Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(118,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.118");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.m (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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.4 | ||
Root | \(1.36166 - 0.381939i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.307 |
Dual form | 525.2.m.b.118.4 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.540143 | − | 0.540143i | −0.381939 | − | 0.381939i | 0.489861 | − | 0.871800i | \(-0.337047\pi\) |
−0.871800 | + | 0.489861i | \(0.837047\pi\) | |||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.41649i | − | 0.708245i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 0.763878i | − | 0.311852i | ||||||
\(7\) | −0.614060 | − | 2.57351i | −0.232093 | − | 0.972694i | ||||
\(8\) | −1.84539 | + | 1.84539i | −0.652445 | + | 0.652445i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.85136 | −1.16123 | −0.580615 | − | 0.814179i | \(-0.697188\pi\) | ||||
−0.580615 | + | 0.814179i | \(0.697188\pi\) | |||||||
\(12\) | 1.00161 | − | 1.00161i | 0.289140 | − | 0.289140i | ||||
\(13\) | −3.66816 | − | 3.66816i | −1.01737 | − | 1.01737i | −0.999847 | − | 0.0175187i | \(-0.994423\pi\) |
−0.0175187 | − | 0.999847i | \(-0.505577\pi\) | |||||||
\(14\) | −1.05838 | + | 1.72174i | −0.282864 | + | 0.460155i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.839427 | −0.209857 | ||||||||
\(17\) | 1.49007 | − | 1.49007i | 0.361395 | − | 0.361395i | −0.502931 | − | 0.864326i | \(-0.667745\pi\) |
0.864326 | + | 0.502931i | \(0.167745\pi\) | |||||||
\(18\) | 0.540143 | − | 0.540143i | 0.127313 | − | 0.127313i | ||||
\(19\) | −0.0697674 | −0.0160057 | −0.00800286 | − | 0.999968i | \(-0.502547\pi\) | ||||
−0.00800286 | + | 0.999968i | \(0.502547\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.38554 | − | 2.25395i | 0.302349 | − | 0.491852i | ||||
\(22\) | 2.08029 | + | 2.08029i | 0.443519 | + | 0.443519i | ||||
\(23\) | 0.534176 | − | 0.534176i | 0.111383 | − | 0.111383i | −0.649218 | − | 0.760602i | \(-0.724904\pi\) |
0.760602 | + | 0.649218i | \(0.224904\pi\) | |||||||
\(24\) | −2.60978 | −0.532719 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.96267i | 0.777143i | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −3.64535 | + | 0.869810i | −0.688906 | + | 0.164379i | ||||
\(29\) | 2.77107i | 0.514576i | 0.966335 | + | 0.257288i | \(0.0828288\pi\) | ||||
−0.966335 | + | 0.257288i | \(0.917171\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.39674i | 0.430467i | 0.976563 | + | 0.215233i | \(0.0690512\pi\) | ||||
−0.976563 | + | 0.215233i | \(0.930949\pi\) | |||||||
\(32\) | 4.14420 | + | 4.14420i | 0.732598 | + | 0.732598i | ||||
\(33\) | −2.72332 | − | 2.72332i | −0.474070 | − | 0.474070i | ||||
\(34\) | −1.60970 | −0.276062 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.41649 | 0.236082 | ||||||||
\(37\) | −6.18757 | − | 6.18757i | −1.01723 | − | 1.01723i | −0.999849 | − | 0.0173805i | \(-0.994467\pi\) |
−0.0173805 | − | 0.999849i | \(-0.505533\pi\) | |||||||
\(38\) | 0.0376844 | + | 0.0376844i | 0.00611321 | + | 0.00611321i | ||||
\(39\) | − | 5.18757i | − | 0.830675i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.68077i | − | 1.35571i | −0.735196 | − | 0.677854i | \(-0.762910\pi\) | ||
0.735196 | − | 0.677854i | \(-0.237090\pi\) | |||||||
\(42\) | −1.96584 | + | 0.469067i | −0.303336 | + | 0.0723786i | ||||
\(43\) | 2.77107 | − | 2.77107i | 0.422585 | − | 0.422585i | −0.463508 | − | 0.886093i | \(-0.653409\pi\) |
0.886093 | + | 0.463508i | \(0.153409\pi\) | |||||||
\(44\) | 5.45542i | 0.822435i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.577063 | −0.0850834 | ||||||||
\(47\) | 5.49042 | − | 5.49042i | 0.800860 | − | 0.800860i | −0.182370 | − | 0.983230i | \(-0.558377\pi\) |
0.983230 | + | 0.182370i | \(0.0583768\pi\) | |||||||
\(48\) | −0.593565 | − | 0.593565i | −0.0856737 | − | 0.0856737i | ||||
\(49\) | −6.24586 | + | 3.16057i | −0.892266 | + | 0.451510i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.10728 | 0.295078 | ||||||||
\(52\) | −5.19592 | + | 5.19592i | −0.720544 | + | 0.720544i | ||||
\(53\) | −6.13823 | + | 6.13823i | −0.843151 | + | 0.843151i | −0.989267 | − | 0.146116i | \(-0.953323\pi\) |
0.146116 | + | 0.989267i | \(0.453323\pi\) | |||||||
\(54\) | 0.763878 | 0.103951 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.88231 | + | 3.61595i | 0.786057 | + | 0.483202i | ||||
\(57\) | −0.0493330 | − | 0.0493330i | −0.00653431 | − | 0.00653431i | ||||
\(58\) | 1.49678 | − | 1.49678i | 0.196536 | − | 0.196536i | ||||
\(59\) | 6.97440 | 0.907990 | 0.453995 | − | 0.891004i | \(-0.349998\pi\) | ||||
0.453995 | + | 0.891004i | \(0.349998\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 14.3107i | − | 1.83230i | −0.400835 | − | 0.916150i | \(-0.631280\pi\) | ||
0.400835 | − | 0.916150i | \(-0.368720\pi\) | |||||||
\(62\) | 1.29458 | − | 1.29458i | 0.164412 | − | 0.164412i | ||||
\(63\) | 2.57351 | − | 0.614060i | 0.324231 | − | 0.0773643i | ||||
\(64\) | − | 2.79807i | − | 0.349758i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.94197i | 0.362131i | ||||||||
\(67\) | −0.416491 | − | 0.416491i | −0.0508824 | − | 0.0508824i | 0.681208 | − | 0.732090i | \(-0.261455\pi\) |
−0.732090 | + | 0.681208i | \(0.761455\pi\) | |||||||
\(68\) | −2.11067 | − | 2.11067i | −0.255957 | − | 0.255957i | ||||
\(69\) | 0.755439 | 0.0909442 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.12783 | −0.964595 | −0.482298 | − | 0.876007i | \(-0.660198\pi\) | ||||
−0.482298 | + | 0.876007i | \(0.660198\pi\) | |||||||
\(72\) | −1.84539 | − | 1.84539i | −0.217482 | − | 0.217482i | ||||
\(73\) | 9.55210 | + | 9.55210i | 1.11799 | + | 1.11799i | 0.992036 | + | 0.125953i | \(0.0401987\pi\) |
0.125953 | + | 0.992036i | \(0.459801\pi\) | |||||||
\(74\) | 6.68434i | 0.777039i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.0988248i | 0.0113360i | ||||||||
\(77\) | 2.36497 | + | 9.91150i | 0.269513 | + | 1.12952i | ||||
\(78\) | −2.80203 | + | 2.80203i | −0.317267 | + | 0.317267i | ||||
\(79\) | − | 9.86329i | − | 1.10971i | −0.831948 | − | 0.554854i | \(-0.812774\pi\) | ||
0.831948 | − | 0.554854i | \(-0.187226\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −4.68886 | + | 4.68886i | −0.517798 | + | 0.517798i | ||||
\(83\) | 1.63570 | + | 1.63570i | 0.179541 | + | 0.179541i | 0.791156 | − | 0.611615i | \(-0.209480\pi\) |
−0.611615 | + | 0.791156i | \(0.709480\pi\) | |||||||
\(84\) | −3.19270 | − | 1.96260i | −0.348352 | − | 0.214137i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.99355 | −0.322803 | ||||||||
\(87\) | −1.95945 | + | 1.95945i | −0.210075 | + | 0.210075i | ||||
\(88\) | 7.10728 | − | 7.10728i | 0.757638 | − | 0.757638i | ||||
\(89\) | 5.05313 | 0.535631 | 0.267815 | − | 0.963470i | \(-0.413698\pi\) | ||||
0.267815 | + | 0.963470i | \(0.413698\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.18757 | + | 11.6925i | −0.753462 | + | 1.22571i | ||||
\(92\) | −0.756656 | − | 0.756656i | −0.0788868 | − | 0.0788868i | ||||
\(93\) | −1.69475 | + | 1.69475i | −0.175737 | + | 0.175737i | ||||
\(94\) | −5.93123 | −0.611759 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.86078i | 0.598164i | ||||||||
\(97\) | 6.85851 | − | 6.85851i | 0.696376 | − | 0.696376i | −0.267251 | − | 0.963627i | \(-0.586115\pi\) |
0.963627 | + | 0.267251i | \(0.0861152\pi\) | |||||||
\(98\) | 5.08082 | + | 1.66650i | 0.513240 | + | 0.168342i | ||||
\(99\) | − | 3.85136i | − | 0.387076i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.1953i | 1.91000i | 0.296605 | + | 0.955000i | \(0.404145\pi\) | ||||
−0.296605 | + | 0.955000i | \(0.595855\pi\) | |||||||
\(102\) | −1.13823 | − | 1.13823i | −0.112702 | − | 0.112702i | ||||
\(103\) | 2.33825 | + | 2.33825i | 0.230394 | + | 0.230394i | 0.812857 | − | 0.582463i | \(-0.197911\pi\) |
−0.582463 | + | 0.812857i | \(0.697911\pi\) | |||||||
\(104\) | 13.5384 | 1.32755 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.63105 | 0.644064 | ||||||||
\(107\) | 6.39747 | + | 6.39747i | 0.618467 | + | 0.618467i | 0.945138 | − | 0.326671i | \(-0.105927\pi\) |
−0.326671 | + | 0.945138i | \(0.605927\pi\) | |||||||
\(108\) | 1.00161 | + | 1.00161i | 0.0963800 | + | 0.0963800i | ||||
\(109\) | − | 2.16057i | − | 0.206945i | −0.994632 | − | 0.103473i | \(-0.967005\pi\) | ||
0.994632 | − | 0.103473i | \(-0.0329954\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 8.75054i | − | 0.830564i | ||||||
\(112\) | 0.515459 | + | 2.16027i | 0.0487063 | + | 0.204126i | ||||
\(113\) | 4.13823 | − | 4.13823i | 0.389292 | − | 0.389292i | −0.485143 | − | 0.874435i | \(-0.661232\pi\) |
0.874435 | + | 0.485143i | \(0.161232\pi\) | |||||||
\(114\) | 0.0532937i | 0.00499142i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.92520 | 0.364446 | ||||||||
\(117\) | 3.66816 | − | 3.66816i | 0.339122 | − | 0.339122i | ||||
\(118\) | −3.76718 | − | 3.76718i | −0.346797 | − | 0.346797i | ||||
\(119\) | −4.74970 | − | 2.91971i | −0.435404 | − | 0.267650i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.83298 | 0.348453 | ||||||||
\(122\) | −7.72984 | + | 7.72984i | −0.699827 | + | 0.699827i | ||||
\(123\) | 6.13823 | − | 6.13823i | 0.553466 | − | 0.553466i | ||||
\(124\) | 3.39496 | 0.304876 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.72174 | − | 1.05838i | −0.153385 | − | 0.0942881i | ||||
\(127\) | 4.83298 | + | 4.83298i | 0.428858 | + | 0.428858i | 0.888239 | − | 0.459381i | \(-0.151929\pi\) |
−0.459381 | + | 0.888239i | \(0.651929\pi\) | |||||||
\(128\) | 6.77704 | − | 6.77704i | 0.599011 | − | 0.599011i | ||||
\(129\) | 3.91889 | 0.345039 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 0.647499i | − | 0.0565722i | −0.999600 | − | 0.0282861i | \(-0.990995\pi\) | ||
0.999600 | − | 0.0282861i | \(-0.00900495\pi\) | |||||||
\(132\) | −3.85756 | + | 3.85756i | −0.335758 | + | 0.335758i | ||||
\(133\) | 0.0428413 | + | 0.179547i | 0.00371481 | + | 0.0155687i | ||||
\(134\) | 0.449929i | 0.0388680i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.49954i | 0.471581i | ||||||||
\(137\) | −10.2369 | − | 10.2369i | −0.874597 | − | 0.874597i | 0.118372 | − | 0.992969i | \(-0.462232\pi\) |
−0.992969 | + | 0.118372i | \(0.962232\pi\) | |||||||
\(138\) | −0.408045 | − | 0.408045i | −0.0347351 | − | 0.0347351i | ||||
\(139\) | 22.1663 | 1.88012 | 0.940060 | − | 0.341009i | \(-0.110769\pi\) | ||||
0.940060 | + | 0.341009i | \(0.110769\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.76463 | 0.653900 | ||||||||
\(142\) | 4.39019 | + | 4.39019i | 0.368417 | + | 0.368417i | ||||
\(143\) | 14.1274 | + | 14.1274i | 1.18139 | + | 1.18139i | ||||
\(144\) | − | 0.839427i | − | 0.0699523i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 10.3190i | − | 0.854007i | ||||||
\(147\) | −6.65135 | − | 2.18163i | −0.548594 | − | 0.179938i | ||||
\(148\) | −8.76463 | + | 8.76463i | −0.720448 | + | 0.720448i | ||||
\(149\) | − | 11.0475i | − | 0.905050i | −0.891752 | − | 0.452525i | \(-0.850523\pi\) | ||
0.891752 | − | 0.452525i | \(-0.149477\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3990 | 1.49729 | 0.748645 | − | 0.662972i | \(-0.230705\pi\) | ||||
0.748645 | + | 0.662972i | \(0.230705\pi\) | |||||||
\(152\) | 0.128748 | − | 0.128748i | 0.0104429 | − | 0.0104429i | ||||
\(153\) | 1.49007 | + | 1.49007i | 0.120465 | + | 0.120465i | ||||
\(154\) | 4.07621 | − | 6.63105i | 0.328470 | − | 0.534345i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.34814 | −0.588322 | ||||||||
\(157\) | −1.04994 | + | 1.04994i | −0.0837946 | + | 0.0837946i | −0.747762 | − | 0.663967i | \(-0.768871\pi\) |
0.663967 | + | 0.747762i | \(0.268871\pi\) | |||||||
\(158\) | −5.32759 | + | 5.32759i | −0.423840 | + | 0.423840i | ||||
\(159\) | −8.68077 | −0.688430 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.70272 | − | 1.04669i | −0.134193 | − | 0.0824907i | ||||
\(162\) | 0.540143 | + | 0.540143i | 0.0424377 | + | 0.0424377i | ||||
\(163\) | −5.50539 | + | 5.50539i | −0.431215 | + | 0.431215i | −0.889042 | − | 0.457826i | \(-0.848628\pi\) |
0.457826 | + | 0.889042i | \(0.348628\pi\) | |||||||
\(164\) | −12.2962 | −0.960174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 1.76702i | − | 0.137147i | ||||||
\(167\) | 1.88968 | − | 1.88968i | 0.146228 | − | 0.146228i | −0.630203 | − | 0.776431i | \(-0.717028\pi\) |
0.776431 | + | 0.630203i | \(0.217028\pi\) | |||||||
\(168\) | 1.60256 | + | 6.71629i | 0.123640 | + | 0.518173i | ||||
\(169\) | 13.9108i | 1.07006i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 0.0697674i | − | 0.00533524i | ||||||
\(172\) | −3.92520 | − | 3.92520i | −0.299294 | − | 0.299294i | ||||
\(173\) | −4.90751 | − | 4.90751i | −0.373111 | − | 0.373111i | 0.495498 | − | 0.868609i | \(-0.334986\pi\) |
−0.868609 | + | 0.495498i | \(0.834986\pi\) | |||||||
\(174\) | 2.11676 | 0.160471 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.23294 | 0.243692 | ||||||||
\(177\) | 4.93165 | + | 4.93165i | 0.370685 | + | 0.370685i | ||||
\(178\) | −2.72941 | − | 2.72941i | −0.204578 | − | 0.204578i | ||||
\(179\) | 18.5857i | 1.38916i | 0.719416 | + | 0.694579i | \(0.244409\pi\) | ||||
−0.719416 | + | 0.694579i | \(0.755591\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.48528i | − | 0.630706i | −0.948974 | − | 0.315353i | \(-0.897877\pi\) | ||
0.948974 | − | 0.315353i | \(-0.102123\pi\) | |||||||
\(182\) | 10.1979 | − | 2.43331i | 0.755922 | − | 0.180369i | ||||
\(183\) | 10.1192 | − | 10.1192i | 0.748034 | − | 0.748034i | ||||
\(184\) | 1.97153i | 0.145343i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.83081 | 0.134242 | ||||||||
\(187\) | −5.73880 | + | 5.73880i | −0.419663 | + | 0.419663i | ||||
\(188\) | −7.77713 | − | 7.77713i | −0.567206 | − | 0.567206i | ||||
\(189\) | 2.25395 | + | 1.38554i | 0.163951 | + | 0.100783i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.39351 | −0.390261 | −0.195130 | − | 0.980777i | \(-0.562513\pi\) | ||||
−0.195130 | + | 0.980777i | \(0.562513\pi\) | |||||||
\(192\) | 1.97853 | − | 1.97853i | 0.142788 | − | 0.142788i | ||||
\(193\) | 4.80599 | − | 4.80599i | 0.345943 | − | 0.345943i | −0.512653 | − | 0.858596i | \(-0.671337\pi\) |
0.858596 | + | 0.512653i | \(0.171337\pi\) | |||||||
\(194\) | −7.40916 | −0.531946 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.47692 | + | 8.84720i | 0.319780 | + | 0.631943i | ||||
\(197\) | −12.6739 | − | 12.6739i | −0.902981 | − | 0.902981i | 0.0927124 | − | 0.995693i | \(-0.470446\pi\) |
−0.995693 | + | 0.0927124i | \(0.970446\pi\) | |||||||
\(198\) | −2.08029 | + | 2.08029i | −0.147840 | + | 0.147840i | ||||
\(199\) | 2.67111 | 0.189350 | 0.0946750 | − | 0.995508i | \(-0.469819\pi\) | ||||
0.0946750 | + | 0.995508i | \(0.469819\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 0.589007i | − | 0.0415453i | ||||||
\(202\) | 10.3682 | − | 10.3682i | 0.729503 | − | 0.729503i | ||||
\(203\) | 7.13138 | − | 1.70161i | 0.500524 | − | 0.119429i | ||||
\(204\) | − | 2.98494i | − | 0.208988i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 2.52597i | − | 0.175993i | ||||||
\(207\) | 0.534176 | + | 0.534176i | 0.0371278 | + | 0.0371278i | ||||
\(208\) | 3.07916 | + | 3.07916i | 0.213501 | + | 0.213501i | ||||
\(209\) | 0.268699 | 0.0185863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0239 | −0.827757 | −0.413879 | − | 0.910332i | \(-0.635826\pi\) | ||||
−0.413879 | + | 0.910332i | \(0.635826\pi\) | |||||||
\(212\) | 8.69475 | + | 8.69475i | 0.597158 | + | 0.597158i | ||||
\(213\) | −5.74724 | − | 5.74724i | −0.393794 | − | 0.393794i | ||||
\(214\) | − | 6.91110i | − | 0.472433i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 2.60978i | − | 0.177573i | ||||||
\(217\) | 6.16802 | − | 1.47174i | 0.418712 | − | 0.0999082i | ||||
\(218\) | −1.16702 | + | 1.16702i | −0.0790405 | + | 0.0790405i | ||||
\(219\) | 13.5087i | 0.912834i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.9316 | −0.735342 | ||||||||
\(222\) | −4.72654 | + | 4.72654i | −0.317225 | + | 0.317225i | ||||
\(223\) | −11.6925 | − | 11.6925i | −0.782988 | − | 0.782988i | 0.197346 | − | 0.980334i | \(-0.436768\pi\) |
−0.980334 | + | 0.197346i | \(0.936768\pi\) | |||||||
\(224\) | 8.12033 | − | 13.2099i | 0.542563 | − | 0.882624i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.47048 | −0.297372 | ||||||||
\(227\) | 1.10518 | − | 1.10518i | 0.0733535 | − | 0.0733535i | −0.669478 | − | 0.742832i | \(-0.733482\pi\) |
0.742832 | + | 0.669478i | \(0.233482\pi\) | |||||||
\(228\) | −0.0698797 | + | 0.0698797i | −0.00462790 | + | 0.00462790i | ||||
\(229\) | −7.83309 | −0.517625 | −0.258812 | − | 0.965928i | \(-0.583331\pi\) | ||||
−0.258812 | + | 0.965928i | \(0.583331\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.33620 | + | 8.68077i | −0.351096 | + | 0.571153i | ||||
\(232\) | −5.11372 | − | 5.11372i | −0.335732 | − | 0.335732i | ||||
\(233\) | −1.00797 | + | 1.00797i | −0.0660345 | + | 0.0660345i | −0.739353 | − | 0.673318i | \(-0.764868\pi\) |
0.673318 | + | 0.739353i | \(0.264868\pi\) | |||||||
\(234\) | −3.96267 | −0.259048 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 9.87918i | − | 0.643080i | ||||||
\(237\) | 6.97440 | − | 6.97440i | 0.453036 | − | 0.453036i | ||||
\(238\) | 0.988454 | + | 4.14258i | 0.0640720 | + | 0.268524i | ||||
\(239\) | − | 20.2805i | − | 1.31183i | −0.754833 | − | 0.655917i | \(-0.772282\pi\) | ||
0.754833 | − | 0.655917i | \(-0.227718\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 2.76994i | − | 0.178427i | −0.996013 | − | 0.0892136i | \(-0.971565\pi\) | ||
0.996013 | − | 0.0892136i | \(-0.0284354\pi\) | |||||||
\(242\) | −2.07036 | − | 2.07036i | −0.133088 | − | 0.133088i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | −20.2710 | −1.29772 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.63105 | −0.422780 | ||||||||
\(247\) | 0.255918 | + | 0.255918i | 0.0162837 | + | 0.0162837i | ||||
\(248\) | −4.42292 | − | 4.42292i | −0.280856 | − | 0.280856i | ||||
\(249\) | 2.31322i | 0.146595i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.09982i | 0.385017i | 0.981295 | + | 0.192509i | \(0.0616623\pi\) | ||||
−0.981295 | + | 0.192509i | \(0.938338\pi\) | |||||||
\(252\) | −0.869810 | − | 3.64535i | −0.0547929 | − | 0.229635i | ||||
\(253\) | −2.05731 | + | 2.05731i | −0.129342 | + | 0.129342i | ||||
\(254\) | − | 5.22100i | − | 0.327595i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9173 | −0.807330 | ||||||||
\(257\) | −2.01843 | + | 2.01843i | −0.125906 | + | 0.125906i | −0.767252 | − | 0.641346i | \(-0.778376\pi\) |
0.641346 | + | 0.767252i | \(0.278376\pi\) | |||||||
\(258\) | −2.11676 | − | 2.11676i | −0.131784 | − | 0.131784i | ||||
\(259\) | −12.1242 | + | 19.7233i | −0.753361 | + | 1.22554i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.77107 | −0.171525 | ||||||||
\(262\) | −0.349742 | + | 0.349742i | −0.0216071 | + | 0.0216071i | ||||
\(263\) | −16.7686 | + | 16.7686i | −1.03400 | + | 1.03400i | −0.0345941 | + | 0.999401i | \(0.511014\pi\) |
−0.999401 | + | 0.0345941i | \(0.988986\pi\) | |||||||
\(264\) | 10.0512 | 0.618609 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0738405 | − | 0.120121i | 0.00452745 | − | 0.00736511i | ||||
\(267\) | 3.57310 | + | 3.57310i | 0.218670 | + | 0.218670i | ||||
\(268\) | −0.589955 | + | 0.589955i | −0.0360372 | + | 0.0360372i | ||||
\(269\) | −24.7351 | −1.50813 | −0.754064 | − | 0.656801i | \(-0.771909\pi\) | ||||
−0.754064 | + | 0.656801i | \(0.771909\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.13470i | − | 0.251165i | −0.992083 | − | 0.125583i | \(-0.959920\pi\) | ||
0.992083 | − | 0.125583i | \(-0.0400800\pi\) | |||||||
\(272\) | −1.25081 | + | 1.25081i | −0.0758413 | + | 0.0758413i | ||||
\(273\) | −13.3502 | + | 3.18548i | −0.807993 | + | 0.192794i | ||||
\(274\) | 11.0588i | 0.668085i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 1.07007i | − | 0.0644108i | ||||||
\(277\) | 12.1128 | + | 12.1128i | 0.727786 | + | 0.727786i | 0.970178 | − | 0.242393i | \(-0.0779322\pi\) |
−0.242393 | + | 0.970178i | \(0.577932\pi\) | |||||||
\(278\) | −11.9730 | − | 11.9730i | −0.718091 | − | 0.718091i | ||||
\(279\) | −2.39674 | −0.143489 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.25279 | 0.313355 | 0.156678 | − | 0.987650i | \(-0.449922\pi\) | ||||
0.156678 | + | 0.987650i | \(0.449922\pi\) | |||||||
\(282\) | −4.19401 | − | 4.19401i | −0.249750 | − | 0.249750i | ||||
\(283\) | −1.66729 | − | 1.66729i | −0.0991101 | − | 0.0991101i | 0.655813 | − | 0.754923i | \(-0.272326\pi\) |
−0.754923 | + | 0.655813i | \(0.772326\pi\) | |||||||
\(284\) | 11.5130i | 0.683170i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 15.2617i | − | 0.902441i | ||||||
\(287\) | −22.3400 | + | 5.33051i | −1.31869 | + | 0.314650i | ||||
\(288\) | −4.14420 | + | 4.14420i | −0.244199 | + | 0.244199i | ||||
\(289\) | 12.5594i | 0.738787i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.69940 | 0.568589 | ||||||||
\(292\) | 13.5305 | − | 13.5305i | 0.791810 | − | 0.791810i | ||||
\(293\) | −15.2556 | − | 15.2556i | −0.891240 | − | 0.891240i | 0.103400 | − | 0.994640i | \(-0.467028\pi\) |
−0.994640 | + | 0.103400i | \(0.967028\pi\) | |||||||
\(294\) | 2.41429 | + | 4.77107i | 0.140804 | + | 0.278255i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 22.8370 | 1.32737 | ||||||||
\(297\) | 2.72332 | − | 2.72332i | 0.158023 | − | 0.158023i | ||||
\(298\) | −5.96725 | + | 5.96725i | −0.345674 | + | 0.345674i | ||||
\(299\) | −3.91889 | −0.226635 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.83298 | − | 5.42977i | −0.509125 | − | 0.312967i | ||||
\(302\) | −9.93809 | − | 9.93809i | −0.571873 | − | 0.571873i | ||||
\(303\) | −13.5731 | + | 13.5731i | −0.779754 | + | 0.779754i | ||||
\(304\) | 0.0585646 | 0.00335891 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 1.60970i | − | 0.0920206i | ||||||
\(307\) | −14.6198 | + | 14.6198i | −0.834394 | + | 0.834394i | −0.988114 | − | 0.153721i | \(-0.950874\pi\) |
0.153721 | + | 0.988114i | \(0.450874\pi\) | |||||||
\(308\) | 14.0395 | − | 3.34995i | 0.799977 | − | 0.190881i | ||||
\(309\) | 3.30678i | 0.188116i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2.86218i | − | 0.162299i | −0.996702 | − | 0.0811497i | \(-0.974141\pi\) | ||
0.996702 | − | 0.0811497i | \(-0.0258592\pi\) | |||||||
\(312\) | 9.57310 | + | 9.57310i | 0.541970 | + | 0.541970i | ||||
\(313\) | −9.41824 | − | 9.41824i | −0.532350 | − | 0.532350i | 0.388921 | − | 0.921271i | \(-0.372848\pi\) |
−0.921271 | + | 0.388921i | \(0.872848\pi\) | |||||||
\(314\) | 1.13424 | 0.0640088 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.9713 | −0.785945 | ||||||||
\(317\) | −7.38310 | − | 7.38310i | −0.414676 | − | 0.414676i | 0.468688 | − | 0.883364i | \(-0.344727\pi\) |
−0.883364 | + | 0.468688i | \(0.844727\pi\) | |||||||
\(318\) | 4.68886 | + | 4.68886i | 0.262938 | + | 0.262938i | ||||
\(319\) | − | 10.6724i | − | 0.597540i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.04739i | 0.504976i | ||||||||
\(322\) | 0.354351 | + | 1.48508i | 0.0197472 | + | 0.0827600i | ||||
\(323\) | −0.103958 | + | 0.103958i | −0.00578440 | + | 0.00578440i | ||||
\(324\) | 1.41649i | 0.0786939i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.94740 | 0.329396 | ||||||||
\(327\) | 1.52776 | − | 1.52776i | 0.0844851 | − | 0.0844851i | ||||
\(328\) | 16.0194 | + | 16.0194i | 0.884526 | + | 0.884526i | ||||
\(329\) | −17.5011 | − | 10.7582i | −0.964866 | − | 0.593118i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.6200 | 1.29827 | 0.649136 | − | 0.760672i | \(-0.275130\pi\) | ||||
0.649136 | + | 0.760672i | \(0.275130\pi\) | |||||||
\(332\) | 2.31695 | − | 2.31695i | 0.127159 | − | 0.127159i | ||||
\(333\) | 6.18757 | − | 6.18757i | 0.339076 | − | 0.339076i | ||||
\(334\) | −2.04139 | −0.111700 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.16306 | + | 1.89203i | −0.0634500 | + | 0.103219i | ||||
\(337\) | 4.93809 | + | 4.93809i | 0.268995 | + | 0.268995i | 0.828695 | − | 0.559700i | \(-0.189084\pi\) |
−0.559700 | + | 0.828695i | \(0.689084\pi\) | |||||||
\(338\) | 7.51384 | − | 7.51384i | 0.408699 | − | 0.408699i | ||||
\(339\) | 5.85234 | 0.317856 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 9.23070i | − | 0.499870i | ||||||
\(342\) | −0.0376844 | + | 0.0376844i | −0.00203774 | + | 0.00203774i | ||||
\(343\) | 11.9691 | + | 14.1330i | 0.646270 | + | 0.763109i | ||||
\(344\) | 10.2274i | 0.551427i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.30151i | 0.285011i | ||||||||
\(347\) | −5.83694 | − | 5.83694i | −0.313343 | − | 0.313343i | 0.532860 | − | 0.846203i | \(-0.321117\pi\) |
−0.846203 | + | 0.532860i | \(0.821117\pi\) | |||||||
\(348\) | 2.77554 | + | 2.77554i | 0.148784 | + | 0.148784i | ||||
\(349\) | 16.9121 | 0.905282 | 0.452641 | − | 0.891693i | \(-0.350482\pi\) | ||||
0.452641 | + | 0.891693i | \(0.350482\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.18757 | 0.276892 | ||||||||
\(352\) | −15.9608 | − | 15.9608i | −0.850714 | − | 0.850714i | ||||
\(353\) | −11.1265 | − | 11.1265i | −0.592202 | − | 0.592202i | 0.346024 | − | 0.938226i | \(-0.387532\pi\) |
−0.938226 | + | 0.346024i | \(0.887532\pi\) | |||||||
\(354\) | − | 5.32759i | − | 0.283158i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 7.15771i | − | 0.379358i | ||||||
\(357\) | −1.29400 | − | 5.42309i | −0.0684855 | − | 0.287021i | ||||
\(358\) | 10.0389 | − | 10.0389i | 0.530574 | − | 0.530574i | ||||
\(359\) | − | 8.14864i | − | 0.430069i | −0.976606 | − | 0.215034i | \(-0.931014\pi\) | ||
0.976606 | − | 0.215034i | \(-0.0689864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9951 | −0.999744 | ||||||||
\(362\) | −4.58327 | + | 4.58327i | −0.240891 | + | 0.240891i | ||||
\(363\) | 2.71033 | + | 2.71033i | 0.142255 | + | 0.142255i | ||||
\(364\) | 16.5623 | + | 10.1811i | 0.868102 | + | 0.533636i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.9316 | −0.571406 | ||||||||
\(367\) | 14.7480 | − | 14.7480i | 0.769840 | − | 0.769840i | −0.208238 | − | 0.978078i | \(-0.566773\pi\) |
0.978078 | + | 0.208238i | \(0.0667728\pi\) | |||||||
\(368\) | −0.448402 | + | 0.448402i | −0.0233746 | + | 0.0233746i | ||||
\(369\) | 8.68077 | 0.451903 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.5660 | + | 12.0275i | 1.01582 | + | 0.624438i | ||||
\(372\) | 2.40060 | + | 2.40060i | 0.124465 | + | 0.124465i | ||||
\(373\) | −1.49461 | + | 1.49461i | −0.0773880 | + | 0.0773880i | −0.744741 | − | 0.667353i | \(-0.767427\pi\) |
0.667353 | + | 0.744741i | \(0.267427\pi\) | |||||||
\(374\) | 6.19955 | 0.320571 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.2640i | 1.04504i | ||||||||
\(377\) | 10.1648 | − | 10.1648i | 0.523511 | − | 0.523511i | ||||
\(378\) | −0.469067 | − | 1.96584i | −0.0241262 | − | 0.101112i | ||||
\(379\) | − | 18.7135i | − | 0.961248i | −0.876927 | − | 0.480624i | \(-0.840410\pi\) | ||
0.876927 | − | 0.480624i | \(-0.159590\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.83487i | 0.350161i | ||||||||
\(382\) | 2.91327 | + | 2.91327i | 0.149056 | + | 0.149056i | ||||
\(383\) | 20.9354 | + | 20.9354i | 1.06975 | + | 1.06975i | 0.997378 | + | 0.0723706i | \(0.0230564\pi\) |
0.0723706 | + | 0.997378i | \(0.476944\pi\) | |||||||
\(384\) | 9.58418 | 0.489091 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.19184 | −0.264258 | ||||||||
\(387\) | 2.77107 | + | 2.77107i | 0.140862 | + | 0.140862i | ||||
\(388\) | −9.71502 | − | 9.71502i | −0.493205 | − | 0.493205i | ||||
\(389\) | − | 25.6611i | − | 1.30107i | −0.759477 | − | 0.650535i | \(-0.774545\pi\) | ||
0.759477 | − | 0.650535i | \(-0.225455\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.59192i | − | 0.0805069i | ||||||
\(392\) | 5.69357 | − | 17.3586i | 0.287569 | − | 0.876741i | ||||
\(393\) | 0.457851 | − | 0.457851i | 0.0230955 | − | 0.0230955i | ||||
\(394\) | 13.6915i | 0.689767i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.45542 | −0.274145 | ||||||||
\(397\) | 6.73585 | − | 6.73585i | 0.338063 | − | 0.338063i | −0.517575 | − | 0.855638i | \(-0.673165\pi\) |
0.855638 | + | 0.517575i | \(0.173165\pi\) | |||||||
\(398\) | −1.44278 | − | 1.44278i | −0.0723201 | − | 0.0723201i | ||||
\(399\) | −0.0966653 | + | 0.157252i | −0.00483932 | + | 0.00787245i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.7503 | 0.736593 | 0.368296 | − | 0.929708i | \(-0.379941\pi\) | ||||
0.368296 | + | 0.929708i | \(0.379941\pi\) | |||||||
\(402\) | −0.318148 | + | 0.318148i | −0.0158678 | + | 0.0158678i | ||||
\(403\) | 8.79162 | − | 8.79162i | 0.437942 | − | 0.437942i | ||||
\(404\) | 27.1899 | 1.35275 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.77107 | − | 2.93285i | −0.236784 | − | 0.145555i | ||||
\(407\) | 23.8305 | + | 23.8305i | 1.18124 | + | 1.18124i | ||||
\(408\) | −3.88876 | + | 3.88876i | −0.192522 | + | 0.192522i | ||||
\(409\) | −10.5604 | −0.522180 | −0.261090 | − | 0.965315i | \(-0.584082\pi\) | ||||
−0.261090 | + | 0.965315i | \(0.584082\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 14.4772i | − | 0.714106i | ||||||
\(412\) | 3.31210 | − | 3.31210i | 0.163176 | − | 0.163176i | ||||
\(413\) | −4.28270 | − | 17.9487i | −0.210738 | − | 0.883196i | ||||
\(414\) | − | 0.577063i | − | 0.0283611i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 30.4032i | − | 1.49064i | ||||||
\(417\) | 15.6739 | + | 15.6739i | 0.767556 | + | 0.767556i | ||||
\(418\) | −0.145136 | − | 0.145136i | −0.00709884 | − | 0.00709884i | ||||
\(419\) | −15.5472 | −0.759532 | −0.379766 | − | 0.925083i | \(-0.623996\pi\) | ||||
−0.379766 | + | 0.925083i | \(0.623996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.29886 | 0.160776 | 0.0803882 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803882 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(422\) | 6.49461 | + | 6.49461i | 0.316153 | + | 0.316153i | ||||
\(423\) | 5.49042 | + | 5.49042i | 0.266953 | + | 0.266953i | ||||
\(424\) | − | 22.6549i | − | 1.10022i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.20867i | 0.300811i | ||||||||
\(427\) | −36.8287 | + | 8.78764i | −1.78227 | + | 0.425264i | ||||
\(428\) | 9.06196 | − | 9.06196i | 0.438026 | − | 0.438026i | ||||
\(429\) | 19.9792i | 0.964604i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.0911 | −0.678743 | −0.339371 | − | 0.940652i | \(-0.610214\pi\) | ||||
−0.339371 | + | 0.940652i | \(0.610214\pi\) | |||||||
\(432\) | 0.593565 | − | 0.593565i | 0.0285579 | − | 0.0285579i | ||||
\(433\) | −1.72650 | − | 1.72650i | −0.0829702 | − | 0.0829702i | 0.664404 | − | 0.747374i | \(-0.268686\pi\) |
−0.747374 | + | 0.664404i | \(0.768686\pi\) | |||||||
\(434\) | −4.12656 | − | 2.53666i | −0.198081 | − | 0.121764i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.06043 | −0.146568 | ||||||||
\(437\) | −0.0372681 | + | 0.0372681i | −0.00178277 | + | 0.00178277i | ||||
\(438\) | 7.29664 | − | 7.29664i | 0.348647 | − | 0.348647i | ||||
\(439\) | 27.1172 | 1.29423 | 0.647116 | − | 0.762392i | \(-0.275975\pi\) | ||||
0.647116 | + | 0.762392i | \(0.275975\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.16057 | − | 6.24586i | −0.150503 | − | 0.297422i | ||||
\(442\) | 5.90465 | + | 5.90465i | 0.280856 | + | 0.280856i | ||||
\(443\) | 24.1502 | − | 24.1502i | 1.14741 | − | 1.14741i | 0.160349 | − | 0.987060i | \(-0.448738\pi\) |
0.987060 | − | 0.160349i | \(-0.0512618\pi\) | |||||||
\(444\) | −12.3951 | −0.588243 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.6313i | 0.598107i | ||||||||
\(447\) | 7.81179 | − | 7.81179i | 0.369485 | − | 0.369485i | ||||
\(448\) | −7.20084 | + | 1.71818i | −0.340208 | + | 0.0811764i | ||||
\(449\) | 9.80267i | 0.462617i | 0.972881 | + | 0.231308i | \(0.0743006\pi\) | ||||
−0.972881 | + | 0.231308i | \(0.925699\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.4328i | 1.57429i | ||||||||
\(452\) | −5.86177 | − | 5.86177i | −0.275714 | − | 0.275714i | ||||
\(453\) | 13.0101 | + | 13.0101i | 0.611266 | + | 0.611266i | ||||
\(454\) | −1.19391 | −0.0560331 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.182078 | 0.00852656 | ||||||||
\(457\) | −0.550071 | − | 0.550071i | −0.0257312 | − | 0.0257312i | 0.694124 | − | 0.719855i | \(-0.255792\pi\) |
−0.719855 | + | 0.694124i | \(0.755792\pi\) | |||||||
\(458\) | 4.23099 | + | 4.23099i | 0.197701 | + | 0.197701i | ||||
\(459\) | 2.10728i | 0.0983594i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 0.831786i | − | 0.0387401i | −0.999812 | − | 0.0193701i | \(-0.993834\pi\) | ||
0.999812 | − | 0.0193701i | \(-0.00616607\pi\) | |||||||
\(462\) | 7.57117 | − | 1.80655i | 0.352243 | − | 0.0840481i | ||||
\(463\) | −5.45140 | + | 5.45140i | −0.253348 | + | 0.253348i | −0.822342 | − | 0.568994i | \(-0.807333\pi\) |
0.568994 | + | 0.822342i | \(0.307333\pi\) | |||||||
\(464\) | − | 2.32612i | − | 0.107987i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.08890 | 0.0504423 | ||||||||
\(467\) | −23.2827 | + | 23.2827i | −1.07740 | + | 1.07740i | −0.0806551 | + | 0.996742i | \(0.525701\pi\) |
−0.996742 | + | 0.0806551i | \(0.974299\pi\) | |||||||
\(468\) | −5.19592 | − | 5.19592i | −0.240181 | − | 0.240181i | ||||
\(469\) | −0.816091 | + | 1.32759i | −0.0376836 | + | 0.0613025i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.48484 | −0.0684180 | ||||||||
\(472\) | −12.8705 | + | 12.8705i | −0.592414 | + | 0.592414i | ||||
\(473\) | −10.6724 | + | 10.6724i | −0.490718 | + | 0.490718i | ||||
\(474\) | −7.53435 | −0.346064 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.13575 | + | 6.72791i | −0.189562 | + | 0.308373i | ||||
\(477\) | −6.13823 | − | 6.13823i | −0.281050 | − | 0.281050i | ||||
\(478\) | −10.9544 | + | 10.9544i | −0.501041 | + | 0.501041i | ||||
\(479\) | 40.4319 | 1.84738 | 0.923691 | − | 0.383138i | \(-0.125157\pi\) | ||||
0.923691 | + | 0.383138i | \(0.125157\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.3940i | 2.06979i | ||||||||
\(482\) | −1.49616 | + | 1.49616i | −0.0681483 | + | 0.0681483i | ||||
\(483\) | −0.463885 | − | 1.94413i | −0.0211075 | − | 0.0884609i | ||||
\(484\) | − | 5.42938i | − | 0.246790i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.763878i | 0.0346502i | ||||||||
\(487\) | 7.22893 | + | 7.22893i | 0.327574 | + | 0.327574i | 0.851663 | − | 0.524089i | \(-0.175594\pi\) |
−0.524089 | + | 0.851663i | \(0.675594\pi\) | |||||||
\(488\) | 26.4089 | + | 26.4089i | 1.19548 | + | 1.19548i | ||||
\(489\) | −7.78580 | −0.352086 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.1040 | 0.907279 | 0.453639 | − | 0.891185i | \(-0.350125\pi\) | ||||
0.453639 | + | 0.891185i | \(0.350125\pi\) | |||||||
\(492\) | −8.69475 | − | 8.69475i | −0.391990 | − | 0.391990i | ||||
\(493\) | 4.12910 | + | 4.12910i | 0.185965 | + | 0.185965i | ||||
\(494\) | − | 0.276465i | − | 0.0124387i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2.01189i | − | 0.0903364i | ||||||
\(497\) | 4.99097 | + | 20.9170i | 0.223876 | + | 0.938256i | ||||
\(498\) | 1.24947 | − | 1.24947i | 0.0559902 | − | 0.0559902i | ||||
\(499\) | − | 15.4227i | − | 0.690414i | −0.938527 | − | 0.345207i | \(-0.887809\pi\) | ||
0.938527 | − | 0.345207i | \(-0.112191\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.67241 | 0.119394 | ||||||||
\(502\) | 3.29478 | − | 3.29478i | 0.147053 | − | 0.147053i | ||||
\(503\) | 25.9985 | + | 25.9985i | 1.15922 | + | 1.15922i | 0.984644 | + | 0.174573i | \(0.0558546\pi\) |
0.174573 | + | 0.984644i | \(0.444145\pi\) | |||||||
\(504\) | −3.61595 | + | 5.88231i | −0.161067 | + | 0.262019i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.22248 | 0.0988013 | ||||||||
\(507\) | −9.83645 | + | 9.83645i | −0.436852 | + | 0.436852i | ||||
\(508\) | 6.84587 | − | 6.84587i | 0.303737 | − | 0.303737i | ||||
\(509\) | −37.1271 | −1.64563 | −0.822816 | − | 0.568309i | \(-0.807598\pi\) | ||||
−0.822816 | + | 0.568309i | \(0.807598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.7168 | − | 30.4479i | 0.827983 | − | 1.34694i | ||||
\(512\) | −6.57690 | − | 6.57690i | −0.290661 | − | 0.290661i | ||||
\(513\) | 0.0493330 | − | 0.0493330i | 0.00217810 | − | 0.00217810i | ||||
\(514\) | 2.18048 | 0.0961768 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 5.55107i | − | 0.244372i | ||||||
\(517\) | −21.1456 | + | 21.1456i | −0.929982 | + | 0.929982i | ||||
\(518\) | 17.2022 | − | 4.10459i | 0.755821 | − | 0.180345i | ||||
\(519\) | − | 6.94026i | − | 0.304644i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.59132i | 0.113528i | 0.998388 | + | 0.0567639i | \(0.0180782\pi\) | ||||
−0.998388 | + | 0.0567639i | \(0.981922\pi\) | |||||||
\(522\) | 1.49678 | + | 1.49678i | 0.0655122 | + | 0.0655122i | ||||
\(523\) | −6.08854 | − | 6.08854i | −0.266233 | − | 0.266233i | 0.561347 | − | 0.827581i | \(-0.310283\pi\) |
−0.827581 | + | 0.561347i | \(0.810283\pi\) | |||||||
\(524\) | −0.917176 | −0.0400670 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.1149 | 0.789846 | ||||||||
\(527\) | 3.57131 | + | 3.57131i | 0.155569 | + | 0.155569i | ||||
\(528\) | 2.28603 | + | 2.28603i | 0.0994868 | + | 0.0994868i | ||||
\(529\) | 22.4293i | 0.975187i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.97440i | 0.302663i | ||||||||
\(532\) | 0.254326 | − | 0.0606843i | 0.0110264 | − | 0.00263100i | ||||
\(533\) | −31.8425 | + | 31.8425i | −1.37925 | + | 1.37925i | ||||
\(534\) | − | 3.85997i | − | 0.167037i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.53718 | 0.0663960 | ||||||||
\(537\) | −13.1421 | + | 13.1421i | −0.567122 | + | 0.567122i | ||||
\(538\) | 13.3605 | + | 13.3605i | 0.576013 | + | 0.576013i | ||||
\(539\) | 24.0551 | − | 12.1725i | 1.03613 | − | 0.524307i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.4638 | −1.43872 | −0.719360 | − | 0.694638i | \(-0.755565\pi\) | ||||
−0.719360 | + | 0.694638i | \(0.755565\pi\) | |||||||
\(542\) | −2.23333 | + | 2.23333i | −0.0959297 | + | 0.0959297i | ||||
\(543\) | 6.00000 | − | 6.00000i | 0.257485 | − | 0.257485i | ||||
\(544\) | 12.3503 | 0.529515 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.93165 | + | 5.49042i | 0.382239 | + | 0.234968i | ||||
\(547\) | 0.828381 | + | 0.828381i | 0.0354190 | + | 0.0354190i | 0.724594 | − | 0.689175i | \(-0.242027\pi\) |
−0.689175 | + | 0.724594i | \(0.742027\pi\) | |||||||
\(548\) | −14.5005 | + | 14.5005i | −0.619429 | + | 0.619429i | ||||
\(549\) | 14.3107 | 0.610767 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 0.193331i | − | 0.00823616i | ||||||
\(552\) | −1.39408 | + | 1.39408i | −0.0593361 | + | 0.0593361i | ||||
\(553\) | −25.3832 | + | 6.05665i | −1.07941 | + | 0.257555i | ||||
\(554\) | − | 13.0853i | − | 0.555939i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 31.3983i | − | 1.33159i | ||||||
\(557\) | −14.7120 | − | 14.7120i | −0.623366 | − | 0.623366i | 0.323024 | − | 0.946391i | \(-0.395300\pi\) |
−0.946391 | + | 0.323024i | \(0.895300\pi\) | |||||||
\(558\) | 1.29458 | + | 1.29458i | 0.0548040 | + | 0.0548040i | ||||
\(559\) | −20.3295 | −0.859846 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.11589 | −0.342653 | ||||||||
\(562\) | −2.83726 | − | 2.83726i | −0.119683 | − | 0.119683i | ||||
\(563\) | −23.9693 | − | 23.9693i | −1.01019 | − | 1.01019i | −0.999948 | − | 0.0102391i | \(-0.996741\pi\) |
−0.0102391 | − | 0.999948i | \(-0.503259\pi\) | |||||||
\(564\) | − | 10.9985i | − | 0.463121i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.80115i | 0.0757080i | ||||||||
\(567\) | 0.614060 | + | 2.57351i | 0.0257881 | + | 0.108077i | ||||
\(568\) | 14.9990 | − | 14.9990i | 0.629346 | − | 0.629346i | ||||
\(569\) | − | 15.6660i | − | 0.656751i | −0.944547 | − | 0.328376i | \(-0.893499\pi\) | ||
0.944547 | − | 0.328376i | \(-0.106501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.9887 | 1.54793 | 0.773964 | − | 0.633229i | \(-0.218271\pi\) | ||||
0.773964 | + | 0.633229i | \(0.218271\pi\) | |||||||
\(572\) | 20.0114 | − | 20.0114i | 0.836717 | − | 0.836717i | ||||
\(573\) | −3.81379 | − | 3.81379i | −0.159323 | − | 0.159323i | ||||
\(574\) | 14.9460 | + | 9.18757i | 0.623836 | + | 0.383482i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.79807 | 0.116586 | ||||||||
\(577\) | 15.5587 | − | 15.5587i | 0.647717 | − | 0.647717i | −0.304724 | − | 0.952441i | \(-0.598564\pi\) |
0.952441 | + | 0.304724i | \(0.0985641\pi\) | |||||||
\(578\) | 6.78386 | − | 6.78386i | 0.282171 | − | 0.282171i | ||||
\(579\) | 6.79669 | 0.282461 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.20506 | − | 5.21389i | 0.132968 | − | 0.216309i | ||||
\(582\) | −5.23907 | − | 5.23907i | −0.217166 | − | 0.217166i | ||||
\(583\) | 23.6405 | − | 23.6405i | 0.979091 | − | 0.979091i | ||||
\(584\) | −35.2548 | −1.45885 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.4804i | 0.680798i | ||||||||
\(587\) | −15.7111 | + | 15.7111i | −0.648468 | + | 0.648468i | −0.952623 | − | 0.304155i | \(-0.901626\pi\) |
0.304155 | + | 0.952623i | \(0.401626\pi\) | |||||||
\(588\) | −3.09026 | + | 9.42158i | −0.127440 | + | 0.388539i | ||||
\(589\) | − | 0.167214i | − | 0.00688993i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 17.9237i | − | 0.737281i | ||||||
\(592\) | 5.19401 | + | 5.19401i | 0.213473 | + | 0.213473i | ||||
\(593\) | −1.85199 | − | 1.85199i | −0.0760523 | − | 0.0760523i | 0.668057 | − | 0.744110i | \(-0.267126\pi\) |
−0.744110 | + | 0.668057i | \(0.767126\pi\) | |||||||
\(594\) | −2.94197 | −0.120710 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.6487 | −0.640997 | ||||||||
\(597\) | 1.88876 | + | 1.88876i | 0.0773018 | + | 0.0773018i | ||||
\(598\) | 2.11676 | + | 2.11676i | 0.0865609 | + | 0.0865609i | ||||
\(599\) | 47.3151i | 1.93324i | 0.256208 | + | 0.966622i | \(0.417527\pi\) | ||||
−0.256208 | + | 0.966622i | \(0.582473\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.0819i | 0.452041i | 0.974123 | + | 0.226021i | \(0.0725717\pi\) | ||||
−0.974123 | + | 0.226021i | \(0.927428\pi\) | |||||||
\(602\) | 1.83822 | + | 7.70393i | 0.0749203 | + | 0.313989i | ||||
\(603\) | 0.416491 | − | 0.416491i | 0.0169608 | − | 0.0169608i | ||||
\(604\) | − | 26.0620i | − | 1.06045i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.6628 | 0.595637 | ||||||||
\(607\) | 7.54653 | − | 7.54653i | 0.306304 | − | 0.306304i | −0.537170 | − | 0.843474i | \(-0.680507\pi\) |
0.843474 | + | 0.537170i | \(0.180507\pi\) | |||||||
\(608\) | −0.289130 | − | 0.289130i | −0.0117258 | − | 0.0117258i | ||||
\(609\) | 6.24586 | + | 3.83943i | 0.253095 | + | 0.155581i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40.2795 | −1.62953 | ||||||||
\(612\) | 2.11067 | − | 2.11067i | 0.0853189 | − | 0.0853189i | ||||
\(613\) | 2.62487 | − | 2.62487i | 0.106017 | − | 0.106017i | −0.652108 | − | 0.758126i | \(-0.726115\pi\) |
0.758126 | + | 0.652108i | \(0.226115\pi\) | |||||||
\(614\) | 15.7935 | 0.637375 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.6549 | − | 13.9263i | −0.912793 | − | 0.561108i | ||||
\(617\) | −11.3212 | − | 11.3212i | −0.455774 | − | 0.455774i | 0.441491 | − | 0.897266i | \(-0.354450\pi\) |
−0.897266 | + | 0.441491i | \(0.854450\pi\) | |||||||
\(618\) | 1.78613 | − | 1.78613i | 0.0718488 | − | 0.0718488i | ||||
\(619\) | 9.06771 | 0.364462 | 0.182231 | − | 0.983256i | \(-0.441668\pi\) | ||||
0.182231 | + | 0.983256i | \(0.441668\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.755439i | 0.0303147i | ||||||||
\(622\) | −1.54599 | + | 1.54599i | −0.0619884 | + | 0.0619884i | ||||
\(623\) | −3.10292 | − | 13.0043i | −0.124316 | − | 0.521005i | ||||
\(624\) | 4.35458i | 0.174323i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.1744i | 0.406651i | ||||||||
\(627\) | 0.189999 | + | 0.189999i | 0.00758783 | + | 0.00758783i | ||||
\(628\) | 1.48723 | + | 1.48723i | 0.0593471 | + | 0.0593471i | ||||
\(629\) | −18.4398 | −0.735244 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.67260 | −0.385060 | −0.192530 | − | 0.981291i | \(-0.561669\pi\) | ||||
−0.192530 | + | 0.981291i | \(0.561669\pi\) | |||||||
\(632\) | 18.2017 | + | 18.2017i | 0.724023 | + | 0.724023i | ||||
\(633\) | −8.50216 | − | 8.50216i | −0.337930 | − | 0.337930i | ||||
\(634\) | 7.97587i | 0.316762i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12.2962i | 0.487577i | ||||||||
\(637\) | 34.5043 | + | 11.3173i | 1.36711 | + | 0.448409i | ||||
\(638\) | −5.76463 | + | 5.76463i | −0.228224 | + | 0.228224i | ||||
\(639\) | − | 8.12783i | − | 0.321532i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.5847 | −1.60300 | −0.801500 | − | 0.597995i | \(-0.795964\pi\) | ||||
−0.801500 | + | 0.597995i | \(0.795964\pi\) | |||||||
\(642\) | 4.88689 | − | 4.88689i | 0.192870 | − | 0.192870i | ||||
\(643\) | 3.89544 | + | 3.89544i | 0.153621 | + | 0.153621i | 0.779733 | − | 0.626112i | \(-0.215355\pi\) |
−0.626112 | + | 0.779733i | \(0.715355\pi\) | |||||||
\(644\) | −1.48263 | + | 2.41189i | −0.0584236 | + | 0.0950418i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.112305 | 0.00441857 | ||||||||
\(647\) | 16.8414 | − | 16.8414i | 0.662104 | − | 0.662104i | −0.293772 | − | 0.955876i | \(-0.594911\pi\) |
0.955876 | + | 0.293772i | \(0.0949106\pi\) | |||||||
\(648\) | 1.84539 | − | 1.84539i | 0.0724939 | − | 0.0724939i | ||||
\(649\) | −26.8609 | −1.05438 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.40212 | + | 3.32077i | 0.211726 | + | 0.130151i | ||||
\(652\) | 7.79833 | + | 7.79833i | 0.305406 | + | 0.305406i | ||||
\(653\) | 22.9951 | − | 22.9951i | 0.899867 | − | 0.899867i | −0.0955569 | − | 0.995424i | \(-0.530463\pi\) |
0.995424 | + | 0.0955569i | \(0.0304632\pi\) | |||||||
\(654\) | −1.65041 | −0.0645363 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.28688i | 0.284505i | ||||||||
\(657\) | −9.55210 | + | 9.55210i | −0.372663 | + | 0.372663i | ||||
\(658\) | 3.64213 | + | 15.2640i | 0.141985 | + | 0.595054i | ||||
\(659\) | 32.7543i | 1.27593i | 0.770067 | + | 0.637963i | \(0.220223\pi\) | ||||
−0.770067 | + | 0.637963i | \(0.779777\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 32.5174i | − | 1.26478i | −0.774650 | − | 0.632391i | \(-0.782074\pi\) | ||
0.774650 | − | 0.632391i | \(-0.217926\pi\) | |||||||
\(662\) | −12.7582 | − | 12.7582i | −0.495861 | − | 0.495861i | ||||
\(663\) | −7.72984 | − | 7.72984i | −0.300202 | − | 0.300202i | ||||
\(664\) | −6.03701 | −0.234281 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.68434 | −0.259013 | ||||||||
\(667\) | 1.48024 | + | 1.48024i | 0.0573152 | + | 0.0573152i | ||||
\(668\) | −2.67671 | − | 2.67671i | −0.103565 | − | 0.103565i | ||||
\(669\) | − | 16.5357i | − | 0.639307i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 55.1158i | 2.12772i | ||||||||
\(672\) | 15.0828 | − | 3.59887i | 0.581830 | − | 0.138829i | ||||
\(673\) | 16.7534 | − | 16.7534i | 0.645796 | − | 0.645796i | −0.306179 | − | 0.951974i | \(-0.599050\pi\) |
0.951974 | + | 0.306179i | \(0.0990504\pi\) | |||||||
\(674\) | − | 5.33455i | − | 0.205479i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.7046 | 0.757868 | ||||||||
\(677\) | −6.85568 | + | 6.85568i | −0.263485 | + | 0.263485i | −0.826468 | − | 0.562983i | \(-0.809654\pi\) |
0.562983 | + | 0.826468i | \(0.309654\pi\) | |||||||
\(678\) | −3.16110 | − | 3.16110i | −0.121401 | − | 0.121401i | ||||
\(679\) | −21.8620 | − | 13.4389i | −0.838985 | − | 0.515737i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.56296 | 0.0598929 | ||||||||
\(682\) | −4.98590 | + | 4.98590i | −0.190920 | + | 0.190920i | ||||
\(683\) | −23.2345 | + | 23.2345i | −0.889042 | + | 0.889042i | −0.994431 | − | 0.105389i | \(-0.966391\pi\) |
0.105389 | + | 0.994431i | \(0.466391\pi\) | |||||||
\(684\) | −0.0988248 | −0.00377866 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.16881 | − | 14.0988i | 0.0446255 | − | 0.538297i | ||||
\(687\) | −5.53883 | − | 5.53883i | −0.211319 | − | 0.211319i | ||||
\(688\) | −2.32612 | + | 2.32612i | −0.0886823 | + | 0.0886823i | ||||
\(689\) | 45.0321 | 1.71559 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 42.4714i | − | 1.61569i | −0.589395 | − | 0.807845i | \(-0.700634\pi\) | ||
0.589395 | − | 0.807845i | \(-0.299366\pi\) | |||||||
\(692\) | −6.95144 | + | 6.95144i | −0.264254 | + | 0.264254i | ||||
\(693\) | −9.91150 | + | 2.36497i | −0.376507 | + | 0.0898376i | ||||
\(694\) | 6.30557i | 0.239356i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 7.23190i | − | 0.274124i | ||||||
\(697\) | −12.9350 | − | 12.9350i | −0.489947 | − | 0.489947i | ||||
\(698\) | −9.13494 | − | 9.13494i | −0.345763 | − | 0.345763i | ||||
\(699\) | −1.42549 | −0.0539169 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.0793 | 0.645077 | 0.322539 | − | 0.946556i | \(-0.395464\pi\) | ||||
0.322539 | + | 0.946556i | \(0.395464\pi\) | |||||||
\(702\) | −2.80203 | − | 2.80203i | −0.105756 | − | 0.105756i | ||||
\(703\) | 0.431690 | + | 0.431690i | 0.0162815 | + | 0.0162815i | ||||
\(704\) | 10.7764i | 0.406150i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.0198i | 0.452370i | ||||||||
\(707\) | 49.3991 | − | 11.7870i | 1.85785 | − | 0.443297i | ||||
\(708\) | 6.98563 | − | 6.98563i | 0.262536 | − | 0.262536i | ||||
\(709\) | 32.6742i | 1.22710i | 0.789654 | + | 0.613552i | \(0.210260\pi\) | ||||
−0.789654 | + | 0.613552i | \(0.789740\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.86329 | 0.369902 | ||||||||
\(712\) | −9.32502 | + | 9.32502i | −0.349470 | + | 0.349470i | ||||
\(713\) | 1.28028 | + | 1.28028i | 0.0479469 | + | 0.0479469i | ||||
\(714\) | −2.23030 | + | 3.62819i | −0.0834670 | + | 0.135782i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26.3264 | 0.983865 | ||||||||
\(717\) | 14.3405 | − | 14.3405i | 0.535554 | − | 0.535554i | ||||
\(718\) | −4.40143 | + | 4.40143i | −0.164260 | + | 0.164260i | ||||
\(719\) | 19.3248 | 0.720693 | 0.360346 | − | 0.932819i | \(-0.382659\pi\) | ||||
0.360346 | + | 0.932819i | \(0.382659\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.58166 | − | 7.45331i | 0.170630 | − | 0.277576i | ||||
\(722\) | 10.2601 | + | 10.2601i | 0.381841 | + | 0.381841i | ||||
\(723\) | 1.95864 | − | 1.95864i | 0.0728426 | − | 0.0728426i | ||||
\(724\) | −12.0193 | −0.446695 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 2.92793i | − | 0.108666i | ||||||
\(727\) | 2.71795 | − | 2.71795i | 0.100803 | − | 0.100803i | −0.654907 | − | 0.755710i | \(-0.727292\pi\) |
0.755710 | + | 0.654907i | \(0.227292\pi\) | |||||||
\(728\) | −8.31339 | − | 34.8412i | −0.308115 | − | 1.29130i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 8.25820i | − | 0.305440i | ||||||
\(732\) | −14.3338 | − | 14.3338i | −0.529791 | − | 0.529791i | ||||
\(733\) | −2.38437 | − | 2.38437i | −0.0880686 | − | 0.0880686i | 0.661700 | − | 0.749769i | \(-0.269835\pi\) |
−0.749769 | + | 0.661700i | \(0.769835\pi\) | |||||||
\(734\) | −15.9321 | −0.588064 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.42747 | 0.163199 | ||||||||
\(737\) | 1.60406 | + | 1.60406i | 0.0590862 | + | 0.0590862i | ||||
\(738\) | −4.68886 | − | 4.68886i | −0.172599 | − | 0.172599i | ||||
\(739\) | 4.95679i | 0.182339i | 0.995835 | + | 0.0911693i | \(0.0290605\pi\) | ||||
−0.995835 | + | 0.0911693i | \(0.970940\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.361923i | 0.0132956i | ||||||||
\(742\) | −4.07186 | − | 17.0650i | −0.149483 | − | 0.626477i | ||||
\(743\) | −15.6556 | + | 15.6556i | −0.574347 | + | 0.574347i | −0.933340 | − | 0.358993i | \(-0.883120\pi\) |
0.358993 | + | 0.933340i | \(0.383120\pi\) | |||||||
\(744\) | − | 6.25496i | − | 0.229318i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.61461 | 0.0591150 | ||||||||
\(747\) | −1.63570 | + | 1.63570i | −0.0598470 | + | 0.0598470i | ||||
\(748\) | 8.12896 | + | 8.12896i | 0.297224 | + | 0.297224i | ||||
\(749\) | 12.5355 | − | 20.3924i | 0.458037 | − | 0.745120i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.1909 | −0.408361 | −0.204181 | − | 0.978933i | \(-0.565453\pi\) | ||||
−0.204181 | + | 0.978933i | \(0.565453\pi\) | |||||||
\(752\) | −4.60881 | + | 4.60881i | −0.168066 | + | 0.168066i | ||||
\(753\) | −4.31322 | + | 4.31322i | −0.157183 | + | 0.157183i | ||||
\(754\) | −10.9808 | −0.399899 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.96260 | − | 3.19270i | 0.0713791 | − | 0.116117i | ||||
\(757\) | −29.4977 | − | 29.4977i | −1.07211 | − | 1.07211i | −0.997189 | − | 0.0749214i | \(-0.976129\pi\) |
−0.0749214 | − | 0.997189i | \(-0.523871\pi\) | |||||||
\(758\) | −10.1080 | + | 10.1080i | −0.367138 | + | 0.367138i | ||||
\(759\) | −2.90947 | −0.105607 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 28.1175i | − | 1.01926i | −0.860395 | − | 0.509629i | \(-0.829783\pi\) | ||
0.860395 | − | 0.509629i | \(-0.170217\pi\) | |||||||
\(762\) | 3.69181 | − | 3.69181i | 0.133740 | − | 0.133740i | ||||
\(763\) | −5.56025 | + | 1.32672i | −0.201294 | + | 0.0480305i | ||||
\(764\) | 7.63986i | 0.276400i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 22.6162i | − | 0.817157i | ||||||
\(767\) | −25.5832 | − | 25.5832i | −0.923757 | − | 0.923757i | ||||
\(768\) | −9.13390 | − | 9.13390i | −0.329591 | − | 0.329591i | ||||
\(769\) | −6.61248 | −0.238452 | −0.119226 | − | 0.992867i | \(-0.538041\pi\) | ||||
−0.119226 | + | 0.992867i | \(0.538041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.85449 | −0.102802 | ||||||||
\(772\) | −6.80764 | − | 6.80764i | −0.245012 | − | 0.245012i | ||||
\(773\) | 31.7247 | + | 31.7247i | 1.14106 | + | 1.14106i | 0.988257 | + | 0.152800i | \(0.0488290\pi\) |
0.152800 | + | 0.988257i | \(0.451171\pi\) | |||||||
\(774\) | − | 2.99355i | − | 0.107601i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 25.3133i | 0.908695i | ||||||||
\(777\) | −22.5196 | + | 5.37335i | −0.807885 | + | 0.192768i | ||||
\(778\) | −13.8607 | + | 13.8607i | −0.496929 | + | 0.496929i | ||||
\(779\) | 0.605634i | 0.0216991i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.3032 | 1.12012 | ||||||||
\(782\) | −0.859866 | + | 0.859866i | −0.0307487 | + | 0.0307487i | ||||
\(783\) | −1.95945 | − | 1.95945i | −0.0700249 | − | 0.0700249i | ||||
\(784\) | 5.24295 | − | 2.65307i | 0.187248 | − | 0.0947525i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.494610 | −0.0176422 | ||||||||
\(787\) | 22.4472 | − | 22.4472i | 0.800155 | − | 0.800155i | −0.182964 | − | 0.983120i | \(-0.558569\pi\) |
0.983120 | + | 0.182964i | \(0.0585693\pi\) | |||||||
\(788\) | −17.9525 | + | 17.9525i | −0.639532 | + | 0.639532i | ||||
\(789\) | −23.7144 | −0.844254 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.1909 | − | 8.10864i | −0.469014 | − | 0.288310i | ||||
\(792\) | 7.10728 | + | 7.10728i | 0.252546 | + | 0.252546i | ||||
\(793\) | −52.4941 | + | 52.4941i | −1.86412 | + | 1.86412i | ||||
\(794\) | −7.27665 | −0.258239 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 3.78360i | − | 0.134106i | ||||||
\(797\) | 5.14677 | − | 5.14677i | 0.182308 | − | 0.182308i | −0.610053 | − | 0.792361i | \(-0.708852\pi\) |
0.792361 | + | 0.610053i | \(0.208852\pi\) | |||||||
\(798\) | 0.137152 | − | 0.0327255i | 0.00485512 | − | 0.00115847i | ||||
\(799\) | − | 16.3622i | − | 0.578854i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.05313i | 0.178544i | ||||||||
\(802\) | −7.96725 | − | 7.96725i | −0.281333 | − | 0.281333i | ||||
\(803\) | −36.7886 | − | 36.7886i | −1.29824 | − | 1.29824i | ||||
\(804\) | −0.834323 | −0.0294243 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.49747 | −0.334534 | ||||||||
\(807\) | −17.4904 | − | 17.4904i | −0.615691 | − | 0.615691i | ||||
\(808\) | −35.4228 | − | 35.4228i | −1.24617 | − | 1.24617i | ||||
\(809\) | 22.5215i | 0.791815i | 0.918290 | + | 0.395907i | \(0.129570\pi\) | ||||
−0.918290 | + | 0.395907i | \(0.870430\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.9145i | 1.22602i | 0.790077 | + | 0.613008i | \(0.210040\pi\) | ||||
−0.790077 | + | 0.613008i | \(0.789960\pi\) | |||||||
\(812\) | −2.41031 | − | 10.1015i | −0.0845852 | − | 0.354494i | ||||
\(813\) | 2.92367 | − | 2.92367i | 0.102538 | − | 0.102538i | ||||
\(814\) | − | 25.7438i | − | 0.902320i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.76891 | −0.0619241 | ||||||||
\(817\) | −0.193331 | + | 0.193331i | −0.00676378 | + | 0.00676378i | ||||
\(818\) | 5.70414 | + | 5.70414i | 0.199441 | + | 0.199441i | ||||
\(819\) | −11.6925 | − | 7.18757i | −0.408569 | − | 0.251154i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.52640 | 0.297573 | 0.148787 | − | 0.988869i | \(-0.452463\pi\) | ||||
0.148787 | + | 0.988869i | \(0.452463\pi\) | |||||||
\(822\) | −7.81974 | + | 7.81974i | −0.272745 | + | 0.272745i | ||||
\(823\) | 33.9044 | − | 33.9044i | 1.18183 | − | 1.18183i | 0.202564 | − | 0.979269i | \(-0.435073\pi\) |
0.979269 | − | 0.202564i | \(-0.0649273\pi\) | |||||||
\(824\) | −8.62997 | −0.300639 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.38158 | + | 12.0081i | −0.256838 | + | 0.417816i | ||||
\(827\) | 37.8440 | + | 37.8440i | 1.31597 | + | 1.31597i | 0.916940 | + | 0.399025i | \(0.130651\pi\) |
0.399025 | + | 0.916940i | \(0.369349\pi\) | |||||||
\(828\) | 0.756656 | − | 0.756656i | 0.0262956 | − | 0.0262956i | ||||
\(829\) | 33.7140 | 1.17094 | 0.585469 | − | 0.810695i | \(-0.300911\pi\) | ||||
0.585469 | + | 0.810695i | \(0.300911\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.1300i | 0.594234i | ||||||||
\(832\) | −10.2638 | + | 10.2638i | −0.355832 | + | 0.355832i | ||||
\(833\) | −4.59730 | + | 14.0163i | −0.159287 | + | 0.485635i | ||||
\(834\) | − | 16.9323i | − | 0.586319i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 0.380610i | − | 0.0131637i | ||||||
\(837\) | −1.69475 | − | 1.69475i | −0.0585791 | − | 0.0585791i | ||||
\(838\) | 8.39773 | + | 8.39773i | 0.290095 | + | 0.290095i | ||||
\(839\) | 16.0665 | 0.554679 | 0.277339 | − | 0.960772i | \(-0.410547\pi\) | ||||
0.277339 | + | 0.960772i | \(0.410547\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.3211 | 0.735212 | ||||||||
\(842\) | −1.78185 | − | 1.78185i | −0.0614068 | − | 0.0614068i | ||||
\(843\) | 3.71429 | + | 3.71429i | 0.127927 | + | 0.127927i | ||||
\(844\) | 17.0317i | 0.586255i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 5.93123i | − | 0.203920i | ||||||
\(847\) | −2.35368 | − | 9.86420i | −0.0808734 | − | 0.338938i | ||||
\(848\) | 5.15260 | − | 5.15260i | 0.176941 | − | 0.176941i | ||||
\(849\) | − | 2.35790i | − | 0.0809231i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.61050 | −0.226605 | ||||||||
\(852\) | −8.14091 | + | 8.14091i | −0.278903 | + | 0.278903i | ||||
\(853\) | 5.14393 | + | 5.14393i | 0.176125 | + | 0.176125i | 0.789664 | − | 0.613539i | \(-0.210255\pi\) |
−0.613539 | + | 0.789664i | \(0.710255\pi\) | |||||||
\(854\) | 24.6394 | + | 15.1462i | 0.843142 | + | 0.518292i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −23.6117 | −0.807032 | ||||||||
\(857\) | −5.65076 | + | 5.65076i | −0.193026 | + | 0.193026i | −0.797002 | − | 0.603976i | \(-0.793582\pi\) |
0.603976 | + | 0.797002i | \(0.293582\pi\) | |||||||
\(858\) | 10.7916 | − | 10.7916i | 0.368420 | − | 0.368420i | ||||
\(859\) | −42.0801 | −1.43575 | −0.717877 | − | 0.696170i | \(-0.754886\pi\) | ||||
−0.717877 | + | 0.696170i | \(0.754886\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.5660 | − | 12.0275i | −0.666808 | − | 0.409897i | ||||
\(862\) | 7.61119 | + | 7.61119i | 0.259238 | + | 0.259238i | ||||
\(863\) | 11.9777 | − | 11.9777i | 0.407724 | − | 0.407724i | −0.473220 | − | 0.880944i | \(-0.656908\pi\) |
0.880944 | + | 0.473220i | \(0.156908\pi\) | |||||||
\(864\) | −5.86078 | −0.199388 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.86511i | 0.0633791i | ||||||||
\(867\) | −8.88082 | + | 8.88082i | −0.301608 | + | 0.301608i | ||||
\(868\) | −2.08471 | − | 8.73694i | −0.0707595 | − | 0.296551i | ||||
\(869\) | 37.9871i | 1.28862i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.05551i | 0.103532i | ||||||||
\(872\) | 3.98711 | + | 3.98711i | 0.135021 | + | 0.135021i | ||||
\(873\) | 6.85851 | + | 6.85851i | 0.232125 | + | 0.232125i | ||||
\(874\) | 0.0402602 | 0.00136182 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.1350 | 0.646510 | ||||||||
\(877\) | 11.5817 | + | 11.5817i | 0.391085 | + | 0.391085i | 0.875074 | − | 0.483989i | \(-0.160813\pi\) |
−0.483989 | + | 0.875074i | \(0.660813\pi\) | |||||||
\(878\) | −14.6471 | − | 14.6471i | −0.494317 | − | 0.494317i | ||||
\(879\) | − | 21.5746i | − | 0.727694i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 8.72058i | − | 0.293804i | −0.989151 | − | 0.146902i | \(-0.953070\pi\) | ||
0.989151 | − | 0.146902i | \(-0.0469301\pi\) | |||||||
\(882\) | −1.66650 | + | 5.08082i | −0.0561139 | + | 0.171080i | ||||
\(883\) | −17.0876 | + | 17.0876i | −0.575044 | + | 0.575044i | −0.933534 | − | 0.358490i | \(-0.883292\pi\) |
0.358490 | + | 0.933534i | \(0.383292\pi\) | |||||||
\(884\) | 15.4846i | 0.520803i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.0891 | −0.876480 | ||||||||
\(887\) | 26.4024 | − | 26.4024i | 0.886507 | − | 0.886507i | −0.107679 | − | 0.994186i | \(-0.534342\pi\) |
0.994186 | + | 0.107679i | \(0.0343419\pi\) | |||||||
\(888\) | 16.1482 | + | 16.1482i | 0.541898 | + | 0.541898i | ||||
\(889\) | 9.46996 | − | 15.4054i | 0.317612 | − | 0.516682i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.85136 | 0.129025 | ||||||||
\(892\) | −16.5623 | + | 16.5623i | −0.554548 | + | 0.554548i | ||||
\(893\) | −0.383052 | + | 0.383052i | −0.0128184 | + | 0.0128184i | ||||
\(894\) | −8.43897 | −0.282241 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −21.6023 | − | 13.2792i | −0.721681 | − | 0.443628i | ||||
\(897\) | −2.77107 | − | 2.77107i | −0.0925235 | − | 0.0925235i | ||||
\(898\) | 5.29484 | − | 5.29484i | 0.176691 | − | 0.176691i | ||||
\(899\) | −6.64154 | −0.221508 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.2928i | 0.609422i | ||||||||
\(902\) | 18.0585 | − | 18.0585i | 0.601282 | − | 0.601282i | ||||
\(903\) | −2.40643 | − | 10.0853i | −0.0800811 | − | 0.335617i | ||||
\(904\) | 15.2733i | 0.507984i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 14.0546i | − | 0.466932i | ||||||
\(907\) | 23.6454 | + | 23.6454i | 0.785133 | + | 0.785133i | 0.980692 | − | 0.195559i | \(-0.0626521\pi\) |
−0.195559 | + | 0.980692i | \(0.562652\pi\) | |||||||
\(908\) | −1.56548 | − | 1.56548i | −0.0519523 | − | 0.0519523i | ||||
\(909\) | −19.1953 | −0.636667 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.8226 | −0.590490 | −0.295245 | − | 0.955422i | \(-0.595401\pi\) | ||||
−0.295245 | + | 0.955422i | \(0.595401\pi\) | |||||||
\(912\) | 0.0414114 | + | 0.0414114i | 0.00137127 | + | 0.00137127i | ||||
\(913\) | −6.29966 | − | 6.29966i | −0.208488 | − | 0.208488i | ||||
\(914\) | 0.594234i | 0.0196555i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.0955i | 0.366605i | ||||||||
\(917\) | −1.66634 | + | 0.397603i | −0.0550274 | + | 0.0131300i | ||||
\(918\) | 1.13823 | − | 1.13823i | 0.0375673 | − | 0.0375673i | ||||
\(919\) | 21.5752i | 0.711701i | 0.934543 | + | 0.355850i | \(0.115809\pi\) | ||||
−0.934543 | + | 0.355850i | \(0.884191\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.6755 | −0.681280 | ||||||||
\(922\) | −0.449284 | + | 0.449284i | −0.0147964 | + | 0.0147964i | ||||
\(923\) | 29.8142 | + | 29.8142i | 0.981346 | + | 0.981346i | ||||
\(924\) | 12.2962 | + | 7.55868i | 0.404516 | + | 0.248662i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.88908 | 0.193527 | ||||||||
\(927\) | −2.33825 | + | 2.33825i | −0.0767980 | + | 0.0767980i | ||||
\(928\) | −11.4839 | + | 11.4839i | −0.376977 | + | 0.376977i | ||||
\(929\) | −38.3070 | −1.25681 | −0.628405 | − | 0.777886i | \(-0.716292\pi\) | ||||
−0.628405 | + | 0.777886i | \(0.716292\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.435757 | − | 0.220505i | 0.0142814 | − | 0.00722675i | ||||
\(932\) | 1.42778 | + | 1.42778i | 0.0467686 | + | 0.0467686i | ||||
\(933\) | 2.02387 | − | 2.02387i | 0.0662584 | − | 0.0662584i | ||||
\(934\) | 25.1520 | 0.823000 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13.5384i | 0.442517i | ||||||||
\(937\) | 13.2317 | − | 13.2317i | 0.432262 | − | 0.432262i | −0.457135 | − | 0.889397i | \(-0.651125\pi\) |
0.889397 | + | 0.457135i | \(0.151125\pi\) | |||||||
\(938\) | 1.15790 | − | 0.276283i | 0.0378066 | − | 0.00902097i | ||||
\(939\) | − | 13.3194i | − | 0.434662i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.58095i | 0.0841366i | 0.999115 | + | 0.0420683i | \(0.0133947\pi\) | ||||
−0.999115 | + | 0.0420683i | \(0.986605\pi\) | |||||||
\(942\) | 0.802028 | + | 0.802028i | 0.0261315 | + | 0.0261315i | ||||
\(943\) | −4.63706 | − | 4.63706i | −0.151004 | − | 0.151004i | ||||
\(944\) | −5.85450 | −0.190548 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.5293 | 0.374848 | ||||||||
\(947\) | −4.94205 | − | 4.94205i | −0.160595 | − | 0.160595i | 0.622235 | − | 0.782830i | \(-0.286225\pi\) |
−0.782830 | + | 0.622235i | \(0.786225\pi\) | |||||||
\(948\) | −9.87918 | − | 9.87918i | −0.320861 | − | 0.320861i | ||||
\(949\) | − | 70.0773i | − | 2.27481i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 10.4413i | − | 0.338582i | ||||||
\(952\) | 14.1531 | − | 3.37705i | 0.458704 | − | 0.109451i | ||||
\(953\) | 16.3558 | − | 16.3558i | 0.529818 | − | 0.529818i | −0.390700 | − | 0.920518i | \(-0.627767\pi\) |
0.920518 | + | 0.390700i | \(0.127767\pi\) | |||||||
\(954\) | 6.63105i | 0.214688i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −28.7271 | −0.929101 | ||||||||
\(957\) | 7.54653 | − | 7.54653i | 0.243945 | − | 0.243945i | ||||
\(958\) | −21.8390 | − | 21.8390i | −0.705587 | − | 0.705587i | ||||
\(959\) | −20.0586 | + | 32.6308i | −0.647727 | + | 1.05370i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.2557 | 0.814698 | ||||||||
\(962\) | 24.5193 | − | 24.5193i | 0.790533 | − | 0.790533i | ||||
\(963\) | −6.39747 | + | 6.39747i | −0.206156 | + | 0.206156i | ||||
\(964\) | −3.92359 | −0.126370 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.799543 | + | 1.30067i | −0.0257249 | + | 0.0418484i | ||||
\(967\) | −8.66781 | − | 8.66781i | −0.278738 | − | 0.278738i | 0.553867 | − | 0.832605i | \(-0.313152\pi\) |
−0.832605 | + | 0.553867i | \(0.813152\pi\) | |||||||
\(968\) | −7.07336 | + | 7.07336i | −0.227346 | + | 0.227346i | ||||
\(969\) | −0.147019 | −0.00472294 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.1861i | 0.423163i | 0.977360 | + | 0.211582i | \(0.0678614\pi\) | ||||
−0.977360 | + | 0.211582i | \(0.932139\pi\) | |||||||
\(972\) | −1.00161 | + | 1.00161i | −0.0321267 | + | 0.0321267i | ||||
\(973\) | −13.6114 | − | 57.0451i | −0.436362 | − | 1.82878i | ||||
\(974\) | − | 7.80931i | − | 0.250226i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.0128i | 0.384521i | ||||||||
\(977\) | 24.4925 | + | 24.4925i | 0.783586 | + | 0.783586i | 0.980434 | − | 0.196848i | \(-0.0630705\pi\) |
−0.196848 | + | 0.980434i | \(0.563071\pi\) | |||||||
\(978\) | 4.20545 | + | 4.20545i | 0.134475 | + | 0.134475i | ||||
\(979\) | −19.4614 | −0.621990 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.16057 | 0.0689818 | ||||||||
\(982\) | −10.8590 | − | 10.8590i | −0.346525 | − | 0.346525i | ||||
\(983\) | 15.7362 | + | 15.7362i | 0.501907 | + | 0.501907i | 0.912030 | − | 0.410123i | \(-0.134514\pi\) |
−0.410123 | + | 0.912030i | \(0.634514\pi\) | |||||||
\(984\) | 22.6549i | 0.722212i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 4.46061i | − | 0.142055i | ||||||
\(987\) | −4.76795 | − | 19.9823i | −0.151765 | − | 0.636044i | ||||
\(988\) | 0.362505 | − | 0.362505i | 0.0115328 | − | 0.0115328i | ||||
\(989\) | − | 2.96048i | − | 0.0941379i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.1031 | −0.956257 | −0.478128 | − | 0.878290i | \(-0.658685\pi\) | ||||
−0.478128 | + | 0.878290i | \(0.658685\pi\) | |||||||
\(992\) | −9.93256 | + | 9.93256i | −0.315359 | + | 0.315359i | ||||
\(993\) | 16.7019 | + | 16.7019i | 0.530018 | + | 0.530018i | ||||
\(994\) | 8.60234 | − | 13.9940i | 0.272850 | − | 0.443863i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.27666 | 0.103825 | ||||||||
\(997\) | −22.8721 | + | 22.8721i | −0.724367 | + | 0.724367i | −0.969491 | − | 0.245125i | \(-0.921171\pi\) |
0.245125 | + | 0.969491i | \(0.421171\pi\) | |||||||
\(998\) | −8.33045 | + | 8.33045i | −0.263696 | + | 0.263696i | ||||
\(999\) | 8.75054 | 0.276855 |
(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 | 525.2.m.b.307.4 | 16 | ||
5.2 | odd | 4 | 105.2.m.a.13.6 | yes | 16 | ||
5.3 | odd | 4 | inner | 525.2.m.b.118.3 | 16 | ||
5.4 | even | 2 | 105.2.m.a.97.5 | yes | 16 | ||
7.6 | odd | 2 | inner | 525.2.m.b.307.3 | 16 | ||
15.2 | even | 4 | 315.2.p.e.118.4 | 16 | |||
15.14 | odd | 2 | 315.2.p.e.307.3 | 16 | |||
20.7 | even | 4 | 1680.2.cz.d.433.2 | 16 | |||
20.19 | odd | 2 | 1680.2.cz.d.97.7 | 16 | |||
35.2 | odd | 12 | 735.2.v.a.178.4 | 32 | |||
35.4 | even | 6 | 735.2.v.a.607.3 | 32 | |||
35.9 | even | 6 | 735.2.v.a.472.6 | 32 | |||
35.12 | even | 12 | 735.2.v.a.178.3 | 32 | |||
35.13 | even | 4 | inner | 525.2.m.b.118.4 | 16 | ||
35.17 | even | 12 | 735.2.v.a.313.6 | 32 | |||
35.19 | odd | 6 | 735.2.v.a.472.5 | 32 | |||
35.24 | odd | 6 | 735.2.v.a.607.4 | 32 | |||
35.27 | even | 4 | 105.2.m.a.13.5 | ✓ | 16 | ||
35.32 | odd | 12 | 735.2.v.a.313.5 | 32 | |||
35.34 | odd | 2 | 105.2.m.a.97.6 | yes | 16 | ||
105.62 | odd | 4 | 315.2.p.e.118.3 | 16 | |||
105.104 | even | 2 | 315.2.p.e.307.4 | 16 | |||
140.27 | odd | 4 | 1680.2.cz.d.433.7 | 16 | |||
140.139 | even | 2 | 1680.2.cz.d.97.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.5 | ✓ | 16 | 35.27 | even | 4 | ||
105.2.m.a.13.6 | yes | 16 | 5.2 | odd | 4 | ||
105.2.m.a.97.5 | yes | 16 | 5.4 | even | 2 | ||
105.2.m.a.97.6 | yes | 16 | 35.34 | odd | 2 | ||
315.2.p.e.118.3 | 16 | 105.62 | odd | 4 | |||
315.2.p.e.118.4 | 16 | 15.2 | even | 4 | |||
315.2.p.e.307.3 | 16 | 15.14 | odd | 2 | |||
315.2.p.e.307.4 | 16 | 105.104 | even | 2 | |||
525.2.m.b.118.3 | 16 | 5.3 | odd | 4 | inner | ||
525.2.m.b.118.4 | 16 | 35.13 | even | 4 | inner | ||
525.2.m.b.307.3 | 16 | 7.6 | odd | 2 | inner | ||
525.2.m.b.307.4 | 16 | 1.1 | even | 1 | trivial | ||
735.2.v.a.178.3 | 32 | 35.12 | even | 12 | |||
735.2.v.a.178.4 | 32 | 35.2 | odd | 12 | |||
735.2.v.a.313.5 | 32 | 35.32 | odd | 12 | |||
735.2.v.a.313.6 | 32 | 35.17 | even | 12 | |||
735.2.v.a.472.5 | 32 | 35.19 | odd | 6 | |||
735.2.v.a.472.6 | 32 | 35.9 | even | 6 | |||
735.2.v.a.607.3 | 32 | 35.4 | even | 6 | |||
735.2.v.a.607.4 | 32 | 35.24 | odd | 6 | |||
1680.2.cz.d.97.2 | 16 | 140.139 | even | 2 | |||
1680.2.cz.d.97.7 | 16 | 20.19 | odd | 2 | |||
1680.2.cz.d.433.2 | 16 | 20.7 | even | 4 | |||
1680.2.cz.d.433.7 | 16 | 140.27 | odd | 4 |