Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(19,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.l (of order \(10\), degree \(4\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 379.2 | ||
Root | \(0.951057 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.379 |
Dual form | 450.2.l.a.19.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.951057 | + | 0.309017i | 0.672499 | + | 0.218508i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.809017 | + | 0.587785i | 0.404508 | + | 0.293893i | ||||
\(5\) | 2.06909 | + | 0.847859i | 0.925325 | + | 0.379174i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.07768i | 1.54122i | 0.637307 | + | 0.770610i | \(0.280048\pi\) | ||||
−0.637307 | + | 0.770610i | \(0.719952\pi\) | |||||||
\(8\) | 0.587785 | + | 0.809017i | 0.207813 | + | 0.286031i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.70582 | + | 1.44575i | 0.539427 | + | 0.457185i | ||||
\(11\) | 1.01484 | − | 3.12334i | 0.305985 | − | 0.941724i | −0.673323 | − | 0.739348i | \(-0.735134\pi\) |
0.979308 | − | 0.202376i | \(-0.0648662\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.15688 | + | 1.67557i | −1.43026 | + | 0.464720i | −0.918847 | − | 0.394615i | \(-0.870878\pi\) |
−0.511413 | + | 0.859335i | \(0.670878\pi\) | |||||||
\(14\) | −1.26007 | + | 3.87811i | −0.336769 | + | 1.03647i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −2.03353 | − | 2.79892i | −0.493204 | − | 0.678837i | 0.487771 | − | 0.872972i | \(-0.337810\pi\) |
−0.980975 | + | 0.194135i | \(0.937810\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.32292 | − | 0.961158i | 0.303499 | − | 0.220505i | −0.425603 | − | 0.904910i | \(-0.639938\pi\) |
0.729102 | + | 0.684405i | \(0.239938\pi\) | |||||||
\(20\) | 1.17557 | + | 1.90211i | 0.262866 | + | 0.425325i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.93033 | − | 2.65688i | 0.411548 | − | 0.566448i | ||||
\(23\) | 0.581542 | + | 0.188954i | 0.121260 | + | 0.0393997i | 0.369018 | − | 0.929422i | \(-0.379694\pi\) |
−0.247758 | + | 0.968822i | \(0.579694\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.56227 | + | 3.50859i | 0.712454 | + | 0.701719i | ||||
\(26\) | −5.42226 | −1.06339 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.39680 | + | 3.29892i | −0.452953 | + | 0.623436i | ||||
\(29\) | 3.78173 | + | 2.74759i | 0.702249 | + | 0.510214i | 0.880664 | − | 0.473741i | \(-0.157097\pi\) |
−0.178415 | + | 0.983955i | \(0.557097\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.71737 | − | 4.88046i | 1.20648 | − | 0.876556i | 0.211570 | − | 0.977363i | \(-0.432142\pi\) |
0.994906 | + | 0.100807i | \(0.0321424\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.06909 | − | 3.29032i | −0.183348 | − | 0.564286i | ||||
\(35\) | −3.45730 | + | 8.43710i | −0.584390 | + | 1.42613i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.28350 | − | 0.741955i | 0.375406 | − | 0.121977i | −0.115236 | − | 0.993338i | \(-0.536762\pi\) |
0.490642 | + | 0.871361i | \(0.336762\pi\) | |||||||
\(38\) | 1.55519 | − | 0.505311i | 0.252285 | − | 0.0819722i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.530249 | + | 2.17229i | 0.0838397 | + | 0.343469i | ||||
\(41\) | −0.905972 | − | 2.78829i | −0.141489 | − | 0.435458i | 0.855054 | − | 0.518539i | \(-0.173524\pi\) |
−0.996543 | + | 0.0830809i | \(0.973524\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.64114i | − | 1.31776i | −0.752247 | − | 0.658881i | \(-0.771030\pi\) | ||
0.752247 | − | 0.658881i | \(-0.228970\pi\) | |||||||
\(44\) | 2.65688 | − | 1.93033i | 0.400539 | − | 0.291009i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.494689 | + | 0.359413i | 0.0729379 | + | 0.0529925i | ||||
\(47\) | 4.06430 | − | 5.59403i | 0.592839 | − | 0.815973i | −0.402190 | − | 0.915556i | \(-0.631751\pi\) |
0.995029 | + | 0.0995832i | \(0.0317509\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.62750 | −1.37536 | ||||||||
\(50\) | 2.30371 | + | 4.43767i | 0.325793 | + | 0.627582i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.15688 | − | 1.67557i | −0.715130 | − | 0.232360i | ||||
\(53\) | −3.99557 | + | 5.49942i | −0.548833 | + | 0.755404i | −0.989853 | − | 0.142093i | \(-0.954617\pi\) |
0.441020 | + | 0.897497i | \(0.354617\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.74794 | − | 5.60205i | 0.640213 | − | 0.755380i | ||||
\(56\) | −3.29892 | + | 2.39680i | −0.440836 | + | 0.320286i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.74759 | + | 3.78173i | 0.360776 | + | 0.496565i | ||||
\(59\) | −4.38081 | − | 13.4828i | −0.570333 | − | 1.75531i | −0.651546 | − | 0.758609i | \(-0.725879\pi\) |
0.0812131 | − | 0.996697i | \(-0.474121\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.88998 | + | 11.9721i | −0.498061 | + | 1.53287i | 0.314070 | + | 0.949400i | \(0.398307\pi\) |
−0.812131 | + | 0.583475i | \(0.801693\pi\) | |||||||
\(62\) | 7.89675 | − | 2.56581i | 1.00289 | − | 0.325858i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.309017 | + | 0.951057i | −0.0386271 | + | 0.118882i | ||||
\(65\) | −12.0907 | − | 0.905395i | −1.49967 | − | 0.112300i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.39169 | + | 8.79741i | 0.780869 | + | 1.07477i | 0.995185 | + | 0.0980099i | \(0.0312477\pi\) |
−0.214316 | + | 0.976764i | \(0.568752\pi\) | |||||||
\(68\) | − | 3.45965i | − | 0.419544i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.89529 | + | 6.95579i | −0.704622 | + | 0.831376i | ||||
\(71\) | −7.33541 | − | 5.32949i | −0.870553 | − | 0.632494i | 0.0601825 | − | 0.998187i | \(-0.480832\pi\) |
−0.930735 | + | 0.365694i | \(0.880832\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.65537 | − | 2.81230i | −1.01303 | − | 0.329155i | −0.244972 | − | 0.969530i | \(-0.578779\pi\) |
−0.768062 | + | 0.640375i | \(0.778779\pi\) | |||||||
\(74\) | 2.40102 | 0.279113 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.63522 | 0.187573 | ||||||||
\(77\) | 12.7360 | + | 4.13818i | 1.45140 | + | 0.471589i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.31375 | − | 2.40758i | −0.372826 | − | 0.270874i | 0.385556 | − | 0.922685i | \(-0.374010\pi\) |
−0.758382 | + | 0.651810i | \(0.774010\pi\) | |||||||
\(80\) | −0.166977 | + | 2.22982i | −0.0186686 | + | 0.249302i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 2.93179i | − | 0.323762i | ||||||
\(83\) | −4.19156 | − | 5.76919i | −0.460083 | − | 0.633250i | 0.514443 | − | 0.857525i | \(-0.327999\pi\) |
−0.974526 | + | 0.224274i | \(0.927999\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.83447 | − | 7.51536i | −0.198977 | − | 0.815155i | ||||
\(86\) | 2.67026 | − | 8.21821i | 0.287942 | − | 0.886193i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.12334 | − | 1.01484i | 0.332950 | − | 0.108182i | ||||
\(89\) | 1.48423 | − | 4.56799i | 0.157328 | − | 0.484206i | −0.841061 | − | 0.540940i | \(-0.818069\pi\) |
0.998389 | + | 0.0567336i | \(0.0180686\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.83245 | − | 21.0281i | −0.716235 | − | 2.20434i | ||||
\(92\) | 0.359413 | + | 0.494689i | 0.0374714 | + | 0.0515749i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.59403 | − | 4.06430i | 0.576980 | − | 0.419200i | ||||
\(95\) | 3.55217 | − | 0.867073i | 0.364445 | − | 0.0889599i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.67557 | − | 11.9409i | 0.880871 | − | 1.21241i | −0.0953083 | − | 0.995448i | \(-0.530384\pi\) |
0.976179 | − | 0.216967i | \(-0.0696163\pi\) | |||||||
\(98\) | −9.15630 | − | 2.97506i | −0.924926 | − | 0.300527i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.819639 | + | 4.93236i | 0.0819639 | + | 0.493236i | ||||
\(101\) | 11.4846 | 1.14276 | 0.571381 | − | 0.820685i | \(-0.306408\pi\) | ||||
0.571381 | + | 0.820685i | \(0.306408\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.20248 | + | 11.2897i | −0.808214 | + | 1.11241i | 0.183382 | + | 0.983042i | \(0.441295\pi\) |
−0.991596 | + | 0.129370i | \(0.958705\pi\) | |||||||
\(104\) | −4.38670 | − | 3.18712i | −0.430151 | − | 0.312523i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.49942 | + | 3.99557i | −0.534151 | + | 0.388084i | ||||
\(107\) | 8.35405i | 0.807616i | 0.914844 | + | 0.403808i | \(0.132314\pi\) | ||||
−0.914844 | + | 0.403808i | \(0.867686\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.164593 | − | 0.506564i | −0.0157651 | − | 0.0485201i | 0.942864 | − | 0.333176i | \(-0.108120\pi\) |
−0.958630 | + | 0.284656i | \(0.908120\pi\) | |||||||
\(110\) | 6.24669 | − | 3.86067i | 0.595598 | − | 0.368100i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.87811 | + | 1.26007i | −0.366447 | + | 0.119066i | ||||
\(113\) | −16.3840 | + | 5.32350i | −1.54128 | + | 0.500792i | −0.951729 | − | 0.306938i | \(-0.900695\pi\) |
−0.589551 | + | 0.807731i | \(0.700695\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.04306 | + | 0.884029i | 0.0972655 | + | 0.0824362i | ||||
\(116\) | 1.44449 | + | 4.44569i | 0.134118 | + | 0.412772i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 14.1766i | − | 1.30506i | ||||||
\(119\) | 11.4131 | − | 8.29210i | 1.04624 | − | 0.760135i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.173797 | + | 0.126271i | 0.0157997 | + | 0.0114792i | ||||
\(122\) | −7.39919 | + | 10.1841i | −0.669891 | + | 0.922026i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.30313 | 0.745643 | ||||||||
\(125\) | 4.39587 | + | 10.2799i | 0.393179 | + | 0.919462i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.09148 | − | 0.354643i | −0.0968532 | − | 0.0314695i | 0.260190 | − | 0.965558i | \(-0.416215\pi\) |
−0.357043 | + | 0.934088i | \(0.616215\pi\) | |||||||
\(128\) | −0.587785 | + | 0.809017i | −0.0519534 | + | 0.0715077i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.2191 | − | 4.59731i | −0.983984 | − | 0.403211i | ||||
\(131\) | −5.35494 | + | 3.89059i | −0.467864 | + | 0.339923i | −0.796608 | − | 0.604496i | \(-0.793374\pi\) |
0.328745 | + | 0.944419i | \(0.393374\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.91930 | + | 5.39445i | 0.339846 | + | 0.467758i | ||||
\(134\) | 3.36031 | + | 10.3420i | 0.290287 | + | 0.893410i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.06909 | − | 3.29032i | 0.0916738 | − | 0.282143i | ||||
\(137\) | 7.05850 | − | 2.29345i | 0.603049 | − | 0.195942i | 0.00844901 | − | 0.999964i | \(-0.497311\pi\) |
0.594600 | + | 0.804022i | \(0.297311\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.63798 | + | 5.04119i | −0.138932 | + | 0.427588i | −0.996181 | − | 0.0873138i | \(-0.972172\pi\) |
0.857249 | + | 0.514902i | \(0.172172\pi\) | |||||||
\(140\) | −7.75621 | + | 4.79360i | −0.655520 | + | 0.405134i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.32949 | − | 7.33541i | −0.447240 | − | 0.615574i | ||||
\(143\) | 17.8071i | 1.48911i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.49517 | + | 8.89138i | 0.456349 | + | 0.738389i | ||||
\(146\) | −7.36269 | − | 5.34931i | −0.609341 | − | 0.442712i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.28350 | + | 0.741955i | 0.187703 | + | 0.0609883i | ||||
\(149\) | −4.79296 | −0.392655 | −0.196327 | − | 0.980538i | \(-0.562902\pi\) | ||||
−0.196327 | + | 0.980538i | \(0.562902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.93533 | 0.564389 | 0.282195 | − | 0.959357i | \(-0.408938\pi\) | ||||
0.282195 | + | 0.959357i | \(0.408938\pi\) | |||||||
\(152\) | 1.55519 | + | 0.505311i | 0.126142 | + | 0.0409861i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.8339 | + | 7.87129i | 0.873020 | + | 0.634286i | ||||
\(155\) | 18.0368 | − | 4.40272i | 1.44875 | − | 0.353635i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.51609i | − | 0.599849i | −0.953963 | − | 0.299925i | \(-0.903038\pi\) | ||
0.953963 | − | 0.299925i | \(-0.0969615\pi\) | |||||||
\(158\) | −2.40758 | − | 3.31375i | −0.191537 | − | 0.263628i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.847859 | + | 2.06909i | −0.0670291 | + | 0.163576i | ||||
\(161\) | −0.770497 | + | 2.37134i | −0.0607236 | + | 0.186888i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.95766 | − | 2.58560i | 0.623292 | − | 0.202520i | 0.0196905 | − | 0.999806i | \(-0.493732\pi\) |
0.603601 | + | 0.797286i | \(0.293732\pi\) | |||||||
\(164\) | 0.905972 | − | 2.78829i | 0.0707445 | − | 0.217729i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.20363 | − | 6.78209i | −0.171035 | − | 0.526392i | ||||
\(167\) | −5.25731 | − | 7.23607i | −0.406823 | − | 0.559944i | 0.555617 | − | 0.831438i | \(-0.312482\pi\) |
−0.962440 | + | 0.271495i | \(0.912482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.2686 | − | 9.64021i | 1.02066 | − | 0.741555i | ||||
\(170\) | 0.577684 | − | 7.71441i | 0.0443063 | − | 0.591668i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.07914 | − | 6.99083i | 0.387280 | − | 0.533046i | ||||
\(173\) | 2.22457 | + | 0.722807i | 0.169131 | + | 0.0549540i | 0.392358 | − | 0.919812i | \(-0.371659\pi\) |
−0.223228 | + | 0.974766i | \(0.571659\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.3069 | + | 14.5258i | −1.08150 | + | 1.09805i | ||||
\(176\) | 3.28408 | 0.247547 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.82318 | − | 3.88577i | 0.211606 | − | 0.291251i | ||||
\(179\) | −4.87811 | − | 3.54415i | −0.364607 | − | 0.264902i | 0.390364 | − | 0.920661i | \(-0.372349\pi\) |
−0.754971 | + | 0.655758i | \(0.772349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.4112 | + | 9.74379i | −0.996844 | + | 0.724250i | −0.961409 | − | 0.275122i | \(-0.911282\pi\) |
−0.0354351 | + | 0.999372i | \(0.511282\pi\) | |||||||
\(182\) | − | 22.1103i | − | 1.63892i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.188954 | + | 0.581542i | 0.0139299 | + | 0.0428718i | ||||
\(185\) | 5.35385 | + | 0.400916i | 0.393623 | + | 0.0294759i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.8057 | + | 3.51098i | −0.790189 | + | 0.256748i | ||||
\(188\) | 6.57617 | − | 2.13673i | 0.479617 | − | 0.155837i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.64625 | + | 0.273045i | 0.264527 | + | 0.0198088i | ||||
\(191\) | −3.08029 | − | 9.48015i | −0.222882 | − | 0.685960i | −0.998500 | − | 0.0547570i | \(-0.982562\pi\) |
0.775618 | − | 0.631203i | \(-0.217438\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.0735i | 1.80483i | 0.430867 | + | 0.902416i | \(0.358208\pi\) | ||||
−0.430867 | + | 0.902416i | \(0.641792\pi\) | |||||||
\(194\) | 11.9409 | − | 8.67557i | 0.857307 | − | 0.622870i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.78881 | − | 5.65890i | −0.556344 | − | 0.404207i | ||||
\(197\) | −15.7749 | + | 21.7123i | −1.12391 | + | 1.54694i | −0.324773 | + | 0.945792i | \(0.605288\pi\) |
−0.799141 | + | 0.601143i | \(0.794712\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.06114 | 0.287887 | 0.143943 | − | 0.989586i | \(-0.454022\pi\) | ||||
0.143943 | + | 0.989586i | \(0.454022\pi\) | |||||||
\(200\) | −0.744661 | + | 4.94424i | −0.0526555 | + | 0.349610i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.9225 | + | 3.54894i | 0.768506 | + | 0.249703i | ||||
\(203\) | −11.2038 | + | 15.4207i | −0.786352 | + | 1.08232i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.489542 | − | 6.53737i | 0.0341911 | − | 0.456590i | ||||
\(206\) | −11.2897 | + | 8.20248i | −0.786594 | + | 0.571494i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.18712 | − | 4.38670i | −0.220987 | − | 0.304163i | ||||
\(209\) | −1.65948 | − | 5.10736i | −0.114789 | − | 0.353283i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.34573 | + | 4.14173i | −0.0926438 | + | 0.285128i | −0.986632 | − | 0.162961i | \(-0.947895\pi\) |
0.893989 | + | 0.448090i | \(0.147895\pi\) | |||||||
\(212\) | −6.46496 | + | 2.10059i | −0.444015 | + | 0.144269i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.58154 | + | 7.94517i | −0.176471 | + | 0.543121i | ||||
\(215\) | 7.32647 | − | 17.8793i | 0.499661 | − | 1.21936i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.9010 | + | 27.3913i | 1.35097 | + | 1.85944i | ||||
\(218\) | − | 0.532633i | − | 0.0360745i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.13397 | − | 1.74138i | 0.480972 | − | 0.117404i | ||||
\(221\) | 15.1764 | + | 11.0263i | 1.02088 | + | 0.741711i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.344164 | − | 0.111826i | −0.0230469 | − | 0.00748840i | 0.297471 | − | 0.954731i | \(-0.403857\pi\) |
−0.320518 | + | 0.947243i | \(0.603857\pi\) | |||||||
\(224\) | −4.07768 | −0.272452 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17.2272 | −1.14594 | ||||||||
\(227\) | 12.2284 | + | 3.97323i | 0.811624 | + | 0.263713i | 0.685286 | − | 0.728274i | \(-0.259677\pi\) |
0.126339 | + | 0.991987i | \(0.459677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.3769 | − | 9.71886i | −0.883968 | − | 0.642240i | 0.0503302 | − | 0.998733i | \(-0.483973\pi\) |
−0.934298 | + | 0.356492i | \(0.883973\pi\) | |||||||
\(230\) | 0.718826 | + | 1.16308i | 0.0473980 | + | 0.0766915i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.67447i | 0.306894i | ||||||||
\(233\) | −6.50714 | − | 8.95631i | −0.426297 | − | 0.586747i | 0.540801 | − | 0.841150i | \(-0.318121\pi\) |
−0.967098 | + | 0.254403i | \(0.918121\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.1523 | − | 8.12860i | 0.857965 | − | 0.530251i | ||||
\(236\) | 4.38081 | − | 13.4828i | 0.285167 | − | 0.877653i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.4169 | − | 4.35941i | 0.869688 | − | 0.282579i | ||||
\(239\) | −1.72654 | + | 5.31375i | −0.111681 | + | 0.343718i | −0.991240 | − | 0.132071i | \(-0.957837\pi\) |
0.879560 | + | 0.475789i | \(0.157837\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.59014 | − | 14.1270i | −0.295677 | − | 0.909999i | −0.982993 | − | 0.183641i | \(-0.941212\pi\) |
0.687317 | − | 0.726358i | \(-0.258788\pi\) | |||||||
\(242\) | 0.126271 | + | 0.173797i | 0.00811700 | + | 0.0111721i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.1841 | + | 7.39919i | −0.651971 | + | 0.473684i | ||||
\(245\) | −19.9202 | − | 8.16276i | −1.27265 | − | 0.521500i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.21165 | + | 7.17322i | −0.331609 | + | 0.456421i | ||||
\(248\) | 7.89675 | + | 2.56581i | 0.501444 | + | 0.162929i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00406 | + | 11.1352i | 0.0635021 | + | 0.704250i | ||||
\(251\) | 12.6802 | 0.800368 | 0.400184 | − | 0.916435i | \(-0.368946\pi\) | ||||
0.400184 | + | 0.916435i | \(0.368946\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.18034 | − | 1.62460i | 0.0742073 | − | 0.102138i | ||||
\(254\) | −0.928468 | − | 0.674572i | −0.0582573 | − | 0.0423264i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 19.1916i | 1.19714i | 0.801071 | + | 0.598570i | \(0.204264\pi\) | ||||
−0.801071 | + | 0.598570i | \(0.795736\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.02546 | + | 9.31140i | 0.187993 | + | 0.578582i | ||||
\(260\) | −9.24940 | − | 7.83921i | −0.573623 | − | 0.486167i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.29511 | + | 2.04541i | −0.388913 | + | 0.126366i | ||||
\(263\) | 28.0323 | − | 9.10825i | 1.72855 | − | 0.561639i | 0.735309 | − | 0.677732i | \(-0.237037\pi\) |
0.993238 | + | 0.116093i | \(0.0370372\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.9299 | + | 7.99113i | −0.794279 | + | 0.490891i | ||||
\(266\) | 2.06050 | + | 6.34156i | 0.126337 | + | 0.388826i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.8742i | 0.664247i | ||||||||
\(269\) | −17.7191 | + | 12.8737i | −1.08035 | + | 0.784922i | −0.977744 | − | 0.209800i | \(-0.932719\pi\) |
−0.102608 | + | 0.994722i | \(0.532719\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.2025 | + | 8.86562i | 0.741248 | + | 0.538548i | 0.893102 | − | 0.449855i | \(-0.148524\pi\) |
−0.151854 | + | 0.988403i | \(0.548524\pi\) | |||||||
\(272\) | 2.03353 | − | 2.79892i | 0.123301 | − | 0.169709i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.42175 | 0.448364 | ||||||||
\(275\) | 14.5737 | − | 7.56555i | 0.878825 | − | 0.456220i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.45721 | − | 0.798395i | −0.147639 | − | 0.0479709i | 0.234265 | − | 0.972173i | \(-0.424732\pi\) |
−0.381904 | + | 0.924202i | \(0.624732\pi\) | |||||||
\(278\) | −3.11563 | + | 4.28829i | −0.186863 | + | 0.257195i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.85790 | + | 2.16219i | −0.529361 | + | 0.129215i | ||||
\(281\) | −14.8843 | + | 10.8141i | −0.887923 | + | 0.645113i | −0.935336 | − | 0.353762i | \(-0.884902\pi\) |
0.0474130 | + | 0.998875i | \(0.484902\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.04234 | + | 2.81105i | 0.121405 | + | 0.167099i | 0.865394 | − | 0.501093i | \(-0.167068\pi\) |
−0.743989 | + | 0.668192i | \(0.767068\pi\) | |||||||
\(284\) | −2.80188 | − | 8.62329i | −0.166261 | − | 0.511698i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.50271 | + | 16.9356i | −0.325382 | + | 1.00142i | ||||
\(287\) | 11.3698 | − | 3.69427i | 0.671137 | − | 0.218066i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.55461 | − | 4.78460i | 0.0914477 | − | 0.281447i | ||||
\(290\) | 2.47863 | + | 10.1543i | 0.145550 | + | 0.596281i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.34931 | − | 7.36269i | −0.313045 | − | 0.430869i | ||||
\(293\) | − | 15.8625i | − | 0.926699i | −0.886176 | − | 0.463349i | \(-0.846647\pi\) | ||
0.886176 | − | 0.463349i | \(-0.153353\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.36717 | − | 31.6114i | 0.137822 | − | 1.84048i | ||||
\(296\) | 1.94246 | + | 1.41128i | 0.112903 | + | 0.0820291i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.55838 | − | 1.48111i | −0.264060 | − | 0.0857982i | ||||
\(299\) | −3.31555 | −0.191743 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 35.2358 | 2.03096 | ||||||||
\(302\) | 6.59589 | + | 2.14314i | 0.379551 | + | 0.123324i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.32292 | + | 0.961158i | 0.0758747 | + | 0.0551262i | ||||
\(305\) | −18.1994 | + | 21.4733i | −1.04210 | + | 1.22956i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.4122i | 1.45035i | 0.688565 | + | 0.725175i | \(0.258241\pi\) | ||||
−0.688565 | + | 0.725175i | \(0.741759\pi\) | |||||||
\(308\) | 7.87129 | + | 10.8339i | 0.448508 | + | 0.617319i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18.5145 | + | 1.38644i | 1.05155 | + | 0.0787443i | ||||
\(311\) | −5.69968 | + | 17.5418i | −0.323199 | + | 0.994704i | 0.649048 | + | 0.760748i | \(0.275167\pi\) |
−0.972247 | + | 0.233957i | \(0.924833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.8396 | − | 6.77121i | 1.17793 | − | 0.382731i | 0.346330 | − | 0.938113i | \(-0.387428\pi\) |
0.831596 | + | 0.555381i | \(0.187428\pi\) | |||||||
\(314\) | 2.32260 | − | 7.14823i | 0.131072 | − | 0.403398i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.26574 | − | 3.89555i | −0.0712035 | − | 0.219142i | ||||
\(317\) | 3.40134 | + | 4.68155i | 0.191039 | + | 0.262942i | 0.893782 | − | 0.448501i | \(-0.148042\pi\) |
−0.702744 | + | 0.711443i | \(0.748042\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4195 | − | 9.02329i | 0.695358 | − | 0.505207i | ||||
\(320\) | −1.44575 | + | 1.70582i | −0.0808196 | + | 0.0953582i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.46557 | + | 2.01719i | −0.0816731 | + | 0.112413i | ||||
\(323\) | −5.38040 | − | 1.74820i | −0.299374 | − | 0.0972724i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.2491 | − | 12.1245i | −1.34510 | − | 0.672549i | ||||
\(326\) | 8.36717 | 0.463415 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.72326 | − | 2.37186i | 0.0951511 | − | 0.130964i | ||||
\(329\) | 22.8107 | + | 16.5729i | 1.25759 | + | 0.913695i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.18384 | − | 4.49282i | 0.339895 | − | 0.246948i | −0.404723 | − | 0.914439i | \(-0.632632\pi\) |
0.744617 | + | 0.667492i | \(0.232632\pi\) | |||||||
\(332\) | − | 7.13111i | − | 0.391370i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.76393 | − | 8.50651i | −0.151236 | − | 0.465455i | ||||
\(335\) | 5.76603 | + | 23.6219i | 0.315032 | + | 1.29060i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.50849 | − | 1.13998i | 0.191119 | − | 0.0620985i | −0.211893 | − | 0.977293i | \(-0.567963\pi\) |
0.403013 | + | 0.915194i | \(0.367963\pi\) | |||||||
\(338\) | 15.5982 | − | 5.06816i | 0.848430 | − | 0.275671i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.93329 | − | 7.15833i | 0.159080 | − | 0.388215i | ||||
\(341\) | −8.42632 | − | 25.9335i | −0.456311 | − | 1.40438i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 10.7141i | − | 0.578508i | ||||||
\(344\) | 6.99083 | − | 5.07914i | 0.376920 | − | 0.273849i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.89233 | + | 1.37486i | 0.101732 | + | 0.0739129i | ||||
\(347\) | 2.13673 | − | 2.94095i | 0.114706 | − | 0.157879i | −0.747804 | − | 0.663920i | \(-0.768892\pi\) |
0.862509 | + | 0.506041i | \(0.168892\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.2270 | −0.654496 | −0.327248 | − | 0.944938i | \(-0.606121\pi\) | ||||
−0.327248 | + | 0.944938i | \(0.606121\pi\) | |||||||
\(350\) | −18.0954 | + | 9.39378i | −0.967241 | + | 0.502119i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.12334 | + | 1.01484i | 0.166475 | + | 0.0540910i | ||||
\(353\) | 9.20711 | − | 12.6725i | 0.490045 | − | 0.674489i | −0.490351 | − | 0.871525i | \(-0.663132\pi\) |
0.980396 | + | 0.197036i | \(0.0631316\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.6590 | − | 17.2466i | −0.565719 | − | 0.915353i | ||||
\(356\) | 3.88577 | − | 2.82318i | 0.205945 | − | 0.149628i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.54415 | − | 4.87811i | −0.187314 | − | 0.257816i | ||||
\(359\) | 2.18529 | + | 6.72564i | 0.115335 | + | 0.354966i | 0.992017 | − | 0.126105i | \(-0.0402478\pi\) |
−0.876681 | + | 0.481071i | \(0.840248\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.04503 | + | 15.5270i | −0.265528 | + | 0.817211i | ||||
\(362\) | −15.7658 | + | 5.12261i | −0.828631 | + | 0.269238i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.83245 | − | 21.0281i | 0.358117 | − | 1.10217i | ||||
\(365\) | −15.5243 | − | 13.1574i | −0.812579 | − | 0.688691i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.7219 | − | 21.6393i | −0.820676 | − | 1.12956i | −0.989588 | − | 0.143932i | \(-0.954025\pi\) |
0.168912 | − | 0.985631i | \(-0.445975\pi\) | |||||||
\(368\) | 0.611469i | 0.0318751i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.96792 | + | 2.03572i | 0.258270 | + | 0.105832i | ||||
\(371\) | −22.4249 | − | 16.2927i | −1.16424 | − | 0.845872i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.3031 | − | 3.67261i | −0.585254 | − | 0.190161i | 0.00139899 | − | 0.999999i | \(-0.499555\pi\) |
−0.586653 | + | 0.809839i | \(0.699555\pi\) | |||||||
\(374\) | −11.3618 | −0.587503 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.91460 | 0.356593 | ||||||||
\(377\) | −24.1057 | − | 7.83241i | −1.24151 | − | 0.403390i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.90398 | − | 2.83641i | −0.200534 | − | 0.145696i | 0.482987 | − | 0.875628i | \(-0.339552\pi\) |
−0.683520 | + | 0.729931i | \(0.739552\pi\) | |||||||
\(380\) | 3.38342 | + | 1.38644i | 0.173566 | + | 0.0711226i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 9.96802i | − | 0.510008i | ||||||
\(383\) | 2.82343 | + | 3.88612i | 0.144271 | + | 0.198572i | 0.875037 | − | 0.484056i | \(-0.160837\pi\) |
−0.730766 | + | 0.682628i | \(0.760837\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 22.8434 | + | 19.3606i | 1.16421 | + | 0.986708i | ||||
\(386\) | −7.74814 | + | 23.8463i | −0.394370 | + | 1.21375i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.0374 | − | 4.56102i | 0.712639 | − | 0.231551i | ||||
\(389\) | −4.15372 | + | 12.7838i | −0.210602 | + | 0.648166i | 0.788835 | + | 0.614605i | \(0.210685\pi\) |
−0.999437 | + | 0.0335605i | \(0.989315\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.653716 | − | 2.01193i | −0.0330599 | − | 0.101748i | ||||
\(392\) | −5.65890 | − | 7.78881i | −0.285818 | − | 0.393394i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.7123 | + | 15.7749i | −1.09385 | + | 0.794727i | ||||
\(395\) | −4.81516 | − | 7.79110i | −0.242277 | − | 0.392013i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.0509156 | + | 0.0700793i | −0.00255538 | + | 0.00351718i | −0.810293 | − | 0.586025i | \(-0.800692\pi\) |
0.807737 | + | 0.589542i | \(0.200692\pi\) | |||||||
\(398\) | 3.86237 | + | 1.25496i | 0.193603 | + | 0.0629055i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.23607 | + | 4.47214i | −0.111803 | + | 0.223607i | ||||
\(401\) | −0.321141 | −0.0160370 | −0.00801851 | − | 0.999968i | \(-0.502552\pi\) | ||||
−0.00801851 | + | 0.999968i | \(0.502552\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.4631 | + | 36.4233i | −1.31822 | + | 1.81438i | ||||
\(404\) | 9.29125 | + | 6.75049i | 0.462257 | + | 0.335850i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.4207 | + | 11.2038i | −0.765316 | + | 0.556035i | ||||
\(407\) | − | 7.88513i | − | 0.390851i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.48890 | − | 23.0485i | −0.370302 | − | 1.13967i | −0.946594 | − | 0.322429i | \(-0.895501\pi\) |
0.576291 | − | 0.817244i | \(-0.304499\pi\) | |||||||
\(410\) | 2.48574 | − | 6.06613i | 0.122762 | − | 0.299585i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.2719 | + | 4.31230i | −0.653859 | + | 0.212452i | ||||
\(413\) | 54.9784 | − | 17.8636i | 2.70531 | − | 0.879009i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.78126 | − | 15.4908i | −0.185615 | − | 0.760414i | ||||
\(416\) | −1.67557 | − | 5.15688i | −0.0821516 | − | 0.252837i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 5.37019i | − | 0.262665i | ||||||
\(419\) | −18.4661 | + | 13.4164i | −0.902128 | + | 0.655434i | −0.939012 | − | 0.343885i | \(-0.888257\pi\) |
0.0368836 | + | 0.999320i | \(0.488257\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.6567 | + | 22.9999i | 1.54285 | + | 1.12095i | 0.948514 | + | 0.316734i | \(0.102586\pi\) |
0.594339 | + | 0.804215i | \(0.297414\pi\) | |||||||
\(422\) | −2.55973 | + | 3.52316i | −0.124606 | + | 0.171505i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.79766 | −0.330124 | ||||||||
\(425\) | 2.57627 | − | 17.1053i | 0.124967 | − | 0.829730i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −48.8186 | − | 15.8621i | −2.36250 | − | 0.767622i | ||||
\(428\) | −4.91038 | + | 6.75856i | −0.237352 | + | 0.326688i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.4929 | − | 14.7402i | 0.602461 | − | 0.710837i | ||||
\(431\) | 19.9676 | − | 14.5073i | 0.961806 | − | 0.698793i | 0.00823646 | − | 0.999966i | \(-0.497378\pi\) |
0.953569 | + | 0.301173i | \(0.0973782\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.6839 | − | 16.0815i | −0.561493 | − | 0.772829i | 0.430023 | − | 0.902818i | \(-0.358506\pi\) |
−0.991515 | + | 0.129990i | \(0.958506\pi\) | |||||||
\(434\) | 10.4626 | + | 32.2004i | 0.502219 | + | 1.54567i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.164593 | − | 0.506564i | 0.00788256 | − | 0.0242600i | ||||
\(437\) | 0.950949 | − | 0.308982i | 0.0454901 | − | 0.0147806i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.56742 | + | 4.82402i | −0.0748088 | + | 0.230238i | −0.981468 | − | 0.191626i | \(-0.938624\pi\) |
0.906659 | + | 0.421864i | \(0.138624\pi\) | |||||||
\(440\) | 7.32292 | + | 0.548367i | 0.349107 | + | 0.0261424i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.0263 | + | 15.1764i | 0.524469 | + | 0.721870i | ||||
\(443\) | − | 10.1873i | − | 0.484015i | −0.970274 | − | 0.242008i | \(-0.922194\pi\) | ||
0.970274 | − | 0.242008i | \(-0.0778059\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.94402 | − | 8.19318i | 0.329178 | − | 0.388394i | ||||
\(446\) | −0.292763 | − | 0.212705i | −0.0138627 | − | 0.0100719i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.87811 | − | 1.26007i | −0.183223 | − | 0.0595329i | ||||
\(449\) | 10.3653 | 0.489169 | 0.244585 | − | 0.969628i | \(-0.421348\pi\) | ||||
0.244585 | + | 0.969628i | \(0.421348\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.62822 | −0.453375 | ||||||||
\(452\) | −16.3840 | − | 5.32350i | −0.770640 | − | 0.250396i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.4021 | + | 7.55754i | 0.488193 | + | 0.354693i | ||||
\(455\) | 3.69192 | − | 49.3020i | 0.173080 | − | 2.31131i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.06165i | 0.189996i | 0.995477 | + | 0.0949980i | \(0.0302845\pi\) | ||||
−0.995477 | + | 0.0949980i | \(0.969716\pi\) | |||||||
\(458\) | −9.71886 | − | 13.3769i | −0.454133 | − | 0.625060i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.324231 | + | 1.32829i | 0.0151173 | + | 0.0619317i | ||||
\(461\) | −2.08929 | + | 6.43019i | −0.0973081 | + | 0.299484i | −0.987848 | − | 0.155421i | \(-0.950327\pi\) |
0.890540 | + | 0.454905i | \(0.150327\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.24602 | − | 3.00421i | 0.429699 | − | 0.139618i | −0.0861791 | − | 0.996280i | \(-0.527466\pi\) |
0.515878 | + | 0.856662i | \(0.327466\pi\) | |||||||
\(464\) | −1.44449 | + | 4.44569i | −0.0670589 | + | 0.206386i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.42101 | − | 10.5288i | −0.158475 | − | 0.487736i | ||||
\(467\) | −22.5722 | − | 31.0679i | −1.04452 | − | 1.43765i | −0.893469 | − | 0.449125i | \(-0.851736\pi\) |
−0.151046 | − | 0.988527i | \(-0.548264\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −35.8730 | + | 26.0633i | −1.65646 | + | 1.20349i | ||||
\(470\) | 15.0205 | − | 3.66646i | 0.692844 | − | 0.169121i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.33280 | − | 11.4691i | 0.383548 | − | 0.527909i | ||||
\(473\) | −26.9893 | − | 8.76934i | −1.24097 | − | 0.403215i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.08492 | + | 1.21768i | 0.370961 | + | 0.0558712i | ||||
\(476\) | 14.1074 | 0.646610 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.28408 | + | 4.52015i | −0.150210 | + | 0.206747i | ||||
\(479\) | −6.85832 | − | 4.98286i | −0.313364 | − | 0.227673i | 0.419974 | − | 0.907536i | \(-0.362039\pi\) |
−0.733339 | + | 0.679863i | \(0.762039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5325 | + | 7.65234i | −0.480243 | + | 0.348917i | ||||
\(482\) | − | 14.8540i | − | 0.676581i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.0663845 | + | 0.204311i | 0.00301748 | + | 0.00928684i | ||||
\(485\) | 28.0747 | − | 17.3511i | 1.27481 | − | 0.787875i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.5559 | − | 8.95344i | 1.24868 | − | 0.405719i | 0.391229 | − | 0.920293i | \(-0.372050\pi\) |
0.857446 | + | 0.514574i | \(0.172050\pi\) | |||||||
\(488\) | −11.9721 | + | 3.88998i | −0.541953 | + | 0.176091i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.4228 | − | 13.9189i | −0.741906 | − | 0.628793i | ||||
\(491\) | 3.16018 | + | 9.72603i | 0.142617 | + | 0.438930i | 0.996697 | − | 0.0812121i | \(-0.0258791\pi\) |
−0.854080 | + | 0.520142i | \(0.825879\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 16.1720i | − | 0.728352i | ||||||
\(494\) | −7.17322 | + | 5.21165i | −0.322738 | + | 0.234483i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.71737 | + | 4.88046i | 0.301619 | + | 0.219139i | ||||
\(497\) | 21.7320 | − | 29.9115i | 0.974811 | − | 1.34171i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0007 | 1.02965 | 0.514827 | − | 0.857294i | \(-0.327856\pi\) | ||||
0.514827 | + | 0.857294i | \(0.327856\pi\) | |||||||
\(500\) | −2.48604 | + | 10.9004i | −0.111179 | + | 0.487483i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0596 | + | 3.91840i | 0.538246 | + | 0.174887i | ||||
\(503\) | −11.1980 | + | 15.4127i | −0.499293 | + | 0.687217i | −0.982068 | − | 0.188527i | \(-0.939629\pi\) |
0.482775 | + | 0.875744i | \(0.339629\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.7627 | + | 9.73734i | 1.05743 | + | 0.433306i | ||||
\(506\) | 1.62460 | − | 1.18034i | 0.0722222 | − | 0.0524725i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.674572 | − | 0.928468i | −0.0299293 | − | 0.0411941i | ||||
\(509\) | −7.33006 | − | 22.5596i | −0.324899 | − | 0.999937i | −0.971486 | − | 0.237097i | \(-0.923804\pi\) |
0.646587 | − | 0.762840i | \(-0.276196\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.4677 | − | 35.2938i | 0.507300 | − | 1.56131i | ||||
\(512\) | −0.951057 | + | 0.309017i | −0.0420312 | + | 0.0136568i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.93053 | + | 18.2523i | −0.261585 | + | 0.805074i | ||||
\(515\) | −26.5438 | + | 16.4050i | −1.16966 | + | 0.722889i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.3475 | − | 18.3712i | −0.587022 | − | 0.807966i | ||||
\(518\) | 9.79059i | 0.430174i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.37425 | − | 10.3138i | −0.279529 | − | 0.452288i | ||||
\(521\) | 23.6577 | + | 17.1883i | 1.03646 | + | 0.753034i | 0.969592 | − | 0.244728i | \(-0.0786985\pi\) |
0.0668706 | + | 0.997762i | \(0.478699\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.3703 | − | 5.96888i | −0.803278 | − | 0.261001i | −0.121530 | − | 0.992588i | \(-0.538780\pi\) |
−0.681748 | + | 0.731587i | \(0.738780\pi\) | |||||||
\(524\) | −6.61907 | −0.289156 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.4749 | 1.28517 | ||||||||
\(527\) | −27.3200 | − | 8.87680i | −1.19008 | − | 0.386679i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.3049 | − | 13.2993i | −0.795865 | − | 0.578230i | ||||
\(530\) | −14.7665 | + | 3.60445i | −0.641415 | + | 0.156567i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.66791i | 0.289091i | ||||||||
\(533\) | 9.34397 | + | 12.8609i | 0.404732 | + | 0.557066i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.08305 | + | 17.2853i | −0.306227 | + | 0.747308i | ||||
\(536\) | −3.36031 | + | 10.3420i | −0.145143 | + | 0.446705i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.8300 | + | 6.76809i | −0.898047 | + | 0.291793i | ||||
\(539\) | −9.77034 | + | 30.0700i | −0.420838 | + | 1.29521i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.95316 | − | 30.6327i | −0.427920 | − | 1.31700i | −0.900170 | − | 0.435538i | \(-0.856558\pi\) |
0.472250 | − | 0.881464i | \(-0.343442\pi\) | |||||||
\(542\) | 8.86562 | + | 12.2025i | 0.380811 | + | 0.524141i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.79892 | − | 2.03353i | 0.120003 | − | 0.0871869i | ||||
\(545\) | 0.0889378 | − | 1.18768i | 0.00380968 | − | 0.0508746i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.0871 | + | 18.0129i | −0.559564 | + | 0.770174i | −0.991271 | − | 0.131840i | \(-0.957912\pi\) |
0.431707 | + | 0.902014i | \(0.357912\pi\) | |||||||
\(548\) | 7.05850 | + | 2.29345i | 0.301524 | + | 0.0979712i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 16.1983 | − | 2.69176i | 0.690696 | − | 0.114777i | ||||
\(551\) | 7.64379 | 0.325637 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.81736 | − | 13.5124i | 0.417476 | − | 0.574607i | ||||
\(554\) | −2.09023 | − | 1.51864i | −0.0888052 | − | 0.0645208i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.28829 | + | 3.11563i | −0.181864 | + | 0.132132i | ||||
\(557\) | 15.1565i | 0.642202i | 0.947045 | + | 0.321101i | \(0.104053\pi\) | ||||
−0.947045 | + | 0.321101i | \(0.895947\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.4788 | + | 44.5613i | 0.612390 | + | 1.88474i | ||||
\(560\) | −9.09252 | − | 0.680881i | −0.384229 | − | 0.0287725i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.4975 | + | 5.68529i | −0.738089 | + | 0.239820i | ||||
\(563\) | −19.8019 | + | 6.43403i | −0.834551 | + | 0.271162i | −0.694961 | − | 0.719047i | \(-0.744579\pi\) |
−0.139590 | + | 0.990209i | \(0.544579\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.4136 | − | 2.87655i | −1.61607 | − | 0.121018i | ||||
\(566\) | 1.07372 | + | 3.30458i | 0.0451320 | + | 0.138902i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 9.06706i | − | 0.380445i | ||||||
\(569\) | −11.9375 | + | 8.67311i | −0.500446 | + | 0.363596i | −0.809187 | − | 0.587551i | \(-0.800092\pi\) |
0.308741 | + | 0.951146i | \(0.400092\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.08805 | + | 2.97014i | 0.171080 | + | 0.124297i | 0.670030 | − | 0.742334i | \(-0.266281\pi\) |
−0.498951 | + | 0.866630i | \(0.666281\pi\) | |||||||
\(572\) | −10.4668 | + | 14.4063i | −0.437638 | + | 0.602356i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.9549 | 0.498988 | ||||||||
\(575\) | 1.40865 | + | 2.71350i | 0.0587446 | + | 0.113161i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.22817 | + | 1.69873i | 0.217651 | + | 0.0707193i | 0.415813 | − | 0.909450i | \(-0.363497\pi\) |
−0.198162 | + | 0.980169i | \(0.563497\pi\) | |||||||
\(578\) | 2.95704 | − | 4.07002i | 0.122997 | − | 0.169291i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.780532 | + | 10.4233i | −0.0324098 | + | 0.432802i | ||||
\(581\) | 23.5249 | − | 17.0919i | 0.975978 | − | 0.709090i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.1218 | + | 18.0605i | 0.543447 | + | 0.747991i | ||||
\(584\) | −2.81230 | − | 8.65537i | −0.116374 | − | 0.358162i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.90179 | − | 15.0862i | 0.202491 | − | 0.623204i | ||||
\(587\) | −40.3229 | + | 13.1017i | −1.66430 | + | 0.540765i | −0.981767 | − | 0.190088i | \(-0.939123\pi\) |
−0.682535 | + | 0.730853i | \(0.739123\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.19566 | − | 12.9129i | 0.172879 | − | 0.532067i | ||||
\(590\) | 12.0198 | − | 29.3327i | 0.494846 | − | 1.20761i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.41128 | + | 1.94246i | 0.0580033 | + | 0.0798348i | ||||
\(593\) | − | 6.76110i | − | 0.277645i | −0.990317 | − | 0.138822i | \(-0.955668\pi\) | ||
0.990317 | − | 0.138822i | \(-0.0443317\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.6452 | − | 7.48041i | 1.25633 | − | 0.306667i | ||||
\(596\) | −3.87759 | − | 2.81723i | −0.158832 | − | 0.115398i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.15327 | − | 1.02456i | −0.128947 | − | 0.0418974i | ||||
\(599\) | 11.7740 | 0.481074 | 0.240537 | − | 0.970640i | \(-0.422676\pi\) | ||||
0.240537 | + | 0.970640i | \(0.422676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.4353 | 0.915154 | 0.457577 | − | 0.889170i | \(-0.348717\pi\) | ||||
0.457577 | + | 0.889170i | \(0.348717\pi\) | |||||||
\(602\) | 33.5113 | + | 10.8885i | 1.36582 | + | 0.443781i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.61080 | + | 4.07649i | 0.228300 | + | 0.165870i | ||||
\(605\) | 0.252542 | + | 0.408621i | 0.0102673 | + | 0.0166128i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 33.0837i | − | 1.34283i | −0.741083 | − | 0.671413i | \(-0.765688\pi\) | ||
0.741083 | − | 0.671413i | \(-0.234312\pi\) | |||||||
\(608\) | 0.961158 | + | 1.32292i | 0.0389801 | + | 0.0536515i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −23.9443 | + | 14.7984i | −0.969475 | + | 0.599169i | ||||
\(611\) | −11.5859 | + | 35.6577i | −0.468715 | + | 1.44256i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.5411 | − | 4.72470i | 0.587311 | − | 0.190829i | −0.000262331 | − | 1.00000i | \(-0.500084\pi\) |
0.587573 | + | 0.809171i | \(0.300084\pi\) | |||||||
\(614\) | −7.85279 | + | 24.1684i | −0.316913 | + | 0.975358i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.13818 | + | 12.7360i | 0.166732 | + | 0.513149i | ||||
\(617\) | 6.25460 | + | 8.60872i | 0.251801 | + | 0.346574i | 0.916141 | − | 0.400856i | \(-0.131287\pi\) |
−0.664340 | + | 0.747430i | \(0.731287\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.3120 | − | 16.9371i | 0.936987 | − | 0.680761i | −0.0107068 | − | 0.999943i | \(-0.503408\pi\) |
0.947693 | + | 0.319182i | \(0.103408\pi\) | |||||||
\(620\) | 17.1799 | + | 7.03988i | 0.689962 | + | 0.282728i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.8414 | + | 14.9219i | −0.434702 | + | 0.598316i | ||||
\(623\) | 18.6268 | + | 6.05223i | 0.746268 | + | 0.242477i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.379550 | + | 24.9971i | 0.0151820 | + | 0.999885i | ||||
\(626\) | 21.9121 | 0.875783 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.41785 | − | 6.08064i | 0.176291 | − | 0.242644i | ||||
\(629\) | −6.72024 | − | 4.88254i | −0.267954 | − | 0.194680i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.3555 | + | 11.8830i | −0.651102 | + | 0.473053i | −0.863646 | − | 0.504098i | \(-0.831825\pi\) |
0.212544 | + | 0.977151i | \(0.431825\pi\) | |||||||
\(632\) | − | 4.09602i | − | 0.162931i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.78819 | + | 5.50349i | 0.0710182 | + | 0.218572i | ||||
\(635\) | −1.95768 | − | 1.65921i | −0.0776883 | − | 0.0658437i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 49.6478 | − | 16.1316i | 1.96712 | − | 0.639156i | ||||
\(638\) | 14.6000 | − | 4.74383i | 0.578019 | − | 0.187810i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.90211 | + | 1.17557i | −0.0751876 | + | 0.0464685i | ||||
\(641\) | 15.4707 | + | 47.6138i | 0.611055 | + | 1.88063i | 0.448053 | + | 0.894007i | \(0.352118\pi\) |
0.163002 | + | 0.986626i | \(0.447882\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.8080i | − | 0.465660i | −0.972517 | − | 0.232830i | \(-0.925201\pi\) | ||
0.972517 | − | 0.232830i | \(-0.0747986\pi\) | |||||||
\(644\) | −2.01719 | + | 1.46557i | −0.0794883 | + | 0.0577516i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.57684 | − | 3.32527i | −0.180073 | − | 0.130831i | ||||
\(647\) | 17.0969 | − | 23.5319i | 0.672148 | − | 0.925133i | −0.327658 | − | 0.944796i | \(-0.606260\pi\) |
0.999807 | + | 0.0196636i | \(0.00625953\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −46.5571 | −1.82753 | ||||||||
\(650\) | −19.3156 | − | 19.0245i | −0.757619 | − | 0.746202i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.95766 | + | 2.58560i | 0.311646 | + | 0.101260i | ||||
\(653\) | 14.5845 | − | 20.0738i | 0.570735 | − | 0.785549i | −0.421906 | − | 0.906639i | \(-0.638639\pi\) |
0.992642 | + | 0.121090i | \(0.0386389\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.3785 | + | 3.50976i | −0.561816 | + | 0.137137i | ||||
\(656\) | 2.37186 | − | 1.72326i | 0.0926057 | − | 0.0672820i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 16.5729 | + | 22.8107i | 0.646080 | + | 0.889253i | ||||
\(659\) | 5.92361 | + | 18.2310i | 0.230751 | + | 0.710179i | 0.997657 | + | 0.0684190i | \(0.0217955\pi\) |
−0.766906 | + | 0.641760i | \(0.778205\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.1363 | + | 43.5071i | −0.549839 | + | 1.69223i | 0.159359 | + | 0.987221i | \(0.449057\pi\) |
−0.709198 | + | 0.705010i | \(0.750943\pi\) | |||||||
\(662\) | 7.26954 | − | 2.36202i | 0.282539 | − | 0.0918024i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.20363 | − | 6.78209i | 0.0855176 | − | 0.263196i | ||||
\(665\) | 3.53565 | + | 14.4846i | 0.137107 | + | 0.561690i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.68007 | + | 2.31241i | 0.0650524 | + | 0.0895370i | ||||
\(668\) | − | 8.94427i | − | 0.346064i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.81575 | + | 24.2475i | −0.0701484 | + | 0.936764i | ||||
\(671\) | 33.4454 | + | 24.2995i | 1.29115 | + | 0.938072i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.2139 | + | 6.56790i | 0.779189 | + | 0.253174i | 0.671494 | − | 0.741010i | \(-0.265653\pi\) |
0.107695 | + | 0.994184i | \(0.465653\pi\) | |||||||
\(674\) | 3.68904 | 0.142097 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.4009 | 0.630804 | ||||||||
\(677\) | −41.2313 | − | 13.3968i | −1.58465 | − | 0.514883i | −0.621398 | − | 0.783495i | \(-0.713435\pi\) |
−0.963248 | + | 0.268613i | \(0.913435\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 48.6912 | + | 35.3762i | 1.86860 | + | 1.35762i | ||||
\(680\) | 5.00177 | − | 5.90154i | 0.191809 | − | 0.226314i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 27.2681i | − | 1.04415i | ||||||
\(683\) | 9.15838 | + | 12.6054i | 0.350436 | + | 0.482334i | 0.947453 | − | 0.319895i | \(-0.103648\pi\) |
−0.597017 | + | 0.802228i | \(0.703648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.5492 | + | 1.23927i | 0.632313 | + | 0.0473499i | ||||
\(686\) | 3.31085 | − | 10.1897i | 0.126409 | − | 0.389046i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.21821 | − | 2.67026i | 0.313316 | − | 0.101803i | ||||
\(689\) | 11.3900 | − | 35.0547i | 0.433923 | − | 1.33548i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.89660 | + | 24.3032i | 0.300401 | + | 0.924539i | 0.981354 | + | 0.192212i | \(0.0615660\pi\) |
−0.680953 | + | 0.732328i | \(0.738434\pi\) | |||||||
\(692\) | 1.37486 | + | 1.89233i | 0.0522643 | + | 0.0719357i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.94095 | − | 2.13673i | 0.111637 | − | 0.0811091i | ||||
\(695\) | −7.66335 | + | 9.04190i | −0.290688 | + | 0.342979i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.96188 | + | 8.20582i | −0.225822 | + | 0.310818i | ||||
\(698\) | −11.6286 | − | 3.77835i | −0.440148 | − | 0.143013i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −20.1126 | + | 3.34223i | −0.760185 | + | 0.126324i | ||||
\(701\) | −24.7063 | −0.933146 | −0.466573 | − | 0.884483i | \(-0.654511\pi\) | ||||
−0.466573 | + | 0.884483i | \(0.654511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.30776 | − | 3.17636i | 0.0870387 | − | 0.119799i | ||||
\(704\) | 2.65688 | + | 1.93033i | 0.100135 | + | 0.0727522i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.6725 | − | 9.20711i | 0.476936 | − | 0.346514i | ||||
\(707\) | 46.8307i | 1.76125i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.22394 | + | 19.1553i | 0.233745 | + | 0.719393i | 0.997285 | + | 0.0736329i | \(0.0234593\pi\) |
−0.763541 | + | 0.645760i | \(0.776541\pi\) | |||||||
\(710\) | −4.80780 | − | 19.6963i | −0.180433 | − | 0.739188i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.56799 | − | 1.48423i | 0.171193 | − | 0.0556239i | ||||
\(713\) | 4.82862 | − | 1.56891i | 0.180833 | − | 0.0587563i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.0979 | + | 36.8446i | −0.564631 | + | 1.37791i | ||||
\(716\) | −1.86327 | − | 5.73456i | −0.0696337 | − | 0.214311i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.07176i | 0.263916i | ||||||||
\(719\) | 21.0273 | − | 15.2772i | 0.784187 | − | 0.569745i | −0.122046 | − | 0.992524i | \(-0.538945\pi\) |
0.906233 | + | 0.422779i | \(0.138945\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −46.0360 | − | 33.4471i | −1.71447 | − | 1.24564i | ||||
\(722\) | −9.59621 | + | 13.2081i | −0.357134 | + | 0.491553i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.5771 | −0.616084 | ||||||||
\(725\) | 3.83138 | + | 23.0562i | 0.142294 | + | 0.856286i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.6799 | + | 10.6183i | 1.21203 | + | 0.393812i | 0.844173 | − | 0.536071i | \(-0.180092\pi\) |
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(728\) | 12.9961 | − | 17.8876i | 0.481667 | − | 0.662958i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.6986 | − | 17.3107i | −0.395974 | − | 0.640699i | ||||
\(731\) | −24.1858 | + | 17.5720i | −0.894545 | + | 0.649925i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.9570 | + | 26.0920i | 0.700192 | + | 0.963731i | 0.999953 | + | 0.00971697i | \(0.00309306\pi\) |
−0.299761 | + | 0.954014i | \(0.596907\pi\) | |||||||
\(734\) | −8.26549 | − | 25.4385i | −0.305085 | − | 0.938954i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.188954 | + | 0.581542i | −0.00696495 | + | 0.0214359i | ||||
\(737\) | 33.9639 | − | 11.0355i | 1.25107 | − | 0.406499i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.7515 | + | 39.2451i | −0.469071 | + | 1.44365i | 0.384718 | + | 0.923034i | \(0.374299\pi\) |
−0.853789 | + | 0.520619i | \(0.825701\pi\) | |||||||
\(740\) | 4.09570 | + | 3.47126i | 0.150561 | + | 0.127606i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.2927 | − | 22.4249i | −0.598122 | − | 0.823244i | ||||
\(743\) | − | 7.06997i | − | 0.259372i | −0.991555 | − | 0.129686i | \(-0.958603\pi\) | ||
0.991555 | − | 0.129686i | \(-0.0413969\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.91707 | − | 4.06375i | −0.363333 | − | 0.148884i | ||||
\(746\) | −9.61502 | − | 6.98572i | −0.352031 | − | 0.255765i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.8057 | − | 3.51098i | −0.395095 | − | 0.128374i | ||||
\(749\) | −34.0652 | −1.24471 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.57240 | −0.166849 | −0.0834246 | − | 0.996514i | \(-0.526586\pi\) | ||||
−0.0834246 | + | 0.996514i | \(0.526586\pi\) | |||||||
\(752\) | 6.57617 | + | 2.13673i | 0.239808 | + | 0.0779185i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20.5055 | − | 14.8981i | −0.746767 | − | 0.542558i | ||||
\(755\) | 14.3498 | + | 5.88018i | 0.522244 | + | 0.214002i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 21.1871i | − | 0.770058i | −0.922904 | − | 0.385029i | \(-0.874191\pi\) | ||
0.922904 | − | 0.385029i | \(-0.125809\pi\) | |||||||
\(758\) | −2.83641 | − | 3.90398i | −0.103023 | − | 0.141799i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.78939 | + | 2.36411i | 0.101182 | + | 0.0857554i | ||||
\(761\) | 9.84246 | − | 30.2920i | 0.356789 | − | 1.09808i | −0.598176 | − | 0.801365i | \(-0.704108\pi\) |
0.954965 | − | 0.296718i | \(-0.0958923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.06561 | − | 0.671157i | 0.0747801 | − | 0.0242975i | ||||
\(764\) | 3.08029 | − | 9.48015i | 0.111441 | − | 0.342980i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.48437 | + | 4.56841i | 0.0536324 | + | 0.165063i | ||||
\(767\) | 45.1826 | + | 62.1885i | 1.63145 | + | 2.24550i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.38487 | + | 5.36542i | −0.266305 | + | 0.193482i | −0.712922 | − | 0.701243i | \(-0.752629\pi\) |
0.446617 | + | 0.894725i | \(0.352629\pi\) | |||||||
\(770\) | 15.7426 | + | 25.4720i | 0.567323 | + | 0.917948i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.7378 | + | 20.2849i | −0.530427 | + | 0.730069i | ||||
\(773\) | −37.1998 | − | 12.0870i | −1.33798 | − | 0.434738i | −0.449351 | − | 0.893355i | \(-0.648345\pi\) |
−0.888634 | + | 0.458618i | \(0.848345\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 41.0526 | + | 6.18302i | 1.47465 | + | 0.222101i | ||||
\(776\) | 14.7598 | 0.529845 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.90084 | + | 10.8746i | −0.283259 | + | 0.389872i | ||||
\(779\) | −3.87852 | − | 2.81791i | −0.138962 | − | 0.100962i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.0901 | + | 17.5025i | −0.862010 | + | 0.626287i | ||||
\(782\) | − | 2.11547i | − | 0.0756491i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.97506 | − | 9.15630i | −0.106252 | − | 0.327011i | ||||
\(785\) | 6.37258 | − | 15.5515i | 0.227447 | − | 0.555056i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.7764 | + | 8.37524i | −0.918828 | + | 0.298545i | −0.729986 | − | 0.683462i | \(-0.760473\pi\) |
−0.188842 | + | 0.982008i | \(0.560473\pi\) | |||||||
\(788\) | −25.5243 | + | 8.29335i | −0.909266 | + | 0.295438i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.17191 | − | 8.89774i | −0.0772731 | − | 0.316567i | ||||
\(791\) | −21.7075 | − | 66.8089i | −0.771831 | − | 2.37545i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 68.2568i | − | 2.42387i | ||||||
\(794\) | −0.0700793 | + | 0.0509156i | −0.00248702 | + | 0.00180693i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.28553 | + | 2.38708i | 0.116453 | + | 0.0846077i | ||||
\(797\) | 7.78292 | − | 10.7123i | 0.275685 | − | 0.379448i | −0.648614 | − | 0.761118i | \(-0.724651\pi\) |
0.924299 | + | 0.381670i | \(0.124651\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.9221 | −0.846303 | ||||||||
\(800\) | −3.50859 | + | 3.56227i | −0.124047 | + | 0.125945i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.305423 | − | 0.0992381i | −0.0107849 | − | 0.00350422i | ||||
\(803\) | −17.5676 | + | 24.1797i | −0.619946 | + | 0.853282i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.60479 | + | 4.25325i | −0.127052 | + | 0.149908i | ||||
\(806\) | −36.4233 | + | 26.4631i | −1.28296 | + | 0.932123i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.75049 | + | 9.29125i | 0.237481 | + | 0.326865i | ||||
\(809\) | −2.32740 | − | 7.16299i | −0.0818269 | − | 0.251837i | 0.901770 | − | 0.432215i | \(-0.142268\pi\) |
−0.983597 | + | 0.180378i | \(0.942268\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.28844 | + | 25.5092i | −0.291046 | + | 0.895749i | 0.693475 | + | 0.720481i | \(0.256079\pi\) |
−0.984521 | + | 0.175267i | \(0.943921\pi\) | |||||||
\(812\) | −18.1281 | + | 5.89018i | −0.636172 | + | 0.206705i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.43664 | − | 7.49920i | 0.0854042 | − | 0.262847i | ||||
\(815\) | 18.6573 | + | 1.39713i | 0.653538 | + | 0.0489393i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.30550 | − | 11.4315i | −0.290573 | − | 0.399939i | ||||
\(818\) | − | 24.2346i | − | 0.847343i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.23862 | − | 5.00110i | 0.148019 | − | 0.174646i | ||||
\(821\) | 30.1027 | + | 21.8709i | 1.05059 | + | 0.763298i | 0.972325 | − | 0.233634i | \(-0.0750618\pi\) |
0.0782654 | + | 0.996933i | \(0.475062\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.0656 | + | 5.54495i | 0.594870 | + | 0.193285i | 0.590951 | − | 0.806707i | \(-0.298753\pi\) |
0.00391871 | + | 0.999992i | \(0.498753\pi\) | |||||||
\(824\) | −13.9549 | −0.486142 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 57.8077 | 2.01139 | ||||||||
\(827\) | −16.0984 | − | 5.23070i | −0.559798 | − | 0.181889i | 0.0154325 | − | 0.999881i | \(-0.495087\pi\) |
−0.575230 | + | 0.817992i | \(0.695087\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.6780 | + | 30.2809i | 1.44754 | + | 1.05170i | 0.986399 | + | 0.164369i | \(0.0525589\pi\) |
0.461138 | + | 0.887328i | \(0.347441\pi\) | |||||||
\(830\) | 1.19073 | − | 15.9011i | 0.0413310 | − | 0.551936i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.42226i | − | 0.187983i | ||||||
\(833\) | 19.5778 | + | 26.9466i | 0.678331 | + | 0.933643i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.74269 | − | 19.4295i | −0.164128 | − | 0.672387i | ||||
\(836\) | 1.65948 | − | 5.10736i | 0.0573943 | − | 0.176642i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.7082 | + | 7.05342i | −0.749897 | + | 0.243656i | ||||
\(839\) | 6.86327 | − | 21.1230i | 0.236946 | − | 0.729246i | −0.759911 | − | 0.650027i | \(-0.774757\pi\) |
0.996857 | − | 0.0792188i | \(-0.0252426\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.20925 | − | 6.79938i | −0.0761811 | − | 0.234461i | ||||
\(842\) | 22.9999 | + | 31.6567i | 0.792630 | + | 1.09096i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.52316 | + | 2.55973i | −0.121272 | + | 0.0881095i | ||||
\(845\) | 35.6275 | − | 8.69656i | 1.22562 | − | 0.299171i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.514893 | + | 0.708689i | −0.0176919 | + | 0.0243508i | ||||
\(848\) | −6.46496 | − | 2.10059i | −0.222008 | − | 0.0721347i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.73601 | − | 15.4720i | 0.265343 | − | 0.530686i | ||||
\(851\) | 1.46815 | 0.0503275 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.8778 | − | 28.7359i | 0.714843 | − | 0.983897i | −0.284836 | − | 0.958576i | \(-0.591939\pi\) |
0.999679 | − | 0.0253210i | \(-0.00806080\pi\) | |||||||
\(854\) | −41.5276 | − | 30.1715i | −1.42104 | − | 1.03245i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.75856 | + | 4.91038i | −0.231003 | + | 0.167833i | ||||
\(857\) | − | 35.9714i | − | 1.22876i | −0.789010 | − | 0.614380i | \(-0.789406\pi\) | ||
0.789010 | − | 0.614380i | \(-0.210594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.5608 | − | 44.8137i | −0.496809 | − | 1.52902i | −0.814118 | − | 0.580700i | \(-0.802779\pi\) |
0.317308 | − | 0.948322i | \(-0.397221\pi\) | |||||||
\(860\) | 16.4364 | − | 10.1583i | 0.560478 | − | 0.346394i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 23.4733 | − | 7.62695i | 0.799505 | − | 0.259775i | ||||
\(863\) | −38.4902 | + | 12.5062i | −1.31022 | + | 0.425716i | −0.879125 | − | 0.476590i | \(-0.841872\pi\) |
−0.431095 | + | 0.902307i | \(0.641872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.99000 | + | 3.38167i | 0.135664 | + | 0.114980i | ||||
\(866\) | −6.14259 | − | 18.9050i | −0.208734 | − | 0.642417i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 33.8575i | 1.14920i | ||||||||
\(869\) | −10.8826 | + | 7.90669i | −0.369168 | + | 0.268216i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47.7018 | − | 34.6574i | −1.61631 | − | 1.17432i | ||||
\(872\) | 0.313074 | − | 0.430909i | 0.0106020 | − | 0.0145924i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.999887 | 0.0338217 | ||||||||
\(875\) | −41.9182 | + | 17.9250i | −1.41709 | + | 0.605974i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.9166 | − | 4.19687i | −0.436164 | − | 0.141718i | 0.0827012 | − | 0.996574i | \(-0.473645\pi\) |
−0.518865 | + | 0.854856i | \(0.673645\pi\) | |||||||
\(878\) | −2.98141 | + | 4.10355i | −0.100618 | + | 0.138488i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.79506 | + | 2.78444i | 0.229061 | + | 0.0938633i | ||||
\(881\) | 24.3625 | − | 17.7004i | 0.820793 | − | 0.596341i | −0.0961468 | − | 0.995367i | \(-0.530652\pi\) |
0.916939 | + | 0.399026i | \(0.130652\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.80047 | + | 3.85451i | 0.0942433 | + | 0.129715i | 0.853535 | − | 0.521036i | \(-0.174454\pi\) |
−0.759291 | + | 0.650751i | \(0.774454\pi\) | |||||||
\(884\) | 5.79689 | + | 17.8410i | 0.194970 | + | 0.600057i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.14806 | − | 9.68874i | 0.105761 | − | 0.325500i | ||||
\(887\) | −38.4028 | + | 12.4778i | −1.28944 | + | 0.418965i | −0.871896 | − | 0.489692i | \(-0.837109\pi\) |
−0.417545 | + | 0.908656i | \(0.637109\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.44612 | − | 4.45071i | 0.0485014 | − | 0.149272i | ||||
\(890\) | 9.13599 | − | 5.64635i | 0.306239 | − | 0.189266i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.212705 | − | 0.292763i | −0.00712189 | − | 0.00980244i | ||||
\(893\) | − | 11.3069i | − | 0.378371i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.08831 | − | 11.4691i | −0.236936 | − | 0.383370i | ||||
\(896\) | −3.29892 | − | 2.39680i | −0.110209 | − | 0.0800715i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.85800 | + | 3.20306i | 0.328966 | + | 0.106887i | ||||
\(899\) | 38.8128 | 1.29448 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.5175 | 0.783482 | ||||||||
\(902\) | −9.15698 | − | 2.97528i | −0.304894 | − | 0.0990661i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.9371 | − | 10.1259i | −0.463541 | − | 0.336782i | ||||
\(905\) | −36.0103 | + | 8.79000i | −1.19702 | + | 0.292189i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.3227i | 0.741214i | 0.928790 | + | 0.370607i | \(0.120850\pi\) | ||||
−0.928790 | + | 0.370607i | \(0.879150\pi\) | |||||||
\(908\) | 7.55754 | + | 10.4021i | 0.250806 | + | 0.345204i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 18.7464 | − | 45.7481i | 0.621436 | − | 1.51654i | ||||
\(911\) | −0.241832 | + | 0.744283i | −0.00801226 | + | 0.0246592i | −0.954983 | − | 0.296661i | \(-0.904127\pi\) |
0.946970 | + | 0.321321i | \(0.104127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.2729 | + | 7.23691i | −0.737126 | + | 0.239507i | ||||
\(914\) | −1.25512 | + | 3.86286i | −0.0415156 | + | 0.127772i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.10951 | − | 15.7254i | −0.168823 | − | 0.519583i | ||||
\(917\) | −15.8646 | − | 21.8358i | −0.523896 | − | 0.721080i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.59426 | + | 1.15830i | −0.0525897 | + | 0.0382087i | −0.613770 | − | 0.789485i | \(-0.710348\pi\) |
0.561180 | + | 0.827694i | \(0.310348\pi\) | |||||||
\(920\) | −0.102102 | + | 1.36347i | −0.00336619 | + | 0.0449523i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.97407 | + | 5.46984i | −0.130879 | + | 0.180140i | ||||
\(923\) | 46.7577 | + | 15.1925i | 1.53905 | + | 0.500067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.7377 | + | 5.36884i | 0.353053 | + | 0.176526i | ||||
\(926\) | 9.72184 | 0.319480 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.74759 | + | 3.78173i | −0.0901940 | + | 0.124141i | ||||
\(929\) | 19.1823 | + | 13.9368i | 0.629352 | + | 0.457251i | 0.856176 | − | 0.516685i | \(-0.172834\pi\) |
−0.226824 | + | 0.973936i | \(0.572834\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.7364 | + | 9.25355i | −0.417419 | + | 0.303273i | ||||
\(932\) | − | 11.0706i | − | 0.362630i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.8669 | − | 36.5225i | −0.388296 | − | 1.19505i | ||||
\(935\) | −25.3347 | − | 1.89716i | −0.828535 | − | 0.0620437i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.8801 | + | 5.48469i | −0.551450 | + | 0.179177i | −0.571471 | − | 0.820623i | \(-0.693627\pi\) |
0.0200205 | + | 0.999800i | \(0.493627\pi\) | |||||||
\(938\) | −42.1713 | + | 13.7023i | −1.37694 | + | 0.447395i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.4183 | + | 1.15458i | 0.502891 | + | 0.0376583i | ||||
\(941\) | −15.3815 | − | 47.3393i | −0.501422 | − | 1.54322i | −0.806703 | − | 0.590956i | \(-0.798750\pi\) |
0.305281 | − | 0.952262i | \(-0.401250\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.79270i | − | 0.0583783i | ||||||
\(944\) | 11.4691 | − | 8.33280i | 0.373288 | − | 0.271210i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.9584 | − | 16.6803i | −0.746443 | − | 0.542323i | ||||
\(947\) | 2.65398 | − | 3.65289i | 0.0862428 | − | 0.118703i | −0.763716 | − | 0.645553i | \(-0.776627\pi\) |
0.849958 | + | 0.526850i | \(0.176627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49.3469 | 1.60187 | ||||||||
\(950\) | 7.31293 | + | 3.65646i | 0.237263 | + | 0.118631i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.4169 | + | 4.35941i | 0.434844 | + | 0.141289i | ||||
\(953\) | −5.48579 | + | 7.55054i | −0.177702 | + | 0.244586i | −0.888572 | − | 0.458738i | \(-0.848302\pi\) |
0.710869 | + | 0.703324i | \(0.248302\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.66444 | − | 22.2269i | 0.0538599 | − | 0.719247i | ||||
\(956\) | −4.52015 | + | 3.28408i | −0.146192 | + | 0.106215i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.98286 | − | 6.85832i | −0.160989 | − | 0.221582i | ||||
\(959\) | 9.35195 | + | 28.7823i | 0.301990 | + | 0.929430i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.7247 | − | 36.0850i | 0.378217 | − | 1.16403i | ||||
\(962\) | −12.3817 | + | 4.02307i | −0.399204 | + | 0.129709i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.59014 | − | 14.1270i | 0.147838 | − | 0.454999i | ||||
\(965\) | −21.2588 | + | 51.8794i | −0.684345 | + | 1.67006i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.0799 | − | 18.0029i | −0.420620 | − | 0.578934i | 0.545148 | − | 0.838340i | \(-0.316473\pi\) |
−0.965769 | + | 0.259405i | \(0.916473\pi\) | |||||||
\(968\) | 0.214825i | 0.00690473i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 32.0625 | − | 7.82635i | 1.02946 | − | 0.251289i | ||||
\(971\) | 3.55705 | + | 2.58435i | 0.114151 | + | 0.0829357i | 0.643396 | − | 0.765533i | \(-0.277525\pi\) |
−0.529245 | + | 0.848469i | \(0.677525\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.5564 | − | 6.67917i | −0.659007 | − | 0.214124i | ||||
\(974\) | 28.9739 | 0.928385 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.5882 | −0.402940 | ||||||||
\(977\) | 14.1016 | + | 4.58190i | 0.451151 | + | 0.146588i | 0.525775 | − | 0.850624i | \(-0.323775\pi\) |
−0.0746235 | + | 0.997212i | \(0.523775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.7612 | − | 9.27153i | −0.407849 | − | 0.296319i | ||||
\(980\) | −11.3178 | − | 18.3126i | −0.361534 | − | 0.584975i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.2266i | 0.326343i | ||||||||
\(983\) | −10.6096 | − | 14.6028i | −0.338393 | − | 0.465758i | 0.605578 | − | 0.795786i | \(-0.292942\pi\) |
−0.943971 | + | 0.330028i | \(0.892942\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.0486 | + | 31.5498i | −1.62654 | + | 1.00526i | ||||
\(986\) | 4.99744 | − | 15.3805i | 0.159151 | − | 0.489816i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.43263 | + | 2.73993i | −0.268278 | + | 0.0871687i | ||||
\(989\) | 1.63278 | − | 5.02519i | 0.0519195 | − | 0.159792i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.0781 | − | 52.5608i | −0.542502 | − | 1.66965i | −0.726856 | − | 0.686790i | \(-0.759019\pi\) |
0.184353 | − | 0.982860i | \(-0.440981\pi\) | |||||||
\(992\) | 4.88046 | + | 6.71737i | 0.154955 | + | 0.213277i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 29.9115 | − | 21.7320i | 0.948734 | − | 0.689296i | ||||
\(995\) | 8.40287 | + | 3.44327i | 0.266389 | + | 0.109159i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.56346 | + | 13.1630i | −0.302878 | + | 0.416875i | −0.933144 | − | 0.359504i | \(-0.882946\pi\) |
0.630266 | + | 0.776379i | \(0.282946\pi\) | |||||||
\(998\) | 21.8750 | + | 7.10761i | 0.692440 | + | 0.224987i | ||||
\(999\) | 0 | 0 |
(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 | 450.2.l.a.379.2 | 8 | ||
3.2 | odd | 2 | 150.2.h.a.79.1 | yes | 8 | ||
15.2 | even | 4 | 750.2.g.c.601.1 | 8 | |||
15.8 | even | 4 | 750.2.g.e.601.2 | 8 | |||
15.14 | odd | 2 | 750.2.h.c.649.2 | 8 | |||
25.19 | even | 10 | inner | 450.2.l.a.19.2 | 8 | ||
75.8 | even | 20 | 750.2.g.e.151.2 | 8 | |||
75.17 | even | 20 | 750.2.g.c.151.1 | 8 | |||
75.38 | even | 20 | 3750.2.a.m.1.4 | 4 | |||
75.41 | odd | 10 | 3750.2.c.e.1249.4 | 8 | |||
75.44 | odd | 10 | 150.2.h.a.19.1 | ✓ | 8 | ||
75.56 | odd | 10 | 750.2.h.c.349.2 | 8 | |||
75.59 | odd | 10 | 3750.2.c.e.1249.5 | 8 | |||
75.62 | even | 20 | 3750.2.a.o.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.h.a.19.1 | ✓ | 8 | 75.44 | odd | 10 | ||
150.2.h.a.79.1 | yes | 8 | 3.2 | odd | 2 | ||
450.2.l.a.19.2 | 8 | 25.19 | even | 10 | inner | ||
450.2.l.a.379.2 | 8 | 1.1 | even | 1 | trivial | ||
750.2.g.c.151.1 | 8 | 75.17 | even | 20 | |||
750.2.g.c.601.1 | 8 | 15.2 | even | 4 | |||
750.2.g.e.151.2 | 8 | 75.8 | even | 20 | |||
750.2.g.e.601.2 | 8 | 15.8 | even | 4 | |||
750.2.h.c.349.2 | 8 | 75.56 | odd | 10 | |||
750.2.h.c.649.2 | 8 | 15.14 | odd | 2 | |||
3750.2.a.m.1.4 | 4 | 75.38 | even | 20 | |||
3750.2.a.o.1.1 | 4 | 75.62 | even | 20 | |||
3750.2.c.e.1249.4 | 8 | 75.41 | odd | 10 | |||
3750.2.c.e.1249.5 | 8 | 75.59 | odd | 10 |