Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(271,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.271");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.bz (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 271.7 | ||
Character | \(\chi\) | \(=\) | 1120.271 |
Dual form | 1120.2.bz.e.591.7 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.725648 | + | 0.418953i | −0.418953 | + | 0.241883i | −0.694629 | − | 0.719368i | \(-0.744432\pi\) |
0.275676 | + | 0.961251i | \(0.411098\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.36913 | − | 1.17781i | 0.895445 | − | 0.445172i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.14896 | + | 1.99005i | −0.382985 | + | 0.663350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.98938 | − | 5.17776i | −0.901332 | − | 1.56115i | −0.825766 | − | 0.564013i | \(-0.809257\pi\) |
−0.0755665 | − | 0.997141i | \(-0.524077\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.87544 | −0.797504 | −0.398752 | − | 0.917059i | \(-0.630557\pi\) | ||||
−0.398752 | + | 0.917059i | \(0.630557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.837906i | − | 0.216346i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.07668 | − | 1.19897i | 0.503670 | − | 0.290794i | −0.226558 | − | 0.973998i | \(-0.572747\pi\) |
0.730228 | + | 0.683204i | \(0.239414\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.05564 | + | 2.34152i | 0.930427 | + | 0.537182i | 0.886947 | − | 0.461872i | \(-0.152822\pi\) |
0.0434803 | + | 0.999054i | \(0.486155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.22570 | + | 1.84723i | −0.267470 | + | 0.403099i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.81623 | − | 3.35800i | −1.21277 | − | 0.700191i | −0.249406 | − | 0.968399i | \(-0.580235\pi\) |
−0.963361 | + | 0.268208i | \(0.913569\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.43915i | − | 0.854316i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.31035i | 0.243325i | 0.992572 | + | 0.121663i | \(0.0388226\pi\) | ||||
−0.992572 | + | 0.121663i | \(0.961177\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.34775 | − | 7.53053i | −0.780879 | − | 1.35252i | −0.931430 | − | 0.363920i | \(-0.881438\pi\) |
0.150551 | − | 0.988602i | \(-0.451895\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.33848 | + | 2.50482i | 0.755232 | + | 0.436034i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.164546 | + | 2.64063i | −0.0278133 | + | 0.446348i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.26889 | − | 1.88729i | −0.537402 | − | 0.310269i | 0.206624 | − | 0.978421i | \(-0.433752\pi\) |
−0.744025 | + | 0.668151i | \(0.767086\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.08656 | − | 1.20468i | 0.334117 | − | 0.192903i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.79404i | − | 0.280181i | −0.990139 | − | 0.140091i | \(-0.955261\pi\) | ||
0.990139 | − | 0.140091i | \(-0.0447394\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.73760 | 1.02747 | 0.513737 | − | 0.857948i | \(-0.328261\pi\) | ||||
0.513737 | + | 0.857948i | \(0.328261\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.14896 | − | 1.99005i | −0.171276 | − | 0.296659i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.874599 | + | 1.51485i | −0.127573 | + | 0.220963i | −0.922736 | − | 0.385433i | \(-0.874052\pi\) |
0.795163 | + | 0.606396i | \(0.207385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.22551 | − | 5.58078i | 0.603644 | − | 0.797254i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00463 | + | 1.74007i | −0.140676 | + | 0.243658i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.0994447 | + | 0.0574144i | −0.0136598 | + | 0.00788648i | −0.506814 | − | 0.862055i | \(-0.669177\pi\) |
0.493155 | + | 0.869942i | \(0.335844\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.97876 | 0.806176 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.92395 | −0.519740 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.61363 | + | 1.50898i | −0.340266 | + | 0.196453i | −0.660390 | − | 0.750923i | \(-0.729609\pi\) |
0.320124 | + | 0.947376i | \(0.396276\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.40120 | − | 7.62310i | 0.563516 | − | 0.976038i | −0.433670 | − | 0.901072i | \(-0.642782\pi\) |
0.997186 | − | 0.0749664i | \(-0.0238850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.378112 | + | 6.06794i | −0.0476376 | + | 0.764488i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.43772 | − | 2.49021i | 0.178327 | − | 0.308872i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.83761 | + | 4.91489i | 0.346670 | + | 0.600449i | 0.985656 | − | 0.168769i | \(-0.0539792\pi\) |
−0.638986 | + | 0.769218i | \(0.720646\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.62738 | 0.677457 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.06734i | − | 0.364026i | −0.983296 | − | 0.182013i | \(-0.941739\pi\) | ||
0.983296 | − | 0.182013i | \(-0.0582613\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.69332 | − | 5.01909i | 1.01748 | − | 0.587440i | 0.104104 | − | 0.994566i | \(-0.466802\pi\) |
0.913372 | + | 0.407126i | \(0.133469\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.725648 | + | 0.418953i | 0.0837906 | + | 0.0483765i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.1807 | − | 8.74583i | −1.50208 | − | 0.996680i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9852 | − | 6.91965i | −1.34844 | − | 0.778522i | −0.360411 | − | 0.932794i | \(-0.617364\pi\) |
−0.988028 | + | 0.154272i | \(0.950697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.58707 | − | 2.74889i | −0.176341 | − | 0.305432i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 17.4215i | − | 1.91226i | −0.292940 | − | 0.956131i | \(-0.594634\pi\) | ||
0.292940 | − | 0.956131i | \(-0.405366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.39795i | 0.260094i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.548973 | − | 0.950850i | −0.0588561 | − | 0.101942i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.0658 | − | 6.38886i | −1.17297 | − | 0.677217i | −0.218596 | − | 0.975815i | \(-0.570148\pi\) |
−0.954379 | + | 0.298598i | \(0.903481\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.81228 | + | 3.38674i | −0.714121 | + | 0.355026i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.30988 | + | 3.64301i | 0.654304 | + | 0.377762i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.05564 | + | 2.34152i | −0.416100 | + | 0.240235i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.76431i | − | 0.382208i | −0.981570 | − | 0.191104i | \(-0.938793\pi\) | ||
0.981570 | − | 0.191104i | \(-0.0612067\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.7387 | 1.38079 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.14097 | − | 14.1006i | −0.810057 | − | 1.40306i | −0.912824 | − | 0.408354i | \(-0.866103\pi\) |
0.102767 | − | 0.994705i | \(-0.467230\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.13180 | + | 1.96034i | −0.111520 | + | 0.193158i | −0.916383 | − | 0.400302i | \(-0.868905\pi\) |
0.804864 | + | 0.593460i | \(0.202238\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.986898 | − | 1.98511i | −0.0963114 | − | 0.193726i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.21095 | + | 2.09743i | −0.117067 | + | 0.202766i | −0.918604 | − | 0.395179i | \(-0.870683\pi\) |
0.801537 | + | 0.597945i | \(0.204016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.35090 | + | 3.66669i | −0.608306 | + | 0.351206i | −0.772302 | − | 0.635255i | \(-0.780895\pi\) |
0.163996 | + | 0.986461i | \(0.447561\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.16275 | 0.300195 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.0661 | 1.41730 | 0.708651 | − | 0.705559i | \(-0.249304\pi\) | ||||
0.708651 | + | 0.705559i | \(0.249304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.81623 | − | 3.35800i | 0.542366 | − | 0.313135i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.30376 | − | 5.72228i | 0.305433 | − | 0.529025i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.50775 | − | 5.28646i | 0.321555 | − | 0.484609i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.3728 | + | 21.4303i | −1.12480 | + | 1.94821i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.751617 | + | 1.30184i | 0.0677710 | + | 0.117383i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.22434i | 0.463585i | 0.972765 | + | 0.231793i | \(0.0744591\pi\) | ||||
−0.972765 | + | 0.231793i | \(0.925541\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.88913 | + | 2.82274i | −0.430464 | + | 0.248528i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.76094 | − | 4.48078i | −0.678076 | − | 0.391487i | 0.121054 | − | 0.992646i | \(-0.461373\pi\) |
−0.799130 | + | 0.601159i | \(0.794706\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.3662 | + | 0.770575i | 1.07228 | + | 0.0668173i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.84442 | + | 2.21958i | 0.330875 | + | 0.191031i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.4348 | + | 18.0735i | 0.891502 | + | 1.54413i | 0.838075 | + | 0.545554i | \(0.183681\pi\) |
0.0534263 | + | 0.998572i | \(0.482986\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.8189i | 1.08728i | 0.839318 | + | 0.543641i | \(0.182955\pi\) | ||||
−0.839318 | + | 0.543641i | \(0.817045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 1.46566i | − | 0.123431i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.59580 | + | 14.8884i | 0.718817 | + | 1.24503i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.13479 | − | 0.655173i | −0.0942394 | − | 0.0544091i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.728148 | + | 5.81997i | −0.0600566 | + | 0.480023i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.696284 | − | 0.402000i | −0.0570418 | − | 0.0329331i | 0.471208 | − | 0.882022i | \(-0.343818\pi\) |
−0.528250 | + | 0.849089i | \(0.677151\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.3405 | + | 6.54743i | −0.922875 | + | 0.532822i | −0.884551 | − | 0.466443i | \(-0.845535\pi\) |
−0.0383242 | + | 0.999265i | \(0.512202\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.51027i | 0.445479i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.69550 | 0.698440 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.58489 | + | 14.8695i | 0.685149 | + | 1.18671i | 0.973390 | + | 0.229155i | \(0.0735962\pi\) |
−0.288241 | + | 0.957558i | \(0.593070\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0481079 | − | 0.0833254i | 0.00381521 | − | 0.00660813i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.7345 | − | 1.10509i | −1.39767 | − | 0.0870932i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.93458 | − | 5.08284i | 0.229854 | − | 0.398119i | −0.727911 | − | 0.685672i | \(-0.759508\pi\) |
0.957765 | + | 0.287553i | \(0.0928418\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.33848 | + | 2.50482i | −0.337750 | + | 0.195000i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.02260 | −0.466043 | −0.233022 | − | 0.972472i | \(-0.574861\pi\) | ||||
−0.233022 | + | 0.972472i | \(0.574861\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.73183 | −0.363987 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.31950 | + | 5.38062i | −0.712680 | + | 0.411466i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.08168 | − | 1.87352i | 0.0822385 | − | 0.142441i | −0.821973 | − | 0.569527i | \(-0.807126\pi\) |
0.904211 | + | 0.427086i | \(0.140460\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.20458 | − | 1.46282i | −0.166651 | − | 0.110578i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.26439 | − | 2.18998i | 0.0950371 | − | 0.164609i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.63498 | − | 9.76008i | −0.421178 | − | 0.729502i | 0.574877 | − | 0.818240i | \(-0.305050\pi\) |
−0.996055 | + | 0.0887377i | \(0.971717\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.2369 | 1.13255 | 0.566274 | − | 0.824217i | \(-0.308384\pi\) | ||||
0.566274 | + | 0.824217i | \(0.308384\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.37559i | 0.545219i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.26889 | − | 1.88729i | 0.240333 | − | 0.138757i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.4160 | − | 7.16838i | −0.907948 | − | 0.524204i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.22850 | − | 10.5169i | −0.380317 | − | 0.764993i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.33642 | + | 3.08099i | 0.386130 | + | 0.222932i | 0.680482 | − | 0.732765i | \(-0.261770\pi\) |
−0.294352 | + | 0.955697i | \(0.595104\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.79750 | + | 10.0416i | 0.417313 | + | 0.722808i | 0.995668 | − | 0.0929776i | \(-0.0296385\pi\) |
−0.578355 | + | 0.815785i | \(0.696305\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.40935i | 0.172537i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.1499i | 0.936892i | 0.883492 | + | 0.468446i | \(0.155186\pi\) | ||||
−0.883492 | + | 0.468446i | \(0.844814\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0683 | + | 17.4388i | 0.713724 | + | 1.23621i | 0.963450 | + | 0.267889i | \(0.0863261\pi\) |
−0.249726 | + | 0.968317i | \(0.580341\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.11822 | − | 2.37765i | −0.290477 | − | 0.167707i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.54334 | + | 3.10437i | 0.108321 | + | 0.217884i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.55368 | + | 0.897018i | 0.108514 | + | 0.0626504i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.3652 | − | 7.71639i | 0.928944 | − | 0.536326i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 27.9988i | − | 1.93672i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.31289 | −0.296912 | −0.148456 | − | 0.988919i | \(-0.547430\pi\) | ||||
−0.148456 | + | 0.988919i | \(0.547430\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.28507 | + | 2.22581i | 0.0880516 | + | 0.152510i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.36880 | + | 5.83493i | −0.229750 | + | 0.397939i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.1699 | − | 12.7199i | −1.30134 | − | 0.863484i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.20553 | + | 7.28419i | −0.284183 | + | 0.492220i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.97138 | + | 3.44758i | −0.401679 | + | 0.231909i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.5948 | 0.776447 | 0.388224 | − | 0.921565i | \(-0.373089\pi\) | ||||
0.388224 | + | 0.921565i | \(0.373089\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.29791 | 0.153194 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.7181 | + | 9.65222i | −1.10962 | + | 0.640640i | −0.938731 | − | 0.344650i | \(-0.887998\pi\) |
−0.170890 | + | 0.985290i | \(0.554664\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.54131 | + | 14.7940i | −0.564425 | + | 0.977613i | 0.432678 | + | 0.901549i | \(0.357569\pi\) |
−0.997103 | + | 0.0760647i | \(0.975764\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.2286 | + | 0.824315i | 0.870379 | + | 0.0542360i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.11671 | + | 10.5945i | −0.400719 | + | 0.694066i | −0.993813 | − | 0.111068i | \(-0.964573\pi\) |
0.593094 | + | 0.805133i | \(0.297906\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.874599 | − | 1.51485i | −0.0570525 | − | 0.0988179i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.5960 | 0.753244 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.56688i | − | 0.101353i | −0.998715 | − | 0.0506767i | \(-0.983862\pi\) | ||
0.998715 | − | 0.0506767i | \(-0.0161378\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.0828 | − | 11.0174i | 1.22923 | − | 0.709695i | 0.262360 | − | 0.964970i | \(-0.415499\pi\) |
0.966869 | + | 0.255275i | \(0.0821659\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.8366 | + | 7.98855i | 0.887617 | + | 0.512466i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.72034 | + | 6.44979i | 0.173796 | + | 0.412062i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.6618 | − | 6.73291i | −0.742019 | − | 0.428405i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.29881 | + | 12.6419i | 0.462543 | + | 0.801148i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 7.68553i | − | 0.485106i | −0.970138 | − | 0.242553i | \(-0.922015\pi\) | ||
0.970138 | − | 0.242553i | \(-0.0779849\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.1534i | 2.52442i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.00463 | − | 1.74007i | −0.0629122 | − | 0.108967i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.93788 | + | 1.11883i | 0.120881 | + | 0.0697909i | 0.559221 | − | 0.829018i | \(-0.311100\pi\) |
−0.438340 | + | 0.898809i | \(0.644433\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.96728 | − | 0.621092i | −0.619337 | − | 0.0385928i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.60765 | − | 1.50553i | −0.161410 | − | 0.0931900i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.0365 | + | 8.68130i | −0.927188 | + | 0.535312i | −0.885921 | − | 0.463836i | \(-0.846473\pi\) |
−0.0412668 | + | 0.999148i | \(0.513139\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.114829i | − | 0.00705388i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.7065 | 0.655229 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.374476 | − | 0.648612i | −0.0228322 | − | 0.0395466i | 0.854384 | − | 0.519643i | \(-0.173935\pi\) |
−0.877216 | + | 0.480096i | \(0.840602\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.8572 | − | 18.8052i | 0.659527 | − | 1.14233i | −0.321211 | − | 0.947008i | \(-0.604090\pi\) |
0.980738 | − | 0.195327i | \(-0.0625767\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.52444 | − | 5.31161i | 0.213309 | − | 0.321473i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.98938 | + | 5.17776i | −0.180266 | + | 0.312231i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.4537 | − | 11.8089i | 1.22894 | − | 0.709531i | 0.262135 | − | 0.965031i | \(-0.415574\pi\) |
0.966809 | + | 0.255500i | \(0.0822402\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.9815 | 1.19626 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.4129 | −0.859803 | −0.429901 | − | 0.902876i | \(-0.641452\pi\) | ||||
−0.429901 | + | 0.902876i | \(0.641452\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.7892 | + | 6.22915i | −0.641351 | + | 0.370284i | −0.785135 | − | 0.619325i | \(-0.787406\pi\) |
0.143784 | + | 0.989609i | \(0.454073\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.96198 | − | 3.39824i | 0.116217 | − | 0.201295i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.11304 | − | 4.25030i | −0.124729 | − | 0.250887i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.62493 | + | 9.74266i | −0.330878 | + | 0.573097i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.57707 | + | 2.73157i | 0.0924495 | + | 0.160127i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.47355 | −0.495030 | −0.247515 | − | 0.968884i | \(-0.579614\pi\) | ||||
−0.247515 | + | 0.968884i | \(0.579614\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.01797i | − | 0.175713i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.9849 | + | 13.2703i | −1.33372 | + | 0.770023i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.7242 | + | 9.65573i | 0.967187 | + | 0.558406i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.9622 | − | 7.93564i | 0.920047 | − | 0.457403i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.8150 | + | 6.82137i | 0.678752 | + | 0.391877i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.40120 | + | 7.62310i | 0.252012 | + | 0.436498i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 11.9420i | − | 0.681565i | −0.940142 | − | 0.340783i | \(-0.889308\pi\) | ||
0.940142 | − | 0.340783i | \(-0.110692\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.89668i | − | 0.107899i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.74793 | − | 13.4198i | −0.439345 | − | 0.760967i | 0.558294 | − | 0.829643i | \(-0.311456\pi\) |
−0.997639 | + | 0.0686757i | \(0.978123\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.9712 | + | 8.64360i | 0.846220 | + | 0.488565i | 0.859374 | − | 0.511348i | \(-0.170854\pi\) |
−0.0131537 | + | 0.999913i | \(0.504187\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.06593 | − | 3.36142i | −0.285433 | − | 0.189395i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.20732 | − | 4.16115i | −0.404803 | − | 0.233713i | 0.283751 | − | 0.958898i | \(-0.408421\pi\) |
−0.688554 | + | 0.725185i | \(0.741754\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.78466 | − | 3.91712i | 0.379868 | − | 0.219317i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 2.02933i | − | 0.113266i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.2297 | 0.624837 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.43772 | + | 2.49021i | 0.0797504 | + | 0.138132i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.07235 | − | 5.32146i | 0.169901 | − | 0.294277i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.287823 | + | 4.61898i | −0.0158682 | + | 0.254653i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.6436 | + | 21.8993i | −0.694953 | + | 1.20369i | 0.275244 | + | 0.961375i | \(0.411241\pi\) |
−0.970197 | + | 0.242319i | \(0.922092\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.51162 | − | 4.33683i | 0.411634 | − | 0.237657i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.67523 | −0.310071 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.379048 | −0.0206481 | −0.0103240 | − | 0.999947i | \(-0.503286\pi\) | ||||
−0.0103240 | + | 0.999947i | \(0.503286\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.9327 | + | 6.31200i | −0.593783 | + | 0.342821i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.9942 | + | 45.0232i | −1.40766 | + | 2.43815i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.43764 | − | 18.1984i | 0.185615 | − | 0.982623i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.81369 | + | 4.87345i | −0.151484 | + | 0.262378i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.89803 | − | 8.48364i | −0.262940 | − | 0.455426i | 0.704082 | − | 0.710119i | \(-0.251359\pi\) |
−0.967022 | + | 0.254693i | \(0.918026\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.73905 | 0.360733 | 0.180366 | − | 0.983599i | \(-0.442272\pi\) | ||||
0.180366 | + | 0.983599i | \(0.442272\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.7645i | 0.681321i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.5926 | − | 10.7345i | 0.989587 | − | 0.571338i | 0.0844361 | − | 0.996429i | \(-0.473091\pi\) |
0.905151 | + | 0.425091i | \(0.139758\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.65639 | + | 1.53367i | 0.140987 | + | 0.0813986i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.330614 | + | 5.30570i | −0.0174980 | + | 0.280807i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.15852 | − | 2.40092i | −0.219478 | − | 0.126716i | 0.386231 | − | 0.922402i | \(-0.373777\pi\) |
−0.605709 | + | 0.795687i | \(0.707110\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.46546 | + | 2.53825i | 0.0771294 | + | 0.133592i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 20.7345i | − | 1.08828i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0382i | 0.525423i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.81465 | − | 10.0713i | −0.303522 | − | 0.525716i | 0.673409 | − | 0.739270i | \(-0.264829\pi\) |
−0.976931 | + | 0.213554i | \(0.931496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.57022 | + | 2.06127i | 0.185858 | + | 0.107305i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.167973 | + | 0.253149i | −0.00872075 | + | 0.0131429i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.2282 | − | 14.5655i | −1.30627 | − | 0.754174i | −0.324797 | − | 0.945784i | \(-0.605296\pi\) |
−0.981471 | + | 0.191610i | \(0.938629\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.725648 | + | 0.418953i | −0.0374723 | + | 0.0216346i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.76782i | − | 0.194053i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.52399 | −0.129649 | −0.0648243 | − | 0.997897i | \(-0.520649\pi\) | ||||
−0.0648243 | + | 0.997897i | \(0.520649\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.18875 | − | 3.79103i | −0.112133 | − | 0.194221i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.6539 | + | 20.1851i | −0.595485 | + | 1.03141i | 0.397993 | + | 0.917388i | \(0.369707\pi\) |
−0.993478 | + | 0.114022i | \(0.963627\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.1644 | − | 7.04187i | 0.721887 | − | 0.358887i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.74121 | + | 13.4082i | −0.393508 | + | 0.681575i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.383453 | − | 0.221387i | 0.0194418 | − | 0.0112248i | −0.490248 | − | 0.871583i | \(-0.663094\pi\) |
0.509689 | + | 0.860358i | \(0.329760\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.1046 | −0.814445 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.50895 | 0.378776 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.9852 | − | 6.91965i | 0.603041 | − | 0.348166i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.05153 | − | 7.01745i | 0.203340 | − | 0.352196i | −0.746262 | − | 0.665652i | \(-0.768154\pi\) |
0.949603 | + | 0.313456i | \(0.101487\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.29634 | + | 4.62169i | −0.465399 | + | 0.231374i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.01905 | + | 1.76504i | −0.0508889 | + | 0.0881421i | −0.890348 | − | 0.455281i | \(-0.849539\pi\) |
0.839459 | + | 0.543423i | \(0.182872\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.5017 | + | 21.6536i | 0.622755 | + | 1.07864i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.17414 | 0.157724 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.5674i | 1.11862i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.1993 | + | 15.7035i | −1.34492 | + | 0.776490i | −0.987525 | − | 0.157463i | \(-0.949668\pi\) |
−0.357395 | + | 0.933953i | \(0.616335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.1439 | − | 8.74335i | −0.746995 | − | 0.431278i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.41473 | + | 6.65334i | −0.217235 | + | 0.327390i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0875 | + | 8.71077i | 0.740616 | + | 0.427595i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.37051 | − | 9.30199i | −0.262995 | − | 0.455521i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 18.1384i | − | 0.886117i | −0.896493 | − | 0.443059i | \(-0.853893\pi\) | ||
0.896493 | − | 0.443059i | \(-0.146107\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 38.6453i | − | 1.88345i | −0.336377 | − | 0.941727i | \(-0.609202\pi\) | ||
0.336377 | − | 0.941727i | \(-0.390798\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.00975 | − | 3.48099i | −0.0977175 | − | 0.169252i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.07668 | − | 1.19897i | −0.100734 | − | 0.0581588i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.44840 | − | 23.2439i | 0.0700928 | − | 1.12485i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.4750 | − | 7.20247i | −0.602301 | − | 0.347739i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.59352 | + | 2.07472i | −0.173094 | + | 0.0999358i | −0.584044 | − | 0.811722i | \(-0.698530\pi\) |
0.410950 | + | 0.911658i | \(0.365197\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 21.7089i | − | 1.04326i | −0.853170 | − | 0.521632i | \(-0.825323\pi\) | ||
0.853170 | − | 0.521632i | \(-0.174677\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.09795 | 0.0526425 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.7257 | − | 27.2376i | −0.752260 | − | 1.30295i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.86516 | − | 6.69465i | 0.184474 | − | 0.319518i | −0.758925 | − | 0.651178i | \(-0.774275\pi\) |
0.943399 | + | 0.331660i | \(0.107609\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.25111 | + | 14.8210i | 0.297672 | + | 0.705764i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.93181 | − | 15.4704i | 0.424363 | − | 0.735019i | −0.571998 | − | 0.820255i | \(-0.693831\pi\) |
0.996361 | + | 0.0852368i | \(0.0271647\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.0658 | − | 6.38886i | 0.524570 | − | 0.302861i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.673676 | 0.0318638 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.3236 | 1.38387 | 0.691933 | − | 0.721961i | \(-0.256759\pi\) | ||||
0.691933 | + | 0.721961i | \(0.256759\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.28909 | + | 5.36306i | −0.437406 | + | 0.252537i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.48613 | − | 9.50226i | 0.257761 | − | 0.446455i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.473142 | − | 7.59298i | 0.0221812 | − | 0.355964i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.64207 | + | 8.04029i | −0.217147 | + | 0.376109i | −0.953935 | − | 0.300015i | \(-0.903008\pi\) |
0.736788 | + | 0.676124i | \(0.236342\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.32243 | − | 9.21872i | −0.248430 | − | 0.430293i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.401756 | 0.0187116 | 0.00935582 | − | 0.999956i | \(-0.497022\pi\) | ||||
0.00935582 | + | 0.999956i | \(0.497022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 9.04694i | − | 0.420447i | −0.977653 | − | 0.210223i | \(-0.932581\pi\) | ||
0.977653 | − | 0.210223i | \(-0.0674191\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.30988 | + | 3.64301i | −0.292614 | + | 0.168940i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.4257 | + | 6.01931i | 0.482446 | + | 0.278540i | 0.721435 | − | 0.692482i | \(-0.243483\pi\) |
−0.238989 | + | 0.971022i | \(0.576816\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.5115 | + | 8.30181i | 0.577727 | + | 0.383342i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.4592 | − | 7.19333i | −0.574091 | − | 0.331451i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.1413 | − | 34.8857i | −0.926096 | − | 1.60405i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 4.68305i | − | 0.214873i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 0.263867i | − | 0.0120816i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.59624 | + | 2.76477i | 0.0729340 | + | 0.126325i | 0.900186 | − | 0.435506i | \(-0.143430\pi\) |
−0.827252 | + | 0.561831i | \(0.810097\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.39950 | + | 5.42680i | 0.428580 | + | 0.247441i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.3320 | − | 6.62800i | 0.606625 | − | 0.301585i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.25999 | + | 1.88216i | 0.148028 | + | 0.0854643i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.30907 | + | 1.91049i | −0.149948 | + | 0.0865727i | −0.573097 | − | 0.819488i | \(-0.694258\pi\) |
0.423149 | + | 0.906060i | \(0.360925\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.91781i | 0.222391i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.7678 | 1.93008 | 0.965041 | − | 0.262097i | \(-0.0844141\pi\) | ||||
0.965041 | + | 0.262097i | \(0.0844141\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.57107 | + | 2.72117i | 0.0707574 | + | 0.122555i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.86934 | + | 11.8980i | −0.308754 | + | 0.534777i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.61275 | − | 7.26690i | −0.162054 | − | 0.325965i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.71383 | − | 6.43253i | 0.166254 | − | 0.287960i | −0.770846 | − | 0.637021i | \(-0.780166\pi\) |
0.937100 | + | 0.349062i | \(0.113500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.37029 | − | 2.52319i | 0.195250 | − | 0.112728i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 41.0916 | 1.83219 | 0.916093 | − | 0.400966i | \(-0.131326\pi\) | ||||
0.916093 | + | 0.400966i | \(0.131326\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.2819 | 0.724537 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.43364 | − | 1.98241i | 0.152493 | − | 0.0880421i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.7683 | − | 30.7755i | 0.787564 | − | 1.36410i | −0.139891 | − | 0.990167i | \(-0.544675\pi\) |
0.927455 | − | 0.373934i | \(-0.121991\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.6840 | − | 22.1300i | 0.649582 | − | 0.978972i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.3944 | − | 18.0036i | 0.458923 | − | 0.794878i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.13180 | − | 1.96034i | −0.0498731 | − | 0.0863827i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.4580 | 0.459944 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.81269i | 0.0795683i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.1264 | + | 17.9708i | −1.36367 | + | 0.787316i | −0.990111 | − | 0.140289i | \(-0.955197\pi\) |
−0.373561 | + | 0.927606i | \(0.621863\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.6453 | + | 15.3837i | 1.16512 | + | 0.672681i | 0.952525 | − | 0.304460i | \(-0.0984760\pi\) |
0.212592 | + | 0.977141i | \(0.431809\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.21260 | + | 0.137874i | 0.0965658 | + | 0.00601731i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.0578 | − | 10.4257i | −0.786610 | − | 0.454150i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0523 | + | 19.1432i | 0.480536 | + | 0.832312i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.93502i | − | 0.300954i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.15865i | 0.223446i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.21095 | − | 2.09743i | −0.0523540 | − | 0.0906798i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.17803 | + | 4.72159i | 0.352908 | + | 0.203752i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −41.5276 | − | 5.19560i | −1.78872 | − | 0.223790i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.51224 | + | 3.75984i | 0.279983 | + | 0.161648i | 0.633416 | − | 0.773812i | \(-0.281652\pi\) |
−0.353433 | + | 0.935460i | \(0.614986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.0566 | + | 6.38354i | −0.474484 | + | 0.273944i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7.33339i | − | 0.314128i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.8177 | −0.462531 | −0.231265 | − | 0.972891i | \(-0.574287\pi\) | ||||
−0.231265 | + | 0.972891i | \(0.574287\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.1136 | + | 17.5172i | 0.431637 | + | 0.747617i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.06820 | + | 5.31428i | −0.130710 | + | 0.226396i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36.5445 | − | 2.27720i | −1.55403 | − | 0.0968364i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.58137 | + | 2.73902i | −0.0671256 | + | 0.116265i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.6521 | + | 11.9235i | −0.875057 | + | 0.505214i | −0.869025 | − | 0.494767i | \(-0.835253\pi\) |
−0.00603158 | + | 0.999982i | \(0.501920\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.3736 | −0.819415 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0129 | 0.507183 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.24064 | − | 0.716284i | 0.0522868 | − | 0.0301878i | −0.473629 | − | 0.880725i | \(-0.657056\pi\) |
0.525916 | + | 0.850537i | \(0.323723\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.53306 | + | 13.0476i | −0.316918 | + | 0.548919i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.99765 | − | 4.64319i | −0.293874 | − | 0.194995i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.6099 | − | 23.5731i | 0.570558 | − | 0.988235i | −0.425951 | − | 0.904746i | \(-0.640060\pi\) |
0.996509 | − | 0.0834885i | \(-0.0266062\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.19271 | + | 10.7261i | 0.259157 | + | 0.448873i | 0.966016 | − | 0.258481i | \(-0.0832220\pi\) |
−0.706859 | + | 0.707354i | \(0.749889\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.16316 | −0.215694 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.71600i | 0.280076i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.3920 | − | 11.7733i | 0.848929 | − | 0.490130i | −0.0113602 | − | 0.999935i | \(-0.503616\pi\) |
0.860289 | + | 0.509806i | \(0.170283\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.41389 | − | 4.85776i | −0.349669 | − | 0.201882i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.5193 | − | 41.2738i | −0.851285 | − | 1.71233i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.594557 | + | 0.343267i | 0.0246240 | + | 0.0142167i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.30376 | + | 5.72228i | 0.136594 | + | 0.236587i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.0077i | 1.15600i | 0.816036 | + | 0.578001i | \(0.196167\pi\) | ||||
−0.816036 | + | 0.578001i | \(0.803833\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 40.7214i | − | 1.67790i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.50920 | − | 9.54221i | −0.226618 | − | 0.392514i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.9741 | − | 16.7282i | −1.18982 | − | 0.686945i | −0.231557 | − | 0.972821i | \(-0.574382\pi\) |
−0.958266 | + | 0.285877i | \(0.907715\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.82434 | + | 5.68104i | 0.115786 | + | 0.232900i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.6121 | − | 8.43630i | −0.598034 | − | 0.345275i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.2436 | + | 21.5026i | −1.52173 | + | 0.878571i | −0.522060 | + | 0.852909i | \(0.674836\pi\) |
−0.999671 | + | 0.0256625i | \(0.991830\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 32.3145i | − | 1.31813i | −0.752084 | − | 0.659067i | \(-0.770951\pi\) | ||
0.752084 | − | 0.659067i | \(-0.229049\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.0412 | −0.531078 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.3728 | − | 21.4303i | −0.503026 | − | 0.871267i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.75765 | − | 11.7046i | 0.274285 | − | 0.475075i | −0.695670 | − | 0.718362i | \(-0.744892\pi\) |
0.969954 | + | 0.243287i | \(0.0782256\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.42051 | − | 1.60609i | −0.0980841 | − | 0.0650822i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.51486 | − | 4.35586i | 0.101740 | − | 0.176219i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.63444 | + | 3.25304i | −0.227573 | + | 0.131389i | −0.609452 | − | 0.792823i | \(-0.708610\pi\) |
0.381879 | + | 0.924212i | \(0.375277\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.50323 | −0.0606162 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.66184 | −0.0669033 | −0.0334516 | − | 0.999440i | \(-0.510650\pi\) | ||||
−0.0334516 | + | 0.999440i | \(0.510650\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.5080 | − | 14.1497i | 0.985061 | − | 0.568725i | 0.0812670 | − | 0.996692i | \(-0.474103\pi\) |
0.903794 | + | 0.427967i | \(0.140770\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.9067 | + | 25.8191i | −0.598184 | + | 1.03609i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −33.7412 | − | 2.10252i | −1.35181 | − | 0.0842356i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.7302 | + | 20.3173i | 0.468459 | + | 0.811395i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.05126 | −0.360897 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 48.7721i | 1.94159i | 0.239918 | + | 0.970793i | \(0.422879\pi\) | ||||
−0.239918 | + | 0.970793i | \(0.577121\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.12964 | − | 1.80690i | 0.124392 | − | 0.0718178i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.52441 | − | 2.61217i | −0.179546 | − | 0.103661i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.1502 | + | 16.0472i | −0.481409 | + | 0.635814i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.10415 | + | 3.52424i | 0.241477 | + | 0.139417i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.8633 | − | 18.8158i | −0.429074 | − | 0.743178i | 0.567717 | − | 0.823224i | \(-0.307827\pi\) |
−0.996791 | + | 0.0800459i | \(0.974493\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.13929i | 0.281546i | 0.990042 | + | 0.140773i | \(0.0449588\pi\) | ||||
−0.990042 | + | 0.140773i | \(0.955041\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 5.64548i | − | 0.222290i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.58700 | + | 7.94492i | 0.180334 | + | 0.312347i | 0.941994 | − | 0.335629i | \(-0.108949\pi\) |
−0.761661 | + | 0.647976i | \(0.775616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.6263 | + | 9.02185i | 0.613386 | + | 0.354139i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.2397 | + | 1.19888i | 0.754062 | + | 0.0469879i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.710174 | + | 0.410019i | 0.0277913 | + | 0.0160453i | 0.513831 | − | 0.857891i | \(-0.328226\pi\) |
−0.486040 | + | 0.873937i | \(0.661559\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.76094 | − | 4.48078i | 0.303245 | − | 0.175079i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.0669i | 0.899924i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.4133 | 0.405645 | 0.202823 | − | 0.979216i | \(-0.434989\pi\) | ||||
0.202823 | + | 0.979216i | \(0.434989\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.76908 | + | 4.79619i | 0.107705 | + | 0.186550i | 0.914840 | − | 0.403816i | \(-0.132317\pi\) |
−0.807135 | + | 0.590367i | \(0.798983\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.88875 | − | 5.00346i | 0.112190 | − | 0.194318i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.85043 | + | 10.3241i | −0.265648 | + | 0.400353i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.40014 | − | 7.62126i | 0.170374 | − | 0.295097i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.41377 | + | 4.85769i | −0.325295 | + | 0.187809i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −52.6275 | −2.03166 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.9492 | 1.11591 | 0.557956 | − | 0.829871i | \(-0.311586\pi\) | ||||
0.557956 | + | 0.829871i | \(0.311586\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.84442 | + | 2.21958i | −0.147972 | + | 0.0854316i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.77831 | − | 4.81218i | 0.106779 | − | 0.184947i | −0.807685 | − | 0.589615i | \(-0.799280\pi\) |
0.914464 | + | 0.404668i | \(0.132613\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.43366 | − | 8.91812i | −0.170148 | − | 0.342246i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.08766 | − | 14.0082i | 0.309920 | − | 0.536797i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.5473 | + | 30.3928i | 0.671428 | + | 1.16295i | 0.977499 | + | 0.210939i | \(0.0676522\pi\) |
−0.306071 | + | 0.952009i | \(0.599014\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.8695 | −0.797383 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 14.3136i | − | 0.546099i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.285948 | − | 0.165092i | 0.0108937 | − | 0.00628950i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.28794 | − | 3.63035i | −0.239205 | − | 0.138105i | 0.375606 | − | 0.926779i | \(-0.377434\pi\) |
−0.614811 | + | 0.788674i | \(0.710768\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 32.5486 | − | 16.1816i | 1.23642 | − | 0.614688i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.1015 | − | 6.40944i | −0.421103 | − | 0.243124i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.15100 | − | 3.72564i | −0.0814750 | − | 0.141119i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 10.2505i | − | 0.387708i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.84288i | − | 0.107374i | −0.998558 | − | 0.0536870i | \(-0.982903\pi\) | ||
0.998558 | − | 0.0536870i | \(-0.0170973\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.83828 | − | 15.3083i | −0.333342 | − | 0.577365i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.26930 | + | 0.732832i | 0.0478047 | + | 0.0276000i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.8948 | − | 23.8175i | −1.34996 | − | 0.895748i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.8464 | + | 8.57155i | 0.557567 | + | 0.321911i | 0.752168 | − | 0.658971i | \(-0.229008\pi\) |
−0.194601 | + | 0.980882i | \(0.562341\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.5409 | − | 15.9008i | 1.03287 | − | 0.596325i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 58.3990i | 2.18706i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.1916 | −0.642929 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.656451 | + | 1.13701i | 0.0245156 | + | 0.0424623i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.0395 | − | 19.1210i | 0.411705 | − | 0.713094i | −0.583371 | − | 0.812206i | \(-0.698267\pi\) |
0.995076 | + | 0.0991116i | \(0.0316001\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.372466 | + | 5.97733i | −0.0138713 | + | 0.222607i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.23158 | + | 15.9896i | −0.343326 | + | 0.594658i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.13479 | − | 0.655173i | 0.0421451 | − | 0.0243325i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 52.6712 | 1.95347 | 0.976733 | − | 0.214459i | \(-0.0687990\pi\) | ||||
0.976733 | + | 0.214459i | \(0.0687990\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.86488 | −0.143144 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.9919 | − | 8.07820i | 0.517507 | − | 0.298783i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.876721 | − | 1.51853i | 0.0323824 | − | 0.0560880i | −0.849380 | − | 0.527782i | \(-0.823024\pi\) |
0.881762 | + | 0.471694i | \(0.156357\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.67617 | − | 3.54058i | −0.172483 | − | 0.130596i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.9654 | − | 29.3850i | 0.624929 | − | 1.08241i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.69575 | − | 16.7935i | −0.356664 | − | 0.617760i | 0.630737 | − | 0.775996i | \(-0.282752\pi\) |
−0.987401 | + | 0.158237i | \(0.949419\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.2831 | 0.414495 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 44.8603i | − | 1.64576i | −0.568213 | − | 0.822882i | \(-0.692365\pi\) | ||
0.568213 | − | 0.822882i | \(-0.307635\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.696284 | − | 0.402000i | 0.0255099 | − | 0.0147281i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.6697 | + | 20.0166i | 1.26850 | + | 0.732368i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.398514 | + | 6.39535i | −0.0145614 | + | 0.233681i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.9012 | + | 23.6143i | 1.49250 | + | 0.861698i | 0.999963 | − | 0.00859066i | \(-0.00273453\pi\) |
0.492542 | + | 0.870289i | \(0.336068\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.21988 | + | 5.57699i | 0.117339 | + | 0.203237i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 13.0949i | − | 0.476571i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.52456i | − | 0.0554110i | −0.999616 | − | 0.0277055i | \(-0.991180\pi\) | ||
0.999616 | − | 0.0277055i | \(-0.00882007\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.8224 | − | 29.1372i | −0.610614 | − | 1.05761i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.6395 | − | 16.5350i | −1.03818 | − | 0.599394i | −0.118863 | − | 0.992911i | \(-0.537925\pi\) |
−0.919317 | + | 0.393517i | \(0.871258\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.7274 | + | 16.1670i | −0.388358 | + | 0.585286i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.77204 | − | 2.75514i | −0.172533 | − | 0.0996122i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.51536 | − | 4.33899i | 0.271364 | − | 0.156672i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.31233i | 0.0473238i | 0.999720 | + | 0.0236619i | \(0.00753252\pi\) | ||||
−0.999720 | + | 0.0236619i | \(0.992467\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.87495 | −0.0675248 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.51479 | − | 14.7480i | −0.306256 | − | 0.530450i | 0.671284 | − | 0.741200i | \(-0.265743\pi\) |
−0.977540 | + | 0.210749i | \(0.932410\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.34775 | + | 7.53053i | −0.156176 | + | 0.270505i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.49295 | − | 3.72513i | 0.268808 | − | 0.133638i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.20078 | − | 7.27596i | 0.150508 | − | 0.260688i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.8819 | + | 9.16944i | −0.568300 | + | 0.328108i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.81683 | 0.207876 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.1698 | −0.612816 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.0083 | − | 15.0159i | 0.927097 | − | 0.535260i | 0.0412045 | − | 0.999151i | \(-0.486880\pi\) |
0.885892 | + | 0.463891i | \(0.153547\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.27412 | − | 12.5991i | 0.258966 | − | 0.448541i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.6935 | − | 17.7451i | 1.26912 | − | 0.630943i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.6554 | + | 21.9198i | −0.449406 | + | 0.778395i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.0481079 | + | 0.0833254i | 0.00170621 | + | 0.00295525i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.7798 | 1.23196 | 0.615981 | − | 0.787761i | \(-0.288760\pi\) | ||||
0.615981 | + | 0.787761i | \(0.288760\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.19448i | 0.148390i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.4283 | − | 14.6810i | 0.898465 | − | 0.518729i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −51.9753 | − | 30.0080i | −1.83417 | − | 1.05896i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.82427 | − | 14.8060i | 0.346260 | − | 0.521841i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.543476 | + | 0.313776i | 0.0191313 | + | 0.0110454i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.61556 | + | 11.4585i | 0.232591 | + | 0.402859i | 0.958570 | − | 0.284858i | \(-0.0919464\pi\) |
−0.725979 | + | 0.687717i | \(0.758613\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17.4547i | − | 0.612917i | −0.951884 | − | 0.306459i | \(-0.900856\pi\) | ||
0.951884 | − | 0.306459i | \(-0.0991441\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.1946i | 0.638113i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.93458 | + | 5.08284i | 0.102794 | + | 0.178044i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.3253 | + | 15.7762i | 0.955990 | + | 0.551941i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.08724 | − | 17.4480i | 0.0379912 | − | 0.609683i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.5407 | + | 23.4062i | 1.41488 | + | 0.816882i | 0.995843 | − | 0.0910860i | \(-0.0290338\pi\) |
0.419039 | + | 0.907968i | \(0.362367\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.7735 | − | 7.95213i | 0.480114 | − | 0.277194i | −0.240350 | − | 0.970686i | \(-0.577262\pi\) |
0.720464 | + | 0.693492i | \(0.243929\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5.00964i | − | 0.174413i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.9258 | −0.519021 | −0.259511 | − | 0.965740i | \(-0.583561\pi\) | ||||
−0.259511 | + | 0.965740i | \(0.583561\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.10972 | − | 15.7785i | −0.316394 | − | 0.548010i | 0.663339 | − | 0.748319i | \(-0.269139\pi\) |
−0.979733 | + | 0.200309i | \(0.935805\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.89479 | + | 17.1383i | −0.343247 | + | 0.594520i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.08384 | − | 16.6558i | 0.0722007 | − | 0.577088i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.01130 | − | 5.21573i | 0.104210 | − | 0.180498i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −33.4292 | + | 19.3003i | −1.15548 | + | 0.667117i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.2947 | −0.976843 | −0.488421 | − | 0.872608i | \(-0.662427\pi\) | ||||
−0.488421 | + | 0.872608i | \(0.662427\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.2830 | 0.940793 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.4587 | − | 6.03834i | 0.360217 | − | 0.207971i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.36591 | − | 4.09788i | 0.0813899 | − | 0.140971i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.07178 | + | 65.3440i | −0.139908 | + | 2.24525i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.21944 | − | 9.04034i | 0.179131 | − | 0.310264i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.6751 | + | 21.9538i | 0.434495 | + | 0.752568i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.5247 | −1.35330 | −0.676650 | − | 0.736305i | \(-0.736569\pi\) | ||||
−0.676650 | + | 0.736305i | \(0.736569\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 10.7612i | − | 0.368026i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.50342 | − | 1.44535i | 0.0855151 | − | 0.0493722i | −0.456633 | − | 0.889655i | \(-0.650945\pi\) |
0.542148 | + | 0.840283i | \(0.317611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6042 | − | 7.27704i | −0.430050 | − | 0.248290i | 0.269318 | − | 0.963051i | \(-0.413202\pi\) |
−0.699368 | + | 0.714762i | \(0.746535\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.31400 | + | 2.19895i | 0.112941 | + | 0.0749402i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.0583 | − | 6.96188i | −0.410470 | − | 0.236985i | 0.280521 | − | 0.959848i | \(-0.409493\pi\) |
−0.690992 | + | 0.722863i | \(0.742826\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.08168 | + | 1.87352i | 0.0367782 | + | 0.0637016i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 9.42632i | − | 0.320135i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 82.7420i | 2.80683i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.15939 | − | 14.1325i | −0.276471 | − | 0.478861i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.49117 | + | 4.32503i | 0.253538 | + | 0.146380i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.36913 | − | 1.17781i | 0.0800910 | − | 0.0398174i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.6311 | − | 7.86992i | −0.460289 | − | 0.265748i | 0.251877 | − | 0.967759i | \(-0.418952\pi\) |
−0.712166 | + | 0.702011i | \(0.752286\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.14882 | − | 3.55002i | 0.207394 | − | 0.119739i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 4.77034i | − | 0.160717i | −0.996766 | − | 0.0803584i | \(-0.974394\pi\) | ||
0.996766 | − | 0.0803584i | \(-0.0256065\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.2410 | −1.05134 | −0.525672 | − | 0.850688i | \(-0.676186\pi\) | ||||
−0.525672 | + | 0.850688i | \(0.676186\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.26439 | + | 2.18998i | 0.0425019 | + | 0.0736154i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.4386 | − | 31.9365i | 0.619106 | − | 1.07232i | −0.370543 | − | 0.928815i | \(-0.620828\pi\) |
0.989649 | − | 0.143508i | \(-0.0458384\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.15330 | + | 12.3771i | 0.206375 | + | 0.415115i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.48872 | + | 16.4350i | −0.317884 | + | 0.550592i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.09411 | + | 4.09579i | −0.237395 | + | 0.137060i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.2700 | 0.376713 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.1812 | −0.540275 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.86759 | − | 5.69706i | 0.329103 | − | 0.190007i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.137677 | + | 0.238463i | −0.00458668 | + | 0.00794436i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.25829 | + | 12.4459i | −0.274819 | + | 0.414174i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.61844 | + | 13.1955i | −0.253245 | + | 0.438634i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.588928 | + | 1.02005i | 0.0195550 | + | 0.0338703i | 0.875637 | − | 0.482969i | \(-0.160442\pi\) |
−0.856082 | + | 0.516840i | \(0.827108\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 37.4145 | 1.24096 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 37.7931i | − | 1.25214i | −0.779766 | − | 0.626071i | \(-0.784662\pi\) | ||
0.779766 | − | 0.626071i | \(-0.215338\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −90.2045 | + | 52.0796i | −2.98533 | + | 1.72358i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.38745 | − | 3.68779i | −0.211162 | − | 0.121915i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.6642 | − | 1.47459i | −0.781459 | − | 0.0486951i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.4585 | − | 21.6267i | −1.23564 | − | 0.713398i | −0.267441 | − | 0.963574i | \(-0.586178\pi\) |
−0.968200 | + | 0.250177i | \(0.919511\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.00313 | + | 8.66568i | 0.164859 | + | 0.285544i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.81995i | 0.290312i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.77459i | 0.124108i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.60078 | − | 4.50468i | −0.0854208 | − | 0.147953i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.3878 | + | 17.5444i | 0.996992 | + | 0.575614i | 0.907357 | − | 0.420361i | \(-0.138097\pi\) |
0.0896350 | + | 0.995975i | \(0.471430\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.2046 | − | 12.7395i | 0.989917 | − | 0.417520i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.2445 | + | 6.49204i | 0.368130 | + | 0.212540i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.4160 | − | 7.16838i | 0.406046 | − | 0.234431i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 44.8914i | − | 1.46654i | −0.679938 | − | 0.733270i | \(-0.737993\pi\) | ||
0.679938 | − | 0.733270i | \(-0.262007\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.4851 | −0.472702 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.7781 | + | 49.8451i | 0.938138 | + | 1.62490i | 0.768941 | + | 0.639320i | \(0.220784\pi\) |
0.169197 | + | 0.985582i | \(0.445882\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.02437 | + | 10.4345i | −0.196180 | + | 0.339795i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.7222 | + | 0.730444i | 0.381322 | + | 0.0237613i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.60454 | − | 14.9035i | 0.279610 | − | 0.484299i | −0.691678 | − | 0.722206i | \(-0.743128\pi\) |
0.971288 | + | 0.237908i | \(0.0764615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.9972 | + | 14.4321i | −0.811442 | + | 0.468486i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.97330 | 0.226125 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.6755 | 0.378207 | 0.189103 | − | 0.981957i | \(-0.439442\pi\) | ||||
0.189103 | + | 0.981957i | \(0.439442\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.33642 | + | 3.08099i | −0.172683 | + | 0.0996984i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.28218 | + | 5.68491i | −0.106098 | + | 0.183767i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46.0085 | + | 30.5283i | 1.48569 | + | 0.985809i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.3059 | + | 38.6349i | −0.719545 | + | 1.24629i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.78266 | − | 4.81971i | −0.0896700 | − | 0.155313i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.5950 | −0.373256 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.1618i | 1.67741i | 0.544586 | + | 0.838705i | \(0.316687\pi\) | ||||
−0.544586 | + | 0.838705i | \(0.683313\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.14881 | + | 4.70472i | −0.261777 | + | 0.151137i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.6994 | − | 8.48673i | −0.471728 | − | 0.272352i | 0.245235 | − | 0.969464i | \(-0.421135\pi\) |
−0.716963 | + | 0.697112i | \(0.754468\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.0982 | + | 30.3695i | 0.484028 | + | 0.973602i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.08656 | − | 1.20468i | −0.0668234 | − | 0.0385805i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.5148 | − | 19.9442i | −0.368390 | − | 0.638071i | 0.620924 | − | 0.783871i | \(-0.286758\pi\) |
−0.989314 | + | 0.145800i | \(0.953424\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 76.3949i | 2.44159i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 16.8515i | − | 0.538027i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.4921 | + | 33.7613i | 0.621701 | + | 1.07682i | 0.989169 | + | 0.146782i | \(0.0468915\pi\) |
−0.367468 | + | 0.930036i | \(0.619775\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.3882 | − | 6.57495i | −0.362857 | − | 0.209495i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.72628 | − | 3.47234i | −0.0549481 | − | 0.110526i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.1874 | − | 22.6249i | −1.24609 | − | 0.719428i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9773 | − | 8.06982i | 0.444005 | − | 0.256346i | −0.261290 | − | 0.965260i | \(-0.584148\pi\) |
0.705295 | + | 0.708914i | \(0.250815\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 21.1882i | − | 0.672388i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.1366 | −0.638374 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.3556 | + | 40.4531i | 0.739679 | + | 1.28116i | 0.952640 | + | 0.304102i | \(0.0983562\pi\) |
−0.212960 | + | 0.977061i | \(0.568310\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.37799 | + | 14.5111i | −0.265068 | + | 0.459111i |
(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 | 1120.2.bz.e.271.7 | 24 | ||
4.3 | odd | 2 | 280.2.bj.f.131.1 | yes | 24 | ||
7.3 | odd | 6 | 1120.2.bz.f.591.7 | 24 | |||
8.3 | odd | 2 | 1120.2.bz.f.271.7 | 24 | |||
8.5 | even | 2 | 280.2.bj.e.131.8 | ✓ | 24 | ||
28.3 | even | 6 | 280.2.bj.e.171.8 | yes | 24 | ||
56.3 | even | 6 | inner | 1120.2.bz.e.591.7 | 24 | ||
56.45 | odd | 6 | 280.2.bj.f.171.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bj.e.131.8 | ✓ | 24 | 8.5 | even | 2 | ||
280.2.bj.e.171.8 | yes | 24 | 28.3 | even | 6 | ||
280.2.bj.f.131.1 | yes | 24 | 4.3 | odd | 2 | ||
280.2.bj.f.171.1 | yes | 24 | 56.45 | odd | 6 | ||
1120.2.bz.e.271.7 | 24 | 1.1 | even | 1 | trivial | ||
1120.2.bz.e.591.7 | 24 | 56.3 | even | 6 | inner | ||
1120.2.bz.f.271.7 | 24 | 8.3 | odd | 2 | |||
1120.2.bz.f.591.7 | 24 | 7.3 | odd | 6 |