Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1537,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3072.1537");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.d (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: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1537.5 | ||
Root | \(0.500000 - 0.691860i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1537 |
Dual form | 3072.2.d.f.1537.4 |
$q$-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 \(\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(2047\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.79793i | − 1.69849i | −0.528001 | − | 0.849244i | \(-0.677058\pi\) | ||||
0.528001 | − | 0.849244i | \(-0.322942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.15894 | −0.816003 | −0.408002 | − | 0.912981i | \(-0.633774\pi\) | ||||
−0.408002 | + | 0.912981i | \(0.633774\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.54266i | − 0.766641i | −0.923615 | − | 0.383321i | \(-0.874780\pi\) | ||||
0.923615 | − | 0.383321i | \(-0.125220\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.95687i | − 0.542739i | −0.962475 | − | 0.271370i | \(-0.912523\pi\) | ||||
0.962475 | − | 0.271370i | \(-0.0874766\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.79793 | 0.980622 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.224777 | 0.0545165 | 0.0272583 | − | 0.999628i | \(-0.491322\pi\) | ||||
0.0272583 | + | 0.999628i | \(0.491322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 0.224777i | − 0.0515675i | −0.999668 | − | 0.0257837i | \(-0.991792\pi\) | ||||
0.999668 | − | 0.0257837i | \(-0.00820813\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 2.15894i | − 0.471120i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.42429 | −1.88486 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 2.62636i | − 0.487703i | −0.969813 | − | 0.243851i | \(-0.921589\pi\) | ||||
0.969813 | − | 0.243851i | \(-0.0784109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.84106 | 0.330664 | 0.165332 | − | 0.986238i | \(-0.447130\pi\) | ||||
0.165332 | + | 0.986238i | \(0.447130\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.54266 | 0.442620 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.19951i | 1.38597i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.18944i | − 0.853138i | −0.904455 | − | 0.426569i | \(-0.859722\pi\) | ||||
0.904455 | − | 0.426569i | \(-0.140278\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.95687 | 0.313351 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.88163 | −0.918557 | −0.459278 | − | 0.888292i | \(-0.651892\pi\) | ||||
−0.459278 | + | 0.888292i | \(0.651892\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.9670i | 1.67244i | 0.548391 | + | 0.836222i | \(0.315241\pi\) | ||||
−0.548391 | + | 0.836222i | \(0.684759\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.79793i | 0.566162i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.33897 | −0.334139 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.224777i | 0.0314751i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 10.6264i | − 1.45964i | −0.683638 | − | 0.729821i | \(-0.739603\pi\) | ||||
0.683638 | − | 0.729821i | \(-0.260397\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.65685 | −1.30213 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.224777 | 0.0297725 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.65685i | 0.736460i | 0.929735 | + | 0.368230i | \(0.120036\pi\) | ||||
−0.929735 | + | 0.368230i | \(0.879964\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.46742i | 1.08414i | 0.840333 | + | 0.542071i | \(0.182360\pi\) | ||||
−0.840333 | + | 0.542071i | \(0.817640\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.15894 | 0.272001 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.43208 | −0.921836 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 14.7422i | − 1.80104i | −0.434811 | − | 0.900522i | \(-0.643185\pi\) | ||||
0.434811 | − | 0.900522i | \(-0.356815\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.82843i | 0.340503i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.31788 | 0.512438 | 0.256219 | − | 0.966619i | \(-0.417523\pi\) | ||||
0.256219 | + | 0.966619i | \(0.417523\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.97474 | −0.699290 | −0.349645 | − | 0.936882i | \(-0.613698\pi\) | ||||
−0.349645 | + | 0.936882i | \(0.613698\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 9.42429i | − 1.08822i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.48946i | 0.625582i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0075 | −1.68848 | −0.844239 | − | 0.535966i | \(-0.819947\pi\) | ||||
−0.844239 | + | 0.535966i | \(0.819947\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.3059i | 1.57028i | 0.619319 | + | 0.785140i | \(0.287409\pi\) | ||||
−0.619319 | + | 0.785140i | \(0.712591\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 0.853690i | − 0.0925956i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.62636 | 0.281575 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.42847 | 0.151417 | 0.0757086 | − | 0.997130i | \(-0.475878\pi\) | ||||
0.0757086 | + | 0.997130i | \(0.475878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.22478i | 0.442877i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.84106i | 0.190909i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.853690 | −0.0875867 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.3990 | −1.66507 | −0.832535 | − | 0.553973i | \(-0.813111\pi\) | ||||
−0.832535 | + | 0.553973i | \(0.813111\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.54266i | 0.255547i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.115816i | 0.0115241i | 0.999983 | + | 0.00576206i | \(0.00183413\pi\) | ||||
−0.999983 | + | 0.00576206i | \(0.998166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.3507 | −1.31548 | −0.657740 | − | 0.753245i | \(-0.728488\pi\) | ||||
−0.657740 | + | 0.753245i | \(0.728488\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.19951 | −0.800191 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.2926i | 0.995025i | 0.867457 | + | 0.497513i | \(0.165753\pi\) | ||||
−0.867457 | + | 0.497513i | \(0.834247\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.95687i | 0.953696i | 0.878986 | + | 0.476848i | \(0.158221\pi\) | ||||
−0.878986 | + | 0.476848i | \(0.841779\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.18944 | 0.492559 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.8486 | −1.77313 | −0.886563 | − | 0.462608i | \(-0.846914\pi\) | ||||
−0.886563 | + | 0.462608i | \(0.846914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 10.7422i | − 1.00171i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.95687i | 0.180913i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.485281 | −0.0444857 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.53488 | 0.412261 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 5.88163i | − 0.530329i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 16.8032i | 1.50292i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.81580 | −0.338597 | −0.169299 | − | 0.985565i | \(-0.554150\pi\) | ||||
−0.169299 | + | 0.985565i | \(0.554150\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.9670 | −0.965586 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.08532i | − 0.0948250i | −0.998875 | − | 0.0474125i | \(-0.984902\pi\) | ||||
0.998875 | − | 0.0474125i | \(-0.0150975\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.485281i | 0.0420792i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.79793 | −0.326874 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.31010 | 0.453672 | 0.226836 | − | 0.973933i | \(-0.427162\pi\) | ||||
0.226836 | + | 0.973933i | \(0.427162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 12.3990i | − 1.05167i | −0.850586 | − | 0.525836i | \(-0.823753\pi\) | ||||
0.850586 | − | 0.525836i | \(-0.176247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82843i | 0.238197i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.97567 | −0.416086 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.97474 | −0.828357 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2.33897i | − 0.192915i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.45479i | 0.119181i | 0.998223 | + | 0.0595904i | \(0.0189795\pi\) | ||||
−0.998223 | + | 0.0595904i | \(0.981021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.03696 | −0.165766 | −0.0828829 | − | 0.996559i | \(-0.526413\pi\) | ||||
−0.0828829 | + | 0.996559i | \(0.526413\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.224777 | −0.0181722 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 6.99222i | − 0.561628i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.61790i | 0.687784i | 0.939009 | + | 0.343892i | \(0.111745\pi\) | ||||
−0.939009 | + | 0.343892i | \(0.888255\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.6264 | 0.842725 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.10641 | −0.481252 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.86054i | 0.380707i | 0.981716 | + | 0.190354i | \(0.0609634\pi\) | ||||
−0.981716 | + | 0.190354i | \(0.939037\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 9.65685i | − 0.751785i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.7023 | 1.67937 | 0.839686 | − | 0.543072i | \(-0.182739\pi\) | ||||
0.839686 | + | 0.543072i | \(0.182739\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.17064 | 0.705434 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.224777i | 0.0171892i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.3695i | 0.940433i | 0.882551 | + | 0.470217i | \(0.155824\pi\) | ||||
−0.882551 | + | 0.470217i | \(0.844176\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.3465 | 1.53805 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.65685 | −0.425195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 11.6413i | − 0.870111i | −0.900404 | − | 0.435055i | \(-0.856729\pi\) | ||||
0.900404 | − | 0.435055i | \(-0.143271\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 9.50732i | − 0.706673i | −0.935496 | − | 0.353337i | \(-0.885047\pi\) | ||||
0.935496 | − | 0.353337i | \(-0.114953\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.46742 | −0.625930 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.7091 | −1.44904 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 0.571533i | − 0.0417946i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.15894i | 0.157040i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.8032 | −1.50526 | −0.752632 | − | 0.658441i | \(-0.771216\pi\) | ||||
−0.752632 | + | 0.658441i | \(0.771216\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1454 | 1.01821 | 0.509103 | − | 0.860705i | \(-0.329977\pi\) | ||||
0.509103 | + | 0.860705i | \(0.329977\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 7.43208i | − 0.532222i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3.43463i | − 0.244707i | −0.992487 | − | 0.122354i | \(-0.960956\pi\) | ||||
0.992487 | − | 0.122354i | \(-0.0390442\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.306182 | −0.0217047 | −0.0108523 | − | 0.999941i | \(-0.503454\pi\) | ||||
−0.0108523 | + | 0.999941i | \(0.503454\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.7422 | 1.03983 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.67016i | 0.397967i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.3380i | 1.56016i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.82843 | −0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.571533 | −0.0395337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 10.2284i | − 0.704151i | −0.935972 | − | 0.352076i | \(-0.885476\pi\) | ||||
0.935972 | − | 0.352076i | \(-0.114524\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.31788i | 0.295856i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 41.6517 | 2.84063 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.97474 | −0.269823 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 5.97474i | − 0.403735i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 0.439861i | − 0.0295883i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.71908 | −0.115118 | −0.0575591 | − | 0.998342i | \(-0.518332\pi\) | ||||
−0.0575591 | + | 0.998342i | \(0.518332\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.42429 | 0.628286 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.3059i | 0.949518i | 0.880116 | + | 0.474759i | \(0.157465\pi\) | ||||
−0.880116 | + | 0.474759i | \(0.842535\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 16.9981i | − 1.12327i | −0.827386 | − | 0.561634i | \(-0.810173\pi\) | ||||
0.827386 | − | 0.561634i | \(-0.189827\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.48946 | −0.361180 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.3779 | −0.876418 | −0.438209 | − | 0.898873i | \(-0.644387\pi\) | ||||
−0.438209 | + | 0.898873i | \(0.644387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 10.7422i | − 0.700742i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 15.0075i | − 0.974844i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.3675 | −0.864670 | −0.432335 | − | 0.901713i | \(-0.642310\pi\) | ||||
−0.432335 | + | 0.901713i | \(0.642310\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.211474 | −0.0136222 | −0.00681112 | − | 0.999977i | \(-0.502168\pi\) | ||||
−0.00681112 | + | 0.999977i | \(0.502168\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.88325i | 0.567530i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.439861 | −0.0279877 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.3059 | −0.906601 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.7555i | 0.931358i | 0.884954 | + | 0.465679i | \(0.154190\pi\) | ||||
−0.884954 | + | 0.465679i | \(0.845810\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 7.19173i | − 0.452140i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.853690 | 0.0534601 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.742176 | −0.0462957 | −0.0231478 | − | 0.999732i | \(-0.507369\pi\) | ||||
−0.0231478 | + | 0.999732i | \(0.507369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.2037i | 0.696163i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.62636i | 0.162568i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.48435 | −0.338180 | −0.169090 | − | 0.985601i | \(-0.554083\pi\) | ||||
−0.169090 | + | 0.985601i | \(0.554083\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −40.3582 | −2.47918 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.42847i | 0.0874208i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 20.4694i | − 1.24804i | −0.781407 | − | 0.624021i | \(-0.785498\pi\) | ||||
0.781407 | − | 0.624021i | \(-0.214502\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0370 | 0.852685 | 0.426342 | − | 0.904562i | \(-0.359802\pi\) | ||||
0.426342 | + | 0.904562i | \(0.359802\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.22478 | −0.255695 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.9628i | 1.44501i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 13.4211i | − 0.806394i | −0.915113 | − | 0.403197i | \(-0.867899\pi\) | ||||
0.915113 | − | 0.403197i | \(-0.132101\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.84106 | −0.110221 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.89359 | −0.232272 | −0.116136 | − | 0.993233i | \(-0.537051\pi\) | ||||
−0.116136 | + | 0.993233i | \(0.537051\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 17.6569i | − 1.04959i | −0.851228 | − | 0.524796i | \(-0.824142\pi\) | ||||
0.851228 | − | 0.524796i | \(-0.175858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 0.853690i | − 0.0505682i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.6981 | 0.749545 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9495 | −0.997028 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 16.3990i | − 0.961328i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 15.7759i | − 0.921639i | −0.887494 | − | 0.460819i | \(-0.847556\pi\) | ||||
0.887494 | − | 0.460819i | \(-0.152444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.4844 | 1.25087 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.54266 | −0.147540 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 5.53488i | − 0.320090i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 23.6770i | − 1.36472i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.115816 | −0.00665345 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.1587 | 1.84140 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.64129i | 0.436111i | 0.975936 | + | 0.218056i | \(0.0699714\pi\) | ||||
−0.975936 | + | 0.218056i | \(0.930029\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 13.3507i | − 0.759493i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.1623 | −1.37012 | −0.685059 | − | 0.728488i | \(-0.740224\pi\) | ||||
−0.685059 | + | 0.728488i | \(0.740224\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.6105 | 0.938881 | 0.469441 | − | 0.882964i | \(-0.344456\pi\) | ||||
0.469441 | + | 0.882964i | \(0.344456\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 8.19951i | − 0.461990i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.56213i | 0.143903i | 0.997408 | + | 0.0719517i | \(0.0229227\pi\) | ||||
−0.997408 | + | 0.0719517i | \(0.977077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.67794 | −0.373893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.2926 | −0.574478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 0.0505249i | − 0.00281128i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.4422i | 1.02299i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.95687 | −0.550616 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.10641 | −0.336657 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 19.1275i | − 1.05134i | −0.850688 | − | 0.525671i | \(-0.823814\pi\) | ||||
0.850688 | − | 0.525671i | \(-0.176186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.18944i | 0.284379i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −55.9898 | −3.05905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.12615 | 0.0613454 | 0.0306727 | − | 0.999529i | \(-0.490235\pi\) | ||||
0.0306727 | + | 0.999529i | \(0.490235\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 18.8486i | − 1.02371i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4.68119i | − 0.253500i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1623 | 1.08866 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.7422 | 0.578339 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.4068i | 1.57864i | 0.613982 | + | 0.789320i | \(0.289567\pi\) | ||||
−0.613982 | + | 0.789320i | \(0.710433\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 27.2738i | − 1.45993i | −0.683482 | − | 0.729967i | \(-0.739535\pi\) | ||||
0.683482 | − | 0.729967i | \(-0.260465\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.95687 | −0.104450 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.5908 | 1.36206 | 0.681029 | − | 0.732256i | \(-0.261533\pi\) | ||||
0.681029 | + | 0.732256i | \(0.261533\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 16.3990i | − 0.870370i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 0.485281i | − 0.0256838i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.77296 | −0.199129 | −0.0995645 | − | 0.995031i | \(-0.531745\pi\) | ||||
−0.0995645 | + | 0.995031i | \(0.531745\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9495 | 0.997341 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.53488i | 0.238019i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.6917i | 1.18774i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.4474 | 1.43274 | 0.716371 | − | 0.697720i | \(-0.245802\pi\) | ||||
0.716371 | + | 0.697720i | \(0.245802\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.88163 | 0.306186 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.9417i | 1.19107i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 17.8518i | − 0.924332i | −0.886794 | − | 0.462166i | \(-0.847072\pi\) | ||||
0.886794 | − | 0.462166i | \(-0.152928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.8032 | −0.867712 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.13946 | −0.264695 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 16.5018i | − 0.847642i | −0.905746 | − | 0.423821i | \(-0.860689\pi\) | ||||
0.905746 | − | 0.423821i | \(-0.139311\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 3.81580i | − 0.195489i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.1885 | −0.878291 | −0.439145 | − | 0.898416i | \(-0.644719\pi\) | ||||
−0.439145 | + | 0.898416i | \(0.644719\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.8486 | 1.06254 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 10.9670i | − 0.557482i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 2.66209i | − 0.134973i | −0.997720 | − | 0.0674866i | \(-0.978502\pi\) | ||||
0.997720 | − | 0.0674866i | \(-0.0214980\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.635767 | 0.0321521 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.08532 | 0.0547472 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 56.9976i | 2.86786i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 11.8959i | − 0.597037i | −0.954404 | − | 0.298519i | \(-0.903507\pi\) | ||||
0.954404 | − | 0.298519i | \(-0.0964925\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.485281 | −0.0242945 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.12389 | −0.0561242 | −0.0280621 | − | 0.999606i | \(-0.508934\pi\) | ||||
−0.0280621 | + | 0.999606i | \(0.508934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 3.60272i | − 0.179464i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 3.79793i | − 0.188721i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.1950 | −0.654051 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.7211 | −0.678464 | −0.339232 | − | 0.940703i | \(-0.610167\pi\) | ||||
−0.339232 | + | 0.940703i | \(0.610167\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.31010i | 0.261928i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 12.2128i | − 0.600953i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 54.3329 | 2.66710 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.3990 | 0.607183 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 13.1629i | − 0.643048i | −0.946901 | − | 0.321524i | \(-0.895805\pi\) | ||||
0.946901 | − | 0.321524i | \(-0.104195\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.9413i | 0.581984i | 0.956726 | + | 0.290992i | \(0.0939852\pi\) | ||||
−0.956726 | + | 0.290992i | \(0.906015\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.82843 | −0.137523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.11837 | −0.102756 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 18.2807i | − 0.884663i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 4.97567i | − 0.240227i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.6054 | 1.47421 | 0.737105 | − | 0.675778i | \(-0.236192\pi\) | ||||
0.737105 | + | 0.675778i | \(0.236192\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.3137 | 0.735930 | 0.367965 | − | 0.929840i | \(-0.380055\pi\) | ||||
0.367965 | + | 0.929840i | \(0.380055\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 9.97474i | − 0.478252i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 0.635767i | − 0.0304128i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.3676 | −1.59255 | −0.796274 | − | 0.604936i | \(-0.793199\pi\) | ||||
−0.796274 | + | 0.604936i | \(0.793199\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.33897 | 0.111380 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.23617i | 0.153755i | 0.997041 | + | 0.0768776i | \(0.0244951\pi\) | ||||
−0.997041 | + | 0.0768776i | \(0.975505\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 5.42522i | − 0.257180i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.45479 | −0.0688091 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.4165 | −1.29387 | −0.646933 | − | 0.762547i | \(-0.723948\pi\) | ||||
−0.646933 | + | 0.762547i | \(0.723948\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.9550i | 0.704203i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 2.03696i | − 0.0957049i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.0454 | 0.752221 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.9147 | 0.510567 | 0.255284 | − | 0.966866i | \(-0.417831\pi\) | ||||
0.255284 | + | 0.966866i | \(0.417831\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 0.224777i | − 0.0104917i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 25.2181i | − 1.17452i | −0.809398 | − | 0.587261i | \(-0.800206\pi\) | ||||
0.809398 | − | 0.587261i | \(-0.199794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.4937 | −1.04537 | −0.522686 | − | 0.852525i | \(-0.675070\pi\) | ||||
−0.522686 | + | 0.852525i | \(0.675070\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.99222 | 0.324256 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 34.2482i | − 1.58482i | −0.609991 | − | 0.792408i | \(-0.708827\pi\) | ||||
0.609991 | − | 0.792408i | \(-0.291173\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.8275i | 1.46966i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.61790 | −0.397092 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.8852 | 1.28216 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.11837i | 0.0971974i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.6264i | 0.486548i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.2362 | −1.65568 | −0.827838 | − | 0.560968i | \(-0.810429\pi\) | ||||
−0.827838 | + | 0.560968i | \(0.810429\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1551 | −0.463032 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 6.10641i | − 0.277851i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 62.2824i | 2.82810i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.8200 | −0.762186 | −0.381093 | − | 0.924537i | \(-0.624452\pi\) | ||||
−0.381093 | + | 0.924537i | \(0.624452\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.86054 | −0.219801 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 8.63577i | − 0.389727i | −0.980830 | − | 0.194863i | \(-0.937574\pi\) | ||||
0.980830 | − | 0.194863i | \(-0.0624263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 0.590346i | − 0.0265879i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.65685 | 0.434043 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.32206 | −0.418151 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.8275i | 1.24573i | 0.782329 | + | 0.622865i | \(0.214031\pi\) | ||||
−0.782329 | + | 0.622865i | \(0.785969\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.7023i | 0.969586i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.7308 | 1.14728 | 0.573639 | − | 0.819108i | \(-0.305531\pi\) | ||||
0.573639 | + | 0.819108i | \(0.305531\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.439861 | 0.0195736 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.17064i | 0.407283i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.45386i | 0.108765i | 0.998520 | + | 0.0543826i | \(0.0173191\pi\) | ||||
−0.998520 | + | 0.0543826i | \(0.982681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8991 | 0.570623 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.224777 | −0.00992417 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 50.7050i | 2.23433i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 7.19173i | − 0.316292i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.3695 | −0.542959 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.5944 | 1.47180 | 0.735898 | − | 0.677092i | \(-0.236760\pi\) | ||||
0.735898 | + | 0.677092i | \(0.236760\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.8522i | 1.34907i | 0.738242 | + | 0.674536i | \(0.235656\pi\) | ||||
−0.738242 | + | 0.674536i | \(0.764344\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.3465i | 0.887994i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.413828 | 0.0180266 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 5.65685i | − 0.245487i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.5096i | 0.498537i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.0907 | 1.69004 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.6413 | 0.502359 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.94721i | 0.256164i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.4825i | 1.65449i | 0.561841 | + | 0.827245i | \(0.310093\pi\) | ||||
−0.561841 | + | 0.827245i | \(0.689907\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.50732 | 0.407998 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 37.8155 | 1.61984 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 9.61829i | − 0.411248i | −0.978631 | − | 0.205624i | \(-0.934078\pi\) | ||||
0.978631 | − | 0.205624i | \(-0.0659224\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 8.46742i | − 0.361381i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.590346 | −0.0251496 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.4004 | 1.37780 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 19.7091i | − 0.836606i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.07174i | 0.257268i | 0.991692 | + | 0.128634i | \(0.0410592\pi\) | ||||
−0.991692 | + | 0.128634i | \(0.958941\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.4609 | 0.907701 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.571533 | 0.0241301 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.2554i | 0.600793i | 0.953814 | + | 0.300397i | \(0.0971191\pi\) | ||||
−0.953814 | + | 0.300397i | \(0.902881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 71.5857i | 3.01163i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.15894 | −0.0906670 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.5018 | 1.36255 | 0.681274 | − | 0.732029i | \(-0.261426\pi\) | ||||
0.681274 | + | 0.732029i | \(0.261426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 12.9706i | − 0.542801i | −0.962466 | − | 0.271401i | \(-0.912513\pi\) | ||||
0.962466 | − | 0.271401i | \(-0.0874868\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 20.8032i | − 0.869065i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.6559 | −1.11163 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.7536 | 0.489308 | 0.244654 | − | 0.969611i | \(-0.421326\pi\) | ||||
0.244654 | + | 0.969611i | \(0.421326\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.1454i | 0.587862i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 30.8857i | − 1.28135i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.0192 | −1.11902 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.43208 | 0.307279 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 9.13585i | − 0.377077i | −0.982066 | − | 0.188538i | \(-0.939625\pi\) | ||||
0.982066 | − | 0.188538i | \(-0.0603750\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 0.413828i | − 0.0170515i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.43463 | 0.141282 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.49270 | −0.225558 | −0.112779 | − | 0.993620i | \(-0.535975\pi\) | ||||
−0.112779 | + | 0.993620i | \(0.535975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.84307i | 0.0755583i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 0.306182i | − 0.0125312i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.4348 | 1.48868 | 0.744342 | − | 0.667799i | \(-0.232763\pi\) | ||||
0.744342 | + | 0.667799i | \(0.232763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.97474 | 0.406878 | 0.203439 | − | 0.979088i | \(-0.434788\pi\) | ||||
0.203439 | + | 0.979088i | \(0.434788\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.7422i | 0.600348i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 17.2232i | − 0.700221i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.51900 | 0.183421 | 0.0917103 | − | 0.995786i | \(-0.470767\pi\) | ||||
0.0917103 | + | 0.995786i | \(0.470767\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.67016 | −0.229766 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 5.53488i | − 0.223917i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 11.9316i | − 0.481913i | −0.970536 | − | 0.240957i | \(-0.922539\pi\) | ||||
0.970536 | − | 0.240957i | \(-0.0774612\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.3380 | −0.900757 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.1201 | 1.29311 | 0.646554 | − | 0.762869i | \(-0.276210\pi\) | ||||
0.646554 | + | 0.762869i | \(0.276210\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 21.2715i | − 0.854975i | −0.904021 | − | 0.427488i | \(-0.859399\pi\) | ||||
0.904021 | − | 0.427488i | \(-0.140601\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.82843i | − 0.113501i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.08398 | −0.123557 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.6958 | 0.667833 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 0.571533i | − 0.0228248i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.16647i | − 0.0465101i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.4685 | −1.45179 | −0.725894 | − | 0.687807i | \(-0.758574\pi\) | ||||
−0.725894 | + | 0.687807i | \(0.758574\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.2284 | 0.406542 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.4921i | 0.575103i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.57707i | 0.181350i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.31788 | −0.170813 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.0036 | 0.553109 | 0.276555 | − | 0.960998i | \(-0.410807\pi\) | ||||
0.276555 | + | 0.960998i | \(0.410807\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.4807i | 0.925990i | 0.886361 | + | 0.462995i | \(0.153225\pi\) | ||||
−0.886361 | + | 0.462995i | \(0.846775\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 41.6517i | 1.64004i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.1908 | 0.479270 | 0.239635 | − | 0.970863i | \(-0.422972\pi\) | ||||
0.239635 | + | 0.970863i | \(0.422972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.3835 | 0.564600 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 3.97474i | − 0.155782i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.39055i | − 0.0544165i | −0.999630 | − | 0.0272083i | \(-0.991338\pi\) | ||||
0.999630 | − | 0.0272083i | \(-0.00866173\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.12198 | −0.161059 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.97474 | 0.233097 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.5349i | 0.994698i | 0.867551 | + | 0.497349i | \(0.165693\pi\) | ||||
−0.867551 | + | 0.497349i | \(0.834307\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.44726i | 0.250769i | 0.992108 | + | 0.125385i | \(0.0400165\pi\) | ||||
−0.992108 | + | 0.125385i | \(0.959983\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.439861 | 0.0170828 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.84307 | 0.0714710 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 7.42847i | − 0.287631i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.71908i | − 0.0664635i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.5298 | 0.831148 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.8569 | −0.418504 | −0.209252 | − | 0.977862i | \(-0.567103\pi\) | ||||
−0.209252 | + | 0.977862i | \(0.567103\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.42429i | 0.362741i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.5262i | 1.28852i | 0.764807 | + | 0.644259i | \(0.222834\pi\) | ||||
−0.764807 | + | 0.644259i | \(0.777166\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 35.4045 | 1.35870 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.3059 | −0.548204 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.2206i | 0.965040i | 0.875885 | + | 0.482520i | \(0.160278\pi\) | ||||
−0.875885 | + | 0.482520i | \(0.839722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 20.1674i | − 0.770557i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.9981 | 0.648519 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.7945 | −0.792205 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 15.3523i | − 0.584028i | −0.956414 | − | 0.292014i | \(-0.905675\pi\) | ||||
0.956414 | − | 0.292014i | \(-0.0943254\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 5.48946i | − 0.208527i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −47.0907 | −1.78625 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.32206 | −0.0500765 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 13.3779i | − 0.506000i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 8.61079i | − 0.325225i | −0.986690 | − | 0.162613i | \(-0.948008\pi\) | ||||
0.986690 | − | 0.162613i | \(-0.0519921\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.16647 | −0.0439942 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.7422 | 0.404574 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 0.250040i | − 0.00940372i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.3624i | 1.21539i | 0.794169 | + | 0.607697i | \(0.207906\pi\) | ||||
−0.794169 | + | 0.607697i | \(0.792094\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.0075 | 0.562826 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.20730 | 0.195015 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.8972i | 0.706717i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 13.3675i | − 0.499218i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.46744 | 0.0547262 | 0.0273631 | − | 0.999626i | \(-0.491289\pi\) | ||||
0.0273631 | + | 0.999626i | \(0.491289\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.8233 | 1.07344 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 0.211474i | − 0.00786481i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.7516i | 0.919251i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.3928 | 0.570889 | 0.285445 | − | 0.958395i | \(-0.407859\pi\) | ||||
0.285445 | + | 0.958395i | \(0.407859\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.46512i | 0.0911759i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 17.5624i | − 0.648683i | −0.945940 | − | 0.324342i | \(-0.894857\pi\) | ||||
0.945940 | − | 0.324342i | \(-0.105143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.88325 | −0.327664 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −37.4844 | −1.38075 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 20.7266i | − 0.762441i | −0.924484 | − | 0.381220i | \(-0.875504\pi\) | ||||
0.924484 | − | 0.381220i | \(-0.124496\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 0.439861i | − 0.0161587i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.7821 | 1.16597 | 0.582986 | − | 0.812482i | \(-0.301884\pi\) | ||||
0.582986 | + | 0.812482i | \(0.301884\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.52518 | 0.202427 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 14.3059i | − 0.523426i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 22.2212i | − 0.811944i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.7594 | −1.08594 | −0.542968 | − | 0.839753i | \(-0.682699\pi\) | ||||
−0.542968 | + | 0.839753i | \(0.682699\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.7555 | −0.537720 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.73625i | 0.281551i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 22.1119i | − 0.803672i | −0.915712 | − | 0.401836i | \(-0.868372\pi\) | ||||
0.915712 | − | 0.401836i | \(-0.131628\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.19173 | 0.261043 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.55957 | 0.165284 | 0.0826422 | − | 0.996579i | \(-0.473664\pi\) | ||||
0.0826422 | + | 0.996579i | \(0.473664\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 21.4963i | − 0.778219i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.853690i | 0.0308652i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.0698 | 0.399706 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.5794 | 1.31909 | 0.659543 | − | 0.751667i | \(-0.270750\pi\) | ||||
0.659543 | + | 0.751667i | \(0.270750\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 0.742176i | − 0.0267288i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 26.4611i | − 0.951739i | −0.879516 | − | 0.475869i | \(-0.842133\pi\) | ||||
0.879516 | − | 0.475869i | \(-0.157867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.3507 | −0.623255 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.2037 | −0.401930 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.32206i | 0.0473676i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 10.9789i | − 0.392856i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.62636 | −0.0938584 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.7302 | 1.16819 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 18.9164i | − 0.674298i | −0.941451 | − | 0.337149i | \(-0.890537\pi\) | ||||
0.941451 | − | 0.337149i | \(-0.109463\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 5.48435i | − 0.195248i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.6930 | 1.44688 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.5697 | 0.588406 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 40.3582i | − 1.43136i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 47.8065i | − 1.69339i | −0.532075 | − | 0.846697i | \(-0.678588\pi\) | ||||
0.532075 | − | 0.846697i | \(-0.321412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.635767 | 0.0224918 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.42847 | −0.0504724 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.1917i | 0.536105i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23.1917i | 0.817401i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.4694 | 0.720558 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.9862 | −1.05426 | −0.527129 | − | 0.849785i | \(-0.676732\pi\) | ||||
−0.527129 | + | 0.849785i | \(0.676732\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.3899i | 0.399954i | 0.979801 | + | 0.199977i | \(0.0640867\pi\) | ||||
−0.979801 | + | 0.199977i | \(0.935913\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0370i | 0.492298i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.4600 | 0.646626 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.46512 | 0.0862438 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 4.22478i | − 0.147626i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 19.6929i | − 0.687286i | −0.939100 | − | 0.343643i | \(-0.888339\pi\) | ||||
0.939100 | − | 0.343643i | \(-0.111661\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.4666 | −0.783137 | −0.391568 | − | 0.920149i | \(-0.628067\pi\) | ||||
−0.391568 | + | 0.920149i | \(0.628067\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −23.9628 | −0.834277 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.7927i | 0.375299i | 0.982236 | + | 0.187649i | \(0.0600869\pi\) | ||||
−0.982236 | + | 0.187649i | \(0.939913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 45.9421i | − 1.59563i | −0.602900 | − | 0.797817i | \(-0.705988\pi\) | ||||
0.602900 | − | 0.797817i | \(-0.294012\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.4211 | 0.465572 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.525748 | −0.0182161 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 82.4238i | − 2.85239i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.84106i | − 0.0636363i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.9142 | −0.791085 | −0.395542 | − | 0.918448i | \(-0.629443\pi\) | ||||
−0.395542 | + | 0.918448i | \(0.629443\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.1022 | 0.762146 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 3.89359i | − 0.134102i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 34.8295i | − 1.19817i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.79053 | −0.336407 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.6569 | 0.605982 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 14.6779i | − 0.503153i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 55.0728i | − 1.88566i | −0.333278 | − | 0.942829i | \(-0.608155\pi\) | ||||
0.333278 | − | 0.942829i | \(-0.391845\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.853690 | 0.0291956 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.79079 | 0.0611723 | 0.0305861 | − | 0.999532i | \(-0.490263\pi\) | ||||
0.0305861 | + | 0.999532i | \(0.490263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5468i | 0.871647i | 0.900032 | + | 0.435823i | \(0.143543\pi\) | ||||
−0.900032 | + | 0.435823i | \(0.856457\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.6981i | 0.432750i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.1150 | 1.43361 | 0.716806 | − | 0.697273i | \(-0.245603\pi\) | ||||
0.716806 | + | 0.697273i | \(0.245603\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 46.9784 | 1.59731 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 16.9495i | − 0.575634i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.1590i | 1.29446i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.8486 | −0.977497 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.3990 | 0.555023 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 36.2771i | − 1.22639i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.01044i | − 0.0341203i | −0.999854 | − | 0.0170601i | \(-0.994569\pi\) | ||||
0.999854 | − | 0.0170601i | \(-0.00543067\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.7759 | 0.532108 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.3972 | 1.49578 | 0.747889 | − | 0.663823i | \(-0.231067\pi\) | ||||
0.747889 | + | 0.663823i | \(0.231067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1.82389i | − 0.0613787i | −0.999529 | − | 0.0306894i | \(-0.990230\pi\) | ||||
0.999529 | − | 0.0306894i | \(-0.00977026\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.4844i | 0.722189i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.38532 | −0.147245 | −0.0736223 | − | 0.997286i | \(-0.523456\pi\) | ||||
−0.0736223 | + | 0.997286i | \(0.523456\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.23808 | 0.276296 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 2.54266i | − 0.0851823i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 0.635767i | − 0.0212751i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.2128 | −1.47787 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.53488 | 0.184804 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 4.83528i | − 0.161266i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2.38857i | − 0.0795747i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.6770 | 0.787922 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −36.1082 | −1.20028 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.06248i | 0.134893i | 0.997723 | + | 0.0674463i | \(0.0214851\pi\) | ||||
−0.997723 | + | 0.0674463i | \(0.978515\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 0.115816i | − 0.00384137i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.3784 | −1.40406 | −0.702029 | − | 0.712149i | \(-0.747722\pi\) | ||||
−0.702029 | + | 0.712149i | \(0.747722\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.3751 | 1.20384 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32.1587i | 1.06313i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.34315i | 0.0773775i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.8603 | −1.47980 | −0.739902 | − | 0.672715i | \(-0.765128\pi\) | ||||
−0.739902 | + | 0.672715i | \(0.765128\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.64129 | −0.251789 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 8.44955i | − 0.278120i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.9068i | 1.60804i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.3507 | 0.438494 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.96695 | −0.0973426 | −0.0486713 | − | 0.998815i | \(-0.515499\pi\) | ||||
−0.0486713 | + | 0.998815i | \(0.515499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.525748i | 0.0172307i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 24.1623i | − 0.791038i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.17064 | −0.0709876 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.7669 | −1.78916 | −0.894579 | − | 0.446910i | \(-0.852524\pi\) | ||||
−0.894579 | + | 0.446910i | \(0.852524\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.6105i | 0.542063i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.89558i | 0.289988i | 0.989433 | + | 0.144994i | \(0.0463162\pi\) | ||||
−0.989433 | + | 0.144994i | \(0.953684\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.6358 | −0.541735 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.19951 | 0.266730 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.8541i | 0.515189i | 0.966253 | + | 0.257595i | \(0.0829299\pi\) | ||||
−0.966253 | + | 0.257595i | \(0.917070\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.6918i | 0.379532i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.56213 | −0.0830826 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.2807 | 0.980887 | 0.490443 | − | 0.871473i | \(-0.336835\pi\) | ||||
0.490443 | + | 0.871473i | \(0.336835\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 79.0090i | 2.55667i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 6.67794i | − 0.215867i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.4642 | −0.370198 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6105 | −0.890661 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 10.2926i | − 0.331675i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 53.7232i | − 1.72941i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.5273 | 0.338537 | 0.169268 | − | 0.985570i | \(-0.445860\pi\) | ||||
0.169268 | + | 0.985570i | \(0.445860\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0505249 | 0.00162309 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 38.7050i | − 1.24210i | −0.783771 | − | 0.621051i | \(-0.786706\pi\) | ||||
0.783771 | − | 0.621051i | \(-0.213294\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.7688i | 0.858168i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18.4422 | −0.590622 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.9009 | 0.540706 | 0.270353 | − | 0.962761i | \(-0.412860\pi\) | ||||
0.270353 | + | 0.962761i | \(0.412860\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 3.63211i | − 0.116083i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 9.95687i | − 0.317899i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.0798 | 0.321496 | 0.160748 | − | 0.986995i | \(-0.448609\pi\) | ||||
0.160748 | + | 0.986995i | \(0.448609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.0445 | −0.415632 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 6.10641i | − 0.194369i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.0192i | 0.986354i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.3446 | −1.34512 | −0.672561 | − | 0.740042i | \(-0.734806\pi\) | ||||
−0.672561 | + | 0.740042i | \(0.734806\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.1275 | 0.606993 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.16286i | 0.0368651i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 47.6132i | − 1.50793i | −0.656917 | − | 0.753963i | \(-0.728140\pi\) | ||||
0.656917 | − | 0.753963i | \(-0.271860\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.18944 | −0.164186 |
(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 | 3072.2.d.f.1537.5 | 8 | ||
4.3 | odd | 2 | 3072.2.d.i.1537.1 | 8 | |||
8.3 | odd | 2 | 3072.2.d.i.1537.8 | 8 | |||
8.5 | even | 2 | inner | 3072.2.d.f.1537.4 | 8 | ||
16.3 | odd | 4 | 3072.2.a.o.1.1 | 4 | |||
16.5 | even | 4 | 3072.2.a.t.1.4 | 4 | |||
16.11 | odd | 4 | 3072.2.a.n.1.4 | 4 | |||
16.13 | even | 4 | 3072.2.a.i.1.1 | 4 | |||
32.3 | odd | 8 | 384.2.j.a.97.4 | 8 | |||
32.5 | even | 8 | 384.2.j.b.289.2 | 8 | |||
32.11 | odd | 8 | 192.2.j.a.145.1 | 8 | |||
32.13 | even | 8 | 48.2.j.a.37.3 | yes | 8 | ||
32.19 | odd | 8 | 192.2.j.a.49.1 | 8 | |||
32.21 | even | 8 | 48.2.j.a.13.3 | ✓ | 8 | ||
32.27 | odd | 8 | 384.2.j.a.289.4 | 8 | |||
32.29 | even | 8 | 384.2.j.b.97.2 | 8 | |||
48.5 | odd | 4 | 9216.2.a.y.1.1 | 4 | |||
48.11 | even | 4 | 9216.2.a.x.1.1 | 4 | |||
48.29 | odd | 4 | 9216.2.a.bo.1.4 | 4 | |||
48.35 | even | 4 | 9216.2.a.bn.1.4 | 4 | |||
96.5 | odd | 8 | 1152.2.k.c.289.1 | 8 | |||
96.11 | even | 8 | 576.2.k.b.145.4 | 8 | |||
96.29 | odd | 8 | 1152.2.k.c.865.1 | 8 | |||
96.35 | even | 8 | 1152.2.k.f.865.1 | 8 | |||
96.53 | odd | 8 | 144.2.k.b.109.2 | 8 | |||
96.59 | even | 8 | 1152.2.k.f.289.1 | 8 | |||
96.77 | odd | 8 | 144.2.k.b.37.2 | 8 | |||
96.83 | even | 8 | 576.2.k.b.433.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.3 | ✓ | 8 | 32.21 | even | 8 | ||
48.2.j.a.37.3 | yes | 8 | 32.13 | even | 8 | ||
144.2.k.b.37.2 | 8 | 96.77 | odd | 8 | |||
144.2.k.b.109.2 | 8 | 96.53 | odd | 8 | |||
192.2.j.a.49.1 | 8 | 32.19 | odd | 8 | |||
192.2.j.a.145.1 | 8 | 32.11 | odd | 8 | |||
384.2.j.a.97.4 | 8 | 32.3 | odd | 8 | |||
384.2.j.a.289.4 | 8 | 32.27 | odd | 8 | |||
384.2.j.b.97.2 | 8 | 32.29 | even | 8 | |||
384.2.j.b.289.2 | 8 | 32.5 | even | 8 | |||
576.2.k.b.145.4 | 8 | 96.11 | even | 8 | |||
576.2.k.b.433.4 | 8 | 96.83 | even | 8 | |||
1152.2.k.c.289.1 | 8 | 96.5 | odd | 8 | |||
1152.2.k.c.865.1 | 8 | 96.29 | odd | 8 | |||
1152.2.k.f.289.1 | 8 | 96.59 | even | 8 | |||
1152.2.k.f.865.1 | 8 | 96.35 | even | 8 | |||
3072.2.a.i.1.1 | 4 | 16.13 | even | 4 | |||
3072.2.a.n.1.4 | 4 | 16.11 | odd | 4 | |||
3072.2.a.o.1.1 | 4 | 16.3 | odd | 4 | |||
3072.2.a.t.1.4 | 4 | 16.5 | even | 4 | |||
3072.2.d.f.1537.4 | 8 | 8.5 | even | 2 | inner | ||
3072.2.d.f.1537.5 | 8 | 1.1 | even | 1 | trivial | ||
3072.2.d.i.1537.1 | 8 | 4.3 | odd | 2 | |||
3072.2.d.i.1537.8 | 8 | 8.3 | odd | 2 | |||
9216.2.a.x.1.1 | 4 | 48.11 | even | 4 | |||
9216.2.a.y.1.1 | 4 | 48.5 | odd | 4 | |||
9216.2.a.bn.1.4 | 4 | 48.35 | even | 4 | |||
9216.2.a.bo.1.4 | 4 | 48.29 | odd | 4 |