Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(89,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.k (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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.3 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.89 |
Dual form | 462.2.k.d.353.3 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −2.09077 | + | 3.62132i | −0.935021 | + | 1.61950i | −0.160424 | + | 0.987048i | \(0.551286\pi\) |
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | −1.73205 | −0.707107 | ||||||||
\(7\) | −1.62132 | − | 2.09077i | −0.612801 | − | 0.790237i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | −3.62132 | + | 2.09077i | −1.14516 | + | 0.661160i | ||||
\(11\) | 0.866025 | − | 0.500000i | 0.261116 | − | 0.150756i | ||||
\(12\) | −1.50000 | − | 0.866025i | −0.433013 | − | 0.250000i | ||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | −0.358719 | − | 2.62132i | −0.0958718 | − | 0.700577i | ||||
\(15\) | − | 7.24264i | − | 1.87004i | ||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.58346 | − | 2.74264i | −0.384047 | − | 0.665188i | 0.607590 | − | 0.794251i | \(-0.292136\pi\) |
−0.991636 | + | 0.129063i | \(0.958803\pi\) | |||||||
\(18\) | 2.59808 | − | 1.50000i | 0.612372 | − | 0.353553i | ||||
\(19\) | −7.24264 | − | 4.18154i | −1.66158 | − | 0.959311i | −0.971963 | − | 0.235133i | \(-0.924448\pi\) |
−0.689612 | − | 0.724179i | \(-0.742219\pi\) | |||||||
\(20\) | −4.18154 | −0.935021 | ||||||||
\(21\) | 4.24264 | + | 1.73205i | 0.925820 | + | 0.377964i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 1.07616 | + | 0.621320i | 0.224395 | + | 0.129554i | 0.607983 | − | 0.793950i | \(-0.291979\pi\) |
−0.383589 | + | 0.923504i | \(0.625312\pi\) | |||||||
\(24\) | −0.866025 | − | 1.50000i | −0.176777 | − | 0.306186i | ||||
\(25\) | −6.24264 | − | 10.8126i | −1.24853 | − | 2.16251i | ||||
\(26\) | −1.73205 | + | 3.00000i | −0.339683 | + | 0.588348i | ||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 1.00000 | − | 2.44949i | 0.188982 | − | 0.462910i | ||||
\(29\) | 8.48528i | 1.57568i | 0.615882 | + | 0.787839i | \(0.288800\pi\) | ||||
−0.615882 | + | 0.787839i | \(0.711200\pi\) | |||||||
\(30\) | 3.62132 | − | 6.27231i | 0.661160 | − | 1.14516i | ||||
\(31\) | 1.24264 | − | 0.717439i | 0.223185 | − | 0.128856i | −0.384239 | − | 0.923234i | \(-0.625536\pi\) |
0.607424 | + | 0.794378i | \(0.292203\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −0.866025 | + | 1.50000i | −0.150756 | + | 0.261116i | ||||
\(34\) | − | 3.16693i | − | 0.543124i | ||||||
\(35\) | 10.9612 | − | 1.50000i | 1.85277 | − | 0.253546i | ||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | −2.00000 | + | 3.46410i | −0.328798 | + | 0.569495i | −0.982274 | − | 0.187453i | \(-0.939977\pi\) |
0.653476 | + | 0.756948i | \(0.273310\pi\) | |||||||
\(38\) | −4.18154 | − | 7.24264i | −0.678335 | − | 1.17491i | ||||
\(39\) | −3.00000 | − | 5.19615i | −0.480384 | − | 0.832050i | ||||
\(40\) | −3.62132 | − | 2.09077i | −0.572581 | − | 0.330580i | ||||
\(41\) | 5.19615 | 0.811503 | 0.405751 | − | 0.913984i | \(-0.367010\pi\) | ||||
0.405751 | + | 0.913984i | \(0.367010\pi\) | |||||||
\(42\) | 2.80821 | + | 3.62132i | 0.433316 | + | 0.558782i | ||||
\(43\) | −4.48528 | −0.683999 | −0.341999 | − | 0.939700i | \(-0.611104\pi\) | ||||
−0.341999 | + | 0.939700i | \(0.611104\pi\) | |||||||
\(44\) | 0.866025 | + | 0.500000i | 0.130558 | + | 0.0753778i | ||||
\(45\) | 6.27231 | + | 10.8640i | 0.935021 | + | 1.61950i | ||||
\(46\) | 0.621320 | + | 1.07616i | 0.0916087 | + | 0.158671i | ||||
\(47\) | −2.09077 | + | 3.62132i | −0.304970 | + | 0.528224i | −0.977255 | − | 0.212069i | \(-0.931980\pi\) |
0.672285 | + | 0.740293i | \(0.265313\pi\) | |||||||
\(48\) | − | 1.73205i | − | 0.250000i | ||||||
\(49\) | −1.74264 | + | 6.77962i | −0.248949 | + | 0.968517i | ||||
\(50\) | − | 12.4853i | − | 1.76569i | ||||||
\(51\) | 4.75039 | + | 2.74264i | 0.665188 | + | 0.384047i | ||||
\(52\) | −3.00000 | + | 1.73205i | −0.416025 | + | 0.240192i | ||||
\(53\) | −7.34847 | + | 4.24264i | −1.00939 | + | 0.582772i | −0.911013 | − | 0.412378i | \(-0.864698\pi\) |
−0.0983769 | + | 0.995149i | \(0.531365\pi\) | |||||||
\(54\) | −2.59808 | + | 4.50000i | −0.353553 | + | 0.612372i | ||||
\(55\) | 4.18154i | 0.563839i | ||||||||
\(56\) | 2.09077 | − | 1.62132i | 0.279391 | − | 0.216658i | ||||
\(57\) | 14.4853 | 1.91862 | ||||||||
\(58\) | −4.24264 | + | 7.34847i | −0.557086 | + | 0.964901i | ||||
\(59\) | 3.16693 | + | 5.48528i | 0.412299 | + | 0.714123i | 0.995141 | − | 0.0984629i | \(-0.0313926\pi\) |
−0.582842 | + | 0.812586i | \(0.698059\pi\) | |||||||
\(60\) | 6.27231 | − | 3.62132i | 0.809752 | − | 0.467510i | ||||
\(61\) | 0.621320 | + | 0.358719i | 0.0795519 | + | 0.0459293i | 0.539248 | − | 0.842147i | \(-0.318708\pi\) |
−0.459696 | + | 0.888076i | \(0.652042\pi\) | |||||||
\(62\) | 1.43488 | 0.182230 | ||||||||
\(63\) | −7.86396 | + | 1.07616i | −0.990766 | + | 0.135583i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −12.5446 | − | 7.24264i | −1.55597 | − | 0.898339i | ||||
\(66\) | −1.50000 | + | 0.866025i | −0.184637 | + | 0.106600i | ||||
\(67\) | 1.74264 | + | 3.01834i | 0.212897 | + | 0.368749i | 0.952620 | − | 0.304163i | \(-0.0983766\pi\) |
−0.739723 | + | 0.672912i | \(0.765043\pi\) | |||||||
\(68\) | 1.58346 | − | 2.74264i | 0.192023 | − | 0.332594i | ||||
\(69\) | −2.15232 | −0.259108 | ||||||||
\(70\) | 10.2426 | + | 4.18154i | 1.22423 | + | 0.499790i | ||||
\(71\) | 6.00000i | 0.712069i | 0.934473 | + | 0.356034i | \(0.115871\pi\) | ||||
−0.934473 | + | 0.356034i | \(0.884129\pi\) | |||||||
\(72\) | 2.59808 | + | 1.50000i | 0.306186 | + | 0.176777i | ||||
\(73\) | −7.24264 | + | 4.18154i | −0.847687 | + | 0.489412i | −0.859870 | − | 0.510513i | \(-0.829455\pi\) |
0.0121828 | + | 0.999926i | \(0.496122\pi\) | |||||||
\(74\) | −3.46410 | + | 2.00000i | −0.402694 | + | 0.232495i | ||||
\(75\) | 18.7279 | + | 10.8126i | 2.16251 | + | 1.24853i | ||||
\(76\) | − | 8.36308i | − | 0.959311i | ||||||
\(77\) | −2.44949 | − | 1.00000i | −0.279145 | − | 0.113961i | ||||
\(78\) | − | 6.00000i | − | 0.679366i | ||||||
\(79\) | 2.62132 | − | 4.54026i | 0.294922 | − | 0.510819i | −0.680045 | − | 0.733170i | \(-0.738040\pi\) |
0.974967 | + | 0.222351i | \(0.0713731\pi\) | |||||||
\(80\) | −2.09077 | − | 3.62132i | −0.233755 | − | 0.404876i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 4.50000 | + | 2.59808i | 0.496942 | + | 0.286910i | ||||
\(83\) | 3.16693 | 0.347616 | 0.173808 | − | 0.984780i | \(-0.444393\pi\) | ||||
0.173808 | + | 0.984780i | \(0.444393\pi\) | |||||||
\(84\) | 0.621320 | + | 4.54026i | 0.0677916 | + | 0.495383i | ||||
\(85\) | 13.2426 | 1.43637 | ||||||||
\(86\) | −3.88437 | − | 2.24264i | −0.418862 | − | 0.241830i | ||||
\(87\) | −7.34847 | − | 12.7279i | −0.787839 | − | 1.36458i | ||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | 1.01461 | − | 1.75736i | 0.107549 | − | 0.186280i | −0.807228 | − | 0.590240i | \(-0.799033\pi\) |
0.914777 | + | 0.403960i | \(0.132367\pi\) | |||||||
\(90\) | 12.5446i | 1.32232i | ||||||||
\(91\) | 7.24264 | − | 5.61642i | 0.759235 | − | 0.588761i | ||||
\(92\) | 1.24264i | 0.129554i | ||||||||
\(93\) | −1.24264 | + | 2.15232i | −0.128856 | + | 0.223185i | ||||
\(94\) | −3.62132 | + | 2.09077i | −0.373511 | + | 0.215646i | ||||
\(95\) | 30.2854 | − | 17.4853i | 3.10722 | − | 1.79395i | ||||
\(96\) | 0.866025 | − | 1.50000i | 0.0883883 | − | 0.153093i | ||||
\(97\) | − | 0.297173i | − | 0.0301733i | −0.999886 | − | 0.0150867i | \(-0.995198\pi\) | ||
0.999886 | − | 0.0150867i | \(-0.00480242\pi\) | |||||||
\(98\) | −4.89898 | + | 5.00000i | −0.494872 | + | 0.505076i | ||||
\(99\) | − | 3.00000i | − | 0.301511i | ||||||
\(100\) | 6.24264 | − | 10.8126i | 0.624264 | − | 1.08126i | ||||
\(101\) | −1.01461 | − | 1.75736i | −0.100958 | − | 0.174864i | 0.811122 | − | 0.584877i | \(-0.198857\pi\) |
−0.912079 | + | 0.410013i | \(0.865524\pi\) | |||||||
\(102\) | 2.74264 | + | 4.75039i | 0.271562 | + | 0.470359i | ||||
\(103\) | 10.2426 | + | 5.91359i | 1.00924 | + | 0.582683i | 0.910968 | − | 0.412476i | \(-0.135336\pi\) |
0.0982691 | + | 0.995160i | \(0.468669\pi\) | |||||||
\(104\) | −3.46410 | −0.339683 | ||||||||
\(105\) | −15.1427 | + | 11.7426i | −1.47778 | + | 1.14596i | ||||
\(106\) | −8.48528 | −0.824163 | ||||||||
\(107\) | −12.9904 | − | 7.50000i | −1.25583 | − | 0.725052i | −0.283567 | − | 0.958952i | \(-0.591518\pi\) |
−0.972261 | + | 0.233900i | \(0.924851\pi\) | |||||||
\(108\) | −4.50000 | + | 2.59808i | −0.433013 | + | 0.250000i | ||||
\(109\) | −1.37868 | − | 2.38794i | −0.132054 | − | 0.228723i | 0.792414 | − | 0.609983i | \(-0.208824\pi\) |
−0.924468 | + | 0.381260i | \(0.875490\pi\) | |||||||
\(110\) | −2.09077 | + | 3.62132i | −0.199347 | + | 0.345279i | ||||
\(111\) | − | 6.92820i | − | 0.657596i | ||||||
\(112\) | 2.62132 | − | 0.358719i | 0.247691 | − | 0.0338958i | ||||
\(113\) | 18.0000i | 1.69330i | 0.532152 | + | 0.846649i | \(0.321383\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678617\pi\) | |||||||
\(114\) | 12.5446 | + | 7.24264i | 1.17491 | + | 0.678335i | ||||
\(115\) | −4.50000 | + | 2.59808i | −0.419627 | + | 0.242272i | ||||
\(116\) | −7.34847 | + | 4.24264i | −0.682288 | + | 0.393919i | ||||
\(117\) | 9.00000 | + | 5.19615i | 0.832050 | + | 0.480384i | ||||
\(118\) | 6.33386i | 0.583079i | ||||||||
\(119\) | −3.16693 | + | 7.75736i | −0.290312 | + | 0.711116i | ||||
\(120\) | 7.24264 | 0.661160 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 0.358719 | + | 0.621320i | 0.0324769 | + | 0.0562517i | ||||
\(123\) | −7.79423 | + | 4.50000i | −0.702782 | + | 0.405751i | ||||
\(124\) | 1.24264 | + | 0.717439i | 0.111592 | + | 0.0644279i | ||||
\(125\) | 31.3000 | 2.79956 | ||||||||
\(126\) | −7.34847 | − | 3.00000i | −0.654654 | − | 0.267261i | ||||
\(127\) | 15.2426 | 1.35257 | 0.676283 | − | 0.736642i | \(-0.263590\pi\) | ||||
0.676283 | + | 0.736642i | \(0.263590\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 6.72792 | − | 3.88437i | 0.592361 | − | 0.341999i | ||||
\(130\) | −7.24264 | − | 12.5446i | −0.635222 | − | 1.10024i | ||||
\(131\) | 3.16693 | − | 5.48528i | 0.276696 | − | 0.479251i | −0.693866 | − | 0.720104i | \(-0.744094\pi\) |
0.970562 | + | 0.240853i | \(0.0774272\pi\) | |||||||
\(132\) | −1.73205 | −0.150756 | ||||||||
\(133\) | 3.00000 | + | 21.9223i | 0.260133 | + | 1.90091i | ||||
\(134\) | 3.48528i | 0.301082i | ||||||||
\(135\) | −18.8169 | − | 10.8640i | −1.61950 | − | 0.935021i | ||||
\(136\) | 2.74264 | − | 1.58346i | 0.235179 | − | 0.135781i | ||||
\(137\) | −12.5446 | + | 7.24264i | −1.07176 | + | 0.618781i | −0.928662 | − | 0.370928i | \(-0.879040\pi\) |
−0.143098 | + | 0.989709i | \(0.545706\pi\) | |||||||
\(138\) | −1.86396 | − | 1.07616i | −0.158671 | − | 0.0916087i | ||||
\(139\) | − | 3.46410i | − | 0.293821i | −0.989150 | − | 0.146911i | \(-0.953067\pi\) | ||
0.989150 | − | 0.146911i | \(-0.0469330\pi\) | |||||||
\(140\) | 6.77962 | + | 8.74264i | 0.572982 | + | 0.738888i | ||||
\(141\) | − | 7.24264i | − | 0.609940i | ||||||
\(142\) | −3.00000 | + | 5.19615i | −0.251754 | + | 0.436051i | ||||
\(143\) | 1.73205 | + | 3.00000i | 0.144841 | + | 0.250873i | ||||
\(144\) | 1.50000 | + | 2.59808i | 0.125000 | + | 0.216506i | ||||
\(145\) | −30.7279 | − | 17.7408i | −2.55182 | − | 1.47329i | ||||
\(146\) | −8.36308 | −0.692134 | ||||||||
\(147\) | −3.25736 | − | 11.6786i | −0.268662 | − | 0.963234i | ||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 10.8126 | + | 18.7279i | 0.882843 | + | 1.52913i | ||||
\(151\) | 0.378680 | + | 0.655892i | 0.0308165 | + | 0.0533758i | 0.881022 | − | 0.473075i | \(-0.156856\pi\) |
−0.850206 | + | 0.526450i | \(0.823523\pi\) | |||||||
\(152\) | 4.18154 | − | 7.24264i | 0.339168 | − | 0.587456i | ||||
\(153\) | −9.50079 | −0.768093 | ||||||||
\(154\) | −1.62132 | − | 2.09077i | −0.130650 | − | 0.168479i | ||||
\(155\) | 6.00000i | 0.481932i | ||||||||
\(156\) | 3.00000 | − | 5.19615i | 0.240192 | − | 0.416025i | ||||
\(157\) | −16.2426 | + | 9.37769i | −1.29630 | + | 0.748421i | −0.979764 | − | 0.200158i | \(-0.935855\pi\) |
−0.316540 | + | 0.948579i | \(0.602521\pi\) | |||||||
\(158\) | 4.54026 | − | 2.62132i | 0.361204 | − | 0.208541i | ||||
\(159\) | 7.34847 | − | 12.7279i | 0.582772 | − | 1.00939i | ||||
\(160\) | − | 4.18154i | − | 0.330580i | ||||||
\(161\) | −0.445759 | − | 3.25736i | −0.0351308 | − | 0.256716i | ||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | 6.50000 | − | 11.2583i | 0.509119 | − | 0.881820i | −0.490825 | − | 0.871258i | \(-0.663305\pi\) |
0.999944 | − | 0.0105623i | \(-0.00336213\pi\) | |||||||
\(164\) | 2.59808 | + | 4.50000i | 0.202876 | + | 0.351391i | ||||
\(165\) | −3.62132 | − | 6.27231i | −0.281919 | − | 0.488299i | ||||
\(166\) | 2.74264 | + | 1.58346i | 0.212870 | + | 0.122901i | ||||
\(167\) | −2.02922 | −0.157026 | −0.0785130 | − | 0.996913i | \(-0.525017\pi\) | ||||
−0.0785130 | + | 0.996913i | \(0.525017\pi\) | |||||||
\(168\) | −1.73205 | + | 4.24264i | −0.133631 | + | 0.327327i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 11.4685 | + | 6.62132i | 0.879591 | + | 0.507832i | ||||
\(171\) | −21.7279 | + | 12.5446i | −1.66158 | + | 0.959311i | ||||
\(172\) | −2.24264 | − | 3.88437i | −0.171000 | − | 0.296180i | ||||
\(173\) | 4.18154 | − | 7.24264i | 0.317917 | − | 0.550648i | −0.662137 | − | 0.749383i | \(-0.730350\pi\) |
0.980053 | + | 0.198735i | \(0.0636835\pi\) | |||||||
\(174\) | − | 14.6969i | − | 1.11417i | ||||||
\(175\) | −12.4853 | + | 30.5826i | −0.943799 | + | 2.31182i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | −9.50079 | − | 5.48528i | −0.714123 | − | 0.412299i | ||||
\(178\) | 1.75736 | − | 1.01461i | 0.131720 | − | 0.0760484i | ||||
\(179\) | −12.5446 | + | 7.24264i | −0.937629 | + | 0.541340i | −0.889216 | − | 0.457487i | \(-0.848750\pi\) |
−0.0484128 | + | 0.998827i | \(0.515416\pi\) | |||||||
\(180\) | −6.27231 | + | 10.8640i | −0.467510 | + | 0.809752i | ||||
\(181\) | − | 16.7262i | − | 1.24325i | −0.783317 | − | 0.621623i | \(-0.786474\pi\) | ||
0.783317 | − | 0.621623i | \(-0.213526\pi\) | |||||||
\(182\) | 9.08052 | − | 1.24264i | 0.673093 | − | 0.0921107i | ||||
\(183\) | −1.24264 | −0.0918586 | ||||||||
\(184\) | −0.621320 | + | 1.07616i | −0.0458043 | + | 0.0793355i | ||||
\(185\) | −8.36308 | − | 14.4853i | −0.614866 | − | 1.06498i | ||||
\(186\) | −2.15232 | + | 1.24264i | −0.157816 | + | 0.0911148i | ||||
\(187\) | −2.74264 | − | 1.58346i | −0.200562 | − | 0.115794i | ||||
\(188\) | −4.18154 | −0.304970 | ||||||||
\(189\) | 10.8640 | − | 8.42463i | 0.790237 | − | 0.612801i | ||||
\(190\) | 34.9706 | 2.53703 | ||||||||
\(191\) | −15.5885 | − | 9.00000i | −1.12794 | − | 0.651217i | −0.184525 | − | 0.982828i | \(-0.559075\pi\) |
−0.943416 | + | 0.331611i | \(0.892408\pi\) | |||||||
\(192\) | 1.50000 | − | 0.866025i | 0.108253 | − | 0.0625000i | ||||
\(193\) | 8.24264 | + | 14.2767i | 0.593318 | + | 1.02766i | 0.993782 | + | 0.111345i | \(0.0355158\pi\) |
−0.400464 | + | 0.916313i | \(0.631151\pi\) | |||||||
\(194\) | 0.148586 | − | 0.257359i | 0.0106679 | − | 0.0184773i | ||||
\(195\) | 25.0892 | 1.79668 | ||||||||
\(196\) | −6.74264 | + | 1.88064i | −0.481617 | + | 0.134331i | ||||
\(197\) | − | 8.48528i | − | 0.604551i | −0.953221 | − | 0.302276i | \(-0.902254\pi\) | ||
0.953221 | − | 0.302276i | \(-0.0977463\pi\) | |||||||
\(198\) | 1.50000 | − | 2.59808i | 0.106600 | − | 0.184637i | ||||
\(199\) | 11.4853 | − | 6.63103i | 0.814170 | − | 0.470061i | −0.0342319 | − | 0.999414i | \(-0.510898\pi\) |
0.848402 | + | 0.529353i | \(0.177565\pi\) | |||||||
\(200\) | 10.8126 | − | 6.24264i | 0.764564 | − | 0.441421i | ||||
\(201\) | −5.22792 | − | 3.01834i | −0.368749 | − | 0.212897i | ||||
\(202\) | − | 2.02922i | − | 0.142776i | ||||||
\(203\) | 17.7408 | − | 13.7574i | 1.24516 | − | 0.965577i | ||||
\(204\) | 5.48528i | 0.384047i | ||||||||
\(205\) | −10.8640 | + | 18.8169i | −0.758772 | + | 1.31423i | ||||
\(206\) | 5.91359 | + | 10.2426i | 0.412019 | + | 0.713639i | ||||
\(207\) | 3.22848 | − | 1.86396i | 0.224395 | − | 0.129554i | ||||
\(208\) | −3.00000 | − | 1.73205i | −0.208013 | − | 0.120096i | ||||
\(209\) | −8.36308 | −0.578486 | ||||||||
\(210\) | −18.9853 | + | 2.59808i | −1.31011 | + | 0.179284i | ||||
\(211\) | 12.4853 | 0.859522 | 0.429761 | − | 0.902943i | \(-0.358598\pi\) | ||||
0.429761 | + | 0.902943i | \(0.358598\pi\) | |||||||
\(212\) | −7.34847 | − | 4.24264i | −0.504695 | − | 0.291386i | ||||
\(213\) | −5.19615 | − | 9.00000i | −0.356034 | − | 0.616670i | ||||
\(214\) | −7.50000 | − | 12.9904i | −0.512689 | − | 0.888004i | ||||
\(215\) | 9.37769 | − | 16.2426i | 0.639553 | − | 1.10774i | ||||
\(216\) | −5.19615 | −0.353553 | ||||||||
\(217\) | −3.51472 | − | 1.43488i | −0.238595 | − | 0.0974059i | ||||
\(218\) | − | 2.75736i | − | 0.186752i | ||||||
\(219\) | 7.24264 | − | 12.5446i | 0.489412 | − | 0.847687i | ||||
\(220\) | −3.62132 | + | 2.09077i | −0.244149 | + | 0.140960i | ||||
\(221\) | 9.50079 | − | 5.48528i | 0.639092 | − | 0.368980i | ||||
\(222\) | 3.46410 | − | 6.00000i | 0.232495 | − | 0.402694i | ||||
\(223\) | 6.33386i | 0.424146i | 0.977254 | + | 0.212073i | \(0.0680215\pi\) | ||||
−0.977254 | + | 0.212073i | \(0.931978\pi\) | |||||||
\(224\) | 2.44949 | + | 1.00000i | 0.163663 | + | 0.0668153i | ||||
\(225\) | −37.4558 | −2.49706 | ||||||||
\(226\) | −9.00000 | + | 15.5885i | −0.598671 | + | 1.03693i | ||||
\(227\) | 10.9612 | + | 18.9853i | 0.727518 | + | 1.26010i | 0.957929 | + | 0.287004i | \(0.0926594\pi\) |
−0.230412 | + | 0.973093i | \(0.574007\pi\) | |||||||
\(228\) | 7.24264 | + | 12.5446i | 0.479656 | + | 0.830788i | ||||
\(229\) | 6.00000 | + | 3.46410i | 0.396491 | + | 0.228914i | 0.684969 | − | 0.728572i | \(-0.259816\pi\) |
−0.288478 | + | 0.957487i | \(0.593149\pi\) | |||||||
\(230\) | −5.19615 | −0.342624 | ||||||||
\(231\) | 4.54026 | − | 0.621320i | 0.298727 | − | 0.0408799i | ||||
\(232\) | −8.48528 | −0.557086 | ||||||||
\(233\) | 22.4912 | + | 12.9853i | 1.47345 | + | 0.850694i | 0.999553 | − | 0.0298888i | \(-0.00951533\pi\) |
0.473892 | + | 0.880583i | \(0.342849\pi\) | |||||||
\(234\) | 5.19615 | + | 9.00000i | 0.339683 | + | 0.588348i | ||||
\(235\) | −8.74264 | − | 15.1427i | −0.570307 | − | 0.987801i | ||||
\(236\) | −3.16693 | + | 5.48528i | −0.206149 | + | 0.357061i | ||||
\(237\) | 9.08052i | 0.589843i | ||||||||
\(238\) | −6.62132 | + | 5.13461i | −0.429196 | + | 0.332827i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 6.27231 | + | 3.62132i | 0.404876 | + | 0.233755i | ||||
\(241\) | 12.0000 | − | 6.92820i | 0.772988 | − | 0.446285i | −0.0609515 | − | 0.998141i | \(-0.519414\pi\) |
0.833939 | + | 0.551856i | \(0.186080\pi\) | |||||||
\(242\) | 0.866025 | − | 0.500000i | 0.0556702 | − | 0.0321412i | ||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | 0.717439i | 0.0459293i | ||||||||
\(245\) | −20.9077 | − | 20.4853i | −1.33574 | − | 1.30876i | ||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | 14.4853 | − | 25.0892i | 0.921676 | − | 1.59639i | ||||
\(248\) | 0.717439 | + | 1.24264i | 0.0455574 | + | 0.0789078i | ||||
\(249\) | −4.75039 | + | 2.74264i | −0.301044 | + | 0.173808i | ||||
\(250\) | 27.1066 | + | 15.6500i | 1.71437 | + | 0.989793i | ||||
\(251\) | −14.6969 | −0.927663 | −0.463831 | − | 0.885924i | \(-0.653526\pi\) | ||||
−0.463831 | + | 0.885924i | \(0.653526\pi\) | |||||||
\(252\) | −4.86396 | − | 6.27231i | −0.306401 | − | 0.395118i | ||||
\(253\) | 1.24264 | 0.0781242 | ||||||||
\(254\) | 13.2005 | + | 7.62132i | 0.828274 | + | 0.478204i | ||||
\(255\) | −19.8640 | + | 11.4685i | −1.24393 | + | 0.718183i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.01461 | + | 1.75736i | −0.0632897 | + | 0.109621i | −0.895934 | − | 0.444187i | \(-0.853493\pi\) |
0.832644 | + | 0.553808i | \(0.186826\pi\) | |||||||
\(258\) | 7.76874 | 0.483660 | ||||||||
\(259\) | 10.4853 | − | 1.43488i | 0.651524 | − | 0.0891590i | ||||
\(260\) | − | 14.4853i | − | 0.898339i | ||||||
\(261\) | 22.0454 | + | 12.7279i | 1.36458 | + | 0.787839i | ||||
\(262\) | 5.48528 | − | 3.16693i | 0.338882 | − | 0.195654i | ||||
\(263\) | −9.50079 | + | 5.48528i | −0.585844 | + | 0.338237i | −0.763452 | − | 0.645864i | \(-0.776497\pi\) |
0.177609 | + | 0.984101i | \(0.443164\pi\) | |||||||
\(264\) | −1.50000 | − | 0.866025i | −0.0923186 | − | 0.0533002i | ||||
\(265\) | − | 35.4815i | − | 2.17961i | ||||||
\(266\) | −8.36308 | + | 20.4853i | −0.512773 | + | 1.25603i | ||||
\(267\) | 3.51472i | 0.215097i | ||||||||
\(268\) | −1.74264 | + | 3.01834i | −0.106449 | + | 0.184375i | ||||
\(269\) | 11.4685 | + | 19.8640i | 0.699245 | + | 1.21113i | 0.968729 | + | 0.248122i | \(0.0798135\pi\) |
−0.269484 | + | 0.963005i | \(0.586853\pi\) | |||||||
\(270\) | −10.8640 | − | 18.8169i | −0.661160 | − | 1.14516i | ||||
\(271\) | 6.72792 | + | 3.88437i | 0.408692 | + | 0.235959i | 0.690228 | − | 0.723592i | \(-0.257510\pi\) |
−0.281535 | + | 0.959551i | \(0.590844\pi\) | |||||||
\(272\) | 3.16693 | 0.192023 | ||||||||
\(273\) | −6.00000 | + | 14.6969i | −0.363137 | + | 0.889499i | ||||
\(274\) | −14.4853 | −0.875088 | ||||||||
\(275\) | −10.8126 | − | 6.24264i | −0.652023 | − | 0.376445i | ||||
\(276\) | −1.07616 | − | 1.86396i | −0.0647771 | − | 0.112197i | ||||
\(277\) | −14.2426 | − | 24.6690i | −0.855757 | − | 1.48222i | −0.875941 | − | 0.482419i | \(-0.839758\pi\) |
0.0201833 | − | 0.999796i | \(-0.493575\pi\) | |||||||
\(278\) | 1.73205 | − | 3.00000i | 0.103882 | − | 0.179928i | ||||
\(279\) | − | 4.30463i | − | 0.257712i | ||||||
\(280\) | 1.50000 | + | 10.9612i | 0.0896421 | + | 0.655054i | ||||
\(281\) | 17.4853i | 1.04308i | 0.853225 | + | 0.521542i | \(0.174643\pi\) | ||||
−0.853225 | + | 0.521542i | \(0.825357\pi\) | |||||||
\(282\) | 3.62132 | − | 6.27231i | 0.215646 | − | 0.373511i | ||||
\(283\) | −21.2132 | + | 12.2474i | −1.26099 | + | 0.728035i | −0.973267 | − | 0.229677i | \(-0.926233\pi\) |
−0.287727 | + | 0.957712i | \(0.592900\pi\) | |||||||
\(284\) | −5.19615 | + | 3.00000i | −0.308335 | + | 0.178017i | ||||
\(285\) | −30.2854 | + | 52.4558i | −1.79395 | + | 3.10722i | ||||
\(286\) | 3.46410i | 0.204837i | ||||||||
\(287\) | −8.42463 | − | 10.8640i | −0.497290 | − | 0.641279i | ||||
\(288\) | 3.00000i | 0.176777i | ||||||||
\(289\) | 3.48528 | − | 6.03668i | 0.205017 | − | 0.355099i | ||||
\(290\) | −17.7408 | − | 30.7279i | −1.04177 | − | 1.80441i | ||||
\(291\) | 0.257359 | + | 0.445759i | 0.0150867 | + | 0.0261309i | ||||
\(292\) | −7.24264 | − | 4.18154i | −0.423843 | − | 0.244706i | ||||
\(293\) | −12.4215 | −0.725673 | −0.362837 | − | 0.931853i | \(-0.618192\pi\) | ||||
−0.362837 | + | 0.931853i | \(0.618192\pi\) | |||||||
\(294\) | 3.01834 | − | 11.7426i | 0.176033 | − | 0.684845i | ||||
\(295\) | −26.4853 | −1.54203 | ||||||||
\(296\) | −3.46410 | − | 2.00000i | −0.201347 | − | 0.116248i | ||||
\(297\) | 2.59808 | + | 4.50000i | 0.150756 | + | 0.261116i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.15232 | + | 3.72792i | −0.124472 | + | 0.215591i | ||||
\(300\) | 21.6251i | 1.24853i | ||||||||
\(301\) | 7.27208 | + | 9.37769i | 0.419156 | + | 0.540521i | ||||
\(302\) | 0.757359i | 0.0435811i | ||||||||
\(303\) | 3.04384 | + | 1.75736i | 0.174864 | + | 0.100958i | ||||
\(304\) | 7.24264 | − | 4.18154i | 0.415394 | − | 0.239828i | ||||
\(305\) | −2.59808 | + | 1.50000i | −0.148765 | + | 0.0858898i | ||||
\(306\) | −8.22792 | − | 4.75039i | −0.470359 | − | 0.271562i | ||||
\(307\) | − | 23.6544i | − | 1.35003i | −0.737806 | − | 0.675013i | \(-0.764138\pi\) | ||
0.737806 | − | 0.675013i | \(-0.235862\pi\) | |||||||
\(308\) | −0.358719 | − | 2.62132i | −0.0204399 | − | 0.149364i | ||||
\(309\) | −20.4853 | −1.16537 | ||||||||
\(310\) | −3.00000 | + | 5.19615i | −0.170389 | + | 0.295122i | ||||
\(311\) | −12.6062 | − | 21.8345i | −0.714830 | − | 1.23812i | −0.963025 | − | 0.269412i | \(-0.913171\pi\) |
0.248195 | − | 0.968710i | \(-0.420163\pi\) | |||||||
\(312\) | 5.19615 | − | 3.00000i | 0.294174 | − | 0.169842i | ||||
\(313\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(314\) | −18.7554 | −1.05843 | ||||||||
\(315\) | 12.5446 | − | 30.7279i | 0.706809 | − | 1.73132i | ||||
\(316\) | 5.24264 | 0.294922 | ||||||||
\(317\) | 21.8608 | + | 12.6213i | 1.22782 | + | 0.708884i | 0.966574 | − | 0.256387i | \(-0.0825323\pi\) |
0.261249 | + | 0.965271i | \(0.415866\pi\) | |||||||
\(318\) | 12.7279 | − | 7.34847i | 0.713746 | − | 0.412082i | ||||
\(319\) | 4.24264 | + | 7.34847i | 0.237542 | + | 0.411435i | ||||
\(320\) | 2.09077 | − | 3.62132i | 0.116878 | − | 0.202438i | ||||
\(321\) | 25.9808 | 1.45010 | ||||||||
\(322\) | 1.24264 | − | 3.04384i | 0.0692497 | − | 0.169626i | ||||
\(323\) | 26.4853i | 1.47368i | ||||||||
\(324\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(325\) | 37.4558 | − | 21.6251i | 2.07768 | − | 1.19955i | ||||
\(326\) | 11.2583 | − | 6.50000i | 0.623541 | − | 0.360002i | ||||
\(327\) | 4.13604 | + | 2.38794i | 0.228723 | + | 0.132054i | ||||
\(328\) | 5.19615i | 0.286910i | ||||||||
\(329\) | 10.9612 | − | 1.50000i | 0.604308 | − | 0.0826977i | ||||
\(330\) | − | 7.24264i | − | 0.398694i | ||||||
\(331\) | −9.50000 | + | 16.4545i | −0.522167 | + | 0.904420i | 0.477500 | + | 0.878632i | \(0.341543\pi\) |
−0.999667 | + | 0.0257885i | \(0.991790\pi\) | |||||||
\(332\) | 1.58346 | + | 2.74264i | 0.0869039 | + | 0.150522i | ||||
\(333\) | 6.00000 | + | 10.3923i | 0.328798 | + | 0.569495i | ||||
\(334\) | −1.75736 | − | 1.01461i | −0.0961584 | − | 0.0555171i | ||||
\(335\) | −14.5738 | −0.796254 | ||||||||
\(336\) | −3.62132 | + | 2.80821i | −0.197559 | + | 0.153200i | ||||
\(337\) | 30.4853 | 1.66064 | 0.830320 | − | 0.557288i | \(-0.188158\pi\) | ||||
0.830320 | + | 0.557288i | \(0.188158\pi\) | |||||||
\(338\) | 0.866025 | + | 0.500000i | 0.0471056 | + | 0.0271964i | ||||
\(339\) | −15.5885 | − | 27.0000i | −0.846649 | − | 1.46644i | ||||
\(340\) | 6.62132 | + | 11.4685i | 0.359092 | + | 0.621965i | ||||
\(341\) | 0.717439 | − | 1.24264i | 0.0388515 | − | 0.0672928i | ||||
\(342\) | −25.0892 | −1.35667 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | − | 4.48528i | − | 0.241830i | ||||||
\(345\) | 4.50000 | − | 7.79423i | 0.242272 | − | 0.419627i | ||||
\(346\) | 7.24264 | − | 4.18154i | 0.389367 | − | 0.224801i | ||||
\(347\) | −0.445759 | + | 0.257359i | −0.0239296 | + | 0.0138158i | −0.511917 | − | 0.859035i | \(-0.671065\pi\) |
0.487987 | + | 0.872851i | \(0.337731\pi\) | |||||||
\(348\) | 7.34847 | − | 12.7279i | 0.393919 | − | 0.682288i | ||||
\(349\) | − | 15.4144i | − | 0.825113i | −0.910932 | − | 0.412556i | \(-0.864636\pi\) | ||
0.910932 | − | 0.412556i | \(-0.135364\pi\) | |||||||
\(350\) | −26.1039 | + | 20.2426i | −1.39531 | + | 1.08201i | ||||
\(351\) | −18.0000 | −0.960769 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | −12.5446 | − | 21.7279i | −0.667683 | − | 1.15646i | −0.978550 | − | 0.206007i | \(-0.933953\pi\) |
0.310868 | − | 0.950453i | \(-0.399380\pi\) | |||||||
\(354\) | −5.48528 | − | 9.50079i | −0.291539 | − | 0.504961i | ||||
\(355\) | −21.7279 | − | 12.5446i | −1.15320 | − | 0.665799i | ||||
\(356\) | 2.02922 | 0.107549 | ||||||||
\(357\) | −1.96768 | − | 14.3787i | −0.104141 | − | 0.761000i | ||||
\(358\) | −14.4853 | −0.765571 | ||||||||
\(359\) | 7.34847 | + | 4.24264i | 0.387837 | + | 0.223918i | 0.681223 | − | 0.732076i | \(-0.261449\pi\) |
−0.293385 | + | 0.955994i | \(0.594782\pi\) | |||||||
\(360\) | −10.8640 | + | 6.27231i | −0.572581 | + | 0.330580i | ||||
\(361\) | 25.4706 | + | 44.1163i | 1.34056 | + | 2.32191i | ||||
\(362\) | 8.36308 | − | 14.4853i | 0.439554 | − | 0.761329i | ||||
\(363\) | 1.73205i | 0.0909091i | ||||||||
\(364\) | 8.48528 | + | 3.46410i | 0.444750 | + | 0.181568i | ||||
\(365\) | − | 34.9706i | − | 1.83044i | ||||||
\(366\) | −1.07616 | − | 0.621320i | −0.0562517 | − | 0.0324769i | ||||
\(367\) | −21.7279 | + | 12.5446i | −1.13419 | + | 0.654824i | −0.944985 | − | 0.327114i | \(-0.893924\pi\) |
−0.189203 | + | 0.981938i | \(0.560591\pi\) | |||||||
\(368\) | −1.07616 | + | 0.621320i | −0.0560986 | + | 0.0323886i | ||||
\(369\) | 7.79423 | − | 13.5000i | 0.405751 | − | 0.702782i | ||||
\(370\) | − | 16.7262i | − | 0.869552i | ||||||
\(371\) | 20.7846 | + | 8.48528i | 1.07908 | + | 0.440534i | ||||
\(372\) | −2.48528 | −0.128856 | ||||||||
\(373\) | −8.86396 | + | 15.3528i | −0.458959 | + | 0.794939i | −0.998906 | − | 0.0467591i | \(-0.985111\pi\) |
0.539948 | + | 0.841699i | \(0.318444\pi\) | |||||||
\(374\) | −1.58346 | − | 2.74264i | −0.0818790 | − | 0.141819i | ||||
\(375\) | −46.9500 | + | 27.1066i | −2.42449 | + | 1.39978i | ||||
\(376\) | −3.62132 | − | 2.09077i | −0.186755 | − | 0.107823i | ||||
\(377\) | −29.3939 | −1.51386 | ||||||||
\(378\) | 13.6208 | − | 1.86396i | 0.700577 | − | 0.0958718i | ||||
\(379\) | −0.0294373 | −0.00151209 | −0.000756045 | − | 1.00000i | \(-0.500241\pi\) | ||||
−0.000756045 | 1.00000i | \(0.500241\pi\) | ||||||||
\(380\) | 30.2854 | + | 17.4853i | 1.55361 | + | 0.896976i | ||||
\(381\) | −22.8640 | + | 13.2005i | −1.17136 | + | 0.676283i | ||||
\(382\) | −9.00000 | − | 15.5885i | −0.460480 | − | 0.797575i | ||||
\(383\) | −15.7116 | + | 27.2132i | −0.802823 | + | 1.39053i | 0.114928 | + | 0.993374i | \(0.463336\pi\) |
−0.917751 | + | 0.397156i | \(0.869997\pi\) | |||||||
\(384\) | 1.73205 | 0.0883883 | ||||||||
\(385\) | 8.74264 | − | 6.77962i | 0.445566 | − | 0.345521i | ||||
\(386\) | 16.4853i | 0.839079i | ||||||||
\(387\) | −6.72792 | + | 11.6531i | −0.341999 | + | 0.592361i | ||||
\(388\) | 0.257359 | − | 0.148586i | 0.0130654 | − | 0.00754334i | ||||
\(389\) | 24.0131 | − | 13.8640i | 1.21751 | − | 0.702931i | 0.253127 | − | 0.967433i | \(-0.418541\pi\) |
0.964385 | + | 0.264502i | \(0.0852077\pi\) | |||||||
\(390\) | 21.7279 | + | 12.5446i | 1.10024 | + | 0.635222i | ||||
\(391\) | − | 3.93535i | − | 0.199019i | ||||||
\(392\) | −6.77962 | − | 1.74264i | −0.342422 | − | 0.0880166i | ||||
\(393\) | 10.9706i | 0.553392i | ||||||||
\(394\) | 4.24264 | − | 7.34847i | 0.213741 | − | 0.370211i | ||||
\(395\) | 10.9612 | + | 18.9853i | 0.551516 | + | 0.955253i | ||||
\(396\) | 2.59808 | − | 1.50000i | 0.130558 | − | 0.0753778i | ||||
\(397\) | 21.2132 | + | 12.2474i | 1.06466 | + | 0.614682i | 0.926718 | − | 0.375758i | \(-0.122618\pi\) |
0.137943 | + | 0.990440i | \(0.455951\pi\) | |||||||
\(398\) | 13.2621 | 0.664767 | ||||||||
\(399\) | −23.4853 | − | 30.2854i | −1.17573 | − | 1.51617i | ||||
\(400\) | 12.4853 | 0.624264 | ||||||||
\(401\) | −7.34847 | − | 4.24264i | −0.366965 | − | 0.211867i | 0.305167 | − | 0.952299i | \(-0.401288\pi\) |
−0.672132 | + | 0.740432i | \(0.734621\pi\) | |||||||
\(402\) | −3.01834 | − | 5.22792i | −0.150541 | − | 0.260745i | ||||
\(403\) | 2.48528 | + | 4.30463i | 0.123801 | + | 0.214429i | ||||
\(404\) | 1.01461 | − | 1.75736i | 0.0504788 | − | 0.0874319i | ||||
\(405\) | 37.6339 | 1.87004 | ||||||||
\(406\) | 22.2426 | − | 3.04384i | 1.10388 | − | 0.151063i | ||||
\(407\) | 4.00000i | 0.198273i | ||||||||
\(408\) | −2.74264 | + | 4.75039i | −0.135781 | + | 0.235179i | ||||
\(409\) | 13.2426 | − | 7.64564i | 0.654806 | − | 0.378053i | −0.135489 | − | 0.990779i | \(-0.543260\pi\) |
0.790295 | + | 0.612726i | \(0.209927\pi\) | |||||||
\(410\) | −18.8169 | + | 10.8640i | −0.929302 | + | 0.536533i | ||||
\(411\) | 12.5446 | − | 21.7279i | 0.618781 | − | 1.07176i | ||||
\(412\) | 11.8272i | 0.582683i | ||||||||
\(413\) | 6.33386 | − | 15.5147i | 0.311669 | − | 0.763429i | ||||
\(414\) | 3.72792 | 0.183217 | ||||||||
\(415\) | −6.62132 | + | 11.4685i | −0.325028 | + | 0.562965i | ||||
\(416\) | −1.73205 | − | 3.00000i | −0.0849208 | − | 0.147087i | ||||
\(417\) | 3.00000 | + | 5.19615i | 0.146911 | + | 0.254457i | ||||
\(418\) | −7.24264 | − | 4.18154i | −0.354249 | − | 0.204526i | ||||
\(419\) | −8.36308 | −0.408563 | −0.204282 | − | 0.978912i | \(-0.565486\pi\) | ||||
−0.204282 | + | 0.978912i | \(0.565486\pi\) | |||||||
\(420\) | −17.7408 | − | 7.24264i | −0.865661 | − | 0.353405i | ||||
\(421\) | 16.4853 | 0.803443 | 0.401722 | − | 0.915762i | \(-0.368412\pi\) | ||||
0.401722 | + | 0.915762i | \(0.368412\pi\) | |||||||
\(422\) | 10.8126 | + | 6.24264i | 0.526348 | + | 0.303887i | ||||
\(423\) | 6.27231 | + | 10.8640i | 0.304970 | + | 0.528224i | ||||
\(424\) | −4.24264 | − | 7.34847i | −0.206041 | − | 0.356873i | ||||
\(425\) | −19.7700 | + | 34.2426i | −0.958986 | + | 1.66101i | ||||
\(426\) | − | 10.3923i | − | 0.503509i | ||||||
\(427\) | −0.257359 | − | 1.88064i | −0.0124545 | − | 0.0910104i | ||||
\(428\) | − | 15.0000i | − | 0.725052i | ||||||
\(429\) | −5.19615 | − | 3.00000i | −0.250873 | − | 0.144841i | ||||
\(430\) | 16.2426 | − | 9.37769i | 0.783290 | − | 0.452233i | ||||
\(431\) | −8.23999 | + | 4.75736i | −0.396906 | + | 0.229154i | −0.685148 | − | 0.728404i | \(-0.740263\pi\) |
0.288242 | + | 0.957558i | \(0.406929\pi\) | |||||||
\(432\) | −4.50000 | − | 2.59808i | −0.216506 | − | 0.125000i | ||||
\(433\) | 28.8505i | 1.38647i | 0.720713 | + | 0.693234i | \(0.243815\pi\) | ||||
−0.720713 | + | 0.693234i | \(0.756185\pi\) | |||||||
\(434\) | −2.32640 | − | 3.00000i | −0.111671 | − | 0.144005i | ||||
\(435\) | 61.4558 | 2.94658 | ||||||||
\(436\) | 1.37868 | − | 2.38794i | 0.0660268 | − | 0.114362i | ||||
\(437\) | −5.19615 | − | 9.00000i | −0.248566 | − | 0.430528i | ||||
\(438\) | 12.5446 | − | 7.24264i | 0.599405 | − | 0.346067i | ||||
\(439\) | 16.3492 | + | 9.43924i | 0.780307 | + | 0.450510i | 0.836539 | − | 0.547907i | \(-0.184575\pi\) |
−0.0562322 | + | 0.998418i | \(0.517909\pi\) | |||||||
\(440\) | −4.18154 | −0.199347 | ||||||||
\(441\) | 15.0000 | + | 14.6969i | 0.714286 | + | 0.699854i | ||||
\(442\) | 10.9706 | 0.521816 | ||||||||
\(443\) | 31.1769 | + | 18.0000i | 1.48126 | + | 0.855206i | 0.999774 | − | 0.0212481i | \(-0.00676401\pi\) |
0.481486 | + | 0.876454i | \(0.340097\pi\) | |||||||
\(444\) | 6.00000 | − | 3.46410i | 0.284747 | − | 0.164399i | ||||
\(445\) | 4.24264 | + | 7.34847i | 0.201120 | + | 0.348351i | ||||
\(446\) | −3.16693 | + | 5.48528i | −0.149958 | + | 0.259736i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.62132 | + | 2.09077i | 0.0766002 | + | 0.0987796i | ||||
\(449\) | 3.51472i | 0.165870i | 0.996555 | + | 0.0829349i | \(0.0264294\pi\) | ||||
−0.996555 | + | 0.0829349i | \(0.973571\pi\) | |||||||
\(450\) | −32.4377 | − | 18.7279i | −1.52913 | − | 0.882843i | ||||
\(451\) | 4.50000 | − | 2.59808i | 0.211897 | − | 0.122339i | ||||
\(452\) | −15.5885 | + | 9.00000i | −0.733219 | + | 0.423324i | ||||
\(453\) | −1.13604 | − | 0.655892i | −0.0533758 | − | 0.0308165i | ||||
\(454\) | 21.9223i | 1.02887i | ||||||||
\(455\) | 5.19615 | + | 37.9706i | 0.243599 | + | 1.78009i | ||||
\(456\) | 14.4853i | 0.678335i | ||||||||
\(457\) | −10.4853 | + | 18.1610i | −0.490481 | + | 0.849538i | −0.999940 | − | 0.0109572i | \(-0.996512\pi\) |
0.509459 | + | 0.860495i | \(0.329845\pi\) | |||||||
\(458\) | 3.46410 | + | 6.00000i | 0.161867 | + | 0.280362i | ||||
\(459\) | 14.2512 | − | 8.22792i | 0.665188 | − | 0.384047i | ||||
\(460\) | −4.50000 | − | 2.59808i | −0.209814 | − | 0.121136i | ||||
\(461\) | 6.33386 | 0.294997 | 0.147499 | − | 0.989062i | \(-0.452878\pi\) | ||||
0.147499 | + | 0.989062i | \(0.452878\pi\) | |||||||
\(462\) | 4.24264 | + | 1.73205i | 0.197386 | + | 0.0805823i | ||||
\(463\) | −29.4558 | −1.36893 | −0.684465 | − | 0.729046i | \(-0.739964\pi\) | ||||
−0.684465 | + | 0.729046i | \(0.739964\pi\) | |||||||
\(464\) | −7.34847 | − | 4.24264i | −0.341144 | − | 0.196960i | ||||
\(465\) | −5.19615 | − | 9.00000i | −0.240966 | − | 0.417365i | ||||
\(466\) | 12.9853 | + | 22.4912i | 0.601532 | + | 1.04188i | ||||
\(467\) | 15.5885 | − | 27.0000i | 0.721348 | − | 1.24941i | −0.239112 | − | 0.970992i | \(-0.576856\pi\) |
0.960460 | − | 0.278419i | \(-0.0898104\pi\) | |||||||
\(468\) | 10.3923i | 0.480384i | ||||||||
\(469\) | 3.48528 | − | 8.53716i | 0.160935 | − | 0.394209i | ||||
\(470\) | − | 17.4853i | − | 0.806536i | ||||||
\(471\) | 16.2426 | − | 28.1331i | 0.748421 | − | 1.29630i | ||||
\(472\) | −5.48528 | + | 3.16693i | −0.252481 | + | 0.145770i | ||||
\(473\) | −3.88437 | + | 2.24264i | −0.178603 | + | 0.103117i | ||||
\(474\) | −4.54026 | + | 7.86396i | −0.208541 | + | 0.361204i | ||||
\(475\) | 104.415i | 4.79091i | ||||||||
\(476\) | −8.30153 | + | 1.13604i | −0.380500 | + | 0.0520703i | ||||
\(477\) | 25.4558i | 1.16554i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.7116 | + | 27.2132i | 0.717879 | + | 1.24340i | 0.961839 | + | 0.273618i | \(0.0882203\pi\) |
−0.243960 | + | 0.969785i | \(0.578446\pi\) | |||||||
\(480\) | 3.62132 | + | 6.27231i | 0.165290 | + | 0.286291i | ||||
\(481\) | −12.0000 | − | 6.92820i | −0.547153 | − | 0.315899i | ||||
\(482\) | 13.8564 | 0.631142 | ||||||||
\(483\) | 3.48960 | + | 4.50000i | 0.158782 | + | 0.204757i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 1.07616 | + | 0.621320i | 0.0488658 | + | 0.0282127i | ||||
\(486\) | 7.79423 | + | 13.5000i | 0.353553 | + | 0.612372i | ||||
\(487\) | −7.48528 | − | 12.9649i | −0.339190 | − | 0.587495i | 0.645090 | − | 0.764106i | \(-0.276820\pi\) |
−0.984281 | + | 0.176611i | \(0.943486\pi\) | |||||||
\(488\) | −0.358719 | + | 0.621320i | −0.0162385 | + | 0.0281259i | ||||
\(489\) | 22.5167i | 1.01824i | ||||||||
\(490\) | −7.86396 | − | 28.1946i | −0.355258 | − | 1.27370i | ||||
\(491\) | − | 19.9706i | − | 0.901259i | −0.892711 | − | 0.450629i | \(-0.851200\pi\) | ||
0.892711 | − | 0.450629i | \(-0.148800\pi\) | |||||||
\(492\) | −7.79423 | − | 4.50000i | −0.351391 | − | 0.202876i | ||||
\(493\) | 23.2721 | − | 13.4361i | 1.04812 | − | 0.605133i | ||||
\(494\) | 25.0892 | − | 14.4853i | 1.12882 | − | 0.651724i | ||||
\(495\) | 10.8640 | + | 6.27231i | 0.488299 | + | 0.281919i | ||||
\(496\) | 1.43488i | 0.0644279i | ||||||||
\(497\) | 12.5446 | − | 9.72792i | 0.562703 | − | 0.436357i | ||||
\(498\) | −5.48528 | −0.245801 | ||||||||
\(499\) | 6.48528 | − | 11.2328i | 0.290321 | − | 0.502851i | −0.683565 | − | 0.729890i | \(-0.739571\pi\) |
0.973886 | + | 0.227039i | \(0.0729046\pi\) | |||||||
\(500\) | 15.6500 | + | 27.1066i | 0.699889 | + | 1.21224i | ||||
\(501\) | 3.04384 | − | 1.75736i | 0.135989 | − | 0.0785130i | ||||
\(502\) | −12.7279 | − | 7.34847i | −0.568075 | − | 0.327978i | ||||
\(503\) | −16.7262 | −0.745783 | −0.372891 | − | 0.927875i | \(-0.621634\pi\) | ||||
−0.372891 | + | 0.927875i | \(0.621634\pi\) | |||||||
\(504\) | −1.07616 | − | 7.86396i | −0.0479359 | − | 0.350289i | ||||
\(505\) | 8.48528 | 0.377590 | ||||||||
\(506\) | 1.07616 | + | 0.621320i | 0.0478411 | + | 0.0276211i | ||||
\(507\) | −1.50000 | + | 0.866025i | −0.0666173 | + | 0.0384615i | ||||
\(508\) | 7.62132 | + | 13.2005i | 0.338141 | + | 0.585678i | ||||
\(509\) | 3.16693 | − | 5.48528i | 0.140372 | − | 0.243131i | −0.787265 | − | 0.616615i | \(-0.788504\pi\) |
0.927637 | + | 0.373484i | \(0.121837\pi\) | |||||||
\(510\) | −22.9369 | −1.01566 | ||||||||
\(511\) | 20.4853 | + | 8.36308i | 0.906215 | + | 0.369961i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 21.7279 | − | 37.6339i | 0.959311 | − | 1.66158i | ||||
\(514\) | −1.75736 | + | 1.01461i | −0.0775138 | + | 0.0447526i | ||||
\(515\) | −42.8300 | + | 24.7279i | −1.88732 | + | 1.08964i | ||||
\(516\) | 6.72792 | + | 3.88437i | 0.296180 | + | 0.171000i | ||||
\(517\) | 4.18154i | 0.183904i | ||||||||
\(518\) | 9.79796 | + | 4.00000i | 0.430498 | + | 0.175750i | ||||
\(519\) | 14.4853i | 0.635833i | ||||||||
\(520\) | 7.24264 | − | 12.5446i | 0.317611 | − | 0.550118i | ||||
\(521\) | 1.13770 | + | 1.97056i | 0.0498438 | + | 0.0863319i | 0.889871 | − | 0.456213i | \(-0.150794\pi\) |
−0.840027 | + | 0.542544i | \(0.817461\pi\) | |||||||
\(522\) | 12.7279 | + | 22.0454i | 0.557086 | + | 0.964901i | ||||
\(523\) | −22.7574 | − | 13.1390i | −0.995110 | − | 0.574527i | −0.0883121 | − | 0.996093i | \(-0.528147\pi\) |
−0.906798 | + | 0.421566i | \(0.861481\pi\) | |||||||
\(524\) | 6.33386 | 0.276696 | ||||||||
\(525\) | −7.75736 | − | 56.6864i | −0.338559 | − | 2.47400i | ||||
\(526\) | −10.9706 | −0.478339 | ||||||||
\(527\) | −3.93535 | − | 2.27208i | −0.171427 | − | 0.0989733i | ||||
\(528\) | −0.866025 | − | 1.50000i | −0.0376889 | − | 0.0652791i | ||||
\(529\) | −10.7279 | − | 18.5813i | −0.466431 | − | 0.807883i | ||||
\(530\) | 17.7408 | − | 30.7279i | 0.770610 | − | 1.33474i | ||||
\(531\) | 19.0016 | 0.824598 | ||||||||
\(532\) | −17.4853 | + | 13.5592i | −0.758083 | + | 0.587867i | ||||
\(533\) | 18.0000i | 0.779667i | ||||||||
\(534\) | −1.75736 | + | 3.04384i | −0.0760484 | + | 0.131720i | ||||
\(535\) | 54.3198 | − | 31.3616i | 2.34845 | − | 1.35588i | ||||
\(536\) | −3.01834 | + | 1.74264i | −0.130373 | + | 0.0752706i | ||||
\(537\) | 12.5446 | − | 21.7279i | 0.541340 | − | 0.937629i | ||||
\(538\) | 22.9369i | 0.988881i | ||||||||
\(539\) | 1.88064 | + | 6.74264i | 0.0810048 | + | 0.290426i | ||||
\(540\) | − | 21.7279i | − | 0.935021i | ||||||
\(541\) | −3.37868 | + | 5.85204i | −0.145261 | + | 0.251599i | −0.929470 | − | 0.368897i | \(-0.879735\pi\) |
0.784209 | + | 0.620496i | \(0.213069\pi\) | |||||||
\(542\) | 3.88437 | + | 6.72792i | 0.166848 | + | 0.288989i | ||||
\(543\) | 14.4853 | + | 25.0892i | 0.621623 | + | 1.07668i | ||||
\(544\) | 2.74264 | + | 1.58346i | 0.117590 | + | 0.0678905i | ||||
\(545\) | 11.5300 | 0.493891 | ||||||||
\(546\) | −12.5446 | + | 9.72792i | −0.536860 | + | 0.416317i | ||||
\(547\) | −11.4558 | −0.489817 | −0.244908 | − | 0.969546i | \(-0.578758\pi\) | ||||
−0.244908 | + | 0.969546i | \(0.578758\pi\) | |||||||
\(548\) | −12.5446 | − | 7.24264i | −0.535880 | − | 0.309390i | ||||
\(549\) | 1.86396 | − | 1.07616i | 0.0795519 | − | 0.0459293i | ||||
\(550\) | −6.24264 | − | 10.8126i | −0.266187 | − | 0.461050i | ||||
\(551\) | 35.4815 | − | 61.4558i | 1.51156 | − | 2.61811i | ||||
\(552\) | − | 2.15232i | − | 0.0916087i | ||||||
\(553\) | −13.7426 | + | 1.88064i | −0.584397 | + | 0.0799728i | ||||
\(554\) | − | 28.4853i | − | 1.21022i | ||||||
\(555\) | 25.0892 | + | 14.4853i | 1.06498 | + | 0.614866i | ||||
\(556\) | 3.00000 | − | 1.73205i | 0.127228 | − | 0.0734553i | ||||
\(557\) | 23.8284 | − | 13.7574i | 1.00964 | − | 0.582918i | 0.0985563 | − | 0.995131i | \(-0.468578\pi\) |
0.911087 | + | 0.412213i | \(0.135244\pi\) | |||||||
\(558\) | 2.15232 | − | 3.72792i | 0.0911148 | − | 0.157816i | ||||
\(559\) | − | 15.5375i | − | 0.657165i | ||||||
\(560\) | −4.18154 | + | 10.2426i | −0.176702 | + | 0.432831i | ||||
\(561\) | 5.48528 | 0.231589 | ||||||||
\(562\) | −8.74264 | + | 15.1427i | −0.368786 | + | 0.638756i | ||||
\(563\) | −13.5592 | − | 23.4853i | −0.571454 | − | 0.989787i | −0.996417 | − | 0.0845761i | \(-0.973046\pi\) |
0.424963 | − | 0.905211i | \(-0.360287\pi\) | |||||||
\(564\) | 6.27231 | − | 3.62132i | 0.264112 | − | 0.152485i | ||||
\(565\) | −65.1838 | − | 37.6339i | −2.74230 | − | 1.58327i | ||||
\(566\) | −24.4949 | −1.02960 | ||||||||
\(567\) | −9.00000 | + | 22.0454i | −0.377964 | + | 0.925820i | ||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | −24.1977 | − | 13.9706i | −1.01442 | − | 0.585676i | −0.101938 | − | 0.994791i | \(-0.532504\pi\) |
−0.912483 | + | 0.409114i | \(0.865838\pi\) | |||||||
\(570\) | −52.4558 | + | 30.2854i | −2.19713 | + | 1.26852i | ||||
\(571\) | −6.48528 | − | 11.2328i | −0.271401 | − | 0.470080i | 0.697820 | − | 0.716273i | \(-0.254153\pi\) |
−0.969221 | + | 0.246193i | \(0.920820\pi\) | |||||||
\(572\) | −1.73205 | + | 3.00000i | −0.0724207 | + | 0.125436i | ||||
\(573\) | 31.1769 | 1.30243 | ||||||||
\(574\) | −1.86396 | − | 13.6208i | −0.0778002 | − | 0.568520i | ||||
\(575\) | − | 15.5147i | − | 0.647008i | ||||||
\(576\) | −1.50000 | + | 2.59808i | −0.0625000 | + | 0.108253i | ||||
\(577\) | 17.7426 | − | 10.2437i | 0.738636 | − | 0.426452i | −0.0829373 | − | 0.996555i | \(-0.526430\pi\) |
0.821573 | + | 0.570103i | \(0.193097\pi\) | |||||||
\(578\) | 6.03668 | − | 3.48528i | 0.251093 | − | 0.144969i | ||||
\(579\) | −24.7279 | − | 14.2767i | −1.02766 | − | 0.593318i | ||||
\(580\) | − | 35.4815i | − | 1.47329i | ||||||
\(581\) | −5.13461 | − | 6.62132i | −0.213019 | − | 0.274699i | ||||
\(582\) | 0.514719i | 0.0213358i | ||||||||
\(583\) | −4.24264 | + | 7.34847i | −0.175712 | + | 0.304342i | ||||
\(584\) | −4.18154 | − | 7.24264i | −0.173033 | − | 0.299703i | ||||
\(585\) | −37.6339 | + | 21.7279i | −1.55597 | + | 0.898339i | ||||
\(586\) | −10.7574 | − | 6.21076i | −0.444382 | − | 0.256564i | ||||
\(587\) | 12.4215 | 0.512691 | 0.256346 | − | 0.966585i | \(-0.417481\pi\) | ||||
0.256346 | + | 0.966585i | \(0.417481\pi\) | |||||||
\(588\) | 8.48528 | − | 8.66025i | 0.349927 | − | 0.357143i | ||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | −22.9369 | − | 13.2426i | −0.944298 | − | 0.545191i | ||||
\(591\) | 7.34847 | + | 12.7279i | 0.302276 | + | 0.523557i | ||||
\(592\) | −2.00000 | − | 3.46410i | −0.0821995 | − | 0.142374i | ||||
\(593\) | −12.4215 | + | 21.5147i | −0.510091 | + | 0.883504i | 0.489841 | + | 0.871812i | \(0.337055\pi\) |
−0.999932 | + | 0.0116916i | \(0.996278\pi\) | |||||||
\(594\) | 5.19615i | 0.213201i | ||||||||
\(595\) | −21.4706 | − | 27.6873i | −0.880207 | − | 1.13507i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.4853 | + | 19.8931i | −0.470061 | + | 0.814170i | ||||
\(598\) | −3.72792 | + | 2.15232i | −0.152446 | + | 0.0880148i | ||||
\(599\) | 24.0131 | − | 13.8640i | 0.981148 | − | 0.566466i | 0.0785315 | − | 0.996912i | \(-0.474977\pi\) |
0.902617 | + | 0.430446i | \(0.141644\pi\) | |||||||
\(600\) | −10.8126 | + | 18.7279i | −0.441421 | + | 0.764564i | ||||
\(601\) | 9.79796i | 0.399667i | 0.979830 | + | 0.199834i | \(0.0640401\pi\) | ||||
−0.979830 | + | 0.199834i | \(0.935960\pi\) | |||||||
\(602\) | 1.60896 | + | 11.7574i | 0.0655762 | + | 0.479194i | ||||
\(603\) | 10.4558 | 0.425795 | ||||||||
\(604\) | −0.378680 | + | 0.655892i | −0.0154083 | + | 0.0266879i | ||||
\(605\) | 2.09077 | + | 3.62132i | 0.0850019 | + | 0.147228i | ||||
\(606\) | 1.75736 | + | 3.04384i | 0.0713878 | + | 0.123647i | ||||
\(607\) | 7.13604 | + | 4.11999i | 0.289643 | + | 0.167225i | 0.637781 | − | 0.770218i | \(-0.279853\pi\) |
−0.348138 | + | 0.937443i | \(0.613186\pi\) | |||||||
\(608\) | 8.36308 | 0.339168 | ||||||||
\(609\) | −14.6969 | + | 36.0000i | −0.595550 | + | 1.45879i | ||||
\(610\) | −3.00000 | −0.121466 | ||||||||
\(611\) | −12.5446 | − | 7.24264i | −0.507501 | − | 0.293006i | ||||
\(612\) | −4.75039 | − | 8.22792i | −0.192023 | − | 0.332594i | ||||
\(613\) | −4.10660 | − | 7.11284i | −0.165864 | − | 0.287285i | 0.771098 | − | 0.636717i | \(-0.219708\pi\) |
−0.936962 | + | 0.349432i | \(0.886375\pi\) | |||||||
\(614\) | 11.8272 | − | 20.4853i | 0.477306 | − | 0.826719i | ||||
\(615\) | − | 37.6339i | − | 1.51754i | ||||||
\(616\) | 1.00000 | − | 2.44949i | 0.0402911 | − | 0.0986928i | ||||
\(617\) | − | 8.48528i | − | 0.341605i | −0.985305 | − | 0.170802i | \(-0.945364\pi\) | ||
0.985305 | − | 0.170802i | \(-0.0546359\pi\) | |||||||
\(618\) | −17.7408 | − | 10.2426i | −0.713639 | − | 0.412019i | ||||
\(619\) | 3.77208 | − | 2.17781i | 0.151613 | − | 0.0875336i | −0.422274 | − | 0.906468i | \(-0.638768\pi\) |
0.573887 | + | 0.818934i | \(0.305435\pi\) | |||||||
\(620\) | −5.19615 | + | 3.00000i | −0.208683 | + | 0.120483i | ||||
\(621\) | −3.22848 | + | 5.59188i | −0.129554 | + | 0.224395i | ||||
\(622\) | − | 25.2123i | − | 1.01092i | ||||||
\(623\) | −5.31925 | + | 0.727922i | −0.213111 | + | 0.0291636i | ||||
\(624\) | 6.00000 | 0.240192 | ||||||||
\(625\) | −34.2279 | + | 59.2845i | −1.36912 | + | 2.37138i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.5446 | − | 7.24264i | 0.500984 | − | 0.289243i | ||||
\(628\) | −16.2426 | − | 9.37769i | −0.648152 | − | 0.374211i | ||||
\(629\) | 12.6677 | 0.505095 | ||||||||
\(630\) | 26.2279 | − | 20.3389i | 1.04495 | − | 0.810319i | ||||
\(631\) | −26.9706 | −1.07368 | −0.536841 | − | 0.843684i | \(-0.680382\pi\) | ||||
−0.536841 | + | 0.843684i | \(0.680382\pi\) | |||||||
\(632\) | 4.54026 | + | 2.62132i | 0.180602 | + | 0.104271i | ||||
\(633\) | −18.7279 | + | 10.8126i | −0.744368 | + | 0.429761i | ||||
\(634\) | 12.6213 | + | 21.8608i | 0.501257 | + | 0.868202i | ||||
\(635\) | −31.8689 | + | 55.1985i | −1.26468 | + | 2.19049i | ||||
\(636\) | 14.6969 | 0.582772 | ||||||||
\(637\) | −23.4853 | − | 6.03668i | −0.930521 | − | 0.239182i | ||||
\(638\) | 8.48528i | 0.335936i | ||||||||
\(639\) | 15.5885 | + | 9.00000i | 0.616670 | + | 0.356034i | ||||
\(640\) | 3.62132 | − | 2.09077i | 0.143145 | − | 0.0826450i | ||||
\(641\) | 4.30463 | − | 2.48528i | 0.170023 | − | 0.0981627i | −0.412574 | − | 0.910924i | \(-0.635370\pi\) |
0.582597 | + | 0.812761i | \(0.302037\pi\) | |||||||
\(642\) | 22.5000 | + | 12.9904i | 0.888004 | + | 0.512689i | ||||
\(643\) | 4.65279i | 0.183488i | 0.995783 | + | 0.0917441i | \(0.0292442\pi\) | ||||
−0.995783 | + | 0.0917441i | \(0.970756\pi\) | |||||||
\(644\) | 2.59808 | − | 2.01472i | 0.102379 | − | 0.0793910i | ||||
\(645\) | 32.4853i | 1.27911i | ||||||||
\(646\) | −13.2426 | + | 22.9369i | −0.521025 | + | 0.902441i | ||||
\(647\) | 7.28692 | + | 12.6213i | 0.286478 | + | 0.496195i | 0.972967 | − | 0.230946i | \(-0.0741820\pi\) |
−0.686488 | + | 0.727141i | \(0.740849\pi\) | |||||||
\(648\) | 7.79423 | − | 4.50000i | 0.306186 | − | 0.176777i | ||||
\(649\) | 5.48528 | + | 3.16693i | 0.215316 | + | 0.124313i | ||||
\(650\) | 43.2503 | 1.69642 | ||||||||
\(651\) | 6.51472 | − | 0.891519i | 0.255332 | − | 0.0349414i | ||||
\(652\) | 13.0000 | 0.509119 | ||||||||
\(653\) | −36.5577 | − | 21.1066i | −1.43061 | − | 0.825965i | −0.433446 | − | 0.901179i | \(-0.642703\pi\) |
−0.997167 | + | 0.0752143i | \(0.976036\pi\) | |||||||
\(654\) | 2.38794 | + | 4.13604i | 0.0933760 | + | 0.161732i | ||||
\(655\) | 13.2426 | + | 22.9369i | 0.517433 | + | 0.896220i | ||||
\(656\) | −2.59808 | + | 4.50000i | −0.101438 | + | 0.175695i | ||||
\(657\) | 25.0892i | 0.978825i | ||||||||
\(658\) | 10.2426 | + | 4.18154i | 0.399300 | + | 0.163013i | ||||
\(659\) | 7.97056i | 0.310489i | 0.987876 | + | 0.155245i | \(0.0496165\pi\) | ||||
−0.987876 | + | 0.155245i | \(0.950383\pi\) | |||||||
\(660\) | 3.62132 | − | 6.27231i | 0.140960 | − | 0.244149i | ||||
\(661\) | −23.4853 | + | 13.5592i | −0.913472 | + | 0.527393i | −0.881546 | − | 0.472097i | \(-0.843497\pi\) |
−0.0319251 | + | 0.999490i | \(0.510164\pi\) | |||||||
\(662\) | −16.4545 | + | 9.50000i | −0.639522 | + | 0.369228i | ||||
\(663\) | −9.50079 | + | 16.4558i | −0.368980 | + | 0.639092i | ||||
\(664\) | 3.16693i | 0.122901i | ||||||||
\(665\) | −85.6600 | − | 34.9706i | −3.32175 | − | 1.35610i | ||||
\(666\) | 12.0000i | 0.464991i | ||||||||
\(667\) | −5.27208 | + | 9.13151i | −0.204136 | + | 0.353573i | ||||
\(668\) | −1.01461 | − | 1.75736i | −0.0392565 | − | 0.0679943i | ||||
\(669\) | −5.48528 | − | 9.50079i | −0.212073 | − | 0.367322i | ||||
\(670\) | −12.6213 | − | 7.28692i | −0.487604 | − | 0.281518i | ||||
\(671\) | 0.717439 | 0.0276964 | ||||||||
\(672\) | −4.54026 | + | 0.621320i | −0.175144 | + | 0.0239680i | ||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | 26.4010 | + | 15.2426i | 1.01693 | + | 0.587125i | ||||
\(675\) | 56.1838 | − | 32.4377i | 2.16251 | − | 1.24853i | ||||
\(676\) | 0.500000 | + | 0.866025i | 0.0192308 | + | 0.0333087i | ||||
\(677\) | 8.48617 | − | 14.6985i | 0.326150 | − | 0.564909i | −0.655594 | − | 0.755113i | \(-0.727582\pi\) |
0.981744 | + | 0.190205i | \(0.0609152\pi\) | |||||||
\(678\) | − | 31.1769i | − | 1.19734i | ||||||
\(679\) | −0.621320 | + | 0.481813i | −0.0238441 | + | 0.0184903i | ||||
\(680\) | 13.2426i | 0.507832i | ||||||||
\(681\) | −32.8835 | − | 18.9853i | −1.26010 | − | 0.727518i | ||||
\(682\) | 1.24264 | − | 0.717439i | 0.0475832 | − | 0.0274722i | ||||
\(683\) | −20.7846 | + | 12.0000i | −0.795301 | + | 0.459167i | −0.841825 | − | 0.539750i | \(-0.818519\pi\) |
0.0465244 | + | 0.998917i | \(0.485185\pi\) | |||||||
\(684\) | −21.7279 | − | 12.5446i | −0.830788 | − | 0.479656i | ||||
\(685\) | − | 60.5708i | − | 2.31429i | ||||||
\(686\) | 18.3967 | + | 2.13604i | 0.702388 | + | 0.0815543i | ||||
\(687\) | −12.0000 | −0.457829 | ||||||||
\(688\) | 2.24264 | − | 3.88437i | 0.0854999 | − | 0.148090i | ||||
\(689\) | −14.6969 | − | 25.4558i | −0.559909 | − | 0.969790i | ||||
\(690\) | 7.79423 | − | 4.50000i | 0.296721 | − | 0.171312i | ||||
\(691\) | 0.257359 | + | 0.148586i | 0.00979041 | + | 0.00565250i | 0.504887 | − | 0.863185i | \(-0.331534\pi\) |
−0.495097 | + | 0.868838i | \(0.664867\pi\) | |||||||
\(692\) | 8.36308 | 0.317917 | ||||||||
\(693\) | −6.27231 | + | 4.86396i | −0.238265 | + | 0.184767i | ||||
\(694\) | −0.514719 | −0.0195385 | ||||||||
\(695\) | 12.5446 | + | 7.24264i | 0.475845 | + | 0.274729i | ||||
\(696\) | 12.7279 | − | 7.34847i | 0.482451 | − | 0.278543i | ||||
\(697\) | −8.22792 | − | 14.2512i | −0.311655 | − | 0.539802i | ||||
\(698\) | 7.70719 | − | 13.3492i | 0.291721 | − | 0.505276i | ||||
\(699\) | −44.9823 | −1.70139 | ||||||||
\(700\) | −32.7279 | + | 4.47871i | −1.23700 | + | 0.169279i | ||||
\(701\) | 14.4853i | 0.547102i | 0.961858 | + | 0.273551i | \(0.0881982\pi\) | ||||
−0.961858 | + | 0.273551i | \(0.911802\pi\) | |||||||
\(702\) | −15.5885 | − | 9.00000i | −0.588348 | − | 0.339683i | ||||
\(703\) | 28.9706 | − | 16.7262i | 1.09265 | − | 0.630839i | ||||
\(704\) | −0.866025 | + | 0.500000i | −0.0326396 | + | 0.0188445i | ||||
\(705\) | 26.2279 | + | 15.1427i | 0.987801 | + | 0.570307i | ||||
\(706\) | − | 25.0892i | − | 0.944246i | ||||||
\(707\) | −2.02922 | + | 4.97056i | −0.0763168 | + | 0.186937i | ||||
\(708\) | − | 10.9706i | − | 0.412299i | ||||||
\(709\) | 11.2426 | − | 19.4728i | 0.422226 | − | 0.731317i | −0.573931 | − | 0.818904i | \(-0.694582\pi\) |
0.996157 | + | 0.0875866i | \(0.0279155\pi\) | |||||||
\(710\) | −12.5446 | − | 21.7279i | −0.470791 | − | 0.815434i | ||||
\(711\) | −7.86396 | − | 13.6208i | −0.294922 | − | 0.510819i | ||||
\(712\) | 1.75736 | + | 1.01461i | 0.0658598 | + | 0.0380242i | ||||
\(713\) | 1.78304 | 0.0667753 | ||||||||
\(714\) | 5.48528 | − | 13.4361i | 0.205281 | − | 0.502835i | ||||
\(715\) | −14.4853 | −0.541719 | ||||||||
\(716\) | −12.5446 | − | 7.24264i | −0.468815 | − | 0.270670i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.24264 | + | 7.34847i | 0.158334 | + | 0.274242i | ||||
\(719\) | −9.31615 | + | 16.1360i | −0.347434 | + | 0.601773i | −0.985793 | − | 0.167966i | \(-0.946280\pi\) |
0.638359 | + | 0.769739i | \(0.279613\pi\) | |||||||
\(720\) | −12.5446 | −0.467510 | ||||||||
\(721\) | −4.24264 | − | 31.0028i | −0.158004 | − | 1.15461i | ||||
\(722\) | 50.9411i | 1.89583i | ||||||||
\(723\) | −12.0000 | + | 20.7846i | −0.446285 | + | 0.772988i | ||||
\(724\) | 14.4853 | − | 8.36308i | 0.538341 | − | 0.310811i | ||||
\(725\) | 91.7477 | − | 52.9706i | 3.40742 | − | 1.96728i | ||||
\(726\) | −0.866025 | + | 1.50000i | −0.0321412 | + | 0.0556702i | ||||
\(727\) | − | 7.76874i | − | 0.288126i | −0.989568 | − | 0.144063i | \(-0.953983\pi\) | ||
0.989568 | − | 0.144063i | \(-0.0460169\pi\) | |||||||
\(728\) | 5.61642 | + | 7.24264i | 0.208158 | + | 0.268430i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 17.4853 | − | 30.2854i | 0.647159 | − | 1.12091i | ||||
\(731\) | 7.10228 | + | 12.3015i | 0.262687 | + | 0.454988i | ||||
\(732\) | −0.621320 | − | 1.07616i | −0.0229647 | − | 0.0397760i | ||||
\(733\) | 4.86396 | + | 2.80821i | 0.179654 | + | 0.103724i | 0.587130 | − | 0.809492i | \(-0.300258\pi\) |
−0.407476 | + | 0.913216i | \(0.633591\pi\) | |||||||
\(734\) | −25.0892 | −0.926061 | ||||||||
\(735\) | 49.1023 | + | 12.6213i | 1.81117 | + | 0.465544i | ||||
\(736\) | −1.24264 | −0.0458043 | ||||||||
\(737\) | 3.01834 | + | 1.74264i | 0.111182 | + | 0.0641910i | ||||
\(738\) | 13.5000 | − | 7.79423i | 0.496942 | − | 0.286910i | ||||
\(739\) | −7.00000 | − | 12.1244i | −0.257499 | − | 0.446002i | 0.708072 | − | 0.706140i | \(-0.249565\pi\) |
−0.965571 | + | 0.260138i | \(0.916232\pi\) | |||||||
\(740\) | 8.36308 | − | 14.4853i | 0.307433 | − | 0.532490i | ||||
\(741\) | 50.1785i | 1.84335i | ||||||||
\(742\) | 13.7574 | + | 17.7408i | 0.505049 | + | 0.651284i | ||||
\(743\) | 12.0000i | 0.440237i | 0.975473 | + | 0.220119i | \(0.0706445\pi\) | ||||
−0.975473 | + | 0.220119i | \(0.929356\pi\) | |||||||
\(744\) | −2.15232 | − | 1.24264i | −0.0789078 | − | 0.0455574i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.3528 | + | 8.86396i | −0.562107 | + | 0.324533i | ||||
\(747\) | 4.75039 | − | 8.22792i | 0.173808 | − | 0.301044i | ||||
\(748\) | − | 3.16693i | − | 0.115794i | ||||||
\(749\) | 5.38079 | + | 39.3198i | 0.196610 | + | 1.43671i | ||||
\(750\) | −54.2132 | −1.97959 | ||||||||
\(751\) | −23.7279 | + | 41.0980i | −0.865844 | + | 1.49969i | 0.000362347 | 1.00000i | \(0.499885\pi\) | |
−0.866207 | + | 0.499686i | \(0.833449\pi\) | |||||||
\(752\) | −2.09077 | − | 3.62132i | −0.0762425 | − | 0.132056i | ||||
\(753\) | 22.0454 | − | 12.7279i | 0.803379 | − | 0.463831i | ||||
\(754\) | −25.4558 | − | 14.6969i | −0.927047 | − | 0.535231i | ||||
\(755\) | −3.16693 | −0.115256 | ||||||||
\(756\) | 12.7279 | + | 5.19615i | 0.462910 | + | 0.188982i | ||||
\(757\) | −47.9411 | −1.74245 | −0.871225 | − | 0.490884i | \(-0.836674\pi\) | ||||
−0.871225 | + | 0.490884i | \(0.836674\pi\) | |||||||
\(758\) | −0.0254934 | − | 0.0147186i | −0.000925962 | − | 0.000534605i | ||||
\(759\) | −1.86396 | + | 1.07616i | −0.0676575 | + | 0.0390621i | ||||
\(760\) | 17.4853 | + | 30.2854i | 0.634258 | + | 1.09857i | ||||
\(761\) | −11.9758 | + | 20.7426i | −0.434121 | + | 0.751920i | −0.997223 | − | 0.0744671i | \(-0.976274\pi\) |
0.563102 | + | 0.826387i | \(0.309608\pi\) | |||||||
\(762\) | −26.4010 | −0.956408 | ||||||||
\(763\) | −2.75736 | + | 6.75412i | −0.0998231 | + | 0.244516i | ||||
\(764\) | − | 18.0000i | − | 0.651217i | ||||||
\(765\) | 19.8640 | − | 34.4054i | 0.718183 | − | 1.24393i | ||||
\(766\) | −27.2132 | + | 15.7116i | −0.983253 | + | 0.567681i | ||||
\(767\) | −19.0016 | + | 10.9706i | −0.686107 | + | 0.396124i | ||||
\(768\) | 1.50000 | + | 0.866025i | 0.0541266 | + | 0.0312500i | ||||
\(769\) | 21.0308i | 0.758390i | 0.925317 | + | 0.379195i | \(0.123799\pi\) | ||||
−0.925317 | + | 0.379195i | \(0.876201\pi\) | |||||||
\(770\) | 10.9612 | − | 1.50000i | 0.395013 | − | 0.0540562i | ||||
\(771\) | − | 3.51472i | − | 0.126579i | ||||||
\(772\) | −8.24264 | + | 14.2767i | −0.296659 | + | 0.513829i | ||||
\(773\) | 11.5916 | + | 20.0772i | 0.416919 | + | 0.722125i | 0.995628 | − | 0.0934090i | \(-0.0297764\pi\) |
−0.578709 | + | 0.815534i | \(0.696443\pi\) | |||||||
\(774\) | −11.6531 | + | 6.72792i | −0.418862 | + | 0.241830i | ||||
\(775\) | −15.5147 | − | 8.95743i | −0.557305 | − | 0.321760i | ||||
\(776\) | 0.297173 | 0.0106679 | ||||||||
\(777\) | −14.4853 | + | 11.2328i | −0.519657 | + | 0.402976i | ||||
\(778\) | 27.7279 | 0.994094 | ||||||||
\(779\) | −37.6339 | − | 21.7279i | −1.34837 | − | 0.778484i | ||||
\(780\) | 12.5446 | + | 21.7279i | 0.449170 | + | 0.777984i | ||||
\(781\) | 3.00000 | + | 5.19615i | 0.107348 | + | 0.185933i | ||||
\(782\) | 1.96768 | − | 3.40812i | 0.0703640 | − | 0.121874i | ||||
\(783\) | −44.0908 | −1.57568 | ||||||||
\(784\) | −5.00000 | − | 4.89898i | −0.178571 | − | 0.174964i | ||||
\(785\) | − | 78.4264i | − | 2.79916i | ||||||
\(786\) | −5.48528 | + | 9.50079i | −0.195654 | + | 0.338882i | ||||
\(787\) | −15.7279 | + | 9.08052i | −0.560640 | + | 0.323686i | −0.753402 | − | 0.657560i | \(-0.771589\pi\) |
0.192762 | + | 0.981245i | \(0.438255\pi\) | |||||||
\(788\) | 7.34847 | − | 4.24264i | 0.261778 | − | 0.151138i | ||||
\(789\) | 9.50079 | − | 16.4558i | 0.338237 | − | 0.585844i | ||||
\(790\) | 21.9223i | 0.779961i | ||||||||
\(791\) | 37.6339 | − | 29.1838i | 1.33811 | − | 1.03766i | ||||
\(792\) | 3.00000 | 0.106600 | ||||||||
\(793\) | −1.24264 | + | 2.15232i | −0.0441275 | + | 0.0764310i | ||||
\(794\) | 12.2474 | + | 21.2132i | 0.434646 | + | 0.752828i | ||||
\(795\) | 30.7279 | + | 53.2223i | 1.08981 | + | 1.88760i | ||||
\(796\) | 11.4853 | + | 6.63103i | 0.407085 | + | 0.235031i | ||||
\(797\) | −1.90613 | −0.0675186 | −0.0337593 | − | 0.999430i | \(-0.510748\pi\) | ||||
−0.0337593 | + | 0.999430i | \(0.510748\pi\) | |||||||
\(798\) | −5.19615 | − | 37.9706i | −0.183942 | − | 1.34414i | ||||
\(799\) | 13.2426 | 0.468491 | ||||||||
\(800\) | 10.8126 | + | 6.24264i | 0.382282 | + | 0.220711i | ||||
\(801\) | −3.04384 | − | 5.27208i | −0.107549 | − | 0.186280i | ||||
\(802\) | −4.24264 | − | 7.34847i | −0.149813 | − | 0.259483i | ||||
\(803\) | −4.18154 | + | 7.24264i | −0.147563 | + | 0.255587i | ||||
\(804\) | − | 6.03668i | − | 0.212897i | ||||||
\(805\) | 12.7279 | + | 5.19615i | 0.448600 | + | 0.183140i | ||||
\(806\) | 4.97056i | 0.175081i | ||||||||
\(807\) | −34.4054 | − | 19.8640i | −1.21113 | − | 0.699245i | ||||
\(808\) | 1.75736 | − | 1.01461i | 0.0618237 | − | 0.0356939i | ||||
\(809\) | −2.59808 | + | 1.50000i | −0.0913435 | + | 0.0527372i | −0.544976 | − | 0.838452i | \(-0.683461\pi\) |
0.453632 | + | 0.891189i | \(0.350128\pi\) | |||||||
\(810\) | 32.5919 | + | 18.8169i | 1.14516 | + | 0.661160i | ||||
\(811\) | 2.27541i | 0.0799004i | 0.999202 | + | 0.0399502i | \(0.0127199\pi\) | ||||
−0.999202 | + | 0.0399502i | \(0.987280\pi\) | |||||||
\(812\) | 20.7846 | + | 8.48528i | 0.729397 | + | 0.297775i | ||||
\(813\) | −13.4558 | −0.471917 | ||||||||
\(814\) | −2.00000 | + | 3.46410i | −0.0701000 | + | 0.121417i | ||||
\(815\) | 27.1800 | + | 47.0772i | 0.952074 | + | 1.64904i | ||||
\(816\) | −4.75039 | + | 2.74264i | −0.166297 | + | 0.0960116i | ||||
\(817\) | 32.4853 | + | 18.7554i | 1.13652 | + | 0.656168i | ||||
\(818\) | 15.2913 | 0.534647 | ||||||||
\(819\) | −3.72792 | − | 27.2416i | −0.130264 | − | 0.951897i | ||||
\(820\) | −21.7279 | −0.758772 | ||||||||
\(821\) | 2.15232 | + | 1.24264i | 0.0751164 | + | 0.0433685i | 0.537088 | − | 0.843526i | \(-0.319524\pi\) |
−0.461971 | + | 0.886895i | \(0.652858\pi\) | |||||||
\(822\) | 21.7279 | − | 12.5446i | 0.757848 | − | 0.437544i | ||||
\(823\) | 6.75736 | + | 11.7041i | 0.235547 | + | 0.407979i | 0.959431 | − | 0.281942i | \(-0.0909786\pi\) |
−0.723885 | + | 0.689921i | \(0.757645\pi\) | |||||||
\(824\) | −5.91359 | + | 10.2426i | −0.206010 | + | 0.356819i | ||||
\(825\) | 21.6251 | 0.752891 | ||||||||
\(826\) | 13.2426 | − | 10.2692i | 0.460770 | − | 0.357312i | ||||
\(827\) | 17.4853i | 0.608023i | 0.952668 | + | 0.304011i | \(0.0983261\pi\) | ||||
−0.952668 | + | 0.304011i | \(0.901674\pi\) | |||||||
\(828\) | 3.22848 | + | 1.86396i | 0.112197 | + | 0.0647771i | ||||
\(829\) | −28.9706 | + | 16.7262i | −1.00619 | + | 0.580924i | −0.910074 | − | 0.414447i | \(-0.863975\pi\) |
−0.0961156 | + | 0.995370i | \(0.530642\pi\) | |||||||
\(830\) | −11.4685 | + | 6.62132i | −0.398076 | + | 0.229829i | ||||
\(831\) | 42.7279 | + | 24.6690i | 1.48222 | + | 0.855757i | ||||
\(832\) | − | 3.46410i | − | 0.120096i | ||||||
\(833\) | 21.3535 | − | 5.95584i | 0.739854 | − | 0.206358i | ||||
\(834\) | 6.00000i | 0.207763i | ||||||||
\(835\) | 4.24264 | − | 7.34847i | 0.146823 | − | 0.254304i | ||||
\(836\) | −4.18154 | − | 7.24264i | −0.144622 | − | 0.250492i | ||||
\(837\) | 3.72792 | + | 6.45695i | 0.128856 | + | 0.223185i | ||||
\(838\) | −7.24264 | − | 4.18154i | −0.250193 | − | 0.144449i | ||||
\(839\) | 14.8200 | 0.511644 | 0.255822 | − | 0.966724i | \(-0.417654\pi\) | ||||
0.255822 | + | 0.966724i | \(0.417654\pi\) | |||||||
\(840\) | −11.7426 | − | 15.1427i | −0.405160 | − | 0.522473i | ||||
\(841\) | −43.0000 | −1.48276 | ||||||||
\(842\) | 14.2767 | + | 8.24264i | 0.492007 | + | 0.284060i | ||||
\(843\) | −15.1427 | − | 26.2279i | −0.521542 | − | 0.903338i | ||||
\(844\) | 6.24264 | + | 10.8126i | 0.214881 | + | 0.372184i | ||||
\(845\) | −2.09077 | + | 3.62132i | −0.0719247 | + | 0.124577i | ||||
\(846\) | 12.5446i | 0.431293i | ||||||||
\(847\) | −2.62132 | + | 0.358719i | −0.0900696 | + | 0.0123257i | ||||
\(848\) | − | 8.48528i | − | 0.291386i | ||||||
\(849\) | 21.2132 | − | 36.7423i | 0.728035 | − | 1.26099i | ||||
\(850\) | −34.2426 | + | 19.7700i | −1.17451 | + | 0.678105i | ||||
\(851\) | −4.30463 | + | 2.48528i | −0.147561 | + | 0.0851943i | ||||
\(852\) | 5.19615 | − | 9.00000i | 0.178017 | − | 0.308335i | ||||
\(853\) | 10.5154i | 0.360040i | 0.983663 | + | 0.180020i | \(0.0576163\pi\) | ||||
−0.983663 | + | 0.180020i | \(0.942384\pi\) | |||||||
\(854\) | 0.717439 | − | 1.75736i | 0.0245503 | − | 0.0601356i | ||||
\(855\) | − | 104.912i | − | 3.58790i | ||||||
\(856\) | 7.50000 | − | 12.9904i | 0.256345 | − | 0.444002i | ||||
\(857\) | −21.3535 | − | 36.9853i | −0.729420 | − | 1.26339i | −0.957128 | − | 0.289664i | \(-0.906457\pi\) |
0.227708 | − | 0.973729i | \(-0.426877\pi\) | |||||||
\(858\) | −3.00000 | − | 5.19615i | −0.102418 | − | 0.177394i | ||||
\(859\) | −41.4411 | − | 23.9260i | −1.41395 | − | 0.816346i | −0.418195 | − | 0.908357i | \(-0.637337\pi\) |
−0.995758 | + | 0.0920112i | \(0.970670\pi\) | |||||||
\(860\) | 18.7554 | 0.639553 | ||||||||
\(861\) | 22.0454 | + | 9.00000i | 0.751305 | + | 0.306719i | ||||
\(862\) | −9.51472 | −0.324073 | ||||||||
\(863\) | −23.1216 | − | 13.3492i | −0.787067 | − | 0.454413i | 0.0518618 | − | 0.998654i | \(-0.483484\pi\) |
−0.838929 | + | 0.544241i | \(0.816818\pi\) | |||||||
\(864\) | −2.59808 | − | 4.50000i | −0.0883883 | − | 0.153093i | ||||
\(865\) | 17.4853 | + | 30.2854i | 0.594517 | + | 1.02973i | ||||
\(866\) | −14.4253 | + | 24.9853i | −0.490190 | + | 0.849034i | ||||
\(867\) | 12.0734i | 0.410033i | ||||||||
\(868\) | −0.514719 | − | 3.76127i | −0.0174707 | − | 0.127666i | ||||
\(869\) | − | 5.24264i | − | 0.177844i | ||||||
\(870\) | 53.2223 | + | 30.7279i | 1.80441 | + | 1.04177i | ||||
\(871\) | −10.4558 | + | 6.03668i | −0.354283 | + | 0.204545i | ||||
\(872\) | 2.38794 | − | 1.37868i | 0.0808660 | − | 0.0466880i | ||||
\(873\) | −0.772078 | − | 0.445759i | −0.0261309 | − | 0.0150867i | ||||
\(874\) | − | 10.3923i | − | 0.351525i | ||||||
\(875\) | −50.7473 | − | 65.4411i | −1.71557 | − | 2.21231i | ||||
\(876\) | 14.4853 | 0.489412 | ||||||||
\(877\) | 3.34924 | − | 5.80106i | 0.113096 | − | 0.195888i | −0.803921 | − | 0.594736i | \(-0.797257\pi\) |
0.917017 | + | 0.398848i | \(0.130590\pi\) | |||||||
\(878\) | 9.43924 | + | 16.3492i | 0.318559 | + | 0.551760i | ||||
\(879\) | 18.6323 | − | 10.7574i | 0.628452 | − | 0.362837i | ||||
\(880\) | −3.62132 | − | 2.09077i | −0.122075 | − | 0.0704799i | ||||
\(881\) | 19.0016 | 0.640179 | 0.320090 | − | 0.947387i | \(-0.396287\pi\) | ||||
0.320090 | + | 0.947387i | \(0.396287\pi\) | |||||||
\(882\) | 5.64191 | + | 20.2279i | 0.189973 | + | 0.681110i | ||||
\(883\) | 32.4558 | 1.09223 | 0.546113 | − | 0.837711i | \(-0.316107\pi\) | ||||
0.546113 | + | 0.837711i | \(0.316107\pi\) | |||||||
\(884\) | 9.50079 | + | 5.48528i | 0.319546 | + | 0.184490i | ||||
\(885\) | 39.7279 | − | 22.9369i | 1.33544 | − | 0.771016i | ||||
\(886\) | 18.0000 | + | 31.1769i | 0.604722 | + | 1.04741i | ||||
\(887\) | −21.9223 | + | 37.9706i | −0.736079 | + | 1.27493i | 0.218169 | + | 0.975911i | \(0.429992\pi\) |
−0.954248 | + | 0.299016i | \(0.903342\pi\) | |||||||
\(888\) | 6.92820 | 0.232495 | ||||||||
\(889\) | −24.7132 | − | 31.8689i | −0.828854 | − | 1.06885i | ||||
\(890\) | 8.48528i | 0.284427i | ||||||||
\(891\) | −7.79423 | − | 4.50000i | −0.261116 | − | 0.150756i | ||||
\(892\) | −5.48528 | + | 3.16693i | −0.183661 | + | 0.106037i | ||||
\(893\) | 30.2854 | − | 17.4853i | 1.01346 | − | 0.585123i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 60.5708i | − | 2.02466i | ||||||
\(896\) | 0.358719 | + | 2.62132i | 0.0119840 | + | 0.0875722i | ||||
\(897\) | − | 7.45584i | − | 0.248943i | ||||||
\(898\) | −1.75736 | + | 3.04384i | −0.0586438 | + | 0.101574i | ||||
\(899\) | 6.08767 | + | 10.5442i | 0.203035 | + | 0.351667i | ||||
\(900\) | −18.7279 | − | 32.4377i | −0.624264 | − | 1.08126i | ||||
\(901\) | 23.2721 | + | 13.4361i | 0.775305 | + | 0.447623i | ||||
\(902\) | 5.19615 | 0.173013 | ||||||||
\(903\) | −19.0294 | − | 7.76874i | −0.633260 | − | 0.258527i | ||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | 60.5708 | + | 34.9706i | 2.01344 | + | 1.16246i | ||||
\(906\) | −0.655892 | − | 1.13604i | −0.0217906 | − | 0.0377424i | ||||
\(907\) | −25.2279 | − | 43.6960i | −0.837679 | − | 1.45090i | −0.891830 | − | 0.452371i | \(-0.850578\pi\) |
0.0541507 | − | 0.998533i | \(-0.482755\pi\) | |||||||
\(908\) | −10.9612 | + | 18.9853i | −0.363759 | + | 0.630049i | ||||
\(909\) | −6.08767 | −0.201915 | ||||||||
\(910\) | −14.4853 | + | 35.4815i | −0.480182 | + | 1.17620i | ||||
\(911\) | − | 2.27208i | − | 0.0752773i | −0.999291 | − | 0.0376387i | \(-0.988016\pi\) | ||
0.999291 | − | 0.0376387i | \(-0.0119836\pi\) | |||||||
\(912\) | −7.24264 | + | 12.5446i | −0.239828 | + | 0.415394i | ||||
\(913\) | 2.74264 | − | 1.58346i | 0.0907682 | − | 0.0524050i | ||||
\(914\) | −18.1610 | + | 10.4853i | −0.600714 | + | 0.346822i | ||||
\(915\) | 2.59808 | − | 4.50000i | 0.0858898 | − | 0.148765i | ||||
\(916\) | 6.92820i | 0.228914i | ||||||||
\(917\) | −16.6031 | + | 2.27208i | −0.548282 | + | 0.0750306i | ||||
\(918\) | 16.4558 | 0.543124 | ||||||||
\(919\) | −12.8640 | + | 22.2810i | −0.424343 | + | 0.734983i | −0.996359 | − | 0.0852590i | \(-0.972828\pi\) |
0.572016 | + | 0.820243i | \(0.306162\pi\) | |||||||
\(920\) | −2.59808 | − | 4.50000i | −0.0856560 | − | 0.148361i | ||||
\(921\) | 20.4853 | + | 35.4815i | 0.675013 | + | 1.16916i | ||||
\(922\) | 5.48528 | + | 3.16693i | 0.180648 | + | 0.104297i | ||||
\(923\) | −20.7846 | −0.684134 | ||||||||
\(924\) | 2.80821 | + | 3.62132i | 0.0923833 | + | 0.119133i | ||||
\(925\) | 49.9411 | 1.64205 | ||||||||
\(926\) | −25.5095 | − | 14.7279i | −0.838294 | − | 0.483990i | ||||
\(927\) | 30.7279 | − | 17.7408i | 1.00924 | − | 0.582683i | ||||
\(928\) | −4.24264 | − | 7.34847i | −0.139272 | − | 0.241225i | ||||
\(929\) | −4.18154 | + | 7.24264i | −0.137192 | + | 0.237623i | −0.926433 | − | 0.376461i | \(-0.877141\pi\) |
0.789241 | + | 0.614084i | \(0.210474\pi\) | |||||||
\(930\) | − | 10.3923i | − | 0.340777i | ||||||
\(931\) | 40.9706 | − | 41.8154i | 1.34276 | − | 1.37044i | ||||
\(932\) | 25.9706i | 0.850694i | ||||||||
\(933\) | 37.8185 | + | 21.8345i | 1.23812 | + | 0.714830i | ||||
\(934\) | 27.0000 | − | 15.5885i | 0.883467 | − | 0.510070i | ||||
\(935\) | 11.4685 | − | 6.62132i | 0.375059 | − | 0.216540i | ||||
\(936\) | −5.19615 | + | 9.00000i | −0.169842 | + | 0.294174i | ||||
\(937\) | − | 45.5257i | − | 1.48726i | −0.668592 | − | 0.743630i | \(-0.733103\pi\) | ||
0.668592 | − | 0.743630i | \(-0.266897\pi\) | |||||||
\(938\) | 7.28692 | − | 5.65076i | 0.237926 | − | 0.184504i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.74264 | − | 15.1427i | 0.285153 | − | 0.493900i | ||||
\(941\) | 5.19615 | + | 9.00000i | 0.169390 | + | 0.293392i | 0.938205 | − | 0.346079i | \(-0.112487\pi\) |
−0.768816 | + | 0.639470i | \(0.779154\pi\) | |||||||
\(942\) | 28.1331 | − | 16.2426i | 0.916625 | − | 0.529214i | ||||
\(943\) | 5.59188 | + | 3.22848i | 0.182097 | + | 0.105134i | ||||
\(944\) | −6.33386 | −0.206149 | ||||||||
\(945\) | 7.79423 | + | 56.9558i | 0.253546 | + | 1.85277i | ||||
\(946\) | −4.48528 | −0.145829 | ||||||||
\(947\) | 30.2854 | + | 17.4853i | 0.984143 | + | 0.568195i | 0.903518 | − | 0.428549i | \(-0.140975\pi\) |
0.0806247 | + | 0.996745i | \(0.474308\pi\) | |||||||
\(948\) | −7.86396 | + | 4.54026i | −0.255410 | + | 0.147461i | ||||
\(949\) | −14.4853 | − | 25.0892i | −0.470212 | − | 0.814431i | ||||
\(950\) | −52.2077 | + | 90.4264i | −1.69384 | + | 2.93382i | ||||
\(951\) | −43.7215 | −1.41777 | ||||||||
\(952\) | −7.75736 | − | 3.16693i | −0.251417 | − | 0.102641i | ||||
\(953\) | − | 25.9706i | − | 0.841269i | −0.907230 | − | 0.420635i | \(-0.861807\pi\) | ||
0.907230 | − | 0.420635i | \(-0.138193\pi\) | |||||||
\(954\) | −12.7279 | + | 22.0454i | −0.412082 | + | 0.713746i | ||||
\(955\) | 65.1838 | − | 37.6339i | 2.10930 | − | 1.21780i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.7279 | − | 7.34847i | −0.411435 | − | 0.237542i | ||||
\(958\) | 31.4231i | 1.01523i | ||||||||
\(959\) | 35.4815 | + | 14.4853i | 1.14576 | + | 0.467754i | ||||
\(960\) | 7.24264i | 0.233755i | ||||||||
\(961\) | −14.4706 | + | 25.0637i | −0.466792 | + | 0.808508i | ||||
\(962\) | −6.92820 | − | 12.0000i | −0.223374 | − | 0.386896i | ||||
\(963\) | −38.9711 | + | 22.5000i | −1.25583 | + | 0.725052i | ||||
\(964\) | 12.0000 | + | 6.92820i | 0.386494 | + | 0.223142i | ||||
\(965\) | −68.9339 | −2.21906 | ||||||||
\(966\) | 0.772078 | + | 5.64191i | 0.0248412 | + | 0.181526i | ||||
\(967\) | 2.21320 | 0.0711718 | 0.0355859 | − | 0.999367i | \(-0.488670\pi\) | ||||
0.0355859 | + | 0.999367i | \(0.488670\pi\) | |||||||
\(968\) | 0.866025 | + | 0.500000i | 0.0278351 | + | 0.0160706i | ||||
\(969\) | −22.9369 | − | 39.7279i | −0.736840 | − | 1.27624i | ||||
\(970\) | 0.621320 | + | 1.07616i | 0.0199494 | + | 0.0345534i | ||||
\(971\) | 21.9223 | − | 37.9706i | 0.703521 | − | 1.21853i | −0.263702 | − | 0.964604i | \(-0.584944\pi\) |
0.967223 | − | 0.253929i | \(-0.0817230\pi\) | |||||||
\(972\) | 15.5885i | 0.500000i | ||||||||
\(973\) | −7.24264 | + | 5.61642i | −0.232188 | + | 0.180054i | ||||
\(974\) | − | 14.9706i | − | 0.479688i | ||||||
\(975\) | −37.4558 | + | 64.8754i | −1.19955 | + | 2.07768i | ||||
\(976\) | −0.621320 | + | 0.358719i | −0.0198880 | + | 0.0114823i | ||||
\(977\) | −0.891519 | + | 0.514719i | −0.0285222 | + | 0.0164673i | −0.514193 | − | 0.857674i | \(-0.671909\pi\) |
0.485671 | + | 0.874142i | \(0.338575\pi\) | |||||||
\(978\) | −11.2583 | + | 19.5000i | −0.360002 | + | 0.623541i | ||||
\(979\) | − | 2.02922i | − | 0.0648543i | ||||||
\(980\) | 7.28692 | − | 28.3492i | 0.232772 | − | 0.905583i | ||||
\(981\) | −8.27208 | −0.264107 | ||||||||
\(982\) | 9.98528 | − | 17.2950i | 0.318643 | − | 0.551906i | ||||
\(983\) | −15.7731 | − | 27.3198i | −0.503084 | − | 0.871366i | −0.999994 | − | 0.00356437i | \(-0.998865\pi\) |
0.496910 | − | 0.867802i | \(-0.334468\pi\) | |||||||
\(984\) | −4.50000 | − | 7.79423i | −0.143455 | − | 0.248471i | ||||
\(985\) | 30.7279 | + | 17.7408i | 0.979073 | + | 0.565268i | ||||
\(986\) | 26.8723 | 0.855788 | ||||||||
\(987\) | −15.1427 | + | 11.7426i | −0.481997 | + | 0.373772i | ||||
\(988\) | 28.9706 | 0.921676 | ||||||||
\(989\) | −4.82687 | − | 2.78680i | −0.153486 | − | 0.0886150i | ||||
\(990\) | 6.27231 | + | 10.8640i | 0.199347 | + | 0.345279i | ||||
\(991\) | 4.00000 | + | 6.92820i | 0.127064 | + | 0.220082i | 0.922538 | − | 0.385906i | \(-0.126111\pi\) |
−0.795474 | + | 0.605988i | \(0.792778\pi\) | |||||||
\(992\) | −0.717439 | + | 1.24264i | −0.0227787 | + | 0.0394539i | ||||
\(993\) | − | 32.9090i | − | 1.04433i | ||||||
\(994\) | 15.7279 | − | 2.15232i | 0.498859 | − | 0.0682673i | ||||
\(995\) | 55.4558i | 1.75807i | ||||||||
\(996\) | −4.75039 | − | 2.74264i | −0.150522 | − | 0.0869039i | ||||
\(997\) | 0.514719 | − | 0.297173i | 0.0163013 | − | 0.00941156i | −0.491827 | − | 0.870693i | \(-0.663671\pi\) |
0.508129 | + | 0.861281i | \(0.330337\pi\) | |||||||
\(998\) | 11.2328 | − | 6.48528i | 0.355569 | − | 0.205288i | ||||
\(999\) | −18.0000 | − | 10.3923i | −0.569495 | − | 0.328798i |
(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 | 462.2.k.d.89.3 | yes | 8 | |
3.2 | odd | 2 | inner | 462.2.k.d.89.2 | ✓ | 8 | |
7.3 | odd | 6 | inner | 462.2.k.d.353.2 | yes | 8 | |
21.17 | even | 6 | inner | 462.2.k.d.353.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.k.d.89.2 | ✓ | 8 | 3.2 | odd | 2 | inner | |
462.2.k.d.89.3 | yes | 8 | 1.1 | even | 1 | trivial | |
462.2.k.d.353.2 | yes | 8 | 7.3 | odd | 6 | inner | |
462.2.k.d.353.3 | yes | 8 | 21.17 | even | 6 | inner |