Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,6,Mod(99,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.99");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.c (of order \(2\), degree \(1\), 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: | \(56.1343369345\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.99 |
Dual form | 350.6.c.a.99.1 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000i | 0.707107i | ||||||||
\(3\) | 17.0000i | 1.09055i | 0.838257 | + | 0.545275i | \(0.183575\pi\) | ||||
−0.838257 | + | 0.545275i | \(0.816425\pi\) | |||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −68.0000 | −0.771136 | ||||||||
\(7\) | − 49.0000i | − 0.377964i | ||||||||
\(8\) | − 64.0000i | − 0.353553i | ||||||||
\(9\) | −46.0000 | −0.189300 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −715.000 | −1.78166 | −0.890829 | − | 0.454339i | \(-0.849876\pi\) | ||||
−0.890829 | + | 0.454339i | \(0.849876\pi\) | |||||||
\(12\) | − 272.000i | − 0.545275i | ||||||||
\(13\) | − 331.000i | − 0.543212i | −0.962408 | − | 0.271606i | \(-0.912445\pi\) | ||||
0.962408 | − | 0.271606i | \(-0.0875548\pi\) | |||||||
\(14\) | 196.000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | − 1699.00i | − 1.42584i | −0.701245 | − | 0.712920i | \(-0.747372\pi\) | ||||
0.701245 | − | 0.712920i | \(-0.252628\pi\) | |||||||
\(18\) | − 184.000i | − 0.133856i | ||||||||
\(19\) | 1718.00 | 1.09179 | 0.545895 | − | 0.837854i | \(-0.316190\pi\) | ||||
0.545895 | + | 0.837854i | \(0.316190\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 833.000 | 0.412189 | ||||||||
\(22\) | − 2860.00i | − 1.25982i | ||||||||
\(23\) | 3950.00i | 1.55696i | 0.627669 | + | 0.778480i | \(0.284009\pi\) | ||||
−0.627669 | + | 0.778480i | \(0.715991\pi\) | |||||||
\(24\) | 1088.00 | 0.385568 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1324.00 | 0.384109 | ||||||||
\(27\) | 3349.00i | 0.884109i | ||||||||
\(28\) | 784.000i | 0.188982i | ||||||||
\(29\) | −4579.00 | −1.01106 | −0.505529 | − | 0.862810i | \(-0.668702\pi\) | ||||
−0.505529 | + | 0.862810i | \(0.668702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6756.00 | 1.26266 | 0.631329 | − | 0.775516i | \(-0.282510\pi\) | ||||
0.631329 | + | 0.775516i | \(0.282510\pi\) | |||||||
\(32\) | 1024.00i | 0.176777i | ||||||||
\(33\) | − 12155.0i | − 1.94299i | ||||||||
\(34\) | 6796.00 | 1.00822 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 736.000 | 0.0946502 | ||||||||
\(37\) | − 16518.0i | − 1.98360i | −0.127816 | − | 0.991798i | \(-0.540797\pi\) | ||||
0.127816 | − | 0.991798i | \(-0.459203\pi\) | |||||||
\(38\) | 6872.00i | 0.772012i | ||||||||
\(39\) | 5627.00 | 0.592400 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18876.0 | 1.75368 | 0.876840 | − | 0.480782i | \(-0.159647\pi\) | ||||
0.876840 | + | 0.480782i | \(0.159647\pi\) | |||||||
\(42\) | 3332.00i | 0.291462i | ||||||||
\(43\) | − 2258.00i | − 0.186231i | −0.995655 | − | 0.0931157i | \(-0.970317\pi\) | ||||
0.995655 | − | 0.0931157i | \(-0.0296826\pi\) | |||||||
\(44\) | 11440.0 | 0.890829 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −15800.0 | −1.10094 | ||||||||
\(47\) | − 537.000i | − 0.0354593i | −0.999843 | − | 0.0177296i | \(-0.994356\pi\) | ||||
0.999843 | − | 0.0177296i | \(-0.00564381\pi\) | |||||||
\(48\) | 4352.00i | 0.272638i | ||||||||
\(49\) | −2401.00 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 28883.0 | 1.55495 | ||||||||
\(52\) | 5296.00i | 0.271606i | ||||||||
\(53\) | 10984.0i | 0.537119i | 0.963263 | + | 0.268560i | \(0.0865477\pi\) | ||||
−0.963263 | + | 0.268560i | \(0.913452\pi\) | |||||||
\(54\) | −13396.0 | −0.625159 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3136.00 | −0.133631 | ||||||||
\(57\) | 29206.0i | 1.19065i | ||||||||
\(58\) | − 18316.0i | − 0.714925i | ||||||||
\(59\) | 25956.0 | 0.970751 | 0.485375 | − | 0.874306i | \(-0.338683\pi\) | ||||
0.485375 | + | 0.874306i | \(0.338683\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 39188.0 | 1.34843 | 0.674215 | − | 0.738535i | \(-0.264482\pi\) | ||||
0.674215 | + | 0.738535i | \(0.264482\pi\) | |||||||
\(62\) | 27024.0i | 0.892833i | ||||||||
\(63\) | 2254.00i | 0.0715488i | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 48620.0 | 1.37390 | ||||||||
\(67\) | 4416.00i | 0.120183i | 0.998193 | + | 0.0600914i | \(0.0191392\pi\) | ||||
−0.998193 | + | 0.0600914i | \(0.980861\pi\) | |||||||
\(68\) | 27184.0i | 0.712920i | ||||||||
\(69\) | −67150.0 | −1.69794 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −31880.0 | −0.750538 | −0.375269 | − | 0.926916i | \(-0.622450\pi\) | ||||
−0.375269 | + | 0.926916i | \(0.622450\pi\) | |||||||
\(72\) | 2944.00i | 0.0669278i | ||||||||
\(73\) | 5018.00i | 0.110211i | 0.998481 | + | 0.0551053i | \(0.0175495\pi\) | ||||
−0.998481 | + | 0.0551053i | \(0.982451\pi\) | |||||||
\(74\) | 66072.0 | 1.40261 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −27488.0 | −0.545895 | ||||||||
\(77\) | 35035.0i | 0.673403i | ||||||||
\(78\) | 22508.0i | 0.418890i | ||||||||
\(79\) | 27977.0 | 0.504352 | 0.252176 | − | 0.967681i | \(-0.418854\pi\) | ||||
0.252176 | + | 0.967681i | \(0.418854\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −68111.0 | −1.15347 | ||||||||
\(82\) | 75504.0i | 1.24004i | ||||||||
\(83\) | − 37644.0i | − 0.599792i | −0.953972 | − | 0.299896i | \(-0.903048\pi\) | ||||
0.953972 | − | 0.299896i | \(-0.0969520\pi\) | |||||||
\(84\) | −13328.0 | −0.206095 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9032.00 | 0.131685 | ||||||||
\(87\) | − 77843.0i | − 1.10261i | ||||||||
\(88\) | 45760.0i | 0.629911i | ||||||||
\(89\) | 17216.0 | 0.230387 | 0.115193 | − | 0.993343i | \(-0.463251\pi\) | ||||
0.115193 | + | 0.993343i | \(0.463251\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16219.0 | −0.205315 | ||||||||
\(92\) | − 63200.0i | − 0.778480i | ||||||||
\(93\) | 114852.i | 1.37699i | ||||||||
\(94\) | 2148.00 | 0.0250735 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −17408.0 | −0.192784 | ||||||||
\(97\) | − 63175.0i | − 0.681736i | −0.940111 | − | 0.340868i | \(-0.889279\pi\) | ||||
0.940111 | − | 0.340868i | \(-0.110721\pi\) | |||||||
\(98\) | − 9604.00i | − 0.101015i | ||||||||
\(99\) | 32890.0 | 0.337269 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −29250.0 | −0.285314 | −0.142657 | − | 0.989772i | \(-0.545565\pi\) | ||||
−0.142657 | + | 0.989772i | \(0.545565\pi\) | |||||||
\(102\) | 115532.i | 1.09952i | ||||||||
\(103\) | 149189.i | 1.38562i | 0.721121 | + | 0.692809i | \(0.243627\pi\) | ||||
−0.721121 | + | 0.692809i | \(0.756373\pi\) | |||||||
\(104\) | −21184.0 | −0.192055 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −43936.0 | −0.379801 | ||||||||
\(107\) | 83742.0i | 0.707105i | 0.935415 | + | 0.353552i | \(0.115026\pi\) | ||||
−0.935415 | + | 0.353552i | \(0.884974\pi\) | |||||||
\(108\) | − 53584.0i | − 0.442054i | ||||||||
\(109\) | −105377. | −0.849532 | −0.424766 | − | 0.905303i | \(-0.639644\pi\) | ||||
−0.424766 | + | 0.905303i | \(0.639644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 280806. | 2.16321 | ||||||||
\(112\) | − 12544.0i | − 0.0944911i | ||||||||
\(113\) | 122754.i | 0.904356i | 0.891928 | + | 0.452178i | \(0.149353\pi\) | ||||
−0.891928 | + | 0.452178i | \(0.850647\pi\) | |||||||
\(114\) | −116824. | −0.841918 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 73264.0 | 0.505529 | ||||||||
\(117\) | 15226.0i | 0.102830i | ||||||||
\(118\) | 103824.i | 0.686424i | ||||||||
\(119\) | −83251.0 | −0.538917 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 350174. | 2.17431 | ||||||||
\(122\) | 156752.i | 0.953484i | ||||||||
\(123\) | 320892.i | 1.91248i | ||||||||
\(124\) | −108096. | −0.631329 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9016.00 | −0.0505927 | ||||||||
\(127\) | − 219196.i | − 1.20593i | −0.797766 | − | 0.602967i | \(-0.793985\pi\) | ||||
0.797766 | − | 0.602967i | \(-0.206015\pi\) | |||||||
\(128\) | − 16384.0i | − 0.0883883i | ||||||||
\(129\) | 38386.0 | 0.203095 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −96682.0 | −0.492229 | −0.246115 | − | 0.969241i | \(-0.579154\pi\) | ||||
−0.246115 | + | 0.969241i | \(0.579154\pi\) | |||||||
\(132\) | 194480.i | 0.971494i | ||||||||
\(133\) | − 84182.0i | − 0.412658i | ||||||||
\(134\) | −17664.0 | −0.0849820 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −108736. | −0.504111 | ||||||||
\(137\) | 187288.i | 0.852528i | 0.904599 | + | 0.426264i | \(0.140170\pi\) | ||||
−0.904599 | + | 0.426264i | \(0.859830\pi\) | |||||||
\(138\) | − 268600.i | − 1.20063i | ||||||||
\(139\) | −176894. | −0.776562 | −0.388281 | − | 0.921541i | \(-0.626931\pi\) | ||||
−0.388281 | + | 0.921541i | \(0.626931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9129.00 | 0.0386701 | ||||||||
\(142\) | − 127520.i | − 0.530710i | ||||||||
\(143\) | 236665.i | 0.967819i | ||||||||
\(144\) | −11776.0 | −0.0473251 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −20072.0 | −0.0779307 | ||||||||
\(147\) | − 40817.0i | − 0.155793i | ||||||||
\(148\) | 264288.i | 0.991798i | ||||||||
\(149\) | 199078. | 0.734611 | 0.367306 | − | 0.930100i | \(-0.380280\pi\) | ||||
0.367306 | + | 0.930100i | \(0.380280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 471583. | 1.68312 | 0.841561 | − | 0.540162i | \(-0.181637\pi\) | ||||
0.841561 | + | 0.540162i | \(0.181637\pi\) | |||||||
\(152\) | − 109952.i | − 0.386006i | ||||||||
\(153\) | 78154.0i | 0.269912i | ||||||||
\(154\) | −140140. | −0.476168 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −90032.0 | −0.296200 | ||||||||
\(157\) | − 72054.0i | − 0.233297i | −0.993173 | − | 0.116648i | \(-0.962785\pi\) | ||||
0.993173 | − | 0.116648i | \(-0.0372151\pi\) | |||||||
\(158\) | 111908.i | 0.356630i | ||||||||
\(159\) | −186728. | −0.585756 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 193550. | 0.588476 | ||||||||
\(162\) | − 272444.i | − 0.815623i | ||||||||
\(163\) | − 385334.i | − 1.13597i | −0.823038 | − | 0.567987i | \(-0.807722\pi\) | ||||
0.823038 | − | 0.567987i | \(-0.192278\pi\) | |||||||
\(164\) | −302016. | −0.876840 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 150576. | 0.424117 | ||||||||
\(167\) | − 542957.i | − 1.50652i | −0.657724 | − | 0.753259i | \(-0.728481\pi\) | ||||
0.657724 | − | 0.753259i | \(-0.271519\pi\) | |||||||
\(168\) | − 53312.0i | − 0.145731i | ||||||||
\(169\) | 261732. | 0.704920 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −79028.0 | −0.206676 | ||||||||
\(172\) | 36128.0i | 0.0931157i | ||||||||
\(173\) | − 370953.i | − 0.942331i | −0.882045 | − | 0.471166i | \(-0.843833\pi\) | ||||
0.882045 | − | 0.471166i | \(-0.156167\pi\) | |||||||
\(174\) | 311372. | 0.779662 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −183040. | −0.445414 | ||||||||
\(177\) | 441252.i | 1.05865i | ||||||||
\(178\) | 68864.0i | 0.162908i | ||||||||
\(179\) | 754172. | 1.75929 | 0.879646 | − | 0.475629i | \(-0.157780\pi\) | ||||
0.879646 | + | 0.475629i | \(0.157780\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 303840. | 0.689364 | 0.344682 | − | 0.938720i | \(-0.387987\pi\) | ||||
0.344682 | + | 0.938720i | \(0.387987\pi\) | |||||||
\(182\) | − 64876.0i | − 0.145180i | ||||||||
\(183\) | 666196.i | 1.47053i | ||||||||
\(184\) | 252800. | 0.550469 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −459408. | −0.973680 | ||||||||
\(187\) | 1.21478e6i | 2.54036i | ||||||||
\(188\) | 8592.00i | 0.0177296i | ||||||||
\(189\) | 164101. | 0.334162 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −186271. | −0.369455 | −0.184728 | − | 0.982790i | \(-0.559140\pi\) | ||||
−0.184728 | + | 0.982790i | \(0.559140\pi\) | |||||||
\(192\) | − 69632.0i | − 0.136319i | ||||||||
\(193\) | − 92504.0i | − 0.178759i | −0.995998 | − | 0.0893794i | \(-0.971512\pi\) | ||||
0.995998 | − | 0.0893794i | \(-0.0284884\pi\) | |||||||
\(194\) | 252700. | 0.482060 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 38416.0 | 0.0714286 | ||||||||
\(197\) | − 736368.i | − 1.35185i | −0.736969 | − | 0.675926i | \(-0.763744\pi\) | ||||
0.736969 | − | 0.675926i | \(-0.236256\pi\) | |||||||
\(198\) | 131560.i | 0.238485i | ||||||||
\(199\) | 481620. | 0.862128 | 0.431064 | − | 0.902321i | \(-0.358138\pi\) | ||||
0.431064 | + | 0.902321i | \(0.358138\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −75072.0 | −0.131065 | ||||||||
\(202\) | − 117000.i | − 0.201747i | ||||||||
\(203\) | 224371.i | 0.382144i | ||||||||
\(204\) | −462128. | −0.777476 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −596756. | −0.979780 | ||||||||
\(207\) | − 181700.i | − 0.294733i | ||||||||
\(208\) | − 84736.0i | − 0.135803i | ||||||||
\(209\) | −1.22837e6 | −1.94520 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 189531. | 0.293072 | 0.146536 | − | 0.989205i | \(-0.453188\pi\) | ||||
0.146536 | + | 0.989205i | \(0.453188\pi\) | |||||||
\(212\) | − 175744.i | − 0.268560i | ||||||||
\(213\) | − 541960.i | − 0.818499i | ||||||||
\(214\) | −334968. | −0.499999 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 214336. | 0.312580 | ||||||||
\(217\) | − 331044.i | − 0.477240i | ||||||||
\(218\) | − 421508.i | − 0.600710i | ||||||||
\(219\) | −85306.0 | −0.120190 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −562369. | −0.774534 | ||||||||
\(222\) | 1.12322e6i | 1.52962i | ||||||||
\(223\) | 22597.0i | 0.0304291i | 0.999884 | + | 0.0152145i | \(0.00484312\pi\) | ||||
−0.999884 | + | 0.0152145i | \(0.995157\pi\) | |||||||
\(224\) | 50176.0 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −491016. | −0.639476 | ||||||||
\(227\) | − 998117.i | − 1.28563i | −0.766020 | − | 0.642816i | \(-0.777766\pi\) | ||||
0.766020 | − | 0.642816i | \(-0.222234\pi\) | |||||||
\(228\) | − 467296.i | − 0.595326i | ||||||||
\(229\) | 854644. | 1.07695 | 0.538476 | − | 0.842641i | \(-0.319000\pi\) | ||||
0.538476 | + | 0.842641i | \(0.319000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −595595. | −0.734380 | ||||||||
\(232\) | 293056.i | 0.357463i | ||||||||
\(233\) | − 1.25818e6i | − 1.51829i | −0.650922 | − | 0.759144i | \(-0.725618\pi\) | ||||
0.650922 | − | 0.759144i | \(-0.274382\pi\) | |||||||
\(234\) | −60904.0 | −0.0727120 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −415296. | −0.485375 | ||||||||
\(237\) | 475609.i | 0.550021i | ||||||||
\(238\) | − 333004.i | − 0.381072i | ||||||||
\(239\) | 706581. | 0.800142 | 0.400071 | − | 0.916484i | \(-0.368985\pi\) | ||||
0.400071 | + | 0.916484i | \(0.368985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 616330. | 0.683551 | 0.341775 | − | 0.939782i | \(-0.388972\pi\) | ||||
0.341775 | + | 0.939782i | \(0.388972\pi\) | |||||||
\(242\) | 1.40070e6i | 1.53747i | ||||||||
\(243\) | − 344080.i | − 0.373804i | ||||||||
\(244\) | −627008. | −0.674215 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.28357e6 | −1.35233 | ||||||||
\(247\) | − 568658.i | − 0.593074i | ||||||||
\(248\) | − 432384.i | − 0.446417i | ||||||||
\(249\) | 639948. | 0.654103 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 190842. | 0.191201 | 0.0956004 | − | 0.995420i | \(-0.469523\pi\) | ||||
0.0956004 | + | 0.995420i | \(0.469523\pi\) | |||||||
\(252\) | − 36064.0i | − 0.0357744i | ||||||||
\(253\) | − 2.82425e6i | − 2.77397i | ||||||||
\(254\) | 876784. | 0.852724 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | − 1.13094e6i | − 1.06809i | −0.845456 | − | 0.534045i | \(-0.820671\pi\) | ||||
0.845456 | − | 0.534045i | \(-0.179329\pi\) | |||||||
\(258\) | 153544.i | 0.143610i | ||||||||
\(259\) | −809382. | −0.749729 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 210634. | 0.191394 | ||||||||
\(262\) | − 386728.i | − 0.348059i | ||||||||
\(263\) | 1.67377e6i | 1.49213i | 0.665874 | + | 0.746065i | \(0.268059\pi\) | ||||
−0.665874 | + | 0.746065i | \(0.731941\pi\) | |||||||
\(264\) | −777920. | −0.686950 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 336728. | 0.291793 | ||||||||
\(267\) | 292672.i | 0.251248i | ||||||||
\(268\) | − 70656.0i | − 0.0600914i | ||||||||
\(269\) | 630942. | 0.531629 | 0.265815 | − | 0.964024i | \(-0.414359\pi\) | ||||
0.265815 | + | 0.964024i | \(0.414359\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −372476. | −0.308088 | −0.154044 | − | 0.988064i | \(-0.549230\pi\) | ||||
−0.154044 | + | 0.988064i | \(0.549230\pi\) | |||||||
\(272\) | − 434944.i | − 0.356460i | ||||||||
\(273\) | − 275723.i | − 0.223906i | ||||||||
\(274\) | −749152. | −0.602828 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.07440e6 | 0.848972 | ||||||||
\(277\) | 867010.i | 0.678930i | 0.940619 | + | 0.339465i | \(0.110246\pi\) | ||||
−0.940619 | + | 0.339465i | \(0.889754\pi\) | |||||||
\(278\) | − 707576.i | − 0.549112i | ||||||||
\(279\) | −310776. | −0.239021 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.94498e6 | −1.46943 | −0.734716 | − | 0.678375i | \(-0.762685\pi\) | ||||
−0.734716 | + | 0.678375i | \(0.762685\pi\) | |||||||
\(282\) | 36516.0i | 0.0273439i | ||||||||
\(283\) | − 1.18501e6i | − 0.879543i | −0.898110 | − | 0.439771i | \(-0.855059\pi\) | ||||
0.898110 | − | 0.439771i | \(-0.144941\pi\) | |||||||
\(284\) | 510080. | 0.375269 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −946660. | −0.684351 | ||||||||
\(287\) | − 924924.i | − 0.662829i | ||||||||
\(288\) | − 47104.0i | − 0.0334639i | ||||||||
\(289\) | −1.46674e6 | −1.03302 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.07398e6 | 0.743467 | ||||||||
\(292\) | − 80288.0i | − 0.0551053i | ||||||||
\(293\) | − 33669.0i | − 0.0229119i | −0.999934 | − | 0.0114560i | \(-0.996353\pi\) | ||||
0.999934 | − | 0.0114560i | \(-0.00364662\pi\) | |||||||
\(294\) | 163268. | 0.110162 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.05715e6 | −0.701307 | ||||||||
\(297\) | − 2.39454e6i | − 1.57518i | ||||||||
\(298\) | 796312.i | 0.519449i | ||||||||
\(299\) | 1.30745e6 | 0.845760 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −110642. | −0.0703888 | ||||||||
\(302\) | 1.88633e6i | 1.19015i | ||||||||
\(303\) | − 497250.i | − 0.311149i | ||||||||
\(304\) | 439808. | 0.272948 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −312616. | −0.190857 | ||||||||
\(307\) | − 27043.0i | − 0.0163760i | −0.999966 | − | 0.00818802i | \(-0.997394\pi\) | ||||
0.999966 | − | 0.00818802i | \(-0.00260636\pi\) | |||||||
\(308\) | − 560560.i | − 0.336702i | ||||||||
\(309\) | −2.53621e6 | −1.51109 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.14919e6 | 1.26001 | 0.630004 | − | 0.776592i | \(-0.283053\pi\) | ||||
0.630004 | + | 0.776592i | \(0.283053\pi\) | |||||||
\(312\) | − 360128.i | − 0.209445i | ||||||||
\(313\) | 2.67052e6i | 1.54076i | 0.637583 | + | 0.770381i | \(0.279934\pi\) | ||||
−0.637583 | + | 0.770381i | \(0.720066\pi\) | |||||||
\(314\) | 288216. | 0.164966 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −447632. | −0.252176 | ||||||||
\(317\) | − 250514.i | − 0.140018i | −0.997546 | − | 0.0700090i | \(-0.977697\pi\) | ||||
0.997546 | − | 0.0700090i | \(-0.0223028\pi\) | |||||||
\(318\) | − 746912.i | − 0.414192i | ||||||||
\(319\) | 3.27398e6 | 1.80136 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.42361e6 | −0.771134 | ||||||||
\(322\) | 774200.i | 0.416115i | ||||||||
\(323\) | − 2.91888e6i | − 1.55672i | ||||||||
\(324\) | 1.08978e6 | 0.576733 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.54134e6 | 0.803255 | ||||||||
\(327\) | − 1.79141e6i | − 0.926457i | ||||||||
\(328\) | − 1.20806e6i | − 0.620019i | ||||||||
\(329\) | −26313.0 | −0.0134023 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.05899e6 | 0.531277 | 0.265639 | − | 0.964073i | \(-0.414417\pi\) | ||||
0.265639 | + | 0.964073i | \(0.414417\pi\) | |||||||
\(332\) | 602304.i | 0.299896i | ||||||||
\(333\) | 759828.i | 0.375495i | ||||||||
\(334\) | 2.17183e6 | 1.06527 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 213248. | 0.103047 | ||||||||
\(337\) | − 2.85025e6i | − 1.36712i | −0.729893 | − | 0.683562i | \(-0.760430\pi\) | ||||
0.729893 | − | 0.683562i | \(-0.239570\pi\) | |||||||
\(338\) | 1.04693e6i | 0.498454i | ||||||||
\(339\) | −2.08682e6 | −0.986246 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.83054e6 | −2.24962 | ||||||||
\(342\) | − 316112.i | − 0.146142i | ||||||||
\(343\) | 117649.i | 0.0539949i | ||||||||
\(344\) | −144512. | −0.0658427 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.48381e6 | 0.666329 | ||||||||
\(347\) | 1.89141e6i | 0.843259i | 0.906768 | + | 0.421630i | \(0.138542\pi\) | ||||
−0.906768 | + | 0.421630i | \(0.861458\pi\) | |||||||
\(348\) | 1.24549e6i | 0.551304i | ||||||||
\(349\) | 1.04232e6 | 0.458075 | 0.229038 | − | 0.973418i | \(-0.426442\pi\) | ||||
0.229038 | + | 0.973418i | \(0.426442\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.10852e6 | 0.480259 | ||||||||
\(352\) | − 732160.i | − 0.314956i | ||||||||
\(353\) | 2.30309e6i | 0.983725i | 0.870673 | + | 0.491862i | \(0.163684\pi\) | ||||
−0.870673 | + | 0.491862i | \(0.836316\pi\) | |||||||
\(354\) | −1.76501e6 | −0.748581 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −275456. | −0.115193 | ||||||||
\(357\) | − 1.41527e6i | − 0.587716i | ||||||||
\(358\) | 3.01669e6i | 1.24401i | ||||||||
\(359\) | 1.67594e6 | 0.686315 | 0.343157 | − | 0.939278i | \(-0.388504\pi\) | ||||
0.343157 | + | 0.939278i | \(0.388504\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 475425. | 0.192006 | ||||||||
\(362\) | 1.21536e6i | 0.487454i | ||||||||
\(363\) | 5.95296e6i | 2.37119i | ||||||||
\(364\) | 259504. | 0.102657 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.66478e6 | −1.03982 | ||||||||
\(367\) | 94663.0i | 0.0366872i | 0.999832 | + | 0.0183436i | \(0.00583928\pi\) | ||||
−0.999832 | + | 0.0183436i | \(0.994161\pi\) | |||||||
\(368\) | 1.01120e6i | 0.389240i | ||||||||
\(369\) | −868296. | −0.331972 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 538216. | 0.203012 | ||||||||
\(372\) | − 1.83763e6i | − 0.688496i | ||||||||
\(373\) | 953536.i | 0.354867i | 0.984133 | + | 0.177433i | \(0.0567794\pi\) | ||||
−0.984133 | + | 0.177433i | \(0.943221\pi\) | |||||||
\(374\) | −4.85914e6 | −1.79631 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −34368.0 | −0.0125367 | ||||||||
\(377\) | 1.51565e6i | 0.549219i | ||||||||
\(378\) | 656404.i | 0.236288i | ||||||||
\(379\) | −3.88824e6 | −1.39045 | −0.695225 | − | 0.718792i | \(-0.744695\pi\) | ||||
−0.695225 | + | 0.718792i | \(0.744695\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.72633e6 | 1.31513 | ||||||||
\(382\) | − 745084.i | − 0.261244i | ||||||||
\(383\) | − 2.93636e6i | − 1.02285i | −0.859328 | − | 0.511425i | \(-0.829118\pi\) | ||||
0.859328 | − | 0.511425i | \(-0.170882\pi\) | |||||||
\(384\) | 278528. | 0.0963920 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 370016. | 0.126402 | ||||||||
\(387\) | 103868.i | 0.0352537i | ||||||||
\(388\) | 1.01080e6i | 0.340868i | ||||||||
\(389\) | −1.70377e6 | −0.570871 | −0.285435 | − | 0.958398i | \(-0.592138\pi\) | ||||
−0.285435 | + | 0.958398i | \(0.592138\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.71105e6 | 2.21998 | ||||||||
\(392\) | 153664.i | 0.0505076i | ||||||||
\(393\) | − 1.64359e6i | − 0.536801i | ||||||||
\(394\) | 2.94547e6 | 0.955904 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −526240. | −0.168634 | ||||||||
\(397\) | 1.19110e6i | 0.379292i | 0.981853 | + | 0.189646i | \(0.0607340\pi\) | ||||
−0.981853 | + | 0.189646i | \(0.939266\pi\) | |||||||
\(398\) | 1.92648e6i | 0.609617i | ||||||||
\(399\) | 1.43109e6 | 0.450024 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.38330e6 | −1.05070 | −0.525351 | − | 0.850885i | \(-0.676066\pi\) | ||||
−0.525351 | + | 0.850885i | \(0.676066\pi\) | |||||||
\(402\) | − 300288.i | − 0.0926772i | ||||||||
\(403\) | − 2.23624e6i | − 0.685891i | ||||||||
\(404\) | 468000. | 0.142657 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −897484. | −0.270216 | ||||||||
\(407\) | 1.18104e7i | 3.53409i | ||||||||
\(408\) | − 1.84851e6i | − 0.549758i | ||||||||
\(409\) | 1.33185e6 | 0.393682 | 0.196841 | − | 0.980435i | \(-0.436932\pi\) | ||||
0.196841 | + | 0.980435i | \(0.436932\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.18390e6 | −0.929725 | ||||||||
\(412\) | − 2.38702e6i | − 0.692809i | ||||||||
\(413\) | − 1.27184e6i | − 0.366909i | ||||||||
\(414\) | 726800. | 0.208408 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 338944. | 0.0960273 | ||||||||
\(417\) | − 3.00720e6i | − 0.846880i | ||||||||
\(418\) | − 4.91348e6i | − 1.37546i | ||||||||
\(419\) | −5.82786e6 | −1.62171 | −0.810856 | − | 0.585246i | \(-0.800998\pi\) | ||||
−0.810856 | + | 0.585246i | \(0.800998\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.47430e6 | 0.680374 | 0.340187 | − | 0.940358i | \(-0.389510\pi\) | ||||
0.340187 | + | 0.940358i | \(0.389510\pi\) | |||||||
\(422\) | 758124.i | 0.207233i | ||||||||
\(423\) | 24702.0i | 0.00671245i | ||||||||
\(424\) | 702976. | 0.189900 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.16784e6 | 0.578766 | ||||||||
\(427\) | − 1.92021e6i | − 0.509659i | ||||||||
\(428\) | − 1.33987e6i | − 0.353552i | ||||||||
\(429\) | −4.02331e6 | −1.05546 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.61851e6 | 1.19759 | 0.598796 | − | 0.800902i | \(-0.295646\pi\) | ||||
0.598796 | + | 0.800902i | \(0.295646\pi\) | |||||||
\(432\) | 857344.i | 0.221027i | ||||||||
\(433\) | − 58606.0i | − 0.0150218i | −0.999972 | − | 0.00751091i | \(-0.997609\pi\) | ||||
0.999972 | − | 0.00751091i | \(-0.00239082\pi\) | |||||||
\(434\) | 1.32418e6 | 0.337459 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.68603e6 | 0.424766 | ||||||||
\(437\) | 6.78610e6i | 1.69987i | ||||||||
\(438\) | − 341224.i | − 0.0849874i | ||||||||
\(439\) | −7.04298e6 | −1.74419 | −0.872097 | − | 0.489332i | \(-0.837241\pi\) | ||||
−0.872097 | + | 0.489332i | \(0.837241\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 110446. | 0.0270429 | ||||||||
\(442\) | − 2.24948e6i | − 0.547678i | ||||||||
\(443\) | − 1.46894e6i | − 0.355627i | −0.984064 | − | 0.177813i | \(-0.943098\pi\) | ||||
0.984064 | − | 0.177813i | \(-0.0569023\pi\) | |||||||
\(444\) | −4.49290e6 | −1.08161 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −90388.0 | −0.0215166 | ||||||||
\(447\) | 3.38433e6i | 0.801131i | ||||||||
\(448\) | 200704.i | 0.0472456i | ||||||||
\(449\) | 7.48414e6 | 1.75197 | 0.875983 | − | 0.482341i | \(-0.160213\pi\) | ||||
0.875983 | + | 0.482341i | \(0.160213\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.34963e7 | −3.12446 | ||||||||
\(452\) | − 1.96406e6i | − 0.452178i | ||||||||
\(453\) | 8.01691e6i | 1.83553i | ||||||||
\(454\) | 3.99247e6 | 0.909079 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.86918e6 | 0.420959 | ||||||||
\(457\) | 170320.i | 0.0381483i | 0.999818 | + | 0.0190741i | \(0.00607186\pi\) | ||||
−0.999818 | + | 0.0190741i | \(0.993928\pi\) | |||||||
\(458\) | 3.41858e6i | 0.761520i | ||||||||
\(459\) | 5.68995e6 | 1.26060 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.28685e6 | −0.939476 | −0.469738 | − | 0.882806i | \(-0.655652\pi\) | ||||
−0.469738 | + | 0.882806i | \(0.655652\pi\) | |||||||
\(462\) | − 2.38238e6i | − 0.519285i | ||||||||
\(463\) | − 3.38317e6i | − 0.733452i | −0.930329 | − | 0.366726i | \(-0.880479\pi\) | ||||
0.930329 | − | 0.366726i | \(-0.119521\pi\) | |||||||
\(464\) | −1.17222e6 | −0.252764 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.03274e6 | 1.07359 | ||||||||
\(467\) | 5.18029e6i | 1.09916i | 0.835440 | + | 0.549581i | \(0.185213\pi\) | ||||
−0.835440 | + | 0.549581i | \(0.814787\pi\) | |||||||
\(468\) | − 243616.i | − 0.0514152i | ||||||||
\(469\) | 216384. | 0.0454248 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.22492e6 | 0.254422 | ||||||||
\(472\) | − 1.66118e6i | − 0.343212i | ||||||||
\(473\) | 1.61447e6i | 0.331801i | ||||||||
\(474\) | −1.90244e6 | −0.388924 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.33202e6 | 0.269459 | ||||||||
\(477\) | − 505264.i | − 0.101677i | ||||||||
\(478\) | 2.82632e6i | 0.565786i | ||||||||
\(479\) | 8.76779e6 | 1.74603 | 0.873014 | − | 0.487695i | \(-0.162162\pi\) | ||||
0.873014 | + | 0.487695i | \(0.162162\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.46746e6 | −1.07751 | ||||||||
\(482\) | 2.46532e6i | 0.483343i | ||||||||
\(483\) | 3.29035e6i | 0.641762i | ||||||||
\(484\) | −5.60278e6 | −1.08715 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.37632e6 | 0.264319 | ||||||||
\(487\) | 270154.i | 0.0516166i | 0.999667 | + | 0.0258083i | \(0.00821594\pi\) | ||||
−0.999667 | + | 0.0258083i | \(0.991784\pi\) | |||||||
\(488\) | − 2.50803e6i | − 0.476742i | ||||||||
\(489\) | 6.55068e6 | 1.23884 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.85550e6 | 0.908930 | 0.454465 | − | 0.890765i | \(-0.349830\pi\) | ||||
0.454465 | + | 0.890765i | \(0.349830\pi\) | |||||||
\(492\) | − 5.13427e6i | − 0.956238i | ||||||||
\(493\) | 7.77972e6i | 1.44161i | ||||||||
\(494\) | 2.27463e6 | 0.419367 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.72954e6 | 0.315664 | ||||||||
\(497\) | 1.56212e6i | 0.283677i | ||||||||
\(498\) | 2.55979e6i | 0.462521i | ||||||||
\(499\) | 2.98576e6 | 0.536789 | 0.268394 | − | 0.963309i | \(-0.413507\pi\) | ||||
0.268394 | + | 0.963309i | \(0.413507\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.23027e6 | 1.64293 | ||||||||
\(502\) | 763368.i | 0.135199i | ||||||||
\(503\) | 8.28783e6i | 1.46057i | 0.683145 | + | 0.730283i | \(0.260612\pi\) | ||||
−0.683145 | + | 0.730283i | \(0.739388\pi\) | |||||||
\(504\) | 144256. | 0.0252963 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.12970e7 | 1.96149 | ||||||||
\(507\) | 4.44944e6i | 0.768751i | ||||||||
\(508\) | 3.50714e6i | 0.602967i | ||||||||
\(509\) | −6.24307e6 | −1.06808 | −0.534040 | − | 0.845459i | \(-0.679327\pi\) | ||||
−0.534040 | + | 0.845459i | \(0.679327\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 245882. | 0.0416557 | ||||||||
\(512\) | 262144.i | 0.0441942i | ||||||||
\(513\) | 5.75358e6i | 0.965261i | ||||||||
\(514\) | 4.52377e6 | 0.755253 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −614176. | −0.101547 | ||||||||
\(517\) | 383955.i | 0.0631763i | ||||||||
\(518\) | − 3.23753e6i | − 0.530138i | ||||||||
\(519\) | 6.30620e6 | 1.02766 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.49509e6 | 1.20971 | 0.604856 | − | 0.796335i | \(-0.293230\pi\) | ||||
0.604856 | + | 0.796335i | \(0.293230\pi\) | |||||||
\(522\) | 842536.i | 0.135336i | ||||||||
\(523\) | − 3.80957e6i | − 0.609007i | −0.952511 | − | 0.304503i | \(-0.901510\pi\) | ||||
0.952511 | − | 0.304503i | \(-0.0984905\pi\) | |||||||
\(524\) | 1.54691e6 | 0.246115 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.69508e6 | −1.05509 | ||||||||
\(527\) | − 1.14784e7i | − 1.80035i | ||||||||
\(528\) | − 3.11168e6i | − 0.485747i | ||||||||
\(529\) | −9.16616e6 | −1.42413 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.19398e6 | −0.183764 | ||||||||
\(532\) | 1.34691e6i | 0.206329i | ||||||||
\(533\) | − 6.24796e6i | − 0.952621i | ||||||||
\(534\) | −1.17069e6 | −0.177659 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 282624. | 0.0424910 | ||||||||
\(537\) | 1.28209e7i | 1.91860i | ||||||||
\(538\) | 2.52377e6i | 0.375919i | ||||||||
\(539\) | 1.71672e6 | 0.254523 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.67156e6 | 1.12691 | 0.563457 | − | 0.826145i | \(-0.309471\pi\) | ||||
0.563457 | + | 0.826145i | \(0.309471\pi\) | |||||||
\(542\) | − 1.48990e6i | − 0.217851i | ||||||||
\(543\) | 5.16528e6i | 0.751786i | ||||||||
\(544\) | 1.73978e6 | 0.252055 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.10289e6 | 0.158326 | ||||||||
\(547\) | − 9.53845e6i | − 1.36304i | −0.731798 | − | 0.681522i | \(-0.761319\pi\) | ||||
0.731798 | − | 0.681522i | \(-0.238681\pi\) | |||||||
\(548\) | − 2.99661e6i | − 0.426264i | ||||||||
\(549\) | −1.80265e6 | −0.255258 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.86672e6 | −1.10386 | ||||||||
\(552\) | 4.29760e6i | 0.600314i | ||||||||
\(553\) | − 1.37087e6i | − 0.190627i | ||||||||
\(554\) | −3.46804e6 | −0.480076 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.83030e6 | 0.388281 | ||||||||
\(557\) | − 7.45022e6i | − 1.01749i | −0.860916 | − | 0.508746i | \(-0.830109\pi\) | ||||
0.860916 | − | 0.508746i | \(-0.169891\pi\) | |||||||
\(558\) | − 1.24310e6i | − 0.169014i | ||||||||
\(559\) | −747398. | −0.101163 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.06513e7 | −2.77039 | ||||||||
\(562\) | − 7.77992e6i | − 1.03905i | ||||||||
\(563\) | − 3.36698e6i | − 0.447682i | −0.974626 | − | 0.223841i | \(-0.928140\pi\) | ||||
0.974626 | − | 0.223841i | \(-0.0718596\pi\) | |||||||
\(564\) | −146064. | −0.0193351 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.74005e6 | 0.621931 | ||||||||
\(567\) | 3.33744e6i | 0.435969i | ||||||||
\(568\) | 2.04032e6i | 0.265355i | ||||||||
\(569\) | 4.05501e6 | 0.525063 | 0.262532 | − | 0.964923i | \(-0.415443\pi\) | ||||
0.262532 | + | 0.964923i | \(0.415443\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.31585e6 | 0.939020 | 0.469510 | − | 0.882927i | \(-0.344431\pi\) | ||||
0.469510 | + | 0.882927i | \(0.344431\pi\) | |||||||
\(572\) | − 3.78664e6i | − 0.483909i | ||||||||
\(573\) | − 3.16661e6i | − 0.402910i | ||||||||
\(574\) | 3.69970e6 | 0.468691 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 188416. | 0.0236626 | ||||||||
\(577\) | − 9.76895e6i | − 1.22154i | −0.791807 | − | 0.610771i | \(-0.790860\pi\) | ||||
0.791807 | − | 0.610771i | \(-0.209140\pi\) | |||||||
\(578\) | − 5.86698e6i | − 0.730457i | ||||||||
\(579\) | 1.57257e6 | 0.194945 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.84456e6 | −0.226700 | ||||||||
\(582\) | 4.29590e6i | 0.525711i | ||||||||
\(583\) | − 7.85356e6i | − 0.956963i | ||||||||
\(584\) | 321152. | 0.0389653 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 134676. | 0.0162012 | ||||||||
\(587\) | 3.75689e6i | 0.450021i | 0.974356 | + | 0.225011i | \(0.0722417\pi\) | ||||
−0.974356 | + | 0.225011i | \(0.927758\pi\) | |||||||
\(588\) | 653072.i | 0.0778965i | ||||||||
\(589\) | 1.16068e7 | 1.37856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.25183e7 | 1.47426 | ||||||||
\(592\) | − 4.22861e6i | − 0.495899i | ||||||||
\(593\) | − 2.89048e6i | − 0.337546i | −0.985655 | − | 0.168773i | \(-0.946020\pi\) | ||||
0.985655 | − | 0.168773i | \(-0.0539805\pi\) | |||||||
\(594\) | 9.57814e6 | 1.11382 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.18525e6 | −0.367306 | ||||||||
\(597\) | 8.18754e6i | 0.940194i | ||||||||
\(598\) | 5.22980e6i | 0.598043i | ||||||||
\(599\) | −1.32233e7 | −1.50582 | −0.752910 | − | 0.658124i | \(-0.771350\pi\) | ||||
−0.752910 | + | 0.658124i | \(0.771350\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.47399e6 | 0.392321 | 0.196161 | − | 0.980572i | \(-0.437153\pi\) | ||||
0.196161 | + | 0.980572i | \(0.437153\pi\) | |||||||
\(602\) | − 442568.i | − 0.0497724i | ||||||||
\(603\) | − 203136.i | − 0.0227506i | ||||||||
\(604\) | −7.54533e6 | −0.841561 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.98900e6 | 0.220015 | ||||||||
\(607\) | 6.45088e6i | 0.710636i | 0.934746 | + | 0.355318i | \(0.115627\pi\) | ||||
−0.934746 | + | 0.355318i | \(0.884373\pi\) | |||||||
\(608\) | 1.75923e6i | 0.193003i | ||||||||
\(609\) | −3.81431e6 | −0.416747 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −177747. | −0.0192619 | ||||||||
\(612\) | − 1.25046e6i | − 0.134956i | ||||||||
\(613\) | − 8.43820e6i | − 0.906982i | −0.891261 | − | 0.453491i | \(-0.850178\pi\) | ||||
0.891261 | − | 0.453491i | \(-0.149822\pi\) | |||||||
\(614\) | 108172. | 0.0115796 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.24224e6 | 0.238084 | ||||||||
\(617\) | 9.45501e6i | 0.999882i | 0.866059 | + | 0.499941i | \(0.166645\pi\) | ||||
−0.866059 | + | 0.499941i | \(0.833355\pi\) | |||||||
\(618\) | − 1.01449e7i | − 1.06850i | ||||||||
\(619\) | −1.43145e6 | −0.150158 | −0.0750790 | − | 0.997178i | \(-0.523921\pi\) | ||||
−0.0750790 | + | 0.997178i | \(0.523921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.32286e7 | −1.37652 | ||||||||
\(622\) | 8.59674e6i | 0.890960i | ||||||||
\(623\) | − 843584.i | − 0.0870780i | ||||||||
\(624\) | 1.44051e6 | 0.148100 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.06821e7 | −1.08948 | ||||||||
\(627\) | − 2.08823e7i | − 2.12134i | ||||||||
\(628\) | 1.15286e6i | 0.116648i | ||||||||
\(629\) | −2.80641e7 | −2.82829 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.01813e7 | −1.01795 | −0.508977 | − | 0.860780i | \(-0.669976\pi\) | ||||
−0.508977 | + | 0.860780i | \(0.669976\pi\) | |||||||
\(632\) | − 1.79053e6i | − 0.178315i | ||||||||
\(633\) | 3.22203e6i | 0.319610i | ||||||||
\(634\) | 1.00206e6 | 0.0990077 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.98765e6 | 0.292878 | ||||||||
\(637\) | 794731.i | 0.0776018i | ||||||||
\(638\) | 1.30959e7i | 1.27375i | ||||||||
\(639\) | 1.46648e6 | 0.142077 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.76908e7 | −1.70060 | −0.850300 | − | 0.526298i | \(-0.823580\pi\) | ||||
−0.850300 | + | 0.526298i | \(0.823580\pi\) | |||||||
\(642\) | − 5.69446e6i | − 0.545274i | ||||||||
\(643\) | − 1.82748e7i | − 1.74311i | −0.490296 | − | 0.871556i | \(-0.663111\pi\) | ||||
0.490296 | − | 0.871556i | \(-0.336889\pi\) | |||||||
\(644\) | −3.09680e6 | −0.294238 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.16755e7 | 1.10077 | ||||||||
\(647\) | 1.52897e6i | 0.143594i | 0.997419 | + | 0.0717972i | \(0.0228734\pi\) | ||||
−0.997419 | + | 0.0717972i | \(0.977127\pi\) | |||||||
\(648\) | 4.35910e6i | 0.407812i | ||||||||
\(649\) | −1.85585e7 | −1.72955 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.62775e6 | 0.520454 | ||||||||
\(652\) | 6.16534e6i | 0.567987i | ||||||||
\(653\) | 9.10088e6i | 0.835219i | 0.908627 | + | 0.417610i | \(0.137132\pi\) | ||||
−0.908627 | + | 0.417610i | \(0.862868\pi\) | |||||||
\(654\) | 7.16564e6 | 0.655104 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.83226e6 | 0.438420 | ||||||||
\(657\) | − 230828.i | − 0.0208629i | ||||||||
\(658\) | − 105252.i | − 0.00947689i | ||||||||
\(659\) | 430119. | 0.0385811 | 0.0192906 | − | 0.999814i | \(-0.493859\pi\) | ||||
0.0192906 | + | 0.999814i | \(0.493859\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.65248e6 | 0.681238 | 0.340619 | − | 0.940202i | \(-0.389363\pi\) | ||||
0.340619 | + | 0.940202i | \(0.389363\pi\) | |||||||
\(662\) | 4.23595e6i | 0.375670i | ||||||||
\(663\) | − 9.56027e6i | − 0.844669i | ||||||||
\(664\) | −2.40922e6 | −0.212058 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.03931e6 | −0.265515 | ||||||||
\(667\) | − 1.80870e7i | − 1.57418i | ||||||||
\(668\) | 8.68731e6i | 0.753259i | ||||||||
\(669\) | −384149. | −0.0331844 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.80194e7 | −2.40244 | ||||||||
\(672\) | 852992.i | 0.0728655i | ||||||||
\(673\) | 2.18404e7i | 1.85876i | 0.369128 | + | 0.929378i | \(0.379656\pi\) | ||||
−0.369128 | + | 0.929378i | \(0.620344\pi\) | |||||||
\(674\) | 1.14010e7 | 0.966702 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.18771e6 | −0.352460 | ||||||||
\(677\) | 1.39504e7i | 1.16981i | 0.811102 | + | 0.584905i | \(0.198868\pi\) | ||||
−0.811102 | + | 0.584905i | \(0.801132\pi\) | |||||||
\(678\) | − 8.34727e6i | − 0.697381i | ||||||||
\(679\) | −3.09558e6 | −0.257672 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.69680e7 | 1.40205 | ||||||||
\(682\) | − 1.93222e7i | − 1.59072i | ||||||||
\(683\) | − 2.29121e7i | − 1.87937i | −0.342040 | − | 0.939686i | \(-0.611118\pi\) | ||||
0.342040 | − | 0.939686i | \(-0.388882\pi\) | |||||||
\(684\) | 1.26445e6 | 0.103338 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −470596. | −0.0381802 | ||||||||
\(687\) | 1.45289e7i | 1.17447i | ||||||||
\(688\) | − 578048.i | − 0.0465578i | ||||||||
\(689\) | 3.63570e6 | 0.291770 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.69127e7 | −1.34747 | −0.673734 | − | 0.738974i | \(-0.735310\pi\) | ||||
−0.673734 | + | 0.738974i | \(0.735310\pi\) | |||||||
\(692\) | 5.93525e6i | 0.471166i | ||||||||
\(693\) | − 1.61161e6i | − 0.127476i | ||||||||
\(694\) | −7.56562e6 | −0.596274 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.98195e6 | −0.389831 | ||||||||
\(697\) | − 3.20703e7i | − 2.50047i | ||||||||
\(698\) | 4.16927e6i | 0.323908i | ||||||||
\(699\) | 2.13891e7 | 1.65577 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.90087e7 | −1.46102 | −0.730510 | − | 0.682902i | \(-0.760718\pi\) | ||||
−0.730510 | + | 0.682902i | \(0.760718\pi\) | |||||||
\(702\) | 4.43408e6i | 0.339594i | ||||||||
\(703\) | − 2.83779e7i | − 2.16567i | ||||||||
\(704\) | 2.92864e6 | 0.222707 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.21235e6 | −0.695598 | ||||||||
\(707\) | 1.43325e6i | 0.107838i | ||||||||
\(708\) | − 7.06003e6i | − 0.529326i | ||||||||
\(709\) | −1.66079e7 | −1.24079 | −0.620396 | − | 0.784289i | \(-0.713028\pi\) | ||||
−0.620396 | + | 0.784289i | \(0.713028\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.28694e6 | −0.0954740 | ||||||||
\(712\) | − 1.10182e6i | − 0.0814540i | ||||||||
\(713\) | 2.66862e7i | 1.96591i | ||||||||
\(714\) | 5.66107e6 | 0.415578 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.20668e7 | −0.879646 | ||||||||
\(717\) | 1.20119e7i | 0.872596i | ||||||||
\(718\) | 6.70378e6i | 0.485298i | ||||||||
\(719\) | −5.93610e6 | −0.428232 | −0.214116 | − | 0.976808i | \(-0.568687\pi\) | ||||
−0.214116 | + | 0.976808i | \(0.568687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.31026e6 | 0.523715 | ||||||||
\(722\) | 1.90170e6i | 0.135768i | ||||||||
\(723\) | 1.04776e7i | 0.745447i | ||||||||
\(724\) | −4.86144e6 | −0.344682 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.38118e7 | −1.67668 | ||||||||
\(727\) | 1.73276e7i | 1.21591i | 0.793970 | + | 0.607957i | \(0.208011\pi\) | ||||
−0.793970 | + | 0.607957i | \(0.791989\pi\) | |||||||
\(728\) | 1.03802e6i | 0.0725898i | ||||||||
\(729\) | −1.07016e7 | −0.745814 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.83634e6 | −0.265536 | ||||||||
\(732\) | − 1.06591e7i | − 0.735266i | ||||||||
\(733\) | − 1.39829e7i | − 0.961255i | −0.876925 | − | 0.480627i | \(-0.840409\pi\) | ||||
0.876925 | − | 0.480627i | \(-0.159591\pi\) | |||||||
\(734\) | −378652. | −0.0259418 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.04480e6 | −0.275234 | ||||||||
\(737\) | − 3.15744e6i | − 0.214125i | ||||||||
\(738\) | − 3.47318e6i | − 0.234740i | ||||||||
\(739\) | 1.14263e7 | 0.769649 | 0.384824 | − | 0.922990i | \(-0.374262\pi\) | ||||
0.384824 | + | 0.922990i | \(0.374262\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.66719e6 | 0.646777 | ||||||||
\(742\) | 2.15286e6i | 0.143551i | ||||||||
\(743\) | − 1.23126e7i | − 0.818236i | −0.912481 | − | 0.409118i | \(-0.865836\pi\) | ||||
0.912481 | − | 0.409118i | \(-0.134164\pi\) | |||||||
\(744\) | 7.35053e6 | 0.486840 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.81414e6 | −0.250929 | ||||||||
\(747\) | 1.73162e6i | 0.113541i | ||||||||
\(748\) | − 1.94366e7i | − 1.27018i | ||||||||
\(749\) | 4.10336e6 | 0.267261 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.43093e7 | −0.925806 | −0.462903 | − | 0.886409i | \(-0.653192\pi\) | ||||
−0.462903 | + | 0.886409i | \(0.653192\pi\) | |||||||
\(752\) | − 137472.i | − 0.00886481i | ||||||||
\(753\) | 3.24431e6i | 0.208514i | ||||||||
\(754\) | −6.06260e6 | −0.388356 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.62562e6 | −0.167081 | ||||||||
\(757\) | − 5.34505e6i | − 0.339010i | −0.985529 | − | 0.169505i | \(-0.945783\pi\) | ||||
0.985529 | − | 0.169505i | \(-0.0542168\pi\) | |||||||
\(758\) | − 1.55530e7i | − 0.983197i | ||||||||
\(759\) | 4.80122e7 | 3.02515 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.22568e6 | 0.389695 | 0.194848 | − | 0.980834i | \(-0.437579\pi\) | ||||
0.194848 | + | 0.980834i | \(0.437579\pi\) | |||||||
\(762\) | 1.49053e7i | 0.929938i | ||||||||
\(763\) | 5.16347e6i | 0.321093i | ||||||||
\(764\) | 2.98034e6 | 0.184728 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.17454e7 | 0.723264 | ||||||||
\(767\) | − 8.59144e6i | − 0.527324i | ||||||||
\(768\) | 1.11411e6i | 0.0681594i | ||||||||
\(769\) | −1.57888e7 | −0.962793 | −0.481397 | − | 0.876503i | \(-0.659870\pi\) | ||||
−0.481397 | + | 0.876503i | \(0.659870\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.92260e7 | 1.16481 | ||||||||
\(772\) | 1.48006e6i | 0.0893794i | ||||||||
\(773\) | 2.50453e7i | 1.50757i | 0.657121 | + | 0.753785i | \(0.271774\pi\) | ||||
−0.657121 | + | 0.753785i | \(0.728226\pi\) | |||||||
\(774\) | −415472. | −0.0249281 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.04320e6 | −0.241030 | ||||||||
\(777\) | − 1.37595e7i | − 0.817617i | ||||||||
\(778\) | − 6.81509e6i | − 0.403667i | ||||||||
\(779\) | 3.24290e7 | 1.91465 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.27942e7 | 1.33720 | ||||||||
\(782\) | 2.68442e7i | 1.56976i | ||||||||
\(783\) | − 1.53351e7i | − 0.893884i | ||||||||
\(784\) | −614656. | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.57438e6 | 0.379576 | ||||||||
\(787\) | − 1.28020e6i | − 0.0736784i | −0.999321 | − | 0.0368392i | \(-0.988271\pi\) | ||||
0.999321 | − | 0.0368392i | \(-0.0117289\pi\) | |||||||
\(788\) | 1.17819e7i | 0.675926i | ||||||||
\(789\) | −2.84541e7 | −1.62724 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.01495e6 | 0.341815 | ||||||||
\(792\) | − 2.10496e6i | − 0.119242i | ||||||||
\(793\) | − 1.29712e7i | − 0.732484i | ||||||||
\(794\) | −4.76442e6 | −0.268200 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.70592e6 | −0.431064 | ||||||||
\(797\) | − 1.13798e7i | − 0.634584i | −0.948328 | − | 0.317292i | \(-0.897226\pi\) | ||||
0.948328 | − | 0.317292i | \(-0.102774\pi\) | |||||||
\(798\) | 5.72438e6i | 0.318215i | ||||||||
\(799\) | −912363. | −0.0505593 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −791936. | −0.0436123 | ||||||||
\(802\) | − 1.35332e7i | − 0.742959i | ||||||||
\(803\) | − 3.58787e6i | − 0.196358i | ||||||||
\(804\) | 1.20115e6 | 0.0655327 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.94494e6 | 0.484998 | ||||||||
\(807\) | 1.07260e7i | 0.579768i | ||||||||
\(808\) | 1.87200e6i | 0.100874i | ||||||||
\(809\) | 1.70542e7 | 0.916138 | 0.458069 | − | 0.888917i | \(-0.348541\pi\) | ||||
0.458069 | + | 0.888917i | \(0.348541\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.21494e7 | −1.18252 | −0.591262 | − | 0.806480i | \(-0.701370\pi\) | ||||
−0.591262 | + | 0.806480i | \(0.701370\pi\) | |||||||
\(812\) | − 3.58994e6i | − 0.191072i | ||||||||
\(813\) | − 6.33209e6i | − 0.335986i | ||||||||
\(814\) | −4.72415e7 | −2.49898 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.39405e6 | 0.388738 | ||||||||
\(817\) | − 3.87924e6i | − 0.203326i | ||||||||
\(818\) | 5.32738e6i | 0.278375i | ||||||||
\(819\) | 746074. | 0.0388662 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.01068e7 | −0.523307 | −0.261654 | − | 0.965162i | \(-0.584268\pi\) | ||||
−0.261654 | + | 0.965162i | \(0.584268\pi\) | |||||||
\(822\) | − 1.27356e7i | − 0.657415i | ||||||||
\(823\) | 1.83993e7i | 0.946895i | 0.880822 | + | 0.473447i | \(0.156991\pi\) | ||||
−0.880822 | + | 0.473447i | \(0.843009\pi\) | |||||||
\(824\) | 9.54810e6 | 0.489890 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.08738e6 | 0.259444 | ||||||||
\(827\) | − 2.48056e7i | − 1.26121i | −0.776105 | − | 0.630604i | \(-0.782807\pi\) | ||||
0.776105 | − | 0.630604i | \(-0.217193\pi\) | |||||||
\(828\) | 2.90720e6i | 0.147367i | ||||||||
\(829\) | 1.19708e6 | 0.0604976 | 0.0302488 | − | 0.999542i | \(-0.490370\pi\) | ||||
0.0302488 | + | 0.999542i | \(0.490370\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.47392e7 | −0.740407 | ||||||||
\(832\) | 1.35578e6i | 0.0679015i | ||||||||
\(833\) | 4.07930e6i | 0.203692i | ||||||||
\(834\) | 1.20288e7 | 0.598835 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.96539e7 | 0.972598 | ||||||||
\(837\) | 2.26258e7i | 1.11633i | ||||||||
\(838\) | − 2.33114e7i | − 1.14672i | ||||||||
\(839\) | 3.17171e7 | 1.55557 | 0.777783 | − | 0.628533i | \(-0.216344\pi\) | ||||
0.777783 | + | 0.628533i | \(0.216344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 456092. | 0.0222363 | ||||||||
\(842\) | 9.89722e6i | 0.481097i | ||||||||
\(843\) | − 3.30647e7i | − 1.60249i | ||||||||
\(844\) | −3.03250e6 | −0.146536 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −98808.0 | −0.00474642 | ||||||||
\(847\) | − 1.71585e7i | − 0.821810i | ||||||||
\(848\) | 2.81190e6i | 0.134280i | ||||||||
\(849\) | 2.01452e7 | 0.959186 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.52461e7 | 3.08838 | ||||||||
\(852\) | 8.67136e6i | 0.409250i | ||||||||
\(853\) | − 3.18237e7i | − 1.49754i | −0.662831 | − | 0.748769i | \(-0.730645\pi\) | ||||
0.662831 | − | 0.748769i | \(-0.269355\pi\) | |||||||
\(854\) | 7.68085e6 | 0.360383 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.35949e6 | 0.249999 | ||||||||
\(857\) | 2.27853e7i | 1.05975i | 0.848076 | + | 0.529874i | \(0.177761\pi\) | ||||
−0.848076 | + | 0.529874i | \(0.822239\pi\) | |||||||
\(858\) | − 1.60932e7i | − 0.746319i | ||||||||
\(859\) | 1.85966e7 | 0.859907 | 0.429953 | − | 0.902851i | \(-0.358530\pi\) | ||||
0.429953 | + | 0.902851i | \(0.358530\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.57237e7 | 0.722848 | ||||||||
\(862\) | 1.84740e7i | 0.846825i | ||||||||
\(863\) | 2.77046e7i | 1.26627i | 0.774043 | + | 0.633133i | \(0.218231\pi\) | ||||
−0.774043 | + | 0.633133i | \(0.781769\pi\) | |||||||
\(864\) | −3.42938e6 | −0.156290 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 234424. | 0.0106220 | ||||||||
\(867\) | − 2.49346e7i | − 1.12656i | ||||||||
\(868\) | 5.29670e6i | 0.238620i | ||||||||
\(869\) | −2.00036e7 | −0.898582 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.46170e6 | 0.0652847 | ||||||||
\(872\) | 6.74413e6i | 0.300355i | ||||||||
\(873\) | 2.90605e6i | 0.129053i | ||||||||
\(874\) | −2.71444e7 | −1.20199 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.36490e6 | 0.0600951 | ||||||||
\(877\) | − 2.41150e7i | − 1.05874i | −0.848391 | − | 0.529370i | \(-0.822428\pi\) | ||||
0.848391 | − | 0.529370i | \(-0.177572\pi\) | |||||||
\(878\) | − 2.81719e7i | − 1.23333i | ||||||||
\(879\) | 572373. | 0.0249866 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.26207e7 | −0.547827 | −0.273914 | − | 0.961754i | \(-0.588318\pi\) | ||||
−0.273914 | + | 0.961754i | \(0.588318\pi\) | |||||||
\(882\) | 441784.i | 0.0191222i | ||||||||
\(883\) | 6.01876e6i | 0.259780i | 0.991528 | + | 0.129890i | \(0.0414624\pi\) | ||||
−0.991528 | + | 0.129890i | \(0.958538\pi\) | |||||||
\(884\) | 8.99790e6 | 0.387267 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.87575e6 | 0.251466 | ||||||||
\(887\) | 2.36901e7i | 1.01102i | 0.862821 | + | 0.505509i | \(0.168695\pi\) | ||||
−0.862821 | + | 0.505509i | \(0.831305\pi\) | |||||||
\(888\) | − 1.79716e7i | − 0.764811i | ||||||||
\(889\) | −1.07406e7 | −0.455800 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.86994e7 | 2.05508 | ||||||||
\(892\) | − 361552.i | − 0.0152145i | ||||||||
\(893\) | − 922566.i | − 0.0387141i | ||||||||
\(894\) | −1.35373e7 | −0.566485 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −802816. | −0.0334077 | ||||||||
\(897\) | 2.22266e7i | 0.922344i | ||||||||
\(898\) | 2.99365e7i | 1.23883i | ||||||||
\(899\) | −3.09357e7 | −1.27662 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.86618e7 | 0.765847 | ||||||||
\(902\) | − 5.39854e7i | − 2.20933i | ||||||||
\(903\) | − 1.88091e6i | − 0.0767626i | ||||||||
\(904\) | 7.85626e6 | 0.319738 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.20676e7 | −1.29792 | ||||||||
\(907\) | − 1.10583e7i | − 0.446346i | −0.974779 | − | 0.223173i | \(-0.928359\pi\) | ||||
0.974779 | − | 0.223173i | \(-0.0716414\pi\) | |||||||
\(908\) | 1.59699e7i | 0.642816i | ||||||||
\(909\) | 1.34550e6 | 0.0540100 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.07573e6 | 0.122787 | 0.0613934 | − | 0.998114i | \(-0.480446\pi\) | ||||
0.0613934 | + | 0.998114i | \(0.480446\pi\) | |||||||
\(912\) | 7.47674e6i | 0.297663i | ||||||||
\(913\) | 2.69155e7i | 1.06862i | ||||||||
\(914\) | −681280. | −0.0269749 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.36743e7 | −0.538476 | ||||||||
\(917\) | 4.73742e6i | 0.186045i | ||||||||
\(918\) | 2.27598e7i | 0.891378i | ||||||||
\(919\) | 1.89018e7 | 0.738270 | 0.369135 | − | 0.929376i | \(-0.379654\pi\) | ||||
0.369135 | + | 0.929376i | \(0.379654\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 459731. | 0.0178589 | ||||||||
\(922\) | − 1.71474e7i | − 0.664310i | ||||||||
\(923\) | 1.05523e7i | 0.407701i | ||||||||
\(924\) | 9.52952e6 | 0.367190 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.35327e7 | 0.518629 | ||||||||
\(927\) | − 6.86269e6i | − 0.262298i | ||||||||
\(928\) | − 4.68890e6i | − 0.178731i | ||||||||
\(929\) | 1.81458e7 | 0.689821 | 0.344911 | − | 0.938636i | \(-0.387909\pi\) | ||||
0.344911 | + | 0.938636i | \(0.387909\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.12492e6 | −0.155970 | ||||||||
\(932\) | 2.01309e7i | 0.759144i | ||||||||
\(933\) | 3.65362e7i | 1.37410i | ||||||||
\(934\) | −2.07212e7 | −0.777225 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 974464. | 0.0363560 | ||||||||
\(937\) | − 2.17350e7i | − 0.808744i | −0.914595 | − | 0.404372i | \(-0.867490\pi\) | ||||
0.914595 | − | 0.404372i | \(-0.132510\pi\) | |||||||
\(938\) | 865536.i | 0.0321202i | ||||||||
\(939\) | −4.53989e7 | −1.68028 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.86808e7 | 0.687735 | 0.343868 | − | 0.939018i | \(-0.388263\pi\) | ||||
0.343868 | + | 0.939018i | \(0.388263\pi\) | |||||||
\(942\) | 4.89967e6i | 0.179904i | ||||||||
\(943\) | 7.45602e7i | 2.73041i | ||||||||
\(944\) | 6.64474e6 | 0.242688 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.45788e6 | −0.234618 | ||||||||
\(947\) | − 2.24778e6i | − 0.0814476i | −0.999170 | − | 0.0407238i | \(-0.987034\pi\) | ||||
0.999170 | − | 0.0407238i | \(-0.0129664\pi\) | |||||||
\(948\) | − 7.60974e6i | − 0.275010i | ||||||||
\(949\) | 1.66096e6 | 0.0598678 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.25874e6 | 0.152697 | ||||||||
\(952\) | 5.32806e6i | 0.190536i | ||||||||
\(953\) | 3.73293e7i | 1.33143i | 0.746207 | + | 0.665714i | \(0.231873\pi\) | ||||
−0.746207 | + | 0.665714i | \(0.768127\pi\) | |||||||
\(954\) | 2.02106e6 | 0.0718964 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.13053e7 | −0.400071 | ||||||||
\(957\) | 5.56577e7i | 1.96447i | ||||||||
\(958\) | 3.50711e7i | 1.23463i | ||||||||
\(959\) | 9.17711e6 | 0.322225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.70144e7 | 0.594303 | ||||||||
\(962\) | − 2.18698e7i | − 0.761917i | ||||||||
\(963\) | − 3.85213e6i | − 0.133855i | ||||||||
\(964\) | −9.86128e6 | −0.341775 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.31614e7 | −0.453795 | ||||||||
\(967\) | 2.61870e7i | 0.900573i | 0.892884 | + | 0.450287i | \(0.148678\pi\) | ||||
−0.892884 | + | 0.450287i | \(0.851322\pi\) | |||||||
\(968\) | − 2.24111e7i | − 0.768733i | ||||||||
\(969\) | 4.96210e7 | 1.69768 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.91957e7 | −1.33410 | −0.667052 | − | 0.745011i | \(-0.732444\pi\) | ||||
−0.667052 | + | 0.745011i | \(0.732444\pi\) | |||||||
\(972\) | 5.50528e6i | 0.186902i | ||||||||
\(973\) | 8.66781e6i | 0.293513i | ||||||||
\(974\) | −1.08062e6 | −0.0364984 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.00321e7 | 0.337108 | ||||||||
\(977\) | 3.03935e6i | 0.101870i | 0.998702 | + | 0.0509348i | \(0.0162201\pi\) | ||||
−0.998702 | + | 0.0509348i | \(0.983780\pi\) | |||||||
\(978\) | 2.62027e7i | 0.875990i | ||||||||
\(979\) | −1.23094e7 | −0.410470 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.84734e6 | 0.160817 | ||||||||
\(982\) | 1.94220e7i | 0.642711i | ||||||||
\(983\) | 1.59937e7i | 0.527915i | 0.964534 | + | 0.263957i | \(0.0850278\pi\) | ||||
−0.964534 | + | 0.263957i | \(0.914972\pi\) | |||||||
\(984\) | 2.05371e7 | 0.676163 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.11189e7 | −1.01937 | ||||||||
\(987\) | − 447321.i | − 0.0146159i | ||||||||
\(988\) | 9.09853e6i | 0.296537i | ||||||||
\(989\) | 8.91910e6 | 0.289955 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.63186e6 | 0.117475 | 0.0587375 | − | 0.998273i | \(-0.481293\pi\) | ||||
0.0587375 | + | 0.998273i | \(0.481293\pi\) | |||||||
\(992\) | 6.91814e6i | 0.223208i | ||||||||
\(993\) | 1.80028e7i | 0.579384i | ||||||||
\(994\) | −6.24848e6 | −0.200590 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.02392e7 | −0.327052 | ||||||||
\(997\) | − 4.33287e7i | − 1.38051i | −0.723568 | − | 0.690253i | \(-0.757499\pi\) | ||||
0.723568 | − | 0.690253i | \(-0.242501\pi\) | |||||||
\(998\) | 1.19430e7i | 0.379567i | ||||||||
\(999\) | 5.53188e7 | 1.75371 |
(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 | 350.6.c.a.99.2 | 2 | ||
5.2 | odd | 4 | 350.6.a.e.1.1 | 1 | |||
5.3 | odd | 4 | 70.6.a.e.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 350.6.c.a.99.1 | 2 | ||
15.8 | even | 4 | 630.6.a.b.1.1 | 1 | |||
20.3 | even | 4 | 560.6.a.h.1.1 | 1 | |||
35.13 | even | 4 | 490.6.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.6.a.e.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
350.6.a.e.1.1 | 1 | 5.2 | odd | 4 | |||
350.6.c.a.99.1 | 2 | 5.4 | even | 2 | inner | ||
350.6.c.a.99.2 | 2 | 1.1 | even | 1 | trivial | ||
490.6.a.m.1.1 | 1 | 35.13 | even | 4 | |||
560.6.a.h.1.1 | 1 | 20.3 | even | 4 | |||
630.6.a.b.1.1 | 1 | 15.8 | even | 4 |