Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(197,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("630.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.m (of order \(4\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 197.4 | ||
Root | \(-3.16053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.197 |
Dual form | 630.2.m.c.323.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.52773 | + | 1.63280i | 0.683220 | + | 0.730213i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.23483 | + | 0.0743018i | 0.706716 | + | 0.0234963i | ||||
\(11\) | − | 2.14860i | − | 0.647828i | −0.946086 | − | 0.323914i | \(-0.895001\pi\) | ||
0.946086 | − | 0.323914i | \(-0.104999\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.16053 | − | 2.16053i | 0.599224 | − | 0.599224i | −0.340882 | − | 0.940106i | \(-0.610726\pi\) |
0.940106 | + | 0.340882i | \(0.110726\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.46967 | − | 4.46967i | 1.08405 | − | 1.08405i | 0.0879263 | − | 0.996127i | \(-0.471976\pi\) |
0.996127 | − | 0.0879263i | \(-0.0280240\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 1.63280 | − | 1.52773i | 0.365106 | − | 0.341610i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.51929 | − | 1.51929i | −0.323914 | − | 0.323914i | ||||
\(23\) | 6.32106 | + | 6.32106i | 1.31803 | + | 1.31803i | 0.915331 | + | 0.402701i | \(0.131929\pi\) |
0.402701 | + | 0.915331i | \(0.368071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.332104 | + | 4.98896i | −0.0664208 | + | 0.997792i | ||||
\(26\) | − | 3.05545i | − | 0.599224i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.707107 | + | 0.707107i | −0.133631 | + | 0.133631i | ||||
\(29\) | 8.20494 | 1.52362 | 0.761810 | − | 0.647801i | \(-0.224311\pi\) | ||||
0.761810 | + | 0.647801i | \(0.224311\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.85140 | −0.332521 | −0.166260 | − | 0.986082i | \(-0.553169\pi\) | ||||
−0.166260 | + | 0.986082i | \(0.553169\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.32106i | − | 1.08405i | ||||||
\(35\) | 0.0743018 | − | 2.23483i | 0.0125593 | − | 0.377756i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.13756 | − | 5.13756i | −0.844610 | − | 0.844610i | 0.144844 | − | 0.989454i | \(-0.453732\pi\) |
−0.989454 | + | 0.144844i | \(0.953732\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0743018 | − | 2.23483i | 0.0117481 | − | 0.353358i | ||||
\(41\) | − | 7.56282i | − | 1.18111i | −0.806996 | − | 0.590557i | \(-0.798908\pi\) | ||
0.806996 | − | 0.590557i | \(-0.201092\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.84035 | + | 7.84035i | −1.19564 | + | 1.19564i | −0.220185 | + | 0.975458i | \(0.570666\pi\) |
−0.975458 | + | 0.220185i | \(0.929334\pi\) | |||||||
\(44\) | −2.14860 | −0.323914 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.93933 | 1.31803 | ||||||||
\(47\) | −5.01193 | + | 5.01193i | −0.731065 | + | 0.731065i | −0.970831 | − | 0.239766i | \(-0.922929\pi\) |
0.239766 | + | 0.970831i | \(0.422929\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 3.29289 | + | 3.76256i | 0.465685 | + | 0.532106i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.16053 | − | 2.16053i | −0.299612 | − | 0.299612i | ||||
\(53\) | 2.35876 | + | 2.35876i | 0.324001 | + | 0.324001i | 0.850300 | − | 0.526299i | \(-0.176421\pi\) |
−0.526299 | + | 0.850300i | \(0.676421\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.50825 | − | 3.28248i | 0.473052 | − | 0.442609i | ||||
\(56\) | 1.00000i | 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.80177 | − | 5.80177i | 0.761810 | − | 0.761810i | ||||
\(59\) | −9.35965 | −1.21852 | −0.609261 | − | 0.792970i | \(-0.708534\pi\) | ||||
−0.609261 | + | 0.792970i | \(0.708534\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.46967 | −0.572282 | −0.286141 | − | 0.958188i | \(-0.592373\pi\) | ||||
−0.286141 | + | 0.958188i | \(0.592373\pi\) | |||||||
\(62\) | −1.30913 | + | 1.30913i | −0.166260 | + | 0.166260i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 6.82843 | + | 0.227026i | 0.846962 | + | 0.0281591i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.84035 | − | 3.84035i | −0.469174 | − | 0.469174i | 0.432473 | − | 0.901647i | \(-0.357641\pi\) |
−0.901647 | + | 0.432473i | \(0.857641\pi\) | |||||||
\(68\) | −4.46967 | − | 4.46967i | −0.542027 | − | 0.542027i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.52773 | − | 1.63280i | −0.182598 | − | 0.195158i | ||||
\(71\) | − | 0.420314i | − | 0.0498821i | −0.999689 | − | 0.0249411i | \(-0.992060\pi\) | ||
0.999689 | − | 0.0249411i | \(-0.00793981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.63020 | + | 2.63020i | −0.307841 | + | 0.307841i | −0.844072 | − | 0.536230i | \(-0.819848\pi\) |
0.536230 | + | 0.844072i | \(0.319848\pi\) | |||||||
\(74\) | −7.26561 | −0.844610 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.51929 | + | 1.51929i | −0.173139 | + | 0.173139i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.23654i | − | 0.589157i | −0.955627 | − | 0.294578i | \(-0.904821\pi\) | ||
0.955627 | − | 0.294578i | \(-0.0951792\pi\) | |||||||
\(80\) | −1.52773 | − | 1.63280i | −0.170805 | − | 0.182553i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.34772 | − | 5.34772i | −0.590557 | − | 0.590557i | ||||
\(83\) | 10.6183 | + | 10.6183i | 1.16551 | + | 1.16551i | 0.983251 | + | 0.182255i | \(0.0583397\pi\) |
0.182255 | + | 0.983251i | \(0.441660\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.1265 | + | 0.469666i | 1.53224 | + | 0.0509425i | ||||
\(86\) | 11.0879i | 1.19564i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.51929 | + | 1.51929i | −0.161957 | + | 0.161957i | ||||
\(89\) | −14.5481 | −1.54209 | −0.771047 | − | 0.636778i | \(-0.780267\pi\) | ||||
−0.771047 | + | 0.636778i | \(0.780267\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.05545 | −0.320298 | ||||||||
\(92\) | 6.32106 | − | 6.32106i | 0.659016 | − | 0.659016i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.08794i | 0.731065i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.606342 | − | 0.606342i | −0.0615647 | − | 0.0615647i | 0.675654 | − | 0.737219i | \(-0.263861\pi\) |
−0.737219 | + | 0.675654i | \(0.763861\pi\) | |||||||
\(98\) | 0.707107 | + | 0.707107i | 0.0714286 | + | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.98896 | + | 0.332104i | 0.498896 | + | 0.0332104i | ||||
\(101\) | − | 5.39860i | − | 0.537181i | −0.963255 | − | 0.268590i | \(-0.913442\pi\) | ||
0.963255 | − | 0.268590i | \(-0.0865578\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.80546 | + | 7.80546i | −0.769095 | + | 0.769095i | −0.977947 | − | 0.208853i | \(-0.933027\pi\) |
0.208853 | + | 0.977947i | \(0.433027\pi\) | |||||||
\(104\) | −3.05545 | −0.299612 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.33579 | 0.324001 | ||||||||
\(107\) | −2.40811 | + | 2.40811i | −0.232801 | + | 0.232801i | −0.813861 | − | 0.581060i | \(-0.802638\pi\) |
0.581060 | + | 0.813861i | \(0.302638\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.90075i | 0.948320i | 0.880439 | + | 0.474160i | \(0.157248\pi\) | ||||
−0.880439 | + | 0.474160i | \(0.842752\pi\) | |||||||
\(110\) | 0.159645 | − | 4.80177i | 0.0152216 | − | 0.457831i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.707107 | + | 0.707107i | 0.0668153 | + | 0.0668153i | ||||
\(113\) | 4.22703 | + | 4.22703i | 0.397645 | + | 0.397645i | 0.877402 | − | 0.479757i | \(-0.159275\pi\) |
−0.479757 | + | 0.877402i | \(0.659275\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.664208 | + | 19.9779i | −0.0619378 | + | 1.86295i | ||||
\(116\) | − | 8.20494i | − | 0.761810i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.61827 | + | 6.61827i | −0.609261 | + | 0.609261i | ||||
\(119\) | −6.32106 | −0.579451 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.38350 | 0.580318 | ||||||||
\(122\) | −3.16053 | + | 3.16053i | −0.286141 | + | 0.286141i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.85140i | 0.166260i | ||||||||
\(125\) | −8.65336 | + | 7.07950i | −0.773980 | + | 0.633210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.32106 | + | 2.32106i | 0.205961 | + | 0.205961i | 0.802548 | − | 0.596587i | \(-0.203477\pi\) |
−0.596587 | + | 0.802548i | \(0.703477\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.98896 | − | 4.66790i | 0.437561 | − | 0.409402i | ||||
\(131\) | 2.37438i | 0.207450i | 0.994606 | + | 0.103725i | \(0.0330762\pi\) | ||||
−0.994606 | + | 0.103725i | \(0.966924\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.43108 | −0.469174 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.32106 | −0.542027 | ||||||||
\(137\) | −9.88388 | + | 9.88388i | −0.844437 | + | 0.844437i | −0.989432 | − | 0.144995i | \(-0.953683\pi\) |
0.144995 | + | 0.989432i | \(0.453683\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.6109i | − | 1.32410i | −0.749459 | − | 0.662050i | \(-0.769687\pi\) | ||
0.749459 | − | 0.662050i | \(-0.230313\pi\) | |||||||
\(140\) | −2.23483 | − | 0.0743018i | −0.188878 | − | 0.00627965i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.297207 | − | 0.297207i | −0.0249411 | − | 0.0249411i | ||||
\(143\) | −4.64213 | − | 4.64213i | −0.388194 | − | 0.388194i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.5349 | + | 13.3971i | 1.04097 | + | 1.11257i | ||||
\(146\) | 3.71966i | 0.307841i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.13756 | + | 5.13756i | −0.422305 | + | 0.422305i | ||||
\(149\) | 9.49962 | 0.778239 | 0.389120 | − | 0.921187i | \(-0.372779\pi\) | ||||
0.389120 | + | 0.921187i | \(0.372779\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.5815 | −1.10524 | −0.552622 | − | 0.833432i | \(-0.686373\pi\) | ||||
−0.552622 | + | 0.833432i | \(0.686373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.14860i | 0.173139i | ||||||||
\(155\) | −2.82843 | − | 3.02297i | −0.227185 | − | 0.242811i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0613 | + | 14.0613i | 1.12221 | + | 1.12221i | 0.991408 | + | 0.130804i | \(0.0417559\pi\) |
0.130804 | + | 0.991408i | \(0.458244\pi\) | |||||||
\(158\) | −3.70279 | − | 3.70279i | −0.294578 | − | 0.294578i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.23483 | − | 0.0743018i | −0.176679 | − | 0.00587407i | ||||
\(161\) | − | 8.93933i | − | 0.704518i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.80177 | − | 8.80177i | 0.689408 | − | 0.689408i | −0.272693 | − | 0.962101i | \(-0.587914\pi\) |
0.962101 | + | 0.272693i | \(0.0879144\pi\) | |||||||
\(164\) | −7.56282 | −0.590557 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.0165 | 1.16551 | ||||||||
\(167\) | 2.66878 | − | 2.66878i | 0.206517 | − | 0.206517i | −0.596269 | − | 0.802785i | \(-0.703351\pi\) |
0.802785 | + | 0.596269i | \(0.203351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.66421i | 0.281862i | ||||||||
\(170\) | 10.3211 | − | 9.65685i | 0.791589 | − | 0.740647i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.84035 | + | 7.84035i | 0.597821 | + | 0.597821i | ||||
\(173\) | −6.70127 | − | 6.70127i | −0.509488 | − | 0.509488i | 0.404881 | − | 0.914369i | \(-0.367313\pi\) |
−0.914369 | + | 0.404881i | \(0.867313\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.76256 | − | 3.29289i | 0.284423 | − | 0.248919i | ||||
\(176\) | 2.14860i | 0.161957i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.2871 | + | 10.2871i | −0.771047 | + | 0.771047i | ||||
\(179\) | −3.50825 | −0.262219 | −0.131109 | − | 0.991368i | \(-0.541854\pi\) | ||||
−0.131109 | + | 0.991368i | \(0.541854\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7981 | 1.02560 | 0.512802 | − | 0.858507i | \(-0.328608\pi\) | ||||
0.512802 | + | 0.858507i | \(0.328608\pi\) | |||||||
\(182\) | −2.16053 | + | 2.16053i | −0.160149 | + | 0.160149i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 8.93933i | − | 0.659016i | ||||||
\(185\) | 0.539848 | − | 16.2374i | 0.0396904 | − | 1.19380i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.60354 | − | 9.60354i | −0.702280 | − | 0.702280i | ||||
\(188\) | 5.01193 | + | 5.01193i | 0.365532 | + | 0.365532i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.519018i | 0.0375548i | 0.999824 | + | 0.0187774i | \(0.00597739\pi\) | ||||
−0.999824 | + | 0.0187774i | \(0.994023\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.1759 | + | 17.1759i | −1.23635 | + | 1.23635i | −0.274863 | + | 0.961483i | \(0.588632\pi\) |
−0.961483 | + | 0.274863i | \(0.911368\pi\) | |||||||
\(194\) | −0.857497 | −0.0615647 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −4.03248 | + | 4.03248i | −0.287303 | + | 0.287303i | −0.836013 | − | 0.548710i | \(-0.815119\pi\) |
0.548710 | + | 0.836013i | \(0.315119\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 21.1651i | − | 1.50035i | −0.661237 | − | 0.750177i | \(-0.729968\pi\) | ||
0.661237 | − | 0.750177i | \(-0.270032\pi\) | |||||||
\(200\) | 3.76256 | − | 3.29289i | 0.266053 | − | 0.232843i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.81739 | − | 3.81739i | −0.268590 | − | 0.268590i | ||||
\(203\) | −5.80177 | − | 5.80177i | −0.407204 | − | 0.407204i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.3486 | − | 11.5539i | 0.862464 | − | 0.806960i | ||||
\(206\) | 11.0386i | 0.769095i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.16053 | + | 2.16053i | −0.149806 | + | 0.149806i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.8787 | 1.50619 | 0.753095 | − | 0.657912i | \(-0.228560\pi\) | ||||
0.753095 | + | 0.657912i | \(0.228560\pi\) | |||||||
\(212\) | 2.35876 | − | 2.35876i | 0.162000 | − | 0.162000i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.40559i | 0.232801i | ||||||||
\(215\) | −24.7797 | − | 0.823854i | −1.68996 | − | 0.0561863i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.30913 | + | 1.30913i | 0.0888699 | + | 0.0888699i | ||||
\(218\) | 7.00089 | + | 7.00089i | 0.474160 | + | 0.474160i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.28248 | − | 3.50825i | −0.221305 | − | 0.236526i | ||||
\(221\) | − | 19.3137i | − | 1.29918i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.42031 | + | 4.42031i | −0.296006 | + | 0.296006i | −0.839447 | − | 0.543441i | \(-0.817121\pi\) |
0.543441 | + | 0.839447i | \(0.317121\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.97792 | 0.397645 | ||||||||
\(227\) | −11.7028 | + | 11.7028i | −0.776742 | + | 0.776742i | −0.979275 | − | 0.202534i | \(-0.935082\pi\) |
0.202534 | + | 0.979275i | \(0.435082\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.6314i | − | 0.900785i | −0.892831 | − | 0.450393i | \(-0.851284\pi\) | ||
0.892831 | − | 0.450393i | \(-0.148716\pi\) | |||||||
\(230\) | 13.6569 | + | 14.5962i | 0.900506 | + | 0.962444i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.80177 | − | 5.80177i | −0.380905 | − | 0.380905i | ||||
\(233\) | 20.6421 | + | 20.6421i | 1.35231 | + | 1.35231i | 0.883071 | + | 0.469240i | \(0.155472\pi\) |
0.469240 | + | 0.883071i | \(0.344528\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.8404 | − | 0.526646i | −1.03331 | − | 0.0343546i | ||||
\(236\) | 9.35965i | 0.609261i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.46967 | + | 4.46967i | −0.289725 | + | 0.289725i | ||||
\(239\) | 10.3744 | 0.671063 | 0.335531 | − | 0.942029i | \(-0.391084\pi\) | ||||
0.335531 | + | 0.942029i | \(0.391084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.7028 | −0.882674 | −0.441337 | − | 0.897341i | \(-0.645496\pi\) | ||||
−0.441337 | + | 0.897341i | \(0.645496\pi\) | |||||||
\(242\) | 4.51382 | − | 4.51382i | 0.290159 | − | 0.290159i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.46967i | 0.286141i | ||||||||
\(245\) | −1.63280 | + | 1.52773i | −0.104316 | + | 0.0976029i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.30913 | + | 1.30913i | 0.0831302 | + | 0.0831302i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.11289 | + | 11.1248i | −0.0703851 | + | 0.703595i | ||||
\(251\) | 7.57969i | 0.478426i | 0.970967 | + | 0.239213i | \(0.0768893\pi\) | ||||
−0.970967 | + | 0.239213i | \(0.923111\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.5815 | − | 13.5815i | 0.853859 | − | 0.853859i | ||||
\(254\) | 3.28248 | 0.205961 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.2929 | − | 19.2929i | 1.20346 | − | 1.20346i | 0.230349 | − | 0.973108i | \(-0.426013\pi\) |
0.973108 | − | 0.230349i | \(-0.0739866\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.26561i | 0.451463i | ||||||||
\(260\) | 0.227026 | − | 6.82843i | 0.0140795 | − | 0.423481i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.67894 | + | 1.67894i | 0.103725 | + | 0.103725i | ||||
\(263\) | 17.6348 | + | 17.6348i | 1.08741 | + | 1.08741i | 0.995795 | + | 0.0916118i | \(0.0292019\pi\) |
0.0916118 | + | 0.995795i | \(0.470798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.247855 | + | 7.45494i | −0.0152256 | + | 0.457953i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.84035 | + | 3.84035i | −0.234587 | + | 0.234587i | ||||
\(269\) | −20.4463 | −1.24663 | −0.623317 | − | 0.781969i | \(-0.714216\pi\) | ||||
−0.623317 | + | 0.781969i | \(0.714216\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.5707 | −1.24958 | −0.624790 | − | 0.780793i | \(-0.714816\pi\) | ||||
−0.624790 | + | 0.780793i | \(0.714816\pi\) | |||||||
\(272\) | −4.46967 | + | 4.46967i | −0.271013 | + | 0.271013i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.9779i | 0.844437i | ||||||||
\(275\) | 10.7193 | + | 0.713560i | 0.646398 | + | 0.0430293i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.22208 | − | 2.22208i | −0.133512 | − | 0.133512i | 0.637193 | − | 0.770705i | \(-0.280096\pi\) |
−0.770705 | + | 0.637193i | \(0.780096\pi\) | |||||||
\(278\) | −11.0386 | − | 11.0386i | −0.662050 | − | 0.662050i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.63280 | + | 1.52773i | −0.0975788 | + | 0.0912991i | ||||
\(281\) | − | 17.4792i | − | 1.04272i | −0.853337 | − | 0.521360i | \(-0.825425\pi\) | ||
0.853337 | − | 0.521360i | \(-0.174575\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.9007 | − | 17.9007i | 1.06409 | − | 1.06409i | 0.0662885 | − | 0.997800i | \(-0.478884\pi\) |
0.997800 | − | 0.0662885i | \(-0.0211158\pi\) | |||||||
\(284\) | −0.420314 | −0.0249411 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.56496 | −0.388194 | ||||||||
\(287\) | −5.34772 | + | 5.34772i | −0.315666 | + | 0.315666i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 22.9558i | − | 1.35034i | ||||||
\(290\) | 18.3367 | + | 0.609642i | 1.07677 | + | 0.0357994i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.63020 | + | 2.63020i | 0.153921 | + | 0.153921i | ||||
\(293\) | −1.36370 | − | 1.36370i | −0.0796683 | − | 0.0796683i | 0.666150 | − | 0.745818i | \(-0.267941\pi\) |
−0.745818 | + | 0.666150i | \(0.767941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.2990 | − | 15.2825i | −0.832519 | − | 0.889780i | ||||
\(296\) | 7.26561i | 0.422305i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.71725 | − | 6.71725i | 0.389120 | − | 0.389120i | ||||
\(299\) | 27.3137 | 1.57959 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.0879 | 0.639098 | ||||||||
\(302\) | −9.60354 | + | 9.60354i | −0.552622 | + | 0.552622i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.82843 | − | 7.29809i | −0.390995 | − | 0.417888i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.70279 | − | 7.70279i | −0.439622 | − | 0.439622i | 0.452263 | − | 0.891885i | \(-0.350617\pi\) |
−0.891885 | + | 0.452263i | \(0.850617\pi\) | |||||||
\(308\) | 1.51929 | + | 1.51929i | 0.0865697 | + | 0.0865697i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.13756 | − | 0.137562i | −0.234998 | − | 0.00781300i | ||||
\(311\) | − | 3.52637i | − | 0.199962i | −0.994989 | − | 0.0999811i | \(-0.968122\pi\) | ||
0.994989 | − | 0.0999811i | \(-0.0318782\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.3330 | + | 12.3330i | −0.697102 | + | 0.697102i | −0.963784 | − | 0.266683i | \(-0.914072\pi\) |
0.266683 | + | 0.963784i | \(0.414072\pi\) | |||||||
\(314\) | 19.8857 | 1.12221 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.23654 | −0.294578 | ||||||||
\(317\) | −6.65597 | + | 6.65597i | −0.373836 | + | 0.373836i | −0.868872 | − | 0.495036i | \(-0.835155\pi\) |
0.495036 | + | 0.868872i | \(0.335155\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 17.6292i | − | 0.987044i | ||||||
\(320\) | −1.63280 | + | 1.52773i | −0.0912766 | + | 0.0854025i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.32106 | − | 6.32106i | −0.352259 | − | 0.352259i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.0613 | + | 11.4963i | 0.558099 | + | 0.637701i | ||||
\(326\) | − | 12.4476i | − | 0.689408i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.34772 | + | 5.34772i | −0.295278 | + | 0.295278i | ||||
\(329\) | 7.08794 | 0.390771 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.7193 | −1.68849 | −0.844243 | − | 0.535961i | \(-0.819949\pi\) | ||||
−0.844243 | + | 0.535961i | \(0.819949\pi\) | |||||||
\(332\) | 10.6183 | − | 10.6183i | 0.582753 | − | 0.582753i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 3.77423i | − | 0.206517i | ||||||
\(335\) | 0.403539 | − | 12.1376i | 0.0220477 | − | 0.663146i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6183 | − | 11.6183i | −0.632887 | − | 0.632887i | 0.315904 | − | 0.948791i | \(-0.397692\pi\) |
−0.948791 | + | 0.315904i | \(0.897692\pi\) | |||||||
\(338\) | 2.59099 | + | 2.59099i | 0.140931 | + | 0.140931i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.469666 | − | 14.1265i | 0.0254712 | − | 0.766118i | ||||
\(341\) | 3.97792i | 0.215416i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | 11.0879 | 0.597821 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.47702 | −0.509488 | ||||||||
\(347\) | −10.8284 | + | 10.8284i | −0.581300 | + | 0.581300i | −0.935261 | − | 0.353960i | \(-0.884835\pi\) |
0.353960 | + | 0.935261i | \(0.384835\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.3318i | − | 0.820694i | −0.911929 | − | 0.410347i | \(-0.865408\pi\) | ||
0.911929 | − | 0.410347i | \(-0.134592\pi\) | |||||||
\(350\) | 0.332104 | − | 4.98896i | 0.0177517 | − | 0.266671i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.51929 | + | 1.51929i | 0.0809785 | + | 0.0809785i | ||||
\(353\) | −6.14860 | − | 6.14860i | −0.327257 | − | 0.327257i | 0.524285 | − | 0.851543i | \(-0.324332\pi\) |
−0.851543 | + | 0.524285i | \(0.824332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.686292 | − | 0.642125i | 0.0364246 | − | 0.0340805i | ||||
\(356\) | 14.5481i | 0.771047i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.48071 | + | 2.48071i | −0.131109 | + | 0.131109i | ||||
\(359\) | 28.6421 | 1.51167 | 0.755837 | − | 0.654760i | \(-0.227230\pi\) | ||||
0.755837 | + | 0.654760i | \(0.227230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 9.75672 | − | 9.75672i | 0.512802 | − | 0.512802i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.05545i | 0.160149i | ||||||||
\(365\) | −8.31282 | − | 0.276378i | −0.435113 | − | 0.0144663i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0732 | − | 10.0732i | −0.525817 | − | 0.525817i | 0.393505 | − | 0.919322i | \(-0.371262\pi\) |
−0.919322 | + | 0.393505i | \(0.871262\pi\) | |||||||
\(368\) | −6.32106 | − | 6.32106i | −0.329508 | − | 0.329508i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.0999 | − | 11.8633i | −0.577054 | − | 0.616745i | ||||
\(371\) | − | 3.33579i | − | 0.173186i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.1614 | − | 19.1614i | 0.992141 | − | 0.992141i | −0.00782876 | − | 0.999969i | \(-0.502492\pi\) |
0.999969 | + | 0.00782876i | \(0.00249200\pi\) | |||||||
\(374\) | −13.5815 | −0.702280 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.08794 | 0.365532 | ||||||||
\(377\) | 17.7270 | − | 17.7270i | 0.912989 | − | 0.912989i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 22.1538i | − | 1.13796i | −0.822350 | − | 0.568982i | \(-0.807337\pi\) | ||
0.822350 | − | 0.568982i | \(-0.192663\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.367001 | + | 0.367001i | 0.0187774 | + | 0.0187774i | ||||
\(383\) | −24.6008 | − | 24.6008i | −1.25704 | − | 1.25704i | −0.952499 | − | 0.304541i | \(-0.901497\pi\) |
−0.304541 | − | 0.952499i | \(-0.598503\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.80177 | − | 0.159645i | −0.244721 | − | 0.00813627i | ||||
\(386\) | 24.2904i | 1.23635i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.606342 | + | 0.606342i | −0.0307824 | + | 0.0307824i | ||||
\(389\) | −9.25341 | −0.469166 | −0.234583 | − | 0.972096i | \(-0.575373\pi\) | ||||
−0.234583 | + | 0.972096i | \(0.575373\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 56.5061 | 2.85764 | ||||||||
\(392\) | 0.707107 | − | 0.707107i | 0.0357143 | − | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.70279i | 0.287303i | ||||||||
\(395\) | 8.55025 | − | 8.00000i | 0.430210 | − | 0.402524i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.8282 | + | 14.8282i | 0.744204 | + | 0.744204i | 0.973384 | − | 0.229180i | \(-0.0736045\pi\) |
−0.229180 | + | 0.973384i | \(0.573605\pi\) | |||||||
\(398\) | −14.9660 | − | 14.9660i | −0.750177 | − | 0.750177i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.332104 | − | 4.98896i | 0.0166052 | − | 0.249448i | ||||
\(401\) | 13.0416i | 0.651267i | 0.945496 | + | 0.325633i | \(0.105578\pi\) | ||||
−0.945496 | + | 0.325633i | \(0.894422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | + | 4.00000i | −0.199254 | + | 0.199254i | ||||
\(404\) | −5.39860 | −0.268590 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.20494 | −0.407204 | ||||||||
\(407\) | −11.0386 | + | 11.0386i | −0.547162 | + | 0.547162i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.9190i | 1.33106i | 0.746371 | + | 0.665530i | \(0.231794\pi\) | ||||
−0.746371 | + | 0.665530i | \(0.768206\pi\) | |||||||
\(410\) | 0.561931 | − | 16.9016i | 0.0277518 | − | 0.834712i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.80546 | + | 7.80546i | 0.384547 | + | 0.384547i | ||||
\(413\) | 6.61827 | + | 6.61827i | 0.325664 | + | 0.325664i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.11575 | + | 33.5594i | −0.0547702 | + | 1.64736i | ||||
\(416\) | 3.05545i | 0.149806i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.9705 | 1.07333 | 0.536666 | − | 0.843795i | \(-0.319684\pi\) | ||||
0.536666 | + | 0.843795i | \(0.319684\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5502 | −0.514188 | −0.257094 | − | 0.966386i | \(-0.582765\pi\) | ||||
−0.257094 | + | 0.966386i | \(0.582765\pi\) | |||||||
\(422\) | 15.4706 | − | 15.4706i | 0.753095 | − | 0.753095i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 3.33579i | − | 0.162000i | ||||||
\(425\) | 20.8146 | + | 23.7834i | 1.00966 | + | 1.15366i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.16053 | + | 3.16053i | 0.152949 | + | 0.152949i | ||||
\(428\) | 2.40811 | + | 2.40811i | 0.116401 | + | 0.116401i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.1044 | + | 16.9393i | −0.873074 | + | 0.816887i | ||||
\(431\) | 22.9853i | 1.10716i | 0.832795 | + | 0.553581i | \(0.186739\pi\) | ||||
−0.832795 | + | 0.553581i | \(0.813261\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.3256 | − | 11.3256i | 0.544275 | − | 0.544275i | −0.380504 | − | 0.924779i | \(-0.624249\pi\) |
0.924779 | + | 0.380504i | \(0.124249\pi\) | |||||||
\(434\) | 1.85140 | 0.0888699 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.90075 | 0.474160 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.416353i | 0.0198715i | 0.999951 | + | 0.00993573i | \(0.00316269\pi\) | ||||
−0.999951 | + | 0.00993573i | \(0.996837\pi\) | |||||||
\(440\) | −4.80177 | − | 0.159645i | −0.228915 | − | 0.00761078i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.6569 | − | 13.6569i | −0.649590 | − | 0.649590i | ||||
\(443\) | −11.2487 | − | 11.2487i | −0.534444 | − | 0.534444i | 0.387448 | − | 0.921892i | \(-0.373357\pi\) |
−0.921892 | + | 0.387448i | \(0.873357\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.2255 | − | 23.7542i | −1.05359 | − | 1.12606i | ||||
\(446\) | 6.25127i | 0.296006i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.707107 | − | 0.707107i | 0.0334077 | − | 0.0334077i | ||||
\(449\) | 20.7929 | 0.981277 | 0.490639 | − | 0.871363i | \(-0.336764\pi\) | ||||
0.490639 | + | 0.871363i | \(0.336764\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.2495 | −0.765159 | ||||||||
\(452\) | 4.22703 | − | 4.22703i | 0.198823 | − | 0.198823i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.5502i | 0.776742i | ||||||||
\(455\) | −4.66790 | − | 4.98896i | −0.218834 | − | 0.233886i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.7028 | + | 12.7028i | 0.594212 | + | 0.594212i | 0.938766 | − | 0.344555i | \(-0.111970\pi\) |
−0.344555 | + | 0.938766i | \(0.611970\pi\) | |||||||
\(458\) | −9.63883 | − | 9.63883i | −0.450393 | − | 0.450393i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 19.9779 | + | 0.664208i | 0.931475 | + | 0.0309689i | ||||
\(461\) | − | 29.8783i | − | 1.39157i | −0.718250 | − | 0.695785i | \(-0.755057\pi\) | ||
0.718250 | − | 0.695785i | \(-0.244943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.2825 | + | 15.2825i | −0.710237 | + | 0.710237i | −0.966585 | − | 0.256348i | \(-0.917481\pi\) |
0.256348 | + | 0.966585i | \(0.417481\pi\) | |||||||
\(464\) | −8.20494 | −0.380905 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 29.1924 | 1.35231 | ||||||||
\(467\) | −18.5429 | + | 18.5429i | −0.858062 | + | 0.858062i | −0.991110 | − | 0.133048i | \(-0.957524\pi\) |
0.133048 | + | 0.991110i | \(0.457524\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.43108i | 0.250784i | ||||||||
\(470\) | −11.5732 | + | 10.8284i | −0.533833 | + | 0.499478i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.61827 | + | 6.61827i | 0.304631 | + | 0.304631i | ||||
\(473\) | 16.8458 | + | 16.8458i | 0.774571 | + | 0.774571i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.32106i | 0.289725i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.33579 | − | 7.33579i | 0.335531 | − | 0.335531i | ||||
\(479\) | −4.91725 | −0.224675 | −0.112337 | − | 0.993670i | \(-0.535834\pi\) | ||||
−0.112337 | + | 0.993670i | \(0.535834\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.1997 | −1.01222 | ||||||||
\(482\) | −9.68934 | + | 9.68934i | −0.441337 | + | 0.441337i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 6.38350i | − | 0.290159i | ||||||
\(485\) | 0.0637136 | − | 1.91636i | 0.00289309 | − | 0.0870176i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.63477 | + | 9.63477i | 0.436593 | + | 0.436593i | 0.890864 | − | 0.454271i | \(-0.150100\pi\) |
−0.454271 | + | 0.890864i | \(0.650100\pi\) | |||||||
\(488\) | 3.16053 | + | 3.16053i | 0.143071 | + | 0.143071i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.0743018 | + | 2.23483i | −0.00335661 | + | 0.100959i | ||||
\(491\) | − | 20.0273i | − | 0.903818i | −0.892064 | − | 0.451909i | \(-0.850743\pi\) | ||
0.892064 | − | 0.451909i | \(-0.149257\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.6734 | − | 36.6734i | 1.65168 | − | 1.65168i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.85140 | 0.0831302 | ||||||||
\(497\) | −0.297207 | + | 0.297207i | −0.0133316 | + | 0.0133316i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.7959i | 1.55768i | 0.627223 | + | 0.778840i | \(0.284191\pi\) | ||||
−0.627223 | + | 0.778840i | \(0.715809\pi\) | |||||||
\(500\) | 7.07950 | + | 8.65336i | 0.316605 | + | 0.386990i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.35965 | + | 5.35965i | 0.239213 | + | 0.239213i | ||||
\(503\) | 3.26320 | + | 3.26320i | 0.145499 | + | 0.145499i | 0.776104 | − | 0.630605i | \(-0.217193\pi\) |
−0.630605 | + | 0.776104i | \(0.717193\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.81486 | − | 8.24758i | 0.392256 | − | 0.367013i | ||||
\(506\) | − | 19.2071i | − | 0.853859i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.32106 | − | 2.32106i | 0.102981 | − | 0.102981i | ||||
\(509\) | 29.3544 | 1.30111 | 0.650556 | − | 0.759458i | \(-0.274536\pi\) | ||||
0.650556 | + | 0.759458i | \(0.274536\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.71966 | 0.164548 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 27.2843i | − | 1.20346i | ||||||
\(515\) | −24.6694 | − | 0.820187i | −1.08706 | − | 0.0361417i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7686 | + | 10.7686i | 0.473605 | + | 0.473605i | ||||
\(518\) | 5.13756 | + | 5.13756i | 0.225732 | + | 0.225732i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.66790 | − | 4.98896i | −0.204701 | − | 0.218780i | ||||
\(521\) | 12.3453i | 0.540858i | 0.962740 | + | 0.270429i | \(0.0871655\pi\) | ||||
−0.962740 | + | 0.270429i | \(0.912835\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.52637 | + | 7.52637i | −0.329105 | + | 0.329105i | −0.852246 | − | 0.523141i | \(-0.824760\pi\) |
0.523141 | + | 0.852246i | \(0.324760\pi\) | |||||||
\(524\) | 2.37438 | 0.103725 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.9393 | 1.08741 | ||||||||
\(527\) | −8.27512 | + | 8.27512i | −0.360470 | + | 0.360470i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.9117i | 2.47442i | ||||||||
\(530\) | 5.09618 | + | 5.44670i | 0.221364 | + | 0.236589i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.3397 | − | 16.3397i | −0.707751 | − | 0.707751i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.61092 | − | 0.253041i | −0.329049 | − | 0.0109399i | ||||
\(536\) | 5.43108i | 0.234587i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.4577 | + | 14.4577i | −0.623317 | + | 0.623317i | ||||
\(539\) | 2.14860 | 0.0925469 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.9172 | −1.75917 | −0.879585 | − | 0.475742i | \(-0.842180\pi\) | ||||
−0.879585 | + | 0.475742i | \(0.842180\pi\) | |||||||
\(542\) | −14.5457 | + | 14.5457i | −0.624790 | + | 0.624790i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.32106i | 0.271013i | ||||||||
\(545\) | −16.1660 | + | 15.1256i | −0.692475 | + | 0.647911i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.8789 | + | 10.8789i | 0.465150 | + | 0.465150i | 0.900339 | − | 0.435189i | \(-0.143319\pi\) |
−0.435189 | + | 0.900339i | \(0.643319\pi\) | |||||||
\(548\) | 9.88388 | + | 9.88388i | 0.422218 | + | 0.422218i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.08425 | − | 7.07512i | 0.344714 | − | 0.301684i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.70279 | + | 3.70279i | −0.157459 | + | 0.157459i | ||||
\(554\) | −3.14250 | −0.133512 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.6109 | −0.662050 | ||||||||
\(557\) | 18.3588 | − | 18.3588i | 0.777886 | − | 0.777886i | −0.201585 | − | 0.979471i | \(-0.564609\pi\) |
0.979471 | + | 0.201585i | \(0.0646093\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.8787i | 1.43291i | ||||||||
\(560\) | −0.0743018 | + | 2.23483i | −0.00313982 | + | 0.0944389i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.3596 | − | 12.3596i | −0.521360 | − | 0.521360i | ||||
\(563\) | −25.6348 | − | 25.6348i | −1.08038 | − | 1.08038i | −0.996474 | − | 0.0839029i | \(-0.973261\pi\) |
−0.0839029 | − | 0.996474i | \(-0.526739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.444170 | + | 13.3596i | −0.0186864 | + | 0.562045i | ||||
\(566\) | − | 25.3155i | − | 1.06409i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.297207 | + | 0.297207i | −0.0124705 | + | 0.0124705i | ||||
\(569\) | −44.9637 | −1.88498 | −0.942488 | − | 0.334239i | \(-0.891521\pi\) | ||||
−0.942488 | + | 0.334239i | \(0.891521\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.0380 | −0.545625 | −0.272812 | − | 0.962067i | \(-0.587954\pi\) | ||||
−0.272812 | + | 0.962067i | \(0.587954\pi\) | |||||||
\(572\) | −4.64213 | + | 4.64213i | −0.194097 | + | 0.194097i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.56282i | 0.315666i | ||||||||
\(575\) | −33.6348 | + | 29.4363i | −1.40267 | + | 1.22758i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.1498 | + | 17.1498i | 0.713954 | + | 0.713954i | 0.967360 | − | 0.253406i | \(-0.0815509\pi\) |
−0.253406 | + | 0.967360i | \(0.581551\pi\) | |||||||
\(578\) | −16.2322 | − | 16.2322i | −0.675172 | − | 0.675172i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.3971 | − | 12.5349i | 0.556283 | − | 0.520484i | ||||
\(581\) | − | 15.0165i | − | 0.622989i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.06804 | − | 5.06804i | 0.209897 | − | 0.209897i | ||||
\(584\) | 3.71966 | 0.153921 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.92857 | −0.0796683 | ||||||||
\(587\) | 7.26040 | − | 7.26040i | 0.299669 | − | 0.299669i | −0.541215 | − | 0.840884i | \(-0.682036\pi\) |
0.840884 | + | 0.541215i | \(0.182036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −20.9172 | − | 0.695439i | −0.861150 | − | 0.0286308i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.13756 | + | 5.13756i | 0.211153 | + | 0.211153i | ||||
\(593\) | 7.97917 | + | 7.97917i | 0.327665 | + | 0.327665i | 0.851698 | − | 0.524033i | \(-0.175573\pi\) |
−0.524033 | + | 0.851698i | \(0.675573\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.65685 | − | 10.3211i | −0.395892 | − | 0.423122i | ||||
\(596\) | − | 9.49962i | − | 0.389120i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 19.3137 | − | 19.3137i | 0.789796 | − | 0.789796i | ||||
\(599\) | −6.17587 | −0.252339 | −0.126170 | − | 0.992009i | \(-0.540268\pi\) | ||||
−0.126170 | + | 0.992009i | \(0.540268\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.8106 | −0.644930 | −0.322465 | − | 0.946581i | \(-0.604511\pi\) | ||||
−0.322465 | + | 0.946581i | \(0.604511\pi\) | |||||||
\(602\) | 7.84035 | − | 7.84035i | 0.319549 | − | 0.319549i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.5815i | 0.552622i | ||||||||
\(605\) | 9.75225 | + | 10.4230i | 0.396485 | + | 0.423756i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.57969 | − | 3.57969i | −0.145295 | − | 0.145295i | 0.630718 | − | 0.776012i | \(-0.282761\pi\) |
−0.776012 | + | 0.630718i | \(0.782761\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.98896 | − | 0.332104i | −0.404441 | − | 0.0134465i | ||||
\(611\) | 21.6569i | 0.876143i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.77056 | − | 6.77056i | 0.273460 | − | 0.273460i | −0.557031 | − | 0.830492i | \(-0.688060\pi\) |
0.830492 | + | 0.557031i | \(0.188060\pi\) | |||||||
\(614\) | −10.8934 | −0.439622 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.14860 | 0.0865697 | ||||||||
\(617\) | −0.889981 | + | 0.889981i | −0.0358293 | + | 0.0358293i | −0.724794 | − | 0.688965i | \(-0.758065\pi\) |
0.688965 | + | 0.724794i | \(0.258065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 40.4436i | − | 1.62557i | −0.582566 | − | 0.812783i | \(-0.697951\pi\) | ||
0.582566 | − | 0.812783i | \(-0.302049\pi\) | |||||||
\(620\) | −3.02297 | + | 2.82843i | −0.121405 | + | 0.113592i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.49352 | − | 2.49352i | −0.0999811 | − | 0.0999811i | ||||
\(623\) | 10.2871 | + | 10.2871i | 0.412142 | + | 0.412142i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.7794 | − | 3.31371i | −0.991177 | − | 0.132548i | ||||
\(626\) | 17.4415i | 0.697102i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.0613 | − | 14.0613i | 0.561106 | − | 0.561106i | ||||
\(629\) | −45.9264 | −1.83120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.38908 | 0.333964 | 0.166982 | − | 0.985960i | \(-0.446598\pi\) | ||||
0.166982 | + | 0.985960i | \(0.446598\pi\) | |||||||
\(632\) | −3.70279 | + | 3.70279i | −0.147289 | + | 0.147289i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.41296i | 0.373836i | ||||||||
\(635\) | −0.243894 | + | 7.33579i | −0.00967864 | + | 0.291112i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.16053 | + | 2.16053i | 0.0856034 | + | 0.0856034i | ||||
\(638\) | −12.4657 | − | 12.4657i | −0.493522 | − | 0.493522i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.0743018 | + | 2.23483i | −0.00293704 | + | 0.0883395i | ||||
\(641\) | 20.6863i | 0.817058i | 0.912745 | + | 0.408529i | \(0.133958\pi\) | ||||
−0.912745 | + | 0.408529i | \(0.866042\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.55583 | − | 1.55583i | 0.0613559 | − | 0.0613559i | −0.675763 | − | 0.737119i | \(-0.736186\pi\) |
0.737119 | + | 0.675763i | \(0.236186\pi\) | |||||||
\(644\) | −8.93933 | −0.352259 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.9053 | − | 31.9053i | 1.25433 | − | 1.25433i | 0.300567 | − | 0.953761i | \(-0.402824\pi\) |
0.953761 | − | 0.300567i | \(-0.0971759\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.1102i | 0.789393i | ||||||||
\(650\) | 15.2435 | + | 1.01473i | 0.597900 | + | 0.0398009i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.80177 | − | 8.80177i | −0.344704 | − | 0.344704i | ||||
\(653\) | −16.1841 | − | 16.1841i | −0.633333 | − | 0.633333i | 0.315569 | − | 0.948903i | \(-0.397805\pi\) |
−0.948903 | + | 0.315569i | \(0.897805\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.87689 | + | 3.62740i | −0.151483 | + | 0.141734i | ||||
\(656\) | 7.56282i | 0.295278i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.01193 | − | 5.01193i | 0.195385 | − | 0.195385i | ||||
\(659\) | −7.13565 | −0.277965 | −0.138983 | − | 0.990295i | \(-0.544383\pi\) | ||||
−0.138983 | + | 0.990295i | \(0.544383\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.3103 | −1.14004 | −0.570019 | − | 0.821631i | \(-0.693064\pi\) | ||||
−0.570019 | + | 0.821631i | \(0.693064\pi\) | |||||||
\(662\) | −21.7218 | + | 21.7218i | −0.844243 | + | 0.844243i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 15.0165i | − | 0.582753i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51.8640 | + | 51.8640i | 2.00818 | + | 2.00818i | ||||
\(668\) | −2.66878 | − | 2.66878i | −0.103258 | − | 0.103258i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.29721 | − | 8.86790i | −0.320549 | − | 0.342597i | ||||
\(671\) | 9.60354i | 0.370741i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.3431 | + | 13.3431i | −0.514340 | + | 0.514340i | −0.915853 | − | 0.401513i | \(-0.868484\pi\) |
0.401513 | + | 0.915853i | \(0.368484\pi\) | |||||||
\(674\) | −16.4307 | −0.632887 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.66421 | 0.140931 | ||||||||
\(677\) | 1.38289 | − | 1.38289i | 0.0531488 | − | 0.0531488i | −0.680033 | − | 0.733182i | \(-0.738035\pi\) |
0.733182 | + | 0.680033i | \(0.238035\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.857497i | 0.0329077i | ||||||||
\(680\) | −9.65685 | − | 10.3211i | −0.370323 | − | 0.395795i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.81281 | + | 2.81281i | 0.107708 | + | 0.107708i | ||||
\(683\) | 24.2907 | + | 24.2907i | 0.929459 | + | 0.929459i | 0.997671 | − | 0.0682116i | \(-0.0217293\pi\) |
−0.0682116 | + | 0.997671i | \(0.521729\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.2383 | − | 1.03858i | −1.19355 | − | 0.0396823i | ||||
\(686\) | − | 1.00000i | − | 0.0381802i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.84035 | − | 7.84035i | 0.298911 | − | 0.298911i | ||||
\(689\) | 10.1924 | 0.388298 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.0642 | 1.02957 | 0.514786 | − | 0.857319i | \(-0.327872\pi\) | ||||
0.514786 | + | 0.857319i | \(0.327872\pi\) | |||||||
\(692\) | −6.70127 | + | 6.70127i | −0.254744 | + | 0.254744i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.3137i | 0.581300i | ||||||||
\(695\) | 25.4896 | − | 23.8492i | 0.966875 | − | 0.904652i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.8033 | − | 33.8033i | −1.28039 | − | 1.28039i | ||||
\(698\) | −10.8412 | − | 10.8412i | −0.410347 | − | 0.410347i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.29289 | − | 3.76256i | −0.124460 | − | 0.142211i | ||||
\(701\) | − | 1.63999i | − | 0.0619414i | −0.999520 | − | 0.0309707i | \(-0.990140\pi\) | ||
0.999520 | − | 0.0309707i | \(-0.00985986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.14860 | 0.0809785 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.69544 | −0.327257 | ||||||||
\(707\) | −3.81739 | + | 3.81739i | −0.143568 | + | 0.143568i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 8.35963i | − | 0.313952i | −0.987602 | − | 0.156976i | \(-0.949825\pi\) | ||
0.987602 | − | 0.156976i | \(-0.0501746\pi\) | |||||||
\(710\) | 0.0312301 | − | 0.939333i | 0.00117205 | − | 0.0352525i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.2871 | + | 10.2871i | 0.385524 | + | 0.385524i | ||||
\(713\) | −11.7028 | − | 11.7028i | −0.438273 | − | 0.438273i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.487788 | − | 14.6716i | 0.0182422 | − | 0.548686i | ||||
\(716\) | 3.50825i | 0.131109i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.2530 | − | 20.2530i | 0.755837 | − | 0.755837i | ||||
\(719\) | 16.9706 | 0.632895 | 0.316448 | − | 0.948610i | \(-0.397510\pi\) | ||||
0.316448 | + | 0.948610i | \(0.397510\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.0386 | 0.411098 | ||||||||
\(722\) | 13.4350 | − | 13.4350i | 0.500000 | − | 0.500000i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 13.7981i | − | 0.512802i | ||||||
\(725\) | −2.72490 | + | 40.9341i | −0.101200 | + | 1.52025i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.221811 | + | 0.221811i | 0.00822652 | + | 0.00822652i | 0.711208 | − | 0.702982i | \(-0.248148\pi\) |
−0.702982 | + | 0.711208i | \(0.748148\pi\) | |||||||
\(728\) | 2.16053 | + | 2.16053i | 0.0800746 | + | 0.0800746i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.07348 | + | 5.68262i | −0.224790 | + | 0.210323i | ||||
\(731\) | 70.0875i | 2.59228i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.28705 | − | 4.28705i | 0.158346 | − | 0.158346i | −0.623487 | − | 0.781833i | \(-0.714285\pi\) |
0.781833 | + | 0.623487i | \(0.214285\pi\) | |||||||
\(734\) | −14.2457 | −0.525817 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.93933 | −0.329508 | ||||||||
\(737\) | −8.25140 | + | 8.25140i | −0.303944 | + | 0.303944i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.6182i | 0.427384i | 0.976901 | + | 0.213692i | \(0.0685489\pi\) | ||||
−0.976901 | + | 0.213692i | \(0.931451\pi\) | |||||||
\(740\) | −16.2374 | − | 0.539848i | −0.596900 | − | 0.0198452i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.35876 | − | 2.35876i | −0.0865928 | − | 0.0865928i | ||||
\(743\) | −7.65508 | − | 7.65508i | −0.280838 | − | 0.280838i | 0.552605 | − | 0.833443i | \(-0.313634\pi\) |
−0.833443 | + | 0.552605i | \(0.813634\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.5128 | + | 15.5110i | 0.531709 | + | 0.568280i | ||||
\(746\) | − | 27.0983i | − | 0.992141i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.60354 | + | 9.60354i | −0.351140 | + | 0.351140i | ||||
\(749\) | 3.40559 | 0.124437 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.7505 | −0.866668 | −0.433334 | − | 0.901233i | \(-0.642663\pi\) | ||||
−0.433334 | + | 0.901233i | \(0.642663\pi\) | |||||||
\(752\) | 5.01193 | − | 5.01193i | 0.182766 | − | 0.182766i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 25.0698i | − | 0.912989i | ||||||
\(755\) | −20.7488 | − | 22.1759i | −0.755124 | − | 0.807063i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.4825 | − | 31.4825i | −1.14425 | − | 1.14425i | −0.987664 | − | 0.156586i | \(-0.949951\pi\) |
−0.156586 | − | 0.987664i | \(-0.550049\pi\) | |||||||
\(758\) | −15.6651 | − | 15.6651i | −0.568982 | − | 0.568982i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.2552i | 0.698000i | 0.937123 | + | 0.349000i | \(0.113479\pi\) | ||||
−0.937123 | + | 0.349000i | \(0.886521\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.00089 | − | 7.00089i | 0.253449 | − | 0.253449i | ||||
\(764\) | 0.519018 | 0.0187774 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34.7907 | −1.25704 | ||||||||
\(767\) | −20.2218 | + | 20.2218i | −0.730167 | + | 0.730167i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 52.3541i | 1.88794i | 0.330037 | + | 0.943968i | \(0.392939\pi\) | ||||
−0.330037 | + | 0.943968i | \(0.607061\pi\) | |||||||
\(770\) | −3.50825 | + | 3.28248i | −0.126429 | + | 0.118292i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.1759 | + | 17.1759i | 0.618173 | + | 0.618173i | ||||
\(773\) | 24.6410 | + | 24.6410i | 0.886274 | + | 0.886274i | 0.994163 | − | 0.107889i | \(-0.0344091\pi\) |
−0.107889 | + | 0.994163i | \(0.534409\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.614857 | − | 9.23654i | 0.0220863 | − | 0.331786i | ||||
\(776\) | 0.857497i | 0.0307824i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.54315 | + | 6.54315i | −0.234583 | + | 0.234583i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.903089 | −0.0323151 | ||||||||
\(782\) | 39.9558 | − | 39.9558i | 1.42882 | − | 1.42882i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | −1.47754 | + | 44.4411i | −0.0527357 | + | 1.58617i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.9264 | + | 33.9264i | 1.20934 | + | 1.20934i | 0.971239 | + | 0.238105i | \(0.0765264\pi\) |
0.238105 | + | 0.971239i | \(0.423474\pi\) | |||||||
\(788\) | 4.03248 | + | 4.03248i | 0.143651 | + | 0.143651i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.389084 | − | 11.7028i | 0.0138430 | − | 0.416367i | ||||
\(791\) | − | 5.97792i | − | 0.212550i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.65685 | + | 9.65685i | −0.342925 | + | 0.342925i | ||||
\(794\) | 20.9702 | 0.744204 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21.1651 | −0.750177 | ||||||||
\(797\) | 13.8269 | − | 13.8269i | 0.489774 | − | 0.489774i | −0.418461 | − | 0.908235i | \(-0.637430\pi\) |
0.908235 | + | 0.418461i | \(0.137430\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.8033i | 1.58503i | ||||||||
\(800\) | −3.29289 | − | 3.76256i | −0.116421 | − | 0.133027i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.22181 | + | 9.22181i | 0.325633 | + | 0.325633i | ||||
\(803\) | 5.65125 | + | 5.65125i | 0.199428 | + | 0.199428i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.5962 | − | 13.6569i | 0.514448 | − | 0.481341i | ||||
\(806\) | 5.65685i | 0.199254i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.81739 | + | 3.81739i | −0.134295 | + | 0.134295i | ||||
\(809\) | 32.8743 | 1.15580 | 0.577900 | − | 0.816108i | \(-0.303872\pi\) | ||||
0.577900 | + | 0.816108i | \(0.303872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.1794 | −1.20020 | −0.600101 | − | 0.799924i | \(-0.704873\pi\) | ||||
−0.600101 | + | 0.799924i | \(0.704873\pi\) | |||||||
\(812\) | −5.80177 | + | 5.80177i | −0.203602 | + | 0.203602i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.6109i | 0.547162i | ||||||||
\(815\) | 27.8183 | + | 0.924878i | 0.974432 | + | 0.0323971i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 19.0346 | + | 19.0346i | 0.665530 | + | 0.665530i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.5539 | − | 12.3486i | −0.403480 | − | 0.431232i | ||||
\(821\) | − | 54.3392i | − | 1.89645i | −0.317600 | − | 0.948225i | \(-0.602877\pi\) | ||
0.317600 | − | 0.948225i | \(-0.397123\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.09365 | − | 2.09365i | 0.0729800 | − | 0.0729800i | −0.669675 | − | 0.742655i | \(-0.733566\pi\) |
0.742655 | + | 0.669675i | \(0.233566\pi\) | |||||||
\(824\) | 11.0386 | 0.384547 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.35965 | 0.325664 | ||||||||
\(827\) | 34.5273 | − | 34.5273i | 1.20063 | − | 1.20063i | 0.226655 | − | 0.973975i | \(-0.427221\pi\) |
0.973975 | − | 0.226655i | \(-0.0727791\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 20.4697i | − | 0.710941i | −0.934688 | − | 0.355470i | \(-0.884321\pi\) | ||
0.934688 | − | 0.355470i | \(-0.115679\pi\) | |||||||
\(830\) | 22.9411 | + | 24.5190i | 0.796297 | + | 0.851068i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.16053 | + | 2.16053i | 0.0749029 | + | 0.0749029i | ||||
\(833\) | 4.46967 | + | 4.46967i | 0.154865 | + | 0.154865i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.43477 | + | 0.280432i | 0.291897 | + | 0.00970475i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.5355 | − | 15.5355i | 0.536666 | − | 0.536666i | ||||
\(839\) | 37.0472 | 1.27901 | 0.639505 | − | 0.768787i | \(-0.279139\pi\) | ||||
0.639505 | + | 0.768787i | \(0.279139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.3211 | 1.32142 | ||||||||
\(842\) | −7.46015 | + | 7.46015i | −0.257094 | + | 0.257094i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 21.8787i | − | 0.753095i | ||||||
\(845\) | −5.98294 | + | 5.59791i | −0.205819 | + | 0.192574i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.51382 | − | 4.51382i | −0.155097 | − | 0.155097i | ||||
\(848\) | −2.35876 | − | 2.35876i | −0.0810002 | − | 0.0810002i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 31.5355 | + | 2.09925i | 1.08166 | + | 0.0720037i | ||||
\(851\) | − | 64.9497i | − | 2.22645i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.806618 | − | 0.806618i | 0.0276181 | − | 0.0276181i | −0.693163 | − | 0.720781i | \(-0.743783\pi\) |
0.720781 | + | 0.693163i | \(0.243783\pi\) | |||||||
\(854\) | 4.46967 | 0.152949 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.40559 | 0.116401 | ||||||||
\(857\) | 17.6075 | − | 17.6075i | 0.601461 | − | 0.601461i | −0.339239 | − | 0.940700i | \(-0.610170\pi\) |
0.940700 | + | 0.339239i | \(0.110170\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 37.4748i | − | 1.27862i | −0.768947 | − | 0.639312i | \(-0.779219\pi\) | ||
0.768947 | − | 0.639312i | \(-0.220781\pi\) | |||||||
\(860\) | −0.823854 | + | 24.7797i | −0.0280932 | + | 0.844980i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.2530 | + | 16.2530i | 0.553581 | + | 0.553581i | ||||
\(863\) | −37.1924 | − | 37.1924i | −1.26604 | − | 1.26604i | −0.948115 | − | 0.317928i | \(-0.897013\pi\) |
−0.317928 | − | 0.948115i | \(-0.602987\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.704160 | − | 21.1796i | 0.0239421 | − | 0.720127i | ||||
\(866\) | − | 16.0169i | − | 0.544275i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.30913 | − | 1.30913i | 0.0444349 | − | 0.0444349i | ||||
\(869\) | −11.2512 | −0.381672 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.5944 | −0.562280 | ||||||||
\(872\) | 7.00089 | − | 7.00089i | 0.237080 | − | 0.237080i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.1248 | + | 1.11289i | 0.376087 | + | 0.0376224i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.3997 | − | 26.3997i | −0.891456 | − | 0.891456i | 0.103205 | − | 0.994660i | \(-0.467090\pi\) |
−0.994660 | + | 0.103205i | \(0.967090\pi\) | |||||||
\(878\) | 0.294406 | + | 0.294406i | 0.00993573 | + | 0.00993573i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.50825 | + | 3.28248i | −0.118263 | + | 0.110652i | ||||
\(881\) | 56.1098i | 1.89039i | 0.326511 | + | 0.945193i | \(0.394127\pi\) | ||||
−0.326511 | + | 0.945193i | \(0.605873\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.55052 | − | 5.55052i | 0.186790 | − | 0.186790i | −0.607517 | − | 0.794307i | \(-0.707834\pi\) |
0.794307 | + | 0.607517i | \(0.207834\pi\) | |||||||
\(884\) | −19.3137 | −0.649590 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.9081 | −0.534444 | ||||||||
\(887\) | 17.9292 | − | 17.9292i | 0.602003 | − | 0.602003i | −0.338841 | − | 0.940844i | \(-0.610035\pi\) |
0.940844 | + | 0.338841i | \(0.110035\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 3.28248i | − | 0.110091i | ||||||
\(890\) | −32.5126 | − | 1.08095i | −1.08982 | − | 0.0362335i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.42031 | + | 4.42031i | 0.148003 | + | 0.148003i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.35965 | − | 5.72829i | −0.179153 | − | 0.191476i | ||||
\(896\) | − | 1.00000i | − | 0.0334077i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.7028 | − | 14.7028i | 0.490639 | − | 0.490639i | ||||
\(899\) | −15.1906 | −0.506635 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.0857 | 0.702468 | ||||||||
\(902\) | −11.4901 | + | 11.4901i | −0.382579 | + | 0.382579i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 5.97792i | − | 0.198823i | ||||||
\(905\) | 21.0797 | + | 22.5296i | 0.700713 | + | 0.748909i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.4734 | − | 11.4734i | −0.380966 | − | 0.380966i | 0.490484 | − | 0.871450i | \(-0.336820\pi\) |
−0.871450 | + | 0.490484i | \(0.836820\pi\) | |||||||
\(908\) | 11.7028 | + | 11.7028i | 0.388371 | + | 0.388371i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.82843 | − | 0.227026i | −0.226360 | − | 0.00752583i | ||||
\(911\) | − | 22.2383i | − | 0.736789i | −0.929670 | − | 0.368394i | \(-0.879908\pi\) | ||
0.929670 | − | 0.368394i | \(-0.120092\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.8145 | − | 22.8145i | 0.755048 | − | 0.755048i | ||||
\(914\) | 17.9645 | 0.594212 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.6314 | −0.450393 | ||||||||
\(917\) | 1.67894 | − | 1.67894i | 0.0554434 | − | 0.0554434i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.25917i | − | 0.107510i | −0.998554 | − | 0.0537551i | \(-0.982881\pi\) | ||
0.998554 | − | 0.0537551i | \(-0.0171190\pi\) | |||||||
\(920\) | 14.5962 | − | 13.6569i | 0.481222 | − | 0.450253i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −21.1271 | − | 21.1271i | −0.695785 | − | 0.695785i | ||||
\(923\) | −0.908103 | − | 0.908103i | −0.0298906 | − | 0.0298906i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.3373 | − | 23.9249i | 0.898845 | − | 0.786645i | ||||
\(926\) | 21.6127i | 0.710237i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.80177 | + | 5.80177i | −0.190452 | + | 0.190452i | ||||
\(929\) | −6.79758 | −0.223022 | −0.111511 | − | 0.993763i | \(-0.535569\pi\) | ||||
−0.111511 | + | 0.993763i | \(0.535569\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.6421 | − | 20.6421i | 0.676155 | − | 0.676155i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26.2236i | 0.858062i | ||||||||
\(935\) | 1.00913 | − | 30.3523i | 0.0330020 | − | 0.992626i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.8061 | − | 40.8061i | −1.33308 | − | 1.33308i | −0.902604 | − | 0.430473i | \(-0.858347\pi\) |
−0.430473 | − | 0.902604i | \(-0.641653\pi\) | |||||||
\(938\) | 3.84035 | + | 3.84035i | 0.125392 | + | 0.125392i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.526646 | + | 15.8404i | −0.0171773 | + | 0.516655i | ||||
\(941\) | − | 28.1400i | − | 0.917337i | −0.888607 | − | 0.458668i | \(-0.848327\pi\) | ||
0.888607 | − | 0.458668i | \(-0.151673\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 47.8050 | − | 47.8050i | 1.55675 | − | 1.55675i | ||||
\(944\) | 9.35965 | 0.304631 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.8236 | 0.774571 | ||||||||
\(947\) | 22.0151 | − | 22.0151i | 0.715394 | − | 0.715394i | −0.252265 | − | 0.967658i | \(-0.581175\pi\) |
0.967658 | + | 0.252265i | \(0.0811754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.3652i | 0.368932i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.46967 | + | 4.46967i | 0.144863 | + | 0.144863i | ||||
\(953\) | 6.51039 | + | 6.51039i | 0.210892 | + | 0.210892i | 0.804646 | − | 0.593754i | \(-0.202355\pi\) |
−0.593754 | + | 0.804646i | \(0.702355\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.847456 | + | 0.792918i | −0.0274230 | + | 0.0256582i | ||||
\(956\) | − | 10.3744i | − | 0.335531i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.47702 | + | 3.47702i | −0.112337 | + | 0.112337i | ||||
\(959\) | 13.9779 | 0.451370 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.5723 | −0.889430 | ||||||||
\(962\) | −15.6976 | + | 15.6976i | −0.506110 | + | 0.506110i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.7028i | 0.441337i | ||||||||
\(965\) | −54.2849 | − | 1.80482i | −1.74749 | − | 0.0580991i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.1299 | + | 28.1299i | 0.904598 | + | 0.904598i | 0.995830 | − | 0.0912320i | \(-0.0290805\pi\) |
−0.0912320 | + | 0.995830i | \(0.529080\pi\) | |||||||
\(968\) | −4.51382 | − | 4.51382i | −0.145080 | − | 0.145080i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.31002 | − | 1.40013i | −0.0420622 | − | 0.0449553i | ||||
\(971\) | 36.6421i | 1.17590i | 0.808897 | + | 0.587951i | \(0.200065\pi\) | ||||
−0.808897 | + | 0.587951i | \(0.799935\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.0386 | + | 11.0386i | −0.353881 | + | 0.353881i | ||||
\(974\) | 13.6256 | 0.436593 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.46967 | 0.143071 | ||||||||
\(977\) | 30.5962 | − | 30.5962i | 0.978859 | − | 0.978859i | −0.0209224 | − | 0.999781i | \(-0.506660\pi\) |
0.999781 | + | 0.0209224i | \(0.00666028\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.2581i | 0.999012i | ||||||||
\(980\) | 1.52773 | + | 1.63280i | 0.0488014 | + | 0.0521580i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14.1614 | − | 14.1614i | −0.451909 | − | 0.451909i | ||||
\(983\) | −4.87234 | − | 4.87234i | −0.155403 | − | 0.155403i | 0.625123 | − | 0.780526i | \(-0.285049\pi\) |
−0.780526 | + | 0.625123i | \(0.785049\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.7448 | − | 0.423728i | −0.406083 | − | 0.0135011i | ||||
\(986\) | − | 51.8640i | − | 1.65168i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −99.1188 | −3.15179 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.1317 | 1.71955 | 0.859775 | − | 0.510673i | \(-0.170604\pi\) | ||||
0.859775 | + | 0.510673i | \(0.170604\pi\) | |||||||
\(992\) | 1.30913 | − | 1.30913i | 0.0415651 | − | 0.0415651i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.420314i | 0.0133316i | ||||||||
\(995\) | 34.5585 | − | 32.3345i | 1.09558 | − | 1.02507i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.5094 | − | 16.5094i | −0.522858 | − | 0.522858i | 0.395575 | − | 0.918434i | \(-0.370545\pi\) |
−0.918434 | + | 0.395575i | \(0.870545\pi\) | |||||||
\(998\) | 24.6044 | + | 24.6044i | 0.778840 | + | 0.778840i | ||||
\(999\) | 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 | 630.2.m.c.197.4 | ✓ | 8 | |
3.2 | odd | 2 | 630.2.m.d.197.1 | yes | 8 | ||
5.2 | odd | 4 | 3150.2.m.j.2843.4 | 8 | |||
5.3 | odd | 4 | 630.2.m.d.323.1 | yes | 8 | ||
5.4 | even | 2 | 3150.2.m.i.1457.2 | 8 | |||
15.2 | even | 4 | 3150.2.m.i.2843.1 | 8 | |||
15.8 | even | 4 | inner | 630.2.m.c.323.4 | yes | 8 | |
15.14 | odd | 2 | 3150.2.m.j.1457.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.m.c.197.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
630.2.m.c.323.4 | yes | 8 | 15.8 | even | 4 | inner | |
630.2.m.d.197.1 | yes | 8 | 3.2 | odd | 2 | ||
630.2.m.d.323.1 | yes | 8 | 5.3 | odd | 4 | ||
3150.2.m.i.1457.2 | 8 | 5.4 | even | 2 | |||
3150.2.m.i.2843.1 | 8 | 15.2 | even | 4 | |||
3150.2.m.j.1457.3 | 8 | 15.14 | odd | 2 | |||
3150.2.m.j.2843.4 | 8 | 5.2 | odd | 4 |