Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(1009,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.bb (of order \(6\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1009.8 | ||
Character | \(\chi\) | \(=\) | 1110.1009 |
Dual form | 1110.2.bb.d.1099.8 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.40108 | + | 1.74269i | 0.626584 | + | 0.779354i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.36459 | − | 1.94255i | 1.27170 | − | 0.734214i | 0.296389 | − | 0.955067i | \(-0.404217\pi\) |
0.975307 | + | 0.220853i | \(0.0708841\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0.342030 | + | 2.20975i | 0.108159 | + | 0.698786i | ||||
\(11\) | −0.297359 | −0.0896572 | −0.0448286 | − | 0.998995i | \(-0.514274\pi\) | ||||
−0.0448286 | + | 0.998995i | \(0.514274\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | −0.273612 | + | 0.157970i | −0.0758863 | + | 0.0438130i | −0.537463 | − | 0.843287i | \(-0.680617\pi\) |
0.461577 | + | 0.887100i | \(0.347284\pi\) | |||||||
\(14\) | 3.88510 | 1.03834 | ||||||||
\(15\) | 2.08472 | + | 0.808671i | 0.538272 | + | 0.208798i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.766516 | − | 0.442548i | −0.185907 | − | 0.107334i | 0.404158 | − | 0.914689i | \(-0.367565\pi\) |
−0.590065 | + | 0.807356i | \(0.700898\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | 1.55178 | + | 2.68777i | 0.356004 | + | 0.616617i | 0.987289 | − | 0.158934i | \(-0.0508057\pi\) |
−0.631285 | + | 0.775551i | \(0.717472\pi\) | |||||||
\(20\) | −0.808671 | + | 2.08472i | −0.180824 | + | 0.466157i | ||||
\(21\) | 1.94255 | − | 3.36459i | 0.423899 | − | 0.734214i | ||||
\(22\) | −0.257521 | − | 0.148680i | −0.0549036 | − | 0.0316986i | ||||
\(23\) | − | 7.33518i | − | 1.52949i | −0.644333 | − | 0.764745i | \(-0.722865\pi\) | ||
0.644333 | − | 0.764745i | \(-0.277135\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −1.07393 | + | 4.88331i | −0.214785 | + | 0.976661i | ||||
\(26\) | −0.315940 | −0.0619609 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 3.36459 | + | 1.94255i | 0.635848 | + | 0.367107i | ||||
\(29\) | −4.88510 | −0.907140 | −0.453570 | − | 0.891221i | \(-0.649850\pi\) | ||||
−0.453570 | + | 0.891221i | \(0.649850\pi\) | |||||||
\(30\) | 1.40108 | + | 1.74269i | 0.255802 | + | 0.318170i | ||||
\(31\) | 1.38670 | 0.249059 | 0.124529 | − | 0.992216i | \(-0.460258\pi\) | ||||
0.124529 | + | 0.992216i | \(0.460258\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −0.257521 | + | 0.148680i | −0.0448286 | + | 0.0258818i | ||||
\(34\) | −0.442548 | − | 0.766516i | −0.0758964 | − | 0.131456i | ||||
\(35\) | 8.09933 | + | 3.14176i | 1.36904 | + | 0.531055i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.88771 | + | 5.78243i | −0.310338 | + | 0.950626i | ||||
\(38\) | 3.10357i | 0.503465i | ||||||||
\(39\) | −0.157970 | + | 0.273612i | −0.0252954 | + | 0.0438130i | ||||
\(40\) | −1.74269 | + | 1.40108i | −0.275543 | + | 0.221531i | ||||
\(41\) | −6.17993 | − | 10.7040i | −0.965143 | − | 1.67168i | −0.709231 | − | 0.704976i | \(-0.750958\pi\) |
−0.255912 | − | 0.966700i | \(-0.582376\pi\) | |||||||
\(42\) | 3.36459 | − | 1.94255i | 0.519168 | − | 0.299742i | ||||
\(43\) | 7.34477i | 1.12007i | 0.828470 | + | 0.560034i | \(0.189212\pi\) | ||||
−0.828470 | + | 0.560034i | \(0.810788\pi\) | |||||||
\(44\) | −0.148680 | − | 0.257521i | −0.0224143 | − | 0.0388227i | ||||
\(45\) | 2.20975 | − | 0.342030i | 0.329411 | − | 0.0509868i | ||||
\(46\) | 3.66759 | − | 6.35245i | 0.540756 | − | 0.936617i | ||||
\(47\) | − | 5.14536i | − | 0.750528i | −0.926918 | − | 0.375264i | \(-0.877552\pi\) | ||
0.926918 | − | 0.375264i | \(-0.122448\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 4.04699 | − | 7.00959i | 0.578141 | − | 1.00137i | ||||
\(50\) | −3.37170 | + | 3.69210i | −0.476831 | + | 0.522142i | ||||
\(51\) | −0.885096 | −0.123938 | ||||||||
\(52\) | −0.273612 | − | 0.157970i | −0.0379431 | − | 0.0219065i | ||||
\(53\) | 4.71160 | + | 2.72024i | 0.647187 | + | 0.373654i | 0.787378 | − | 0.616471i | \(-0.211438\pi\) |
−0.140190 | + | 0.990125i | \(0.544771\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | −0.416625 | − | 0.518205i | −0.0561778 | − | 0.0698747i | ||||
\(56\) | 1.94255 | + | 3.36459i | 0.259584 | + | 0.449613i | ||||
\(57\) | 2.68777 | + | 1.55178i | 0.356004 | + | 0.205539i | ||||
\(58\) | −4.23062 | − | 2.44255i | −0.555507 | − | 0.320722i | ||||
\(59\) | −6.37254 | + | 11.0376i | −0.829634 | + | 1.43697i | 0.0686908 | + | 0.997638i | \(0.478118\pi\) |
−0.898325 | + | 0.439331i | \(0.855216\pi\) | |||||||
\(60\) | 0.342030 | + | 2.20975i | 0.0441559 | + | 0.285278i | ||||
\(61\) | −1.26241 | − | 2.18655i | −0.161635 | − | 0.279960i | 0.773820 | − | 0.633405i | \(-0.218343\pi\) |
−0.935455 | + | 0.353446i | \(0.885010\pi\) | |||||||
\(62\) | 1.20092 | + | 0.693350i | 0.152517 | + | 0.0880556i | ||||
\(63\) | − | 3.88510i | − | 0.489476i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.658645 | − | 0.255491i | −0.0816949 | − | 0.0316898i | ||||
\(66\) | −0.297359 | −0.0366024 | ||||||||
\(67\) | 0.512438 | − | 0.295856i | 0.0626042 | − | 0.0361446i | −0.468371 | − | 0.883532i | \(-0.655159\pi\) |
0.530975 | + | 0.847387i | \(0.321826\pi\) | |||||||
\(68\) | − | 0.885096i | − | 0.107334i | ||||||
\(69\) | −3.66759 | − | 6.35245i | −0.441526 | − | 0.764745i | ||||
\(70\) | 5.44335 | + | 6.77051i | 0.650604 | + | 0.809231i | ||||
\(71\) | −2.61853 | − | 4.53542i | −0.310762 | − | 0.538256i | 0.667766 | − | 0.744372i | \(-0.267251\pi\) |
−0.978528 | + | 0.206116i | \(0.933918\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 14.4291i | 1.68880i | 0.535710 | + | 0.844402i | \(0.320044\pi\) | ||||
−0.535710 | + | 0.844402i | \(0.679956\pi\) | |||||||
\(74\) | −4.52602 | + | 4.06388i | −0.526139 | + | 0.472417i | ||||
\(75\) | 1.51161 | + | 4.76603i | 0.174545 | + | 0.550334i | ||||
\(76\) | −1.55178 | + | 2.68777i | −0.178002 | + | 0.308308i | ||||
\(77\) | −1.00049 | + | 0.577635i | −0.114017 | + | 0.0658276i | ||||
\(78\) | −0.273612 | + | 0.157970i | −0.0309804 | + | 0.0178866i | ||||
\(79\) | 1.22680 | + | 2.12488i | 0.138026 | + | 0.239067i | 0.926749 | − | 0.375681i | \(-0.122591\pi\) |
−0.788724 | + | 0.614748i | \(0.789258\pi\) | |||||||
\(80\) | −2.20975 | + | 0.342030i | −0.247058 | + | 0.0382401i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | − | 12.3599i | − | 1.36492i | ||||||
\(83\) | 5.62000 | + | 3.24471i | 0.616875 | + | 0.356153i | 0.775651 | − | 0.631162i | \(-0.217422\pi\) |
−0.158777 | + | 0.987315i | \(0.550755\pi\) | |||||||
\(84\) | 3.88510 | 0.423899 | ||||||||
\(85\) | −0.302730 | − | 1.95585i | −0.0328356 | − | 0.212141i | ||||
\(86\) | −3.67239 | + | 6.36076i | −0.396004 | + | 0.685898i | ||||
\(87\) | −4.23062 | + | 2.44255i | −0.453570 | + | 0.261869i | ||||
\(88\) | − | 0.297359i | − | 0.0316986i | ||||||
\(89\) | 2.65348 | − | 4.59596i | 0.281268 | − | 0.487171i | −0.690429 | − | 0.723400i | \(-0.742578\pi\) |
0.971697 | + | 0.236229i | \(0.0759116\pi\) | |||||||
\(90\) | 2.08472 | + | 0.808671i | 0.219749 | + | 0.0852414i | ||||
\(91\) | −0.613728 | + | 1.06301i | −0.0643362 | + | 0.111434i | ||||
\(92\) | 6.35245 | − | 3.66759i | 0.662288 | − | 0.382372i | ||||
\(93\) | 1.20092 | − | 0.693350i | 0.124529 | − | 0.0718971i | ||||
\(94\) | 2.57268 | − | 4.45601i | 0.265352 | − | 0.459603i | ||||
\(95\) | −2.50977 | + | 6.47007i | −0.257496 | + | 0.663815i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | − | 8.87683i | − | 0.901306i | −0.892699 | − | 0.450653i | \(-0.851191\pi\) | ||
0.892699 | − | 0.450653i | \(-0.148809\pi\) | |||||||
\(98\) | 7.00959 | − | 4.04699i | 0.708075 | − | 0.408807i | ||||
\(99\) | −0.148680 | + | 0.257521i | −0.0149429 | + | 0.0258818i | ||||
\(100\) | −4.76603 | + | 1.51161i | −0.476603 | + | 0.151161i | ||||
\(101\) | −7.05378 | −0.701877 | −0.350939 | − | 0.936398i | \(-0.614137\pi\) | ||||
−0.350939 | + | 0.936398i | \(0.614137\pi\) | |||||||
\(102\) | −0.766516 | − | 0.442548i | −0.0758964 | − | 0.0438188i | ||||
\(103\) | 5.94035i | 0.585320i | 0.956217 | + | 0.292660i | \(0.0945404\pi\) | ||||
−0.956217 | + | 0.292660i | \(0.905460\pi\) | |||||||
\(104\) | −0.157970 | − | 0.273612i | −0.0154902 | − | 0.0268298i | ||||
\(105\) | 8.58511 | − | 1.32882i | 0.837821 | − | 0.129680i | ||||
\(106\) | 2.72024 | + | 4.71160i | 0.264213 | + | 0.457631i | ||||
\(107\) | 11.9668 | − | 6.90904i | 1.15688 | − | 0.667922i | 0.206322 | − | 0.978484i | \(-0.433850\pi\) |
0.950553 | + | 0.310562i | \(0.100517\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 3.08116 | − | 5.33672i | 0.295121 | − | 0.511165i | −0.679892 | − | 0.733313i | \(-0.737973\pi\) |
0.975013 | + | 0.222147i | \(0.0713065\pi\) | |||||||
\(110\) | −0.101706 | − | 0.657091i | −0.00969727 | − | 0.0626512i | ||||
\(111\) | 1.25641 | + | 5.95159i | 0.119253 | + | 0.564900i | ||||
\(112\) | 3.88510i | 0.367107i | ||||||||
\(113\) | 3.83100 | + | 2.21183i | 0.360390 | + | 0.208071i | 0.669252 | − | 0.743036i | \(-0.266615\pi\) |
−0.308862 | + | 0.951107i | \(0.599948\pi\) | |||||||
\(114\) | 1.55178 | + | 2.68777i | 0.145338 | + | 0.251733i | ||||
\(115\) | 12.7829 | − | 10.2772i | 1.19201 | − | 0.958354i | ||||
\(116\) | −2.44255 | − | 4.23062i | −0.226785 | − | 0.392803i | ||||
\(117\) | 0.315940i | 0.0292086i | ||||||||
\(118\) | −11.0376 | + | 6.37254i | −1.01609 | + | 0.586640i | ||||
\(119\) | −3.43868 | −0.315224 | ||||||||
\(120\) | −0.808671 | + | 2.08472i | −0.0738212 | + | 0.190308i | ||||
\(121\) | −10.9116 | −0.991962 | ||||||||
\(122\) | − | 2.52482i | − | 0.228586i | ||||||
\(123\) | −10.7040 | − | 6.17993i | −0.965143 | − | 0.557225i | ||||
\(124\) | 0.693350 | + | 1.20092i | 0.0622647 | + | 0.107846i | ||||
\(125\) | −10.0147 | + | 4.97040i | −0.895746 | + | 0.444566i | ||||
\(126\) | 1.94255 | − | 3.36459i | 0.173056 | − | 0.299742i | ||||
\(127\) | −9.86467 | − | 5.69537i | −0.875348 | − | 0.505382i | −0.00622607 | − | 0.999981i | \(-0.501982\pi\) |
−0.869122 | + | 0.494598i | \(0.835315\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 3.67239 | + | 6.36076i | 0.323336 | + | 0.560034i | ||||
\(130\) | −0.442658 | − | 0.550585i | −0.0388237 | − | 0.0482895i | ||||
\(131\) | −7.22034 | + | 12.5060i | −0.630844 | + | 1.09265i | 0.356535 | + | 0.934282i | \(0.383958\pi\) |
−0.987379 | + | 0.158372i | \(0.949375\pi\) | |||||||
\(132\) | −0.257521 | − | 0.148680i | −0.0224143 | − | 0.0129409i | ||||
\(133\) | 10.4422 | + | 6.02883i | 0.905457 | + | 0.522766i | ||||
\(134\) | 0.591712 | 0.0511161 | ||||||||
\(135\) | 1.74269 | − | 1.40108i | 0.149987 | − | 0.120586i | ||||
\(136\) | 0.442548 | − | 0.766516i | 0.0379482 | − | 0.0657282i | ||||
\(137\) | − | 14.0285i | − | 1.19854i | −0.800548 | − | 0.599269i | \(-0.795458\pi\) | ||
0.800548 | − | 0.599269i | \(-0.204542\pi\) | |||||||
\(138\) | − | 7.33518i | − | 0.624412i | ||||||
\(139\) | 9.79333 | − | 16.9625i | 0.830659 | − | 1.43874i | −0.0668571 | − | 0.997763i | \(-0.521297\pi\) |
0.897516 | − | 0.440981i | \(-0.145370\pi\) | |||||||
\(140\) | 1.32882 | + | 8.58511i | 0.112306 | + | 0.725574i | ||||
\(141\) | −2.57268 | − | 4.45601i | −0.216659 | − | 0.375264i | ||||
\(142\) | − | 5.23705i | − | 0.439484i | ||||||
\(143\) | 0.0813610 | − | 0.0469738i | 0.00680375 | − | 0.00392815i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −6.84443 | − | 8.51320i | −0.568399 | − | 0.706983i | ||||
\(146\) | −7.21457 | + | 12.4960i | −0.597082 | + | 1.03418i | ||||
\(147\) | − | 8.09397i | − | 0.667580i | ||||||
\(148\) | −5.95159 | + | 1.25641i | −0.489218 | + | 0.103277i | ||||
\(149\) | 4.89601 | 0.401097 | 0.200548 | − | 0.979684i | \(-0.435728\pi\) | ||||
0.200548 | + | 0.979684i | \(0.435728\pi\) | |||||||
\(150\) | −1.07393 | + | 4.88331i | −0.0876858 | + | 0.398720i | ||||
\(151\) | −2.85747 | − | 4.94928i | −0.232538 | − | 0.402767i | 0.726017 | − | 0.687677i | \(-0.241370\pi\) |
−0.958554 | + | 0.284910i | \(0.908036\pi\) | |||||||
\(152\) | −2.68777 | + | 1.55178i | −0.218007 | + | 0.125866i | ||||
\(153\) | −0.766516 | + | 0.442548i | −0.0619691 | + | 0.0357779i | ||||
\(154\) | −1.15527 | −0.0930943 | ||||||||
\(155\) | 1.94288 | + | 2.41659i | 0.156056 | + | 0.194105i | ||||
\(156\) | −0.315940 | −0.0252954 | ||||||||
\(157\) | 0.444121 | + | 0.256413i | 0.0354447 | + | 0.0204640i | 0.517618 | − | 0.855612i | \(-0.326819\pi\) |
−0.482173 | + | 0.876076i | \(0.660152\pi\) | |||||||
\(158\) | 2.45360i | 0.195198i | ||||||||
\(159\) | 5.44048 | 0.431458 | ||||||||
\(160\) | −2.08472 | − | 0.808671i | −0.164811 | − | 0.0639310i | ||||
\(161\) | −14.2489 | − | 24.6799i | −1.12297 | − | 1.94505i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −4.81112 | − | 2.77770i | −0.376836 | − | 0.217566i | 0.299605 | − | 0.954063i | \(-0.403145\pi\) |
−0.676441 | + | 0.736497i | \(0.736479\pi\) | |||||||
\(164\) | 6.17993 | − | 10.7040i | 0.482571 | − | 0.835838i | ||||
\(165\) | −0.619910 | − | 0.240466i | −0.0482600 | − | 0.0187202i | ||||
\(166\) | 3.24471 | + | 5.62000i | 0.251838 | + | 0.436196i | ||||
\(167\) | 4.57289 | − | 2.64016i | 0.353861 | − | 0.204302i | −0.312524 | − | 0.949910i | \(-0.601174\pi\) |
0.666384 | + | 0.745608i | \(0.267841\pi\) | |||||||
\(168\) | 3.36459 | + | 1.94255i | 0.259584 | + | 0.149871i | ||||
\(169\) | −6.45009 | + | 11.1719i | −0.496161 | + | 0.859376i | ||||
\(170\) | 0.715751 | − | 1.84518i | 0.0548956 | − | 0.141519i | ||||
\(171\) | 3.10357 | 0.237336 | ||||||||
\(172\) | −6.36076 | + | 3.67239i | −0.485003 | + | 0.280017i | ||||
\(173\) | −18.4308 | − | 10.6410i | −1.40127 | − | 0.809022i | −0.406745 | − | 0.913542i | \(-0.633336\pi\) |
−0.994523 | + | 0.104520i | \(0.966669\pi\) | |||||||
\(174\) | −4.88510 | −0.370338 | ||||||||
\(175\) | 5.87273 | + | 18.5165i | 0.443937 | + | 1.39971i | ||||
\(176\) | 0.148680 | − | 0.257521i | 0.0112071 | − | 0.0194114i | ||||
\(177\) | 12.7451i | 0.957979i | ||||||||
\(178\) | 4.59596 | − | 2.65348i | 0.344482 | − | 0.198887i | ||||
\(179\) | −18.3439 | −1.37109 | −0.685544 | − | 0.728032i | \(-0.740435\pi\) | ||||
−0.685544 | + | 0.728032i | \(0.740435\pi\) | |||||||
\(180\) | 1.40108 | + | 1.74269i | 0.104431 | + | 0.129892i | ||||
\(181\) | 7.21545 | + | 12.4975i | 0.536320 | + | 0.928934i | 0.999098 | + | 0.0424598i | \(0.0135194\pi\) |
−0.462778 | + | 0.886474i | \(0.653147\pi\) | |||||||
\(182\) | −1.06301 | + | 0.613728i | −0.0787954 | + | 0.0454926i | ||||
\(183\) | −2.18655 | − | 1.26241i | −0.161635 | − | 0.0933199i | ||||
\(184\) | 7.33518 | 0.540756 | ||||||||
\(185\) | −12.7218 | + | 4.81199i | −0.935327 | + | 0.353784i | ||||
\(186\) | 1.38670 | 0.101678 | ||||||||
\(187\) | 0.227931 | + | 0.131596i | 0.0166679 | + | 0.00962324i | ||||
\(188\) | 4.45601 | − | 2.57268i | 0.324988 | − | 0.187632i | ||||
\(189\) | −1.94255 | − | 3.36459i | −0.141300 | − | 0.244738i | ||||
\(190\) | −5.40855 | + | 4.34836i | −0.392378 | + | 0.315463i | ||||
\(191\) | 6.95331 | 0.503124 | 0.251562 | − | 0.967841i | \(-0.419056\pi\) | ||||
0.251562 | + | 0.967841i | \(0.419056\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | − | 24.4671i | − | 1.76118i | −0.473877 | − | 0.880591i | \(-0.657146\pi\) | ||
0.473877 | − | 0.880591i | \(-0.342854\pi\) | |||||||
\(194\) | 4.43842 | − | 7.68756i | 0.318660 | − | 0.551935i | ||||
\(195\) | −0.698149 | + | 0.108061i | −0.0499955 | + | 0.00773840i | ||||
\(196\) | 8.09397 | 0.578141 | ||||||||
\(197\) | −18.9041 | − | 10.9143i | −1.34686 | − | 0.777609i | −0.359055 | − | 0.933317i | \(-0.616901\pi\) |
−0.987803 | + | 0.155708i | \(0.950234\pi\) | |||||||
\(198\) | −0.257521 | + | 0.148680i | −0.0183012 | + | 0.0105662i | ||||
\(199\) | −9.32319 | −0.660903 | −0.330452 | − | 0.943823i | \(-0.607201\pi\) | ||||
−0.330452 | + | 0.943823i | \(0.607201\pi\) | |||||||
\(200\) | −4.88331 | − | 1.07393i | −0.345302 | − | 0.0759381i | ||||
\(201\) | 0.295856 | − | 0.512438i | 0.0208681 | − | 0.0361446i | ||||
\(202\) | −6.10875 | − | 3.52689i | −0.429810 | − | 0.248151i | ||||
\(203\) | −16.4364 | + | 9.48953i | −1.15361 | + | 0.666035i | ||||
\(204\) | −0.442548 | − | 0.766516i | −0.0309846 | − | 0.0536668i | ||||
\(205\) | 9.99505 | − | 25.7668i | 0.698085 | − | 1.79963i | ||||
\(206\) | −2.97017 | + | 5.14449i | −0.206942 | + | 0.358434i | ||||
\(207\) | −6.35245 | − | 3.66759i | −0.441526 | − | 0.254915i | ||||
\(208\) | − | 0.315940i | − | 0.0219065i | ||||||
\(209\) | −0.461438 | − | 0.799233i | −0.0319183 | − | 0.0552841i | ||||
\(210\) | 8.09933 | + | 3.14176i | 0.558907 | + | 0.216802i | ||||
\(211\) | 5.22728 | 0.359861 | 0.179930 | − | 0.983679i | \(-0.442413\pi\) | ||||
0.179930 | + | 0.983679i | \(0.442413\pi\) | |||||||
\(212\) | 5.44048i | 0.373654i | ||||||||
\(213\) | −4.53542 | − | 2.61853i | −0.310762 | − | 0.179419i | ||||
\(214\) | 13.8181 | 0.944585 | ||||||||
\(215\) | −12.7997 | + | 10.2906i | −0.872929 | + | 0.701816i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 4.66568 | − | 2.69373i | 0.316727 | − | 0.182863i | ||||
\(218\) | 5.33672 | − | 3.08116i | 0.361449 | − | 0.208682i | ||||
\(219\) | 7.21457 | + | 12.4960i | 0.487516 | + | 0.844402i | ||||
\(220\) | 0.240466 | − | 0.619910i | 0.0162122 | − | 0.0417944i | ||||
\(221\) | 0.279637 | 0.0188104 | ||||||||
\(222\) | −1.88771 | + | 5.78243i | −0.126695 | + | 0.388092i | ||||
\(223\) | 14.3590i | 0.961551i | 0.876844 | + | 0.480776i | \(0.159645\pi\) | ||||
−0.876844 | + | 0.480776i | \(0.840355\pi\) | |||||||
\(224\) | −1.94255 | + | 3.36459i | −0.129792 | + | 0.224806i | ||||
\(225\) | 3.69210 | + | 3.37170i | 0.246140 | + | 0.224780i | ||||
\(226\) | 2.21183 | + | 3.83100i | 0.147129 | + | 0.254834i | ||||
\(227\) | −4.35717 | + | 2.51561i | −0.289195 | + | 0.166967i | −0.637579 | − | 0.770385i | \(-0.720064\pi\) |
0.348384 | + | 0.937352i | \(0.386731\pi\) | |||||||
\(228\) | 3.10357i | 0.205539i | ||||||||
\(229\) | 1.24438 | + | 2.15533i | 0.0822309 | + | 0.142428i | 0.904208 | − | 0.427093i | \(-0.140462\pi\) |
−0.821977 | + | 0.569521i | \(0.807129\pi\) | |||||||
\(230\) | 16.2089 | − | 2.50885i | 1.06879 | − | 0.165429i | ||||
\(231\) | −0.577635 | + | 1.00049i | −0.0380056 | + | 0.0658276i | ||||
\(232\) | − | 4.88510i | − | 0.320722i | ||||||
\(233\) | 23.9097i | 1.56638i | 0.621785 | + | 0.783188i | \(0.286408\pi\) | ||||
−0.621785 | + | 0.783188i | \(0.713592\pi\) | |||||||
\(234\) | −0.157970 | + | 0.273612i | −0.0103268 | + | 0.0178866i | ||||
\(235\) | 8.96676 | − | 7.20908i | 0.584927 | − | 0.470269i | ||||
\(236\) | −12.7451 | −0.829634 | ||||||||
\(237\) | 2.12488 | + | 1.22680i | 0.138026 | + | 0.0796891i | ||||
\(238\) | −2.97799 | − | 1.71934i | −0.193034 | − | 0.111448i | ||||
\(239\) | −14.9600 | + | 25.9114i | −0.967679 | + | 1.67607i | −0.265442 | + | 0.964127i | \(0.585518\pi\) |
−0.702237 | + | 0.711943i | \(0.747815\pi\) | |||||||
\(240\) | −1.74269 | + | 1.40108i | −0.112490 | + | 0.0904396i | ||||
\(241\) | 6.46707 | + | 11.2013i | 0.416580 | + | 0.721538i | 0.995593 | − | 0.0937802i | \(-0.0298951\pi\) |
−0.579013 | + | 0.815319i | \(0.696562\pi\) | |||||||
\(242\) | −9.44970 | − | 5.45579i | −0.607450 | − | 0.350711i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 1.26241 | − | 2.18655i | 0.0808174 | − | 0.139980i | ||||
\(245\) | 17.8857 | − | 2.76838i | 1.14267 | − | 0.176865i | ||||
\(246\) | −6.17993 | − | 10.7040i | −0.394018 | − | 0.682459i | ||||
\(247\) | −0.849173 | − | 0.490270i | −0.0540316 | − | 0.0311952i | ||||
\(248\) | 1.38670i | 0.0880556i | ||||||||
\(249\) | 6.48941 | 0.411250 | ||||||||
\(250\) | −11.1582 | − | 0.702877i | −0.705708 | − | 0.0444538i | ||||
\(251\) | −11.5353 | −0.728100 | −0.364050 | − | 0.931379i | \(-0.618606\pi\) | ||||
−0.364050 | + | 0.931379i | \(0.618606\pi\) | |||||||
\(252\) | 3.36459 | − | 1.94255i | 0.211949 | − | 0.122369i | ||||
\(253\) | 2.18118i | 0.137130i | ||||||||
\(254\) | −5.69537 | − | 9.86467i | −0.357359 | − | 0.618964i | ||||
\(255\) | −1.24009 | − | 1.54245i | −0.0776577 | − | 0.0965918i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −8.97268 | − | 5.18038i | −0.559701 | − | 0.323143i | 0.193325 | − | 0.981135i | \(-0.438073\pi\) |
−0.753025 | + | 0.657992i | \(0.771406\pi\) | |||||||
\(258\) | 7.34477i | 0.457266i | ||||||||
\(259\) | 4.88129 | + | 23.1225i | 0.303308 | + | 1.43676i | ||||
\(260\) | −0.108061 | − | 0.698149i | −0.00670165 | − | 0.0432974i | ||||
\(261\) | −2.44255 | + | 4.23062i | −0.151190 | + | 0.261869i | ||||
\(262\) | −12.5060 | + | 7.22034i | −0.772623 | + | 0.446074i | ||||
\(263\) | −2.92053 | + | 1.68617i | −0.180088 | + | 0.103974i | −0.587334 | − | 0.809345i | \(-0.699822\pi\) |
0.407246 | + | 0.913318i | \(0.366489\pi\) | |||||||
\(264\) | −0.148680 | − | 0.257521i | −0.00915060 | − | 0.0158493i | ||||
\(265\) | 1.86081 | + | 12.0221i | 0.114309 | + | 0.738513i | ||||
\(266\) | 6.02883 | + | 10.4422i | 0.369651 | + | 0.640255i | ||||
\(267\) | − | 5.30696i | − | 0.324780i | ||||||
\(268\) | 0.512438 | + | 0.295856i | 0.0313021 | + | 0.0180723i | ||||
\(269\) | 13.5925 | 0.828752 | 0.414376 | − | 0.910106i | \(-0.364000\pi\) | ||||
0.414376 | + | 0.910106i | \(0.364000\pi\) | |||||||
\(270\) | 2.20975 | − | 0.342030i | 0.134481 | − | 0.0208153i | ||||
\(271\) | 5.79573 | − | 10.0385i | 0.352066 | − | 0.609796i | −0.634546 | − | 0.772885i | \(-0.718813\pi\) |
0.986611 | + | 0.163090i | \(0.0521460\pi\) | |||||||
\(272\) | 0.766516 | − | 0.442548i | 0.0464768 | − | 0.0268334i | ||||
\(273\) | 1.22746i | 0.0742890i | ||||||||
\(274\) | 7.01426 | − | 12.1491i | 0.423747 | − | 0.733951i | ||||
\(275\) | 0.319342 | − | 1.45210i | 0.0192571 | − | 0.0875647i | ||||
\(276\) | 3.66759 | − | 6.35245i | 0.220763 | − | 0.382372i | ||||
\(277\) | 13.0002 | − | 7.50570i | 0.781109 | − | 0.450974i | −0.0557140 | − | 0.998447i | \(-0.517743\pi\) |
0.836823 | + | 0.547473i | \(0.184410\pi\) | |||||||
\(278\) | 16.9625 | − | 9.79333i | 1.01735 | − | 0.587365i | ||||
\(279\) | 0.693350 | − | 1.20092i | 0.0415098 | − | 0.0718971i | ||||
\(280\) | −3.14176 | + | 8.09933i | −0.187756 | + | 0.484028i | ||||
\(281\) | 10.4127 | − | 18.0352i | 0.621167 | − | 1.07589i | −0.368102 | − | 0.929785i | \(-0.619992\pi\) |
0.989269 | − | 0.146107i | \(-0.0466744\pi\) | |||||||
\(282\) | − | 5.14536i | − | 0.306402i | ||||||
\(283\) | −6.88151 | + | 3.97304i | −0.409063 | + | 0.236173i | −0.690387 | − | 0.723440i | \(-0.742560\pi\) |
0.281324 | + | 0.959613i | \(0.409226\pi\) | |||||||
\(284\) | 2.61853 | − | 4.53542i | 0.155381 | − | 0.269128i | ||||
\(285\) | 1.06151 | + | 6.85813i | 0.0628787 | + | 0.406240i | ||||
\(286\) | 0.0939476 | 0.00555524 | ||||||||
\(287\) | −41.5859 | − | 24.0096i | −2.45474 | − | 1.41724i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −8.10830 | − | 14.0440i | −0.476959 | − | 0.826117i | ||||
\(290\) | −1.67085 | − | 10.7949i | −0.0981157 | − | 0.633896i | ||||
\(291\) | −4.43842 | − | 7.68756i | −0.260185 | − | 0.450653i | ||||
\(292\) | −12.4960 | + | 7.21457i | −0.731274 | + | 0.422201i | ||||
\(293\) | 16.9408 | − | 9.78077i | 0.989692 | − | 0.571399i | 0.0845098 | − | 0.996423i | \(-0.473068\pi\) |
0.905182 | + | 0.425024i | \(0.139734\pi\) | |||||||
\(294\) | 4.04699 | − | 7.00959i | 0.236025 | − | 0.408807i | ||||
\(295\) | −28.1635 | + | 4.35920i | −1.63974 | + | 0.253803i | ||||
\(296\) | −5.78243 | − | 1.88771i | −0.336097 | − | 0.109721i | ||||
\(297\) | 0.297359i | 0.0172545i | ||||||||
\(298\) | 4.24007 | + | 2.44800i | 0.245621 | + | 0.141809i | ||||
\(299\) | 1.15874 | + | 2.00699i | 0.0670115 | + | 0.116067i | ||||
\(300\) | −3.37170 | + | 3.69210i | −0.194665 | + | 0.213164i | ||||
\(301\) | 14.2676 | + | 24.7122i | 0.822369 | + | 1.42439i | ||||
\(302\) | − | 5.71494i | − | 0.328858i | ||||||
\(303\) | −6.10875 | + | 3.52689i | −0.350939 | + | 0.202615i | ||||
\(304\) | −3.10357 | −0.178002 | ||||||||
\(305\) | 2.04174 | − | 5.26353i | 0.116910 | − | 0.301389i | ||||
\(306\) | −0.885096 | −0.0505976 | ||||||||
\(307\) | 7.16588i | 0.408978i | 0.978869 | + | 0.204489i | \(0.0655533\pi\) | ||||
−0.978869 | + | 0.204489i | \(0.934447\pi\) | |||||||
\(308\) | −1.00049 | − | 0.577635i | −0.0570084 | − | 0.0329138i | ||||
\(309\) | 2.97017 | + | 5.14449i | 0.168967 | + | 0.292660i | ||||
\(310\) | 0.474294 | + | 3.06427i | 0.0269381 | + | 0.174039i | ||||
\(311\) | 12.7074 | − | 22.0099i | 0.720571 | − | 1.24807i | −0.240200 | − | 0.970723i | \(-0.577213\pi\) |
0.960771 | − | 0.277343i | \(-0.0894537\pi\) | |||||||
\(312\) | −0.273612 | − | 0.157970i | −0.0154902 | − | 0.00894328i | ||||
\(313\) | 2.73391 | + | 1.57843i | 0.154530 | + | 0.0892179i | 0.575271 | − | 0.817963i | \(-0.304897\pi\) |
−0.420741 | + | 0.907181i | \(0.638230\pi\) | |||||||
\(314\) | 0.256413 | + | 0.444121i | 0.0144702 | + | 0.0250632i | ||||
\(315\) | 6.77051 | − | 5.44335i | 0.381475 | − | 0.306698i | ||||
\(316\) | −1.22680 | + | 2.12488i | −0.0690128 | + | 0.119534i | ||||
\(317\) | −4.88564 | − | 2.82073i | −0.274405 | − | 0.158428i | 0.356483 | − | 0.934302i | \(-0.383976\pi\) |
−0.630888 | + | 0.775874i | \(0.717309\pi\) | |||||||
\(318\) | 4.71160 | + | 2.72024i | 0.264213 | + | 0.152544i | ||||
\(319\) | 1.45263 | 0.0813316 | ||||||||
\(320\) | −1.40108 | − | 1.74269i | −0.0783230 | − | 0.0974193i | ||||
\(321\) | 6.90904 | − | 11.9668i | 0.385625 | − | 0.667922i | ||||
\(322\) | − | 28.4979i | − | 1.58812i | ||||||
\(323\) | − | 2.74696i | − | 0.152845i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −0.477576 | − | 1.50578i | −0.0264912 | − | 0.0835256i | ||||
\(326\) | −2.77770 | − | 4.81112i | −0.153843 | − | 0.266463i | ||||
\(327\) | − | 6.16232i | − | 0.340777i | ||||||
\(328\) | 10.7040 | − | 6.17993i | 0.591027 | − | 0.341230i | ||||
\(329\) | −9.99511 | − | 17.3120i | −0.551048 | − | 0.954444i | ||||
\(330\) | −0.416625 | − | 0.518205i | −0.0229345 | − | 0.0285262i | ||||
\(331\) | −1.01400 | + | 1.75630i | −0.0557346 | + | 0.0965351i | −0.892547 | − | 0.450955i | \(-0.851083\pi\) |
0.836812 | + | 0.547490i | \(0.184417\pi\) | |||||||
\(332\) | 6.48941i | 0.356153i | ||||||||
\(333\) | 4.06388 | + | 4.52602i | 0.222699 | + | 0.248024i | ||||
\(334\) | 5.28032 | 0.288926 | ||||||||
\(335\) | 1.23355 | + | 0.478500i | 0.0673962 | + | 0.0261433i | ||||
\(336\) | 1.94255 | + | 3.36459i | 0.105975 | + | 0.183554i | ||||
\(337\) | 27.6085 | − | 15.9398i | 1.50393 | − | 0.868294i | 0.503939 | − | 0.863739i | \(-0.331884\pi\) |
0.999990 | − | 0.00455466i | \(-0.00144980\pi\) | |||||||
\(338\) | −11.1719 | + | 6.45009i | −0.607670 | + | 0.350839i | ||||
\(339\) | 4.42366 | 0.240260 | ||||||||
\(340\) | 1.54245 | − | 1.24009i | 0.0836509 | − | 0.0672535i | ||||
\(341\) | −0.412348 | −0.0223299 | ||||||||
\(342\) | 2.68777 | + | 1.55178i | 0.145338 | + | 0.0839109i | ||||
\(343\) | − | 4.25019i | − | 0.229488i | ||||||
\(344\) | −7.34477 | −0.396004 | ||||||||
\(345\) | 5.93174 | − | 15.2918i | 0.319354 | − | 0.823282i | ||||
\(346\) | −10.6410 | − | 18.4308i | −0.572065 | − | 0.990846i | ||||
\(347\) | − | 8.51155i | − | 0.456924i | −0.973553 | − | 0.228462i | \(-0.926630\pi\) | ||
0.973553 | − | 0.228462i | \(-0.0733696\pi\) | |||||||
\(348\) | −4.23062 | − | 2.44255i | −0.226785 | − | 0.130934i | ||||
\(349\) | −7.55902 | + | 13.0926i | −0.404625 | + | 0.700831i | −0.994278 | − | 0.106826i | \(-0.965931\pi\) |
0.589653 | + | 0.807657i | \(0.299265\pi\) | |||||||
\(350\) | −4.17231 | + | 18.9721i | −0.223019 | + | 1.01410i | ||||
\(351\) | 0.157970 | + | 0.273612i | 0.00843181 | + | 0.0146043i | ||||
\(352\) | 0.257521 | − | 0.148680i | 0.0137259 | − | 0.00792465i | ||||
\(353\) | 22.8657 | + | 13.2015i | 1.21702 | + | 0.702645i | 0.964279 | − | 0.264890i | \(-0.0853358\pi\) |
0.252738 | + | 0.967535i | \(0.418669\pi\) | |||||||
\(354\) | −6.37254 | + | 11.0376i | −0.338697 | + | 0.586640i | ||||
\(355\) | 4.23505 | − | 10.9178i | 0.224773 | − | 0.579456i | ||||
\(356\) | 5.30696 | 0.281268 | ||||||||
\(357\) | −2.97799 | + | 1.71934i | −0.157612 | + | 0.0909972i | ||||
\(358\) | −15.8863 | − | 9.17195i | −0.839616 | − | 0.484752i | ||||
\(359\) | −15.8538 | −0.836730 | −0.418365 | − | 0.908279i | \(-0.637397\pi\) | ||||
−0.418365 | + | 0.908279i | \(0.637397\pi\) | |||||||
\(360\) | 0.342030 | + | 2.20975i | 0.0180266 | + | 0.116464i | ||||
\(361\) | 4.68393 | − | 8.11280i | 0.246523 | − | 0.426990i | ||||
\(362\) | 14.4309i | 0.758472i | ||||||||
\(363\) | −9.44970 | + | 5.45579i | −0.495981 | + | 0.286355i | ||||
\(364\) | −1.22746 | −0.0643362 | ||||||||
\(365\) | −25.1455 | + | 20.2164i | −1.31618 | + | 1.05818i | ||||
\(366\) | −1.26241 | − | 2.18655i | −0.0659871 | − | 0.114293i | ||||
\(367\) | 24.6085 | − | 14.2077i | 1.28455 | − | 0.741637i | 0.306876 | − | 0.951749i | \(-0.400716\pi\) |
0.977677 | + | 0.210112i | \(0.0673828\pi\) | |||||||
\(368\) | 6.35245 | + | 3.66759i | 0.331144 | + | 0.191186i | ||||
\(369\) | −12.3599 | −0.643429 | ||||||||
\(370\) | −13.4234 | − | 2.19361i | −0.697850 | − | 0.114040i | ||||
\(371\) | 21.1368 | 1.09737 | ||||||||
\(372\) | 1.20092 | + | 0.693350i | 0.0622647 | + | 0.0359485i | ||||
\(373\) | −4.25045 | + | 2.45400i | −0.220080 | + | 0.127063i | −0.605987 | − | 0.795474i | \(-0.707222\pi\) |
0.385907 | + | 0.922538i | \(0.373888\pi\) | |||||||
\(374\) | 0.131596 | + | 0.227931i | 0.00680466 | + | 0.0117860i | ||||
\(375\) | −6.18782 | + | 9.31187i | −0.319538 | + | 0.480863i | ||||
\(376\) | 5.14536 | 0.265352 | ||||||||
\(377\) | 1.33662 | − | 0.771698i | 0.0688394 | − | 0.0397445i | ||||
\(378\) | − | 3.88510i | − | 0.199828i | ||||||
\(379\) | −10.9001 | + | 18.8795i | −0.559899 | + | 0.969773i | 0.437605 | + | 0.899167i | \(0.355827\pi\) |
−0.997504 | + | 0.0706062i | \(0.977507\pi\) | |||||||
\(380\) | −6.85813 | + | 1.06151i | −0.351814 | + | 0.0544545i | ||||
\(381\) | −11.3907 | −0.583565 | ||||||||
\(382\) | 6.02174 | + | 3.47665i | 0.308099 | + | 0.177881i | ||||
\(383\) | 18.7573 | − | 10.8295i | 0.958453 | − | 0.553363i | 0.0627565 | − | 0.998029i | \(-0.480011\pi\) |
0.895697 | + | 0.444666i | \(0.146678\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −2.40841 | − | 0.934232i | −0.122744 | − | 0.0476129i | ||||
\(386\) | 12.2336 | − | 21.1891i | 0.622672 | − | 1.07850i | ||||
\(387\) | 6.36076 | + | 3.67239i | 0.323336 | + | 0.186678i | ||||
\(388\) | 7.68756 | − | 4.43842i | 0.390277 | − | 0.225326i | ||||
\(389\) | 10.1405 | + | 17.5639i | 0.514144 | + | 0.890524i | 0.999865 | + | 0.0164099i | \(0.00522367\pi\) |
−0.485721 | + | 0.874114i | \(0.661443\pi\) | |||||||
\(390\) | −0.658645 | − | 0.255491i | −0.0333518 | − | 0.0129373i | ||||
\(391\) | −3.24617 | + | 5.62253i | −0.164166 | + | 0.284343i | ||||
\(392\) | 7.00959 | + | 4.04699i | 0.354038 | + | 0.204404i | ||||
\(393\) | 14.4407i | 0.728436i | ||||||||
\(394\) | −10.9143 | − | 18.9041i | −0.549852 | − | 0.952372i | ||||
\(395\) | −1.98415 | + | 5.11506i | −0.0998335 | + | 0.257367i | ||||
\(396\) | −0.297359 | −0.0149429 | ||||||||
\(397\) | − | 12.4857i | − | 0.626638i | −0.949648 | − | 0.313319i | \(-0.898559\pi\) | ||
0.949648 | − | 0.313319i | \(-0.101441\pi\) | |||||||
\(398\) | −8.07412 | − | 4.66159i | −0.404719 | − | 0.233665i | ||||
\(399\) | 12.0577 | 0.603638 | ||||||||
\(400\) | −3.69210 | − | 3.37170i | −0.184605 | − | 0.168585i | ||||
\(401\) | −4.29869 | −0.214667 | −0.107333 | − | 0.994223i | \(-0.534231\pi\) | ||||
−0.107333 | + | 0.994223i | \(0.534231\pi\) | |||||||
\(402\) | 0.512438 | − | 0.295856i | 0.0255581 | − | 0.0147560i | ||||
\(403\) | −0.379418 | + | 0.219057i | −0.0189001 | + | 0.0109120i | ||||
\(404\) | −3.52689 | − | 6.10875i | −0.175469 | − | 0.303922i | ||||
\(405\) | 0.808671 | − | 2.08472i | 0.0401832 | − | 0.103591i | ||||
\(406\) | −18.9791 | −0.941915 | ||||||||
\(407\) | 0.561328 | − | 1.71946i | 0.0278240 | − | 0.0852305i | ||||
\(408\) | − | 0.885096i | − | 0.0438188i | ||||||
\(409\) | 2.94848 | − | 5.10692i | 0.145793 | − | 0.252521i | −0.783876 | − | 0.620918i | \(-0.786760\pi\) |
0.929668 | + | 0.368397i | \(0.120093\pi\) | |||||||
\(410\) | 21.5394 | − | 17.3172i | 1.06375 | − | 0.855236i | ||||
\(411\) | −7.01426 | − | 12.1491i | −0.345988 | − | 0.599269i | ||||
\(412\) | −5.14449 | + | 2.97017i | −0.253451 | + | 0.146330i | ||||
\(413\) | 49.5159i | 2.43652i | ||||||||
\(414\) | −3.66759 | − | 6.35245i | −0.180252 | − | 0.312206i | ||||
\(415\) | 2.21957 | + | 14.3400i | 0.108955 | + | 0.703923i | ||||
\(416\) | 0.157970 | − | 0.273612i | 0.00774511 | − | 0.0134149i | ||||
\(417\) | − | 19.5867i | − | 0.959163i | ||||||
\(418\) | − | 0.922875i | − | 0.0451393i | ||||||
\(419\) | 5.97334 | − | 10.3461i | 0.291817 | − | 0.505441i | −0.682423 | − | 0.730958i | \(-0.739074\pi\) |
0.974239 | + | 0.225517i | \(0.0724070\pi\) | |||||||
\(420\) | 5.44335 | + | 6.77051i | 0.265608 | + | 0.330367i | ||||
\(421\) | 30.2064 | 1.47217 | 0.736086 | − | 0.676888i | \(-0.236672\pi\) | ||||
0.736086 | + | 0.676888i | \(0.236672\pi\) | |||||||
\(422\) | 4.52695 | + | 2.61364i | 0.220369 | + | 0.127230i | ||||
\(423\) | −4.45601 | − | 2.57268i | −0.216659 | − | 0.125088i | ||||
\(424\) | −2.72024 | + | 4.71160i | −0.132107 | + | 0.228815i | ||||
\(425\) | 2.98428 | − | 3.26787i | 0.144759 | − | 0.158515i | ||||
\(426\) | −2.61853 | − | 4.53542i | −0.126868 | − | 0.219742i | ||||
\(427\) | −8.49497 | − | 4.90458i | −0.411101 | − | 0.237349i | ||||
\(428\) | 11.9668 | + | 6.90904i | 0.578438 | + | 0.333961i | ||||
\(429\) | 0.0469738 | − | 0.0813610i | 0.00226792 | − | 0.00392815i | ||||
\(430\) | −16.2301 | + | 2.51213i | −0.782687 | + | 0.121146i | ||||
\(431\) | 10.9678 | + | 18.9968i | 0.528300 | + | 0.915042i | 0.999456 | + | 0.0329922i | \(0.0105037\pi\) |
−0.471156 | + | 0.882050i | \(0.656163\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 41.5595i | − | 1.99722i | −0.0526686 | − | 0.998612i | \(-0.516773\pi\) | ||
0.0526686 | − | 0.998612i | \(-0.483227\pi\) | |||||||
\(434\) | 5.38747 | 0.258607 | ||||||||
\(435\) | −10.1841 | − | 3.95043i | −0.488288 | − | 0.189409i | ||||
\(436\) | 6.16232 | 0.295121 | ||||||||
\(437\) | 19.7153 | − | 11.3826i | 0.943109 | − | 0.544504i | ||||
\(438\) | 14.4291i | 0.689451i | ||||||||
\(439\) | 11.2929 | + | 19.5599i | 0.538982 | + | 0.933543i | 0.998959 | + | 0.0456130i | \(0.0145241\pi\) |
−0.459978 | + | 0.887931i | \(0.652143\pi\) | |||||||
\(440\) | 0.518205 | − | 0.416625i | 0.0247044 | − | 0.0198618i | ||||
\(441\) | −4.04699 | − | 7.00959i | −0.192714 | − | 0.333790i | ||||
\(442\) | 0.242173 | + | 0.139819i | 0.0115190 | + | 0.00665049i | ||||
\(443\) | − | 4.84155i | − | 0.230029i | −0.993364 | − | 0.115014i | \(-0.963309\pi\) | ||
0.993364 | − | 0.115014i | \(-0.0366914\pi\) | |||||||
\(444\) | −4.52602 | + | 4.06388i | −0.214795 | + | 0.192863i | ||||
\(445\) | 11.7271 | − | 1.81514i | 0.555917 | − | 0.0860458i | ||||
\(446\) | −7.17951 | + | 12.4353i | −0.339960 | + | 0.588828i | ||||
\(447\) | 4.24007 | − | 2.44800i | 0.200548 | − | 0.115787i | ||||
\(448\) | −3.36459 | + | 1.94255i | −0.158962 | + | 0.0917768i | ||||
\(449\) | 17.8372 | + | 30.8949i | 0.841789 | + | 1.45802i | 0.888381 | + | 0.459107i | \(0.151830\pi\) |
−0.0465924 | + | 0.998914i | \(0.514836\pi\) | |||||||
\(450\) | 1.51161 | + | 4.76603i | 0.0712578 | + | 0.224673i | ||||
\(451\) | 1.83766 | + | 3.18292i | 0.0865320 | + | 0.149878i | ||||
\(452\) | 4.42366i | 0.208071i | ||||||||
\(453\) | −4.94928 | − | 2.85747i | −0.232538 | − | 0.134256i | ||||
\(454\) | −5.03122 | −0.236127 | ||||||||
\(455\) | −2.71238 | + | 0.419827i | −0.127158 | + | 0.0196818i | ||||
\(456\) | −1.55178 | + | 2.68777i | −0.0726690 | + | 0.125866i | ||||
\(457\) | −7.99977 | + | 4.61867i | −0.374213 | + | 0.216052i | −0.675298 | − | 0.737545i | \(-0.735985\pi\) |
0.301084 | + | 0.953598i | \(0.402651\pi\) | |||||||
\(458\) | 2.48876i | 0.116292i | ||||||||
\(459\) | −0.442548 | + | 0.766516i | −0.0206564 | + | 0.0357779i | ||||
\(460\) | 15.2918 | + | 5.93174i | 0.712983 | + | 0.276569i | ||||
\(461\) | −2.17760 | + | 3.77172i | −0.101421 | + | 0.175666i | −0.912270 | − | 0.409589i | \(-0.865672\pi\) |
0.810849 | + | 0.585255i | \(0.199006\pi\) | |||||||
\(462\) | −1.00049 | + | 0.577635i | −0.0465471 | + | 0.0268740i | ||||
\(463\) | −4.84239 | + | 2.79576i | −0.225045 | + | 0.129930i | −0.608284 | − | 0.793719i | \(-0.708142\pi\) |
0.383239 | + | 0.923649i | \(0.374809\pi\) | |||||||
\(464\) | 2.44255 | − | 4.23062i | 0.113392 | − | 0.196401i | ||||
\(465\) | 2.89088 | + | 1.12138i | 0.134061 | + | 0.0520029i | ||||
\(466\) | −11.9548 | + | 20.7064i | −0.553797 | + | 0.959205i | ||||
\(467\) | 13.0932i | 0.605881i | 0.953009 | + | 0.302941i | \(0.0979684\pi\) | ||||
−0.953009 | + | 0.302941i | \(0.902032\pi\) | |||||||
\(468\) | −0.273612 | + | 0.157970i | −0.0126477 | + | 0.00730216i | ||||
\(469\) | 1.14943 | − | 1.99087i | 0.0530757 | − | 0.0919298i | ||||
\(470\) | 11.3700 | − | 1.75987i | 0.524458 | − | 0.0811767i | ||||
\(471\) | 0.512826 | 0.0236298 | ||||||||
\(472\) | −11.0376 | − | 6.37254i | −0.508045 | − | 0.293320i | ||||
\(473\) | − | 2.18404i | − | 0.100422i | ||||||
\(474\) | 1.22680 | + | 2.12488i | 0.0563487 | + | 0.0975989i | ||||
\(475\) | −14.7917 | + | 4.69137i | −0.678690 | + | 0.215255i | ||||
\(476\) | −1.71934 | − | 2.97799i | −0.0788059 | − | 0.136496i | ||||
\(477\) | 4.71160 | − | 2.72024i | 0.215729 | − | 0.124551i | ||||
\(478\) | −25.9114 | + | 14.9600i | −1.18516 | + | 0.684253i | ||||
\(479\) | −12.5645 | + | 21.7624i | −0.574088 | + | 0.994349i | 0.422052 | + | 0.906572i | \(0.361310\pi\) |
−0.996140 | + | 0.0877779i | \(0.972023\pi\) | |||||||
\(480\) | −2.20975 | + | 0.342030i | −0.100861 | + | 0.0156115i | ||||
\(481\) | −0.396951 | − | 1.88034i | −0.0180994 | − | 0.0857363i | ||||
\(482\) | 12.9341i | 0.589134i | ||||||||
\(483\) | −24.6799 | − | 14.2489i | −1.12297 | − | 0.648349i | ||||
\(484\) | −5.45579 | − | 9.44970i | −0.247990 | − | 0.429532i | ||||
\(485\) | 15.4696 | − | 12.4372i | 0.702436 | − | 0.564744i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | − | 4.67830i | − | 0.211994i | −0.994366 | − | 0.105997i | \(-0.966197\pi\) | ||
0.994366 | − | 0.105997i | \(-0.0338034\pi\) | |||||||
\(488\) | 2.18655 | − | 1.26241i | 0.0989807 | − | 0.0571465i | ||||
\(489\) | −5.55541 | −0.251224 | ||||||||
\(490\) | 16.8737 | + | 6.54536i | 0.762274 | + | 0.295689i | ||||
\(491\) | −8.10382 | −0.365720 | −0.182860 | − | 0.983139i | \(-0.558536\pi\) | ||||
−0.182860 | + | 0.983139i | \(0.558536\pi\) | |||||||
\(492\) | − | 12.3599i | − | 0.557225i | ||||||
\(493\) | 3.74450 | + | 2.16189i | 0.168644 | + | 0.0973666i | ||||
\(494\) | −0.490270 | − | 0.849173i | −0.0220583 | − | 0.0382061i | ||||
\(495\) | −0.657091 | + | 0.101706i | −0.0295340 | + | 0.00457134i | ||||
\(496\) | −0.693350 | + | 1.20092i | −0.0311324 | + | 0.0539228i | ||||
\(497\) | −17.6205 | − | 10.1732i | −0.790390 | − | 0.456332i | ||||
\(498\) | 5.62000 | + | 3.24471i | 0.251838 | + | 0.145399i | ||||
\(499\) | 6.68241 | + | 11.5743i | 0.299146 | + | 0.518136i | 0.975941 | − | 0.218036i | \(-0.0699649\pi\) |
−0.676795 | + | 0.736172i | \(0.736632\pi\) | |||||||
\(500\) | −9.31187 | − | 6.18782i | −0.416439 | − | 0.276728i | ||||
\(501\) | 2.64016 | − | 4.57289i | 0.117954 | − | 0.204302i | ||||
\(502\) | −9.98983 | − | 5.76763i | −0.445868 | − | 0.257422i | ||||
\(503\) | 21.1165 | + | 12.1916i | 0.941539 | + | 0.543598i | 0.890443 | − | 0.455096i | \(-0.150395\pi\) |
0.0510969 | + | 0.998694i | \(0.483728\pi\) | |||||||
\(504\) | 3.88510 | 0.173056 | ||||||||
\(505\) | −9.88294 | − | 12.2925i | −0.439785 | − | 0.547011i | ||||
\(506\) | −1.09059 | + | 1.88896i | −0.0484827 | + | 0.0839745i | ||||
\(507\) | 12.9002i | 0.572917i | ||||||||
\(508\) | − | 11.3907i | − | 0.505382i | ||||||
\(509\) | −5.64271 | + | 9.77345i | −0.250109 | + | 0.433201i | −0.963555 | − | 0.267509i | \(-0.913800\pi\) |
0.713447 | + | 0.700709i | \(0.247133\pi\) | |||||||
\(510\) | −0.302730 | − | 1.95585i | −0.0134051 | − | 0.0866063i | ||||
\(511\) | 28.0293 | + | 48.5482i | 1.23994 | + | 2.14765i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 2.68777 | − | 1.55178i | 0.118668 | − | 0.0685130i | ||||
\(514\) | −5.18038 | − | 8.97268i | −0.228497 | − | 0.395768i | ||||
\(515\) | −10.3522 | + | 8.32293i | −0.456172 | + | 0.366752i | ||||
\(516\) | −3.67239 | + | 6.36076i | −0.161668 | + | 0.280017i | ||||
\(517\) | 1.53002i | 0.0672902i | ||||||||
\(518\) | −7.33393 | + | 22.4653i | −0.322234 | + | 0.987069i | ||||
\(519\) | −21.2820 | −0.934178 | ||||||||
\(520\) | 0.255491 | − | 0.658645i | 0.0112040 | − | 0.0288835i | ||||
\(521\) | −8.10569 | − | 14.0395i | −0.355117 | − | 0.615080i | 0.632021 | − | 0.774951i | \(-0.282225\pi\) |
−0.987138 | + | 0.159871i | \(0.948892\pi\) | |||||||
\(522\) | −4.23062 | + | 2.44255i | −0.185169 | + | 0.106907i | ||||
\(523\) | 19.3660 | − | 11.1810i | 0.846817 | − | 0.488910i | −0.0127588 | − | 0.999919i | \(-0.504061\pi\) |
0.859575 | + | 0.511009i | \(0.170728\pi\) | |||||||
\(524\) | −14.4407 | −0.630844 | ||||||||
\(525\) | 14.3442 | + | 13.0994i | 0.626031 | + | 0.571704i | ||||
\(526\) | −3.37234 | −0.147041 | ||||||||
\(527\) | −1.06293 | − | 0.613682i | −0.0463019 | − | 0.0267324i | ||||
\(528\) | − | 0.297359i | − | 0.0129409i | ||||||
\(529\) | −30.8048 | −1.33934 | ||||||||
\(530\) | −4.39956 | + | 11.3419i | −0.191105 | + | 0.492659i | ||||
\(531\) | 6.37254 | + | 11.0376i | 0.276545 | + | 0.478990i | ||||
\(532\) | 12.0577i | 0.522766i | ||||||||
\(533\) | 3.38180 | + | 1.95249i | 0.146482 | + | 0.0845715i | ||||
\(534\) | 2.65348 | − | 4.59596i | 0.114827 | − | 0.198887i | ||||
\(535\) | 28.8068 | + | 11.1743i | 1.24543 | + | 0.483106i | ||||
\(536\) | 0.295856 | + | 0.512438i | 0.0127790 | + | 0.0221339i | ||||
\(537\) | −15.8863 | + | 9.17195i | −0.685544 | + | 0.395799i | ||||
\(538\) | 11.7715 | + | 6.79627i | 0.507505 | + | 0.293008i | ||||
\(539\) | −1.20341 | + | 2.08437i | −0.0518345 | + | 0.0897800i | ||||
\(540\) | 2.08472 | + | 0.808671i | 0.0897120 | + | 0.0347996i | ||||
\(541\) | 19.8953 | 0.855368 | 0.427684 | − | 0.903928i | \(-0.359330\pi\) | ||||
0.427684 | + | 0.903928i | \(0.359330\pi\) | |||||||
\(542\) | 10.0385 | − | 5.79573i | 0.431191 | − | 0.248948i | ||||
\(543\) | 12.4975 | + | 7.21545i | 0.536320 | + | 0.309645i | ||||
\(544\) | 0.885096 | 0.0379482 | ||||||||
\(545\) | 13.6172 | − | 2.10770i | 0.583297 | − | 0.0902839i | ||||
\(546\) | −0.613728 | + | 1.06301i | −0.0262651 | + | 0.0454926i | ||||
\(547\) | 36.1842i | 1.54712i | 0.633721 | + | 0.773562i | \(0.281527\pi\) | ||||
−0.633721 | + | 0.773562i | \(0.718473\pi\) | |||||||
\(548\) | 12.1491 | − | 7.01426i | 0.518982 | − | 0.299634i | ||||
\(549\) | −2.52482 | −0.107757 | ||||||||
\(550\) | 1.00261 | − | 1.09788i | 0.0427513 | − | 0.0468138i | ||||
\(551\) | −7.58062 | − | 13.1300i | −0.322945 | − | 0.559357i | ||||
\(552\) | 6.35245 | − | 3.66759i | 0.270378 | − | 0.156103i | ||||
\(553\) | 8.25535 | + | 4.76623i | 0.351053 | + | 0.202681i | ||||
\(554\) | 15.0114 | 0.637773 | ||||||||
\(555\) | −8.61143 | + | 10.5282i | −0.365535 | + | 0.446898i | ||||
\(556\) | 19.5867 | 0.830659 | ||||||||
\(557\) | −7.64850 | − | 4.41586i | −0.324077 | − | 0.187106i | 0.329131 | − | 0.944284i | \(-0.393244\pi\) |
−0.653209 | + | 0.757178i | \(0.726578\pi\) | |||||||
\(558\) | 1.20092 | − | 0.693350i | 0.0508389 | − | 0.0293519i | ||||
\(559\) | −1.16025 | − | 2.00962i | −0.0490735 | − | 0.0849977i | ||||
\(560\) | −6.77051 | + | 5.44335i | −0.286106 | + | 0.230023i | ||||
\(561\) | 0.263192 | 0.0111120 | ||||||||
\(562\) | 18.0352 | − | 10.4127i | 0.760771 | − | 0.439231i | ||||
\(563\) | 23.4622i | 0.988815i | 0.869230 | + | 0.494407i | \(0.164615\pi\) | ||||
−0.869230 | + | 0.494407i | \(0.835385\pi\) | |||||||
\(564\) | 2.57268 | − | 4.45601i | 0.108329 | − | 0.187632i | ||||
\(565\) | 1.51302 | + | 9.77520i | 0.0636534 | + | 0.411246i | ||||
\(566\) | −7.94608 | −0.333999 | ||||||||
\(567\) | −3.36459 | − | 1.94255i | −0.141300 | − | 0.0815794i | ||||
\(568\) | 4.53542 | − | 2.61853i | 0.190302 | − | 0.109871i | ||||
\(569\) | 22.5086 | 0.943612 | 0.471806 | − | 0.881702i | \(-0.343602\pi\) | ||||
0.471806 | + | 0.881702i | \(0.343602\pi\) | |||||||
\(570\) | −2.50977 | + | 6.47007i | −0.105122 | + | 0.271001i | ||||
\(571\) | 7.70572 | − | 13.3467i | 0.322474 | − | 0.558542i | −0.658524 | − | 0.752560i | \(-0.728819\pi\) |
0.980998 | + | 0.194018i | \(0.0621520\pi\) | |||||||
\(572\) | 0.0813610 | + | 0.0469738i | 0.00340188 | + | 0.00196407i | ||||
\(573\) | 6.02174 | − | 3.47665i | 0.251562 | − | 0.145239i | ||||
\(574\) | −24.0096 | − | 41.5859i | −1.00214 | − | 1.73576i | ||||
\(575\) | 35.8199 | + | 7.87744i | 1.49379 | + | 0.328512i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 8.01405 | + | 4.62692i | 0.333629 | + | 0.192621i | 0.657451 | − | 0.753497i | \(-0.271635\pi\) |
−0.323822 | + | 0.946118i | \(0.604968\pi\) | |||||||
\(578\) | − | 16.2166i | − | 0.674522i | ||||||
\(579\) | −12.2336 | − | 21.1891i | −0.508409 | − | 0.880591i | ||||
\(580\) | 3.95043 | − | 10.1841i | 0.164033 | − | 0.422870i | ||||
\(581\) | 25.2120 | 1.04597 | ||||||||
\(582\) | − | 8.87683i | − | 0.367957i | ||||||
\(583\) | −1.40104 | − | 0.808889i | −0.0580250 | − | 0.0335008i | ||||
\(584\) | −14.4291 | −0.597082 | ||||||||
\(585\) | −0.550585 | + | 0.442658i | −0.0227639 | + | 0.0183017i | ||||
\(586\) | 19.5615 | 0.808080 | ||||||||
\(587\) | 15.3642 | − | 8.87053i | 0.634149 | − | 0.366126i | −0.148208 | − | 0.988956i | \(-0.547351\pi\) |
0.782357 | + | 0.622830i | \(0.214017\pi\) | |||||||
\(588\) | 7.00959 | − | 4.04699i | 0.289070 | − | 0.166895i | ||||
\(589\) | 2.15186 | + | 3.72713i | 0.0886659 | + | 0.153574i | ||||
\(590\) | −26.5699 | − | 10.3066i | −1.09387 | − | 0.424315i | ||||
\(591\) | −21.8285 | −0.897905 | ||||||||
\(592\) | −4.06388 | − | 4.52602i | −0.167024 | − | 0.186018i | ||||
\(593\) | − | 0.121693i | − | 0.00499735i | −0.999997 | − | 0.00249867i | \(-0.999205\pi\) | ||
0.999997 | − | 0.00249867i | \(-0.000795353\pi\) | |||||||
\(594\) | −0.148680 | + | 0.257521i | −0.00610040 | + | 0.0105662i | ||||
\(595\) | −4.81788 | − | 5.99255i | −0.197514 | − | 0.245671i | ||||
\(596\) | 2.44800 | + | 4.24007i | 0.100274 | + | 0.173680i | ||||
\(597\) | −8.07412 | + | 4.66159i | −0.330452 | + | 0.190786i | ||||
\(598\) | 2.31747i | 0.0947685i | ||||||||
\(599\) | 18.4792 | + | 32.0069i | 0.755039 | + | 1.30777i | 0.945355 | + | 0.326042i | \(0.105715\pi\) |
−0.190317 | + | 0.981723i | \(0.560951\pi\) | |||||||
\(600\) | −4.76603 | + | 1.51161i | −0.194572 | + | 0.0617110i | ||||
\(601\) | −6.53316 | + | 11.3158i | −0.266493 | + | 0.461580i | −0.967954 | − | 0.251129i | \(-0.919198\pi\) |
0.701461 | + | 0.712708i | \(0.252532\pi\) | |||||||
\(602\) | 28.5351i | 1.16301i | ||||||||
\(603\) | − | 0.591712i | − | 0.0240964i | ||||||
\(604\) | 2.85747 | − | 4.94928i | 0.116269 | − | 0.201383i | ||||
\(605\) | −15.2880 | − | 19.0155i | −0.621547 | − | 0.773089i | ||||
\(606\) | −7.05378 | −0.286540 | ||||||||
\(607\) | 32.7606 | + | 18.9143i | 1.32971 | + | 0.767710i | 0.985255 | − | 0.171093i | \(-0.0547297\pi\) |
0.344457 | + | 0.938802i | \(0.388063\pi\) | |||||||
\(608\) | −2.68777 | − | 1.55178i | −0.109003 | − | 0.0629332i | ||||
\(609\) | −9.48953 | + | 16.4364i | −0.384535 | + | 0.666035i | ||||
\(610\) | 4.39997 | − | 3.53748i | 0.178149 | − | 0.143228i | ||||
\(611\) | 0.812812 | + | 1.40783i | 0.0328829 | + | 0.0569548i | ||||
\(612\) | −0.766516 | − | 0.442548i | −0.0309846 | − | 0.0178889i | ||||
\(613\) | 15.6579 | + | 9.04011i | 0.632418 | + | 0.365127i | 0.781688 | − | 0.623670i | \(-0.214359\pi\) |
−0.149270 | + | 0.988796i | \(0.547692\pi\) | |||||||
\(614\) | −3.58294 | + | 6.20583i | −0.144596 | + | 0.250447i | ||||
\(615\) | −4.22744 | − | 27.3123i | −0.170467 | − | 1.10134i | ||||
\(616\) | −0.577635 | − | 1.00049i | −0.0232736 | − | 0.0403110i | ||||
\(617\) | 24.4225 | + | 14.1003i | 0.983213 | + | 0.567658i | 0.903239 | − | 0.429139i | \(-0.141183\pi\) |
0.0799744 | + | 0.996797i | \(0.474516\pi\) | |||||||
\(618\) | 5.94035i | 0.238956i | ||||||||
\(619\) | −28.9547 | −1.16379 | −0.581894 | − | 0.813264i | \(-0.697688\pi\) | ||||
−0.581894 | + | 0.813264i | \(0.697688\pi\) | |||||||
\(620\) | −1.12138 | + | 2.89088i | −0.0450359 | + | 0.116101i | ||||
\(621\) | −7.33518 | −0.294350 | ||||||||
\(622\) | 22.0099 | − | 12.7074i | 0.882516 | − | 0.509521i | ||||
\(623\) | − | 20.6180i | − | 0.826044i | ||||||
\(624\) | −0.157970 | − | 0.273612i | −0.00632386 | − | 0.0109532i | ||||
\(625\) | −22.6934 | − | 10.4886i | −0.907735 | − | 0.419545i | ||||
\(626\) | 1.57843 | + | 2.73391i | 0.0630866 | + | 0.109269i | ||||
\(627\) | −0.799233 | − | 0.461438i | −0.0319183 | − | 0.0184280i | ||||
\(628\) | 0.512826i | 0.0204640i | ||||||||
\(629\) | 4.00596 | − | 3.59693i | 0.159728 | − | 0.143419i | ||||
\(630\) | 8.58511 | − | 1.32882i | 0.342039 | − | 0.0529415i | ||||
\(631\) | −24.6501 | + | 42.6952i | −0.981304 | + | 1.69967i | −0.323974 | + | 0.946066i | \(0.605019\pi\) |
−0.657330 | + | 0.753603i | \(0.728314\pi\) | |||||||
\(632\) | −2.12488 | + | 1.22680i | −0.0845231 | + | 0.0487994i | ||||
\(633\) | 4.52695 | − | 2.61364i | 0.179930 | − | 0.103883i | ||||
\(634\) | −2.82073 | − | 4.88564i | −0.112025 | − | 0.194034i | ||||
\(635\) | −3.89598 | − | 25.1707i | −0.154607 | − | 0.998870i | ||||
\(636\) | 2.72024 | + | 4.71160i | 0.107865 | + | 0.186827i | ||||
\(637\) | 2.55721i | 0.101320i | ||||||||
\(638\) | 1.25801 | + | 0.726314i | 0.0498052 | + | 0.0287551i | ||||
\(639\) | −5.23705 | −0.207175 | ||||||||
\(640\) | −0.342030 | − | 2.20975i | −0.0135199 | − | 0.0873482i | ||||
\(641\) | −6.83132 | + | 11.8322i | −0.269821 | + | 0.467344i | −0.968815 | − | 0.247783i | \(-0.920298\pi\) |
0.698995 | + | 0.715127i | \(0.253631\pi\) | |||||||
\(642\) | 11.9668 | − | 6.90904i | 0.472292 | − | 0.272678i | ||||
\(643\) | − | 25.4872i | − | 1.00512i | −0.864544 | − | 0.502558i | \(-0.832392\pi\) | ||
0.864544 | − | 0.502558i | \(-0.167608\pi\) | |||||||
\(644\) | 14.2489 | − | 24.6799i | 0.561487 | − | 0.972523i | ||||
\(645\) | −5.93950 | + | 15.3118i | −0.233868 | + | 0.602901i | ||||
\(646\) | 1.37348 | − | 2.37893i | 0.0540388 | − | 0.0935979i | ||||
\(647\) | 12.9156 | − | 7.45681i | 0.507764 | − | 0.293158i | −0.224150 | − | 0.974555i | \(-0.571961\pi\) |
0.731914 | + | 0.681397i | \(0.238627\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 1.89493 | − | 3.28212i | 0.0743827 | − | 0.128835i | ||||
\(650\) | 0.339296 | − | 1.54283i | 0.0133083 | − | 0.0605148i | ||||
\(651\) | 2.69373 | − | 4.66568i | 0.105576 | − | 0.182863i | ||||
\(652\) | − | 5.55541i | − | 0.217566i | ||||||
\(653\) | −19.5857 | + | 11.3078i | −0.766449 | + | 0.442510i | −0.831606 | − | 0.555365i | \(-0.812578\pi\) |
0.0651574 | + | 0.997875i | \(0.479245\pi\) | |||||||
\(654\) | 3.08116 | − | 5.33672i | 0.120483 | − | 0.208682i | ||||
\(655\) | −31.9104 | + | 4.93915i | −1.24684 | + | 0.192988i | ||||
\(656\) | 12.3599 | 0.482571 | ||||||||
\(657\) | 12.4960 | + | 7.21457i | 0.487516 | + | 0.281467i | ||||
\(658\) | − | 19.9902i | − | 0.779300i | ||||||
\(659\) | 15.3180 | + | 26.5316i | 0.596705 | + | 1.03352i | 0.993304 | + | 0.115531i | \(0.0368569\pi\) |
−0.396599 | + | 0.917992i | \(0.629810\pi\) | |||||||
\(660\) | −0.101706 | − | 0.657091i | −0.00395889 | − | 0.0255772i | ||||
\(661\) | −21.5266 | − | 37.2852i | −0.837289 | − | 1.45023i | −0.892153 | − | 0.451733i | \(-0.850806\pi\) |
0.0548648 | − | 0.998494i | \(-0.482527\pi\) | |||||||
\(662\) | −1.75630 | + | 1.01400i | −0.0682607 | + | 0.0394103i | ||||
\(663\) | 0.242173 | − | 0.139819i | 0.00940521 | − | 0.00543010i | ||||
\(664\) | −3.24471 | + | 5.62000i | −0.125919 | + | 0.218098i | ||||
\(665\) | 4.12409 | + | 26.6445i | 0.159925 | + | 1.03323i | ||||
\(666\) | 1.25641 | + | 5.95159i | 0.0486850 | + | 0.230619i | ||||
\(667\) | 35.8330i | 1.38746i | ||||||||
\(668\) | 4.57289 | + | 2.64016i | 0.176930 | + | 0.102151i | ||||
\(669\) | 7.17951 | + | 12.4353i | 0.277576 | + | 0.480776i | ||||
\(670\) | 0.829039 | + | 1.03117i | 0.0320286 | + | 0.0398376i | ||||
\(671\) | 0.375389 | + | 0.650192i | 0.0144917 | + | 0.0251004i | ||||
\(672\) | 3.88510i | 0.149871i | ||||||||
\(673\) | −4.54995 | + | 2.62692i | −0.175388 | + | 0.101260i | −0.585124 | − | 0.810944i | \(-0.698954\pi\) |
0.409736 | + | 0.912204i | \(0.365621\pi\) | |||||||
\(674\) | 31.8795 | 1.22795 | ||||||||
\(675\) | 4.88331 | + | 1.07393i | 0.187959 | + | 0.0413355i | ||||
\(676\) | −12.9002 | −0.496161 | ||||||||
\(677\) | − | 32.3513i | − | 1.24336i | −0.783271 | − | 0.621680i | \(-0.786450\pi\) | ||
0.783271 | − | 0.621680i | \(-0.213550\pi\) | |||||||
\(678\) | 3.83100 | + | 2.21183i | 0.147129 | + | 0.0849448i | ||||
\(679\) | −17.2437 | − | 29.8669i | −0.661752 | − | 1.14619i | ||||
\(680\) | 1.95585 | − | 0.302730i | 0.0750032 | − | 0.0116091i | ||||
\(681\) | −2.51561 | + | 4.35717i | −0.0963985 | + | 0.166967i | ||||
\(682\) | −0.357104 | − | 0.206174i | −0.0136742 | − | 0.00789482i | ||||
\(683\) | −10.1060 | − | 5.83471i | −0.386696 | − | 0.223259i | 0.294032 | − | 0.955796i | \(-0.405003\pi\) |
−0.680728 | + | 0.732537i | \(0.738336\pi\) | |||||||
\(684\) | 1.55178 | + | 2.68777i | 0.0593340 | + | 0.102769i | ||||
\(685\) | 24.4473 | − | 19.6551i | 0.934085 | − | 0.750984i | ||||
\(686\) | 2.12509 | − | 3.68077i | 0.0811364 | − | 0.140532i | ||||
\(687\) | 2.15533 | + | 1.24438i | 0.0822309 | + | 0.0474760i | ||||
\(688\) | −6.36076 | − | 3.67239i | −0.242502 | − | 0.140008i | ||||
\(689\) | −1.71886 | −0.0654835 | ||||||||
\(690\) | 12.7829 | − | 10.2772i | 0.486638 | − | 0.391246i | ||||
\(691\) | −12.3043 | + | 21.3117i | −0.468077 | + | 0.810734i | −0.999334 | − | 0.0364770i | \(-0.988386\pi\) |
0.531257 | + | 0.847211i | \(0.321720\pi\) | |||||||
\(692\) | − | 21.2820i | − | 0.809022i | ||||||
\(693\) | 1.15527i | 0.0438851i | ||||||||
\(694\) | 4.25577 | − | 7.37122i | 0.161547 | − | 0.279807i | ||||
\(695\) | 43.2817 | − | 6.69923i | 1.64177 | − | 0.254116i | ||||
\(696\) | −2.44255 | − | 4.23062i | −0.0925845 | − | 0.160361i | ||||
\(697\) | 10.9397i | 0.414369i | ||||||||
\(698\) | −13.0926 | + | 7.55902i | −0.495562 | + | 0.286113i | ||||
\(699\) | 11.9548 | + | 20.7064i | 0.452174 | + | 0.783188i | ||||
\(700\) | −13.0994 | + | 14.3442i | −0.495110 | + | 0.542159i | ||||
\(701\) | −4.03627 | + | 6.99102i | −0.152448 | + | 0.264047i | −0.932127 | − | 0.362132i | \(-0.882049\pi\) |
0.779679 | + | 0.626179i | \(0.215382\pi\) | |||||||
\(702\) | 0.315940i | 0.0119244i | ||||||||
\(703\) | −18.4712 | + | 3.89937i | −0.696654 | + | 0.147067i | ||||
\(704\) | 0.297359 | 0.0112071 | ||||||||
\(705\) | 4.16090 | − | 10.7266i | 0.156709 | − | 0.403988i | ||||
\(706\) | 13.2015 | + | 22.8657i | 0.496845 | + | 0.860560i | ||||
\(707\) | −23.7331 | + | 13.7023i | −0.892575 | + | 0.515328i | ||||
\(708\) | −11.0376 | + | 6.37254i | −0.414817 | + | 0.239495i | ||||
\(709\) | 42.1290 | 1.58219 | 0.791094 | − | 0.611694i | \(-0.209512\pi\) | ||||
0.791094 | + | 0.611694i | \(0.209512\pi\) | |||||||
\(710\) | 9.12655 | − | 7.33755i | 0.342513 | − | 0.275373i | ||||
\(711\) | 2.45360 | 0.0920171 | ||||||||
\(712\) | 4.59596 | + | 2.65348i | 0.172241 | + | 0.0994433i | ||||
\(713\) | − | 10.1717i | − | 0.380933i | ||||||
\(714\) | −3.43868 | −0.128689 | ||||||||
\(715\) | 0.195854 | + | 0.0759727i | 0.00732454 | + | 0.00284122i | ||||
\(716\) | −9.17195 | − | 15.8863i | −0.342772 | − | 0.593698i | ||||
\(717\) | 29.9199i | 1.11738i | ||||||||
\(718\) | −13.7298 | − | 7.92689i | −0.512391 | − | 0.295829i | ||||
\(719\) | 20.1969 | − | 34.9821i | 0.753218 | − | 1.30461i | −0.193037 | − | 0.981192i | \(-0.561834\pi\) |
0.946255 | − | 0.323421i | \(-0.104833\pi\) | |||||||
\(720\) | −0.808671 | + | 2.08472i | −0.0301374 | + | 0.0776929i | ||||
\(721\) | 11.5394 | + | 19.9869i | 0.429750 | + | 0.744349i | ||||
\(722\) | 8.11280 | − | 4.68393i | 0.301927 | − | 0.174318i | ||||
\(723\) | 11.2013 | + | 6.46707i | 0.416580 | + | 0.240513i | ||||
\(724\) | −7.21545 | + | 12.4975i | −0.268160 | + | 0.464467i | ||||
\(725\) | 5.24624 | − | 23.8554i | 0.194840 | − | 0.885968i | ||||
\(726\) | −10.9116 | −0.404967 | ||||||||
\(727\) | −37.6222 | + | 21.7212i | −1.39533 | + | 0.805594i | −0.993899 | − | 0.110296i | \(-0.964820\pi\) |
−0.401430 | + | 0.915890i | \(0.631487\pi\) | |||||||
\(728\) | −1.06301 | − | 0.613728i | −0.0393977 | − | 0.0227463i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −31.8849 | + | 4.93520i | −1.18011 | + | 0.182660i | ||||
\(731\) | 3.25041 | − | 5.62988i | 0.120221 | − | 0.208229i | ||||
\(732\) | − | 2.52482i | − | 0.0933199i | ||||||
\(733\) | −6.68259 | + | 3.85819i | −0.246827 | + | 0.142506i | −0.618310 | − | 0.785934i | \(-0.712183\pi\) |
0.371484 | + | 0.928440i | \(0.378849\pi\) | |||||||
\(734\) | 28.4155 | 1.04883 | ||||||||
\(735\) | 14.1053 | − | 11.3403i | 0.520281 | − | 0.418295i | ||||
\(736\) | 3.66759 | + | 6.35245i | 0.135189 | + | 0.234154i | ||||
\(737\) | −0.152378 | + | 0.0879756i | −0.00561292 | + | 0.00324062i | ||||
\(738\) | −10.7040 | − | 6.17993i | −0.394018 | − | 0.227486i | ||||
\(739\) | −41.2019 | −1.51564 | −0.757818 | − | 0.652466i | \(-0.773735\pi\) | ||||
−0.757818 | + | 0.652466i | \(0.773735\pi\) | |||||||
\(740\) | −10.5282 | − | 8.61143i | −0.387025 | − | 0.316562i | ||||
\(741\) | −0.980541 | −0.0360211 | ||||||||
\(742\) | 18.3050 | + | 10.5684i | 0.671998 | + | 0.387978i | ||||
\(743\) | 15.5183 | − | 8.95952i | 0.569313 | − | 0.328693i | −0.187562 | − | 0.982253i | \(-0.560059\pi\) |
0.756875 | + | 0.653560i | \(0.226725\pi\) | |||||||
\(744\) | 0.693350 | + | 1.20092i | 0.0254195 | + | 0.0440278i | ||||
\(745\) | 6.85972 | + | 8.53222i | 0.251321 | + | 0.312596i | ||||
\(746\) | −4.90800 | −0.179695 | ||||||||
\(747\) | 5.62000 | − | 3.24471i | 0.205625 | − | 0.118718i | ||||
\(748\) | 0.263192i | 0.00962324i | ||||||||
\(749\) | 26.8423 | − | 46.4922i | 0.980796 | − | 1.69879i | ||||
\(750\) | −10.0147 | + | 4.97040i | −0.365687 | + | 0.181493i | ||||
\(751\) | 25.5716 | 0.933120 | 0.466560 | − | 0.884490i | \(-0.345493\pi\) | ||||
0.466560 | + | 0.884490i | \(0.345493\pi\) | |||||||
\(752\) | 4.45601 | + | 2.57268i | 0.162494 | + | 0.0938160i | ||||
\(753\) | −9.98983 | + | 5.76763i | −0.364050 | + | 0.210184i | ||||
\(754\) | 1.54340 | 0.0562072 | ||||||||
\(755\) | 4.62150 | − | 11.9140i | 0.168194 | − | 0.433596i | ||||
\(756\) | 1.94255 | − | 3.36459i | 0.0706498 | − | 0.122369i | ||||
\(757\) | −4.64047 | − | 2.67918i | −0.168661 | − | 0.0973763i | 0.413293 | − | 0.910598i | \(-0.364378\pi\) |
−0.581954 | + | 0.813222i | \(0.697712\pi\) | |||||||
\(758\) | −18.8795 | + | 10.9001i | −0.685733 | + | 0.395908i | ||||
\(759\) | 1.09059 | + | 1.88896i | 0.0395860 | + | 0.0685649i | ||||
\(760\) | −6.47007 | − | 2.50977i | −0.234694 | − | 0.0910387i | ||||
\(761\) | −26.4595 | + | 45.8292i | −0.959156 | + | 1.66131i | −0.234598 | + | 0.972092i | \(0.575377\pi\) |
−0.724558 | + | 0.689214i | \(0.757956\pi\) | |||||||
\(762\) | −9.86467 | − | 5.69537i | −0.357359 | − | 0.206321i | ||||
\(763\) | − | 23.9412i | − | 0.866729i | ||||||
\(764\) | 3.47665 | + | 6.02174i | 0.125781 | + | 0.217859i | ||||
\(765\) | −1.84518 | − | 0.715751i | −0.0667125 | − | 0.0258780i | ||||
\(766\) | 21.6591 | 0.782574 | ||||||||
\(767\) | − | 4.02668i | − | 0.145395i | ||||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | −17.6816 | −0.637615 | −0.318808 | − | 0.947819i | \(-0.603282\pi\) | ||||
−0.318808 | + | 0.947819i | \(0.603282\pi\) | |||||||
\(770\) | −1.61863 | − | 2.01327i | −0.0583314 | − | 0.0725534i | ||||
\(771\) | −10.3608 | −0.373134 | ||||||||
\(772\) | 21.1891 | − | 12.2336i | 0.762614 | − | 0.440295i | ||||
\(773\) | 16.7129 | − | 9.64917i | 0.601120 | − | 0.347057i | −0.168362 | − | 0.985725i | \(-0.553848\pi\) |
0.769482 | + | 0.638669i | \(0.220514\pi\) | |||||||
\(774\) | 3.67239 | + | 6.36076i | 0.132001 | + | 0.228633i | ||||
\(775\) | −1.48922 | + | 6.77169i | −0.0534942 | + | 0.243246i | ||||
\(776\) | 8.87683 | 0.318660 | ||||||||
\(777\) | 15.7886 | + | 17.5840i | 0.566412 | + | 0.630824i | ||||
\(778\) | 20.2810i | 0.727110i | ||||||||
\(779\) | 19.1798 | − | 33.2205i | 0.687189 | − | 1.19025i | ||||
\(780\) | −0.442658 | − | 0.550585i | −0.0158497 | − | 0.0197141i | ||||
\(781\) | 0.778643 | + | 1.34865i | 0.0278620 | + | 0.0482585i | ||||
\(782\) | −5.62253 | + | 3.24617i | −0.201061 | + | 0.116083i | ||||
\(783\) | 4.88510i | 0.174579i | ||||||||
\(784\) | 4.04699 | + | 7.00959i | 0.144535 | + | 0.250342i | ||||
\(785\) | 0.175402 | + | 1.13322i | 0.00626037 | + | 0.0404464i | ||||
\(786\) | −7.22034 | + | 12.5060i | −0.257541 | + | 0.446074i | ||||
\(787\) | − | 29.5664i | − | 1.05393i | −0.849888 | − | 0.526963i | \(-0.823330\pi\) | ||
0.849888 | − | 0.526963i | \(-0.176670\pi\) | |||||||
\(788\) | − | 21.8285i | − | 0.777609i | ||||||
\(789\) | −1.68617 | + | 2.92053i | −0.0600292 | + | 0.103974i | ||||
\(790\) | −4.27586 | + | 3.43770i | −0.152128 | + | 0.122308i | ||||
\(791\) | 17.1863 | 0.611076 | ||||||||
\(792\) | −0.257521 | − | 0.148680i | −0.00915060 | − | 0.00528310i | ||||
\(793\) | 0.690819 | + | 0.398845i | 0.0245317 | + | 0.0141634i | ||||
\(794\) | 6.24284 | − | 10.8129i | 0.221550 | − | 0.383736i | ||||
\(795\) | 7.62257 | + | 9.48106i | 0.270345 | + | 0.336259i | ||||
\(796\) | −4.66159 | − | 8.07412i | −0.165226 | − | 0.286179i | ||||
\(797\) | 47.5797 | + | 27.4702i | 1.68536 | + | 0.973043i | 0.957992 | + | 0.286795i | \(0.0925899\pi\) |
0.727368 | + | 0.686248i | \(0.240743\pi\) | |||||||
\(798\) | 10.4422 | + | 6.02883i | 0.369651 | + | 0.213418i | ||||
\(799\) | −2.27707 | + | 3.94400i | −0.0805569 | + | 0.139529i | ||||
\(800\) | −1.51161 | − | 4.76603i | −0.0534433 | − | 0.168505i | ||||
\(801\) | −2.65348 | − | 4.59596i | −0.0937561 | − | 0.162390i | ||||
\(802\) | −3.72278 | − | 2.14935i | −0.131456 | − | 0.0758961i | ||||
\(803\) | − | 4.29064i | − | 0.151413i | ||||||
\(804\) | 0.591712 | 0.0208681 | ||||||||
\(805\) | 23.0454 | − | 59.4100i | 0.812243 | − | 2.09393i | ||||
\(806\) | −0.438114 | −0.0154319 | ||||||||
\(807\) | 11.7715 | − | 6.79627i | 0.414376 | − | 0.239240i | ||||
\(808\) | − | 7.05378i | − | 0.248151i | ||||||
\(809\) | 12.2224 | + | 21.1698i | 0.429716 | + | 0.744289i | 0.996848 | − | 0.0793374i | \(-0.0252805\pi\) |
−0.567132 | + | 0.823627i | \(0.691947\pi\) | |||||||
\(810\) | 1.74269 | − | 1.40108i | 0.0612318 | − | 0.0492291i | ||||
\(811\) | 15.4561 | + | 26.7707i | 0.542737 | + | 0.940048i | 0.998746 | + | 0.0500725i | \(0.0159452\pi\) |
−0.456009 | + | 0.889975i | \(0.650721\pi\) | |||||||
\(812\) | −16.4364 | − | 9.48953i | −0.576803 | − | 0.333017i | ||||
\(813\) | − | 11.5915i | − | 0.406530i | ||||||
\(814\) | 1.34585 | − | 1.20843i | 0.0471722 | − | 0.0423555i | ||||
\(815\) | −1.90012 | − | 12.2761i | −0.0665582 | − | 0.430012i | ||||
\(816\) | 0.442548 | − | 0.766516i | 0.0154923 | − | 0.0268334i | ||||
\(817\) | −19.7411 | + | 11.3975i | −0.690652 | + | 0.398748i | ||||
\(818\) | 5.10692 | − | 2.94848i | 0.178559 | − | 0.103091i | ||||
\(819\) | 0.613728 | + | 1.06301i | 0.0214454 | + | 0.0371445i | ||||
\(820\) | 27.3123 | − | 4.22744i | 0.953785 | − | 0.147629i | ||||
\(821\) | −16.4835 | − | 28.5503i | −0.575279 | − | 0.996412i | −0.996011 | − | 0.0892274i | \(-0.971560\pi\) |
0.420732 | − | 0.907185i | \(-0.361773\pi\) | |||||||
\(822\) | − | 14.0285i | − | 0.489301i | ||||||
\(823\) | 33.4584 | + | 19.3172i | 1.16629 | + | 0.673356i | 0.952803 | − | 0.303590i | \(-0.0981854\pi\) |
0.213485 | + | 0.976946i | \(0.431519\pi\) | |||||||
\(824\) | −5.94035 | −0.206942 | ||||||||
\(825\) | −0.449490 | − | 1.41722i | −0.0156492 | − | 0.0493414i | ||||
\(826\) | −24.7579 | + | 42.8820i | −0.861439 | + | 1.49206i | ||||
\(827\) | −29.9212 | + | 17.2750i | −1.04046 | + | 0.600711i | −0.919964 | − | 0.392003i | \(-0.871782\pi\) |
−0.120498 | + | 0.992714i | \(0.538449\pi\) | |||||||
\(828\) | − | 7.33518i | − | 0.254915i | ||||||
\(829\) | 26.1312 | − | 45.2606i | 0.907575 | − | 1.57197i | 0.0901510 | − | 0.995928i | \(-0.471265\pi\) |
0.817424 | − | 0.576037i | \(-0.195402\pi\) | |||||||
\(830\) | −5.24780 | + | 13.5286i | −0.182154 | + | 0.469585i | ||||
\(831\) | 7.50570 | − | 13.0002i | 0.260370 | − | 0.450974i | ||||
\(832\) | 0.273612 | − | 0.157970i | 0.00948578 | − | 0.00547662i | ||||
\(833\) | −6.20416 | + | 3.58197i | −0.214961 | + | 0.124108i | ||||
\(834\) | 9.79333 | − | 16.9625i | 0.339115 | − | 0.587365i | ||||
\(835\) | 11.0080 | + | 4.27004i | 0.380947 | + | 0.147771i | ||||
\(836\) | 0.461438 | − | 0.799233i | 0.0159592 | − | 0.0276421i | ||||
\(837\) | − | 1.38670i | − | 0.0479314i | ||||||
\(838\) | 10.3461 | − | 5.97334i | 0.357401 | − | 0.206345i | ||||
\(839\) | −13.3565 | + | 23.1341i | −0.461117 | + | 0.798679i | −0.999017 | − | 0.0443302i | \(-0.985885\pi\) |
0.537900 | + | 0.843009i | \(0.319218\pi\) | |||||||
\(840\) | 1.32882 | + | 8.58511i | 0.0458486 | + | 0.296214i | ||||
\(841\) | −5.13584 | −0.177098 | ||||||||
\(842\) | 26.1596 | + | 15.1032i | 0.901518 | + | 0.520491i | ||||
\(843\) | − | 20.8253i | − | 0.717262i | ||||||
\(844\) | 2.61364 | + | 4.52695i | 0.0899652 | + | 0.155824i | ||||
\(845\) | −28.5062 | + | 4.41225i | −0.980644 | + | 0.151786i | ||||
\(846\) | −2.57268 | − | 4.45601i | −0.0884506 | − | 0.153201i | ||||
\(847\) | −36.7130 | + | 21.1963i | −1.26147 | + | 0.728312i | ||||
\(848\) | −4.71160 | + | 2.72024i | −0.161797 | + | 0.0934134i | ||||
\(849\) | −3.97304 | + | 6.88151i | −0.136354 | + | 0.236173i | ||||
\(850\) | 4.21840 | − | 1.33792i | 0.144690 | − | 0.0458901i | ||||
\(851\) | 42.4152 | + | 13.8467i | 1.45397 | + | 0.474658i | ||||
\(852\) | − | 5.23705i | − | 0.179419i | ||||||
\(853\) | −21.1020 | − | 12.1832i | −0.722518 | − | 0.417146i | 0.0931608 | − | 0.995651i | \(-0.470303\pi\) |
−0.815679 | + | 0.578505i | \(0.803636\pi\) | |||||||
\(854\) | −4.90458 | − | 8.49497i | −0.167831 | − | 0.290692i | ||||
\(855\) | 4.34836 | + | 5.40855i | 0.148711 | + | 0.184969i | ||||
\(856\) | 6.90904 | + | 11.9668i | 0.236146 | + | 0.409017i | ||||
\(857\) | 0.352479i | 0.0120404i | 0.999982 | + | 0.00602022i | \(0.00191631\pi\) | ||||
−0.999982 | + | 0.00602022i | \(0.998084\pi\) | |||||||
\(858\) | 0.0813610 | − | 0.0469738i | 0.00277762 | − | 0.00160366i | ||||
\(859\) | −5.53671 | −0.188910 | −0.0944551 | − | 0.995529i | \(-0.530111\pi\) | ||||
−0.0944551 | + | 0.995529i | \(0.530111\pi\) | |||||||
\(860\) | −15.3118 | − | 5.93950i | −0.522128 | − | 0.202535i | ||||
\(861\) | −48.0192 | −1.63649 | ||||||||
\(862\) | 21.9356i | 0.747129i | ||||||||
\(863\) | 1.01152 | + | 0.584003i | 0.0344326 | + | 0.0198797i | 0.517118 | − | 0.855914i | \(-0.327005\pi\) |
−0.482685 | + | 0.875794i | \(0.660338\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −7.27910 | − | 47.0281i | −0.247497 | − | 1.59900i | ||||
\(866\) | 20.7798 | − | 35.9916i | 0.706125 | − | 1.22304i | ||||
\(867\) | −14.0440 | − | 8.10830i | −0.476959 | − | 0.275372i | ||||
\(868\) | 4.66568 | + | 2.69373i | 0.158364 | + | 0.0914313i | ||||
\(869\) | −0.364800 | − | 0.631852i | −0.0123750 | − | 0.0214341i | ||||
\(870\) | −6.84443 | − | 8.51320i | −0.232048 | − | 0.288625i | ||||
\(871\) | −0.0934727 | + | 0.161899i | −0.00316720 | + | 0.00548575i | ||||
\(872\) | 5.33672 | + | 3.08116i | 0.180724 | + | 0.104341i | ||||
\(873\) | −7.68756 | − | 4.43842i | −0.260185 | − | 0.150218i | ||||
\(874\) | 22.7652 | 0.770045 | ||||||||
\(875\) | −24.0403 | + | 36.1775i | −0.812710 | + | 1.22302i | ||||
\(876\) | −7.21457 | + | 12.4960i | −0.243758 | + | 0.422201i | ||||
\(877\) | 34.1036i | 1.15160i | 0.817592 | + | 0.575799i | \(0.195309\pi\) | ||||
−0.817592 | + | 0.575799i | \(0.804691\pi\) | |||||||
\(878\) | 22.5858i | 0.762235i | ||||||||
\(879\) | 9.78077 | − | 16.9408i | 0.329897 | − | 0.571399i | ||||
\(880\) | 0.657091 | − | 0.101706i | 0.0221505 | − | 0.00342850i | ||||
\(881\) | 9.15065 | + | 15.8494i | 0.308293 | + | 0.533980i | 0.977989 | − | 0.208656i | \(-0.0669088\pi\) |
−0.669696 | + | 0.742636i | \(0.733576\pi\) | |||||||
\(882\) | − | 8.09397i | − | 0.272538i | ||||||
\(883\) | −17.1687 | + | 9.91237i | −0.577774 | + | 0.333578i | −0.760248 | − | 0.649633i | \(-0.774923\pi\) |
0.182474 | + | 0.983211i | \(0.441589\pi\) | |||||||
\(884\) | 0.139819 | + | 0.242173i | 0.00470261 | + | 0.00814515i | ||||
\(885\) | −22.2107 | + | 17.8569i | −0.746605 | + | 0.600254i | ||||
\(886\) | 2.42077 | − | 4.19290i | 0.0813275 | − | 0.140863i | ||||
\(887\) | − | 57.3569i | − | 1.92586i | −0.269759 | − | 0.962928i | \(-0.586944\pi\) | ||
0.269759 | − | 0.962928i | \(-0.413056\pi\) | |||||||
\(888\) | −5.95159 | + | 1.25641i | −0.199722 | + | 0.0421625i | ||||
\(889\) | −44.2541 | −1.48424 | ||||||||
\(890\) | 11.0635 | + | 4.29158i | 0.370850 | + | 0.143854i | ||||
\(891\) | 0.148680 | + | 0.257521i | 0.00498096 | + | 0.00862727i | ||||
\(892\) | −12.4353 | + | 7.17951i | −0.416364 | + | 0.240388i | ||||
\(893\) | 13.8295 | − | 7.98449i | 0.462788 | − | 0.267191i | ||||
\(894\) | 4.89601 | 0.163747 | ||||||||
\(895\) | −25.7013 | − | 31.9677i | −0.859101 | − | 1.06856i | ||||
\(896\) | −3.88510 | −0.129792 | ||||||||
\(897\) | 2.00699 | + | 1.15874i | 0.0670115 | + | 0.0386891i | ||||
\(898\) | 35.6744i | 1.19047i | ||||||||
\(899\) | −6.77417 | −0.225931 | ||||||||
\(900\) | −1.07393 | + | 4.88331i | −0.0357976 | + | 0.162777i | ||||
\(901\) | −2.40767 | − | 4.17021i | −0.0802113 | − | 0.138930i | ||||
\(902\) | 3.67532i | 0.122375i | ||||||||
\(903\) | 24.7122 | + | 14.2676i | 0.822369 | + | 0.474795i | ||||
\(904\) | −2.21183 | + | 3.83100i | −0.0735643 | + | 0.127417i | ||||
\(905\) | −11.6698 | + | 30.0844i | −0.387919 | + | 1.00004i | ||||
\(906\) | −2.85747 | − | 4.94928i | −0.0949331 | − | 0.164429i | ||||
\(907\) | −21.9044 | + | 12.6465i | −0.727324 | + | 0.419921i | −0.817442 | − | 0.576010i | \(-0.804609\pi\) |
0.0901186 | + | 0.995931i | \(0.471275\pi\) | |||||||
\(908\) | −4.35717 | − | 2.51561i | −0.144598 | − | 0.0834835i | ||||
\(909\) | −3.52689 | + | 6.10875i | −0.116980 | + | 0.202615i | ||||
\(910\) | −2.55890 | − | 0.992608i | −0.0848267 | − | 0.0329046i | ||||
\(911\) | 43.5990 | 1.44450 | 0.722250 | − | 0.691632i | \(-0.243108\pi\) | ||||
0.722250 | + | 0.691632i | \(0.243108\pi\) | |||||||
\(912\) | −2.68777 | + | 1.55178i | −0.0890010 | + | 0.0513847i | ||||
\(913\) | −1.67116 | − | 0.964843i | −0.0553073 | − | 0.0319317i | ||||
\(914\) | −9.23734 | −0.305544 | ||||||||
\(915\) | −0.863563 | − | 5.57922i | −0.0285485 | − | 0.184443i | ||||
\(916\) | −1.24438 | + | 2.15533i | −0.0411154 | + | 0.0712140i | ||||
\(917\) | 56.1034i | 1.85270i | ||||||||
\(918\) | −0.766516 | + | 0.442548i | −0.0252988 | + | 0.0146063i | ||||
\(919\) | −23.4361 | −0.773086 | −0.386543 | − | 0.922271i | \(-0.626331\pi\) | ||||
−0.386543 | + | 0.922271i | \(0.626331\pi\) | |||||||
\(920\) | 10.2772 | + | 12.7829i | 0.338829 | + | 0.421441i | ||||
\(921\) | 3.58294 | + | 6.20583i | 0.118062 | + | 0.204489i | ||||
\(922\) | −3.77172 | + | 2.17760i | −0.124215 | + | 0.0717155i | ||||
\(923\) | 1.43292 | + | 0.827297i | 0.0471651 | + | 0.0272308i | ||||
\(924\) | −1.15527 | −0.0380056 | ||||||||
\(925\) | −26.2101 | − | 15.4282i | −0.861784 | − | 0.507275i | ||||
\(926\) | −5.59151 | −0.183749 | ||||||||
\(927\) | 5.14449 | + | 2.97017i | 0.168967 | + | 0.0975533i | ||||
\(928\) | 4.23062 | − | 2.44255i | 0.138877 | − | 0.0801806i | ||||
\(929\) | −21.8232 | − | 37.7989i | −0.715996 | − | 1.24014i | −0.962574 | − | 0.271019i | \(-0.912639\pi\) |
0.246578 | − | 0.969123i | \(-0.420694\pi\) | |||||||
\(930\) | 1.94288 | + | 2.41659i | 0.0637097 | + | 0.0792430i | ||||
\(931\) | 25.1202 | 0.823281 | ||||||||
\(932\) | −20.7064 | + | 11.9548i | −0.678260 | + | 0.391594i | ||||
\(933\) | − | 25.4148i | − | 0.832044i | ||||||
\(934\) | −6.54660 | + | 11.3390i | −0.214211 | + | 0.371025i | ||||
\(935\) | 0.0900194 | + | 0.581589i | 0.00294395 | + | 0.0190200i | ||||
\(936\) | −0.315940 | −0.0103268 | ||||||||
\(937\) | 25.9384 | + | 14.9756i | 0.847371 | + | 0.489230i | 0.859763 | − | 0.510693i | \(-0.170611\pi\) |
−0.0123919 | + | 0.999923i | \(0.503945\pi\) | |||||||
\(938\) | 1.99087 | − | 1.14943i | 0.0650042 | − | 0.0375302i | ||||
\(939\) | 3.15685 | 0.103020 | ||||||||
\(940\) | 10.7266 | + | 4.16090i | 0.349864 | + | 0.135714i | ||||
\(941\) | 15.7396 | − | 27.2617i | 0.513095 | − | 0.888707i | −0.486789 | − | 0.873519i | \(-0.661832\pi\) |
0.999885 | − | 0.0151878i | \(-0.00483460\pi\) | |||||||
\(942\) | 0.444121 | + | 0.256413i | 0.0144702 | + | 0.00835439i | ||||
\(943\) | −78.5154 | + | 45.3309i | −2.55681 | + | 1.47618i | ||||
\(944\) | −6.37254 | − | 11.0376i | −0.207409 | − | 0.359242i | ||||
\(945\) | 3.14176 | − | 8.09933i | 0.102202 | − | 0.263471i | ||||
\(946\) | 1.09202 | − | 1.89143i | 0.0355046 | − | 0.0614957i | ||||
\(947\) | −13.9000 | − | 8.02515i | −0.451688 | − | 0.260782i | 0.256855 | − | 0.966450i | \(-0.417314\pi\) |
−0.708543 | + | 0.705668i | \(0.750647\pi\) | |||||||
\(948\) | 2.45360i | 0.0796891i | ||||||||
\(949\) | −2.27937 | − | 3.94799i | −0.0739915 | − | 0.128157i | ||||
\(950\) | −15.1557 | − | 3.33301i | −0.491715 | − | 0.108137i | ||||
\(951\) | −5.64145 | −0.182937 | ||||||||
\(952\) | − | 3.43868i | − | 0.111448i | ||||||
\(953\) | −48.1223 | − | 27.7834i | −1.55883 | − | 0.899994i | −0.997369 | − | 0.0724935i | \(-0.976904\pi\) |
−0.561466 | − | 0.827500i | \(-0.689762\pi\) | |||||||
\(954\) | 5.44048 | 0.176142 | ||||||||
\(955\) | 9.74217 | + | 12.1174i | 0.315249 | + | 0.392111i | ||||
\(956\) | −29.9199 | −0.967679 | ||||||||
\(957\) | 1.25801 | − | 0.726314i | 0.0406658 | − | 0.0234784i | ||||
\(958\) | −21.7624 | + | 12.5645i | −0.703111 | + | 0.405941i | ||||
\(959\) | −27.2511 | − | 47.2003i | −0.879983 | − | 1.52418i | ||||
\(960\) | −2.08472 | − | 0.808671i | −0.0672840 | − | 0.0260997i | ||||
\(961\) | −29.0771 | −0.937970 | ||||||||
\(962\) | 0.596402 | − | 1.82690i | 0.0192288 | − | 0.0589016i | ||||
\(963\) | − | 13.8181i | − | 0.445282i | ||||||
\(964\) | −6.46707 | + | 11.2013i | −0.208290 | + | 0.360769i | ||||
\(965\) | 42.6386 | − | 34.2805i | 1.37258 | − | 1.10353i | ||||
\(966\) | −14.2489 | − | 24.6799i | −0.458452 | − | 0.794062i | ||||
\(967\) | 28.9931 | − | 16.7392i | 0.932354 | − | 0.538295i | 0.0447986 | − | 0.998996i | \(-0.485735\pi\) |
0.887555 | + | 0.460701i | \(0.152402\pi\) | |||||||
\(968\) | − | 10.9116i | − | 0.350711i | ||||||
\(969\) | −1.37348 | − | 2.37893i | −0.0441225 | − | 0.0764224i | ||||
\(970\) | 19.6156 | − | 3.03614i | 0.629820 | − | 0.0974847i | ||||
\(971\) | 14.1086 | − | 24.4368i | 0.452766 | − | 0.784213i | −0.545791 | − | 0.837921i | \(-0.683771\pi\) |
0.998557 | + | 0.0537083i | \(0.0171041\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | − | 76.0960i | − | 2.43953i | ||||||
\(974\) | 2.33915 | − | 4.05153i | 0.0749512 | − | 0.129819i | ||||
\(975\) | −1.16648 | − | 1.06525i | −0.0373573 | − | 0.0341154i | ||||
\(976\) | 2.52482 | 0.0808174 | ||||||||
\(977\) | 42.6720 | + | 24.6367i | 1.36520 | + | 0.788197i | 0.990310 | − | 0.138873i | \(-0.0443480\pi\) |
0.374888 | + | 0.927070i | \(0.377681\pi\) | |||||||
\(978\) | −4.81112 | − | 2.77770i | −0.153843 | − | 0.0888211i | ||||
\(979\) | −0.789036 | + | 1.36665i | −0.0252177 | + | 0.0436784i | ||||
\(980\) | 11.3403 | + | 14.1053i | 0.362254 | + | 0.450576i | ||||
\(981\) | −3.08116 | − | 5.33672i | −0.0983738 | − | 0.170388i | ||||
\(982\) | −7.01811 | − | 4.05191i | −0.223957 | − | 0.129302i | ||||
\(983\) | 21.2400 | + | 12.2629i | 0.677451 | + | 0.391126i | 0.798894 | − | 0.601472i | \(-0.205419\pi\) |
−0.121443 | + | 0.992598i | \(0.538752\pi\) | |||||||
\(984\) | 6.17993 | − | 10.7040i | 0.197009 | − | 0.341230i | ||||
\(985\) | −7.46601 | − | 48.2357i | −0.237887 | − | 1.53692i | ||||
\(986\) | 2.16189 | + | 3.74450i | 0.0688486 | + | 0.119249i | ||||
\(987\) | −17.3120 | − | 9.99511i | −0.551048 | − | 0.318148i | ||||
\(988\) | − | 0.980541i | − | 0.0311952i | ||||||
\(989\) | 53.8752 | 1.71313 | ||||||||
\(990\) | −0.619910 | − | 0.240466i | −0.0197020 | − | 0.00764250i | ||||
\(991\) | 30.8951 | 0.981416 | 0.490708 | − | 0.871324i | \(-0.336738\pi\) | ||||
0.490708 | + | 0.871324i | \(0.336738\pi\) | |||||||
\(992\) | −1.20092 | + | 0.693350i | −0.0381292 | + | 0.0220139i | ||||
\(993\) | 2.02800i | 0.0643568i | ||||||||
\(994\) | −10.1732 | − | 17.6205i | −0.322675 | − | 0.558890i | ||||
\(995\) | −13.0626 | − | 16.2474i | −0.414111 | − | 0.515077i | ||||
\(996\) | 3.24471 | + | 5.62000i | 0.102812 | + | 0.178076i | ||||
\(997\) | −44.2485 | − | 25.5469i | −1.40137 | − | 0.809079i | −0.406832 | − | 0.913503i | \(-0.633367\pi\) |
−0.994533 | + | 0.104424i | \(0.966700\pi\) | |||||||
\(998\) | 13.3648i | 0.423056i | ||||||||
\(999\) | 5.78243 | + | 1.88771i | 0.182948 | + | 0.0597245i |
(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 | 1110.2.bb.d.1009.8 | yes | 28 | |
5.4 | even | 2 | inner | 1110.2.bb.d.1009.7 | ✓ | 28 | |
37.26 | even | 3 | inner | 1110.2.bb.d.1099.7 | yes | 28 | |
185.174 | even | 6 | inner | 1110.2.bb.d.1099.8 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.bb.d.1009.7 | ✓ | 28 | 5.4 | even | 2 | inner | |
1110.2.bb.d.1009.8 | yes | 28 | 1.1 | even | 1 | trivial | |
1110.2.bb.d.1099.7 | yes | 28 | 37.26 | even | 3 | inner | |
1110.2.bb.d.1099.8 | yes | 28 | 185.174 | even | 6 | inner |