Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 372.6 | ||
Character | \(\chi\) | \(=\) | 847.372 |
Dual form | 847.2.f.z.148.6 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.428283 | − | 1.31812i | 0.302842 | − | 0.932051i | −0.677632 | − | 0.735401i | \(-0.736994\pi\) |
0.980474 | − | 0.196650i | \(-0.0630062\pi\) | |||||||
\(3\) | 0.0990877 | − | 0.0719914i | 0.0572083 | − | 0.0415643i | −0.558814 | − | 0.829293i | \(-0.688743\pi\) |
0.616022 | + | 0.787729i | \(0.288743\pi\) | |||||||
\(4\) | 0.0640220 | + | 0.0465147i | 0.0320110 | + | 0.0232574i | ||||
\(5\) | −0.0411006 | − | 0.126495i | −0.0183808 | − | 0.0565702i | 0.941445 | − | 0.337165i | \(-0.109468\pi\) |
−0.959826 | + | 0.280595i | \(0.909468\pi\) | |||||||
\(6\) | −0.0524557 | − | 0.161442i | −0.0214150 | − | 0.0659084i | ||||
\(7\) | 0.809017 | + | 0.587785i | 0.305780 | + | 0.222162i | ||||
\(8\) | 2.33125 | − | 1.69375i | 0.824221 | − | 0.598832i | ||||
\(9\) | −0.922415 | + | 2.83890i | −0.307472 | + | 0.946301i | ||||
\(10\) | −0.184338 | −0.0582928 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.00969245 | 0.00279797 | ||||||||
\(13\) | 0.198215 | − | 0.610042i | 0.0549749 | − | 0.169195i | −0.919799 | − | 0.392390i | \(-0.871648\pi\) |
0.974774 | + | 0.223194i | \(0.0716485\pi\) | |||||||
\(14\) | 1.12126 | − | 0.814642i | 0.299669 | − | 0.217722i | ||||
\(15\) | −0.0131791 | − | 0.00957518i | −0.00340283 | − | 0.00247230i | ||||
\(16\) | −1.18522 | − | 3.64775i | −0.296306 | − | 0.911936i | ||||
\(17\) | 0.440294 | + | 1.35508i | 0.106787 | + | 0.328656i | 0.990146 | − | 0.140041i | \(-0.0447235\pi\) |
−0.883359 | + | 0.468697i | \(0.844723\pi\) | |||||||
\(18\) | 3.34696 | + | 2.43171i | 0.788885 | + | 0.573159i | ||||
\(19\) | 5.81115 | − | 4.22204i | 1.33317 | − | 0.968603i | 0.333502 | − | 0.942749i | \(-0.391769\pi\) |
0.999666 | − | 0.0258541i | \(-0.00823055\pi\) | |||||||
\(20\) | 0.00325252 | − | 0.0100102i | 0.000727286 | − | 0.00223836i | ||||
\(21\) | 0.122479 | 0.0267271 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.66655 | 0.347500 | 0.173750 | − | 0.984790i | \(-0.444412\pi\) | ||||
0.173750 | + | 0.984790i | \(0.444412\pi\) | |||||||
\(24\) | 0.109063 | − | 0.335660i | 0.0222623 | − | 0.0685163i | ||||
\(25\) | 4.03077 | − | 2.92853i | 0.806155 | − | 0.585706i | ||||
\(26\) | −0.719216 | − | 0.522541i | −0.141050 | − | 0.102479i | ||||
\(27\) | 0.226521 | + | 0.697160i | 0.0435940 | + | 0.134168i | ||||
\(28\) | 0.0244542 | + | 0.0752624i | 0.00462141 | + | 0.0142233i | ||||
\(29\) | 3.62162 | + | 2.63126i | 0.672518 | + | 0.488613i | 0.870867 | − | 0.491519i | \(-0.163558\pi\) |
−0.198349 | + | 0.980131i | \(0.563558\pi\) | |||||||
\(30\) | −0.0182656 | + | 0.0132707i | −0.00333483 | + | 0.00242290i | ||||
\(31\) | −2.11115 | + | 6.49745i | −0.379174 | + | 1.16698i | 0.561446 | + | 0.827514i | \(0.310245\pi\) |
−0.940619 | + | 0.339463i | \(0.889755\pi\) | |||||||
\(32\) | 0.447392 | 0.0790885 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.97473 | 0.338664 | ||||||||
\(35\) | 0.0411006 | − | 0.126495i | 0.00694728 | − | 0.0213815i | ||||
\(36\) | −0.191106 | + | 0.138846i | −0.0318509 | + | 0.0231411i | ||||
\(37\) | −3.04890 | − | 2.21515i | −0.501235 | − | 0.364169i | 0.308253 | − | 0.951304i | \(-0.400256\pi\) |
−0.809489 | + | 0.587135i | \(0.800256\pi\) | |||||||
\(38\) | −3.07634 | − | 9.46801i | −0.499049 | − | 1.53591i | ||||
\(39\) | −0.0242772 | − | 0.0747174i | −0.00388746 | − | 0.0119644i | ||||
\(40\) | −0.310067 | − | 0.225277i | −0.0490258 | − | 0.0356194i | ||||
\(41\) | 4.99395 | − | 3.62832i | 0.779924 | − | 0.566648i | −0.125032 | − | 0.992153i | \(-0.539904\pi\) |
0.904956 | + | 0.425505i | \(0.139904\pi\) | |||||||
\(42\) | 0.0524557 | − | 0.161442i | 0.00809409 | − | 0.0249110i | ||||
\(43\) | 1.03970 | 0.158553 | 0.0792764 | − | 0.996853i | \(-0.474739\pi\) | ||||
0.0792764 | + | 0.996853i | \(0.474739\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.397018 | 0.0591840 | ||||||||
\(46\) | 0.713755 | − | 2.19671i | 0.105237 | − | 0.323887i | ||||
\(47\) | −7.67707 | + | 5.57771i | −1.11982 | + | 0.813593i | −0.984181 | − | 0.177166i | \(-0.943307\pi\) |
−0.135634 | + | 0.990759i | \(0.543307\pi\) | |||||||
\(48\) | −0.380047 | − | 0.276121i | −0.0548551 | − | 0.0398546i | ||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | −2.13384 | − | 6.56728i | −0.301770 | − | 0.928753i | ||||
\(51\) | 0.141182 | + | 0.102575i | 0.0197695 | + | 0.0143633i | ||||
\(52\) | 0.0410660 | − | 0.0298362i | 0.00569483 | − | 0.00413754i | ||||
\(53\) | −0.205975 | + | 0.633926i | −0.0282928 | + | 0.0870764i | −0.964206 | − | 0.265155i | \(-0.914577\pi\) |
0.935913 | + | 0.352231i | \(0.114577\pi\) | |||||||
\(54\) | 1.01595 | 0.138254 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.88158 | 0.385068 | ||||||||
\(57\) | 0.271862 | − | 0.836705i | 0.0360090 | − | 0.110824i | ||||
\(58\) | 5.01939 | − | 3.64680i | 0.659078 | − | 0.478849i | ||||
\(59\) | −6.62338 | − | 4.81217i | −0.862291 | − | 0.626491i | 0.0662165 | − | 0.997805i | \(-0.478907\pi\) |
−0.928507 | + | 0.371314i | \(0.878907\pi\) | |||||||
\(60\) | −0.000398366 | − | 0.00122604i | −5.14288e−5 | − | 0.000158282i | ||||
\(61\) | −2.93506 | − | 9.03320i | −0.375796 | − | 1.15658i | −0.942940 | − | 0.332963i | \(-0.891951\pi\) |
0.567143 | − | 0.823619i | \(-0.308049\pi\) | |||||||
\(62\) | 7.66024 | + | 5.56549i | 0.972852 | + | 0.706818i | ||||
\(63\) | −2.41491 | + | 1.75454i | −0.304251 | + | 0.221051i | ||||
\(64\) | 2.56206 | − | 7.88521i | 0.320257 | − | 0.985651i | ||||
\(65\) | −0.0853139 | −0.0105819 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0398 | 1.47089 | 0.735446 | − | 0.677583i | \(-0.236973\pi\) | ||||
0.735446 | + | 0.677583i | \(0.236973\pi\) | |||||||
\(68\) | −0.0348429 | + | 0.107235i | −0.00422532 | + | 0.0130042i | ||||
\(69\) | 0.165134 | − | 0.119977i | 0.0198799 | − | 0.0144436i | ||||
\(70\) | −0.149132 | − | 0.108351i | −0.0178247 | − | 0.0129504i | ||||
\(71\) | 1.49384 | + | 4.59758i | 0.177287 | + | 0.545632i | 0.999731 | − | 0.0232143i | \(-0.00738999\pi\) |
−0.822444 | + | 0.568846i | \(0.807390\pi\) | |||||||
\(72\) | 2.65802 | + | 8.18053i | 0.313250 | + | 0.964085i | ||||
\(73\) | −7.16585 | − | 5.20629i | −0.838699 | − | 0.609351i | 0.0833078 | − | 0.996524i | \(-0.473452\pi\) |
−0.922007 | + | 0.387173i | \(0.873452\pi\) | |||||||
\(74\) | −4.22563 | + | 3.07010i | −0.491219 | + | 0.356891i | ||||
\(75\) | 0.188571 | − | 0.580362i | 0.0217743 | − | 0.0670144i | ||||
\(76\) | 0.568428 | 0.0652032 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.108884 | −0.0123287 | ||||||||
\(79\) | −3.55081 | + | 10.9283i | −0.399497 | + | 1.22953i | 0.525906 | + | 0.850543i | \(0.323726\pi\) |
−0.925403 | + | 0.378984i | \(0.876274\pi\) | |||||||
\(80\) | −0.412707 | + | 0.299849i | −0.0461421 | + | 0.0335242i | ||||
\(81\) | −7.17211 | − | 5.21084i | −0.796901 | − | 0.578983i | ||||
\(82\) | −2.64373 | − | 8.13656i | −0.291951 | − | 0.898533i | ||||
\(83\) | −2.96038 | − | 9.11111i | −0.324944 | − | 1.00007i | −0.971466 | − | 0.237179i | \(-0.923777\pi\) |
0.646522 | − | 0.762895i | \(-0.276223\pi\) | |||||||
\(84\) | 0.00784136 | + | 0.00569708i | 0.000855562 | + | 0.000621602i | ||||
\(85\) | 0.153315 | − | 0.111390i | 0.0166293 | − | 0.0120819i | ||||
\(86\) | 0.445286 | − | 1.37045i | 0.0480164 | − | 0.147779i | ||||
\(87\) | 0.548286 | 0.0587824 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.7001 | −1.87621 | −0.938104 | − | 0.346353i | \(-0.887420\pi\) | ||||
−0.938104 | + | 0.346353i | \(0.887420\pi\) | |||||||
\(90\) | 0.170036 | − | 0.523317i | 0.0179234 | − | 0.0551625i | ||||
\(91\) | 0.518933 | − | 0.377027i | 0.0543989 | − | 0.0395231i | ||||
\(92\) | 0.106696 | + | 0.0775190i | 0.0111238 | + | 0.00808192i | ||||
\(93\) | 0.258572 | + | 0.795802i | 0.0268126 | + | 0.0825208i | ||||
\(94\) | 4.06414 | + | 12.5081i | 0.419184 | + | 1.29011i | ||||
\(95\) | −0.772908 | − | 0.561551i | −0.0792987 | − | 0.0576139i | ||||
\(96\) | 0.0443310 | − | 0.0322084i | 0.00452452 | − | 0.00328725i | ||||
\(97\) | 2.03376 | − | 6.25927i | 0.206497 | − | 0.635533i | −0.793151 | − | 0.609024i | \(-0.791561\pi\) |
0.999649 | − | 0.0265084i | \(-0.00843888\pi\) | |||||||
\(98\) | 1.38595 | 0.140002 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.394278 | 0.0394278 | ||||||||
\(101\) | −5.75402 | + | 17.7091i | −0.572547 | + | 1.76212i | 0.0718388 | + | 0.997416i | \(0.477113\pi\) |
−0.644385 | + | 0.764701i | \(0.722887\pi\) | |||||||
\(102\) | 0.195672 | − | 0.142164i | 0.0193744 | − | 0.0140763i | ||||
\(103\) | 5.60128 | + | 4.06957i | 0.551910 | + | 0.400986i | 0.828489 | − | 0.560005i | \(-0.189201\pi\) |
−0.276579 | + | 0.960991i | \(0.589201\pi\) | |||||||
\(104\) | −0.571172 | − | 1.75789i | −0.0560080 | − | 0.172375i | ||||
\(105\) | −0.00503397 | − | 0.0154930i | −0.000491265 | − | 0.00151196i | ||||
\(106\) | 0.747374 | + | 0.542999i | 0.0725914 | + | 0.0527408i | ||||
\(107\) | −4.40466 | + | 3.20017i | −0.425814 | + | 0.309372i | −0.779973 | − | 0.625813i | \(-0.784767\pi\) |
0.354159 | + | 0.935185i | \(0.384767\pi\) | |||||||
\(108\) | −0.0179259 | + | 0.0551701i | −0.00172492 | + | 0.00530875i | ||||
\(109\) | 9.22316 | 0.883419 | 0.441709 | − | 0.897158i | \(-0.354372\pi\) | ||||
0.441709 | + | 0.897158i | \(0.354372\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.461580 | −0.0438112 | ||||||||
\(112\) | 1.18522 | − | 3.64775i | 0.111993 | − | 0.344680i | ||||
\(113\) | −7.59038 | + | 5.51474i | −0.714043 | + | 0.518783i | −0.884476 | − | 0.466587i | \(-0.845484\pi\) |
0.170432 | + | 0.985369i | \(0.445484\pi\) | |||||||
\(114\) | −0.986443 | − | 0.716693i | −0.0923889 | − | 0.0671244i | ||||
\(115\) | −0.0684962 | − | 0.210810i | −0.00638731 | − | 0.0196581i | ||||
\(116\) | 0.109471 | + | 0.336917i | 0.0101641 | + | 0.0312820i | ||||
\(117\) | 1.54901 | + | 1.12542i | 0.143206 | + | 0.104046i | ||||
\(118\) | −9.17969 | + | 6.66944i | −0.845059 | + | 0.613971i | ||||
\(119\) | −0.440294 | + | 1.35508i | −0.0403617 | + | 0.124220i | ||||
\(120\) | −0.0469418 | −0.00428518 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −13.1639 | −1.19180 | ||||||||
\(123\) | 0.233631 | − | 0.719043i | 0.0210658 | − | 0.0648339i | ||||
\(124\) | −0.437387 | + | 0.317780i | −0.0392785 | + | 0.0285375i | ||||
\(125\) | −1.07413 | − | 0.780398i | −0.0960727 | − | 0.0698009i | ||||
\(126\) | 1.27842 | + | 3.93458i | 0.113891 | + | 0.350521i | ||||
\(127\) | −4.77616 | − | 14.6995i | −0.423816 | − | 1.30437i | −0.904123 | − | 0.427271i | \(-0.859475\pi\) |
0.480308 | − | 0.877100i | \(-0.340525\pi\) | |||||||
\(128\) | −8.57246 | − | 6.22826i | −0.757706 | − | 0.550505i | ||||
\(129\) | 0.103022 | − | 0.0748495i | 0.00907054 | − | 0.00659013i | ||||
\(130\) | −0.0365385 | + | 0.112454i | −0.00320464 | + | 0.00986286i | ||||
\(131\) | −17.6675 | −1.54362 | −0.771810 | − | 0.635854i | \(-0.780648\pi\) | ||||
−0.771810 | + | 0.635854i | \(0.780648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.18297 | 0.622843 | ||||||||
\(134\) | 5.15643 | − | 15.8699i | 0.445448 | − | 1.37095i | ||||
\(135\) | 0.0788769 | − | 0.0573074i | 0.00678865 | − | 0.00493224i | ||||
\(136\) | 3.32161 | + | 2.41329i | 0.284826 | + | 0.206938i | ||||
\(137\) | 5.88131 | + | 18.1008i | 0.502474 | + | 1.54646i | 0.804975 | + | 0.593308i | \(0.202178\pi\) |
−0.302501 | + | 0.953149i | \(0.597822\pi\) | |||||||
\(138\) | −0.0874200 | − | 0.269051i | −0.00744169 | − | 0.0229032i | ||||
\(139\) | −11.3800 | − | 8.26808i | −0.965242 | − | 0.701289i | −0.0108796 | − | 0.999941i | \(-0.503463\pi\) |
−0.954362 | + | 0.298652i | \(0.903463\pi\) | |||||||
\(140\) | 0.00851521 | − | 0.00618666i | 0.000719667 | − | 0.000522869i | ||||
\(141\) | −0.359155 | + | 1.10537i | −0.0302463 | + | 0.0930886i | ||||
\(142\) | 6.69994 | 0.562247 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 11.4489 | 0.954072 | ||||||||
\(145\) | 0.183990 | − | 0.566262i | 0.0152795 | − | 0.0470255i | ||||
\(146\) | −9.93153 | + | 7.21568i | −0.821939 | + | 0.597174i | ||||
\(147\) | 0.0990877 | + | 0.0719914i | 0.00817261 | + | 0.00593775i | ||||
\(148\) | −0.0921593 | − | 0.283637i | −0.00757544 | − | 0.0233148i | ||||
\(149\) | 3.41052 | + | 10.4965i | 0.279401 | + | 0.859907i | 0.988021 | + | 0.154317i | \(0.0493178\pi\) |
−0.708621 | + | 0.705590i | \(0.750682\pi\) | |||||||
\(150\) | −0.684225 | − | 0.497118i | −0.0558667 | − | 0.0405895i | ||||
\(151\) | −13.0535 | + | 9.48391i | −1.06228 | + | 0.771789i | −0.974508 | − | 0.224351i | \(-0.927974\pi\) |
−0.0877688 | + | 0.996141i | \(0.527974\pi\) | |||||||
\(152\) | 6.39614 | − | 19.6853i | 0.518795 | − | 1.59669i | ||||
\(153\) | −4.25309 | −0.343842 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.908663 | 0.0729856 | ||||||||
\(156\) | 0.00192119 | − | 0.00591280i | 0.000153818 | − | 0.000473403i | ||||
\(157\) | 12.0300 | − | 8.74029i | 0.960096 | − | 0.697551i | 0.00692325 | − | 0.999976i | \(-0.497796\pi\) |
0.953173 | + | 0.302425i | \(0.0977962\pi\) | |||||||
\(158\) | 12.8840 | + | 9.36078i | 1.02500 | + | 0.744704i | ||||
\(159\) | 0.0252276 | + | 0.0776427i | 0.00200068 | + | 0.00615747i | ||||
\(160\) | −0.0183881 | − | 0.0565927i | −0.00145371 | − | 0.00447405i | ||||
\(161\) | 1.34827 | + | 0.979573i | 0.106258 | + | 0.0772012i | ||||
\(162\) | −9.94020 | + | 7.22198i | −0.780976 | + | 0.567412i | ||||
\(163\) | −5.08454 | + | 15.6486i | −0.398252 | + | 1.22569i | 0.528148 | + | 0.849152i | \(0.322887\pi\) |
−0.926400 | + | 0.376541i | \(0.877113\pi\) | |||||||
\(164\) | 0.488493 | 0.0381449 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.2774 | −1.03053 | ||||||||
\(167\) | 5.91825 | − | 18.2145i | 0.457968 | − | 1.40948i | −0.409648 | − | 0.912244i | \(-0.634348\pi\) |
0.867615 | − | 0.497236i | \(-0.165652\pi\) | |||||||
\(168\) | 0.285529 | − | 0.207449i | 0.0220291 | − | 0.0160051i | ||||
\(169\) | 10.1844 | + | 7.39937i | 0.783412 | + | 0.569182i | ||||
\(170\) | −0.0811628 | − | 0.249793i | −0.00622490 | − | 0.0191583i | ||||
\(171\) | 6.62568 | + | 20.3918i | 0.506679 | + | 1.55940i | ||||
\(172\) | 0.0665637 | + | 0.0483614i | 0.00507544 | + | 0.00368752i | ||||
\(173\) | 12.3169 | − | 8.94879i | 0.936440 | − | 0.680364i | −0.0111210 | − | 0.999938i | \(-0.503540\pi\) |
0.947561 | + | 0.319575i | \(0.103540\pi\) | |||||||
\(174\) | 0.234821 | − | 0.722706i | 0.0178018 | − | 0.0547882i | ||||
\(175\) | 4.98231 | 0.376627 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.00273 | −0.0753698 | ||||||||
\(178\) | −7.58066 | + | 23.3309i | −0.568194 | + | 1.74872i | ||||
\(179\) | −0.913077 | + | 0.663389i | −0.0682465 | + | 0.0495840i | −0.621385 | − | 0.783505i | \(-0.713430\pi\) |
0.553139 | + | 0.833089i | \(0.313430\pi\) | |||||||
\(180\) | 0.0254179 | + | 0.0184672i | 0.00189454 | + | 0.00137646i | ||||
\(181\) | 5.70986 | + | 17.5731i | 0.424410 | + | 1.30620i | 0.903558 | + | 0.428466i | \(0.140946\pi\) |
−0.479147 | + | 0.877735i | \(0.659054\pi\) | |||||||
\(182\) | −0.274716 | − | 0.845489i | −0.0203633 | − | 0.0626718i | ||||
\(183\) | −0.941141 | − | 0.683779i | −0.0695712 | − | 0.0505464i | ||||
\(184\) | 3.88514 | − | 2.82272i | 0.286416 | − | 0.208094i | ||||
\(185\) | −0.154894 | + | 0.476714i | −0.0113880 | + | 0.0350487i | ||||
\(186\) | 1.15970 | 0.0850336 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.750947 | −0.0547684 | ||||||||
\(189\) | −0.226521 | + | 0.697160i | −0.0164770 | + | 0.0507109i | ||||
\(190\) | −1.07121 | + | 0.778283i | −0.0777141 | + | 0.0564626i | ||||
\(191\) | 1.96576 | + | 1.42821i | 0.142237 | + | 0.103342i | 0.656628 | − | 0.754214i | \(-0.271982\pi\) |
−0.514391 | + | 0.857556i | \(0.671982\pi\) | |||||||
\(192\) | −0.313799 | − | 0.965773i | −0.0226465 | − | 0.0696987i | ||||
\(193\) | 0.0813717 | + | 0.250436i | 0.00585726 | + | 0.0180268i | 0.953942 | − | 0.299990i | \(-0.0969833\pi\) |
−0.948085 | + | 0.318017i | \(0.896983\pi\) | |||||||
\(194\) | −7.37944 | − | 5.36148i | −0.529813 | − | 0.384932i | ||||
\(195\) | −0.00845355 | + | 0.00614187i | −0.000605372 | + | 0.000439828i | ||||
\(196\) | −0.0244542 | + | 0.0752624i | −0.00174673 | + | 0.00537588i | ||||
\(197\) | −17.4681 | −1.24455 | −0.622276 | − | 0.782798i | \(-0.713792\pi\) | ||||
−0.622276 | + | 0.782798i | \(0.713792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.1415 | −1.42780 | −0.713898 | − | 0.700250i | \(-0.753072\pi\) | ||||
−0.713898 | + | 0.700250i | \(0.753072\pi\) | |||||||
\(200\) | 4.43654 | − | 13.6543i | 0.313711 | − | 0.965502i | ||||
\(201\) | 1.19299 | − | 0.866760i | 0.0841473 | − | 0.0611366i | ||||
\(202\) | 20.8783 | + | 15.1690i | 1.46899 | + | 1.06729i | ||||
\(203\) | 1.38334 | + | 4.25747i | 0.0970911 | + | 0.298816i | ||||
\(204\) | 0.00426752 | + | 0.0131341i | 0.000298786 | + | 0.000919570i | ||||
\(205\) | −0.664217 | − | 0.482582i | −0.0463910 | − | 0.0337050i | ||||
\(206\) | 7.76310 | − | 5.64023i | 0.540881 | − | 0.392973i | ||||
\(207\) | −1.53725 | + | 4.73117i | −0.106846 | + | 0.328839i | ||||
\(208\) | −2.46021 | −0.170585 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.0225775 | −0.00155800 | ||||||||
\(211\) | 4.35102 | − | 13.3911i | 0.299536 | − | 0.921879i | −0.682123 | − | 0.731237i | \(-0.738943\pi\) |
0.981660 | − | 0.190641i | \(-0.0610567\pi\) | |||||||
\(212\) | −0.0426738 | + | 0.0310043i | −0.00293085 | + | 0.00212939i | ||||
\(213\) | 0.479007 | + | 0.348019i | 0.0328210 | + | 0.0238459i | ||||
\(214\) | 2.33177 | + | 7.17644i | 0.159396 | + | 0.490572i | ||||
\(215\) | −0.0427324 | − | 0.131517i | −0.00291432 | − | 0.00896937i | ||||
\(216\) | 1.70889 | + | 1.24158i | 0.116275 | + | 0.0844791i | ||||
\(217\) | −5.52706 | + | 4.01565i | −0.375201 | + | 0.272600i | ||||
\(218\) | 3.95012 | − | 12.1572i | 0.267536 | − | 0.823391i | ||||
\(219\) | −1.08486 | −0.0733078 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.913931 | 0.0614777 | ||||||||
\(222\) | −0.197687 | + | 0.608417i | −0.0132679 | + | 0.0408343i | ||||
\(223\) | 7.79378 | − | 5.66251i | 0.521910 | − | 0.379190i | −0.295413 | − | 0.955370i | \(-0.595457\pi\) |
0.817323 | + | 0.576180i | \(0.195457\pi\) | |||||||
\(224\) | 0.361948 | + | 0.262970i | 0.0241836 | + | 0.0175704i | ||||
\(225\) | 4.59576 | + | 14.1443i | 0.306384 | + | 0.942953i | ||||
\(226\) | 4.01825 | + | 12.3669i | 0.267290 | + | 0.822634i | ||||
\(227\) | −8.42119 | − | 6.11835i | −0.558934 | − | 0.406089i | 0.272135 | − | 0.962259i | \(-0.412270\pi\) |
−0.831069 | + | 0.556170i | \(0.812270\pi\) | |||||||
\(228\) | 0.0563242 | − | 0.0409220i | 0.00373016 | − | 0.00271012i | ||||
\(229\) | −2.88167 | + | 8.86887i | −0.190426 | + | 0.586072i | −1.00000 | 0.000947117i | \(-0.999699\pi\) | |
0.809573 | + | 0.587019i | \(0.199699\pi\) | |||||||
\(230\) | −0.307208 | −0.0202567 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.8996 | 0.846900 | ||||||||
\(233\) | −5.23969 | + | 16.1261i | −0.343264 | + | 1.05646i | 0.619243 | + | 0.785199i | \(0.287440\pi\) |
−0.962507 | + | 0.271258i | \(0.912560\pi\) | |||||||
\(234\) | 2.14686 | − | 1.55978i | 0.140345 | − | 0.101966i | ||||
\(235\) | 1.02108 | + | 0.741861i | 0.0666082 | + | 0.0483937i | ||||
\(236\) | −0.200206 | − | 0.616169i | −0.0130323 | − | 0.0401092i | ||||
\(237\) | 0.434900 | + | 1.33848i | 0.0282498 | + | 0.0869439i | ||||
\(238\) | 1.59759 | + | 1.16072i | 0.103557 | + | 0.0752382i | ||||
\(239\) | 6.69837 | − | 4.86665i | 0.433281 | − | 0.314797i | −0.349678 | − | 0.936870i | \(-0.613709\pi\) |
0.782960 | + | 0.622073i | \(0.213709\pi\) | |||||||
\(240\) | −0.0193076 | + | 0.0594228i | −0.00124630 | + | 0.00383572i | ||||
\(241\) | −9.31212 | −0.599846 | −0.299923 | − | 0.953963i | \(-0.596961\pi\) | ||||
−0.299923 | + | 0.953963i | \(0.596961\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.28492 | −0.210727 | ||||||||
\(244\) | 0.232268 | − | 0.714847i | 0.0148694 | − | 0.0457634i | ||||
\(245\) | 0.107603 | − | 0.0781781i | 0.00687450 | − | 0.00499461i | ||||
\(246\) | −0.847724 | − | 0.615907i | −0.0540489 | − | 0.0392688i | ||||
\(247\) | −1.42377 | − | 4.38191i | −0.0905923 | − | 0.278815i | ||||
\(248\) | 6.08345 | + | 18.7229i | 0.386300 | + | 1.18891i | ||||
\(249\) | −0.949258 | − | 0.689676i | −0.0601568 | − | 0.0437065i | ||||
\(250\) | −1.48869 | + | 1.08159i | −0.0941528 | + | 0.0684060i | ||||
\(251\) | −1.52510 | + | 4.69377i | −0.0962633 | + | 0.296268i | −0.987581 | − | 0.157112i | \(-0.949782\pi\) |
0.891318 | + | 0.453379i | \(0.149782\pi\) | |||||||
\(252\) | −0.236220 | −0.0148804 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −21.4213 | −1.34409 | ||||||||
\(255\) | 0.00717250 | − | 0.0220747i | 0.000449160 | − | 0.00138237i | ||||
\(256\) | 1.53409 | − | 1.11458i | 0.0958807 | − | 0.0696614i | ||||
\(257\) | 13.6044 | + | 9.88415i | 0.848617 | + | 0.616556i | 0.924764 | − | 0.380540i | \(-0.124262\pi\) |
−0.0761474 | + | 0.997097i | \(0.524262\pi\) | |||||||
\(258\) | −0.0545382 | − | 0.167851i | −0.00339540 | − | 0.0104500i | ||||
\(259\) | −1.16457 | − | 3.58419i | −0.0723632 | − | 0.222711i | ||||
\(260\) | −0.00546197 | − | 0.00396835i | −0.000338737 | − | 0.000246107i | ||||
\(261\) | −10.8105 | + | 7.85431i | −0.669155 | + | 0.486170i | ||||
\(262\) | −7.56670 | + | 23.2879i | −0.467472 | + | 1.43873i | ||||
\(263\) | −4.11162 | −0.253533 | −0.126767 | − | 0.991933i | \(-0.540460\pi\) | ||||
−0.126767 | + | 0.991933i | \(0.540460\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0886540 | 0.00544597 | ||||||||
\(266\) | 3.07634 | − | 9.46801i | 0.188623 | − | 0.580521i | ||||
\(267\) | −1.75386 | + | 1.27426i | −0.107335 | + | 0.0779832i | ||||
\(268\) | 0.770811 | + | 0.560027i | 0.0470847 | + | 0.0342091i | ||||
\(269\) | −7.40664 | − | 22.7953i | −0.451591 | − | 1.38985i | −0.875091 | − | 0.483958i | \(-0.839199\pi\) |
0.423500 | − | 0.905896i | \(-0.360801\pi\) | |||||||
\(270\) | −0.0417564 | − | 0.128513i | −0.00254121 | − | 0.00782105i | ||||
\(271\) | −4.86050 | − | 3.53136i | −0.295254 | − | 0.214515i | 0.430289 | − | 0.902691i | \(-0.358412\pi\) |
−0.725544 | + | 0.688176i | \(0.758412\pi\) | |||||||
\(272\) | 4.42116 | − | 3.21216i | 0.268072 | − | 0.194766i | ||||
\(273\) | 0.0242772 | − | 0.0747174i | 0.00146932 | − | 0.00452210i | ||||
\(274\) | 26.3779 | 1.59355 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.0161529 | 0.000972293 | ||||||||
\(277\) | 2.83123 | − | 8.71363i | 0.170112 | − | 0.523552i | −0.829264 | − | 0.558857i | \(-0.811240\pi\) |
0.999377 | + | 0.0353050i | \(0.0112403\pi\) | |||||||
\(278\) | −15.7722 | + | 11.4592i | −0.945953 | + | 0.687275i | ||||
\(279\) | −16.4983 | − | 11.9867i | −0.987726 | − | 0.717625i | ||||
\(280\) | −0.118435 | − | 0.364505i | −0.00707784 | − | 0.0217834i | ||||
\(281\) | −4.00423 | − | 12.3237i | −0.238872 | − | 0.735173i | −0.996584 | − | 0.0825836i | \(-0.973683\pi\) |
0.757712 | − | 0.652589i | \(-0.226317\pi\) | |||||||
\(282\) | 1.30318 | + | 0.946818i | 0.0776034 | + | 0.0563822i | ||||
\(283\) | −3.06440 | + | 2.22642i | −0.182160 | + | 0.132347i | −0.675128 | − | 0.737700i | \(-0.735912\pi\) |
0.492969 | + | 0.870047i | \(0.335912\pi\) | |||||||
\(284\) | −0.118216 | + | 0.363832i | −0.00701483 | + | 0.0215894i | ||||
\(285\) | −0.117013 | −0.00693122 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.17286 | 0.364372 | ||||||||
\(288\) | −0.412681 | + | 1.27010i | −0.0243175 | + | 0.0748415i | ||||
\(289\) | 12.1109 | − | 8.79908i | 0.712405 | − | 0.517593i | ||||
\(290\) | −0.667602 | − | 0.485041i | −0.0392029 | − | 0.0284826i | ||||
\(291\) | −0.249093 | − | 0.766630i | −0.0146021 | − | 0.0449407i | ||||
\(292\) | −0.216603 | − | 0.666635i | −0.0126757 | − | 0.0390118i | ||||
\(293\) | 17.2879 | + | 12.5604i | 1.00997 | + | 0.733785i | 0.964202 | − | 0.265168i | \(-0.0854273\pi\) |
0.0457656 | + | 0.998952i | \(0.485427\pi\) | |||||||
\(294\) | 0.137331 | − | 0.0997767i | 0.00800930 | − | 0.00581909i | ||||
\(295\) | −0.336489 | + | 1.03561i | −0.0195911 | + | 0.0602953i | ||||
\(296\) | −10.8597 | −0.631205 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.2963 | 0.886091 | ||||||||
\(299\) | 0.330334 | − | 1.01667i | 0.0191037 | − | 0.0587953i | ||||
\(300\) | 0.0390681 | − | 0.0283846i | 0.00225560 | − | 0.00163879i | ||||
\(301\) | 0.841136 | + | 0.611121i | 0.0484822 | + | 0.0352244i | ||||
\(302\) | 6.91034 | + | 21.2678i | 0.397645 | + | 1.22383i | ||||
\(303\) | 0.704747 | + | 2.16899i | 0.0404867 | + | 0.124605i | ||||
\(304\) | −22.2885 | − | 16.1935i | −1.27833 | − | 0.928761i | ||||
\(305\) | −1.02202 | + | 0.742540i | −0.0585207 | + | 0.0425177i | ||||
\(306\) | −1.82152 | + | 5.60608i | −0.104130 | + | 0.320478i | ||||
\(307\) | 8.44677 | 0.482082 | 0.241041 | − | 0.970515i | \(-0.422511\pi\) | ||||
0.241041 | + | 0.970515i | \(0.422511\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.847991 | 0.0482405 | ||||||||
\(310\) | 0.389165 | − | 1.19773i | 0.0221031 | − | 0.0680263i | ||||
\(311\) | −14.5777 | + | 10.5913i | −0.826624 | + | 0.600577i | −0.918602 | − | 0.395184i | \(-0.870681\pi\) |
0.0919783 | + | 0.995761i | \(0.470681\pi\) | |||||||
\(312\) | −0.183149 | − | 0.133065i | −0.0103688 | − | 0.00753335i | ||||
\(313\) | 0.0730332 | + | 0.224773i | 0.00412808 | + | 0.0127049i | 0.953099 | − | 0.302658i | \(-0.0978739\pi\) |
−0.948971 | + | 0.315363i | \(0.897874\pi\) | |||||||
\(314\) | −6.36851 | − | 19.6003i | −0.359396 | − | 1.10611i | ||||
\(315\) | 0.321194 | + | 0.233361i | 0.0180973 | + | 0.0131484i | ||||
\(316\) | −0.735655 | + | 0.534485i | −0.0413838 | + | 0.0300671i | ||||
\(317\) | 5.28206 | − | 16.2565i | 0.296670 | − | 0.913056i | −0.685985 | − | 0.727615i | \(-0.740629\pi\) |
0.982655 | − | 0.185441i | \(-0.0593714\pi\) | |||||||
\(318\) | 0.113147 | 0.00634496 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.10274 | −0.0616450 | ||||||||
\(321\) | −0.206062 | + | 0.634195i | −0.0115013 | + | 0.0353973i | ||||
\(322\) | 1.86863 | − | 1.35764i | 0.104135 | − | 0.0756584i | ||||
\(323\) | 8.27984 | + | 6.01565i | 0.460703 | + | 0.334720i | ||||
\(324\) | −0.216792 | − | 0.667217i | −0.0120440 | − | 0.0370676i | ||||
\(325\) | −0.987567 | − | 3.03942i | −0.0547804 | − | 0.168597i | ||||
\(326\) | 18.4491 | + | 13.4041i | 1.02180 | + | 0.742382i | ||||
\(327\) | 0.913902 | − | 0.663988i | 0.0505389 | − | 0.0367186i | ||||
\(328\) | 5.49667 | − | 16.9170i | 0.303503 | − | 0.934086i | ||||
\(329\) | −9.48937 | −0.523166 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.41186 | 0.242498 | 0.121249 | − | 0.992622i | \(-0.461310\pi\) | ||||
0.121249 | + | 0.992622i | \(0.461310\pi\) | |||||||
\(332\) | 0.234271 | − | 0.721012i | 0.0128573 | − | 0.0395707i | ||||
\(333\) | 9.10095 | − | 6.61223i | 0.498729 | − | 0.362348i | ||||
\(334\) | −21.4742 | − | 15.6019i | −1.17502 | − | 0.853699i | ||||
\(335\) | −0.494843 | − | 1.52297i | −0.0270361 | − | 0.0832087i | ||||
\(336\) | −0.145165 | − | 0.446773i | −0.00791941 | − | 0.0243734i | ||||
\(337\) | 22.4809 | + | 16.3333i | 1.22461 | + | 0.889733i | 0.996475 | − | 0.0838961i | \(-0.0267364\pi\) |
0.228138 | + | 0.973629i | \(0.426736\pi\) | |||||||
\(338\) | 14.1150 | − | 10.2552i | 0.767757 | − | 0.557808i | ||||
\(339\) | −0.355100 | + | 1.09289i | −0.0192864 | + | 0.0593574i | ||||
\(340\) | 0.0149968 | 0.000813315 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 29.7164 | 1.60688 | ||||||||
\(343\) | −0.309017 | + | 0.951057i | −0.0166853 | + | 0.0513522i | ||||
\(344\) | 2.42380 | − | 1.76100i | 0.130683 | − | 0.0949465i | ||||
\(345\) | −0.0219636 | − | 0.0159575i | −0.00118248 | − | 0.000859123i | ||||
\(346\) | −6.52043 | − | 20.0678i | −0.350540 | − | 1.07885i | ||||
\(347\) | −9.65724 | − | 29.7219i | −0.518428 | − | 1.59556i | −0.776958 | − | 0.629553i | \(-0.783238\pi\) |
0.258530 | − | 0.966003i | \(-0.416762\pi\) | |||||||
\(348\) | 0.0351024 | + | 0.0255034i | 0.00188168 | + | 0.00136712i | ||||
\(349\) | −0.439651 | + | 0.319425i | −0.0235340 | + | 0.0170984i | −0.599490 | − | 0.800382i | \(-0.704630\pi\) |
0.575956 | + | 0.817481i | \(0.304630\pi\) | |||||||
\(350\) | 2.13384 | − | 6.56728i | 0.114058 | − | 0.351036i | ||||
\(351\) | 0.470197 | 0.0250972 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.8517 | −0.950148 | −0.475074 | − | 0.879946i | \(-0.657579\pi\) | ||||
−0.475074 | + | 0.879946i | \(0.657579\pi\) | |||||||
\(354\) | −0.429452 | + | 1.32172i | −0.0228251 | + | 0.0702485i | ||||
\(355\) | 0.520171 | − | 0.377927i | 0.0276078 | − | 0.0200583i | ||||
\(356\) | −1.13320 | − | 0.823316i | −0.0600593 | − | 0.0436356i | ||||
\(357\) | 0.0539268 | + | 0.165970i | 0.00285411 | + | 0.00878404i | ||||
\(358\) | 0.483371 | + | 1.48766i | 0.0255469 | + | 0.0786254i | ||||
\(359\) | −9.70081 | − | 7.04805i | −0.511989 | − | 0.371982i | 0.301588 | − | 0.953438i | \(-0.402483\pi\) |
−0.813578 | + | 0.581456i | \(0.802483\pi\) | |||||||
\(360\) | 0.925549 | − | 0.672450i | 0.0487807 | − | 0.0354413i | ||||
\(361\) | 10.0724 | − | 30.9998i | 0.530128 | − | 1.63157i | ||||
\(362\) | 25.6089 | 1.34598 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0507604 | 0.00266057 | ||||||||
\(365\) | −0.364048 | + | 1.12042i | −0.0190551 | + | 0.0586457i | ||||
\(366\) | −1.30438 | + | 0.947685i | −0.0681809 | + | 0.0495363i | ||||
\(367\) | −23.9435 | − | 17.3960i | −1.24984 | − | 0.908062i | −0.251628 | − | 0.967824i | \(-0.580966\pi\) |
−0.998213 | + | 0.0597620i | \(0.980966\pi\) | |||||||
\(368\) | −1.97523 | − | 6.07915i | −0.102966 | − | 0.316897i | ||||
\(369\) | 5.69394 | + | 17.5241i | 0.296415 | + | 0.912271i | ||||
\(370\) | 0.562027 | + | 0.408337i | 0.0292184 | + | 0.0212284i | ||||
\(371\) | −0.539250 | + | 0.391788i | −0.0279964 | + | 0.0203406i | ||||
\(372\) | −0.0204622 | + | 0.0629762i | −0.00106092 | + | 0.00326516i | ||||
\(373\) | −10.5209 | −0.544753 | −0.272377 | − | 0.962191i | \(-0.587810\pi\) | ||||
−0.272377 | + | 0.962191i | \(0.587810\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.162615 | −0.00839738 | ||||||||
\(376\) | −8.44989 | + | 26.0061i | −0.435770 | + | 1.34116i | ||||
\(377\) | 2.32304 | − | 1.68779i | 0.119643 | − | 0.0869254i | ||||
\(378\) | 0.821925 | + | 0.597163i | 0.0422752 | + | 0.0307148i | ||||
\(379\) | −2.58002 | − | 7.94050i | −0.132527 | − | 0.407876i | 0.862670 | − | 0.505767i | \(-0.168790\pi\) |
−0.995197 | + | 0.0978908i | \(0.968790\pi\) | |||||||
\(380\) | −0.0233628 | − | 0.0719032i | −0.00119848 | − | 0.00368856i | ||||
\(381\) | −1.53150 | − | 1.11270i | −0.0784610 | − | 0.0570053i | ||||
\(382\) | 2.72445 | − | 1.97943i | 0.139395 | − | 0.101276i | ||||
\(383\) | −5.70870 | + | 17.5696i | −0.291701 | + | 0.897764i | 0.692609 | + | 0.721314i | \(0.256461\pi\) |
−0.984310 | + | 0.176450i | \(0.943539\pi\) | |||||||
\(384\) | −1.29781 | −0.0662284 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.364955 | 0.0185757 | ||||||||
\(387\) | −0.959036 | + | 2.95161i | −0.0487505 | + | 0.150039i | ||||
\(388\) | 0.421354 | − | 0.306131i | 0.0213910 | − | 0.0155415i | ||||
\(389\) | −18.8145 | − | 13.6695i | −0.953934 | − | 0.693074i | −0.00219987 | − | 0.999998i | \(-0.500700\pi\) |
−0.951734 | + | 0.306924i | \(0.900700\pi\) | |||||||
\(390\) | 0.00447520 | + | 0.0137732i | 0.000226611 | + | 0.000697436i | ||||
\(391\) | 0.733771 | + | 2.25832i | 0.0371084 | + | 0.114208i | ||||
\(392\) | 2.33125 | + | 1.69375i | 0.117746 | + | 0.0855474i | ||||
\(393\) | −1.75063 | + | 1.27191i | −0.0883078 | + | 0.0641594i | ||||
\(394\) | −7.48130 | + | 23.0251i | −0.376902 | + | 1.15999i | ||||
\(395\) | 1.52831 | 0.0768976 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.6794 | 1.08806 | 0.544029 | − | 0.839066i | \(-0.316898\pi\) | ||||
0.544029 | + | 0.839066i | \(0.316898\pi\) | |||||||
\(398\) | −8.62627 | + | 26.5489i | −0.432396 | + | 1.33078i | ||||
\(399\) | 0.711744 | − | 0.517112i | 0.0356318 | − | 0.0258880i | ||||
\(400\) | −15.4599 | − | 11.2323i | −0.772995 | − | 0.561614i | ||||
\(401\) | −10.7561 | − | 33.1039i | −0.537135 | − | 1.65313i | −0.738990 | − | 0.673717i | \(-0.764697\pi\) |
0.201855 | − | 0.979415i | \(-0.435303\pi\) | |||||||
\(402\) | −0.631555 | − | 1.94373i | −0.0314991 | − | 0.0969443i | ||||
\(403\) | 3.54526 | + | 2.57578i | 0.176602 | + | 0.128309i | ||||
\(404\) | −1.19212 | + | 0.866123i | −0.0593100 | + | 0.0430912i | ||||
\(405\) | −0.364366 | + | 1.12140i | −0.0181055 | + | 0.0557230i | ||||
\(406\) | 6.20431 | 0.307915 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.502867 | 0.0248956 | ||||||||
\(409\) | −5.03471 | + | 15.4952i | −0.248950 | + | 0.766190i | 0.746011 | + | 0.665933i | \(0.231967\pi\) |
−0.994962 | + | 0.100257i | \(0.968033\pi\) | |||||||
\(410\) | −0.920574 | + | 0.668836i | −0.0454639 | + | 0.0330315i | ||||
\(411\) | 1.88587 | + | 1.37016i | 0.0930231 | + | 0.0675852i | ||||
\(412\) | 0.169310 | + | 0.521084i | 0.00834132 | + | 0.0256719i | ||||
\(413\) | −2.52991 | − | 7.78625i | −0.124489 | − | 0.383136i | ||||
\(414\) | 5.57787 | + | 4.05256i | 0.274137 | + | 0.199172i | ||||
\(415\) | −1.03083 | + | 0.748945i | −0.0506016 | + | 0.0367642i | ||||
\(416\) | 0.0886796 | − | 0.272928i | 0.00434788 | − | 0.0133814i | ||||
\(417\) | −1.72285 | −0.0843684 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.6536 | −1.10670 | −0.553350 | − | 0.832949i | \(-0.686651\pi\) | ||||
−0.553350 | + | 0.832949i | \(0.686651\pi\) | |||||||
\(420\) | 0.000398366 | − | 0.00122604i | 1.94383e−5 | − | 5.98248e-5i | ||||
\(421\) | 12.3020 | − | 8.93795i | 0.599564 | − | 0.435609i | −0.246160 | − | 0.969229i | \(-0.579169\pi\) |
0.845724 | + | 0.533620i | \(0.179169\pi\) | |||||||
\(422\) | −15.7875 | − | 11.4703i | −0.768526 | − | 0.558367i | ||||
\(423\) | −8.75314 | − | 26.9394i | −0.425592 | − | 1.30984i | ||||
\(424\) | 0.593534 | + | 1.82671i | 0.0288246 | + | 0.0887129i | ||||
\(425\) | 5.74313 | + | 4.17263i | 0.278583 | + | 0.202402i | ||||
\(426\) | 0.663882 | − | 0.482338i | 0.0321652 | − | 0.0233694i | ||||
\(427\) | 2.93506 | − | 9.03320i | 0.142038 | − | 0.437147i | ||||
\(428\) | −0.430850 | −0.0208259 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.191656 | −0.00924249 | ||||||||
\(431\) | 0.990988 | − | 3.04995i | 0.0477342 | − | 0.146911i | −0.924348 | − | 0.381549i | \(-0.875391\pi\) |
0.972083 | + | 0.234639i | \(0.0753906\pi\) | |||||||
\(432\) | 2.27458 | − | 1.65258i | 0.109436 | − | 0.0795099i | ||||
\(433\) | −4.84800 | − | 3.52228i | −0.232980 | − | 0.169270i | 0.465170 | − | 0.885221i | \(-0.345993\pi\) |
−0.698150 | + | 0.715951i | \(0.745993\pi\) | |||||||
\(434\) | 2.92595 | + | 9.00516i | 0.140450 | + | 0.432261i | ||||
\(435\) | −0.0225349 | − | 0.0693553i | −0.00108047 | − | 0.00332533i | ||||
\(436\) | 0.590485 | + | 0.429013i | 0.0282791 | + | 0.0205460i | ||||
\(437\) | 9.68456 | − | 7.03624i | 0.463275 | − | 0.336589i | ||||
\(438\) | −0.464625 | + | 1.42997i | −0.0222007 | + | 0.0683266i | ||||
\(439\) | 7.68712 | 0.366886 | 0.183443 | − | 0.983030i | \(-0.441276\pi\) | ||||
0.183443 | + | 0.983030i | \(0.441276\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.98500 | −0.142143 | ||||||||
\(442\) | 0.391421 | − | 1.20467i | 0.0186180 | − | 0.0573003i | ||||
\(443\) | −30.1358 | + | 21.8950i | −1.43180 | + | 1.04026i | −0.442117 | + | 0.896957i | \(0.645772\pi\) |
−0.989679 | + | 0.143303i | \(0.954228\pi\) | |||||||
\(444\) | −0.0295513 | − | 0.0214703i | −0.00140244 | − | 0.00101893i | ||||
\(445\) | 0.727486 | + | 2.23897i | 0.0344861 | + | 0.106137i | ||||
\(446\) | −4.12592 | − | 12.6983i | −0.195368 | − | 0.601281i | ||||
\(447\) | 1.09360 | + | 0.794546i | 0.0517254 | + | 0.0375807i | ||||
\(448\) | 6.70756 | − | 4.87333i | 0.316902 | − | 0.230243i | ||||
\(449\) | 3.42156 | − | 10.5305i | 0.161473 | − | 0.496964i | −0.837286 | − | 0.546766i | \(-0.815859\pi\) |
0.998759 | + | 0.0498016i | \(0.0158589\pi\) | |||||||
\(450\) | 20.6121 | 0.971666 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.742468 | −0.0349228 | ||||||||
\(453\) | −0.610679 | + | 1.87948i | −0.0286922 | + | 0.0883055i | ||||
\(454\) | −11.6714 | + | 8.47975i | −0.547764 | + | 0.397974i | ||||
\(455\) | −0.0690204 | − | 0.0501462i | −0.00323573 | − | 0.00235089i | ||||
\(456\) | −0.783393 | − | 2.41104i | −0.0366857 | − | 0.112907i | ||||
\(457\) | −8.77488 | − | 27.0063i | −0.410472 | − | 1.26330i | −0.916239 | − | 0.400632i | \(-0.868791\pi\) |
0.505768 | − | 0.862670i | \(-0.331209\pi\) | |||||||
\(458\) | 10.4561 | + | 7.59677i | 0.488580 | + | 0.354974i | ||||
\(459\) | −0.844975 | + | 0.613910i | −0.0394401 | + | 0.0286549i | ||||
\(460\) | 0.00542049 | − | 0.0166825i | 0.000252732 | − | 0.000777828i | ||||
\(461\) | 25.7420 | 1.19892 | 0.599462 | − | 0.800403i | \(-0.295381\pi\) | ||||
0.599462 | + | 0.800403i | \(0.295381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.6543 | 1.74995 | 0.874973 | − | 0.484172i | \(-0.160879\pi\) | ||||
0.874973 | + | 0.484172i | \(0.160879\pi\) | |||||||
\(464\) | 5.30574 | − | 16.3294i | 0.246313 | − | 0.758072i | ||||
\(465\) | 0.0900373 | − | 0.0654159i | 0.00417538 | − | 0.00303359i | ||||
\(466\) | 19.0121 | + | 13.8131i | 0.880717 | + | 0.639879i | ||||
\(467\) | −4.75498 | − | 14.6343i | −0.220034 | − | 0.677196i | −0.998758 | − | 0.0498289i | \(-0.984132\pi\) |
0.778723 | − | 0.627367i | \(-0.215868\pi\) | |||||||
\(468\) | 0.0468222 | + | 0.144104i | 0.00216436 | + | 0.00666120i | ||||
\(469\) | 9.74038 | + | 7.07680i | 0.449769 | + | 0.326776i | ||||
\(470\) | 1.41517 | − | 1.02818i | 0.0652771 | − | 0.0474266i | ||||
\(471\) | 0.562796 | − | 1.73211i | 0.0259323 | − | 0.0798114i | ||||
\(472\) | −23.5914 | −1.08588 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.95054 | 0.0895914 | ||||||||
\(475\) | 11.0590 | − | 34.0362i | 0.507423 | − | 1.56169i | ||||
\(476\) | −0.0912198 | + | 0.0662751i | −0.00418105 | + | 0.00303771i | ||||
\(477\) | −1.60966 | − | 1.16949i | −0.0737012 | − | 0.0535471i | ||||
\(478\) | −3.54603 | − | 10.9135i | −0.162191 | − | 0.499174i | ||||
\(479\) | 0.185465 | + | 0.570803i | 0.00847412 | + | 0.0260807i | 0.955204 | − | 0.295948i | \(-0.0956354\pi\) |
−0.946730 | + | 0.322028i | \(0.895635\pi\) | |||||||
\(480\) | −0.00589622 | − | 0.00428386i | −0.000269125 | − | 0.000195530i | ||||
\(481\) | −1.95567 | + | 1.42088i | −0.0891710 | + | 0.0647865i | ||||
\(482\) | −3.98822 | + | 12.2745i | −0.181658 | + | 0.559087i | ||||
\(483\) | 0.204117 | 0.00928767 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.875354 | −0.0397478 | ||||||||
\(486\) | −1.40687 | + | 4.32991i | −0.0638171 | + | 0.196409i | ||||
\(487\) | −8.33216 | + | 6.05367i | −0.377566 | + | 0.274318i | −0.760341 | − | 0.649524i | \(-0.774968\pi\) |
0.382775 | + | 0.923842i | \(0.374968\pi\) | |||||||
\(488\) | −22.1424 | − | 16.0874i | −1.00234 | − | 0.728241i | ||||
\(489\) | 0.622750 | + | 1.91663i | 0.0281617 | + | 0.0866729i | ||||
\(490\) | −0.0569635 | − | 0.175316i | −0.00257335 | − | 0.00791996i | ||||
\(491\) | −8.16497 | − | 5.93220i | −0.368480 | − | 0.267716i | 0.388100 | − | 0.921617i | \(-0.373131\pi\) |
−0.756580 | + | 0.653901i | \(0.773131\pi\) | |||||||
\(492\) | 0.0484036 | − | 0.0351673i | 0.00218220 | − | 0.00158546i | ||||
\(493\) | −1.97100 | + | 6.06613i | −0.0887696 | + | 0.273205i | ||||
\(494\) | −6.38566 | −0.287304 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.2032 | 1.17656 | ||||||||
\(497\) | −1.49384 | + | 4.59758i | −0.0670080 | + | 0.206229i | ||||
\(498\) | −1.31563 | + | 0.955859i | −0.0589546 | + | 0.0428331i | ||||
\(499\) | −16.0149 | − | 11.6355i | −0.716926 | − | 0.520877i | 0.168474 | − | 0.985706i | \(-0.446116\pi\) |
−0.885401 | + | 0.464829i | \(0.846116\pi\) | |||||||
\(500\) | −0.0324677 | − | 0.0999252i | −0.00145200 | − | 0.00446879i | ||||
\(501\) | −0.724862 | − | 2.23089i | −0.0323844 | − | 0.0996690i | ||||
\(502\) | 5.53377 | + | 4.02052i | 0.246984 | + | 0.179445i | ||||
\(503\) | −11.5717 | + | 8.40733i | −0.515956 | + | 0.374864i | −0.815078 | − | 0.579351i | \(-0.803306\pi\) |
0.299122 | + | 0.954215i | \(0.403306\pi\) | |||||||
\(504\) | −2.65802 | + | 8.18053i | −0.118397 | + | 0.364390i | ||||
\(505\) | 2.47660 | 0.110207 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.54184 | 0.0684753 | ||||||||
\(508\) | 0.377964 | − | 1.16325i | 0.0167695 | − | 0.0516111i | ||||
\(509\) | 34.0576 | − | 24.7443i | 1.50958 | − | 1.09677i | 0.543214 | − | 0.839594i | \(-0.317207\pi\) |
0.966364 | − | 0.257178i | \(-0.0827927\pi\) | |||||||
\(510\) | −0.0260252 | − | 0.0189084i | −0.00115242 | − | 0.000837279i | ||||
\(511\) | −2.73711 | − | 8.42396i | −0.121083 | − | 0.372654i | ||||
\(512\) | −7.36090 | − | 22.6545i | −0.325309 | − | 1.00120i | ||||
\(513\) | 4.25979 | + | 3.09492i | 0.188074 | + | 0.136644i | ||||
\(514\) | 18.8550 | − | 13.6990i | 0.831659 | − | 0.604235i | ||||
\(515\) | 0.284563 | − | 0.875794i | 0.0125393 | − | 0.0385921i | ||||
\(516\) | 0.0100772 | 0.000443626 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −5.22316 | −0.229492 | ||||||||
\(519\) | 0.576222 | − | 1.77343i | 0.0252933 | − | 0.0778449i | ||||
\(520\) | −0.198888 | + | 0.144501i | −0.00872181 | + | 0.00633677i | ||||
\(521\) | 17.3512 | + | 12.6064i | 0.760168 | + | 0.552294i | 0.898962 | − | 0.438027i | \(-0.144323\pi\) |
−0.138794 | + | 0.990321i | \(0.544323\pi\) | |||||||
\(522\) | 5.72295 | + | 17.6134i | 0.250487 | + | 0.770919i | ||||
\(523\) | 10.9993 | + | 33.8525i | 0.480968 | + | 1.48027i | 0.837737 | + | 0.546074i | \(0.183878\pi\) |
−0.356769 | + | 0.934193i | \(0.616122\pi\) | |||||||
\(524\) | −1.13111 | − | 0.821800i | −0.0494128 | − | 0.0359005i | ||||
\(525\) | 0.493685 | − | 0.358684i | 0.0215462 | − | 0.0156542i | ||||
\(526\) | −1.76094 | + | 5.41960i | −0.0767804 | + | 0.236306i | ||||
\(527\) | −9.73412 | −0.424025 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.2226 | −0.879244 | ||||||||
\(530\) | 0.0379690 | − | 0.116857i | 0.00164927 | − | 0.00507593i | ||||
\(531\) | 19.7708 | − | 14.3643i | 0.857979 | − | 0.623358i | ||||
\(532\) | 0.459868 | + | 0.334114i | 0.0199378 | + | 0.0144857i | ||||
\(533\) | −1.22355 | − | 3.76570i | −0.0529979 | − | 0.163111i | ||||
\(534\) | 0.928472 | + | 2.85754i | 0.0401789 | + | 0.123658i | ||||
\(535\) | 0.585839 | + | 0.425637i | 0.0253280 | + | 0.0184019i | ||||
\(536\) | 28.0677 | − | 20.3924i | 1.21234 | − | 0.880817i | ||||
\(537\) | −0.0427163 | + | 0.131467i | −0.00184335 | + | 0.00567323i | ||||
\(538\) | −33.2191 | −1.43218 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.00771550 | 0.000332022 | ||||||||
\(541\) | −5.23320 | + | 16.1061i | −0.224993 | + | 0.692457i | 0.773300 | + | 0.634041i | \(0.218605\pi\) |
−0.998292 | + | 0.0584158i | \(0.981395\pi\) | |||||||
\(542\) | −6.73642 | + | 4.89430i | −0.289354 | + | 0.210228i | ||||
\(543\) | 1.83089 | + | 1.33022i | 0.0785711 | + | 0.0570852i | ||||
\(544\) | 0.196984 | + | 0.606254i | 0.00844561 | + | 0.0259929i | ||||
\(545\) | −0.379078 | − | 1.16668i | −0.0162379 | − | 0.0499752i | ||||
\(546\) | −0.0880889 | − | 0.0640004i | −0.00376986 | − | 0.00273896i | ||||
\(547\) | −7.11192 | + | 5.16711i | −0.304084 | + | 0.220930i | −0.729354 | − | 0.684137i | \(-0.760179\pi\) |
0.425270 | + | 0.905067i | \(0.360179\pi\) | |||||||
\(548\) | −0.465421 | + | 1.43242i | −0.0198818 | + | 0.0611899i | ||||
\(549\) | 28.3517 | 1.21002 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.1551 | 1.36985 | ||||||||
\(552\) | 0.181758 | − | 0.559394i | 0.00773614 | − | 0.0238094i | ||||
\(553\) | −9.29614 | + | 6.75404i | −0.395312 | + | 0.287211i | ||||
\(554\) | −10.2730 | − | 7.46380i | −0.436460 | − | 0.317107i | ||||
\(555\) | 0.0189712 | + | 0.0583875i | 0.000805284 | + | 0.00247841i | ||||
\(556\) | −0.343985 | − | 1.05868i | −0.0145882 | − | 0.0448979i | ||||
\(557\) | 17.5780 | + | 12.7712i | 0.744805 | + | 0.541132i | 0.894212 | − | 0.447643i | \(-0.147737\pi\) |
−0.149407 | + | 0.988776i | \(0.547737\pi\) | |||||||
\(558\) | −22.8658 | + | 16.6130i | −0.967987 | + | 0.703284i | ||||
\(559\) | 0.206084 | − | 0.634261i | 0.00871642 | − | 0.0268264i | ||||
\(560\) | −0.510134 | −0.0215571 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.9591 | −0.757559 | ||||||||
\(563\) | 0.562827 | − | 1.73220i | 0.0237203 | − | 0.0730036i | −0.938496 | − | 0.345291i | \(-0.887780\pi\) |
0.962216 | + | 0.272288i | \(0.0877802\pi\) | |||||||
\(564\) | −0.0744096 | + | 0.0540617i | −0.00313321 | + | 0.00227641i | ||||
\(565\) | 1.00956 | + | 0.733485i | 0.0424723 | + | 0.0308579i | ||||
\(566\) | 1.62225 | + | 4.99278i | 0.0681884 | + | 0.209862i | ||||
\(567\) | −2.73950 | − | 8.43132i | −0.115048 | − | 0.354082i | ||||
\(568\) | 11.2697 | + | 8.18790i | 0.472865 | + | 0.343557i | ||||
\(569\) | 26.6505 | − | 19.3627i | 1.11725 | − | 0.811726i | 0.133456 | − | 0.991055i | \(-0.457392\pi\) |
0.983789 | + | 0.179328i | \(0.0573924\pi\) | |||||||
\(570\) | −0.0501145 | + | 0.154236i | −0.00209906 | + | 0.00646025i | ||||
\(571\) | 23.4394 | 0.980908 | 0.490454 | − | 0.871467i | \(-0.336831\pi\) | ||||
0.490454 | + | 0.871467i | \(0.336831\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.297601 | 0.0124325 | ||||||||
\(574\) | 2.64373 | − | 8.13656i | 0.110347 | − | 0.339614i | ||||
\(575\) | 6.71748 | − | 4.88054i | 0.280138 | − | 0.203532i | ||||
\(576\) | 20.0221 | + | 14.5469i | 0.834252 | + | 0.606120i | ||||
\(577\) | 10.6468 | + | 32.7676i | 0.443233 | + | 1.36413i | 0.884410 | + | 0.466711i | \(0.154561\pi\) |
−0.441177 | + | 0.897420i | \(0.645439\pi\) | |||||||
\(578\) | −6.41135 | − | 19.7321i | −0.266677 | − | 0.820747i | ||||
\(579\) | 0.0260922 | + | 0.0189571i | 0.00108435 | + | 0.000787830i | ||||
\(580\) | 0.0381189 | − | 0.0276950i | 0.00158280 | − | 0.00114997i | ||||
\(581\) | 2.96038 | − | 9.11111i | 0.122817 | − | 0.377992i | ||||
\(582\) | −1.11719 | −0.0463091 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −25.5236 | −1.05617 | ||||||||
\(585\) | 0.0786948 | − | 0.242198i | 0.00325363 | − | 0.0100136i | ||||
\(586\) | 23.9602 | − | 17.4081i | 0.989785 | − | 0.719121i | ||||
\(587\) | 16.8818 | + | 12.2653i | 0.696786 | + | 0.506244i | 0.878884 | − | 0.477036i | \(-0.158289\pi\) |
−0.182098 | + | 0.983280i | \(0.558289\pi\) | |||||||
\(588\) | 0.00299513 | + | 0.00921807i | 0.000123517 | + | 0.000380147i | ||||
\(589\) | 15.1643 | + | 46.6710i | 0.624835 | + | 1.92304i | ||||
\(590\) | 1.22094 | + | 0.887065i | 0.0502653 | + | 0.0365199i | ||||
\(591\) | −1.73088 | + | 1.25755i | −0.0711987 | + | 0.0517289i | ||||
\(592\) | −4.46669 | + | 13.7471i | −0.183580 | + | 0.565000i | ||||
\(593\) | −26.6381 | −1.09389 | −0.546947 | − | 0.837167i | \(-0.684210\pi\) | ||||
−0.546947 | + | 0.837167i | \(0.684210\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.189507 | 0.00776905 | ||||||||
\(596\) | −0.269893 | + | 0.830646i | −0.0110553 | + | 0.0340246i | ||||
\(597\) | −1.99578 | + | 1.45002i | −0.0816817 | + | 0.0593453i | ||||
\(598\) | −1.19861 | − | 0.870840i | −0.0490148 | − | 0.0356113i | ||||
\(599\) | −6.38775 | − | 19.6595i | −0.260996 | − | 0.803264i | −0.992589 | − | 0.121522i | \(-0.961223\pi\) |
0.731592 | − | 0.681742i | \(-0.238777\pi\) | |||||||
\(600\) | −0.543383 | − | 1.67236i | −0.0221835 | − | 0.0682739i | ||||
\(601\) | −4.00312 | − | 2.90843i | −0.163290 | − | 0.118637i | 0.503139 | − | 0.864205i | \(-0.332178\pi\) |
−0.666430 | + | 0.745568i | \(0.732178\pi\) | |||||||
\(602\) | 1.16577 | − | 0.846984i | 0.0475134 | − | 0.0345205i | ||||
\(603\) | −11.1057 | + | 34.1798i | −0.452258 | + | 1.39191i | ||||
\(604\) | −1.27685 | −0.0519543 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.16082 | 0.128399 | ||||||||
\(607\) | 8.53154 | − | 26.2574i | 0.346285 | − | 1.06575i | −0.614608 | − | 0.788833i | \(-0.710686\pi\) |
0.960893 | − | 0.276922i | \(-0.0893142\pi\) | |||||||
\(608\) | 2.59986 | − | 1.88891i | 0.105438 | − | 0.0766053i | ||||
\(609\) | 0.443573 | + | 0.322274i | 0.0179745 | + | 0.0130592i | ||||
\(610\) | 0.541043 | + | 1.66516i | 0.0219062 | + | 0.0674204i | ||||
\(611\) | 1.88093 | + | 5.78892i | 0.0760944 | + | 0.234195i | ||||
\(612\) | −0.272291 | − | 0.197831i | −0.0110067 | − | 0.00799685i | ||||
\(613\) | 5.81617 | − | 4.22570i | 0.234913 | − | 0.170674i | −0.464101 | − | 0.885782i | \(-0.653623\pi\) |
0.699014 | + | 0.715108i | \(0.253623\pi\) | |||||||
\(614\) | 3.61760 | − | 11.1338i | 0.145995 | − | 0.449325i | ||||
\(615\) | −0.100558 | −0.00405487 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.1215 | 0.850320 | 0.425160 | − | 0.905118i | \(-0.360218\pi\) | ||||
0.425160 | + | 0.905118i | \(0.360218\pi\) | |||||||
\(618\) | 0.363180 | − | 1.11775i | 0.0146092 | − | 0.0449626i | ||||
\(619\) | −2.24431 | + | 1.63059i | −0.0902064 | + | 0.0655388i | −0.631974 | − | 0.774989i | \(-0.717755\pi\) |
0.541768 | + | 0.840528i | \(0.317755\pi\) | |||||||
\(620\) | 0.0581744 | + | 0.0422662i | 0.00233634 | + | 0.00169745i | ||||
\(621\) | 0.377508 | + | 1.16185i | 0.0151489 | + | 0.0466235i | ||||
\(622\) | 7.71723 | + | 23.7512i | 0.309433 | + | 0.952336i | ||||
\(623\) | −14.3197 | − | 10.4039i | −0.573706 | − | 0.416822i | ||||
\(624\) | −0.243776 | + | 0.177114i | −0.00975886 | + | 0.00709022i | ||||
\(625\) | 7.64352 | − | 23.5243i | 0.305741 | − | 0.940974i | ||||
\(626\) | 0.327556 | 0.0130918 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.17673 | 0.0469568 | ||||||||
\(629\) | 1.65931 | − | 5.10683i | 0.0661610 | − | 0.203623i | ||||
\(630\) | 0.445160 | − | 0.323428i | 0.0177356 | − | 0.0128857i | ||||
\(631\) | 19.5855 | + | 14.2297i | 0.779685 | + | 0.566474i | 0.904884 | − | 0.425657i | \(-0.139957\pi\) |
−0.125200 | + | 0.992132i | \(0.539957\pi\) | |||||||
\(632\) | 10.2320 | + | 31.4907i | 0.407005 | + | 1.25263i | ||||
\(633\) | −0.532909 | − | 1.64012i | −0.0211812 | − | 0.0651891i | ||||
\(634\) | −19.1658 | − | 13.9248i | −0.761171 | − | 0.553023i | ||||
\(635\) | −1.66311 | + | 1.20832i | −0.0659985 | + | 0.0479507i | ||||
\(636\) | −0.00199640 | + | 0.00614430i | −7.91625e−5 | + | 0.000243637i | ||||
\(637\) | 0.641436 | 0.0254146 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.4300 | −0.570843 | ||||||||
\(640\) | −0.435508 | + | 1.34036i | −0.0172150 | + | 0.0529823i | ||||
\(641\) | −35.1839 | + | 25.5626i | −1.38968 | + | 1.00966i | −0.393782 | + | 0.919204i | \(0.628834\pi\) |
−0.995900 | + | 0.0904593i | \(0.971166\pi\) | |||||||
\(642\) | 0.747692 | + | 0.543230i | 0.0295090 | + | 0.0214396i | ||||
\(643\) | −5.30017 | − | 16.3122i | −0.209018 | − | 0.643292i | −0.999524 | − | 0.0308379i | \(-0.990182\pi\) |
0.790506 | − | 0.612454i | \(-0.209818\pi\) | |||||||
\(644\) | 0.0407542 | + | 0.125428i | 0.00160594 | + | 0.00494257i | ||||
\(645\) | −0.0137023 | − | 0.00995532i | −0.000539529 | − | 0.000391990i | ||||
\(646\) | 11.4755 | − | 8.33741i | 0.451496 | − | 0.328031i | ||||
\(647\) | 4.41613 | − | 13.5914i | 0.173616 | − | 0.534335i | −0.825952 | − | 0.563741i | \(-0.809362\pi\) |
0.999568 | + | 0.0294062i | \(0.00936164\pi\) | |||||||
\(648\) | −25.5459 | −1.00354 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.42927 | −0.173730 | ||||||||
\(651\) | −0.258572 | + | 0.795802i | −0.0101342 | + | 0.0311899i | ||||
\(652\) | −1.05341 | + | 0.765349i | −0.0412548 | + | 0.0299734i | ||||
\(653\) | 30.6228 | + | 22.2487i | 1.19836 | + | 0.870660i | 0.994123 | − | 0.108261i | \(-0.0345282\pi\) |
0.204239 | + | 0.978921i | \(0.434528\pi\) | |||||||
\(654\) | −0.483807 | − | 1.48901i | −0.0189184 | − | 0.0582247i | ||||
\(655\) | 0.726147 | + | 2.23485i | 0.0283729 | + | 0.0873228i | ||||
\(656\) | −19.1541 | − | 13.9163i | −0.747843 | − | 0.543340i | ||||
\(657\) | 21.3901 | − | 15.5408i | 0.834505 | − | 0.606304i | ||||
\(658\) | −4.06414 | + | 12.5081i | −0.158437 | + | 0.487618i | ||||
\(659\) | −8.13829 | −0.317023 | −0.158511 | − | 0.987357i | \(-0.550669\pi\) | ||||
−0.158511 | + | 0.987357i | \(0.550669\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.33161 | −0.207375 | −0.103688 | − | 0.994610i | \(-0.533064\pi\) | ||||
−0.103688 | + | 0.994610i | \(0.533064\pi\) | |||||||
\(662\) | 1.88952 | − | 5.81535i | 0.0734384 | − | 0.226020i | ||||
\(663\) | 0.0905593 | − | 0.0657952i | 0.00351703 | − | 0.00255527i | ||||
\(664\) | −22.3333 | − | 16.2261i | −0.866701 | − | 0.629695i | ||||
\(665\) | −0.295225 | − | 0.908608i | −0.0114483 | − | 0.0352343i | ||||
\(666\) | −4.81792 | − | 14.8280i | −0.186691 | − | 0.574575i | ||||
\(667\) | 6.03561 | + | 4.38512i | 0.233700 | + | 0.169793i | ||||
\(668\) | 1.22614 | − | 0.890843i | 0.0474408 | − | 0.0344677i | ||||
\(669\) | 0.364615 | − | 1.12217i | 0.0140968 | − | 0.0433856i | ||||
\(670\) | −2.21939 | −0.0857424 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.0547962 | 0.00211381 | ||||||||
\(673\) | 6.01023 | − | 18.4976i | 0.231677 | − | 0.713030i | −0.765867 | − | 0.642999i | \(-0.777690\pi\) |
0.997545 | − | 0.0700313i | \(-0.0223099\pi\) | |||||||
\(674\) | 31.1574 | − | 22.6372i | 1.20014 | − | 0.871953i | ||||
\(675\) | 2.95471 | + | 2.14672i | 0.113727 | + | 0.0826273i | ||||
\(676\) | 0.307844 | + | 0.947445i | 0.0118401 | + | 0.0364402i | ||||
\(677\) | 11.2186 | + | 34.5274i | 0.431167 | + | 1.32699i | 0.896964 | + | 0.442103i | \(0.145768\pi\) |
−0.465797 | + | 0.884891i | \(0.654232\pi\) | |||||||
\(678\) | 1.28847 | + | 0.936128i | 0.0494834 | + | 0.0359518i | ||||
\(679\) | 5.32446 | − | 3.86844i | 0.204334 | − | 0.148457i | ||||
\(680\) | 0.168748 | − | 0.519354i | 0.00647121 | − | 0.0199163i | ||||
\(681\) | −1.27490 | −0.0488545 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.7805 | −0.795142 | −0.397571 | − | 0.917571i | \(-0.630147\pi\) | ||||
−0.397571 | + | 0.917571i | \(0.630147\pi\) | |||||||
\(684\) | −0.524327 | + | 1.61371i | −0.0200481 | + | 0.0617018i | ||||
\(685\) | 2.04793 | − | 1.48791i | 0.0782475 | − | 0.0568501i | ||||
\(686\) | 1.12126 | + | 0.814642i | 0.0428099 | + | 0.0311032i | ||||
\(687\) | 0.352945 | + | 1.08625i | 0.0134657 | + | 0.0414431i | ||||
\(688\) | −1.23228 | − | 3.79256i | −0.0469802 | − | 0.144590i | ||||
\(689\) | 0.345894 | + | 0.251307i | 0.0131775 | + | 0.00957403i | ||||
\(690\) | −0.0304405 | + | 0.0221163i | −0.00115885 | + | 0.000841955i | ||||
\(691\) | −15.4833 | + | 47.6527i | −0.589012 | + | 1.81279i | −0.00649001 | + | 0.999979i | \(0.502066\pi\) |
−0.582522 | + | 0.812815i | \(0.697934\pi\) | |||||||
\(692\) | 1.20481 | 0.0457998 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −43.3131 | −1.64414 | ||||||||
\(695\) | −0.578142 | + | 1.77934i | −0.0219302 | + | 0.0674941i | ||||
\(696\) | 1.27819 | − | 0.928660i | 0.0484497 | − | 0.0352008i | ||||
\(697\) | 7.11548 | + | 5.16970i | 0.269518 | + | 0.195816i | ||||
\(698\) | 0.232745 | + | 0.716316i | 0.00880954 | + | 0.0271130i | ||||
\(699\) | 0.641753 | + | 1.97511i | 0.0242733 | + | 0.0747056i | ||||
\(700\) | 0.318977 | + | 0.231751i | 0.0120562 | + | 0.00875935i | ||||
\(701\) | −13.2055 | + | 9.59437i | −0.498765 | + | 0.362374i | −0.808545 | − | 0.588434i | \(-0.799745\pi\) |
0.309780 | + | 0.950808i | \(0.399745\pi\) | |||||||
\(702\) | 0.201377 | − | 0.619775i | 0.00760049 | − | 0.0233919i | ||||
\(703\) | −27.0701 | −1.02097 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.154584 | 0.00582199 | ||||||||
\(706\) | −7.64556 | + | 23.5306i | −0.287745 | + | 0.885587i | ||||
\(707\) | −15.0642 | + | 10.9448i | −0.566548 | + | 0.411622i | ||||
\(708\) | −0.0641968 | − | 0.0466417i | −0.00241266 | − | 0.00175290i | ||||
\(709\) | 10.2686 | + | 31.6035i | 0.385646 | + | 1.18690i | 0.936011 | + | 0.351971i | \(0.114489\pi\) |
−0.550365 | + | 0.834924i | \(0.685511\pi\) | |||||||
\(710\) | −0.275372 | − | 0.847507i | −0.0103345 | − | 0.0318064i | ||||
\(711\) | −27.7490 | − | 20.1608i | −1.04067 | − | 0.756089i | ||||
\(712\) | −41.2634 | + | 29.9796i | −1.54641 | + | 1.12353i | ||||
\(713\) | −3.51833 | + | 10.8283i | −0.131763 | + | 0.405524i | ||||
\(714\) | 0.241864 | 0.00905152 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.0893143 | −0.00333783 | ||||||||
\(717\) | 0.313369 | − | 0.964450i | 0.0117030 | − | 0.0360180i | ||||
\(718\) | −13.4449 | + | 9.76827i | −0.501758 | + | 0.364548i | ||||
\(719\) | 20.4240 | + | 14.8389i | 0.761688 | + | 0.553399i | 0.899428 | − | 0.437070i | \(-0.143984\pi\) |
−0.137740 | + | 0.990468i | \(0.543984\pi\) | |||||||
\(720\) | −0.470556 | − | 1.44822i | −0.0175366 | − | 0.0539720i | ||||
\(721\) | 2.13950 | + | 6.58470i | 0.0796791 | + | 0.245227i | ||||
\(722\) | −36.5475 | − | 26.5533i | −1.36016 | − | 0.988212i | ||||
\(723\) | −0.922716 | + | 0.670392i | −0.0343162 | + | 0.0249322i | ||||
\(724\) | −0.451853 | + | 1.39066i | −0.0167930 | + | 0.0516835i | ||||
\(725\) | 22.3036 | 0.828337 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.86242 | 0.0690733 | 0.0345366 | − | 0.999403i | \(-0.489004\pi\) | ||||
0.0345366 | + | 0.999403i | \(0.489004\pi\) | |||||||
\(728\) | 0.571172 | − | 1.75789i | 0.0211690 | − | 0.0651516i | ||||
\(729\) | 21.1908 | − | 15.3960i | 0.784846 | − | 0.570224i | ||||
\(730\) | 1.32094 | + | 0.959717i | 0.0488901 | + | 0.0355207i | ||||
\(731\) | 0.457774 | + | 1.40888i | 0.0169314 | + | 0.0521094i | ||||
\(732\) | −0.0284480 | − | 0.0875538i | −0.00105147 | − | 0.00323608i | ||||
\(733\) | 16.2330 | + | 11.7940i | 0.599581 | + | 0.435621i | 0.845730 | − | 0.533611i | \(-0.179165\pi\) |
−0.246149 | + | 0.969232i | \(0.579165\pi\) | |||||||
\(734\) | −33.1845 | + | 24.1100i | −1.22486 | + | 0.889916i | ||||
\(735\) | 0.00503397 | − | 0.0154930i | 0.000185681 | − | 0.000571467i | ||||
\(736\) | 0.745601 | 0.0274832 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 25.5375 | 0.940049 | ||||||||
\(739\) | 6.92104 | − | 21.3008i | 0.254595 | − | 0.783562i | −0.739315 | − | 0.673360i | \(-0.764850\pi\) |
0.993909 | − | 0.110202i | \(-0.0351497\pi\) | |||||||
\(740\) | −0.0320908 | + | 0.0233153i | −0.00117968 | + | 0.000857089i | ||||
\(741\) | −0.456538 | − | 0.331694i | −0.0167714 | − | 0.0121851i | ||||
\(742\) | 0.285472 | + | 0.878591i | 0.0104800 | + | 0.0322541i | ||||
\(743\) | 11.2082 | + | 34.4953i | 0.411189 | + | 1.26551i | 0.915616 | + | 0.402054i | \(0.131704\pi\) |
−0.504427 | + | 0.863454i | \(0.668296\pi\) | |||||||
\(744\) | 1.95069 | + | 1.41726i | 0.0715156 | + | 0.0519591i | ||||
\(745\) | 1.18758 | − | 0.862826i | 0.0435095 | − | 0.0316115i | ||||
\(746\) | −4.50593 | + | 13.8678i | −0.164974 | + | 0.507738i | ||||
\(747\) | 28.5962 | 1.04628 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.44446 | −0.198936 | ||||||||
\(750\) | −0.0696450 | + | 0.214345i | −0.00254308 | + | 0.00782678i | ||||
\(751\) | −36.1013 | + | 26.2291i | −1.31736 | + | 0.957115i | −0.317394 | + | 0.948294i | \(0.602808\pi\) |
−0.999961 | + | 0.00882107i | \(0.997192\pi\) | |||||||
\(752\) | 29.4451 | + | 21.3931i | 1.07375 | + | 0.780127i | ||||
\(753\) | 0.186793 | + | 0.574888i | 0.00680710 | + | 0.0209501i | ||||
\(754\) | −1.22979 | − | 3.78489i | −0.0447861 | − | 0.137838i | ||||
\(755\) | 1.73617 | + | 1.26140i | 0.0631857 | + | 0.0459071i | ||||
\(756\) | −0.0469305 | + | 0.0340970i | −0.00170685 | + | 0.00124010i | ||||
\(757\) | 2.78104 | − | 8.55916i | 0.101079 | − | 0.311088i | −0.887711 | − | 0.460400i | \(-0.847706\pi\) |
0.988790 | + | 0.149312i | \(0.0477059\pi\) | |||||||
\(758\) | −11.5715 | −0.420296 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.75297 | −0.0998607 | ||||||||
\(761\) | −1.59192 | + | 4.89941i | −0.0577069 | + | 0.177604i | −0.975755 | − | 0.218865i | \(-0.929765\pi\) |
0.918048 | + | 0.396469i | \(0.129765\pi\) | |||||||
\(762\) | −2.12258 | + | 1.54215i | −0.0768931 | + | 0.0558661i | ||||
\(763\) | 7.46169 | + | 5.42124i | 0.270131 | + | 0.196262i | ||||
\(764\) | 0.0594192 | + | 0.182874i | 0.00214971 | + | 0.00661613i | ||||
\(765\) | 0.174805 | + | 0.537993i | 0.00632007 | + | 0.0194512i | ||||
\(766\) | 20.7139 | + | 15.0495i | 0.748422 | + | 0.543761i | ||||
\(767\) | −4.24848 | + | 3.08670i | −0.153404 | + | 0.111454i | ||||
\(768\) | 0.0717691 | − | 0.220883i | 0.00258975 | − | 0.00797042i | ||||
\(769\) | 38.5242 | 1.38922 | 0.694608 | − | 0.719388i | \(-0.255578\pi\) | ||||
0.694608 | + | 0.719388i | \(0.255578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.05960 | 0.0741746 | ||||||||
\(772\) | −0.00643939 | + | 0.0198184i | −0.000231759 | + | 0.000713280i | ||||
\(773\) | 5.65522 | − | 4.10876i | 0.203404 | − | 0.147782i | −0.481420 | − | 0.876490i | \(-0.659879\pi\) |
0.684824 | + | 0.728708i | \(0.259879\pi\) | |||||||
\(774\) | 3.47983 | + | 2.52825i | 0.125080 | + | 0.0908760i | ||||
\(775\) | 10.5184 | + | 32.3723i | 0.377832 | + | 1.16285i | ||||
\(776\) | −5.86045 | − | 18.0366i | −0.210378 | − | 0.647477i | ||||
\(777\) | −0.373426 | − | 0.271310i | −0.0133966 | − | 0.00973319i | ||||
\(778\) | −26.0760 | + | 18.9453i | −0.934871 | + | 0.679223i | ||||
\(779\) | 13.7016 | − | 42.1693i | 0.490912 | − | 1.51087i | ||||
\(780\) | −0.000826901 | 0 | −2.96078e−5 | 0 | ||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 3.29099 | 0.117686 | ||||||||
\(783\) | −1.01404 | + | 3.12088i | −0.0362387 | + | 0.111531i | ||||
\(784\) | 3.10296 | − | 2.25443i | 0.110820 | − | 0.0805154i | ||||
\(785\) | −1.60004 | − | 1.16250i | −0.0571079 | − | 0.0414913i | ||||
\(786\) | 0.926763 | + | 2.85228i | 0.0330565 | + | 0.101738i | ||||
\(787\) | −9.69877 | − | 29.8497i | −0.345724 | − | 1.06403i | −0.961195 | − | 0.275869i | \(-0.911034\pi\) |
0.615471 | − | 0.788159i | \(-0.288966\pi\) | |||||||
\(788\) | −1.11834 | − | 0.812524i | −0.0398394 | − | 0.0289450i | ||||
\(789\) | −0.407411 | + | 0.296001i | −0.0145042 | + | 0.0105379i | ||||
\(790\) | 0.654549 | − | 2.01449i | 0.0232878 | − | 0.0716725i | ||||
\(791\) | −9.38223 | −0.333594 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.09240 | −0.216348 | ||||||||
\(794\) | 9.28492 | − | 28.5760i | 0.329509 | − | 1.01413i | ||||
\(795\) | 0.00878452 | − | 0.00638233i | 0.000311555 | − | 0.000226358i | ||||
\(796\) | −1.28950 | − | 0.936878i | −0.0457052 | − | 0.0332067i | ||||
\(797\) | 8.12629 | + | 25.0102i | 0.287848 | + | 0.885905i | 0.985531 | + | 0.169498i | \(0.0542147\pi\) |
−0.697682 | + | 0.716407i | \(0.745785\pi\) | |||||||
\(798\) | −0.376788 | − | 1.15963i | −0.0133381 | − | 0.0410506i | ||||
\(799\) | −10.9384 | − | 7.94724i | −0.386974 | − | 0.281153i | ||||
\(800\) | 1.80334 | − | 1.31020i | 0.0637575 | − | 0.0463226i | ||||
\(801\) | 16.3269 | − | 50.2489i | 0.576881 | − | 1.77546i | ||||
\(802\) | −48.2416 | −1.70347 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.116695 | 0.00411551 | ||||||||
\(805\) | 0.0684962 | − | 0.210810i | 0.00241418 | − | 0.00743007i | ||||
\(806\) | 4.91356 | − | 3.56991i | 0.173073 | − | 0.125745i | ||||
\(807\) | −2.37497 | − | 1.72552i | −0.0836030 | − | 0.0607412i | ||||
\(808\) | 16.5807 | + | 51.0301i | 0.583307 | + | 1.79523i | ||||
\(809\) | −3.63508 | − | 11.1876i | −0.127802 | − | 0.393336i | 0.866599 | − | 0.499006i | \(-0.166301\pi\) |
−0.994401 | + | 0.105670i | \(0.966301\pi\) | |||||||
\(810\) | 1.32209 | + | 0.960556i | 0.0464536 | + | 0.0337505i | ||||
\(811\) | −6.69303 | + | 4.86277i | −0.235024 | + | 0.170755i | −0.699064 | − | 0.715060i | \(-0.746400\pi\) |
0.464040 | + | 0.885814i | \(0.346400\pi\) | |||||||
\(812\) | −0.109471 | + | 0.336917i | −0.00384168 | + | 0.0118235i | ||||
\(813\) | −0.735843 | −0.0258071 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.18844 | 0.0766579 | ||||||||
\(816\) | 0.206834 | − | 0.636571i | 0.00724065 | − | 0.0222844i | ||||
\(817\) | 6.04185 | − | 4.38966i | 0.211378 | − | 0.153575i | ||||
\(818\) | 18.2683 | + | 13.2727i | 0.638736 | + | 0.464069i | ||||
\(819\) | 0.591671 | + | 1.82097i | 0.0206746 | + | 0.0636300i | ||||
\(820\) | −0.0200774 | − | 0.0617918i | −0.000701132 | − | 0.00215786i | ||||
\(821\) | −5.97470 | − | 4.34087i | −0.208518 | − | 0.151497i | 0.478625 | − | 0.878020i | \(-0.341135\pi\) |
−0.687143 | + | 0.726522i | \(0.741135\pi\) | |||||||
\(822\) | 2.61372 | − | 1.89898i | 0.0911641 | − | 0.0662346i | ||||
\(823\) | 15.2788 | − | 47.0234i | 0.532587 | − | 1.63913i | −0.216220 | − | 0.976345i | \(-0.569373\pi\) |
0.748807 | − | 0.662788i | \(-0.230627\pi\) | |||||||
\(824\) | 19.9508 | 0.695019 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.3467 | −0.394803 | ||||||||
\(827\) | −7.17967 | + | 22.0968i | −0.249662 | + | 0.768380i | 0.745173 | + | 0.666871i | \(0.232367\pi\) |
−0.994835 | + | 0.101509i | \(0.967633\pi\) | |||||||
\(828\) | −0.318487 | + | 0.231394i | −0.0110682 | + | 0.00804151i | ||||
\(829\) | −24.4273 | − | 17.7474i | −0.848394 | − | 0.616394i | 0.0763089 | − | 0.997084i | \(-0.475686\pi\) |
−0.924703 | + | 0.380690i | \(0.875686\pi\) | |||||||
\(830\) | 0.545710 | + | 1.67952i | 0.0189419 | + | 0.0582971i | ||||
\(831\) | −0.346767 | − | 1.06724i | −0.0120292 | − | 0.0370221i | ||||
\(832\) | −4.30247 | − | 3.12593i | −0.149161 | − | 0.108372i | ||||
\(833\) | −1.15270 | + | 0.837488i | −0.0399388 | + | 0.0290173i | ||||
\(834\) | −0.737868 | + | 2.27092i | −0.0255503 | + | 0.0786357i | ||||
\(835\) | −2.54728 | −0.0881523 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.00798 | −0.173101 | ||||||||
\(838\) | −9.70214 | + | 29.8601i | −0.335155 | + | 1.03150i | ||||
\(839\) | −13.4398 | + | 9.76461i | −0.463995 | + | 0.337112i | −0.795096 | − | 0.606483i | \(-0.792580\pi\) |
0.331102 | + | 0.943595i | \(0.392580\pi\) | |||||||
\(840\) | −0.0379767 | − | 0.0275917i | −0.00131032 | − | 0.000952003i | ||||
\(841\) | −2.76890 | − | 8.52180i | −0.0954793 | − | 0.293855i | ||||
\(842\) | −6.51253 | − | 20.0435i | −0.224437 | − | 0.690745i | ||||
\(843\) | −1.28397 | − | 0.932861i | −0.0442224 | − | 0.0321294i | ||||
\(844\) | 0.901442 | − | 0.654936i | 0.0310289 | − | 0.0225438i | ||||
\(845\) | 0.517398 | − | 1.59239i | 0.0177990 | − | 0.0547798i | ||||
\(846\) | −39.2582 | −1.34972 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.55653 | 0.0877915 | ||||||||
\(849\) | −0.143361 | + | 0.441221i | −0.00492015 | + | 0.0151427i | ||||
\(850\) | 7.95970 | − | 5.78306i | 0.273016 | − | 0.198357i | ||||
\(851\) | −5.08114 | − | 3.69166i | −0.174179 | − | 0.126549i | ||||
\(852\) | 0.0144790 | + | 0.0445618i | 0.000496042 | + | 0.00152666i | ||||
\(853\) | 12.3763 | + | 38.0904i | 0.423758 | + | 1.30419i | 0.904179 | + | 0.427154i | \(0.140484\pi\) |
−0.480421 | + | 0.877038i | \(0.659516\pi\) | |||||||
\(854\) | −10.6498 | − | 7.73753i | −0.364428 | − | 0.264773i | ||||
\(855\) | 2.30713 | − | 1.67623i | 0.0789022 | − | 0.0573258i | ||||
\(856\) | −4.84806 | + | 14.9208i | −0.165703 | + | 0.509982i | ||||
\(857\) | 31.7070 | 1.08309 | 0.541546 | − | 0.840671i | \(-0.317839\pi\) | ||||
0.541546 | + | 0.840671i | \(0.317839\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.63654 | 0.0558381 | 0.0279190 | − | 0.999610i | \(-0.491112\pi\) | ||||
0.0279190 | + | 0.999610i | \(0.491112\pi\) | |||||||
\(860\) | 0.00338165 | − | 0.0104076i | 0.000115313 | − | 0.000354898i | ||||
\(861\) | 0.611654 | − | 0.444393i | 0.0208451 | − | 0.0151449i | ||||
\(862\) | −3.59577 | − | 2.61248i | −0.122472 | − | 0.0889815i | ||||
\(863\) | −5.37858 | − | 16.5536i | −0.183089 | − | 0.563490i | 0.816821 | − | 0.576891i | \(-0.195734\pi\) |
−0.999910 | + | 0.0134007i | \(0.995734\pi\) | |||||||
\(864\) | 0.101344 | + | 0.311904i | 0.00344778 | + | 0.0106112i | ||||
\(865\) | −1.63821 | − | 1.19023i | −0.0557008 | − | 0.0404690i | ||||
\(866\) | −6.71910 | + | 4.88171i | −0.228324 | + | 0.165887i | ||||
\(867\) | 0.566582 | − | 1.74376i | 0.0192421 | − | 0.0592212i | ||||
\(868\) | −0.540640 | −0.0183505 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.101070 | −0.00342659 | ||||||||
\(871\) | 2.38646 | − | 7.34477i | 0.0808621 | − | 0.248868i | ||||
\(872\) | 21.5015 | − | 15.6217i | 0.728132 | − | 0.529019i | ||||
\(873\) | 15.8935 | + | 11.5473i | 0.537913 | + | 0.390817i | ||||
\(874\) | −5.12688 | − | 15.7789i | −0.173419 | − | 0.533729i | ||||
\(875\) | −0.410279 | − | 1.26271i | −0.0138700 | − | 0.0426874i | ||||
\(876\) | −0.0694546 | − | 0.0504617i | −0.00234665 | − | 0.00170494i | ||||
\(877\) | −38.9677 | + | 28.3117i | −1.31584 | + | 0.956017i | −0.315871 | + | 0.948802i | \(0.602297\pi\) |
−0.999974 | + | 0.00721510i | \(0.997703\pi\) | |||||||
\(878\) | 3.29226 | − | 10.1325i | 0.111108 | − | 0.341957i | ||||
\(879\) | 2.61725 | 0.0882778 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0141 | −1.01120 | −0.505601 | − | 0.862767i | \(-0.668729\pi\) | ||||
−0.505601 | + | 0.862767i | \(0.668729\pi\) | |||||||
\(882\) | −1.27842 | + | 3.93458i | −0.0430468 | + | 0.132484i | ||||
\(883\) | −45.5764 | + | 33.1132i | −1.53377 | + | 1.11435i | −0.579671 | + | 0.814851i | \(0.696819\pi\) |
−0.954097 | + | 0.299497i | \(0.903181\pi\) | |||||||
\(884\) | 0.0585117 | + | 0.0425112i | 0.00196796 | + | 0.00142981i | ||||
\(885\) | 0.0412129 | + | 0.126840i | 0.00138536 | + | 0.00426368i | ||||
\(886\) | 15.9535 | + | 49.0998i | 0.535968 | + | 1.64954i | ||||
\(887\) | −3.66562 | − | 2.66323i | −0.123079 | − | 0.0894224i | 0.524543 | − | 0.851384i | \(-0.324236\pi\) |
−0.647622 | + | 0.761962i | \(0.724236\pi\) | |||||||
\(888\) | −1.07606 | + | 0.781802i | −0.0361102 | + | 0.0262356i | ||||
\(889\) | 4.77616 | − | 14.6995i | 0.160187 | − | 0.493006i | ||||
\(890\) | 3.26280 | 0.109369 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.762363 | 0.0255258 | ||||||||
\(893\) | −21.0632 | + | 64.8258i | −0.704853 | + | 2.16931i | ||||
\(894\) | 1.51568 | − | 1.10120i | 0.0506918 | − | 0.0368297i | ||||
\(895\) | 0.121443 | + | 0.0882337i | 0.00405940 | + | 0.00294933i | ||||
\(896\) | −3.27439 | − | 10.0775i | −0.109390 | − | 0.336667i | ||||
\(897\) | −0.0404591 | − | 0.124520i | −0.00135089 | − | 0.00415761i | ||||
\(898\) | −12.4150 | − | 9.02005i | −0.414295 | − | 0.301003i | ||||
\(899\) | −24.7423 | + | 17.9763i | −0.825201 | + | 0.599543i | ||||
\(900\) | −0.363688 | + | 1.11932i | −0.0121229 | + | 0.0373105i | ||||
\(901\) | −0.949713 | −0.0316395 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.127342 | 0.00423766 | ||||||||
\(904\) | −8.35448 | + | 25.7125i | −0.277866 | + | 0.855184i | ||||
\(905\) | 1.98823 | − | 1.44453i | 0.0660910 | − | 0.0480180i | ||||
\(906\) | 2.21583 | + | 1.60990i | 0.0736161 | + | 0.0534852i | ||||
\(907\) | −6.41548 | − | 19.7448i | −0.213023 | − | 0.655616i | −0.999288 | − | 0.0377272i | \(-0.987988\pi\) |
0.786266 | − | 0.617889i | \(-0.212012\pi\) | |||||||
\(908\) | −0.254548 | − | 0.783418i | −0.00844747 | − | 0.0259986i | ||||
\(909\) | −44.9667 | − | 32.6702i | −1.49145 | − | 1.08360i | ||||
\(910\) | −0.0956590 | + | 0.0695003i | −0.00317106 | + | 0.00230391i | ||||
\(911\) | −4.75738 | + | 14.6417i | −0.157619 | + | 0.485102i | −0.998417 | − | 0.0562476i | \(-0.982086\pi\) |
0.840798 | + | 0.541349i | \(0.182086\pi\) | |||||||
\(912\) | −3.37430 | −0.111734 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −39.3557 | −1.30177 | ||||||||
\(915\) | −0.0478130 | + | 0.147153i | −0.00158065 | + | 0.00486474i | ||||
\(916\) | −0.597023 | + | 0.433763i | −0.0197262 | + | 0.0143319i | ||||
\(917\) | −14.2933 | − | 10.3847i | −0.472007 | − | 0.342933i | ||||
\(918\) | 0.447319 | + | 1.37670i | 0.0147637 | + | 0.0454380i | ||||
\(919\) | −6.60003 | − | 20.3128i | −0.217715 | − | 0.670057i | −0.998950 | − | 0.0458201i | \(-0.985410\pi\) |
0.781235 | − | 0.624237i | \(-0.214590\pi\) | |||||||
\(920\) | −0.516741 | − | 0.375435i | −0.0170365 | − | 0.0123777i | ||||
\(921\) | 0.836970 | − | 0.608095i | 0.0275791 | − | 0.0200374i | ||||
\(922\) | 11.0248 | − | 33.9310i | 0.363084 | − | 1.11746i | ||||
\(923\) | 3.10082 | 0.102065 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.7765 | −0.617369 | ||||||||
\(926\) | 16.1267 | − | 49.6329i | 0.529956 | − | 1.63104i | ||||
\(927\) | −16.7198 | + | 12.1477i | −0.549150 | + | 0.398981i | ||||
\(928\) | 1.62028 | + | 1.17720i | 0.0531884 | + | 0.0386436i | ||||
\(929\) | 4.98554 | + | 15.3439i | 0.163570 | + | 0.503418i | 0.998928 | − | 0.0462888i | \(-0.0147395\pi\) |
−0.835358 | + | 0.549707i | \(0.814739\pi\) | |||||||
\(930\) | −0.0476646 | − | 0.146696i | −0.00156298 | − | 0.00481037i | ||||
\(931\) | 5.81115 | + | 4.22204i | 0.190453 | + | 0.138372i | ||||
\(932\) | −1.08556 | + | 0.788704i | −0.0355586 | + | 0.0258348i | ||||
\(933\) | −0.681985 | + | 2.09893i | −0.0223272 | + | 0.0687160i | ||||
\(934\) | −21.3263 | −0.697817 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.51733 | 0.180339 | ||||||||
\(937\) | 1.41006 | − | 4.33973i | 0.0460648 | − | 0.141773i | −0.925379 | − | 0.379044i | \(-0.876253\pi\) |
0.971443 | + | 0.237271i | \(0.0762530\pi\) | |||||||
\(938\) | 13.4997 | − | 9.80811i | 0.440781 | − | 0.320246i | ||||
\(939\) | 0.0234184 | + | 0.0170145i | 0.000764231 | + | 0.000555246i | ||||
\(940\) | 0.0308644 | + | 0.0949908i | 0.00100669 | + | 0.00309826i | ||||
\(941\) | −3.87827 | − | 11.9361i | −0.126428 | − | 0.389106i | 0.867730 | − | 0.497035i | \(-0.165578\pi\) |
−0.994159 | + | 0.107929i | \(0.965578\pi\) | |||||||
\(942\) | −2.04209 | − | 1.48367i | −0.0665349 | − | 0.0483404i | ||||
\(943\) | 8.32266 | − | 6.04677i | 0.271023 | − | 0.196910i | ||||
\(944\) | −9.70337 | + | 29.8639i | −0.315818 | + | 0.971987i | ||||
\(945\) | 0.0974972 | 0.00317159 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.6790 | 1.67934 | 0.839672 | − | 0.543094i | \(-0.182747\pi\) | ||||
0.839672 | + | 0.543094i | \(0.182747\pi\) | |||||||
\(948\) | −0.0344161 | + | 0.105922i | −0.00111778 | + | 0.00344018i | ||||
\(949\) | −4.59643 | + | 3.33951i | −0.149207 | + | 0.108405i | ||||
\(950\) | −40.1274 | − | 29.1542i | −1.30190 | − | 0.945889i | ||||
\(951\) | −0.646942 | − | 1.99108i | −0.0209785 | − | 0.0645653i | ||||
\(952\) | 1.26874 | + | 3.90479i | 0.0411202 | + | 0.126555i | ||||
\(953\) | 1.06993 | + | 0.777352i | 0.0346585 | + | 0.0251809i | 0.604980 | − | 0.796241i | \(-0.293181\pi\) |
−0.570321 | + | 0.821422i | \(0.693181\pi\) | |||||||
\(954\) | −2.23091 | + | 1.62085i | −0.0722284 | + | 0.0524770i | ||||
\(955\) | 0.0998669 | − | 0.307359i | 0.00323162 | − | 0.00994589i | ||||
\(956\) | 0.655213 | 0.0211911 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.831818 | 0.0268748 | ||||||||
\(959\) | −5.88131 | + | 18.1008i | −0.189917 | + | 0.584506i | ||||
\(960\) | −0.109268 | + | 0.0793878i | −0.00352661 | + | 0.00256223i | ||||
\(961\) | −12.6804 | − | 9.21284i | −0.409045 | − | 0.297188i | ||||
\(962\) | 1.03531 | + | 3.18635i | 0.0333796 | + | 0.102732i | ||||
\(963\) | −5.02205 | − | 15.4563i | −0.161833 | − | 0.498072i | ||||
\(964\) | −0.596180 | − | 0.433150i | −0.0192017 | − | 0.0139508i | ||||
\(965\) | 0.0283345 | − | 0.0205862i | 0.000912118 | − | 0.000662693i | ||||
\(966\) | 0.0874200 | − | 0.269051i | 0.00281269 | − | 0.00865658i | ||||
\(967\) | 44.1214 | 1.41885 | 0.709425 | − | 0.704781i | \(-0.248955\pi\) | ||||
0.709425 | + | 0.704781i | \(0.248955\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.25351 | 0.0402684 | ||||||||
\(970\) | −0.374899 | + | 1.15382i | −0.0120373 | + | 0.0370470i | ||||
\(971\) | 1.06119 | − | 0.770998i | 0.0340551 | − | 0.0247425i | −0.570627 | − | 0.821209i | \(-0.693300\pi\) |
0.604683 | + | 0.796467i | \(0.293300\pi\) | |||||||
\(972\) | −0.210307 | − | 0.152797i | −0.00674560 | − | 0.00490096i | ||||
\(973\) | −4.34679 | − | 13.3780i | −0.139352 | − | 0.428880i | ||||
\(974\) | 4.41094 | + | 13.5755i | 0.141335 | + | 0.434986i | ||||
\(975\) | −0.316668 | − | 0.230073i | −0.0101415 | − | 0.00736822i | ||||
\(976\) | −29.4721 | + | 21.4127i | −0.943379 | + | 0.685405i | ||||
\(977\) | −3.83495 | + | 11.8028i | −0.122691 | + | 0.377604i | −0.993473 | − | 0.114065i | \(-0.963613\pi\) |
0.870782 | + | 0.491669i | \(0.163613\pi\) | |||||||
\(978\) | 2.79306 | 0.0893121 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.0105254 | 0.000336221 | ||||||||
\(981\) | −8.50758 | + | 26.1837i | −0.271626 | + | 0.835980i | ||||
\(982\) | −11.3163 | + | 8.22174i | −0.361116 | + | 0.262366i | ||||
\(983\) | 25.8533 | + | 18.7836i | 0.824594 | + | 0.599102i | 0.918025 | − | 0.396523i | \(-0.129783\pi\) |
−0.0934309 | + | 0.995626i | \(0.529783\pi\) | |||||||
\(984\) | −0.673228 | − | 2.07198i | −0.0214617 | − | 0.0660523i | ||||
\(985\) | 0.717951 | + | 2.20963i | 0.0228758 | + | 0.0704045i | ||||
\(986\) | 7.15173 | + | 5.19604i | 0.227758 | + | 0.165476i | ||||
\(987\) | −0.940280 | + | 0.683153i | −0.0299294 | + | 0.0217450i | ||||
\(988\) | 0.112671 | − | 0.346765i | 0.00358454 | − | 0.0110321i | ||||
\(989\) | 1.73271 | 0.0550970 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.17926 | −0.291589 | −0.145794 | − | 0.989315i | \(-0.546574\pi\) | ||||
−0.145794 | + | 0.989315i | \(0.546574\pi\) | |||||||
\(992\) | −0.944511 | + | 2.90691i | −0.0299883 | + | 0.0922944i | ||||
\(993\) | 0.437161 | − | 0.317616i | 0.0138729 | − | 0.0100792i | ||||
\(994\) | 5.42037 | + | 3.93813i | 0.171924 | + | 0.124910i | ||||
\(995\) | 0.827830 | + | 2.54780i | 0.0262440 | + | 0.0807707i | ||||
\(996\) | −0.0286933 | − | 0.0883089i | −0.000909182 | − | 0.00279818i | ||||
\(997\) | 11.6036 | + | 8.43050i | 0.367489 | + | 0.266996i | 0.756169 | − | 0.654376i | \(-0.227069\pi\) |
−0.388680 | + | 0.921373i | \(0.627069\pi\) | |||||||
\(998\) | −22.1959 | + | 16.1263i | −0.702600 | + | 0.510468i | ||||
\(999\) | 0.853677 | − | 2.62735i | 0.0270091 | − | 0.0831256i |
(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 | 847.2.f.z.372.6 | 24 | ||
11.2 | odd | 10 | 847.2.f.y.729.6 | 24 | |||
11.3 | even | 5 | inner | 847.2.f.z.323.1 | 24 | ||
11.4 | even | 5 | 847.2.a.m.1.6 | ✓ | 6 | ||
11.5 | even | 5 | inner | 847.2.f.z.148.6 | 24 | ||
11.6 | odd | 10 | 847.2.f.y.148.1 | 24 | |||
11.7 | odd | 10 | 847.2.a.n.1.1 | yes | 6 | ||
11.8 | odd | 10 | 847.2.f.y.323.6 | 24 | |||
11.9 | even | 5 | inner | 847.2.f.z.729.1 | 24 | ||
11.10 | odd | 2 | 847.2.f.y.372.1 | 24 | |||
33.26 | odd | 10 | 7623.2.a.cs.1.1 | 6 | |||
33.29 | even | 10 | 7623.2.a.cp.1.6 | 6 | |||
77.48 | odd | 10 | 5929.2.a.bj.1.6 | 6 | |||
77.62 | even | 10 | 5929.2.a.bm.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.m.1.6 | ✓ | 6 | 11.4 | even | 5 | ||
847.2.a.n.1.1 | yes | 6 | 11.7 | odd | 10 | ||
847.2.f.y.148.1 | 24 | 11.6 | odd | 10 | |||
847.2.f.y.323.6 | 24 | 11.8 | odd | 10 | |||
847.2.f.y.372.1 | 24 | 11.10 | odd | 2 | |||
847.2.f.y.729.6 | 24 | 11.2 | odd | 10 | |||
847.2.f.z.148.6 | 24 | 11.5 | even | 5 | inner | ||
847.2.f.z.323.1 | 24 | 11.3 | even | 5 | inner | ||
847.2.f.z.372.6 | 24 | 1.1 | even | 1 | trivial | ||
847.2.f.z.729.1 | 24 | 11.9 | even | 5 | inner | ||
5929.2.a.bj.1.6 | 6 | 77.48 | odd | 10 | |||
5929.2.a.bm.1.1 | 6 | 77.62 | even | 10 | |||
7623.2.a.cp.1.6 | 6 | 33.29 | even | 10 | |||
7623.2.a.cs.1.1 | 6 | 33.26 | odd | 10 |