Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(451,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.451");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bj (of order \(6\), 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Relative dimension: | \(42\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 451.3 | ||
Character | \(\chi\) | \(=\) | 756.451 |
Dual form | 756.2.bj.b.523.4 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36675 | − | 0.363308i | −0.966439 | − | 0.256897i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.73601 | + | 0.993103i | 0.868007 | + | 0.496551i | ||||
\(5\) | −1.43430 | − | 0.828095i | −0.641439 | − | 0.370335i | 0.143729 | − | 0.989617i | \(-0.454091\pi\) |
−0.785169 | + | 0.619282i | \(0.787424\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.375983 | − | 2.61890i | −0.142108 | − | 0.989851i | ||||
\(8\) | −2.01190 | − | 1.98803i | −0.711313 | − | 0.702875i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.65948 | + | 1.65289i | 0.524774 | + | 0.522690i | ||||
\(11\) | −2.34869 | + | 1.35602i | −0.708157 | + | 0.408855i | −0.810378 | − | 0.585907i | \(-0.800738\pi\) |
0.102221 | + | 0.994762i | \(0.467405\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.25755 | + | 2.45810i | −1.18083 | + | 0.681753i | −0.956207 | − | 0.292692i | \(-0.905449\pi\) |
−0.224625 | + | 0.974445i | \(0.572116\pi\) | |||||||
\(14\) | −0.437592 | + | 3.71598i | −0.116952 | + | 0.993138i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.02749 | + | 3.44808i | 0.506874 | + | 0.862020i | ||||
\(17\) | 2.86290 | + | 1.65289i | 0.694354 | + | 0.400886i | 0.805241 | − | 0.592947i | \(-0.202036\pi\) |
−0.110887 | + | 0.993833i | \(0.535369\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.756379 | + | 1.31009i | 0.173525 | + | 0.300555i | 0.939650 | − | 0.342137i | \(-0.111151\pi\) |
−0.766125 | + | 0.642692i | \(0.777818\pi\) | |||||||
\(20\) | −1.66759 | − | 2.86199i | −0.372884 | − | 0.639961i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.70273 | − | 1.00004i | 0.789424 | − | 0.213209i | ||||
\(23\) | 3.45097 | + | 1.99242i | 0.719577 | + | 0.415448i | 0.814597 | − | 0.580028i | \(-0.196958\pi\) |
−0.0950202 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.12852 | − | 1.95465i | −0.225704 | − | 0.390930i | ||||
\(26\) | 6.71205 | − | 1.81280i | 1.31634 | − | 0.355520i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.94812 | − | 4.91984i | 0.368161 | − | 0.929762i | ||||
\(29\) | −3.66717 | + | 6.35172i | −0.680976 | + | 1.17948i | 0.293708 | + | 0.955895i | \(0.405111\pi\) |
−0.974683 | + | 0.223589i | \(0.928223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.31513 | 1.13423 | 0.567116 | − | 0.823638i | \(-0.308059\pi\) | ||||
0.567116 | + | 0.823638i | \(0.308059\pi\) | |||||||
\(32\) | −1.51836 | − | 5.44927i | −0.268412 | − | 0.963304i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.31236 | − | 3.29921i | −0.568064 | − | 0.565809i | ||||
\(35\) | −1.62942 | + | 4.06764i | −0.275423 | + | 0.687557i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.46089 | + | 7.72649i | 0.733366 | + | 1.27023i | 0.955436 | + | 0.295197i | \(0.0953853\pi\) |
−0.222070 | + | 0.975031i | \(0.571281\pi\) | |||||||
\(38\) | −0.557817 | − | 2.06536i | −0.0904898 | − | 0.335046i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.23939 | + | 4.51748i | 0.195965 | + | 0.714276i | ||||
\(41\) | −0.879545 | + | 0.507805i | −0.137362 | + | 0.0793059i | −0.567106 | − | 0.823645i | \(-0.691937\pi\) |
0.429744 | + | 0.902951i | \(0.358604\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.68989 | − | 3.28506i | −0.867701 | − | 0.500967i | −0.00111731 | − | 0.999999i | \(-0.500356\pi\) |
−0.866584 | + | 0.499032i | \(0.833689\pi\) | |||||||
\(44\) | −5.42403 | + | 0.0215753i | −0.817703 | + | 0.00325260i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.99275 | − | 3.97690i | −0.588699 | − | 0.586362i | ||||
\(47\) | 1.95291 | 0.284861 | 0.142430 | − | 0.989805i | \(-0.454508\pi\) | ||||
0.142430 | + | 0.989805i | \(0.454508\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.71727 | + | 1.96932i | −0.959611 | + | 0.281332i | ||||
\(50\) | 0.832263 | + | 3.08152i | 0.117700 | + | 0.435793i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.83231 | + | 0.0391102i | −1.36350 | + | 0.00542362i | ||||
\(53\) | −5.20840 | + | 9.02122i | −0.715429 | + | 1.23916i | 0.247365 | + | 0.968922i | \(0.420435\pi\) |
−0.962794 | + | 0.270237i | \(0.912898\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.49164 | 0.605653 | ||||||||
\(56\) | −4.45002 | + | 6.01642i | −0.594659 | + | 0.803978i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.31973 | − | 7.34891i | 0.961128 | − | 0.964959i | ||||
\(59\) | 6.50576 | 0.846978 | 0.423489 | − | 0.905901i | \(-0.360805\pi\) | ||||
0.423489 | + | 0.905901i | \(0.360805\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3099i | 1.44809i | 0.689755 | + | 0.724043i | \(0.257718\pi\) | ||||
−0.689755 | + | 0.724043i | \(0.742282\pi\) | |||||||
\(62\) | −8.63121 | − | 2.29434i | −1.09617 | − | 0.291381i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.0954627 | + | 7.99943i | 0.0119328 | + | 0.999929i | ||||
\(65\) | 8.14215 | 1.00991 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.23288i | − | 0.517128i | −0.965994 | − | 0.258564i | \(-0.916751\pi\) | ||
0.965994 | − | 0.258564i | \(-0.0832493\pi\) | |||||||
\(68\) | 3.32854 | + | 5.71260i | 0.403644 | + | 0.692754i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.70482 | − | 4.96747i | 0.442811 | − | 0.593726i | ||||
\(71\) | 2.11040i | 0.250459i | 0.992128 | + | 0.125229i | \(0.0399666\pi\) | ||||
−0.992128 | + | 0.125229i | \(0.960033\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.56368 | − | 2.63484i | −0.534139 | − | 0.308385i | 0.208561 | − | 0.978009i | \(-0.433122\pi\) |
−0.742700 | + | 0.669624i | \(0.766455\pi\) | |||||||
\(74\) | −3.28983 | − | 12.1809i | −0.382435 | − | 1.41600i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.0120346 | + | 3.02549i | 0.00138046 | + | 0.347048i | ||||
\(77\) | 4.43434 | + | 5.64115i | 0.505340 | + | 0.642868i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.2086i | 1.71110i | 0.517717 | + | 0.855552i | \(0.326782\pi\) | ||||
−0.517717 | + | 0.855552i | \(0.673218\pi\) | |||||||
\(80\) | −0.0527021 | − | 6.62455i | −0.00589228 | − | 0.740647i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.38661 | − | 0.374498i | 0.153125 | − | 0.0413564i | ||||
\(83\) | 7.30362 | − | 12.6502i | 0.801676 | − | 1.38854i | −0.116836 | − | 0.993151i | \(-0.537275\pi\) |
0.918512 | − | 0.395393i | \(-0.129391\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.73751 | − | 4.74150i | −0.296924 | − | 0.514288i | ||||
\(86\) | 6.58318 | + | 6.55704i | 0.709882 | + | 0.707064i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.42113 | + | 1.94110i | 0.791095 | + | 0.206922i | ||||
\(89\) | −4.61689 | + | 2.66556i | −0.489389 | + | 0.282549i | −0.724321 | − | 0.689463i | \(-0.757847\pi\) |
0.234932 | + | 0.972012i | \(0.424513\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.03827 | + | 10.2259i | 0.842640 | + | 1.07196i | ||||
\(92\) | 4.01226 | + | 6.88603i | 0.418307 | + | 0.717918i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.66914 | − | 0.709507i | −0.275301 | − | 0.0731800i | ||||
\(95\) | − | 2.50541i | − | 0.257050i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.20504 | − | 2.42778i | −0.426957 | − | 0.246504i | 0.271092 | − | 0.962553i | \(-0.412615\pi\) |
−0.698049 | + | 0.716050i | \(0.745948\pi\) | |||||||
\(98\) | 9.89631 | − | 0.251133i | 0.999678 | − | 0.0253683i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.0179556 | − | 4.51404i | −0.00179556 | − | 0.451404i | ||||
\(101\) | −2.44236 | + | 1.41010i | −0.243024 | + | 0.140310i | −0.616566 | − | 0.787303i | \(-0.711477\pi\) |
0.373542 | + | 0.927613i | \(0.378143\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.797304 | − | 1.38097i | 0.0785607 | − | 0.136071i | −0.824068 | − | 0.566490i | \(-0.808301\pi\) |
0.902629 | + | 0.430419i | \(0.141634\pi\) | |||||||
\(104\) | 13.4525 | + | 3.51870i | 1.31913 | + | 0.345037i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.3961 | − | 10.4375i | 1.00976 | − | 1.01378i | ||||
\(107\) | −4.75730 | + | 2.74663i | −0.459906 | + | 0.265527i | −0.712005 | − | 0.702175i | \(-0.752213\pi\) |
0.252099 | + | 0.967701i | \(0.418879\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.81189 | + | 11.7985i | −0.652461 | + | 1.13010i | 0.330063 | + | 0.943959i | \(0.392930\pi\) |
−0.982524 | + | 0.186136i | \(0.940403\pi\) | |||||||
\(110\) | −6.13896 | − | 1.63185i | −0.585326 | − | 0.155591i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.26788 | − | 6.60622i | 0.781241 | − | 0.624230i | ||||
\(113\) | 0.261159 | + | 0.452340i | 0.0245677 | + | 0.0425526i | 0.878048 | − | 0.478573i | \(-0.158846\pi\) |
−0.853480 | + | 0.521125i | \(0.825512\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.29982 | − | 5.71546i | −0.307710 | − | 0.532969i | ||||
\(116\) | −12.6742 | + | 7.38481i | −1.17677 | + | 0.685662i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.89175 | − | 2.36359i | −0.818552 | − | 0.217586i | ||||
\(119\) | 3.25236 | − | 8.11910i | 0.298144 | − | 0.744276i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.82244 | + | 3.15655i | −0.165676 | + | 0.286959i | ||||
\(122\) | 4.10898 | − | 15.4578i | 0.372010 | − | 1.39949i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.9632 | + | 6.27158i | 0.984521 | + | 0.563204i | ||||
\(125\) | 12.0190i | 1.07501i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.34549i | 0.740543i | 0.928924 | + | 0.370271i | \(0.120735\pi\) | ||||
−0.928924 | + | 0.370271i | \(0.879265\pi\) | |||||||
\(128\) | 2.77578 | − | 10.9679i | 0.245347 | − | 0.969435i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.1283 | − | 2.95811i | −0.976015 | − | 0.259443i | ||||
\(131\) | −8.56896 | + | 14.8419i | −0.748673 | + | 1.29674i | 0.199786 | + | 0.979840i | \(0.435975\pi\) |
−0.948459 | + | 0.316900i | \(0.897358\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.14660 | − | 2.47345i | 0.272845 | − | 0.214475i | ||||
\(134\) | −1.53784 | + | 5.78529i | −0.132849 | + | 0.499773i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.47385 | − | 9.01698i | −0.212131 | − | 0.773200i | ||||
\(137\) | −0.0749253 | − | 0.129774i | −0.00640130 | − | 0.0110874i | 0.862807 | − | 0.505533i | \(-0.168704\pi\) |
−0.869208 | + | 0.494446i | \(0.835371\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.06467 | − | 10.5043i | −0.514399 | − | 0.890965i | −0.999860 | − | 0.0167067i | \(-0.994682\pi\) |
0.485462 | − | 0.874258i | \(-0.338651\pi\) | |||||||
\(140\) | −6.86829 | + | 5.44330i | −0.580477 | + | 0.460043i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.766725 | − | 2.88439i | 0.0643422 | − | 0.242053i | ||||
\(143\) | 6.66644 | − | 11.5466i | 0.557476 | − | 0.965577i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.5197 | − | 6.07352i | 0.873609 | − | 0.504379i | ||||
\(146\) | 5.28016 | + | 5.25920i | 0.436989 | + | 0.435254i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.0709763 | + | 17.8434i | 0.00583422 | + | 1.46672i | ||||
\(149\) | 8.27619 | − | 14.3348i | 0.678012 | − | 1.17435i | −0.297567 | − | 0.954701i | \(-0.596175\pi\) |
0.975579 | − | 0.219650i | \(-0.0704916\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.7206 | + | 8.49894i | −1.19794 | + | 0.691634i | −0.960097 | − | 0.279669i | \(-0.909775\pi\) |
−0.237848 | + | 0.971302i | \(0.576442\pi\) | |||||||
\(152\) | 1.08274 | − | 4.13947i | 0.0878216 | − | 0.335755i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.01116 | − | 9.32107i | −0.323229 | − | 0.751113i | ||||
\(155\) | −9.05781 | − | 5.22953i | −0.727541 | − | 0.420046i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 15.1129i | − | 1.20614i | −0.797687 | − | 0.603071i | \(-0.793943\pi\) | ||
0.797687 | − | 0.603071i | \(-0.206057\pi\) | |||||||
\(158\) | 5.52541 | − | 20.7864i | 0.439578 | − | 1.65368i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.33472 | + | 9.07325i | −0.184576 | + | 0.717304i | ||||
\(161\) | 3.92044 | − | 9.78686i | 0.308974 | − | 0.771312i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.13064 | + | 2.96218i | −0.401863 | + | 0.232015i | −0.687287 | − | 0.726386i | \(-0.741199\pi\) |
0.285425 | + | 0.958401i | \(0.407865\pi\) | |||||||
\(164\) | −2.03121 | + | 0.00807958i | −0.158610 | + | 0.000630909i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.5782 | + | 14.6363i | −1.13148 | + | 1.13599i | ||||
\(167\) | −8.25628 | − | 14.3003i | −0.638890 | − | 1.10659i | −0.985677 | − | 0.168646i | \(-0.946061\pi\) |
0.346787 | − | 0.937944i | \(-0.387273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.58448 | − | 9.67261i | 0.429576 | − | 0.744047i | ||||
\(170\) | 2.01886 | + | 7.47500i | 0.154840 | + | 0.573307i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.61534 | − | 11.3536i | −0.504415 | − | 0.865701i | ||||
\(173\) | − | 16.2245i | − | 1.23353i | −0.787148 | − | 0.616764i | \(-0.788443\pi\) | ||
0.787148 | − | 0.616764i | \(-0.211557\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.69473 | + | 3.69039i | −0.354888 | + | 0.278967i | ||||
\(176\) | −9.43762 | − | 5.34916i | −0.711387 | − | 0.403208i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.27856 | − | 1.96581i | 0.545551 | − | 0.147343i | ||||
\(179\) | −15.1520 | − | 8.74799i | −1.13251 | − | 0.653855i | −0.187945 | − | 0.982180i | \(-0.560183\pi\) |
−0.944565 | + | 0.328324i | \(0.893516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.17571i | − | 0.682025i | −0.940059 | − | 0.341013i | \(-0.889230\pi\) | ||
0.940059 | − | 0.341013i | \(-0.110770\pi\) | |||||||
\(182\) | −7.27117 | − | 16.8966i | −0.538975 | − | 1.25246i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.98201 | − | 10.8692i | −0.219836 | − | 0.801286i | ||||
\(185\) | − | 14.7762i | − | 1.08637i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.96541 | −0.655616 | ||||||||
\(188\) | 3.39028 | + | 1.93944i | 0.247261 | + | 0.141448i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.910237 | + | 3.42428i | −0.0660355 | + | 0.248423i | ||||
\(191\) | − | 0.746176i | − | 0.0539914i | −0.999636 | − | 0.0269957i | \(-0.991406\pi\) | ||
0.999636 | − | 0.0269957i | \(-0.00859404\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.27175 | 0.379469 | 0.189734 | − | 0.981835i | \(-0.439237\pi\) | ||||
0.189734 | + | 0.981835i | \(0.439237\pi\) | |||||||
\(194\) | 4.86521 | + | 4.84590i | 0.349302 | + | 0.347915i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.6170 | − | 3.25217i | −0.972645 | − | 0.232298i | ||||
\(197\) | 12.9993 | 0.926162 | 0.463081 | − | 0.886316i | \(-0.346744\pi\) | ||||
0.463081 | + | 0.886316i | \(0.346744\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.92545 | − | 8.53113i | 0.349156 | − | 0.604756i | −0.636944 | − | 0.770910i | \(-0.719802\pi\) |
0.986100 | + | 0.166154i | \(0.0531350\pi\) | |||||||
\(200\) | −1.61544 | + | 6.17609i | −0.114229 | + | 0.436715i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.85040 | − | 1.03992i | 0.270913 | − | 0.0731687i | ||||
\(203\) | 18.0133 | + | 7.21581i | 1.26429 | + | 0.506450i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.68204 | 0.117479 | ||||||||
\(206\) | −1.59143 | + | 1.59778i | −0.110880 | + | 0.111322i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −17.1079 | − | 9.69660i | −1.18622 | − | 0.672338i | ||||
\(209\) | −3.55300 | − | 2.05133i | −0.245766 | − | 0.141893i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.4282 | − | 11.7942i | 1.40633 | − | 0.811946i | 0.411300 | − | 0.911500i | \(-0.365075\pi\) |
0.995032 | + | 0.0995535i | \(0.0317414\pi\) | |||||||
\(212\) | −18.0009 | + | 10.4885i | −1.23630 | + | 0.720352i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.49992 | − | 2.02559i | 0.512684 | − | 0.138467i | ||||
\(215\) | 5.44069 | + | 9.42354i | 0.371052 | + | 0.642680i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.37438 | − | 16.5387i | −0.161183 | − | 1.12272i | ||||
\(218\) | 13.5967 | − | 13.6508i | 0.920882 | − | 0.924552i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.79756 | + | 4.46066i | 0.525711 | + | 0.300738i | ||||
\(221\) | −16.2519 | −1.09322 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.37545 | − | 4.11440i | 0.159072 | − | 0.275520i | −0.775462 | − | 0.631394i | \(-0.782483\pi\) |
0.934534 | + | 0.355873i | \(0.115817\pi\) | |||||||
\(224\) | −13.7002 | + | 6.02528i | −0.915384 | + | 0.402581i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.192600 | − | 0.713117i | −0.0128116 | − | 0.0474358i | ||||
\(227\) | 13.8419 | + | 23.9749i | 0.918720 | + | 1.59127i | 0.801361 | + | 0.598180i | \(0.204109\pi\) |
0.117359 | + | 0.993090i | \(0.462557\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.76512 | + | 5.06054i | 0.579215 | + | 0.334410i | 0.760822 | − | 0.648961i | \(-0.224796\pi\) |
−0.181606 | + | 0.983371i | \(0.558130\pi\) | |||||||
\(230\) | 2.43356 | + | 9.01046i | 0.160464 | + | 0.594132i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.0054 | − | 5.48856i | 1.31342 | − | 0.360342i | ||||
\(233\) | −6.75115 | − | 11.6933i | −0.442283 | − | 0.766056i | 0.555576 | − | 0.831466i | \(-0.312498\pi\) |
−0.997858 | + | 0.0654097i | \(0.979165\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.80106 | − | 1.61719i | −0.182721 | − | 0.105494i | ||||
\(236\) | 11.2941 | + | 6.46088i | 0.735183 | + | 0.420568i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.39490 | + | 9.91517i | −0.479340 | + | 0.642705i | ||||
\(239\) | −21.6423 | + | 12.4952i | −1.39992 | + | 0.808246i | −0.994384 | − | 0.105831i | \(-0.966250\pi\) |
−0.405540 | + | 0.914077i | \(0.632916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.04255 | + | 5.22072i | −0.582482 | + | 0.336296i | −0.762119 | − | 0.647437i | \(-0.775841\pi\) |
0.179637 | + | 0.983733i | \(0.442508\pi\) | |||||||
\(242\) | 3.63761 | − | 3.65211i | 0.233835 | − | 0.234767i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.2319 | + | 19.6342i | −0.719049 | + | 1.25695i | ||||
\(245\) | 11.2654 | + | 2.73794i | 0.719719 | + | 0.174920i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.44064 | − | 3.71851i | −0.409808 | − | 0.236603i | ||||
\(248\) | −12.7054 | − | 12.5547i | −0.806794 | − | 0.797223i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.36661 | − | 16.4270i | 0.276168 | − | 1.03894i | ||||
\(251\) | −4.59012 | −0.289726 | −0.144863 | − | 0.989452i | \(-0.546274\pi\) | ||||
−0.144863 | + | 0.989452i | \(0.546274\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.8070 | −0.679431 | ||||||||
\(254\) | 3.03198 | − | 11.4062i | 0.190244 | − | 0.715689i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.77853 | + | 13.9819i | −0.486158 | + | 0.873871i | ||||
\(257\) | 22.6947 | + | 13.1028i | 1.41566 | + | 0.817331i | 0.995914 | − | 0.0903116i | \(-0.0287863\pi\) |
0.419745 | + | 0.907642i | \(0.362120\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.5577 | − | 14.5877i | 1.15312 | − | 0.906433i | ||||
\(260\) | 14.1349 | + | 8.08599i | 0.876609 | + | 0.501472i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.1038 | − | 17.1720i | 1.05668 | − | 1.06089i | ||||
\(263\) | −5.13861 | + | 2.96678i | −0.316860 | + | 0.182939i | −0.649992 | − | 0.759941i | \(-0.725228\pi\) |
0.333132 | + | 0.942880i | \(0.391895\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.9408 | − | 8.62610i | 0.917809 | − | 0.529897i | ||||
\(266\) | −5.19924 | + | 2.23741i | −0.318786 | + | 0.137184i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.20368 | − | 7.34834i | 0.256781 | − | 0.448871i | ||||
\(269\) | 1.49698 | + | 0.864283i | 0.0912726 | + | 0.0526963i | 0.544942 | − | 0.838474i | \(-0.316552\pi\) |
−0.453669 | + | 0.891170i | \(0.649885\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.37150 | − | 5.83961i | −0.204804 | − | 0.354731i | 0.745266 | − | 0.666767i | \(-0.232322\pi\) |
−0.950070 | + | 0.312036i | \(0.898989\pi\) | |||||||
\(272\) | 0.105194 | + | 13.2227i | 0.00637835 | + | 0.801746i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.0552561 | + | 0.204590i | 0.00333814 | + | 0.0123597i | ||||
\(275\) | 5.30108 | + | 3.06058i | 0.319667 | + | 0.184560i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.53023 | + | 6.11454i | 0.212111 | + | 0.367387i | 0.952375 | − | 0.304929i | \(-0.0986328\pi\) |
−0.740264 | + | 0.672316i | \(0.765300\pi\) | |||||||
\(278\) | 4.47259 | + | 16.5601i | 0.268248 | + | 0.993210i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.3648 | − | 4.94433i | 0.679179 | − | 0.295480i | ||||
\(281\) | −0.814975 | + | 1.41158i | −0.0486174 | + | 0.0842077i | −0.889310 | − | 0.457305i | \(-0.848815\pi\) |
0.840693 | + | 0.541513i | \(0.182148\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.1027 | −1.49220 | −0.746101 | − | 0.665833i | \(-0.768076\pi\) | ||||
−0.746101 | + | 0.665833i | \(0.768076\pi\) | |||||||
\(284\) | −2.09584 | + | 3.66369i | −0.124366 | + | 0.217400i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.3063 | + | 13.3594i | −0.786821 | + | 0.789957i | ||||
\(287\) | 1.66058 | + | 2.11251i | 0.0980212 | + | 0.124698i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.03589 | − | 5.25831i | −0.178581 | − | 0.309312i | ||||
\(290\) | −16.5843 | + | 4.47912i | −0.973864 | + | 0.263023i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.30595 | − | 9.10633i | −0.310507 | − | 0.532908i | ||||
\(293\) | −17.8533 | + | 10.3076i | −1.04300 | + | 0.602175i | −0.920681 | − | 0.390316i | \(-0.872366\pi\) |
−0.122317 | + | 0.992491i | \(0.539033\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.33122 | − | 5.38738i | −0.543285 | − | 0.313666i | ||||
\(296\) | 6.38565 | − | 24.4133i | 0.371159 | − | 1.41899i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.5194 | + | 16.5853i | −0.956945 | + | 0.960759i | ||||
\(299\) | −19.5902 | −1.13293 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.46395 | + | 16.1364i | −0.372576 | + | 0.930086i | ||||
\(302\) | 23.2071 | − | 6.26782i | 1.33542 | − | 0.360673i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.98373 | + | 5.26425i | −0.171129 | + | 0.301926i | ||||
\(305\) | 9.36568 | − | 16.2218i | 0.536277 | − | 0.928860i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.7340 | 1.63993 | 0.819967 | − | 0.572410i | \(-0.193992\pi\) | ||||
0.819967 | + | 0.572410i | \(0.193992\pi\) | |||||||
\(308\) | 2.09584 | + | 14.1969i | 0.119422 | + | 0.808942i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.4798 | + | 10.4382i | 0.595215 | + | 0.592852i | ||||
\(311\) | 10.2429 | 0.580824 | 0.290412 | − | 0.956902i | \(-0.406208\pi\) | ||||
0.290412 | + | 0.956902i | \(0.406208\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.107424i | 0.00607194i | 0.999995 | + | 0.00303597i | \(0.000966381\pi\) | ||||
−0.999995 | + | 0.00303597i | \(0.999034\pi\) | |||||||
\(314\) | −5.49064 | + | 20.6556i | −0.309855 | + | 1.16566i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.1037 | + | 26.4024i | −0.849651 | + | 1.48525i | ||||
\(317\) | −14.3346 | −0.805113 | −0.402556 | − | 0.915395i | \(-0.631878\pi\) | ||||
−0.402556 | + | 0.915395i | \(0.631878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 19.8910i | − | 1.11368i | ||||||
\(320\) | 6.48736 | − | 11.5527i | 0.362655 | − | 0.645813i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.91390 | + | 11.9519i | −0.496752 | + | 0.666051i | ||||
\(323\) | 5.00086i | 0.278255i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.60944 | + | 5.54801i | 0.533036 | + | 0.307748i | ||||
\(326\) | 8.08848 | − | 2.18455i | 0.447980 | − | 0.120991i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.77909 | + | 0.726910i | 0.153449 | + | 0.0401369i | ||||
\(329\) | −0.734259 | − | 5.11447i | −0.0404810 | − | 0.281970i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.9762i | 0.768202i | 0.923291 | + | 0.384101i | \(0.125489\pi\) | ||||
−0.923291 | + | 0.384101i | \(0.874511\pi\) | |||||||
\(332\) | 25.2422 | − | 14.7078i | 1.38534 | − | 0.807193i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.08886 | + | 22.5445i | 0.333168 | + | 1.23358i | ||||
\(335\) | −3.50522 | + | 6.07123i | −0.191511 | + | 0.331706i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.48571 | + | 14.6977i | 0.462246 | + | 0.800634i | 0.999073 | − | 0.0430591i | \(-0.0137104\pi\) |
−0.536827 | + | 0.843693i | \(0.680377\pi\) | |||||||
\(338\) | −11.1467 | + | 11.1912i | −0.606302 | + | 0.608719i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.0435559 | − | 10.9499i | −0.00236215 | − | 0.593844i | ||||
\(341\) | −14.8323 | + | 8.56343i | −0.803214 | + | 0.463736i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.68303 | + | 16.8514i | 0.414845 | + | 0.909892i | ||||
\(344\) | 4.91668 | + | 17.9209i | 0.265090 | + | 0.966230i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.89449 | + | 22.1749i | −0.316890 | + | 1.19213i | ||||
\(347\) | − | 17.6139i | − | 0.945561i | −0.881180 | − | 0.472781i | \(-0.843250\pi\) | ||
0.881180 | − | 0.472781i | \(-0.156750\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.0589 | + | 13.8904i | 1.28785 | + | 0.743538i | 0.978270 | − | 0.207337i | \(-0.0664796\pi\) |
0.309576 | + | 0.950875i | \(0.399813\pi\) | |||||||
\(350\) | 7.75727 | − | 3.33821i | 0.414644 | − | 0.178435i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.9555 | + | 10.7397i | 0.583929 | + | 0.572429i | ||||
\(353\) | −17.6109 | + | 10.1677i | −0.937335 | + | 0.541170i | −0.889124 | − | 0.457667i | \(-0.848685\pi\) |
−0.0482109 | + | 0.998837i | \(0.515352\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.74761 | − | 3.02695i | 0.0927536 | − | 0.160654i | ||||
\(356\) | −10.6622 | + | 0.0424112i | −0.565094 | + | 0.00224779i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.5307 | + | 17.4611i | 0.926528 | + | 0.922850i | ||||
\(359\) | −9.00180 | + | 5.19719i | −0.475097 | + | 0.274297i | −0.718371 | − | 0.695660i | \(-0.755112\pi\) |
0.243274 | + | 0.969958i | \(0.421779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.35578 | − | 14.4726i | 0.439778 | − | 0.761718i | ||||
\(362\) | −3.33361 | + | 12.5409i | −0.175211 | + | 0.659136i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.79920 | + | 25.7351i | 0.199132 | + | 1.34889i | ||||
\(365\) | 4.36380 | + | 7.55833i | 0.228412 | + | 0.395621i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.21836 | + | 10.7705i | 0.324596 | + | 0.562216i | 0.981430 | − | 0.191818i | \(-0.0614385\pi\) |
−0.656835 | + | 0.754034i | \(0.728105\pi\) | |||||||
\(368\) | 0.126803 | + | 15.9388i | 0.00661005 | + | 0.830869i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.36830 | + | 20.1953i | −0.279085 | + | 1.04991i | ||||
\(371\) | 25.5839 | + | 10.2485i | 1.32825 | + | 0.532074i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.52422 | + | 6.10412i | −0.182477 | + | 0.316059i | −0.942723 | − | 0.333575i | \(-0.891745\pi\) |
0.760246 | + | 0.649635i | \(0.225078\pi\) | |||||||
\(374\) | 12.2535 | + | 3.25720i | 0.633612 | + | 0.168426i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.92905 | − | 3.88244i | −0.202625 | − | 0.200222i | ||||
\(377\) | − | 36.0570i | − | 1.85703i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5.49479i | − | 0.282248i | −0.989992 | − | 0.141124i | \(-0.954928\pi\) | ||
0.989992 | − | 0.141124i | \(-0.0450717\pi\) | |||||||
\(380\) | 2.48813 | − | 4.34944i | 0.127639 | − | 0.223121i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.271092 | + | 1.01984i | −0.0138703 | + | 0.0521794i | ||||
\(383\) | 14.9307 | − | 25.8607i | 0.762923 | − | 1.32142i | −0.178414 | − | 0.983955i | \(-0.557097\pi\) |
0.941338 | − | 0.337466i | \(-0.109570\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.68878 | − | 11.7632i | −0.0860682 | − | 0.599506i | ||||
\(386\) | −7.20517 | − | 1.91527i | −0.366733 | − | 0.0974846i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.88898 | − | 8.39070i | −0.248200 | − | 0.425973i | ||||
\(389\) | −1.85969 | − | 3.22107i | −0.0942899 | − | 0.163315i | 0.815022 | − | 0.579430i | \(-0.196725\pi\) |
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.58651 | + | 11.4082i | 0.333094 | + | 0.576936i | ||||
\(392\) | 17.4295 | + | 9.39208i | 0.880325 | + | 0.474372i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.7668 | − | 4.72275i | −0.895079 | − | 0.237929i | ||||
\(395\) | 12.5942 | − | 21.8138i | 0.633682 | − | 1.09757i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.9038 | − | 9.18206i | 0.798189 | − | 0.460834i | −0.0446487 | − | 0.999003i | \(-0.514217\pi\) |
0.842837 | + | 0.538168i | \(0.180884\pi\) | |||||||
\(398\) | −9.83129 | + | 9.87047i | −0.492798 | + | 0.494762i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.45173 | − | 7.85427i | 0.222586 | − | 0.392713i | ||||
\(401\) | −12.0156 | + | 20.8116i | −0.600029 | + | 1.03928i | 0.392787 | + | 0.919629i | \(0.371511\pi\) |
−0.992816 | + | 0.119651i | \(0.961822\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.8870 | + | 15.5232i | −1.33934 | + | 0.773266i | ||||
\(404\) | −5.64035 | + | 0.0224358i | −0.280618 | + | 0.00111622i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.9981 | − | 16.4066i | −1.09175 | − | 0.814245i | ||||
\(407\) | −20.9545 | − | 12.0981i | −1.03868 | − | 0.599680i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.31574i | − | 0.163953i | −0.996634 | − | 0.0819764i | \(-0.973877\pi\) | ||
0.996634 | − | 0.0819764i | \(-0.0261232\pi\) | |||||||
\(410\) | −2.29893 | − | 0.611100i | −0.113536 | − | 0.0301801i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.75558 | − | 1.60558i | 0.135758 | − | 0.0791013i | ||||
\(413\) | −2.44605 | − | 17.0379i | −0.120362 | − | 0.838382i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.9512 | + | 12.0962i | −1.02845 | + | 0.593778i | ||||
\(416\) | 19.8594 | + | 19.4683i | 0.973685 | + | 0.954510i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.11080 | + | 4.09448i | 0.201066 | + | 0.200268i | ||||
\(419\) | −1.19685 | − | 2.07300i | −0.0584698 | − | 0.101273i | 0.835309 | − | 0.549781i | \(-0.185289\pi\) |
−0.893779 | + | 0.448508i | \(0.851955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.27117 | + | 5.66583i | −0.159427 | + | 0.276135i | −0.934662 | − | 0.355537i | \(-0.884298\pi\) |
0.775235 | + | 0.631673i | \(0.217631\pi\) | |||||||
\(422\) | −32.2051 | + | 8.69802i | −1.56772 | + | 0.423413i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 28.4132 | − | 7.79530i | 1.37987 | − | 0.378573i | ||||
\(425\) | − | 7.46128i | − | 0.361925i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.6195 | − | 4.25233i | 1.43339 | − | 0.205785i | ||||
\(428\) | −10.9864 | + | 0.0437010i | −0.531049 | + | 0.00211237i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.01241 | − | 14.8563i | −0.193496 | − | 0.716433i | ||||
\(431\) | 19.2653 | + | 11.1228i | 0.927978 | + | 0.535768i | 0.886172 | − | 0.463357i | \(-0.153355\pi\) |
0.0418066 | + | 0.999126i | \(0.486689\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.03561i | − | 0.241996i | −0.992653 | − | 0.120998i | \(-0.961391\pi\) | ||
0.992653 | − | 0.120998i | \(-0.0386094\pi\) | |||||||
\(434\) | −2.76346 | + | 23.4669i | −0.132650 | + | 1.12645i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.5427 | + | 13.7175i | −1.12749 | + | 0.656951i | ||||
\(437\) | 6.02809i | 0.288363i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.4591 | 0.785551 | 0.392776 | − | 0.919634i | \(-0.371515\pi\) | ||||
0.392776 | + | 0.919634i | \(0.371515\pi\) | |||||||
\(440\) | −9.03672 | − | 8.92953i | −0.430809 | − | 0.425698i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.2123 | + | 5.90444i | 1.05653 | + | 0.280846i | ||||
\(443\) | 26.8092i | 1.27374i | 0.770969 | + | 0.636872i | \(0.219772\pi\) | ||||
−0.770969 | + | 0.636872i | \(0.780228\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.82935 | 0.418551 | ||||||||
\(446\) | −4.74144 | + | 4.76034i | −0.224514 | + | 0.225408i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.9138 | − | 3.25765i | 0.988085 | − | 0.153910i | ||||
\(449\) | 7.27030 | 0.343107 | 0.171553 | − | 0.985175i | \(-0.445121\pi\) | ||||
0.171553 | + | 0.985175i | \(0.445121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.37719 | − | 2.38535i | 0.0648491 | − | 0.112322i | ||||
\(452\) | 0.00415524 | + | 1.04463i | 0.000195446 | + | 0.0491351i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.2082 | − | 37.7966i | −0.479093 | − | 1.77388i | ||||
\(455\) | −3.06131 | − | 21.3235i | −0.143516 | − | 0.999660i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.18531 | 0.429670 | 0.214835 | − | 0.976650i | \(-0.431079\pi\) | ||||
0.214835 | + | 0.976650i | \(0.431079\pi\) | |||||||
\(458\) | −10.1412 | − | 10.1009i | −0.473867 | − | 0.471986i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.0525027 | − | 13.1992i | −0.00244795 | − | 0.615415i | ||||
\(461\) | −19.8154 | − | 11.4404i | −0.922894 | − | 0.532833i | −0.0383369 | − | 0.999265i | \(-0.512206\pi\) |
−0.884557 | + | 0.466432i | \(0.845539\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.96359 | + | 5.17513i | −0.416573 | + | 0.240509i | −0.693610 | − | 0.720351i | \(-0.743981\pi\) |
0.277037 | + | 0.960859i | \(0.410648\pi\) | |||||||
\(464\) | −29.3364 | + | 0.233388i | −1.36191 | + | 0.0108348i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.97886 | + | 18.4346i | 0.230641 | + | 0.853968i | ||||
\(467\) | 2.05702 | + | 3.56287i | 0.0951876 | + | 0.164870i | 0.909687 | − | 0.415295i | \(-0.136322\pi\) |
−0.814499 | + | 0.580165i | \(0.802988\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.0855 | + | 1.59149i | −0.511880 | + | 0.0734881i | ||||
\(470\) | 3.24081 | + | 3.22795i | 0.149488 | + | 0.148894i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.0889 | − | 12.9337i | −0.602466 | − | 0.595320i | ||||
\(473\) | 17.8184 | 0.819291 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.70718 | − | 2.95691i | 0.0783306 | − | 0.135673i | ||||
\(476\) | 13.7092 | − | 10.8649i | 0.628362 | − | 0.497994i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 34.1192 | − | 9.21499i | 1.56058 | − | 0.421484i | ||||
\(479\) | −4.35898 | − | 7.54998i | −0.199167 | − | 0.344967i | 0.749092 | − | 0.662466i | \(-0.230490\pi\) |
−0.948259 | + | 0.317499i | \(0.897157\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.9849 | − | 21.9306i | −1.73196 | − | 0.999950i | ||||
\(482\) | 14.2556 | − | 3.85019i | 0.649326 | − | 0.175371i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.29855 | + | 3.66995i | −0.286298 | + | 0.166816i | ||||
\(485\) | 4.02087 | + | 6.96434i | 0.182578 | + | 0.316235i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.6495 | − | 17.1181i | −1.34355 | − | 0.775697i | −0.356221 | − | 0.934402i | \(-0.615935\pi\) |
−0.987326 | + | 0.158704i | \(0.949268\pi\) | |||||||
\(488\) | 22.4845 | − | 22.7544i | 1.01782 | − | 1.03004i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −14.4023 | − | 7.83488i | −0.650628 | − | 0.353944i | ||||
\(491\) | −34.6007 | + | 19.9767i | −1.56151 | + | 0.901537i | −0.564403 | + | 0.825499i | \(0.690894\pi\) |
−0.997105 | + | 0.0760381i | \(0.975773\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.9974 | + | 12.1229i | −0.945677 | + | 0.545987i | ||||
\(494\) | 7.45179 | + | 7.42221i | 0.335272 | + | 0.333941i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.8039 | + | 21.7751i | 0.574912 | + | 0.977731i | ||||
\(497\) | 5.52693 | − | 0.793474i | 0.247917 | − | 0.0355922i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.4941 | + | 7.79083i | 0.604080 | + | 0.348766i | 0.770645 | − | 0.637265i | \(-0.219934\pi\) |
−0.166565 | + | 0.986030i | \(0.553268\pi\) | |||||||
\(500\) | −11.9361 | + | 20.8652i | −0.533800 | + | 0.933121i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.27355 | + | 1.66763i | 0.280002 | + | 0.0744299i | ||||
\(503\) | 9.03852 | 0.403008 | 0.201504 | − | 0.979488i | \(-0.435417\pi\) | ||||
0.201504 | + | 0.979488i | \(0.435417\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.67078 | 0.207847 | ||||||||
\(506\) | 14.7705 | + | 3.92627i | 0.656628 | + | 0.174544i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.28793 | + | 14.4879i | −0.367717 | + | 0.642797i | ||||
\(509\) | −13.0489 | − | 7.53379i | −0.578382 | − | 0.333929i | 0.182108 | − | 0.983279i | \(-0.441708\pi\) |
−0.760490 | + | 0.649349i | \(0.775041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.18453 | + | 12.9425i | −0.229350 | + | 0.572542i | ||||
\(512\) | 15.7111 | − | 16.2838i | 0.694337 | − | 0.719650i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.2577 | − | 26.1534i | −1.15818 | − | 1.15358i | ||||
\(515\) | −2.28715 | + | 1.32049i | −0.100784 | + | 0.0581876i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.58678 | + | 2.64818i | −0.201726 | + | 0.116467i | ||||
\(518\) | −30.6636 | + | 13.1955i | −1.34728 | + | 0.579779i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −16.3812 | − | 16.1868i | −0.718362 | − | 0.709840i | ||||
\(521\) | 9.24459 | + | 5.33737i | 0.405013 | + | 0.233834i | 0.688645 | − | 0.725099i | \(-0.258206\pi\) |
−0.283632 | + | 0.958933i | \(0.591539\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.88205 | + | 10.1880i | 0.257204 | + | 0.445490i | 0.965492 | − | 0.260433i | \(-0.0838654\pi\) |
−0.708288 | + | 0.705924i | \(0.750532\pi\) | |||||||
\(524\) | −29.6153 | + | 17.2558i | −1.29375 | + | 0.753825i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.10106 | − | 2.18795i | 0.353223 | − | 0.0953991i | ||||
\(527\) | 18.0796 | + | 10.4382i | 0.787558 | + | 0.454697i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.56054 | − | 6.16704i | −0.154806 | − | 0.268132i | ||||
\(530\) | −23.5543 | + | 6.36160i | −1.02314 | + | 0.276330i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.91894 | − | 1.16905i | 0.343329 | − | 0.0506847i | ||||
\(533\) | 2.49647 | − | 4.32401i | 0.108134 | − | 0.187294i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.09788 | 0.393336 | ||||||||
\(536\) | −8.41509 | + | 8.51612i | −0.363477 | + | 0.367840i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.73200 | − | 1.72512i | −0.0746718 | − | 0.0743754i | ||||
\(539\) | 13.1064 | − | 13.7341i | 0.564531 | − | 0.591568i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.31831 | + | 12.6757i | 0.314639 | + | 0.544970i | 0.979361 | − | 0.202120i | \(-0.0647833\pi\) |
−0.664722 | + | 0.747091i | \(0.731450\pi\) | |||||||
\(542\) | 2.48643 | + | 9.20619i | 0.106801 | + | 0.395440i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.66015 | − | 18.1104i | 0.199802 | − | 0.776477i | ||||
\(545\) | 19.5406 | − | 11.2818i | 0.837028 | − | 0.483258i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.3730 | − | 16.3812i | −1.21314 | − | 0.700408i | −0.249699 | − | 0.968323i | \(-0.580332\pi\) |
−0.963442 | + | 0.267916i | \(0.913665\pi\) | |||||||
\(548\) | −0.00119212 | − | 0.299699i | −5.09248e−5 | − | 0.0128025i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.13332 | − | 6.10897i | −0.261526 | − | 0.260487i | ||||
\(551\) | −11.0951 | −0.472666 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 39.8299 | − | 5.71818i | 1.69374 | − | 0.243162i | ||||
\(554\) | −2.60348 | − | 9.63961i | −0.110611 | − | 0.409548i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0964937 | − | 24.2585i | −0.00409224 | − | 1.02879i | ||||
\(557\) | −7.70165 | + | 13.3397i | −0.326330 | + | 0.565219i | −0.981781 | − | 0.190018i | \(-0.939145\pi\) |
0.655451 | + | 0.755238i | \(0.272479\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.3000 | 1.36614 | ||||||||
\(560\) | −17.3292 | + | 2.62874i | −0.732293 | + | 0.111084i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.62671 | − | 1.63319i | 0.0686184 | − | 0.0688919i | ||||
\(563\) | −30.9832 | −1.30579 | −0.652893 | − | 0.757450i | \(-0.726445\pi\) | ||||
−0.652893 | + | 0.757450i | \(0.726445\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 0.865056i | − | 0.0363932i | ||||||
\(566\) | 34.3092 | + | 9.12001i | 1.44212 | + | 0.383343i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.19554 | − | 4.24591i | 0.176041 | − | 0.178154i | ||||
\(569\) | 38.2081 | 1.60177 | 0.800884 | − | 0.598820i | \(-0.204363\pi\) | ||||
0.800884 | + | 0.598820i | \(0.204363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.2007i | 0.426886i | 0.976955 | + | 0.213443i | \(0.0684678\pi\) | ||||
−0.976955 | + | 0.213443i | \(0.931532\pi\) | |||||||
\(572\) | 23.0400 | − | 13.4246i | 0.963352 | − | 0.561312i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.50211 | − | 3.49058i | −0.0626970 | − | 0.145694i | ||||
\(575\) | − | 8.99392i | − | 0.375072i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.2579 | + | 16.3147i | 1.17639 | + | 0.679191i | 0.955177 | − | 0.296035i | \(-0.0956643\pi\) |
0.221215 | + | 0.975225i | \(0.428998\pi\) | |||||||
\(578\) | 2.23891 | + | 8.28976i | 0.0931265 | + | 0.344808i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 24.2939 | − | 0.0966345i | 1.00875 | − | 0.00401253i | ||||
\(581\) | −35.8757 | − | 14.3712i | −1.48838 | − | 0.596217i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 28.2507i | − | 1.17003i | ||||||
\(584\) | 3.94351 | + | 14.3738i | 0.163184 | + | 0.594791i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.1458 | − | 7.60167i | 1.16269 | − | 0.314022i | ||||
\(587\) | 17.3247 | − | 30.0073i | 0.715067 | − | 1.23853i | −0.247867 | − | 0.968794i | \(-0.579729\pi\) |
0.962934 | − | 0.269738i | \(-0.0869372\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.77664 | + | 8.27338i | 0.196818 | + | 0.340898i | ||||
\(590\) | 10.7962 | + | 10.7533i | 0.444472 | + | 0.442707i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.5971 | + | 31.0470i | −0.723238 | + | 1.27602i | ||||
\(593\) | −4.42792 | + | 2.55646i | −0.181833 | + | 0.104981i | −0.588153 | − | 0.808749i | \(-0.700145\pi\) |
0.406321 | + | 0.913731i | \(0.366812\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.3883 | + | 8.95197i | −0.466873 | + | 0.366995i | ||||
\(596\) | 28.6035 | − | 16.6663i | 1.17165 | − | 0.682678i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26.7750 | + | 7.11728i | 1.09491 | + | 0.291047i | ||||
\(599\) | 23.2794i | 0.951171i | 0.879669 | + | 0.475586i | \(0.157764\pi\) | ||||
−0.879669 | + | 0.475586i | \(0.842236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.2417 | − | 20.3468i | −1.43754 | − | 0.829964i | −0.439862 | − | 0.898066i | \(-0.644973\pi\) |
−0.997678 | + | 0.0681014i | \(0.978306\pi\) | |||||||
\(602\) | 14.6971 | − | 19.7060i | 0.599008 | − | 0.803157i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −33.9955 | + | 0.135225i | −1.38326 | + | 0.00550222i | ||||
\(605\) | 5.22785 | − | 3.01830i | 0.212542 | − | 0.122711i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.67342 | + | 4.63049i | −0.108511 | + | 0.187946i | −0.915167 | − | 0.403075i | \(-0.867941\pi\) |
0.806656 | + | 0.591021i | \(0.201275\pi\) | |||||||
\(608\) | 5.99056 | − | 6.11091i | 0.242949 | − | 0.247830i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.6941 | + | 18.7686i | −0.756901 | + | 0.759917i | ||||
\(611\) | −8.31460 | + | 4.80044i | −0.336373 | + | 0.194205i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.3074 | + | 36.9055i | −0.860597 | + | 1.49060i | 0.0107566 | + | 0.999942i | \(0.496576\pi\) |
−0.871354 | + | 0.490656i | \(0.836757\pi\) | |||||||
\(614\) | −39.2722 | − | 10.4393i | −1.58490 | − | 0.421295i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.29334 | − | 20.1650i | 0.0924013 | − | 0.812472i | ||||
\(617\) | 3.10687 | + | 5.38126i | 0.125078 | + | 0.216641i | 0.921763 | − | 0.387753i | \(-0.126749\pi\) |
−0.796685 | + | 0.604394i | \(0.793415\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.91636 | + | 3.31923i | 0.0770249 | + | 0.133411i | 0.901965 | − | 0.431809i | \(-0.142125\pi\) |
−0.824940 | + | 0.565220i | \(0.808791\pi\) | |||||||
\(620\) | −10.5310 | − | 18.0739i | −0.422937 | − | 0.725864i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.9995 | − | 3.72134i | −0.561331 | − | 0.149212i | ||||
\(623\) | 8.71671 | + | 11.0890i | 0.349228 | + | 0.444270i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.31030 | − | 7.46567i | 0.172412 | − | 0.298627i | ||||
\(626\) | 0.0390279 | − | 0.146821i | 0.00155987 | − | 0.00586816i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.0087 | − | 26.2363i | 0.598912 | − | 1.04694i | ||||
\(629\) | 29.4935i | 1.17598i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 31.3249i | − | 1.24703i | −0.781813 | − | 0.623513i | \(-0.785705\pi\) | ||
0.781813 | − | 0.623513i | \(-0.214295\pi\) | |||||||
\(632\) | 30.2352 | − | 30.5982i | 1.20269 | − | 1.21713i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.5919 | + | 5.20788i | 0.778092 | + | 0.206831i | ||||
\(635\) | 6.91086 | − | 11.9700i | 0.274249 | − | 0.475013i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.7583 | − | 24.8962i | 0.941340 | − | 0.986423i | ||||
\(638\) | −7.22654 | + | 27.1860i | −0.286102 | + | 1.07630i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.0638 | + | 13.4327i | −0.516391 | + | 0.530974i | ||||
\(641\) | 10.2056 | + | 17.6766i | 0.403097 | + | 0.698185i | 0.994098 | − | 0.108486i | \(-0.0346002\pi\) |
−0.591001 | + | 0.806671i | \(0.701267\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.30287 | − | 12.6489i | −0.287997 | − | 0.498826i | 0.685334 | − | 0.728228i | \(-0.259656\pi\) |
−0.973332 | + | 0.229403i | \(0.926323\pi\) | |||||||
\(644\) | 16.5253 | − | 13.0967i | 0.651188 | − | 0.516083i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.81685 | − | 6.83492i | 0.0714830 | − | 0.268917i | ||||
\(647\) | −16.1015 | + | 27.8887i | −0.633017 | + | 1.09642i | 0.353915 | + | 0.935278i | \(0.384850\pi\) |
−0.986932 | + | 0.161140i | \(0.948483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.2800 | + | 8.82192i | −0.599793 | + | 0.346291i | ||||
\(650\) | −11.1181 | − | 11.0739i | −0.436087 | − | 0.434356i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.8486 | + | 0.0471305i | −0.464027 | + | 0.00184577i | ||||
\(653\) | −17.9103 | + | 31.0215i | −0.700883 | + | 1.21397i | 0.267274 | + | 0.963621i | \(0.413877\pi\) |
−0.968157 | + | 0.250344i | \(0.919456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.5809 | − | 14.1918i | 0.960457 | − | 0.554520i | ||||
\(656\) | −3.53423 | − | 2.00317i | −0.137988 | − | 0.0782106i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.854578 | + | 7.25697i | −0.0333149 | + | 0.282906i | ||||
\(659\) | 0.326746 | + | 0.188647i | 0.0127282 | + | 0.00734865i | 0.506351 | − | 0.862328i | \(-0.330994\pi\) |
−0.493622 | + | 0.869676i | \(0.664327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 39.3987i | − | 1.53243i | −0.642584 | − | 0.766216i | \(-0.722137\pi\) | ||
0.642584 | − | 0.766216i | \(-0.277863\pi\) | |||||||
\(662\) | 5.07767 | − | 19.1020i | 0.197349 | − | 0.742420i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −39.8432 | + | 10.9312i | −1.54622 | + | 0.424211i | ||||
\(665\) | −6.56143 | + | 0.941992i | −0.254441 | + | 0.0365289i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.3106 | + | 14.6131i | −0.980029 | + | 0.565820i | ||||
\(668\) | −0.131364 | − | 33.0248i | −0.00508262 | − | 1.27777i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.99649 | − | 7.02438i | 0.270298 | − | 0.271375i | ||||
\(671\) | −15.3364 | − | 26.5635i | −0.592057 | − | 1.02547i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.6511 | + | 28.8406i | −0.641853 | + | 1.11172i | 0.343166 | + | 0.939275i | \(0.388501\pi\) |
−0.985019 | + | 0.172447i | \(0.944833\pi\) | |||||||
\(674\) | −6.25807 | − | 23.1710i | −0.241052 | − | 0.892513i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.3006 | − | 11.2458i | 0.742332 | − | 0.432532i | ||||
\(677\) | 9.32909i | 0.358546i | 0.983799 | + | 0.179273i | \(0.0573745\pi\) | ||||
−0.983799 | + | 0.179273i | \(0.942625\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.77709 | + | 11.9254i | −0.183328 | + | 0.457654i | ||||
\(680\) | −3.91867 | + | 14.9817i | −0.150274 | + | 0.574520i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23.3832 | − | 6.31538i | 0.895389 | − | 0.241829i | ||||
\(683\) | −1.57689 | − | 0.910416i | −0.0603379 | − | 0.0348361i | 0.469528 | − | 0.882918i | \(-0.344424\pi\) |
−0.529865 | + | 0.848082i | \(0.677758\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.248181i | 0.00948251i | ||||||||
\(686\) | −4.37853 | − | 25.8230i | −0.167173 | − | 0.985928i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.209070 | − | 26.2797i | −0.00797072 | − | 1.00190i | ||||
\(689\) | − | 51.2110i | − | 1.95098i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.82516 | 0.107474 | 0.0537371 | − | 0.998555i | \(-0.482887\pi\) | ||||
0.0537371 | + | 0.998555i | \(0.482887\pi\) | |||||||
\(692\) | 16.1126 | − | 28.1660i | 0.612509 | − | 1.07071i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.39925 | + | 24.0737i | −0.242912 | + | 0.913827i | ||||
\(695\) | 20.0885i | 0.762000i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.35739 | −0.127170 | ||||||||
\(698\) | −27.8361 | − | 27.7256i | −1.05361 | − | 1.04943i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.8151 | + | 1.74422i | −0.446567 | + | 0.0659254i | ||||
\(701\) | −21.7145 | −0.820146 | −0.410073 | − | 0.912053i | \(-0.634497\pi\) | ||||
−0.410073 | + | 0.912053i | \(0.634497\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.74825 | + | 11.6883i | −0.254515 | + | 0.440833i | ||||
\(704\) | −11.0716 | − | 18.6587i | −0.417276 | − | 0.703228i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.7637 | − | 7.49848i | 1.04490 | − | 0.282209i | ||||
\(707\) | 4.61119 | + | 5.86613i | 0.173422 | + | 0.220618i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.2252 | 0.684460 | 0.342230 | − | 0.939616i | \(-0.388818\pi\) | ||||
0.342230 | + | 0.939616i | \(0.388818\pi\) | |||||||
\(710\) | −3.48827 | + | 3.50217i | −0.130912 | + | 0.131434i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.5879 | + | 3.81568i | 0.546706 | + | 0.142999i | ||||
\(713\) | 21.7933 | + | 12.5824i | 0.816167 | + | 0.471214i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.1234 | + | 11.0409i | −0.715174 | + | 0.412906i | ||||
\(716\) | −17.6164 | − | 30.2341i | −0.658355 | − | 1.12990i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.1914 | − | 3.83284i | 0.529618 | − | 0.143040i | ||||
\(719\) | −0.946279 | − | 1.63900i | −0.0352903 | − | 0.0611245i | 0.847841 | − | 0.530251i | \(-0.177902\pi\) |
−0.883131 | + | 0.469126i | \(0.844569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.91640 | − | 1.56884i | −0.145854 | − | 0.0584266i | ||||
\(722\) | −16.6783 | + | 16.7448i | −0.620702 | + | 0.623176i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.11242 | − | 15.9292i | 0.338660 | − | 0.592003i | ||||
\(725\) | 16.5539 | 0.614795 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.6125 | − | 28.7738i | 0.616125 | − | 1.06716i | −0.374061 | − | 0.927404i | \(-0.622035\pi\) |
0.990186 | − | 0.139756i | \(-0.0446317\pi\) | |||||||
\(728\) | 4.15721 | − | 36.5538i | 0.154077 | − | 1.35477i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.21823 | − | 11.9157i | −0.119112 | − | 0.441022i | ||||
\(731\) | −10.8597 | − | 18.8096i | −0.401661 | − | 0.695698i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.05539 | − | 4.07343i | −0.260597 | − | 0.150456i | 0.364010 | − | 0.931395i | \(-0.381407\pi\) |
−0.624607 | + | 0.780939i | \(0.714741\pi\) | |||||||
\(734\) | −4.58593 | − | 16.9798i | −0.169270 | − | 0.626735i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.61740 | − | 21.8305i | 0.207060 | − | 0.804682i | ||||
\(737\) | 5.73985 | + | 9.94172i | 0.211430 | + | 0.366208i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.33522 | + | 2.50294i | 0.159474 | + | 0.0920722i | 0.577613 | − | 0.816311i | \(-0.303984\pi\) |
−0.418139 | + | 0.908383i | \(0.637318\pi\) | |||||||
\(740\) | 14.6743 | − | 25.6517i | 0.539436 | − | 0.942973i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −31.2435 | − | 23.3019i | −1.14699 | − | 0.855441i | ||||
\(743\) | 23.9292 | − | 13.8155i | 0.877877 | − | 0.506842i | 0.00791898 | − | 0.999969i | \(-0.497479\pi\) |
0.869958 | + | 0.493126i | \(0.164146\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.7411 | + | 13.7069i | −0.869807 | + | 0.502184i | ||||
\(746\) | 7.03440 | − | 7.06243i | 0.257548 | − | 0.258574i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15.5641 | − | 8.90357i | −0.569079 | − | 0.325547i | ||||
\(749\) | 8.98181 | + | 11.4262i | 0.328188 | + | 0.417505i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.3094 | − | 16.3445i | −1.03303 | − | 0.596418i | −0.115176 | − | 0.993345i | \(-0.536743\pi\) |
−0.917850 | + | 0.396927i | \(0.870077\pi\) | |||||||
\(752\) | 3.95951 | + | 6.73379i | 0.144388 | + | 0.245556i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.0998 | + | 49.2809i | −0.477066 | + | 1.79471i | ||||
\(755\) | 28.1517 | 1.02455 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.8021 | −0.719720 | −0.359860 | − | 0.933006i | \(-0.617176\pi\) | ||||
−0.359860 | + | 0.933006i | \(0.617176\pi\) | |||||||
\(758\) | −1.99630 | + | 7.51001i | −0.0725089 | + | 0.272776i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.98084 | + | 5.04064i | −0.180674 | + | 0.182843i | ||||
\(761\) | 41.0380 | + | 23.6933i | 1.48763 | + | 0.858881i | 0.999900 | − | 0.0141164i | \(-0.00449353\pi\) |
0.487725 | + | 0.872997i | \(0.337827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.4603 | + | 13.4036i | 1.21135 | + | 0.485243i | ||||
\(764\) | 0.741029 | − | 1.29537i | 0.0268095 | − | 0.0468649i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29.8020 | + | 29.9207i | −1.07679 | + | 1.08108i | ||||
\(767\) | −27.6986 | + | 15.9918i | −1.00014 | + | 0.577430i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.6592 | + | 24.0520i | −1.50227 | + | 0.867336i | −0.502273 | + | 0.864709i | \(0.667503\pi\) |
−0.999997 | + | 0.00262643i | \(0.999164\pi\) | |||||||
\(770\) | −1.96551 | + | 16.6909i | −0.0708320 | + | 0.601497i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.15184 | + | 5.23539i | 0.329382 | + | 0.188426i | ||||
\(773\) | 0.506957 | + | 0.292692i | 0.0182340 | + | 0.0105274i | 0.509089 | − | 0.860714i | \(-0.329982\pi\) |
−0.490855 | + | 0.871241i | \(0.663316\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.12674 | − | 12.3439i | −0.256000 | − | 0.443405i | ||||
\(776\) | 3.63360 | + | 13.2442i | 0.130439 | + | 0.475439i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.37149 | + | 5.07804i | 0.0491702 | + | 0.182057i | ||||
\(779\) | −1.33054 | − | 0.768187i | −0.0476715 | − | 0.0275231i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.86174 | − | 4.95668i | −0.102401 | − | 0.177364i | ||||
\(782\) | −4.85744 | − | 17.9851i | −0.173702 | − | 0.643144i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −20.4096 | − | 19.1689i | −0.728915 | − | 0.684604i | ||||
\(785\) | −12.5149 | + | 21.6765i | −0.446677 | + | 0.773667i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.22833 | −0.0437851 | −0.0218926 | − | 0.999760i | \(-0.506969\pi\) | ||||
−0.0218926 | + | 0.999760i | \(0.506969\pi\) | |||||||
\(788\) | 22.5670 | + | 12.9096i | 0.803915 | + | 0.459887i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −25.1382 | + | 25.2384i | −0.894378 | + | 0.897942i | ||||
\(791\) | 1.08644 | − | 0.854020i | 0.0386294 | − | 0.0303655i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.8009 | − | 48.1525i | −0.987238 | − | 1.70995i | ||||
\(794\) | −25.0724 | + | 6.77161i | −0.889788 | + | 0.240316i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.0229 | − | 9.91869i | 0.603362 | − | 0.351559i | ||||
\(797\) | 10.3748 | − | 5.98989i | 0.367494 | − | 0.212173i | −0.304869 | − | 0.952394i | \(-0.598613\pi\) |
0.672363 | + | 0.740222i | \(0.265279\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.59097 | + | 3.22795i | 0.197794 | + | 0.114197i | ||||
\(800\) | −8.93792 | + | 9.11747i | −0.316003 | + | 0.322351i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 23.9833 | − | 24.0789i | 0.846880 | − | 0.850255i | ||||
\(803\) | 14.2916 | 0.504339 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.7275 | + | 10.7908i | −0.483832 | + | 0.380326i | ||||
\(806\) | 42.3875 | − | 11.4481i | 1.49304 | − | 0.403242i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.71710 | + | 2.01852i | 0.271487 | + | 0.0710112i | ||||
\(809\) | 3.43996 | − | 5.95818i | 0.120943 | − | 0.209479i | −0.799197 | − | 0.601069i | \(-0.794742\pi\) |
0.920140 | + | 0.391590i | \(0.128075\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.6994 | −0.445938 | −0.222969 | − | 0.974826i | \(-0.571575\pi\) | ||||
−0.222969 | + | 0.974826i | \(0.571575\pi\) | |||||||
\(812\) | 24.1053 | + | 30.4158i | 0.845931 | + | 1.06739i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 24.2443 | + | 24.1480i | 0.849761 | + | 0.846388i | ||||
\(815\) | 9.81185 | 0.343694 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 9.93901i | − | 0.347722i | ||||||
\(818\) | −1.20464 | + | 4.53179i | −0.0421191 | + | 0.158450i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.92005 | + | 1.67044i | 0.101973 | + | 0.0583344i | ||||
\(821\) | 40.0401 | 1.39741 | 0.698704 | − | 0.715411i | \(-0.253761\pi\) | ||||
0.698704 | + | 0.715411i | \(0.253761\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.4514i | 1.23576i | 0.786274 | + | 0.617878i | \(0.212008\pi\) | ||||
−0.786274 | + | 0.617878i | \(0.787992\pi\) | |||||||
\(824\) | −4.34951 | + | 1.19331i | −0.151522 | + | 0.0415708i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.84687 | + | 24.1753i | −0.0990553 | + | 0.841165i | ||||
\(827\) | − | 51.5618i | − | 1.79298i | −0.443064 | − | 0.896490i | \(-0.646109\pi\) | ||
0.443064 | − | 0.896490i | \(-0.353891\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.0577 | + | 20.2406i | 1.21760 | + | 0.702984i | 0.964405 | − | 0.264431i | \(-0.0851840\pi\) |
0.253199 | + | 0.967414i | \(0.418517\pi\) | |||||||
\(830\) | 33.0297 | − | 8.92072i | 1.14648 | − | 0.309643i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.0698 | − | 33.8233i | −0.695796 | − | 1.17261i | ||||
\(833\) | −22.4859 | − | 5.46498i | −0.779091 | − | 0.189350i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.3479i | 0.946414i | ||||||||
\(836\) | −4.13089 | − | 7.08963i | −0.142870 | − | 0.245200i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.882654 | + | 3.26810i | 0.0304908 | + | 0.112895i | ||||
\(839\) | −3.71303 | + | 6.43115i | −0.128188 | + | 0.222028i | −0.922975 | − | 0.384861i | \(-0.874249\pi\) |
0.794787 | + | 0.606889i | \(0.207583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.3962 | − | 21.4709i | −0.427456 | − | 0.740375i | ||||
\(842\) | 6.52931 | − | 6.55533i | 0.225015 | − | 0.225912i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 47.1764 | − | 0.187655i | 1.62388 | − | 0.00645935i | ||||
\(845\) | −16.0197 | + | 9.24896i | −0.551093 | + | 0.318174i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.95189 | + | 3.58597i | 0.307591 | + | 0.123215i | ||||
\(848\) | −41.6659 | + | 0.331476i | −1.43081 | + | 0.0113829i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.71074 | + | 10.1977i | −0.0929777 | + | 0.349779i | ||||
\(851\) | 35.5519i | 1.21870i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.86973 | + | 5.12094i | 0.303694 | + | 0.175338i | 0.644101 | − | 0.764940i | \(-0.277232\pi\) |
−0.340407 | + | 0.940278i | \(0.610565\pi\) | |||||||
\(854\) | −42.0274 | − | 4.94913i | −1.43815 | − | 0.169356i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.0316 | + | 3.93173i | 0.513769 | + | 0.134384i | ||||
\(857\) | 15.5246 | − | 8.96315i | 0.530311 | − | 0.306175i | −0.210832 | − | 0.977522i | \(-0.567617\pi\) |
0.741143 | + | 0.671347i | \(0.234284\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.5755 | + | 30.4417i | −0.599670 | + | 1.03866i | 0.393200 | + | 0.919453i | \(0.371368\pi\) |
−0.992870 | + | 0.119205i | \(0.961965\pi\) | |||||||
\(860\) | 0.0865656 | + | 21.7626i | 0.00295186 | + | 0.742098i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.2899 | − | 22.2014i | −0.759196 | − | 0.756183i | ||||
\(863\) | 13.3132 | − | 7.68639i | 0.453187 | − | 0.261648i | −0.255988 | − | 0.966680i | \(-0.582401\pi\) |
0.709175 | + | 0.705032i | \(0.249068\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.4354 | + | 23.2709i | −0.456819 | + | 0.791233i | ||||
\(866\) | −1.82948 | + | 6.88242i | −0.0621681 | + | 0.233874i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.3027 | − | 31.0694i | 0.417580 | − | 1.05457i | ||||
\(869\) | −20.6232 | − | 35.7204i | −0.699593 | − | 1.21173i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.4048 | + | 18.0217i | 0.352554 | + | 0.610641i | ||||
\(872\) | 37.1607 | − | 10.1952i | 1.25842 | − | 0.345253i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.19005 | − | 8.23890i | 0.0740797 | − | 0.278685i | ||||
\(875\) | 31.4766 | − | 4.51894i | 1.06410 | − | 0.152768i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.2020 | + | 19.4025i | −0.378265 | + | 0.655174i | −0.990810 | − | 0.135261i | \(-0.956813\pi\) |
0.612545 | + | 0.790436i | \(0.290146\pi\) | |||||||
\(878\) | −22.4955 | − | 5.97973i | −0.759187 | − | 0.201806i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.10678 | + | 15.4875i | 0.306990 | + | 0.522085i | ||||
\(881\) | 29.1250i | 0.981247i | 0.871372 | + | 0.490624i | \(0.163231\pi\) | ||||
−0.871372 | + | 0.490624i | \(0.836769\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 20.8057i | − | 0.700168i | −0.936718 | − | 0.350084i | \(-0.886153\pi\) | ||
0.936718 | − | 0.350084i | \(-0.113847\pi\) | |||||||
\(884\) | −28.2135 | − | 16.1398i | −0.948924 | − | 0.542840i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.74000 | − | 36.6415i | 0.327222 | − | 1.23100i | ||||
\(887\) | −6.23363 | + | 10.7970i | −0.209305 | + | 0.362526i | −0.951496 | − | 0.307662i | \(-0.900453\pi\) |
0.742191 | + | 0.670188i | \(0.233787\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.8560 | − | 3.13776i | 0.733027 | − | 0.105237i | ||||
\(890\) | −12.0675 | − | 3.20777i | −0.404504 | − | 0.107525i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.20983 | − | 4.78359i | 0.274886 | − | 0.160166i | ||||
\(893\) | 1.47714 | + | 2.55848i | 0.0494306 | + | 0.0856162i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.4883 | + | 25.0945i | 0.484291 | + | 0.838817i | ||||
\(896\) | −29.7675 | − | 3.14575i | −0.994462 | − | 0.105092i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.93668 | − | 2.64136i | −0.331591 | − | 0.0881432i | ||||
\(899\) | −23.1586 | + | 40.1120i | −0.772384 | + | 1.33781i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.8222 | + | 17.2179i | −0.993522 | + | 0.573610i | ||||
\(902\) | −2.74889 | + | 2.75984i | −0.0915279 | + | 0.0918927i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.373842 | − | 1.42925i | 0.0124338 | − | 0.0475363i | ||||
\(905\) | −7.59836 | + | 13.1607i | −0.252578 | + | 0.437478i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.9315 | − | 13.8169i | 0.794634 | − | 0.458782i | −0.0469575 | − | 0.998897i | \(-0.514953\pi\) |
0.841591 | + | 0.540115i | \(0.181619\pi\) | |||||||
\(908\) | 0.220236 | + | 55.3672i | 0.00730878 | + | 1.83743i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.56294 | + | 30.2561i | −0.118110 | + | 1.00298i | ||||
\(911\) | 16.9835 | + | 9.80544i | 0.562689 | + | 0.324869i | 0.754224 | − | 0.656617i | \(-0.228013\pi\) |
−0.191535 | + | 0.981486i | \(0.561347\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.6153i | 1.31108i | ||||||||
\(914\) | −12.5540 | − | 3.33709i | −0.415250 | − | 0.110381i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.1907 | + | 17.4898i | 0.336711 | + | 0.577881i | ||||
\(917\) | 42.0911 | + | 16.8610i | 1.38997 | + | 0.556798i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.8847 | − | 15.5219i | 0.886843 | − | 0.512019i | 0.0139343 | − | 0.999903i | \(-0.495564\pi\) |
0.872908 | + | 0.487884i | \(0.162231\pi\) | |||||||
\(920\) | −4.72361 | + | 18.0591i | −0.155733 | + | 0.595390i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.9263 | + | 22.8353i | 0.755037 | + | 0.752040i | ||||
\(923\) | −5.18757 | − | 8.98514i | −0.170751 | − | 0.295749i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0684 | − | 17.4390i | 0.331047 | − | 0.573390i | ||||
\(926\) | 14.1312 | − | 3.81657i | 0.464378 | − | 0.125420i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 40.1803 | + | 10.3392i | 1.31898 | + | 0.339400i | ||||
\(929\) | − | 8.72104i | − | 0.286128i | −0.989713 | − | 0.143064i | \(-0.954305\pi\) | ||
0.989713 | − | 0.143064i | \(-0.0456955\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.66079 | − | 7.31066i | −0.251072 | − | 0.239597i | ||||
\(932\) | −0.107416 | − | 27.0044i | −0.00351853 | − | 0.884558i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.51702 | − | 5.61688i | −0.0496384 | − | 0.183790i | ||||
\(935\) | 12.8591 | + | 7.42421i | 0.420538 | + | 0.242798i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.0809i | − | 0.492672i | −0.969185 | − | 0.246336i | \(-0.920773\pi\) | ||
0.969185 | − | 0.246336i | \(-0.0792266\pi\) | |||||||
\(938\) | 15.7293 | + | 1.85228i | 0.513580 | + | 0.0604789i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.25664 | − | 5.58921i | −0.106220 | − | 0.182300i | ||||
\(941\) | 52.4732i | 1.71058i | 0.518151 | + | 0.855289i | \(0.326620\pi\) | ||||
−0.518151 | + | 0.855289i | \(0.673380\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.04704 | −0.131790 | ||||||||
\(944\) | 13.1904 | + | 22.4324i | 0.429311 | + | 0.730112i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.3533 | − | 6.47357i | −0.791795 | − | 0.210474i | ||||
\(947\) | − | 44.4680i | − | 1.44501i | −0.691363 | − | 0.722507i | \(-0.742990\pi\) | ||
0.691363 | − | 0.722507i | \(-0.257010\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.9068 | 0.840971 | ||||||||
\(950\) | −3.40755 | + | 3.42113i | −0.110556 | + | 0.110996i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −22.6844 | + | 9.86899i | −0.735207 | + | 0.319856i | ||||
\(953\) | −13.0081 | −0.421374 | −0.210687 | − | 0.977554i | \(-0.567570\pi\) | ||||
−0.210687 | + | 0.977554i | \(0.567570\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.617905 | + | 1.07024i | −0.0199949 | + | 0.0346322i | ||||
\(956\) | −49.9803 | + | 0.198808i | −1.61648 | + | 0.00642992i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.21468 | + | 11.9026i | 0.103861 | + | 0.384555i | ||||
\(959\) | −0.311696 | + | 0.245015i | −0.0100652 | + | 0.00791194i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.88091 | 0.286481 | ||||||||
\(962\) | 43.9484 | + | 43.7739i | 1.41695 | + | 1.41133i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.8827 | + | 0.0830657i | −0.672587 | + | 0.00267537i | ||||
\(965\) | −7.56128 | − | 4.36551i | −0.243406 | − | 0.140531i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.2347 | − | 13.9919i | 0.779335 | − | 0.449949i | −0.0568598 | − | 0.998382i | \(-0.518109\pi\) |
0.836194 | + | 0.548433i | \(0.184775\pi\) | |||||||
\(968\) | 9.94187 | − | 2.72760i | 0.319544 | − | 0.0876683i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.96532 | − | 10.9793i | −0.0952107 | − | 0.352525i | ||||
\(971\) | −4.21204 | − | 7.29547i | −0.135171 | − | 0.234123i | 0.790492 | − | 0.612473i | \(-0.209825\pi\) |
−0.925663 | + | 0.378350i | \(0.876492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.2295 | + | 19.8322i | −0.808822 | + | 0.635791i | ||||
\(974\) | 34.3043 | + | 34.1681i | 1.09918 | + | 1.09482i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.9975 | + | 22.9308i | −1.24828 | + | 0.733997i | ||||
\(977\) | −0.704020 | −0.0225236 | −0.0112618 | − | 0.999937i | \(-0.503585\pi\) | ||||
−0.0112618 | + | 0.999937i | \(0.503585\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.22910 | − | 12.5212i | 0.231043 | − | 0.400178i | ||||
\(980\) | 16.8378 | + | 15.9408i | 0.537865 | + | 0.509210i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 54.5483 | − | 14.7325i | 1.74070 | − | 0.470133i | ||||
\(983\) | 15.3077 | + | 26.5137i | 0.488240 | + | 0.845656i | 0.999909 | − | 0.0135267i | \(-0.00430580\pi\) |
−0.511669 | + | 0.859183i | \(0.670972\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.6449 | − | 10.7647i | −0.594077 | − | 0.342990i | ||||
\(986\) | 33.1026 | − | 8.94041i | 1.05420 | − | 0.284721i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.48819 | − | 12.8516i | −0.238231 | − | 0.408864i | ||||
\(989\) | −13.0904 | − | 22.6733i | −0.416252 | − | 0.720969i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.1803 | + | 22.0434i | 1.21284 | + | 0.700232i | 0.963376 | − | 0.268153i | \(-0.0864134\pi\) |
0.249460 | + | 0.968385i | \(0.419747\pi\) | |||||||
\(992\) | −9.58868 | − | 34.4129i | −0.304441 | − | 1.09261i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.84221 | − | 0.923496i | −0.248740 | − | 0.0292915i | ||||
\(995\) | −14.1292 | + | 8.15748i | −0.447925 | + | 0.258609i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.37914 | − | 3.68300i | 0.202030 | − | 0.116642i | −0.395572 | − | 0.918435i | \(-0.629454\pi\) |
0.597602 | + | 0.801793i | \(0.296120\pi\) | |||||||
\(998\) | −15.6126 | − | 15.5506i | −0.494209 | − | 0.492247i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 756.2.bj.b.451.3 | 84 | ||
3.2 | odd | 2 | 252.2.bj.b.115.40 | yes | 84 | ||
4.3 | odd | 2 | inner | 756.2.bj.b.451.4 | 84 | ||
7.5 | odd | 6 | 756.2.n.b.19.26 | 84 | |||
9.4 | even | 3 | 756.2.n.b.199.32 | 84 | |||
9.5 | odd | 6 | 252.2.n.b.31.11 | ✓ | 84 | ||
12.11 | even | 2 | 252.2.bj.b.115.39 | yes | 84 | ||
21.5 | even | 6 | 252.2.n.b.187.17 | yes | 84 | ||
28.19 | even | 6 | 756.2.n.b.19.32 | 84 | |||
36.23 | even | 6 | 252.2.n.b.31.17 | yes | 84 | ||
36.31 | odd | 6 | 756.2.n.b.199.26 | 84 | |||
63.5 | even | 6 | 252.2.bj.b.103.40 | yes | 84 | ||
63.40 | odd | 6 | inner | 756.2.bj.b.523.3 | 84 | ||
84.47 | odd | 6 | 252.2.n.b.187.11 | yes | 84 | ||
252.103 | even | 6 | inner | 756.2.bj.b.523.4 | 84 | ||
252.131 | odd | 6 | 252.2.bj.b.103.39 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.n.b.31.11 | ✓ | 84 | 9.5 | odd | 6 | ||
252.2.n.b.31.17 | yes | 84 | 36.23 | even | 6 | ||
252.2.n.b.187.11 | yes | 84 | 84.47 | odd | 6 | ||
252.2.n.b.187.17 | yes | 84 | 21.5 | even | 6 | ||
252.2.bj.b.103.39 | yes | 84 | 252.131 | odd | 6 | ||
252.2.bj.b.103.40 | yes | 84 | 63.5 | even | 6 | ||
252.2.bj.b.115.39 | yes | 84 | 12.11 | even | 2 | ||
252.2.bj.b.115.40 | yes | 84 | 3.2 | odd | 2 | ||
756.2.n.b.19.26 | 84 | 7.5 | odd | 6 | |||
756.2.n.b.19.32 | 84 | 28.19 | even | 6 | |||
756.2.n.b.199.26 | 84 | 36.31 | odd | 6 | |||
756.2.n.b.199.32 | 84 | 9.4 | even | 3 | |||
756.2.bj.b.451.3 | 84 | 1.1 | even | 1 | trivial | ||
756.2.bj.b.451.4 | 84 | 4.3 | odd | 2 | inner | ||
756.2.bj.b.523.3 | 84 | 63.40 | odd | 6 | inner | ||
756.2.bj.b.523.4 | 84 | 252.103 | even | 6 | inner |