Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(214,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.h (of order \(3\), degree \(2\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.1 | ||
Character | \(\chi\) | \(=\) | 441.373 |
Dual form | 441.2.h.h.214.1 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71513 | −1.91989 | −0.959944 | − | 0.280191i | \(-0.909602\pi\) | ||||
−0.959944 | + | 0.280191i | \(0.909602\pi\) | |||||||
\(3\) | −1.16958 | + | 1.27753i | −0.675255 | + | 0.737584i | ||||
\(4\) | 5.37195 | 2.68597 | ||||||||
\(5\) | −0.793197 | − | 1.37386i | −0.354728 | − | 0.614407i | 0.632343 | − | 0.774688i | \(-0.282093\pi\) |
−0.987071 | + | 0.160281i | \(0.948760\pi\) | |||||||
\(6\) | 3.17555 | − | 3.46867i | 1.29641 | − | 1.41608i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −9.15528 | −3.23688 | ||||||||
\(9\) | −0.264183 | − | 2.98835i | −0.0880610 | − | 0.996115i | ||||
\(10\) | 2.15363 | + | 3.73020i | 0.681039 | + | 1.17959i | ||||
\(11\) | 0.674376 | − | 1.16805i | 0.203332 | − | 0.352181i | −0.746268 | − | 0.665646i | \(-0.768156\pi\) |
0.949600 | + | 0.313464i | \(0.101490\pi\) | |||||||
\(12\) | −6.28290 | + | 6.86284i | −1.81372 | + | 1.98113i | ||||
\(13\) | −1.58916 | + | 2.75251i | −0.440754 | + | 0.763409i | −0.997746 | − | 0.0671096i | \(-0.978622\pi\) |
0.556991 | + | 0.830518i | \(0.311956\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.68285 | + | 0.593495i | 0.692709 | + | 0.153240i | ||||
\(16\) | 14.1139 | 3.52848 | ||||||||
\(17\) | 1.40027 | + | 2.42534i | 0.339615 | + | 0.588230i | 0.984360 | − | 0.176167i | \(-0.0563699\pi\) |
−0.644745 | + | 0.764397i | \(0.723037\pi\) | |||||||
\(18\) | 0.717292 | + | 8.11375i | 0.169067 | + | 1.91243i | ||||
\(19\) | 0.312846 | − | 0.541866i | 0.0717719 | − | 0.124313i | −0.827906 | − | 0.560867i | \(-0.810468\pi\) |
0.899678 | + | 0.436554i | \(0.143801\pi\) | |||||||
\(20\) | −4.26101 | − | 7.38028i | −0.952791 | − | 1.65028i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.83102 | + | 3.17142i | −0.390375 | + | 0.676149i | ||||
\(23\) | 0.142434 | + | 0.246702i | 0.0296995 | + | 0.0514410i | 0.880493 | − | 0.474059i | \(-0.157212\pi\) |
−0.850794 | + | 0.525500i | \(0.823878\pi\) | |||||||
\(24\) | 10.7078 | − | 11.6962i | 2.18572 | − | 2.38747i | ||||
\(25\) | 1.24168 | − | 2.15065i | 0.248336 | − | 0.430130i | ||||
\(26\) | 4.31479 | − | 7.47343i | 0.846199 | − | 1.46566i | ||||
\(27\) | 4.12669 | + | 3.15760i | 0.794182 | + | 0.607679i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.27396 | + | 3.93861i | 0.422264 | + | 0.731382i | 0.996161 | − | 0.0875454i | \(-0.0279023\pi\) |
−0.573897 | + | 0.818928i | \(0.694569\pi\) | |||||||
\(30\) | −7.28430 | − | 1.61142i | −1.32992 | − | 0.294203i | ||||
\(31\) | −7.43005 | −1.33448 | −0.667238 | − | 0.744845i | \(-0.732524\pi\) | ||||
−0.667238 | + | 0.744845i | \(0.732524\pi\) | |||||||
\(32\) | −20.0106 | −3.53741 | ||||||||
\(33\) | 0.703493 | + | 2.22767i | 0.122462 | + | 0.387787i | ||||
\(34\) | −3.80191 | − | 6.58511i | −0.652023 | − | 1.12934i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.41918 | − | 16.0532i | −0.236529 | − | 2.67554i | ||||
\(37\) | −4.01126 | + | 6.94770i | −0.659447 | + | 1.14220i | 0.321312 | + | 0.946973i | \(0.395876\pi\) |
−0.980759 | + | 0.195222i | \(0.937457\pi\) | |||||||
\(38\) | −0.849420 | + | 1.47124i | −0.137794 | + | 0.238666i | ||||
\(39\) | −1.65778 | − | 5.24948i | −0.265457 | − | 0.840589i | ||||
\(40\) | 7.26194 | + | 12.5780i | 1.14821 | + | 1.98876i | ||||
\(41\) | −5.01329 | + | 8.68327i | −0.782944 | + | 1.35610i | 0.147275 | + | 0.989096i | \(0.452950\pi\) |
−0.930219 | + | 0.367004i | \(0.880384\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.12937 | − | 5.42022i | −0.477224 | − | 0.826576i | 0.522435 | − | 0.852679i | \(-0.325024\pi\) |
−0.999659 | + | 0.0261027i | \(0.991690\pi\) | |||||||
\(44\) | 3.62271 | − | 6.27472i | 0.546144 | − | 0.945950i | ||||
\(45\) | −3.89601 | + | 2.73329i | −0.580783 | + | 0.407455i | ||||
\(46\) | −0.386726 | − | 0.669829i | −0.0570197 | − | 0.0987609i | ||||
\(47\) | −11.1477 | −1.62605 | −0.813026 | − | 0.582227i | \(-0.802181\pi\) | ||||
−0.813026 | + | 0.582227i | \(0.802181\pi\) | |||||||
\(48\) | −16.5073 | + | 18.0310i | −2.38262 | + | 2.60255i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.37132 | + | 5.83930i | −0.476777 | + | 0.825802i | ||||
\(51\) | −4.73617 | − | 1.04773i | −0.663196 | − | 0.146711i | ||||
\(52\) | −8.53689 | + | 14.7863i | −1.18385 | + | 2.05049i | ||||
\(53\) | −1.39349 | − | 2.41359i | −0.191410 | − | 0.331532i | 0.754308 | − | 0.656521i | \(-0.227973\pi\) |
−0.945718 | + | 0.324989i | \(0.894639\pi\) | |||||||
\(54\) | −11.2045 | − | 8.57329i | −1.52474 | − | 1.16668i | ||||
\(55\) | −2.13965 | −0.288510 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.326354 | + | 1.03343i | 0.0432266 | + | 0.136881i | ||||
\(58\) | −6.17410 | − | 10.6939i | −0.810699 | − | 1.40417i | ||||
\(59\) | −4.57469 | −0.595574 | −0.297787 | − | 0.954632i | \(-0.596248\pi\) | ||||
−0.297787 | + | 0.954632i | \(0.596248\pi\) | |||||||
\(60\) | 14.4121 | + | 3.18822i | 1.86060 | + | 0.411598i | ||||
\(61\) | 0.385014 | 0.0492960 | 0.0246480 | − | 0.999696i | \(-0.492154\pi\) | ||||
0.0246480 | + | 0.999696i | \(0.492154\pi\) | |||||||
\(62\) | 20.1736 | 2.56205 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 26.1036 | 3.26295 | ||||||||
\(65\) | 5.04207 | 0.625392 | ||||||||
\(66\) | −1.91008 | − | 6.04841i | −0.235114 | − | 0.744508i | ||||
\(67\) | −2.53916 | −0.310208 | −0.155104 | − | 0.987898i | \(-0.549571\pi\) | ||||
−0.155104 | + | 0.987898i | \(0.549571\pi\) | |||||||
\(68\) | 7.52217 | + | 13.0288i | 0.912197 | + | 1.57997i | ||||
\(69\) | −0.481757 | − | 0.106573i | −0.0579968 | − | 0.0128299i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.45208 | −0.172330 | −0.0861651 | − | 0.996281i | \(-0.527461\pi\) | ||||
−0.0861651 | + | 0.996281i | \(0.527461\pi\) | |||||||
\(72\) | 2.41867 | + | 27.3591i | 0.285043 | + | 3.22431i | ||||
\(73\) | −0.234067 | − | 0.405416i | −0.0273955 | − | 0.0474503i | 0.852003 | − | 0.523538i | \(-0.175388\pi\) |
−0.879398 | + | 0.476087i | \(0.842055\pi\) | |||||||
\(74\) | 10.8911 | − | 18.8639i | 1.26606 | − | 2.19289i | ||||
\(75\) | 1.29529 | + | 4.10164i | 0.149567 | + | 0.473616i | ||||
\(76\) | 1.68059 | − | 2.91087i | 0.192777 | − | 0.333900i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.50108 | + | 14.2530i | 0.509647 | + | 1.61384i | ||||
\(79\) | −15.7124 | −1.76778 | −0.883892 | − | 0.467691i | \(-0.845086\pi\) | ||||
−0.883892 | + | 0.467691i | \(0.845086\pi\) | |||||||
\(80\) | −11.1951 | − | 19.3905i | −1.25165 | − | 2.16792i | ||||
\(81\) | −8.86041 | + | 1.57894i | −0.984491 | + | 0.175438i | ||||
\(82\) | 13.6117 | − | 23.5762i | 1.50317 | − | 2.60356i | ||||
\(83\) | 6.99338 | + | 12.1129i | 0.767623 | + | 1.32956i | 0.938848 | + | 0.344331i | \(0.111894\pi\) |
−0.171225 | + | 0.985232i | \(0.554772\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.22138 | − | 3.84754i | 0.240942 | − | 0.417324i | ||||
\(86\) | 8.49665 | + | 14.7166i | 0.916217 | + | 1.58693i | ||||
\(87\) | −7.69128 | − | 1.70145i | −0.824592 | − | 0.182415i | ||||
\(88\) | −6.17410 | + | 10.6939i | −0.658162 | + | 1.13997i | ||||
\(89\) | −1.29353 | + | 2.24046i | −0.137114 | + | 0.237488i | −0.926403 | − | 0.376534i | \(-0.877116\pi\) |
0.789289 | + | 0.614022i | \(0.210449\pi\) | |||||||
\(90\) | 10.5782 | − | 7.42126i | 1.11504 | − | 0.782269i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.765146 | + | 1.32527i | 0.0797719 | + | 0.138169i | ||||
\(93\) | 8.69001 | − | 9.49213i | 0.901112 | − | 0.984288i | ||||
\(94\) | 30.2674 | 3.12184 | ||||||||
\(95\) | −0.992595 | −0.101838 | ||||||||
\(96\) | 23.4039 | − | 25.5642i | 2.38865 | − | 2.60913i | ||||
\(97\) | −7.22962 | − | 12.5221i | −0.734057 | − | 1.27142i | −0.955136 | − | 0.296168i | \(-0.904291\pi\) |
0.221079 | − | 0.975256i | \(-0.429042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.66871 | − | 1.70669i | −0.368719 | − | 0.171529i | ||||
\(100\) | 6.67023 | − | 11.5532i | 0.667023 | − | 1.15532i | ||||
\(101\) | 4.91888 | − | 8.51975i | 0.489447 | − | 0.847747i | −0.510479 | − | 0.859890i | \(-0.670532\pi\) |
0.999926 | + | 0.0121430i | \(0.00386534\pi\) | |||||||
\(102\) | 12.8593 | + | 2.84471i | 1.27326 | + | 0.281669i | ||||
\(103\) | 5.52897 | + | 9.57646i | 0.544786 | + | 0.943597i | 0.998620 | + | 0.0525110i | \(0.0167225\pi\) |
−0.453834 | + | 0.891086i | \(0.649944\pi\) | |||||||
\(104\) | 14.5492 | − | 25.2000i | 1.42667 | − | 2.47106i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.78350 | + | 6.55322i | 0.367486 | + | 0.636505i | ||||
\(107\) | 0.962153 | − | 1.66650i | 0.0930149 | − | 0.161106i | −0.815764 | − | 0.578386i | \(-0.803683\pi\) |
0.908778 | + | 0.417279i | \(0.137016\pi\) | |||||||
\(108\) | 22.1684 | + | 16.9624i | 2.13315 | + | 1.63221i | ||||
\(109\) | 9.30341 | + | 16.1140i | 0.891105 | + | 1.54344i | 0.838553 | + | 0.544821i | \(0.183402\pi\) |
0.0525523 | + | 0.998618i | \(0.483264\pi\) | |||||||
\(110\) | 5.80944 | 0.553908 | ||||||||
\(111\) | −4.18445 | − | 13.2504i | −0.397170 | − | 1.25767i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.59338 | − | 2.75982i | 0.149893 | − | 0.259622i | −0.781295 | − | 0.624162i | \(-0.785440\pi\) |
0.931188 | + | 0.364540i | \(0.118774\pi\) | |||||||
\(114\) | −0.886094 | − | 2.80589i | −0.0829903 | − | 0.262795i | ||||
\(115\) | 0.225956 | − | 0.391367i | 0.0210705 | − | 0.0364951i | ||||
\(116\) | 12.2156 | + | 21.1580i | 1.13419 | + | 1.96447i | ||||
\(117\) | 8.64528 | + | 4.02180i | 0.799256 | + | 0.371815i | ||||
\(118\) | 12.4209 | 1.14344 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −24.5623 | − | 5.43361i | −2.24222 | − | 0.496019i | ||||
\(121\) | 4.59043 | + | 7.95086i | 0.417312 | + | 0.722806i | ||||
\(122\) | −1.04536 | −0.0946428 | ||||||||
\(123\) | −5.22975 | − | 16.5604i | −0.471550 | − | 1.49320i | ||||
\(124\) | −39.9138 | −3.58437 | ||||||||
\(125\) | −11.8715 | −1.06182 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.37387 | −0.743061 | −0.371530 | − | 0.928421i | \(-0.621167\pi\) | ||||
−0.371530 | + | 0.928421i | \(0.621167\pi\) | |||||||
\(128\) | −30.8535 | −2.72709 | ||||||||
\(129\) | 10.5845 | + | 2.34149i | 0.931918 | + | 0.206157i | ||||
\(130\) | −13.6899 | −1.20068 | ||||||||
\(131\) | −5.98629 | − | 10.3686i | −0.523024 | − | 0.905905i | −0.999641 | − | 0.0267937i | \(-0.991470\pi\) |
0.476616 | − | 0.879111i | \(-0.341863\pi\) | |||||||
\(132\) | 3.77913 | + | 11.9669i | 0.328931 | + | 1.04158i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.89415 | 0.595564 | ||||||||
\(135\) | 1.06480 | − | 8.17408i | 0.0916438 | − | 0.703513i | ||||
\(136\) | −12.8199 | − | 22.2046i | −1.09929 | − | 1.90403i | ||||
\(137\) | −8.27525 | + | 14.3332i | −0.707003 | + | 1.22456i | 0.258961 | + | 0.965888i | \(0.416620\pi\) |
−0.965964 | + | 0.258677i | \(0.916714\pi\) | |||||||
\(138\) | 1.30803 | + | 0.289361i | 0.111347 | + | 0.0246320i | ||||
\(139\) | −3.95119 | + | 6.84367i | −0.335136 | + | 0.580472i | −0.983511 | − | 0.180849i | \(-0.942116\pi\) |
0.648375 | + | 0.761321i | \(0.275449\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.0380 | − | 14.2415i | 1.09800 | − | 1.19935i | ||||
\(142\) | 3.94259 | 0.330855 | ||||||||
\(143\) | 2.14339 | + | 3.71245i | 0.179239 | + | 0.310451i | ||||
\(144\) | −3.72865 | − | 42.1772i | −0.310721 | − | 3.51477i | ||||
\(145\) | 3.60739 | − | 6.24819i | 0.299578 | − | 0.518884i | ||||
\(146\) | 0.635523 | + | 1.10076i | 0.0525962 | + | 0.0910994i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −21.5483 | + | 37.3227i | −1.77126 | + | 3.06791i | ||||
\(149\) | 6.83427 | + | 11.8373i | 0.559885 | + | 0.969749i | 0.997505 | + | 0.0705895i | \(0.0224881\pi\) |
−0.437620 | + | 0.899160i | \(0.644179\pi\) | |||||||
\(150\) | −3.51688 | − | 11.1365i | −0.287152 | − | 0.909290i | ||||
\(151\) | −1.94982 | + | 3.37718i | −0.158674 | + | 0.274831i | −0.934391 | − | 0.356250i | \(-0.884055\pi\) |
0.775717 | + | 0.631081i | \(0.217389\pi\) | |||||||
\(152\) | −2.86420 | + | 4.96093i | −0.232317 | + | 0.402385i | ||||
\(153\) | 6.87781 | − | 4.82522i | 0.556038 | − | 0.390096i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.89349 | + | 10.2078i | 0.473376 | + | 0.819912i | ||||
\(156\) | −8.90548 | − | 28.1999i | −0.713009 | − | 2.25780i | ||||
\(157\) | 0.294352 | 0.0234919 | 0.0117459 | − | 0.999931i | \(-0.496261\pi\) | ||||
0.0117459 | + | 0.999931i | \(0.496261\pi\) | |||||||
\(158\) | 42.6613 | 3.39395 | ||||||||
\(159\) | 4.71323 | + | 1.04265i | 0.373784 | + | 0.0826877i | ||||
\(160\) | 15.8723 | + | 27.4917i | 1.25482 | + | 2.17341i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 24.0572 | − | 4.28703i | 1.89011 | − | 0.336821i | ||||
\(163\) | −5.35455 | + | 9.27436i | −0.419401 | + | 0.726424i | −0.995879 | − | 0.0906886i | \(-0.971093\pi\) |
0.576478 | + | 0.817112i | \(0.304427\pi\) | |||||||
\(164\) | −26.9311 | + | 46.6461i | −2.10297 | + | 3.64245i | ||||
\(165\) | 2.50249 | − | 2.73348i | 0.194818 | − | 0.212801i | ||||
\(166\) | −18.9880 | − | 32.8881i | −1.47375 | − | 2.55261i | ||||
\(167\) | −1.59872 | + | 2.76907i | −0.123713 | + | 0.214277i | −0.921229 | − | 0.389020i | \(-0.872814\pi\) |
0.797516 | + | 0.603298i | \(0.206147\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.44913 | + | 2.50997i | 0.111472 | + | 0.193074i | ||||
\(170\) | −6.03133 | + | 10.4466i | −0.462582 | + | 0.801215i | ||||
\(171\) | −1.70193 | − | 0.791741i | −0.130150 | − | 0.0605460i | ||||
\(172\) | −16.8108 | − | 29.1171i | −1.28181 | − | 2.22016i | ||||
\(173\) | 11.4375 | 0.869577 | 0.434789 | − | 0.900533i | \(-0.356823\pi\) | ||||
0.434789 | + | 0.900533i | \(0.356823\pi\) | |||||||
\(174\) | 20.8828 | + | 4.61966i | 1.58312 | + | 0.350216i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.51809 | − | 16.4858i | 0.717453 | − | 1.24266i | ||||
\(177\) | 5.35045 | − | 5.84432i | 0.402164 | − | 0.439286i | ||||
\(178\) | 3.51210 | − | 6.08314i | 0.263243 | − | 0.455951i | ||||
\(179\) | −0.549275 | − | 0.951372i | −0.0410547 | − | 0.0711089i | 0.844768 | − | 0.535133i | \(-0.179738\pi\) |
−0.885823 | + | 0.464024i | \(0.846405\pi\) | |||||||
\(180\) | −20.9292 | + | 14.6831i | −1.55997 | + | 1.09441i | ||||
\(181\) | −3.19013 | −0.237120 | −0.118560 | − | 0.992947i | \(-0.537828\pi\) | ||||
−0.118560 | + | 0.992947i | \(0.537828\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.450303 | + | 0.491868i | −0.0332874 | + | 0.0363599i | ||||
\(184\) | −1.30402 | − | 2.25863i | −0.0961336 | − | 0.166508i | ||||
\(185\) | 12.7269 | 0.935698 | ||||||||
\(186\) | −23.5945 | + | 25.7724i | −1.73003 | + | 1.88972i | ||||
\(187\) | 3.77723 | 0.276218 | ||||||||
\(188\) | −59.8846 | −4.36753 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.69503 | 0.195518 | ||||||||
\(191\) | 3.86815 | 0.279889 | 0.139945 | − | 0.990159i | \(-0.455308\pi\) | ||||
0.139945 | + | 0.990159i | \(0.455308\pi\) | |||||||
\(192\) | −30.5301 | + | 33.3482i | −2.20332 | + | 2.40670i | ||||
\(193\) | −4.13585 | −0.297705 | −0.148853 | − | 0.988859i | \(-0.547558\pi\) | ||||
−0.148853 | + | 0.988859i | \(0.547558\pi\) | |||||||
\(194\) | 19.6294 | + | 33.9991i | 1.40931 | + | 2.44099i | ||||
\(195\) | −5.89709 | + | 6.44141i | −0.422299 | + | 0.461279i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.889267 | −0.0633576 | −0.0316788 | − | 0.999498i | \(-0.510085\pi\) | ||||
−0.0316788 | + | 0.999498i | \(0.510085\pi\) | |||||||
\(198\) | 9.96102 | + | 4.63389i | 0.707899 | + | 0.329316i | ||||
\(199\) | 3.16193 | + | 5.47663i | 0.224143 | + | 0.388228i | 0.956062 | − | 0.293164i | \(-0.0947083\pi\) |
−0.731919 | + | 0.681392i | \(0.761375\pi\) | |||||||
\(200\) | −11.3679 | + | 19.6898i | −0.803833 | + | 1.39228i | ||||
\(201\) | 2.96974 | − | 3.24386i | 0.209469 | − | 0.228804i | ||||
\(202\) | −13.3554 | + | 23.1323i | −0.939684 | + | 1.62758i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −25.4424 | − | 5.62833i | −1.78133 | − | 0.394062i | ||||
\(205\) | 15.9061 | 1.11093 | ||||||||
\(206\) | −15.0119 | − | 26.0014i | −1.04593 | − | 1.81160i | ||||
\(207\) | 0.699603 | − | 0.490815i | 0.0486258 | − | 0.0341140i | ||||
\(208\) | −22.4293 | + | 38.8487i | −1.55519 | + | 2.69367i | ||||
\(209\) | −0.421952 | − | 0.730843i | −0.0291870 | − | 0.0505535i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.71291 | − | 9.89505i | 0.393293 | − | 0.681204i | −0.599589 | − | 0.800308i | \(-0.704669\pi\) |
0.992882 | + | 0.119105i | \(0.0380025\pi\) | |||||||
\(212\) | −7.48574 | − | 12.9657i | −0.514123 | − | 0.890487i | ||||
\(213\) | 1.69832 | − | 1.85508i | 0.116367 | − | 0.127108i | ||||
\(214\) | −2.61237 | + | 4.52476i | −0.178578 | + | 0.309307i | ||||
\(215\) | −4.96441 | + | 8.59860i | −0.338570 | + | 0.586420i | ||||
\(216\) | −37.7810 | − | 28.9087i | −2.57067 | − | 1.96699i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −25.2600 | − | 43.7516i | −1.71082 | − | 2.96323i | ||||
\(219\) | 0.791691 | + | 0.175136i | 0.0534975 | + | 0.0118346i | ||||
\(220\) | −11.4941 | −0.774931 | ||||||||
\(221\) | −8.90101 | −0.598747 | ||||||||
\(222\) | 11.3613 | + | 35.9766i | 0.762523 | + | 2.41459i | ||||
\(223\) | −8.35953 | − | 14.4791i | −0.559796 | − | 0.969595i | −0.997513 | − | 0.0704822i | \(-0.977546\pi\) |
0.437717 | − | 0.899113i | \(-0.355787\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.75492 | − | 3.14240i | −0.450328 | − | 0.209493i | ||||
\(226\) | −4.32625 | + | 7.49328i | −0.287778 | + | 0.498446i | ||||
\(227\) | 8.53501 | − | 14.7831i | 0.566489 | − | 0.981187i | −0.430421 | − | 0.902628i | \(-0.641635\pi\) |
0.996909 | − | 0.0785588i | \(-0.0250318\pi\) | |||||||
\(228\) | 1.75316 | + | 5.55150i | 0.116106 | + | 0.367657i | ||||
\(229\) | 9.89471 | + | 17.1381i | 0.653861 | + | 1.13252i | 0.982178 | + | 0.187953i | \(0.0601851\pi\) |
−0.328317 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(230\) | −0.613500 | + | 1.06261i | −0.0404530 | + | 0.0700666i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20.8187 | − | 36.0591i | −1.36682 | − | 2.36740i | ||||
\(233\) | −2.96579 | + | 5.13691i | −0.194296 | + | 0.336530i | −0.946669 | − | 0.322207i | \(-0.895575\pi\) |
0.752374 | + | 0.658736i | \(0.228909\pi\) | |||||||
\(234\) | −23.4731 | − | 10.9197i | −1.53448 | − | 0.713844i | ||||
\(235\) | 8.84228 | + | 15.3153i | 0.576807 | + | 0.999058i | ||||
\(236\) | −24.5750 | −1.59969 | ||||||||
\(237\) | 18.3769 | − | 20.0731i | 1.19371 | − | 1.30389i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.0277 | + | 17.3685i | −0.648637 | + | 1.12347i | 0.334812 | + | 0.942285i | \(0.391327\pi\) |
−0.983449 | + | 0.181187i | \(0.942006\pi\) | |||||||
\(240\) | 37.8655 | + | 8.37654i | 2.44421 | + | 0.540703i | ||||
\(241\) | 14.6444 | − | 25.3648i | 0.943326 | − | 1.63389i | 0.184256 | − | 0.982878i | \(-0.441012\pi\) |
0.759069 | − | 0.651010i | \(-0.225654\pi\) | |||||||
\(242\) | −12.4636 | − | 21.5877i | −0.801193 | − | 1.38771i | ||||
\(243\) | 8.34578 | − | 13.1662i | 0.535382 | − | 0.844610i | ||||
\(244\) | 2.06827 | 0.132408 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.1995 | + | 44.9637i | 0.905324 | + | 2.86678i | ||||
\(247\) | 0.994327 | + | 1.72223i | 0.0632675 | + | 0.109583i | ||||
\(248\) | 68.0242 | 4.31954 | ||||||||
\(249\) | −23.6539 | − | 5.23267i | −1.49901 | − | 0.331607i | ||||
\(250\) | 32.2328 | 2.03858 | ||||||||
\(251\) | 22.7856 | 1.43821 | 0.719106 | − | 0.694901i | \(-0.244552\pi\) | ||||
0.719106 | + | 0.694901i | \(0.244552\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.384215 | 0.0241554 | ||||||||
\(254\) | 22.7362 | 1.42659 | ||||||||
\(255\) | 2.31729 | + | 7.33787i | 0.145114 | + | 0.459515i | ||||
\(256\) | 31.5642 | 1.97276 | ||||||||
\(257\) | −12.1444 | − | 21.0348i | −0.757550 | − | 1.31211i | −0.944097 | − | 0.329668i | \(-0.893063\pi\) |
0.186547 | − | 0.982446i | \(-0.440270\pi\) | |||||||
\(258\) | −28.7385 | − | 6.35747i | −1.78918 | − | 0.395798i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 27.0857 | 1.67979 | ||||||||
\(261\) | 11.1692 | − | 7.83589i | 0.691356 | − | 0.485030i | ||||
\(262\) | 16.2536 | + | 28.1520i | 1.00415 | + | 1.73924i | ||||
\(263\) | 4.30578 | − | 7.45782i | 0.265506 | − | 0.459869i | −0.702190 | − | 0.711989i | \(-0.747794\pi\) |
0.967696 | + | 0.252120i | \(0.0811278\pi\) | |||||||
\(264\) | −6.44068 | − | 20.3949i | −0.396396 | − | 1.25522i | ||||
\(265\) | −2.21062 | + | 3.82890i | −0.135797 | + | 0.235208i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.34938 | − | 4.27291i | −0.0825807 | − | 0.261498i | ||||
\(268\) | −13.6402 | −0.833209 | ||||||||
\(269\) | −7.61561 | − | 13.1906i | −0.464332 | − | 0.804247i | 0.534839 | − | 0.844954i | \(-0.320372\pi\) |
−0.999171 | + | 0.0407073i | \(0.987039\pi\) | |||||||
\(270\) | −2.89109 | + | 22.1937i | −0.175946 | + | 1.35067i | ||||
\(271\) | −2.33910 | + | 4.05144i | −0.142090 | + | 0.246108i | −0.928284 | − | 0.371873i | \(-0.878716\pi\) |
0.786193 | + | 0.617981i | \(0.212049\pi\) | |||||||
\(272\) | 19.7633 | + | 34.2310i | 1.19832 | + | 2.07556i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.4684 | − | 38.9164i | 1.35737 | − | 2.35103i | ||||
\(275\) | −1.67472 | − | 2.90069i | −0.100989 | − | 0.174918i | ||||
\(276\) | −2.58797 | − | 0.572507i | −0.155778 | − | 0.0344608i | ||||
\(277\) | 8.19537 | − | 14.1948i | 0.492412 | − | 0.852883i | −0.507550 | − | 0.861622i | \(-0.669449\pi\) |
0.999962 | + | 0.00873986i | \(0.00278202\pi\) | |||||||
\(278\) | 10.7280 | − | 18.5815i | 0.643423 | − | 1.11444i | ||||
\(279\) | 1.96289 | + | 22.2035i | 0.117515 | + | 1.32929i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.75702 | + | 3.04325i | 0.104815 | + | 0.181545i | 0.913663 | − | 0.406473i | \(-0.133242\pi\) |
−0.808848 | + | 0.588018i | \(0.799908\pi\) | |||||||
\(282\) | −35.4000 | + | 38.6676i | −2.10804 | + | 2.30262i | ||||
\(283\) | −26.0708 | −1.54975 | −0.774874 | − | 0.632116i | \(-0.782187\pi\) | ||||
−0.774874 | + | 0.632116i | \(0.782187\pi\) | |||||||
\(284\) | −7.80050 | −0.462874 | ||||||||
\(285\) | 1.16092 | − | 1.26807i | 0.0687667 | − | 0.0751142i | ||||
\(286\) | −5.81958 | − | 10.0798i | −0.344119 | − | 0.596031i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.28645 | + | 59.7985i | 0.311507 | + | 3.52366i | ||||
\(289\) | 4.57850 | − | 7.93019i | 0.269323 | − | 0.466482i | ||||
\(290\) | −9.79455 | + | 16.9647i | −0.575156 | + | 0.996199i | ||||
\(291\) | 24.4530 | + | 5.40944i | 1.43346 | + | 0.317107i | ||||
\(292\) | −1.25740 | − | 2.17787i | −0.0735835 | − | 0.127450i | ||||
\(293\) | 9.44192 | − | 16.3539i | 0.551603 | − | 0.955404i | −0.446556 | − | 0.894756i | \(-0.647350\pi\) |
0.998159 | − | 0.0606487i | \(-0.0193169\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.62863 | + | 6.28497i | 0.211267 | + | 0.365925i | ||||
\(296\) | 36.7242 | − | 63.6082i | 2.13455 | − | 3.69715i | ||||
\(297\) | 6.47118 | − | 2.69079i | 0.375496 | − | 0.156136i | ||||
\(298\) | −18.5559 | − | 32.1398i | −1.07492 | − | 1.86181i | ||||
\(299\) | −0.905400 | −0.0523606 | ||||||||
\(300\) | 6.95823 | + | 22.0338i | 0.401733 | + | 1.27212i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.29401 | − | 9.16950i | 0.304636 | − | 0.527645i | ||||
\(303\) | 5.13126 | + | 16.2485i | 0.294783 | + | 0.933454i | ||||
\(304\) | 4.41549 | − | 7.64785i | 0.253246 | − | 0.438634i | ||||
\(305\) | −0.305392 | − | 0.528954i | −0.0174867 | − | 0.0302878i | ||||
\(306\) | −18.6742 | + | 13.1011i | −1.06753 | + | 0.748940i | ||||
\(307\) | 21.6407 | 1.23510 | 0.617551 | − | 0.786531i | \(-0.288125\pi\) | ||||
0.617551 | + | 0.786531i | \(0.288125\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.7008 | − | 4.13696i | −1.06385 | − | 0.235343i | ||||
\(310\) | −16.0016 | − | 27.7156i | −0.908830 | − | 1.57414i | ||||
\(311\) | −4.49448 | −0.254859 | −0.127429 | − | 0.991848i | \(-0.540673\pi\) | ||||
−0.127429 | + | 0.991848i | \(0.540673\pi\) | |||||||
\(312\) | 15.1774 | + | 48.0604i | 0.859251 | + | 2.72089i | ||||
\(313\) | −8.60204 | −0.486216 | −0.243108 | − | 0.969999i | \(-0.578167\pi\) | ||||
−0.243108 | + | 0.969999i | \(0.578167\pi\) | |||||||
\(314\) | −0.799206 | −0.0451018 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84.4062 | −4.74822 | ||||||||
\(317\) | −8.06255 | −0.452838 | −0.226419 | − | 0.974030i | \(-0.572702\pi\) | ||||
−0.226419 | + | 0.974030i | \(0.572702\pi\) | |||||||
\(318\) | −12.7971 | − | 2.83094i | −0.717623 | − | 0.158751i | ||||
\(319\) | 6.13402 | 0.343439 | ||||||||
\(320\) | −20.7053 | − | 35.8626i | −1.15746 | − | 2.00478i | ||||
\(321\) | 1.00370 | + | 3.17828i | 0.0560208 | + | 0.177394i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.75228 | 0.0974992 | ||||||||
\(324\) | −47.5977 | + | 8.48198i | −2.64432 | + | 0.471221i | ||||
\(325\) | 3.94646 | + | 6.83546i | 0.218910 | + | 0.379163i | ||||
\(326\) | 14.5383 | − | 25.1811i | 0.805203 | − | 1.39465i | ||||
\(327\) | −31.4672 | − | 6.96111i | −1.74014 | − | 0.384950i | ||||
\(328\) | 45.8981 | − | 79.4978i | 2.53430 | − | 4.38953i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.79458 | + | 7.42175i | −0.374029 | + | 0.408554i | ||||
\(331\) | −22.9026 | −1.25884 | −0.629419 | − | 0.777066i | \(-0.716707\pi\) | ||||
−0.629419 | + | 0.777066i | \(0.716707\pi\) | |||||||
\(332\) | 37.5681 | + | 65.0698i | 2.06182 | + | 3.57117i | ||||
\(333\) | 21.8218 | + | 10.1516i | 1.19583 | + | 0.556302i | ||||
\(334\) | 4.34075 | − | 7.51840i | 0.237515 | − | 0.411388i | ||||
\(335\) | 2.01405 | + | 3.48844i | 0.110039 | + | 0.190594i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.81891 | + | 11.8107i | −0.371450 | + | 0.643369i | −0.989789 | − | 0.142542i | \(-0.954472\pi\) |
0.618339 | + | 0.785911i | \(0.287806\pi\) | |||||||
\(338\) | −3.93458 | − | 6.81489i | −0.214013 | − | 0.370681i | ||||
\(339\) | 1.66218 | + | 5.26342i | 0.0902772 | + | 0.285870i | ||||
\(340\) | 11.9331 | − | 20.6688i | 0.647164 | − | 1.12092i | ||||
\(341\) | −5.01065 | + | 8.67869i | −0.271342 | + | 0.469978i | ||||
\(342\) | 4.62097 | + | 2.14968i | 0.249873 | + | 0.116242i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 28.6502 | + | 49.6237i | 1.54472 | + | 2.67553i | ||||
\(345\) | 0.235712 | + | 0.746399i | 0.0126903 | + | 0.0401848i | ||||
\(346\) | −31.0543 | −1.66949 | ||||||||
\(347\) | −2.82563 | −0.151688 | −0.0758440 | − | 0.997120i | \(-0.524165\pi\) | ||||
−0.0758440 | + | 0.997120i | \(0.524165\pi\) | |||||||
\(348\) | −41.3171 | − | 9.14010i | −2.21483 | − | 0.489961i | ||||
\(349\) | 1.81202 | + | 3.13851i | 0.0969951 | + | 0.168000i | 0.910440 | − | 0.413642i | \(-0.135744\pi\) |
−0.813444 | + | 0.581643i | \(0.802410\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.2493 | + | 6.34083i | −0.813947 | + | 0.338448i | ||||
\(352\) | −13.4947 | + | 23.3734i | −0.719268 | + | 1.24581i | ||||
\(353\) | −1.37701 | + | 2.38504i | −0.0732907 | + | 0.126943i | −0.900342 | − | 0.435184i | \(-0.856683\pi\) |
0.827051 | + | 0.562127i | \(0.190017\pi\) | |||||||
\(354\) | −14.5272 | + | 15.8681i | −0.772110 | + | 0.843380i | ||||
\(355\) | 1.15179 | + | 1.99495i | 0.0611304 | + | 0.105881i | ||||
\(356\) | −6.94877 | + | 12.0356i | −0.368284 | + | 0.637887i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.49135 | + | 2.58310i | 0.0788205 | + | 0.136521i | ||||
\(359\) | 8.40076 | − | 14.5505i | 0.443375 | − | 0.767948i | −0.554562 | − | 0.832142i | \(-0.687114\pi\) |
0.997937 | + | 0.0641941i | \(0.0204477\pi\) | |||||||
\(360\) | 35.6691 | − | 25.0241i | 1.87992 | − | 1.31888i | ||||
\(361\) | 9.30425 | + | 16.1154i | 0.489698 | + | 0.848181i | ||||
\(362\) | 8.66163 | 0.455245 | ||||||||
\(363\) | −15.5264 | − | 3.43471i | −0.814922 | − | 0.180276i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.371322 | + | 0.643149i | −0.0194359 | + | 0.0336640i | ||||
\(366\) | 1.22263 | − | 1.33549i | 0.0639080 | − | 0.0698070i | ||||
\(367\) | −11.9670 | + | 20.7274i | −0.624670 | + | 1.08196i | 0.363934 | + | 0.931425i | \(0.381433\pi\) |
−0.988605 | + | 0.150536i | \(0.951900\pi\) | |||||||
\(368\) | 2.01030 | + | 3.48193i | 0.104794 | + | 0.181508i | ||||
\(369\) | 27.2730 | + | 12.6875i | 1.41978 | + | 0.660483i | ||||
\(370\) | −34.5551 | −1.79644 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 46.6822 | − | 50.9912i | 2.42036 | − | 2.64377i | ||||
\(373\) | 9.58030 | + | 16.5936i | 0.496049 | + | 0.859182i | 0.999990 | − | 0.00455622i | \(-0.00145030\pi\) |
−0.503941 | + | 0.863738i | \(0.668117\pi\) | |||||||
\(374\) | −10.2557 | −0.530309 | ||||||||
\(375\) | 13.8847 | − | 15.1663i | 0.717002 | − | 0.783184i | ||||
\(376\) | 102.060 | 5.26334 | ||||||||
\(377\) | −14.4548 | −0.744458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0770 | 0.517622 | 0.258811 | − | 0.965928i | \(-0.416669\pi\) | ||||
0.258811 | + | 0.965928i | \(0.416669\pi\) | |||||||
\(380\) | −5.33217 | −0.273534 | ||||||||
\(381\) | 9.79388 | − | 10.6979i | 0.501756 | − | 0.548070i | ||||
\(382\) | −10.5025 | −0.537357 | ||||||||
\(383\) | −10.0718 | − | 17.4448i | −0.514643 | − | 0.891388i | −0.999856 | − | 0.0169915i | \(-0.994591\pi\) |
0.485213 | − | 0.874396i | \(-0.338742\pi\) | |||||||
\(384\) | 36.0855 | − | 39.4164i | 1.84148 | − | 2.01146i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.2294 | 0.571561 | ||||||||
\(387\) | −15.3708 | + | 10.7836i | −0.781340 | + | 0.548159i | ||||
\(388\) | −38.8372 | − | 67.2679i | −1.97166 | − | 3.41501i | ||||
\(389\) | −6.69736 | + | 11.6002i | −0.339570 | + | 0.588152i | −0.984352 | − | 0.176215i | \(-0.943615\pi\) |
0.644782 | + | 0.764366i | \(0.276948\pi\) | |||||||
\(390\) | 16.0114 | − | 17.4893i | 0.810767 | − | 0.885605i | ||||
\(391\) | −0.398891 | + | 0.690899i | −0.0201728 | + | 0.0349402i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.2476 | + | 4.47913i | 1.02136 | + | 0.225942i | ||||
\(394\) | 2.41448 | 0.121640 | ||||||||
\(395\) | 12.4630 | + | 21.5866i | 0.627083 | + | 1.08614i | ||||
\(396\) | −19.7081 | − | 9.16824i | −0.990369 | − | 0.460721i | ||||
\(397\) | −9.00664 | + | 15.6000i | −0.452031 | + | 0.782940i | −0.998512 | − | 0.0545313i | \(-0.982634\pi\) |
0.546482 | + | 0.837471i | \(0.315967\pi\) | |||||||
\(398\) | −8.58506 | − | 14.8698i | −0.430330 | − | 0.745354i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.5249 | − | 30.3541i | 0.876247 | − | 1.51770i | ||||
\(401\) | −14.4337 | − | 25.0000i | −0.720787 | − | 1.24844i | −0.960685 | − | 0.277642i | \(-0.910447\pi\) |
0.239898 | − | 0.970798i | \(-0.422886\pi\) | |||||||
\(402\) | −8.06324 | + | 8.80751i | −0.402158 | + | 0.439279i | ||||
\(403\) | 11.8075 | − | 20.4513i | 0.588176 | − | 1.01875i | ||||
\(404\) | 26.4240 | − | 45.7676i | 1.31464 | − | 2.27703i | ||||
\(405\) | 9.19729 | + | 10.9205i | 0.457017 | + | 0.542646i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.41019 | + | 9.37073i | 0.268173 | + | 0.464490i | ||||
\(408\) | 43.3610 | + | 9.59222i | 2.14669 | + | 0.474886i | ||||
\(409\) | 10.8587 | 0.536931 | 0.268465 | − | 0.963289i | \(-0.413484\pi\) | ||||
0.268465 | + | 0.963289i | \(0.413484\pi\) | |||||||
\(410\) | −43.1872 | −2.13286 | ||||||||
\(411\) | −8.63255 | − | 27.3356i | −0.425812 | − | 1.34837i | ||||
\(412\) | 29.7014 | + | 51.4443i | 1.46328 | + | 2.53448i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.89951 | + | 1.33263i | −0.0933561 | + | 0.0654951i | ||||
\(415\) | 11.0943 | − | 19.2158i | 0.544595 | − | 0.943267i | ||||
\(416\) | 31.8001 | − | 55.0793i | 1.55913 | − | 2.70049i | ||||
\(417\) | −4.12179 | − | 13.0520i | −0.201845 | − | 0.639158i | ||||
\(418\) | 1.14566 | + | 1.98434i | 0.0560359 | + | 0.0970570i | ||||
\(419\) | 0.247572 | − | 0.428807i | 0.0120947 | − | 0.0209486i | −0.859915 | − | 0.510438i | \(-0.829483\pi\) |
0.872009 | + | 0.489489i | \(0.162817\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.50320 | + | 16.4600i | 0.463158 | + | 0.802212i | 0.999116 | − | 0.0420318i | \(-0.0133831\pi\) |
−0.535959 | + | 0.844244i | \(0.680050\pi\) | |||||||
\(422\) | −15.5113 | + | 26.8664i | −0.755079 | + | 1.30784i | ||||
\(423\) | 2.94502 | + | 33.3130i | 0.143192 | + | 1.61974i | ||||
\(424\) | 12.7578 | + | 22.0971i | 0.619572 | + | 1.07313i | ||||
\(425\) | 6.95473 | 0.337354 | ||||||||
\(426\) | −4.61116 | + | 5.03679i | −0.223411 | + | 0.244033i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.16864 | − | 8.95234i | 0.249835 | − | 0.432728i | ||||
\(429\) | −7.24963 | − | 1.60375i | −0.350016 | − | 0.0774298i | ||||
\(430\) | 13.4790 | − | 23.3464i | 0.650016 | − | 1.12586i | ||||
\(431\) | 8.46073 | + | 14.6544i | 0.407539 | + | 0.705878i | 0.994613 | − | 0.103655i | \(-0.0330538\pi\) |
−0.587074 | + | 0.809533i | \(0.699720\pi\) | |||||||
\(432\) | 58.2438 | + | 44.5660i | 2.80226 | + | 2.14418i | ||||
\(433\) | 33.4740 | 1.60866 | 0.804330 | − | 0.594183i | \(-0.202524\pi\) | ||||
0.804330 | + | 0.594183i | \(0.202524\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.76315 | + | 11.9163i | 0.180429 | + | 0.571343i | ||||
\(436\) | 49.9774 | + | 86.5634i | 2.39348 | + | 4.14564i | ||||
\(437\) | 0.178239 | 0.00852634 | ||||||||
\(438\) | −2.14955 | − | 0.475519i | −0.102709 | − | 0.0227212i | ||||
\(439\) | −20.9315 | −0.999005 | −0.499502 | − | 0.866313i | \(-0.666484\pi\) | ||||
−0.499502 | + | 0.866313i | \(0.666484\pi\) | |||||||
\(440\) | 19.5891 | 0.933874 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.1674 | 1.14953 | ||||||||
\(443\) | −30.8580 | −1.46611 | −0.733054 | − | 0.680170i | \(-0.761906\pi\) | ||||
−0.733054 | + | 0.680170i | \(0.761906\pi\) | |||||||
\(444\) | −22.4786 | − | 71.1804i | −1.06679 | − | 3.37807i | ||||
\(445\) | 4.10409 | 0.194553 | ||||||||
\(446\) | 22.6972 | + | 39.3128i | 1.07475 | + | 1.86151i | ||||
\(447\) | −23.1157 | − | 5.11362i | −1.09334 | − | 0.241866i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.2789 | −1.57053 | −0.785263 | − | 0.619162i | \(-0.787472\pi\) | ||||
−0.785263 | + | 0.619162i | \(0.787472\pi\) | |||||||
\(450\) | 18.3405 | + | 8.53203i | 0.864579 | + | 0.402204i | ||||
\(451\) | 6.76168 | + | 11.7116i | 0.318395 | + | 0.551477i | ||||
\(452\) | 8.55957 | − | 14.8256i | 0.402608 | − | 0.697338i | ||||
\(453\) | −2.03400 | − | 6.44083i | −0.0955658 | − | 0.302617i | ||||
\(454\) | −23.1737 | + | 40.1380i | −1.08760 | + | 1.88377i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.98786 | − | 9.46130i | −0.139919 | − | 0.443066i | ||||
\(457\) | 23.7904 | 1.11287 | 0.556434 | − | 0.830892i | \(-0.312169\pi\) | ||||
0.556434 | + | 0.830892i | \(0.312169\pi\) | |||||||
\(458\) | −26.8654 | − | 46.5323i | −1.25534 | − | 2.17431i | ||||
\(459\) | −1.87975 | + | 14.4301i | −0.0877393 | + | 0.673539i | ||||
\(460\) | 1.21382 | − | 2.10240i | 0.0565947 | − | 0.0980249i | ||||
\(461\) | −8.53122 | − | 14.7765i | −0.397339 | − | 0.688211i | 0.596058 | − | 0.802941i | \(-0.296733\pi\) |
−0.993397 | + | 0.114731i | \(0.963400\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1243 | − | 31.3922i | 0.842306 | − | 1.45892i | −0.0456338 | − | 0.998958i | \(-0.514531\pi\) |
0.887940 | − | 0.459959i | \(-0.152136\pi\) | |||||||
\(464\) | 32.0945 | + | 55.5893i | 1.48995 | + | 2.58067i | ||||
\(465\) | −19.9337 | − | 4.40970i | −0.924404 | − | 0.204495i | ||||
\(466\) | 8.05253 | − | 13.9474i | 0.373026 | − | 0.646100i | ||||
\(467\) | −4.09580 | + | 7.09413i | −0.189531 | + | 0.328277i | −0.945094 | − | 0.326799i | \(-0.894030\pi\) |
0.755563 | + | 0.655076i | \(0.227363\pi\) | |||||||
\(468\) | 46.4420 | + | 21.6049i | 2.14678 | + | 0.998686i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −24.0080 | − | 41.5830i | −1.10740 | − | 1.91808i | ||||
\(471\) | −0.344268 | + | 0.376045i | −0.0158630 | + | 0.0173272i | ||||
\(472\) | 41.8826 | 1.92780 | ||||||||
\(473\) | −8.44148 | −0.388140 | ||||||||
\(474\) | −49.8956 | + | 54.5012i | −2.29178 | + | 2.50332i | ||||
\(475\) | −0.776909 | − | 1.34565i | −0.0356470 | − | 0.0617425i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.84451 | + | 4.80185i | −0.313389 | + | 0.219862i | ||||
\(478\) | 27.2265 | − | 47.1577i | 1.24531 | − | 2.15694i | ||||
\(479\) | −12.7775 | + | 22.1312i | −0.583817 | + | 1.01120i | 0.411205 | + | 0.911543i | \(0.365108\pi\) |
−0.995022 | + | 0.0996574i | \(0.968225\pi\) | |||||||
\(480\) | −53.6854 | − | 11.8762i | −2.45039 | − | 0.542071i | ||||
\(481\) | −12.7491 | − | 22.0820i | −0.581308 | − | 1.00685i | ||||
\(482\) | −39.7614 | + | 68.8687i | −1.81108 | + | 3.13688i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 24.6596 | + | 42.7116i | 1.12089 | + | 1.94144i | ||||
\(485\) | −11.4690 | + | 19.8649i | −0.520782 | + | 0.902020i | ||||
\(486\) | −22.6599 | + | 35.7479i | −1.02787 | + | 1.62156i | ||||
\(487\) | 3.46140 | + | 5.99533i | 0.156851 | + | 0.271674i | 0.933732 | − | 0.357974i | \(-0.116532\pi\) |
−0.776880 | + | 0.629648i | \(0.783199\pi\) | |||||||
\(488\) | −3.52491 | −0.159565 | ||||||||
\(489\) | −5.58574 | − | 17.6877i | −0.252596 | − | 0.799865i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.7262 | − | 32.4348i | 0.845103 | − | 1.46376i | −0.0404294 | − | 0.999182i | \(-0.512873\pi\) |
0.885532 | − | 0.464578i | \(-0.153794\pi\) | |||||||
\(492\) | −28.0939 | − | 88.9615i | −1.26657 | − | 4.01070i | ||||
\(493\) | −6.36831 | + | 11.0302i | −0.286814 | + | 0.496777i | ||||
\(494\) | −2.69973 | − | 4.67607i | −0.121467 | − | 0.210386i | ||||
\(495\) | 0.565259 | + | 6.39402i | 0.0254065 | + | 0.287390i | ||||
\(496\) | −104.867 | −4.70867 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 64.2235 | + | 14.2074i | 2.87793 | + | 0.636649i | ||||
\(499\) | −12.8125 | − | 22.1919i | −0.573566 | − | 0.993446i | −0.996196 | − | 0.0871432i | \(-0.972226\pi\) |
0.422630 | − | 0.906302i | \(-0.361107\pi\) | |||||||
\(500\) | −63.7733 | −2.85203 | ||||||||
\(501\) | −1.66775 | − | 5.28106i | −0.0745096 | − | 0.235941i | ||||
\(502\) | −61.8658 | −2.76121 | ||||||||
\(503\) | 5.79692 | 0.258472 | 0.129236 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129236 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6066 | −0.694483 | ||||||||
\(506\) | −1.04320 | −0.0463757 | ||||||||
\(507\) | −4.90143 | − | 1.08429i | −0.217680 | − | 0.0481548i | ||||
\(508\) | −44.9840 | −1.99584 | ||||||||
\(509\) | 12.5697 | + | 21.7714i | 0.557144 | + | 0.965002i | 0.997733 | + | 0.0672931i | \(0.0214363\pi\) |
−0.440589 | + | 0.897709i | \(0.645230\pi\) | |||||||
\(510\) | −6.29174 | − | 19.9233i | −0.278603 | − | 0.882218i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −23.9940 | −1.06039 | ||||||||
\(513\) | 3.00201 | − | 1.24827i | 0.132542 | − | 0.0551125i | ||||
\(514\) | 32.9738 | + | 57.1123i | 1.45441 | + | 2.51911i | ||||
\(515\) | 8.77113 | − | 15.1920i | 0.386502 | − | 0.669441i | ||||
\(516\) | 56.8596 | + | 12.5784i | 2.50311 | + | 0.553732i | ||||
\(517\) | −7.51771 | + | 13.0211i | −0.330629 | + | 0.572665i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.3770 | + | 14.6118i | −0.587186 | + | 0.641386i | ||||
\(520\) | −46.1616 | −2.02432 | ||||||||
\(521\) | 3.64828 | + | 6.31900i | 0.159834 | + | 0.276841i | 0.934809 | − | 0.355152i | \(-0.115571\pi\) |
−0.774975 | + | 0.631992i | \(0.782237\pi\) | |||||||
\(522\) | −30.3259 | + | 21.2755i | −1.32733 | + | 0.931203i | ||||
\(523\) | 8.38637 | − | 14.5256i | 0.366710 | − | 0.635161i | −0.622339 | − | 0.782748i | \(-0.713817\pi\) |
0.989049 | + | 0.147587i | \(0.0471506\pi\) | |||||||
\(524\) | −32.1580 | − | 55.6993i | −1.40483 | − | 2.43324i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.6908 | + | 20.2490i | −0.509741 | + | 0.882898i | ||||
\(527\) | −10.4041 | − | 18.0204i | −0.453208 | − | 0.784979i | ||||
\(528\) | 9.92904 | + | 31.4411i | 0.432106 | + | 1.36830i | ||||
\(529\) | 11.4594 | − | 19.8483i | 0.498236 | − | 0.862970i | ||||
\(530\) | 6.00212 | − | 10.3960i | 0.260716 | − | 0.451573i | ||||
\(531\) | 1.20855 | + | 13.6707i | 0.0524468 | + | 0.593260i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.9339 | − | 27.5982i | −0.690172 | − | 1.19541i | ||||
\(534\) | 3.66374 | + | 11.6015i | 0.158546 | + | 0.502047i | ||||
\(535\) | −3.05271 | −0.131980 | ||||||||
\(536\) | 23.2467 | 1.00411 | ||||||||
\(537\) | 1.85783 | + | 0.410985i | 0.0801712 | + | 0.0177353i | ||||
\(538\) | 20.6774 | + | 35.8143i | 0.891466 | + | 1.54406i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.72007 | − | 43.9107i | 0.246153 | − | 1.88962i | ||||
\(541\) | 2.64908 | − | 4.58834i | 0.113893 | − | 0.197268i | −0.803444 | − | 0.595381i | \(-0.797001\pi\) |
0.917337 | + | 0.398112i | \(0.130335\pi\) | |||||||
\(542\) | 6.35097 | − | 11.0002i | 0.272798 | − | 0.472499i | ||||
\(543\) | 3.73110 | − | 4.07550i | 0.160117 | − | 0.174896i | ||||
\(544\) | −28.0202 | − | 48.5324i | −1.20136 | − | 2.08081i | ||||
\(545\) | 14.7589 | − | 25.5631i | 0.632200 | − | 1.09500i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4325 | + | 28.4619i | 0.702603 | + | 1.21694i | 0.967550 | + | 0.252681i | \(0.0813123\pi\) |
−0.264947 | + | 0.964263i | \(0.585354\pi\) | |||||||
\(548\) | −44.4542 | + | 76.9970i | −1.89899 | + | 3.28915i | ||||
\(549\) | −0.101714 | − | 1.15055i | −0.00434105 | − | 0.0491045i | ||||
\(550\) | 4.54708 | + | 7.87577i | 0.193888 | + | 0.335824i | ||||
\(551\) | 2.84560 | 0.121227 | ||||||||
\(552\) | 4.41062 | + | 0.975709i | 0.187729 | + | 0.0415290i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −22.2515 | + | 38.5408i | −0.945376 | + | 1.63744i | ||||
\(555\) | −14.8850 | + | 16.2590i | −0.631835 | + | 0.690156i | ||||
\(556\) | −21.2256 | + | 36.7638i | −0.900166 | + | 1.55913i | ||||
\(557\) | 9.40798 | + | 16.2951i | 0.398629 | + | 0.690446i | 0.993557 | − | 0.113333i | \(-0.0361527\pi\) |
−0.594928 | + | 0.803779i | \(0.702819\pi\) | |||||||
\(558\) | −5.32951 | − | 60.2856i | −0.225616 | − | 2.55209i | ||||
\(559\) | 19.8923 | 0.841354 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.41776 | + | 4.82554i | −0.186518 | + | 0.203734i | ||||
\(562\) | −4.77054 | − | 8.26282i | −0.201233 | − | 0.348546i | ||||
\(563\) | −27.6650 | −1.16594 | −0.582970 | − | 0.812494i | \(-0.698109\pi\) | ||||
−0.582970 | + | 0.812494i | \(0.698109\pi\) | |||||||
\(564\) | 70.0396 | − | 76.5046i | 2.94920 | − | 3.22142i | ||||
\(565\) | −5.05547 | −0.212685 | ||||||||
\(566\) | 70.7856 | 2.97534 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.2942 | 0.557812 | ||||||||
\(569\) | −40.1831 | −1.68456 | −0.842282 | − | 0.539037i | \(-0.818788\pi\) | ||||
−0.842282 | + | 0.539037i | \(0.818788\pi\) | |||||||
\(570\) | −3.15204 | + | 3.44299i | −0.132024 | + | 0.144211i | ||||
\(571\) | −6.81129 | −0.285044 | −0.142522 | − | 0.989792i | \(-0.545521\pi\) | ||||
−0.142522 | + | 0.989792i | \(0.545521\pi\) | |||||||
\(572\) | 11.5142 | + | 19.9431i | 0.481431 | + | 0.833863i | ||||
\(573\) | −4.52409 | + | 4.94169i | −0.188997 | + | 0.206442i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.707427 | 0.0295017 | ||||||||
\(576\) | −6.89612 | − | 78.0065i | −0.287338 | − | 3.25027i | ||||
\(577\) | −18.2111 | − | 31.5425i | −0.758138 | − | 1.31313i | −0.943799 | − | 0.330519i | \(-0.892776\pi\) |
0.185661 | − | 0.982614i | \(-0.440557\pi\) | |||||||
\(578\) | −12.4312 | + | 21.5315i | −0.517071 | + | 0.895593i | ||||
\(579\) | 4.83720 | − | 5.28369i | 0.201027 | − | 0.219583i | ||||
\(580\) | 19.3787 | − | 33.5649i | 0.804658 | − | 1.39371i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −66.3930 | − | 14.6873i | −2.75208 | − | 0.608810i | ||||
\(583\) | −3.75894 | −0.155679 | ||||||||
\(584\) | 2.14295 | + | 3.71170i | 0.0886759 | + | 0.153591i | ||||
\(585\) | −1.33203 | − | 15.0674i | −0.0550726 | − | 0.622962i | ||||
\(586\) | −25.6361 | + | 44.4030i | −1.05902 | + | 1.83427i | ||||
\(587\) | −5.57943 | − | 9.66385i | −0.230288 | − | 0.398870i | 0.727605 | − | 0.685996i | \(-0.240633\pi\) |
−0.957893 | + | 0.287126i | \(0.907300\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.32446 | + | 4.02609i | −0.0957779 | + | 0.165892i | ||||
\(590\) | −9.85220 | − | 17.0645i | −0.405609 | − | 0.702535i | ||||
\(591\) | 1.04007 | − | 1.13607i | 0.0427826 | − | 0.0467316i | ||||
\(592\) | −56.6145 | + | 98.0593i | −2.32684 | + | 4.03021i | ||||
\(593\) | 9.90427 | − | 17.1547i | 0.406720 | − | 0.704459i | −0.587800 | − | 0.809006i | \(-0.700006\pi\) |
0.994520 | + | 0.104547i | \(0.0333392\pi\) | |||||||
\(594\) | −17.5701 | + | 7.30586i | −0.720911 | + | 0.299763i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 36.7133 | + | 63.5893i | 1.50384 | + | 2.60472i | ||||
\(597\) | −10.6947 | − | 2.36586i | −0.437705 | − | 0.0968281i | ||||
\(598\) | 2.45828 | 0.100527 | ||||||||
\(599\) | −18.1320 | −0.740853 | −0.370427 | − | 0.928862i | \(-0.620789\pi\) | ||||
−0.370427 | + | 0.928862i | \(0.620789\pi\) | |||||||
\(600\) | −11.8587 | − | 37.5516i | −0.484131 | − | 1.53304i | ||||
\(601\) | 12.3285 | + | 21.3536i | 0.502889 | + | 0.871030i | 0.999994 | + | 0.00333942i | \(0.00106297\pi\) |
−0.497105 | + | 0.867690i | \(0.665604\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.670802 | + | 7.58788i | 0.0273172 | + | 0.309003i | ||||
\(604\) | −10.4743 | + | 18.1420i | −0.426194 | + | 0.738189i | ||||
\(605\) | 7.28223 | − | 12.6132i | 0.296065 | − | 0.512799i | ||||
\(606\) | −13.9321 | − | 44.1169i | −0.565951 | − | 1.79213i | ||||
\(607\) | 8.63876 | + | 14.9628i | 0.350637 | + | 0.607320i | 0.986361 | − | 0.164596i | \(-0.0526319\pi\) |
−0.635725 | + | 0.771916i | \(0.719299\pi\) | |||||||
\(608\) | −6.26024 | + | 10.8431i | −0.253886 | + | 0.439744i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.829179 | + | 1.43618i | 0.0335725 | + | 0.0581492i | ||||
\(611\) | 17.7154 | − | 30.6840i | 0.716689 | − | 1.24134i | ||||
\(612\) | 36.9472 | − | 25.9208i | 1.49350 | − | 1.04779i | ||||
\(613\) | −9.77828 | − | 16.9365i | −0.394941 | − | 0.684058i | 0.598153 | − | 0.801382i | \(-0.295902\pi\) |
−0.993094 | + | 0.117324i | \(0.962568\pi\) | |||||||
\(614\) | −58.7575 | −2.37126 | ||||||||
\(615\) | −18.6034 | + | 20.3206i | −0.750161 | + | 0.819404i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.8723 | − | 18.8314i | 0.437702 | − | 0.758122i | −0.559810 | − | 0.828621i | \(-0.689126\pi\) |
0.997512 | + | 0.0704988i | \(0.0224591\pi\) | |||||||
\(618\) | 50.7752 | + | 11.2324i | 2.04248 | + | 0.451833i | ||||
\(619\) | 16.9024 | − | 29.2758i | 0.679366 | − | 1.17670i | −0.295807 | − | 0.955248i | \(-0.595588\pi\) |
0.975172 | − | 0.221448i | \(-0.0710782\pi\) | |||||||
\(620\) | 31.6595 | + | 54.8359i | 1.27148 | + | 2.20226i | ||||
\(621\) | −0.191206 | + | 1.46781i | −0.00767284 | + | 0.0589013i | ||||
\(622\) | 12.2031 | 0.489300 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −23.3977 | − | 74.0906i | −0.936658 | − | 2.96600i | ||||
\(625\) | 3.20808 | + | 5.55655i | 0.128323 | + | 0.222262i | ||||
\(626\) | 23.3557 | 0.933481 | ||||||||
\(627\) | 1.42718 | + | 0.315718i | 0.0569961 | + | 0.0126086i | ||||
\(628\) | 1.58125 | 0.0630986 | ||||||||
\(629\) | −22.4674 | −0.895832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.6410 | −0.941134 | −0.470567 | − | 0.882364i | \(-0.655951\pi\) | ||||
−0.470567 | + | 0.882364i | \(0.655951\pi\) | |||||||
\(632\) | 143.852 | 5.72211 | ||||||||
\(633\) | 5.95957 | + | 18.8715i | 0.236872 | + | 0.750073i | ||||
\(634\) | 21.8909 | 0.869399 | ||||||||
\(635\) | 6.64213 | + | 11.5045i | 0.263585 | + | 0.456542i | ||||
\(636\) | 25.3192 | + | 5.60107i | 1.00397 | + | 0.222097i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.6547 | −0.659365 | ||||||||
\(639\) | 0.383615 | + | 4.33932i | 0.0151756 | + | 0.171661i | ||||
\(640\) | 24.4729 | + | 42.3883i | 0.967375 | + | 1.67554i | ||||
\(641\) | −7.95901 | + | 13.7854i | −0.314362 | + | 0.544491i | −0.979302 | − | 0.202406i | \(-0.935124\pi\) |
0.664940 | + | 0.746897i | \(0.268457\pi\) | |||||||
\(642\) | −2.72517 | − | 8.62945i | −0.107554 | − | 0.340577i | ||||
\(643\) | 13.2527 | − | 22.9544i | 0.522636 | − | 0.905231i | −0.477017 | − | 0.878894i | \(-0.658282\pi\) |
0.999653 | − | 0.0263376i | \(-0.00838450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.17875 | − | 16.3989i | −0.203913 | − | 0.645707i | ||||
\(646\) | −4.75766 | −0.187188 | ||||||||
\(647\) | 0.00801958 | + | 0.0138903i | 0.000315282 | + | 0.000546085i | 0.866183 | − | 0.499727i | \(-0.166566\pi\) |
−0.865868 | + | 0.500273i | \(0.833233\pi\) | |||||||
\(648\) | 81.1196 | − | 14.4556i | 3.18668 | − | 0.567871i | ||||
\(649\) | −3.08506 | + | 5.34348i | −0.121099 | + | 0.209750i | ||||
\(650\) | −10.7152 | − | 18.5592i | −0.420283 | − | 0.727951i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −28.7644 | + | 49.8214i | −1.12650 | + | 1.95115i | ||||
\(653\) | 16.6440 | + | 28.8282i | 0.651328 | + | 1.12813i | 0.982801 | + | 0.184669i | \(0.0591212\pi\) |
−0.331473 | + | 0.943465i | \(0.607545\pi\) | |||||||
\(654\) | 85.4376 | + | 18.9003i | 3.34087 | + | 0.739062i | ||||
\(655\) | −9.49661 | + | 16.4486i | −0.371063 | + | 0.642700i | ||||
\(656\) | −70.7571 | + | 122.555i | −2.76260 | + | 4.78497i | ||||
\(657\) | −1.14969 | + | 0.806577i | −0.0448535 | + | 0.0314676i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.4156 | + | 33.6288i | 0.756324 | + | 1.30999i | 0.944713 | + | 0.327897i | \(0.106340\pi\) |
−0.188389 | + | 0.982094i | \(0.560327\pi\) | |||||||
\(660\) | 13.4432 | − | 14.6841i | 0.523276 | − | 0.571577i | ||||
\(661\) | −5.30644 | −0.206397 | −0.103198 | − | 0.994661i | \(-0.532908\pi\) | ||||
−0.103198 | + | 0.994661i | \(0.532908\pi\) | |||||||
\(662\) | 62.1835 | 2.41683 | ||||||||
\(663\) | 10.4104 | − | 11.3713i | 0.404307 | − | 0.441626i | ||||
\(664\) | −64.0264 | − | 110.897i | −2.48471 | − | 4.30364i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −59.2492 | − | 27.5628i | −2.29586 | − | 1.06804i | ||||
\(667\) | −0.647777 | + | 1.12198i | −0.0250820 | + | 0.0434433i | ||||
\(668\) | −8.58826 | + | 14.8753i | −0.332290 | + | 0.575543i | ||||
\(669\) | 28.2747 | + | 6.25487i | 1.09316 | + | 0.241827i | ||||
\(670\) | −5.46842 | − | 9.47158i | −0.211263 | − | 0.365919i | ||||
\(671\) | 0.259644 | − | 0.449717i | 0.0100235 | − | 0.0173611i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.03565 | − | 5.25789i | −0.117016 | − | 0.202677i | 0.801568 | − | 0.597903i | \(-0.203999\pi\) |
−0.918584 | + | 0.395227i | \(0.870666\pi\) | |||||||
\(674\) | 18.5142 | − | 32.0676i | 0.713142 | − | 1.23520i | ||||
\(675\) | 11.9149 | − | 4.95435i | 0.458605 | − | 0.190693i | ||||
\(676\) | 7.78465 | + | 13.4834i | 0.299410 | + | 0.518593i | ||||
\(677\) | 34.7850 | 1.33690 | 0.668449 | − | 0.743758i | \(-0.266959\pi\) | ||||
0.668449 | + | 0.743758i | \(0.266959\pi\) | |||||||
\(678\) | −4.51304 | − | 14.2909i | −0.173322 | − | 0.548838i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −20.3373 | + | 35.2253i | −0.779901 | + | 1.35083i | ||||
\(681\) | 8.90352 | + | 28.1937i | 0.341184 | + | 1.08038i | ||||
\(682\) | 13.6046 | − | 23.5638i | 0.520946 | − | 0.902305i | ||||
\(683\) | −9.71206 | − | 16.8218i | −0.371622 | − | 0.643667i | 0.618194 | − | 0.786026i | \(-0.287865\pi\) |
−0.989815 | + | 0.142358i | \(0.954531\pi\) | |||||||
\(684\) | −9.14268 | − | 4.25319i | −0.349579 | − | 0.162625i | ||||
\(685\) | 26.2556 | 1.00318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.4672 | − | 7.40354i | −1.27685 | − | 0.282463i | ||||
\(688\) | −44.1676 | − | 76.5006i | −1.68387 | − | 2.91656i | ||||
\(689\) | 8.85791 | 0.337459 | ||||||||
\(690\) | −0.639988 | − | 2.02657i | −0.0243639 | − | 0.0771503i | ||||
\(691\) | 6.63675 | 0.252474 | 0.126237 | − | 0.992000i | \(-0.459710\pi\) | ||||
0.126237 | + | 0.992000i | \(0.459710\pi\) | |||||||
\(692\) | 61.4416 | 2.33566 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.67197 | 0.291224 | ||||||||
\(695\) | 12.5363 | 0.475529 | ||||||||
\(696\) | 70.4158 | + | 15.5773i | 2.66911 | + | 0.590454i | ||||
\(697\) | −28.0798 | −1.06360 | ||||||||
\(698\) | −4.91987 | − | 8.52147i | −0.186220 | − | 0.322542i | ||||
\(699\) | −3.09385 | − | 9.79690i | −0.117020 | − | 0.370553i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.9153 | −0.525574 | −0.262787 | − | 0.964854i | \(-0.584642\pi\) | ||||
−0.262787 | + | 0.964854i | \(0.584642\pi\) | |||||||
\(702\) | 41.4038 | − | 17.2162i | 1.56269 | − | 0.649783i | ||||
\(703\) | 2.50982 | + | 4.34713i | 0.0946595 | + | 0.163955i | ||||
\(704\) | 17.6036 | − | 30.4904i | 0.663462 | − | 1.14915i | ||||
\(705\) | −29.9075 | − | 6.61608i | −1.12638 | − | 0.249176i | ||||
\(706\) | 3.73876 | − | 6.47571i | 0.140710 | − | 0.243717i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 28.7423 | − | 31.3954i | 1.08020 | − | 1.17991i | ||||
\(709\) | 34.1556 | 1.28274 | 0.641370 | − | 0.767231i | \(-0.278366\pi\) | ||||
0.641370 | + | 0.767231i | \(0.278366\pi\) | |||||||
\(710\) | −3.12725 | − | 5.41655i | −0.117364 | − | 0.203280i | ||||
\(711\) | 4.15095 | + | 46.9541i | 0.155673 | + | 1.76092i | ||||
\(712\) | 11.8426 | − | 20.5120i | 0.443821 | − | 0.768721i | ||||
\(713\) | −1.05829 | − | 1.83301i | −0.0396332 | − | 0.0686467i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.40025 | − | 5.88941i | 0.127162 | − | 0.220251i | ||||
\(716\) | −2.95068 | − | 5.11072i | −0.110272 | − | 0.190997i | ||||
\(717\) | −10.4606 | − | 33.1244i | −0.390660 | − | 1.23705i | ||||
\(718\) | −22.8092 | + | 39.5066i | −0.851231 | + | 1.47437i | ||||
\(719\) | −22.1450 | + | 38.3563i | −0.825870 | + | 1.43045i | 0.0753825 | + | 0.997155i | \(0.475982\pi\) |
−0.901253 | + | 0.433294i | \(0.857351\pi\) | |||||||
\(720\) | −54.9879 | + | 38.5775i | −2.04928 | + | 1.43770i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −25.2623 | − | 43.7556i | −0.940165 | − | 1.62841i | ||||
\(723\) | 15.2766 | + | 48.3747i | 0.568144 | + | 1.79907i | ||||
\(724\) | −17.1372 | −0.636899 | ||||||||
\(725\) | 11.2941 | 0.419453 | ||||||||
\(726\) | 42.1561 | + | 9.32569i | 1.56456 | + | 0.346109i | ||||
\(727\) | −14.1247 | − | 24.4647i | −0.523857 | − | 0.907346i | −0.999614 | − | 0.0277700i | \(-0.991159\pi\) |
0.475758 | − | 0.879576i | \(-0.342174\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.05919 | + | 26.0608i | 0.261451 | + | 0.965217i | ||||
\(730\) | 1.00819 | − | 1.74623i | 0.0373147 | − | 0.0646310i | ||||
\(731\) | 8.76391 | − | 15.1795i | 0.324145 | − | 0.561435i | ||||
\(732\) | −2.41900 | + | 2.64229i | −0.0894090 | + | 0.0976618i | ||||
\(733\) | −12.5084 | − | 21.6653i | −0.462010 | − | 0.800225i | 0.537051 | − | 0.843550i | \(-0.319538\pi\) |
−0.999061 | + | 0.0433249i | \(0.986205\pi\) | |||||||
\(734\) | 32.4919 | − | 56.2776i | 1.19930 | − | 2.07724i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.85018 | − | 4.93666i | −0.105059 | − | 0.181968i | ||||
\(737\) | −1.71235 | + | 2.96587i | −0.0630752 | + | 0.109249i | ||||
\(738\) | −74.0499 | − | 34.4482i | −2.72582 | − | 1.26805i | ||||
\(739\) | −16.0115 | − | 27.7327i | −0.588992 | − | 1.02016i | −0.994365 | − | 0.106013i | \(-0.966192\pi\) |
0.405373 | − | 0.914151i | \(-0.367142\pi\) | |||||||
\(740\) | 68.3680 | 2.51326 | ||||||||
\(741\) | −3.36314 | − | 0.743987i | −0.123548 | − | 0.0273311i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.4031 | − | 33.6072i | 0.711833 | − | 1.23293i | −0.252336 | − | 0.967640i | \(-0.581199\pi\) |
0.964169 | − | 0.265290i | \(-0.0854678\pi\) | |||||||
\(744\) | −79.5595 | + | 86.9032i | −2.91679 | + | 3.18602i | ||||
\(745\) | 10.8418 | − | 18.7786i | 0.397214 | − | 0.687995i | ||||
\(746\) | −26.0118 | − | 45.0537i | −0.952359 | − | 1.64953i | ||||
\(747\) | 34.3500 | − | 24.0987i | 1.25680 | − | 0.881724i | ||||
\(748\) | 20.2911 | 0.741915 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −37.6987 | + | 41.1785i | −1.37656 | + | 1.50363i | ||||
\(751\) | −10.8495 | − | 18.7920i | −0.395905 | − | 0.685728i | 0.597311 | − | 0.802010i | \(-0.296236\pi\) |
−0.993216 | + | 0.116282i | \(0.962903\pi\) | |||||||
\(752\) | −157.337 | −5.73749 | ||||||||
\(753\) | −26.6494 | + | 29.1093i | −0.971160 | + | 1.06080i | ||||
\(754\) | 39.2466 | 1.42928 | ||||||||
\(755\) | 6.18635 | 0.225144 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5242 | 1.21846 | 0.609229 | − | 0.792995i | \(-0.291479\pi\) | ||||
0.609229 | + | 0.792995i | \(0.291479\pi\) | |||||||
\(758\) | −27.3605 | −0.993778 | ||||||||
\(759\) | −0.449369 | + | 0.490848i | −0.0163111 | + | 0.0178166i | ||||
\(760\) | 9.08748 | 0.329638 | ||||||||
\(761\) | −6.66048 | − | 11.5363i | −0.241442 | − | 0.418190i | 0.719683 | − | 0.694303i | \(-0.244287\pi\) |
−0.961125 | + | 0.276113i | \(0.910954\pi\) | |||||||
\(762\) | −26.5917 | + | 29.0462i | −0.963315 | + | 1.05223i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.7795 | 0.751775 | ||||||||
\(765\) | −12.0846 | − | 5.62179i | −0.436920 | − | 0.203256i | ||||
\(766\) | 27.3462 | + | 47.3649i | 0.988057 | + | 1.71137i | ||||
\(767\) | 7.26992 | − | 12.5919i | 0.262502 | − | 0.454666i | ||||
\(768\) | −36.9167 | + | 40.3243i | −1.33212 | + | 1.45508i | ||||
\(769\) | −27.3568 | + | 47.3833i | −0.986510 | + | 1.70869i | −0.351488 | + | 0.936192i | \(0.614324\pi\) |
−0.635022 | + | 0.772494i | \(0.719009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.0765 | + | 9.08686i | 1.47933 | + | 0.327255i | ||||
\(772\) | −22.2176 | −0.799628 | ||||||||
\(773\) | 1.18021 | + | 2.04418i | 0.0424491 | + | 0.0735240i | 0.886469 | − | 0.462787i | \(-0.153151\pi\) |
−0.844020 | + | 0.536311i | \(0.819817\pi\) | |||||||
\(774\) | 41.7337 | − | 29.2788i | 1.50009 | − | 1.05240i | ||||
\(775\) | −9.22573 | + | 15.9794i | −0.331398 | + | 0.573998i | ||||
\(776\) | 66.1892 | + | 114.643i | 2.37606 | + | 4.11545i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.1842 | − | 31.4960i | 0.651936 | − | 1.12919i | ||||
\(779\) | 3.13678 | + | 5.43306i | 0.112387 | + | 0.194660i | ||||
\(780\) | −31.6788 | + | 34.6029i | −1.13428 | + | 1.23898i | ||||
\(781\) | −0.979248 | + | 1.69611i | −0.0350403 | + | 0.0606915i | ||||
\(782\) | 1.08304 | − | 1.87588i | 0.0387295 | − | 0.0670814i | ||||
\(783\) | −3.05261 | + | 23.4337i | −0.109092 | + | 0.837452i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.233479 | − | 0.404398i | −0.00833323 | − | 0.0144336i | ||||
\(786\) | −54.9749 | − | 12.1614i | −1.96089 | − | 0.433784i | ||||
\(787\) | 1.66794 | 0.0594557 | 0.0297278 | − | 0.999558i | \(-0.490536\pi\) | ||||
0.0297278 | + | 0.999558i | \(0.490536\pi\) | |||||||
\(788\) | −4.77709 | −0.170177 | ||||||||
\(789\) | 4.49168 | + | 14.2233i | 0.159908 | + | 0.506362i | ||||
\(790\) | −33.8388 | − | 58.6105i | −1.20393 | − | 2.08527i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 33.5880 | + | 15.6252i | 1.19350 | + | 0.555218i | ||||
\(793\) | −0.611849 | + | 1.05975i | −0.0217274 | + | 0.0376330i | ||||
\(794\) | 24.4542 | − | 42.3560i | 0.867848 | − | 1.50316i | ||||
\(795\) | −2.30607 | − | 7.30234i | −0.0817877 | − | 0.258987i | ||||
\(796\) | 16.9857 | + | 29.4201i | 0.602043 | + | 1.04277i | ||||
\(797\) | 14.3148 | − | 24.7939i | 0.507055 | − | 0.878244i | −0.492912 | − | 0.870079i | \(-0.664068\pi\) |
0.999967 | − | 0.00816511i | \(-0.00259906\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.6097 | − | 27.0368i | −0.552232 | − | 0.956493i | ||||
\(800\) | −24.8467 | + | 43.0358i | −0.878464 | + | 1.52154i | ||||
\(801\) | 7.03699 | + | 3.27362i | 0.248640 | + | 0.115668i | ||||
\(802\) | 39.1895 | + | 67.8783i | 1.38383 | + | 2.39687i | ||||
\(803\) | −0.631397 | −0.0222815 | ||||||||
\(804\) | 15.9533 | − | 17.4258i | 0.562629 | − | 0.614562i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −32.0591 | + | 55.5279i | −1.12923 | + | 1.95589i | ||||
\(807\) | 25.7585 | + | 5.69824i | 0.906742 | + | 0.200588i | ||||
\(808\) | −45.0337 | + | 78.0007i | −1.58428 | + | 2.74406i | ||||
\(809\) | 1.42846 | + | 2.47416i | 0.0502219 | + | 0.0869868i | 0.890043 | − | 0.455876i | \(-0.150674\pi\) |
−0.839822 | + | 0.542862i | \(0.817340\pi\) | |||||||
\(810\) | −24.9719 | − | 29.6507i | −0.877422 | − | 1.04182i | ||||
\(811\) | −26.2917 | −0.923225 | −0.461613 | − | 0.887082i | \(-0.652729\pi\) | ||||
−0.461613 | + | 0.887082i | \(0.652729\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.44010 | − | 7.72675i | −0.0855779 | − | 0.270989i | ||||
\(814\) | −14.6894 | − | 25.4428i | −0.514863 | − | 0.891769i | ||||
\(815\) | 16.9889 | 0.595094 | ||||||||
\(816\) | −66.8459 | − | 14.7875i | −2.34007 | − | 0.517666i | ||||
\(817\) | −3.91605 | −0.137005 | ||||||||
\(818\) | −29.4829 | −1.03085 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 85.4467 | 2.98393 | ||||||||
\(821\) | −2.65849 | −0.0927821 | −0.0463910 | − | 0.998923i | \(-0.514772\pi\) | ||||
−0.0463910 | + | 0.998923i | \(0.514772\pi\) | |||||||
\(822\) | 23.4385 | + | 74.2199i | 0.817512 | + | 2.58872i | ||||
\(823\) | −12.2154 | −0.425801 | −0.212901 | − | 0.977074i | \(-0.568291\pi\) | ||||
−0.212901 | + | 0.977074i | \(0.568291\pi\) | |||||||
\(824\) | −50.6193 | − | 87.6752i | −1.76341 | − | 3.05431i | ||||
\(825\) | 5.66444 | + | 1.25308i | 0.197211 | + | 0.0436265i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.15812 | 0.318459 | 0.159230 | − | 0.987242i | \(-0.449099\pi\) | ||||
0.159230 | + | 0.987242i | \(0.449099\pi\) | |||||||
\(828\) | 3.75823 | − | 2.63663i | 0.130607 | − | 0.0916293i | ||||
\(829\) | 9.17156 | + | 15.8856i | 0.318541 | + | 0.551730i | 0.980184 | − | 0.198089i | \(-0.0634737\pi\) |
−0.661642 | + | 0.749819i | \(0.730140\pi\) | |||||||
\(830\) | −30.1224 | + | 52.1735i | −1.04556 | + | 1.81097i | ||||
\(831\) | 8.54922 | + | 27.0718i | 0.296569 | + | 0.939109i | ||||
\(832\) | −41.4828 | + | 71.8503i | −1.43816 | + | 2.49096i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 11.1912 | + | 35.4378i | 0.387520 | + | 1.22711i | ||||
\(835\) | 5.07241 | 0.175538 | ||||||||
\(836\) | −2.26670 | − | 3.92605i | −0.0783956 | − | 0.135785i | ||||
\(837\) | −30.6615 | − | 23.4611i | −1.05982 | − | 0.810934i | ||||
\(838\) | −0.672190 | + | 1.16427i | −0.0232204 | + | 0.0402190i | ||||
\(839\) | 9.47055 | + | 16.4035i | 0.326960 | + | 0.566311i | 0.981907 | − | 0.189364i | \(-0.0606425\pi\) |
−0.654947 | + | 0.755675i | \(0.727309\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.15821 | − | 7.20224i | 0.143387 | − | 0.248353i | ||||
\(842\) | −25.8024 | − | 44.6911i | −0.889211 | − | 1.54016i | ||||
\(843\) | −5.94282 | − | 1.31466i | −0.204682 | − | 0.0452793i | ||||
\(844\) | 30.6895 | − | 53.1557i | 1.05637 | − | 1.82969i | ||||
\(845\) | 2.29889 | − | 3.98179i | 0.0790842 | − | 0.136978i | ||||
\(846\) | −7.99612 | − | 90.4493i | −0.274912 | − | 3.10971i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.6676 | − | 34.0652i | −0.675387 | − | 1.16980i | ||||
\(849\) | 30.4918 | − | 33.3063i | 1.04647 | − | 1.14307i | ||||
\(850\) | −18.8830 | −0.647682 | ||||||||
\(851\) | −2.28535 | −0.0783408 | ||||||||
\(852\) | 9.12328 | − | 9.96540i | 0.312558 | − | 0.341409i | ||||
\(853\) | 9.97922 | + | 17.2845i | 0.341682 | + | 0.591811i | 0.984745 | − | 0.174002i | \(-0.0556701\pi\) |
−0.643063 | + | 0.765813i | \(0.722337\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.262227 | + | 2.96622i | 0.00896796 | + | 0.101442i | ||||
\(856\) | −8.80878 | + | 15.2573i | −0.301078 | + | 0.521482i | ||||
\(857\) | −8.20001 | + | 14.2028i | −0.280107 | + | 0.485159i | −0.971411 | − | 0.237405i | \(-0.923703\pi\) |
0.691304 | + | 0.722564i | \(0.257037\pi\) | |||||||
\(858\) | 19.6837 | + | 4.35439i | 0.671991 | + | 0.148657i | ||||
\(859\) | 16.8575 | + | 29.1981i | 0.575172 | + | 0.996226i | 0.996023 | + | 0.0890968i | \(0.0283980\pi\) |
−0.420851 | + | 0.907130i | \(0.638269\pi\) | |||||||
\(860\) | −26.6685 | + | 46.1912i | −0.909389 | + | 1.57511i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.9720 | − | 39.7887i | −0.782429 | − | 1.35521i | ||||
\(863\) | 14.3415 | − | 24.8403i | 0.488191 | − | 0.845572i | −0.511716 | − | 0.859154i | \(-0.670990\pi\) |
0.999908 | + | 0.0135822i | \(0.00432348\pi\) | |||||||
\(864\) | −82.5775 | − | 63.1853i | −2.80934 | − | 2.14961i | ||||
\(865\) | −9.07219 | − | 15.7135i | −0.308464 | − | 0.534275i | ||||
\(866\) | −90.8865 | −3.08845 | ||||||||
\(867\) | 4.77618 | + | 15.1241i | 0.162208 | + | 0.513643i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.5961 | + | 18.3529i | −0.359447 | + | 0.622581i | ||||
\(870\) | −10.2174 | − | 32.3543i | −0.346404 | − | 1.09691i | ||||
\(871\) | 4.03513 | − | 6.98906i | 0.136725 | − | 0.236815i | ||||
\(872\) | −85.1753 | − | 147.528i | −2.88440 | − | 4.99593i | ||||
\(873\) | −35.5103 | + | 24.9127i | −1.20184 | + | 0.843168i | ||||
\(874\) | −0.483944 | −0.0163696 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.25292 | + | 0.940823i | 0.143693 | + | 0.0317875i | ||||
\(877\) | 14.7621 | + | 25.5688i | 0.498482 | + | 0.863396i | 0.999998 | − | 0.00175202i | \(-0.000557684\pi\) |
−0.501517 | + | 0.865148i | \(0.667224\pi\) | |||||||
\(878\) | 56.8317 | 1.91798 | ||||||||
\(879\) | 9.84959 | + | 31.1895i | 0.332218 | + | 1.05200i | ||||
\(880\) | −30.1988 | −1.01800 | ||||||||
\(881\) | −57.5032 | −1.93733 | −0.968666 | − | 0.248366i | \(-0.920107\pi\) | ||||
−0.968666 | + | 0.248366i | \(0.920107\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8715 | 0.668730 | 0.334365 | − | 0.942444i | \(-0.391478\pi\) | ||||
0.334365 | + | 0.942444i | \(0.391478\pi\) | |||||||
\(884\) | −47.8158 | −1.60822 | ||||||||
\(885\) | −12.2732 | − | 2.71505i | −0.412559 | − | 0.0912656i | ||||
\(886\) | 83.7836 | 2.81477 | ||||||||
\(887\) | 18.5475 | + | 32.1253i | 0.622766 | + | 1.07866i | 0.988968 | + | 0.148127i | \(0.0473243\pi\) |
−0.366203 | + | 0.930535i | \(0.619342\pi\) | |||||||
\(888\) | 38.3098 | + | 121.311i | 1.28559 | + | 4.07093i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −11.1432 | −0.373519 | ||||||||
\(891\) | −4.13097 | + | 11.4142i | −0.138393 | + | 0.382391i | ||||
\(892\) | −44.9070 | − | 77.7812i | −1.50360 | − | 2.60431i | ||||
\(893\) | −3.48750 | + | 6.04053i | −0.116705 | + | 0.202139i | ||||
\(894\) | 62.7623 | + | 13.8842i | 2.09909 | + | 0.464356i | ||||
\(895\) | −0.871366 | + | 1.50925i | −0.0291266 | + | 0.0504487i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.05893 | − | 1.15668i | 0.0353568 | − | 0.0386204i | ||||
\(898\) | 90.3565 | 3.01524 | ||||||||
\(899\) | −16.8956 | − | 29.2641i | −0.563501 | − | 0.976012i | ||||
\(900\) | −36.2870 | − | 16.8808i | −1.20957 | − | 0.562693i | ||||
\(901\) | 3.90251 | − | 6.75935i | 0.130012 | − | 0.225187i | ||||
\(902\) | −18.3589 | − | 31.7985i | −0.611284 | − | 1.05877i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.5879 | + | 25.2669i | −0.485185 | + | 0.840366i | ||||
\(905\) | 2.53040 | + | 4.38278i | 0.0841133 | + | 0.145689i | ||||
\(906\) | 5.52259 | + | 17.4877i | 0.183476 | + | 0.580990i | ||||
\(907\) | −12.2044 | + | 21.1386i | −0.405240 | + | 0.701896i | −0.994349 | − | 0.106157i | \(-0.966145\pi\) |
0.589110 | + | 0.808053i | \(0.299479\pi\) | |||||||
\(908\) | 45.8496 | − | 79.4139i | 1.52157 | − | 2.63544i | ||||
\(909\) | −26.7594 | − | 12.4485i | −0.887555 | − | 0.412892i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.5493 | − | 21.7360i | −0.415776 | − | 0.720146i | 0.579733 | − | 0.814806i | \(-0.303157\pi\) |
−0.995510 | + | 0.0946604i | \(0.969823\pi\) | |||||||
\(912\) | 4.60613 | + | 14.5857i | 0.152524 | + | 0.482980i | ||||
\(913\) | 18.8647 | 0.624330 | ||||||||
\(914\) | −64.5941 | −2.13658 | ||||||||
\(915\) | 1.03294 | + | 0.228504i | 0.0341478 | + | 0.00755411i | ||||
\(916\) | 53.1538 | + | 92.0652i | 1.75625 | + | 3.04192i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.10378 | − | 39.1796i | 0.168450 | − | 1.29312i | ||||
\(919\) | 14.2988 | − | 24.7662i | 0.471674 | − | 0.816963i | −0.527801 | − | 0.849368i | \(-0.676983\pi\) |
0.999475 | + | 0.0324050i | \(0.0103167\pi\) | |||||||
\(920\) | −2.06869 | + | 3.58307i | −0.0682026 | + | 0.118130i | ||||
\(921\) | −25.3105 | + | 27.6468i | −0.834009 | + | 0.910992i | ||||
\(922\) | 23.1634 | + | 40.1202i | 0.762846 | + | 1.32129i | ||||
\(923\) | 2.30759 | − | 3.99686i | 0.0759553 | − | 0.131558i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.96139 | + | 17.2536i | 0.327528 | + | 0.567296i | ||||
\(926\) | −49.2098 | + | 85.2339i | −1.61713 | + | 2.80096i | ||||
\(927\) | 27.1571 | − | 19.0524i | 0.891957 | − | 0.625764i | ||||
\(928\) | −45.5033 | − | 78.8140i | −1.49372 | − | 2.58720i | ||||
\(929\) | 45.4570 | 1.49140 | 0.745698 | − | 0.666284i | \(-0.232116\pi\) | ||||
0.745698 | + | 0.666284i | \(0.232116\pi\) | |||||||
\(930\) | 54.1227 | + | 11.9729i | 1.77475 | + | 0.392607i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.9321 | + | 27.5952i | −0.521873 | + | 0.903910i | ||||
\(933\) | 5.25664 | − | 5.74185i | 0.172095 | − | 0.187980i | ||||
\(934\) | 11.1206 | − | 19.2615i | 0.363878 | − | 0.630256i | ||||
\(935\) | −2.99609 | − | 5.18937i | −0.0979825 | − | 0.169711i | ||||
\(936\) | −79.1499 | − | 36.8207i | −2.58710 | − | 1.20352i | ||||
\(937\) | −27.0083 | −0.882322 | −0.441161 | − | 0.897428i | \(-0.645433\pi\) | ||||
−0.441161 | + | 0.897428i | \(0.645433\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0607 | − | 10.9894i | 0.328320 | − | 0.358625i | ||||
\(940\) | 47.5002 | + | 82.2728i | 1.54929 | + | 2.68344i | ||||
\(941\) | −12.7131 | −0.414436 | −0.207218 | − | 0.978295i | \(-0.566441\pi\) | ||||
−0.207218 | + | 0.978295i | \(0.566441\pi\) | |||||||
\(942\) | 0.934732 | − | 1.02101i | 0.0304552 | − | 0.0332664i | ||||
\(943\) | −2.85624 | −0.0930121 | ||||||||
\(944\) | −64.5667 | −2.10147 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.9197 | 0.745185 | ||||||||
\(947\) | 47.5447 | 1.54500 | 0.772498 | − | 0.635017i | \(-0.219007\pi\) | ||||
0.772498 | + | 0.635017i | \(0.219007\pi\) | |||||||
\(948\) | 98.7195 | − | 107.832i | 3.20626 | − | 3.50221i | ||||
\(949\) | 1.48788 | 0.0482987 | ||||||||
\(950\) | 2.10941 | + | 3.65361i | 0.0684384 | + | 0.118539i | ||||
\(951\) | 9.42977 | − | 10.3002i | 0.305781 | − | 0.334006i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.2355 | 1.23857 | 0.619285 | − | 0.785166i | \(-0.287423\pi\) | ||||
0.619285 | + | 0.785166i | \(0.287423\pi\) | |||||||
\(954\) | 18.5838 | − | 13.0377i | 0.601671 | − | 0.422110i | ||||
\(955\) | −3.06820 | − | 5.31428i | −0.0992847 | − | 0.171966i | ||||
\(956\) | −53.8682 | + | 93.3024i | −1.74222 | + | 3.01762i | ||||
\(957\) | −7.17420 | + | 7.83641i | −0.231909 | + | 0.253315i | ||||
\(958\) | 34.6925 | − | 60.0891i | 1.12086 | − | 1.94139i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 70.0320 | + | 15.4923i | 2.26027 | + | 0.500013i | ||||
\(961\) | 24.2056 | 0.780826 | ||||||||
\(962\) | 34.6154 | + | 59.9557i | 1.11605 | + | 1.93305i | ||||
\(963\) | −5.23426 | − | 2.43499i | −0.168672 | − | 0.0784663i | ||||
\(964\) | 78.6687 | − | 136.258i | 2.53375 | − | 4.38858i | ||||
\(965\) | 3.28054 | + | 5.68207i | 0.105604 | + | 0.182912i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.4093 | + | 35.3499i | −0.656317 | + | 1.13678i | 0.325244 | + | 0.945630i | \(0.394553\pi\) |
−0.981562 | + | 0.191145i | \(0.938780\pi\) | |||||||
\(968\) | −42.0267 | − | 72.7924i | −1.35079 | − | 2.33964i | ||||
\(969\) | −2.04942 | + | 2.23859i | −0.0658369 | + | 0.0719139i | ||||
\(970\) | 31.1399 | − | 53.9359i | 0.999843 | − | 1.73178i | ||||
\(971\) | 22.4735 | − | 38.9253i | 0.721210 | − | 1.24917i | −0.239305 | − | 0.970944i | \(-0.576920\pi\) |
0.960515 | − | 0.278228i | \(-0.0897470\pi\) | |||||||
\(972\) | 44.8331 | − | 70.7279i | 1.43802 | − | 2.26860i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.39817 | − | 16.2781i | −0.301137 | − | 0.521584i | ||||
\(975\) | −13.3482 | − | 2.95287i | −0.427485 | − | 0.0945674i | ||||
\(976\) | 5.43405 | 0.173940 | ||||||||
\(977\) | 53.5104 | 1.71195 | 0.855974 | − | 0.517018i | \(-0.172958\pi\) | ||||
0.855974 | + | 0.517018i | \(0.172958\pi\) | |||||||
\(978\) | 15.1660 | + | 48.0244i | 0.484956 | + | 1.53565i | ||||
\(979\) | 1.74465 | + | 3.02182i | 0.0557593 | + | 0.0965779i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.6963 | − | 32.0588i | 1.45897 | − | 1.02356i | ||||
\(982\) | −50.8442 | + | 88.0647i | −1.62250 | + | 2.81026i | ||||
\(983\) | 5.80278 | − | 10.0507i | 0.185080 | − | 0.320568i | −0.758524 | − | 0.651646i | \(-0.774079\pi\) |
0.943603 | + | 0.331078i | \(0.107412\pi\) | |||||||
\(984\) | 47.8798 | + | 151.615i | 1.52635 | + | 4.83331i | ||||
\(985\) | 0.705363 | + | 1.22172i | 0.0224747 | + | 0.0389274i | ||||
\(986\) | 17.2908 | − | 29.9485i | 0.550651 | − | 0.953756i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.34147 | + | 9.25170i | 0.169935 | + | 0.294336i | ||||
\(989\) | 0.891454 | − | 1.54404i | 0.0283466 | − | 0.0490977i | ||||
\(990\) | −1.53475 | − | 17.3606i | −0.0487777 | − | 0.551756i | ||||
\(991\) | −13.0046 | − | 22.5246i | −0.413104 | − | 0.715517i | 0.582123 | − | 0.813100i | \(-0.302222\pi\) |
−0.995227 | + | 0.0975835i | \(0.968889\pi\) | |||||||
\(992\) | 148.680 | 4.72058 | ||||||||
\(993\) | 26.7863 | − | 29.2588i | 0.850037 | − | 0.928500i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.01607 | − | 8.68808i | 0.159020 | − | 0.275431i | ||||
\(996\) | −127.068 | − | 28.1096i | −4.02629 | − | 0.890688i | ||||
\(997\) | −23.4499 | + | 40.6164i | −0.742666 | + | 1.28633i | 0.208612 | + | 0.977999i | \(0.433105\pi\) |
−0.951277 | + | 0.308336i | \(0.900228\pi\) | |||||||
\(998\) | 34.7876 | + | 60.2539i | 1.10118 | + | 1.90731i | ||||
\(999\) | −38.4913 | + | 16.0051i | −1.21781 | + | 0.506379i |
(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 | 441.2.h.h.373.1 | 24 | ||
3.2 | odd | 2 | 1323.2.h.h.226.11 | 24 | |||
7.2 | even | 3 | 441.2.f.h.148.11 | ✓ | 24 | ||
7.3 | odd | 6 | 441.2.g.h.67.11 | 24 | |||
7.4 | even | 3 | 441.2.g.h.67.12 | 24 | |||
7.5 | odd | 6 | 441.2.f.h.148.12 | yes | 24 | ||
7.6 | odd | 2 | inner | 441.2.h.h.373.2 | 24 | ||
9.2 | odd | 6 | 1323.2.g.h.667.2 | 24 | |||
9.7 | even | 3 | 441.2.g.h.79.12 | 24 | |||
21.2 | odd | 6 | 1323.2.f.h.442.1 | 24 | |||
21.5 | even | 6 | 1323.2.f.h.442.2 | 24 | |||
21.11 | odd | 6 | 1323.2.g.h.361.2 | 24 | |||
21.17 | even | 6 | 1323.2.g.h.361.1 | 24 | |||
21.20 | even | 2 | 1323.2.h.h.226.12 | 24 | |||
63.2 | odd | 6 | 1323.2.f.h.883.1 | 24 | |||
63.5 | even | 6 | 3969.2.a.bi.1.12 | 12 | |||
63.11 | odd | 6 | 1323.2.h.h.802.11 | 24 | |||
63.16 | even | 3 | 441.2.f.h.295.11 | yes | 24 | ||
63.20 | even | 6 | 1323.2.g.h.667.1 | 24 | |||
63.23 | odd | 6 | 3969.2.a.bi.1.11 | 12 | |||
63.25 | even | 3 | inner | 441.2.h.h.214.1 | 24 | ||
63.34 | odd | 6 | 441.2.g.h.79.11 | 24 | |||
63.38 | even | 6 | 1323.2.h.h.802.12 | 24 | |||
63.40 | odd | 6 | 3969.2.a.bh.1.1 | 12 | |||
63.47 | even | 6 | 1323.2.f.h.883.2 | 24 | |||
63.52 | odd | 6 | inner | 441.2.h.h.214.2 | 24 | ||
63.58 | even | 3 | 3969.2.a.bh.1.2 | 12 | |||
63.61 | odd | 6 | 441.2.f.h.295.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.11 | ✓ | 24 | 7.2 | even | 3 | ||
441.2.f.h.148.12 | yes | 24 | 7.5 | odd | 6 | ||
441.2.f.h.295.11 | yes | 24 | 63.16 | even | 3 | ||
441.2.f.h.295.12 | yes | 24 | 63.61 | odd | 6 | ||
441.2.g.h.67.11 | 24 | 7.3 | odd | 6 | |||
441.2.g.h.67.12 | 24 | 7.4 | even | 3 | |||
441.2.g.h.79.11 | 24 | 63.34 | odd | 6 | |||
441.2.g.h.79.12 | 24 | 9.7 | even | 3 | |||
441.2.h.h.214.1 | 24 | 63.25 | even | 3 | inner | ||
441.2.h.h.214.2 | 24 | 63.52 | odd | 6 | inner | ||
441.2.h.h.373.1 | 24 | 1.1 | even | 1 | trivial | ||
441.2.h.h.373.2 | 24 | 7.6 | odd | 2 | inner | ||
1323.2.f.h.442.1 | 24 | 21.2 | odd | 6 | |||
1323.2.f.h.442.2 | 24 | 21.5 | even | 6 | |||
1323.2.f.h.883.1 | 24 | 63.2 | odd | 6 | |||
1323.2.f.h.883.2 | 24 | 63.47 | even | 6 | |||
1323.2.g.h.361.1 | 24 | 21.17 | even | 6 | |||
1323.2.g.h.361.2 | 24 | 21.11 | odd | 6 | |||
1323.2.g.h.667.1 | 24 | 63.20 | even | 6 | |||
1323.2.g.h.667.2 | 24 | 9.2 | odd | 6 | |||
1323.2.h.h.226.11 | 24 | 3.2 | odd | 2 | |||
1323.2.h.h.226.12 | 24 | 21.20 | even | 2 | |||
1323.2.h.h.802.11 | 24 | 63.11 | odd | 6 | |||
1323.2.h.h.802.12 | 24 | 63.38 | even | 6 | |||
3969.2.a.bh.1.1 | 12 | 63.40 | odd | 6 | |||
3969.2.a.bh.1.2 | 12 | 63.58 | even | 3 | |||
3969.2.a.bi.1.11 | 12 | 63.23 | odd | 6 | |||
3969.2.a.bi.1.12 | 12 | 63.5 | even | 6 |