Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(881,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1386.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0672657201\) |
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: | \( x^{16} - 4x^{14} + 8x^{12} + 80x^{10} + 1189x^{8} - 2028x^{6} + 1800x^{4} + 1080x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.9 | ||
Root | \(-0.876932 + 2.11710i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.881 |
Dual form | 1386.2.g.a.881.1 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −4.23420 | −1.89359 | −0.946796 | − | 0.321834i | \(-0.895701\pi\) | ||||
−0.946796 | + | 0.321834i | \(0.895701\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.59178 | − | 0.531652i | −0.979602 | − | 0.200946i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 4.23420i | − | 1.33897i | ||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0.531652 | − | 2.59178i | 0.142090 | − | 0.692683i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.29751 | −1.28483 | −0.642417 | − | 0.766355i | \(-0.722068\pi\) | ||||
−0.642417 | + | 0.766355i | \(0.722068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.250123i | 0.0573822i | 0.999588 | + | 0.0286911i | \(0.00913392\pi\) | ||||
−0.999588 | + | 0.0286911i | \(0.990866\pi\) | |||||||
\(20\) | 4.23420 | 0.946796 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 4.50225i | 0.938783i | 0.882990 | + | 0.469392i | \(0.155527\pi\) | ||||
−0.882990 | + | 0.469392i | \(0.844473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.9285 | 2.58569 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.59178 | + | 0.531652i | 0.489801 | + | 0.100473i | ||||
\(29\) | 1.05907i | 0.196665i | 0.995154 | + | 0.0983324i | \(0.0313508\pi\) | ||||
−0.995154 | + | 0.0983324i | \(0.968649\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.32489i | − | 1.13598i | −0.823034 | − | 0.567992i | \(-0.807720\pi\) | ||
0.823034 | − | 0.567992i | \(-0.192280\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5.29751i | − | 0.908515i | ||||||
\(35\) | 10.9741 | + | 2.25112i | 1.85497 | + | 0.380509i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50225 | 0.411367 | 0.205683 | − | 0.978619i | \(-0.434058\pi\) | ||||
0.205683 | + | 0.978619i | \(0.434058\pi\) | |||||||
\(38\) | −0.250123 | −0.0405754 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.23420i | 0.669486i | ||||||||
\(41\) | −1.31343 | −0.205123 | −0.102562 | − | 0.994727i | \(-0.532704\pi\) | ||||
−0.102562 | + | 0.994727i | \(0.532704\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.18357 | 1.09548 | 0.547742 | − | 0.836647i | \(-0.315488\pi\) | ||||
0.547742 | + | 0.836647i | \(0.315488\pi\) | |||||||
\(44\) | 1.00000i | 0.150756i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.50225 | −0.663820 | ||||||||
\(47\) | 7.15497 | 1.04366 | 0.521830 | − | 0.853049i | \(-0.325250\pi\) | ||||
0.521830 | + | 0.853049i | \(0.325250\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.43469 | + | 2.75586i | 0.919242 | + | 0.393694i | ||||
\(50\) | 12.9285i | 1.82836i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.68132i | − | 0.643029i | −0.946905 | − | 0.321515i | \(-0.895808\pi\) | ||
0.946905 | − | 0.321515i | \(-0.104192\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.23420i | 0.570939i | ||||||||
\(56\) | −0.531652 | + | 2.59178i | −0.0710450 | + | 0.346342i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.05907 | −0.139063 | ||||||||
\(59\) | −8.46840 | −1.10249 | −0.551246 | − | 0.834343i | \(-0.685847\pi\) | ||||
−0.551246 | + | 0.834343i | \(0.685847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.8102i | 1.89625i | 0.317896 | + | 0.948125i | \(0.397024\pi\) | ||||
−0.317896 | + | 0.948125i | \(0.602976\pi\) | |||||||
\(62\) | 6.32489 | 0.803262 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.42621 | 1.15159 | 0.575797 | − | 0.817592i | \(-0.304692\pi\) | ||||
0.575797 | + | 0.817592i | \(0.304692\pi\) | |||||||
\(68\) | 5.29751 | 0.642417 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.25112 | + | 10.9741i | −0.269061 | + | 1.31166i | ||||
\(71\) | 12.9875i | 1.54134i | 0.637237 | + | 0.770668i | \(0.280077\pi\) | ||||
−0.637237 | + | 0.770668i | \(0.719923\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.15497i | − | 0.837426i | −0.908119 | − | 0.418713i | \(-0.862481\pi\) | ||
0.908119 | − | 0.418713i | \(-0.137519\pi\) | |||||||
\(74\) | 2.50225i | 0.290880i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 0.250123i | − | 0.0286911i | ||||||
\(77\) | −0.531652 | + | 2.59178i | −0.0605874 | + | 0.295361i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.377749 | −0.0425001 | −0.0212501 | − | 0.999774i | \(-0.506765\pi\) | ||||
−0.0212501 | + | 0.999774i | \(0.506765\pi\) | |||||||
\(80\) | −4.23420 | −0.473398 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 1.31343i | − | 0.145044i | ||||||
\(83\) | 1.84057 | 0.202029 | 0.101014 | − | 0.994885i | \(-0.467791\pi\) | ||||
0.101014 | + | 0.994885i | \(0.467791\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.4307 | 2.43295 | ||||||||
\(86\) | 7.18357i | 0.774624i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −1.56355 | −0.165736 | −0.0828681 | − | 0.996561i | \(-0.526408\pi\) | ||||
−0.0828681 | + | 0.996561i | \(0.526408\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 4.50225i | − | 0.469392i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.15497i | 0.737979i | ||||||||
\(95\) | − | 1.05907i | − | 0.108659i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.96815i | − | 0.809044i | −0.914528 | − | 0.404522i | \(-0.867438\pi\) | ||
0.914528 | − | 0.404522i | \(-0.132562\pi\) | |||||||
\(98\) | −2.75586 | + | 6.43469i | −0.278384 | + | 0.650002i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −12.9285 | −1.29285 | ||||||||
\(101\) | 15.6065 | 1.55290 | 0.776451 | − | 0.630177i | \(-0.217018\pi\) | ||||
0.776451 | + | 0.630177i | \(0.217018\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.84057i | 0.181357i | 0.995880 | + | 0.0906784i | \(0.0289035\pi\) | ||||
−0.995880 | + | 0.0906784i | \(0.971096\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.68132 | 0.454690 | ||||||||
\(107\) | − | 17.2365i | − | 1.66632i | −0.553034 | − | 0.833159i | \(-0.686530\pi\) | ||
0.553034 | − | 0.833159i | \(-0.313470\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.8103 | −1.70592 | −0.852959 | − | 0.521978i | \(-0.825194\pi\) | ||||
−0.852959 | + | 0.521978i | \(0.825194\pi\) | |||||||
\(110\) | −4.23420 | −0.403715 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.59178 | − | 0.531652i | −0.244901 | − | 0.0502364i | ||||
\(113\) | 9.80396i | 0.922279i | 0.887328 | + | 0.461139i | \(0.152559\pi\) | ||||
−0.887328 | + | 0.461139i | \(0.847441\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 19.0634i | − | 1.77767i | ||||||
\(116\) | − | 1.05907i | − | 0.0983324i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 8.46840i | − | 0.779580i | ||||||
\(119\) | 13.7300 | + | 2.81643i | 1.25863 | + | 0.258182i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −14.8102 | −1.34085 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.32489i | 0.567992i | ||||||||
\(125\) | −33.5707 | −3.00265 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.1120 | −1.16350 | −0.581752 | − | 0.813366i | \(-0.697633\pi\) | ||||
−0.581752 | + | 0.813366i | \(0.697633\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.3928 | 1.43224 | 0.716121 | − | 0.697976i | \(-0.245916\pi\) | ||||
0.716121 | + | 0.697976i | \(0.245916\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.132979 | − | 0.648266i | 0.0115307 | − | 0.0562118i | ||||
\(134\) | 9.42621i | 0.814300i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.29751i | 0.454257i | ||||||||
\(137\) | − | 17.6688i | − | 1.50955i | −0.655983 | − | 0.754776i | \(-0.727746\pi\) | ||
0.655983 | − | 0.754776i | \(-0.272254\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.8840i | − | 1.43208i | −0.698059 | − | 0.716041i | \(-0.745952\pi\) | ||
0.698059 | − | 0.716041i | \(-0.254048\pi\) | |||||||
\(140\) | −10.9741 | − | 2.25112i | −0.927484 | − | 0.190255i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.9875 | −1.08989 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.48432i | − | 0.372403i | ||||||
\(146\) | 7.15497 | 0.592150 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.50225 | −0.205683 | ||||||||
\(149\) | 10.8694i | 0.890455i | 0.895418 | + | 0.445227i | \(0.146877\pi\) | ||||
−0.895418 | + | 0.445227i | \(0.853123\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.17110 | 0.664954 | 0.332477 | − | 0.943111i | \(-0.392116\pi\) | ||||
0.332477 | + | 0.943111i | \(0.392116\pi\) | |||||||
\(152\) | 0.250123 | 0.0202877 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.59178 | − | 0.531652i | −0.208852 | − | 0.0428418i | ||||
\(155\) | 26.7809i | 2.15109i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.6348i | − | 1.64684i | −0.567433 | − | 0.823420i | \(-0.692063\pi\) | ||
0.567433 | − | 0.823420i | \(-0.307937\pi\) | |||||||
\(158\) | − | 0.377749i | − | 0.0300521i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 4.23420i | − | 0.334743i | ||||||
\(161\) | 2.39363 | − | 11.6688i | 0.188644 | − | 0.919634i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.62039 | 0.675201 | 0.337601 | − | 0.941289i | \(-0.390385\pi\) | ||||
0.337601 | + | 0.941289i | \(0.390385\pi\) | |||||||
\(164\) | 1.31343 | 0.102562 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.84057i | 0.142856i | ||||||||
\(167\) | −2.88486 | −0.223237 | −0.111618 | − | 0.993751i | \(-0.535603\pi\) | ||||
−0.111618 | + | 0.993751i | \(0.535603\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 22.4307i | 1.72036i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.18357 | −0.547742 | ||||||||
\(173\) | 11.8535 | 0.901205 | 0.450603 | − | 0.892725i | \(-0.351209\pi\) | ||||
0.450603 | + | 0.892725i | \(0.351209\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −33.5078 | − | 6.87344i | −2.53295 | − | 0.519584i | ||||
\(176\) | − | 1.00000i | − | 0.0753778i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 1.56355i | − | 0.117193i | ||||||
\(179\) | − | 13.4262i | − | 1.00352i | −0.865006 | − | 0.501761i | \(-0.832686\pi\) | ||
0.865006 | − | 0.501761i | \(-0.167314\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.8766i | 1.47742i | 0.674026 | + | 0.738708i | \(0.264564\pi\) | ||||
−0.674026 | + | 0.738708i | \(0.735436\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.50225 | 0.331910 | ||||||||
\(185\) | −10.5950 | −0.778961 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.29751i | 0.387392i | ||||||||
\(188\) | −7.15497 | −0.521830 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.05907 | 0.0768332 | ||||||||
\(191\) | − | 0.253253i | − | 0.0183247i | −0.999958 | − | 0.00916237i | \(-0.997083\pi\) | ||
0.999958 | − | 0.00916237i | \(-0.00291651\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.8524 | 0.925137 | 0.462569 | − | 0.886583i | \(-0.346928\pi\) | ||||
0.462569 | + | 0.886583i | \(0.346928\pi\) | |||||||
\(194\) | 7.96815 | 0.572080 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.43469 | − | 2.75586i | −0.459621 | − | 0.196847i | ||||
\(197\) | − | 25.4352i | − | 1.81218i | −0.423082 | − | 0.906091i | \(-0.639052\pi\) | ||
0.423082 | − | 0.906091i | \(-0.360948\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.7615i | 1.61352i | 0.590882 | + | 0.806758i | \(0.298780\pi\) | ||||
−0.590882 | + | 0.806758i | \(0.701220\pi\) | |||||||
\(200\) | − | 12.9285i | − | 0.914180i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.6065i | 1.09807i | ||||||||
\(203\) | 0.563058 | − | 2.74489i | 0.0395189 | − | 0.192653i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.56132 | 0.388419 | ||||||||
\(206\) | −1.84057 | −0.128239 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.250123 | 0.0173014 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.6733 | −1.14784 | −0.573920 | − | 0.818911i | \(-0.694578\pi\) | ||||
−0.573920 | + | 0.818911i | \(0.694578\pi\) | |||||||
\(212\) | 4.68132i | 0.321515i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.2365 | 1.17826 | ||||||||
\(215\) | −30.4167 | −2.07440 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.36265 | + | 16.3928i | −0.228271 | + | 1.11281i | ||||
\(218\) | − | 17.8103i | − | 1.20627i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 4.23420i | − | 0.285470i | ||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.0085i | 1.27290i | 0.771317 | + | 0.636451i | \(0.219598\pi\) | ||||
−0.771317 | + | 0.636451i | \(0.780402\pi\) | |||||||
\(224\) | 0.531652 | − | 2.59178i | 0.0355225 | − | 0.173171i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.80396 | −0.652150 | ||||||||
\(227\) | 11.1122 | 0.737540 | 0.368770 | − | 0.929521i | \(-0.379779\pi\) | ||||
0.368770 | + | 0.929521i | \(0.379779\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.34032i | − | 0.0885711i | −0.999019 | − | 0.0442856i | \(-0.985899\pi\) | ||
0.999019 | − | 0.0442856i | \(-0.0141011\pi\) | |||||||
\(230\) | 19.0634 | 1.25700 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.05907 | 0.0695315 | ||||||||
\(233\) | 14.4853i | 0.948962i | 0.880266 | + | 0.474481i | \(0.157364\pi\) | ||||
−0.880266 | + | 0.474481i | \(0.842636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.2956 | −1.97627 | ||||||||
\(236\) | 8.46840 | 0.551246 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.81643 | + | 13.7300i | −0.182562 | + | 0.889983i | ||||
\(239\) | − | 2.01696i | − | 0.130467i | −0.997870 | − | 0.0652333i | \(-0.979221\pi\) | ||
0.997870 | − | 0.0652333i | \(-0.0207792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 12.1395i | − | 0.781977i | −0.920396 | − | 0.390988i | \(-0.872133\pi\) | ||
0.920396 | − | 0.390988i | \(-0.127867\pi\) | |||||||
\(242\) | − | 1.00000i | − | 0.0642824i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 14.8102i | − | 0.948125i | ||||||
\(245\) | −27.2458 | − | 11.6688i | −1.74067 | − | 0.745495i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.32489 | −0.401631 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 33.5707i | − | 2.12320i | ||||||
\(251\) | 6.34179 | 0.400290 | 0.200145 | − | 0.979766i | \(-0.435859\pi\) | ||||
0.200145 | + | 0.979766i | \(0.435859\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.50225 | 0.283054 | ||||||||
\(254\) | − | 13.1120i | − | 0.822722i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.56355 | 0.0975317 | 0.0487658 | − | 0.998810i | \(-0.484471\pi\) | ||||
0.0487658 | + | 0.998810i | \(0.484471\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.48528 | − | 1.33032i | −0.402976 | − | 0.0826624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.3928i | 1.01275i | ||||||||
\(263\) | − | 6.18171i | − | 0.381180i | −0.981670 | − | 0.190590i | \(-0.938960\pi\) | ||
0.981670 | − | 0.190590i | \(-0.0610402\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.8217i | 1.21763i | ||||||||
\(266\) | 0.648266 | + | 0.132979i | 0.0397477 | + | 0.00815344i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.42621 | −0.575797 | ||||||||
\(269\) | 25.0832 | 1.52935 | 0.764676 | − | 0.644415i | \(-0.222899\pi\) | ||||
0.764676 | + | 0.644415i | \(0.222899\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.15188i | − | 0.191463i | −0.995407 | − | 0.0957315i | \(-0.969481\pi\) | ||
0.995407 | − | 0.0957315i | \(-0.0305190\pi\) | |||||||
\(272\) | −5.29751 | −0.321208 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.6688 | 1.06741 | ||||||||
\(275\) | − | 12.9285i | − | 0.779615i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.04211 | 0.0626142 | 0.0313071 | − | 0.999510i | \(-0.490033\pi\) | ||||
0.0313071 | + | 0.999510i | \(0.490033\pi\) | |||||||
\(278\) | 16.8840 | 1.01263 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.25112 | − | 10.9741i | 0.134530 | − | 0.655830i | ||||
\(281\) | 22.9706i | 1.37031i | 0.728398 | + | 0.685154i | \(0.240265\pi\) | ||||
−0.728398 | + | 0.685154i | \(0.759735\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.7979i | 1.41464i | 0.706896 | + | 0.707318i | \(0.250095\pi\) | ||||
−0.706896 | + | 0.707318i | \(0.749905\pi\) | |||||||
\(284\) | − | 12.9875i | − | 0.770668i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.40412 | + | 0.698287i | 0.200939 | + | 0.0412186i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.0636 | 0.650798 | ||||||||
\(290\) | 4.48432 | 0.263329 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.15497i | 0.418713i | ||||||||
\(293\) | 13.9801 | 0.816727 | 0.408364 | − | 0.912819i | \(-0.366100\pi\) | ||||
0.408364 | + | 0.912819i | \(0.366100\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 35.8569 | 2.08767 | ||||||||
\(296\) | − | 2.50225i | − | 0.145440i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.8694 | −0.629646 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.6183 | − | 3.81916i | −1.07314 | − | 0.220133i | ||||
\(302\) | 8.17110i | 0.470194i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.250123i | 0.0143456i | ||||||||
\(305\) | − | 62.7093i | − | 3.59073i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.5897i | 1.91706i | 0.284984 | + | 0.958532i | \(0.408012\pi\) | ||||
−0.284984 | + | 0.958532i | \(0.591988\pi\) | |||||||
\(308\) | 0.531652 | − | 2.59178i | 0.0302937 | − | 0.147681i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −26.7809 | −1.52105 | ||||||||
\(311\) | −11.6393 | −0.660004 | −0.330002 | − | 0.943980i | \(-0.607049\pi\) | ||||
−0.330002 | + | 0.943980i | \(0.607049\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.83057i | 0.103470i | 0.998661 | + | 0.0517350i | \(0.0164751\pi\) | ||||
−0.998661 | + | 0.0517350i | \(0.983525\pi\) | |||||||
\(314\) | 20.6348 | 1.16449 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.377749 | 0.0212501 | ||||||||
\(317\) | − | 29.9348i | − | 1.68131i | −0.541574 | − | 0.840653i | \(-0.682171\pi\) | ||
0.541574 | − | 0.840653i | \(-0.317829\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.05907 | 0.0592967 | ||||||||
\(320\) | 4.23420 | 0.236699 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.6688 | + | 2.39363i | 0.650280 | + | 0.133392i | ||||
\(323\) | − | 1.32503i | − | 0.0737266i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.62039i | 0.477439i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.31343i | 0.0725219i | ||||||||
\(329\) | −18.5441 | − | 3.80396i | −1.02237 | − | 0.209719i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.69643 | −0.313104 | −0.156552 | − | 0.987670i | \(-0.550038\pi\) | ||||
−0.156552 | + | 0.987670i | \(0.550038\pi\) | |||||||
\(332\) | −1.84057 | −0.101014 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 2.88486i | − | 0.157852i | ||||||
\(335\) | −39.9125 | −2.18065 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.637355 | 0.0347189 | 0.0173595 | − | 0.999849i | \(-0.494474\pi\) | ||||
0.0173595 | + | 0.999849i | \(0.494474\pi\) | |||||||
\(338\) | 13.0000i | 0.707107i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −22.4307 | −1.21648 | ||||||||
\(341\) | −6.32489 | −0.342512 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.2122 | − | 10.5636i | −0.821380 | − | 0.570381i | ||||
\(344\) | − | 7.18357i | − | 0.387312i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.8535i | 0.637248i | ||||||||
\(347\) | − | 21.4728i | − | 1.15272i | −0.817196 | − | 0.576360i | \(-0.804472\pi\) | ||
0.817196 | − | 0.576360i | \(-0.195528\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9.52269i | − | 0.509738i | −0.966976 | − | 0.254869i | \(-0.917968\pi\) | ||
0.966976 | − | 0.254869i | \(-0.0820323\pi\) | |||||||
\(350\) | 6.87344 | − | 33.5078i | 0.367401 | − | 1.79107i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 32.3101 | 1.71969 | 0.859845 | − | 0.510555i | \(-0.170560\pi\) | ||||
0.859845 | + | 0.510555i | \(0.170560\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 54.9918i | − | 2.91866i | ||||||
\(356\) | 1.56355 | 0.0828681 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.4262 | 0.709597 | ||||||||
\(359\) | − | 3.07604i | − | 0.162347i | −0.996700 | − | 0.0811735i | \(-0.974133\pi\) | ||
0.996700 | − | 0.0811735i | \(-0.0258668\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9374 | 0.996707 | ||||||||
\(362\) | −19.8766 | −1.04469 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.2956i | 1.58574i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.6508i | 0.869163i | 0.900633 | + | 0.434581i | \(0.143104\pi\) | ||||
−0.900633 | + | 0.434581i | \(0.856896\pi\) | |||||||
\(368\) | 4.50225i | 0.234696i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 10.5950i | − | 0.550808i | ||||||
\(371\) | −2.48884 | + | 12.1330i | −0.129214 | + | 0.629913i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.37163 | −0.381688 | −0.190844 | − | 0.981620i | \(-0.561123\pi\) | ||||
−0.190844 | + | 0.981620i | \(0.561123\pi\) | |||||||
\(374\) | −5.29751 | −0.273927 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 7.15497i | − | 0.368990i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.62039 | 0.237333 | 0.118667 | − | 0.992934i | \(-0.462138\pi\) | ||||
0.118667 | + | 0.992934i | \(0.462138\pi\) | |||||||
\(380\) | 1.05907i | 0.0543293i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.253253 | 0.0129576 | ||||||||
\(383\) | −26.9159 | −1.37534 | −0.687670 | − | 0.726023i | \(-0.741366\pi\) | ||||
−0.687670 | + | 0.726023i | \(0.741366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.25112 | − | 10.9741i | 0.114728 | − | 0.559294i | ||||
\(386\) | 12.8524i | 0.654171i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.96815i | 0.404522i | ||||||||
\(389\) | 5.20053i | 0.263677i | 0.991271 | + | 0.131839i | \(0.0420881\pi\) | ||||
−0.991271 | + | 0.131839i | \(0.957912\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 23.8507i | − | 1.20618i | ||||||
\(392\) | 2.75586 | − | 6.43469i | 0.139192 | − | 0.325001i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25.4352 | 1.28141 | ||||||||
\(395\) | 1.59947 | 0.0804779 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 7.38608i | − | 0.370697i | −0.982673 | − | 0.185348i | \(-0.940659\pi\) | ||
0.982673 | − | 0.185348i | \(-0.0593413\pi\) | |||||||
\(398\) | −22.7615 | −1.14093 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.9285 | 0.646423 | ||||||||
\(401\) | − | 16.0699i | − | 0.802493i | −0.915970 | − | 0.401247i | \(-0.868577\pi\) | ||
0.915970 | − | 0.401247i | \(-0.131423\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −15.6065 | −0.776451 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.74489 | + | 0.563058i | 0.136226 | + | 0.0279441i | ||||
\(407\) | − | 2.50225i | − | 0.124032i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.1625i | 1.09586i | 0.836523 | + | 0.547932i | \(0.184585\pi\) | ||||
−0.836523 | + | 0.547932i | \(0.815415\pi\) | |||||||
\(410\) | 5.56132i | 0.274654i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 1.84057i | − | 0.0906784i | ||||||
\(413\) | 21.9483 | + | 4.50225i | 1.08000 | + | 0.221541i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.79335 | −0.382560 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.250123i | 0.0122339i | ||||||||
\(419\) | 24.9050 | 1.21669 | 0.608343 | − | 0.793674i | \(-0.291834\pi\) | ||||
0.608343 | + | 0.793674i | \(0.291834\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.47281 | −0.364202 | −0.182101 | − | 0.983280i | \(-0.558290\pi\) | ||||
−0.182101 | + | 0.983280i | \(0.558290\pi\) | |||||||
\(422\) | − | 16.6733i | − | 0.811646i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.68132 | −0.227345 | ||||||||
\(425\) | −68.4886 | −3.32218 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.87387 | − | 38.3848i | 0.381043 | − | 1.85757i | ||||
\(428\) | 17.2365i | 0.833159i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 30.4167i | − | 1.46682i | ||||||
\(431\) | 14.6797i | 0.707096i | 0.935416 | + | 0.353548i | \(0.115025\pi\) | ||||
−0.935416 | + | 0.353548i | \(0.884975\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 32.4714i | − | 1.56048i | −0.625481 | − | 0.780239i | \(-0.715097\pi\) | ||
0.625481 | − | 0.780239i | \(-0.284903\pi\) | |||||||
\(434\) | −16.3928 | − | 3.36265i | −0.786878 | − | 0.161412i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.8103 | 0.852959 | ||||||||
\(437\) | −1.12612 | −0.0538695 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.3643i | 1.59239i | 0.605038 | + | 0.796197i | \(0.293158\pi\) | ||||
−0.605038 | + | 0.796197i | \(0.706842\pi\) | |||||||
\(440\) | 4.23420 | 0.201858 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.9205i | 1.32654i | 0.748379 | + | 0.663271i | \(0.230832\pi\) | ||||
−0.748379 | + | 0.663271i | \(0.769168\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.62039 | 0.313837 | ||||||||
\(446\) | −19.0085 | −0.900078 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.59178 | + | 0.531652i | 0.122450 | + | 0.0251182i | ||||
\(449\) | 12.4413i | 0.587142i | 0.955937 | + | 0.293571i | \(0.0948437\pi\) | ||||
−0.955937 | + | 0.293571i | \(0.905156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.31343i | 0.0618469i | ||||||||
\(452\) | − | 9.80396i | − | 0.461139i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.1122i | 0.521519i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.48528 | 0.303369 | 0.151684 | − | 0.988429i | \(-0.451530\pi\) | ||||
0.151684 | + | 0.988429i | \(0.451530\pi\) | |||||||
\(458\) | 1.34032 | 0.0626292 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 19.0634i | 0.888836i | ||||||||
\(461\) | −2.38461 | −0.111062 | −0.0555312 | − | 0.998457i | \(-0.517685\pi\) | ||||
−0.0555312 | + | 0.998457i | \(0.517685\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.35815 | 0.388436 | 0.194218 | − | 0.980958i | \(-0.437783\pi\) | ||||
0.194218 | + | 0.980958i | \(0.437783\pi\) | |||||||
\(464\) | 1.05907i | 0.0491662i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.4853 | −0.671018 | ||||||||
\(467\) | 25.8336 | 1.19544 | 0.597719 | − | 0.801706i | \(-0.296074\pi\) | ||||
0.597719 | + | 0.801706i | \(0.296074\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.4307 | − | 5.01147i | −1.12810 | − | 0.231408i | ||||
\(470\) | − | 30.2956i | − | 1.39743i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.46840i | 0.389790i | ||||||||
\(473\) | − | 7.18357i | − | 0.330301i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.23371i | 0.148373i | ||||||||
\(476\) | −13.7300 | − | 2.81643i | −0.629313 | − | 0.129091i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.01696 | 0.0922538 | ||||||||
\(479\) | −21.9102 | −1.00110 | −0.500552 | − | 0.865706i | \(-0.666870\pi\) | ||||
−0.500552 | + | 0.865706i | \(0.666870\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 12.1395 | 0.552941 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 33.7388i | 1.53200i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.4898 | −1.15505 | −0.577526 | − | 0.816372i | \(-0.695982\pi\) | ||||
−0.577526 | + | 0.816372i | \(0.695982\pi\) | |||||||
\(488\) | 14.8102 | 0.670426 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.6688 | − | 27.2458i | 0.527145 | − | 1.23084i | ||||
\(491\) | − | 13.5067i | − | 0.609551i | −0.952424 | − | 0.304775i | \(-0.901419\pi\) | ||
0.952424 | − | 0.304775i | \(-0.0985814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.61044i | − | 0.252682i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 6.32489i | − | 0.283996i | ||||||
\(497\) | 6.90485 | − | 33.6609i | 0.309725 | − | 1.50990i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.90700 | 0.219667 | 0.109834 | − | 0.993950i | \(-0.464968\pi\) | ||||
0.109834 | + | 0.993950i | \(0.464968\pi\) | |||||||
\(500\) | 33.5707 | 1.50133 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.34179i | 0.283048i | ||||||||
\(503\) | −14.0519 | −0.626545 | −0.313273 | − | 0.949663i | \(-0.601425\pi\) | ||||
−0.313273 | + | 0.949663i | \(0.601425\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −66.0810 | −2.94056 | ||||||||
\(506\) | 4.50225i | 0.200149i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.1120 | 0.581752 | ||||||||
\(509\) | 42.0201 | 1.86251 | 0.931253 | − | 0.364373i | \(-0.118717\pi\) | ||||
0.931253 | + | 0.364373i | \(0.118717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.80396 | + | 18.5441i | −0.168277 | + | 0.820345i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.56355i | 0.0689653i | ||||||||
\(515\) | − | 7.79335i | − | 0.343416i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 7.15497i | − | 0.314675i | ||||||
\(518\) | 1.33032 | − | 6.48528i | 0.0584511 | − | 0.284947i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 43.4053 | 1.90162 | 0.950811 | − | 0.309773i | \(-0.100253\pi\) | ||||
0.950811 | + | 0.309773i | \(0.100253\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.60734i | 0.0702843i | 0.999382 | + | 0.0351421i | \(0.0111884\pi\) | ||||
−0.999382 | + | 0.0351421i | \(0.988812\pi\) | |||||||
\(524\) | −16.3928 | −0.716121 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.18171 | 0.269535 | ||||||||
\(527\) | 33.5062i | 1.45955i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.72978 | 0.118686 | ||||||||
\(530\) | −19.8217 | −0.860998 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.132979 | + | 0.648266i | −0.00576536 | + | 0.0281059i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 72.9829i | 3.15533i | ||||||||
\(536\) | − | 9.42621i | − | 0.407150i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.0832i | 1.08142i | ||||||||
\(539\) | 2.75586 | − | 6.43469i | 0.118703 | − | 0.277162i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.9955 | 0.472734 | 0.236367 | − | 0.971664i | \(-0.424043\pi\) | ||||
0.236367 | + | 0.971664i | \(0.424043\pi\) | |||||||
\(542\) | 3.15188 | 0.135385 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 5.29751i | − | 0.227129i | ||||||
\(545\) | 75.4124 | 3.23031 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.6733 | 1.22598 | 0.612992 | − | 0.790089i | \(-0.289966\pi\) | ||||
0.612992 | + | 0.790089i | \(0.289966\pi\) | |||||||
\(548\) | 17.6688i | 0.754776i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.9285 | 0.551271 | ||||||||
\(551\) | −0.264899 | −0.0112851 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.979045 | + | 0.200831i | 0.0416332 | + | 0.00854022i | ||||
\(554\) | 1.04211i | 0.0442749i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.8840i | 0.716041i | ||||||||
\(557\) | − | 25.4352i | − | 1.07772i | −0.842394 | − | 0.538862i | \(-0.818854\pi\) | ||
0.842394 | − | 0.538862i | \(-0.181146\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 10.9741 | + | 2.25112i | 0.463742 | + | 0.0951273i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −22.9706 | −0.968955 | ||||||||
\(563\) | −14.4973 | −0.610987 | −0.305493 | − | 0.952194i | \(-0.598821\pi\) | ||||
−0.305493 | + | 0.952194i | \(0.598821\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 41.5119i | − | 1.74642i | ||||||
\(566\) | −23.7979 | −1.00030 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.9875 | 0.544945 | ||||||||
\(569\) | 2.48528i | 0.104188i | 0.998642 | + | 0.0520942i | \(0.0165896\pi\) | ||||
−0.998642 | + | 0.0520942i | \(0.983410\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.9141 | −1.58666 | −0.793328 | − | 0.608794i | \(-0.791654\pi\) | ||||
−0.793328 | + | 0.608794i | \(0.791654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.698287 | + | 3.40412i | −0.0291459 | + | 0.142085i | ||||
\(575\) | 58.2071i | 2.42740i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.572077i | 0.0238159i | 0.999929 | + | 0.0119079i | \(0.00379051\pi\) | ||||
−0.999929 | + | 0.0119079i | \(0.996209\pi\) | |||||||
\(578\) | 11.0636i | 0.460184i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.48432i | 0.186201i | ||||||||
\(581\) | −4.77036 | − | 0.978544i | −0.197908 | − | 0.0405968i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.68132 | −0.193881 | ||||||||
\(584\) | −7.15497 | −0.296075 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.9801i | 0.577513i | ||||||||
\(587\) | 19.0296 | 0.785436 | 0.392718 | − | 0.919659i | \(-0.371535\pi\) | ||||
0.392718 | + | 0.919659i | \(0.371535\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.58200 | 0.0651853 | ||||||||
\(590\) | 35.8569i | 1.47621i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.50225 | 0.102842 | ||||||||
\(593\) | −7.58339 | −0.311412 | −0.155706 | − | 0.987803i | \(-0.549765\pi\) | ||||
−0.155706 | + | 0.987803i | \(0.549765\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −58.1355 | − | 11.9253i | −2.38332 | − | 0.488891i | ||||
\(596\) | − | 10.8694i | − | 0.445227i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.5067i | 1.04218i | 0.853503 | + | 0.521089i | \(0.174474\pi\) | ||||
−0.853503 | + | 0.521089i | \(0.825526\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 32.8631i | − | 1.34051i | −0.742129 | − | 0.670257i | \(-0.766184\pi\) | ||
0.742129 | − | 0.670257i | \(-0.233816\pi\) | |||||||
\(602\) | 3.81916 | − | 18.6183i | 0.155657 | − | 0.758824i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.17110 | −0.332477 | ||||||||
\(605\) | 4.23420 | 0.172145 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.8646i | 1.37452i | 0.726411 | + | 0.687261i | \(0.241187\pi\) | ||||
−0.726411 | + | 0.687261i | \(0.758813\pi\) | |||||||
\(608\) | −0.250123 | −0.0101438 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 62.7093 | 2.53903 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.4434 | 1.14882 | 0.574408 | − | 0.818569i | \(-0.305232\pi\) | ||||
0.574408 | + | 0.818569i | \(0.305232\pi\) | |||||||
\(614\) | −33.5897 | −1.35557 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.59178 | + | 0.531652i | 0.104426 | + | 0.0214209i | ||||
\(617\) | − | 12.0064i | − | 0.483358i | −0.970356 | − | 0.241679i | \(-0.922302\pi\) | ||
0.970356 | − | 0.241679i | \(-0.0776980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.71494i | 0.149316i | 0.997209 | + | 0.0746579i | \(0.0237865\pi\) | ||||
−0.997209 | + | 0.0746579i | \(0.976214\pi\) | |||||||
\(620\) | − | 26.7809i | − | 1.07555i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 11.6393i | − | 0.466693i | ||||||
\(623\) | 4.05239 | + | 0.831266i | 0.162355 | + | 0.0333040i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 77.5027 | 3.10011 | ||||||||
\(626\) | −1.83057 | −0.0731644 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.6348i | 0.823420i | ||||||||
\(629\) | −13.2557 | −0.528538 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.9795 | −1.07404 | −0.537019 | − | 0.843570i | \(-0.680450\pi\) | ||||
−0.537019 | + | 0.843570i | \(0.680450\pi\) | |||||||
\(632\) | 0.377749i | 0.0150261i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29.9348 | 1.18886 | ||||||||
\(635\) | 55.5189 | 2.20320 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.05907i | 0.0419291i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.23420i | 0.167371i | ||||||||
\(641\) | 20.4916i | 0.809371i | 0.914456 | + | 0.404685i | \(0.132619\pi\) | ||||
−0.914456 | + | 0.404685i | \(0.867381\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 9.59452i | − | 0.378371i | −0.981941 | − | 0.189185i | \(-0.939415\pi\) | ||
0.981941 | − | 0.189185i | \(-0.0605847\pi\) | |||||||
\(644\) | −2.39363 | + | 11.6688i | −0.0943222 | + | 0.459817i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.32503 | 0.0521326 | ||||||||
\(647\) | −37.5110 | −1.47471 | −0.737354 | − | 0.675507i | \(-0.763925\pi\) | ||||
−0.737354 | + | 0.675507i | \(0.763925\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.46840i | 0.332414i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.62039 | −0.337601 | ||||||||
\(653\) | − | 28.8964i | − | 1.13080i | −0.824816 | − | 0.565401i | \(-0.808721\pi\) | ||
0.824816 | − | 0.565401i | \(-0.191279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −69.4102 | −2.71208 | ||||||||
\(656\) | −1.31343 | −0.0512808 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.80396 | − | 18.5441i | 0.148294 | − | 0.722926i | ||||
\(659\) | 45.5957i | 1.77616i | 0.459693 | + | 0.888078i | \(0.347959\pi\) | ||||
−0.459693 | + | 0.888078i | \(0.652041\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.42890i | 0.133369i | 0.997774 | + | 0.0666843i | \(0.0212420\pi\) | ||||
−0.997774 | + | 0.0666843i | \(0.978758\pi\) | |||||||
\(662\) | − | 5.69643i | − | 0.221398i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1.84057i | − | 0.0714280i | ||||||
\(665\) | −0.563058 | + | 2.74489i | −0.0218345 | + | 0.106442i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.76820 | −0.184626 | ||||||||
\(668\) | 2.88486 | 0.111618 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 39.9125i | − | 1.54195i | ||||||
\(671\) | 14.8102 | 0.571741 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.2069 | −0.894558 | −0.447279 | − | 0.894394i | \(-0.647607\pi\) | ||||
−0.447279 | + | 0.894394i | \(0.647607\pi\) | |||||||
\(674\) | 0.637355i | 0.0245500i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | −8.06674 | −0.310030 | −0.155015 | − | 0.987912i | \(-0.549543\pi\) | ||||
−0.155015 | + | 0.987912i | \(0.549543\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.23629 | + | 20.6517i | −0.162574 | + | 0.792541i | ||||
\(680\) | − | 22.4307i | − | 0.860178i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 6.32489i | − | 0.242193i | ||||||
\(683\) | 34.2876i | 1.31198i | 0.754770 | + | 0.655989i | \(0.227748\pi\) | ||||
−0.754770 | + | 0.655989i | \(0.772252\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 74.8135i | 2.85848i | ||||||||
\(686\) | 10.5636 | − | 15.2122i | 0.403320 | − | 0.580804i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.18357 | 0.273871 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.1840i | 1.87105i | 0.353261 | + | 0.935525i | \(0.385073\pi\) | ||||
−0.353261 | + | 0.935525i | \(0.614927\pi\) | |||||||
\(692\) | −11.8535 | −0.450603 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.4728 | 0.815097 | ||||||||
\(695\) | 71.4902i | 2.71178i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.95789 | 0.263549 | ||||||||
\(698\) | 9.52269 | 0.360439 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 33.5078 | + | 6.87344i | 1.26647 | + | 0.259792i | ||||
\(701\) | 37.6079i | 1.42043i | 0.703984 | + | 0.710216i | \(0.251403\pi\) | ||||
−0.703984 | + | 0.710216i | \(0.748597\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.625870i | 0.0236051i | ||||||||
\(704\) | 1.00000i | 0.0376889i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.3101i | 1.21600i | ||||||||
\(707\) | −40.4486 | − | 8.29722i | −1.52123 | − | 0.312049i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.7093 | 1.37865 | 0.689324 | − | 0.724453i | \(-0.257908\pi\) | ||||
0.689324 | + | 0.724453i | \(0.257908\pi\) | |||||||
\(710\) | 54.9918 | 2.06381 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.56355i | 0.0585966i | ||||||||
\(713\) | 28.4762 | 1.06644 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.4262i | 0.501761i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.07604 | 0.114797 | ||||||||
\(719\) | 50.7486 | 1.89260 | 0.946301 | − | 0.323286i | \(-0.104788\pi\) | ||||
0.946301 | + | 0.323286i | \(0.104788\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.978544 | − | 4.77036i | 0.0364429 | − | 0.177658i | ||||
\(722\) | 18.9374i | 0.704778i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 19.8766i | − | 0.738708i | ||||||
\(725\) | 13.6922i | 0.508514i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.570936i | 0.0211748i | 0.999944 | + | 0.0105874i | \(0.00337014\pi\) | ||||
−0.999944 | + | 0.0105874i | \(0.996630\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −30.2956 | −1.12129 | ||||||||
\(731\) | −38.0550 | −1.40751 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.6836i | 0.468479i | 0.972179 | + | 0.234239i | \(0.0752600\pi\) | ||||
−0.972179 | + | 0.234239i | \(0.924740\pi\) | |||||||
\(734\) | −16.6508 | −0.614591 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.50225 | −0.165955 | ||||||||
\(737\) | − | 9.42621i | − | 0.347219i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.0360 | 0.957749 | 0.478875 | − | 0.877883i | \(-0.341045\pi\) | ||||
0.478875 | + | 0.877883i | \(0.341045\pi\) | |||||||
\(740\) | 10.5950 | 0.389480 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.1330 | − | 2.48884i | −0.445416 | − | 0.0913681i | ||||
\(743\) | 30.8355i | 1.13124i | 0.824665 | + | 0.565622i | \(0.191364\pi\) | ||||
−0.824665 | + | 0.565622i | \(0.808636\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 46.0231i | − | 1.68616i | ||||||
\(746\) | − | 7.37163i | − | 0.269895i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 5.29751i | − | 0.193696i | ||||||
\(749\) | −9.16384 | + | 44.6733i | −0.334839 | + | 1.63233i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.9616 | 0.545956 | 0.272978 | − | 0.962020i | \(-0.411991\pi\) | ||||
0.272978 | + | 0.962020i | \(0.411991\pi\) | |||||||
\(752\) | 7.15497 | 0.260915 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34.5981 | −1.25915 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.6294 | 0.822479 | 0.411239 | − | 0.911527i | \(-0.365096\pi\) | ||||
0.411239 | + | 0.911527i | \(0.365096\pi\) | |||||||
\(758\) | 4.62039i | 0.167820i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.05907 | −0.0384166 | ||||||||
\(761\) | −35.1870 | −1.27553 | −0.637764 | − | 0.770231i | \(-0.720141\pi\) | ||||
−0.637764 | + | 0.770231i | \(0.720141\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.1605 | + | 9.46889i | 1.67112 | + | 0.342797i | ||||
\(764\) | 0.253253i | 0.00916237i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 26.9159i | − | 0.972513i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.4721i | − | 1.13491i | −0.823403 | − | 0.567456i | \(-0.807928\pi\) | ||
0.823403 | − | 0.567456i | \(-0.192072\pi\) | |||||||
\(770\) | 10.9741 | + | 2.25112i | 0.395480 | + | 0.0811248i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.8524 | −0.462569 | ||||||||
\(773\) | 29.3365 | 1.05516 | 0.527580 | − | 0.849506i | \(-0.323100\pi\) | ||||
0.527580 | + | 0.849506i | \(0.323100\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 81.7711i | − | 2.93731i | ||||||
\(776\) | −7.96815 | −0.286040 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.20053 | −0.186448 | ||||||||
\(779\) | − | 0.328519i | − | 0.0117704i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.9875 | 0.464730 | ||||||||
\(782\) | 23.8507 | 0.852898 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.43469 | + | 2.75586i | 0.229810 | + | 0.0984235i | ||||
\(785\) | 87.3721i | 3.11844i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 27.7101i | − | 0.987759i | −0.869530 | − | 0.493879i | \(-0.835578\pi\) | ||
0.869530 | − | 0.493879i | \(-0.164422\pi\) | |||||||
\(788\) | 25.4352i | 0.906091i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.59947i | 0.0569065i | ||||||||
\(791\) | 5.21230 | − | 25.4097i | 0.185328 | − | 0.903467i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 7.38608 | 0.262122 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 22.7615i | − | 0.806758i | ||||||
\(797\) | 21.4739 | 0.760646 | 0.380323 | − | 0.924854i | \(-0.375813\pi\) | ||||
0.380323 | + | 0.924854i | \(0.375813\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.9035 | −1.34093 | ||||||||
\(800\) | 12.9285i | 0.457090i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.0699 | 0.567448 | ||||||||
\(803\) | −7.15497 | −0.252494 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.1351 | + | 49.4083i | −0.357216 | + | 1.74141i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 15.6065i | − | 0.549034i | ||||||
\(809\) | 9.89084i | 0.347743i | 0.984768 | + | 0.173872i | \(0.0556278\pi\) | ||||
−0.984768 | + | 0.173872i | \(0.944372\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 14.7574i | − | 0.518202i | −0.965850 | − | 0.259101i | \(-0.916574\pi\) | ||
0.965850 | − | 0.259101i | \(-0.0834262\pi\) | |||||||
\(812\) | −0.563058 | + | 2.74489i | −0.0197595 | + | 0.0963266i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.50225 | 0.0877037 | ||||||||
\(815\) | −36.5005 | −1.27856 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.79678i | 0.0628613i | ||||||||
\(818\) | −22.1625 | −0.774893 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.56132 | −0.194210 | ||||||||
\(821\) | − | 33.3716i | − | 1.16468i | −0.812946 | − | 0.582339i | \(-0.802138\pi\) | ||
0.812946 | − | 0.582339i | \(-0.197862\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.02944 | 0.105600 | 0.0527998 | − | 0.998605i | \(-0.483185\pi\) | ||||
0.0527998 | + | 0.998605i | \(0.483185\pi\) | |||||||
\(824\) | 1.84057 | 0.0641193 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.50225 | + | 21.9483i | −0.156653 | + | 0.763678i | ||||
\(827\) | − | 0.468317i | − | 0.0162850i | −0.999967 | − | 0.00814249i | \(-0.997408\pi\) | ||
0.999967 | − | 0.00814249i | \(-0.00259186\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 44.4855i | − | 1.54505i | −0.634987 | − | 0.772523i | \(-0.718995\pi\) | ||
0.634987 | − | 0.772523i | \(-0.281005\pi\) | |||||||
\(830\) | − | 7.79335i | − | 0.270511i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.0878 | − | 14.5992i | −1.18107 | − | 0.505831i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.2151 | 0.422720 | ||||||||
\(836\) | −0.250123 | −0.00865069 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.9050i | 0.860327i | ||||||||
\(839\) | −18.4095 | −0.635567 | −0.317783 | − | 0.948163i | \(-0.602938\pi\) | ||||
−0.317783 | + | 0.948163i | \(0.602938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.8784 | 0.961323 | ||||||||
\(842\) | − | 7.47281i | − | 0.257530i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.6733 | 0.573920 | ||||||||
\(845\) | −55.0446 | −1.89359 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.59178 | + | 0.531652i | 0.0890548 | + | 0.0182678i | ||||
\(848\) | − | 4.68132i | − | 0.160757i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 68.4886i | − | 2.34914i | ||||||
\(851\) | 11.2657i | 0.386184i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 39.0555i | − | 1.33723i | −0.743607 | − | 0.668617i | \(-0.766887\pi\) | ||
0.743607 | − | 0.668617i | \(-0.233113\pi\) | |||||||
\(854\) | 38.3848 | + | 7.87387i | 1.31350 | + | 0.269438i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.2365 | −0.589132 | ||||||||
\(857\) | −52.9808 | −1.80979 | −0.904895 | − | 0.425635i | \(-0.860051\pi\) | ||||
−0.904895 | + | 0.425635i | \(0.860051\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 57.1564i | − | 1.95015i | −0.221870 | − | 0.975076i | \(-0.571216\pi\) | ||
0.221870 | − | 0.975076i | \(-0.428784\pi\) | |||||||
\(860\) | 30.4167 | 1.03720 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.6797 | −0.499992 | ||||||||
\(863\) | − | 36.4683i | − | 1.24140i | −0.784050 | − | 0.620698i | \(-0.786849\pi\) | ||
0.784050 | − | 0.620698i | \(-0.213151\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.1901 | −1.70652 | ||||||||
\(866\) | 32.4714 | 1.10342 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.36265 | − | 16.3928i | 0.114136 | − | 0.556407i | ||||
\(869\) | 0.377749i | 0.0128143i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 17.8103i | 0.603133i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1.12612i | − | 0.0380915i | ||||||
\(875\) | 87.0079 | + | 17.8479i | 2.94141 | + | 0.603370i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.4566 | 0.893378 | 0.446689 | − | 0.894689i | \(-0.352603\pi\) | ||||
0.446689 | + | 0.894689i | \(0.352603\pi\) | |||||||
\(878\) | −33.3643 | −1.12599 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.23420i | 0.142735i | ||||||||
\(881\) | 11.5527 | 0.389220 | 0.194610 | − | 0.980881i | \(-0.437656\pi\) | ||||
0.194610 | + | 0.980881i | \(0.437656\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.1274 | 1.45135 | 0.725676 | − | 0.688037i | \(-0.241527\pi\) | ||||
0.725676 | + | 0.688037i | \(0.241527\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.9205 | −0.938007 | ||||||||
\(887\) | 11.6293 | 0.390474 | 0.195237 | − | 0.980756i | \(-0.437452\pi\) | ||||
0.195237 | + | 0.980756i | \(0.437452\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.9835 | + | 6.97104i | 1.13977 | + | 0.233801i | ||||
\(890\) | 6.62039i | 0.221916i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 19.0085i | − | 0.636451i | ||||||
\(893\) | 1.78963i | 0.0598875i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 56.8493i | 1.90026i | ||||||||
\(896\) | −0.531652 | + | 2.59178i | −0.0177613 | + | 0.0865854i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.4413 | −0.415172 | ||||||||
\(899\) | 6.69852 | 0.223408 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.7993i | 0.826186i | ||||||||
\(902\) | −1.31343 | −0.0437324 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.80396 | 0.326075 | ||||||||
\(905\) | − | 84.1615i | − | 2.79762i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.6413 | −1.11704 | −0.558520 | − | 0.829491i | \(-0.688631\pi\) | ||||
−0.558520 | + | 0.829491i | \(0.688631\pi\) | |||||||
\(908\) | −11.1122 | −0.368770 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.13062i | − | 0.0374590i | −0.999825 | − | 0.0187295i | \(-0.994038\pi\) | ||
0.999825 | − | 0.0187295i | \(-0.00596214\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.84057i | − | 0.0609140i | ||||||
\(914\) | 6.48528i | 0.214514i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.34032i | 0.0442856i | ||||||||
\(917\) | −42.4865 | − | 8.71525i | −1.40303 | − | 0.287803i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.2095 | −0.831585 | −0.415793 | − | 0.909459i | \(-0.636496\pi\) | ||||
−0.415793 | + | 0.909459i | \(0.636496\pi\) | |||||||
\(920\) | −19.0634 | −0.628502 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 2.38461i | − | 0.0785330i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.3502 | 1.06367 | ||||||||
\(926\) | 8.35815i | 0.274666i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.05907 | −0.0347657 | ||||||||
\(929\) | 39.1521 | 1.28454 | 0.642269 | − | 0.766479i | \(-0.277993\pi\) | ||||
0.642269 | + | 0.766479i | \(0.277993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.689304 | + | 1.60947i | −0.0225910 | + | 0.0527481i | ||||
\(932\) | − | 14.4853i | − | 0.474481i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 25.8336i | 0.845302i | ||||||||
\(935\) | − | 22.4307i | − | 0.733562i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 10.9079i | − | 0.356347i | −0.983999 | − | 0.178174i | \(-0.942981\pi\) | ||
0.983999 | − | 0.178174i | \(-0.0570188\pi\) | |||||||
\(938\) | 5.01147 | − | 24.4307i | 0.163630 | − | 0.797691i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 30.2956 | 0.988133 | ||||||||
\(941\) | −20.8940 | −0.681124 | −0.340562 | − | 0.940222i | \(-0.610617\pi\) | ||||
−0.340562 | + | 0.940222i | \(0.610617\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.91338i | − | 0.192566i | ||||||
\(944\) | −8.46840 | −0.275623 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.18357 | 0.233558 | ||||||||
\(947\) | − | 35.5999i | − | 1.15684i | −0.815738 | − | 0.578421i | \(-0.803669\pi\) | ||
0.815738 | − | 0.578421i | \(-0.196331\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.23371 | −0.104915 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.81643 | − | 13.7300i | 0.0912811 | − | 0.444992i | ||||
\(953\) | 42.7343i | 1.38430i | 0.721754 | + | 0.692149i | \(0.243336\pi\) | ||||
−0.721754 | + | 0.692149i | \(0.756664\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.07232i | 0.0346996i | ||||||||
\(956\) | 2.01696i | 0.0652333i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 21.9102i | − | 0.707887i | ||||||
\(959\) | −9.39369 | + | 45.7938i | −0.303338 | + | 1.47876i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00429 | −0.290461 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.1395i | 0.390988i | ||||||||
\(965\) | −54.4197 | −1.75183 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.5891 | −0.662102 | −0.331051 | − | 0.943613i | \(-0.607403\pi\) | ||||
−0.331051 | + | 0.943613i | \(0.607403\pi\) | |||||||
\(968\) | 1.00000i | 0.0321412i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −33.7388 | −1.08329 | ||||||||
\(971\) | 44.8252 | 1.43851 | 0.719255 | − | 0.694747i | \(-0.244483\pi\) | ||||
0.719255 | + | 0.694747i | \(0.244483\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.97641 | + | 43.7597i | −0.287771 | + | 1.40287i | ||||
\(974\) | − | 25.4898i | − | 0.816745i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.8102i | 0.474063i | ||||||||
\(977\) | 23.9936i | 0.767625i | 0.923411 | + | 0.383812i | \(0.125389\pi\) | ||||
−0.923411 | + | 0.383812i | \(0.874611\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.56355i | 0.0499713i | ||||||||
\(980\) | 27.2458 | + | 11.6688i | 0.870334 | + | 0.372748i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.5067 | 0.431017 | ||||||||
\(983\) | 21.9314 | 0.699502 | 0.349751 | − | 0.936843i | \(-0.386266\pi\) | ||||
0.349751 | + | 0.936843i | \(0.386266\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 107.698i | 3.43153i | ||||||||
\(986\) | 5.61044 | 0.178673 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.3422i | 1.02842i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.5957 | −1.70252 | −0.851261 | − | 0.524742i | \(-0.824162\pi\) | ||||
−0.851261 | + | 0.524742i | \(0.824162\pi\) | |||||||
\(992\) | 6.32489 | 0.200816 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 33.6609 | + | 6.90485i | 1.06766 | + | 0.219009i | ||||
\(995\) | − | 96.3765i | − | 3.05534i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.3191i | 1.02356i | 0.859118 | + | 0.511778i | \(0.171013\pi\) | ||||
−0.859118 | + | 0.511778i | \(0.828987\pi\) | |||||||
\(998\) | 4.90700i | 0.155328i | ||||||||
\(999\) | 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 | 1386.2.g.a.881.9 | yes | 16 | |
3.2 | odd | 2 | inner | 1386.2.g.a.881.8 | yes | 16 | |
7.6 | odd | 2 | inner | 1386.2.g.a.881.16 | yes | 16 | |
21.20 | even | 2 | inner | 1386.2.g.a.881.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.g.a.881.1 | ✓ | 16 | 21.20 | even | 2 | inner | |
1386.2.g.a.881.8 | yes | 16 | 3.2 | odd | 2 | inner | |
1386.2.g.a.881.9 | yes | 16 | 1.1 | even | 1 | trivial | |
1386.2.g.a.881.16 | yes | 16 | 7.6 | odd | 2 | inner |