Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(101,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.bh (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 10.0.29471584693248.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 341.4 | ||
Root | \(1.15038 - 1.29484i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 420.341 |
Dual form | 420.2.bh.a.101.4 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.546177 | − | 1.64368i | 0.315336 | − | 0.948980i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.08214 | − | 2.41433i | −0.409009 | − | 0.912531i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.40338 | − | 1.79548i | −0.801127 | − | 0.598494i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.17086 | + | 0.675999i | −0.353029 | + | 0.203821i | −0.666018 | − | 0.745935i | \(-0.732003\pi\) |
0.312990 | + | 0.949757i | \(0.398669\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.94296i | − | 1.37093i | −0.728105 | − | 0.685466i | \(-0.759599\pi\) | ||
0.728105 | − | 0.685466i | \(-0.240401\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.15038 | + | 1.29484i | 0.297027 | + | 0.334327i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.87105 | − | 4.97280i | −0.696332 | − | 1.20608i | −0.969730 | − | 0.244181i | \(-0.921481\pi\) |
0.273398 | − | 0.961901i | \(-0.411852\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.84694 | + | 1.64368i | 0.653133 | + | 0.377087i | 0.789656 | − | 0.613550i | \(-0.210259\pi\) |
−0.136523 | + | 0.990637i | \(0.543593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.55943 | + | 0.460035i | −0.994948 | + | 0.100388i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.33480 | + | 2.50270i | 0.903868 | + | 0.521849i | 0.878453 | − | 0.477828i | \(-0.158576\pi\) |
0.0254150 | + | 0.999677i | \(0.491909\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.26388 | + | 2.96974i | −0.820583 | + | 0.571527i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.68630i | − | 1.05592i | −0.849270 | − | 0.527959i | \(-0.822957\pi\) | ||
0.849270 | − | 0.527959i | \(-0.177043\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.45160 | + | 1.41543i | −0.440320 | + | 0.254219i | −0.703733 | − | 0.710464i | \(-0.748485\pi\) |
0.263414 | + | 0.964683i | \(0.415152\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.471628 | + | 2.29374i | 0.0820998 | + | 0.399289i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.63194 | + | 0.270008i | 0.444879 | + | 0.0456397i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.92545 | + | 3.33498i | −0.316542 | + | 0.548267i | −0.979764 | − | 0.200156i | \(-0.935855\pi\) |
0.663222 | + | 0.748423i | \(0.269189\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.12466 | − | 2.69973i | −1.30099 | − | 0.432303i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.73802 | 0.583781 | 0.291890 | − | 0.956452i | \(-0.405716\pi\) | ||||
0.291890 | + | 0.956452i | \(0.405716\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.06339 | 0.619661 | 0.309830 | − | 0.950792i | \(-0.399728\pi\) | ||||
0.309830 | + | 0.950792i | \(0.399728\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.75662 | − | 1.18365i | 0.410933 | − | 0.176448i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.84298 | − | 4.92419i | 0.414691 | − | 0.718266i | −0.580705 | − | 0.814114i | \(-0.697223\pi\) |
0.995396 | + | 0.0958478i | \(0.0305562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.65797 | + | 5.22526i | −0.665424 | + | 0.746466i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.74181 | + | 2.00306i | −1.36413 | + | 0.280484i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.26574 | + | 0.730773i | −0.173862 | + | 0.100379i | −0.584406 | − | 0.811462i | \(-0.698672\pi\) |
0.410544 | + | 0.911841i | \(0.365339\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.35200i | − | 0.182303i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.25662 | − | 3.78172i | 0.563804 | − | 0.500902i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.34239 | + | 7.52123i | 0.565330 | + | 0.979181i | 0.997019 | + | 0.0771582i | \(0.0245846\pi\) |
−0.431688 | + | 0.902023i | \(0.642082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.65306 | + | 0.954394i | 0.211653 | + | 0.122198i | 0.602079 | − | 0.798436i | \(-0.294339\pi\) |
−0.390427 | + | 0.920634i | \(0.627672\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.73410 | + | 7.74551i | −0.218477 | + | 0.975842i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.28073 | + | 2.47148i | 0.530959 | + | 0.306550i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.51939 | − | 4.36371i | −0.307793 | − | 0.533113i | 0.670086 | − | 0.742283i | \(-0.266257\pi\) |
−0.977879 | + | 0.209170i | \(0.932924\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.48121 | − | 5.75812i | 0.780246 | − | 0.693196i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.38259i | 0.401440i | 0.979649 | + | 0.200720i | \(0.0643281\pi\) | ||||
−0.979649 | + | 0.200720i | \(0.935672\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.1398 | − | 8.16364i | 1.65494 | − | 0.955481i | 0.679945 | − | 0.733263i | \(-0.262004\pi\) |
0.974997 | − | 0.222218i | \(-0.0713298\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.69656 | + | 0.348838i | −0.195902 | + | 0.0402803i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.89912 | + | 2.09533i | 0.330385 | + | 0.238785i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.41693 | + | 4.18625i | −0.271926 | + | 0.470990i | −0.969355 | − | 0.245664i | \(-0.920994\pi\) |
0.697429 | + | 0.716654i | \(0.254327\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.55248 | + | 8.63046i | 0.283609 | + | 0.958940i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.6525 | 1.82785 | 0.913927 | − | 0.405879i | \(-0.133035\pi\) | ||||
0.913927 | + | 0.405879i | \(0.133035\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.74210 | 0.622818 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.34646 | − | 3.10572i | −1.00205 | − | 0.332969i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.08150 | − | 13.9976i | 0.856637 | − | 1.48374i | −0.0184813 | − | 0.999829i | \(-0.505883\pi\) |
0.875118 | − | 0.483909i | \(-0.160784\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.9339 | + | 5.34895i | −1.25102 | + | 0.560723i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.987510 | + | 4.80272i | 0.102400 | + | 0.498019i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.84694 | + | 1.64368i | −0.292090 | + | 0.168638i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0577i | 1.22427i | 0.790751 | + | 0.612137i | \(0.209690\pi\) | ||||
−0.790751 | + | 0.612137i | \(0.790310\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.02778 | + | 0.477584i | 0.404807 | + | 0.0479990i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.01683 | − | 15.6176i | −0.897208 | − | 1.55401i | −0.831048 | − | 0.556201i | \(-0.812258\pi\) |
−0.0661605 | − | 0.997809i | \(-0.521075\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.533615 | + | 0.308083i | 0.0525787 | + | 0.0303563i | 0.526059 | − | 0.850448i | \(-0.323669\pi\) |
−0.473480 | + | 0.880804i | \(0.657002\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.88131 | − | 4.17860i | 0.183597 | − | 0.407789i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.3374 | + | 8.85503i | 1.48272 | + | 0.856048i | 0.999807 | − | 0.0196209i | \(-0.00624594\pi\) |
0.482912 | + | 0.875669i | \(0.339579\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.855282 | + | 1.48139i | 0.0819211 | + | 0.141892i | 0.904075 | − | 0.427374i | \(-0.140561\pi\) |
−0.822154 | + | 0.569265i | \(0.807228\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.43001 | + | 4.98632i | 0.420478 | + | 0.473280i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.1214i | 1.23436i | 0.786822 | + | 0.617180i | \(0.211725\pi\) | ||||
−0.786822 | + | 0.617180i | \(0.788275\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.33480 | + | 2.50270i | −0.404222 | + | 0.233378i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.87501 | + | 11.8798i | −0.820495 | + | 1.09829i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.89912 | + | 12.3129i | −0.815781 | + | 1.12872i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.58605 | + | 7.94327i | −0.416914 | + | 0.722116i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.04162 | − | 6.14412i | 0.184087 | − | 0.553996i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.5324 | −1.37828 | −0.689139 | − | 0.724629i | \(-0.742011\pi\) | ||||
−0.689139 | + | 0.724629i | \(0.742011\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.21933 | − | 6.67892i | 0.195401 | − | 0.588046i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.47822 | − | 7.75651i | 0.391264 | − | 0.677689i | −0.601353 | − | 0.798984i | \(-0.705371\pi\) |
0.992617 | + | 0.121295i | \(0.0387046\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.887614 | − | 8.65214i | 0.0769659 | − | 0.750235i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.439934 | − | 5.17750i | −0.0378635 | − | 0.445608i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.4047 | + | 7.73923i | −1.14524 | + | 0.661207i | −0.947724 | − | 0.319092i | \(-0.896622\pi\) |
−0.197520 | + | 0.980299i | \(0.563289\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.1547i | 1.70950i | 0.519044 | + | 0.854748i | \(0.326288\pi\) | ||||
−0.519044 | + | 0.854748i | \(0.673712\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.54103 | − | 7.36243i | −0.550854 | − | 0.620029i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.34144 | + | 5.78754i | 0.279425 | + | 0.483978i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.92448 | + | 2.84315i | 0.408955 | + | 0.236111i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.04459 | + | 10.5101i | 0.498549 | + | 0.866861i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.24947 | + | 0.721384i | 0.102361 | + | 0.0590981i | 0.550307 | − | 0.834963i | \(-0.314511\pi\) |
−0.447946 | + | 0.894061i | \(0.647844\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.12108 | − | 14.0661i | −0.660884 | − | 1.14468i | −0.980384 | − | 0.197098i | \(-0.936848\pi\) |
0.319500 | − | 0.947586i | \(-0.396485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.02836 | + | 17.1065i | −0.163983 | + | 1.38298i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.83086i | − | 0.227380i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7942 | − | 9.11876i | 1.26051 | − | 0.727756i | 0.287338 | − | 0.957829i | \(-0.407230\pi\) |
0.973173 | + | 0.230073i | \(0.0738965\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.509842 | + | 2.47960i | 0.0404331 | + | 0.196645i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.35150 | − | 13.1739i | 0.106513 | − | 1.03825i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.1630 | − | 21.0669i | 0.952679 | − | 1.65009i | 0.213087 | − | 0.977033i | \(-0.431648\pi\) |
0.739592 | − | 0.673055i | \(-0.235018\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.22225 | − | 0.738430i | −0.173002 | − | 0.0574867i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.5007 | −0.967336 | −0.483668 | − | 0.875252i | \(-0.660696\pi\) | ||||
−0.483668 | + | 0.875252i | \(0.660696\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4329 | −0.879453 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.89108 | − | 9.06203i | −0.297558 | − | 0.692991i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.42089 | − | 12.8534i | 0.564200 | − | 0.977223i | −0.432923 | − | 0.901431i | \(-0.642518\pi\) |
0.997124 | − | 0.0757927i | \(-0.0241487\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.54980 | + | 2.14432i | −0.117154 | + | 0.162095i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.7342 | − | 3.02957i | 1.10749 | − | 0.227717i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.93533 | + | 5.73617i | −0.742602 | + | 0.428741i | −0.823015 | − | 0.568020i | \(-0.807709\pi\) |
0.0804127 | + | 0.996762i | \(0.474376\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.91099i | − | 0.439361i | −0.975572 | − | 0.219680i | \(-0.929499\pi\) | ||
0.975572 | − | 0.219680i | \(-0.0705014\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.47158 | − | 2.19584i | 0.182705 | − | 0.162321i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.92545 | − | 3.33498i | −0.141562 | − | 0.245192i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.72322 | + | 3.88165i | 0.491650 | + | 0.283854i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.7840 | + | 7.08073i | 0.857162 | + | 0.515048i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.15764 | − | 5.28716i | −0.662623 | − | 0.382566i | 0.130652 | − | 0.991428i | \(-0.458293\pi\) |
−0.793276 | + | 0.608862i | \(0.791626\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.03231 | − | 10.4483i | −0.434215 | − | 0.752082i | 0.563016 | − | 0.826446i | \(-0.309641\pi\) |
−0.997231 | + | 0.0743635i | \(0.976307\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.40037 | − | 5.68630i | 0.458340 | − | 0.407204i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.2423i | − | 1.22846i | −0.789126 | − | 0.614231i | \(-0.789466\pi\) | ||
0.789126 | − | 0.614231i | \(-0.210534\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.46400 | − | 1.42259i | 0.174668 | − | 0.100845i | −0.410117 | − | 0.912033i | \(-0.634512\pi\) |
0.584785 | + | 0.811188i | \(0.301179\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.54859 | + | 1.75772i | −0.602971 | + | 0.123980i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.7286 | + | 6.15334i | −0.963558 | + | 0.431880i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.86901 | + | 3.23722i | −0.130537 | + | 0.226097i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.92462 | − | 13.7980i | −0.411790 | − | 0.959027i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.44451 | −0.307433 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.4677 | 1.54674 | 0.773372 | − | 0.633953i | \(-0.218569\pi\) | ||||
0.773372 | + | 0.633953i | \(0.218569\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.55991 | + | 1.84749i | 0.380958 | + | 0.126588i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.03169 | + | 3.51900i | −0.138560 | + | 0.239994i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.07027 | + | 4.38727i | 0.412077 | + | 0.297828i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.69557 | − | 27.7002i | −0.384871 | − | 1.87180i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.5804 | + | 14.1915i | −1.65346 | + | 0.954623i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5.27620i | − | 0.353321i | −0.984272 | − | 0.176660i | \(-0.943471\pi\) | ||
0.984272 | − | 0.176660i | \(-0.0565294\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.353244 | + | 2.97913i | −0.0235496 | + | 0.198609i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.24055 | − | 10.8090i | −0.414200 | − | 0.717416i | 0.581144 | − | 0.813801i | \(-0.302605\pi\) |
−0.995344 | + | 0.0963851i | \(0.969272\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0882 | − | 8.13380i | −0.930971 | − | 0.537496i | −0.0438526 | − | 0.999038i | \(-0.513963\pi\) |
−0.887119 | + | 0.461542i | \(0.847297\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.02749 | − | 3.62080i | 0.330784 | − | 0.238231i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.64788 | − | 4.41551i | −0.501029 | − | 0.289269i | 0.228109 | − | 0.973636i | \(-0.426746\pi\) |
−0.729139 | + | 0.684366i | \(0.760079\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.84298 | + | 4.92419i | 0.185456 | + | 0.321219i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.56079 | + | 6.25911i | 0.361212 | + | 0.406573i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.3333i | 0.797773i | 0.917000 | + | 0.398886i | \(0.130603\pi\) | ||||
−0.917000 | + | 0.398886i | \(0.869397\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.88815 | − | 3.97688i | 0.443705 | − | 0.256173i | −0.261463 | − | 0.965214i | \(-0.584205\pi\) |
0.705168 | + | 0.709040i | \(0.250872\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5798 | + | 0.518295i | 0.999447 | + | 0.0332486i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.19622 | − | 6.64655i | −0.140312 | − | 0.424632i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.12466 | − | 14.0723i | 0.516960 | − | 0.895401i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.09524 | − | 27.3715i | 0.576387 | − | 1.73460i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.64756 | 0.482710 | 0.241355 | − | 0.970437i | \(-0.422408\pi\) | ||||
0.241355 | + | 0.970437i | \(0.422408\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.76728 | −0.425455 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.13620 | − | 9.43818i | 0.196397 | − | 0.591042i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.7478 | + | 23.8118i | −0.857563 | + | 1.48534i | 0.0166841 | + | 0.999861i | \(0.494689\pi\) |
−0.874247 | + | 0.485482i | \(0.838644\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.1353 | + | 1.03977i | 0.629779 | + | 0.0646084i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.2096 | + | 13.6663i | −0.631961 | + | 0.845925i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.4738 | + | 9.51115i | −1.01582 | + | 0.586483i | −0.912890 | − | 0.408206i | \(-0.866155\pi\) |
−0.102928 | + | 0.994689i | \(0.532821\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.46155i | − | 0.0897821i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.5936 | − | 20.9286i | −1.13791 | − | 1.28081i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.46010 | − | 7.72512i | −0.271937 | − | 0.471009i | 0.697421 | − | 0.716662i | \(-0.254331\pi\) |
−0.969358 | + | 0.245653i | \(0.920998\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.53123 | + | 3.77081i | 0.396744 | + | 0.229060i | 0.685078 | − | 0.728470i | \(-0.259768\pi\) |
−0.288334 | + | 0.957530i | \(0.593101\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.27393 | + | 22.5371i | 0.137625 | + | 1.36401i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.17086 | + | 0.675999i | 0.0706058 | + | 0.0407643i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.888562 | + | 1.53903i | 0.0533885 | + | 0.0924716i | 0.891485 | − | 0.453051i | \(-0.149664\pi\) |
−0.838096 | + | 0.545523i | \(0.816331\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.43350 | + | 0.999983i | 0.504900 | + | 0.0598674i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.3819i | 1.51416i | 0.653324 | + | 0.757079i | \(0.273374\pi\) | ||||
−0.653324 | + | 0.757079i | \(0.726626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.9774 | + | 8.06987i | −0.830872 | + | 0.479704i | −0.854151 | − | 0.520025i | \(-0.825923\pi\) |
0.0232795 | + | 0.999729i | \(0.492589\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.14676 | + | 5.57721i | 0.0679280 | + | 0.330365i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.04504 | − | 9.02481i | −0.238771 | − | 0.532718i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.98584 | + | 13.8319i | −0.469755 | + | 0.813640i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.8190 | + | 6.58564i | 1.16181 | + | 0.386057i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.5542 | −1.14237 | −0.571186 | − | 0.820821i | \(-0.693516\pi\) | ||||
−0.571186 | + | 0.820821i | \(0.693516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.68477 | −0.505647 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.98488 | − | 6.35954i | 0.173200 | − | 0.369018i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.3707 | − | 21.4268i | 0.715419 | − | 1.23914i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.39713 | − | 9.81035i | −0.253447 | − | 0.565459i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −30.5952 | + | 6.29082i | −1.75765 | + | 0.361398i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.65306 | + | 0.954394i | −0.0946539 | + | 0.0546485i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.8231i | 0.674777i | 0.941365 | + | 0.337389i | \(0.109544\pi\) | ||||
−0.941365 | + | 0.337389i | \(0.890456\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.797839 | − | 0.708826i | 0.0453875 | − | 0.0403237i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.1689 | + | 19.3451i | 0.633331 | + | 1.09696i | 0.986866 | + | 0.161540i | \(0.0516462\pi\) |
−0.353535 | + | 0.935421i | \(0.615020\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.5250 | − | 6.65398i | −0.651433 | − | 0.376105i | 0.137572 | − | 0.990492i | \(-0.456070\pi\) |
−0.789005 | + | 0.614387i | \(0.789404\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.84075 | − | 5.37453i | −0.329089 | − | 0.302821i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.3395 | + | 16.9392i | 1.64787 | + | 0.951400i | 0.977915 | + | 0.209001i | \(0.0670212\pi\) |
0.669958 | + | 0.742399i | \(0.266312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.84393 | + | 6.65788i | 0.215219 | + | 0.372770i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.9318 | − | 20.3733i | 1.27993 | − | 1.13713i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 18.8764i | − | 1.05031i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.28073 | + | 2.47148i | −0.237452 | + | 0.137093i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.90207 | − | 0.596709i | 0.160485 | − | 0.0329981i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.9651 | − | 1.53525i | −0.825052 | − | 0.0846413i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.989824 | − | 1.71443i | 0.0544057 | − | 0.0942334i | −0.837540 | − | 0.546376i | \(-0.816007\pi\) |
0.891946 | + | 0.452143i | \(0.149340\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.6155 | − | 4.55811i | 0.581725 | − | 0.249783i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.03878 | 0.275298 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.0217 | −0.654862 | −0.327431 | − | 0.944875i | \(-0.606183\pi\) | ||||
−0.327431 | + | 0.944875i | \(0.606183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.5674 | + | 7.16662i | 1.17138 | + | 0.389237i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.91366 | − | 3.31455i | 0.103630 | − | 0.179493i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6560 | + | 5.59143i | 0.953337 | + | 0.301909i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.74607 | + | 8.49195i | 0.0940053 | + | 0.457191i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.6992 | − | 7.33186i | 0.681726 | − | 0.393595i | −0.118779 | − | 0.992921i | \(-0.537898\pi\) |
0.800505 | + | 0.599326i | \(0.204565\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.0573i | 1.34129i | 0.741780 | + | 0.670644i | \(0.233982\pi\) | ||||
−0.741780 | + | 0.670644i | \(0.766018\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.6793 | + | 21.0762i | 0.783525 | + | 1.12496i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.88365 | − | 6.72669i | −0.206706 | − | 0.358025i | 0.743969 | − | 0.668214i | \(-0.232941\pi\) |
−0.950675 | + | 0.310189i | \(0.899608\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.92941 | − | 1.69130i | −0.155477 | − | 0.0897647i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.3780 | + | 21.3523i | 0.813890 | + | 1.13009i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.86952 | + | 2.23407i | 0.204225 | + | 0.117910i | 0.598625 | − | 0.801030i | \(-0.295714\pi\) |
−0.394399 | + | 0.918939i | \(0.629047\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.09662 | − | 7.09555i | −0.215612 | − | 0.373450i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.5514 | + | 11.8764i | 0.553806 | + | 0.623352i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.3273i | 0.854608i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.45880 | − | 0.842240i | 0.0761489 | − | 0.0439646i | −0.461442 | − | 0.887170i | \(-0.652668\pi\) |
0.537591 | + | 0.843206i | \(0.319334\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.98389 | − | 6.71155i | −0.467682 | − | 0.349389i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.13402 | + | 2.26511i | 0.162710 | + | 0.117599i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.92322 | + | 11.9914i | −0.358471 | + | 0.620890i | −0.987706 | − | 0.156325i | \(-0.950035\pi\) |
0.629235 | + | 0.777215i | \(0.283368\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.546177 | − | 1.64368i | 0.0282045 | − | 0.0848794i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.1072 | −1.44759 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.15603 | −0.110748 | −0.0553739 | − | 0.998466i | \(-0.517635\pi\) | ||||
−0.0553739 | + | 0.998466i | \(0.517635\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.48345 | + | 25.5303i | −0.434620 | + | 1.30796i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.86598 | − | 3.23197i | 0.0953471 | − | 0.165146i | −0.814406 | − | 0.580295i | \(-0.802937\pi\) |
0.909753 | + | 0.415149i | \(0.136271\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.26417 | + | 1.46304i | −0.166357 | + | 0.0745636i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.76587 | − | 7.29574i | −0.496427 | − | 0.370863i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.9512 | − | 6.90001i | 0.605948 | − | 0.349844i | −0.165430 | − | 0.986222i | \(-0.552901\pi\) |
0.771378 | + | 0.636377i | \(0.219568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 28.7415i | − | 1.45352i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.3033 | − | 11.5972i | −0.519734 | − | 0.585001i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.41693 | − | 4.18625i | −0.121609 | − | 0.210633i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.1606 | − | 8.17565i | −0.710702 | − | 0.410324i | 0.100619 | − | 0.994925i | \(-0.467918\pi\) |
−0.811321 | + | 0.584601i | \(0.801251\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.7366 | − | 6.18456i | −0.687688 | − | 0.309615i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.9669 | + | 6.90910i | 0.597599 | + | 0.345024i | 0.768096 | − | 0.640334i | \(-0.221204\pi\) |
−0.170497 | + | 0.985358i | \(0.554537\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.99642 | + | 12.1182i | 0.348516 | + | 0.603648i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.75044 | − | 2.10472i | −0.434813 | − | 0.104584i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.20641i | − | 0.258072i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.26987 | + | 4.77461i | −0.408919 | + | 0.236089i | −0.690325 | − | 0.723499i | \(-0.742533\pi\) |
0.281406 | + | 0.959589i | \(0.409199\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.39947 | + | 26.2601i | 0.266336 | + | 1.29532i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.4597 | − | 18.6229i | 0.662307 | − | 0.916375i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.32627 | + | 14.4215i | −0.408721 | + | 0.707925i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.1278 | + | 11.0080i | 1.62228 | + | 0.539065i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.71886 | −0.474797 | −0.237399 | − | 0.971412i | \(-0.576295\pi\) | ||||
−0.237399 | + | 0.971412i | \(0.576295\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.8713 | 1.69953 | 0.849763 | − | 0.527165i | \(-0.176745\pi\) | ||||
0.849763 | + | 0.527165i | \(0.176745\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.6741 | + | 6.73017i | −0.762099 | + | 0.327232i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.87105 | + | 4.97280i | −0.139266 | + | 0.241216i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.515388 | − | 5.02381i | 0.0249414 | − | 0.243119i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.3379 | − | 2.33124i | 0.547399 | − | 0.112553i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.57279 | − | 0.908052i | 0.0757587 | − | 0.0437393i | −0.461642 | − | 0.887066i | \(-0.652740\pi\) |
0.537401 | + | 0.843327i | \(0.319406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.6773i | − | 0.513117i | −0.966529 | − | 0.256558i | \(-0.917411\pi\) | ||
0.966529 | − | 0.256558i | \(-0.0825886\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.36287 | − | 6.54141i | 0.353022 | − | 0.313637i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.22728 | + | 14.2501i | 0.393564 | + | 0.681673i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.6759 | + | 15.4013i | 1.27317 | + | 0.735066i | 0.975584 | − | 0.219628i | \(-0.0704845\pi\) |
0.297588 | + | 0.954694i | \(0.403818\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.5767 | − | 4.19499i | 0.979845 | − | 0.199761i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.3178 | + | 8.26640i | 0.680260 | + | 0.392749i | 0.799953 | − | 0.600062i | \(-0.204858\pi\) |
−0.119693 | + | 0.992811i | \(0.538191\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.08150 | + | 13.9976i | 0.383100 | + | 0.663548i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.86816 | − | 1.65974i | 0.0883610 | − | 0.0785028i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.59098i | − | 0.122276i | −0.998129 | − | 0.0611380i | \(-0.980527\pi\) | ||
0.998129 | − | 0.0611380i | \(-0.0194730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.37671 | + | 2.52690i | −0.206091 | + | 0.118987i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −27.5558 | + | 5.66588i | −1.29468 | + | 0.266206i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.33464 | − | 13.0096i | 0.0625689 | − | 0.609898i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0874 | − | 19.2040i | 0.518647 | − | 0.898323i | −0.481118 | − | 0.876656i | \(-0.659769\pi\) |
0.999765 | − | 0.0216672i | \(-0.00689744\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 27.0097 | + | 12.6771i | 1.26071 | + | 0.591718i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.5304 | 1.42194 | 0.710971 | − | 0.703221i | \(-0.248256\pi\) | ||||
0.710971 | + | 0.703221i | \(0.248256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.54824 | 0.164901 | 0.0824504 | − | 0.996595i | \(-0.473725\pi\) | ||||
0.0824504 | + | 0.996595i | \(0.473725\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.65303 | − | 1.54615i | −0.215779 | − | 0.0717010i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.1564 | − | 29.7157i | 0.793901 | − | 1.37508i | −0.129633 | − | 0.991562i | \(-0.541380\pi\) |
0.923534 | − | 0.383515i | \(-0.125287\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.80912 | + | 10.8048i | −0.360592 | + | 0.498918i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.36193 | − | 30.9410i | −0.293142 | − | 1.42569i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.75767 | + | 2.74684i | −0.218758 | + | 0.126300i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.28736i | − | 0.150835i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.35414 | + | 0.516282i | 0.199362 | + | 0.0236389i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.78624 | + | 16.9503i | 0.447145 | + | 0.774477i | 0.998199 | − | 0.0599923i | \(-0.0191076\pi\) |
−0.551054 | + | 0.834469i | \(0.685774\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.4847 | + | 9.51743i | 0.751637 | + | 0.433958i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.9155 | − | 9.41671i | −0.951689 | − | 0.428475i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.4423 | − | 6.02885i | −0.474160 | − | 0.273756i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.6133 | − | 21.8468i | −0.571561 | − | 0.989973i | −0.996406 | − | 0.0847071i | \(-0.973005\pi\) |
0.424844 | − | 0.905266i | \(-0.360329\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −27.9842 | − | 31.4984i | −1.26549 | − | 1.42441i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.6556i | 1.74450i | 0.489057 | + | 0.872252i | \(0.337341\pi\) | ||||
−0.489057 | + | 0.872252i | \(0.662659\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.2768 | + | 16.3256i | −1.27352 | + | 0.735269i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.42749 | + | 3.24936i | −0.109108 | + | 0.146048i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.16669 | − | 3.66042i | 0.366326 | − | 0.164192i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.80910 | + | 4.86551i | −0.125753 | + | 0.217810i | −0.922027 | − | 0.387126i | \(-0.873468\pi\) |
0.796274 | + | 0.604936i | \(0.206801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.82761 | + | 20.5472i | −0.305035 | + | 0.917982i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.8655 | −1.15329 | −0.576644 | − | 0.816996i | \(-0.695638\pi\) | ||||
−0.576644 | + | 0.816996i | \(0.695638\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0337 | 0.802487 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.24438 | + | 18.7920i | −0.277323 | + | 0.834584i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.2306 | + | 26.3801i | −0.675082 | + | 1.16928i | 0.301362 | + | 0.953510i | \(0.402559\pi\) |
−0.976445 | + | 0.215767i | \(0.930775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.0109 | − | 25.3040i | −1.54879 | − | 1.11939i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.0203 | + | 1.44622i | −0.751465 | + | 0.0638524i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.533615 | + | 0.308083i | −0.0235139 | + | 0.0135758i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.68740i | 0.338092i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.0737 | − | 19.2178i | −0.749453 | − | 0.843568i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.6182 | + | 18.3913i | 0.465192 | + | 0.805737i | 0.999210 | − | 0.0397366i | \(-0.0126519\pi\) |
−0.534018 | + | 0.845473i | \(0.679319\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.7227 | − | 6.19077i | −0.468872 | − | 0.270704i | 0.246895 | − | 0.969042i | \(-0.420590\pi\) |
−0.715768 | + | 0.698339i | \(0.753923\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.67811 | + | 3.71856i | 0.116883 | + | 0.162291i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.0773 | + | 8.12754i | 0.613217 | + | 0.354041i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.02699 | + | 1.77880i | 0.0446518 | + | 0.0773392i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.06784 | − | 25.8731i | 0.133133 | − | 1.12280i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 18.4769i | − | 0.800323i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.3374 | + | 8.85503i | −0.663092 | + | 0.382836i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.00198 | + | 19.4635i | 0.172698 | + | 0.839912i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.92158 | − | 9.26685i | 0.0827682 | − | 0.399151i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.93001 | + | 12.0031i | −0.297944 | + | 0.516055i | −0.975665 | − | 0.219264i | \(-0.929634\pi\) |
0.677721 | + | 0.735319i | \(0.262968\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.71579 | − | 3.22845i | −0.416945 | − | 0.138546i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.71056 | −0.0732725 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.7100 | 0.757226 | 0.378613 | − | 0.925555i | \(-0.376401\pi\) | ||||
0.378613 | + | 0.925555i | \(0.376401\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.25933 | − | 5.26181i | −0.0964260 | − | 0.224569i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.34646 | − | 16.1885i | 0.398173 | − | 0.689655i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.7224 | + | 1.30518i | 0.541013 | + | 0.0555020i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.53328 | + | 1.34334i | −0.277322 | + | 0.0570216i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.01129 | + | 1.73857i | −0.127593 | + | 0.0736656i | −0.562438 | − | 0.826840i | \(-0.690136\pi\) |
0.434845 | + | 0.900505i | \(0.356803\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 20.0852i | − | 0.849512i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.0523 | − | 8.93076i | 0.424407 | − | 0.377057i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.02897 | + | 10.4425i | 0.254091 | + | 0.440098i | 0.964648 | − | 0.263541i | \(-0.0848904\pi\) |
−0.710557 | + | 0.703639i | \(0.751557\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.3635 | − | 6.56071i | −0.478065 | − | 0.276011i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.0746 | − | 15.5019i | 0.759064 | − | 0.651017i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.8065 | + | 6.81650i | 0.494955 | + | 0.285762i | 0.726628 | − | 0.687031i | \(-0.241087\pi\) |
−0.231673 | + | 0.972794i | \(0.574420\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.0474 | + | 38.1873i | 0.922657 | + | 1.59809i | 0.795287 | + | 0.606233i | \(0.207320\pi\) |
0.127369 | + | 0.991855i | \(0.459347\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.6921 | + | 12.1645i | −0.571996 | + | 0.508180i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.00540i | − | 0.208739i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.06103 | + | 3.49934i | −0.252324 | + | 0.145679i | −0.620828 | − | 0.783947i | \(-0.713203\pi\) |
0.368504 | + | 0.929626i | \(0.379870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.4683 | + | 4.20859i | −0.850635 | + | 0.174903i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0203 | − | 40.2047i | −0.747608 | − | 1.66797i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.988003 | − | 1.71127i | 0.0409189 | − | 0.0708736i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.85073 | − | 13.6259i | −0.241898 | − | 0.563361i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.9161 | −1.23477 | −0.617385 | − | 0.786661i | \(-0.711808\pi\) | ||||
−0.617385 | + | 0.786661i | \(0.711808\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.30607 | −0.383450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.3408 | − | 9.41734i | −1.16579 | − | 0.387378i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.0426 | − | 20.8583i | 0.494529 | − | 0.856549i | −0.505451 | − | 0.862855i | \(-0.668674\pi\) |
0.999980 | + | 0.00630583i | \(0.00200722\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.21372 | − | 13.8633i | −0.254738 | − | 0.568340i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.992506 | − | 4.82702i | −0.0406206 | − | 0.197557i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.14773 | − | 2.97205i | 0.210331 | − | 0.121434i | −0.391134 | − | 0.920334i | \(-0.627917\pi\) |
0.601465 | + | 0.798899i | \(0.294584\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 46.9992i | − | 1.91714i | −0.284863 | − | 0.958568i | \(-0.591948\pi\) | ||
0.284863 | − | 0.958568i | \(-0.408052\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.77992 | + | 15.0112i | −0.0724839 | + | 0.611303i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.58605 | − | 7.94327i | −0.186450 | − | 0.322940i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.61387 | − | 4.97322i | −0.349626 | − | 0.201857i | 0.314894 | − | 0.949127i | \(-0.398031\pi\) |
−0.664521 | + | 0.747270i | \(0.731364\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.61589 | + | 25.9262i | 0.106001 | + | 1.05058i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.3401 | − | 14.0528i | −0.984694 | − | 0.568513i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.2739 | + | 28.1873i | 0.657298 | + | 1.13847i | 0.981312 | + | 0.192421i | \(0.0616340\pi\) |
−0.324014 | + | 0.946052i | \(0.605033\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.30015 | + | 4.84015i | 0.173399 | + | 0.195174i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.69843i | 0.309927i | 0.987920 | + | 0.154964i | \(0.0495260\pi\) | ||||
−0.987920 | + | 0.154964i | \(0.950474\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.76170 | − | 1.59447i | 0.111002 | − | 0.0640872i | −0.443471 | − | 0.896289i | \(-0.646253\pi\) |
0.554473 | + | 0.832202i | \(0.312920\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.9154 | + | 2.20205i | −1.03995 | + | 0.0883650i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −42.5400 | − | 4.36414i | −1.70433 | − | 0.174845i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.42749 | + | 7.30536i | −0.0969446 | + | 0.291748i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.1122 | 0.881673 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.97461 | 0.317464 | 0.158732 | − | 0.987322i | \(-0.449259\pi\) | ||||
0.158732 | + | 0.987322i | \(0.449259\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.2714 | − | 36.9298i | 0.487743 | − | 1.46783i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.76620 | − | 13.4515i | 0.308192 | − | 0.533805i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.8283 | + | 23.0242i | 1.02335 | + | 0.912251i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.07339 | − | 8.12966i | 0.240259 | − | 0.321604i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.7774 | − | 13.7279i | 0.939152 | − | 0.542219i | 0.0494573 | − | 0.998776i | \(-0.484251\pi\) |
0.889694 | + | 0.456557i | \(0.150917\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 29.0919i | − | 1.14727i | −0.819110 | − | 0.573637i | \(-0.805532\pi\) | ||
0.819110 | − | 0.573637i | \(-0.194468\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.67445 | + | 5.26145i | 0.184056 | + | 0.207170i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.5999 | + | 37.4122i | 0.849181 | + | 1.47082i | 0.881940 | + | 0.471361i | \(0.156237\pi\) |
−0.0327597 | + | 0.999463i | \(0.510430\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.1687 | − | 5.87089i | −0.399156 | − | 0.230453i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.5267 | − | 7.58137i | 0.412575 | − | 0.297137i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.27142 | + | 3.62080i | 0.245420 | + | 0.141693i | 0.617665 | − | 0.786441i | \(-0.288079\pi\) |
−0.372246 | + | 0.928134i | \(0.621412\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.47822 | + | 7.75651i | 0.174979 | + | 0.303072i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −48.6411 | − | 5.76750i | −1.89767 | − | 0.225012i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.29324i | 0.206196i | 0.994671 | + | 0.103098i | \(0.0328755\pi\) | ||||
−0.994671 | + | 0.103098i | \(0.967125\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.2638 | − | 24.9783i | 1.68276 | − | 0.971545i | 0.722954 | − | 0.690896i | \(-0.242784\pi\) |
0.959810 | − | 0.280649i | \(-0.0905497\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.90105 | + | 48.1534i | 0.384525 | + | 1.87012i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.04916 | + | 5.09477i | 0.273355 | + | 0.197567i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.2311 | − | 24.6490i | 0.551030 | − | 0.954411i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.67240 | − | 2.88174i | −0.335294 | − | 0.111415i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.58068 | −0.0996259 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.8855 | −0.843625 | −0.421812 | − | 0.906683i | \(-0.638606\pi\) | ||||
−0.421812 | + | 0.906683i | \(0.638606\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.70381 | + | 2.20775i | 0.181050 | + | 0.0849765i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.87236 | − | 11.9033i | 0.264126 | − | 0.457480i | −0.703208 | − | 0.710984i | \(-0.748250\pi\) |
0.967334 | + | 0.253504i | \(0.0815831\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.1113 | − | 13.0481i | 1.11719 | − | 0.500739i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.1749 | + | 4.35388i | −0.811425 | + | 0.166841i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.1547 | − | 21.4513i | 1.42169 | − | 0.820811i | 0.425243 | − | 0.905079i | \(-0.360189\pi\) |
0.996443 | + | 0.0842682i | \(0.0268552\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 15.4785i | − | 0.591401i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.0640 | + | 18.7139i | −0.803642 | + | 0.713982i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.61218 | + | 6.25649i | 0.137613 | + | 0.238353i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.5494 | − | 11.8642i | −0.781735 | − | 0.451335i | 0.0553098 | − | 0.998469i | \(-0.482385\pi\) |
−0.837045 | + | 0.547134i | \(0.815719\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.20555 | − | 10.2412i | −0.121769 | − | 0.389031i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.4544 | − | 10.0773i | −0.662085 | − | 0.382255i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.7320 | − | 18.5884i | −0.406505 | − | 0.704087i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.4348 | + | 10.1590i | −0.432503 | + | 0.384250i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.2721i | − | 0.803436i | −0.915763 | − | 0.401718i | \(-0.868413\pi\) | ||
0.915763 | − | 0.401718i | \(-0.131587\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.9633 | + | 6.32966i | −0.413488 | + | 0.238728i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.64657 | − | 1.98348i | 0.363311 | − | 0.0747021i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.9486 | + | 38.6700i | −1.05112 | + | 1.45433i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.8069 | − | 39.5026i | 0.856529 | − | 1.48355i | −0.0186897 | − | 0.999825i | \(-0.505949\pi\) |
0.875219 | − | 0.483727i | \(-0.160717\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.3252 | − | 5.72160i | 0.499733 | − | 0.214577i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.1696 | −0.530655 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.68287 | −0.249925 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.2720 | + | 6.73615i | 0.757071 | + | 0.251566i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.50850 | − | 16.4692i | 0.354607 | − | 0.614198i | −0.632443 | − | 0.774607i | \(-0.717948\pi\) |
0.987051 | + | 0.160409i | \(0.0512812\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.166370 | − | 1.62171i | 0.00619593 | − | 0.0603956i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.77457 | − | 13.4940i | −0.103187 | − | 0.501848i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.92448 | + | 2.84315i | −0.182890 | + | 0.105592i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.0540i | 1.26299i | 0.775379 | + | 0.631496i | \(0.217559\pi\) | ||||
−0.775379 | + | 0.631496i | \(0.782441\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.36126 | − | 25.3252i | 0.346714 | − | 0.937971i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.6662 | − | 20.2064i | −0.431489 | − | 0.747361i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.71837 | − | 3.87885i | −0.248148 | − | 0.143269i | 0.370768 | − | 0.928726i | \(-0.379095\pi\) |
−0.618916 | + | 0.785457i | \(0.712428\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.1243 | − | 0.0202988i | −0.447213 | − | 0.000748733i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.89973 | + | 3.40621i | 0.217319 | + | 0.125469i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.19659 | + | 7.26871i | 0.154374 | + | 0.267384i | 0.932831 | − | 0.360314i | \(-0.117331\pi\) |
−0.778457 | + | 0.627698i | \(0.783997\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.6929 | − | 21.0403i | −0.686702 | − | 0.772936i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.7540i | 0.541273i | 0.962682 | + | 0.270636i | \(0.0872341\pi\) | ||||
−0.962682 | + | 0.270636i | \(0.912766\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.24947 | + | 0.721384i | −0.0457772 | + | 0.0264295i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −40.0224 | − | 29.8994i | −1.46434 | − | 1.09396i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.78186 | − | 46.6118i | 0.174725 | − | 1.70316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.6067 | + | 35.6918i | −0.751948 | + | 1.30241i | 0.194929 | + | 0.980817i | \(0.437552\pi\) |
−0.946877 | + | 0.321595i | \(0.895781\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.17692 | − | 12.5702i | 0.152216 | − | 0.458082i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.2422 | 0.591113 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.8681 | −0.431354 | −0.215677 | − | 0.976465i | \(-0.569196\pi\) | ||||
−0.215677 | + | 0.976465i | \(0.569196\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.69613 | + | 11.1233i | −0.134161 | + | 0.403749i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.7705 | + | 30.7795i | −0.644181 | + | 1.11575i | 0.340309 | + | 0.940314i | \(0.389468\pi\) |
−0.984490 | + | 0.175441i | \(0.943865\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.65104 | − | 3.66800i | 0.0959739 | − | 0.132790i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.8004 | − | 10.3098i | −0.498956 | − | 0.372753i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.1772 | − | 21.4643i | 1.34239 | − | 0.775029i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 6.25608i | − | 0.225600i | −0.993618 | − | 0.112800i | \(-0.964018\pi\) | ||
0.993618 | − | 0.112800i | \(-0.0359820\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.6304 | + | 35.6025i | 1.13914 | + | 1.28219i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.0161 | + | 17.3483i | 0.360253 | + | 0.623977i | 0.988002 | − | 0.154439i | \(-0.0493570\pi\) |
−0.627749 | + | 0.778416i | \(0.716024\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.45160 | + | 1.41543i | 0.0880639 | + | 0.0508437i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.24474 | − | 16.0914i | 0.259904 | − | 0.577274i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.6419 | + | 6.14412i | 0.381286 | + | 0.220136i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.28663 | − | 3.96056i | −0.0818220 | − | 0.141720i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.8868 | + | 24.2457i | 0.603486 | + | 0.866469i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.2375i | 0.650925i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.27835 | + | 0.738053i | −0.0455681 | + | 0.0263088i | −0.522611 | − | 0.852571i | \(-0.675042\pi\) |
0.477043 | + | 0.878880i | \(0.341709\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.63570 | + | 32.2725i | 0.236237 | + | 1.14893i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.6794 | − | 14.1991i | 1.12639 | − | 0.504863i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.71754 | − | 8.17101i | 0.167525 | − | 0.290161i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.40232 | − | 0.798263i | −0.0852014 | − | 0.0283115i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.9470 | 0.812823 | 0.406411 | − | 0.913690i | \(-0.366780\pi\) | ||||
0.406411 | + | 0.913690i | \(0.366780\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.6493 | −1.15505 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.5553 | + | 19.1313i | −1.57428 | + | 0.675971i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.0372 | + | 19.1170i | −0.389495 | + | 0.674625i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.7332 | + | 7.75737i | 0.378295 | + | 0.273412i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.1336 | + | 3.11170i | −0.532729 | + | 0.109537i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.5613 | + | 11.2937i | −0.687739 | + | 0.397066i | −0.802764 | − | 0.596296i | \(-0.796638\pi\) |
0.115026 | + | 0.993363i | \(0.463305\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.9366i | 1.47259i | 0.676659 | + | 0.736296i | \(0.263427\pi\) | ||||
−0.676659 | + | 0.736296i | \(0.736573\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.76522 | − | 8.67573i | 0.342481 | − | 0.304271i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.1630 | + | 21.0669i | 0.426051 | + | 0.737942i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.5682 | + | 6.67892i | 0.404721 | + | 0.233666i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 38.2858 | + | 8.57161i | 1.33781 | + | 0.299516i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.447025 | − | 0.258090i | −0.0156013 | − | 0.00900741i | 0.492179 | − | 0.870494i | \(-0.336201\pi\) |
−0.507780 | + | 0.861487i | \(0.669534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.2841 | + | 17.8125i | 0.358480 | + | 0.620906i | 0.987707 | − | 0.156316i | \(-0.0499618\pi\) |
−0.629227 | + | 0.777222i | \(0.716628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.75063 | − | 1.55531i | 0.0609490 | − | 0.0541491i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 24.0587i | − | 0.836603i | −0.908308 | − | 0.418301i | \(-0.862626\pi\) | ||
0.908308 | − | 0.418301i | \(-0.137374\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.3074 | + | 22.6941i | −1.36520 | + | 0.788200i | −0.990311 | − | 0.138869i | \(-0.955653\pi\) |
−0.374891 | + | 0.927069i | \(0.622320\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.01500 | − | 0.619928i | 0.104589 | − | 0.0215051i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 39.3574 | + | 8.16117i | 1.36365 | + | 0.282768i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.25037 | − | 10.8260i | 0.216303 | − | 0.374647i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.24984 | − | 13.3158i | 0.216026 | − | 0.460262i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.8758 | −1.37666 | −0.688332 | − | 0.725395i | \(-0.741657\pi\) | ||||
−0.688332 | + | 0.725395i | \(0.741657\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.33396 | −0.114964 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 41.7198 | + | 13.8630i | 1.43691 | + | 0.477468i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.71645 | − | 9.90117i | 0.196652 | − | 0.340611i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.1404 | + | 2.47654i | 0.829474 | + | 0.0850949i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.63015 | + | 27.3820i | 0.193226 | + | 0.939748i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.6929 | + | 9.63764i | −0.572225 | + | 0.330374i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 16.9504i | − | 0.580372i | −0.956970 | − | 0.290186i | \(-0.906283\pi\) | ||
0.956970 | − | 0.290186i | \(-0.0937172\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.79349 | + | 1.16124i | 0.334930 | + | 0.0397136i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.315644 | + | 0.546711i | 0.0107822 | + | 0.0186753i | 0.871366 | − | 0.490633i | \(-0.163235\pi\) |
−0.860584 | + | 0.509309i | \(0.829901\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.59642 | − | 3.23109i | −0.190947 | − | 0.110243i | 0.401479 | − | 0.915868i | \(-0.368496\pi\) |
−0.592426 | + | 0.805625i | \(0.701830\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.0432 | + | 1.71962i | −0.580832 | + | 0.0586045i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.31821 | + | 3.64782i | 0.215074 | + | 0.124173i | 0.603667 | − | 0.797236i | \(-0.293705\pi\) |
−0.388593 | + | 0.921409i | \(0.627039\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.42089 | + | 12.8534i | 0.252318 | + | 0.437028i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.3735 | + | 20.6808i | 0.623998 | + | 0.702358i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 6.53538i | − | 0.221698i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.5697 | + | 12.4533i | −0.730861 | + | 0.421963i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.6494 | − | 28.9793i | 0.732722 | − | 0.980800i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.08214 | − | 2.41433i | −0.0365828 | − | 0.0816192i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.8442 | + | 25.7109i | −0.501253 | + | 0.868196i | 0.498746 | + | 0.866748i | \(0.333794\pi\) |
−0.999999 | + | 0.00144772i | \(0.999539\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.6801 | + | 32.1410i | −0.360230 | + | 1.08409i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.6272 | 0.728638 | 0.364319 | − | 0.931274i | \(-0.381302\pi\) | ||||
0.364319 | + | 0.931274i | \(0.381302\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.9462 | −1.00777 | −0.503884 | − | 0.863771i | \(-0.668096\pi\) | ||||
−0.503884 | + | 0.863771i | \(0.668096\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.74342 | + | 14.2750i | −0.159448 | + | 0.479849i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.89821 | − | 10.2160i | 0.198043 | − | 0.343020i | −0.749851 | − | 0.661607i | \(-0.769875\pi\) |
0.947894 | + | 0.318587i | \(0.103208\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.8082 | + | 37.5003i | 0.563728 | + | 1.25772i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.82279 | − | 8.37962i | −0.295574 | − | 0.280728i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.1876 | − | 9.34591i | 0.541697 | − | 0.312749i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 11.4723i | − | 0.383478i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.4622 | − | 32.0364i | −0.950324 | − | 1.06966i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.04855 | + | 13.9405i | 0.268434 | + | 0.464942i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.26798 | + | 4.19617i | 0.242131 | + | 0.139795i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.5267 | + | 1.86930i | −0.616530 | + | 0.0622064i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.11907 | + | 2.95550i | 0.170164 | + | 0.0982440i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.2455 | + | 24.6739i | 0.473014 | + | 0.819284i | 0.999523 | − | 0.0308855i | \(-0.00983273\pi\) |
−0.526509 | + | 0.850169i | \(0.676499\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.37028 | + | 53.7246i | −0.211289 | + | 1.78193i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.4884i | 0.480023i | 0.970770 | + | 0.240011i | \(0.0771511\pi\) | ||||
−0.970770 | + | 0.240011i | \(0.922849\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.4979 | + | 11.2571i | −0.645285 | + | 0.372555i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.665857 | + | 3.23837i | 0.0220126 | + | 0.107057i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.5728 | − | 2.41831i | −0.778442 | − | 0.0798597i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.83403 | − | 4.90869i | 0.0934861 | − | 0.161923i | −0.815490 | − | 0.578772i | \(-0.803532\pi\) |
0.908976 | + | 0.416849i | \(0.136866\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.4333 | + | 6.45748i | 0.640350 | + | 0.212781i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.7200 | 0.550346 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.85090 | 0.126617 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.729323 | − | 1.69854i | −0.0239541 | − | 0.0557873i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.51159 | + | 14.7425i | −0.279256 | + | 0.483686i | −0.971200 | − | 0.238265i | \(-0.923421\pi\) |
0.691944 | + | 0.721951i | \(0.256755\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.8496 | + | 7.21979i | −0.716092 | + | 0.236619i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 37.8974 | − | 7.79228i | 1.24071 | − | 0.255108i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.72322 | + | 3.88165i | −0.219873 | + | 0.126944i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.1936i | 0.365678i | 0.983143 | + | 0.182839i | \(0.0585287\pi\) | ||||
−0.983143 | + | 0.182839i | \(0.941471\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.2317 | + | 15.3092i | −0.562336 | + | 0.499598i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.0101 | − | 19.0700i | −0.358919 | − | 0.621665i | 0.628862 | − | 0.777517i | \(-0.283521\pi\) |
−0.987780 | + | 0.155852i | \(0.950188\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.2036 | + | 9.35513i | 0.527661 | + | 0.304645i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.0241 | + | 6.66490i | −0.391144 | + | 0.216809i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.7743 | − | 14.3035i | −0.805057 | − | 0.464800i | 0.0401795 | − | 0.999192i | \(-0.487207\pi\) |
−0.845236 | + | 0.534393i | \(0.820540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.3526 | − | 69.8927i | −1.30990 | − | 2.26881i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.8672 | − | 38.9731i | 1.42249 | − | 1.26379i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.2210i | 1.46485i | 0.680846 | + | 0.732426i | \(0.261612\pi\) | ||||
−0.680846 | + | 0.732426i | \(0.738388\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.15764 | − | 5.28716i | 0.296334 | − | 0.171089i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.0429 | − | 2.68181i | 0.421617 | − | 0.0866907i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.1908 | + | 23.9886i | 1.07179 | + | 0.774631i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.4931 | + | 19.9067i | −0.370746 | + | 0.642150i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.9625 | − | 48.8200i | −0.675506 | − | 1.57320i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.0646 | 0.388374 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.5961 | −1.75569 | −0.877846 | − | 0.478943i | \(-0.841020\pi\) | ||||
−0.877846 | + | 0.478943i | \(0.841020\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31.0267 | − | 10.3098i | −0.996722 | − | 0.331200i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.1591 | + | 21.0603i | −0.390206 | + | 0.675856i | −0.992476 | − | 0.122436i | \(-0.960929\pi\) |
0.602271 | + | 0.798292i | \(0.294263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.6600 | − | 21.8101i | 1.55997 | − | 0.699198i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.72429 | + | 8.38603i | 0.0552215 | + | 0.268568i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.94835 | + | 4.58898i | −0.254290 | + | 0.146815i | −0.621727 | − | 0.783234i | \(-0.713569\pi\) |
0.367437 | + | 0.930048i | \(0.380235\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.8523i | 0.698403i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.604246 | − | 5.09599i | 0.0192921 | − | 0.162703i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.29768 | − | 14.3720i | −0.264655 | − | 0.458396i | 0.702818 | − | 0.711369i | \(-0.251925\pi\) |
−0.967473 | + | 0.252974i | \(0.918591\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.9323 | + | 8.62114i | 0.475781 | + | 0.274692i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.6971 | + | 23.7593i | −0.340491 | + | 0.756268i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.6140 | + | 10.1694i | 0.560092 | + | 0.323369i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.44914 | − | 16.3664i | −0.300162 | − | 0.519895i | 0.676011 | − | 0.736892i | \(-0.263707\pi\) |
−0.976172 | + | 0.216996i | \(0.930374\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.27735 | − | 2.56334i | −0.0722696 | − | 0.0813450i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.84518i | 0.0901983i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.7670 | − | 7.37103i | 0.404335 | − | 0.233443i | −0.284018 | − | 0.958819i | \(-0.591667\pi\) |
0.688353 | + | 0.725376i | \(0.258334\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.69414 | − | 19.9380i | −0.0536003 | − | 0.630811i |
(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 | 420.2.bh.a.341.4 | yes | 10 | |
3.2 | odd | 2 | 420.2.bh.b.341.5 | yes | 10 | ||
5.2 | odd | 4 | 2100.2.bo.h.1349.2 | 20 | |||
5.3 | odd | 4 | 2100.2.bo.h.1349.9 | 20 | |||
5.4 | even | 2 | 2100.2.bi.k.1601.2 | 10 | |||
7.2 | even | 3 | 2940.2.d.b.881.8 | 10 | |||
7.3 | odd | 6 | 420.2.bh.b.101.5 | yes | 10 | ||
7.5 | odd | 6 | 2940.2.d.a.881.3 | 10 | |||
15.2 | even | 4 | 2100.2.bo.g.1349.6 | 20 | |||
15.8 | even | 4 | 2100.2.bo.g.1349.5 | 20 | |||
15.14 | odd | 2 | 2100.2.bi.j.1601.1 | 10 | |||
21.2 | odd | 6 | 2940.2.d.a.881.4 | 10 | |||
21.5 | even | 6 | 2940.2.d.b.881.7 | 10 | |||
21.17 | even | 6 | inner | 420.2.bh.a.101.4 | ✓ | 10 | |
35.3 | even | 12 | 2100.2.bo.g.1949.6 | 20 | |||
35.17 | even | 12 | 2100.2.bo.g.1949.5 | 20 | |||
35.24 | odd | 6 | 2100.2.bi.j.101.1 | 10 | |||
105.17 | odd | 12 | 2100.2.bo.h.1949.9 | 20 | |||
105.38 | odd | 12 | 2100.2.bo.h.1949.2 | 20 | |||
105.59 | even | 6 | 2100.2.bi.k.101.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bh.a.101.4 | ✓ | 10 | 21.17 | even | 6 | inner | |
420.2.bh.a.341.4 | yes | 10 | 1.1 | even | 1 | trivial | |
420.2.bh.b.101.5 | yes | 10 | 7.3 | odd | 6 | ||
420.2.bh.b.341.5 | yes | 10 | 3.2 | odd | 2 | ||
2100.2.bi.j.101.1 | 10 | 35.24 | odd | 6 | |||
2100.2.bi.j.1601.1 | 10 | 15.14 | odd | 2 | |||
2100.2.bi.k.101.2 | 10 | 105.59 | even | 6 | |||
2100.2.bi.k.1601.2 | 10 | 5.4 | even | 2 | |||
2100.2.bo.g.1349.5 | 20 | 15.8 | even | 4 | |||
2100.2.bo.g.1349.6 | 20 | 15.2 | even | 4 | |||
2100.2.bo.g.1949.5 | 20 | 35.17 | even | 12 | |||
2100.2.bo.g.1949.6 | 20 | 35.3 | even | 12 | |||
2100.2.bo.h.1349.2 | 20 | 5.2 | odd | 4 | |||
2100.2.bo.h.1349.9 | 20 | 5.3 | odd | 4 | |||
2100.2.bo.h.1949.2 | 20 | 105.38 | odd | 12 | |||
2100.2.bo.h.1949.9 | 20 | 105.17 | odd | 12 | |||
2940.2.d.a.881.3 | 10 | 7.5 | odd | 6 | |||
2940.2.d.a.881.4 | 10 | 21.2 | odd | 6 | |||
2940.2.d.b.881.7 | 10 | 21.5 | even | 6 | |||
2940.2.d.b.881.8 | 10 | 7.2 | even | 3 |