Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,7,Mod(511,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.511");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(176.681536220\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 511.1 | ||
Root | \(-0.780776 - 1.35234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.511 |
Dual form | 768.7.g.c.511.4 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 15.5885i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −20.0000 | −0.160000 | −0.0800000 | − | 0.996795i | \(-0.525492\pi\) | ||||
−0.0800000 | + | 0.996795i | \(0.525492\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | − 2306.46i | − 1.73288i | −0.499282 | − | 0.866439i | \(-0.666403\pi\) | ||||
0.499282 | − | 0.866439i | \(-0.333597\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3221.18 | 1.46617 | 0.733086 | − | 0.680136i | \(-0.238079\pi\) | ||||
0.733086 | + | 0.680136i | \(0.238079\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | − 3926.40i | − 0.572445i | −0.958163 | − | 0.286223i | \(-0.907600\pi\) | ||||
0.958163 | − | 0.286223i | \(-0.0923997\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2427.54 | −0.262126 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 3788.00i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −44713.3 | −1.83334 | −0.916669 | − | 0.399648i | \(-0.869132\pi\) | ||||
−0.916669 | + | 0.399648i | \(0.869132\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 30636.4i | 1.02838i | 0.857677 | + | 0.514188i | \(0.171907\pi\) | ||||
−0.857677 | + | 0.514188i | \(0.828093\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −35954.2 | −1.00048 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3114.54i | 0.0726424i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44158.1 | 0.871776 | 0.435888 | − | 0.900001i | \(-0.356434\pi\) | ||||
0.435888 | + | 0.900001i | \(0.356434\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 50213.3i | − 0.846495i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9008.18 | −0.130703 | −0.0653515 | − | 0.997862i | \(-0.520817\pi\) | ||||
−0.0653515 | + | 0.997862i | \(0.520817\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 25270.3i | − 0.317838i | −0.987292 | − | 0.158919i | \(-0.949199\pi\) | ||||
0.987292 | − | 0.158919i | \(-0.0508008\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4860.00 | 0.0533333 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 175606.i | − 1.69140i | −0.533658 | − | 0.845700i | \(-0.679183\pi\) | ||||
0.533658 | − | 0.845700i | \(-0.320817\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 93398.1 | 0.793871 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 102365.i | 0.771688i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −96206.3 | −0.646214 | −0.323107 | − | 0.946363i | \(-0.604727\pi\) | ||||
−0.323107 | + | 0.946363i | \(0.604727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 46129.2i | 0.277261i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −61206.5 | −0.330501 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 35018.3i | 0.170506i | 0.996359 | + | 0.0852529i | \(0.0271698\pi\) | ||||
−0.996359 | + | 0.0852529i | \(0.972830\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −86135.7 | −0.379484 | −0.189742 | − | 0.981834i | \(-0.560765\pi\) | ||||
−0.189742 | + | 0.981834i | \(0.560765\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 37841.7i | 0.151338i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −64423.6 | −0.234588 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 424605.i | − 1.41176i | −0.708332 | − | 0.705880i | \(-0.750552\pi\) | ||||
0.708332 | − | 0.705880i | \(-0.249448\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 271114. | 0.825287 | ||||||||
\(70\) | 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 | \(-0.339860\pi\) | ||||
0.482140 | + | 0.876094i | \(0.339860\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 237334.i | 0.562570i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −359179. | −0.786753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 520323.i | − 1.05534i | −0.849450 | − | 0.527670i | \(-0.823066\pi\) | ||||
0.849450 | − | 0.527670i | \(-0.176934\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 594208.i | 1.03921i | 0.854406 | + | 0.519606i | \(0.173921\pi\) | ||||
−0.854406 | + | 0.519606i | \(0.826079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 131335. | 0.213856 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 697011.i | 1.05848i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −901101. | −1.27821 | −0.639107 | − | 0.769118i | \(-0.720696\pi\) | ||||
−0.639107 | + | 0.769118i | \(0.720696\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 501625.i | − 0.665664i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 477574. | 0.593733 | ||||||||
\(94\) | 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.i | 0.577626i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −391040. | −0.379539 | −0.189770 | − | 0.981829i | \(-0.560774\pi\) | ||||
−0.189770 | + | 0.981829i | \(0.560774\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | 1.28620e6i | 1.04992i | 0.851127 | + | 0.524960i | \(0.175920\pi\) | ||||
−0.851127 | + | 0.524960i | \(0.824080\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.75763e6 | 1.35721 | 0.678605 | − | 0.734504i | \(-0.262585\pi\) | ||||
0.678605 | + | 0.734504i | \(0.262585\pi\) | |||||||
\(110\) | 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.i | − 0.228710i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −782747. | −0.488724 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.02262e6i | 0.606837i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.54820e6 | −2.00287 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 140424.i | 0.0754614i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 617000. | 0.315904 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2.59678e6i | − 1.26772i | −0.773448 | − | 0.633860i | \(-0.781469\pi\) | ||||
0.773448 | − | 0.633860i | \(-0.218531\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −393925. | −0.183504 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 605543.i | 0.269359i | 0.990889 | + | 0.134679i | \(0.0430005\pi\) | ||||
−0.990889 | + | 0.134679i | \(0.957000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −611447. | −0.259899 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 75759.9i | − 0.0307920i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.75932e6 | 0.684199 | 0.342100 | − | 0.939664i | \(-0.388862\pi\) | ||||
0.342100 | + | 0.939664i | \(0.388862\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 303680.i | − 0.113076i | −0.998400 | − | 0.0565382i | \(-0.981994\pi\) | ||||
0.998400 | − | 0.0565382i | \(-0.0180063\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.73743e6 | −0.976531 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 7.42953e6i | − 2.54070i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 894265. | 0.293334 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.45593e6i | − 0.458341i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.32218e6 | 0.399696 | 0.199848 | − | 0.979827i | \(-0.435955\pi\) | ||||
0.199848 | + | 0.979827i | \(0.435955\pi\) | |||||||
\(150\) | 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.i | − 0.164540i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.44769e6 | −0.632495 | −0.316247 | − | 0.948677i | \(-0.602423\pi\) | ||||
−0.316247 | + | 0.948677i | \(0.602423\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.49971e6i | 0.373092i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.70840e6 | 0.648987 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.62033e6i | 1.52868i | 0.644813 | + | 0.764340i | \(0.276935\pi\) | ||||
−0.644813 | + | 0.764340i | \(0.723065\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 719084. | 0.160076 | ||||||||
\(166\) | 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.i | 0.190815i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.72601e6 | 0.719623 | 0.359812 | − | 0.933025i | \(-0.382841\pi\) | ||||
0.359812 | + | 0.933025i | \(0.382841\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.37094e6i | 0.442392i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 545881. | 0.0984415 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 201811.i | − 0.0351873i | −0.999845 | − | 0.0175937i | \(-0.994399\pi\) | ||||
0.999845 | − | 0.0175937i | \(-0.00560053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.43440e6 | −0.916466 | −0.458233 | − | 0.888832i | \(-0.651517\pi\) | ||||
−0.458233 | + | 0.888832i | \(0.651517\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.34272e6i | 0.219095i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −883162. | −0.139484 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.51459e7i | 2.31617i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 589893. | 0.0873752 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 6.82608e6i | − 0.979650i | −0.871821 | − | 0.489825i | \(-0.837061\pi\) | ||||
0.871821 | − | 0.489825i | \(-0.162939\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.30841e6 | 0.182001 | 0.0910004 | − | 0.995851i | \(-0.470994\pi\) | ||||
0.0910004 | + | 0.995851i | \(0.470994\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00427e6i | 0.135439i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.61375e6 | 0.995863 | 0.497932 | − | 0.867216i | \(-0.334093\pi\) | ||||
0.497932 | + | 0.867216i | \(0.334093\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 6.96307e6i | 0.832362i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 180164. | 0.0209125 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 4.22625e6i | − 0.476480i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.05609e6 | −0.991978 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.58058e7i | 1.68256i | 0.540603 | + | 0.841278i | \(0.318196\pi\) | ||||
−0.540603 | + | 0.841278i | \(0.681804\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 570108. | 0.0589954 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 505406.i | 0.0508540i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.77091e6 | 0.466898 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 5.84756e6i | − 0.556727i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.11526e7 | −1.95969 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2.07099e7i | − 1.86751i | −0.357907 | − | 0.933757i | \(-0.616509\pi\) | ||||
0.357907 | − | 0.933757i | \(-0.383491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.69967e6 | 0.324800 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.06179e6i | 0.603722i | 0.953352 | + | 0.301861i | \(0.0976079\pi\) | ||||
−0.953352 | + | 0.301861i | \(0.902392\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.64766e6 | 0.387015 | 0.193507 | − | 0.981099i | \(-0.438014\pi\) | ||||
0.193507 | + | 0.981099i | \(0.438014\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.59904e6i | 0.454232i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.13777e7 | −0.899469 | −0.449735 | − | 0.893162i | \(-0.648481\pi\) | ||||
−0.449735 | + | 0.893162i | \(0.648481\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.51213e6i | 0.270624i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.11104e6 | −0.609300 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.93765e7i | 1.41932i | 0.704542 | + | 0.709662i | \(0.251152\pi\) | ||||
−0.704542 | + | 0.709662i | \(0.748848\pi\) | |||||||
\(240\) | 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.i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.86796e6 | −0.127019 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.26477e7i | − 0.839304i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.26279e6 | 0.599989 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 129527.i | 0.00819104i | 0.999992 | + | 0.00409552i | \(0.00130365\pi\) | ||||
−0.999992 | + | 0.00409552i | \(0.998696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.01140e7 | 2.47705 | ||||||||
\(254\) | 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 | ||||||||
\(259\) | − 6.87661e6i | − 0.395799i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.08653e7 | 0.611113 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 1.40468e7i | 0.737977i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.71231e7 | 0.879680 | 0.439840 | − | 0.898076i | \(-0.355035\pi\) | ||||
0.439840 | + | 0.898076i | \(0.355035\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 320201.i | − 0.0160885i | −0.999968 | − | 0.00804423i | \(-0.997439\pi\) | ||||
0.999968 | − | 0.00804423i | \(-0.00256058\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.81956e6 | −0.384321 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.51159e7i | 1.68852i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.50949e7 | −0.710216 | −0.355108 | − | 0.934825i | \(-0.615556\pi\) | ||||
−0.355108 | + | 0.934825i | \(0.615556\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 7.44463e6i | − 0.342792i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.32580e7 | 1.94961 | 0.974804 | − | 0.223063i | \(-0.0716056\pi\) | ||||
0.974804 | + | 0.223063i | \(0.0716056\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.22002e7i | 1.42069i | 0.703854 | + | 0.710345i | \(0.251461\pi\) | ||||
−0.703854 | + | 0.710345i | \(0.748539\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.22413e6 | 0.0528802 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.40282e6i | 0.0593411i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.89843e7 | 0.786505 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.96015e7i | 0.795444i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.01307e7 | −1.19786 | −0.598931 | − | 0.800801i | \(-0.704408\pi\) | ||||
−0.598931 | + | 0.800801i | \(0.704408\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 700366.i | − 0.0272809i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.73687e6 | 0.333493 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.60228e7i | 2.09581i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.93527e6 | −0.144303 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.09571e6i | 0.219127i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.72271e6 | 0.0607175 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.09501e7i | 0.724053i | 0.932168 | + | 0.362026i | \(0.117915\pi\) | ||||
−0.932168 | + | 0.362026i | \(0.882085\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.12128e7 | 0.718990 | ||||||||
\(310\) | 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 | \(-0.643637\pi\) | ||||
−0.436091 | + | 0.899903i | \(0.643637\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 756834.i | − 0.0242141i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.74499e7 | −1.48956 | −0.744779 | − | 0.667311i | \(-0.767445\pi\) | ||||
−0.744779 | + | 0.667311i | \(0.767445\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.03129e8i | 3.17695i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.00498e7 | 0.606172 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.57836e7i | 0.765131i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.90425e7 | −1.42864 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 2.73987e7i | − 0.783585i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.73467e7 | −0.767921 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4.84318e7i | − 1.33551i | −0.744382 | − | 0.667754i | \(-0.767256\pi\) | ||||
0.744382 | − | 0.667754i | \(-0.232744\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.07304e7 | −0.290592 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 1.13913e7i | 0.292397i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.06616e7 | 1.78205 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3.28657e7i | − 0.814444i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.42229e6 | −0.132046 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.95157e7i | 0.706423i | 0.935544 | + | 0.353211i | \(0.114910\pi\) | ||||
−0.935544 | + | 0.353211i | \(0.885090\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.55247e7 | 1.30620 | 0.653100 | − | 0.757272i | \(-0.273468\pi\) | ||||
0.653100 | + | 0.757272i | \(0.273468\pi\) | |||||||
\(350\) | 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.i | − 0.0163493i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.59410e7 | 0.350358 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 5.53110e7i | 1.15636i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.50242e6 | −0.154285 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 4.83247e7i | − 0.977623i | −0.872389 | − | 0.488811i | \(-0.837431\pi\) | ||||
0.872389 | − | 0.488811i | \(-0.162569\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.18899e6 | 0.0435677 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.49819e7i | 0.293391i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.98844e7 | −1.73204 | −0.866020 | − | 0.500010i | \(-0.833330\pi\) | ||||
−0.866020 | + | 0.500010i | \(0.833330\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 9.61808e6i | − 0.182387i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.44030e8 | −2.68799 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.60279e7i | 1.58024i | 0.612955 | + | 0.790118i | \(0.289981\pi\) | ||||
−0.612955 | + | 0.790118i | \(0.710019\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.04798e7 | −0.731919 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.65042e7i | 1.18373i | 0.806037 | + | 0.591865i | \(0.201608\pi\) | ||||
−0.806037 | + | 0.591865i | \(0.798392\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.18357e6 | 0.125880 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.14069e6i | 0.105946i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.66889e7 | 0.963050 | 0.481525 | − | 0.876432i | \(-0.340083\pi\) | ||||
0.481525 | + | 0.876432i | \(0.340083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 1.14208e8i | − 1.91059i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.43949e6 | 0.155514 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.04065e7i | 0.168854i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.21267e7 | 0.513446 | 0.256723 | − | 0.966485i | \(-0.417357\pi\) | ||||
0.256723 | + | 0.966485i | \(0.417357\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 9.86853e7i | 1.50778i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.18098e6 | −0.0177778 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.01849e8i | − 1.51068i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.07185e7 | 0.302823 | 0.151412 | − | 0.988471i | \(-0.451618\pi\) | ||||
0.151412 | + | 0.988471i | \(0.451618\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 2.74251e7i | − 0.395023i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.45330e6 | 0.0774121 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 1.18842e7i | − 0.166274i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.73390e6 | −0.0652846 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.79561e7i | 0.923818i | 0.886927 | + | 0.461909i | \(0.152835\pi\) | ||||
−0.886927 | + | 0.461909i | \(0.847165\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 522580. | 0.00700336 | 0.00350168 | − | 0.999994i | \(-0.498885\pi\) | ||||
0.00350168 | + | 0.999994i | \(0.498885\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.26723e7i | 0.563800i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.99784e7 | 1.30239 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.34137e7i | 0.172291i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.15815e8 | −1.46687 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.10533e8i | 1.38057i | 0.723538 | + | 0.690285i | \(0.242515\pi\) | ||||
−0.723538 | + | 0.690285i | \(0.757485\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.65239e7 | 0.819435 | 0.409717 | − | 0.912213i | \(-0.365627\pi\) | ||||
0.409717 | + | 0.912213i | \(0.365627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 1.39402e7i | − 0.169356i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.82879e7 | 0.818276 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | − 1.01597e7i | − 0.116861i | −0.998291 | − | 0.0584304i | \(-0.981390\pi\) | ||||
0.998291 | − | 0.0584304i | \(-0.0186096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.80220e7 | 0.204514 | ||||||||
\(446\) | 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 | ||||||||
\(451\) | 2.07770e7i | 0.226492i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.28789e7 | 0.783984 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00325e7i | 0.106506i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.92987e6 | 0.0621293 | 0.0310646 | − | 0.999517i | \(-0.490110\pi\) | ||||
0.0310646 | + | 0.999517i | \(0.490110\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2.48747e7i | − 0.257229i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.31145e7 | −0.440069 | −0.220035 | − | 0.975492i | \(-0.570617\pi\) | ||||
−0.220035 | + | 0.975492i | \(0.570617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.09555e7i | 0.815649i | 0.913060 | + | 0.407825i | \(0.133712\pi\) | ||||
−0.913060 | + | 0.407825i | \(0.866288\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.55147e6 | −0.0949973 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1.20309e8i | − 1.18127i | −0.806940 | − | 0.590633i | \(-0.798878\pi\) | ||||
0.806940 | − | 0.590633i | \(-0.201122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.61225e7 | −0.640960 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.81557e7i | 0.365171i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.82850e7 | −0.550774 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.97795e7i | 0.557791i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.33781e7 | 0.215405 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 1.54238e8i | − 1.40341i | −0.712468 | − | 0.701705i | \(-0.752422\pi\) | ||||
0.712468 | − | 0.701705i | \(-0.247578\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.42241e8 | 1.27817 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 4.22198e7i | − 0.374693i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.51487e7 | 0.220440 | ||||||||
\(486\) | 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 | ||||||||
\(491\) | 4.51212e7i | 0.381185i | 0.981669 | + | 0.190593i | \(0.0610410\pi\) | ||||
−0.981669 | + | 0.190593i | \(0.938959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.93620e8 | 2.45044 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 1.12094e7i | − 0.0924202i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.69532e6 | 0.0463926 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.03581e7i | 0.405292i | 0.979252 | + | 0.202646i | \(0.0649540\pi\) | ||||
−0.979252 | + | 0.202646i | \(0.935046\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.13412e8 | 0.901872 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | − 8.65035e7i | − 0.663758i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.44005e7 | −0.185031 | −0.0925156 | − | 0.995711i | \(-0.529491\pi\) | ||||
−0.0925156 | + | 0.995711i | \(0.529491\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 5.84165e7i | − 0.437797i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.48732e7 | 0.110167 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2.72160e7i | − 0.199252i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.05029e8 | −2.93099 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 5.80827e7i | − 0.415475i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.53917e7 | −0.462391 | −0.231195 | − | 0.972907i | \(-0.574264\pi\) | ||||
−0.231195 | + | 0.972907i | \(0.574264\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.19428e8i | 0.834833i | 0.908715 | + | 0.417417i | \(0.137064\pi\) | ||||
−0.908715 | + | 0.417417i | \(0.862936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.69594e7 | 0.255415 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.01181e8i | − 1.37453i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.54446e8 | −1.04330 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 8.50945e6i | − 0.0568352i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.90170e7 | −0.191633 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 2.57240e7i | − 0.167987i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.14593e6 | −0.0203154 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.15419e8i | − 1.37568i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.06540e7 | 0.193596 | 0.0967979 | − | 0.995304i | \(-0.469140\pi\) | ||||
0.0967979 | + | 0.995304i | \(0.469140\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.47140e7i | 0.529122i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.51525e7 | −0.217153 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.60733e8i | − 0.982071i | −0.871140 | − | 0.491035i | \(-0.836619\pi\) | ||||
0.871140 | − | 0.491035i | \(-0.163381\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.09310e7 | 0.126495 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.75562e8i | 1.04949i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.10284e7 | −0.479140 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.37671e7i | 0.0805313i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.11683e8 | −1.80363 | −0.901814 | − | 0.432125i | \(-0.857764\pi\) | ||||
−0.901814 | + | 0.432125i | \(0.857764\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 8.14003e7i | − 0.466005i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.36101e8 | 1.33724 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.81653e8i | 1.57830i | 0.614201 | + | 0.789149i | \(0.289478\pi\) | ||||
−0.614201 | + | 0.789149i | \(0.710522\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.46150e7 | 0.0810313 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 9.19553e6i | − 0.0504461i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.82677e7 | −0.479143 | −0.239571 | − | 0.970879i | \(-0.577007\pi\) | ||||
−0.239571 | + | 0.970879i | \(0.577007\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1.66103e8i | − 0.892217i | −0.894979 | − | 0.446108i | \(-0.852810\pi\) | ||||
0.894979 | − | 0.446108i | \(-0.147190\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.06408e8 | −0.565601 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | − 2.03962e7i | − 0.105078i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.25343e7 | 0.471818 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.21896e8i | 1.11981i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.56549e7 | 0.0781959 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.88069e7i | 0.191865i | 0.995388 | + | 0.0959323i | \(0.0305832\pi\) | ||||
−0.995388 | + | 0.0959323i | \(0.969417\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.20291e8 | 0.588689 | ||||||||
\(590\) | 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 | ||||||||
\(595\) | − 2.04523e7i | − 0.0970939i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.00965e8 | 0.474514 | ||||||||
\(598\) | 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 | \(-0.129148\pi\) | ||||
0.918815 | + | 0.394689i | \(0.129148\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.03179e8i | 0.470586i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.09641e7 | 0.320459 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 2.46327e8i | − 1.10140i | −0.834703 | − | 0.550701i | \(-0.814361\pi\) | ||||
0.834703 | − | 0.550701i | \(-0.185639\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.08543e8 | 0.480565 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 5.65660e8i | − 2.47989i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.16670e8 | 0.940628 | 0.470314 | − | 0.882499i | \(-0.344141\pi\) | ||||
0.470314 | + | 0.882499i | \(0.344141\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 2.80847e6i | − 0.0120738i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.27942e8 | −0.544699 | −0.272350 | − | 0.962198i | \(-0.587801\pi\) | ||||
−0.272350 | + | 0.962198i | \(0.587801\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1.96738e8i | − 0.829499i | −0.909936 | − | 0.414749i | \(-0.863869\pi\) | ||||
0.909936 | − | 0.414749i | \(-0.136131\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.58808e7 | −0.275096 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.40326e8i | 0.580328i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.25551e8 | 0.923855 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.41171e8i | 0.572719i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.89974e8 | −1.16522 | ||||||||
\(630\) | 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 | ||||||||
\(635\) | 5.19355e7i | 0.202835i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00852e8 | 1.16395 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | − 2.98146e8i | − 1.12149i | −0.827988 | − | 0.560745i | \(-0.810515\pi\) | ||||
0.827988 | − | 0.560745i | \(-0.189485\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.87850e6 | 0.0293606 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | − 7.43711e7i | − 0.269564i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.67190e7 | −0.347354 | −0.173677 | − | 0.984803i | \(-0.555565\pi\) | ||||
−0.173677 | + | 0.984803i | \(0.555565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1.21109e7i | − 0.0430974i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.11545e7 | −0.321427 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 6.49525e7i | − 0.226955i | −0.993541 | − | 0.113477i | \(-0.963801\pi\) | ||||
0.993541 | − | 0.113477i | \(-0.0361990\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.29739e8 | −1.14174 | −0.570868 | − | 0.821042i | \(-0.693393\pi\) | ||||
−0.570868 | + | 0.821042i | \(0.693393\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.29737e8i | 1.13143i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.22289e7 | 0.0415838 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 7.77653e8i | − 2.62065i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.22836e8 | −1.07821 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | − 5.76722e7i | − 0.187523i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.25473e8 | 1.04894 | 0.524469 | − | 0.851430i | \(-0.324264\pi\) | ||||
0.524469 | + | 0.851430i | \(0.324264\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.95817e8i | 0.625519i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.10082e8 | 0.348559 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5.37538e8i | − 1.68713i | −0.537031 | − | 0.843563i | \(-0.680454\pi\) | ||||
0.537031 | − | 0.843563i | \(-0.319546\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.51864e7 | −0.109472 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 7.24498e7i | − 0.223443i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.09898e8 | −0.947461 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 4.64528e8i | − 1.40792i | −0.710239 | − | 0.703960i | \(-0.751413\pi\) | ||||
0.710239 | − | 0.703960i | \(-0.248587\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.72804e7 | 0.262251 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.07360e6i | 0.0180922i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.91543e7 | 0.174698 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.77361e8i | 0.519309i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.59130e7 | −0.104255 | −0.0521275 | − | 0.998640i | \(-0.516600\pi\) | ||||
−0.0521275 | + | 0.998640i | \(0.516600\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.73382e8i | − 0.499044i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.47486e7 | 0.156245 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.08955e7i | 0.172317i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.86788e8 | 0.524094 | 0.262047 | − | 0.965055i | \(-0.415602\pi\) | ||||
0.262047 | + | 0.965055i | \(0.415602\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.26439e8i | 0.351780i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.32827e8 | −1.47000 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.48591e8i | 0.406512i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.02050e8 | 0.819447 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 3.76368e7i | − 0.101257i | −0.998718 | − | 0.0506286i | \(-0.983878\pi\) | ||||
0.998718 | − | 0.0506286i | \(-0.0161225\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.11914e8 | 0.565397 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1.06763e8i | − 0.282491i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.80760e8 | 1.78640 | ||||||||
\(726\) | 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 | ||||||||
\(731\) | 1.65943e8i | 0.424822i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.31872e8 | −1.35050 | −0.675251 | − | 0.737588i | \(-0.735965\pi\) | ||||
−0.675251 | + | 0.737588i | \(0.735965\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.91186e7i | 0.0733346i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.79335e8 | −2.44641 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.70943e8i | − 0.423564i | −0.977317 | − | 0.211782i | \(-0.932073\pi\) | ||||
0.977317 | − | 0.211782i | \(-0.0679267\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.97157e8 | −0.484572 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | − 1.44393e8i | − 0.346404i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.00296e8 | 0.476679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 3.04170e8i | − 0.718118i | −0.933315 | − | 0.359059i | \(-0.883098\pi\) | ||||
0.933315 | − | 0.359059i | \(-0.116902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.01912e6 | 0.00472910 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 9.35037e7i | − 0.217264i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.06435e8 | −0.706401 | −0.353201 | − | 0.935548i | \(-0.614907\pi\) | ||||
−0.353201 | + | 0.935548i | \(0.614907\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 6.25315e8i | − 1.43012i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.23923e8 | −0.961907 | −0.480954 | − | 0.876746i | \(-0.659709\pi\) | ||||
−0.480954 | + | 0.876746i | \(0.659709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.73710e8i | − 0.616193i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.19143e7 | −0.0712854 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | − 1.85338e8i | − 0.404391i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.89126e7 | −0.0409462 | −0.0204731 | − | 0.999790i | \(-0.506517\pi\) | ||||
−0.0204731 | + | 0.999790i | \(0.506517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 4.66439e8i | − 1.00205i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.07196e8 | −0.228515 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.53697e7i | 0.0748203i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.43529e7 | 0.177071 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 1.69374e8i | − 0.352826i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.89537e7 | 0.101199 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.65036e8i | 0.543726i | 0.962336 | + | 0.271863i | \(0.0876398\pi\) | ||||
−0.962336 | + | 0.271863i | \(0.912360\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.11495e8 | −0.430594 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.13797e8i | 0.229934i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.77459e8 | −0.556390 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 2.99942e7i | − 0.0596947i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.82061e8 | 1.34725 | 0.673626 | − | 0.739073i | \(-0.264736\pi\) | ||||
0.673626 | + | 0.739073i | \(0.264736\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.15316e9i | 2.26073i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.18968e8 | 0.426071 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 8.65203e8i | − 1.67098i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.41681e7 | −0.103838 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 2.66922e8i | − 0.507884i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.50511e8 | −1.03973 | −0.519865 | − | 0.854248i | \(-0.674018\pi\) | ||||
−0.519865 | + | 0.854248i | \(0.674018\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.11549e8i | 0.584068i | 0.956408 | + | 0.292034i | \(0.0943321\pi\) | ||||
−0.956408 | + | 0.292034i | \(0.905668\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.99143e6 | −0.00928867 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1.32407e8i | − 0.244589i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.92214e7 | −0.181945 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.21895e8i | 0.221888i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.17579e8 | −1.29670 | −0.648351 | − | 0.761342i | \(-0.724541\pi\) | ||||
−0.648351 | + | 0.761342i | \(0.724541\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | − 8.79442e8i | − 1.55486i | −0.628971 | − | 0.777429i | \(-0.716524\pi\) | ||||
0.628971 | − | 0.777429i | \(-0.283476\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.29123e8 | 0.753213 | 0.376607 | − | 0.926373i | \(-0.377091\pi\) | ||||
0.376607 | + | 0.926373i | \(0.377091\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.35306e8i | 0.410043i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.13320e8 | −1.06109 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1.45507e8i | − 0.249934i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.16050e8 | −0.197911 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | − 6.74325e8i | − 1.12561i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.10984e8 | −0.183946 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.52552e8i | 0.909332i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.01951e8 | 0.820236 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.67997e8i | 1.24615i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.00029e8 | 1.12790 | 0.563948 | − | 0.825810i | \(-0.309282\pi\) | ||||
0.563948 | + | 0.825810i | \(0.309282\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 1.90823e7i | − 0.0305304i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.52114e8 | −1.51268 | −0.756339 | − | 0.654180i | \(-0.773014\pi\) | ||||
−0.756339 | + | 0.654180i | \(0.773014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 4.16968e8i | − 0.657844i | −0.944357 | − | 0.328922i | \(-0.893315\pi\) | ||||
0.944357 | − | 0.328922i | \(-0.106685\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.18678e7 | 0.0342606 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.62686e8i | 0.719869i | 0.932978 | + | 0.359935i | \(0.117201\pi\) | ||||
−0.932978 | + | 0.359935i | \(0.882799\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.45201e7 | −0.115140 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 2.95936e8i | − 0.454089i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.20011e9 | −1.82877 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1.36773e9i | − 2.06988i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.05557e8 | 0.459250 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 9.60836e7i | − 0.143425i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.73329e8 | −0.998225 | −0.499113 | − | 0.866537i | \(-0.666341\pi\) | ||||
−0.499113 | + | 0.866537i | \(0.666341\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 1.35707e8i | 0.197115i | 0.995131 | + | 0.0985574i | \(0.0314228\pi\) | ||||
−0.995131 | + | 0.0985574i | \(0.968577\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.09176e7 | −0.0157506 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | − 1.36194e8i | − 0.192542i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.89501e8 | −0.968234 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.03623e6i | 0.00562997i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.73309e8 | 1.21001 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.36985e9i | − 1.88536i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.31761e8 | 0.863731 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.13448e7i | 0.0833133i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.08688e8 | 0.146635 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.34159e9i | 1.79803i | 0.437917 | + | 0.899015i | \(0.355716\pi\) | ||||
−0.437917 | + | 0.899015i | \(0.644284\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.50227e7 | 0.126513 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.16107e9i | 1.53569i | 0.640638 | + | 0.767843i | \(0.278670\pi\) | ||||
−0.640638 | + | 0.767843i | \(0.721330\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.37052e9 | 1.80083 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 2.68545e7i | − 0.0350553i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.42995e7 | 0.122293 | ||||||||
\(918\) | 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 | ||||||||
\(923\) | 1.17806e8i | 0.149818i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.72307e8 | −0.849459 | ||||||||
\(926\) | 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 | ||||||||
\(931\) | − 3.66718e8i | − 0.454447i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.70227e7 | 0.0948361 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 3.02918e8i | − 0.370587i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.90868e8 | −0.596686 | −0.298343 | − | 0.954459i | \(-0.596434\pi\) | ||||
−0.298343 | + | 0.954459i | \(0.596434\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.16911e8i | 0.503555i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.54536e8 | 0.185464 | 0.0927321 | − | 0.995691i | \(-0.470440\pi\) | ||||
0.0927321 | + | 0.995691i | \(0.470440\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.56670e8i | − 0.186832i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.17979e7 | −0.0139800 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.24667e9i | 1.46792i | 0.679192 | + | 0.733961i | \(0.262331\pi\) | ||||
−0.679192 | + | 0.733961i | \(0.737669\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.20833e9 | 1.41380 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.39671e8i | 0.859997i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.21385e8 | 0.486856 | 0.243428 | − | 0.969919i | \(-0.421728\pi\) | ||||
0.243428 | + | 0.969919i | \(0.421728\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.36522e8i | 0.156744i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.60763e9 | 1.83421 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2.73973e8i | − 0.310637i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.10826e7 | −0.0575576 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 3.12546e8i | − 0.349973i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.61683e7 | −0.0291201 | ||||||||
\(966\) | 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 | ||||||||
\(971\) | − 2.75696e8i | − 0.301143i | −0.988599 | − | 0.150571i | \(-0.951889\pi\) | ||||
0.988599 | − | 0.150571i | \(-0.0481113\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.72912e7 | −0.0513383 | ||||||||
\(974\) | 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 | ||||||||
\(979\) | 2.07836e9i | 2.21499i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.27103e8 | −0.452403 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 4.26292e8i | 0.443359i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.39501e8 | 0.454330 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 5.76213e8i | − 0.592056i | −0.955179 | − | 0.296028i | \(-0.904338\pi\) | ||||
0.955179 | − | 0.296028i | \(-0.0956621\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.54976e8 | −0.771055 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.29538e8i | − 0.131501i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.84682e7 | 0.0892692 | 0.0446346 | − | 0.999003i | \(-0.485788\pi\) | ||||
0.0446346 | + | 0.999003i | \(0.485788\pi\) | |||||||
\(998\) | 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 | 768.7.g.c.511.1 | 4 | ||
4.3 | odd | 2 | inner | 768.7.g.c.511.4 | 4 | ||
8.3 | odd | 2 | 768.7.g.e.511.2 | 4 | |||
8.5 | even | 2 | 768.7.g.e.511.3 | 4 | |||
16.3 | odd | 4 | 384.7.b.d.319.3 | yes | 8 | ||
16.5 | even | 4 | 384.7.b.d.319.2 | ✓ | 8 | ||
16.11 | odd | 4 | 384.7.b.d.319.5 | yes | 8 | ||
16.13 | even | 4 | 384.7.b.d.319.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.7.b.d.319.2 | ✓ | 8 | 16.5 | even | 4 | ||
384.7.b.d.319.3 | yes | 8 | 16.3 | odd | 4 | ||
384.7.b.d.319.5 | yes | 8 | 16.11 | odd | 4 | ||
384.7.b.d.319.8 | yes | 8 | 16.13 | even | 4 | ||
768.7.g.c.511.1 | 4 | 1.1 | even | 1 | trivial | ||
768.7.g.c.511.4 | 4 | 4.3 | odd | 2 | inner | ||
768.7.g.e.511.2 | 4 | 8.3 | odd | 2 | |||
768.7.g.e.511.3 | 4 | 8.5 | even | 2 |