Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,7,Mod(415,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.415");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(132.511152165\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1301023109376.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 45x^{6} + 1541x^{4} - 21780x^{2} + 234256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 64) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 415.4 | ||
Root | \(-4.51805 - 2.60850i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.415 |
Dual form | 576.7.b.e.415.5 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 51.5041i | − 0.412033i | −0.978549 | − | 0.206017i | \(-0.933950\pi\) | ||||
0.978549 | − | 0.206017i | \(-0.0660501\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 316.831i | 0.923706i | 0.886957 | + | 0.461853i | \(0.152815\pi\) | ||||
−0.886957 | + | 0.461853i | \(0.847185\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 455.953 | 0.342564 | 0.171282 | − | 0.985222i | \(-0.445209\pi\) | ||||
0.171282 | + | 0.985222i | \(0.445209\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2324.48i | 1.05802i | 0.848614 | + | 0.529012i | \(0.177437\pi\) | ||||
−0.848614 | + | 0.529012i | \(0.822563\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5962.31 | −1.21358 | −0.606789 | − | 0.794863i | \(-0.707543\pi\) | ||||
−0.606789 | + | 0.794863i | \(0.707543\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −11298.5 | −1.64725 | −0.823624 | − | 0.567137i | \(-0.808051\pi\) | ||||
−0.823624 | + | 0.567137i | \(0.808051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 7529.20i | − 0.618821i | −0.950929 | − | 0.309411i | \(-0.899868\pi\) | ||||
0.950929 | − | 0.309411i | \(-0.100132\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12972.3 | 0.830229 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 48632.1i | − 1.99402i | −0.0772777 | − | 0.997010i | \(-0.524623\pi\) | ||||
0.0772777 | − | 0.997010i | \(-0.475377\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 21236.6i | 0.712852i | 0.934324 | + | 0.356426i | \(0.116005\pi\) | ||||
−0.934324 | + | 0.356426i | \(0.883995\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 16318.1 | 0.380597 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 12803.2i | − 0.252762i | −0.991982 | − | 0.126381i | \(-0.959664\pi\) | ||||
0.991982 | − | 0.126381i | \(-0.0403362\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −19217.2 | −0.278829 | −0.139414 | − | 0.990234i | \(-0.544522\pi\) | ||||
−0.139414 | + | 0.990234i | \(0.544522\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8941.24 | 0.112459 | 0.0562293 | − | 0.998418i | \(-0.482092\pi\) | ||||
0.0562293 | + | 0.998418i | \(0.482092\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 162741.i | 1.56749i | 0.621085 | + | 0.783743i | \(0.286692\pi\) | ||||
−0.621085 | + | 0.783743i | \(0.713308\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17267.1 | 0.146768 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 167076.i | 1.12224i | 0.827734 | + | 0.561120i | \(0.189629\pi\) | ||||
−0.827734 | + | 0.561120i | \(0.810371\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 23483.5i | − 0.141148i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −136253. | −0.663421 | −0.331711 | − | 0.943381i | \(-0.607626\pi\) | ||||
−0.331711 | + | 0.943381i | \(0.607626\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 254875.i | − 1.12289i | −0.827514 | − | 0.561445i | \(-0.810246\pi\) | ||||
0.827514 | − | 0.561445i | \(-0.189754\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 119720. | 0.435941 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 291121. | 0.967941 | 0.483970 | − | 0.875084i | \(-0.339194\pi\) | ||||
0.483970 | + | 0.875084i | \(0.339194\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 372162.i | − 1.03982i | −0.854222 | − | 0.519908i | \(-0.825966\pi\) | ||||
0.854222 | − | 0.519908i | \(-0.174034\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 28637.2 | 0.0736143 | 0.0368071 | − | 0.999322i | \(-0.488281\pi\) | ||||
0.0368071 | + | 0.999322i | \(0.488281\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 144460.i | 0.316429i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 747327.i | − 1.51576i | −0.652396 | − | 0.757878i | \(-0.726236\pi\) | ||||
0.652396 | − | 0.757878i | \(-0.273764\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 926047. | 1.61957 | 0.809783 | − | 0.586730i | \(-0.199585\pi\) | ||||
0.809783 | + | 0.586730i | \(0.199585\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 307084.i | 0.500034i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −821138. | −1.16479 | −0.582393 | − | 0.812907i | \(-0.697883\pi\) | ||||
−0.582393 | + | 0.812907i | \(0.697883\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −736467. | −0.977303 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 581918.i | 0.678720i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 675688. | 0.740339 | 0.370170 | − | 0.928964i | \(-0.379300\pi\) | ||||
0.370170 | + | 0.928964i | \(0.379300\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.26530e6i | − 1.22809i | −0.789272 | − | 0.614044i | \(-0.789542\pi\) | ||||
0.789272 | − | 0.614044i | \(-0.210458\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.56235e6i | 1.42977i | 0.699242 | + | 0.714885i | \(0.253521\pi\) | ||||
−0.699242 | + | 0.714885i | \(0.746479\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 876393. | 0.715398 | 0.357699 | − | 0.933837i | \(-0.383561\pi\) | ||||
0.357699 | + | 0.933837i | \(0.383561\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 646317.i | 0.499075i | 0.968365 | + | 0.249538i | \(0.0802787\pi\) | ||||
−0.968365 | + | 0.249538i | \(0.919721\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −196814. | −0.136402 | −0.0682010 | − | 0.997672i | \(-0.521726\pi\) | ||||
−0.0682010 | + | 0.997672i | \(0.521726\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −387785. | −0.254975 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 1.88905e6i | − 1.12099i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.56367e6 | −0.882650 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.47288e6i | − 0.754115i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3.31510e6i | − 1.61840i | −0.587536 | − | 0.809198i | \(-0.699902\pi\) | ||||
0.587536 | − | 0.809198i | \(-0.300098\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.46157e6 | −0.650137 | −0.325069 | − | 0.945690i | \(-0.605387\pi\) | ||||
−0.325069 | + | 0.945690i | \(0.605387\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.57971e6i | − 1.52157i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.31324e6 | −0.899621 | −0.449811 | − | 0.893124i | \(-0.648509\pi\) | ||||
−0.449811 | + | 0.893124i | \(0.648509\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.08798e6 | 1.14982 | 0.574910 | − | 0.818216i | \(-0.305037\pi\) | ||||
0.574910 | + | 0.818216i | \(0.305037\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.05985e6i | 0.362441i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.50476e6 | −0.821602 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 506312.i | 0.153059i | 0.997067 | + | 0.0765297i | \(0.0243840\pi\) | ||||
−0.997067 | + | 0.0765297i | \(0.975616\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 540989.i | 0.157129i | 0.996909 | + | 0.0785647i | \(0.0250337\pi\) | ||||
−0.996909 | + | 0.0785647i | \(0.974966\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.09377e6 | 0.293719 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2.59485e6i | − 0.670522i | −0.942125 | − | 0.335261i | \(-0.891176\pi\) | ||||
0.942125 | − | 0.335261i | \(-0.108824\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.38548e6 | 0.571609 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.27225e6 | 1.21740 | 0.608700 | − | 0.793400i | \(-0.291691\pi\) | ||||
0.608700 | + | 0.793400i | \(0.291691\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 2.04949e6i | − 0.440043i | −0.975495 | − | 0.220022i | \(-0.929387\pi\) | ||||
0.975495 | − | 0.220022i | \(-0.0706128\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −576396. | −0.119416 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 6.44436e6i | − 1.24463i | −0.782766 | − | 0.622317i | \(-0.786192\pi\) | ||||
0.782766 | − | 0.622317i | \(-0.213808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.11004e6i | 0.766887i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.00130e7 | 1.74584 | 0.872918 | − | 0.487866i | \(-0.162225\pi\) | ||||
0.872918 | + | 0.487866i | \(0.162225\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.09474e6i | 0.521901i | 0.965352 | + | 0.260951i | \(0.0840360\pi\) | ||||
−0.965352 | + | 0.260951i | \(0.915964\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −659415. | −0.104146 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.71853e6 | −0.415729 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 1.26300e7i | − 1.81260i | −0.422634 | − | 0.906301i | \(-0.638894\pi\) | ||||
0.422634 | − | 0.906301i | \(-0.361106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.50418e6 | 0.904733 | 0.452366 | − | 0.891832i | \(-0.350580\pi\) | ||||
0.452366 | + | 0.891832i | \(0.350580\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.04312e7i | − 1.36438i | −0.731173 | − | 0.682192i | \(-0.761027\pi\) | ||||
0.731173 | − | 0.682192i | \(-0.238973\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 6.15168e6i | − 0.780611i | −0.920685 | − | 0.390305i | \(-0.872369\pi\) | ||||
0.920685 | − | 0.390305i | \(-0.127631\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.54082e7 | 1.84189 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 989763.i | 0.114887i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.15157e6 | −0.564288 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.17218e6 | 0.550587 | 0.275294 | − | 0.961360i | \(-0.411225\pi\) | ||||
0.275294 | + | 0.961360i | \(0.411225\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 460511.i | − 0.0463367i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.72841e6 | −0.658465 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.38593e7i | − 1.28400i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.16411e7i | 1.04973i | 0.851185 | + | 0.524866i | \(0.175885\pi\) | ||||
−0.851185 | + | 0.524866i | \(0.824115\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.01124e6 | 0.684892 | 0.342446 | − | 0.939538i | \(-0.388745\pi\) | ||||
0.342446 | + | 0.939538i | \(0.388745\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1.11134e7i | − 0.925424i | −0.886509 | − | 0.462712i | \(-0.846876\pi\) | ||||
0.886509 | − | 0.462712i | \(-0.153124\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.52724e7 | −1.20737 | −0.603683 | − | 0.797224i | \(-0.706301\pi\) | ||||
−0.603683 | + | 0.797224i | \(0.706301\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.38184e6 | 0.645856 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 1.58629e7i | − 1.16195i | −0.813920 | − | 0.580976i | \(-0.802671\pi\) | ||||
0.813920 | − | 0.580976i | \(-0.197329\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.30600e7 | −1.64743 | −0.823716 | − | 0.567003i | \(-0.808103\pi\) | ||||
−0.823716 | + | 0.567003i | \(0.808103\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 889325.i | − 0.0604731i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2.62631e7i | − 1.74283i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.60894e6 | −0.607651 | −0.303826 | − | 0.952728i | \(-0.598264\pi\) | ||||
−0.303826 | + | 0.952728i | \(0.598264\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 3.43296e6i | − 0.211986i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.97448e7 | −1.16320 | −0.581598 | − | 0.813477i | \(-0.697572\pi\) | ||||
−0.581598 | + | 0.813477i | \(0.697572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.05644e6 | 0.233478 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.10803e7i | 1.15880i | 0.815043 | + | 0.579401i | \(0.196713\pi\) | ||||
−0.815043 | + | 0.579401i | \(0.803287\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.60509e6 | 0.462400 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 8.65879e6i | − 0.444836i | −0.974951 | − | 0.222418i | \(-0.928605\pi\) | ||||
0.974951 | − | 0.222418i | \(-0.0713950\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 1.35042e7i | − 0.678518i | −0.940693 | − | 0.339259i | \(-0.889824\pi\) | ||||
0.940693 | − | 0.339259i | \(-0.110176\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.91477e6 | 0.284407 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3.94224e7i | − 1.85483i | −0.374036 | − | 0.927414i | \(-0.622027\pi\) | ||||
0.374036 | − | 0.927414i | \(-0.377973\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.52689e7 | 1.13885 | 0.569426 | − | 0.822043i | \(-0.307165\pi\) | ||||
0.569426 | + | 0.822043i | \(0.307165\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 889757. | 0.0392566 | 0.0196283 | − | 0.999807i | \(-0.493752\pi\) | ||||
0.0196283 | + | 0.999807i | \(0.493752\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 6.08859e6i | − 0.257556i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.14116e7 | 0.472773 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.86906e7i | − 0.743054i | −0.928422 | − | 0.371527i | \(-0.878834\pi\) | ||||
0.928422 | − | 0.371527i | \(-0.121166\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.01758e6i | 0.273352i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.75015e7 | 0.654728 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.83286e6i | 0.103879i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.31271e7 | −0.462668 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.12497e7 | 0.734410 | 0.367205 | − | 0.930140i | \(-0.380315\pi\) | ||||
0.367205 | + | 0.930140i | \(0.380315\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 2.14152e7i | − 0.711934i | −0.934498 | − | 0.355967i | \(-0.884151\pi\) | ||||
0.934498 | − | 0.355967i | \(-0.115849\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.54992e7 | −0.505449 | −0.252724 | − | 0.967538i | \(-0.581327\pi\) | ||||
−0.252724 | + | 0.967538i | \(0.581327\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.20284e7i | − 0.691521i | −0.938323 | − | 0.345761i | \(-0.887621\pi\) | ||||
0.938323 | − | 0.345761i | \(-0.112379\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 2.21740e7i | − 0.683080i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.73650e7 | 1.99906 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.01539e7i | 0.878402i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.15614e7 | −1.44790 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.25702e7 | −0.622375 | −0.311187 | − | 0.950349i | \(-0.600727\pi\) | ||||
−0.311187 | + | 0.950349i | \(0.600727\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 1.49939e7i | − 0.398824i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.10276e7 | −0.288132 | −0.144066 | − | 0.989568i | \(-0.546018\pi\) | ||||
−0.144066 | + | 0.989568i | \(0.546018\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.68288e6i | 0.244198i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.27456e7i | 1.05928i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.85304e7 | 0.922178 | 0.461089 | − | 0.887354i | \(-0.347459\pi\) | ||||
0.461089 | + | 0.887354i | \(0.347459\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.67472e6i | 0.0393972i | 0.999806 | + | 0.0196986i | \(0.00627067\pi\) | ||||
−0.999806 | + | 0.0196986i | \(0.993729\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.39273e7 | −0.998643 | −0.499321 | − | 0.866417i | \(-0.666417\pi\) | ||||
−0.499321 | + | 0.866417i | \(0.666417\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.91679e7 | −0.428439 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 7.13472e6i | − 0.154203i | −0.997023 | − | 0.0771017i | \(-0.975433\pi\) | ||||
0.997023 | − | 0.0771017i | \(-0.0245666\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.06096e7 | 1.71342 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.47493e6i | − 0.0303315i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.37831e7i | − 0.481139i | −0.970632 | − | 0.240570i | \(-0.922666\pi\) | ||||
0.970632 | − | 0.240570i | \(-0.0773343\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.29348e7 | −1.03662 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.75669e7i | 0.531205i | 0.964083 | + | 0.265602i | \(0.0855708\pi\) | ||||
−0.964083 | + | 0.265602i | \(0.914429\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.13044e8 | 2.10972 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.70623e7 | 1.04817 | 0.524085 | − | 0.851666i | \(-0.324407\pi\) | ||||
0.524085 | + | 0.851666i | \(0.324407\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.45219e7i | 0.258480i | 0.991613 | + | 0.129240i | \(0.0412538\pi\) | ||||
−0.991613 | + | 0.129240i | \(0.958746\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.44029e6 | 0.130379 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.83034e7i | 0.650711i | 0.945592 | + | 0.325355i | \(0.105484\pi\) | ||||
−0.945592 | + | 0.325355i | \(0.894516\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.48914e7i | 0.750988i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.84904e7 | −0.624542 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.93337e7i | − 0.468808i | −0.972139 | − | 0.234404i | \(-0.924686\pi\) | ||||
0.972139 | − | 0.234404i | \(-0.0753139\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.33165e7 | 1.29211 | 0.646053 | − | 0.763293i | \(-0.276419\pi\) | ||||
0.646053 | + | 0.763293i | \(0.276419\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.93640e7 | −0.754215 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 5.83764e6i | − 0.0865872i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.28360e8 | −1.87612 | −0.938062 | − | 0.346469i | \(-0.887381\pi\) | ||||
−0.938062 | + | 0.346469i | \(0.887381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.31691e7i | − 0.612806i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 4.76952e7i | − 0.667315i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.31253e8 | −1.78430 | −0.892148 | − | 0.451744i | \(-0.850802\pi\) | ||||
−0.892148 | + | 0.451744i | \(0.850802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.08565e8i | − 1.45493i | −0.686145 | − | 0.727465i | \(-0.740698\pi\) | ||||
0.686145 | − | 0.727465i | \(-0.259302\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.73450e7 | −1.00755 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.07522e7 | 1.03722 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.30324e8i | 1.62777i | 0.581024 | + | 0.813886i | \(0.302652\pi\) | ||||
−0.581024 | + | 0.813886i | \(0.697348\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.54168e6 | −0.0805797 | −0.0402899 | − | 0.999188i | \(-0.512828\pi\) | ||||
−0.0402899 | + | 0.999188i | \(0.512828\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.50684e7i | 1.01935i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.19410e7i | 0.259336i | 0.991557 | + | 0.129668i | \(0.0413911\pi\) | ||||
−0.991557 | + | 0.129668i | \(0.958609\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.92753e7 | 0.221713 | 0.110856 | − | 0.993836i | \(-0.464641\pi\) | ||||
0.110856 | + | 0.993836i | \(0.464641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.22920e7i | 0.479930i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.47464e7 | 0.273384 | 0.136692 | − | 0.990614i | \(-0.456353\pi\) | ||||
0.136692 | + | 0.990614i | \(0.456353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.76213e6 | −0.0955168 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.79311e7i | 0.402681i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.77220e7 | 0.604773 | 0.302387 | − | 0.953185i | \(-0.402217\pi\) | ||||
0.302387 | + | 0.953185i | \(0.402217\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.06314e7i | 0.720934i | 0.932772 | + | 0.360467i | \(0.117383\pi\) | ||||
−0.932772 | + | 0.360467i | \(0.882617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.26034e7i | 0.529994i | 0.964249 | + | 0.264997i | \(0.0853710\pi\) | ||||
−0.964249 | + | 0.264997i | \(0.914629\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.10121e7 | −0.697239 | −0.348620 | − | 0.937264i | \(-0.613350\pi\) | ||||
−0.348620 | + | 0.937264i | \(0.613350\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.22361e7i | 0.894093i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.07679e6 | 0.0385243 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.46567e8 | −1.36759 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 1.40741e8i | − 1.28060i | −0.768125 | − | 0.640299i | \(-0.778810\pi\) | ||||
0.768125 | − | 0.640299i | \(-0.221190\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.97607e7 | 0.267428 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 3.48007e7i | − 0.305044i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.35775e7i | 0.550448i | 0.961380 | + | 0.275224i | \(0.0887521\pi\) | ||||
−0.961380 | + | 0.275224i | \(0.911248\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.59327e8 | −1.34600 | −0.672999 | − | 0.739644i | \(-0.734994\pi\) | ||||
−0.672999 | + | 0.739644i | \(0.734994\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.89960e8i | 2.41990i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.17912e8 | 0.960485 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.22399e8 | −0.985088 | −0.492544 | − | 0.870288i | \(-0.663933\pi\) | ||||
−0.492544 | + | 0.870288i | \(0.663933\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 1.79127e7i | − 0.140753i | −0.997521 | − | 0.0703763i | \(-0.977580\pi\) | ||||
0.997521 | − | 0.0703763i | \(-0.0224200\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.51682e7 | −0.506013 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.60087e8i | 1.21395i | 0.794720 | + | 0.606976i | \(0.207618\pi\) | ||||
−0.794720 | + | 0.606976i | \(0.792382\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.07316e6i | 0.0679979i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.04674e7 | 0.589113 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.42023e7i | 0.536965i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.93475e7 | −0.207519 | −0.103759 | − | 0.994602i | \(-0.533087\pi\) | ||||
−0.103759 | + | 0.994602i | \(0.533087\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.69326e8 | −1.18363 | −0.591817 | − | 0.806072i | \(-0.701589\pi\) | ||||
−0.591817 | + | 0.806072i | \(0.701589\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.26619e8i | − 0.865102i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.13471e7 | 0.617061 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4.46699e7i | − 0.295008i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 4.51379e7i | − 0.294768i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.87297e6 | 0.0502773 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 1.45276e8i | − 0.917493i | −0.888567 | − | 0.458746i | \(-0.848299\pi\) | ||||
0.888567 | − | 0.458746i | \(-0.151701\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.32880e7 | 0.205636 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.72469e8 | 1.05378 | 0.526889 | − | 0.849934i | \(-0.323358\pi\) | ||||
0.526889 | + | 0.849934i | \(0.323358\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.49469e8i | 3.28464i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.36776e8 | 1.40011 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.52417e8i | 1.46067i | 0.683089 | + | 0.730335i | \(0.260636\pi\) | ||||
−0.683089 | + | 0.730335i | \(0.739364\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.07837e7i | 0.118984i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.43419e7 | 0.416589 | 0.208295 | − | 0.978066i | \(-0.433209\pi\) | ||||
0.208295 | + | 0.978066i | \(0.433209\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.01367e7i | 0.0562022i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.44911e8 | 0.786620 | 0.393310 | − | 0.919406i | \(-0.371330\pi\) | ||||
0.393310 | + | 0.919406i | \(0.371330\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.51024e8 | 0.811218 | 0.405609 | − | 0.914047i | \(-0.367059\pi\) | ||||
0.405609 | + | 0.914047i | \(0.367059\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 9.76712e7i | − 0.513763i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.65008e7 | −0.190009 | −0.0950046 | − | 0.995477i | \(-0.530287\pi\) | ||||
−0.0950046 | + | 0.995477i | \(0.530287\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.93400e8i | 1.49600i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.61787e7i | 0.384439i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.97585e8 | −1.47129 | −0.735643 | − | 0.677370i | \(-0.763120\pi\) | ||||
−0.735643 | + | 0.677370i | \(0.763120\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 2.39941e8i | − 1.17424i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.59264e8 | 0.763755 | 0.381878 | − | 0.924213i | \(-0.375278\pi\) | ||||
0.381878 | + | 0.924213i | \(0.375278\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.72936e7 | −0.461885 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.93971e8i | 1.36781i | 0.729573 | + | 0.683903i | \(0.239719\pi\) | ||||
−0.729573 | + | 0.683903i | \(0.760281\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.17935e8 | −0.543277 | −0.271638 | − | 0.962399i | \(-0.587565\pi\) | ||||
−0.271638 | + | 0.962399i | \(0.587565\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.05354e7i | 0.363681i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 7.36776e7i | − 0.329435i | −0.986341 | − | 0.164717i | \(-0.947329\pi\) | ||||
0.986341 | − | 0.164717i | \(-0.0526712\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.78288e8 | −1.65844 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.85901e8i | 0.807050i | 0.914969 | + | 0.403525i | \(0.132215\pi\) | ||||
−0.914969 | + | 0.403525i | \(0.867785\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.32115e7 | 0.141395 | 0.0706973 | − | 0.997498i | \(-0.477478\pi\) | ||||
0.0706973 | + | 0.997498i | \(0.477478\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.24234e7 | 0.221031 | 0.110516 | − | 0.993874i | \(-0.464750\pi\) | ||||
0.110516 | + | 0.993874i | \(0.464750\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2.60162e8i | − 1.07592i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.26833e8 | 0.519509 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.63364e7i | 0.306747i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 1.32736e8i | − 0.528326i | −0.964478 | − | 0.264163i | \(-0.914904\pi\) | ||||
0.964478 | − | 0.264163i | \(-0.0850957\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.70741e8 | −0.666833 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.01369e7i | 0.155284i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.42334e7 | −0.319823 | −0.159912 | − | 0.987131i | \(-0.551121\pi\) | ||||
−0.159912 | + | 0.987131i | \(0.551121\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.11219e8 | −1.17067 | −0.585334 | − | 0.810792i | \(-0.699037\pi\) | ||||
−0.585334 | + | 0.810792i | \(0.699037\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.82536e8i | 1.41241i | 0.708010 | + | 0.706203i | \(0.249593\pi\) | ||||
−0.708010 | + | 0.706203i | \(0.750407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.21249e7 | −0.227265 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 3.98790e8i | − 1.43220i | −0.697996 | − | 0.716102i | \(-0.745925\pi\) | ||||
0.697996 | − | 0.716102i | \(-0.254075\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.52768e7i | 0.267878i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.89798e7 | −0.241027 | −0.120513 | − | 0.992712i | \(-0.538454\pi\) | ||||
−0.120513 | + | 0.992712i | \(0.538454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 2.51486e8i | − 0.870782i | −0.900241 | − | 0.435391i | \(-0.856610\pi\) | ||||
0.900241 | − | 0.435391i | \(-0.143390\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.84370e8 | −0.626938 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.66161e8 | −1.23394 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1.16211e8i | − 0.384662i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.23586e8 | 0.733499 | 0.366750 | − | 0.930320i | \(-0.380471\pi\) | ||||
0.366750 | + | 0.930320i | \(0.380471\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.72443e8i | 0.555751i | 0.960617 | + | 0.277876i | \(0.0896303\pi\) | ||||
−0.960617 | + | 0.277876i | \(0.910370\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.14079e8i | 0.683856i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.18442e8 | 1.62719 | 0.813594 | − | 0.581433i | \(-0.197508\pi\) | ||||
0.813594 | + | 0.581433i | \(0.197508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.19142e8i | 0.370674i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.88364e8 | −1.18736 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.12317e8 | 1.24967 | 0.624837 | − | 0.780755i | \(-0.285166\pi\) | ||||
0.624837 | + | 0.780755i | \(0.285166\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1.59044e8i | − 0.473764i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.14579e8 | 0.338381 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 4.19721e7i | − 0.121845i | −0.998143 | − | 0.0609224i | \(-0.980596\pi\) | ||||
0.998143 | − | 0.0609224i | \(-0.0194042\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.44656e8i | 0.416362i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.00886e8 | 1.13439 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.94810e8i | 1.66894i | 0.551057 | + | 0.834468i | \(0.314225\pi\) | ||||
−0.551057 | + | 0.834468i | \(0.685775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.59894e8 | 0.441128 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.45868e7 | 0.149338 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 7.17679e7i | − 0.193083i | −0.995329 | − | 0.0965414i | \(-0.969222\pi\) | ||||
0.995329 | − | 0.0965414i | \(-0.0307780\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.95001e8 | −1.32069 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 6.30872e8i | − 1.65549i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.60152e7i | 0.119756i | 0.998206 | + | 0.0598781i | \(0.0190712\pi\) | ||||
−0.998206 | + | 0.0598781i | \(0.980929\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.33105e7 | −0.136477 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 3.14277e7i | − 0.0797995i | −0.999204 | − | 0.0398997i | \(-0.987296\pi\) | ||||
0.999204 | − | 0.0398997i | \(-0.0127039\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.32737e8 | 0.331582 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.30671e8 | −0.323778 | −0.161889 | − | 0.986809i | \(-0.551759\pi\) | ||||
−0.161889 | + | 0.986809i | \(0.551759\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 2.39517e8i | − 0.583942i | −0.956427 | − | 0.291971i | \(-0.905689\pi\) | ||||
0.956427 | − | 0.291971i | \(-0.0943111\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.60772e7 | 0.0630655 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.77669e8i | 0.660817i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 5.07976e8i | − 1.19929i | −0.800267 | − | 0.599644i | \(-0.795309\pi\) | ||||
0.800267 | − | 0.599644i | \(-0.204691\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.78632e7 | 0.0647425 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 3.35592e8i | − 0.773614i | −0.922161 | − | 0.386807i | \(-0.873578\pi\) | ||||
0.922161 | − | 0.386807i | \(-0.126422\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.91901e8 | 0.662341 | 0.331171 | − | 0.943571i | \(-0.392556\pi\) | ||||
0.331171 | + | 0.943571i | \(0.392556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.04773e8 | −0.460999 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 3.16717e8i | − 0.701916i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.38154e8 | −0.523695 | −0.261847 | − | 0.965109i | \(-0.584332\pi\) | ||||
−0.261847 | + | 0.965109i | \(0.584332\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 3.03506e8i | − 0.657096i | −0.944487 | − | 0.328548i | \(-0.893441\pi\) | ||||
0.944487 | − | 0.328548i | \(-0.106559\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.75488e8i | 0.591830i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.17125e8 | 0.459300 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.69688e8i | − 0.356204i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.33645e8 | −0.276277 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.21311e8 | 1.27463 | 0.637316 | − | 0.770603i | \(-0.280045\pi\) | ||||
0.637316 | + | 0.770603i | \(0.280045\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 6.23568e7i | − 0.125995i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.92451e8 | 1.18804 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.14212e8i | 1.01570i | 0.861444 | + | 0.507852i | \(0.169560\pi\) | ||||
−0.861444 | + | 0.507852i | \(0.830440\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 9.70313e8i | − 1.90227i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.30572e7 | 0.0252176 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.22862e8i | − 0.235522i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.15875e8 | 0.407715 | 0.203858 | − | 0.979001i | \(-0.434652\pi\) | ||||
0.203858 | + | 0.979001i | \(0.434652\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.81893e8 | 1.27836 | 0.639181 | − | 0.769056i | \(-0.279273\pi\) | ||||
0.639181 | + | 0.769056i | \(0.279273\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 2.71543e8i | − 0.501609i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.01022e8 | −0.185247 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 3.70599e8i | − 0.669692i | −0.942273 | − | 0.334846i | \(-0.891316\pi\) | ||||
0.942273 | − | 0.334846i | \(-0.108684\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.80700e8i | 1.22111i | 0.791972 | + | 0.610557i | \(0.209054\pi\) | ||||
−0.791972 | + | 0.610557i | \(0.790946\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.55416e7 | −0.151238 | −0.0756189 | − | 0.997137i | \(-0.524093\pi\) | ||||
−0.0756189 | + | 0.997137i | \(0.524093\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 5.12614e8i | − 0.899761i | −0.893089 | − | 0.449880i | \(-0.851467\pi\) | ||||
0.893089 | − | 0.449880i | \(-0.148533\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.02952e8 | −0.178114 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.05557e8 | −0.181312 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.25162e8i | 0.381249i | 0.981663 | + | 0.190625i | \(0.0610513\pi\) | ||||
−0.981663 | + | 0.190625i | \(0.938949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.77026e9 | −2.97611 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.96868e7i | 0.0492031i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 4.95419e8i | − 0.815309i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.63975e7 | −0.156414 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.68109e8i | 0.270860i | 0.990787 | + | 0.135430i | \(0.0432416\pi\) | ||||
−0.990787 | + | 0.135430i | \(0.956758\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.61928e8 | −1.05164 | −0.525822 | − | 0.850595i | \(-0.676242\pi\) | ||||
−0.525822 | + | 0.850595i | \(0.676242\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.46051e8 | 1.17703 | 0.588517 | − | 0.808485i | \(-0.299712\pi\) | ||||
0.588517 | + | 0.808485i | \(0.299712\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 9.52742e8i | − 1.48232i | −0.671326 | − | 0.741162i | \(-0.734275\pi\) | ||||
0.671326 | − | 0.741162i | \(-0.265725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.31911e8 | −0.512830 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 3.40746e8i | − 0.519244i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.76704e8i | 1.02411i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.66654e8 | 0.696580 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.38880e7i | 0.0798902i | 0.999202 | + | 0.0399451i | \(0.0127183\pi\) | ||||
−0.999202 | + | 0.0399451i | \(0.987282\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.06501e9 | −1.55750 | −0.778749 | − | 0.627336i | \(-0.784145\pi\) | ||||
−0.778749 | + | 0.627336i | \(0.784145\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.06768e8 | 0.155081 | 0.0775405 | − | 0.996989i | \(-0.475293\pi\) | ||||
0.0775405 | + | 0.996989i | \(0.475293\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.57318e8i | 1.22849i | 0.789116 | + | 0.614244i | \(0.210539\pi\) | ||||
−0.789116 | + | 0.614244i | \(0.789461\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.05033e9 | 1.49492 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.83873e9i | − 2.58204i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 5.15709e8i | − 0.719342i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.03278e9 | 1.42144 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 9.96157e8i | − 1.36193i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.59392e8 | 0.215041 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.55579e8 | −0.744601 | −0.372301 | − | 0.928112i | \(-0.621431\pi\) | ||||
−0.372301 | + | 0.928112i | \(0.621431\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 4.58157e8i | − 0.605981i | −0.952994 | − | 0.302991i | \(-0.902015\pi\) | ||||
0.952994 | − | 0.302991i | \(-0.0979851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.22234e8 | 0.554805 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.63070e8i | − 0.600536i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.63186e8i | 1.11214i | 0.831137 | + | 0.556068i | \(0.187691\pi\) | ||||
−0.831137 | + | 0.556068i | \(0.812309\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.65082e8 | 1.10015 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1.66087e8i | − 0.209850i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.00351e8 | 0.998237 | 0.499118 | − | 0.866534i | \(-0.333657\pi\) | ||||
0.499118 | + | 0.866534i | \(0.333657\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.95091e8 | −0.241763 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.40016e8i | 0.171294i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.02009e8 | 0.610228 | 0.305114 | − | 0.952316i | \(-0.401305\pi\) | ||||
0.305114 | + | 0.952316i | \(0.401305\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1.18725e9i | − 1.42486i | −0.701744 | − | 0.712429i | \(-0.747595\pi\) | ||||
0.701744 | − | 0.712429i | \(-0.252405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.44690e8i | 0.172545i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.32279e9 | 1.55755 | 0.778775 | − | 0.627303i | \(-0.215841\pi\) | ||||
0.778775 | + | 0.627303i | \(0.215841\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.65666e7i | 0.0778857i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.30974e9 | −1.51324 | −0.756618 | − | 0.653858i | \(-0.773149\pi\) | ||||
−0.756618 | + | 0.653858i | \(0.773149\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.50496e8 | −0.746852 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 7.32908e8i | − 0.830986i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.36512e8 | 0.491842 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 3.34992e8i | − 0.372780i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 9.99874e8i | − 1.10577i | −0.833257 | − | 0.552886i | \(-0.813526\pi\) | ||||
0.833257 | − | 0.552886i | \(-0.186474\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.22800e9 | −1.34135 | −0.670675 | − | 0.741751i | \(-0.733996\pi\) | ||||
−0.670675 | + | 0.741751i | \(0.733996\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.78368e8i | 1.06210i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.12283e8 | 0.334861 | 0.167430 | − | 0.985884i | \(-0.446453\pi\) | ||||
0.167430 | + | 0.985884i | \(0.446453\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.74400e8 | −0.399014 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.52567e8i | 0.687013i | 0.939150 | + | 0.343506i | \(0.111615\pi\) | ||||
−0.939150 | + | 0.343506i | \(0.888385\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.37251e8 | −0.562171 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 6.73204e7i | − 0.0695917i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.47356e8i | 0.356906i | 0.983948 | + | 0.178453i | \(0.0571092\pi\) | ||||
−0.983948 | + | 0.178453i | \(0.942891\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.16837e8 | −0.321637 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.98519e8i | 0.200317i | 0.994972 | + | 0.100158i | \(0.0319350\pi\) | ||||
−0.994972 | + | 0.100158i | \(0.968065\pi\) | |||||||
\(998\) | 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 | 576.7.b.e.415.4 | 8 | ||
3.2 | odd | 2 | 64.7.d.b.31.6 | yes | 8 | ||
4.3 | odd | 2 | inner | 576.7.b.e.415.3 | 8 | ||
8.3 | odd | 2 | inner | 576.7.b.e.415.5 | 8 | ||
8.5 | even | 2 | inner | 576.7.b.e.415.6 | 8 | ||
12.11 | even | 2 | 64.7.d.b.31.4 | yes | 8 | ||
24.5 | odd | 2 | 64.7.d.b.31.3 | ✓ | 8 | ||
24.11 | even | 2 | 64.7.d.b.31.5 | yes | 8 | ||
48.5 | odd | 4 | 256.7.c.k.255.3 | 8 | |||
48.11 | even | 4 | 256.7.c.k.255.5 | 8 | |||
48.29 | odd | 4 | 256.7.c.k.255.6 | 8 | |||
48.35 | even | 4 | 256.7.c.k.255.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
64.7.d.b.31.3 | ✓ | 8 | 24.5 | odd | 2 | ||
64.7.d.b.31.4 | yes | 8 | 12.11 | even | 2 | ||
64.7.d.b.31.5 | yes | 8 | 24.11 | even | 2 | ||
64.7.d.b.31.6 | yes | 8 | 3.2 | odd | 2 | ||
256.7.c.k.255.3 | 8 | 48.5 | odd | 4 | |||
256.7.c.k.255.4 | 8 | 48.35 | even | 4 | |||
256.7.c.k.255.5 | 8 | 48.11 | even | 4 | |||
256.7.c.k.255.6 | 8 | 48.29 | odd | 4 | |||
576.7.b.e.415.3 | 8 | 4.3 | odd | 2 | inner | ||
576.7.b.e.415.4 | 8 | 1.1 | even | 1 | trivial | ||
576.7.b.e.415.5 | 8 | 8.3 | odd | 2 | inner | ||
576.7.b.e.415.6 | 8 | 8.5 | even | 2 | inner |