Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,7,Mod(319,384)]
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, 1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.319");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(88.3407681100\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.5 | ||
Root | \(1.35234 - 0.780776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.7.b.d.319.8 |
$q$-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 | ||||||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 20.0000i | − 0.160000i | −0.996795 | − | 0.0800000i | \(-0.974508\pi\) | ||||
0.996795 | − | 0.0800000i | \(-0.0254920\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 155.727i | − 0.454015i | −0.973893 | − | 0.227007i | \(-0.927106\pi\) | ||||
0.973893 | − | 0.227007i | \(-0.0728942\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2306.46 | −1.73288 | −0.866439 | − | 0.499282i | \(-0.833597\pi\) | ||||
−0.866439 | + | 0.499282i | \(0.833597\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3221.18i | − 1.46617i | −0.680136 | − | 0.733086i | \(-0.738079\pi\) | ||||
0.680136 | − | 0.733086i | \(-0.261921\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 311.769i | − 0.0923760i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6566.73 | −1.33660 | −0.668301 | − | 0.743891i | \(-0.732978\pi\) | ||||
−0.668301 | + | 0.743891i | \(0.732978\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3926.40 | 0.572445 | 0.286223 | − | 0.958163i | \(-0.407600\pi\) | ||||
0.286223 | + | 0.958163i | \(0.407600\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 2427.54i | − 0.262126i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17392.0i | 1.42944i | 0.699411 | + | 0.714720i | \(0.253446\pi\) | ||||
−0.699411 | + | 0.714720i | \(0.746554\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15225.0 | 0.974400 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 44713.3i | 1.83334i | 0.399648 | + | 0.916669i | \(0.369132\pi\) | ||||
−0.399648 | + | 0.916669i | \(0.630868\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 30636.4i | − 1.02838i | −0.857677 | − | 0.514188i | \(-0.828093\pi\) | ||||
0.857677 | − | 0.514188i | \(-0.171907\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −35954.2 | −1.00048 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3114.54 | −0.0726424 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44158.1i | 0.871776i | 0.900001 | + | 0.435888i | \(0.143566\pi\) | ||||
−0.900001 | + | 0.435888i | \(0.856434\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 50213.3i | − 0.846495i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9008.18 | 0.130703 | 0.0653515 | − | 0.997862i | \(-0.479183\pi\) | ||||
0.0653515 | + | 0.997862i | \(0.479183\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −25270.3 | −0.317838 | −0.158919 | − | 0.987292i | \(-0.550801\pi\) | ||||
−0.158919 | + | 0.987292i | \(0.550801\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 4860.00i | − 0.0533333i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 175606.i | 1.69140i | 0.533658 | + | 0.845700i | \(0.320817\pi\) | ||||
−0.533658 | + | 0.845700i | \(0.679183\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 93398.1 | 0.793871 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −102365. | −0.771688 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 96206.3i | − 0.646214i | −0.946363 | − | 0.323107i | \(-0.895273\pi\) | ||||
0.946363 | − | 0.323107i | \(-0.104727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 46129.2i | 0.277261i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 61206.5 | 0.330501 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 35018.3 | 0.170506 | 0.0852529 | − | 0.996359i | \(-0.472830\pi\) | ||||
0.0852529 | + | 0.996359i | \(0.472830\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 86135.7i | 0.379484i | 0.981834 | + | 0.189742i | \(0.0607652\pi\) | ||||
−0.981834 | + | 0.189742i | \(0.939235\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 37841.7i | − 0.151338i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −64423.6 | −0.234588 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 424605. | 1.41176 | 0.705880 | − | 0.708332i | \(-0.250552\pi\) | ||||
0.705880 | + | 0.708332i | \(0.250552\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 271114.i | 0.825287i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36572.4i | 0.102183i | 0.998694 | + | 0.0510915i | \(0.0162700\pi\) | ||||
−0.998694 | + | 0.0510915i | \(0.983730\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −375121. | −0.964280 | −0.482140 | − | 0.876094i | \(-0.660140\pi\) | ||||
−0.482140 | + | 0.876094i | \(0.660140\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 237334. | 0.562570 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 359179.i | 0.786753i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 520323.i | 1.05534i | 0.849450 | + | 0.527670i | \(0.176934\pi\) | ||||
−0.849450 | + | 0.527670i | \(0.823066\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −594208. | −1.03921 | −0.519606 | − | 0.854406i | \(-0.673921\pi\) | ||||
−0.519606 | + | 0.854406i | \(0.673921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 131335.i | 0.213856i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 697011.i | 1.05848i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 901101. | 1.27821 | 0.639107 | − | 0.769118i | \(-0.279304\pi\) | ||||
0.639107 | + | 0.769118i | \(0.279304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −501625. | −0.665664 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 477574.i | − 0.593733i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 78528.0i | − 0.0915912i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.25744e6 | −1.37775 | −0.688875 | − | 0.724880i | \(-0.741895\pi\) | ||||
−0.688875 | + | 0.724880i | \(0.741895\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −560470. | −0.577626 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 391040.i | − 0.379539i | −0.981829 | − | 0.189770i | \(-0.939226\pi\) | ||||
0.981829 | − | 0.189770i | \(-0.0607741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.36080e6i | 1.24533i | 0.782490 | + | 0.622663i | \(0.213949\pi\) | ||||
−0.782490 | + | 0.622663i | \(0.786051\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −48550.9 | −0.0419401 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.28620e6 | 1.04992 | 0.524960 | − | 0.851127i | \(-0.324080\pi\) | ||||
0.524960 | + | 0.851127i | \(0.324080\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.75763e6i | − 1.35721i | −0.734504 | − | 0.678605i | \(-0.762585\pi\) | ||||
0.734504 | − | 0.678605i | \(-0.237415\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 688357.i | 0.503320i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −730749. | −0.506446 | −0.253223 | − | 0.967408i | \(-0.581491\pi\) | ||||
−0.253223 | + | 0.967408i | \(0.581491\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 347840. | 0.228710 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 782747.i | − 0.488724i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.02262e6i | 0.606837i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.54820e6 | 2.00287 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 140424. | 0.0754614 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 617000.i | − 0.315904i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.59678e6i | 1.26772i | 0.773448 | + | 0.633860i | \(0.218531\pi\) | ||||
−0.773448 | + | 0.633860i | \(0.781469\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −393925. | −0.183504 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −605543. | −0.269359 | −0.134679 | − | 0.990889i | \(-0.543000\pi\) | ||||
−0.134679 | + | 0.990889i | \(0.543000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 611447.i | − 0.259899i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 75759.9i | − 0.0307920i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.75932e6 | −0.684199 | −0.342100 | − | 0.939664i | \(-0.611138\pi\) | ||||
−0.342100 | + | 0.939664i | \(0.611138\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −303680. | −0.113076 | −0.0565382 | − | 0.998400i | \(-0.518006\pi\) | ||||
−0.0565382 | + | 0.998400i | \(0.518006\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.73743e6i | 0.976531i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.42953e6i | 2.54070i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 894265. | 0.293334 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.45593e6 | 0.458341 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.32218e6i | 0.399696i | 0.979827 | + | 0.199848i | \(0.0640449\pi\) | ||||
−0.979827 | + | 0.199848i | \(0.935955\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.67518e6i | 1.35790i | 0.734184 | + | 0.678950i | \(0.237565\pi\) | ||||
−0.734184 | + | 0.678950i | \(0.762435\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.59571e6 | −0.445534 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −612727. | −0.164540 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.44769e6i | 0.632495i | 0.948677 | + | 0.316247i | \(0.102423\pi\) | ||||
−0.948677 | + | 0.316247i | \(0.897577\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 1.49971e6i | − 0.373092i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.70840e6 | 0.648987 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.62033e6 | −1.52868 | −0.764340 | − | 0.644813i | \(-0.776935\pi\) | ||||
−0.764340 | + | 0.644813i | \(0.776935\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 719084.i | 0.160076i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.27537e6i | 1.56209i | 0.624476 | + | 0.781044i | \(0.285313\pi\) | ||||
−0.624476 | + | 0.781044i | \(0.714687\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.54920e6 | −1.14966 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 954116. | 0.190815 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 3.72601e6i | − 0.719623i | −0.933025 | − | 0.359812i | \(-0.882841\pi\) | ||||
0.933025 | − | 0.359812i | \(-0.117159\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 2.37094e6i | − 0.442392i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 545881. | 0.0984415 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 201811. | 0.0351873 | 0.0175937 | − | 0.999845i | \(-0.494399\pi\) | ||||
0.0175937 | + | 0.999845i | \(0.494399\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 5.43440e6i | − 0.916466i | −0.888832 | − | 0.458233i | \(-0.848483\pi\) | ||||
0.888832 | − | 0.458233i | \(-0.151517\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.34272e6i | 0.219095i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 883162. | 0.139484 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.51459e7 | 2.31617 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 589893.i | − 0.0873752i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.82608e6i | 0.979650i | 0.871821 | + | 0.489825i | \(0.162939\pi\) | ||||
−0.871821 | + | 0.489825i | \(0.837061\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.30841e6 | 0.182001 | 0.0910004 | − | 0.995851i | \(-0.470994\pi\) | ||||
0.0910004 | + | 0.995851i | \(0.470994\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00427e6 | −0.135439 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.61375e6i | 0.995863i | 0.867216 | + | 0.497932i | \(0.165907\pi\) | ||||
−0.867216 | + | 0.497932i | \(0.834093\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.47692e6i | 0.821882i | 0.911662 | + | 0.410941i | \(0.134800\pi\) | ||||
−0.911662 | + | 0.410941i | \(0.865200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.61894e6 | 0.815080 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.96307e6 | 0.832362 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 180164.i | − 0.0209125i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.22625e6i | 0.476480i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.05609e6 | −0.991978 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.58058e7 | −1.68256 | −0.841278 | − | 0.540603i | \(-0.818196\pi\) | ||||
−0.841278 | + | 0.540603i | \(0.818196\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 570108.i | 0.0589954i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 505406.i | 0.0508540i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.77091e6 | −0.466898 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.84756e6 | −0.556727 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.11526e7i | 1.95969i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.07099e7i | 1.86751i | 0.357907 | + | 0.933757i | \(0.383491\pi\) | ||||
−0.357907 | + | 0.933757i | \(0.616509\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.69967e6 | 0.324800 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.06179e6 | −0.603722 | −0.301861 | − | 0.953352i | \(-0.597608\pi\) | ||||
−0.301861 | + | 0.953352i | \(0.597608\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.64766e6i | 0.387015i | 0.981099 | + | 0.193507i | \(0.0619863\pi\) | ||||
−0.981099 | + | 0.193507i | \(0.938014\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.59904e6i | 0.454232i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.13777e7 | 0.899469 | 0.449735 | − | 0.893162i | \(-0.351519\pi\) | ||||
0.449735 | + | 0.893162i | \(0.351519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.51213e6 | 0.270624 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.11104e6i | 0.609300i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 1.93765e7i | − 1.41932i | −0.704542 | − | 0.709662i | \(-0.748848\pi\) | ||||
0.704542 | − | 0.709662i | \(-0.251152\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.84883e6 | 0.489289 | 0.244644 | − | 0.969613i | \(-0.421329\pi\) | ||||
0.244644 | + | 0.969613i | \(0.421329\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.86796e6i | − 0.127019i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.26477e7i | − 0.839304i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.26279e6 | −0.599989 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 129527. | 0.00819104 | 0.00409552 | − | 0.999992i | \(-0.498696\pi\) | ||||
0.00409552 | + | 0.999992i | \(0.498696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4.01140e7i | − 2.47705i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.04730e6i | 0.123470i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.18895e7 | 0.700427 | 0.350213 | − | 0.936670i | \(-0.386109\pi\) | ||||
0.350213 | + | 0.936670i | \(0.386109\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.87661e6 | 0.395799 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.08653e7i | 0.611113i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 1.35674e7i | − 0.745811i | −0.927869 | − | 0.372906i | \(-0.878362\pi\) | ||||
0.927869 | − | 0.372906i | \(-0.121638\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.92413e6 | −0.103394 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.40468e7 | 0.737977 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1.71231e7i | − 0.879680i | −0.898076 | − | 0.439840i | \(-0.855035\pi\) | ||||
0.898076 | − | 0.439840i | \(-0.144965\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 320201.i | 0.0160885i | 0.999968 | + | 0.00804423i | \(0.00256058\pi\) | ||||
−0.999968 | + | 0.00804423i | \(0.997439\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.81956e6 | −0.384321 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.51159e7 | −1.68852 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.50949e7i | − 0.710216i | −0.934825 | − | 0.355108i | \(-0.884444\pi\) | ||||
0.934825 | − | 0.355108i | \(-0.115556\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 7.44463e6i | − 0.342792i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.32580e7 | −1.94961 | −0.974804 | − | 0.223063i | \(-0.928394\pi\) | ||||
−0.974804 | + | 0.223063i | \(0.928394\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.22002e7 | 1.42069 | 0.710345 | − | 0.703854i | \(-0.248539\pi\) | ||||
0.710345 | + | 0.703854i | \(0.248539\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.22413e6i | − 0.0528802i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.40282e6i | − 0.0593411i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.89843e7 | 0.786505 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.96015e7 | −0.795444 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3.01307e7i | − 1.19786i | −0.800801 | − | 0.598931i | \(-0.795592\pi\) | ||||
0.800801 | − | 0.598931i | \(-0.204408\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 700366.i | − 0.0272809i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.73687e6 | −0.333493 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.60228e7 | 2.09581 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.93527e6i | 0.144303i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 6.09571e6i | − 0.219127i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.72271e6 | 0.0607175 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.09501e7 | −0.724053 | −0.362026 | − | 0.932168i | \(-0.617915\pi\) | ||||
−0.362026 | + | 0.932168i | \(0.617915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.12128e7i | 0.718990i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.94101e6i | 0.164261i | 0.996622 | + | 0.0821305i | \(0.0261724\pi\) | ||||
−0.996622 | + | 0.0821305i | \(0.973828\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.67449e7 | 0.872182 | 0.436091 | − | 0.899903i | \(-0.356363\pi\) | ||||
0.436091 | + | 0.899903i | \(0.356363\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −756834. | −0.0242141 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.74499e7i | 1.48956i | 0.667311 | + | 0.744779i | \(0.267445\pi\) | ||||
−0.667311 | + | 0.744779i | \(0.732555\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 1.03129e8i | − 3.17695i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.00498e7 | 0.606172 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.57836e7 | −0.765131 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.90425e7i | − 1.42864i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 2.73987e7i | − 0.783585i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.73467e7 | 0.767921 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.84318e7 | −1.33551 | −0.667754 | − | 0.744382i | \(-0.732744\pi\) | ||||
−0.667754 | + | 0.744382i | \(0.732744\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.07304e7i | 0.290592i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 8.49210e6i | − 0.225881i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.96066e7 | −1.55742 | −0.778709 | − | 0.627386i | \(-0.784125\pi\) | ||||
−0.778709 | + | 0.627386i | \(0.784125\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.13913e7 | −0.292397 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.06616e7i | 1.78205i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3.28657e7i | − 0.814444i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.42229e6 | 0.132046 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.95157e7 | 0.706423 | 0.353211 | − | 0.935544i | \(-0.385090\pi\) | ||||
0.353211 | + | 0.935544i | \(0.385090\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 5.55247e7i | − 1.30620i | −0.757272 | − | 0.653100i | \(-0.773468\pi\) | ||||
0.757272 | − | 0.653100i | \(-0.226532\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 1.22018e7i | − 0.282165i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.81396e7 | −0.412386 | −0.206193 | − | 0.978511i | \(-0.566107\pi\) | ||||
−0.206193 | + | 0.978511i | \(0.566107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 731449. | 0.0163493 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.59410e7i | 0.350358i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 8.83261e6i | − 0.190900i | −0.995434 | − | 0.0954499i | \(-0.969571\pi\) | ||||
0.995434 | − | 0.0954499i | \(-0.0304290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.16293e7 | −0.672307 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.53110e7 | 1.15636 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.50242e6i | 0.154285i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.83247e7i | 0.977623i | 0.872389 | + | 0.488811i | \(0.162569\pi\) | ||||
−0.872389 | + | 0.488811i | \(0.837431\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.18899e6 | 0.0435677 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.49819e7 | −0.293391 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 8.98844e7i | − 1.73204i | −0.500010 | − | 0.866020i | \(-0.666670\pi\) | ||||
0.500010 | − | 0.866020i | \(-0.333330\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 9.61808e6i | − 0.182387i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.44030e8 | 2.68799 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.60279e7 | 1.58024 | 0.790118 | − | 0.612955i | \(-0.210019\pi\) | ||||
0.790118 | + | 0.612955i | \(0.210019\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.04798e7i | 0.731919i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 6.65042e7i | − 1.18373i | −0.806037 | − | 0.591865i | \(-0.798392\pi\) | ||||
0.806037 | − | 0.591865i | \(-0.201608\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.18357e6 | 0.125880 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.14069e6 | −0.105946 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.66889e7i | 0.963050i | 0.876432 | + | 0.481525i | \(0.159917\pi\) | ||||
−0.876432 | + | 0.481525i | \(0.840083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 1.14208e8i | − 1.91059i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.43949e6 | −0.155514 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.04065e7 | 0.168854 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3.21267e7i | − 0.513446i | −0.966485 | − | 0.256723i | \(-0.917357\pi\) | ||||
0.966485 | − | 0.256723i | \(-0.0826429\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 9.53152e6i | − 0.150053i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.28625e7 | −1.12998 | −0.564991 | − | 0.825097i | \(-0.691120\pi\) | ||||
−0.564991 | + | 0.825097i | \(0.691120\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.86853e7 | −1.50778 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.18098e6i | − 0.0177778i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.01849e8i | − 1.51068i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.07185e7 | −0.302823 | −0.151412 | − | 0.988471i | \(-0.548382\pi\) | ||||
−0.151412 | + | 0.988471i | \(0.548382\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.74251e7 | −0.395023 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5.45330e6i | − 0.0774121i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.18842e7i | 0.166274i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.73390e6 | −0.0652846 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.79561e7 | −0.923818 | −0.461909 | − | 0.886927i | \(-0.652835\pi\) | ||||
−0.461909 | + | 0.886927i | \(0.652835\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 522580.i | 0.00700336i | 0.999994 | + | 0.00350168i | \(0.00111462\pi\) | ||||
−0.999994 | + | 0.00350168i | \(0.998885\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.26723e7i | 0.563800i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.99784e7 | −1.30239 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.34137e7 | 0.172291 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.15815e8i | 1.46687i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 1.10533e8i | − 1.38057i | −0.723538 | − | 0.690285i | \(-0.757485\pi\) | ||||
0.723538 | − | 0.690285i | \(-0.242515\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.65239e7 | 0.819435 | 0.409717 | − | 0.912213i | \(-0.365627\pi\) | ||||
0.409717 | + | 0.912213i | \(0.365627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.39402e7 | 0.169356 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.82879e7i | 0.818276i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.06995e8i | 1.26465i | 0.774702 | + | 0.632327i | \(0.217900\pi\) | ||||
−0.774702 | + | 0.632327i | \(0.782100\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.26957e7 | 0.264624 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.01597e7 | −0.116861 | −0.0584304 | − | 0.998291i | \(-0.518610\pi\) | ||||
−0.0584304 | + | 0.998291i | \(0.518610\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.80220e7i | − 0.204514i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.06107e7i | 0.230765i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.39511e7 | −0.485546 | −0.242773 | − | 0.970083i | \(-0.578057\pi\) | ||||
−0.242773 | + | 0.970083i | \(0.578057\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.07770e7 | −0.226492 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.28789e7i | 0.783984i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00325e7i | 0.106506i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.92987e6 | −0.0621293 | −0.0310646 | − | 0.999517i | \(-0.509890\pi\) | ||||
−0.0310646 | + | 0.999517i | \(0.509890\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.48747e7 | −0.257229 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.31145e7i | 0.440069i | 0.975492 | + | 0.220035i | \(0.0706170\pi\) | ||||
−0.975492 | + | 0.220035i | \(0.929383\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 8.09555e7i | − 0.815649i | −0.913060 | − | 0.407825i | \(-0.866288\pi\) | ||||
0.913060 | − | 0.407825i | \(-0.133712\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.55147e6 | −0.0949973 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.20309e8 | 1.18127 | 0.590633 | − | 0.806940i | \(-0.298878\pi\) | ||||
0.590633 | + | 0.806940i | \(0.298878\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 6.61225e7i | − 0.640960i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.81557e7i | 0.365171i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.82850e7 | 0.550774 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.97795e7 | 0.557791 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.33781e7i | − 0.215405i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.54238e8i | 1.40341i | 0.712468 | + | 0.701705i | \(0.247578\pi\) | ||||
−0.712468 | + | 0.701705i | \(0.752422\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.42241e8 | 1.27817 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.22198e7 | 0.374693 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.51487e7i | 0.220440i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.53601e7i | 0.565882i | 0.959137 | + | 0.282941i | \(0.0913101\pi\) | ||||
−0.959137 | + | 0.282941i | \(0.908690\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.03201e8 | −0.882584 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.51212e7 | 0.381185 | 0.190593 | − | 0.981669i | \(-0.438959\pi\) | ||||
0.190593 | + | 0.981669i | \(0.438959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 2.93620e8i | − 2.45044i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.12094e7i | 0.0924202i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.69532e6 | 0.0463926 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.03581e7 | −0.405292 | −0.202646 | − | 0.979252i | \(-0.564954\pi\) | ||||
−0.202646 | + | 0.979252i | \(0.564954\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.13412e8i | 0.901872i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 4.41054e6i | − 0.0346567i | −0.999850 | − | 0.0173284i | \(-0.994484\pi\) | ||||
0.999850 | − | 0.0173284i | \(-0.00551607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.82080e6 | −0.0607263 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.65035e7 | −0.663758 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.44005e7i | 0.185031i | 0.995711 | + | 0.0925156i | \(0.0294908\pi\) | ||||
−0.995711 | + | 0.0925156i | \(0.970509\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.84165e7i | 0.437797i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.48732e7 | 0.110167 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.72160e7 | 0.199252 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 4.05029e8i | − 2.93099i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 5.80827e7i | − 0.415475i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.53917e7 | 0.462391 | 0.231195 | − | 0.972907i | \(-0.425736\pi\) | ||||
0.231195 | + | 0.972907i | \(0.425736\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.19428e8 | 0.834833 | 0.417417 | − | 0.908715i | \(-0.362936\pi\) | ||||
0.417417 | + | 0.908715i | \(0.362936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 3.69594e7i | − 0.255415i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.01181e8i | 1.37453i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.54446e8 | −1.04330 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.50945e6 | 0.0568352 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 2.90170e7i | − 0.191633i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 2.57240e7i | − 0.167987i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.14593e6 | 0.0203154 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.15419e8 | −1.37568 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 3.06540e7i | − 0.193596i | −0.995304 | − | 0.0967979i | \(-0.969140\pi\) | ||||
0.995304 | − | 0.0967979i | \(-0.0308600\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 8.47140e7i | − 0.529122i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.51525e7 | −0.217153 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.60733e8 | 0.982071 | 0.491035 | − | 0.871140i | \(-0.336619\pi\) | ||||
0.491035 | + | 0.871140i | \(0.336619\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.09310e7i | 0.126495i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.75562e8i | 1.04949i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.10284e7 | 0.479140 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.37671e7 | 0.0805313 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.11683e8i | 1.80363i | 0.432125 | + | 0.901814i | \(0.357764\pi\) | ||||
−0.432125 | + | 0.901814i | \(0.642236\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.14003e7i | 0.466005i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.36101e8 | 1.33724 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.81653e8 | −1.57830 | −0.789149 | − | 0.614201i | \(-0.789478\pi\) | ||||
−0.789149 | + | 0.614201i | \(0.789478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.46150e7i | 0.0810313i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 9.19553e6i | − 0.0504461i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.82677e7 | 0.479143 | 0.239571 | − | 0.970879i | \(-0.422993\pi\) | ||||
0.239571 | + | 0.970879i | \(0.422993\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.66103e8 | −0.892217 | −0.446108 | − | 0.894979i | \(-0.647190\pi\) | ||||
−0.446108 | + | 0.894979i | \(0.647190\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.06408e8i | 0.565601i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.64793e8i | 1.39285i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.26455e7 | −0.274053 | −0.137026 | − | 0.990567i | \(-0.543754\pi\) | ||||
−0.137026 | + | 0.990567i | \(0.543754\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.03962e7 | 0.105078 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.25343e7i | 0.471818i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.21896e8i | 1.11981i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.56549e7 | −0.0781959 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.88069e7 | 0.191865 | 0.0959323 | − | 0.995388i | \(-0.469417\pi\) | ||||
0.0959323 | + | 0.995388i | \(0.469417\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.20291e8i | − 0.588689i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.18687e8i | 0.574962i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.26100e8 | −1.56382 | −0.781909 | − | 0.623392i | \(-0.785754\pi\) | ||||
−0.781909 | + | 0.623392i | \(0.785754\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.04523e7 | 0.0970939 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.00965e8i | 0.474514i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.03039e8i | 1.41000i | 0.709210 | + | 0.704998i | \(0.249052\pi\) | ||||
−0.709210 | + | 0.704998i | \(0.750948\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.98916e8 | −1.83763 | −0.918815 | − | 0.394689i | \(-0.870852\pi\) | ||||
−0.918815 | + | 0.394689i | \(0.870852\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.03179e8 | 0.470586 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 7.09641e7i | − 0.320459i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.46327e8i | 1.10140i | 0.834703 | + | 0.550701i | \(0.185639\pi\) | ||||
−0.834703 | + | 0.550701i | \(0.814361\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.08543e8 | 0.480565 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.65660e8 | 2.47989 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.16670e8i | 0.940628i | 0.882499 | + | 0.470314i | \(0.155859\pi\) | ||||
−0.882499 | + | 0.470314i | \(0.844141\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 2.80847e6i | − 0.0120738i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.27942e8 | 0.544699 | 0.272350 | − | 0.962198i | \(-0.412199\pi\) | ||||
0.272350 | + | 0.962198i | \(0.412199\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.96738e8 | −0.829499 | −0.414749 | − | 0.909936i | \(-0.636131\pi\) | ||||
−0.414749 | + | 0.909936i | \(0.636131\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.58808e7i | 0.275096i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.40326e8i | − 0.580328i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.25551e8 | 0.923855 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.41171e8 | −0.572719 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 2.89974e8i | − 1.16522i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.81163e7i | 0.390529i | 0.980751 | + | 0.195264i | \(0.0625565\pi\) | ||||
−0.980751 | + | 0.195264i | \(0.937443\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.46388e8 | −0.971424 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.19355e7 | 0.202835 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.00852e8i | − 1.16395i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.88710e6i | 0.0340610i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.85929e8 | 1.08564 | 0.542819 | − | 0.839850i | \(-0.317357\pi\) | ||||
0.542819 | + | 0.839850i | \(0.317357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.98146e8 | 1.12149 | 0.560745 | − | 0.827988i | \(-0.310515\pi\) | ||||
0.560745 | + | 0.827988i | \(0.310515\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.87850e6i | 0.0293606i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 3.84615e7i | − 0.142008i | −0.997476 | − | 0.0710042i | \(-0.977380\pi\) | ||||
0.997476 | − | 0.0710042i | \(-0.0226204\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.07684e7 | −0.295466 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.43711e7 | −0.269564 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.67190e7i | 0.347354i | 0.984803 | + | 0.173677i | \(0.0555648\pi\) | ||||
−0.984803 | + | 0.173677i | \(0.944435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.21109e7i | 0.0430974i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.11545e7 | −0.321427 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.49525e7 | 0.226955 | 0.113477 | − | 0.993541i | \(-0.463801\pi\) | ||||
0.113477 | + | 0.993541i | \(0.463801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 3.29739e8i | − 1.14174i | −0.821042 | − | 0.570868i | \(-0.806607\pi\) | ||||
0.821042 | − | 0.570868i | \(-0.193393\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.29737e8i | 1.13143i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.22289e7 | −0.0415838 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.77653e8 | −2.62065 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.22836e8i | 1.07821i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1.98669e8i | − 0.657600i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.17571e8 | 1.69795 | 0.848975 | − | 0.528433i | \(-0.177220\pi\) | ||||
0.848975 | + | 0.528433i | \(0.177220\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.76722e7 | 0.187523 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.25473e8i | 1.04894i | 0.851430 | + | 0.524469i | \(0.175736\pi\) | ||||
−0.851430 | + | 0.524469i | \(0.824264\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.95817e8i | 0.625519i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.10082e8 | −0.348559 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.37538e8 | −1.68713 | −0.843563 | − | 0.537031i | \(-0.819546\pi\) | ||||
−0.843563 | + | 0.537031i | \(0.819546\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.51864e7i | 0.109472i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.24498e7i | 0.223443i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.09898e8 | −0.947461 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.64528e8 | 1.40792 | 0.703960 | − | 0.710239i | \(-0.251413\pi\) | ||||
0.703960 | + | 0.710239i | \(0.251413\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.72804e7i | 0.262251i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.07360e6i | 0.0180922i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.91543e7 | −0.174698 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.77361e8 | 0.519309 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.59130e7i | 0.104255i | 0.998640 | + | 0.0521275i | \(0.0166002\pi\) | ||||
−0.998640 | + | 0.0521275i | \(0.983400\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.73382e8i | 0.499044i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.47486e7 | 0.156245 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.08955e7 | −0.172317 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.86788e8i | 0.524094i | 0.965055 | + | 0.262047i | \(0.0843976\pi\) | ||||
−0.965055 | + | 0.262047i | \(0.915602\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.26439e8i | 0.351780i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.32827e8 | 1.47000 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.48591e8 | 0.406512 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 3.02050e8i | − 0.819447i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.76368e7i | 0.101257i | 0.998718 | + | 0.0506286i | \(0.0161225\pi\) | ||||
−0.998718 | + | 0.0506286i | \(0.983878\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.11914e8 | 0.565397 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.06763e8 | 0.282491 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.80760e8i | 1.78640i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 2.58872e8i | − 0.673724i | −0.941554 | − | 0.336862i | \(-0.890634\pi\) | ||||
0.941554 | − | 0.336862i | \(-0.109366\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.65943e8 | 0.424822 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.31872e8i | 1.35050i | 0.737588 | + | 0.675251i | \(0.235965\pi\) | ||||
−0.737588 | + | 0.675251i | \(0.764035\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 2.91186e7i | − 0.0733346i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.79335e8 | −2.44641 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.70943e8 | 0.423564 | 0.211782 | − | 0.977317i | \(-0.432073\pi\) | ||||
0.211782 | + | 0.977317i | \(0.432073\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1.97157e8i | − 0.484572i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 4.23377e8i | − 1.03219i | −0.856531 | − | 0.516096i | \(-0.827385\pi\) | ||||
0.856531 | − | 0.516096i | \(-0.172615\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.64435e7 | 0.0639514 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.44393e8 | −0.346404 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 2.00296e8i | − 0.476679i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.04170e8i | 0.718118i | 0.933315 | + | 0.359059i | \(0.116902\pi\) | ||||
−0.933315 | + | 0.359059i | \(0.883098\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.01912e6 | 0.00472910 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.35037e7 | 0.217264 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 3.06435e8i | − 0.706401i | −0.935548 | − | 0.353201i | \(-0.885093\pi\) | ||||
0.935548 | − | 0.353201i | \(-0.114907\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 6.25315e8i | − 1.43012i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.23923e8 | 0.961907 | 0.480954 | − | 0.876746i | \(-0.340291\pi\) | ||||
0.480954 | + | 0.876746i | \(0.340291\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.73710e8 | −0.616193 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.19143e7i | 0.0712854i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.12800e8i | − 0.249991i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.19668e8 | −1.14274 | −0.571369 | − | 0.820693i | \(-0.693588\pi\) | ||||
−0.571369 | + | 0.820693i | \(0.693588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.85338e8 | 0.404391 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.89126e7i | − 0.0409462i | −0.999790 | − | 0.0204731i | \(-0.993483\pi\) | ||||
0.999790 | − | 0.0204731i | \(-0.00651724\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 4.66439e8i | − 1.00205i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.07196e8 | 0.228515 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.53697e7 | 0.0748203 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 8.43529e7i | − 0.177071i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.69374e8i | 0.352826i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.89537e7 | 0.101199 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.65036e8 | −0.543726 | −0.271863 | − | 0.962336i | \(-0.587640\pi\) | ||||
−0.271863 | + | 0.962336i | \(0.587640\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 2.11495e8i | − 0.430594i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.13797e8i | 0.229934i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.77459e8 | 0.556390 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.99942e7 | −0.0596947 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 6.82061e8i | − 1.34725i | −0.739073 | − | 0.673626i | \(-0.764736\pi\) | ||||
0.739073 | − | 0.673626i | \(-0.235264\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1.15316e9i | − 2.26073i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.18968e8 | 0.426071 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.65203e8 | 1.67098 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 5.41681e7i | − 0.103838i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 2.66922e8i | − 0.507884i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.50511e8 | 1.03973 | 0.519865 | − | 0.854248i | \(-0.325982\pi\) | ||||
0.519865 | + | 0.854248i | \(0.325982\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.11549e8 | 0.584068 | 0.292034 | − | 0.956408i | \(-0.405668\pi\) | ||||
0.292034 | + | 0.956408i | \(0.405668\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.99143e6i | 0.00928867i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.32407e8i | 0.244589i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.92214e7 | −0.181945 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.21895e8 | −0.221888 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 7.17579e8i | − 1.29670i | −0.761342 | − | 0.648351i | \(-0.775459\pi\) | ||||
0.761342 | − | 0.648351i | \(-0.224541\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.41195e8i | 0.970854i | 0.874277 | + | 0.485427i | \(0.161336\pi\) | ||||
−0.874277 | + | 0.485427i | \(0.838664\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.47402e8 | −0.974866 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.79442e8 | −1.55486 | −0.777429 | − | 0.628971i | \(-0.783476\pi\) | ||||
−0.777429 | + | 0.628971i | \(0.783476\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 4.29123e8i | − 0.753213i | −0.926373 | − | 0.376607i | \(-0.877091\pi\) | ||||
0.926373 | − | 0.376607i | \(-0.122909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 2.35306e8i | − 0.410043i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.13320e8 | −1.06109 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.45507e8 | 0.249934 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.16050e8i | − 0.197911i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.86636e8i | 0.993305i | 0.867949 | + | 0.496653i | \(0.165438\pi\) | ||||
−0.867949 | + | 0.496653i | \(0.834562\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.40445e9 | −2.36113 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.74325e8 | −1.12561 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.10984e8i | 0.183946i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 5.52552e8i | − 0.909332i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.01951e8 | 0.820236 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.67997e8 | −1.24615 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.00029e8i | 1.12790i | 0.825810 | + | 0.563948i | \(0.190718\pi\) | ||||
−0.825810 | + | 0.563948i | \(0.809282\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 1.90823e7i | − 0.0305304i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.52114e8 | 1.51268 | 0.756339 | − | 0.654180i | \(-0.226986\pi\) | ||||
0.756339 | + | 0.654180i | \(0.226986\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.16968e8 | −0.657844 | −0.328922 | − | 0.944357i | \(-0.606685\pi\) | ||||
−0.328922 | + | 0.944357i | \(0.606685\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 2.18678e7i | − 0.0342606i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 4.62686e8i | − 0.719869i | −0.932978 | − | 0.359935i | \(-0.882799\pi\) | ||||
0.932978 | − | 0.359935i | \(-0.117201\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.45201e7 | −0.115140 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.95936e8 | 0.454089 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.20011e9i | − 1.82877i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1.36773e9i | − 2.06988i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.05557e8 | −0.459250 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.60836e7 | −0.143425 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.73329e8i | 0.998225i | 0.866537 | + | 0.499113i | \(0.166341\pi\) | ||||
−0.866537 | + | 0.499113i | \(0.833659\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 4.69692e8i | − 0.691586i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.77155e8 | 0.259074 | 0.129537 | − | 0.991575i | \(-0.458651\pi\) | ||||
0.129537 | + | 0.991575i | \(0.458651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.35707e8 | −0.197115 | −0.0985574 | − | 0.995131i | \(-0.531423\pi\) | ||||
−0.0985574 | + | 0.995131i | \(0.531423\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 1.09176e7i | − 0.0157506i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1.09553e9i | − 1.56984i | −0.619598 | − | 0.784919i | \(-0.712704\pi\) | ||||
0.619598 | − | 0.784919i | \(-0.287296\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.04389e8 | 0.575564 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.36194e8 | −0.192542 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.89501e8i | 0.968234i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 4.03623e6i | − 0.00562997i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.73309e8 | 1.21001 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.36985e9 | 1.88536 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.31761e8i | 0.863731i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.13448e7i | 0.0833133i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.08688e8 | −0.146635 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.34159e9 | 1.79803 | 0.899015 | − | 0.437917i | \(-0.144284\pi\) | ||||
0.899015 | + | 0.437917i | \(0.144284\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 9.50227e7i | − 0.126513i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.16107e9i | − 1.53569i | −0.640638 | − | 0.767843i | \(-0.721330\pi\) | ||||
0.640638 | − | 0.767843i | \(-0.278670\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.37052e9 | 1.80083 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.68545e7 | 0.0350553 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.42995e7i | 0.122293i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1.03538e9i | − 1.33399i | −0.745061 | − | 0.666996i | \(-0.767580\pi\) | ||||
0.745061 | − | 0.666996i | \(-0.232420\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.26579e8 | −0.418032 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.17806e8 | 0.149818 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.72307e8i | 0.849459i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.30675e8i | 0.415109i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.47698e9 | −1.84217 | −0.921083 | − | 0.389367i | \(-0.872694\pi\) | ||||
−0.921083 | + | 0.389367i | \(0.872694\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.66718e8 | 0.454447 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.70227e7i | 0.0948361i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 3.02918e8i | − 0.370587i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.90868e8 | 0.596686 | 0.298343 | − | 0.954459i | \(-0.403566\pi\) | ||||
0.298343 | + | 0.954459i | \(0.403566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.16911e8 | 0.503555 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1.54536e8i | − 0.185464i | −0.995691 | − | 0.0927321i | \(-0.970440\pi\) | ||||
0.995691 | − | 0.0927321i | \(-0.0295600\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.56670e8i | 0.186832i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.17979e7 | −0.0139800 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.24667e9 | −1.46792 | −0.733961 | − | 0.679192i | \(-0.762331\pi\) | ||||
−0.733961 | + | 0.679192i | \(0.762331\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.20833e9i | 1.41380i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.39671e8i | 0.859997i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.21385e8 | −0.486856 | −0.243428 | − | 0.969919i | \(-0.578272\pi\) | ||||
−0.243428 | + | 0.969919i | \(0.578272\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.36522e8 | 0.156744 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.60763e9i | − 1.83421i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.73973e8i | 0.310637i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.10826e7 | −0.0575576 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.12546e8 | 0.349973 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 2.61683e7i | − 0.0291201i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.35010e9i | 1.49309i | 0.665334 | + | 0.746546i | \(0.268289\pi\) | ||||
−0.665334 | + | 0.746546i | \(0.731711\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.01927e8 | −0.441749 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.75696e8 | −0.301143 | −0.150571 | − | 0.988599i | \(-0.548111\pi\) | ||||
−0.150571 | + | 0.988599i | \(0.548111\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.72912e7i | 0.0513383i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 7.64497e8i | − 0.824825i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.86639e8 | −0.521823 | −0.260911 | − | 0.965363i | \(-0.584023\pi\) | ||||
−0.260911 | + | 0.965363i | \(0.584023\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.07836e9 | −2.21499 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 4.27103e8i | − 0.452403i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.34935e9i | − 1.42058i | −0.703909 | − | 0.710290i | \(-0.748564\pi\) | ||||
0.703909 | − | 0.710290i | \(-0.251436\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.52275e8 | 0.159338 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.26292e8 | 0.443359 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 4.39501e8i | − 0.454330i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.76213e8i | 0.592056i | 0.955179 | + | 0.296028i | \(0.0956621\pi\) | ||||
−0.955179 | + | 0.296028i | \(0.904338\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.54976e8 | −0.771055 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.29538e8 | 0.131501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.84682e7i | 0.0892692i | 0.999003 | + | 0.0446346i | \(0.0142124\pi\) | ||||
−0.999003 | + | 0.0446346i | \(0.985788\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.67271e8i | 0.167773i |
(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 | 384.7.b.d.319.5 | yes | 8 | |
4.3 | odd | 2 | inner | 384.7.b.d.319.2 | ✓ | 8 | |
8.3 | odd | 2 | inner | 384.7.b.d.319.8 | yes | 8 | |
8.5 | even | 2 | inner | 384.7.b.d.319.3 | yes | 8 | |
16.3 | odd | 4 | 768.7.g.c.511.1 | 4 | |||
16.5 | even | 4 | 768.7.g.e.511.2 | 4 | |||
16.11 | odd | 4 | 768.7.g.e.511.3 | 4 | |||
16.13 | even | 4 | 768.7.g.c.511.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.7.b.d.319.2 | ✓ | 8 | 4.3 | odd | 2 | inner | |
384.7.b.d.319.3 | yes | 8 | 8.5 | even | 2 | inner | |
384.7.b.d.319.5 | yes | 8 | 1.1 | even | 1 | trivial | |
384.7.b.d.319.8 | yes | 8 | 8.3 | odd | 2 | inner | |
768.7.g.c.511.1 | 4 | 16.3 | odd | 4 | |||
768.7.g.c.511.4 | 4 | 16.13 | even | 4 | |||
768.7.g.e.511.2 | 4 | 16.5 | even | 4 | |||
768.7.g.e.511.3 | 4 | 16.11 | odd | 4 |