Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,2,Mod(75,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.75");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.42745222145\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Relative dimension: | \(38\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 75.9 | ||
Character | \(\chi\) | \(=\) | 304.75 |
Dual form | 304.2.m.a.227.9 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.18010 | − | 0.779343i | −0.834453 | − | 0.551079i | ||||
\(3\) | 1.07779 | − | 1.07779i | 0.622265 | − | 0.622265i | −0.323845 | − | 0.946110i | \(-0.604976\pi\) |
0.946110 | + | 0.323845i | \(0.104976\pi\) | |||||||
\(4\) | 0.785249 | + | 1.83940i | 0.392624 | + | 0.919699i | ||||
\(5\) | −1.37400 | − | 1.37400i | −0.614472 | − | 0.614472i | 0.329636 | − | 0.944108i | \(-0.393074\pi\) |
−0.944108 | + | 0.329636i | \(0.893074\pi\) | |||||||
\(6\) | −2.11187 | + | 0.431928i | −0.862167 | + | 0.176334i | ||||
\(7\) | −4.00321 | −1.51307 | −0.756535 | − | 0.653954i | \(-0.773109\pi\) | ||||
−0.756535 | + | 0.653954i | \(0.773109\pi\) | |||||||
\(8\) | 0.506854 | − | 2.78264i | 0.179200 | − | 0.983813i | ||||
\(9\) | 0.676721i | 0.225574i | ||||||||
\(10\) | 0.550634 | + | 2.69227i | 0.174126 | + | 0.851371i | ||||
\(11\) | −2.44045 | + | 2.44045i | −0.735822 | + | 0.735822i | −0.971767 | − | 0.235945i | \(-0.924182\pi\) |
0.235945 | + | 0.971767i | \(0.424182\pi\) | |||||||
\(12\) | 2.82883 | + | 1.13616i | 0.816612 | + | 0.327980i | ||||
\(13\) | −3.86163 | − | 3.86163i | −1.07102 | − | 1.07102i | −0.997277 | − | 0.0737474i | \(-0.976504\pi\) |
−0.0737474 | − | 0.997277i | \(-0.523496\pi\) | |||||||
\(14\) | 4.72416 | + | 3.11987i | 1.26259 | + | 0.833820i | ||||
\(15\) | −2.96178 | −0.764729 | ||||||||
\(16\) | −2.76677 | + | 2.88877i | −0.691692 | + | 0.722192i | ||||
\(17\) | 0.770883 | 0.186967 | 0.0934833 | − | 0.995621i | \(-0.470200\pi\) | ||||
0.0934833 | + | 0.995621i | \(0.470200\pi\) | |||||||
\(18\) | 0.527398 | − | 0.798595i | 0.124309 | − | 0.188231i | ||||
\(19\) | −2.90179 | − | 3.25263i | −0.665717 | − | 0.746205i | ||||
\(20\) | 1.44840 | − | 3.60627i | 0.323873 | − | 0.806386i | ||||
\(21\) | −4.31463 | + | 4.31463i | −0.941529 | + | 0.941529i | ||||
\(22\) | 4.78190 | − | 0.978013i | 1.01950 | − | 0.208513i | ||||
\(23\) | 7.83638 | 1.63400 | 0.816999 | − | 0.576639i | \(-0.195636\pi\) | ||||
0.816999 | + | 0.576639i | \(0.195636\pi\) | |||||||
\(24\) | −2.45283 | − | 3.54540i | −0.500682 | − | 0.723702i | ||||
\(25\) | − | 1.22424i | − | 0.244848i | ||||||
\(26\) | 1.54756 | + | 7.56663i | 0.303501 | + | 1.48394i | ||||
\(27\) | 3.96275 | + | 3.96275i | 0.762631 | + | 0.762631i | ||||
\(28\) | −3.14351 | − | 7.36349i | −0.594068 | − | 1.39157i | ||||
\(29\) | −4.22402 | − | 4.22402i | −0.784380 | − | 0.784380i | 0.196186 | − | 0.980567i | \(-0.437144\pi\) |
−0.980567 | + | 0.196186i | \(0.937144\pi\) | |||||||
\(30\) | 3.49518 | + | 2.30824i | 0.638130 | + | 0.421426i | ||||
\(31\) | −6.35498 | −1.14139 | −0.570694 | − | 0.821163i | \(-0.693326\pi\) | ||||
−0.570694 | + | 0.821163i | \(0.693326\pi\) | |||||||
\(32\) | 5.51639 | − | 1.25276i | 0.975170 | − | 0.221459i | ||||
\(33\) | 5.26059i | 0.915752i | ||||||||
\(34\) | −0.909715 | − | 0.600782i | −0.156015 | − | 0.103033i | ||||
\(35\) | 5.50041 | + | 5.50041i | 0.929739 | + | 0.929739i | ||||
\(36\) | −1.24476 | + | 0.531394i | −0.207460 | + | 0.0885657i | ||||
\(37\) | −1.65503 | + | 1.65503i | −0.272085 | + | 0.272085i | −0.829939 | − | 0.557854i | \(-0.811625\pi\) |
0.557854 | + | 0.829939i | \(0.311625\pi\) | |||||||
\(38\) | 0.889474 | + | 6.09990i | 0.144292 | + | 0.989535i | ||||
\(39\) | −8.32409 | −1.33292 | ||||||||
\(40\) | −4.51977 | + | 3.12694i | −0.714639 | + | 0.494412i | ||||
\(41\) | 2.19975 | 0.343544 | 0.171772 | − | 0.985137i | \(-0.445051\pi\) | ||||
0.171772 | + | 0.985137i | \(0.445051\pi\) | |||||||
\(42\) | 8.45425 | − | 1.72910i | 1.30452 | − | 0.266805i | ||||
\(43\) | −7.25972 | + | 7.25972i | −1.10710 | + | 1.10710i | −0.113566 | + | 0.993530i | \(0.536227\pi\) |
−0.993530 | + | 0.113566i | \(0.963773\pi\) | |||||||
\(44\) | −6.40531 | − | 2.57259i | −0.965636 | − | 0.387833i | ||||
\(45\) | 0.929815 | − | 0.929815i | 0.138609 | − | 0.138609i | ||||
\(46\) | −9.24767 | − | 6.10723i | −1.36349 | − | 0.900462i | ||||
\(47\) | 3.06973i | 0.447767i | 0.974616 | + | 0.223883i | \(0.0718735\pi\) | ||||
−0.974616 | + | 0.223883i | \(0.928127\pi\) | |||||||
\(48\) | 0.131491 | + | 6.09550i | 0.0189792 | + | 0.879810i | ||||
\(49\) | 9.02565 | 1.28938 | ||||||||
\(50\) | −0.954102 | + | 1.44472i | −0.134930 | + | 0.204314i | ||||
\(51\) | 0.830853 | − | 0.830853i | 0.116343 | − | 0.116343i | ||||
\(52\) | 4.07074 | − | 10.1354i | 0.564510 | − | 1.40553i | ||||
\(53\) | 8.94960 | − | 8.94960i | 1.22932 | − | 1.22932i | 0.265102 | − | 0.964220i | \(-0.414594\pi\) |
0.964220 | − | 0.265102i | \(-0.0854058\pi\) | |||||||
\(54\) | −1.58808 | − | 7.76476i | −0.216110 | − | 1.05665i | ||||
\(55\) | 6.70635 | 0.904284 | ||||||||
\(56\) | −2.02904 | + | 11.1395i | −0.271142 | + | 1.48858i | ||||
\(57\) | −6.63320 | − | 0.378133i | −0.878589 | − | 0.0500849i | ||||
\(58\) | 1.69278 | + | 8.27670i | 0.222273 | + | 1.08678i | ||||
\(59\) | −8.06369 | − | 8.06369i | −1.04980 | − | 1.04980i | −0.998693 | − | 0.0511094i | \(-0.983724\pi\) |
−0.0511094 | − | 0.998693i | \(-0.516276\pi\) | |||||||
\(60\) | −2.32573 | − | 5.44789i | −0.300251 | − | 0.703320i | ||||
\(61\) | 5.67621 | − | 5.67621i | 0.726764 | − | 0.726764i | −0.243209 | − | 0.969974i | \(-0.578200\pi\) |
0.969974 | + | 0.243209i | \(0.0782002\pi\) | |||||||
\(62\) | 7.49948 | + | 4.95271i | 0.952435 | + | 0.628995i | ||||
\(63\) | − | 2.70905i | − | 0.341308i | ||||||
\(64\) | −7.48620 | − | 2.82079i | −0.935775 | − | 0.352598i | ||||
\(65\) | 10.6118i | 1.31623i | ||||||||
\(66\) | 4.09981 | − | 6.20800i | 0.504651 | − | 0.764152i | ||||
\(67\) | 6.75376 | − | 6.75376i | 0.825103 | − | 0.825103i | −0.161732 | − | 0.986835i | \(-0.551708\pi\) |
0.986835 | + | 0.161732i | \(0.0517079\pi\) | |||||||
\(68\) | 0.605335 | + | 1.41796i | 0.0734076 | + | 0.171953i | ||||
\(69\) | 8.44600 | − | 8.44600i | 1.01678 | − | 1.01678i | ||||
\(70\) | −2.20430 | − | 10.7777i | −0.263464 | − | 1.28818i | ||||
\(71\) | 5.29590i | 0.628507i | 0.949339 | + | 0.314254i | \(0.101754\pi\) | ||||
−0.949339 | + | 0.314254i | \(0.898246\pi\) | |||||||
\(72\) | 1.88307 | + | 0.342999i | 0.221922 | + | 0.0404228i | ||||
\(73\) | − | 7.64027i | − | 0.894226i | −0.894478 | − | 0.447113i | \(-0.852452\pi\) | ||
0.894478 | − | 0.447113i | \(-0.147548\pi\) | |||||||
\(74\) | 3.24292 | − | 0.663255i | 0.376982 | − | 0.0771018i | ||||
\(75\) | −1.31948 | − | 1.31948i | −0.152360 | − | 0.152360i | ||||
\(76\) | 3.70425 | − | 7.89167i | 0.424907 | − | 0.905237i | ||||
\(77\) | 9.76960 | − | 9.76960i | 1.11335 | − | 1.11335i | ||||
\(78\) | 9.82322 | + | 6.48732i | 1.11226 | + | 0.734545i | ||||
\(79\) | −4.93934 | −0.555719 | −0.277860 | − | 0.960622i | \(-0.589625\pi\) | ||||
−0.277860 | + | 0.960622i | \(0.589625\pi\) | |||||||
\(80\) | 7.77072 | − | 0.167629i | 0.868793 | − | 0.0187415i | ||||
\(81\) | 6.51189 | 0.723543 | ||||||||
\(82\) | −2.59592 | − | 1.71436i | −0.286671 | − | 0.189320i | ||||
\(83\) | 1.44386 | + | 1.44386i | 0.158484 | + | 0.158484i | 0.781895 | − | 0.623411i | \(-0.214254\pi\) |
−0.623411 | + | 0.781895i | \(0.714254\pi\) | |||||||
\(84\) | −11.3244 | − | 4.54826i | −1.23559 | − | 0.496256i | ||||
\(85\) | −1.05919 | − | 1.05919i | −0.114886 | − | 0.114886i | ||||
\(86\) | 14.2250 | − | 2.90935i | 1.53392 | − | 0.313723i | ||||
\(87\) | −9.10524 | −0.976184 | ||||||||
\(88\) | 5.55394 | + | 8.02784i | 0.592052 | + | 0.855770i | ||||
\(89\) | −0.971859 | −0.103017 | −0.0515084 | − | 0.998673i | \(-0.516403\pi\) | ||||
−0.0515084 | + | 0.998673i | \(0.516403\pi\) | |||||||
\(90\) | −1.82192 | + | 0.372625i | −0.192047 | + | 0.0392782i | ||||
\(91\) | 15.4589 | + | 15.4589i | 1.62053 | + | 1.62053i | ||||
\(92\) | 6.15351 | + | 14.4142i | 0.641547 | + | 1.50279i | ||||
\(93\) | −6.84936 | + | 6.84936i | −0.710245 | + | 0.710245i | ||||
\(94\) | 2.39238 | − | 3.62258i | 0.246755 | − | 0.373640i | ||||
\(95\) | −0.482054 | + | 8.45619i | −0.0494577 | + | 0.867586i | ||||
\(96\) | 4.59532 | − | 7.29575i | 0.469008 | − | 0.744620i | ||||
\(97\) | − | 6.62675i | − | 0.672845i | −0.941711 | − | 0.336422i | \(-0.890783\pi\) | ||
0.941711 | − | 0.336422i | \(-0.109217\pi\) | |||||||
\(98\) | −10.6511 | − | 7.03408i | −1.07593 | − | 0.710549i | ||||
\(99\) | −1.65150 | − | 1.65150i | −0.165982 | − | 0.165982i | ||||
\(100\) | 2.25186 | − | 0.961332i | 0.225186 | − | 0.0961332i | ||||
\(101\) | −8.93505 | − | 8.93505i | −0.889070 | − | 0.889070i | 0.105363 | − | 0.994434i | \(-0.466399\pi\) |
−0.994434 | + | 0.105363i | \(0.966399\pi\) | |||||||
\(102\) | −1.62801 | + | 0.332966i | −0.161197 | + | 0.0329685i | ||||
\(103\) | 2.76517i | 0.272460i | 0.990677 | + | 0.136230i | \(0.0434986\pi\) | ||||
−0.990677 | + | 0.136230i | \(0.956501\pi\) | |||||||
\(104\) | −12.7028 | + | 8.78826i | −1.24561 | + | 0.861760i | ||||
\(105\) | 11.8566 | 1.15709 | ||||||||
\(106\) | −17.5362 | + | 3.58657i | −1.70327 | + | 0.348359i | ||||
\(107\) | −2.29005 | − | 2.29005i | −0.221387 | − | 0.221387i | 0.587695 | − | 0.809082i | \(-0.300035\pi\) |
−0.809082 | + | 0.587695i | \(0.800035\pi\) | |||||||
\(108\) | −4.17733 | + | 10.4008i | −0.401963 | + | 1.00082i | ||||
\(109\) | 7.12660 | + | 7.12660i | 0.682604 | + | 0.682604i | 0.960586 | − | 0.277982i | \(-0.0896655\pi\) |
−0.277982 | + | 0.960586i | \(0.589666\pi\) | |||||||
\(110\) | −7.91413 | − | 5.22655i | −0.754583 | − | 0.498332i | ||||
\(111\) | 3.56756i | 0.338617i | ||||||||
\(112\) | 11.0759 | − | 11.5643i | 1.04658 | − | 1.09273i | ||||
\(113\) | − | 4.01320i | − | 0.377530i | −0.982022 | − | 0.188765i | \(-0.939552\pi\) | ||
0.982022 | − | 0.188765i | \(-0.0604485\pi\) | |||||||
\(114\) | 7.53311 | + | 5.61577i | 0.705540 | + | 0.525965i | ||||
\(115\) | −10.7672 | − | 10.7672i | −1.00405 | − | 1.00405i | ||||
\(116\) | 4.45274 | − | 11.0865i | 0.413427 | − | 1.02936i | ||||
\(117\) | 2.61325 | − | 2.61325i | 0.241595 | − | 0.241595i | ||||
\(118\) | 3.23154 | + | 15.8003i | 0.297487 | + | 1.45453i | ||||
\(119\) | −3.08600 | −0.282893 | ||||||||
\(120\) | −1.50119 | + | 8.24158i | −0.137039 | + | 0.752350i | ||||
\(121\) | − | 0.911546i | − | 0.0828678i | ||||||
\(122\) | −11.1222 | + | 2.27475i | −1.00696 | + | 0.205946i | ||||
\(123\) | 2.37088 | − | 2.37088i | 0.213775 | − | 0.213775i | ||||
\(124\) | −4.99024 | − | 11.6893i | −0.448137 | − | 1.04973i | ||||
\(125\) | −8.55211 | + | 8.55211i | −0.764924 | + | 0.764924i | ||||
\(126\) | −2.11128 | + | 3.19694i | −0.188088 | + | 0.284806i | ||||
\(127\) | −21.0423 | −1.86721 | −0.933603 | − | 0.358309i | \(-0.883354\pi\) | ||||
−0.933603 | + | 0.358309i | \(0.883354\pi\) | |||||||
\(128\) | 6.63607 | + | 9.16311i | 0.586551 | + | 0.809912i | ||||
\(129\) | 15.6490i | 1.37781i | ||||||||
\(130\) | 8.27022 | − | 12.5229i | 0.725346 | − | 1.09833i | ||||
\(131\) | 5.90211 | + | 5.90211i | 0.515669 | + | 0.515669i | 0.916258 | − | 0.400589i | \(-0.131194\pi\) |
−0.400589 | + | 0.916258i | \(0.631194\pi\) | |||||||
\(132\) | −9.67632 | + | 4.13087i | −0.842216 | + | 0.359546i | ||||
\(133\) | 11.6165 | + | 13.0209i | 1.00728 | + | 1.12906i | ||||
\(134\) | −13.2336 | + | 2.70658i | −1.14321 | + | 0.233813i | ||||
\(135\) | − | 10.8896i | − | 0.937231i | ||||||
\(136\) | 0.390725 | − | 2.14509i | 0.0335044 | − | 0.183940i | ||||
\(137\) | 0.836629i | 0.0714781i | 0.999361 | + | 0.0357390i | \(0.0113785\pi\) | ||||
−0.999361 | + | 0.0357390i | \(0.988621\pi\) | |||||||
\(138\) | −16.5494 | + | 3.38475i | −1.40878 | + | 0.288129i | ||||
\(139\) | 9.52338 | − | 9.52338i | 0.807762 | − | 0.807762i | −0.176533 | − | 0.984295i | \(-0.556488\pi\) |
0.984295 | + | 0.176533i | \(0.0564881\pi\) | |||||||
\(140\) | −5.79825 | + | 14.4366i | −0.490042 | + | 1.22012i | ||||
\(141\) | 3.30854 | + | 3.30854i | 0.278629 | + | 0.278629i | ||||
\(142\) | 4.12732 | − | 6.24966i | 0.346357 | − | 0.524460i | ||||
\(143\) | 18.8482 | 1.57617 | ||||||||
\(144\) | −1.95489 | − | 1.87233i | −0.162908 | − | 0.156027i | ||||
\(145\) | 11.6076i | 0.963960i | ||||||||
\(146\) | −5.95439 | + | 9.01624i | −0.492789 | + | 0.746190i | ||||
\(147\) | 9.72779 | − | 9.72779i | 0.802335 | − | 0.802335i | ||||
\(148\) | −4.34386 | − | 1.74464i | −0.357063 | − | 0.143409i | ||||
\(149\) | 6.00097 | + | 6.00097i | 0.491619 | + | 0.491619i | 0.908816 | − | 0.417197i | \(-0.136988\pi\) |
−0.417197 | + | 0.908816i | \(0.636988\pi\) | |||||||
\(150\) | 0.528783 | + | 2.58543i | 0.0431750 | + | 0.211100i | ||||
\(151\) | 18.9950i | 1.54579i | 0.634533 | + | 0.772895i | \(0.281192\pi\) | ||||
−0.634533 | + | 0.772895i | \(0.718808\pi\) | |||||||
\(152\) | −10.5217 | + | 6.42604i | −0.853422 | + | 0.521221i | ||||
\(153\) | 0.521673i | 0.0421747i | ||||||||
\(154\) | −19.1429 | + | 3.91519i | −1.54258 | + | 0.315495i | ||||
\(155\) | 8.73175 | + | 8.73175i | 0.701351 | + | 0.701351i | ||||
\(156\) | −6.53648 | − | 15.3113i | −0.523337 | − | 1.22589i | ||||
\(157\) | −0.417157 | + | 0.417157i | −0.0332928 | + | 0.0332928i | −0.723557 | − | 0.690264i | \(-0.757494\pi\) |
0.690264 | + | 0.723557i | \(0.257494\pi\) | |||||||
\(158\) | 5.82889 | + | 3.84944i | 0.463722 | + | 0.306245i | ||||
\(159\) | − | 19.2917i | − | 1.52993i | ||||||
\(160\) | −9.30083 | − | 5.85824i | −0.735295 | − | 0.463134i | ||||
\(161\) | −31.3706 | −2.47235 | ||||||||
\(162\) | −7.68465 | − | 5.07499i | −0.603763 | − | 0.398729i | ||||
\(163\) | −6.53608 | − | 6.53608i | −0.511945 | − | 0.511945i | 0.403177 | − | 0.915122i | \(-0.367906\pi\) |
−0.915122 | + | 0.403177i | \(0.867906\pi\) | |||||||
\(164\) | 1.72735 | + | 4.04622i | 0.134884 | + | 0.315957i | ||||
\(165\) | 7.22806 | − | 7.22806i | 0.562704 | − | 0.562704i | ||||
\(166\) | −0.578628 | − | 2.82915i | −0.0449103 | − | 0.219584i | ||||
\(167\) | − | 6.23492i | − | 0.482473i | −0.970466 | − | 0.241236i | \(-0.922447\pi\) | ||
0.970466 | − | 0.241236i | \(-0.0775529\pi\) | |||||||
\(168\) | 9.81919 | + | 14.1930i | 0.757567 | + | 1.09501i | ||||
\(169\) | 16.8244i | 1.29419i | ||||||||
\(170\) | 0.424474 | + | 2.07543i | 0.0325557 | + | 0.159178i | ||||
\(171\) | 2.20112 | − | 1.96370i | 0.168324 | − | 0.150168i | ||||
\(172\) | −19.0542 | − | 7.65283i | −1.45287 | − | 0.583523i | ||||
\(173\) | −9.89033 | − | 9.89033i | −0.751948 | − | 0.751948i | 0.222895 | − | 0.974843i | \(-0.428449\pi\) |
−0.974843 | + | 0.222895i | \(0.928449\pi\) | |||||||
\(174\) | 10.7450 | + | 7.09610i | 0.814580 | + | 0.537954i | ||||
\(175\) | 4.90088i | 0.370472i | ||||||||
\(176\) | −0.297736 | − | 13.8020i | −0.0224427 | − | 1.04037i | ||||
\(177\) | −17.3820 | −1.30651 | ||||||||
\(178\) | 1.14689 | + | 0.757412i | 0.0859627 | + | 0.0567704i | ||||
\(179\) | −0.867301 | + | 0.867301i | −0.0648251 | + | 0.0648251i | −0.738776 | − | 0.673951i | \(-0.764596\pi\) |
0.673951 | + | 0.738776i | \(0.264596\pi\) | |||||||
\(180\) | 2.44044 | + | 0.980164i | 0.181899 | + | 0.0730571i | ||||
\(181\) | −12.5035 | + | 12.5035i | −0.929379 | + | 0.929379i | −0.997666 | − | 0.0682866i | \(-0.978247\pi\) |
0.0682866 | + | 0.997666i | \(0.478247\pi\) | |||||||
\(182\) | −6.19519 | − | 30.2908i | −0.459218 | − | 2.24530i | ||||
\(183\) | − | 12.2356i | − | 0.904479i | ||||||
\(184\) | 3.97190 | − | 21.8058i | 0.292812 | − | 1.60755i | ||||
\(185\) | 4.54802 | 0.334377 | ||||||||
\(186\) | 13.4209 | − | 2.74489i | 0.984068 | − | 0.201265i | ||||
\(187\) | −1.88130 | + | 1.88130i | −0.137574 | + | 0.137574i | ||||
\(188\) | −5.64646 | + | 2.41050i | −0.411811 | + | 0.175804i | ||||
\(189\) | −15.8637 | − | 15.8637i | −1.15391 | − | 1.15391i | ||||
\(190\) | 7.15914 | − | 9.60342i | 0.519379 | − | 0.696705i | ||||
\(191\) | 8.81392i | 0.637753i | 0.947796 | + | 0.318876i | \(0.103305\pi\) | ||||
−0.947796 | + | 0.318876i | \(0.896695\pi\) | |||||||
\(192\) | −11.1088 | + | 5.02835i | −0.801709 | + | 0.362890i | ||||
\(193\) | − | 6.79503i | − | 0.489117i | −0.969635 | − | 0.244558i | \(-0.921357\pi\) | ||
0.969635 | − | 0.244558i | \(-0.0786430\pi\) | |||||||
\(194\) | −5.16451 | + | 7.82020i | −0.370790 | + | 0.561457i | ||||
\(195\) | 11.4373 | + | 11.4373i | 0.819043 | + | 0.819043i | ||||
\(196\) | 7.08738 | + | 16.6018i | 0.506242 | + | 1.18584i | ||||
\(197\) | 5.37965 | + | 5.37965i | 0.383284 | + | 0.383284i | 0.872284 | − | 0.489000i | \(-0.162638\pi\) |
−0.489000 | + | 0.872284i | \(0.662638\pi\) | |||||||
\(198\) | 0.661842 | + | 3.23601i | 0.0470351 | + | 0.229973i | ||||
\(199\) | −2.55317 | −0.180990 | −0.0904949 | − | 0.995897i | \(-0.528845\pi\) | ||||
−0.0904949 | + | 0.995897i | \(0.528845\pi\) | |||||||
\(200\) | −3.40662 | − | 0.620510i | −0.240884 | − | 0.0438767i | ||||
\(201\) | − | 14.5583i | − | 1.02686i | ||||||
\(202\) | 3.58074 | + | 17.5077i | 0.251940 | + | 1.23184i | ||||
\(203\) | 16.9096 | + | 16.9096i | 1.18682 | + | 1.18682i | ||||
\(204\) | 2.18070 | + | 0.875843i | 0.152679 | + | 0.0613213i | ||||
\(205\) | −3.02247 | − | 3.02247i | −0.211098 | − | 0.211098i | ||||
\(206\) | 2.15501 | − | 3.26316i | 0.150147 | − | 0.227355i | ||||
\(207\) | 5.30304i | 0.368587i | ||||||||
\(208\) | 21.8396 | − | 0.471122i | 1.51430 | − | 0.0326664i | ||||
\(209\) | 15.0195 | + | 0.856205i | 1.03892 | + | 0.0592250i | ||||
\(210\) | −13.9919 | − | 9.24037i | −0.965535 | − | 0.637646i | ||||
\(211\) | −7.16054 | + | 7.16054i | −0.492952 | + | 0.492952i | −0.909235 | − | 0.416283i | \(-0.863333\pi\) |
0.416283 | + | 0.909235i | \(0.363333\pi\) | |||||||
\(212\) | 23.4895 | + | 9.43422i | 1.61327 | + | 0.647945i | ||||
\(213\) | 5.70789 | + | 5.70789i | 0.391098 | + | 0.391098i | ||||
\(214\) | 0.917741 | + | 4.48721i | 0.0627355 | + | 0.306739i | ||||
\(215\) | 19.9497 | 1.36056 | ||||||||
\(216\) | 13.0354 | − | 9.01837i | 0.886949 | − | 0.613623i | ||||
\(217\) | 25.4403 | 1.72700 | ||||||||
\(218\) | −2.85600 | − | 13.9641i | −0.193433 | − | 0.945770i | ||||
\(219\) | −8.23463 | − | 8.23463i | −0.556445 | − | 0.556445i | ||||
\(220\) | 5.26615 | + | 12.3356i | 0.355044 | + | 0.831669i | ||||
\(221\) | −2.97687 | − | 2.97687i | −0.200246 | − | 0.200246i | ||||
\(222\) | 2.78035 | − | 4.21005i | 0.186605 | − | 0.282560i | ||||
\(223\) | 0.364568 | 0.0244133 | 0.0122066 | − | 0.999925i | \(-0.496114\pi\) | ||||
0.0122066 | + | 0.999925i | \(0.496114\pi\) | |||||||
\(224\) | −22.0833 | + | 5.01506i | −1.47550 | + | 0.335083i | ||||
\(225\) | 0.828468 | 0.0552312 | ||||||||
\(226\) | −3.12766 | + | 4.73596i | −0.208049 | + | 0.315031i | ||||
\(227\) | 12.1764 | − | 12.1764i | 0.808178 | − | 0.808178i | −0.176180 | − | 0.984358i | \(-0.556374\pi\) |
0.984358 | + | 0.176180i | \(0.0563741\pi\) | |||||||
\(228\) | −4.51317 | − | 12.4980i | −0.298892 | − | 0.827702i | ||||
\(229\) | −3.93799 | − | 3.93799i | −0.260230 | − | 0.260230i | 0.564917 | − | 0.825147i | \(-0.308908\pi\) |
−0.825147 | + | 0.564917i | \(0.808908\pi\) | |||||||
\(230\) | 4.31498 | + | 21.0977i | 0.284521 | + | 1.39114i | ||||
\(231\) | − | 21.0592i | − | 1.38560i | ||||||
\(232\) | −13.8949 | + | 9.61297i | −0.912244 | + | 0.631122i | ||||
\(233\) | 0.107442i | 0.00703876i | 0.999994 | + | 0.00351938i | \(0.00112026\pi\) | ||||
−0.999994 | + | 0.00351938i | \(0.998880\pi\) | |||||||
\(234\) | −5.12050 | + | 1.04726i | −0.334737 | + | 0.0684618i | ||||
\(235\) | 4.21782 | − | 4.21782i | 0.275140 | − | 0.275140i | ||||
\(236\) | 8.50033 | − | 21.1643i | 0.553324 | − | 1.37768i | ||||
\(237\) | −5.32359 | + | 5.32359i | −0.345804 | + | 0.345804i | ||||
\(238\) | 3.64178 | + | 2.40506i | 0.236061 | + | 0.155897i | ||||
\(239\) | 5.60709i | 0.362692i | 0.983419 | + | 0.181346i | \(0.0580455\pi\) | ||||
−0.983419 | + | 0.181346i | \(0.941955\pi\) | |||||||
\(240\) | 8.19456 | − | 8.55590i | 0.528957 | − | 0.552281i | ||||
\(241\) | 25.7917i | 1.66139i | 0.556727 | + | 0.830695i | \(0.312057\pi\) | ||||
−0.556727 | + | 0.830695i | \(0.687943\pi\) | |||||||
\(242\) | −0.710407 | + | 1.07571i | −0.0456667 | + | 0.0691493i | ||||
\(243\) | −4.86977 | + | 4.86977i | −0.312396 | + | 0.312396i | ||||
\(244\) | 14.8980 | + | 5.98357i | 0.953750 | + | 0.383059i | ||||
\(245\) | −12.4013 | − | 12.4013i | −0.792288 | − | 0.792288i | ||||
\(246\) | −4.64560 | + | 0.950135i | −0.296192 | + | 0.0605784i | ||||
\(247\) | −1.35481 | + | 23.7661i | −0.0862048 | + | 1.51220i | ||||
\(248\) | −3.22105 | + | 17.6836i | −0.204537 | + | 1.12291i | ||||
\(249\) | 3.11236 | 0.197238 | ||||||||
\(250\) | 16.7573 | − | 3.42728i | 1.05983 | − | 0.216760i | ||||
\(251\) | 11.9794 | − | 11.9794i | 0.756132 | − | 0.756132i | −0.219484 | − | 0.975616i | \(-0.570437\pi\) |
0.975616 | + | 0.219484i | \(0.0704374\pi\) | |||||||
\(252\) | 4.98302 | − | 2.12728i | 0.313901 | − | 0.134006i | ||||
\(253\) | −19.1243 | + | 19.1243i | −1.20233 | + | 1.20233i | ||||
\(254\) | 24.8320 | + | 16.3992i | 1.55810 | + | 1.02898i | ||||
\(255\) | −2.28319 | −0.142979 | ||||||||
\(256\) | −0.689979 | − | 15.9851i | −0.0431237 | − | 0.999070i | ||||
\(257\) | − | 21.1739i | − | 1.32079i | −0.750917 | − | 0.660396i | \(-0.770388\pi\) | ||
0.750917 | − | 0.660396i | \(-0.229612\pi\) | |||||||
\(258\) | 12.1959 | − | 18.4673i | 0.759284 | − | 1.14972i | ||||
\(259\) | 6.62541 | − | 6.62541i | 0.411683 | − | 0.411683i | ||||
\(260\) | −19.5193 | + | 8.33289i | −1.21053 | + | 0.516784i | ||||
\(261\) | 2.85848 | − | 2.85848i | 0.176935 | − | 0.176935i | ||||
\(262\) | −2.36528 | − | 11.5648i | −0.146128 | − | 0.714477i | ||||
\(263\) | −3.56210 | −0.219648 | −0.109824 | − | 0.993951i | \(-0.535029\pi\) | ||||
−0.109824 | + | 0.993951i | \(0.535029\pi\) | |||||||
\(264\) | 14.6384 | + | 2.66635i | 0.900928 | + | 0.164103i | ||||
\(265\) | −24.5935 | −1.51077 | ||||||||
\(266\) | −3.56075 | − | 24.4192i | −0.218323 | − | 1.49724i | ||||
\(267\) | −1.04746 | + | 1.04746i | −0.0641037 | + | 0.0641037i | ||||
\(268\) | 17.7262 | + | 7.11947i | 1.08280 | + | 0.434891i | ||||
\(269\) | −6.71180 | − | 6.71180i | −0.409226 | − | 0.409226i | 0.472243 | − | 0.881469i | \(-0.343445\pi\) |
−0.881469 | + | 0.472243i | \(0.843445\pi\) | |||||||
\(270\) | −8.48677 | + | 12.8508i | −0.516488 | + | 0.782076i | ||||
\(271\) | − | 17.8380i | − | 1.08358i | −0.840514 | − | 0.541789i | \(-0.817747\pi\) | ||
0.840514 | − | 0.541789i | \(-0.182253\pi\) | |||||||
\(272\) | −2.13286 | + | 2.22690i | −0.129323 | + | 0.135026i | ||||
\(273\) | 33.3230 | 2.01680 | ||||||||
\(274\) | 0.652021 | − | 0.987302i | 0.0393900 | − | 0.0596451i | ||||
\(275\) | 2.98769 | + | 2.98769i | 0.180164 | + | 0.180164i | ||||
\(276\) | 22.1678 | + | 8.90334i | 1.33434 | + | 0.535918i | ||||
\(277\) | −4.31985 | − | 4.31985i | −0.259555 | − | 0.259555i | 0.565318 | − | 0.824873i | \(-0.308753\pi\) |
−0.824873 | + | 0.565318i | \(0.808753\pi\) | |||||||
\(278\) | −18.6605 | + | 3.81651i | −1.11918 | + | 0.228899i | ||||
\(279\) | − | 4.30055i | − | 0.257467i | ||||||
\(280\) | 18.0936 | − | 12.5178i | 1.08130 | − | 0.748080i | ||||
\(281\) | −10.9456 | −0.652961 | −0.326480 | − | 0.945204i | \(-0.605863\pi\) | ||||
−0.326480 | + | 0.945204i | \(0.605863\pi\) | |||||||
\(282\) | −1.32590 | − | 6.48288i | −0.0789565 | − | 0.386050i | ||||
\(283\) | 12.7625 | − | 12.7625i | 0.758651 | − | 0.758651i | −0.217426 | − | 0.976077i | \(-0.569766\pi\) |
0.976077 | + | 0.217426i | \(0.0697660\pi\) | |||||||
\(284\) | −9.74126 | + | 4.15860i | −0.578038 | + | 0.246767i | ||||
\(285\) | 8.59447 | + | 9.63358i | 0.509092 | + | 0.570644i | ||||
\(286\) | −22.2427 | − | 14.6892i | −1.31524 | − | 0.868592i | ||||
\(287\) | −8.80607 | −0.519806 | ||||||||
\(288\) | 0.847769 | + | 3.73306i | 0.0499553 | + | 0.219973i | ||||
\(289\) | −16.4057 | −0.965043 | ||||||||
\(290\) | 9.04631 | − | 13.6981i | 0.531218 | − | 0.804379i | ||||
\(291\) | −7.14227 | − | 7.14227i | −0.418687 | − | 0.418687i | ||||
\(292\) | 14.0535 | − | 5.99951i | 0.822418 | − | 0.351095i | ||||
\(293\) | −15.2720 | + | 15.2720i | −0.892202 | + | 0.892202i | −0.994730 | − | 0.102529i | \(-0.967307\pi\) |
0.102529 | + | 0.994730i | \(0.467307\pi\) | |||||||
\(294\) | −19.0610 | + | 3.89843i | −1.11166 | + | 0.227361i | ||||
\(295\) | 22.1590i | 1.29015i | ||||||||
\(296\) | 3.76649 | + | 5.44420i | 0.218923 | + | 0.316438i | ||||
\(297\) | −19.3417 | −1.12232 | ||||||||
\(298\) | −2.40490 | − | 11.7585i | −0.139312 | − | 0.681153i | ||||
\(299\) | −30.2612 | − | 30.2612i | −1.75005 | − | 1.75005i | ||||
\(300\) | 1.39093 | − | 3.46316i | 0.0803051 | − | 0.199946i | ||||
\(301\) | 29.0621 | − | 29.0621i | 1.67511 | − | 1.67511i | ||||
\(302\) | 14.8036 | − | 22.4159i | 0.851853 | − | 1.28989i | ||||
\(303\) | −19.2603 | −1.10647 | ||||||||
\(304\) | 17.4247 | + | 0.616672i | 0.999374 | + | 0.0353686i | ||||
\(305\) | −15.5982 | −0.893153 | ||||||||
\(306\) | 0.406562 | − | 0.615623i | 0.0232416 | − | 0.0351928i | ||||
\(307\) | −3.37715 | + | 3.37715i | −0.192744 | + | 0.192744i | −0.796881 | − | 0.604137i | \(-0.793518\pi\) |
0.604137 | + | 0.796881i | \(0.293518\pi\) | |||||||
\(308\) | 25.6418 | + | 10.2986i | 1.46107 | + | 0.586818i | ||||
\(309\) | 2.98028 | + | 2.98028i | 0.169542 | + | 0.169542i | ||||
\(310\) | −3.49927 | − | 17.1093i | −0.198745 | − | 0.971745i | ||||
\(311\) | −1.49807 | −0.0849477 | −0.0424738 | − | 0.999098i | \(-0.513524\pi\) | ||||
−0.0424738 | + | 0.999098i | \(0.513524\pi\) | |||||||
\(312\) | −4.21910 | + | 23.1630i | −0.238859 | + | 1.31134i | ||||
\(313\) | 18.4107i | 1.04064i | 0.853973 | + | 0.520318i | \(0.174187\pi\) | ||||
−0.853973 | + | 0.520318i | \(0.825813\pi\) | |||||||
\(314\) | 0.817394 | − | 0.167177i | 0.0461282 | − | 0.00943432i | ||||
\(315\) | −3.72224 | + | 3.72224i | −0.209725 | + | 0.209725i | ||||
\(316\) | −3.87861 | − | 9.08541i | −0.218189 | − | 0.511094i | ||||
\(317\) | 16.6166 | + | 16.6166i | 0.933283 | + | 0.933283i | 0.997910 | − | 0.0646267i | \(-0.0205857\pi\) |
−0.0646267 | + | 0.997910i | \(0.520586\pi\) | |||||||
\(318\) | −15.0348 | + | 22.7660i | −0.843111 | + | 1.27665i | ||||
\(319\) | 20.6170 | 1.15433 | ||||||||
\(320\) | 6.41028 | + | 14.1618i | 0.358346 | + | 0.791669i | ||||
\(321\) | −4.93640 | −0.275523 | ||||||||
\(322\) | 37.0203 | + | 24.4485i | 2.06306 | + | 1.36246i | ||||
\(323\) | −2.23694 | − | 2.50740i | −0.124467 | − | 0.139515i | ||||
\(324\) | 5.11345 | + | 11.9780i | 0.284081 | + | 0.665442i | ||||
\(325\) | −4.72756 | + | 4.72756i | −0.262238 | + | 0.262238i | ||||
\(326\) | 2.61935 | + | 12.8070i | 0.145072 | + | 0.709317i | ||||
\(327\) | 15.3620 | 0.849521 | ||||||||
\(328\) | 1.11495 | − | 6.12113i | 0.0615630 | − | 0.337983i | ||||
\(329\) | − | 12.2888i | − | 0.677502i | ||||||
\(330\) | −14.1629 | + | 2.89666i | −0.779644 | + | 0.159456i | ||||
\(331\) | −13.9808 | − | 13.9808i | −0.768453 | − | 0.768453i | 0.209381 | − | 0.977834i | \(-0.432855\pi\) |
−0.977834 | + | 0.209381i | \(0.932855\pi\) | |||||||
\(332\) | −1.52204 | + | 3.78961i | −0.0835328 | + | 0.207982i | ||||
\(333\) | −1.11999 | − | 1.11999i | −0.0613751 | − | 0.0613751i | ||||
\(334\) | −4.85915 | + | 7.35780i | −0.265881 | + | 0.402601i | ||||
\(335\) | −18.5594 | −1.01401 | ||||||||
\(336\) | −0.526387 | − | 24.4016i | −0.0287168 | − | 1.33121i | ||||
\(337\) | − | 17.8920i | − | 0.974641i | −0.873223 | − | 0.487320i | \(-0.837974\pi\) | ||
0.873223 | − | 0.487320i | \(-0.162026\pi\) | |||||||
\(338\) | 13.1120 | − | 19.8544i | 0.713199 | − | 1.07994i | ||||
\(339\) | −4.32540 | − | 4.32540i | −0.234924 | − | 0.234924i | ||||
\(340\) | 1.11655 | − | 2.78001i | 0.0605534 | − | 0.150767i | ||||
\(341\) | 15.5090 | − | 15.5090i | 0.839858 | − | 0.839858i | ||||
\(342\) | −4.12793 | + | 0.601926i | −0.223213 | + | 0.0325484i | ||||
\(343\) | −8.10910 | −0.437850 | ||||||||
\(344\) | 16.5216 | + | 23.8808i | 0.890784 | + | 1.28757i | ||||
\(345\) | −23.2096 | −1.24956 | ||||||||
\(346\) | 3.96357 | + | 19.3795i | 0.213083 | + | 1.04185i | ||||
\(347\) | −0.120595 | + | 0.120595i | −0.00647386 | + | 0.00647386i | −0.710336 | − | 0.703862i | \(-0.751457\pi\) |
0.703862 | + | 0.710336i | \(0.251457\pi\) | |||||||
\(348\) | −7.14988 | − | 16.7482i | −0.383274 | − | 0.897795i | ||||
\(349\) | −0.280410 | + | 0.280410i | −0.0150100 | + | 0.0150100i | −0.714572 | − | 0.699562i | \(-0.753379\pi\) |
0.699562 | + | 0.714572i | \(0.253379\pi\) | |||||||
\(350\) | 3.81947 | − | 5.78350i | 0.204159 | − | 0.309141i | ||||
\(351\) | − | 30.6054i | − | 1.63359i | ||||||
\(352\) | −10.4052 | + | 16.5197i | −0.554597 | + | 0.880506i | ||||
\(353\) | 16.6801 | 0.887792 | 0.443896 | − | 0.896078i | \(-0.353596\pi\) | ||||
0.443896 | + | 0.896078i | \(0.353596\pi\) | |||||||
\(354\) | 20.5124 | + | 13.5465i | 1.09022 | + | 0.719990i | ||||
\(355\) | 7.27657 | − | 7.27657i | 0.386200 | − | 0.386200i | ||||
\(356\) | −0.763151 | − | 1.78764i | −0.0404469 | − | 0.0947445i | ||||
\(357\) | −3.32608 | + | 3.32608i | −0.176035 | + | 0.176035i | ||||
\(358\) | 1.69942 | − | 0.347573i | 0.0898173 | − | 0.0183698i | ||||
\(359\) | 23.6765 | 1.24960 | 0.624800 | − | 0.780785i | \(-0.285180\pi\) | ||||
0.624800 | + | 0.780785i | \(0.285180\pi\) | |||||||
\(360\) | −2.11606 | − | 3.05862i | −0.111526 | − | 0.161204i | ||||
\(361\) | −2.15922 | + | 18.8769i | −0.113643 | + | 0.993522i | ||||
\(362\) | 24.4999 | − | 5.01081i | 1.28768 | − | 0.263362i | ||||
\(363\) | −0.982458 | − | 0.982458i | −0.0515657 | − | 0.0515657i | ||||
\(364\) | −16.2960 | + | 40.5742i | −0.854142 | + | 2.12666i | ||||
\(365\) | −10.4977 | + | 10.4977i | −0.549477 | + | 0.549477i | ||||
\(366\) | −9.53571 | + | 14.4391i | −0.498439 | + | 0.754746i | ||||
\(367\) | − | 8.49939i | − | 0.443665i | −0.975085 | − | 0.221832i | \(-0.928796\pi\) | ||
0.975085 | − | 0.221832i | \(-0.0712038\pi\) | |||||||
\(368\) | −21.6814 | + | 22.6375i | −1.13022 | + | 1.18006i | ||||
\(369\) | 1.48862i | 0.0774944i | ||||||||
\(370\) | −5.36709 | − | 3.54447i | −0.279022 | − | 0.184268i | ||||
\(371\) | −35.8271 | + | 35.8271i | −1.86005 | + | 1.86005i | ||||
\(372\) | −17.9771 | − | 7.22025i | −0.932072 | − | 0.374352i | ||||
\(373\) | 15.0345 | − | 15.0345i | 0.778457 | − | 0.778457i | −0.201111 | − | 0.979568i | \(-0.564455\pi\) |
0.979568 | + | 0.201111i | \(0.0644553\pi\) | |||||||
\(374\) | 3.68629 | − | 0.753934i | 0.190613 | − | 0.0389850i | ||||
\(375\) | 18.4348i | 0.951971i | ||||||||
\(376\) | 8.54197 | + | 1.55591i | 0.440519 | + | 0.0802398i | ||||
\(377\) | 32.6232i | 1.68018i | ||||||||
\(378\) | 6.35741 | + | 31.0839i | 0.326990 | + | 1.59878i | ||||
\(379\) | −10.6125 | − | 10.6125i | −0.545128 | − | 0.545128i | 0.379900 | − | 0.925028i | \(-0.375958\pi\) |
−0.925028 | + | 0.379900i | \(0.875958\pi\) | |||||||
\(380\) | −15.9328 | + | 5.75352i | −0.817337 | + | 0.295149i | ||||
\(381\) | −22.6793 | + | 22.6793i | −1.16190 | + | 1.16190i | ||||
\(382\) | 6.86907 | − | 10.4013i | 0.351452 | − | 0.532175i | ||||
\(383\) | −6.01982 | −0.307599 | −0.153799 | − | 0.988102i | \(-0.549151\pi\) | ||||
−0.153799 | + | 0.988102i | \(0.549151\pi\) | |||||||
\(384\) | 17.0283 | + | 2.72364i | 0.868970 | + | 0.138990i | ||||
\(385\) | −26.8469 | −1.36824 | ||||||||
\(386\) | −5.29566 | + | 8.01878i | −0.269542 | + | 0.408145i | ||||
\(387\) | −4.91280 | − | 4.91280i | −0.249732 | − | 0.249732i | ||||
\(388\) | 12.1892 | − | 5.20365i | 0.618815 | − | 0.264175i | ||||
\(389\) | 9.78130 | + | 9.78130i | 0.495932 | + | 0.495932i | 0.910169 | − | 0.414237i | \(-0.135952\pi\) |
−0.414237 | + | 0.910169i | \(0.635952\pi\) | |||||||
\(390\) | −4.58353 | − | 22.4107i | −0.232096 | − | 1.13481i | ||||
\(391\) | 6.04093 | 0.305503 | ||||||||
\(392\) | 4.57469 | − | 25.1152i | 0.231057 | − | 1.26851i | ||||
\(393\) | 12.7225 | 0.641766 | ||||||||
\(394\) | −2.15591 | − | 10.5411i | −0.108613 | − | 0.531053i | ||||
\(395\) | 6.78666 | + | 6.78666i | 0.341474 | + | 0.341474i | ||||
\(396\) | 1.74093 | − | 4.33460i | 0.0874849 | − | 0.217822i | ||||
\(397\) | −17.2798 | + | 17.2798i | −0.867247 | + | 0.867247i | −0.992167 | − | 0.124920i | \(-0.960133\pi\) |
0.124920 | + | 0.992167i | \(0.460133\pi\) | |||||||
\(398\) | 3.01299 | + | 1.98980i | 0.151027 | + | 0.0997396i | ||||
\(399\) | 26.5541 | + | 1.51374i | 1.32937 | + | 0.0757820i | ||||
\(400\) | 3.53654 | + | 3.38719i | 0.176827 | + | 0.169359i | ||||
\(401\) | − | 21.0663i | − | 1.05200i | −0.850485 | − | 0.526000i | \(-0.823691\pi\) | ||
0.850485 | − | 0.526000i | \(-0.176309\pi\) | |||||||
\(402\) | −11.3459 | + | 17.1802i | −0.565883 | + | 0.856871i | ||||
\(403\) | 24.5406 | + | 24.5406i | 1.22245 | + | 1.22245i | ||||
\(404\) | 9.41887 | − | 23.4513i | 0.468606 | − | 1.16675i | ||||
\(405\) | −8.94734 | − | 8.94734i | −0.444597 | − | 0.444597i | ||||
\(406\) | −6.77656 | − | 33.1333i | −0.336315 | − | 1.64438i | ||||
\(407\) | − | 8.07800i | − | 0.400412i | ||||||
\(408\) | −1.89085 | − | 2.73309i | −0.0936108 | − | 0.135308i | ||||
\(409\) | 30.6366 | 1.51488 | 0.757441 | − | 0.652904i | \(-0.226449\pi\) | ||||
0.757441 | + | 0.652904i | \(0.226449\pi\) | |||||||
\(410\) | 1.21126 | + | 5.92234i | 0.0598198 | + | 0.292483i | ||||
\(411\) | 0.901714 | + | 0.901714i | 0.0444783 | + | 0.0444783i | ||||
\(412\) | −5.08624 | + | 2.17134i | −0.250581 | + | 0.106974i | ||||
\(413\) | 32.2806 | + | 32.2806i | 1.58842 | + | 1.58842i | ||||
\(414\) | 4.13289 | − | 6.25809i | 0.203120 | − | 0.307568i | ||||
\(415\) | − | 3.96772i | − | 0.194768i | ||||||
\(416\) | −26.1400 | − | 16.4646i | −1.28162 | − | 0.807243i | ||||
\(417\) | − | 20.5285i | − | 1.00528i | ||||||
\(418\) | −17.0572 | − | 12.7158i | −0.834295 | − | 0.621949i | ||||
\(419\) | −11.0415 | − | 11.0415i | −0.539415 | − | 0.539415i | 0.383942 | − | 0.923357i | \(-0.374566\pi\) |
−0.923357 | + | 0.383942i | \(0.874566\pi\) | |||||||
\(420\) | 9.31039 | + | 21.8090i | 0.454301 | + | 1.06417i | ||||
\(421\) | −9.18271 | + | 9.18271i | −0.447538 | + | 0.447538i | −0.894535 | − | 0.446997i | \(-0.852493\pi\) |
0.446997 | + | 0.894535i | \(0.352493\pi\) | |||||||
\(422\) | 14.0306 | − | 2.86960i | 0.683001 | − | 0.139690i | ||||
\(423\) | −2.07735 | −0.101004 | ||||||||
\(424\) | −20.3674 | − | 29.4397i | −0.989129 | − | 1.42972i | ||||
\(425\) | − | 0.943745i | − | 0.0457784i | ||||||
\(426\) | −2.28745 | − | 11.1842i | −0.110827 | − | 0.541879i | ||||
\(427\) | −22.7230 | + | 22.7230i | −1.09964 | + | 1.09964i | ||||
\(428\) | 2.41405 | − | 6.01057i | 0.116688 | − | 0.290532i | ||||
\(429\) | 20.3145 | − | 20.3145i | 0.980793 | − | 0.980793i | ||||
\(430\) | −23.5426 | − | 15.5477i | −1.13532 | − | 0.749776i | ||||
\(431\) | 34.1955 | 1.64714 | 0.823570 | − | 0.567215i | \(-0.191979\pi\) | ||||
0.823570 | + | 0.567215i | \(0.191979\pi\) | |||||||
\(432\) | −22.4115 | + | 0.483457i | −1.07827 | + | 0.0232604i | ||||
\(433\) | − | 7.12873i | − | 0.342585i | −0.985220 | − | 0.171292i | \(-0.945206\pi\) | ||
0.985220 | − | 0.171292i | \(-0.0547943\pi\) | |||||||
\(434\) | −30.0220 | − | 19.8267i | −1.44110 | − | 0.951713i | ||||
\(435\) | 12.5106 | + | 12.5106i | 0.599838 | + | 0.599838i | ||||
\(436\) | −7.51250 | + | 18.7048i | −0.359783 | + | 0.895798i | ||||
\(437\) | −22.7395 | − | 25.4888i | −1.08778 | − | 1.21930i | ||||
\(438\) | 3.30005 | + | 16.1353i | 0.157682 | + | 0.770972i | ||||
\(439\) | − | 13.3329i | − | 0.636347i | −0.948033 | − | 0.318173i | \(-0.896931\pi\) | ||
0.948033 | − | 0.318173i | \(-0.103069\pi\) | |||||||
\(440\) | 3.39914 | − | 18.6614i | 0.162048 | − | 0.889646i | ||||
\(441\) | 6.10785i | 0.290850i | ||||||||
\(442\) | 1.19299 | + | 5.83299i | 0.0567445 | + | 0.277447i | ||||
\(443\) | −6.00022 | + | 6.00022i | −0.285079 | + | 0.285079i | −0.835131 | − | 0.550052i | \(-0.814608\pi\) |
0.550052 | + | 0.835131i | \(0.314608\pi\) | |||||||
\(444\) | −6.56215 | + | 2.80142i | −0.311426 | + | 0.132949i | ||||
\(445\) | 1.33534 | + | 1.33534i | 0.0633010 | + | 0.0633010i | ||||
\(446\) | −0.430224 | − | 0.284123i | −0.0203717 | − | 0.0134536i | ||||
\(447\) | 12.9356 | 0.611834 | ||||||||
\(448\) | 29.9688 | + | 11.2922i | 1.41589 | + | 0.533506i | ||||
\(449\) | 24.8792i | 1.17412i | 0.809542 | + | 0.587061i | \(0.199715\pi\) | ||||
−0.809542 | + | 0.587061i | \(0.800285\pi\) | |||||||
\(450\) | −0.977671 | − | 0.645661i | −0.0460878 | − | 0.0304367i | ||||
\(451\) | −5.36838 | + | 5.36838i | −0.252787 | + | 0.252787i | ||||
\(452\) | 7.38188 | − | 3.15136i | 0.347214 | − | 0.148228i | ||||
\(453\) | 20.4727 | + | 20.4727i | 0.961891 | + | 0.961891i | ||||
\(454\) | −23.8590 | + | 4.87973i | −1.11976 | + | 0.229017i | ||||
\(455\) | − | 42.4811i | − | 1.99155i | ||||||
\(456\) | −4.41427 | + | 18.2662i | −0.206717 | + | 0.855391i | ||||
\(457\) | − | 35.0890i | − | 1.64140i | −0.571363 | − | 0.820698i | \(-0.693585\pi\) | ||
0.571363 | − | 0.820698i | \(-0.306415\pi\) | |||||||
\(458\) | 1.57816 | + | 7.71625i | 0.0737425 | + | 0.360557i | ||||
\(459\) | 3.05481 | + | 3.05481i | 0.142587 | + | 0.142587i | ||||
\(460\) | 11.3502 | − | 28.2601i | 0.529207 | − | 1.31763i | ||||
\(461\) | 3.40782 | − | 3.40782i | 0.158718 | − | 0.158718i | −0.623280 | − | 0.781998i | \(-0.714200\pi\) |
0.781998 | + | 0.623280i | \(0.214200\pi\) | |||||||
\(462\) | −16.4124 | + | 24.8519i | −0.763573 | + | 1.15622i | ||||
\(463\) | 5.08661i | 0.236395i | 0.992990 | + | 0.118197i | \(0.0377115\pi\) | ||||
−0.992990 | + | 0.118197i | \(0.962288\pi\) | |||||||
\(464\) | 23.8891 | − | 0.515332i | 1.10902 | − | 0.0239237i | ||||
\(465\) | 18.8221 | 0.872852 | ||||||||
\(466\) | 0.0837341 | − | 0.126792i | 0.00387891 | − | 0.00587351i | ||||
\(467\) | −10.1565 | − | 10.1565i | −0.469989 | − | 0.469989i | 0.431922 | − | 0.901911i | \(-0.357836\pi\) |
−0.901911 | + | 0.431922i | \(0.857836\pi\) | |||||||
\(468\) | 6.85885 | + | 2.75475i | 0.317050 | + | 0.127338i | ||||
\(469\) | −27.0367 | + | 27.0367i | −1.24844 | + | 1.24844i | ||||
\(470\) | −8.26456 | + | 1.69030i | −0.381216 | + | 0.0779677i | ||||
\(471\) | 0.899219i | 0.0414338i | ||||||||
\(472\) | −26.5255 | + | 18.3512i | −1.22093 | + | 0.844684i | ||||
\(473\) | − | 35.4339i | − | 1.62925i | ||||||
\(474\) | 10.4312 | − | 2.13344i | 0.479123 | − | 0.0979921i | ||||
\(475\) | −3.98200 | + | 3.55249i | −0.182707 | + | 0.162999i | ||||
\(476\) | −2.42328 | − | 5.67639i | −0.111071 | − | 0.260177i | ||||
\(477\) | 6.05638 | + | 6.05638i | 0.277303 | + | 0.277303i | ||||
\(478\) | 4.36985 | − | 6.61690i | 0.199872 | − | 0.302650i | ||||
\(479\) | − | 5.47969i | − | 0.250373i | −0.992133 | − | 0.125187i | \(-0.960047\pi\) | ||
0.992133 | − | 0.125187i | \(-0.0399530\pi\) | |||||||
\(480\) | −16.3383 | + | 3.71040i | −0.745740 | + | 0.169356i | ||||
\(481\) | 12.7822 | 0.582819 | ||||||||
\(482\) | 20.1006 | − | 30.4367i | 0.915557 | − | 1.38635i | ||||
\(483\) | −33.8111 | + | 33.8111i | −1.53846 | + | 1.53846i | ||||
\(484\) | 1.67670 | − | 0.715790i | 0.0762134 | − | 0.0325359i | ||||
\(485\) | −9.10517 | + | 9.10517i | −0.413444 | + | 0.413444i | ||||
\(486\) | 9.54201 | − | 1.95157i | 0.432834 | − | 0.0885250i | ||||
\(487\) | − | 40.0620i | − | 1.81538i | −0.419636 | − | 0.907692i | \(-0.637842\pi\) | ||
0.419636 | − | 0.907692i | \(-0.362158\pi\) | |||||||
\(488\) | −12.9179 | − | 18.6719i | −0.584764 | − | 0.845236i | ||||
\(489\) | −14.0891 | −0.637131 | ||||||||
\(490\) | 4.96983 | + | 24.2995i | 0.224514 | + | 1.09774i | ||||
\(491\) | −22.1640 | + | 22.1640i | −1.00025 | + | 1.00025i | −0.000247972 | 1.00000i | \(0.500079\pi\) | |
−1.00000 | 0.000247972i | \(0.999921\pi\) | ||||||||
\(492\) | 6.22273 | + | 2.49926i | 0.280542 | + | 0.112675i | ||||
\(493\) | −3.25622 | − | 3.25622i | −0.146653 | − | 0.146653i | ||||
\(494\) | 20.1208 | − | 26.9904i | 0.905276 | − | 1.21436i | ||||
\(495\) | 4.53833i | 0.203983i | ||||||||
\(496\) | 17.5828 | − | 18.3581i | 0.789489 | − | 0.824302i | ||||
\(497\) | − | 21.2006i | − | 0.950975i | ||||||
\(498\) | −3.67288 | − | 2.42560i | −0.164586 | − | 0.108694i | ||||
\(499\) | 6.12304 | + | 6.12304i | 0.274105 | + | 0.274105i | 0.830750 | − | 0.556645i | \(-0.187912\pi\) |
−0.556645 | + | 0.830750i | \(0.687912\pi\) | |||||||
\(500\) | −22.4463 | − | 9.01520i | −1.00383 | − | 0.403172i | ||||
\(501\) | −6.71996 | − | 6.71996i | −0.300226 | − | 0.300226i | ||||
\(502\) | −23.4729 | + | 4.80076i | −1.04765 | + | 0.214269i | ||||
\(503\) | −22.7361 | −1.01375 | −0.506876 | − | 0.862019i | \(-0.669200\pi\) | ||||
−0.506876 | + | 0.862019i | \(0.669200\pi\) | |||||||
\(504\) | −7.53832 | − | 1.37309i | −0.335784 | − | 0.0611625i | ||||
\(505\) | 24.5535i | 1.09262i | ||||||||
\(506\) | 37.4728 | − | 7.66408i | 1.66587 | − | 0.340710i | ||||
\(507\) | 18.1333 | + | 18.1333i | 0.805326 | + | 0.805326i | ||||
\(508\) | −16.5235 | − | 38.7053i | −0.733111 | − | 1.71727i | ||||
\(509\) | −10.5574 | − | 10.5574i | −0.467948 | − | 0.467948i | 0.433301 | − | 0.901249i | \(-0.357349\pi\) |
−0.901249 | + | 0.433301i | \(0.857349\pi\) | |||||||
\(510\) | 2.69438 | + | 1.77939i | 0.119309 | + | 0.0787925i | ||||
\(511\) | 30.5856i | 1.35303i | ||||||||
\(512\) | −11.6436 | + | 19.4017i | −0.514581 | + | 0.857442i | ||||
\(513\) | 1.39029 | − | 24.3884i | 0.0613828 | − | 1.07677i | ||||
\(514\) | −16.5017 | + | 24.9872i | −0.727861 | + | 1.10214i | ||||
\(515\) | 3.79934 | − | 3.79934i | 0.167419 | − | 0.167419i | ||||
\(516\) | −28.7847 | + | 12.2883i | −1.26717 | + | 0.540963i | ||||
\(517\) | −7.49152 | − | 7.49152i | −0.329477 | − | 0.329477i | ||||
\(518\) | −12.9821 | + | 2.65515i | −0.570400 | + | 0.116660i | ||||
\(519\) | −21.3195 | −0.935821 | ||||||||
\(520\) | 29.5288 | + | 5.37862i | 1.29492 | + | 0.235868i | ||||
\(521\) | 25.0157 | 1.09596 | 0.547979 | − | 0.836492i | \(-0.315397\pi\) | ||||
0.547979 | + | 0.836492i | \(0.315397\pi\) | |||||||
\(522\) | −5.60101 | + | 1.14554i | −0.245150 | + | 0.0501390i | ||||
\(523\) | −0.0726825 | − | 0.0726825i | −0.00317819 | − | 0.00317819i | 0.705516 | − | 0.708694i | \(-0.250715\pi\) |
−0.708694 | + | 0.705516i | \(0.750715\pi\) | |||||||
\(524\) | −6.22170 | + | 15.4909i | −0.271796 | + | 0.676725i | ||||
\(525\) | 5.28214 | + | 5.28214i | 0.230531 | + | 0.230531i | ||||
\(526\) | 4.20361 | + | 2.77610i | 0.183286 | + | 0.121044i | ||||
\(527\) | −4.89895 | −0.213401 | ||||||||
\(528\) | −15.1966 | − | 14.5548i | −0.661349 | − | 0.633418i | ||||
\(529\) | 38.4088 | 1.66995 | ||||||||
\(530\) | 29.0227 | + | 19.1668i | 1.26067 | + | 0.832553i | ||||
\(531\) | 5.45686 | − | 5.45686i | 0.236808 | − | 0.236808i | ||||
\(532\) | −14.8289 | + | 31.5920i | −0.642914 | + | 1.36969i | ||||
\(533\) | −8.49464 | − | 8.49464i | −0.367944 | − | 0.367944i | ||||
\(534\) | 2.05244 | − | 0.419773i | 0.0888178 | − | 0.0181654i | ||||
\(535\) | 6.29306i | 0.272073i | ||||||||
\(536\) | −15.3701 | − | 22.2165i | −0.663888 | − | 0.959605i | ||||
\(537\) | 1.86954i | 0.0806767i | ||||||||
\(538\) | 2.68977 | + | 13.1514i | 0.115964 | + | 0.566995i | ||||
\(539\) | −22.0266 | + | 22.0266i | −0.948753 | + | 0.948753i | ||||
\(540\) | 20.0304 | − | 8.55108i | 0.861971 | − | 0.367980i | ||||
\(541\) | 26.1537 | − | 26.1537i | 1.12444 | − | 1.12444i | 0.133371 | − | 0.991066i | \(-0.457420\pi\) |
0.991066 | − | 0.133371i | \(-0.0425801\pi\) | |||||||
\(542\) | −13.9019 | + | 21.0505i | −0.597137 | + | 0.904196i | ||||
\(543\) | 26.9524i | 1.15664i | ||||||||
\(544\) | 4.25249 | − | 0.965732i | 0.182324 | − | 0.0414054i | ||||
\(545\) | − | 19.5839i | − | 0.838883i | ||||||
\(546\) | −39.3244 | − | 25.9701i | −1.68293 | − | 1.11142i | ||||
\(547\) | −14.2992 | + | 14.2992i | −0.611388 | + | 0.611388i | −0.943308 | − | 0.331919i | \(-0.892304\pi\) |
0.331919 | + | 0.943308i | \(0.392304\pi\) | |||||||
\(548\) | −1.53889 | + | 0.656962i | −0.0657383 | + | 0.0280640i | ||||
\(549\) | 3.84121 | + | 3.84121i | 0.163939 | + | 0.163939i | ||||
\(550\) | −1.19732 | − | 5.85419i | −0.0510540 | − | 0.249623i | ||||
\(551\) | −1.48195 | + | 25.9964i | −0.0631333 | + | 1.10748i | ||||
\(552\) | −19.2213 | − | 27.7831i | −0.818113 | − | 1.18253i | ||||
\(553\) | 19.7732 | 0.840842 | ||||||||
\(554\) | 1.73119 | + | 8.46448i | 0.0735512 | + | 0.359621i | ||||
\(555\) | 4.90183 | − | 4.90183i | 0.208071 | − | 0.208071i | ||||
\(556\) | 24.9955 | + | 10.0391i | 1.06005 | + | 0.425751i | ||||
\(557\) | 21.0678 | − | 21.0678i | 0.892670 | − | 0.892670i | −0.102103 | − | 0.994774i | \(-0.532557\pi\) |
0.994774 | + | 0.102103i | \(0.0325573\pi\) | |||||||
\(558\) | −3.35160 | + | 5.07505i | −0.141885 | + | 0.214844i | ||||
\(559\) | 56.0687 | 2.37146 | ||||||||
\(560\) | −31.1078 | + | 0.671053i | −1.31454 | + | 0.0283572i | ||||
\(561\) | 4.05530i | 0.171215i | ||||||||
\(562\) | 12.9169 | + | 8.53039i | 0.544865 | + | 0.359833i | ||||
\(563\) | −6.74038 | + | 6.74038i | −0.284073 | + | 0.284073i | −0.834731 | − | 0.550658i | \(-0.814377\pi\) |
0.550658 | + | 0.834731i | \(0.314377\pi\) | |||||||
\(564\) | −3.48770 | + | 8.68375i | −0.146858 | + | 0.365652i | ||||
\(565\) | −5.51415 | + | 5.51415i | −0.231982 | + | 0.231982i | ||||
\(566\) | −25.0073 | + | 5.11459i | −1.05114 | + | 0.214982i | ||||
\(567\) | −26.0684 | −1.09477 | ||||||||
\(568\) | 14.7366 | + | 2.68425i | 0.618334 | + | 0.112628i | ||||
\(569\) | −34.0576 | −1.42777 | −0.713885 | − | 0.700263i | \(-0.753066\pi\) | ||||
−0.713885 | + | 0.700263i | \(0.753066\pi\) | |||||||
\(570\) | −2.63443 | − | 18.0666i | −0.110344 | − | 0.756726i | ||||
\(571\) | −4.22887 | + | 4.22887i | −0.176973 | + | 0.176973i | −0.790035 | − | 0.613062i | \(-0.789938\pi\) |
0.613062 | + | 0.790035i | \(0.289938\pi\) | |||||||
\(572\) | 14.8005 | + | 34.6694i | 0.618841 | + | 1.44960i | ||||
\(573\) | 9.49959 | + | 9.49959i | 0.396851 | + | 0.396851i | ||||
\(574\) | 10.3920 | + | 6.86295i | 0.433754 | + | 0.286454i | ||||
\(575\) | − | 9.59360i | − | 0.400081i | ||||||
\(576\) | 1.90888 | − | 5.06607i | 0.0795369 | − | 0.211086i | ||||
\(577\) | −36.3517 | −1.51334 | −0.756671 | − | 0.653795i | \(-0.773176\pi\) | ||||
−0.756671 | + | 0.653795i | \(0.773176\pi\) | |||||||
\(578\) | 19.3603 | + | 12.7857i | 0.805284 | + | 0.531815i | ||||
\(579\) | −7.32364 | − | 7.32364i | −0.304360 | − | 0.304360i | ||||
\(580\) | −21.3510 | + | 9.11486i | −0.886553 | + | 0.378474i | ||||
\(581\) | −5.78006 | − | 5.78006i | −0.239797 | − | 0.239797i | ||||
\(582\) | 2.86228 | + | 13.9948i | 0.118645 | + | 0.580105i | ||||
\(583\) | 43.6820i | 1.80913i | ||||||||
\(584\) | −21.2601 | − | 3.87250i | −0.879751 | − | 0.160245i | ||||
\(585\) | −7.18121 | −0.296907 | ||||||||
\(586\) | 29.9246 | − | 6.12030i | 1.23617 | − | 0.252827i | ||||
\(587\) | 26.7919 | − | 26.7919i | 1.10582 | − | 1.10582i | 0.112124 | − | 0.993694i | \(-0.464235\pi\) |
0.993694 | − | 0.112124i | \(-0.0357654\pi\) | |||||||
\(588\) | 25.5320 | + | 10.2545i | 1.05292 | + | 0.422890i | ||||
\(589\) | 18.4408 | + | 20.6704i | 0.759841 | + | 0.851709i | ||||
\(590\) | 17.2695 | − | 26.1498i | 0.710974 | − | 1.07657i | ||||
\(591\) | 11.5963 | 0.477009 | ||||||||
\(592\) | −0.201914 | − | 9.36007i | −0.00829862 | − | 0.384696i | ||||
\(593\) | −5.90642 | −0.242548 | −0.121274 | − | 0.992619i | \(-0.538698\pi\) | ||||
−0.121274 | + | 0.992619i | \(0.538698\pi\) | |||||||
\(594\) | 22.8251 | + | 15.0738i | 0.936525 | + | 0.618487i | ||||
\(595\) | 4.24017 | + | 4.24017i | 0.173830 | + | 0.173830i | ||||
\(596\) | −6.32592 | + | 15.7504i | −0.259120 | + | 0.645163i | ||||
\(597\) | −2.75180 | + | 2.75180i | −0.112623 | + | 0.112623i | ||||
\(598\) | 12.1272 | + | 59.2950i | 0.495920 | + | 2.42475i | ||||
\(599\) | − | 34.2515i | − | 1.39948i | −0.714398 | − | 0.699739i | \(-0.753300\pi\) | ||
0.714398 | − | 0.699739i | \(-0.246700\pi\) | |||||||
\(600\) | −4.34042 | + | 3.00285i | −0.177197 | + | 0.122591i | ||||
\(601\) | −6.25234 | −0.255038 | −0.127519 | − | 0.991836i | \(-0.540701\pi\) | ||||
−0.127519 | + | 0.991836i | \(0.540701\pi\) | |||||||
\(602\) | −56.9455 | + | 11.6467i | −2.32092 | + | 0.474685i | ||||
\(603\) | 4.57041 | + | 4.57041i | 0.186121 | + | 0.186121i | ||||
\(604\) | −34.9394 | + | 14.9158i | −1.42166 | + | 0.606915i | ||||
\(605\) | −1.25247 | + | 1.25247i | −0.0509200 | + | 0.0509200i | ||||
\(606\) | 22.7290 | + | 15.0104i | 0.923301 | + | 0.609754i | ||||
\(607\) | 34.1961 | 1.38798 | 0.693988 | − | 0.719987i | \(-0.255852\pi\) | ||||
0.693988 | + | 0.719987i | \(0.255852\pi\) | |||||||
\(608\) | −20.0822 | − | 14.3075i | −0.814440 | − | 0.580247i | ||||
\(609\) | 36.4501 | 1.47703 | ||||||||
\(610\) | 18.4074 | + | 12.1564i | 0.745294 | + | 0.492198i | ||||
\(611\) | 11.8542 | − | 11.8542i | 0.479569 | − | 0.479569i | ||||
\(612\) | −0.959563 | + | 0.409643i | −0.0387881 | + | 0.0165588i | ||||
\(613\) | 5.80803 | + | 5.80803i | 0.234584 | + | 0.234584i | 0.814603 | − | 0.580019i | \(-0.196955\pi\) |
−0.580019 | + | 0.814603i | \(0.696955\pi\) | |||||||
\(614\) | 6.61732 | − | 1.35340i | 0.267053 | − | 0.0546188i | ||||
\(615\) | −6.51519 | −0.262718 | ||||||||
\(616\) | −22.2336 | − | 32.1371i | −0.895815 | − | 1.29484i | ||||
\(617\) | − | 33.1368i | − | 1.33404i | −0.745041 | − | 0.667019i | \(-0.767570\pi\) | ||
0.745041 | − | 0.667019i | \(-0.232430\pi\) | |||||||
\(618\) | −1.19435 | − | 5.83967i | −0.0480439 | − | 0.234906i | ||||
\(619\) | −3.63801 | + | 3.63801i | −0.146224 | + | 0.146224i | −0.776429 | − | 0.630205i | \(-0.782971\pi\) |
0.630205 | + | 0.776429i | \(0.282971\pi\) | |||||||
\(620\) | −9.20457 | + | 22.9178i | −0.369664 | + | 0.920400i | ||||
\(621\) | 31.0536 | + | 31.0536i | 1.24614 | + | 1.24614i | ||||
\(622\) | 1.76786 | + | 1.16751i | 0.0708849 | + | 0.0468129i | ||||
\(623\) | 3.89055 | 0.155872 | ||||||||
\(624\) | 23.0308 | − | 24.0464i | 0.921971 | − | 0.962625i | ||||
\(625\) | 17.3800 | 0.695202 | ||||||||
\(626\) | 14.3483 | − | 21.7264i | 0.573472 | − | 0.868362i | ||||
\(627\) | 17.1108 | − | 15.2651i | 0.683338 | − | 0.609631i | ||||
\(628\) | −1.09489 | − | 0.439746i | −0.0436909 | − | 0.0175478i | ||||
\(629\) | −1.27583 | + | 1.27583i | −0.0508708 | + | 0.0508708i | ||||
\(630\) | 7.29350 | − | 1.49170i | 0.290580 | − | 0.0594306i | ||||
\(631\) | 8.04038 | 0.320083 | 0.160041 | − | 0.987110i | \(-0.448837\pi\) | ||||
0.160041 | + | 0.987110i | \(0.448837\pi\) | |||||||
\(632\) | −2.50352 | + | 13.7444i | −0.0995849 | + | 0.546724i | ||||
\(633\) | 15.4352i | 0.613493i | ||||||||
\(634\) | −6.65915 | − | 32.5593i | −0.264468 | − | 1.29309i | ||||
\(635\) | 28.9122 | + | 28.9122i | 1.14735 | + | 1.14735i | ||||
\(636\) | 35.4850 | − | 15.1487i | 1.40707 | − | 0.600687i | ||||
\(637\) | −34.8538 | − | 34.8538i | −1.38096 | − | 1.38096i | ||||
\(638\) | −24.3300 | − | 16.0677i | −0.963233 | − | 0.636126i | ||||
\(639\) | −3.58384 | −0.141775 | ||||||||
\(640\) | 3.47217 | − | 21.7081i | 0.137249 | − | 0.858088i | ||||
\(641\) | − | 4.50914i | − | 0.178100i | −0.996027 | − | 0.0890501i | \(-0.971617\pi\) | ||
0.996027 | − | 0.0890501i | \(-0.0283831\pi\) | |||||||
\(642\) | 5.82542 | + | 3.84715i | 0.229911 | + | 0.151835i | ||||
\(643\) | −9.49870 | − | 9.49870i | −0.374592 | − | 0.374592i | 0.494554 | − | 0.869147i | \(-0.335331\pi\) |
−0.869147 | + | 0.494554i | \(0.835331\pi\) | |||||||
\(644\) | −24.6337 | − | 57.7031i | −0.970706 | − | 2.27382i | ||||
\(645\) | 21.5017 | − | 21.5017i | 0.846629 | − | 0.846629i | ||||
\(646\) | 0.685680 | + | 4.70231i | 0.0269777 | + | 0.185010i | ||||
\(647\) | 31.7571 | 1.24850 | 0.624250 | − | 0.781225i | \(-0.285405\pi\) | ||||
0.624250 | + | 0.781225i | \(0.285405\pi\) | |||||||
\(648\) | 3.30058 | − | 18.1203i | 0.129659 | − | 0.711831i | ||||
\(649\) | 39.3580 | 1.54494 | ||||||||
\(650\) | 9.26336 | − | 1.89458i | 0.363339 | − | 0.0743115i | ||||
\(651\) | 27.4194 | − | 27.4194i | 1.07465 | − | 1.07465i | ||||
\(652\) | 6.89000 | − | 17.1549i | 0.269833 | − | 0.671838i | ||||
\(653\) | 19.7023 | − | 19.7023i | 0.771009 | − | 0.771009i | −0.207274 | − | 0.978283i | \(-0.566459\pi\) |
0.978283 | + | 0.207274i | \(0.0664591\pi\) | |||||||
\(654\) | −18.1286 | − | 11.9723i | −0.708886 | − | 0.468153i | ||||
\(655\) | − | 16.2190i | − | 0.633729i | ||||||
\(656\) | −6.08621 | + | 6.35458i | −0.237627 | + | 0.248105i | ||||
\(657\) | 5.17033 | 0.201714 | ||||||||
\(658\) | −9.57717 | + | 14.5019i | −0.373357 | + | 0.565344i | ||||
\(659\) | 3.40326 | − | 3.40326i | 0.132572 | − | 0.132572i | −0.637707 | − | 0.770279i | \(-0.720117\pi\) |
0.770279 | + | 0.637707i | \(0.220117\pi\) | |||||||
\(660\) | 18.9711 | + | 7.61946i | 0.738450 | + | 0.296587i | ||||
\(661\) | −7.77011 | + | 7.77011i | −0.302222 | + | 0.302222i | −0.841883 | − | 0.539660i | \(-0.818553\pi\) |
0.539660 | + | 0.841883i | \(0.318553\pi\) | |||||||
\(662\) | 5.60282 | + | 27.3945i | 0.217760 | + | 1.06472i | ||||
\(663\) | −6.41690 | −0.249212 | ||||||||
\(664\) | 4.74956 | − | 3.28591i | 0.184319 | − | 0.127518i | ||||
\(665\) | 1.92976 | − | 33.8518i | 0.0748330 | − | 1.31272i | ||||
\(666\) | 0.448839 | + | 2.19455i | 0.0173921 | + | 0.0850372i | ||||
\(667\) | −33.1010 | − | 33.1010i | −1.28168 | − | 1.28168i | ||||
\(668\) | 11.4685 | − | 4.89597i | 0.443730 | − | 0.189431i | ||||
\(669\) | 0.392929 | − | 0.392929i | 0.0151915 | − | 0.0151915i | ||||
\(670\) | 21.9018 | + | 14.4641i | 0.846140 | + | 0.558797i | ||||
\(671\) | 27.7050i | 1.06954i | ||||||||
\(672\) | −18.3960 | + | 29.2064i | −0.709641 | + | 1.12666i | ||||
\(673\) | 19.7481i | 0.761232i | 0.924733 | + | 0.380616i | \(0.124288\pi\) | ||||
−0.924733 | + | 0.380616i | \(0.875712\pi\) | |||||||
\(674\) | −13.9440 | + | 21.1143i | −0.537104 | + | 0.813292i | ||||
\(675\) | 4.85135 | − | 4.85135i | 0.186729 | − | 0.186729i | ||||
\(676\) | −30.9468 | + | 13.2114i | −1.19026 | + | 0.508129i | ||||
\(677\) | −8.64520 | + | 8.64520i | −0.332262 | + | 0.332262i | −0.853445 | − | 0.521183i | \(-0.825491\pi\) |
0.521183 | + | 0.853445i | \(0.325491\pi\) | |||||||
\(678\) | 1.73341 | + | 8.47536i | 0.0665714 | + | 0.325494i | ||||
\(679\) | 26.5282i | 1.01806i | ||||||||
\(680\) | −3.48422 | + | 2.41050i | −0.133614 | + | 0.0924386i | ||||
\(681\) | − | 26.2474i | − | 1.00580i | ||||||
\(682\) | −30.3889 | + | 6.21525i | −1.16365 | + | 0.237994i | ||||
\(683\) | 7.82187 | + | 7.82187i | 0.299295 | + | 0.299295i | 0.840738 | − | 0.541442i | \(-0.182122\pi\) |
−0.541442 | + | 0.840738i | \(0.682122\pi\) | |||||||
\(684\) | 5.34046 | + | 2.50675i | 0.204198 | + | 0.0958478i | ||||
\(685\) | 1.14953 | − | 1.14953i | 0.0439213 | − | 0.0439213i | ||||
\(686\) | 9.56951 | + | 6.31977i | 0.365366 | + | 0.241290i | ||||
\(687\) | −8.48869 | −0.323864 | ||||||||
\(688\) | −0.885690 | − | 41.0576i | −0.0337666 | − | 1.56531i | ||||
\(689\) | −69.1202 | −2.63327 | ||||||||
\(690\) | 27.3896 | + | 18.0883i | 1.04270 | + | 0.688609i | ||||
\(691\) | −23.2422 | − | 23.2422i | −0.884173 | − | 0.884173i | 0.109782 | − | 0.993956i | \(-0.464985\pi\) |
−0.993956 | + | 0.109782i | \(0.964985\pi\) | |||||||
\(692\) | 10.4259 | − | 25.9586i | 0.396333 | − | 0.986799i | ||||
\(693\) | 6.61129 | + | 6.61129i | 0.251142 | + | 0.251142i | ||||
\(694\) | 0.236298 | − | 0.0483286i | 0.00896975 | − | 0.00183453i | ||||
\(695\) | −26.1703 | −0.992695 | ||||||||
\(696\) | −4.61503 | + | 25.3366i | −0.174932 | + | 0.960382i | ||||
\(697\) | 1.69575 | 0.0642312 | ||||||||
\(698\) | 0.549446 | − | 0.112375i | 0.0207968 | − | 0.00425345i | ||||
\(699\) | 0.115800 | + | 0.115800i | 0.00437997 | + | 0.00437997i | ||||
\(700\) | −9.01467 | + | 3.84841i | −0.340722 | + | 0.145456i | ||||
\(701\) | −4.21154 | + | 4.21154i | −0.159068 | + | 0.159068i | −0.782153 | − | 0.623086i | \(-0.785879\pi\) |
0.623086 | + | 0.782153i | \(0.285879\pi\) | |||||||
\(702\) | −23.8521 | + | 36.1172i | −0.900238 | + | 1.36316i | ||||
\(703\) | 10.1857 | + | 0.580649i | 0.384162 | + | 0.0218996i | ||||
\(704\) | 25.1536 | − | 11.3857i | 0.948013 | − | 0.429114i | ||||
\(705\) | − | 9.09188i | − | 0.342420i | ||||||
\(706\) | −19.6841 | − | 12.9995i | −0.740821 | − | 0.489243i | ||||
\(707\) | 35.7688 | + | 35.7688i | 1.34523 | + | 1.34523i | ||||
\(708\) | −13.6492 | − | 31.9724i | −0.512968 | − | 1.20160i | ||||
\(709\) | 30.2765 | + | 30.2765i | 1.13706 | + | 1.13706i | 0.988975 | + | 0.148083i | \(0.0473102\pi\) |
0.148083 | + | 0.988975i | \(0.452690\pi\) | |||||||
\(710\) | −14.2580 | + | 2.91610i | −0.535093 | + | 0.109439i | ||||
\(711\) | − | 3.34255i | − | 0.125356i | ||||||
\(712\) | −0.492590 | + | 2.70434i | −0.0184606 | + | 0.101349i | ||||
\(713\) | −49.8000 | −1.86503 | ||||||||
\(714\) | 6.51724 | − | 1.33293i | 0.243902 | − | 0.0498837i | ||||
\(715\) | −25.8975 | − | 25.8975i | −0.968510 | − | 0.968510i | ||||
\(716\) | −2.27636 | − | 0.914264i | −0.0850715 | − | 0.0341677i | ||||
\(717\) | 6.04329 | + | 6.04329i | 0.225691 | + | 0.225691i | ||||
\(718\) | −27.9406 | − | 18.4522i | −1.04273 | − | 0.688628i | ||||
\(719\) | − | 34.3034i | − | 1.27930i | −0.768665 | − | 0.639651i | \(-0.779079\pi\) | ||
0.768665 | − | 0.639651i | \(-0.220921\pi\) | |||||||
\(720\) | 0.113438 | + | 5.25861i | 0.00422759 | + | 0.195977i | ||||
\(721\) | − | 11.0695i | − | 0.412251i | ||||||
\(722\) | 17.2597 | − | 20.5938i | 0.642338 | − | 0.766421i | ||||
\(723\) | 27.7982 | + | 27.7982i | 1.03382 | + | 1.03382i | ||||
\(724\) | −32.8173 | − | 13.1806i | −1.21965 | − | 0.489852i | ||||
\(725\) | −5.17120 | + | 5.17120i | −0.192054 | + | 0.192054i | ||||
\(726\) | 0.393722 | + | 1.92507i | 0.0146124 | + | 0.0714459i | ||||
\(727\) | 49.1242 | 1.82192 | 0.910958 | − | 0.412499i | \(-0.135344\pi\) | ||||
0.910958 | + | 0.412499i | \(0.135344\pi\) | |||||||
\(728\) | 50.8520 | − | 35.1812i | 1.88470 | − | 1.30390i | ||||
\(729\) | 30.0329i | 1.11233i | ||||||||
\(730\) | 20.5697 | − | 4.20699i | 0.761318 | − | 0.155708i | ||||
\(731\) | −5.59639 | + | 5.59639i | −0.206990 | + | 0.206990i | ||||
\(732\) | 22.5061 | − | 9.60797i | 0.831849 | − | 0.355121i | ||||
\(733\) | −15.2256 | + | 15.2256i | −0.562372 | + | 0.562372i | −0.929981 | − | 0.367609i | \(-0.880177\pi\) |
0.367609 | + | 0.929981i | \(0.380177\pi\) | |||||||
\(734\) | −6.62394 | + | 10.0301i | −0.244494 | + | 0.370217i | ||||
\(735\) | −26.7320 | −0.986025 | ||||||||
\(736\) | 43.2285 | − | 9.81710i | 1.59343 | − | 0.361863i | ||||
\(737\) | 32.9644i | 1.21426i | ||||||||
\(738\) | 1.16015 | − | 1.75671i | 0.0427055 | − | 0.0646655i | ||||
\(739\) | −37.2945 | − | 37.2945i | −1.37190 | − | 1.37190i | −0.857623 | − | 0.514278i | \(-0.828060\pi\) |
−0.514278 | − | 0.857623i | \(-0.671940\pi\) | |||||||
\(740\) | 3.57133 | + | 8.36562i | 0.131285 | + | 0.307526i | ||||
\(741\) | 24.1548 | + | 27.0752i | 0.887348 | + | 0.994632i | ||||
\(742\) | 70.2010 | − | 14.3578i | 2.57716 | − | 0.527091i | ||||
\(743\) | − | 24.9289i | − | 0.914553i | −0.889325 | − | 0.457276i | \(-0.848825\pi\) | ||
0.889325 | − | 0.457276i | \(-0.151175\pi\) | |||||||
\(744\) | 15.5877 | + | 22.5309i | 0.571473 | + | 0.826024i | ||||
\(745\) | − | 16.4907i | − | 0.604172i | ||||||
\(746\) | −29.4592 | + | 6.02511i | −1.07858 | + | 0.220595i | ||||
\(747\) | −0.977088 | + | 0.977088i | −0.0357498 | + | 0.0357498i | ||||
\(748\) | −4.93774 | − | 1.98317i | −0.180542 | − | 0.0725118i | ||||
\(749\) | 9.16753 | + | 9.16753i | 0.334974 | + | 0.334974i | ||||
\(750\) | 14.3671 | − | 21.7549i | 0.524611 | − | 0.794375i | ||||
\(751\) | −23.5788 | −0.860404 | −0.430202 | − | 0.902733i | \(-0.641558\pi\) | ||||
−0.430202 | + | 0.902733i | \(0.641558\pi\) | |||||||
\(752\) | −8.86776 | − | 8.49325i | −0.323374 | − | 0.309717i | ||||
\(753\) | − | 25.8226i | − | 0.941028i | ||||||
\(754\) | 25.4247 | − | 38.4985i | 0.925912 | − | 1.40203i | ||||
\(755\) | 26.0992 | − | 26.0992i | 0.949846 | − | 0.949846i | ||||
\(756\) | 16.7227 | − | 41.6366i | 0.608199 | − | 1.51431i | ||||
\(757\) | 4.74247 | + | 4.74247i | 0.172368 | + | 0.172368i | 0.788019 | − | 0.615651i | \(-0.211107\pi\) |
−0.615651 | + | 0.788019i | \(0.711107\pi\) | |||||||
\(758\) | 4.25298 | + | 20.7945i | 0.154475 | + | 0.755292i | ||||
\(759\) | 41.2240i | 1.49634i | ||||||||
\(760\) | 23.2862 | + | 5.62744i | 0.844680 | + | 0.204129i | ||||
\(761\) | 51.4004i | 1.86326i | 0.363402 | + | 0.931632i | \(0.381615\pi\) | ||||
−0.363402 | + | 0.931632i | \(0.618385\pi\) | |||||||
\(762\) | 44.4387 | − | 9.08878i | 1.60984 | − | 0.329252i | ||||
\(763\) | −28.5292 | − | 28.5292i | −1.03283 | − | 1.03283i | ||||
\(764\) | −16.2123 | + | 6.92112i | −0.586540 | + | 0.250397i | ||||
\(765\) | 0.716779 | − | 0.716779i | 0.0259152 | − | 0.0259152i | ||||
\(766\) | 7.10397 | + | 4.69151i | 0.256677 | + | 0.169511i | ||||
\(767\) | 62.2780i | 2.24873i | ||||||||
\(768\) | −17.9723 | − | 16.4850i | −0.648520 | − | 0.594851i | ||||
\(769\) | 3.83126 | 0.138159 | 0.0690794 | − | 0.997611i | \(-0.477994\pi\) | ||||
0.0690794 | + | 0.997611i | \(0.477994\pi\) | |||||||
\(770\) | 31.6819 | + | 20.9229i | 1.14174 | + | 0.754011i | ||||
\(771\) | −22.8211 | − | 22.8211i | −0.821882 | − | 0.821882i | ||||
\(772\) | 12.4988 | − | 5.33579i | 0.449840 | − | 0.192039i | ||||
\(773\) | 27.6605 | − | 27.6605i | 0.994880 | − | 0.994880i | −0.00510728 | − | 0.999987i | \(-0.501626\pi\) |
0.999987 | + | 0.00510728i | \(0.00162571\pi\) | |||||||
\(774\) | 1.96882 | + | 9.62633i | 0.0707676 | + | 0.346011i | ||||
\(775\) | 7.78001i | 0.279466i | ||||||||
\(776\) | −18.4399 | − | 3.35879i | −0.661953 | − | 0.120574i | ||||
\(777\) | − | 14.2817i | − | 0.512352i | ||||||
\(778\) | −3.91988 | − | 19.1659i | −0.140534 | − | 0.687129i | ||||
\(779\) | −6.38323 | − | 7.15499i | −0.228703 | − | 0.256354i | ||||
\(780\) | −12.0566 | + | 30.0189i | −0.431697 | + | 1.07485i | ||||
\(781\) | −12.9243 | − | 12.9243i | −0.462470 | − | 0.462470i | ||||
\(782\) | −7.12887 | − | 4.70796i | −0.254928 | − | 0.168356i | ||||
\(783\) | − | 33.4774i | − | 1.19639i | ||||||
\(784\) | −24.9719 | + | 26.0730i | −0.891853 | + | 0.931180i | ||||
\(785\) | 1.14635 | 0.0409150 | ||||||||
\(786\) | −15.0138 | − | 9.91520i | −0.535523 | − | 0.353663i | ||||
\(787\) | 4.34463 | − | 4.34463i | 0.154869 | − | 0.154869i | −0.625419 | − | 0.780289i | \(-0.715072\pi\) |
0.780289 | + | 0.625419i | \(0.215072\pi\) | |||||||
\(788\) | −5.67096 | + | 14.1197i | −0.202020 | + | 0.502993i | ||||
\(789\) | −3.83921 | + | 3.83921i | −0.136679 | + | 0.136679i | ||||
\(790\) | −2.71977 | − | 13.2980i | −0.0967650 | − | 0.473123i | ||||
\(791\) | 16.0657i | 0.571230i | ||||||||
\(792\) | −5.43260 | + | 3.75846i | −0.193039 | + | 0.133551i | ||||
\(793\) | −43.8389 | −1.55676 | ||||||||
\(794\) | 33.8586 | − | 6.92490i | 1.20160 | − | 0.245756i | ||||
\(795\) | −26.5068 | + | 26.5068i | −0.940098 | + | 0.940098i | ||||
\(796\) | −2.00488 | − | 4.69630i | −0.0710610 | − | 0.166456i | ||||
\(797\) | 26.1675 | + | 26.1675i | 0.926899 | + | 0.926899i | 0.997504 | − | 0.0706057i | \(-0.0224932\pi\) |
−0.0706057 | + | 0.997504i | \(0.522493\pi\) | |||||||
\(798\) | −30.1566 | − | 22.4811i | −1.06753 | − | 0.795822i | ||||
\(799\) | 2.36641i | 0.0837174i | ||||||||
\(800\) | −1.53368 | − | 6.75338i | −0.0542237 | − | 0.238768i | ||||
\(801\) | − | 0.657677i | − | 0.0232379i | ||||||
\(802\) | −16.4179 | + | 24.8602i | −0.579735 | + | 0.877845i | ||||
\(803\) | 18.6457 | + | 18.6457i | 0.657991 | + | 0.657991i | ||||
\(804\) | 26.7785 | − | 11.4319i | 0.944407 | − | 0.403172i | ||||
\(805\) | 43.1033 | + | 43.1033i | 1.51919 | + | 1.51919i | ||||
\(806\) | −9.83469 | − | 48.0858i | −0.346412 | − | 1.69375i | ||||
\(807\) | −14.4679 | −0.509293 | ||||||||
\(808\) | −29.3918 | + | 20.3343i | −1.03400 | + | 0.715357i | ||||
\(809\) | − | 37.4714i | − | 1.31742i | −0.752395 | − | 0.658712i | \(-0.771102\pi\) | ||
0.752395 | − | 0.658712i | \(-0.228898\pi\) | |||||||
\(810\) | 3.58567 | + | 17.5318i | 0.125987 | + | 0.616003i | ||||
\(811\) | −7.02259 | − | 7.02259i | −0.246597 | − | 0.246597i | 0.572976 | − | 0.819572i | \(-0.305789\pi\) |
−0.819572 | + | 0.572976i | \(0.805789\pi\) | |||||||
\(812\) | −17.8252 | + | 44.3817i | −0.625543 | + | 1.55749i | ||||
\(813\) | −19.2256 | − | 19.2256i | −0.674273 | − | 0.674273i | ||||
\(814\) | −6.29554 | + | 9.53281i | −0.220658 | + | 0.334125i | ||||
\(815\) | 17.9612i | 0.629152i | ||||||||
\(816\) | 0.101365 | + | 4.69892i | 0.00354847 | + | 0.164495i | ||||
\(817\) | 44.6794 | + | 2.54700i | 1.56313 | + | 0.0891082i | ||||
\(818\) | −36.1541 | − | 23.8764i | −1.26410 | − | 0.834819i | ||||
\(819\) | −10.4614 | + | 10.4614i | −0.365550 | + | 0.365550i | ||||
\(820\) | 3.18613 | − | 7.93290i | 0.111264 | − | 0.277029i | ||||
\(821\) | −25.4236 | − | 25.4236i | −0.887290 | − | 0.887290i | 0.106972 | − | 0.994262i | \(-0.465885\pi\) |
−0.994262 | + | 0.106972i | \(0.965885\pi\) | |||||||
\(822\) | −0.361364 | − | 1.76685i | −0.0126040 | − | 0.0616261i | ||||
\(823\) | −39.4688 | −1.37579 | −0.687897 | − | 0.725808i | \(-0.741466\pi\) | ||||
−0.687897 | + | 0.725808i | \(0.741466\pi\) | |||||||
\(824\) | 7.69447 | + | 1.40153i | 0.268049 | + | 0.0488248i | ||||
\(825\) | 6.44022 | 0.224220 | ||||||||
\(826\) | −12.9365 | − | 63.2518i | −0.450119 | − | 2.20081i | ||||
\(827\) | 9.50078 | + | 9.50078i | 0.330375 | + | 0.330375i | 0.852729 | − | 0.522354i | \(-0.174946\pi\) |
−0.522354 | + | 0.852729i | \(0.674946\pi\) | |||||||
\(828\) | −9.75440 | + | 4.16421i | −0.338989 | + | 0.144716i | ||||
\(829\) | −33.9168 | − | 33.9168i | −1.17798 | − | 1.17798i | −0.980259 | − | 0.197720i | \(-0.936646\pi\) |
−0.197720 | − | 0.980259i | \(-0.563354\pi\) | |||||||
\(830\) | −3.09222 | + | 4.68229i | −0.107332 | + | 0.162525i | ||||
\(831\) | −9.31182 | −0.323023 | ||||||||
\(832\) | 18.0161 | + | 39.8018i | 0.624596 | + | 1.37988i | ||||
\(833\) | 6.95772 | 0.241071 | ||||||||
\(834\) | −15.9987 | + | 24.2256i | −0.553991 | + | 0.838862i | ||||
\(835\) | −8.56680 | + | 8.56680i | −0.296466 | + | 0.296466i | ||||
\(836\) | 10.2192 | + | 28.2992i | 0.353437 | + | 0.978749i | ||||
\(837\) | −25.1832 | − | 25.1832i | −0.870458 | − | 0.870458i | ||||
\(838\) | 4.42492 | + | 21.6352i | 0.152856 | + | 0.747377i | ||||
\(839\) | 36.5254i | 1.26100i | 0.776190 | + | 0.630499i | \(0.217150\pi\) | ||||
−0.776190 | + | 0.630499i | \(0.782850\pi\) | |||||||
\(840\) | 6.00957 | − | 32.9927i | 0.207350 | − | 1.13836i | ||||
\(841\) | 6.68463i | 0.230504i | ||||||||
\(842\) | 17.9930 | − | 3.67999i | 0.620078 | − | 0.126821i | ||||
\(843\) | −11.7971 | + | 11.7971i | −0.406314 | + | 0.406314i | ||||
\(844\) | −18.7939 | − | 7.54828i | −0.646912 | − | 0.259822i | ||||
\(845\) | 23.1168 | − | 23.1168i | 0.795242 | − | 0.795242i | ||||
\(846\) | 2.45147 | + | 1.61897i | 0.0842834 | + | 0.0556614i | ||||
\(847\) | 3.64910i | 0.125385i | ||||||||
\(848\) | 1.09186 | + | 50.6148i | 0.0374945 | + | 1.73812i | ||||
\(849\) | − | 27.5107i | − | 0.944164i | ||||||
\(850\) | −0.735501 | + | 1.11371i | −0.0252275 | + | 0.0381999i | ||||
\(851\) | −12.9694 | + | 12.9694i | −0.444586 | + | 0.444586i | ||||
\(852\) | −6.01696 | + | 14.9812i | −0.206138 | + | 0.513247i | ||||
\(853\) | −32.1854 | − | 32.1854i | −1.10201 | − | 1.10201i | −0.994168 | − | 0.107838i | \(-0.965607\pi\) |
−0.107838 | − | 0.994168i | \(-0.534393\pi\) | |||||||
\(854\) | 44.5244 | − | 9.10630i | 1.52359 | − | 0.311611i | ||||
\(855\) | −5.72248 | − | 0.326216i | −0.195705 | − | 0.0111564i | ||||
\(856\) | −7.53311 | + | 5.21167i | −0.257476 | + | 0.178131i | ||||
\(857\) | 3.04400 | 0.103981 | 0.0519905 | − | 0.998648i | \(-0.483443\pi\) | ||||
0.0519905 | + | 0.998648i | \(0.483443\pi\) | |||||||
\(858\) | −39.8050 | + | 8.14107i | −1.35892 | + | 0.277932i | ||||
\(859\) | −3.14985 | + | 3.14985i | −0.107472 | + | 0.107472i | −0.758798 | − | 0.651326i | \(-0.774213\pi\) |
0.651326 | + | 0.758798i | \(0.274213\pi\) | |||||||
\(860\) | 15.6655 | + | 36.6955i | 0.534189 | + | 1.25131i | ||||
\(861\) | −9.49113 | + | 9.49113i | −0.323457 | + | 0.323457i | ||||
\(862\) | −40.3539 | − | 26.6500i | −1.37446 | − | 0.907703i | ||||
\(863\) | −11.5197 | −0.392134 | −0.196067 | − | 0.980590i | \(-0.562817\pi\) | ||||
−0.196067 | + | 0.980590i | \(0.562817\pi\) | |||||||
\(864\) | 26.8244 | + | 16.8957i | 0.912586 | + | 0.574803i | ||||
\(865\) | 27.1787i | 0.924102i | ||||||||
\(866\) | −5.55572 | + | 8.41258i | −0.188791 | + | 0.285871i | ||||
\(867\) | −17.6820 | + | 17.6820i | −0.600512 | + | 0.600512i | ||||
\(868\) | 19.9770 | + | 46.7948i | 0.678062 | + | 1.58832i | ||||
\(869\) | 12.0542 | − | 12.0542i | 0.408910 | − | 0.408910i | ||||
\(870\) | −5.01365 | − | 24.5138i | −0.169979 | − | 0.831095i | ||||
\(871\) | −52.1611 | −1.76741 | ||||||||
\(872\) | 23.4429 | − | 16.2186i | 0.793878 | − | 0.549232i | ||||
\(873\) | 4.48446 | 0.151776 | ||||||||
\(874\) | 6.97026 | + | 47.8012i | 0.235772 | + | 1.61690i | ||||
\(875\) | 34.2359 | − | 34.2359i | 1.15738 | − | 1.15738i | ||||
\(876\) | 8.68053 | − | 21.6130i | 0.293288 | − | 0.730236i | ||||
\(877\) | −14.6976 | − | 14.6976i | −0.496304 | − | 0.496304i | 0.413981 | − | 0.910285i | \(-0.364138\pi\) |
−0.910285 | + | 0.413981i | \(0.864138\pi\) | |||||||
\(878\) | −10.3909 | + | 15.7341i | −0.350677 | + | 0.531001i | ||||
\(879\) | 32.9202i | 1.11037i | ||||||||
\(880\) | −18.5549 | + | 19.3731i | −0.625486 | + | 0.653067i | ||||
\(881\) | 21.0495 | 0.709174 | 0.354587 | − | 0.935023i | \(-0.384621\pi\) | ||||
0.354587 | + | 0.935023i | \(0.384621\pi\) | |||||||
\(882\) | 4.76011 | − | 7.20784i | 0.160281 | − | 0.242701i | ||||
\(883\) | 14.6536 | + | 14.6536i | 0.493134 | + | 0.493134i | 0.909292 | − | 0.416158i | \(-0.136624\pi\) |
−0.416158 | + | 0.909292i | \(0.636624\pi\) | |||||||
\(884\) | 3.13806 | − | 7.81323i | 0.105544 | − | 0.262787i | ||||
\(885\) | 23.8829 | + | 23.8829i | 0.802814 | + | 0.802814i | ||||
\(886\) | 11.7571 | − | 2.40460i | 0.394986 | − | 0.0807841i | ||||
\(887\) | − | 32.4528i | − | 1.08966i | −0.838547 | − | 0.544830i | \(-0.816594\pi\) | ||
0.838547 | − | 0.544830i | \(-0.183406\pi\) | |||||||
\(888\) | 9.92723 | + | 1.80823i | 0.333136 | + | 0.0606802i | ||||
\(889\) | 84.2368 | 2.82521 | ||||||||
\(890\) | −0.535138 | − | 2.61651i | −0.0179379 | − | 0.0877055i | ||||
\(891\) | −15.8919 | + | 15.8919i | −0.532399 | + | 0.532399i | ||||
\(892\) | 0.286276 | + | 0.670585i | 0.00958524 | + | 0.0224528i | ||||
\(893\) | 9.98471 | − | 8.90773i | 0.334126 | − | 0.298086i | ||||
\(894\) | −15.2653 | − | 10.0813i | −0.510547 | − | 0.337169i | ||||
\(895\) | 2.38335 | 0.0796665 | ||||||||
\(896\) | −26.5655 | − | 36.6818i | −0.887492 | − | 1.22545i | ||||
\(897\) | −65.2307 | −2.17799 | ||||||||
\(898\) | 19.3894 | − | 29.3598i | 0.647034 | − | 0.979750i | ||||
\(899\) | 26.8435 | + | 26.8435i | 0.895282 | + | 0.895282i | ||||
\(900\) | 0.650553 | + | 1.52388i | 0.0216851 | + | 0.0507961i | ||||
\(901\) | 6.89910 | − | 6.89910i | 0.229842 | − | 0.229842i | ||||
\(902\) | 10.5190 | − | 2.15139i | 0.350245 | − | 0.0716334i | ||||
\(903\) | − | 62.6460i | − | 2.08473i | ||||||
\(904\) | −11.1673 | − | 2.03411i | −0.371419 | − | 0.0676534i | ||||
\(905\) | 34.3597 | 1.14216 | ||||||||
\(906\) | −8.20447 | − | 40.1150i | −0.272575 | − | 1.33273i | ||||
\(907\) | −3.07200 | − | 3.07200i | −0.102004 | − | 0.102004i | 0.654263 | − | 0.756267i | \(-0.272979\pi\) |
−0.756267 | + | 0.654263i | \(0.772979\pi\) | |||||||
\(908\) | 31.9588 | + | 12.8358i | 1.06059 | + | 0.425970i | ||||
\(909\) | 6.04653 | − | 6.04653i | 0.200551 | − | 0.200551i | ||||
\(910\) | −33.1074 | + | 50.1318i | −1.09750 | + | 1.66185i | ||||
\(911\) | −33.6220 | −1.11395 | −0.556973 | − | 0.830531i | \(-0.688037\pi\) | ||||
−0.556973 | + | 0.830531i | \(0.688037\pi\) | |||||||
\(912\) | 19.4449 | − | 18.1156i | 0.643884 | − | 0.599867i | ||||
\(913\) | −7.04731 | −0.233232 | ||||||||
\(914\) | −27.3464 | + | 41.4084i | −0.904538 | + | 1.36967i | ||||
\(915\) | −16.8117 | + | 16.8117i | −0.555777 | + | 0.555777i | ||||
\(916\) | 4.15123 | − | 10.3358i | 0.137161 | − | 0.341506i | ||||
\(917\) | −23.6273 | − | 23.6273i | −0.780244 | − | 0.780244i | ||||
\(918\) | −1.22422 | − | 5.98572i | −0.0404054 | − | 0.197558i | ||||
\(919\) | −29.3209 | −0.967208 | −0.483604 | − | 0.875287i | \(-0.660673\pi\) | ||||
−0.483604 | + | 0.875287i | \(0.660673\pi\) | |||||||
\(920\) | −35.4187 | + | 24.5039i | −1.16772 | + | 0.807868i | ||||
\(921\) | 7.27974i | 0.239876i | ||||||||
\(922\) | −6.67741 | + | 1.36569i | −0.219909 | + | 0.0449766i | ||||
\(923\) | 20.4508 | − | 20.4508i | 0.673147 | − | 0.673147i | ||||
\(924\) | 38.7363 | − | 16.5367i | 1.27433 | − | 0.544019i | ||||
\(925\) | 2.02615 | + | 2.02615i | 0.0666193 | + | 0.0666193i | ||||
\(926\) | 3.96421 | − | 6.00268i | 0.130272 | − | 0.197260i | ||||
\(927\) | −1.87124 | −0.0614597 | ||||||||
\(928\) | −28.5930 | − | 18.0097i | −0.938612 | − | 0.591196i | ||||
\(929\) | −20.0624 | −0.658227 | −0.329114 | − | 0.944290i | \(-0.606750\pi\) | ||||
−0.329114 | + | 0.944290i | \(0.606750\pi\) | |||||||
\(930\) | −22.2118 | − | 14.6688i | −0.728354 | − | 0.481010i | ||||
\(931\) | −26.1906 | − | 29.3571i | −0.858361 | − | 0.962141i | ||||
\(932\) | −0.197628 | + | 0.0843686i | −0.00647354 | + | 0.00276359i | ||||
\(933\) | −1.61461 | + | 1.61461i | −0.0528599 | + | 0.0528599i | ||||
\(934\) | 4.07025 | + | 19.9011i | 0.133183 | + | 0.651185i | ||||
\(935\) | 5.16981 | 0.169071 | ||||||||
\(936\) | −5.94720 | − | 8.59627i | −0.194390 | − | 0.280978i | ||||
\(937\) | 22.1788i | 0.724549i | 0.932072 | + | 0.362274i | \(0.118000\pi\) | ||||
−0.932072 | + | 0.362274i | \(0.882000\pi\) | |||||||
\(938\) | 52.9767 | − | 10.8350i | 1.72975 | − | 0.353775i | ||||
\(939\) | 19.8430 | + | 19.8430i | 0.647551 | + | 0.647551i | ||||
\(940\) | 11.0703 | + | 4.44621i | 0.361073 | + | 0.145019i | ||||
\(941\) | 8.50754 | + | 8.50754i | 0.277338 | + | 0.277338i | 0.832045 | − | 0.554708i | \(-0.187170\pi\) |
−0.554708 | + | 0.832045i | \(0.687170\pi\) | |||||||
\(942\) | 0.700800 | − | 1.06116i | 0.0228333 | − | 0.0345746i | ||||
\(943\) | 17.2381 | 0.561350 | ||||||||
\(944\) | 45.6045 | − | 0.983774i | 1.48430 | − | 0.0320191i | ||||
\(945\) | 43.5935i | 1.41810i | ||||||||
\(946\) | −27.6152 | + | 41.8154i | −0.897846 | + | 1.35953i | ||||
\(947\) | −15.8585 | − | 15.8585i | −0.515333 | − | 0.515333i | 0.400823 | − | 0.916156i | \(-0.368724\pi\) |
−0.916156 | + | 0.400823i | \(0.868724\pi\) | |||||||
\(948\) | −13.9725 | − | 5.61186i | −0.453807 | − | 0.182265i | ||||
\(949\) | −29.5039 | + | 29.5039i | −0.957738 | + | 0.957738i | ||||
\(950\) | 7.46774 | − | 1.08893i | 0.242285 | − | 0.0353295i | ||||
\(951\) | 35.8186 | 1.16150 | ||||||||
\(952\) | −1.56415 | + | 8.58724i | −0.0506945 | + | 0.278314i | ||||
\(953\) | −37.2019 | −1.20509 | −0.602543 | − | 0.798086i | \(-0.705846\pi\) | ||||
−0.602543 | + | 0.798086i | \(0.705846\pi\) | |||||||
\(954\) | −2.42711 | − | 11.8671i | −0.0785805 | − | 0.384212i | ||||
\(955\) | 12.1103 | − | 12.1103i | 0.391881 | − | 0.391881i | ||||
\(956\) | −10.3137 | + | 4.40296i | −0.333568 | + | 0.142402i | ||||
\(957\) | 22.2208 | − | 22.2208i | 0.718298 | − | 0.718298i | ||||
\(958\) | −4.27056 | + | 6.46655i | −0.137975 | + | 0.208925i | ||||
\(959\) | − | 3.34920i | − | 0.108151i | ||||||
\(960\) | 22.1725 | + | 8.35455i | 0.715614 | + | 0.269642i | ||||
\(961\) | 9.38577 | 0.302767 | ||||||||
\(962\) | −15.0842 | − | 9.96173i | −0.486335 | − | 0.321179i | ||||
\(963\) | 1.54972 | − | 1.54972i | 0.0499391 | − | 0.0499391i | ||||
\(964\) | −47.4412 | + | 20.2529i | −1.52798 | + | 0.652302i | ||||
\(965\) | −9.33638 | + | 9.33638i | −0.300549 | + | 0.300549i | ||||
\(966\) | 66.2507 | − | 13.5499i | 2.13158 | − | 0.435959i | ||||
\(967\) | 54.2359 | 1.74411 | 0.872054 | − | 0.489409i | \(-0.162788\pi\) | ||||
0.872054 | + | 0.489409i | \(0.162788\pi\) | |||||||
\(968\) | −2.53651 | − | 0.462020i | −0.0815264 | − | 0.0148499i | ||||
\(969\) | −5.11342 | − | 0.291496i | −0.164267 | − | 0.00936421i | ||||
\(970\) | 17.8410 | − | 3.64891i | 0.572840 | − | 0.117160i | ||||
\(971\) | 26.3041 | + | 26.3041i | 0.844137 | + | 0.844137i | 0.989394 | − | 0.145257i | \(-0.0464008\pi\) |
−0.145257 | + | 0.989394i | \(0.546401\pi\) | |||||||
\(972\) | −12.7814 | − | 5.13346i | −0.409964 | − | 0.164656i | ||||
\(973\) | −38.1240 | + | 38.1240i | −1.22220 | + | 1.22220i | ||||
\(974\) | −31.2221 | + | 47.2770i | −1.00042 | + | 1.51485i | ||||
\(975\) | 10.1907i | 0.326363i | ||||||||
\(976\) | 0.692501 | + | 32.1020i | 0.0221664 | + | 1.02756i | ||||
\(977\) | 53.5665i | 1.71374i | 0.515529 | + | 0.856872i | \(0.327596\pi\) | ||||
−0.515529 | + | 0.856872i | \(0.672404\pi\) | |||||||
\(978\) | 16.6265 | + | 10.9802i | 0.531656 | + | 0.351109i | ||||
\(979\) | 2.37177 | − | 2.37177i | 0.0758021 | − | 0.0758021i | ||||
\(980\) | 13.0728 | − | 32.5489i | 0.417595 | − | 1.03974i | ||||
\(981\) | −4.82272 | + | 4.82272i | −0.153978 | + | 0.153978i | ||||
\(982\) | 43.4290 | − | 8.88227i | 1.38588 | − | 0.283445i | ||||
\(983\) | 11.9694i | 0.381765i | 0.981613 | + | 0.190882i | \(0.0611349\pi\) | ||||
−0.981613 | + | 0.190882i | \(0.938865\pi\) | |||||||
\(984\) | −5.39563 | − | 7.79901i | −0.172006 | − | 0.248623i | ||||
\(985\) | − | 14.7833i | − | 0.471035i | ||||||
\(986\) | 1.30494 | + | 6.38037i | 0.0415577 | + | 0.203192i | ||||
\(987\) | −13.2448 | − | 13.2448i | −0.421586 | − | 0.421586i | ||||
\(988\) | −44.7792 | + | 16.1703i | −1.42462 | + | 0.514445i | ||||
\(989\) | −56.8899 | + | 56.8899i | −1.80899 | + | 1.80899i | ||||
\(990\) | 3.53691 | − | 5.35566i | 0.112411 | − | 0.170214i | ||||
\(991\) | −2.57961 | −0.0819439 | −0.0409720 | − | 0.999160i | \(-0.513045\pi\) | ||||
−0.0409720 | + | 0.999160i | \(0.513045\pi\) | |||||||
\(992\) | −35.0566 | + | 7.96127i | −1.11305 | + | 0.252770i | ||||
\(993\) | −30.1368 | −0.956362 | ||||||||
\(994\) | −16.5225 | + | 25.0187i | −0.524062 | + | 0.793544i | ||||
\(995\) | 3.50807 | + | 3.50807i | 0.111213 | + | 0.111213i | ||||
\(996\) | 2.44398 | + | 5.72487i | 0.0774404 | + | 0.181399i | ||||
\(997\) | −4.59126 | − | 4.59126i | −0.145407 | − | 0.145407i | 0.630656 | − | 0.776063i | \(-0.282786\pi\) |
−0.776063 | + | 0.630656i | \(0.782786\pi\) | |||||||
\(998\) | −2.45382 | − | 11.9977i | −0.0776743 | − | 0.379781i | ||||
\(999\) | −13.1169 | −0.415000 |
(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 | 304.2.m.a.75.9 | ✓ | 76 | |
4.3 | odd | 2 | 1216.2.m.a.911.11 | 76 | |||
16.3 | odd | 4 | inner | 304.2.m.a.227.30 | yes | 76 | |
16.13 | even | 4 | 1216.2.m.a.303.28 | 76 | |||
19.18 | odd | 2 | inner | 304.2.m.a.75.30 | yes | 76 | |
76.75 | even | 2 | 1216.2.m.a.911.28 | 76 | |||
304.189 | odd | 4 | 1216.2.m.a.303.11 | 76 | |||
304.227 | even | 4 | inner | 304.2.m.a.227.9 | yes | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
304.2.m.a.75.9 | ✓ | 76 | 1.1 | even | 1 | trivial | |
304.2.m.a.75.30 | yes | 76 | 19.18 | odd | 2 | inner | |
304.2.m.a.227.9 | yes | 76 | 304.227 | even | 4 | inner | |
304.2.m.a.227.30 | yes | 76 | 16.3 | odd | 4 | inner | |
1216.2.m.a.303.11 | 76 | 304.189 | odd | 4 | |||
1216.2.m.a.303.28 | 76 | 16.13 | even | 4 | |||
1216.2.m.a.911.11 | 76 | 4.3 | odd | 2 | |||
1216.2.m.a.911.28 | 76 | 76.75 | even | 2 |