Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(37,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.37");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 175x^{8} + 8800x^{6} + 124623x^{4} + 498609x^{2} + 442368 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{16} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.3 | ||
Root | \(7.64342i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.37 |
Dual form | 108.6.e.a.73.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.88422 | + | 8.45972i | −0.0873716 | + | 0.151332i | −0.906399 | − | 0.422422i | \(-0.861180\pi\) |
0.819028 | + | 0.573754i | \(0.194513\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −68.3340 | − | 118.358i | −0.527099 | − | 0.912962i | −0.999501 | − | 0.0315789i | \(-0.989946\pi\) |
0.472403 | − | 0.881383i | \(-0.343387\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 326.660 | + | 565.792i | 0.813982 | + | 1.40986i | 0.910057 | + | 0.414484i | \(0.136038\pi\) |
−0.0960745 | + | 0.995374i | \(0.530629\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −125.247 | + | 216.934i | −0.205546 | + | 0.356016i | −0.950307 | − | 0.311316i | \(-0.899230\pi\) |
0.744761 | + | 0.667332i | \(0.232564\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −249.768 | −0.209611 | −0.104806 | − | 0.994493i | \(-0.533422\pi\) | ||||
−0.104806 | + | 0.994493i | \(0.533422\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1754.03 | −1.11469 | −0.557343 | − | 0.830282i | \(-0.688179\pi\) | ||||
−0.557343 | + | 0.830282i | \(0.688179\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −827.440 | + | 1433.17i | −0.326150 | + | 0.564908i | −0.981744 | − | 0.190205i | \(-0.939085\pi\) |
0.655595 | + | 0.755113i | \(0.272418\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1514.79 | + | 2623.69i | 0.484732 | + | 0.839581i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2123.96 | + | 3678.81i | 0.468977 | + | 0.812292i | 0.999371 | − | 0.0354595i | \(-0.0112895\pi\) |
−0.530394 | + | 0.847751i | \(0.677956\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4493.72 | + | 7783.34i | −0.839849 | + | 1.45466i | 0.0501712 | + | 0.998741i | \(0.484023\pi\) |
−0.890020 | + | 0.455921i | \(0.849310\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1335.03 | 0.184214 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6000.33 | −0.720561 | −0.360280 | − | 0.932844i | \(-0.617319\pi\) | ||||
−0.360280 | + | 0.932844i | \(0.617319\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5372.59 | + | 9305.61i | −0.499142 | + | 0.864540i | −1.00000 | 0.000990010i | \(-0.999685\pi\) | |
0.500857 | + | 0.865530i | \(0.333018\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5023.30 | − | 8700.62i | −0.414303 | − | 0.717594i | 0.581052 | − | 0.813867i | \(-0.302641\pi\) |
−0.995355 | + | 0.0962724i | \(0.969308\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11743.3 | + | 20340.0i | 0.775435 | + | 1.34309i | 0.934550 | + | 0.355833i | \(0.115803\pi\) |
−0.159114 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −935.582 | + | 1620.48i | −0.0556662 | + | 0.0964167i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9411.34 | −0.460216 | −0.230108 | − | 0.973165i | \(-0.573908\pi\) | ||||
−0.230108 | + | 0.973165i | \(0.573908\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6381.93 | −0.284476 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 22083.4 | − | 38249.5i | 0.825915 | − | 1.43053i | −0.0753026 | − | 0.997161i | \(-0.523992\pi\) |
0.901218 | − | 0.433366i | \(-0.142674\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11202.4 | + | 19403.2i | 0.385467 | + | 0.667649i | 0.991834 | − | 0.127536i | \(-0.0407069\pi\) |
−0.606366 | + | 0.795185i | \(0.707374\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1223.47 | − | 2119.11i | −0.0359177 | − | 0.0622113i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 18001.5 | − | 31179.5i | 0.489916 | − | 0.848560i | −0.510016 | − | 0.860165i | \(-0.670361\pi\) |
0.999933 | + | 0.0116049i | \(0.00369404\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −78538.5 | −1.84900 | −0.924499 | − | 0.381184i | \(-0.875517\pi\) | ||||
−0.924499 | + | 0.381184i | \(0.875517\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 61305.5 | 1.34646 | 0.673229 | − | 0.739434i | \(-0.264907\pi\) | ||||
0.673229 | + | 0.739434i | \(0.264907\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 44644.1 | − | 77325.8i | 0.858098 | − | 1.48627i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13745.0 | − | 23807.1i | −0.247787 | − | 0.429180i | 0.715125 | − | 0.698997i | \(-0.246370\pi\) |
−0.962911 | + | 0.269817i | \(0.913037\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −32403.2 | − | 56124.0i | −0.516289 | − | 0.894238i | −0.999821 | − | 0.0189117i | \(-0.993980\pi\) |
0.483533 | − | 0.875326i | \(-0.339353\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1219.92 | − | 2112.97i | 0.0183141 | − | 0.0317209i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 34652.4 | 0.463722 | 0.231861 | − | 0.972749i | \(-0.425518\pi\) | ||||
0.231861 | + | 0.972749i | \(0.425518\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 34234.5 | 0.433372 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8567.06 | − | 14838.6i | 0.0973919 | − | 0.168688i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8056.14 | − | 13953.6i | −0.0869356 | − | 0.150577i | 0.819279 | − | 0.573395i | \(-0.194374\pi\) |
−0.906214 | + | 0.422819i | \(0.861041\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 93469.6 | + | 161894.i | 0.911731 | + | 1.57916i | 0.811618 | + | 0.584189i | \(0.198587\pi\) |
0.100113 | + | 0.994976i | \(0.468079\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 84293.8 | − | 146001.i | 0.782893 | − | 1.35601i | −0.147357 | − | 0.989083i | \(-0.547077\pi\) |
0.930250 | − | 0.366927i | \(-0.119590\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −155131. | −1.30991 | −0.654953 | − | 0.755669i | \(-0.727312\pi\) | ||||
−0.654953 | + | 0.755669i | \(0.727312\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −115289. | −0.929439 | −0.464720 | − | 0.885458i | \(-0.653845\pi\) | ||||
−0.464720 | + | 0.885458i | \(0.653845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 62693.8 | − | 108589.i | 0.461880 | − | 0.799999i | −0.537175 | − | 0.843471i | \(-0.680509\pi\) |
0.999055 | + | 0.0434719i | \(0.0138419\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8082.80 | − | 13999.8i | −0.0569924 | − | 0.0987138i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17067.7 | + | 29562.1i | 0.110486 | + | 0.191367i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −132889. | + | 230170.i | −0.825134 | + | 1.42917i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −60120.6 | −0.344151 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17459.4 | 0.0960548 | 0.0480274 | − | 0.998846i | \(-0.484707\pi\) | ||||
0.0480274 | + | 0.998846i | \(0.484707\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14464.0 | + | 25052.4i | −0.0736395 | + | 0.127547i | −0.900494 | − | 0.434869i | \(-0.856795\pi\) |
0.826854 | + | 0.562416i | \(0.190128\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 119860. | + | 207603.i | 0.587549 | + | 1.01767i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 204277. | + | 353818.i | 0.929862 | + | 1.61057i | 0.783550 | + | 0.621329i | \(0.213407\pi\) |
0.146312 | + | 0.989239i | \(0.453260\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −144577. | + | 250415.i | −0.634693 | + | 1.09932i | 0.351888 | + | 0.936042i | \(0.385540\pi\) |
−0.986580 | + | 0.163278i | \(0.947793\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −163653. | −0.669243 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −41495.6 | −0.163901 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −169.673 | + | 293.882i | −0.000626104 | + | 0.00108444i | −0.866338 | − | 0.499458i | \(-0.833533\pi\) |
0.865712 | + | 0.500542i | \(0.166866\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −178737. | − | 309581.i | −0.637928 | − | 1.10492i | −0.985887 | − | 0.167414i | \(-0.946458\pi\) |
0.347958 | − | 0.937510i | \(-0.386875\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −43896.6 | − | 76031.1i | −0.146758 | − | 0.254192i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 376.310 | − | 651.789i | 0.00121842 | − | 0.00211037i | −0.865416 | − | 0.501055i | \(-0.832945\pi\) |
0.866634 | + | 0.498944i | \(0.166279\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 226169. | 0.687653 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −358488. | −1.05683 | −0.528416 | − | 0.848986i | \(-0.677214\pi\) | ||||
−0.528416 | + | 0.848986i | \(0.677214\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −246875. | + | 427601.i | −0.684994 | + | 1.18644i | 0.288445 | + | 0.957496i | \(0.406862\pi\) |
−0.973439 | + | 0.228948i | \(0.926472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 154273. | + | 267209.i | 0.415502 | + | 0.719670i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 83924.6 | + | 145362.i | 0.213193 | + | 0.369262i | 0.952712 | − | 0.303874i | \(-0.0982802\pi\) |
−0.739519 | + | 0.673136i | \(0.764947\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 207023. | − | 358575.i | 0.511004 | − | 0.885084i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 483862. | 1.12873 | 0.564364 | − | 0.825526i | \(-0.309122\pi\) | ||||
0.564364 | + | 0.825526i | \(0.309122\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 74732.3 | 0.169555 | 0.0847777 | − | 0.996400i | \(-0.472982\pi\) | ||||
0.0847777 | + | 0.996400i | \(0.472982\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 29306.9 | − | 50761.1i | 0.0629565 | − | 0.109044i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −81589.4 | − | 141317.i | −0.170620 | − | 0.295522i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −297130. | − | 514645.i | −0.589337 | − | 1.02076i | −0.994319 | − | 0.106437i | \(-0.966056\pi\) |
0.404983 | − | 0.914324i | \(-0.367277\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 44949.8 | − | 77855.4i | 0.0868630 | − | 0.150451i | −0.819321 | − | 0.573336i | \(-0.805649\pi\) |
0.906184 | + | 0.422885i | \(0.138982\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −425161. | −0.780527 | −0.390263 | − | 0.920703i | \(-0.627616\pi\) | ||||
−0.390263 | + | 0.920703i | \(0.627616\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 374339. | 0.670089 | 0.335044 | − | 0.942202i | \(-0.391249\pi\) | ||||
0.335044 | + | 0.942202i | \(0.391249\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 290278. | − | 502775.i | 0.494394 | − | 0.856316i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −52481.9 | − | 90901.3i | −0.0872217 | − | 0.151072i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −572971. | − | 992416.i | −0.907334 | − | 1.57155i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 82302.7 | − | 142552.i | 0.127265 | − | 0.220429i | −0.795351 | − | 0.606149i | \(-0.792714\pi\) |
0.922616 | + | 0.385720i | \(0.126047\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 98139.7 | 0.144793 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.22829e6 | 1.77073 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31282.7 | − | 54183.2i | 0.0430848 | − | 0.0746250i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 162339. | + | 281179.i | 0.218605 | + | 0.378635i | 0.954382 | − | 0.298589i | \(-0.0965160\pi\) |
−0.735777 | + | 0.677224i | \(0.763183\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −354884. | − | 614677.i | −0.457111 | − | 0.791739i | 0.541696 | − | 0.840575i | \(-0.317782\pi\) |
−0.998807 | + | 0.0488351i | \(0.984449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 126953. | − | 219889.i | 0.159976 | − | 0.277086i | −0.774884 | − | 0.632104i | \(-0.782192\pi\) |
0.934860 | + | 0.355017i | \(0.115525\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 557666. | 0.672952 | 0.336476 | − | 0.941692i | \(-0.390765\pi\) | ||||
0.336476 | + | 0.941692i | \(0.390765\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −229427. | −0.271004 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −266147. | + | 460981.i | −0.301389 | + | 0.522021i | −0.976451 | − | 0.215740i | \(-0.930784\pi\) |
0.675062 | + | 0.737761i | \(0.264117\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −332544. | − | 575984.i | −0.368814 | − | 0.638804i | 0.620567 | − | 0.784154i | \(-0.286903\pi\) |
−0.989380 | + | 0.145350i | \(0.953569\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9139.17 | − | 15829.5i | −0.00972729 | − | 0.0168482i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 219687. | − | 380508.i | 0.229119 | − | 0.396846i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 906446. | 0.908150 | 0.454075 | − | 0.890963i | \(-0.349970\pi\) | ||||
0.454075 | + | 0.890963i | \(0.349970\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.08117e6 | −1.06192 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −362420. | + | 627731.i | −0.342279 | + | 0.592844i | −0.984855 | − | 0.173377i | \(-0.944532\pi\) |
0.642577 | + | 0.766221i | \(0.277865\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 410027. | + | 710187.i | 0.379807 | + | 0.657844i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 126262. | + | 218692.i | 0.112560 | + | 0.194959i | 0.916802 | − | 0.399343i | \(-0.130762\pi\) |
−0.804242 | + | 0.594302i | \(0.797428\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 45967.1 | − | 79617.3i | 0.0402098 | − | 0.0696455i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 191107. | 0.161026 | 0.0805131 | − | 0.996754i | \(-0.474344\pi\) | ||||
0.0805131 | + | 0.996754i | \(0.474344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 86694.8 | 0.0717084 | 0.0358542 | − | 0.999357i | \(-0.488585\pi\) | ||||
0.0358542 | + | 0.999357i | \(0.488585\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −989643. | + | 1.71411e6i | −0.789127 | + | 1.36681i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −635239. | − | 1.10027e6i | −0.497437 | − | 0.861586i | 0.502559 | − | 0.864543i | \(-0.332392\pi\) |
−0.999996 | + | 0.00295734i | \(0.999059\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28414.8 | − | 49215.9i | −0.0214674 | − | 0.0371826i | 0.855092 | − | 0.518476i | \(-0.173500\pi\) |
−0.876560 | + | 0.481293i | \(0.840167\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −676798. | + | 1.17225e6i | −0.502335 | + | 0.870069i | 0.497662 | + | 0.867371i | \(0.334192\pi\) |
−0.999996 | + | 0.00269796i | \(0.999141\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.46852e6 | 1.05239 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.35747e6 | −0.956063 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −263851. | + | 457003.i | −0.179552 | + | 0.310993i | −0.941727 | − | 0.336378i | \(-0.890798\pi\) |
0.762175 | + | 0.647371i | \(0.224131\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 215720. | + | 373638.i | 0.144323 | + | 0.249975i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −207269. | − | 359000.i | −0.134077 | − | 0.232229i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −686525. | + | 1.18910e6i | −0.436757 | + | 0.756486i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −218861. | −0.134716 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.15348e6 | 0.698497 | 0.349249 | − | 0.937030i | \(-0.386437\pi\) | ||||
0.349249 | + | 0.937030i | \(0.386437\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −758833. | + | 1.31434e6i | −0.444883 | + | 0.770559i | −0.998044 | − | 0.0625148i | \(-0.980088\pi\) |
0.553161 | + | 0.833074i | \(0.313421\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 979958. | + | 1.69734e6i | 0.565388 | + | 0.979281i | 0.997013 | + | 0.0772280i | \(0.0246069\pi\) |
−0.431625 | + | 0.902053i | \(0.642060\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 916140. | + | 1.58680e6i | 0.512052 | + | 0.886899i | 0.999902 | + | 0.0139724i | \(0.00444770\pi\) |
−0.487851 | + | 0.872927i | \(0.662219\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.38763e6 | + | 2.40344e6i | −0.763477 | + | 1.32238i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 438100. | 0.233651 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −758891. | −0.398539 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.60493e6 | − | 2.77983e6i | 0.817462 | − | 1.41589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 360056. | + | 623635.i | 0.180634 | + | 0.312868i | 0.942097 | − | 0.335341i | \(-0.108852\pi\) |
−0.761462 | + | 0.648209i | \(0.775518\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 175847. | + | 304575.i | 0.0856095 | + | 0.148280i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.55433e6 | − | 2.69218e6i | 0.745537 | − | 1.29131i | −0.204406 | − | 0.978886i | \(-0.565526\pi\) |
0.949943 | − | 0.312422i | \(-0.101140\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.87168e6 | −2.73449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.04125e6 | −0.936831 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 136034. | − | 235618.i | 0.0606490 | − | 0.105047i | −0.834107 | − | 0.551603i | \(-0.814016\pi\) |
0.894756 | + | 0.446556i | \(0.147350\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.51024e6 | − | 2.61582e6i | −0.663718 | − | 1.14959i | −0.979631 | − | 0.200805i | \(-0.935644\pi\) |
0.315913 | − | 0.948788i | \(-0.397689\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 526944. | + | 912695.i | 0.225075 | + | 0.389842i | 0.956342 | − | 0.292250i | \(-0.0944038\pi\) |
−0.731267 | + | 0.682092i | \(0.761070\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 383599. | − | 664413.i | 0.161550 | − | 0.279813i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.26085e6 | 1.74486 | 0.872430 | − | 0.488739i | \(-0.162543\pi\) | ||||
0.872430 | + | 0.488739i | \(0.162543\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 600514. | 0.242524 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −299430. | + | 518628.i | −0.117642 | + | 0.203762i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 155650. | + | 269594.i | 0.0603231 | + | 0.104483i | 0.894610 | − | 0.446848i | \(-0.147454\pi\) |
−0.834287 | + | 0.551331i | \(0.814120\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 643115. | + | 1.11391e6i | 0.242579 | + | 0.420160i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.13768e6 | − | 1.97052e6i | 0.423397 | − | 0.733345i | −0.572872 | − | 0.819645i | \(-0.694171\pi\) |
0.996269 | + | 0.0862997i | \(0.0275043\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.06408e6 | −0.385585 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.28710e6 | 1.17548 | 0.587739 | − | 0.809050i | \(-0.300018\pi\) | ||||
0.587739 | + | 0.809050i | \(0.300018\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.12336e6 | − | 1.94572e6i | 0.391311 | − | 0.677770i | −0.601312 | − | 0.799014i | \(-0.705355\pi\) |
0.992623 | + | 0.121244i | \(0.0386885\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 436103. | + | 755352.i | 0.149947 | + | 0.259715i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −683723. | − | 1.18424e6i | −0.229090 | − | 0.396796i | 0.728449 | − | 0.685100i | \(-0.240242\pi\) |
−0.957539 | + | 0.288305i | \(0.906908\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 206668. | − | 357960.i | 0.0683647 | − | 0.118411i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 268535. | 0.0865982 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.52652e6 | 0.486099 | 0.243050 | − | 0.970014i | \(-0.421852\pi\) | ||||
0.243050 | + | 0.970014i | \(0.421852\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.36998e6 | − | 4.10493e6i | 0.736011 | − | 1.27481i | −0.218267 | − | 0.975889i | \(-0.570040\pi\) |
0.954278 | − | 0.298920i | \(-0.0966263\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.12565e6 | − | 1.94968e6i | −0.345255 | − | 0.597999i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.96007e6 | − | 3.39494e6i | −0.586523 | − | 1.01589i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −478468. | + | 828731.i | −0.141431 | + | 0.244966i | −0.928036 | − | 0.372491i | \(-0.878504\pi\) |
0.786605 | + | 0.617457i | \(0.211837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.03619e6 | −1.74136 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 633057. | 0.180436 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 885418. | − | 1.53359e6i | 0.246384 | − | 0.426750i | −0.716135 | − | 0.697961i | \(-0.754091\pi\) |
0.962520 | + | 0.271211i | \(0.0874241\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.54265e6 | − | 2.67194e6i | −0.424190 | − | 0.734719i | 0.572154 | − | 0.820146i | \(-0.306108\pi\) |
−0.996344 | + | 0.0854269i | \(0.972775\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −378346. | − | 655315.i | −0.101605 | − | 0.175986i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.53101e6 | − | 2.65180e6i | 0.406359 | − | 0.703834i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.16873e6 | −0.562356 | −0.281178 | − | 0.959656i | \(-0.590725\pi\) | ||||
−0.281178 | + | 0.959656i | \(0.590725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.69677e6 | 1.71651 | 0.858253 | − | 0.513226i | \(-0.171550\pi\) | ||||
0.858253 | + | 0.513226i | \(0.171550\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.45135e6 | − | 2.51382e6i | 0.363554 | − | 0.629695i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.23130e6 | + | 5.59677e6i | 0.800231 | + | 1.38604i | 0.919464 | + | 0.393175i | \(0.128623\pi\) |
−0.119232 | + | 0.992866i | \(0.538043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 877362. | + | 1.51964e6i | 0.212407 | + | 0.367900i | 0.952467 | − | 0.304640i | \(-0.0985363\pi\) |
−0.740060 | + | 0.672541i | \(0.765203\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −169250. | + | 293149.i | −0.0405162 | + | 0.0701761i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 515131. | 0.120587 | 0.0602937 | − | 0.998181i | \(-0.480796\pi\) | ||||
0.0602937 | + | 0.998181i | \(0.480796\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.02006e6 | −1.62517 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −167209. | + | 289614.i | −0.0378644 | + | 0.0655830i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.46694e6 | + | 4.27287e6i | 0.552546 | + | 0.957038i | 0.998090 | + | 0.0617782i | \(0.0196771\pi\) |
−0.445543 | + | 0.895260i | \(0.646990\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.12932e6 | + | 7.15219e6i | 0.904953 | + | 1.56742i | 0.820981 | + | 0.570956i | \(0.193427\pi\) |
0.0839718 | + | 0.996468i | \(0.473239\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.09543e6 | + | 1.89734e6i | −0.237482 | + | 0.411331i | −0.959991 | − | 0.280030i | \(-0.909655\pi\) |
0.722509 | + | 0.691362i | \(0.242989\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.29374e6 | −0.486691 | −0.243345 | − | 0.969940i | \(-0.578245\pi\) | ||||
−0.243345 | + | 0.969940i | \(0.578245\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.92046e6 | −1.03294 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.28183e6 | − | 5.68429e6i | 0.674471 | − | 1.16822i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.65698e6 | − | 4.60203e6i | −0.540324 | − | 0.935869i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 46443.2 | + | 80442.0i | 0.00924876 | + | 0.0160193i | 0.870613 | − | 0.491969i | \(-0.163723\pi\) |
−0.861364 | + | 0.507988i | \(0.830389\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 751522. | − | 1.30168e6i | 0.148108 | − | 0.256531i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 157392. | 0.0303828 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.13899e6 | −0.217620 | −0.108810 | − | 0.994063i | \(-0.534704\pi\) | ||||
−0.108810 | + | 0.994063i | \(0.534704\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.36473e6 | + | 7.55993e6i | −0.817060 | + | 1.41519i | 0.0907800 | + | 0.995871i | \(0.471064\pi\) |
−0.907840 | + | 0.419318i | \(0.862269\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −530498. | − | 918849.i | −0.0983029 | − | 0.170266i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.36685e6 | + | 9.29566e6i | 0.974605 | + | 1.68807i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 738810. | − | 1.27966e6i | 0.132825 | − | 0.230061i | −0.791939 | − | 0.610600i | \(-0.790928\pi\) |
0.924765 | + | 0.380539i | \(0.124262\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 743514. | 0.131029 | 0.0655147 | − | 0.997852i | \(-0.479131\pi\) | ||||
0.0655147 | + | 0.997852i | \(0.479131\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.82610e6 | −0.318638 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.43560e6 | + | 7.68269e6i | −0.758854 | + | 1.31437i | 0.184582 | + | 0.982817i | \(0.440907\pi\) |
−0.943435 | + | 0.331556i | \(0.892426\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.18926e6 | − | 7.25600e6i | −0.709716 | − | 1.22926i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 823419. | + | 1.42620e6i | 0.136805 | + | 0.236954i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.67214e6 | + | 1.32885e7i | −1.26238 | + | 2.18651i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.00935e6 | 0.324311 | 0.162155 | − | 0.986765i | \(-0.448155\pi\) | ||||
0.162155 | + | 0.986765i | \(0.448155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.39895e6 | 1.02295 | 0.511475 | − | 0.859298i | \(-0.329099\pi\) | ||||
0.511475 | + | 0.859298i | \(0.329099\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.12239e6 | − | 1.94403e6i | 0.176042 | − | 0.304914i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.84886e6 | + | 3.20231e6i | 0.287253 | + | 0.497536i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.34580e6 | − | 2.33100e6i | −0.205193 | − | 0.355405i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 757696. | − | 1.31237e6i | 0.114449 | − | 0.198231i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.22247e6 | −0.181245 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.26335e7 | −1.85580 | −0.927899 | − | 0.372832i | \(-0.878387\pi\) | ||||
−0.927899 | + | 0.372832i | \(0.878387\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 563096. | − | 975311.i | 0.0812066 | − | 0.140654i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.51776e6 | + | 9.55704e6i | 0.788487 | + | 1.36570i | 0.926894 | + | 0.375323i | \(0.122468\pi\) |
−0.138407 | + | 0.990375i | \(0.544198\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.72548e6 | − | 6.45273e6i | −0.522762 | − | 0.905450i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.87851e6 | + | 3.25367e6i | −0.261216 | + | 0.452440i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.08374e7 | 1.48009 | 0.740046 | − | 0.672557i | \(-0.234804\pi\) | ||||
0.740046 | + | 0.672557i | \(0.234804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.51661e6 | 0.340633 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.65688e6 | + | 2.86981e6i | −0.220303 | + | 0.381577i | −0.954900 | − | 0.296927i | \(-0.904038\pi\) |
0.734597 | + | 0.678504i | \(0.237371\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 612421. | + | 1.06074e6i | 0.0807103 | + | 0.139794i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −774757. | − | 1.34192e6i | −0.100319 | − | 0.173758i | 0.811497 | − | 0.584357i | \(-0.198653\pi\) |
−0.911816 | + | 0.410599i | \(0.865320\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.59557e6 | + | 2.76361e6i | −0.204798 | + | 0.354720i | −0.950068 | − | 0.312042i | \(-0.898987\pi\) |
0.745271 | + | 0.666762i | \(0.232320\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.01359e6 | −0.632381 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.55234e6 | 1.19446 | 0.597228 | − | 0.802072i | \(-0.296269\pi\) | ||||
0.597228 | + | 0.802072i | \(0.296269\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.42848e6 | + | 7.67035e6i | −0.544270 | + | 0.942704i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.07431e6 | − | 5.32487e6i | −0.374608 | − | 0.648840i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.64410e6 | − | 9.77587e6i | −0.676083 | − | 1.17101i | −0.976151 | − | 0.217092i | \(-0.930343\pi\) |
0.300069 | − | 0.953918i | \(-0.402990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.88210e6 | − | 1.36522e7i | 0.936168 | − | 1.62149i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.91815e6 | 0.924671 | 0.462336 | − | 0.886705i | \(-0.347012\pi\) | ||||
0.462336 | + | 0.886705i | \(0.347012\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −333449. | −0.0386133 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.60914e6 | + | 2.78711e6i | −0.183242 | + | 0.317385i | −0.942983 | − | 0.332841i | \(-0.891993\pi\) |
0.759740 | + | 0.650227i | \(0.225326\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.74304e6 | + | 6.48314e6i | 0.422706 | + | 0.732149i | 0.996203 | − | 0.0870589i | \(-0.0277468\pi\) |
−0.573497 | + | 0.819208i | \(0.694414\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.29811e6 | − | 2.24840e6i | −0.144186 | − | 0.249738i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.06061e6 | − | 8.76524e6i | 0.557483 | − | 0.965588i | −0.440223 | − | 0.897888i | \(-0.645101\pi\) |
0.997706 | − | 0.0676999i | \(-0.0215661\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.88325e6 | −0.637550 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.34715e6 | −0.467254 | −0.233627 | − | 0.972326i | \(-0.575059\pi\) | ||||
−0.233627 | + | 0.972326i | \(0.575059\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.29590e6 | − | 1.61010e7i | 0.983056 | − | 1.70270i | 0.332781 | − | 0.943004i | \(-0.392013\pi\) |
0.650275 | − | 0.759699i | \(-0.274654\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.83014e6 | − | 1.18301e7i | −0.716478 | − | 1.24098i | −0.962387 | − | 0.271683i | \(-0.912420\pi\) |
0.245909 | − | 0.969293i | \(-0.420914\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.36794e6 | − | 4.10139e6i | −0.244428 | − | 0.423361i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.44007e6 | + | 7.69043e6i | −0.454663 | + | 0.787500i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.49869e6 | 0.151038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.33121e6 | −0.333065 | −0.166532 | − | 0.986036i | \(-0.553257\pi\) | ||||
−0.166532 | + | 0.986036i | \(0.553257\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −85275.4 | + | 147701.i | −0.00839246 | + | 0.0145362i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −234358. | − | 405919.i | −0.0228839 | − | 0.0396361i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.14477e6 | + | 1.98280e6i | 0.110046 | + | 0.190604i | 0.915788 | − | 0.401661i | \(-0.131567\pi\) |
−0.805743 | + | 0.592266i | \(0.798234\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.40519e6 | − | 5.89797e6i | 0.324799 | − | 0.562568i | −0.656673 | − | 0.754176i | \(-0.728037\pi\) |
0.981472 | + | 0.191608i | \(0.0613701\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.48250e7 | 1.39231 | 0.696153 | − | 0.717894i | \(-0.254894\pi\) | ||||
0.696153 | + | 0.717894i | \(0.254894\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.88551e7 | 2.68912 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.06356e6 | + | 7.03829e6i | −0.372927 | + | 0.645928i | −0.990014 | − | 0.140966i | \(-0.954979\pi\) |
0.617088 | + | 0.786894i | \(0.288312\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −141291. | − | 244723.i | −0.0128680 | − | 0.0222880i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.07616e6 | − | 7.06011e6i | −0.365626 | − | 0.633283i | 0.623250 | − | 0.782023i | \(-0.285812\pi\) |
−0.988876 | + | 0.148739i | \(0.952478\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.37958e6 | − | 7.58565e6i | 0.389878 | − | 0.675288i | −0.602555 | − | 0.798077i | \(-0.705851\pi\) |
0.992433 | + | 0.122789i | \(0.0391839\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.34169e6 | −0.205341 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.02980e6 | −0.611827 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.31878e6 | + | 1.26765e7i | −0.627527 | + | 1.08691i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.26745e6 | − | 7.39143e6i | −0.363187 | − | 0.629058i | 0.625296 | − | 0.780387i | \(-0.284978\pi\) |
−0.988483 | + | 0.151329i | \(0.951645\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.58162e6 | − | 1.31317e7i | −0.635755 | − | 1.10116i | −0.986355 | − | 0.164635i | \(-0.947355\pi\) |
0.350599 | − | 0.936526i | \(-0.385978\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.10102e6 | + | 1.90702e6i | −0.0916473 | + | 0.158738i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.33221e7 | 1.09275 | 0.546376 | − | 0.837540i | \(-0.316007\pi\) | ||||
0.546376 | + | 0.837540i | \(0.316007\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.99094e6 | −0.324974 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.17874e6 | − | 2.04164e6i | 0.0945956 | − | 0.163844i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 981739. | + | 1.70042e6i | 0.0782169 | + | 0.135476i | 0.902481 | − | 0.430730i | \(-0.141744\pi\) |
−0.824264 | + | 0.566206i | \(0.808411\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.41230e6 | − | 2.44617e6i | −0.110908 | − | 0.192099i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.34190e6 | − | 2.32425e6i | 0.104626 | − | 0.181217i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.36605e7 | −1.81856 | −0.909282 | − | 0.416180i | \(-0.863369\pi\) | ||||
−0.909282 | + | 0.416180i | \(0.863369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.05247e7 | 0.803199 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.27743e7 | − | 2.21257e7i | 0.961145 | − | 1.66475i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.39194e6 | + | 1.45353e7i | 0.626970 | + | 1.08594i | 0.988156 | + | 0.153451i | \(0.0490386\pi\) |
−0.361186 | + | 0.932494i | \(0.617628\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.43656e6 | − | 1.28805e7i | −0.547833 | − | 0.948875i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 799317. | − | 1.38446e6i | 0.0584728 | − | 0.101278i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.89621e6 | 0.425355 | 0.212677 | − | 0.977123i | \(-0.431782\pi\) | ||||
0.212677 | + | 0.977123i | \(0.431782\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.30405e7 | −1.65065 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.43470e6 | + | 1.11452e7i | −0.454656 | + | 0.787488i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.15459e6 | + | 8.92800e6i | 0.361708 | + | 0.626496i | 0.988242 | − | 0.152898i | \(-0.0488605\pi\) |
−0.626534 | + | 0.779394i | \(0.715527\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.25466e6 | + | 2.17314e6i | 0.0868427 | + | 0.150416i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.66868e6 | + | 1.32825e7i | −0.527182 | + | 0.913106i | 0.472316 | + | 0.881429i | \(0.343418\pi\) |
−0.999498 | + | 0.0316768i | \(0.989915\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.35215e7 | 1.59513 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.97929e6 | −0.133321 | −0.0666606 | − | 0.997776i | \(-0.521234\pi\) | ||||
−0.0666606 | + | 0.997776i | \(0.521234\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.44874e7 | + | 2.50929e7i | −0.962758 | + | 1.66755i | −0.247238 | + | 0.968955i | \(0.579523\pi\) |
−0.715520 | + | 0.698592i | \(0.753810\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1657.44 | − | 2870.77i | −0.000109407 | − | 0.000189499i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.06008e7 | + | 1.83611e7i | 0.690450 | + | 1.19589i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.21827e6 | + | 9.03831e6i | −0.337619 | + | 0.584773i | −0.983984 | − | 0.178255i | \(-0.942955\pi\) |
0.646366 | + | 0.763028i | \(0.276288\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.49196e6 | 0.222947 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.51464e7 | 0.960661 | 0.480331 | − | 0.877087i | \(-0.340517\pi\) | ||||
0.480331 | + | 0.877087i | \(0.340517\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.10900e7 | + | 1.92084e7i | −0.694176 | + | 1.20235i | 0.276282 | + | 0.961077i | \(0.410898\pi\) |
−0.970458 | + | 0.241271i | \(0.922436\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.87815e6 | + | 1.36454e7i | 0.489906 | + | 0.848542i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.53175e6 | + | 9.58127e6i | 0.339527 | + | 0.588078i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.21191e6 | − | 5.56319e6i | 0.195861 | − | 0.339241i | −0.751322 | − | 0.659936i | \(-0.770583\pi\) |
0.947182 | + | 0.320695i | \(0.103917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.34346e6 | −0.141062 | −0.0705308 | − | 0.997510i | \(-0.522469\pi\) | ||||
−0.0705308 | + | 0.997510i | \(0.522469\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.72281e7 | −1.62841 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.42368e6 | − | 1.63223e7i | 0.556387 | − | 0.963690i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.56554e7 | − | 4.44365e7i | −1.50505 | − | 2.60683i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3675.97 | + | 6366.96i | 0.000212911 | + | 0.000368772i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.42540e7 | + | 2.46887e7i | −0.820354 | + | 1.42089i | 0.0850650 | + | 0.996375i | \(0.472890\pi\) |
−0.905419 | + | 0.424519i | \(0.860443\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.71365e7 | −0.973824 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.61228e6 | −0.316925 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.77498e6 | − | 6.53845e6i | 0.210508 | − | 0.364611i | −0.741366 | − | 0.671101i | \(-0.765822\pi\) |
0.951874 | + | 0.306491i | \(0.0991549\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.93310e6 | − | 5.08028e6i | −0.162540 | − | 0.281528i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.00261e7 | + | 3.46862e7i | 1.09599 | + | 1.89831i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.10466e6 | + | 1.91333e6i | −0.0600813 | + | 0.104064i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.98225e6 | −0.321361 | −0.160680 | − | 0.987006i | \(-0.551369\pi\) | ||||
−0.160680 | + | 0.987006i | \(0.551369\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.22339e6 | 0.492423 | 0.246212 | − | 0.969216i | \(-0.420814\pi\) | ||||
0.246212 | + | 0.969216i | \(0.420814\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.75093e6 | − | 3.03271e6i | 0.0923370 | − | 0.159932i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.81101e6 | + | 1.52611e7i | 0.461818 | + | 0.799892i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.48011e6 | + | 1.12239e7i | 0.335525 | + | 0.581146i | 0.983585 | − | 0.180443i | \(-0.0577531\pi\) |
−0.648061 | + | 0.761589i | \(0.724420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.76675e6 | − | 6.52421e6i | 0.193851 | − | 0.335759i | −0.752672 | − | 0.658395i | \(-0.771236\pi\) |
0.946523 | + | 0.322636i | \(0.104569\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.59694e7 | −0.811942 | −0.405971 | − | 0.913886i | \(-0.633067\pi\) | ||||
−0.405971 | + | 0.913886i | \(0.633067\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.71049e7 | −1.36981 | −0.684907 | − | 0.728631i | \(-0.740157\pi\) | ||||
−0.684907 | + | 0.728631i | \(0.740157\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 233679. | − | 404743.i | 0.0116683 | − | 0.0202100i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.41159e6 | − | 4.17699e6i | −0.119698 | − | 0.207323i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.38138e7 | + | 2.39261e7i | 0.677497 | + | 1.17346i | 0.975732 | + | 0.218967i | \(0.0702686\pi\) |
−0.298236 | + | 0.954492i | \(0.596398\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.23316e6 | − | 2.13590e6i | 0.0601216 | − | 0.104134i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.01401e6 | −0.145212 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.63233e7 | 1.73971 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.96491e6 | − | 8.59948e6i | 0.235011 | − | 0.407050i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.66982e6 | + | 1.67486e7i | 0.455036 | + | 0.788145i | 0.998690 | − | 0.0511638i | \(-0.0162931\pi\) |
−0.543654 | + | 0.839309i | \(0.682960\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.37449e7 | − | 2.38068e7i | −0.639277 | − | 1.10726i | −0.985592 | − | 0.169142i | \(-0.945900\pi\) |
0.346315 | − | 0.938118i | \(-0.387433\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.33195e6 | + | 4.03905e6i | −0.107829 | + | 0.186765i | −0.914891 | − | 0.403702i | \(-0.867723\pi\) |
0.807061 | + | 0.590467i | \(0.201057\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.10059e6 | 0.141716 | 0.0708578 | − | 0.997486i | \(-0.477426\pi\) | ||||
0.0708578 | + | 0.997486i | \(0.477426\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.63962e6 | −0.0745082 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.97993e6 | − | 1.55537e7i | 0.403388 | − | 0.698689i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.50927e6 | + | 7.81028e6i | 0.201400 | + | 0.348836i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.10829e6 | + | 7.11576e6i | 0.181401 | + | 0.314196i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.22715e6 | − | 1.42498e7i | 0.361202 | − | 0.625621i | −0.626957 | − | 0.779054i | \(-0.715700\pi\) |
0.988159 | + | 0.153433i | \(0.0490330\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.06332e6 | −0.0895626 | −0.0447813 | − | 0.998997i | \(-0.514259\pi\) | ||||
−0.0447813 | + | 0.998997i | \(0.514259\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00336e7 | −0.864683 | −0.432342 | − | 0.901710i | \(-0.642313\pi\) | ||||
−0.432342 | + | 0.901710i | \(0.642313\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.41621e7 | − | 2.45295e7i | 0.604393 | − | 1.04684i | −0.387754 | − | 0.921763i | \(-0.626749\pi\) |
0.992147 | − | 0.125077i | \(-0.0399177\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.19307e6 | − | 2.06646e6i | −0.0506304 | − | 0.0876944i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.05981e7 | − | 3.56769e7i | −0.864366 | − | 1.49713i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.36329e6 | + | 4.09334e6i | −0.0986187 | + | 0.170813i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.81779e7 | −1.57548 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.35066e6 | 0.0964666 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −365009. | + | 632214.i | −0.0148143 | + | 0.0256592i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.40375e7 | + | 2.43137e7i | 0.566593 | + | 0.981369i | 0.996899 | + | 0.0786856i | \(0.0250723\pi\) |
−0.430306 | + | 0.902683i | \(0.641594\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.35864e7 | − | 2.35324e7i | −0.542387 | − | 0.939443i | −0.998766 | − | 0.0496571i | \(-0.984187\pi\) |
0.456379 | − | 0.889786i | \(-0.349146\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.11697e7 | − | 3.66670e7i | 0.840499 | − | 1.45579i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.95354e6 | 0.155261 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.48360e7 | 1.75121 | 0.875604 | − | 0.483029i | \(-0.160464\pi\) | ||||
0.875604 | + | 0.483029i | \(0.160464\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.83670e6 | − | 1.70377e7i | 0.380054 | − | 0.658273i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.08923e6 | − | 1.57430e7i | −0.349279 | − | 0.604969i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −786592. | − | 1.36242e6i | −0.0299027 | − | 0.0517930i | 0.850687 | − | 0.525673i | \(-0.176186\pi\) |
−0.880589 | + | 0.473880i | \(0.842853\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.64104e6 | − | 2.84236e6i | 0.0620503 | − | 0.107474i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.59400e6 | 0.0596293 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.08278e6 | 0.0774986 | 0.0387493 | − | 0.999249i | \(-0.487663\pi\) | ||||
0.0387493 | + | 0.999249i | \(0.487663\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.15451e6 | + | 7.19583e6i | −0.152949 | + | 0.264915i | −0.932310 | − | 0.361659i | \(-0.882210\pi\) |
0.779361 | + | 0.626575i | \(0.215544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.89100e6 | − | 1.53997e7i | −0.325590 | − | 0.563939i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.34570e7 | + | 4.06287e7i | 0.849958 | + | 1.47217i | 0.881245 | + | 0.472659i | \(0.156706\pi\) |
−0.0312875 | + | 0.999510i | \(0.509961\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.67833e6 | + | 1.32993e7i | −0.276759 | + | 0.479360i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.19875e7 | −0.427559 | −0.213779 | − | 0.976882i | \(-0.568577\pi\) | ||||
−0.213779 | + | 0.976882i | \(0.568577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.80500e6 | 0.205965 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.79182e7 | − | 4.83557e7i | 0.980258 | − | 1.69786i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.60724e7 | − | 4.51587e7i | −0.910693 | − | 1.57737i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 439090. | + | 760525.i | 0.0151787 | + | 0.0262903i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.44190e7 | − | 2.49745e7i | 0.495872 | − | 0.858876i | −0.504116 | − | 0.863636i | \(-0.668182\pi\) |
0.999989 | + | 0.00475965i | \(0.00151505\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.30199e7 | −0.443158 | −0.221579 | − | 0.975142i | \(-0.571121\pi\) | ||||
−0.221579 | + | 0.975142i | \(0.571121\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.95182e7 | 1.33818 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.14539e6 | + | 1.58403e7i | −0.306525 | + | 0.530917i | −0.977600 | − | 0.210473i | \(-0.932500\pi\) |
0.671075 | + | 0.741390i | \(0.265833\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.13196e7 | + | 1.96061e7i | 0.377462 | + | 0.653783i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 484901. | + | 839872.i | 0.0160055 | + | 0.0277223i | 0.873917 | − | 0.486075i | \(-0.161572\pi\) |
−0.857912 | + | 0.513797i | \(0.828238\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.07658e6 | − | 3.59674e6i | 0.0681959 | − | 0.118119i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.66259e7 | 0.540500 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.04589e7 | −1.63213 | −0.816063 | − | 0.577962i | \(-0.803848\pi\) | ||||
−0.816063 | + | 0.577962i | \(0.803848\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.82835e6 | + | 3.16680e6i | −0.0585467 | + | 0.101406i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.90625e6 | − | 1.54261e7i | −0.283764 | − | 0.491493i | 0.688545 | − | 0.725194i | \(-0.258250\pi\) |
−0.972309 | + | 0.233700i | \(0.924917\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 108.6.e.a.37.3 | 10 | ||
3.2 | odd | 2 | 36.6.e.a.13.2 | ✓ | 10 | ||
4.3 | odd | 2 | 432.6.i.d.145.3 | 10 | |||
9.2 | odd | 6 | 36.6.e.a.25.2 | yes | 10 | ||
9.4 | even | 3 | 324.6.a.d.1.3 | 5 | |||
9.5 | odd | 6 | 324.6.a.e.1.3 | 5 | |||
9.7 | even | 3 | inner | 108.6.e.a.73.3 | 10 | ||
12.11 | even | 2 | 144.6.i.d.49.4 | 10 | |||
36.7 | odd | 6 | 432.6.i.d.289.3 | 10 | |||
36.11 | even | 6 | 144.6.i.d.97.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.e.a.13.2 | ✓ | 10 | 3.2 | odd | 2 | ||
36.6.e.a.25.2 | yes | 10 | 9.2 | odd | 6 | ||
108.6.e.a.37.3 | 10 | 1.1 | even | 1 | trivial | ||
108.6.e.a.73.3 | 10 | 9.7 | even | 3 | inner | ||
144.6.i.d.49.4 | 10 | 12.11 | even | 2 | |||
144.6.i.d.97.4 | 10 | 36.11 | even | 6 | |||
324.6.a.d.1.3 | 5 | 9.4 | even | 3 | |||
324.6.a.e.1.3 | 5 | 9.5 | odd | 6 | |||
432.6.i.d.145.3 | 10 | 4.3 | odd | 2 | |||
432.6.i.d.289.3 | 10 | 36.7 | odd | 6 |