Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,2,Mod(13,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, 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("105.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(0.838429221223\) |
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: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.5 | ||
Root | \(-1.36166 - 0.381939i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.13 |
Dual form | 105.2.m.a.97.5 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 | \(-0.662953\pi\) |
0.871800 | + | 0.489861i | \(0.162953\pi\) | |||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 1.41649i | 0.708245i | ||||||||
\(5\) | 1.03649 | + | 1.98133i | 0.463534 | + | 0.886079i | ||||
\(6\) | 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 | ||||||
\(10\) | 1.63006 | + | 0.510348i | 0.515470 | + | 0.161386i | ||||
\(11\) | −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 | 0.0175187 | − | 0.999847i | \(-0.494423\pi\) |
0.999847 | − | 0.0175187i | \(-0.00557667\pi\) | |||||||
\(14\) | −1.05838 | − | 1.72174i | −0.282864 | − | 0.460155i | ||||
\(15\) | −2.13393 | − | 0.668102i | −0.550977 | − | 0.172503i | ||||
\(16\) | −0.839427 | −0.209857 | ||||||||
\(17\) | −1.49007 | − | 1.49007i | −0.361395 | − | 0.361395i | 0.502931 | − | 0.864326i | \(-0.332255\pi\) |
−0.864326 | + | 0.502931i | \(0.832255\pi\) | |||||||
\(18\) | −0.540143 | − | 0.540143i | −0.127313 | − | 0.127313i | ||||
\(19\) | −0.0697674 | −0.0160057 | −0.00800286 | − | 0.999968i | \(-0.502547\pi\) | ||||
−0.00800286 | + | 0.999968i | \(0.502547\pi\) | |||||||
\(20\) | −2.80654 | + | 1.46818i | −0.627561 | + | 0.328296i | ||||
\(21\) | 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 | \(-0.275096\pi\) |
−0.760602 | + | 0.649218i | \(0.775096\pi\) | |||||||
\(24\) | −2.60978 | −0.532719 | ||||||||
\(25\) | −2.85136 | + | 4.10728i | −0.570272 | + | 0.821456i | ||||
\(26\) | − | 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 | \(-0.917171\pi\) | ||
0.966335 | − | 0.257288i | \(-0.0828288\pi\) | |||||||
\(30\) | −1.51350 | + | 0.791755i | −0.276325 | + | 0.144554i | ||||
\(31\) | − | 2.39674i | − | 0.430467i | −0.976563 | − | 0.215233i | \(-0.930949\pi\) | ||
0.976563 | − | 0.215233i | \(-0.0690512\pi\) | |||||||
\(32\) | −4.14420 | + | 4.14420i | −0.732598 | + | 0.732598i | ||||
\(33\) | 2.72332 | − | 2.72332i | 0.474070 | − | 0.474070i | ||||
\(34\) | −1.60970 | −0.276062 | ||||||||
\(35\) | 5.73544 | − | 1.45077i | 0.969466 | − | 0.245224i | ||||
\(36\) | 1.41649 | 0.236082 | ||||||||
\(37\) | 6.18757 | − | 6.18757i | 1.01723 | − | 1.01723i | 0.0173805 | − | 0.999849i | \(-0.494467\pi\) |
0.999849 | − | 0.0173805i | \(-0.00553267\pi\) | |||||||
\(38\) | −0.0376844 | + | 0.0376844i | −0.00611321 | + | 0.00611321i | ||||
\(39\) | 5.18757i | 0.830675i | ||||||||
\(40\) | −1.74360 | + | 5.56908i | −0.275687 | + | 0.880549i | ||||
\(41\) | 8.68077i | 1.35571i | 0.735196 | + | 0.677854i | \(0.237090\pi\) | ||||
−0.735196 | + | 0.677854i | \(0.762910\pi\) | |||||||
\(42\) | 1.96584 | + | 0.469067i | 0.303336 | + | 0.0723786i | ||||
\(43\) | −2.77107 | − | 2.77107i | −0.422585 | − | 0.422585i | 0.463508 | − | 0.886093i | \(-0.346591\pi\) |
−0.886093 | + | 0.463508i | \(0.846591\pi\) | |||||||
\(44\) | − | 5.45542i | − | 0.822435i | ||||||
\(45\) | 1.98133 | − | 1.03649i | 0.295360 | − | 0.154511i | ||||
\(46\) | −0.577063 | −0.0850834 | ||||||||
\(47\) | −5.49042 | − | 5.49042i | −0.800860 | − | 0.800860i | 0.182370 | − | 0.983230i | \(-0.441623\pi\) |
−0.983230 | + | 0.182370i | \(0.941623\pi\) | |||||||
\(48\) | 0.593565 | − | 0.593565i | 0.0856737 | − | 0.0856737i | ||||
\(49\) | −6.24586 | − | 3.16057i | −0.892266 | − | 0.451510i | ||||
\(50\) | 0.678376 | + | 3.75866i | 0.0959368 | + | 0.531555i | ||||
\(51\) | 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 | \(-0.0466774\pi\) |
−0.146116 | + | 0.989267i | \(0.546677\pi\) | |||||||
\(54\) | 0.763878 | 0.103951 | ||||||||
\(55\) | −3.99191 | − | 7.63083i | −0.538269 | − | 1.02894i | ||||
\(56\) | 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 | \(0.349998\pi\) | |||||||
\(60\) | 0.946361 | − | 3.02269i | 0.122175 | − | 0.390227i | ||||
\(61\) | 14.3107i | 1.83230i | 0.400835 | + | 0.916150i | \(0.368720\pi\) | ||||
−0.400835 | + | 0.916150i | \(0.631280\pi\) | |||||||
\(62\) | −1.29458 | − | 1.29458i | −0.164412 | − | 0.164412i | ||||
\(63\) | −2.57351 | − | 0.614060i | −0.324231 | − | 0.0773643i | ||||
\(64\) | 2.79807i | 0.349758i | ||||||||
\(65\) | 11.0699 | + | 3.46582i | 1.37305 | + | 0.429883i | ||||
\(66\) | − | 2.94197i | − | 0.362131i | ||||||
\(67\) | 0.416491 | − | 0.416491i | 0.0508824 | − | 0.0508824i | −0.681208 | − | 0.732090i | \(-0.738545\pi\) |
0.732090 | + | 0.681208i | \(0.238545\pi\) | |||||||
\(68\) | 2.11067 | − | 2.11067i | 0.255957 | − | 0.255957i | ||||
\(69\) | 0.755439 | 0.0909442 | ||||||||
\(70\) | 2.31434 | − | 3.88158i | 0.276616 | − | 0.463938i | ||||
\(71\) | −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 | −0.125953 | + | 0.992036i | \(0.540199\pi\) |
−0.992036 | + | 0.125953i | \(0.959801\pi\) | |||||||
\(74\) | − | 6.68434i | − | 0.777039i | ||||||
\(75\) | −0.888068 | − | 4.92050i | −0.102545 | − | 0.568171i | ||||
\(76\) | − | 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 | \(0.187226\pi\) | ||||
−0.831948 | + | 0.554854i | \(0.812774\pi\) | |||||||
\(80\) | −0.870061 | − | 1.66319i | −0.0972758 | − | 0.185950i | ||||
\(81\) | −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 | \(-0.790520\pi\) |
0.611615 | + | 0.791156i | \(0.290520\pi\) | |||||||
\(84\) | −3.19270 | + | 1.96260i | −0.348352 | + | 0.214137i | ||||
\(85\) | 1.40788 | − | 4.49678i | 0.152706 | − | 0.487744i | ||||
\(86\) | −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 | \(0.413698\pi\) | |||||||
\(90\) | 0.510348 | − | 1.63006i | 0.0537954 | − | 0.171823i | ||||
\(91\) | −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 | ||||||||
\(95\) | −0.0723134 | − | 0.138232i | −0.00741920 | − | 0.0141823i | ||||
\(96\) | − | 5.86078i | − | 0.598164i | ||||||
\(97\) | −6.85851 | − | 6.85851i | −0.696376 | − | 0.696376i | 0.267251 | − | 0.963627i | \(-0.413885\pi\) |
−0.963627 | + | 0.267251i | \(0.913885\pi\) | |||||||
\(98\) | −5.08082 | + | 1.66650i | −0.513240 | + | 0.168342i | ||||
\(99\) | 3.85136i | 0.387076i | ||||||||
\(100\) | −5.81792 | − | 4.03893i | −0.581792 | − | 0.403893i | ||||
\(101\) | − | 19.1953i | − | 1.91000i | −0.296605 | − | 0.955000i | \(-0.595855\pi\) | ||
0.296605 | − | 0.955000i | \(-0.404145\pi\) | |||||||
\(102\) | 1.13823 | − | 1.13823i | 0.112702 | − | 0.112702i | ||||
\(103\) | −2.33825 | + | 2.33825i | −0.230394 | + | 0.230394i | −0.812857 | − | 0.582463i | \(-0.802089\pi\) |
0.582463 | + | 0.812857i | \(0.302089\pi\) | |||||||
\(104\) | 13.5384 | 1.32755 | ||||||||
\(105\) | −3.02972 | + | 5.08142i | −0.295671 | + | 0.495895i | ||||
\(106\) | 6.63105 | 0.644064 | ||||||||
\(107\) | −6.39747 | + | 6.39747i | −0.618467 | + | 0.618467i | −0.945138 | − | 0.326671i | \(-0.894073\pi\) |
0.326671 | + | 0.945138i | \(0.394073\pi\) | |||||||
\(108\) | −1.00161 | + | 1.00161i | −0.0963800 | + | 0.0963800i | ||||
\(109\) | 2.16057i | 0.206945i | 0.994632 | + | 0.103473i | \(0.0329954\pi\) | ||||
−0.994632 | + | 0.103473i | \(0.967005\pi\) | |||||||
\(110\) | −6.27794 | − | 1.96554i | −0.598578 | − | 0.187407i | ||||
\(111\) | 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 | \(-0.338768\pi\) |
−0.874435 | + | 0.485143i | \(0.838768\pi\) | |||||||
\(114\) | − | 0.0532937i | − | 0.00499142i | ||||||
\(115\) | 0.504711 | − | 1.61205i | 0.0470645 | − | 0.150325i | ||||
\(116\) | 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 | ||||
\(120\) | −2.70502 | − | 5.17085i | −0.246934 | − | 0.472032i | ||||
\(121\) | 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 | ||||||||
\(125\) | −11.0933 | − | 1.39233i | −0.992215 | − | 0.124533i | ||||
\(126\) | −1.72174 | + | 1.05838i | −0.153385 | + | 0.0942881i | ||||
\(127\) | −4.83298 | + | 4.83298i | −0.428858 | + | 0.428858i | −0.888239 | − | 0.459381i | \(-0.848071\pi\) |
0.459381 | + | 0.888239i | \(0.348071\pi\) | |||||||
\(128\) | −6.77704 | − | 6.77704i | −0.599011 | − | 0.599011i | ||||
\(129\) | 3.91889 | 0.345039 | ||||||||
\(130\) | 7.85136 | − | 4.10728i | 0.688610 | − | 0.360232i | ||||
\(131\) | 0.647499i | 0.0565722i | 0.999600 | + | 0.0282861i | \(0.00900495\pi\) | ||||
−0.999600 | + | 0.0282861i | \(0.990995\pi\) | |||||||
\(132\) | 3.85756 | + | 3.85756i | 0.335758 | + | 0.335758i | ||||
\(133\) | −0.0428413 | + | 0.179547i | −0.00371481 | + | 0.0155687i | ||||
\(134\) | − | 0.449929i | − | 0.0388680i | ||||||
\(135\) | −0.668102 | + | 2.13393i | −0.0575011 | + | 0.183659i | ||||
\(136\) | − | 5.49954i | − | 0.471581i | ||||||
\(137\) | 10.2369 | − | 10.2369i | 0.874597 | − | 0.874597i | −0.118372 | − | 0.992969i | \(-0.537768\pi\) |
0.992969 | + | 0.118372i | \(0.0377676\pi\) | |||||||
\(138\) | 0.408045 | − | 0.408045i | 0.0347351 | − | 0.0347351i | ||||
\(139\) | 22.1663 | 1.88012 | 0.940060 | − | 0.341009i | \(-0.110769\pi\) | ||||
0.940060 | + | 0.341009i | \(0.110769\pi\) | |||||||
\(140\) | 2.05500 | + | 8.12420i | 0.173679 | + | 0.686620i | ||||
\(141\) | 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 | ||||||||
\(145\) | 5.49042 | − | 2.87220i | 0.455955 | − | 0.238523i | ||||
\(146\) | 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 | \(0.149477\pi\) | ||||
−0.891752 | + | 0.452525i | \(0.850523\pi\) | |||||||
\(150\) | −3.13746 | − | 2.17809i | −0.256172 | − | 0.177840i | ||||
\(151\) | 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 | ||||
\(155\) | 4.74873 | − | 2.48420i | 0.381428 | − | 0.199536i | ||||
\(156\) | −7.34814 | −0.588322 | ||||||||
\(157\) | 1.04994 | + | 1.04994i | 0.0837946 | + | 0.0837946i | 0.747762 | − | 0.663967i | \(-0.231129\pi\) |
−0.663967 | + | 0.747762i | \(0.731129\pi\) | |||||||
\(158\) | 5.32759 | + | 5.32759i | 0.423840 | + | 0.423840i | ||||
\(159\) | −8.68077 | −0.688430 | ||||||||
\(160\) | −12.5065 | − | 3.91560i | −0.988724 | − | 0.309555i | ||||
\(161\) | −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 | \(-0.151372\pi\) |
−0.457826 | + | 0.889042i | \(0.651372\pi\) | |||||||
\(164\) | −12.2962 | −0.960174 | ||||||||
\(165\) | 8.21852 | + | 2.57310i | 0.639811 | + | 0.200316i | ||||
\(166\) | 1.76702i | 0.137147i | ||||||||
\(167\) | −1.88968 | − | 1.88968i | −0.146228 | − | 0.146228i | 0.630203 | − | 0.776431i | \(-0.282972\pi\) |
−0.776431 | + | 0.630203i | \(0.782972\pi\) | |||||||
\(168\) | −1.60256 | + | 6.71629i | −0.123640 | + | 0.518173i | ||||
\(169\) | − | 13.9108i | − | 1.07006i | ||||||
\(170\) | −1.66845 | − | 3.18936i | −0.127964 | − | 0.244613i | ||||
\(171\) | 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 | \(-0.665014\pi\) |
0.868609 | + | 0.495498i | \(0.165014\pi\) | |||||||
\(174\) | 2.11676 | 0.160471 | ||||||||
\(175\) | 8.81920 | + | 9.86011i | 0.666669 | + | 0.745354i | ||||
\(176\) | 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 | \(-0.755591\pi\) | ||
0.719416 | − | 0.694579i | \(-0.244409\pi\) | |||||||
\(180\) | 1.46818 | + | 2.80654i | 0.109432 | + | 0.209187i | ||||
\(181\) | 8.48528i | 0.630706i | 0.948974 | + | 0.315353i | \(0.102123\pi\) | ||||
−0.948974 | + | 0.315353i | \(0.897877\pi\) | |||||||
\(182\) | −10.1979 | − | 2.43331i | −0.755922 | − | 0.180369i | ||||
\(183\) | −10.1192 | − | 10.1192i | −0.748034 | − | 0.748034i | ||||
\(184\) | − | 1.97153i | − | 0.145343i | ||||||
\(185\) | 18.6730 | + | 5.84625i | 1.37287 | + | 0.429825i | ||||
\(186\) | 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 | ||||
\(190\) | −0.113725 | − | 0.0356057i | −0.00825047 | − | 0.00258311i | ||||
\(191\) | −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 | \(-0.328663\pi\) |
−0.858596 | + | 0.512653i | \(0.828663\pi\) | |||||||
\(194\) | −7.40916 | −0.531946 | ||||||||
\(195\) | −10.2783 | + | 5.37688i | −0.736044 | + | 0.385046i | ||||
\(196\) | 4.47692 | − | 8.84720i | 0.319780 | − | 0.631943i | ||||
\(197\) | 12.6739 | − | 12.6739i | 0.902981 | − | 0.902981i | −0.0927124 | − | 0.995693i | \(-0.529554\pi\) |
0.995693 | + | 0.0927124i | \(0.0295537\pi\) | |||||||
\(198\) | 2.08029 | + | 2.08029i | 0.147840 | + | 0.147840i | ||||
\(199\) | 2.67111 | 0.189350 | 0.0946750 | − | 0.995508i | \(-0.469819\pi\) | ||||
0.0946750 | + | 0.995508i | \(0.469819\pi\) | |||||||
\(200\) | −12.8414 | + | 2.31766i | −0.908026 | + | 0.163884i | ||||
\(201\) | 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 | ||||||||
\(205\) | −17.1995 | + | 8.99757i | −1.20127 | + | 0.628417i | ||||
\(206\) | 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 | ||||||||
\(210\) | 1.10821 | + | 4.38118i | 0.0764736 | + | 0.302330i | ||||
\(211\) | −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 | ||||||||
\(215\) | 2.61822 | − | 8.36262i | 0.178561 | − | 0.570326i | ||||
\(216\) | 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 | ||||||
\(220\) | 10.8090 | − | 5.65451i | 0.728742 | − | 0.381227i | ||||
\(221\) | −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 | \(-0.563232\pi\) |
0.980334 | + | 0.197346i | \(0.0632321\pi\) | |||||||
\(224\) | 8.12033 | + | 13.2099i | 0.542563 | + | 0.882624i | ||||
\(225\) | 4.10728 | + | 2.85136i | 0.273819 | + | 0.190091i | ||||
\(226\) | −4.47048 | −0.297372 | ||||||||
\(227\) | −1.10518 | − | 1.10518i | −0.0733535 | − | 0.0733535i | 0.669478 | − | 0.742832i | \(-0.266518\pi\) |
−0.742832 | + | 0.669478i | \(0.766518\pi\) | |||||||
\(228\) | 0.0698797 | + | 0.0698797i | 0.00462790 | + | 0.00462790i | ||||
\(229\) | −7.83309 | −0.517625 | −0.258812 | − | 0.965928i | \(-0.583331\pi\) | ||||
−0.258812 | + | 0.965928i | \(0.583331\pi\) | |||||||
\(230\) | −0.598123 | − | 1.14335i | −0.0394390 | − | 0.0753906i | ||||
\(231\) | −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 | \(-0.235132\pi\) |
−0.673318 | + | 0.739353i | \(0.735132\pi\) | |||||||
\(234\) | −3.96267 | −0.259048 | ||||||||
\(235\) | 5.18757 | − | 16.5691i | 0.338399 | − | 1.08085i | ||||
\(236\) | 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 | \(0.227718\pi\) | ||||
−0.754833 | + | 0.655917i | \(0.772282\pi\) | |||||||
\(240\) | 1.79128 | + | 0.560823i | 0.115626 | + | 0.0362010i | ||||
\(241\) | 2.76994i | 0.178427i | 0.996013 | + | 0.0892136i | \(0.0284354\pi\) | ||||
−0.996013 | + | 0.0892136i | \(0.971565\pi\) | |||||||
\(242\) | 2.07036 | − | 2.07036i | 0.133088 | − | 0.133088i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −20.2710 | −1.29772 | ||||||||
\(245\) | −0.211650 | − | 15.6510i | −0.0135218 | − | 0.999909i | ||||
\(246\) | −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 | ||||||
\(250\) | −6.74403 | + | 5.23992i | −0.426530 | + | 0.331401i | ||||
\(251\) | − | 6.09982i | − | 0.385017i | −0.981295 | − | 0.192509i | \(-0.938338\pi\) | ||
0.981295 | − | 0.192509i | \(-0.0616623\pi\) | |||||||
\(252\) | 0.869810 | − | 3.64535i | 0.0547929 | − | 0.229635i | ||||
\(253\) | 2.05731 | + | 2.05731i | 0.129342 | + | 0.129342i | ||||
\(254\) | 5.22100i | 0.327595i | ||||||||
\(255\) | 2.18418 | + | 4.17522i | 0.136779 | + | 0.261463i | ||||
\(256\) | −12.9173 | −0.807330 | ||||||||
\(257\) | 2.01843 | + | 2.01843i | 0.125906 | + | 0.125906i | 0.767252 | − | 0.641346i | \(-0.221624\pi\) |
−0.641346 | + | 0.767252i | \(0.721624\pi\) | |||||||
\(258\) | 2.11676 | − | 2.11676i | 0.131784 | − | 0.131784i | ||||
\(259\) | −12.1242 | − | 19.7233i | −0.753361 | − | 1.22554i | ||||
\(260\) | −4.90931 | + | 15.6804i | −0.304462 | + | 0.972456i | ||||
\(261\) | −2.77107 | −0.171525 | ||||||||
\(262\) | 0.349742 | + | 0.349742i | 0.0216071 | + | 0.0216071i | ||||
\(263\) | 16.7686 | + | 16.7686i | 1.03400 | + | 1.03400i | 0.999401 | + | 0.0345941i | \(0.0110138\pi\) |
0.0345941 | + | 0.999401i | \(0.488986\pi\) | |||||||
\(264\) | 10.0512 | 0.618609 | ||||||||
\(265\) | −5.79964 | + | 18.5241i | −0.356269 | + | 1.13793i | ||||
\(266\) | 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 | \(0.771909\pi\) | |||||||
\(270\) | 0.791755 | + | 1.51350i | 0.0481847 | + | 0.0921085i | ||||
\(271\) | 4.13470i | 0.251165i | 0.992083 | + | 0.125583i | \(0.0400800\pi\) | ||||
−0.992083 | + | 0.125583i | \(0.959920\pi\) | |||||||
\(272\) | 1.25081 | + | 1.25081i | 0.0758413 | + | 0.0758413i | ||||
\(273\) | 13.3502 | + | 3.18548i | 0.807993 | + | 0.192794i | ||||
\(274\) | − | 11.0588i | − | 0.668085i | ||||||
\(275\) | 10.9816 | − | 15.8186i | 0.662217 | − | 0.953898i | ||||
\(276\) | 1.07007i | 0.0644108i | ||||||||
\(277\) | −12.1128 | + | 12.1128i | −0.727786 | + | 0.727786i | −0.970178 | − | 0.242393i | \(-0.922068\pi\) |
0.242393 | + | 0.970178i | \(0.422068\pi\) | |||||||
\(278\) | 11.9730 | − | 11.9730i | 0.718091 | − | 0.718091i | ||||
\(279\) | −2.39674 | −0.143489 | ||||||||
\(280\) | 13.2614 | + | 7.90691i | 0.792519 | + | 0.472528i | ||||
\(281\) | 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 | \(-0.727674\pi\) |
0.754923 | + | 0.655813i | \(0.227674\pi\) | |||||||
\(284\) | − | 11.5130i | − | 0.683170i | ||||||
\(285\) | 0.148878 | + | 0.0466117i | 0.00881879 | + | 0.00276104i | ||||
\(286\) | 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 | ||||||
\(290\) | 1.41421 | − | 4.51701i | 0.0830455 | − | 0.265248i | ||||
\(291\) | 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 | \(-0.532972\pi\) |
0.994640 | + | 0.103400i | \(0.0329722\pi\) | |||||||
\(294\) | 2.41429 | − | 4.77107i | 0.140804 | − | 0.278255i | ||||
\(295\) | 7.22893 | + | 13.8186i | 0.420884 | + | 0.804551i | ||||
\(296\) | 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 | ||||||||
\(300\) | 6.96984 | − | 1.25794i | 0.402404 | − | 0.0726272i | ||||
\(301\) | −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 | ||||||||
\(305\) | −28.3543 | + | 14.8330i | −1.62356 | + | 0.849334i | ||||
\(306\) | 1.60970i | 0.0920206i | ||||||||
\(307\) | 14.6198 | + | 14.6198i | 0.834394 | + | 0.834394i | 0.988114 | − | 0.153721i | \(-0.0491256\pi\) |
−0.153721 | + | 0.988114i | \(0.549126\pi\) | |||||||
\(308\) | −14.0395 | − | 3.34995i | −0.799977 | − | 0.190881i | ||||
\(309\) | − | 3.30678i | − | 0.188116i | ||||||
\(310\) | 1.22317 | − | 3.90682i | 0.0694714 | − | 0.221893i | ||||
\(311\) | 2.86218i | 0.162299i | 0.996702 | + | 0.0811497i | \(0.0258592\pi\) | ||||
−0.996702 | + | 0.0811497i | \(0.974141\pi\) | |||||||
\(312\) | −9.57310 | + | 9.57310i | −0.541970 | + | 0.541970i | ||||
\(313\) | 9.41824 | − | 9.41824i | 0.532350 | − | 0.532350i | −0.388921 | − | 0.921271i | \(-0.627152\pi\) |
0.921271 | + | 0.388921i | \(0.127152\pi\) | |||||||
\(314\) | 1.13424 | 0.0640088 | ||||||||
\(315\) | −1.45077 | − | 5.73544i | −0.0817414 | − | 0.323155i | ||||
\(316\) | −13.9713 | −0.785945 | ||||||||
\(317\) | 7.38310 | − | 7.38310i | 0.414676 | − | 0.414676i | −0.468688 | − | 0.883364i | \(-0.655273\pi\) |
0.883364 | + | 0.468688i | \(0.155273\pi\) | |||||||
\(318\) | −4.68886 | + | 4.68886i | −0.262938 | + | 0.262938i | ||||
\(319\) | 10.6724i | 0.597540i | ||||||||
\(320\) | −5.54390 | + | 2.90018i | −0.309914 | + | 0.162125i | ||||
\(321\) | − | 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 | ||||||
\(325\) | 4.60691 | + | 25.5254i | 0.255545 | + | 1.41590i | ||||
\(326\) | 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 | ||||
\(330\) | 5.82902 | − | 3.04933i | 0.320877 | − | 0.167860i | ||||
\(331\) | 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 | ||||||||
\(335\) | 1.25690 | + | 0.393517i | 0.0686716 | + | 0.0215001i | ||||
\(336\) | −1.16306 | − | 1.89203i | −0.0634500 | − | 0.103219i | ||||
\(337\) | −4.93809 | + | 4.93809i | −0.268995 | + | 0.268995i | −0.828695 | − | 0.559700i | \(-0.810916\pi\) |
0.559700 | + | 0.828695i | \(0.310916\pi\) | |||||||
\(338\) | −7.51384 | − | 7.51384i | −0.408699 | − | 0.408699i | ||||
\(339\) | 5.85234 | 0.317856 | ||||||||
\(340\) | 6.36964 | + | 1.99425i | 0.345442 | + | 0.108153i | ||||
\(341\) | 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 | ||||||
\(345\) | 0.783008 | + | 1.49678i | 0.0421558 | + | 0.0805838i | ||||
\(346\) | − | 5.30151i | − | 0.285011i | ||||||
\(347\) | 5.83694 | − | 5.83694i | 0.313343 | − | 0.313343i | −0.532860 | − | 0.846203i | \(-0.678883\pi\) |
0.846203 | + | 0.532860i | \(0.178883\pi\) | |||||||
\(348\) | −2.77554 | + | 2.77554i | −0.148784 | + | 0.148784i | ||||
\(349\) | 16.9121 | 0.905282 | 0.452641 | − | 0.891693i | \(-0.350482\pi\) | ||||
0.452641 | + | 0.891693i | \(0.350482\pi\) | |||||||
\(350\) | 10.0895 | + | 0.562240i | 0.539306 | + | 0.0300530i | ||||
\(351\) | 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 | \(-0.612468\pi\) |
0.938226 | + | 0.346024i | \(0.112468\pi\) | |||||||
\(354\) | 5.32759i | 0.283158i | ||||||||
\(355\) | −8.42444 | − | 16.1039i | −0.447123 | − | 0.854708i | ||||
\(356\) | 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 | \(0.0689864\pi\) | ||||
−0.976606 | + | 0.215034i | \(0.931014\pi\) | |||||||
\(360\) | 5.56908 | + | 1.74360i | 0.293516 | + | 0.0918958i | ||||
\(361\) | −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 | ||||
\(365\) | −28.8266 | − | 9.02520i | −1.50885 | − | 0.472401i | ||||
\(366\) | −10.9316 | −0.571406 | ||||||||
\(367\) | −14.7480 | − | 14.7480i | −0.769840 | − | 0.769840i | 0.208238 | − | 0.978078i | \(-0.433227\pi\) |
−0.978078 | + | 0.208238i | \(0.933227\pi\) | |||||||
\(368\) | 0.448402 | + | 0.448402i | 0.0233746 | + | 0.0233746i | ||||
\(369\) | 8.68077 | 0.451903 | ||||||||
\(370\) | 13.2439 | − | 6.92828i | 0.688518 | − | 0.360184i | ||||
\(371\) | 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 | \(-0.232573\pi\) |
−0.667353 | + | 0.744741i | \(0.732573\pi\) | |||||||
\(374\) | 6.19955 | 0.320571 | ||||||||
\(375\) | 8.82867 | − | 6.85963i | 0.455911 | − | 0.354230i | ||||
\(376\) | − | 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 | \(0.159590\pi\) | ||||
−0.876927 | + | 0.480624i | \(0.840410\pi\) | |||||||
\(380\) | 0.195805 | − | 0.102431i | 0.0100446 | − | 0.00525461i | ||||
\(381\) | − | 6.83487i | − | 0.350161i | ||||||
\(382\) | −2.91327 | + | 2.91327i | −0.149056 | + | 0.149056i | ||||
\(383\) | −20.9354 | + | 20.9354i | −1.06975 | + | 1.06975i | −0.0723706 | + | 0.997378i | \(0.523056\pi\) |
−0.997378 | + | 0.0723706i | \(0.976944\pi\) | |||||||
\(384\) | 9.58418 | 0.489091 | ||||||||
\(385\) | −22.0893 | + | 5.58742i | −1.12577 | + | 0.284761i | ||||
\(386\) | −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 | \(0.225455\pi\) | ||||
−0.759477 | + | 0.650535i | \(0.774545\pi\) | |||||||
\(390\) | −2.64747 | + | 8.45604i | −0.134060 | + | 0.428188i | ||||
\(391\) | 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 | ||||||
\(395\) | −19.5425 | + | 10.2232i | −0.983288 | + | 0.514387i | ||||
\(396\) | −5.45542 | −0.274145 | ||||||||
\(397\) | −6.73585 | − | 6.73585i | −0.338063 | − | 0.338063i | 0.517575 | − | 0.855638i | \(-0.326835\pi\) |
−0.855638 | + | 0.517575i | \(0.826835\pi\) | |||||||
\(398\) | 1.44278 | − | 1.44278i | 0.0723201 | − | 0.0723201i | ||||
\(399\) | −0.0966653 | − | 0.157252i | −0.00483932 | − | 0.00787245i | ||||
\(400\) | 2.39351 | − | 3.44776i | 0.119676 | − | 0.172388i | ||||
\(401\) | 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 | ||||||||
\(405\) | −1.03649 | − | 1.98133i | −0.0515038 | − | 0.0984532i | ||||
\(406\) | −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 | \(0.584082\pi\) | |||||||
\(410\) | −4.43022 | + | 14.1502i | −0.218793 | + | 0.698827i | ||||
\(411\) | 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 | ||||||||
\(415\) | −4.93625 | − | 1.54547i | −0.242311 | − | 0.0758641i | ||||
\(416\) | 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 | \(0.623996\pi\) | |||||||
\(420\) | −7.19778 | − | 4.29157i | −0.351216 | − | 0.209407i | ||||
\(421\) | 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 | ||||||||
\(425\) | 10.3689 | − | 1.87141i | 0.502964 | − | 0.0907766i | ||||
\(426\) | − | 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 | ||||||
\(430\) | −3.10280 | − | 5.93123i | −0.149630 | − | 0.286029i | ||||
\(431\) | −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 | \(-0.731314\pi\) |
0.747374 | + | 0.664404i | \(0.231314\pi\) | |||||||
\(434\) | −4.12656 | + | 2.53666i | −0.198081 | + | 0.121764i | ||||
\(435\) | −1.85136 | + | 5.91327i | −0.0887660 | + | 0.283519i | ||||
\(436\) | −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 | \(0.275975\pi\) | |||||||
\(440\) | 6.71524 | − | 21.4485i | 0.320136 | − | 1.02252i | ||||
\(441\) | −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 | −0.987060 | − | 0.160349i | \(-0.948738\pi\) |
−0.160349 | − | 0.987060i | \(-0.551262\pi\) | |||||||
\(444\) | −12.3951 | −0.588243 | ||||||||
\(445\) | 5.23754 | + | 10.0119i | 0.248283 | + | 0.474611i | ||||
\(446\) | − | 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 | \(-0.925699\pi\) | ||
0.972881 | − | 0.231308i | \(-0.0743006\pi\) | |||||||
\(450\) | 3.75866 | − | 0.678376i | 0.177185 | − | 0.0319789i | ||||
\(451\) | − | 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 | ||||||||
\(455\) | 15.7169 | − | 26.3602i | 0.736819 | − | 1.23578i | ||||
\(456\) | 0.182078 | 0.00852656 | ||||||||
\(457\) | 0.550071 | − | 0.550071i | 0.0257312 | − | 0.0257312i | −0.694124 | − | 0.719855i | \(-0.744208\pi\) |
0.719855 | + | 0.694124i | \(0.244208\pi\) | |||||||
\(458\) | −4.23099 | + | 4.23099i | −0.197701 | + | 0.197701i | ||||
\(459\) | − | 2.10728i | − | 0.0983594i | ||||||
\(460\) | 2.28346 | + | 0.714918i | 0.106467 | + | 0.0333332i | ||||
\(461\) | 0.831786i | 0.0387401i | 0.999812 | + | 0.0193701i | \(0.00616607\pi\) | ||||
−0.999812 | + | 0.0193701i | \(0.993834\pi\) | |||||||
\(462\) | −7.57117 | − | 1.80655i | −0.352243 | − | 0.0840481i | ||||
\(463\) | 5.45140 | + | 5.45140i | 0.253348 | + | 0.253348i | 0.822342 | − | 0.568994i | \(-0.192667\pi\) |
−0.568994 | + | 0.822342i | \(0.692667\pi\) | |||||||
\(464\) | 2.32612i | 0.107987i | ||||||||
\(465\) | −1.60127 | + | 5.11446i | −0.0742569 | + | 0.237177i | ||||
\(466\) | 1.08890 | 0.0504423 | ||||||||
\(467\) | 23.2827 | + | 23.2827i | 1.07740 | + | 1.07740i | 0.996742 | + | 0.0806551i | \(0.0257012\pi\) |
0.0806551 | + | 0.996742i | \(0.474299\pi\) | |||||||
\(468\) | 5.19592 | − | 5.19592i | 0.240181 | − | 0.240181i | ||||
\(469\) | −0.816091 | − | 1.32759i | −0.0376836 | − | 0.0613025i | ||||
\(470\) | −6.14768 | − | 11.7517i | −0.283571 | − | 0.542067i | ||||
\(471\) | −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 | ||||||||
\(475\) | 0.198932 | − | 0.286554i | 0.00912762 | − | 0.0131480i | ||||
\(476\) | −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 | \(0.125157\pi\) | |||||||
\(480\) | 11.6122 | − | 6.07467i | 0.530020 | − | 0.277269i | ||||
\(481\) | − | 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 | ||||||||
\(485\) | 6.48019 | − | 20.6978i | 0.294250 | − | 0.939839i | ||||
\(486\) | − | 0.763878i | − | 0.0346502i | ||||||
\(487\) | −7.22893 | + | 7.22893i | −0.327574 | + | 0.327574i | −0.851663 | − | 0.524089i | \(-0.824406\pi\) |
0.524089 | + | 0.851663i | \(0.324406\pi\) | |||||||
\(488\) | −26.4089 | + | 26.4089i | −1.19548 | + | 1.19548i | ||||
\(489\) | −7.78580 | −0.352086 | ||||||||
\(490\) | −8.56813 | − | 8.33948i | −0.387068 | − | 0.376739i | ||||
\(491\) | 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 | ||||||||
\(495\) | −7.63083 | + | 3.99191i | −0.342980 | + | 0.179423i | ||||
\(496\) | 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 | \(0.112191\pi\) | ||||
−0.938527 | + | 0.345207i | \(0.887809\pi\) | |||||||
\(500\) | 1.97222 | − | 15.7136i | 0.0882002 | − | 0.702732i | ||||
\(501\) | 2.67241 | 0.119394 | ||||||||
\(502\) | −3.29478 | − | 3.29478i | −0.147053 | − | 0.147053i | ||||
\(503\) | −25.9985 | + | 25.9985i | −1.15922 | + | 1.15922i | −0.174573 | + | 0.984644i | \(0.555855\pi\) |
−0.984644 | + | 0.174573i | \(0.944145\pi\) | |||||||
\(504\) | −3.61595 | − | 5.88231i | −0.161067 | − | 0.262019i | ||||
\(505\) | 38.0322 | − | 19.8958i | 1.69241 | − | 0.885350i | ||||
\(506\) | 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 | \(0.807598\pi\) | |||||||
\(510\) | 3.43499 | + | 1.07545i | 0.152104 | + | 0.0476216i | ||||
\(511\) | 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 | ||||||||
\(515\) | −7.05642 | − | 2.20927i | −0.310943 | − | 0.0973519i | ||||
\(516\) | 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 | ||||||||
\(520\) | 14.0325 | + | 26.8241i | 0.615365 | + | 1.17631i | ||||
\(521\) | − | 2.59132i | − | 0.113528i | −0.998388 | − | 0.0567639i | \(-0.981922\pi\) | ||
0.998388 | − | 0.0567639i | \(-0.0180782\pi\) | |||||||
\(522\) | −1.49678 | + | 1.49678i | −0.0655122 | + | 0.0655122i | ||||
\(523\) | 6.08854 | − | 6.08854i | 0.266233 | − | 0.266233i | −0.561347 | − | 0.827581i | \(-0.689717\pi\) |
0.827581 | + | 0.561347i | \(0.189717\pi\) | |||||||
\(524\) | −0.917176 | −0.0400670 | ||||||||
\(525\) | −13.2083 | − | 0.736034i | −0.576456 | − | 0.0321232i | ||||
\(526\) | 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 | ||||||
\(530\) | 6.87304 | + | 13.1383i | 0.298546 | + | 0.570692i | ||||
\(531\) | − | 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 | ||||||||
\(535\) | −19.3065 | − | 6.04458i | −0.834691 | − | 0.261330i | ||||
\(536\) | 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 | ||||
\(540\) | −3.02269 | − | 0.946361i | −0.130076 | − | 0.0407249i | ||||
\(541\) | −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 | ||||||||
\(545\) | −4.28081 | + | 2.23942i | −0.183370 | + | 0.0959262i | ||||
\(546\) | 8.93165 | − | 5.49042i | 0.382239 | − | 0.234968i | ||||
\(547\) | −0.828381 | + | 0.828381i | −0.0354190 | + | 0.0354190i | −0.724594 | − | 0.689175i | \(-0.757973\pi\) |
0.689175 | + | 0.724594i | \(0.257973\pi\) | |||||||
\(548\) | 14.5005 | + | 14.5005i | 0.619429 | + | 0.619429i | ||||
\(549\) | 14.3107 | 0.610767 | ||||||||
\(550\) | −2.61267 | − | 14.4760i | −0.111405 | − | 0.617257i | ||||
\(551\) | 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 | ||||||||
\(555\) | −17.3377 | + | 9.06988i | −0.735946 | + | 0.384995i | ||||
\(556\) | 31.3983i | 1.33159i | ||||||||
\(557\) | 14.7120 | − | 14.7120i | 0.623366 | − | 0.623366i | −0.323024 | − | 0.946391i | \(-0.604700\pi\) |
0.946391 | + | 0.323024i | \(0.104700\pi\) | |||||||
\(558\) | −1.29458 | + | 1.29458i | −0.0548040 | + | 0.0548040i | ||||
\(559\) | −20.3295 | −0.859846 | ||||||||
\(560\) | −4.81449 | + | 1.21781i | −0.203449 | + | 0.0514620i | ||||
\(561\) | −8.11589 | −0.342653 | ||||||||
\(562\) | 2.83726 | − | 2.83726i | 0.119683 | − | 0.119683i | ||||
\(563\) | 23.9693 | − | 23.9693i | 1.01019 | − | 1.01019i | 0.0102391 | − | 0.999948i | \(-0.496741\pi\) |
0.999948 | − | 0.0102391i | \(-0.00325926\pi\) | |||||||
\(564\) | 10.9985i | 0.463121i | ||||||||
\(565\) | 3.90996 | − | 12.4885i | 0.164493 | − | 0.525394i | ||||
\(566\) | − | 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 | \(0.106501\pi\) | ||||
−0.944547 | + | 0.328376i | \(0.893499\pi\) | |||||||
\(570\) | 0.105593 | − | 0.0552386i | 0.00442279 | − | 0.00231369i | ||||
\(571\) | 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 | ||||
\(575\) | 3.71714 | − | 0.670882i | 0.155015 | − | 0.0279777i | ||||
\(576\) | 2.79807 | 0.116586 | ||||||||
\(577\) | −15.5587 | − | 15.5587i | −0.647717 | − | 0.647717i | 0.304724 | − | 0.952441i | \(-0.401436\pi\) |
−0.952441 | + | 0.304724i | \(0.901436\pi\) | |||||||
\(578\) | −6.78386 | − | 6.78386i | −0.282171 | − | 0.282171i | ||||
\(579\) | 6.79669 | 0.282461 | ||||||||
\(580\) | 4.06845 | + | 7.77713i | 0.168933 | + | 0.322928i | ||||
\(581\) | 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 | ||||||||
\(585\) | 3.46582 | − | 11.0699i | 0.143294 | − | 0.457683i | ||||
\(586\) | − | 16.4804i | − | 0.680798i | ||||||
\(587\) | 15.7111 | + | 15.7111i | 0.648468 | + | 0.648468i | 0.952623 | − | 0.304155i | \(-0.0983740\pi\) |
−0.304155 | + | 0.952623i | \(0.598374\pi\) | |||||||
\(588\) | 3.09026 | + | 9.42158i | 0.127440 | + | 0.388539i | ||||
\(589\) | 0.167214i | 0.00688993i | ||||||||
\(590\) | 11.3687 | + | 3.55938i | 0.468041 | + | 0.146537i | ||||
\(591\) | 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 | \(-0.732874\pi\) |
0.744110 | + | 0.668057i | \(0.232874\pi\) | |||||||
\(594\) | −2.94197 | −0.120710 | ||||||||
\(595\) | −10.7080 | − | 6.38447i | −0.438984 | − | 0.261738i | ||||
\(596\) | −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 | \(-0.582473\pi\) | ||
0.256208 | − | 0.966622i | \(-0.417527\pi\) | |||||||
\(600\) | 7.44143 | − | 10.7191i | 0.303795 | − | 0.437605i | ||||
\(601\) | − | 11.0819i | − | 0.452041i | −0.974123 | − | 0.226021i | \(-0.927428\pi\) | ||
0.974123 | − | 0.226021i | \(-0.0725717\pi\) | |||||||
\(602\) | −1.83822 | + | 7.70393i | −0.0749203 | + | 0.313989i | ||||
\(603\) | −0.416491 | − | 0.416491i | −0.0169608 | − | 0.0169608i | ||||
\(604\) | 26.0620i | 1.06045i | ||||||||
\(605\) | 3.97286 | + | 7.59441i | 0.161520 | + | 0.308757i | ||||
\(606\) | 14.6628 | 0.595637 | ||||||||
\(607\) | −7.54653 | − | 7.54653i | −0.306304 | − | 0.306304i | 0.537170 | − | 0.843474i | \(-0.319493\pi\) |
−0.843474 | + | 0.537170i | \(0.819493\pi\) | |||||||
\(608\) | 0.289130 | − | 0.289130i | 0.0117258 | − | 0.0117258i | ||||
\(609\) | 6.24586 | − | 3.83943i | 0.253095 | − | 0.155581i | ||||
\(610\) | −7.30346 | + | 23.3273i | −0.295708 | + | 0.944496i | ||||
\(611\) | −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 | \(-0.273885\pi\) |
−0.758126 | + | 0.652108i | \(0.773885\pi\) | |||||||
\(614\) | 15.7935 | 0.637375 | ||||||||
\(615\) | 5.79964 | − | 18.5241i | 0.233864 | − | 0.746965i | ||||
\(616\) | −22.6549 | + | 13.9263i | −0.912793 | + | 0.561108i | ||||
\(617\) | 11.3212 | − | 11.3212i | 0.455774 | − | 0.455774i | −0.441491 | − | 0.897266i | \(-0.645550\pi\) |
0.897266 | + | 0.441491i | \(0.145550\pi\) | |||||||
\(618\) | −1.78613 | − | 1.78613i | −0.0718488 | − | 0.0718488i | ||||
\(619\) | 9.06771 | 0.364462 | 0.182231 | − | 0.983256i | \(-0.441668\pi\) | ||||
0.182231 | + | 0.983256i | \(0.441668\pi\) | |||||||
\(620\) | 3.51885 | + | 6.72654i | 0.141320 | + | 0.270144i | ||||
\(621\) | − | 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 | ||||||
\(625\) | −8.73948 | − | 23.4227i | −0.349579 | − | 0.936907i | ||||
\(626\) | − | 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 | ||||||||
\(630\) | −3.88158 | − | 2.31434i | −0.154646 | − | 0.0922054i | ||||
\(631\) | −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 | ||||||
\(635\) | −14.5851 | − | 4.56639i | −0.578792 | − | 0.181212i | ||||
\(636\) | − | 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 | ||||||||
\(640\) | 6.40321 | − | 20.4519i | 0.253109 | − | 0.808434i | ||||
\(641\) | −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 | \(-0.784645\pi\) |
0.626112 | + | 0.779733i | \(0.284645\pi\) | |||||||
\(644\) | −1.48263 | − | 2.41189i | −0.0584236 | − | 0.0950418i | ||||
\(645\) | 4.06191 | + | 7.76463i | 0.159937 | + | 0.305732i | ||||
\(646\) | 0.112305 | 0.00441857 | ||||||||
\(647\) | −16.8414 | − | 16.8414i | −0.662104 | − | 0.662104i | 0.293772 | − | 0.955876i | \(-0.405089\pi\) |
−0.955876 | + | 0.293772i | \(0.905089\pi\) | |||||||
\(648\) | −1.84539 | − | 1.84539i | −0.0724939 | − | 0.0724939i | ||||
\(649\) | −26.8609 | −1.05438 | ||||||||
\(650\) | 16.2758 | + | 11.2990i | 0.638388 | + | 0.443183i | ||||
\(651\) | 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 | \(-0.469537\pi\) |
−0.995424 | + | 0.0955569i | \(0.969537\pi\) | |||||||
\(654\) | −1.65041 | −0.0645363 | ||||||||
\(655\) | −1.28291 | + | 0.671128i | −0.0501275 | + | 0.0262232i | ||||
\(656\) | − | 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 | \(-0.779777\pi\) | ||
0.770067 | − | 0.637963i | \(-0.220223\pi\) | |||||||
\(660\) | −3.64478 | + | 11.6415i | −0.141873 | + | 0.453143i | ||||
\(661\) | 32.5174i | 1.26478i | 0.774650 | + | 0.632391i | \(0.217926\pi\) | ||||
−0.774650 | + | 0.632391i | \(0.782074\pi\) | |||||||
\(662\) | 12.7582 | − | 12.7582i | 0.495861 | − | 0.495861i | ||||
\(663\) | 7.72984 | − | 7.72984i | 0.300202 | − | 0.300202i | ||||
\(664\) | −6.03701 | −0.234281 | ||||||||
\(665\) | −0.400147 | + | 0.101216i | −0.0155170 | + | 0.00392499i | ||||
\(666\) | −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 | ||||||||
\(670\) | 0.891460 | − | 0.466349i | 0.0344401 | − | 0.0180166i | ||||
\(671\) | − | 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 | \(-0.400950\pi\) |
−0.951974 | + | 0.306179i | \(0.900950\pi\) | |||||||
\(674\) | 5.33455i | 0.205479i | ||||||||
\(675\) | −4.92050 | + | 0.888068i | −0.189390 | + | 0.0341818i | ||||
\(676\) | 19.7046 | 0.757868 | ||||||||
\(677\) | 6.85568 | + | 6.85568i | 0.263485 | + | 0.263485i | 0.826468 | − | 0.562983i | \(-0.190346\pi\) |
−0.562983 | + | 0.826468i | \(0.690346\pi\) | |||||||
\(678\) | 3.16110 | − | 3.16110i | 0.121401 | − | 0.121401i | ||||
\(679\) | −21.8620 | + | 13.4389i | −0.838985 | + | 0.515737i | ||||
\(680\) | 10.8964 | − | 5.70024i | 0.417858 | − | 0.218594i | ||||
\(681\) | 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 | \(-0.0336088\pi\) |
−0.105389 | + | 0.994431i | \(0.533609\pi\) | |||||||
\(684\) | −0.0988248 | −0.00377866 | ||||||||
\(685\) | 30.8932 | + | 9.67222i | 1.18037 | + | 0.369557i | ||||
\(686\) | 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 | ||||||||
\(690\) | 1.23141 | + | 0.385537i | 0.0468790 | + | 0.0146772i | ||||
\(691\) | 42.4714i | 1.61569i | 0.589395 | + | 0.807845i | \(0.299366\pi\) | ||||
−0.589395 | + | 0.807845i | \(0.700634\pi\) | |||||||
\(692\) | 6.95144 | + | 6.95144i | 0.264254 | + | 0.264254i | ||||
\(693\) | 9.91150 | + | 2.36497i | 0.376507 | + | 0.0898376i | ||||
\(694\) | − | 6.30557i | − | 0.239356i | ||||||
\(695\) | 22.9752 | + | 43.9188i | 0.871500 | + | 1.66594i | ||||
\(696\) | 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 | ||||||||
\(700\) | −13.9668 | + | 12.4923i | −0.527894 | + | 0.472165i | ||||
\(701\) | 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 | ||||||
\(705\) | 8.04799 | + | 15.3843i | 0.303105 | + | 0.579407i | ||||
\(706\) | − | 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 | \(-0.789740\pi\) | ||
0.789654 | − | 0.613552i | \(-0.210260\pi\) | |||||||
\(710\) | −13.2488 | − | 4.14802i | −0.497220 | − | 0.155673i | ||||
\(711\) | 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 | ||||
\(715\) | −42.6341 | − | 13.3481i | −1.59443 | − | 0.499192i | ||||
\(716\) | 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 | \(0.382659\pi\) | |||||||
\(720\) | −1.66319 | + | 0.870061i | −0.0619832 | + | 0.0324253i | ||||
\(721\) | 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 | ||||||||
\(725\) | 11.3816 | + | 7.90133i | 0.422701 | + | 0.293448i | ||||
\(726\) | 2.92793i | 0.108666i | ||||||||
\(727\) | −2.71795 | − | 2.71795i | −0.100803 | − | 0.100803i | 0.654907 | − | 0.755710i | \(-0.272708\pi\) |
−0.755710 | + | 0.654907i | \(0.772708\pi\) | |||||||
\(728\) | 8.31339 | − | 34.8412i | 0.308115 | − | 1.29130i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −20.4454 | + | 10.6956i | −0.756718 | + | 0.395861i | ||||
\(731\) | 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 | \(-0.730165\pi\) |
0.749769 | + | 0.661700i | \(0.230165\pi\) | |||||||
\(734\) | −15.9321 | −0.588064 | ||||||||
\(735\) | 11.2166 | + | 10.9173i | 0.413731 | + | 0.402691i | ||||
\(736\) | 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 | \(-0.970940\pi\) | ||
0.995835 | − | 0.0911693i | \(-0.0290605\pi\) | |||||||
\(740\) | −8.28116 | + | 26.4501i | −0.304422 | + | 0.972326i | ||||
\(741\) | − | 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 | \(-0.116880\pi\) |
−0.358993 | + | 0.933340i | \(0.616880\pi\) | |||||||
\(744\) | 6.25496i | 0.229318i | ||||||||
\(745\) | −21.8889 | + | 11.4507i | −0.801946 | + | 0.419521i | ||||
\(746\) | 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 | ||||
\(750\) | 1.06357 | − | 8.47393i | 0.0388360 | − | 0.309424i | ||||
\(751\) | −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 | ||||||||
\(755\) | 19.0704 | + | 36.4545i | 0.694045 | + | 1.32672i | ||||
\(756\) | 1.96260 | + | 3.19270i | 0.0713791 | + | 0.116117i | ||||
\(757\) | 29.4977 | − | 29.4977i | 1.07211 | − | 1.07211i | 0.0749214 | − | 0.997189i | \(-0.476129\pi\) |
0.997189 | − | 0.0749214i | \(-0.0238706\pi\) | |||||||
\(758\) | 10.1080 | + | 10.1080i | 0.367138 | + | 0.367138i | ||||
\(759\) | −2.90947 | −0.105607 | ||||||||
\(760\) | 0.121646 | − | 0.388540i | 0.00441258 | − | 0.0140938i | ||||
\(761\) | 28.1175i | 1.01926i | 0.860395 | + | 0.509629i | \(0.170217\pi\) | ||||
−0.860395 | + | 0.509629i | \(0.829783\pi\) | |||||||
\(762\) | −3.69181 | − | 3.69181i | −0.133740 | − | 0.133740i | ||||
\(763\) | 5.56025 | + | 1.32672i | 0.201294 | + | 0.0480305i | ||||
\(764\) | − | 7.63986i | − | 0.276400i | ||||||
\(765\) | −4.49678 | − | 1.40788i | −0.162581 | − | 0.0509019i | ||||
\(766\) | 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 | \(0.538041\pi\) | |||||||
\(770\) | −8.91335 | + | 14.9494i | −0.321215 | + | 0.538738i | ||||
\(771\) | −2.85449 | −0.102802 | ||||||||
\(772\) | 6.80764 | − | 6.80764i | 0.245012 | − | 0.245012i | ||||
\(773\) | −31.7247 | + | 31.7247i | −1.14106 | + | 1.14106i | −0.152800 | + | 0.988257i | \(0.548829\pi\) |
−0.988257 | + | 0.152800i | \(0.951171\pi\) | |||||||
\(774\) | 2.99355i | 0.107601i | ||||||||
\(775\) | 9.84407 | + | 6.83396i | 0.353609 | + | 0.245483i | ||||
\(776\) | − | 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 | ||||||
\(780\) | −7.61630 | − | 14.5591i | −0.272707 | − | 0.521300i | ||||
\(781\) | 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 | ||||
\(785\) | −0.992027 | + | 3.16855i | −0.0354070 | + | 0.113090i | ||||
\(786\) | −0.494610 | −0.0176422 | ||||||||
\(787\) | −22.4472 | − | 22.4472i | −0.800155 | − | 0.800155i | 0.182964 | − | 0.983120i | \(-0.441431\pi\) |
−0.983120 | + | 0.182964i | \(0.941431\pi\) | |||||||
\(788\) | 17.9525 | + | 17.9525i | 0.639532 | + | 0.639532i | ||||
\(789\) | −23.7144 | −0.844254 | ||||||||
\(790\) | −5.03372 | + | 16.0777i | −0.179092 | + | 0.572021i | ||||
\(791\) | −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 | ||||||||
\(795\) | −8.99757 | − | 17.1995i | −0.319111 | − | 0.610003i | ||||
\(796\) | 3.78360i | 0.134106i | ||||||||
\(797\) | −5.14677 | − | 5.14677i | −0.182308 | − | 0.182308i | 0.610053 | − | 0.792361i | \(-0.291148\pi\) |
−0.792361 | + | 0.610053i | \(0.791148\pi\) | |||||||
\(798\) | −0.137152 | − | 0.0327255i | −0.00485512 | − | 0.00115847i | ||||
\(799\) | 16.3622i | 0.578854i | ||||||||
\(800\) | −5.20477 | − | 28.8380i | −0.184017 | − | 1.01958i | ||||
\(801\) | − | 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 | ||||||||
\(805\) | −3.83870 | − | 2.28877i | −0.135296 | − | 0.0806686i | ||||
\(806\) | −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 | \(-0.870430\pi\) | ||
0.918290 | − | 0.395907i | \(-0.129570\pi\) | |||||||
\(810\) | −1.63006 | − | 0.510348i | −0.0572744 | − | 0.0179318i | ||||
\(811\) | − | 34.9145i | − | 1.22602i | −0.790077 | − | 0.613008i | \(-0.789960\pi\) | ||
0.790077 | − | 0.613008i | \(-0.210040\pi\) | |||||||
\(812\) | 2.41031 | − | 10.1015i | 0.0845852 | − | 0.354494i | ||||
\(813\) | −2.92367 | − | 2.92367i | −0.102538 | − | 0.102538i | ||||
\(814\) | 25.7438i | 0.902320i | ||||||||
\(815\) | −5.20171 | + | 16.6143i | −0.182208 | + | 0.581974i | ||||
\(816\) | −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 | ||||
\(820\) | −12.7450 | − | 24.3629i | −0.445074 | − | 0.850790i | ||||
\(821\) | 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 | −0.979269 | − | 0.202564i | \(-0.935073\pi\) |
−0.202564 | − | 0.979269i | \(-0.564927\pi\) | |||||||
\(824\) | −8.62997 | −0.300639 | ||||||||
\(825\) | 3.42027 | + | 18.9506i | 0.119079 | + | 0.659776i | ||||
\(826\) | −7.38158 | − | 12.0081i | −0.256838 | − | 0.417816i | ||||
\(827\) | −37.8440 | + | 37.8440i | −1.31597 | + | 1.31597i | −0.399025 | + | 0.916940i | \(0.630651\pi\) |
−0.916940 | + | 0.399025i | \(0.869349\pi\) | |||||||
\(828\) | −0.756656 | − | 0.756656i | −0.0262956 | − | 0.0262956i | ||||
\(829\) | 33.7140 | 1.17094 | 0.585469 | − | 0.810695i | \(-0.300911\pi\) | ||||
0.585469 | + | 0.810695i | \(0.300911\pi\) | |||||||
\(830\) | −3.50106 | + | 1.83151i | −0.121523 | + | 0.0635725i | ||||
\(831\) | − | 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 | ||||||||
\(835\) | 1.78544 | − | 5.70272i | 0.0617878 | − | 0.197351i | ||||
\(836\) | 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 | \(0.410547\pi\) | |||||||
\(840\) | −14.9682 | + | 3.78618i | −0.516454 | + | 0.130636i | ||||
\(841\) | 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 | ||||||
\(845\) | 27.5620 | − | 14.4185i | 0.948161 | − | 0.496011i | ||||
\(846\) | 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 | ||||||||
\(850\) | 4.58985 | − | 6.61150i | 0.157430 | − | 0.226773i | ||||
\(851\) | −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 | \(-0.789745\pi\) |
0.613539 | + | 0.789664i | \(0.289745\pi\) | |||||||
\(854\) | 24.6394 | − | 15.1462i | 0.843142 | − | 0.518292i | ||||
\(855\) | −0.138232 | + | 0.0723134i | −0.00472745 | + | 0.00247307i | ||||
\(856\) | −23.6117 | −0.807032 | ||||||||
\(857\) | 5.65076 | + | 5.65076i | 0.193026 | + | 0.193026i | 0.797002 | − | 0.603976i | \(-0.206418\pi\) |
−0.603976 | + | 0.797002i | \(0.706418\pi\) | |||||||
\(858\) | −10.7916 | − | 10.7916i | −0.368420 | − | 0.368420i | ||||
\(859\) | −42.0801 | −1.43575 | −0.717877 | − | 0.696170i | \(-0.754886\pi\) | ||||
−0.717877 | + | 0.696170i | \(0.754886\pi\) | |||||||
\(860\) | 11.8456 | + | 3.70868i | 0.403931 | + | 0.126465i | ||||
\(861\) | −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 | \(-0.343092\pi\) |
−0.880944 | + | 0.473220i | \(0.843092\pi\) | |||||||
\(864\) | −5.86078 | −0.199388 | ||||||||
\(865\) | 14.8100 | + | 4.63680i | 0.503555 | + | 0.157656i | ||||
\(866\) | − | 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 | ||||||
\(870\) | 2.19401 | + | 4.19401i | 0.0743839 | + | 0.142190i | ||||
\(871\) | − | 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 | ||||||||
\(875\) | −10.3951 | + | 27.6937i | −0.351419 | + | 0.936218i | ||||
\(876\) | 19.1350 | 0.646510 | ||||||||
\(877\) | −11.5817 | + | 11.5817i | −0.391085 | + | 0.391085i | −0.875074 | − | 0.483989i | \(-0.839187\pi\) |
0.483989 | + | 0.875074i | \(0.339187\pi\) | |||||||
\(878\) | 14.6471 | − | 14.6471i | 0.494317 | − | 0.494317i | ||||
\(879\) | 21.5746i | 0.727694i | ||||||||
\(880\) | 3.35092 | + | 6.40553i | 0.112959 | + | 0.215930i | ||||
\(881\) | 8.72058i | 0.293804i | 0.989151 | + | 0.146902i | \(0.0469301\pi\) | ||||
−0.989151 | + | 0.146902i | \(0.953070\pi\) | |||||||
\(882\) | 1.66650 | + | 5.08082i | 0.0561139 | + | 0.171080i | ||||
\(883\) | 17.0876 | + | 17.0876i | 0.575044 | + | 0.575044i | 0.933534 | − | 0.358490i | \(-0.116708\pi\) |
−0.358490 | + | 0.933534i | \(0.616708\pi\) | |||||||
\(884\) | − | 15.4846i | − | 0.520803i | ||||||
\(885\) | −14.8829 | − | 4.65961i | −0.500282 | − | 0.156631i | ||||
\(886\) | −26.0891 | −0.876480 | ||||||||
\(887\) | −26.4024 | − | 26.4024i | −0.886507 | − | 0.886507i | 0.107679 | − | 0.994186i | \(-0.465658\pi\) |
−0.994186 | + | 0.107679i | \(0.965658\pi\) | |||||||
\(888\) | −16.1482 | + | 16.1482i | −0.541898 | + | 0.541898i | ||||
\(889\) | 9.46996 | + | 15.4054i | 0.317612 | + | 0.516682i | ||||
\(890\) | 8.23690 | + | 2.57886i | 0.276101 | + | 0.0864435i | ||||
\(891\) | 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 | ||||||||
\(895\) | 36.8244 | − | 19.2639i | 1.23090 | − | 0.643922i | ||||
\(896\) | −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 | ||||||||
\(900\) | −4.03893 | + | 5.81792i | −0.134631 | + | 0.193931i | ||||
\(901\) | − | 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 | ||||||
\(905\) | −16.8122 | + | 8.79494i | −0.558855 | + | 0.292354i | ||||
\(906\) | 14.0546i | 0.466932i | ||||||||
\(907\) | −23.6454 | + | 23.6454i | −0.785133 | + | 0.785133i | −0.980692 | − | 0.195559i | \(-0.937348\pi\) |
0.195559 | + | 0.980692i | \(0.437348\pi\) | |||||||
\(908\) | 1.56548 | − | 1.56548i | 0.0519523 | − | 0.0519523i | ||||
\(909\) | −19.1953 | −0.636667 | ||||||||
\(910\) | −5.74890 | − | 22.7276i | −0.190574 | − | 0.753414i | ||||
\(911\) | −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 | ||||||
\(915\) | 9.56103 | − | 30.5380i | 0.316078 | − | 1.00956i | ||||
\(916\) | − | 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 | \(-0.884191\pi\) | ||
0.934543 | − | 0.355850i | \(-0.115809\pi\) | |||||||
\(920\) | 3.90626 | − | 2.04348i | 0.128786 | − | 0.0673716i | ||||
\(921\) | −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 | ||||
\(925\) | 7.77107 | + | 43.0570i | 0.255511 | + | 1.41571i | ||||
\(926\) | 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 | \(0.716292\pi\) | |||||||
\(930\) | 1.89763 | + | 3.62745i | 0.0622257 | + | 0.118949i | ||||
\(931\) | 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 | ||||||||
\(935\) | −5.42225 | + | 17.3187i | −0.177326 | + | 0.566382i | ||||
\(936\) | − | 13.5384i | − | 0.442517i | ||||||
\(937\) | −13.2317 | − | 13.2317i | −0.432262 | − | 0.432262i | 0.457135 | − | 0.889397i | \(-0.348875\pi\) |
−0.889397 | + | 0.457135i | \(0.848875\pi\) | |||||||
\(938\) | −1.15790 | − | 0.276283i | −0.0378066 | − | 0.00902097i | ||||
\(939\) | 13.3194i | 0.434662i | ||||||||
\(940\) | 23.4700 | + | 7.34814i | 0.765508 | + | 0.239670i | ||||
\(941\) | − | 2.58095i | − | 0.0841366i | −0.999115 | − | 0.0420683i | \(-0.986605\pi\) | ||
0.999115 | − | 0.0420683i | \(-0.0133947\pi\) | |||||||
\(942\) | −0.802028 | + | 0.802028i | −0.0261315 | + | 0.0261315i | ||||
\(943\) | 4.63706 | − | 4.63706i | 0.151004 | − | 0.151004i | ||||
\(944\) | −5.85450 | −0.190548 | ||||||||
\(945\) | 5.08142 | + | 3.02972i | 0.165298 | + | 0.0985569i | ||||
\(946\) | 11.5293 | 0.374848 | ||||||||
\(947\) | 4.94205 | − | 4.94205i | 0.160595 | − | 0.160595i | −0.622235 | − | 0.782830i | \(-0.713775\pi\) |
0.782830 | + | 0.622235i | \(0.213775\pi\) | |||||||
\(948\) | 9.87918 | − | 9.87918i | 0.320861 | − | 0.320861i | ||||
\(949\) | 70.0773i | 2.27481i | ||||||||
\(950\) | −0.0473285 | − | 0.262232i | −0.00153554 | − | 0.00850793i | ||||
\(951\) | 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 | \(-0.372233\pi\) |
−0.920518 | + | 0.390700i | \(0.872233\pi\) | |||||||
\(954\) | − | 6.63105i | − | 0.214688i | ||||||
\(955\) | −5.59034 | − | 10.6863i | −0.180899 | − | 0.345802i | ||||
\(956\) | −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 | ||||
\(960\) | 1.86939 | − | 5.97087i | 0.0603345 | − | 0.192709i | ||||
\(961\) | 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 | ||||||||
\(965\) | 4.54089 | − | 14.5036i | 0.146176 | − | 0.466889i | ||||
\(966\) | −0.799543 | − | 1.30067i | −0.0257249 | − | 0.0418484i | ||||
\(967\) | 8.66781 | − | 8.66781i | 0.278738 | − | 0.278738i | −0.553867 | − | 0.832605i | \(-0.686848\pi\) |
0.832605 | + | 0.553867i | \(0.186848\pi\) | |||||||
\(968\) | 7.07336 | + | 7.07336i | 0.227346 | + | 0.227346i | ||||
\(969\) | −0.147019 | −0.00472294 | ||||||||
\(970\) | −7.67955 | − | 14.6800i | −0.246575 | − | 0.471347i | ||||
\(971\) | − | 13.1861i | − | 0.423163i | −0.977360 | − | 0.211582i | \(-0.932139\pi\) | ||
0.977360 | − | 0.211582i | \(-0.0678614\pi\) | |||||||
\(972\) | 1.00161 | + | 1.00161i | 0.0321267 | + | 0.0321267i | ||||
\(973\) | 13.6114 | − | 57.0451i | 0.436362 | − | 1.82878i | ||||
\(974\) | 7.80931i | 0.250226i | ||||||||
\(975\) | −21.3068 | − | 14.7916i | −0.682363 | − | 0.473711i | ||||
\(976\) | − | 12.0128i | − | 0.384521i | ||||||
\(977\) | −24.4925 | + | 24.4925i | −0.783586 | + | 0.783586i | −0.980434 | − | 0.196848i | \(-0.936929\pi\) |
0.196848 | + | 0.980434i | \(0.436929\pi\) | |||||||
\(978\) | −4.20545 | + | 4.20545i | −0.134475 | + | 0.134475i | ||||
\(979\) | −19.4614 | −0.621990 | ||||||||
\(980\) | 22.1696 | − | 0.299800i | 0.708181 | − | 0.00957675i | ||||
\(981\) | 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 | \(-0.865486\pi\) |
0.410123 | + | 0.912030i | \(0.365486\pi\) | |||||||
\(984\) | − | 22.6549i | − | 0.722212i | ||||||
\(985\) | 38.2477 | + | 11.9748i | 1.21867 | + | 0.381550i | ||||
\(986\) | 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 | ||||||||
\(990\) | −1.96554 | + | 6.27794i | −0.0624688 | + | 0.199526i | ||||
\(991\) | −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 | ||||
\(995\) | 2.76859 | + | 5.29236i | 0.0877702 | + | 0.167779i | ||||
\(996\) | 3.27666 | 0.103825 | ||||||||
\(997\) | 22.8721 | + | 22.8721i | 0.724367 | + | 0.724367i | 0.969491 | − | 0.245125i | \(-0.0788290\pi\) |
−0.245125 | + | 0.969491i | \(0.578829\pi\) | |||||||
\(998\) | 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 | 105.2.m.a.13.5 | ✓ | 16 | |
3.2 | odd | 2 | 315.2.p.e.118.3 | 16 | |||
4.3 | odd | 2 | 1680.2.cz.d.433.7 | 16 | |||
5.2 | odd | 4 | inner | 105.2.m.a.97.6 | yes | 16 | |
5.3 | odd | 4 | 525.2.m.b.307.3 | 16 | |||
5.4 | even | 2 | 525.2.m.b.118.4 | 16 | |||
7.2 | even | 3 | 735.2.v.a.178.3 | 32 | |||
7.3 | odd | 6 | 735.2.v.a.313.5 | 32 | |||
7.4 | even | 3 | 735.2.v.a.313.6 | 32 | |||
7.5 | odd | 6 | 735.2.v.a.178.4 | 32 | |||
7.6 | odd | 2 | inner | 105.2.m.a.13.6 | yes | 16 | |
15.2 | even | 4 | 315.2.p.e.307.4 | 16 | |||
20.7 | even | 4 | 1680.2.cz.d.97.2 | 16 | |||
21.20 | even | 2 | 315.2.p.e.118.4 | 16 | |||
28.27 | even | 2 | 1680.2.cz.d.433.2 | 16 | |||
35.2 | odd | 12 | 735.2.v.a.472.5 | 32 | |||
35.12 | even | 12 | 735.2.v.a.472.6 | 32 | |||
35.13 | even | 4 | 525.2.m.b.307.4 | 16 | |||
35.17 | even | 12 | 735.2.v.a.607.3 | 32 | |||
35.27 | even | 4 | inner | 105.2.m.a.97.5 | yes | 16 | |
35.32 | odd | 12 | 735.2.v.a.607.4 | 32 | |||
35.34 | odd | 2 | 525.2.m.b.118.3 | 16 | |||
105.62 | odd | 4 | 315.2.p.e.307.3 | 16 | |||
140.27 | odd | 4 | 1680.2.cz.d.97.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
105.2.m.a.13.6 | yes | 16 | 7.6 | odd | 2 | inner | |
105.2.m.a.97.5 | yes | 16 | 35.27 | even | 4 | inner | |
105.2.m.a.97.6 | yes | 16 | 5.2 | odd | 4 | inner | |
315.2.p.e.118.3 | 16 | 3.2 | odd | 2 | |||
315.2.p.e.118.4 | 16 | 21.20 | even | 2 | |||
315.2.p.e.307.3 | 16 | 105.62 | odd | 4 | |||
315.2.p.e.307.4 | 16 | 15.2 | even | 4 | |||
525.2.m.b.118.3 | 16 | 35.34 | odd | 2 | |||
525.2.m.b.118.4 | 16 | 5.4 | even | 2 | |||
525.2.m.b.307.3 | 16 | 5.3 | odd | 4 | |||
525.2.m.b.307.4 | 16 | 35.13 | even | 4 | |||
735.2.v.a.178.3 | 32 | 7.2 | even | 3 | |||
735.2.v.a.178.4 | 32 | 7.5 | odd | 6 | |||
735.2.v.a.313.5 | 32 | 7.3 | odd | 6 | |||
735.2.v.a.313.6 | 32 | 7.4 | even | 3 | |||
735.2.v.a.472.5 | 32 | 35.2 | odd | 12 | |||
735.2.v.a.472.6 | 32 | 35.12 | even | 12 | |||
735.2.v.a.607.3 | 32 | 35.17 | even | 12 | |||
735.2.v.a.607.4 | 32 | 35.32 | odd | 12 | |||
1680.2.cz.d.97.2 | 16 | 20.7 | even | 4 | |||
1680.2.cz.d.97.7 | 16 | 140.27 | odd | 4 | |||
1680.2.cz.d.433.2 | 16 | 28.27 | even | 2 | |||
1680.2.cz.d.433.7 | 16 | 4.3 | odd | 2 |