Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(127,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.bj (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: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + \cdots + 97344 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1135.7 | ||
Root | \(2.24849 - 2.24849i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.1135 |
Dual form | 1638.2.bj.i.127.6 |
$q$-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 \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.24768i | 0.557981i | 0.960294 | + | 0.278991i | \(0.0899998\pi\) | ||||
−0.960294 | + | 0.278991i | \(0.910000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | − | 0.500000i | 0.327327 | − | 0.188982i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.623842 | + | 1.08053i | −0.197276 | + | 0.341692i | ||||
\(11\) | −1.41441 | − | 0.816612i | −0.426461 | − | 0.246218i | 0.271377 | − | 0.962473i | \(-0.412521\pi\) |
−0.697838 | + | 0.716256i | \(0.745854\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.60364 | − | 0.117447i | 0.999469 | − | 0.0325741i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.78174 | + | 4.81811i | 0.674671 | + | 1.16856i | 0.976565 | + | 0.215223i | \(0.0690477\pi\) |
−0.301894 | + | 0.953341i | \(0.597619\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.23947 | + | 2.44766i | −0.972601 | + | 0.561531i | −0.900028 | − | 0.435832i | \(-0.856454\pi\) |
−0.0725725 | + | 0.997363i | \(0.523121\pi\) | |||||||
\(20\) | −1.08053 | + | 0.623842i | −0.241613 | + | 0.139495i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.816612 | − | 1.41441i | −0.174102 | − | 0.301554i | ||||
\(23\) | −2.83571 | + | 4.91159i | −0.591286 | + | 1.02414i | 0.402773 | + | 0.915300i | \(0.368046\pi\) |
−0.994059 | + | 0.108838i | \(0.965287\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.44329 | 0.688657 | ||||||||
\(26\) | 3.17957 | + | 1.70011i | 0.623564 | + | 0.333418i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.866025 | + | 0.500000i | 0.163663 | + | 0.0944911i | ||||
\(29\) | 1.59985 | − | 2.77102i | 0.297085 | − | 0.514566i | −0.678383 | − | 0.734708i | \(-0.737319\pi\) |
0.975468 | + | 0.220143i | \(0.0706523\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.53063i | − | 0.634121i | −0.948405 | − | 0.317060i | \(-0.897304\pi\) | ||
0.948405 | − | 0.317060i | \(-0.102696\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.56348i | 0.954129i | ||||||||
\(35\) | 0.623842 | + | 1.08053i | 0.105449 | + | 0.182642i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.12562 | + | 3.53663i | 1.00705 | + | 0.581418i | 0.910325 | − | 0.413894i | \(-0.135832\pi\) |
0.0967201 | + | 0.995312i | \(0.469165\pi\) | |||||||
\(38\) | −4.89532 | −0.794125 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.24768 | −0.197276 | ||||||||
\(41\) | −3.46229 | − | 1.99895i | −0.540718 | − | 0.312184i | 0.204652 | − | 0.978835i | \(-0.434394\pi\) |
−0.745370 | + | 0.666651i | \(0.767727\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.69078 | + | 4.66057i | 0.410341 | + | 0.710731i | 0.994927 | − | 0.100601i | \(-0.0320765\pi\) |
−0.584586 | + | 0.811332i | \(0.698743\pi\) | |||||||
\(44\) | − | 1.63322i | − | 0.246218i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.91159 | + | 2.83571i | −0.724175 | + | 0.418103i | ||||
\(47\) | 11.4980i | 1.67716i | 0.544778 | + | 0.838580i | \(0.316614\pi\) | ||||
−0.544778 | + | 0.838580i | \(0.683386\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | − | 0.866025i | 0.0714286 | − | 0.123718i | ||||
\(50\) | 2.98197 | + | 1.72164i | 0.421715 | + | 0.243477i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.90353 | + | 3.06212i | 0.263972 | + | 0.424639i | ||||
\(53\) | 4.82030 | 0.662120 | 0.331060 | − | 0.943610i | \(-0.392594\pi\) | ||||
0.331060 | + | 0.943610i | \(0.392594\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.01887 | − | 1.76474i | 0.137385 | − | 0.237957i | ||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.77102 | − | 1.59985i | 0.363853 | − | 0.210071i | ||||
\(59\) | 4.48259 | − | 2.58803i | 0.583584 | − | 0.336932i | −0.178972 | − | 0.983854i | \(-0.557277\pi\) |
0.762556 | + | 0.646922i | \(0.223944\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.97263 | − | 5.14874i | −0.380606 | − | 0.659229i | 0.610543 | − | 0.791983i | \(-0.290951\pi\) |
−0.991149 | + | 0.132754i | \(0.957618\pi\) | |||||||
\(62\) | 1.76532 | − | 3.05762i | 0.224196 | − | 0.388318i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.146537 | + | 4.49620i | 0.0181757 | + | 0.557685i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.48962 | − | 3.16943i | −0.670664 | − | 0.387208i | 0.125664 | − | 0.992073i | \(-0.459894\pi\) |
−0.796328 | + | 0.604865i | \(0.793227\pi\) | |||||||
\(68\) | −2.78174 | + | 4.81811i | −0.337335 | + | 0.584282i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.24768i | 0.149127i | ||||||||
\(71\) | −11.3538 | + | 6.55514i | −1.34745 | + | 0.777952i | −0.987888 | − | 0.155168i | \(-0.950408\pi\) |
−0.359565 | + | 0.933120i | \(0.617075\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.62310i | 0.775175i | 0.921833 | + | 0.387588i | \(0.126692\pi\) | ||||
−0.921833 | + | 0.387588i | \(0.873308\pi\) | |||||||
\(74\) | 3.53663 | + | 6.12562i | 0.411125 | + | 0.712089i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.23947 | − | 2.44766i | −0.486300 | − | 0.280766i | ||||
\(77\) | −1.63322 | −0.186123 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.21115 | −0.923827 | −0.461914 | − | 0.886925i | \(-0.652837\pi\) | ||||
−0.461914 | + | 0.886925i | \(0.652837\pi\) | |||||||
\(80\) | −1.08053 | − | 0.623842i | −0.120806 | − | 0.0697476i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.99895 | − | 3.46229i | −0.220747 | − | 0.382346i | ||||
\(83\) | 11.1721i | 1.22630i | 0.789968 | + | 0.613148i | \(0.210097\pi\) | ||||
−0.789968 | + | 0.613148i | \(0.789903\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.01148 | + | 3.47073i | −0.652037 | + | 0.376453i | ||||
\(86\) | 5.38157i | 0.580309i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.816612 | − | 1.41441i | 0.0870511 | − | 0.150777i | ||||
\(89\) | −2.16375 | − | 1.24924i | −0.229357 | − | 0.132419i | 0.380918 | − | 0.924609i | \(-0.375608\pi\) |
−0.610275 | + | 0.792189i | \(0.708941\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.06212 | − | 1.90353i | 0.320997 | − | 0.199544i | ||||
\(92\) | −5.67142 | −0.591286 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.74902 | + | 9.95759i | −0.592966 | + | 1.02705i | ||||
\(95\) | −3.05390 | − | 5.28951i | −0.313324 | − | 0.542693i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.02271 | − | 5.20926i | 0.916117 | − | 0.528920i | 0.0337228 | − | 0.999431i | \(-0.489264\pi\) |
0.882394 | + | 0.470511i | \(0.155930\pi\) | |||||||
\(98\) | 0.866025 | − | 0.500000i | 0.0874818 | − | 0.0505076i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.72164 | + | 2.98197i | 0.172164 | + | 0.298197i | ||||
\(101\) | 1.78522 | − | 3.09210i | 0.177636 | − | 0.307675i | −0.763434 | − | 0.645886i | \(-0.776488\pi\) |
0.941071 | + | 0.338210i | \(0.109822\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.63810 | 0.949670 | 0.474835 | − | 0.880075i | \(-0.342508\pi\) | ||||
0.474835 | + | 0.880075i | \(0.342508\pi\) | |||||||
\(104\) | 0.117447 | + | 3.60364i | 0.0115167 | + | 0.353366i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.17451 | + | 2.41015i | 0.405464 | + | 0.234095i | ||||
\(107\) | −2.18140 | + | 3.77830i | −0.210884 | + | 0.365262i | −0.951991 | − | 0.306125i | \(-0.900968\pi\) |
0.741107 | + | 0.671387i | \(0.234301\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 19.3037i | − | 1.84896i | −0.381230 | − | 0.924480i | \(-0.624499\pi\) | ||
0.381230 | − | 0.924480i | \(-0.375501\pi\) | |||||||
\(110\) | 1.76474 | − | 1.01887i | 0.168261 | − | 0.0971457i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | −4.73647 | − | 8.20380i | −0.445569 | − | 0.771748i | 0.552522 | − | 0.833498i | \(-0.313665\pi\) |
−0.998092 | + | 0.0617495i | \(0.980332\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.12812 | − | 3.53807i | −0.571450 | − | 0.329927i | ||||
\(116\) | 3.19970 | 0.297085 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.17605 | 0.476494 | ||||||||
\(119\) | 4.81811 | + | 2.78174i | 0.441676 | + | 0.255002i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.16629 | − | 7.21623i | −0.378754 | − | 0.656021i | ||||
\(122\) | − | 5.94526i | − | 0.538258i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.05762 | − | 1.76532i | 0.274582 | − | 0.158530i | ||||
\(125\) | 10.5345i | 0.942239i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.47672 | − | 12.9501i | 0.663452 | − | 1.14913i | −0.316251 | − | 0.948676i | \(-0.602424\pi\) |
0.979703 | − | 0.200457i | \(-0.0642425\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.12119 | + | 3.96709i | −0.186041 | + | 0.347937i | ||||
\(131\) | 13.3546 | 1.16680 | 0.583398 | − | 0.812187i | \(-0.301723\pi\) | ||||
0.583398 | + | 0.812187i | \(0.301723\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.44766 | + | 4.23947i | −0.212239 | + | 0.367608i | ||||
\(134\) | −3.16943 | − | 5.48962i | −0.273797 | − | 0.474231i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.81811 | + | 2.78174i | −0.413150 | + | 0.238532i | ||||
\(137\) | −6.27707 | + | 3.62407i | −0.536286 | + | 0.309625i | −0.743573 | − | 0.668655i | \(-0.766870\pi\) |
0.207286 | + | 0.978280i | \(0.433537\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.86534 | + | 13.6232i | 0.667129 | + | 1.15550i | 0.978703 | + | 0.205280i | \(0.0658104\pi\) |
−0.311574 | + | 0.950222i | \(0.600856\pi\) | |||||||
\(140\) | −0.623842 | + | 1.08053i | −0.0527243 | + | 0.0913211i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.1103 | −1.10019 | ||||||||
\(143\) | −5.19294 | − | 2.77665i | −0.434255 | − | 0.232195i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.45736 | + | 1.99611i | 0.287118 | + | 0.165768i | ||||
\(146\) | −3.31155 | + | 5.73577i | −0.274066 | + | 0.474696i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.07325i | 0.581418i | ||||||||
\(149\) | 2.20523 | − | 1.27319i | 0.180659 | − | 0.104304i | −0.406943 | − | 0.913454i | \(-0.633405\pi\) |
0.587602 | + | 0.809150i | \(0.300072\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9.89437i | − | 0.805192i | −0.915378 | − | 0.402596i | \(-0.868108\pi\) | ||
0.915378 | − | 0.402596i | \(-0.131892\pi\) | |||||||
\(152\) | −2.44766 | − | 4.23947i | −0.198531 | − | 0.343866i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.41441 | − | 0.816612i | −0.113977 | − | 0.0658044i | ||||
\(155\) | 4.40511 | 0.353827 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.96414 | 0.715416 | 0.357708 | − | 0.933833i | \(-0.383558\pi\) | ||||
0.357708 | + | 0.933833i | \(0.383558\pi\) | |||||||
\(158\) | −7.11107 | − | 4.10558i | −0.565726 | − | 0.326622i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.623842 | − | 1.08053i | −0.0493190 | − | 0.0854231i | ||||
\(161\) | 5.67142i | 0.446971i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.371849 | − | 0.214687i | 0.0291254 | − | 0.0168156i | −0.485367 | − | 0.874311i | \(-0.661314\pi\) |
0.514492 | + | 0.857495i | \(0.327981\pi\) | |||||||
\(164\) | − | 3.99790i | − | 0.312184i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.58604 | + | 9.67531i | −0.433561 | + | 0.750949i | ||||
\(167\) | 19.5072 | + | 11.2625i | 1.50951 | + | 0.871516i | 0.999939 | + | 0.0110885i | \(0.00352966\pi\) |
0.509572 | + | 0.860428i | \(0.329804\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9724 | − | 0.846476i | 0.997878 | − | 0.0651136i | ||||
\(170\) | −6.94146 | −0.532386 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.69078 | + | 4.66057i | −0.205170 | + | 0.355365i | ||||
\(173\) | 5.50562 | + | 9.53601i | 0.418584 | + | 0.725010i | 0.995797 | − | 0.0915841i | \(-0.0291930\pi\) |
−0.577213 | + | 0.816594i | \(0.695860\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.98197 | − | 1.72164i | 0.225416 | − | 0.130144i | ||||
\(176\) | 1.41441 | − | 0.816612i | 0.106615 | − | 0.0615544i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.24924 | − | 2.16375i | −0.0936347 | − | 0.162180i | ||||
\(179\) | −1.09732 | + | 1.90062i | −0.0820179 | + | 0.142059i | −0.904117 | − | 0.427286i | \(-0.859470\pi\) |
0.822099 | + | 0.569345i | \(0.192803\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.81625 | −0.357989 | −0.178995 | − | 0.983850i | \(-0.557284\pi\) | ||||
−0.178995 | + | 0.983850i | \(0.557284\pi\) | |||||||
\(182\) | 3.60364 | − | 0.117447i | 0.267119 | − | 0.00870579i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.91159 | − | 2.83571i | −0.362088 | − | 0.209051i | ||||
\(185\) | −4.41259 | + | 7.64283i | −0.324420 | + | 0.561912i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.08640i | − | 0.664463i | ||||||
\(188\) | −9.95759 | + | 5.74902i | −0.726232 | + | 0.419290i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 6.10780i | − | 0.443107i | ||||||
\(191\) | −6.13215 | − | 10.6212i | −0.443707 | − | 0.768523i | 0.554254 | − | 0.832347i | \(-0.313004\pi\) |
−0.997961 | + | 0.0638244i | \(0.979670\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.2180 | − | 9.36349i | −1.16740 | − | 0.673999i | −0.214334 | − | 0.976760i | \(-0.568758\pi\) |
−0.953066 | + | 0.302762i | \(0.902091\pi\) | |||||||
\(194\) | 10.4185 | 0.748006 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −15.7761 | − | 9.10832i | −1.12400 | − | 0.648941i | −0.181580 | − | 0.983376i | \(-0.558121\pi\) |
−0.942419 | + | 0.334435i | \(0.891454\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.60392 | − | 7.97423i | −0.326364 | − | 0.565278i | 0.655424 | − | 0.755261i | \(-0.272490\pi\) |
−0.981787 | + | 0.189983i | \(0.939157\pi\) | |||||||
\(200\) | 3.44329i | 0.243477i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.09210 | − | 1.78522i | 0.217559 | − | 0.125608i | ||||
\(203\) | − | 3.19970i | − | 0.224575i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.49406 | − | 4.31984i | 0.174193 | − | 0.301711i | ||||
\(206\) | 8.34684 | + | 4.81905i | 0.581552 | + | 0.335759i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.70011 | + | 3.17957i | −0.117881 | + | 0.220463i | ||||
\(209\) | 7.99514 | 0.553036 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.17384 | + | 3.76520i | −0.149653 | + | 0.259207i | −0.931099 | − | 0.364766i | \(-0.881149\pi\) |
0.781446 | + | 0.623973i | \(0.214482\pi\) | |||||||
\(212\) | 2.41015 | + | 4.17451i | 0.165530 | + | 0.286706i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.77830 | + | 2.18140i | −0.258279 | + | 0.149118i | ||||
\(215\) | −5.81492 | + | 3.35725i | −0.396574 | + | 0.228962i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.76532 | − | 3.05762i | −0.119838 | − | 0.207565i | ||||
\(218\) | 9.65186 | − | 16.7175i | 0.653706 | − | 1.13225i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.03775 | 0.137385 | ||||||||
\(221\) | 10.5903 | + | 17.0360i | 0.712378 | + | 1.14597i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.15095 | − | 2.39655i | −0.277968 | − | 0.160485i | 0.354535 | − | 0.935043i | \(-0.384639\pi\) |
−0.632503 | + | 0.774558i | \(0.717973\pi\) | |||||||
\(224\) | −0.500000 | + | 0.866025i | −0.0334077 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 9.47293i | − | 0.630130i | ||||||
\(227\) | 4.71526 | − | 2.72236i | 0.312963 | − | 0.180689i | −0.335289 | − | 0.942115i | \(-0.608834\pi\) |
0.648252 | + | 0.761426i | \(0.275500\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 15.0809i | − | 0.996573i | −0.867012 | − | 0.498287i | \(-0.833963\pi\) | ||
0.867012 | − | 0.498287i | \(-0.166037\pi\) | |||||||
\(230\) | −3.53807 | − | 6.12812i | −0.233293 | − | 0.404076i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.77102 | + | 1.59985i | 0.181927 | + | 0.105035i | ||||
\(233\) | −5.27514 | −0.345586 | −0.172793 | − | 0.984958i | \(-0.555279\pi\) | ||||
−0.172793 | + | 0.984958i | \(0.555279\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.3459 | −0.935824 | ||||||||
\(236\) | 4.48259 | + | 2.58803i | 0.291792 | + | 0.168466i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.78174 | + | 4.81811i | 0.180313 | + | 0.312312i | ||||
\(239\) | − | 29.0721i | − | 1.88052i | −0.340461 | − | 0.940259i | \(-0.610583\pi\) | ||
0.340461 | − | 0.940259i | \(-0.389417\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.5375 | − | 14.7441i | 1.64502 | − | 0.949751i | 0.666006 | − | 0.745947i | \(-0.268003\pi\) |
0.979012 | − | 0.203805i | \(-0.0653307\pi\) | |||||||
\(242\) | − | 8.33258i | − | 0.535639i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.97263 | − | 5.14874i | 0.190303 | − | 0.329615i | ||||
\(245\) | 1.08053 | + | 0.623842i | 0.0690323 | + | 0.0398558i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.9900 | + | 9.31839i | −0.953793 | + | 0.592915i | ||||
\(248\) | 3.53063 | 0.224196 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.26727 | + | 9.12319i | −0.333132 | + | 0.577001i | ||||
\(251\) | −1.04396 | − | 1.80819i | −0.0658941 | − | 0.114132i | 0.831196 | − | 0.555979i | \(-0.187657\pi\) |
−0.897090 | + | 0.441847i | \(0.854323\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.02173 | − | 4.63135i | 0.504322 | − | 0.291170i | ||||
\(254\) | 12.9501 | − | 7.47672i | 0.812559 | − | 0.469131i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 14.1891 | − | 24.5763i | 0.885094 | − | 1.53303i | 0.0394885 | − | 0.999220i | \(-0.487427\pi\) |
0.845606 | − | 0.533808i | \(-0.179240\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.07325 | 0.439511 | ||||||||
\(260\) | −3.82055 | + | 2.37500i | −0.236941 | + | 0.147292i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.5654 | + | 6.67729i | 0.714513 | + | 0.412524i | ||||
\(263\) | 12.2799 | − | 21.2695i | 0.757214 | − | 1.31153i | −0.187053 | − | 0.982350i | \(-0.559894\pi\) |
0.944266 | − | 0.329183i | \(-0.106773\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.01421i | 0.369450i | ||||||||
\(266\) | −4.23947 | + | 2.44766i | −0.259938 | + | 0.150076i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 6.33887i | − | 0.387208i | ||||||
\(269\) | −13.3076 | − | 23.0494i | −0.811379 | − | 1.40535i | −0.911899 | − | 0.410414i | \(-0.865384\pi\) |
0.100521 | − | 0.994935i | \(-0.467949\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.9931 | − | 9.81095i | −1.03225 | − | 0.595973i | −0.114625 | − | 0.993409i | \(-0.536567\pi\) |
−0.917630 | + | 0.397436i | \(0.869900\pi\) | |||||||
\(272\) | −5.56348 | −0.337335 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.24814 | −0.437876 | ||||||||
\(275\) | −4.87023 | − | 2.81183i | −0.293686 | − | 0.169560i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.6675 | + | 20.2087i | 0.701034 | + | 1.21423i | 0.968104 | + | 0.250549i | \(0.0806110\pi\) |
−0.267070 | + | 0.963677i | \(0.586056\pi\) | |||||||
\(278\) | 15.7307i | 0.943463i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.08053 | + | 0.623842i | −0.0645738 | + | 0.0372817i | ||||
\(281\) | − | 21.2604i | − | 1.26829i | −0.773215 | − | 0.634143i | \(-0.781353\pi\) | ||
0.773215 | − | 0.634143i | \(-0.218647\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.32039 | + | 16.1434i | −0.554039 | + | 0.959625i | 0.443938 | + | 0.896057i | \(0.353581\pi\) |
−0.997978 | + | 0.0635671i | \(0.979752\pi\) | |||||||
\(284\) | −11.3538 | − | 6.55514i | −0.673726 | − | 0.388976i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.10889 | − | 5.00112i | −0.183833 | − | 0.295723i | ||||
\(287\) | −3.99790 | −0.235989 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.97614 | + | 12.0830i | −0.410361 | + | 0.710767i | ||||
\(290\) | 1.99611 | + | 3.45736i | 0.117215 | + | 0.203023i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.73577 | + | 3.31155i | −0.335661 | + | 0.193794i | ||||
\(293\) | 10.0804 | − | 5.81994i | 0.588905 | − | 0.340004i | −0.175760 | − | 0.984433i | \(-0.556238\pi\) |
0.764664 | + | 0.644429i | \(0.222905\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.22904 | + | 5.59286i | 0.188002 | + | 0.325629i | ||||
\(296\) | −3.53663 | + | 6.12562i | −0.205562 | + | 0.356044i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.54638 | 0.147508 | ||||||||
\(299\) | −9.64202 | + | 18.0327i | −0.557612 | + | 1.04286i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.66057 | + | 2.69078i | 0.268631 | + | 0.155094i | ||||
\(302\) | 4.94718 | − | 8.56877i | 0.284678 | − | 0.493077i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 4.89532i | − | 0.280766i | ||||||
\(305\) | 6.42400 | − | 3.70890i | 0.367837 | − | 0.212371i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.802209i | 0.0457845i | 0.999738 | + | 0.0228922i | \(0.00728747\pi\) | ||||
−0.999738 | + | 0.0228922i | \(0.992713\pi\) | |||||||
\(308\) | −0.816612 | − | 1.41441i | −0.0465308 | − | 0.0805936i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.81494 | + | 2.20256i | 0.216674 | + | 0.125097i | ||||
\(311\) | 10.2961 | 0.583838 | 0.291919 | − | 0.956443i | \(-0.405706\pi\) | ||||
0.291919 | + | 0.956443i | \(0.405706\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.2030 | −0.689752 | −0.344876 | − | 0.938648i | \(-0.612079\pi\) | ||||
−0.344876 | + | 0.938648i | \(0.612079\pi\) | |||||||
\(314\) | 7.76317 | + | 4.48207i | 0.438101 | + | 0.252938i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.10558 | − | 7.11107i | −0.230957 | − | 0.400029i | ||||
\(317\) | 8.53952i | 0.479627i | 0.970819 | + | 0.239814i | \(0.0770863\pi\) | ||||
−0.970819 | + | 0.239814i | \(0.922914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.52570 | + | 2.61291i | −0.253390 | + | 0.146295i | ||||
\(320\) | − | 1.24768i | − | 0.0697476i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.83571 | + | 4.91159i | −0.158028 | + | 0.273712i | ||||
\(323\) | −23.5862 | − | 13.6175i | −1.31237 | − | 0.757697i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.4084 | − | 0.404405i | 0.688292 | − | 0.0224324i | ||||
\(326\) | 0.429374 | 0.0237808 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.99895 | − | 3.46229i | 0.110374 | − | 0.191173i | ||||
\(329\) | 5.74902 | + | 9.95759i | 0.316954 | + | 0.548980i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.3998 | − | 13.5099i | 1.28617 | − | 0.742571i | 0.308202 | − | 0.951321i | \(-0.400273\pi\) |
0.977969 | + | 0.208750i | \(0.0669396\pi\) | |||||||
\(332\) | −9.67531 | + | 5.58604i | −0.531001 | + | 0.306574i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.2625 | + | 19.5072i | 0.616255 | + | 1.06739i | ||||
\(335\) | 3.95445 | − | 6.84931i | 0.216055 | − | 0.374218i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.48883 | 0.190048 | 0.0950242 | − | 0.995475i | \(-0.469707\pi\) | ||||
0.0950242 | + | 0.995475i | \(0.469707\pi\) | |||||||
\(338\) | 11.6577 | + | 5.75314i | 0.634094 | + | 0.312929i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.01148 | − | 3.47073i | −0.326018 | − | 0.188227i | ||||
\(341\) | −2.88316 | + | 4.99377i | −0.156132 | + | 0.270428i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −4.66057 | + | 2.69078i | −0.251281 | + | 0.145077i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.0112i | 0.591968i | ||||||||
\(347\) | −10.8293 | − | 18.7569i | −0.581347 | − | 1.00692i | −0.995320 | − | 0.0966337i | \(-0.969192\pi\) |
0.413973 | − | 0.910289i | \(-0.364141\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.8664 | + | 15.5113i | 1.43813 | + | 0.830303i | 0.997720 | − | 0.0674949i | \(-0.0215007\pi\) |
0.440407 | + | 0.897798i | \(0.354834\pi\) | |||||||
\(350\) | 3.44329 | 0.184051 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.63322 | 0.0870511 | ||||||||
\(353\) | −25.8321 | − | 14.9142i | −1.37491 | − | 0.793802i | −0.383365 | − | 0.923597i | \(-0.625235\pi\) |
−0.991541 | + | 0.129795i | \(0.958568\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.17874 | − | 14.1660i | −0.434083 | − | 0.751853i | ||||
\(356\) | − | 2.49848i | − | 0.132419i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.90062 | + | 1.09732i | −0.100451 | + | 0.0579954i | ||||
\(359\) | 21.5254i | 1.13607i | 0.823006 | + | 0.568033i | \(0.192295\pi\) | ||||
−0.823006 | + | 0.568033i | \(0.807705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.48206 | − | 4.29905i | 0.130635 | − | 0.226266i | ||||
\(362\) | −4.17100 | − | 2.40813i | −0.219223 | − | 0.126568i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.17957 | + | 1.70011i | 0.166655 | + | 0.0891098i | ||||
\(365\) | −8.26353 | −0.432533 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.21213 | + | 3.83153i | −0.115472 | + | 0.200004i | −0.917969 | − | 0.396653i | \(-0.870172\pi\) |
0.802496 | + | 0.596657i | \(0.203505\pi\) | |||||||
\(368\) | −2.83571 | − | 4.91159i | −0.147822 | − | 0.256035i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.64283 | + | 4.41259i | −0.397332 | + | 0.229400i | ||||
\(371\) | 4.17451 | − | 2.41015i | 0.216730 | − | 0.125129i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.3688 | + | 23.1554i | 0.692209 | + | 1.19894i | 0.971112 | + | 0.238622i | \(0.0766958\pi\) |
−0.278903 | + | 0.960319i | \(0.589971\pi\) | |||||||
\(374\) | 4.54320 | − | 7.86905i | 0.234923 | − | 0.406899i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.4980 | −0.592966 | ||||||||
\(377\) | 5.43983 | − | 10.1737i | 0.280166 | − | 0.523970i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.0198 | − | 8.09436i | −0.720151 | − | 0.415780i | 0.0946571 | − | 0.995510i | \(-0.469825\pi\) |
−0.814808 | + | 0.579730i | \(0.803158\pi\) | |||||||
\(380\) | 3.05390 | − | 5.28951i | 0.156662 | − | 0.271346i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 12.2643i | − | 0.627496i | ||||||
\(383\) | −0.351106 | + | 0.202711i | −0.0179407 | + | 0.0103580i | −0.508944 | − | 0.860800i | \(-0.669964\pi\) |
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 2.03775i | − | 0.103853i | ||||||
\(386\) | −9.36349 | − | 16.2180i | −0.476589 | − | 0.825477i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.02271 | + | 5.20926i | 0.458058 | + | 0.264460i | ||||
\(389\) | −2.18998 | −0.111037 | −0.0555183 | − | 0.998458i | \(-0.517681\pi\) | ||||
−0.0555183 | + | 0.998458i | \(0.517681\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.5528 | −1.59569 | ||||||||
\(392\) | 0.866025 | + | 0.500000i | 0.0437409 | + | 0.0252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.10832 | − | 15.7761i | −0.458871 | − | 0.794787i | ||||
\(395\) | − | 10.2449i | − | 0.515478i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.24673 | + | 3.60655i | −0.313515 | + | 0.181008i | −0.648498 | − | 0.761216i | \(-0.724603\pi\) |
0.334984 | + | 0.942224i | \(0.391269\pi\) | |||||||
\(398\) | − | 9.20785i | − | 0.461548i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.72164 | + | 2.98197i | −0.0860821 | + | 0.149099i | ||||
\(401\) | −2.39085 | − | 1.38036i | −0.119393 | − | 0.0689318i | 0.439114 | − | 0.898431i | \(-0.355292\pi\) |
−0.558507 | + | 0.829500i | \(0.688626\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.414664 | − | 12.7231i | −0.0206559 | − | 0.633784i | ||||
\(404\) | 3.57045 | 0.177636 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.59985 | − | 2.77102i | 0.0793992 | − | 0.137524i | ||||
\(407\) | −5.77610 | − | 10.0045i | −0.286311 | − | 0.495905i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.60545 | − | 4.96836i | 0.425512 | − | 0.245670i | −0.271921 | − | 0.962320i | \(-0.587659\pi\) |
0.697433 | + | 0.716650i | \(0.254325\pi\) | |||||||
\(410\) | 4.31984 | − | 2.49406i | 0.213342 | − | 0.123173i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.81905 | + | 8.34684i | 0.237418 | + | 0.411219i | ||||
\(413\) | 2.58803 | − | 4.48259i | 0.127348 | − | 0.220574i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.9392 | −0.684249 | ||||||||
\(416\) | −3.06212 | + | 1.90353i | −0.150133 | + | 0.0933283i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.92400 | + | 3.99757i | 0.338664 | + | 0.195528i | ||||
\(419\) | −9.01445 | + | 15.6135i | −0.440385 | + | 0.762769i | −0.997718 | − | 0.0675201i | \(-0.978491\pi\) |
0.557333 | + | 0.830289i | \(0.311825\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.61265i | 0.176070i | 0.996117 | + | 0.0880348i | \(0.0280587\pi\) | ||||
−0.996117 | + | 0.0880348i | \(0.971941\pi\) | |||||||
\(422\) | −3.76520 | + | 2.17384i | −0.183287 | + | 0.105821i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.82030i | 0.234095i | ||||||||
\(425\) | 9.57832 | + | 16.5901i | 0.464617 | + | 0.804740i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.14874 | − | 2.97263i | −0.249165 | − | 0.143856i | ||||
\(428\) | −4.36280 | −0.210884 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.71449 | −0.323802 | ||||||||
\(431\) | −24.7893 | − | 14.3121i | −1.19406 | − | 0.689389i | −0.234833 | − | 0.972036i | \(-0.575454\pi\) |
−0.959224 | + | 0.282646i | \(0.908788\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.3338 | + | 21.3627i | 0.592723 | + | 1.02663i | 0.993864 | + | 0.110610i | \(0.0352804\pi\) |
−0.401141 | + | 0.916016i | \(0.631386\pi\) | |||||||
\(434\) | − | 3.53063i | − | 0.169476i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.7175 | − | 9.65186i | 0.800623 | − | 0.462240i | ||||
\(437\) | − | 27.7634i | − | 1.32810i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.13469 | − | 12.3576i | 0.340520 | − | 0.589798i | −0.644009 | − | 0.765018i | \(-0.722730\pi\) |
0.984529 | + | 0.175219i | \(0.0560635\pi\) | |||||||
\(440\) | 1.76474 | + | 1.01887i | 0.0841306 | + | 0.0485729i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.653416 | + | 20.0488i | 0.0310799 | + | 0.953622i | ||||
\(443\) | 32.2838 | 1.53385 | 0.766925 | − | 0.641736i | \(-0.221786\pi\) | ||||
0.766925 | + | 0.641736i | \(0.221786\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.55866 | − | 2.69968i | 0.0738875 | − | 0.127977i | ||||
\(446\) | −2.39655 | − | 4.15095i | −0.113480 | − | 0.196553i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.866025 | + | 0.500000i | −0.0409159 | + | 0.0236228i | ||||
\(449\) | 18.8020 | − | 10.8554i | 0.887323 | − | 0.512296i | 0.0142572 | − | 0.999898i | \(-0.495462\pi\) |
0.873066 | + | 0.487602i | \(0.162128\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.26473 | + | 5.65469i | 0.153730 | + | 0.266269i | ||||
\(452\) | 4.73647 | − | 8.20380i | 0.222785 | − | 0.385874i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.44472 | 0.255533 | ||||||||
\(455\) | 2.37500 | + | 3.82055i | 0.111342 | + | 0.179110i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.41901 | + | 1.39662i | 0.113156 | + | 0.0653309i | 0.555510 | − | 0.831510i | \(-0.312523\pi\) |
−0.442354 | + | 0.896841i | \(0.645856\pi\) | |||||||
\(458\) | 7.54045 | − | 13.0604i | 0.352342 | − | 0.610274i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 7.07614i | − | 0.329927i | ||||||
\(461\) | −12.4200 | + | 7.17070i | −0.578458 | + | 0.333973i | −0.760520 | − | 0.649314i | \(-0.775056\pi\) |
0.182062 | + | 0.983287i | \(0.441723\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.1760i | 1.77419i | 0.461588 | + | 0.887095i | \(0.347280\pi\) | ||||
−0.461588 | + | 0.887095i | \(0.652720\pi\) | |||||||
\(464\) | 1.59985 | + | 2.77102i | 0.0742712 | + | 0.128641i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.56841 | − | 2.63757i | −0.211627 | − | 0.122183i | ||||
\(467\) | 13.0228 | 0.602622 | 0.301311 | − | 0.953526i | \(-0.402576\pi\) | ||||
0.301311 | + | 0.953526i | \(0.402576\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.33887 | −0.292702 | ||||||||
\(470\) | −12.4239 | − | 7.17295i | −0.573073 | − | 0.330864i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.58803 | + | 4.48259i | 0.119124 | + | 0.206328i | ||||
\(473\) | − | 8.78930i | − | 0.404132i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.5977 | + | 8.42799i | −0.669788 | + | 0.386702i | ||||
\(476\) | 5.56348i | 0.255002i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.5360 | − | 25.1772i | 0.664863 | − | 1.15158i | ||||
\(479\) | −17.5949 | − | 10.1584i | −0.803932 | − | 0.464150i | 0.0409123 | − | 0.999163i | \(-0.486974\pi\) |
−0.844844 | + | 0.535012i | \(0.820307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.4899 | + | 12.0253i | 1.02545 | + | 0.548306i | ||||
\(482\) | 29.4882 | 1.34315 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.16629 | − | 7.21623i | 0.189377 | − | 0.328010i | ||||
\(485\) | 6.49951 | + | 11.2575i | 0.295128 | + | 0.511176i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.36922 | + | 2.52257i | −0.197988 | + | 0.114309i | −0.595717 | − | 0.803195i | \(-0.703132\pi\) |
0.397728 | + | 0.917503i | \(0.369799\pi\) | |||||||
\(488\) | 5.14874 | − | 2.97263i | 0.233073 | − | 0.134565i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.623842 | + | 1.08053i | 0.0281823 | + | 0.0488132i | ||||
\(491\) | 17.9099 | − | 31.0208i | 0.808261 | − | 1.39995i | −0.105807 | − | 0.994387i | \(-0.533742\pi\) |
0.914067 | − | 0.405562i | \(-0.132924\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.8015 | 0.801738 | ||||||||
\(494\) | −17.6409 | + | 0.574942i | −0.793704 | + | 0.0258679i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.05762 | + | 1.76532i | 0.137291 | + | 0.0792651i | ||||
\(497\) | −6.55514 | + | 11.3538i | −0.294038 | + | 0.509289i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.0174i | 1.47806i | 0.673670 | + | 0.739032i | \(0.264717\pi\) | ||||
−0.673670 | + | 0.739032i | \(0.735283\pi\) | |||||||
\(500\) | −9.12319 | + | 5.26727i | −0.408001 | + | 0.235560i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 2.08792i | − | 0.0931883i | ||||||
\(503\) | 3.46368 | + | 5.99927i | 0.154438 | + | 0.267494i | 0.932854 | − | 0.360254i | \(-0.117310\pi\) |
−0.778416 | + | 0.627748i | \(0.783977\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.85796 | + | 2.22740i | 0.171677 | + | 0.0991178i | ||||
\(506\) | 9.26269 | 0.411777 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.9534 | 0.663452 | ||||||||
\(509\) | −4.11620 | − | 2.37649i | −0.182447 | − | 0.105336i | 0.405995 | − | 0.913875i | \(-0.366925\pi\) |
−0.588442 | + | 0.808539i | \(0.700258\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.31155 | + | 5.73577i | 0.146494 | + | 0.253736i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.5763 | − | 14.1891i | 1.08401 | − | 0.625856i | ||||
\(515\) | 12.0253i | 0.529898i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.38943 | − | 16.2630i | 0.412946 | − | 0.715244i | ||||
\(518\) | 6.12562 | + | 3.53663i | 0.269144 | + | 0.155390i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.49620 | + | 0.146537i | −0.197171 | + | 0.00642609i | ||||
\(521\) | 0.0344780 | 0.00151051 | 0.000755255 | − | 1.00000i | \(-0.499760\pi\) | ||||
0.000755255 | 1.00000i | \(0.499760\pi\) | ||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.60834 | + | 2.78573i | −0.0703278 | + | 0.121811i | −0.899045 | − | 0.437856i | \(-0.855738\pi\) |
0.828717 | + | 0.559668i | \(0.189071\pi\) | |||||||
\(524\) | 6.67729 | + | 11.5654i | 0.291699 | + | 0.505237i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.2695 | − | 12.2799i | 0.927393 | − | 0.535431i | ||||
\(527\) | 17.0110 | − | 9.82130i | 0.741011 | − | 0.427823i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.58250 | − | 7.93713i | −0.199239 | − | 0.345093i | ||||
\(530\) | −3.00711 | + | 5.20846i | −0.130620 | + | 0.226241i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.89532 | −0.212239 | ||||||||
\(533\) | −12.7116 | − | 6.79686i | −0.550600 | − | 0.294405i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.71412 | − | 2.72170i | −0.203809 | − | 0.117669i | ||||
\(536\) | 3.16943 | − | 5.48962i | 0.136899 | − | 0.237115i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 26.6152i | − | 1.14746i | ||||||
\(539\) | −1.41441 | + | 0.816612i | −0.0609231 | + | 0.0351739i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.4438i | 1.78181i | 0.454190 | + | 0.890905i | \(0.349929\pi\) | ||||
−0.454190 | + | 0.890905i | \(0.650071\pi\) | |||||||
\(542\) | −9.81095 | − | 16.9931i | −0.421416 | − | 0.729915i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.81811 | − | 2.78174i | −0.206575 | − | 0.119266i | ||||
\(545\) | 24.0849 | 1.03168 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.9393 | −1.23736 | −0.618678 | − | 0.785645i | \(-0.712331\pi\) | ||||
−0.618678 | + | 0.785645i | \(0.712331\pi\) | |||||||
\(548\) | −6.27707 | − | 3.62407i | −0.268143 | − | 0.154813i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.81183 | − | 4.87023i | −0.119897 | − | 0.207667i | ||||
\(551\) | 15.6635i | 0.667289i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.11107 | + | 4.10558i | −0.302393 | + | 0.174587i | ||||
\(554\) | 23.3350i | 0.991411i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.86534 | + | 13.6232i | −0.333565 | + | 0.577751i | ||||
\(557\) | −27.8019 | − | 16.0514i | −1.17800 | − | 0.680121i | −0.222453 | − | 0.974944i | \(-0.571406\pi\) |
−0.955552 | + | 0.294822i | \(0.904740\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.2440 | + | 16.4790i | 0.433274 | + | 0.696987i | ||||
\(560\) | −1.24768 | −0.0527243 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.6302 | − | 18.4120i | 0.448407 | − | 0.776664i | ||||
\(563\) | 1.79857 | + | 3.11521i | 0.0758006 | + | 0.131291i | 0.901434 | − | 0.432916i | \(-0.142515\pi\) |
−0.825634 | + | 0.564207i | \(0.809182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.2357 | − | 5.90961i | 0.430621 | − | 0.248619i | ||||
\(566\) | −16.1434 | + | 9.32039i | −0.678557 | + | 0.391765i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.55514 | − | 11.3538i | −0.275048 | − | 0.476396i | ||||
\(569\) | 18.3294 | − | 31.7474i | 0.768407 | − | 1.33092i | −0.170019 | − | 0.985441i | \(-0.554383\pi\) |
0.938426 | − | 0.345480i | \(-0.112284\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −47.5969 | −1.99187 | −0.995934 | − | 0.0900902i | \(-0.971284\pi\) | ||||
−0.995934 | + | 0.0900902i | \(0.971284\pi\) | |||||||
\(572\) | −0.191818 | − | 5.88554i | −0.00802031 | − | 0.246087i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.46229 | − | 1.99895i | −0.144513 | − | 0.0834346i | ||||
\(575\) | −9.76416 | + | 16.9120i | −0.407194 | + | 0.705280i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 25.7012i | − | 1.06996i | −0.844866 | − | 0.534978i | \(-0.820320\pi\) | ||
0.844866 | − | 0.534978i | \(-0.179680\pi\) | |||||||
\(578\) | −12.0830 | + | 6.97614i | −0.502588 | + | 0.290169i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.99221i | 0.165768i | ||||||||
\(581\) | 5.58604 | + | 9.67531i | 0.231748 | + | 0.401399i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.81790 | − | 3.93632i | −0.282368 | − | 0.163026i | ||||
\(584\) | −6.62310 | −0.274066 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.6399 | 0.480839 | ||||||||
\(587\) | −25.7531 | − | 14.8686i | −1.06294 | − | 0.613691i | −0.136699 | − | 0.990613i | \(-0.543649\pi\) |
−0.926245 | + | 0.376921i | \(0.876983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.64179 | + | 14.9680i | 0.356079 | + | 0.616746i | ||||
\(590\) | 6.45808i | 0.265875i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.12562 | + | 3.53663i | −0.251761 | + | 0.145354i | ||||
\(593\) | 38.5870i | 1.58458i | 0.610146 | + | 0.792289i | \(0.291111\pi\) | ||||
−0.610146 | + | 0.792289i | \(0.708889\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.47073 | + | 6.01148i | −0.142286 | + | 0.246447i | ||||
\(596\) | 2.20523 | + | 1.27319i | 0.0903297 | + | 0.0521519i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −17.3666 | + | 10.7957i | −0.710171 | + | 0.441470i | ||||
\(599\) | 24.8717 | 1.01623 | 0.508114 | − | 0.861290i | \(-0.330343\pi\) | ||||
0.508114 | + | 0.861290i | \(0.330343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.82588 | + | 3.16252i | −0.0744792 | + | 0.129002i | −0.900860 | − | 0.434110i | \(-0.857063\pi\) |
0.826380 | + | 0.563112i | \(0.190396\pi\) | |||||||
\(602\) | 2.69078 | + | 4.66057i | 0.109668 | + | 0.189951i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.56877 | − | 4.94718i | 0.348658 | − | 0.201298i | ||||
\(605\) | 9.00357 | − | 5.19821i | 0.366047 | − | 0.211337i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.01855 | − | 13.8885i | −0.325463 | − | 0.563718i | 0.656143 | − | 0.754636i | \(-0.272187\pi\) |
−0.981606 | + | 0.190918i | \(0.938853\pi\) | |||||||
\(608\) | 2.44766 | − | 4.23947i | 0.0992656 | − | 0.171933i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.41780 | 0.300338 | ||||||||
\(611\) | 1.35041 | + | 41.4347i | 0.0546319 | + | 1.67627i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.1663 | + | 9.33363i | 0.652952 | + | 0.376982i | 0.789586 | − | 0.613640i | \(-0.210295\pi\) |
−0.136635 | + | 0.990622i | \(0.543629\pi\) | |||||||
\(614\) | −0.401105 | + | 0.694734i | −0.0161873 | + | 0.0280372i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 1.63322i | − | 0.0658044i | ||||||
\(617\) | 15.3613 | − | 8.86883i | 0.618422 | − | 0.357046i | −0.157833 | − | 0.987466i | \(-0.550451\pi\) |
0.776254 | + | 0.630420i | \(0.217117\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 25.3244i | − | 1.01787i | −0.860804 | − | 0.508937i | \(-0.830039\pi\) | ||
0.860804 | − | 0.508937i | \(-0.169961\pi\) | |||||||
\(620\) | 2.20256 | + | 3.81494i | 0.0884568 | + | 0.153212i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.91668 | + | 5.14805i | 0.357526 | + | 0.206418i | ||||
\(623\) | −2.49848 | −0.100100 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.07265 | 0.162906 | ||||||||
\(626\) | −10.5681 | − | 6.10148i | −0.422385 | − | 0.243864i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.48207 | + | 7.76317i | 0.178854 | + | 0.309784i | ||||
\(629\) | 39.3519i | 1.56906i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.68116 | + | 2.12532i | −0.146545 | + | 0.0846075i | −0.571479 | − | 0.820616i | \(-0.693630\pi\) |
0.424935 | + | 0.905224i | \(0.360297\pi\) | |||||||
\(632\) | − | 8.21115i | − | 0.326622i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.26976 | + | 7.39544i | −0.169574 | + | 0.293710i | ||||
\(635\) | 16.1576 | + | 9.32858i | 0.641194 | + | 0.370194i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.70011 | − | 3.17957i | 0.0673607 | − | 0.125979i | ||||
\(638\) | −5.22582 | −0.206892 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.623842 | − | 1.08053i | 0.0246595 | − | 0.0427115i | ||||
\(641\) | 17.2678 | + | 29.9086i | 0.682036 | + | 1.18132i | 0.974359 | + | 0.225001i | \(0.0722384\pi\) |
−0.292323 | + | 0.956320i | \(0.594428\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.67586 | + | 5.00901i | −0.342143 | + | 0.197536i | −0.661219 | − | 0.750193i | \(-0.729961\pi\) |
0.319077 | + | 0.947729i | \(0.396627\pi\) | |||||||
\(644\) | −4.91159 | + | 2.83571i | −0.193544 | + | 0.111743i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.6175 | − | 23.5862i | −0.535773 | − | 0.927986i | ||||
\(647\) | 7.91081 | − | 13.7019i | 0.311006 | − | 0.538678i | −0.667574 | − | 0.744543i | \(-0.732667\pi\) |
0.978580 | + | 0.205865i | \(0.0660007\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.45365 | −0.331835 | ||||||||
\(650\) | 10.9482 | + | 5.85395i | 0.429422 | + | 0.229611i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.371849 | + | 0.214687i | 0.0145627 | + | 0.00840779i | ||||
\(653\) | −5.37123 | + | 9.30325i | −0.210193 | + | 0.364064i | −0.951775 | − | 0.306798i | \(-0.900742\pi\) |
0.741582 | + | 0.670862i | \(0.234076\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.6623i | 0.651050i | ||||||||
\(656\) | 3.46229 | − | 1.99895i | 0.135180 | − | 0.0780460i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.4980i | 0.448240i | ||||||||
\(659\) | −8.19715 | − | 14.1979i | −0.319315 | − | 0.553071i | 0.661030 | − | 0.750360i | \(-0.270120\pi\) |
−0.980345 | + | 0.197289i | \(0.936786\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.7580 | − | 9.67522i | −0.651809 | − | 0.376322i | 0.137340 | − | 0.990524i | \(-0.456145\pi\) |
−0.789149 | + | 0.614202i | \(0.789478\pi\) | |||||||
\(662\) | 27.0198 | 1.05015 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.1721 | −0.433561 | ||||||||
\(665\) | −5.28951 | − | 3.05390i | −0.205119 | − | 0.118425i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.07342 | + | 15.7156i | 0.351324 | + | 0.608512i | ||||
\(668\) | 22.5249i | 0.871516i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.84931 | − | 3.95445i | 0.264612 | − | 0.152774i | ||||
\(671\) | 9.70993i | 0.374848i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.4635 | − | 19.8553i | 0.441884 | − | 0.765366i | −0.555945 | − | 0.831219i | \(-0.687643\pi\) |
0.997829 | + | 0.0658530i | \(0.0209768\pi\) | |||||||
\(674\) | 3.02141 | + | 1.74441i | 0.116380 | + | 0.0671923i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.21928 | + | 10.8112i | 0.277664 | + | 0.415815i | ||||
\(677\) | −22.8391 | −0.877776 | −0.438888 | − | 0.898542i | \(-0.644628\pi\) | ||||
−0.438888 | + | 0.898542i | \(0.644628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.20926 | − | 9.02271i | 0.199913 | − | 0.346260i | ||||
\(680\) | −3.47073 | − | 6.01148i | −0.133096 | − | 0.230530i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.99377 | + | 2.88316i | −0.191222 | + | 0.110402i | ||||
\(683\) | −6.52984 | + | 3.77001i | −0.249857 | + | 0.144255i | −0.619699 | − | 0.784840i | \(-0.712745\pi\) |
0.369842 | + | 0.929095i | \(0.379412\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.52169 | − | 7.83180i | −0.172765 | − | 0.299238i | ||||
\(686\) | 0.500000 | − | 0.866025i | 0.0190901 | − | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.38157 | −0.205170 | ||||||||
\(689\) | 17.3706 | − | 0.566133i | 0.661768 | − | 0.0215679i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.6929 | + | 13.1017i | 0.863278 | + | 0.498414i | 0.865109 | − | 0.501584i | \(-0.167249\pi\) |
−0.00183036 | + | 0.999998i | \(0.500583\pi\) | |||||||
\(692\) | −5.50562 | + | 9.53601i | −0.209292 | + | 0.362505i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 21.6586i | − | 0.822149i | ||||||
\(695\) | −16.9974 | + | 9.81345i | −0.644748 | + | 0.372245i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 22.2422i | − | 0.842485i | ||||||
\(698\) | 15.5113 | + | 26.8664i | 0.587113 | + | 1.01691i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.98197 | + | 1.72164i | 0.112708 | + | 0.0650720i | ||||
\(701\) | −37.4467 | −1.41434 | −0.707171 | − | 0.707043i | \(-0.750029\pi\) | ||||
−0.707171 | + | 0.707043i | \(0.750029\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34.6258 | −1.30594 | ||||||||
\(704\) | 1.41441 | + | 0.816612i | 0.0533077 | + | 0.0307772i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.9142 | − | 25.8321i | −0.561303 | − | 0.972205i | ||||
\(707\) | − | 3.57045i | − | 0.134281i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.1468 | + | 16.8279i | −1.09463 | + | 0.631986i | −0.934806 | − | 0.355159i | \(-0.884427\pi\) |
−0.159826 | + | 0.987145i | \(0.551093\pi\) | |||||||
\(710\) | − | 16.3575i | − | 0.613885i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.24924 | − | 2.16375i | 0.0468173 | − | 0.0810900i | ||||
\(713\) | 17.3410 | + | 10.0119i | 0.649427 | + | 0.374947i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.46438 | − | 6.47915i | 0.129561 | − | 0.242306i | ||||
\(716\) | −2.19465 | −0.0820179 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.7627 | + | 18.6415i | −0.401660 | + | 0.695695i | ||||
\(719\) | 10.7899 | + | 18.6887i | 0.402396 | + | 0.696971i | 0.994015 | − | 0.109247i | \(-0.0348441\pi\) |
−0.591618 | + | 0.806218i | \(0.701511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.34684 | − | 4.81905i | 0.310853 | − | 0.179471i | ||||
\(722\) | 4.29905 | − | 2.48206i | 0.159994 | − | 0.0923726i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.40813 | − | 4.17100i | −0.0894973 | − | 0.155014i | ||||
\(725\) | 5.50874 | − | 9.54142i | 0.204590 | − | 0.354359i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.5309 | 0.983978 | 0.491989 | − | 0.870601i | \(-0.336270\pi\) | ||||
0.491989 | + | 0.870601i | \(0.336270\pi\) | |||||||
\(728\) | 1.90353 | + | 3.06212i | 0.0705496 | + | 0.113490i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.15643 | − | 4.13177i | −0.264871 | − | 0.152924i | ||||
\(731\) | −14.9701 | + | 25.9290i | −0.553690 | + | 0.959019i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.0423i | 0.555599i | 0.960639 | + | 0.277799i | \(0.0896050\pi\) | ||||
−0.960639 | + | 0.277799i | \(0.910395\pi\) | |||||||
\(734\) | −3.83153 | + | 2.21213i | −0.141424 | + | 0.0816514i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 5.67142i | − | 0.209051i | ||||||
\(737\) | 5.17639 | + | 8.96577i | 0.190675 | + | 0.330258i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1481 | − | 7.59105i | −0.483660 | − | 0.279241i | 0.238280 | − | 0.971196i | \(-0.423416\pi\) |
−0.721941 | + | 0.691955i | \(0.756750\pi\) | |||||||
\(740\) | −8.82518 | −0.324420 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.82030 | 0.176959 | ||||||||
\(743\) | −31.1626 | − | 17.9917i | −1.14324 | − | 0.660052i | −0.196012 | − | 0.980602i | \(-0.562799\pi\) |
−0.947232 | + | 0.320550i | \(0.896132\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.58854 | + | 2.75143i | 0.0581995 | + | 0.100804i | ||||
\(746\) | 26.7376i | 0.978932i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.86905 | − | 4.54320i | 0.287721 | − | 0.166116i | ||||
\(749\) | 4.36280i | 0.159413i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.91824 | − | 15.4468i | 0.325431 | − | 0.563663i | −0.656168 | − | 0.754614i | \(-0.727824\pi\) |
0.981599 | + | 0.190951i | \(0.0611573\pi\) | |||||||
\(752\) | −9.95759 | − | 5.74902i | −0.363116 | − | 0.209645i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.79786 | − | 6.09073i | 0.356817 | − | 0.221811i | ||||
\(755\) | 12.3450 | 0.449282 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.850916 | − | 1.47383i | 0.0309271 | − | 0.0535673i | −0.850148 | − | 0.526544i | \(-0.823487\pi\) |
0.881075 | + | 0.472977i | \(0.156821\pi\) | |||||||
\(758\) | −8.09436 | − | 14.0198i | −0.294001 | − | 0.509224i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.28951 | − | 3.05390i | 0.191871 | − | 0.110777i | ||||
\(761\) | −13.2906 | + | 7.67330i | −0.481782 | + | 0.278157i | −0.721159 | − | 0.692770i | \(-0.756390\pi\) |
0.239377 | + | 0.970927i | \(0.423057\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.65186 | − | 16.7175i | −0.349421 | − | 0.605214i | ||||
\(764\) | 6.13215 | − | 10.6212i | 0.221854 | − | 0.384262i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.405422 | −0.0146485 | ||||||||
\(767\) | 15.8497 | − | 9.85278i | 0.572299 | − | 0.355763i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.5852 | − | 11.3075i | −0.706259 | − | 0.407759i | 0.103415 | − | 0.994638i | \(-0.467023\pi\) |
−0.809674 | + | 0.586880i | \(0.800356\pi\) | |||||||
\(770\) | 1.01887 | − | 1.76474i | 0.0367176 | − | 0.0635968i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 18.7270i | − | 0.673999i | ||||||
\(773\) | −37.9606 | + | 21.9166i | −1.36535 | + | 0.788285i | −0.990330 | − | 0.138732i | \(-0.955697\pi\) |
−0.375019 | + | 0.927017i | \(0.622364\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 12.1570i | − | 0.436692i | ||||||
\(776\) | 5.20926 | + | 9.02271i | 0.187002 | + | 0.323896i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.89658 | − | 1.09499i | −0.0679957 | − | 0.0392573i | ||||
\(779\) | 19.5710 | 0.701204 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.4120 | 0.766182 | ||||||||
\(782\) | −27.3255 | − | 15.7764i | −0.977159 | − | 0.564163i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.500000 | + | 0.866025i | 0.0178571 | + | 0.0309295i | ||||
\(785\) | 11.1844i | 0.399189i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.630664 | − | 0.364114i | 0.0224808 | − | 0.0129793i | −0.488718 | − | 0.872442i | \(-0.662535\pi\) |
0.511198 | + | 0.859463i | \(0.329202\pi\) | |||||||
\(788\) | − | 18.2166i | − | 0.648941i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.12246 | − | 8.87236i | 0.182249 | − | 0.315665i | ||||
\(791\) | −8.20380 | − | 4.73647i | −0.291694 | − | 0.168409i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.3170 | − | 18.2051i | −0.401878 | − | 0.646481i | ||||
\(794\) | −7.21311 | −0.255984 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.60392 | − | 7.97423i | 0.163182 | − | 0.282639i | ||||
\(797\) | 19.4943 | + | 33.7652i | 0.690525 | + | 1.19602i | 0.971666 | + | 0.236357i | \(0.0759536\pi\) |
−0.281142 | + | 0.959666i | \(0.590713\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.3988 | + | 31.9845i | −1.95987 | + | 1.13153i | ||||
\(800\) | −2.98197 | + | 1.72164i | −0.105429 | + | 0.0608693i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.38036 | − | 2.39085i | −0.0487421 | − | 0.0844238i | ||||
\(803\) | 5.40850 | − | 9.36780i | 0.190862 | − | 0.330582i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.07614 | −0.249401 | ||||||||
\(806\) | 6.00245 | − | 11.2259i | 0.211427 | − | 0.395415i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.09210 | + | 1.78522i | 0.108780 | + | 0.0628040i | ||||
\(809\) | −13.9625 | + | 24.1838i | −0.490895 | + | 0.850256i | −0.999945 | − | 0.0104813i | \(-0.996664\pi\) |
0.509050 | + | 0.860737i | \(0.329997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.8777i | − | 0.592655i | −0.955086 | − | 0.296327i | \(-0.904238\pi\) | ||
0.955086 | − | 0.296327i | \(-0.0957619\pi\) | |||||||
\(812\) | 2.77102 | − | 1.59985i | 0.0972438 | − | 0.0561437i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 11.5522i | − | 0.404904i | ||||||
\(815\) | 0.267861 | + | 0.463950i | 0.00938278 | + | 0.0162514i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.8150 | − | 13.1722i | −0.798195 | − | 0.460838i | ||||
\(818\) | 9.93672 | 0.347429 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.98812 | 0.174193 | ||||||||
\(821\) | 37.6774 | + | 21.7531i | 1.31495 | + | 0.759187i | 0.982912 | − | 0.184078i | \(-0.0589300\pi\) |
0.332039 | + | 0.943266i | \(0.392263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.0681 | + | 20.9025i | 0.420667 | + | 0.728617i | 0.996005 | − | 0.0892992i | \(-0.0284627\pi\) |
−0.575338 | + | 0.817916i | \(0.695129\pi\) | |||||||
\(824\) | 9.63810i | 0.335759i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.48259 | − | 2.58803i | 0.155969 | − | 0.0900490i | ||||
\(827\) | − | 23.2109i | − | 0.807121i | −0.914953 | − | 0.403560i | \(-0.867773\pi\) | ||
0.914953 | − | 0.403560i | \(-0.132227\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.0392158 | − | 0.0679238i | 0.00136202 | − | 0.00235909i | −0.865344 | − | 0.501179i | \(-0.832900\pi\) |
0.866706 | + | 0.498820i | \(0.166233\pi\) | |||||||
\(830\) | −12.0717 | − | 6.96961i | −0.419016 | − | 0.241919i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.60364 | + | 0.117447i | −0.124934 | + | 0.00407176i | ||||
\(833\) | 5.56348 | 0.192763 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0520 | + | 24.3388i | −0.486290 | + | 0.842278i | ||||
\(836\) | 3.99757 | + | 6.92400i | 0.138259 | + | 0.239471i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.6135 | + | 9.01445i | −0.539359 | + | 0.311399i | ||||
\(839\) | 41.7182 | − | 24.0860i | 1.44027 | − | 0.831541i | 0.442404 | − | 0.896816i | \(-0.354126\pi\) |
0.997867 | + | 0.0652750i | \(0.0207925\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.38096 | + | 16.2483i | 0.323481 | + | 0.560286i | ||||
\(842\) | −1.80632 | + | 3.12864i | −0.0622500 | + | 0.107820i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.34768 | −0.149653 | ||||||||
\(845\) | 1.05613 | + | 16.1855i | 0.0363321 | + | 0.556797i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.21623 | − | 4.16629i | −0.247953 | − | 0.143155i | ||||
\(848\) | −2.41015 | + | 4.17451i | −0.0827649 | + | 0.143353i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 19.1566i | 0.657067i | ||||||||
\(851\) | −34.7410 | + | 20.0577i | −1.19090 | + | 0.687569i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.8560i | 1.33040i | 0.746664 | + | 0.665201i | \(0.231654\pi\) | ||||
−0.746664 | + | 0.665201i | \(0.768346\pi\) | |||||||
\(854\) | −2.97263 | − | 5.14874i | −0.101721 | − | 0.176186i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.77830 | − | 2.18140i | −0.129140 | − | 0.0745588i | ||||
\(857\) | 27.1368 | 0.926974 | 0.463487 | − | 0.886104i | \(-0.346598\pi\) | ||||
0.463487 | + | 0.886104i | \(0.346598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.1359 | −0.448191 | −0.224096 | − | 0.974567i | \(-0.571943\pi\) | ||||
−0.224096 | + | 0.974567i | \(0.571943\pi\) | |||||||
\(860\) | −5.81492 | − | 3.35725i | −0.198287 | − | 0.114481i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.3121 | − | 24.7893i | −0.487472 | − | 0.844326i | ||||
\(863\) | − | 5.98646i | − | 0.203781i | −0.994796 | − | 0.101891i | \(-0.967511\pi\) | ||
0.994796 | − | 0.101891i | \(-0.0324892\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.8979 | + | 6.86927i | −0.404542 | + | 0.233562i | ||||
\(866\) | 24.6675i | 0.838237i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.76532 | − | 3.05762i | 0.0599188 | − | 0.103782i | ||||
\(869\) | 11.6140 | + | 6.70532i | 0.393977 | + | 0.227463i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.1548 | − | 10.7767i | −0.682921 | − | 0.365156i | ||||
\(872\) | 19.3037 | 0.653706 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.8817 | − | 24.0438i | 0.469555 | − | 0.813294i | ||||
\(875\) | 5.26727 | + | 9.12319i | 0.178066 | + | 0.308420i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.51170 | + | 1.45013i | −0.0848142 | + | 0.0489675i | −0.541807 | − | 0.840503i | \(-0.682260\pi\) |
0.456993 | + | 0.889470i | \(0.348926\pi\) | |||||||
\(878\) | 12.3576 | − | 7.13469i | 0.417050 | − | 0.240784i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.01887 | + | 1.76474i | 0.0343462 | + | 0.0594894i | ||||
\(881\) | −28.6722 | + | 49.6617i | −0.965991 | + | 1.67315i | −0.259063 | + | 0.965860i | \(0.583414\pi\) |
−0.706928 | + | 0.707285i | \(0.749920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.5545 | −1.06189 | −0.530947 | − | 0.847405i | \(-0.678164\pi\) | ||||
−0.530947 | + | 0.847405i | \(0.678164\pi\) | |||||||
\(884\) | −9.45850 | + | 17.6894i | −0.318124 | + | 0.594960i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.9586 | + | 16.1419i | 0.939288 | + | 0.542298i | ||||
\(887\) | 5.63687 | − | 9.76335i | 0.189268 | − | 0.327821i | −0.755739 | − | 0.654873i | \(-0.772722\pi\) |
0.945006 | + | 0.327052i | \(0.106055\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 14.9534i | − | 0.501522i | ||||||
\(890\) | 2.69968 | − | 1.55866i | 0.0904934 | − | 0.0522464i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 4.79311i | − | 0.160485i | ||||||
\(893\) | −28.1432 | − | 48.7455i | −0.941778 | − | 1.63121i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.37137 | − | 1.36911i | −0.0792663 | − | 0.0457644i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.7107 | 0.724496 | ||||||||
\(899\) | −9.78347 | − | 5.64849i | −0.326297 | − | 0.188388i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.4088 | + | 23.2248i | 0.446713 | + | 0.773729i | ||||
\(902\) | 6.52947i | 0.217408i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.20380 | − | 4.73647i | 0.272854 | − | 0.157532i | ||||
\(905\) | − | 6.00916i | − | 0.199751i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.5237 | − | 40.7443i | 0.781092 | − | 1.35289i | −0.150214 | − | 0.988654i | \(-0.547996\pi\) |
0.931306 | − | 0.364238i | \(-0.118670\pi\) | |||||||
\(908\) | 4.71526 | + | 2.72236i | 0.156481 | + | 0.0903446i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.146537 | + | 4.49620i | 0.00485766 | + | 0.149048i | ||||
\(911\) | −8.82281 | −0.292313 | −0.146156 | − | 0.989261i | \(-0.546690\pi\) | ||||
−0.146156 | + | 0.989261i | \(0.546690\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.12325 | − | 15.8019i | 0.301936 | − | 0.522968i | ||||
\(914\) | 1.39662 | + | 2.41901i | 0.0461959 | + | 0.0800137i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.0604 | − | 7.54045i | 0.431529 | − | 0.249143i | ||||
\(917\) | 11.5654 | − | 6.67729i | 0.381923 | − | 0.220504i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.6953 | + | 23.7209i | 0.451765 | + | 0.782481i | 0.998496 | − | 0.0548280i | \(-0.0174611\pi\) |
−0.546730 | + | 0.837309i | \(0.684128\pi\) | |||||||
\(920\) | 3.53807 | − | 6.12812i | 0.116647 | − | 0.202038i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.3414 | −0.472309 | ||||||||
\(923\) | −40.1452 | + | 24.9558i | −1.32140 | + | 0.821431i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.0923 | + | 12.1776i | 0.693509 | + | 0.400398i | ||||
\(926\) | −19.0880 | + | 33.0614i | −0.627271 | + | 1.08646i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.19970i | 0.105035i | ||||||||
\(929\) | 5.78441 | − | 3.33963i | 0.189780 | − | 0.109570i | −0.402099 | − | 0.915596i | \(-0.631719\pi\) |
0.591880 | + | 0.806026i | \(0.298386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.89532i | 0.160437i | ||||||||
\(932\) | −2.63757 | − | 4.56841i | −0.0863966 | − | 0.149643i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.2780 | + | 6.51138i | 0.369029 | + | 0.213059i | ||||
\(935\) | 11.3370 | 0.370758 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.8852 | −0.976307 | −0.488153 | − | 0.872758i | \(-0.662329\pi\) | ||||
−0.488153 | + | 0.872758i | \(0.662329\pi\) | |||||||
\(938\) | −5.48962 | − | 3.16943i | −0.179242 | − | 0.103486i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.17295 | − | 12.4239i | −0.233956 | − | 0.405224i | ||||
\(941\) | 50.3008i | 1.63976i | 0.572537 | + | 0.819879i | \(0.305959\pi\) | ||||
−0.572537 | + | 0.819879i | \(0.694041\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.6361 | − | 11.3369i | 0.639439 | − | 0.369180i | ||||
\(944\) | 5.17605i | 0.168466i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.39465 | − | 7.61176i | 0.142882 | − | 0.247480i | ||||
\(947\) | −18.6830 | − | 10.7866i | −0.607116 | − | 0.350519i | 0.164720 | − | 0.986340i | \(-0.447328\pi\) |
−0.771836 | + | 0.635822i | \(0.780661\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.777866 | + | 23.8673i | 0.0252506 | + | 0.774764i | ||||
\(950\) | −16.8560 | −0.546880 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.78174 | + | 4.81811i | −0.0901567 | + | 0.156156i | ||||
\(953\) | −5.75014 | − | 9.95953i | −0.186265 | − | 0.322621i | 0.757737 | − | 0.652560i | \(-0.226305\pi\) |
−0.944002 | + | 0.329939i | \(0.892972\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.2519 | − | 7.65099i | 0.428821 | − | 0.247580i | ||||
\(956\) | 25.1772 | − | 14.5360i | 0.814288 | − | 0.470129i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.1584 | − | 17.5949i | −0.328204 | − | 0.568466i | ||||
\(959\) | −3.62407 | + | 6.27707i | −0.117027 | + | 0.202697i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.5346 | 0.597891 | ||||||||
\(962\) | 13.4642 | + | 21.6591i | 0.434102 | + | 0.698319i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25.5375 | + | 14.7441i | 0.822509 | + | 0.474876i | ||||
\(965\) | 11.6827 | − | 20.2350i | 0.376079 | − | 0.651387i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.86045i | 0.124144i | 0.998072 | + | 0.0620719i | \(0.0197708\pi\) | ||||
−0.998072 | + | 0.0620719i | \(0.980229\pi\) | |||||||
\(968\) | 7.21623 | − | 4.16629i | 0.231938 | − | 0.133910i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.9990i | 0.417373i | ||||||||
\(971\) | −1.67410 | − | 2.89962i | −0.0537243 | − | 0.0930532i | 0.837913 | − | 0.545805i | \(-0.183776\pi\) |
−0.891637 | + | 0.452751i | \(0.850443\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.6232 | + | 7.86534i | 0.436739 | + | 0.252151i | ||||
\(974\) | −5.04515 | −0.161657 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.94526 | 0.190303 | ||||||||
\(977\) | −40.4030 | − | 23.3267i | −1.29261 | − | 0.746287i | −0.313492 | − | 0.949591i | \(-0.601499\pi\) |
−0.979116 | + | 0.203304i | \(0.934832\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.04029 | + | 3.53389i | 0.0652080 | + | 0.112944i | ||||
\(980\) | 1.24768i | 0.0398558i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 31.0208 | − | 17.9099i | 0.989913 | − | 0.571527i | ||||
\(983\) | 35.4073i | 1.12932i | 0.825324 | + | 0.564659i | \(0.190992\pi\) | ||||
−0.825324 | + | 0.564659i | \(0.809008\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.3643 | − | 19.6835i | 0.362097 | − | 0.627170i | ||||
\(986\) | 15.4165 | + | 8.90073i | 0.490962 | + | 0.283457i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.5650 | − | 8.32256i | −0.495188 | − | 0.264776i | ||||
\(989\) | −30.5211 | −0.970516 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.95560 | − | 6.85131i | 0.125654 | − | 0.217639i | −0.796334 | − | 0.604857i | \(-0.793230\pi\) |
0.921988 | + | 0.387218i | \(0.126564\pi\) | |||||||
\(992\) | 1.76532 | + | 3.05762i | 0.0560489 | + | 0.0970795i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.3538 | + | 6.55514i | −0.360122 | + | 0.207916i | ||||
\(995\) | 9.94932 | − | 5.74424i | 0.315415 | − | 0.182105i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.5503 | + | 42.5223i | 0.777515 | + | 1.34669i | 0.933370 | + | 0.358915i | \(0.116853\pi\) |
−0.155855 | + | 0.987780i | \(0.549813\pi\) | |||||||
\(998\) | −16.5087 | + | 28.5939i | −0.522574 | + | 0.905125i | ||||
\(999\) | 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 | 1638.2.bj.i.1135.7 | yes | 16 | |
3.2 | odd | 2 | 1638.2.bj.h.1135.2 | yes | 16 | ||
13.10 | even | 6 | inner | 1638.2.bj.i.127.6 | yes | 16 | |
39.23 | odd | 6 | 1638.2.bj.h.127.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1638.2.bj.h.127.3 | ✓ | 16 | 39.23 | odd | 6 | ||
1638.2.bj.h.1135.2 | yes | 16 | 3.2 | odd | 2 | ||
1638.2.bj.i.127.6 | yes | 16 | 13.10 | even | 6 | inner | |
1638.2.bj.i.1135.7 | yes | 16 | 1.1 | even | 1 | trivial |