Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [406,2,Mod(233,406)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(406, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("406.233");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 406 = 2 \cdot 7 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 406.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.24192632206\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.3118758597603.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 233.4 | ||
Root | \(2.31940 - 0.319028i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 406.233 |
Dual form | 406.2.e.a.291.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/406\mathbb{Z}\right)^\times\).
\(n\) | \(59\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0.357289 | + | 0.618843i | 0.206281 | + | 0.357289i | 0.950540 | − | 0.310602i | \(-0.100531\pi\) |
−0.744259 | + | 0.667891i | \(0.767197\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.116584 | + | 0.201930i | −0.0521381 | + | 0.0903058i | −0.890917 | − | 0.454167i | \(-0.849937\pi\) |
0.838778 | + | 0.544473i | \(0.183270\pi\) | |||||||
\(6\) | −0.714579 | −0.291726 | ||||||||
\(7\) | 2.36799 | + | 1.18009i | 0.895017 | + | 0.446033i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.24469 | − | 2.15586i | 0.414896 | − | 0.718621i | ||||
\(10\) | −0.116584 | − | 0.201930i | −0.0368672 | − | 0.0638559i | ||||
\(11\) | −0.146694 | − | 0.254082i | −0.0442299 | − | 0.0766085i | 0.843063 | − | 0.537815i | \(-0.180750\pi\) |
−0.887293 | + | 0.461206i | \(0.847417\pi\) | |||||||
\(12\) | 0.357289 | − | 0.618843i | 0.103141 | − | 0.178645i | ||||
\(13\) | 4.15740 | 1.15305 | 0.576527 | − | 0.817078i | \(-0.304408\pi\) | ||||
0.576527 | + | 0.817078i | \(0.304408\pi\) | |||||||
\(14\) | −2.20598 | + | 1.46070i | −0.589574 | + | 0.390387i | ||||
\(15\) | −0.166617 | −0.0430204 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.304717 | − | 0.527786i | −0.0739048 | − | 0.128007i | 0.826705 | − | 0.562636i | \(-0.190213\pi\) |
−0.900610 | + | 0.434629i | \(0.856879\pi\) | |||||||
\(18\) | 1.24469 | + | 2.15586i | 0.293376 | + | 0.508142i | ||||
\(19\) | −3.33870 | + | 5.78280i | −0.765950 | + | 1.32666i | 0.173793 | + | 0.984782i | \(0.444398\pi\) |
−0.939743 | + | 0.341882i | \(0.888936\pi\) | |||||||
\(20\) | 0.233169 | 0.0521381 | ||||||||
\(21\) | 0.115767 | + | 1.88705i | 0.0252624 | + | 0.411788i | ||||
\(22\) | 0.293388 | 0.0625506 | ||||||||
\(23\) | 0.743871 | − | 1.28842i | 0.155108 | − | 0.268655i | −0.777990 | − | 0.628276i | \(-0.783761\pi\) |
0.933098 | + | 0.359621i | \(0.117094\pi\) | |||||||
\(24\) | 0.357289 | + | 0.618843i | 0.0729314 | + | 0.126321i | ||||
\(25\) | 2.47282 | + | 4.28304i | 0.494563 | + | 0.856609i | ||||
\(26\) | −2.07870 | + | 3.60041i | −0.407666 | + | 0.706099i | ||||
\(27\) | 3.92259 | 0.754903 | ||||||||
\(28\) | −0.162007 | − | 2.64079i | −0.0306164 | − | 0.499062i | ||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0.0833087 | − | 0.144295i | 0.0152100 | − | 0.0263445i | ||||
\(31\) | 0.675875 | + | 1.17065i | 0.121391 | + | 0.210255i | 0.920316 | − | 0.391175i | \(-0.127931\pi\) |
−0.798926 | + | 0.601430i | \(0.794598\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.104824 | − | 0.181561i | 0.0182476 | − | 0.0316058i | ||||
\(34\) | 0.609435 | 0.104517 | ||||||||
\(35\) | −0.514366 | + | 0.340588i | −0.0869438 | + | 0.0575699i | ||||
\(36\) | −2.48938 | −0.414896 | ||||||||
\(37\) | −0.318586 | + | 0.551807i | −0.0523752 | + | 0.0907164i | −0.891024 | − | 0.453956i | \(-0.850012\pi\) |
0.838649 | + | 0.544672i | \(0.183346\pi\) | |||||||
\(38\) | −3.33870 | − | 5.78280i | −0.541609 | − | 0.938094i | ||||
\(39\) | 1.48539 | + | 2.57278i | 0.237853 | + | 0.411974i | ||||
\(40\) | −0.116584 | + | 0.201930i | −0.0184336 | + | 0.0319279i | ||||
\(41\) | 3.31605 | 0.517880 | 0.258940 | − | 0.965893i | \(-0.416627\pi\) | ||||
0.258940 | + | 0.965893i | \(0.416627\pi\) | |||||||
\(42\) | −1.69212 | − | 0.843268i | −0.261099 | − | 0.130119i | ||||
\(43\) | −3.29502 | −0.502486 | −0.251243 | − | 0.967924i | \(-0.580839\pi\) | ||||
−0.251243 | + | 0.967924i | \(0.580839\pi\) | |||||||
\(44\) | −0.146694 | + | 0.254082i | −0.0221150 | + | 0.0383042i | ||||
\(45\) | 0.290222 | + | 0.502680i | 0.0432638 | + | 0.0749351i | ||||
\(46\) | 0.743871 | + | 1.28842i | 0.109678 | + | 0.189967i | ||||
\(47\) | −1.09046 | + | 1.88873i | −0.159060 | + | 0.275499i | −0.934530 | − | 0.355885i | \(-0.884180\pi\) |
0.775470 | + | 0.631384i | \(0.217513\pi\) | |||||||
\(48\) | −0.714579 | −0.103141 | ||||||||
\(49\) | 4.21477 | + | 5.58889i | 0.602110 | + | 0.798413i | ||||
\(50\) | −4.94563 | −0.699418 | ||||||||
\(51\) | 0.217745 | − | 0.377145i | 0.0304903 | − | 0.0528108i | ||||
\(52\) | −2.07870 | − | 3.60041i | −0.288264 | − | 0.499287i | ||||
\(53\) | −5.99610 | − | 10.3855i | −0.823627 | − | 1.42656i | −0.902964 | − | 0.429716i | \(-0.858614\pi\) |
0.0793369 | − | 0.996848i | \(-0.474720\pi\) | |||||||
\(54\) | −1.96130 | + | 3.39706i | −0.266899 | + | 0.462282i | ||||
\(55\) | 0.0684089 | 0.00922426 | ||||||||
\(56\) | 2.36799 | + | 1.18009i | 0.316436 | + | 0.157696i | ||||
\(57\) | −4.77153 | −0.632004 | ||||||||
\(58\) | 0.500000 | − | 0.866025i | 0.0656532 | − | 0.113715i | ||||
\(59\) | −2.15057 | − | 3.72489i | −0.279980 | − | 0.484939i | 0.691400 | − | 0.722473i | \(-0.256994\pi\) |
−0.971379 | + | 0.237533i | \(0.923661\pi\) | |||||||
\(60\) | 0.0833087 | + | 0.144295i | 0.0107551 | + | 0.0186284i | ||||
\(61\) | −1.82401 | + | 3.15928i | −0.233541 | + | 0.404505i | −0.958848 | − | 0.283921i | \(-0.908365\pi\) |
0.725307 | + | 0.688426i | \(0.241698\pi\) | |||||||
\(62\) | −1.35175 | −0.171672 | ||||||||
\(63\) | 5.49153 | − | 3.63622i | 0.691868 | − | 0.458121i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.484687 | + | 0.839503i | −0.0601180 | + | 0.104128i | ||||
\(66\) | 0.104824 | + | 0.181561i | 0.0129030 | + | 0.0223487i | ||||
\(67\) | −2.47824 | − | 4.29245i | −0.302766 | − | 0.524406i | 0.673996 | − | 0.738735i | \(-0.264577\pi\) |
−0.976761 | + | 0.214330i | \(0.931243\pi\) | |||||||
\(68\) | −0.304717 | + | 0.527786i | −0.0369524 | + | 0.0640035i | ||||
\(69\) | 1.06311 | 0.127983 | ||||||||
\(70\) | −0.0377749 | − | 0.615749i | −0.00451497 | − | 0.0735960i | ||||
\(71\) | 4.21106 | 0.499761 | 0.249881 | − | 0.968277i | \(-0.419609\pi\) | ||||
0.249881 | + | 0.968277i | \(0.419609\pi\) | |||||||
\(72\) | 1.24469 | − | 2.15586i | 0.146688 | − | 0.254071i | ||||
\(73\) | −2.92149 | − | 5.06017i | −0.341935 | − | 0.592248i | 0.642857 | − | 0.765986i | \(-0.277749\pi\) |
−0.984792 | + | 0.173738i | \(0.944416\pi\) | |||||||
\(74\) | −0.318586 | − | 0.551807i | −0.0370348 | − | 0.0641462i | ||||
\(75\) | −1.76702 | + | 3.06057i | −0.204038 | + | 0.353404i | ||||
\(76\) | 6.67740 | 0.765950 | ||||||||
\(77\) | −0.0475309 | − | 0.774776i | −0.00541665 | − | 0.0882939i | ||||
\(78\) | −2.97079 | −0.336375 | ||||||||
\(79\) | −1.05339 | + | 1.82452i | −0.118516 | + | 0.205275i | −0.919180 | − | 0.393839i | \(-0.871147\pi\) |
0.800664 | + | 0.599114i | \(0.204480\pi\) | |||||||
\(80\) | −0.116584 | − | 0.201930i | −0.0130345 | − | 0.0225765i | ||||
\(81\) | −2.33257 | − | 4.04012i | −0.259174 | − | 0.448902i | ||||
\(82\) | −1.65802 | + | 2.87178i | −0.183098 | + | 0.317135i | ||||
\(83\) | 6.73621 | 0.739395 | 0.369697 | − | 0.929152i | \(-0.379461\pi\) | ||||
0.369697 | + | 0.929152i | \(0.379461\pi\) | |||||||
\(84\) | 1.57635 | − | 1.04378i | 0.171994 | − | 0.113886i | ||||
\(85\) | 0.142101 | 0.0154130 | ||||||||
\(86\) | 1.64751 | − | 2.85357i | 0.177656 | − | 0.307709i | ||||
\(87\) | −0.357289 | − | 0.618843i | −0.0383054 | − | 0.0663470i | ||||
\(88\) | −0.146694 | − | 0.254082i | −0.0156376 | − | 0.0270852i | ||||
\(89\) | 6.31233 | − | 10.9333i | 0.669106 | − | 1.15893i | −0.309048 | − | 0.951046i | \(-0.600011\pi\) |
0.978154 | − | 0.207879i | \(-0.0666561\pi\) | |||||||
\(90\) | −0.580445 | −0.0611842 | ||||||||
\(91\) | 9.84468 | + | 4.90611i | 1.03200 | + | 0.514300i | ||||
\(92\) | −1.48774 | −0.155108 | ||||||||
\(93\) | −0.482966 | + | 0.836522i | −0.0500812 | + | 0.0867433i | ||||
\(94\) | −1.09046 | − | 1.88873i | −0.112472 | − | 0.194807i | ||||
\(95\) | −0.778480 | − | 1.34837i | −0.0798704 | − | 0.138340i | ||||
\(96\) | 0.357289 | − | 0.618843i | 0.0364657 | − | 0.0631604i | ||||
\(97\) | 5.70498 | 0.579253 | 0.289626 | − | 0.957140i | \(-0.406469\pi\) | ||||
0.289626 | + | 0.957140i | \(0.406469\pi\) | |||||||
\(98\) | −6.94751 | + | 0.855651i | −0.701804 | + | 0.0864338i | ||||
\(99\) | −0.730354 | −0.0734033 | ||||||||
\(100\) | 2.47282 | − | 4.28304i | 0.247282 | − | 0.428304i | ||||
\(101\) | −7.86693 | − | 13.6259i | −0.782789 | − | 1.35583i | −0.930311 | − | 0.366772i | \(-0.880463\pi\) |
0.147522 | − | 0.989059i | \(-0.452870\pi\) | |||||||
\(102\) | 0.217745 | + | 0.377145i | 0.0215599 | + | 0.0373429i | ||||
\(103\) | 2.44775 | − | 4.23962i | 0.241184 | − | 0.417742i | −0.719868 | − | 0.694111i | \(-0.755798\pi\) |
0.961052 | + | 0.276369i | \(0.0891310\pi\) | |||||||
\(104\) | 4.15740 | 0.407666 | ||||||||
\(105\) | −0.394549 | − | 0.196624i | −0.0385040 | − | 0.0191885i | ||||
\(106\) | 11.9922 | 1.16478 | ||||||||
\(107\) | −5.61573 | + | 9.72674i | −0.542894 | + | 0.940319i | 0.455843 | + | 0.890060i | \(0.349338\pi\) |
−0.998736 | + | 0.0502589i | \(0.983995\pi\) | |||||||
\(108\) | −1.96130 | − | 3.39706i | −0.188726 | − | 0.326883i | ||||
\(109\) | −7.59327 | − | 13.1519i | −0.727304 | − | 1.25973i | −0.958019 | − | 0.286705i | \(-0.907440\pi\) |
0.230715 | − | 0.973021i | \(-0.425893\pi\) | |||||||
\(110\) | −0.0342045 | + | 0.0592439i | −0.00326127 | + | 0.00564868i | ||||
\(111\) | −0.455309 | −0.0432160 | ||||||||
\(112\) | −2.20598 | + | 1.46070i | −0.208446 | + | 0.138023i | ||||
\(113\) | −10.2976 | −0.968717 | −0.484359 | − | 0.874870i | \(-0.660947\pi\) | ||||
−0.484359 | + | 0.874870i | \(0.660947\pi\) | |||||||
\(114\) | 2.38576 | − | 4.13226i | 0.223447 | − | 0.387022i | ||||
\(115\) | 0.173447 | + | 0.300420i | 0.0161741 | + | 0.0280143i | ||||
\(116\) | 0.500000 | + | 0.866025i | 0.0464238 | + | 0.0804084i | ||||
\(117\) | 5.17466 | − | 8.96278i | 0.478398 | − | 0.828609i | ||||
\(118\) | 4.30113 | 0.395951 | ||||||||
\(119\) | −0.0987327 | − | 1.60939i | −0.00905081 | − | 0.147532i | ||||
\(120\) | −0.166617 | −0.0152100 | ||||||||
\(121\) | 5.45696 | − | 9.45173i | 0.496087 | − | 0.859249i | ||||
\(122\) | −1.82401 | − | 3.15928i | −0.165138 | − | 0.286028i | ||||
\(123\) | 1.18479 | + | 2.05211i | 0.106829 | + | 0.185033i | ||||
\(124\) | 0.675875 | − | 1.17065i | 0.0606954 | − | 0.105127i | ||||
\(125\) | −2.31901 | −0.207419 | ||||||||
\(126\) | 0.403296 | + | 6.57391i | 0.0359285 | + | 0.585651i | ||||
\(127\) | −15.3053 | −1.35813 | −0.679065 | − | 0.734078i | \(-0.737615\pi\) | ||||
−0.679065 | + | 0.734078i | \(0.737615\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.17728 | − | 2.03910i | −0.103653 | − | 0.179533i | ||||
\(130\) | −0.484687 | − | 0.839503i | −0.0425099 | − | 0.0736293i | ||||
\(131\) | −6.10878 | + | 10.5807i | −0.533726 | + | 0.924441i | 0.465498 | + | 0.885049i | \(0.345875\pi\) |
−0.999224 | + | 0.0393918i | \(0.987458\pi\) | |||||||
\(132\) | −0.209649 | −0.0182476 | ||||||||
\(133\) | −14.7302 | + | 9.75365i | −1.27727 | + | 0.845748i | ||||
\(134\) | 4.95649 | 0.428175 | ||||||||
\(135\) | −0.457313 | + | 0.792089i | −0.0393592 | + | 0.0681722i | ||||
\(136\) | −0.304717 | − | 0.527786i | −0.0261293 | − | 0.0452573i | ||||
\(137\) | −8.91455 | − | 15.4405i | −0.761622 | − | 1.31917i | −0.942014 | − | 0.335573i | \(-0.891070\pi\) |
0.180393 | − | 0.983595i | \(-0.442263\pi\) | |||||||
\(138\) | −0.531554 | + | 0.920679i | −0.0452489 | + | 0.0783734i | ||||
\(139\) | 7.99852 | 0.678426 | 0.339213 | − | 0.940710i | \(-0.389839\pi\) | ||||
0.339213 | + | 0.940710i | \(0.389839\pi\) | |||||||
\(140\) | 0.552141 | + | 0.275160i | 0.0466645 | + | 0.0232553i | ||||
\(141\) | −1.55844 | −0.131244 | ||||||||
\(142\) | −2.10553 | + | 3.64689i | −0.176692 | + | 0.306040i | ||||
\(143\) | −0.609865 | − | 1.05632i | −0.0509995 | − | 0.0883338i | ||||
\(144\) | 1.24469 | + | 2.15586i | 0.103724 | + | 0.179655i | ||||
\(145\) | 0.116584 | − | 0.201930i | 0.00968180 | − | 0.0167694i | ||||
\(146\) | 5.84298 | 0.483569 | ||||||||
\(147\) | −1.95276 | + | 4.60513i | −0.161061 | + | 0.379825i | ||||
\(148\) | 0.637171 | 0.0523752 | ||||||||
\(149\) | −3.90799 | + | 6.76883i | −0.320155 | + | 0.554524i | −0.980520 | − | 0.196421i | \(-0.937068\pi\) |
0.660365 | + | 0.750945i | \(0.270402\pi\) | |||||||
\(150\) | −1.76702 | − | 3.06057i | −0.144277 | − | 0.249895i | ||||
\(151\) | 8.10878 | + | 14.0448i | 0.659883 | + | 1.14295i | 0.980646 | + | 0.195791i | \(0.0627274\pi\) |
−0.320763 | + | 0.947160i | \(0.603939\pi\) | |||||||
\(152\) | −3.33870 | + | 5.78280i | −0.270804 | + | 0.469047i | ||||
\(153\) | −1.51711 | −0.122651 | ||||||||
\(154\) | 0.694741 | + | 0.346225i | 0.0559838 | + | 0.0278996i | ||||
\(155\) | −0.315186 | −0.0253163 | ||||||||
\(156\) | 1.48539 | − | 2.57278i | 0.118927 | − | 0.205987i | ||||
\(157\) | 11.8227 | + | 20.4776i | 0.943556 | + | 1.63429i | 0.758616 | + | 0.651538i | \(0.225876\pi\) |
0.184940 | + | 0.982750i | \(0.440791\pi\) | |||||||
\(158\) | −1.05339 | − | 1.82452i | −0.0838032 | − | 0.145151i | ||||
\(159\) | 4.28468 | − | 7.42129i | 0.339797 | − | 0.588546i | ||||
\(160\) | 0.233169 | 0.0184336 | ||||||||
\(161\) | 3.28194 | − | 2.17314i | 0.258653 | − | 0.171267i | ||||
\(162\) | 4.66513 | 0.366527 | ||||||||
\(163\) | 6.80624 | − | 11.7888i | 0.533106 | − | 0.923367i | −0.466146 | − | 0.884708i | \(-0.654358\pi\) |
0.999252 | − | 0.0386591i | \(-0.0123086\pi\) | |||||||
\(164\) | −1.65802 | − | 2.87178i | −0.129470 | − | 0.224248i | ||||
\(165\) | 0.0244418 | + | 0.0423344i | 0.00190279 | + | 0.00329573i | ||||
\(166\) | −3.36810 | + | 5.83373i | −0.261415 | + | 0.452785i | ||||
\(167\) | −3.59710 | −0.278352 | −0.139176 | − | 0.990268i | \(-0.544445\pi\) | ||||
−0.139176 | + | 0.990268i | \(0.544445\pi\) | |||||||
\(168\) | 0.115767 | + | 1.88705i | 0.00893159 | + | 0.145589i | ||||
\(169\) | 4.28394 | 0.329534 | ||||||||
\(170\) | −0.0710506 | + | 0.123063i | −0.00544933 | + | 0.00943851i | ||||
\(171\) | 8.31128 | + | 14.3956i | 0.635580 | + | 1.10086i | ||||
\(172\) | 1.64751 | + | 2.85357i | 0.125622 | + | 0.217583i | ||||
\(173\) | −6.19782 | + | 10.7349i | −0.471212 | + | 0.816162i | −0.999458 | − | 0.0329288i | \(-0.989517\pi\) |
0.528246 | + | 0.849091i | \(0.322850\pi\) | |||||||
\(174\) | 0.714579 | 0.0541721 | ||||||||
\(175\) | 0.801226 | + | 13.0604i | 0.0605670 | + | 0.987270i | ||||
\(176\) | 0.293388 | 0.0221150 | ||||||||
\(177\) | 1.53675 | − | 2.66173i | 0.115509 | − | 0.200068i | ||||
\(178\) | 6.31233 | + | 10.9333i | 0.473129 | + | 0.819484i | ||||
\(179\) | −4.79172 | − | 8.29950i | −0.358150 | − | 0.620334i | 0.629502 | − | 0.776999i | \(-0.283259\pi\) |
−0.987652 | + | 0.156665i | \(0.949926\pi\) | |||||||
\(180\) | 0.290222 | − | 0.502680i | 0.0216319 | − | 0.0374675i | ||||
\(181\) | 0.148655 | 0.0110495 | 0.00552473 | − | 0.999985i | \(-0.498241\pi\) | ||||
0.00552473 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(182\) | −9.17115 | + | 6.07269i | −0.679811 | + | 0.450138i | ||||
\(183\) | −2.60680 | −0.192700 | ||||||||
\(184\) | 0.743871 | − | 1.28842i | 0.0548389 | − | 0.0949837i | ||||
\(185\) | −0.0742842 | − | 0.128664i | −0.00546148 | − | 0.00945956i | ||||
\(186\) | −0.482966 | − | 0.836522i | −0.0354128 | − | 0.0613367i | ||||
\(187\) | −0.0894005 | + | 0.154846i | −0.00653761 | + | 0.0113235i | ||||
\(188\) | 2.18092 | 0.159060 | ||||||||
\(189\) | 9.28867 | + | 4.62902i | 0.675651 | + | 0.336711i | ||||
\(190\) | 1.55696 | 0.112954 | ||||||||
\(191\) | −5.14154 | + | 8.90541i | −0.372029 | + | 0.644373i | −0.989878 | − | 0.141924i | \(-0.954671\pi\) |
0.617849 | + | 0.786297i | \(0.288004\pi\) | |||||||
\(192\) | 0.357289 | + | 0.618843i | 0.0257851 | + | 0.0446612i | ||||
\(193\) | −6.23407 | − | 10.7977i | −0.448738 | − | 0.777237i | 0.549566 | − | 0.835450i | \(-0.314793\pi\) |
−0.998304 | + | 0.0582133i | \(0.981460\pi\) | |||||||
\(194\) | −2.85249 | + | 4.94065i | −0.204797 | + | 0.354718i | ||||
\(195\) | −0.692694 | −0.0496049 | ||||||||
\(196\) | 2.73274 | − | 6.44454i | 0.195196 | − | 0.460325i | ||||
\(197\) | −19.0312 | −1.35591 | −0.677957 | − | 0.735101i | \(-0.737135\pi\) | ||||
−0.677957 | + | 0.735101i | \(0.737135\pi\) | |||||||
\(198\) | 0.365177 | − | 0.632505i | 0.0259520 | − | 0.0449502i | ||||
\(199\) | 5.30417 | + | 9.18709i | 0.376003 | + | 0.651256i | 0.990477 | − | 0.137681i | \(-0.0439650\pi\) |
−0.614474 | + | 0.788937i | \(0.710632\pi\) | |||||||
\(200\) | 2.47282 | + | 4.28304i | 0.174855 | + | 0.302857i | ||||
\(201\) | 1.77090 | − | 3.06729i | 0.124910 | − | 0.216350i | ||||
\(202\) | 15.7339 | 1.10703 | ||||||||
\(203\) | −2.36799 | − | 1.18009i | −0.166200 | − | 0.0828262i | ||||
\(204\) | −0.435489 | −0.0304903 | ||||||||
\(205\) | −0.386599 | + | 0.669609i | −0.0270012 | + | 0.0467675i | ||||
\(206\) | 2.44775 | + | 4.23962i | 0.170543 | + | 0.295389i | ||||
\(207\) | −1.85178 | − | 3.20737i | −0.128707 | − | 0.222928i | ||||
\(208\) | −2.07870 | + | 3.60041i | −0.144132 | + | 0.249644i | ||||
\(209\) | 1.95907 | 0.135512 | ||||||||
\(210\) | 0.367555 | − | 0.243377i | 0.0253637 | − | 0.0167946i | ||||
\(211\) | −8.69020 | −0.598258 | −0.299129 | − | 0.954213i | \(-0.596696\pi\) | ||||
−0.299129 | + | 0.954213i | \(0.596696\pi\) | |||||||
\(212\) | −5.99610 | + | 10.3855i | −0.411814 | + | 0.713282i | ||||
\(213\) | 1.50457 | + | 2.60599i | 0.103091 | + | 0.178559i | ||||
\(214\) | −5.61573 | − | 9.72674i | −0.383884 | − | 0.664906i | ||||
\(215\) | 0.384148 | − | 0.665364i | 0.0261987 | − | 0.0453774i | ||||
\(216\) | 3.92259 | 0.266899 | ||||||||
\(217\) | 0.218993 | + | 3.56968i | 0.0148662 | + | 0.242326i | ||||
\(218\) | 15.1865 | 1.02856 | ||||||||
\(219\) | 2.08764 | − | 3.61589i | 0.141069 | − | 0.244339i | ||||
\(220\) | −0.0342045 | − | 0.0592439i | −0.00230606 | − | 0.00399422i | ||||
\(221\) | −1.26683 | − | 2.19422i | −0.0852163 | − | 0.147599i | ||||
\(222\) | 0.227655 | − | 0.394309i | 0.0152792 | − | 0.0264643i | ||||
\(223\) | 9.99383 | 0.669236 | 0.334618 | − | 0.942354i | \(-0.391393\pi\) | ||||
0.334618 | + | 0.942354i | \(0.391393\pi\) | |||||||
\(224\) | −0.162007 | − | 2.64079i | −0.0108245 | − | 0.176445i | ||||
\(225\) | 12.3115 | 0.820770 | ||||||||
\(226\) | 5.14880 | − | 8.91799i | 0.342493 | − | 0.593216i | ||||
\(227\) | 12.6545 | + | 21.9183i | 0.839910 | + | 1.45477i | 0.889969 | + | 0.456020i | \(0.150726\pi\) |
−0.0500595 | + | 0.998746i | \(0.515941\pi\) | |||||||
\(228\) | 2.38576 | + | 4.13226i | 0.158001 | + | 0.273666i | ||||
\(229\) | −9.23923 | + | 16.0028i | −0.610545 | + | 1.05750i | 0.380603 | + | 0.924738i | \(0.375716\pi\) |
−0.991149 | + | 0.132757i | \(0.957617\pi\) | |||||||
\(230\) | −0.346895 | −0.0228736 | ||||||||
\(231\) | 0.462482 | − | 0.306233i | 0.0304291 | − | 0.0201487i | ||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 4.67954 | − | 8.10520i | 0.306567 | − | 0.530989i | −0.671042 | − | 0.741419i | \(-0.734153\pi\) |
0.977609 | + | 0.210430i | \(0.0674864\pi\) | |||||||
\(234\) | 5.17466 | + | 8.96278i | 0.338278 | + | 0.585915i | ||||
\(235\) | −0.254261 | − | 0.440392i | −0.0165861 | − | 0.0287280i | ||||
\(236\) | −2.15057 | + | 3.72489i | −0.139990 | + | 0.242470i | ||||
\(237\) | −1.50546 | −0.0977901 | ||||||||
\(238\) | 1.44314 | + | 0.719189i | 0.0935447 | + | 0.0466181i | ||||
\(239\) | −17.5424 | −1.13473 | −0.567363 | − | 0.823468i | \(-0.692036\pi\) | ||||
−0.567363 | + | 0.823468i | \(0.692036\pi\) | |||||||
\(240\) | 0.0833087 | − | 0.144295i | 0.00537755 | − | 0.00931419i | ||||
\(241\) | −1.52113 | − | 2.63467i | −0.0979845 | − | 0.169714i | 0.812866 | − | 0.582451i | \(-0.197906\pi\) |
−0.910850 | + | 0.412737i | \(0.864573\pi\) | |||||||
\(242\) | 5.45696 | + | 9.45173i | 0.350787 | + | 0.607581i | ||||
\(243\) | 7.55069 | − | 13.0782i | 0.484377 | − | 0.838966i | ||||
\(244\) | 3.64803 | 0.233541 | ||||||||
\(245\) | −1.61994 | + | 0.199511i | −0.103494 | + | 0.0127463i | ||||
\(246\) | −2.36958 | −0.151079 | ||||||||
\(247\) | −13.8803 | + | 24.0414i | −0.883182 | + | 1.52972i | ||||
\(248\) | 0.675875 | + | 1.17065i | 0.0429181 | + | 0.0743363i | ||||
\(249\) | 2.40677 | + | 4.16866i | 0.152523 | + | 0.264178i | ||||
\(250\) | 1.15950 | − | 2.00832i | 0.0733335 | − | 0.127017i | ||||
\(251\) | −17.2275 | −1.08739 | −0.543694 | − | 0.839283i | \(-0.682975\pi\) | ||||
−0.543694 | + | 0.839283i | \(0.682975\pi\) | |||||||
\(252\) | −5.89482 | − | 2.93769i | −0.371339 | − | 0.185057i | ||||
\(253\) | −0.436486 | −0.0274416 | ||||||||
\(254\) | 7.65267 | − | 13.2548i | 0.480172 | − | 0.831681i | ||||
\(255\) | 0.0507712 | + | 0.0879383i | 0.00317942 | + | 0.00550691i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −10.3227 | + | 17.8795i | −0.643913 | + | 1.11529i | 0.340638 | + | 0.940195i | \(0.389357\pi\) |
−0.984551 | + | 0.175096i | \(0.943976\pi\) | |||||||
\(258\) | 2.35455 | 0.146588 | ||||||||
\(259\) | −1.40559 | + | 0.930713i | −0.0873391 | + | 0.0578317i | ||||
\(260\) | 0.969374 | 0.0601180 | ||||||||
\(261\) | −1.24469 | + | 2.15586i | −0.0770443 | + | 0.133445i | ||||
\(262\) | −6.10878 | − | 10.5807i | −0.377401 | − | 0.653678i | ||||
\(263\) | 8.28531 | + | 14.3506i | 0.510894 | + | 0.884895i | 0.999920 | + | 0.0126254i | \(0.00401891\pi\) |
−0.489026 | + | 0.872269i | \(0.662648\pi\) | |||||||
\(264\) | 0.104824 | − | 0.181561i | 0.00645150 | − | 0.0111743i | ||||
\(265\) | 2.79620 | 0.171769 | ||||||||
\(266\) | −1.08178 | − | 17.6336i | −0.0663285 | − | 1.08118i | ||||
\(267\) | 9.02132 | 0.552096 | ||||||||
\(268\) | −2.47824 | + | 4.29245i | −0.151383 | + | 0.262203i | ||||
\(269\) | 1.31413 | + | 2.27614i | 0.0801239 | + | 0.138779i | 0.903303 | − | 0.429003i | \(-0.141135\pi\) |
−0.823179 | + | 0.567782i | \(0.807802\pi\) | |||||||
\(270\) | −0.457313 | − | 0.792089i | −0.0278312 | − | 0.0482050i | ||||
\(271\) | 6.31120 | − | 10.9313i | 0.383378 | − | 0.664030i | −0.608165 | − | 0.793811i | \(-0.708094\pi\) |
0.991543 | + | 0.129781i | \(0.0414274\pi\) | |||||||
\(272\) | 0.609435 | 0.0369524 | ||||||||
\(273\) | 0.481288 | + | 7.84522i | 0.0291289 | + | 0.474814i | ||||
\(274\) | 17.8291 | 1.07710 | ||||||||
\(275\) | 0.725495 | − | 1.25659i | 0.0437490 | − | 0.0757755i | ||||
\(276\) | −0.531554 | − | 0.920679i | −0.0319958 | − | 0.0554184i | ||||
\(277\) | −9.72977 | − | 16.8525i | −0.584605 | − | 1.01257i | −0.994924 | − | 0.100624i | \(-0.967916\pi\) |
0.410319 | − | 0.911942i | \(-0.365417\pi\) | |||||||
\(278\) | −3.99926 | + | 6.92692i | −0.239860 | + | 0.415449i | ||||
\(279\) | 3.36502 | 0.201458 | ||||||||
\(280\) | −0.514366 | + | 0.340588i | −0.0307393 | + | 0.0203540i | ||||
\(281\) | 15.9906 | 0.953917 | 0.476958 | − | 0.878926i | \(-0.341739\pi\) | ||||
0.476958 | + | 0.878926i | \(0.341739\pi\) | |||||||
\(282\) | 0.779218 | − | 1.34965i | 0.0464018 | − | 0.0803702i | ||||
\(283\) | −13.9913 | − | 24.2337i | −0.831699 | − | 1.44054i | −0.896690 | − | 0.442659i | \(-0.854035\pi\) |
0.0649910 | − | 0.997886i | \(-0.479298\pi\) | |||||||
\(284\) | −2.10553 | − | 3.64689i | −0.124940 | − | 0.216403i | ||||
\(285\) | 0.556285 | − | 0.963514i | 0.0329515 | − | 0.0570737i | ||||
\(286\) | 1.21973 | 0.0721242 | ||||||||
\(287\) | 7.85237 | + | 3.91324i | 0.463511 | + | 0.230991i | ||||
\(288\) | −2.48938 | −0.146688 | ||||||||
\(289\) | 8.31429 | − | 14.4008i | 0.489076 | − | 0.847105i | ||||
\(290\) | 0.116584 | + | 0.201930i | 0.00684607 | + | 0.0118577i | ||||
\(291\) | 2.03833 | + | 3.53049i | 0.119489 | + | 0.206961i | ||||
\(292\) | −2.92149 | + | 5.06017i | −0.170967 | + | 0.296124i | ||||
\(293\) | 20.6845 | 1.20840 | 0.604202 | − | 0.796832i | \(-0.293492\pi\) | ||||
0.604202 | + | 0.796832i | \(0.293492\pi\) | |||||||
\(294\) | −3.01178 | − | 3.99370i | −0.175651 | − | 0.232918i | ||||
\(295\) | 1.00289 | 0.0583905 | ||||||||
\(296\) | −0.318586 | + | 0.551807i | −0.0185174 | + | 0.0320731i | ||||
\(297\) | −0.575421 | − | 0.996659i | −0.0333893 | − | 0.0578320i | ||||
\(298\) | −3.90799 | − | 6.76883i | −0.226384 | − | 0.392108i | ||||
\(299\) | 3.09257 | − | 5.35648i | 0.178848 | − | 0.309773i | ||||
\(300\) | 3.53404 | 0.204038 | ||||||||
\(301\) | −7.80259 | − | 3.88843i | −0.449734 | − | 0.224125i | ||||
\(302\) | −16.2176 | −0.933215 | ||||||||
\(303\) | 5.62154 | − | 9.73680i | 0.322949 | − | 0.559365i | ||||
\(304\) | −3.33870 | − | 5.78280i | −0.191488 | − | 0.331666i | ||||
\(305\) | −0.425303 | − | 0.736646i | −0.0243528 | − | 0.0421802i | ||||
\(306\) | 0.758557 | − | 1.31386i | 0.0433638 | − | 0.0751083i | ||||
\(307\) | −28.6540 | −1.63537 | −0.817686 | − | 0.575664i | \(-0.804744\pi\) | ||||
−0.817686 | + | 0.575664i | \(0.804744\pi\) | |||||||
\(308\) | −0.647210 | + | 0.428551i | −0.0368782 | + | 0.0244189i | ||||
\(309\) | 3.49822 | 0.199007 | ||||||||
\(310\) | 0.157593 | − | 0.272959i | 0.00895067 | − | 0.0155030i | ||||
\(311\) | −5.23235 | − | 9.06270i | −0.296699 | − | 0.513898i | 0.678679 | − | 0.734435i | \(-0.262553\pi\) |
−0.975379 | + | 0.220536i | \(0.929219\pi\) | |||||||
\(312\) | 1.48539 | + | 2.57278i | 0.0840939 | + | 0.145655i | ||||
\(313\) | 15.7086 | − | 27.2081i | 0.887901 | − | 1.53789i | 0.0455495 | − | 0.998962i | \(-0.485496\pi\) |
0.842352 | − | 0.538928i | \(-0.181171\pi\) | |||||||
\(314\) | −23.6455 | −1.33439 | ||||||||
\(315\) | 0.0940360 | + | 1.53283i | 0.00529833 | + | 0.0863652i | ||||
\(316\) | 2.10678 | 0.118516 | ||||||||
\(317\) | −6.37389 | + | 11.0399i | −0.357993 | + | 0.620062i | −0.987625 | − | 0.156831i | \(-0.949872\pi\) |
0.629632 | + | 0.776893i | \(0.283206\pi\) | |||||||
\(318\) | 4.28468 | + | 7.42129i | 0.240273 | + | 0.416165i | ||||
\(319\) | 0.146694 | + | 0.254082i | 0.00821329 | + | 0.0142258i | ||||
\(320\) | −0.116584 | + | 0.201930i | −0.00651726 | + | 0.0112882i | ||||
\(321\) | −8.02577 | −0.447955 | ||||||||
\(322\) | 0.241024 | + | 3.92881i | 0.0134318 | + | 0.218944i | ||||
\(323\) | 4.06944 | 0.226430 | ||||||||
\(324\) | −2.33257 | + | 4.04012i | −0.129587 | + | 0.224451i | ||||
\(325\) | 10.2805 | + | 17.8063i | 0.570258 | + | 0.987716i | ||||
\(326\) | 6.80624 | + | 11.7888i | 0.376963 | + | 0.652919i | ||||
\(327\) | 5.42599 | − | 9.39809i | 0.300058 | − | 0.519716i | ||||
\(328\) | 3.31605 | 0.183098 | ||||||||
\(329\) | −4.81107 | + | 3.18565i | −0.265243 | + | 0.175631i | ||||
\(330\) | −0.0488836 | −0.00269095 | ||||||||
\(331\) | 5.13096 | − | 8.88709i | 0.282023 | − | 0.488479i | −0.689860 | − | 0.723943i | \(-0.742328\pi\) |
0.971883 | + | 0.235465i | \(0.0756612\pi\) | |||||||
\(332\) | −3.36810 | − | 5.83373i | −0.184849 | − | 0.320167i | ||||
\(333\) | 0.793080 | + | 1.37365i | 0.0434605 | + | 0.0752758i | ||||
\(334\) | 1.79855 | − | 3.11518i | 0.0984123 | − | 0.170455i | ||||
\(335\) | 1.15570 | 0.0631425 | ||||||||
\(336\) | −1.69212 | − | 0.843268i | −0.0923125 | − | 0.0460040i | ||||
\(337\) | −26.9868 | −1.47007 | −0.735033 | − | 0.678031i | \(-0.762833\pi\) | ||||
−0.735033 | + | 0.678031i | \(0.762833\pi\) | |||||||
\(338\) | −2.14197 | + | 3.71001i | −0.116508 | + | 0.201798i | ||||
\(339\) | −3.67923 | − | 6.37260i | −0.199828 | − | 0.346112i | ||||
\(340\) | −0.0710506 | − | 0.123063i | −0.00385326 | − | 0.00667404i | ||||
\(341\) | 0.198294 | − | 0.343455i | 0.0107382 | − | 0.0185991i | ||||
\(342\) | −16.6226 | −0.898845 | ||||||||
\(343\) | 3.38514 | + | 18.2083i | 0.182780 | + | 0.983154i | ||||
\(344\) | −3.29502 | −0.177656 | ||||||||
\(345\) | −0.123942 | + | 0.214674i | −0.00667280 | + | 0.0115576i | ||||
\(346\) | −6.19782 | − | 10.7349i | −0.333197 | − | 0.577114i | ||||
\(347\) | −0.0149934 | − | 0.0259694i | −0.000804890 | − | 0.00139411i | 0.865623 | − | 0.500697i | \(-0.166923\pi\) |
−0.866428 | + | 0.499303i | \(0.833590\pi\) | |||||||
\(348\) | −0.357289 | + | 0.618843i | −0.0191527 | + | 0.0331735i | ||||
\(349\) | 6.30027 | 0.337246 | 0.168623 | − | 0.985681i | \(-0.446068\pi\) | ||||
0.168623 | + | 0.985681i | \(0.446068\pi\) | |||||||
\(350\) | −11.7112 | − | 5.83630i | −0.625991 | − | 0.311963i | ||||
\(351\) | 16.3078 | 0.870444 | ||||||||
\(352\) | −0.146694 | + | 0.254082i | −0.00781882 | + | 0.0135426i | ||||
\(353\) | −13.8172 | − | 23.9321i | −0.735415 | − | 1.27378i | −0.954541 | − | 0.298079i | \(-0.903654\pi\) |
0.219126 | − | 0.975696i | \(-0.429679\pi\) | |||||||
\(354\) | 1.53675 | + | 2.66173i | 0.0816773 | + | 0.141469i | ||||
\(355\) | −0.490944 | + | 0.850340i | −0.0260566 | + | 0.0451313i | ||||
\(356\) | −12.6247 | −0.669106 | ||||||||
\(357\) | 0.960683 | − | 0.636117i | 0.0508447 | − | 0.0336669i | ||||
\(358\) | 9.58344 | 0.506501 | ||||||||
\(359\) | 9.23986 | − | 16.0039i | 0.487661 | − | 0.844654i | −0.512238 | − | 0.858843i | \(-0.671184\pi\) |
0.999899 | + | 0.0141898i | \(0.00451691\pi\) | |||||||
\(360\) | 0.290222 | + | 0.502680i | 0.0152961 | + | 0.0264936i | ||||
\(361\) | −12.7938 | − | 22.1596i | −0.673359 | − | 1.16629i | ||||
\(362\) | −0.0743276 | + | 0.128739i | −0.00390657 | + | 0.00676638i | ||||
\(363\) | 7.79886 | 0.409334 | ||||||||
\(364\) | −0.673527 | − | 10.9788i | −0.0353024 | − | 0.575445i | ||||
\(365\) | 1.36240 | 0.0713113 | ||||||||
\(366\) | 1.30340 | − | 2.25756i | 0.0681299 | − | 0.118004i | ||||
\(367\) | 8.86676 | + | 15.3577i | 0.462841 | + | 0.801665i | 0.999101 | − | 0.0423883i | \(-0.0134967\pi\) |
−0.536260 | + | 0.844053i | \(0.680163\pi\) | |||||||
\(368\) | 0.743871 | + | 1.28842i | 0.0387770 | + | 0.0671637i | ||||
\(369\) | 4.12745 | − | 7.14895i | 0.214866 | − | 0.372159i | ||||
\(370\) | 0.148568 | 0.00772370 | ||||||||
\(371\) | −1.94282 | − | 31.6688i | −0.100866 | − | 1.64416i | ||||
\(372\) | 0.965932 | 0.0500812 | ||||||||
\(373\) | −7.11961 | + | 12.3315i | −0.368639 | + | 0.638502i | −0.989353 | − | 0.145535i | \(-0.953510\pi\) |
0.620714 | + | 0.784037i | \(0.286843\pi\) | |||||||
\(374\) | −0.0894005 | − | 0.154846i | −0.00462279 | − | 0.00800691i | ||||
\(375\) | −0.828558 | − | 1.43510i | −0.0427865 | − | 0.0741084i | ||||
\(376\) | −1.09046 | + | 1.88873i | −0.0562361 | + | 0.0974037i | ||||
\(377\) | −4.15740 | −0.214117 | ||||||||
\(378\) | −8.65318 | + | 5.72971i | −0.445072 | + | 0.294705i | ||||
\(379\) | 33.9879 | 1.74584 | 0.872920 | − | 0.487863i | \(-0.162224\pi\) | ||||
0.872920 | + | 0.487863i | \(0.162224\pi\) | |||||||
\(380\) | −0.778480 | + | 1.34837i | −0.0399352 | + | 0.0691698i | ||||
\(381\) | −5.46844 | − | 9.47161i | −0.280157 | − | 0.485246i | ||||
\(382\) | −5.14154 | − | 8.90541i | −0.263064 | − | 0.455641i | ||||
\(383\) | 8.54059 | − | 14.7927i | 0.436404 | − | 0.755873i | −0.561005 | − | 0.827812i | \(-0.689585\pi\) |
0.997409 | + | 0.0719387i | \(0.0229186\pi\) | |||||||
\(384\) | −0.714579 | −0.0364657 | ||||||||
\(385\) | 0.161992 | + | 0.0807288i | 0.00825586 | + | 0.00411432i | ||||
\(386\) | 12.4681 | 0.634611 | ||||||||
\(387\) | −4.10128 | + | 7.10362i | −0.208480 | + | 0.361097i | ||||
\(388\) | −2.85249 | − | 4.94065i | −0.144813 | − | 0.250824i | ||||
\(389\) | 5.65882 | + | 9.80136i | 0.286913 | + | 0.496949i | 0.973071 | − | 0.230504i | \(-0.0740375\pi\) |
−0.686158 | + | 0.727453i | \(0.740704\pi\) | |||||||
\(390\) | 0.346347 | − | 0.599891i | 0.0175380 | − | 0.0303767i | ||||
\(391\) | −0.906682 | −0.0458529 | ||||||||
\(392\) | 4.21477 | + | 5.58889i | 0.212878 | + | 0.282282i | ||||
\(393\) | −8.73040 | −0.440391 | ||||||||
\(394\) | 9.51558 | − | 16.4815i | 0.479388 | − | 0.830325i | ||||
\(395\) | −0.245617 | − | 0.425422i | −0.0123584 | − | 0.0214053i | ||||
\(396\) | 0.365177 | + | 0.632505i | 0.0183508 | + | 0.0317846i | ||||
\(397\) | −5.12573 | + | 8.87803i | −0.257253 | + | 0.445575i | −0.965505 | − | 0.260384i | \(-0.916151\pi\) |
0.708252 | + | 0.705960i | \(0.249484\pi\) | |||||||
\(398\) | −10.6083 | −0.531748 | ||||||||
\(399\) | −11.2989 | − | 5.63084i | −0.565654 | − | 0.281894i | ||||
\(400\) | −4.94563 | −0.247282 | ||||||||
\(401\) | 8.80508 | − | 15.2509i | 0.439705 | − | 0.761591i | −0.557962 | − | 0.829867i | \(-0.688416\pi\) |
0.997667 | + | 0.0682755i | \(0.0217497\pi\) | |||||||
\(402\) | 1.77090 | + | 3.06729i | 0.0883245 | + | 0.152983i | ||||
\(403\) | 2.80988 | + | 4.86686i | 0.139970 | + | 0.242435i | ||||
\(404\) | −7.86693 | + | 13.6259i | −0.391395 | + | 0.677915i | ||||
\(405\) | 1.08776 | 0.0540513 | ||||||||
\(406\) | 2.20598 | − | 1.46070i | 0.109481 | − | 0.0724931i | ||||
\(407\) | 0.186939 | 0.00926620 | ||||||||
\(408\) | 0.217745 | − | 0.377145i | 0.0107800 | − | 0.0186714i | ||||
\(409\) | 19.4479 | + | 33.6848i | 0.961639 | + | 1.66561i | 0.718386 | + | 0.695645i | \(0.244881\pi\) |
0.243254 | + | 0.969963i | \(0.421785\pi\) | |||||||
\(410\) | −0.386599 | − | 0.669609i | −0.0190928 | − | 0.0330696i | ||||
\(411\) | 6.37015 | − | 11.0334i | 0.314216 | − | 0.544239i | ||||
\(412\) | −4.89549 | −0.241184 | ||||||||
\(413\) | −0.696813 | − | 11.3584i | −0.0342879 | − | 0.558909i | ||||
\(414\) | 3.70355 | 0.182020 | ||||||||
\(415\) | −0.785336 | + | 1.36024i | −0.0385506 | + | 0.0667716i | ||||
\(416\) | −2.07870 | − | 3.60041i | −0.101917 | − | 0.176525i | ||||
\(417\) | 2.85779 | + | 4.94983i | 0.139946 | + | 0.242394i | ||||
\(418\) | −0.979535 | + | 1.69660i | −0.0479106 | + | 0.0829836i | ||||
\(419\) | −12.6437 | −0.617683 | −0.308842 | − | 0.951113i | \(-0.599941\pi\) | ||||
−0.308842 | + | 0.951113i | \(0.599941\pi\) | |||||||
\(420\) | 0.0269932 | + | 0.440001i | 0.00131713 | + | 0.0214698i | ||||
\(421\) | −10.7981 | −0.526267 | −0.263133 | − | 0.964759i | \(-0.584756\pi\) | ||||
−0.263133 | + | 0.964759i | \(0.584756\pi\) | |||||||
\(422\) | 4.34510 | − | 7.52593i | 0.211516 | − | 0.366357i | ||||
\(423\) | 2.71456 | + | 4.70176i | 0.131986 | + | 0.228607i | ||||
\(424\) | −5.99610 | − | 10.3855i | −0.291196 | − | 0.504367i | ||||
\(425\) | 1.50702 | − | 2.61024i | 0.0731012 | − | 0.126615i | ||||
\(426\) | −3.00914 | −0.145793 | ||||||||
\(427\) | −8.04749 | + | 5.32866i | −0.389445 | + | 0.257872i | ||||
\(428\) | 11.2315 | 0.542894 | ||||||||
\(429\) | 0.435797 | − | 0.754822i | 0.0210405 | − | 0.0364432i | ||||
\(430\) | 0.384148 | + | 0.665364i | 0.0185253 | + | 0.0320867i | ||||
\(431\) | 18.0906 | + | 31.3339i | 0.871394 | + | 1.50930i | 0.860555 | + | 0.509358i | \(0.170117\pi\) |
0.0108397 | + | 0.999941i | \(0.496550\pi\) | |||||||
\(432\) | −1.96130 | + | 3.39706i | −0.0943629 | + | 0.163441i | ||||
\(433\) | 10.6350 | 0.511084 | 0.255542 | − | 0.966798i | \(-0.417746\pi\) | ||||
0.255542 | + | 0.966798i | \(0.417746\pi\) | |||||||
\(434\) | −3.20093 | − | 1.59519i | −0.153650 | − | 0.0765715i | ||||
\(435\) | 0.166617 | 0.00798869 | ||||||||
\(436\) | −7.59327 | + | 13.1519i | −0.363652 | + | 0.629863i | ||||
\(437\) | 4.96712 | + | 8.60331i | 0.237610 | + | 0.411552i | ||||
\(438\) | 2.08764 | + | 3.61589i | 0.0997511 | + | 0.172774i | ||||
\(439\) | 1.48753 | − | 2.57648i | 0.0709961 | − | 0.122969i | −0.828342 | − | 0.560223i | \(-0.810716\pi\) |
0.899338 | + | 0.437254i | \(0.144049\pi\) | |||||||
\(440\) | 0.0684089 | 0.00326127 | ||||||||
\(441\) | 17.2950 | − | 2.13004i | 0.823570 | − | 0.101430i | ||||
\(442\) | 2.53366 | 0.120514 | ||||||||
\(443\) | 13.9715 | − | 24.1993i | 0.663804 | − | 1.14974i | −0.315805 | − | 0.948824i | \(-0.602274\pi\) |
0.979608 | − | 0.200917i | \(-0.0643923\pi\) | |||||||
\(444\) | 0.227655 | + | 0.394309i | 0.0108040 | + | 0.0187131i | ||||
\(445\) | 1.47184 | + | 2.54930i | 0.0697718 | + | 0.120848i | ||||
\(446\) | −4.99691 | + | 8.65491i | −0.236611 | + | 0.409822i | ||||
\(447\) | −5.58513 | −0.264167 | ||||||||
\(448\) | 2.36799 | + | 1.18009i | 0.111877 | + | 0.0557541i | ||||
\(449\) | −0.604431 | −0.0285248 | −0.0142624 | − | 0.999898i | \(-0.504540\pi\) | ||||
−0.0142624 | + | 0.999898i | \(0.504540\pi\) | |||||||
\(450\) | −6.15577 | + | 10.6621i | −0.290186 | + | 0.502617i | ||||
\(451\) | −0.486444 | − | 0.842547i | −0.0229058 | − | 0.0396740i | ||||
\(452\) | 5.14880 | + | 8.91799i | 0.242179 | + | 0.419467i | ||||
\(453\) | −5.79436 | + | 10.0361i | −0.272243 | + | 0.471538i | ||||
\(454\) | −25.3090 | −1.18781 | ||||||||
\(455\) | −2.13843 | + | 1.41596i | −0.100251 | + | 0.0663813i | ||||
\(456\) | −4.77153 | −0.223447 | ||||||||
\(457\) | 3.55156 | − | 6.15148i | 0.166135 | − | 0.287754i | −0.770923 | − | 0.636929i | \(-0.780205\pi\) |
0.937058 | + | 0.349175i | \(0.113538\pi\) | |||||||
\(458\) | −9.23923 | − | 16.0028i | −0.431721 | − | 0.747762i | ||||
\(459\) | −1.19528 | − | 2.07029i | −0.0557910 | − | 0.0966329i | ||||
\(460\) | 0.173447 | − | 0.300420i | 0.00808703 | − | 0.0140071i | ||||
\(461\) | 3.81028 | 0.177462 | 0.0887312 | − | 0.996056i | \(-0.471719\pi\) | ||||
0.0887312 | + | 0.996056i | \(0.471719\pi\) | |||||||
\(462\) | 0.0339646 | + | 0.553638i | 0.00158018 | + | 0.0257576i | ||||
\(463\) | −3.42327 | −0.159093 | −0.0795464 | − | 0.996831i | \(-0.525347\pi\) | ||||
−0.0795464 | + | 0.996831i | \(0.525347\pi\) | |||||||
\(464\) | 0.500000 | − | 0.866025i | 0.0232119 | − | 0.0402042i | ||||
\(465\) | −0.112613 | − | 0.195051i | −0.00522228 | − | 0.00904525i | ||||
\(466\) | 4.67954 | + | 8.10520i | 0.216775 | + | 0.375466i | ||||
\(467\) | −11.4351 | + | 19.8061i | −0.529151 | + | 0.916517i | 0.470271 | + | 0.882522i | \(0.344156\pi\) |
−0.999422 | + | 0.0339945i | \(0.989177\pi\) | |||||||
\(468\) | −10.3493 | −0.478398 | ||||||||
\(469\) | −0.802985 | − | 13.0890i | −0.0370784 | − | 0.604395i | ||||
\(470\) | 0.508521 | 0.0234563 | ||||||||
\(471\) | −8.44827 | + | 14.6328i | −0.389276 | + | 0.674245i | ||||
\(472\) | −2.15057 | − | 3.72489i | −0.0989878 | − | 0.171452i | ||||
\(473\) | 0.483360 | + | 0.837205i | 0.0222249 | + | 0.0384947i | ||||
\(474\) | 0.752730 | − | 1.30377i | 0.0345740 | − | 0.0598840i | ||||
\(475\) | −33.0240 | −1.51524 | ||||||||
\(476\) | −1.34440 | + | 0.890199i | −0.0616207 | + | 0.0408022i | ||||
\(477\) | −29.8531 | −1.36688 | ||||||||
\(478\) | 8.77121 | − | 15.1922i | 0.401186 | − | 0.694874i | ||||
\(479\) | 2.28610 | + | 3.95963i | 0.104454 | + | 0.180920i | 0.913515 | − | 0.406805i | \(-0.133357\pi\) |
−0.809061 | + | 0.587725i | \(0.800024\pi\) | |||||||
\(480\) | 0.0833087 | + | 0.144295i | 0.00380250 | + | 0.00658613i | ||||
\(481\) | −1.32449 | + | 2.29408i | −0.0603914 | + | 0.104601i | ||||
\(482\) | 3.04226 | 0.138571 | ||||||||
\(483\) | 2.51743 | + | 1.25457i | 0.114547 | + | 0.0570847i | ||||
\(484\) | −10.9139 | −0.496087 | ||||||||
\(485\) | −0.665111 | + | 1.15201i | −0.0302011 | + | 0.0523099i | ||||
\(486\) | 7.55069 | + | 13.0782i | 0.342506 | + | 0.593238i | ||||
\(487\) | −10.8284 | − | 18.7554i | −0.490683 | − | 0.849889i | 0.509259 | − | 0.860613i | \(-0.329919\pi\) |
−0.999942 | + | 0.0107247i | \(0.996586\pi\) | |||||||
\(488\) | −1.82401 | + | 3.15928i | −0.0825692 | + | 0.143014i | ||||
\(489\) | 9.72719 | 0.439879 | ||||||||
\(490\) | 0.637189 | − | 1.50267i | 0.0287853 | − | 0.0678835i | ||||
\(491\) | 32.0537 | 1.44656 | 0.723281 | − | 0.690554i | \(-0.242633\pi\) | ||||
0.723281 | + | 0.690554i | \(0.242633\pi\) | |||||||
\(492\) | 1.18479 | − | 2.05211i | 0.0534144 | − | 0.0925164i | ||||
\(493\) | 0.304717 | + | 0.527786i | 0.0137238 | + | 0.0237703i | ||||
\(494\) | −13.8803 | − | 24.0414i | −0.624504 | − | 1.08167i | ||||
\(495\) | 0.0851478 | − | 0.147480i | 0.00382711 | − | 0.00662875i | ||||
\(496\) | −1.35175 | −0.0606954 | ||||||||
\(497\) | 9.97176 | + | 4.96944i | 0.447295 | + | 0.222910i | ||||
\(498\) | −4.81355 | −0.215700 | ||||||||
\(499\) | −12.3057 | + | 21.3140i | −0.550877 | + | 0.954147i | 0.447335 | + | 0.894367i | \(0.352373\pi\) |
−0.998212 | + | 0.0597801i | \(0.980960\pi\) | |||||||
\(500\) | 1.15950 | + | 2.00832i | 0.0518546 | + | 0.0898149i | ||||
\(501\) | −1.28521 | − | 2.22604i | −0.0574188 | − | 0.0994523i | ||||
\(502\) | 8.61374 | − | 14.9194i | 0.384450 | − | 0.665887i | ||||
\(503\) | −35.0600 | −1.56325 | −0.781623 | − | 0.623751i | \(-0.785608\pi\) | ||||
−0.781623 | + | 0.623751i | \(0.785608\pi\) | |||||||
\(504\) | 5.49153 | − | 3.63622i | 0.244612 | − | 0.161970i | ||||
\(505\) | 3.66864 | 0.163253 | ||||||||
\(506\) | 0.218243 | − | 0.378008i | 0.00970208 | − | 0.0168045i | ||||
\(507\) | 1.53061 | + | 2.65109i | 0.0679767 | + | 0.117739i | ||||
\(508\) | 7.65267 | + | 13.2548i | 0.339533 | + | 0.588088i | ||||
\(509\) | 15.8796 | − | 27.5043i | 0.703851 | − | 1.21910i | −0.263254 | − | 0.964726i | \(-0.584796\pi\) |
0.967105 | − | 0.254378i | \(-0.0818708\pi\) | |||||||
\(510\) | −0.101542 | −0.00449638 | ||||||||
\(511\) | −0.946604 | − | 15.4301i | −0.0418753 | − | 0.682586i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −13.0964 | + | 22.6836i | −0.578218 | + | 1.00150i | ||||
\(514\) | −10.3227 | − | 17.8795i | −0.455315 | − | 0.788630i | ||||
\(515\) | 0.570738 | + | 0.988547i | 0.0251497 | + | 0.0435606i | ||||
\(516\) | −1.17728 | + | 2.03910i | −0.0518267 | + | 0.0897665i | ||||
\(517\) | 0.639855 | 0.0281408 | ||||||||
\(518\) | −0.103226 | − | 1.68263i | −0.00453550 | − | 0.0739307i | ||||
\(519\) | −8.85766 | −0.388808 | ||||||||
\(520\) | −0.484687 | + | 0.839503i | −0.0212549 | + | 0.0368146i | ||||
\(521\) | 7.08405 | + | 12.2699i | 0.310358 | + | 0.537556i | 0.978440 | − | 0.206532i | \(-0.0662178\pi\) |
−0.668082 | + | 0.744088i | \(0.732884\pi\) | |||||||
\(522\) | −1.24469 | − | 2.15586i | −0.0544785 | − | 0.0943596i | ||||
\(523\) | 9.85144 | − | 17.0632i | 0.430774 | − | 0.746122i | −0.566167 | − | 0.824291i | \(-0.691574\pi\) |
0.996940 | + | 0.0781692i | \(0.0249075\pi\) | |||||||
\(524\) | 12.2176 | 0.533726 | ||||||||
\(525\) | −7.79605 | + | 5.16216i | −0.340247 | + | 0.225295i | ||||
\(526\) | −16.5706 | −0.722513 | ||||||||
\(527\) | 0.411902 | − | 0.713435i | 0.0179427 | − | 0.0310777i | ||||
\(528\) | 0.104824 | + | 0.181561i | 0.00456190 | + | 0.00790144i | ||||
\(529\) | 10.3933 | + | 18.0017i | 0.451883 | + | 0.782685i | ||||
\(530\) | −1.39810 | + | 2.42158i | −0.0607296 | + | 0.105187i | ||||
\(531\) | −10.7071 | −0.464650 | ||||||||
\(532\) | 15.8120 | + | 7.87994i | 0.685538 | + | 0.341639i | ||||
\(533\) | 13.7861 | 0.597143 | ||||||||
\(534\) | −4.51066 | + | 7.81269i | −0.195195 | + | 0.338088i | ||||
\(535\) | −1.30941 | − | 2.26797i | −0.0566109 | − | 0.0980529i | ||||
\(536\) | −2.47824 | − | 4.29245i | −0.107044 | − | 0.185405i | ||||
\(537\) | 3.42406 | − | 5.93065i | 0.147759 | − | 0.255926i | ||||
\(538\) | −2.62826 | −0.113312 | ||||||||
\(539\) | 0.801753 | − | 1.89075i | 0.0345339 | − | 0.0814405i | ||||
\(540\) | 0.914626 | 0.0393592 | ||||||||
\(541\) | 6.64270 | − | 11.5055i | 0.285592 | − | 0.494660i | −0.687161 | − | 0.726505i | \(-0.741143\pi\) |
0.972753 | + | 0.231846i | \(0.0744765\pi\) | |||||||
\(542\) | 6.31120 | + | 10.9313i | 0.271089 | + | 0.469540i | ||||
\(543\) | 0.0531129 | + | 0.0919943i | 0.00227929 | + | 0.00394785i | ||||
\(544\) | −0.304717 | + | 0.527786i | −0.0130647 | + | 0.0226286i | ||||
\(545\) | 3.54103 | 0.151681 | ||||||||
\(546\) | −7.03480 | − | 3.50580i | −0.301062 | − | 0.150034i | ||||
\(547\) | −3.77149 | −0.161257 | −0.0806287 | − | 0.996744i | \(-0.525693\pi\) | ||||
−0.0806287 | + | 0.996744i | \(0.525693\pi\) | |||||||
\(548\) | −8.91455 | + | 15.4405i | −0.380811 | + | 0.659584i | ||||
\(549\) | 4.54066 | + | 7.86465i | 0.193791 | + | 0.335655i | ||||
\(550\) | 0.725495 | + | 1.25659i | 0.0309352 | + | 0.0535814i | ||||
\(551\) | 3.33870 | − | 5.78280i | 0.142233 | − | 0.246355i | ||||
\(552\) | 1.06311 | 0.0452489 | ||||||||
\(553\) | −4.64752 | + | 3.07736i | −0.197633 | + | 0.130863i | ||||
\(554\) | 19.4595 | 0.826757 | ||||||||
\(555\) | 0.0530819 | − | 0.0919405i | 0.00225320 | − | 0.00390266i | ||||
\(556\) | −3.99926 | − | 6.92692i | −0.169606 | − | 0.293767i | ||||
\(557\) | 20.6721 | + | 35.8052i | 0.875907 | + | 1.51712i | 0.855793 | + | 0.517318i | \(0.173069\pi\) |
0.0201136 | + | 0.999798i | \(0.493597\pi\) | |||||||
\(558\) | −1.68251 | + | 2.91419i | −0.0712262 | + | 0.123367i | ||||
\(559\) | −13.6987 | −0.579394 | ||||||||
\(560\) | −0.0377749 | − | 0.615749i | −0.00159628 | − | 0.0260201i | ||||
\(561\) | −0.127767 | −0.00539434 | ||||||||
\(562\) | −7.99528 | + | 13.8482i | −0.337260 | + | 0.584152i | ||||
\(563\) | 3.31295 | + | 5.73821i | 0.139624 | + | 0.241837i | 0.927354 | − | 0.374184i | \(-0.122077\pi\) |
−0.787730 | + | 0.616021i | \(0.788744\pi\) | |||||||
\(564\) | 0.779218 | + | 1.34965i | 0.0328110 | + | 0.0568303i | ||||
\(565\) | 1.20054 | − | 2.07939i | 0.0505071 | − | 0.0874808i | ||||
\(566\) | 27.9827 | 1.17620 | ||||||||
\(567\) | −0.755783 | − | 12.3196i | −0.0317399 | − | 0.517375i | ||||
\(568\) | 4.21106 | 0.176692 | ||||||||
\(569\) | 6.97747 | − | 12.0853i | 0.292511 | − | 0.506644i | −0.681892 | − | 0.731453i | \(-0.738843\pi\) |
0.974403 | + | 0.224809i | \(0.0721759\pi\) | |||||||
\(570\) | 0.556285 | + | 0.963514i | 0.0233002 | + | 0.0403572i | ||||
\(571\) | 1.05581 | + | 1.82871i | 0.0441841 | + | 0.0765291i | 0.887272 | − | 0.461247i | \(-0.152598\pi\) |
−0.843088 | + | 0.537776i | \(0.819265\pi\) | |||||||
\(572\) | −0.609865 | + | 1.05632i | −0.0254998 | + | 0.0441669i | ||||
\(573\) | −7.34807 | −0.306970 | ||||||||
\(574\) | −7.31515 | + | 4.84373i | −0.305328 | + | 0.202174i | ||||
\(575\) | 7.35782 | 0.306842 | ||||||||
\(576\) | 1.24469 | − | 2.15586i | 0.0518620 | − | 0.0898277i | ||||
\(577\) | −1.39881 | − | 2.42281i | −0.0582331 | − | 0.100863i | 0.835439 | − | 0.549583i | \(-0.185213\pi\) |
−0.893672 | + | 0.448720i | \(0.851880\pi\) | |||||||
\(578\) | 8.31429 | + | 14.4008i | 0.345829 | + | 0.598994i | ||||
\(579\) | 4.45473 | − | 7.71582i | 0.185132 | − | 0.320659i | ||||
\(580\) | −0.233169 | −0.00968180 | ||||||||
\(581\) | 15.9513 | + | 7.94934i | 0.661771 | + | 0.329794i | ||||
\(582\) | −4.07666 | −0.168983 | ||||||||
\(583\) | −1.75918 | + | 3.04700i | −0.0728579 | + | 0.126194i | ||||
\(584\) | −2.92149 | − | 5.06017i | −0.120892 | − | 0.209391i | ||||
\(585\) | 1.20657 | + | 2.08984i | 0.0498855 | + | 0.0864042i | ||||
\(586\) | −10.3423 | + | 17.9133i | −0.427235 | + | 0.739993i | ||||
\(587\) | 6.93586 | 0.286274 | 0.143137 | − | 0.989703i | \(-0.454281\pi\) | ||||
0.143137 | + | 0.989703i | \(0.454281\pi\) | |||||||
\(588\) | 4.96454 | − | 0.611430i | 0.204734 | − | 0.0252150i | ||||
\(589\) | −9.02617 | −0.371917 | ||||||||
\(590\) | −0.501445 | + | 0.868528i | −0.0206441 | + | 0.0357567i | ||||
\(591\) | −6.79963 | − | 11.7773i | −0.279700 | − | 0.484454i | ||||
\(592\) | −0.318586 | − | 0.551807i | −0.0130938 | − | 0.0226791i | ||||
\(593\) | −1.69542 | + | 2.93655i | −0.0696225 | + | 0.120590i | −0.898735 | − | 0.438492i | \(-0.855513\pi\) |
0.829113 | + | 0.559082i | \(0.188846\pi\) | |||||||
\(594\) | 1.15084 | 0.0472196 | ||||||||
\(595\) | 0.336494 | + | 0.167692i | 0.0137949 | + | 0.00687471i | ||||
\(596\) | 7.81597 | 0.320155 | ||||||||
\(597\) | −3.79025 | + | 6.56490i | −0.155124 | + | 0.268684i | ||||
\(598\) | 3.09257 | + | 5.35648i | 0.126464 | + | 0.219043i | ||||
\(599\) | 15.3624 | + | 26.6084i | 0.627689 | + | 1.08719i | 0.988014 | + | 0.154363i | \(0.0493325\pi\) |
−0.360325 | + | 0.932827i | \(0.617334\pi\) | |||||||
\(600\) | −1.76702 | + | 3.06057i | −0.0721384 | + | 0.124947i | ||||
\(601\) | 32.5720 | 1.32864 | 0.664320 | − | 0.747448i | \(-0.268721\pi\) | ||||
0.664320 | + | 0.747448i | \(0.268721\pi\) | |||||||
\(602\) | 7.26877 | − | 4.81303i | 0.296253 | − | 0.196164i | ||||
\(603\) | −12.3386 | −0.502465 | ||||||||
\(604\) | 8.10878 | − | 14.0448i | 0.329941 | − | 0.571475i | ||||
\(605\) | 1.27239 | + | 2.20385i | 0.0517301 | + | 0.0895992i | ||||
\(606\) | 5.62154 | + | 9.73680i | 0.228360 | + | 0.395530i | ||||
\(607\) | 0.960031 | − | 1.66282i | 0.0389664 | − | 0.0674919i | −0.845884 | − | 0.533366i | \(-0.820927\pi\) |
0.884851 | + | 0.465874i | \(0.154260\pi\) | |||||||
\(608\) | 6.67740 | 0.270804 | ||||||||
\(609\) | −0.115767 | − | 1.88705i | −0.00469110 | − | 0.0764671i | ||||
\(610\) | 0.850606 | 0.0344400 | ||||||||
\(611\) | −4.53347 | + | 7.85219i | −0.183404 | + | 0.317666i | ||||
\(612\) | 0.758557 | + | 1.31386i | 0.0306628 | + | 0.0531096i | ||||
\(613\) | 14.4028 | + | 24.9463i | 0.581722 | + | 1.00757i | 0.995275 | + | 0.0970922i | \(0.0309542\pi\) |
−0.413553 | + | 0.910480i | \(0.635713\pi\) | |||||||
\(614\) | 14.3270 | − | 24.8151i | 0.578191 | − | 1.00146i | ||||
\(615\) | −0.552511 | −0.0222794 | ||||||||
\(616\) | −0.0475309 | − | 0.774776i | −0.00191507 | − | 0.0312166i | ||||
\(617\) | 41.9416 | 1.68850 | 0.844252 | − | 0.535946i | \(-0.180045\pi\) | ||||
0.844252 | + | 0.535946i | \(0.180045\pi\) | |||||||
\(618\) | −1.74911 | + | 3.02954i | −0.0703595 | + | 0.121866i | ||||
\(619\) | 0.376352 | + | 0.651862i | 0.0151269 | + | 0.0262005i | 0.873490 | − | 0.486843i | \(-0.161851\pi\) |
−0.858363 | + | 0.513043i | \(0.828518\pi\) | |||||||
\(620\) | 0.157593 | + | 0.272959i | 0.00632908 | + | 0.0109623i | ||||
\(621\) | 2.91790 | − | 5.05396i | 0.117091 | − | 0.202808i | ||||
\(622\) | 10.4647 | 0.419596 | ||||||||
\(623\) | 27.8498 | − | 18.4408i | 1.11578 | − | 0.738815i | ||||
\(624\) | −2.97079 | −0.118927 | ||||||||
\(625\) | −12.0937 | + | 20.9469i | −0.483749 | + | 0.837878i | ||||
\(626\) | 15.7086 | + | 27.2081i | 0.627841 | + | 1.08745i | ||||
\(627\) | 0.699955 | + | 1.21236i | 0.0279535 | + | 0.0484169i | ||||
\(628\) | 11.8227 | − | 20.4776i | 0.471778 | − | 0.817144i | ||||
\(629\) | 0.388314 | 0.0154831 | ||||||||
\(630\) | −1.37449 | − | 0.684978i | −0.0547609 | − | 0.0272902i | ||||
\(631\) | −36.3961 | −1.44891 | −0.724453 | − | 0.689325i | \(-0.757907\pi\) | ||||
−0.724453 | + | 0.689325i | \(0.757907\pi\) | |||||||
\(632\) | −1.05339 | + | 1.82452i | −0.0419016 | + | 0.0725757i | ||||
\(633\) | −3.10492 | − | 5.37787i | −0.123409 | − | 0.213751i | ||||
\(634\) | −6.37389 | − | 11.0399i | −0.253139 | − | 0.438450i | ||||
\(635\) | 1.78436 | − | 3.09061i | 0.0708103 | − | 0.122647i | ||||
\(636\) | −8.56937 | −0.339797 | ||||||||
\(637\) | 17.5225 | + | 23.2352i | 0.694265 | + | 0.920614i | ||||
\(638\) | −0.293388 | −0.0116153 | ||||||||
\(639\) | 5.24146 | − | 9.07848i | 0.207349 | − | 0.359139i | ||||
\(640\) | −0.116584 | − | 0.201930i | −0.00460840 | − | 0.00798198i | ||||
\(641\) | 10.2287 | + | 17.7167i | 0.404010 | + | 0.699766i | 0.994206 | − | 0.107494i | \(-0.0342827\pi\) |
−0.590195 | + | 0.807260i | \(0.700949\pi\) | |||||||
\(642\) | 4.01289 | − | 6.95052i | 0.158376 | − | 0.274315i | ||||
\(643\) | −36.0350 | −1.42108 | −0.710541 | − | 0.703656i | \(-0.751550\pi\) | ||||
−0.710541 | + | 0.703656i | \(0.751550\pi\) | |||||||
\(644\) | −3.52296 | − | 1.75567i | −0.138824 | − | 0.0691831i | ||||
\(645\) | 0.549008 | 0.0216172 | ||||||||
\(646\) | −2.03472 | + | 3.52424i | −0.0800550 | + | 0.138659i | ||||
\(647\) | −21.3888 | − | 37.0464i | −0.840879 | − | 1.45645i | −0.889152 | − | 0.457611i | \(-0.848705\pi\) |
0.0482734 | − | 0.998834i | \(-0.484628\pi\) | |||||||
\(648\) | −2.33257 | − | 4.04012i | −0.0916318 | − | 0.158711i | ||||
\(649\) | −0.630951 | + | 1.09284i | −0.0247670 | + | 0.0428977i | ||||
\(650\) | −20.5610 | −0.806467 | ||||||||
\(651\) | −2.13083 | + | 1.41093i | −0.0835139 | + | 0.0552988i | ||||
\(652\) | −13.6125 | −0.533106 | ||||||||
\(653\) | −14.0161 | + | 24.2766i | −0.548493 | + | 0.950017i | 0.449885 | + | 0.893086i | \(0.351465\pi\) |
−0.998378 | + | 0.0569310i | \(0.981868\pi\) | |||||||
\(654\) | 5.42599 | + | 9.39809i | 0.212173 | + | 0.367495i | ||||
\(655\) | −1.42437 | − | 2.46709i | −0.0556549 | − | 0.0963972i | ||||
\(656\) | −1.65802 | + | 2.87178i | −0.0647349 | + | 0.112124i | ||||
\(657\) | −14.5454 | −0.567470 | ||||||||
\(658\) | −0.353323 | − | 5.75933i | −0.0137740 | − | 0.224522i | ||||
\(659\) | 36.2772 | 1.41316 | 0.706579 | − | 0.707634i | \(-0.250238\pi\) | ||||
0.706579 | + | 0.707634i | \(0.250238\pi\) | |||||||
\(660\) | 0.0244418 | − | 0.0423344i | 0.000951395 | − | 0.00164786i | ||||
\(661\) | 3.01525 | + | 5.22256i | 0.117279 | + | 0.203134i | 0.918689 | − | 0.394983i | \(-0.129249\pi\) |
−0.801409 | + | 0.598116i | \(0.795916\pi\) | |||||||
\(662\) | 5.13096 | + | 8.88709i | 0.199421 | + | 0.345406i | ||||
\(663\) | 0.905251 | − | 1.56794i | 0.0351570 | − | 0.0608938i | ||||
\(664\) | 6.73621 | 0.261415 | ||||||||
\(665\) | −0.252238 | − | 4.11160i | −0.00978138 | − | 0.159441i | ||||
\(666\) | −1.58616 | −0.0614624 | ||||||||
\(667\) | −0.743871 | + | 1.28842i | −0.0288028 | + | 0.0498879i | ||||
\(668\) | 1.79855 | + | 3.11518i | 0.0695880 | + | 0.120530i | ||||
\(669\) | 3.57069 | + | 6.18461i | 0.138051 | + | 0.239111i | ||||
\(670\) | −0.577849 | + | 1.00086i | −0.0223242 | + | 0.0386667i | ||||
\(671\) | 1.07029 | 0.0413180 | ||||||||
\(672\) | 1.57635 | − | 1.04378i | 0.0608090 | − | 0.0402648i | ||||
\(673\) | 16.7412 | 0.645327 | 0.322663 | − | 0.946514i | \(-0.395422\pi\) | ||||
0.322663 | + | 0.946514i | \(0.395422\pi\) | |||||||
\(674\) | 13.4934 | − | 23.3713i | 0.519747 | − | 0.900228i | ||||
\(675\) | 9.69985 | + | 16.8006i | 0.373347 | + | 0.646657i | ||||
\(676\) | −2.14197 | − | 3.71001i | −0.0823836 | − | 0.142693i | ||||
\(677\) | −20.4963 | + | 35.5007i | −0.787737 | + | 1.36440i | 0.139613 | + | 0.990206i | \(0.455414\pi\) |
−0.927350 | + | 0.374195i | \(0.877919\pi\) | |||||||
\(678\) | 7.35845 | 0.282600 | ||||||||
\(679\) | 13.5093 | + | 6.73239i | 0.518441 | + | 0.258366i | ||||
\(680\) | 0.142101 | 0.00544933 | ||||||||
\(681\) | −9.04265 | + | 15.6623i | −0.346515 | + | 0.600182i | ||||
\(682\) | 0.198294 | + | 0.343455i | 0.00759306 | + | 0.0131516i | ||||
\(683\) | 17.0734 | + | 29.5720i | 0.653296 | + | 1.13154i | 0.982318 | + | 0.187220i | \(0.0599477\pi\) |
−0.329022 | + | 0.944322i | \(0.606719\pi\) | |||||||
\(684\) | 8.31128 | − | 14.3956i | 0.317790 | − | 0.550428i | ||||
\(685\) | 4.15719 | 0.158838 | ||||||||
\(686\) | −17.4614 | − | 6.17252i | −0.666679 | − | 0.235668i | ||||
\(687\) | −13.2043 | −0.503776 | ||||||||
\(688\) | 1.64751 | − | 2.85357i | 0.0628108 | − | 0.108791i | ||||
\(689\) | −24.9281 | − | 43.1768i | −0.949687 | − | 1.64491i | ||||
\(690\) | −0.123942 | − | 0.214674i | −0.00471838 | − | 0.00817248i | ||||
\(691\) | 11.3172 | − | 19.6019i | 0.430525 | − | 0.745692i | −0.566393 | − | 0.824135i | \(-0.691662\pi\) |
0.996919 | + | 0.0784434i | \(0.0249950\pi\) | |||||||
\(692\) | 12.3956 | 0.471212 | ||||||||
\(693\) | −1.72947 | − | 0.861884i | −0.0656972 | − | 0.0327403i | ||||
\(694\) | 0.0299869 | 0.00113829 | ||||||||
\(695\) | −0.932502 | + | 1.61514i | −0.0353718 | + | 0.0612658i | ||||
\(696\) | −0.357289 | − | 0.618843i | −0.0135430 | − | 0.0234572i | ||||
\(697\) | −1.01046 | − | 1.75016i | −0.0382738 | − | 0.0662922i | ||||
\(698\) | −3.15014 | + | 5.45620i | −0.119234 | + | 0.206520i | ||||
\(699\) | 6.68780 | 0.252956 | ||||||||
\(700\) | 10.9100 | − | 7.22406i | 0.412359 | − | 0.273044i | ||||
\(701\) | −15.1951 | −0.573911 | −0.286955 | − | 0.957944i | \(-0.592643\pi\) | ||||
−0.286955 | + | 0.957944i | \(0.592643\pi\) | |||||||
\(702\) | −8.15389 | + | 14.1229i | −0.307749 | + | 0.533036i | ||||
\(703\) | −2.12732 | − | 3.68463i | −0.0802335 | − | 0.138969i | ||||
\(704\) | −0.146694 | − | 0.254082i | −0.00552874 | − | 0.00957606i | ||||
\(705\) | 0.181689 | − | 0.314695i | 0.00684281 | − | 0.0118521i | ||||
\(706\) | 27.6344 | 1.04003 | ||||||||
\(707\) | −2.54899 | − | 41.5498i | −0.0958648 | − | 1.56264i | ||||
\(708\) | −3.07350 | −0.115509 | ||||||||
\(709\) | −4.00781 | + | 6.94172i | −0.150516 | + | 0.260702i | −0.931417 | − | 0.363953i | \(-0.881427\pi\) |
0.780901 | + | 0.624655i | \(0.214760\pi\) | |||||||
\(710\) | −0.490944 | − | 0.850340i | −0.0184248 | − | 0.0319127i | ||||
\(711\) | 2.62228 | + | 4.54193i | 0.0983433 | + | 0.170336i | ||||
\(712\) | 6.31233 | − | 10.9333i | 0.236565 | − | 0.409742i | ||||
\(713\) | 2.01106 | 0.0753146 | ||||||||
\(714\) | 0.0705523 | + | 1.15003i | 0.00264035 | + | 0.0430390i | ||||
\(715\) | 0.284403 | 0.0106361 | ||||||||
\(716\) | −4.79172 | + | 8.29950i | −0.179075 | + | 0.310167i | ||||
\(717\) | −6.26772 | − | 10.8560i | −0.234072 | − | 0.405425i | ||||
\(718\) | 9.23986 | + | 16.0039i | 0.344828 | + | 0.597260i | ||||
\(719\) | −1.08801 | + | 1.88448i | −0.0405757 | + | 0.0702793i | −0.885600 | − | 0.464449i | \(-0.846253\pi\) |
0.845024 | + | 0.534728i | \(0.179586\pi\) | |||||||
\(720\) | −0.580445 | −0.0216319 | ||||||||
\(721\) | 10.7994 | − | 7.15083i | 0.402190 | − | 0.266311i | ||||
\(722\) | 25.5877 | 0.952274 | ||||||||
\(723\) | 1.08697 | − | 1.88268i | 0.0404247 | − | 0.0700177i | ||||
\(724\) | −0.0743276 | − | 0.128739i | −0.00276236 | − | 0.00478455i | ||||
\(725\) | −2.47282 | − | 4.28304i | −0.0918381 | − | 0.159068i | ||||
\(726\) | −3.89943 | + | 6.75401i | −0.144721 | + | 0.250665i | ||||
\(727\) | −53.7791 | −1.99456 | −0.997278 | − | 0.0737366i | \(-0.976508\pi\) | ||||
−0.997278 | + | 0.0737366i | \(0.976508\pi\) | |||||||
\(728\) | 9.84468 | + | 4.90611i | 0.364868 | + | 0.181832i | ||||
\(729\) | −3.20426 | −0.118676 | ||||||||
\(730\) | −0.681200 | + | 1.17987i | −0.0252124 | + | 0.0436691i | ||||
\(731\) | 1.00405 | + | 1.73907i | 0.0371362 | + | 0.0643217i | ||||
\(732\) | 1.30340 | + | 2.25756i | 0.0481751 | + | 0.0834417i | ||||
\(733\) | −13.3872 | + | 23.1874i | −0.494469 | + | 0.856445i | −0.999980 | − | 0.00637498i | \(-0.997971\pi\) |
0.505511 | + | 0.862820i | \(0.331304\pi\) | |||||||
\(734\) | −17.7335 | −0.654556 | ||||||||
\(735\) | −0.702254 | − | 0.931206i | −0.0259030 | − | 0.0343481i | ||||
\(736\) | −1.48774 | −0.0548389 | ||||||||
\(737\) | −0.727088 | + | 1.25935i | −0.0267826 | + | 0.0463889i | ||||
\(738\) | 4.12745 | + | 7.14895i | 0.151933 | + | 0.263156i | ||||
\(739\) | −14.6468 | − | 25.3690i | −0.538791 | − | 0.933213i | −0.998969 | − | 0.0453869i | \(-0.985548\pi\) |
0.460179 | − | 0.887826i | \(-0.347785\pi\) | |||||||
\(740\) | −0.0742842 | + | 0.128664i | −0.00273074 | + | 0.00472978i | ||||
\(741\) | −19.8371 | −0.728735 | ||||||||
\(742\) | 28.3974 | + | 14.1519i | 1.04250 | + | 0.519532i | ||||
\(743\) | 6.53498 | 0.239745 | 0.119873 | − | 0.992789i | \(-0.461751\pi\) | ||||
0.119873 | + | 0.992789i | \(0.461751\pi\) | |||||||
\(744\) | −0.482966 | + | 0.836522i | −0.0177064 | + | 0.0306684i | ||||
\(745\) | −0.911220 | − | 1.57828i | −0.0333845 | − | 0.0578237i | ||||
\(746\) | −7.11961 | − | 12.3315i | −0.260667 | − | 0.451489i | ||||
\(747\) | 8.38448 | − | 14.5223i | 0.306772 | − | 0.531345i | ||||
\(748\) | 0.178801 | 0.00653761 | ||||||||
\(749\) | −24.7765 | + | 16.4058i | −0.905312 | + | 0.599453i | ||||
\(750\) | 1.65712 | 0.0605093 | ||||||||
\(751\) | −15.0999 | + | 26.1537i | −0.551002 | + | 0.954363i | 0.447201 | + | 0.894434i | \(0.352421\pi\) |
−0.998203 | + | 0.0599296i | \(0.980912\pi\) | |||||||
\(752\) | −1.09046 | − | 1.88873i | −0.0397649 | − | 0.0688748i | ||||
\(753\) | −6.15519 | − | 10.6611i | −0.224308 | − | 0.388512i | ||||
\(754\) | 2.07870 | − | 3.60041i | 0.0757017 | − | 0.131119i | ||||
\(755\) | −3.78142 | −0.137620 | ||||||||
\(756\) | −0.635487 | − | 10.3587i | −0.0231124 | − | 0.376743i | ||||
\(757\) | −26.5008 | −0.963189 | −0.481595 | − | 0.876394i | \(-0.659942\pi\) | ||||
−0.481595 | + | 0.876394i | \(0.659942\pi\) | |||||||
\(758\) | −16.9939 | + | 29.4344i | −0.617248 | + | 1.06910i | ||||
\(759\) | −0.155952 | − | 0.270116i | −0.00566069 | − | 0.00980460i | ||||
\(760\) | −0.778480 | − | 1.34837i | −0.0282384 | − | 0.0489104i | ||||
\(761\) | −2.18705 | + | 3.78808i | −0.0792805 | + | 0.137318i | −0.902940 | − | 0.429767i | \(-0.858596\pi\) |
0.823659 | + | 0.567085i | \(0.191929\pi\) | |||||||
\(762\) | 10.9369 | 0.396201 | ||||||||
\(763\) | −2.46032 | − | 40.1044i | −0.0890697 | − | 1.45188i | ||||
\(764\) | 10.2831 | 0.372029 | ||||||||
\(765\) | 0.176872 | − | 0.306351i | 0.00639481 | − | 0.0110761i | ||||
\(766\) | 8.54059 | + | 14.7927i | 0.308584 | + | 0.534483i | ||||
\(767\) | −8.94076 | − | 15.4858i | −0.322832 | − | 0.559161i | ||||
\(768\) | 0.357289 | − | 0.618843i | 0.0128926 | − | 0.0223306i | ||||
\(769\) | 43.7523 | 1.57775 | 0.788874 | − | 0.614555i | \(-0.210665\pi\) | ||||
0.788874 | + | 0.614555i | \(0.210665\pi\) | |||||||
\(770\) | −0.150909 | + | 0.0999246i | −0.00543838 | + | 0.00360103i | ||||
\(771\) | −14.7528 | −0.531309 | ||||||||
\(772\) | −6.23407 | + | 10.7977i | −0.224369 | + | 0.388618i | ||||
\(773\) | −7.17176 | − | 12.4219i | −0.257950 | − | 0.446783i | 0.707742 | − | 0.706471i | \(-0.249714\pi\) |
−0.965693 | + | 0.259687i | \(0.916380\pi\) | |||||||
\(774\) | −4.10128 | − | 7.10362i | −0.147417 | − | 0.255334i | ||||
\(775\) | −3.34263 | + | 5.78960i | −0.120071 | + | 0.207969i | ||||
\(776\) | 5.70498 | 0.204797 | ||||||||
\(777\) | −1.07817 | − | 0.537306i | −0.0386791 | − | 0.0192758i | ||||
\(778\) | −11.3176 | −0.405757 | ||||||||
\(779\) | −11.0713 | + | 19.1760i | −0.396670 | + | 0.687052i | ||||
\(780\) | 0.346347 | + | 0.599891i | 0.0124012 | + | 0.0214795i | ||||
\(781\) | −0.617738 | − | 1.06995i | −0.0221044 | − | 0.0382859i | ||||
\(782\) | 0.453341 | − | 0.785210i | 0.0162114 | − | 0.0280790i | ||||
\(783\) | −3.92259 | −0.140182 | ||||||||
\(784\) | −6.94751 | + | 0.855651i | −0.248125 | + | 0.0305590i | ||||
\(785\) | −5.51338 | −0.196781 | ||||||||
\(786\) | 4.36520 | − | 7.56075i | 0.155702 | − | 0.269683i | ||||
\(787\) | 15.8209 | + | 27.4025i | 0.563953 | + | 0.976794i | 0.997146 | + | 0.0754936i | \(0.0240532\pi\) |
−0.433194 | + | 0.901301i | \(0.642613\pi\) | |||||||
\(788\) | 9.51558 | + | 16.4815i | 0.338979 | + | 0.587128i | ||||
\(789\) | −5.92051 | + | 10.2546i | −0.210776 | + | 0.365074i | ||||
\(790\) | 0.491235 | 0.0174773 | ||||||||
\(791\) | −24.3846 | − | 12.1521i | −0.867018 | − | 0.432079i | ||||
\(792\) | −0.730354 | −0.0259520 | ||||||||
\(793\) | −7.58315 | + | 13.1344i | −0.269285 | + | 0.466416i | ||||
\(794\) | −5.12573 | − | 8.87803i | −0.181905 | − | 0.315069i | ||||
\(795\) | 0.999054 | + | 1.73041i | 0.0354328 | + | 0.0613714i | ||||
\(796\) | 5.30417 | − | 9.18709i | 0.188001 | − | 0.325628i | ||||
\(797\) | −12.6909 | −0.449536 | −0.224768 | − | 0.974412i | \(-0.572162\pi\) | ||||
−0.224768 | + | 0.974412i | \(0.572162\pi\) | |||||||
\(798\) | 10.5259 | − | 6.96975i | 0.372613 | − | 0.246726i | ||||
\(799\) | 1.32913 | 0.0470211 | ||||||||
\(800\) | 2.47282 | − | 4.28304i | 0.0874273 | − | 0.151428i | ||||
\(801\) | −15.7138 | − | 27.2171i | −0.555219 | − | 0.961668i | ||||
\(802\) | 8.80508 | + | 15.2509i | 0.310918 | + | 0.538526i | ||||
\(803\) | −0.857131 | + | 1.48460i | −0.0302475 | + | 0.0523902i | ||||
\(804\) | −3.54180 | −0.124910 | ||||||||
\(805\) | 0.0561993 | + | 0.916075i | 0.00198077 | + | 0.0322874i | ||||
\(806\) | −5.61976 | −0.197948 | ||||||||
\(807\) | −0.939049 | + | 1.62648i | −0.0330561 | + | 0.0572548i | ||||
\(808\) | −7.86693 | − | 13.6259i | −0.276758 | − | 0.479359i | ||||
\(809\) | −5.29226 | − | 9.16647i | −0.186066 | − | 0.322276i | 0.757869 | − | 0.652407i | \(-0.226241\pi\) |
−0.943935 | + | 0.330131i | \(0.892907\pi\) | |||||||
\(810\) | −0.543881 | + | 0.942030i | −0.0191100 | + | 0.0330995i | ||||
\(811\) | −47.2614 | −1.65957 | −0.829786 | − | 0.558082i | \(-0.811537\pi\) | ||||
−0.829786 | + | 0.558082i | \(0.811537\pi\) | |||||||
\(812\) | 0.162007 | + | 2.64079i | 0.00568533 | + | 0.0926734i | ||||
\(813\) | 9.01969 | 0.316334 | ||||||||
\(814\) | −0.0934693 | + | 0.161894i | −0.00327610 | + | 0.00567436i | ||||
\(815\) | 1.58700 | + | 2.74877i | 0.0555903 | + | 0.0962851i | ||||
\(816\) | 0.217745 | + | 0.377145i | 0.00762259 | + | 0.0132027i | ||||
\(817\) | 11.0011 | − | 19.0545i | 0.384880 | − | 0.666631i | ||||
\(818\) | −38.8959 | −1.35996 | ||||||||
\(819\) | 22.8305 | − | 15.1172i | 0.797761 | − | 0.528238i | ||||
\(820\) | 0.773198 | 0.0270012 | ||||||||
\(821\) | 0.410163 | − | 0.710423i | 0.0143148 | − | 0.0247939i | −0.858779 | − | 0.512346i | \(-0.828777\pi\) |
0.873094 | + | 0.487552i | \(0.162110\pi\) | |||||||
\(822\) | 6.37015 | + | 11.0334i | 0.222184 | + | 0.384835i | ||||
\(823\) | −20.5851 | − | 35.6544i | −0.717551 | − | 1.24283i | −0.961967 | − | 0.273165i | \(-0.911930\pi\) |
0.244416 | − | 0.969670i | \(-0.421404\pi\) | |||||||
\(824\) | 2.44775 | − | 4.23962i | 0.0852713 | − | 0.147694i | ||||
\(825\) | 1.03685 | 0.0360984 | ||||||||
\(826\) | 10.1850 | + | 5.07573i | 0.354383 | + | 0.176607i | ||||
\(827\) | −24.2372 | −0.842810 | −0.421405 | − | 0.906872i | \(-0.638463\pi\) | ||||
−0.421405 | + | 0.906872i | \(0.638463\pi\) | |||||||
\(828\) | −1.85178 | + | 3.20737i | −0.0643536 | + | 0.111464i | ||||
\(829\) | 14.8873 | + | 25.7855i | 0.517057 | + | 0.895568i | 0.999804 | + | 0.0198086i | \(0.00630570\pi\) |
−0.482747 | + | 0.875760i | \(0.660361\pi\) | |||||||
\(830\) | −0.785336 | − | 1.36024i | −0.0272594 | − | 0.0472147i | ||||
\(831\) | 6.95269 | − | 12.0424i | 0.241186 | − | 0.417747i | ||||
\(832\) | 4.15740 | 0.144132 | ||||||||
\(833\) | 1.66543 | − | 3.92753i | 0.0577036 | − | 0.136081i | ||||
\(834\) | −5.71558 | −0.197914 | ||||||||
\(835\) | 0.419366 | − | 0.726363i | 0.0145127 | − | 0.0251368i | ||||
\(836\) | −0.979535 | − | 1.69660i | −0.0338779 | − | 0.0586783i | ||||
\(837\) | 2.65118 | + | 4.59198i | 0.0916383 | + | 0.158722i | ||||
\(838\) | 6.32183 | − | 10.9497i | 0.218384 | − | 0.378252i | ||||
\(839\) | 14.8726 | 0.513459 | 0.256730 | − | 0.966483i | \(-0.417355\pi\) | ||||
0.256730 | + | 0.966483i | \(0.417355\pi\) | |||||||
\(840\) | −0.394549 | − | 0.196624i | −0.0136132 | − | 0.00678416i | ||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 5.39905 | − | 9.35143i | 0.186063 | − | 0.322271i | ||||
\(843\) | 5.71326 | + | 9.89565i | 0.196775 | + | 0.340824i | ||||
\(844\) | 4.34510 | + | 7.52593i | 0.149564 | + | 0.259053i | ||||
\(845\) | −0.499441 | + | 0.865057i | −0.0171813 | + | 0.0297589i | ||||
\(846\) | −5.42912 | −0.186657 | ||||||||
\(847\) | 24.0759 | − | 15.9419i | 0.827259 | − | 0.547771i | ||||
\(848\) | 11.9922 | 0.411814 | ||||||||
\(849\) | 9.99792 | − | 17.3169i | 0.343128 | − | 0.594314i | ||||
\(850\) | 1.50702 | + | 2.61024i | 0.0516904 | + | 0.0895304i | ||||
\(851\) | 0.473973 | + | 0.820946i | 0.0162476 | + | 0.0281417i | ||||
\(852\) | 1.50457 | − | 2.60599i | 0.0515456 | − | 0.0892797i | ||||
\(853\) | 48.2468 | 1.65194 | 0.825970 | − | 0.563715i | \(-0.190628\pi\) | ||||
0.825970 | + | 0.563715i | \(0.190628\pi\) | |||||||
\(854\) | −0.591006 | − | 9.63366i | −0.0202238 | − | 0.329657i | ||||
\(855\) | −3.87586 | −0.132552 | ||||||||
\(856\) | −5.61573 | + | 9.72674i | −0.191942 | + | 0.332453i | ||||
\(857\) | 11.1442 | + | 19.3023i | 0.380677 | + | 0.659352i | 0.991159 | − | 0.132678i | \(-0.0423576\pi\) |
−0.610482 | + | 0.792030i | \(0.709024\pi\) | |||||||
\(858\) | 0.435797 | + | 0.754822i | 0.0148779 | + | 0.0257692i | ||||
\(859\) | −16.5053 | + | 28.5881i | −0.563155 | + | 0.975413i | 0.434063 | + | 0.900882i | \(0.357079\pi\) |
−0.997219 | + | 0.0745311i | \(0.976254\pi\) | |||||||
\(860\) | −0.768296 | −0.0261987 | ||||||||
\(861\) | 0.383888 | + | 6.25755i | 0.0130829 | + | 0.213257i | ||||
\(862\) | −36.1812 | −1.23234 | ||||||||
\(863\) | −1.49100 | + | 2.58249i | −0.0507543 | + | 0.0879090i | −0.890286 | − | 0.455401i | \(-0.849496\pi\) |
0.839532 | + | 0.543310i | \(0.182829\pi\) | |||||||
\(864\) | −1.96130 | − | 3.39706i | −0.0667247 | − | 0.115570i | ||||
\(865\) | −1.44514 | − | 2.50305i | −0.0491361 | − | 0.0851063i | ||||
\(866\) | −5.31749 | + | 9.21016i | −0.180696 | + | 0.312974i | ||||
\(867\) | 11.8824 | 0.403549 | ||||||||
\(868\) | 2.98194 | − | 1.97450i | 0.101214 | − | 0.0670187i | ||||
\(869\) | 0.618104 | 0.0209677 | ||||||||
\(870\) | −0.0833087 | + | 0.144295i | −0.00282443 | + | 0.00489205i | ||||
\(871\) | −10.3030 | − | 17.8454i | −0.349105 | − | 0.604668i | ||||
\(872\) | −7.59327 | − | 13.1519i | −0.257141 | − | 0.445381i | ||||
\(873\) | 7.10092 | − | 12.2992i | 0.240330 | − | 0.416263i | ||||
\(874\) | −9.93425 | −0.336031 | ||||||||
\(875\) | −5.49140 | − | 2.73664i | −0.185643 | − | 0.0925154i | ||||
\(876\) | −4.17527 | −0.141069 | ||||||||
\(877\) | 4.80059 | − | 8.31486i | 0.162104 | − | 0.280773i | −0.773519 | − | 0.633773i | \(-0.781505\pi\) |
0.935623 | + | 0.353000i | \(0.114839\pi\) | |||||||
\(878\) | 1.48753 | + | 2.57648i | 0.0502018 | + | 0.0869521i | ||||
\(879\) | 7.39036 | + | 12.8005i | 0.249271 | + | 0.431750i | ||||
\(880\) | −0.0342045 | + | 0.0592439i | −0.00115303 | + | 0.00199711i | ||||
\(881\) | 11.0461 | 0.372153 | 0.186076 | − | 0.982535i | \(-0.440423\pi\) | ||||
0.186076 | + | 0.982535i | \(0.440423\pi\) | |||||||
\(882\) | −6.80282 | + | 16.0429i | −0.229063 | + | 0.540193i | ||||
\(883\) | −30.8011 | −1.03654 | −0.518269 | − | 0.855218i | \(-0.673423\pi\) | ||||
−0.518269 | + | 0.855218i | \(0.673423\pi\) | |||||||
\(884\) | −1.26683 | + | 2.19422i | −0.0426081 | + | 0.0737995i | ||||
\(885\) | 0.358322 | + | 0.620631i | 0.0120449 | + | 0.0208623i | ||||
\(886\) | 13.9715 | + | 24.1993i | 0.469380 | + | 0.812990i | ||||
\(887\) | 19.5367 | − | 33.8386i | 0.655980 | − | 1.13619i | −0.325667 | − | 0.945484i | \(-0.605589\pi\) |
0.981647 | − | 0.190706i | \(-0.0610777\pi\) | |||||||
\(888\) | −0.455309 | −0.0152792 | ||||||||
\(889\) | −36.2429 | − | 18.0617i | −1.21555 | − | 0.605770i | ||||
\(890\) | −2.94368 | −0.0986723 | ||||||||
\(891\) | −0.684347 | + | 1.18532i | −0.0229265 | + | 0.0397098i | ||||
\(892\) | −4.99691 | − | 8.65491i | −0.167309 | − | 0.289788i | ||||
\(893\) | −7.28142 | − | 12.6118i | −0.243664 | − | 0.422038i | ||||
\(894\) | 2.79256 | − | 4.83686i | 0.0933973 | − | 0.161769i | ||||
\(895\) | 2.23456 | 0.0746930 | ||||||||
\(896\) | −2.20598 | + | 1.46070i | −0.0736968 | + | 0.0487984i | ||||
\(897\) | 4.41976 | 0.147572 | ||||||||
\(898\) | 0.302215 | − | 0.523452i | 0.0100851 | − | 0.0174678i | ||||
\(899\) | −0.675875 | − | 1.17065i | −0.0225417 | − | 0.0390434i | ||||
\(900\) | −6.15577 | − | 10.6621i | −0.205192 | − | 0.355404i | ||||
\(901\) | −3.65423 | + | 6.32931i | −0.121740 | + | 0.210860i | ||||
\(902\) | 0.972889 | 0.0323937 | ||||||||
\(903\) | −0.381454 | − | 6.21787i | −0.0126940 | − | 0.206918i | ||||
\(904\) | −10.2976 | −0.342493 | ||||||||
\(905\) | −0.0173309 | + | 0.0300179i | −0.000576097 | + | 0.000997830i | ||||
\(906\) | −5.79436 | − | 10.0361i | −0.192505 | − | 0.333428i | ||||
\(907\) | 0.206207 | + | 0.357160i | 0.00684697 | + | 0.0118593i | 0.869429 | − | 0.494059i | \(-0.164487\pi\) |
−0.862582 | + | 0.505918i | \(0.831154\pi\) | |||||||
\(908\) | 12.6545 | − | 21.9183i | 0.419955 | − | 0.727383i | ||||
\(909\) | −39.1675 | −1.29911 | ||||||||
\(910\) | −0.157045 | − | 2.55991i | −0.00520600 | − | 0.0848602i | ||||
\(911\) | 31.6863 | 1.04981 | 0.524907 | − | 0.851160i | \(-0.324100\pi\) | ||||
0.524907 | + | 0.851160i | \(0.324100\pi\) | |||||||
\(912\) | 2.38576 | − | 4.13226i | 0.0790005 | − | 0.136833i | ||||
\(913\) | −0.988162 | − | 1.71155i | −0.0327034 | − | 0.0566439i | ||||
\(914\) | 3.55156 | + | 6.15148i | 0.117475 | + | 0.203473i | ||||
\(915\) | 0.303912 | − | 0.526392i | 0.0100470 | − | 0.0174020i | ||||
\(916\) | 18.4785 | 0.610545 | ||||||||
\(917\) | −26.9517 | + | 17.8461i | −0.890025 | + | 0.589331i | ||||
\(918\) | 2.39057 | 0.0789004 | ||||||||
\(919\) | 27.5749 | − | 47.7611i | 0.909611 | − | 1.57549i | 0.0950047 | − | 0.995477i | \(-0.469713\pi\) |
0.814606 | − | 0.580015i | \(-0.196953\pi\) | |||||||
\(920\) | 0.173447 | + | 0.300420i | 0.00571839 | + | 0.00990454i | ||||
\(921\) | −10.2378 | − | 17.7324i | −0.337346 | − | 0.584301i | ||||
\(922\) | −1.90514 | + | 3.29980i | −0.0627424 | + | 0.108673i | ||||
\(923\) | 17.5071 | 0.576252 | ||||||||
\(924\) | −0.496447 | − | 0.247405i | −0.0163319 | − | 0.00813902i | ||||
\(925\) | −3.15122 | −0.103611 | ||||||||
\(926\) | 1.71164 | − | 2.96464i | 0.0562478 | − | 0.0974241i | ||||
\(927\) | −6.09337 | − | 10.5540i | −0.200132 | − | 0.346640i | ||||
\(928\) | 0.500000 | + | 0.866025i | 0.0164133 | + | 0.0284287i | ||||
\(929\) | −19.8498 | + | 34.3809i | −0.651251 | + | 1.12800i | 0.331569 | + | 0.943431i | \(0.392422\pi\) |
−0.982820 | + | 0.184568i | \(0.940911\pi\) | |||||||
\(930\) | 0.225225 | 0.00738542 | ||||||||
\(931\) | −46.3913 | + | 5.71352i | −1.52041 | + | 0.187253i | ||||
\(932\) | −9.35908 | −0.306567 | ||||||||
\(933\) | 3.73893 | − | 6.47601i | 0.122407 | − | 0.212015i | ||||
\(934\) | −11.4351 | − | 19.8061i | −0.374166 | − | 0.648075i | ||||
\(935\) | −0.0208454 | − | 0.0361053i | −0.000681717 | − | 0.00118077i | ||||
\(936\) | 5.17466 | − | 8.96278i | 0.169139 | − | 0.292958i | ||||
\(937\) | 2.47672 | 0.0809108 | 0.0404554 | − | 0.999181i | \(-0.487119\pi\) | ||||
0.0404554 | + | 0.999181i | \(0.487119\pi\) | |||||||
\(938\) | 11.7369 | + | 5.84911i | 0.383224 | + | 0.190980i | ||||
\(939\) | 22.4500 | 0.732629 | ||||||||
\(940\) | −0.254261 | + | 0.440392i | −0.00829307 | + | 0.0143640i | ||||
\(941\) | −12.5890 | − | 21.8048i | −0.410390 | − | 0.710817i | 0.584542 | − | 0.811363i | \(-0.301274\pi\) |
−0.994932 | + | 0.100547i | \(0.967941\pi\) | |||||||
\(942\) | −8.44827 | − | 14.6328i | −0.275260 | − | 0.476764i | ||||
\(943\) | 2.46671 | − | 4.27247i | 0.0803272 | − | 0.139131i | ||||
\(944\) | 4.30113 | 0.139990 | ||||||||
\(945\) | −2.01765 | + | 1.33599i | −0.0656342 | + | 0.0434597i | ||||
\(946\) | −0.966721 | −0.0314308 | ||||||||
\(947\) | 19.0860 | − | 33.0579i | 0.620212 | − | 1.07424i | −0.369234 | − | 0.929336i | \(-0.620380\pi\) |
0.989446 | − | 0.144902i | \(-0.0462867\pi\) | |||||||
\(948\) | 0.752730 | + | 1.30377i | 0.0244475 | + | 0.0423444i | ||||
\(949\) | −12.1458 | − | 21.0371i | −0.394269 | − | 0.682895i | ||||
\(950\) | 16.5120 | − | 28.5996i | 0.535719 | − | 0.927893i | ||||
\(951\) | −9.10929 | −0.295389 | ||||||||
\(952\) | −0.0987327 | − | 1.60939i | −0.00319994 | − | 0.0521606i | ||||
\(953\) | 41.3605 | 1.33980 | 0.669900 | − | 0.742452i | \(-0.266337\pi\) | ||||
0.669900 | + | 0.742452i | \(0.266337\pi\) | |||||||
\(954\) | 14.9265 | − | 25.8535i | 0.483265 | − | 0.837039i | ||||
\(955\) | −1.19885 | − | 2.07646i | −0.0387938 | − | 0.0671928i | ||||
\(956\) | 8.77121 | + | 15.1922i | 0.283681 | + | 0.491350i | ||||
\(957\) | −0.104824 | + | 0.181561i | −0.00338849 | + | 0.00586904i | ||||
\(958\) | −4.57219 | −0.147721 | ||||||||
\(959\) | −2.88844 | − | 47.0829i | −0.0932725 | − | 1.52038i | ||||
\(960\) | −0.166617 | −0.00537755 | ||||||||
\(961\) | 14.5864 | − | 25.2644i | 0.470529 | − | 0.814979i | ||||
\(962\) | −1.32449 | − | 2.29408i | −0.0427032 | − | 0.0739641i | ||||
\(963\) | 13.9797 | + | 24.2135i | 0.450489 | + | 0.780270i | ||||
\(964\) | −1.52113 | + | 2.63467i | −0.0489923 | + | 0.0848571i | ||||
\(965\) | 2.90718 | 0.0935853 | ||||||||
\(966\) | −2.34520 | + | 1.55288i | −0.0754556 | + | 0.0499630i | ||||
\(967\) | 7.05786 | 0.226965 | 0.113483 | − | 0.993540i | \(-0.463799\pi\) | ||||
0.113483 | + | 0.993540i | \(0.463799\pi\) | |||||||
\(968\) | 5.45696 | − | 9.45173i | 0.175393 | − | 0.303790i | ||||
\(969\) | 1.45397 | + | 2.51835i | 0.0467082 | + | 0.0809009i | ||||
\(970\) | −0.665111 | − | 1.15201i | −0.0213554 | − | 0.0369887i | ||||
\(971\) | −17.7494 | + | 30.7428i | −0.569605 | + | 0.986585i | 0.427000 | + | 0.904252i | \(0.359570\pi\) |
−0.996605 | + | 0.0823332i | \(0.973763\pi\) | |||||||
\(972\) | −15.1014 | −0.484377 | ||||||||
\(973\) | 18.9404 | + | 9.43899i | 0.607203 | + | 0.302600i | ||||
\(974\) | 21.6569 | 0.693931 | ||||||||
\(975\) | −7.34621 | + | 12.7240i | −0.235267 | + | 0.407494i | ||||
\(976\) | −1.82401 | − | 3.15928i | −0.0583853 | − | 0.101126i | ||||
\(977\) | −7.43503 | − | 12.8778i | −0.237868 | − | 0.411999i | 0.722235 | − | 0.691648i | \(-0.243115\pi\) |
−0.960102 | + | 0.279649i | \(0.909782\pi\) | |||||||
\(978\) | −4.86360 | + | 8.42400i | −0.155521 | + | 0.269370i | ||||
\(979\) | −3.70393 | −0.118378 | ||||||||
\(980\) | 0.982752 | + | 1.30315i | 0.0313929 | + | 0.0416277i | ||||
\(981\) | −37.8050 | −1.20702 | ||||||||
\(982\) | −16.0268 | + | 27.7593i | −0.511437 | + | 0.885834i | ||||
\(983\) | −18.3841 | − | 31.8422i | −0.586362 | − | 1.01561i | −0.994704 | − | 0.102779i | \(-0.967226\pi\) |
0.408343 | − | 0.912829i | \(-0.366107\pi\) | |||||||
\(984\) | 1.18479 | + | 2.05211i | 0.0377697 | + | 0.0654190i | ||||
\(985\) | 2.21874 | − | 3.84296i | 0.0706948 | − | 0.122447i | ||||
\(986\) | −0.609435 | −0.0194084 | ||||||||
\(987\) | −3.69036 | − | 1.83910i | −0.117466 | − | 0.0585391i | ||||
\(988\) | 27.7606 | 0.883182 | ||||||||
\(989\) | −2.45107 | + | 4.24538i | −0.0779396 | + | 0.134995i | ||||
\(990\) | 0.0851478 | + | 0.147480i | 0.00270617 | + | 0.00468723i | ||||
\(991\) | 13.4811 | + | 23.3500i | 0.428242 | + | 0.741736i | 0.996717 | − | 0.0809641i | \(-0.0257999\pi\) |
−0.568475 | + | 0.822700i | \(0.692467\pi\) | |||||||
\(992\) | 0.675875 | − | 1.17065i | 0.0214591 | − | 0.0371682i | ||||
\(993\) | 7.33295 | 0.232704 | ||||||||
\(994\) | −9.28954 | + | 6.15108i | −0.294646 | + | 0.195100i | ||||
\(995\) | −2.47353 | −0.0784162 | ||||||||
\(996\) | 2.40677 | − | 4.16866i | 0.0762616 | − | 0.132089i | ||||
\(997\) | −3.73465 | − | 6.46860i | −0.118278 | − | 0.204863i | 0.800808 | − | 0.598922i | \(-0.204404\pi\) |
−0.919085 | + | 0.394059i | \(0.871071\pi\) | |||||||
\(998\) | −12.3057 | − | 21.3140i | −0.389529 | − | 0.674684i | ||||
\(999\) | −1.24968 | + | 2.16451i | −0.0395382 | + | 0.0684821i |
(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 | 406.2.e.a.233.4 | ✓ | 10 | |
7.2 | even | 3 | 2842.2.a.z.1.2 | 5 | |||
7.4 | even | 3 | inner | 406.2.e.a.291.4 | yes | 10 | |
7.5 | odd | 6 | 2842.2.a.x.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
406.2.e.a.233.4 | ✓ | 10 | 1.1 | even | 1 | trivial | |
406.2.e.a.291.4 | yes | 10 | 7.4 | even | 3 | inner | |
2842.2.a.x.1.4 | 5 | 7.5 | odd | 6 | |||
2842.2.a.z.1.2 | 5 | 7.2 | even | 3 |