Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(229,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.229");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.c (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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.14077504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 14x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.2 | ||
Root | \(-1.23277i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.229 |
Dual form | 380.2.c.b.229.5 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.62236i | − | 0.936672i | −0.883551 | − | 0.468336i | \(-0.844854\pi\) | ||
0.883551 | − | 0.468336i | \(-0.155146\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.92411 | + | 1.13921i | −0.860487 | + | 0.509472i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.74397i | 1.79305i | 0.442993 | + | 0.896525i | \(0.353917\pi\) | ||||
−0.442993 | + | 0.896525i | \(0.646083\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.367938 | 0.122646 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.48028 | 1.35085 | 0.675427 | − | 0.737426i | \(-0.263959\pi\) | ||||
0.675427 | + | 0.737426i | \(0.263959\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.843176i | − | 0.233855i | −0.993140 | − | 0.116928i | \(-0.962695\pi\) | ||
0.993140 | − | 0.116928i | \(-0.0373045\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.84822 | + | 3.12160i | 0.477208 | + | 0.805994i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.52315i | 1.33956i | 0.742559 | + | 0.669781i | \(0.233612\pi\) | ||||
−0.742559 | + | 0.669781i | \(0.766388\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.69643 | 1.67950 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.779187i | 0.162472i | 0.996695 | + | 0.0812358i | \(0.0258867\pi\) | ||||
−0.996695 | + | 0.0812358i | \(0.974113\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.40439 | − | 4.38394i | 0.480877 | − | 0.876788i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.46402i | − | 1.05155i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.6570 | 1.97895 | 0.989477 | − | 0.144691i | \(-0.0462189\pi\) | ||||
0.989477 | + | 0.144691i | \(0.0462189\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.65699 | −1.55484 | −0.777421 | − | 0.628981i | \(-0.783472\pi\) | ||||
−0.777421 | + | 0.628981i | \(0.783472\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 7.26864i | − | 1.26531i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.40439 | − | 9.12790i | −0.913508 | − | 1.54290i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.62236i | 0.266715i | 0.991068 | + | 0.133357i | \(0.0425758\pi\) | ||||
−0.991068 | + | 0.133357i | \(0.957424\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.36794 | −0.219045 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.73588 | 0.739620 | 0.369810 | − | 0.929107i | \(-0.379423\pi\) | ||||
0.369810 | + | 0.929107i | \(0.379423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.67504i | 1.47543i | 0.675112 | + | 0.737715i | \(0.264095\pi\) | ||||
−0.675112 | + | 0.737715i | \(0.735905\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.707953 | + | 0.419160i | −0.105535 | + | 0.0624847i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.18559i | 0.464666i | 0.972636 | + | 0.232333i | \(0.0746360\pi\) | ||||
−0.972636 | + | 0.232333i | \(0.925364\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.5052 | −2.21503 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.96056 | 1.25473 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.17922i | 0.848780i | 0.905479 | + | 0.424390i | \(0.139512\pi\) | ||||
−0.905479 | + | 0.424390i | \(0.860488\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.62054 | + | 5.10399i | −1.16239 | + | 0.688222i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.62236i | 0.214887i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.6964 | −1.52275 | −0.761373 | − | 0.648314i | \(-0.775474\pi\) | ||||
−0.761373 | + | 0.648314i | \(0.775474\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.48028 | 0.829715 | 0.414857 | − | 0.909886i | \(-0.363831\pi\) | ||||
0.414857 | + | 0.909886i | \(0.363831\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.74549i | 0.219911i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.960558 | + | 1.62236i | 0.119143 | + | 0.201229i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 14.8880i | − | 1.81885i | −0.415864 | − | 0.909427i | \(-0.636521\pi\) | ||
0.415864 | − | 0.909427i | \(-0.363479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.26412 | 0.152183 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.303566 | 0.0360266 | 0.0180133 | − | 0.999838i | \(-0.494266\pi\) | ||||
0.0180133 | + | 0.999838i | \(0.494266\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.0800i | − | 1.17978i | −0.807485 | − | 0.589888i | \(-0.799172\pi\) | ||
0.807485 | − | 0.589888i | \(-0.200828\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.11234 | − | 3.90079i | −0.821262 | − | 0.450424i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 21.2543i | 2.42215i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.76081 | −0.862312 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 0.779187i | − | 0.0855268i | −0.999085 | − | 0.0427634i | \(-0.986384\pi\) | ||
0.999085 | − | 0.0427634i | \(-0.0136162\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.29205 | − | 10.6271i | −0.682468 | − | 1.15268i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 17.2895i | − | 1.85363i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.69643 | 0.603821 | 0.301910 | − | 0.953336i | \(-0.402376\pi\) | ||||
0.301910 | + | 0.953336i | \(0.402376\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.0448i | 1.45638i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.92411 | − | 1.13921i | 0.197409 | − | 0.116881i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.17922i | − | 0.627404i | −0.949521 | − | 0.313702i | \(-0.898431\pi\) | ||
0.949521 | − | 0.313702i | \(-0.101569\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.64847 | 0.165677 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.36794 | 0.335122 | 0.167561 | − | 0.985862i | \(-0.446411\pi\) | ||||
0.167561 | + | 0.985862i | \(0.446411\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.71368i | − | 0.365919i | −0.983120 | − | 0.182960i | \(-0.941432\pi\) | ||
0.983120 | − | 0.182960i | \(-0.0585678\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.8088 | + | 8.76788i | −1.44519 | + | 0.855657i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.2031i | − | 0.986374i | −0.869923 | − | 0.493187i | \(-0.835832\pi\) | ||
0.869923 | − | 0.493187i | \(-0.164168\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.96056 | −0.283570 | −0.141785 | − | 0.989897i | \(-0.545284\pi\) | ||||
−0.141785 | + | 0.989897i | \(0.545284\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.63206 | 0.249824 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 7.08638i | − | 0.666631i | −0.942815 | − | 0.333315i | \(-0.891833\pi\) | ||
0.942815 | − | 0.333315i | \(-0.108167\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.887659 | − | 1.49924i | −0.0827747 | − | 0.139805i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.310237i | − | 0.0286814i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −26.2016 | −2.40190 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.07290 | 0.824809 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 7.68331i | − | 0.692781i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.367938 | + | 11.1743i | 0.0329094 | + | 0.999458i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.79817i | − | 0.869447i | −0.900564 | − | 0.434723i | \(-0.856846\pi\) | ||
0.900564 | − | 0.434723i | \(-0.143154\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.6964 | 1.38199 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.5841 | 1.09948 | 0.549739 | − | 0.835337i | \(-0.314727\pi\) | ||||
0.549739 | + | 0.835337i | \(0.314727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 4.74397i | − | 0.411354i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.22468 | + | 10.5134i | 0.535735 | + | 0.904846i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.89586i | − | 0.760024i | −0.924981 | − | 0.380012i | \(-0.875920\pi\) | ||
0.924981 | − | 0.380012i | \(-0.124080\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.25560 | −0.530593 | −0.265296 | − | 0.964167i | \(-0.585470\pi\) | ||||
−0.265296 | + | 0.964167i | \(0.585470\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.16819 | 0.435240 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3.77767i | − | 0.315904i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.5052 | + | 12.1406i | −1.70286 | + | 1.00822i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 25.1551i | 2.07476i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.48028 | −0.203192 | −0.101596 | − | 0.994826i | \(-0.532395\pi\) | ||||
−0.101596 | + | 0.994826i | \(0.532395\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.69643 | 0.300812 | 0.150406 | − | 0.988624i | \(-0.451942\pi\) | ||||
0.150406 | + | 0.988624i | \(0.451942\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.03218i | 0.164292i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.6570 | − | 9.86216i | 1.33792 | − | 0.792148i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 18.8479i | − | 1.50422i | −0.659035 | − | 0.752112i | \(-0.729035\pi\) | ||
0.659035 | − | 0.752112i | \(-0.270965\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.0249 | 0.795029 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.69643 | −0.291320 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.46554i | 0.193116i | 0.995327 | + | 0.0965580i | \(0.0307833\pi\) | ||||
−0.995327 | + | 0.0965580i | \(0.969217\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.28053 | + | 13.9856i | 0.644638 | + | 1.08878i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.49134i | 0.579697i | 0.957072 | + | 0.289849i | \(0.0936050\pi\) | ||||
−0.957072 | + | 0.289849i | \(0.906395\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2891 | 0.945312 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.367938 | −0.0281369 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 20.0653i | − | 1.52554i | −0.646673 | − | 0.762768i | \(-0.723840\pi\) | ||
0.646673 | − | 0.762768i | \(-0.276160\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.7973 | + | 11.4063i | 1.57212 | + | 0.862238i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.9759i | 1.42631i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.69643 | 0.276284 | 0.138142 | − | 0.990412i | \(-0.455887\pi\) | ||||
0.138142 | + | 0.990412i | \(0.455887\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 10.5134i | − | 0.777170i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.84822 | − | 3.12160i | −0.135884 | − | 0.229505i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.7453i | 1.80955i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 25.9211 | 1.88548 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.887659 | 0.0642288 | 0.0321144 | − | 0.999484i | \(-0.489776\pi\) | ||||
0.0321144 | + | 0.999484i | \(0.489776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.1581i | 1.37903i | 0.724271 | + | 0.689516i | \(0.242177\pi\) | ||||
−0.724271 | + | 0.689516i | \(0.757823\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.63206 | − | 1.55837i | 0.188486 | − | 0.111597i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.37271i | − | 0.240295i | −0.992756 | − | 0.120148i | \(-0.961663\pi\) | ||
0.992756 | − | 0.120148i | \(-0.0383368\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.58409 | −0.324958 | −0.162479 | − | 0.986712i | \(-0.551949\pi\) | ||||
−0.162479 | + | 0.986712i | \(0.551949\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24.1537 | −1.70367 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 50.5564i | 3.54836i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.11234 | + | 5.39517i | −0.636433 | + | 0.376815i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.286693i | 0.0199265i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.48028 | −0.309907 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.8817 | −1.02450 | −0.512248 | − | 0.858837i | \(-0.671187\pi\) | ||||
−0.512248 | + | 0.858837i | \(0.671187\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 0.492494i | − | 0.0337451i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.0219 | − | 18.6158i | −0.751690 | − | 1.26959i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 41.0685i | − | 2.78791i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.3534 | −1.10506 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.65699 | 0.313263 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7839i | 1.25786i | 0.777461 | + | 0.628931i | \(0.216507\pi\) | ||||
−0.777461 | + | 0.628931i | \(0.783493\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.884666 | − | 1.61302i | 0.0589777 | − | 0.107535i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.843176i | 0.0559636i | 0.999608 | + | 0.0279818i | \(0.00890804\pi\) | ||||
−0.999608 | + | 0.0279818i | \(0.991092\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.86273 | 0.321338 | 0.160669 | − | 0.987008i | \(-0.448635\pi\) | ||||
0.160669 | + | 0.987008i | \(0.448635\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 34.4822 | 2.26876 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.90268i | − | 0.321185i | −0.987021 | − | 0.160593i | \(-0.948659\pi\) | ||
0.987021 | − | 0.160593i | \(-0.0513405\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.62907 | − | 6.12943i | −0.236734 | − | 0.399840i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.48945i | 0.421535i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.20164 | 0.401151 | 0.200575 | − | 0.979678i | \(-0.435719\pi\) | ||||
0.200575 | + | 0.979678i | \(0.435719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.26412 | −0.210261 | −0.105130 | − | 0.994458i | \(-0.533526\pi\) | ||||
−0.105130 | + | 0.994458i | \(0.533526\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 3.80121i | − | 0.243848i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 29.8337 | − | 17.6637i | 1.90601 | − | 1.12849i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.843176i | 0.0536500i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.26412 | −0.0801106 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.4263 | 1.79425 | 0.897127 | − | 0.441773i | \(-0.145650\pi\) | ||||
0.897127 | + | 0.441773i | \(0.145650\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.49097i | 0.219476i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.2411 | + | 10.2080i | −1.07968 | + | 0.639249i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.55192i | 0.595832i | 0.954592 | + | 0.297916i | \(0.0962916\pi\) | ||||
−0.954592 | + | 0.297916i | \(0.903708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.69643 | −0.478233 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.92112 | 0.242711 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 9.54706i | − | 0.588697i | −0.955698 | − | 0.294349i | \(-0.904897\pi\) | ||
0.955698 | − | 0.294349i | \(-0.0951027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.03944 | − | 11.8895i | −0.432430 | − | 0.730365i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 9.24168i | − | 0.565582i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.3534 | 0.875144 | 0.437572 | − | 0.899183i | \(-0.355839\pi\) | ||||
0.437572 | + | 0.899183i | \(0.355839\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.1038 | −0.735254 | −0.367627 | − | 0.929973i | \(-0.619830\pi\) | ||||
−0.367627 | + | 0.929973i | \(0.619830\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 6.48945i | − | 0.392760i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.7723 | − | 19.6413i | 0.649596 | − | 1.18441i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3.59055i | − | 0.215735i | −0.994165 | − | 0.107868i | \(-0.965598\pi\) | ||
0.994165 | − | 0.107868i | \(-0.0344023\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.18524 | −0.190695 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.7069 | 1.59320 | 0.796599 | − | 0.604509i | \(-0.206631\pi\) | ||||
0.796599 | + | 0.604509i | \(0.206631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.4751i | − | 1.21712i | −0.793508 | − | 0.608559i | \(-0.791748\pi\) | ||
0.793508 | − | 0.608559i | \(-0.208252\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.84822 | − | 3.12160i | −0.109479 | − | 0.184908i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.4668i | 1.32618i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5052 | −0.794424 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0249 | −0.587672 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.1581i | 1.11923i | 0.828753 | + | 0.559615i | \(0.189051\pi\) | ||||
−0.828753 | + | 0.559615i | \(0.810949\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.5052 | − | 13.3247i | 1.31030 | − | 0.775796i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 24.4803i | − | 1.42049i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.656992 | 0.0379948 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −45.8981 | −2.64552 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 5.46402i | − | 0.313900i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.4688 | + | 7.38242i | −0.713959 | + | 0.422716i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.0495i | 1.82916i | 0.404404 | + | 0.914580i | \(0.367479\pi\) | ||||
−0.404404 | + | 0.914580i | \(0.632521\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.02493 | −0.342746 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.5301 | −1.16416 | −0.582079 | − | 0.813132i | \(-0.697760\pi\) | ||||
−0.582079 | + | 0.813132i | \(0.697760\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.7932i | 0.836163i | 0.908409 | + | 0.418082i | \(0.137297\pi\) | ||||
−0.908409 | + | 0.418082i | \(0.862703\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.98848 | − | 3.35851i | −0.112038 | − | 0.189230i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 16.9485i | − | 0.951925i | −0.879466 | − | 0.475962i | \(-0.842100\pi\) | ||
0.879466 | − | 0.475962i | \(-0.157900\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 47.7463 | 2.67328 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.5532 | −0.923908 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.52315i | − | 0.307316i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.69643 | − | 2.02732i | −0.205041 | − | 0.112456i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.80310i | 0.265612i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.1123 | −0.833170 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.1287 | −1.21631 | −0.608153 | − | 0.793820i | \(-0.708089\pi\) | ||||
−0.608153 | + | 0.793820i | \(0.708089\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.596929i | 0.0327115i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.9606 | + | 28.6461i | 0.926654 | + | 1.56510i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.9948i | 1.52498i | 0.647002 | + | 0.762488i | \(0.276022\pi\) | ||||
−0.647002 | + | 0.762488i | \(0.723978\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.4967 | −0.624414 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −38.7857 | −2.10037 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 40.3484i | − | 2.17861i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.43231 | + | 1.44011i | −0.130951 | + | 0.0775327i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 17.1024i | − | 0.918105i | −0.888409 | − | 0.459052i | \(-0.848189\pi\) | ||
0.888409 | − | 0.459052i | \(-0.151811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.2411 | 1.02995 | 0.514976 | − | 0.857205i | \(-0.327801\pi\) | ||||
0.514976 | + | 0.857205i | \(0.327801\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.60713 | −0.245910 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 7.42735i | − | 0.395318i | −0.980271 | − | 0.197659i | \(-0.936666\pi\) | ||
0.980271 | − | 0.197659i | \(-0.0633339\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.584094 | + | 0.345826i | −0.0310005 | + | 0.0183545i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 42.5086i | 2.24979i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.1767 | −1.48711 | −0.743555 | − | 0.668675i | \(-0.766862\pi\) | ||||
−0.743555 | + | 0.668675i | \(0.766862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 14.7195i | − | 0.772575i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.4833 | + | 19.3950i | 0.601062 | + | 1.01518i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 26.1165i | − | 1.36327i | −0.731692 | − | 0.681636i | \(-0.761269\pi\) | ||
0.731692 | − | 0.681636i | \(-0.238731\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.74251 | 0.0907115 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.3140 | −1.52191 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.438217i | 0.0226900i | 0.999936 | + | 0.0113450i | \(0.00361130\pi\) | ||||
−0.999936 | + | 0.0113450i | \(0.996389\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.1287 | − | 0.596929i | 0.936164 | − | 0.0308253i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.98572i | − | 0.462788i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.7753 | 0.707591 | 0.353795 | − | 0.935323i | \(-0.384891\pi\) | ||||
0.353795 | + | 0.935323i | \(0.384891\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8962 | −0.814386 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.3153i | 1.14026i | 0.821555 | + | 0.570130i | \(0.193107\pi\) | ||||
−0.821555 | + | 0.570130i | \(0.806893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.2132 | − | 40.8956i | −1.23402 | − | 2.08423i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.55982i | 0.180956i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.4263 | −0.731444 | −0.365722 | − | 0.930724i | \(-0.619178\pi\) | ||||
−0.365722 | + | 0.930724i | \(0.619178\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.30357 | −0.217641 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 20.4160i | − | 1.02985i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.69643 | − | 4.55685i | 0.387250 | − | 0.229280i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.4512i | − | 0.825662i | −0.910808 | − | 0.412831i | \(-0.864540\pi\) | ||
0.910808 | − | 0.412831i | \(-0.135460\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.69643 | −0.385304 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.96056 | 0.147843 | 0.0739216 | − | 0.997264i | \(-0.476449\pi\) | ||||
0.0739216 | + | 0.997264i | \(0.476449\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.29937i | 0.363608i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.9326 | − | 8.84121i | 0.742009 | − | 0.439323i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.26864i | 0.360293i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.0893 | −0.845012 | −0.422506 | − | 0.906360i | \(-0.638849\pi\) | ||||
−0.422506 | + | 0.906360i | \(0.638849\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.4323 | −0.711893 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 55.4875i | − | 2.73036i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.887659 | + | 1.49924i | 0.0435735 | + | 0.0735948i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.1489i | 0.496991i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.3929 | 0.751991 | 0.375995 | − | 0.926622i | \(-0.377301\pi\) | ||||
0.375995 | + | 0.926622i | \(0.377301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.4323 | −0.800862 | −0.400431 | − | 0.916327i | \(-0.631140\pi\) | ||||
−0.400431 | + | 0.916327i | \(0.631140\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.17210i | 0.0569895i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.2132 | + | 13.2798i | 1.17451 | + | 0.644165i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 30.7422i | 1.48772i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.12874 | −0.295899 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.1852 | 0.731447 | 0.365724 | − | 0.930724i | \(-0.380822\pi\) | ||||
0.365724 | + | 0.930724i | \(0.380822\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 23.4380i | − | 1.12636i | −0.826335 | − | 0.563179i | \(-0.809578\pi\) | ||
0.826335 | − | 0.563179i | \(-0.190422\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.6964 | + | 33.2669i | 0.944372 | + | 1.59503i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 0.779187i | − | 0.0372735i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.511196 | −0.0243980 | −0.0121990 | − | 0.999926i | \(-0.503883\pi\) | ||||
−0.0121990 | + | 0.999926i | \(0.503883\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.70496 | −0.271665 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.7834i | 0.939940i | 0.882682 | + | 0.469970i | \(0.155735\pi\) | ||||
−0.882682 | + | 0.469970i | \(0.844265\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.9606 | + | 6.48945i | −0.519580 | + | 0.307630i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.02391i | 0.190325i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.1682 | −1.47092 | −0.735459 | − | 0.677569i | \(-0.763033\pi\) | ||||
−0.735459 | + | 0.677569i | \(0.763033\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.2180 | 0.999119 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 5.99696i | − | 0.281762i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.69643 | + | 4.55685i | −0.360814 | + | 0.213629i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 7.20950i | − | 0.337246i | −0.985681 | − | 0.168623i | \(-0.946068\pi\) | ||
0.985681 | − | 0.168623i | \(-0.0539321\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 30.1786 | 1.40862 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.41591 | −0.252244 | −0.126122 | − | 0.992015i | \(-0.540253\pi\) | ||||
−0.126122 | + | 0.992015i | \(0.540253\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.73715i | − | 0.406050i | −0.979174 | − | 0.203025i | \(-0.934923\pi\) | ||
0.979174 | − | 0.203025i | \(-0.0650772\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.0000 | − | 27.0237i | −0.741982 | − | 1.25319i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 17.3584i | − | 0.803249i | −0.915804 | − | 0.401624i | \(-0.868446\pi\) | ||
0.915804 | − | 0.401624i | \(-0.131554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 70.6280 | 3.26130 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.5781 | −1.40896 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 43.3469i | 1.99309i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.40439 | + | 4.38394i | −0.110321 | + | 0.201149i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.27357i | 0.104100i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.44682 | −0.340254 | −0.170127 | − | 0.985422i | \(-0.554418\pi\) | ||||
−0.170127 | + | 0.985422i | \(0.554418\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.36794 | 0.0623726 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.99696i | 0.272871i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.03944 | + | 11.8895i | 0.319645 | + | 0.539874i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.15530i | 0.0976661i | 0.998807 | + | 0.0488330i | \(0.0155502\pi\) | ||||
−0.998807 | + | 0.0488330i | \(0.984450\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.3140 | 1.32292 | 0.661461 | − | 0.749980i | \(-0.269937\pi\) | ||||
0.661461 | + | 0.749980i | \(0.269937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 58.8602i | 2.65093i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.17183 | + | 1.87795i | −0.142563 | + | 0.0844078i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.44011i | 0.0645976i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.5696 | 1.05512 | 0.527560 | − | 0.849518i | \(-0.323107\pi\) | ||||
0.527560 | + | 0.849518i | \(0.323107\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.1537 | 0.542986 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.08297i | 0.404990i | 0.979283 | + | 0.202495i | \(0.0649049\pi\) | ||||
−0.979283 | + | 0.202495i | \(0.935095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.48028 | + | 3.83680i | −0.288369 | + | 0.170735i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 19.9373i | − | 0.885447i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.5112 | 0.820494 | 0.410247 | − | 0.911974i | \(-0.365442\pi\) | ||||
0.410247 | + | 0.911974i | \(0.365442\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 47.8192 | 2.11540 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.46402i | 0.241242i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.23067 | + | 7.14552i | 0.186425 | + | 0.314869i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.2723i | 0.627697i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.5532 | −1.42893 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.0893 | −1.09918 | −0.549591 | − | 0.835434i | \(-0.685216\pi\) | ||||
−0.549591 | + | 0.835434i | \(0.685216\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 28.5181i | − | 1.24701i | −0.781820 | − | 0.623504i | \(-0.785708\pi\) | ||
0.781820 | − | 0.623504i | \(-0.214292\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.5052 | − | 33.7407i | 0.807634 | − | 1.47256i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 47.8139i | − | 2.08281i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3929 | 0.973603 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.30357 | −0.186759 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.99318i | − | 0.172964i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.6235 | + | 19.6319i | 0.502529 | + | 0.848762i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 5.99696i | − | 0.258788i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −69.4677 | −2.99218 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.6485 | −0.672780 | −0.336390 | − | 0.941723i | \(-0.609206\pi\) | ||||
−0.336390 | + | 0.941723i | \(0.609206\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.24473i | 0.139245i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.69643 | − | 3.37271i | 0.244008 | − | 0.144471i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.8543i | 0.464098i | 0.972704 | + | 0.232049i | \(0.0745429\pi\) | ||||
−0.972704 | + | 0.232049i | \(0.925457\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.38434 | 0.101761 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.6570 | −0.454003 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 18.9759i | − | 0.806936i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.06437 | + | 2.99848i | −0.214971 | + | 0.127278i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 18.8763i | − | 0.799814i | −0.916556 | − | 0.399907i | \(-0.869042\pi\) | ||
0.916556 | − | 0.399907i | \(-0.130958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.15777 | 0.345037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.1458 | 1.69496 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 22.2846i | − | 0.939183i | −0.882884 | − | 0.469591i | \(-0.844401\pi\) | ||
0.882884 | − | 0.469591i | \(-0.155599\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.07290 | + | 13.6350i | 0.339629 | + | 0.573627i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 36.8170i | − | 1.54617i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.11833 | 0.298416 | 0.149208 | − | 0.988806i | \(-0.452328\pi\) | ||||
0.149208 | + | 0.988806i | \(0.452328\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.21017 | 0.0506440 | 0.0253220 | − | 0.999679i | \(-0.491939\pi\) | ||||
0.0253220 | + | 0.999679i | \(0.491939\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.44011i | − | 0.0601613i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.41591 | + | 1.87347i | 0.142453 | + | 0.0781289i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.4143i | 1.72410i | 0.506823 | + | 0.862050i | \(0.330820\pi\) | ||||
−0.506823 | + | 0.862050i | \(0.669180\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 31.0814 | 1.29170 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.69643 | 0.153354 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.6846i | 1.14658i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.353426 | + | 0.596929i | 0.0146124 | + | 0.0246800i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.0591336i | 0.00244071i | 0.999999 | + | 0.00122035i | \(0.000388450\pi\) | ||||
−0.999999 | + | 0.00122035i | \(0.999612\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.65699 | 0.356705 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.47175 | −0.225078 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.8828i | 1.76099i | 0.474059 | + | 0.880493i | \(0.342788\pi\) | ||||
−0.474059 | + | 0.880493i | \(0.657212\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 50.4148 | − | 29.8493i | 2.06681 | − | 1.22370i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.43706i | 0.304379i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.3430 | −0.626898 | −0.313449 | − | 0.949605i | \(-0.601485\pi\) | ||||
−0.313449 | + | 0.949605i | \(0.601485\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5781 | −0.513072 | −0.256536 | − | 0.966535i | \(-0.582581\pi\) | ||||
−0.256536 | + | 0.966535i | \(0.582581\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 5.47785i | − | 0.223075i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.4572 | + | 10.3360i | −0.709738 | + | 0.420217i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.65751i | − | 0.107865i | −0.998545 | − | 0.0539325i | \(-0.982824\pi\) | ||
0.998545 | − | 0.0539325i | \(-0.0171756\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 82.0208 | 3.32365 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.68602 | 0.108665 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.1052i | 1.37750i | 0.725001 | + | 0.688748i | \(0.241839\pi\) | ||||
−0.725001 | + | 0.688748i | \(0.758161\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.75293 | + | 14.7835i | 0.352952 | + | 0.596129i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 29.9226i | − | 1.20464i | −0.798255 | − | 0.602319i | \(-0.794244\pi\) | ||
0.798255 | − | 0.602319i | \(-0.205756\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.2102 | −0.691735 | −0.345868 | − | 0.938283i | \(-0.612415\pi\) | ||||
−0.345868 | + | 0.938283i | \(0.612415\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.25749 | 0.170847 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.0237i | 1.08268i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.4378 | − | 21.0814i | −0.537514 | − | 0.843255i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.26864i | 0.290281i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.96056 | −0.357281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.36195 | −0.133837 | −0.0669186 | − | 0.997758i | \(-0.521317\pi\) | ||||
−0.0669186 | + | 0.997758i | \(0.521317\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.1435i | 0.959617i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.1622 | + | 18.8527i | 0.442958 | + | 0.748148i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.0736i | 0.517996i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.111693 | 0.00441853 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.2745 | −0.642806 | −0.321403 | − | 0.946943i | \(-0.604154\pi\) | ||||
−0.321403 | + | 0.946943i | \(0.604154\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.7040i | 1.40803i | 0.710185 | + | 0.704015i | \(0.248611\pi\) | ||||
−0.710185 | + | 0.704015i | \(0.751389\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.2016 | + | 17.8816i | −1.18919 | + | 0.704087i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 15.2881i | − | 0.601036i | −0.953776 | − | 0.300518i | \(-0.902840\pi\) | ||
0.953776 | − | 0.300518i | \(-0.0971595\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −52.4033 | −2.05701 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −66.6280 | −2.61136 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.4512i | 0.643785i | 0.946776 | + | 0.321892i | \(0.104319\pi\) | ||||
−0.946776 | + | 0.321892i | \(0.895681\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.2132 | + | 14.3360i | −0.946087 | + | 0.560152i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 3.70882i | − | 0.144695i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.03944 | −0.274218 | −0.137109 | − | 0.990556i | \(-0.543781\pi\) | ||||
−0.137109 | + | 0.990556i | \(0.543781\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.35343 | 0.247120 | 0.123560 | − | 0.992337i | \(-0.460569\pi\) | ||||
0.123560 | + | 0.992337i | \(0.460569\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 7.55533i | − | 0.293425i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.40439 | + | 9.12790i | 0.209573 | + | 0.353965i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.30378i | 0.321524i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 30.4743 | 1.17820 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.0335 | 1.12082 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.08638i | 0.273160i | 0.990629 | + | 0.136580i | \(0.0436111\pi\) | ||||
−0.990629 | + | 0.136580i | \(0.956389\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.9539 | − | 13.1376i | −0.921987 | − | 0.505667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.6095i | 0.676786i | 0.941005 | + | 0.338393i | \(0.109883\pi\) | ||||
−0.941005 | + | 0.338393i | \(0.890117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.3140 | 1.12497 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.36794 | 0.0524195 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 26.5855i | − | 1.01726i | −0.860984 | − | 0.508632i | \(-0.830151\pi\) | ||
0.860984 | − | 0.508632i | \(-0.169849\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.1343 | + | 17.1166i | 0.387211 | + | 0.653992i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.88911i | − | 0.300988i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.21017 | 0.198492 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.4907 | 1.88271 | 0.941357 | − | 0.337411i | \(-0.109551\pi\) | ||||
0.941357 | + | 0.337411i | \(0.109551\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.82027i | 0.297067i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.0364 | − | 7.12646i | 0.456569 | − | 0.270322i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.1570i | 0.990766i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.95392 | −0.300845 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.3389 | 1.10812 | 0.554058 | − | 0.832478i | \(-0.313079\pi\) | ||||
0.554058 | + | 0.832478i | \(0.313079\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.62236i | − | 0.0611886i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.94415 | + | 5.88767i | −0.374518 | + | 0.221742i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.9774i | 0.600891i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.7359 | −0.928975 | −0.464488 | − | 0.885580i | \(-0.653762\pi\) | ||||
−0.464488 | + | 0.885580i | \(0.653762\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.47175 | −0.0551951 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.74541i | − | 0.252618i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.30357 | + | 7.26864i | 0.160944 | + | 0.271832i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 10.0613i | − | 0.375747i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.7548 | −0.997786 | −0.498893 | − | 0.866663i | \(-0.666260\pi\) | ||||
−0.498893 | + | 0.866663i | \(0.666260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.6175 | 0.656112 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.29559i | 0.196945i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.6235 | − | 46.7196i | 0.951634 | − | 1.73512i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 27.2108i | − | 1.00919i | −0.863355 | − | 0.504596i | \(-0.831641\pi\) | ||
0.863355 | − | 0.504596i | \(-0.168359\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.4494 | −1.09072 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.4367 | −1.97643 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 40.0026i | − | 1.47753i | −0.673963 | − | 0.738765i | \(-0.735409\pi\) | ||
0.673963 | − | 0.738765i | \(-0.264591\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −28.6570 | − | 48.4011i | −1.05703 | − | 1.78530i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 66.7022i | − | 2.45701i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.1123 | −1.29163 | −0.645814 | − | 0.763495i | \(-0.723482\pi\) | ||||
−0.645814 | + | 0.763495i | \(0.723482\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.36794 | 0.0502525 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 25.6476i | − | 0.940918i | −0.882422 | − | 0.470459i | \(-0.844088\pi\) | ||
0.882422 | − | 0.470459i | \(-0.155912\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.77233 | − | 2.82557i | 0.174844 | − | 0.103521i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 0.286693i | − | 0.0104895i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.4033 | 1.76862 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.2641 | −0.484015 | −0.242007 | − | 0.970274i | \(-0.577806\pi\) | ||||
−0.242007 | + | 0.970274i | \(0.577806\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 46.1178i | − | 1.68063i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.11234 | + | 4.21103i | −0.258845 | + | 0.153255i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.77092i | 0.100711i | 0.998731 | + | 0.0503554i | \(0.0160354\pi\) | ||||
−0.998731 | + | 0.0503554i | \(0.983965\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.66363 | 0.205577 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.7838 | 0.390914 | 0.195457 | − | 0.980712i | \(-0.437381\pi\) | ||||
0.195457 | + | 0.980712i | \(0.437381\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 14.0448i | − | 0.508455i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.31508 | − | 3.91013i | −0.0837021 | − | 0.141371i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.86216i | 0.356102i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.6090 | 1.46440 | 0.732199 | − | 0.681090i | \(-0.238494\pi\) | ||||
0.732199 | + | 0.681090i | \(0.238494\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.4967 | 0.558099 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.4410i | 0.627310i | 0.949537 | + | 0.313655i | \(0.101554\pi\) | ||||
−0.949537 | + | 0.313655i | \(0.898446\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.8148 | + | 37.9517i | −0.747688 | + | 1.36327i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.4864i | 0.447947i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.73588 | −0.169680 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.36006 | 0.0486668 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 58.2300i | − | 2.08097i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.4718 | + | 36.2654i | 0.766360 | + | 1.29437i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.8346i | 1.09914i | 0.835449 | + | 0.549568i | \(0.185208\pi\) | ||||
−0.835449 | + | 0.549568i | \(0.814792\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.4888 | −0.551416 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.6175 | 1.19530 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.46402i | − | 0.194033i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.2891 | + | 11.4205i | −0.684112 | + | 0.405044i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 38.1340i | − | 1.35077i | −0.737463 | − | 0.675387i | \(-0.763976\pi\) | ||
0.737463 | − | 0.675387i | \(-0.236024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.5945 | −0.622449 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.09594 | 0.0740563 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 45.1612i | − | 1.59371i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.11234 | − | 4.21103i | 0.250677 | − | 0.148419i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 23.2865i | − | 0.819722i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.7917 | −1.08258 | −0.541290 | − | 0.840836i | \(-0.682064\pi\) | ||||
−0.541290 | + | 0.840836i | \(0.682064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.0275 | −0.668145 | −0.334072 | − | 0.942547i | \(-0.608423\pi\) | ||||
−0.334072 | + | 0.942547i | \(0.608423\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.6368i | 0.688692i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.80877 | − | 4.74397i | −0.0983871 | − | 0.166174i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 9.67504i | − | 0.338487i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.47175 | 0.0514272 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.1228 | −1.47009 | −0.735047 | − | 0.678016i | \(-0.762840\pi\) | ||||
−0.735047 | + | 0.678016i | \(0.762840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.6298i | 1.45112i | 0.688157 | + | 0.725562i | \(0.258420\pi\) | ||||
−0.688157 | + | 0.725562i | \(0.741580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −31.8653 | − | 17.4766i | −1.10941 | − | 0.608458i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.54814i | 0.262475i | 0.991351 | + | 0.131237i | \(0.0418950\pi\) | ||||
−0.991351 | + | 0.131237i | \(0.958105\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.6674 | −1.79448 | −0.897242 | − | 0.441540i | \(-0.854432\pi\) | ||||
−0.897242 | + | 0.441540i | \(0.854432\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.82518 | −0.202073 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 85.6376i | − | 2.96717i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.53423 | − | 14.4142i | −0.295339 | − | 0.498822i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 47.3020i | 1.63500i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.1682 | −1.55938 | −0.779689 | − | 0.626166i | \(-0.784623\pi\) | ||||
−0.779689 | + | 0.626166i | \(0.784623\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 84.5715 | 2.91626 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 43.3282i | − | 1.49230i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.6455 | + | 13.9998i | −0.813429 | + | 0.481609i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 43.0415i | 1.47892i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −33.2180 | −1.14004 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.26412 | −0.0433336 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 10.6721i | − | 0.365405i | −0.983168 | − | 0.182702i | \(-0.941515\pi\) | ||
0.983168 | − | 0.182702i | \(-0.0584845\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.707953 | − | 0.419160i | 0.0242115 | − | 0.0143350i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.7119i | 1.01494i | 0.861669 | + | 0.507470i | \(0.169419\pi\) | ||||
−0.861669 | + | 0.507470i | \(0.830581\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.6734 | 0.534769 | 0.267385 | − | 0.963590i | \(-0.413841\pi\) | ||||
0.267385 | + | 0.963590i | \(0.413841\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.4494 | 1.24219 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 39.5741i | − | 1.34712i | −0.739134 | − | 0.673559i | \(-0.764765\pi\) | ||
0.739134 | − | 0.673559i | \(-0.235235\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.8586 | + | 38.6078i | 0.777217 | + | 1.31270i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.9104i | 0.744115i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.9211 | −0.607932 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.5532 | −0.425348 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.27357i | − | 0.0769487i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −53.0104 | + | 1.74549i | −1.79208 | + | 0.0590082i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 47.9393i | − | 1.61880i | −0.587260 | − | 0.809398i | \(-0.699793\pi\) | ||
0.587260 | − | 0.809398i | \(-0.300207\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.0814 | 1.04835 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.32251 | −0.0782473 | −0.0391237 | − | 0.999234i | \(-0.512457\pi\) | ||||
−0.0391237 | + | 0.999234i | \(0.512457\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.3919i | 1.15738i | 0.815548 | + | 0.578690i | \(0.196436\pi\) | ||||
−0.815548 | + | 0.578690i | \(0.803564\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.6175 | − | 36.5116i | −0.726666 | − | 1.22732i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.1002i | 1.48074i | 0.672200 | + | 0.740370i | \(0.265350\pi\) | ||||
−0.672200 | + | 0.740370i | \(0.734650\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 46.4822 | 1.55896 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.7706 | −1.16486 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 3.18559i | − | 0.106602i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.11234 | + | 4.21103i | −0.237739 | + | 0.140759i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1.06588i | − | 0.0355887i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −92.2575 | −3.07696 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.1287 | −1.13699 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 74.4633i | 2.47798i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.84822 | − | 2.27843i | 0.127919 | − | 0.0757374i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 25.3706i | − | 0.842417i | −0.906964 | − | 0.421208i | \(-0.861606\pi\) | ||
0.906964 | − | 0.421208i | \(-0.138394\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.23919 | 0.0411015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.8252 | 0.988152 | 0.494076 | − | 0.869419i | \(-0.335506\pi\) | ||||
0.494076 | + | 0.869419i | \(0.335506\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 3.49097i | − | 0.115534i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.9770 | + | 20.2289i | 0.395946 | + | 0.668745i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 59.6985i | 1.97142i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.8422 | 0.522587 | 0.261293 | − | 0.965259i | \(-0.415851\pi\) | ||||
0.261293 | + | 0.965259i | \(0.415851\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51.9959 | 1.71332 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 0.255960i | − | 0.00842501i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.11234 | + | 3.90079i | 0.233852 | + | 0.128257i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1.36640i | − | 0.0448786i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.97098 | 0.261519 | 0.130760 | − | 0.991414i | \(-0.458258\pi\) | ||||
0.130760 | + | 0.991414i | \(0.458258\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.5052 | 0.508163 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.3073i | 1.09043i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −28.1901 | − | 47.6126i | −0.921916 | − | 1.55710i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 0.848033i | − | 0.0277040i | −0.999904 | − | 0.0138520i | \(-0.995591\pi\) | ||
0.999904 | − | 0.0138520i | \(-0.00440937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.0000 | 0.783210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.3140 | 1.02081 | 0.510403 | − | 0.859935i | \(-0.329496\pi\) | ||||
0.510403 | + | 0.859935i | \(0.329496\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.69013i | 0.120167i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −49.8750 | + | 29.5297i | −1.62244 | + | 0.960600i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.9885i | 0.844514i | 0.906476 | + | 0.422257i | \(0.138762\pi\) | ||||
−0.906476 | + | 0.422257i | \(0.861238\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.49922 | −0.275896 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.4967 | −0.891641 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.6347i | 1.34868i | 0.738421 | + | 0.674340i | \(0.235572\pi\) | ||||
−0.738421 | + | 0.674340i | \(0.764428\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.70795 | + | 1.01123i | −0.0552681 | + | 0.0327227i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 77.4618i | − | 2.50399i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.2016 | 1.36276 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.9435 | 1.41753 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 3.75412i | − | 0.120975i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.8252 | − | 36.8623i | −0.702577 | − | 1.18664i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 13.2656i | − | 0.426593i | −0.976988 | − | 0.213296i | \(-0.931580\pi\) | ||
0.976988 | − | 0.213296i | \(-0.0684200\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.96056 | −0.287855 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.3140 | 0.812364 | 0.406182 | − | 0.913792i | \(-0.366860\pi\) | ||||
0.406182 | + | 0.913792i | \(0.366860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 29.6763i | − | 0.951380i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.28905 | + | 5.99696i | −0.105334 | + | 0.192056i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.7694i | 1.62426i | 0.583479 | + | 0.812128i | \(0.301691\pi\) | ||||
−0.583479 | + | 0.812128i | \(0.698309\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.5216 | 0.815674 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.08930 | −0.0347788 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.4123i | 1.44843i | 0.689575 | + | 0.724214i | \(0.257797\pi\) | ||||
−0.689575 | + | 0.724214i | \(0.742203\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.84223 | + | 6.48945i | 0.122424 | + | 0.206771i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.5177i | 0.780407i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.53866 | −0.239716 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.6175 | 1.44909 | 0.724545 | − | 0.689228i | \(-0.242050\pi\) | ||||
0.724545 | + | 0.689228i | \(0.242050\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 35.9009i | 1.13928i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.82029 | − | 5.22226i | 0.279622 | − | 0.165557i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 59.5705i | − | 1.88662i | −0.331917 | − | 0.943309i | \(-0.607695\pi\) | ||
0.331917 | − | 0.943309i | \(-0.392305\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.86462 | 0.280464 |
(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 | 380.2.c.b.229.2 | ✓ | 6 | |
3.2 | odd | 2 | 3420.2.f.c.1369.5 | 6 | |||
4.3 | odd | 2 | 1520.2.d.i.609.5 | 6 | |||
5.2 | odd | 4 | 1900.2.a.k.1.2 | 6 | |||
5.3 | odd | 4 | 1900.2.a.k.1.5 | 6 | |||
5.4 | even | 2 | inner | 380.2.c.b.229.5 | yes | 6 | |
15.14 | odd | 2 | 3420.2.f.c.1369.6 | 6 | |||
20.3 | even | 4 | 7600.2.a.cj.1.2 | 6 | |||
20.7 | even | 4 | 7600.2.a.cj.1.5 | 6 | |||
20.19 | odd | 2 | 1520.2.d.i.609.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.c.b.229.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
380.2.c.b.229.5 | yes | 6 | 5.4 | even | 2 | inner | |
1520.2.d.i.609.2 | 6 | 20.19 | odd | 2 | |||
1520.2.d.i.609.5 | 6 | 4.3 | odd | 2 | |||
1900.2.a.k.1.2 | 6 | 5.2 | odd | 4 | |||
1900.2.a.k.1.5 | 6 | 5.3 | odd | 4 | |||
3420.2.f.c.1369.5 | 6 | 3.2 | odd | 2 | |||
3420.2.f.c.1369.6 | 6 | 15.14 | odd | 2 | |||
7600.2.a.cj.1.2 | 6 | 20.3 | even | 4 | |||
7600.2.a.cj.1.5 | 6 | 20.7 | even | 4 |