Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(829,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1380.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 27x^{12} + 283x^{10} + 1441x^{8} + 3596x^{6} + 3740x^{4} + 772x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 829.13 | ||
Root | \(-0.0729221i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1380.829 |
Dual form | 1380.2.f.b.829.6 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 1.54426 | + | 1.61718i | 0.690613 | + | 0.723225i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.99468i | 1.50985i | 0.655812 | + | 0.754924i | \(0.272326\pi\) | ||||
−0.655812 | + | 0.754924i | \(0.727674\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.31084 | 0.696745 | 0.348372 | − | 0.937356i | \(-0.386734\pi\) | ||||
0.348372 | + | 0.937356i | \(0.386734\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.60596i | 1.55481i | 0.628998 | + | 0.777407i | \(0.283465\pi\) | ||||
−0.628998 | + | 0.777407i | \(0.716535\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.61718 | + | 1.54426i | −0.417554 | + | 0.398726i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.27777i | − | 0.794976i | −0.917607 | − | 0.397488i | \(-0.869882\pi\) | ||
0.917607 | − | 0.397488i | \(-0.130118\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.49731 | −0.343507 | −0.171754 | − | 0.985140i | \(-0.554943\pi\) | ||||
−0.171754 | + | 0.985140i | \(0.554943\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.99468 | −0.871711 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.230539 | + | 4.99468i | −0.0461077 | + | 0.998936i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.51213 | 0.837882 | 0.418941 | − | 0.908014i | \(-0.362401\pi\) | ||||
0.418941 | + | 0.908014i | \(0.362401\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.38895 | −0.429069 | −0.214534 | − | 0.976716i | \(-0.568823\pi\) | ||||
−0.214534 | + | 0.976716i | \(0.568823\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.31084i | 0.402266i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.46012 | + | 6.16882i | −1.09196 | + | 1.04272i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.66237i | − | 1.09529i | −0.836712 | − | 0.547643i | \(-0.815525\pi\) | ||
0.836712 | − | 0.547643i | \(-0.184475\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.60596 | −0.897672 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.07468 | 0.167837 | 0.0839184 | − | 0.996473i | \(-0.473257\pi\) | ||||
0.0839184 | + | 0.996473i | \(0.473257\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12.5260i | − | 1.91019i | −0.296297 | − | 0.955096i | \(-0.595752\pi\) | ||
0.296297 | − | 0.955096i | \(-0.404248\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.54426 | − | 1.61718i | −0.230204 | − | 0.241075i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.43129i | 0.646370i | 0.946336 | + | 0.323185i | \(0.104754\pi\) | ||||
−0.946336 | + | 0.323185i | \(0.895246\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.95749 | −1.27964 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.27777 | 0.458980 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.01735i | 0.277104i | 0.990355 | + | 0.138552i | \(0.0442449\pi\) | ||||
−0.990355 | + | 0.138552i | \(0.955755\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.56853 | + | 3.73705i | 0.481181 | + | 0.503903i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.49731i | − | 0.198324i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.1502 | −1.71202 | −0.856008 | − | 0.516963i | \(-0.827062\pi\) | ||||
−0.856008 | + | 0.516963i | \(0.827062\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1266 | 1.42462 | 0.712308 | − | 0.701867i | \(-0.247650\pi\) | ||||
0.712308 | + | 0.701867i | \(0.247650\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 3.99468i | − | 0.503283i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.06585 | + | 8.65705i | −1.12448 | + | 1.07377i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.91149i | 1.21088i | 0.795891 | + | 0.605440i | \(0.207003\pi\) | ||||
−0.795891 | + | 0.605440i | \(0.792997\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.94360 | 0.586697 | 0.293348 | − | 0.956006i | \(-0.405230\pi\) | ||||
0.293348 | + | 0.956006i | \(0.405230\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.38340i | − | 0.513038i | −0.966539 | − | 0.256519i | \(-0.917424\pi\) | ||
0.966539 | − | 0.256519i | \(-0.0825757\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.99468 | − | 0.230539i | −0.576736 | − | 0.0266203i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.23108i | 1.05198i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.35481 | −1.05250 | −0.526249 | − | 0.850331i | \(-0.676402\pi\) | ||||
−0.526249 | + | 0.850331i | \(0.676402\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.95659i | 0.434292i | 0.976139 | + | 0.217146i | \(0.0696748\pi\) | ||||
−0.976139 | + | 0.217146i | \(0.930325\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.30074 | − | 5.06172i | 0.574946 | − | 0.549021i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.51213i | 0.483751i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.6996 | 1.24015 | 0.620076 | − | 0.784542i | \(-0.287102\pi\) | ||||
0.620076 | + | 0.784542i | \(0.287102\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.3940 | −2.34753 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 2.38895i | − | 0.247723i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.31224 | − | 2.42142i | −0.237231 | − | 0.248433i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 16.4888i | − | 1.67418i | −0.547064 | − | 0.837090i | \(-0.684255\pi\) | ||
0.547064 | − | 0.837090i | \(-0.315745\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.31084 | −0.232248 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3994 | 1.03478 | 0.517390 | − | 0.855750i | \(-0.326904\pi\) | ||||
0.517390 | + | 0.855750i | \(0.326904\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4044i | 1.22225i | 0.791536 | + | 0.611123i | \(0.209282\pi\) | ||||
−0.791536 | + | 0.611123i | \(0.790718\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.16882 | − | 6.46012i | −0.602015 | − | 0.630443i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.51748i | − | 0.146700i | −0.997306 | − | 0.0733502i | \(-0.976631\pi\) | ||
0.997306 | − | 0.0733502i | \(-0.0233691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.86276 | −0.465767 | −0.232884 | − | 0.972505i | \(-0.574816\pi\) | ||||
−0.232884 | + | 0.972505i | \(0.574816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.66237 | 0.632364 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.72566i | 0.162337i | 0.996700 | + | 0.0811683i | \(0.0258651\pi\) | ||||
−0.996700 | + | 0.0811683i | \(0.974135\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.61718 | − | 1.54426i | 0.150803 | − | 0.144003i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.60596i | − | 0.518271i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.0937 | 1.20029 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.66001 | −0.514546 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.07468i | 0.0969006i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.43331 | + | 7.34025i | −0.754298 | + | 0.656532i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.1962i | 1.25971i | 0.776713 | + | 0.629855i | \(0.216886\pi\) | ||||
−0.776713 | + | 0.629855i | \(0.783114\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.5260 | 1.10285 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.34301 | −0.466821 | −0.233410 | − | 0.972378i | \(-0.574989\pi\) | ||||
−0.233410 | + | 0.972378i | \(0.574989\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.98129i | − | 0.518644i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.61718 | − | 1.54426i | 0.139185 | − | 0.132909i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.1842i | 1.55358i | 0.629759 | + | 0.776791i | \(0.283154\pi\) | ||||
−0.629759 | + | 0.776791i | \(0.716846\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.86064 | −0.157817 | −0.0789086 | − | 0.996882i | \(-0.525144\pi\) | ||||
−0.0789086 | + | 0.996882i | \(0.525144\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.43129 | −0.373182 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.9545i | 1.08331i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.96789 | + | 7.29692i | 0.578652 | + | 0.605977i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 8.95749i | − | 0.738801i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.33848 | −0.519268 | −0.259634 | − | 0.965707i | \(-0.583602\pi\) | ||||
−0.259634 | + | 0.965707i | \(0.583602\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.44809 | 0.606117 | 0.303058 | − | 0.952972i | \(-0.401992\pi\) | ||||
0.303058 | + | 0.952972i | \(0.401992\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.27777i | 0.264992i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.68916 | − | 3.86337i | −0.296320 | − | 0.310313i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.10147i | − | 0.407142i | −0.979060 | − | 0.203571i | \(-0.934745\pi\) | ||
0.979060 | − | 0.203571i | \(-0.0652547\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.01735 | −0.159986 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.99468 | 0.314825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.41321i | − | 0.345669i | −0.984951 | − | 0.172835i | \(-0.944707\pi\) | ||
0.984951 | − | 0.172835i | \(-0.0552927\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.73705 | + | 3.56853i | −0.290929 | + | 0.277810i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.3349i | 0.799739i | 0.916572 | + | 0.399869i | \(0.130945\pi\) | ||||
−0.916572 | + | 0.399869i | \(0.869055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.4268 | −1.41745 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.49731 | 0.114502 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.56659i | 0.727335i | 0.931529 | + | 0.363667i | \(0.118475\pi\) | ||||
−0.931529 | + | 0.363667i | \(0.881525\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.9522 | − | 0.920929i | −1.50824 | − | 0.0696157i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 13.1502i | − | 0.988432i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.9657 | 1.41757 | 0.708783 | − | 0.705427i | \(-0.249245\pi\) | ||||
0.708783 | + | 0.705427i | \(0.249245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.4964 | 1.82080 | 0.910401 | − | 0.413727i | \(-0.135773\pi\) | ||||
0.910401 | + | 0.413727i | \(0.135773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.1266i | 0.822503i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.7742 | − | 10.2884i | 0.792138 | − | 0.756419i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.57441i | − | 0.553896i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.99468 | 0.290570 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.3403 | 1.10998 | 0.554992 | − | 0.831856i | \(-0.312721\pi\) | ||||
0.554992 | + | 0.831856i | \(0.312721\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 11.4740i | − | 0.825915i | −0.910750 | − | 0.412958i | \(-0.864496\pi\) | ||
0.910750 | − | 0.412958i | \(-0.135504\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.65705 | − | 9.06585i | −0.619944 | − | 0.649219i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.8530i | − | 1.34322i | −0.740904 | − | 0.671611i | \(-0.765603\pi\) | ||
0.740904 | − | 0.671611i | \(-0.234397\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.3152 | −1.44011 | −0.720053 | − | 0.693919i | \(-0.755883\pi\) | ||||
−0.720053 | + | 0.693919i | \(0.755883\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.91149 | −0.699102 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.0245i | 1.26507i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.65958 | + | 1.73795i | 0.115910 | + | 0.121384i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.46005 | −0.239337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0136020 | −0.000936399 | −0.000468199 | − | 1.00000i | \(-0.500149\pi\) | ||||
−0.000468199 | 1.00000i | \(0.500149\pi\) | ||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.94360i | 0.338730i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.2567 | − | 19.3433i | 1.38150 | − | 1.31920i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.54311i | − | 0.647828i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.38340 | 0.296203 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.3751 | 1.23604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.61622i | − | 0.576985i | −0.957482 | − | 0.288493i | \(-0.906846\pi\) | ||
0.957482 | − | 0.288493i | \(-0.0931540\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.230539 | − | 4.99468i | 0.0153692 | − | 0.332979i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 16.2173i | − | 1.07638i | −0.842824 | − | 0.538190i | \(-0.819108\pi\) | ||
0.842824 | − | 0.538190i | \(-0.180892\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.2202 | −0.741450 | −0.370725 | − | 0.928743i | \(-0.620891\pi\) | ||||
−0.370725 | + | 0.928743i | \(0.620891\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.23108 | −0.607360 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.24723i | 0.0817090i | 0.999165 | + | 0.0408545i | \(0.0130080\pi\) | ||||
−0.999165 | + | 0.0408545i | \(0.986992\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.16619 | + | 6.84305i | −0.467471 | + | 0.446391i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 9.35481i | − | 0.607660i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.8930 | −0.898663 | −0.449332 | − | 0.893365i | \(-0.648338\pi\) | ||||
−0.449332 | + | 0.893365i | \(0.648338\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.1962 | 1.04329 | 0.521645 | − | 0.853163i | \(-0.325319\pi\) | ||||
0.521645 | + | 0.853163i | \(0.325319\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.8327 | − | 14.4859i | −0.883737 | − | 0.925468i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.39388i | − | 0.534090i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.95659 | −0.250739 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.451519 | −0.0284996 | −0.0142498 | − | 0.999898i | \(-0.504536\pi\) | ||||
−0.0142498 | + | 0.999898i | \(0.504536\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.31084i | − | 0.145281i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.06172 | + | 5.30074i | 0.316977 | + | 0.331945i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3.94554i | − | 0.246116i | −0.992399 | − | 0.123058i | \(-0.960730\pi\) | ||
0.992399 | − | 0.123058i | \(-0.0392701\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.6140 | 1.65372 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.51213 | −0.279294 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 21.7884i | − | 1.34353i | −0.740765 | − | 0.671764i | \(-0.765537\pi\) | ||
0.740765 | − | 0.671764i | \(-0.234463\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.26242 | + | 3.11531i | −0.200409 | + | 0.191372i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.6996i | 0.716002i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.3071 | 1.78688 | 0.893442 | − | 0.449179i | \(-0.148283\pi\) | ||||
0.893442 | + | 0.449179i | \(0.148283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.6009 | 0.947685 | 0.473842 | − | 0.880610i | \(-0.342867\pi\) | ||||
0.473842 | + | 0.880610i | \(0.342867\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 22.3940i | − | 1.35535i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.532739 | + | 11.5419i | −0.0321253 | + | 0.696004i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.76382i | − | 0.105977i | −0.998595 | − | 0.0529887i | \(-0.983125\pi\) | ||
0.998595 | − | 0.0529887i | \(-0.0168747\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.38895 | 0.143023 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.6750 | 1.71061 | 0.855305 | − | 0.518125i | \(-0.173370\pi\) | ||||
0.855305 | + | 0.518125i | \(0.173370\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.6822i | 1.40776i | 0.710319 | + | 0.703880i | \(0.248551\pi\) | ||||
−0.710319 | + | 0.703880i | \(0.751449\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.42142 | − | 2.31224i | 0.143433 | − | 0.136965i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.29300i | 0.253408i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.25621 | 0.368013 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.4888 | 0.966589 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.7897i | 1.91559i | 0.287444 | + | 0.957797i | \(0.407195\pi\) | ||||
−0.287444 | + | 0.957797i | \(0.592805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.3073 | − | 21.2663i | −1.18234 | − | 1.23817i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.31084i | − | 0.134089i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.60596 | 0.324201 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 50.0373 | 2.88410 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.3994i | 0.597431i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.1823 | + | 17.9937i | 0.983858 | + | 1.03032i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.50214i | − | 0.142804i | −0.997448 | − | 0.0714022i | \(-0.977253\pi\) | ||
0.997448 | − | 0.0714022i | \(-0.0227474\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.4044 | −0.705664 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.4641 | 1.89757 | 0.948787 | − | 0.315918i | \(-0.102312\pi\) | ||||
0.948787 | + | 0.315918i | \(0.102312\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 24.5389i | − | 1.38702i | −0.720446 | − | 0.693511i | \(-0.756063\pi\) | ||
0.720446 | − | 0.693511i | \(-0.243937\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.46012 | − | 6.16882i | 0.363986 | − | 0.347573i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 24.5232i | − | 1.37736i | −0.725066 | − | 0.688680i | \(-0.758191\pi\) | ||
0.725066 | − | 0.688680i | \(-0.241809\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.4268 | 0.583790 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.51748 | 0.0846975 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.90785i | 0.273080i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28.0000 | − | 1.29239i | −1.55316 | − | 0.0716890i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 4.86276i | − | 0.268911i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.7016 | −0.975920 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.00518 | −0.165179 | −0.0825897 | − | 0.996584i | \(-0.526319\pi\) | ||||
−0.0825897 | + | 0.996584i | \(0.526319\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.66237i | 0.365095i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.0287 | + | 15.3059i | −0.875739 | + | 0.836250i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.83422i | 0.0999162i | 0.998751 | + | 0.0499581i | \(0.0159088\pi\) | ||||
−0.998751 | + | 0.0499581i | \(0.984091\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.72566 | −0.0937250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.52049 | −0.298951 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 7.81954i | − | 0.422215i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.54426 | + | 1.61718i | 0.0831400 | + | 0.0870660i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 19.7001i | − | 1.05756i | −0.848759 | − | 0.528779i | \(-0.822650\pi\) | ||
0.848759 | − | 0.528779i | \(-0.177350\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.1625 | −1.02575 | −0.512874 | − | 0.858464i | \(-0.671419\pi\) | ||||
−0.512874 | + | 0.858464i | \(0.671419\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.60596 | 0.299224 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.9329i | 1.16737i | 0.811979 | + | 0.583686i | \(0.198390\pi\) | ||||
−0.811979 | + | 0.583686i | \(0.801610\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.63418 | + | 7.99468i | 0.405180 | + | 0.424314i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.0937i | 0.692990i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.0257 | 0.634693 | 0.317347 | − | 0.948310i | \(-0.397208\pi\) | ||||
0.317347 | + | 0.948310i | \(0.397208\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7581 | −0.882003 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 5.66001i | − | 0.297074i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.08875 | − | 6.76910i | 0.371042 | − | 0.354311i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.39198i | − | 0.177060i | −0.996074 | − | 0.0885298i | \(-0.971783\pi\) | ||
0.996074 | − | 0.0885298i | \(-0.0282169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.07468 | −0.0559456 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.05867 | −0.418385 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 14.4907i | − | 0.750299i | −0.926964 | − | 0.375150i | \(-0.877591\pi\) | ||
0.926964 | − | 0.375150i | \(-0.122409\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.34025 | − | 8.43331i | −0.379049 | − | 0.435494i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.2948i | 1.30275i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.2473 | 0.526366 | 0.263183 | − | 0.964746i | \(-0.415228\pi\) | ||||
0.263183 | + | 0.964746i | \(0.415228\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.1962 | −0.727294 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 21.0326i | − | 1.07471i | −0.843355 | − | 0.537357i | \(-0.819423\pi\) | ||
0.843355 | − | 0.537357i | \(-0.180577\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.9283 | + | 14.2552i | −0.760817 | + | 0.726510i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.5260i | 0.636731i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.4421 | −0.985754 | −0.492877 | − | 0.870099i | \(-0.664055\pi\) | ||||
−0.492877 | + | 0.870099i | \(0.664055\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.27777 | −0.165764 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5.34301i | − | 0.269519i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.4462 | − | 15.1284i | −0.726869 | − | 0.761192i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.53486i | − | 0.227598i | −0.993504 | − | 0.113799i | \(-0.963698\pi\) | ||
0.993504 | − | 0.113799i | \(-0.0363020\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.98129 | 0.299439 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.8076 | 1.33871 | 0.669353 | − | 0.742944i | \(-0.266571\pi\) | ||||
0.669353 | + | 0.742944i | \(0.266571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 13.3924i | − | 0.667122i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.54426 | + | 1.61718i | 0.0767348 | + | 0.0803583i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 15.3957i | − | 0.763135i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.5992 | 1.26580 | 0.632899 | − | 0.774234i | \(-0.281865\pi\) | ||||
0.632899 | + | 0.774234i | \(0.281865\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.1842 | −0.896961 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 52.5310i | − | 2.58488i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.39851 | + | 6.10999i | −0.314091 | + | 0.299928i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.86064i | − | 0.0911158i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.9334 | −1.80431 | −0.902157 | − | 0.431407i | \(-0.858017\pi\) | ||||
−0.902157 | + | 0.431407i | \(0.858017\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.4129 | 0.897391 | 0.448696 | − | 0.893685i | \(-0.351889\pi\) | ||||
0.448696 | + | 0.893685i | \(0.351889\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 4.43129i | − | 0.215457i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.3714 | + | 0.755653i | 0.794131 | + | 0.0366546i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 44.4473i | 2.15095i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.9545 | −0.625449 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.2149 | −1.55174 | −0.775869 | − | 0.630894i | \(-0.782688\pi\) | ||||
−0.775869 | + | 0.630894i | \(0.782688\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 38.7313i | − | 1.86131i | −0.365900 | − | 0.930654i | \(-0.619239\pi\) | ||
0.365900 | − | 0.930654i | \(-0.380761\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.29692 | + | 6.96789i | −0.349861 | + | 0.334085i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.49731i | 0.0716262i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.4945 | −0.596329 | −0.298165 | − | 0.954514i | \(-0.596374\pi\) | ||||
−0.298165 | + | 0.954514i | \(0.596374\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.95749 | 0.426547 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.8438i | 1.18036i | 0.807270 | + | 0.590182i | \(0.200944\pi\) | ||||
−0.807270 | + | 0.590182i | \(0.799056\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0671 | + | 18.9203i | 0.856464 | + | 0.896908i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 6.33848i | − | 0.299800i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.3084 | 0.675254 | 0.337627 | − | 0.941280i | \(-0.390376\pi\) | ||||
0.337627 | + | 0.941280i | \(0.390376\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.48341 | 0.116939 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.44809i | 0.349942i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −34.5822 | − | 36.2152i | −1.62124 | − | 1.69779i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.0544i | 1.40589i | 0.711247 | + | 0.702943i | \(0.248131\pi\) | ||||
−0.711247 | + | 0.702943i | \(0.751869\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.27777 | −0.152993 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.27280 | −0.199004 | −0.0995021 | − | 0.995037i | \(-0.531725\pi\) | ||||
−0.0995021 | + | 0.995037i | \(0.531725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 36.5765i | − | 1.69986i | −0.526899 | − | 0.849928i | \(-0.676646\pi\) | ||
0.526899 | − | 0.849928i | \(-0.323354\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.86337 | − | 3.68916i | 0.179159 | − | 0.171081i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.4252i | 1.59301i | 0.604634 | + | 0.796503i | \(0.293319\pi\) | ||||
−0.604634 | + | 0.796503i | \(0.706681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −39.5932 | −1.82825 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.10147 | 0.235063 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 28.9455i | − | 1.33092i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.345189 | − | 7.47860i | 0.0158383 | − | 0.343142i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2.01735i | − | 0.0923681i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.31790 | 0.425746 | 0.212873 | − | 0.977080i | \(-0.431718\pi\) | ||||
0.212873 | + | 0.977080i | \(0.431718\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.3490 | 1.70297 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.99468i | 0.181764i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.6653 | − | 25.4629i | 1.21081 | − | 1.15621i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.49269i | 0.248897i | 0.992226 | + | 0.124449i | \(0.0397162\pi\) | ||||
−0.992226 | + | 0.124449i | \(0.960284\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.41321 | 0.199572 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.97963 | 0.134469 | 0.0672344 | − | 0.997737i | \(-0.478582\pi\) | ||||
0.0672344 | + | 0.997737i | \(0.478582\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 14.7897i | − | 0.666096i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.56853 | − | 3.73705i | −0.160394 | − | 0.167968i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.7481i | 0.885823i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.38895 | −0.106944 | −0.0534721 | − | 0.998569i | \(-0.517029\pi\) | ||||
−0.0534721 | + | 0.998569i | \(0.517029\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.3349 | −0.461730 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.4790i | 1.13605i | 0.823010 | + | 0.568027i | \(0.192293\pi\) | ||||
−0.823010 | + | 0.568027i | \(0.807707\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.0594 | + | 16.8177i | 0.714632 | + | 0.748378i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 18.4268i | − | 0.818364i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.3695 | 0.503942 | 0.251971 | − | 0.967735i | \(-0.418921\pi\) | ||||
0.251971 | + | 0.967735i | \(0.418921\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.5103 | 0.774610 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.49731i | 0.0661080i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.0602 | + | 19.1556i | −0.883958 | + | 0.844099i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.2400i | 0.450355i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.56659 | −0.419927 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.6336 | 0.772543 | 0.386271 | − | 0.922385i | \(-0.373763\pi\) | ||||
0.386271 | + | 0.922385i | \(0.373763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.47209i | − | 0.151824i | −0.997115 | − | 0.0759120i | \(-0.975813\pi\) | ||
0.997115 | − | 0.0759120i | \(-0.0241868\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.920929 | − | 19.9522i | 0.0401926 | − | 0.870784i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.83044i | 0.341099i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.1502 | 0.570672 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.02461i | 0.260955i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.45404 | − | 2.34338i | 0.106097 | − | 0.101313i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.9657i | 0.818432i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.6993 | −0.891583 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.0785 | −1.85209 | −0.926046 | − | 0.377411i | \(-0.876814\pi\) | ||||
−0.926046 | + | 0.377411i | \(0.876814\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.4964i | 1.05124i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.50935 | − | 7.86395i | −0.321665 | − | 0.336855i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3.12643i | − | 0.133677i | −0.997764 | − | 0.0668383i | \(-0.978709\pi\) | ||
0.997764 | − | 0.0668383i | \(-0.0212912\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.1266 | −0.474872 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.75607 | −0.287818 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 37.3695i | − | 1.58911i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.2884 | + | 10.7742i | 0.436719 | + | 0.457341i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.9391i | 1.39567i | 0.716257 | + | 0.697837i | \(0.245854\pi\) | ||||
−0.716257 | + | 0.697837i | \(0.754146\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 70.2201 | 2.96999 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.57441 | 0.319792 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.4548i | 1.03065i | 0.856996 | + | 0.515324i | \(0.172328\pi\) | ||||
−0.856996 | + | 0.515324i | \(0.827672\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.79070 | + | 2.66486i | −0.117406 | + | 0.112112i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.99468i | 0.167761i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.16894 | 0.216693 | 0.108347 | − | 0.994113i | \(-0.465444\pi\) | ||||
0.108347 | + | 0.994113i | \(0.465444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.0392 | −0.713070 | −0.356535 | − | 0.934282i | \(-0.616042\pi\) | ||||
−0.356535 | + | 0.934282i | \(0.616042\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.3403i | 0.640849i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.99468 | + | 0.230539i | 0.208293 | + | 0.00961413i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.2584i | 1.59272i | 0.604824 | + | 0.796359i | \(0.293243\pi\) | ||||
−0.604824 | + | 0.796359i | \(0.706757\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.4740 | 0.476842 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.8053 | −0.655715 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.66178i | 0.193071i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.06585 | − | 8.65705i | 0.374827 | − | 0.357925i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 25.6094i | − | 1.05701i | −0.848929 | − | 0.528506i | \(-0.822752\pi\) | ||
0.848929 | − | 0.528506i | \(-0.177248\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.57701 | 0.147388 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.8530 | 0.775510 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 5.83920i | − | 0.239787i | −0.992787 | − | 0.119894i | \(-0.961745\pi\) | ||
0.992787 | − | 0.119894i | \(-0.0382553\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.2200 | + | 21.1748i | 0.828938 | + | 0.868082i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 20.3152i | − | 0.831446i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −43.4013 | −1.77333 | −0.886665 | − | 0.462413i | \(-0.846984\pi\) | ||||
−0.886665 | + | 0.462413i | \(0.846984\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.3983 | −1.44393 | −0.721964 | − | 0.691931i | \(-0.756760\pi\) | ||||
−0.721964 | + | 0.691931i | \(0.756760\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 9.91149i | − | 0.403627i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.74051 | − | 9.15325i | −0.355352 | − | 0.372133i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.9548i | 1.45936i | 0.683788 | + | 0.729681i | \(0.260331\pi\) | ||||
−0.683788 | + | 0.729681i | \(0.739669\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.0245 | −0.730391 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.8416 | −1.00499 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.70382i | 0.270765i | 0.990793 | + | 0.135382i | \(0.0432263\pi\) | ||||
−0.990793 | + | 0.135382i | \(0.956774\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.73795 | + | 1.65958i | −0.0700809 | + | 0.0669208i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.0722i | − | 0.486010i | −0.970025 | − | 0.243005i | \(-0.921867\pi\) | ||
0.970025 | − | 0.243005i | \(-0.0781332\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.3418 | 0.536254 | 0.268127 | − | 0.963384i | \(-0.413595\pi\) | ||||
0.268127 | + | 0.963384i | \(0.413595\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 46.7360i | 1.87244i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.8937 | − | 2.30294i | −0.995748 | − | 0.0921174i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 3.46005i | − | 0.138181i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.8377 | −0.870727 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.3182 | 1.20695 | 0.603474 | − | 0.797383i | \(-0.293783\pi\) | ||||
0.603474 | + | 0.797383i | \(0.293783\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 0.0136020i | − | 0.000540630i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.9578 | + | 21.9226i | −0.911053 | + | 0.869972i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 50.2153i | − | 1.98960i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.94360 | −0.195566 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.3840 | −1.16060 | −0.580299 | − | 0.814403i | \(-0.697064\pi\) | ||||
−0.580299 | + | 0.814403i | \(0.697064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.3568i | 1.31546i | 0.753252 | + | 0.657732i | \(0.228484\pi\) | ||||
−0.753252 | + | 0.657732i | \(0.771516\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.3433 | + | 20.2567i | 0.761642 | + | 0.797608i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 29.5633i | − | 1.16225i | −0.813814 | − | 0.581126i | \(-0.802612\pi\) | ||
0.813814 | − | 0.581126i | \(-0.197388\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.3881 | −1.19284 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.54311 | 0.374024 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 26.4562i | − | 1.03531i | −0.855589 | − | 0.517655i | \(-0.826805\pi\) | ||
0.855589 | − | 0.517655i | \(-0.173195\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.25098 | − | 8.64060i | −0.322392 | − | 0.337616i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.38340i | 0.171013i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.9043 | −1.24282 | −0.621408 | − | 0.783487i | \(-0.713439\pi\) | ||||
−0.621408 | + | 0.783487i | \(0.713439\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.3266 | 0.440553 | 0.220277 | − | 0.975437i | \(-0.429304\pi\) | ||||
0.220277 | + | 0.975437i | \(0.429304\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.3751i | 0.713628i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.67282 | − | 9.23665i | 0.375096 | − | 0.358182i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4.51213i | − | 0.174710i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.61622 | 0.333122 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.7118 | 0.992594 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15.1178i | − | 0.582749i | −0.956609 | − | 0.291375i | \(-0.905887\pi\) | ||
0.956609 | − | 0.291375i | \(-0.0941126\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.99468 | + | 0.230539i | 0.192245 | + | 0.00887344i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.77610i | 0.375726i | 0.982195 | + | 0.187863i | \(0.0601561\pi\) | ||||
−0.982195 | + | 0.187863i | \(0.939844\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 65.8674 | 2.52776 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.2173 | 0.621448 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 2.52943i | − | 0.0967861i | −0.998828 | − | 0.0483931i | \(-0.984590\pi\) | ||
0.998828 | − | 0.0483931i | \(-0.0154100\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.4071 | + | 28.0811i | −1.12359 | + | 1.07292i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 11.2202i | − | 0.428076i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.3092 | −0.430846 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.95336 | −0.226476 | −0.113238 | − | 0.993568i | \(-0.536122\pi\) | ||||
−0.113238 | + | 0.993568i | \(0.536122\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 9.23108i | − | 0.350660i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.87330 | − | 3.00898i | −0.108991 | − | 0.114137i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.52255i | − | 0.133426i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.24723 | −0.0471747 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0260 | −0.454215 | −0.227108 | − | 0.973870i | \(-0.572927\pi\) | ||||
−0.227108 | + | 0.973870i | \(0.572927\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.97565i | 0.376239i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.84305 | − | 7.16619i | −0.257724 | − | 0.269894i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 41.5423i | 1.56236i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.49518 | −0.281488 | −0.140744 | − | 0.990046i | \(-0.544949\pi\) | ||||
−0.140744 | + | 0.990046i | \(0.544949\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.35481 | 0.350833 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.38895i | 0.0894670i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.9497 | + | 20.0051i | −0.783476 | + | 0.748147i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 13.8930i | − | 0.518844i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.2523 | 1.38928 | 0.694639 | − | 0.719359i | \(-0.255564\pi\) | ||||
0.694639 | + | 0.719359i | \(0.255564\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −49.5518 | −1.84541 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.1962i | 0.602343i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.04022 | + | 22.5367i | −0.0386328 | + | 0.836990i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.5588i | 1.17045i | 0.810870 | + | 0.585226i | \(0.198994\pi\) | ||||
−0.810870 | + | 0.585226i | \(0.801006\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.0573 | −1.51856 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 3.54807i | − | 0.131051i | −0.997851 | − | 0.0655254i | \(-0.979128\pi\) | ||
0.997851 | − | 0.0655254i | \(-0.0208723\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.4859 | − | 13.8327i | 0.534319 | − | 0.510226i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.9039i | 0.843675i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.75173 | −0.174795 | −0.0873976 | − | 0.996174i | \(-0.527855\pi\) | ||||
−0.0873976 | + | 0.996174i | \(0.527855\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.39388 | 0.308357 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 31.7958i | − | 1.16647i | −0.812302 | − | 0.583237i | \(-0.801786\pi\) | ||
0.812302 | − | 0.583237i | \(-0.198214\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.78824 | − | 10.2505i | −0.358613 | − | 0.375548i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 3.95659i | − | 0.144764i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.06186 | 0.221495 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.7363 | −0.574225 | −0.287113 | − | 0.957897i | \(-0.592695\pi\) | ||||
−0.287113 | + | 0.957897i | \(0.592695\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 0.451519i | − | 0.0164543i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.5018 | + | 12.0449i | 0.418592 | + | 0.438359i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.2259i | 0.953198i | 0.879121 | + | 0.476599i | \(0.158131\pi\) | ||||
−0.879121 | + | 0.476599i | \(0.841869\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.31084 | 0.0838782 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.1436 | 1.34646 | 0.673228 | − | 0.739435i | \(-0.264907\pi\) | ||||
0.673228 | + | 0.739435i | \(0.264907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 19.4252i | − | 0.703238i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.30074 | + | 5.06172i | −0.191649 | + | 0.183007i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 73.7197i | − | 2.66187i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.4226 | 0.772519 | 0.386259 | − | 0.922390i | \(-0.373767\pi\) | ||||
0.386259 | + | 0.922390i | \(0.373767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.94554 | 0.142095 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 52.0313i | 1.87143i | 0.352751 | + | 0.935717i | \(0.385246\pi\) | ||||
−0.352751 | + | 0.935717i | \(0.614754\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.550746 | − | 11.9321i | 0.0197834 | − | 0.428612i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.6140i | 0.954773i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.60913 | −0.0576531 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4239 | 0.408778 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 4.51213i | − | 0.161250i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.25000 | − | 7.87799i | 0.294455 | − | 0.281177i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.3028i | 1.04453i | 0.852782 | + | 0.522266i | \(0.174913\pi\) | ||||
−0.852782 | + | 0.522266i | \(0.825087\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.7884 | 0.775686 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.89347 | −0.245103 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 62.3754i | 2.21501i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.11531 | − | 3.26242i | −0.110489 | − | 0.115706i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 25.3855i | − | 0.899200i | −0.893230 | − | 0.449600i | \(-0.851566\pi\) | ||
0.893230 | − | 0.449600i | \(-0.148434\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.5248 | 0.513849 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.6996 | −0.413384 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 10.1293i | − | 0.357457i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.16882 | + | 6.46012i | 0.217422 | + | 0.227689i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.3071i | 1.03166i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.0003 | −1.51181 | −0.755905 | − | 0.654681i | \(-0.772803\pi\) | ||||
−0.755905 | + | 0.654681i | \(0.772803\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0750 | −0.564470 | −0.282235 | − | 0.959345i | \(-0.591076\pi\) | ||||
−0.282235 | + | 0.959345i | \(0.591076\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.6009i | 0.547146i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.13696 | − | 6.81514i | 0.249997 | − | 0.238724i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.7553i | 0.656165i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 22.3940 | 0.782511 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.9668 | −0.696846 | −0.348423 | − | 0.937337i | \(-0.613283\pi\) | ||||
−0.348423 | + | 0.937337i | \(0.613283\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 22.9199i | − | 0.798939i | −0.916747 | − | 0.399469i | \(-0.869194\pi\) | ||
0.916747 | − | 0.399469i | \(-0.130806\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.5419 | − | 0.532739i | −0.401838 | − | 0.0185476i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 20.2103i | − | 0.702779i | −0.936229 | − | 0.351390i | \(-0.885709\pi\) | ||
0.936229 | − | 0.351390i | \(-0.114291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.7839 | −1.34702 | −0.673510 | − | 0.739178i | \(-0.735214\pi\) | ||||
−0.673510 | + | 0.739178i | \(0.735214\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.76382 | 0.0611861 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.3606i | 1.01728i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.7134 | + | 15.9598i | −0.578391 | + | 0.552310i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.38895i | 0.0825743i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.6947 | 1.61208 | 0.806040 | − | 0.591861i | \(-0.201607\pi\) | ||||
0.806040 | + | 0.591861i | \(0.201607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.64068 | −0.297954 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.6750i | 0.987621i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.4557 | − | 29.7995i | −0.978907 | − | 1.02513i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 22.6099i | − | 0.776887i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.6822 | −0.812771 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.66237 | −0.228383 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.3238i | 0.935549i | 0.883848 | + | 0.467775i | \(0.154944\pi\) | ||||
−0.883848 | + | 0.467775i | \(0.845056\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.31224 | + | 2.42142i | 0.0790768 | + | 0.0828110i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.8111i | 0.847530i | 0.905772 | + | 0.423765i | \(0.139292\pi\) | ||||
−0.905772 | + | 0.423765i | \(0.860708\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.1139 | −1.16395 | −0.581975 | − | 0.813207i | \(-0.697720\pi\) | ||||
−0.581975 | + | 0.813207i | \(0.697720\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.29300 | −0.146305 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 25.8989i | − | 0.881609i | −0.897603 | − | 0.440805i | \(-0.854693\pi\) | ||
0.897603 | − | 0.440805i | \(-0.145307\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.4709 | + | 14.7733i | −0.526026 | + | 0.502307i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.25621i | 0.212472i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.6175 | −0.733323 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −55.5634 | −1.88269 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.4888i | 0.558060i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.3220 | − | 33.6884i | −0.991264 | − | 1.13888i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.59319i | − | 0.0537980i | −0.999638 | − | 0.0268990i | \(-0.991437\pi\) | ||
0.999638 | − | 0.0268990i | \(-0.00856326\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.7897 | −1.10597 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.7424 | 1.54110 | 0.770551 | − | 0.637379i | \(-0.219981\pi\) | ||||
0.770551 | + | 0.637379i | \(0.219981\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 38.8682i | − | 1.30802i | −0.756487 | − | 0.654009i | \(-0.773086\pi\) | ||
0.756487 | − | 0.654009i | \(-0.226914\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.2663 | − | 20.3073i | 0.714859 | − | 0.682624i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 56.7934i | − | 1.90694i | −0.301495 | − | 0.953468i | \(-0.597486\pi\) | ||
0.301495 | − | 0.953468i | \(-0.402514\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −56.7093 | −1.90197 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.31084 | 0.0774161 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 6.63503i | − | 0.222033i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.2880 | + | 30.6710i | 0.978989 | + | 1.02522i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.60596i | 0.187178i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.7793 | −0.359509 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.61241 | 0.220291 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 50.0373i | 1.66514i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.8287 | + | 39.6151i | 1.25747 | + | 1.31685i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 38.7967i | − | 1.28822i | −0.764931 | − | 0.644112i | \(-0.777227\pi\) | ||
0.764931 | − | 0.644112i | \(-0.222773\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.3994 | −0.344927 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.2655 | 1.03587 | 0.517936 | − | 0.855419i | \(-0.326700\pi\) | ||||
0.517936 | + | 0.855419i | \(0.326700\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.14305i | 0.302591i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.9937 | + | 17.1823i | −0.594854 | + | 0.568031i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 21.3436i | − | 0.704828i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.1623 | 0.961976 | 0.480988 | − | 0.876727i | \(-0.340278\pi\) | ||||
0.480988 | + | 0.876727i | \(0.340278\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.50214 | 0.0824482 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.7136i | 0.912205i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.2764 | + | 1.53593i | 1.09412 | + | 0.0505012i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 12.4044i | − | 0.407415i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.4054 | 1.06319 | 0.531593 | − | 0.847000i | \(-0.321594\pi\) | ||||
0.531593 | + | 0.847000i | \(0.321594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.4122 | 0.439566 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.4641i | 1.09556i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.2492 | − | 11.6968i | 0.400591 | − | 0.382528i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 35.1464i | − | 1.14818i | −0.818792 | − | 0.574091i | \(-0.805356\pi\) | ||
0.818792 | − | 0.574091i | \(-0.194644\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.5389 | 0.800798 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.1574 | 0.331121 | 0.165561 | − | 0.986200i | \(-0.447057\pi\) | ||||
0.165561 | + | 0.986200i | \(0.447057\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.07468i | − | 0.0349964i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.16882 | + | 6.46012i | 0.200672 | + | 0.210148i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.8674i | 0.483126i | 0.970385 | + | 0.241563i | \(0.0776601\pi\) | ||||
−0.970385 | + | 0.241563i | \(0.922340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.5732 | 0.797679 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.5232 | 0.795219 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.40621i | − | 0.110338i | −0.998477 | − | 0.0551690i | \(-0.982430\pi\) | ||
0.998477 | − | 0.0551690i | \(-0.0175698\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.6893 | + | 24.8080i | 0.766569 | + | 0.802767i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.4268i | 0.337051i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −72.6401 | −2.34567 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.2929 | −0.815900 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.51748i | 0.0489001i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.5555 | − | 17.7188i | 0.597322 | − | 0.570388i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.5021i | 0.852251i | 0.904664 | + | 0.426126i | \(0.140122\pi\) | ||||
−0.904664 | + | 0.426126i | \(0.859878\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.90785 | −0.157663 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.8259 | −0.507878 | −0.253939 | − | 0.967220i | \(-0.581726\pi\) | ||||
−0.253939 | + | 0.967220i | \(0.581726\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 7.43265i | − | 0.238280i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.29239 | − | 28.0000i | 0.0413897 | − | 0.896718i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0343i | 0.576968i | 0.957485 | + | 0.288484i | \(0.0931512\pi\) | ||||
−0.957485 | + | 0.288484i | \(0.906849\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.0358 | 0.864069 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.86276 | 0.155256 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 42.4751i | − | 1.35475i | −0.735640 | − | 0.677373i | \(-0.763118\pi\) | ||
0.735640 | − | 0.677373i | \(-0.236882\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.4887 | − | 29.1139i | 0.971451 | − | 0.927646i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 17.7016i | − | 0.563448i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.5260 | −0.398303 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.8613 | −1.04387 | −0.521936 | − | 0.852985i | \(-0.674790\pi\) | ||||
−0.521936 | + | 0.852985i | \(0.674790\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 3.00518i | − | 0.0953664i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31.3719 | − | 32.8533i | −0.994556 | − | 1.04152i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.7690i | 0.562750i | 0.959598 | + | 0.281375i | \(0.0907904\pi\) | ||||
−0.959598 | + | 0.281375i | \(0.909210\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.66237 | −0.210788 |
(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 | 1380.2.f.b.829.13 | yes | 14 | |
3.2 | odd | 2 | 4140.2.f.c.829.3 | 14 | |||
5.2 | odd | 4 | 6900.2.a.bd.1.1 | 7 | |||
5.3 | odd | 4 | 6900.2.a.bc.1.7 | 7 | |||
5.4 | even | 2 | inner | 1380.2.f.b.829.6 | ✓ | 14 | |
15.14 | odd | 2 | 4140.2.f.c.829.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.f.b.829.6 | ✓ | 14 | 5.4 | even | 2 | inner | |
1380.2.f.b.829.13 | yes | 14 | 1.1 | even | 1 | trivial | |
4140.2.f.c.829.3 | 14 | 3.2 | odd | 2 | |||
4140.2.f.c.829.4 | 14 | 15.14 | odd | 2 | |||
6900.2.a.bc.1.7 | 7 | 5.3 | odd | 4 | |||
6900.2.a.bd.1.1 | 7 | 5.2 | odd | 4 |