Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(31,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.f (of order \(4\), 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: | \(13.2313552747\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} + \cdots + 2097152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{42} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(1.03712 - 2.63142i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.31 |
Dual form | 128.5.f.b.95.1 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −11.5209 | − | 11.5209i | −1.28010 | − | 1.28010i | −0.940612 | − | 0.339485i | \(-0.889747\pi\) |
−0.339485 | − | 0.940612i | \(-0.610253\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.6016 | + | 14.6016i | 0.584063 | + | 0.584063i | 0.936017 | − | 0.351954i | \(-0.114483\pi\) |
−0.351954 | + | 0.936017i | \(0.614483\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.0210 | −0.490224 | −0.245112 | − | 0.969495i | \(-0.578825\pi\) | ||||
−0.245112 | + | 0.969495i | \(0.578825\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 184.461i | 2.27729i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −61.7287 | + | 61.7287i | −0.510154 | + | 0.510154i | −0.914574 | − | 0.404419i | \(-0.867474\pi\) |
0.404419 | + | 0.914574i | \(0.367474\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37.5611 | − | 37.5611i | 0.222255 | − | 0.222255i | −0.587192 | − | 0.809447i | \(-0.699767\pi\) |
0.809447 | + | 0.587192i | \(0.199767\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 336.446i | − | 1.49531i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 96.8718 | 0.335197 | 0.167598 | − | 0.985855i | \(-0.446399\pi\) | ||||
0.167598 | + | 0.985855i | \(0.446399\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 156.751 | + | 156.751i | 0.434214 | + | 0.434214i | 0.890059 | − | 0.455845i | \(-0.150663\pi\) |
−0.455845 | + | 0.890059i | \(0.650663\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 276.742 | + | 276.742i | 0.627534 | + | 0.627534i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 959.783 | 1.81433 | 0.907167 | − | 0.420770i | \(-0.138240\pi\) | ||||
0.907167 | + | 0.420770i | \(0.138240\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 198.587i | − | 0.317740i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1191.96 | − | 1191.96i | 1.63506 | − | 1.63506i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 350.180 | − | 350.180i | 0.416385 | − | 0.416385i | −0.467571 | − | 0.883956i | \(-0.654871\pi\) |
0.883956 | + | 0.467571i | \(0.154871\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 237.885i | − | 0.247539i | −0.992311 | − | 0.123769i | \(-0.960502\pi\) | ||
0.992311 | − | 0.123769i | \(-0.0394983\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1422.34 | 1.30609 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −350.744 | − | 350.744i | −0.286322 | − | 0.286322i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 560.815 | + | 560.815i | 0.409653 | + | 0.409653i | 0.881617 | − | 0.471965i | \(-0.156455\pi\) |
−0.471965 | + | 0.881617i | \(0.656455\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −865.473 | −0.569016 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1802.95i | 1.07255i | 0.844044 | + | 0.536274i | \(0.180169\pi\) | ||||
−0.844044 | + | 0.536274i | \(0.819831\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −206.090 | + | 206.090i | −0.111460 | + | 0.111460i | −0.760637 | − | 0.649177i | \(-0.775113\pi\) |
0.649177 | + | 0.760637i | \(0.275113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2693.42 | + | 2693.42i | −1.33008 | + | 1.33008i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1599.92i | 0.724274i | 0.932125 | + | 0.362137i | \(0.117953\pi\) | ||||
−0.932125 | + | 0.362137i | \(0.882047\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1823.99 | −0.759681 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1116.05 | − | 1116.05i | −0.429084 | − | 0.429084i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2234.17 | + | 2234.17i | 0.795360 | + | 0.795360i | 0.982360 | − | 0.187000i | \(-0.0598765\pi\) |
−0.187000 | + | 0.982360i | \(0.559876\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1802.67 | −0.595925 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3611.82i | − | 1.11167i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2353.11 | + | 2353.11i | −0.675988 | + | 0.675988i | −0.959090 | − | 0.283102i | \(-0.908636\pi\) |
0.283102 | + | 0.959090i | \(0.408636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4443.45 | − | 4443.45i | 1.19415 | − | 1.19415i | 0.218264 | − | 0.975890i | \(-0.429961\pi\) |
0.975890 | − | 0.218264i | \(-0.0700395\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 4430.92i | − | 1.11638i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1096.90 | 0.259622 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3995.40 | + | 3995.40i | 0.890042 | + | 0.890042i | 0.994527 | − | 0.104485i | \(-0.0333193\pi\) |
−0.104485 | + | 0.994527i | \(0.533319\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11057.5 | − | 11057.5i | −2.32252 | − | 2.32252i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4929.25 | 0.977832 | 0.488916 | − | 0.872331i | \(-0.337392\pi\) | ||||
0.488916 | + | 0.872331i | \(0.337392\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2651.57i | 0.497574i | 0.968558 | + | 0.248787i | \(0.0800319\pi\) | ||||
−0.968558 | + | 0.248787i | \(0.919968\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2287.90 | + | 2287.90i | −0.406737 | + | 0.406737i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1482.78 | − | 1482.78i | 0.250090 | − | 0.250090i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8792.34i | 1.40880i | 0.709801 | + | 0.704402i | \(0.248785\pi\) | ||||
−0.709801 | + | 0.704402i | \(0.751215\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −12523.4 | −1.90877 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 228.231 | + | 228.231i | 0.0331298 | + | 0.0331298i | 0.723478 | − | 0.690348i | \(-0.242542\pi\) |
−0.690348 | + | 0.723478i | \(0.742542\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1414.48 | + | 1414.48i | 0.195776 | + | 0.195776i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8068.75 | −1.06603 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10596.7i | − | 1.33780i | −0.743353 | − | 0.668899i | \(-0.766766\pi\) | ||
0.743353 | − | 0.668899i | \(-0.233234\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −902.254 | + | 902.254i | −0.108955 | + | 0.108955i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2740.64 | + | 2740.64i | −0.316873 | + | 0.316873i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4577.63i | 0.507217i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11048.3 | 1.17422 | 0.587111 | − | 0.809506i | \(-0.300265\pi\) | ||||
0.587111 | + | 0.809506i | \(0.300265\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11386.5 | − | 11386.5i | −1.16177 | − | 1.16177i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7543.12 | + | 7543.12i | 0.739449 | + | 0.739449i | 0.972471 | − | 0.233022i | \(-0.0748615\pi\) |
−0.233022 | + | 0.972471i | \(0.574861\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6124.81 | −0.577322 | −0.288661 | − | 0.957431i | \(-0.593210\pi\) | ||||
−0.288661 | + | 0.957431i | \(0.593210\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8081.75i | 0.733039i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4636.79 | + | 4636.79i | −0.404995 | + | 0.404995i | −0.879989 | − | 0.474994i | \(-0.842450\pi\) |
0.474994 | + | 0.879989i | \(0.342450\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15235.6 | + | 15235.6i | −1.28235 | + | 1.28235i | −0.343022 | + | 0.939327i | \(0.611451\pi\) |
−0.939327 | + | 0.343022i | \(0.888549\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 12922.1i | − | 1.04879i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2902.13 | 0.227279 | 0.113639 | − | 0.993522i | \(-0.463749\pi\) | ||||
0.113639 | + | 0.993522i | \(0.463749\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14014.4 | + | 14014.4i | 1.05969 | + | 1.05969i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6928.55 | + | 6928.55i | 0.506140 | + | 0.506140i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2326.95 | −0.164321 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7020.14i | 0.479485i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20771.6 | − | 20771.6i | 1.37296 | − | 1.37296i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12025.7 | − | 12025.7i | 0.769644 | − | 0.769644i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3992.46i | 0.247533i | 0.992311 | + | 0.123766i | \(0.0394974\pi\) | ||||
−0.992311 | + | 0.123766i | \(0.960503\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4748.66 | 0.285359 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16640.1 | − | 16640.1i | −0.969645 | − | 0.969645i | 0.0299081 | − | 0.999553i | \(-0.490479\pi\) |
−0.999553 | + | 0.0299081i | \(0.990479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3765.31 | − | 3765.31i | −0.212862 | − | 0.212862i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 34808.9 | 1.90995 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10746.6i | − | 0.572573i | −0.958144 | − | 0.286286i | \(-0.907579\pi\) | ||
0.958144 | − | 0.286286i | \(-0.0924209\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7583.76 | − | 7583.76i | 0.392514 | − | 0.392514i | −0.483069 | − | 0.875582i | \(-0.660478\pi\) |
0.875582 | + | 0.483069i | \(0.160478\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18432.5 | − | 18432.5i | 0.927140 | − | 0.927140i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4637.20i | 0.226769i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10226.4 | 0.486390 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21014.0 | + | 21014.0i | 0.972464 | + | 0.972464i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3385.37 | − | 3385.37i | −0.152487 | − | 0.152487i | 0.626741 | − | 0.779228i | \(-0.284389\pi\) |
−0.779228 | + | 0.626741i | \(0.784389\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21697.8 | 0.951617 | 0.475809 | − | 0.879549i | \(-0.342155\pi\) | ||||
0.475809 | + | 0.879549i | \(0.342155\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17869.0i | 0.763341i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3473.49 | − | 3473.49i | 0.144578 | − | 0.144578i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14212.7 | + | 14212.7i | −0.576603 | + | 0.576603i | −0.933966 | − | 0.357363i | \(-0.883676\pi\) |
0.357363 | + | 0.933966i | \(0.383676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 51479.0i | − | 2.03627i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23054.9 | −0.889430 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7450.28 | + | 7450.28i | 0.280412 | + | 0.280412i | 0.833273 | − | 0.552861i | \(-0.186464\pi\) |
−0.552861 | + | 0.833273i | \(0.686464\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 20768.4 | + | 20768.4i | 0.762841 | + | 0.762841i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3997.25 | −0.143327 | −0.0716635 | − | 0.997429i | \(-0.522831\pi\) | ||||
−0.0716635 | + | 0.997429i | \(0.522831\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25739.3i | 0.901205i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −28914.4 | + | 28914.4i | −0.988832 | + | 0.988832i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16996.8 | − | 16996.8i | 0.567903 | − | 0.567903i | −0.363638 | − | 0.931540i | \(-0.618465\pi\) |
0.931540 | + | 0.363638i | \(0.118465\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4770.26i | 0.155764i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 54219.8 | 1.73066 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24121.3 | − | 24121.3i | −0.752826 | − | 0.752826i | 0.222180 | − | 0.975006i | \(-0.428683\pi\) |
−0.975006 | + | 0.222180i | \(0.928683\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13837.8 | − | 13837.8i | −0.422386 | − | 0.422386i | 0.463638 | − | 0.886025i | \(-0.346544\pi\) |
−0.886025 | + | 0.463638i | \(0.846544\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −102385. | −3.05726 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16377.6i | 0.478526i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5979.77 | + | 5979.77i | −0.171002 | + | 0.171002i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −28632.0 | + | 28632.0i | −0.801544 | + | 0.801544i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11717.4i | − | 0.321193i | −0.987020 | − | 0.160596i | \(-0.948658\pi\) | ||
0.987020 | − | 0.160596i | \(-0.0513417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −68633.2 | −1.84255 | −0.921276 | − | 0.388910i | \(-0.872852\pi\) | ||||
−0.921276 | + | 0.388910i | \(0.872852\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12637.3 | − | 12637.3i | −0.332341 | − | 0.332341i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22885.3 | + | 22885.3i | 0.589689 | + | 0.589689i | 0.937547 | − | 0.347858i | \(-0.113091\pi\) |
−0.347858 | + | 0.937547i | \(0.613091\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 59936.9 | 1.51352 | 0.756761 | − | 0.653692i | \(-0.226781\pi\) | ||||
0.756761 | + | 0.653692i | \(0.226781\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 92060.9i | − | 2.27868i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8411.65 | + | 8411.65i | −0.204122 | + | 0.204122i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26326.0 | + | 26326.0i | −0.626436 | + | 0.626436i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 177042.i | 4.13177i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −19352.1 | −0.443032 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12558.8 | + | 12558.8i | 0.282086 | + | 0.282086i | 0.833941 | − | 0.551854i | \(-0.186080\pi\) |
−0.551854 | + | 0.833941i | \(0.686080\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −56789.2 | − | 56789.2i | −1.25172 | − | 1.25172i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6018.47 | −0.130199 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5714.22i | 0.121349i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 30548.4 | − | 30548.4i | 0.636943 | − | 0.636943i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3638.61 | − | 3638.61i | 0.0744992 | − | 0.0744992i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 22761.5i | − | 0.457711i | −0.973460 | − | 0.228856i | \(-0.926502\pi\) | ||
0.973460 | − | 0.228856i | \(-0.0734983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 36631.6 | 0.723586 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6480.30 | − | 6480.30i | −0.125760 | − | 0.125760i | 0.641425 | − | 0.767186i | \(-0.278343\pi\) |
−0.767186 | + | 0.641425i | \(0.778343\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −36068.6 | − | 36068.6i | −0.687795 | − | 0.687795i | 0.273949 | − | 0.961744i | \(-0.411670\pi\) |
−0.961744 | + | 0.273949i | \(0.911670\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −34165.9 | −0.640278 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 68226.4i | − | 1.25673i | −0.777920 | − | 0.628363i | \(-0.783725\pi\) | ||
0.777920 | − | 0.628363i | \(-0.216275\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23361.4 | + | 23361.4i | −0.423022 | + | 0.423022i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 101295. | − | 101295.i | 1.80340 | − | 1.80340i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 100556.i | − | 1.76040i | −0.474599 | − | 0.880202i | \(-0.657407\pi\) | ||
0.474599 | − | 0.880202i | \(-0.342593\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −35563.1 | −0.612302 | −0.306151 | − | 0.951983i | \(-0.599041\pi\) | ||||
−0.306151 | + | 0.951983i | \(0.599041\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 47732.3 | + | 47732.3i | 0.808351 | + | 0.808351i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −26633.2 | − | 26633.2i | −0.443702 | − | 0.443702i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11775.5 | 0.193013 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 5258.84i | − | 0.0848186i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29206.3 | − | 29206.3i | 0.463585 | − | 0.463585i | −0.436244 | − | 0.899829i | \(-0.643691\pi\) |
0.899829 | + | 0.436244i | \(0.143691\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −59246.1 | + | 59246.1i | −0.925591 | + | 0.925591i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 32592.1i | − | 0.501224i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2932.77 | 0.0444029 | 0.0222015 | − | 0.999754i | \(-0.492932\pi\) | ||||
0.0222015 | + | 0.999754i | \(0.492932\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13471.3 | − | 13471.3i | −0.200821 | − | 0.200821i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 64594.4 | + | 64594.4i | 0.948230 | + | 0.948230i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23253.5 | 0.336184 | 0.168092 | − | 0.985771i | \(-0.446239\pi\) | ||||
0.168092 | + | 0.985771i | \(0.446239\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 65244.7i | 0.929081i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −122083. | + | 122083.i | −1.71251 | + | 1.71251i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −56836.3 | + | 56836.3i | −0.785455 | + | 0.785455i | −0.980745 | − | 0.195290i | \(-0.937435\pi\) |
0.195290 | + | 0.980745i | \(0.437435\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 91679.6i | 1.24834i | 0.781287 | + | 0.624172i | \(0.214564\pi\) | ||||
−0.781287 | + | 0.624172i | \(0.785436\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 20789.5 | 0.278945 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12258.5 | + | 12258.5i | 0.162096 | + | 0.162096i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 75831.0 | + | 75831.0i | 0.988297 | + | 0.988297i | 0.999932 | − | 0.0116353i | \(-0.00370370\pi\) |
−0.0116353 | + | 0.999932i | \(0.503704\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 43880.4 | 0.563718 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 77682.2i | 0.983805i | 0.870650 | + | 0.491903i | \(0.163698\pi\) | ||||
−0.870650 | + | 0.491903i | \(0.836302\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 43834.7 | − | 43834.7i | 0.547325 | − | 0.547325i | −0.378341 | − | 0.925666i | \(-0.623505\pi\) |
0.925666 | + | 0.378341i | \(0.123505\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 52738.3 | − | 52738.3i | 0.649286 | − | 0.649286i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 43308.7i | − | 0.525788i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −74136.9 | −0.887643 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −127286. | − | 127286.i | −1.50312 | − | 1.50312i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −61916.9 | − | 61916.9i | −0.721231 | − | 0.721231i | 0.247625 | − | 0.968856i | \(-0.420350\pi\) |
−0.968856 | + | 0.247625i | \(0.920350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −68718.4 | −0.789639 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 147156.i | 1.66826i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36050.5 | − | 36050.5i | 0.403245 | − | 0.403245i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4950.47 | − | 4950.47i | 0.0546404 | − | 0.0546404i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 173807.i | − | 1.89313i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 129763. | 1.39492 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 99698.5 | + | 99698.5i | 1.05782 | + | 1.05782i | 0.998223 | + | 0.0595972i | \(0.0189816\pi\) |
0.0595972 | + | 0.998223i | \(0.481018\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 70563.1 | + | 70563.1i | 0.739028 | + | 0.739028i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −127678. | −1.32006 | −0.660031 | − | 0.751238i | \(-0.729457\pi\) | ||||
−0.660031 | + | 0.751238i | \(0.729457\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24132.5i | 0.246328i | 0.992386 | + | 0.123164i | \(0.0393042\pi\) | ||||
−0.992386 | + | 0.123164i | \(0.960696\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 64698.5 | − | 64698.5i | 0.652039 | − | 0.652039i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 63739.0 | − | 63739.0i | 0.634289 | − | 0.634289i | −0.314852 | − | 0.949141i | \(-0.601955\pi\) |
0.949141 | + | 0.314852i | \(0.101955\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 43232.3i | 0.424841i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 106840. | 1.03687 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15184.8 | + | 15184.8i | 0.145547 | + | 0.145547i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7459.16 | − | 7459.16i | −0.0706193 | − | 0.0706193i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 351055. | 3.28306 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 38431.6i | − | 0.355056i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 111266. | − | 111266.i | 1.01556 | − | 1.01556i | 0.0156868 | − | 0.999877i | \(-0.495007\pi\) |
0.999877 | − | 0.0156868i | \(-0.00499346\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −103448. | + | 103448.i | −0.932899 | + | 0.932899i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 116678.i | 1.03968i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −89183.5 | −0.785280 | −0.392640 | − | 0.919692i | \(-0.628438\pi\) | ||||
−0.392640 | + | 0.919692i | \(0.628438\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −33435.0 | − | 33435.0i | −0.290939 | − | 0.290939i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14684.3 | + | 14684.3i | 0.126283 | + | 0.126283i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 101488. | 0.862637 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 322915.i | − | 2.71300i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17075.7 | − | 17075.7i | 0.141814 | − | 0.141814i | −0.632635 | − | 0.774450i | \(-0.718027\pi\) |
0.774450 | + | 0.632635i | \(0.218027\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25961.7 | − | 25961.7i | 0.213149 | − | 0.213149i | −0.592455 | − | 0.805604i | \(-0.701841\pi\) |
0.805604 | + | 0.592455i | \(0.201841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 89542.5i | − | 0.726800i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 221897. | 1.78075 | 0.890374 | − | 0.455230i | \(-0.150443\pi\) | ||||
0.890374 | + | 0.455230i | \(0.150443\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 71974.9 | + | 71974.9i | 0.571116 | + | 0.571116i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 26808.5 | + | 26808.5i | 0.210347 | + | 0.210347i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −106831. | −0.828908 | −0.414454 | − | 0.910070i | \(-0.636027\pi\) | ||||
−0.414454 | + | 0.910070i | \(0.636027\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 81179.1i | − | 0.622917i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 80878.1 | − | 80878.1i | 0.613787 | − | 0.613787i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −38717.2 | + | 38717.2i | −0.290615 | + | 0.290615i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 79074.9i | 0.587093i | 0.955945 | + | 0.293546i | \(0.0948355\pi\) | ||||
−0.955945 | + | 0.293546i | \(0.905164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −332574. | −2.44250 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −53666.8 | − | 53666.8i | −0.389904 | − | 0.389904i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 86341.4 | + | 86341.4i | 0.620585 | + | 0.620585i | 0.945681 | − | 0.325096i | \(-0.105397\pi\) |
−0.325096 | + | 0.945681i | \(0.605397\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −277093. | −1.97044 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 26306.3i | − | 0.185087i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −168223. | + | 168223.i | −1.17114 | + | 1.17114i | −0.189199 | + | 0.981939i | \(0.560589\pi\) |
−0.981939 | + | 0.189199i | \(0.939411\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 45996.6 | − | 45996.6i | 0.316866 | − | 0.316866i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22177.8i | 0.151189i | 0.997139 | + | 0.0755946i | \(0.0240855\pi\) | ||||
−0.997139 | + | 0.0755946i | \(0.975915\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 43301.9 | 0.292137 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −38015.4 | − | 38015.4i | −0.253827 | − | 0.253827i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −163109. | − | 163109.i | −1.07790 | − | 1.07790i | −0.996698 | − | 0.0812004i | \(-0.974125\pi\) |
−0.0812004 | − | 0.996698i | \(-0.525875\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 92975.9 | 0.608159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 383416.i | 2.48248i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −128382. | + | 128382.i | −0.822831 | + | 0.822831i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −110463. | + | 110463.i | −0.700868 | + | 0.700868i | −0.964597 | − | 0.263729i | \(-0.915047\pi\) |
0.263729 | + | 0.964597i | \(0.415047\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 86759.4i | 0.544968i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 43913.8 | 0.273094 | 0.136547 | − | 0.990634i | \(-0.456399\pi\) | ||||
0.136547 | + | 0.990634i | \(0.456399\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8935.22 | − | 8935.22i | −0.0550168 | − | 0.0550168i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −182862. | − | 182862.i | −1.11484 | − | 1.11484i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −69236.7 | −0.417972 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 188666.i | 1.12784i | 0.825830 | + | 0.563919i | \(0.190707\pi\) | ||||
−0.825830 | + | 0.563919i | \(0.809293\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −123810. | + | 123810.i | −0.732948 | + | 0.732948i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 56524.0 | − | 56524.0i | 0.331385 | − | 0.331385i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6665.07i | 0.0386998i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −174743. | −1.00491 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 88556.3 | + | 88556.3i | 0.504419 | + | 0.504419i | 0.912808 | − | 0.408389i | \(-0.133909\pi\) |
−0.408389 | + | 0.912808i | \(0.633909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 42983.4 | + | 42983.4i | 0.242514 | + | 0.242514i | 0.817889 | − | 0.575375i | \(-0.195144\pi\) |
−0.575375 | + | 0.817889i | \(0.695144\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −295123. | −1.64938 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 19237.5i | − | 0.106505i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −106736. | + | 106736.i | −0.585403 | + | 0.585403i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 53424.5 | − | 53424.5i | 0.290286 | − | 0.290286i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 163696.i | − | 0.881219i | −0.897699 | − | 0.440609i | \(-0.854762\pi\) | ||
0.897699 | − | 0.440609i | \(-0.145238\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 49710.2 | 0.265137 | 0.132568 | − | 0.991174i | \(-0.457678\pi\) | ||||
0.132568 | + | 0.991174i | \(0.457678\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −117816. | − | 117816.i | −0.622626 | − | 0.622626i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 150447. | + | 150447.i | 0.787809 | + | 0.787809i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 182166. | 0.945233 | 0.472617 | − | 0.881268i | \(-0.343310\pi\) | ||||
0.472617 | + | 0.881268i | \(0.343310\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 336455.i | − | 1.73002i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3141.28 | − | 3141.28i | 0.0160066 | − | 0.0160066i | −0.699058 | − | 0.715065i | \(-0.746397\pi\) |
0.715065 | + | 0.699058i | \(0.246397\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 154729. | − | 154729.i | 0.781359 | − | 0.781359i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 78004.9i | 0.390397i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −108328. | −0.537341 | −0.268670 | − | 0.963232i | \(-0.586584\pi\) | ||||
−0.268670 | + | 0.963232i | \(0.586584\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −111294. | − | 111294.i | −0.547165 | − | 0.547165i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −249978. | − | 249978.i | −1.21816 | − | 1.21816i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −26348.7 | −0.127273 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 220908.i | − | 1.05774i | −0.848703 | − | 0.528870i | \(-0.822616\pi\) | ||
0.848703 | − | 0.528870i | \(-0.177384\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 115467. | − | 115467.i | 0.548066 | − | 0.548066i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 137539. | − | 137539.i | 0.647176 | − | 0.647176i | −0.305133 | − | 0.952310i | \(-0.598701\pi\) |
0.952310 | + | 0.305133i | \(0.0987010\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 53332.6i | 0.248789i | 0.992233 | + | 0.124394i | \(0.0396988\pi\) | ||||
−0.992233 | + | 0.124394i | \(0.960301\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −80035.3 | −0.370148 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 207164. | + | 207164.i | 0.949908 | + | 0.949908i | 0.998804 | − | 0.0488961i | \(-0.0155703\pi\) |
−0.0488961 | + | 0.998804i | \(0.515570\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −95973.3 | − | 95973.3i | −0.436320 | − | 0.436320i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 327485. | 1.47622 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 25443.3i | − | 0.113724i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31128.8 | − | 31128.8i | 0.137967 | − | 0.137967i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −412116. | + | 412116.i | −1.81127 | + | 1.81127i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 269434.i | 1.17430i | 0.809477 | + | 0.587152i | \(0.199751\pi\) | ||||
−0.809477 | + | 0.587152i | \(0.800249\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42129.6 | 0.182095 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 265613. | + | 265613.i | 1.13856 | + | 1.13856i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 161322. | + | 161322.i | 0.685821 | + | 0.685821i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −114893. | −0.484436 | −0.242218 | − | 0.970222i | \(-0.577875\pi\) | ||||
−0.242218 | + | 0.970222i | \(0.577875\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 171667.i | − | 0.717910i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −83485.8 | + | 83485.8i | −0.346298 | + | 0.346298i | −0.858728 | − | 0.512431i | \(-0.828745\pi\) |
0.512431 | + | 0.858728i | \(0.328745\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33922.5 | − | 33922.5i | 0.139571 | − | 0.139571i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 332522.i | − | 1.35710i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −118405. | −0.479356 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8291.04 | + | 8291.04i | 0.0332972 | + | 0.0332972i | 0.723559 | − | 0.690262i | \(-0.242505\pi\) |
−0.690262 | + | 0.723559i | \(0.742505\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 46051.8 | + | 46051.8i | 0.183472 | + | 0.183472i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 302384. | 1.19515 | 0.597575 | − | 0.801813i | \(-0.296131\pi\) | ||||
0.597575 | + | 0.801813i | \(0.296131\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 220283.i | 0.863770i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 296539. | − | 296539.i | 1.15363 | − | 1.15363i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41954.6 | − | 41954.6i | 0.161936 | − | 0.161936i | −0.621488 | − | 0.783424i | \(-0.713471\pi\) |
0.783424 | + | 0.621488i | \(0.213471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 63693.3i | − | 0.243923i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 373681. | 1.41993 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −89431.9 | − | 89431.9i | −0.337193 | − | 0.337193i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −98761.0 | − | 98761.0i | −0.369492 | − | 0.369492i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −391635. | −1.45394 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 16852.7i | − | 0.0620860i | −0.999518 | − | 0.0310430i | \(-0.990117\pi\) | ||
0.999518 | − | 0.0310430i | \(-0.00988289\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 92911.9 | − | 92911.9i | 0.339678 | − | 0.339678i | −0.516568 | − | 0.856246i | \(-0.672791\pi\) |
0.856246 | + | 0.516568i | \(0.172791\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 54957.5 | − | 54957.5i | 0.199392 | − | 0.199392i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 23044.3i | − | 0.0829741i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 641343. | 2.29181 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −434057. | − | 434057.i | −1.53942 | − | 1.53942i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 67720.9 | + | 67720.9i | 0.238379 | + | 0.238379i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −135409. | −0.473086 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 555796.i | 1.92738i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 112593. | − | 112593.i | 0.387554 | − | 0.387554i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40690.8 | − | 40690.8i | 0.139028 | − | 0.139028i | −0.634168 | − | 0.773196i | \(-0.718657\pi\) |
0.773196 | + | 0.634168i | \(0.218657\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 318847.i | 1.08139i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −444928. | −1.49795 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −222264. | − | 222264.i | −0.742839 | − | 0.742839i | 0.230284 | − | 0.973123i | \(-0.426034\pi\) |
−0.973123 | + | 0.230284i | \(0.926034\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 819641. | + | 819641.i | 2.71944 | + | 2.71944i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 109782. | 0.361600 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 211201.i | − | 0.690629i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 188684. | − | 188684.i | 0.612560 | − | 0.612560i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −223795. | + | 223795.i | −0.721341 | + | 0.721341i | −0.968878 | − | 0.247537i | \(-0.920379\pi\) |
0.247537 | + | 0.968878i | \(0.420379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15481.9i | 0.0495451i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 137784. | 0.437798 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −201474. | − | 201474.i | −0.635626 | − | 0.635626i | 0.313847 | − | 0.949474i | \(-0.398382\pi\) |
−0.949474 | + | 0.313847i | \(0.898382\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 42375.6 | + | 42375.6i | 0.132745 | + | 0.132745i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 300825. | 0.935724 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 473995.i | 1.46403i | 0.681289 | + | 0.732014i | \(0.261420\pi\) | ||||
−0.681289 | + | 0.732014i | \(0.738580\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −303262. | + | 303262.i | −0.930133 | + | 0.930133i | −0.997714 | − | 0.0675806i | \(-0.978472\pi\) |
0.0675806 | + | 0.997714i | \(0.478472\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −134995. | + | 134995.i | −0.411158 | + | 0.411158i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 190601.i | − | 0.576486i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −340809. | −1.02367 | −0.511834 | − | 0.859084i | \(-0.671034\pi\) | ||||
−0.511834 | + | 0.859084i | \(0.671034\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 790714. | + | 790714.i | 2.35864 | + | 2.35864i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5482.33 | − | 5482.33i | −0.0162410 | − | 0.0162410i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −275824. | −0.811512 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 202336.i | 0.591236i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 253433. | − | 253433.i | 0.735507 | − | 0.735507i | −0.236198 | − | 0.971705i | \(-0.575901\pi\) |
0.971705 | + | 0.236198i | \(0.0759014\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37288.7 | − | 37288.7i | 0.107485 | − | 0.107485i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 527316.i | − | 1.50972i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 117236. | 0.333390 | 0.166695 | − | 0.986009i | \(-0.446691\pi\) | ||||
0.166695 | + | 0.986009i | \(0.446691\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −33977.2 | − | 33977.2i | −0.0959741 | − | 0.0959741i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −690526. | − | 690526.i | −1.93745 | − | 1.93745i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 277087. | 0.772257 | 0.386129 | − | 0.922445i | \(-0.373812\pi\) | ||||
0.386129 | + | 0.922445i | \(0.373812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 323876.i | − | 0.896665i | −0.893867 | − | 0.448333i | \(-0.852018\pi\) | ||
0.893867 | − | 0.448333i | \(-0.147982\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −736994. | + | 736994.i | −2.02689 | + | 2.02689i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −102505. | + | 102505.i | −0.280050 | + | 0.280050i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 715467.i | − | 1.94184i | −0.239414 | − | 0.970918i | \(-0.576955\pi\) | ||
0.239414 | − | 0.970918i | \(-0.423045\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 193819. | 0.522591 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 60094.8 | + | 60094.8i | 0.160974 | + | 0.160974i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −137200. | − | 137200.i | −0.365117 | − | 0.365117i | 0.500576 | − | 0.865693i | \(-0.333122\pi\) |
−0.865693 | + | 0.500576i | \(0.833122\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 606596. | 1.60380 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 106650.i | − | 0.280149i | −0.990141 | − | 0.140074i | \(-0.955266\pi\) | ||
0.990141 | − | 0.140074i | \(-0.0447342\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 373667. | − | 373667.i | 0.975221 | − | 0.975221i | −0.0244790 | − | 0.999700i | \(-0.507793\pi\) |
0.999700 | + | 0.0244790i | \(0.00779267\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.14402e6 | − | 1.14402e6i | 2.96654 | − | 2.96654i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 254543.i | 0.655820i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 227071. | 0.581302 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 222953. | + | 222953.i | 0.567124 | + | 0.567124i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 54327.1 | + | 54327.1i | 0.137314 | + | 0.137314i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −445762. | −1.11955 | −0.559777 | − | 0.828644i | \(-0.689113\pi\) | ||||
−0.559777 | + | 0.828644i | \(0.689113\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 289376.i | − | 0.722195i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −58296.2 | + | 58296.2i | −0.144575 | + | 0.144575i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −68511.2 | + | 68511.2i | −0.168843 | + | 0.168843i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 909253.i | 2.22681i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −412550. | −1.00406 | −0.502031 | − | 0.864850i | \(-0.667414\pi\) | ||||
−0.502031 | + | 0.864850i | \(0.667414\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 71290.0 | + | 71290.0i | 0.172428 | + | 0.172428i | 0.788045 | − | 0.615617i | \(-0.211093\pi\) |
−0.615617 | + | 0.788045i | \(0.711093\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 69338.0 | + | 69338.0i | 0.166668 | + | 0.166668i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 138722. | 0.331388 | 0.165694 | − | 0.986177i | \(-0.447014\pi\) | ||||
0.165694 | + | 0.986177i | \(0.447014\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 290509.i | − | 0.689716i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 65832.7 | − | 65832.7i | 0.155339 | − | 0.155339i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −467444. | + | 467444.i | −1.09623 | + | 1.09623i | −0.101387 | + | 0.994847i | \(0.532328\pi\) |
−0.994847 | + | 0.101387i | \(0.967672\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 485943.i | − | 1.13267i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −489111. | −1.13312 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −180573. | − | 180573.i | −0.415797 | − | 0.415797i | 0.467955 | − | 0.883752i | \(-0.344991\pi\) |
−0.883752 | + | 0.467955i | \(0.844991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −142726. | − | 142726.i | −0.326664 | − | 0.326664i | 0.524652 | − | 0.851317i | \(-0.324195\pi\) |
−0.851317 | + | 0.524652i | \(0.824195\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −83840.0 | −0.190732 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 109959.i | − | 0.248650i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 336097. | − | 336097.i | 0.755462 | − | 0.755462i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −262232. | + | 262232.i | −0.585914 | + | 0.585914i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 548576.i | 1.21841i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −272445. | −0.601517 | −0.300759 | − | 0.953700i | \(-0.597240\pi\) | ||||
−0.300759 | + | 0.953700i | \(0.597240\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −236708. | − | 236708.i | −0.519523 | − | 0.519523i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −285404. | − | 285404.i | −0.622706 | − | 0.622706i | 0.323517 | − | 0.946222i | \(-0.395135\pi\) |
−0.946222 | + | 0.323517i | \(0.895135\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −265390. | −0.575632 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 149317.i | 0.321970i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −186551. | + | 186551.i | −0.399904 | + | 0.399904i | −0.878199 | − | 0.478295i | \(-0.841255\pi\) |
0.478295 | + | 0.878199i | \(0.341255\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 156918. | − | 156918.i | 0.334419 | − | 0.334419i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 831084.i | 1.76089i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 167836. | 0.353546 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −544261. | − | 544261.i | −1.13986 | − | 1.13986i | −0.988475 | − | 0.151383i | \(-0.951627\pi\) |
−0.151383 | − | 0.988475i | \(-0.548373\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 273515. | + | 273515.i | 0.569528 | + | 0.569528i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 221470. | 0.458506 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 174655.i | 0.359514i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −786027. | + | 786027.i | −1.60873 | + | 1.60873i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 69213.2 | − | 69213.2i | 0.140849 | − | 0.140849i | −0.633167 | − | 0.774015i | \(-0.718245\pi\) |
0.774015 | + | 0.633167i | \(0.218245\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 175817.i | 0.355754i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 538287. | 1.08302 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −181193. | − | 181193.i | −0.362496 | − | 0.362496i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −133745. | − | 133745.i | −0.266063 | − | 0.266063i | 0.561448 | − | 0.827512i | \(-0.310244\pi\) |
−0.827512 | + | 0.561448i | \(0.810244\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.62184e6 | −3.20826 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 228318.i | − | 0.449118i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −67710.4 | + | 67710.4i | −0.132447 | + | 0.132447i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.15849e6 | + | 1.15849e6i | −2.25349 | + | 2.25349i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 762270.i | − | 1.47452i | −0.675609 | − | 0.737261i | \(-0.736119\pi\) | ||
0.675609 | − | 0.737261i | \(-0.263881\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 147124. | 0.283017 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 409718. | + | 409718.i | 0.783805 | + | 0.783805i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −69541.2 | − | 69541.2i | −0.132302 | − | 0.132302i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −664888. | −1.25800 | −0.628999 | − | 0.777406i | \(-0.716535\pi\) | ||||
−0.628999 | + | 0.777406i | \(0.716535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 85436.8i | − | 0.160764i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19964.3 | + | 19964.3i | −0.0373610 | + | 0.0373610i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 616942. | − | 616942.i | 1.14825 | − | 1.14825i | 0.161352 | − | 0.986897i | \(-0.448414\pi\) |
0.986897 | − | 0.161352i | \(-0.0515856\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 613675.i | 1.13596i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −493261. | −0.908117 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 204895. | + | 204895.i | 0.375182 | + | 0.375182i | 0.869360 | − | 0.494179i | \(-0.164531\pi\) |
−0.494179 | + | 0.869360i | \(0.664531\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −135664. | − | 135664.i | −0.247075 | − | 0.247075i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 183598. | 0.332576 | 0.166288 | − | 0.986077i | \(-0.446822\pi\) | ||||
0.166288 | + | 0.986077i | \(0.446822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 98863.7i | − | 0.178125i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −42099.7 | + | 42099.7i | −0.0754462 | + | 0.0754462i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 111380. | − | 111380.i | 0.198538 | − | 0.198538i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 167996.i | − | 0.297864i | −0.988847 | − | 0.148932i | \(-0.952416\pi\) | ||
0.988847 | − | 0.148932i | \(-0.0475836\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −672964. | −1.18687 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 316823. | + | 316823.i | 0.555805 | + | 0.555805i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 414105. | + | 414105.i | 0.722634 | + | 0.722634i | 0.969141 | − | 0.246507i | \(-0.0792828\pi\) |
−0.246507 | + | 0.969141i | \(0.579283\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.36513e6 | 2.36969 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 315375.i | − | 0.544575i | −0.962216 | − | 0.272287i | \(-0.912220\pi\) | ||
0.962216 | − | 0.272287i | \(-0.0877801\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 365974. | − | 365974.i | 0.628638 | − | 0.628638i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −260916. | + | 260916.i | −0.445839 | + | 0.445839i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 176771.i | 0.300483i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 156016. | 0.263825 | 0.131913 | − | 0.991261i | \(-0.457888\pi\) | ||||
0.131913 | + | 0.991261i | \(0.457888\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33788.0 | − | 33788.0i | −0.0568400 | − | 0.0568400i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 151026. | + | 151026.i | 0.252751 | + | 0.252751i | 0.822098 | − | 0.569347i | \(-0.192804\pi\) |
−0.569347 | + | 0.822098i | \(0.692804\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47240.9 | −0.0786529 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 310402.i | 0.514142i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −282615. | + | 282615.i | −0.465715 | + | 0.465715i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −304276. | + | 304276.i | −0.498845 | + | 0.498845i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 834798.i | − | 1.36163i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −415056. | −0.673546 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −95574.5 | − | 95574.5i | −0.154310 | − | 0.154310i | 0.625730 | − | 0.780040i | \(-0.284801\pi\) |
−0.780040 | + | 0.625730i | \(0.784801\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −267901. | − | 267901.i | −0.430348 | − | 0.430348i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −69711.8 | −0.111418 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 333802.i | − | 0.530814i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 751676. | − | 751676.i | 1.18931 | − | 1.18931i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 497721. | − | 497721.i | 0.783555 | − | 0.783555i | −0.196874 | − | 0.980429i | \(-0.563079\pi\) |
0.980429 | + | 0.196874i | \(0.0630790\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 154987.i | 0.242774i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.95467e6 | 3.04656 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −163678. | − | 163678.i | −0.253840 | − | 0.253840i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −336638. | − | 336638.i | −0.519484 | − | 0.519484i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.30961e6 | 2.01092 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 363878.i | 0.555979i | 0.960584 | + | 0.277990i | \(0.0896681\pi\) | ||||
−0.960584 | + | 0.277990i | \(0.910332\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53046.1 | − | 53046.1i | 0.0806513 | − | 0.0806513i | −0.665630 | − | 0.746282i | \(-0.731837\pi\) |
0.746282 | + | 0.665630i | \(0.231837\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.05623e6 | − | 1.05623e6i | 1.59800 | − | 1.59800i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 217572.i | 0.327557i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −64609.6 | −0.0967950 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −166430. | − | 166430.i | −0.248122 | − | 0.248122i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 540562. | + | 540562.i | 0.801972 | + | 0.801972i | 0.983404 | − | 0.181432i | \(-0.0580731\pi\) |
−0.181432 | + | 0.983404i | \(0.558073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 956590. | 1.41230 | 0.706148 | − | 0.708064i | \(-0.250431\pi\) | ||||
0.706148 | + | 0.708064i | \(0.250431\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 282458.i | − | 0.414998i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 83207.7 | − | 83207.7i | 0.121661 | − | 0.121661i | −0.643655 | − | 0.765316i | \(-0.722583\pi\) |
0.765316 | + | 0.643655i | \(0.222583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 673529. | − | 673529.i | 0.980048 | − | 0.980048i | −0.0197565 | − | 0.999805i | \(-0.506289\pi\) |
0.999805 | + | 0.0197565i | \(0.00628909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1.74728e6i | − | 2.53023i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −176694. | −0.254642 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −58366.2 | − | 58366.2i | −0.0837121 | − | 0.0837121i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −283548. | − | 283548.i | −0.404740 | − | 0.404740i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −488503. | −0.693975 | −0.346987 | − | 0.937870i | \(-0.612795\pi\) | ||||
−0.346987 | + | 0.937870i | \(0.612795\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 462029.i | 0.653247i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 894967. | − | 894967.i | 1.25937 | − | 1.25937i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −375835. | + | 375835.i | −0.526361 | + | 0.526361i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 168631.i | − | 0.235055i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.01003e6 | −1.40126 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 538260. | + | 538260.i | 0.743247 | + | 0.743247i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 462565. | + | 462565.i | 0.635733 | + | 0.635733i | 0.949500 | − | 0.313767i | \(-0.101591\pi\) |
−0.313767 | + | 0.949500i | \(0.601591\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −844393. | −1.15508 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.08100e6i | 1.47185i | 0.677064 | + | 0.735924i | \(0.263252\pi\) | ||||
−0.677064 | + | 0.735924i | \(0.736748\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −911196. | + | 911196.i | −1.23488 | + | 1.23488i | −0.272816 | + | 0.962066i | \(0.587955\pi\) |
−0.962066 | + | 0.272816i | \(0.912045\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −498953. | + | 498953.i | −0.673060 | + | 0.673060i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35108.9i | 0.0471406i | 0.999722 | + | 0.0235703i | \(0.00750335\pi\) | ||||
−0.999722 | + | 0.0235703i | \(0.992497\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 496359. | 0.663382 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 854121. | + | 854121.i | 1.13627 | + | 1.13627i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −542740. | − | 542740.i | −0.718707 | − | 0.718707i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 300143. | 0.395633 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.03797e6i | 2.67405i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −288868. | + | 288868.i | −0.377298 | + | 0.377298i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −134545. | + | 134545.i | −0.174931 | + | 0.174931i | −0.789142 | − | 0.614211i | \(-0.789474\pi\) |
0.614211 | + | 0.789142i | \(0.289474\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.42667e6i | 1.84649i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.27287e6 | 1.63995 | 0.819975 | − | 0.572399i | \(-0.193987\pi\) | ||||
0.819975 | + | 0.572399i | \(0.193987\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −484264. | − | 484264.i | −0.621098 | − | 0.621098i | 0.324714 | − | 0.945812i | \(-0.394732\pi\) |
−0.945812 | + | 0.324714i | \(0.894732\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 791695. | + | 791695.i | 1.01081 | + | 1.01081i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −66348.3 | −0.0843301 | −0.0421650 | − | 0.999111i | \(-0.513426\pi\) | ||||
−0.0421650 | + | 0.999111i | \(0.513426\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 95902.7i | − | 0.121347i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 773055. | − | 773055.i | 0.973767 | − | 0.973767i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −250790. | + | 250790.i | −0.314490 | + | 0.314490i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 704418.i | − | 0.879396i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −830667. | −1.03239 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −83302.4 | − | 83302.4i | −0.103071 | − | 0.103071i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 216428. | + | 216428.i | 0.266602 | + | 0.266602i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −114067. | −0.139890 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 404107.i | − | 0.493401i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −846133. | + | 846133.i | −1.02855 | + | 1.02855i | −0.0289661 | + | 0.999580i | \(0.509221\pi\) |
−0.999580 | + | 0.0289661i | \(0.990779\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.39141e6 | + | 1.39141e6i | −1.68394 | + | 1.68394i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 133938.i | − | 0.161386i | −0.996739 | − | 0.0806932i | \(-0.974287\pi\) | ||
0.996739 | − | 0.0806932i | \(-0.0257134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28176.8 | −0.0338026 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.49498e6 | − | 1.49498e6i | −1.78564 | − | 1.78564i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 399711. | + | 399711.i | 0.475343 | + | 0.475343i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −469228. | −0.555589 | −0.277794 | − | 0.960641i | \(-0.589603\pi\) | ||||
−0.277794 | + | 0.960641i | \(0.589603\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 2.29723e6i | − | 2.70822i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 185148. | − | 185148.i | 0.217328 | − | 0.217328i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 111371. | − | 111371.i | 0.130163 | − | 0.130163i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1.12979e6i | − | 1.31473i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 728330. | 0.843911 | 0.421955 | − | 0.906617i | \(-0.361344\pi\) | ||||
0.421955 | + | 0.906617i | \(0.361344\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −285913. | − | 285913.i | −0.329864 | − | 0.329864i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.47096e6 | + | 1.47096e6i | 1.68981 | + | 1.68981i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −174628. | −0.199752 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 572084.i | − | 0.651599i | −0.945439 | − | 0.325800i | \(-0.894366\pi\) | ||
0.945439 | − | 0.325800i | \(-0.105634\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 278028. | − | 278028.i | 0.315324 | − | 0.315324i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 270062. | − | 270062.i | 0.304989 | − | 0.304989i | −0.537973 | − | 0.842962i | \(-0.680810\pi\) |
0.842962 | + | 0.537973i | \(0.180810\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.73044e6i | 1.94596i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −836144. | −0.936305 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 803359. | + | 803359.i | 0.895797 | + | 0.895797i | 0.995061 | − | 0.0992642i | \(-0.0316489\pi\) |
−0.0992642 | + | 0.995061i | \(0.531649\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 99596.1 | + | 99596.1i | 0.110588 | + | 0.110588i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.46866e6 | −1.62390 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 188445.i | − | 0.207491i | −0.994604 | − | 0.103746i | \(-0.966917\pi\) | ||
0.994604 | − | 0.103746i | \(-0.0330827\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 171093. | − | 171093.i | 0.187597 | − | 0.187597i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 498073. | − | 498073.i | 0.543837 | − | 0.543837i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 258144.i | 0.280689i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 866932. | 0.938725 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −855306. | − | 855306.i | −0.922293 | − | 0.922293i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.00215e6 | − | 1.00215e6i | −1.07617 | − | 1.07617i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.17554e6 | 1.25715 | 0.628573 | − | 0.777751i | \(-0.283639\pi\) | ||||
0.628573 | + | 0.777751i | \(0.283639\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 349883.i | − | 0.372628i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 784226. | − | 784226.i | 0.831769 | − | 0.831769i | −0.155989 | − | 0.987759i | \(-0.549857\pi\) |
0.987759 | + | 0.155989i | \(0.0498565\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −182169. | + | 182169.i | −0.192420 | + | 0.192420i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 171872.i | 0.180799i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 710097. | 0.743924 | 0.371962 | − | 0.928248i | \(-0.378685\pi\) | ||||
0.371962 | + | 0.928248i | \(0.378685\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 654120. | + | 654120.i | 0.682483 | + | 0.682483i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.81037e6 | − | 2.81037e6i | −2.92029 | − | 2.92029i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 471799. | 0.488259 | 0.244129 | − | 0.969743i | \(-0.421498\pi\) | ||||
0.244129 | + | 0.969743i | \(0.421498\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 668322.i | 0.688832i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −442766. | + | 442766.i | −0.454506 | + | 0.454506i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −197801. | + | 197801.i | −0.202226 | + | 0.202226i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.06681e6i | 1.08627i | 0.839644 | + | 0.543137i | \(0.182763\pi\) | ||||
−0.839644 | + | 0.543137i | \(0.817237\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.56377e6 | −2.60004 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 875175. | + | 875175.i | 0.883992 | + | 0.883992i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 303115. | + | 303115.i | 0.304942 | + | 0.304942i | 0.842944 | − | 0.538002i | \(-0.180821\pi\) |
−0.538002 | + | 0.842944i | \(0.680821\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.33693e6 | 1.33961 |
(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 | 128.5.f.b.31.1 | 14 | ||
4.3 | odd | 2 | 128.5.f.a.31.7 | 14 | |||
8.3 | odd | 2 | 64.5.f.a.15.1 | 14 | |||
8.5 | even | 2 | 16.5.f.a.11.5 | yes | 14 | ||
16.3 | odd | 4 | inner | 128.5.f.b.95.1 | 14 | ||
16.5 | even | 4 | 64.5.f.a.47.1 | 14 | |||
16.11 | odd | 4 | 16.5.f.a.3.5 | ✓ | 14 | ||
16.13 | even | 4 | 128.5.f.a.95.7 | 14 | |||
24.5 | odd | 2 | 144.5.m.a.91.3 | 14 | |||
24.11 | even | 2 | 576.5.m.a.271.6 | 14 | |||
48.5 | odd | 4 | 576.5.m.a.559.6 | 14 | |||
48.11 | even | 4 | 144.5.m.a.19.3 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.f.a.3.5 | ✓ | 14 | 16.11 | odd | 4 | ||
16.5.f.a.11.5 | yes | 14 | 8.5 | even | 2 | ||
64.5.f.a.15.1 | 14 | 8.3 | odd | 2 | |||
64.5.f.a.47.1 | 14 | 16.5 | even | 4 | |||
128.5.f.a.31.7 | 14 | 4.3 | odd | 2 | |||
128.5.f.a.95.7 | 14 | 16.13 | even | 4 | |||
128.5.f.b.31.1 | 14 | 1.1 | even | 1 | trivial | ||
128.5.f.b.95.1 | 14 | 16.3 | odd | 4 | inner | ||
144.5.m.a.19.3 | 14 | 48.11 | even | 4 | |||
144.5.m.a.91.3 | 14 | 24.5 | odd | 2 | |||
576.5.m.a.271.6 | 14 | 24.11 | even | 2 | |||
576.5.m.a.559.6 | 14 | 48.5 | odd | 4 |