Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(99,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.u (of order \(18\), degree \(6\), not 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 99.8 | ||
Character | \(\chi\) | \(=\) | 950.99 |
Dual form | 950.2.u.h.499.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.342020 | − | 0.939693i | 0.241845 | − | 0.664463i | ||||
\(3\) | 2.84564 | − | 0.501764i | 1.64293 | − | 0.289693i | 0.725690 | − | 0.688022i | \(-0.241521\pi\) |
0.917243 | + | 0.398328i | \(0.130410\pi\) | |||||||
\(4\) | −0.766044 | − | 0.642788i | −0.383022 | − | 0.321394i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.501764 | − | 2.84564i | 0.204844 | − | 1.16173i | ||||
\(7\) | 3.49580 | + | 2.01830i | 1.32129 | + | 0.762846i | 0.983934 | − | 0.178531i | \(-0.0571346\pi\) |
0.337354 | + | 0.941378i | \(0.390468\pi\) | |||||||
\(8\) | −0.866025 | + | 0.500000i | −0.306186 | + | 0.176777i | ||||
\(9\) | 5.02684 | − | 1.82962i | 1.67561 | − | 0.609873i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.11161 | + | 3.65741i | 0.636674 | + | 1.10275i | 0.986158 | + | 0.165809i | \(0.0530234\pi\) |
−0.349484 | + | 0.936942i | \(0.613643\pi\) | |||||||
\(12\) | −2.50242 | − | 1.44477i | −0.722385 | − | 0.417069i | ||||
\(13\) | −5.44192 | − | 0.959556i | −1.50932 | − | 0.266133i | −0.643092 | − | 0.765789i | \(-0.722349\pi\) |
−0.866224 | + | 0.499656i | \(0.833460\pi\) | |||||||
\(14\) | 3.09222 | − | 2.59468i | 0.826430 | − | 0.693457i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.173648 | + | 0.984808i | 0.0434120 | + | 0.246202i | ||||
\(17\) | −0.523948 | + | 1.43954i | −0.127076 | + | 0.349139i | −0.986873 | − | 0.161497i | \(-0.948368\pi\) |
0.859797 | + | 0.510636i | \(0.170590\pi\) | |||||||
\(18\) | − | 5.34945i | − | 1.26088i | ||||||
\(19\) | 0.805977 | − | 4.28374i | 0.184904 | − | 0.982757i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.9605 | + | 3.98930i | 2.39178 | + | 0.870537i | ||||
\(22\) | 4.15905 | − | 0.733353i | 0.886713 | − | 0.156351i | ||||
\(23\) | 3.83470 | − | 4.57002i | 0.799591 | − | 0.952915i | −0.200048 | − | 0.979786i | \(-0.564110\pi\) |
0.999639 | + | 0.0268711i | \(0.00855436\pi\) | |||||||
\(24\) | −2.21352 | + | 1.85736i | −0.451832 | + | 0.379132i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.76293 | + | 4.78554i | −0.541856 | + | 0.938522i | ||||
\(27\) | 5.87931 | − | 3.39442i | 1.13147 | − | 0.653257i | ||||
\(28\) | −1.38060 | − | 3.79317i | −0.260909 | − | 0.716841i | ||||
\(29\) | −4.97373 | + | 1.81029i | −0.923598 | + | 0.336162i | −0.759669 | − | 0.650310i | \(-0.774639\pi\) |
−0.163929 | + | 0.986472i | \(0.552417\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.35962 | + | 2.35493i | −0.244195 | + | 0.422958i | −0.961905 | − | 0.273384i | \(-0.911857\pi\) |
0.717710 | + | 0.696342i | \(0.245190\pi\) | |||||||
\(32\) | 0.984808 | + | 0.173648i | 0.174091 | + | 0.0306970i | ||||
\(33\) | 7.84404 | + | 9.34816i | 1.36547 | + | 1.62731i | ||||
\(34\) | 1.17352 | + | 0.984700i | 0.201257 | + | 0.168875i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.02684 | − | 1.82962i | −0.837807 | − | 0.304937i | ||||
\(37\) | 8.71589i | 1.43288i | 0.697647 | + | 0.716442i | \(0.254231\pi\) | ||||
−0.697647 | + | 0.716442i | \(0.745769\pi\) | |||||||
\(38\) | −3.74974 | − | 2.22249i | −0.608287 | − | 0.360536i | ||||
\(39\) | −15.9672 | −2.55680 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.560056 | − | 3.17623i | −0.0874660 | − | 0.496044i | −0.996797 | − | 0.0799712i | \(-0.974517\pi\) |
0.909331 | − | 0.416073i | \(-0.136594\pi\) | |||||||
\(42\) | 7.49743 | − | 8.93509i | 1.15688 | − | 1.37871i | ||||
\(43\) | −1.46718 | − | 1.74851i | −0.223743 | − | 0.266646i | 0.642482 | − | 0.766301i | \(-0.277905\pi\) |
−0.866225 | + | 0.499655i | \(0.833460\pi\) | |||||||
\(44\) | 0.733353 | − | 4.15905i | 0.110557 | − | 0.627001i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.98287 | − | 5.16648i | −0.439800 | − | 0.761756i | ||||
\(47\) | −3.61462 | − | 9.93108i | −0.527246 | − | 1.44860i | −0.862300 | − | 0.506398i | \(-0.830977\pi\) |
0.335053 | − | 0.942199i | \(-0.391246\pi\) | |||||||
\(48\) | 0.988282 | + | 2.71528i | 0.142646 | + | 0.391917i | ||||
\(49\) | 4.64708 | + | 8.04898i | 0.663869 | + | 1.14985i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.768663 | + | 4.35930i | −0.107634 | + | 0.610424i | ||||
\(52\) | 3.55196 | + | 4.23306i | 0.492568 | + | 0.587020i | ||||
\(53\) | 1.66137 | − | 1.97995i | 0.228207 | − | 0.271966i | −0.639775 | − | 0.768562i | \(-0.720972\pi\) |
0.867982 | + | 0.496596i | \(0.165417\pi\) | |||||||
\(54\) | −1.17887 | − | 6.68570i | −0.160424 | − | 0.909809i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.03660 | −0.539414 | ||||||||
\(57\) | 0.144099 | − | 12.5944i | 0.0190864 | − | 1.66817i | ||||
\(58\) | 5.29293i | 0.694996i | ||||||||
\(59\) | −9.90460 | − | 3.60498i | −1.28947 | − | 0.469328i | −0.395916 | − | 0.918287i | \(-0.629573\pi\) |
−0.893553 | + | 0.448958i | \(0.851795\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.45129 | − | 2.89597i | −0.441892 | − | 0.370792i | 0.394525 | − | 0.918885i | \(-0.370909\pi\) |
−0.836417 | + | 0.548094i | \(0.815354\pi\) | |||||||
\(62\) | 1.74789 | + | 2.08306i | 0.221982 | + | 0.264548i | ||||
\(63\) | 21.2656 | + | 3.74969i | 2.67921 | + | 0.472417i | ||||
\(64\) | 0.500000 | − | 0.866025i | 0.0625000 | − | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11.4672 | − | 4.17372i | 1.41152 | − | 0.513750i | ||||
\(67\) | −3.76316 | − | 10.3392i | −0.459743 | − | 1.26313i | −0.925677 | − | 0.378314i | \(-0.876504\pi\) |
0.465934 | − | 0.884819i | \(-0.345718\pi\) | |||||||
\(68\) | 1.32668 | − | 0.765961i | 0.160884 | − | 0.0928864i | ||||
\(69\) | 8.61912 | − | 14.9288i | 1.03762 | − | 1.79721i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.73392 | + | 4.81133i | −0.680491 | + | 0.570999i | −0.916150 | − | 0.400836i | \(-0.868720\pi\) |
0.235659 | + | 0.971836i | \(0.424275\pi\) | |||||||
\(72\) | −3.43856 | + | 4.09792i | −0.405238 | + | 0.482944i | ||||
\(73\) | 1.94167 | − | 0.342370i | 0.227256 | − | 0.0400713i | −0.0588605 | − | 0.998266i | \(-0.518747\pi\) |
0.286116 | + | 0.958195i | \(0.407636\pi\) | |||||||
\(74\) | 8.19026 | + | 2.98101i | 0.952099 | + | 0.346536i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.37095 | + | 2.76346i | −0.386674 | + | 0.316991i | ||||
\(77\) | 17.0474i | 1.94274i | ||||||||
\(78\) | −5.46111 | + | 15.0043i | −0.618349 | + | 1.69890i | ||||
\(79\) | −2.15982 | − | 12.2490i | −0.242999 | − | 1.37812i | −0.825094 | − | 0.564995i | \(-0.808878\pi\) |
0.582095 | − | 0.813120i | \(-0.302233\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.73346 | − | 2.29365i | 0.303718 | − | 0.254850i | ||||
\(82\) | −3.17623 | − | 0.560056i | −0.350756 | − | 0.0618478i | ||||
\(83\) | 3.32355 | + | 1.91885i | 0.364807 | + | 0.210621i | 0.671187 | − | 0.741288i | \(-0.265785\pi\) |
−0.306381 | + | 0.951909i | \(0.599118\pi\) | |||||||
\(84\) | −5.83197 | − | 10.1013i | −0.636320 | − | 1.10214i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.14487 | + | 0.780669i | −0.231287 | + | 0.0841817i | ||||
\(87\) | −13.2451 | + | 7.64707i | −1.42003 | + | 0.819852i | ||||
\(88\) | −3.65741 | − | 2.11161i | −0.389881 | − | 0.225098i | ||||
\(89\) | −1.96650 | + | 11.1526i | −0.208448 | + | 1.18217i | 0.683472 | + | 0.729976i | \(0.260469\pi\) |
−0.891921 | + | 0.452192i | \(0.850642\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.0872 | − | 14.3378i | −1.79122 | − | 1.50301i | ||||
\(92\) | −5.87510 | + | 1.03594i | −0.612522 | + | 0.108004i | ||||
\(93\) | −2.68737 | + | 7.38349i | −0.278667 | + | 0.765632i | ||||
\(94\) | −10.5684 | −1.09005 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.88954 | 0.294913 | ||||||||
\(97\) | 4.66803 | − | 12.8253i | 0.473967 | − | 1.30221i | −0.440573 | − | 0.897717i | \(-0.645225\pi\) |
0.914540 | − | 0.404496i | \(-0.132553\pi\) | |||||||
\(98\) | 9.15296 | − | 1.61391i | 0.924589 | − | 0.163030i | ||||
\(99\) | 17.3064 | + | 14.5218i | 1.73936 | + | 1.45949i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.46911 | + | 14.0030i | −0.245686 | + | 1.39335i | 0.573209 | + | 0.819409i | \(0.305698\pi\) |
−0.818895 | + | 0.573944i | \(0.805413\pi\) | |||||||
\(102\) | 3.83351 | + | 2.21328i | 0.379574 | + | 0.219147i | ||||
\(103\) | −6.93582 | + | 4.00440i | −0.683406 | + | 0.394565i | −0.801137 | − | 0.598481i | \(-0.795771\pi\) |
0.117731 | + | 0.993046i | \(0.462438\pi\) | |||||||
\(104\) | 5.19261 | − | 1.88996i | 0.509178 | − | 0.185326i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.29232 | − | 2.23836i | −0.125521 | − | 0.217409i | ||||
\(107\) | 15.1979 | + | 8.77452i | 1.46924 | + | 0.848265i | 0.999405 | − | 0.0344902i | \(-0.0109807\pi\) |
0.469833 | + | 0.882755i | \(0.344314\pi\) | |||||||
\(108\) | −6.68570 | − | 1.17887i | −0.643332 | − | 0.113437i | ||||
\(109\) | −6.11656 | + | 5.13241i | −0.585861 | + | 0.491595i | −0.886866 | − | 0.462027i | \(-0.847122\pi\) |
0.301005 | + | 0.953622i | \(0.402678\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.37332 | + | 24.8023i | 0.415097 | + | 2.35413i | ||||
\(112\) | −1.38060 | + | 3.79317i | −0.130454 | + | 0.358421i | ||||
\(113\) | − | 7.86032i | − | 0.739436i | −0.929144 | − | 0.369718i | \(-0.879454\pi\) | ||
0.929144 | − | 0.369718i | \(-0.120546\pi\) | |||||||
\(114\) | −11.7856 | − | 4.44295i | −1.10382 | − | 0.416120i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.97373 | + | 1.81029i | 0.461799 | + | 0.168081i | ||||
\(117\) | −29.1113 | + | 5.13310i | −2.69134 | + | 0.474555i | ||||
\(118\) | −6.77514 | + | 8.07430i | −0.623703 | + | 0.743300i | ||||
\(119\) | −4.73703 | + | 3.97484i | −0.434243 | + | 0.364373i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.41777 | + | 5.91975i | −0.310706 | + | 0.538159i | ||||
\(122\) | −3.90174 | + | 2.25267i | −0.353247 | + | 0.203947i | ||||
\(123\) | −3.18744 | − | 8.75741i | −0.287402 | − | 0.789629i | ||||
\(124\) | 2.55525 | − | 0.930034i | 0.229468 | − | 0.0835195i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 10.7968 | − | 18.7006i | 0.961856 | − | 1.66598i | ||||
\(127\) | 18.2700 | + | 3.22150i | 1.62120 | + | 0.285862i | 0.909214 | − | 0.416328i | \(-0.136683\pi\) |
0.711989 | + | 0.702190i | \(0.247794\pi\) | |||||||
\(128\) | −0.642788 | − | 0.766044i | −0.0568149 | − | 0.0677094i | ||||
\(129\) | −5.05241 | − | 4.23947i | −0.444840 | − | 0.373265i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.22255 | + | 3.35673i | 0.805778 | + | 0.293279i | 0.711878 | − | 0.702303i | \(-0.247845\pi\) |
0.0938991 | + | 0.995582i | \(0.470067\pi\) | |||||||
\(132\) | − | 12.2032i | − | 1.06215i | ||||||
\(133\) | 11.4634 | − | 13.3484i | 0.994003 | − | 1.15745i | ||||
\(134\) | −11.0027 | −0.950492 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.266015 | − | 1.50865i | −0.0228106 | − | 0.129366i | ||||
\(137\) | −2.10023 | + | 2.50295i | −0.179434 | + | 0.213842i | −0.848263 | − | 0.529575i | \(-0.822351\pi\) |
0.668829 | + | 0.743417i | \(0.266796\pi\) | |||||||
\(138\) | −11.0805 | − | 13.2053i | −0.943237 | − | 1.12411i | ||||
\(139\) | −0.274807 | + | 1.55851i | −0.0233089 | + | 0.132191i | −0.994242 | − | 0.107161i | \(-0.965824\pi\) |
0.970933 | + | 0.239352i | \(0.0769351\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.2690 | − | 26.4466i | −1.28588 | − | 2.22721i | ||||
\(142\) | 2.56005 | + | 7.03369i | 0.214835 | + | 0.590254i | ||||
\(143\) | −7.98169 | − | 21.9295i | −0.667463 | − | 1.83384i | ||||
\(144\) | 2.67473 | + | 4.63276i | 0.222894 | + | 0.386063i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.342370 | − | 1.94167i | 0.0283347 | − | 0.160694i | ||||
\(147\) | 17.2626 | + | 20.5728i | 1.42380 | + | 1.69682i | ||||
\(148\) | 5.60247 | − | 6.67676i | 0.460520 | − | 0.548827i | ||||
\(149\) | 2.09553 | + | 11.8843i | 0.171672 | + | 0.973603i | 0.941915 | + | 0.335852i | \(0.109024\pi\) |
−0.770242 | + | 0.637751i | \(0.779865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.98455 | 0.405637 | 0.202818 | − | 0.979216i | \(-0.434990\pi\) | ||||
0.202818 | + | 0.979216i | \(0.434990\pi\) | |||||||
\(152\) | 1.44387 | + | 4.11281i | 0.117113 | + | 0.333593i | ||||
\(153\) | 8.19494i | 0.662522i | ||||||||
\(154\) | 16.0194 | + | 5.83057i | 1.29088 | + | 0.469841i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 12.2316 | + | 10.2635i | 0.979312 | + | 0.821740i | ||||
\(157\) | −10.0731 | − | 12.0046i | −0.803919 | − | 0.958073i | 0.195827 | − | 0.980639i | \(-0.437261\pi\) |
−0.999745 | + | 0.0225655i | \(0.992817\pi\) | |||||||
\(158\) | −12.2490 | − | 2.15982i | −0.974475 | − | 0.171826i | ||||
\(159\) | 3.73421 | − | 6.46783i | 0.296142 | − | 0.512933i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.6290 | − | 8.23629i | 1.78342 | − | 0.649111i | ||||
\(162\) | −1.22042 | − | 3.35309i | −0.0958856 | − | 0.263444i | ||||
\(163\) | 7.28558 | − | 4.20633i | 0.570651 | − | 0.329465i | −0.186758 | − | 0.982406i | \(-0.559798\pi\) |
0.757409 | + | 0.652940i | \(0.226465\pi\) | |||||||
\(164\) | −1.61262 | + | 2.79313i | −0.125924 | + | 0.218107i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.93985 | − | 2.46683i | 0.228177 | − | 0.191463i | ||||
\(167\) | 2.05862 | − | 2.45336i | 0.159300 | − | 0.189847i | −0.680490 | − | 0.732757i | \(-0.738233\pi\) |
0.839791 | + | 0.542910i | \(0.182678\pi\) | |||||||
\(168\) | −11.4867 | + | 2.02542i | −0.886221 | + | 0.156265i | ||||
\(169\) | 16.4777 | + | 5.99739i | 1.26751 | + | 0.461338i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.78609 | − | 23.0083i | −0.289530 | − | 1.75949i | ||||
\(172\) | 2.28252i | 0.174041i | ||||||||
\(173\) | −4.83471 | + | 13.2833i | −0.367576 | + | 1.00991i | 0.608704 | + | 0.793397i | \(0.291690\pi\) |
−0.976280 | + | 0.216510i | \(0.930533\pi\) | |||||||
\(174\) | 2.65580 | + | 15.0618i | 0.201336 | + | 1.14183i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.23517 | + | 2.71463i | −0.243860 | + | 0.204623i | ||||
\(177\) | −29.9938 | − | 5.28872i | −2.25447 | − | 0.397524i | ||||
\(178\) | 9.80739 | + | 5.66230i | 0.735095 | + | 0.424407i | ||||
\(179\) | 8.50106 | + | 14.7243i | 0.635399 | + | 1.10054i | 0.986430 | + | 0.164180i | \(0.0524978\pi\) |
−0.351031 | + | 0.936364i | \(0.614169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.7494 | + | 6.82423i | −1.39363 | + | 0.507241i | −0.926282 | − | 0.376830i | \(-0.877014\pi\) |
−0.467352 | + | 0.884072i | \(0.654792\pi\) | |||||||
\(182\) | −19.3173 | + | 11.1529i | −1.43190 | + | 0.826705i | ||||
\(183\) | −11.2742 | − | 6.50918i | −0.833415 | − | 0.481172i | ||||
\(184\) | −1.03594 | + | 5.87510i | −0.0763705 | + | 0.433118i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.01908 | + | 5.05061i | 0.441340 | + | 0.370328i | ||||
\(187\) | −6.37135 | + | 1.12344i | −0.465919 | + | 0.0821541i | ||||
\(188\) | −3.61462 | + | 9.93108i | −0.263623 | + | 0.724299i | ||||
\(189\) | 27.4039 | 1.99334 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.0735 | 0.728896 | 0.364448 | − | 0.931224i | \(-0.381258\pi\) | ||||
0.364448 | + | 0.931224i | \(0.381258\pi\) | |||||||
\(192\) | 0.988282 | − | 2.71528i | 0.0713231 | − | 0.195959i | ||||
\(193\) | 4.53351 | − | 0.799380i | 0.326329 | − | 0.0575407i | −0.00808358 | − | 0.999967i | \(-0.502573\pi\) |
0.334413 | + | 0.942427i | \(0.391462\pi\) | |||||||
\(194\) | −10.4553 | − | 8.77303i | −0.750646 | − | 0.629867i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.61391 | − | 9.15296i | 0.115280 | − | 0.653783i | ||||
\(197\) | 0.940940 | + | 0.543252i | 0.0670392 | + | 0.0387051i | 0.533145 | − | 0.846024i | \(-0.321010\pi\) |
−0.466106 | + | 0.884729i | \(0.654343\pi\) | |||||||
\(198\) | 19.5651 | − | 11.2959i | 1.39043 | − | 0.802768i | ||||
\(199\) | −1.22137 | + | 0.444543i | −0.0865808 | + | 0.0315128i | −0.384947 | − | 0.922939i | \(-0.625780\pi\) |
0.298367 | + | 0.954451i | \(0.403558\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.8964 | − | 27.5334i | −1.12125 | − | 1.94206i | ||||
\(202\) | 12.3141 | + | 7.10952i | 0.866414 | + | 0.500224i | ||||
\(203\) | −21.0409 | − | 3.71007i | −1.47678 | − | 0.260396i | ||||
\(204\) | 3.39094 | − | 2.84533i | 0.237413 | − | 0.199213i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.39071 | + | 7.88712i | 0.0968955 | + | 0.549522i | ||||
\(207\) | 10.9150 | − | 29.9888i | 0.758647 | − | 2.08437i | ||||
\(208\) | − | 5.52587i | − | 0.383150i | ||||||
\(209\) | 17.3693 | − | 6.09778i | 1.20146 | − | 0.421792i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.86776 | − | 1.77172i | −0.335111 | − | 0.121970i | 0.168984 | − | 0.985619i | \(-0.445951\pi\) |
−0.504094 | + | 0.863649i | \(0.668174\pi\) | |||||||
\(212\) | −2.54537 | + | 0.448817i | −0.174817 | + | 0.0308249i | ||||
\(213\) | −13.9025 | + | 16.5684i | −0.952586 | + | 1.13525i | ||||
\(214\) | 13.4433 | − | 11.2803i | 0.918968 | − | 0.771106i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.39442 | + | 5.87931i | −0.230961 | + | 0.400036i | ||||
\(217\) | −9.50591 | + | 5.48824i | −0.645303 | + | 0.372566i | ||||
\(218\) | 2.73090 | + | 7.50308i | 0.184960 | + | 0.508172i | ||||
\(219\) | 5.35352 | − | 1.94852i | 0.361758 | − | 0.131669i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.23260 | − | 7.33107i | 0.284715 | − | 0.493141i | ||||
\(222\) | 24.8023 | + | 4.37332i | 1.66462 | + | 0.293518i | ||||
\(223\) | −5.19927 | − | 6.19625i | −0.348169 | − | 0.414932i | 0.563331 | − | 0.826231i | \(-0.309520\pi\) |
−0.911500 | + | 0.411299i | \(0.865075\pi\) | |||||||
\(224\) | 3.09222 | + | 2.59468i | 0.206607 | + | 0.173364i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.38628 | − | 2.68839i | −0.491328 | − | 0.178829i | ||||
\(227\) | 6.53426i | 0.433694i | 0.976206 | + | 0.216847i | \(0.0695773\pi\) | ||||
−0.976206 | + | 0.216847i | \(0.930423\pi\) | |||||||
\(228\) | −8.20591 | + | 9.55524i | −0.543450 | + | 0.632811i | ||||
\(229\) | −25.8896 | −1.71084 | −0.855418 | − | 0.517939i | \(-0.826699\pi\) | ||||
−0.855418 | + | 0.517939i | \(0.826699\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.55379 | + | 48.5109i | 0.562798 | + | 3.19179i | ||||
\(232\) | 3.40223 | − | 4.05462i | 0.223367 | − | 0.266199i | ||||
\(233\) | 14.5918 | + | 17.3898i | 0.955937 | + | 1.13924i | 0.990176 | + | 0.139828i | \(0.0446550\pi\) |
−0.0342384 | + | 0.999414i | \(0.510901\pi\) | |||||||
\(234\) | −5.13310 | + | 29.1113i | −0.335561 | + | 1.90306i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.27013 | + | 9.12813i | 0.343056 | + | 0.594190i | ||||
\(237\) | −12.2922 | − | 33.7724i | −0.798462 | − | 2.19376i | ||||
\(238\) | 2.11497 | + | 5.81083i | 0.137093 | + | 0.376660i | ||||
\(239\) | −4.47880 | − | 7.75751i | −0.289710 | − | 0.501792i | 0.684031 | − | 0.729453i | \(-0.260225\pi\) |
−0.973740 | + | 0.227661i | \(0.926892\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.582502 | − | 3.30353i | 0.0375223 | − | 0.212799i | −0.960282 | − | 0.279031i | \(-0.909987\pi\) |
0.997804 | + | 0.0662321i | \(0.0210978\pi\) | |||||||
\(242\) | 4.39380 | + | 5.23633i | 0.282444 | + | 0.336604i | ||||
\(243\) | −6.46376 | + | 7.70320i | −0.414650 | + | 0.494161i | ||||
\(244\) | 0.782343 | + | 4.43689i | 0.0500844 | + | 0.284043i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.31944 | −0.594186 | ||||||||
\(247\) | −8.49655 | + | 22.5384i | −0.540622 | + | 1.43408i | ||||
\(248\) | − | 2.71924i | − | 0.172672i | ||||||
\(249\) | 10.4204 | + | 3.79273i | 0.660369 | + | 0.240354i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.0959 | + | 14.3452i | 1.07909 | + | 0.905460i | 0.995845 | − | 0.0910693i | \(-0.0290285\pi\) |
0.0832408 | + | 0.996529i | \(0.473473\pi\) | |||||||
\(252\) | −13.8801 | − | 16.5417i | −0.874365 | − | 1.04203i | ||||
\(253\) | 24.8118 | + | 4.37499i | 1.55991 | + | 0.275054i | ||||
\(254\) | 9.27594 | − | 16.0664i | 0.582024 | − | 1.00810i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.939693 | + | 0.342020i | −0.0587308 | + | 0.0213763i | ||||
\(257\) | 0.319330 | + | 0.877351i | 0.0199192 | + | 0.0547277i | 0.949254 | − | 0.314511i | \(-0.101841\pi\) |
−0.929334 | + | 0.369239i | \(0.879618\pi\) | |||||||
\(258\) | −5.71183 | + | 3.29772i | −0.355603 | + | 0.205307i | ||||
\(259\) | −17.5913 | + | 30.4690i | −1.09307 | + | 1.89325i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.6900 | + | 18.2001i | −1.34258 | + | 1.12656i | ||||
\(262\) | 6.30859 | − | 7.51829i | 0.389746 | − | 0.464481i | ||||
\(263\) | 14.6030 | − | 2.57491i | 0.900462 | − | 0.158776i | 0.295793 | − | 0.955252i | \(-0.404416\pi\) |
0.604670 | + | 0.796476i | \(0.293305\pi\) | |||||||
\(264\) | −11.4672 | − | 4.17372i | −0.705758 | − | 0.256875i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.62266 | − | 15.3375i | −0.528689 | − | 0.940402i | ||||
\(267\) | 32.7229i | 2.00261i | ||||||||
\(268\) | −3.76316 | + | 10.3392i | −0.229872 | + | 0.631567i | ||||
\(269\) | 0.487261 | + | 2.76340i | 0.0297088 | + | 0.168487i | 0.996052 | − | 0.0887681i | \(-0.0282930\pi\) |
−0.966343 | + | 0.257255i | \(0.917182\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.28912 | − | 5.27720i | 0.382037 | − | 0.320567i | −0.431464 | − | 0.902130i | \(-0.642003\pi\) |
0.813502 | + | 0.581563i | \(0.197559\pi\) | |||||||
\(272\) | −1.50865 | − | 0.266015i | −0.0914752 | − | 0.0161296i | ||||
\(273\) | −55.8182 | − | 32.2267i | −3.37827 | − | 1.95045i | ||||
\(274\) | 1.63369 | + | 2.82963i | 0.0986946 | + | 0.170944i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −16.1987 | + | 5.89583i | −0.975044 | + | 0.354887i | ||||
\(277\) | 17.4575 | − | 10.0791i | 1.04892 | − | 0.605595i | 0.126574 | − | 0.991957i | \(-0.459602\pi\) |
0.922347 | + | 0.386362i | \(0.126268\pi\) | |||||||
\(278\) | 1.37053 | + | 0.791276i | 0.0821990 | + | 0.0474576i | ||||
\(279\) | −2.52596 | + | 14.3254i | −0.151225 | + | 0.857641i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.80083 | + | 3.18928i | 0.226739 | + | 0.190256i | 0.749079 | − | 0.662481i | \(-0.230496\pi\) |
−0.522340 | + | 0.852737i | \(0.674941\pi\) | |||||||
\(282\) | −30.0740 | + | 5.30286i | −1.79088 | + | 0.315781i | ||||
\(283\) | −5.16552 | + | 14.1921i | −0.307058 | + | 0.843635i | 0.686168 | + | 0.727443i | \(0.259291\pi\) |
−0.993227 | + | 0.116193i | \(0.962931\pi\) | |||||||
\(284\) | 7.48509 | 0.444159 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.3369 | −1.37994 | ||||||||
\(287\) | 4.45275 | − | 12.2338i | 0.262838 | − | 0.722141i | ||||
\(288\) | 5.26818 | − | 0.928923i | 0.310431 | − | 0.0547373i | ||||
\(289\) | 11.2250 | + | 9.41891i | 0.660295 | + | 0.554053i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.84828 | − | 38.8385i | 0.401453 | − | 2.27675i | ||||
\(292\) | −1.70748 | − | 0.985814i | −0.0999227 | − | 0.0576904i | ||||
\(293\) | −2.35283 | + | 1.35841i | −0.137454 | + | 0.0793589i | −0.567150 | − | 0.823615i | \(-0.691954\pi\) |
0.429696 | + | 0.902974i | \(0.358621\pi\) | |||||||
\(294\) | 25.2363 | − | 9.18525i | 1.47181 | − | 0.535695i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.35795 | − | 7.54819i | −0.253301 | − | 0.438729i | ||||
\(297\) | 24.8296 | + | 14.3354i | 1.44076 | + | 0.831822i | ||||
\(298\) | 11.8843 | + | 2.09553i | 0.688441 | + | 0.121391i | ||||
\(299\) | −25.2533 | + | 21.1900i | −1.46044 | + | 1.22545i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.59993 | − | 9.07367i | −0.0922186 | − | 0.522997i | ||||
\(302\) | 1.70482 | − | 4.68394i | 0.0981011 | − | 0.269531i | ||||
\(303\) | 41.0865i | 2.36036i | ||||||||
\(304\) | 4.35861 | + | 0.0498692i | 0.249984 | + | 0.00286019i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.70073 | + | 2.80284i | 0.440221 | + | 0.160227i | ||||
\(307\) | 24.9663 | − | 4.40223i | 1.42490 | − | 0.251248i | 0.592566 | − | 0.805522i | \(-0.298115\pi\) |
0.832335 | + | 0.554273i | \(0.187004\pi\) | |||||||
\(308\) | 10.9579 | − | 13.0591i | 0.624383 | − | 0.744111i | ||||
\(309\) | −17.7276 | + | 14.8752i | −1.00849 | + | 0.846222i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.87719 | + | 3.25139i | −0.106446 | + | 0.184370i | −0.914328 | − | 0.404974i | \(-0.867280\pi\) |
0.807882 | + | 0.589344i | \(0.200614\pi\) | |||||||
\(312\) | 13.8280 | − | 7.98361i | 0.782857 | − | 0.451983i | ||||
\(313\) | −7.30618 | − | 20.0736i | −0.412970 | − | 1.13463i | −0.955604 | − | 0.294656i | \(-0.904795\pi\) |
0.542634 | − | 0.839969i | \(-0.317427\pi\) | |||||||
\(314\) | −14.7258 | + | 5.35977i | −0.831028 | + | 0.302469i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.21896 | + | 10.7716i | −0.349844 | + | 0.605947i | ||||
\(317\) | 20.2025 | + | 3.56224i | 1.13468 | + | 0.200075i | 0.709279 | − | 0.704928i | \(-0.249021\pi\) |
0.425404 | + | 0.905003i | \(0.360132\pi\) | |||||||
\(318\) | −4.80060 | − | 5.72114i | −0.269204 | − | 0.320825i | ||||
\(319\) | −17.1235 | − | 14.3683i | −0.958733 | − | 0.804473i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 47.6506 | + | 17.3434i | 2.65960 | + | 0.968014i | ||||
\(322\) | − | 24.0813i | − | 1.34200i | ||||||
\(323\) | 5.74430 | + | 3.40469i | 0.319621 | + | 0.189442i | ||||
\(324\) | −3.56828 | −0.198238 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.46084 | − | 8.28486i | −0.0809087 | − | 0.458856i | ||||
\(327\) | −14.8303 | + | 17.6741i | −0.820118 | + | 0.977378i | ||||
\(328\) | 2.07314 | + | 2.47067i | 0.114470 | + | 0.136420i | ||||
\(329\) | 7.40793 | − | 42.0125i | 0.408413 | − | 2.31622i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.3737 | − | 28.3601i | −0.899982 | − | 1.55881i | −0.827515 | − | 0.561443i | \(-0.810246\pi\) |
−0.0724661 | − | 0.997371i | \(-0.523087\pi\) | |||||||
\(332\) | −1.31257 | − | 3.60626i | −0.0720367 | − | 0.197919i | ||||
\(333\) | 15.9468 | + | 43.8134i | 0.873878 | + | 2.40096i | ||||
\(334\) | −1.60132 | − | 2.77357i | −0.0876203 | − | 0.151763i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.02542 | + | 11.4867i | −0.110496 | + | 0.626653i | ||||
\(337\) | −15.3643 | − | 18.3105i | −0.836948 | − | 0.997435i | −0.999942 | − | 0.0108083i | \(-0.996560\pi\) |
0.162994 | − | 0.986627i | \(-0.447885\pi\) | |||||||
\(338\) | 11.2714 | − | 13.4327i | 0.613083 | − | 0.730644i | ||||
\(339\) | −3.94402 | − | 22.3677i | −0.214210 | − | 1.21484i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.4839 | −0.621889 | ||||||||
\(342\) | −22.9156 | − | 4.31153i | −1.23914 | − | 0.233141i | ||||
\(343\) | 9.26063i | 0.500027i | ||||||||
\(344\) | 2.14487 | + | 0.780669i | 0.115644 | + | 0.0420909i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.8286 | + | 9.08628i | 0.582150 | + | 0.488482i | ||||
\(347\) | −8.78538 | − | 10.4700i | −0.471624 | − | 0.562059i | 0.476822 | − | 0.879000i | \(-0.341789\pi\) |
−0.948445 | + | 0.316941i | \(0.897344\pi\) | |||||||
\(348\) | 15.0618 | + | 2.65580i | 0.807397 | + | 0.142366i | ||||
\(349\) | −12.6829 | + | 21.9674i | −0.678899 | + | 1.17589i | 0.296414 | + | 0.955060i | \(0.404209\pi\) |
−0.975313 | + | 0.220828i | \(0.929124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −35.2518 | + | 12.8306i | −1.88160 | + | 0.684848i | ||||
\(352\) | 1.44442 | + | 3.96852i | 0.0769881 | + | 0.211523i | ||||
\(353\) | −15.6173 | + | 9.01663i | −0.831223 | + | 0.479907i | −0.854271 | − | 0.519828i | \(-0.825996\pi\) |
0.0230484 | + | 0.999734i | \(0.492663\pi\) | |||||||
\(354\) | −15.2283 | + | 26.3761i | −0.809372 | + | 1.40187i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.67515 | − | 7.27931i | 0.459782 | − | 0.385803i | ||||
\(357\) | −11.4855 | + | 13.6879i | −0.607876 | + | 0.724438i | ||||
\(358\) | 16.7438 | − | 2.95239i | 0.884939 | − | 0.156039i | ||||
\(359\) | −15.1395 | − | 5.51032i | −0.799031 | − | 0.290824i | −0.0899463 | − | 0.995947i | \(-0.528670\pi\) |
−0.709085 | + | 0.705123i | \(0.750892\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7008 | − | 6.90519i | −0.931621 | − | 0.363431i | ||||
\(362\) | 19.9527i | 1.04869i | ||||||||
\(363\) | −6.75544 | + | 18.5604i | −0.354569 | + | 0.974169i | ||||
\(364\) | 3.87335 | + | 21.9669i | 0.203019 | + | 1.15138i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.97264 | + | 8.36804i | −0.521278 | + | 0.437404i | ||||
\(367\) | 9.75596 | + | 1.72024i | 0.509257 | + | 0.0897957i | 0.422372 | − | 0.906423i | \(-0.361198\pi\) |
0.0868849 | + | 0.996218i | \(0.472309\pi\) | |||||||
\(368\) | 5.16648 | + | 2.98287i | 0.269321 | + | 0.155493i | ||||
\(369\) | −8.62661 | − | 14.9417i | −0.449084 | − | 0.777835i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.80395 | − | 3.56835i | 0.508996 | − | 0.185259i | ||||
\(372\) | 6.80466 | − | 3.92867i | 0.352805 | − | 0.203692i | ||||
\(373\) | 7.58731 | + | 4.38054i | 0.392856 | + | 0.226816i | 0.683397 | − | 0.730047i | \(-0.260502\pi\) |
−0.290541 | + | 0.956863i | \(0.593835\pi\) | |||||||
\(374\) | −1.12344 | + | 6.37135i | −0.0580917 | + | 0.329454i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.09589 | + | 6.79326i | 0.417514 | + | 0.350336i | ||||
\(377\) | 28.8037 | − | 5.07886i | 1.48346 | − | 0.261575i | ||||
\(378\) | 9.37267 | − | 25.7512i | 0.482078 | − | 1.32450i | ||||
\(379\) | −9.49485 | −0.487718 | −0.243859 | − | 0.969811i | \(-0.578413\pi\) | ||||
−0.243859 | + | 0.969811i | \(0.578413\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 53.6064 | 2.74634 | ||||||||
\(382\) | 3.44536 | − | 9.46604i | 0.176280 | − | 0.484325i | ||||
\(383\) | −28.8836 | + | 5.09296i | −1.47588 | + | 0.260238i | −0.852932 | − | 0.522022i | \(-0.825178\pi\) |
−0.622952 | + | 0.782260i | \(0.714067\pi\) | |||||||
\(384\) | −2.21352 | − | 1.85736i | −0.112958 | − | 0.0947831i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.799380 | − | 4.53351i | 0.0406874 | − | 0.230750i | ||||
\(387\) | −10.5744 | − | 6.10513i | −0.537526 | − | 0.310341i | ||||
\(388\) | −11.8199 | + | 6.82421i | −0.600063 | + | 0.346447i | ||||
\(389\) | 11.3431 | − | 4.12854i | 0.575117 | − | 0.209325i | −0.0380542 | − | 0.999276i | \(-0.512116\pi\) |
0.613171 | + | 0.789950i | \(0.289894\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.56952 | + | 7.91464i | 0.231091 | + | 0.400261i | ||||
\(392\) | −8.04898 | − | 4.64708i | −0.406535 | − | 0.234713i | ||||
\(393\) | 27.9284 | + | 4.92452i | 1.40880 | + | 0.248409i | ||||
\(394\) | 0.832311 | − | 0.698392i | 0.0419312 | − | 0.0351845i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.92304 | − | 22.2487i | −0.197140 | − | 1.11804i | ||||
\(397\) | −3.91763 | + | 10.7636i | −0.196620 | + | 0.540210i | −0.998347 | − | 0.0574815i | \(-0.981693\pi\) |
0.801726 | + | 0.597691i | \(0.203915\pi\) | |||||||
\(398\) | 1.29976i | 0.0651509i | ||||||||
\(399\) | 25.9230 | − | 43.7367i | 1.29777 | − | 2.18957i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.66865 | + | 1.69925i | 0.233141 | + | 0.0848564i | 0.455949 | − | 0.890006i | \(-0.349300\pi\) |
−0.222808 | + | 0.974862i | \(0.571522\pi\) | |||||||
\(402\) | −31.3099 | + | 5.52078i | −1.56159 | + | 0.275351i | ||||
\(403\) | 9.65861 | − | 11.5107i | 0.481130 | − | 0.573388i | ||||
\(404\) | 10.8924 | − | 9.13983i | 0.541918 | − | 0.454723i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.6827 | + | 18.5030i | −0.530175 | + | 0.918290i | ||||
\(407\) | −31.8776 | + | 18.4045i | −1.58011 | + | 0.912280i | ||||
\(408\) | −1.51397 | − | 4.15960i | −0.0749527 | − | 0.205931i | ||||
\(409\) | 1.22014 | − | 0.444093i | 0.0603318 | − | 0.0219590i | −0.311678 | − | 0.950188i | \(-0.600891\pi\) |
0.372010 | + | 0.928229i | \(0.378669\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.72061 | + | 8.17633i | −0.232850 | + | 0.403309i | ||||
\(412\) | 7.88712 | + | 1.39071i | 0.388571 | + | 0.0685155i | ||||
\(413\) | −27.3486 | − | 32.5928i | −1.34573 | − | 1.60378i | ||||
\(414\) | −24.4471 | − | 20.5136i | −1.20151 | − | 1.00819i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.19261 | − | 1.88996i | −0.254589 | − | 0.0926628i | ||||
\(417\) | 4.57285i | 0.223934i | ||||||||
\(418\) | 0.210608 | − | 18.4074i | 0.0103012 | − | 0.900333i | ||||
\(419\) | 36.1438 | 1.76574 | 0.882870 | − | 0.469617i | \(-0.155608\pi\) | ||||
0.882870 | + | 0.469617i | \(0.155608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.28902 | − | 29.9955i | −0.257771 | − | 1.46189i | −0.788859 | − | 0.614574i | \(-0.789328\pi\) |
0.531088 | − | 0.847317i | \(-0.321783\pi\) | |||||||
\(422\) | −3.32975 | + | 3.96824i | −0.162089 | + | 0.193171i | ||||
\(423\) | −36.3402 | − | 43.3086i | −1.76692 | − | 2.10574i | ||||
\(424\) | −0.448817 | + | 2.54537i | −0.0217965 | + | 0.123614i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.8142 | + | 18.7308i | 0.523952 | + | 0.907511i | ||||
\(427\) | −6.22007 | − | 17.0895i | −0.301010 | − | 0.827018i | ||||
\(428\) | −6.00213 | − | 16.4907i | −0.290124 | − | 0.797108i | ||||
\(429\) | −33.7165 | − | 58.3987i | −1.62785 | − | 2.81952i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.25630 | + | 35.4813i | −0.301355 | + | 1.70907i | 0.338827 | + | 0.940849i | \(0.389970\pi\) |
−0.640182 | + | 0.768223i | \(0.721141\pi\) | |||||||
\(432\) | 4.36378 | + | 5.20055i | 0.209953 | + | 0.250212i | ||||
\(433\) | 18.7188 | − | 22.3082i | 0.899568 | − | 1.07206i | −0.0974763 | − | 0.995238i | \(-0.531077\pi\) |
0.997045 | − | 0.0768258i | \(-0.0244785\pi\) | |||||||
\(434\) | 1.90605 | + | 10.8097i | 0.0914931 | + | 0.518883i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.98461 | 0.382393 | ||||||||
\(437\) | −16.4861 | − | 20.1102i | −0.788636 | − | 0.962001i | ||||
\(438\) | − | 5.69710i | − | 0.272218i | ||||||
\(439\) | 3.06643 | + | 1.11609i | 0.146353 | + | 0.0532681i | 0.414158 | − | 0.910205i | \(-0.364076\pi\) |
−0.267805 | + | 0.963473i | \(0.586298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 38.0867 | + | 31.9586i | 1.81365 | + | 1.52184i | ||||
\(442\) | −5.44132 | − | 6.48471i | −0.258817 | − | 0.308446i | ||||
\(443\) | 33.5612 | + | 5.91774i | 1.59454 | + | 0.281160i | 0.899206 | − | 0.437526i | \(-0.144145\pi\) |
0.695334 | + | 0.718687i | \(0.255256\pi\) | |||||||
\(444\) | 12.5925 | − | 21.8108i | 0.597612 | − | 1.03509i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.60083 | + | 2.76648i | −0.359910 | + | 0.130996i | ||||
\(447\) | 11.9263 | + | 32.7671i | 0.564093 | + | 1.54983i | ||||
\(448\) | 3.49580 | − | 2.01830i | 0.165161 | − | 0.0953558i | ||||
\(449\) | 16.0584 | − | 27.8139i | 0.757841 | − | 1.31262i | −0.186109 | − | 0.982529i | \(-0.559588\pi\) |
0.943950 | − | 0.330089i | \(-0.107079\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.4342 | − | 8.75531i | 0.491326 | − | 0.412272i | ||||
\(452\) | −5.05251 | + | 6.02135i | −0.237650 | + | 0.283221i | ||||
\(453\) | 14.1842 | − | 2.50106i | 0.666434 | − | 0.117510i | ||||
\(454\) | 6.14020 | + | 2.23485i | 0.288174 | + | 0.104887i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.17240 | + | 10.9791i | 0.289049 | + | 0.514144i | ||||
\(457\) | 8.66519i | 0.405341i | 0.979247 | + | 0.202670i | \(0.0649620\pi\) | ||||
−0.979247 | + | 0.202670i | \(0.935038\pi\) | |||||||
\(458\) | −8.85478 | + | 24.3283i | −0.413756 | + | 1.13679i | ||||
\(459\) | 1.80594 | + | 10.2420i | 0.0842939 | + | 0.478054i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.5892 | + | 11.4027i | −0.632911 | + | 0.531076i | −0.901832 | − | 0.432087i | \(-0.857777\pi\) |
0.268921 | + | 0.963162i | \(0.413333\pi\) | |||||||
\(462\) | 48.5109 | + | 8.55379i | 2.25693 | + | 0.397958i | ||||
\(463\) | −22.9510 | − | 13.2507i | −1.06662 | − | 0.615814i | −0.139365 | − | 0.990241i | \(-0.544506\pi\) |
−0.927257 | + | 0.374427i | \(0.877840\pi\) | |||||||
\(464\) | −2.64646 | − | 4.58381i | −0.122859 | − | 0.212798i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.3317 | − | 7.76411i | 0.988173 | − | 0.359665i | ||||
\(467\) | 13.6094 | − | 7.85739i | 0.629768 | − | 0.363597i | −0.150894 | − | 0.988550i | \(-0.548215\pi\) |
0.780662 | + | 0.624953i | \(0.214882\pi\) | |||||||
\(468\) | 25.6000 | + | 14.7802i | 1.18336 | + | 0.683214i | ||||
\(469\) | 7.71236 | − | 43.7390i | 0.356124 | − | 2.01968i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −34.6879 | − | 29.1066i | −1.59833 | − | 1.34116i | ||||
\(472\) | 10.3801 | − | 1.83030i | 0.477784 | − | 0.0842462i | ||||
\(473\) | 3.29693 | − | 9.05825i | 0.151593 | − | 0.416499i | ||||
\(474\) | −35.9399 | −1.65077 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.18376 | 0.283432 | ||||||||
\(477\) | 4.72890 | − | 12.9926i | 0.216522 | − | 0.594888i | ||||
\(478\) | −8.82152 | + | 1.55547i | −0.403487 | + | 0.0711456i | ||||
\(479\) | 7.03049 | + | 5.89928i | 0.321231 | + | 0.269545i | 0.789116 | − | 0.614245i | \(-0.210539\pi\) |
−0.467884 | + | 0.883790i | \(0.654984\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.36339 | − | 47.4312i | 0.381338 | − | 2.16267i | ||||
\(482\) | −2.90508 | − | 1.67725i | −0.132323 | − | 0.0763965i | ||||
\(483\) | 60.2615 | − | 34.7920i | 2.74199 | − | 1.58309i | ||||
\(484\) | 6.42331 | − | 2.33789i | 0.291968 | − | 0.106268i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.02791 | + | 8.70859i | 0.228071 | + | 0.395030i | ||||
\(487\) | 23.0303 | + | 13.2965i | 1.04360 | + | 0.602524i | 0.920852 | − | 0.389913i | \(-0.127495\pi\) |
0.122751 | + | 0.992438i | \(0.460828\pi\) | |||||||
\(488\) | 4.43689 | + | 0.782343i | 0.200849 | + | 0.0354150i | ||||
\(489\) | 18.6216 | − | 15.6254i | 0.842097 | − | 0.706603i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.89000 | − | 33.4038i | −0.265812 | − | 1.50749i | −0.766713 | − | 0.641990i | \(-0.778109\pi\) |
0.500901 | − | 0.865504i | \(-0.333002\pi\) | |||||||
\(492\) | −3.18744 | + | 8.75741i | −0.143701 | + | 0.394815i | ||||
\(493\) | − | 8.10835i | − | 0.365182i | ||||||
\(494\) | 18.2731 | + | 15.6927i | 0.822147 | + | 0.706048i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.55525 | − | 0.930034i | −0.114734 | − | 0.0417597i | ||||
\(497\) | −29.7553 | + | 5.24667i | −1.33471 | + | 0.235345i | ||||
\(498\) | 7.12800 | − | 8.49482i | 0.319413 | − | 0.380662i | ||||
\(499\) | 21.1761 | − | 17.7689i | 0.947973 | − | 0.795444i | −0.0309820 | − | 0.999520i | \(-0.509863\pi\) |
0.978955 | + | 0.204076i | \(0.0654190\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.62708 | − | 8.01433i | 0.206723 | − | 0.358054i | ||||
\(502\) | 19.3272 | − | 11.1586i | 0.862616 | − | 0.498032i | ||||
\(503\) | −7.38317 | − | 20.2851i | −0.329199 | − | 0.904468i | −0.988315 | − | 0.152426i | \(-0.951291\pi\) |
0.659116 | − | 0.752042i | \(-0.270931\pi\) | |||||||
\(504\) | −20.2914 | + | 7.38545i | −0.903849 | + | 0.328974i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12.5973 | − | 21.8192i | 0.560018 | − | 0.969980i | ||||
\(507\) | 49.8989 | + | 8.79852i | 2.21609 | + | 0.390756i | ||||
\(508\) | −11.9249 | − | 14.2116i | −0.529083 | − | 0.630536i | ||||
\(509\) | 1.78133 | + | 1.49471i | 0.0789560 | + | 0.0662520i | 0.681411 | − | 0.731901i | \(-0.261366\pi\) |
−0.602455 | + | 0.798152i | \(0.705811\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.47871 | + | 2.72203i | 0.330839 | + | 0.120415i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −9.80222 | − | 27.9212i | −0.432778 | − | 1.23275i | ||||
\(514\) | 0.933658 | 0.0411819 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.14529 | + | 6.49525i | 0.0504185 | + | 0.285937i | ||||
\(517\) | 28.6894 | − | 34.1907i | 1.26176 | − | 1.50371i | ||||
\(518\) | 22.6149 | + | 26.9514i | 0.993644 | + | 1.18418i | ||||
\(519\) | −7.09280 | + | 40.2253i | −0.311340 | + | 1.76569i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.81228 | + | 4.87102i | 0.123208 | + | 0.213403i | 0.921031 | − | 0.389489i | \(-0.127348\pi\) |
−0.797823 | + | 0.602892i | \(0.794015\pi\) | |||||||
\(522\) | 9.68405 | + | 26.6067i | 0.423859 | + | 1.16454i | ||||
\(523\) | 14.2976 | + | 39.2824i | 0.625192 | + | 1.71770i | 0.693908 | + | 0.720064i | \(0.255887\pi\) |
−0.0687164 | + | 0.997636i | \(0.521890\pi\) | |||||||
\(524\) | −4.90721 | − | 8.49954i | −0.214373 | − | 0.371304i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.57491 | − | 14.6030i | 0.112271 | − | 0.636723i | ||||
\(527\) | −2.67763 | − | 3.19108i | −0.116640 | − | 0.139006i | ||||
\(528\) | −7.84404 | + | 9.34816i | −0.341368 | + | 0.406826i | ||||
\(529\) | −2.18623 | − | 12.3987i | −0.0950536 | − | 0.539076i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −56.3846 | −2.44688 | ||||||||
\(532\) | −17.3617 | + | 2.85692i | −0.752723 | + | 0.123863i | ||||
\(533\) | 17.8222i | 0.771965i | ||||||||
\(534\) | 30.7495 | + | 11.1919i | 1.33066 | + | 0.484321i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.42859 | + | 7.07243i | 0.364060 | + | 0.305482i | ||||
\(537\) | 31.5791 | + | 37.6345i | 1.36274 | + | 1.62405i | ||||
\(538\) | 2.76340 | + | 0.487261i | 0.119138 | + | 0.0210073i | ||||
\(539\) | −19.6256 | + | 33.9926i | −0.845335 | + | 1.46416i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.0797 | − | 6.94444i | 0.820300 | − | 0.298565i | 0.102428 | − | 0.994740i | \(-0.467339\pi\) |
0.717871 | + | 0.696176i | \(0.245117\pi\) | |||||||
\(542\) | −2.80794 | − | 7.71475i | −0.120611 | − | 0.331377i | ||||
\(543\) | −49.9300 | + | 28.8271i | −2.14270 | + | 1.23709i | ||||
\(544\) | −0.765961 | + | 1.32668i | −0.0328403 | + | 0.0568811i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −49.3741 | + | 41.4298i | −2.11302 | + | 1.77303i | ||||
\(547\) | −23.7651 | + | 28.3221i | −1.01612 | + | 1.21097i | −0.0387920 | + | 0.999247i | \(0.512351\pi\) |
−0.977330 | + | 0.211720i | \(0.932093\pi\) | |||||||
\(548\) | 3.21773 | − | 0.567373i | 0.137455 | − | 0.0242370i | ||||
\(549\) | −22.6476 | − | 8.24306i | −0.966576 | − | 0.351805i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.74609 | + | 22.7652i | 0.159589 | + | 0.969829i | ||||
\(552\) | 17.2382i | 0.733708i | ||||||||
\(553\) | 17.1718 | − | 47.1791i | 0.730219 | − | 2.00626i | ||||
\(554\) | −3.50044 | − | 19.8520i | −0.148719 | − | 0.843430i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.21231 | − | 1.01725i | 0.0514132 | − | 0.0431408i | ||||
\(557\) | 12.2041 | + | 2.15190i | 0.517102 | + | 0.0911791i | 0.426108 | − | 0.904672i | \(-0.359884\pi\) |
0.0909943 | + | 0.995851i | \(0.470995\pi\) | |||||||
\(558\) | 12.5976 | + | 7.27321i | 0.533298 | + | 0.307900i | ||||
\(559\) | 6.30646 | + | 10.9231i | 0.266735 | + | 0.461998i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.5669 | + | 6.39382i | −0.741674 | + | 0.269947i | ||||
\(562\) | 4.29690 | − | 2.48082i | 0.181254 | − | 0.104647i | ||||
\(563\) | 8.54424 | + | 4.93302i | 0.360097 | + | 0.207902i | 0.669123 | − | 0.743152i | \(-0.266670\pi\) |
−0.309027 | + | 0.951053i | \(0.600003\pi\) | |||||||
\(564\) | −5.30286 | + | 30.0740i | −0.223291 | + | 1.26634i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.5695 | + | 9.70800i | 0.486304 | + | 0.408058i | ||||
\(567\) | 14.1849 | − | 2.50118i | 0.595711 | − | 0.105040i | ||||
\(568\) | 2.56005 | − | 7.03369i | 0.107417 | − | 0.295127i | ||||
\(569\) | −15.2083 | −0.637565 | −0.318782 | − | 0.947828i | \(-0.603274\pi\) | ||||
−0.318782 | + | 0.947828i | \(0.603274\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.6461 | −1.11511 | −0.557553 | − | 0.830141i | \(-0.688260\pi\) | ||||
−0.557553 | + | 0.830141i | \(0.688260\pi\) | |||||||
\(572\) | −7.98169 | + | 21.9295i | −0.333731 | + | 0.916920i | ||||
\(573\) | 28.6657 | − | 5.05454i | 1.19753 | − | 0.211156i | ||||
\(574\) | −9.97312 | − | 8.36844i | −0.416270 | − | 0.349292i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.928923 | − | 5.26818i | 0.0387051 | − | 0.219508i | ||||
\(577\) | −29.6874 | − | 17.1401i | −1.23590 | − | 0.713550i | −0.267650 | − | 0.963516i | \(-0.586247\pi\) |
−0.968254 | + | 0.249967i | \(0.919580\pi\) | |||||||
\(578\) | 12.6901 | − | 7.32661i | 0.527837 | − | 0.304747i | ||||
\(579\) | 12.4997 | − | 4.54950i | 0.519468 | − | 0.189071i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.74564 | + | 13.4158i | 0.321343 | + | 0.556583i | ||||
\(582\) | −34.1540 | − | 19.7188i | −1.41573 | − | 0.817372i | ||||
\(583\) | 10.7496 | + | 1.89545i | 0.445205 | + | 0.0785016i | ||||
\(584\) | −1.51035 | + | 1.26734i | −0.0624989 | + | 0.0524428i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.471769 | + | 2.67554i | 0.0194886 | + | 0.110525i | ||||
\(587\) | 10.9423 | − | 30.0636i | 0.451636 | − | 1.24086i | −0.479937 | − | 0.877303i | \(-0.659340\pi\) |
0.931572 | − | 0.363556i | \(-0.118437\pi\) | |||||||
\(588\) | − | 26.8559i | − | 1.10752i | ||||||
\(589\) | 8.99207 | + | 7.72226i | 0.370512 | + | 0.318190i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.95016 | + | 1.07377i | 0.121354 | + | 0.0441691i | ||||
\(592\) | −8.58348 | + | 1.51350i | −0.352779 | + | 0.0622044i | ||||
\(593\) | −10.8774 | + | 12.9632i | −0.446683 | + | 0.532336i | −0.941658 | − | 0.336571i | \(-0.890733\pi\) |
0.494975 | + | 0.868907i | \(0.335177\pi\) | |||||||
\(594\) | 21.9631 | − | 18.4292i | 0.901155 | − | 0.756159i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.03384 | − | 10.4509i | 0.247156 | − | 0.428086i | ||||
\(597\) | −3.25253 | + | 1.87785i | −0.133117 | + | 0.0768554i | ||||
\(598\) | 11.2750 | + | 30.9778i | 0.461069 | + | 1.26678i | ||||
\(599\) | −16.3401 | + | 5.94730i | −0.667637 | + | 0.243000i | −0.653530 | − | 0.756901i | \(-0.726713\pi\) |
−0.0141069 | + | 0.999900i | \(0.504491\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.18870 | − | 3.79093i | 0.0892787 | − | 0.154635i | −0.817928 | − | 0.575321i | \(-0.804877\pi\) |
0.907206 | + | 0.420686i | \(0.138210\pi\) | |||||||
\(602\) | −9.07367 | − | 1.59993i | −0.369815 | − | 0.0652084i | ||||
\(603\) | −37.8336 | − | 45.0883i | −1.54070 | − | 1.83614i | ||||
\(604\) | −3.81838 | − | 3.20400i | −0.155368 | − | 0.130369i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 38.6087 | + | 14.0524i | 1.56837 | + | 0.570841i | ||||
\(607\) | − | 36.1181i | − | 1.46599i | −0.680234 | − | 0.732995i | \(-0.738122\pi\) | ||
0.680234 | − | 0.732995i | \(-0.261878\pi\) | |||||||
\(608\) | 1.53760 | − | 4.07870i | 0.0623577 | − | 0.165413i | ||||
\(609\) | −61.7364 | −2.50168 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.1410 | + | 57.5126i | 0.410262 | + | 2.32671i | ||||
\(612\) | 5.26761 | − | 6.27769i | 0.212930 | − | 0.253761i | ||||
\(613\) | −8.07763 | − | 9.62654i | −0.326252 | − | 0.388812i | 0.577840 | − | 0.816150i | \(-0.303896\pi\) |
−0.904092 | + | 0.427338i | \(0.859451\pi\) | |||||||
\(614\) | 4.40223 | − | 24.9663i | 0.177660 | − | 1.00756i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.52372 | − | 14.7635i | −0.343430 | − | 0.594839i | ||||
\(617\) | −8.14855 | − | 22.3880i | −0.328048 | − | 0.901305i | −0.988605 | − | 0.150530i | \(-0.951902\pi\) |
0.660557 | − | 0.750776i | \(-0.270320\pi\) | |||||||
\(618\) | 7.91494 | + | 21.7461i | 0.318386 | + | 0.874757i | ||||
\(619\) | −0.743546 | − | 1.28786i | −0.0298856 | − | 0.0517635i | 0.850696 | − | 0.525658i | \(-0.176181\pi\) |
−0.880581 | + | 0.473895i | \(0.842848\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.03283 | − | 39.8851i | 0.282218 | − | 1.60054i | ||||
\(622\) | 2.41327 | + | 2.87603i | 0.0967634 | + | 0.115318i | ||||
\(623\) | −29.3837 | + | 35.0181i | −1.17723 | + | 1.40297i | ||||
\(624\) | −2.77268 | − | 15.7246i | −0.110996 | − | 0.629489i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −21.3618 | −0.853791 | ||||||||
\(627\) | 46.3672 | − | 26.0674i | 1.85173 | − | 1.04103i | ||||
\(628\) | 15.6709i | 0.625338i | ||||||||
\(629\) | −12.5468 | − | 4.56668i | −0.500275 | − | 0.182085i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.1333 | + | 16.8939i | 0.801495 | + | 0.672534i | 0.948562 | − | 0.316592i | \(-0.102539\pi\) |
−0.147067 | + | 0.989127i | \(0.546983\pi\) | |||||||
\(632\) | 7.99494 | + | 9.52800i | 0.318022 | + | 0.379003i | ||||
\(633\) | −14.7409 | − | 2.59922i | −0.585898 | − | 0.103310i | ||||
\(634\) | 10.2571 | − | 17.7657i | 0.407360 | − | 0.705568i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.01801 | + | 2.55435i | −0.278282 | + | 0.101286i | ||||
\(637\) | −17.5656 | − | 48.2610i | −0.695973 | − | 1.91217i | ||||
\(638\) | −19.3584 | + | 11.1766i | −0.766407 | + | 0.442485i | ||||
\(639\) | −20.0206 | + | 34.6767i | −0.792002 | + | 1.37179i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.77655 | + | 3.16890i | −0.149165 | + | 0.125164i | −0.714316 | − | 0.699823i | \(-0.753262\pi\) |
0.565151 | + | 0.824987i | \(0.308818\pi\) | |||||||
\(642\) | 32.5949 | − | 38.8451i | 1.28642 | − | 1.53309i | ||||
\(643\) | −7.58704 | + | 1.33780i | −0.299204 | + | 0.0527577i | −0.321235 | − | 0.947000i | \(-0.604098\pi\) |
0.0220310 | + | 0.999757i | \(0.492987\pi\) | |||||||
\(644\) | −22.6290 | − | 8.23629i | −0.891709 | − | 0.324555i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.16403 | − | 4.23341i | 0.203176 | − | 0.166561i | ||||
\(647\) | − | 33.7875i | − | 1.32832i | −0.747590 | − | 0.664161i | \(-0.768789\pi\) | ||
0.747590 | − | 0.664161i | \(-0.231211\pi\) | |||||||
\(648\) | −1.22042 | + | 3.35309i | −0.0479428 | + | 0.131722i | ||||
\(649\) | −7.72973 | − | 43.8375i | −0.303418 | − | 1.72077i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.2966 | + | 20.3873i | −0.952260 | + | 0.799041i | ||||
\(652\) | −8.28486 | − | 1.46084i | −0.324460 | − | 0.0572111i | ||||
\(653\) | 10.7184 | + | 6.18826i | 0.419442 | + | 0.242165i | 0.694839 | − | 0.719166i | \(-0.255476\pi\) |
−0.275396 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(654\) | 11.5359 | + | 19.9808i | 0.451091 | + | 0.781312i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.03073 | − | 1.10309i | 0.118330 | − | 0.0430686i | ||||
\(657\) | 9.13408 | − | 5.27357i | 0.356355 | − | 0.205741i | ||||
\(658\) | −36.9452 | − | 21.3303i | −1.44027 | − | 0.831542i | ||||
\(659\) | −1.69829 | + | 9.63145i | −0.0661558 | + | 0.375188i | 0.933698 | + | 0.358063i | \(0.116563\pi\) |
−0.999853 | + | 0.0171255i | \(0.994549\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.0726 | + | 10.9692i | 0.508466 | + | 0.426654i | 0.860589 | − | 0.509300i | \(-0.170096\pi\) |
−0.352123 | + | 0.935954i | \(0.614540\pi\) | |||||||
\(662\) | −32.2500 | + | 5.68654i | −1.25343 | + | 0.221014i | ||||
\(663\) | 8.36599 | − | 22.9854i | 0.324908 | − | 0.892678i | ||||
\(664\) | −3.83770 | −0.148932 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 46.6253 | 1.80669 | ||||||||
\(667\) | −10.7997 | + | 29.6719i | −0.418166 | + | 1.14890i | ||||
\(668\) | −3.15398 | + | 0.556132i | −0.122031 | + | 0.0215174i | ||||
\(669\) | −17.9043 | − | 15.0235i | −0.692221 | − | 0.580843i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.30400 | − | 18.7379i | 0.127550 | − | 0.723370i | ||||
\(672\) | 10.1013 | + | 5.83197i | 0.389665 | + | 0.224973i | ||||
\(673\) | −21.1903 | + | 12.2342i | −0.816826 | + | 0.471595i | −0.849321 | − | 0.527877i | \(-0.822988\pi\) |
0.0324944 | + | 0.999472i | \(0.489655\pi\) | |||||||
\(674\) | −22.4611 | + | 8.17518i | −0.865170 | + | 0.314896i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.76759 | − | 15.1859i | −0.337215 | − | 0.584074i | ||||
\(677\) | 2.20353 | + | 1.27221i | 0.0846884 | + | 0.0488949i | 0.541746 | − | 0.840542i | \(-0.317763\pi\) |
−0.457058 | + | 0.889437i | \(0.651097\pi\) | |||||||
\(678\) | −22.3677 | − | 3.94402i | −0.859025 | − | 0.151469i | ||||
\(679\) | 42.2039 | − | 35.4132i | 1.61964 | − | 1.35904i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.27866 | + | 18.5942i | 0.125638 | + | 0.712531i | ||||
\(682\) | −3.92773 | + | 10.7914i | −0.150401 | + | 0.413222i | ||||
\(683\) | 13.2825i | 0.508240i | 0.967173 | + | 0.254120i | \(0.0817857\pi\) | ||||
−0.967173 | + | 0.254120i | \(0.918214\pi\) | |||||||
\(684\) | −11.8891 | + | 20.0590i | −0.454592 | + | 0.766976i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.70214 | + | 3.16732i | 0.332249 | + | 0.120929i | ||||
\(687\) | −73.6727 | + | 12.9905i | −2.81079 | + | 0.495618i | ||||
\(688\) | 1.46718 | − | 1.74851i | 0.0559356 | − | 0.0666615i | ||||
\(689\) | −10.9409 | + | 9.18052i | −0.416816 | + | 0.349750i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.25288 | − | 5.63415i | 0.123745 | − | 0.214333i | −0.797497 | − | 0.603324i | \(-0.793843\pi\) |
0.921242 | + | 0.388990i | \(0.127176\pi\) | |||||||
\(692\) | 12.2419 | − | 7.06787i | 0.465368 | − | 0.268680i | ||||
\(693\) | 31.1903 | + | 85.6948i | 1.18482 | + | 3.25528i | ||||
\(694\) | −12.8434 | + | 4.67460i | −0.487527 | + | 0.177445i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.64707 | − | 13.2451i | 0.289861 | − | 0.502055i | ||||
\(697\) | 4.86574 | + | 0.857961i | 0.184303 | + | 0.0324976i | ||||
\(698\) | 16.3048 | + | 19.4313i | 0.617145 | + | 0.735485i | ||||
\(699\) | 50.2485 | + | 42.1635i | 1.90057 | + | 1.59477i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.89524 | − | 2.14569i | −0.222660 | − | 0.0810417i | 0.228281 | − | 0.973595i | \(-0.426689\pi\) |
−0.450941 | + | 0.892554i | \(0.648912\pi\) | |||||||
\(702\) | 37.5142i | 1.41588i | ||||||||
\(703\) | 37.3366 | + | 7.02481i | 1.40818 | + | 0.264946i | ||||
\(704\) | 4.22321 | 0.159168 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.13144 | + | 17.7593i | 0.117853 | + | 0.668380i | ||||
\(707\) | −36.8939 | + | 43.9684i | −1.38754 | + | 1.65360i | ||||
\(708\) | 19.5771 | + | 23.3310i | 0.735751 | + | 0.876834i | ||||
\(709\) | −1.34174 | + | 7.60941i | −0.0503903 | + | 0.285777i | −0.999582 | − | 0.0289219i | \(-0.990793\pi\) |
0.949191 | + | 0.314699i | \(0.101904\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.2680 | − | 57.6219i | −1.24765 | − | 2.16099i | ||||
\(712\) | −3.87324 | − | 10.6416i | −0.145156 | − | 0.398812i | ||||
\(713\) | 5.54834 | + | 15.2439i | 0.207787 | + | 0.570890i | ||||
\(714\) | 8.93412 | + | 15.4743i | 0.334351 | + | 0.579113i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.95239 | − | 16.7438i | 0.110336 | − | 0.625746i | ||||
\(717\) | −16.6375 | − | 19.8278i | −0.621339 | − | 0.740483i | ||||
\(718\) | −10.3560 | + | 12.3418i | −0.386483 | + | 0.460593i | ||||
\(719\) | 1.92572 | + | 10.9213i | 0.0718173 | + | 0.407296i | 0.999430 | + | 0.0337534i | \(0.0107461\pi\) |
−0.927613 | + | 0.373543i | \(0.878143\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.3283 | −1.20397 | ||||||||
\(722\) | −12.5428 | + | 14.2716i | −0.466794 | + | 0.531134i | ||||
\(723\) | − | 9.69296i | − | 0.360485i | ||||||
\(724\) | 18.7494 | + | 6.82423i | 0.696817 | + | 0.253621i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 15.1306 | + | 12.6961i | 0.561549 | + | 0.471195i | ||||
\(727\) | −19.0466 | − | 22.6989i | −0.706401 | − | 0.841855i | 0.286834 | − | 0.957980i | \(-0.407397\pi\) |
−0.993235 | + | 0.116125i | \(0.962953\pi\) | |||||||
\(728\) | 21.9669 | + | 3.87335i | 0.814146 | + | 0.143556i | ||||
\(729\) | −19.8808 | + | 34.4345i | −0.736325 | + | 1.27535i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.28577 | − | 1.19592i | 0.121529 | − | 0.0442328i | ||||
\(732\) | 4.45254 | + | 12.2333i | 0.164571 | + | 0.452154i | ||||
\(733\) | 22.9943 | − | 13.2758i | 0.849314 | − | 0.490352i | −0.0111055 | − | 0.999938i | \(-0.503535\pi\) |
0.860419 | + | 0.509587i | \(0.170202\pi\) | |||||||
\(734\) | 4.95323 | − | 8.57924i | 0.182827 | − | 0.316666i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.57002 | − | 3.83470i | 0.168453 | − | 0.141349i | ||||
\(737\) | 29.8684 | − | 35.5957i | 1.10022 | − | 1.31119i | ||||
\(738\) | −16.9911 | + | 2.99599i | −0.625451 | + | 0.110284i | ||||
\(739\) | 16.6006 | + | 6.04212i | 0.610663 | + | 0.222263i | 0.628793 | − | 0.777573i | \(-0.283549\pi\) |
−0.0181306 | + | 0.999836i | \(0.505771\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.8692 | + | 68.3994i | −0.472762 | + | 2.51271i | ||||
\(742\) | − | 10.4331i | − | 0.383013i | ||||||
\(743\) | −2.83848 | + | 7.79867i | −0.104134 | + | 0.286105i | −0.980807 | − | 0.194981i | \(-0.937535\pi\) |
0.876673 | + | 0.481086i | \(0.159758\pi\) | |||||||
\(744\) | −1.36441 | − | 7.73798i | −0.0500219 | − | 0.283688i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.71137 | − | 5.63151i | 0.245721 | − | 0.206184i | ||||
\(747\) | 20.2177 | + | 3.56493i | 0.739727 | + | 0.130434i | ||||
\(748\) | 5.60287 | + | 3.23482i | 0.204861 | + | 0.118277i | ||||
\(749\) | 35.4193 | + | 61.3480i | 1.29419 | + | 2.24161i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.43969 | + | 1.25195i | −0.125516 | + | 0.0456841i | −0.404015 | − | 0.914753i | \(-0.632386\pi\) |
0.278498 | + | 0.960437i | \(0.410163\pi\) | |||||||
\(752\) | 9.15254 | − | 5.28422i | 0.333759 | − | 0.192696i | ||||
\(753\) | 55.8468 | + | 32.2432i | 2.03517 | + | 1.17501i | ||||
\(754\) | 5.07886 | − | 28.8037i | 0.184961 | − | 1.04897i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −20.9926 | − | 17.6149i | −0.763492 | − | 0.640646i | ||||
\(757\) | 39.8461 | − | 7.02594i | 1.44823 | − | 0.255362i | 0.606424 | − | 0.795141i | \(-0.292603\pi\) |
0.841807 | + | 0.539779i | \(0.181492\pi\) | |||||||
\(758\) | −3.24743 | + | 8.92224i | −0.117952 | + | 0.324070i | ||||
\(759\) | 72.8008 | 2.64250 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.2575 | −0.589335 | −0.294667 | − | 0.955600i | \(-0.595209\pi\) | ||||
−0.294667 | + | 0.955600i | \(0.595209\pi\) | |||||||
\(762\) | 18.3345 | − | 50.3736i | 0.664188 | − | 1.82484i | ||||
\(763\) | −31.7410 | + | 5.59680i | −1.14910 | + | 0.202618i | ||||
\(764\) | −7.71678 | − | 6.47515i | −0.279183 | − | 0.234263i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.09296 | + | 28.8836i | −0.184016 | + | 1.04361i | ||||
\(767\) | 50.4408 | + | 29.1220i | 1.82131 | + | 1.05153i | ||||
\(768\) | −2.50242 | + | 1.44477i | −0.0902982 | + | 0.0521337i | ||||
\(769\) | −4.84451 | + | 1.76326i | −0.174697 | + | 0.0635846i | −0.427888 | − | 0.903832i | \(-0.640742\pi\) |
0.253191 | + | 0.967416i | \(0.418520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.34892 | + | 2.33640i | 0.0485802 | + | 0.0841434i | ||||
\(772\) | −3.98670 | − | 2.30172i | −0.143485 | − | 0.0828409i | ||||
\(773\) | −34.6179 | − | 6.10407i | −1.24512 | − | 0.219548i | −0.488012 | − | 0.872837i | \(-0.662278\pi\) |
−0.757109 | + | 0.653289i | \(0.773389\pi\) | |||||||
\(774\) | −9.35359 | + | 7.84860i | −0.336208 | + | 0.282112i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.37002 | + | 13.4411i | 0.0850788 | + | 0.482506i | ||||
\(777\) | −34.7703 | + | 95.5307i | −1.24738 | + | 3.42714i | ||||
\(778\) | − | 12.0710i | − | 0.432768i | ||||||
\(779\) | −14.0575 | − | 0.160840i | −0.503664 | − | 0.00576268i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.7048 | − | 10.8117i | −1.06292 | − | 0.386871i | ||||
\(782\) | 9.00020 | − | 1.58698i | 0.321846 | − | 0.0567502i | ||||
\(783\) | −23.0972 | + | 27.5262i | −0.825426 | + | 0.983705i | ||||
\(784\) | −7.11974 | + | 5.97417i | −0.254277 | + | 0.213363i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 14.1796 | − | 24.5598i | 0.505770 | − | 0.876019i | ||||
\(787\) | 23.3860 | − | 13.5019i | 0.833622 | − | 0.481292i | −0.0214692 | − | 0.999770i | \(-0.506834\pi\) |
0.855091 | + | 0.518478i | \(0.173501\pi\) | |||||||
\(788\) | −0.371606 | − | 1.02098i | −0.0132379 | − | 0.0363709i | ||||
\(789\) | 40.2631 | − | 14.6546i | 1.43340 | − | 0.521716i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.8645 | − | 27.4781i | 0.564076 | − | 0.977009i | ||||
\(792\) | −22.2487 | − | 3.92304i | −0.790572 | − | 0.139399i | ||||
\(793\) | 16.0028 | + | 19.0714i | 0.568275 | + | 0.677244i | ||||
\(794\) | 8.77457 | + | 7.36274i | 0.311398 | + | 0.261294i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.22137 | + | 0.444543i | 0.0432904 | + | 0.0157564i | ||||
\(797\) | − | 19.8667i | − | 0.703715i | −0.936054 | − | 0.351857i | \(-0.885550\pi\) | ||
0.936054 | − | 0.351857i | \(-0.114450\pi\) | |||||||
\(798\) | −32.2328 | − | 39.3185i | −1.14103 | − | 1.39186i | ||||
\(799\) | 16.1900 | 0.572762 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.5197 | + | 59.6601i | 0.371695 | + | 2.10798i | ||||
\(802\) | 3.19354 | − | 3.80592i | 0.112768 | − | 0.134392i | ||||
\(803\) | 5.35224 | + | 6.37855i | 0.188876 | + | 0.225094i | ||||
\(804\) | −5.52078 | + | 31.3099i | −0.194703 | + | 1.10421i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.51307 | − | 13.0130i | −0.264637 | − | 0.458364i | ||||
\(807\) | 2.77314 | + | 7.61915i | 0.0976193 | + | 0.268207i | ||||
\(808\) | −4.86320 | − | 13.3615i | −0.171087 | − | 0.470057i | ||||
\(809\) | −9.17170 | − | 15.8859i | −0.322460 | − | 0.558517i | 0.658535 | − | 0.752550i | \(-0.271176\pi\) |
−0.980995 | + | 0.194033i | \(0.937843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.96210 | − | 45.1553i | 0.279587 | − | 1.58562i | −0.444416 | − | 0.895820i | \(-0.646589\pi\) |
0.724003 | − | 0.689796i | \(-0.242300\pi\) | |||||||
\(812\) | 13.7334 | + | 16.3669i | 0.481950 | + | 0.574365i | ||||
\(813\) | 15.2487 | − | 18.1727i | 0.534795 | − | 0.637344i | ||||
\(814\) | 6.39183 | + | 36.2499i | 0.224034 | + | 1.27056i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.42655 | −0.154960 | ||||||||
\(817\) | −8.67269 | + | 4.87574i | −0.303419 | + | 0.170581i | ||||
\(818\) | − | 1.29844i | − | 0.0453989i | ||||||
\(819\) | −112.127 | − | 40.8110i | −3.91805 | − | 1.42605i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.8300 | − | 10.7656i | −0.447769 | − | 0.375723i | 0.390838 | − | 0.920459i | \(-0.372185\pi\) |
−0.838607 | + | 0.544737i | \(0.816630\pi\) | |||||||
\(822\) | 6.06869 | + | 7.23239i | 0.211670 | + | 0.252258i | ||||
\(823\) | −14.3394 | − | 2.52843i | −0.499841 | − | 0.0881355i | −0.0819572 | − | 0.996636i | \(-0.526117\pi\) |
−0.417884 | + | 0.908500i | \(0.637228\pi\) | |||||||
\(824\) | 4.00440 | − | 6.93582i | 0.139500 | − | 0.241621i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −39.9809 | + | 14.5519i | −1.39111 | + | 0.506324i | ||||
\(827\) | −1.27214 | − | 3.49518i | −0.0442367 | − | 0.121539i | 0.915607 | − | 0.402074i | \(-0.131710\pi\) |
−0.959844 | + | 0.280535i | \(0.909488\pi\) | |||||||
\(828\) | −27.6378 | + | 15.9567i | −0.960481 | + | 0.554534i | ||||
\(829\) | −9.26652 | + | 16.0501i | −0.321840 | + | 0.557442i | −0.980868 | − | 0.194676i | \(-0.937634\pi\) |
0.659028 | + | 0.752118i | \(0.270968\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 44.6206 | − | 37.4411i | 1.54787 | − | 1.29882i | ||||
\(832\) | −3.55196 | + | 4.23306i | −0.123142 | + | 0.146755i | ||||
\(833\) | −14.0216 | + | 2.47239i | −0.485820 | + | 0.0856633i | ||||
\(834\) | 4.29708 | + | 1.56401i | 0.148796 | + | 0.0541572i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −17.2252 | − | 6.49360i | −0.595747 | − | 0.224586i | ||||
\(837\) | 18.4605i | 0.638087i | ||||||||
\(838\) | 12.3619 | − | 33.9641i | 0.427035 | − | 1.17327i | ||||
\(839\) | −4.49001 | − | 25.4641i | −0.155013 | − | 0.879120i | −0.958774 | − | 0.284168i | \(-0.908282\pi\) |
0.803762 | − | 0.594951i | \(-0.202829\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.754479 | + | 0.633083i | −0.0260165 | + | 0.0218305i | ||||
\(842\) | −29.9955 | − | 5.28902i | −1.03371 | − | 0.182272i | ||||
\(843\) | 12.4161 | + | 7.16843i | 0.427633 | + | 0.246894i | ||||
\(844\) | 2.59008 | + | 4.48615i | 0.0891543 | + | 0.154420i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −53.1259 | + | 19.3362i | −1.82650 | + | 0.664793i | ||||
\(847\) | −23.8957 | + | 13.7962i | −0.821066 | + | 0.474042i | ||||
\(848\) | 2.23836 | + | 1.29232i | 0.0768656 | + | 0.0443784i | ||||
\(849\) | −7.57812 | + | 42.9777i | −0.260080 | + | 1.47499i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.8318 | + | 33.4229i | 1.36542 | + | 1.14572i | ||||
\(852\) | 21.2999 | − | 3.75575i | 0.729723 | − | 0.128670i | ||||
\(853\) | −10.7040 | + | 29.4089i | −0.366497 | + | 1.00694i | 0.610186 | + | 0.792258i | \(0.291095\pi\) |
−0.976683 | + | 0.214685i | \(0.931128\pi\) | |||||||
\(854\) | −18.1863 | −0.622321 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.5490 | −0.599814 | ||||||||
\(857\) | −1.15540 | + | 3.17443i | −0.0394677 | + | 0.108437i | −0.957861 | − | 0.287232i | \(-0.907265\pi\) |
0.918393 | + | 0.395669i | \(0.129487\pi\) | |||||||
\(858\) | −66.4085 | + | 11.7096i | −2.26715 | + | 0.399760i | ||||
\(859\) | 39.0805 | + | 32.7924i | 1.33341 | + | 1.11886i | 0.983268 | + | 0.182167i | \(0.0583112\pi\) |
0.350142 | + | 0.936697i | \(0.386133\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.53245 | − | 37.0474i | 0.222625 | − | 1.26257i | ||||
\(862\) | 31.2017 | + | 18.0143i | 1.06273 | + | 0.613570i | ||||
\(863\) | 21.3865 | − | 12.3475i | 0.728006 | − | 0.420315i | −0.0896861 | − | 0.995970i | \(-0.528586\pi\) |
0.817692 | + | 0.575656i | \(0.195253\pi\) | |||||||
\(864\) | 6.37942 | − | 2.32192i | 0.217032 | − | 0.0789933i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.5606 | − | 25.2198i | −0.494791 | − | 0.857003i | ||||
\(867\) | 36.6685 | + | 21.1705i | 1.24533 | + | 0.718989i | ||||
\(868\) | 10.8097 | + | 1.90605i | 0.366906 | + | 0.0646954i | ||||
\(869\) | 40.2388 | − | 33.7643i | 1.36501 | − | 1.14538i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5578 | + | 59.8760i | 0.357736 | + | 2.02882i | ||||
\(872\) | 2.73090 | − | 7.50308i | 0.0924798 | − | 0.254086i | ||||
\(873\) | − | 73.0115i | − | 2.47107i | ||||||
\(874\) | −24.5360 | + | 8.61376i | −0.829941 | + | 0.291365i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.35352 | − | 1.94852i | −0.180879 | − | 0.0658345i | ||||
\(877\) | −6.87335 | + | 1.21196i | −0.232096 | + | 0.0409249i | −0.288487 | − | 0.957484i | \(-0.593152\pi\) |
0.0563901 | + | 0.998409i | \(0.482041\pi\) | |||||||
\(878\) | 2.09756 | − | 2.49978i | 0.0707894 | − | 0.0843635i | ||||
\(879\) | −6.01371 | + | 5.04610i | −0.202837 | + | 0.170201i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.780822 | + | 1.35242i | −0.0263065 | + | 0.0455643i | −0.878879 | − | 0.477045i | \(-0.841708\pi\) |
0.852572 | + | 0.522609i | \(0.175041\pi\) | |||||||
\(882\) | 43.0576 | − | 24.8593i | 1.44983 | − | 0.837058i | ||||
\(883\) | −18.4078 | − | 50.5749i | −0.619471 | − | 1.70198i | −0.708278 | − | 0.705933i | \(-0.750528\pi\) |
0.0888076 | − | 0.996049i | \(-0.471694\pi\) | |||||||
\(884\) | −7.95468 | + | 2.89527i | −0.267545 | + | 0.0973783i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.0395 | − | 29.5132i | 0.572452 | − | 0.991516i | ||||
\(887\) | −49.2169 | − | 8.67826i | −1.65254 | − | 0.291388i | −0.731787 | − | 0.681533i | \(-0.761314\pi\) |
−0.920753 | + | 0.390145i | \(0.872425\pi\) | |||||||
\(888\) | −16.1886 | − | 19.2928i | −0.543253 | − | 0.647424i | ||||
\(889\) | 57.3665 | + | 48.1362i | 1.92401 | + | 1.61444i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.1608 | + | 5.15412i | 0.474405 | + | 0.172669i | ||||
\(892\) | 8.08863i | 0.270827i | ||||||||
\(893\) | −45.4555 | + | 7.47985i | −1.52111 | + | 0.250304i | ||||
\(894\) | 34.8700 | 1.16623 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.700949 | − | 3.97528i | −0.0234171 | − | 0.132805i | ||||
\(897\) | −61.2295 | + | 72.9705i | −2.04439 | + | 2.43641i | ||||
\(898\) | −20.6442 | − | 24.6028i | −0.688907 | − | 0.821007i | ||||
\(899\) | 2.49927 | − | 14.1741i | 0.0833553 | − | 0.472732i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.97973 | + | 3.42899i | 0.0659543 | + | 0.114236i | ||||
\(902\) | −4.65860 | − | 12.7994i | −0.155115 | − | 0.426174i | ||||
\(903\) | −9.10567 | − | 25.0176i | −0.303018 | − | 0.832535i | ||||
\(904\) | 3.93016 | + | 6.80723i | 0.130715 | + | 0.226405i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.50106 | − | 14.1842i | 0.0830923 | − | 0.471240i | ||||
\(907\) | −32.7593 | − | 39.0410i | −1.08776 | − | 1.29634i | −0.952169 | − | 0.305571i | \(-0.901153\pi\) |
−0.135586 | − | 0.990766i | \(-0.543292\pi\) | |||||||
\(908\) | 4.20014 | − | 5.00554i | 0.139387 | − | 0.166115i | ||||
\(909\) | 13.2084 | + | 74.9085i | 0.438095 | + | 2.48456i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.8444 | −1.22071 | −0.610355 | − | 0.792128i | \(-0.708973\pi\) | ||||
−0.610355 | + | 0.792128i | \(0.708973\pi\) | |||||||
\(912\) | 12.4281 | − | 2.04508i | 0.411535 | − | 0.0677195i | ||||
\(913\) | 16.2074i | 0.536388i | ||||||||
\(914\) | 8.14262 | + | 2.96367i | 0.269334 | + | 0.0980295i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.8326 | + | 16.6415i | 0.655288 | + | 0.549852i | ||||
\(917\) | 25.4653 | + | 30.3483i | 0.840938 | + | 1.00219i | ||||
\(918\) | 10.2420 | + | 1.80594i | 0.338035 | + | 0.0596048i | ||||
\(919\) | −7.33804 | + | 12.7099i | −0.242060 | + | 0.419260i | −0.961301 | − | 0.275501i | \(-0.911156\pi\) |
0.719241 | + | 0.694761i | \(0.244490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 68.8363 | − | 25.0543i | 2.26823 | − | 0.825569i | ||||
\(922\) | 6.06724 | + | 16.6696i | 0.199814 | + | 0.548984i | ||||
\(923\) | 35.8202 | − | 20.6808i | 1.17904 | − | 0.680717i | ||||
\(924\) | 24.6296 | − | 42.6598i | 0.810256 | − | 1.40340i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −20.3013 | + | 17.0348i | −0.667143 | + | 0.559799i | ||||
\(927\) | −27.5387 | + | 32.8194i | −0.904490 | + | 1.07793i | ||||
\(928\) | −5.21252 | + | 0.919107i | −0.171109 | + | 0.0301712i | ||||
\(929\) | 35.9586 | + | 13.0879i | 1.17976 | + | 0.429399i | 0.856119 | − | 0.516780i | \(-0.172869\pi\) |
0.323645 | + | 0.946178i | \(0.395092\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.2252 | − | 13.4196i | 1.25278 | − | 0.439809i | ||||
\(932\) | − | 22.7007i | − | 0.743587i | ||||||
\(933\) | −3.71039 | + | 10.1942i | −0.121473 | + | 0.333744i | ||||
\(934\) | −2.72884 | − | 15.4760i | −0.0892905 | − | 0.506392i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 22.6445 | − | 19.0010i | 0.740160 | − | 0.621068i | ||||
\(937\) | 9.32123 | + | 1.64359i | 0.304511 | + | 0.0536936i | 0.323816 | − | 0.946120i | \(-0.395034\pi\) |
−0.0193046 | + | 0.999814i | \(0.506145\pi\) | |||||||
\(938\) | −38.4634 | − | 22.2069i | −1.25587 | − | 0.725079i | ||||
\(939\) | −30.8630 | − | 53.4562i | −1.00717 | − | 1.74448i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.1763 | + | 7.70755i | −0.690328 | + | 0.251259i | −0.663276 | − | 0.748375i | \(-0.730834\pi\) |
−0.0270523 | + | 0.999634i | \(0.508612\pi\) | |||||||
\(942\) | −39.2152 | + | 22.6409i | −1.27770 | + | 0.737680i | ||||
\(943\) | −16.6631 | − | 9.62044i | −0.542625 | − | 0.313285i | ||||
\(944\) | 1.83030 | − | 10.3801i | 0.0595710 | − | 0.337844i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.38435 | − | 6.19621i | −0.240086 | − | 0.201456i | ||||
\(947\) | −40.7294 | + | 7.18168i | −1.32353 | + | 0.233373i | −0.790363 | − | 0.612639i | \(-0.790108\pi\) |
−0.533163 | + | 0.846012i | \(0.678997\pi\) | |||||||
\(948\) | −12.2922 | + | 33.7724i | −0.399231 | + | 1.09688i | ||||
\(949\) | −10.8950 | −0.353665 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 59.2764 | 1.92217 | ||||||||
\(952\) | 2.11497 | − | 5.81083i | 0.0685466 | − | 0.188330i | ||||
\(953\) | −1.63331 | + | 0.287997i | −0.0529083 | + | 0.00932915i | −0.200040 | − | 0.979788i | \(-0.564107\pi\) |
0.147131 | + | 0.989117i | \(0.452996\pi\) | |||||||
\(954\) | −10.5916 | − | 8.88743i | −0.342916 | − | 0.287741i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.55547 | + | 8.82152i | −0.0503076 | + | 0.285308i | ||||
\(957\) | −55.9370 | − | 32.2952i | −1.80819 | − | 1.04396i | ||||
\(958\) | 7.94808 | − | 4.58883i | 0.256791 | − | 0.148258i | ||||
\(959\) | −12.3937 | + | 4.51093i | −0.400213 | + | 0.145666i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.8029 | + | 20.4432i | 0.380738 | + | 0.659457i | ||||
\(962\) | −41.7103 | − | 24.0814i | −1.34479 | − | 0.776416i | ||||
\(963\) | 92.4516 | + | 16.3017i | 2.97921 | + | 0.525315i | ||||
\(964\) | −2.56969 | + | 2.15623i | −0.0827642 | + | 0.0694474i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.0831 | − | 68.5268i | −0.388768 | − | 2.20481i | ||||
\(967\) | −13.8597 | + | 38.0792i | −0.445697 | + | 1.22454i | 0.489994 | + | 0.871726i | \(0.336999\pi\) |
−0.935692 | + | 0.352818i | \(0.885223\pi\) | |||||||
\(968\) | − | 6.83554i | − | 0.219703i | ||||||
\(969\) | 18.0546 | + | 6.80625i | 0.579997 | + | 0.218648i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.2395 | + | 10.2783i | 0.906248 | + | 0.329847i | 0.752754 | − | 0.658302i | \(-0.228725\pi\) |
0.153494 | + | 0.988150i | \(0.450947\pi\) | |||||||
\(972\) | 9.90305 | − | 1.74617i | 0.317640 | − | 0.0560086i | ||||
\(973\) | −4.10622 | + | 4.89360i | −0.131639 | + | 0.156882i | ||||
\(974\) | 20.3715 | − | 17.0937i | 0.652745 | − | 0.547718i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.25267 | − | 3.90174i | 0.0721061 | − | 0.124892i | ||||
\(977\) | 26.0144 | − | 15.0194i | 0.832273 | − | 0.480513i | −0.0223570 | − | 0.999750i | \(-0.507117\pi\) |
0.854630 | + | 0.519237i | \(0.173784\pi\) | |||||||
\(978\) | −8.31408 | − | 22.8427i | −0.265855 | − | 0.730431i | ||||
\(979\) | −44.9419 | + | 16.3575i | −1.43635 | + | 0.522789i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.3566 | + | 36.9908i | −0.681865 | + | 1.18102i | ||||
\(982\) | −33.4038 | − | 5.89000i | −1.06596 | − | 0.187957i | ||||
\(983\) | 12.4389 | + | 14.8241i | 0.396740 | + | 0.472816i | 0.927023 | − | 0.375004i | \(-0.122359\pi\) |
−0.530283 | + | 0.847821i | \(0.677914\pi\) | |||||||
\(984\) | 7.13911 | + | 5.99042i | 0.227586 | + | 0.190968i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.61936 | − | 2.77322i | −0.242650 | − | 0.0883173i | ||||
\(987\) | − | 123.270i | − | 3.92371i | ||||||
\(988\) | 20.9961 | − | 11.8039i | 0.667975 | − | 0.375532i | ||||
\(989\) | −13.6169 | −0.432993 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.11302 | + | 17.6548i | 0.0988885 | + | 0.560824i | 0.993486 | + | 0.113952i | \(0.0363510\pi\) |
−0.894598 | + | 0.446872i | \(0.852538\pi\) | |||||||
\(992\) | −1.74789 | + | 2.08306i | −0.0554956 | + | 0.0661371i | ||||
\(993\) | −60.8239 | − | 72.4871i | −1.93019 | − | 2.30031i | ||||
\(994\) | −5.24667 | + | 29.7553i | −0.166414 | + | 0.943782i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.54460 | − | 9.60353i | −0.175687 | − | 0.304299i | ||||
\(997\) | 14.1528 | + | 38.8845i | 0.448224 | + | 1.23149i | 0.933959 | + | 0.357380i | \(0.116330\pi\) |
−0.485735 | + | 0.874106i | \(0.661448\pi\) | |||||||
\(998\) | −9.45462 | − | 25.9763i | −0.299281 | − | 0.822267i | ||||
\(999\) | 29.5854 | + | 51.2434i | 0.936041 | + | 1.62127i |
(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 | 950.2.u.h.99.8 | 48 | ||
5.2 | odd | 4 | 950.2.l.j.251.1 | ✓ | 24 | ||
5.3 | odd | 4 | 950.2.l.k.251.4 | yes | 24 | ||
5.4 | even | 2 | inner | 950.2.u.h.99.1 | 48 | ||
19.5 | even | 9 | inner | 950.2.u.h.499.1 | 48 | ||
95.24 | even | 18 | inner | 950.2.u.h.499.8 | 48 | ||
95.43 | odd | 36 | 950.2.l.k.651.4 | yes | 24 | ||
95.62 | odd | 36 | 950.2.l.j.651.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.l.j.251.1 | ✓ | 24 | 5.2 | odd | 4 | ||
950.2.l.j.651.1 | yes | 24 | 95.62 | odd | 36 | ||
950.2.l.k.251.4 | yes | 24 | 5.3 | odd | 4 | ||
950.2.l.k.651.4 | yes | 24 | 95.43 | odd | 36 | ||
950.2.u.h.99.1 | 48 | 5.4 | even | 2 | inner | ||
950.2.u.h.99.8 | 48 | 1.1 | even | 1 | trivial | ||
950.2.u.h.499.1 | 48 | 19.5 | even | 9 | inner | ||
950.2.u.h.499.8 | 48 | 95.24 | even | 18 | inner |