Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(239,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 239.13 | ||
Character | \(\chi\) | \(=\) | 507.239 |
Dual form | 507.2.f.g.437.14 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.249216 | + | 0.249216i | 0.176222 | + | 0.176222i | 0.789707 | − | 0.613485i | \(-0.210233\pi\) |
−0.613485 | + | 0.789707i | \(0.710233\pi\) | |||||||
\(3\) | 0.892053 | − | 1.48467i | 0.515027 | − | 0.857174i | ||||
\(4\) | − | 1.87578i | − | 0.937892i | ||||||
\(5\) | 2.45719 | + | 2.45719i | 1.09889 | + | 1.09889i | 0.994541 | + | 0.104350i | \(0.0332761\pi\) |
0.104350 | + | 0.994541i | \(0.466724\pi\) | |||||||
\(6\) | 0.592316 | − | 0.147689i | 0.241812 | − | 0.0602939i | ||||
\(7\) | −0.821655 | − | 0.821655i | −0.310556 | − | 0.310556i | 0.534569 | − | 0.845125i | \(-0.320474\pi\) |
−0.845125 | + | 0.534569i | \(0.820474\pi\) | |||||||
\(8\) | 0.965906 | − | 0.965906i | 0.341499 | − | 0.341499i | ||||
\(9\) | −1.40848 | − | 2.64881i | −0.469495 | − | 0.882935i | ||||
\(10\) | 1.22474i | 0.387298i | ||||||||
\(11\) | 1.32603 | − | 1.32603i | 0.399814 | − | 0.399814i | −0.478353 | − | 0.878167i | \(-0.658766\pi\) |
0.878167 | + | 0.478353i | \(0.158766\pi\) | |||||||
\(12\) | −2.78492 | − | 1.67330i | −0.803936 | − | 0.483039i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | − | 0.409539i | − | 0.109454i | ||||||
\(15\) | 5.84006 | − | 1.45617i | 1.50790 | − | 0.375982i | ||||
\(16\) | −3.27013 | −0.817532 | ||||||||
\(17\) | 5.90167 | 1.43136 | 0.715682 | − | 0.698426i | \(-0.246116\pi\) | ||||
0.715682 | + | 0.698426i | \(0.246116\pi\) | |||||||
\(18\) | 0.309108 | − | 1.01114i | 0.0728573 | − | 0.238328i | ||||
\(19\) | −3.48387 | + | 3.48387i | −0.799255 | + | 0.799255i | −0.982978 | − | 0.183723i | \(-0.941185\pi\) |
0.183723 | + | 0.982978i | \(0.441185\pi\) | |||||||
\(20\) | 4.60916 | − | 4.60916i | 1.03064 | − | 1.03064i | ||||
\(21\) | −1.95284 | + | 0.486926i | −0.426146 | + | 0.106256i | ||||
\(22\) | 0.660937 | 0.140912 | ||||||||
\(23\) | −2.70965 | −0.565001 | −0.282500 | − | 0.959267i | \(-0.591164\pi\) | ||||
−0.282500 | + | 0.959267i | \(0.591164\pi\) | |||||||
\(24\) | −0.572412 | − | 2.29569i | −0.116843 | − | 0.468606i | ||||
\(25\) | 7.07560i | 1.41512i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.18904 | − | 0.271740i | −0.998632 | − | 0.0522964i | ||||
\(28\) | −1.54125 | + | 1.54125i | −0.291268 | + | 0.291268i | ||||
\(29\) | 2.68706i | 0.498975i | 0.968378 | + | 0.249488i | \(0.0802622\pi\) | ||||
−0.968378 | + | 0.249488i | \(0.919738\pi\) | |||||||
\(30\) | 1.81834 | + | 1.09253i | 0.331981 | + | 0.199469i | ||||
\(31\) | 3.22500 | − | 3.22500i | 0.579227 | − | 0.579227i | −0.355463 | − | 0.934690i | \(-0.615677\pi\) |
0.934690 | + | 0.355463i | \(0.115677\pi\) | |||||||
\(32\) | −2.74678 | − | 2.74678i | −0.485567 | − | 0.485567i | ||||
\(33\) | −0.785829 | − | 3.15161i | −0.136795 | − | 0.548625i | ||||
\(34\) | 1.47079 | + | 1.47079i | 0.252238 | + | 0.252238i | ||||
\(35\) | − | 4.03793i | − | 0.682535i | ||||||
\(36\) | −4.96858 | + | 2.64201i | −0.828097 | + | 0.440335i | ||||
\(37\) | −1.52785 | − | 1.52785i | −0.251177 | − | 0.251177i | 0.570276 | − | 0.821453i | \(-0.306836\pi\) |
−0.821453 | + | 0.570276i | \(0.806836\pi\) | |||||||
\(38\) | −1.73647 | −0.281693 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.74684 | 0.750541 | ||||||||
\(41\) | 4.81276 | + | 4.81276i | 0.751627 | + | 0.751627i | 0.974783 | − | 0.223156i | \(-0.0716358\pi\) |
−0.223156 | + | 0.974783i | \(0.571636\pi\) | |||||||
\(42\) | −0.608029 | − | 0.365330i | −0.0938210 | − | 0.0563716i | ||||
\(43\) | − | 5.55122i | − | 0.846553i | −0.906001 | − | 0.423276i | \(-0.860880\pi\) | ||
0.906001 | − | 0.423276i | \(-0.139120\pi\) | |||||||
\(44\) | −2.48735 | − | 2.48735i | −0.374982 | − | 0.374982i | ||||
\(45\) | 3.04771 | − | 9.96955i | 0.454326 | − | 1.48617i | ||||
\(46\) | −0.675287 | − | 0.675287i | −0.0995657 | − | 0.0995657i | ||||
\(47\) | −2.23192 | + | 2.23192i | −0.325559 | + | 0.325559i | −0.850895 | − | 0.525336i | \(-0.823940\pi\) |
0.525336 | + | 0.850895i | \(0.323940\pi\) | |||||||
\(48\) | −2.91713 | + | 4.85506i | −0.421051 | + | 0.700767i | ||||
\(49\) | − | 5.64977i | − | 0.807110i | ||||||
\(50\) | −1.76335 | + | 1.76335i | −0.249375 | + | 0.249375i | ||||
\(51\) | 5.26460 | − | 8.76202i | 0.737191 | − | 1.22693i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.46136i | 0.338093i | 0.985608 | + | 0.169047i | \(0.0540689\pi\) | ||||
−0.985608 | + | 0.169047i | \(0.945931\pi\) | |||||||
\(54\) | −1.22547 | − | 1.36091i | −0.166765 | − | 0.185197i | ||||
\(55\) | 6.51664 | 0.878704 | ||||||||
\(56\) | −1.58728 | −0.212110 | ||||||||
\(57\) | 2.06460 | + | 8.28020i | 0.273463 | + | 1.09674i | ||||
\(58\) | −0.669659 | + | 0.669659i | −0.0879305 | + | 0.0879305i | ||||
\(59\) | −7.07657 | + | 7.07657i | −0.921291 | + | 0.921291i | −0.997121 | − | 0.0758301i | \(-0.975839\pi\) |
0.0758301 | + | 0.997121i | \(0.475839\pi\) | |||||||
\(60\) | −2.73147 | − | 10.9547i | −0.352631 | − | 1.41424i | ||||
\(61\) | −2.66269 | −0.340922 | −0.170461 | − | 0.985364i | \(-0.554526\pi\) | ||||
−0.170461 | + | 0.985364i | \(0.554526\pi\) | |||||||
\(62\) | 1.60744 | 0.204145 | ||||||||
\(63\) | −1.01912 | + | 3.33369i | −0.128397 | + | 0.420006i | ||||
\(64\) | 5.17117i | 0.646397i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.589590 | − | 0.981273i | 0.0725736 | − | 0.120786i | ||||
\(67\) | −4.81080 | + | 4.81080i | −0.587732 | + | 0.587732i | −0.937017 | − | 0.349284i | \(-0.886425\pi\) |
0.349284 | + | 0.937017i | \(0.386425\pi\) | |||||||
\(68\) | − | 11.0702i | − | 1.34246i | ||||||
\(69\) | −2.41715 | + | 4.02293i | −0.290991 | + | 0.484304i | ||||
\(70\) | 1.00632 | − | 1.00632i | 0.120278 | − | 0.120278i | ||||
\(71\) | 8.20749 | + | 8.20749i | 0.974050 | + | 0.974050i | 0.999672 | − | 0.0256220i | \(-0.00815664\pi\) |
−0.0256220 | + | 0.999672i | \(0.508157\pi\) | |||||||
\(72\) | −3.91896 | − | 1.19803i | −0.461854 | − | 0.141190i | ||||
\(73\) | 9.13263 | + | 9.13263i | 1.06889 | + | 1.06889i | 0.997444 | + | 0.0714492i | \(0.0227624\pi\) |
0.0714492 | + | 0.997444i | \(0.477238\pi\) | |||||||
\(74\) | − | 0.761529i | − | 0.0885259i | ||||||
\(75\) | 10.5049 | + | 6.31180i | 1.21300 | + | 0.728824i | ||||
\(76\) | 6.53499 | + | 6.53499i | 0.749615 | + | 0.749615i | ||||
\(77\) | −2.17908 | −0.248330 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.10008 | 0.123769 | 0.0618844 | − | 0.998083i | \(-0.480289\pi\) | ||||
0.0618844 | + | 0.998083i | \(0.480289\pi\) | |||||||
\(80\) | −8.03534 | − | 8.03534i | −0.898378 | − | 0.898378i | ||||
\(81\) | −5.03234 | + | 7.46160i | −0.559149 | + | 0.829067i | ||||
\(82\) | 2.39883i | 0.264907i | ||||||||
\(83\) | −4.58922 | − | 4.58922i | −0.503732 | − | 0.503732i | 0.408864 | − | 0.912596i | \(-0.365925\pi\) |
−0.912596 | + | 0.408864i | \(0.865925\pi\) | |||||||
\(84\) | 0.913368 | + | 3.66311i | 0.0996566 | + | 0.399678i | ||||
\(85\) | 14.5015 | + | 14.5015i | 1.57291 | + | 1.57291i | ||||
\(86\) | 1.38345 | − | 1.38345i | 0.149181 | − | 0.149181i | ||||
\(87\) | 3.98940 | + | 2.39700i | 0.427709 | + | 0.256986i | ||||
\(88\) | − | 2.56165i | − | 0.273073i | ||||||
\(89\) | 3.02216 | − | 3.02216i | 0.320348 | − | 0.320348i | −0.528553 | − | 0.848901i | \(-0.677265\pi\) |
0.848901 | + | 0.528553i | \(0.177265\pi\) | |||||||
\(90\) | 3.24410 | − | 1.72503i | 0.341959 | − | 0.181834i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.08271i | 0.529909i | ||||||||
\(93\) | −1.91119 | − | 7.66492i | −0.198181 | − | 0.794815i | ||||
\(94\) | −1.11246 | −0.114742 | ||||||||
\(95\) | −17.1211 | −1.75659 | ||||||||
\(96\) | −6.52833 | + | 1.62779i | −0.666295 | + | 0.166135i | ||||
\(97\) | −8.67443 | + | 8.67443i | −0.880755 | + | 0.880755i | −0.993611 | − | 0.112856i | \(-0.964000\pi\) |
0.112856 | + | 0.993611i | \(0.464000\pi\) | |||||||
\(98\) | 1.40801 | − | 1.40801i | 0.142231 | − | 0.142231i | ||||
\(99\) | −5.38010 | − | 1.64471i | −0.540721 | − | 0.165299i | ||||
\(100\) | 13.2723 | 1.32723 | ||||||||
\(101\) | 11.0956 | 1.10405 | 0.552026 | − | 0.833827i | \(-0.313855\pi\) | ||||
0.552026 | + | 0.833827i | \(0.313855\pi\) | |||||||
\(102\) | 3.49565 | − | 0.871614i | 0.346121 | − | 0.0863026i | ||||
\(103\) | − | 4.43285i | − | 0.436782i | −0.975861 | − | 0.218391i | \(-0.929919\pi\) | ||
0.975861 | − | 0.218391i | \(-0.0700808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.99499 | − | 3.60205i | −0.585051 | − | 0.351524i | ||||
\(106\) | −0.613409 | + | 0.613409i | −0.0595796 | + | 0.0595796i | ||||
\(107\) | 13.0554i | 1.26211i | 0.775738 | + | 0.631055i | \(0.217378\pi\) | ||||
−0.775738 | + | 0.631055i | \(0.782622\pi\) | |||||||
\(108\) | −0.509725 | + | 9.73352i | −0.0490484 | + | 0.936608i | ||||
\(109\) | −4.48829 | + | 4.48829i | −0.429901 | + | 0.429901i | −0.888594 | − | 0.458694i | \(-0.848318\pi\) |
0.458694 | + | 0.888594i | \(0.348318\pi\) | |||||||
\(110\) | 1.62405 | + | 1.62405i | 0.154847 | + | 0.154847i | ||||
\(111\) | −3.63127 | + | 0.905429i | −0.344665 | + | 0.0859396i | ||||
\(112\) | 2.68692 | + | 2.68692i | 0.253890 | + | 0.253890i | ||||
\(113\) | 13.0126i | 1.22413i | 0.790809 | + | 0.612063i | \(0.209660\pi\) | ||||
−0.790809 | + | 0.612063i | \(0.790340\pi\) | |||||||
\(114\) | −1.54902 | + | 2.57809i | −0.145079 | + | 0.241460i | ||||
\(115\) | −6.65813 | − | 6.65813i | −0.620874 | − | 0.620874i | ||||
\(116\) | 5.04035 | 0.467985 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.52718 | −0.324704 | ||||||||
\(119\) | −4.84913 | − | 4.84913i | −0.444519 | − | 0.444519i | ||||
\(120\) | 4.23443 | − | 7.04748i | 0.386549 | − | 0.643344i | ||||
\(121\) | 7.48327i | 0.680297i | ||||||||
\(122\) | −0.663584 | − | 0.663584i | −0.0600781 | − | 0.0600781i | ||||
\(123\) | 11.4386 | − | 2.85212i | 1.03138 | − | 0.257167i | ||||
\(124\) | −6.04940 | − | 6.04940i | −0.543252 | − | 0.543252i | ||||
\(125\) | −5.10014 | + | 5.10014i | −0.456171 | + | 0.456171i | ||||
\(126\) | −1.08479 | + | 0.576829i | −0.0966406 | + | 0.0513880i | ||||
\(127\) | − | 7.79402i | − | 0.691607i | −0.938307 | − | 0.345804i | \(-0.887606\pi\) | ||
0.938307 | − | 0.345804i | \(-0.112394\pi\) | |||||||
\(128\) | −6.78230 | + | 6.78230i | −0.599476 | + | 0.599476i | ||||
\(129\) | −8.24172 | − | 4.95198i | −0.725643 | − | 0.435997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 18.5420i | − | 1.62003i | −0.586412 | − | 0.810013i | \(-0.699460\pi\) | ||
0.586412 | − | 0.810013i | \(-0.300540\pi\) | |||||||
\(132\) | −5.91174 | + | 1.47405i | −0.514551 | + | 0.128299i | ||||
\(133\) | 5.72508 | 0.496428 | ||||||||
\(134\) | −2.39785 | −0.207143 | ||||||||
\(135\) | −12.0828 | − | 13.4182i | −1.03992 | − | 1.15485i | ||||
\(136\) | 5.70046 | − | 5.70046i | 0.488810 | − | 0.488810i | ||||
\(137\) | −5.32795 | + | 5.32795i | −0.455197 | + | 0.455197i | −0.897075 | − | 0.441878i | \(-0.854312\pi\) |
0.441878 | + | 0.897075i | \(0.354312\pi\) | |||||||
\(138\) | −1.60497 | + | 0.400186i | −0.136624 | + | 0.0340661i | ||||
\(139\) | −5.39232 | −0.457371 | −0.228685 | − | 0.973500i | \(-0.573443\pi\) | ||||
−0.228685 | + | 0.973500i | \(0.573443\pi\) | |||||||
\(140\) | −7.57428 | −0.640143 | ||||||||
\(141\) | 1.32267 | + | 5.30466i | 0.111389 | + | 0.446733i | ||||
\(142\) | 4.09087i | 0.343298i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.60592 | + | 8.66193i | 0.383827 | + | 0.721828i | ||||
\(145\) | −6.60264 | + | 6.60264i | −0.548319 | + | 0.548319i | ||||
\(146\) | 4.55199i | 0.376725i | ||||||||
\(147\) | −8.38803 | − | 5.03989i | −0.691833 | − | 0.415683i | ||||
\(148\) | −2.86592 | + | 2.86592i | −0.235577 | + | 0.235577i | ||||
\(149\) | −16.1312 | − | 16.1312i | −1.32152 | − | 1.32152i | −0.912545 | − | 0.408977i | \(-0.865886\pi\) |
−0.408977 | − | 0.912545i | \(-0.634114\pi\) | |||||||
\(150\) | 1.04499 | + | 4.19099i | 0.0853231 | + | 0.342193i | ||||
\(151\) | −6.61873 | − | 6.61873i | −0.538625 | − | 0.538625i | 0.384500 | − | 0.923125i | \(-0.374374\pi\) |
−0.923125 | + | 0.384500i | \(0.874374\pi\) | |||||||
\(152\) | 6.73019i | 0.545891i | ||||||||
\(153\) | −8.31241 | − | 15.6324i | −0.672018 | − | 1.26380i | ||||
\(154\) | −0.543062 | − | 0.543062i | −0.0437612 | − | 0.0437612i | ||||
\(155\) | 15.8489 | 1.27301 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.6785 | 1.25128 | 0.625640 | − | 0.780112i | \(-0.284838\pi\) | ||||
0.625640 | + | 0.780112i | \(0.284838\pi\) | |||||||
\(158\) | 0.274158 | + | 0.274158i | 0.0218108 | + | 0.0218108i | ||||
\(159\) | 3.65430 | + | 2.19566i | 0.289805 | + | 0.174127i | ||||
\(160\) | − | 13.4987i | − | 1.06717i | ||||||
\(161\) | 2.22640 | + | 2.22640i | 0.175465 | + | 0.175465i | ||||
\(162\) | −3.11369 | + | 0.605410i | −0.244634 | + | 0.0475655i | ||||
\(163\) | −2.44403 | − | 2.44403i | −0.191432 | − | 0.191432i | 0.604883 | − | 0.796314i | \(-0.293220\pi\) |
−0.796314 | + | 0.604883i | \(0.793220\pi\) | |||||||
\(164\) | 9.02770 | − | 9.02770i | 0.704945 | − | 0.704945i | ||||
\(165\) | 5.81319 | − | 9.67506i | 0.452556 | − | 0.753202i | ||||
\(166\) | − | 2.28741i | − | 0.177537i | ||||||
\(167\) | −3.70756 | + | 3.70756i | −0.286899 | + | 0.286899i | −0.835853 | − | 0.548954i | \(-0.815026\pi\) |
0.548954 | + | 0.835853i | \(0.315026\pi\) | |||||||
\(168\) | −1.41594 | + | 2.35659i | −0.109242 | + | 0.181815i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 7.22802i | 0.554364i | ||||||||
\(171\) | 14.1351 | + | 4.32112i | 1.08094 | + | 0.330444i | ||||
\(172\) | −10.4129 | −0.793975 | ||||||||
\(173\) | 14.2512 | 1.08350 | 0.541751 | − | 0.840539i | \(-0.317762\pi\) | ||||
0.541751 | + | 0.840539i | \(0.317762\pi\) | |||||||
\(174\) | 0.396851 | + | 1.59159i | 0.0300852 | + | 0.120658i | ||||
\(175\) | 5.81370 | − | 5.81370i | 0.439474 | − | 0.439474i | ||||
\(176\) | −4.33630 | + | 4.33630i | −0.326861 | + | 0.326861i | ||||
\(177\) | 4.19369 | + | 16.8190i | 0.315217 | + | 1.26420i | ||||
\(178\) | 1.50634 | 0.112905 | ||||||||
\(179\) | −4.36667 | −0.326381 | −0.163190 | − | 0.986595i | \(-0.552178\pi\) | ||||
−0.163190 | + | 0.986595i | \(0.552178\pi\) | |||||||
\(180\) | −18.7007 | − | 5.71684i | −1.39387 | − | 0.426108i | ||||
\(181\) | 2.10738i | 0.156640i | 0.996928 | + | 0.0783201i | \(0.0249556\pi\) | ||||
−0.996928 | + | 0.0783201i | \(0.975044\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.37526 | + | 3.95321i | −0.175584 | + | 0.292230i | ||||
\(184\) | −2.61727 | + | 2.61727i | −0.192947 | + | 0.192947i | ||||
\(185\) | − | 7.50845i | − | 0.552032i | ||||||
\(186\) | 1.43392 | − | 2.38652i | 0.105140 | − | 0.174988i | ||||
\(187\) | 7.82581 | − | 7.82581i | 0.572280 | − | 0.572280i | ||||
\(188\) | 4.18660 | + | 4.18660i | 0.305339 | + | 0.305339i | ||||
\(189\) | 4.04033 | + | 4.48688i | 0.293890 | + | 0.326372i | ||||
\(190\) | −4.26685 | − | 4.26685i | −0.309550 | − | 0.309550i | ||||
\(191\) | − | 6.79779i | − | 0.491871i | −0.969286 | − | 0.245935i | \(-0.920905\pi\) | ||
0.969286 | − | 0.245935i | \(-0.0790951\pi\) | |||||||
\(192\) | 7.67748 | + | 4.61296i | 0.554075 | + | 0.332912i | ||||
\(193\) | 7.86036 | + | 7.86036i | 0.565801 | + | 0.565801i | 0.930949 | − | 0.365148i | \(-0.118982\pi\) |
−0.365148 | + | 0.930949i | \(0.618982\pi\) | |||||||
\(194\) | −4.32361 | −0.310417 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.5977 | −0.756981 | ||||||||
\(197\) | 1.61492 | + | 1.61492i | 0.115058 | + | 0.115058i | 0.762292 | − | 0.647233i | \(-0.224074\pi\) |
−0.647233 | + | 0.762292i | \(0.724074\pi\) | |||||||
\(198\) | −0.930919 | − | 1.75069i | −0.0661576 | − | 0.124416i | ||||
\(199\) | 18.3431i | 1.30031i | 0.759801 | + | 0.650155i | \(0.225296\pi\) | ||||
−0.759801 | + | 0.650155i | \(0.774704\pi\) | |||||||
\(200\) | 6.83436 | + | 6.83436i | 0.483262 | + | 0.483262i | ||||
\(201\) | 2.85096 | + | 11.4339i | 0.201091 | + | 0.806487i | ||||
\(202\) | 2.76519 | + | 2.76519i | 0.194558 | + | 0.194558i | ||||
\(203\) | 2.20784 | − | 2.20784i | 0.154960 | − | 0.154960i | ||||
\(204\) | −16.4357 | − | 9.87524i | −1.15073 | − | 0.691405i | ||||
\(205\) | 23.6518i | 1.65191i | ||||||||
\(206\) | 1.10474 | − | 1.10474i | 0.0769706 | − | 0.0769706i | ||||
\(207\) | 3.81650 | + | 7.17733i | 0.265265 | + | 0.498859i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.23947i | 0.639107i | ||||||||
\(210\) | −0.596359 | − | 2.39173i | −0.0411527 | − | 0.165045i | ||||
\(211\) | −8.00723 | −0.551241 | −0.275620 | − | 0.961267i | \(-0.588883\pi\) | ||||
−0.275620 | + | 0.961267i | \(0.588883\pi\) | |||||||
\(212\) | 4.61697 | 0.317095 | ||||||||
\(213\) | 19.5069 | − | 4.86389i | 1.33659 | − | 0.333269i | ||||
\(214\) | −3.25361 | + | 3.25361i | −0.222412 | + | 0.222412i | ||||
\(215\) | 13.6404 | − | 13.6404i | 0.930269 | − | 0.930269i | ||||
\(216\) | −5.27460 | + | 4.74965i | −0.358891 | + | 0.323173i | ||||
\(217\) | −5.29967 | −0.359765 | ||||||||
\(218\) | −2.23711 | −0.151516 | ||||||||
\(219\) | 21.7057 | − | 5.41215i | 1.46674 | − | 0.365719i | ||||
\(220\) | − | 12.2238i | − | 0.824129i | ||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.13062 | − | 0.679324i | −0.0758821 | − | 0.0455932i | ||||
\(223\) | 20.0214 | − | 20.0214i | 1.34073 | − | 1.34073i | 0.445400 | − | 0.895332i | \(-0.353062\pi\) |
0.895332 | − | 0.445400i | \(-0.146938\pi\) | |||||||
\(224\) | 4.51381i | 0.301592i | ||||||||
\(225\) | 18.7419 | − | 9.96587i | 1.24946 | − | 0.664391i | ||||
\(226\) | −3.24295 | + | 3.24295i | −0.215718 | + | 0.215718i | ||||
\(227\) | 5.20089 | + | 5.20089i | 0.345195 | + | 0.345195i | 0.858316 | − | 0.513121i | \(-0.171511\pi\) |
−0.513121 | + | 0.858316i | \(0.671511\pi\) | |||||||
\(228\) | 15.5319 | − | 3.87274i | 1.02862 | − | 0.256479i | ||||
\(229\) | −11.4094 | − | 11.4094i | −0.753951 | − | 0.753951i | 0.221263 | − | 0.975214i | \(-0.428982\pi\) |
−0.975214 | + | 0.221263i | \(0.928982\pi\) | |||||||
\(230\) | − | 3.31862i | − | 0.218823i | ||||||
\(231\) | −1.94386 | + | 3.23522i | −0.127896 | + | 0.212862i | ||||
\(232\) | 2.59545 | + | 2.59545i | 0.170400 | + | 0.170400i | ||||
\(233\) | −18.1554 | −1.18940 | −0.594700 | − | 0.803947i | \(-0.702729\pi\) | ||||
−0.594700 | + | 0.803947i | \(0.702729\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.9685 | −0.715508 | ||||||||
\(236\) | 13.2741 | + | 13.2741i | 0.864071 | + | 0.864071i | ||||
\(237\) | 0.981330 | − | 1.63326i | 0.0637442 | − | 0.106091i | ||||
\(238\) | − | 2.41696i | − | 0.156668i | ||||||
\(239\) | 6.54262 | + | 6.54262i | 0.423207 | + | 0.423207i | 0.886306 | − | 0.463099i | \(-0.153263\pi\) |
−0.463099 | + | 0.886306i | \(0.653263\pi\) | |||||||
\(240\) | −19.0978 | + | 4.76187i | −1.23275 | + | 0.307378i | ||||
\(241\) | −19.5707 | − | 19.5707i | −1.26066 | − | 1.26066i | −0.950775 | − | 0.309883i | \(-0.899710\pi\) |
−0.309883 | − | 0.950775i | \(-0.600290\pi\) | |||||||
\(242\) | −1.86495 | + | 1.86495i | −0.119883 | + | 0.119883i | ||||
\(243\) | 6.58890 | + | 14.1275i | 0.422678 | + | 0.906280i | ||||
\(244\) | 4.99463i | 0.319748i | ||||||||
\(245\) | 13.8826 | − | 13.8826i | 0.886925 | − | 0.886925i | ||||
\(246\) | 3.56147 | + | 2.13988i | 0.227071 | + | 0.136434i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 6.23009i | − | 0.395611i | ||||||
\(249\) | −10.9073 | + | 2.71965i | −0.691221 | + | 0.172351i | ||||
\(250\) | −2.54207 | −0.160775 | ||||||||
\(251\) | 5.60006 | 0.353473 | 0.176736 | − | 0.984258i | \(-0.443446\pi\) | ||||
0.176736 | + | 0.984258i | \(0.443446\pi\) | |||||||
\(252\) | 6.25328 | + | 1.91164i | 0.393920 | + | 0.120422i | ||||
\(253\) | −3.59308 | + | 3.59308i | −0.225895 | + | 0.225895i | ||||
\(254\) | 1.94239 | − | 1.94239i | 0.121877 | − | 0.121877i | ||||
\(255\) | 34.4661 | − | 8.59385i | 2.15835 | − | 0.538168i | ||||
\(256\) | 6.96184 | 0.435115 | ||||||||
\(257\) | 6.81357 | 0.425019 | 0.212510 | − | 0.977159i | \(-0.431836\pi\) | ||||
0.212510 | + | 0.977159i | \(0.431836\pi\) | |||||||
\(258\) | −0.819856 | − | 3.28808i | −0.0510420 | − | 0.204707i | ||||
\(259\) | 2.51073i | 0.156009i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.11751 | − | 3.78469i | 0.440563 | − | 0.234266i | ||||
\(262\) | 4.62097 | − | 4.62097i | 0.285485 | − | 0.285485i | ||||
\(263\) | − | 22.6317i | − | 1.39553i | −0.716326 | − | 0.697765i | \(-0.754178\pi\) | ||
0.716326 | − | 0.697765i | \(-0.245822\pi\) | |||||||
\(264\) | −3.80320 | − | 2.28512i | −0.234071 | − | 0.140640i | ||||
\(265\) | −6.04803 | + | 6.04803i | −0.371528 | + | 0.371528i | ||||
\(266\) | 1.42678 | + | 1.42678i | 0.0874816 | + | 0.0874816i | ||||
\(267\) | −1.79098 | − | 7.18283i | −0.109606 | − | 0.439582i | ||||
\(268\) | 9.02401 | + | 9.02401i | 0.551229 | + | 0.551229i | ||||
\(269\) | − | 26.1029i | − | 1.59152i | −0.605610 | − | 0.795762i | \(-0.707071\pi\) | ||
0.605610 | − | 0.795762i | \(-0.292929\pi\) | |||||||
\(270\) | 0.332812 | − | 6.35524i | 0.0202543 | − | 0.386768i | ||||
\(271\) | −12.5033 | − | 12.5033i | −0.759521 | − | 0.759521i | 0.216714 | − | 0.976235i | \(-0.430466\pi\) |
−0.976235 | + | 0.216714i | \(0.930466\pi\) | |||||||
\(272\) | −19.2992 | −1.17019 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.65562 | −0.160432 | ||||||||
\(275\) | 9.38248 | + | 9.38248i | 0.565785 | + | 0.565785i | ||||
\(276\) | 7.54615 | + | 4.53405i | 0.454225 | + | 0.272918i | ||||
\(277\) | − | 22.7007i | − | 1.36395i | −0.731375 | − | 0.681975i | \(-0.761121\pi\) | ||
0.731375 | − | 0.681975i | \(-0.238879\pi\) | |||||||
\(278\) | −1.34385 | − | 1.34385i | −0.0805989 | − | 0.0805989i | ||||
\(279\) | −13.0848 | − | 4.00003i | −0.783364 | − | 0.239476i | ||||
\(280\) | −3.90026 | − | 3.90026i | −0.233085 | − | 0.233085i | ||||
\(281\) | −8.55751 | + | 8.55751i | −0.510498 | + | 0.510498i | −0.914679 | − | 0.404181i | \(-0.867557\pi\) |
0.404181 | + | 0.914679i | \(0.367557\pi\) | |||||||
\(282\) | −0.992373 | + | 1.65164i | −0.0590950 | + | 0.0983535i | ||||
\(283\) | 7.10558i | 0.422383i | 0.977445 | + | 0.211192i | \(0.0677344\pi\) | ||||
−0.977445 | + | 0.211192i | \(0.932266\pi\) | |||||||
\(284\) | 15.3955 | − | 15.3955i | 0.913553 | − | 0.913553i | ||||
\(285\) | −15.2729 | + | 25.4192i | −0.904690 | + | 1.50570i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 7.90886i | − | 0.466845i | ||||||
\(288\) | −3.40689 | + | 11.1445i | −0.200753 | + | 0.656695i | ||||
\(289\) | 17.8297 | 1.04880 | ||||||||
\(290\) | −3.29096 | −0.193252 | ||||||||
\(291\) | 5.14061 | + | 20.6167i | 0.301348 | + | 1.20857i | ||||
\(292\) | 17.1308 | − | 17.1308i | 1.00251 | − | 1.00251i | ||||
\(293\) | 11.2394 | − | 11.2394i | 0.656615 | − | 0.656615i | −0.297963 | − | 0.954578i | \(-0.596307\pi\) |
0.954578 | + | 0.297963i | \(0.0963071\pi\) | |||||||
\(294\) | −0.834411 | − | 3.34645i | −0.0486638 | − | 0.195169i | ||||
\(295\) | −34.7770 | −2.02479 | ||||||||
\(296\) | −2.95152 | −0.171554 | ||||||||
\(297\) | −7.24118 | + | 6.52051i | −0.420176 | + | 0.378358i | ||||
\(298\) | − | 8.04031i | − | 0.465763i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 11.8396 | − | 19.7050i | 0.683558 | − | 1.13767i | ||||
\(301\) | −4.56119 | + | 4.56119i | −0.262902 | + | 0.262902i | ||||
\(302\) | − | 3.29899i | − | 0.189835i | ||||||
\(303\) | 9.89784 | − | 16.4733i | 0.568616 | − | 0.946364i | ||||
\(304\) | 11.3927 | − | 11.3927i | 0.653417 | − | 0.653417i | ||||
\(305\) | −6.54274 | − | 6.54274i | −0.374636 | − | 0.374636i | ||||
\(306\) | 1.82425 | − | 5.96742i | 0.104285 | − | 0.341134i | ||||
\(307\) | −14.3846 | − | 14.3846i | −0.820970 | − | 0.820970i | 0.165277 | − | 0.986247i | \(-0.447148\pi\) |
−0.986247 | + | 0.165277i | \(0.947148\pi\) | |||||||
\(308\) | 4.08749i | 0.232906i | ||||||||
\(309\) | −6.58132 | − | 3.95433i | −0.374398 | − | 0.224954i | ||||
\(310\) | 3.94979 | + | 3.94979i | 0.224333 | + | 0.224333i | ||||
\(311\) | 7.62181 | 0.432193 | 0.216097 | − | 0.976372i | \(-0.430667\pi\) | ||||
0.216097 | + | 0.976372i | \(0.430667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.51488 | −0.368243 | −0.184121 | − | 0.982904i | \(-0.558944\pi\) | ||||
−0.184121 | + | 0.982904i | \(0.558944\pi\) | |||||||
\(314\) | 3.90733 | + | 3.90733i | 0.220503 | + | 0.220503i | ||||
\(315\) | −10.6957 | + | 5.68736i | −0.602634 | + | 0.320447i | ||||
\(316\) | − | 2.06351i | − | 0.116082i | ||||||
\(317\) | −6.29415 | − | 6.29415i | −0.353515 | − | 0.353515i | 0.507901 | − | 0.861416i | \(-0.330422\pi\) |
−0.861416 | + | 0.507901i | \(0.830422\pi\) | |||||||
\(318\) | 0.363516 | + | 1.45790i | 0.0203850 | + | 0.0817551i | ||||
\(319\) | 3.56314 | + | 3.56314i | 0.199497 | + | 0.199497i | ||||
\(320\) | −12.7066 | + | 12.7066i | −0.710319 | + | 0.710319i | ||||
\(321\) | 19.3829 | + | 11.6461i | 1.08185 | + | 0.650021i | ||||
\(322\) | 1.10971i | 0.0618415i | ||||||||
\(323\) | −20.5607 | + | 20.5607i | −1.14403 | + | 1.14403i | ||||
\(324\) | 13.9963 | + | 9.43958i | 0.777575 | + | 0.524421i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 1.21818i | − | 0.0674689i | ||||||
\(327\) | 2.65984 | + | 10.6674i | 0.147089 | + | 0.589910i | ||||
\(328\) | 9.29736 | 0.513361 | ||||||||
\(329\) | 3.66774 | 0.202209 | ||||||||
\(330\) | 3.85991 | − | 0.962439i | 0.212481 | − | 0.0529805i | ||||
\(331\) | 11.3679 | − | 11.3679i | 0.624836 | − | 0.624836i | −0.321928 | − | 0.946764i | \(-0.604331\pi\) |
0.946764 | + | 0.321928i | \(0.104331\pi\) | |||||||
\(332\) | −8.60838 | + | 8.60838i | −0.472446 | + | 0.472446i | ||||
\(333\) | −1.89502 | + | 6.19893i | −0.103847 | + | 0.339699i | ||||
\(334\) | −1.84796 | −0.101116 | ||||||||
\(335\) | −23.6421 | −1.29171 | ||||||||
\(336\) | 6.38605 | − | 1.59231i | 0.348388 | − | 0.0868677i | ||||
\(337\) | − | 28.3556i | − | 1.54463i | −0.635243 | − | 0.772313i | \(-0.719100\pi\) | ||
0.635243 | − | 0.772313i | \(-0.280900\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.3195 | + | 11.6080i | 1.04929 | + | 0.630457i | ||||
\(340\) | 27.2017 | − | 27.2017i | 1.47522 | − | 1.47522i | ||||
\(341\) | − | 8.55291i | − | 0.463166i | ||||||
\(342\) | 2.44579 | + | 4.59958i | 0.132253 | + | 0.248717i | ||||
\(343\) | −10.3937 | + | 10.3937i | −0.561209 | + | 0.561209i | ||||
\(344\) | −5.36196 | − | 5.36196i | −0.289097 | − | 0.289097i | ||||
\(345\) | −15.8245 | + | 3.94572i | −0.851964 | + | 0.212430i | ||||
\(346\) | 3.55163 | + | 3.55163i | 0.190937 | + | 0.190937i | ||||
\(347\) | − | 11.0739i | − | 0.594476i | −0.954803 | − | 0.297238i | \(-0.903935\pi\) | ||
0.954803 | − | 0.297238i | \(-0.0960655\pi\) | |||||||
\(348\) | 4.49626 | − | 7.48325i | 0.241025 | − | 0.401144i | ||||
\(349\) | −21.1548 | − | 21.1548i | −1.13239 | − | 1.13239i | −0.989779 | − | 0.142610i | \(-0.954450\pi\) |
−0.142610 | − | 0.989779i | \(-0.545550\pi\) | |||||||
\(350\) | 2.89773 | 0.154890 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.28464 | −0.388273 | ||||||||
\(353\) | −8.96336 | − | 8.96336i | −0.477072 | − | 0.477072i | 0.427122 | − | 0.904194i | \(-0.359527\pi\) |
−0.904194 | + | 0.427122i | \(0.859527\pi\) | |||||||
\(354\) | −3.14643 | + | 5.23670i | −0.167231 | + | 0.278328i | ||||
\(355\) | 40.3348i | 2.14075i | ||||||||
\(356\) | −5.66891 | − | 5.66891i | −0.300452 | − | 0.300452i | ||||
\(357\) | −11.5250 | + | 2.87368i | −0.609970 | + | 0.152091i | ||||
\(358\) | −1.08824 | − | 1.08824i | −0.0575155 | − | 0.0575155i | ||||
\(359\) | 20.3859 | − | 20.3859i | 1.07593 | − | 1.07593i | 0.0790589 | − | 0.996870i | \(-0.474808\pi\) |
0.996870 | − | 0.0790589i | \(-0.0251915\pi\) | |||||||
\(360\) | −6.68585 | − | 12.5734i | −0.352375 | − | 0.662679i | ||||
\(361\) | − | 5.27475i | − | 0.277619i | ||||||
\(362\) | −0.525192 | + | 0.525192i | −0.0276035 | + | 0.0276035i | ||||
\(363\) | 11.1102 | + | 6.67547i | 0.583133 | + | 0.350371i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 44.8813i | 2.34919i | ||||||||
\(366\) | −1.57715 | + | 0.393251i | −0.0824392 | + | 0.0205556i | ||||
\(367\) | −23.1390 | −1.20784 | −0.603922 | − | 0.797043i | \(-0.706396\pi\) | ||||
−0.603922 | + | 0.797043i | \(0.706396\pi\) | |||||||
\(368\) | 8.86090 | 0.461906 | ||||||||
\(369\) | 5.96937 | − | 19.5268i | 0.310753 | − | 1.01652i | ||||
\(370\) | 1.87122 | − | 1.87122i | 0.0972803 | − | 0.0972803i | ||||
\(371\) | 2.02239 | − | 2.02239i | 0.104997 | − | 0.104997i | ||||
\(372\) | −14.3777 | + | 3.58497i | −0.745451 | + | 0.185872i | ||||
\(373\) | 20.4816 | 1.06050 | 0.530249 | − | 0.847842i | \(-0.322098\pi\) | ||||
0.530249 | + | 0.847842i | \(0.322098\pi\) | |||||||
\(374\) | 3.90063 | 0.201697 | ||||||||
\(375\) | 3.02243 | + | 12.1216i | 0.156078 | + | 0.625958i | ||||
\(376\) | 4.31166i | 0.222357i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.111288 | + | 2.12511i | −0.00572404 | + | 0.109304i | ||||
\(379\) | −2.80816 | + | 2.80816i | −0.144246 | + | 0.144246i | −0.775542 | − | 0.631296i | \(-0.782523\pi\) |
0.631296 | + | 0.775542i | \(0.282523\pi\) | |||||||
\(380\) | 32.1155i | 1.64749i | ||||||||
\(381\) | −11.5715 | − | 6.95267i | −0.592828 | − | 0.356196i | ||||
\(382\) | 1.69412 | − | 1.69412i | 0.0866785 | − | 0.0866785i | ||||
\(383\) | 18.8170 | + | 18.8170i | 0.961502 | + | 0.961502i | 0.999286 | − | 0.0377843i | \(-0.0120300\pi\) |
−0.0377843 | + | 0.999286i | \(0.512030\pi\) | |||||||
\(384\) | 4.01930 | + | 16.1196i | 0.205109 | + | 0.822602i | ||||
\(385\) | −5.35443 | − | 5.35443i | −0.272887 | − | 0.272887i | ||||
\(386\) | 3.91785i | 0.199413i | ||||||||
\(387\) | −14.7041 | + | 7.81881i | −0.747451 | + | 0.397452i | ||||
\(388\) | 16.2714 | + | 16.2714i | 0.826053 | + | 0.826053i | ||||
\(389\) | 6.17335 | 0.313001 | 0.156501 | − | 0.987678i | \(-0.449979\pi\) | ||||
0.156501 | + | 0.987678i | \(0.449979\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.9914 | −0.808722 | ||||||||
\(392\) | −5.45714 | − | 5.45714i | −0.275627 | − | 0.275627i | ||||
\(393\) | −27.5288 | − | 16.5405i | −1.38864 | − | 0.834357i | ||||
\(394\) | 0.804928i | 0.0405517i | ||||||||
\(395\) | 2.70311 | + | 2.70311i | 0.136008 | + | 0.136008i | ||||
\(396\) | −3.08511 | + | 10.0919i | −0.155033 | + | 0.507137i | ||||
\(397\) | 16.8721 | + | 16.8721i | 0.846785 | + | 0.846785i | 0.989731 | − | 0.142946i | \(-0.0456575\pi\) |
−0.142946 | + | 0.989731i | \(0.545657\pi\) | |||||||
\(398\) | −4.57140 | + | 4.57140i | −0.229143 | + | 0.229143i | ||||
\(399\) | 5.10708 | − | 8.49985i | 0.255674 | − | 0.425525i | ||||
\(400\) | − | 23.1381i | − | 1.15691i | ||||||
\(401\) | −16.4059 | + | 16.4059i | −0.819274 | + | 0.819274i | −0.986003 | − | 0.166729i | \(-0.946679\pi\) |
0.166729 | + | 0.986003i | \(0.446679\pi\) | |||||||
\(402\) | −2.13901 | + | 3.56002i | −0.106684 | + | 0.177558i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 20.8129i | − | 1.03548i | ||||||
\(405\) | −30.7000 | + | 5.96917i | −1.52550 | + | 0.296610i | ||||
\(406\) | 1.10046 | 0.0546147 | ||||||||
\(407\) | −4.05196 | −0.200848 | ||||||||
\(408\) | −3.37818 | − | 13.5484i | −0.167245 | − | 0.670746i | ||||
\(409\) | −8.88715 | + | 8.88715i | −0.439441 | + | 0.439441i | −0.891824 | − | 0.452383i | \(-0.850574\pi\) |
0.452383 | + | 0.891824i | \(0.350574\pi\) | |||||||
\(410\) | −5.89440 | + | 5.89440i | −0.291103 | + | 0.291103i | ||||
\(411\) | 3.15743 | + | 12.6630i | 0.155744 | + | 0.624622i | ||||
\(412\) | −8.31506 | −0.409654 | ||||||||
\(413\) | 11.6290 | 0.572225 | ||||||||
\(414\) | −0.837573 | + | 2.73984i | −0.0411645 | + | 0.134656i | ||||
\(415\) | − | 22.5532i | − | 1.10709i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.81024 | + | 8.00582i | −0.235558 | + | 0.392047i | ||||
\(418\) | −2.30262 | + | 2.30262i | −0.112625 | + | 0.112625i | ||||
\(419\) | 26.8089i | 1.30970i | 0.755758 | + | 0.654851i | \(0.227269\pi\) | ||||
−0.755758 | + | 0.654851i | \(0.772731\pi\) | |||||||
\(420\) | −6.75666 | + | 11.2453i | −0.329691 | + | 0.548714i | ||||
\(421\) | 8.93430 | − | 8.93430i | 0.435431 | − | 0.435431i | −0.455040 | − | 0.890471i | \(-0.650375\pi\) |
0.890471 | + | 0.455040i | \(0.150375\pi\) | |||||||
\(422\) | −1.99553 | − | 1.99553i | −0.0971408 | − | 0.0971408i | ||||
\(423\) | 9.05556 | + | 2.76830i | 0.440296 | + | 0.134599i | ||||
\(424\) | 2.37744 | + | 2.37744i | 0.115459 | + | 0.115459i | ||||
\(425\) | 41.7578i | 2.02555i | ||||||||
\(426\) | 6.07359 | + | 3.64927i | 0.294266 | + | 0.176808i | ||||
\(427\) | 2.18781 | + | 2.18781i | 0.105876 | + | 0.105876i | ||||
\(428\) | 24.4891 | 1.18372 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.79881 | 0.327868 | ||||||||
\(431\) | −15.0091 | − | 15.0091i | −0.722961 | − | 0.722961i | 0.246246 | − | 0.969207i | \(-0.420803\pi\) |
−0.969207 | + | 0.246246i | \(0.920803\pi\) | |||||||
\(432\) | 16.9688 | + | 0.888625i | 0.816413 | + | 0.0427540i | ||||
\(433\) | 1.85372i | 0.0890840i | 0.999008 | + | 0.0445420i | \(0.0141828\pi\) | ||||
−0.999008 | + | 0.0445420i | \(0.985817\pi\) | |||||||
\(434\) | −1.32076 | − | 1.32076i | −0.0633986 | − | 0.0633986i | ||||
\(435\) | 3.91283 | + | 15.6926i | 0.187606 | + | 0.752404i | ||||
\(436\) | 8.41907 | + | 8.41907i | 0.403200 | + | 0.403200i | ||||
\(437\) | 9.44007 | − | 9.44007i | 0.451580 | − | 0.451580i | ||||
\(438\) | 6.75820 | + | 4.06061i | 0.322919 | + | 0.194024i | ||||
\(439\) | 14.4053i | 0.687526i | 0.939056 | + | 0.343763i | \(0.111702\pi\) | ||||
−0.939056 | + | 0.343763i | \(0.888298\pi\) | |||||||
\(440\) | 6.29446 | − | 6.29446i | 0.300077 | − | 0.300077i | ||||
\(441\) | −14.9651 | + | 7.95761i | −0.712625 | + | 0.378934i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 22.2330i | − | 1.05632i | −0.849144 | − | 0.528162i | \(-0.822881\pi\) | ||
0.849144 | − | 0.528162i | \(-0.177119\pi\) | |||||||
\(444\) | 1.69839 | + | 6.81148i | 0.0806020 | + | 0.323259i | ||||
\(445\) | 14.8521 | 0.704055 | ||||||||
\(446\) | 9.97929 | 0.472533 | ||||||||
\(447\) | −38.3394 | + | 9.55963i | −1.81339 | + | 0.452155i | ||||
\(448\) | 4.24892 | − | 4.24892i | 0.200743 | − | 0.200743i | ||||
\(449\) | −17.3832 | + | 17.3832i | −0.820362 | + | 0.820362i | −0.986160 | − | 0.165798i | \(-0.946980\pi\) |
0.165798 | + | 0.986160i | \(0.446980\pi\) | |||||||
\(450\) | 7.15442 | + | 2.18712i | 0.337263 | + | 0.103102i | ||||
\(451\) | 12.7638 | 0.601022 | ||||||||
\(452\) | 24.4089 | 1.14810 | ||||||||
\(453\) | −15.7309 | + | 3.92237i | −0.739102 | + | 0.184289i | ||||
\(454\) | 2.59229i | 0.121662i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.99211 | + | 6.00368i | 0.467923 | + | 0.281148i | ||||
\(457\) | 4.78633 | − | 4.78633i | 0.223895 | − | 0.223895i | −0.586241 | − | 0.810136i | \(-0.699393\pi\) |
0.810136 | + | 0.586241i | \(0.199393\pi\) | |||||||
\(458\) | − | 5.68678i | − | 0.265726i | ||||||
\(459\) | −30.6240 | − | 1.60372i | −1.42941 | − | 0.0748552i | ||||
\(460\) | −12.4892 | + | 12.4892i | −0.582312 | + | 0.582312i | ||||
\(461\) | −8.76156 | − | 8.76156i | −0.408067 | − | 0.408067i | 0.472997 | − | 0.881064i | \(-0.343172\pi\) |
−0.881064 | + | 0.472997i | \(0.843172\pi\) | |||||||
\(462\) | −1.29071 | + | 0.321828i | −0.0600491 | + | 0.0149728i | ||||
\(463\) | −6.97385 | − | 6.97385i | −0.324102 | − | 0.324102i | 0.526236 | − | 0.850339i | \(-0.323603\pi\) |
−0.850339 | + | 0.526236i | \(0.823603\pi\) | |||||||
\(464\) | − | 8.78704i | − | 0.407928i | ||||||
\(465\) | 14.1380 | − | 23.5304i | 0.655636 | − | 1.09119i | ||||
\(466\) | −4.52462 | − | 4.52462i | −0.209599 | − | 0.209599i | ||||
\(467\) | 9.19934 | 0.425695 | 0.212847 | − | 0.977085i | \(-0.431726\pi\) | ||||
0.212847 | + | 0.977085i | \(0.431726\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.90563 | 0.365048 | ||||||||
\(470\) | −2.73353 | − | 2.73353i | −0.126088 | − | 0.126088i | ||||
\(471\) | 13.9860 | − | 23.2774i | 0.644443 | − | 1.07257i | ||||
\(472\) | 13.6706i | 0.629240i | ||||||||
\(473\) | −7.36110 | − | 7.36110i | −0.338464 | − | 0.338464i | ||||
\(474\) | 0.651596 | − | 0.162470i | 0.0299288 | − | 0.00746251i | ||||
\(475\) | −24.6505 | − | 24.6505i | −1.13104 | − | 1.13104i | ||||
\(476\) | −9.09592 | + | 9.09592i | −0.416911 | + | 0.416911i | ||||
\(477\) | 6.51966 | − | 3.46678i | 0.298515 | − | 0.158733i | ||||
\(478\) | 3.26105i | 0.149157i | ||||||||
\(479\) | 16.2278 | − | 16.2278i | 0.741469 | − | 0.741469i | −0.231392 | − | 0.972861i | \(-0.574328\pi\) |
0.972861 | + | 0.231392i | \(0.0743279\pi\) | |||||||
\(480\) | −20.0412 | − | 12.0416i | −0.914750 | − | 0.549621i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 9.75464i | − | 0.444312i | ||||||
\(483\) | 5.29152 | − | 1.31940i | 0.240773 | − | 0.0600347i | ||||
\(484\) | 14.0370 | 0.638045 | ||||||||
\(485\) | −42.6295 | −1.93571 | ||||||||
\(486\) | −1.87874 | + | 5.16285i | −0.0852213 | + | 0.234192i | ||||
\(487\) | 20.8383 | − | 20.8383i | 0.944271 | − | 0.944271i | −0.0542557 | − | 0.998527i | \(-0.517279\pi\) |
0.998527 | + | 0.0542557i | \(0.0172786\pi\) | |||||||
\(488\) | −2.57191 | + | 2.57191i | −0.116425 | + | 0.116425i | ||||
\(489\) | −5.80879 | + | 1.44838i | −0.262682 | + | 0.0654978i | ||||
\(490\) | 6.91951 | 0.312592 | ||||||||
\(491\) | 15.3239 | 0.691558 | 0.345779 | − | 0.938316i | \(-0.387615\pi\) | ||||
0.345779 | + | 0.938316i | \(0.387615\pi\) | |||||||
\(492\) | −5.34996 | − | 21.4563i | −0.241195 | − | 0.967326i | ||||
\(493\) | 15.8582i | 0.714215i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.17859 | − | 17.2613i | −0.412547 | − | 0.775838i | ||||
\(496\) | −10.5462 | + | 10.5462i | −0.473536 | + | 0.473536i | ||||
\(497\) | − | 13.4874i | − | 0.604995i | ||||||
\(498\) | −3.39605 | − | 2.04049i | −0.152181 | − | 0.0914365i | ||||
\(499\) | −29.5332 | + | 29.5332i | −1.32209 | + | 1.32209i | −0.410004 | + | 0.912084i | \(0.634473\pi\) |
−0.912084 | + | 0.410004i | \(0.865527\pi\) | |||||||
\(500\) | 9.56676 | + | 9.56676i | 0.427839 | + | 0.427839i | ||||
\(501\) | 2.19716 | + | 8.81183i | 0.0981618 | + | 0.393683i | ||||
\(502\) | 1.39562 | + | 1.39562i | 0.0622897 | + | 0.0622897i | ||||
\(503\) | 34.7649i | 1.55009i | 0.631905 | + | 0.775046i | \(0.282273\pi\) | ||||
−0.631905 | + | 0.775046i | \(0.717727\pi\) | |||||||
\(504\) | 2.23566 | + | 4.20440i | 0.0995844 | + | 0.187279i | ||||
\(505\) | 27.2640 | + | 27.2640i | 1.21323 | + | 1.21323i | ||||
\(506\) | −1.79091 | −0.0796155 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.6199 | −0.648653 | ||||||||
\(509\) | −31.3223 | − | 31.3223i | −1.38834 | − | 1.38834i | −0.828814 | − | 0.559525i | \(-0.810984\pi\) |
−0.559525 | − | 0.828814i | \(-0.689016\pi\) | |||||||
\(510\) | 10.7312 | + | 6.44778i | 0.475186 | + | 0.285512i | ||||
\(511\) | − | 15.0077i | − | 0.663903i | ||||||
\(512\) | 15.2996 | + | 15.2996i | 0.676153 | + | 0.676153i | ||||
\(513\) | 19.0247 | − | 17.1313i | 0.839960 | − | 0.756364i | ||||
\(514\) | 1.69805 | + | 1.69805i | 0.0748978 | + | 0.0748978i | ||||
\(515\) | 10.8924 | − | 10.8924i | 0.479975 | − | 0.479975i | ||||
\(516\) | −9.28884 | + | 15.4597i | −0.408918 | + | 0.680575i | ||||
\(517\) | 5.91921i | 0.260326i | ||||||||
\(518\) | −0.625714 | + | 0.625714i | −0.0274923 | + | 0.0274923i | ||||
\(519\) | 12.7128 | − | 21.1584i | 0.558032 | − | 0.928749i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.93372i | − | 0.0847179i | −0.999102 | − | 0.0423590i | \(-0.986513\pi\) | ||
0.999102 | − | 0.0423590i | \(-0.0134873\pi\) | |||||||
\(522\) | 2.71700 | + | 0.830592i | 0.118920 | + | 0.0363540i | ||||
\(523\) | 1.50610 | 0.0658572 | 0.0329286 | − | 0.999458i | \(-0.489517\pi\) | ||||
0.0329286 | + | 0.999458i | \(0.489517\pi\) | |||||||
\(524\) | −34.7809 | −1.51941 | ||||||||
\(525\) | −3.44529 | − | 13.8175i | −0.150365 | − | 0.603047i | ||||
\(526\) | 5.64018 | − | 5.64018i | 0.245923 | − | 0.245923i | ||||
\(527\) | 19.0329 | − | 19.0329i | 0.829085 | − | 0.829085i | ||||
\(528\) | 2.56976 | + | 10.3062i | 0.111835 | + | 0.448519i | ||||
\(529\) | −15.6578 | −0.680774 | ||||||||
\(530\) | −3.01453 | −0.130943 | ||||||||
\(531\) | 28.7117 | + | 8.77722i | 1.24598 | + | 0.380899i | ||||
\(532\) | − | 10.7390i | − | 0.465595i | ||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.34373 | − | 2.23641i | 0.0581490 | − | 0.0967791i | ||||
\(535\) | −32.0796 | + | 32.0796i | −1.38692 | + | 1.38692i | ||||
\(536\) | 9.29356i | 0.401421i | ||||||||
\(537\) | −3.89530 | + | 6.48307i | −0.168095 | + | 0.279765i | ||||
\(538\) | 6.50526 | − | 6.50526i | 0.280462 | − | 0.280462i | ||||
\(539\) | −7.49178 | − | 7.49178i | −0.322694 | − | 0.322694i | ||||
\(540\) | −25.1696 | + | 22.6646i | −1.08313 | + | 0.975331i | ||||
\(541\) | 2.56375 | + | 2.56375i | 0.110224 | + | 0.110224i | 0.760068 | − | 0.649844i | \(-0.225166\pi\) |
−0.649844 | + | 0.760068i | \(0.725166\pi\) | |||||||
\(542\) | − | 6.23204i | − | 0.267689i | ||||||
\(543\) | 3.12876 | + | 1.87989i | 0.134268 | + | 0.0806739i | ||||
\(544\) | −16.2106 | − | 16.2106i | −0.695023 | − | 0.695023i | ||||
\(545\) | −22.0572 | −0.944827 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.1549 | 0.990030 | 0.495015 | − | 0.868884i | \(-0.335163\pi\) | ||||
0.495015 | + | 0.868884i | \(0.335163\pi\) | |||||||
\(548\) | 9.99407 | + | 9.99407i | 0.426926 | + | 0.426926i | ||||
\(549\) | 3.75036 | + | 7.05295i | 0.160061 | + | 0.301012i | ||||
\(550\) | 4.67652i | 0.199408i | ||||||||
\(551\) | −9.36139 | − | 9.36139i | −0.398809 | − | 0.398809i | ||||
\(552\) | 1.55104 | + | 6.22051i | 0.0660165 | + | 0.264763i | ||||
\(553\) | −0.903887 | − | 0.903887i | −0.0384372 | − | 0.0384372i | ||||
\(554\) | 5.65736 | − | 5.65736i | 0.240358 | − | 0.240358i | ||||
\(555\) | −11.1476 | − | 6.69793i | −0.473188 | − | 0.284311i | ||||
\(556\) | 10.1148i | 0.428964i | ||||||||
\(557\) | −2.53023 | + | 2.53023i | −0.107209 | + | 0.107209i | −0.758677 | − | 0.651467i | \(-0.774154\pi\) |
0.651467 | + | 0.758677i | \(0.274154\pi\) | |||||||
\(558\) | −2.26406 | − | 4.25780i | −0.0958451 | − | 0.180247i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 13.2045i | 0.557994i | ||||||||
\(561\) | −4.63770 | − | 18.5998i | −0.195804 | − | 0.785283i | ||||
\(562\) | −4.26533 | −0.179922 | ||||||||
\(563\) | 19.6742 | 0.829169 | 0.414585 | − | 0.910011i | \(-0.363927\pi\) | ||||
0.414585 | + | 0.910011i | \(0.363927\pi\) | |||||||
\(564\) | 9.95039 | − | 2.48105i | 0.418987 | − | 0.104471i | ||||
\(565\) | −31.9746 | + | 31.9746i | −1.34518 | + | 1.34518i | ||||
\(566\) | −1.77082 | + | 1.77082i | −0.0744332 | + | 0.0744332i | ||||
\(567\) | 10.2657 | − | 1.99601i | 0.431119 | − | 0.0838247i | ||||
\(568\) | 15.8553 | 0.665275 | ||||||||
\(569\) | −9.56462 | −0.400970 | −0.200485 | − | 0.979697i | \(-0.564252\pi\) | ||||
−0.200485 | + | 0.979697i | \(0.564252\pi\) | |||||||
\(570\) | −10.1411 | + | 2.52861i | −0.424764 | + | 0.105912i | ||||
\(571\) | 17.9785i | 0.752375i | 0.926544 | + | 0.376187i | \(0.122765\pi\) | ||||
−0.926544 | + | 0.376187i | \(0.877235\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.0925 | − | 6.06399i | −0.421619 | − | 0.253327i | ||||
\(574\) | 1.97101 | − | 1.97101i | 0.0822685 | − | 0.0822685i | ||||
\(575\) | − | 19.1724i | − | 0.799544i | ||||||
\(576\) | 13.6974 | − | 7.28352i | 0.570726 | − | 0.303480i | ||||
\(577\) | 6.37509 | − | 6.37509i | 0.265398 | − | 0.265398i | −0.561844 | − | 0.827243i | \(-0.689908\pi\) |
0.827243 | + | 0.561844i | \(0.189908\pi\) | |||||||
\(578\) | 4.44343 | + | 4.44343i | 0.184823 | + | 0.184823i | ||||
\(579\) | 18.6819 | − | 4.65818i | 0.776393 | − | 0.193587i | ||||
\(580\) | 12.3851 | + | 12.3851i | 0.514264 | + | 0.514264i | ||||
\(581\) | 7.54150i | 0.312874i | ||||||||
\(582\) | −3.85689 | + | 6.41913i | −0.159873 | + | 0.266082i | ||||
\(583\) | 3.26384 | + | 3.26384i | 0.135175 | + | 0.135175i | ||||
\(584\) | 17.6425 | 0.730053 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.60209 | 0.231420 | ||||||||
\(587\) | 22.1906 | + | 22.1906i | 0.915902 | + | 0.915902i | 0.996728 | − | 0.0808262i | \(-0.0257559\pi\) |
−0.0808262 | + | 0.996728i | \(0.525756\pi\) | |||||||
\(588\) | −9.45374 | + | 15.7341i | −0.389866 | + | 0.648865i | ||||
\(589\) | 22.4710i | 0.925900i | ||||||||
\(590\) | −8.66697 | − | 8.66697i | −0.356814 | − | 0.356814i | ||||
\(591\) | 3.83822 | − | 0.957029i | 0.157883 | − | 0.0393669i | ||||
\(592\) | 4.99627 | + | 4.99627i | 0.205345 | + | 0.205345i | ||||
\(593\) | −23.7211 | + | 23.7211i | −0.974108 | + | 0.974108i | −0.999673 | − | 0.0255650i | \(-0.991862\pi\) |
0.0255650 | + | 0.999673i | \(0.491862\pi\) | |||||||
\(594\) | −3.42963 | − | 0.179603i | −0.140719 | − | 0.00736920i | ||||
\(595\) | − | 23.8305i | − | 0.976956i | ||||||
\(596\) | −30.2587 | + | 30.2587i | −1.23944 | + | 1.23944i | ||||
\(597\) | 27.2335 | + | 16.3630i | 1.11459 | + | 0.669695i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.7915i | 1.38068i | 0.723484 | + | 0.690341i | \(0.242540\pi\) | ||||
−0.723484 | + | 0.690341i | \(0.757460\pi\) | |||||||
\(600\) | 16.2434 | − | 4.05016i | 0.663133 | − | 0.165347i | ||||
\(601\) | −30.1484 | −1.22978 | −0.614888 | − | 0.788614i | \(-0.710799\pi\) | ||||
−0.614888 | + | 0.788614i | \(0.710799\pi\) | |||||||
\(602\) | −2.27344 | −0.0926584 | ||||||||
\(603\) | 19.5188 | + | 5.96693i | 0.794867 | + | 0.242992i | ||||
\(604\) | −12.4153 | + | 12.4153i | −0.505172 | + | 0.505172i | ||||
\(605\) | −18.3878 | + | 18.3878i | −0.747572 | + | 0.747572i | ||||
\(606\) | 6.57209 | − | 1.63870i | 0.266973 | − | 0.0665676i | ||||
\(607\) | 22.0396 | 0.894561 | 0.447281 | − | 0.894394i | \(-0.352392\pi\) | ||||
0.447281 | + | 0.894394i | \(0.352392\pi\) | |||||||
\(608\) | 19.1389 | 0.776184 | ||||||||
\(609\) | −1.30840 | − | 5.24742i | −0.0530191 | − | 0.212636i | ||||
\(610\) | − | 3.26111i | − | 0.132038i | ||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −29.3229 | + | 15.5923i | −1.18531 | + | 0.630280i | ||||
\(613\) | −0.418180 | + | 0.418180i | −0.0168901 | + | 0.0168901i | −0.715501 | − | 0.698611i | \(-0.753802\pi\) |
0.698611 | + | 0.715501i | \(0.253802\pi\) | |||||||
\(614\) | − | 7.16972i | − | 0.289346i | ||||||
\(615\) | 35.1151 | + | 21.0986i | 1.41598 | + | 0.850779i | ||||
\(616\) | −2.10479 | + | 2.10479i | −0.0848044 | + | 0.0848044i | ||||
\(617\) | 20.5560 | + | 20.5560i | 0.827552 | + | 0.827552i | 0.987178 | − | 0.159626i | \(-0.0510288\pi\) |
−0.159626 | + | 0.987178i | \(0.551029\pi\) | |||||||
\(618\) | −0.654685 | − | 2.62565i | −0.0263353 | − | 0.105619i | ||||
\(619\) | −22.7868 | − | 22.7868i | −0.915881 | − | 0.915881i | 0.0808459 | − | 0.996727i | \(-0.474238\pi\) |
−0.996727 | + | 0.0808459i | \(0.974238\pi\) | |||||||
\(620\) | − | 29.7291i | − | 1.19395i | ||||||
\(621\) | 14.0605 | + | 0.736320i | 0.564228 | + | 0.0295475i | ||||
\(622\) | 1.89948 | + | 1.89948i | 0.0761620 | + | 0.0761620i | ||||
\(623\) | −4.96634 | −0.198972 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.3139 | 0.412556 | ||||||||
\(626\) | −1.62361 | − | 1.62361i | −0.0648925 | − | 0.0648925i | ||||
\(627\) | 13.7175 | + | 8.24209i | 0.547826 | + | 0.329157i | ||||
\(628\) | − | 29.4095i | − | 1.17357i | ||||||
\(629\) | −9.01686 | − | 9.01686i | −0.359526 | − | 0.359526i | ||||
\(630\) | −4.08291 | − | 1.24815i | −0.162667 | − | 0.0497277i | ||||
\(631\) | 28.6918 | + | 28.6918i | 1.14220 | + | 1.14220i | 0.988047 | + | 0.154155i | \(0.0492656\pi\) |
0.154155 | + | 0.988047i | \(0.450734\pi\) | |||||||
\(632\) | 1.06258 | − | 1.06258i | 0.0422670 | − | 0.0422670i | ||||
\(633\) | −7.14287 | + | 11.8881i | −0.283904 | + | 0.472509i | ||||
\(634\) | − | 3.13720i | − | 0.124594i | ||||||
\(635\) | 19.1514 | − | 19.1514i | 0.760001 | − | 0.760001i | ||||
\(636\) | 4.11858 | − | 6.85468i | 0.163312 | − | 0.271806i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.77598i | 0.0703117i | ||||||||
\(639\) | 10.1799 | − | 33.3002i | 0.402711 | − | 1.31733i | ||||
\(640\) | −33.3308 | −1.31752 | ||||||||
\(641\) | 25.7121 | 1.01557 | 0.507783 | − | 0.861485i | \(-0.330465\pi\) | ||||
0.507783 | + | 0.861485i | \(0.330465\pi\) | |||||||
\(642\) | 1.92814 | + | 7.73291i | 0.0760976 | + | 0.305194i | ||||
\(643\) | 0.448106 | − | 0.448106i | 0.0176716 | − | 0.0176716i | −0.698216 | − | 0.715887i | \(-0.746022\pi\) |
0.715887 | + | 0.698216i | \(0.246022\pi\) | |||||||
\(644\) | 4.17624 | − | 4.17624i | 0.164567 | − | 0.164567i | ||||
\(645\) | −8.08354 | − | 32.4195i | −0.318289 | − | 1.27652i | ||||
\(646\) | −10.2481 | −0.403205 | ||||||||
\(647\) | −47.0248 | −1.84874 | −0.924368 | − | 0.381501i | \(-0.875407\pi\) | ||||
−0.924368 | + | 0.381501i | \(0.875407\pi\) | |||||||
\(648\) | 2.34644 | + | 12.0680i | 0.0921768 | + | 0.474075i | ||||
\(649\) | 18.7675i | 0.736690i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.72758 | + | 7.86826i | −0.185289 | + | 0.308381i | ||||
\(652\) | −4.58448 | + | 4.58448i | −0.179542 | + | 0.179542i | ||||
\(653\) | 28.9755i | 1.13390i | 0.823753 | + | 0.566949i | \(0.191876\pi\) | ||||
−0.823753 | + | 0.566949i | \(0.808124\pi\) | |||||||
\(654\) | −1.99562 | + | 3.32136i | −0.0780348 | + | 0.129876i | ||||
\(655\) | 45.5614 | − | 45.5614i | 1.78023 | − | 1.78023i | ||||
\(656\) | −15.7384 | − | 15.7384i | −0.614479 | − | 0.614479i | ||||
\(657\) | 11.3274 | − | 37.0537i | 0.441924 | − | 1.44560i | ||||
\(658\) | 0.914059 | + | 0.914059i | 0.0356337 | + | 0.0356337i | ||||
\(659\) | − | 46.6822i | − | 1.81848i | −0.416271 | − | 0.909241i | \(-0.636663\pi\) | ||
0.416271 | − | 0.909241i | \(-0.363337\pi\) | |||||||
\(660\) | −18.1483 | − | 10.9043i | −0.706422 | − | 0.424448i | ||||
\(661\) | 4.90953 | + | 4.90953i | 0.190959 | + | 0.190959i | 0.796110 | − | 0.605152i | \(-0.206887\pi\) |
−0.605152 | + | 0.796110i | \(0.706887\pi\) | |||||||
\(662\) | 5.66611 | 0.220220 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.86551 | −0.344048 | ||||||||
\(665\) | 14.0676 | + | 14.0676i | 0.545520 | + | 0.545520i | ||||
\(666\) | −2.01714 | + | 1.07260i | −0.0781627 | + | 0.0415625i | ||||
\(667\) | − | 7.28100i | − | 0.281921i | ||||||
\(668\) | 6.95457 | + | 6.95457i | 0.269080 | + | 0.269080i | ||||
\(669\) | −11.8650 | − | 47.5853i | −0.458728 | − | 1.83975i | ||||
\(670\) | −5.89199 | − | 5.89199i | −0.227627 | − | 0.227627i | ||||
\(671\) | −3.53081 | + | 3.53081i | −0.136306 | + | 0.136306i | ||||
\(672\) | 6.70151 | + | 4.02656i | 0.258517 | + | 0.155328i | ||||
\(673\) | 26.1949i | 1.00974i | 0.863196 | + | 0.504870i | \(0.168459\pi\) | ||||
−0.863196 | + | 0.504870i | \(0.831541\pi\) | |||||||
\(674\) | 7.06665 | − | 7.06665i | 0.272197 | − | 0.272197i | ||||
\(675\) | 1.92272 | − | 36.7156i | 0.0740057 | − | 1.41318i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 21.9298i | − | 0.842829i | −0.906868 | − | 0.421415i | \(-0.861534\pi\) | ||
0.906868 | − | 0.421415i | \(-0.138466\pi\) | |||||||
\(678\) | 1.92183 | + | 7.70760i | 0.0738074 | + | 0.296008i | ||||
\(679\) | 14.2548 | 0.547048 | ||||||||
\(680\) | 28.0142 | 1.07430 | ||||||||
\(681\) | 12.3611 | − | 3.08213i | 0.473677 | − | 0.118108i | ||||
\(682\) | 2.13152 | − | 2.13152i | 0.0816201 | − | 0.0816201i | ||||
\(683\) | −5.39035 | + | 5.39035i | −0.206256 | + | 0.206256i | −0.802674 | − | 0.596418i | \(-0.796590\pi\) |
0.596418 | + | 0.802674i | \(0.296590\pi\) | |||||||
\(684\) | 8.10549 | − | 26.5144i | 0.309921 | − | 1.01380i | ||||
\(685\) | −26.1836 | −1.00042 | ||||||||
\(686\) | −5.18057 | −0.197795 | ||||||||
\(687\) | −27.1169 | + | 6.76137i | −1.03457 | + | 0.257962i | ||||
\(688\) | 18.1532i | 0.692084i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −4.92706 | − | 2.96039i | −0.187570 | − | 0.112700i | ||||
\(691\) | 11.2800 | − | 11.2800i | 0.429113 | − | 0.429113i | −0.459213 | − | 0.888326i | \(-0.651869\pi\) |
0.888326 | + | 0.459213i | \(0.151869\pi\) | |||||||
\(692\) | − | 26.7322i | − | 1.01621i | ||||||
\(693\) | 3.06921 | + | 5.77197i | 0.116589 | + | 0.219259i | ||||
\(694\) | 2.75978 | − | 2.75978i | 0.104760 | − | 0.104760i | ||||
\(695\) | −13.2500 | − | 13.2500i | −0.502600 | − | 0.502600i | ||||
\(696\) | 6.16867 | − | 1.53811i | 0.233823 | − | 0.0583018i | ||||
\(697\) | 28.4033 | + | 28.4033i | 1.07585 | + | 1.07585i | ||||
\(698\) | − | 10.5442i | − | 0.399104i | ||||||
\(699\) | −16.1956 | + | 26.9548i | −0.612573 | + | 1.01952i | ||||
\(700\) | −10.9052 | − | 10.9052i | −0.412179 | − | 0.412179i | ||||
\(701\) | −30.3059 | −1.14464 | −0.572319 | − | 0.820031i | \(-0.693956\pi\) | ||||
−0.572319 | + | 0.820031i | \(0.693956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.6457 | 0.401509 | ||||||||
\(704\) | 6.85715 | + | 6.85715i | 0.258439 | + | 0.258439i | ||||
\(705\) | −9.78451 | + | 16.2846i | −0.368506 | + | 0.613315i | ||||
\(706\) | − | 4.46762i | − | 0.168141i | ||||||
\(707\) | −9.11674 | − | 9.11674i | −0.342870 | − | 0.342870i | ||||
\(708\) | 31.5489 | − | 7.86646i | 1.18568 | − | 0.295639i | ||||
\(709\) | −24.0489 | − | 24.0489i | −0.903174 | − | 0.903174i | 0.0925354 | − | 0.995709i | \(-0.470503\pi\) |
−0.995709 | + | 0.0925354i | \(0.970503\pi\) | |||||||
\(710\) | −10.0521 | + | 10.0521i | −0.377247 | + | 0.377247i | ||||
\(711\) | −1.54945 | − | 2.91390i | −0.0581088 | − | 0.109280i | ||||
\(712\) | − | 5.83824i | − | 0.218797i | ||||||
\(713\) | −8.73861 | + | 8.73861i | −0.327264 | + | 0.327264i | ||||
\(714\) | −3.58839 | − | 2.15606i | −0.134292 | − | 0.0806884i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.19093i | 0.306110i | ||||||||
\(717\) | 15.5500 | − | 3.87727i | 0.580725 | − | 0.144799i | ||||
\(718\) | 10.1610 | 0.379205 | ||||||||
\(719\) | −7.89679 | −0.294500 | −0.147250 | − | 0.989099i | \(-0.547042\pi\) | ||||
−0.147250 | + | 0.989099i | \(0.547042\pi\) | |||||||
\(720\) | −9.96640 | + | 32.6017i | −0.371426 | + | 1.21499i | ||||
\(721\) | −3.64227 | + | 3.64227i | −0.135645 | + | 0.135645i | ||||
\(722\) | 1.31455 | − | 1.31455i | 0.0489225 | − | 0.0489225i | ||||
\(723\) | −46.5140 | + | 11.5979i | −1.72988 | + | 0.431331i | ||||
\(724\) | 3.95299 | 0.146912 | ||||||||
\(725\) | −19.0126 | −0.706110 | ||||||||
\(726\) | 1.10520 | + | 4.43246i | 0.0410178 | + | 0.164504i | ||||
\(727\) | 24.6824i | 0.915420i | 0.889102 | + | 0.457710i | \(0.151330\pi\) | ||||
−0.889102 | + | 0.457710i | \(0.848670\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.8523 | + | 2.82014i | 0.994530 | + | 0.104450i | ||||
\(730\) | −11.1851 | + | 11.1851i | −0.413980 | + | 0.413980i | ||||
\(731\) | − | 32.7614i | − | 1.21173i | ||||||
\(732\) | 7.41537 | + | 4.45547i | 0.274080 | + | 0.164679i | ||||
\(733\) | −34.3405 | + | 34.3405i | −1.26839 | + | 1.26839i | −0.321476 | + | 0.946918i | \(0.604179\pi\) |
−0.946918 | + | 0.321476i | \(0.895821\pi\) | |||||||
\(734\) | −5.76659 | − | 5.76659i | −0.212849 | − | 0.212849i | ||||
\(735\) | −8.22704 | − | 32.9950i | −0.303459 | − | 1.21704i | ||||
\(736\) | 7.44281 | + | 7.44281i | 0.274346 | + | 0.274346i | ||||
\(737\) | 12.7586i | 0.469967i | ||||||||
\(738\) | 6.35404 | − | 3.37872i | 0.233896 | − | 0.124372i | ||||
\(739\) | −27.4710 | − | 27.4710i | −1.01054 | − | 1.01054i | −0.999944 | − | 0.0105933i | \(-0.996628\pi\) |
−0.0105933 | − | 0.999944i | \(-0.503372\pi\) | |||||||
\(740\) | −14.0842 | −0.517746 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.00802 | 0.0370056 | ||||||||
\(743\) | 36.8590 | + | 36.8590i | 1.35223 | + | 1.35223i | 0.883167 | + | 0.469058i | \(0.155407\pi\) |
0.469058 | + | 0.883167i | \(0.344593\pi\) | |||||||
\(744\) | −9.24962 | − | 5.55757i | −0.339108 | − | 0.203750i | ||||
\(745\) | − | 79.2751i | − | 2.90441i | ||||||
\(746\) | 5.10435 | + | 5.10435i | 0.186883 | + | 0.186883i | ||||
\(747\) | −5.69210 | + | 18.6198i | −0.208263 | + | 0.681262i | ||||
\(748\) | −14.6795 | − | 14.6795i | −0.536736 | − | 0.536736i | ||||
\(749\) | 10.7270 | − | 10.7270i | 0.391957 | − | 0.391957i | ||||
\(750\) | −2.26766 | + | 3.77414i | −0.0828033 | + | 0.137812i | ||||
\(751\) | − | 49.3601i | − | 1.80118i | −0.434674 | − | 0.900588i | \(-0.643136\pi\) | ||
0.434674 | − | 0.900588i | \(-0.356864\pi\) | |||||||
\(752\) | 7.29867 | − | 7.29867i | 0.266155 | − | 0.266155i | ||||
\(753\) | 4.99555 | − | 8.31423i | 0.182048 | − | 0.302987i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 32.5270i | − | 1.18378i | ||||||
\(756\) | 8.41641 | − | 7.57877i | 0.306102 | − | 0.275637i | ||||
\(757\) | 18.8564 | 0.685346 | 0.342673 | − | 0.939455i | \(-0.388668\pi\) | ||||
0.342673 | + | 0.939455i | \(0.388668\pi\) | |||||||
\(758\) | −1.39968 | −0.0508385 | ||||||||
\(759\) | 2.12932 | + | 8.53976i | 0.0772895 | + | 0.309974i | ||||
\(760\) | −16.5374 | + | 16.5374i | −0.599874 | + | 0.599874i | ||||
\(761\) | 27.2152 | − | 27.2152i | 0.986549 | − | 0.986549i | −0.0133615 | − | 0.999911i | \(-0.504253\pi\) |
0.999911 | + | 0.0133615i | \(0.00425321\pi\) | |||||||
\(762\) | −1.15109 | − | 4.61653i | −0.0416997 | − | 0.167239i | ||||
\(763\) | 7.37566 | 0.267017 | ||||||||
\(764\) | −12.7512 | −0.461321 | ||||||||
\(765\) | 17.9866 | − | 58.8369i | 0.650305 | − | 2.12725i | ||||
\(766\) | 9.37896i | 0.338876i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 6.21032 | − | 10.3360i | 0.224096 | − | 0.372969i | ||||
\(769\) | 2.01778 | − | 2.01778i | 0.0727631 | − | 0.0727631i | −0.669789 | − | 0.742552i | \(-0.733615\pi\) |
0.742552 | + | 0.669789i | \(0.233615\pi\) | |||||||
\(770\) | − | 2.66882i | − | 0.0961775i | ||||||
\(771\) | 6.07807 | − | 10.1159i | 0.218896 | − | 0.364315i | ||||
\(772\) | 14.7443 | − | 14.7443i | 0.530660 | − | 0.530660i | ||||
\(773\) | −4.54435 | − | 4.54435i | −0.163449 | − | 0.163449i | 0.620644 | − | 0.784093i | \(-0.286871\pi\) |
−0.784093 | + | 0.620644i | \(0.786871\pi\) | |||||||
\(774\) | −5.61306 | − | 1.71592i | −0.201757 | − | 0.0616776i | ||||
\(775\) | 22.8188 | + | 22.8188i | 0.819675 | + | 0.819675i | ||||
\(776\) | 16.7574i | 0.601555i | ||||||||
\(777\) | 3.72761 | + | 2.23970i | 0.133727 | + | 0.0803489i | ||||
\(778\) | 1.53850 | + | 1.53850i | 0.0551578 | + | 0.0551578i | ||||
\(779\) | −33.5341 | −1.20148 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.7668 | 0.778878 | ||||||||
\(782\) | −3.98532 | − | 3.98532i | −0.142515 | − | 0.142515i | ||||
\(783\) | 0.730183 | − | 13.9433i | 0.0260946 | − | 0.498292i | ||||
\(784\) | 18.4755i | 0.659838i | ||||||||
\(785\) | 38.5251 | + | 38.5251i | 1.37502 | + | 1.37502i | ||||
\(786\) | −2.73846 | − | 10.9828i | −0.0976778 | − | 0.391742i | ||||
\(787\) | 10.7255 | + | 10.7255i | 0.382322 | + | 0.382322i | 0.871938 | − | 0.489616i | \(-0.162863\pi\) |
−0.489616 | + | 0.871938i | \(0.662863\pi\) | |||||||
\(788\) | 3.02924 | − | 3.02924i | 0.107912 | − | 0.107912i | ||||
\(789\) | −33.6006 | − | 20.1887i | −1.19621 | − | 0.718736i | ||||
\(790\) | 1.34732i | 0.0479354i | ||||||||
\(791\) | 10.6919 | − | 10.6919i | 0.380160 | − | 0.380160i | ||||
\(792\) | −6.78531 | + | 3.60804i | −0.241105 | + | 0.128206i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 8.40957i | 0.298444i | ||||||||
\(795\) | 3.58416 | + | 14.3745i | 0.127117 | + | 0.509811i | ||||
\(796\) | 34.4077 | 1.21955 | ||||||||
\(797\) | 1.57925 | 0.0559399 | 0.0279700 | − | 0.999609i | \(-0.491096\pi\) | ||||
0.0279700 | + | 0.999609i | \(0.491096\pi\) | |||||||
\(798\) | 3.39106 | − | 0.845534i | 0.120042 | − | 0.0299316i | ||||
\(799\) | −13.1721 | + | 13.1721i | −0.465994 | + | 0.465994i | ||||
\(800\) | 19.4351 | − | 19.4351i | 0.687135 | − | 0.687135i | ||||
\(801\) | −12.2618 | − | 3.74845i | −0.433248 | − | 0.132445i | ||||
\(802\) | −8.17724 | −0.288748 | ||||||||
\(803\) | 24.2203 | 0.854717 | ||||||||
\(804\) | 21.4476 | − | 5.34778i | 0.756397 | − | 0.188602i | ||||
\(805\) | 10.9414i | 0.385633i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38.7542 | − | 23.2852i | −1.36421 | − | 0.819677i | ||||
\(808\) | 10.7173 | − | 10.7173i | 0.377033 | − | 0.377033i | ||||
\(809\) | 12.2119i | 0.429348i | 0.976686 | + | 0.214674i | \(0.0688689\pi\) | ||||
−0.976686 | + | 0.214674i | \(0.931131\pi\) | |||||||
\(810\) | −9.13854 | − | 6.16332i | −0.321096 | − | 0.216557i | ||||
\(811\) | 29.6037 | − | 29.6037i | 1.03952 | − | 1.03952i | 0.0403387 | − | 0.999186i | \(-0.487156\pi\) |
0.999186 | − | 0.0403387i | \(-0.0128437\pi\) | |||||||
\(812\) | −4.14143 | − | 4.14143i | −0.145336 | − | 0.145336i | ||||
\(813\) | −29.7169 | + | 7.40966i | −1.04222 | + | 0.259868i | ||||
\(814\) | −1.00981 | − | 1.00981i | −0.0353939 | − | 0.0353939i | ||||
\(815\) | − | 12.0109i | − | 0.420724i | ||||||
\(816\) | −17.2159 | + | 28.6529i | −0.602677 | + | 1.00305i | ||||
\(817\) | 19.3397 | + | 19.3397i | 0.676612 | + | 0.676612i | ||||
\(818\) | −4.42964 | −0.154879 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 44.3656 | 1.54931 | ||||||||
\(821\) | −13.1586 | − | 13.1586i | −0.459237 | − | 0.459237i | 0.439168 | − | 0.898405i | \(-0.355273\pi\) |
−0.898405 | + | 0.439168i | \(0.855273\pi\) | |||||||
\(822\) | −2.36895 | + | 3.94271i | −0.0826266 | + | 0.137518i | ||||
\(823\) | 0.516417i | 0.0180012i | 0.999959 | + | 0.00900059i | \(0.00286501\pi\) | ||||
−0.999959 | + | 0.00900059i | \(0.997135\pi\) | |||||||
\(824\) | −4.28172 | − | 4.28172i | −0.149161 | − | 0.149161i | ||||
\(825\) | 22.2995 | − | 5.56021i | 0.776370 | − | 0.193582i | ||||
\(826\) | 2.89813 | + | 2.89813i | 0.100839 | + | 0.100839i | ||||
\(827\) | 21.0701 | − | 21.0701i | 0.732678 | − | 0.732678i | −0.238472 | − | 0.971149i | \(-0.576646\pi\) |
0.971149 | + | 0.238472i | \(0.0766464\pi\) | |||||||
\(828\) | 13.4631 | − | 7.15892i | 0.467876 | − | 0.248790i | ||||
\(829\) | 1.68723i | 0.0586000i | 0.999571 | + | 0.0293000i | \(0.00932781\pi\) | ||||
−0.999571 | + | 0.0293000i | \(0.990672\pi\) | |||||||
\(830\) | 5.62061 | − | 5.62061i | 0.195094 | − | 0.195094i | ||||
\(831\) | −33.7030 | − | 20.2502i | −1.16914 | − | 0.702471i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 33.3430i | − | 1.15527i | ||||||
\(834\) | −3.19396 | + | 0.796389i | −0.110598 | + | 0.0275767i | ||||
\(835\) | −18.2204 | −0.630542 | ||||||||
\(836\) | 17.3312 | 0.599413 | ||||||||
\(837\) | −17.6110 | + | 15.8583i | −0.608726 | + | 0.548143i | ||||
\(838\) | −6.68121 | + | 6.68121i | −0.230799 | + | 0.230799i | ||||
\(839\) | 7.66187 | − | 7.66187i | 0.264517 | − | 0.264517i | −0.562369 | − | 0.826886i | \(-0.690110\pi\) |
0.826886 | + | 0.562369i | \(0.190110\pi\) | |||||||
\(840\) | −9.26984 | + | 2.31136i | −0.319840 | + | 0.0797495i | ||||
\(841\) | 21.7797 | 0.751024 | ||||||||
\(842\) | 4.45314 | 0.153465 | ||||||||
\(843\) | 5.07132 | + | 20.3388i | 0.174666 | + | 0.700506i | ||||
\(844\) | 15.0198i | 0.517004i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.56688 | + | 2.94669i | 0.0538706 | + | 0.101309i | ||||
\(847\) | 6.14867 | − | 6.14867i | 0.211271 | − | 0.211271i | ||||
\(848\) | − | 8.04895i | − | 0.276402i | ||||||
\(849\) | 10.5494 | + | 6.33855i | 0.362056 | + | 0.217539i | ||||
\(850\) | −10.4067 | + | 10.4067i | −0.356947 | + | 0.356947i | ||||
\(851\) | 4.13994 | + | 4.13994i | 0.141915 | + | 0.141915i | ||||
\(852\) | −9.12361 | − | 36.5907i | −0.312570 | − | 1.25358i | ||||
\(853\) | 30.1644 | + | 30.1644i | 1.03281 | + | 1.03281i | 0.999443 | + | 0.0333670i | \(0.0106230\pi\) |
0.0333670 | + | 0.999443i | \(0.489377\pi\) | |||||||
\(854\) | 1.09047i | 0.0373153i | ||||||||
\(855\) | 24.1148 | + | 45.3505i | 0.824709 | + | 1.55095i | ||||
\(856\) | 12.6103 | + | 12.6103i | 0.431010 | + | 0.431010i | ||||
\(857\) | 36.7949 | 1.25689 | 0.628444 | − | 0.777855i | \(-0.283692\pi\) | ||||
0.628444 | + | 0.777855i | \(0.283692\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.7044 | −1.66177 | −0.830886 | − | 0.556442i | \(-0.812166\pi\) | ||||
−0.830886 | + | 0.556442i | \(0.812166\pi\) | |||||||
\(860\) | −25.5865 | − | 25.5865i | −0.872491 | − | 0.872491i | ||||
\(861\) | −11.7420 | − | 7.05512i | −0.400168 | − | 0.240438i | ||||
\(862\) | − | 7.48099i | − | 0.254803i | ||||||
\(863\) | 25.4155 | + | 25.4155i | 0.865153 | + | 0.865153i | 0.991931 | − | 0.126779i | \(-0.0404637\pi\) |
−0.126779 | + | 0.991931i | \(0.540464\pi\) | |||||||
\(864\) | 13.5067 | + | 14.9996i | 0.459509 | + | 0.510296i | ||||
\(865\) | 35.0180 | + | 35.0180i | 1.19065 | + | 1.19065i | ||||
\(866\) | −0.461976 | + | 0.461976i | −0.0156986 | + | 0.0156986i | ||||
\(867\) | 15.9050 | − | 26.4712i | 0.540162 | − | 0.899008i | ||||
\(868\) | 9.94103i | 0.337421i | ||||||||
\(869\) | 1.45874 | − | 1.45874i | 0.0494845 | − | 0.0494845i | ||||
\(870\) | −2.93571 | + | 4.88599i | −0.0995299 | + | 0.165651i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.67054i | 0.293622i | ||||||||
\(873\) | 35.1947 | + | 10.7591i | 1.19116 | + | 0.364140i | ||||
\(874\) | 4.70523 | 0.159157 | ||||||||
\(875\) | 8.38112 | 0.283333 | ||||||||
\(876\) | −10.1520 | − | 40.7152i | −0.343005 | − | 1.37564i | ||||
\(877\) | −12.9567 | + | 12.9567i | −0.437516 | + | 0.437516i | −0.891175 | − | 0.453659i | \(-0.850118\pi\) |
0.453659 | + | 0.891175i | \(0.350118\pi\) | |||||||
\(878\) | −3.59002 | + | 3.59002i | −0.121157 | + | 0.121157i | ||||
\(879\) | −6.66068 | − | 26.7130i | −0.224659 | − | 0.901007i | ||||
\(880\) | −21.3102 | −0.718368 | ||||||||
\(881\) | 31.1077 | 1.04805 | 0.524023 | − | 0.851704i | \(-0.324431\pi\) | ||||
0.524023 | + | 0.851704i | \(0.324431\pi\) | |||||||
\(882\) | −5.71271 | − | 1.74639i | −0.192357 | − | 0.0588039i | ||||
\(883\) | − | 9.56660i | − | 0.321942i | −0.986959 | − | 0.160971i | \(-0.948537\pi\) | ||
0.986959 | − | 0.160971i | \(-0.0514625\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −31.0229 | + | 51.6323i | −1.04282 | + | 1.73560i | ||||
\(886\) | 5.54082 | − | 5.54082i | 0.186148 | − | 0.186148i | ||||
\(887\) | 24.6546i | 0.827819i | 0.910318 | + | 0.413910i | \(0.135837\pi\) | ||||
−0.910318 | + | 0.413910i | \(0.864163\pi\) | |||||||
\(888\) | −2.63291 | + | 4.38203i | −0.0883547 | + | 0.147051i | ||||
\(889\) | −6.40399 | + | 6.40399i | −0.214783 | + | 0.214783i | ||||
\(890\) | 3.70137 | + | 3.70137i | 0.124070 | + | 0.124070i | ||||
\(891\) | 3.22128 | + | 16.5674i | 0.107917 | + | 0.555028i | ||||
\(892\) | −37.5558 | − | 37.5558i | −1.25746 | − | 1.25746i | ||||
\(893\) | − | 15.5515i | − | 0.520410i | ||||||
\(894\) | −11.9372 | − | 7.17238i | −0.399240 | − | 0.239880i | ||||
\(895\) | −10.7298 | − | 10.7298i | −0.358656 | − | 0.358656i | ||||
\(896\) | 11.1454 | 0.372342 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.66432 | −0.289132 | ||||||||
\(899\) | 8.66578 | + | 8.66578i | 0.289020 | + | 0.289020i | ||||
\(900\) | −18.6938 | − | 35.1557i | −0.623127 | − | 1.17186i | ||||
\(901\) | 14.5261i | 0.483935i | ||||||||
\(902\) | 3.18093 | + | 3.18093i | 0.105913 | + | 0.105913i | ||||
\(903\) | 2.70303 | + | 10.8407i | 0.0899513 | + | 0.360755i | ||||
\(904\) | 12.5690 | + | 12.5690i | 0.418038 | + | 0.418038i | ||||
\(905\) | −5.17824 | + | 5.17824i | −0.172130 | + | 0.172130i | ||||
\(906\) | −4.89790 | − | 2.94287i | −0.162722 | − | 0.0977703i | ||||
\(907\) | − | 1.68516i | − | 0.0559549i | −0.999609 | − | 0.0279775i | \(-0.991093\pi\) | ||
0.999609 | − | 0.0279775i | \(-0.00890666\pi\) | |||||||
\(908\) | 9.75575 | − | 9.75575i | 0.323756 | − | 0.323756i | ||||
\(909\) | −15.6280 | − | 29.3900i | −0.518346 | − | 0.974806i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.9421i | 1.45587i | 0.685648 | + | 0.727933i | \(0.259519\pi\) | ||||
−0.685648 | + | 0.727933i | \(0.740481\pi\) | |||||||
\(912\) | −6.75151 | − | 27.0773i | −0.223565 | − | 0.896619i | ||||
\(913\) | −12.1709 | −0.402798 | ||||||||
\(914\) | 2.38566 | 0.0789106 | ||||||||
\(915\) | −15.5503 | + | 3.87734i | −0.514076 | + | 0.128181i | ||||
\(916\) | −21.4015 | + | 21.4015i | −0.707124 | + | 0.707124i | ||||
\(917\) | −15.2352 | + | 15.2352i | −0.503109 | + | 0.503109i | ||||
\(918\) | −7.23231 | − | 8.03165i | −0.238702 | − | 0.265084i | ||||
\(919\) | 8.41429 | 0.277562 | 0.138781 | − | 0.990323i | \(-0.455682\pi\) | ||||
0.138781 | + | 0.990323i | \(0.455682\pi\) | |||||||
\(920\) | −12.8623 | −0.424056 | ||||||||
\(921\) | −34.1881 | + | 8.52453i | −1.12654 | + | 0.280893i | ||||
\(922\) | − | 4.36704i | − | 0.143821i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 6.06857 | + | 3.64625i | 0.199641 | + | 0.119953i | ||||
\(925\) | 10.8105 | − | 10.8105i | 0.355446 | − | 0.355446i | ||||
\(926\) | − | 3.47599i | − | 0.114228i | ||||||
\(927\) | −11.7418 | + | 6.24360i | −0.385650 | + | 0.205067i | ||||
\(928\) | 7.38077 | − | 7.38077i | 0.242286 | − | 0.242286i | ||||
\(929\) | 1.62237 | + | 1.62237i | 0.0532282 | + | 0.0532282i | 0.733220 | − | 0.679992i | \(-0.238017\pi\) |
−0.679992 | + | 0.733220i | \(0.738017\pi\) | |||||||
\(930\) | 9.38756 | − | 2.34071i | 0.307830 | − | 0.0767550i | ||||
\(931\) | 19.6831 | + | 19.6831i | 0.645087 | + | 0.645087i | ||||
\(932\) | 34.0556i | 1.11553i | ||||||||
\(933\) | 6.79906 | − | 11.3159i | 0.222591 | − | 0.370465i | ||||
\(934\) | 2.29262 | + | 2.29262i | 0.0750168 | + | 0.0750168i | ||||
\(935\) | 38.4590 | 1.25775 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.10985 | 0.232269 | 0.116134 | − | 0.993234i | \(-0.462950\pi\) | ||||
0.116134 | + | 0.993234i | \(0.462950\pi\) | |||||||
\(938\) | 1.97021 | + | 1.97021i | 0.0643296 | + | 0.0643296i | ||||
\(939\) | −5.81161 | + | 9.67244i | −0.189655 | + | 0.315648i | ||||
\(940\) | 20.5746i | 0.671069i | ||||||||
\(941\) | 22.6506 | + | 22.6506i | 0.738390 | + | 0.738390i | 0.972266 | − | 0.233877i | \(-0.0751412\pi\) |
−0.233877 | + | 0.972266i | \(0.575141\pi\) | |||||||
\(942\) | 9.28664 | − | 2.31555i | 0.302575 | − | 0.0754447i | ||||
\(943\) | −13.0409 | − | 13.0409i | −0.424670 | − | 0.424670i | ||||
\(944\) | 23.1413 | − | 23.1413i | 0.753185 | − | 0.753185i | ||||
\(945\) | −1.09727 | + | 20.9530i | −0.0356941 | + | 0.681601i | ||||
\(946\) | − | 3.66900i | − | 0.119290i | ||||||
\(947\) | −9.45582 | + | 9.45582i | −0.307273 | + | 0.307273i | −0.843851 | − | 0.536578i | \(-0.819717\pi\) |
0.536578 | + | 0.843851i | \(0.319717\pi\) | |||||||
\(948\) | −3.06363 | − | 1.84076i | −0.0995022 | − | 0.0597852i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | − | 12.2866i | − | 0.398629i | ||||||
\(951\) | −14.9594 | + | 3.73002i | −0.485093 | + | 0.120954i | ||||
\(952\) | −9.36762 | −0.303606 | ||||||||
\(953\) | 17.7883 | 0.576219 | 0.288110 | − | 0.957597i | \(-0.406973\pi\) | ||||
0.288110 | + | 0.957597i | \(0.406973\pi\) | |||||||
\(954\) | 2.48878 | + | 0.760824i | 0.0805772 | + | 0.0246326i | ||||
\(955\) | 16.7035 | − | 16.7035i | 0.540512 | − | 0.540512i | ||||
\(956\) | 12.2725 | − | 12.2725i | 0.396922 | − | 0.396922i | ||||
\(957\) | 8.46858 | − | 2.11157i | 0.273750 | − | 0.0682575i | ||||
\(958\) | 8.08847 | 0.261327 | ||||||||
\(959\) | 8.75547 | 0.282729 | ||||||||
\(960\) | 7.53013 | + | 30.2000i | 0.243034 | + | 0.974700i | ||||
\(961\) | 10.1988i | 0.328993i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 34.5812 | − | 18.3883i | 1.11436 | − | 0.592555i | ||||
\(964\) | −36.7103 | + | 36.7103i | −1.18236 | + | 1.18236i | ||||
\(965\) | 38.6288i | 1.24351i | ||||||||
\(966\) | 1.64755 | + | 0.989916i | 0.0530089 | + | 0.0318500i | ||||
\(967\) | 29.0154 | − | 29.0154i | 0.933072 | − | 0.933072i | −0.0648250 | − | 0.997897i | \(-0.520649\pi\) |
0.997897 | + | 0.0648250i | \(0.0206489\pi\) | |||||||
\(968\) | 7.22814 | + | 7.22814i | 0.232321 | + | 0.232321i | ||||
\(969\) | 12.1846 | + | 48.8670i | 0.391425 | + | 1.56983i | ||||
\(970\) | −10.6239 | − | 10.6239i | −0.341114 | − | 0.341114i | ||||
\(971\) | 22.5895i | 0.724933i | 0.931997 | + | 0.362466i | \(0.118065\pi\) | ||||
−0.931997 | + | 0.362466i | \(0.881935\pi\) | |||||||
\(972\) | 26.5001 | − | 12.3593i | 0.849992 | − | 0.396426i | ||||
\(973\) | 4.43063 | + | 4.43063i | 0.142039 | + | 0.142039i | ||||
\(974\) | 10.3864 | 0.332803 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.70733 | 0.278715 | ||||||||
\(977\) | −1.88475 | − | 1.88475i | −0.0602986 | − | 0.0602986i | 0.676314 | − | 0.736613i | \(-0.263576\pi\) |
−0.736613 | + | 0.676314i | \(0.763576\pi\) | |||||||
\(978\) | −1.80860 | − | 1.08668i | −0.0578326 | − | 0.0347483i | ||||
\(979\) | − | 8.01496i | − | 0.256159i | ||||||
\(980\) | −26.0407 | − | 26.0407i | −0.831839 | − | 0.831839i | ||||
\(981\) | 18.2103 | + | 5.56693i | 0.581411 | + | 0.177738i | ||||
\(982\) | 3.81896 | + | 3.81896i | 0.121868 | + | 0.121868i | ||||
\(983\) | −38.5049 | + | 38.5049i | −1.22812 | + | 1.22812i | −0.263440 | + | 0.964676i | \(0.584857\pi\) |
−0.964676 | + | 0.263440i | \(0.915143\pi\) | |||||||
\(984\) | 8.29373 | − | 13.8035i | 0.264394 | − | 0.440039i | ||||
\(985\) | 7.93635i | 0.252873i | ||||||||
\(986\) | −3.95210 | + | 3.95210i | −0.125861 | + | 0.125861i | ||||
\(987\) | 3.27182 | − | 5.44538i | 0.104143 | − | 0.173328i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.0419i | 0.478303i | ||||||||
\(990\) | 2.01434 | − | 6.58924i | 0.0640200 | − | 0.209420i | ||||
\(991\) | 13.2443 | 0.420720 | 0.210360 | − | 0.977624i | \(-0.432536\pi\) | ||||
0.210360 | + | 0.977624i | \(0.432536\pi\) | |||||||
\(992\) | −17.7167 | −0.562506 | ||||||||
\(993\) | −6.73680 | − | 27.0183i | −0.213786 | − | 0.857400i | ||||
\(994\) | 3.36128 | − | 3.36128i | 0.106613 | − | 0.106613i | ||||
\(995\) | −45.0726 | + | 45.0726i | −1.42890 | + | 1.42890i | ||||
\(996\) | 5.10147 | + | 20.4597i | 0.161646 | + | 0.648291i | ||||
\(997\) | −31.5812 | −1.00019 | −0.500093 | − | 0.865972i | \(-0.666701\pi\) | ||||
−0.500093 | + | 0.865972i | \(0.666701\pi\) | |||||||
\(998\) | −14.7203 | −0.465962 | ||||||||
\(999\) | 7.51290 | + | 8.34326i | 0.237698 | + | 0.263969i |
(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 | 507.2.f.g.239.13 | yes | 48 | |
3.2 | odd | 2 | inner | 507.2.f.g.239.12 | yes | 48 | |
13.2 | odd | 12 | 507.2.k.k.488.14 | 96 | |||
13.3 | even | 3 | 507.2.k.k.188.12 | 96 | |||
13.4 | even | 6 | 507.2.k.k.80.11 | 96 | |||
13.5 | odd | 4 | inner | 507.2.f.g.437.13 | yes | 48 | |
13.6 | odd | 12 | 507.2.k.k.89.11 | 96 | |||
13.7 | odd | 12 | 507.2.k.k.89.13 | 96 | |||
13.8 | odd | 4 | inner | 507.2.f.g.437.11 | yes | 48 | |
13.9 | even | 3 | 507.2.k.k.80.13 | 96 | |||
13.10 | even | 6 | 507.2.k.k.188.14 | 96 | |||
13.11 | odd | 12 | 507.2.k.k.488.12 | 96 | |||
13.12 | even | 2 | inner | 507.2.f.g.239.11 | ✓ | 48 | |
39.2 | even | 12 | 507.2.k.k.488.11 | 96 | |||
39.5 | even | 4 | inner | 507.2.f.g.437.12 | yes | 48 | |
39.8 | even | 4 | inner | 507.2.f.g.437.14 | yes | 48 | |
39.11 | even | 12 | 507.2.k.k.488.13 | 96 | |||
39.17 | odd | 6 | 507.2.k.k.80.14 | 96 | |||
39.20 | even | 12 | 507.2.k.k.89.12 | 96 | |||
39.23 | odd | 6 | 507.2.k.k.188.11 | 96 | |||
39.29 | odd | 6 | 507.2.k.k.188.13 | 96 | |||
39.32 | even | 12 | 507.2.k.k.89.14 | 96 | |||
39.35 | odd | 6 | 507.2.k.k.80.12 | 96 | |||
39.38 | odd | 2 | inner | 507.2.f.g.239.14 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.f.g.239.11 | ✓ | 48 | 13.12 | even | 2 | inner | |
507.2.f.g.239.12 | yes | 48 | 3.2 | odd | 2 | inner | |
507.2.f.g.239.13 | yes | 48 | 1.1 | even | 1 | trivial | |
507.2.f.g.239.14 | yes | 48 | 39.38 | odd | 2 | inner | |
507.2.f.g.437.11 | yes | 48 | 13.8 | odd | 4 | inner | |
507.2.f.g.437.12 | yes | 48 | 39.5 | even | 4 | inner | |
507.2.f.g.437.13 | yes | 48 | 13.5 | odd | 4 | inner | |
507.2.f.g.437.14 | yes | 48 | 39.8 | even | 4 | inner | |
507.2.k.k.80.11 | 96 | 13.4 | even | 6 | |||
507.2.k.k.80.12 | 96 | 39.35 | odd | 6 | |||
507.2.k.k.80.13 | 96 | 13.9 | even | 3 | |||
507.2.k.k.80.14 | 96 | 39.17 | odd | 6 | |||
507.2.k.k.89.11 | 96 | 13.6 | odd | 12 | |||
507.2.k.k.89.12 | 96 | 39.20 | even | 12 | |||
507.2.k.k.89.13 | 96 | 13.7 | odd | 12 | |||
507.2.k.k.89.14 | 96 | 39.32 | even | 12 | |||
507.2.k.k.188.11 | 96 | 39.23 | odd | 6 | |||
507.2.k.k.188.12 | 96 | 13.3 | even | 3 | |||
507.2.k.k.188.13 | 96 | 39.29 | odd | 6 | |||
507.2.k.k.188.14 | 96 | 13.10 | even | 6 | |||
507.2.k.k.488.11 | 96 | 39.2 | even | 12 | |||
507.2.k.k.488.12 | 96 | 13.11 | odd | 12 | |||
507.2.k.k.488.13 | 96 | 39.11 | even | 12 | |||
507.2.k.k.488.14 | 96 | 13.2 | odd | 12 |