Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1839,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1839");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.m (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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{6}, \sqrt{-14})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1839.4 | ||
Root | \(-1.22474 + 1.87083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1839 |
Dual form | 1840.2.m.d.1839.3 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.22474 | + | 1.87083i | 0.547723 | + | 0.836660i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.89898 | −1.47710 | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.58258i | − | 1.27098i | −0.772110 | − | 0.635489i | \(-0.780799\pi\) | ||
0.772110 | − | 0.635489i | \(-0.219201\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.22474 | + | 1.87083i | 0.316228 | + | 0.483046i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.44949 | −0.594089 | −0.297044 | − | 0.954864i | \(-0.596001\pi\) | ||||
−0.297044 | + | 0.954864i | \(0.596001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.44949 | −0.561951 | −0.280976 | − | 0.959715i | \(-0.590658\pi\) | ||||
−0.280976 | + | 0.959715i | \(0.590658\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | + | 3.74166i | −0.625543 | + | 0.780189i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 4.58258i | −0.400000 | + | 0.916515i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.58258i | 0.823055i | 0.911397 | + | 0.411527i | \(0.135005\pi\) | ||||
−0.911397 | + | 0.411527i | \(0.864995\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.89898 | −0.852803 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.89898 | 0.805387 | 0.402694 | − | 0.915335i | \(-0.368074\pi\) | ||||
0.402694 | + | 0.915335i | \(0.368074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.58258i | − | 0.733799i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.2250i | 1.71179i | 0.517148 | + | 0.855896i | \(0.326994\pi\) | ||||
−0.517148 | + | 0.855896i | \(0.673006\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.44949 | − | 3.74166i | −0.365148 | − | 0.557773i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.00000 | −1.31278 | −0.656392 | − | 0.754420i | \(-0.727918\pi\) | ||||
−0.656392 | + | 0.754420i | \(0.727918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.44949 | −0.342997 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.89898 | −0.672927 | −0.336463 | − | 0.941697i | \(-0.609231\pi\) | ||||
−0.336463 | + | 0.941697i | \(0.609231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | − | 9.16515i | −0.809040 | − | 1.23583i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.44949 | −0.324443 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 9.16515i | − | 1.19320i | −0.802538 | − | 0.596601i | \(-0.796518\pi\) | ||
0.802538 | − | 0.596601i | \(-0.203482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2250i | 1.43721i | 0.695418 | + | 0.718605i | \(0.255219\pi\) | ||||
−0.695418 | + | 0.718605i | \(0.744781\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.57321 | − | 5.61249i | 1.06338 | − | 0.696143i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.00000 | + | 3.74166i | −0.361158 | + | 0.450443i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.7477i | − | 1.63156i | −0.578366 | − | 0.815778i | \(-0.696309\pi\) | ||
0.578366 | − | 0.815778i | \(-0.303691\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.58258i | − | 0.536350i | −0.963370 | − | 0.268175i | \(-0.913579\pi\) | ||
0.963370 | − | 0.268175i | \(-0.0864205\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.00000 | + | 4.58258i | −0.230940 | + | 0.529150i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.34847 | −0.826767 | −0.413384 | − | 0.910557i | \(-0.635653\pi\) | ||||
−0.413384 | + | 0.910557i | \(0.635653\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.74166i | − | 0.410700i | −0.978689 | − | 0.205350i | \(-0.934167\pi\) | ||
0.978689 | − | 0.205350i | \(-0.0658333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | − | 4.58258i | −0.325396 | − | 0.497050i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.00000 | −0.321634 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.74166i | − | 0.396615i | −0.980140 | − | 0.198307i | \(-0.936456\pi\) | ||
0.980140 | − | 0.198307i | \(-0.0635444\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.58258i | 0.475191i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00000 | − | 4.58258i | −0.307794 | − | 0.470162i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.79796 | 0.994832 | 0.497416 | − | 0.867512i | \(-0.334282\pi\) | ||||
0.497416 | + | 0.867512i | \(0.334282\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.79796 | 0.984732 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000 | 1.19404 | 0.597022 | − | 0.802225i | \(-0.296350\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.2250i | 1.10603i | 0.833172 | + | 0.553015i | \(0.186523\pi\) | ||||
−0.833172 | + | 0.553015i | \(0.813477\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.74166i | 0.361720i | 0.983509 | + | 0.180860i | \(0.0578880\pi\) | ||||
−0.983509 | + | 0.180860i | \(0.942112\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.2250i | − | 1.07516i | −0.843214 | − | 0.537579i | \(-0.819339\pi\) | ||
0.843214 | − | 0.537579i | \(-0.180661\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.89898 | 0.464991 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.6969 | 1.38257 | 0.691286 | − | 0.722581i | \(-0.257045\pi\) | ||||
0.691286 | + | 0.722581i | \(0.257045\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.6742 | − | 1.02991i | −0.995378 | − | 0.0960396i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.16515i | 0.847319i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.00000 | −0.270501 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0227 | + | 1.87083i | −0.985901 | + | 0.167332i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0000 | −0.976092 | −0.488046 | − | 0.872818i | \(-0.662290\pi\) | ||||
−0.488046 | + | 0.872818i | \(0.662290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.2250i | 0.988304i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.58258i | − | 0.400381i | −0.979757 | − | 0.200191i | \(-0.935844\pi\) | ||
0.979757 | − | 0.200191i | \(-0.0641562\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.12372 | − | 9.35414i | −0.527046 | − | 0.805076i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.6969 | −1.25564 | −0.627822 | − | 0.778357i | \(-0.716053\pi\) | ||||
−0.627822 | + | 0.778357i | \(0.716053\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.9129i | 1.94344i | 0.236126 | + | 0.971722i | \(0.424122\pi\) | ||||
−0.236126 | + | 0.971722i | \(0.575878\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.00000 | −0.757937 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.4499i | 1.87736i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.67423 | − | 5.61249i | −0.305129 | − | 0.466092i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.00000 | 0.577350 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 14.9666i | − | 1.22611i | −0.790039 | − | 0.613057i | \(-0.789940\pi\) | ||
0.790039 | − | 0.613057i | \(-0.210060\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 13.7477i | − | 1.11877i | −0.828907 | − | 0.559387i | \(-0.811037\pi\) | ||
0.828907 | − | 0.559387i | \(-0.188963\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.89898 | 0.396059 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.57321 | + | 5.61249i | −0.688617 | + | 0.450806i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.44949 | 0.195491 | 0.0977453 | − | 0.995211i | \(-0.468837\pi\) | ||||
0.0977453 | + | 0.995211i | \(0.468837\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.89898 | −0.388514 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.0000 | 1.01824 | 0.509119 | − | 0.860696i | \(-0.329971\pi\) | ||||
0.509119 | + | 0.860696i | \(0.329971\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00000 | − | 9.16515i | −0.467099 | − | 0.713506i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.0000 | −1.39288 | −0.696441 | − | 0.717614i | \(-0.745234\pi\) | ||||
−0.696441 | + | 0.717614i | \(0.745234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.00000 | −0.615385 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.89898 | 0.374634 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.3303i | 1.39363i | 0.717252 | + | 0.696814i | \(0.245400\pi\) | ||||
−0.717252 | + | 0.696814i | \(0.754600\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 9.16515i | − | 0.688895i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 13.7477i | − | 1.02755i | −0.857924 | − | 0.513777i | \(-0.828246\pi\) | ||
0.857924 | − | 0.513777i | \(-0.171754\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2250i | 0.829774i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | + | 9.16515i | 0.441129 | + | 0.673835i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0000 | 0.877527 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.2474 | −0.886194 | −0.443097 | − | 0.896474i | \(-0.646120\pi\) | ||||
−0.443097 | + | 0.896474i | \(0.646120\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.9129i | 1.64931i | 0.565640 | + | 0.824653i | \(0.308629\pi\) | ||||
−0.565640 | + | 0.824653i | \(0.691371\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.57321 | − | 5.61249i | 0.613941 | − | 0.401918i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.58258i | − | 0.326495i | −0.986585 | − | 0.163247i | \(-0.947803\pi\) | ||
0.986585 | − | 0.163247i | \(-0.0521969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.5959 | −1.38912 | −0.694559 | − | 0.719436i | \(-0.744400\pi\) | ||||
−0.694559 | + | 0.719436i | \(0.744400\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.67423 | − | 5.61249i | −0.256620 | − | 0.391993i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | − | 7.48331i | 0.417029 | − | 0.520126i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.3303i | 1.26191i | 0.775819 | + | 0.630955i | \(0.217337\pi\) | ||||
−0.775819 | + | 0.630955i | \(0.782663\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 13.7477i | − | 0.941979i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.0000 | + | 13.7477i | −1.43219 | + | 0.937587i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 4.58258i | − | 0.309662i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.2250i | 0.755073i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.0000 | 1.47323 | 0.736614 | − | 0.676313i | \(-0.236423\pi\) | ||||
0.736614 | + | 0.676313i | \(0.236423\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | − | 9.16515i | 0.266667 | − | 0.611010i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 7.48331i | − | 0.496685i | −0.968672 | − | 0.248343i | \(-0.920114\pi\) | ||
0.968672 | − | 0.248343i | \(-0.0798858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.2250i | 0.741767i | 0.928679 | + | 0.370884i | \(0.120945\pi\) | ||||
−0.928679 | + | 0.370884i | \(0.879055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.58258i | 0.300215i | 0.988670 | + | 0.150107i | \(0.0479619\pi\) | ||||
−0.988670 | + | 0.150107i | \(0.952038\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.0227 | − | 16.8375i | −0.719042 | − | 1.09835i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.34847 | −0.477334 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.58258i | 0.296422i | 0.988956 | + | 0.148211i | \(0.0473515\pi\) | ||||
−0.988956 | + | 0.148211i | \(0.952648\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.2250i | − | 0.723064i | −0.932360 | − | 0.361532i | \(-0.882254\pi\) | ||
0.932360 | − | 0.361532i | \(-0.117746\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.57321 | + | 13.0958i | 0.547723 | + | 0.836660i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.2250i | 0.714228i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 3.74166i | − | 0.237118i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.2474 | 0.773052 | 0.386526 | − | 0.922278i | \(-0.373675\pi\) | ||||
0.386526 | + | 0.922278i | \(0.373675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.6969 | − | 18.3303i | 0.923989 | − | 1.15242i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.00000 | − | 4.58258i | −0.187867 | − | 0.286972i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 22.9129i | − | 1.42927i | −0.699500 | − | 0.714633i | \(-0.746594\pi\) | ||
0.699500 | − | 0.714633i | \(-0.253406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.7083i | 1.15360i | 0.816885 | + | 0.576801i | \(0.195699\pi\) | ||||
−0.816885 | + | 0.576801i | \(0.804301\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | − | 9.16515i | −0.368577 | − | 0.563011i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.74166i | − | 0.228986i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.00000 | −0.548740 | −0.274370 | − | 0.961624i | \(-0.588469\pi\) | ||||
−0.274370 | + | 0.961624i | \(0.588469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.16515i | 0.556743i | 0.960473 | + | 0.278372i | \(0.0897947\pi\) | ||||
−0.960473 | + | 0.278372i | \(0.910205\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.79796 | − | 22.4499i | 0.590839 | − | 1.35378i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.9129i | 1.37670i | 0.725378 | + | 0.688351i | \(0.241665\pi\) | ||||
−0.725378 | + | 0.688351i | \(0.758335\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 9.16515i | − | 0.548703i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.9666i | 0.892834i | 0.894825 | + | 0.446417i | \(0.147300\pi\) | ||||
−0.894825 | + | 0.446417i | \(0.852700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 11.2250i | − | 0.667255i | −0.942705 | − | 0.333628i | \(-0.891727\pi\) | ||
0.942705 | − | 0.333628i | \(-0.108273\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00000 | − | 4.58258i | −0.177705 | − | 0.271448i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.0000 | −0.647059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.79796 | 0.574367 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.79796 | 0.572403 | 0.286201 | − | 0.958169i | \(-0.407607\pi\) | ||||
0.286201 | + | 0.958169i | \(0.407607\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.1464 | − | 11.2250i | 0.998304 | − | 0.653543i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.4949 | 1.42134 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.1464 | + | 13.7477i | 0.991604 | + | 0.795052i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.0000 | 0.689382 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.0000 | + | 13.7477i | −1.20246 | + | 0.787193i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0000 | 1.25561 | 0.627803 | − | 0.778372i | \(-0.283954\pi\) | ||||
0.627803 | + | 0.778372i | \(0.283954\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.2250i | 0.638566i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.58258i | 0.259854i | 0.991524 | + | 0.129927i | \(0.0414743\pi\) | ||||
−0.991524 | + | 0.129927i | \(0.958526\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.3939 | −1.66144 | −0.830720 | − | 0.556690i | \(-0.812071\pi\) | ||||
−0.830720 | + | 0.556690i | \(0.812071\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 18.3303i | − | 1.02953i | −0.857331 | − | 0.514766i | \(-0.827879\pi\) | ||
0.857331 | − | 0.514766i | \(-0.172121\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.6969 | 0.822871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.74166i | 0.208839i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.0000 | + | 9.16515i | 1.16487 | + | 0.508391i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 11.2250i | − | 0.620742i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.58258i | 0.251881i | 0.992038 | + | 0.125941i | \(0.0401949\pi\) | ||||
−0.992038 | + | 0.125941i | \(0.959805\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.79796 | −0.536925 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.8434 | −1.73462 | −0.867309 | − | 0.497770i | \(-0.834153\pi\) | ||||
−0.867309 | + | 0.497770i | \(0.834153\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.6969 | 0.798228 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 22.4499i | − | 1.21573i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.6742 | − | 1.02991i | −0.574681 | − | 0.0554485i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | 0.322097 | 0.161048 | − | 0.986947i | \(-0.448512\pi\) | ||||
0.161048 | + | 0.986947i | \(0.448512\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.00000 | 0.0535288 | 0.0267644 | − | 0.999642i | \(-0.491480\pi\) | ||||
0.0267644 | + | 0.999642i | \(0.491480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.9129i | 1.22300i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4.58258i | − | 0.243906i | −0.992536 | − | 0.121953i | \(-0.961084\pi\) | ||
0.992536 | − | 0.121953i | \(-0.0389157\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.7196 | − | 16.8375i | 1.36506 | − | 0.893639i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.2474 | 0.646396 | 0.323198 | − | 0.946331i | \(-0.395242\pi\) | ||||
0.323198 | + | 0.946331i | \(0.395242\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0000 | −0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.0000 | 0.682323 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.57321 | − | 5.61249i | 0.448743 | − | 0.293771i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 33.6749i | − | 1.75782i | −0.476991 | − | 0.878908i | \(-0.658273\pi\) | ||
0.476991 | − | 0.878908i | \(-0.341727\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0454 | −1.14147 | −0.570734 | − | 0.821135i | \(-0.693341\pi\) | ||||
−0.570734 | + | 0.821135i | \(0.693341\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.0227 | + | 1.87083i | −0.569210 | + | 0.0966092i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.7477i | 0.708044i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.5959 | −1.00657 | −0.503287 | − | 0.864119i | \(-0.667876\pi\) | ||||
−0.503287 | + | 0.864119i | \(0.667876\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.0000 | −0.563547 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.1916i | 1.33833i | 0.743115 | + | 0.669164i | \(0.233348\pi\) | ||||
−0.743115 | + | 0.669164i | \(0.766652\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 22.4499i | − | 1.14119i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 14.9666i | − | 0.758838i | −0.925225 | − | 0.379419i | \(-0.876124\pi\) | ||
0.925225 | − | 0.379419i | \(-0.123876\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.34847 | − | 9.16515i | 0.371628 | − | 0.463502i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.58258i | − | 0.231160i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.00000 | − | 13.7477i | −0.452839 | − | 0.691723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.7477i | 0.689979i | 0.938607 | + | 0.344989i | \(0.112117\pi\) | ||||
−0.938607 | + | 0.344989i | \(0.887883\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.1916i | 1.30795i | 0.756518 | + | 0.653973i | \(0.226899\pi\) | ||||
−0.756518 | + | 0.653973i | \(0.773101\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.0000 | 1.04608 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.22474 | + | 1.87083i | 0.0608581 | + | 0.0929622i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.0000 | −1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.00000 | 0.0494468 | 0.0247234 | − | 0.999694i | \(-0.492129\pi\) | ||||
0.0247234 | + | 0.999694i | \(0.492129\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.6969 | −0.724947 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.00000 | − | 4.58258i | 0.343616 | − | 0.224950i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.9129i | 1.12205i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.9444 | 1.31632 | 0.658160 | − | 0.752878i | \(-0.271335\pi\) | ||||
0.658160 | + | 0.752878i | \(0.271335\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.0000 | 0.875190 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.89898 | − | 11.2250i | 0.237635 | − | 0.544491i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.4499i | 1.08389i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.8434 | −1.53384 | −0.766921 | − | 0.641742i | \(-0.778212\pi\) | ||||
−0.766921 | + | 0.641742i | \(0.778212\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.34847 | 0.353145 | 0.176572 | − | 0.984288i | \(-0.443499\pi\) | ||||
0.176572 | + | 0.984288i | \(0.443499\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.67423 | − | 5.61249i | −0.176166 | − | 0.269098i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.34847 | − | 9.16515i | 0.351525 | − | 0.438429i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.58258i | 0.218714i | 0.994003 | + | 0.109357i | \(0.0348792\pi\) | ||||
−0.994003 | + | 0.109357i | \(0.965121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.0000 | −0.666667 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.0000 | 1.56788 | 0.783939 | − | 0.620838i | \(-0.213208\pi\) | ||||
0.783939 | + | 0.620838i | \(0.213208\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.00000 | − | 4.58258i | 0.331832 | − | 0.217235i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 14.9666i | − | 0.707897i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.6969 | 0.692052 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 13.7477i | − | 0.645925i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.2474 | 0.572911 | 0.286456 | − | 0.958093i | \(-0.407523\pi\) | ||||
0.286456 | + | 0.958093i | \(0.407523\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.2474 | 0.571662 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0000 | 0.698620 | 0.349310 | − | 0.937007i | \(-0.386416\pi\) | ||||
0.349310 | + | 0.937007i | \(0.386416\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.57321 | + | 5.61249i | −0.397573 | + | 0.260273i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 7.48331i | − | 0.346287i | −0.984897 | − | 0.173143i | \(-0.944608\pi\) | ||
0.984897 | − | 0.173143i | \(-0.0553924\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.44949 | 0.112867 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 54.9909i | − | 2.52848i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.89898 | − | 11.2250i | 0.224781 | − | 0.515037i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.79796 | 0.448618 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.8434 | −1.45496 | −0.727480 | − | 0.686129i | \(-0.759309\pi\) | ||||
−0.727480 | + | 0.686129i | \(0.759309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 22.4499i | − | 1.02363i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0000 | + | 18.3303i | 0.544892 | + | 0.832336i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00000 | −0.0453143 | −0.0226572 | − | 0.999743i | \(-0.507213\pi\) | ||||
−0.0226572 | + | 0.999743i | \(0.507213\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.0000 | 0.587880 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.58258i | − | 0.206809i | −0.994639 | − | 0.103404i | \(-0.967026\pi\) | ||
0.994639 | − | 0.103404i | \(-0.0329736\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.34847 | 0.330958 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0000 | + | 18.3303i | 0.539360 | + | 0.823886i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.9129i | 1.02572i | 0.858472 | + | 0.512861i | \(0.171414\pi\) | ||||
−0.858472 | + | 0.512861i | \(0.828586\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.0000 | −0.804181 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.9666i | 0.667329i | 0.942692 | + | 0.333665i | \(0.108285\pi\) | ||||
−0.942692 | + | 0.333665i | \(0.891715\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.6969 | + | 22.4499i | 0.654005 | + | 0.999009i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.00000 | −0.355292 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.00000 | −0.398918 | −0.199459 | − | 0.979906i | \(-0.563918\pi\) | ||||
−0.199459 | + | 0.979906i | \(0.563918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.2474 | 0.540738 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.0000 | + | 13.7477i | −0.925371 | + | 0.605797i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.0908 | 1.93911 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.3303i | 0.804611i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.48331i | − | 0.327850i | −0.986473 | − | 0.163925i | \(-0.947584\pi\) | ||
0.986473 | − | 0.163925i | \(-0.0524155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.4499i | 0.981668i | 0.871253 | + | 0.490834i | \(0.163308\pi\) | ||||
−0.871253 | + | 0.490834i | \(0.836692\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 11.2250i | − | 0.488967i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.00000 | − | 22.4499i | −0.217391 | − | 0.976085i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.3303i | 0.795467i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.7477i | 0.595480i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.00000 | + | 4.58258i | −0.302636 | + | 0.198122i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 13.7477i | − | 0.593258i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.2929 | −1.47710 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.0000 | 0.558914 | 0.279457 | − | 0.960158i | \(-0.409846\pi\) | ||||
0.279457 | + | 0.960158i | \(0.409846\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.0000 | − | 13.7477i | 0.899541 | − | 0.588888i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0000 | 0.812381 | 0.406191 | − | 0.913788i | \(-0.366857\pi\) | ||||
0.406191 | + | 0.913788i | \(0.366857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 22.4499i | − | 0.958140i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.34847 | 0.313055 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.00000 | + | 9.16515i | 0.254686 | + | 0.389039i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.7423 | −1.55682 | −0.778412 | − | 0.627754i | \(-0.783974\pi\) | ||||
−0.778412 | + | 0.627754i | \(0.783974\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.4393 | 2.17565 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0000 | 0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.9333i | 1.26154i | 0.775971 | + | 0.630768i | \(0.217260\pi\) | ||||
−0.775971 | + | 0.630768i | \(0.782740\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.0000 | + | 27.4955i | 0.757266 | + | 1.15674i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.7083i | 0.784292i | 0.919903 | + | 0.392146i | \(0.128267\pi\) | ||||
−0.919903 | + | 0.392146i | \(0.871733\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.8434 | 1.33260 | 0.666302 | − | 0.745682i | \(-0.267876\pi\) | ||||
0.666302 | + | 0.745682i | \(0.267876\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.2474 | −0.511645 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.1464 | − | 21.2310i | −0.464838 | − | 0.885396i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.9129i | 0.953876i | 0.878937 | + | 0.476938i | \(0.158253\pi\) | ||||
−0.878937 | + | 0.476938i | \(0.841747\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.9129i | 0.952227i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.0000 | 0.993978 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.1464 | + | 11.2250i | −0.708918 | + | 0.464095i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.00000 | −0.123823 | −0.0619116 | − | 0.998082i | \(-0.519720\pi\) | ||||
−0.0619116 | + | 0.998082i | \(0.519720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 11.2250i | − | 0.462517i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 4.58258i | − | 0.188502i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.6606i | 1.50547i | 0.658323 | + | 0.752735i | \(0.271266\pi\) | ||||
−0.658323 | + | 0.752735i | \(0.728734\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.5959 | −0.802008 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 45.8258i | − | 1.87239i | −0.351481 | − | 0.936195i | \(-0.614322\pi\) | ||
0.351481 | − | 0.936195i | \(-0.385678\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.0000 | −0.448699 | −0.224350 | − | 0.974509i | \(-0.572026\pi\) | ||||
−0.224350 | + | 0.974509i | \(0.572026\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.9217 | + | 24.3208i | 0.647308 | + | 0.988780i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.00000 | −0.162355 | −0.0811775 | − | 0.996700i | \(-0.525868\pi\) | ||||
−0.0811775 | + | 0.996700i | \(0.525868\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 41.2432i | 1.66852i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.0454 | −0.890406 | −0.445203 | − | 0.895430i | \(-0.646868\pi\) | ||||
−0.445203 | + | 0.895430i | \(0.646868\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.67423 | − | 5.61249i | −0.148159 | − | 0.226317i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.34847 | 0.295838 | 0.147919 | − | 0.988999i | \(-0.452742\pi\) | ||||
0.147919 | + | 0.988999i | \(0.452742\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.6969 | −0.590720 | −0.295360 | − | 0.955386i | \(-0.595440\pi\) | ||||
−0.295360 | + | 0.955386i | \(0.595440\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.0000 | − | 18.7083i | 0.601929 | − | 0.750738i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.0000 | − | 18.3303i | −0.680000 | − | 0.733212i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.0000 | 0.479234 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.34847 | −0.292538 | −0.146269 | − | 0.989245i | \(-0.546726\pi\) | ||||
−0.146269 | + | 0.989245i | \(0.546726\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.3303i | 0.728564i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.4722 | − | 20.5791i | −0.534628 | − | 0.816657i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 32.0780i | − | 1.27098i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.4955i | 1.08770i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 48.6415i | − | 1.92123i | −0.277890 | − | 0.960613i | \(-0.589635\pi\) | ||
0.277890 | − | 0.960613i | \(-0.410365\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.2250i | − | 0.442670i | −0.975198 | − | 0.221335i | \(-0.928959\pi\) | ||
0.975198 | − | 0.221335i | \(-0.0710414\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21.0000 | + | 13.7477i | −0.826874 | + | 0.541316i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.0000 | −1.29736 | −0.648682 | − | 0.761060i | \(-0.724679\pi\) | ||||
−0.648682 | + | 0.761060i | \(0.724679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44.8999i | 1.76247i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 50.4083i | 1.97263i | 0.164870 | + | 0.986315i | \(0.447279\pi\) | ||||
−0.164870 | + | 0.986315i | \(0.552721\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.57321 | − | 5.61249i | 0.334983 | − | 0.219298i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.16515i | 0.357567i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.6413 | −1.62212 | −0.811058 | − | 0.584966i | \(-0.801108\pi\) | ||||
−0.811058 | + | 0.584966i | \(0.801108\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 22.4499i | − | 0.873202i | −0.899655 | − | 0.436601i | \(-0.856182\pi\) | ||
0.899655 | − | 0.436601i | \(-0.143818\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.2250i | 0.435942i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | − | 11.2250i | 0.348481 | − | 0.434633i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.0000 | 0.850569 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 54.9909i | − | 2.12290i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 13.7477i | − | 0.529936i | −0.964257 | − | 0.264968i | \(-0.914639\pi\) | ||
0.964257 | − | 0.264968i | \(-0.0853614\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0000 | − | 22.9129i | 0.384900 | − | 0.881917i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.89898 | 0.188283 | 0.0941415 | − | 0.995559i | \(-0.469989\pi\) | ||||
0.0941415 | + | 0.995559i | \(0.469989\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 7.48331i | − | 0.286761i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.00000 | 0.114792 | 0.0573959 | − | 0.998351i | \(-0.481720\pi\) | ||||
0.0573959 | + | 0.998351i | \(0.481720\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | − | 27.4955i | −0.687745 | − | 1.05055i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.2250i | 0.428259i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.4499i | 0.855275i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 9.16515i | − | 0.348659i | −0.984687 | − | 0.174329i | \(-0.944224\pi\) | ||
0.984687 | − | 0.174329i | \(-0.0557758\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −42.8661 | + | 28.0624i | −1.62600 | + | 1.06447i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.34847 | 0.278343 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.58258i | 0.173329i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.9666i | − | 0.565282i | −0.959226 | − | 0.282641i | \(-0.908790\pi\) | ||
0.959226 | − | 0.282641i | \(-0.0912105\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | −0.452589 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.0227 | − | 16.8375i | −0.415139 | − | 0.634135i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 44.8999i | − | 1.68625i | −0.537717 | − | 0.843125i | \(-0.680713\pi\) | ||
0.537717 | − | 0.843125i | \(-0.319287\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.6969 | 0.551178 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.1464 | − | 13.7477i | −0.642139 | − | 0.514856i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42.0000 | + | 27.4955i | −1.57071 | + | 1.02827i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.58258i | 0.171139i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 27.4955i | − | 1.02541i | −0.858566 | − | 0.512704i | \(-0.828644\pi\) | ||
0.858566 | − | 0.512704i | \(-0.171356\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 11.2250i | − | 0.417461i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.00000 | − | 13.7477i | 0.222834 | − | 0.510578i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 33.6749i | − | 1.24893i | −0.781051 | − | 0.624467i | \(-0.785316\pi\) | ||
0.781051 | − | 0.624467i | \(-0.214684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 27.4955i | − | 1.01696i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.4393 | 1.89995 | 0.949977 | − | 0.312321i | \(-0.101106\pi\) | ||||
0.949977 | + | 0.312321i | \(0.101106\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.57321 | + | 13.0958i | 0.316228 | + | 0.483046i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4.58258i | − | 0.168573i | −0.996442 | − | 0.0842864i | \(-0.973139\pi\) | ||
0.996442 | − | 0.0842864i | \(-0.0268611\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.2250i | 0.412360i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.1916i | 0.960877i | 0.877029 | + | 0.480438i | \(0.159522\pi\) | ||||
−0.877029 | + | 0.480438i | \(0.840478\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.0000 | − | 18.3303i | 1.02584 | − | 0.671570i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.48331i | 0.273800i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.2474 | 0.446916 | 0.223458 | − | 0.974714i | \(-0.428265\pi\) | ||||
0.223458 | + | 0.974714i | \(0.428265\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.2474 | 0.446322 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.7196 | − | 16.8375i | 0.936034 | − | 0.612778i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.9898 | −1.78056 | −0.890282 | − | 0.455409i | \(-0.849493\pi\) | ||||
−0.890282 | + | 0.455409i | \(0.849493\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.6969 | − | 18.3303i | 0.533465 | − | 0.665348i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.0000 | −1.63125 | −0.815624 | − | 0.578582i | \(-0.803606\pi\) | ||||
−0.815624 | + | 0.578582i | \(0.803606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.00000 | + | 9.16515i | 0.216930 | + | 0.331367i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −42.0000 | −1.51653 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.6749i | 1.21435i | 0.794569 | + | 0.607174i | \(0.207697\pi\) | ||||
−0.794569 | + | 0.607174i | \(0.792303\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 22.9129i | − | 0.825187i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.1464 | 0.616714 | 0.308357 | − | 0.951271i | \(-0.400221\pi\) | ||||
0.308357 | + | 0.951271i | \(0.400221\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.0000 | − | 9.16515i | −0.754342 | − | 0.329222i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.34847 | 0.263286 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 67.3498i | 2.40997i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.0000 | 0.536056 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.00000 | + | 4.58258i | 0.107075 | + | 0.163559i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.8999i | 1.60051i | 0.599661 | + | 0.800254i | \(0.295302\pi\) | ||||
−0.599661 | + | 0.800254i | \(0.704698\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.7083i | 0.666033i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 51.4393 | 1.82666 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.00000 | − | 9.16515i | −0.212798 | − | 0.325054i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.34847 | −0.260296 | −0.130148 | − | 0.991495i | \(-0.541545\pi\) | ||||
−0.130148 | + | 0.991495i | \(0.541545\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.0454 | 0.779910 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.48331i | 0.264410i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.4499i | 0.792241i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.00000 | −0.316815 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 41.2432i | − | 1.44824i | −0.689672 | − | 0.724122i | \(-0.742245\pi\) | ||
0.689672 | − | 0.724122i | \(-0.257755\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.16515i | 0.321436i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.9217 | + | 24.3208i | 0.557712 | + | 0.851920i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 27.4955i | − | 0.961944i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.0000 | −1.04701 | −0.523504 | − | 0.852023i | \(-0.675375\pi\) | ||||
−0.523504 | + | 0.852023i | \(0.675375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.0000 | −1.91718 | −0.958590 | − | 0.284791i | \(-0.908076\pi\) | ||||
−0.958590 | + | 0.284791i | \(0.908076\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.79796 | − | 22.4499i | 0.341121 | − | 0.781607i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.4166i | 1.30110i | 0.759463 | + | 0.650551i | \(0.225462\pi\) | ||||
−0.759463 | + | 0.650551i | \(0.774538\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.0000 | 0.555703 | 0.277851 | − | 0.960624i | \(-0.410378\pi\) | ||||
0.277851 | + | 0.960624i | \(0.410378\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.9129i | 0.794839i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.1464 | −0.594089 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.0454 | − | 33.6749i | −0.762913 | − | 1.16537i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 22.9129i | − | 0.791985i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.1918 | −1.35305 | −0.676526 | − | 0.736419i | \(-0.736515\pi\) | ||||
−0.676526 | + | 0.736419i | \(0.736515\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.9666i | 0.515478i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.79796 | − | 14.9666i | −0.337060 | − | 0.514868i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 11.2250i | − | 0.385240i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.6969 | + | 18.3303i | −0.503805 | + | 0.628355i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 9.16515i | − | 0.313809i | −0.987614 | − | 0.156904i | \(-0.949849\pi\) | ||
0.987614 | − | 0.156904i | \(-0.0501515\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | + | 9.16515i | 0.205196 | + | 0.313442i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.58258i | 0.156538i | 0.996932 | + | 0.0782689i | \(0.0249393\pi\) | ||||
−0.996932 | + | 0.0782689i | \(0.975061\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 41.2432i | − | 1.40720i | −0.710597 | − | 0.703600i | \(-0.751575\pi\) | ||
0.710597 | − | 0.703600i | \(-0.248425\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.0000 | −0.714848 | −0.357424 | − | 0.933942i | \(-0.616345\pi\) | ||||
−0.357424 | + | 0.933942i | \(0.616345\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.2929 | + | 22.4499i | −1.16599 | + | 0.763321i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.0000 | −0.373580 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.0000 | 1.22122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.5959 | −0.663221 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 18.3303i | − | 0.618970i | −0.950904 | − | 0.309485i | \(-0.899843\pi\) | ||
0.950904 | − | 0.309485i | \(-0.100157\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.79796 | 0.330477 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.74166i | 0.126060i | 0.998012 | + | 0.0630298i | \(0.0200763\pi\) | ||||
−0.998012 | + | 0.0630298i | \(0.979924\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.0000 | 0.538443 | 0.269221 | − | 0.963078i | \(-0.413234\pi\) | ||||
0.269221 | + | 0.963078i | \(0.413234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.1464 | − | 11.2250i | 0.576371 | − | 0.377323i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.0000 | −1.30949 | −0.654746 | − | 0.755849i | \(-0.727224\pi\) | ||||
−0.654746 | + | 0.755849i | \(0.727224\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.89898 | −0.164122 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.0454 | 0.737721 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.7196 | − | 16.8375i | 0.859713 | − | 0.562814i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.1464 | + | 13.7477i | 0.572503 | + | 0.459023i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 13.7477i | − | 0.458512i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.6749i | 1.11816i | 0.829115 | + | 0.559079i | \(0.188845\pi\) | ||||
−0.829115 | + | 0.559079i | \(0.811155\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.0000 | −0.796030 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.34847 | −0.243466 | −0.121733 | − | 0.992563i | \(-0.538845\pi\) | ||||
−0.121733 | + | 0.992563i | \(0.538845\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.3303i | 0.606644i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.0000 | + | 13.7477i | −0.694239 | + | 0.454486i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.89898 | 0.161602 | 0.0808012 | − | 0.996730i | \(-0.474252\pi\) | ||||
0.0808012 | + | 0.996730i | \(0.474252\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.0000 | 0.724925 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −63.0000 | −2.07367 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.79796 | + | 22.4499i | −0.322155 | + | 0.738150i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 22.4499i | − | 0.737353i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.0000 | −1.08269 | −0.541347 | − | 0.840799i | \(-0.682086\pi\) | ||||
−0.541347 | + | 0.840799i | \(0.682086\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.1464 | −0.561951 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.58258i | 0.150027i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.6969 | + | 22.4499i | 0.480641 | + | 0.734192i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.89898 | −0.160043 | −0.0800213 | − | 0.996793i | \(-0.525499\pi\) | ||||
−0.0800213 | + | 0.996793i | \(0.525499\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.3939 | −0.959233 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.74166i | − | 0.121975i | −0.998139 | − | 0.0609873i | \(-0.980575\pi\) | ||
0.998139 | − | 0.0609873i | \(-0.0194249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | − | 11.2250i | 0.293080 | − | 0.365535i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.0000 | 0.682408 | 0.341204 | − | 0.939989i | \(-0.389165\pi\) | ||||
0.341204 | + | 0.939989i | \(0.389165\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.0000 | −0.681689 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 18.3303i | − | 0.594401i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.8888 | −1.74563 | −0.872814 | − | 0.488052i | \(-0.837707\pi\) | ||||
−0.872814 | + | 0.488052i | \(0.837707\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0000 | − | 22.9129i | −0.485389 | − | 0.741443i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.6969 | 0.475085 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.0000 | 0.322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 7.48331i | − | 0.241146i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42.8661 | + | 28.0624i | −1.37991 | + | 0.903362i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.0000 | 1.12552 | 0.562762 | − | 0.826619i | \(-0.309739\pi\) | ||||
0.562762 | + | 0.826619i | \(0.309739\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.00000 | 0.192748 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.1918 | −1.25773 | −0.628863 | − | 0.777516i | \(-0.716479\pi\) | ||||
−0.628863 | + | 0.777516i | \(0.716479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.0000 | + | 9.16515i | 0.672538 | + | 0.293520i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.3939 | 0.940393 | 0.470197 | − | 0.882562i | \(-0.344183\pi\) | ||||
0.470197 | + | 0.882562i | \(0.344183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.3303i | 0.585839i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.4499i | 0.716772i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.3832i | 1.67076i | 0.549669 | + | 0.835382i | \(0.314754\pi\) | ||||
−0.549669 | + | 0.835382i | \(0.685246\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.57321 | − | 5.61249i | 0.273165 | − | 0.178829i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.0000 | − | 33.6749i | −1.33552 | − | 1.07080i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.6606i | 1.16456i | 0.812987 | + | 0.582281i | \(0.197840\pi\) | ||||
−0.812987 | + | 0.582281i | \(0.802160\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.58258i | 0.145424i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.0000 | − | 36.6606i | −0.760851 | − | 1.16222i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.4955i | 0.870790i | 0.900240 | + | 0.435395i | \(0.143391\pi\) | ||||
−0.900240 | + | 0.435395i | \(0.856609\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.4949 | −0.774984 |
(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 | 1840.2.m.d.1839.4 | yes | 4 | |
4.3 | odd | 2 | 1840.2.m.a.1839.4 | yes | 4 | ||
5.4 | even | 2 | 1840.2.m.a.1839.2 | yes | 4 | ||
20.19 | odd | 2 | inner | 1840.2.m.d.1839.2 | yes | 4 | |
23.22 | odd | 2 | inner | 1840.2.m.d.1839.1 | yes | 4 | |
92.91 | even | 2 | 1840.2.m.a.1839.1 | ✓ | 4 | ||
115.114 | odd | 2 | 1840.2.m.a.1839.3 | yes | 4 | ||
460.459 | even | 2 | inner | 1840.2.m.d.1839.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1840.2.m.a.1839.1 | ✓ | 4 | 92.91 | even | 2 | ||
1840.2.m.a.1839.2 | yes | 4 | 5.4 | even | 2 | ||
1840.2.m.a.1839.3 | yes | 4 | 115.114 | odd | 2 | ||
1840.2.m.a.1839.4 | yes | 4 | 4.3 | odd | 2 | ||
1840.2.m.d.1839.1 | yes | 4 | 23.22 | odd | 2 | inner | |
1840.2.m.d.1839.2 | yes | 4 | 20.19 | odd | 2 | inner | |
1840.2.m.d.1839.3 | yes | 4 | 460.459 | even | 2 | inner | |
1840.2.m.d.1839.4 | yes | 4 | 1.1 | even | 1 | trivial |