Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(459,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 459.7 | ||
Character | \(\chi\) | \(=\) | 460.459 |
Dual form | 460.2.g.c.459.5 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.28797 | + | 0.584066i | −0.910733 | + | 0.412997i | ||||
\(3\) | 2.56426 | 1.48048 | 0.740239 | − | 0.672344i | \(-0.234712\pi\) | ||||
0.740239 | + | 0.672344i | \(0.234712\pi\) | |||||||
\(4\) | 1.31773 | − | 1.50452i | 0.658867 | − | 0.752259i | ||||
\(5\) | −0.662839 | + | 2.13557i | −0.296430 | + | 0.955054i | ||||
\(6\) | −3.30269 | + | 1.49770i | −1.34832 | + | 0.611432i | ||||
\(7\) | 1.62105i | 0.612700i | 0.951919 | + | 0.306350i | \(0.0991078\pi\) | ||||
−0.951919 | + | 0.306350i | \(0.900892\pi\) | |||||||
\(8\) | −0.818466 | + | 2.70742i | −0.289371 | + | 0.957217i | ||||
\(9\) | 3.57544 | 1.19181 | ||||||||
\(10\) | −0.393594 | − | 3.13769i | −0.124465 | − | 0.992224i | ||||
\(11\) | 1.26237 | 0.380619 | 0.190310 | − | 0.981724i | \(-0.439051\pi\) | ||||
0.190310 | + | 0.981724i | \(0.439051\pi\) | |||||||
\(12\) | 3.37902 | − | 3.85798i | 0.975439 | − | 1.11370i | ||||
\(13\) | 3.70421i | 1.02736i | 0.857981 | + | 0.513681i | \(0.171719\pi\) | ||||
−0.857981 | + | 0.513681i | \(0.828281\pi\) | |||||||
\(14\) | −0.946800 | − | 2.08787i | −0.253043 | − | 0.558006i | ||||
\(15\) | −1.69969 | + | 5.47615i | −0.438859 | + | 1.41394i | ||||
\(16\) | −0.527150 | − | 3.96511i | −0.131787 | − | 0.991278i | ||||
\(17\) | −7.74004 | −1.87724 | −0.938618 | − | 0.344959i | \(-0.887893\pi\) | ||||
−0.938618 | + | 0.344959i | \(0.887893\pi\) | |||||||
\(18\) | −4.60507 | + | 2.08829i | −1.08542 | + | 0.492215i | ||||
\(19\) | 3.73366 | 0.856560 | 0.428280 | − | 0.903646i | \(-0.359120\pi\) | ||||
0.428280 | + | 0.903646i | \(0.359120\pi\) | |||||||
\(20\) | 2.33955 | + | 3.81136i | 0.523140 | + | 0.852247i | ||||
\(21\) | 4.15680i | 0.907089i | ||||||||
\(22\) | −1.62590 | + | 0.737308i | −0.346642 | + | 0.157195i | ||||
\(23\) | 3.86984 | + | 2.83273i | 0.806917 | + | 0.590665i | ||||
\(24\) | −2.09876 | + | 6.94253i | −0.428408 | + | 1.41714i | ||||
\(25\) | −4.12129 | − | 2.83107i | −0.824258 | − | 0.566214i | ||||
\(26\) | −2.16350 | − | 4.77091i | −0.424297 | − | 0.935652i | ||||
\(27\) | 1.47559 | 0.283977 | ||||||||
\(28\) | 2.43890 | + | 2.13612i | 0.460909 | + | 0.403688i | ||||
\(29\) | 3.07514 | 0.571038 | 0.285519 | − | 0.958373i | \(-0.407834\pi\) | ||||
0.285519 | + | 0.958373i | \(0.407834\pi\) | |||||||
\(30\) | −1.00928 | − | 8.04586i | −0.184268 | − | 1.46897i | ||||
\(31\) | − | 7.06240i | − | 1.26844i | −0.773151 | − | 0.634222i | \(-0.781321\pi\) | ||
0.773151 | − | 0.634222i | \(-0.218679\pi\) | |||||||
\(32\) | 2.99484 | + | 4.79906i | 0.529418 | + | 0.848361i | ||||
\(33\) | 3.23705 | 0.563499 | ||||||||
\(34\) | 9.96894 | − | 4.52069i | 1.70966 | − | 0.775292i | ||||
\(35\) | −3.46186 | − | 1.07450i | −0.585162 | − | 0.181623i | ||||
\(36\) | 4.71149 | − | 5.37932i | 0.785248 | − | 0.896553i | ||||
\(37\) | 9.94153 | 1.63438 | 0.817189 | − | 0.576370i | \(-0.195531\pi\) | ||||
0.817189 | + | 0.576370i | \(0.195531\pi\) | |||||||
\(38\) | −4.80884 | + | 2.18070i | −0.780097 | + | 0.353757i | ||||
\(39\) | 9.49856i | 1.52099i | ||||||||
\(40\) | −5.23936 | − | 3.54247i | −0.828416 | − | 0.560114i | ||||
\(41\) | 0.611252 | 0.0954615 | 0.0477308 | − | 0.998860i | \(-0.484801\pi\) | ||||
0.0477308 | + | 0.998860i | \(0.484801\pi\) | |||||||
\(42\) | −2.42784 | − | 5.35384i | −0.374625 | − | 0.826115i | ||||
\(43\) | − | 6.59717i | − | 1.00606i | −0.864269 | − | 0.503029i | \(-0.832219\pi\) | ||
0.864269 | − | 0.503029i | \(-0.167781\pi\) | |||||||
\(44\) | 1.66347 | − | 1.89926i | 0.250778 | − | 0.286324i | ||||
\(45\) | −2.36994 | + | 7.63560i | −0.353290 | + | 1.13825i | ||||
\(46\) | −6.63874 | − | 1.38823i | −0.978828 | − | 0.204684i | ||||
\(47\) | −2.33340 | −0.340361 | −0.170180 | − | 0.985413i | \(-0.554435\pi\) | ||||
−0.170180 | + | 0.985413i | \(0.554435\pi\) | |||||||
\(48\) | −1.35175 | − | 10.1676i | −0.195108 | − | 1.46757i | ||||
\(49\) | 4.37219 | 0.624599 | ||||||||
\(50\) | 6.96163 | + | 1.23923i | 0.984523 | + | 0.175254i | ||||
\(51\) | −19.8475 | −2.77921 | ||||||||
\(52\) | 5.57305 | + | 4.88116i | 0.772843 | + | 0.676896i | ||||
\(53\) | −0.331215 | −0.0454959 | −0.0227480 | − | 0.999741i | \(-0.507242\pi\) | ||||
−0.0227480 | + | 0.999741i | \(0.507242\pi\) | |||||||
\(54\) | −1.90051 | + | 0.861841i | −0.258627 | + | 0.117282i | ||||
\(55\) | −0.836749 | + | 2.69588i | −0.112827 | + | 0.363512i | ||||
\(56\) | −4.38886 | − | 1.32678i | −0.586487 | − | 0.177298i | ||||
\(57\) | 9.57409 | 1.26812 | ||||||||
\(58\) | −3.96068 | + | 1.79608i | −0.520063 | + | 0.235837i | ||||
\(59\) | 9.13726i | 1.18957i | 0.803885 | + | 0.594785i | \(0.202763\pi\) | ||||
−0.803885 | + | 0.594785i | \(0.797237\pi\) | |||||||
\(60\) | 5.99923 | + | 9.77334i | 0.774497 | + | 1.26173i | ||||
\(61\) | 7.91039i | 1.01282i | 0.862292 | + | 0.506411i | \(0.169028\pi\) | ||||
−0.862292 | + | 0.506411i | \(0.830972\pi\) | |||||||
\(62\) | 4.12490 | + | 9.09616i | 0.523863 | + | 1.15521i | ||||
\(63\) | 5.79598i | 0.730225i | ||||||||
\(64\) | −6.66023 | − | 4.43186i | −0.832528 | − | 0.553983i | ||||
\(65\) | −7.91058 | − | 2.45529i | −0.981187 | − | 0.304542i | ||||
\(66\) | −4.16923 | + | 1.89065i | −0.513196 | + | 0.232723i | ||||
\(67\) | − | 10.5612i | − | 1.29026i | −0.764073 | − | 0.645130i | \(-0.776803\pi\) | ||
0.764073 | − | 0.645130i | \(-0.223197\pi\) | |||||||
\(68\) | −10.1993 | + | 11.6450i | −1.23685 | + | 1.41217i | ||||
\(69\) | 9.92328 | + | 7.26386i | 1.19462 | + | 0.874466i | ||||
\(70\) | 5.08635 | − | 0.638037i | 0.607935 | − | 0.0762600i | ||||
\(71\) | 2.77876i | 0.329778i | 0.986312 | + | 0.164889i | \(0.0527266\pi\) | ||||
−0.986312 | + | 0.164889i | \(0.947273\pi\) | |||||||
\(72\) | −2.92638 | + | 9.68022i | −0.344877 | + | 1.14083i | ||||
\(73\) | 5.23380i | 0.612569i | 0.951940 | + | 0.306285i | \(0.0990860\pi\) | ||||
−0.951940 | + | 0.306285i | \(0.900914\pi\) | |||||||
\(74\) | −12.8044 | + | 5.80651i | −1.48848 | + | 0.674993i | ||||
\(75\) | −10.5681 | − | 7.25961i | −1.22030 | − | 0.838268i | ||||
\(76\) | 4.91997 | − | 5.61736i | 0.564360 | − | 0.644355i | ||||
\(77\) | 2.04637i | 0.233205i | ||||||||
\(78\) | −5.54778 | − | 12.2339i | −0.628163 | − | 1.38521i | ||||
\(79\) | −1.62920 | −0.183300 | −0.0916498 | − | 0.995791i | \(-0.529214\pi\) | ||||
−0.0916498 | + | 0.995791i | \(0.529214\pi\) | |||||||
\(80\) | 8.81718 | + | 1.50247i | 0.985790 | + | 0.167981i | ||||
\(81\) | −6.94253 | −0.771393 | ||||||||
\(82\) | −0.787274 | + | 0.357011i | −0.0869399 | + | 0.0394253i | ||||
\(83\) | − | 13.2717i | − | 1.45676i | −0.685173 | − | 0.728381i | \(-0.740273\pi\) | ||
0.685173 | − | 0.728381i | \(-0.259727\pi\) | |||||||
\(84\) | 6.25398 | + | 5.47756i | 0.682366 | + | 0.597651i | ||||
\(85\) | 5.13040 | − | 16.5294i | 0.556470 | − | 1.79286i | ||||
\(86\) | 3.85318 | + | 8.49696i | 0.415499 | + | 0.916250i | ||||
\(87\) | 7.88546 | 0.845410 | ||||||||
\(88\) | −1.03321 | + | 3.41777i | −0.110140 | + | 0.364335i | ||||
\(89\) | − | 12.2047i | − | 1.29370i | −0.762618 | − | 0.646850i | \(-0.776086\pi\) | ||
0.762618 | − | 0.646850i | \(-0.223914\pi\) | |||||||
\(90\) | −1.40727 | − | 11.2186i | −0.148340 | − | 1.18255i | ||||
\(91\) | −6.00471 | −0.629465 | ||||||||
\(92\) | 9.36131 | − | 2.08946i | 0.975984 | − | 0.217841i | ||||
\(93\) | − | 18.1098i | − | 1.87790i | ||||||
\(94\) | 3.00535 | − | 1.36286i | 0.309978 | − | 0.140568i | ||||
\(95\) | −2.47481 | + | 7.97348i | −0.253911 | + | 0.818062i | ||||
\(96\) | 7.67955 | + | 12.3060i | 0.783791 | + | 1.25598i | ||||
\(97\) | 9.85230 | 1.00035 | 0.500175 | − | 0.865924i | \(-0.333269\pi\) | ||||
0.500175 | + | 0.865924i | \(0.333269\pi\) | |||||||
\(98\) | −5.63125 | + | 2.55365i | −0.568842 | + | 0.257957i | ||||
\(99\) | 4.51354 | 0.453628 | ||||||||
\(100\) | −9.69017 | + | 2.46995i | −0.969017 | + | 0.246995i | ||||
\(101\) | 2.75584 | 0.274216 | 0.137108 | − | 0.990556i | \(-0.456219\pi\) | ||||
0.137108 | + | 0.990556i | \(0.456219\pi\) | |||||||
\(102\) | 25.5630 | − | 11.5922i | 2.53111 | − | 1.14780i | ||||
\(103\) | − | 9.45350i | − | 0.931481i | −0.884921 | − | 0.465740i | \(-0.845788\pi\) | ||
0.884921 | − | 0.465740i | \(-0.154212\pi\) | |||||||
\(104\) | −10.0288 | − | 3.03177i | −0.983409 | − | 0.297289i | ||||
\(105\) | −8.87713 | − | 2.75529i | −0.866319 | − | 0.268889i | ||||
\(106\) | 0.426596 | − | 0.193451i | 0.0414346 | − | 0.0187897i | ||||
\(107\) | 3.34030i | 0.322919i | 0.986879 | + | 0.161460i | \(0.0516201\pi\) | ||||
−0.986879 | + | 0.161460i | \(0.948380\pi\) | |||||||
\(108\) | 1.94443 | − | 2.22005i | 0.187103 | − | 0.213624i | ||||
\(109\) | − | 12.7148i | − | 1.21785i | −0.793227 | − | 0.608926i | \(-0.791600\pi\) | ||
0.793227 | − | 0.608926i | \(-0.208400\pi\) | |||||||
\(110\) | −0.496862 | − | 3.96093i | −0.0473740 | − | 0.377660i | ||||
\(111\) | 25.4927 | 2.41966 | ||||||||
\(112\) | 6.42765 | − | 0.854537i | 0.607356 | − | 0.0807461i | ||||
\(113\) | 13.7089 | 1.28963 | 0.644813 | − | 0.764341i | \(-0.276935\pi\) | ||||
0.644813 | + | 0.764341i | \(0.276935\pi\) | |||||||
\(114\) | −12.3311 | + | 5.59189i | −1.15492 | + | 0.523729i | ||||
\(115\) | −8.61456 | + | 6.38665i | −0.803312 | + | 0.595559i | ||||
\(116\) | 4.05221 | − | 4.62660i | 0.376239 | − | 0.429569i | ||||
\(117\) | 13.2442i | 1.22443i | ||||||||
\(118\) | −5.33676 | − | 11.7685i | −0.491288 | − | 1.08338i | ||||
\(119\) | − | 12.5470i | − | 1.15018i | ||||||
\(120\) | −13.4351 | − | 9.08383i | −1.22645 | − | 0.829236i | ||||
\(121\) | −9.40642 | −0.855129 | ||||||||
\(122\) | −4.62018 | − | 10.1883i | −0.418292 | − | 0.922409i | ||||
\(123\) | 1.56741 | 0.141329 | ||||||||
\(124\) | −10.6255 | − | 9.30637i | −0.954198 | − | 0.835736i | ||||
\(125\) | 8.77769 | − | 6.92474i | 0.785101 | − | 0.619368i | ||||
\(126\) | −3.38523 | − | 7.46505i | −0.301580 | − | 0.665039i | ||||
\(127\) | −11.9753 | −1.06263 | −0.531317 | − | 0.847173i | \(-0.678303\pi\) | ||||
−0.531317 | + | 0.847173i | \(0.678303\pi\) | |||||||
\(128\) | 11.1667 | + | 1.81810i | 0.987004 | + | 0.160698i | ||||
\(129\) | − | 16.9169i | − | 1.48945i | ||||||
\(130\) | 11.6226 | − | 1.45796i | 1.01937 | − | 0.127871i | ||||
\(131\) | − | 5.21493i | − | 0.455630i | −0.973704 | − | 0.227815i | \(-0.926842\pi\) | ||
0.973704 | − | 0.227815i | \(-0.0731582\pi\) | |||||||
\(132\) | 4.26558 | − | 4.87020i | 0.371271 | − | 0.423897i | ||||
\(133\) | 6.05246i | 0.524814i | ||||||||
\(134\) | 6.16846 | + | 13.6026i | 0.532873 | + | 1.17508i | ||||
\(135\) | −0.978077 | + | 3.15122i | −0.0841795 | + | 0.271214i | ||||
\(136\) | 6.33496 | − | 20.9555i | 0.543218 | − | 1.79692i | ||||
\(137\) | −12.8474 | −1.09762 | −0.548812 | − | 0.835946i | \(-0.684920\pi\) | ||||
−0.548812 | + | 0.835946i | \(0.684920\pi\) | |||||||
\(138\) | −17.0235 | − | 3.55979i | −1.44913 | − | 0.303030i | ||||
\(139\) | 6.09860i | 0.517277i | 0.965974 | + | 0.258638i | \(0.0832738\pi\) | ||||
−0.965974 | + | 0.258638i | \(0.916726\pi\) | |||||||
\(140\) | −6.17842 | + | 3.79254i | −0.522171 | + | 0.320528i | ||||
\(141\) | −5.98344 | −0.503897 | ||||||||
\(142\) | −1.62298 | − | 3.57896i | −0.136197 | − | 0.300339i | ||||
\(143\) | 4.67609i | 0.391034i | ||||||||
\(144\) | −1.88479 | − | 14.1770i | −0.157066 | − | 1.18142i | ||||
\(145\) | −2.03832 | + | 6.56716i | −0.169273 | + | 0.545373i | ||||
\(146\) | −3.05688 | − | 6.74097i | −0.252989 | − | 0.557887i | ||||
\(147\) | 11.2114 | 0.924705 | ||||||||
\(148\) | 13.1003 | − | 14.9572i | 1.07684 | − | 1.22948i | ||||
\(149\) | 10.3256i | 0.845907i | 0.906151 | + | 0.422953i | \(0.139007\pi\) | ||||
−0.906151 | + | 0.422953i | \(0.860993\pi\) | |||||||
\(150\) | 17.8515 | + | 3.17772i | 1.45756 | + | 0.259460i | ||||
\(151\) | − | 11.9160i | − | 0.969711i | −0.874594 | − | 0.484856i | \(-0.838872\pi\) | ||
0.874594 | − | 0.484856i | \(-0.161128\pi\) | |||||||
\(152\) | −3.05587 | + | 10.1086i | −0.247864 | + | 0.819914i | ||||
\(153\) | −27.6741 | −2.23732 | ||||||||
\(154\) | −1.19521 | − | 2.63566i | −0.0963131 | − | 0.212388i | ||||
\(155\) | 15.0822 | + | 4.68123i | 1.21143 | + | 0.376005i | ||||
\(156\) | 14.2908 | + | 12.5166i | 1.14418 | + | 1.00213i | ||||
\(157\) | −12.3832 | −0.988289 | −0.494144 | − | 0.869380i | \(-0.664519\pi\) | ||||
−0.494144 | + | 0.869380i | \(0.664519\pi\) | |||||||
\(158\) | 2.09836 | − | 0.951561i | 0.166937 | − | 0.0757021i | ||||
\(159\) | −0.849323 | −0.0673557 | ||||||||
\(160\) | −12.2338 | + | 3.21468i | −0.967167 | + | 0.254142i | ||||
\(161\) | −4.59200 | + | 6.27321i | −0.361900 | + | 0.494398i | ||||
\(162\) | 8.94178 | − | 4.05489i | 0.702532 | − | 0.318583i | ||||
\(163\) | 11.9253 | 0.934062 | 0.467031 | − | 0.884241i | \(-0.345324\pi\) | ||||
0.467031 | + | 0.884241i | \(0.345324\pi\) | |||||||
\(164\) | 0.805468 | − | 0.919639i | 0.0628965 | − | 0.0718118i | ||||
\(165\) | −2.14564 | + | 6.91294i | −0.167038 | + | 0.538172i | ||||
\(166\) | 7.75156 | + | 17.0936i | 0.601638 | + | 1.32672i | ||||
\(167\) | 10.1226 | 0.783310 | 0.391655 | − | 0.920112i | \(-0.371903\pi\) | ||||
0.391655 | + | 0.920112i | \(0.371903\pi\) | |||||||
\(168\) | −11.2542 | − | 3.40220i | −0.868280 | − | 0.262486i | ||||
\(169\) | −0.721160 | −0.0554738 | ||||||||
\(170\) | 3.04644 | + | 24.2858i | 0.233651 | + | 1.86264i | ||||
\(171\) | 13.3495 | 1.02086 | ||||||||
\(172\) | −9.92556 | − | 8.69332i | −0.756817 | − | 0.662859i | ||||
\(173\) | 4.77722i | 0.363205i | 0.983372 | + | 0.181603i | \(0.0581284\pi\) | ||||
−0.983372 | + | 0.181603i | \(0.941872\pi\) | |||||||
\(174\) | −10.1562 | + | 4.60562i | −0.769942 | + | 0.349151i | ||||
\(175\) | 4.58931 | − | 6.68082i | 0.346920 | − | 0.505023i | ||||
\(176\) | −0.665459 | − | 5.00545i | −0.0501608 | − | 0.377300i | ||||
\(177\) | 23.4303i | 1.76113i | ||||||||
\(178\) | 7.12837 | + | 15.7193i | 0.534294 | + | 1.17821i | ||||
\(179\) | − | 25.2785i | − | 1.88941i | −0.327925 | − | 0.944704i | \(-0.606349\pi\) | ||
0.327925 | − | 0.944704i | \(-0.393651\pi\) | |||||||
\(180\) | 8.36494 | + | 13.6273i | 0.623486 | + | 1.01572i | ||||
\(181\) | − | 1.32658i | − | 0.0986036i | −0.998784 | − | 0.0493018i | \(-0.984300\pi\) | ||
0.998784 | − | 0.0493018i | \(-0.0156996\pi\) | |||||||
\(182\) | 7.73389 | − | 3.50715i | 0.573274 | − | 0.259967i | ||||
\(183\) | 20.2843i | 1.49946i | ||||||||
\(184\) | −10.8367 | + | 8.15878i | −0.798893 | + | 0.601473i | ||||
\(185\) | −6.58963 | + | 21.2308i | −0.484479 | + | 1.56092i | ||||
\(186\) | 10.5773 | + | 23.3249i | 0.775568 | + | 1.71027i | ||||
\(187\) | −9.77081 | −0.714512 | ||||||||
\(188\) | −3.07480 | + | 3.51064i | −0.224253 | + | 0.256040i | ||||
\(189\) | 2.39201i | 0.173993i | ||||||||
\(190\) | −1.46955 | − | 11.7151i | −0.106612 | − | 0.849900i | ||||
\(191\) | −17.3904 | −1.25832 | −0.629162 | − | 0.777274i | \(-0.716602\pi\) | ||||
−0.629162 | + | 0.777274i | \(0.716602\pi\) | |||||||
\(192\) | −17.0786 | − | 11.3645i | −1.23254 | − | 0.820159i | ||||
\(193\) | − | 16.0635i | − | 1.15627i | −0.815940 | − | 0.578137i | \(-0.803780\pi\) | ||
0.815940 | − | 0.578137i | \(-0.196220\pi\) | |||||||
\(194\) | −12.6895 | + | 5.75439i | −0.911051 | + | 0.413141i | ||||
\(195\) | −20.2848 | − | 6.29602i | −1.45263 | − | 0.450867i | ||||
\(196\) | 5.76139 | − | 6.57804i | 0.411528 | − | 0.469860i | ||||
\(197\) | − | 13.1841i | − | 0.939328i | −0.882845 | − | 0.469664i | \(-0.844375\pi\) | ||
0.882845 | − | 0.469664i | \(-0.155625\pi\) | |||||||
\(198\) | −5.81330 | + | 2.63620i | −0.413134 | + | 0.187347i | ||||
\(199\) | 4.84781 | 0.343652 | 0.171826 | − | 0.985127i | \(-0.445033\pi\) | ||||
0.171826 | + | 0.985127i | \(0.445033\pi\) | |||||||
\(200\) | 11.0380 | − | 8.84092i | 0.780507 | − | 0.625147i | ||||
\(201\) | − | 27.0818i | − | 1.91020i | ||||||
\(202\) | −3.54944 | + | 1.60959i | −0.249738 | + | 0.113250i | ||||
\(203\) | 4.98495i | 0.349875i | ||||||||
\(204\) | −26.1537 | + | 29.8609i | −1.83113 | + | 2.09068i | ||||
\(205\) | −0.405161 | + | 1.30537i | −0.0282977 | + | 0.0911709i | ||||
\(206\) | 5.52146 | + | 12.1758i | 0.384699 | + | 0.848330i | ||||
\(207\) | 13.8364 | + | 10.1283i | 0.961695 | + | 0.703963i | ||||
\(208\) | 14.6876 | − | 1.95267i | 1.01840 | − | 0.135393i | ||||
\(209\) | 4.71327 | 0.326024 | ||||||||
\(210\) | 13.0427 | − | 1.63609i | 0.900035 | − | 0.112901i | ||||
\(211\) | 22.3882i | 1.54126i | 0.637280 | + | 0.770632i | \(0.280059\pi\) | ||||
−0.637280 | + | 0.770632i | \(0.719941\pi\) | |||||||
\(212\) | −0.436454 | + | 0.498320i | −0.0299758 | + | 0.0342247i | ||||
\(213\) | 7.12546i | 0.488229i | ||||||||
\(214\) | −1.95095 | − | 4.30221i | −0.133364 | − | 0.294093i | ||||
\(215\) | 14.0887 | + | 4.37286i | 0.960841 | + | 0.298226i | ||||
\(216\) | −1.20772 | + | 3.99504i | −0.0821749 | + | 0.271828i | ||||
\(217\) | 11.4485 | 0.777175 | ||||||||
\(218\) | 7.42625 | + | 16.3762i | 0.502969 | + | 1.10914i | ||||
\(219\) | 13.4208i | 0.906896i | ||||||||
\(220\) | 2.95339 | + | 4.81136i | 0.199117 | + | 0.324382i | ||||
\(221\) | − | 28.6707i | − | 1.92860i | ||||||
\(222\) | −32.8338 | + | 14.8894i | −2.20366 | + | 0.999312i | ||||
\(223\) | −13.4927 | −0.903539 | −0.451770 | − | 0.892135i | \(-0.649207\pi\) | ||||
−0.451770 | + | 0.892135i | \(0.649207\pi\) | |||||||
\(224\) | −7.77952 | + | 4.85479i | −0.519791 | + | 0.324374i | ||||
\(225\) | −14.7354 | − | 10.1223i | −0.982363 | − | 0.674823i | ||||
\(226\) | −17.6567 | + | 8.00690i | −1.17450 | + | 0.532611i | ||||
\(227\) | 2.65450i | 0.176185i | 0.996112 | + | 0.0880927i | \(0.0280772\pi\) | ||||
−0.996112 | + | 0.0880927i | \(0.971923\pi\) | |||||||
\(228\) | 12.6161 | − | 14.4044i | 0.835522 | − | 0.953954i | ||||
\(229\) | 17.5942i | 1.16266i | 0.813669 | + | 0.581328i | \(0.197467\pi\) | ||||
−0.813669 | + | 0.581328i | \(0.802533\pi\) | |||||||
\(230\) | 7.36507 | − | 13.2573i | 0.485639 | − | 0.874160i | ||||
\(231\) | 5.24743i | 0.345256i | ||||||||
\(232\) | −2.51689 | + | 8.32568i | −0.165242 | + | 0.546608i | ||||
\(233\) | 3.11938i | 0.204357i | 0.994766 | + | 0.102179i | \(0.0325813\pi\) | ||||
−0.994766 | + | 0.102179i | \(0.967419\pi\) | |||||||
\(234\) | −7.73547 | − | 17.0581i | −0.505684 | − | 1.11512i | ||||
\(235\) | 1.54667 | − | 4.98313i | 0.100893 | − | 0.325063i | ||||
\(236\) | 13.7472 | + | 12.0405i | 0.894864 | + | 0.783769i | ||||
\(237\) | −4.17770 | −0.271371 | ||||||||
\(238\) | 7.32827 | + | 16.1602i | 0.475021 | + | 1.04751i | ||||
\(239\) | 5.17786i | 0.334928i | 0.985878 | + | 0.167464i | \(0.0535577\pi\) | ||||
−0.985878 | + | 0.167464i | \(0.946442\pi\) | |||||||
\(240\) | 22.6096 | + | 3.85272i | 1.45944 | + | 0.248692i | ||||
\(241\) | 30.9351i | 1.99270i | 0.0853470 | + | 0.996351i | \(0.472800\pi\) | ||||
−0.0853470 | + | 0.996351i | \(0.527200\pi\) | |||||||
\(242\) | 12.1152 | − | 5.49396i | 0.778794 | − | 0.353165i | ||||
\(243\) | −22.2292 | −1.42601 | ||||||||
\(244\) | 11.9013 | + | 10.4238i | 0.761904 | + | 0.667315i | ||||
\(245\) | −2.89806 | + | 9.33711i | −0.185150 | + | 0.596526i | ||||
\(246\) | −2.01878 | + | 0.915470i | −0.128713 | + | 0.0583683i | ||||
\(247\) | 13.8303i | 0.879998i | ||||||||
\(248\) | 19.1209 | + | 5.78033i | 1.21418 | + | 0.367051i | ||||
\(249\) | − | 34.0322i | − | 2.15670i | ||||||
\(250\) | −7.26090 | + | 14.0456i | −0.459220 | + | 0.888323i | ||||
\(251\) | 6.68143 | 0.421728 | 0.210864 | − | 0.977515i | \(-0.432372\pi\) | ||||
0.210864 | + | 0.977515i | \(0.432372\pi\) | |||||||
\(252\) | 8.72015 | + | 7.63756i | 0.549318 | + | 0.481121i | ||||
\(253\) | 4.88517 | + | 3.57596i | 0.307128 | + | 0.224819i | ||||
\(254\) | 15.4238 | − | 6.99434i | 0.967775 | − | 0.438864i | ||||
\(255\) | 13.1557 | − | 42.3856i | 0.823841 | − | 2.65429i | ||||
\(256\) | −15.4442 | + | 4.18041i | −0.965264 | + | 0.261276i | ||||
\(257\) | − | 23.9916i | − | 1.49655i | −0.663386 | − | 0.748277i | \(-0.730881\pi\) | ||
0.663386 | − | 0.748277i | \(-0.269119\pi\) | |||||||
\(258\) | 9.88056 | + | 21.7884i | 0.615137 | + | 1.35649i | ||||
\(259\) | 16.1157i | 1.00138i | ||||||||
\(260\) | −14.1181 | + | 8.66619i | −0.875566 | + | 0.537454i | ||||
\(261\) | 10.9950 | 0.680572 | ||||||||
\(262\) | 3.04586 | + | 6.71667i | 0.188174 | + | 0.414957i | ||||
\(263\) | 1.22644i | 0.0756257i | 0.999285 | + | 0.0378128i | \(0.0120391\pi\) | ||||
−0.999285 | + | 0.0378128i | \(0.987961\pi\) | |||||||
\(264\) | −2.64942 | + | 8.76406i | −0.163060 | + | 0.539390i | ||||
\(265\) | 0.219542 | − | 0.707332i | 0.0134864 | − | 0.0434511i | ||||
\(266\) | −3.53503 | − | 7.79538i | −0.216747 | − | 0.477966i | ||||
\(267\) | − | 31.2961i | − | 1.91529i | ||||||
\(268\) | −15.8896 | − | 13.9169i | −0.970610 | − | 0.850111i | ||||
\(269\) | −16.6973 | −1.01805 | −0.509027 | − | 0.860750i | \(-0.669995\pi\) | ||||
−0.509027 | + | 0.860750i | \(0.669995\pi\) | |||||||
\(270\) | −0.580783 | − | 4.62994i | −0.0353454 | − | 0.281769i | ||||
\(271\) | 23.7737i | 1.44415i | 0.691816 | + | 0.722074i | \(0.256811\pi\) | ||||
−0.691816 | + | 0.722074i | \(0.743189\pi\) | |||||||
\(272\) | 4.08016 | + | 30.6901i | 0.247396 | + | 1.86086i | ||||
\(273\) | −15.3977 | −0.931909 | ||||||||
\(274\) | 16.5470 | − | 7.50371i | 0.999643 | − | 0.453315i | ||||
\(275\) | −5.20260 | − | 3.57387i | −0.313729 | − | 0.215512i | ||||
\(276\) | 24.0049 | − | 5.35791i | 1.44492 | − | 0.322508i | ||||
\(277\) | 0.193125i | 0.0116038i | 0.999983 | + | 0.00580189i | \(0.00184681\pi\) | ||||
−0.999983 | + | 0.00580189i | \(0.998153\pi\) | |||||||
\(278\) | −3.56198 | − | 7.85482i | −0.213634 | − | 0.471101i | ||||
\(279\) | − | 25.2512i | − | 1.51175i | ||||||
\(280\) | 5.74253 | − | 8.49327i | 0.343182 | − | 0.507570i | ||||
\(281\) | 0.685427i | 0.0408892i | 0.999791 | + | 0.0204446i | \(0.00650816\pi\) | ||||
−0.999791 | + | 0.0204446i | \(0.993492\pi\) | |||||||
\(282\) | 7.70650 | − | 3.49472i | 0.458915 | − | 0.208108i | ||||
\(283\) | − | 6.29825i | − | 0.374392i | −0.982323 | − | 0.187196i | \(-0.940060\pi\) | ||
0.982323 | − | 0.187196i | \(-0.0599400\pi\) | |||||||
\(284\) | 4.18069 | + | 3.66167i | 0.248078 | + | 0.217280i | ||||
\(285\) | −6.34608 | + | 20.4461i | −0.375909 | + | 1.21112i | ||||
\(286\) | −2.73114 | − | 6.02266i | −0.161496 | − | 0.356127i | ||||
\(287\) | 0.990871i | 0.0584892i | ||||||||
\(288\) | 10.7079 | + | 17.1588i | 0.630968 | + | 1.01109i | ||||
\(289\) | 42.9082 | 2.52401 | ||||||||
\(290\) | −1.21036 | − | 9.64882i | −0.0710746 | − | 0.566598i | ||||
\(291\) | 25.2639 | 1.48100 | ||||||||
\(292\) | 7.87434 | + | 6.89676i | 0.460811 | + | 0.403602i | ||||
\(293\) | −25.1421 | −1.46882 | −0.734408 | − | 0.678708i | \(-0.762540\pi\) | ||||
−0.734408 | + | 0.678708i | \(0.762540\pi\) | |||||||
\(294\) | −14.4400 | + | 6.54822i | −0.842159 | + | 0.381900i | ||||
\(295\) | −19.5132 | − | 6.05653i | −1.13610 | − | 0.352625i | ||||
\(296\) | −8.13681 | + | 26.9159i | −0.472942 | + | 1.56445i | ||||
\(297\) | 1.86274 | 0.108087 | ||||||||
\(298\) | −6.03083 | − | 13.2991i | −0.349357 | − | 0.770395i | ||||
\(299\) | −10.4930 | + | 14.3347i | −0.606827 | + | 0.828996i | ||||
\(300\) | −24.8481 | + | 6.33361i | −1.43461 | + | 0.365671i | ||||
\(301\) | 10.6943 | 0.616412 | ||||||||
\(302\) | 6.95973 | + | 15.3475i | 0.400488 | + | 0.883148i | ||||
\(303\) | 7.06669 | 0.405971 | ||||||||
\(304\) | −1.96820 | − | 14.8044i | −0.112884 | − | 0.849090i | ||||
\(305\) | −16.8932 | − | 5.24331i | −0.967299 | − | 0.300231i | ||||
\(306\) | 35.6434 | − | 16.1635i | 2.03760 | − | 0.924004i | ||||
\(307\) | −0.393652 | −0.0224669 | −0.0112334 | − | 0.999937i | \(-0.503576\pi\) | ||||
−0.0112334 | + | 0.999937i | \(0.503576\pi\) | |||||||
\(308\) | 3.07880 | + | 2.69657i | 0.175431 | + | 0.153651i | ||||
\(309\) | − | 24.2413i | − | 1.37904i | ||||||
\(310\) | −22.1596 | + | 2.77972i | −1.25858 | + | 0.157877i | ||||
\(311\) | − | 2.70456i | − | 0.153362i | −0.997056 | − | 0.0766808i | \(-0.975568\pi\) | ||
0.997056 | − | 0.0766808i | \(-0.0244322\pi\) | |||||||
\(312\) | −25.7166 | − | 7.77425i | −1.45591 | − | 0.440130i | ||||
\(313\) | 12.4169 | 0.701843 | 0.350922 | − | 0.936405i | \(-0.385868\pi\) | ||||
0.350922 | + | 0.936405i | \(0.385868\pi\) | |||||||
\(314\) | 15.9492 | − | 7.23262i | 0.900067 | − | 0.408160i | ||||
\(315\) | −12.3777 | − | 3.84180i | −0.697404 | − | 0.216461i | ||||
\(316\) | −2.14686 | + | 2.45116i | −0.120770 | + | 0.137889i | ||||
\(317\) | 19.2978i | 1.08387i | 0.840420 | + | 0.541935i | \(0.182308\pi\) | ||||
−0.840420 | + | 0.541935i | \(0.817692\pi\) | |||||||
\(318\) | 1.09390 | − | 0.496060i | 0.0613430 | − | 0.0278177i | ||||
\(319\) | 3.88196 | 0.217348 | ||||||||
\(320\) | 13.8792 | − | 11.2857i | 0.775870 | − | 0.630893i | ||||
\(321\) | 8.56541i | 0.478074i | ||||||||
\(322\) | 2.25040 | − | 10.7617i | 0.125410 | − | 0.599728i | ||||
\(323\) | −28.8987 | −1.60797 | ||||||||
\(324\) | −9.14842 | + | 10.4452i | −0.508245 | + | 0.580287i | ||||
\(325\) | 10.4869 | − | 15.2661i | 0.581708 | − | 0.846812i | ||||
\(326\) | −15.3594 | + | 6.96516i | −0.850681 | + | 0.385765i | ||||
\(327\) | − | 32.6040i | − | 1.80300i | ||||||
\(328\) | −0.500289 | + | 1.65491i | −0.0276238 | + | 0.0913774i | ||||
\(329\) | − | 3.78256i | − | 0.208539i | ||||||
\(330\) | −1.27409 | − | 10.1569i | −0.0701361 | − | 0.559117i | ||||
\(331\) | − | 24.6944i | − | 1.35733i | −0.734449 | − | 0.678664i | \(-0.762559\pi\) | ||
0.734449 | − | 0.678664i | \(-0.237441\pi\) | |||||||
\(332\) | −19.9676 | − | 17.4886i | −1.09586 | − | 0.959813i | ||||
\(333\) | 35.5454 | 1.94788 | ||||||||
\(334\) | −13.0376 | + | 5.91226i | −0.713386 | + | 0.323505i | ||||
\(335\) | 22.5542 | + | 7.00040i | 1.23227 | + | 0.382473i | ||||
\(336\) | 16.4822 | − | 2.19126i | 0.899177 | − | 0.119543i | ||||
\(337\) | −0.810102 | −0.0441291 | −0.0220645 | − | 0.999757i | \(-0.507024\pi\) | ||||
−0.0220645 | + | 0.999757i | \(0.507024\pi\) | |||||||
\(338\) | 0.928833 | − | 0.421205i | 0.0505218 | − | 0.0229105i | ||||
\(339\) | 35.1532 | 1.90926 | ||||||||
\(340\) | −18.1082 | − | 29.5001i | −0.982057 | − | 1.59987i | ||||
\(341\) | − | 8.91537i | − | 0.482794i | ||||||
\(342\) | −17.1938 | + | 7.79698i | −0.929732 | + | 0.421612i | ||||
\(343\) | 18.4349i | 0.995392i | ||||||||
\(344\) | 17.8613 | + | 5.39956i | 0.963016 | + | 0.291125i | ||||
\(345\) | −22.0900 | + | 16.3771i | −1.18929 | + | 0.881711i | ||||
\(346\) | −2.79021 | − | 6.15291i | −0.150002 | − | 0.330783i | ||||
\(347\) | −20.6572 | −1.10894 | −0.554469 | − | 0.832204i | \(-0.687079\pi\) | ||||
−0.554469 | + | 0.832204i | \(0.687079\pi\) | |||||||
\(348\) | 10.3909 | − | 11.8638i | 0.557013 | − | 0.635967i | ||||
\(349\) | −9.11873 | −0.488115 | −0.244057 | − | 0.969761i | \(-0.578479\pi\) | ||||
−0.244057 | + | 0.969761i | \(0.578479\pi\) | |||||||
\(350\) | −2.00886 | + | 11.2852i | −0.107378 | + | 0.603217i | ||||
\(351\) | 5.46589i | 0.291748i | ||||||||
\(352\) | 3.78060 | + | 6.05819i | 0.201507 | + | 0.322903i | ||||
\(353\) | 18.5400i | 0.986783i | 0.869807 | + | 0.493391i | \(0.164243\pi\) | ||||
−0.869807 | + | 0.493391i | \(0.835757\pi\) | |||||||
\(354\) | −13.6848 | − | 30.1776i | −0.727341 | − | 1.60392i | ||||
\(355\) | −5.93422 | − | 1.84187i | −0.314956 | − | 0.0977562i | ||||
\(356\) | −18.3622 | − | 16.0826i | −0.973197 | − | 0.852376i | ||||
\(357\) | − | 32.1738i | − | 1.70282i | ||||||
\(358\) | 14.7643 | + | 32.5580i | 0.780319 | + | 1.72074i | ||||
\(359\) | 24.8931 | 1.31381 | 0.656905 | − | 0.753973i | \(-0.271865\pi\) | ||||
0.656905 | + | 0.753973i | \(0.271865\pi\) | |||||||
\(360\) | −18.7330 | − | 12.6659i | −0.987318 | − | 0.667552i | ||||
\(361\) | −5.05978 | −0.266304 | ||||||||
\(362\) | 0.774807 | + | 1.70859i | 0.0407230 | + | 0.0898015i | ||||
\(363\) | −24.1205 | −1.26600 | ||||||||
\(364\) | −7.91262 | + | 9.03420i | −0.414734 | + | 0.473521i | ||||
\(365\) | −11.1771 | − | 3.46916i | −0.585037 | − | 0.181584i | ||||
\(366\) | −11.8474 | − | 26.1256i | −0.619272 | − | 1.36561i | ||||
\(367\) | 33.2237i | 1.73427i | 0.498077 | + | 0.867133i | \(0.334040\pi\) | ||||
−0.498077 | + | 0.867133i | \(0.665960\pi\) | |||||||
\(368\) | 9.19210 | − | 16.8376i | 0.479172 | − | 0.877721i | ||||
\(369\) | 2.18550 | 0.113772 | ||||||||
\(370\) | −3.91293 | − | 31.1934i | −0.203424 | − | 1.62167i | ||||
\(371\) | − | 0.536917i | − | 0.0278753i | ||||||
\(372\) | −27.2466 | − | 23.8640i | −1.41267 | − | 1.23729i | ||||
\(373\) | 15.0397 | 0.778727 | 0.389363 | − | 0.921084i | \(-0.372695\pi\) | ||||
0.389363 | + | 0.921084i | \(0.372695\pi\) | |||||||
\(374\) | 12.5845 | − | 5.70679i | 0.650729 | − | 0.295091i | ||||
\(375\) | 22.5083 | − | 17.7569i | 1.16232 | − | 0.916961i | ||||
\(376\) | 1.90981 | − | 6.31748i | 0.0984908 | − | 0.325799i | ||||
\(377\) | 11.3909i | 0.586663i | ||||||||
\(378\) | −1.39709 | − | 3.08083i | −0.0718585 | − | 0.158461i | ||||
\(379\) | −31.0601 | −1.59545 | −0.797724 | − | 0.603023i | \(-0.793963\pi\) | ||||
−0.797724 | + | 0.603023i | \(0.793963\pi\) | |||||||
\(380\) | 8.73510 | + | 14.2303i | 0.448101 | + | 0.730001i | ||||
\(381\) | −30.7077 | −1.57321 | ||||||||
\(382\) | 22.3983 | − | 10.1571i | 1.14600 | − | 0.519684i | ||||
\(383\) | 3.54400i | 0.181090i | 0.995892 | + | 0.0905449i | \(0.0288609\pi\) | ||||
−0.995892 | + | 0.0905449i | \(0.971139\pi\) | |||||||
\(384\) | 28.6343 | + | 4.66208i | 1.46124 | + | 0.237911i | ||||
\(385\) | −4.37016 | − | 1.35641i | −0.222724 | − | 0.0691292i | ||||
\(386\) | 9.38212 | + | 20.6893i | 0.477537 | + | 1.05306i | ||||
\(387\) | − | 23.5878i | − | 1.19904i | ||||||
\(388\) | 12.9827 | − | 14.8230i | 0.659098 | − | 0.752522i | ||||
\(389\) | 8.58051i | 0.435049i | 0.976055 | + | 0.217525i | \(0.0697982\pi\) | ||||
−0.976055 | + | 0.217525i | \(0.930202\pi\) | |||||||
\(390\) | 29.8035 | − | 3.73858i | 1.50916 | − | 0.189310i | ||||
\(391\) | −29.9527 | − | 21.9254i | −1.51477 | − | 1.10882i | ||||
\(392\) | −3.57849 | + | 11.8374i | −0.180741 | + | 0.597877i | ||||
\(393\) | − | 13.3724i | − | 0.674550i | ||||||
\(394\) | 7.70037 | + | 16.9807i | 0.387939 | + | 0.855476i | ||||
\(395\) | 1.07990 | − | 3.47927i | 0.0543356 | − | 0.175061i | ||||
\(396\) | 5.94765 | − | 6.79070i | 0.298881 | − | 0.341246i | ||||
\(397\) | − | 12.9361i | − | 0.649246i | −0.945843 | − | 0.324623i | \(-0.894763\pi\) | ||
0.945843 | − | 0.324623i | \(-0.105237\pi\) | |||||||
\(398\) | −6.24384 | + | 2.83144i | −0.312975 | + | 0.141927i | ||||
\(399\) | 15.5201i | 0.776976i | ||||||||
\(400\) | −9.05298 | + | 17.8338i | −0.452649 | + | 0.891689i | ||||
\(401\) | 24.7106i | 1.23399i | 0.786967 | + | 0.616995i | \(0.211650\pi\) | ||||
−0.786967 | + | 0.616995i | \(0.788350\pi\) | |||||||
\(402\) | 15.8175 | + | 34.8805i | 0.788907 | + | 1.73968i | ||||
\(403\) | 26.1606 | 1.30315 | ||||||||
\(404\) | 3.63146 | − | 4.14621i | 0.180672 | − | 0.206282i | ||||
\(405\) | 4.60178 | − | 14.8262i | 0.228664 | − | 0.736722i | ||||
\(406\) | −2.91154 | − | 6.42047i | −0.144497 | − | 0.318643i | ||||
\(407\) | 12.5499 | 0.622076 | ||||||||
\(408\) | 16.2445 | − | 53.7355i | 0.804223 | − | 2.66030i | ||||
\(409\) | 7.62265 | 0.376916 | 0.188458 | − | 0.982081i | \(-0.439651\pi\) | ||||
0.188458 | + | 0.982081i | \(0.439651\pi\) | |||||||
\(410\) | −0.240585 | − | 1.91792i | −0.0118817 | − | 0.0947192i | ||||
\(411\) | −32.9440 | −1.62501 | ||||||||
\(412\) | −14.2230 | − | 12.4572i | −0.700715 | − | 0.613722i | ||||
\(413\) | −14.8120 | −0.728849 | ||||||||
\(414\) | −23.7364 | − | 4.96355i | −1.16658 | − | 0.243945i | ||||
\(415\) | 28.3427 | + | 8.79701i | 1.39129 | + | 0.431828i | ||||
\(416\) | −17.7767 | + | 11.0935i | −0.871575 | + | 0.543904i | ||||
\(417\) | 15.6384i | 0.765817i | ||||||||
\(418\) | −6.07055 | + | 2.75286i | −0.296920 | + | 0.134647i | ||||
\(419\) | −5.55318 | −0.271291 | −0.135645 | − | 0.990757i | \(-0.543311\pi\) | ||||
−0.135645 | + | 0.990757i | \(0.543311\pi\) | |||||||
\(420\) | −15.8431 | + | 9.72506i | −0.773063 | + | 0.474534i | ||||
\(421\) | 9.55340i | 0.465604i | 0.972524 | + | 0.232802i | \(0.0747894\pi\) | ||||
−0.972524 | + | 0.232802i | \(0.925211\pi\) | |||||||
\(422\) | −13.0762 | − | 28.8353i | −0.636537 | − | 1.40368i | ||||
\(423\) | −8.34293 | −0.405647 | ||||||||
\(424\) | 0.271089 | − | 0.896738i | 0.0131652 | − | 0.0435495i | ||||
\(425\) | 31.8989 | + | 21.9126i | 1.54733 | + | 1.06292i | ||||
\(426\) | −4.16174 | − | 9.17739i | −0.201637 | − | 0.444646i | ||||
\(427\) | −12.8231 | −0.620555 | ||||||||
\(428\) | 5.02554 | + | 4.40163i | 0.242919 | + | 0.212761i | ||||
\(429\) | 11.9907i | 0.578917i | ||||||||
\(430\) | −20.6999 | + | 2.59661i | −0.998236 | + | 0.125220i | ||||
\(431\) | 36.8035 | 1.77276 | 0.886381 | − | 0.462956i | \(-0.153211\pi\) | ||||
0.886381 | + | 0.462956i | \(0.153211\pi\) | |||||||
\(432\) | −0.777856 | − | 5.85087i | −0.0374246 | − | 0.281500i | ||||
\(433\) | 16.1069 | 0.774049 | 0.387025 | − | 0.922069i | \(-0.373503\pi\) | ||||
0.387025 | + | 0.922069i | \(0.373503\pi\) | |||||||
\(434\) | −14.7453 | + | 6.68668i | −0.707799 | + | 0.320971i | ||||
\(435\) | −5.22679 | + | 16.8399i | −0.250605 | + | 0.807412i | ||||
\(436\) | −19.1296 | − | 16.7547i | −0.916141 | − | 0.802404i | ||||
\(437\) | 14.4487 | + | 10.5764i | 0.691173 | + | 0.505940i | ||||
\(438\) | −7.83864 | − | 17.2856i | −0.374545 | − | 0.825939i | ||||
\(439\) | 30.9144i | 1.47546i | 0.675095 | + | 0.737731i | \(0.264103\pi\) | ||||
−0.675095 | + | 0.737731i | \(0.735897\pi\) | |||||||
\(440\) | −6.61402 | − | 4.47191i | −0.315311 | − | 0.213190i | ||||
\(441\) | 15.6325 | 0.744406 | ||||||||
\(442\) | 16.7456 | + | 36.9270i | 0.796506 | + | 1.75644i | ||||
\(443\) | −1.86842 | −0.0887711 | −0.0443855 | − | 0.999014i | \(-0.514133\pi\) | ||||
−0.0443855 | + | 0.999014i | \(0.514133\pi\) | |||||||
\(444\) | 33.5926 | − | 38.3542i | 1.59424 | − | 1.82021i | ||||
\(445\) | 26.0640 | + | 8.08977i | 1.23555 | + | 0.383492i | ||||
\(446\) | 17.3782 | − | 7.88063i | 0.822883 | − | 0.373159i | ||||
\(447\) | 26.4776i | 1.25235i | ||||||||
\(448\) | 7.18427 | − | 10.7966i | 0.339425 | − | 0.510090i | ||||
\(449\) | 33.1765 | 1.56570 | 0.782848 | − | 0.622213i | \(-0.213766\pi\) | ||||
0.782848 | + | 0.622213i | \(0.213766\pi\) | |||||||
\(450\) | 24.8909 | + | 4.43081i | 1.17337 | + | 0.208870i | ||||
\(451\) | 0.771627 | 0.0363345 | ||||||||
\(452\) | 18.0647 | − | 20.6253i | 0.849692 | − | 0.970132i | ||||
\(453\) | − | 30.5558i | − | 1.43564i | ||||||
\(454\) | −1.55040 | − | 3.41892i | −0.0727640 | − | 0.160458i | ||||
\(455\) | 3.98016 | − | 12.8235i | 0.186593 | − | 0.601173i | ||||
\(456\) | −7.83607 | + | 25.9211i | −0.366957 | + | 1.21386i | ||||
\(457\) | −16.4071 | −0.767491 | −0.383746 | − | 0.923439i | \(-0.625366\pi\) | ||||
−0.383746 | + | 0.923439i | \(0.625366\pi\) | |||||||
\(458\) | −10.2762 | − | 22.6608i | −0.480173 | − | 1.05887i | ||||
\(459\) | −11.4211 | −0.533092 | ||||||||
\(460\) | −1.74287 | + | 21.3767i | −0.0812617 | + | 0.996693i | ||||
\(461\) | −12.2226 | −0.569262 | −0.284631 | − | 0.958637i | \(-0.591871\pi\) | ||||
−0.284631 | + | 0.958637i | \(0.591871\pi\) | |||||||
\(462\) | −3.06484 | − | 6.75853i | −0.142589 | − | 0.314435i | ||||
\(463\) | 38.5395 | 1.79108 | 0.895540 | − | 0.444980i | \(-0.146789\pi\) | ||||
0.895540 | + | 0.444980i | \(0.146789\pi\) | |||||||
\(464\) | −1.62106 | − | 12.1933i | −0.0752557 | − | 0.566058i | ||||
\(465\) | 38.6748 | + | 12.0039i | 1.79350 | + | 0.556668i | ||||
\(466\) | −1.82192 | − | 4.01767i | −0.0843989 | − | 0.186115i | ||||
\(467\) | − | 9.00046i | − | 0.416492i | −0.978077 | − | 0.208246i | \(-0.933225\pi\) | ||
0.978077 | − | 0.208246i | \(-0.0667754\pi\) | |||||||
\(468\) | 19.9261 | + | 17.4523i | 0.921085 | + | 0.806734i | ||||
\(469\) | 17.1203 | 0.790543 | ||||||||
\(470\) | 0.918412 | + | 7.32147i | 0.0423632 | + | 0.337714i | ||||
\(471\) | −31.7538 | −1.46314 | ||||||||
\(472\) | −24.7384 | − | 7.47854i | −1.13868 | − | 0.344227i | ||||
\(473\) | − | 8.32808i | − | 0.382925i | ||||||
\(474\) | 5.38076 | − | 2.44005i | 0.247146 | − | 0.112075i | ||||
\(475\) | −15.3875 | − | 10.5703i | −0.706027 | − | 0.484997i | ||||
\(476\) | −18.8772 | − | 16.5336i | −0.865235 | − | 0.757817i | ||||
\(477\) | −1.18424 | −0.0542227 | ||||||||
\(478\) | −3.02421 | − | 6.66893i | −0.138324 | − | 0.305030i | ||||
\(479\) | −20.2212 | −0.923929 | −0.461965 | − | 0.886898i | \(-0.652855\pi\) | ||||
−0.461965 | + | 0.886898i | \(0.652855\pi\) | |||||||
\(480\) | −31.3707 | + | 8.24327i | −1.43187 | + | 0.376252i | ||||
\(481\) | 36.8255i | 1.67910i | ||||||||
\(482\) | −18.0681 | − | 39.8434i | −0.822980 | − | 1.81482i | ||||
\(483\) | −11.7751 | + | 16.0862i | −0.535785 | + | 0.731945i | ||||
\(484\) | −12.3952 | + | 14.1521i | −0.563417 | + | 0.643278i | ||||
\(485\) | −6.53049 | + | 21.0403i | −0.296534 | + | 0.955389i | ||||
\(486\) | 28.6306 | − | 12.9833i | 1.29871 | − | 0.588936i | ||||
\(487\) | −21.7271 | −0.984547 | −0.492274 | − | 0.870440i | \(-0.663834\pi\) | ||||
−0.492274 | + | 0.870440i | \(0.663834\pi\) | |||||||
\(488\) | −21.4167 | − | 6.47438i | −0.969490 | − | 0.293082i | ||||
\(489\) | 30.5796 | 1.38286 | ||||||||
\(490\) | −1.72087 | − | 13.7186i | −0.0777410 | − | 0.619742i | ||||
\(491\) | − | 11.6459i | − | 0.525572i | −0.964854 | − | 0.262786i | \(-0.915359\pi\) | ||
0.964854 | − | 0.262786i | \(-0.0846413\pi\) | |||||||
\(492\) | 2.06543 | − | 2.35820i | 0.0931168 | − | 0.106316i | ||||
\(493\) | −23.8017 | −1.07197 | ||||||||
\(494\) | −8.07778 | − | 17.8130i | −0.363436 | − | 0.801443i | ||||
\(495\) | −2.99175 | + | 9.63896i | −0.134469 | + | 0.433239i | ||||
\(496\) | −28.0032 | + | 3.72294i | −1.25738 | + | 0.167165i | ||||
\(497\) | −4.50451 | −0.202055 | ||||||||
\(498\) | 19.8770 | + | 43.8325i | 0.890711 | + | 1.96418i | ||||
\(499\) | 20.6465i | 0.924263i | 0.886811 | + | 0.462132i | \(0.152915\pi\) | ||||
−0.886811 | + | 0.462132i | \(0.847085\pi\) | |||||||
\(500\) | 1.14827 | − | 22.3312i | 0.0513522 | − | 0.998681i | ||||
\(501\) | 25.9570 | 1.15967 | ||||||||
\(502\) | −8.60548 | + | 3.90239i | −0.384081 | + | 0.174172i | ||||
\(503\) | 19.9699i | 0.890413i | 0.895428 | + | 0.445207i | \(0.146870\pi\) | ||||
−0.895428 | + | 0.445207i | \(0.853130\pi\) | |||||||
\(504\) | −15.6921 | − | 4.74381i | −0.698983 | − | 0.211306i | ||||
\(505\) | −1.82668 | + | 5.88528i | −0.0812860 | + | 0.261891i | ||||
\(506\) | −8.38055 | − | 1.75246i | −0.372561 | − | 0.0779066i | ||||
\(507\) | −1.84924 | −0.0821278 | ||||||||
\(508\) | −15.7802 | + | 18.0170i | −0.700135 | + | 0.799376i | ||||
\(509\) | −21.2795 | −0.943197 | −0.471598 | − | 0.881813i | \(-0.656323\pi\) | ||||
−0.471598 | + | 0.881813i | \(0.656323\pi\) | |||||||
\(510\) | 7.81186 | + | 62.2752i | 0.345915 | + | 2.75759i | ||||
\(511\) | −8.48425 | −0.375321 | ||||||||
\(512\) | 17.4501 | − | 14.4047i | 0.771191 | − | 0.636603i | ||||
\(513\) | 5.50935 | 0.243244 | ||||||||
\(514\) | 14.0127 | + | 30.9005i | 0.618072 | + | 1.36296i | ||||
\(515\) | 20.1886 | + | 6.26615i | 0.889615 | + | 0.276119i | ||||
\(516\) | −25.4517 | − | 22.2920i | −1.12045 | − | 0.981349i | ||||
\(517\) | −2.94561 | −0.129548 | ||||||||
\(518\) | −9.41265 | − | 20.7566i | −0.413568 | − | 0.911992i | ||||
\(519\) | 12.2500i | 0.537717i | ||||||||
\(520\) | 13.1220 | − | 19.4077i | 0.575440 | − | 0.851083i | ||||
\(521\) | − | 6.12734i | − | 0.268444i | −0.990951 | − | 0.134222i | \(-0.957147\pi\) | ||
0.990951 | − | 0.134222i | \(-0.0428535\pi\) | |||||||
\(522\) | −14.1612 | + | 6.42179i | −0.619819 | + | 0.281074i | ||||
\(523\) | − | 3.52313i | − | 0.154056i | −0.997029 | − | 0.0770278i | \(-0.975457\pi\) | ||
0.997029 | − | 0.0770278i | \(-0.0245430\pi\) | |||||||
\(524\) | −7.84595 | − | 6.87189i | −0.342752 | − | 0.300200i | ||||
\(525\) | 11.7682 | − | 17.1314i | 0.513607 | − | 0.747675i | ||||
\(526\) | −0.716323 | − | 1.57962i | −0.0312332 | − | 0.0688748i | ||||
\(527\) | 54.6632i | 2.38117i | ||||||||
\(528\) | −1.70641 | − | 12.8353i | −0.0742620 | − | 0.558584i | ||||
\(529\) | 6.95129 | + | 21.9244i | 0.302230 | + | 0.953235i | ||||
\(530\) | 0.130364 | + | 1.03925i | 0.00566267 | + | 0.0451421i | ||||
\(531\) | 32.6697i | 1.41775i | ||||||||
\(532\) | 9.10603 | + | 7.97553i | 0.394796 | + | 0.345783i | ||||
\(533\) | 2.26420i | 0.0980736i | ||||||||
\(534\) | 18.2790 | + | 40.3085i | 0.791010 | + | 1.74432i | ||||
\(535\) | −7.13343 | − | 2.21408i | −0.308405 | − | 0.0957230i | ||||
\(536\) | 28.5937 | + | 8.64402i | 1.23506 | + | 0.373365i | ||||
\(537\) | − | 64.8208i | − | 2.79723i | ||||||
\(538\) | 21.5057 | − | 9.75234i | 0.927175 | − | 0.420453i | ||||
\(539\) | 5.51933 | 0.237734 | ||||||||
\(540\) | 3.45222 | + | 5.62401i | 0.148560 | + | 0.242019i | ||||
\(541\) | −21.0618 | −0.905518 | −0.452759 | − | 0.891633i | \(-0.649560\pi\) | ||||
−0.452759 | + | 0.891633i | \(0.649560\pi\) | |||||||
\(542\) | −13.8854 | − | 30.6198i | −0.596428 | − | 1.31523i | ||||
\(543\) | − | 3.40169i | − | 0.145980i | ||||||
\(544\) | −23.1802 | − | 37.1449i | −0.993841 | − | 1.59257i | ||||
\(545\) | 27.1532 | + | 8.42783i | 1.16312 | + | 0.361009i | ||||
\(546\) | 19.8317 | − | 8.99324i | 0.848720 | − | 0.384875i | ||||
\(547\) | 44.2233 | 1.89085 | 0.945425 | − | 0.325839i | \(-0.105647\pi\) | ||||
0.945425 | + | 0.325839i | \(0.105647\pi\) | |||||||
\(548\) | −16.9294 | + | 19.3291i | −0.723189 | + | 0.825698i | ||||
\(549\) | 28.2831i | 1.20710i | ||||||||
\(550\) | 8.78817 | + | 1.56437i | 0.374729 | + | 0.0667051i | ||||
\(551\) | 11.4815 | 0.489129 | ||||||||
\(552\) | −27.7882 | + | 20.9212i | −1.18274 | + | 0.890467i | ||||
\(553\) | − | 2.64102i | − | 0.112308i | ||||||
\(554\) | −0.112798 | − | 0.248740i | −0.00479232 | − | 0.0105679i | ||||
\(555\) | −16.8975 | + | 54.4414i | −0.717261 | + | 2.31091i | ||||
\(556\) | 9.17546 | + | 8.03634i | 0.389126 | + | 0.340817i | ||||
\(557\) | −11.8698 | −0.502938 | −0.251469 | − | 0.967865i | \(-0.580914\pi\) | ||||
−0.251469 | + | 0.967865i | \(0.580914\pi\) | |||||||
\(558\) | 14.7484 | + | 32.5228i | 0.624348 | + | 1.37680i | ||||
\(559\) | 24.4373 | 1.03359 | ||||||||
\(560\) | −2.43558 | + | 14.2931i | −0.102922 | + | 0.603994i | ||||
\(561\) | −25.0549 | −1.05782 | ||||||||
\(562\) | −0.400334 | − | 0.882810i | −0.0168871 | − | 0.0372391i | ||||
\(563\) | − | 27.1163i | − | 1.14282i | −0.820666 | − | 0.571408i | \(-0.806397\pi\) | ||
0.820666 | − | 0.571408i | \(-0.193603\pi\) | |||||||
\(564\) | −7.88459 | + | 9.00220i | −0.332001 | + | 0.379061i | ||||
\(565\) | −9.08679 | + | 29.2763i | −0.382284 | + | 1.23166i | ||||
\(566\) | 3.67859 | + | 8.11196i | 0.154623 | + | 0.340971i | ||||
\(567\) | − | 11.2542i | − | 0.472632i | ||||||
\(568\) | −7.52326 | − | 2.27432i | −0.315669 | − | 0.0954283i | ||||
\(569\) | − | 16.5698i | − | 0.694644i | −0.937746 | − | 0.347322i | \(-0.887091\pi\) | ||
0.937746 | − | 0.347322i | \(-0.112909\pi\) | |||||||
\(570\) | −3.76831 | − | 30.0405i | −0.157837 | − | 1.25826i | ||||
\(571\) | −26.2174 | −1.09717 | −0.548583 | − | 0.836096i | \(-0.684833\pi\) | ||||
−0.548583 | + | 0.836096i | \(0.684833\pi\) | |||||||
\(572\) | 7.03526 | + | 6.16184i | 0.294159 | + | 0.257640i | ||||
\(573\) | −44.5935 | −1.86292 | ||||||||
\(574\) | −0.578733 | − | 1.27621i | −0.0241559 | − | 0.0532681i | ||||
\(575\) | −7.92906 | − | 22.6303i | −0.330665 | − | 0.943748i | ||||
\(576\) | −23.8133 | − | 15.8459i | −0.992219 | − | 0.660244i | ||||
\(577\) | − | 35.5566i | − | 1.48024i | −0.672473 | − | 0.740121i | \(-0.734768\pi\) | ||
0.672473 | − | 0.740121i | \(-0.265232\pi\) | |||||||
\(578\) | −55.2645 | + | 25.0612i | −2.29870 | + | 1.04241i | ||||
\(579\) | − | 41.1910i | − | 1.71184i | ||||||
\(580\) | 7.19444 | + | 11.7205i | 0.298733 | + | 0.486666i | ||||
\(581\) | 21.5142 | 0.892557 | ||||||||
\(582\) | −32.5391 | + | 14.7558i | −1.34879 | + | 0.611646i | ||||
\(583\) | −0.418117 | −0.0173166 | ||||||||
\(584\) | −14.1701 | − | 4.28368i | −0.586362 | − | 0.177260i | ||||
\(585\) | −28.2838 | − | 8.77876i | −1.16939 | − | 0.362957i | ||||
\(586\) | 32.3823 | − | 14.6846i | 1.33770 | − | 0.606616i | ||||
\(587\) | −21.4550 | −0.885542 | −0.442771 | − | 0.896635i | \(-0.646005\pi\) | ||||
−0.442771 | + | 0.896635i | \(0.646005\pi\) | |||||||
\(588\) | 14.7737 | − | 16.8678i | 0.609258 | − | 0.695618i | ||||
\(589\) | − | 26.3686i | − | 1.08650i | ||||||
\(590\) | 28.6699 | − | 3.59637i | 1.18032 | − | 0.148060i | ||||
\(591\) | − | 33.8075i | − | 1.39065i | ||||||
\(592\) | −5.24067 | − | 39.4193i | −0.215390 | − | 1.62012i | ||||
\(593\) | − | 24.9201i | − | 1.02335i | −0.859180 | − | 0.511673i | \(-0.829026\pi\) | ||
0.859180 | − | 0.511673i | \(-0.170974\pi\) | |||||||
\(594\) | −2.39916 | + | 1.08796i | −0.0984386 | + | 0.0446397i | ||||
\(595\) | 26.7950 | + | 8.31664i | 1.09849 | + | 0.340949i | ||||
\(596\) | 15.5351 | + | 13.6064i | 0.636341 | + | 0.557340i | ||||
\(597\) | 12.4311 | 0.508770 | ||||||||
\(598\) | 5.14230 | − | 24.5913i | 0.210284 | − | 1.00561i | ||||
\(599\) | − | 42.3392i | − | 1.72993i | −0.501831 | − | 0.864965i | \(-0.667340\pi\) | ||
0.501831 | − | 0.864965i | \(-0.332660\pi\) | |||||||
\(600\) | 28.3044 | − | 22.6704i | 1.15552 | − | 0.925517i | ||||
\(601\) | 11.3211 | 0.461796 | 0.230898 | − | 0.972978i | \(-0.425834\pi\) | ||||
0.230898 | + | 0.972978i | \(0.425834\pi\) | |||||||
\(602\) | −13.7740 | + | 6.24620i | −0.561386 | + | 0.254576i | ||||
\(603\) | − | 37.7611i | − | 1.53775i | ||||||
\(604\) | −17.9279 | − | 15.7021i | −0.729474 | − | 0.638911i | ||||
\(605\) | 6.23494 | − | 20.0880i | 0.253486 | − | 0.816695i | ||||
\(606\) | −9.10169 | + | 4.12741i | −0.369731 | + | 0.167665i | ||||
\(607\) | −44.0794 | −1.78913 | −0.894564 | − | 0.446940i | \(-0.852514\pi\) | ||||
−0.894564 | + | 0.446940i | \(0.852514\pi\) | |||||||
\(608\) | 11.1817 | + | 17.9180i | 0.453478 | + | 0.726673i | ||||
\(609\) | 12.7827i | 0.517982i | ||||||||
\(610\) | 24.8203 | − | 3.11348i | 1.00495 | − | 0.126061i | ||||
\(611\) | − | 8.64339i | − | 0.349674i | ||||||
\(612\) | −36.4671 | + | 41.6361i | −1.47409 | + | 1.68304i | ||||
\(613\) | 39.7817 | 1.60677 | 0.803384 | − | 0.595462i | \(-0.203031\pi\) | ||||
0.803384 | + | 0.595462i | \(0.203031\pi\) | |||||||
\(614\) | 0.507012 | − | 0.229918i | 0.0204613 | − | 0.00927875i | ||||
\(615\) | −1.03894 | + | 3.34731i | −0.0418941 | + | 0.134977i | ||||
\(616\) | −5.54038 | − | 1.67488i | −0.223228 | − | 0.0674830i | ||||
\(617\) | 1.72131 | 0.0692972 | 0.0346486 | − | 0.999400i | \(-0.488969\pi\) | ||||
0.0346486 | + | 0.999400i | \(0.488969\pi\) | |||||||
\(618\) | 14.1585 | + | 31.2220i | 0.569538 | + | 1.25593i | ||||
\(619\) | 12.8611 | 0.516933 | 0.258467 | − | 0.966020i | \(-0.416783\pi\) | ||||
0.258467 | + | 0.966020i | \(0.416783\pi\) | |||||||
\(620\) | 26.9174 | − | 16.5228i | 1.08103 | − | 0.663574i | ||||
\(621\) | 5.71029 | + | 4.17994i | 0.229146 | + | 0.167735i | ||||
\(622\) | 1.57964 | + | 3.48339i | 0.0633378 | + | 0.139671i | ||||
\(623\) | 19.7845 | 0.792649 | ||||||||
\(624\) | 37.6629 | − | 5.00716i | 1.50772 | − | 0.200447i | ||||
\(625\) | 8.97006 | + | 23.3353i | 0.358802 | + | 0.933414i | ||||
\(626\) | −15.9926 | + | 7.25227i | −0.639192 | + | 0.289859i | ||||
\(627\) | 12.0861 | 0.482671 | ||||||||
\(628\) | −16.3178 | + | 18.6308i | −0.651151 | + | 0.743449i | ||||
\(629\) | −76.9478 | −3.06811 | ||||||||
\(630\) | 18.1860 | − | 2.28126i | 0.724546 | − | 0.0908877i | ||||
\(631\) | 7.22744 | 0.287720 | 0.143860 | − | 0.989598i | \(-0.454049\pi\) | ||||
0.143860 | + | 0.989598i | \(0.454049\pi\) | |||||||
\(632\) | 1.33345 | − | 4.41093i | 0.0530417 | − | 0.175457i | ||||
\(633\) | 57.4091i | 2.28181i | ||||||||
\(634\) | −11.2712 | − | 24.8550i | −0.447635 | − | 0.987116i | ||||
\(635\) | 7.93767 | − | 25.5740i | 0.314997 | − | 1.01487i | ||||
\(636\) | −1.11918 | + | 1.27782i | −0.0443785 | + | 0.0506689i | ||||
\(637\) | 16.1955i | 0.641689i | ||||||||
\(638\) | −4.99986 | + | 2.26732i | −0.197946 | + | 0.0897641i | ||||
\(639\) | 9.93529i | 0.393034i | ||||||||
\(640\) | −11.2844 | + | 22.6421i | −0.446054 | + | 0.895006i | ||||
\(641\) | − | 6.18142i | − | 0.244151i | −0.992521 | − | 0.122076i | \(-0.961045\pi\) | ||
0.992521 | − | 0.122076i | \(-0.0389551\pi\) | |||||||
\(642\) | −5.00276 | − | 11.0320i | −0.197443 | − | 0.435398i | ||||
\(643\) | 1.29026i | 0.0508828i | 0.999676 | + | 0.0254414i | \(0.00809912\pi\) | ||||
−0.999676 | + | 0.0254414i | \(0.991901\pi\) | |||||||
\(644\) | 3.38711 | + | 15.1752i | 0.133471 | + | 0.597985i | ||||
\(645\) | 36.1271 | + | 11.2132i | 1.42250 | + | 0.441518i | ||||
\(646\) | 37.2206 | − | 16.8787i | 1.46443 | − | 0.664084i | ||||
\(647\) | −6.12824 | −0.240926 | −0.120463 | − | 0.992718i | \(-0.538438\pi\) | ||||
−0.120463 | + | 0.992718i | \(0.538438\pi\) | |||||||
\(648\) | 5.68223 | − | 18.7963i | 0.223219 | − | 0.738390i | ||||
\(649\) | 11.5346i | 0.452773i | ||||||||
\(650\) | −4.59038 | + | 25.7873i | −0.180050 | + | 1.01146i | ||||
\(651\) | 29.3570 | 1.15059 | ||||||||
\(652\) | 15.7144 | − | 17.9418i | 0.615423 | − | 0.702657i | ||||
\(653\) | − | 7.74694i | − | 0.303161i | −0.988445 | − | 0.151581i | \(-0.951564\pi\) | ||
0.988445 | − | 0.151581i | \(-0.0484363\pi\) | |||||||
\(654\) | 19.0429 | + | 41.9930i | 0.744635 | + | 1.64205i | ||||
\(655\) | 11.1368 | + | 3.45665i | 0.435152 | + | 0.135063i | ||||
\(656\) | −0.322221 | − | 2.42368i | −0.0125806 | − | 0.0946289i | ||||
\(657\) | 18.7131i | 0.730069i | ||||||||
\(658\) | 2.20926 | + | 4.87182i | 0.0861260 | + | 0.189923i | ||||
\(659\) | −36.4649 | −1.42047 | −0.710235 | − | 0.703965i | \(-0.751411\pi\) | ||||
−0.710235 | + | 0.703965i | \(0.751411\pi\) | |||||||
\(660\) | 7.57326 | + | 12.3376i | 0.294789 | + | 0.480240i | ||||
\(661\) | − | 39.3779i | − | 1.53162i | −0.643064 | − | 0.765812i | \(-0.722337\pi\) | ||
0.643064 | − | 0.765812i | \(-0.277663\pi\) | |||||||
\(662\) | 14.4232 | + | 31.8057i | 0.560572 | + | 1.23616i | ||||
\(663\) | − | 73.5193i | − | 2.85525i | ||||||
\(664\) | 35.9321 | + | 10.8625i | 1.39444 | + | 0.421545i | ||||
\(665\) | −12.9254 | − | 4.01180i | −0.501226 | − | 0.155571i | ||||
\(666\) | −45.7814 | + | 20.7608i | −1.77399 | + | 0.804466i | ||||
\(667\) | 11.9003 | + | 8.71103i | 0.460781 | + | 0.337292i | ||||
\(668\) | 13.3389 | − | 15.2296i | 0.516098 | − | 0.589252i | ||||
\(669\) | −34.5989 | −1.33767 | ||||||||
\(670\) | −33.1379 | + | 4.15684i | −1.28023 | + | 0.160593i | ||||
\(671\) | 9.98585i | 0.385499i | ||||||||
\(672\) | −19.9487 | + | 12.4489i | −0.769539 | + | 0.480229i | ||||
\(673\) | 43.3599i | 1.67140i | 0.549186 | + | 0.835700i | \(0.314938\pi\) | ||||
−0.549186 | + | 0.835700i | \(0.685062\pi\) | |||||||
\(674\) | 1.04339 | − | 0.473153i | 0.0401898 | − | 0.0182252i | ||||
\(675\) | −6.08133 | − | 4.17750i | −0.234070 | − | 0.160792i | ||||
\(676\) | −0.950298 | + | 1.08500i | −0.0365499 | + | 0.0417307i | ||||
\(677\) | −26.2636 | −1.00939 | −0.504696 | − | 0.863297i | \(-0.668395\pi\) | ||||
−0.504696 | + | 0.863297i | \(0.668395\pi\) | |||||||
\(678\) | −45.2763 | + | 20.5318i | −1.73883 | + | 0.788519i | ||||
\(679\) | 15.9711i | 0.612914i | ||||||||
\(680\) | 40.5529 | + | 27.4189i | 1.55513 | + | 1.05147i | ||||
\(681\) | 6.80684i | 0.260838i | ||||||||
\(682\) | 5.20716 | + | 11.4827i | 0.199392 | + | 0.439696i | ||||
\(683\) | −1.55833 | −0.0596279 | −0.0298139 | − | 0.999555i | \(-0.509491\pi\) | ||||
−0.0298139 | + | 0.999555i | \(0.509491\pi\) | |||||||
\(684\) | 17.5911 | − | 20.0846i | 0.672612 | − | 0.767952i | ||||
\(685\) | 8.51573 | − | 27.4364i | 0.325369 | − | 1.04829i | ||||
\(686\) | −10.7672 | − | 23.7436i | −0.411093 | − | 0.906535i | ||||
\(687\) | 45.1161i | 1.72129i | ||||||||
\(688\) | −26.1585 | + | 3.47769i | −0.997284 | + | 0.132586i | ||||
\(689\) | − | 1.22689i | − | 0.0467408i | ||||||
\(690\) | 18.8860 | − | 33.9952i | 0.718977 | − | 1.29417i | ||||
\(691\) | − | 20.9491i | − | 0.796941i | −0.917181 | − | 0.398471i | \(-0.869541\pi\) | ||
0.917181 | − | 0.398471i | \(-0.130459\pi\) | |||||||
\(692\) | 7.18741 | + | 6.29511i | 0.273224 | + | 0.239304i | ||||
\(693\) | 7.31668i | 0.277938i | ||||||||
\(694\) | 26.6059 | − | 12.0652i | 1.00995 | − | 0.457988i | ||||
\(695\) | −13.0240 | − | 4.04239i | −0.494028 | − | 0.153337i | ||||
\(696\) | −6.45398 | + | 21.3492i | −0.244637 | + | 0.809240i | ||||
\(697\) | −4.73111 | −0.179204 | ||||||||
\(698\) | 11.7447 | − | 5.32594i | 0.444542 | − | 0.201590i | ||||
\(699\) | 7.99890i | 0.302546i | ||||||||
\(700\) | −4.00392 | − | 15.7083i | −0.151334 | − | 0.593716i | ||||
\(701\) | − | 32.8322i | − | 1.24005i | −0.784580 | − | 0.620027i | \(-0.787121\pi\) | ||
0.784580 | − | 0.620027i | \(-0.212879\pi\) | |||||||
\(702\) | −3.19244 | − | 7.03990i | −0.120491 | − | 0.265704i | ||||
\(703\) | 37.1183 | 1.39994 | ||||||||
\(704\) | −8.40768 | − | 5.59466i | −0.316876 | − | 0.210857i | ||||
\(705\) | 3.96606 | − | 12.7780i | 0.149370 | − | 0.481249i | ||||
\(706\) | −10.8286 | − | 23.8789i | −0.407538 | − | 0.898695i | ||||
\(707\) | 4.46736i | 0.168012i | ||||||||
\(708\) | 35.2514 | + | 30.8750i | 1.32483 | + | 1.16035i | ||||
\(709\) | 39.9184i | 1.49917i | 0.661910 | + | 0.749584i | \(0.269746\pi\) | ||||
−0.661910 | + | 0.749584i | \(0.730254\pi\) | |||||||
\(710\) | 8.71887 | − | 1.09370i | 0.327213 | − | 0.0410459i | ||||
\(711\) | −5.82512 | −0.218459 | ||||||||
\(712\) | 33.0433 | + | 9.98916i | 1.23835 | + | 0.374360i | ||||
\(713\) | 20.0059 | − | 27.3303i | 0.749225 | − | 1.02353i | ||||
\(714\) | 18.7916 | + | 41.4389i | 0.703259 | + | 1.55081i | ||||
\(715\) | −9.98610 | − | 3.09949i | −0.373459 | − | 0.115914i | ||||
\(716\) | −38.0320 | − | 33.3104i | −1.42132 | − | 1.24487i | ||||
\(717\) | 13.2774i | 0.495853i | ||||||||
\(718\) | −32.0616 | + | 14.5392i | −1.19653 | + | 0.542599i | ||||
\(719\) | − | 24.6272i | − | 0.918438i | −0.888323 | − | 0.459219i | \(-0.848129\pi\) | ||
0.888323 | − | 0.459219i | \(-0.151871\pi\) | |||||||
\(720\) | 31.5253 | + | 5.37199i | 1.17488 | + | 0.200202i | ||||
\(721\) | 15.3246 | 0.570718 | ||||||||
\(722\) | 6.51684 | − | 2.95524i | 0.242532 | − | 0.109983i | ||||
\(723\) | 79.3256i | 2.95015i | ||||||||
\(724\) | −1.99586 | − | 1.74808i | −0.0741755 | − | 0.0649667i | ||||
\(725\) | −12.6735 | − | 8.70593i | −0.470683 | − | 0.323330i | ||||
\(726\) | 31.0665 | − | 14.0880i | 1.15299 | − | 0.522854i | ||||
\(727\) | − | 4.57658i | − | 0.169736i | −0.996392 | − | 0.0848679i | \(-0.972953\pi\) | ||
0.996392 | − | 0.0848679i | \(-0.0270468\pi\) | |||||||
\(728\) | 4.91465 | − | 16.2573i | 0.182149 | − | 0.602534i | ||||
\(729\) | −36.1740 | −1.33978 | ||||||||
\(730\) | 16.4220 | − | 2.05999i | 0.607806 | − | 0.0762437i | ||||
\(731\) | 51.0623i | 1.88861i | ||||||||
\(732\) | 30.5181 | + | 26.7293i | 1.12798 | + | 0.987945i | ||||
\(733\) | 28.9459 | 1.06914 | 0.534571 | − | 0.845123i | \(-0.320473\pi\) | ||||
0.534571 | + | 0.845123i | \(0.320473\pi\) | |||||||
\(734\) | −19.4048 | − | 42.7912i | −0.716246 | − | 1.57945i | ||||
\(735\) | −7.43138 | + | 23.9428i | −0.274111 | + | 0.883143i | ||||
\(736\) | −2.00489 | + | 27.0551i | −0.0739012 | + | 0.997266i | ||||
\(737\) | − | 13.3322i | − | 0.491098i | ||||||
\(738\) | −2.81485 | + | 1.27647i | −0.103616 | + | 0.0469876i | ||||
\(739\) | − | 40.4785i | − | 1.48903i | −0.667608 | − | 0.744513i | \(-0.732682\pi\) | ||
0.667608 | − | 0.744513i | \(-0.267318\pi\) | |||||||
\(740\) | 23.2587 | + | 37.8908i | 0.855008 | + | 1.39289i | ||||
\(741\) | 35.4644i | 1.30282i | ||||||||
\(742\) | 0.313595 | + | 0.691533i | 0.0115124 | + | 0.0253870i | ||||
\(743\) | − | 32.9024i | − | 1.20707i | −0.797335 | − | 0.603537i | \(-0.793758\pi\) | ||
0.797335 | − | 0.603537i | \(-0.206242\pi\) | |||||||
\(744\) | 49.0309 | + | 14.8223i | 1.79756 | + | 0.543412i | ||||
\(745\) | −22.0510 | − | 6.84421i | −0.807887 | − | 0.250753i | ||||
\(746\) | −19.3707 | + | 8.78418i | −0.709212 | + | 0.321612i | ||||
\(747\) | − | 47.4523i | − | 1.73619i | ||||||
\(748\) | −12.8753 | + | 14.7004i | −0.470769 | + | 0.537498i | ||||
\(749\) | −5.41480 | −0.197852 | ||||||||
\(750\) | −18.6189 | + | 36.0166i | −0.679865 | + | 1.31514i | ||||
\(751\) | −19.3003 | −0.704279 | −0.352139 | − | 0.935948i | \(-0.614546\pi\) | ||||
−0.352139 | + | 0.935948i | \(0.614546\pi\) | |||||||
\(752\) | 1.23005 | + | 9.25218i | 0.0448553 | + | 0.337392i | ||||
\(753\) | 17.1329 | 0.624359 | ||||||||
\(754\) | −6.65306 | − | 14.6712i | −0.242290 | − | 0.534294i | ||||
\(755\) | 25.4474 | + | 7.89840i | 0.926127 | + | 0.287452i | ||||
\(756\) | 3.59882 | + | 3.15203i | 0.130888 | + | 0.114638i | ||||
\(757\) | −44.6128 | −1.62148 | −0.810739 | − | 0.585408i | \(-0.800935\pi\) | ||||
−0.810739 | + | 0.585408i | \(0.800935\pi\) | |||||||
\(758\) | 40.0044 | − | 18.1411i | 1.45303 | − | 0.658915i | ||||
\(759\) | 12.5269 | + | 9.16969i | 0.454697 | + | 0.332839i | ||||
\(760\) | −19.5620 | − | 13.2264i | −0.709588 | − | 0.479771i | ||||
\(761\) | 38.6678 | 1.40171 | 0.700854 | − | 0.713305i | \(-0.252803\pi\) | ||||
0.700854 | + | 0.713305i | \(0.252803\pi\) | |||||||
\(762\) | 39.5507 | − | 17.9353i | 1.43277 | − | 0.649729i | ||||
\(763\) | 20.6113 | 0.746178 | ||||||||
\(764\) | −22.9159 | + | 26.1642i | −0.829069 | + | 0.946586i | ||||
\(765\) | 18.3434 | − | 59.0998i | 0.663209 | − | 2.13676i | ||||
\(766\) | −2.06993 | − | 4.56457i | −0.0747895 | − | 0.164924i | ||||
\(767\) | −33.8463 | −1.22212 | ||||||||
\(768\) | −39.6031 | + | 10.7197i | −1.42905 | + | 0.386813i | ||||
\(769\) | 27.9367i | 1.00742i | 0.863872 | + | 0.503711i | \(0.168032\pi\) | ||||
−0.863872 | + | 0.503711i | \(0.831968\pi\) | |||||||
\(770\) | 6.42087 | − | 0.805439i | 0.231392 | − | 0.0290260i | ||||
\(771\) | − | 61.5208i | − | 2.21562i | ||||||
\(772\) | −24.1678 | − | 21.1674i | −0.869817 | − | 0.761831i | ||||
\(773\) | 9.02065 | 0.324450 | 0.162225 | − | 0.986754i | \(-0.448133\pi\) | ||||
0.162225 | + | 0.986754i | \(0.448133\pi\) | |||||||
\(774\) | 13.7768 | + | 30.3804i | 0.495198 | + | 1.09200i | ||||
\(775\) | −19.9942 | + | 29.1062i | −0.718211 | + | 1.04552i | ||||
\(776\) | −8.06378 | + | 26.6743i | −0.289473 | + | 0.957552i | ||||
\(777\) | 41.3250i | 1.48253i | ||||||||
\(778\) | −5.01158 | − | 11.0514i | −0.179674 | − | 0.396213i | ||||
\(779\) | 2.28221 | 0.0817685 | ||||||||
\(780\) | −36.2025 | + | 22.2224i | −1.29626 | + | 0.795689i | ||||
\(781\) | 3.50782i | 0.125520i | ||||||||
\(782\) | 51.3841 | + | 10.7450i | 1.83749 | + | 0.384239i | ||||
\(783\) | 4.53764 | 0.162162 | ||||||||
\(784\) | −2.30480 | − | 17.3362i | −0.0823143 | − | 0.619151i | ||||
\(785\) | 8.20808 | − | 26.4452i | 0.292959 | − | 0.943870i | ||||
\(786\) | 7.81038 | + | 17.2233i | 0.278587 | + | 0.614335i | ||||
\(787\) | 22.2563i | 0.793352i | 0.917959 | + | 0.396676i | \(0.129836\pi\) | ||||
−0.917959 | + | 0.396676i | \(0.870164\pi\) | |||||||
\(788\) | −19.8357 | − | 17.3731i | −0.706618 | − | 0.618892i | ||||
\(789\) | 3.14492i | 0.111962i | ||||||||
\(790\) | 0.641245 | + | 5.11193i | 0.0228145 | + | 0.181874i | ||||
\(791\) | 22.2228i | 0.790153i | ||||||||
\(792\) | −3.69418 | + | 12.2200i | −0.131267 | + | 0.434220i | ||||
\(793\) | −29.3017 | −1.04053 | ||||||||
\(794\) | 7.55555 | + | 16.6614i | 0.268137 | + | 0.591290i | ||||
\(795\) | 0.562964 | − | 1.81379i | 0.0199663 | − | 0.0643284i | ||||
\(796\) | 6.38813 | − | 7.29362i | 0.226421 | − | 0.258516i | ||||
\(797\) | 26.3482 | 0.933300 | 0.466650 | − | 0.884442i | \(-0.345461\pi\) | ||||
0.466650 | + | 0.884442i | \(0.345461\pi\) | |||||||
\(798\) | −9.06475 | − | 19.9894i | −0.320889 | − | 0.707618i | ||||
\(799\) | 18.0606 | 0.638938 | ||||||||
\(800\) | 1.24388 | − | 28.2569i | 0.0439778 | − | 0.999033i | ||||
\(801\) | − | 43.6373i | − | 1.54185i | ||||||
\(802\) | −14.4326 | − | 31.8266i | −0.509634 | − | 1.12384i | ||||
\(803\) | 6.60700i | 0.233156i | ||||||||
\(804\) | −40.7450 | − | 35.6866i | −1.43697 | − | 1.25857i | ||||
\(805\) | −10.3531 | − | 13.9646i | −0.364899 | − | 0.492189i | ||||
\(806\) | −33.6941 | + | 15.2795i | −1.18682 | + | 0.538197i | ||||
\(807\) | −42.8164 | −1.50721 | ||||||||
\(808\) | −2.25556 | + | 7.46121i | −0.0793503 | + | 0.262484i | ||||
\(809\) | −21.6638 | −0.761657 | −0.380829 | − | 0.924646i | \(-0.624361\pi\) | ||||
−0.380829 | + | 0.924646i | \(0.624361\pi\) | |||||||
\(810\) | 2.73254 | + | 21.7835i | 0.0960117 | + | 0.765394i | ||||
\(811\) | 0.319681i | 0.0112255i | 0.999984 | + | 0.00561275i | \(0.00178660\pi\) | ||||
−0.999984 | + | 0.00561275i | \(0.998213\pi\) | |||||||
\(812\) | 7.49995 | + | 6.56885i | 0.263197 | + | 0.230521i | ||||
\(813\) | 60.9619i | 2.13803i | ||||||||
\(814\) | −16.1639 | + | 7.32997i | −0.566545 | + | 0.256915i | ||||
\(815\) | −7.90456 | + | 25.4673i | −0.276885 | + | 0.892080i | ||||
\(816\) | 10.4626 | + | 78.6975i | 0.366264 | + | 2.75496i | ||||
\(817\) | − | 24.6316i | − | 0.861750i | ||||||
\(818\) | −9.81775 | + | 4.45213i | −0.343270 | + | 0.155665i | ||||
\(819\) | −21.4695 | −0.750205 | ||||||||
\(820\) | 1.43006 | + | 2.32970i | 0.0499397 | + | 0.0813568i | ||||
\(821\) | 12.4488 | 0.434466 | 0.217233 | − | 0.976120i | \(-0.430297\pi\) | ||||
0.217233 | + | 0.976120i | \(0.430297\pi\) | |||||||
\(822\) | 42.4309 | − | 19.2415i | 1.47995 | − | 0.671123i | ||||
\(823\) | −24.9542 | −0.869850 | −0.434925 | − | 0.900467i | \(-0.643225\pi\) | ||||
−0.434925 | + | 0.900467i | \(0.643225\pi\) | |||||||
\(824\) | 25.5946 | + | 7.73737i | 0.891629 | + | 0.269544i | ||||
\(825\) | −13.3408 | − | 9.16433i | −0.464468 | − | 0.319061i | ||||
\(826\) | 19.0774 | − | 8.65116i | 0.663787 | − | 0.301012i | ||||
\(827\) | − | 37.0949i | − | 1.28992i | −0.764218 | − | 0.644958i | \(-0.776875\pi\) | ||
0.764218 | − | 0.644958i | \(-0.223125\pi\) | |||||||
\(828\) | 33.4708 | − | 7.47073i | 1.16319 | − | 0.259626i | ||||
\(829\) | −30.2201 | −1.04959 | −0.524794 | − | 0.851230i | \(-0.675858\pi\) | ||||
−0.524794 | + | 0.851230i | \(0.675858\pi\) | |||||||
\(830\) | −41.6425 | + | 5.22368i | −1.44543 | + | 0.181316i | ||||
\(831\) | 0.495224i | 0.0171791i | ||||||||
\(832\) | 16.4165 | − | 24.6709i | 0.569141 | − | 0.855308i | ||||
\(833\) | −33.8409 | −1.17252 | ||||||||
\(834\) | −9.13386 | − | 20.1418i | −0.316280 | − | 0.697454i | ||||
\(835\) | −6.70965 | + | 21.6175i | −0.232197 | + | 0.748104i | ||||
\(836\) | 6.21084 | − | 7.09120i | 0.214806 | − | 0.245254i | ||||
\(837\) | − | 10.4212i | − | 0.360209i | ||||||
\(838\) | 7.15233 | − | 3.24342i | 0.247073 | − | 0.112042i | ||||
\(839\) | −18.5073 | −0.638942 | −0.319471 | − | 0.947596i | \(-0.603505\pi\) | ||||
−0.319471 | + | 0.947596i | \(0.603505\pi\) | |||||||
\(840\) | 14.7253 | − | 21.7790i | 0.508073 | − | 0.751446i | ||||
\(841\) | −19.5435 | −0.673915 | ||||||||
\(842\) | −5.57981 | − | 12.3045i | −0.192293 | − | 0.424041i | ||||
\(843\) | 1.75762i | 0.0605355i | ||||||||
\(844\) | 33.6834 | + | 29.5017i | 1.15943 | + | 1.01549i | ||||
\(845\) | 0.478013 | − | 1.54009i | 0.0164441 | − | 0.0529805i | ||||
\(846\) | 10.7454 | − | 4.87282i | 0.369436 | − | 0.167531i | ||||
\(847\) | − | 15.2483i | − | 0.523937i | ||||||
\(848\) | 0.174600 | + | 1.31331i | 0.00599579 | + | 0.0450991i | ||||
\(849\) | − | 16.1504i | − | 0.554280i | ||||||
\(850\) | −53.8833 | − | 9.59172i | −1.84818 | − | 0.328993i | ||||
\(851\) | 38.4721 | + | 28.1617i | 1.31881 | + | 0.965369i | ||||
\(852\) | 10.7204 | + | 9.38947i | 0.367275 | + | 0.321678i | ||||
\(853\) | 42.7030i | 1.46212i | 0.682312 | + | 0.731061i | \(0.260975\pi\) | ||||
−0.682312 | + | 0.731061i | \(0.739025\pi\) | |||||||
\(854\) | 16.5158 | − | 7.48956i | 0.565160 | − | 0.256287i | ||||
\(855\) | −8.84856 | + | 28.5087i | −0.302614 | + | 0.974978i | ||||
\(856\) | −9.04359 | − | 2.73392i | −0.309104 | − | 0.0934436i | ||||
\(857\) | 20.9362i | 0.715168i | 0.933881 | + | 0.357584i | \(0.116399\pi\) | ||||
−0.933881 | + | 0.357584i | \(0.883601\pi\) | |||||||
\(858\) | −7.00337 | − | 15.4437i | −0.239091 | − | 0.527239i | ||||
\(859\) | − | 36.7363i | − | 1.25343i | −0.779250 | − | 0.626714i | \(-0.784400\pi\) | ||
0.779250 | − | 0.626714i | \(-0.215600\pi\) | |||||||
\(860\) | 25.1442 | − | 15.4344i | 0.857410 | − | 0.526309i | ||||
\(861\) | 2.54085i | 0.0865920i | ||||||||
\(862\) | −47.4018 | + | 21.4957i | −1.61451 | + | 0.732145i | ||||
\(863\) | 47.2340 | 1.60786 | 0.803932 | − | 0.594721i | \(-0.202737\pi\) | ||||
0.803932 | + | 0.594721i | \(0.202737\pi\) | |||||||
\(864\) | 4.41915 | + | 7.08143i | 0.150343 | + | 0.240915i | ||||
\(865\) | −10.2021 | − | 3.16652i | −0.346881 | − | 0.107665i | ||||
\(866\) | −20.7452 | + | 9.40750i | −0.704952 | + | 0.319680i | ||||
\(867\) | 110.028 | 3.73674 | ||||||||
\(868\) | 15.0861 | − | 17.2245i | 0.512055 | − | 0.584637i | ||||
\(869\) | −2.05666 | −0.0697673 | ||||||||
\(870\) | −3.10367 | − | 24.7421i | −0.105224 | − | 0.838836i | ||||
\(871\) | 39.1210 | 1.32557 | ||||||||
\(872\) | 34.4242 | + | 10.4066i | 1.16575 | + | 0.352412i | ||||
\(873\) | 35.2264 | 1.19223 | ||||||||
\(874\) | −24.7868 | − | 5.18319i | −0.838426 | − | 0.175324i | ||||
\(875\) | 11.2254 | + | 14.2291i | 0.379487 | + | 0.481031i | ||||
\(876\) | 20.1919 | + | 17.6851i | 0.682220 | + | 0.597524i | ||||
\(877\) | − | 0.341245i | − | 0.0115230i | −0.999983 | − | 0.00576151i | \(-0.998166\pi\) | ||
0.999983 | − | 0.00576151i | \(-0.00183396\pi\) | |||||||
\(878\) | −18.0560 | − | 39.8168i | −0.609361 | − | 1.34375i | ||||
\(879\) | −64.4709 | −2.17455 | ||||||||
\(880\) | 11.1306 | + | 1.89667i | 0.375211 | + | 0.0639368i | ||||
\(881\) | − | 37.6366i | − | 1.26801i | −0.773329 | − | 0.634005i | \(-0.781410\pi\) | ||
0.773329 | − | 0.634005i | \(-0.218590\pi\) | |||||||
\(882\) | −20.1342 | + | 9.13042i | −0.677955 | + | 0.307437i | ||||
\(883\) | −10.8974 | −0.366725 | −0.183363 | − | 0.983045i | \(-0.558698\pi\) | ||||
−0.183363 | + | 0.983045i | \(0.558698\pi\) | |||||||
\(884\) | −43.1356 | − | 37.7804i | −1.45081 | − | 1.27069i | ||||
\(885\) | −50.0370 | − | 15.5305i | −1.68198 | − | 0.522053i | ||||
\(886\) | 2.40646 | − | 1.09128i | 0.0808467 | − | 0.0366622i | ||||
\(887\) | −17.9288 | −0.601991 | −0.300995 | − | 0.953626i | \(-0.597319\pi\) | ||||
−0.300995 | + | 0.953626i | \(0.597319\pi\) | |||||||
\(888\) | −20.8649 | + | 69.0194i | −0.700181 | + | 2.31614i | ||||
\(889\) | − | 19.4125i | − | 0.651075i | ||||||
\(890\) | −38.2946 | + | 4.80371i | −1.28364 | + | 0.161021i | ||||
\(891\) | −8.76406 | −0.293607 | ||||||||
\(892\) | −17.7798 | + | 20.3000i | −0.595313 | + | 0.679696i | ||||
\(893\) | −8.71211 | −0.291540 | ||||||||
\(894\) | −15.4646 | − | 34.1023i | −0.517215 | − | 1.14055i | ||||
\(895\) | 53.9840 | + | 16.7556i | 1.80449 | + | 0.560078i | ||||
\(896\) | −2.94723 | + | 18.1017i | −0.0984599 | + | 0.604737i | ||||
\(897\) | −26.9069 | + | 36.7579i | −0.898394 | + | 1.22731i | ||||
\(898\) | −42.7304 | + | 19.3773i | −1.42593 | + | 0.646627i | ||||
\(899\) | − | 21.7178i | − | 0.724330i | ||||||
\(900\) | −34.6466 | + | 8.83117i | −1.15489 | + | 0.294372i | ||||
\(901\) | 2.56362 | 0.0854066 | ||||||||
\(902\) | −0.993833 | + | 0.450681i | −0.0330910 | + | 0.0150060i | ||||
\(903\) | 27.4231 | 0.912584 | ||||||||
\(904\) | −11.2203 | + | 37.1157i | −0.373181 | + | 1.23445i | ||||
\(905\) | 2.83299 | + | 0.879306i | 0.0941718 | + | 0.0292291i | ||||
\(906\) | 17.8466 | + | 39.3550i | 0.592913 | + | 1.30748i | ||||
\(907\) | 56.2830i | 1.86885i | 0.356164 | + | 0.934423i | \(0.384084\pi\) | ||||
−0.356164 | + | 0.934423i | \(0.615916\pi\) | |||||||
\(908\) | 3.99374 | + | 3.49793i | 0.132537 | + | 0.116083i | ||||
\(909\) | 9.85334 | 0.326815 | ||||||||
\(910\) | 2.36342 | + | 18.8409i | 0.0783466 | + | 0.624570i | ||||
\(911\) | 26.0399 | 0.862742 | 0.431371 | − | 0.902175i | \(-0.358030\pi\) | ||||
0.431371 | + | 0.902175i | \(0.358030\pi\) | |||||||
\(912\) | −5.04698 | − | 37.9623i | −0.167122 | − | 1.25706i | ||||
\(913\) | − | 16.7539i | − | 0.554472i | ||||||
\(914\) | 21.1318 | − | 9.58281i | 0.698979 | − | 0.316971i | ||||
\(915\) | −43.3185 | − | 13.4452i | −1.43207 | − | 0.444485i | ||||
\(916\) | 26.4708 | + | 23.1845i | 0.874619 | + | 0.766037i | ||||
\(917\) | 8.45366 | 0.279165 | ||||||||
\(918\) | 14.7101 | − | 6.67068i | 0.485504 | − | 0.220165i | ||||
\(919\) | −20.8262 | −0.686992 | −0.343496 | − | 0.939154i | \(-0.611611\pi\) | ||||
−0.343496 | + | 0.939154i | \(0.611611\pi\) | |||||||
\(920\) | −10.2406 | − | 28.5505i | −0.337623 | − | 0.941281i | ||||
\(921\) | −1.00943 | −0.0332617 | ||||||||
\(922\) | 15.7423 | − | 7.13879i | 0.518446 | − | 0.235103i | ||||
\(923\) | −10.2931 | −0.338801 | ||||||||
\(924\) | 7.89485 | + | 6.91472i | 0.259722 | + | 0.227478i | ||||
\(925\) | −40.9719 | − | 28.1452i | −1.34715 | − | 0.925408i | ||||
\(926\) | −49.6377 | + | 22.5096i | −1.63120 | + | 0.739711i | ||||
\(927\) | − | 33.8005i | − | 1.11015i | ||||||
\(928\) | 9.20953 | + | 14.7578i | 0.302318 | + | 0.484447i | ||||
\(929\) | 34.6067 | 1.13541 | 0.567704 | − | 0.823233i | \(-0.307832\pi\) | ||||
0.567704 | + | 0.823233i | \(0.307832\pi\) | |||||||
\(930\) | −56.8230 | + | 7.12793i | −1.86330 | + | 0.233734i | ||||
\(931\) | 16.3243 | 0.535007 | ||||||||
\(932\) | 4.69316 | + | 4.11051i | 0.153730 | + | 0.134644i | ||||
\(933\) | − | 6.93520i | − | 0.227048i | ||||||
\(934\) | 5.25686 | + | 11.5923i | 0.172010 | + | 0.379313i | ||||
\(935\) | 6.47647 | − | 20.8662i | 0.211803 | − | 0.682398i | ||||
\(936\) | −35.8576 | − | 10.8399i | −1.17204 | − | 0.354314i | ||||
\(937\) | −28.5789 | −0.933633 | −0.466817 | − | 0.884354i | \(-0.654599\pi\) | ||||
−0.466817 | + | 0.884354i | \(0.654599\pi\) | |||||||
\(938\) | −22.0505 | + | 9.99938i | −0.719973 | + | 0.326491i | ||||
\(939\) | 31.8401 | 1.03906 | ||||||||
\(940\) | −5.45911 | − | 8.89343i | −0.178056 | − | 0.290072i | ||||
\(941\) | − | 30.7312i | − | 1.00181i | −0.865502 | − | 0.500905i | \(-0.833001\pi\) | ||
0.865502 | − | 0.500905i | \(-0.166999\pi\) | |||||||
\(942\) | 40.8980 | − | 18.5463i | 1.33253 | − | 0.604272i | ||||
\(943\) | 2.36545 | + | 1.73151i | 0.0770295 | + | 0.0563858i | ||||
\(944\) | 36.2302 | − | 4.81670i | 1.17919 | − | 0.156770i | ||||
\(945\) | −5.10829 | − | 1.58551i | −0.166173 | − | 0.0515768i | ||||
\(946\) | 4.86414 | + | 10.7263i | 0.158147 | + | 0.348743i | ||||
\(947\) | 6.09604 | 0.198095 | 0.0990474 | − | 0.995083i | \(-0.468420\pi\) | ||||
0.0990474 | + | 0.995083i | \(0.468420\pi\) | |||||||
\(948\) | −5.50510 | + | 6.28543i | −0.178797 | + | 0.204141i | ||||
\(949\) | −19.3871 | −0.629331 | ||||||||
\(950\) | 25.9924 | + | 4.62688i | 0.843304 | + | 0.150116i | ||||
\(951\) | 49.4846i | 1.60465i | ||||||||
\(952\) | 33.9700 | + | 10.2693i | 1.10097 | + | 0.332830i | ||||
\(953\) | −14.7724 | −0.478526 | −0.239263 | − | 0.970955i | \(-0.576906\pi\) | ||||
−0.239263 | + | 0.970955i | \(0.576906\pi\) | |||||||
\(954\) | 1.52527 | − | 0.691675i | 0.0493824 | − | 0.0223938i | ||||
\(955\) | 11.5270 | − | 37.1383i | 0.373006 | − | 1.20177i | ||||
\(956\) | 7.79018 | + | 6.82304i | 0.251952 | + | 0.220673i | ||||
\(957\) | 9.95438 | 0.321779 | ||||||||
\(958\) | 26.0443 | − | 11.8105i | 0.841453 | − | 0.381580i | ||||
\(959\) | − | 20.8262i | − | 0.672515i | ||||||
\(960\) | 35.5899 | − | 28.9396i | 1.14866 | − | 0.934022i | ||||
\(961\) | −18.8774 | −0.608949 | ||||||||
\(962\) | −21.5085 | − | 47.4302i | −0.693462 | − | 1.52921i | ||||
\(963\) | 11.9431i | 0.384860i | ||||||||
\(964\) | 46.5424 | + | 40.7642i | 1.49903 | + | 1.31293i | ||||
\(965\) | 34.3046 | + | 10.6475i | 1.10430 | + | 0.342755i | ||||
\(966\) | 5.77061 | − | 27.5959i | 0.185666 | − | 0.887884i | ||||
\(967\) | −6.31871 | −0.203196 | −0.101598 | − | 0.994826i | \(-0.532396\pi\) | ||||
−0.101598 | + | 0.994826i | \(0.532396\pi\) | |||||||
\(968\) | 7.69883 | − | 25.4671i | 0.247450 | − | 0.818544i | ||||
\(969\) | −74.1038 | −2.38056 | ||||||||
\(970\) | −3.87781 | − | 30.9135i | −0.124509 | − | 0.992571i | ||||
\(971\) | 1.24147 | 0.0398407 | 0.0199204 | − | 0.999802i | \(-0.493659\pi\) | ||||
0.0199204 | + | 0.999802i | \(0.493659\pi\) | |||||||
\(972\) | −29.2923 | + | 33.4443i | −0.939549 | + | 1.07273i | ||||
\(973\) | −9.88615 | −0.316935 | ||||||||
\(974\) | 27.9838 | − | 12.6900i | 0.896659 | − | 0.406615i | ||||
\(975\) | 26.8911 | − | 39.1463i | 0.861205 | − | 1.25369i | ||||
\(976\) | 31.3656 | − | 4.16996i | 1.00399 | − | 0.133477i | ||||
\(977\) | 52.9476 | 1.69394 | 0.846972 | − | 0.531637i | \(-0.178423\pi\) | ||||
0.846972 | + | 0.531637i | \(0.178423\pi\) | |||||||
\(978\) | −39.3856 | + | 17.8605i | −1.25941 | + | 0.571116i | ||||
\(979\) | − | 15.4069i | − | 0.492407i | ||||||
\(980\) | 10.2290 | + | 16.6640i | 0.326753 | + | 0.532312i | ||||
\(981\) | − | 45.4609i | − | 1.45145i | ||||||
\(982\) | 6.80197 | + | 14.9996i | 0.217059 | + | 0.478655i | ||||
\(983\) | 24.3193i | 0.775664i | 0.921730 | + | 0.387832i | \(0.126776\pi\) | ||||
−0.921730 | + | 0.387832i | \(0.873224\pi\) | |||||||
\(984\) | −1.28287 | + | 4.24364i | −0.0408965 | + | 0.135282i | ||||
\(985\) | 28.1555 | + | 8.73893i | 0.897109 | + | 0.278445i | ||||
\(986\) | 30.6558 | − | 13.9017i | 0.976281 | − | 0.442722i | ||||
\(987\) | − | 9.69947i | − | 0.308738i | ||||||
\(988\) | 20.8079 | + | 18.2246i | 0.661987 | + | 0.579802i | ||||
\(989\) | 18.6880 | − | 25.5300i | 0.594244 | − | 0.811806i | ||||
\(990\) | −1.77650 | − | 14.1621i | −0.0564610 | − | 0.450100i | ||||
\(991\) | 26.9879i | 0.857299i | 0.903471 | + | 0.428650i | \(0.141011\pi\) | ||||
−0.903471 | + | 0.428650i | \(0.858989\pi\) | |||||||
\(992\) | 33.8928 | − | 21.1507i | 1.07610 | − | 0.671536i | ||||
\(993\) | − | 63.3229i | − | 2.00949i | ||||||
\(994\) | 5.80167 | − | 2.63093i | 0.184018 | − | 0.0834480i | ||||
\(995\) | −3.21332 | + | 10.3528i | −0.101869 | + | 0.328207i | ||||
\(996\) | −51.2021 | − | 44.8454i | −1.62240 | − | 1.42098i | ||||
\(997\) | 1.51921i | 0.0481140i | 0.999711 | + | 0.0240570i | \(0.00765832\pi\) | ||||
−0.999711 | + | 0.0240570i | \(0.992342\pi\) | |||||||
\(998\) | −12.0589 | − | 26.5920i | −0.381718 | − | 0.841756i | ||||
\(999\) | 14.6696 | 0.464126 |
(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 | 460.2.g.c.459.7 | yes | 56 | |
4.3 | odd | 2 | inner | 460.2.g.c.459.51 | yes | 56 | |
5.4 | even | 2 | inner | 460.2.g.c.459.50 | yes | 56 | |
20.19 | odd | 2 | inner | 460.2.g.c.459.6 | yes | 56 | |
23.22 | odd | 2 | inner | 460.2.g.c.459.8 | yes | 56 | |
92.91 | even | 2 | inner | 460.2.g.c.459.52 | yes | 56 | |
115.114 | odd | 2 | inner | 460.2.g.c.459.49 | yes | 56 | |
460.459 | even | 2 | inner | 460.2.g.c.459.5 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.g.c.459.5 | ✓ | 56 | 460.459 | even | 2 | inner | |
460.2.g.c.459.6 | yes | 56 | 20.19 | odd | 2 | inner | |
460.2.g.c.459.7 | yes | 56 | 1.1 | even | 1 | trivial | |
460.2.g.c.459.8 | yes | 56 | 23.22 | odd | 2 | inner | |
460.2.g.c.459.49 | yes | 56 | 115.114 | odd | 2 | inner | |
460.2.g.c.459.50 | yes | 56 | 5.4 | even | 2 | inner | |
460.2.g.c.459.51 | yes | 56 | 4.3 | odd | 2 | inner | |
460.2.g.c.459.52 | yes | 56 | 92.91 | even | 2 | inner |