Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(196,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.196");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.i (of order \(3\), 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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 196.5 | ||
Character | \(\chi\) | \(=\) | 585.196 |
Dual form | 585.2.i.h.391.5 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.644173 | + | 1.11574i | −0.455499 | + | 0.788948i | −0.998717 | − | 0.0506441i | \(-0.983873\pi\) |
0.543217 | + | 0.839592i | \(0.317206\pi\) | |||||||
\(3\) | −0.971694 | − | 1.43381i | −0.561008 | − | 0.827810i | ||||
\(4\) | 0.170081 | + | 0.294590i | 0.0850407 | + | 0.147295i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 2.22570 | − | 0.160537i | 0.908638 | − | 0.0655391i | ||||
\(7\) | 1.40888 | − | 2.44026i | 0.532508 | − | 0.922330i | −0.466772 | − | 0.884378i | \(-0.654583\pi\) |
0.999280 | − | 0.0379524i | \(-0.0120835\pi\) | |||||||
\(8\) | −3.01494 | −1.06594 | ||||||||
\(9\) | −1.11162 | + | 2.78645i | −0.370540 | + | 0.928817i | ||||
\(10\) | −1.28835 | −0.407411 | ||||||||
\(11\) | 2.57577 | − | 4.46137i | 0.776625 | − | 1.34515i | −0.157252 | − | 0.987558i | \(-0.550264\pi\) |
0.933877 | − | 0.357595i | \(-0.116403\pi\) | |||||||
\(12\) | 0.257118 | − | 0.530116i | 0.0742237 | − | 0.153031i | ||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | ||||
\(14\) | 1.81513 | + | 3.14390i | 0.485114 | + | 0.840242i | ||||
\(15\) | 0.755868 | − | 1.55842i | 0.195164 | − | 0.402382i | ||||
\(16\) | 1.60198 | − | 2.77471i | 0.400495 | − | 0.693678i | ||||
\(17\) | −6.95944 | −1.68791 | −0.843956 | − | 0.536413i | \(-0.819779\pi\) | ||||
−0.843956 | + | 0.536413i | \(0.819779\pi\) | |||||||
\(18\) | −2.39288 | − | 3.03524i | −0.564007 | − | 0.715412i | ||||
\(19\) | 5.29545 | 1.21486 | 0.607430 | − | 0.794373i | \(-0.292200\pi\) | ||||
0.607430 | + | 0.794373i | \(0.292200\pi\) | |||||||
\(20\) | −0.170081 | + | 0.294590i | −0.0380314 | + | 0.0658723i | ||||
\(21\) | −4.86787 | + | 0.351114i | −1.06226 | + | 0.0766194i | ||||
\(22\) | 3.31849 | + | 5.74779i | 0.707504 | + | 1.22543i | ||||
\(23\) | −0.178608 | − | 0.309358i | −0.0372423 | − | 0.0645055i | 0.846803 | − | 0.531906i | \(-0.178524\pi\) |
−0.884046 | + | 0.467400i | \(0.845191\pi\) | |||||||
\(24\) | 2.92960 | + | 4.32285i | 0.598002 | + | 0.882398i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 1.28835 | 0.252666 | ||||||||
\(27\) | 5.07539 | − | 1.11373i | 0.976760 | − | 0.214337i | ||||
\(28\) | 0.958499 | 0.181139 | ||||||||
\(29\) | 2.41921 | − | 4.19019i | 0.449235 | − | 0.778099i | −0.549101 | − | 0.835756i | \(-0.685030\pi\) |
0.998336 | + | 0.0576574i | \(0.0183631\pi\) | |||||||
\(30\) | 1.25188 | + | 1.84724i | 0.228561 | + | 0.337259i | ||||
\(31\) | −3.69084 | − | 6.39272i | −0.662894 | − | 1.14817i | −0.979852 | − | 0.199727i | \(-0.935994\pi\) |
0.316957 | − | 0.948440i | \(-0.397339\pi\) | |||||||
\(32\) | −0.951033 | − | 1.64724i | −0.168121 | − | 0.291193i | ||||
\(33\) | −8.89962 | + | 0.641920i | −1.54922 | + | 0.111744i | ||||
\(34\) | 4.48308 | − | 7.76493i | 0.768843 | − | 1.33167i | ||||
\(35\) | 2.81777 | 0.476289 | ||||||||
\(36\) | −1.00993 | + | 0.146452i | −0.168321 | + | 0.0244086i | ||||
\(37\) | 5.70885 | 0.938530 | 0.469265 | − | 0.883058i | \(-0.344519\pi\) | ||||
0.469265 | + | 0.883058i | \(0.344519\pi\) | |||||||
\(38\) | −3.41119 | + | 5.90835i | −0.553368 | + | 0.958461i | ||||
\(39\) | −0.755868 | + | 1.55842i | −0.121036 | + | 0.249546i | ||||
\(40\) | −1.50747 | − | 2.61102i | −0.238352 | − | 0.412838i | ||||
\(41\) | 3.03414 | + | 5.25529i | 0.473854 | + | 0.820739i | 0.999552 | − | 0.0299323i | \(-0.00952917\pi\) |
−0.525698 | + | 0.850671i | \(0.676196\pi\) | |||||||
\(42\) | 2.74400 | − | 5.65746i | 0.423408 | − | 0.872964i | ||||
\(43\) | 4.89119 | − | 8.47179i | 0.745900 | − | 1.29194i | −0.203873 | − | 0.978997i | \(-0.565353\pi\) |
0.949773 | − | 0.312939i | \(-0.101314\pi\) | |||||||
\(44\) | 1.75236 | 0.264179 | ||||||||
\(45\) | −2.96895 | + | 0.430534i | −0.442584 | + | 0.0641802i | ||||
\(46\) | 0.460217 | 0.0678553 | ||||||||
\(47\) | 3.06257 | − | 5.30452i | 0.446721 | − | 0.773744i | −0.551449 | − | 0.834208i | \(-0.685925\pi\) |
0.998170 | + | 0.0604648i | \(0.0192583\pi\) | |||||||
\(48\) | −5.53505 | + | 0.399237i | −0.798915 | + | 0.0576249i | ||||
\(49\) | −0.469900 | − | 0.813891i | −0.0671286 | − | 0.116270i | ||||
\(50\) | −0.644173 | − | 1.11574i | −0.0910999 | − | 0.157790i | ||||
\(51\) | 6.76245 | + | 9.97851i | 0.946932 | + | 1.39727i | ||||
\(52\) | 0.170081 | − | 0.294590i | 0.0235861 | − | 0.0408522i | ||||
\(53\) | 3.26565 | 0.448572 | 0.224286 | − | 0.974523i | \(-0.427995\pi\) | ||||
0.224286 | + | 0.974523i | \(0.427995\pi\) | |||||||
\(54\) | −2.02680 | + | 6.38026i | −0.275813 | + | 0.868243i | ||||
\(55\) | 5.15154 | 0.694634 | ||||||||
\(56\) | −4.24770 | + | 7.35723i | −0.567623 | + | 0.983151i | ||||
\(57\) | −5.14556 | − | 7.59267i | −0.681546 | − | 1.00567i | ||||
\(58\) | 3.11678 | + | 5.39842i | 0.409253 | + | 0.708847i | ||||
\(59\) | −0.656449 | − | 1.13700i | −0.0854624 | − | 0.148025i | 0.820126 | − | 0.572183i | \(-0.193903\pi\) |
−0.905588 | + | 0.424158i | \(0.860570\pi\) | |||||||
\(60\) | 0.587653 | − | 0.0423868i | 0.0758657 | − | 0.00547211i | ||||
\(61\) | 4.58881 | − | 7.94805i | 0.587537 | − | 1.01764i | −0.407017 | − | 0.913421i | \(-0.633431\pi\) |
0.994554 | − | 0.104223i | \(-0.0332356\pi\) | |||||||
\(62\) | 9.51016 | 1.20779 | ||||||||
\(63\) | 5.23351 | + | 6.63842i | 0.659360 | + | 0.836362i | ||||
\(64\) | 8.85845 | 1.10731 | ||||||||
\(65\) | 0.500000 | − | 0.866025i | 0.0620174 | − | 0.107417i | ||||
\(66\) | 5.01668 | − | 10.3432i | 0.617510 | − | 1.27316i | ||||
\(67\) | −0.894026 | − | 1.54850i | −0.109223 | − | 0.189179i | 0.806233 | − | 0.591598i | \(-0.201503\pi\) |
−0.915456 | + | 0.402419i | \(0.868169\pi\) | |||||||
\(68\) | −1.18367 | − | 2.05018i | −0.143541 | − | 0.248621i | ||||
\(69\) | −0.270008 | + | 0.556691i | −0.0325051 | + | 0.0670177i | ||||
\(70\) | −1.81513 | + | 3.14390i | −0.216949 | + | 0.375767i | ||||
\(71\) | −4.91564 | −0.583379 | −0.291689 | − | 0.956513i | \(-0.594217\pi\) | ||||
−0.291689 | + | 0.956513i | \(0.594217\pi\) | |||||||
\(72\) | 3.35147 | − | 8.40098i | 0.394974 | − | 0.990065i | ||||
\(73\) | 4.67778 | 0.547493 | 0.273746 | − | 0.961802i | \(-0.411737\pi\) | ||||
0.273746 | + | 0.961802i | \(0.411737\pi\) | |||||||
\(74\) | −3.67749 | + | 6.36960i | −0.427500 | + | 0.740451i | ||||
\(75\) | 1.72756 | − | 0.124607i | 0.199482 | − | 0.0143884i | ||||
\(76\) | 0.900658 | + | 1.55999i | 0.103313 | + | 0.178943i | ||||
\(77\) | −7.25792 | − | 12.5711i | −0.827117 | − | 1.43261i | ||||
\(78\) | −1.25188 | − | 1.84724i | −0.141747 | − | 0.209159i | ||||
\(79\) | −4.43554 | + | 7.68258i | −0.499037 | + | 0.864358i | −0.999999 | − | 0.00111120i | \(-0.999646\pi\) |
0.500962 | + | 0.865469i | \(0.332980\pi\) | |||||||
\(80\) | 3.20396 | 0.358214 | ||||||||
\(81\) | −6.52860 | − | 6.19494i | −0.725400 | − | 0.688327i | ||||
\(82\) | −7.81806 | −0.863360 | ||||||||
\(83\) | −7.47911 | + | 12.9542i | −0.820939 | + | 1.42191i | 0.0840448 | + | 0.996462i | \(0.473216\pi\) |
−0.904984 | + | 0.425446i | \(0.860117\pi\) | |||||||
\(84\) | −0.931368 | − | 1.37431i | −0.101621 | − | 0.149949i | ||||
\(85\) | −3.47972 | − | 6.02705i | −0.377429 | − | 0.653725i | ||||
\(86\) | 6.30155 | + | 10.9146i | 0.679514 | + | 1.17695i | ||||
\(87\) | −8.35866 | + | 0.602902i | −0.896143 | + | 0.0646379i | ||||
\(88\) | −7.76580 | + | 13.4508i | −0.827837 | + | 1.43386i | ||||
\(89\) | 6.44960 | 0.683656 | 0.341828 | − | 0.939763i | \(-0.388954\pi\) | ||||
0.341828 | + | 0.939763i | \(0.388954\pi\) | |||||||
\(90\) | 1.43215 | − | 3.58991i | 0.150962 | − | 0.378410i | ||||
\(91\) | −2.81777 | −0.295382 | ||||||||
\(92\) | 0.0607557 | − | 0.105232i | 0.00633422 | − | 0.0109712i | ||||
\(93\) | −5.57958 | + | 11.5037i | −0.578575 | + | 1.19288i | ||||
\(94\) | 3.94565 | + | 6.83406i | 0.406962 | + | 0.704879i | ||||
\(95\) | 2.64773 | + | 4.58600i | 0.271651 | + | 0.470513i | ||||
\(96\) | −1.43771 | + | 2.96421i | −0.146736 | + | 0.302534i | ||||
\(97\) | −5.62800 | + | 9.74798i | −0.571437 | + | 0.989757i | 0.424982 | + | 0.905202i | \(0.360280\pi\) |
−0.996419 | + | 0.0845556i | \(0.973053\pi\) | |||||||
\(98\) | 1.21079 | 0.122308 | ||||||||
\(99\) | 9.56810 | + | 12.1366i | 0.961630 | + | 1.21977i | ||||
\(100\) | −0.340163 | −0.0340163 | ||||||||
\(101\) | −4.87922 | + | 8.45106i | −0.485501 | + | 0.840912i | −0.999861 | − | 0.0166623i | \(-0.994696\pi\) |
0.514361 | + | 0.857574i | \(0.328029\pi\) | |||||||
\(102\) | −15.4896 | + | 1.11725i | −1.53370 | + | 0.110624i | ||||
\(103\) | −3.96888 | − | 6.87431i | −0.391066 | − | 0.677345i | 0.601525 | − | 0.798854i | \(-0.294560\pi\) |
−0.992590 | + | 0.121509i | \(0.961227\pi\) | |||||||
\(104\) | 1.50747 | + | 2.61102i | 0.147820 | + | 0.256031i | ||||
\(105\) | −2.73801 | − | 4.04014i | −0.267202 | − | 0.394277i | ||||
\(106\) | −2.10365 | + | 3.64362i | −0.204324 | + | 0.353900i | ||||
\(107\) | 4.45095 | 0.430290 | 0.215145 | − | 0.976582i | \(-0.430978\pi\) | ||||
0.215145 | + | 0.976582i | \(0.430978\pi\) | |||||||
\(108\) | 1.19132 | + | 1.30573i | 0.114635 | + | 0.125644i | ||||
\(109\) | −8.58876 | −0.822654 | −0.411327 | − | 0.911488i | \(-0.634935\pi\) | ||||
−0.411327 | + | 0.911488i | \(0.634935\pi\) | |||||||
\(110\) | −3.31849 | + | 5.74779i | −0.316405 | + | 0.548030i | ||||
\(111\) | −5.54726 | − | 8.18541i | −0.526523 | − | 0.776924i | ||||
\(112\) | −4.51401 | − | 7.81849i | −0.426534 | − | 0.738778i | ||||
\(113\) | −9.61749 | − | 16.6580i | −0.904738 | − | 1.56705i | −0.821269 | − | 0.570541i | \(-0.806733\pi\) |
−0.0834690 | − | 0.996510i | \(-0.526600\pi\) | |||||||
\(114\) | 11.7861 | − | 0.850118i | 1.10387 | − | 0.0796209i | ||||
\(115\) | 0.178608 | − | 0.309358i | 0.0166553 | − | 0.0288477i | ||||
\(116\) | 1.64585 | 0.152813 | ||||||||
\(117\) | 2.96895 | − | 0.430534i | 0.274479 | − | 0.0398029i | ||||
\(118\) | 1.69147 | 0.155712 | ||||||||
\(119\) | −9.80503 | + | 16.9828i | −0.898826 | + | 1.55681i | ||||
\(120\) | −2.27890 | + | 4.69854i | −0.208034 | + | 0.428916i | ||||
\(121\) | −7.76921 | − | 13.4567i | −0.706291 | − | 1.22333i | ||||
\(122\) | 5.91198 | + | 10.2398i | 0.535245 | + | 0.927072i | ||||
\(123\) | 4.58683 | − | 9.45693i | 0.413580 | − | 0.852702i | ||||
\(124\) | 1.25549 | − | 2.17457i | 0.112746 | − | 0.195282i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −10.7780 | + | 1.56295i | −0.960184 | + | 0.139239i | ||||
\(127\) | 7.98997 | 0.708995 | 0.354497 | − | 0.935057i | \(-0.384652\pi\) | ||||
0.354497 | + | 0.935057i | \(0.384652\pi\) | |||||||
\(128\) | −3.80431 | + | 6.58926i | −0.336257 | + | 0.582414i | ||||
\(129\) | −16.8997 | + | 1.21896i | −1.48793 | + | 0.107323i | ||||
\(130\) | 0.644173 | + | 1.11574i | 0.0564977 | + | 0.0978570i | ||||
\(131\) | 1.73503 | + | 3.00516i | 0.151590 | + | 0.262562i | 0.931812 | − | 0.362941i | \(-0.118227\pi\) |
−0.780222 | + | 0.625503i | \(0.784894\pi\) | |||||||
\(132\) | −1.70276 | − | 2.51256i | −0.148206 | − | 0.218690i | ||||
\(133\) | 7.46067 | − | 12.9223i | 0.646922 | − | 1.12050i | ||||
\(134\) | 2.30363 | 0.199003 | ||||||||
\(135\) | 3.50221 | + | 3.83856i | 0.301422 | + | 0.330370i | ||||
\(136\) | 20.9823 | 1.79922 | ||||||||
\(137\) | −2.87915 | + | 4.98683i | −0.245982 | + | 0.426054i | −0.962407 | − | 0.271610i | \(-0.912444\pi\) |
0.716425 | + | 0.697664i | \(0.245777\pi\) | |||||||
\(138\) | −0.447191 | − | 0.659864i | −0.0380674 | − | 0.0561713i | ||||
\(139\) | 3.79217 | + | 6.56823i | 0.321647 | + | 0.557110i | 0.980828 | − | 0.194875i | \(-0.0624301\pi\) |
−0.659181 | + | 0.751985i | \(0.729097\pi\) | |||||||
\(140\) | 0.479250 | + | 0.830085i | 0.0405040 | + | 0.0701550i | ||||
\(141\) | −10.5815 | + | 0.763236i | −0.891127 | + | 0.0642761i | ||||
\(142\) | 3.16652 | − | 5.48458i | 0.265729 | − | 0.460256i | ||||
\(143\) | −5.15154 | −0.430794 | ||||||||
\(144\) | 5.95081 | + | 7.54827i | 0.495900 | + | 0.629022i | ||||
\(145\) | 4.83841 | 0.401808 | ||||||||
\(146\) | −3.01330 | + | 5.21919i | −0.249383 | + | 0.431943i | ||||
\(147\) | −0.710365 | + | 1.46460i | −0.0585899 | + | 0.120798i | ||||
\(148\) | 0.970970 | + | 1.68177i | 0.0798132 | + | 0.138241i | ||||
\(149\) | −3.00953 | − | 5.21267i | −0.246551 | − | 0.427038i | 0.716016 | − | 0.698084i | \(-0.245964\pi\) |
−0.962566 | + | 0.271046i | \(0.912631\pi\) | |||||||
\(150\) | −0.973820 | + | 2.00778i | −0.0795121 | + | 0.163935i | ||||
\(151\) | −4.91595 | + | 8.51467i | −0.400054 | + | 0.692914i | −0.993732 | − | 0.111789i | \(-0.964342\pi\) |
0.593678 | + | 0.804703i | \(0.297675\pi\) | |||||||
\(152\) | −15.9655 | −1.29497 | ||||||||
\(153\) | 7.73625 | − | 19.3921i | 0.625439 | − | 1.56776i | ||||
\(154\) | 18.7014 | 1.50700 | ||||||||
\(155\) | 3.69084 | − | 6.39272i | 0.296455 | − | 0.513476i | ||||
\(156\) | −0.587653 | + | 0.0423868i | −0.0470499 | + | 0.00339366i | ||||
\(157\) | 1.25443 | + | 2.17274i | 0.100115 | + | 0.173403i | 0.911732 | − | 0.410786i | \(-0.134746\pi\) |
−0.811617 | + | 0.584190i | \(0.801412\pi\) | |||||||
\(158\) | −5.71451 | − | 9.89783i | −0.454622 | − | 0.787429i | ||||
\(159\) | −3.17322 | − | 4.68233i | −0.251653 | − | 0.371333i | ||||
\(160\) | 0.951033 | − | 1.64724i | 0.0751858 | − | 0.130226i | ||||
\(161\) | −1.00655 | −0.0793272 | ||||||||
\(162\) | 11.1175 | − | 3.29361i | 0.873474 | − | 0.258771i | ||||
\(163\) | −19.8235 | −1.55269 | −0.776347 | − | 0.630306i | \(-0.782929\pi\) | ||||
−0.776347 | + | 0.630306i | \(0.782929\pi\) | |||||||
\(164\) | −1.03210 | + | 1.78766i | −0.0805938 | + | 0.139592i | ||||
\(165\) | −5.00573 | − | 7.38633i | −0.389695 | − | 0.575025i | ||||
\(166\) | −9.63569 | − | 16.6895i | −0.747874 | − | 1.29536i | ||||
\(167\) | 11.8886 | + | 20.5916i | 0.919964 | + | 1.59342i | 0.799467 | + | 0.600710i | \(0.205115\pi\) |
0.120497 | + | 0.992714i | \(0.461551\pi\) | |||||||
\(168\) | 14.6763 | − | 1.05859i | 1.13230 | − | 0.0816719i | ||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 8.96617 | 0.687674 | ||||||||
\(171\) | −5.88653 | + | 14.7555i | −0.450154 | + | 1.12838i | ||||
\(172\) | 3.32760 | 0.253727 | ||||||||
\(173\) | 2.89292 | − | 5.01068i | 0.219944 | − | 0.380955i | −0.734846 | − | 0.678234i | \(-0.762746\pi\) |
0.954791 | + | 0.297279i | \(0.0960791\pi\) | |||||||
\(174\) | 4.71175 | − | 9.71448i | 0.357197 | − | 0.736452i | ||||
\(175\) | 1.40888 | + | 2.44026i | 0.106502 | + | 0.184466i | ||||
\(176\) | −8.25268 | − | 14.2941i | −0.622069 | − | 1.07746i | ||||
\(177\) | −0.992378 | + | 2.04604i | −0.0745917 | + | 0.153790i | ||||
\(178\) | −4.15466 | + | 7.19608i | −0.311405 | + | 0.539369i | ||||
\(179\) | −20.1982 | −1.50969 | −0.754844 | − | 0.655905i | \(-0.772287\pi\) | ||||
−0.754844 | + | 0.655905i | \(0.772287\pi\) | |||||||
\(180\) | −0.631794 | − | 0.801395i | −0.0470911 | − | 0.0597325i | ||||
\(181\) | −10.0801 | −0.749249 | −0.374625 | − | 0.927177i | \(-0.622228\pi\) | ||||
−0.374625 | + | 0.927177i | \(0.622228\pi\) | |||||||
\(182\) | 1.81513 | − | 3.14390i | 0.134546 | − | 0.233041i | ||||
\(183\) | −15.8549 | + | 1.14360i | −1.17203 | + | 0.0845372i | ||||
\(184\) | 0.538492 | + | 0.932695i | 0.0396981 | + | 0.0687592i | ||||
\(185\) | 2.85443 | + | 4.94401i | 0.209862 | + | 0.363491i | ||||
\(186\) | −9.24097 | − | 13.6358i | −0.677581 | − | 0.999823i | ||||
\(187\) | −17.9259 | + | 31.0486i | −1.31087 | + | 2.27050i | ||||
\(188\) | 2.08354 | 0.151958 | ||||||||
\(189\) | 4.43285 | − | 13.9544i | 0.322443 | − | 1.01503i | ||||
\(190\) | −6.82238 | −0.494947 | ||||||||
\(191\) | 9.12892 | − | 15.8118i | 0.660545 | − | 1.14410i | −0.319927 | − | 0.947442i | \(-0.603658\pi\) |
0.980473 | − | 0.196656i | \(-0.0630082\pi\) | |||||||
\(192\) | −8.60770 | − | 12.7013i | −0.621208 | − | 0.916639i | ||||
\(193\) | 1.08415 | + | 1.87780i | 0.0780388 | + | 0.135167i | 0.902404 | − | 0.430892i | \(-0.141801\pi\) |
−0.824365 | + | 0.566059i | \(0.808468\pi\) | |||||||
\(194\) | −7.25081 | − | 12.5588i | −0.520578 | − | 0.901668i | ||||
\(195\) | −1.72756 | + | 0.124607i | −0.123713 | + | 0.00892332i | ||||
\(196\) | 0.159843 | − | 0.276856i | 0.0114173 | − | 0.0197754i | ||||
\(197\) | 14.9589 | 1.06578 | 0.532890 | − | 0.846185i | \(-0.321106\pi\) | ||||
0.532890 | + | 0.846185i | \(0.321106\pi\) | |||||||
\(198\) | −19.7048 | + | 2.85744i | −1.40036 | + | 0.203070i | ||||
\(199\) | 4.81279 | 0.341170 | 0.170585 | − | 0.985343i | \(-0.445434\pi\) | ||||
0.170585 | + | 0.985343i | \(0.445434\pi\) | |||||||
\(200\) | 1.50747 | − | 2.61102i | 0.106594 | − | 0.184627i | ||||
\(201\) | −1.35153 | + | 2.78653i | −0.0953297 | + | 0.196547i | ||||
\(202\) | −6.28613 | − | 10.8879i | −0.442290 | − | 0.766069i | ||||
\(203\) | −6.81676 | − | 11.8070i | −0.478443 | − | 0.828687i | ||||
\(204\) | −1.78940 | + | 3.68931i | −0.125283 | + | 0.258303i | ||||
\(205\) | −3.03414 | + | 5.25529i | −0.211914 | + | 0.367046i | ||||
\(206\) | 10.2266 | 0.712520 | ||||||||
\(207\) | 1.06055 | − | 0.153793i | 0.0737135 | − | 0.0106894i | ||||
\(208\) | −3.20396 | −0.222155 | ||||||||
\(209\) | 13.6399 | − | 23.6250i | 0.943490 | − | 1.63417i | ||||
\(210\) | 6.27150 | − | 0.452357i | 0.432775 | − | 0.0312156i | ||||
\(211\) | −4.80298 | − | 8.31901i | −0.330651 | − | 0.572704i | 0.651989 | − | 0.758229i | \(-0.273935\pi\) |
−0.982640 | + | 0.185524i | \(0.940602\pi\) | |||||||
\(212\) | 0.555427 | + | 0.962028i | 0.0381469 | + | 0.0660724i | ||||
\(213\) | 4.77650 | + | 7.04809i | 0.327280 | + | 0.482927i | ||||
\(214\) | −2.86718 | + | 4.96611i | −0.195997 | + | 0.339476i | ||||
\(215\) | 9.78238 | 0.667153 | ||||||||
\(216\) | −15.3020 | + | 3.35782i | −1.04117 | + | 0.228471i | ||||
\(217\) | −20.7998 | −1.41199 | ||||||||
\(218\) | 5.53265 | − | 9.58283i | 0.374718 | − | 0.649031i | ||||
\(219\) | −4.54537 | − | 6.70704i | −0.307148 | − | 0.453220i | ||||
\(220\) | 0.876182 | + | 1.51759i | 0.0590722 | + | 0.102316i | ||||
\(221\) | 3.47972 | + | 6.02705i | 0.234071 | + | 0.405423i | ||||
\(222\) | 12.7062 | − | 0.916484i | 0.852784 | − | 0.0615104i | ||||
\(223\) | 3.17548 | − | 5.50009i | 0.212646 | − | 0.368313i | −0.739896 | − | 0.672721i | \(-0.765125\pi\) |
0.952542 | + | 0.304408i | \(0.0984587\pi\) | |||||||
\(224\) | −5.35958 | −0.358102 | ||||||||
\(225\) | −1.85733 | − | 2.35592i | −0.123822 | − | 0.157061i | ||||
\(226\) | 24.7813 | 1.64843 | ||||||||
\(227\) | −2.84962 | + | 4.93569i | −0.189136 | + | 0.327593i | −0.944962 | − | 0.327179i | \(-0.893902\pi\) |
0.755826 | + | 0.654772i | \(0.227235\pi\) | |||||||
\(228\) | 1.36156 | − | 2.80720i | 0.0901714 | − | 0.185912i | ||||
\(229\) | 10.9728 | + | 19.0054i | 0.725102 | + | 1.25591i | 0.958932 | + | 0.283636i | \(0.0915407\pi\) |
−0.233830 | + | 0.972277i | \(0.575126\pi\) | |||||||
\(230\) | 0.230109 | + | 0.398560i | 0.0151729 | + | 0.0262803i | ||||
\(231\) | −10.9721 | + | 22.6217i | −0.721909 | + | 1.48840i | ||||
\(232\) | −7.29377 | + | 12.6332i | −0.478859 | + | 0.829408i | ||||
\(233\) | 25.7672 | 1.68806 | 0.844031 | − | 0.536294i | \(-0.180176\pi\) | ||||
0.844031 | + | 0.536294i | \(0.180176\pi\) | |||||||
\(234\) | −1.43215 | + | 3.58991i | −0.0936227 | + | 0.234680i | ||||
\(235\) | 6.12513 | 0.399560 | ||||||||
\(236\) | 0.223300 | − | 0.386766i | 0.0145356 | − | 0.0251763i | ||||
\(237\) | 15.3254 | − | 1.10540i | 0.995489 | − | 0.0718036i | ||||
\(238\) | −12.6323 | − | 21.8797i | −0.818829 | − | 1.41825i | ||||
\(239\) | 2.97550 | + | 5.15372i | 0.192469 | + | 0.333366i | 0.946068 | − | 0.323968i | \(-0.105017\pi\) |
−0.753599 | + | 0.657335i | \(0.771684\pi\) | |||||||
\(240\) | −3.11327 | − | 4.59387i | −0.200961 | − | 0.296533i | ||||
\(241\) | −11.6495 | + | 20.1774i | −0.750407 | + | 1.29974i | 0.197218 | + | 0.980360i | \(0.436809\pi\) |
−0.947625 | + | 0.319384i | \(0.896524\pi\) | |||||||
\(242\) | 20.0189 | 1.28686 | ||||||||
\(243\) | −2.53856 | + | 15.3804i | −0.162849 | + | 0.986651i | ||||
\(244\) | 3.12189 | 0.199858 | ||||||||
\(245\) | 0.469900 | − | 0.813891i | 0.0300208 | − | 0.0519976i | ||||
\(246\) | 7.59677 | + | 11.2096i | 0.484352 | + | 0.714699i | ||||
\(247\) | −2.64773 | − | 4.58600i | −0.168471 | − | 0.291800i | ||||
\(248\) | 11.1277 | + | 19.2737i | 0.706607 | + | 1.22388i | ||||
\(249\) | 25.8413 | − | 1.86390i | 1.63762 | − | 0.118120i | ||||
\(250\) | 0.644173 | − | 1.11574i | 0.0407411 | − | 0.0705657i | ||||
\(251\) | 16.6483 | 1.05083 | 0.525417 | − | 0.850845i | \(-0.323909\pi\) | ||||
0.525417 | + | 0.850845i | \(0.323909\pi\) | |||||||
\(252\) | −1.06549 | + | 2.67081i | −0.0671194 | + | 0.168245i | ||||
\(253\) | −1.84021 | −0.115693 | ||||||||
\(254\) | −5.14692 | + | 8.91473i | −0.322947 | + | 0.559360i | ||||
\(255\) | −5.26042 | + | 10.8457i | −0.329420 | + | 0.679184i | ||||
\(256\) | 3.95718 | + | 6.85404i | 0.247324 | + | 0.428377i | ||||
\(257\) | 3.29768 | + | 5.71175i | 0.205704 | + | 0.356289i | 0.950357 | − | 0.311163i | \(-0.100718\pi\) |
−0.744653 | + | 0.667452i | \(0.767385\pi\) | |||||||
\(258\) | 9.52628 | − | 19.6409i | 0.593081 | − | 1.22279i | ||||
\(259\) | 8.04310 | − | 13.9311i | 0.499774 | − | 0.865634i | ||||
\(260\) | 0.340163 | 0.0210960 | ||||||||
\(261\) | 8.98651 | + | 11.3989i | 0.556251 | + | 0.705574i | ||||
\(262\) | −4.47064 | −0.276197 | ||||||||
\(263\) | 8.83438 | − | 15.3016i | 0.544751 | − | 0.943536i | −0.453872 | − | 0.891067i | \(-0.649958\pi\) |
0.998623 | − | 0.0524693i | \(-0.0167092\pi\) | |||||||
\(264\) | 26.8318 | − | 1.93535i | 1.65138 | − | 0.119113i | ||||
\(265\) | 1.63283 | + | 2.82814i | 0.100304 | + | 0.173731i | ||||
\(266\) | 9.61193 | + | 16.6484i | 0.589345 | + | 1.02078i | ||||
\(267\) | −6.26704 | − | 9.24750i | −0.383537 | − | 0.565938i | ||||
\(268\) | 0.304115 | − | 0.526742i | 0.0185768 | − | 0.0321759i | ||||
\(269\) | −6.09803 | −0.371804 | −0.185902 | − | 0.982568i | \(-0.559521\pi\) | ||||
−0.185902 | + | 0.982568i | \(0.559521\pi\) | |||||||
\(270\) | −6.53887 | + | 1.43487i | −0.397943 | + | 0.0873232i | ||||
\(271\) | −19.9160 | −1.20981 | −0.604906 | − | 0.796297i | \(-0.706789\pi\) | ||||
−0.604906 | + | 0.796297i | \(0.706789\pi\) | |||||||
\(272\) | −11.1489 | + | 19.3104i | −0.676001 | + | 1.17087i | ||||
\(273\) | 2.73801 | + | 4.04014i | 0.165712 | + | 0.244520i | ||||
\(274\) | −3.70934 | − | 6.42477i | −0.224090 | − | 0.388134i | ||||
\(275\) | 2.57577 | + | 4.46137i | 0.155325 | + | 0.269031i | ||||
\(276\) | −0.209919 | + | 0.0151412i | −0.0126356 | + | 0.000911394i | ||||
\(277\) | −16.1804 | + | 28.0254i | −0.972189 | + | 1.68388i | −0.283272 | + | 0.959040i | \(0.591420\pi\) |
−0.688916 | + | 0.724841i | \(0.741913\pi\) | |||||||
\(278\) | −9.77125 | −0.586041 | ||||||||
\(279\) | 21.9158 | − | 3.17806i | 1.31207 | − | 0.190266i | ||||
\(280\) | −8.49540 | −0.507697 | ||||||||
\(281\) | 16.0058 | − | 27.7228i | 0.954825 | − | 1.65381i | 0.220057 | − | 0.975487i | \(-0.429376\pi\) |
0.734768 | − | 0.678319i | \(-0.237291\pi\) | |||||||
\(282\) | 5.96478 | − | 12.2979i | 0.355197 | − | 0.732331i | ||||
\(283\) | 14.4870 | + | 25.0921i | 0.861160 | + | 1.49157i | 0.870810 | + | 0.491620i | \(0.163595\pi\) |
−0.00965008 | + | 0.999953i | \(0.503072\pi\) | |||||||
\(284\) | −0.836059 | − | 1.44810i | −0.0496110 | − | 0.0859287i | ||||
\(285\) | 4.00266 | − | 8.25252i | 0.237097 | − | 0.488837i | ||||
\(286\) | 3.31849 | − | 5.74779i | 0.196226 | − | 0.339874i | ||||
\(287\) | 17.0990 | 1.00932 | ||||||||
\(288\) | 5.64713 | − | 0.818904i | 0.332761 | − | 0.0482544i | ||||
\(289\) | 31.4338 | 1.84905 | ||||||||
\(290\) | −3.11678 | + | 5.39842i | −0.183023 | + | 0.317006i | ||||
\(291\) | 19.4454 | − | 1.40258i | 1.13991 | − | 0.0822207i | ||||
\(292\) | 0.795603 | + | 1.37803i | 0.0465592 | + | 0.0806429i | ||||
\(293\) | −2.02909 | − | 3.51448i | −0.118541 | − | 0.205318i | 0.800649 | − | 0.599134i | \(-0.204488\pi\) |
−0.919190 | + | 0.393815i | \(0.871155\pi\) | |||||||
\(294\) | −1.17652 | − | 1.73604i | −0.0686158 | − | 0.101248i | ||||
\(295\) | 0.656449 | − | 1.13700i | 0.0382199 | − | 0.0661989i | ||||
\(296\) | −17.2119 | −1.00042 | ||||||||
\(297\) | 8.10431 | − | 25.5119i | 0.470260 | − | 1.48035i | ||||
\(298\) | 7.75465 | 0.449215 | ||||||||
\(299\) | −0.178608 | + | 0.309358i | −0.0103292 | + | 0.0178906i | ||||
\(300\) | 0.330534 | + | 0.487729i | 0.0190834 | + | 0.0281590i | ||||
\(301\) | −13.7822 | − | 23.8715i | −0.794395 | − | 1.37593i | ||||
\(302\) | −6.33345 | − | 10.9698i | −0.364449 | − | 0.631244i | ||||
\(303\) | 16.8583 | − | 1.21597i | 0.968485 | − | 0.0698558i | ||||
\(304\) | 8.48322 | − | 14.6934i | 0.486546 | − | 0.842722i | ||||
\(305\) | 9.17762 | 0.525509 | ||||||||
\(306\) | 16.6531 | + | 21.1235i | 0.951994 | + | 1.20755i | ||||
\(307\) | 10.2358 | 0.584185 | 0.292093 | − | 0.956390i | \(-0.405648\pi\) | ||||
0.292093 | + | 0.956390i | \(0.405648\pi\) | |||||||
\(308\) | 2.46888 | − | 4.27622i | 0.140677 | − | 0.243660i | ||||
\(309\) | −5.99990 | + | 12.3703i | −0.341323 | + | 0.703724i | ||||
\(310\) | 4.75508 | + | 8.23604i | 0.270070 | + | 0.467776i | ||||
\(311\) | −11.1128 | − | 19.2479i | −0.630149 | − | 1.09145i | −0.987521 | − | 0.157488i | \(-0.949660\pi\) |
0.357372 | − | 0.933962i | \(-0.383673\pi\) | |||||||
\(312\) | 2.27890 | − | 4.69854i | 0.129017 | − | 0.266002i | ||||
\(313\) | 4.81602 | − | 8.34160i | 0.272218 | − | 0.471495i | −0.697212 | − | 0.716865i | \(-0.745576\pi\) |
0.969429 | + | 0.245370i | \(0.0789096\pi\) | |||||||
\(314\) | −3.23228 | −0.182408 | ||||||||
\(315\) | −3.13228 | + | 7.85156i | −0.176484 | + | 0.442385i | ||||
\(316\) | −3.01761 | −0.169754 | ||||||||
\(317\) | −15.3523 | + | 26.5910i | −0.862273 | + | 1.49350i | 0.00745758 | + | 0.999972i | \(0.497626\pi\) |
−0.869730 | + | 0.493528i | \(0.835707\pi\) | |||||||
\(318\) | 7.26837 | − | 0.524260i | 0.407590 | − | 0.0293990i | ||||
\(319\) | −12.4627 | − | 21.5859i | −0.697775 | − | 1.20858i | ||||
\(320\) | 4.42922 | + | 7.67164i | 0.247601 | + | 0.428858i | ||||
\(321\) | −4.32496 | − | 6.38181i | −0.241396 | − | 0.356198i | ||||
\(322\) | 0.648392 | − | 1.12305i | 0.0361335 | − | 0.0625850i | ||||
\(323\) | −36.8534 | −2.05058 | ||||||||
\(324\) | 0.714573 | − | 2.97690i | 0.0396985 | − | 0.165384i | ||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 12.7697 | − | 22.1179i | 0.707251 | − | 1.22499i | ||||
\(327\) | 8.34565 | + | 12.3146i | 0.461516 | + | 0.681002i | ||||
\(328\) | −9.14777 | − | 15.8444i | −0.505101 | − | 0.874861i | ||||
\(329\) | −8.62959 | − | 14.9469i | −0.475765 | − | 0.824049i | ||||
\(330\) | 11.4658 | − | 0.827016i | 0.631171 | − | 0.0455257i | ||||
\(331\) | 1.75825 | − | 3.04538i | 0.0966424 | − | 0.167389i | −0.813651 | − | 0.581354i | \(-0.802523\pi\) |
0.910293 | + | 0.413965i | \(0.135856\pi\) | |||||||
\(332\) | −5.08823 | −0.279253 | ||||||||
\(333\) | −6.34607 | + | 15.9074i | −0.347763 | + | 0.871722i | ||||
\(334\) | −30.6331 | −1.67617 | ||||||||
\(335\) | 0.894026 | − | 1.54850i | 0.0488459 | − | 0.0846035i | ||||
\(336\) | −6.82399 | + | 14.0694i | −0.372279 | + | 0.767549i | ||||
\(337\) | 9.81302 | + | 16.9967i | 0.534549 | + | 0.925867i | 0.999185 | + | 0.0403646i | \(0.0128520\pi\) |
−0.464636 | + | 0.885502i | \(0.653815\pi\) | |||||||
\(338\) | −0.644173 | − | 1.11574i | −0.0350384 | − | 0.0606883i | ||||
\(339\) | −14.5391 | + | 29.9761i | −0.789656 | + | 1.62808i | ||||
\(340\) | 1.18367 | − | 2.05018i | 0.0641936 | − | 0.111187i | ||||
\(341\) | −38.0271 | −2.05928 | ||||||||
\(342\) | −12.6714 | − | 16.0729i | −0.685190 | − | 0.869126i | ||||
\(343\) | 17.0762 | 0.922029 | ||||||||
\(344\) | −14.7467 | + | 25.5420i | −0.795086 | + | 1.37713i | ||||
\(345\) | −0.617112 | + | 0.0445117i | −0.0332242 | + | 0.00239643i | ||||
\(346\) | 3.72708 | + | 6.45549i | 0.200369 | + | 0.347049i | ||||
\(347\) | −12.6960 | − | 21.9902i | −0.681559 | − | 1.18049i | −0.974505 | − | 0.224366i | \(-0.927969\pi\) |
0.292946 | − | 0.956129i | \(-0.405364\pi\) | |||||||
\(348\) | −1.59926 | − | 2.35983i | −0.0857295 | − | 0.126500i | ||||
\(349\) | 6.09864 | − | 10.5632i | 0.326453 | − | 0.565433i | −0.655352 | − | 0.755323i | \(-0.727480\pi\) |
0.981805 | + | 0.189890i | \(0.0608132\pi\) | |||||||
\(350\) | −3.63026 | −0.194045 | ||||||||
\(351\) | −3.50221 | − | 3.83856i | −0.186934 | − | 0.204887i | ||||
\(352\) | −9.79858 | −0.522266 | ||||||||
\(353\) | 8.97537 | − | 15.5458i | 0.477711 | − | 0.827419i | −0.521963 | − | 0.852968i | \(-0.674800\pi\) |
0.999674 | + | 0.0255491i | \(0.00813343\pi\) | |||||||
\(354\) | −1.64359 | − | 2.42524i | −0.0873558 | − | 0.128900i | ||||
\(355\) | −2.45782 | − | 4.25707i | −0.130447 | − | 0.225942i | ||||
\(356\) | 1.09696 | + | 1.89999i | 0.0581386 | + | 0.100699i | ||||
\(357\) | 33.8776 | − | 2.44356i | 1.79299 | − | 0.129327i | ||||
\(358\) | 13.0112 | − | 22.5360i | 0.687662 | − | 1.19106i | ||||
\(359\) | 20.1656 | 1.06430 | 0.532149 | − | 0.846651i | \(-0.321385\pi\) | ||||
0.532149 | + | 0.846651i | \(0.321385\pi\) | |||||||
\(360\) | 8.95120 | − | 1.29803i | 0.471770 | − | 0.0684124i | ||||
\(361\) | 9.04182 | 0.475885 | ||||||||
\(362\) | 6.49334 | − | 11.2468i | 0.341283 | − | 0.591119i | ||||
\(363\) | −11.7450 | + | 24.2153i | −0.616452 | + | 1.27097i | ||||
\(364\) | −0.479250 | − | 0.830085i | −0.0251195 | − | 0.0435083i | ||||
\(365\) | 2.33889 | + | 4.05108i | 0.122423 | + | 0.212043i | ||||
\(366\) | 8.93735 | − | 18.4266i | 0.467163 | − | 0.963176i | ||||
\(367\) | −14.9418 | + | 25.8799i | −0.779953 | + | 1.35092i | 0.152015 | + | 0.988378i | \(0.451424\pi\) |
−0.931968 | + | 0.362540i | \(0.881910\pi\) | |||||||
\(368\) | −1.14451 | −0.0596615 | ||||||||
\(369\) | −18.0164 | + | 2.61260i | −0.937898 | + | 0.136007i | ||||
\(370\) | −7.35498 | −0.382367 | ||||||||
\(371\) | 4.60092 | − | 7.96903i | 0.238868 | − | 0.413732i | ||||
\(372\) | −4.33786 | + | 0.312886i | −0.224908 | + | 0.0162224i | ||||
\(373\) | 1.82808 | + | 3.16632i | 0.0946542 | + | 0.163946i | 0.909464 | − | 0.415782i | \(-0.136492\pi\) |
−0.814810 | + | 0.579728i | \(0.803159\pi\) | |||||||
\(374\) | −23.0948 | − | 40.0014i | −1.19420 | − | 2.06842i | ||||
\(375\) | 0.971694 | + | 1.43381i | 0.0501781 | + | 0.0740416i | ||||
\(376\) | −9.23346 | + | 15.9928i | −0.476179 | + | 0.824766i | ||||
\(377\) | −4.83841 | −0.249191 | ||||||||
\(378\) | 12.7139 | + | 13.9349i | 0.653934 | + | 0.716736i | ||||
\(379\) | 24.0635 | 1.23606 | 0.618028 | − | 0.786156i | \(-0.287932\pi\) | ||||
0.618028 | + | 0.786156i | \(0.287932\pi\) | |||||||
\(380\) | −0.900658 | + | 1.55999i | −0.0462028 | + | 0.0800256i | ||||
\(381\) | −7.76381 | − | 11.4561i | −0.397752 | − | 0.586913i | ||||
\(382\) | 11.7612 | + | 20.3710i | 0.601756 | + | 1.04227i | ||||
\(383\) | 14.8405 | + | 25.7045i | 0.758314 | + | 1.31344i | 0.943710 | + | 0.330775i | \(0.107310\pi\) |
−0.185396 | + | 0.982664i | \(0.559357\pi\) | |||||||
\(384\) | 13.1444 | − | 0.948089i | 0.670771 | − | 0.0483820i | ||||
\(385\) | 7.25792 | − | 12.5711i | 0.369898 | − | 0.640682i | ||||
\(386\) | −2.79352 | −0.142187 | ||||||||
\(387\) | 18.1691 | + | 23.0465i | 0.923586 | + | 1.17152i | ||||
\(388\) | −3.82887 | −0.194382 | ||||||||
\(389\) | −2.84354 | + | 4.92516i | −0.144173 | + | 0.249715i | −0.929064 | − | 0.369919i | \(-0.879386\pi\) |
0.784891 | + | 0.619634i | \(0.212719\pi\) | |||||||
\(390\) | 0.973820 | − | 2.00778i | 0.0493113 | − | 0.101668i | ||||
\(391\) | 1.24301 | + | 2.15296i | 0.0628617 | + | 0.108880i | ||||
\(392\) | 1.41672 | + | 2.45383i | 0.0715552 | + | 0.123937i | ||||
\(393\) | 2.62291 | − | 5.40780i | 0.132308 | − | 0.272788i | ||||
\(394\) | −9.63614 | + | 16.6903i | −0.485462 | + | 0.840845i | ||||
\(395\) | −8.87108 | −0.446353 | ||||||||
\(396\) | −1.94796 | + | 4.88288i | −0.0978888 | + | 0.245374i | ||||
\(397\) | −1.64080 | −0.0823496 | −0.0411748 | − | 0.999152i | \(-0.513110\pi\) | ||||
−0.0411748 | + | 0.999152i | \(0.513110\pi\) | |||||||
\(398\) | −3.10027 | + | 5.36983i | −0.155403 | + | 0.269165i | ||||
\(399\) | −25.7776 | + | 1.85931i | −1.29049 | + | 0.0930818i | ||||
\(400\) | 1.60198 | + | 2.77471i | 0.0800991 | + | 0.138736i | ||||
\(401\) | 6.65233 | + | 11.5222i | 0.332201 | + | 0.575390i | 0.982943 | − | 0.183909i | \(-0.0588753\pi\) |
−0.650742 | + | 0.759299i | \(0.725542\pi\) | |||||||
\(402\) | −2.23843 | − | 3.30297i | −0.111643 | − | 0.164737i | ||||
\(403\) | −3.69084 | + | 6.39272i | −0.183854 | + | 0.318444i | ||||
\(404\) | −3.31946 | −0.165149 | ||||||||
\(405\) | 2.10068 | − | 8.75141i | 0.104384 | − | 0.434861i | ||||
\(406\) | 17.5647 | 0.871721 | ||||||||
\(407\) | 14.7047 | − | 25.4693i | 0.728885 | − | 1.26247i | ||||
\(408\) | −20.3884 | − | 30.0846i | −1.00938 | − | 1.48941i | ||||
\(409\) | −5.27938 | − | 9.14416i | −0.261049 | − | 0.452150i | 0.705472 | − | 0.708738i | \(-0.250735\pi\) |
−0.966521 | + | 0.256588i | \(0.917402\pi\) | |||||||
\(410\) | −3.90903 | − | 6.77064i | −0.193053 | − | 0.334378i | ||||
\(411\) | 9.94782 | − | 0.717526i | 0.490690 | − | 0.0353930i | ||||
\(412\) | 1.35007 | − | 2.33838i | 0.0665130 | − | 0.115204i | ||||
\(413\) | −3.69944 | −0.182037 | ||||||||
\(414\) | −0.511587 | + | 1.28237i | −0.0251431 | + | 0.0630252i | ||||
\(415\) | −14.9582 | −0.734270 | ||||||||
\(416\) | −0.951033 | + | 1.64724i | −0.0466282 | + | 0.0807625i | ||||
\(417\) | 5.73276 | − | 11.8196i | 0.280734 | − | 0.578806i | ||||
\(418\) | 17.5729 | + | 30.4371i | 0.859518 | + | 1.48873i | ||||
\(419\) | −10.2745 | − | 17.7960i | −0.501944 | − | 0.869393i | −0.999997 | − | 0.00224654i | \(-0.999285\pi\) |
0.498053 | − | 0.867146i | \(-0.334048\pi\) | |||||||
\(420\) | 0.724499 | − | 1.49374i | 0.0353519 | − | 0.0728871i | ||||
\(421\) | 18.1358 | − | 31.4121i | 0.883885 | − | 1.53093i | 0.0368980 | − | 0.999319i | \(-0.488252\pi\) |
0.846987 | − | 0.531614i | \(-0.178414\pi\) | |||||||
\(422\) | 12.3758 | 0.602445 | ||||||||
\(423\) | 11.3764 | + | 14.4303i | 0.553138 | + | 0.701625i | ||||
\(424\) | −9.84576 | −0.478152 | ||||||||
\(425\) | 3.47972 | − | 6.02705i | 0.168791 | − | 0.292355i | ||||
\(426\) | −10.9407 | + | 0.789144i | −0.530080 | + | 0.0382341i | ||||
\(427\) | −12.9302 | − | 22.3957i | −0.625736 | − | 1.08381i | ||||
\(428\) | 0.757024 | + | 1.31120i | 0.0365921 | + | 0.0633794i | ||||
\(429\) | 5.00573 | + | 7.38633i | 0.241679 | + | 0.356616i | ||||
\(430\) | −6.30155 | + | 10.9146i | −0.303888 | + | 0.526349i | ||||
\(431\) | 15.4318 | 0.743323 | 0.371661 | − | 0.928368i | \(-0.378788\pi\) | ||||
0.371661 | + | 0.928368i | \(0.378788\pi\) | |||||||
\(432\) | 5.04041 | − | 15.8669i | 0.242507 | − | 0.763398i | ||||
\(433\) | −23.3484 | −1.12205 | −0.561027 | − | 0.827797i | \(-0.689594\pi\) | ||||
−0.561027 | + | 0.827797i | \(0.689594\pi\) | |||||||
\(434\) | 13.3987 | − | 23.2072i | 0.643158 | − | 1.11398i | ||||
\(435\) | −4.70146 | − | 6.93736i | −0.225418 | − | 0.332621i | ||||
\(436\) | −1.46079 | − | 2.53016i | −0.0699591 | − | 0.121173i | ||||
\(437\) | −0.945809 | − | 1.63819i | −0.0452442 | − | 0.0783652i | ||||
\(438\) | 10.4113 | − | 0.750959i | 0.497473 | − | 0.0358822i | ||||
\(439\) | −6.22486 | + | 10.7818i | −0.297096 | + | 0.514586i | −0.975470 | − | 0.220131i | \(-0.929352\pi\) |
0.678374 | + | 0.734717i | \(0.262685\pi\) | |||||||
\(440\) | −15.5316 | −0.740440 | ||||||||
\(441\) | 2.79022 | − | 0.404616i | 0.132867 | − | 0.0192674i | ||||
\(442\) | −8.96617 | −0.426477 | ||||||||
\(443\) | 3.63184 | − | 6.29053i | 0.172554 | − | 0.298872i | −0.766758 | − | 0.641936i | \(-0.778131\pi\) |
0.939312 | + | 0.343064i | \(0.111465\pi\) | |||||||
\(444\) | 1.46785 | − | 3.02635i | 0.0696611 | − | 0.143624i | ||||
\(445\) | 3.22480 | + | 5.58552i | 0.152870 | + | 0.264779i | ||||
\(446\) | 4.09111 | + | 7.08602i | 0.193720 | + | 0.335533i | ||||
\(447\) | −4.54962 | + | 9.38022i | −0.215190 | + | 0.443669i | ||||
\(448\) | 12.4805 | − | 21.6169i | 0.589649 | − | 1.02130i | ||||
\(449\) | −14.7385 | −0.695555 | −0.347777 | − | 0.937577i | \(-0.613064\pi\) | ||||
−0.347777 | + | 0.937577i | \(0.613064\pi\) | |||||||
\(450\) | 3.82503 | − | 0.554677i | 0.180314 | − | 0.0261477i | ||||
\(451\) | 31.2611 | 1.47203 | ||||||||
\(452\) | 3.27152 | − | 5.66643i | 0.153879 | − | 0.266526i | ||||
\(453\) | 16.9852 | − | 1.22513i | 0.798035 | − | 0.0575615i | ||||
\(454\) | −3.67130 | − | 6.35888i | −0.172303 | − | 0.298437i | ||||
\(455\) | −1.40888 | − | 2.44026i | −0.0660494 | − | 0.114401i | ||||
\(456\) | 15.5136 | + | 22.8915i | 0.726489 | + | 1.07199i | ||||
\(457\) | −3.70139 | + | 6.41099i | −0.173143 | + | 0.299893i | −0.939517 | − | 0.342502i | \(-0.888726\pi\) |
0.766374 | + | 0.642395i | \(0.222059\pi\) | |||||||
\(458\) | −28.2735 | −1.32113 | ||||||||
\(459\) | −35.3219 | + | 7.75091i | −1.64868 | + | 0.361782i | ||||
\(460\) | 0.121511 | 0.00566550 | ||||||||
\(461\) | 1.52205 | − | 2.63626i | 0.0708888 | − | 0.122783i | −0.828402 | − | 0.560134i | \(-0.810750\pi\) |
0.899291 | + | 0.437351i | \(0.144083\pi\) | |||||||
\(462\) | −18.1721 | − | 26.8143i | −0.845442 | − | 1.24751i | ||||
\(463\) | −6.99042 | − | 12.1078i | −0.324872 | − | 0.562695i | 0.656614 | − | 0.754227i | \(-0.271988\pi\) |
−0.981487 | + | 0.191531i | \(0.938655\pi\) | |||||||
\(464\) | −7.75105 | − | 13.4252i | −0.359833 | − | 0.623250i | ||||
\(465\) | −12.7523 | + | 0.919811i | −0.591374 | + | 0.0426552i | ||||
\(466\) | −16.5985 | + | 28.7495i | −0.768911 | + | 1.33179i | ||||
\(467\) | 30.6445 | 1.41806 | 0.709030 | − | 0.705178i | \(-0.249133\pi\) | ||||
0.709030 | + | 0.705178i | \(0.249133\pi\) | |||||||
\(468\) | 0.631794 | + | 0.801395i | 0.0292047 | + | 0.0370445i | ||||
\(469\) | −5.03831 | −0.232648 | ||||||||
\(470\) | −3.94565 | + | 6.83406i | −0.181999 | + | 0.315232i | ||||
\(471\) | 1.89637 | − | 3.90985i | 0.0873801 | − | 0.180157i | ||||
\(472\) | 1.97915 | + | 3.42800i | 0.0910980 | + | 0.157786i | ||||
\(473\) | −25.1972 | − | 43.6428i | −1.15857 | − | 2.00670i | ||||
\(474\) | −8.63884 | + | 17.8112i | −0.396795 | + | 0.818095i | ||||
\(475\) | −2.64773 | + | 4.58600i | −0.121486 | + | 0.210420i | ||||
\(476\) | −6.67062 | −0.305747 | ||||||||
\(477\) | −3.63017 | + | 9.09958i | −0.166214 | + | 0.416641i | ||||
\(478\) | −7.66695 | −0.350678 | ||||||||
\(479\) | 1.48202 | − | 2.56693i | 0.0677152 | − | 0.117286i | −0.830180 | − | 0.557495i | \(-0.811762\pi\) |
0.897895 | + | 0.440209i | \(0.145096\pi\) | |||||||
\(480\) | −3.28594 | + | 0.237011i | −0.149982 | + | 0.0108180i | ||||
\(481\) | −2.85443 | − | 4.94401i | −0.130151 | − | 0.225428i | ||||
\(482\) | −15.0085 | − | 25.9955i | −0.683620 | − | 1.18406i | ||||
\(483\) | 0.978058 | + | 1.44320i | 0.0445032 | + | 0.0656679i | ||||
\(484\) | 2.64280 | − | 4.57746i | 0.120127 | − | 0.208066i | ||||
\(485\) | −11.2560 | −0.511109 | ||||||||
\(486\) | −15.5252 | − | 12.7400i | −0.704239 | − | 0.577898i | ||||
\(487\) | −17.5341 | −0.794546 | −0.397273 | − | 0.917700i | \(-0.630043\pi\) | ||||
−0.397273 | + | 0.917700i | \(0.630043\pi\) | |||||||
\(488\) | −13.8350 | + | 23.9629i | −0.626281 | + | 1.08475i | ||||
\(489\) | 19.2624 | + | 28.4231i | 0.871074 | + | 1.28534i | ||||
\(490\) | 0.605394 | + | 1.04857i | 0.0273489 | + | 0.0473697i | ||||
\(491\) | 10.5572 | + | 18.2856i | 0.476439 | + | 0.825216i | 0.999636 | − | 0.0269956i | \(-0.00859399\pi\) |
−0.523197 | + | 0.852212i | \(0.675261\pi\) | |||||||
\(492\) | 3.56605 | − | 0.257215i | 0.160770 | − | 0.0115962i | ||||
\(493\) | −16.8363 | + | 29.1614i | −0.758270 | + | 1.31336i | ||||
\(494\) | 6.82238 | 0.306953 | ||||||||
\(495\) | −5.72656 | + | 14.3545i | −0.257390 | + | 0.645188i | ||||
\(496\) | −23.6506 | −1.06194 | ||||||||
\(497\) | −6.92556 | + | 11.9954i | −0.310654 | + | 0.538068i | ||||
\(498\) | −14.5666 | + | 30.0328i | −0.652746 | + | 1.34580i | ||||
\(499\) | −16.5523 | − | 28.6694i | −0.740981 | − | 1.28342i | −0.952049 | − | 0.305945i | \(-0.901028\pi\) |
0.211068 | − | 0.977471i | \(-0.432306\pi\) | |||||||
\(500\) | −0.170081 | − | 0.294590i | −0.00760627 | − | 0.0131745i | ||||
\(501\) | 17.9724 | − | 37.0546i | 0.802946 | − | 1.65548i | ||||
\(502\) | −10.7244 | + | 18.5752i | −0.478654 | + | 0.829053i | ||||
\(503\) | 20.4002 | 0.909601 | 0.454800 | − | 0.890593i | \(-0.349711\pi\) | ||||
0.454800 | + | 0.890593i | \(0.349711\pi\) | |||||||
\(504\) | −15.7787 | − | 20.0144i | −0.702840 | − | 0.891514i | ||||
\(505\) | −9.75844 | −0.434245 | ||||||||
\(506\) | 1.18541 | − | 2.05320i | 0.0526981 | − | 0.0912758i | ||||
\(507\) | 1.72756 | − | 0.124607i | 0.0767238 | − | 0.00553401i | ||||
\(508\) | 1.35895 | + | 2.35376i | 0.0602934 | + | 0.104431i | ||||
\(509\) | 15.9675 | + | 27.6564i | 0.707745 | + | 1.22585i | 0.965692 | + | 0.259691i | \(0.0836207\pi\) |
−0.257947 | + | 0.966159i | \(0.583046\pi\) | |||||||
\(510\) | −8.71238 | − | 12.8558i | −0.385791 | − | 0.569263i | ||||
\(511\) | 6.59044 | − | 11.4150i | 0.291544 | − | 0.504969i | ||||
\(512\) | −25.4137 | −1.12314 | ||||||||
\(513\) | 26.8765 | − | 5.89769i | 1.18663 | − | 0.260389i | ||||
\(514\) | −8.49711 | −0.374791 | ||||||||
\(515\) | 3.96888 | − | 6.87431i | 0.174890 | − | 0.302918i | ||||
\(516\) | −3.23341 | − | 4.77115i | −0.142343 | − | 0.210038i | ||||
\(517\) | −15.7769 | − | 27.3265i | −0.693869 | − | 1.20182i | ||||
\(518\) | 10.3623 | + | 17.9480i | 0.455294 | + | 0.788591i | ||||
\(519\) | −9.99539 | + | 0.720957i | −0.438749 | + | 0.0316465i | ||||
\(520\) | −1.50747 | + | 2.61102i | −0.0661070 | + | 0.114501i | ||||
\(521\) | −20.4121 | −0.894270 | −0.447135 | − | 0.894467i | \(-0.647556\pi\) | ||||
−0.447135 | + | 0.894467i | \(0.647556\pi\) | |||||||
\(522\) | −18.5071 | + | 2.68376i | −0.810033 | + | 0.117465i | ||||
\(523\) | 16.5405 | 0.723264 | 0.361632 | − | 0.932321i | \(-0.382220\pi\) | ||||
0.361632 | + | 0.932321i | \(0.382220\pi\) | |||||||
\(524\) | −0.590193 | + | 1.02224i | −0.0257827 | + | 0.0446570i | ||||
\(525\) | 2.12986 | − | 4.39125i | 0.0929547 | − | 0.191650i | ||||
\(526\) | 11.3817 | + | 19.7138i | 0.496267 | + | 0.859560i | ||||
\(527\) | 25.6862 | + | 44.4898i | 1.11891 | + | 1.93800i | ||||
\(528\) | −12.4759 | + | 25.7222i | −0.542943 | + | 1.11942i | ||||
\(529\) | 11.4362 | − | 19.8081i | 0.497226 | − | 0.861221i | ||||
\(530\) | −4.20729 | −0.182753 | ||||||||
\(531\) | 3.89792 | − | 0.565247i | 0.169155 | − | 0.0245296i | ||||
\(532\) | 5.07569 | 0.220059 | ||||||||
\(533\) | 3.03414 | − | 5.25529i | 0.131423 | − | 0.227632i | ||||
\(534\) | 14.3549 | − | 1.03540i | 0.621196 | − | 0.0448062i | ||||
\(535\) | 2.22547 | + | 3.85464i | 0.0962157 | + | 0.166650i | ||||
\(536\) | 2.69544 | + | 4.66863i | 0.116425 | + | 0.201654i | ||||
\(537\) | 19.6265 | + | 28.9604i | 0.846947 | + | 1.24973i | ||||
\(538\) | 3.92819 | − | 6.80382i | 0.169356 | − | 0.293334i | ||||
\(539\) | −4.84142 | −0.208535 | ||||||||
\(540\) | −0.535138 | + | 1.68458i | −0.0230287 | + | 0.0724929i | ||||
\(541\) | 13.3791 | 0.575211 | 0.287606 | − | 0.957749i | \(-0.407141\pi\) | ||||
0.287606 | + | 0.957749i | \(0.407141\pi\) | |||||||
\(542\) | 12.8294 | − | 22.2211i | 0.551069 | − | 0.954479i | ||||
\(543\) | 9.79480 | + | 14.4530i | 0.420335 | + | 0.620236i | ||||
\(544\) | 6.61866 | + | 11.4639i | 0.283773 | + | 0.491509i | ||||
\(545\) | −4.29438 | − | 7.43809i | −0.183951 | − | 0.318613i | ||||
\(546\) | −6.27150 | + | 0.452357i | −0.268395 | + | 0.0193591i | ||||
\(547\) | −13.9133 | + | 24.0986i | −0.594892 | + | 1.03038i | 0.398671 | + | 0.917094i | \(0.369472\pi\) |
−0.993562 | + | 0.113288i | \(0.963862\pi\) | |||||||
\(548\) | −1.95876 | −0.0836741 | ||||||||
\(549\) | 17.0458 | + | 21.6217i | 0.727498 | + | 0.922791i | ||||
\(550\) | −6.63698 | −0.283002 | ||||||||
\(551\) | 12.8108 | − | 22.1889i | 0.545758 | − | 0.945281i | ||||
\(552\) | 0.814058 | − | 1.67839i | 0.0346486 | − | 0.0714370i | ||||
\(553\) | 12.4983 | + | 21.6477i | 0.531482 | + | 0.920554i | ||||
\(554\) | −20.8460 | − | 36.1064i | −0.885663 | − | 1.53401i | ||||
\(555\) | 4.31514 | − | 8.89677i | 0.183168 | − | 0.377647i | ||||
\(556\) | −1.28995 | + | 2.23427i | −0.0547063 | + | 0.0947540i | ||||
\(557\) | −6.61513 | −0.280292 | −0.140146 | − | 0.990131i | \(-0.544757\pi\) | ||||
−0.140146 | + | 0.990131i | \(0.544757\pi\) | |||||||
\(558\) | −10.5717 | + | 26.4996i | −0.447535 | + | 1.12182i | ||||
\(559\) | −9.78238 | −0.413751 | ||||||||
\(560\) | 4.51401 | − | 7.81849i | 0.190752 | − | 0.330392i | ||||
\(561\) | 61.9363 | − | 4.46740i | 2.61495 | − | 0.188614i | ||||
\(562\) | 20.6210 | + | 35.7166i | 0.869844 | + | 1.50661i | ||||
\(563\) | −8.40891 | − | 14.5647i | −0.354393 | − | 0.613827i | 0.632621 | − | 0.774462i | \(-0.281979\pi\) |
−0.987014 | + | 0.160634i | \(0.948646\pi\) | |||||||
\(564\) | −2.02457 | − | 2.98740i | −0.0852496 | − | 0.125792i | ||||
\(565\) | 9.61749 | − | 16.6580i | 0.404611 | − | 0.700807i | ||||
\(566\) | −37.3284 | −1.56903 | ||||||||
\(567\) | −24.3153 | + | 7.20351i | −1.02115 | + | 0.302519i | ||||
\(568\) | 14.8204 | 0.621848 | ||||||||
\(569\) | 14.8185 | − | 25.6664i | 0.621223 | − | 1.07599i | −0.368035 | − | 0.929812i | \(-0.619969\pi\) |
0.989258 | − | 0.146178i | \(-0.0466972\pi\) | |||||||
\(570\) | 6.62927 | + | 9.78199i | 0.277669 | + | 0.409723i | ||||
\(571\) | −12.4637 | − | 21.5878i | −0.521590 | − | 0.903421i | −0.999685 | − | 0.0251123i | \(-0.992006\pi\) |
0.478094 | − | 0.878308i | \(-0.341328\pi\) | |||||||
\(572\) | −0.876182 | − | 1.51759i | −0.0366350 | − | 0.0634537i | ||||
\(573\) | −31.5416 | + | 2.27506i | −1.31767 | + | 0.0950420i | ||||
\(574\) | −11.0147 | + | 19.0781i | −0.459746 | + | 0.796303i | ||||
\(575\) | 0.357215 | 0.0148969 | ||||||||
\(576\) | −9.84723 | + | 24.6836i | −0.410301 | + | 1.02848i | ||||
\(577\) | 25.6134 | 1.06630 | 0.533151 | − | 0.846020i | \(-0.321008\pi\) | ||||
0.533151 | + | 0.846020i | \(0.321008\pi\) | |||||||
\(578\) | −20.2488 | + | 35.0720i | −0.842239 | + | 1.45880i | ||||
\(579\) | 1.63895 | − | 3.37912i | 0.0681124 | − | 0.140431i | ||||
\(580\) | 0.822924 | + | 1.42535i | 0.0341701 | + | 0.0591843i | ||||
\(581\) | 21.0744 | + | 36.5019i | 0.874312 | + | 1.51435i | ||||
\(582\) | −10.9613 | + | 22.5996i | −0.454361 | + | 0.936783i | ||||
\(583\) | 8.41158 | − | 14.5693i | 0.348372 | − | 0.603398i | ||||
\(584\) | −14.1032 | −0.583596 | ||||||||
\(585\) | 1.85733 | + | 2.35592i | 0.0767910 | + | 0.0974051i | ||||
\(586\) | 5.22834 | 0.215981 | ||||||||
\(587\) | −13.1566 | + | 22.7878i | −0.543029 | + | 0.940554i | 0.455699 | + | 0.890134i | \(0.349389\pi\) |
−0.998728 | + | 0.0504202i | \(0.983944\pi\) | |||||||
\(588\) | −0.552276 | + | 0.0398351i | −0.0227755 | + | 0.00164277i | ||||
\(589\) | −19.5447 | − | 33.8524i | −0.805324 | − | 1.39486i | ||||
\(590\) | 0.845734 | + | 1.46485i | 0.0348183 | + | 0.0603071i | ||||
\(591\) | −14.5355 | − | 21.4483i | −0.597911 | − | 0.882263i | ||||
\(592\) | 9.14548 | − | 15.8404i | 0.375877 | − | 0.651038i | ||||
\(593\) | −28.9470 | −1.18871 | −0.594356 | − | 0.804202i | \(-0.702593\pi\) | ||||
−0.594356 | + | 0.804202i | \(0.702593\pi\) | |||||||
\(594\) | 23.2441 | + | 25.4764i | 0.953717 | + | 1.04531i | ||||
\(595\) | −19.6101 | −0.803934 | ||||||||
\(596\) | 1.02373 | − | 1.77316i | 0.0419337 | − | 0.0726313i | ||||
\(597\) | −4.67656 | − | 6.90063i | −0.191399 | − | 0.282424i | ||||
\(598\) | −0.230109 | − | 0.398560i | −0.00940984 | − | 0.0162983i | ||||
\(599\) | 17.8935 | + | 30.9925i | 0.731110 | + | 1.26632i | 0.956409 | + | 0.292031i | \(0.0943309\pi\) |
−0.225299 | + | 0.974290i | \(0.572336\pi\) | |||||||
\(600\) | −5.20850 | + | 0.375684i | −0.212636 | + | 0.0153372i | ||||
\(601\) | −23.1849 | + | 40.1574i | −0.945731 | + | 1.63805i | −0.191450 | + | 0.981502i | \(0.561319\pi\) |
−0.754281 | + | 0.656552i | \(0.772014\pi\) | |||||||
\(602\) | 35.5126 | 1.44738 | ||||||||
\(603\) | 5.30863 | − | 0.769817i | 0.216184 | − | 0.0313494i | ||||
\(604\) | −3.34445 | −0.136084 | ||||||||
\(605\) | 7.76921 | − | 13.4567i | 0.315863 | − | 0.547091i | ||||
\(606\) | −9.50297 | + | 19.5928i | −0.386032 | + | 0.795904i | ||||
\(607\) | −1.97001 | − | 3.41216i | −0.0799603 | − | 0.138495i | 0.823272 | − | 0.567647i | \(-0.192146\pi\) |
−0.903233 | + | 0.429151i | \(0.858813\pi\) | |||||||
\(608\) | −5.03615 | − | 8.72287i | −0.204243 | − | 0.353759i | ||||
\(609\) | −10.3051 | + | 21.2467i | −0.417585 | + | 0.860960i | ||||
\(610\) | −5.91198 | + | 10.2398i | −0.239369 | + | 0.414599i | ||||
\(611\) | −6.12513 | −0.247796 | ||||||||
\(612\) | 7.02851 | − | 1.01922i | 0.284111 | − | 0.0411996i | ||||
\(613\) | −36.4623 | −1.47270 | −0.736349 | − | 0.676602i | \(-0.763452\pi\) | ||||
−0.736349 | + | 0.676602i | \(0.763452\pi\) | |||||||
\(614\) | −6.59360 | + | 11.4205i | −0.266096 | + | 0.460892i | ||||
\(615\) | 10.4834 | − | 0.756153i | 0.422730 | − | 0.0304910i | ||||
\(616\) | 21.8822 | + | 37.9011i | 0.881659 | + | 1.52708i | ||||
\(617\) | −6.07505 | − | 10.5223i | −0.244572 | − | 0.423612i | 0.717439 | − | 0.696621i | \(-0.245314\pi\) |
−0.962011 | + | 0.273010i | \(0.911981\pi\) | |||||||
\(618\) | −9.93712 | − | 14.6630i | −0.399730 | − | 0.589832i | ||||
\(619\) | −4.37235 | + | 7.57314i | −0.175740 | + | 0.304390i | −0.940417 | − | 0.340023i | \(-0.889565\pi\) |
0.764677 | + | 0.644413i | \(0.222898\pi\) | |||||||
\(620\) | 2.51097 | 0.100843 | ||||||||
\(621\) | −1.25104 | − | 1.37119i | −0.0502027 | − | 0.0550240i | ||||
\(622\) | 28.6343 | 1.14813 | ||||||||
\(623\) | 9.08673 | − | 15.7387i | 0.364052 | − | 0.630557i | ||||
\(624\) | 3.11327 | + | 4.59387i | 0.124631 | + | 0.183902i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 6.20471 | + | 10.7469i | 0.247990 | + | 0.429531i | ||||
\(627\) | −47.1275 | + | 3.39926i | −1.88209 | + | 0.135753i | ||||
\(628\) | −0.426711 | + | 0.739085i | −0.0170276 | + | 0.0294927i | ||||
\(629\) | −39.7304 | −1.58415 | ||||||||
\(630\) | −6.74257 | − | 8.55258i | −0.268631 | − | 0.340743i | ||||
\(631\) | 8.53562 | 0.339798 | 0.169899 | − | 0.985462i | \(-0.445656\pi\) | ||||
0.169899 | + | 0.985462i | \(0.445656\pi\) | |||||||
\(632\) | 13.3729 | − | 23.1625i | 0.531945 | − | 0.921356i | ||||
\(633\) | −7.26085 | + | 14.9701i | −0.288593 | + | 0.595008i | ||||
\(634\) | −19.7791 | − | 34.2584i | −0.785529 | − | 1.36058i | ||||
\(635\) | 3.99498 | + | 6.91951i | 0.158536 | + | 0.274592i | ||||
\(636\) | 0.839660 | − | 1.73117i | 0.0332947 | − | 0.0686455i | ||||
\(637\) | −0.469900 | + | 0.813891i | −0.0186181 | + | 0.0322475i | ||||
\(638\) | 32.1124 | 1.27134 | ||||||||
\(639\) | 5.46432 | − | 13.6972i | 0.216165 | − | 0.541852i | ||||
\(640\) | −7.60862 | −0.300757 | ||||||||
\(641\) | −9.66780 | + | 16.7451i | −0.381855 | + | 0.661393i | −0.991327 | − | 0.131415i | \(-0.958048\pi\) |
0.609472 | + | 0.792807i | \(0.291381\pi\) | |||||||
\(642\) | 9.90648 | − | 0.714544i | 0.390977 | − | 0.0282008i | ||||
\(643\) | 19.7501 | + | 34.2082i | 0.778868 | + | 1.34904i | 0.932594 | + | 0.360926i | \(0.117539\pi\) |
−0.153726 | + | 0.988113i | \(0.549127\pi\) | |||||||
\(644\) | −0.171195 | − | 0.296519i | −0.00674604 | − | 0.0116845i | ||||
\(645\) | −9.50549 | − | 14.0261i | −0.374278 | − | 0.552276i | ||||
\(646\) | 23.7400 | − | 41.1188i | 0.934036 | − | 1.61780i | ||||
\(647\) | 35.0901 | 1.37954 | 0.689768 | − | 0.724031i | \(-0.257713\pi\) | ||||
0.689768 | + | 0.724031i | \(0.257713\pi\) | |||||||
\(648\) | 19.6834 | + | 18.6774i | 0.773235 | + | 0.733717i | ||||
\(649\) | −6.76345 | −0.265489 | ||||||||
\(650\) | −0.644173 | + | 1.11574i | −0.0252666 | + | 0.0437630i | ||||
\(651\) | 20.2111 | + | 29.8230i | 0.792135 | + | 1.16886i | ||||
\(652\) | −3.37160 | − | 5.83979i | −0.132042 | − | 0.228704i | ||||
\(653\) | 5.16552 | + | 8.94694i | 0.202142 | + | 0.350121i | 0.949218 | − | 0.314618i | \(-0.101876\pi\) |
−0.747076 | + | 0.664738i | \(0.768543\pi\) | |||||||
\(654\) | −19.1160 | + | 1.37882i | −0.747495 | + | 0.0539160i | ||||
\(655\) | −1.73503 | + | 3.00516i | −0.0677933 | + | 0.117421i | ||||
\(656\) | 19.4426 | 0.759105 | ||||||||
\(657\) | −5.19991 | + | 13.0344i | −0.202868 | + | 0.508520i | ||||
\(658\) | 22.2358 | 0.866842 | ||||||||
\(659\) | −16.6368 | + | 28.8158i | −0.648078 | + | 1.12250i | 0.335504 | + | 0.942039i | \(0.391094\pi\) |
−0.983581 | + | 0.180465i | \(0.942240\pi\) | |||||||
\(660\) | 1.32456 | − | 2.73091i | 0.0515583 | − | 0.106301i | ||||
\(661\) | 10.6134 | + | 18.3829i | 0.412812 | + | 0.715011i | 0.995196 | − | 0.0979025i | \(-0.0312133\pi\) |
−0.582384 | + | 0.812914i | \(0.697880\pi\) | |||||||
\(662\) | 2.26524 | + | 3.92351i | 0.0880411 | + | 0.152492i | ||||
\(663\) | 5.26042 | − | 10.8457i | 0.204298 | − | 0.421212i | ||||
\(664\) | 22.5491 | − | 39.0561i | 0.875074 | − | 1.51567i | ||||
\(665\) | 14.9213 | 0.578625 | ||||||||
\(666\) | −13.6606 | − | 17.3277i | −0.529337 | − | 0.671435i | ||||
\(667\) | −1.72836 | −0.0669222 | ||||||||
\(668\) | −4.04404 | + | 7.00449i | −0.156469 | + | 0.271012i | ||||
\(669\) | −10.9717 | + | 0.791375i | −0.424189 | + | 0.0305963i | ||||
\(670\) | 1.15182 | + | 1.99500i | 0.0444985 | + | 0.0770737i | ||||
\(671\) | −23.6395 | − | 40.9447i | −0.912591 | − | 1.58065i | ||||
\(672\) | 5.20787 | + | 7.68461i | 0.200898 | + | 0.296440i | ||||
\(673\) | 0.618753 | − | 1.07171i | 0.0238512 | − | 0.0413115i | −0.853853 | − | 0.520513i | \(-0.825741\pi\) |
0.877705 | + | 0.479202i | \(0.159074\pi\) | |||||||
\(674\) | −25.2851 | −0.973947 | ||||||||
\(675\) | −1.57318 | + | 4.95228i | −0.0605518 | + | 0.190613i | ||||
\(676\) | −0.340163 | −0.0130832 | ||||||||
\(677\) | −11.3996 | + | 19.7446i | −0.438121 | + | 0.758848i | −0.997545 | − | 0.0700341i | \(-0.977689\pi\) |
0.559424 | + | 0.828882i | \(0.311023\pi\) | |||||||
\(678\) | −24.0799 | − | 35.5317i | −0.924782 | − | 1.36459i | ||||
\(679\) | 15.8584 | + | 27.4675i | 0.608589 | + | 1.05411i | ||||
\(680\) | 10.4911 | + | 18.1712i | 0.402317 | + | 0.696834i | ||||
\(681\) | 9.84581 | − | 0.710168i | 0.377292 | − | 0.0272137i | ||||
\(682\) | 24.4960 | − | 42.4283i | 0.938001 | − | 1.62467i | ||||
\(683\) | 2.63501 | 0.100826 | 0.0504130 | − | 0.998728i | \(-0.483946\pi\) | ||||
0.0504130 | + | 0.998728i | \(0.483946\pi\) | |||||||
\(684\) | −5.34801 | + | 0.775528i | −0.204486 | + | 0.0296531i | ||||
\(685\) | −5.75830 | −0.220013 | ||||||||
\(686\) | −11.0000 | + | 19.0526i | −0.419984 | + | 0.727433i | ||||
\(687\) | 16.5880 | − | 34.2003i | 0.632870 | − | 1.30482i | ||||
\(688\) | −15.6712 | − | 27.1433i | −0.597459 | − | 1.03483i | ||||
\(689\) | −1.63283 | − | 2.82814i | −0.0622058 | − | 0.107744i | ||||
\(690\) | 0.347864 | − | 0.717210i | 0.0132429 | − | 0.0273037i | ||||
\(691\) | 11.8570 | − | 20.5370i | 0.451063 | − | 0.781264i | −0.547389 | − | 0.836878i | \(-0.684378\pi\) |
0.998452 | + | 0.0556138i | \(0.0177116\pi\) | |||||||
\(692\) | 1.96813 | 0.0748169 | ||||||||
\(693\) | 43.0968 | − | 6.24956i | 1.63711 | − | 0.237401i | ||||
\(694\) | 32.7138 | 1.24180 | ||||||||
\(695\) | −3.79217 | + | 6.56823i | −0.143845 | + | 0.249147i | ||||
\(696\) | 25.2009 | − | 1.81771i | 0.955237 | − | 0.0689002i | ||||
\(697\) | −21.1159 | − | 36.5739i | −0.799823 | − | 1.38533i | ||||
\(698\) | 7.85717 | + | 13.6090i | 0.297398 | + | 0.515109i | ||||
\(699\) | −25.0378 | − | 36.9452i | −0.947017 | − | 1.39740i | ||||
\(700\) | −0.479250 | + | 0.830085i | −0.0181139 | + | 0.0313743i | ||||
\(701\) | 36.6440 | 1.38403 | 0.692013 | − | 0.721885i | \(-0.256724\pi\) | ||||
0.692013 | + | 0.721885i | \(0.256724\pi\) | |||||||
\(702\) | 6.53887 | − | 1.43487i | 0.246794 | − | 0.0541555i | ||||
\(703\) | 30.2310 | 1.14018 | ||||||||
\(704\) | 22.8173 | − | 39.5208i | 0.859961 | − | 1.48950i | ||||
\(705\) | −5.95176 | − | 8.78227i | −0.224156 | − | 0.330760i | ||||
\(706\) | 11.5634 | + | 20.0284i | 0.435194 | + | 0.753778i | ||||
\(707\) | 13.7485 | + | 23.8131i | 0.517065 | + | 0.895584i | ||||
\(708\) | −0.771528 | + | 0.0556495i | −0.0289958 | + | 0.00209144i | ||||
\(709\) | −12.7783 | + | 22.1327i | −0.479900 | + | 0.831211i | −0.999734 | − | 0.0230560i | \(-0.992660\pi\) |
0.519834 | + | 0.854267i | \(0.325994\pi\) | |||||||
\(710\) | 6.33305 | 0.237675 | ||||||||
\(711\) | −16.4765 | − | 20.8995i | −0.617917 | − | 0.783793i | ||||
\(712\) | −19.4452 | −0.728738 | ||||||||
\(713\) | −1.31842 | + | 2.28358i | −0.0493754 | + | 0.0855207i | ||||
\(714\) | −19.0967 | + | 39.3727i | −0.714675 | + | 1.47349i | ||||
\(715\) | −2.57577 | − | 4.46137i | −0.0963284 | − | 0.166846i | ||||
\(716\) | −3.43535 | − | 5.95019i | −0.128385 | − | 0.222369i | ||||
\(717\) | 4.49817 | − | 9.27414i | 0.167987 | − | 0.346349i | ||||
\(718\) | −12.9901 | + | 22.4996i | −0.484787 | + | 0.839676i | ||||
\(719\) | 3.51637 | 0.131139 | 0.0655693 | − | 0.997848i | \(-0.479114\pi\) | ||||
0.0655693 | + | 0.997848i | \(0.479114\pi\) | |||||||
\(720\) | −3.56159 | + | 8.92768i | −0.132733 | + | 0.332715i | ||||
\(721\) | −22.3668 | −0.832981 | ||||||||
\(722\) | −5.82450 | + | 10.0883i | −0.216765 | + | 0.375449i | ||||
\(723\) | 40.2503 | − | 2.90321i | 1.49693 | − | 0.107972i | ||||
\(724\) | −1.71444 | − | 2.96950i | −0.0637167 | − | 0.110361i | ||||
\(725\) | 2.41921 | + | 4.19019i | 0.0898471 | + | 0.155620i | ||||
\(726\) | −19.4522 | − | 28.7032i | −0.721939 | − | 1.06528i | ||||
\(727\) | 9.54123 | − | 16.5259i | 0.353865 | − | 0.612912i | −0.633058 | − | 0.774104i | \(-0.718201\pi\) |
0.986923 | + | 0.161192i | \(0.0515340\pi\) | |||||||
\(728\) | 8.49540 | 0.314860 | ||||||||
\(729\) | 24.5192 | − | 11.3052i | 0.908119 | − | 0.418711i | ||||
\(730\) | −6.02660 | −0.223054 | ||||||||
\(731\) | −34.0399 | + | 58.9589i | −1.25901 | + | 2.18067i | ||||
\(732\) | −3.03352 | − | 4.47619i | −0.112122 | − | 0.165445i | ||||
\(733\) | 8.11234 | + | 14.0510i | 0.299636 | + | 0.518985i | 0.976053 | − | 0.217534i | \(-0.0698014\pi\) |
−0.676417 | + | 0.736519i | \(0.736468\pi\) | |||||||
\(734\) | −19.2502 | − | 33.3423i | −0.710536 | − | 1.23068i | ||||
\(735\) | −1.62356 | + | 0.117106i | −0.0598861 | + | 0.00431952i | ||||
\(736\) | −0.339724 | + | 0.588419i | −0.0125224 | + | 0.0216894i | ||||
\(737\) | −9.21123 | −0.339300 | ||||||||
\(738\) | 8.69071 | − | 21.7846i | 0.319909 | − | 0.801903i | ||||
\(739\) | 17.3100 | 0.636760 | 0.318380 | − | 0.947963i | \(-0.396861\pi\) | ||||
0.318380 | + | 0.947963i | \(0.396861\pi\) | |||||||
\(740\) | −0.970970 | + | 1.68177i | −0.0356936 | + | 0.0618231i | ||||
\(741\) | −4.00266 | + | 8.25252i | −0.147042 | + | 0.303164i | ||||
\(742\) | 5.92758 | + | 10.2669i | 0.217608 | + | 0.376909i | ||||
\(743\) | 22.3620 | + | 38.7321i | 0.820381 | + | 1.42094i | 0.905399 | + | 0.424562i | \(0.139572\pi\) |
−0.0850183 | + | 0.996379i | \(0.527095\pi\) | |||||||
\(744\) | 16.8221 | − | 34.6831i | 0.616728 | − | 1.27154i | ||||
\(745\) | 3.00953 | − | 5.21267i | 0.110261 | − | 0.190977i | ||||
\(746\) | −4.71039 | −0.172460 | ||||||||
\(747\) | −27.7823 | − | 35.2403i | −1.01650 | − | 1.28938i | ||||
\(748\) | −12.1955 | −0.445911 | ||||||||
\(749\) | 6.27086 | − | 10.8615i | 0.229132 | − | 0.396869i | ||||
\(750\) | −2.22570 | + | 0.160537i | −0.0812711 | + | 0.00586200i | ||||
\(751\) | −14.4998 | − | 25.1143i | −0.529104 | − | 0.916435i | −0.999424 | − | 0.0339392i | \(-0.989195\pi\) |
0.470320 | − | 0.882496i | \(-0.344139\pi\) | |||||||
\(752\) | −9.81235 | − | 16.9955i | −0.357820 | − | 0.619762i | ||||
\(753\) | −16.1771 | − | 23.8705i | −0.589526 | − | 0.869891i | ||||
\(754\) | 3.11678 | − | 5.39842i | 0.113506 | − | 0.196599i | ||||
\(755\) | −9.83190 | −0.357819 | ||||||||
\(756\) | 4.86476 | − | 1.06751i | 0.176930 | − | 0.0388248i | ||||
\(757\) | 32.0762 | 1.16583 | 0.582914 | − | 0.812534i | \(-0.301912\pi\) | ||||
0.582914 | + | 0.812534i | \(0.301912\pi\) | |||||||
\(758\) | −15.5010 | + | 26.8486i | −0.563023 | + | 0.975184i | ||||
\(759\) | 1.78812 | + | 2.63851i | 0.0649048 | + | 0.0957719i | ||||
\(760\) | −7.98274 | − | 13.8265i | −0.289564 | − | 0.501540i | ||||
\(761\) | 12.4399 | + | 21.5465i | 0.450944 | + | 0.781059i | 0.998445 | − | 0.0557467i | \(-0.0177539\pi\) |
−0.547501 | + | 0.836805i | \(0.684421\pi\) | |||||||
\(762\) | 17.7833 | − | 1.28269i | 0.644220 | − | 0.0464669i | ||||
\(763\) | −12.1006 | + | 20.9588i | −0.438070 | + | 0.758759i | ||||
\(764\) | 6.21064 | 0.224693 | ||||||||
\(765\) | 20.6622 | − | 2.99627i | 0.747043 | − | 0.108331i | ||||
\(766\) | −38.2394 | −1.38165 | ||||||||
\(767\) | −0.656449 | + | 1.13700i | −0.0237030 | + | 0.0410548i | ||||
\(768\) | 5.98221 | − | 12.3339i | 0.215864 | − | 0.445060i | ||||
\(769\) | 20.1005 | + | 34.8150i | 0.724842 | + | 1.25546i | 0.959039 | + | 0.283273i | \(0.0914204\pi\) |
−0.234198 | + | 0.972189i | \(0.575246\pi\) | |||||||
\(770\) | 9.35072 | + | 16.1959i | 0.336977 | + | 0.583660i | ||||
\(771\) | 4.98522 | − | 10.2783i | 0.179538 | − | 0.370165i | ||||
\(772\) | −0.368788 | + | 0.638759i | −0.0132730 | + | 0.0229894i | ||||
\(773\) | −2.03131 | −0.0730612 | −0.0365306 | − | 0.999333i | \(-0.511631\pi\) | ||||
−0.0365306 | + | 0.999333i | \(0.511631\pi\) | |||||||
\(774\) | −37.4179 | + | 5.42606i | −1.34496 | + | 0.195036i | ||||
\(775\) | 7.38168 | 0.265158 | ||||||||
\(776\) | 16.9681 | − | 29.3896i | 0.609119 | − | 1.05502i | ||||
\(777\) | −27.7899 | + | 2.00446i | −0.996958 | + | 0.0719096i | ||||
\(778\) | −3.66346 | − | 6.34531i | −0.131342 | − | 0.227490i | ||||
\(779\) | 16.0672 | + | 27.8292i | 0.575666 | + | 0.997083i | ||||
\(780\) | −0.330534 | − | 0.487729i | −0.0118350 | − | 0.0174635i | ||||
\(781\) | −12.6616 | + | 21.9305i | −0.453066 | + | 0.784734i | ||||
\(782\) | −3.20285 | −0.114534 | ||||||||
\(783\) | 7.61170 | − | 23.9612i | 0.272020 | − | 0.856303i | ||||
\(784\) | −3.01109 | −0.107539 | ||||||||
\(785\) | −1.25443 | + | 2.17274i | −0.0447726 | + | 0.0775484i | ||||
\(786\) | 4.34410 | + | 6.41005i | 0.154949 | + | 0.228639i | ||||
\(787\) | −18.7372 | − | 32.4537i | −0.667908 | − | 1.15685i | −0.978488 | − | 0.206303i | \(-0.933857\pi\) |
0.310580 | − | 0.950547i | \(-0.399477\pi\) | |||||||
\(788\) | 2.54424 | + | 4.40675i | 0.0906347 | + | 0.156984i | ||||
\(789\) | −30.5239 | + | 2.20166i | −1.08668 | + | 0.0783810i | ||||
\(790\) | 5.71451 | − | 9.89783i | 0.203313 | − | 0.352149i | ||||
\(791\) | −54.1997 | −1.92712 | ||||||||
\(792\) | −28.8473 | − | 36.5911i | −1.02504 | − | 1.30021i | ||||
\(793\) | −9.17762 | −0.325907 | ||||||||
\(794\) | 1.05696 | − | 1.83071i | 0.0375102 | − | 0.0649696i | ||||
\(795\) | 2.46840 | − | 5.08925i | 0.0875453 | − | 0.180497i | ||||
\(796\) | 0.818567 | + | 1.41780i | 0.0290133 | + | 0.0502526i | ||||
\(797\) | 6.95827 | + | 12.0521i | 0.246475 | + | 0.426907i | 0.962545 | − | 0.271121i | \(-0.0873944\pi\) |
−0.716070 | + | 0.698028i | \(0.754061\pi\) | |||||||
\(798\) | 14.5307 | − | 29.9588i | 0.514381 | − | 1.06053i | ||||
\(799\) | −21.3137 | + | 36.9165i | −0.754026 | + | 1.30601i | ||||
\(800\) | 1.90207 | 0.0672482 | ||||||||
\(801\) | −7.16950 | + | 17.9715i | −0.253322 | + | 0.634991i | ||||
\(802\) | −17.1410 | −0.605270 | ||||||||
\(803\) | 12.0489 | − | 20.8693i | 0.425196 | − | 0.736461i | ||||
\(804\) | −1.05075 | + | 0.0757898i | −0.0370572 | + | 0.00267290i | ||||
\(805\) | −0.503275 | − | 0.871697i | −0.0177381 | − | 0.0307233i | ||||
\(806\) | −4.75508 | − | 8.23604i | −0.167491 | − | 0.290102i | ||||
\(807\) | 5.92542 | + | 8.74342i | 0.208585 | + | 0.307783i | ||||
\(808\) | 14.7106 | − | 25.4794i | 0.517516 | − | 0.896364i | ||||
\(809\) | 7.77442 | 0.273334 | 0.136667 | − | 0.990617i | \(-0.456361\pi\) | ||||
0.136667 | + | 0.990617i | \(0.456361\pi\) | |||||||
\(810\) | 8.41110 | + | 7.98124i | 0.295536 | + | 0.280432i | ||||
\(811\) | −29.5307 | −1.03696 | −0.518482 | − | 0.855089i | \(-0.673503\pi\) | ||||
−0.518482 | + | 0.855089i | \(0.673503\pi\) | |||||||
\(812\) | 2.31881 | − | 4.01629i | 0.0813742 | − | 0.140944i | ||||
\(813\) | 19.3523 | + | 28.5558i | 0.678714 | + | 1.00150i | ||||
\(814\) | 18.9448 | + | 32.8133i | 0.664013 | + | 1.15010i | ||||
\(815\) | −9.91173 | − | 17.1676i | −0.347193 | − | 0.601356i | ||||
\(816\) | 38.5208 | − | 2.77847i | 1.34850 | − | 0.0972658i | ||||
\(817\) | 25.9011 | − | 44.8620i | 0.906164 | − | 1.56952i | ||||
\(818\) | 13.6034 | 0.475630 | ||||||||
\(819\) | 3.13228 | − | 7.85156i | 0.109451 | − | 0.274356i | ||||
\(820\) | −2.06421 | −0.0720852 | ||||||||
\(821\) | 9.69370 | − | 16.7900i | 0.338312 | − | 0.585974i | −0.645803 | − | 0.763504i | \(-0.723477\pi\) |
0.984115 | + | 0.177530i | \(0.0568106\pi\) | |||||||
\(822\) | −5.60755 | + | 11.5614i | −0.195586 | + | 0.403250i | ||||
\(823\) | −19.9843 | − | 34.6138i | −0.696609 | − | 1.20656i | −0.969635 | − | 0.244555i | \(-0.921358\pi\) |
0.273027 | − | 0.962006i | \(-0.411975\pi\) | |||||||
\(824\) | 11.9659 | + | 20.7256i | 0.416853 | + | 0.722011i | ||||
\(825\) | 3.89389 | − | 8.02825i | 0.135568 | − | 0.279508i | ||||
\(826\) | 2.38308 | − | 4.12761i | 0.0829179 | − | 0.143618i | ||||
\(827\) | 39.8289 | 1.38499 | 0.692494 | − | 0.721424i | \(-0.256512\pi\) | ||||
0.692494 | + | 0.721424i | \(0.256512\pi\) | |||||||
\(828\) | 0.225686 | + | 0.286271i | 0.00784314 | + | 0.00994860i | ||||
\(829\) | 32.8078 | 1.13946 | 0.569731 | − | 0.821831i | \(-0.307047\pi\) | ||||
0.569731 | + | 0.821831i | \(0.307047\pi\) | |||||||
\(830\) | 9.63569 | − | 16.6895i | 0.334460 | − | 0.579301i | ||||
\(831\) | 55.9055 | − | 4.03240i | 1.93934 | − | 0.139883i | ||||
\(832\) | −4.42922 | − | 7.67164i | −0.153556 | − | 0.265966i | ||||
\(833\) | 3.27024 | + | 5.66422i | 0.113307 | + | 0.196254i | ||||
\(834\) | 9.49467 | + | 14.0101i | 0.328774 | + | 0.485131i | ||||
\(835\) | −11.8886 | + | 20.5916i | −0.411420 | + | 0.712601i | ||||
\(836\) | 9.27956 | 0.320940 | ||||||||
\(837\) | −25.8522 | − | 28.3350i | −0.893583 | − | 0.979400i | ||||
\(838\) | 26.4743 | 0.914541 | ||||||||
\(839\) | −24.7549 | + | 42.8767i | −0.854633 | + | 1.48027i | 0.0223528 | + | 0.999750i | \(0.492884\pi\) |
−0.876985 | + | 0.480517i | \(0.840449\pi\) | |||||||
\(840\) | 8.25493 | + | 12.1808i | 0.284822 | + | 0.420277i | ||||
\(841\) | 2.79488 | + | 4.84087i | 0.0963751 | + | 0.166927i | ||||
\(842\) | 23.3652 | + | 40.4697i | 0.805218 | + | 1.39468i | ||||
\(843\) | −55.3020 | + | 3.98888i | −1.90470 | + | 0.137384i | ||||
\(844\) | 1.63380 | − | 2.82982i | 0.0562376 | − | 0.0974064i | ||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | −23.4288 | + | 3.39747i | −0.805499 | + | 0.116807i | ||||
\(847\) | −43.7836 | −1.50442 | ||||||||
\(848\) | 5.23152 | − | 9.06126i | 0.179651 | − | 0.311165i | ||||
\(849\) | 21.9005 | − | 45.1534i | 0.751622 | − | 1.54966i | ||||
\(850\) | 4.48308 | + | 7.76493i | 0.153769 | + | 0.266335i | ||||
\(851\) | −1.01965 | − | 1.76608i | −0.0349530 | − | 0.0605403i | ||||
\(852\) | −1.26390 | + | 2.60586i | −0.0433005 | + | 0.0892752i | ||||
\(853\) | 9.43866 | − | 16.3482i | 0.323174 | − | 0.559753i | −0.657967 | − | 0.753046i | \(-0.728584\pi\) |
0.981141 | + | 0.193293i | \(0.0619168\pi\) | |||||||
\(854\) | 33.3171 | 1.14009 | ||||||||
\(855\) | −15.7219 | + | 2.27987i | −0.537678 | + | 0.0779700i | ||||
\(856\) | −13.4193 | −0.458664 | ||||||||
\(857\) | 19.0881 | − | 33.0616i | 0.652037 | − | 1.12936i | −0.330591 | − | 0.943774i | \(-0.607248\pi\) |
0.982628 | − | 0.185587i | \(-0.0594187\pi\) | |||||||
\(858\) | −11.4658 | + | 0.827016i | −0.391436 | + | 0.0282338i | ||||
\(859\) | −17.1791 | − | 29.7551i | −0.586144 | − | 1.01523i | −0.994732 | − | 0.102512i | \(-0.967312\pi\) |
0.408588 | − | 0.912719i | \(-0.366021\pi\) | |||||||
\(860\) | 1.66380 | + | 2.88179i | 0.0567352 | + | 0.0982682i | ||||
\(861\) | −16.6150 | − | 24.5167i | −0.566238 | − | 0.835528i | ||||
\(862\) | −9.94074 | + | 17.2179i | −0.338583 | + | 0.586443i | ||||
\(863\) | 38.0198 | 1.29421 | 0.647105 | − | 0.762401i | \(-0.275980\pi\) | ||||
0.647105 | + | 0.762401i | \(0.275980\pi\) | |||||||
\(864\) | −6.66144 | − | 7.30119i | −0.226627 | − | 0.248392i | ||||
\(865\) | 5.78584 | 0.196724 | ||||||||
\(866\) | 15.0404 | − | 26.0508i | 0.511095 | − | 0.885243i | ||||
\(867\) | −30.5440 | − | 45.0700i | −1.03733 | − | 1.53066i | ||||
\(868\) | −3.53767 | − | 6.12742i | −0.120076 | − | 0.207978i | ||||
\(869\) | 22.8499 | + | 39.5772i | 0.775129 | + | 1.34256i | ||||
\(870\) | 10.7689 | − | 0.776746i | 0.365098 | − | 0.0263342i | ||||
\(871\) | −0.894026 | + | 1.54850i | −0.0302929 | + | 0.0524689i | ||||
\(872\) | 25.8946 | 0.876902 | ||||||||
\(873\) | −20.9061 | − | 26.5182i | −0.707563 | − | 0.897504i | ||||
\(874\) | 2.43706 | 0.0824347 | ||||||||
\(875\) | −1.40888 | + | 2.44026i | −0.0476289 | + | 0.0824957i | ||||
\(876\) | 1.20274 | − | 2.47976i | 0.0406369 | − | 0.0837835i | ||||
\(877\) | 15.8916 | + | 27.5251i | 0.536622 | + | 0.929456i | 0.999083 | + | 0.0428167i | \(0.0136331\pi\) |
−0.462461 | + | 0.886640i | \(0.653034\pi\) | |||||||
\(878\) | −8.01978 | − | 13.8907i | −0.270654 | − | 0.468787i | ||||
\(879\) | −3.06745 | + | 6.32433i | −0.103462 | + | 0.213314i | ||||
\(880\) | 8.25268 | − | 14.2941i | 0.278198 | − | 0.481853i | ||||
\(881\) | −9.08373 | −0.306039 | −0.153019 | − | 0.988223i | \(-0.548900\pi\) | ||||
−0.153019 | + | 0.988223i | \(0.548900\pi\) | |||||||
\(882\) | −1.34594 | + | 3.37380i | −0.0453200 | + | 0.113602i | ||||
\(883\) | 49.6414 | 1.67057 | 0.835283 | − | 0.549820i | \(-0.185304\pi\) | ||||
0.835283 | + | 0.549820i | \(0.185304\pi\) | |||||||
\(884\) | −1.18367 | + | 2.05018i | −0.0398112 | + | 0.0689550i | ||||
\(885\) | −2.26811 | + | 0.163597i | −0.0762418 | + | 0.00549924i | ||||
\(886\) | 4.67907 | + | 8.10438i | 0.157196 | + | 0.272272i | ||||
\(887\) | −14.9338 | − | 25.8661i | −0.501429 | − | 0.868500i | −0.999999 | − | 0.00165060i | \(-0.999475\pi\) |
0.498570 | − | 0.866850i | \(-0.333859\pi\) | |||||||
\(888\) | 16.7247 | + | 24.6785i | 0.561243 | + | 0.828157i | ||||
\(889\) | 11.2569 | − | 19.4976i | 0.377545 | − | 0.653927i | ||||
\(890\) | −8.30932 | −0.278529 | ||||||||
\(891\) | −44.4541 | + | 13.1697i | −1.48927 | + | 0.441203i | ||||
\(892\) | 2.16036 | 0.0723342 | ||||||||
\(893\) | 16.2177 | − | 28.0898i | 0.542704 | − | 0.939990i | ||||
\(894\) | −7.53515 | − | 11.1187i | −0.252013 | − | 0.371865i | ||||
\(895\) | −10.0991 | − | 17.4922i | −0.337576 | − | 0.584699i | ||||
\(896\) | 10.7196 | + | 18.5670i | 0.358118 | + | 0.620279i | ||||
\(897\) | 0.617112 | − | 0.0445117i | 0.0206048 | − | 0.00148620i | ||||
\(898\) | 9.49418 | − | 16.4444i | 0.316825 | − | 0.548757i | ||||
\(899\) | −35.7156 | −1.19118 | ||||||||
\(900\) | 0.378132 | − | 0.947847i | 0.0126044 | − | 0.0315949i | ||||
\(901\) | −22.7271 | −0.757150 | ||||||||
\(902\) | −20.1375 | + | 34.8793i | −0.670507 | + | 1.16135i | ||||
\(903\) | −20.8351 | + | 42.9569i | −0.693349 | + | 1.42952i | ||||
\(904\) | 28.9962 | + | 50.2229i | 0.964399 | + | 1.67039i | ||||
\(905\) | −5.04006 | − | 8.72964i | −0.167537 | − | 0.290183i | ||||
\(906\) | −9.57450 | + | 19.7403i | −0.318091 | + | 0.655827i | ||||
\(907\) | 9.22113 | − | 15.9715i | 0.306183 | − | 0.530324i | −0.671341 | − | 0.741148i | \(-0.734282\pi\) |
0.977524 | + | 0.210824i | \(0.0676148\pi\) | |||||||
\(908\) | −1.93867 | −0.0643371 | ||||||||
\(909\) | −18.1246 | − | 22.9901i | −0.601155 | − | 0.762532i | ||||
\(910\) | 3.63026 | 0.120342 | ||||||||
\(911\) | 4.10456 | − | 7.10930i | 0.135990 | − | 0.235542i | −0.789985 | − | 0.613126i | \(-0.789912\pi\) |
0.925975 | + | 0.377584i | \(0.123245\pi\) | |||||||
\(912\) | −29.3106 | + | 2.11414i | −0.970570 | + | 0.0700062i | ||||
\(913\) | 38.5290 | + | 66.7341i | 1.27512 | + | 2.20858i | ||||
\(914\) | −4.76867 | − | 8.25957i | −0.157733 | − | 0.273202i | ||||
\(915\) | −8.91784 | − | 13.1590i | −0.294815 | − | 0.435022i | ||||
\(916\) | −3.73253 | + | 6.46494i | −0.123326 | + | 0.213608i | ||||
\(917\) | 9.77782 | 0.322892 | ||||||||
\(918\) | 14.1054 | − | 44.4030i | 0.465548 | − | 1.46552i | ||||
\(919\) | −1.11177 | −0.0366738 | −0.0183369 | − | 0.999832i | \(-0.505837\pi\) | ||||
−0.0183369 | + | 0.999832i | \(0.505837\pi\) | |||||||
\(920\) | −0.538492 | + | 0.932695i | −0.0177535 | + | 0.0307500i | ||||
\(921\) | −9.94603 | − | 14.6761i | −0.327733 | − | 0.483595i | ||||
\(922\) | 1.96093 | + | 3.39642i | 0.0645796 | + | 0.111855i | ||||
\(923\) | 2.45782 | + | 4.25707i | 0.0809001 | + | 0.140123i | ||||
\(924\) | −8.53028 | + | 0.615280i | −0.280625 | + | 0.0202412i | ||||
\(925\) | −2.85443 | + | 4.94401i | −0.0938530 | + | 0.162558i | ||||
\(926\) | 18.0122 | 0.591916 | ||||||||
\(927\) | 23.5668 | − | 3.41748i | 0.774035 | − | 0.112245i | ||||
\(928\) | −9.20299 | −0.302103 | ||||||||
\(929\) | −5.88119 | + | 10.1865i | −0.192956 | + | 0.334209i | −0.946228 | − | 0.323499i | \(-0.895141\pi\) |
0.753273 | + | 0.657708i | \(0.228474\pi\) | |||||||
\(930\) | 7.18843 | − | 14.8208i | 0.235718 | − | 0.485993i | ||||
\(931\) | −2.48833 | − | 4.30992i | −0.0815519 | − | 0.141252i | ||||
\(932\) | 4.38252 | + | 7.59074i | 0.143554 | + | 0.248643i | ||||
\(933\) | −16.7996 | + | 34.6368i | −0.549995 | + | 1.13396i | ||||
\(934\) | −19.7404 | + | 34.1914i | −0.645926 | + | 1.11878i | ||||
\(935\) | −35.8519 | −1.17248 | ||||||||
\(936\) | −8.95120 | + | 1.29803i | −0.292579 | + | 0.0424276i | ||||
\(937\) | −50.7176 | −1.65687 | −0.828436 | − | 0.560084i | \(-0.810769\pi\) | ||||
−0.828436 | + | 0.560084i | \(0.810769\pi\) | |||||||
\(938\) | 3.24555 | − | 5.62145i | 0.105971 | − | 0.183547i | ||||
\(939\) | −16.6400 | + | 1.20022i | −0.543025 | + | 0.0391678i | ||||
\(940\) | 1.04177 | + | 1.80440i | 0.0339788 | + | 0.0588531i | ||||
\(941\) | −13.3852 | − | 23.1839i | −0.436345 | − | 0.755772i | 0.561059 | − | 0.827776i | \(-0.310394\pi\) |
−0.997404 | + | 0.0720035i | \(0.977061\pi\) | |||||||
\(942\) | 3.14079 | + | 4.63448i | 0.102333 | + | 0.151000i | ||||
\(943\) | 1.08384 | − | 1.87727i | 0.0352948 | − | 0.0611324i | ||||
\(944\) | −4.20648 | −0.136909 | ||||||||
\(945\) | 14.3013 | − | 3.13822i | 0.465220 | − | 0.102086i | ||||
\(946\) | 64.9254 | 2.11091 | ||||||||
\(947\) | 11.4159 | − | 19.7730i | 0.370968 | − | 0.642536i | −0.618746 | − | 0.785591i | \(-0.712359\pi\) |
0.989715 | + | 0.143055i | \(0.0456925\pi\) | |||||||
\(948\) | 2.93220 | + | 4.32668i | 0.0952334 | + | 0.140524i | ||||
\(949\) | −2.33889 | − | 4.05108i | −0.0759236 | − | 0.131503i | ||||
\(950\) | −3.41119 | − | 5.90835i | −0.110674 | − | 0.191692i | ||||
\(951\) | 53.0442 | − | 3.82602i | 1.72008 | − | 0.124067i | ||||
\(952\) | 29.5616 | − | 51.2022i | 0.958097 | − | 1.65947i | ||||
\(953\) | −4.98857 | −0.161596 | −0.0807979 | − | 0.996731i | \(-0.525747\pi\) | ||||
−0.0807979 | + | 0.996731i | \(0.525747\pi\) | |||||||
\(954\) | −7.81432 | − | 9.91203i | −0.252998 | − | 0.320914i | ||||
\(955\) | 18.2578 | 0.590810 | ||||||||
\(956\) | −1.01216 | + | 1.75310i | −0.0327354 | + | 0.0566994i | ||||
\(957\) | −18.8402 | + | 38.8440i | −0.609019 | + | 1.25565i | ||||
\(958\) | 1.90936 | + | 3.30710i | 0.0616885 | + | 0.106848i | ||||
\(959\) | 8.11277 | + | 14.0517i | 0.261975 | + | 0.453754i | ||||
\(960\) | 6.69582 | − | 13.8052i | 0.216107 | − | 0.445559i | ||||
\(961\) | −11.7446 | + | 20.3422i | −0.378858 | + | 0.656201i | ||||
\(962\) | 7.35498 | 0.237134 | ||||||||
\(963\) | −4.94776 | + | 12.4023i | −0.159439 | + | 0.399660i | ||||
\(964\) | −7.92542 | −0.255261 | ||||||||
\(965\) | −1.08415 | + | 1.87780i | −0.0349000 | + | 0.0604486i | ||||
\(966\) | −2.24028 | + | 0.161589i | −0.0720797 | + | 0.00519903i | ||||
\(967\) | 8.44142 | + | 14.6210i | 0.271458 | + | 0.470179i | 0.969235 | − | 0.246136i | \(-0.0791610\pi\) |
−0.697778 | + | 0.716314i | \(0.745828\pi\) | |||||||
\(968\) | 23.4237 | + | 40.5710i | 0.752866 | + | 1.30400i | ||||
\(969\) | 35.8102 | + | 52.8407i | 1.15039 | + | 1.69749i | ||||
\(970\) | 7.25081 | − | 12.5588i | 0.232810 | − | 0.403238i | ||||
\(971\) | −12.3303 | −0.395699 | −0.197850 | − | 0.980232i | \(-0.563396\pi\) | ||||
−0.197850 | + | 0.980232i | \(0.563396\pi\) | |||||||
\(972\) | −4.96266 | + | 1.86808i | −0.159177 | + | 0.0599187i | ||||
\(973\) | 21.3709 | 0.685119 | ||||||||
\(974\) | 11.2950 | − | 19.5635i | 0.361915 | − | 0.626856i | ||||
\(975\) | −0.971694 | − | 1.43381i | −0.0311191 | − | 0.0459187i | ||||
\(976\) | −14.7024 | − | 25.4653i | −0.470612 | − | 0.815123i | ||||
\(977\) | −30.0983 | − | 52.1317i | −0.962929 | − | 1.66784i | −0.715079 | − | 0.699044i | \(-0.753609\pi\) |
−0.247850 | − | 0.968798i | \(-0.579724\pi\) | |||||||
\(978\) | −44.1211 | + | 3.18241i | −1.41084 | + | 0.101762i | ||||
\(979\) | 16.6127 | − | 28.7740i | 0.530944 | − | 0.919622i | ||||
\(980\) | 0.319685 | 0.0102120 | ||||||||
\(981\) | 9.54744 | − | 23.9322i | 0.304826 | − | 0.764095i | ||||
\(982\) | −27.2026 | −0.868070 | ||||||||
\(983\) | 1.13564 | − | 1.96698i | 0.0362212 | − | 0.0627370i | −0.847346 | − | 0.531040i | \(-0.821801\pi\) |
0.883568 | + | 0.468303i | \(0.155135\pi\) | |||||||
\(984\) | −13.8290 | + | 28.5121i | −0.440853 | + | 0.908932i | ||||
\(985\) | 7.47946 | + | 12.9548i | 0.238316 | + | 0.412775i | ||||
\(986\) | −21.6910 | − | 37.5699i | −0.690783 | − | 1.19647i | ||||
\(987\) | −13.0457 | + | 26.8970i | −0.415248 | + | 0.856141i | ||||
\(988\) | 0.900658 | − | 1.55999i | 0.0286538 | − | 0.0496298i | ||||
\(989\) | −3.49442 | −0.111116 | ||||||||
\(990\) | −12.3270 | − | 15.6362i | −0.391779 | − | 0.496950i | ||||
\(991\) | 55.9580 | 1.77756 | 0.888782 | − | 0.458331i | \(-0.151552\pi\) | ||||
0.888782 | + | 0.458331i | \(0.151552\pi\) | |||||||
\(992\) | −7.02022 | + | 12.1594i | −0.222892 | + | 0.386061i | ||||
\(993\) | −6.07499 | + | 0.438183i | −0.192784 | + | 0.0139053i | ||||
\(994\) | −8.92252 | − | 15.4543i | −0.283005 | − | 0.490179i | ||||
\(995\) | 2.40640 | + | 4.16800i | 0.0762879 | + | 0.132135i | ||||
\(996\) | 4.94421 | + | 7.29556i | 0.156663 | + | 0.231169i | ||||
\(997\) | −1.41267 | + | 2.44682i | −0.0447397 | + | 0.0774915i | −0.887528 | − | 0.460754i | \(-0.847579\pi\) |
0.842788 | + | 0.538245i | \(0.180913\pi\) | |||||||
\(998\) | 42.6501 | 1.35007 | ||||||||
\(999\) | 28.9747 | − | 6.35810i | 0.916718 | − | 0.201161i |
(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 | 585.2.i.h.196.5 | ✓ | 30 | |
3.2 | odd | 2 | 1755.2.i.h.586.11 | 30 | |||
9.2 | odd | 6 | 5265.2.a.bl.1.5 | 15 | |||
9.4 | even | 3 | inner | 585.2.i.h.391.5 | yes | 30 | |
9.5 | odd | 6 | 1755.2.i.h.1171.11 | 30 | |||
9.7 | even | 3 | 5265.2.a.bk.1.11 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.i.h.196.5 | ✓ | 30 | 1.1 | even | 1 | trivial | |
585.2.i.h.391.5 | yes | 30 | 9.4 | even | 3 | inner | |
1755.2.i.h.586.11 | 30 | 3.2 | odd | 2 | |||
1755.2.i.h.1171.11 | 30 | 9.5 | odd | 6 | |||
5265.2.a.bk.1.11 | 15 | 9.7 | even | 3 | |||
5265.2.a.bl.1.5 | 15 | 9.2 | odd | 6 |