Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.383");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.c (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: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 306 x^{18} + 37827 x^{16} + 2442168 x^{14} + 88368509 x^{12} + 1774000974 x^{10} + 18093172325 x^{8} + 74958811500 x^{6} + 79355888475 x^{4} + \cdots + 2870280625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{88}\cdot 3^{14}\cdot 41^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.10 | ||
Root | \(-5.94193i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.6.c.a.383.9 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.25525 | + | 15.4245i | −0.144674 | + | 0.989479i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 86.6842i | 1.55065i | 0.631560 | + | 0.775327i | \(0.282415\pi\) | ||||
−0.631560 | + | 0.775327i | \(0.717585\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 110.468i | − | 0.852101i | −0.904699 | − | 0.426051i | \(-0.859905\pi\) | ||
0.904699 | − | 0.426051i | \(-0.140095\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −232.828 | − | 69.5720i | −0.958139 | − | 0.286304i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 212.115 | 0.528555 | 0.264278 | − | 0.964447i | \(-0.414866\pi\) | ||||
0.264278 | + | 0.964447i | \(0.414866\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 539.316 | 0.885084 | 0.442542 | − | 0.896748i | \(-0.354077\pi\) | ||||
0.442542 | + | 0.896748i | \(0.354077\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1337.06 | − | 195.494i | −1.53434 | − | 0.224340i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 24.1619i | 0.0202773i | 0.999949 | + | 0.0101386i | \(0.00322728\pi\) | ||||
−0.999949 | + | 0.0101386i | \(0.996773\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1930.54i | − | 1.22686i | −0.789749 | − | 0.613430i | \(-0.789789\pi\) | ||
0.789749 | − | 0.613430i | \(-0.210211\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1703.91 | + | 249.133i | 0.843137 | + | 0.123277i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −275.110 | −0.108439 | −0.0542197 | − | 0.998529i | \(-0.517267\pi\) | ||||
−0.0542197 | + | 0.998529i | \(0.517267\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4389.15 | −1.40453 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1598.19 | − | 3434.34i | 0.421910 | − | 0.906638i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7337.17i | − | 1.62007i | −0.586382 | − | 0.810034i | \(-0.699448\pi\) | ||
0.586382 | − | 0.810034i | \(-0.300552\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7478.16i | − | 1.39762i | −0.715305 | − | 0.698812i | \(-0.753712\pi\) | ||
0.715305 | − | 0.698812i | \(-0.246288\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −478.373 | + | 3271.76i | −0.0764683 | + | 0.522995i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9575.83 | 1.32131 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7681.01 | −0.922389 | −0.461195 | − | 0.887299i | \(-0.652579\pi\) | ||||
−0.461195 | + | 0.887299i | \(0.652579\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1216.29 | + | 8318.65i | −0.128049 | + | 0.875773i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 19394.9i | − | 1.80188i | −0.433939 | − | 0.900942i | \(-0.642877\pi\) | ||
0.433939 | − | 0.900942i | \(-0.357123\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4494.69i | 0.370705i | 0.982672 | + | 0.185352i | \(0.0593427\pi\) | ||||
−0.982672 | + | 0.185352i | \(0.940657\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6030.79 | − | 20182.5i | 0.443959 | − | 1.48574i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3629.25 | 0.239647 | 0.119824 | − | 0.992795i | \(-0.461767\pi\) | ||||
0.119824 | + | 0.992795i | \(0.461767\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4603.83 | 0.273923 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −372.684 | − | 54.4911i | −0.0200639 | − | 0.00293360i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3676.39i | 0.179776i | 0.995952 | + | 0.0898880i | \(0.0286509\pi\) | ||||
−0.995952 | + | 0.0898880i | \(0.971349\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18387.1i | 0.819606i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 29777.5 | + | 4353.85i | 1.21395 | + | 0.177495i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 23949.3 | 0.895702 | 0.447851 | − | 0.894108i | \(-0.352189\pi\) | ||||
0.447851 | + | 0.894108i | \(0.352189\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −43340.3 | −1.49131 | −0.745653 | − | 0.666334i | \(-0.767863\pi\) | ||||
−0.745653 | + | 0.666334i | \(0.767863\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7685.47 | + | 25720.0i | −0.243960 | + | 0.816431i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 46750.1i | 1.37246i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 65528.4i | 1.78337i | 0.452652 | + | 0.891687i | \(0.350478\pi\) | ||||
−0.452652 | + | 0.891687i | \(0.649522\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 620.442 | − | 4243.43i | 0.0156884 | − | 0.107299i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 30068.2 | 0.707882 | 0.353941 | − | 0.935268i | \(-0.384841\pi\) | ||||
0.353941 | + | 0.935268i | \(0.384841\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −43260.2 | −0.950127 | −0.475063 | − | 0.879952i | \(-0.657575\pi\) | ||||
−0.475063 | + | 0.879952i | \(0.657575\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9898.63 | − | 67700.3i | 0.203199 | − | 1.38975i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 23432.0i | − | 0.450383i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 90539.6i | − | 1.63219i | −0.577917 | − | 0.816096i | \(-0.696134\pi\) | ||
0.577917 | − | 0.816096i | \(-0.303866\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 49368.5 | + | 32396.6i | 0.836060 | + | 0.548639i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 109867. | 1.75053 | 0.875266 | − | 0.483641i | \(-0.160686\pi\) | ||||
0.875266 | + | 0.483641i | \(0.160686\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2094.46 | −0.0314430 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 113172. | + | 16547.1i | 1.60302 | + | 0.234382i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 138798.i | 1.85741i | 0.370822 | + | 0.928704i | \(0.379076\pi\) | ||||
−0.370822 | + | 0.928704i | \(0.620924\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 59577.1i | − | 0.754181i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 115347. | + | 16865.1i | 1.38292 | + | 0.202200i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 167347. | 1.90243 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4237.49 | −0.0457277 | −0.0228638 | − | 0.999739i | \(-0.507278\pi\) | ||||
−0.0228638 | + | 0.999739i | \(0.507278\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −49386.3 | − | 14757.3i | −0.506429 | − | 0.151328i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 162305.i | − | 1.58317i | −0.611057 | − | 0.791587i | \(-0.709255\pi\) | ||
0.611057 | − | 0.791587i | \(-0.290745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 91064.8i | − | 0.845780i | −0.906181 | − | 0.422890i | \(-0.861016\pi\) | ||
0.906181 | − | 0.422890i | \(-0.138984\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −21595.9 | + | 147702.i | −0.191160 | + | 1.30741i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −156580. | −1.32214 | −0.661068 | − | 0.750326i | \(-0.729897\pi\) | ||||
−0.661068 | + | 0.750326i | \(0.729897\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 113832. | 0.917692 | 0.458846 | − | 0.888516i | \(-0.348263\pi\) | ||||
0.458846 | + | 0.888516i | \(0.348263\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17322.6 | − | 118475.i | 0.133446 | − | 0.912685i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9212.03i | − | 0.0678671i | −0.999424 | − | 0.0339336i | \(-0.989197\pi\) | ||
0.999424 | − | 0.0339336i | \(-0.0108035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 23847.7i | − | 0.168152i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −125568. | − | 37521.2i | −0.848033 | − | 0.253403i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2669.12 | 0.0172783 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −116058. | −0.720629 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 299155. | + | 43740.2i | 1.78293 | + | 0.260686i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 109582.i | − | 0.627284i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 82080.7i | 0.451577i | 0.974176 | + | 0.225788i | \(0.0724958\pi\) | ||||
−0.974176 | + | 0.225788i | \(0.927504\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −69328.1 | − | 10136.6i | −0.366805 | − | 0.0536315i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 192564. | 0.980387 | 0.490193 | − | 0.871614i | \(-0.336926\pi\) | ||||
0.490193 | + | 0.871614i | \(0.336926\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −213263. | −1.04541 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 297703. | + | 138538.i | 1.40588 | + | 0.654237i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 262306.i | 1.19401i | 0.802238 | + | 0.597004i | \(0.203642\pi\) | ||||
−0.802238 | + | 0.597004i | \(0.796358\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 33737.6i | 0.148108i | 0.997254 | + | 0.0740539i | \(0.0235937\pi\) | ||||
−0.997254 | + | 0.0740539i | \(0.976406\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8184.86 | + | 55979.2i | −0.0346708 | + | 0.237126i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 114397. | 0.467816 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 636017. | 2.51217 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10382.8 | + | 71011.5i | −0.0396296 | + | 0.271041i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 322123.i | − | 1.18866i | −0.804223 | − | 0.594328i | \(-0.797418\pi\) | ||
0.804223 | − | 0.594328i | \(-0.202582\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 190296.i | 0.679183i | 0.940573 | + | 0.339592i | \(0.110289\pi\) | ||||
−0.940573 | + | 0.339592i | \(0.889711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1680.99 | − | 5625.56i | 0.00580547 | − | 0.0194284i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 648238. | 2.16723 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6464.74 | 0.0209316 | 0.0104658 | − | 0.999945i | \(-0.496669\pi\) | ||||
0.0104658 | + | 0.999945i | \(0.496669\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −56706.3 | − | 8291.16i | −0.177885 | − | 0.0260089i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 30390.9i | 0.0924014i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 333250.i | − | 0.982428i | −0.871039 | − | 0.491214i | \(-0.836553\pi\) | ||
0.871039 | − | 0.491214i | \(-0.163447\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −283610. | − | 41467.4i | −0.810984 | − | 0.118576i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −430857. | −1.19548 | −0.597740 | − | 0.801690i | \(-0.703934\pi\) | ||||
−0.597740 | + | 0.801690i | \(0.703934\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −80431.7 | −0.216626 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −134311. | + | 449483.i | −0.351255 | + | 1.17550i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 720397.i | − | 1.83002i | −0.403428 | − | 0.915011i | \(-0.632181\pi\) | ||
0.403428 | − | 0.915011i | \(-0.367819\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 484861.i | 1.19680i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −54011.7 | + | 369406.i | −0.129585 | + | 0.886279i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 822982. | 1.91981 | 0.959904 | − | 0.280329i | \(-0.0904437\pi\) | ||||
0.959904 | + | 0.280329i | \(0.0904437\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −86567.9 | −0.196409 | −0.0982043 | − | 0.995166i | \(-0.531310\pi\) | ||||
−0.0982043 | + | 0.995166i | \(0.531310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 97743.1 | − | 668500.i | 0.215754 | − | 1.47562i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 665822.i | − | 1.43031i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5125.11i | 0.0107176i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −379384. | − | 176549.i | −0.772547 | − | 0.359510i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 93397.9 | 0.185248 | 0.0926240 | − | 0.995701i | \(-0.470475\pi\) | ||||
0.0926240 | + | 0.995701i | \(0.470475\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 63345.4 | 0.122411 | 0.0612057 | − | 0.998125i | \(-0.480505\pi\) | ||||
0.0612057 | + | 0.998125i | \(0.480505\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −721096. | − | 105433.i | −1.35802 | − | 0.198560i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 603734.i | 1.10836i | 0.832397 | + | 0.554179i | \(0.186968\pi\) | ||||
−0.832397 | + | 0.554179i | \(0.813032\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 324247.i | − | 0.580420i | −0.956963 | − | 0.290210i | \(-0.906275\pi\) | ||
0.956963 | − | 0.290210i | \(-0.0937252\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.01074e6 | − | 147783.i | −1.76461 | − | 0.258008i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −810522. | −1.38046 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.68123e6 | 2.79410 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 64053.3 | + | 19140.0i | 0.103900 | + | 0.0310467i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 409497.i | − | 0.648463i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 660510.i | − | 1.02135i | −0.859775 | − | 0.510673i | \(-0.829396\pi\) | ||
0.859775 | − | 0.510673i | \(-0.170604\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −67811.2 | + | 463785.i | −0.102412 | + | 0.700435i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −389618. | −0.574835 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −826097. | −1.19092 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 97562.5 | − | 667265.i | 0.137459 | − | 0.940131i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13030.9i | 0.0179471i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 162536.i | 0.218870i | 0.993994 | + | 0.109435i | \(0.0349042\pi\) | ||||
−0.993994 | + | 0.109435i | \(0.965096\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.02192e6 | + | 305362.i | 1.34573 | + | 0.402123i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −667969. | −0.860383 | −0.430192 | − | 0.902738i | \(-0.641554\pi\) | ||||
−0.430192 | + | 0.902738i | \(0.641554\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −945355. | −1.19126 | −0.595630 | − | 0.803259i | \(-0.703097\pi\) | ||||
−0.595630 | + | 0.803259i | \(0.703097\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 361425. | + | 52844.9i | 0.445644 | + | 0.0651588i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 666944.i | − | 0.804821i | −0.915459 | − | 0.402411i | \(-0.868172\pi\) | ||
0.915459 | − | 0.402411i | \(-0.131828\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 314599.i | 0.371610i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.39652e6 | + | 204189.i | 1.61502 | + | 0.236136i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −409633. | −0.463874 | −0.231937 | − | 0.972731i | \(-0.574506\pi\) | ||||
−0.231937 | + | 0.972731i | \(0.574506\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 427196. | 0.473789 | 0.236894 | − | 0.971535i | \(-0.423870\pi\) | ||||
0.236894 | + | 0.971535i | \(0.423870\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −611038. | + | 688420.i | −0.663823 | + | 0.747890i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 399079.i | 0.424760i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.04117e6i | − | 1.08587i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −247776. | + | 1.69463e6i | −0.253257 | + | 1.73212i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 881998. | 0.883656 | 0.441828 | − | 0.897100i | \(-0.354330\pi\) | ||||
0.441828 | + | 0.897100i | \(0.354330\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −58355.1 | −0.0573162 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4723.52 | − | 32305.9i | 0.00454899 | − | 0.0311122i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 599689.i | − | 0.566361i | −0.959067 | − | 0.283181i | \(-0.908610\pi\) | ||
0.959067 | − | 0.283181i | \(-0.0913896\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 848506.i | 0.785969i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −510461. | + | 1.70830e6i | −0.463833 | + | 1.55225i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −456966. | −0.407375 | −0.203687 | − | 0.979036i | \(-0.565293\pi\) | ||||
−0.203687 | + | 0.979036i | \(0.565293\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −318685. | −0.278770 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.14088e6 | − | 313023.i | −1.83787 | − | 0.268719i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.10405e6i | 0.930267i | 0.885241 | + | 0.465134i | \(0.153994\pi\) | ||||
−0.885241 | + | 0.465134i | \(0.846006\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 33195.9i | − | 0.0274575i | −0.999906 | − | 0.0137287i | \(-0.995630\pi\) | ||
0.999906 | − | 0.0137287i | \(-0.00437013\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 918944. | + | 134361.i | 0.746247 | + | 0.109111i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −931006. | −0.742371 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.31847e6 | −1.03246 | −0.516229 | − | 0.856451i | \(-0.672664\pi\) | ||||
−0.516229 | + | 0.856451i | \(0.672664\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −520270. | + | 1.74112e6i | −0.400146 | + | 1.33912i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 401388.i | − | 0.303248i | −0.988438 | − | 0.151624i | \(-0.951550\pi\) | ||
0.988438 | − | 0.151624i | \(-0.0484504\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.13872e6i | 1.58741i | 0.608305 | + | 0.793703i | \(0.291850\pi\) | ||||
−0.608305 | + | 0.793703i | \(0.708150\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −377410. | + | 2.58124e6i | −0.275233 | + | 1.88242i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.14251e6 | −1.53539 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.41927e6 | 0.999589 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9556.58 | − | 65360.9i | 0.00661561 | − | 0.0452466i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.22189e6i | − | 0.831499i | −0.909479 | − | 0.415750i | \(-0.863519\pi\) | ||
0.909479 | − | 0.415750i | \(-0.136481\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.07603e6i | 1.38892i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 339001. | − | 728476.i | 0.223003 | − | 0.479208i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −148371. | −0.0959781 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 496519. | 0.315878 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.50347e6 | + | 366038.i | 1.56652 | + | 0.229044i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3.75692e6i | − | 2.31250i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 58956.8i | − | 0.0357016i | −0.999841 | − | 0.0178508i | \(-0.994318\pi\) | ||
0.999841 | − | 0.0178508i | \(-0.00568240\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.40463e6 | + | 205374.i | 0.836882 | + | 0.122363i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.02518e6 | −0.601034 | −0.300517 | − | 0.953776i | \(-0.597159\pi\) | ||||
−0.300517 | + | 0.953776i | \(0.597159\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.63335e6 | −0.942365 | −0.471183 | − | 0.882036i | \(-0.656173\pi\) | ||||
−0.471183 | + | 0.882036i | \(0.656173\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.22952e6 | − | 666209.i | −1.26600 | − | 0.378298i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 596082.i | 0.333164i | 0.986028 | + | 0.166582i | \(0.0532731\pi\) | ||||
−0.986028 | + | 0.166582i | \(0.946727\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.55633e6i | − | 0.856296i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 353126. | − | 2.41516e6i | 0.191279 | − | 1.30823i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 46645.5 | 0.0248773 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.36714e6 | −1.24313 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −256719. | + | 1.75579e6i | −0.132766 | + | 0.908038i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 400916.i | − | 0.204204i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.40214e6i | − | 0.703428i | −0.936107 | − | 0.351714i | \(-0.885599\pi\) | ||
0.936107 | − | 0.351714i | \(-0.114401\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.78835e6 | + | 534383.i | 0.883777 | + | 0.264084i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.68028e6 | −2.76540 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.84572e6 | −1.36495 | −0.682477 | − | 0.730907i | \(-0.739097\pi\) | ||||
−0.682477 | + | 0.730907i | \(0.739097\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 142091. | + | 20775.4i | 0.0671531 | + | 0.00981862i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.58623e6i | − | 0.738722i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.36521e6i | − | 1.08551i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 367838. | + | 53782.5i | 0.166383 | + | 0.0243273i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 121815. | 0.0543098 | 0.0271549 | − | 0.999631i | \(-0.491355\pi\) | ||||
0.0271549 | + | 0.999631i | \(0.491355\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 324699. | 0.142698 | 0.0713488 | − | 0.997451i | \(-0.477270\pi\) | ||||
0.0713488 | + | 0.997451i | \(0.477270\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 861931. | − | 1.85219e6i | 0.373426 | − | 0.802451i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 244816.i | − | 0.104569i | −0.998632 | − | 0.0522846i | \(-0.983350\pi\) | ||
0.998632 | − | 0.0522846i | \(-0.0166503\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.60643e6i | 1.09768i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6019.52 | + | 41169.7i | −0.00249972 | + | 0.0170965i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −793556. | −0.324969 | −0.162484 | − | 0.986711i | \(-0.551951\pi\) | ||||
−0.162484 | + | 0.986711i | \(0.551951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.25088e6 | −0.505183 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 261740. | − | 1.79013e6i | 0.104257 | − | 0.713048i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.74998e6i | − | 1.47332i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 785525.i | − | 0.304435i | −0.988347 | − | 0.152218i | \(-0.951359\pi\) | ||
0.988347 | − | 0.152218i | \(-0.0486415\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.34934e6 | + | 4.51566e6i | −0.515887 | + | 1.72646i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 406123. | 0.153187 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.97945e6 | 0.736671 | 0.368335 | − | 0.929693i | \(-0.379928\pi\) | ||||
0.368335 | + | 0.929693i | \(0.379928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.69024e6 | + | 247135.i | 0.620684 | + | 0.0907518i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.95705e6i | − | 1.43390i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.50429e6i | − | 1.25315i | −0.779362 | − | 0.626574i | \(-0.784456\pi\) | ||
0.779362 | − | 0.626574i | \(-0.215544\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.26605e6 | − | 185112.i | −0.446826 | − | 0.0653315i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.16489e6 | −0.405779 | −0.202889 | − | 0.979202i | \(-0.565033\pi\) | ||||
−0.202889 | + | 0.979202i | \(0.565033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.03118e6 | 0.698388 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 312704. | − | 1.04649e6i | 0.106134 | − | 0.355187i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 65857.4i | − | 0.0220664i | −0.999939 | − | 0.0110332i | \(-0.996488\pi\) | ||
0.999939 | − | 0.0110332i | \(-0.00351204\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6647.19i | − | 0.00219885i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −434280. | + | 2.97020e6i | −0.141837 | + | 0.970073i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.84836e6 | 2.53096 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.01996e6 | 1.28011 | 0.640053 | − | 0.768331i | \(-0.278913\pi\) | ||||
0.640053 | + | 0.768331i | \(0.278913\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 480960. | − | 3.28946e6i | 0.151244 | − | 1.03441i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.82280e6i | − | 0.566081i | −0.959108 | − | 0.283040i | \(-0.908657\pi\) | ||
0.959108 | − | 0.283040i | \(-0.0913430\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.03309e6i | − | 1.23702i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.80827e6 | + | 4.27947e6i | −0.850749 | + | 1.29644i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.62926e6 | −0.487534 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.23169e6 | −0.364077 | −0.182039 | − | 0.983291i | \(-0.558270\pi\) | ||||
−0.182039 | + | 0.983291i | \(0.558270\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.04593e6 | − | 591566.i | −1.18145 | − | 0.172742i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 2.64564e6i | − | 0.763229i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.52369e6i | 2.71447i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −520385. | − | 76086.8i | −0.146550 | − | 0.0214274i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.26757e6 | 0.909264 | 0.454632 | − | 0.890679i | \(-0.349771\pi\) | ||||
0.454632 | + | 0.890679i | \(0.349771\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.58190e6 | 0.709961 | 0.354981 | − | 0.934874i | \(-0.384487\pi\) | ||||
0.354981 | + | 0.934874i | \(0.384487\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −844990. | − | 252494.i | −0.229615 | − | 0.0686120i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 106050.i | − | 0.0284800i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.78771e6i | 1.27074i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −257994. | + | 1.76451e6i | −0.0676809 | + | 0.462894i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.97814e6 | 1.03154 | 0.515771 | − | 0.856727i | \(-0.327506\pi\) | ||||
0.515771 | + | 0.856727i | \(0.327506\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.30560e6 | 1.35992 | 0.679962 | − | 0.733247i | \(-0.261996\pi\) | ||||
0.679962 | + | 0.733247i | \(0.261996\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.43438e6 | + | 9.81021e6i | −0.363446 | + | 2.48574i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 531111.i | 0.133040i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.79565e6i | − | 0.692344i | −0.938171 | − | 0.346172i | \(-0.887481\pi\) | ||
0.938171 | − | 0.346172i | \(-0.112519\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.07190e6 | − | 320297.i | −0.262456 | − | 0.0784254i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.79176e6 | −0.917976 | −0.458988 | − | 0.888442i | \(-0.651788\pi\) | ||||
−0.458988 | + | 0.888442i | \(0.651788\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.20316e7 | −2.88020 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.96858e6 | + | 726468.i | 1.17615 | + | 0.171968i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.90181e6i | 1.61565i | 0.589422 | + | 0.807825i | \(0.299355\pi\) | ||||
−0.589422 | + | 0.807825i | \(0.700645\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.11395e6i | − | 0.952396i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.93521e6 | − | 429164.i | −0.672038 | − | 0.0982603i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.16439e6 | 1.16947 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.98001e6 | 1.33940 | 0.669702 | − | 0.742630i | \(-0.266422\pi\) | ||||
0.669702 | + | 0.742630i | \(0.266422\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 82980.2 | + | 38615.4i | 0.0183841 | + | 0.00855518i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 5.66582e6i | − | 1.24168i | −0.783936 | − | 0.620841i | \(-0.786791\pi\) | ||
0.783936 | − | 0.620841i | \(-0.213209\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.78722e6i | − | 0.387458i | −0.981055 | − | 0.193729i | \(-0.937942\pi\) | ||
0.981055 | − | 0.193729i | \(-0.0620583\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.46194e6 | + | 9.99872e6i | −0.313543 | + | 2.14443i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −654822. | −0.138941 | −0.0694706 | − | 0.997584i | \(-0.522131\pi\) | ||||
−0.0694706 | + | 0.997584i | \(0.522131\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.23879e6 | 1.51962 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14579.6 | + | 99715.0i | −0.00302826 | + | 0.0207114i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 953392.i | 0.195938i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.47343e6i | 1.72316i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 255773. | − | 855965.i | 0.0514706 | − | 0.172250i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.61770e6 | 0.919575 | 0.459788 | − | 0.888029i | \(-0.347926\pi\) | ||||
0.459788 | + | 0.888029i | \(0.347926\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.14249e6 | −0.816392 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −468763. | − | 68539.0i | −0.0914293 | − | 0.0133681i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 367323.i | − | 0.0709078i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.36141e6i | 0.451178i | 0.974223 | + | 0.225589i | \(0.0724307\pi\) | ||||
−0.974223 | + | 0.225589i | \(0.927569\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.14020e6 | + | 751561.i | 0.972093 | + | 0.142132i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.12401e6 | 1.52078 | 0.760390 | − | 0.649466i | \(-0.225008\pi\) | ||||
0.760390 | + | 0.649466i | \(0.225008\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 177280. | 0.0328505 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.27922e6 | − | 4.28102e6i | 0.234657 | − | 0.785297i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 3.32157e6i | − | 0.603187i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6.53711e6i | − | 1.17526i | −0.809129 | − | 0.587631i | \(-0.800061\pi\) | ||
0.809129 | − | 0.587631i | \(-0.199939\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 971689. | − | 6.64573e6i | 0.172955 | − | 1.18290i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.65689e6 | 1.34937 | 0.674687 | − | 0.738104i | \(-0.264279\pi\) | ||||
0.674687 | + | 0.738104i | \(0.264279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.40693e7 | 2.45495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 181393. | − | 1.24061e6i | 0.0313402 | − | 0.214347i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.52236e6i | 0.431532i | 0.976445 | + | 0.215766i | \(0.0692248\pi\) | ||||
−0.976445 | + | 0.215766i | \(0.930775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.77887e6i | 0.809604i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.63013e6 | − | 3.08538e6i | −1.11232 | − | 0.517624i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.89388e6 | 1.31151 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 769820. | 0.126667 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.11117e7 | + | 1.62467e6i | 1.81077 | + | 0.264757i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.05284e6i | 0.654131i | 0.945002 | + | 0.327065i | \(0.106060\pi\) | ||||
−0.945002 | + | 0.327065i | \(0.893940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.38894e6i | − | 0.701625i | −0.936446 | − | 0.350813i | \(-0.885905\pi\) | ||
0.936446 | − | 0.350813i | \(-0.114095\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.47871e6 | − | 1.09348e6i | −1.18421 | − | 0.173146i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 180687. | 0.0283400 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.36066e6 | −0.988241 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.57607e6 | − | 1.66620e6i | −0.858207 | − | 0.256443i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.04600e7i | − | 1.59482i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.35730e7i | − | 2.05018i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.85603e6 | + | 1.26940e7i | −0.277747 | + | 1.89961i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 976543. | 0.144784 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.53968e6 | 0.813751 | 0.406875 | − | 0.913484i | \(-0.366618\pi\) | ||||
0.406875 | + | 0.913484i | \(0.366618\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 195232. | − | 1.33526e6i | 0.0284153 | − | 0.194342i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.86741e6i | 1.42302i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.15951e7i | − | 1.65694i | −0.560034 | − | 0.828470i | \(-0.689212\pi\) | ||
0.560034 | − | 0.828470i | \(-0.310788\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.00908e7 | + | 3.01527e6i | 1.42888 | + | 0.426968i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.41647e7 | −1.98760 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.00017e7 | −1.39079 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.02699e7 | + | 1.50159e6i | 1.41526 | + | 0.206929i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.96541e6i | 1.08785i | 0.839133 | + | 0.543927i | \(0.183063\pi\) | ||||
−0.839133 | + | 0.543927i | \(0.816937\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.42405e6i | 0.328105i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −79052.1 | − | 11558.4i | −0.0106049 | − | 0.00155057i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.14209e6 | 0.683705 | 0.341853 | − | 0.939754i | \(-0.388946\pi\) | ||||
0.341853 | + | 0.939754i | \(0.388946\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 798538. | 0.105238 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.57878e6 | − | 5.45364e6i | 0.467496 | − | 0.712408i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.04215e6i | 0.393913i | 0.980412 | + | 0.196956i | \(0.0631057\pi\) | ||||
−0.980412 | + | 0.196956i | \(0.936894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.13371e6i | 1.17235i | 0.810185 | + | 0.586175i | \(0.199367\pi\) | ||||
−0.810185 | + | 0.586175i | \(0.800633\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −210635. | + | 1.44061e6i | −0.0268006 | + | 0.183299i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.20750e6 | 0.152306 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.31021e6 | −1.16418 | −0.582090 | − | 0.813125i | \(-0.697765\pi\) | ||||
−0.582090 | + | 0.813125i | \(0.697765\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −142860. | + | 977069.i | −0.0177098 | + | 0.121124i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.21367e7i | − | 1.49163i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 779818.i | 0.0950215i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.25250e6 | − | 1.08847e7i | 0.392941 | − | 1.31501i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.65177e6 | −0.677001 | −0.338500 | − | 0.940966i | \(-0.609920\pi\) | ||||
−0.338500 | + | 0.940966i | \(0.609920\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.44369e7 | −1.71469 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.31227e6 | − | 1.36157e6i | −1.09670 | − | 0.160351i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.25646e7i | − | 1.46728i | −0.679541 | − | 0.733638i | \(-0.737821\pi\) | ||
0.679541 | − | 0.733638i | \(-0.262179\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 231370.i | 0.0267926i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.00133e6 | + | 731256.i | 0.574314 | + | 0.0839719i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.66264e7 | −1.89335 | −0.946676 | − | 0.322186i | \(-0.895582\pi\) | ||||
−0.946676 | + | 0.322186i | \(0.895582\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.65512e6 | 0.525708 | 0.262854 | − | 0.964836i | \(-0.415336\pi\) | ||||
0.262854 | + | 0.964836i | \(0.415336\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.55894e6 | − | 1.52568e7i | 0.510588 | − | 1.70872i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 1.00604e7i | − | 1.11745i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 4.60458e6i | − | 0.507245i | −0.967303 | − | 0.253623i | \(-0.918378\pi\) | ||
0.967303 | − | 0.253623i | \(-0.0816222\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.82793e6 | − | 1.25019e7i | 0.199717 | − | 1.36594i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.95731e6 | 0.212108 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.06680e6 | 0.544606 | 0.272303 | − | 0.962212i | \(-0.412215\pi\) | ||||
0.272303 | + | 0.962212i | \(0.412215\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.79159e6 | + | 2.59320e7i | −0.404234 | + | 2.76470i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.69843e6i | 0.602618i | 0.953527 | + | 0.301309i | \(0.0974235\pi\) | ||||
−0.953527 | + | 0.301309i | \(0.902576\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.94045e6i | 0.518251i | 0.965844 | + | 0.259125i | \(0.0834343\pi\) | ||||
−0.965844 | + | 0.259125i | \(0.916566\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −439680. | + | 944822.i | −0.0457517 | + | 0.0983153i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.53327e7 | 1.58270 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.21707e6 | −0.431828 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.31627e6 | + | 923518.i | 0.641641 | + | 0.0938159i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 185588.i | − | 0.0187035i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.04200e7i | − | 1.04182i | −0.853612 | − | 0.520910i | \(-0.825593\pi\) | ||
0.853612 | − | 0.520910i | \(-0.174407\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.01880e7 | + | 1.48961e6i | 1.01060 | + | 0.147762i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.11510e6 | −0.700240 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.48292e6 | 0.242445 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.00070e6 | − | 2.09190e6i | −0.678249 | − | 0.202670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.75177e6i | 0.264525i | 0.991215 | + | 0.132263i | \(0.0422242\pi\) | ||||
−0.991215 | + | 0.132263i | \(0.957776\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.96874e7i | 1.87785i | 0.344123 | + | 0.938925i | \(0.388176\pi\) | ||||
−0.344123 | + | 0.938925i | \(0.611824\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 878686. | − | 6.00965e6i | 0.0831638 | − | 0.568787i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.00089e7 | 1.87915 | 0.939575 | − | 0.342343i | \(-0.111220\pi\) | ||||
0.939575 | + | 0.342343i | \(0.111220\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.08002e6 | 0.473428 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.86305e6 | − | 1.27421e7i | 0.172295 | − | 1.17839i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.44288e6i | 0.315965i | 0.987442 | + | 0.157982i | \(0.0504989\pi\) | ||||
−0.987442 | + | 0.157982i | \(0.949501\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.66923e7i | 1.52024i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.00722e7 | + | 3.00970e6i | 0.910353 | + | 0.272025i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.86205e6 | 0.256722 | 0.128361 | − | 0.991727i | \(-0.459028\pi\) | ||||
0.128361 | + | 0.991727i | \(0.459028\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.51348e7 | −1.34733 | −0.673663 | − | 0.739039i | \(-0.735280\pi\) | ||||
−0.673663 | + | 0.739039i | \(0.735280\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −200995. | − | 29387.9i | −0.0177583 | − | 0.00259648i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.84865e7i | − | 1.62107i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.01853e6i | 0.175679i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.50703e6 | − | 366559.i | −0.216568 | − | 0.0316649i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.19314e6 | −0.788238 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.06636e6 | −0.516286 | −0.258143 | − | 0.966107i | \(-0.583111\pi\) | ||||
−0.258143 | + | 0.966107i | \(0.583111\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.01472e6 | + | 1.50738e7i | −0.592585 | + | 1.27340i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.23983e7i | 1.03966i | 0.854270 | + | 0.519829i | \(0.174005\pi\) | ||||
−0.854270 | + | 0.519829i | \(0.825995\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 468106.i | 0.0389646i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.50644e6 | − | 1.03031e7i | 0.124475 | − | 0.851331i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.41080e7 | −1.15722 | −0.578608 | − | 0.815605i | \(-0.696404\pi\) | ||||
−0.578608 | + | 0.815605i | \(0.696404\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.27378e7 | −1.85149 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.13201e6 | − | 1.45816e7i | 0.172345 | − | 1.17873i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.98273e6i | 0.159117i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 5.34373e6i | − | 0.425745i | −0.977080 | − | 0.212872i | \(-0.931718\pi\) | ||
0.977080 | − | 0.212872i | \(-0.0682818\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.63021e6 | + | 5.45561e6i | −0.128947 | + | 0.431529i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.92452e6 | −0.229664 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 468617. | 0.0365373 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.02872e7 | + | 1.50412e6i | 0.796354 | + | 0.116437i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.64930e6i | 0.357349i | 0.983908 | + | 0.178674i | \(0.0571809\pi\) | ||||
−0.983908 | + | 0.178674i | \(0.942819\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.48285e7i | 1.13164i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.85251e6 | − | 709498.i | −0.367700 | − | 0.0537624i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.79295e7 | −1.34902 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.37828e6 | 0.551239 | 0.275619 | − | 0.961267i | \(-0.411117\pi\) | ||||
0.275619 | + | 0.961267i | \(0.411117\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.29902e6 | + | 2.10801e7i | −0.467303 | + | 1.56387i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.05732e6i | 0.151558i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.91642e6i | 0.725421i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 923823. | − | 6.31836e6i | 0.0671106 | − | 0.458994i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.11646e7 | −1.52682 | −0.763410 | − | 0.645914i | \(-0.776477\pi\) | ||||
−0.763410 | + | 0.645914i | \(0.776477\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.00597e7 | −0.720691 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −963434. | + | 6.58927e6i | −0.0685451 | + | 0.468804i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.22039e7i | 2.27543i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.97307e7i | − | 1.38454i | −0.721636 | − | 0.692272i | \(-0.756610\pi\) | ||
0.721636 | − | 0.692272i | \(-0.243390\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.24046e6 | − | 1.09775e7i | −0.643984 | − | 0.765039i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −108600. | −0.00751688 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.30762e7 | 0.898924 | 0.449462 | − | 0.893299i | \(-0.351616\pi\) | ||||
0.449462 | + | 0.893299i | \(0.351616\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.15558e6 | − | 900023.i | −0.420291 | − | 0.0614519i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.38996e7i | 0.942612i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 9.42776e6i | − | 0.635035i | −0.948252 | − | 0.317517i | \(-0.897151\pi\) | ||
0.948252 | − | 0.317517i | \(-0.102849\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.60595e7 | + | 2.34810e6i | 1.07445 | + | 0.157098i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.00117e6 | −0.332353 | −0.166177 | − | 0.986096i | \(-0.553142\pi\) | ||||
−0.166177 | + | 0.986096i | \(0.553142\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.79230e7 | 1.84320 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.55800e7 | − | 7.64363e6i | −1.67725 | − | 0.501185i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.72971e7i | 1.12659i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2.94559e7i | − | 1.90578i | −0.303314 | − | 0.952891i | \(-0.598093\pi\) | ||
0.303314 | − | 0.952891i | \(-0.401907\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.98912e6 | + | 1.36043e7i | −0.127842 | + | 0.874360i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.64956e7 | −1.05318 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.64703e7 | 1.67888 | 0.839440 | − | 0.543452i | \(-0.182883\pi\) | ||||
0.839440 | + | 0.543452i | \(0.182883\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 131605. | − | 900096.i | 0.00829218 | − | 0.0567132i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.16223e7i | − | 0.727494i | −0.931498 | − | 0.363747i | \(-0.881497\pi\) | ||
0.931498 | − | 0.363747i | \(-0.118503\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.25748e7i | − | 0.781967i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 487648. | + | 145715.i | 0.0301268 | + | 0.00900227i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.29163e7 | 0.792772 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.74960e6 | −0.289628 | −0.144814 | − | 0.989459i | \(-0.546258\pi\) | ||||
−0.144814 | + | 0.989459i | \(0.546258\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.24988e6 | + | 1.35245e6i | 0.560403 | + | 0.0819379i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.39153e7i | 1.43955i | 0.694208 | + | 0.719774i | \(0.255755\pi\) | ||||
−0.694208 | + | 0.719774i | \(0.744245\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.28228e7i | 1.96300i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.30877e7 | − | 1.91359e6i | −0.777700 | − | 0.113709i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.74425e7 | −2.21066 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.37792e6 | 0.374155 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.51983e7 | − | 1.17262e7i | −1.46882 | − | 0.683524i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 560391.i | 0.0324576i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 773120.i | − | 0.0444949i | −0.999752 | − | 0.0222475i | \(-0.992918\pi\) | ||
0.999752 | − | 0.0222475i | \(-0.00708217\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.03057e6 | − | 7.04844e6i | 0.0589366 | − | 0.403089i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.01763e6 | −0.0578297 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.33741e7 | −1.31993 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 718713. | − | 4.91554e6i | 0.0403309 | − | 0.275837i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.84342e7i | 1.58560i | 0.609480 | + | 0.792802i | \(0.291378\pi\) | ||||
−0.609480 | + | 0.792802i | \(0.708622\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 87689.7i | 0.00485939i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.65643e6 | − | 3.23160e7i | 0.531784 | − | 1.77965i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.17616e6 | −0.502194 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.63441e6 | −0.143283 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.70294e7 | − | 2.48990e6i | −0.920480 | − | 0.134586i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.04767e7i | 0.562800i | 0.959591 | + | 0.281400i | \(0.0907988\pi\) | ||||
−0.959591 | + | 0.281400i | \(0.909201\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.11593e7i | 0.595776i | 0.954601 | + | 0.297888i | \(0.0962822\pi\) | ||||
−0.954601 | + | 0.297888i | \(0.903718\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 512028. | + | 74864.9i | 0.0271686 | + | 0.00397239i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.88875e7 | 1.52341 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.67717e6 | 0.454803 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.14490e6 | + | 1.38712e7i | −0.215925 | + | 0.722611i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.20649e7i | 0.624690i | 0.949969 | + | 0.312345i | \(0.101114\pi\) | ||||
−0.949969 | + | 0.312345i | \(0.898886\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.97522e7i | − | 1.53115i | −0.643344 | − | 0.765577i | \(-0.722454\pi\) | ||
0.643344 | − | 0.765577i | \(-0.277546\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.09965e6 | − | 1.43603e7i | 0.107402 | − | 0.734561i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.54258e7 | 1.29274 | 0.646369 | − | 0.763025i | \(-0.276287\pi\) | ||||
0.646369 | + | 0.763025i | \(0.276287\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.74678e7 | 1.38815 | 0.694077 | − | 0.719901i | \(-0.255813\pi\) | ||||
0.694077 | + | 0.719901i | \(0.255813\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.97349e6 | − | 2.03367e7i | 0.149370 | − | 1.02159i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 111237.i | 0.00555441i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3.73485e7i | − | 1.85377i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.56825e7 | − | 1.19515e7i | −1.26714 | − | 0.589672i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.10051e7 | 1.03019 | 0.515097 | − | 0.857132i | \(-0.327756\pi\) | ||||
0.515097 | + | 0.857132i | \(0.327756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.33229e7 | −1.62462 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.19119e6 | + | 905230.i | 0.300058 | + | 0.0438722i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 6.97216e6i | − | 0.335912i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.28207e7i | 0.614049i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.29886e7 | − | 4.82335e6i | −1.57071 | − | 0.229657i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.11313e6 | 0.100023 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.25309e7 | −1.06024 | −0.530121 | − | 0.847922i | \(-0.677854\pi\) | ||||
−0.530121 | + | 0.847922i | \(0.677854\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.89631e7 | − | 1.16427e7i | −1.82280 | − | 0.544675i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.37134e7i | 1.10292i | 0.834203 | + | 0.551458i | \(0.185928\pi\) | ||||
−0.834203 | + | 0.551458i | \(0.814072\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.08107e7i | 0.499887i | 0.968260 | + | 0.249944i | \(0.0804121\pi\) | ||||
−0.968260 | + | 0.249944i | \(0.919588\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.83189e6 | − | 3.30471e7i | 0.222131 | − | 1.51924i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.86848e7 | −0.854006 | −0.427003 | − | 0.904250i | \(-0.640431\pi\) | ||||
−0.427003 | + | 0.904250i | \(0.640431\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.24470e7 | 2.83773 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.20081e6 | + | 2.18915e7i | −0.144615 | + | 0.989072i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.92048e7i | − | 0.862703i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.53405e7i | 1.57844i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 986604. | + | 294810.i | 0.0438134 | + | 0.0130920i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.21053e7 | −0.534509 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.16971e7 | −0.513544 | −0.256772 | − | 0.966472i | \(-0.582659\pi\) | ||||
−0.256772 | + | 0.966472i | \(0.582659\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.88469e7 | + | 2.75566e6i | 0.822751 | + | 0.120296i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.81207e7i | − | 1.22064i | −0.792156 | − | 0.610318i | \(-0.791042\pi\) | ||
0.792156 | − | 0.610318i | \(-0.208958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.71174e7i | − | 0.738816i | −0.929267 | − | 0.369408i | \(-0.879561\pi\) | ||
0.929267 | − | 0.369408i | \(-0.120439\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.20216e7 | − | 4.68196e6i | −1.37431 | − | 0.200942i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.58331e7 | 1.10247 | 0.551237 | − | 0.834349i | \(-0.314156\pi\) | ||||
0.551237 | + | 0.834349i | \(0.314156\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.06729e6 | 0.384789 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.04718e7 | + | 6.87181e6i | 0.441904 | + | 0.289986i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 7.00641e6i | − | 0.294013i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.13395e7i | 2.97696i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 334614. | − | 2.28855e6i | 0.0138856 | − | 0.0949683i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.48685e7 | −2.26425 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −88828.6 | −0.00364536 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.11977e6 | + | 7.65854e6i | −0.0456994 | + | 0.312555i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 7.50407e6i | − | 0.304562i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.84483e7i | 1.14825i | 0.818766 | + | 0.574127i | \(0.194659\pi\) | ||||
−0.818766 | + | 0.574127i | \(0.805341\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.12919e7 | + | 3.77891e7i | −0.453269 | + | 1.51690i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.51021e7 | −1.80053 | −0.900266 | − | 0.435340i | \(-0.856628\pi\) | ||||
−0.900266 | + | 0.435340i | \(0.856628\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.33044e7 | 0.925253 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.79484e7 | + | 8.47278e6i | 2.28817 | + | 0.334559i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.12722e7i | − | 0.835389i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.39345e7i | − | 1.71600i | −0.513651 | − | 0.857999i | \(-0.671707\pi\) | ||
0.513651 | − | 0.857999i | \(-0.328293\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 909377. | + | 132962.i | 0.0353260 | + | 0.00516511i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.62162e7 | 0.626535 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.37131e7 | 1.29552 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.33556e6 | + | 2.12024e7i | −0.242151 | + | 0.810375i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 2.25804e7i | − | 0.858405i | −0.903208 | − | 0.429203i | \(-0.858795\pi\) | ||
0.903208 | − | 0.429203i | \(-0.141205\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 8.88787e6i | − | 0.336065i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.31204e6 | − | 1.58128e7i | 0.0869542 | − | 0.594711i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −444266. | −0.0166194 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.13233e6 | 0.302598 | 0.151299 | − | 0.988488i | \(-0.451654\pi\) | ||||
0.151299 | + | 0.988488i | \(0.451654\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.68362e6 | − | 2.51936e7i | 0.136336 | − | 0.932451i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.83529e7i | 0.675665i | 0.941206 | + | 0.337833i | \(0.109694\pi\) | ||||
−0.941206 | + | 0.337833i | \(0.890306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.33573e6i | 0.195395i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.53040e7 | − | 3.28866e7i | 0.557476 | − | 1.19795i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.42017e6 | 0.123929 | 0.0619644 | − | 0.998078i | \(-0.480263\pi\) | ||||
0.0619644 | + | 0.998078i | \(0.480263\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.33309e7 | −0.840942 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.19425e6 | − | 1.34431e6i | −0.329659 | − | 0.0482003i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.57241e7i | 1.63084i | 0.578867 | + | 0.815422i | \(0.303495\pi\) | ||||
−0.578867 | + | 0.815422i | \(0.696505\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.09612e6i | 0.287256i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.40055e7 | + | 3.50990e6i | 0.847287 | + | 0.123884i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.89765e7 | 1.01742 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.72937e7 | −0.953354 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.64561e7 | + | 1.08936e7i | 1.26679 | + | 0.378533i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.49105e6i | 0.189818i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 6.01434e6i | − | 0.206834i | −0.994638 | − | 0.103417i | \(-0.967022\pi\) | ||
0.994638 | − | 0.103417i | \(-0.0329776\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −105197. | + | 719482.i | −0.00359911 | + | 0.0246156i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.11774e7 | 1.40156 | 0.700779 | − | 0.713378i | \(-0.252836\pi\) | ||||
0.700779 | + | 0.713378i | \(0.252836\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.72693e6 | 0.126203 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.33848e6 | − | 3.65118e7i | 0.179848 | − | 1.23005i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.82069e7i | 0.945409i | 0.881221 | + | 0.472704i | \(0.156722\pi\) | ||||
−0.881221 | + | 0.472704i | \(0.843278\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.94411e7i | 0.981743i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.65032e7 | − | 7.91950e6i | −0.879277 | − | 0.262739i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.06646e6 | −0.200240 | −0.100120 | − | 0.994975i | \(-0.531923\pi\) | ||||
−0.100120 | + | 0.994975i | \(0.531923\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.23342e7 | −1.71868 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.18391e6 | + | 904165.i | 0.202055 | + | 0.0295430i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.23653e6i | − | 0.0401990i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.99468e7i | 0.968649i | 0.874888 | + | 0.484324i | \(0.160935\pi\) | ||||
−0.874888 | + | 0.484324i | \(0.839065\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.16272e7 | + | 3.16216e6i | 0.696028 | + | 0.101768i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.81071e7 | 0.900031 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.82255e7 | −1.21791 | −0.608954 | − | 0.793205i | \(-0.708411\pi\) | ||||
−0.608954 | + | 0.793205i | \(0.708411\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.22757e7 | + | 2.63792e7i | −0.389165 | + | 0.836273i |
(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 | 384.6.c.a.383.10 | yes | 20 | |
3.2 | odd | 2 | 384.6.c.d.383.12 | yes | 20 | ||
4.3 | odd | 2 | 384.6.c.d.383.11 | yes | 20 | ||
8.3 | odd | 2 | 384.6.c.b.383.10 | yes | 20 | ||
8.5 | even | 2 | 384.6.c.c.383.11 | yes | 20 | ||
12.11 | even | 2 | inner | 384.6.c.a.383.9 | ✓ | 20 | |
24.5 | odd | 2 | 384.6.c.b.383.9 | yes | 20 | ||
24.11 | even | 2 | 384.6.c.c.383.12 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.c.a.383.9 | ✓ | 20 | 12.11 | even | 2 | inner | |
384.6.c.a.383.10 | yes | 20 | 1.1 | even | 1 | trivial | |
384.6.c.b.383.9 | yes | 20 | 24.5 | odd | 2 | ||
384.6.c.b.383.10 | yes | 20 | 8.3 | odd | 2 | ||
384.6.c.c.383.11 | yes | 20 | 8.5 | even | 2 | ||
384.6.c.c.383.12 | yes | 20 | 24.11 | even | 2 | ||
384.6.c.d.383.11 | yes | 20 | 4.3 | odd | 2 | ||
384.6.c.d.383.12 | yes | 20 | 3.2 | odd | 2 |