Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(113,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(8))
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("896.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.u (of order \(8\), degree \(4\), 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: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(13\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 113.4 | ||
Character | \(\chi\) | \(=\) | 896.113 |
Dual form | 896.2.u.c.785.4 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) |
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 | ||||||||
\(3\) | −0.694865 | − | 1.67755i | −0.401180 | − | 0.968535i | −0.987380 | − | 0.158369i | \(-0.949377\pi\) |
0.586200 | − | 0.810167i | \(-0.300623\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.286541 | − | 0.118689i | −0.128145 | − | 0.0530795i | 0.317689 | − | 0.948195i | \(-0.397093\pi\) |
−0.445835 | + | 0.895115i | \(0.647093\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.210023 | + | 0.210023i | −0.0700078 | + | 0.0700078i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.06259 | − | 2.56533i | 0.320384 | − | 0.773476i | −0.678847 | − | 0.734280i | \(-0.737520\pi\) |
0.999232 | − | 0.0391965i | \(-0.0124798\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.401442 | + | 0.166283i | −0.111340 | + | 0.0461185i | −0.437658 | − | 0.899142i | \(-0.644192\pi\) |
0.326318 | + | 0.945260i | \(0.394192\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.563161i | 0.145408i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.58480i | 0.384370i | 0.981359 | + | 0.192185i | \(0.0615573\pi\) | ||||
−0.981359 | + | 0.192185i | \(0.938443\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.27546 | − | 3.01360i | 1.66911 | − | 0.691366i | 0.670389 | − | 0.742010i | \(-0.266127\pi\) |
0.998717 | + | 0.0506436i | \(0.0161272\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.694865 | − | 1.67755i | 0.151632 | − | 0.366072i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.26201 | + | 1.26201i | −0.263147 | + | 0.263147i | −0.826331 | − | 0.563184i | \(-0.809576\pi\) |
0.563184 | + | 0.826331i | \(0.309576\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.46752 | − | 3.46752i | −0.693503 | − | 0.693503i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.53439 | − | 1.87821i | −0.872644 | − | 0.361461i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.29808 | − | 7.96227i | −0.612438 | − | 1.47856i | −0.860314 | − | 0.509765i | \(-0.829732\pi\) |
0.247876 | − | 0.968792i | \(-0.420268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0589875 | 0.0105945 | 0.00529724 | − | 0.999986i | \(-0.498314\pi\) | ||||
0.00529724 | + | 0.999986i | \(0.498314\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.04183 | −0.877671 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.118689 | − | 0.286541i | −0.0200622 | − | 0.0484343i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.50897 | + | 0.625037i | 0.248074 | + | 0.102755i | 0.503256 | − | 0.864138i | \(-0.332135\pi\) |
−0.255182 | + | 0.966893i | \(0.582135\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.557896 | + | 0.557896i | 0.0893348 | + | 0.0893348i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.22267 | − | 2.22267i | 0.347122 | − | 0.347122i | −0.511914 | − | 0.859037i | \(-0.671063\pi\) |
0.859037 | + | 0.511914i | \(0.171063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.16639 | − | 2.81591i | 0.177873 | − | 0.429423i | −0.809647 | − | 0.586917i | \(-0.800342\pi\) |
0.987520 | + | 0.157494i | \(0.0503415\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0851079 | − | 0.0352528i | 0.0126871 | − | 0.00525518i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.51458i | 0.804385i | 0.915555 | + | 0.402192i | \(0.131752\pi\) | ||||
−0.915555 | + | 0.402192i | \(0.868248\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.65858 | − | 1.10122i | 0.372275 | − | 0.154202i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.25750 | + | 3.03587i | −0.172731 | + | 0.417009i | −0.986409 | − | 0.164306i | \(-0.947462\pi\) |
0.813679 | + | 0.581315i | \(0.197462\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.608955 | + | 0.608955i | −0.0821114 | + | 0.0821114i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.1109 | − | 10.1109i | −1.33922 | − | 1.33922i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.1068 | − | 4.18638i | −1.31579 | − | 0.545020i | −0.389224 | − | 0.921143i | \(-0.627257\pi\) |
−0.926570 | + | 0.376123i | \(0.877257\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.240133 | + | 0.579733i | 0.0307459 | + | 0.0742272i | 0.938507 | − | 0.345261i | \(-0.112210\pi\) |
−0.907761 | + | 0.419488i | \(0.862210\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.297018 | −0.0374207 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.134766 | 0.0167156 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.03571 | − | 14.5715i | −0.737379 | − | 1.78019i | −0.616246 | − | 0.787554i | \(-0.711347\pi\) |
−0.121133 | − | 0.992636i | \(-0.538653\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.99401 | + | 1.24016i | 0.360436 | + | 0.149298i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.06754 | − | 5.06754i | −0.601406 | − | 0.601406i | 0.339280 | − | 0.940686i | \(-0.389817\pi\) |
−0.940686 | + | 0.339280i | \(0.889817\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.46348 | + | 6.46348i | −0.756493 | + | 0.756493i | −0.975682 | − | 0.219190i | \(-0.929659\pi\) |
0.219190 | + | 0.975682i | \(0.429659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.40748 | + | 8.22639i | −0.393462 | + | 0.949902i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.56533 | − | 1.06259i | 0.292346 | − | 0.121094i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.34488i | − | 0.826363i | −0.910649 | − | 0.413182i | \(-0.864417\pi\) | ||
0.910649 | − | 0.413182i | \(-0.135583\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.80283i | 1.08920i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.41929 | − | 3.07317i | 0.814373 | − | 0.337324i | 0.0636756 | − | 0.997971i | \(-0.479718\pi\) |
0.750697 | + | 0.660646i | \(0.229718\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.188098 | − | 0.454110i | 0.0204021 | − | 0.0492551i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.0654 | + | 11.0654i | −1.18634 | + | 1.18634i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.60338 | − | 5.60338i | −0.593958 | − | 0.593958i | 0.344741 | − | 0.938698i | \(-0.387967\pi\) |
−0.938698 | + | 0.344741i | \(0.887967\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.401442 | − | 0.166283i | −0.0420825 | − | 0.0174312i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.0409884 | − | 0.0989547i | −0.00425030 | − | 0.0102611i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.44240 | −0.250585 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.6589 | 1.08225 | 0.541125 | − | 0.840942i | \(-0.317999\pi\) | ||||
0.541125 | + | 0.840942i | \(0.317999\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.315609 | + | 0.761949i | 0.0317199 | + | 0.0765787i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6268 | + | 4.81597i | 1.15691 | + | 0.479207i | 0.876844 | − | 0.480775i | \(-0.159645\pi\) |
0.280063 | + | 0.959982i | \(0.409645\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.2382 | + | 10.2382i | 1.00880 | + | 1.00880i | 0.999961 | + | 0.00883982i | \(0.00281384\pi\) |
0.00883982 | + | 0.999961i | \(0.497186\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.398215 | + | 0.398215i | −0.0388618 | + | 0.0388618i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.42716 | + | 10.6881i | −0.427989 | + | 1.03326i | 0.551935 | + | 0.833887i | \(0.313890\pi\) |
−0.979924 | + | 0.199370i | \(0.936110\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.9220 | − | 5.76668i | 1.33349 | − | 0.552348i | 0.401838 | − | 0.915711i | \(-0.368371\pi\) |
0.931648 | + | 0.363363i | \(0.118371\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.96570i | − | 0.281491i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.04001i | − | 0.756340i | −0.925736 | − | 0.378170i | \(-0.876553\pi\) | ||
0.925736 | − | 0.378170i | \(-0.123447\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.511404 | − | 0.211831i | 0.0476887 | − | 0.0197533i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0493889 | − | 0.119235i | 0.00456601 | − | 0.0110233i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.12062 | + | 1.12062i | −0.102727 | + | 0.102727i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.32636 | + | 2.32636i | 0.211488 | + | 0.211488i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.27309 | − | 2.18419i | −0.475459 | − | 0.196941i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.17548 | + | 2.83785i | 0.105138 | + | 0.253825i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.950863 | 0.0843754 | 0.0421877 | − | 0.999110i | \(-0.486567\pi\) | ||||
0.0421877 | + | 0.999110i | \(0.486567\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.53433 | −0.487270 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.54070 | + | 3.71958i | 0.134611 | + | 0.324981i | 0.976784 | − | 0.214228i | \(-0.0687235\pi\) |
−0.842172 | + | 0.539209i | \(0.818723\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.27546 | + | 3.01360i | 0.630863 | + | 0.261312i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.07637 | + | 1.07637i | 0.0926390 | + | 0.0926390i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.92167 | − | 8.92167i | 0.762230 | − | 0.762230i | −0.214495 | − | 0.976725i | \(-0.568811\pi\) |
0.976725 | + | 0.214495i | \(0.0688106\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.64625 | − | 3.97441i | 0.139633 | − | 0.337105i | −0.838557 | − | 0.544813i | \(-0.816600\pi\) |
0.978191 | + | 0.207708i | \(0.0666005\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.25100 | − | 3.83189i | 0.779075 | − | 0.322703i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.20652i | 0.100894i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.67297i | 0.221978i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.67755 | − | 0.694865i | 0.138362 | − | 0.0573115i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.15685 | + | 10.0355i | −0.340543 | + | 0.822142i | 0.657119 | + | 0.753787i | \(0.271775\pi\) |
−0.997661 | + | 0.0683551i | \(0.978225\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.51727 | − | 6.51727i | 0.530368 | − | 0.530368i | −0.390314 | − | 0.920682i | \(-0.627634\pi\) |
0.920682 | + | 0.390314i | \(0.127634\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.332844 | − | 0.332844i | −0.0269089 | − | 0.0269089i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.0169024 | − | 0.00700119i | −0.00135763 | − | 0.000562349i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.42079 | + | 3.43009i | 0.113391 | + | 0.273751i | 0.970380 | − | 0.241585i | \(-0.0776672\pi\) |
−0.856988 | + | 0.515336i | \(0.827667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.96663 | 0.473184 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.78475 | −0.140658 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.70768 | + | 16.1938i | 0.525386 | + | 1.26839i | 0.934517 | + | 0.355919i | \(0.115832\pi\) |
−0.409131 | + | 0.912476i | \(0.634168\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.44469 | + | 0.598412i | 0.112469 | + | 0.0465863i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.90516 | + | 8.90516i | 0.689102 | + | 0.689102i | 0.962033 | − | 0.272932i | \(-0.0879933\pi\) |
−0.272932 | + | 0.962033i | \(0.587993\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.05888 | + | 9.05888i | −0.696837 | + | 0.696837i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.895092 | + | 2.16094i | −0.0684494 | + | 0.165251i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.4231 | − | 8.45954i | 1.55274 | − | 0.643167i | 0.568933 | − | 0.822384i | \(-0.307356\pi\) |
0.983810 | + | 0.179217i | \(0.0573563\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.90381i | − | 0.370693i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19.8637i | 1.49304i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.69861 | + | 2.77466i | −0.500678 | + | 0.207388i | −0.618706 | − | 0.785623i | \(-0.712343\pi\) |
0.118028 | + | 0.993010i | \(0.462343\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.85410 | + | 16.5473i | −0.509461 | + | 1.22995i | 0.434733 | + | 0.900559i | \(0.356843\pi\) |
−0.944194 | + | 0.329389i | \(0.893157\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.805672 | − | 0.805672i | 0.0595570 | − | 0.0595570i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.358198 | − | 0.358198i | −0.0263352 | − | 0.0263352i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.06553 | + | 1.68400i | 0.297301 | + | 0.123146i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.87821 | − | 4.53439i | −0.136619 | − | 0.329829i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.2866 | −1.68496 | −0.842478 | − | 0.538730i | \(-0.818904\pi\) | ||||
−0.842478 | + | 0.538730i | \(0.818904\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.5900 | 0.762288 | 0.381144 | − | 0.924516i | \(-0.375530\pi\) | ||||
0.381144 | + | 0.924516i | \(0.375530\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0936439 | − | 0.226076i | −0.00670598 | − | 0.0161897i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.6629 | − | 5.65934i | −0.973438 | − | 0.403211i | −0.161447 | − | 0.986881i | \(-0.551616\pi\) |
−0.811991 | + | 0.583670i | \(0.801616\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.9071 | + | 18.9071i | 1.34029 | + | 1.34029i | 0.895769 | + | 0.444519i | \(0.146626\pi\) |
0.444519 | + | 0.895769i | \(0.353374\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.2504 | + | 20.2504i | −1.42835 | + | 1.42835i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.29808 | − | 7.96227i | 0.231480 | − | 0.558842i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.900693 | + | 0.373079i | −0.0629071 | + | 0.0260570i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.530102i | − | 0.0368446i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 21.8662i | − | 1.51252i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.4979 | − | 9.31893i | 1.54882 | − | 0.641542i | 0.565716 | − | 0.824600i | \(-0.308600\pi\) |
0.983102 | + | 0.183058i | \(0.0585997\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.97980 | + | 12.0223i | −0.341211 | + | 0.823755i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.668438 | + | 0.668438i | −0.0455871 | + | 0.0455871i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0417105 | + | 0.0417105i | 0.00283149 | + | 0.00283149i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.3341 | + | 6.35158i | 1.03618 | + | 0.429200i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.263524 | − | 0.636204i | −0.0177266 | − | 0.0427957i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.1991 | 1.28567 | 0.642834 | − | 0.766005i | \(-0.277758\pi\) | ||||
0.642834 | + | 0.766005i | \(0.277758\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.45652 | 0.0971012 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.57737 | + | 13.4650i | 0.370183 | + | 0.893701i | 0.993719 | + | 0.111906i | \(0.0356956\pi\) |
−0.623536 | + | 0.781795i | \(0.714304\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.5925 | − | 7.70125i | −1.22862 | − | 0.508913i | −0.328482 | − | 0.944510i | \(-0.606537\pi\) |
−0.900142 | + | 0.435597i | \(0.856537\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.56511 | − | 3.56511i | −0.234567 | − | 0.234567i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.44778 | − | 9.44778i | 0.618945 | − | 0.618945i | −0.326316 | − | 0.945261i | \(-0.605807\pi\) |
0.945261 | + | 0.326316i | \(0.105807\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.654522 | − | 1.58016i | 0.0426963 | − | 0.103078i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.3214 | + | 5.10370i | −0.800362 | + | 0.331521i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 29.8950i | − | 1.93375i | −0.255254 | − | 0.966874i | \(-0.582159\pi\) | ||
0.255254 | − | 0.966874i | \(-0.417841\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.5234i | 0.677874i | 0.940809 | + | 0.338937i | \(0.110067\pi\) | ||||
−0.940809 | + | 0.338937i | \(0.889933\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.84158 | − | 1.17702i | 0.182288 | − | 0.0755060i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.118689 | − | 0.286541i | 0.00758278 | − | 0.0183065i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.41957 | + | 2.41957i | −0.153953 | + | 0.153953i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.3108 | − | 10.3108i | −0.653421 | − | 0.653421i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.7000 | − | 4.84628i | −0.738495 | − | 0.305895i | −0.0184573 | − | 0.999830i | \(-0.505875\pi\) |
−0.720038 | + | 0.693935i | \(0.755875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.89646 | + | 4.57847i | 0.119230 | + | 0.287846i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.892496 | −0.0558902 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.39861 | 0.461513 | 0.230756 | − | 0.973012i | \(-0.425880\pi\) | ||||
0.230756 | + | 0.973012i | \(0.425880\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.625037 | + | 1.50897i | 0.0388379 | + | 0.0937630i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.36494 | + | 0.979589i | 0.146386 | + | 0.0606350i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.1801 | + | 14.1801i | 0.874385 | + | 0.874385i | 0.992947 | − | 0.118562i | \(-0.0378284\pi\) |
−0.118562 | + | 0.992947i | \(0.537828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.720651 | − | 0.720651i | 0.0442693 | − | 0.0442693i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.50637 | + | 13.2936i | −0.336985 | + | 0.813553i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.9345 | + | 9.91400i | −1.45931 | + | 0.604468i | −0.964394 | − | 0.264471i | \(-0.914803\pi\) |
−0.494920 | + | 0.868939i | \(0.664803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.7120i | 1.25816i | 0.777339 | + | 0.629082i | \(0.216569\pi\) | ||||
−0.777339 | + | 0.629082i | \(0.783431\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.788984i | 0.0477515i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.5799 | + | 5.21076i | −0.758595 | + | 0.314221i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.88572 | + | 9.38096i | −0.233470 | + | 0.563647i | −0.996581 | − | 0.0826204i | \(-0.973671\pi\) |
0.763111 | + | 0.646268i | \(0.223671\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.0123888 | + | 0.0123888i | −0.000741696 | + | 0.000741696i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.1224 | + | 19.1224i | 1.14075 | + | 1.14075i | 0.988314 | + | 0.152432i | \(0.0487104\pi\) |
0.152432 | + | 0.988314i | \(0.451290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.71215 | − | 2.36605i | −0.339552 | − | 0.140647i | 0.206391 | − | 0.978470i | \(-0.433828\pi\) |
−0.545942 | + | 0.837823i | \(0.683828\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.69714 | + | 4.09726i | 0.100530 | + | 0.242701i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.14333 | 0.185545 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4884 | 0.852260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.40651 | − | 17.8809i | −0.434177 | − | 1.04820i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.7513 | − | 9.42391i | −1.32915 | − | 0.550551i | −0.398735 | − | 0.917066i | \(-0.630551\pi\) |
−0.930412 | + | 0.366516i | \(0.880551\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.39914 | + | 2.39914i | 0.139683 | + | 0.139683i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.63644 | + | 9.63644i | −0.559163 | + | 0.559163i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.296773 | − | 0.716473i | 0.0171628 | − | 0.0414347i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.81591 | − | 1.16639i | 0.162307 | − | 0.0672296i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 22.8510i | − | 1.31275i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 0.194619i | − | 0.0111438i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.81779 | + | 1.99559i | −0.274966 | + | 0.113895i | −0.515905 | − | 0.856646i | \(-0.672544\pi\) |
0.240940 | + | 0.970540i | \(0.422544\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.0610 | − | 24.2893i | 0.572348 | − | 1.38177i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.8134 | + | 12.8134i | −0.726582 | + | 0.726582i | −0.969937 | − | 0.243356i | \(-0.921752\pi\) |
0.243356 | + | 0.969937i | \(0.421752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.20989 | − | 1.20989i | −0.0683871 | − | 0.0683871i | 0.672086 | − | 0.740473i | \(-0.265399\pi\) |
−0.740473 | + | 0.672086i | \(0.765399\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0851079 | + | 0.0352528i | 0.00479529 | + | 0.00198627i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.324788 | + | 0.784107i | 0.0182419 | + | 0.0440398i | 0.932738 | − | 0.360555i | \(-0.117413\pi\) |
−0.914496 | + | 0.404595i | \(0.867413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.9304 | −1.33984 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.0061 | 1.17245 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.77594 | + | 11.5301i | 0.265740 | + | 0.641553i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.96859 | + | 0.815418i | 0.109198 | + | 0.0452313i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.3478 | − | 19.3478i | −1.06994 | − | 1.06994i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.89940 | + | 3.89940i | −0.214981 | + | 0.214981i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.967319 | + | 2.33531i | −0.0531686 | + | 0.128360i | −0.948232 | − | 0.317579i | \(-0.897130\pi\) |
0.895063 | + | 0.445939i | \(0.147130\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.448192 | + | 0.185647i | −0.0245608 | + | 0.0101734i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.89171i | 0.267263i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.25318i | − | 0.286159i | −0.989711 | − | 0.143079i | \(-0.954300\pi\) | ||
0.989711 | − | 0.143079i | \(-0.0457004\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.4875 | + | 5.58672i | −0.732542 | + | 0.303429i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0626798 | − | 0.151323i | 0.00339430 | − | 0.00819457i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.710714 | − | 0.710714i | −0.0382635 | − | 0.0382635i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.2993 | + | 9.23669i | 1.19709 | + | 0.495851i | 0.890058 | − | 0.455847i | \(-0.150664\pi\) |
0.307033 | + | 0.951699i | \(0.400664\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.7749 | − | 28.4272i | −0.630298 | − | 1.52167i | −0.839249 | − | 0.543748i | \(-0.817005\pi\) |
0.208951 | − | 0.977926i | \(-0.432995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.13261 | 0.113830 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.78602 | 0.414408 | 0.207204 | − | 0.978298i | \(-0.433564\pi\) | ||||
0.207204 | + | 0.978298i | \(0.433564\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.850597 | + | 2.05352i | 0.0451450 | + | 0.108990i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.65858 | + | 1.10122i | 0.140707 | + | 0.0582827i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.7745 | − | 16.7745i | −0.885325 | − | 0.885325i | 0.108745 | − | 0.994070i | \(-0.465317\pi\) |
−0.994070 | + | 0.108745i | \(0.965317\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.4156 | − | 30.4156i | 1.60082 | − | 1.60082i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.28609 | − | 5.51911i | 0.119989 | − | 0.289678i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.61920 | − | 1.08491i | 0.137095 | − | 0.0567867i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.18075i | − | 0.218234i | −0.994029 | − | 0.109117i | \(-0.965198\pi\) | ||
0.994029 | − | 0.109117i | \(-0.0348022\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.933624i | 0.0486025i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.03587 | + | 1.25750i | −0.157615 | + | 0.0652861i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.80301 | + | 11.5955i | −0.248691 | + | 0.600392i | −0.998093 | − | 0.0617222i | \(-0.980341\pi\) |
0.749403 | + | 0.662114i | \(0.230341\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.94385 | − | 3.94385i | 0.203659 | − | 0.203659i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.64798 | + | 2.64798i | 0.136378 | + | 0.136378i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.48718 | − | 2.27286i | −0.281857 | − | 0.116749i | 0.237276 | − | 0.971442i | \(-0.423745\pi\) |
−0.519134 | + | 0.854693i | \(0.673745\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.660721 | − | 1.59512i | −0.0338498 | − | 0.0817206i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.7157 | −1.05852 | −0.529262 | − | 0.848459i | \(-0.677531\pi\) | ||||
−0.529262 | + | 0.848459i | \(0.677531\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.861192 | −0.0438904 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.346439 | + | 0.836377i | 0.0176105 | + | 0.0425154i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.5609 | − | 10.5877i | −1.29599 | − | 0.536815i | −0.375223 | − | 0.926935i | \(-0.622434\pi\) |
−0.920764 | + | 0.390119i | \(0.872434\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.00002 | − | 2.00002i | −0.101146 | − | 0.101146i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.16920 | − | 5.16920i | 0.260752 | − | 0.260752i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.871759 | + | 2.10461i | −0.0438629 | + | 0.105895i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.9912 | − | 4.96691i | 0.601820 | − | 0.249282i | −0.0609066 | − | 0.998143i | \(-0.519399\pi\) |
0.662727 | + | 0.748861i | \(0.269399\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 14.2990i | − | 0.715846i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0744i | 0.503094i | 0.967845 | + | 0.251547i | \(0.0809393\pi\) | ||||
−0.967845 | + | 0.251547i | \(0.919061\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0236801 | + | 0.00980861i | −0.00117959 | + | 0.000488601i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.16349 | − | 2.80892i | 0.0578144 | − | 0.139576i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.20685 | − | 3.20685i | 0.158958 | − | 0.158958i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.7261 | + | 20.7261i | 1.02484 | + | 1.02484i | 0.999684 | + | 0.0251572i | \(0.00800864\pi\) |
0.0251572 | + | 0.999684i | \(0.491991\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.1659 | − | 8.76722i | −1.04404 | − | 0.432455i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.18638 | − | 10.1068i | −0.205998 | − | 0.497323i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.49069 | −0.122263 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.81120 | −0.382516 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.64415 | + | 3.96932i | 0.0803218 | + | 0.193914i | 0.958939 | − | 0.283613i | \(-0.0915332\pi\) |
−0.878617 | + | 0.477527i | \(0.841533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.7236 | + | 11.0693i | 1.30243 | + | 0.539484i | 0.922666 | − | 0.385599i | \(-0.126005\pi\) |
0.379764 | + | 0.925084i | \(0.376005\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.15819 | − | 1.15819i | −0.0563132 | − | 0.0563132i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.49531 | − | 5.49531i | 0.266561 | − | 0.266561i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.240133 | + | 0.579733i | −0.0116209 | + | 0.0280552i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.02400 | − | 0.838369i | 0.0977198 | − | 0.0404769i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8.46979i | − | 0.407975i | −0.978973 | − | 0.203988i | \(-0.934610\pi\) | ||
0.978973 | − | 0.203988i | \(-0.0653902\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 41.2749i | − | 1.98354i | −0.128017 | − | 0.991772i | \(-0.540861\pi\) | ||
0.128017 | − | 0.991772i | \(-0.459139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.48404 | − | 1.85735i | 0.214993 | − | 0.0890532i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.37851 | + | 12.9849i | −0.257289 | + | 0.621151i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.1447 | − | 28.1447i | 1.34327 | − | 1.34327i | 0.450497 | − | 0.892778i | \(-0.351247\pi\) |
0.892778 | − | 0.450497i | \(-0.148753\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.210023 | − | 0.210023i | −0.0100011 | − | 0.0100011i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.7826 | + | 7.78002i | 0.892390 | + | 0.369640i | 0.781289 | − | 0.624169i | \(-0.214562\pi\) |
0.111101 | + | 0.993809i | \(0.464562\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.940540 | + | 2.27066i | 0.0445859 | + | 0.107640i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.7236 | 0.932893 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.56124 | 0.309644 | 0.154822 | − | 0.987942i | \(-0.450520\pi\) | ||||
0.154822 | + | 0.987942i | \(0.450520\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.34008 | − | 8.06367i | −0.157278 | − | 0.379703i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.4617 | − | 6.40444i | −0.726453 | − | 0.300907i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0952937 | + | 0.0952937i | 0.00446744 | + | 0.00446744i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.5764 | + | 22.5764i | −1.05608 | + | 1.05608i | −0.0577483 | + | 0.998331i | \(0.518392\pi\) |
−0.998331 | + | 0.0577483i | \(0.981608\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.97658 | − | 7.18609i | 0.138935 | − | 0.335418i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.6098 | + | 13.0932i | −1.47222 | + | 0.609812i | −0.967364 | − | 0.253393i | \(-0.918454\pi\) |
−0.504854 | + | 0.863205i | \(0.668454\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.26935i | 0.198413i | 0.995067 | + | 0.0992067i | \(0.0316305\pi\) | ||||
−0.995067 | + | 0.0992067i | \(0.968370\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.0332195i | 0.00154052i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.1292 | − | 5.85251i | 0.653822 | − | 0.270822i | −0.0310145 | − | 0.999519i | \(-0.509874\pi\) |
0.684836 | + | 0.728697i | \(0.259874\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.03571 | − | 14.5715i | 0.278703 | − | 0.672849i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.76690 | − | 4.76690i | 0.219647 | − | 0.219647i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.98435 | − | 5.98435i | −0.275161 | − | 0.275161i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.6775 | − | 14.7781i | −1.63699 | − | 0.678065i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.373500 | − | 0.901708i | −0.0171014 | − | 0.0412864i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.7054 | 0.626217 | 0.313108 | − | 0.949717i | \(-0.398630\pi\) | ||||
0.313108 | + | 0.949717i | \(0.398630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.709698 | −0.0323594 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.24016 | + | 2.99401i | 0.0564292 | + | 0.136232i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.05422 | − | 1.26510i | −0.138685 | − | 0.0574453i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.3828 | + | 15.3828i | 0.697063 | + | 0.697063i | 0.963776 | − | 0.266713i | \(-0.0859375\pi\) |
−0.266713 | + | 0.963776i | \(0.585938\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.5050 | − | 22.5050i | 1.01771 | − | 1.01771i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.87621 | − | 6.94379i | 0.129802 | − | 0.313369i | −0.845595 | − | 0.533824i | \(-0.820754\pi\) |
0.975397 | + | 0.220456i | \(0.0707544\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.6186 | − | 5.22679i | 0.568312 | − | 0.235403i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 0.255789i | − | 0.0114969i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 7.16658i | − | 0.321465i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.9429 | + | 7.01799i | −0.758470 | + | 0.314168i | −0.728192 | − | 0.685373i | \(-0.759639\pi\) |
−0.0302776 | + | 0.999542i | \(0.509639\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.75098 | − | 21.1267i | 0.390965 | − | 0.943873i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.67325 | + | 4.67325i | −0.208370 | + | 0.208370i | −0.803574 | − | 0.595204i | \(-0.797071\pi\) |
0.595204 | + | 0.803574i | \(0.297071\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.75995 | − | 2.75995i | −0.122816 | − | 0.122816i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.4914 | + | 8.90205i | 0.954469 | + | 0.395354i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.28515 | + | 20.0021i | 0.367233 | + | 0.886578i | 0.994201 | + | 0.107534i | \(0.0342954\pi\) |
−0.626969 | + | 0.779044i | \(0.715705\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.14074 | −0.404362 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −38.6500 | −1.70644 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.71850 | − | 4.14884i | −0.0757264 | − | 0.182820i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.1467 | + | 5.85977i | 0.622172 | + | 0.257712i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.3826 | − | 28.3826i | −1.24586 | − | 1.24586i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.8777 | − | 19.8777i | 0.870857 | − | 0.870857i | −0.121709 | − | 0.992566i | \(-0.538838\pi\) |
0.992566 | + | 0.121709i | \(0.0388376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.8527 | + | 38.2718i | −0.693190 | + | 1.67351i | 0.0450633 | + | 0.998984i | \(0.485651\pi\) |
−0.738253 | + | 0.674524i | \(0.764349\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.22639 | + | 3.40748i | −0.359029 | + | 0.148715i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.0934833i | 0.00407219i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.8147i | 0.861508i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.00190 | − | 1.24343i | 0.130271 | − | 0.0539602i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.522681 | + | 1.26186i | −0.0226398 | + | 0.0546573i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.53713 | − | 2.53713i | 0.109690 | − | 0.109690i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.30926 | + | 9.30926i | 0.401724 | + | 0.401724i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.56533 | + | 1.06259i | 0.110497 | + | 0.0457692i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.4194 | − | 29.9831i | −0.533952 | − | 1.28907i | −0.928886 | − | 0.370365i | \(-0.879233\pi\) |
0.394934 | − | 0.918709i | \(-0.370767\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32.5216 | 1.39563 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.67367 | −0.200198 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.86098 | + | 23.8065i | 0.421625 | + | 1.01789i | 0.981868 | + | 0.189564i | \(0.0607076\pi\) |
−0.560243 | + | 0.828328i | \(0.689292\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.172191 | − | 0.0713238i | −0.00734893 | − | 0.00304403i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −47.9901 | − | 47.9901i | −2.04445 | − | 2.04445i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.19361 | − | 5.19361i | 0.220855 | − | 0.220855i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.351996 | + | 0.849795i | −0.0149414 | + | 0.0360718i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.4760 | + | 11.3809i | −1.16420 | + | 0.482226i | −0.879270 | − | 0.476323i | \(-0.841969\pi\) |
−0.284927 | + | 0.958549i | \(0.591969\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.32438i | 0.0560151i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 7.99028i | − | 0.337350i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.7852 | + | 9.43795i | −0.960282 | + | 0.397762i | −0.807086 | − | 0.590434i | \(-0.798957\pi\) |
−0.153196 | + | 0.988196i | \(0.548957\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.954263 | + | 2.30379i | −0.0401461 | + | 0.0969214i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.93165 | + | 6.93165i | −0.291102 | + | 0.291102i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.7197 | − | 14.7197i | −0.617080 | − | 0.617080i | 0.327701 | − | 0.944781i | \(-0.393726\pi\) |
−0.944781 | + | 0.327701i | \(0.893726\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.4362 | + | 7.63654i | 0.771533 | + | 0.319579i | 0.733493 | − | 0.679697i | \(-0.237889\pi\) |
0.0380396 | + | 0.999276i | \(0.487889\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.1810 | + | 39.0644i | 0.675972 | + | 1.63194i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.75206 | 0.364986 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.73589 | −0.155527 | −0.0777635 | − | 0.996972i | \(-0.524778\pi\) | ||||
−0.0777635 | + | 0.996972i | \(0.524778\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.35865 | − | 17.7653i | −0.305815 | − | 0.738302i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.41929 | + | 3.07317i | 0.307804 | + | 0.127497i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.45180 | + | 6.45180i | 0.267206 | + | 0.267206i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0283039 | + | 0.0283039i | −0.00117022 | + | 0.00117022i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.25930 | − | 7.86864i | 0.134526 | − | 0.324773i | −0.842234 | − | 0.539112i | \(-0.818760\pi\) |
0.976759 | + | 0.214339i | \(0.0687598\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.429162 | − | 0.177765i | 0.0176833 | − | 0.00732466i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.8526i | 1.10457i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 8.91561i | − | 0.366120i | −0.983102 | − | 0.183060i | \(-0.941400\pi\) | ||
0.983102 | − | 0.183060i | \(-0.0586003\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.454110 | − | 0.188098i | 0.0186167 | − | 0.00771128i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.5798 | − | 44.8555i | 0.760419 | − | 1.83581i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.4876 | − | 20.4876i | 0.837100 | − | 0.837100i | −0.151376 | − | 0.988476i | \(-0.548371\pi\) |
0.988476 | + | 0.151376i | \(0.0483706\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.48561 | + | 4.48561i | 0.182972 | + | 0.182972i | 0.792650 | − | 0.609678i | \(-0.208701\pi\) |
−0.609678 | + | 0.792650i | \(0.708701\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.32799 | + | 1.79271i | 0.176249 | + | 0.0730049i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.390485 | − | 0.942714i | −0.0158755 | − | 0.0383268i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.9396 | −0.484615 | −0.242307 | − | 0.970200i | \(-0.577904\pi\) | ||||
−0.242307 | + | 0.970200i | \(0.577904\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.6488 | −0.634123 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.916980 | − | 2.21378i | −0.0370970 | − | 0.0895602i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.9328 | + | 8.25643i | 0.805078 | + | 0.333474i | 0.746988 | − | 0.664837i | \(-0.231499\pi\) |
0.0580894 | + | 0.998311i | \(0.481499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.25172 | + | 1.25172i | 0.0504742 | + | 0.0504742i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.7234 | + | 22.7234i | −0.914808 | + | 0.914808i | −0.996646 | − | 0.0818380i | \(-0.973921\pi\) |
0.0818380 | + | 0.996646i | \(0.473921\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.70370 | + | 6.52730i | −0.108671 | + | 0.262354i | −0.968855 | − | 0.247629i | \(-0.920349\pi\) |
0.860184 | + | 0.509984i | \(0.170349\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.09275 | − | 3.35213i | 0.324751 | − | 0.134516i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 7.92438i | − | 0.317484i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.5664i | 0.942654i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −36.6817 | + | 15.1940i | −1.46492 | + | 0.606792i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.990556 | + | 2.39141i | −0.0394961 | + | 0.0953519i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.43447 | − | 3.43447i | 0.136724 | − | 0.136724i | −0.635432 | − | 0.772157i | \(-0.719178\pi\) |
0.772157 | + | 0.635432i | \(0.219178\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −31.2660 | − | 31.2660i | −1.24271 | − | 1.24271i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.272462 | − | 0.112857i | −0.0108123 | − | 0.00447860i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.166283 | − | 0.401442i | −0.00658836 | − | 0.0159057i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.12860 | 0.0842062 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.3679 | −0.685992 | −0.342996 | − | 0.939337i | \(-0.611442\pi\) | ||||
−0.342996 | + | 0.939337i | \(0.611442\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.1938 | − | 39.0954i | −0.638622 | − | 1.54177i | −0.828516 | − | 0.559966i | \(-0.810814\pi\) |
0.189893 | − | 0.981805i | \(-0.439186\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.58581 | + | 0.656865i | 0.0624413 | + | 0.0258641i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.10802 | − | 7.10802i | −0.279445 | − | 0.279445i | 0.553442 | − | 0.832888i | \(-0.313314\pi\) |
−0.832888 | + | 0.553442i | \(0.813314\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.4789 | + | 21.4789i | −0.843119 | + | 0.843119i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0409884 | − | 0.0989547i | 0.00160646 | − | 0.00387834i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.59052 | + | 2.72988i | −0.257907 | + | 0.106829i | −0.507891 | − | 0.861421i | \(-0.669575\pi\) |
0.249984 | + | 0.968250i | \(0.419575\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1.24868i | − | 0.0487898i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2.71496i | − | 0.105921i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.47271 | − | 3.50951i | 0.330050 | − | 0.136711i | −0.211504 | − | 0.977377i | \(-0.567836\pi\) |
0.541554 | + | 0.840666i | \(0.317836\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.0390952 | + | 0.0943841i | −0.00152063 | + | 0.00367111i | −0.924638 | − | 0.380847i | \(-0.875632\pi\) |
0.923117 | + | 0.384518i | \(0.125632\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.884151 | + | 0.884151i | −0.0343376 | + | 0.0343376i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.72704 | − | 1.72704i | −0.0669717 | − | 0.0669717i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.2106 | + | 5.88624i | 0.550239 | + | 0.227916i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.3408 | − | 32.2075i | −0.515785 | − | 1.24522i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.74237 | 0.0672634 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.92984 | 0.151484 | 0.0757421 | − | 0.997127i | \(-0.475867\pi\) | ||||
0.0757421 | + | 0.997127i | \(0.475867\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.21037 | + | 22.2358i | 0.354507 | + | 0.855856i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.1313 | − | 7.51024i | −0.696844 | − | 0.288642i | 0.00600459 | − | 0.999982i | \(-0.498089\pi\) |
−0.702848 | + | 0.711340i | \(0.748089\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.53700 | + | 7.53700i | 0.289243 | + | 0.289243i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.7127 | − | 18.7127i | 0.717071 | − | 0.717071i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.18867 | − | 5.28391i | 0.0837471 | − | 0.202183i | −0.876459 | − | 0.481477i | \(-0.840100\pi\) |
0.960206 | + | 0.279294i | \(0.0901004\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.61534 | + | 1.49752i | −0.138135 | + | 0.0572174i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.5411i | 1.39413i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.42783i | − | 0.0543959i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.9531 | − | 9.92169i | 0.911218 | − | 0.377439i | 0.122695 | − | 0.992444i | \(-0.460846\pi\) |
0.788523 | + | 0.615006i | \(0.210846\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.315609 | + | 0.761949i | −0.0119890 | + | 0.0289440i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.943440 | + | 0.943440i | −0.0357867 | + | 0.0357867i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.52247 | + | 3.52247i | 0.133423 | + | 0.133423i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.4141 | − | 9.28422i | −0.847778 | − | 0.351161i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.87457 | + | 19.0109i | 0.297418 | + | 0.718031i | 0.999979 | + | 0.00640805i | \(0.00203976\pi\) |
−0.702561 | + | 0.711623i | \(0.747960\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.8621 | 0.485103 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.10560 | −0.116964 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.81597 | + | 11.6268i | 0.181123 | + | 0.437270i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.4087 | + | 11.7673i | 1.06691 | + | 0.441929i | 0.845900 | − | 0.533342i | \(-0.179064\pi\) |
0.221012 | + | 0.975271i | \(0.429064\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.54260 | + | 1.54260i | 0.0578519 | + | 0.0578519i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.0744427 | + | 0.0744427i | −0.00278790 | + | 0.00278790i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.143201 | − | 0.345718i | 0.00535542 | − | 0.0129291i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −50.1505 | + | 20.7730i | −1.87290 | + | 0.775782i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.7491i | 0.848398i | 0.905569 | + | 0.424199i | \(0.139444\pi\) | ||||
−0.905569 | + | 0.424199i | \(0.860556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.4790i | 0.539227i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.6536 | − | 7.31237i | 0.656545 | − | 0.271950i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.1732 | + | 39.0454i | −0.600656 | + | 1.45011i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.54966 | + | 4.54966i | −0.168737 | + | 0.168737i | −0.786424 | − | 0.617687i | \(-0.788070\pi\) |
0.617687 | + | 0.786424i | \(0.288070\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.8459 | + | 16.8459i | 0.623923 | + | 0.623923i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.46265 | + | 1.84849i | 0.165057 | + | 0.0683689i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.9141 | + | 36.0057i | 0.550864 | + | 1.32990i | 0.916831 | + | 0.399275i | \(0.130738\pi\) |
−0.365968 | + | 0.930628i | \(0.619262\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.563161 | −0.0207725 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −43.7942 | −1.61318 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.49399 | − | 10.8494i | −0.165314 | − | 0.399103i | 0.819414 | − | 0.573202i | \(-0.194299\pi\) |
−0.984728 | + | 0.174099i | \(0.944299\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.74022 | + | 2.37768i | 0.210872 | + | 0.0873462i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.2587 | − | 27.2587i | −1.00003 | − | 1.00003i | −1.00000 | 2.62449e-5i | \(-0.999992\pi\) | |
−2.62449e−5 | − | 1.00000i | \(-0.500008\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.38222 | − | 2.38222i | 0.0872778 | − | 0.0872778i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.912786 | + | 2.20366i | −0.0333971 | + | 0.0806277i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.6881 | + | 4.42716i | −0.390535 | + | 0.161765i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.0673i | 1.09717i | 0.836095 | + | 0.548585i | \(0.184833\pi\) | ||||
−0.836095 | + | 0.548585i | \(0.815167\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.9948i | 0.837977i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.64100 | + | 1.09394i | −0.0961158 | + | 0.0398125i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.77290 | − | 16.3512i | 0.246165 | − | 0.594296i | −0.751707 | − | 0.659497i | \(-0.770769\pi\) |
0.997872 | + | 0.0652018i | \(0.0207691\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.36283 | − | 6.36283i | 0.230956 | − | 0.230956i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.7438 | + | 25.7438i | 0.933212 | + | 0.933212i | 0.997905 | − | 0.0646936i | \(-0.0206070\pi\) |
−0.0646936 | + | 0.997905i | \(0.520607\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.9220 | + | 5.76668i | 0.504010 | + | 0.208768i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0558686 | + | 0.134879i | 0.00201993 | + | 0.00487655i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.75342 | 0.171636 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.19445 | 0.0791339 | 0.0395669 | − | 0.999217i | \(-0.487402\pi\) | ||||
0.0395669 | + | 0.999217i | \(0.487402\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.14103 | − | 12.4116i | −0.185150 | − | 0.446991i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.7318 | + | 11.0727i | 0.961476 | + | 0.398256i | 0.807532 | − | 0.589823i | \(-0.200803\pi\) |
0.153944 | + | 0.988080i | \(0.450803\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.204540 | − | 0.204540i | −0.00734730 | − | 0.00734730i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.09706 | − | 2.09706i | 0.0752317 | − | 0.0752317i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.47271 | − | 22.8692i | 0.339395 | − | 0.819372i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.3846 | + | 7.61517i | −0.657854 | + | 0.272492i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.2985i | 1.51163i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.15150i | − | 0.0410986i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.67661 | − | 1.93712i | 0.166703 | − | 0.0690507i | −0.297771 | − | 0.954637i | \(-0.596243\pi\) |
0.464474 | + | 0.885587i | \(0.346243\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.9346 | − | 33.6412i | 0.496086 | − | 1.19766i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.68514 | − | 5.68514i | 0.202140 | − | 0.202140i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.192799 | − | 0.192799i | −0.00684649 | − | 0.00684649i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.70969 | − | 0.708175i | −0.0606363 | − | 0.0251164i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.4293 | + | 34.8354i | 0.511112 | + | 1.23393i | 0.943237 | + | 0.332120i | \(0.107764\pi\) |
−0.432125 | + | 0.901814i | \(0.642236\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.73949 | −0.309181 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.35368 | 0.0831633 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.71289 | + | 23.4490i | 0.342761 | + | 0.827497i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.511404 | + | 0.211831i | 0.0180246 | + | 0.00746605i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.2625 | + | 33.2625i | 1.17090 | + | 1.17090i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.5198 | − | 34.5198i | 1.21365 | − | 1.21365i | 0.243836 | − | 0.969816i | \(-0.421594\pi\) |
0.969816 | − | 0.243836i | \(-0.0784059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.88782 | − | 19.0429i | 0.276979 | − | 0.668686i | −0.722770 | − | 0.691088i | \(-0.757132\pi\) |
0.999749 | + | 0.0224024i | \(0.00713151\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.7455 | − | 14.3920i | 1.21858 | − | 0.504751i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 5.43632i | − | 0.190426i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 24.0021i | − | 0.839728i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.119235 | − | 0.0493889i | 0.00416642 | − | 0.00172579i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.0386 | − | 26.6495i | 0.385250 | − | 0.930076i | −0.605682 | − | 0.795707i | \(-0.707099\pi\) |
0.990931 | − | 0.134368i | \(-0.0429005\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.5633 | + | 17.5633i | −0.612216 | + | 0.612216i | −0.943523 | − | 0.331307i | \(-0.892511\pi\) |
0.331307 | + | 0.943523i | \(0.392511\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.4826 | + | 17.4826i | 0.608667 | + | 0.608667i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.69624 | + | 0.702605i | 0.0589840 | + | 0.0244320i | 0.411980 | − | 0.911193i | \(-0.364837\pi\) |
−0.352996 | + | 0.935625i | \(0.614837\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.6418 | − | 25.6915i | −0.369603 | − | 0.892302i | −0.993815 | − | 0.111047i | \(-0.964580\pi\) |
0.624212 | − | 0.781255i | \(-0.285420\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.4371 | 0.639576 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.58480 | −0.0549099 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.49475 | − | 3.60864i | −0.0517279 | − | 0.124882i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.267473 | − | 0.110791i | −0.00924521 | − | 0.00382949i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.5414 | + | 13.5414i | 0.467500 | + | 0.467500i | 0.901104 | − | 0.433604i | \(-0.142758\pi\) |
−0.433604 | + | 0.901104i | \(0.642758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −32.0143 | + | 32.0143i | −1.10394 | + | 1.10394i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.7913 | − | 45.3663i | 0.647207 | − | 1.56250i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.67094 | − | 1.52055i | 0.126284 | − | 0.0523086i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.28998i | 0.113045i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.2265i | 0.385293i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.69314 | + | 1.11553i | −0.0923195 | + | 0.0382400i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.32133 | − | 10.4326i | 0.147960 | − | 0.357206i | −0.832472 | − | 0.554067i | \(-0.813075\pi\) |
0.980431 | + | 0.196862i | \(0.0630750\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.512962 | − | 0.512962i | 0.0175429 | − | 0.0175429i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.0539 | + | 22.0539i | 0.753349 | + | 0.753349i | 0.975103 | − | 0.221754i | \(-0.0711782\pi\) |
−0.221754 | + | 0.975103i | \(0.571178\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.1538 | + | 9.59062i | 0.789997 | + | 0.327228i | 0.740943 | − | 0.671568i | \(-0.234379\pi\) |
0.0490549 | + | 0.998796i | \(0.484379\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.18419 | − | 5.27309i | −0.0744369 | − | 0.179707i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.96957 | 0.169166 | 0.0845830 | − | 0.996416i | \(-0.473044\pi\) | ||||
0.0845830 | + | 0.996416i | \(0.473044\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.85613 | −0.233116 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.0675 | − | 24.3051i | −0.341910 | − | 0.825444i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.8420 | − | 7.80463i | −0.639172 | − | 0.264754i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.84597 | + | 4.84597i | 0.164199 | + | 0.164199i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.23862 | + | 2.23862i | −0.0757659 | + | 0.0757659i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.17548 | + | 2.83785i | −0.0397383 | + | 0.0959369i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.6215 | − | 12.6839i | 1.03402 | − | 0.428304i | 0.199856 | − | 0.979825i | \(-0.435953\pi\) |
0.834160 | + | 0.551522i | \(0.185953\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 44.7149i | 1.50820i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.9074i | 0.670697i | 0.942094 | + | 0.335349i | \(0.108854\pi\) | ||||
−0.942094 | + | 0.335349i | \(0.891146\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.54376 | + | 3.53894i | −0.287521 | + | 0.119095i | −0.521782 | − | 0.853079i | \(-0.674733\pi\) |
0.234262 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.35760 | − | 5.69176i | 0.0792500 | − | 0.191326i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.05704 | + | 8.05704i | −0.270529 | + | 0.270529i | −0.829313 | − | 0.558784i | \(-0.811268\pi\) |
0.558784 | + | 0.829313i | \(0.311268\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.672361 | + | 0.672361i | 0.0225503 | + | 0.0225503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 25.1475 | + | 10.4164i | 0.842473 | + | 0.348964i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.6187 | + | 40.1212i | 0.556125 | + | 1.34260i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.24875 | 0.0751675 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.40814 | −0.0470163 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.194546 | − | 0.469675i | −0.00648846 | − | 0.0156645i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.81124 | − | 1.99288i | −0.160286 | − | 0.0663925i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.91336 | − | 3.91336i | −0.130228 | − | 0.130228i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.92797 | − | 3.92797i | 0.130570 | − | 0.130570i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.39566 | − | 13.0263i | 0.179160 | − | 0.432531i | −0.808631 | − | 0.588316i | \(-0.799791\pi\) |
0.987791 | + | 0.155786i | \(0.0497910\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.45336 | + | 1.43043i | −0.114541 | + | 0.0474443i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.0139i | 0.928141i | 0.885798 | + | 0.464071i | \(0.153612\pi\) | ||||
−0.885798 | + | 0.464071i | \(0.846388\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 22.2985i | − | 0.737971i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.326483 | + | 0.135234i | −0.0107932 | + | 0.00447069i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.54070 | + | 3.71958i | −0.0508784 | + | 0.122831i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.5061 | + | 18.5061i | −0.610461 | + | 0.610461i | −0.943066 | − | 0.332605i | \(-0.892072\pi\) |
0.332605 | + | 0.943066i | \(0.392072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.69543 | + | 6.69543i | 0.220622 | + | 0.220622i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.87696 | + | 1.19168i | 0.0946964 | + | 0.0392246i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.06506 | − | 7.39971i | −0.100779 | − | 0.243301i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.30053 | −0.141248 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.4795 | 1.62337 | 0.811685 | − | 0.584095i | \(-0.198550\pi\) | ||||
0.811685 | + | 0.584095i | \(0.198550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.01360 | + | 7.27546i | 0.0987666 | + | 0.238444i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.3987 | + | 12.5916i | 0.995210 | + | 0.412230i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.965069 | − | 0.965069i | −0.0315611 | − | 0.0315611i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.8520 | + | 23.8520i | −0.779212 | + | 0.779212i | −0.979697 | − | 0.200485i | \(-0.935748\pi\) |
0.200485 | + | 0.979697i | \(0.435748\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.18894 | + | 2.87037i | −0.0387997 | + | 0.0936709i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.35340 | − | 2.21745i | 0.174516 | − | 0.0722868i | −0.293715 | − | 0.955893i | \(-0.594892\pi\) |
0.468231 | + | 0.883606i | \(0.344892\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.61004i | 0.182688i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.52221i | 0.0495176i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.8691 | + | 11.5438i | −0.905624 | + | 0.375122i | −0.786380 | − | 0.617743i | \(-0.788047\pi\) |
−0.119244 | + | 0.992865i | \(0.538047\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.51995 | − | 3.66947i | 0.0493395 | − | 0.119116i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.08970 | − | 1.08970i | 0.0353358 | − | 0.0353358i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.9681 | − | 21.9681i | −0.711616 | − | 0.711616i | 0.255257 | − | 0.966873i | \(-0.417840\pi\) |
−0.966873 | + | 0.255257i | \(0.917840\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.67257 | + | 2.76387i | 0.215919 | + | 0.0894366i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.6284 | + | 40.1444i | 0.537519 | + | 1.29769i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.6172 | 0.407429 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9965 | −0.999888 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.31494 | − | 3.17456i | −0.0423735 | − | 0.102299i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.03448 | − | 1.25692i | −0.0976835 | − | 0.0404618i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.9430 | + | 23.9430i | 0.769956 | + | 0.769956i | 0.978098 | − | 0.208143i | \(-0.0667418\pi\) |
−0.208143 | + | 0.978098i | \(0.566742\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.0238 | − | 16.0238i | 0.514757 | − | 0.514757i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.212732 | − | 0.513581i | 0.00682690 | − | 0.0164816i | −0.920429 | − | 0.390909i | \(-0.872161\pi\) |
0.927256 | + | 0.374427i | \(0.122161\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.97441 | − | 1.64625i | 0.127414 | − | 0.0527765i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 3.86902i | − | 0.123908i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 27.3205i | − | 0.874061i | −0.899447 | − | 0.437031i | \(-0.856030\pi\) | ||
0.899447 | − | 0.437031i | \(-0.143970\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.3287 | + | 8.42040i | −0.649707 | + | 0.269117i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.71281 | + | 4.13508i | −0.0546857 | + | 0.132023i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.92072 | − | 4.92072i | 0.156947 | − | 0.156947i | −0.624266 | − | 0.781212i | \(-0.714602\pi\) |
0.781212 | + | 0.624266i | \(0.214602\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.24327 | + | 3.24327i | 0.103339 | + | 0.103339i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.25100 | + | 3.83189i | 0.294463 | + | 0.121970i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.08171 | + | 5.02570i | 0.0661946 | + | 0.159808i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.4505 | −1.38025 | −0.690126 | − | 0.723689i | \(-0.742445\pi\) | ||||
−0.690126 | + | 0.723689i | \(0.742445\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.58977 | 0.145652 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.17360 | − | 7.66174i | −0.100610 | − | 0.242893i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.2304 | − | 6.30863i | −0.482351 | − | 0.199796i | 0.128239 | − | 0.991743i | \(-0.459068\pi\) |
−0.610590 | + | 0.791947i | \(0.709068\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.66833 | − | 5.66833i | −0.179338 | − | 0.179338i |
(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 | 896.2.u.c.113.4 | 52 | ||
4.3 | odd | 2 | 224.2.u.c.197.12 | yes | 52 | ||
32.13 | even | 8 | inner | 896.2.u.c.785.4 | 52 | ||
32.19 | odd | 8 | 224.2.u.c.141.12 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.u.c.141.12 | ✓ | 52 | 32.19 | odd | 8 | ||
224.2.u.c.197.12 | yes | 52 | 4.3 | odd | 2 | ||
896.2.u.c.113.4 | 52 | 1.1 | even | 1 | trivial | ||
896.2.u.c.785.4 | 52 | 32.13 | even | 8 | inner |