Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2520,2,Mod(361,2520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2520.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2520.bi (of order \(3\), degree \(2\), 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: | \(20.1223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2520.361 |
Dual form | 2520.2.bi.l.1801.1 |
$q$-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 \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(1081\) | \(1261\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.62132 | + | 0.358719i | −0.990766 | + | 0.135583i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.707107 | + | 1.22474i | −0.213201 | + | 0.369274i | −0.952714 | − | 0.303867i | \(-0.901722\pi\) |
0.739514 | + | 0.673141i | \(0.235055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.24264 | 0.899347 | 0.449673 | − | 0.893193i | \(-0.351540\pi\) | ||||
0.449673 | + | 0.893193i | \(0.351540\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.29289 | + | 2.23936i | −0.313573 | + | 0.543124i | −0.979133 | − | 0.203220i | \(-0.934859\pi\) |
0.665560 | + | 0.746344i | \(0.268193\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.91421 | + | 5.04757i | 0.668566 | + | 1.15799i | 0.978305 | + | 0.207169i | \(0.0664251\pi\) |
−0.309739 | + | 0.950822i | \(0.600242\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.53553 | − | 6.12372i | −0.737210 | − | 1.27688i | −0.953747 | − | 0.300610i | \(-0.902810\pi\) |
0.216537 | − | 0.976274i | \(-0.430524\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.07107 | −0.941674 | −0.470837 | − | 0.882220i | \(-0.656048\pi\) | ||||
−0.470837 | + | 0.882220i | \(0.656048\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50000 | − | 4.33013i | 0.449013 | − | 0.777714i | −0.549309 | − | 0.835619i | \(-0.685109\pi\) |
0.998322 | + | 0.0579057i | \(0.0184423\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.62132 | − | 2.09077i | −0.274053 | − | 0.353405i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.20711 | + | 9.01897i | 0.856043 | + | 1.48271i | 0.875674 | + | 0.482903i | \(0.160418\pi\) |
−0.0196309 | + | 0.999807i | \(0.506249\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.242641 | −0.0378941 | −0.0189471 | − | 0.999820i | \(-0.506031\pi\) | ||||
−0.0189471 | + | 0.999820i | \(0.506031\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8995 | −1.66216 | −0.831079 | − | 0.556155i | \(-0.812276\pi\) | ||||
−0.831079 | + | 0.556155i | \(0.812276\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.82843 | − | 6.63103i | −0.558433 | − | 0.967235i | −0.997628 | − | 0.0688429i | \(-0.978069\pi\) |
0.439194 | − | 0.898392i | \(-0.355264\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.74264 | − | 1.88064i | 0.963234 | − | 0.268662i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.41421 | + | 5.91359i | −0.468978 | + | 0.812294i | −0.999371 | − | 0.0354577i | \(-0.988711\pi\) |
0.530393 | + | 0.847752i | \(0.322044\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.41421 | −0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.87868 | + | 4.98602i | −0.374772 | + | 0.649124i | −0.990293 | − | 0.138996i | \(-0.955612\pi\) |
0.615521 | + | 0.788121i | \(0.288946\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.58579 | − | 7.94282i | −0.587150 | − | 1.01697i | −0.994604 | − | 0.103747i | \(-0.966917\pi\) |
0.407454 | − | 0.913226i | \(-0.366417\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.62132 | + | 2.80821i | 0.201100 | + | 0.348315i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.44975 | + | 7.70719i | −0.543623 | + | 0.941583i | 0.455069 | + | 0.890456i | \(0.349615\pi\) |
−0.998692 | + | 0.0511268i | \(0.983719\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0711 | −1.31389 | −0.656947 | − | 0.753937i | \(-0.728152\pi\) | ||||
−0.656947 | + | 0.753937i | \(0.728152\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.621320 | + | 1.07616i | −0.0727200 | + | 0.125955i | −0.900093 | − | 0.435699i | \(-0.856501\pi\) |
0.827372 | + | 0.561654i | \(0.189835\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.41421 | − | 3.46410i | 0.161165 | − | 0.394771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.91421 | + | 10.2437i | 0.665401 | + | 1.15251i | 0.979176 | + | 0.203011i | \(0.0650728\pi\) |
−0.313775 | + | 0.949497i | \(0.601594\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.24264 | −0.685219 | −0.342609 | − | 0.939478i | \(-0.611311\pi\) | ||||
−0.342609 | + | 0.939478i | \(0.611311\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.58579 | −0.280468 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.12132 | + | 1.94218i | 0.118860 | + | 0.205871i | 0.919316 | − | 0.393520i | \(-0.128743\pi\) |
−0.800456 | + | 0.599391i | \(0.795409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.50000 | + | 1.16320i | −0.891042 | + | 0.121936i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.91421 | + | 5.04757i | −0.298992 | + | 0.517869i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.48528 | −0.861550 | −0.430775 | − | 0.902459i | \(-0.641760\pi\) | ||||
−0.430775 | + | 0.902459i | \(0.641760\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.77817 | + | 13.4722i | −0.773957 | + | 1.34053i | 0.161421 | + | 0.986886i | \(0.448392\pi\) |
−0.935379 | + | 0.353648i | \(0.884941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.378680 | + | 0.655892i | 0.0373124 | + | 0.0646270i | 0.884079 | − | 0.467338i | \(-0.154787\pi\) |
−0.846766 | + | 0.531965i | \(0.821454\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.707107 | − | 1.22474i | −0.0683586 | − | 0.118401i | 0.829820 | − | 0.558031i | \(-0.188443\pi\) |
−0.898179 | + | 0.439630i | \(0.855110\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.742641 | − | 1.28629i | 0.0711321 | − | 0.123204i | −0.828266 | − | 0.560336i | \(-0.810672\pi\) |
0.899398 | + | 0.437131i | \(0.144005\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.3137 | −1.25245 | −0.626224 | − | 0.779643i | \(-0.715401\pi\) | ||||
−0.626224 | + | 0.779643i | \(0.715401\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.53553 | − | 6.12372i | 0.329690 | − | 0.571040i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.58579 | − | 6.33386i | 0.237039 | − | 0.580624i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.50000 | + | 7.79423i | 0.409091 | + | 0.708566i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.07107 | 0.716191 | 0.358096 | − | 0.933685i | \(-0.383426\pi\) | ||||
0.358096 | + | 0.933685i | \(0.383426\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.24264 | + | 5.61642i | 0.283311 | + | 0.490709i | 0.972198 | − | 0.234160i | \(-0.0752339\pi\) |
−0.688887 | + | 0.724868i | \(0.741901\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.44975 | − | 12.1859i | −0.819397 | − | 1.05665i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.53553 | − | 13.0519i | 0.643804 | − | 1.11510i | −0.340772 | − | 0.940146i | \(-0.610688\pi\) |
0.984576 | − | 0.174956i | \(-0.0559782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.3137 | −1.89262 | −0.946312 | − | 0.323255i | \(-0.895223\pi\) | ||||
−0.946312 | + | 0.323255i | \(0.895223\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.29289 | + | 3.97141i | −0.191741 | + | 0.332106i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.53553 | − | 4.39167i | −0.210565 | − | 0.364709i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000 | + | 3.46410i | 0.163846 | + | 0.283790i | 0.936245 | − | 0.351348i | \(-0.114277\pi\) |
−0.772399 | + | 0.635138i | \(0.780943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.24264 | − | 9.08052i | 0.426640 | − | 0.738962i | −0.569932 | − | 0.821692i | \(-0.693030\pi\) |
0.996572 | + | 0.0827296i | \(0.0263638\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.00000 | 0.401610 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.75736 | − | 4.77589i | 0.220061 | − | 0.381157i | −0.734765 | − | 0.678322i | \(-0.762708\pi\) |
0.954826 | + | 0.297164i | \(0.0960409\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.4645 | + | 14.7840i | 0.903527 | + | 1.16514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3137 | − | 19.5959i | −0.886158 | − | 1.53487i | −0.844381 | − | 0.535744i | \(-0.820031\pi\) |
−0.0417775 | − | 0.999127i | \(-0.513302\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.89949 | −0.611281 | −0.305641 | − | 0.952147i | \(-0.598871\pi\) | ||||
−0.305641 | + | 0.952147i | \(0.598871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.48528 | −0.191175 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.41421 | + | 9.37769i | 0.411635 | + | 0.712973i | 0.995069 | − | 0.0991880i | \(-0.0316245\pi\) |
−0.583434 | + | 0.812161i | \(0.698291\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | − | 2.44949i | 0.0755929 | − | 0.185164i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.17157 | − | 7.22538i | 0.311798 | − | 0.540050i | −0.666954 | − | 0.745099i | \(-0.732402\pi\) |
0.978752 | + | 0.205049i | \(0.0657354\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.3137 | 1.06393 | 0.531965 | − | 0.846766i | \(-0.321454\pi\) | ||||
0.531965 | + | 0.846766i | \(0.321454\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.20711 | + | 9.01897i | −0.382834 | + | 0.663088i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.82843 | − | 3.16693i | −0.133708 | − | 0.231589i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.82843 | + | 13.5592i | 0.566445 | + | 0.981112i | 0.996914 | + | 0.0785061i | \(0.0250150\pi\) |
−0.430469 | + | 0.902606i | \(0.641652\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.20711 | + | 10.7510i | −0.446797 | + | 0.773876i | −0.998175 | − | 0.0603798i | \(-0.980769\pi\) |
0.551378 | + | 0.834255i | \(0.314102\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.0416 | 1.71290 | 0.856448 | − | 0.516234i | \(-0.172666\pi\) | ||||
0.856448 | + | 0.516234i | \(0.172666\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.24264 | + | 9.08052i | −0.371641 | + | 0.643701i | −0.989818 | − | 0.142338i | \(-0.954538\pi\) |
0.618177 | + | 0.786039i | \(0.287871\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.2929 | − | 1.81909i | 0.932978 | − | 0.127675i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.121320 | − | 0.210133i | −0.00847338 | − | 0.0146763i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.24264 | −0.570155 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.828427 | 0.0570313 | 0.0285156 | − | 0.999593i | \(-0.490922\pi\) | ||||
0.0285156 | + | 0.999593i | \(0.490922\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.44975 | − | 9.43924i | −0.371670 | − | 0.643751i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.00000 | + | 12.2474i | −0.339422 | + | 0.831411i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.19239 | + | 7.26143i | −0.282011 | + | 0.488457i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.1421 | −1.48275 | −0.741374 | − | 0.671093i | \(-0.765825\pi\) | ||||
−0.741374 | + | 0.671093i | \(0.765825\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.5355 | + | 25.1763i | −0.964757 | + | 1.67101i | −0.254491 | + | 0.967075i | \(0.581908\pi\) |
−0.710266 | + | 0.703934i | \(0.751425\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.98528 | + | 13.8309i | 0.527682 | + | 0.913972i | 0.999479 | + | 0.0322653i | \(0.0102721\pi\) |
−0.471797 | + | 0.881707i | \(0.656395\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.2426 | − | 19.4728i | −0.736530 | − | 1.27571i | −0.954049 | − | 0.299651i | \(-0.903130\pi\) |
0.217519 | − | 0.976056i | \(-0.430204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.82843 | − | 6.63103i | 0.249739 | − | 0.432561i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.68629 | −0.432500 | −0.216250 | − | 0.976338i | \(-0.569383\pi\) | ||||
−0.216250 | + | 0.976338i | \(0.569383\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.828427 | − | 1.43488i | 0.0533637 | − | 0.0924286i | −0.838110 | − | 0.545502i | \(-0.816339\pi\) |
0.891473 | + | 0.453073i | \(0.149672\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.00000 | + | 4.89898i | 0.319438 | + | 0.312984i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.44975 | + | 16.3674i | 0.601273 | + | 1.04144i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.8995 | 1.25604 | 0.628022 | − | 0.778195i | \(-0.283865\pi\) | ||||
0.628022 | + | 0.778195i | \(0.283865\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.0000 | 0.628695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.77817 | − | 11.7401i | −0.422811 | − | 0.732330i | 0.573402 | − | 0.819274i | \(-0.305623\pi\) |
−0.996213 | + | 0.0869440i | \(0.972290\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.8848 | − | 21.7737i | −1.04917 | − | 1.35295i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.89949 | − | 17.1464i | 0.610429 | − | 1.05729i | −0.380739 | − | 0.924683i | \(-0.624330\pi\) |
0.991168 | − | 0.132612i | \(-0.0423363\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.82843 | −0.419467 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.24264 | − | 5.61642i | 0.197707 | − | 0.342439i | −0.750077 | − | 0.661350i | \(-0.769984\pi\) |
0.947785 | + | 0.318911i | \(0.103317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.24264 | − | 2.15232i | −0.0754850 | − | 0.130744i | 0.825812 | − | 0.563945i | \(-0.190717\pi\) |
−0.901297 | + | 0.433201i | \(0.857384\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.707107 | − | 1.22474i | −0.0426401 | − | 0.0738549i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.6924 | + | 20.2518i | −0.702528 | + | 1.21681i | 0.265049 | + | 0.964235i | \(0.414612\pi\) |
−0.967576 | + | 0.252578i | \(0.918721\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.34315 | −0.139780 | −0.0698902 | − | 0.997555i | \(-0.522265\pi\) | ||||
−0.0698902 | + | 0.997555i | \(0.522265\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.863961 | − | 1.49642i | 0.0513572 | − | 0.0889532i | −0.839204 | − | 0.543817i | \(-0.816979\pi\) |
0.890561 | + | 0.454864i | \(0.150312\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.636039 | − | 0.0870399i | 0.0375442 | − | 0.00513781i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.15685 | + | 8.93193i | 0.303344 | + | 0.525408i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.65685 | 0.0967945 | 0.0483972 | − | 0.998828i | \(-0.484589\pi\) | ||||
0.0483972 | + | 0.998828i | \(0.484589\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.75736 | −0.335206 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.4645 | − | 19.8570i | −0.663007 | − | 1.14836i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 28.5711 | − | 3.90986i | 1.64681 | − | 0.225361i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.58579 | − | 7.94282i | 0.262581 | − | 0.454804i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.07107 | 0.346494 | 0.173247 | − | 0.984878i | \(-0.444574\pi\) | ||||
0.173247 | + | 0.984878i | \(0.444574\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.1213 | + | 17.5306i | −0.573927 | + | 0.994071i | 0.422230 | + | 0.906489i | \(0.361248\pi\) |
−0.996157 | + | 0.0875826i | \(0.972086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.03553 | − | 8.72180i | −0.284625 | − | 0.492985i | 0.687893 | − | 0.725812i | \(-0.258536\pi\) |
−0.972518 | + | 0.232827i | \(0.925202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.29289 | − | 9.16756i | −0.297279 | − | 0.514901i | 0.678234 | − | 0.734846i | \(-0.262746\pi\) |
−0.975512 | + | 0.219945i | \(0.929412\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.58579 | − | 6.21076i | 0.200765 | − | 0.347736i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.0711 | −0.838577 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.62132 | + | 2.80821i | −0.0899347 | + | 0.155771i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.4142 | + | 16.0087i | 0.684418 | + | 0.882589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.08579 | − | 1.88064i | −0.0596802 | − | 0.103369i | 0.834642 | − | 0.550793i | \(-0.185675\pi\) |
−0.894322 | + | 0.447424i | \(0.852341\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.89949 | −0.486231 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.89949 | 0.484786 | 0.242393 | − | 0.970178i | \(-0.422068\pi\) | ||||
0.242393 | + | 0.970178i | \(0.422068\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.53553 | + | 6.12372i | 0.191460 | + | 0.331618i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.82843 | + | 8.36308i | −0.259204 | + | 0.448954i | −0.966029 | − | 0.258435i | \(-0.916793\pi\) |
0.706825 | + | 0.707388i | \(0.250127\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.31371 | 0.498551 | 0.249276 | − | 0.968433i | \(-0.419807\pi\) | ||||
0.249276 | + | 0.968433i | \(0.419807\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.87868 | + | 11.9142i | −0.366115 | + | 0.634130i | −0.988954 | − | 0.148220i | \(-0.952646\pi\) |
0.622839 | + | 0.782350i | \(0.285979\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.53553 | − | 9.58783i | −0.293796 | − | 0.508869i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.1213 | + | 22.7268i | 0.692517 | + | 1.19947i | 0.971011 | + | 0.239036i | \(0.0768315\pi\) |
−0.278494 | + | 0.960438i | \(0.589835\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.48528 | + | 12.9649i | −0.393962 | + | 0.682363i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.24264 | −0.0650428 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.20711 | − | 15.9472i | 0.480607 | − | 0.832436i | −0.519145 | − | 0.854686i | \(-0.673750\pi\) |
0.999752 | + | 0.0222501i | \(0.00708301\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.82843 | − | 16.7262i | 0.354514 | − | 0.868379i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.4497 | + | 25.0277i | 0.748180 | + | 1.29589i | 0.948694 | + | 0.316194i | \(0.102405\pi\) |
−0.200515 | + | 0.979691i | \(0.564261\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.4437 | −0.846891 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.31371 | −0.118847 | −0.0594236 | − | 0.998233i | \(-0.518926\pi\) | ||||
−0.0594236 | + | 0.998233i | \(0.518926\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.8995 | − | 27.5387i | −0.812426 | − | 1.40716i | −0.911161 | − | 0.412050i | \(-0.864813\pi\) |
0.0987351 | − | 0.995114i | \(-0.468520\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.70711 | − | 0.507306i | 0.188932 | − | 0.0258547i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.6066 | − | 25.2994i | 0.740584 | − | 1.28273i | −0.211646 | − | 0.977346i | \(-0.567882\pi\) |
0.952230 | − | 0.305383i | \(-0.0987844\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.2843 | 0.924675 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.91421 | + | 10.2437i | −0.297576 | + | 0.515417i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.79289 | − | 8.30153i | −0.240548 | − | 0.416642i | 0.720322 | − | 0.693640i | \(-0.243994\pi\) |
−0.960871 | + | 0.276998i | \(0.910661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.0711 | + | 19.1757i | 0.552863 | + | 0.957586i | 0.998066 | + | 0.0621570i | \(0.0197980\pi\) |
−0.445204 | + | 0.895429i | \(0.646869\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.10660 | − | 14.0410i | 0.403819 | − | 0.699434i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.7279 | −0.730036 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.67157 | − | 15.0196i | 0.428782 | − | 0.742672i | −0.567984 | − | 0.823040i | \(-0.692276\pi\) |
0.996765 | + | 0.0803682i | \(0.0256096\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.75736 | − | 14.1026i | 0.283301 | − | 0.693943i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.12132 | − | 5.40629i | −0.153220 | − | 0.265384i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.1716 | 0.936593 | 0.468296 | − | 0.883571i | \(-0.344868\pi\) | ||||
0.468296 | + | 0.883571i | \(0.344868\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.4558 | 1.19190 | 0.595952 | − | 0.803020i | \(-0.296775\pi\) | ||||
0.595952 | + | 0.803020i | \(0.296775\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.29289 | − | 2.23936i | −0.0627145 | − | 0.108625i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.8701 | + | 19.1757i | 0.719613 | + | 0.927975i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.4142 | − | 21.5020i | 0.597972 | − | 1.03572i | −0.395149 | − | 0.918617i | \(-0.629307\pi\) |
0.993120 | − | 0.117100i | \(-0.0373598\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.4142 | −0.981044 | −0.490522 | − | 0.871429i | \(-0.663194\pi\) | ||||
−0.490522 | + | 0.871429i | \(0.663194\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.6066 | − | 35.6917i | 0.985747 | − | 1.70736i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.17157 | + | 10.6895i | 0.294553 | + | 0.510181i | 0.974881 | − | 0.222727i | \(-0.0714959\pi\) |
−0.680328 | + | 0.732908i | \(0.738163\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.2426 | + | 28.1331i | 0.771711 | + | 1.33664i | 0.936625 | + | 0.350335i | \(0.113932\pi\) |
−0.164913 | + | 0.986308i | \(0.552734\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.12132 | + | 1.94218i | −0.0531557 | + | 0.0920683i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.3137 | −1.19463 | −0.597314 | − | 0.802008i | \(-0.703765\pi\) | ||||
−0.597314 | + | 0.802008i | \(0.703765\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.171573 | − | 0.297173i | 0.00807905 | − | 0.0139933i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.25736 | − | 6.77962i | −0.246469 | − | 0.317833i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.3787 | + | 21.4405i | 0.579050 | + | 1.00294i | 0.995589 | + | 0.0938263i | \(0.0299098\pi\) |
−0.416538 | + | 0.909118i | \(0.636757\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.72792 | 0.127052 | 0.0635260 | − | 0.997980i | \(-0.479765\pi\) | ||||
0.0635260 | + | 0.997980i | \(0.479765\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.7574 | 1.24352 | 0.621760 | − | 0.783208i | \(-0.286418\pi\) | ||||
0.621760 | + | 0.783208i | \(0.286418\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.6569 | + | 18.4582i | 0.493140 | + | 0.854144i | 0.999969 | − | 0.00790275i | \(-0.00251555\pi\) |
−0.506828 | + | 0.862047i | \(0.669182\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.89949 | − | 21.7992i | 0.410940 | − | 1.00659i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.70711 | − | 13.3491i | 0.354373 | − | 0.613792i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.82843 | −0.267427 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.34315 | − | 10.9867i | 0.289826 | − | 0.501993i | −0.683942 | − | 0.729536i | \(-0.739736\pi\) |
0.973768 | + | 0.227543i | \(0.0730693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.8848 | + | 29.2453i | 0.769880 | + | 1.33347i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.24264 | − | 7.34847i | −0.192648 | − | 0.333677i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.4497 | − | 37.1521i | 0.971981 | − | 1.68352i | 0.282422 | − | 0.959290i | \(-0.408862\pi\) |
0.689558 | − | 0.724230i | \(-0.257805\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.85786 | −0.444879 | −0.222440 | − | 0.974946i | \(-0.571402\pi\) | ||||
−0.222440 | + | 0.974946i | \(0.571402\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.55635 | − | 11.3559i | 0.295283 | − | 0.511445i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.0208 | − | 3.97141i | 1.30176 | − | 0.178142i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.32843 | + | 12.6932i | 0.328065 | + | 0.568226i | 0.982128 | − | 0.188214i | \(-0.0602700\pi\) |
−0.654062 | + | 0.756441i | \(0.726937\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.142136 | 0.00633751 | 0.00316876 | − | 0.999995i | \(-0.498991\pi\) | ||||
0.00316876 | + | 0.999995i | \(0.498991\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.5563 | −0.692248 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.2426 | − | 26.4010i | −0.675618 | − | 1.17020i | −0.976288 | − | 0.216477i | \(-0.930543\pi\) |
0.300670 | − | 0.953728i | \(-0.402790\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.24264 | − | 3.04384i | 0.0549712 | − | 0.134651i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.378680 | + | 0.655892i | −0.0166866 | + | 0.0289021i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.8284 | 0.476234 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0711 | − | 22.6398i | 0.572654 | − | 0.991866i | −0.423638 | − | 0.905831i | \(-0.639247\pi\) |
0.996292 | − | 0.0860342i | \(-0.0274194\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.2782 | − | 19.5344i | −0.493160 | − | 0.854178i | 0.506809 | − | 0.862058i | \(-0.330825\pi\) |
−0.999969 | + | 0.00788006i | \(0.997492\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.46447 | + | 11.1968i | 0.281597 | + | 0.487740i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.5000 | + | 23.3827i | −0.586957 | + | 1.01664i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.786797 | −0.0340799 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.707107 | − | 1.22474i | 0.0305709 | − | 0.0529503i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.46447 | + | 9.58783i | −0.106152 | + | 0.412977i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.64214 | + | 16.7007i | 0.414548 | + | 0.718018i | 0.995381 | − | 0.0960049i | \(-0.0306064\pi\) |
−0.580833 | + | 0.814023i | \(0.697273\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.48528 | 0.0636225 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.1716 | −0.563176 | −0.281588 | − | 0.959535i | \(-0.590861\pi\) | ||||
−0.281588 | + | 0.959535i | \(0.590861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.7782 | − | 25.5965i | −0.629571 | − | 1.09045i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.1777 | − | 24.7305i | −0.815517 | − | 1.05165i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.48528 | − | 16.4290i | 0.401904 | − | 0.696119i | −0.592051 | − | 0.805900i | \(-0.701682\pi\) |
0.993956 | + | 0.109782i | \(0.0350151\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.3431 | −1.49486 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.48528 | − | 12.9649i | 0.315467 | − | 0.546405i | −0.664070 | − | 0.747671i | \(-0.731172\pi\) |
0.979537 | + | 0.201266i | \(0.0645055\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.65685 | − | 11.5300i | −0.280056 | − | 0.485071i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.87868 | + | 17.1104i | 0.414136 | + | 0.717304i | 0.995337 | − | 0.0964554i | \(-0.0307505\pi\) |
−0.581202 | + | 0.813760i | \(0.697417\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.25736 | − | 12.5701i | 0.303711 | − | 0.526043i | −0.673262 | − | 0.739404i | \(-0.735108\pi\) |
0.976974 | + | 0.213361i | \(0.0684409\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.07107 | 0.294884 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.7929 | − | 18.6938i | 0.449314 | − | 0.778235i | −0.549027 | − | 0.835804i | \(-0.685002\pi\) |
0.998341 | + | 0.0575696i | \(0.0183351\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.3640 | − | 2.23936i | 0.678891 | − | 0.0929042i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.82843 | − | 8.36308i | −0.199973 | − | 0.346363i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.2426 | 1.00060 | 0.500300 | − | 0.865852i | \(-0.333223\pi\) | ||||
0.500300 | + | 0.865852i | \(0.333223\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.1421 | 1.20078 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.12132 | − | 5.40629i | −0.128177 | − | 0.222010i | 0.794793 | − | 0.606880i | \(-0.207579\pi\) |
−0.922970 | + | 0.384871i | \(0.874246\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.77817 | − | 0.927572i | 0.277878 | − | 0.0380267i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.89949 | − | 17.1464i | 0.404482 | − | 0.700584i | −0.589779 | − | 0.807565i | \(-0.700785\pi\) |
0.994261 | + | 0.106981i | \(0.0341184\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.1127 | −1.06516 | −0.532580 | − | 0.846380i | \(-0.678777\pi\) | ||||
−0.532580 | + | 0.846380i | \(0.678777\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.50000 | + | 7.79423i | −0.182951 | + | 0.316880i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.3492 | + | 26.5857i | 0.623007 | + | 1.07908i | 0.988923 | + | 0.148431i | \(0.0474223\pi\) |
−0.365916 | + | 0.930648i | \(0.619244\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.4142 | − | 21.5020i | −0.502225 | − | 0.869880i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.7279 | − | 25.5095i | 0.594855 | − | 1.03032i | −0.398712 | − | 0.917076i | \(-0.630543\pi\) |
0.993567 | − | 0.113243i | \(-0.0361239\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.4853 | 1.71039 | 0.855197 | − | 0.518304i | \(-0.173436\pi\) | ||||
0.855197 | + | 0.518304i | \(0.173436\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.257359 | + | 0.445759i | −0.0103441 | + | 0.0179166i | −0.871151 | − | 0.491015i | \(-0.836626\pi\) |
0.860807 | + | 0.508932i | \(0.169959\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.63604 | − | 4.68885i | −0.145675 | − | 0.187855i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.9289 | −1.07373 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.6569 | 0.543671 | 0.271835 | − | 0.962344i | \(-0.412369\pi\) | ||||
0.271835 | + | 0.962344i | \(0.412369\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.03553 | + | 6.98975i | 0.160145 | + | 0.277380i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.8640 | − | 6.09823i | 0.866282 | − | 0.241621i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.4350 | + | 25.0022i | −0.570149 | + | 0.987528i | 0.426401 | + | 0.904534i | \(0.359781\pi\) |
−0.996550 | + | 0.0829933i | \(0.973552\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.58579 | −0.220282 | −0.110141 | − | 0.993916i | \(-0.535130\pi\) | ||||
−0.110141 | + | 0.993916i | \(0.535130\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.9497 | + | 27.6258i | −0.627049 | + | 1.08608i | 0.361091 | + | 0.932530i | \(0.382404\pi\) |
−0.988141 | + | 0.153551i | \(0.950929\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.07107 | − | 7.05130i | −0.159803 | − | 0.276788i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.3640 | + | 23.1471i | 0.522972 | + | 0.905814i | 0.999643 | + | 0.0267324i | \(0.00851019\pi\) |
−0.476670 | + | 0.879082i | \(0.658156\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.24264 | + | 5.61642i | −0.126700 | + | 0.219452i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.9706 | 1.12853 | 0.564266 | − | 0.825593i | \(-0.309159\pi\) | ||||
0.564266 | + | 0.825593i | \(0.309159\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.6421 | + | 42.6814i | −0.958468 | + | 1.66012i | −0.232243 | + | 0.972658i | \(0.574607\pi\) |
−0.726225 | + | 0.687458i | \(0.758727\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.82843 | − | 14.2767i | 0.226017 | − | 0.553626i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.9289 | + | 31.0538i | 0.694211 | + | 1.20241i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.9706 | 0.500723 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.89949 | −0.343050 | −0.171525 | − | 0.985180i | \(-0.554869\pi\) | ||||
−0.171525 | + | 0.985180i | \(0.554869\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.9203 | + | 37.9671i | 0.842466 | + | 1.45919i | 0.887804 | + | 0.460222i | \(0.152230\pi\) |
−0.0453378 | + | 0.998972i | \(0.514436\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.2426 | − | 3.04384i | 0.853594 | − | 0.116812i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.2635 | + | 24.7050i | −0.545776 | + | 0.945312i | 0.452782 | + | 0.891621i | \(0.350432\pi\) |
−0.998558 | + | 0.0536903i | \(0.982902\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.0711 | 0.575836 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.0711 | + | 19.1757i | −0.421774 | + | 0.730534i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.2279 | + | 38.4999i | 0.845590 | + | 1.46460i | 0.885108 | + | 0.465386i | \(0.154084\pi\) |
−0.0395178 | + | 0.999219i | \(0.512582\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.1569 | − | 19.3242i | −0.423204 | − | 0.733010i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.313708 | − | 0.543359i | 0.0118826 | − | 0.0205812i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.4142 | 1.03542 | 0.517710 | − | 0.855556i | \(-0.326785\pi\) | ||||
0.517710 | + | 0.855556i | \(0.326785\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.3492 | + | 52.5664i | −1.14464 | + | 1.98258i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.5563 | − | 38.1051i | 0.585057 | − | 1.43309i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.0711 | − | 43.4244i | −0.941564 | − | 1.63084i | −0.762489 | − | 0.647001i | \(-0.776023\pi\) |
−0.179074 | − | 0.983836i | \(-0.557310\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.3553 | −1.32407 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.58579 | −0.171499 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.5563 | + | 42.5328i | 0.915797 | + | 1.58621i | 0.805730 | + | 0.592283i | \(0.201773\pi\) |
0.110068 | + | 0.993924i | \(0.464893\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.22792 | − | 1.58346i | −0.0457302 | − | 0.0589713i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.53553 | − | 4.39167i | 0.0941674 | − | 0.163103i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.7574 | −1.14073 | −0.570364 | − | 0.821392i | \(-0.693198\pi\) | ||||
−0.570364 | + | 0.821392i | \(0.693198\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.0919 | − | 24.4079i | 0.521207 | − | 0.902757i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.3787 | − | 37.0290i | −0.789640 | − | 1.36770i | −0.926188 | − | 0.377062i | \(-0.876934\pi\) |
0.136548 | − | 0.990633i | \(-0.456399\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.29289 | − | 10.8996i | −0.231802 | − | 0.401492i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.6716 | − | 18.4837i | 0.392560 | − | 0.679934i | −0.600226 | − | 0.799830i | \(-0.704923\pi\) |
0.992786 | + | 0.119896i | \(0.0382561\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.0711 | −0.773023 | −0.386511 | − | 0.922285i | \(-0.626320\pi\) | ||||
−0.386511 | + | 0.922285i | \(0.626320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00000 | + | 3.46410i | −0.0732743 | + | 0.126915i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.29289 | + | 2.95680i | 0.0837805 | + | 0.108039i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.39949 | + | 4.15605i | 0.0875588 | + | 0.151656i | 0.906479 | − | 0.422252i | \(-0.138760\pi\) |
−0.818920 | + | 0.573908i | \(0.805427\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.4853 | 0.381598 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0000 | −1.38113 | −0.690567 | − | 0.723269i | \(-0.742639\pi\) | ||||
−0.690567 | + | 0.723269i | \(0.742639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.8492 | + | 27.4517i | 0.574535 | + | 0.995123i | 0.996092 | + | 0.0883214i | \(0.0281503\pi\) |
−0.421557 | + | 0.906802i | \(0.638516\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.48528 | + | 3.63818i | −0.0537708 | + | 0.131711i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.33452 | + | 16.1679i | −0.337050 | + | 0.583788i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.9411 | 1.11577 | 0.557883 | − | 0.829920i | \(-0.311614\pi\) | ||||
0.557883 | + | 0.829920i | \(0.311614\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.6360 | − | 21.8863i | 0.454487 | − | 0.787194i | −0.544172 | − | 0.838974i | \(-0.683156\pi\) |
0.998659 | + | 0.0517797i | \(0.0164894\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.50000 | + | 4.33013i | 0.0898027 | + | 0.155543i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.707107 | − | 1.22474i | −0.0253347 | − | 0.0438810i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.82843 | − | 13.5592i | 0.280123 | − | 0.485188i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.51472 | 0.196829 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.5858 | − | 35.6556i | 0.733804 | − | 1.27099i | −0.221442 | − | 0.975174i | \(-0.571076\pi\) |
0.955246 | − | 0.295812i | \(-0.0955903\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.8995 | − | 4.77589i | 1.24088 | − | 0.169811i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.8701 | − | 25.7557i | −0.528051 | − | 0.914612i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −49.4142 | −1.75034 | −0.875171 | − | 0.483814i | \(-0.839251\pi\) | ||||
−0.875171 | + | 0.483814i | \(0.839251\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.7990 | 0.700438 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.878680 | − | 1.52192i | −0.0310079 | − | 0.0537073i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.07107 | + | 17.3205i | −0.249222 | + | 0.610468i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.34315 | − | 16.1828i | 0.328488 | − | 0.568957i | −0.653724 | − | 0.756733i | \(-0.726794\pi\) |
0.982212 | + | 0.187776i | \(0.0601278\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.6863 | 0.796623 | 0.398312 | − | 0.917250i | \(-0.369596\pi\) | ||||
0.398312 | + | 0.917250i | \(0.369596\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.3137 | − | 19.5959i | 0.396302 | − | 0.686415i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.7635 | − | 55.0159i | −1.11126 | − | 1.92476i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.7782 | + | 20.4004i | 0.411061 | + | 0.711979i | 0.995006 | − | 0.0998145i | \(-0.0318249\pi\) |
−0.583945 | + | 0.811793i | \(0.698492\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.51472 | − | 11.2838i | 0.227089 | − | 0.393329i | −0.729855 | − | 0.683602i | \(-0.760413\pi\) |
0.956944 | + | 0.290272i | \(0.0937459\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.85786 | 0.134151 | 0.0670755 | − | 0.997748i | \(-0.478633\pi\) | ||||
0.0670755 | + | 0.997748i | \(0.478633\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.642136 | − | 1.11221i | 0.0223023 | − | 0.0386287i | −0.854659 | − | 0.519190i | \(-0.826234\pi\) |
0.876961 | + | 0.480561i | \(0.159567\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.50610 | + | 17.5306i | −0.156127 | + | 0.607401i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.94975 | − | 6.84116i | −0.136687 | − | 0.236748i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.38478 | 0.151379 | 0.0756896 | − | 0.997131i | \(-0.475884\pi\) | ||||
0.0756896 | + | 0.997131i | \(0.475884\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.28427 | −0.113251 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.24264 | − | 2.15232i | −0.0427481 | − | 0.0740419i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.5919 | − | 18.8169i | −0.501383 | − | 0.646557i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.8198 | − | 63.7738i | 1.26217 | − | 2.18614i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.6985 | −1.73588 | −0.867942 | − | 0.496666i | \(-0.834557\pi\) | ||||
−0.867942 | + | 0.496666i | \(0.834557\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.7782 | + | 48.1132i | −0.948884 | + | 1.64352i | −0.201104 | + | 0.979570i | \(0.564453\pi\) |
−0.747781 | + | 0.663946i | \(0.768880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.4853 | + | 33.7495i | 0.664829 | + | 1.15152i | 0.979332 | + | 0.202261i | \(0.0648290\pi\) |
−0.314502 | + | 0.949257i | \(0.601838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.4142 | + | 38.8226i | 0.762989 | + | 1.32154i | 0.941303 | + | 0.337562i | \(0.109602\pi\) |
−0.178315 | + | 0.983974i | \(0.557065\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.41421 | + | 9.37769i | −0.184089 | + | 0.318851i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.7279 | −0.567456 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.4289 | + | 24.9916i | −0.488906 | + | 0.846810i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.62132 | − | 0.358719i | 0.0886168 | − | 0.0121269i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.51472 | − | 11.2838i | −0.219986 | − | 0.381028i | 0.734817 | − | 0.678265i | \(-0.237268\pi\) |
−0.954804 | + | 0.297238i | \(0.903935\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.2843 | −1.62674 | −0.813369 | − | 0.581748i | \(-0.802369\pi\) | ||||
−0.813369 | + | 0.581748i | \(0.802369\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.4142 | −1.62927 | −0.814634 | − | 0.579975i | \(-0.803062\pi\) | ||||
−0.814634 | + | 0.579975i | \(0.803062\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.5061 | + | 26.8573i | 0.520644 | + | 0.901781i | 0.999712 | + | 0.0240037i | \(0.00764136\pi\) |
−0.479068 | + | 0.877778i | \(0.659025\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.1569 | + | 2.89525i | −0.709578 | + | 0.0971035i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.3137 | − | 38.6485i | 0.746700 | − | 1.29332i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.34315 | 0.278881 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.6777 | + | 21.9584i | −0.422824 | + | 0.732353i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.82843 | − | 15.2913i | −0.294118 | − | 0.509427i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.15685 | + | 12.3960i | 0.237902 | + | 0.412058i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.89340 | − | 5.01151i | 0.0960737 | − | 0.166405i | −0.813983 | − | 0.580889i | \(-0.802705\pi\) |
0.910056 | + | 0.414485i | \(0.136038\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.2132 | 0.371510 | 0.185755 | − | 0.982596i | \(-0.440527\pi\) | ||||
0.185755 | + | 0.982596i | \(0.440527\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.41421 | − | 7.64564i | 0.146089 | − | 0.253034i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.5147 | − | 13.5592i | −0.347227 | − | 0.447765i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.22792 | − | 12.5191i | −0.238427 | − | 0.412968i | 0.721836 | − | 0.692064i | \(-0.243298\pi\) |
−0.960263 | + | 0.279096i | \(0.909965\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.8995 | −1.18165 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.4142 | −0.342417 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.0208 | − | 34.6771i | −0.656862 | − | 1.13772i | −0.981424 | − | 0.191853i | \(-0.938550\pi\) |
0.324562 | − | 0.945864i | \(-0.394783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.1421 | + | 28.5533i | 0.955095 | + | 0.935798i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.82843 | − | 3.16693i | 0.0597960 | − | 0.103570i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.3848 | −1.02530 | −0.512648 | − | 0.858599i | \(-0.671335\pi\) | ||||
−0.512648 | + | 0.858599i | \(0.671335\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.0919 | + | 41.7284i | −0.785373 | + | 1.36031i | 0.143403 | + | 0.989664i | \(0.454195\pi\) |
−0.928776 | + | 0.370641i | \(0.879138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.857864 | + | 1.48586i | 0.0279359 | + | 0.0483864i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.4350 | + | 49.2509i | 0.924014 | + | 1.60044i | 0.793139 | + | 0.609041i | \(0.208445\pi\) |
0.130875 | + | 0.991399i | \(0.458221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.01472 | + | 3.48960i | −0.0654005 | + | 0.113277i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.85786 | −0.0601821 | −0.0300911 | − | 0.999547i | \(-0.509580\pi\) | ||||
−0.0300911 | + | 0.999547i | \(0.509580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.82843 | + | 13.5592i | −0.253322 | + | 0.438766i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.0711 | + | 36.9164i | −0.486670 | + | 1.19209i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.4142 | −0.399628 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.7279 | −1.40620 | −0.703098 | − | 0.711093i | \(-0.748200\pi\) | ||||
−0.703098 | + | 0.711093i | \(0.748200\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.1421 | − | 24.4949i | −0.453843 | − | 0.786079i | 0.544778 | − | 0.838580i | \(-0.316614\pi\) |
−0.998621 | + | 0.0525016i | \(0.983281\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 58.4914 | − | 8.00436i | 1.87515 | − | 0.256608i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.7782 | + | 18.6683i | −0.344824 | + | 0.597253i | −0.985322 | − | 0.170707i | \(-0.945395\pi\) |
0.640497 | + | 0.767960i | \(0.278728\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.17157 | −0.101364 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.1924 | − | 33.2422i | 0.612142 | − | 1.06026i | −0.378737 | − | 0.925505i | \(-0.623641\pi\) |
0.990879 | − | 0.134757i | \(-0.0430253\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0208 | + | 20.8207i | 0.383015 | + | 0.663401i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.5355 | + | 66.7455i | 1.22536 | + | 2.12238i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.4289 | − | 21.5275i | 0.394818 | − | 0.683845i | −0.598260 | − | 0.801302i | \(-0.704141\pi\) |
0.993078 | + | 0.117457i | \(0.0374743\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.4853 | −0.332406 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.6630 | − | 42.7175i | 0.781083 | − | 1.35288i | −0.150228 | − | 0.988651i | \(-0.548001\pi\) |
0.931311 | − | 0.364225i | \(-0.118666\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2520.2.bi.l.361.1 | 4 | ||
3.2 | odd | 2 | 840.2.bg.g.361.1 | yes | 4 | ||
7.2 | even | 3 | inner | 2520.2.bi.l.1801.1 | 4 | ||
12.11 | even | 2 | 1680.2.bg.r.1201.2 | 4 | |||
21.2 | odd | 6 | 840.2.bg.g.121.1 | ✓ | 4 | ||
21.11 | odd | 6 | 5880.2.a.bs.1.1 | 2 | |||
21.17 | even | 6 | 5880.2.a.bm.1.1 | 2 | |||
84.23 | even | 6 | 1680.2.bg.r.961.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.bg.g.121.1 | ✓ | 4 | 21.2 | odd | 6 | ||
840.2.bg.g.361.1 | yes | 4 | 3.2 | odd | 2 | ||
1680.2.bg.r.961.2 | 4 | 84.23 | even | 6 | |||
1680.2.bg.r.1201.2 | 4 | 12.11 | even | 2 | |||
2520.2.bi.l.361.1 | 4 | 1.1 | even | 1 | trivial | ||
2520.2.bi.l.1801.1 | 4 | 7.2 | even | 3 | inner | ||
5880.2.a.bm.1.1 | 2 | 21.17 | even | 6 | |||
5880.2.a.bs.1.1 | 2 | 21.11 | odd | 6 |