Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(4409,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4410.4409");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.d (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: | \(35.2140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} - 6 x^{8} - 420 x^{7} + 4650 x^{6} - 21000 x^{5} + 70625 x^{4} - 168750 x^{3} + \cdots + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4409.8 | ||
Root | \(2.11423 - 0.728019i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.4409 |
Dual form | 4410.2.d.b.4409.7 |
$q$-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 \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.426635 | + | 2.19499i | −0.190797 | + | 0.981630i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.426635 | + | 2.19499i | −0.134914 | + | 0.694117i | ||||
\(11\) | 1.28310i | 0.386869i | 0.981113 | + | 0.193435i | \(0.0619627\pi\) | ||||
−0.981113 | + | 0.193435i | \(0.938037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.14864 | 1.70533 | 0.852663 | − | 0.522462i | \(-0.174986\pi\) | ||||
0.852663 | + | 0.522462i | \(0.174986\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 6.52257i | − | 1.58195i | −0.611846 | − | 0.790977i | \(-0.709573\pi\) | ||
0.611846 | − | 0.790977i | \(-0.290427\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.03756i | − | 1.38511i | −0.721365 | − | 0.692555i | \(-0.756485\pi\) | ||
0.721365 | − | 0.692555i | \(-0.243515\pi\) | |||||||
\(20\) | −0.426635 | + | 2.19499i | −0.0953985 | + | 0.490815i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.28310i | 0.273558i | ||||||||
\(23\) | 2.87917 | 0.600348 | 0.300174 | − | 0.953884i | \(-0.402955\pi\) | ||||
0.300174 | + | 0.953884i | \(0.402955\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.63597 | − | 1.87292i | −0.927193 | − | 0.374584i | ||||
\(26\) | 6.14864 | 1.20585 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.35052i | 0.250785i | 0.992107 | + | 0.125393i | \(0.0400191\pi\) | ||||
−0.992107 | + | 0.125393i | \(0.959981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.65515i | − | 1.55451i | −0.629185 | − | 0.777255i | \(-0.716611\pi\) | ||
0.629185 | − | 0.777255i | \(-0.283389\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.52257i | − | 1.11861i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.53381i | − | 1.56735i | −0.621172 | − | 0.783674i | \(-0.713343\pi\) | ||
0.621172 | − | 0.783674i | \(-0.286657\pi\) | |||||||
\(38\) | − | 6.03756i | − | 0.979421i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.426635 | + | 2.19499i | −0.0674569 | + | 0.347058i | ||||
\(41\) | 8.71759 | 1.36146 | 0.680730 | − | 0.732535i | \(-0.261663\pi\) | ||||
0.680730 | + | 0.732535i | \(0.261663\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.35859i | 0.817177i | 0.912719 | + | 0.408588i | \(0.133979\pi\) | ||||
−0.912719 | + | 0.408588i | \(0.866021\pi\) | |||||||
\(44\) | 1.28310i | 0.193435i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.87917 | 0.424510 | ||||||||
\(47\) | − | 0.806172i | − | 0.117592i | −0.998270 | − | 0.0587961i | \(-0.981274\pi\) | ||
0.998270 | − | 0.0587961i | \(-0.0187262\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.63597 | − | 1.87292i | −0.655625 | − | 0.264871i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.14864 | 0.852663 | ||||||||
\(53\) | −6.66826 | −0.915956 | −0.457978 | − | 0.888964i | \(-0.651426\pi\) | ||||
−0.457978 | + | 0.888964i | \(0.651426\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.81639 | − | 0.547415i | −0.379762 | − | 0.0738134i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.35052i | 0.177332i | ||||||||
\(59\) | 1.59622 | 0.207810 | 0.103905 | − | 0.994587i | \(-0.466866\pi\) | ||||
0.103905 | + | 0.994587i | \(0.466866\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.35361i | 0.813497i | 0.913540 | + | 0.406748i | \(0.133337\pi\) | ||||
−0.913540 | + | 0.406748i | \(0.866663\pi\) | |||||||
\(62\) | − | 8.65515i | − | 1.09921i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.62322 | + | 13.4962i | −0.325371 | + | 1.67400i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.39463i | 0.659059i | 0.944145 | + | 0.329529i | \(0.106890\pi\) | ||||
−0.944145 | + | 0.329529i | \(0.893110\pi\) | |||||||
\(68\) | − | 6.52257i | − | 0.790977i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.6787i | 1.86072i | 0.366650 | + | 0.930359i | \(0.380505\pi\) | ||||
−0.366650 | + | 0.930359i | \(0.619495\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.4167 | 1.45327 | 0.726635 | − | 0.687024i | \(-0.241083\pi\) | ||||
0.726635 | + | 0.687024i | \(0.241083\pi\) | |||||||
\(74\) | − | 9.53381i | − | 1.10828i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 6.03756i | − | 0.692555i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1819 | 1.25806 | 0.629028 | − | 0.777382i | \(-0.283453\pi\) | ||||
0.629028 | + | 0.777382i | \(0.283453\pi\) | |||||||
\(80\) | −0.426635 | + | 2.19499i | −0.0476992 | + | 0.245407i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.71759 | 0.962697 | ||||||||
\(83\) | − | 3.74493i | − | 0.411059i | −0.978651 | − | 0.205530i | \(-0.934108\pi\) | ||
0.978651 | − | 0.205530i | \(-0.0658917\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.3170 | + | 2.78275i | 1.55289 | + | 0.301832i | ||||
\(86\) | 5.35859i | 0.577831i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.28310i | 0.136779i | ||||||||
\(89\) | −3.63941 | −0.385777 | −0.192889 | − | 0.981221i | \(-0.561786\pi\) | ||||
−0.192889 | + | 0.981221i | \(0.561786\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.87917 | 0.300174 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 0.806172i | − | 0.0831503i | ||||||
\(95\) | 13.2524 | + | 2.57583i | 1.35967 | + | 0.264275i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.76818 | −0.890274 | −0.445137 | − | 0.895463i | \(-0.646845\pi\) | ||||
−0.445137 | + | 0.895463i | \(0.646845\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.63597 | − | 1.87292i | −0.463597 | − | 0.187292i | ||||
\(101\) | −1.70654 | −0.169807 | −0.0849035 | − | 0.996389i | \(-0.527058\pi\) | ||||
−0.0849035 | + | 0.996389i | \(0.527058\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3644 | −1.02123 | −0.510617 | − | 0.859808i | \(-0.670583\pi\) | ||||
−0.510617 | + | 0.859808i | \(0.670583\pi\) | |||||||
\(104\) | 6.14864 | 0.602923 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.66826 | −0.647679 | ||||||||
\(107\) | −11.5136 | −1.11306 | −0.556531 | − | 0.830827i | \(-0.687868\pi\) | ||||
−0.556531 | + | 0.830827i | \(0.687868\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −2.81639 | − | 0.547415i | −0.268532 | − | 0.0521940i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3875 | 1.25939 | 0.629695 | − | 0.776843i | \(-0.283180\pi\) | ||||
0.629695 | + | 0.776843i | \(0.283180\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.22835 | + | 6.31975i | −0.114545 | + | 0.589319i | ||||
\(116\) | 1.35052i | 0.125393i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.59622 | 0.146944 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.35366 | 0.850332 | ||||||||
\(122\) | 6.35361i | 0.575229i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 8.65515i | − | 0.777255i | ||||||
\(125\) | 6.08890 | − | 9.37685i | 0.544608 | − | 0.838691i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.65313i | − | 0.501634i | −0.968035 | − | 0.250817i | \(-0.919301\pi\) | ||
0.968035 | − | 0.250817i | \(-0.0806992\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.62322 | + | 13.4962i | −0.230072 | + | 1.18369i | ||||
\(131\) | 12.4673 | 1.08928 | 0.544638 | − | 0.838671i | \(-0.316667\pi\) | ||||
0.544638 | + | 0.838671i | \(0.316667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.39463i | 0.466025i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 6.52257i | − | 0.559305i | ||||||
\(137\) | −0.0509686 | −0.00435454 | −0.00217727 | − | 0.999998i | \(-0.500693\pi\) | ||||
−0.00217727 | + | 0.999998i | \(0.500693\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.05069i | − | 0.0891184i | −0.999007 | − | 0.0445592i | \(-0.985812\pi\) | ||
0.999007 | − | 0.0445592i | \(-0.0141883\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.6787i | 1.31573i | ||||||||
\(143\) | 7.88931i | 0.659738i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.96438 | − | 0.576179i | −0.246178 | − | 0.0478491i | ||||
\(146\) | 12.4167 | 1.02762 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 9.53381i | − | 0.783674i | ||||||
\(149\) | 8.22305i | 0.673659i | 0.941566 | + | 0.336829i | \(0.109355\pi\) | ||||
−0.941566 | + | 0.336829i | \(0.890645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.26715 | −0.347256 | −0.173628 | − | 0.984811i | \(-0.555549\pi\) | ||||
−0.173628 | + | 0.984811i | \(0.555549\pi\) | |||||||
\(152\) | − | 6.03756i | − | 0.489710i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.9980 | + | 3.69259i | 1.52595 | + | 0.296596i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.83203 | −0.385638 | −0.192819 | − | 0.981234i | \(-0.561763\pi\) | ||||
−0.192819 | + | 0.981234i | \(0.561763\pi\) | |||||||
\(158\) | 11.1819 | 0.889581 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.426635 | + | 2.19499i | −0.0337285 | + | 0.173529i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 10.7532i | − | 0.842257i | −0.907001 | − | 0.421128i | \(-0.861634\pi\) | ||
0.907001 | − | 0.421128i | \(-0.138366\pi\) | |||||||
\(164\) | 8.71759 | 0.680730 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 3.74493i | − | 0.290663i | ||||||
\(167\) | 18.9267i | 1.46459i | 0.680988 | + | 0.732295i | \(0.261551\pi\) | ||||
−0.680988 | + | 0.732295i | \(0.738449\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.8057 | 1.90813 | ||||||||
\(170\) | 14.3170 | + | 2.78275i | 1.09806 | + | 0.213427i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.35859i | 0.408588i | ||||||||
\(173\) | 11.8435i | 0.900447i | 0.892916 | + | 0.450223i | \(0.148656\pi\) | ||||
−0.892916 | + | 0.450223i | \(0.851344\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.28310i | 0.0967173i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.63941 | −0.272786 | ||||||||
\(179\) | − | 3.78561i | − | 0.282949i | −0.989942 | − | 0.141475i | \(-0.954816\pi\) | ||
0.989942 | − | 0.141475i | \(-0.0451844\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.0033i | − | 1.41251i | −0.707960 | − | 0.706253i | \(-0.750384\pi\) | ||
0.707960 | − | 0.706253i | \(-0.249616\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.87917 | 0.212255 | ||||||||
\(185\) | 20.9266 | + | 4.06745i | 1.53856 | + | 0.299045i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.36910 | 0.612009 | ||||||||
\(188\) | − | 0.806172i | − | 0.0587961i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.2524 | + | 2.57583i | 0.961428 | + | 0.186871i | ||||
\(191\) | 2.82843i | 0.204658i | 0.994751 | + | 0.102329i | \(0.0326294\pi\) | ||||
−0.994751 | + | 0.102329i | \(0.967371\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.53892i | 0.254737i | 0.991855 | + | 0.127368i | \(0.0406530\pi\) | ||||
−0.991855 | + | 0.127368i | \(0.959347\pi\) | |||||||
\(194\) | −8.76818 | −0.629519 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.36728 | −0.168662 | −0.0843308 | − | 0.996438i | \(-0.526875\pi\) | ||||
−0.0843308 | + | 0.996438i | \(0.526875\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.46410i | − | 0.245564i | −0.992434 | − | 0.122782i | \(-0.960818\pi\) | ||
0.992434 | − | 0.122782i | \(-0.0391815\pi\) | |||||||
\(200\) | −4.63597 | − | 1.87292i | −0.327812 | − | 0.132435i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.70654 | −0.120072 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.71923 | + | 19.1350i | −0.259762 | + | 1.33645i | ||||
\(206\) | −10.3644 | −0.722122 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.14864 | 0.426331 | ||||||||
\(209\) | 7.74679 | 0.535856 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.3620 | −0.988721 | −0.494361 | − | 0.869257i | \(-0.664598\pi\) | ||||
−0.494361 | + | 0.869257i | \(0.664598\pi\) | |||||||
\(212\) | −6.66826 | −0.457978 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.5136 | −0.787053 | ||||||||
\(215\) | −11.7620 | − | 2.28616i | −0.802165 | − | 0.155915i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.00000 | 0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.81639 | − | 0.547415i | −0.189881 | − | 0.0369067i | ||||
\(221\) | − | 40.1049i | − | 2.69775i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.5975 | −0.910557 | −0.455279 | − | 0.890349i | \(-0.650460\pi\) | ||||
−0.455279 | + | 0.890349i | \(0.650460\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.3875 | 0.890523 | ||||||||
\(227\) | − | 12.3559i | − | 0.820092i | −0.912065 | − | 0.410046i | \(-0.865513\pi\) | ||
0.912065 | − | 0.410046i | \(-0.134487\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.41341i | 0.159483i | 0.996816 | + | 0.0797414i | \(0.0254094\pi\) | ||||
−0.996816 | + | 0.0797414i | \(0.974591\pi\) | |||||||
\(230\) | −1.22835 | + | 6.31975i | −0.0809952 | + | 0.416712i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.35052i | 0.0886660i | ||||||||
\(233\) | −12.8756 | −0.843509 | −0.421754 | − | 0.906710i | \(-0.638586\pi\) | ||||
−0.421754 | + | 0.906710i | \(0.638586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.76954 | + | 0.343941i | 0.115432 | + | 0.0224362i | ||||
\(236\) | 1.59622 | 0.103905 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.2546i | 1.76296i | 0.472226 | + | 0.881478i | \(0.343451\pi\) | ||||
−0.472226 | + | 0.881478i | \(0.656549\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.61759i | 0.168614i | 0.996440 | + | 0.0843070i | \(0.0268677\pi\) | ||||
−0.996440 | + | 0.0843070i | \(0.973132\pi\) | |||||||
\(242\) | 9.35366 | 0.601276 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.35361i | 0.406748i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 37.1227i | − | 2.36206i | ||||||
\(248\) | − | 8.65515i | − | 0.549603i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.08890 | − | 9.37685i | 0.385096 | − | 0.593044i | ||||
\(251\) | 26.7173 | 1.68638 | 0.843190 | − | 0.537615i | \(-0.180675\pi\) | ||||
0.843190 | + | 0.537615i | \(0.180675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.69426i | 0.232256i | ||||||||
\(254\) | − | 5.65313i | − | 0.354709i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 10.5613i | − | 0.658793i | −0.944192 | − | 0.329397i | \(-0.893155\pi\) | ||
0.944192 | − | 0.329397i | \(-0.106845\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.62322 | + | 13.4962i | −0.162685 | + | 0.836999i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.4673 | 0.770234 | ||||||||
\(263\) | −8.33174 | −0.513757 | −0.256879 | − | 0.966444i | \(-0.582694\pi\) | ||||
−0.256879 | + | 0.966444i | \(0.582694\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.84491 | − | 14.6368i | 0.174762 | − | 0.899130i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.39463i | 0.329529i | ||||||||
\(269\) | 14.2834 | 0.870876 | 0.435438 | − | 0.900219i | \(-0.356594\pi\) | ||||
0.435438 | + | 0.900219i | \(0.356594\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.60446i | 0.461938i | 0.972961 | + | 0.230969i | \(0.0741896\pi\) | ||||
−0.972961 | + | 0.230969i | \(0.925810\pi\) | |||||||
\(272\) | − | 6.52257i | − | 0.395489i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.0509686 | −0.00307912 | ||||||||
\(275\) | 2.40314 | − | 5.94841i | 0.144915 | − | 0.358702i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 12.0400i | − | 0.723416i | −0.932291 | − | 0.361708i | \(-0.882194\pi\) | ||
0.932291 | − | 0.361708i | \(-0.117806\pi\) | |||||||
\(278\) | − | 1.05069i | − | 0.0630162i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.7879i | − | 0.762861i | −0.924397 | − | 0.381431i | \(-0.875431\pi\) | ||
0.924397 | − | 0.381431i | \(-0.124569\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.5521 | −0.924479 | −0.462239 | − | 0.886755i | \(-0.652954\pi\) | ||||
−0.462239 | + | 0.886755i | \(0.652954\pi\) | |||||||
\(284\) | 15.6787i | 0.930359i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.88931i | 0.466505i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −25.5439 | −1.50258 | ||||||||
\(290\) | −2.96438 | − | 0.576179i | −0.174074 | − | 0.0338344i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.4167 | 0.726635 | ||||||||
\(293\) | − | 11.5536i | − | 0.674967i | −0.941331 | − | 0.337483i | \(-0.890424\pi\) | ||
0.941331 | − | 0.337483i | \(-0.109576\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.681003 | + | 3.50369i | −0.0396495 | + | 0.203993i | ||||
\(296\) | − | 9.53381i | − | 0.554141i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.22305i | 0.476349i | ||||||||
\(299\) | 17.7030 | 1.02379 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.26715 | −0.245547 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 6.03756i | − | 0.346278i | ||||||
\(305\) | −13.9461 | − | 2.71067i | −0.798553 | − | 0.155213i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.57617 | −0.147030 | −0.0735150 | − | 0.997294i | \(-0.523422\pi\) | ||||
−0.0735150 | + | 0.997294i | \(0.523422\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18.9980 | + | 3.69259i | 1.07901 | + | 0.209725i | ||||
\(311\) | −24.7140 | −1.40140 | −0.700702 | − | 0.713454i | \(-0.747130\pi\) | ||||
−0.700702 | + | 0.713454i | \(0.747130\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.00173 | −0.508808 | −0.254404 | − | 0.967098i | \(-0.581879\pi\) | ||||
−0.254404 | + | 0.967098i | \(0.581879\pi\) | |||||||
\(314\) | −4.83203 | −0.272687 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.1819 | 0.629028 | ||||||||
\(317\) | 23.9059 | 1.34269 | 0.671344 | − | 0.741146i | \(-0.265717\pi\) | ||||
0.671344 | + | 0.741146i | \(0.265717\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.73285 | −0.0970211 | ||||||||
\(320\) | −0.426635 | + | 2.19499i | −0.0238496 | + | 0.122704i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −39.3804 | −2.19118 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28.5049 | − | 11.5159i | −1.58117 | − | 0.638787i | ||||
\(326\) | − | 10.7532i | − | 0.595565i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.71759 | 0.481349 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.36728 | 0.240047 | 0.120024 | − | 0.992771i | \(-0.461703\pi\) | ||||
0.120024 | + | 0.992771i | \(0.461703\pi\) | |||||||
\(332\) | − | 3.74493i | − | 0.205530i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.9267i | 1.03562i | ||||||||
\(335\) | −11.8412 | − | 2.30154i | −0.646951 | − | 0.125746i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.5159i | 1.06310i | 0.847028 | + | 0.531549i | \(0.178390\pi\) | ||||
−0.847028 | + | 0.531549i | \(0.821610\pi\) | |||||||
\(338\) | 24.8057 | 1.34925 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.3170 | + | 2.78275i | 0.776447 | + | 0.150916i | ||||
\(341\) | 11.1054 | 0.601392 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.35859i | 0.288916i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.8435i | 0.636712i | ||||||||
\(347\) | −26.9147 | −1.44486 | −0.722429 | − | 0.691446i | \(-0.756974\pi\) | ||||
−0.722429 | + | 0.691446i | \(0.756974\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.3821i | − | 0.555741i | −0.960619 | − | 0.277870i | \(-0.910371\pi\) | ||
0.960619 | − | 0.277870i | \(-0.0896286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.28310i | 0.0683894i | ||||||||
\(353\) | − | 0.168951i | − | 0.00899236i | −0.999990 | − | 0.00449618i | \(-0.998569\pi\) | ||
0.999990 | − | 0.00449618i | \(-0.00143118\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −34.4146 | − | 6.68908i | −1.82654 | − | 0.355019i | ||||
\(356\) | −3.63941 | −0.192889 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 3.78561i | − | 0.200075i | ||||||
\(359\) | 37.6661i | 1.98794i | 0.109655 | + | 0.993970i | \(0.465025\pi\) | ||||
−0.109655 | + | 0.993970i | \(0.534975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4521 | −0.918531 | ||||||||
\(362\) | − | 19.0033i | − | 0.998792i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.29741 | + | 27.2546i | −0.277279 | + | 1.42657i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.1557 | 0.791124 | 0.395562 | − | 0.918439i | \(-0.370550\pi\) | ||||
0.395562 | + | 0.918439i | \(0.370550\pi\) | |||||||
\(368\) | 2.87917 | 0.150087 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 20.9266 | + | 4.06745i | 1.08792 | + | 0.211457i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0400i | 0.623410i | 0.950179 | + | 0.311705i | \(0.100900\pi\) | ||||
−0.950179 | + | 0.311705i | \(0.899100\pi\) | |||||||
\(374\) | 8.36910 | 0.432756 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 0.806172i | − | 0.0415751i | ||||||
\(377\) | 8.30386i | 0.427671i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0918 | 0.929312 | 0.464656 | − | 0.885491i | \(-0.346178\pi\) | ||||
0.464656 | + | 0.885491i | \(0.346178\pi\) | |||||||
\(380\) | 13.2524 | + | 2.57583i | 0.679833 | + | 0.132137i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.82843i | 0.144715i | ||||||||
\(383\) | 29.1538i | 1.48969i | 0.667237 | + | 0.744846i | \(0.267477\pi\) | ||||
−0.667237 | + | 0.744846i | \(0.732523\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.53892i | 0.180126i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.76818 | −0.445137 | ||||||||
\(389\) | 19.6641i | 0.997012i | 0.866886 | + | 0.498506i | \(0.166118\pi\) | ||||
−0.866886 | + | 0.498506i | \(0.833882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 18.7796i | − | 0.949723i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.36728 | −0.119262 | ||||||||
\(395\) | −4.77057 | + | 24.5441i | −0.240033 | + | 1.23495i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.68454 | −0.285299 | −0.142649 | − | 0.989773i | \(-0.545562\pi\) | ||||
−0.142649 | + | 0.989773i | \(0.545562\pi\) | |||||||
\(398\) | − | 3.46410i | − | 0.173640i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.63597 | − | 1.87292i | −0.231798 | − | 0.0936460i | ||||
\(401\) | 10.2166i | 0.510195i | 0.966915 | + | 0.255097i | \(0.0821075\pi\) | ||||
−0.966915 | + | 0.255097i | \(0.917892\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 53.2174i | − | 2.65095i | ||||||
\(404\) | −1.70654 | −0.0849035 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.2328 | 0.606359 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.9683i | 0.690687i | 0.938476 | + | 0.345344i | \(0.112238\pi\) | ||||
−0.938476 | + | 0.345344i | \(0.887762\pi\) | |||||||
\(410\) | −3.71923 | + | 19.1350i | −0.183680 | + | 0.945012i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.3644 | −0.510617 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.22008 | + | 1.59772i | 0.403508 | + | 0.0784288i | ||||
\(416\) | 6.14864 | 0.301462 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.74679 | 0.378908 | ||||||||
\(419\) | 11.3181 | 0.552924 | 0.276462 | − | 0.961025i | \(-0.410838\pi\) | ||||
0.276462 | + | 0.961025i | \(0.410838\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.9099 | −0.677928 | −0.338964 | − | 0.940799i | \(-0.610077\pi\) | ||||
−0.338964 | + | 0.940799i | \(0.610077\pi\) | |||||||
\(422\) | −14.3620 | −0.699132 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.66826 | −0.323839 | ||||||||
\(425\) | −12.2162 | + | 30.2384i | −0.592575 | + | 1.46678i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11.5136 | −0.556531 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.7620 | − | 2.28616i | −0.567216 | − | 0.110248i | ||||
\(431\) | 26.0901i | 1.25672i | 0.777924 | + | 0.628359i | \(0.216273\pi\) | ||||
−0.777924 | + | 0.628359i | \(0.783727\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.42614 | 0.404935 | 0.202467 | − | 0.979289i | \(-0.435104\pi\) | ||||
0.202467 | + | 0.979289i | \(0.435104\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | − | 17.3831i | − | 0.831548i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.6585i | 1.32007i | 0.751236 | + | 0.660033i | \(0.229458\pi\) | ||||
−0.751236 | + | 0.660033i | \(0.770542\pi\) | |||||||
\(440\) | −2.81639 | − | 0.547415i | −0.134266 | − | 0.0260970i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 40.1049i | − | 1.90759i | ||||||
\(443\) | 2.35722 | 0.111995 | 0.0559975 | − | 0.998431i | \(-0.482166\pi\) | ||||
0.0559975 | + | 0.998431i | \(0.482166\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.55270 | − | 7.98848i | 0.0736051 | − | 0.378690i | ||||
\(446\) | −13.5975 | −0.643861 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 12.8021i | − | 0.604169i | −0.953281 | − | 0.302084i | \(-0.902318\pi\) | ||
0.953281 | − | 0.302084i | \(-0.0976824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.1855i | 0.526707i | ||||||||
\(452\) | 13.3875 | 0.629695 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 12.3559i | − | 0.579893i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 34.5242i | − | 1.61498i | −0.589884 | − | 0.807488i | \(-0.700827\pi\) | ||
0.589884 | − | 0.807488i | \(-0.299173\pi\) | |||||||
\(458\) | 2.41341i | 0.112771i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.22835 | + | 6.31975i | −0.0572723 | + | 0.294660i | ||||
\(461\) | 20.2692 | 0.944032 | 0.472016 | − | 0.881590i | \(-0.343526\pi\) | ||||
0.472016 | + | 0.881590i | \(0.343526\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.1246i | − | 0.609952i | −0.952360 | − | 0.304976i | \(-0.901352\pi\) | ||
0.952360 | − | 0.304976i | \(-0.0986485\pi\) | |||||||
\(464\) | 1.35052i | 0.0626963i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.8756 | −0.596451 | ||||||||
\(467\) | − | 1.53167i | − | 0.0708773i | −0.999372 | − | 0.0354387i | \(-0.988717\pi\) | ||
0.999372 | − | 0.0354387i | \(-0.0112828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.76954 | + | 0.343941i | 0.0816228 | + | 0.0158648i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.59622 | 0.0734720 | ||||||||
\(473\) | −6.87560 | −0.316140 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.3079 | + | 27.9899i | −0.518840 | + | 1.28426i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.2546i | 1.24660i | ||||||||
\(479\) | −29.3170 | −1.33953 | −0.669764 | − | 0.742574i | \(-0.733605\pi\) | ||||
−0.669764 | + | 0.742574i | \(0.733605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 58.6199i | − | 2.67284i | ||||||
\(482\) | 2.61759i | 0.119228i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.35366 | 0.425166 | ||||||||
\(485\) | 3.74081 | − | 19.2461i | 0.169862 | − | 0.873919i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8.19540i | − | 0.371369i | −0.982609 | − | 0.185685i | \(-0.940550\pi\) | ||
0.982609 | − | 0.185685i | \(-0.0594502\pi\) | |||||||
\(488\) | 6.35361i | 0.287615i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 40.4383i | − | 1.82495i | −0.409129 | − | 0.912477i | \(-0.634167\pi\) | ||
0.409129 | − | 0.912477i | \(-0.365833\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.80886 | 0.396731 | ||||||||
\(494\) | − | 37.1227i | − | 1.67023i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.65515i | − | 0.388628i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.4490 | 0.781125 | 0.390562 | − | 0.920576i | \(-0.372281\pi\) | ||||
0.390562 | + | 0.920576i | \(0.372281\pi\) | |||||||
\(500\) | 6.08890 | − | 9.37685i | 0.272304 | − | 0.419345i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 26.7173 | 1.19245 | ||||||||
\(503\) | − | 1.91949i | − | 0.0855860i | −0.999084 | − | 0.0427930i | \(-0.986374\pi\) | ||
0.999084 | − | 0.0427930i | \(-0.0136256\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.728069 | − | 3.74584i | 0.0323987 | − | 0.166688i | ||||
\(506\) | 3.69426i | 0.164230i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 5.65313i | − | 0.250817i | ||||||
\(509\) | 11.0910 | 0.491599 | 0.245800 | − | 0.969321i | \(-0.420949\pi\) | ||||
0.245800 | + | 0.969321i | \(0.420949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 10.5613i | − | 0.465837i | ||||||
\(515\) | 4.42181 | − | 22.7498i | 0.194848 | − | 1.00247i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.03440 | 0.0454928 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.62322 | + | 13.4962i | −0.115036 | + | 0.591847i | ||||
\(521\) | 39.7412 | 1.74109 | 0.870546 | − | 0.492088i | \(-0.163766\pi\) | ||||
0.870546 | + | 0.492088i | \(0.163766\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.2808 | −1.36781 | −0.683907 | − | 0.729570i | \(-0.739720\pi\) | ||||
−0.683907 | + | 0.729570i | \(0.739720\pi\) | |||||||
\(524\) | 12.4673 | 0.544638 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.33174 | −0.363281 | ||||||||
\(527\) | −56.4538 | −2.45917 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.7104 | −0.639582 | ||||||||
\(530\) | 2.84491 | − | 14.6368i | 0.123575 | − | 0.635781i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 53.6013 | 2.32173 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.91210 | − | 25.2722i | 0.212369 | − | 1.09261i | ||||
\(536\) | 5.39463i | 0.233012i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.2834 | 0.615802 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.7974 | −1.06612 | −0.533061 | − | 0.846077i | \(-0.678959\pi\) | ||||
−0.533061 | + | 0.846077i | \(0.678959\pi\) | |||||||
\(542\) | 7.60446i | 0.326640i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 6.52257i | − | 0.279653i | ||||||
\(545\) | −0.853270 | + | 4.38998i | −0.0365501 | + | 0.188046i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 40.5380i | − | 1.73328i | −0.498934 | − | 0.866640i | \(-0.666275\pi\) | ||
0.498934 | − | 0.866640i | \(-0.333725\pi\) | |||||||
\(548\) | −0.0509686 | −0.00217727 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.40314 | − | 5.94841i | 0.102470 | − | 0.253641i | ||||
\(551\) | 8.15384 | 0.347365 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 12.0400i | − | 0.511532i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 1.05069i | − | 0.0445592i | ||||||
\(557\) | −23.7464 | −1.00617 | −0.503084 | − | 0.864238i | \(-0.667801\pi\) | ||||
−0.503084 | + | 0.864238i | \(0.667801\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.9480i | 1.39355i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 12.7879i | − | 0.539424i | ||||||
\(563\) | 8.42867i | 0.355226i | 0.984100 | + | 0.177613i | \(0.0568375\pi\) | ||||
−0.984100 | + | 0.177613i | \(0.943162\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.71157 | + | 29.3854i | −0.240288 | + | 1.23625i | ||||
\(566\) | −15.5521 | −0.653705 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.6787i | 0.657863i | ||||||||
\(569\) | − | 23.4565i | − | 0.983348i | −0.870779 | − | 0.491674i | \(-0.836385\pi\) | ||
0.870779 | − | 0.491674i | \(-0.163615\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.3589 | 0.642751 | 0.321376 | − | 0.946952i | \(-0.395855\pi\) | ||||
0.321376 | + | 0.946952i | \(0.395855\pi\) | |||||||
\(572\) | 7.88931i | 0.329869i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.3477 | − | 5.39245i | −0.556639 | − | 0.224881i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.2408 | 0.592853 | 0.296426 | − | 0.955056i | \(-0.404205\pi\) | ||||
0.296426 | + | 0.955056i | \(0.404205\pi\) | |||||||
\(578\) | −25.5439 | −1.06248 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.96438 | − | 0.576179i | −0.123089 | − | 0.0239245i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.55604i | − | 0.354355i | ||||||
\(584\) | 12.4167 | 0.513808 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 11.5536i | − | 0.477274i | ||||||
\(587\) | 12.5249i | 0.516958i | 0.966017 | + | 0.258479i | \(0.0832212\pi\) | ||||
−0.966017 | + | 0.258479i | \(0.916779\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −52.2560 | −2.15317 | ||||||||
\(590\) | −0.681003 | + | 3.50369i | −0.0280365 | + | 0.144245i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 9.53381i | − | 0.391837i | ||||||
\(593\) | − | 14.7150i | − | 0.604273i | −0.953265 | − | 0.302136i | \(-0.902300\pi\) | ||
0.953265 | − | 0.302136i | \(-0.0976998\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.22305i | 0.336829i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 17.7030 | 0.723928 | ||||||||
\(599\) | 27.6324i | 1.12903i | 0.825423 | + | 0.564515i | \(0.190937\pi\) | ||||
−0.825423 | + | 0.564515i | \(0.809063\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 8.82137i | − | 0.359831i | −0.983682 | − | 0.179916i | \(-0.942418\pi\) | ||
0.983682 | − | 0.179916i | \(-0.0575825\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.26715 | −0.173628 | ||||||||
\(605\) | −3.99060 | + | 20.5312i | −0.162241 | + | 0.834711i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.5354 | 1.07704 | 0.538519 | − | 0.842613i | \(-0.318984\pi\) | ||||
0.538519 | + | 0.842613i | \(0.318984\pi\) | |||||||
\(608\) | − | 6.03756i | − | 0.244855i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.9461 | − | 2.71067i | −0.564662 | − | 0.109752i | ||||
\(611\) | − | 4.95686i | − | 0.200533i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.913683i | 0.0369033i | 0.999830 | + | 0.0184517i | \(0.00587368\pi\) | ||||
−0.999830 | + | 0.0184517i | \(0.994126\pi\) | |||||||
\(614\) | −2.57617 | −0.103966 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.0558 | −1.41129 | −0.705646 | − | 0.708565i | \(-0.749343\pi\) | ||||
−0.705646 | + | 0.708565i | \(0.749343\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.0967i | 0.767561i | 0.923424 | + | 0.383781i | \(0.125378\pi\) | ||||
−0.923424 | + | 0.383781i | \(0.874622\pi\) | |||||||
\(620\) | 18.9980 | + | 3.69259i | 0.762977 | + | 0.148298i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.7140 | −0.990942 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.9843 | + | 17.3656i | 0.719374 | + | 0.694623i | ||||
\(626\) | −9.00173 | −0.359782 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.83203 | −0.192819 | ||||||||
\(629\) | −62.1849 | −2.47947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.5350 | 0.857296 | 0.428648 | − | 0.903472i | \(-0.358990\pi\) | ||||
0.428648 | + | 0.903472i | \(0.358990\pi\) | |||||||
\(632\) | 11.1819 | 0.444790 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23.9059 | 0.949423 | ||||||||
\(635\) | 12.4086 | + | 2.41182i | 0.492419 | + | 0.0957102i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.73285 | −0.0686043 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.426635 | + | 2.19499i | −0.0168642 | + | 0.0867646i | ||||
\(641\) | 33.1131i | 1.30789i | 0.756543 | + | 0.653943i | \(0.226887\pi\) | ||||
−0.756543 | + | 0.653943i | \(0.773113\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.31191 | −0.130609 | −0.0653044 | − | 0.997865i | \(-0.520802\pi\) | ||||
−0.0653044 | + | 0.997865i | \(0.520802\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −39.3804 | −1.54940 | ||||||||
\(647\) | 23.3338i | 0.917348i | 0.888605 | + | 0.458674i | \(0.151675\pi\) | ||||
−0.888605 | + | 0.458674i | \(0.848325\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.04811i | 0.0803953i | ||||||||
\(650\) | −28.5049 | − | 11.5159i | −1.11805 | − | 0.451691i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 10.7532i | − | 0.421128i | ||||||
\(653\) | −17.4604 | −0.683277 | −0.341639 | − | 0.939831i | \(-0.610982\pi\) | ||||
−0.341639 | + | 0.939831i | \(0.610982\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.31900 | + | 27.3657i | −0.207830 | + | 1.06926i | ||||
\(656\) | 8.71759 | 0.340365 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.29864i | 0.0505877i | 0.999680 | + | 0.0252939i | \(0.00805215\pi\) | ||||
−0.999680 | + | 0.0252939i | \(0.991948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.07917i | 0.197557i | 0.995109 | + | 0.0987785i | \(0.0314935\pi\) | ||||
−0.995109 | + | 0.0987785i | \(0.968506\pi\) | |||||||
\(662\) | 4.36728 | 0.169739 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 3.74493i | − | 0.145331i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.88838i | 0.150559i | ||||||||
\(668\) | 18.9267i | 0.732295i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.8412 | − | 2.30154i | −0.457464 | − | 0.0889161i | ||||
\(671\) | −8.15232 | −0.314717 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.4124i | 0.709747i | 0.934914 | + | 0.354873i | \(0.115476\pi\) | ||||
−0.934914 | + | 0.354873i | \(0.884524\pi\) | |||||||
\(674\) | 19.5159i | 0.751723i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.8057 | 0.954067 | ||||||||
\(677\) | − | 41.2795i | − | 1.58650i | −0.608896 | − | 0.793250i | \(-0.708388\pi\) | ||
0.608896 | − | 0.793250i | \(-0.291612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 14.3170 | + | 2.78275i | 0.549031 | + | 0.106714i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.1054 | 0.425249 | ||||||||
\(683\) | 22.9793 | 0.879278 | 0.439639 | − | 0.898174i | \(-0.355106\pi\) | ||||
0.439639 | + | 0.898174i | \(0.355106\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.0217450 | − | 0.111876i | 0.000830833 | − | 0.00427454i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.35859i | 0.204294i | ||||||||
\(689\) | −41.0007 | −1.56200 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 12.7072i | − | 0.483406i | −0.970350 | − | 0.241703i | \(-0.922294\pi\) | ||
0.970350 | − | 0.241703i | \(-0.0777059\pi\) | |||||||
\(692\) | 11.8435i | 0.450223i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.9147 | −1.02167 | ||||||||
\(695\) | 2.30625 | + | 0.448261i | 0.0874812 | + | 0.0170035i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 56.8611i | − | 2.15377i | ||||||
\(698\) | − | 10.3821i | − | 0.392968i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 26.5441i | − | 1.00256i | −0.865286 | − | 0.501279i | \(-0.832863\pi\) | ||
0.865286 | − | 0.501279i | \(-0.167137\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −57.5609 | −2.17095 | ||||||||
\(704\) | 1.28310i | 0.0483586i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 0.168951i | − | 0.00635856i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.3532 | 1.59061 | 0.795303 | − | 0.606212i | \(-0.207312\pi\) | ||||
0.795303 | + | 0.606212i | \(0.207312\pi\) | |||||||
\(710\) | −34.4146 | − | 6.68908i | −1.29156 | − | 0.251037i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.63941 | −0.136393 | ||||||||
\(713\) | − | 24.9196i | − | 0.933248i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.3170 | − | 3.36586i | −0.647618 | − | 0.125876i | ||||
\(716\) | − | 3.78561i | − | 0.141475i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 37.6661i | 1.40569i | ||||||||
\(719\) | −23.9014 | −0.891373 | −0.445686 | − | 0.895189i | \(-0.647040\pi\) | ||||
−0.445686 | + | 0.895189i | \(0.647040\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.4521 | −0.649499 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 19.0033i | − | 0.706253i | ||||||
\(725\) | 2.52942 | − | 6.26097i | 0.0939401 | − | 0.232526i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.4529 | −0.832731 | −0.416365 | − | 0.909197i | \(-0.636696\pi\) | ||||
−0.416365 | + | 0.909197i | \(0.636696\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.29741 | + | 27.2546i | −0.196066 | + | 1.00874i | ||||
\(731\) | 34.9517 | 1.29274 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.5450 | −1.01740 | −0.508700 | − | 0.860944i | \(-0.669874\pi\) | ||||
−0.508700 | + | 0.860944i | \(0.669874\pi\) | |||||||
\(734\) | 15.1557 | 0.559409 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.87917 | 0.106128 | ||||||||
\(737\) | −6.92184 | −0.254969 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.0913 | 1.14371 | 0.571856 | − | 0.820354i | \(-0.306224\pi\) | ||||
0.571856 | + | 0.820354i | \(0.306224\pi\) | |||||||
\(740\) | 20.9266 | + | 4.06745i | 0.769278 | + | 0.149523i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.12610 | 0.0413127 | 0.0206564 | − | 0.999787i | \(-0.493424\pi\) | ||||
0.0206564 | + | 0.999787i | \(0.493424\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0495 | − | 3.50824i | −0.661283 | − | 0.128532i | ||||
\(746\) | 12.0400i | 0.440817i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.36910 | 0.306005 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.54216 | −0.348198 | −0.174099 | − | 0.984728i | \(-0.555701\pi\) | ||||
−0.174099 | + | 0.984728i | \(0.555701\pi\) | |||||||
\(752\) | − | 0.806172i | − | 0.0293981i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.30386i | 0.302409i | ||||||||
\(755\) | 1.82051 | − | 9.36635i | 0.0662553 | − | 0.340876i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.1687i | 1.20554i | 0.797917 | + | 0.602768i | \(0.205935\pi\) | ||||
−0.797917 | + | 0.602768i | \(0.794065\pi\) | |||||||
\(758\) | 18.0918 | 0.657123 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.2524 | + | 2.57583i | 0.480714 | + | 0.0934353i | ||||
\(761\) | 4.34245 | 0.157414 | 0.0787068 | − | 0.996898i | \(-0.474921\pi\) | ||||
0.0787068 | + | 0.996898i | \(0.474921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.82843i | 0.102329i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.1538i | 1.05337i | ||||||||
\(767\) | 9.81458 | 0.354384 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.1795i | 1.66528i | 0.553818 | + | 0.832638i | \(0.313170\pi\) | ||||
−0.553818 | + | 0.832638i | \(0.686830\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.53892i | 0.127368i | ||||||||
\(773\) | 17.9745i | 0.646497i | 0.946314 | + | 0.323248i | \(0.104775\pi\) | ||||
−0.946314 | + | 0.323248i | \(0.895225\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.2104 | + | 40.1250i | −0.582295 | + | 1.44133i | ||||
\(776\) | −8.76818 | −0.314759 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.6641i | 0.704994i | ||||||||
\(779\) | − | 52.6330i | − | 1.88577i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.1173 | −0.719854 | ||||||||
\(782\) | − | 18.7796i | − | 0.671556i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.06151 | − | 10.6063i | 0.0735785 | − | 0.378554i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.8417 | 0.493405 | 0.246702 | − | 0.969091i | \(-0.420653\pi\) | ||||
0.246702 | + | 0.969091i | \(0.420653\pi\) | |||||||
\(788\) | −2.36728 | −0.0843308 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.77057 | + | 24.5441i | −0.169729 | + | 0.873239i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.0661i | 1.38728i | ||||||||
\(794\) | −5.68454 | −0.201737 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 3.46410i | − | 0.122782i | ||||||
\(797\) | − | 7.46138i | − | 0.264296i | −0.991230 | − | 0.132148i | \(-0.957813\pi\) | ||
0.991230 | − | 0.132148i | \(-0.0421874\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.25831 | −0.186026 | ||||||||
\(800\) | −4.63597 | − | 1.87292i | −0.163906 | − | 0.0662177i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.2166i | 0.360762i | ||||||||
\(803\) | 15.9319i | 0.562225i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 53.2174i | − | 1.87450i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.70654 | −0.0600359 | ||||||||
\(809\) | 1.48668i | 0.0522689i | 0.999658 | + | 0.0261344i | \(0.00831980\pi\) | ||||
−0.999658 | + | 0.0261344i | \(0.991680\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.5494i | 1.10785i | 0.832567 | + | 0.553925i | \(0.186871\pi\) | ||||
−0.832567 | + | 0.553925i | \(0.813129\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.2328 | 0.428760 | ||||||||
\(815\) | 23.6032 | + | 4.58770i | 0.826784 | + | 0.160700i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32.3528 | 1.13188 | ||||||||
\(818\) | 13.9683i | 0.488390i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.71923 | + | 19.1350i | −0.129881 | + | 0.668224i | ||||
\(821\) | − | 31.8039i | − | 1.10996i | −0.831862 | − | 0.554982i | \(-0.812725\pi\) | ||
0.831862 | − | 0.554982i | \(-0.187275\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.6371i | 1.27709i | 0.769585 | + | 0.638545i | \(0.220463\pi\) | ||||
−0.769585 | + | 0.638545i | \(0.779537\pi\) | |||||||
\(824\) | −10.3644 | −0.361061 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.9864 | −0.764541 | −0.382271 | − | 0.924050i | \(-0.624858\pi\) | ||||
−0.382271 | + | 0.924050i | \(0.624858\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 24.3062i | − | 0.844191i | −0.906551 | − | 0.422095i | \(-0.861295\pi\) | ||
0.906551 | − | 0.422095i | \(-0.138705\pi\) | |||||||
\(830\) | 8.22008 | + | 1.59772i | 0.285323 | + | 0.0554576i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.14864 | 0.213166 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.5439 | − | 8.07478i | −1.43768 | − | 0.279439i | ||||
\(836\) | 7.74679 | 0.267928 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.3181 | 0.390977 | ||||||||
\(839\) | −27.3914 | −0.945655 | −0.472827 | − | 0.881155i | \(-0.656767\pi\) | ||||
−0.472827 | + | 0.881155i | \(0.656767\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.1761 | 0.937107 | ||||||||
\(842\) | −13.9099 | −0.479368 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.3620 | −0.494361 | ||||||||
\(845\) | −10.5830 | + | 54.4484i | −0.364066 | + | 1.87308i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.66826 | −0.228989 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.2162 | + | 30.2384i | −0.419013 | + | 1.03717i | ||||
\(851\) | − | 27.4494i | − | 0.940954i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.6073 | 0.774060 | 0.387030 | − | 0.922067i | \(-0.373501\pi\) | ||||
0.387030 | + | 0.922067i | \(0.373501\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.5136 | −0.393527 | ||||||||
\(857\) | − | 47.8578i | − | 1.63479i | −0.576076 | − | 0.817396i | \(-0.695417\pi\) | ||
0.576076 | − | 0.817396i | \(-0.304583\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 48.0090i | − | 1.63804i | −0.573762 | − | 0.819022i | \(-0.694516\pi\) | ||
0.573762 | − | 0.819022i | \(-0.305484\pi\) | |||||||
\(860\) | −11.7620 | − | 2.28616i | −0.401082 | − | 0.0779574i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.0901i | 0.888634i | ||||||||
\(863\) | 47.5569 | 1.61886 | 0.809428 | − | 0.587218i | \(-0.199777\pi\) | ||||
0.809428 | + | 0.587218i | \(0.199777\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.9964 | − | 5.05286i | −0.883905 | − | 0.171802i | ||||
\(866\) | 8.42614 | 0.286332 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.3474i | 0.486703i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.1696i | 1.12391i | ||||||||
\(872\) | 2.00000 | 0.0677285 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 17.3831i | − | 0.587993i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 37.0004i | − | 1.24941i | −0.780859 | − | 0.624707i | \(-0.785218\pi\) | ||
0.780859 | − | 0.624707i | \(-0.214782\pi\) | |||||||
\(878\) | 27.6585i | 0.933428i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.81639 | − | 0.547415i | −0.0949405 | − | 0.0184534i | ||||
\(881\) | 5.97213 | 0.201206 | 0.100603 | − | 0.994927i | \(-0.467923\pi\) | ||||
0.100603 | + | 0.994927i | \(0.467923\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 11.0589i | − | 0.372163i | −0.982534 | − | 0.186081i | \(-0.940421\pi\) | ||
0.982534 | − | 0.186081i | \(-0.0595788\pi\) | |||||||
\(884\) | − | 40.1049i | − | 1.34887i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.35722 | 0.0791925 | ||||||||
\(887\) | 5.95070i | 0.199805i | 0.994997 | + | 0.0999026i | \(0.0318531\pi\) | ||||
−0.994997 | + | 0.0999026i | \(0.968147\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.55270 | − | 7.98848i | 0.0520467 | − | 0.267774i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.5975 | −0.455279 | ||||||||
\(893\) | −4.86731 | −0.162878 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.30937 | + | 1.61507i | 0.277752 | + | 0.0539859i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 12.8021i | − | 0.427212i | ||||||
\(899\) | 11.6890 | 0.389849 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.4942i | 1.44900i | ||||||||
\(902\) | 11.1855i | 0.372438i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.3875 | 0.445261 | ||||||||
\(905\) | 41.7121 | + | 8.10748i | 1.38656 | + | 0.269502i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.3144i | 1.83669i | 0.395786 | + | 0.918343i | \(0.370472\pi\) | ||||
−0.395786 | + | 0.918343i | \(0.629528\pi\) | |||||||
\(908\) | − | 12.3559i | − | 0.410046i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 35.2080i | − | 1.16649i | −0.812295 | − | 0.583246i | \(-0.801782\pi\) | ||
0.812295 | − | 0.583246i | \(-0.198218\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.80512 | 0.159026 | ||||||||
\(914\) | − | 34.5242i | − | 1.14196i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.41341i | 0.0797414i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.8875 | −1.67862 | −0.839311 | − | 0.543651i | \(-0.817041\pi\) | ||||
−0.839311 | + | 0.543651i | \(0.817041\pi\) | |||||||
\(920\) | −1.22835 | + | 6.31975i | −0.0404976 | + | 0.208356i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.2692 | 0.667531 | ||||||||
\(923\) | 96.4026i | 3.17313i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.8560 | + | 44.1984i | −0.587103 | + | 1.45323i | ||||
\(926\) | − | 13.1246i | − | 0.431301i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.35052i | 0.0443330i | ||||||||
\(929\) | −59.6810 | −1.95807 | −0.979036 | − | 0.203689i | \(-0.934707\pi\) | ||||
−0.979036 | + | 0.203689i | \(0.934707\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.8756 | −0.421754 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 1.53167i | − | 0.0501179i | ||||||
\(935\) | −3.57055 | + | 18.3701i | −0.116770 | + | 0.600766i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.2579 | 0.792471 | 0.396235 | − | 0.918149i | \(-0.370316\pi\) | ||||
0.396235 | + | 0.918149i | \(0.370316\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.76954 | + | 0.343941i | 0.0577160 | + | 0.0112181i | ||||
\(941\) | −30.1079 | −0.981488 | −0.490744 | − | 0.871304i | \(-0.663275\pi\) | ||||
−0.490744 | + | 0.871304i | \(0.663275\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.0994 | 0.817350 | ||||||||
\(944\) | 1.59622 | 0.0519525 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.87560 | −0.223545 | ||||||||
\(947\) | −46.1625 | −1.50008 | −0.750039 | − | 0.661393i | \(-0.769965\pi\) | ||||
−0.750039 | + | 0.661393i | \(0.769965\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 76.3460 | 2.47830 | ||||||||
\(950\) | −11.3079 | + | 27.9899i | −0.366875 | + | 0.908112i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.7121 | 0.768110 | 0.384055 | − | 0.923310i | \(-0.374527\pi\) | ||||
0.384055 | + | 0.923310i | \(0.374527\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.20837 | − | 1.20671i | −0.200898 | − | 0.0390481i | ||||
\(956\) | 27.2546i | 0.881478i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −29.3170 | −0.947190 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −43.9116 | −1.41650 | ||||||||
\(962\) | − | 58.6199i | − | 1.88998i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.61759i | 0.0843070i | ||||||||
\(965\) | −7.76789 | − | 1.50983i | −0.250057 | − | 0.0486030i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.0922780i | 0.00296746i | 0.999999 | + | 0.00148373i | \(0.000472286\pi\) | ||||
−0.999999 | + | 0.00148373i | \(0.999528\pi\) | |||||||
\(968\) | 9.35366 | 0.300638 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.74081 | − | 19.2461i | 0.120110 | − | 0.617954i | ||||
\(971\) | −39.7005 | −1.27405 | −0.637024 | − | 0.770844i | \(-0.719835\pi\) | ||||
−0.637024 | + | 0.770844i | \(0.719835\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 8.19540i | − | 0.262598i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.35361i | 0.203374i | ||||||||
\(977\) | 36.8070 | 1.17756 | 0.588779 | − | 0.808294i | \(-0.299609\pi\) | ||||
0.588779 | + | 0.808294i | \(0.299609\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4.66973i | − | 0.149245i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 40.4383i | − | 1.29044i | ||||||
\(983\) | − | 62.5731i | − | 1.99577i | −0.0650009 | − | 0.997885i | \(-0.520705\pi\) | ||
0.0650009 | − | 0.997885i | \(-0.479295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.00996 | − | 5.19615i | 0.0321801 | − | 0.165563i | ||||
\(986\) | 8.80886 | 0.280531 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 37.1227i | − | 1.18103i | ||||||
\(989\) | 15.4283i | 0.490591i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.8039 | −1.10558 | −0.552791 | − | 0.833320i | \(-0.686437\pi\) | ||||
−0.552791 | + | 0.833320i | \(0.686437\pi\) | |||||||
\(992\) | − | 8.65515i | − | 0.274801i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.60367 | + | 1.47791i | 0.241053 | + | 0.0468528i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.8631 | 1.54751 | 0.773755 | − | 0.633485i | \(-0.218376\pi\) | ||||
0.773755 | + | 0.633485i | \(0.218376\pi\) | |||||||
\(998\) | 17.4490 | 0.552339 | ||||||||
\(999\) | 0 | 0 |
(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 | 4410.2.d.b.4409.8 | 16 | ||
3.2 | odd | 2 | 4410.2.d.a.4409.9 | 16 | |||
5.4 | even | 2 | 4410.2.d.a.4409.7 | 16 | |||
7.4 | even | 3 | 630.2.bo.a.89.3 | yes | 16 | ||
7.5 | odd | 6 | 630.2.bo.a.269.1 | yes | 16 | ||
7.6 | odd | 2 | inner | 4410.2.d.b.4409.9 | 16 | ||
15.14 | odd | 2 | inner | 4410.2.d.b.4409.10 | 16 | ||
21.5 | even | 6 | 630.2.bo.b.269.8 | yes | 16 | ||
21.11 | odd | 6 | 630.2.bo.b.89.6 | yes | 16 | ||
21.20 | even | 2 | 4410.2.d.a.4409.8 | 16 | |||
35.4 | even | 6 | 630.2.bo.b.89.8 | yes | 16 | ||
35.12 | even | 12 | 3150.2.bf.f.1151.9 | 32 | |||
35.18 | odd | 12 | 3150.2.bf.f.1601.10 | 32 | |||
35.19 | odd | 6 | 630.2.bo.b.269.6 | yes | 16 | ||
35.32 | odd | 12 | 3150.2.bf.f.1601.7 | 32 | |||
35.33 | even | 12 | 3150.2.bf.f.1151.8 | 32 | |||
35.34 | odd | 2 | 4410.2.d.a.4409.10 | 16 | |||
105.32 | even | 12 | 3150.2.bf.f.1601.9 | 32 | |||
105.47 | odd | 12 | 3150.2.bf.f.1151.7 | 32 | |||
105.53 | even | 12 | 3150.2.bf.f.1601.8 | 32 | |||
105.68 | odd | 12 | 3150.2.bf.f.1151.10 | 32 | |||
105.74 | odd | 6 | 630.2.bo.a.89.1 | ✓ | 16 | ||
105.89 | even | 6 | 630.2.bo.a.269.3 | yes | 16 | ||
105.104 | even | 2 | inner | 4410.2.d.b.4409.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.1 | ✓ | 16 | 105.74 | odd | 6 | ||
630.2.bo.a.89.3 | yes | 16 | 7.4 | even | 3 | ||
630.2.bo.a.269.1 | yes | 16 | 7.5 | odd | 6 | ||
630.2.bo.a.269.3 | yes | 16 | 105.89 | even | 6 | ||
630.2.bo.b.89.6 | yes | 16 | 21.11 | odd | 6 | ||
630.2.bo.b.89.8 | yes | 16 | 35.4 | even | 6 | ||
630.2.bo.b.269.6 | yes | 16 | 35.19 | odd | 6 | ||
630.2.bo.b.269.8 | yes | 16 | 21.5 | even | 6 | ||
3150.2.bf.f.1151.7 | 32 | 105.47 | odd | 12 | |||
3150.2.bf.f.1151.8 | 32 | 35.33 | even | 12 | |||
3150.2.bf.f.1151.9 | 32 | 35.12 | even | 12 | |||
3150.2.bf.f.1151.10 | 32 | 105.68 | odd | 12 | |||
3150.2.bf.f.1601.7 | 32 | 35.32 | odd | 12 | |||
3150.2.bf.f.1601.8 | 32 | 105.53 | even | 12 | |||
3150.2.bf.f.1601.9 | 32 | 105.32 | even | 12 | |||
3150.2.bf.f.1601.10 | 32 | 35.18 | odd | 12 | |||
4410.2.d.a.4409.7 | 16 | 5.4 | even | 2 | |||
4410.2.d.a.4409.8 | 16 | 21.20 | even | 2 | |||
4410.2.d.a.4409.9 | 16 | 3.2 | odd | 2 | |||
4410.2.d.a.4409.10 | 16 | 35.34 | odd | 2 | |||
4410.2.d.b.4409.7 | 16 | 105.104 | even | 2 | inner | ||
4410.2.d.b.4409.8 | 16 | 1.1 | even | 1 | trivial | ||
4410.2.d.b.4409.9 | 16 | 7.6 | odd | 2 | inner | ||
4410.2.d.b.4409.10 | 16 | 15.14 | odd | 2 | inner |