Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(311,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.t (of order \(6\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 551.2 | ||
Character | \(\chi\) | \(=\) | 630.551 |
Dual form | 630.2.t.b.311.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −1.18136 | + | 1.26664i | −0.682059 | + | 0.731297i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.389766 | − | 1.68763i | 0.159121 | − | 0.688971i | ||||
\(7\) | 2.05946 | − | 1.66090i | 0.778404 | − | 0.627763i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.208774 | − | 2.99273i | −0.0695914 | − | 0.997576i | ||||
\(10\) | 0.866025 | − | 0.500000i | 0.273861 | − | 0.158114i | ||||
\(11\) | 3.95684i | 1.19303i | 0.802601 | + | 0.596516i | \(0.203449\pi\) | ||||
−0.802601 | + | 0.596516i | \(0.796551\pi\) | |||||||
\(12\) | 0.506266 | + | 1.65641i | 0.146146 | + | 0.478164i | ||||
\(13\) | −2.82686 | + | 1.63209i | −0.784030 | + | 0.452660i | −0.837857 | − | 0.545890i | \(-0.816191\pi\) |
0.0538267 | + | 0.998550i | \(0.482858\pi\) | |||||||
\(14\) | −0.953096 | + | 2.46812i | −0.254726 | + | 0.659632i | ||||
\(15\) | 1.18136 | − | 1.26664i | 0.305026 | − | 0.327046i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.497322 | + | 0.861388i | 0.120618 | + | 0.208917i | 0.920012 | − | 0.391891i | \(-0.128179\pi\) |
−0.799393 | + | 0.600808i | \(0.794846\pi\) | |||||||
\(18\) | 1.67717 | + | 2.48739i | 0.395312 | + | 0.586284i | ||||
\(19\) | −4.90846 | − | 2.83390i | −1.12608 | − | 0.650141i | −0.183132 | − | 0.983088i | \(-0.558624\pi\) |
−0.942945 | + | 0.332947i | \(0.891957\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | −0.329195 | + | 4.57074i | −0.0718363 | + | 0.997416i | ||||
\(22\) | −1.97842 | − | 3.42673i | −0.421801 | − | 0.730580i | ||||
\(23\) | 7.70987i | 1.60762i | 0.594886 | + | 0.803810i | \(0.297197\pi\) | ||||
−0.594886 | + | 0.803810i | \(0.702803\pi\) | |||||||
\(24\) | −1.26664 | − | 1.18136i | −0.258553 | − | 0.241144i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.63209 | − | 2.82686i | 0.320079 | − | 0.554393i | ||||
\(27\) | 4.03736 | + | 3.27105i | 0.776990 | + | 0.629513i | ||||
\(28\) | −0.408654 | − | 2.61400i | −0.0772283 | − | 0.494000i | ||||
\(29\) | −4.10273 | − | 2.36871i | −0.761858 | − | 0.439859i | 0.0681041 | − | 0.997678i | \(-0.478305\pi\) |
−0.829963 | + | 0.557819i | \(0.811638\pi\) | |||||||
\(30\) | −0.389766 | + | 1.68763i | −0.0711613 | + | 0.308117i | ||||
\(31\) | −4.83278 | − | 2.79020i | −0.867992 | − | 0.501135i | −0.00131164 | − | 0.999999i | \(-0.500418\pi\) |
−0.866680 | + | 0.498864i | \(0.833751\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −5.01191 | − | 4.67446i | −0.872462 | − | 0.813719i | ||||
\(34\) | −0.861388 | − | 0.497322i | −0.147727 | − | 0.0852901i | ||||
\(35\) | −2.05946 | + | 1.66090i | −0.348113 | + | 0.280744i | ||||
\(36\) | −2.69616 | − | 1.31556i | −0.449361 | − | 0.219260i | ||||
\(37\) | −5.05548 | + | 8.75634i | −0.831115 | + | 1.43953i | 0.0660393 | + | 0.997817i | \(0.478964\pi\) |
−0.897155 | + | 0.441717i | \(0.854370\pi\) | |||||||
\(38\) | 5.66780 | 0.919438 | ||||||||
\(39\) | 1.27227 | − | 5.50871i | 0.203726 | − | 0.882100i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | −5.16567 | − | 8.94721i | −0.806743 | − | 1.39732i | −0.915108 | − | 0.403208i | \(-0.867895\pi\) |
0.108365 | − | 0.994111i | \(-0.465438\pi\) | |||||||
\(42\) | −2.00028 | − | 4.12297i | −0.308649 | − | 0.636188i | ||||
\(43\) | 5.10292 | − | 8.83852i | 0.778188 | − | 1.34786i | −0.154797 | − | 0.987946i | \(-0.549472\pi\) |
0.932985 | − | 0.359915i | \(-0.117194\pi\) | |||||||
\(44\) | 3.42673 | + | 1.97842i | 0.516598 | + | 0.298258i | ||||
\(45\) | 0.208774 | + | 2.99273i | 0.0311222 | + | 0.446129i | ||||
\(46\) | −3.85494 | − | 6.67695i | −0.568379 | − | 0.984462i | ||||
\(47\) | −2.36963 | − | 4.10432i | −0.345646 | − | 0.598677i | 0.639825 | − | 0.768521i | \(-0.279007\pi\) |
−0.985471 | + | 0.169844i | \(0.945674\pi\) | |||||||
\(48\) | 1.68763 | + | 0.389766i | 0.243588 | + | 0.0562579i | ||||
\(49\) | 1.48279 | − | 6.84115i | 0.211827 | − | 0.977307i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | −1.67859 | − | 0.387679i | −0.235049 | − | 0.0542859i | ||||
\(52\) | 3.26418i | 0.452660i | ||||||||
\(53\) | −8.82289 | + | 5.09390i | −1.21192 | + | 0.699701i | −0.963177 | − | 0.268869i | \(-0.913350\pi\) |
−0.248741 | + | 0.968570i | \(0.580017\pi\) | |||||||
\(54\) | −5.13198 | − | 0.814131i | −0.698374 | − | 0.110789i | ||||
\(55\) | − | 3.95684i | − | 0.533540i | ||||||
\(56\) | 1.66090 | + | 2.05946i | 0.221948 | + | 0.275208i | ||||
\(57\) | 9.38820 | − | 2.86941i | 1.24350 | − | 0.380063i | ||||
\(58\) | 4.73743 | 0.622055 | ||||||||
\(59\) | −1.70360 | + | 2.95072i | −0.221790 | + | 0.384152i | −0.955352 | − | 0.295471i | \(-0.904523\pi\) |
0.733562 | + | 0.679623i | \(0.237857\pi\) | |||||||
\(60\) | −0.506266 | − | 1.65641i | −0.0653586 | − | 0.213842i | ||||
\(61\) | 5.45543 | − | 3.14969i | 0.698496 | − | 0.403277i | −0.108291 | − | 0.994119i | \(-0.534538\pi\) |
0.806787 | + | 0.590842i | \(0.201204\pi\) | |||||||
\(62\) | 5.58041 | 0.708713 | ||||||||
\(63\) | −5.40060 | − | 5.81666i | −0.680411 | − | 0.732830i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.82686 | − | 1.63209i | 0.350629 | − | 0.202436i | ||||
\(66\) | 6.67767 | + | 1.54224i | 0.821964 | + | 0.189837i | ||||
\(67\) | −4.61095 | + | 7.98640i | −0.563317 | + | 0.975694i | 0.433887 | + | 0.900967i | \(0.357142\pi\) |
−0.997204 | + | 0.0747267i | \(0.976192\pi\) | |||||||
\(68\) | 0.994645 | 0.120618 | ||||||||
\(69\) | −9.76567 | − | 9.10814i | −1.17565 | − | 1.09649i | ||||
\(70\) | 0.953096 | − | 2.46812i | 0.113917 | − | 0.294997i | ||||
\(71\) | − | 2.74965i | − | 0.326324i | −0.986599 | − | 0.163162i | \(-0.947831\pi\) | ||
0.986599 | − | 0.163162i | \(-0.0521693\pi\) | |||||||
\(72\) | 2.99273 | − | 0.208774i | 0.352696 | − | 0.0246043i | ||||
\(73\) | −12.7539 | + | 7.36348i | −1.49273 | + | 0.861830i | −0.999965 | − | 0.00833139i | \(-0.997348\pi\) |
−0.492767 | + | 0.870161i | \(0.664015\pi\) | |||||||
\(74\) | − | 10.1110i | − | 1.17537i | ||||||
\(75\) | −1.18136 | + | 1.26664i | −0.136412 | + | 0.146259i | ||||
\(76\) | −4.90846 | + | 2.83390i | −0.563039 | + | 0.325071i | ||||
\(77\) | 6.57194 | + | 8.14898i | 0.748942 | + | 0.928662i | ||||
\(78\) | 1.65254 | + | 5.40682i | 0.187113 | + | 0.612201i | ||||
\(79\) | 0.920736 | + | 1.59476i | 0.103591 | + | 0.179425i | 0.913162 | − | 0.407598i | \(-0.133633\pi\) |
−0.809571 | + | 0.587022i | \(0.800300\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −8.91283 | + | 1.24961i | −0.990314 | + | 0.138845i | ||||
\(82\) | 8.94721 | + | 5.16567i | 0.988054 | + | 0.570453i | ||||
\(83\) | 0.789829 | − | 1.36802i | 0.0866950 | − | 0.150160i | −0.819417 | − | 0.573198i | \(-0.805703\pi\) |
0.906112 | + | 0.423037i | \(0.139036\pi\) | |||||||
\(84\) | 3.79378 | + | 2.57046i | 0.413935 | + | 0.280460i | ||||
\(85\) | −0.497322 | − | 0.861388i | −0.0539422 | − | 0.0934306i | ||||
\(86\) | 10.2058i | 1.10052i | ||||||||
\(87\) | 7.84713 | − | 2.39840i | 0.841300 | − | 0.257135i | ||||
\(88\) | −3.95684 | −0.421801 | ||||||||
\(89\) | −6.92781 | + | 11.9993i | −0.734347 | + | 1.27193i | 0.220663 | + | 0.975350i | \(0.429178\pi\) |
−0.955009 | + | 0.296576i | \(0.904155\pi\) | |||||||
\(90\) | −1.67717 | − | 2.48739i | −0.176789 | − | 0.262194i | ||||
\(91\) | −3.11107 | + | 8.05637i | −0.326129 | + | 0.844537i | ||||
\(92\) | 6.67695 | + | 3.85494i | 0.696120 | + | 0.401905i | ||||
\(93\) | 9.24345 | − | 2.82517i | 0.958501 | − | 0.292956i | ||||
\(94\) | 4.10432 | + | 2.36963i | 0.423329 | + | 0.244409i | ||||
\(95\) | 4.90846 | + | 2.83390i | 0.503597 | + | 0.290752i | ||||
\(96\) | −1.65641 | + | 0.506266i | −0.169057 | + | 0.0516705i | ||||
\(97\) | 0.776974 | + | 0.448586i | 0.0788897 | + | 0.0455470i | 0.538926 | − | 0.842353i | \(-0.318830\pi\) |
−0.460036 | + | 0.887900i | \(0.652164\pi\) | |||||||
\(98\) | 2.13644 | + | 6.66600i | 0.215813 | + | 0.673368i | ||||
\(99\) | 11.8417 | − | 0.826087i | 1.19014 | − | 0.0830249i | ||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −0.215695 | −0.0214624 | −0.0107312 | − | 0.999942i | \(-0.503416\pi\) | ||||
−0.0107312 | + | 0.999942i | \(0.503416\pi\) | |||||||
\(102\) | 1.64754 | − | 0.503554i | 0.163131 | − | 0.0498593i | ||||
\(103\) | − | 11.3535i | − | 1.11869i | −0.828934 | − | 0.559346i | \(-0.811052\pi\) | ||
0.828934 | − | 0.559346i | \(-0.188948\pi\) | |||||||
\(104\) | −1.63209 | − | 2.82686i | −0.160039 | − | 0.277196i | ||||
\(105\) | 0.329195 | − | 4.57074i | 0.0321261 | − | 0.446058i | ||||
\(106\) | 5.09390 | − | 8.82289i | 0.494763 | − | 0.856955i | ||||
\(107\) | −5.53564 | − | 3.19600i | −0.535151 | − | 0.308969i | 0.207961 | − | 0.978137i | \(-0.433317\pi\) |
−0.743111 | + | 0.669168i | \(0.766651\pi\) | |||||||
\(108\) | 4.85149 | − | 1.86093i | 0.466835 | − | 0.179068i | ||||
\(109\) | 0.615666 | + | 1.06636i | 0.0589701 | + | 0.102139i | 0.894003 | − | 0.448060i | \(-0.147885\pi\) |
−0.835033 | + | 0.550199i | \(0.814552\pi\) | |||||||
\(110\) | 1.97842 | + | 3.42673i | 0.188635 | + | 0.326725i | ||||
\(111\) | −5.11883 | − | 16.7479i | −0.485858 | − | 1.58964i | ||||
\(112\) | −2.46812 | − | 0.953096i | −0.233215 | − | 0.0900591i | ||||
\(113\) | −7.32005 | + | 4.22623i | −0.688612 | + | 0.397571i | −0.803092 | − | 0.595855i | \(-0.796813\pi\) |
0.114480 | + | 0.993426i | \(0.463480\pi\) | |||||||
\(114\) | −6.69571 | + | 7.17908i | −0.627111 | + | 0.672383i | ||||
\(115\) | − | 7.70987i | − | 0.718949i | ||||||
\(116\) | −4.10273 | + | 2.36871i | −0.380929 | + | 0.219930i | ||||
\(117\) | 5.47457 | + | 8.11928i | 0.506124 | + | 0.750628i | ||||
\(118\) | − | 3.40720i | − | 0.313658i | ||||||
\(119\) | 2.45490 | + | 0.947992i | 0.225040 | + | 0.0869023i | ||||
\(120\) | 1.26664 | + | 1.18136i | 0.115628 | + | 0.107843i | ||||
\(121\) | −4.65660 | −0.423327 | ||||||||
\(122\) | −3.14969 | + | 5.45543i | −0.285160 | + | 0.493911i | ||||
\(123\) | 17.4355 | + | 4.02681i | 1.57210 | + | 0.363085i | ||||
\(124\) | −4.83278 | + | 2.79020i | −0.433996 | + | 0.250568i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 7.58539 | + | 2.33708i | 0.675760 | + | 0.208203i | ||||
\(127\) | 20.5777 | 1.82598 | 0.912988 | − | 0.407985i | \(-0.133769\pi\) | ||||
0.912988 | + | 0.407985i | \(0.133769\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 5.16687 | + | 16.9051i | 0.454917 | + | 1.48841i | ||||
\(130\) | −1.63209 | + | 2.82686i | −0.143144 | + | 0.247932i | ||||
\(131\) | 5.00917 | 0.437654 | 0.218827 | − | 0.975764i | \(-0.429777\pi\) | ||||
0.218827 | + | 0.975764i | \(0.429777\pi\) | |||||||
\(132\) | −6.55415 | + | 2.00321i | −0.570466 | + | 0.174357i | ||||
\(133\) | −14.8156 | + | 2.31617i | −1.28468 | + | 0.200837i | ||||
\(134\) | − | 9.22190i | − | 0.796651i | ||||||
\(135\) | −4.03736 | − | 3.27105i | −0.347480 | − | 0.281527i | ||||
\(136\) | −0.861388 | + | 0.497322i | −0.0738634 | + | 0.0426450i | ||||
\(137\) | 9.23672i | 0.789147i | 0.918864 | + | 0.394573i | \(0.129108\pi\) | ||||
−0.918864 | + | 0.394573i | \(0.870892\pi\) | |||||||
\(138\) | 13.0114 | + | 3.00505i | 1.10760 | + | 0.255807i | ||||
\(139\) | −11.2919 | + | 6.51936i | −0.957763 | + | 0.552965i | −0.895484 | − | 0.445094i | \(-0.853170\pi\) |
−0.0622791 | + | 0.998059i | \(0.519837\pi\) | |||||||
\(140\) | 0.408654 | + | 2.61400i | 0.0345375 | + | 0.220923i | ||||
\(141\) | 7.99811 | + | 1.84721i | 0.673562 | + | 0.155563i | ||||
\(142\) | 1.37483 | + | 2.38127i | 0.115373 | + | 0.199832i | ||||
\(143\) | −6.45792 | − | 11.1854i | −0.540038 | − | 0.935373i | ||||
\(144\) | −2.48739 | + | 1.67717i | −0.207283 | + | 0.139764i | ||||
\(145\) | 4.10273 | + | 2.36871i | 0.340713 | + | 0.196711i | ||||
\(146\) | 7.36348 | − | 12.7539i | 0.609406 | − | 1.05552i | ||||
\(147\) | 6.91359 | + | 9.96003i | 0.570224 | + | 0.821490i | ||||
\(148\) | 5.05548 | + | 8.75634i | 0.415558 | + | 0.719767i | ||||
\(149\) | 22.0661i | 1.80773i | 0.427821 | + | 0.903863i | \(0.359281\pi\) | ||||
−0.427821 | + | 0.903863i | \(0.640719\pi\) | |||||||
\(150\) | 0.389766 | − | 1.68763i | 0.0318243 | − | 0.137794i | ||||
\(151\) | 5.53782 | 0.450661 | 0.225331 | − | 0.974282i | \(-0.427654\pi\) | ||||
0.225331 | + | 0.974282i | \(0.427654\pi\) | |||||||
\(152\) | 2.83390 | − | 4.90846i | 0.229860 | − | 0.398128i | ||||
\(153\) | 2.47407 | − | 1.66819i | 0.200017 | − | 0.134865i | ||||
\(154\) | −9.76595 | − | 3.77125i | −0.786963 | − | 0.303896i | ||||
\(155\) | 4.83278 | + | 2.79020i | 0.388178 | + | 0.224115i | ||||
\(156\) | −4.13455 | − | 3.85617i | −0.331029 | − | 0.308741i | ||||
\(157\) | 14.5468 | + | 8.39860i | 1.16096 | + | 0.670281i | 0.951534 | − | 0.307543i | \(-0.0995068\pi\) |
0.209427 | + | 0.977824i | \(0.432840\pi\) | |||||||
\(158\) | −1.59476 | − | 0.920736i | −0.126872 | − | 0.0732498i | ||||
\(159\) | 3.97086 | − | 17.1932i | 0.314910 | − | 1.36351i | ||||
\(160\) | −0.866025 | − | 0.500000i | −0.0684653 | − | 0.0395285i | ||||
\(161\) | 12.8054 | + | 15.8782i | 1.00920 | + | 1.25138i | ||||
\(162\) | 7.09393 | − | 5.53861i | 0.557352 | − | 0.435154i | ||||
\(163\) | 0.864749 | − | 1.49779i | 0.0677324 | − | 0.117316i | −0.830170 | − | 0.557510i | \(-0.811757\pi\) |
0.897903 | + | 0.440194i | \(0.145090\pi\) | |||||||
\(164\) | −10.3313 | −0.806743 | ||||||||
\(165\) | 5.01191 | + | 4.67446i | 0.390177 | + | 0.363906i | ||||
\(166\) | 1.57966i | 0.122605i | ||||||||
\(167\) | −0.371022 | − | 0.642629i | −0.0287105 | − | 0.0497281i | 0.851313 | − | 0.524658i | \(-0.175807\pi\) |
−0.880024 | + | 0.474930i | \(0.842473\pi\) | |||||||
\(168\) | −4.57074 | − | 0.329195i | −0.352640 | − | 0.0253979i | ||||
\(169\) | −1.17257 | + | 2.03096i | −0.0901981 | + | 0.156228i | ||||
\(170\) | 0.861388 | + | 0.497322i | 0.0660654 | + | 0.0381429i | ||||
\(171\) | −7.45633 | + | 15.2813i | −0.570200 | + | 1.16859i | ||||
\(172\) | −5.10292 | − | 8.83852i | −0.389094 | − | 0.673930i | ||||
\(173\) | 0.482119 | + | 0.835055i | 0.0366548 | + | 0.0634881i | 0.883771 | − | 0.467920i | \(-0.154996\pi\) |
−0.847116 | + | 0.531408i | \(0.821663\pi\) | |||||||
\(174\) | −5.59661 | + | 6.00064i | −0.424278 | + | 0.454907i | ||||
\(175\) | 2.05946 | − | 1.66090i | 0.155681 | − | 0.125553i | ||||
\(176\) | 3.42673 | − | 1.97842i | 0.258299 | − | 0.149129i | ||||
\(177\) | −1.72495 | − | 5.64373i | −0.129655 | − | 0.424208i | ||||
\(178\) | − | 13.8556i | − | 1.03852i | ||||||
\(179\) | −0.186006 | + | 0.107391i | −0.0139028 | + | 0.00802676i | −0.506935 | − | 0.861984i | \(-0.669222\pi\) |
0.493033 | + | 0.870011i | \(0.335888\pi\) | |||||||
\(180\) | 2.69616 | + | 1.31556i | 0.200960 | + | 0.0980560i | ||||
\(181\) | 11.1757i | 0.830681i | 0.909666 | + | 0.415341i | \(0.136338\pi\) | ||||
−0.909666 | + | 0.415341i | \(0.863662\pi\) | |||||||
\(182\) | −1.33392 | − | 8.53256i | −0.0988765 | − | 0.632476i | ||||
\(183\) | −2.45529 | + | 10.6310i | −0.181500 | + | 0.785867i | ||||
\(184\) | −7.70987 | −0.568379 | ||||||||
\(185\) | 5.05548 | − | 8.75634i | 0.371686 | − | 0.643779i | ||||
\(186\) | −6.59247 | + | 7.06839i | −0.483384 | + | 0.518280i | ||||
\(187\) | −3.40837 | + | 1.96783i | −0.249245 | + | 0.143902i | ||||
\(188\) | −4.73926 | −0.345646 | ||||||||
\(189\) | 13.7477 | + | 0.0309387i | 0.999997 | + | 0.00225046i | ||||
\(190\) | −5.66780 | −0.411185 | ||||||||
\(191\) | 16.3524 | − | 9.44109i | 1.18322 | − | 0.683133i | 0.226464 | − | 0.974020i | \(-0.427284\pi\) |
0.956758 | + | 0.290886i | \(0.0939502\pi\) | |||||||
\(192\) | 1.18136 | − | 1.26664i | 0.0852574 | − | 0.0914122i | ||||
\(193\) | 2.94509 | − | 5.10105i | 0.211992 | − | 0.367181i | −0.740346 | − | 0.672226i | \(-0.765338\pi\) |
0.952338 | + | 0.305045i | \(0.0986715\pi\) | |||||||
\(194\) | −0.897172 | −0.0644132 | ||||||||
\(195\) | −1.27227 | + | 5.50871i | −0.0911089 | + | 0.394487i | ||||
\(196\) | −5.18322 | − | 4.70471i | −0.370230 | − | 0.336051i | ||||
\(197\) | − | 24.0786i | − | 1.71553i | −0.514043 | − | 0.857764i | \(-0.671853\pi\) | ||
0.514043 | − | 0.857764i | \(-0.328147\pi\) | |||||||
\(198\) | −9.84221 | + | 6.63629i | −0.699455 | + | 0.471620i | ||||
\(199\) | 13.1750 | − | 7.60658i | 0.933950 | − | 0.539216i | 0.0458914 | − | 0.998946i | \(-0.485387\pi\) |
0.888059 | + | 0.459730i | \(0.152054\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −4.66873 | − | 15.2753i | −0.329307 | − | 1.07743i | ||||
\(202\) | 0.186797 | − | 0.107847i | 0.0131430 | − | 0.00758812i | ||||
\(203\) | −12.3836 | + | 1.93597i | −0.869161 | + | 0.135878i | ||||
\(204\) | −1.17503 | + | 1.25986i | −0.0822688 | + | 0.0882079i | ||||
\(205\) | 5.16567 | + | 8.94721i | 0.360786 | + | 0.624900i | ||||
\(206\) | 5.67674 | + | 9.83240i | 0.395517 | + | 0.685056i | ||||
\(207\) | 23.0735 | − | 1.60962i | 1.60372 | − | 0.111877i | ||||
\(208\) | 2.82686 | + | 1.63209i | 0.196007 | + | 0.113165i | ||||
\(209\) | 11.2133 | − | 19.4220i | 0.775640 | − | 1.34345i | ||||
\(210\) | 2.00028 | + | 4.12297i | 0.138032 | + | 0.284512i | ||||
\(211\) | −3.11109 | − | 5.38856i | −0.214176 | − | 0.370964i | 0.738841 | − | 0.673879i | \(-0.235373\pi\) |
−0.953017 | + | 0.302916i | \(0.902040\pi\) | |||||||
\(212\) | 10.1878i | 0.699701i | ||||||||
\(213\) | 3.48283 | + | 3.24833i | 0.238640 | + | 0.222572i | ||||
\(214\) | 6.39201 | 0.436949 | ||||||||
\(215\) | −5.10292 | + | 8.83852i | −0.348016 | + | 0.602782i | ||||
\(216\) | −3.27105 | + | 4.03736i | −0.222567 | + | 0.274707i | ||||
\(217\) | −14.5872 | + | 2.28045i | −0.990243 | + | 0.154807i | ||||
\(218\) | −1.06636 | − | 0.615666i | −0.0722233 | − | 0.0416982i | ||||
\(219\) | 5.74007 | − | 24.8536i | 0.387878 | − | 1.67945i | ||||
\(220\) | −3.42673 | − | 1.97842i | −0.231030 | − | 0.133385i | ||||
\(221\) | −2.81172 | − | 1.62335i | −0.189137 | − | 0.109198i | ||||
\(222\) | 12.8070 | + | 11.9447i | 0.859548 | + | 0.801675i | ||||
\(223\) | −4.37102 | − | 2.52361i | −0.292705 | − | 0.168994i | 0.346456 | − | 0.938066i | \(-0.387385\pi\) |
−0.639161 | + | 0.769073i | \(0.720718\pi\) | |||||||
\(224\) | 2.61400 | − | 0.408654i | 0.174655 | − | 0.0273043i | ||||
\(225\) | −0.208774 | − | 2.99273i | −0.0139183 | − | 0.199515i | ||||
\(226\) | 4.22623 | − | 7.32005i | 0.281125 | − | 0.486922i | ||||
\(227\) | −5.07962 | −0.337146 | −0.168573 | − | 0.985689i | \(-0.553916\pi\) | ||||
−0.168573 | + | 0.985689i | \(0.553916\pi\) | |||||||
\(228\) | 2.20912 | − | 9.56513i | 0.146302 | − | 0.633466i | ||||
\(229\) | 29.6559i | 1.95972i | 0.199692 | + | 0.979859i | \(0.436006\pi\) | ||||
−0.199692 | + | 0.979859i | \(0.563994\pi\) | |||||||
\(230\) | 3.85494 | + | 6.67695i | 0.254187 | + | 0.440265i | ||||
\(231\) | −18.0857 | − | 1.30257i | −1.18995 | − | 0.0857030i | ||||
\(232\) | 2.36871 | − | 4.10273i | 0.155514 | − | 0.269358i | ||||
\(233\) | −15.8420 | − | 9.14639i | −1.03784 | − | 0.599200i | −0.118622 | − | 0.992939i | \(-0.537848\pi\) |
−0.919222 | + | 0.393740i | \(0.871181\pi\) | |||||||
\(234\) | −8.80076 | − | 4.29422i | −0.575324 | − | 0.280722i | ||||
\(235\) | 2.36963 | + | 4.10432i | 0.154578 | + | 0.267737i | ||||
\(236\) | 1.70360 | + | 2.95072i | 0.110895 | + | 0.192076i | ||||
\(237\) | −3.10772 | − | 0.717744i | −0.201868 | − | 0.0466225i | ||||
\(238\) | −2.60000 | + | 0.406465i | −0.168533 | + | 0.0263472i | ||||
\(239\) | 6.05638 | − | 3.49665i | 0.391755 | − | 0.226180i | −0.291165 | − | 0.956673i | \(-0.594043\pi\) |
0.682920 | + | 0.730493i | \(0.260710\pi\) | |||||||
\(240\) | −1.68763 | − | 0.389766i | −0.108936 | − | 0.0251593i | ||||
\(241\) | − | 5.51586i | − | 0.355308i | −0.984093 | − | 0.177654i | \(-0.943149\pi\) | ||
0.984093 | − | 0.177654i | \(-0.0568507\pi\) | |||||||
\(242\) | 4.03273 | − | 2.32830i | 0.259234 | − | 0.149669i | ||||
\(243\) | 8.94645 | − | 12.7656i | 0.573915 | − | 0.818915i | ||||
\(244\) | − | 6.29939i | − | 0.403277i | ||||||
\(245\) | −1.48279 | + | 6.84115i | −0.0947319 | + | 0.437065i | ||||
\(246\) | −17.1130 | + | 5.23041i | −1.09108 | + | 0.333479i | ||||
\(247\) | 18.5007 | 1.17717 | ||||||||
\(248\) | 2.79020 | − | 4.83278i | 0.177178 | − | 0.306882i | ||||
\(249\) | 0.799727 | + | 2.61656i | 0.0506806 | + | 0.165818i | ||||
\(250\) | 0.866025 | − | 0.500000i | 0.0547723 | − | 0.0316228i | ||||
\(251\) | 0.276363 | 0.0174439 | 0.00872195 | − | 0.999962i | \(-0.497224\pi\) | ||||
0.00872195 | + | 0.999962i | \(0.497224\pi\) | |||||||
\(252\) | −7.73767 | + | 1.76872i | −0.487428 | + | 0.111419i | ||||
\(253\) | −30.5068 | −1.91794 | ||||||||
\(254\) | −17.8208 | + | 10.2889i | −1.11818 | + | 0.645580i | ||||
\(255\) | 1.67859 | + | 0.387679i | 0.105117 | + | 0.0242774i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −16.4912 | −1.02870 | −0.514348 | − | 0.857582i | \(-0.671966\pi\) | ||||
−0.514348 | + | 0.857582i | \(0.671966\pi\) | |||||||
\(258\) | −12.9272 | − | 12.0568i | −0.804810 | − | 0.750622i | ||||
\(259\) | 4.13188 | + | 26.4300i | 0.256742 | + | 1.64228i | ||||
\(260\) | − | 3.26418i | − | 0.202436i | ||||||
\(261\) | −6.23237 | + | 12.7729i | −0.385774 | + | 0.790622i | ||||
\(262\) | −4.33807 | + | 2.50459i | −0.268007 | + | 0.154734i | ||||
\(263\) | − | 2.50928i | − | 0.154729i | −0.997003 | − | 0.0773646i | \(-0.975349\pi\) | ||
0.997003 | − | 0.0773646i | \(-0.0246505\pi\) | |||||||
\(264\) | 4.67446 | − | 5.01191i | 0.287693 | − | 0.308462i | ||||
\(265\) | 8.82289 | − | 5.09390i | 0.541986 | − | 0.312916i | ||||
\(266\) | 11.6726 | − | 9.41368i | 0.715695 | − | 0.577189i | ||||
\(267\) | −7.01463 | − | 22.9506i | −0.429288 | − | 1.40455i | ||||
\(268\) | 4.61095 | + | 7.98640i | 0.281659 | + | 0.487847i | ||||
\(269\) | −13.3603 | − | 23.1408i | −0.814594 | − | 1.41092i | −0.909619 | − | 0.415444i | \(-0.863626\pi\) |
0.0950245 | − | 0.995475i | \(-0.469707\pi\) | |||||||
\(270\) | 5.13198 | + | 0.814131i | 0.312322 | + | 0.0495464i | ||||
\(271\) | 12.9500 | + | 7.47668i | 0.786656 | + | 0.454176i | 0.838784 | − | 0.544464i | \(-0.183267\pi\) |
−0.0521278 | + | 0.998640i | \(0.516600\pi\) | |||||||
\(272\) | 0.497322 | − | 0.861388i | 0.0301546 | − | 0.0522293i | ||||
\(273\) | −6.52926 | − | 13.4581i | −0.395169 | − | 0.814522i | ||||
\(274\) | −4.61836 | − | 7.99924i | −0.279005 | − | 0.483252i | ||||
\(275\) | 3.95684i | 0.238607i | ||||||||
\(276\) | −12.7707 | + | 3.90324i | −0.768707 | + | 0.234948i | ||||
\(277\) | −14.2293 | −0.854956 | −0.427478 | − | 0.904026i | \(-0.640598\pi\) | ||||
−0.427478 | + | 0.904026i | \(0.640598\pi\) | |||||||
\(278\) | 6.51936 | − | 11.2919i | 0.391005 | − | 0.677241i | ||||
\(279\) | −7.34136 | + | 15.0457i | −0.439516 | + | 0.900762i | ||||
\(280\) | −1.66090 | − | 2.05946i | −0.0992581 | − | 0.123077i | ||||
\(281\) | 21.5588 | + | 12.4470i | 1.28609 | + | 0.742524i | 0.977954 | − | 0.208819i | \(-0.0669620\pi\) |
0.308135 | + | 0.951343i | \(0.400295\pi\) | |||||||
\(282\) | −7.85017 | + | 2.39933i | −0.467471 | + | 0.142878i | ||||
\(283\) | 14.8780 | + | 8.58983i | 0.884407 | + | 0.510612i | 0.872109 | − | 0.489312i | \(-0.162752\pi\) |
0.0122977 | + | 0.999924i | \(0.496085\pi\) | |||||||
\(284\) | −2.38127 | − | 1.37483i | −0.141302 | − | 0.0815810i | ||||
\(285\) | −9.38820 | + | 2.86941i | −0.556109 | + | 0.169969i | ||||
\(286\) | 11.1854 | + | 6.45792i | 0.661409 | + | 0.381865i | ||||
\(287\) | −25.4990 | − | 9.84677i | −1.50516 | − | 0.581236i | ||||
\(288\) | 1.31556 | − | 2.69616i | 0.0775201 | − | 0.158873i | ||||
\(289\) | 8.00534 | − | 13.8657i | 0.470902 | − | 0.815627i | ||||
\(290\) | −4.73743 | −0.278191 | ||||||||
\(291\) | −1.48609 | + | 0.454207i | −0.0871159 | + | 0.0266261i | ||||
\(292\) | 14.7270i | 0.861830i | ||||||||
\(293\) | −3.98706 | − | 6.90578i | −0.232926 | − | 0.403440i | 0.725742 | − | 0.687967i | \(-0.241497\pi\) |
−0.958668 | + | 0.284527i | \(0.908163\pi\) | |||||||
\(294\) | −10.9674 | − | 5.16884i | −0.639630 | − | 0.301453i | ||||
\(295\) | 1.70360 | − | 2.95072i | 0.0991875 | − | 0.171798i | ||||
\(296\) | −8.75634 | − | 5.05548i | −0.508952 | − | 0.293844i | ||||
\(297\) | −12.9430 | + | 15.9752i | −0.751030 | + | 0.926974i | ||||
\(298\) | −11.0331 | − | 19.1098i | −0.639128 | − | 1.10700i | ||||
\(299\) | −12.5832 | − | 21.7947i | −0.727705 | − | 1.26042i | ||||
\(300\) | 0.506266 | + | 1.65641i | 0.0292293 | + | 0.0956329i | ||||
\(301\) | −4.17065 | − | 26.6781i | −0.240392 | − | 1.53770i | ||||
\(302\) | −4.79589 | + | 2.76891i | −0.275973 | + | 0.159333i | ||||
\(303\) | 0.254814 | − | 0.273209i | 0.0146387 | − | 0.0156954i | ||||
\(304\) | 5.66780i | 0.325071i | ||||||||
\(305\) | −5.45543 | + | 3.14969i | −0.312377 | + | 0.180351i | ||||
\(306\) | −1.30851 | + | 2.68173i | −0.0748028 | + | 0.153304i | ||||
\(307\) | 15.5665i | 0.888429i | 0.895920 | + | 0.444215i | \(0.146517\pi\) | ||||
−0.895920 | + | 0.444215i | \(0.853483\pi\) | |||||||
\(308\) | 10.3432 | − | 1.61698i | 0.589358 | − | 0.0921358i | ||||
\(309\) | 14.3808 | + | 13.4126i | 0.818096 | + | 0.763014i | ||||
\(310\) | −5.58041 | −0.316946 | ||||||||
\(311\) | −10.0834 | + | 17.4650i | −0.571779 | + | 0.990350i | 0.424604 | + | 0.905379i | \(0.360413\pi\) |
−0.996383 | + | 0.0849714i | \(0.972920\pi\) | |||||||
\(312\) | 5.50871 | + | 1.27227i | 0.311869 | + | 0.0720279i | ||||
\(313\) | −5.77815 | + | 3.33602i | −0.326600 | + | 0.188563i | −0.654331 | − | 0.756209i | \(-0.727050\pi\) |
0.327730 | + | 0.944771i | \(0.393716\pi\) | |||||||
\(314\) | −16.7972 | −0.947921 | ||||||||
\(315\) | 5.40060 | + | 5.81666i | 0.304289 | + | 0.327732i | ||||
\(316\) | 1.84147 | 0.103591 | ||||||||
\(317\) | 22.1197 | − | 12.7708i | 1.24236 | − | 0.717279i | 0.272789 | − | 0.962074i | \(-0.412054\pi\) |
0.969575 | + | 0.244795i | \(0.0787207\pi\) | |||||||
\(318\) | 5.15773 | + | 16.8752i | 0.289231 | + | 0.946313i | ||||
\(319\) | 9.37263 | − | 16.2339i | 0.524766 | − | 0.908922i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 10.5878 | − | 3.23605i | 0.590953 | − | 0.180619i | ||||
\(322\) | −19.0289 | − | 7.34825i | −1.06044 | − | 0.409502i | ||||
\(323\) | − | 5.63745i | − | 0.313676i | ||||||
\(324\) | −3.37422 | + | 8.34354i | −0.187457 | + | 0.463530i | ||||
\(325\) | −2.82686 | + | 1.63209i | −0.156806 | + | 0.0905320i | ||||
\(326\) | 1.72950i | 0.0957881i | ||||||||
\(327\) | −2.07803 | − | 0.479932i | −0.114915 | − | 0.0265403i | ||||
\(328\) | 8.94721 | − | 5.16567i | 0.494027 | − | 0.285227i | ||||
\(329\) | −11.6971 | − | 4.51697i | −0.644880 | − | 0.249029i | ||||
\(330\) | −6.67767 | − | 1.54224i | −0.367594 | − | 0.0848977i | ||||
\(331\) | −0.906390 | − | 1.56991i | −0.0498197 | − | 0.0862903i | 0.840040 | − | 0.542524i | \(-0.182531\pi\) |
−0.889860 | + | 0.456234i | \(0.849198\pi\) | |||||||
\(332\) | −0.789829 | − | 1.36802i | −0.0433475 | − | 0.0750801i | ||||
\(333\) | 27.2608 | + | 13.3016i | 1.49388 | + | 0.728921i | ||||
\(334\) | 0.642629 | + | 0.371022i | 0.0351631 | + | 0.0203014i | ||||
\(335\) | 4.61095 | − | 7.98640i | 0.251923 | − | 0.436344i | ||||
\(336\) | 4.12297 | − | 2.00028i | 0.224927 | − | 0.109124i | ||||
\(337\) | 7.15488 | + | 12.3926i | 0.389751 | + | 0.675069i | 0.992416 | − | 0.122926i | \(-0.0392277\pi\) |
−0.602665 | + | 0.797995i | \(0.705894\pi\) | |||||||
\(338\) | − | 2.34515i | − | 0.127559i | ||||||
\(339\) | 3.29449 | − | 14.2646i | 0.178932 | − | 0.774747i | ||||
\(340\) | −0.994645 | −0.0539422 | ||||||||
\(341\) | 11.0404 | − | 19.1225i | 0.597871 | − | 1.03554i | ||||
\(342\) | −1.18329 | − | 16.9622i | −0.0639850 | − | 0.917209i | ||||
\(343\) | −8.30875 | − | 16.5519i | −0.448630 | − | 0.893717i | ||||
\(344\) | 8.83852 | + | 5.10292i | 0.476541 | + | 0.275131i | ||||
\(345\) | 9.76567 | + | 9.10814i | 0.525766 | + | 0.490366i | ||||
\(346\) | −0.835055 | − | 0.482119i | −0.0448928 | − | 0.0259189i | ||||
\(347\) | −5.20049 | − | 3.00250i | −0.279177 | − | 0.161183i | 0.353874 | − | 0.935293i | \(-0.384864\pi\) |
−0.633051 | + | 0.774110i | \(0.718198\pi\) | |||||||
\(348\) | 1.84649 | − | 7.99501i | 0.0989822 | − | 0.428577i | ||||
\(349\) | −11.6157 | − | 6.70633i | −0.621775 | − | 0.358982i | 0.155785 | − | 0.987791i | \(-0.450209\pi\) |
−0.777560 | + | 0.628809i | \(0.783543\pi\) | |||||||
\(350\) | −0.953096 | + | 2.46812i | −0.0509451 | + | 0.131926i | ||||
\(351\) | −16.7517 | − | 2.65747i | −0.894139 | − | 0.141845i | ||||
\(352\) | −1.97842 | + | 3.42673i | −0.105450 | + | 0.182645i | ||||
\(353\) | −0.505383 | −0.0268988 | −0.0134494 | − | 0.999910i | \(-0.504281\pi\) | ||||
−0.0134494 | + | 0.999910i | \(0.504281\pi\) | |||||||
\(354\) | 4.31571 | + | 4.02513i | 0.229378 | + | 0.213933i | ||||
\(355\) | 2.74965i | 0.145937i | ||||||||
\(356\) | 6.92781 | + | 11.9993i | 0.367173 | + | 0.635963i | ||||
\(357\) | −4.10089 | + | 1.98956i | −0.217042 | + | 0.105299i | ||||
\(358\) | 0.107391 | − | 0.186006i | 0.00567578 | − | 0.00983073i | ||||
\(359\) | 11.2748 | + | 6.50952i | 0.595062 | + | 0.343559i | 0.767097 | − | 0.641532i | \(-0.221701\pi\) |
−0.172034 | + | 0.985091i | \(0.555034\pi\) | |||||||
\(360\) | −2.99273 | + | 0.208774i | −0.157731 | + | 0.0110034i | ||||
\(361\) | 6.56197 | + | 11.3657i | 0.345367 | + | 0.598193i | ||||
\(362\) | −5.58784 | − | 9.67842i | −0.293690 | − | 0.508686i | ||||
\(363\) | 5.50112 | − | 5.89826i | 0.288734 | − | 0.309578i | ||||
\(364\) | 5.42149 | + | 6.72246i | 0.284163 | + | 0.352352i | ||||
\(365\) | 12.7539 | − | 7.36348i | 0.667570 | − | 0.385422i | ||||
\(366\) | −3.18916 | − | 10.4344i | −0.166700 | − | 0.545413i | ||||
\(367\) | 32.0287i | 1.67188i | 0.548819 | + | 0.835942i | \(0.315078\pi\) | ||||
−0.548819 | + | 0.835942i | \(0.684922\pi\) | |||||||
\(368\) | 6.67695 | − | 3.85494i | 0.348060 | − | 0.200952i | ||||
\(369\) | −25.6981 | + | 17.3274i | −1.33779 | + | 0.902028i | ||||
\(370\) | 10.1110i | 0.525643i | ||||||||
\(371\) | −9.70995 | + | 25.1447i | −0.504116 | + | 1.30545i | ||||
\(372\) | 2.17506 | − | 9.41764i | 0.112771 | − | 0.488282i | ||||
\(373\) | 6.80077 | 0.352130 | 0.176065 | − | 0.984379i | \(-0.443663\pi\) | ||||
0.176065 | + | 0.984379i | \(0.443663\pi\) | |||||||
\(374\) | 1.96783 | − | 3.40837i | 0.101754 | − | 0.176243i | ||||
\(375\) | 1.18136 | − | 1.26664i | 0.0610052 | − | 0.0654092i | ||||
\(376\) | 4.10432 | − | 2.36963i | 0.211664 | − | 0.122204i | ||||
\(377\) | 15.4638 | 0.796426 | ||||||||
\(378\) | −11.9213 | + | 6.84705i | −0.613167 | + | 0.352174i | ||||
\(379\) | 2.14646 | 0.110256 | 0.0551281 | − | 0.998479i | \(-0.482443\pi\) | ||||
0.0551281 | + | 0.998479i | \(0.482443\pi\) | |||||||
\(380\) | 4.90846 | − | 2.83390i | 0.251799 | − | 0.145376i | ||||
\(381\) | −24.3097 | + | 26.0646i | −1.24542 | + | 1.33533i | ||||
\(382\) | −9.44109 | + | 16.3524i | −0.483048 | + | 0.836664i | ||||
\(383\) | 0.710547 | 0.0363072 | 0.0181536 | − | 0.999835i | \(-0.494221\pi\) | ||||
0.0181536 | + | 0.999835i | \(0.494221\pi\) | |||||||
\(384\) | −0.389766 | + | 1.68763i | −0.0198902 | + | 0.0861213i | ||||
\(385\) | −6.57194 | − | 8.14898i | −0.334937 | − | 0.415310i | ||||
\(386\) | 5.89018i | 0.299802i | ||||||||
\(387\) | −27.5166 | − | 13.4264i | −1.39875 | − | 0.682502i | ||||
\(388\) | 0.776974 | − | 0.448586i | 0.0394449 | − | 0.0227735i | ||||
\(389\) | 19.6149i | 0.994517i | 0.867603 | + | 0.497258i | \(0.165660\pi\) | ||||
−0.867603 | + | 0.497258i | \(0.834340\pi\) | |||||||
\(390\) | −1.65254 | − | 5.40682i | −0.0836796 | − | 0.273785i | ||||
\(391\) | −6.64119 | + | 3.83429i | −0.335859 | + | 0.193908i | ||||
\(392\) | 6.84115 | + | 1.48279i | 0.345530 | + | 0.0748922i | ||||
\(393\) | −5.91764 | + | 6.34484i | −0.298505 | + | 0.320055i | ||||
\(394\) | 12.0393 | + | 20.8527i | 0.606531 | + | 1.05054i | ||||
\(395\) | −0.920736 | − | 1.59476i | −0.0463273 | − | 0.0802412i | ||||
\(396\) | 5.20546 | − | 10.6683i | 0.261584 | − | 0.536102i | ||||
\(397\) | 20.7322 | + | 11.9697i | 1.04052 | + | 0.600743i | 0.919980 | − | 0.391965i | \(-0.128205\pi\) |
0.120538 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(398\) | −7.60658 | + | 13.1750i | −0.381284 | + | 0.660402i | ||||
\(399\) | 14.5688 | − | 21.5024i | 0.729355 | − | 1.07646i | ||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | − | 0.675625i | − | 0.0337391i | −0.999858 | − | 0.0168696i | \(-0.994630\pi\) | ||
0.999858 | − | 0.0168696i | \(-0.00537000\pi\) | |||||||
\(402\) | 11.6809 | + | 10.8944i | 0.582589 | + | 0.543363i | ||||
\(403\) | 18.2154 | 0.907376 | ||||||||
\(404\) | −0.107847 | + | 0.186797i | −0.00536561 | + | 0.00929351i | ||||
\(405\) | 8.91283 | − | 1.24961i | 0.442882 | − | 0.0620936i | ||||
\(406\) | 9.75657 | − | 7.86842i | 0.484210 | − | 0.390503i | ||||
\(407\) | −34.6475 | − | 20.0037i | −1.71741 | − | 0.991548i | ||||
\(408\) | 0.387679 | − | 1.67859i | 0.0191930 | − | 0.0831025i | ||||
\(409\) | −26.2888 | − | 15.1779i | −1.29990 | − | 0.750497i | −0.319513 | − | 0.947582i | \(-0.603519\pi\) |
−0.980386 | + | 0.197085i | \(0.936853\pi\) | |||||||
\(410\) | −8.94721 | − | 5.16567i | −0.441871 | − | 0.255114i | ||||
\(411\) | −11.6996 | − | 10.9119i | −0.577101 | − | 0.538244i | ||||
\(412\) | −9.83240 | − | 5.67674i | −0.484408 | − | 0.279673i | ||||
\(413\) | 1.39237 | + | 8.90643i | 0.0685138 | + | 0.438257i | ||||
\(414\) | −19.1775 | + | 12.9307i | −0.942521 | + | 0.635512i | ||||
\(415\) | −0.789829 | + | 1.36802i | −0.0387712 | + | 0.0671537i | ||||
\(416\) | −3.26418 | −0.160039 | ||||||||
\(417\) | 5.08205 | − | 22.0045i | 0.248869 | − | 1.07756i | ||||
\(418\) | 22.4266i | 1.09692i | ||||||||
\(419\) | −5.87786 | − | 10.1808i | −0.287152 | − | 0.497363i | 0.685976 | − | 0.727624i | \(-0.259375\pi\) |
−0.973129 | + | 0.230261i | \(0.926042\pi\) | |||||||
\(420\) | −3.79378 | − | 2.57046i | −0.185117 | − | 0.125426i | ||||
\(421\) | 14.4557 | − | 25.0380i | 0.704526 | − | 1.22028i | −0.262336 | − | 0.964977i | \(-0.584493\pi\) |
0.966862 | − | 0.255299i | \(-0.0821739\pi\) | |||||||
\(422\) | 5.38856 | + | 3.11109i | 0.262311 | + | 0.151445i | ||||
\(423\) | −11.7884 | + | 7.94854i | −0.573172 | + | 0.386471i | ||||
\(424\) | −5.09390 | − | 8.82289i | −0.247382 | − | 0.428477i | ||||
\(425\) | 0.497322 | + | 0.861388i | 0.0241237 | + | 0.0417834i | ||||
\(426\) | −4.64039 | − | 1.07172i | −0.224828 | − | 0.0519251i | ||||
\(427\) | 6.00392 | − | 15.5476i | 0.290550 | − | 0.752402i | ||||
\(428\) | −5.53564 | + | 3.19600i | −0.267575 | + | 0.154485i | ||||
\(429\) | 21.7971 | + | 5.03416i | 1.05237 | + | 0.243051i | ||||
\(430\) | − | 10.2058i | − | 0.492169i | ||||||
\(431\) | −17.2762 | + | 9.97444i | −0.832167 | + | 0.480452i | −0.854594 | − | 0.519297i | \(-0.826194\pi\) |
0.0224273 | + | 0.999748i | \(0.492861\pi\) | |||||||
\(432\) | 0.814131 | − | 5.13198i | 0.0391699 | − | 0.246912i | ||||
\(433\) | 28.8157i | 1.38479i | 0.721517 | + | 0.692397i | \(0.243445\pi\) | ||||
−0.721517 | + | 0.692397i | \(0.756555\pi\) | |||||||
\(434\) | 11.4927 | − | 9.26853i | 0.551665 | − | 0.444904i | ||||
\(435\) | −7.84713 | + | 2.39840i | −0.376241 | + | 0.114994i | ||||
\(436\) | 1.23133 | 0.0589701 | ||||||||
\(437\) | 21.8490 | − | 37.8436i | 1.04518 | − | 1.81030i | ||||
\(438\) | 7.45575 | + | 24.3939i | 0.356249 | + | 1.16558i | ||||
\(439\) | 7.07993 | − | 4.08760i | 0.337907 | − | 0.195091i | −0.321439 | − | 0.946930i | \(-0.604167\pi\) |
0.659346 | + | 0.751840i | \(0.270833\pi\) | |||||||
\(440\) | 3.95684 | 0.188635 | ||||||||
\(441\) | −20.7833 | − | 3.00933i | −0.989679 | − | 0.143301i | ||||
\(442\) | 3.24670 | 0.154430 | ||||||||
\(443\) | −22.7505 | + | 13.1350i | −1.08091 | + | 0.624063i | −0.931141 | − | 0.364659i | \(-0.881186\pi\) |
−0.149767 | + | 0.988721i | \(0.547852\pi\) | |||||||
\(444\) | −17.0635 | − | 3.94091i | −0.809798 | − | 0.187027i | ||||
\(445\) | 6.92781 | − | 11.9993i | 0.328410 | − | 0.568822i | ||||
\(446\) | 5.04722 | 0.238993 | ||||||||
\(447\) | −27.9499 | − | 26.0680i | −1.32199 | − | 1.23298i | ||||
\(448\) | −2.05946 | + | 1.66090i | −0.0973006 | + | 0.0784704i | ||||
\(449\) | − | 6.39690i | − | 0.301888i | −0.988542 | − | 0.150944i | \(-0.951769\pi\) | ||
0.988542 | − | 0.150944i | \(-0.0482314\pi\) | |||||||
\(450\) | 1.67717 | + | 2.48739i | 0.0790624 | + | 0.117257i | ||||
\(451\) | 35.4027 | − | 20.4398i | 1.66705 | − | 0.962471i | ||||
\(452\) | 8.45246i | 0.397571i | ||||||||
\(453\) | −6.54216 | + | 7.01444i | −0.307378 | + | 0.329567i | ||||
\(454\) | 4.39908 | − | 2.53981i | 0.206459 | − | 0.119199i | ||||
\(455\) | 3.11107 | − | 8.05637i | 0.145849 | − | 0.377689i | ||||
\(456\) | 2.86941 | + | 9.38820i | 0.134373 | + | 0.439643i | ||||
\(457\) | 5.16337 | + | 8.94322i | 0.241532 | + | 0.418346i | 0.961151 | − | 0.276023i | \(-0.0890167\pi\) |
−0.719619 | + | 0.694369i | \(0.755683\pi\) | |||||||
\(458\) | −14.8280 | − | 25.6828i | −0.692865 | − | 1.20008i | ||||
\(459\) | −0.809771 | + | 5.10449i | −0.0377969 | + | 0.238257i | ||||
\(460\) | −6.67695 | − | 3.85494i | −0.311314 | − | 0.179737i | ||||
\(461\) | 4.00379 | − | 6.93476i | 0.186475 | − | 0.322984i | −0.757598 | − | 0.652722i | \(-0.773627\pi\) |
0.944073 | + | 0.329738i | \(0.106960\pi\) | |||||||
\(462\) | 16.3139 | − | 7.91478i | 0.758994 | − | 0.368229i | ||||
\(463\) | 15.2865 | + | 26.4770i | 0.710425 | + | 1.23049i | 0.964698 | + | 0.263359i | \(0.0848304\pi\) |
−0.254273 | + | 0.967132i | \(0.581836\pi\) | |||||||
\(464\) | 4.73743i | 0.219930i | ||||||||
\(465\) | −9.24345 | + | 2.82517i | −0.428655 | + | 0.131014i | ||||
\(466\) | 18.2928 | 0.847396 | ||||||||
\(467\) | 3.61017 | − | 6.25300i | 0.167059 | − | 0.289354i | −0.770326 | − | 0.637651i | \(-0.779906\pi\) |
0.937385 | + | 0.348296i | \(0.113240\pi\) | |||||||
\(468\) | 9.76879 | − | 0.681476i | 0.451562 | − | 0.0315012i | ||||
\(469\) | 3.76856 | + | 24.1061i | 0.174016 | + | 1.11311i | ||||
\(470\) | −4.10432 | − | 2.36963i | −0.189318 | − | 0.109303i | ||||
\(471\) | −27.8231 | + | 8.50385i | −1.28202 | + | 0.391837i | ||||
\(472\) | −2.95072 | − | 1.70360i | −0.135818 | − | 0.0784146i | ||||
\(473\) | 34.9726 | + | 20.1914i | 1.60804 | + | 0.928404i | ||||
\(474\) | 3.05023 | − | 0.932274i | 0.140102 | − | 0.0428208i | ||||
\(475\) | −4.90846 | − | 2.83390i | −0.225215 | − | 0.130028i | ||||
\(476\) | 2.04844 | − | 1.65201i | 0.0938899 | − | 0.0757198i | ||||
\(477\) | 17.0866 | + | 25.3410i | 0.782344 | + | 1.16029i | ||||
\(478\) | −3.49665 | + | 6.05638i | −0.159933 | + | 0.277012i | ||||
\(479\) | 18.2719 | 0.834864 | 0.417432 | − | 0.908708i | \(-0.362930\pi\) | ||||
0.417432 | + | 0.908708i | \(0.362930\pi\) | |||||||
\(480\) | 1.65641 | − | 0.506266i | 0.0756044 | − | 0.0231078i | ||||
\(481\) | − | 33.0039i | − | 1.50485i | ||||||
\(482\) | 2.75793 | + | 4.77687i | 0.125620 | + | 0.217581i | ||||
\(483\) | −35.2398 | − | 2.53805i | −1.60347 | − | 0.115485i | ||||
\(484\) | −2.32830 | + | 4.03273i | −0.105832 | + | 0.183306i | ||||
\(485\) | −0.776974 | − | 0.448586i | −0.0352806 | − | 0.0203692i | ||||
\(486\) | −1.36505 | + | 15.5286i | −0.0619198 | + | 0.704390i | ||||
\(487\) | −19.2868 | − | 33.4057i | −0.873967 | − | 1.51375i | −0.857859 | − | 0.513885i | \(-0.828206\pi\) |
−0.0161074 | − | 0.999870i | \(-0.505127\pi\) | |||||||
\(488\) | 3.14969 | + | 5.45543i | 0.142580 | + | 0.246956i | ||||
\(489\) | 0.875586 | + | 2.86476i | 0.0395954 | + | 0.129549i | ||||
\(490\) | −2.13644 | − | 6.66600i | −0.0965146 | − | 0.301139i | ||||
\(491\) | 21.3449 | − | 12.3235i | 0.963282 | − | 0.556151i | 0.0661005 | − | 0.997813i | \(-0.478944\pi\) |
0.897182 | + | 0.441662i | \(0.145611\pi\) | |||||||
\(492\) | 12.2050 | − | 13.0861i | 0.550246 | − | 0.589969i | ||||
\(493\) | − | 4.71206i | − | 0.212220i | ||||||
\(494\) | −16.0221 | + | 9.25035i | −0.720867 | + | 0.416193i | ||||
\(495\) | −11.8417 | + | 0.826087i | −0.532247 | + | 0.0371298i | ||||
\(496\) | 5.58041i | 0.250568i | ||||||||
\(497\) | −4.56691 | − | 5.66282i | −0.204854 | − | 0.254012i | ||||
\(498\) | −2.00087 | − | 1.86615i | −0.0896609 | − | 0.0836240i | ||||
\(499\) | 10.5180 | 0.470850 | 0.235425 | − | 0.971893i | \(-0.424352\pi\) | ||||
0.235425 | + | 0.971893i | \(0.424352\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 1.25229 | + | 0.289224i | 0.0559483 | + | 0.0129216i | ||||
\(502\) | −0.239338 | + | 0.138182i | −0.0106822 | + | 0.00616735i | ||||
\(503\) | 19.4315 | 0.866406 | 0.433203 | − | 0.901296i | \(-0.357383\pi\) | ||||
0.433203 | + | 0.901296i | \(0.357383\pi\) | |||||||
\(504\) | 5.81666 | − | 5.40060i | 0.259095 | − | 0.240562i | ||||
\(505\) | 0.215695 | 0.00959830 | ||||||||
\(506\) | 26.4196 | − | 15.2534i | 1.17450 | − | 0.678095i | ||||
\(507\) | −1.18727 | − | 3.88453i | −0.0527285 | − | 0.172518i | ||||
\(508\) | 10.2889 | − | 17.8208i | 0.456494 | − | 0.790671i | ||||
\(509\) | 23.3328 | 1.03421 | 0.517105 | − | 0.855922i | \(-0.327010\pi\) | ||||
0.517105 | + | 0.855922i | \(0.327010\pi\) | |||||||
\(510\) | −1.64754 | + | 0.503554i | −0.0729543 | + | 0.0222978i | ||||
\(511\) | −14.0362 | + | 36.3479i | −0.620925 | + | 1.60793i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −10.5474 | − | 27.4973i | −0.465678 | − | 1.21403i | ||||
\(514\) | 14.2818 | − | 8.24562i | 0.629945 | − | 0.363699i | ||||
\(515\) | 11.3535i | 0.500294i | ||||||||
\(516\) | 17.2236 | + | 3.97789i | 0.758229 | + | 0.175117i | ||||
\(517\) | 16.2402 | − | 9.37626i | 0.714241 | − | 0.412367i | ||||
\(518\) | −16.7933 | − | 20.8232i | −0.737857 | − | 0.914917i | ||||
\(519\) | −1.62727 | − | 0.375828i | −0.0714294 | − | 0.0164970i | ||||
\(520\) | 1.63209 | + | 2.82686i | 0.0715718 | + | 0.123966i | ||||
\(521\) | −11.8637 | − | 20.5486i | −0.519759 | − | 0.900249i | −0.999736 | − | 0.0229682i | \(-0.992688\pi\) |
0.479977 | − | 0.877281i | \(-0.340645\pi\) | |||||||
\(522\) | −0.989053 | − | 14.1778i | −0.0432897 | − | 0.620547i | ||||
\(523\) | 15.7239 | + | 9.07818i | 0.687556 | + | 0.396961i | 0.802696 | − | 0.596388i | \(-0.203398\pi\) |
−0.115140 | + | 0.993349i | \(0.536732\pi\) | |||||||
\(524\) | 2.50459 | − | 4.33807i | 0.109413 | − | 0.189510i | ||||
\(525\) | −0.329195 | + | 4.57074i | −0.0143673 | + | 0.199483i | ||||
\(526\) | 1.25464 | + | 2.17310i | 0.0547050 | + | 0.0947519i | ||||
\(527\) | − | 5.55052i | − | 0.241785i | ||||||
\(528\) | −1.54224 | + | 6.67767i | −0.0671175 | + | 0.290608i | ||||
\(529\) | −36.4421 | −1.58444 | ||||||||
\(530\) | −5.09390 | + | 8.82289i | −0.221265 | + | 0.383242i | ||||
\(531\) | 9.18638 | + | 4.48238i | 0.398655 | + | 0.194519i | ||||
\(532\) | −5.40196 | + | 13.9888i | −0.234205 | + | 0.606491i | ||||
\(533\) | 29.2053 | + | 16.8617i | 1.26502 | + | 0.730360i | ||||
\(534\) | 17.5501 | + | 16.3685i | 0.759469 | + | 0.708334i | ||||
\(535\) | 5.53564 | + | 3.19600i | 0.239327 | + | 0.138175i | ||||
\(536\) | −7.98640 | − | 4.61095i | −0.344960 | − | 0.199163i | ||||
\(537\) | 0.0837146 | − | 0.362471i | 0.00361255 | − | 0.0156418i | ||||
\(538\) | 23.1408 | + | 13.3603i | 0.997670 | + | 0.576005i | ||||
\(539\) | 27.0694 | + | 5.86716i | 1.16596 | + | 0.252717i | ||||
\(540\) | −4.85149 | + | 1.86093i | −0.208775 | + | 0.0800817i | ||||
\(541\) | 5.56494 | − | 9.63875i | 0.239255 | − | 0.414402i | −0.721245 | − | 0.692680i | \(-0.756430\pi\) |
0.960501 | + | 0.278277i | \(0.0897634\pi\) | |||||||
\(542\) | −14.9534 | −0.642302 | ||||||||
\(543\) | −14.1556 | − | 13.2025i | −0.607475 | − | 0.566574i | ||||
\(544\) | 0.994645i | 0.0426450i | ||||||||
\(545\) | −0.615666 | − | 1.06636i | −0.0263722 | − | 0.0456781i | ||||
\(546\) | 12.3836 | + | 8.39043i | 0.529967 | + | 0.359077i | ||||
\(547\) | −15.8512 | + | 27.4550i | −0.677747 | + | 1.17389i | 0.297911 | + | 0.954594i | \(0.403710\pi\) |
−0.975658 | + | 0.219299i | \(0.929623\pi\) | |||||||
\(548\) | 7.99924 | + | 4.61836i | 0.341711 | + | 0.197287i | ||||
\(549\) | −10.5651 | − | 15.6690i | −0.450908 | − | 0.668738i | ||||
\(550\) | −1.97842 | − | 3.42673i | −0.0843602 | − | 0.146116i | ||||
\(551\) | 13.4254 | + | 23.2535i | 0.571941 | + | 0.990631i | ||||
\(552\) | 9.10814 | − | 9.76567i | 0.387668 | − | 0.415654i | ||||
\(553\) | 4.54497 | + | 1.75510i | 0.193272 | + | 0.0746345i | ||||
\(554\) | 12.3229 | − | 7.11465i | 0.523552 | − | 0.302273i | ||||
\(555\) | 5.11883 | + | 16.7479i | 0.217282 | + | 0.710908i | ||||
\(556\) | 13.0387i | 0.552965i | ||||||||
\(557\) | −28.2949 | + | 16.3360i | −1.19889 | + | 0.692181i | −0.960308 | − | 0.278941i | \(-0.910016\pi\) |
−0.238584 | + | 0.971122i | \(0.576683\pi\) | |||||||
\(558\) | −1.16505 | − | 16.7006i | −0.0493203 | − | 0.706994i | ||||
\(559\) | 33.3137i | 1.40902i | ||||||||
\(560\) | 2.46812 | + | 0.953096i | 0.104297 | + | 0.0402757i | ||||
\(561\) | 1.53398 | − | 6.64191i | 0.0647649 | − | 0.280422i | ||||
\(562\) | −24.8939 | −1.05009 | ||||||||
\(563\) | −12.2498 | + | 21.2172i | −0.516267 | + | 0.894200i | 0.483555 | + | 0.875314i | \(0.339345\pi\) |
−0.999822 | + | 0.0188863i | \(0.993988\pi\) | |||||||
\(564\) | 5.59878 | − | 6.00296i | 0.235751 | − | 0.252770i | ||||
\(565\) | 7.32005 | − | 4.22623i | 0.307957 | − | 0.177799i | ||||
\(566\) | −17.1797 | −0.722115 | ||||||||
\(567\) | −16.2802 | + | 17.3769i | −0.683703 | + | 0.729760i | ||||
\(568\) | 2.74965 | 0.115373 | ||||||||
\(569\) | 18.5002 | − | 10.6811i | 0.775567 | − | 0.447774i | −0.0592899 | − | 0.998241i | \(-0.518884\pi\) |
0.834857 | + | 0.550467i | \(0.185550\pi\) | |||||||
\(570\) | 6.69571 | − | 7.17908i | 0.280453 | − | 0.300699i | ||||
\(571\) | 8.22432 | − | 14.2449i | 0.344177 | − | 0.596132i | −0.641027 | − | 0.767518i | \(-0.721491\pi\) |
0.985204 | + | 0.171386i | \(0.0548246\pi\) | |||||||
\(572\) | −12.9158 | −0.540038 | ||||||||
\(573\) | −7.35963 | + | 31.8661i | −0.307453 | + | 1.33122i | ||||
\(574\) | 27.0062 | − | 4.22194i | 1.12722 | − | 0.176220i | ||||
\(575\) | 7.70987i | 0.321524i | ||||||||
\(576\) | 0.208774 | + | 2.99273i | 0.00869893 | + | 0.124697i | ||||
\(577\) | 17.2606 | − | 9.96542i | 0.718569 | − | 0.414866i | −0.0956570 | − | 0.995414i | \(-0.530495\pi\) |
0.814226 | + | 0.580549i | \(0.197162\pi\) | |||||||
\(578\) | 16.0107i | 0.665957i | ||||||||
\(579\) | 2.98200 | + | 9.75656i | 0.123928 | + | 0.405469i | ||||
\(580\) | 4.10273 | − | 2.36871i | 0.170357 | − | 0.0983555i | ||||
\(581\) | −0.645533 | − | 4.12923i | −0.0267812 | − | 0.171309i | ||||
\(582\) | 1.05988 | − | 1.13640i | 0.0439336 | − | 0.0471052i | ||||
\(583\) | −20.1558 | − | 34.9108i | −0.834766 | − | 1.44586i | ||||
\(584\) | −7.36348 | − | 12.7539i | −0.304703 | − | 0.527761i | ||||
\(585\) | −5.47457 | − | 8.11928i | −0.226346 | − | 0.335691i | ||||
\(586\) | 6.90578 | + | 3.98706i | 0.285275 | + | 0.164704i | ||||
\(587\) | 1.94532 | − | 3.36939i | 0.0802918 | − | 0.139070i | −0.823083 | − | 0.567920i | \(-0.807748\pi\) |
0.903375 | + | 0.428851i | \(0.141081\pi\) | |||||||
\(588\) | 12.0824 | − | 1.00733i | 0.498271 | − | 0.0415416i | ||||
\(589\) | 15.8143 | + | 27.3912i | 0.651618 | + | 1.12863i | ||||
\(590\) | 3.40720i | 0.140272i | ||||||||
\(591\) | 30.4990 | + | 28.4455i | 1.25456 | + | 1.17009i | ||||
\(592\) | 10.1110 | 0.415558 | ||||||||
\(593\) | −7.52066 | + | 13.0262i | −0.308836 | + | 0.534920i | −0.978108 | − | 0.208097i | \(-0.933273\pi\) |
0.669272 | + | 0.743018i | \(0.266606\pi\) | |||||||
\(594\) | 3.22139 | − | 20.3064i | 0.132175 | − | 0.833183i | ||||
\(595\) | −2.45490 | − | 0.947992i | −0.100641 | − | 0.0388639i | ||||
\(596\) | 19.1098 | + | 11.0331i | 0.782769 | + | 0.451932i | ||||
\(597\) | −5.92958 | + | 25.6741i | −0.242681 | + | 1.05077i | ||||
\(598\) | 21.7947 | + | 12.5832i | 0.891253 | + | 0.514565i | ||||
\(599\) | 23.6663 | + | 13.6638i | 0.966979 | + | 0.558286i | 0.898314 | − | 0.439354i | \(-0.144793\pi\) |
0.0686653 | + | 0.997640i | \(0.478126\pi\) | |||||||
\(600\) | −1.26664 | − | 1.18136i | −0.0517105 | − | 0.0482288i | ||||
\(601\) | −10.2307 | − | 5.90670i | −0.417319 | − | 0.240939i | 0.276610 | − | 0.960982i | \(-0.410789\pi\) |
−0.693930 | + | 0.720043i | \(0.744122\pi\) | |||||||
\(602\) | 16.9509 | + | 21.0186i | 0.690868 | + | 0.856653i | ||||
\(603\) | 24.8638 | + | 12.1320i | 1.01253 | + | 0.494052i | ||||
\(604\) | 2.76891 | − | 4.79589i | 0.112665 | − | 0.195142i | ||||
\(605\) | 4.65660 | 0.189318 | ||||||||
\(606\) | −0.0840706 | + | 0.364012i | −0.00341514 | + | 0.0147870i | ||||
\(607\) | 0.740209i | 0.0300441i | 0.999887 | + | 0.0150221i | \(0.00478185\pi\) | ||||
−0.999887 | + | 0.0150221i | \(0.995218\pi\) | |||||||
\(608\) | −2.83390 | − | 4.90846i | −0.114930 | − | 0.199064i | ||||
\(609\) | 12.1774 | − | 17.9727i | 0.493452 | − | 0.728292i | ||||
\(610\) | 3.14969 | − | 5.45543i | 0.127527 | − | 0.220884i | ||||
\(611\) | 13.3972 | + | 7.73490i | 0.541994 | + | 0.312920i | ||||
\(612\) | −0.207656 | − | 2.97670i | −0.00839400 | − | 0.120326i | ||||
\(613\) | 8.29710 | + | 14.3710i | 0.335117 | + | 0.580439i | 0.983507 | − | 0.180869i | \(-0.0578909\pi\) |
−0.648390 | + | 0.761308i | \(0.724558\pi\) | |||||||
\(614\) | −7.78327 | − | 13.4810i | −0.314107 | − | 0.544050i | ||||
\(615\) | −17.4355 | − | 4.02681i | −0.703065 | − | 0.162377i | ||||
\(616\) | −8.14898 | + | 6.57194i | −0.328332 | + | 0.264791i | ||||
\(617\) | −40.0027 | + | 23.0956i | −1.61045 | + | 0.929793i | −0.621184 | + | 0.783665i | \(0.713348\pi\) |
−0.989266 | + | 0.146128i | \(0.953319\pi\) | |||||||
\(618\) | −19.1604 | − | 4.42520i | −0.770746 | − | 0.178008i | ||||
\(619\) | − | 18.0967i | − | 0.727366i | −0.931523 | − | 0.363683i | \(-0.881519\pi\) | ||
0.931523 | − | 0.363683i | \(-0.118481\pi\) | |||||||
\(620\) | 4.83278 | − | 2.79020i | 0.194089 | − | 0.112057i | ||||
\(621\) | −25.2194 | + | 31.1275i | −1.01202 | + | 1.24910i | ||||
\(622\) | − | 20.1669i | − | 0.808618i | ||||||
\(623\) | 5.66215 | + | 36.2186i | 0.226849 | + | 1.45107i | ||||
\(624\) | −5.40682 | + | 1.65254i | −0.216446 | + | 0.0661546i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.33602 | − | 5.77815i | 0.133334 | − | 0.230941i | ||||
\(627\) | 11.3538 | + | 37.1476i | 0.453427 | + | 1.48353i | ||||
\(628\) | 14.5468 | − | 8.39860i | 0.580481 | − | 0.335141i | ||||
\(629\) | −10.0568 | −0.400991 | ||||||||
\(630\) | −7.58539 | − | 2.33708i | −0.302209 | − | 0.0931114i | ||||
\(631\) | 8.36756 | 0.333107 | 0.166554 | − | 0.986032i | \(-0.446736\pi\) | ||||
0.166554 | + | 0.986032i | \(0.446736\pi\) | |||||||
\(632\) | −1.59476 | + | 0.920736i | −0.0634362 | + | 0.0366249i | ||||
\(633\) | 10.5007 | + | 2.42519i | 0.417365 | + | 0.0963928i | ||||
\(634\) | −12.7708 | + | 22.1197i | −0.507193 | + | 0.878484i | ||||
\(635\) | −20.5777 | −0.816602 | ||||||||
\(636\) | −12.9043 | − | 12.0355i | −0.511689 | − | 0.477237i | ||||
\(637\) | 6.97372 | + | 21.7590i | 0.276309 | + | 0.862124i | ||||
\(638\) | 18.7453i | 0.742132i | ||||||||
\(639\) | −8.22896 | + | 0.574057i | −0.325533 | + | 0.0227093i | ||||
\(640\) | −0.866025 | + | 0.500000i | −0.0342327 | + | 0.0197642i | ||||
\(641\) | 17.2032i | 0.679485i | 0.940518 | + | 0.339743i | \(0.110340\pi\) | ||||
−0.940518 | + | 0.339743i | \(0.889660\pi\) | |||||||
\(642\) | −7.55127 | + | 8.09640i | −0.298025 | + | 0.319539i | ||||
\(643\) | −33.1046 | + | 19.1129i | −1.30552 | + | 0.753740i | −0.981344 | − | 0.192258i | \(-0.938419\pi\) |
−0.324172 | + | 0.945998i | \(0.605086\pi\) | |||||||
\(644\) | 20.1536 | − | 3.15067i | 0.794164 | − | 0.124154i | ||||
\(645\) | −5.16687 | − | 16.9051i | −0.203445 | − | 0.665636i | ||||
\(646\) | 2.81872 | + | 4.88217i | 0.110901 | + | 0.192086i | ||||
\(647\) | −7.26184 | − | 12.5779i | −0.285492 | − | 0.494487i | 0.687236 | − | 0.726434i | \(-0.258824\pi\) |
−0.972728 | + | 0.231947i | \(0.925490\pi\) | |||||||
\(648\) | −1.24961 | − | 8.91283i | −0.0490893 | − | 0.350129i | ||||
\(649\) | −11.6755 | − | 6.74088i | −0.458305 | − | 0.264603i | ||||
\(650\) | 1.63209 | − | 2.82686i | 0.0640158 | − | 0.110879i | ||||
\(651\) | 14.3442 | − | 21.1708i | 0.562194 | − | 0.829750i | ||||
\(652\) | −0.864749 | − | 1.49779i | −0.0338662 | − | 0.0586580i | ||||
\(653\) | − | 20.8516i | − | 0.815987i | −0.912985 | − | 0.407994i | \(-0.866229\pi\) | ||
0.912985 | − | 0.407994i | \(-0.133771\pi\) | |||||||
\(654\) | 2.03959 | − | 0.623381i | 0.0797543 | − | 0.0243761i | ||||
\(655\) | −5.00917 | −0.195725 | ||||||||
\(656\) | −5.16567 | + | 8.94721i | −0.201686 | + | 0.349330i | ||||
\(657\) | 24.6996 | + | 36.6317i | 0.963622 | + | 1.42914i | ||||
\(658\) | 12.3884 | − | 1.93672i | 0.482952 | − | 0.0755011i | ||||
\(659\) | −19.3743 | − | 11.1857i | −0.754715 | − | 0.435735i | 0.0726801 | − | 0.997355i | \(-0.476845\pi\) |
−0.827395 | + | 0.561621i | \(0.810178\pi\) | |||||||
\(660\) | 6.55415 | − | 2.00321i | 0.255120 | − | 0.0779750i | ||||
\(661\) | −38.5676 | − | 22.2670i | −1.50011 | − | 0.866086i | −1.00000 | 0.000121967i | \(-0.999961\pi\) | |
−0.500106 | − | 0.865964i | \(-0.666705\pi\) | |||||||
\(662\) | 1.56991 | + | 0.906390i | 0.0610164 | + | 0.0352279i | ||||
\(663\) | 5.37786 | − | 1.64369i | 0.208859 | − | 0.0638357i | ||||
\(664\) | 1.36802 | + | 0.789829i | 0.0530896 | + | 0.0306513i | ||||
\(665\) | 14.8156 | − | 2.31617i | 0.574526 | − | 0.0898171i | ||||
\(666\) | −30.2593 | + | 2.11091i | −1.17252 | + | 0.0817960i | ||||
\(667\) | 18.2625 | − | 31.6316i | 0.707126 | − | 1.22478i | ||||
\(668\) | −0.742044 | −0.0287105 | ||||||||
\(669\) | 8.36027 | − | 2.55524i | 0.323227 | − | 0.0987911i | ||||
\(670\) | 9.22190i | 0.356273i | ||||||||
\(671\) | 12.4628 | + | 21.5863i | 0.481123 | + | 0.833329i | ||||
\(672\) | −2.57046 | + | 3.79378i | −0.0991576 | + | 0.146348i | ||||
\(673\) | −2.10536 | + | 3.64659i | −0.0811557 | + | 0.140566i | −0.903747 | − | 0.428068i | \(-0.859194\pi\) |
0.822591 | + | 0.568634i | \(0.192528\pi\) | |||||||
\(674\) | −12.3926 | − | 7.15488i | −0.477346 | − | 0.275596i | ||||
\(675\) | 4.03736 | + | 3.27105i | 0.155398 | + | 0.125903i | ||||
\(676\) | 1.17257 | + | 2.03096i | 0.0450990 | + | 0.0781138i | ||||
\(677\) | −19.8282 | − | 34.3434i | −0.762059 | − | 1.31992i | −0.941788 | − | 0.336209i | \(-0.890855\pi\) |
0.179729 | − | 0.983716i | \(-0.442478\pi\) | |||||||
\(678\) | 4.27919 | + | 14.0007i | 0.164341 | + | 0.537696i | ||||
\(679\) | 2.34521 | − | 0.366633i | 0.0900009 | − | 0.0140701i | ||||
\(680\) | 0.861388 | − | 0.497322i | 0.0330327 | − | 0.0190714i | ||||
\(681\) | 6.00086 | − | 6.43407i | 0.229953 | − | 0.246554i | ||||
\(682\) | 22.0808i | 0.845517i | ||||||||
\(683\) | 39.4682 | − | 22.7869i | 1.51021 | − | 0.871918i | 0.510278 | − | 0.860010i | \(-0.329543\pi\) |
0.999929 | − | 0.0119087i | \(-0.00379073\pi\) | |||||||
\(684\) | 9.50585 | + | 14.0980i | 0.363465 | + | 0.539052i | ||||
\(685\) | − | 9.23672i | − | 0.352917i | ||||||
\(686\) | 15.4715 | + | 10.1800i | 0.590706 | + | 0.388673i | ||||
\(687\) | −37.5635 | − | 35.0343i | −1.43314 | − | 1.33664i | ||||
\(688\) | −10.2058 | −0.389094 | ||||||||
\(689\) | 16.6274 | − | 28.7995i | 0.633453 | − | 1.09717i | ||||
\(690\) | −13.0114 | − | 3.00505i | −0.495335 | − | 0.114400i | ||||
\(691\) | −17.0955 | + | 9.87010i | −0.650344 | + | 0.375476i | −0.788588 | − | 0.614922i | \(-0.789187\pi\) |
0.138244 | + | 0.990398i | \(0.455854\pi\) | |||||||
\(692\) | 0.964238 | 0.0366548 | ||||||||
\(693\) | 23.0156 | − | 21.3693i | 0.874291 | − | 0.811753i | ||||
\(694\) | 6.00500 | 0.227947 | ||||||||
\(695\) | 11.2919 | − | 6.51936i | 0.428325 | − | 0.247293i | ||||
\(696\) | 2.39840 | + | 7.84713i | 0.0909110 | + | 0.297445i | ||||
\(697\) | 5.13801 | − | 8.89930i | 0.194616 | − | 0.337085i | ||||
\(698\) | 13.4127 | 0.507677 | ||||||||
\(699\) | 30.3003 | − | 9.26100i | 1.14606 | − | 0.350283i | ||||
\(700\) | −0.408654 | − | 2.61400i | −0.0154457 | − | 0.0988000i | ||||
\(701\) | 13.6845i | 0.516855i | 0.966031 | + | 0.258427i | \(0.0832043\pi\) | ||||
−0.966031 | + | 0.258427i | \(0.916796\pi\) | |||||||
\(702\) | 15.8361 | − | 6.07441i | 0.597696 | − | 0.229264i | ||||
\(703\) | 49.6292 | − | 28.6534i | 1.87180 | − | 1.08068i | ||||
\(704\) | − | 3.95684i | − | 0.149129i | ||||||
\(705\) | −7.99811 | − | 1.84721i | −0.301226 | − | 0.0695698i | ||||
\(706\) | 0.437675 | − | 0.252692i | 0.0164721 | − | 0.00951017i | ||||
\(707\) | −0.444216 | + | 0.358249i | −0.0167065 | + | 0.0134733i | ||||
\(708\) | −5.75008 | − | 1.32801i | −0.216101 | − | 0.0499098i | ||||
\(709\) | 3.49061 | + | 6.04592i | 0.131093 | + | 0.227059i | 0.924098 | − | 0.382155i | \(-0.124818\pi\) |
−0.793005 | + | 0.609215i | \(0.791485\pi\) | |||||||
\(710\) | −1.37483 | − | 2.38127i | −0.0515963 | − | 0.0893675i | ||||
\(711\) | 4.58046 | − | 3.08846i | 0.171781 | − | 0.115826i | ||||
\(712\) | −11.9993 | − | 6.92781i | −0.449694 | − | 0.259631i | ||||
\(713\) | 21.5121 | − | 37.2601i | 0.805635 | − | 1.39540i | ||||
\(714\) | 2.55669 | − | 3.77346i | 0.0956819 | − | 0.141218i | ||||
\(715\) | 6.45792 | + | 11.1854i | 0.241512 | + | 0.418312i | ||||
\(716\) | 0.214781i | 0.00802676i | ||||||||
\(717\) | −2.72576 | + | 11.8021i | −0.101795 | + | 0.440757i | ||||
\(718\) | −13.0190 | −0.485866 | ||||||||
\(719\) | −7.49920 | + | 12.9890i | −0.279673 | + | 0.484408i | −0.971303 | − | 0.237844i | \(-0.923559\pi\) |
0.691630 | + | 0.722252i | \(0.256893\pi\) | |||||||
\(720\) | 2.48739 | − | 1.67717i | 0.0926996 | − | 0.0625043i | ||||
\(721\) | −18.8571 | − | 23.3821i | −0.702273 | − | 0.870795i | ||||
\(722\) | −11.3657 | − | 6.56197i | −0.422986 | − | 0.244211i | ||||
\(723\) | 6.98663 | + | 6.51622i | 0.259835 | + | 0.242341i | ||||
\(724\) | 9.67842 | + | 5.58784i | 0.359696 | + | 0.207670i | ||||
\(725\) | −4.10273 | − | 2.36871i | −0.152372 | − | 0.0879718i | ||||
\(726\) | −1.81499 | + | 7.85860i | −0.0673604 | + | 0.291660i | ||||
\(727\) | 22.4642 | + | 12.9697i | 0.833152 | + | 0.481020i | 0.854931 | − | 0.518742i | \(-0.173600\pi\) |
−0.0217788 | + | 0.999763i | \(0.506933\pi\) | |||||||
\(728\) | −8.05637 | − | 3.11107i | −0.298589 | − | 0.115304i | ||||
\(729\) | 5.60051 | + | 26.4128i | 0.207426 | + | 0.978251i | ||||
\(730\) | −7.36348 | + | 12.7539i | −0.272534 | + | 0.472044i | ||||
\(731\) | 10.1512 | 0.375455 | ||||||||
\(732\) | 7.97908 | + | 7.44185i | 0.294915 | + | 0.275059i | ||||
\(733\) | − | 22.7143i | − | 0.838973i | −0.907762 | − | 0.419486i | \(-0.862210\pi\) | ||
0.907762 | − | 0.419486i | \(-0.137790\pi\) | |||||||
\(734\) | −16.0143 | − | 27.7376i | −0.591100 | − | 1.02382i | ||||
\(735\) | −6.91359 | − | 9.96003i | −0.255012 | − | 0.367381i | ||||
\(736\) | −3.85494 | + | 6.67695i | −0.142095 | + | 0.246116i | ||||
\(737\) | −31.6009 | − | 18.2448i | −1.16404 | − | 0.672056i | ||||
\(738\) | 13.5915 | − | 27.8550i | 0.500310 | − | 1.02536i | ||||
\(739\) | −6.74623 | − | 11.6848i | −0.248164 | − | 0.429833i | 0.714852 | − | 0.699275i | \(-0.246494\pi\) |
−0.963016 | + | 0.269443i | \(0.913161\pi\) | |||||||
\(740\) | −5.05548 | − | 8.75634i | −0.185843 | − | 0.321890i | ||||
\(741\) | −21.8560 | + | 23.4338i | −0.802900 | + | 0.860862i | ||||
\(742\) | −4.16328 | − | 26.6309i | −0.152839 | − | 0.977652i | ||||
\(743\) | −32.3371 | + | 18.6698i | −1.18633 | + | 0.684930i | −0.957471 | − | 0.288529i | \(-0.906834\pi\) |
−0.228862 | + | 0.973459i | \(0.573500\pi\) | |||||||
\(744\) | 2.82517 | + | 9.24345i | 0.103576 | + | 0.338881i | ||||
\(745\) | − | 22.0661i | − | 0.808440i | ||||||
\(746\) | −5.88964 | + | 3.40038i | −0.215635 | + | 0.124497i | ||||
\(747\) | −4.25902 | − | 2.07813i | −0.155829 | − | 0.0760350i | ||||
\(748\) | 3.93565i | 0.143902i | ||||||||
\(749\) | −16.7087 | + | 2.61212i | −0.610523 | + | 0.0954447i | ||||
\(750\) | −0.389766 | + | 1.68763i | −0.0142323 | + | 0.0616234i | ||||
\(751\) | −30.6698 | −1.11916 | −0.559579 | − | 0.828777i | \(-0.689037\pi\) | ||||
−0.559579 | + | 0.828777i | \(0.689037\pi\) | |||||||
\(752\) | −2.36963 | + | 4.10432i | −0.0864116 | + | 0.149669i | ||||
\(753\) | −0.326485 | + | 0.350054i | −0.0118978 | + | 0.0127567i | ||||
\(754\) | −13.3920 | + | 7.73190i | −0.487710 | + | 0.281579i | ||||
\(755\) | −5.53782 | −0.201542 | ||||||||
\(756\) | 6.90064 | − | 11.8904i | 0.250974 | − | 0.432449i | ||||
\(757\) | −22.5697 | −0.820308 | −0.410154 | − | 0.912016i | \(-0.634525\pi\) | ||||
−0.410154 | + | 0.912016i | \(0.634525\pi\) | |||||||
\(758\) | −1.85889 | + | 1.07323i | −0.0675179 | + | 0.0389815i | ||||
\(759\) | 36.0395 | − | 38.6412i | 1.30815 | − | 1.40259i | ||||
\(760\) | −2.83390 | + | 4.90846i | −0.102796 | + | 0.178048i | ||||
\(761\) | 20.2312 | 0.733382 | 0.366691 | − | 0.930343i | \(-0.380491\pi\) | ||||
0.366691 | + | 0.930343i | \(0.380491\pi\) | |||||||
\(762\) | 8.02050 | − | 34.7275i | 0.290552 | − | 1.25804i | ||||
\(763\) | 3.03907 | + | 1.17358i | 0.110022 | + | 0.0424864i | ||||
\(764\) | − | 18.8822i | − | 0.683133i | ||||||
\(765\) | −2.47407 | + | 1.66819i | −0.0894502 | + | 0.0603134i | ||||
\(766\) | −0.615351 | + | 0.355273i | −0.0222335 | + | 0.0128365i | ||||
\(767\) | − | 11.1217i | − | 0.401582i | ||||||
\(768\) | −0.506266 | − | 1.65641i | −0.0182683 | − | 0.0597706i | ||||
\(769\) | −29.9888 | + | 17.3140i | −1.08142 | + | 0.624359i | −0.931280 | − | 0.364305i | \(-0.881307\pi\) |
−0.150143 | + | 0.988664i | \(0.547973\pi\) | |||||||
\(770\) | 9.76595 | + | 3.77125i | 0.351941 | + | 0.135906i | ||||
\(771\) | 19.4821 | − | 20.8885i | 0.701631 | − | 0.752282i | ||||
\(772\) | −2.94509 | − | 5.10105i | −0.105996 | − | 0.183591i | ||||
\(773\) | 9.02636 | + | 15.6341i | 0.324656 | + | 0.562320i | 0.981443 | − | 0.191756i | \(-0.0614183\pi\) |
−0.656787 | + | 0.754076i | \(0.728085\pi\) | |||||||
\(774\) | 30.5433 | − | 2.13072i | 1.09786 | − | 0.0765870i | ||||
\(775\) | −4.83278 | − | 2.79020i | −0.173598 | − | 0.100227i | ||||
\(776\) | −0.448586 | + | 0.776974i | −0.0161033 | + | 0.0278917i | ||||
\(777\) | −38.3587 | − | 25.9898i | −1.37611 | − | 0.932379i | ||||
\(778\) | −9.80747 | − | 16.9870i | −0.351615 | − | 0.609015i | ||||
\(779\) | 58.5560i | 2.09799i | ||||||||
\(780\) | 4.13455 | + | 3.85617i | 0.148041 | + | 0.138073i | ||||
\(781\) | 10.8799 | 0.389315 | ||||||||
\(782\) | 3.83429 | − | 6.64119i | 0.137114 | − | 0.237488i | ||||
\(783\) | −8.81603 | − | 22.9836i | −0.315059 | − | 0.821366i | ||||
\(784\) | −6.66600 | + | 2.13644i | −0.238072 | + | 0.0763015i | ||||
\(785\) | −14.5468 | − | 8.39860i | −0.519198 | − | 0.299759i | ||||
\(786\) | 1.95241 | − | 8.45361i | 0.0696400 | − | 0.301530i | ||||
\(787\) | 1.54781 | + | 0.893627i | 0.0551734 | + | 0.0318544i | 0.527333 | − | 0.849659i | \(-0.323192\pi\) |
−0.472160 | + | 0.881513i | \(0.656525\pi\) | |||||||
\(788\) | −20.8527 | − | 12.0393i | −0.742846 | − | 0.428882i | ||||
\(789\) | 3.17837 | + | 2.96437i | 0.113153 | + | 0.105534i | ||||
\(790\) | 1.59476 | + | 0.920736i | 0.0567391 | + | 0.0327583i | ||||
\(791\) | −8.05601 | + | 20.8617i | −0.286439 | + | 0.741756i | ||||
\(792\) | 0.826087 | + | 11.8417i | 0.0293537 | + | 0.420778i | ||||
\(793\) | −10.2812 | + | 17.8075i | −0.365094 | + | 0.632362i | ||||
\(794\) | −23.9395 | −0.849580 | ||||||||
\(795\) | −3.97086 | + | 17.1932i | −0.140832 | + | 0.609780i | ||||
\(796\) | − | 15.2132i | − | 0.539216i | ||||||
\(797\) | 21.5468 | + | 37.3202i | 0.763227 | + | 1.32195i | 0.941179 | + | 0.337909i | \(0.109720\pi\) |
−0.177951 | + | 0.984039i | \(0.556947\pi\) | |||||||
\(798\) | −1.86581 | + | 25.9060i | −0.0660490 | + | 0.917063i | ||||
\(799\) | 2.35694 | − | 4.08234i | 0.0833826 | − | 0.144423i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 37.3570 | + | 18.2279i | 1.31995 | + | 0.644051i | ||||
\(802\) | 0.337812 | + | 0.585108i | 0.0119286 | + | 0.0206609i | ||||
\(803\) | −29.1361 | − | 50.4652i | −1.02819 | − | 1.78088i | ||||
\(804\) | −15.5631 | − | 3.59439i | −0.548869 | − | 0.126764i | ||||
\(805\) | −12.8054 | − | 15.8782i | −0.451330 | − | 0.559633i | ||||
\(806\) | −15.7750 | + | 9.10772i | −0.555652 | + | 0.320806i | ||||
\(807\) | 45.0945 | + | 10.4148i | 1.58740 | + | 0.366619i | ||||
\(808\) | − | 0.215695i | − | 0.00758812i | ||||||
\(809\) | −31.6514 | + | 18.2739i | −1.11280 | + | 0.642478i | −0.939554 | − | 0.342400i | \(-0.888760\pi\) |
−0.173250 | + | 0.984878i | \(0.555427\pi\) | |||||||
\(810\) | −7.09393 | + | 5.53861i | −0.249255 | + | 0.194607i | ||||
\(811\) | 0.856906i | 0.0300900i | 0.999887 | + | 0.0150450i | \(0.00478916\pi\) | ||||
−0.999887 | + | 0.0150450i | \(0.995211\pi\) | |||||||
\(812\) | −4.51523 | + | 11.6925i | −0.158453 | + | 0.410327i | ||||
\(813\) | −24.7689 | + | 7.57038i | −0.868684 | + | 0.265505i | ||||
\(814\) | 40.0074 | 1.40226 | ||||||||
\(815\) | −0.864749 | + | 1.49779i | −0.0302908 | + | 0.0524653i | ||||
\(816\) | 0.503554 | + | 1.64754i | 0.0176279 | + | 0.0576754i | ||||
\(817\) | −50.0949 | + | 28.9223i | −1.75260 | + | 1.01186i | ||||
\(818\) | 30.3557 | 1.06136 | ||||||||
\(819\) | 24.7600 | + | 7.62863i | 0.865186 | + | 0.266566i | ||||
\(820\) | 10.3313 | 0.360786 | ||||||||
\(821\) | −11.7056 | + | 6.75824i | −0.408529 | + | 0.235864i | −0.690157 | − | 0.723659i | \(-0.742459\pi\) |
0.281629 | + | 0.959523i | \(0.409125\pi\) | |||||||
\(822\) | 15.5881 | + | 3.60016i | 0.543699 | + | 0.125570i | ||||
\(823\) | 7.48663 | − | 12.9672i | 0.260968 | − | 0.452009i | −0.705532 | − | 0.708678i | \(-0.749292\pi\) |
0.966499 | + | 0.256669i | \(0.0826251\pi\) | |||||||
\(824\) | 11.3535 | 0.395517 | ||||||||
\(825\) | −5.01191 | − | 4.67446i | −0.174492 | − | 0.162744i | ||||
\(826\) | −5.65904 | − | 7.01701i | −0.196903 | − | 0.244153i | ||||
\(827\) | − | 14.6192i | − | 0.508361i | −0.967157 | − | 0.254180i | \(-0.918194\pi\) | ||
0.967157 | − | 0.254180i | \(-0.0818057\pi\) | |||||||
\(828\) | 10.1428 | − | 20.7871i | 0.352487 | − | 0.722401i | ||||
\(829\) | 3.40972 | − | 1.96860i | 0.118425 | − | 0.0683724i | −0.439618 | − | 0.898185i | \(-0.644886\pi\) |
0.558042 | + | 0.829813i | \(0.311553\pi\) | |||||||
\(830\) | − | 1.57966i | − | 0.0548308i | ||||||
\(831\) | 16.8099 | − | 18.0235i | 0.583130 | − | 0.625227i | ||||
\(832\) | 2.82686 | − | 1.63209i | 0.0980037 | − | 0.0565825i | ||||
\(833\) | 6.63031 | − | 2.12500i | 0.229726 | − | 0.0736269i | ||||
\(834\) | 6.60105 | + | 21.5975i | 0.228576 | + | 0.747859i | ||||
\(835\) | 0.371022 | + | 0.642629i | 0.0128397 | + | 0.0222391i | ||||
\(836\) | −11.2133 | − | 19.4220i | −0.387820 | − | 0.671724i | ||||
\(837\) | −10.3848 | − | 27.0733i | −0.358950 | − | 0.935790i | ||||
\(838\) | 10.1808 | + | 5.87786i | 0.351688 | + | 0.203047i | ||||
\(839\) | −16.9706 | + | 29.3940i | −0.585891 | + | 1.01479i | 0.408872 | + | 0.912592i | \(0.365922\pi\) |
−0.994764 | + | 0.102202i | \(0.967411\pi\) | |||||||
\(840\) | 4.57074 | + | 0.329195i | 0.157705 | + | 0.0113583i | ||||
\(841\) | −3.27839 | − | 5.67833i | −0.113048 | − | 0.195804i | ||||
\(842\) | 28.9113i | 0.996351i | ||||||||
\(843\) | −41.2346 | + | 12.6029i | −1.42019 | + | 0.434068i | ||||
\(844\) | −6.22217 | −0.214176 | ||||||||
\(845\) | 1.17257 | − | 2.03096i | 0.0403378 | − | 0.0698671i | ||||
\(846\) | 6.23478 | − | 12.7778i | 0.214356 | − | 0.439311i | ||||
\(847\) | −9.59010 | + | 7.73417i | −0.329520 | + | 0.265749i | ||||
\(848\) | 8.82289 | + | 5.09390i | 0.302979 | + | 0.174925i | ||||
\(849\) | −28.4566 | + | 8.69747i | −0.976627 | + | 0.298496i | ||||
\(850\) | −0.861388 | − | 0.497322i | −0.0295453 | − | 0.0170580i | ||||
\(851\) | −67.5103 | − | 38.9771i | −2.31422 | − | 1.33612i | ||||
\(852\) | 4.55456 | − | 1.39206i | 0.156037 | − | 0.0476910i | ||||
\(853\) | −27.7997 | − | 16.0501i | −0.951843 | − | 0.549547i | −0.0581898 | − | 0.998306i | \(-0.518533\pi\) |
−0.893653 | + | 0.448759i | \(0.851866\pi\) | |||||||
\(854\) | 2.57427 | + | 16.4666i | 0.0880896 | + | 0.563476i | ||||
\(855\) | 7.45633 | − | 15.2813i | 0.255001 | − | 0.522610i | ||||
\(856\) | 3.19600 | − | 5.53564i | 0.109237 | − | 0.189204i | ||||
\(857\) | −14.7405 | −0.503525 | −0.251763 | − | 0.967789i | \(-0.581010\pi\) | ||||
−0.251763 | + | 0.967789i | \(0.581010\pi\) | |||||||
\(858\) | −21.3939 | + | 6.53884i | −0.730376 | + | 0.223232i | ||||
\(859\) | − | 1.58168i | − | 0.0539661i | −0.999636 | − | 0.0269831i | \(-0.991410\pi\) | ||
0.999636 | − | 0.0269831i | \(-0.00859002\pi\) | |||||||
\(860\) | 5.10292 | + | 8.83852i | 0.174008 | + | 0.301391i | ||||
\(861\) | 42.5959 | − | 20.6656i | 1.45166 | − | 0.704280i | ||||
\(862\) | 9.97444 | − | 17.2762i | 0.339731 | − | 0.588431i | ||||
\(863\) | −5.03980 | − | 2.90973i | −0.171557 | − | 0.0990483i | 0.411763 | − | 0.911291i | \(-0.364913\pi\) |
−0.583320 | + | 0.812243i | \(0.698247\pi\) | |||||||
\(864\) | 1.86093 | + | 4.85149i | 0.0633101 | + | 0.165051i | ||||
\(865\) | −0.482119 | − | 0.835055i | −0.0163925 | − | 0.0283927i | ||||
\(866\) | −14.4078 | − | 24.9551i | −0.489598 | − | 0.848009i | ||||
\(867\) | 8.10566 | + | 26.5203i | 0.275283 | + | 0.900675i | ||||
\(868\) | −5.31867 | + | 13.7731i | −0.180527 | + | 0.467490i | ||||
\(869\) | −6.31022 | + | 3.64321i | −0.214060 | + | 0.123587i | ||||
\(870\) | 5.59661 | − | 6.00064i | 0.189743 | − | 0.203441i | ||||
\(871\) | − | 30.1019i | − | 1.01996i | ||||||
\(872\) | −1.06636 | + | 0.615666i | −0.0361117 | + | 0.0208491i | ||||
\(873\) | 1.18028 | − | 2.41892i | 0.0399465 | − | 0.0818682i | ||||
\(874\) | 43.6980i | 1.47811i | ||||||||
\(875\) | −2.05946 | + | 1.66090i | −0.0696226 | + | 0.0561488i | ||||
\(876\) | −18.6538 | − | 17.3978i | −0.630254 | − | 0.587819i | ||||
\(877\) | −48.1745 | −1.62674 | −0.813369 | − | 0.581748i | \(-0.802369\pi\) | ||||
−0.813369 | + | 0.581748i | \(0.802369\pi\) | |||||||
\(878\) | −4.08760 | + | 7.07993i | −0.137950 | + | 0.238936i | ||||
\(879\) | 13.4573 | + | 3.10804i | 0.453904 | + | 0.104832i | ||||
\(880\) | −3.42673 | + | 1.97842i | −0.115515 | + | 0.0666926i | ||||
\(881\) | 53.9354 | 1.81713 | 0.908566 | − | 0.417742i | \(-0.137178\pi\) | ||||
0.908566 | + | 0.417742i | \(0.137178\pi\) | |||||||
\(882\) | 19.5035 | − | 7.78548i | 0.656717 | − | 0.262151i | ||||
\(883\) | −42.9089 | −1.44400 | −0.722000 | − | 0.691893i | \(-0.756777\pi\) | ||||
−0.722000 | + | 0.691893i | \(0.756777\pi\) | |||||||
\(884\) | −2.81172 | + | 1.62335i | −0.0945684 | + | 0.0545991i | ||||
\(885\) | 1.72495 | + | 5.64373i | 0.0579835 | + | 0.189712i | ||||
\(886\) | 13.1350 | − | 22.7505i | 0.441279 | − | 0.764317i | ||||
\(887\) | 19.1085 | 0.641600 | 0.320800 | − | 0.947147i | \(-0.396048\pi\) | ||||
0.320800 | + | 0.947147i | \(0.396048\pi\) | |||||||
\(888\) | 16.7479 | − | 5.11883i | 0.562022 | − | 0.171777i | ||||
\(889\) | 42.3791 | − | 34.1776i | 1.42135 | − | 1.14628i | ||||
\(890\) | 13.8556i | 0.464442i | ||||||||
\(891\) | −4.94450 | − | 35.2666i | −0.165647 | − | 1.18148i | ||||
\(892\) | −4.37102 | + | 2.52361i | −0.146353 | + | 0.0844968i | ||||
\(893\) | 26.8612i | 0.898876i | ||||||||
\(894\) | 37.2394 | + | 8.60063i | 1.24547 | + | 0.287648i | ||||
\(895\) | 0.186006 | − | 0.107391i | 0.00621750 | − | 0.00358968i | ||||
\(896\) | 0.953096 | − | 2.46812i | 0.0318407 | − | 0.0824540i | ||||
\(897\) | 42.4715 | + | 9.80901i | 1.41808 | + | 0.327513i | ||||
\(898\) | 3.19845 | + | 5.53988i | 0.106734 | + | 0.184868i | ||||
\(899\) | 13.2184 | + | 22.8949i | 0.440858 | + | 0.763589i | ||||
\(900\) | −2.69616 | − | 1.31556i | −0.0898722 | − | 0.0438520i | ||||
\(901\) | −8.77564 | − | 5.06662i | −0.292359 | − | 0.168794i | ||||
\(902\) | −20.4398 | + | 35.4027i | −0.680570 | + | 1.17878i | ||||
\(903\) | 38.7187 | + | 26.2337i | 1.28848 | + | 0.873003i | ||||
\(904\) | −4.22623 | − | 7.32005i | −0.140562 | − | 0.243461i | ||||
\(905\) | − | 11.1757i | − | 0.371492i | ||||||
\(906\) | 2.15845 | − | 9.34577i | 0.0717099 | − | 0.310492i | ||||
\(907\) | −27.0455 | −0.898032 | −0.449016 | − | 0.893524i | \(-0.648225\pi\) | ||||
−0.449016 | + | 0.893524i | \(0.648225\pi\) | |||||||
\(908\) | −2.53981 | + | 4.39908i | −0.0842865 | + | 0.145989i | ||||
\(909\) | 0.0450316 | + | 0.645516i | 0.00149360 | + | 0.0214104i | ||||
\(910\) | 1.33392 | + | 8.53256i | 0.0442189 | + | 0.282852i | ||||
\(911\) | 4.11941 | + | 2.37834i | 0.136482 | + | 0.0787979i | 0.566686 | − | 0.823934i | \(-0.308225\pi\) |
−0.430204 | + | 0.902732i | \(0.641558\pi\) | |||||||
\(912\) | −7.17908 | − | 6.69571i | −0.237723 | − | 0.221717i | ||||
\(913\) | 5.41306 | + | 3.12523i | 0.179146 | + | 0.103430i | ||||
\(914\) | −8.94322 | − | 5.16337i | −0.295815 | − | 0.170789i | ||||
\(915\) | 2.45529 | − | 10.6310i | 0.0811693 | − | 0.351450i | ||||
\(916\) | 25.6828 | + | 14.8280i | 0.848582 | + | 0.489929i | ||||
\(917\) | 10.3162 | − | 8.31976i | 0.340671 | − | 0.274743i | ||||
\(918\) | −1.85096 | − | 4.82551i | −0.0610909 | − | 0.159265i | ||||
\(919\) | −17.3173 | + | 29.9945i | −0.571245 | + | 0.989426i | 0.425193 | + | 0.905103i | \(0.360206\pi\) |
−0.996438 | + | 0.0843232i | \(0.973127\pi\) | |||||||
\(920\) | 7.70987 | 0.254187 | ||||||||
\(921\) | −19.7173 | − | 18.3897i | −0.649706 | − | 0.605961i | ||||
\(922\) | 8.00758i | 0.263715i | ||||||||
\(923\) | 4.48768 | + | 7.77289i | 0.147714 | + | 0.255848i | ||||
\(924\) | −10.1709 | + | 15.0114i | −0.334598 | + | 0.493838i | ||||
\(925\) | −5.05548 | + | 8.75634i | −0.166223 | + | 0.287907i | ||||
\(926\) | −26.4770 | − | 15.2865i | −0.870089 | − | 0.502346i | ||||
\(927\) | −33.9779 | + | 2.37032i | −1.11598 | + | 0.0778514i | ||||
\(928\) | −2.36871 | − | 4.10273i | −0.0777569 | − | 0.134679i | ||||
\(929\) | −14.6395 | − | 25.3564i | −0.480307 | − | 0.831917i | 0.519437 | − | 0.854509i | \(-0.326142\pi\) |
−0.999745 | + | 0.0225917i | \(0.992808\pi\) | |||||||
\(930\) | 6.59247 | − | 7.06839i | 0.216176 | − | 0.231782i | ||||
\(931\) | −26.6653 | + | 29.3774i | −0.873921 | + | 0.962806i | ||||
\(932\) | −15.8420 | + | 9.14639i | −0.518922 | + | 0.299600i | ||||
\(933\) | −10.2098 | − | 33.4046i | −0.334254 | − | 1.09362i | ||||
\(934\) | 7.22034i | 0.236257i | ||||||||
\(935\) | 3.40837 | − | 1.96783i | 0.111466 | − | 0.0643548i | ||||
\(936\) | −8.11928 | + | 5.47457i | −0.265387 | + | 0.178942i | ||||
\(937\) | − | 25.3740i | − | 0.828932i | −0.910065 | − | 0.414466i | \(-0.863968\pi\) | ||
0.910065 | − | 0.414466i | \(-0.136032\pi\) | |||||||
\(938\) | −15.3167 | − | 18.9922i | −0.500108 | − | 0.620117i | ||||
\(939\) | 2.60053 | − | 11.2599i | 0.0848652 | − | 0.367453i | ||||
\(940\) | 4.73926 | 0.154578 | ||||||||
\(941\) | −6.09522 | + | 10.5572i | −0.198699 | + | 0.344156i | −0.948107 | − | 0.317952i | \(-0.897005\pi\) |
0.749408 | + | 0.662108i | \(0.230338\pi\) | |||||||
\(942\) | 19.8436 | − | 21.2761i | 0.646538 | − | 0.693212i | ||||
\(943\) | 68.9819 | − | 39.8267i | 2.24636 | − | 1.29694i | ||||
\(944\) | 3.40720 | 0.110895 | ||||||||
\(945\) | −13.7477 | − | 0.0309387i | −0.447212 | − | 0.00100644i | ||||
\(946\) | −40.3829 | −1.31296 | ||||||||
\(947\) | 14.1104 | − | 8.14666i | 0.458527 | − | 0.264731i | −0.252898 | − | 0.967493i | \(-0.581384\pi\) |
0.711425 | + | 0.702762i | \(0.248050\pi\) | |||||||
\(948\) | −2.17544 | + | 2.33249i | −0.0706551 | + | 0.0757558i | ||||
\(949\) | 24.0357 | − | 41.6310i | 0.780231 | − | 1.35140i | ||||
\(950\) | 5.66780 | 0.183888 | ||||||||
\(951\) | −9.95524 | + | 43.1046i | −0.322821 | + | 1.39776i | ||||
\(952\) | −0.947992 | + | 2.45490i | −0.0307246 | + | 0.0795638i | ||||
\(953\) | − | 58.2513i | − | 1.88695i | −0.331449 | − | 0.943473i | \(-0.607538\pi\) | ||
0.331449 | − | 0.943473i | \(-0.392462\pi\) | |||||||
\(954\) | −27.4680 | − | 13.4027i | −0.889309 | − | 0.433927i | ||||
\(955\) | −16.3524 | + | 9.44109i | −0.529153 | + | 0.305506i | ||||
\(956\) | − | 6.99331i | − | 0.226180i | ||||||
\(957\) | 9.49008 | + | 31.0498i | 0.306771 | + | 1.00370i | ||||
\(958\) | −15.8239 | + | 9.13594i | −0.511248 | + | 0.295169i | ||||
\(959\) | 15.3413 | + | 19.0227i | 0.495397 | + | 0.614275i | ||||
\(960\) | −1.18136 | + | 1.26664i | −0.0381282 | + | 0.0408808i | ||||
\(961\) | 0.0704801 | + | 0.122075i | 0.00227355 | + | 0.00393791i | ||||
\(962\) | 16.5020 | + | 28.5822i | 0.532045 | + | 0.921529i | ||||
\(963\) | −8.40907 | + | 17.2339i | −0.270978 | + | 0.555355i | ||||
\(964\) | −4.77687 | − | 2.75793i | −0.153853 | − | 0.0888269i | ||||
\(965\) | −2.94509 | + | 5.10105i | −0.0948058 | + | 0.164209i | ||||
\(966\) | 31.7876 | − | 15.4219i | 1.02275 | − | 0.496191i | ||||
\(967\) | 5.61342 | + | 9.72273i | 0.180515 | + | 0.312662i | 0.942056 | − | 0.335455i | \(-0.108890\pi\) |
−0.761541 | + | 0.648117i | \(0.775557\pi\) | |||||||
\(968\) | − | 4.65660i | − | 0.149669i | ||||||
\(969\) | 7.14064 | + | 6.65986i | 0.229390 | + | 0.213945i | ||||
\(970\) | 0.897172 | 0.0288065 | ||||||||
\(971\) | −8.18607 | + | 14.1787i | −0.262704 | + | 0.455016i | −0.966959 | − | 0.254930i | \(-0.917947\pi\) |
0.704256 | + | 0.709946i | \(0.251281\pi\) | |||||||
\(972\) | −6.58212 | − | 14.1307i | −0.211122 | − | 0.453241i | ||||
\(973\) | −12.4272 | + | 32.1811i | −0.398396 | + | 1.03168i | ||||
\(974\) | 33.4057 | + | 19.2868i | 1.07039 | + | 0.617988i | ||||
\(975\) | 1.27227 | − | 5.50871i | 0.0407451 | − | 0.176420i | ||||
\(976\) | −5.45543 | − | 3.14969i | −0.174624 | − | 0.100819i | ||||
\(977\) | −50.6299 | − | 29.2312i | −1.61979 | − | 0.935189i | −0.986972 | − | 0.160892i | \(-0.948563\pi\) |
−0.632823 | − | 0.774297i | \(-0.718104\pi\) | |||||||
\(978\) | −2.19066 | − | 2.04316i | −0.0700496 | − | 0.0653331i | ||||
\(979\) | −47.4794 | − | 27.4123i | −1.51745 | − | 0.876100i | ||||
\(980\) | 5.18322 | + | 4.70471i | 0.165572 | + | 0.150286i | ||||
\(981\) | 3.06280 | − | 2.06515i | 0.0977878 | − | 0.0659352i | ||||
\(982\) | −12.3235 | + | 21.3449i | −0.393258 | + | 0.681143i | ||||
\(983\) | −25.3666 | −0.809070 | −0.404535 | − | 0.914522i | \(-0.632567\pi\) | ||||
−0.404535 | + | 0.914522i | \(0.632567\pi\) | |||||||
\(984\) | −4.02681 | + | 17.4355i | −0.128370 | + | 0.555822i | ||||
\(985\) | 24.0786i | 0.767208i | ||||||||
\(986\) | 2.35603 | + | 4.08076i | 0.0750312 | + | 0.129958i | ||||
\(987\) | 19.5398 | − | 9.47984i | 0.621960 | − | 0.301747i | ||||
\(988\) | 9.25035 | − | 16.0221i | 0.294293 | − | 0.509730i | ||||
\(989\) | 68.1438 | + | 39.3429i | 2.16685 | + | 1.25103i | ||||
\(990\) | 9.84221 | − | 6.63629i | 0.312806 | − | 0.210915i | ||||
\(991\) | −11.2022 | − | 19.4028i | −0.355850 | − | 0.616349i | 0.631413 | − | 0.775446i | \(-0.282475\pi\) |
−0.987263 | + | 0.159097i | \(0.949142\pi\) | |||||||
\(992\) | −2.79020 | − | 4.83278i | −0.0885891 | − | 0.153441i | ||||
\(993\) | 3.05930 | + | 0.706561i | 0.0970838 | + | 0.0224220i | ||||
\(994\) | 6.78647 | + | 2.62069i | 0.215254 | + | 0.0831231i | ||||
\(995\) | −13.1750 | + | 7.60658i | −0.417675 | + | 0.241145i | ||||
\(996\) | 2.66587 | + | 0.615698i | 0.0844714 | + | 0.0195091i | ||||
\(997\) | − | 24.3980i | − | 0.772693i | −0.922354 | − | 0.386346i | \(-0.873737\pi\) | ||
0.922354 | − | 0.386346i | \(-0.126263\pi\) | |||||||
\(998\) | −9.10884 | + | 5.25899i | −0.288335 | + | 0.166470i | ||||
\(999\) | −49.0532 | + | 18.8158i | −1.55197 | + | 0.595305i |
(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 | 630.2.t.b.551.2 | yes | 28 | |
3.2 | odd | 2 | 1890.2.t.b.1601.9 | 28 | |||
7.3 | odd | 6 | 630.2.bk.b.101.1 | yes | 28 | ||
9.4 | even | 3 | 1890.2.bk.b.341.12 | 28 | |||
9.5 | odd | 6 | 630.2.bk.b.131.8 | yes | 28 | ||
21.17 | even | 6 | 1890.2.bk.b.521.12 | 28 | |||
63.31 | odd | 6 | 1890.2.t.b.1151.9 | 28 | |||
63.59 | even | 6 | inner | 630.2.t.b.311.2 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.b.311.2 | ✓ | 28 | 63.59 | even | 6 | inner | |
630.2.t.b.551.2 | yes | 28 | 1.1 | even | 1 | trivial | |
630.2.bk.b.101.1 | yes | 28 | 7.3 | odd | 6 | ||
630.2.bk.b.131.8 | yes | 28 | 9.5 | odd | 6 | ||
1890.2.t.b.1151.9 | 28 | 63.31 | odd | 6 | |||
1890.2.t.b.1601.9 | 28 | 3.2 | odd | 2 | |||
1890.2.bk.b.341.12 | 28 | 9.4 | even | 3 | |||
1890.2.bk.b.521.12 | 28 | 21.17 | even | 6 |