Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(293,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.w (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.79102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 293.8 | ||
Character | \(\chi\) | \(=\) | 600.293 |
Dual form | 600.2.w.k.557.8 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.18496 | + | 0.771921i | −0.837895 | + | 0.545831i | ||||
\(3\) | 1.57845 | − | 0.713099i | 0.911316 | − | 0.411708i | ||||
\(4\) | 0.808275 | − | 1.82940i | 0.404138 | − | 0.914698i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.31994 | + | 2.06343i | −0.538864 | + | 0.842392i | ||||
\(7\) | −1.44651 | + | 1.44651i | −0.546728 | + | 0.546728i | −0.925493 | − | 0.378765i | \(-0.876349\pi\) |
0.378765 | + | 0.925493i | \(0.376349\pi\) | |||||||
\(8\) | 0.454373 | + | 2.79169i | 0.160645 | + | 0.987012i | ||||
\(9\) | 1.98298 | − | 2.25118i | 0.660993 | − | 0.750392i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.641278 | 0.193353 | 0.0966764 | − | 0.995316i | \(-0.469179\pi\) | ||||
0.0966764 | + | 0.995316i | \(0.469179\pi\) | |||||||
\(12\) | −0.0287228 | − | 3.46398i | −0.00829157 | − | 0.999966i | ||||
\(13\) | 2.03304 | − | 2.03304i | 0.563863 | − | 0.563863i | −0.366540 | − | 0.930402i | \(-0.619458\pi\) |
0.930402 | + | 0.366540i | \(0.119458\pi\) | |||||||
\(14\) | 0.597468 | − | 2.83065i | 0.159680 | − | 0.756522i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.69338 | − | 2.95731i | −0.673346 | − | 0.739328i | ||||
\(17\) | 4.37963 | + | 4.37963i | 1.06222 | + | 1.06222i | 0.997932 | + | 0.0642843i | \(0.0204764\pi\) |
0.0642843 | + | 0.997932i | \(0.479524\pi\) | |||||||
\(18\) | −0.612026 | + | 4.19826i | −0.144256 | + | 0.989540i | ||||
\(19\) | 4.93129 | 1.13131 | 0.565657 | − | 0.824640i | \(-0.308622\pi\) | ||||
0.565657 | + | 0.824640i | \(0.308622\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.25173 | + | 3.31474i | −0.273150 | + | 0.723335i | ||||
\(22\) | −0.759891 | + | 0.495016i | −0.162009 | + | 0.105538i | ||||
\(23\) | −3.73619 | + | 3.73619i | −0.779050 | + | 0.779050i | −0.979669 | − | 0.200619i | \(-0.935705\pi\) |
0.200619 | + | 0.979669i | \(0.435705\pi\) | |||||||
\(24\) | 2.70796 | + | 4.08252i | 0.552759 | + | 0.833341i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.839729 | + | 3.97842i | −0.164684 | + | 0.780232i | ||||
\(27\) | 1.52471 | − | 4.96742i | 0.293431 | − | 0.955980i | ||||
\(28\) | 1.47706 | + | 3.81541i | 0.279138 | + | 0.721045i | ||||
\(29\) | − | 9.84421i | − | 1.82802i | −0.405687 | − | 0.914012i | \(-0.632968\pi\) | ||
0.405687 | − | 0.914012i | \(-0.367032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.23032 | 0.939394 | 0.469697 | − | 0.882828i | \(-0.344363\pi\) | ||||
0.469697 | + | 0.882828i | \(0.344363\pi\) | |||||||
\(32\) | 5.47437 | + | 1.42523i | 0.967741 | + | 0.251947i | ||||
\(33\) | 1.01222 | − | 0.457295i | 0.176205 | − | 0.0796049i | ||||
\(34\) | −8.57043 | − | 1.80897i | −1.46982 | − | 0.310236i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.51550 | − | 5.44722i | −0.419250 | − | 0.907871i | ||||
\(37\) | 3.44271 | + | 3.44271i | 0.565978 | + | 0.565978i | 0.930999 | − | 0.365022i | \(-0.118938\pi\) |
−0.365022 | + | 0.930999i | \(0.618938\pi\) | |||||||
\(38\) | −5.84339 | + | 3.80656i | −0.947923 | + | 0.617506i | ||||
\(39\) | 1.75928 | − | 4.65879i | 0.281710 | − | 0.746004i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.20930i | − | 1.12590i | −0.826490 | − | 0.562951i | \(-0.809666\pi\) | ||
0.826490 | − | 0.562951i | \(-0.190334\pi\) | |||||||
\(42\) | −1.07546 | − | 4.89408i | −0.165947 | − | 0.755172i | ||||
\(43\) | 4.37139 | − | 4.37139i | 0.666630 | − | 0.666630i | −0.290304 | − | 0.956934i | \(-0.593756\pi\) |
0.956934 | + | 0.290304i | \(0.0937564\pi\) | |||||||
\(44\) | 0.518329 | − | 1.17315i | 0.0781411 | − | 0.176859i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.54320 | − | 7.31130i | 0.227533 | − | 1.07799i | ||||
\(47\) | −4.08462 | − | 4.08462i | −0.595803 | − | 0.595803i | 0.343390 | − | 0.939193i | \(-0.388425\pi\) |
−0.939193 | + | 0.343390i | \(0.888425\pi\) | |||||||
\(48\) | −6.36021 | − | 2.74731i | −0.918018 | − | 0.396539i | ||||
\(49\) | 2.81523i | 0.402176i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.0361 | + | 3.78989i | 1.40534 | + | 0.530691i | ||||
\(52\) | −2.07598 | − | 5.36248i | −0.287886 | − | 0.743642i | ||||
\(53\) | −3.83383 | − | 3.83383i | −0.526616 | − | 0.526616i | 0.392945 | − | 0.919562i | \(-0.371456\pi\) |
−0.919562 | + | 0.392945i | \(0.871456\pi\) | |||||||
\(54\) | 2.02773 | + | 7.06317i | 0.275939 | + | 0.961175i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.69546 | − | 3.38095i | −0.627457 | − | 0.451798i | ||||
\(57\) | 7.78377 | − | 3.51650i | 1.03098 | − | 0.465771i | ||||
\(58\) | 7.59896 | + | 11.6650i | 0.997792 | + | 1.53169i | ||||
\(59\) | 2.50346i | 0.325923i | 0.986632 | + | 0.162961i | \(0.0521046\pi\) | ||||
−0.986632 | + | 0.162961i | \(0.947895\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.64270i | 1.23462i | 0.786720 | + | 0.617311i | \(0.211778\pi\) | ||||
−0.786720 | + | 0.617311i | \(0.788222\pi\) | |||||||
\(62\) | −6.19774 | + | 4.03740i | −0.787114 | + | 0.512750i | ||||
\(63\) | 0.387949 | + | 6.12474i | 0.0488770 | + | 0.771644i | ||||
\(64\) | −7.58709 | + | 2.53694i | −0.948386 | + | 0.317118i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.846451 | + | 1.32323i | −0.104191 | + | 0.162879i | ||||
\(67\) | 2.59686 | + | 2.59686i | 0.317257 | + | 0.317257i | 0.847713 | − | 0.530456i | \(-0.177979\pi\) |
−0.530456 | + | 0.847713i | \(0.677979\pi\) | |||||||
\(68\) | 11.5520 | − | 4.47213i | 1.40089 | − | 0.542326i | ||||
\(69\) | −3.23310 | + | 8.56166i | −0.389220 | + | 1.03070i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.7173i | 1.98398i | 0.126324 | + | 0.991989i | \(0.459682\pi\) | ||||
−0.126324 | + | 0.991989i | \(0.540318\pi\) | |||||||
\(72\) | 7.18560 | + | 4.51299i | 0.846832 | + | 0.531861i | ||||
\(73\) | −8.40725 | − | 8.40725i | −0.983994 | − | 0.983994i | 0.0158800 | − | 0.999874i | \(-0.494945\pi\) |
−0.999874 | + | 0.0158800i | \(0.994945\pi\) | |||||||
\(74\) | −6.73698 | − | 1.42198i | −0.783158 | − | 0.165302i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.98584 | − | 9.02128i | 0.457207 | − | 1.03481i | ||||
\(77\) | −0.927614 | + | 0.927614i | −0.105711 | + | 0.105711i | ||||
\(78\) | 1.51154 | + | 6.87852i | 0.171148 | + | 0.778839i | ||||
\(79\) | 5.31759i | 0.598275i | 0.954210 | + | 0.299138i | \(0.0966989\pi\) | ||||
−0.954210 | + | 0.299138i | \(0.903301\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.13559 | − | 8.92807i | −0.126176 | − | 0.992008i | ||||
\(82\) | 5.56501 | + | 8.54275i | 0.614552 | + | 0.943389i | ||||
\(83\) | 2.20075 | + | 2.20075i | 0.241564 | + | 0.241564i | 0.817497 | − | 0.575933i | \(-0.195361\pi\) |
−0.575933 | + | 0.817497i | \(0.695361\pi\) | |||||||
\(84\) | 5.05222 | + | 4.96913i | 0.551243 | + | 0.542176i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.80557 | + | 8.55430i | −0.194699 | + | 0.922434i | ||||
\(87\) | −7.01990 | − | 15.5386i | −0.752612 | − | 1.66591i | ||||
\(88\) | 0.291380 | + | 1.79025i | 0.0310612 | + | 0.190841i | ||||
\(89\) | −3.96596 | −0.420391 | −0.210195 | − | 0.977659i | \(-0.567410\pi\) | ||||
−0.210195 | + | 0.977659i | \(0.567410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.88160i | 0.616560i | ||||||||
\(92\) | 3.81511 | + | 9.85485i | 0.397752 | + | 1.02744i | ||||
\(93\) | 8.25578 | − | 3.72974i | 0.856085 | − | 0.386756i | ||||
\(94\) | 7.99313 | + | 1.68712i | 0.824428 | + | 0.174013i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.65732 | − | 1.65413i | 0.985646 | − | 0.168824i | ||||
\(97\) | 1.11334 | − | 1.11334i | 0.113043 | − | 0.113043i | −0.648323 | − | 0.761366i | \(-0.724529\pi\) |
0.761366 | + | 0.648323i | \(0.224529\pi\) | |||||||
\(98\) | −2.17314 | − | 3.33595i | −0.219520 | − | 0.336982i | ||||
\(99\) | 1.27164 | − | 1.44363i | 0.127805 | − | 0.145090i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.32234 | 0.430089 | 0.215045 | − | 0.976604i | \(-0.431010\pi\) | ||||
0.215045 | + | 0.976604i | \(0.431010\pi\) | |||||||
\(102\) | −14.8179 | + | 3.25620i | −1.46719 | + | 0.322412i | ||||
\(103\) | −8.51865 | − | 8.51865i | −0.839368 | − | 0.839368i | 0.149408 | − | 0.988776i | \(-0.452263\pi\) |
−0.988776 | + | 0.149408i | \(0.952263\pi\) | |||||||
\(104\) | 6.59937 | + | 4.75185i | 0.647121 | + | 0.465958i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.50235 | + | 1.58353i | 0.728693 | + | 0.153806i | ||||
\(107\) | −10.3436 | + | 10.3436i | −0.999957 | + | 0.999957i | −1.00000 | 4.33477e-5i | \(-0.999986\pi\) | |
4.33477e−5 | 1.00000i | \(0.499986\pi\) | ||||||||
\(108\) | −7.85499 | − | 6.80434i | −0.755847 | − | 0.654748i | ||||
\(109\) | 11.4461 | 1.09634 | 0.548169 | − | 0.836368i | \(-0.315325\pi\) | ||||
0.548169 | + | 0.836368i | \(0.315325\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.88912 | + | 2.97913i | 0.748802 | + | 0.282767i | ||||
\(112\) | 8.17377 | + | 0.381776i | 0.772349 | + | 0.0360744i | ||||
\(113\) | 7.28974 | − | 7.28974i | 0.685761 | − | 0.685761i | −0.275531 | − | 0.961292i | \(-0.588854\pi\) |
0.961292 | + | 0.275531i | \(0.0888537\pi\) | |||||||
\(114\) | −6.50902 | + | 10.1754i | −0.609625 | + | 0.953011i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −18.0090 | − | 7.95683i | −1.67209 | − | 0.738773i | ||||
\(117\) | −0.545254 | − | 8.60819i | −0.0504088 | − | 0.795827i | ||||
\(118\) | −1.93247 | − | 2.96651i | −0.177899 | − | 0.273089i | ||||
\(119\) | −12.6703 | −1.16149 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5888 | −0.962615 | ||||||||
\(122\) | −7.44340 | − | 11.4262i | −0.673894 | − | 1.03448i | ||||
\(123\) | −5.14094 | − | 11.3795i | −0.463543 | − | 1.02605i | ||||
\(124\) | 4.22754 | − | 9.56834i | 0.379644 | − | 0.859262i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.18752 | − | 6.95812i | −0.462141 | − | 0.619879i | ||||
\(127\) | −11.4720 | + | 11.4720i | −1.01797 | + | 1.01797i | −0.0181391 | + | 0.999835i | \(0.505774\pi\) |
−0.999835 | + | 0.0181391i | \(0.994226\pi\) | |||||||
\(128\) | 7.03210 | − | 8.86282i | 0.621556 | − | 0.783370i | ||||
\(129\) | 3.78276 | − | 10.0172i | 0.333054 | − | 0.881968i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.6449 | −1.36690 | −0.683452 | − | 0.729995i | \(-0.739522\pi\) | ||||
−0.683452 | + | 0.729995i | \(0.739522\pi\) | |||||||
\(132\) | −0.0184193 | − | 2.22138i | −0.00160320 | − | 0.193346i | ||||
\(133\) | −7.13314 | + | 7.13314i | −0.618522 | + | 0.618522i | ||||
\(134\) | −5.08176 | − | 1.07261i | −0.438997 | − | 0.0926596i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.2366 | + | 14.2166i | −0.877780 | + | 1.21906i | ||||
\(137\) | 8.94191 | + | 8.94191i | 0.763959 | + | 0.763959i | 0.977035 | − | 0.213077i | \(-0.0683485\pi\) |
−0.213077 | + | 0.977035i | \(0.568348\pi\) | |||||||
\(138\) | −2.77782 | − | 12.6409i | −0.236464 | − | 1.07607i | ||||
\(139\) | −1.01636 | −0.0862063 | −0.0431031 | − | 0.999071i | \(-0.513724\pi\) | ||||
−0.0431031 | + | 0.999071i | \(0.513724\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.36009 | − | 3.53461i | −0.788262 | − | 0.297668i | ||||
\(142\) | −12.9044 | − | 19.8094i | −1.08292 | − | 1.66237i | ||||
\(143\) | 1.30374 | − | 1.30374i | 0.109024 | − | 0.109024i | ||||
\(144\) | −11.9983 | + | 0.198991i | −0.999862 | + | 0.0165826i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.4520 | + | 3.47255i | 1.36158 | + | 0.287390i | ||||
\(147\) | 2.00754 | + | 4.44369i | 0.165579 | + | 0.366510i | ||||
\(148\) | 9.08073 | − | 3.51542i | 0.746432 | − | 0.288966i | ||||
\(149\) | 3.01841i | 0.247278i | 0.992327 | + | 0.123639i | \(0.0394565\pi\) | ||||
−0.992327 | + | 0.123639i | \(0.960544\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.46150 | −0.607208 | −0.303604 | − | 0.952798i | \(-0.598190\pi\) | ||||
−0.303604 | + | 0.952798i | \(0.598190\pi\) | |||||||
\(152\) | 2.24065 | + | 13.7666i | 0.181740 | + | 1.11662i | ||||
\(153\) | 18.5440 | − | 1.17460i | 1.49920 | − | 0.0949611i | ||||
\(154\) | 0.383143 | − | 1.81523i | 0.0308746 | − | 0.146276i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.10080 | − | 6.98401i | −0.568519 | − | 0.559168i | ||||
\(157\) | −6.08638 | − | 6.08638i | −0.485746 | − | 0.485746i | 0.421215 | − | 0.906961i | \(-0.361604\pi\) |
−0.906961 | + | 0.421215i | \(0.861604\pi\) | |||||||
\(158\) | −4.10476 | − | 6.30114i | −0.326557 | − | 0.501292i | ||||
\(159\) | −8.78538 | − | 3.31759i | −0.696726 | − | 0.263102i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 10.8089i | − | 0.851858i | ||||||
\(162\) | 8.23740 | + | 9.70285i | 0.647191 | + | 0.762328i | ||||
\(163\) | −13.5483 | + | 13.5483i | −1.06119 | + | 1.06119i | −0.0631867 | + | 0.998002i | \(0.520126\pi\) |
−0.998002 | + | 0.0631867i | \(0.979874\pi\) | |||||||
\(164\) | −13.1887 | − | 5.82710i | −1.02986 | − | 0.455020i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.30662 | − | 0.909003i | −0.334258 | − | 0.0705523i | ||||
\(167\) | −8.77613 | − | 8.77613i | −0.679117 | − | 0.679117i | 0.280683 | − | 0.959800i | \(-0.409439\pi\) |
−0.959800 | + | 0.280683i | \(0.909439\pi\) | |||||||
\(168\) | −9.82247 | − | 1.98832i | −0.757820 | − | 0.153402i | ||||
\(169\) | 4.73353i | 0.364118i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.77864 | − | 11.1012i | 0.747791 | − | 0.848930i | ||||
\(172\) | −4.46372 | − | 11.5303i | −0.340355 | − | 0.879176i | ||||
\(173\) | −15.2826 | − | 15.2826i | −1.16192 | − | 1.16192i | −0.984056 | − | 0.177862i | \(-0.943082\pi\) |
−0.177862 | − | 0.984056i | \(-0.556918\pi\) | |||||||
\(174\) | 20.3129 | + | 12.9938i | 1.53991 | + | 0.985057i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.72721 | − | 1.89646i | −0.130193 | − | 0.142951i | ||||
\(177\) | 1.78521 | + | 3.95157i | 0.134185 | + | 0.297018i | ||||
\(178\) | 4.69951 | − | 3.06141i | 0.352243 | − | 0.229462i | ||||
\(179\) | − | 2.11966i | − | 0.158431i | −0.996858 | − | 0.0792153i | \(-0.974759\pi\) | ||
0.996858 | − | 0.0792153i | \(-0.0252415\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.4392i | − | 1.44491i | −0.691420 | − | 0.722453i | \(-0.743014\pi\) | ||
0.691420 | − | 0.722453i | \(-0.256986\pi\) | |||||||
\(182\) | −4.54013 | − | 6.96948i | −0.336537 | − | 0.516612i | ||||
\(183\) | 6.87620 | + | 15.2205i | 0.508303 | + | 1.12513i | ||||
\(184\) | −12.1279 | − | 8.73268i | −0.894083 | − | 0.643781i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.90373 | + | 10.7924i | −0.506206 | + | 0.791338i | ||||
\(187\) | 2.80856 | + | 2.80856i | 0.205382 | + | 0.205382i | ||||
\(188\) | −10.7739 | + | 4.17089i | −0.785766 | + | 0.304194i | ||||
\(189\) | 4.97990 | + | 9.39092i | 0.362235 | + | 0.683089i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.66510i | − | 0.192840i | −0.995341 | − | 0.0964198i | \(-0.969261\pi\) | ||
0.995341 | − | 0.0964198i | \(-0.0307391\pi\) | |||||||
\(192\) | −10.1667 | + | 9.41477i | −0.733719 | + | 0.679453i | ||||
\(193\) | −7.73743 | − | 7.73743i | −0.556952 | − | 0.556952i | 0.371486 | − | 0.928439i | \(-0.378848\pi\) |
−0.928439 | + | 0.371486i | \(0.878848\pi\) | |||||||
\(194\) | −0.459857 | + | 2.17868i | −0.0330158 | + | 0.156420i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.15018 | + | 2.27548i | 0.367870 | + | 0.162535i | ||||
\(197\) | 7.82754 | − | 7.82754i | 0.557689 | − | 0.557689i | −0.370960 | − | 0.928649i | \(-0.620971\pi\) |
0.928649 | + | 0.370960i | \(0.120971\pi\) | |||||||
\(198\) | −0.392479 | + | 2.69226i | −0.0278923 | + | 0.191330i | ||||
\(199\) | 16.8608i | 1.19523i | 0.801783 | + | 0.597615i | \(0.203885\pi\) | ||||
−0.801783 | + | 0.597615i | \(0.796115\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.95082 | + | 2.24718i | 0.419739 | + | 0.158504i | ||||
\(202\) | −5.12182 | + | 3.33651i | −0.360370 | + | 0.234756i | ||||
\(203\) | 14.2397 | + | 14.2397i | 0.999433 | + | 0.999433i | ||||
\(204\) | 15.0452 | − | 15.2968i | 1.05337 | − | 1.07099i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.6700 | + | 3.51856i | 1.16145 | + | 0.245150i | ||||
\(207\) | 1.00204 | + | 15.8196i | 0.0696464 | + | 1.09954i | ||||
\(208\) | −11.4881 | − | 0.536578i | −0.796554 | − | 0.0372050i | ||||
\(209\) | 3.16233 | 0.218743 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 6.45821i | − | 0.444602i | −0.974978 | − | 0.222301i | \(-0.928643\pi\) | ||
0.974978 | − | 0.222301i | \(-0.0713567\pi\) | |||||||
\(212\) | −10.1124 | + | 3.91480i | −0.694521 | + | 0.268870i | ||||
\(213\) | 11.9211 | + | 26.3873i | 0.816820 | + | 1.80803i | ||||
\(214\) | 4.27235 | − | 20.2413i | 0.292052 | − | 1.38367i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.5603 | + | 1.99946i | 0.990702 | + | 0.136046i | ||||
\(217\) | −7.56570 | + | 7.56570i | −0.513593 | + | 0.513593i | ||||
\(218\) | −13.5632 | + | 8.83549i | −0.918617 | + | 0.598415i | ||||
\(219\) | −19.2656 | − | 7.27518i | −1.30185 | − | 0.491611i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.8079 | 1.19789 | ||||||||
\(222\) | −11.6480 | + | 2.55961i | −0.781760 | + | 0.171790i | ||||
\(223\) | 8.41178 | + | 8.41178i | 0.563294 | + | 0.563294i | 0.930242 | − | 0.366947i | \(-0.119597\pi\) |
−0.366947 | + | 0.930242i | \(0.619597\pi\) | |||||||
\(224\) | −9.98032 | + | 5.85712i | −0.666838 | + | 0.391345i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.01097 | + | 14.2652i | −0.200287 | + | 0.948905i | ||||
\(227\) | 0.0799436 | − | 0.0799436i | 0.00530604 | − | 0.00530604i | −0.704449 | − | 0.709755i | \(-0.748806\pi\) |
0.709755 | + | 0.704449i | \(0.248806\pi\) | |||||||
\(228\) | −0.141640 | − | 17.0819i | −0.00938037 | − | 1.13128i | ||||
\(229\) | −12.9730 | −0.857282 | −0.428641 | − | 0.903475i | \(-0.641007\pi\) | ||||
−0.428641 | + | 0.903475i | \(0.641007\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.802707 | + | 2.12567i | −0.0528142 | + | 0.139859i | ||||
\(232\) | 27.4820 | − | 4.47295i | 1.80428 | − | 0.293663i | ||||
\(233\) | −2.12983 | + | 2.12983i | −0.139530 | + | 0.139530i | −0.773422 | − | 0.633892i | \(-0.781456\pi\) |
0.633892 | + | 0.773422i | \(0.281456\pi\) | |||||||
\(234\) | 7.29095 | + | 9.77949i | 0.476624 | + | 0.639306i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.57982 | + | 2.02348i | 0.298121 | + | 0.131718i | ||||
\(237\) | 3.79197 | + | 8.39352i | 0.246315 | + | 0.545218i | ||||
\(238\) | 15.0139 | − | 9.78050i | 0.973205 | − | 0.633975i | ||||
\(239\) | 16.7173 | 1.08135 | 0.540676 | − | 0.841231i | \(-0.318168\pi\) | ||||
0.540676 | + | 0.841231i | \(0.318168\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.68712 | −0.301924 | −0.150962 | − | 0.988540i | \(-0.548237\pi\) | ||||
−0.150962 | + | 0.988540i | \(0.548237\pi\) | |||||||
\(242\) | 12.5473 | − | 8.17369i | 0.806571 | − | 0.525425i | ||||
\(243\) | −8.15906 | − | 13.2827i | −0.523404 | − | 0.852085i | ||||
\(244\) | 17.6403 | + | 7.79396i | 1.12931 | + | 0.498957i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.8759 | + | 9.51586i | 0.948452 | + | 0.606709i | ||||
\(247\) | 10.0255 | − | 10.0255i | 0.637906 | − | 0.637906i | ||||
\(248\) | 2.37652 | + | 14.6015i | 0.150909 | + | 0.927193i | ||||
\(249\) | 5.04312 | + | 1.90441i | 0.319595 | + | 0.120687i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.3364 | −1.15738 | −0.578691 | − | 0.815547i | \(-0.696436\pi\) | ||||
−0.578691 | + | 0.815547i | \(0.696436\pi\) | |||||||
\(252\) | 11.5181 | + | 4.24076i | 0.725575 | + | 0.267143i | ||||
\(253\) | −2.39594 | + | 2.39594i | −0.150632 | + | 0.150632i | ||||
\(254\) | 4.73841 | − | 22.4494i | 0.297314 | − | 1.40860i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.49138 | + | 15.9303i | −0.0932115 | + | 0.995646i | ||||
\(257\) | −1.28687 | − | 1.28687i | −0.0802726 | − | 0.0802726i | 0.665830 | − | 0.746103i | \(-0.268077\pi\) |
−0.746103 | + | 0.665830i | \(0.768077\pi\) | |||||||
\(258\) | 3.25008 | + | 14.7900i | 0.202341 | + | 0.920788i | ||||
\(259\) | −9.95980 | −0.618872 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.1611 | − | 19.5209i | −1.37173 | − | 1.20831i | ||||
\(262\) | 18.5387 | − | 12.0767i | 1.14532 | − | 0.746098i | ||||
\(263\) | −3.96091 | + | 3.96091i | −0.244240 | + | 0.244240i | −0.818602 | − | 0.574361i | \(-0.805250\pi\) |
0.574361 | + | 0.818602i | \(0.305250\pi\) | |||||||
\(264\) | 1.73655 | + | 2.61803i | 0.106878 | + | 0.161129i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.94629 | − | 13.9587i | 0.180648 | − | 0.855865i | ||||
\(267\) | −6.26005 | + | 2.82812i | −0.383109 | + | 0.173078i | ||||
\(268\) | 6.84967 | − | 2.65171i | 0.418410 | − | 0.161979i | ||||
\(269\) | 1.81888i | 0.110899i | 0.998461 | + | 0.0554497i | \(0.0176592\pi\) | ||||
−0.998461 | + | 0.0554497i | \(0.982341\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.54876 | 0.458555 | 0.229277 | − | 0.973361i | \(-0.426364\pi\) | ||||
0.229277 | + | 0.973361i | \(0.426364\pi\) | |||||||
\(272\) | 1.15591 | − | 24.7479i | 0.0700875 | − | 1.50056i | ||||
\(273\) | 4.19417 | + | 9.28379i | 0.253843 | + | 0.561880i | ||||
\(274\) | −17.4983 | − | 3.69338i | −1.05711 | − | 0.223125i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.0494 | + | 12.8348i | 0.785483 | + | 0.772564i | ||||
\(277\) | −6.09911 | − | 6.09911i | −0.366460 | − | 0.366460i | 0.499724 | − | 0.866184i | \(-0.333435\pi\) |
−0.866184 | + | 0.499724i | \(0.833435\pi\) | |||||||
\(278\) | 1.20435 | − | 0.784548i | 0.0722318 | − | 0.0470540i | ||||
\(279\) | 10.3716 | − | 11.7744i | 0.620933 | − | 0.704914i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4.32219i | − | 0.257840i | −0.991655 | − | 0.128920i | \(-0.958849\pi\) | ||
0.991655 | − | 0.128920i | \(-0.0411511\pi\) | |||||||
\(282\) | 13.8198 | − | 3.03687i | 0.822957 | − | 0.180843i | ||||
\(283\) | −6.55658 | + | 6.55658i | −0.389748 | + | 0.389748i | −0.874598 | − | 0.484849i | \(-0.838874\pi\) |
0.484849 | + | 0.874598i | \(0.338874\pi\) | |||||||
\(284\) | 30.5826 | + | 13.5122i | 1.81474 | + | 0.801800i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.538500 | + | 2.55127i | −0.0318422 | + | 0.150860i | ||||
\(287\) | 10.4283 | + | 10.4283i | 0.615563 | + | 0.615563i | ||||
\(288\) | 14.0640 | − | 9.49758i | 0.828729 | − | 0.559650i | ||||
\(289\) | 21.3623i | 1.25661i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.963426 | − | 2.55127i | 0.0564770 | − | 0.149558i | ||||
\(292\) | −22.1756 | + | 8.58482i | −1.29773 | + | 0.502388i | ||||
\(293\) | 3.85667 | + | 3.85667i | 0.225309 | + | 0.225309i | 0.810730 | − | 0.585421i | \(-0.199071\pi\) |
−0.585421 | + | 0.810730i | \(0.699071\pi\) | |||||||
\(294\) | −5.80904 | − | 3.71595i | −0.338790 | − | 0.216718i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.04670 | + | 11.1753i | −0.467705 | + | 0.649548i | ||||
\(297\) | 0.977765 | − | 3.18550i | 0.0567357 | − | 0.184841i | ||||
\(298\) | −2.32998 | − | 3.57671i | −0.134972 | − | 0.207193i | ||||
\(299\) | 15.1916i | 0.878555i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.6465i | 0.728932i | ||||||||
\(302\) | 8.84160 | − | 5.75969i | 0.508777 | − | 0.331433i | ||||
\(303\) | 6.82258 | − | 3.08226i | 0.391947 | − | 0.177071i | ||||
\(304\) | −13.2818 | − | 14.5834i | −0.761766 | − | 0.836413i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −21.0673 | + | 15.7064i | −1.20434 | + | 0.897875i | ||||
\(307\) | −3.22023 | − | 3.22023i | −0.183788 | − | 0.183788i | 0.609216 | − | 0.793004i | \(-0.291484\pi\) |
−0.793004 | + | 0.609216i | \(0.791484\pi\) | |||||||
\(308\) | 0.947206 | + | 2.44674i | 0.0539721 | + | 0.139416i | ||||
\(309\) | −19.5209 | − | 7.37158i | −1.11050 | − | 0.419355i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.3453i | 0.700036i | 0.936743 | + | 0.350018i | \(0.113825\pi\) | ||||
−0.936743 | + | 0.350018i | \(0.886175\pi\) | |||||||
\(312\) | 13.8053 | + | 2.79454i | 0.781570 | + | 0.158209i | ||||
\(313\) | 11.6983 | + | 11.6983i | 0.661226 | + | 0.661226i | 0.955669 | − | 0.294443i | \(-0.0951341\pi\) |
−0.294443 | + | 0.955669i | \(0.595134\pi\) | |||||||
\(314\) | 11.9103 | + | 2.51393i | 0.672139 | + | 0.141869i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.72797 | + | 4.29807i | 0.547241 | + | 0.241785i | ||||
\(317\) | 5.15672 | − | 5.15672i | 0.289631 | − | 0.289631i | −0.547304 | − | 0.836934i | \(-0.684346\pi\) |
0.836934 | + | 0.547304i | \(0.184346\pi\) | |||||||
\(318\) | 12.9713 | − | 2.85041i | 0.727393 | − | 0.159843i | ||||
\(319\) | − | 6.31288i | − | 0.353453i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.95082 | + | 23.7029i | −0.499586 | + | 1.32297i | ||||
\(322\) | 8.34359 | + | 12.8081i | 0.464970 | + | 0.713768i | ||||
\(323\) | 21.5972 | + | 21.5972i | 1.20170 | + | 1.20170i | ||||
\(324\) | −17.2508 | − | 5.13890i | −0.958380 | − | 0.285494i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.59604 | − | 26.5125i | 0.309936 | − | 1.46839i | ||||
\(327\) | 18.0670 | − | 8.16221i | 0.999110 | − | 0.451371i | ||||
\(328\) | 20.1261 | − | 3.27571i | 1.11128 | − | 0.180871i | ||||
\(329\) | 11.8169 | 0.651485 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 14.0460i | − | 0.772037i | −0.922491 | − | 0.386019i | \(-0.873850\pi\) | ||
0.922491 | − | 0.386019i | \(-0.126150\pi\) | |||||||
\(332\) | 5.80486 | − | 2.24723i | 0.318583 | − | 0.123333i | ||||
\(333\) | 14.5770 | − | 0.923324i | 0.798812 | − | 0.0505979i | ||||
\(334\) | 17.1739 | + | 3.62491i | 0.939713 | + | 0.198346i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 13.1741 | − | 5.22610i | 0.718706 | − | 0.285107i | ||||
\(337\) | 10.5701 | − | 10.5701i | 0.575791 | − | 0.575791i | −0.357950 | − | 0.933741i | \(-0.616524\pi\) |
0.933741 | + | 0.357950i | \(0.116524\pi\) | |||||||
\(338\) | −3.65391 | − | 5.60906i | −0.198747 | − | 0.305092i | ||||
\(339\) | 6.30815 | − | 16.7048i | 0.342612 | − | 0.907278i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.35409 | 0.181634 | ||||||||
\(342\) | −3.01808 | + | 20.7028i | −0.163199 | + | 1.11948i | ||||
\(343\) | −14.1978 | − | 14.1978i | −0.766609 | − | 0.766609i | ||||
\(344\) | 14.1898 | + | 10.2173i | 0.765063 | + | 0.550881i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.9063 | + | 6.31237i | 1.60778 | + | 0.339355i | ||||
\(347\) | 20.2172 | − | 20.2172i | 1.08532 | − | 1.08532i | 0.0893127 | − | 0.996004i | \(-0.471533\pi\) |
0.996004 | − | 0.0893127i | \(-0.0284671\pi\) | |||||||
\(348\) | −34.1002 | + | 0.282754i | −1.82796 | + | 0.0151572i | ||||
\(349\) | −0.603017 | −0.0322788 | −0.0161394 | − | 0.999870i | \(-0.505138\pi\) | ||||
−0.0161394 | + | 0.999870i | \(0.505138\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.99915 | − | 13.1987i | −0.373587 | − | 0.704496i | ||||
\(352\) | 3.51060 | + | 0.913967i | 0.187115 | + | 0.0487146i | ||||
\(353\) | −19.6483 | + | 19.6483i | −1.04578 | + | 1.04578i | −0.0468748 | + | 0.998901i | \(0.514926\pi\) |
−0.998901 | + | 0.0468748i | \(0.985074\pi\) | |||||||
\(354\) | −5.16572 | − | 3.30442i | −0.274555 | − | 0.175628i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.20559 | + | 7.25531i | −0.169896 | + | 0.384531i | ||||
\(357\) | −19.9994 | + | 9.03520i | −1.05848 | + | 0.478194i | ||||
\(358\) | 1.63621 | + | 2.51171i | 0.0864763 | + | 0.132748i | ||||
\(359\) | 12.6703 | 0.668714 | 0.334357 | − | 0.942446i | \(-0.391481\pi\) | ||||
0.334357 | + | 0.942446i | \(0.391481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.31759 | 0.279873 | ||||||||
\(362\) | 15.0056 | + | 23.0348i | 0.788674 | + | 1.21068i | ||||
\(363\) | −16.7138 | + | 7.55084i | −0.877246 | + | 0.396316i | ||||
\(364\) | 10.7598 | + | 4.75395i | 0.563966 | + | 0.249175i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −19.8971 | − | 12.7278i | −1.04004 | − | 0.665293i | ||||
\(367\) | −2.17316 | + | 2.17316i | −0.113438 | + | 0.113438i | −0.761547 | − | 0.648109i | \(-0.775560\pi\) |
0.648109 | + | 0.761547i | \(0.275560\pi\) | |||||||
\(368\) | 21.1121 | + | 0.986092i | 1.10054 | + | 0.0514036i | ||||
\(369\) | −16.2294 | − | 14.2959i | −0.844868 | − | 0.744214i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.0913 | 0.575832 | ||||||||
\(372\) | −0.150230 | − | 18.1178i | −0.00778905 | − | 0.939362i | ||||
\(373\) | −19.7420 | + | 19.7420i | −1.02220 | + | 1.02220i | −0.0224556 | + | 0.999748i | \(0.507148\pi\) |
−0.999748 | + | 0.0224556i | \(0.992852\pi\) | |||||||
\(374\) | −5.49603 | − | 1.16005i | −0.284193 | − | 0.0599849i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.54706 | − | 13.2589i | 0.492352 | − | 0.683778i | ||||
\(377\) | −20.0136 | − | 20.0136i | −1.03075 | − | 1.03075i | ||||
\(378\) | −13.1500 | − | 7.28380i | −0.676365 | − | 0.374638i | ||||
\(379\) | 8.76740 | 0.450351 | 0.225176 | − | 0.974318i | \(-0.427704\pi\) | ||||
0.225176 | + | 0.974318i | \(0.427704\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.92724 | + | 26.2886i | −0.508588 | + | 1.34680i | ||||
\(382\) | 2.05724 | + | 3.15804i | 0.105258 | + | 0.161579i | ||||
\(383\) | 16.7382 | − | 16.7382i | 0.855284 | − | 0.855284i | −0.135495 | − | 0.990778i | \(-0.543262\pi\) |
0.990778 | + | 0.135495i | \(0.0432623\pi\) | |||||||
\(384\) | 4.77972 | − | 19.0041i | 0.243914 | − | 0.969797i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.1413 | + | 3.19588i | 0.770670 | + | 0.162666i | ||||
\(387\) | −1.17239 | − | 18.5091i | −0.0595961 | − | 0.940872i | ||||
\(388\) | −1.13686 | − | 2.93663i | −0.0577152 | − | 0.149085i | ||||
\(389\) | − | 20.9924i | − | 1.06435i | −0.846633 | − | 0.532177i | \(-0.821374\pi\) | ||
0.846633 | − | 0.532177i | \(-0.178626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.7263 | −1.65504 | ||||||||
\(392\) | −7.85926 | + | 1.27917i | −0.396953 | + | 0.0646077i | ||||
\(393\) | −24.6947 | + | 11.1564i | −1.24568 | + | 0.562765i | ||||
\(394\) | −3.23310 | + | 15.3176i | −0.162881 | + | 0.771689i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.61314 | − | 3.49319i | −0.0810631 | − | 0.175539i | ||||
\(397\) | 22.7486 | + | 22.7486i | 1.14172 | + | 1.14172i | 0.988136 | + | 0.153584i | \(0.0490815\pi\) |
0.153584 | + | 0.988136i | \(0.450918\pi\) | |||||||
\(398\) | −13.0152 | − | 19.9794i | −0.652393 | − | 1.00148i | ||||
\(399\) | −6.17264 | + | 16.3459i | −0.309018 | + | 0.818319i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.2516i | 1.21107i | 0.795819 | + | 0.605535i | \(0.207041\pi\) | ||||
−0.795819 | + | 0.605535i | \(0.792959\pi\) | |||||||
\(402\) | −8.78615 | + | 1.93074i | −0.438213 | + | 0.0962964i | ||||
\(403\) | 10.6334 | − | 10.6334i | 0.529689 | − | 0.529689i | ||||
\(404\) | 3.49364 | − | 7.90728i | 0.173815 | − | 0.393402i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −27.8655 | − | 5.88160i | −1.38294 | − | 0.291899i | ||||
\(407\) | 2.20773 | + | 2.20773i | 0.109433 | + | 0.109433i | ||||
\(408\) | −6.02007 | + | 29.7398i | −0.298038 | + | 1.47234i | ||||
\(409\) | − | 24.0958i | − | 1.19146i | −0.803184 | − | 0.595731i | \(-0.796863\pi\) | ||
0.803184 | − | 0.595731i | \(-0.203137\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.4908 | + | 7.73784i | 1.01074 | + | 0.381680i | ||||
\(412\) | −22.4694 | + | 8.69857i | −1.10699 | + | 0.428548i | ||||
\(413\) | −3.62127 | − | 3.62127i | −0.178191 | − | 0.178191i | ||||
\(414\) | −13.3989 | − | 17.9722i | −0.658519 | − | 0.883284i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 14.0271 | − | 8.23206i | 0.687737 | − | 0.403610i | ||||
\(417\) | −1.60426 | + | 0.724763i | −0.0785611 | + | 0.0354918i | ||||
\(418\) | −3.74724 | + | 2.44107i | −0.183284 | + | 0.119397i | ||||
\(419\) | 39.9565i | 1.95200i | 0.217767 | + | 0.976001i | \(0.430123\pi\) | ||||
−0.217767 | + | 0.976001i | \(0.569877\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 27.1153i | − | 1.32152i | −0.750599 | − | 0.660758i | \(-0.770235\pi\) | ||
0.750599 | − | 0.660758i | \(-0.229765\pi\) | |||||||
\(422\) | 4.98523 | + | 7.65274i | 0.242677 | + | 0.372530i | ||||
\(423\) | −17.2949 | + | 1.09548i | −0.840907 | + | 0.0532642i | ||||
\(424\) | 8.96087 | − | 12.4448i | 0.435178 | − | 0.604375i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −34.4950 | − | 22.0659i | −1.67129 | − | 1.06910i | ||||
\(427\) | −13.9482 | − | 13.9482i | −0.675002 | − | 0.675002i | ||||
\(428\) | 10.5621 | + | 27.2831i | 0.510538 | + | 1.31878i | ||||
\(429\) | 1.12819 | − | 2.98758i | 0.0544694 | − | 0.144242i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 30.9739i | − | 1.49196i | −0.665969 | − | 0.745979i | \(-0.731982\pi\) | ||
0.665969 | − | 0.745979i | \(-0.268018\pi\) | |||||||
\(432\) | −18.7968 | + | 8.87011i | −0.904363 | + | 0.426763i | ||||
\(433\) | 8.18096 | + | 8.18096i | 0.393152 | + | 0.393152i | 0.875809 | − | 0.482658i | \(-0.160328\pi\) |
−0.482658 | + | 0.875809i | \(0.660328\pi\) | |||||||
\(434\) | 3.12495 | − | 14.8052i | 0.150002 | − | 0.710673i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.25160 | − | 20.9395i | 0.443071 | − | 1.00282i | ||||
\(437\) | −18.4242 | + | 18.4242i | −0.881351 | + | 0.881351i | ||||
\(438\) | 28.4449 | − | 6.25069i | 1.35915 | − | 0.298670i | ||||
\(439\) | − | 9.63432i | − | 0.459821i | −0.973212 | − | 0.229910i | \(-0.926157\pi\) | ||
0.973212 | − | 0.229910i | \(-0.0738433\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.33759 | + | 5.58255i | 0.301790 | + | 0.265836i | ||||
\(442\) | −21.1017 | + | 13.7463i | −1.00370 | + | 0.653844i | ||||
\(443\) | −5.86218 | − | 5.86218i | −0.278521 | − | 0.278521i | 0.553998 | − | 0.832518i | \(-0.313102\pi\) |
−0.832518 | + | 0.553998i | \(0.813102\pi\) | |||||||
\(444\) | 11.8266 | − | 12.0244i | 0.561265 | − | 0.570651i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.4609 | − | 3.47442i | −0.779445 | − | 0.164518i | ||||
\(447\) | 2.15243 | + | 4.76440i | 0.101806 | + | 0.225348i | ||||
\(448\) | 7.30508 | − | 14.6445i | 0.345132 | − | 0.691887i | ||||
\(449\) | −6.40566 | −0.302302 | −0.151151 | − | 0.988511i | \(-0.548298\pi\) | ||||
−0.151151 | + | 0.988511i | \(0.548298\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.62317i | − | 0.217696i | ||||||
\(452\) | −7.44371 | − | 19.2279i | −0.350122 | − | 0.904406i | ||||
\(453\) | −11.7776 | + | 5.32079i | −0.553358 | + | 0.249993i | ||||
\(454\) | −0.0330201 | + | 0.156440i | −0.00154971 | + | 0.00734211i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.3537 | + | 20.1321i | 0.625345 | + | 0.942771i | ||||
\(457\) | −16.7031 | + | 16.7031i | −0.781338 | + | 0.781338i | −0.980057 | − | 0.198719i | \(-0.936322\pi\) |
0.198719 | + | 0.980057i | \(0.436322\pi\) | |||||||
\(458\) | 15.3726 | − | 10.0142i | 0.718313 | − | 0.467931i | ||||
\(459\) | 28.4331 | − | 15.0778i | 1.32714 | − | 0.703770i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.5078 | 1.65376 | 0.826882 | − | 0.562376i | \(-0.190113\pi\) | ||||
0.826882 | + | 0.562376i | \(0.190113\pi\) | |||||||
\(462\) | −0.689670 | − | 3.13847i | −0.0320864 | − | 0.146015i | ||||
\(463\) | 9.79796 | + | 9.79796i | 0.455350 | + | 0.455350i | 0.897126 | − | 0.441776i | \(-0.145651\pi\) |
−0.441776 | + | 0.897126i | \(0.645651\pi\) | |||||||
\(464\) | −29.1124 | + | 26.5142i | −1.35151 | + | 1.23089i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.879707 | − | 4.16782i | 0.0407517 | − | 0.193071i | ||||
\(467\) | −8.06737 | + | 8.06737i | −0.373313 | + | 0.373313i | −0.868683 | − | 0.495369i | \(-0.835033\pi\) |
0.495369 | + | 0.868683i | \(0.335033\pi\) | |||||||
\(468\) | −16.1885 | − | 5.96030i | −0.748314 | − | 0.275515i | ||||
\(469\) | −7.51276 | −0.346907 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.9472 | − | 5.26682i | −0.642653 | − | 0.242682i | ||||
\(472\) | −6.98889 | + | 1.13751i | −0.321690 | + | 0.0523579i | ||||
\(473\) | 2.80328 | − | 2.80328i | 0.128895 | − | 0.128895i | ||||
\(474\) | −10.9725 | − | 7.01891i | −0.503982 | − | 0.322389i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.2411 | + | 23.1791i | −0.469401 | + | 1.06241i | ||||
\(477\) | −16.2330 | + | 1.02822i | −0.743258 | + | 0.0470790i | ||||
\(478\) | −19.8094 | + | 12.9044i | −0.906060 | + | 0.590235i | ||||
\(479\) | 4.04697 | 0.184911 | 0.0924553 | − | 0.995717i | \(-0.470528\pi\) | ||||
0.0924553 | + | 0.995717i | \(0.470528\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.9983 | 0.638267 | ||||||||
\(482\) | 5.55406 | − | 3.61809i | 0.252981 | − | 0.164799i | ||||
\(483\) | −7.70779 | − | 17.0612i | −0.350717 | − | 0.776312i | ||||
\(484\) | −8.55863 | + | 19.3710i | −0.389029 | + | 0.880502i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.9214 | + | 9.44134i | 0.903652 | + | 0.428268i | ||||
\(487\) | −6.28516 | + | 6.28516i | −0.284808 | + | 0.284808i | −0.835023 | − | 0.550215i | \(-0.814546\pi\) |
0.550215 | + | 0.835023i | \(0.314546\pi\) | |||||||
\(488\) | −26.9194 | + | 4.38139i | −1.21859 | + | 0.198336i | ||||
\(489\) | −11.7240 | + | 31.0466i | −0.530178 | + | 1.40398i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.1486 | −1.13494 | −0.567471 | − | 0.823393i | \(-0.692078\pi\) | ||||
−0.567471 | + | 0.823393i | \(0.692078\pi\) | |||||||
\(492\) | −24.9729 | + | 0.207071i | −1.12586 | + | 0.00933550i | ||||
\(493\) | 43.1140 | − | 43.1140i | 1.94176 | − | 1.94176i | ||||
\(494\) | −4.14094 | + | 19.6187i | −0.186310 | + | 0.882688i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.0873 | − | 15.4677i | −0.632537 | − | 0.694520i | ||||
\(497\) | −24.1817 | − | 24.1817i | −1.08470 | − | 1.08470i | ||||
\(498\) | −7.44597 | + | 1.63623i | −0.333662 | + | 0.0733214i | ||||
\(499\) | 4.01216 | 0.179609 | 0.0898044 | − | 0.995959i | \(-0.471376\pi\) | ||||
0.0898044 | + | 0.995959i | \(0.471376\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.1109 | − | 7.59439i | −0.898488 | − | 0.339292i | ||||
\(502\) | 21.7279 | − | 14.1542i | 0.969765 | − | 0.631734i | ||||
\(503\) | 13.7823 | − | 13.7823i | 0.614523 | − | 0.614523i | −0.329598 | − | 0.944121i | \(-0.606913\pi\) |
0.944121 | + | 0.329598i | \(0.106913\pi\) | |||||||
\(504\) | −16.9221 | + | 3.86595i | −0.753770 | + | 0.172203i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.989624 | − | 4.68858i | 0.0439942 | − | 0.208433i | ||||
\(507\) | 3.37548 | + | 7.47162i | 0.149910 | + | 0.331826i | ||||
\(508\) | 11.7143 | + | 30.2593i | 0.519738 | + | 1.34254i | ||||
\(509\) | − | 10.5288i | − | 0.466680i | −0.972395 | − | 0.233340i | \(-0.925034\pi\) | ||
0.972395 | − | 0.233340i | \(-0.0749656\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.3223 | 1.07595 | ||||||||
\(512\) | −10.5297 | − | 20.0281i | −0.465353 | − | 0.885125i | ||||
\(513\) | 7.51879 | − | 24.4958i | 0.331963 | − | 1.08151i | ||||
\(514\) | 2.51825 | + | 0.531531i | 0.111075 | + | 0.0234448i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −15.2680 | − | 15.0169i | −0.672135 | − | 0.661080i | ||||
\(517\) | −2.61938 | − | 2.61938i | −0.115200 | − | 0.115200i | ||||
\(518\) | 11.8020 | − | 7.68818i | 0.518550 | − | 0.337799i | ||||
\(519\) | −35.0208 | − | 13.2248i | −1.53724 | − | 0.580503i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.5500i | 1.42604i | 0.701144 | + | 0.713020i | \(0.252673\pi\) | ||||
−0.701144 | + | 0.713020i | \(0.747327\pi\) | |||||||
\(522\) | 41.3286 | + | 6.02492i | 1.80890 | + | 0.263703i | ||||
\(523\) | 9.90568 | − | 9.90568i | 0.433145 | − | 0.433145i | −0.456552 | − | 0.889697i | \(-0.650916\pi\) |
0.889697 | + | 0.456552i | \(0.150916\pi\) | |||||||
\(524\) | −12.6454 | + | 28.6208i | −0.552417 | + | 1.25030i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.63602 | − | 7.75105i | 0.0713340 | − | 0.337962i | ||||
\(527\) | 22.9069 | + | 22.9069i | 0.997839 | + | 0.997839i | ||||
\(528\) | −4.07867 | − | 1.76179i | −0.177501 | − | 0.0766720i | ||||
\(529\) | − | 4.91829i | − | 0.213839i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.63573 | + | 4.96431i | 0.244570 | + | 0.215433i | ||||
\(532\) | 7.28380 | + | 18.8149i | 0.315793 | + | 0.815729i | ||||
\(533\) | −14.6568 | − | 14.6568i | −0.634855 | − | 0.634855i | ||||
\(534\) | 5.23484 | − | 8.18348i | 0.226534 | − | 0.354134i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.06969 | + | 8.42958i | −0.262171 | + | 0.364102i | ||||
\(537\) | −1.51153 | − | 3.34576i | −0.0652271 | − | 0.144380i | ||||
\(538\) | −1.40404 | − | 2.15531i | −0.0605322 | − | 0.0929220i | ||||
\(539\) | 1.80535i | 0.0777619i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.0216i | 1.89264i | 0.323234 | + | 0.946319i | \(0.395230\pi\) | ||||
−0.323234 | + | 0.946319i | \(0.604770\pi\) | |||||||
\(542\) | −8.94500 | + | 5.82705i | −0.384221 | + | 0.250293i | ||||
\(543\) | −13.8621 | − | 30.6838i | −0.594880 | − | 1.31677i | ||||
\(544\) | 17.7337 | + | 30.2177i | 0.760328 | + | 1.29557i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.1363 | − | 7.76338i | −0.519385 | − | 0.332242i | ||||
\(547\) | 5.74698 | + | 5.74698i | 0.245723 | + | 0.245723i | 0.819213 | − | 0.573490i | \(-0.194411\pi\) |
−0.573490 | + | 0.819213i | \(0.694411\pi\) | |||||||
\(548\) | 23.5858 | − | 9.13077i | 1.00754 | − | 0.390047i | ||||
\(549\) | 21.7074 | + | 19.1213i | 0.926450 | + | 0.816076i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 48.5446i | − | 2.06807i | ||||||
\(552\) | −25.3705 | − | 5.13563i | −1.07984 | − | 0.218587i | ||||
\(553\) | −7.69193 | − | 7.69193i | −0.327094 | − | 0.327094i | ||||
\(554\) | 11.9352 | + | 2.51919i | 0.507080 | + | 0.107030i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.821496 | + | 1.85932i | −0.0348392 | + | 0.0788527i | ||||
\(557\) | 24.0378 | − | 24.0378i | 1.01851 | − | 1.01851i | 0.0186883 | − | 0.999825i | \(-0.494051\pi\) |
0.999825 | − | 0.0186883i | \(-0.00594902\pi\) | |||||||
\(558\) | −3.20110 | + | 21.9583i | −0.135513 | + | 0.929568i | ||||
\(559\) | − | 17.7744i | − | 0.751776i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.43594 | + | 2.43038i | 0.271726 | + | 0.102611i | ||||
\(562\) | 3.33639 | + | 5.12164i | 0.140737 | + | 0.216043i | ||||
\(563\) | −14.5105 | − | 14.5105i | −0.611544 | − | 0.611544i | 0.331805 | − | 0.943348i | \(-0.392343\pi\) |
−0.943348 | + | 0.331805i | \(0.892343\pi\) | |||||||
\(564\) | −14.0317 | + | 14.2664i | −0.590842 | + | 0.600723i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.70814 | − | 12.8305i | 0.113832 | − | 0.539305i | ||||
\(567\) | 14.5572 | + | 11.2719i | 0.611343 | + | 0.473375i | ||||
\(568\) | −46.6695 | + | 7.59590i | −1.95821 | + | 0.318717i | ||||
\(569\) | −31.0050 | −1.29980 | −0.649900 | − | 0.760020i | \(-0.725189\pi\) | ||||
−0.649900 | + | 0.760020i | \(0.725189\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.0629i | 1.38364i | 0.722070 | + | 0.691820i | \(0.243191\pi\) | ||||
−0.722070 | + | 0.691820i | \(0.756809\pi\) | |||||||
\(572\) | −1.33128 | − | 3.43884i | −0.0556636 | − | 0.143785i | ||||
\(573\) | −1.90048 | − | 4.20671i | −0.0793936 | − | 0.175738i | ||||
\(574\) | −20.4070 | − | 4.30732i | −0.851771 | − | 0.179784i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −9.33394 | + | 22.1106i | −0.388914 | + | 0.921274i | ||||
\(577\) | −17.5957 | + | 17.5957i | −0.732519 | + | 0.732519i | −0.971118 | − | 0.238599i | \(-0.923312\pi\) |
0.238599 | + | 0.971118i | \(0.423312\pi\) | |||||||
\(578\) | −16.4900 | − | 25.3135i | −0.685894 | − | 1.05290i | ||||
\(579\) | −17.7307 | − | 6.69556i | −0.736861 | − | 0.278258i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.36681 | −0.264140 | ||||||||
\(582\) | 0.827757 | + | 3.76685i | 0.0343116 | + | 0.156141i | ||||
\(583\) | −2.45855 | − | 2.45855i | −0.101823 | − | 0.101823i | ||||
\(584\) | 19.6504 | − | 27.2905i | 0.813140 | − | 1.12929i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.54706 | − | 1.59297i | −0.311766 | − | 0.0658048i | ||||
\(587\) | 6.48696 | − | 6.48696i | 0.267746 | − | 0.267746i | −0.560446 | − | 0.828191i | \(-0.689370\pi\) |
0.828191 | + | 0.560446i | \(0.189370\pi\) | |||||||
\(588\) | 9.75192 | − | 0.0808615i | 0.402162 | − | 0.00333467i | ||||
\(589\) | 25.7922 | 1.06275 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.77353 | − | 17.9372i | 0.278626 | − | 0.737836i | ||||
\(592\) | 0.908632 | − | 19.4537i | 0.0373445 | − | 0.799542i | ||||
\(593\) | 2.17189 | − | 2.17189i | 0.0891890 | − | 0.0891890i | −0.661105 | − | 0.750294i | \(-0.729912\pi\) |
0.750294 | + | 0.661105i | \(0.229912\pi\) | |||||||
\(594\) | 1.30034 | + | 4.52946i | 0.0533535 | + | 0.185846i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.52187 | + | 2.43971i | 0.226185 | + | 0.0999343i | ||||
\(597\) | 12.0234 | + | 26.6138i | 0.492086 | + | 1.08923i | ||||
\(598\) | −11.7267 | − | 18.0015i | −0.479542 | − | 0.736137i | ||||
\(599\) | 7.56553 | 0.309119 | 0.154560 | − | 0.987983i | \(-0.450604\pi\) | ||||
0.154560 | + | 0.987983i | \(0.450604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.2389 | 1.19268 | 0.596339 | − | 0.802732i | \(-0.296621\pi\) | ||||
0.596339 | + | 0.802732i | \(0.296621\pi\) | |||||||
\(602\) | −9.76209 | − | 14.9856i | −0.397873 | − | 0.610768i | ||||
\(603\) | 10.9955 | − | 0.696471i | 0.447772 | − | 0.0283625i | ||||
\(604\) | −6.03095 | + | 13.6500i | −0.245396 | + | 0.555412i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.70525 | + | 8.91886i | −0.231760 | + | 0.362304i | ||||
\(607\) | 28.6094 | − | 28.6094i | 1.16122 | − | 1.16122i | 0.177009 | − | 0.984209i | \(-0.443358\pi\) |
0.984209 | − | 0.177009i | \(-0.0566421\pi\) | |||||||
\(608\) | 26.9957 | + | 7.02820i | 1.09482 | + | 0.285031i | ||||
\(609\) | 32.6310 | + | 12.3223i | 1.32227 | + | 0.499324i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.6084 | −0.671902 | ||||||||
\(612\) | 12.8399 | − | 34.8738i | 0.519021 | − | 1.40969i | ||||
\(613\) | −9.80228 | + | 9.80228i | −0.395910 | + | 0.395910i | −0.876788 | − | 0.480878i | \(-0.840318\pi\) |
0.480878 | + | 0.876788i | \(0.340318\pi\) | |||||||
\(614\) | 6.30161 | + | 1.33009i | 0.254312 | + | 0.0536780i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.01110 | − | 2.16813i | −0.121321 | − | 0.0873564i | ||||
\(617\) | −6.03941 | − | 6.03941i | −0.243138 | − | 0.243138i | 0.575009 | − | 0.818147i | \(-0.304998\pi\) |
−0.818147 | + | 0.575009i | \(0.804998\pi\) | |||||||
\(618\) | 28.8218 | − | 6.33352i | 1.15938 | − | 0.254772i | ||||
\(619\) | 16.8314 | 0.676509 | 0.338255 | − | 0.941055i | \(-0.390163\pi\) | ||||
0.338255 | + | 0.941055i | \(0.390163\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.8626 | + | 24.2559i | 0.516159 | + | 0.973354i | ||||
\(622\) | −9.52958 | − | 14.6287i | −0.382101 | − | 0.586557i | ||||
\(623\) | 5.73679 | − | 5.73679i | 0.229840 | − | 0.229840i | ||||
\(624\) | −18.5159 | + | 7.34517i | −0.741230 | + | 0.294042i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.8922 | − | 4.83188i | −0.914956 | − | 0.193121i | ||||
\(627\) | 4.99156 | − | 2.25505i | 0.199344 | − | 0.0900582i | ||||
\(628\) | −16.0539 | + | 6.21493i | −0.640619 | + | 0.248003i | ||||
\(629\) | 30.1556i | 1.20238i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.4913 | 0.815744 | 0.407872 | − | 0.913039i | \(-0.366271\pi\) | ||||
0.407872 | + | 0.913039i | \(0.366271\pi\) | |||||||
\(632\) | −14.8451 | + | 2.41617i | −0.590505 | + | 0.0961101i | ||||
\(633\) | −4.60535 | − | 10.1939i | −0.183046 | − | 0.405173i | ||||
\(634\) | −2.12994 | + | 10.0911i | −0.0845909 | + | 0.400769i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.1702 | + | 13.3904i | −0.522232 | + | 0.530965i | ||||
\(637\) | 5.72347 | + | 5.72347i | 0.226772 | + | 0.226772i | ||||
\(638\) | 4.87305 | + | 7.48053i | 0.192926 | + | 0.296157i | ||||
\(639\) | 37.6336 | + | 33.1500i | 1.48876 | + | 1.31140i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 25.3407i | − | 1.00090i | −0.865767 | − | 0.500448i | \(-0.833169\pi\) | ||
0.865767 | − | 0.500448i | \(-0.166831\pi\) | |||||||
\(642\) | −7.69037 | − | 34.9964i | −0.303515 | − | 1.38120i | ||||
\(643\) | 16.2516 | − | 16.2516i | 0.640899 | − | 0.640899i | −0.309878 | − | 0.950776i | \(-0.600288\pi\) |
0.950776 | + | 0.309878i | \(0.100288\pi\) | |||||||
\(644\) | −19.7737 | − | 8.73654i | −0.779193 | − | 0.344268i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −42.2632 | − | 8.92055i | −1.66282 | − | 0.350974i | ||||
\(647\) | 3.30434 | + | 3.30434i | 0.129907 | + | 0.129907i | 0.769071 | − | 0.639164i | \(-0.220719\pi\) |
−0.639164 | + | 0.769071i | \(0.720719\pi\) | |||||||
\(648\) | 24.4084 | − | 7.22689i | 0.958854 | − | 0.283899i | ||||
\(649\) | 1.60541i | 0.0630180i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.54695 | + | 17.3371i | −0.256595 | + | 0.679496i | ||||
\(652\) | 13.8345 | + | 35.7361i | 0.541801 | + | 1.39953i | ||||
\(653\) | −2.00144 | − | 2.00144i | −0.0783225 | − | 0.0783225i | 0.666860 | − | 0.745183i | \(-0.267638\pi\) |
−0.745183 | + | 0.666860i | \(0.767638\pi\) | |||||||
\(654\) | −15.1082 | + | 23.6183i | −0.590778 | + | 0.923547i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −21.3201 | + | 19.4174i | −0.832411 | + | 0.758122i | ||||
\(657\) | −35.5976 | + | 2.25480i | −1.38879 | + | 0.0879681i | ||||
\(658\) | −14.0025 | + | 9.12169i | −0.545876 | + | 0.355600i | ||||
\(659\) | − | 14.5552i | − | 0.566989i | −0.958974 | − | 0.283495i | \(-0.908506\pi\) | ||
0.958974 | − | 0.283495i | \(-0.0914938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 10.7204i | − | 0.416977i | −0.978025 | − | 0.208488i | \(-0.933146\pi\) | ||
0.978025 | − | 0.208488i | \(-0.0668544\pi\) | |||||||
\(662\) | 10.8424 | + | 16.6440i | 0.421402 | + | 0.646887i | ||||
\(663\) | 28.1088 | − | 12.6988i | 1.09165 | − | 0.493180i | ||||
\(664\) | −5.14386 | + | 7.14379i | −0.199620 | + | 0.277233i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.5604 | + | 12.3464i | −0.641703 | + | 0.478412i | ||||
\(667\) | 36.7799 | + | 36.7799i | 1.42412 | + | 1.42412i | ||||
\(668\) | −23.1486 | + | 8.96149i | −0.895644 | + | 0.346731i | ||||
\(669\) | 19.2760 | + | 7.27910i | 0.745252 | + | 0.281426i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.18365i | 0.238717i | ||||||||
\(672\) | −11.5767 | + | 16.3621i | −0.446580 | + | 0.631181i | ||||
\(673\) | 12.2384 | + | 12.2384i | 0.471755 | + | 0.471755i | 0.902482 | − | 0.430727i | \(-0.141743\pi\) |
−0.430727 | + | 0.902482i | \(0.641743\pi\) | |||||||
\(674\) | −4.36590 | + | 20.6845i | −0.168168 | + | 0.796737i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.65950 | + | 3.82599i | 0.333058 | + | 0.147154i | ||||
\(677\) | −3.99371 | + | 3.99371i | −0.153491 | + | 0.153491i | −0.779675 | − | 0.626184i | \(-0.784616\pi\) |
0.626184 | + | 0.779675i | \(0.284616\pi\) | |||||||
\(678\) | 5.41984 | + | 24.6639i | 0.208148 | + | 0.947212i | ||||
\(679\) | 3.22091i | 0.123607i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0691789 | − | 0.183194i | 0.00265094 | − | 0.00702002i | ||||
\(682\) | −3.97448 | + | 2.58910i | −0.152191 | + | 0.0991416i | ||||
\(683\) | −7.19759 | − | 7.19759i | −0.275408 | − | 0.275408i | 0.555865 | − | 0.831273i | \(-0.312387\pi\) |
−0.831273 | + | 0.555865i | \(0.812387\pi\) | |||||||
\(684\) | −12.4047 | − | 26.8618i | −0.474304 | − | 1.02709i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 27.7835 | + | 5.86429i | 1.06078 | + | 0.223900i | ||||
\(687\) | −20.4772 | + | 9.25106i | −0.781255 | + | 0.352950i | ||||
\(688\) | −24.7014 | − | 1.15374i | −0.941731 | − | 0.0439859i | ||||
\(689\) | −15.5886 | −0.593879 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.1691i | 0.919434i | 0.888065 | + | 0.459717i | \(0.152049\pi\) | ||||
−0.888065 | + | 0.459717i | \(0.847951\pi\) | |||||||
\(692\) | −40.3106 | + | 15.6054i | −1.53238 | + | 0.593229i | ||||
\(693\) | 0.248783 | + | 3.92766i | 0.00945050 | + | 0.149200i | ||||
\(694\) | −8.35055 | + | 39.5627i | −0.316983 | + | 1.50178i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 40.1892 | − | 26.6577i | 1.52337 | − | 1.01046i | ||||
\(697\) | 31.5740 | − | 31.5740i | 1.19595 | − | 1.19595i | ||||
\(698\) | 0.714553 | − | 0.465482i | 0.0270462 | − | 0.0176187i | ||||
\(699\) | −1.84304 | + | 4.88059i | −0.0697100 | + | 0.184601i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.9018 | 1.16714 | 0.583572 | − | 0.812061i | \(-0.301655\pi\) | ||||
0.583572 | + | 0.812061i | \(0.301655\pi\) | |||||||
\(702\) | 18.4821 | + | 10.2372i | 0.697563 | + | 0.386379i | ||||
\(703\) | 16.9770 | + | 16.9770i | 0.640299 | + | 0.640299i | ||||
\(704\) | −4.86544 | + | 1.62689i | −0.183373 | + | 0.0613156i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.11559 | − | 38.4495i | 0.305434 | − | 1.44707i | ||||
\(707\) | −6.25230 | + | 6.25230i | −0.235142 | + | 0.235142i | ||||
\(708\) | 8.67194 | − | 0.0719064i | 0.325911 | − | 0.00270241i | ||||
\(709\) | −20.8029 | −0.781269 | −0.390634 | − | 0.920546i | \(-0.627744\pi\) | ||||
−0.390634 | + | 0.920546i | \(0.627744\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.9708 | + | 10.5447i | 0.448941 | + | 0.395456i | ||||
\(712\) | −1.80203 | − | 11.0717i | −0.0675338 | − | 0.414931i | ||||
\(713\) | −19.5415 | + | 19.5415i | −0.731835 | + | 0.731835i | ||||
\(714\) | 16.7241 | − | 26.1444i | 0.625884 | − | 0.978428i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.87769 | − | 1.71327i | −0.144916 | − | 0.0640277i | ||||
\(717\) | 26.3873 | − | 11.9211i | 0.985453 | − | 0.445201i | ||||
\(718\) | −15.0139 | + | 9.78050i | −0.560313 | + | 0.365005i | ||||
\(719\) | −34.2881 | −1.27873 | −0.639364 | − | 0.768904i | \(-0.720802\pi\) | ||||
−0.639364 | + | 0.768904i | \(0.720802\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.6446 | 0.917812 | ||||||||
\(722\) | −6.30114 | + | 4.10476i | −0.234504 | + | 0.152763i | ||||
\(723\) | −7.39836 | + | 3.34238i | −0.275148 | + | 0.124304i | ||||
\(724\) | −35.5621 | − | 15.7123i | −1.32165 | − | 0.583941i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.9766 | − | 21.8492i | 0.518719 | − | 0.810899i | ||||
\(727\) | 2.33356 | − | 2.33356i | 0.0865468 | − | 0.0865468i | −0.662508 | − | 0.749055i | \(-0.730508\pi\) |
0.749055 | + | 0.662508i | \(0.230508\pi\) | |||||||
\(728\) | −16.4196 | + | 2.67244i | −0.608552 | + | 0.0990474i | ||||
\(729\) | −22.3505 | − | 15.1478i | −0.827797 | − | 0.561028i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.2901 | 1.41621 | ||||||||
\(732\) | 33.4021 | − | 0.276966i | 1.23458 | − | 0.0102369i | ||||
\(733\) | 35.6179 | − | 35.6179i | 1.31558 | − | 1.31558i | 0.398342 | − | 0.917237i | \(-0.369586\pi\) |
0.917237 | − | 0.398342i | \(-0.130414\pi\) | |||||||
\(734\) | 0.897608 | − | 4.25263i | 0.0331313 | − | 0.156967i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25.7782 | + | 15.1284i | −0.950198 | + | 0.557640i | ||||
\(737\) | 1.66531 | + | 1.66531i | 0.0613425 | + | 0.0613425i | ||||
\(738\) | 30.2665 | + | 4.41228i | 1.11413 | + | 0.162418i | ||||
\(739\) | −14.3621 | −0.528318 | −0.264159 | − | 0.964479i | \(-0.585094\pi\) | ||||
−0.264159 | + | 0.964479i | \(0.585094\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.67551 | − | 22.9738i | 0.318703 | − | 0.843965i | ||||
\(742\) | −13.1428 | + | 8.56162i | −0.482487 | + | 0.314307i | ||||
\(743\) | 1.87689 | − | 1.87689i | 0.0688563 | − | 0.0688563i | −0.671840 | − | 0.740696i | \(-0.734496\pi\) |
0.740696 | + | 0.671840i | \(0.234496\pi\) | |||||||
\(744\) | 14.1635 | + | 21.3529i | 0.519259 | + | 0.782835i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.15428 | − | 38.6329i | 0.298550 | − | 1.41445i | ||||
\(747\) | 9.31833 | − | 0.590235i | 0.340940 | − | 0.0215956i | ||||
\(748\) | 7.40806 | − | 2.86788i | 0.270866 | − | 0.104860i | ||||
\(749\) | − | 29.9243i | − | 1.09341i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.0439 | −1.09632 | −0.548158 | − | 0.836375i | \(-0.684671\pi\) | ||||
−0.548158 | + | 0.836375i | \(0.684671\pi\) | |||||||
\(752\) | −1.07805 | + | 23.0809i | −0.0393125 | + | 0.841675i | ||||
\(753\) | −28.9430 | + | 13.0757i | −1.05474 | + | 0.476503i | ||||
\(754\) | 39.1644 | + | 8.26647i | 1.42628 | + | 0.301047i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 21.2048 | − | 1.51977i | 0.771212 | − | 0.0552735i | ||||
\(757\) | −34.9468 | − | 34.9468i | −1.27016 | − | 1.27016i | −0.946002 | − | 0.324162i | \(-0.894918\pi\) |
−0.324162 | − | 0.946002i | \(-0.605082\pi\) | |||||||
\(758\) | −10.3891 | + | 6.76775i | −0.377347 | + | 0.245816i | ||||
\(759\) | −2.07332 | + | 5.49040i | −0.0752567 | + | 0.199289i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.88711i | − | 0.104657i | −0.998630 | − | 0.0523287i | \(-0.983336\pi\) | ||
0.998630 | − | 0.0523287i | \(-0.0166644\pi\) | |||||||
\(762\) | −8.52929 | − | 38.8140i | −0.308984 | − | 1.40608i | ||||
\(763\) | −16.5569 | + | 16.5569i | −0.599399 | + | 0.599399i | ||||
\(764\) | −4.87552 | − | 2.15413i | −0.176390 | − | 0.0779337i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.91359 | + | 32.7548i | −0.249798 | + | 1.18348i | ||||
\(767\) | 5.08962 | + | 5.08962i | 0.183776 | + | 0.183776i | ||||
\(768\) | 9.00584 | + | 26.2087i | 0.324970 | + | 0.945724i | ||||
\(769\) | − | 19.0345i | − | 0.686400i | −0.939262 | − | 0.343200i | \(-0.888489\pi\) | ||
0.939262 | − | 0.343200i | \(-0.111511\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.94892 | − | 1.11359i | −0.106203 | − | 0.0401048i | ||||
\(772\) | −20.4088 | + | 7.90085i | −0.734529 | + | 0.284358i | ||||
\(773\) | 18.9794 | + | 18.9794i | 0.682642 | + | 0.682642i | 0.960595 | − | 0.277953i | \(-0.0896558\pi\) |
−0.277953 | + | 0.960595i | \(0.589656\pi\) | |||||||
\(774\) | 15.6768 | + | 21.0276i | 0.563492 | + | 0.755823i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.61398 | + | 2.60223i | 0.129734 | + | 0.0934148i | ||||
\(777\) | −15.7210 | + | 7.10233i | −0.563988 | + | 0.254795i | ||||
\(778\) | 16.2044 | + | 24.8752i | 0.580958 | + | 0.891818i | ||||
\(779\) | − | 35.5511i | − | 1.27375i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7204i | 0.383608i | ||||||||
\(782\) | 38.7794 | − | 25.2621i | 1.38675 | − | 0.903371i | ||||
\(783\) | −48.9003 | − | 15.0096i | −1.74756 | − | 0.536399i | ||||
\(784\) | 8.32552 | − | 7.58250i | 0.297340 | − | 0.270804i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 20.6504 | − | 32.2823i | 0.736576 | − | 1.15147i | ||||
\(787\) | −28.3424 | − | 28.3424i | −1.01030 | − | 1.01030i | −0.999946 | − | 0.0103521i | \(-0.996705\pi\) |
−0.0103521 | − | 0.999946i | \(-0.503295\pi\) | |||||||
\(788\) | −7.99286 | − | 20.6465i | −0.284734 | − | 0.735500i | ||||
\(789\) | −3.42756 | + | 9.07661i | −0.122024 | + | 0.323136i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.0893i | 0.749850i | ||||||||
\(792\) | 4.60797 | + | 2.89408i | 0.163737 | + | 0.102837i | ||||
\(793\) | 19.6040 | + | 19.6040i | 0.696157 | + | 0.696157i | ||||
\(794\) | −44.5164 | − | 9.39613i | −1.57983 | − | 0.333456i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 30.8451 | + | 13.6282i | 1.09327 | + | 0.483037i | ||||
\(797\) | −15.8150 | + | 15.8150i | −0.560195 | + | 0.560195i | −0.929363 | − | 0.369168i | \(-0.879643\pi\) |
0.369168 | + | 0.929363i | \(0.379643\pi\) | |||||||
\(798\) | −5.30341 | − | 24.1341i | −0.187739 | − | 0.854338i | ||||
\(799\) | − | 35.7782i | − | 1.26574i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.86441 | + | 8.92807i | −0.277875 | + | 0.315458i | ||||
\(802\) | −18.7204 | − | 28.7373i | −0.661039 | − | 1.01475i | ||||
\(803\) | −5.39139 | − | 5.39139i | −0.190258 | − | 0.190258i | ||||
\(804\) | 8.92089 | − | 9.07007i | 0.314616 | − | 0.319877i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.39206 | + | 20.8084i | −0.154704 | + | 0.732945i | ||||
\(807\) | 1.29704 | + | 2.87101i | 0.0456581 | + | 0.101064i | ||||
\(808\) | 1.96396 | + | 12.0666i | 0.0690918 | + | 0.424503i | ||||
\(809\) | 49.0232 | 1.72356 | 0.861782 | − | 0.507279i | \(-0.169349\pi\) | ||||
0.861782 | + | 0.507279i | \(0.169349\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 21.1676i | − | 0.743295i | −0.928374 | − | 0.371648i | \(-0.878793\pi\) | ||
0.928374 | − | 0.371648i | \(-0.121207\pi\) | |||||||
\(812\) | 37.5597 | − | 14.5405i | 1.31809 | − | 0.510271i | ||||
\(813\) | 11.9153 | − | 5.38302i | 0.417888 | − | 0.188791i | ||||
\(814\) | −4.32028 | − | 0.911887i | −0.151426 | − | 0.0319616i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −15.8232 | − | 39.8875i | −0.553922 | − | 1.39634i | ||||
\(817\) | 21.5566 | − | 21.5566i | 0.754169 | − | 0.754169i | ||||
\(818\) | 18.6001 | + | 28.5527i | 0.650336 | + | 0.998320i | ||||
\(819\) | 13.2405 | + | 11.6631i | 0.462661 | + | 0.407542i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.4855 | −0.470649 | −0.235324 | − | 0.971917i | \(-0.575615\pi\) | ||||
−0.235324 | + | 0.971917i | \(0.575615\pi\) | |||||||
\(822\) | −30.2538 | + | 6.64821i | −1.05522 | + | 0.231883i | ||||
\(823\) | −19.8632 | − | 19.8632i | −0.692387 | − | 0.692387i | 0.270370 | − | 0.962757i | \(-0.412854\pi\) |
−0.962757 | + | 0.270370i | \(0.912854\pi\) | |||||||
\(824\) | 19.9108 | − | 27.6521i | 0.693626 | − | 0.963306i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.08641 | + | 1.49574i | 0.246568 | + | 0.0520433i | ||||
\(827\) | −36.8216 | + | 36.8216i | −1.28041 | + | 1.28041i | −0.339982 | + | 0.940432i | \(0.610421\pi\) |
−0.940432 | + | 0.339982i | \(0.889579\pi\) | |||||||
\(828\) | 29.7503 | + | 10.9535i | 1.03389 | + | 0.380660i | ||||
\(829\) | 34.1845 | 1.18728 | 0.593638 | − | 0.804732i | \(-0.297691\pi\) | ||||
0.593638 | + | 0.804732i | \(0.297691\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.9764 | − | 5.27784i | −0.484835 | − | 0.183086i | ||||
\(832\) | −10.2671 | + | 20.5825i | −0.355949 | + | 0.713571i | ||||
\(833\) | −12.3297 | + | 12.3297i | −0.427198 | + | 0.427198i | ||||
\(834\) | 1.34153 | − | 2.09718i | 0.0464535 | − | 0.0726195i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.55603 | − | 5.78515i | 0.0884022 | − | 0.200084i | ||||
\(837\) | 7.97474 | − | 25.9812i | 0.275647 | − | 0.898042i | ||||
\(838\) | −30.8432 | − | 47.3469i | −1.06546 | − | 1.63557i | ||||
\(839\) | 19.6854 | 0.679616 | 0.339808 | − | 0.940495i | \(-0.389638\pi\) | ||||
0.339808 | + | 0.940495i | \(0.389638\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −67.9085 | −2.34167 | ||||||||
\(842\) | 20.9308 | + | 32.1306i | 0.721324 | + | 1.10729i | ||||
\(843\) | −3.08215 | − | 6.82234i | −0.106155 | − | 0.234974i | ||||
\(844\) | −11.8146 | − | 5.22001i | −0.406676 | − | 0.179680i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 19.6482 | − | 14.6484i | 0.675519 | − | 0.503623i | ||||
\(847\) | 15.3167 | − | 15.3167i | 0.526289 | − | 0.526289i | ||||
\(848\) | −1.01186 | + | 21.6638i | −0.0347474 | + | 0.743937i | ||||
\(849\) | −5.67371 | + | 15.0247i | −0.194721 | + | 0.515647i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.7252 | −0.881850 | ||||||||
\(852\) | 57.9084 | − | 0.480168i | 1.98391 | − | 0.0164503i | ||||
\(853\) | −29.0954 | + | 29.0954i | −0.996209 | + | 0.996209i | −0.999993 | − | 0.00378410i | \(-0.998795\pi\) |
0.00378410 | + | 0.999993i | \(0.498795\pi\) | |||||||
\(854\) | 27.2951 | + | 5.76121i | 0.934018 | + | 0.197144i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −33.5761 | − | 24.1764i | −1.14761 | − | 0.826331i | ||||
\(857\) | 8.71719 | + | 8.71719i | 0.297773 | + | 0.297773i | 0.840141 | − | 0.542368i | \(-0.182472\pi\) |
−0.542368 | + | 0.840141i | \(0.682472\pi\) | |||||||
\(858\) | 0.969317 | + | 4.41105i | 0.0330920 | + | 0.150591i | ||||
\(859\) | −49.6253 | −1.69319 | −0.846597 | − | 0.532235i | \(-0.821352\pi\) | ||||
−0.846597 | + | 0.532235i | \(0.821352\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.8969 | + | 9.02409i | 0.814405 | + | 0.307540i | ||||
\(862\) | 23.9094 | + | 36.7029i | 0.814357 | + | 1.25011i | ||||
\(863\) | −26.7844 | + | 26.7844i | −0.911750 | + | 0.911750i | −0.996410 | − | 0.0846599i | \(-0.973020\pi\) |
0.0846599 | + | 0.996410i | \(0.473020\pi\) | |||||||
\(864\) | 15.4265 | − | 25.0204i | 0.524821 | − | 0.851212i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.0092 | − | 3.37908i | −0.544014 | − | 0.114826i | ||||
\(867\) | 15.2334 | + | 33.7192i | 0.517354 | + | 1.14516i | ||||
\(868\) | 7.72550 | + | 19.9558i | 0.262220 | + | 0.677345i | ||||
\(869\) | 3.41005i | 0.115678i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5590 | 0.357779 | ||||||||
\(872\) | 5.20081 | + | 31.9540i | 0.176122 | + | 1.08210i | ||||
\(873\) | −0.298595 | − | 4.71406i | −0.0101059 | − | 0.159547i | ||||
\(874\) | 7.60998 | − | 36.0541i | 0.257412 | − | 1.21955i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −28.8811 | + | 29.3640i | −0.975801 | + | 0.992119i | ||||
\(877\) | −13.3952 | − | 13.3952i | −0.452323 | − | 0.452323i | 0.443802 | − | 0.896125i | \(-0.353629\pi\) |
−0.896125 | + | 0.443802i | \(0.853629\pi\) | |||||||
\(878\) | 7.43694 | + | 11.4163i | 0.250984 | + | 0.385282i | ||||
\(879\) | 8.83773 | + | 3.33735i | 0.298089 | + | 0.112566i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.8169i | 0.398120i | 0.979987 | + | 0.199060i | \(0.0637889\pi\) | ||||
−0.979987 | + | 0.199060i | \(0.936211\pi\) | |||||||
\(882\) | −11.8191 | − | 1.72300i | −0.397970 | − | 0.0580163i | ||||
\(883\) | 19.7888 | − | 19.7888i | 0.665947 | − | 0.665947i | −0.290828 | − | 0.956775i | \(-0.593931\pi\) |
0.956775 | + | 0.290828i | \(0.0939308\pi\) | |||||||
\(884\) | 14.3937 | − | 32.5777i | 0.484112 | − | 1.09571i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.4716 | + | 2.42133i | 0.385396 | + | 0.0813461i | ||||
\(887\) | −0.472133 | − | 0.472133i | −0.0158527 | − | 0.0158527i | 0.699136 | − | 0.714989i | \(-0.253568\pi\) |
−0.714989 | + | 0.699136i | \(0.753568\pi\) | |||||||
\(888\) | −4.73222 | + | 23.3776i | −0.158803 | + | 0.784502i | ||||
\(889\) | − | 33.1886i | − | 1.11311i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.728228 | − | 5.72538i | −0.0243966 | − | 0.191807i | ||||
\(892\) | 22.1875 | − | 8.58944i | 0.742893 | − | 0.287596i | ||||
\(893\) | −20.1424 | − | 20.1424i | −0.674041 | − | 0.674041i | ||||
\(894\) | −6.22828 | − | 3.98413i | −0.208305 | − | 0.133249i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.64814 | + | 22.9921i | 0.0884683 | + | 0.768113i | ||||
\(897\) | 10.8331 | + | 23.9792i | 0.361708 | + | 0.800641i | ||||
\(898\) | 7.59048 | − | 4.94467i | 0.253297 | − | 0.165006i | ||||
\(899\) | − | 51.4884i | − | 1.71723i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 33.5815i | − | 1.11876i | ||||||
\(902\) | 3.56872 | + | 5.47828i | 0.118825 | + | 0.182407i | ||||
\(903\) | 9.01820 | + | 19.9618i | 0.300107 | + | 0.664287i | ||||
\(904\) | 23.6630 | + | 17.0384i | 0.787019 | + | 0.566690i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.84875 | − | 15.3963i | 0.327203 | − | 0.511508i | ||||
\(907\) | −38.0394 | − | 38.0394i | −1.26308 | − | 1.26308i | −0.949594 | − | 0.313482i | \(-0.898505\pi\) |
−0.313482 | − | 0.949594i | \(-0.601495\pi\) | |||||||
\(908\) | −0.0816321 | − | 0.210865i | −0.00270906 | − | 0.00699780i | ||||
\(909\) | 8.57111 | − | 9.73035i | 0.284286 | − | 0.322735i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.1309i | 1.66091i | 0.557086 | + | 0.830455i | \(0.311919\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(912\) | −31.3640 | − | 13.5478i | −1.03857 | − | 0.448611i | ||||
\(913\) | 1.41129 | + | 1.41129i | 0.0467070 | + | 0.0467070i | ||||
\(914\) | 6.89908 | − | 32.6860i | 0.228201 | − | 1.08116i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.4858 | + | 23.7328i | −0.346460 | + | 0.784154i | ||||
\(917\) | 22.6305 | − | 22.6305i | 0.747325 | − | 0.747325i | ||||
\(918\) | −22.0533 | + | 39.8147i | −0.727869 | + | 1.31408i | ||||
\(919\) | 21.5999i | 0.712514i | 0.934388 | + | 0.356257i | \(0.115947\pi\) | ||||
−0.934388 | + | 0.356257i | \(0.884053\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.37929 | − | 2.78661i | −0.243156 | − | 0.0918219i | ||||
\(922\) | −42.0754 | + | 27.4092i | −1.38568 | + | 0.902675i | ||||
\(923\) | 33.9869 | + | 33.9869i | 1.11869 | + | 1.11869i | ||||
\(924\) | 3.23988 | + | 3.18659i | 0.106584 | + | 0.104831i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −19.1735 | − | 4.04697i | −0.630079 | − | 0.132992i | ||||
\(927\) | −36.0693 | + | 2.28468i | −1.18467 | + | 0.0750387i | ||||
\(928\) | 14.0302 | − | 53.8909i | 0.460565 | − | 1.76905i | ||||
\(929\) | 0.457555 | 0.0150119 | 0.00750595 | − | 0.999972i | \(-0.497611\pi\) | ||||
0.00750595 | + | 0.999972i | \(0.497611\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.8827i | 0.454988i | ||||||||
\(932\) | 2.17481 | + | 5.61778i | 0.0712383 | + | 0.184017i | ||||
\(933\) | 8.80340 | + | 19.4863i | 0.288211 | + | 0.637954i | ||||
\(934\) | 3.33216 | − | 15.7869i | 0.109032 | − | 0.516563i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 23.7837 | − | 5.43352i | 0.777394 | − | 0.177600i | ||||
\(937\) | −7.63736 | + | 7.63736i | −0.249502 | + | 0.249502i | −0.820766 | − | 0.571264i | \(-0.806453\pi\) |
0.571264 | + | 0.820766i | \(0.306453\pi\) | |||||||
\(938\) | 8.90234 | − | 5.79926i | 0.290672 | − | 0.189352i | ||||
\(939\) | 26.8071 | + | 10.1231i | 0.874818 | + | 0.330354i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52.1835 | −1.70113 | −0.850567 | − | 0.525867i | \(-0.823741\pi\) | ||||
−0.850567 | + | 0.525867i | \(0.823741\pi\) | |||||||
\(942\) | 20.5925 | − | 4.52515i | 0.670940 | − | 0.147437i | ||||
\(943\) | 26.9353 | + | 26.9353i | 0.877135 | + | 0.877135i | ||||
\(944\) | 7.40351 | − | 6.74277i | 0.240964 | − | 0.219459i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.15787 | + | 5.48569i | −0.0376456 | + | 0.178355i | ||||
\(947\) | 28.3995 | − | 28.3995i | 0.922860 | − | 0.922860i | −0.0743707 | − | 0.997231i | \(-0.523695\pi\) |
0.997231 | + | 0.0743707i | \(0.0236948\pi\) | |||||||
\(948\) | 18.4200 | − | 0.152736i | 0.598255 | − | 0.00496064i | ||||
\(949\) | −34.1845 | −1.10968 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.46235 | − | 11.8169i | 0.144702 | − | 0.383188i | ||||
\(952\) | −5.75706 | − | 35.3717i | −0.186587 | − | 1.14640i | ||||
\(953\) | 23.6130 | − | 23.6130i | 0.764900 | − | 0.764900i | −0.212304 | − | 0.977204i | \(-0.568097\pi\) |
0.977204 | + | 0.212304i | \(0.0680967\pi\) | |||||||
\(954\) | 18.4418 | − | 13.7490i | 0.597076 | − | 0.445141i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.5122 | − | 30.5826i | 0.437015 | − | 0.989111i | ||||
\(957\) | −4.50171 | − | 9.96454i | −0.145520 | − | 0.322108i | ||||
\(958\) | −4.79551 | + | 3.12394i | −0.154936 | + | 0.100930i | ||||
\(959\) | −25.8691 | −0.835356 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.64371 | −0.117539 | ||||||||
\(962\) | −16.5875 | + | 10.8056i | −0.534801 | + | 0.348386i | ||||
\(963\) | 2.77413 | + | 43.7965i | 0.0893952 | + | 1.41132i | ||||
\(964\) | −3.78848 | + | 8.57460i | −0.122019 | + | 0.276169i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 22.3034 | + | 14.2671i | 0.717599 | + | 0.459036i | ||||
\(967\) | 3.10676 | − | 3.10676i | 0.0999067 | − | 0.0999067i | −0.655387 | − | 0.755293i | \(-0.727494\pi\) |
0.755293 | + | 0.655387i | \(0.227494\pi\) | |||||||
\(968\) | −4.81125 | − | 29.5606i | −0.154640 | − | 0.950112i | ||||
\(969\) | 49.4909 | + | 18.6891i | 1.58988 | + | 0.600379i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.7395 | −0.537196 | −0.268598 | − | 0.963252i | \(-0.586560\pi\) | ||||
−0.268598 | + | 0.963252i | \(0.586560\pi\) | |||||||
\(972\) | −30.8941 | + | 4.19010i | −0.990928 | + | 0.134397i | ||||
\(973\) | 1.47017 | − | 1.47017i | 0.0471314 | − | 0.0471314i | ||||
\(974\) | 2.59603 | − | 12.2993i | 0.0831823 | − | 0.394096i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28.5165 | − | 25.9715i | 0.912790 | − | 0.831327i | ||||
\(977\) | 38.9727 | + | 38.9727i | 1.24685 | + | 1.24685i | 0.957104 | + | 0.289745i | \(0.0935704\pi\) |
0.289745 | + | 0.957104i | \(0.406430\pi\) | |||||||
\(978\) | −10.0730 | − | 45.8391i | −0.322100 | − | 1.46577i | ||||
\(979\) | −2.54328 | −0.0812837 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.6974 | − | 25.7672i | 0.724672 | − | 0.822683i | ||||
\(982\) | 29.8002 | − | 19.4128i | 0.950963 | − | 0.619486i | ||||
\(983\) | −21.8279 | + | 21.8279i | −0.696200 | + | 0.696200i | −0.963589 | − | 0.267388i | \(-0.913839\pi\) |
0.267388 | + | 0.963589i | \(0.413839\pi\) | |||||||
\(984\) | 29.4321 | − | 19.5225i | 0.938261 | − | 0.622353i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −17.8079 | + | 84.3691i | −0.567119 | + | 2.68686i | ||||
\(987\) | 18.6523 | − | 8.42660i | 0.593708 | − | 0.268222i | ||||
\(988\) | −10.2372 | − | 26.4439i | −0.325690 | − | 0.841294i | ||||
\(989\) | 32.6647i | 1.03868i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.28868 | −0.0409363 | −0.0204681 | − | 0.999791i | \(-0.506516\pi\) | ||||
−0.0204681 | + | 0.999791i | \(0.506516\pi\) | |||||||
\(992\) | 28.6327 | + | 7.45440i | 0.909090 | + | 0.236677i | ||||
\(993\) | −10.0162 | − | 22.1708i | −0.317854 | − | 0.703570i | ||||
\(994\) | 47.3208 | + | 9.98805i | 1.50092 | + | 0.316802i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.56016 | − | 7.68658i | 0.239553 | − | 0.243559i | ||||
\(997\) | 17.8369 | + | 17.8369i | 0.564900 | + | 0.564900i | 0.930695 | − | 0.365795i | \(-0.119203\pi\) |
−0.365795 | + | 0.930695i | \(0.619203\pi\) | |||||||
\(998\) | −4.75426 | + | 3.09707i | −0.150493 | + | 0.0980361i | ||||
\(999\) | 22.3505 | − | 11.8522i | 0.707139 | − | 0.374988i |
(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 | 600.2.w.k.293.8 | yes | 64 | |
3.2 | odd | 2 | inner | 600.2.w.k.293.26 | yes | 64 | |
5.2 | odd | 4 | inner | 600.2.w.k.557.9 | yes | 64 | |
5.3 | odd | 4 | inner | 600.2.w.k.557.24 | yes | 64 | |
5.4 | even | 2 | inner | 600.2.w.k.293.25 | yes | 64 | |
8.5 | even | 2 | inner | 600.2.w.k.293.23 | yes | 64 | |
15.2 | even | 4 | inner | 600.2.w.k.557.23 | yes | 64 | |
15.8 | even | 4 | inner | 600.2.w.k.557.10 | yes | 64 | |
15.14 | odd | 2 | inner | 600.2.w.k.293.7 | ✓ | 64 | |
24.5 | odd | 2 | inner | 600.2.w.k.293.9 | yes | 64 | |
40.13 | odd | 4 | inner | 600.2.w.k.557.7 | yes | 64 | |
40.29 | even | 2 | inner | 600.2.w.k.293.10 | yes | 64 | |
40.37 | odd | 4 | inner | 600.2.w.k.557.26 | yes | 64 | |
120.29 | odd | 2 | inner | 600.2.w.k.293.24 | yes | 64 | |
120.53 | even | 4 | inner | 600.2.w.k.557.25 | yes | 64 | |
120.77 | even | 4 | inner | 600.2.w.k.557.8 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.2.w.k.293.7 | ✓ | 64 | 15.14 | odd | 2 | inner | |
600.2.w.k.293.8 | yes | 64 | 1.1 | even | 1 | trivial | |
600.2.w.k.293.9 | yes | 64 | 24.5 | odd | 2 | inner | |
600.2.w.k.293.10 | yes | 64 | 40.29 | even | 2 | inner | |
600.2.w.k.293.23 | yes | 64 | 8.5 | even | 2 | inner | |
600.2.w.k.293.24 | yes | 64 | 120.29 | odd | 2 | inner | |
600.2.w.k.293.25 | yes | 64 | 5.4 | even | 2 | inner | |
600.2.w.k.293.26 | yes | 64 | 3.2 | odd | 2 | inner | |
600.2.w.k.557.7 | yes | 64 | 40.13 | odd | 4 | inner | |
600.2.w.k.557.8 | yes | 64 | 120.77 | even | 4 | inner | |
600.2.w.k.557.9 | yes | 64 | 5.2 | odd | 4 | inner | |
600.2.w.k.557.10 | yes | 64 | 15.8 | even | 4 | inner | |
600.2.w.k.557.23 | yes | 64 | 15.2 | even | 4 | inner | |
600.2.w.k.557.24 | yes | 64 | 5.3 | odd | 4 | inner | |
600.2.w.k.557.25 | yes | 64 | 120.53 | even | 4 | inner | |
600.2.w.k.557.26 | yes | 64 | 40.37 | odd | 4 | inner |