Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(889,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.d (of order \(2\), degree \(1\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 889.6 | ||
Root | \(1.32001 + 1.32001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.889 |
Dual form | 1110.2.d.i.889.3 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.80487 | − | 1.32001i | 0.807164 | − | 0.590327i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | − | 3.64002i | − | 1.37580i | −0.725806 | − | 0.687900i | \(-0.758533\pi\) | ||
0.725806 | − | 0.687900i | \(-0.241467\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.32001 | + | 1.80487i | 0.417424 | + | 0.570751i | ||||
\(11\) | −4.60975 | −1.38989 | −0.694946 | − | 0.719062i | \(-0.744572\pi\) | ||||
−0.694946 | + | 0.719062i | \(0.744572\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 2.12489i | 0.589337i | 0.955600 | + | 0.294669i | \(0.0952093\pi\) | ||||
−0.955600 | + | 0.294669i | \(0.904791\pi\) | |||||||
\(14\) | 3.64002 | 0.972837 | ||||||||
\(15\) | 1.32001 | + | 1.80487i | 0.340826 | + | 0.466016i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 0.609747i | − | 0.147885i | −0.997262 | − | 0.0739427i | \(-0.976442\pi\) | ||
0.997262 | − | 0.0739427i | \(-0.0235582\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −3.48486 | −0.799482 | −0.399741 | − | 0.916628i | \(-0.630900\pi\) | ||||
−0.399741 | + | 0.916628i | \(0.630900\pi\) | |||||||
\(20\) | −1.80487 | + | 1.32001i | −0.403582 | + | 0.295164i | ||||
\(21\) | 3.64002 | 0.794318 | ||||||||
\(22\) | − | 4.60975i | − | 0.982801i | ||||||
\(23\) | − | 8.76491i | − | 1.82761i | −0.406153 | − | 0.913805i | \(-0.633130\pi\) | ||
0.406153 | − | 0.913805i | \(-0.366870\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.51514 | − | 4.76491i | 0.303028 | − | 0.952982i | ||||
\(26\) | −2.12489 | −0.416724 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 3.64002i | 0.687900i | ||||||||
\(29\) | 8.15516 | 1.51438 | 0.757188 | − | 0.653197i | \(-0.226573\pi\) | ||||
0.757188 | + | 0.653197i | \(0.226573\pi\) | |||||||
\(30\) | −1.80487 | + | 1.32001i | −0.329523 | + | 0.241000i | ||||
\(31\) | −5.76491 | −1.03541 | −0.517704 | − | 0.855560i | \(-0.673213\pi\) | ||||
−0.517704 | + | 0.855560i | \(0.673213\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 4.60975i | − | 0.802454i | ||||||
\(34\) | 0.609747 | 0.104571 | ||||||||
\(35\) | −4.80487 | − | 6.56978i | −0.812172 | − | 1.11050i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | − | 3.48486i | − | 0.565319i | ||||||
\(39\) | −2.12489 | −0.340254 | ||||||||
\(40\) | −1.32001 | − | 1.80487i | −0.208712 | − | 0.285376i | ||||
\(41\) | −11.3747 | −1.77642 | −0.888211 | − | 0.459435i | \(-0.848052\pi\) | ||||
−0.888211 | + | 0.459435i | \(0.848052\pi\) | |||||||
\(42\) | 3.64002i | 0.561668i | ||||||||
\(43\) | − | 12.0147i | − | 1.83222i | −0.400925 | − | 0.916111i | \(-0.631311\pi\) | ||
0.400925 | − | 0.916111i | \(-0.368689\pi\) | |||||||
\(44\) | 4.60975 | 0.694946 | ||||||||
\(45\) | −1.80487 | + | 1.32001i | −0.269055 | + | 0.196776i | ||||
\(46\) | 8.76491 | 1.29232 | ||||||||
\(47\) | − | 1.60975i | − | 0.234806i | −0.993084 | − | 0.117403i | \(-0.962543\pi\) | ||
0.993084 | − | 0.117403i | \(-0.0374569\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −6.24977 | −0.892824 | ||||||||
\(50\) | 4.76491 | + | 1.51514i | 0.673860 | + | 0.214273i | ||||
\(51\) | 0.609747 | 0.0853817 | ||||||||
\(52\) | − | 2.12489i | − | 0.294669i | ||||||
\(53\) | − | 9.24977i | − | 1.27055i | −0.772284 | − | 0.635277i | \(-0.780886\pi\) | ||
0.772284 | − | 0.635277i | \(-0.219114\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −8.32001 | + | 6.08492i | −1.12187 | + | 0.820491i | ||||
\(56\) | −3.64002 | −0.486419 | ||||||||
\(57\) | − | 3.48486i | − | 0.461581i | ||||||
\(58\) | 8.15516i | 1.07083i | ||||||||
\(59\) | 3.67030 | 0.477832 | 0.238916 | − | 0.971040i | \(-0.423208\pi\) | ||||
0.238916 | + | 0.971040i | \(0.423208\pi\) | |||||||
\(60\) | −1.32001 | − | 1.80487i | −0.170413 | − | 0.233008i | ||||
\(61\) | 1.45459 | 0.186241 | 0.0931203 | − | 0.995655i | \(-0.470316\pi\) | ||||
0.0931203 | + | 0.995655i | \(0.470316\pi\) | |||||||
\(62\) | − | 5.76491i | − | 0.732144i | ||||||
\(63\) | 3.64002i | 0.458600i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.80487 | + | 3.83515i | 0.347902 | + | 0.475692i | ||||
\(66\) | 4.60975 | 0.567421 | ||||||||
\(67\) | 3.75023i | 0.458163i | 0.973407 | + | 0.229082i | \(0.0735723\pi\) | ||||
−0.973407 | + | 0.229082i | \(0.926428\pi\) | |||||||
\(68\) | 0.609747i | 0.0739427i | ||||||||
\(69\) | 8.76491 | 1.05517 | ||||||||
\(70\) | 6.56978 | − | 4.80487i | 0.785239 | − | 0.574292i | ||||
\(71\) | 14.1698 | 1.68165 | 0.840825 | − | 0.541306i | \(-0.182070\pi\) | ||||
0.840825 | + | 0.541306i | \(0.182070\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 6.76491i | 0.791773i | 0.918300 | + | 0.395886i | \(0.129563\pi\) | ||||
−0.918300 | + | 0.395886i | \(0.870437\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 4.76491 | + | 1.51514i | 0.550204 | + | 0.174953i | ||||
\(76\) | 3.48486 | 0.399741 | ||||||||
\(77\) | 16.7796i | 1.91221i | ||||||||
\(78\) | − | 2.12489i | − | 0.240596i | ||||||
\(79\) | 6.64002 | 0.747061 | 0.373531 | − | 0.927618i | \(-0.378147\pi\) | ||||
0.373531 | + | 0.927618i | \(0.378147\pi\) | |||||||
\(80\) | 1.80487 | − | 1.32001i | 0.201791 | − | 0.147582i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 11.3747i | − | 1.25612i | ||||||
\(83\) | − | 2.90539i | − | 0.318908i | −0.987205 | − | 0.159454i | \(-0.949027\pi\) | ||
0.987205 | − | 0.159454i | \(-0.0509734\pi\) | |||||||
\(84\) | −3.64002 | −0.397159 | ||||||||
\(85\) | −0.804874 | − | 1.10052i | −0.0873008 | − | 0.119368i | ||||
\(86\) | 12.0147 | 1.29558 | ||||||||
\(87\) | 8.15516i | 0.874325i | ||||||||
\(88\) | 4.60975i | 0.491401i | ||||||||
\(89\) | −10.3747 | −1.09971 | −0.549856 | − | 0.835260i | \(-0.685317\pi\) | ||||
−0.549856 | + | 0.835260i | \(0.685317\pi\) | |||||||
\(90\) | −1.32001 | − | 1.80487i | −0.139141 | − | 0.190250i | ||||
\(91\) | 7.73463 | 0.810810 | ||||||||
\(92\) | 8.76491i | 0.913805i | ||||||||
\(93\) | − | 5.76491i | − | 0.597793i | ||||||
\(94\) | 1.60975 | 0.166033 | ||||||||
\(95\) | −6.28974 | + | 4.60006i | −0.645313 | + | 0.471956i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 16.5942i | 1.68488i | 0.538790 | + | 0.842440i | \(0.318882\pi\) | ||||
−0.538790 | + | 0.842440i | \(0.681118\pi\) | |||||||
\(98\) | − | 6.24977i | − | 0.631322i | ||||||
\(99\) | 4.60975 | 0.463297 | ||||||||
\(100\) | −1.51514 | + | 4.76491i | −0.151514 | + | 0.476491i | ||||
\(101\) | 4.06055 | 0.404040 | 0.202020 | − | 0.979381i | \(-0.435249\pi\) | ||||
0.202020 | + | 0.979381i | \(0.435249\pi\) | |||||||
\(102\) | 0.609747i | 0.0603740i | ||||||||
\(103\) | 3.13957i | 0.309351i | 0.987965 | + | 0.154675i | \(0.0494331\pi\) | ||||
−0.987965 | + | 0.154675i | \(0.950567\pi\) | |||||||
\(104\) | 2.12489 | 0.208362 | ||||||||
\(105\) | 6.56978 | − | 4.80487i | 0.641145 | − | 0.468908i | ||||
\(106\) | 9.24977 | 0.898417 | ||||||||
\(107\) | − | 13.9045i | − | 1.34420i | −0.740462 | − | 0.672098i | \(-0.765393\pi\) | ||
0.740462 | − | 0.672098i | \(-0.234607\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 6.85952 | 0.657023 | 0.328511 | − | 0.944500i | \(-0.393453\pi\) | ||||
0.328511 | + | 0.944500i | \(0.393453\pi\) | |||||||
\(110\) | −6.08492 | − | 8.32001i | −0.580174 | − | 0.793282i | ||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | − | 3.64002i | − | 0.343950i | ||||||
\(113\) | − | 10.9844i | − | 1.03333i | −0.856189 | − | 0.516663i | \(-0.827174\pi\) | ||
0.856189 | − | 0.516663i | \(-0.172826\pi\) | |||||||
\(114\) | 3.48486 | 0.326387 | ||||||||
\(115\) | −11.5698 | − | 15.8196i | −1.07889 | − | 1.47518i | ||||
\(116\) | −8.15516 | −0.757188 | ||||||||
\(117\) | − | 2.12489i | − | 0.196446i | ||||||
\(118\) | 3.67030i | 0.337878i | ||||||||
\(119\) | −2.21949 | −0.203461 | ||||||||
\(120\) | 1.80487 | − | 1.32001i | 0.164762 | − | 0.120500i | ||||
\(121\) | 10.2498 | 0.931797 | ||||||||
\(122\) | 1.45459i | 0.131692i | ||||||||
\(123\) | − | 11.3747i | − | 1.02562i | ||||||
\(124\) | 5.76491 | 0.517704 | ||||||||
\(125\) | −3.55510 | − | 10.6001i | −0.317978 | − | 0.948098i | ||||
\(126\) | −3.64002 | −0.324279 | ||||||||
\(127\) | 19.6547i | 1.74407i | 0.489441 | + | 0.872036i | \(0.337201\pi\) | ||||
−0.489441 | + | 0.872036i | \(0.662799\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 12.0147 | 1.05783 | ||||||||
\(130\) | −3.83515 | + | 2.80487i | −0.336365 | + | 0.246004i | ||||
\(131\) | −1.54920 | −0.135354 | −0.0676769 | − | 0.997707i | \(-0.521559\pi\) | ||||
−0.0676769 | + | 0.997707i | \(0.521559\pi\) | |||||||
\(132\) | 4.60975i | 0.401227i | ||||||||
\(133\) | 12.6850i | 1.09993i | ||||||||
\(134\) | −3.75023 | −0.323970 | ||||||||
\(135\) | −1.32001 | − | 1.80487i | −0.113609 | − | 0.155339i | ||||
\(136\) | −0.609747 | −0.0522854 | ||||||||
\(137\) | 16.6400i | 1.42165i | 0.703367 | + | 0.710827i | \(0.251679\pi\) | ||||
−0.703367 | + | 0.710827i | \(0.748321\pi\) | |||||||
\(138\) | 8.76491i | 0.746119i | ||||||||
\(139\) | −3.04496 | −0.258270 | −0.129135 | − | 0.991627i | \(-0.541220\pi\) | ||||
−0.129135 | + | 0.991627i | \(0.541220\pi\) | |||||||
\(140\) | 4.80487 | + | 6.56978i | 0.406086 | + | 0.555248i | ||||
\(141\) | 1.60975 | 0.135565 | ||||||||
\(142\) | 14.1698i | 1.18911i | ||||||||
\(143\) | − | 9.79518i | − | 0.819115i | ||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 14.7190 | − | 10.7649i | 1.22235 | − | 0.893977i | ||||
\(146\) | −6.76491 | −0.559868 | ||||||||
\(147\) | − | 6.24977i | − | 0.515472i | ||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | −19.8401 | −1.62537 | −0.812684 | − | 0.582705i | \(-0.801994\pi\) | ||||
−0.812684 | + | 0.582705i | \(0.801994\pi\) | |||||||
\(150\) | −1.51514 | + | 4.76491i | −0.123711 | + | 0.389053i | ||||
\(151\) | 6.59507 | 0.536699 | 0.268349 | − | 0.963322i | \(-0.413522\pi\) | ||||
0.268349 | + | 0.963322i | \(0.413522\pi\) | |||||||
\(152\) | 3.48486i | 0.282660i | ||||||||
\(153\) | 0.609747i | 0.0492952i | ||||||||
\(154\) | −16.7796 | −1.35214 | ||||||||
\(155\) | −10.4049 | + | 7.60975i | −0.835744 | + | 0.611230i | ||||
\(156\) | 2.12489 | 0.170127 | ||||||||
\(157\) | 10.6741i | 0.851884i | 0.904750 | + | 0.425942i | \(0.140057\pi\) | ||||
−0.904750 | + | 0.425942i | \(0.859943\pi\) | |||||||
\(158\) | 6.64002i | 0.528252i | ||||||||
\(159\) | 9.24977 | 0.733555 | ||||||||
\(160\) | 1.32001 | + | 1.80487i | 0.104356 | + | 0.142688i | ||||
\(161\) | −31.9045 | −2.51442 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − | 7.00000i | − | 0.548282i | −0.961689 | − | 0.274141i | \(-0.911606\pi\) | ||
0.961689 | − | 0.274141i | \(-0.0883936\pi\) | |||||||
\(164\) | 11.3747 | 0.888211 | ||||||||
\(165\) | −6.08492 | − | 8.32001i | −0.473710 | − | 0.647712i | ||||
\(166\) | 2.90539 | 0.225502 | ||||||||
\(167\) | 3.17454i | 0.245653i | 0.992428 | + | 0.122827i | \(0.0391959\pi\) | ||||
−0.992428 | + | 0.122827i | \(0.960804\pi\) | |||||||
\(168\) | − | 3.64002i | − | 0.280834i | ||||||
\(169\) | 8.48486 | 0.652682 | ||||||||
\(170\) | 1.10052 | − | 0.804874i | 0.0844058 | − | 0.0617310i | ||||
\(171\) | 3.48486 | 0.266494 | ||||||||
\(172\) | 12.0147i | 0.916111i | ||||||||
\(173\) | 1.96972i | 0.149755i | 0.997193 | + | 0.0748777i | \(0.0238566\pi\) | ||||
−0.997193 | + | 0.0748777i | \(0.976143\pi\) | |||||||
\(174\) | −8.15516 | −0.618241 | ||||||||
\(175\) | −17.3444 | − | 5.51514i | −1.31111 | − | 0.416905i | ||||
\(176\) | −4.60975 | −0.347473 | ||||||||
\(177\) | 3.67030i | 0.275877i | ||||||||
\(178\) | − | 10.3747i | − | 0.777613i | ||||||
\(179\) | −22.7493 | −1.70036 | −0.850182 | − | 0.526489i | \(-0.823508\pi\) | ||||
−0.850182 | + | 0.526489i | \(0.823508\pi\) | |||||||
\(180\) | 1.80487 | − | 1.32001i | 0.134527 | − | 0.0983879i | ||||
\(181\) | 11.6703 | 0.867447 | 0.433723 | − | 0.901046i | \(-0.357200\pi\) | ||||
0.433723 | + | 0.901046i | \(0.357200\pi\) | |||||||
\(182\) | 7.73463i | 0.573329i | ||||||||
\(183\) | 1.45459i | 0.107526i | ||||||||
\(184\) | −8.76491 | −0.646158 | ||||||||
\(185\) | 1.32001 | + | 1.80487i | 0.0970492 | + | 0.132697i | ||||
\(186\) | 5.76491 | 0.422704 | ||||||||
\(187\) | 2.81078i | 0.205545i | ||||||||
\(188\) | 1.60975i | 0.117403i | ||||||||
\(189\) | −3.64002 | −0.264773 | ||||||||
\(190\) | −4.60006 | − | 6.28974i | −0.333723 | − | 0.456305i | ||||
\(191\) | 10.2800 | 0.743838 | 0.371919 | − | 0.928265i | \(-0.378700\pi\) | ||||
0.371919 | + | 0.928265i | \(0.378700\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | 6.00000i | 0.431889i | 0.976406 | + | 0.215945i | \(0.0692831\pi\) | ||||
−0.976406 | + | 0.215945i | \(0.930717\pi\) | |||||||
\(194\) | −16.5942 | −1.19139 | ||||||||
\(195\) | −3.83515 | + | 2.80487i | −0.274641 | + | 0.200861i | ||||
\(196\) | 6.24977 | 0.446412 | ||||||||
\(197\) | − | 22.4839i | − | 1.60191i | −0.598721 | − | 0.800957i | \(-0.704324\pi\) | ||
0.598721 | − | 0.800957i | \(-0.295676\pi\) | |||||||
\(198\) | 4.60975i | 0.327600i | ||||||||
\(199\) | −26.5601 | −1.88280 | −0.941398 | − | 0.337299i | \(-0.890487\pi\) | ||||
−0.941398 | + | 0.337299i | \(0.890487\pi\) | |||||||
\(200\) | −4.76491 | − | 1.51514i | −0.336930 | − | 0.107136i | ||||
\(201\) | −3.75023 | −0.264521 | ||||||||
\(202\) | 4.06055i | 0.285699i | ||||||||
\(203\) | − | 29.6850i | − | 2.08348i | ||||||
\(204\) | −0.609747 | −0.0426909 | ||||||||
\(205\) | −20.5298 | + | 15.0147i | −1.43386 | + | 1.04867i | ||||
\(206\) | −3.13957 | −0.218744 | ||||||||
\(207\) | 8.76491i | 0.609203i | ||||||||
\(208\) | 2.12489i | 0.147334i | ||||||||
\(209\) | 16.0643 | 1.11119 | ||||||||
\(210\) | 4.80487 | + | 6.56978i | 0.331568 | + | 0.453358i | ||||
\(211\) | 17.7455 | 1.22165 | 0.610826 | − | 0.791765i | \(-0.290837\pi\) | ||||
0.610826 | + | 0.791765i | \(0.290837\pi\) | |||||||
\(212\) | 9.24977i | 0.635277i | ||||||||
\(213\) | 14.1698i | 0.970902i | ||||||||
\(214\) | 13.9045 | 0.950490 | ||||||||
\(215\) | −15.8595 | − | 21.6850i | −1.08161 | − | 1.47890i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 20.9844i | 1.42451i | ||||||||
\(218\) | 6.85952i | 0.464585i | ||||||||
\(219\) | −6.76491 | −0.457130 | ||||||||
\(220\) | 8.32001 | − | 6.08492i | 0.560935 | − | 0.410245i | ||||
\(221\) | 1.29564 | 0.0871544 | ||||||||
\(222\) | − | 1.00000i | − | 0.0671156i | ||||||
\(223\) | 5.20482i | 0.348540i | 0.984698 | + | 0.174270i | \(0.0557566\pi\) | ||||
−0.984698 | + | 0.174270i | \(0.944243\pi\) | |||||||
\(224\) | 3.64002 | 0.243209 | ||||||||
\(225\) | −1.51514 | + | 4.76491i | −0.101009 | + | 0.317661i | ||||
\(226\) | 10.9844 | 0.730672 | ||||||||
\(227\) | − | 16.3856i | − | 1.08755i | −0.839232 | − | 0.543774i | \(-0.816995\pi\) | ||
0.839232 | − | 0.543774i | \(-0.183005\pi\) | |||||||
\(228\) | 3.48486i | 0.230791i | ||||||||
\(229\) | 20.6694 | 1.36587 | 0.682936 | − | 0.730479i | \(-0.260703\pi\) | ||||
0.682936 | + | 0.730479i | \(0.260703\pi\) | |||||||
\(230\) | 15.8196 | − | 11.5698i | 1.04311 | − | 0.762889i | ||||
\(231\) | −16.7796 | −1.10402 | ||||||||
\(232\) | − | 8.15516i | − | 0.535413i | ||||||
\(233\) | 3.28005i | 0.214883i | 0.994211 | + | 0.107442i | \(0.0342658\pi\) | ||||
−0.994211 | + | 0.107442i | \(0.965734\pi\) | |||||||
\(234\) | 2.12489 | 0.138908 | ||||||||
\(235\) | −2.12489 | − | 2.90539i | −0.138612 | − | 0.189527i | ||||
\(236\) | −3.67030 | −0.238916 | ||||||||
\(237\) | 6.64002i | 0.431316i | ||||||||
\(238\) | − | 2.21949i | − | 0.143868i | ||||||
\(239\) | 23.3553 | 1.51073 | 0.755364 | − | 0.655306i | \(-0.227460\pi\) | ||||
0.755364 | + | 0.655306i | \(0.227460\pi\) | |||||||
\(240\) | 1.32001 | + | 1.80487i | 0.0852064 | + | 0.116504i | ||||
\(241\) | −11.7309 | −0.755651 | −0.377825 | − | 0.925877i | \(-0.623328\pi\) | ||||
−0.377825 | + | 0.925877i | \(0.623328\pi\) | |||||||
\(242\) | 10.2498i | 0.658880i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −1.45459 | −0.0931203 | ||||||||
\(245\) | −11.2800 | + | 8.24977i | −0.720656 | + | 0.527059i | ||||
\(246\) | 11.3747 | 0.725222 | ||||||||
\(247\) | − | 7.40493i | − | 0.471165i | ||||||
\(248\) | 5.76491i | 0.366072i | ||||||||
\(249\) | 2.90539 | 0.184122 | ||||||||
\(250\) | 10.6001 | − | 3.55510i | 0.670407 | − | 0.224844i | ||||
\(251\) | 18.6888 | 1.17962 | 0.589812 | − | 0.807541i | \(-0.299202\pi\) | ||||
0.589812 | + | 0.807541i | \(0.299202\pi\) | |||||||
\(252\) | − | 3.64002i | − | 0.229300i | ||||||
\(253\) | 40.4040i | 2.54018i | ||||||||
\(254\) | −19.6547 | −1.23325 | ||||||||
\(255\) | 1.10052 | − | 0.804874i | 0.0689170 | − | 0.0504031i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 30.1542i | − | 1.88097i | −0.339835 | − | 0.940485i | \(-0.610371\pi\) | ||
0.339835 | − | 0.940485i | \(-0.389629\pi\) | |||||||
\(258\) | 12.0147i | 0.748001i | ||||||||
\(259\) | 3.64002 | 0.226180 | ||||||||
\(260\) | −2.80487 | − | 3.83515i | −0.173951 | − | 0.237846i | ||||
\(261\) | −8.15516 | −0.504792 | ||||||||
\(262\) | − | 1.54920i | − | 0.0957096i | ||||||
\(263\) | 15.3141i | 0.944308i | 0.881516 | + | 0.472154i | \(0.156523\pi\) | ||||
−0.881516 | + | 0.472154i | \(0.843477\pi\) | |||||||
\(264\) | −4.60975 | −0.283710 | ||||||||
\(265\) | −12.2098 | − | 16.6947i | −0.750042 | − | 1.02555i | ||||
\(266\) | −12.6850 | −0.777766 | ||||||||
\(267\) | − | 10.3747i | − | 0.634919i | ||||||
\(268\) | − | 3.75023i | − | 0.229082i | ||||||
\(269\) | −7.98440 | −0.486818 | −0.243409 | − | 0.969924i | \(-0.578266\pi\) | ||||
−0.243409 | + | 0.969924i | \(0.578266\pi\) | |||||||
\(270\) | 1.80487 | − | 1.32001i | 0.109841 | − | 0.0803334i | ||||
\(271\) | −13.3094 | −0.808489 | −0.404244 | − | 0.914651i | \(-0.632465\pi\) | ||||
−0.404244 | + | 0.914651i | \(0.632465\pi\) | |||||||
\(272\) | − | 0.609747i | − | 0.0369714i | ||||||
\(273\) | 7.73463i | 0.468121i | ||||||||
\(274\) | −16.6400 | −1.00526 | ||||||||
\(275\) | −6.98440 | + | 21.9650i | −0.421175 | + | 1.32454i | ||||
\(276\) | −8.76491 | −0.527586 | ||||||||
\(277\) | − | 0.435208i | − | 0.0261491i | −0.999915 | − | 0.0130746i | \(-0.995838\pi\) | ||
0.999915 | − | 0.0130746i | \(-0.00416188\pi\) | |||||||
\(278\) | − | 3.04496i | − | 0.182624i | ||||||
\(279\) | 5.76491 | 0.345136 | ||||||||
\(280\) | −6.56978 | + | 4.80487i | −0.392620 | + | 0.287146i | ||||
\(281\) | −4.65562 | −0.277731 | −0.138865 | − | 0.990311i | \(-0.544346\pi\) | ||||
−0.138865 | + | 0.990311i | \(0.544346\pi\) | |||||||
\(282\) | 1.60975i | 0.0958591i | ||||||||
\(283\) | − | 10.2947i | − | 0.611958i | −0.952038 | − | 0.305979i | \(-0.901016\pi\) | ||
0.952038 | − | 0.305979i | \(-0.0989837\pi\) | |||||||
\(284\) | −14.1698 | −0.840825 | ||||||||
\(285\) | −4.60006 | − | 6.28974i | −0.272484 | − | 0.372572i | ||||
\(286\) | 9.79518 | 0.579201 | ||||||||
\(287\) | 41.4040i | 2.44400i | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 16.6282 | 0.978130 | ||||||||
\(290\) | 10.7649 | + | 14.7190i | 0.632137 | + | 0.864332i | ||||
\(291\) | −16.5942 | −0.972766 | ||||||||
\(292\) | − | 6.76491i | − | 0.395886i | ||||||
\(293\) | − | 11.9092i | − | 0.695741i | −0.937543 | − | 0.347871i | \(-0.886905\pi\) | ||
0.937543 | − | 0.347871i | \(-0.113095\pi\) | |||||||
\(294\) | 6.24977 | 0.364494 | ||||||||
\(295\) | 6.62443 | − | 4.84484i | 0.385689 | − | 0.282077i | ||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 4.60975i | 0.267485i | ||||||||
\(298\) | − | 19.8401i | − | 1.14931i | ||||||
\(299\) | 18.6244 | 1.07708 | ||||||||
\(300\) | −4.76491 | − | 1.51514i | −0.275102 | − | 0.0874765i | ||||
\(301\) | −43.7337 | −2.52077 | ||||||||
\(302\) | 6.59507i | 0.379503i | ||||||||
\(303\) | 4.06055i | 0.233273i | ||||||||
\(304\) | −3.48486 | −0.199871 | ||||||||
\(305\) | 2.62534 | − | 1.92007i | 0.150327 | − | 0.109943i | ||||
\(306\) | −0.609747 | −0.0348569 | ||||||||
\(307\) | 13.8595i | 0.791004i | 0.918465 | + | 0.395502i | \(0.129429\pi\) | ||||
−0.918465 | + | 0.395502i | \(0.870571\pi\) | |||||||
\(308\) | − | 16.7796i | − | 0.956106i | ||||||
\(309\) | −3.13957 | −0.178604 | ||||||||
\(310\) | −7.60975 | − | 10.4049i | −0.432205 | − | 0.590960i | ||||
\(311\) | 7.54450 | 0.427809 | 0.213905 | − | 0.976855i | \(-0.431382\pi\) | ||||
0.213905 | + | 0.976855i | \(0.431382\pi\) | |||||||
\(312\) | 2.12489i | 0.120298i | ||||||||
\(313\) | 4.64002i | 0.262270i | 0.991365 | + | 0.131135i | \(0.0418621\pi\) | ||||
−0.991365 | + | 0.131135i | \(0.958138\pi\) | |||||||
\(314\) | −10.6741 | −0.602373 | ||||||||
\(315\) | 4.80487 | + | 6.56978i | 0.270724 | + | 0.370165i | ||||
\(316\) | −6.64002 | −0.373531 | ||||||||
\(317\) | 10.5142i | 0.590538i | 0.955414 | + | 0.295269i | \(0.0954092\pi\) | ||||
−0.955414 | + | 0.295269i | \(0.904591\pi\) | |||||||
\(318\) | 9.24977i | 0.518701i | ||||||||
\(319\) | −37.5932 | −2.10482 | ||||||||
\(320\) | −1.80487 | + | 1.32001i | −0.100896 | + | 0.0737909i | ||||
\(321\) | 13.9045 | 0.776072 | ||||||||
\(322\) | − | 31.9045i | − | 1.77797i | ||||||
\(323\) | 2.12489i | 0.118232i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 10.1249 | + | 3.21949i | 0.561628 | + | 0.178585i | ||||
\(326\) | 7.00000 | 0.387694 | ||||||||
\(327\) | 6.85952i | 0.379332i | ||||||||
\(328\) | 11.3747i | 0.628060i | ||||||||
\(329\) | −5.85952 | −0.323046 | ||||||||
\(330\) | 8.32001 | − | 6.08492i | 0.458002 | − | 0.334964i | ||||
\(331\) | −1.34060 | −0.0736860 | −0.0368430 | − | 0.999321i | \(-0.511730\pi\) | ||||
−0.0368430 | + | 0.999321i | \(0.511730\pi\) | |||||||
\(332\) | 2.90539i | 0.159454i | ||||||||
\(333\) | − | 1.00000i | − | 0.0547997i | ||||||
\(334\) | −3.17454 | −0.173703 | ||||||||
\(335\) | 4.95035 | + | 6.76869i | 0.270466 | + | 0.369813i | ||||
\(336\) | 3.64002 | 0.198580 | ||||||||
\(337\) | − | 20.1055i | − | 1.09522i | −0.836735 | − | 0.547608i | \(-0.815538\pi\) | ||
0.836735 | − | 0.547608i | \(-0.184462\pi\) | |||||||
\(338\) | 8.48486i | 0.461516i | ||||||||
\(339\) | 10.9844 | 0.596591 | ||||||||
\(340\) | 0.804874 | + | 1.10052i | 0.0436504 | + | 0.0596839i | ||||
\(341\) | 26.5748 | 1.43910 | ||||||||
\(342\) | 3.48486i | 0.188440i | ||||||||
\(343\) | − | 2.73085i | − | 0.147452i | ||||||
\(344\) | −12.0147 | −0.647788 | ||||||||
\(345\) | 15.8196 | − | 11.5698i | 0.851696 | − | 0.622896i | ||||
\(346\) | −1.96972 | −0.105893 | ||||||||
\(347\) | 4.70058i | 0.252340i | 0.992009 | + | 0.126170i | \(0.0402685\pi\) | ||||
−0.992009 | + | 0.126170i | \(0.959731\pi\) | |||||||
\(348\) | − | 8.15516i | − | 0.437163i | ||||||
\(349\) | 9.54920 | 0.511157 | 0.255578 | − | 0.966788i | \(-0.417734\pi\) | ||||
0.255578 | + | 0.966788i | \(0.417734\pi\) | |||||||
\(350\) | 5.51514 | − | 17.3444i | 0.294797 | − | 0.927096i | ||||
\(351\) | 2.12489 | 0.113418 | ||||||||
\(352\) | − | 4.60975i | − | 0.245700i | ||||||
\(353\) | 14.4537i | 0.769291i | 0.923064 | + | 0.384646i | \(0.125676\pi\) | ||||
−0.923064 | + | 0.384646i | \(0.874324\pi\) | |||||||
\(354\) | −3.67030 | −0.195074 | ||||||||
\(355\) | 25.5748 | − | 18.7044i | 1.35737 | − | 0.992724i | ||||
\(356\) | 10.3747 | 0.549856 | ||||||||
\(357\) | − | 2.21949i | − | 0.117468i | ||||||
\(358\) | − | 22.7493i | − | 1.20234i | ||||||
\(359\) | 11.0790 | 0.584728 | 0.292364 | − | 0.956307i | \(-0.405558\pi\) | ||||
0.292364 | + | 0.956307i | \(0.405558\pi\) | |||||||
\(360\) | 1.32001 | + | 1.80487i | 0.0695707 | + | 0.0951252i | ||||
\(361\) | −6.85574 | −0.360828 | ||||||||
\(362\) | 11.6703i | 0.613377i | ||||||||
\(363\) | 10.2498i | 0.537973i | ||||||||
\(364\) | −7.73463 | −0.405405 | ||||||||
\(365\) | 8.92976 | + | 12.2098i | 0.467405 | + | 0.639090i | ||||
\(366\) | −1.45459 | −0.0760324 | ||||||||
\(367\) | 10.9201i | 0.570023i | 0.958524 | + | 0.285012i | \(0.0919974\pi\) | ||||
−0.958524 | + | 0.285012i | \(0.908003\pi\) | |||||||
\(368\) | − | 8.76491i | − | 0.456902i | ||||||
\(369\) | 11.3747 | 0.592141 | ||||||||
\(370\) | −1.80487 | + | 1.32001i | −0.0938309 | + | 0.0686241i | ||||
\(371\) | −33.6694 | −1.74803 | ||||||||
\(372\) | 5.76491i | 0.298897i | ||||||||
\(373\) | − | 5.92007i | − | 0.306530i | −0.988185 | − | 0.153265i | \(-0.951021\pi\) | ||
0.988185 | − | 0.153265i | \(-0.0489787\pi\) | |||||||
\(374\) | −2.81078 | −0.145342 | ||||||||
\(375\) | 10.6001 | − | 3.55510i | 0.547385 | − | 0.183585i | ||||
\(376\) | −1.60975 | −0.0830164 | ||||||||
\(377\) | 17.3288i | 0.892478i | ||||||||
\(378\) | − | 3.64002i | − | 0.187223i | ||||||
\(379\) | −22.5189 | −1.15672 | −0.578360 | − | 0.815782i | \(-0.696307\pi\) | ||||
−0.578360 | + | 0.815782i | \(0.696307\pi\) | |||||||
\(380\) | 6.28974 | − | 4.60006i | 0.322657 | − | 0.235978i | ||||
\(381\) | −19.6547 | −1.00694 | ||||||||
\(382\) | 10.2800i | 0.525973i | ||||||||
\(383\) | − | 27.2039i | − | 1.39005i | −0.718984 | − | 0.695027i | \(-0.755392\pi\) | ||
0.718984 | − | 0.695027i | \(-0.244608\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 22.1493 | + | 30.2850i | 1.12883 | + | 1.54347i | ||||
\(386\) | −6.00000 | −0.305392 | ||||||||
\(387\) | 12.0147i | 0.610740i | ||||||||
\(388\) | − | 16.5942i | − | 0.842440i | ||||||
\(389\) | 0.295643 | 0.0149897 | 0.00749486 | − | 0.999972i | \(-0.497614\pi\) | ||||
0.00749486 | + | 0.999972i | \(0.497614\pi\) | |||||||
\(390\) | −2.80487 | − | 3.83515i | −0.142030 | − | 0.194200i | ||||
\(391\) | −5.34438 | −0.270277 | ||||||||
\(392\) | 6.24977i | 0.315661i | ||||||||
\(393\) | − | 1.54920i | − | 0.0781466i | ||||||
\(394\) | 22.4839 | 1.13272 | ||||||||
\(395\) | 11.9844 | − | 8.76491i | 0.603001 | − | 0.441010i | ||||
\(396\) | −4.60975 | −0.231649 | ||||||||
\(397\) | − | 14.1287i | − | 0.709097i | −0.935038 | − | 0.354549i | \(-0.884635\pi\) | ||
0.935038 | − | 0.354549i | \(-0.115365\pi\) | |||||||
\(398\) | − | 26.5601i | − | 1.33134i | ||||||
\(399\) | −12.6850 | −0.635043 | ||||||||
\(400\) | 1.51514 | − | 4.76491i | 0.0757569 | − | 0.238245i | ||||
\(401\) | 17.2838 | 0.863113 | 0.431557 | − | 0.902086i | \(-0.357965\pi\) | ||||
0.431557 | + | 0.902086i | \(0.357965\pi\) | |||||||
\(402\) | − | 3.75023i | − | 0.187044i | ||||||
\(403\) | − | 12.2498i | − | 0.610205i | ||||||
\(404\) | −4.06055 | −0.202020 | ||||||||
\(405\) | 1.80487 | − | 1.32001i | 0.0896849 | − | 0.0655919i | ||||
\(406\) | 29.6850 | 1.47324 | ||||||||
\(407\) | − | 4.60975i | − | 0.228497i | ||||||
\(408\) | − | 0.609747i | − | 0.0301870i | ||||||
\(409\) | −5.73085 | −0.283372 | −0.141686 | − | 0.989912i | \(-0.545252\pi\) | ||||
−0.141686 | + | 0.989912i | \(0.545252\pi\) | |||||||
\(410\) | −15.0147 | − | 20.5298i | −0.741522 | − | 1.01390i | ||||
\(411\) | −16.6400 | −0.820792 | ||||||||
\(412\) | − | 3.13957i | − | 0.154675i | ||||||
\(413\) | − | 13.3600i | − | 0.657401i | ||||||
\(414\) | −8.76491 | −0.430772 | ||||||||
\(415\) | −3.83515 | − | 5.24386i | −0.188260 | − | 0.257411i | ||||
\(416\) | −2.12489 | −0.104181 | ||||||||
\(417\) | − | 3.04496i | − | 0.149112i | ||||||
\(418\) | 16.0643i | 0.785732i | ||||||||
\(419\) | −4.06433 | −0.198556 | −0.0992778 | − | 0.995060i | \(-0.531653\pi\) | ||||
−0.0992778 | + | 0.995060i | \(0.531653\pi\) | |||||||
\(420\) | −6.56978 | + | 4.80487i | −0.320573 | + | 0.234454i | ||||
\(421\) | 34.7493 | 1.69358 | 0.846789 | − | 0.531929i | \(-0.178533\pi\) | ||||
0.846789 | + | 0.531929i | \(0.178533\pi\) | |||||||
\(422\) | 17.7455i | 0.863839i | ||||||||
\(423\) | 1.60975i | 0.0782686i | ||||||||
\(424\) | −9.24977 | −0.449209 | ||||||||
\(425\) | −2.90539 | − | 0.923851i | −0.140932 | − | 0.0448134i | ||||
\(426\) | −14.1698 | −0.686531 | ||||||||
\(427\) | − | 5.29473i | − | 0.256230i | ||||||
\(428\) | 13.9045i | 0.672098i | ||||||||
\(429\) | 9.79518 | 0.472916 | ||||||||
\(430\) | 21.6850 | − | 15.8595i | 1.04574 | − | 0.764814i | ||||
\(431\) | −9.68120 | −0.466327 | −0.233163 | − | 0.972438i | \(-0.574908\pi\) | ||||
−0.233163 | + | 0.972438i | \(0.574908\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | − | 23.7346i | − | 1.14061i | −0.821432 | − | 0.570307i | \(-0.806824\pi\) | ||
0.821432 | − | 0.570307i | \(-0.193176\pi\) | |||||||
\(434\) | −20.9844 | −1.00728 | ||||||||
\(435\) | 10.7649 | + | 14.7190i | 0.516138 | + | 0.705724i | ||||
\(436\) | −6.85952 | −0.328511 | ||||||||
\(437\) | 30.5445i | 1.46114i | ||||||||
\(438\) | − | 6.76491i | − | 0.323240i | ||||||
\(439\) | −7.49576 | −0.357753 | −0.178877 | − | 0.983872i | \(-0.557246\pi\) | ||||
−0.178877 | + | 0.983872i | \(0.557246\pi\) | |||||||
\(440\) | 6.08492 | + | 8.32001i | 0.290087 | + | 0.396641i | ||||
\(441\) | 6.24977 | 0.297608 | ||||||||
\(442\) | 1.29564i | 0.0616275i | ||||||||
\(443\) | 27.1202i | 1.28852i | 0.764807 | + | 0.644260i | \(0.222834\pi\) | ||||
−0.764807 | + | 0.644260i | \(0.777166\pi\) | |||||||
\(444\) | 1.00000 | 0.0474579 | ||||||||
\(445\) | −18.7249 | + | 13.6947i | −0.887647 | + | 0.649190i | ||||
\(446\) | −5.20482 | −0.246455 | ||||||||
\(447\) | − | 19.8401i | − | 0.938406i | ||||||
\(448\) | 3.64002i | 0.171975i | ||||||||
\(449\) | 33.2489 | 1.56911 | 0.784555 | − | 0.620059i | \(-0.212891\pi\) | ||||
0.784555 | + | 0.620059i | \(0.212891\pi\) | |||||||
\(450\) | −4.76491 | − | 1.51514i | −0.224620 | − | 0.0714243i | ||||
\(451\) | 52.4343 | 2.46903 | ||||||||
\(452\) | 10.9844i | 0.516663i | ||||||||
\(453\) | 6.59507i | 0.309863i | ||||||||
\(454\) | 16.3856 | 0.769012 | ||||||||
\(455\) | 13.9600 | − | 10.2098i | 0.654457 | − | 0.478643i | ||||
\(456\) | −3.48486 | −0.163194 | ||||||||
\(457\) | 37.2635i | 1.74311i | 0.490294 | + | 0.871557i | \(0.336890\pi\) | ||||
−0.490294 | + | 0.871557i | \(0.663110\pi\) | |||||||
\(458\) | 20.6694i | 0.965817i | ||||||||
\(459\) | −0.609747 | −0.0284606 | ||||||||
\(460\) | 11.5698 | + | 15.8196i | 0.539444 | + | 0.737590i | ||||
\(461\) | −23.5151 | −1.09521 | −0.547605 | − | 0.836737i | \(-0.684460\pi\) | ||||
−0.547605 | + | 0.836737i | \(0.684460\pi\) | |||||||
\(462\) | − | 16.7796i | − | 0.780657i | ||||||
\(463\) | − | 32.4196i | − | 1.50667i | −0.657639 | − | 0.753334i | \(-0.728445\pi\) | ||
0.657639 | − | 0.753334i | \(-0.271555\pi\) | |||||||
\(464\) | 8.15516 | 0.378594 | ||||||||
\(465\) | −7.60975 | − | 10.4049i | −0.352894 | − | 0.482517i | ||||
\(466\) | −3.28005 | −0.151945 | ||||||||
\(467\) | 33.6244i | 1.55595i | 0.628293 | + | 0.777976i | \(0.283754\pi\) | ||||
−0.628293 | + | 0.777976i | \(0.716246\pi\) | |||||||
\(468\) | 2.12489i | 0.0982229i | ||||||||
\(469\) | 13.6509 | 0.630341 | ||||||||
\(470\) | 2.90539 | − | 2.12489i | 0.134016 | − | 0.0980137i | ||||
\(471\) | −10.6741 | −0.491836 | ||||||||
\(472\) | − | 3.67030i | − | 0.168939i | ||||||
\(473\) | 55.3846i | 2.54659i | ||||||||
\(474\) | −6.64002 | −0.304986 | ||||||||
\(475\) | −5.28005 | + | 16.6050i | −0.242265 | + | 0.761892i | ||||
\(476\) | 2.21949 | 0.101730 | ||||||||
\(477\) | 9.24977i | 0.423518i | ||||||||
\(478\) | 23.3553i | 1.06825i | ||||||||
\(479\) | −13.7952 | −0.630318 | −0.315159 | − | 0.949039i | \(-0.602058\pi\) | ||||
−0.315159 | + | 0.949039i | \(0.602058\pi\) | |||||||
\(480\) | −1.80487 | + | 1.32001i | −0.0823808 | + | 0.0602500i | ||||
\(481\) | −2.12489 | −0.0968864 | ||||||||
\(482\) | − | 11.7309i | − | 0.534326i | ||||||
\(483\) | − | 31.9045i | − | 1.45170i | ||||||
\(484\) | −10.2498 | −0.465899 | ||||||||
\(485\) | 21.9045 | + | 29.9503i | 0.994631 | + | 1.35998i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 9.03028i | 0.409201i | 0.978846 | + | 0.204600i | \(0.0655895\pi\) | ||||
−0.978846 | + | 0.204600i | \(0.934411\pi\) | |||||||
\(488\) | − | 1.45459i | − | 0.0658460i | ||||||
\(489\) | 7.00000 | 0.316551 | ||||||||
\(490\) | −8.24977 | − | 11.2800i | −0.372687 | − | 0.509581i | ||||
\(491\) | −27.3737 | −1.23536 | −0.617680 | − | 0.786430i | \(-0.711927\pi\) | ||||
−0.617680 | + | 0.786430i | \(0.711927\pi\) | |||||||
\(492\) | 11.3747i | 0.512809i | ||||||||
\(493\) | − | 4.97259i | − | 0.223954i | ||||||
\(494\) | 7.40493 | 0.333164 | ||||||||
\(495\) | 8.32001 | − | 6.08492i | 0.373957 | − | 0.273497i | ||||
\(496\) | −5.76491 | −0.258852 | ||||||||
\(497\) | − | 51.5786i | − | 2.31361i | ||||||
\(498\) | 2.90539i | 0.130194i | ||||||||
\(499\) | −0.333481 | −0.0149287 | −0.00746434 | − | 0.999972i | \(-0.502376\pi\) | ||||
−0.00746434 | + | 0.999972i | \(0.502376\pi\) | |||||||
\(500\) | 3.55510 | + | 10.6001i | 0.158989 | + | 0.474049i | ||||
\(501\) | −3.17454 | −0.141828 | ||||||||
\(502\) | 18.6888i | 0.834120i | ||||||||
\(503\) | − | 12.4390i | − | 0.554627i | −0.960779 | − | 0.277314i | \(-0.910556\pi\) | ||
0.960779 | − | 0.277314i | \(-0.0894441\pi\) | |||||||
\(504\) | 3.64002 | 0.162140 | ||||||||
\(505\) | 7.32878 | − | 5.35998i | 0.326127 | − | 0.238516i | ||||
\(506\) | −40.4040 | −1.79618 | ||||||||
\(507\) | 8.48486i | 0.376826i | ||||||||
\(508\) | − | 19.6547i | − | 0.872036i | ||||||
\(509\) | 36.4234 | 1.61444 | 0.807219 | − | 0.590252i | \(-0.200972\pi\) | ||||
0.807219 | + | 0.590252i | \(0.200972\pi\) | |||||||
\(510\) | 0.804874 | + | 1.10052i | 0.0356404 | + | 0.0487317i | ||||
\(511\) | 24.6244 | 1.08932 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 3.48486i | 0.153860i | ||||||||
\(514\) | 30.1542 | 1.33005 | ||||||||
\(515\) | 4.14426 | + | 5.66652i | 0.182618 | + | 0.249697i | ||||
\(516\) | −12.0147 | −0.528917 | ||||||||
\(517\) | 7.42053i | 0.326354i | ||||||||
\(518\) | 3.64002i | 0.159933i | ||||||||
\(519\) | −1.96972 | −0.0864613 | ||||||||
\(520\) | 3.83515 | − | 2.80487i | 0.168182 | − | 0.123002i | ||||
\(521\) | 40.8733 | 1.79069 | 0.895345 | − | 0.445372i | \(-0.146929\pi\) | ||||
0.895345 | + | 0.445372i | \(0.146929\pi\) | |||||||
\(522\) | − | 8.15516i | − | 0.356942i | ||||||
\(523\) | 19.4693i | 0.851332i | 0.904880 | + | 0.425666i | \(0.139960\pi\) | ||||
−0.904880 | + | 0.425666i | \(0.860040\pi\) | |||||||
\(524\) | 1.54920 | 0.0676769 | ||||||||
\(525\) | 5.51514 | − | 17.3444i | 0.240700 | − | 0.756971i | ||||
\(526\) | −15.3141 | −0.667727 | ||||||||
\(527\) | 3.51514i | 0.153122i | ||||||||
\(528\) | − | 4.60975i | − | 0.200614i | ||||||
\(529\) | −53.8236 | −2.34016 | ||||||||
\(530\) | 16.6947 | − | 12.2098i | 0.725170 | − | 0.530360i | ||||
\(531\) | −3.67030 | −0.159277 | ||||||||
\(532\) | − | 12.6850i | − | 0.549964i | ||||||
\(533\) | − | 24.1698i | − | 1.04691i | ||||||
\(534\) | 10.3747 | 0.448955 | ||||||||
\(535\) | −18.3541 | − | 25.0958i | −0.793516 | − | 1.08499i | ||||
\(536\) | 3.75023 | 0.161985 | ||||||||
\(537\) | − | 22.7493i | − | 0.981705i | ||||||
\(538\) | − | 7.98440i | − | 0.344232i | ||||||
\(539\) | 28.8099 | 1.24093 | ||||||||
\(540\) | 1.32001 | + | 1.80487i | 0.0568043 | + | 0.0776694i | ||||
\(541\) | 1.15516 | 0.0496643 | 0.0248321 | − | 0.999692i | \(-0.492095\pi\) | ||||
0.0248321 | + | 0.999692i | \(0.492095\pi\) | |||||||
\(542\) | − | 13.3094i | − | 0.571688i | ||||||
\(543\) | 11.6703i | 0.500820i | ||||||||
\(544\) | 0.609747 | 0.0261427 | ||||||||
\(545\) | 12.3806 | − | 9.05464i | 0.530325 | − | 0.387858i | ||||
\(546\) | −7.73463 | −0.331012 | ||||||||
\(547\) | − | 7.59885i | − | 0.324903i | −0.986717 | − | 0.162452i | \(-0.948060\pi\) | ||
0.986717 | − | 0.162452i | \(-0.0519402\pi\) | |||||||
\(548\) | − | 16.6400i | − | 0.710827i | ||||||
\(549\) | −1.45459 | −0.0620802 | ||||||||
\(550\) | −21.9650 | − | 6.98440i | −0.936592 | − | 0.297816i | ||||
\(551\) | −28.4196 | −1.21072 | ||||||||
\(552\) | − | 8.76491i | − | 0.373059i | ||||||
\(553\) | − | 24.1698i | − | 1.02781i | ||||||
\(554\) | 0.435208 | 0.0184902 | ||||||||
\(555\) | −1.80487 | + | 1.32001i | −0.0766126 | + | 0.0560314i | ||||
\(556\) | 3.04496 | 0.129135 | ||||||||
\(557\) | − | 3.73841i | − | 0.158402i | −0.996859 | − | 0.0792008i | \(-0.974763\pi\) | ||
0.996859 | − | 0.0792008i | \(-0.0252368\pi\) | |||||||
\(558\) | 5.76491i | 0.244048i | ||||||||
\(559\) | 25.5298 | 1.07980 | ||||||||
\(560\) | −4.80487 | − | 6.56978i | −0.203043 | − | 0.277624i | ||||
\(561\) | −2.81078 | −0.118671 | ||||||||
\(562\) | − | 4.65562i | − | 0.196385i | ||||||
\(563\) | − | 23.5033i | − | 0.990547i | −0.868737 | − | 0.495273i | \(-0.835068\pi\) | ||
0.868737 | − | 0.495273i | \(-0.164932\pi\) | |||||||
\(564\) | −1.60975 | −0.0677826 | ||||||||
\(565\) | −14.4995 | − | 19.8255i | −0.610000 | − | 0.834063i | ||||
\(566\) | 10.2947 | 0.432720 | ||||||||
\(567\) | − | 3.64002i | − | 0.152867i | ||||||
\(568\) | − | 14.1698i | − | 0.594553i | ||||||
\(569\) | 45.2526 | 1.89709 | 0.948545 | − | 0.316644i | \(-0.102556\pi\) | ||||
0.948545 | + | 0.316644i | \(0.102556\pi\) | |||||||
\(570\) | 6.28974 | − | 4.60006i | 0.263448 | − | 0.192675i | ||||
\(571\) | 20.4655 | 0.856454 | 0.428227 | − | 0.903671i | \(-0.359138\pi\) | ||||
0.428227 | + | 0.903671i | \(0.359138\pi\) | |||||||
\(572\) | 9.79518i | 0.409557i | ||||||||
\(573\) | 10.2800i | 0.429455i | ||||||||
\(574\) | −41.4040 | −1.72817 | ||||||||
\(575\) | −41.7640 | − | 13.2800i | −1.74168 | − | 0.553816i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 23.7796i | − | 0.989957i | −0.868905 | − | 0.494979i | \(-0.835176\pi\) | ||
0.868905 | − | 0.494979i | \(-0.164824\pi\) | |||||||
\(578\) | 16.6282i | 0.691642i | ||||||||
\(579\) | −6.00000 | −0.249351 | ||||||||
\(580\) | −14.7190 | + | 10.7649i | −0.611175 | + | 0.446989i | ||||
\(581\) | −10.5757 | −0.438754 | ||||||||
\(582\) | − | 16.5942i | − | 0.687850i | ||||||
\(583\) | 42.6391i | 1.76593i | ||||||||
\(584\) | 6.76491 | 0.279934 | ||||||||
\(585\) | −2.80487 | − | 3.83515i | −0.115967 | − | 0.158564i | ||||
\(586\) | 11.9092 | 0.491963 | ||||||||
\(587\) | 10.8633i | 0.448376i | 0.974546 | + | 0.224188i | \(0.0719730\pi\) | ||||
−0.974546 | + | 0.224188i | \(0.928027\pi\) | |||||||
\(588\) | 6.24977i | 0.257736i | ||||||||
\(589\) | 20.0899 | 0.827790 | ||||||||
\(590\) | 4.84484 | + | 6.62443i | 0.199459 | + | 0.272723i | ||||
\(591\) | 22.4839 | 0.924866 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | 11.5005i | 0.472267i | 0.971721 | + | 0.236134i | \(0.0758803\pi\) | ||||
−0.971721 | + | 0.236134i | \(0.924120\pi\) | |||||||
\(594\) | −4.60975 | −0.189140 | ||||||||
\(595\) | −4.00591 | + | 2.92976i | −0.164226 | + | 0.120108i | ||||
\(596\) | 19.8401 | 0.812684 | ||||||||
\(597\) | − | 26.5601i | − | 1.08703i | ||||||
\(598\) | 18.6244i | 0.761609i | ||||||||
\(599\) | −32.7905 | −1.33978 | −0.669891 | − | 0.742459i | \(-0.733659\pi\) | ||||
−0.669891 | + | 0.742459i | \(0.733659\pi\) | |||||||
\(600\) | 1.51514 | − | 4.76491i | 0.0618553 | − | 0.194527i | ||||
\(601\) | −13.4390 | −0.548188 | −0.274094 | − | 0.961703i | \(-0.588378\pi\) | ||||
−0.274094 | + | 0.961703i | \(0.588378\pi\) | |||||||
\(602\) | − | 43.7337i | − | 1.78245i | ||||||
\(603\) | − | 3.75023i | − | 0.152721i | ||||||
\(604\) | −6.59507 | −0.268349 | ||||||||
\(605\) | 18.4995 | − | 13.5298i | 0.752113 | − | 0.550065i | ||||
\(606\) | −4.06055 | −0.164949 | ||||||||
\(607\) | 27.9007i | 1.13245i | 0.824249 | + | 0.566227i | \(0.191597\pi\) | ||||
−0.824249 | + | 0.566227i | \(0.808403\pi\) | |||||||
\(608\) | − | 3.48486i | − | 0.141330i | ||||||
\(609\) | 29.6850 | 1.20290 | ||||||||
\(610\) | 1.92007 | + | 2.62534i | 0.0777414 | + | 0.106297i | ||||
\(611\) | 3.42053 | 0.138380 | ||||||||
\(612\) | − | 0.609747i | − | 0.0246476i | ||||||
\(613\) | − | 27.3553i | − | 1.10487i | −0.833556 | − | 0.552435i | \(-0.813699\pi\) | ||
0.833556 | − | 0.552435i | \(-0.186301\pi\) | |||||||
\(614\) | −13.8595 | −0.559325 | ||||||||
\(615\) | −15.0147 | − | 20.5298i | −0.605450 | − | 0.827842i | ||||
\(616\) | 16.7796 | 0.676069 | ||||||||
\(617\) | − | 38.2985i | − | 1.54184i | −0.636932 | − | 0.770920i | \(-0.719797\pi\) | ||
0.636932 | − | 0.770920i | \(-0.280203\pi\) | |||||||
\(618\) | − | 3.13957i | − | 0.126292i | ||||||
\(619\) | 26.4948 | 1.06492 | 0.532459 | − | 0.846456i | \(-0.321268\pi\) | ||||
0.532459 | + | 0.846456i | \(0.321268\pi\) | |||||||
\(620\) | 10.4049 | − | 7.60975i | 0.417872 | − | 0.305615i | ||||
\(621\) | −8.76491 | −0.351724 | ||||||||
\(622\) | 7.54450i | 0.302507i | ||||||||
\(623\) | 37.7640i | 1.51298i | ||||||||
\(624\) | −2.12489 | −0.0850635 | ||||||||
\(625\) | −20.4087 | − | 14.4390i | −0.816349 | − | 0.577560i | ||||
\(626\) | −4.64002 | −0.185453 | ||||||||
\(627\) | 16.0643i | 0.641548i | ||||||||
\(628\) | − | 10.6741i | − | 0.425942i | ||||||
\(629\) | 0.609747 | 0.0243122 | ||||||||
\(630\) | −6.56978 | + | 4.80487i | −0.261746 | + | 0.191431i | ||||
\(631\) | 0.666519 | 0.0265337 | 0.0132668 | − | 0.999912i | \(-0.495777\pi\) | ||||
0.0132668 | + | 0.999912i | \(0.495777\pi\) | |||||||
\(632\) | − | 6.64002i | − | 0.264126i | ||||||
\(633\) | 17.7455i | 0.705322i | ||||||||
\(634\) | −10.5142 | −0.417573 | ||||||||
\(635\) | 25.9444 | + | 35.4743i | 1.02957 | + | 1.40775i | ||||
\(636\) | −9.24977 | −0.366777 | ||||||||
\(637\) | − | 13.2800i | − | 0.526175i | ||||||
\(638\) | − | 37.5932i | − | 1.48833i | ||||||
\(639\) | −14.1698 | −0.560550 | ||||||||
\(640\) | −1.32001 | − | 1.80487i | −0.0521780 | − | 0.0713439i | ||||
\(641\) | 22.5436 | 0.890418 | 0.445209 | − | 0.895427i | \(-0.353129\pi\) | ||||
0.445209 | + | 0.895427i | \(0.353129\pi\) | |||||||
\(642\) | 13.9045i | 0.548766i | ||||||||
\(643\) | 6.52982i | 0.257511i | 0.991676 | + | 0.128755i | \(0.0410982\pi\) | ||||
−0.991676 | + | 0.128755i | \(0.958902\pi\) | |||||||
\(644\) | 31.9045 | 1.25721 | ||||||||
\(645\) | 21.6850 | − | 15.8595i | 0.853845 | − | 0.624468i | ||||
\(646\) | −2.12489 | −0.0836025 | ||||||||
\(647\) | 0.294727i | 0.0115869i | 0.999983 | + | 0.00579345i | \(0.00184412\pi\) | ||||
−0.999983 | + | 0.00579345i | \(0.998156\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −16.9192 | −0.664135 | ||||||||
\(650\) | −3.21949 | + | 10.1249i | −0.126279 | + | 0.397131i | ||||
\(651\) | −20.9844 | −0.822444 | ||||||||
\(652\) | 7.00000i | 0.274141i | ||||||||
\(653\) | − | 7.68968i | − | 0.300920i | −0.988616 | − | 0.150460i | \(-0.951924\pi\) | ||
0.988616 | − | 0.150460i | \(-0.0480755\pi\) | |||||||
\(654\) | −6.85952 | −0.268228 | ||||||||
\(655\) | −2.79610 | + | 2.04496i | −0.109253 | + | 0.0799030i | ||||
\(656\) | −11.3747 | −0.444106 | ||||||||
\(657\) | − | 6.76491i | − | 0.263924i | ||||||
\(658\) | − | 5.85952i | − | 0.228428i | ||||||
\(659\) | 2.22041 | 0.0864949 | 0.0432475 | − | 0.999064i | \(-0.486230\pi\) | ||||
0.0432475 | + | 0.999064i | \(0.486230\pi\) | |||||||
\(660\) | 6.08492 | + | 8.32001i | 0.236855 | + | 0.323856i | ||||
\(661\) | 7.76869 | 0.302167 | 0.151084 | − | 0.988521i | \(-0.451724\pi\) | ||||
0.151084 | + | 0.988521i | \(0.451724\pi\) | |||||||
\(662\) | − | 1.34060i | − | 0.0521039i | ||||||
\(663\) | 1.29564i | 0.0503186i | ||||||||
\(664\) | −2.90539 | −0.112751 | ||||||||
\(665\) | 16.7443 | + | 22.8948i | 0.649317 | + | 0.887822i | ||||
\(666\) | 1.00000 | 0.0387492 | ||||||||
\(667\) | − | 71.4792i | − | 2.76769i | ||||||
\(668\) | − | 3.17454i | − | 0.122827i | ||||||
\(669\) | −5.20482 | −0.201230 | ||||||||
\(670\) | −6.76869 | + | 4.95035i | −0.261497 | + | 0.191249i | ||||
\(671\) | −6.70527 | −0.258854 | ||||||||
\(672\) | 3.64002i | 0.140417i | ||||||||
\(673\) | − | 10.9853i | − | 0.423453i | −0.977329 | − | 0.211726i | \(-0.932091\pi\) | ||
0.977329 | − | 0.211726i | \(-0.0679086\pi\) | |||||||
\(674\) | 20.1055 | 0.774435 | ||||||||
\(675\) | −4.76491 | − | 1.51514i | −0.183401 | − | 0.0583177i | ||||
\(676\) | −8.48486 | −0.326341 | ||||||||
\(677\) | − | 32.9229i | − | 1.26533i | −0.774425 | − | 0.632666i | \(-0.781961\pi\) | ||
0.774425 | − | 0.632666i | \(-0.218039\pi\) | |||||||
\(678\) | 10.9844i | 0.421853i | ||||||||
\(679\) | 60.4031 | 2.31806 | ||||||||
\(680\) | −1.10052 | + | 0.804874i | −0.0422029 | + | 0.0308655i | ||||
\(681\) | 16.3856 | 0.627896 | ||||||||
\(682\) | 26.5748i | 1.01760i | ||||||||
\(683\) | − | 34.4343i | − | 1.31759i | −0.752322 | − | 0.658796i | \(-0.771066\pi\) | ||
0.752322 | − | 0.658796i | \(-0.228934\pi\) | |||||||
\(684\) | −3.48486 | −0.133247 | ||||||||
\(685\) | 21.9650 | + | 30.0331i | 0.839241 | + | 1.14751i | ||||
\(686\) | 2.73085 | 0.104264 | ||||||||
\(687\) | 20.6694i | 0.788586i | ||||||||
\(688\) | − | 12.0147i | − | 0.458055i | ||||||
\(689\) | 19.6547 | 0.748785 | ||||||||
\(690\) | 11.5698 | + | 15.8196i | 0.440454 | + | 0.602240i | ||||
\(691\) | 7.02558 | 0.267266 | 0.133633 | − | 0.991031i | \(-0.457336\pi\) | ||||
0.133633 | + | 0.991031i | \(0.457336\pi\) | |||||||
\(692\) | − | 1.96972i | − | 0.0748777i | ||||||
\(693\) | − | 16.7796i | − | 0.637404i | ||||||
\(694\) | −4.70058 | −0.178431 | ||||||||
\(695\) | −5.49576 | + | 4.01938i | −0.208466 | + | 0.152464i | ||||
\(696\) | 8.15516 | 0.309121 | ||||||||
\(697\) | 6.93567i | 0.262707i | ||||||||
\(698\) | 9.54920i | 0.361442i | ||||||||
\(699\) | −3.28005 | −0.124063 | ||||||||
\(700\) | 17.3444 | + | 5.51514i | 0.655556 | + | 0.208453i | ||||
\(701\) | 19.6509 | 0.742205 | 0.371103 | − | 0.928592i | \(-0.378980\pi\) | ||||
0.371103 | + | 0.928592i | \(0.378980\pi\) | |||||||
\(702\) | 2.12489i | 0.0801986i | ||||||||
\(703\) | − | 3.48486i | − | 0.131434i | ||||||
\(704\) | 4.60975 | 0.173736 | ||||||||
\(705\) | 2.90539 | − | 2.12489i | 0.109423 | − | 0.0800278i | ||||
\(706\) | −14.4537 | −0.543971 | ||||||||
\(707\) | − | 14.7805i | − | 0.555878i | ||||||
\(708\) | − | 3.67030i | − | 0.137938i | ||||||
\(709\) | 28.7990 | 1.08157 | 0.540784 | − | 0.841162i | \(-0.318128\pi\) | ||||
0.540784 | + | 0.841162i | \(0.318128\pi\) | |||||||
\(710\) | 18.7044 | + | 25.5748i | 0.701962 | + | 0.959804i | ||||
\(711\) | −6.64002 | −0.249020 | ||||||||
\(712\) | 10.3747i | 0.388807i | ||||||||
\(713\) | 50.5289i | 1.89232i | ||||||||
\(714\) | 2.21949 | 0.0830625 | ||||||||
\(715\) | −12.9298 | − | 17.6791i | −0.483546 | − | 0.661160i | ||||
\(716\) | 22.7493 | 0.850182 | ||||||||
\(717\) | 23.3553i | 0.872219i | ||||||||
\(718\) | 11.0790i | 0.413465i | ||||||||
\(719\) | 52.2598 | 1.94896 | 0.974480 | − | 0.224475i | \(-0.0720666\pi\) | ||||
0.974480 | + | 0.224475i | \(0.0720666\pi\) | |||||||
\(720\) | −1.80487 | + | 1.32001i | −0.0672637 | + | 0.0491939i | ||||
\(721\) | 11.4281 | 0.425604 | ||||||||
\(722\) | − | 6.85574i | − | 0.255144i | ||||||
\(723\) | − | 11.7309i | − | 0.436275i | ||||||
\(724\) | −11.6703 | −0.433723 | ||||||||
\(725\) | 12.3562 | − | 38.8586i | 0.458898 | − | 1.44317i | ||||
\(726\) | −10.2498 | −0.380405 | ||||||||
\(727\) | − | 20.3591i | − | 0.755076i | −0.925994 | − | 0.377538i | \(-0.876771\pi\) | ||
0.925994 | − | 0.377538i | \(-0.123229\pi\) | |||||||
\(728\) | − | 7.73463i | − | 0.286665i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −12.2098 | + | 8.92976i | −0.451905 | + | 0.330505i | ||||
\(731\) | −7.32592 | −0.270959 | ||||||||
\(732\) | − | 1.45459i | − | 0.0537630i | ||||||
\(733\) | 22.1433i | 0.817883i | 0.912561 | + | 0.408942i | \(0.134102\pi\) | ||||
−0.912561 | + | 0.408942i | \(0.865898\pi\) | |||||||
\(734\) | −10.9201 | −0.403067 | ||||||||
\(735\) | −8.24977 | − | 11.2800i | −0.304297 | − | 0.416071i | ||||
\(736\) | 8.76491 | 0.323079 | ||||||||
\(737\) | − | 17.2876i | − | 0.636797i | ||||||
\(738\) | 11.3747i | 0.418707i | ||||||||
\(739\) | −34.6429 | −1.27436 | −0.637180 | − | 0.770715i | \(-0.719899\pi\) | ||||
−0.637180 | + | 0.770715i | \(0.719899\pi\) | |||||||
\(740\) | −1.32001 | − | 1.80487i | −0.0485246 | − | 0.0663485i | ||||
\(741\) | 7.40493 | 0.272027 | ||||||||
\(742\) | − | 33.6694i | − | 1.23604i | ||||||
\(743\) | 46.4049i | 1.70243i | 0.524816 | + | 0.851216i | \(0.324134\pi\) | ||||
−0.524816 | + | 0.851216i | \(0.675866\pi\) | |||||||
\(744\) | −5.76491 | −0.211352 | ||||||||
\(745\) | −35.8089 | + | 26.1892i | −1.31194 | + | 0.959499i | ||||
\(746\) | 5.92007 | 0.216749 | ||||||||
\(747\) | 2.90539i | 0.106303i | ||||||||
\(748\) | − | 2.81078i | − | 0.102772i | ||||||
\(749\) | −50.6126 | −1.84934 | ||||||||
\(750\) | 3.55510 | + | 10.6001i | 0.129814 | + | 0.387059i | ||||
\(751\) | −25.6585 | −0.936291 | −0.468146 | − | 0.883651i | \(-0.655078\pi\) | ||||
−0.468146 | + | 0.883651i | \(0.655078\pi\) | |||||||
\(752\) | − | 1.60975i | − | 0.0587014i | ||||||
\(753\) | 18.6888i | 0.681056i | ||||||||
\(754\) | −17.3288 | −0.631077 | ||||||||
\(755\) | 11.9033 | − | 8.70557i | 0.433204 | − | 0.316828i | ||||
\(756\) | 3.64002 | 0.132386 | ||||||||
\(757\) | 21.2157i | 0.771098i | 0.922687 | + | 0.385549i | \(0.125988\pi\) | ||||
−0.922687 | + | 0.385549i | \(0.874012\pi\) | |||||||
\(758\) | − | 22.5189i | − | 0.817924i | ||||||
\(759\) | −40.4040 | −1.46657 | ||||||||
\(760\) | 4.60006 | + | 6.28974i | 0.166862 | + | 0.228153i | ||||
\(761\) | −41.2654 | −1.49587 | −0.747934 | − | 0.663773i | \(-0.768954\pi\) | ||||
−0.747934 | + | 0.663773i | \(0.768954\pi\) | |||||||
\(762\) | − | 19.6547i | − | 0.712015i | ||||||
\(763\) | − | 24.9688i | − | 0.903932i | ||||||
\(764\) | −10.2800 | −0.371919 | ||||||||
\(765\) | 0.804874 | + | 1.10052i | 0.0291003 | + | 0.0397893i | ||||
\(766\) | 27.2039 | 0.982917 | ||||||||
\(767\) | 7.79897i | 0.281604i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −15.2607 | −0.550314 | −0.275157 | − | 0.961399i | \(-0.588730\pi\) | ||||
−0.275157 | + | 0.961399i | \(0.588730\pi\) | |||||||
\(770\) | −30.2850 | + | 22.1493i | −1.09140 | + | 0.798204i | ||||
\(771\) | 30.1542 | 1.08598 | ||||||||
\(772\) | − | 6.00000i | − | 0.215945i | ||||||
\(773\) | − | 26.4693i | − | 0.952033i | −0.879436 | − | 0.476017i | \(-0.842080\pi\) | ||
0.879436 | − | 0.476017i | \(-0.157920\pi\) | |||||||
\(774\) | −12.0147 | −0.431859 | ||||||||
\(775\) | −8.73463 | + | 27.4693i | −0.313757 | + | 0.986725i | ||||
\(776\) | 16.5942 | 0.595695 | ||||||||
\(777\) | 3.64002i | 0.130585i | ||||||||
\(778\) | 0.295643i | 0.0105993i | ||||||||
\(779\) | 39.6391 | 1.42022 | ||||||||
\(780\) | 3.83515 | − | 2.80487i | 0.137320 | − | 0.100431i | ||||
\(781\) | −65.3194 | −2.33731 | ||||||||
\(782\) | − | 5.34438i | − | 0.191115i | ||||||
\(783\) | − | 8.15516i | − | 0.291442i | ||||||
\(784\) | −6.24977 | −0.223206 | ||||||||
\(785\) | 14.0899 | + | 19.2654i | 0.502891 | + | 0.687610i | ||||
\(786\) | 1.54920 | 0.0552580 | ||||||||
\(787\) | 37.7190i | 1.34454i | 0.740307 | + | 0.672269i | \(0.234680\pi\) | ||||
−0.740307 | + | 0.672269i | \(0.765320\pi\) | |||||||
\(788\) | 22.4839i | 0.800957i | ||||||||
\(789\) | −15.3141 | −0.545197 | ||||||||
\(790\) | 8.76491 | + | 11.9844i | 0.311841 | + | 0.426386i | ||||
\(791\) | −39.9835 | −1.42165 | ||||||||
\(792\) | − | 4.60975i | − | 0.163800i | ||||||
\(793\) | 3.09083i | 0.109759i | ||||||||
\(794\) | 14.1287 | 0.501408 | ||||||||
\(795\) | 16.6947 | − | 12.2098i | 0.592099 | − | 0.433037i | ||||
\(796\) | 26.5601 | 0.941398 | ||||||||
\(797\) | − | 26.6013i | − | 0.942265i | −0.882062 | − | 0.471133i | \(-0.843845\pi\) | ||
0.882062 | − | 0.471133i | \(-0.156155\pi\) | |||||||
\(798\) | − | 12.6850i | − | 0.449043i | ||||||
\(799\) | −0.981539 | −0.0347244 | ||||||||
\(800\) | 4.76491 | + | 1.51514i | 0.168465 | + | 0.0535682i | ||||
\(801\) | 10.3747 | 0.366570 | ||||||||
\(802\) | 17.2838i | 0.610313i | ||||||||
\(803\) | − | 31.1845i | − | 1.10048i | ||||||
\(804\) | 3.75023 | 0.132260 | ||||||||
\(805\) | −57.5835 | + | 42.1143i | −2.02955 | + | 1.48433i | ||||
\(806\) | 12.2498 | 0.431480 | ||||||||
\(807\) | − | 7.98440i | − | 0.281064i | ||||||
\(808\) | − | 4.06055i | − | 0.142850i | ||||||
\(809\) | 39.7834 | 1.39871 | 0.699354 | − | 0.714775i | \(-0.253471\pi\) | ||||
0.699354 | + | 0.714775i | \(0.253471\pi\) | |||||||
\(810\) | 1.32001 | + | 1.80487i | 0.0463805 | + | 0.0634168i | ||||
\(811\) | −3.62156 | −0.127170 | −0.0635851 | − | 0.997976i | \(-0.520253\pi\) | ||||
−0.0635851 | + | 0.997976i | \(0.520253\pi\) | |||||||
\(812\) | 29.6850i | 1.04174i | ||||||||
\(813\) | − | 13.3094i | − | 0.466781i | ||||||
\(814\) | 4.60975 | 0.161572 | ||||||||
\(815\) | −9.24008 | − | 12.6341i | −0.323666 | − | 0.442554i | ||||
\(816\) | 0.609747 | 0.0213454 | ||||||||
\(817\) | 41.8695i | 1.46483i | ||||||||
\(818\) | − | 5.73085i | − | 0.200375i | ||||||
\(819\) | −7.73463 | −0.270270 | ||||||||
\(820\) | 20.5298 | − | 15.0147i | 0.716932 | − | 0.524335i | ||||
\(821\) | 29.4537 | 1.02794 | 0.513970 | − | 0.857808i | \(-0.328174\pi\) | ||||
0.513970 | + | 0.857808i | \(0.328174\pi\) | |||||||
\(822\) | − | 16.6400i | − | 0.580387i | ||||||
\(823\) | − | 31.6159i | − | 1.10206i | −0.834485 | − | 0.551031i | \(-0.814234\pi\) | ||
0.834485 | − | 0.551031i | \(-0.185766\pi\) | |||||||
\(824\) | 3.13957 | 0.109372 | ||||||||
\(825\) | −21.9650 | − | 6.98440i | −0.764724 | − | 0.243166i | ||||
\(826\) | 13.3600 | 0.464853 | ||||||||
\(827\) | 27.3359i | 0.950562i | 0.879834 | + | 0.475281i | \(0.157654\pi\) | ||||
−0.879834 | + | 0.475281i | \(0.842346\pi\) | |||||||
\(828\) | − | 8.76491i | − | 0.304602i | ||||||
\(829\) | −14.6391 | −0.508437 | −0.254219 | − | 0.967147i | \(-0.581818\pi\) | ||||
−0.254219 | + | 0.967147i | \(0.581818\pi\) | |||||||
\(830\) | 5.24386 | − | 3.83515i | 0.182017 | − | 0.133120i | ||||
\(831\) | 0.435208 | 0.0150972 | ||||||||
\(832\) | − | 2.12489i | − | 0.0736671i | ||||||
\(833\) | 3.81078i | 0.132036i | ||||||||
\(834\) | 3.04496 | 0.105438 | ||||||||
\(835\) | 4.19043 | + | 5.72964i | 0.145016 | + | 0.198282i | ||||
\(836\) | −16.0643 | −0.555597 | ||||||||
\(837\) | 5.76491i | 0.199264i | ||||||||
\(838\) | − | 4.06433i | − | 0.140400i | ||||||
\(839\) | −16.1386 | −0.557168 | −0.278584 | − | 0.960412i | \(-0.589865\pi\) | ||||
−0.278584 | + | 0.960412i | \(0.589865\pi\) | |||||||
\(840\) | −4.80487 | − | 6.56978i | −0.165784 | − | 0.226679i | ||||
\(841\) | 37.5067 | 1.29333 | ||||||||
\(842\) | 34.7493i | 1.19754i | ||||||||
\(843\) | − | 4.65562i | − | 0.160348i | ||||||
\(844\) | −17.7455 | −0.610826 | ||||||||
\(845\) | 15.3141 | − | 11.2001i | 0.526821 | − | 0.385296i | ||||
\(846\) | −1.60975 | −0.0553443 | ||||||||
\(847\) | − | 37.3094i | − | 1.28197i | ||||||
\(848\) | − | 9.24977i | − | 0.317638i | ||||||
\(849\) | 10.2947 | 0.353314 | ||||||||
\(850\) | 0.923851 | − | 2.90539i | 0.0316878 | − | 0.0996541i | ||||
\(851\) | 8.76491 | 0.300457 | ||||||||
\(852\) | − | 14.1698i | − | 0.485451i | ||||||
\(853\) | 9.44369i | 0.323346i | 0.986844 | + | 0.161673i | \(0.0516889\pi\) | ||||
−0.986844 | + | 0.161673i | \(0.948311\pi\) | |||||||
\(854\) | 5.29473 | 0.181182 | ||||||||
\(855\) | 6.28974 | − | 4.60006i | 0.215104 | − | 0.157319i | ||||
\(856\) | −13.9045 | −0.475245 | ||||||||
\(857\) | 40.0091i | 1.36668i | 0.730099 | + | 0.683342i | \(0.239474\pi\) | ||||
−0.730099 | + | 0.683342i | \(0.760526\pi\) | |||||||
\(858\) | 9.79518i | 0.334402i | ||||||||
\(859\) | −24.5739 | −0.838449 | −0.419225 | − | 0.907883i | \(-0.637698\pi\) | ||||
−0.419225 | + | 0.907883i | \(0.637698\pi\) | |||||||
\(860\) | 15.8595 | + | 21.6850i | 0.540805 | + | 0.739452i | ||||
\(861\) | −41.4040 | −1.41105 | ||||||||
\(862\) | − | 9.68120i | − | 0.329743i | ||||||
\(863\) | − | 2.43613i | − | 0.0829267i | −0.999140 | − | 0.0414633i | \(-0.986798\pi\) | ||
0.999140 | − | 0.0414633i | \(-0.0132020\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 2.60006 | + | 3.55510i | 0.0884046 | + | 0.120877i | ||||
\(866\) | 23.7346 | 0.806536 | ||||||||
\(867\) | 16.6282i | 0.564724i | ||||||||
\(868\) | − | 20.9844i | − | 0.712257i | ||||||
\(869\) | −30.6088 | −1.03833 | ||||||||
\(870\) | −14.7190 | + | 10.7649i | −0.499022 | + | 0.364965i | ||||
\(871\) | −7.96881 | −0.270013 | ||||||||
\(872\) | − | 6.85952i | − | 0.232293i | ||||||
\(873\) | − | 16.5942i | − | 0.561627i | ||||||
\(874\) | −30.5445 | −1.03318 | ||||||||
\(875\) | −38.5845 | + | 12.9407i | −1.30439 | + | 0.437474i | ||||
\(876\) | 6.76491 | 0.228565 | ||||||||
\(877\) | − | 13.0861i | − | 0.441887i | −0.975287 | − | 0.220944i | \(-0.929086\pi\) | ||
0.975287 | − | 0.220944i | \(-0.0709137\pi\) | |||||||
\(878\) | − | 7.49576i | − | 0.252970i | ||||||
\(879\) | 11.9092 | 0.401686 | ||||||||
\(880\) | −8.32001 | + | 6.08492i | −0.280468 | + | 0.205123i | ||||
\(881\) | −38.8539 | −1.30902 | −0.654511 | − | 0.756053i | \(-0.727125\pi\) | ||||
−0.654511 | + | 0.756053i | \(0.727125\pi\) | |||||||
\(882\) | 6.24977i | 0.210441i | ||||||||
\(883\) | 9.40023i | 0.316343i | 0.987412 | + | 0.158172i | \(0.0505599\pi\) | ||||
−0.987412 | + | 0.158172i | \(0.949440\pi\) | |||||||
\(884\) | −1.29564 | −0.0435772 | ||||||||
\(885\) | 4.84484 | + | 6.62443i | 0.162857 | + | 0.222678i | ||||
\(886\) | −27.1202 | −0.911121 | ||||||||
\(887\) | − | 23.0156i | − | 0.772788i | −0.922334 | − | 0.386394i | \(-0.873720\pi\) | ||
0.922334 | − | 0.386394i | \(-0.126280\pi\) | |||||||
\(888\) | 1.00000i | 0.0335578i | ||||||||
\(889\) | 71.5436 | 2.39949 | ||||||||
\(890\) | −13.6947 | − | 18.7249i | −0.459046 | − | 0.627662i | ||||
\(891\) | −4.60975 | −0.154432 | ||||||||
\(892\) | − | 5.20482i | − | 0.174270i | ||||||
\(893\) | 5.60975i | 0.187723i | ||||||||
\(894\) | 19.8401 | 0.663554 | ||||||||
\(895\) | −41.0596 | + | 30.0294i | −1.37247 | + | 1.00377i | ||||
\(896\) | −3.64002 | −0.121605 | ||||||||
\(897\) | 18.6244i | 0.621852i | ||||||||
\(898\) | 33.2489i | 1.10953i | ||||||||
\(899\) | −47.0138 | −1.56800 | ||||||||
\(900\) | 1.51514 | − | 4.76491i | 0.0505046 | − | 0.158830i | ||||
\(901\) | −5.64002 | −0.187896 | ||||||||
\(902\) | 52.4343i | 1.74587i | ||||||||
\(903\) | − | 43.7337i | − | 1.45537i | ||||||
\(904\) | −10.9844 | −0.365336 | ||||||||
\(905\) | 21.0634 | − | 15.4049i | 0.700172 | − | 0.512077i | ||||
\(906\) | −6.59507 | −0.219106 | ||||||||
\(907\) | − | 24.8860i | − | 0.826327i | −0.910657 | − | 0.413163i | \(-0.864424\pi\) | ||
0.910657 | − | 0.413163i | \(-0.135576\pi\) | |||||||
\(908\) | 16.3856i | 0.543774i | ||||||||
\(909\) | −4.06055 | −0.134680 | ||||||||
\(910\) | 10.2098 | + | 13.9600i | 0.338452 | + | 0.462771i | ||||
\(911\) | −5.49863 | −0.182178 | −0.0910888 | − | 0.995843i | \(-0.529035\pi\) | ||||
−0.0910888 | + | 0.995843i | \(0.529035\pi\) | |||||||
\(912\) | − | 3.48486i | − | 0.115395i | ||||||
\(913\) | 13.3931i | 0.443247i | ||||||||
\(914\) | −37.2635 | −1.23257 | ||||||||
\(915\) | 1.92007 | + | 2.62534i | 0.0634756 | + | 0.0867912i | ||||
\(916\) | −20.6694 | −0.682936 | ||||||||
\(917\) | 5.63911i | 0.186220i | ||||||||
\(918\) | − | 0.609747i | − | 0.0201247i | ||||||
\(919\) | 29.0790 | 0.959228 | 0.479614 | − | 0.877480i | \(-0.340777\pi\) | ||||
0.479614 | + | 0.877480i | \(0.340777\pi\) | |||||||
\(920\) | −15.8196 | + | 11.5698i | −0.521555 | + | 0.381444i | ||||
\(921\) | −13.8595 | −0.456687 | ||||||||
\(922\) | − | 23.5151i | − | 0.774430i | ||||||
\(923\) | 30.1093i | 0.991059i | ||||||||
\(924\) | 16.7796 | 0.552008 | ||||||||
\(925\) | 4.76491 | + | 1.51514i | 0.156669 | + | 0.0498174i | ||||
\(926\) | 32.4196 | 1.06537 | ||||||||
\(927\) | − | 3.13957i | − | 0.103117i | ||||||
\(928\) | 8.15516i | 0.267706i | ||||||||
\(929\) | 48.3931 | 1.58773 | 0.793863 | − | 0.608096i | \(-0.208067\pi\) | ||||
0.793863 | + | 0.608096i | \(0.208067\pi\) | |||||||
\(930\) | 10.4049 | − | 7.60975i | 0.341191 | − | 0.249533i | ||||
\(931\) | 21.7796 | 0.713797 | ||||||||
\(932\) | − | 3.28005i | − | 0.107442i | ||||||
\(933\) | 7.54450i | 0.246996i | ||||||||
\(934\) | −33.6244 | −1.10022 | ||||||||
\(935\) | 3.71026 | + | 5.07311i | 0.121339 | + | 0.165908i | ||||
\(936\) | −2.12489 | −0.0694541 | ||||||||
\(937\) | − | 13.4399i | − | 0.439063i | −0.975605 | − | 0.219531i | \(-0.929547\pi\) | ||
0.975605 | − | 0.219531i | \(-0.0704528\pi\) | |||||||
\(938\) | 13.6509i | 0.445718i | ||||||||
\(939\) | −4.64002 | −0.151421 | ||||||||
\(940\) | 2.12489 | + | 2.90539i | 0.0693061 | + | 0.0947634i | ||||
\(941\) | −29.3482 | −0.956723 | −0.478361 | − | 0.878163i | \(-0.658769\pi\) | ||||
−0.478361 | + | 0.878163i | \(0.658769\pi\) | |||||||
\(942\) | − | 10.6741i | − | 0.347780i | ||||||
\(943\) | 99.6978i | 3.24661i | ||||||||
\(944\) | 3.67030 | 0.119458 | ||||||||
\(945\) | −6.56978 | + | 4.80487i | −0.213715 | + | 0.156303i | ||||
\(946\) | −55.3846 | −1.80071 | ||||||||
\(947\) | − | 21.3435i | − | 0.693569i | −0.937945 | − | 0.346785i | \(-0.887273\pi\) | ||
0.937945 | − | 0.346785i | \(-0.112727\pi\) | |||||||
\(948\) | − | 6.64002i | − | 0.215658i | ||||||
\(949\) | −14.3747 | −0.466621 | ||||||||
\(950\) | −16.6050 | − | 5.28005i | −0.538739 | − | 0.171307i | ||||
\(951\) | −10.5142 | −0.340947 | ||||||||
\(952\) | 2.21949i | 0.0719342i | ||||||||
\(953\) | − | 19.2389i | − | 0.623208i | −0.950212 | − | 0.311604i | \(-0.899134\pi\) | ||
0.950212 | − | 0.311604i | \(-0.100866\pi\) | |||||||
\(954\) | −9.24977 | −0.299472 | ||||||||
\(955\) | 18.5542 | − | 13.5698i | 0.600399 | − | 0.439108i | ||||
\(956\) | −23.3553 | −0.755364 | ||||||||
\(957\) | − | 37.5932i | − | 1.21522i | ||||||
\(958\) | − | 13.7952i | − | 0.445702i | ||||||
\(959\) | 60.5701 | 1.95591 | ||||||||
\(960\) | −1.32001 | − | 1.80487i | −0.0426032 | − | 0.0582520i | ||||
\(961\) | 2.23417 | 0.0720701 | ||||||||
\(962\) | − | 2.12489i | − | 0.0685091i | ||||||
\(963\) | 13.9045i | 0.448065i | ||||||||
\(964\) | 11.7309 | 0.377825 | ||||||||
\(965\) | 7.92007 | + | 10.8292i | 0.254956 | + | 0.348606i | ||||
\(966\) | 31.9045 | 1.02651 | ||||||||
\(967\) | − | 21.8813i | − | 0.703656i | −0.936065 | − | 0.351828i | \(-0.885560\pi\) | ||
0.936065 | − | 0.351828i | \(-0.114440\pi\) | |||||||
\(968\) | − | 10.2498i | − | 0.329440i | ||||||
\(969\) | −2.12489 | −0.0682612 | ||||||||
\(970\) | −29.9503 | + | 21.9045i | −0.961648 | + | 0.703310i | ||||
\(971\) | −49.8236 | −1.59892 | −0.799458 | − | 0.600722i | \(-0.794880\pi\) | ||||
−0.799458 | + | 0.600722i | \(0.794880\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 11.0837i | 0.355327i | ||||||||
\(974\) | −9.03028 | −0.289349 | ||||||||
\(975\) | −3.21949 | + | 10.1249i | −0.103106 | + | 0.324256i | ||||
\(976\) | 1.45459 | 0.0465602 | ||||||||
\(977\) | 1.98910i | 0.0636370i | 0.999494 | + | 0.0318185i | \(0.0101299\pi\) | ||||
−0.999494 | + | 0.0318185i | \(0.989870\pi\) | |||||||
\(978\) | 7.00000i | 0.223835i | ||||||||
\(979\) | 47.8245 | 1.52848 | ||||||||
\(980\) | 11.2800 | − | 8.24977i | 0.360328 | − | 0.263529i | ||||
\(981\) | −6.85952 | −0.219008 | ||||||||
\(982\) | − | 27.3737i | − | 0.873531i | ||||||
\(983\) | − | 35.6950i | − | 1.13849i | −0.822167 | − | 0.569246i | \(-0.807235\pi\) | ||
0.822167 | − | 0.569246i | \(-0.192765\pi\) | |||||||
\(984\) | −11.3747 | −0.362611 | ||||||||
\(985\) | −29.6791 | − | 40.5807i | −0.945654 | − | 1.29301i | ||||
\(986\) | 4.97259 | 0.158359 | ||||||||
\(987\) | − | 5.85952i | − | 0.186511i | ||||||
\(988\) | 7.40493i | 0.235582i | ||||||||
\(989\) | −105.308 | −3.34859 | ||||||||
\(990\) | 6.08492 | + | 8.32001i | 0.193391 | + | 0.264427i | ||||
\(991\) | 50.2333 | 1.59571 | 0.797856 | − | 0.602848i | \(-0.205967\pi\) | ||||
0.797856 | + | 0.602848i | \(0.205967\pi\) | |||||||
\(992\) | − | 5.76491i | − | 0.183036i | ||||||
\(993\) | − | 1.34060i | − | 0.0425426i | ||||||
\(994\) | 51.5786 | 1.63597 | ||||||||
\(995\) | −47.9376 | + | 35.0596i | −1.51972 | + | 1.11147i | ||||
\(996\) | −2.90539 | −0.0920608 | ||||||||
\(997\) | 36.9036i | 1.16875i | 0.811485 | + | 0.584374i | \(0.198660\pi\) | ||||
−0.811485 | + | 0.584374i | \(0.801340\pi\) | |||||||
\(998\) | − | 0.333481i | − | 0.0105562i | ||||||
\(999\) | 1.00000 | 0.0316386 |
(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 | 1110.2.d.i.889.6 | yes | 6 | |
3.2 | odd | 2 | 3330.2.d.n.1999.1 | 6 | |||
5.2 | odd | 4 | 5550.2.a.cf.1.3 | 3 | |||
5.3 | odd | 4 | 5550.2.a.cg.1.1 | 3 | |||
5.4 | even | 2 | inner | 1110.2.d.i.889.3 | ✓ | 6 | |
15.14 | odd | 2 | 3330.2.d.n.1999.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.d.i.889.3 | ✓ | 6 | 5.4 | even | 2 | inner | |
1110.2.d.i.889.6 | yes | 6 | 1.1 | even | 1 | trivial | |
3330.2.d.n.1999.1 | 6 | 3.2 | odd | 2 | |||
3330.2.d.n.1999.4 | 6 | 15.14 | odd | 2 | |||
5550.2.a.cf.1.3 | 3 | 5.2 | odd | 4 | |||
5550.2.a.cg.1.1 | 3 | 5.3 | odd | 4 |