4502i | −0.708929 | − | 0.705280i | ||||
\(926\) | 13.3316 | 0.438102 | ||||||||
\(927\) | 3.62121 | 0.118936 | ||||||||
\(928\) | −1.37472 | − | 1.37472i | −0.0451274 | − | 0.0451274i | ||||
\(929\) | −16.6531 | −0.546370 | −0.273185 | − | 0.961962i | \(-0.588077\pi\) | ||||
−0.273185 | + | 0.961962i | \(0.588077\pi\) | |||||||
\(930\) | −14.1457 | − | 12.1942i | −0.463857 | − | 0.399865i | ||||
\(931\) | 19.3139 | + | 19.3139i | 0.632988 | + | 0.632988i | ||||
\(932\) | 2.23686 | + | 2.23686i | 0.0732706 | + | 0.0732706i | ||||
\(933\) | 17.2862 | 0.565926 | ||||||||
\(934\) | − | 32.1997i | − | 1.05361i | ||||||
\(935\) | 49.9621 | + | 43.0695i | 1.63394 | + | 1.40852i | ||||
\(936\) | − | 1.00869i | − | 0.0329699i | ||||||
\(937\) | 17.3416 | + | 17.3416i | 0.566526 | + | 0.566526i | 0.931154 | − | 0.364627i | \(-0.118804\pi\) |
−0.364627 | + | 0.931154i | \(0.618804\pi\) | |||||||
\(938\) | 2.33124 | 0.0761178 | ||||||||
\(939\) | −29.9322 | − | 29.9322i | −0.976802 | − | 0.976802i | ||||
\(940\) | −0.962160 | − | 12.9865i | −0.0313822 | − | 0.423572i | ||||
\(941\) | −13.4862 | −0.439637 | −0.219818 | − | 0.975541i | \(-0.570547\pi\) | ||||
−0.219818 | + | 0.975541i | \(0.570547\pi\) | |||||||
\(942\) | − | 17.7383i | − | 0.577944i | ||||||
\(943\) | − | 72.5394i | − | 2.36221i | ||||||
\(944\) | −6.16388 | + | 6.16388i | −0.200617 | + | 0.200617i | ||||
\(945\) | 6.77485 | + | 5.84021i | 0.220386 | + | 0.189982i | ||||
\(946\) | − | 39.8032i | − | 1.29411i | ||||||
\(947\) | − | 22.9700i | − | 0.746424i | −0.927746 | − | 0.373212i | \(-0.878256\pi\) | ||
0.927746 | − | 0.373212i | \(-0.121744\pi\) | |||||||
\(948\) | 1.96207 | 0.0637249 | ||||||||
\(949\) | −28.9812 | − | 28.9812i | −0.940769 | − | 0.940769i | ||||
\(950\) | 17.3442 | + | 12.8460i | 0.562720 | + | 0.416778i | ||||
\(951\) | −39.6325 | −1.28517 | ||||||||
\(952\) | −4.69107 | + | 4.69107i | −0.152038 | + | 0.152038i | ||||
\(953\) | 24.2716 | + | 24.2716i | 0.786234 | + | 0.786234i | 0.980875 | − | 0.194641i | \(-0.0623541\pi\) |
−0.194641 | + | 0.980875i | \(0.562354\pi\) | |||||||
\(954\) | −0.144972 | − | 0.144972i | −0.00469365 | − | 0.00469365i | ||||
\(955\) | 0.0646480 | + | 0.872568i | 0.00209196 | + | 0.0282356i | ||||
\(956\) | 4.53542 | − | 4.53542i | 0.146686 | − | 0.146686i | ||||
\(957\) | −12.9258 | −0.417832 | ||||||||
\(958\) | −10.6512 | + | 10.6512i | −0.344124 | + | 0.344124i | ||||
\(959\) | − | 13.2806i | − | 0.428854i | ||||||
\(960\) | 0.301249 | + | 4.06602i | 0.00972276 | + | 0.131230i | ||||
\(961\) | 10.0172i | 0.323136i | ||||||||
\(962\) | 15.1583 | − | 11.2877i | 0.488723 | − | 0.363929i | ||||
\(963\) | 1.26064 | − | 1.26064i | 0.0406234 | − | 0.0406234i | ||||
\(964\) | 2.95256 | + | 2.95256i | 0.0950957 | + | 0.0950957i | ||||
\(965\) | 14.8834 | + | 12.8301i | 0.479113 | + | 0.413016i | ||||
\(966\) | 11.6485i | 0.374786i | ||||||||
\(967\) | − | 20.1548i | − | 0.648135i | −0.946034 | − | 0.324068i | \(-0.894949\pi\) | ||
0.946034 | − | 0.324068i | \(-0.105051\pi\) | |||||||
\(968\) | 2.29574 | 0.0737879 | ||||||||
\(969\) | 63.6772i | 2.04561i | ||||||||
\(970\) | −21.3459 | + | 24.7620i | −0.685375 | + | 0.795060i | ||||
\(971\) | 35.4771 | 1.13852 | 0.569258 | − | 0.822159i | \(-0.307231\pi\) | ||||
0.569258 | + | 0.822159i | \(0.307231\pi\) | |||||||
\(972\) | 2.37553 | + | 2.37553i | 0.0761952 | + | 0.0761952i | ||||
\(973\) | −1.39989 | − | 1.39989i | −0.0448785 | − | 0.0448785i | ||||
\(974\) | − | 17.1695i | − | 0.550145i | ||||||
\(975\) | −16.8592 | + | 22.7628i | −0.539927 | + | 0.728992i | ||||
\(976\) | 8.71382 | − | 8.71382i | 0.278923 | − | 0.278923i | ||||
\(977\) | 2.60048 | 0.0831967 | 0.0415983 | − | 0.999134i | \(-0.486755\pi\) | ||||
0.0415983 | + | 0.999134i | \(0.486755\pi\) | |||||||
\(978\) | 13.7612 | − | 13.7612i | 0.440033 | − | 0.440033i | ||||
\(979\) | 21.1493 | − | 21.1493i | 0.675935 | − | 0.675935i | ||||
\(980\) | 9.23820 | − | 10.7166i | 0.295103 | − | 0.342330i | ||||
\(981\) | 0.654431 | + | 0.654431i | 0.0208944 | + | 0.0208944i | ||||
\(982\) | 9.04897 | 0.288764 | ||||||||
\(983\) | 35.9359 | + | 35.9359i | 1.14618 | + | 1.14618i | 0.987298 | + | 0.158880i | \(0.0507881\pi\) |
0.158880 | + | 0.987298i | \(0.449212\pi\) | |||||||
\(984\) | 12.0049 | − | 12.0049i | 0.382701 | − | 0.382701i | ||||
\(985\) | 1.96614 | + | 26.5374i | 0.0626465 | + | 0.845552i | ||||
\(986\) | −11.1218 | + | 11.1218i | −0.354192 | + | 0.354192i | ||||
\(987\) | 6.15711 | − | 6.15711i | 0.195983 | − | 0.195983i | ||||
\(988\) | −9.48374 | + | 9.48374i | −0.301718 | + | 0.301718i | ||||
\(989\) | −85.0426 | −2.70420 | ||||||||
\(990\) | 2.00488 | + | 1.72829i | 0.0637192 | + | 0.0549286i | ||||
\(991\) | −24.9318 | + | 24.9318i | −0.791984 | + | 0.791984i | −0.981816 | − | 0.189833i | \(-0.939205\pi\) |
0.189833 | + | 0.981816i | \(0.439205\pi\) | |||||||
\(992\) | −3.23904 | + | 3.23904i | −0.102840 | + | 0.102840i | ||||
\(993\) | − | 14.7713i | − | 0.468755i | ||||||
\(994\) | −0.000879026 | 0 | 0.000879026i | −2.78810e−5 | 0 | 2.78810e-5i | ||||
\(995\) | 0.981600 | + | 13.2489i | 0.0311188 | + | 0.420017i | ||||
\(996\) | 8.17374 | 0.258995 | ||||||||
\(997\) | 23.9821i | 0.759520i | 0.925085 | + | 0.379760i | \(0.123993\pi\) | ||||
−0.925085 | + | 0.379760i | \(0.876007\pi\) | |||||||
\(998\) | 8.81194 | + | 8.81194i | 0.278937 | + | 0.278937i | ||||
\(999\) | −4.29708 | + | 29.3598i | −0.135954 | + | 0.928902i |
(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 | 370.2.h.e.117.7 | yes | 20 | |
5.3 | odd | 4 | 370.2.g.e.43.4 | ✓ | 20 | ||
37.31 | odd | 4 | 370.2.g.e.327.4 | yes | 20 | ||
185.68 | even | 4 | inner | 370.2.h.e.253.7 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.e.43.4 | ✓ | 20 | 5.3 | odd | 4 | ||
370.2.g.e.327.4 | yes | 20 | 37.31 | odd | 4 | ||
370.2.h.e.117.7 | yes | 20 | 1.1 | even | 1 | trivial | |
370.2.h.e.253.7 | yes | 20 | 185.68 | even | 4 | inner |