Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(161,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("320.161");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.d (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: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 343 x^{10} - 696 x^{9} + 44406 x^{8} + 179640 x^{7} - 2401691 x^{6} - 15554592 x^{5} + \cdots + 653157349 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.6 | ||
Root | \(-3.41426 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.161 |
Dual form | 320.6.d.c.161.7 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 3.09968i | − 0.198845i | −0.995045 | − | 0.0994223i | \(-0.968301\pi\) | ||||
0.995045 | − | 0.0994223i | \(-0.0316995\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 118.821 | 0.916533 | 0.458266 | − | 0.888815i | \(-0.348471\pi\) | ||||
0.458266 | + | 0.888815i | \(0.348471\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 233.392 | 0.960461 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 355.467i | 0.885763i | 0.896580 | + | 0.442881i | \(0.146044\pi\) | ||||
−0.896580 | + | 0.442881i | \(0.853956\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 370.735i | 0.608422i | 0.952605 | + | 0.304211i | \(0.0983928\pi\) | ||||
−0.952605 | + | 0.304211i | \(0.901607\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 77.4920 | 0.0889260 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −586.019 | −0.491801 | −0.245900 | − | 0.969295i | \(-0.579084\pi\) | ||||
−0.245900 | + | 0.969295i | \(0.579084\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 972.770i | 0.618196i | 0.951030 | + | 0.309098i | \(0.100027\pi\) | ||||
−0.951030 | + | 0.309098i | \(0.899973\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 368.307i | − 0.182248i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1298.93 | 0.511996 | 0.255998 | − | 0.966677i | \(-0.417596\pi\) | ||||
0.255998 | + | 0.966677i | \(0.417596\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1476.66i | − 0.389827i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 5226.75i | − 1.15408i | −0.816715 | − | 0.577041i | \(-0.804207\pi\) | ||||
0.816715 | − | 0.577041i | \(-0.195793\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4622.64 | −0.863944 | −0.431972 | − | 0.901887i | \(-0.642182\pi\) | ||||
−0.431972 | + | 0.901887i | \(0.642182\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1101.83 | 0.176129 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2970.52i | 0.409886i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5296.01i | 0.635982i | 0.948094 | + | 0.317991i | \(0.103008\pi\) | ||||
−0.948094 | + | 0.317991i | \(0.896992\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1149.16 | 0.120981 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14042.0 | 1.30457 | 0.652286 | − | 0.757973i | \(-0.273810\pi\) | ||||
0.652286 | + | 0.757973i | \(0.273810\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4229.77i | 0.348856i | 0.984670 | + | 0.174428i | \(0.0558076\pi\) | ||||
−0.984670 | + | 0.174428i | \(0.944192\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5834.80i | 0.429531i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −18577.1 | −1.22668 | −0.613341 | − | 0.789818i | \(-0.710175\pi\) | ||||
−0.613341 | + | 0.789818i | \(0.710175\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2688.58 | −0.159968 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1816.47i | 0.0977920i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 20963.9i | 1.02514i | 0.858645 | + | 0.512570i | \(0.171306\pi\) | ||||
−0.858645 | + | 0.512570i | \(0.828694\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8886.67 | −0.396125 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3015.28 | 0.122925 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 48573.7i | 1.81665i | 0.418265 | + | 0.908325i | \(0.362638\pi\) | ||||
−0.418265 | + | 0.908325i | \(0.637362\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3620.88i | 0.124592i | 0.998058 | + | 0.0622958i | \(0.0198422\pi\) | ||||
−0.998058 | + | 0.0622958i | \(0.980158\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 27731.9 | 0.880294 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9268.37 | −0.272095 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1683.52i | 0.0458174i | 0.999738 | + | 0.0229087i | \(0.00729270\pi\) | ||||
−0.999738 | + | 0.0229087i | \(0.992707\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 4026.27i | − 0.101808i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5332.40 | −0.125538 | −0.0627692 | − | 0.998028i | \(-0.519993\pi\) | ||||
−0.0627692 | + | 0.998028i | \(0.519993\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 80560.7 | 1.76936 | 0.884680 | − | 0.466199i | \(-0.154377\pi\) | ||||
0.884680 | + | 0.466199i | \(0.154377\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1937.30i | 0.0397689i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 42236.9i | 0.811831i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −39272.8 | −0.707985 | −0.353992 | − | 0.935248i | \(-0.615176\pi\) | ||||
−0.353992 | + | 0.935248i | \(0.615176\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 52137.1 | 0.882946 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18385.7i | 0.292944i | 0.989215 | + | 0.146472i | \(0.0467918\pi\) | ||||
−0.989215 | + | 0.146472i | \(0.953208\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 14650.5i | − 0.219940i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16201.3 | −0.229483 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 43137.3 | 0.577269 | 0.288635 | − | 0.957439i | \(-0.406799\pi\) | ||||
0.288635 | + | 0.957439i | \(0.406799\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 44051.1i | 0.557639i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14328.7i | 0.171791i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24319.2 | −0.276466 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 134744. | 1.45405 | 0.727027 | − | 0.686609i | \(-0.240902\pi\) | ||||
0.727027 | + | 0.686609i | \(0.240902\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 82963.1i | 0.850740i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 39471.3i | 0.385015i | 0.981296 | + | 0.192507i | \(0.0616620\pi\) | ||||
−0.981296 | + | 0.192507i | \(0.938338\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −164437. | −1.52724 | −0.763620 | − | 0.645666i | \(-0.776580\pi\) | ||||
−0.763620 | + | 0.645666i | \(0.776580\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9207.68 | 0.0815036 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 203860.i | 1.72137i | 0.509142 | + | 0.860683i | \(0.329963\pi\) | ||||
−0.509142 | + | 0.860683i | \(0.670037\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 65561.7i | 0.528548i | 0.964448 | + | 0.264274i | \(0.0851322\pi\) | ||||
−0.964448 | + | 0.264274i | \(0.914868\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16415.9 | 0.126462 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 35057.0 | 0.258273 | 0.129136 | − | 0.991627i | \(-0.458780\pi\) | ||||
0.129136 | + | 0.991627i | \(0.458780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 32473.3i | 0.228972i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 86526.6i | 0.584366i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −69631.3 | −0.450752 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 34694.3 | 0.215424 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 43525.6i | − 0.259407i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 15625.0i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 157228. | 0.865007 | 0.432503 | − | 0.901632i | \(-0.357630\pi\) | ||||
0.432503 | + | 0.901632i | \(0.357630\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13110.9 | 0.0693681 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 85680.9i | 0.436220i | 0.975924 | + | 0.218110i | \(0.0699892\pi\) | ||||
−0.975924 | + | 0.218110i | \(0.930011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 115585.i | 0.566597i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 36916.6 | 0.174336 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −99340.8 | −0.452196 | −0.226098 | − | 0.974105i | \(-0.572597\pi\) | ||||
−0.226098 | + | 0.974105i | \(0.572597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 36370.0i | − 0.159664i | −0.996808 | − | 0.0798319i | \(-0.974562\pi\) | ||||
0.996808 | − | 0.0798319i | \(-0.0254384\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 57582.9i | 0.243919i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −131784. | −0.538918 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 130669. | 0.516121 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8333.74i | 0.0318088i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 241962.i | 0.892857i | 0.894819 | + | 0.446428i | \(0.147304\pi\) | ||||
−0.894819 | + | 0.446428i | \(0.852696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −241079. | −0.860433 | −0.430217 | − | 0.902726i | \(-0.641563\pi\) | ||||
−0.430217 | + | 0.902726i | \(0.641563\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −136772. | −0.472356 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 115566.i | − 0.386367i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 450362.i | − 1.45818i | −0.684416 | − | 0.729092i | \(-0.739943\pi\) | ||||
0.684416 | − | 0.729092i | \(-0.260057\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 64981.5 | 0.203844 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 154340. | 0.469261 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 388586.i | 1.14556i | 0.819709 | + | 0.572780i | \(0.194135\pi\) | ||||
−0.819709 | + | 0.572780i | \(0.805865\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 27545.8i | 0.0787674i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16419.7 | −0.0455589 | −0.0227794 | − | 0.999741i | \(-0.507252\pi\) | ||||
−0.0227794 | + | 0.999741i | \(0.507252\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 233849. | 0.629822 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 227037.i | 0.593753i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 111836.i | 0.284097i | 0.989860 | + | 0.142048i | \(0.0453689\pi\) | ||||
−0.989860 | + | 0.142048i | \(0.954631\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −74263.1 | −0.183307 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 150563. | 0.361231 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 432673.i | − 1.00932i | −0.863319 | − | 0.504658i | \(-0.831619\pi\) | ||||
0.863319 | − | 0.504658i | \(-0.168381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 800005.i | − 1.81508i | −0.419962 | − | 0.907542i | \(-0.637957\pi\) | ||||
0.419962 | − | 0.907542i | \(-0.362043\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11223.6 | 0.0247744 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −132400. | −0.284420 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 208310.i | − 0.435619i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 175459.i | − 0.357289i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 372676. | 0.739177 | 0.369588 | − | 0.929196i | \(-0.379499\pi\) | ||||
0.369588 | + | 0.929196i | \(0.379499\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −784772. | −1.51653 | −0.758263 | − | 0.651948i | \(-0.773952\pi\) | ||||
−0.758263 | + | 0.651948i | \(0.773952\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 28729.0i | 0.0541046i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 328945.i | 0.603889i | 0.953325 | + | 0.301945i | \(0.0976358\pi\) | ||||
−0.953325 | + | 0.301945i | \(0.902364\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 473709. | 0.847968 | 0.423984 | − | 0.905670i | \(-0.360631\pi\) | ||||
0.423984 | + | 0.905670i | \(0.360631\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5218.36 | 0.00911054 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 621047.i | − 1.05775i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 351049.i | 0.583423i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 303160. | 0.491752 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −345787. | −0.547575 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 704656.i | − 1.08961i | −0.838563 | − | 0.544805i | \(-0.816604\pi\) | ||||
0.838563 | − | 0.544805i | \(-0.183396\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16528.7i | 0.0249626i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −105744. | −0.156013 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −549266. | −0.791833 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 249712.i | − 0.351828i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 217258.i | − 0.299223i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 487789. | 0.656855 | 0.328427 | − | 0.944529i | \(-0.393481\pi\) | ||||
0.328427 | + | 0.944529i | \(0.393481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −145870. | −0.192092 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 280630.i | − 0.361467i | −0.983532 | − | 0.180734i | \(-0.942153\pi\) | ||||
0.983532 | − | 0.180734i | \(-0.0578472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 336464.i | − 0.423984i | −0.977271 | − | 0.211992i | \(-0.932005\pi\) | ||||
0.977271 | − | 0.211992i | \(-0.0679950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 130921. | 0.161428 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −248441. | −0.299802 | −0.149901 | − | 0.988701i | \(-0.547895\pi\) | ||||
−0.149901 | + | 0.988701i | \(0.547895\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 464426.i | − 0.548589i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 121733.i | 0.140779i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 685682. | 0.776476 | 0.388238 | − | 0.921559i | \(-0.373084\pi\) | ||||
0.388238 | + | 0.921559i | \(0.373084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −762667. | −0.845848 | −0.422924 | − | 0.906165i | \(-0.638996\pi\) | ||||
−0.422924 | + | 0.906165i | \(0.638996\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 520437.i | − 0.565396i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 67214.5i | − 0.0715398i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −360640. | −0.376124 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 56989.8 | 0.0582504 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 92462.4i | 0.0926362i | 0.998927 | + | 0.0463181i | \(0.0147488\pi\) | ||||
−0.998927 | + | 0.0463181i | \(0.985251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 461727.i | 0.453507i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −45411.8 | −0.0437339 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −715466. | −0.675704 | −0.337852 | − | 0.941199i | \(-0.609700\pi\) | ||||
−0.337852 | + | 0.941199i | \(0.609700\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 629277.i | 0.582898i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 1.21988e6i | − 1.10845i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.07592e6 | −1.85064 | −0.925320 | − | 0.379187i | \(-0.876204\pi\) | ||||
−0.925320 | + | 0.379187i | \(0.876204\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −524098. | −0.458457 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 133712.i | − 0.114787i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1.61680e6i | − 1.36231i | −0.732140 | − | 0.681154i | \(-0.761478\pi\) | ||||
0.732140 | − | 0.681154i | \(-0.238522\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.21414e6 | 1.83139 | 0.915695 | − | 0.401873i | \(-0.131641\pi\) | ||||
0.915695 | + | 0.401873i | \(0.131641\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 136544. | 0.110883 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 222167.i | − 0.177153i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 568957.i | − 0.445533i | −0.974872 | − | 0.222767i | \(-0.928491\pi\) | ||||
0.974872 | − | 0.222767i | \(-0.0715088\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.07889e6 | −0.829784 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 786523. | 0.594217 | 0.297109 | − | 0.954844i | \(-0.403978\pi\) | ||||
0.297109 | + | 0.954844i | \(0.403978\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.33703e6i | − 1.73460i | −0.497789 | − | 0.867298i | \(-0.665855\pi\) | ||||
0.497789 | − | 0.867298i | \(-0.334145\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 75381.9i | 0.0549737i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.66848e6 | 1.19568 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.07644e6 | −0.758132 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 417664.i | − 0.289131i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.06744e6i | 0.726398i | 0.931712 | + | 0.363199i | \(0.118315\pi\) | ||||
−0.931712 | + | 0.363199i | \(0.881685\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.21434e6 | −0.812431 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 524905. | 0.345294 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 481559.i | 0.311510i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 502585.i | 0.319738i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 122348. | 0.0765582 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −90521.9 | −0.0557191 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 345396.i | − 0.209156i | −0.994517 | − | 0.104578i | \(-0.966651\pi\) | ||||
0.994517 | − | 0.104578i | \(-0.0333492\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 509703.i | 0.303683i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.38990e6 | 0.814860 | 0.407430 | − | 0.913236i | \(-0.366425\pi\) | ||||
0.407430 | + | 0.913236i | \(0.366425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.35897e6 | −0.784061 | −0.392031 | − | 0.919952i | \(-0.628227\pi\) | ||||
−0.392031 | + | 0.919952i | \(0.628227\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 693296.i | 0.393679i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.04882e6i | − 1.14513i | −0.819859 | − | 0.572565i | \(-0.805948\pi\) | ||||
0.819859 | − | 0.572565i | \(-0.194052\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.85794e6 | 1.02224 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 631902. | 0.342284 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 570061.i | − 0.304029i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 231709.i | − 0.121684i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 203220. | 0.105099 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.20734e6 | −1.12429 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.75605e6i | 1.38267i | 0.722536 | + | 0.691333i | \(0.242976\pi\) | ||||
−0.722536 | + | 0.691333i | \(0.757024\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.23605e6i | 0.610836i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −42087.9 | −0.0204902 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.96450e6 | 0.942275 | 0.471137 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471137 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 108665.i | − 0.0513561i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1.64319e6i | − 0.765249i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.31648e6 | −1.06315 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 100657. | 0.0455298 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.37477e6i | 1.05876i | 0.848384 | + | 0.529381i | \(0.177576\pi\) | ||||
−0.848384 | + | 0.529381i | \(0.822424\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.89577e6i | 0.833146i | 0.909102 | + | 0.416573i | \(0.136769\pi\) | ||||
−0.909102 | + | 0.416573i | \(0.863231\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 547451. | 0.237179 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 89473.2 | 0.0382170 | 0.0191085 | − | 0.999817i | \(-0.493917\pi\) | ||||
0.0191085 | + | 0.999817i | \(0.493917\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 133310.i | − 0.0561425i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 215835.i | 0.0896295i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.27153e6 | −1.74923 | −0.874615 | − | 0.484818i | \(-0.838886\pi\) | ||||
−0.874615 | + | 0.484818i | \(0.838886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.52982e6 | 0.617834 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 107541.i | − 0.0428360i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.01402e6i | 0.791282i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.20466e6 | 0.854429 | 0.427214 | − | 0.904150i | \(-0.359495\pi\) | ||||
0.427214 | + | 0.904150i | \(0.359495\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.27728e6 | 1.25299 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.49095e6i | 0.939574i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.02519e6i | 1.87017i | 0.354427 | + | 0.935084i | \(0.384676\pi\) | ||||
−0.354427 | + | 0.935084i | \(0.615324\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −48432.5 | −0.0177852 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.93774e6 | 0.702169 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 128535.i | − 0.0459647i | −0.999736 | − | 0.0229823i | \(-0.992684\pi\) | ||||
0.999736 | − | 0.0229823i | \(-0.00731615\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 487355.i | − 0.172002i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.97607e6 | −1.38502 | −0.692512 | − | 0.721406i | \(-0.743496\pi\) | ||||
−0.692512 | + | 0.721406i | \(0.743496\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.05592e6 | −0.363062 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 987195.i | 0.335062i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 724285.i | − 0.242681i | −0.992611 | − | 0.121340i | \(-0.961281\pi\) | ||||
0.992611 | − | 0.121340i | \(-0.0387192\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −761198. | −0.251800 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 265584. | 0.0867401 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 981819.i | − 0.316620i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3.92474e6i | − 1.24978i | −0.780711 | − | 0.624892i | \(-0.785143\pi\) | ||||
0.780711 | − | 0.624892i | \(-0.214857\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 358278. | 0.112665 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.85395e6 | 1.81798 | 0.908988 | − | 0.416822i | \(-0.136856\pi\) | ||||
0.908988 | + | 0.416822i | \(0.136856\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.71377e6i | − 0.525643i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.30343e6i | 0.394865i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.88256e6 | −0.563329 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.05857e6 | 0.608496 | 0.304248 | − | 0.952593i | \(-0.401595\pi\) | ||||
0.304248 | + | 0.952593i | \(0.401595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 307925.i | 0.0899167i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.77158e6i | 1.66502i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −459642. | −0.131009 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −112735. | −0.0317483 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.30873e6i | 0.364180i | 0.983282 | + | 0.182090i | \(0.0582863\pi\) | ||||
−0.983282 | + | 0.182090i | \(0.941714\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 4.48649e6i | − 1.23368i | −0.787089 | − | 0.616839i | \(-0.788413\pi\) | ||||
0.787089 | − | 0.616839i | \(-0.211587\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.33574e6 | −1.17818 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 366262. | 0.0983602 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 430236.i | 0.114192i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 408488.i | 0.107161i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.60957e6 | 1.71388 | 0.856940 | − | 0.515417i | \(-0.172363\pi\) | ||||
0.856940 | + | 0.515417i | \(0.172363\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.04227e6 | −1.54875 | −0.774373 | − | 0.632729i | \(-0.781935\pi\) | ||||
−0.774373 | + | 0.632729i | \(0.781935\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 405031.i | − 0.102628i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.26356e6i | 0.316514i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 656087. | 0.162480 | 0.0812401 | − | 0.996695i | \(-0.474112\pi\) | ||||
0.0812401 | + | 0.996695i | \(0.474112\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −627493. | −0.153643 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.38448e6i | 1.30357i | 0.758403 | + | 0.651786i | \(0.225980\pi\) | ||||
−0.758403 | + | 0.651786i | \(0.774020\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.07843e6i | 0.258163i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 750006. | 0.177540 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.00212e6 | 1.63913 | 0.819565 | − | 0.572986i | \(-0.194215\pi\) | ||||
0.819565 | + | 0.572986i | \(0.194215\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.99145e6i | 1.15554i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 747268.i | 0.171093i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.10128e6 | −0.249384 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.95736e6 | 1.33433 | 0.667165 | − | 0.744910i | \(-0.267508\pi\) | ||||
0.667165 | + | 0.744910i | \(0.267508\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 865353.i | 0.191717i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2.60215e6i | − 0.570269i | −0.958487 | − | 0.285135i | \(-0.907962\pi\) | ||||
0.958487 | − | 0.285135i | \(-0.0920383\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.68993e6 | −0.583160 | −0.291580 | − | 0.956546i | \(-0.594181\pi\) | ||||
−0.291580 | + | 0.956546i | \(0.594181\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −358217. | −0.0768271 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.49920e6i | 1.37901i | 0.724280 | + | 0.689506i | \(0.242172\pi\) | ||||
−0.724280 | + | 0.689506i | \(0.757828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 200037.i | 0.0419931i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.39598e6 | −0.289952 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.50354e6 | −0.309003 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 607981.i | − 0.123639i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.89281e6i | 0.984607i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.30319e6 | 1.45437 | 0.727183 | − | 0.686443i | \(-0.240829\pi\) | ||||
0.727183 | + | 0.686443i | \(0.240829\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.96342e6 | −0.386945 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 478406.i | − 0.0933100i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.36860e6i | 0.650272i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.25953e6 | −0.813841 | −0.406921 | − | 0.913464i | \(-0.633397\pi\) | ||||
−0.406921 | + | 0.913464i | \(0.633397\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.20449e6 | 0.227789 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 888023.i | 0.166234i | 0.996540 | + | 0.0831171i | \(0.0264876\pi\) | ||||
−0.996540 | + | 0.0831171i | \(0.973512\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.06297e6i | 0.567579i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.07408e6 | −0.380463 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −633601. | −0.115060 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 597315.i | 0.107387i | 0.998557 | + | 0.0536935i | \(0.0170994\pi\) | ||||
−0.998557 | + | 0.0536935i | \(0.982901\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 50895.7i | 0.00905914i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.67283e6 | −1.70464 | −0.852322 | − | 0.523018i | \(-0.824806\pi\) | ||||
−0.852322 | + | 0.523018i | \(0.824806\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −986782. | −0.172184 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 724856.i | − 0.125237i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 2.66674e6i | − 0.456232i | −0.973634 | − | 0.228116i | \(-0.926743\pi\) | ||||
0.973634 | − | 0.228116i | \(-0.0732566\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.57230e6 | 1.62168 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.43645e6 | 0.240989 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.11093e6i | − 0.683002i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 6.60353e6i | − 1.08655i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 346656. | 0.0564911 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.96858e6 | 0.963333 | 0.481667 | − | 0.876355i | \(-0.340032\pi\) | ||||
0.481667 | + | 0.876355i | \(0.340032\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 9.24654e6i | − 1.47817i | −0.673611 | − | 0.739086i | \(-0.735258\pi\) | ||||
0.673611 | − | 0.739086i | \(-0.264742\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 230192.i | 0.0364495i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.70895e6 | 0.424888 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.74912e6 | −0.737860 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.13367e7i | 1.74482i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.20585e6i | 0.793731i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.09651e6 | −0.769818 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.34115e6 | −0.200697 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 955702.i | − 0.141694i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 1.19550e7i | − 1.75612i | −0.478547 | − | 0.878062i | \(-0.658836\pi\) | ||||
0.478547 | − | 0.878062i | \(-0.341164\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.47976e6 | −0.360919 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.63904e6 | −0.236374 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.07515e7i | − 1.53638i | −0.640221 | − | 0.768190i | \(-0.721157\pi\) | ||||
0.640221 | − | 0.768190i | \(-0.278843\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 845083.i | 0.119665i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.08442e6 | 0.713449 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.66643e6 | −0.648891 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 410399.i | 0.0565553i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 3.09710e6i | − 0.422978i | −0.977380 | − | 0.211489i | \(-0.932169\pi\) | ||||
0.977380 | − | 0.211489i | \(-0.0678313\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.56812e6 | −0.212252 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −645696. | −0.0866205 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.01607e7i | − 1.35100i | −0.737361 | − | 0.675499i | \(-0.763928\pi\) | ||||
0.737361 | − | 0.675499i | \(-0.236072\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 876424.i | 0.115503i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.19498e6 | 0.809249 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.86628e6 | −0.371141 | −0.185570 | − | 0.982631i | \(-0.559413\pi\) | ||||
−0.185570 | + | 0.982631i | \(0.559413\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 6.30651e6i | − 0.809466i | −0.914435 | − | 0.404733i | \(-0.867364\pi\) | ||||
0.914435 | − | 0.404733i | \(-0.132636\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.15518e6i | − 0.146981i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −811832. | −0.102399 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.94056e6 | −1.11796 | −0.558979 | − | 0.829182i | \(-0.688807\pi\) | ||||
−0.558979 | + | 0.829182i | \(0.688807\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.43254e6i | 0.301553i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.18461e6i | 0.268493i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.45199e6 | −0.908031 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.16316e6 | −0.261336 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.46374e6i | 0.894049i | 0.894522 | + | 0.447024i | \(0.147516\pi\) | ||||
−0.894522 | + | 0.447024i | \(0.852484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 4.49676e6i | − 0.534086i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.01962e6 | 0.120080 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.68119e6 | −0.896999 | −0.448500 | − | 0.893783i | \(-0.648041\pi\) | ||||
−0.448500 | + | 0.893783i | \(0.648041\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.74078e6i | − 0.201582i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.46835e6i | − 0.168614i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.04401e6 | −0.460517 | −0.230258 | − | 0.973130i | \(-0.573957\pi\) | ||||
−0.230258 | + | 0.973130i | \(0.573957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 733125. | 0.0827927 | 0.0413963 | − | 0.999143i | \(-0.486819\pi\) | ||||
0.0413963 | + | 0.999143i | \(0.486819\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 392919.i | 0.0440058i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 867357.i | 0.0963407i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.38418e7 | 1.52483 | 0.762413 | − | 0.647091i | \(-0.224015\pi\) | ||||
0.762413 | + | 0.647091i | \(0.224015\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.92505e6 | −0.210329 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 6.88716e6i | − 0.746341i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.82596e6i | 0.518719i | 0.965781 | + | 0.259360i | \(0.0835115\pi\) | ||||
−0.965781 | + | 0.259360i | \(0.916489\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.08814e6 | 0.116010 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.36275e6 | −0.355616 | −0.177808 | − | 0.984065i | \(-0.556901\pi\) | ||||
−0.177808 | + | 0.984065i | \(0.556901\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 9.71613e6i | − 1.01922i | −0.860406 | − | 0.509608i | \(-0.829790\pi\) | ||||
0.860406 | − | 0.509608i | \(-0.170210\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 1.91808e6i | − 0.199590i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.12562e6 | 0.529086 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.07183e6i | 0.108882i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 3.10356e6i | − 0.312776i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.51112e7 | 1.51086 | 0.755432 | − | 0.655227i | \(-0.227427\pi\) | ||||
0.755432 | + | 0.655227i | \(0.227427\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.18421e6 | −0.216663 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.93069e6i | 0.386843i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 996751.i | − 0.0973281i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.24454e6 | −0.120575 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.92719e6 | 0.954292 | 0.477146 | − | 0.878824i | \(-0.341671\pi\) | ||||
0.477146 | + | 0.878824i | \(0.341671\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.34898e7i | − 1.28670i | −0.765573 | − | 0.643349i | \(-0.777544\pi\) | ||||
0.765573 | − | 0.643349i | \(-0.222456\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 327773.i | 0.0310223i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.20615e6 | 0.582857 | 0.291428 | − | 0.956593i | \(-0.405869\pi\) | ||||
0.291428 | + | 0.956593i | \(0.405869\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.72664e7 | −1.60912 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.70255e6i | 0.157452i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.72472e7i | 1.58283i | 0.611277 | + | 0.791417i | \(0.290656\pi\) | ||||
−0.611277 | + | 0.791417i | \(0.709344\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.14202e6 | −0.195084 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.88022e7 | 1.69940 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.84307e6i | 0.434418i | 0.976125 | + | 0.217209i | \(0.0696952\pi\) | ||||
−0.976125 | + | 0.217209i | \(0.930305\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1.29176e7i | − 1.14995i | −0.818172 | − | 0.574973i | \(-0.805013\pi\) | ||||
0.818172 | − | 0.574973i | \(-0.194987\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −673429. | −0.0594988 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.88964e6 | −0.253390 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6.78919e6i | − 0.590885i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.51199e6i | − 0.130612i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.28710e6 | −0.110359 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.16137e6 | −0.524372 | −0.262186 | − | 0.965017i | \(-0.584443\pi\) | ||||
−0.262186 | + | 0.965017i | \(0.584443\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 922914.i | 0.0779654i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.95790e7i | − 1.64179i | −0.571077 | − | 0.820896i | \(-0.693474\pi\) | ||||
0.571077 | − | 0.820896i | \(-0.306526\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.60104e7 | 1.33269 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −869862. | −0.0718758 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.33176e7i | − 1.09238i | −0.837661 | − | 0.546190i | \(-0.816078\pi\) | ||||
0.837661 | − | 0.546190i | \(-0.183922\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 2.48352e6i | − 0.202228i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.04293e6 | −0.0843069 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.77206e6 | −0.623718 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 8.17155e6i | − 0.651043i | −0.945535 | − | 0.325521i | \(-0.894460\pi\) | ||||
0.945535 | − | 0.325521i | \(-0.105540\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.85776e6i | 0.779731i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 909250. | 0.0714038 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.22886e6 | −0.641590 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 770089.i | 0.0596140i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.90780e7i | − 1.46635i | −0.680041 | − | 0.733174i | \(-0.738038\pi\) | ||||
0.680041 | − | 0.733174i | \(-0.261962\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.15180e6 | −0.393161 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.43957e6 | −0.109084 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.69001e6i | 0.352879i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.13159e7i | − 0.845422i | −0.906265 | − | 0.422711i | \(-0.861079\pi\) | ||||
0.906265 | − | 0.422711i | \(-0.138921\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.16595e6 | −0.679992 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.00449e6 | −0.442336 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 3.29460e6i | − 0.241011i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.12540e6i | − 0.154398i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.63847e7 | −1.18200 | −0.590998 | − | 0.806673i | \(-0.701266\pi\) | ||||
−0.590998 | + | 0.806673i | \(0.701266\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.95386e7 | −1.39976 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.36402e6i | 0.168192i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.26672e6i | 0.230816i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.06838e6 | 0.566175 | 0.283087 | − | 0.959094i | \(-0.408641\pi\) | ||||
0.283087 | + | 0.959094i | \(0.408641\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.10561e7 | 0.770520 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 2.47873e6i | − 0.171568i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 563282.i | 0.0387227i | 0.999813 | + | 0.0193614i | \(0.00616330\pi\) | ||||
−0.999813 | + | 0.0193614i | \(0.993837\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −208344. | −0.0142253 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −598434. | −0.0405833 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 6.99287e6i | − 0.471026i | −0.971871 | − | 0.235513i | \(-0.924323\pi\) | ||||
0.971871 | − | 0.235513i | \(-0.0756770\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.11787e6i | 0.0747902i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −690902. | −0.0459139 | −0.0229570 | − | 0.999736i | \(-0.507308\pi\) | ||||
−0.0229570 | + | 0.999736i | \(0.507308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.04906e6 | −0.399298 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.29107e6i | 0.281361i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.42229e7i | 1.57769i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.61091e6 | 0.104225 | 0.0521123 | − | 0.998641i | \(-0.483405\pi\) | ||||
0.0521123 | + | 0.998641i | \(0.483405\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 286604. | 0.0184202 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 6.02698e6i | − 0.384797i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.75412e6i | 0.618655i | 0.950956 | + | 0.309327i | \(0.100104\pi\) | ||||
−0.950956 | + | 0.309327i | \(0.899896\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.43121e6 | 0.0901774 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.42949e7 | 0.894786 | 0.447393 | − | 0.894337i | \(-0.352352\pi\) | ||||
0.447393 | + | 0.894337i | \(0.352352\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.79011e6i | 0.484431i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 3.41930e6i | − 0.211244i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.80080e7 | −1.10529 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.02217e7 | 0.623313 | 0.311656 | − | 0.950195i | \(-0.399116\pi\) | ||||
0.311656 | + | 0.950195i | \(0.399116\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.21772e6i | 0.134360i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 6.53435e6i | − 0.393327i | −0.980471 | − | 0.196663i | \(-0.936989\pi\) | ||||
0.980471 | − | 0.196663i | \(-0.0630106\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.88915e6 | 0.172789 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.95056e6 | 0.115906 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.36596e7i | 0.806481i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.89549e6i | − 0.111197i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.71815e6 | −0.449892 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.12590e7 | 0.652120 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.32185e7i | − 0.760756i | −0.924831 | − | 0.380378i | \(-0.875794\pi\) | ||||
0.924831 | − | 0.380378i | \(-0.124206\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.43470e6i | 0.367990i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.16550e6 | 0.236715 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.34238e6 | −0.0758043 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.62454e6i | 0.0911616i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.45286e7i | 0.810173i | 0.914278 | + | 0.405087i | \(0.132759\pi\) | ||||
−0.914278 | + | 0.405087i | \(0.867241\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.08865e7 | 0.603284 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.00679e7 | 0.554444 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.86367e7i | 1.56723i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.85851e6i | 0.209860i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.01156e6 | −0.270888 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.59141e7 | 0.854891 | 0.427445 | − | 0.904041i | \(-0.359414\pi\) | ||||
0.427445 | + | 0.904041i | \(0.359414\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.87197e7i | 0.999418i | 0.866193 | + | 0.499709i | \(0.166560\pi\) | ||||
−0.866193 | + | 0.499709i | \(0.833440\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 6.86311e6i | − 0.364162i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.71465e6 | −0.512310 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.11459e6 | −0.215661 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.02812e7i | 0.535590i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.44309e7i | 1.78275i | 0.453267 | + | 0.891375i | \(0.350258\pi\) | ||||
−0.453267 | + | 0.891375i | \(0.649742\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.98856e7 | 1.02338 | 0.511692 | − | 0.859169i | \(-0.329019\pi\) | ||||
0.511692 | + | 0.859169i | \(0.329019\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −688646. | −0.0352258 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.39990e7i | 1.22019i | 0.792327 | + | 0.610097i | \(0.208869\pi\) | ||||
−0.792327 | + | 0.610097i | \(0.791131\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1.03074e7i | − 0.520908i | −0.965486 | − | 0.260454i | \(-0.916128\pi\) | ||||
0.965486 | − | 0.260454i | \(-0.0838722\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.76359e6 | −0.0885919 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.57556e6 | 0.0786724 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 410492.i | − 0.0203746i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.82608e6i | 0.336789i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 808698. | 0.0396626 | 0.0198313 | − | 0.999803i | \(-0.493687\pi\) | ||||
0.0198313 | + | 0.999803i | \(0.493687\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.80776e6 | −0.331905 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.43797e6i | − 0.118157i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.84622e6i | 0.281665i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.12241e6 | 0.197443 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.24405e6 | −0.344915 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.87916e6i | 0.325620i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.48576e7i | − 0.699161i | −0.936906 | − | 0.349580i | \(-0.886324\pi\) | ||||
0.936906 | − | 0.349580i | \(-0.113676\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.67592e6 | −0.265534 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 873459. | 0.0406247 | 0.0203124 | − | 0.999794i | \(-0.493534\pi\) | ||||
0.0203124 | + | 0.999794i | \(0.493534\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 3.79173e7i | − 1.75329i | −0.481135 | − | 0.876647i | \(-0.659775\pi\) | ||||
0.481135 | − | 0.876647i | \(-0.340225\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 5.17175e6i | − 0.237755i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.76129e7 | −1.71914 | −0.859568 | − | 0.511022i | \(-0.829267\pi\) | ||||
−0.859568 | + | 0.511022i | \(0.829267\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.79590e6 | −0.127052 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.33662e6i | 0.150750i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.39602e7i | − 0.627107i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −624138. | −0.0278763 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.14482e7 | 1.39656 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.85658e6i | − 0.0819772i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.68861e7i | 0.741360i | 0.928761 | + | 0.370680i | \(0.120875\pi\) | ||||
−0.928761 | + | 0.370680i | \(0.879125\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.30872e6 | 0.144440 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.09397e7 | 0.474858 | 0.237429 | − | 0.971405i | \(-0.423695\pi\) | ||||
0.237429 | + | 0.971405i | \(0.423695\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.07162e7i | 0.462530i | 0.972891 | + | 0.231265i | \(0.0742864\pi\) | ||||
−0.972891 | + | 0.231265i | \(0.925714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.76408e6i | 0.161547i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.53953e6 | −0.151056 | −0.0755278 | − | 0.997144i | \(-0.524064\pi\) | ||||
−0.0755278 | + | 0.997144i | \(0.524064\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.86819e7 | 0.792807 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.85330e7i | 0.782081i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.80712e7i | − 0.758330i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.08168e7 | 0.451380 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.49268e6 | 0.0619420 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.41614e7i | 0.997062i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.22853e7i | − 0.504165i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.55785e6 | 0.0635781 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.00001e7 | 0.811730 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.70933e7i | 0.689935i | 0.938615 | + | 0.344967i | \(0.112110\pi\) | ||||
−0.938615 | + | 0.344967i | \(0.887890\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.21228e6i | 0.369792i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.54600e7 | −1.01639 | −0.508196 | − | 0.861241i | \(-0.669688\pi\) | ||||
−0.508196 | + | 0.861241i | \(0.669688\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.53550e6 | −0.259479 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 280589.i | 0.0110794i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.01807e7i | 0.399810i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.02310e6 | 0.118077 | 0.0590383 | − | 0.998256i | \(-0.481197\pi\) | ||||
0.0590383 | + | 0.998256i | \(0.481197\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.07062e6 | −0.0415896 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.97691e6i | − 0.0763804i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 3.31001e6i | − 0.127196i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.83783e7 | −1.46685 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.67045e7 | 1.39534 | 0.697669 | − | 0.716420i | \(-0.254220\pi\) | ||||
0.697669 | + | 0.716420i | \(0.254220\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2.61537e6i | − 0.0988915i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 4.30825e6i | − 0.162031i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.20776e6 | 0.194815 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.27722e6 | −0.0847338 | −0.0423669 | − | 0.999102i | \(-0.513490\pi\) | ||||
−0.0423669 | + | 0.999102i | \(0.513490\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.21238e6i | 0.155906i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.68229e7i | 1.72379i | 0.507087 | + | 0.861895i | \(0.330722\pi\) | ||||
−0.507087 | + | 0.861895i | \(0.669278\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.82395e7 | 0.667936 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.38646e6 | 0.159785 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.27905e7i | − 1.55050i | −0.631654 | − | 0.775250i | \(-0.717624\pi\) | ||||
0.631654 | − | 0.775250i | \(-0.282376\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.98667e7i | 1.07652i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.35067e6 | −0.227703 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.95519e7 | 1.41070 | 0.705351 | − | 0.708858i | \(-0.250789\pi\) | ||||
0.705351 | + | 0.708858i | \(0.250789\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.31691e6i | 0.330570i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 5.75901e6i | − 0.203267i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.18038e7 | −0.414452 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.26038e6 | −0.253601 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.75793e7i | 1.65330i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1.96193e7i | − 0.678211i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.15339e7 | 0.740553 | 0.370277 | − | 0.928922i | \(-0.379263\pi\) | ||||
0.370277 | + | 0.928922i | \(0.379263\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.76701e6 | −0.0604546 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 559354.i | − 0.0190388i | −0.999955 | − | 0.00951939i | \(-0.996970\pi\) | ||||
0.999955 | − | 0.00951939i | \(-0.00303016\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.32152e6i | − 0.146337i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −718225. | −0.0241963 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.11889e7 | 0.710187 | 0.355094 | − | 0.934831i | \(-0.384449\pi\) | ||||
0.355094 | + | 0.934831i | \(0.384449\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.53339e7i | 0.511324i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.53016e7i | 0.507649i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.00893e7 | 1.32326 | 0.661630 | − | 0.749830i | \(-0.269865\pi\) | ||||
0.661630 | + | 0.749830i | \(0.269865\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.22362e6 | −0.270067 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.84206e6i | 0.223560i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.49418e6i | 0.178613i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.50729e7 | −1.78137 | −0.890684 | − | 0.454623i | \(-0.849774\pi\) | ||||
−0.890684 | + | 0.454623i | \(0.849774\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.54288e6 | 0.274936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.18427e7i | 0.379223i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.44969e7i | − 0.461889i | −0.972967 | − | 0.230944i | \(-0.925818\pi\) | ||||
0.972967 | − | 0.230944i | \(-0.0741816\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.82043e6 | 0.247923 |
(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 | 320.6.d.c.161.6 | ✓ | 12 | |
4.3 | odd | 2 | 320.6.d.d.161.7 | yes | 12 | ||
8.3 | odd | 2 | 320.6.d.d.161.6 | yes | 12 | ||
8.5 | even | 2 | inner | 320.6.d.c.161.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.d.c.161.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
320.6.d.c.161.7 | yes | 12 | 8.5 | even | 2 | inner | |
320.6.d.d.161.6 | yes | 12 | 8.3 | odd | 2 | ||
320.6.d.d.161.7 | yes | 12 | 4.3 | odd | 2 |