Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.5 | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.k.1084.20 |
$q$-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 \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.78468i | − | 1.26196i | −0.775800 | − | 0.630979i | \(-0.782653\pi\) | ||
0.775800 | − | 0.630979i | \(-0.217347\pi\) | |||||||
\(3\) | 2.38377i | 1.37627i | 0.725583 | + | 0.688134i | \(0.241570\pi\) | ||||
−0.725583 | + | 0.688134i | \(0.758430\pi\) | |||||||
\(4\) | −1.18508 | −0.592538 | ||||||||
\(5\) | −1.16534 | + | 1.90840i | −0.521156 | + | 0.853461i | ||||
\(6\) | 4.25426 | 1.73679 | ||||||||
\(7\) | − | 4.23911i | − | 1.60223i | −0.598509 | − | 0.801116i | \(-0.704240\pi\) | ||
0.598509 | − | 0.801116i | \(-0.295760\pi\) | |||||||
\(8\) | − | 1.45438i | − | 0.514199i | ||||||
\(9\) | −2.68235 | −0.894116 | ||||||||
\(10\) | 3.40588 | + | 2.07976i | 1.07703 | + | 0.657677i | ||||
\(11\) | −0.490889 | −0.148009 | −0.0740043 | − | 0.997258i | \(-0.523578\pi\) | ||||
−0.0740043 | + | 0.997258i | \(0.523578\pi\) | |||||||
\(12\) | − | 2.82495i | − | 0.815492i | ||||||
\(13\) | 4.16199i | 1.15433i | 0.816628 | + | 0.577165i | \(0.195841\pi\) | ||||
−0.816628 | + | 0.577165i | \(0.804159\pi\) | |||||||
\(14\) | −7.56544 | −2.02195 | ||||||||
\(15\) | −4.54918 | − | 2.77790i | −1.17459 | − | 0.717251i | ||||
\(16\) | −4.96575 | −1.24144 | ||||||||
\(17\) | 2.03619i | 0.493850i | 0.969035 | + | 0.246925i | \(0.0794201\pi\) | ||||
−0.969035 | + | 0.246925i | \(0.920580\pi\) | |||||||
\(18\) | 4.78713i | 1.12834i | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.38102 | − | 2.26160i | 0.308805 | − | 0.505709i | ||||
\(21\) | 10.1050 | 2.20510 | ||||||||
\(22\) | 0.876080i | 0.186781i | ||||||||
\(23\) | 4.39525i | 0.916472i | 0.888830 | + | 0.458236i | \(0.151519\pi\) | ||||
−0.888830 | + | 0.458236i | \(0.848481\pi\) | |||||||
\(24\) | 3.46689 | 0.707677 | ||||||||
\(25\) | −2.28396 | − | 4.44787i | −0.456793 | − | 0.889573i | ||||
\(26\) | 7.42782 | 1.45672 | ||||||||
\(27\) | 0.757211i | 0.145725i | ||||||||
\(28\) | 5.02367i | 0.949384i | ||||||||
\(29\) | 3.26270 | 0.605869 | 0.302934 | − | 0.953011i | \(-0.402034\pi\) | ||||
0.302934 | + | 0.953011i | \(0.402034\pi\) | |||||||
\(30\) | −4.95766 | + | 8.11882i | −0.905140 | + | 1.48229i | ||||
\(31\) | 4.08833 | 0.734285 | 0.367143 | − | 0.930165i | \(-0.380336\pi\) | ||||
0.367143 | + | 0.930165i | \(0.380336\pi\) | |||||||
\(32\) | 5.95351i | 1.05244i | ||||||||
\(33\) | − | 1.17017i | − | 0.203700i | ||||||
\(34\) | 3.63395 | 0.623218 | ||||||||
\(35\) | 8.08990 | + | 4.94000i | 1.36744 | + | 0.835013i | ||||
\(36\) | 3.17879 | 0.529798 | ||||||||
\(37\) | 2.14440i | 0.352538i | 0.984342 | + | 0.176269i | \(0.0564028\pi\) | ||||
−0.984342 | + | 0.176269i | \(0.943597\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.92123 | −1.58867 | ||||||||
\(40\) | 2.77553 | + | 1.69484i | 0.438849 | + | 0.267978i | ||||
\(41\) | 4.36602 | 0.681857 | 0.340929 | − | 0.940089i | \(-0.389259\pi\) | ||||
0.340929 | + | 0.940089i | \(0.389259\pi\) | |||||||
\(42\) | − | 18.0343i | − | 2.78275i | ||||||
\(43\) | 10.6241i | 1.62015i | 0.586324 | + | 0.810077i | \(0.300575\pi\) | ||||
−0.586324 | + | 0.810077i | \(0.699425\pi\) | |||||||
\(44\) | 0.581742 | 0.0877008 | ||||||||
\(45\) | 3.12585 | − | 5.11898i | 0.465974 | − | 0.763093i | ||||
\(46\) | 7.84410 | 1.15655 | ||||||||
\(47\) | − | 2.62142i | − | 0.382373i | −0.981554 | − | 0.191187i | \(-0.938766\pi\) | ||
0.981554 | − | 0.191187i | \(-0.0612336\pi\) | |||||||
\(48\) | − | 11.8372i | − | 1.70855i | ||||||
\(49\) | −10.9700 | −1.56715 | ||||||||
\(50\) | −7.93801 | + | 4.07614i | −1.12260 | + | 0.576453i | ||||
\(51\) | −4.85381 | −0.679670 | ||||||||
\(52\) | − | 4.93228i | − | 0.683985i | ||||||
\(53\) | 11.4341i | 1.57059i | 0.619121 | + | 0.785296i | \(0.287489\pi\) | ||||
−0.619121 | + | 0.785296i | \(0.712511\pi\) | |||||||
\(54\) | 1.35138 | 0.183899 | ||||||||
\(55\) | 0.572053 | − | 0.936812i | 0.0771356 | − | 0.126320i | ||||
\(56\) | −6.16526 | −0.823867 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 5.82287i | − | 0.764581i | ||||||
\(59\) | 0.542306 | 0.0706022 | 0.0353011 | − | 0.999377i | \(-0.488761\pi\) | ||||
0.0353011 | + | 0.999377i | \(0.488761\pi\) | |||||||
\(60\) | 5.39112 | + | 3.29203i | 0.695991 | + | 0.424999i | ||||
\(61\) | −13.6423 | −1.74671 | −0.873356 | − | 0.487083i | \(-0.838061\pi\) | ||||
−0.873356 | + | 0.487083i | \(0.838061\pi\) | |||||||
\(62\) | − | 7.29635i | − | 0.926637i | ||||||
\(63\) | 11.3708i | 1.43258i | ||||||||
\(64\) | 0.693606 | 0.0867007 | ||||||||
\(65\) | −7.94274 | − | 4.85014i | −0.985176 | − | 0.601586i | ||||
\(66\) | −2.08837 | −0.257061 | ||||||||
\(67\) | 7.15699i | 0.874365i | 0.899373 | + | 0.437182i | \(0.144024\pi\) | ||||
−0.899373 | + | 0.437182i | \(0.855976\pi\) | |||||||
\(68\) | − | 2.41305i | − | 0.292625i | ||||||
\(69\) | −10.4772 | −1.26131 | ||||||||
\(70\) | 8.81632 | − | 14.4379i | 1.05375 | − | 1.72566i | ||||
\(71\) | 6.03858 | 0.716647 | 0.358324 | − | 0.933597i | \(-0.383348\pi\) | ||||
0.358324 | + | 0.933597i | \(0.383348\pi\) | |||||||
\(72\) | 3.90114i | 0.459754i | ||||||||
\(73\) | 2.05419i | 0.240425i | 0.992748 | + | 0.120212i | \(0.0383576\pi\) | ||||
−0.992748 | + | 0.120212i | \(0.961642\pi\) | |||||||
\(74\) | 3.82707 | 0.444888 | ||||||||
\(75\) | 10.6027 | − | 5.44444i | 1.22429 | − | 0.628670i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.08093i | 0.237144i | ||||||||
\(78\) | 17.7062i | 2.00483i | ||||||||
\(79\) | −5.34029 | −0.600830 | −0.300415 | − | 0.953809i | \(-0.597125\pi\) | ||||
−0.300415 | + | 0.953809i | \(0.597125\pi\) | |||||||
\(80\) | 5.78678 | − | 9.47662i | 0.646982 | − | 1.05952i | ||||
\(81\) | −9.85206 | −1.09467 | ||||||||
\(82\) | − | 7.79193i | − | 0.860475i | ||||||
\(83\) | 8.11578i | 0.890823i | 0.895326 | + | 0.445411i | \(0.146943\pi\) | ||||
−0.895326 | + | 0.445411i | \(0.853057\pi\) | |||||||
\(84\) | −11.9753 | −1.30661 | ||||||||
\(85\) | −3.88587 | − | 2.37286i | −0.421482 | − | 0.257373i | ||||
\(86\) | 18.9605 | 2.04457 | ||||||||
\(87\) | 7.77752i | 0.833838i | ||||||||
\(88\) | 0.713937i | 0.0761060i | ||||||||
\(89\) | 4.34099 | 0.460144 | 0.230072 | − | 0.973174i | \(-0.426104\pi\) | ||||
0.230072 | + | 0.973174i | \(0.426104\pi\) | |||||||
\(90\) | −9.13574 | − | 5.57863i | −0.962992 | − | 0.588039i | ||||
\(91\) | 17.6431 | 1.84950 | ||||||||
\(92\) | − | 5.20871i | − | 0.543045i | ||||||
\(93\) | 9.74562i | 1.01057i | ||||||||
\(94\) | −4.67839 | −0.482539 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −14.1918 | −1.44844 | ||||||||
\(97\) | − | 5.64669i | − | 0.573335i | −0.958030 | − | 0.286667i | \(-0.907453\pi\) | ||
0.958030 | − | 0.286667i | \(-0.0925475\pi\) | |||||||
\(98\) | 19.5780i | 1.97768i | ||||||||
\(99\) | 1.31674 | 0.132337 | ||||||||
\(100\) | 2.70667 | + | 5.27106i | 0.270667 | + | 0.527106i | ||||
\(101\) | −3.30082 | −0.328444 | −0.164222 | − | 0.986423i | \(-0.552511\pi\) | ||||
−0.164222 | + | 0.986423i | \(0.552511\pi\) | |||||||
\(102\) | 8.66250i | 0.857715i | ||||||||
\(103\) | − | 3.41567i | − | 0.336556i | −0.985740 | − | 0.168278i | \(-0.946179\pi\) | ||
0.985740 | − | 0.168278i | \(-0.0538206\pi\) | |||||||
\(104\) | 6.05310 | 0.593556 | ||||||||
\(105\) | −11.7758 | + | 19.2844i | −1.14920 | + | 1.88197i | ||||
\(106\) | 20.4062 | 1.98202 | ||||||||
\(107\) | 1.75252i | 0.169422i | 0.996406 | + | 0.0847110i | \(0.0269967\pi\) | ||||
−0.996406 | + | 0.0847110i | \(0.973003\pi\) | |||||||
\(108\) | − | 0.897354i | − | 0.0863479i | ||||||
\(109\) | 3.51923 | 0.337081 | 0.168541 | − | 0.985695i | \(-0.446095\pi\) | ||||
0.168541 | + | 0.985695i | \(0.446095\pi\) | |||||||
\(110\) | −1.67191 | − | 1.02093i | −0.159410 | − | 0.0973419i | ||||
\(111\) | −5.11176 | −0.485186 | ||||||||
\(112\) | 21.0503i | 1.98907i | ||||||||
\(113\) | 13.2583i | 1.24723i | 0.781731 | + | 0.623616i | \(0.214337\pi\) | ||||
−0.781731 | + | 0.623616i | \(0.785663\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.38788 | − | 5.12196i | −0.782174 | − | 0.477625i | ||||
\(116\) | −3.86655 | −0.359000 | ||||||||
\(117\) | − | 11.1639i | − | 1.03210i | ||||||
\(118\) | − | 0.967842i | − | 0.0890971i | ||||||
\(119\) | 8.63165 | 0.791262 | ||||||||
\(120\) | −4.04011 | + | 6.61621i | −0.368810 | + | 0.603975i | ||||
\(121\) | −10.7590 | −0.978093 | ||||||||
\(122\) | 24.3470i | 2.20428i | ||||||||
\(123\) | 10.4076i | 0.938419i | ||||||||
\(124\) | −4.84498 | −0.435092 | ||||||||
\(125\) | 11.1499 | + | 0.824566i | 0.997277 | + | 0.0737514i | ||||
\(126\) | 20.2931 | 1.80786 | ||||||||
\(127\) | 19.8082i | 1.75769i | 0.477105 | + | 0.878846i | \(0.341686\pi\) | ||||
−0.477105 | + | 0.878846i | \(0.658314\pi\) | |||||||
\(128\) | 10.6692i | 0.943029i | ||||||||
\(129\) | −25.3253 | −2.22977 | ||||||||
\(130\) | −8.65594 | + | 14.1752i | −0.759176 | + | 1.24325i | ||||
\(131\) | −3.43004 | −0.299684 | −0.149842 | − | 0.988710i | \(-0.547876\pi\) | ||||
−0.149842 | + | 0.988710i | \(0.547876\pi\) | |||||||
\(132\) | 1.38674i | 0.120700i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.7729 | 1.10341 | ||||||||
\(135\) | −1.44506 | − | 0.882409i | −0.124371 | − | 0.0759457i | ||||
\(136\) | 2.96139 | 0.253937 | ||||||||
\(137\) | − | 0.608296i | − | 0.0519702i | −0.999662 | − | 0.0259851i | \(-0.991728\pi\) | ||
0.999662 | − | 0.0259851i | \(-0.00827225\pi\) | |||||||
\(138\) | 18.6985i | 1.59172i | ||||||||
\(139\) | 8.45799 | 0.717397 | 0.358699 | − | 0.933453i | \(-0.383221\pi\) | ||||
0.358699 | + | 0.933453i | \(0.383221\pi\) | |||||||
\(140\) | −9.58716 | − | 5.85428i | −0.810263 | − | 0.494777i | ||||
\(141\) | 6.24885 | 0.526248 | ||||||||
\(142\) | − | 10.7769i | − | 0.904379i | ||||||
\(143\) | − | 2.04308i | − | 0.170851i | ||||||
\(144\) | 13.3199 | 1.10999 | ||||||||
\(145\) | −3.80216 | + | 6.22653i | −0.315752 | + | 0.517085i | ||||
\(146\) | 3.66607 | 0.303406 | ||||||||
\(147\) | − | 26.1500i | − | 2.15682i | ||||||
\(148\) | − | 2.54128i | − | 0.208892i | ||||||
\(149\) | 4.63735 | 0.379907 | 0.189953 | − | 0.981793i | \(-0.439166\pi\) | ||||
0.189953 | + | 0.981793i | \(0.439166\pi\) | |||||||
\(150\) | −9.71657 | − | 18.9224i | −0.793355 | − | 1.54500i | ||||
\(151\) | 14.2109 | 1.15646 | 0.578232 | − | 0.815872i | \(-0.303743\pi\) | ||||
0.578232 | + | 0.815872i | \(0.303743\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 5.46178i | − | 0.441559i | ||||||
\(154\) | 3.71380 | 0.299266 | ||||||||
\(155\) | −4.76429 | + | 7.80215i | −0.382677 | + | 0.626684i | ||||
\(156\) | 11.7574 | 0.941347 | ||||||||
\(157\) | − | 10.7281i | − | 0.856194i | −0.903733 | − | 0.428097i | \(-0.859184\pi\) | ||
0.903733 | − | 0.428097i | \(-0.140816\pi\) | |||||||
\(158\) | 9.53071i | 0.758222i | ||||||||
\(159\) | −27.2562 | −2.16156 | ||||||||
\(160\) | −11.3617 | − | 6.93786i | −0.898218 | − | 0.548486i | ||||
\(161\) | 18.6319 | 1.46840 | ||||||||
\(162\) | 17.5828i | 1.38143i | ||||||||
\(163\) | − | 16.9366i | − | 1.32658i | −0.748363 | − | 0.663289i | \(-0.769160\pi\) | ||
0.748363 | − | 0.663289i | \(-0.230840\pi\) | |||||||
\(164\) | −5.17406 | −0.404027 | ||||||||
\(165\) | 2.23314 | + | 1.36364i | 0.173850 | + | 0.106159i | ||||
\(166\) | 14.4841 | 1.12418 | ||||||||
\(167\) | − | 16.2567i | − | 1.25798i | −0.777412 | − | 0.628991i | \(-0.783468\pi\) | ||
0.777412 | − | 0.628991i | \(-0.216532\pi\) | |||||||
\(168\) | − | 14.6965i | − | 1.13386i | ||||||
\(169\) | −4.32219 | −0.332476 | ||||||||
\(170\) | −4.23479 | + | 6.93503i | −0.324794 | + | 0.531892i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 12.5903i | − | 0.960003i | ||||||
\(173\) | 8.59112i | 0.653171i | 0.945168 | + | 0.326585i | \(0.105898\pi\) | ||||
−0.945168 | + | 0.326585i | \(0.894102\pi\) | |||||||
\(174\) | 13.8804 | 1.05227 | ||||||||
\(175\) | −18.8550 | + | 9.68197i | −1.42530 | + | 0.731888i | ||||
\(176\) | 2.43763 | 0.183743 | ||||||||
\(177\) | 1.29273i | 0.0971677i | ||||||||
\(178\) | − | 7.74728i | − | 0.580683i | ||||||
\(179\) | 23.5276 | 1.75853 | 0.879267 | − | 0.476330i | \(-0.158033\pi\) | ||||
0.879267 | + | 0.476330i | \(0.158033\pi\) | |||||||
\(180\) | −3.70437 | + | 6.06639i | −0.276107 | + | 0.452162i | ||||
\(181\) | −16.6135 | −1.23487 | −0.617434 | − | 0.786623i | \(-0.711828\pi\) | ||||
−0.617434 | + | 0.786623i | \(0.711828\pi\) | |||||||
\(182\) | − | 31.4873i | − | 2.33400i | ||||||
\(183\) | − | 32.5200i | − | 2.40394i | ||||||
\(184\) | 6.39234 | 0.471250 | ||||||||
\(185\) | −4.09237 | − | 2.49896i | −0.300877 | − | 0.183727i | ||||
\(186\) | 17.3928 | 1.27530 | ||||||||
\(187\) | − | 0.999546i | − | 0.0730941i | ||||||
\(188\) | 3.10658i | 0.226571i | ||||||||
\(189\) | 3.20990 | 0.233486 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.8109 | −0.926965 | −0.463482 | − | 0.886106i | \(-0.653400\pi\) | ||||
−0.463482 | + | 0.886106i | \(0.653400\pi\) | |||||||
\(192\) | 1.65339i | 0.119323i | ||||||||
\(193\) | 9.63983i | 0.693890i | 0.937885 | + | 0.346945i | \(0.112781\pi\) | ||||
−0.937885 | + | 0.346945i | \(0.887219\pi\) | |||||||
\(194\) | −10.0775 | −0.723525 | ||||||||
\(195\) | 11.5616 | − | 18.9336i | 0.827944 | − | 1.35587i | ||||
\(196\) | 13.0003 | 0.928596 | ||||||||
\(197\) | − | 3.10241i | − | 0.221038i | −0.993874 | − | 0.110519i | \(-0.964749\pi\) | ||
0.993874 | − | 0.110519i | \(-0.0352513\pi\) | |||||||
\(198\) | − | 2.34995i | − | 0.167004i | ||||||
\(199\) | −0.524290 | −0.0371659 | −0.0185830 | − | 0.999827i | \(-0.505915\pi\) | ||||
−0.0185830 | + | 0.999827i | \(0.505915\pi\) | |||||||
\(200\) | −6.46887 | + | 3.32174i | −0.457418 | + | 0.234883i | ||||
\(201\) | −17.0606 | −1.20336 | ||||||||
\(202\) | 5.89091i | 0.414483i | ||||||||
\(203\) | − | 13.8309i | − | 0.970742i | ||||||
\(204\) | 5.75214 | 0.402731 | ||||||||
\(205\) | −5.08789 | + | 8.33209i | −0.355354 | + | 0.581939i | ||||
\(206\) | −6.09586 | −0.424719 | ||||||||
\(207\) | − | 11.7896i | − | 0.819432i | ||||||
\(208\) | − | 20.6674i | − | 1.43303i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 34.4165 | + | 21.0160i | 2.37497 | + | 1.45025i | ||||
\(211\) | −19.0637 | −1.31240 | −0.656201 | − | 0.754586i | \(-0.727838\pi\) | ||||
−0.656201 | + | 0.754586i | \(0.727838\pi\) | |||||||
\(212\) | − | 13.5503i | − | 0.930636i | ||||||
\(213\) | 14.3946i | 0.986299i | ||||||||
\(214\) | 3.12768 | 0.213804 | ||||||||
\(215\) | −20.2749 | − | 12.3806i | −1.38274 | − | 0.844353i | ||||
\(216\) | 1.10127 | 0.0749319 | ||||||||
\(217\) | − | 17.3309i | − | 1.17650i | ||||||
\(218\) | − | 6.28069i | − | 0.425382i | ||||||
\(219\) | −4.89671 | −0.330889 | ||||||||
\(220\) | −0.677927 | + | 1.11019i | −0.0457058 | + | 0.0748493i | ||||
\(221\) | −8.47463 | −0.570065 | ||||||||
\(222\) | 9.12284i | 0.612285i | ||||||||
\(223\) | − | 3.16283i | − | 0.211799i | −0.994377 | − | 0.105899i | \(-0.966228\pi\) | ||
0.994377 | − | 0.105899i | \(-0.0337721\pi\) | |||||||
\(224\) | 25.2376 | 1.68626 | ||||||||
\(225\) | 6.12638 | + | 11.9307i | 0.408426 | + | 0.795381i | ||||
\(226\) | 23.6617 | 1.57395 | ||||||||
\(227\) | 9.04654i | 0.600440i | 0.953870 | + | 0.300220i | \(0.0970600\pi\) | ||||
−0.953870 | + | 0.300220i | \(0.902940\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.8920 | 1.18234 | 0.591168 | − | 0.806549i | \(-0.298667\pi\) | ||||
0.591168 | + | 0.806549i | \(0.298667\pi\) | |||||||
\(230\) | −9.14105 | + | 14.9697i | −0.602743 | + | 0.987071i | ||||
\(231\) | −4.96046 | −0.326374 | ||||||||
\(232\) | − | 4.74519i | − | 0.311537i | ||||||
\(233\) | 6.44330i | 0.422114i | 0.977474 | + | 0.211057i | \(0.0676906\pi\) | ||||
−0.977474 | + | 0.211057i | \(0.932309\pi\) | |||||||
\(234\) | −19.9240 | −1.30247 | ||||||||
\(235\) | 5.00271 | + | 3.05485i | 0.326341 | + | 0.199276i | ||||
\(236\) | −0.642674 | −0.0418345 | ||||||||
\(237\) | − | 12.7300i | − | 0.826903i | ||||||
\(238\) | − | 15.4047i | − | 0.998539i | ||||||
\(239\) | 13.4742 | 0.871571 | 0.435785 | − | 0.900051i | \(-0.356471\pi\) | ||||
0.435785 | + | 0.900051i | \(0.356471\pi\) | |||||||
\(240\) | 22.5901 | + | 13.7943i | 1.45818 | + | 0.890421i | ||||
\(241\) | −17.6351 | −1.13598 | −0.567990 | − | 0.823036i | \(-0.692279\pi\) | ||||
−0.567990 | + | 0.823036i | \(0.692279\pi\) | |||||||
\(242\) | 19.2014i | 1.23431i | ||||||||
\(243\) | − | 21.2134i | − | 1.36084i | ||||||
\(244\) | 16.1671 | 1.03499 | ||||||||
\(245\) | 12.7838 | − | 20.9352i | 0.816729 | − | 1.33750i | ||||
\(246\) | 18.5742 | 1.18424 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 5.94596i | − | 0.377569i | ||||||
\(249\) | −19.3461 | −1.22601 | ||||||||
\(250\) | 1.47158 | − | 19.8990i | 0.0930712 | − | 1.25852i | ||||
\(251\) | 17.7326 | 1.11927 | 0.559636 | − | 0.828738i | \(-0.310941\pi\) | ||||
0.559636 | + | 0.828738i | \(0.310941\pi\) | |||||||
\(252\) | − | 13.4752i | − | 0.848859i | ||||||
\(253\) | − | 2.15758i | − | 0.135646i | ||||||
\(254\) | 35.3513 | 2.21813 | ||||||||
\(255\) | 5.65635 | − | 9.26301i | 0.354214 | − | 0.580072i | ||||
\(256\) | 20.4282 | 1.27676 | ||||||||
\(257\) | − | 27.7475i | − | 1.73084i | −0.501046 | − | 0.865421i | \(-0.667051\pi\) | ||
0.501046 | − | 0.865421i | \(-0.332949\pi\) | |||||||
\(258\) | 45.1975i | 2.81387i | ||||||||
\(259\) | 9.09035 | 0.564847 | ||||||||
\(260\) | 9.41276 | + | 5.74779i | 0.583754 | + | 0.356463i | ||||
\(261\) | −8.75170 | −0.541716 | ||||||||
\(262\) | 6.12152i | 0.378189i | ||||||||
\(263\) | − | 5.56032i | − | 0.342864i | −0.985196 | − | 0.171432i | \(-0.945161\pi\) | ||
0.985196 | − | 0.171432i | \(-0.0548393\pi\) | |||||||
\(264\) | −1.70186 | −0.104742 | ||||||||
\(265\) | −21.8208 | − | 13.3246i | −1.34044 | − | 0.818523i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.3479i | 0.633282i | ||||||||
\(268\) | − | 8.48158i | − | 0.518095i | ||||||
\(269\) | 4.62765 | 0.282153 | 0.141076 | − | 0.989999i | \(-0.454944\pi\) | ||||
0.141076 | + | 0.989999i | \(0.454944\pi\) | |||||||
\(270\) | −1.57482 | + | 2.57897i | −0.0958403 | + | 0.156951i | ||||
\(271\) | −7.60838 | −0.462176 | −0.231088 | − | 0.972933i | \(-0.574229\pi\) | ||||
−0.231088 | + | 0.972933i | \(0.574229\pi\) | |||||||
\(272\) | − | 10.1112i | − | 0.613083i | ||||||
\(273\) | 42.0571i | 2.54541i | ||||||||
\(274\) | −1.08561 | −0.0655843 | ||||||||
\(275\) | 1.12117 | + | 2.18341i | 0.0676093 | + | 0.131665i | ||||
\(276\) | 12.4163 | 0.747376 | ||||||||
\(277\) | 7.53544i | 0.452761i | 0.974039 | + | 0.226380i | \(0.0726892\pi\) | ||||
−0.974039 | + | 0.226380i | \(0.927311\pi\) | |||||||
\(278\) | − | 15.0948i | − | 0.905325i | ||||||
\(279\) | −10.9663 | −0.656536 | ||||||||
\(280\) | 7.18462 | − | 11.7658i | 0.429363 | − | 0.703139i | ||||
\(281\) | −18.2549 | −1.08900 | −0.544499 | − | 0.838762i | \(-0.683280\pi\) | ||||
−0.544499 | + | 0.838762i | \(0.683280\pi\) | |||||||
\(282\) | − | 11.1522i | − | 0.664103i | ||||||
\(283\) | 30.9333i | 1.83880i | 0.393328 | + | 0.919398i | \(0.371324\pi\) | ||||
−0.393328 | + | 0.919398i | \(0.628676\pi\) | |||||||
\(284\) | −7.15618 | −0.424641 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.64624 | −0.215607 | ||||||||
\(287\) | − | 18.5080i | − | 1.09249i | ||||||
\(288\) | − | 15.9694i | − | 0.941004i | ||||||
\(289\) | 12.8539 | 0.756112 | ||||||||
\(290\) | 11.1124 | + | 6.78563i | 0.652540 | + | 0.398466i | ||||
\(291\) | 13.4604 | 0.789063 | ||||||||
\(292\) | − | 2.43437i | − | 0.142461i | ||||||
\(293\) | − | 21.8992i | − | 1.27937i | −0.768639 | − | 0.639683i | \(-0.779066\pi\) | ||
0.768639 | − | 0.639683i | \(-0.220934\pi\) | |||||||
\(294\) | −46.6694 | −2.72181 | ||||||||
\(295\) | −0.631971 | + | 1.03494i | −0.0367948 | + | 0.0602563i | ||||
\(296\) | 3.11877 | 0.181275 | ||||||||
\(297\) | − | 0.371707i | − | 0.0215686i | ||||||
\(298\) | − | 8.27618i | − | 0.479426i | ||||||
\(299\) | −18.2930 | −1.05791 | ||||||||
\(300\) | −12.5650 | + | 6.45208i | −0.725440 | + | 0.372511i | ||||
\(301\) | 45.0365 | 2.59586 | ||||||||
\(302\) | − | 25.3618i | − | 1.45941i | ||||||
\(303\) | − | 7.86840i | − | 0.452028i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.8979 | − | 26.0349i | 0.910309 | − | 1.49075i | ||||
\(306\) | −9.74752 | −0.557229 | ||||||||
\(307\) | − | 5.45543i | − | 0.311358i | −0.987808 | − | 0.155679i | \(-0.950243\pi\) | ||
0.987808 | − | 0.155679i | \(-0.0497565\pi\) | |||||||
\(308\) | − | 2.46607i | − | 0.140517i | ||||||
\(309\) | 8.14215 | 0.463191 | ||||||||
\(310\) | 13.9243 | + | 8.50273i | 0.790849 | + | 0.482922i | ||||
\(311\) | 6.69721 | 0.379764 | 0.189882 | − | 0.981807i | \(-0.439189\pi\) | ||||
0.189882 | + | 0.981807i | \(0.439189\pi\) | |||||||
\(312\) | 14.4292i | 0.816892i | ||||||||
\(313\) | − | 4.58279i | − | 0.259035i | −0.991577 | − | 0.129517i | \(-0.958657\pi\) | ||
0.991577 | − | 0.129517i | \(-0.0413428\pi\) | |||||||
\(314\) | −19.1462 | −1.08048 | ||||||||
\(315\) | −21.6999 | − | 13.2508i | −1.22265 | − | 0.746598i | ||||
\(316\) | 6.32866 | 0.356015 | ||||||||
\(317\) | − | 27.6794i | − | 1.55463i | −0.629113 | − | 0.777314i | \(-0.716582\pi\) | ||
0.629113 | − | 0.777314i | \(-0.283418\pi\) | |||||||
\(318\) | 48.6435i | 2.72779i | ||||||||
\(319\) | −1.60163 | −0.0896738 | ||||||||
\(320\) | −0.808286 | + | 1.32368i | −0.0451846 | + | 0.0739957i | ||||
\(321\) | −4.17759 | −0.233170 | ||||||||
\(322\) | − | 33.2520i | − | 1.85306i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 11.6754 | 0.648636 | ||||||||
\(325\) | 18.5120 | − | 9.50584i | 1.02686 | − | 0.527289i | ||||
\(326\) | −30.2264 | −1.67409 | ||||||||
\(327\) | 8.38903i | 0.463914i | ||||||||
\(328\) | − | 6.34983i | − | 0.350611i | ||||||
\(329\) | −11.1125 | −0.612651 | ||||||||
\(330\) | 2.43366 | − | 3.98544i | 0.133969 | − | 0.219391i | ||||
\(331\) | −14.1302 | −0.776665 | −0.388332 | − | 0.921519i | \(-0.626949\pi\) | ||||
−0.388332 | + | 0.921519i | \(0.626949\pi\) | |||||||
\(332\) | − | 9.61782i | − | 0.527847i | ||||||
\(333\) | − | 5.75203i | − | 0.315209i | ||||||
\(334\) | −29.0130 | −1.58752 | ||||||||
\(335\) | −13.6584 | − | 8.34032i | −0.746237 | − | 0.455681i | ||||
\(336\) | −50.1791 | −2.73749 | ||||||||
\(337\) | 14.9974i | 0.816962i | 0.912767 | + | 0.408481i | \(0.133941\pi\) | ||||
−0.912767 | + | 0.408481i | \(0.866059\pi\) | |||||||
\(338\) | 7.71372i | 0.419571i | ||||||||
\(339\) | −31.6046 | −1.71653 | ||||||||
\(340\) | 4.60505 | + | 2.81202i | 0.249744 | + | 0.152503i | ||||
\(341\) | −2.00692 | −0.108681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8294i | 0.908703i | ||||||||
\(344\) | 15.4514 | 0.833082 | ||||||||
\(345\) | 12.2096 | − | 19.9948i | 0.657341 | − | 1.07648i | ||||
\(346\) | 15.3324 | 0.824274 | ||||||||
\(347\) | − | 20.9133i | − | 1.12268i | −0.827584 | − | 0.561342i | \(-0.810285\pi\) | ||
0.827584 | − | 0.561342i | \(-0.189715\pi\) | |||||||
\(348\) | − | 9.21696i | − | 0.494081i | ||||||
\(349\) | 3.13055 | 0.167574 | 0.0837872 | − | 0.996484i | \(-0.473298\pi\) | ||||
0.0837872 | + | 0.996484i | \(0.473298\pi\) | |||||||
\(350\) | 17.2792 | + | 33.6501i | 0.923612 | + | 1.79867i | ||||
\(351\) | −3.15151 | −0.168215 | ||||||||
\(352\) | − | 2.92251i | − | 0.155771i | ||||||
\(353\) | − | 8.04538i | − | 0.428212i | −0.976810 | − | 0.214106i | \(-0.931316\pi\) | ||
0.976810 | − | 0.214106i | \(-0.0686838\pi\) | |||||||
\(354\) | 2.30711 | 0.122622 | ||||||||
\(355\) | −7.03700 | + | 11.5240i | −0.373485 | + | 0.611631i | ||||
\(356\) | −5.14441 | −0.272653 | ||||||||
\(357\) | 20.5758i | 1.08899i | ||||||||
\(358\) | − | 41.9891i | − | 2.21920i | ||||||
\(359\) | −30.5842 | −1.61417 | −0.807087 | − | 0.590432i | \(-0.798957\pi\) | ||||
−0.807087 | + | 0.590432i | \(0.798957\pi\) | |||||||
\(360\) | −7.44493 | − | 4.54616i | −0.392382 | − | 0.239603i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 29.6497i | 1.55835i | ||||||||
\(363\) | − | 25.6470i | − | 1.34612i | ||||||
\(364\) | −20.9085 | −1.09590 | ||||||||
\(365\) | −3.92021 | − | 2.39383i | −0.205193 | − | 0.125299i | ||||
\(366\) | −58.0377 | −3.03368 | ||||||||
\(367\) | − | 9.95175i | − | 0.519477i | −0.965679 | − | 0.259739i | \(-0.916364\pi\) | ||
0.965679 | − | 0.259739i | \(-0.0836364\pi\) | |||||||
\(368\) | − | 21.8257i | − | 1.13774i | ||||||
\(369\) | −11.7112 | −0.609659 | ||||||||
\(370\) | −4.45984 | + | 7.30357i | −0.231856 | + | 0.379694i | ||||
\(371\) | 48.4703 | 2.51645 | ||||||||
\(372\) | − | 11.5493i | − | 0.598804i | ||||||
\(373\) | 9.27611i | 0.480299i | 0.970736 | + | 0.240149i | \(0.0771964\pi\) | ||||
−0.970736 | + | 0.240149i | \(0.922804\pi\) | |||||||
\(374\) | −1.78387 | −0.0922416 | ||||||||
\(375\) | −1.96557 | + | 26.5787i | −0.101502 | + | 1.37252i | ||||
\(376\) | −3.81253 | −0.196616 | ||||||||
\(377\) | 13.5793i | 0.699372i | ||||||||
\(378\) | − | 5.72864i | − | 0.294649i | ||||||
\(379\) | 21.1472 | 1.08626 | 0.543129 | − | 0.839649i | \(-0.317239\pi\) | ||||
0.543129 | + | 0.839649i | \(0.317239\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −47.2181 | −2.41906 | ||||||||
\(382\) | 22.8634i | 1.16979i | ||||||||
\(383\) | 15.1501i | 0.774136i | 0.922051 | + | 0.387068i | \(0.126512\pi\) | ||||
−0.922051 | + | 0.387068i | \(0.873488\pi\) | |||||||
\(384\) | −25.4328 | −1.29786 | ||||||||
\(385\) | −3.97125 | − | 2.42499i | −0.202394 | − | 0.123589i | ||||
\(386\) | 17.2040 | 0.875660 | ||||||||
\(387\) | − | 28.4974i | − | 1.44860i | ||||||
\(388\) | 6.69177i | 0.339723i | ||||||||
\(389\) | 31.4483 | 1.59449 | 0.797247 | − | 0.603653i | \(-0.206289\pi\) | ||||
0.797247 | + | 0.603653i | \(0.206289\pi\) | |||||||
\(390\) | −33.7905 | − | 20.6337i | −1.71105 | − | 1.04483i | ||||
\(391\) | −8.94958 | −0.452600 | ||||||||
\(392\) | 15.9546i | 0.805827i | ||||||||
\(393\) | − | 8.17642i | − | 0.412446i | ||||||
\(394\) | −5.53681 | −0.278940 | ||||||||
\(395\) | 6.22326 | − | 10.1914i | 0.313126 | − | 0.512785i | ||||
\(396\) | −1.56043 | −0.0784147 | ||||||||
\(397\) | − | 9.38559i | − | 0.471049i | −0.971868 | − | 0.235525i | \(-0.924319\pi\) | ||
0.971868 | − | 0.235525i | \(-0.0756808\pi\) | |||||||
\(398\) | 0.935689i | 0.0469019i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.3416 | + | 22.0870i | 0.567079 | + | 1.10435i | ||||
\(401\) | 6.16049 | 0.307640 | 0.153820 | − | 0.988099i | \(-0.450842\pi\) | ||||
0.153820 | + | 0.988099i | \(0.450842\pi\) | |||||||
\(402\) | 30.4477i | 1.51859i | ||||||||
\(403\) | 17.0156i | 0.847607i | ||||||||
\(404\) | 3.91173 | 0.194616 | ||||||||
\(405\) | 11.4810 | − | 18.8016i | 0.570495 | − | 0.934261i | ||||
\(406\) | −24.6838 | −1.22504 | ||||||||
\(407\) | − | 1.05266i | − | 0.0521786i | ||||||
\(408\) | 7.05927i | 0.349486i | ||||||||
\(409\) | −2.28482 | −0.112977 | −0.0564885 | − | 0.998403i | \(-0.517990\pi\) | ||||
−0.0564885 | + | 0.998403i | \(0.517990\pi\) | |||||||
\(410\) | 14.8701 | + | 9.08025i | 0.734382 | + | 0.448442i | ||||
\(411\) | 1.45004 | 0.0715250 | ||||||||
\(412\) | 4.04783i | 0.199422i | ||||||||
\(413\) | − | 2.29889i | − | 0.113121i | ||||||
\(414\) | −21.0406 | −1.03409 | ||||||||
\(415\) | −15.4881 | − | 9.45765i | −0.760283 | − | 0.464258i | ||||
\(416\) | −24.7785 | −1.21486 | ||||||||
\(417\) | 20.1619i | 0.987332i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.6494 | 1.10649 | 0.553247 | − | 0.833017i | \(-0.313389\pi\) | ||||
0.553247 | + | 0.833017i | \(0.313389\pi\) | |||||||
\(420\) | 13.9553 | − | 22.8536i | 0.680947 | − | 1.11514i | ||||
\(421\) | −22.9969 | −1.12080 | −0.560400 | − | 0.828222i | \(-0.689353\pi\) | ||||
−0.560400 | + | 0.828222i | \(0.689353\pi\) | |||||||
\(422\) | 34.0226i | 1.65620i | ||||||||
\(423\) | 7.03155i | 0.341886i | ||||||||
\(424\) | 16.6294 | 0.807597 | ||||||||
\(425\) | 9.05672 | − | 4.65059i | 0.439315 | − | 0.225587i | ||||
\(426\) | 25.6897 | 1.24467 | ||||||||
\(427\) | 57.8310i | 2.79864i | ||||||||
\(428\) | − | 2.07687i | − | 0.100389i | ||||||
\(429\) | 4.87022 | 0.235137 | ||||||||
\(430\) | −22.0955 | + | 36.1842i | −1.06554 | + | 1.74496i | ||||
\(431\) | 25.6319 | 1.23465 | 0.617323 | − | 0.786710i | \(-0.288217\pi\) | ||||
0.617323 | + | 0.786710i | \(0.288217\pi\) | |||||||
\(432\) | − | 3.76012i | − | 0.180909i | ||||||
\(433\) | 2.36330i | 0.113573i | 0.998386 | + | 0.0567864i | \(0.0180854\pi\) | ||||
−0.998386 | + | 0.0567864i | \(0.981915\pi\) | |||||||
\(434\) | −30.9300 | −1.48469 | ||||||||
\(435\) | −14.8426 | − | 9.06346i | −0.711648 | − | 0.434560i | ||||
\(436\) | −4.17056 | −0.199734 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 8.73906i | 0.417568i | ||||||||
\(439\) | 6.31659 | 0.301474 | 0.150737 | − | 0.988574i | \(-0.451835\pi\) | ||||
0.150737 | + | 0.988574i | \(0.451835\pi\) | |||||||
\(440\) | −1.36248 | − | 0.831980i | −0.0649535 | − | 0.0396631i | ||||
\(441\) | 29.4254 | 1.40121 | ||||||||
\(442\) | 15.1245i | 0.719399i | ||||||||
\(443\) | 31.5246i | 1.49778i | 0.662694 | + | 0.748890i | \(0.269413\pi\) | ||||
−0.662694 | + | 0.748890i | \(0.730587\pi\) | |||||||
\(444\) | 6.05782 | 0.287492 | ||||||||
\(445\) | −5.05874 | + | 8.28434i | −0.239807 | + | 0.392716i | ||||
\(446\) | −5.64463 | −0.267281 | ||||||||
\(447\) | 11.0544i | 0.522854i | ||||||||
\(448\) | − | 2.94027i | − | 0.138915i | ||||||
\(449\) | 15.0828 | 0.711803 | 0.355902 | − | 0.934523i | \(-0.384174\pi\) | ||||
0.355902 | + | 0.934523i | \(0.384174\pi\) | |||||||
\(450\) | 21.2925 | − | 10.9336i | 1.00374 | − | 0.515416i | ||||
\(451\) | −2.14323 | −0.100921 | ||||||||
\(452\) | − | 15.7121i | − | 0.739033i | ||||||
\(453\) | 33.8754i | 1.59161i | ||||||||
\(454\) | 16.1452 | 0.757730 | ||||||||
\(455\) | −20.5603 | + | 33.6701i | −0.963880 | + | 1.57848i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 20.1347i | − | 0.941861i | −0.882170 | − | 0.470930i | \(-0.843918\pi\) | ||
0.882170 | − | 0.470930i | \(-0.156082\pi\) | |||||||
\(458\) | − | 31.9314i | − | 1.49206i | ||||||
\(459\) | −1.54183 | −0.0719664 | ||||||||
\(460\) | 9.94028 | + | 6.06992i | 0.463468 | + | 0.283011i | ||||
\(461\) | −7.48489 | −0.348606 | −0.174303 | − | 0.984692i | \(-0.555767\pi\) | ||||
−0.174303 | + | 0.984692i | \(0.555767\pi\) | |||||||
\(462\) | 8.85283i | 0.411871i | ||||||||
\(463\) | − | 21.5973i | − | 1.00371i | −0.864952 | − | 0.501855i | \(-0.832651\pi\) | ||
0.864952 | − | 0.501855i | \(-0.167349\pi\) | |||||||
\(464\) | −16.2017 | −0.752147 | ||||||||
\(465\) | −18.5985 | − | 11.3570i | −0.862486 | − | 0.526666i | ||||
\(466\) | 11.4992 | 0.532691 | ||||||||
\(467\) | 27.0503i | 1.25174i | 0.779927 | + | 0.625870i | \(0.215256\pi\) | ||||
−0.779927 | + | 0.625870i | \(0.784744\pi\) | |||||||
\(468\) | 13.2301i | 0.611561i | ||||||||
\(469\) | 30.3392 | 1.40094 | ||||||||
\(470\) | 5.45192 | − | 8.92823i | 0.251478 | − | 0.411828i | ||||
\(471\) | 25.5732 | 1.17835 | ||||||||
\(472\) | − | 0.788717i | − | 0.0363036i | ||||||
\(473\) | − | 5.21524i | − | 0.239797i | ||||||
\(474\) | −22.7190 | −1.04352 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.2292 | −0.468853 | ||||||||
\(477\) | − | 30.6702i | − | 1.40429i | ||||||
\(478\) | − | 24.0470i | − | 1.09989i | ||||||
\(479\) | 38.0534 | 1.73870 | 0.869352 | − | 0.494193i | \(-0.164536\pi\) | ||||
0.869352 | + | 0.494193i | \(0.164536\pi\) | |||||||
\(480\) | 16.5383 | − | 27.0836i | 0.754865 | − | 1.23619i | ||||
\(481\) | −8.92499 | −0.406944 | ||||||||
\(482\) | 31.4731i | 1.43356i | ||||||||
\(483\) | 44.4142i | 2.02092i | ||||||||
\(484\) | 12.7503 | 0.579558 | ||||||||
\(485\) | 10.7761 | + | 6.58032i | 0.489319 | + | 0.298797i | ||||
\(486\) | −37.8591 | −1.71732 | ||||||||
\(487\) | 18.3353i | 0.830851i | 0.909627 | + | 0.415426i | \(0.136367\pi\) | ||||
−0.909627 | + | 0.415426i | \(0.863633\pi\) | |||||||
\(488\) | 19.8410i | 0.898158i | ||||||||
\(489\) | 40.3730 | 1.82573 | ||||||||
\(490\) | −37.3626 | − | 22.8150i | −1.68787 | − | 1.03068i | ||||
\(491\) | −15.0675 | −0.679986 | −0.339993 | − | 0.940428i | \(-0.610425\pi\) | ||||
−0.339993 | + | 0.940428i | \(0.610425\pi\) | |||||||
\(492\) | − | 12.3338i | − | 0.556049i | ||||||
\(493\) | 6.64350i | 0.299208i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.53444 | + | 2.51285i | −0.0689682 | + | 0.112944i | ||||
\(496\) | −20.3016 | −0.911568 | ||||||||
\(497\) | − | 25.5982i | − | 1.14824i | ||||||
\(498\) | 34.5266i | 1.54717i | ||||||||
\(499\) | −34.5299 | −1.54577 | −0.772886 | − | 0.634545i | \(-0.781188\pi\) | ||||
−0.772886 | + | 0.634545i | \(0.781188\pi\) | |||||||
\(500\) | −13.2135 | − | 0.977174i | −0.590925 | − | 0.0437005i | ||||
\(501\) | 38.7522 | 1.73132 | ||||||||
\(502\) | − | 31.6470i | − | 1.41247i | ||||||
\(503\) | − | 30.8704i | − | 1.37644i | −0.725501 | − | 0.688221i | \(-0.758392\pi\) | ||
0.725501 | − | 0.688221i | \(-0.241608\pi\) | |||||||
\(504\) | 16.5374 | 0.736632 | ||||||||
\(505\) | 3.84658 | − | 6.29929i | 0.171171 | − | 0.280315i | ||||
\(506\) | −3.85059 | −0.171179 | ||||||||
\(507\) | − | 10.3031i | − | 0.457577i | ||||||
\(508\) | − | 23.4742i | − | 1.04150i | ||||||
\(509\) | −10.1777 | −0.451118 | −0.225559 | − | 0.974230i | \(-0.572421\pi\) | ||||
−0.225559 | + | 0.974230i | \(0.572421\pi\) | |||||||
\(510\) | −16.5315 | − | 10.0948i | −0.732027 | − | 0.447003i | ||||
\(511\) | 8.70794 | 0.385217 | ||||||||
\(512\) | − | 15.1195i | − | 0.668194i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −49.5204 | −2.18425 | ||||||||
\(515\) | 6.51845 | + | 3.98041i | 0.287237 | + | 0.175398i | ||||
\(516\) | 30.0124 | 1.32122 | ||||||||
\(517\) | 1.28683i | 0.0565946i | ||||||||
\(518\) | − | 16.2234i | − | 0.712813i | ||||||
\(519\) | −20.4792 | −0.898938 | ||||||||
\(520\) | −7.05392 | + | 11.5517i | −0.309335 | + | 0.506577i | ||||
\(521\) | 16.5423 | 0.724732 | 0.362366 | − | 0.932036i | \(-0.381969\pi\) | ||||
0.362366 | + | 0.932036i | \(0.381969\pi\) | |||||||
\(522\) | 15.6190i | 0.683624i | ||||||||
\(523\) | − | 7.99801i | − | 0.349729i | −0.984593 | − | 0.174864i | \(-0.944051\pi\) | ||
0.984593 | − | 0.174864i | \(-0.0559487\pi\) | |||||||
\(524\) | 4.06486 | 0.177574 | ||||||||
\(525\) | −23.0796 | − | 44.9459i | −1.00727 | − | 1.96160i | ||||
\(526\) | −9.92338 | −0.432680 | ||||||||
\(527\) | 8.32463i | 0.362626i | ||||||||
\(528\) | 5.81075i | 0.252880i | ||||||||
\(529\) | 3.68180 | 0.160078 | ||||||||
\(530\) | −23.7801 | + | 38.9431i | −1.03294 | + | 1.69158i | ||||
\(531\) | −1.45465 | −0.0631266 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.1713i | 0.787088i | ||||||||
\(534\) | 18.4677 | 0.799176 | ||||||||
\(535\) | −3.34450 | − | 2.04228i | −0.144595 | − | 0.0882953i | ||||
\(536\) | 10.4089 | 0.449598 | ||||||||
\(537\) | 56.0843i | 2.42021i | ||||||||
\(538\) | − | 8.25886i | − | 0.356065i | ||||||
\(539\) | 5.38507 | 0.231952 | ||||||||
\(540\) | 1.71251 | + | 1.04572i | 0.0736946 | + | 0.0450007i | ||||
\(541\) | 5.20048 | 0.223586 | 0.111793 | − | 0.993732i | \(-0.464341\pi\) | ||||
0.111793 | + | 0.993732i | \(0.464341\pi\) | |||||||
\(542\) | 13.5785i | 0.583247i | ||||||||
\(543\) | − | 39.6026i | − | 1.69951i | ||||||
\(544\) | −12.1225 | −0.519748 | ||||||||
\(545\) | −4.10110 | + | 6.71609i | −0.175672 | + | 0.287686i | ||||
\(546\) | 75.0585 | 3.21221 | ||||||||
\(547\) | − | 11.0339i | − | 0.471777i | −0.971780 | − | 0.235889i | \(-0.924200\pi\) | ||
0.971780 | − | 0.235889i | \(-0.0758001\pi\) | |||||||
\(548\) | 0.720878i | 0.0307944i | ||||||||
\(549\) | 36.5933 | 1.56176 | ||||||||
\(550\) | 3.89668 | − | 2.00093i | 0.166155 | − | 0.0853201i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 15.2379i | 0.648566i | ||||||||
\(553\) | 22.6381i | 0.962669i | ||||||||
\(554\) | 13.4483 | 0.571365 | ||||||||
\(555\) | 5.95694 | − | 9.75526i | 0.252858 | − | 0.414088i | ||||
\(556\) | −10.0234 | −0.425086 | ||||||||
\(557\) | 21.2817i | 0.901735i | 0.892591 | + | 0.450867i | \(0.148885\pi\) | ||||
−0.892591 | + | 0.450867i | \(0.851115\pi\) | |||||||
\(558\) | 19.5713i | 0.828521i | ||||||||
\(559\) | −44.2173 | −1.87019 | ||||||||
\(560\) | −40.1724 | − | 24.5308i | −1.69759 | − | 1.03662i | ||||
\(561\) | 2.38269 | 0.100597 | ||||||||
\(562\) | 32.5792i | 1.37427i | ||||||||
\(563\) | 14.7072i | 0.619833i | 0.950764 | + | 0.309917i | \(0.100301\pi\) | ||||
−0.950764 | + | 0.309917i | \(0.899699\pi\) | |||||||
\(564\) | −7.40537 | −0.311822 | ||||||||
\(565\) | −25.3020 | − | 15.4504i | −1.06446 | − | 0.650003i | ||||
\(566\) | 55.2061 | 2.32048 | ||||||||
\(567\) | 41.7639i | 1.75392i | ||||||||
\(568\) | − | 8.78236i | − | 0.368500i | ||||||
\(569\) | −40.6551 | −1.70435 | −0.852174 | − | 0.523258i | \(-0.824716\pi\) | ||||
−0.852174 | + | 0.523258i | \(0.824716\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.3240 | −1.01793 | −0.508964 | − | 0.860788i | \(-0.669972\pi\) | ||||
−0.508964 | + | 0.860788i | \(0.669972\pi\) | |||||||
\(572\) | 2.42120i | 0.101236i | ||||||||
\(573\) | − | 30.5382i | − | 1.27575i | ||||||
\(574\) | −33.0308 | −1.37868 | ||||||||
\(575\) | 19.5495 | − | 10.0386i | 0.815269 | − | 0.418638i | ||||
\(576\) | −1.86049 | −0.0775204 | ||||||||
\(577\) | − | 33.6876i | − | 1.40243i | −0.712949 | − | 0.701216i | \(-0.752641\pi\) | ||
0.712949 | − | 0.701216i | \(-0.247359\pi\) | |||||||
\(578\) | − | 22.9401i | − | 0.954182i | ||||||
\(579\) | −22.9791 | −0.954979 | ||||||||
\(580\) | 4.50585 | − | 7.37892i | 0.187095 | − | 0.306393i | ||||
\(581\) | 34.4037 | 1.42730 | ||||||||
\(582\) | − | 24.0225i | − | 0.995764i | ||||||
\(583\) | − | 5.61287i | − | 0.232461i | ||||||
\(584\) | 2.98757 | 0.123626 | ||||||||
\(585\) | 21.3052 | + | 13.0098i | 0.880861 | + | 0.537887i | ||||
\(586\) | −39.0830 | −1.61451 | ||||||||
\(587\) | 2.24977i | 0.0928580i | 0.998922 | + | 0.0464290i | \(0.0147841\pi\) | ||||
−0.998922 | + | 0.0464290i | \(0.985216\pi\) | |||||||
\(588\) | 30.9898i | 1.27800i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.84703 | + | 1.12787i | 0.0760409 | + | 0.0464335i | ||||
\(591\) | 7.39543 | 0.304207 | ||||||||
\(592\) | − | 10.6486i | − | 0.437653i | ||||||
\(593\) | − | 31.3871i | − | 1.28891i | −0.764640 | − | 0.644457i | \(-0.777083\pi\) | ||
0.764640 | − | 0.644457i | \(-0.222917\pi\) | |||||||
\(594\) | −0.663377 | −0.0272187 | ||||||||
\(595\) | −10.0588 | + | 16.4726i | −0.412371 | + | 0.675312i | ||||
\(596\) | −5.49562 | −0.225109 | ||||||||
\(597\) | − | 1.24979i | − | 0.0511503i | ||||||
\(598\) | 32.6471i | 1.33504i | ||||||||
\(599\) | −10.4068 | −0.425212 | −0.212606 | − | 0.977138i | \(-0.568195\pi\) | ||||
−0.212606 | + | 0.977138i | \(0.568195\pi\) | |||||||
\(600\) | −7.91826 | − | 15.4203i | −0.323262 | − | 0.629530i | ||||
\(601\) | −1.29592 | −0.0528616 | −0.0264308 | − | 0.999651i | \(-0.508414\pi\) | ||||
−0.0264308 | + | 0.999651i | \(0.508414\pi\) | |||||||
\(602\) | − | 80.3757i | − | 3.27587i | ||||||
\(603\) | − | 19.1975i | − | 0.781783i | ||||||
\(604\) | −16.8410 | −0.685249 | ||||||||
\(605\) | 12.5379 | − | 20.5325i | 0.509739 | − | 0.834765i | ||||
\(606\) | −14.0426 | −0.570440 | ||||||||
\(607\) | − | 5.50902i | − | 0.223604i | −0.993730 | − | 0.111802i | \(-0.964338\pi\) | ||
0.993730 | − | 0.111802i | \(-0.0356623\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 32.9698 | 1.33600 | ||||||||
\(610\) | −46.4638 | − | 28.3726i | −1.88127 | − | 1.14877i | ||||
\(611\) | 10.9103 | 0.441385 | ||||||||
\(612\) | 6.47263i | 0.261641i | ||||||||
\(613\) | − | 40.6727i | − | 1.64275i | −0.570386 | − | 0.821376i | \(-0.693207\pi\) | ||
0.570386 | − | 0.821376i | \(-0.306793\pi\) | |||||||
\(614\) | −9.73619 | −0.392921 | ||||||||
\(615\) | −19.8618 | − | 12.1284i | −0.800904 | − | 0.489062i | ||||
\(616\) | 3.02646 | 0.121939 | ||||||||
\(617\) | − | 30.5053i | − | 1.22810i | −0.789268 | − | 0.614049i | \(-0.789540\pi\) | ||
0.789268 | − | 0.614049i | \(-0.210460\pi\) | |||||||
\(618\) | − | 14.5311i | − | 0.584527i | ||||||
\(619\) | −5.80411 | −0.233287 | −0.116643 | − | 0.993174i | \(-0.537213\pi\) | ||||
−0.116643 | + | 0.993174i | \(0.537213\pi\) | |||||||
\(620\) | 5.64605 | − | 9.24615i | 0.226751 | − | 0.371334i | ||||
\(621\) | −3.32813 | −0.133553 | ||||||||
\(622\) | − | 11.9524i | − | 0.479246i | ||||||
\(623\) | − | 18.4019i | − | 0.737258i | ||||||
\(624\) | 49.2663 | 1.97223 | ||||||||
\(625\) | −14.5670 | + | 20.3175i | −0.582681 | + | 0.812701i | ||||
\(626\) | −8.17881 | −0.326891 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.7136i | 0.507328i | ||||||||
\(629\) | −4.36642 | −0.174101 | ||||||||
\(630\) | −23.6484 | + | 38.7274i | −0.942176 | + | 1.54294i | ||||
\(631\) | −23.3642 | −0.930116 | −0.465058 | − | 0.885280i | \(-0.653967\pi\) | ||||
−0.465058 | + | 0.885280i | \(0.653967\pi\) | |||||||
\(632\) | 7.76679i | 0.308946i | ||||||||
\(633\) | − | 45.4435i | − | 1.80622i | ||||||
\(634\) | −49.3987 | −1.96187 | ||||||||
\(635\) | −37.8019 | − | 23.0833i | −1.50012 | − | 0.916032i | ||||
\(636\) | 32.3007 | 1.28080 | ||||||||
\(637\) | − | 45.6572i | − | 1.80901i | ||||||
\(638\) | 2.85839i | 0.113165i | ||||||||
\(639\) | −16.1976 | −0.640766 | ||||||||
\(640\) | −20.3610 | − | 12.4332i | −0.804839 | − | 0.491465i | ||||
\(641\) | 18.3459 | 0.724621 | 0.362311 | − | 0.932057i | \(-0.381988\pi\) | ||||
0.362311 | + | 0.932057i | \(0.381988\pi\) | |||||||
\(642\) | 7.45565i | 0.294251i | ||||||||
\(643\) | 15.7630i | 0.621633i | 0.950470 | + | 0.310817i | \(0.100603\pi\) | ||||
−0.950470 | + | 0.310817i | \(0.899397\pi\) | |||||||
\(644\) | −22.0803 | −0.870084 | ||||||||
\(645\) | 29.5126 | − | 48.3307i | 1.16206 | − | 1.90302i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.0443i | 0.984592i | 0.870428 | + | 0.492296i | \(0.163842\pi\) | ||||
−0.870428 | + | 0.492296i | \(0.836158\pi\) | |||||||
\(648\) | 14.3286i | 0.562880i | ||||||||
\(649\) | −0.266212 | −0.0104497 | ||||||||
\(650\) | −16.9649 | − | 33.0379i | −0.665417 | − | 1.29585i | ||||
\(651\) | 41.3127 | 1.61917 | ||||||||
\(652\) | 20.0712i | 0.786049i | ||||||||
\(653\) | 2.98852i | 0.116950i | 0.998289 | + | 0.0584749i | \(0.0186238\pi\) | ||||
−0.998289 | + | 0.0584749i | \(0.981376\pi\) | |||||||
\(654\) | 14.9717 | 0.585440 | ||||||||
\(655\) | 3.99716 | − | 6.54588i | 0.156182 | − | 0.255769i | ||||
\(656\) | −21.6805 | −0.846482 | ||||||||
\(657\) | − | 5.51005i | − | 0.214968i | ||||||
\(658\) | 19.8322i | 0.773140i | ||||||||
\(659\) | 35.7695 | 1.39338 | 0.696691 | − | 0.717372i | \(-0.254655\pi\) | ||||
0.696691 | + | 0.717372i | \(0.254655\pi\) | |||||||
\(660\) | −2.64644 | − | 1.61602i | −0.103013 | − | 0.0629035i | ||||
\(661\) | 3.22147 | 0.125301 | 0.0626503 | − | 0.998036i | \(-0.480045\pi\) | ||||
0.0626503 | + | 0.998036i | \(0.480045\pi\) | |||||||
\(662\) | 25.2178i | 0.980118i | ||||||||
\(663\) | − | 20.2015i | − | 0.784563i | ||||||
\(664\) | 11.8034 | 0.458061 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.2655 | −0.397781 | ||||||||
\(667\) | 14.3404i | 0.555262i | ||||||||
\(668\) | 19.2655i | 0.745403i | ||||||||
\(669\) | 7.53945 | 0.291492 | ||||||||
\(670\) | −14.8848 | + | 24.3758i | −0.575050 | + | 0.941720i | ||||
\(671\) | 6.69684 | 0.258529 | ||||||||
\(672\) | 60.1605i | 2.32074i | ||||||||
\(673\) | − | 0.639706i | − | 0.0246588i | −0.999924 | − | 0.0123294i | \(-0.996075\pi\) | ||
0.999924 | − | 0.0123294i | \(-0.00392468\pi\) | |||||||
\(674\) | 26.7656 | 1.03097 | ||||||||
\(675\) | 3.36797 | − | 1.72944i | 0.129633 | − | 0.0665663i | ||||
\(676\) | 5.12213 | 0.197005 | ||||||||
\(677\) | − | 25.8005i | − | 0.991592i | −0.868439 | − | 0.495796i | \(-0.834876\pi\) | ||
0.868439 | − | 0.495796i | \(-0.165124\pi\) | |||||||
\(678\) | 56.4041i | 2.16618i | ||||||||
\(679\) | −23.9369 | −0.918616 | ||||||||
\(680\) | −3.45103 | + | 5.65151i | −0.132341 | + | 0.216726i | ||||
\(681\) | −21.5648 | −0.826366 | ||||||||
\(682\) | 3.58170i | 0.137150i | ||||||||
\(683\) | 5.33696i | 0.204213i | 0.994773 | + | 0.102107i | \(0.0325583\pi\) | ||||
−0.994773 | + | 0.102107i | \(0.967442\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.16087 | + | 0.708872i | 0.0443546 | + | 0.0270846i | ||||
\(686\) | 30.0351 | 1.14675 | ||||||||
\(687\) | 42.6503i | 1.62721i | ||||||||
\(688\) | − | 52.7564i | − | 2.01132i | ||||||
\(689\) | −47.5886 | −1.81298 | ||||||||
\(690\) | −35.6842 | − | 21.7901i | −1.35847 | − | 0.829536i | ||||
\(691\) | 13.2507 | 0.504079 | 0.252040 | − | 0.967717i | \(-0.418899\pi\) | ||||
0.252040 | + | 0.967717i | \(0.418899\pi\) | |||||||
\(692\) | − | 10.1811i | − | 0.387029i | ||||||
\(693\) | − | 5.58178i | − | 0.212034i | ||||||
\(694\) | −37.3235 | −1.41678 | ||||||||
\(695\) | −9.85644 | + | 16.1412i | −0.373876 | + | 0.612271i | ||||
\(696\) | 11.3114 | 0.428759 | ||||||||
\(697\) | 8.89006i | 0.336735i | ||||||||
\(698\) | − | 5.58702i | − | 0.211472i | ||||||
\(699\) | −15.3593 | −0.580943 | ||||||||
\(700\) | 22.3446 | − | 11.4739i | 0.844547 | − | 0.433672i | ||||
\(701\) | 40.8699 | 1.54363 | 0.771817 | − | 0.635845i | \(-0.219348\pi\) | ||||
0.771817 | + | 0.635845i | \(0.219348\pi\) | |||||||
\(702\) | 5.62443i | 0.212280i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.340484 | −0.0128325 | ||||||||
\(705\) | −7.28204 | + | 11.9253i | −0.274257 | + | 0.449133i | ||||
\(706\) | −14.3584 | −0.540386 | ||||||||
\(707\) | 13.9925i | 0.526244i | ||||||||
\(708\) | − | 1.53199i | − | 0.0575756i | ||||||
\(709\) | −7.35745 | −0.276315 | −0.138157 | − | 0.990410i | \(-0.544118\pi\) | ||||
−0.138157 | + | 0.990410i | \(0.544118\pi\) | |||||||
\(710\) | 20.5666 | + | 12.5588i | 0.771853 | + | 0.471323i | ||||
\(711\) | 14.3245 | 0.537211 | ||||||||
\(712\) | − | 6.31344i | − | 0.236606i | ||||||
\(713\) | 17.9692i | 0.672952i | ||||||||
\(714\) | 36.7213 | 1.37426 | ||||||||
\(715\) | 3.89901 | + | 2.38088i | 0.145815 | + | 0.0890399i | ||||
\(716\) | −27.8820 | −1.04200 | ||||||||
\(717\) | 32.1193i | 1.19952i | ||||||||
\(718\) | 54.5830i | 2.03702i | ||||||||
\(719\) | 31.9597 | 1.19190 | 0.595948 | − | 0.803023i | \(-0.296776\pi\) | ||||
0.595948 | + | 0.803023i | \(0.296776\pi\) | |||||||
\(720\) | −15.5222 | + | 25.4196i | −0.578477 | + | 0.947332i | ||||
\(721\) | −14.4794 | −0.539240 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 42.0381i | − | 1.56341i | ||||||
\(724\) | 19.6882 | 0.731707 | ||||||||
\(725\) | −7.45189 | − | 14.5121i | −0.276756 | − | 0.538964i | ||||
\(726\) | −45.7717 | −1.69875 | ||||||||
\(727\) | 29.3883i | 1.08995i | 0.838452 | + | 0.544976i | \(0.183461\pi\) | ||||
−0.838452 | + | 0.544976i | \(0.816539\pi\) | |||||||
\(728\) | − | 25.6598i | − | 0.951014i | ||||||
\(729\) | 21.0116 | 0.778207 | ||||||||
\(730\) | −4.27222 | + | 6.99632i | −0.158122 | + | 0.258945i | ||||
\(731\) | −21.6326 | −0.800112 | ||||||||
\(732\) | 38.5387i | 1.42443i | ||||||||
\(733\) | − | 50.8285i | − | 1.87739i | −0.344745 | − | 0.938696i | \(-0.612035\pi\) | ||
0.344745 | − | 0.938696i | \(-0.387965\pi\) | |||||||
\(734\) | −17.7607 | −0.655559 | ||||||||
\(735\) | 49.9046 | + | 30.4737i | 1.84076 | + | 1.12404i | ||||
\(736\) | −26.1671 | −0.964534 | ||||||||
\(737\) | − | 3.51329i | − | 0.129414i | ||||||
\(738\) | 20.9007i | 0.769364i | ||||||||
\(739\) | −14.7245 | −0.541650 | −0.270825 | − | 0.962629i | \(-0.587296\pi\) | ||||
−0.270825 | + | 0.962629i | \(0.587296\pi\) | |||||||
\(740\) | 4.84978 | + | 2.96146i | 0.178281 | + | 0.108865i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 86.5039i | − | 3.17566i | ||||||
\(743\) | 34.6568i | 1.27144i | 0.771922 | + | 0.635718i | \(0.219296\pi\) | ||||
−0.771922 | + | 0.635718i | \(0.780704\pi\) | |||||||
\(744\) | 14.1738 | 0.519636 | ||||||||
\(745\) | −5.40409 | + | 8.84991i | −0.197991 | + | 0.324236i | ||||
\(746\) | 16.5549 | 0.606117 | ||||||||
\(747\) | − | 21.7693i | − | 0.796498i | ||||||
\(748\) | 1.18454i | 0.0433110i | ||||||||
\(749\) | 7.42910 | 0.271453 | ||||||||
\(750\) | 47.4345 | + | 3.50792i | 1.73206 | + | 0.128091i | ||||
\(751\) | −8.35539 | −0.304893 | −0.152446 | − | 0.988312i | \(-0.548715\pi\) | ||||
−0.152446 | + | 0.988312i | \(0.548715\pi\) | |||||||
\(752\) | 13.0173i | 0.474692i | ||||||||
\(753\) | 42.2704i | 1.54042i | ||||||||
\(754\) | 24.2348 | 0.882578 | ||||||||
\(755\) | −16.5605 | + | 27.1200i | −0.602698 | + | 0.986998i | ||||
\(756\) | −3.80398 | −0.138349 | ||||||||
\(757\) | − | 13.8709i | − | 0.504146i | −0.967708 | − | 0.252073i | \(-0.918888\pi\) | ||
0.967708 | − | 0.252073i | \(-0.0811123\pi\) | |||||||
\(758\) | − | 37.7410i | − | 1.37081i | ||||||
\(759\) | 5.14317 | 0.186685 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.3970 | 1.60939 | 0.804696 | − | 0.593687i | \(-0.202328\pi\) | ||||
0.804696 | + | 0.593687i | \(0.202328\pi\) | |||||||
\(762\) | 84.2692i | 3.05275i | ||||||||
\(763\) | − | 14.9184i | − | 0.540082i | ||||||
\(764\) | 15.1819 | 0.549262 | ||||||||
\(765\) | 10.4232 | + | 6.36483i | 0.376853 | + | 0.230121i | ||||
\(766\) | 27.0381 | 0.976927 | ||||||||
\(767\) | 2.25707i | 0.0814983i | ||||||||
\(768\) | 48.6961i | 1.75717i | ||||||||
\(769\) | −19.0001 | −0.685160 | −0.342580 | − | 0.939489i | \(-0.611301\pi\) | ||||
−0.342580 | + | 0.939489i | \(0.611301\pi\) | |||||||
\(770\) | −4.32784 | + | 7.08740i | −0.155964 | + | 0.255412i | ||||
\(771\) | 66.1436 | 2.38210 | ||||||||
\(772\) | − | 11.4239i | − | 0.411157i | ||||||
\(773\) | − | 1.86738i | − | 0.0671650i | −0.999436 | − | 0.0335825i | \(-0.989308\pi\) | ||
0.999436 | − | 0.0335825i | \(-0.0106917\pi\) | |||||||
\(774\) | −50.8587 | −1.82808 | ||||||||
\(775\) | −9.33759 | − | 18.1843i | −0.335416 | − | 0.653200i | ||||
\(776\) | −8.21241 | −0.294808 | ||||||||
\(777\) | 21.6693i | 0.777381i | ||||||||
\(778\) | − | 56.1252i | − | 2.01218i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −13.7014 | + | 22.4378i | −0.490588 | + | 0.803403i | ||||
\(781\) | −2.96427 | −0.106070 | ||||||||
\(782\) | 15.9721i | 0.571162i | ||||||||
\(783\) | 2.47055i | 0.0882904i | ||||||||
\(784\) | 54.4744 | 1.94552 | ||||||||
\(785\) | 20.4734 | + | 12.5019i | 0.730728 | + | 0.446211i | ||||
\(786\) | −14.5923 | −0.520489 | ||||||||
\(787\) | − | 12.9689i | − | 0.462291i | −0.972919 | − | 0.231146i | \(-0.925753\pi\) | ||
0.972919 | − | 0.231146i | \(-0.0742474\pi\) | |||||||
\(788\) | 3.67660i | 0.130973i | ||||||||
\(789\) | 13.2545 | 0.471873 | ||||||||
\(790\) | −18.1884 | − | 11.1065i | −0.647113 | − | 0.395152i | ||||
\(791\) | 56.2032 | 1.99836 | ||||||||
\(792\) | − | 1.91503i | − | 0.0680476i | ||||||
\(793\) | − | 56.7790i | − | 2.01628i | ||||||
\(794\) | −16.7503 | −0.594444 | ||||||||
\(795\) | 31.7627 | − | 52.0156i | 1.12651 | − | 1.84480i | ||||
\(796\) | 0.621324 | 0.0220222 | ||||||||
\(797\) | 29.9226i | 1.05991i | 0.848025 | + | 0.529956i | \(0.177791\pi\) | ||||
−0.848025 | + | 0.529956i | \(0.822209\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.33772 | 0.188835 | ||||||||
\(800\) | 26.4804 | − | 13.5976i | 0.936224 | − | 0.480748i | ||||
\(801\) | −11.6441 | −0.411422 | ||||||||
\(802\) | − | 10.9945i | − | 0.388229i | ||||||
\(803\) | − | 1.00838i | − | 0.0355850i | ||||||
\(804\) | 20.2181 | 0.713038 | ||||||||
\(805\) | −21.7125 | + | 35.5571i | −0.765266 | + | 1.25322i | ||||
\(806\) | 30.3674 | 1.06964 | ||||||||
\(807\) | 11.0312i | 0.388318i | ||||||||
\(808\) | 4.80064i | 0.168886i | ||||||||
\(809\) | −42.4578 | −1.49274 | −0.746369 | − | 0.665532i | \(-0.768205\pi\) | ||||
−0.746369 | + | 0.665532i | \(0.768205\pi\) | |||||||
\(810\) | −33.5549 | − | 20.4899i | −1.17900 | − | 0.719941i | ||||
\(811\) | −31.1514 | −1.09387 | −0.546936 | − | 0.837174i | \(-0.684206\pi\) | ||||
−0.546936 | + | 0.837174i | \(0.684206\pi\) | |||||||
\(812\) | 16.3907i | 0.575202i | ||||||||
\(813\) | − | 18.1366i | − | 0.636079i | ||||||
\(814\) | −1.87867 | −0.0658472 | ||||||||
\(815\) | 32.3218 | + | 19.7369i | 1.13218 | + | 0.691354i | ||||
\(816\) | 24.1028 | 0.843767 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 4.07767i | 0.142572i | ||||||||
\(819\) | −47.3250 | −1.65367 | ||||||||
\(820\) | 6.02955 | − | 9.87417i | 0.210561 | − | 0.344821i | ||||
\(821\) | −6.20740 | −0.216640 | −0.108320 | − | 0.994116i | \(-0.534547\pi\) | ||||
−0.108320 | + | 0.994116i | \(0.534547\pi\) | |||||||
\(822\) | − | 2.58785i | − | 0.0902616i | ||||||
\(823\) | 35.9702i | 1.25384i | 0.779083 | + | 0.626921i | \(0.215685\pi\) | ||||
−0.779083 | + | 0.626921i | \(0.784315\pi\) | |||||||
\(824\) | −4.96766 | −0.173057 | ||||||||
\(825\) | −5.20474 | + | 2.67262i | −0.181206 | + | 0.0930486i | ||||
\(826\) | −4.10279 | −0.142754 | ||||||||
\(827\) | 15.3837i | 0.534945i | 0.963565 | + | 0.267473i | \(0.0861885\pi\) | ||||
−0.963565 | + | 0.267473i | \(0.913811\pi\) | |||||||
\(828\) | 13.9716i | 0.485545i | ||||||||
\(829\) | 24.1941 | 0.840295 | 0.420148 | − | 0.907456i | \(-0.361978\pi\) | ||||
0.420148 | + | 0.907456i | \(0.361978\pi\) | |||||||
\(830\) | −16.8789 | + | 27.6413i | −0.585874 | + | 0.959445i | ||||
\(831\) | −17.9627 | −0.623120 | ||||||||
\(832\) | 2.88678i | 0.100081i | ||||||||
\(833\) | − | 22.3371i | − | 0.773936i | ||||||
\(834\) | 35.9825 | 1.24597 | ||||||||
\(835\) | 31.0243 | + | 18.9446i | 1.07364 | + | 0.655605i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.09573i | 0.107004i | ||||||||
\(838\) | − | 40.4218i | − | 1.39635i | ||||||
\(839\) | −12.4265 | −0.429012 | −0.214506 | − | 0.976723i | \(-0.568814\pi\) | ||||
−0.214506 | + | 0.976723i | \(0.568814\pi\) | |||||||
\(840\) | 28.0468 | + | 17.1265i | 0.967708 | + | 0.590919i | ||||
\(841\) | −18.3548 | −0.632923 | ||||||||
\(842\) | 41.0420i | 1.41440i | ||||||||
\(843\) | − | 43.5155i | − | 1.49875i | ||||||
\(844\) | 22.5920 | 0.777649 | ||||||||
\(845\) | 5.03683 | − | 8.24846i | 0.173272 | − | 0.283756i | ||||
\(846\) | 12.5491 | 0.431446 | ||||||||
\(847\) | 45.6087i | 1.56713i | ||||||||
\(848\) | − | 56.7787i | − | 1.94979i | ||||||
\(849\) | −73.7379 | −2.53068 | ||||||||
\(850\) | −8.29982 | − | 16.1633i | −0.284681 | − | 0.554398i | ||||
\(851\) | −9.42518 | −0.323091 | ||||||||
\(852\) | − | 17.0587i | − | 0.584420i | ||||||
\(853\) | − | 23.1527i | − | 0.792734i | −0.918092 | − | 0.396367i | \(-0.870271\pi\) | ||
0.918092 | − | 0.396367i | \(-0.129729\pi\) | |||||||
\(854\) | 103.210 | 3.53176 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.54882 | 0.0871167 | ||||||||
\(857\) | − | 2.84272i | − | 0.0971054i | −0.998821 | − | 0.0485527i | \(-0.984539\pi\) | ||
0.998821 | − | 0.0485527i | \(-0.0154609\pi\) | |||||||
\(858\) | − | 8.69178i | − | 0.296733i | ||||||
\(859\) | 25.8715 | 0.882725 | 0.441363 | − | 0.897329i | \(-0.354495\pi\) | ||||
0.441363 | + | 0.897329i | \(0.354495\pi\) | |||||||
\(860\) | 24.0273 | + | 14.6720i | 0.819326 | + | 0.500311i | ||||
\(861\) | 44.1188 | 1.50356 | ||||||||
\(862\) | − | 45.7447i | − | 1.55807i | ||||||
\(863\) | 38.0032i | 1.29365i | 0.762641 | + | 0.646823i | \(0.223903\pi\) | ||||
−0.762641 | + | 0.646823i | \(0.776097\pi\) | |||||||
\(864\) | −4.50806 | −0.153367 | ||||||||
\(865\) | −16.3953 | − | 10.0116i | −0.557456 | − | 0.340404i | ||||
\(866\) | 4.21773 | 0.143324 | ||||||||
\(867\) | 30.6407i | 1.04061i | ||||||||
\(868\) | 20.5384i | 0.697119i | ||||||||
\(869\) | 2.62149 | 0.0889281 | ||||||||
\(870\) | −16.1754 | + | 26.4893i | −0.548396 | + | 0.898071i | ||||
\(871\) | −29.7873 | −1.00931 | ||||||||
\(872\) | − | 5.11828i | − | 0.173327i | ||||||
\(873\) | 15.1464i | 0.512628i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.49542 | − | 47.2656i | 0.118167 | − | 1.59787i | ||||
\(876\) | 5.80298 | 0.196065 | ||||||||
\(877\) | 49.0943i | 1.65780i | 0.559400 | + | 0.828898i | \(0.311032\pi\) | ||||
−0.559400 | + | 0.828898i | \(0.688968\pi\) | |||||||
\(878\) | − | 11.2731i | − | 0.380448i | ||||||
\(879\) | 52.2026 | 1.76075 | ||||||||
\(880\) | −2.84067 | + | 4.65197i | −0.0957590 | + | 0.156818i | ||||
\(881\) | −55.7494 | −1.87825 | −0.939123 | − | 0.343581i | \(-0.888360\pi\) | ||||
−0.939123 | + | 0.343581i | \(0.888360\pi\) | |||||||
\(882\) | − | 52.5150i | − | 1.76827i | ||||||
\(883\) | 16.6355i | 0.559828i | 0.960025 | + | 0.279914i | \(0.0903060\pi\) | ||||
−0.960025 | + | 0.279914i | \(0.909694\pi\) | |||||||
\(884\) | 10.0431 | 0.337786 | ||||||||
\(885\) | −2.46705 | − | 1.50647i | −0.0829289 | − | 0.0506395i | ||||
\(886\) | 56.2613 | 1.89014 | ||||||||
\(887\) | 43.3883i | 1.45684i | 0.685133 | + | 0.728418i | \(0.259744\pi\) | ||||
−0.685133 | + | 0.728418i | \(0.740256\pi\) | |||||||
\(888\) | 7.43441i | 0.249483i | ||||||||
\(889\) | 83.9691 | 2.81623 | ||||||||
\(890\) | 14.7849 | + | 9.02822i | 0.495591 | + | 0.302626i | ||||
\(891\) | 4.83627 | 0.162021 | ||||||||
\(892\) | 3.74820i | 0.125499i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 19.7285 | 0.659819 | ||||||||
\(895\) | −27.4176 | + | 44.9000i | −0.916470 | + | 1.50084i | ||||
\(896\) | 45.2277 | 1.51095 | ||||||||
\(897\) | − | 43.6062i | − | 1.45597i | ||||||
\(898\) | − | 26.9180i | − | 0.898266i | ||||||
\(899\) | 13.3390 | 0.444880 | ||||||||
\(900\) | −7.26023 | − | 14.1388i | −0.242008 | − | 0.471294i | ||||
\(901\) | −23.2820 | −0.775636 | ||||||||
\(902\) | 3.82498i | 0.127358i | ||||||||
\(903\) | 107.357i | 3.57260i | ||||||||
\(904\) | 19.2825 | 0.641326 | ||||||||
\(905\) | 19.3603 | − | 31.7051i | 0.643559 | − | 1.05391i | ||||
\(906\) | 60.4567 | 2.00854 | ||||||||
\(907\) | 19.8364i | 0.658656i | 0.944216 | + | 0.329328i | \(0.106822\pi\) | ||||
−0.944216 | + | 0.329328i | \(0.893178\pi\) | |||||||
\(908\) | − | 10.7208i | − | 0.355784i | ||||||
\(909\) | 8.85395 | 0.293667 | ||||||||
\(910\) | 60.0904 | + | 36.6935i | 1.99198 | + | 1.21638i | ||||
\(911\) | 15.4076 | 0.510478 | 0.255239 | − | 0.966878i | \(-0.417846\pi\) | ||||
0.255239 | + | 0.966878i | \(0.417846\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 3.98395i | − | 0.131849i | ||||||
\(914\) | −35.9339 | −1.18859 | ||||||||
\(915\) | 62.0610 | + | 37.8968i | 2.05167 | + | 1.25283i | ||||
\(916\) | −21.2034 | −0.700579 | ||||||||
\(917\) | 14.5403i | 0.480163i | ||||||||
\(918\) | 2.75167i | 0.0908186i | ||||||||
\(919\) | 13.2561 | 0.437278 | 0.218639 | − | 0.975806i | \(-0.429838\pi\) | ||||
0.218639 | + | 0.975806i | \(0.429838\pi\) | |||||||
\(920\) | −7.44925 | + | 12.1991i | −0.245595 | + | 0.402193i | ||||
\(921\) | 13.0045 | 0.428512 | ||||||||
\(922\) | 13.3581i | 0.439926i | ||||||||
\(923\) | 25.1325i | 0.827247i | ||||||||
\(924\) | 5.87853 | 0.193389 | ||||||||
\(925\) | 9.53801 | − | 4.89774i | 0.313608 | − | 0.161037i | ||||
\(926\) | −38.5442 | −1.26664 | ||||||||
\(927\) | 9.16200i | 0.300920i | ||||||||
\(928\) | 19.4245i | 0.637641i | ||||||||
\(929\) | −31.2016 | −1.02369 | −0.511846 | − | 0.859077i | \(-0.671038\pi\) | ||||
−0.511846 | + | 0.859077i | \(0.671038\pi\) | |||||||
\(930\) | −20.2685 | + | 33.1924i | −0.664631 | + | 1.08842i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 7.63580i | − | 0.250119i | ||||||
\(933\) | 15.9646i | 0.522658i | ||||||||
\(934\) | 48.2762 | 1.57964 | ||||||||
\(935\) | 1.90753 | + | 1.16481i | 0.0623830 | + | 0.0380934i | ||||
\(936\) | −16.2365 | −0.530707 | ||||||||
\(937\) | − | 16.2187i | − | 0.529840i | −0.964270 | − | 0.264920i | \(-0.914654\pi\) | ||
0.964270 | − | 0.264920i | \(-0.0853456\pi\) | |||||||
\(938\) | − | 54.1458i | − | 1.76792i | ||||||
\(939\) | 10.9243 | 0.356502 | ||||||||
\(940\) | −5.92860 | − | 3.62023i | −0.193369 | − | 0.118079i | ||||
\(941\) | 35.1748 | 1.14666 | 0.573332 | − | 0.819323i | \(-0.305650\pi\) | ||||
0.573332 | + | 0.819323i | \(0.305650\pi\) | |||||||
\(942\) | − | 45.6400i | − | 1.48703i | ||||||
\(943\) | 19.1897i | 0.624903i | ||||||||
\(944\) | −2.69295 | −0.0876482 | ||||||||
\(945\) | −3.74063 | + | 6.12577i | −0.121683 | + | 0.199271i | ||||
\(946\) | −9.30752 | −0.302614 | ||||||||
\(947\) | − | 22.2784i | − | 0.723950i | −0.932188 | − | 0.361975i | \(-0.882103\pi\) | ||
0.932188 | − | 0.361975i | \(-0.117897\pi\) | |||||||
\(948\) | 15.0860i | 0.489972i | ||||||||
\(949\) | −8.54953 | −0.277530 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 65.9811 | 2.13958 | ||||||||
\(952\) | − | 12.5537i | − | 0.406866i | ||||||
\(953\) | 4.25996i | 0.137994i | 0.997617 | + | 0.0689968i | \(0.0219798\pi\) | ||||
−0.997617 | + | 0.0689968i | \(0.978020\pi\) | |||||||
\(954\) | −54.7364 | −1.77216 | ||||||||
\(955\) | 14.9291 | − | 24.4483i | 0.483093 | − | 0.791129i | ||||
\(956\) | −15.9679 | −0.516439 | ||||||||
\(957\) | − | 3.81790i | − | 0.123415i | ||||||
\(958\) | − | 67.9131i | − | 2.19417i | ||||||
\(959\) | −2.57863 | −0.0832684 | ||||||||
\(960\) | −3.15533 | − | 1.92677i | −0.101838 | − | 0.0621861i | ||||
\(961\) | −14.2856 | −0.460825 | ||||||||
\(962\) | 15.9282i | 0.513547i | ||||||||
\(963\) | − | 4.70085i | − | 0.151483i | ||||||
\(964\) | 20.8990 | 0.673111 | ||||||||
\(965\) | −18.3966 | − | 11.2337i | −0.592208 | − | 0.361625i | ||||
\(966\) | 79.2650 | 2.55031 | ||||||||
\(967\) | − | 1.21906i | − | 0.0392023i | −0.999808 | − | 0.0196012i | \(-0.993760\pi\) | ||
0.999808 | − | 0.0196012i | \(-0.00623964\pi\) | |||||||
\(968\) | 15.6477i | 0.502935i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.7438 | − | 19.2319i | 0.377069 | − | 0.617500i | ||||
\(971\) | −4.34003 | −0.139278 | −0.0696391 | − | 0.997572i | \(-0.522185\pi\) | ||||
−0.0696391 | + | 0.997572i | \(0.522185\pi\) | |||||||
\(972\) | 25.1395i | 0.806349i | ||||||||
\(973\) | − | 35.8543i | − | 1.14944i | ||||||
\(974\) | 32.7226 | 1.04850 | ||||||||
\(975\) | 22.6597 | + | 44.1283i | 0.725692 | + | 1.41324i | ||||
\(976\) | 67.7440 | 2.16843 | ||||||||
\(977\) | 21.5270i | 0.688710i | 0.938840 | + | 0.344355i | \(0.111902\pi\) | ||||
−0.938840 | + | 0.344355i | \(0.888098\pi\) | |||||||
\(978\) | − | 72.0527i | − | 2.30399i | ||||||
\(979\) | −2.13095 | −0.0681054 | ||||||||
\(980\) | −15.1498 | + | 24.8098i | −0.483943 | + | 0.792520i | ||||
\(981\) | −9.43980 | −0.301389 | ||||||||
\(982\) | 26.8906i | 0.858114i | ||||||||
\(983\) | − | 14.5998i | − | 0.465661i | −0.972517 | − | 0.232830i | \(-0.925201\pi\) | ||
0.972517 | − | 0.232830i | \(-0.0747987\pi\) | |||||||
\(984\) | 15.1365 | 0.482534 | ||||||||
\(985\) | 5.92064 | + | 3.61537i | 0.188647 | + | 0.115195i | ||||
\(986\) | 11.8565 | 0.377588 | ||||||||
\(987\) | − | 26.4896i | − | 0.843172i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46.6954 | −1.48483 | ||||||||
\(990\) | 4.48464 | + | 2.73849i | 0.142531 | + | 0.0870349i | ||||
\(991\) | 31.9286 | 1.01425 | 0.507123 | − | 0.861874i | \(-0.330709\pi\) | ||||
0.507123 | + | 0.861874i | \(0.330709\pi\) | |||||||
\(992\) | 24.3399i | 0.772792i | ||||||||
\(993\) | − | 33.6831i | − | 1.06890i | ||||||
\(994\) | −45.6845 | −1.44903 | ||||||||
\(995\) | 0.610976 | − | 1.00055i | 0.0193692 | − | 0.0317197i | ||||
\(996\) | 22.9267 | 0.726459 | ||||||||
\(997\) | 55.1812i | 1.74761i | 0.486280 | + | 0.873803i | \(0.338353\pi\) | ||||
−0.486280 | + | 0.873803i | \(0.661647\pi\) | |||||||
\(998\) | 61.6248i | 1.95070i | ||||||||
\(999\) | −1.62377 | −0.0513737 |
(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 | 1805.2.b.k.1084.5 | 24 | ||
5.2 | odd | 4 | 9025.2.a.cu.1.20 | 24 | |||
5.3 | odd | 4 | 9025.2.a.cu.1.5 | 24 | |||
5.4 | even | 2 | inner | 1805.2.b.k.1084.20 | 24 | ||
19.4 | even | 9 | 95.2.p.a.54.7 | yes | 48 | ||
19.5 | even | 9 | 95.2.p.a.44.2 | ✓ | 48 | ||
19.18 | odd | 2 | 1805.2.b.l.1084.20 | 24 | |||
57.5 | odd | 18 | 855.2.da.b.424.7 | 48 | |||
57.23 | odd | 18 | 855.2.da.b.244.2 | 48 | |||
95.4 | even | 18 | 95.2.p.a.54.2 | yes | 48 | ||
95.18 | even | 4 | 9025.2.a.ct.1.20 | 24 | |||
95.23 | odd | 36 | 475.2.l.f.301.2 | 48 | |||
95.24 | even | 18 | 95.2.p.a.44.7 | yes | 48 | ||
95.37 | even | 4 | 9025.2.a.ct.1.5 | 24 | |||
95.42 | odd | 36 | 475.2.l.f.301.7 | 48 | |||
95.43 | odd | 36 | 475.2.l.f.101.2 | 48 | |||
95.62 | odd | 36 | 475.2.l.f.101.7 | 48 | |||
95.94 | odd | 2 | 1805.2.b.l.1084.5 | 24 | |||
285.119 | odd | 18 | 855.2.da.b.424.2 | 48 | |||
285.194 | odd | 18 | 855.2.da.b.244.7 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.44.2 | ✓ | 48 | 19.5 | even | 9 | ||
95.2.p.a.44.7 | yes | 48 | 95.24 | even | 18 | ||
95.2.p.a.54.2 | yes | 48 | 95.4 | even | 18 | ||
95.2.p.a.54.7 | yes | 48 | 19.4 | even | 9 | ||
475.2.l.f.101.2 | 48 | 95.43 | odd | 36 | |||
475.2.l.f.101.7 | 48 | 95.62 | odd | 36 | |||
475.2.l.f.301.2 | 48 | 95.23 | odd | 36 | |||
475.2.l.f.301.7 | 48 | 95.42 | odd | 36 | |||
855.2.da.b.244.2 | 48 | 57.23 | odd | 18 | |||
855.2.da.b.244.7 | 48 | 285.194 | odd | 18 | |||
855.2.da.b.424.2 | 48 | 285.119 | odd | 18 | |||
855.2.da.b.424.7 | 48 | 57.5 | odd | 18 | |||
1805.2.b.k.1084.5 | 24 | 1.1 | even | 1 | trivial | ||
1805.2.b.k.1084.20 | 24 | 5.4 | even | 2 | inner | ||
1805.2.b.l.1084.5 | 24 | 95.94 | odd | 2 | |||
1805.2.b.l.1084.20 | 24 | 19.18 | odd | 2 | |||
9025.2.a.ct.1.5 | 24 | 95.37 | even | 4 | |||
9025.2.a.ct.1.20 | 24 | 95.18 | even | 4 | |||
9025.2.a.cu.1.5 | 24 | 5.3 | odd | 4 | |||
9025.2.a.cu.1.20 | 24 | 5.2 | odd | 4 |