Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(881,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.m (of order \(6\), degree \(2\), not 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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 882) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1763.14 | ||
Character | \(\chi\) | \(=\) | 2646.1763 |
Dual form | 2646.2.m.c.881.14 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.35026 | + | 2.33872i | 0.603856 | + | 1.04591i | 0.992231 | + | 0.124408i | \(0.0397032\pi\) |
−0.388375 | + | 0.921501i | \(0.626963\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.70053i | 0.853982i | ||||||||
\(11\) | 0.205998 | + | 0.118933i | 0.0621106 | + | 0.0358596i | 0.530734 | − | 0.847539i | \(-0.321916\pi\) |
−0.468623 | + | 0.883398i | \(0.655250\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.31418 | + | 1.33609i | −0.641839 | + | 0.370566i | −0.785322 | − | 0.619087i | \(-0.787503\pi\) |
0.143484 | + | 0.989653i | \(0.454169\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −5.86724 | −1.42301 | −0.711507 | − | 0.702679i | \(-0.751987\pi\) | ||||
−0.711507 | + | 0.702679i | \(0.751987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.15274i | 0.264456i | 0.991219 | + | 0.132228i | \(0.0422131\pi\) | ||||
−0.991219 | + | 0.132228i | \(0.957787\pi\) | |||||||
\(20\) | −1.35026 | + | 2.33872i | −0.301928 | + | 0.522955i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.118933 | + | 0.205998i | 0.0253566 | + | 0.0439188i | ||||
\(23\) | −7.02271 | + | 4.05456i | −1.46434 | + | 0.845435i | −0.999207 | − | 0.0398080i | \(-0.987325\pi\) |
−0.465129 | + | 0.885243i | \(0.653992\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.14642 | + | 1.98566i | −0.229284 | + | 0.397132i | ||||
\(26\) | −2.67219 | −0.524059 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.88796 | − | 5.13146i | −1.65045 | − | 0.952889i | −0.976886 | − | 0.213762i | \(-0.931428\pi\) |
−0.673566 | − | 0.739127i | \(-0.735238\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.21902 | + | 3.01320i | −0.937364 | + | 0.541187i | −0.889133 | − | 0.457649i | \(-0.848692\pi\) |
−0.0482307 | + | 0.998836i | \(0.515358\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.08118 | − | 2.93362i | −0.871415 | − | 0.503112i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.68488 | 1.59218 | 0.796092 | − | 0.605175i | \(-0.206897\pi\) | ||||
0.796092 | + | 0.605175i | \(0.206897\pi\) | |||||||
\(38\) | −0.576368 | + | 0.998299i | −0.0934993 | + | 0.161945i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.33872 | + | 1.35026i | −0.369785 | + | 0.213495i | ||||
\(41\) | 3.81891 | + | 6.61455i | 0.596414 | + | 1.03302i | 0.993346 | + | 0.115171i | \(0.0367416\pi\) |
−0.396932 | + | 0.917848i | \(0.629925\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.69219 | − | 4.66301i | 0.410555 | − | 0.711103i | −0.584395 | − | 0.811469i | \(-0.698668\pi\) |
0.994951 | + | 0.100366i | \(0.0320015\pi\) | |||||||
\(44\) | 0.237866i | 0.0358596i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.10913 | −1.19563 | ||||||||
\(47\) | −0.221142 | + | 0.383029i | −0.0322568 | + | 0.0558705i | −0.881703 | − | 0.471805i | \(-0.843603\pi\) |
0.849446 | + | 0.527675i | \(0.176936\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.98566 | + | 1.14642i | −0.280815 | + | 0.162129i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.31418 | − | 1.33609i | −0.320919 | − | 0.185283i | ||||
\(53\) | − | 0.219155i | − | 0.0301032i | −0.999887 | − | 0.0150516i | \(-0.995209\pi\) | ||
0.999887 | − | 0.0150516i | \(-0.00479126\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.642362i | 0.0866161i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.13146 | − | 8.88796i | −0.673794 | − | 1.16705i | ||||
\(59\) | 0.983559 | + | 1.70357i | 0.128048 | + | 0.221786i | 0.922920 | − | 0.384991i | \(-0.125795\pi\) |
−0.794872 | + | 0.606777i | \(0.792462\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8615 | + | 6.27087i | 1.39067 | + | 0.802902i | 0.993389 | − | 0.114796i | \(-0.0366214\pi\) |
0.397278 | + | 0.917698i | \(0.369955\pi\) | |||||||
\(62\) | −6.02640 | −0.765354 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −6.24951 | − | 3.60816i | −0.775156 | − | 0.447537i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.48336 | + | 7.76541i | 0.547730 | + | 0.948696i | 0.998430 | + | 0.0560206i | \(0.0178412\pi\) |
−0.450700 | + | 0.892676i | \(0.648825\pi\) | |||||||
\(68\) | −2.93362 | − | 5.08118i | −0.355754 | − | 0.616183i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.24510i | − | 0.266445i | −0.991086 | − | 0.133222i | \(-0.957468\pi\) | ||
0.991086 | − | 0.133222i | \(-0.0425324\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.25634i | 0.849291i | 0.905360 | + | 0.424645i | \(0.139601\pi\) | ||||
−0.905360 | + | 0.424645i | \(0.860399\pi\) | |||||||
\(74\) | 8.38735 | + | 4.84244i | 0.975010 | + | 0.562922i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.998299 | + | 0.576368i | −0.114513 | + | 0.0661140i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.43592 | − | 9.41528i | 0.611588 | − | 1.05930i | −0.379385 | − | 0.925239i | \(-0.623864\pi\) |
0.990973 | − | 0.134063i | \(-0.0428024\pi\) | |||||||
\(80\) | −2.70053 | −0.301928 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.63782i | 0.843456i | ||||||||
\(83\) | 0.762403 | − | 1.32052i | 0.0836846 | − | 0.144946i | −0.821145 | − | 0.570719i | \(-0.806665\pi\) |
0.904830 | + | 0.425773i | \(0.139998\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.92232 | − | 13.7219i | −0.859296 | − | 1.48834i | ||||
\(86\) | 4.66301 | − | 2.69219i | 0.502826 | − | 0.290307i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.118933 | + | 0.205998i | −0.0126783 | + | 0.0219594i | ||||
\(89\) | −13.5277 | −1.43393 | −0.716967 | − | 0.697107i | \(-0.754470\pi\) | ||||
−0.716967 | + | 0.697107i | \(0.754470\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.02271 | − | 4.05456i | −0.732168 | − | 0.422717i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.383029 | + | 0.221142i | −0.0395064 | + | 0.0228090i | ||||
\(95\) | −2.69593 | + | 1.55650i | −0.276597 | + | 0.159693i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.37708 | + | 0.795057i | 0.139821 | + | 0.0807258i | 0.568279 | − | 0.822836i | \(-0.307610\pi\) |
−0.428458 | + | 0.903562i | \(0.640943\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.29284 | −0.229284 | ||||||||
\(101\) | −6.48353 | + | 11.2298i | −0.645135 | + | 1.11741i | 0.339135 | + | 0.940738i | \(0.389866\pi\) |
−0.984270 | + | 0.176670i | \(0.943468\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.9765 | + | 9.22402i | −1.57421 | + | 0.908870i | −0.578564 | + | 0.815637i | \(0.696387\pi\) |
−0.995644 | + | 0.0932327i | \(0.970280\pi\) | |||||||
\(104\) | −1.33609 | − | 2.31418i | −0.131015 | − | 0.226924i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.109577 | − | 0.189794i | 0.0106431 | − | 0.0184344i | ||||
\(107\) | − | 4.65158i | − | 0.449686i | −0.974395 | − | 0.224843i | \(-0.927813\pi\) | ||
0.974395 | − | 0.224843i | \(-0.0721868\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0651 | 0.964066 | 0.482033 | − | 0.876153i | \(-0.339898\pi\) | ||||
0.482033 | + | 0.876153i | \(0.339898\pi\) | |||||||
\(110\) | −0.321181 | + | 0.556302i | −0.0306234 | + | 0.0530413i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.33618 | − | 4.81290i | 0.784202 | − | 0.452759i | −0.0537156 | − | 0.998556i | \(-0.517106\pi\) |
0.837917 | + | 0.545797i | \(0.183773\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.9650 | − | 10.9495i | −1.76850 | − | 1.02104i | ||||
\(116\) | − | 10.2629i | − | 0.952889i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.96712i | 0.181088i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.47171 | − | 9.47728i | −0.497428 | − | 0.861571i | ||||
\(122\) | 6.27087 | + | 10.8615i | 0.567738 | + | 0.983350i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.21902 | − | 3.01320i | −0.468682 | − | 0.270594i | ||||
\(125\) | 7.31075 | 0.653893 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.69657 | −0.416753 | −0.208377 | − | 0.978049i | \(-0.566818\pi\) | ||||
−0.208377 | + | 0.978049i | \(0.566818\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.60816 | − | 6.24951i | −0.316456 | − | 0.548118i | ||||
\(131\) | 7.02151 | + | 12.1616i | 0.613472 | + | 1.06257i | 0.990650 | + | 0.136424i | \(0.0435611\pi\) |
−0.377178 | + | 0.926141i | \(0.623106\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.96673i | 0.774607i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 5.86724i | − | 0.503112i | ||||||
\(137\) | 9.39626 | + | 5.42494i | 0.802777 | + | 0.463483i | 0.844441 | − | 0.535648i | \(-0.179933\pi\) |
−0.0416643 | + | 0.999132i | \(0.513266\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.5606 | − | 11.2933i | 1.65911 | − | 0.957886i | 0.685980 | − | 0.727620i | \(-0.259374\pi\) |
0.973128 | − | 0.230266i | \(-0.0739597\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.12255 | − | 1.94432i | 0.0942024 | − | 0.163163i | ||||
\(143\) | −0.635621 | −0.0531533 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 27.7153i | − | 2.30163i | ||||||
\(146\) | −3.62817 | + | 6.28418i | −0.300270 | + | 0.520082i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.84244 | + | 8.38735i | 0.398046 | + | 0.689436i | ||||
\(149\) | −0.236156 | + | 0.136345i | −0.0193467 | + | 0.0111698i | −0.509642 | − | 0.860386i | \(-0.670222\pi\) |
0.490295 | + | 0.871556i | \(0.336889\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.42148 | + | 16.3185i | −0.766709 | + | 1.32798i | 0.172629 | + | 0.984987i | \(0.444774\pi\) |
−0.939338 | + | 0.342992i | \(0.888560\pi\) | |||||||
\(152\) | −1.15274 | −0.0934993 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.0941 | − | 8.13723i | −1.13207 | − | 0.653598i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.82310 | − | 1.62992i | 0.225308 | − | 0.130082i | −0.383098 | − | 0.923708i | \(-0.625143\pi\) |
0.608406 | + | 0.793626i | \(0.291809\pi\) | |||||||
\(158\) | 9.41528 | − | 5.43592i | 0.749040 | − | 0.432458i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.33872 | − | 1.35026i | −0.184892 | − | 0.106748i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.13675 | −0.245689 | −0.122844 | − | 0.992426i | \(-0.539202\pi\) | ||||
−0.122844 | + | 0.992426i | \(0.539202\pi\) | |||||||
\(164\) | −3.81891 | + | 6.61455i | −0.298207 | + | 0.516509i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.32052 | − | 0.762403i | 0.102492 | − | 0.0591739i | ||||
\(167\) | −3.19575 | − | 5.53520i | −0.247295 | − | 0.428327i | 0.715480 | − | 0.698634i | \(-0.246208\pi\) |
−0.962774 | + | 0.270307i | \(0.912875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.92971 | + | 5.07440i | −0.225362 | + | 0.390339i | ||||
\(170\) | − | 15.8446i | − | 1.21523i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.38438 | 0.410555 | ||||||||
\(173\) | 0.146767 | − | 0.254207i | 0.0111585 | − | 0.0193270i | −0.860392 | − | 0.509632i | \(-0.829781\pi\) |
0.871551 | + | 0.490305i | \(0.163115\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.205998 | + | 0.118933i | −0.0155277 | + | 0.00896490i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.7153 | − | 6.76386i | −0.878102 | − | 0.506972i | ||||
\(179\) | 23.0747i | 1.72468i | 0.506326 | + | 0.862342i | \(0.331003\pi\) | ||||
−0.506326 | + | 0.862342i | \(0.668997\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9176i | 0.811500i | 0.913984 | + | 0.405750i | \(0.132990\pi\) | ||||
−0.913984 | + | 0.405750i | \(0.867010\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.05456 | − | 7.02271i | −0.298906 | − | 0.517721i | ||||
\(185\) | 13.0771 | + | 22.6503i | 0.961451 | + | 1.66528i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.20864 | − | 0.697807i | −0.0883843 | − | 0.0510287i | ||||
\(188\) | −0.442283 | −0.0322568 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.11300 | −0.225840 | ||||||||
\(191\) | −11.1456 | − | 6.43490i | −0.806465 | − | 0.465613i | 0.0392616 | − | 0.999229i | \(-0.487499\pi\) |
−0.845727 | + | 0.533616i | \(0.820833\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.11771 | + | 8.86414i | 0.368381 | + | 0.638054i | 0.989313 | − | 0.145810i | \(-0.0465789\pi\) |
−0.620932 | + | 0.783865i | \(0.713246\pi\) | |||||||
\(194\) | 0.795057 | + | 1.37708i | 0.0570818 | + | 0.0988686i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.89068i | 0.277200i | 0.990348 | + | 0.138600i | \(0.0442602\pi\) | ||||
−0.990348 | + | 0.138600i | \(0.955740\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.33150i | 0.165276i | 0.996580 | + | 0.0826378i | \(0.0263345\pi\) | ||||
−0.996580 | + | 0.0826378i | \(0.973666\pi\) | |||||||
\(200\) | −1.98566 | − | 1.14642i | −0.140407 | − | 0.0810643i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.2298 | + | 6.48353i | −0.790126 | + | 0.456180i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.3131 | + | 17.8628i | −0.720296 | + | 1.24759i | ||||
\(206\) | −18.4480 | −1.28534 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 2.67219i | − | 0.185283i | ||||||
\(209\) | −0.137098 | + | 0.237461i | −0.00948328 | + | 0.0164255i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.48854 | − | 12.9705i | −0.515532 | − | 0.892928i | −0.999837 | − | 0.0180288i | \(-0.994261\pi\) |
0.484305 | − | 0.874899i | \(-0.339072\pi\) | |||||||
\(212\) | 0.189794 | − | 0.109577i | 0.0130351 | − | 0.00752581i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.32579 | − | 4.02839i | 0.158988 | − | 0.275375i | ||||
\(215\) | 14.5407 | 0.991666 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.71667 | + | 5.03257i | 0.590368 | + | 0.340849i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.556302 | + | 0.321181i | −0.0375059 | + | 0.0216540i | ||||
\(221\) | 13.5779 | − | 7.83918i | 0.913345 | − | 0.527320i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.5517 | − | 10.1335i | −1.17535 | − | 0.678590i | −0.220417 | − | 0.975406i | \(-0.570742\pi\) |
−0.954935 | + | 0.296816i | \(0.904075\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.62579 | 0.640298 | ||||||||
\(227\) | 5.15484 | − | 8.92845i | 0.342139 | − | 0.592602i | −0.642691 | − | 0.766126i | \(-0.722182\pi\) |
0.984830 | + | 0.173524i | \(0.0555153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.57314 | − | 4.37235i | 0.500447 | − | 0.288933i | −0.228451 | − | 0.973555i | \(-0.573366\pi\) |
0.728898 | + | 0.684622i | \(0.240033\pi\) | |||||||
\(230\) | −10.9495 | − | 18.9650i | −0.721986 | − | 1.25052i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.13146 | − | 8.88796i | 0.336897 | − | 0.583523i | ||||
\(233\) | 15.6014i | 1.02208i | 0.859557 | + | 0.511039i | \(0.170739\pi\) | ||||
−0.859557 | + | 0.511039i | \(0.829261\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.19440 | −0.0779139 | ||||||||
\(236\) | −0.983559 | + | 1.70357i | −0.0640242 | + | 0.110893i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.2977 | − | 11.1415i | 1.24827 | − | 0.720686i | 0.277502 | − | 0.960725i | \(-0.410494\pi\) |
0.970763 | + | 0.240039i | \(0.0771602\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.568566 | + | 0.328262i | 0.0366245 | + | 0.0211452i | 0.518200 | − | 0.855259i | \(-0.326602\pi\) |
−0.481576 | + | 0.876404i | \(0.659935\pi\) | |||||||
\(242\) | − | 10.9434i | − | 0.703470i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.5417i | 0.802902i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.54016 | − | 2.66764i | −0.0979983 | − | 0.169738i | ||||
\(248\) | −3.01320 | − | 5.21902i | −0.191339 | − | 0.331408i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.33129 | + | 3.65537i | 0.400426 | + | 0.231186i | ||||
\(251\) | −3.48276 | −0.219830 | −0.109915 | − | 0.993941i | \(-0.535058\pi\) | ||||
−0.109915 | + | 0.993941i | \(0.535058\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.92888 | −0.121268 | ||||||||
\(254\) | −4.06735 | − | 2.34829i | −0.255208 | − | 0.147345i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.02515 | + | 1.77562i | 0.0639474 | + | 0.110760i | 0.896227 | − | 0.443597i | \(-0.146298\pi\) |
−0.832279 | + | 0.554357i | \(0.812964\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 7.21631i | − | 0.447537i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.0430i | 0.867581i | ||||||||
\(263\) | −8.81710 | − | 5.09055i | −0.543686 | − | 0.313897i | 0.202886 | − | 0.979202i | \(-0.434968\pi\) |
−0.746571 | + | 0.665305i | \(0.768301\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.512543 | − | 0.295917i | 0.0314853 | − | 0.0181780i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.48336 | + | 7.76541i | −0.273865 | + | 0.474348i | ||||
\(269\) | 0.349999 | 0.0213398 | 0.0106699 | − | 0.999943i | \(-0.496604\pi\) | ||||
0.0106699 | + | 0.999943i | \(0.496604\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.9073i | − | 0.844807i | −0.906408 | − | 0.422403i | \(-0.861187\pi\) | ||
0.906408 | − | 0.422403i | \(-0.138813\pi\) | |||||||
\(272\) | 2.93362 | − | 5.08118i | 0.177877 | − | 0.308092i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.42494 | + | 9.39626i | 0.327732 | + | 0.567649i | ||||
\(275\) | −0.472321 | + | 0.272694i | −0.0284820 | + | 0.0164441i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.90100 | + | 13.6849i | −0.474725 | + | 0.822248i | −0.999581 | − | 0.0289428i | \(-0.990786\pi\) |
0.524856 | + | 0.851191i | \(0.324119\pi\) | |||||||
\(278\) | 22.5866 | 1.35466 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.2334 | + | 12.8365i | 1.32633 | + | 0.765759i | 0.984731 | − | 0.174086i | \(-0.0556970\pi\) |
0.341603 | + | 0.939844i | \(0.389030\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.73018 | − | 3.30832i | 0.340624 | − | 0.196659i | −0.319924 | − | 0.947443i | \(-0.603657\pi\) |
0.660548 | + | 0.750784i | \(0.270324\pi\) | |||||||
\(284\) | 1.94432 | − | 1.12255i | 0.115374 | − | 0.0666112i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.550464 | − | 0.317811i | −0.0325496 | − | 0.0187925i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.4245 | 1.02497 | ||||||||
\(290\) | 13.8577 | − | 24.0022i | 0.813750 | − | 1.40946i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.28418 | + | 3.62817i | −0.367754 | + | 0.212323i | ||||
\(293\) | 8.68306 | + | 15.0395i | 0.507270 | + | 0.878617i | 0.999965 | + | 0.00841456i | \(0.00267847\pi\) |
−0.492695 | + | 0.870202i | \(0.663988\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.65613 | + | 4.60055i | −0.154646 | + | 0.267854i | ||||
\(296\) | 9.68488i | 0.562922i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.272690 | −0.0157965 | ||||||||
\(299\) | 10.8346 | − | 18.7660i | 0.626578 | − | 1.08527i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −16.3185 | + | 9.42148i | −0.939023 | + | 0.542145i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.998299 | − | 0.576368i | −0.0572564 | − | 0.0330570i | ||||
\(305\) | 33.8693i | 1.93935i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.18328i | 0.0675336i | 0.999430 | + | 0.0337668i | \(0.0107504\pi\) | ||||
−0.999430 | + | 0.0337668i | \(0.989250\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.13723 | − | 14.0941i | −0.462164 | − | 0.800491i | ||||
\(311\) | −12.6616 | − | 21.9306i | −0.717975 | − | 1.24357i | −0.961801 | − | 0.273751i | \(-0.911736\pi\) |
0.243825 | − | 0.969819i | \(-0.421598\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.58789 | − | 0.916770i | −0.0897530 | − | 0.0518189i | 0.454452 | − | 0.890771i | \(-0.349835\pi\) |
−0.544205 | + | 0.838952i | \(0.683169\pi\) | |||||||
\(314\) | 3.25984 | 0.183963 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.8718 | 0.611588 | ||||||||
\(317\) | −8.23307 | − | 4.75337i | −0.462415 | − | 0.266976i | 0.250644 | − | 0.968079i | \(-0.419358\pi\) |
−0.713059 | + | 0.701104i | \(0.752691\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.22060 | − | 2.11414i | −0.0683404 | − | 0.118369i | ||||
\(320\) | −1.35026 | − | 2.33872i | −0.0754820 | − | 0.130739i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.76338i | − | 0.376324i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.12691i | − | 0.339860i | ||||||
\(326\) | −2.71650 | − | 1.56837i | −0.150453 | − | 0.0868642i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.61455 | + | 3.81891i | −0.365227 | + | 0.210864i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.26852 | + | 16.0535i | −0.509444 | + | 0.882382i | 0.490496 | + | 0.871443i | \(0.336815\pi\) |
−0.999940 | + | 0.0109393i | \(0.996518\pi\) | |||||||
\(332\) | 1.52481 | 0.0836846 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 6.39150i | − | 0.349727i | ||||||
\(335\) | −12.1074 | + | 20.9707i | −0.661500 | + | 1.14575i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.70730 | + | 8.15329i | 0.256423 | + | 0.444138i | 0.965281 | − | 0.261213i | \(-0.0841226\pi\) |
−0.708858 | + | 0.705351i | \(0.750789\pi\) | |||||||
\(338\) | −5.07440 | + | 2.92971i | −0.276011 | + | 0.159355i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.92232 | − | 13.7219i | 0.429648 | − | 0.744172i | ||||
\(341\) | −1.43347 | −0.0776270 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.66301 | + | 2.69219i | 0.251413 | + | 0.145153i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.254207 | − | 0.146767i | 0.0136663 | − | 0.00789022i | ||||
\(347\) | −9.73647 | + | 5.62136i | −0.522681 | + | 0.301770i | −0.738031 | − | 0.674767i | \(-0.764244\pi\) |
0.215350 | + | 0.976537i | \(0.430911\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.889499 | − | 0.513552i | −0.0476138 | − | 0.0274898i | 0.476004 | − | 0.879443i | \(-0.342085\pi\) |
−0.523618 | + | 0.851953i | \(0.675418\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.237866 | −0.0126783 | ||||||||
\(353\) | −12.3144 | + | 21.3291i | −0.655429 | + | 1.13524i | 0.326357 | + | 0.945246i | \(0.394179\pi\) |
−0.981786 | + | 0.189990i | \(0.939155\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.25068 | − | 3.03148i | 0.278677 | − | 0.160894i | ||||
\(356\) | −6.76386 | − | 11.7153i | −0.358484 | − | 0.620912i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.5374 | + | 19.9833i | −0.609768 | + | 1.05615i | ||||
\(359\) | 10.5234i | 0.555402i | 0.960668 | + | 0.277701i | \(0.0895725\pi\) | ||||
−0.960668 | + | 0.277701i | \(0.910428\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.6712 | 0.930063 | ||||||||
\(362\) | −5.45881 | + | 9.45493i | −0.286908 | + | 0.496940i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.9706 | + | 9.79797i | −0.888281 | + | 0.512849i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.00271 | − | 3.46567i | −0.313339 | − | 0.180906i | 0.335081 | − | 0.942189i | \(-0.391236\pi\) |
−0.648420 | + | 0.761283i | \(0.724570\pi\) | |||||||
\(368\) | − | 8.10913i | − | 0.422717i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 26.1543i | 1.35970i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.950237 | − | 1.64586i | −0.0492014 | − | 0.0852193i | 0.840376 | − | 0.542004i | \(-0.182334\pi\) |
−0.889577 | + | 0.456785i | \(0.849001\pi\) | |||||||
\(374\) | −0.697807 | − | 1.20864i | −0.0360827 | − | 0.0624971i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.383029 | − | 0.221142i | −0.0197532 | − | 0.0114045i | ||||
\(377\) | 27.4245 | 1.41243 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.4655 | 1.92447 | 0.962236 | − | 0.272217i | \(-0.0877569\pi\) | ||||
0.962236 | + | 0.272217i | \(0.0877569\pi\) | |||||||
\(380\) | −2.69593 | − | 1.55650i | −0.138298 | − | 0.0798467i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.43490 | − | 11.1456i | −0.329238 | − | 0.570257i | ||||
\(383\) | 0.740653 | + | 1.28285i | 0.0378456 | + | 0.0655505i | 0.884328 | − | 0.466867i | \(-0.154617\pi\) |
−0.846482 | + | 0.532417i | \(0.821284\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.2354i | 0.520969i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.59011i | 0.0807258i | ||||||||
\(389\) | −11.0008 | − | 6.35131i | −0.557763 | − | 0.322024i | 0.194484 | − | 0.980906i | \(-0.437697\pi\) |
−0.752247 | + | 0.658881i | \(0.771030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.2039 | − | 23.7891i | 2.08377 | − | 1.20307i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.94534 | + | 3.36943i | −0.0980049 | + | 0.169749i | ||||
\(395\) | 29.3597 | 1.47725 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.3486i | 0.971080i | 0.874215 | + | 0.485540i | \(0.161377\pi\) | ||||
−0.874215 | + | 0.485540i | \(0.838623\pi\) | |||||||
\(398\) | −1.16575 | + | 2.01914i | −0.0584338 | + | 0.101210i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.14642 | − | 1.98566i | −0.0573211 | − | 0.0992831i | ||||
\(401\) | 9.43887 | − | 5.44954i | 0.471355 | − | 0.272137i | −0.245452 | − | 0.969409i | \(-0.578936\pi\) |
0.716807 | + | 0.697272i | \(0.245603\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.05184 | − | 13.9462i | 0.401091 | − | 0.694709i | ||||
\(404\) | −12.9671 | −0.645135 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.99506 | + | 1.15185i | 0.0988916 | + | 0.0570951i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.7691 | − | 10.2590i | 0.878627 | − | 0.507275i | 0.00842142 | − | 0.999965i | \(-0.497319\pi\) |
0.870205 | + | 0.492689i | \(0.163986\pi\) | |||||||
\(410\) | −17.8628 | + | 10.3131i | −0.882179 | + | 0.509326i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.9765 | − | 9.22402i | −0.787104 | − | 0.454435i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.11778 | 0.202134 | ||||||||
\(416\) | 1.33609 | − | 2.31418i | 0.0655074 | − | 0.113462i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.237461 | + | 0.137098i | −0.0116146 | + | 0.00670569i | ||||
\(419\) | −2.73087 | − | 4.73000i | −0.133412 | − | 0.231076i | 0.791578 | − | 0.611068i | \(-0.209260\pi\) |
−0.924990 | + | 0.379993i | \(0.875927\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.2759 | − | 24.7265i | 0.695763 | − | 1.20510i | −0.274160 | − | 0.961684i | \(-0.588400\pi\) |
0.969923 | − | 0.243412i | \(-0.0782669\pi\) | |||||||
\(422\) | − | 14.9771i | − | 0.729073i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.219155 | 0.0106431 | ||||||||
\(425\) | 6.72633 | − | 11.6504i | 0.326275 | − | 0.565125i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.02839 | − | 2.32579i | 0.194720 | − | 0.112421i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.5926 | + | 7.27034i | 0.607269 | + | 0.350607i | ||||
\(431\) | − | 9.55639i | − | 0.460315i | −0.973153 | − | 0.230157i | \(-0.926076\pi\) | ||
0.973153 | − | 0.230157i | \(-0.0739241\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 19.7122i | − | 0.947309i | −0.880711 | − | 0.473654i | \(-0.842935\pi\) | ||
0.880711 | − | 0.473654i | \(-0.157065\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.03257 | + | 8.71667i | 0.241017 | + | 0.417453i | ||||
\(437\) | −4.67384 | − | 8.09533i | −0.223580 | − | 0.387252i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.1001 | + | 12.1822i | 1.00706 | + | 0.581424i | 0.910328 | − | 0.413887i | \(-0.135829\pi\) |
0.0967271 | + | 0.995311i | \(0.469163\pi\) | |||||||
\(440\) | −0.642362 | −0.0306234 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.6784 | 0.745743 | ||||||||
\(443\) | 32.4731 | + | 18.7483i | 1.54284 | + | 0.890760i | 0.998658 | + | 0.0517947i | \(0.0164941\pi\) |
0.544184 | + | 0.838966i | \(0.316839\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.2660 | − | 31.6376i | −0.865890 | − | 1.49977i | ||||
\(446\) | −10.1335 | − | 17.5517i | −0.479835 | − | 0.831099i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.6997i | 1.07127i | 0.844451 | + | 0.535633i | \(0.179927\pi\) | ||||
−0.844451 | + | 0.535633i | \(0.820073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.81678i | 0.0855486i | ||||||||
\(452\) | 8.33618 | + | 4.81290i | 0.392101 | + | 0.226380i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.92845 | − | 5.15484i | 0.419033 | − | 0.241929i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.9116 | + | 34.4878i | −0.931424 | + | 1.61327i | −0.150533 | + | 0.988605i | \(0.548099\pi\) |
−0.780890 | + | 0.624668i | \(0.785234\pi\) | |||||||
\(458\) | 8.74471 | 0.408613 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 21.8989i | − | 1.02104i | ||||||
\(461\) | 4.33763 | − | 7.51299i | 0.202024 | − | 0.349915i | −0.747157 | − | 0.664648i | \(-0.768582\pi\) |
0.949180 | + | 0.314733i | \(0.101915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.06605 | + | 12.2388i | 0.328387 | + | 0.568783i | 0.982192 | − | 0.187880i | \(-0.0601616\pi\) |
−0.653805 | + | 0.756663i | \(0.726828\pi\) | |||||||
\(464\) | 8.88796 | − | 5.13146i | 0.412613 | − | 0.238222i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.80068 | + | 13.5112i | −0.361359 | + | 0.625893i | ||||
\(467\) | −24.6082 | −1.13873 | −0.569366 | − | 0.822084i | \(-0.692811\pi\) | ||||
−0.569366 | + | 0.822084i | \(0.692811\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.03438 | − | 0.597199i | −0.0477124 | − | 0.0275467i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.70357 | + | 0.983559i | −0.0784133 | + | 0.0452720i | ||||
\(473\) | 1.10917 | − | 0.640380i | 0.0509997 | − | 0.0294447i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.28894 | − | 1.32152i | −0.105024 | − | 0.0606356i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.2831 | 1.01920 | ||||||||
\(479\) | 14.7674 | − | 25.5779i | 0.674741 | − | 1.16869i | −0.301804 | − | 0.953370i | \(-0.597589\pi\) |
0.976545 | − | 0.215315i | \(-0.0690779\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.4126 | + | 12.9399i | −1.02193 | + | 0.590009i | ||||
\(482\) | 0.328262 | + | 0.568566i | 0.0149519 | + | 0.0258975i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.47171 | − | 9.47728i | 0.248714 | − | 0.430785i | ||||
\(485\) | 4.29415i | 0.194987i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.08694 | 0.0492538 | 0.0246269 | − | 0.999697i | \(-0.492160\pi\) | ||||
0.0246269 | + | 0.999697i | \(0.492160\pi\) | |||||||
\(488\) | −6.27087 | + | 10.8615i | −0.283869 | + | 0.491675i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.43373 | − | 5.44657i | 0.425738 | − | 0.245800i | −0.271791 | − | 0.962356i | \(-0.587616\pi\) |
0.697529 | + | 0.716556i | \(0.254283\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 52.1478 | + | 30.1075i | 2.34862 | + | 1.35597i | ||||
\(494\) | − | 3.08033i | − | 0.138590i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 6.02640i | − | 0.270594i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0342 | − | 34.7002i | −0.896853 | − | 1.55340i | −0.831494 | − | 0.555534i | \(-0.812514\pi\) |
−0.0653593 | − | 0.997862i | \(-0.520819\pi\) | |||||||
\(500\) | 3.65537 | + | 6.33129i | 0.163473 | + | 0.283144i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.01616 | − | 1.74138i | −0.134618 | − | 0.0777216i | ||||
\(503\) | 27.5061 | 1.22644 | 0.613219 | − | 0.789913i | \(-0.289874\pi\) | ||||
0.613219 | + | 0.789913i | \(0.289874\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.0179 | −1.55828 | ||||||||
\(506\) | −1.67046 | − | 0.964441i | −0.0742610 | − | 0.0428746i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.34829 | − | 4.06735i | −0.104188 | − | 0.180459i | ||||
\(509\) | −4.17535 | − | 7.23192i | −0.185069 | − | 0.320549i | 0.758531 | − | 0.651637i | \(-0.225918\pi\) |
−0.943600 | + | 0.331088i | \(0.892584\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.05031i | 0.0904353i | ||||||||
\(515\) | −43.1449 | − | 24.9097i | −1.90119 | − | 1.09765i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0911093 | + | 0.0526020i | −0.00400698 | + | 0.00231343i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.60816 | − | 6.24951i | 0.158228 | − | 0.274059i | ||||
\(521\) | 8.33273 | 0.365064 | 0.182532 | − | 0.983200i | \(-0.441571\pi\) | ||||
0.182532 | + | 0.983200i | \(0.441571\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.4297i | 0.674694i | 0.941380 | + | 0.337347i | \(0.109530\pi\) | ||||
−0.941380 | + | 0.337347i | \(0.890470\pi\) | |||||||
\(524\) | −7.02151 | + | 12.1616i | −0.306736 | + | 0.531283i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.09055 | − | 8.81710i | −0.221959 | − | 0.384444i | ||||
\(527\) | 30.6212 | − | 17.6792i | 1.33388 | − | 0.770117i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.3790 | − | 37.0295i | 0.929521 | − | 1.60998i | ||||
\(530\) | 0.591834 | 0.0257076 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.6753 | − | 10.2048i | −0.765603 | − | 0.442021i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.8788 | − | 6.28086i | 0.470330 | − | 0.271545i | ||||
\(536\) | −7.76541 | + | 4.48336i | −0.335415 | + | 0.193652i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.303108 | + | 0.174999i | 0.0130679 | + | 0.00754476i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.27007 | −0.269571 | −0.134786 | − | 0.990875i | \(-0.543035\pi\) | ||||
−0.134786 | + | 0.990875i | \(0.543035\pi\) | |||||||
\(542\) | 6.95364 | − | 12.0441i | 0.298684 | − | 0.517336i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.08118 | − | 2.93362i | 0.217854 | − | 0.125778i | ||||
\(545\) | 13.5906 | + | 23.5396i | 0.582157 | + | 1.00833i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.8501 | + | 25.7211i | −0.634945 | + | 1.09976i | 0.351582 | + | 0.936157i | \(0.385644\pi\) |
−0.986527 | + | 0.163600i | \(0.947690\pi\) | |||||||
\(548\) | 10.8499i | 0.463483i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.545389 | −0.0232555 | ||||||||
\(551\) | 5.91523 | − | 10.2455i | 0.251997 | − | 0.436472i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13.6849 | + | 7.90100i | −0.581417 | + | 0.335682i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.5606 | + | 11.2933i | 0.829554 | + | 0.478943i | ||||
\(557\) | − | 17.9103i | − | 0.758883i | −0.925216 | − | 0.379442i | \(-0.876116\pi\) | ||
0.925216 | − | 0.379442i | \(-0.123884\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.3881i | 0.608551i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.8365 | + | 22.2334i | 0.541473 | + | 0.937859i | ||||
\(563\) | −21.7205 | − | 37.6210i | −0.915409 | − | 1.58553i | −0.806302 | − | 0.591504i | \(-0.798534\pi\) |
−0.109107 | − | 0.994030i | \(-0.534799\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.5121 | + | 12.9974i | 0.947090 | + | 0.546803i | ||||
\(566\) | 6.61664 | 0.278118 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.24510 | 0.0942024 | ||||||||
\(569\) | 4.14890 | + | 2.39537i | 0.173931 | + | 0.100419i | 0.584438 | − | 0.811438i | \(-0.301315\pi\) |
−0.410507 | + | 0.911857i | \(0.634648\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.69405 | + | 11.5944i | 0.280137 | + | 0.485212i | 0.971418 | − | 0.237374i | \(-0.0762867\pi\) |
−0.691281 | + | 0.722586i | \(0.742953\pi\) | |||||||
\(572\) | −0.317811 | − | 0.550464i | −0.0132883 | − | 0.0230161i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 18.5930i | − | 0.775380i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.7792i | 0.448746i | 0.974503 | + | 0.224373i | \(0.0720334\pi\) | ||||
−0.974503 | + | 0.224373i | \(0.927967\pi\) | |||||||
\(578\) | 15.0900 | + | 8.71224i | 0.627663 | + | 0.362381i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 24.0022 | − | 13.8577i | 0.996636 | − | 0.575408i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.0260647 | − | 0.0451454i | 0.00107949 | − | 0.00186973i | ||||
\(584\) | −7.25634 | −0.300270 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.3661i | 0.717387i | ||||||||
\(587\) | 10.0173 | − | 17.3504i | 0.413458 | − | 0.716130i | −0.581808 | − | 0.813326i | \(-0.697654\pi\) |
0.995265 | + | 0.0971969i | \(0.0309877\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.47343 | − | 6.01615i | −0.143120 | − | 0.247891i | ||||
\(590\) | −4.60055 | + | 2.65613i | −0.189402 | + | 0.109351i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.84244 | + | 8.38735i | −0.199023 | + | 0.344718i | ||||
\(593\) | 22.7549 | 0.934433 | 0.467217 | − | 0.884143i | \(-0.345257\pi\) | ||||
0.467217 | + | 0.884143i | \(0.345257\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.236156 | − | 0.136345i | −0.00967333 | − | 0.00558490i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 18.7660 | − | 10.8346i | 0.767399 | − | 0.443058i | ||||
\(599\) | 22.0525 | − | 12.7320i | 0.901040 | − | 0.520216i | 0.0235025 | − | 0.999724i | \(-0.492518\pi\) |
0.877537 | + | 0.479508i | \(0.159185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.94631 | + | 5.16515i | 0.364928 | + | 0.210691i | 0.671240 | − | 0.741240i | \(-0.265762\pi\) |
−0.306313 | + | 0.951931i | \(0.599095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −18.8430 | −0.766709 | ||||||||
\(605\) | 14.7765 | − | 25.5936i | 0.600750 | − | 1.04053i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.05553 | + | 3.49616i | −0.245786 | + | 0.141905i | −0.617833 | − | 0.786309i | \(-0.711989\pi\) |
0.372047 | + | 0.928214i | \(0.378656\pi\) | |||||||
\(608\) | −0.576368 | − | 0.998299i | −0.0233748 | − | 0.0404864i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.9346 | + | 29.3317i | −0.685664 | + | 1.18760i | ||||
\(611\) | − | 1.18186i | − | 0.0478131i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.3097 | 0.416405 | 0.208203 | − | 0.978086i | \(-0.433239\pi\) | ||||
0.208203 | + | 0.978086i | \(0.433239\pi\) | |||||||
\(614\) | −0.591642 | + | 1.02475i | −0.0238767 | + | 0.0413557i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.11226 | + | 1.79686i | −0.125295 | + | 0.0723389i | −0.561337 | − | 0.827587i | \(-0.689713\pi\) |
0.436043 | + | 0.899926i | \(0.356380\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.4694 | − | 15.8594i | −1.10409 | − | 0.637445i | −0.166796 | − | 0.985991i | \(-0.553342\pi\) |
−0.937291 | + | 0.348547i | \(0.886675\pi\) | |||||||
\(620\) | − | 16.2745i | − | 0.653598i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 25.3233i | − | 1.01537i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6035 | + | 27.0261i | 0.624142 | + | 1.08105i | ||||
\(626\) | −0.916770 | − | 1.58789i | −0.0366415 | − | 0.0634649i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.82310 | + | 1.62992i | 0.112654 | + | 0.0650408i | ||||
\(629\) | −56.8235 | −2.26570 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.92443 | 0.196038 | 0.0980192 | − | 0.995185i | \(-0.468749\pi\) | ||||
0.0980192 | + | 0.995185i | \(0.468749\pi\) | |||||||
\(632\) | 9.41528 | + | 5.43592i | 0.374520 | + | 0.216229i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.75337 | − | 8.23307i | −0.188780 | − | 0.326977i | ||||
\(635\) | −6.34161 | − | 10.9840i | −0.251659 | − | 0.435886i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 2.44120i | − | 0.0966479i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 2.70053i | − | 0.106748i | ||||||
\(641\) | −7.27479 | − | 4.20010i | −0.287337 | − | 0.165894i | 0.349403 | − | 0.936972i | \(-0.386384\pi\) |
−0.636740 | + | 0.771078i | \(0.719718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.34290 | + | 3.66208i | −0.250140 | + | 0.144418i | −0.619828 | − | 0.784738i | \(-0.712798\pi\) |
0.369689 | + | 0.929156i | \(0.379464\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.38169 | − | 5.85726i | 0.133051 | − | 0.230451i | ||||
\(647\) | −3.89938 | −0.153301 | −0.0766503 | − | 0.997058i | \(-0.524422\pi\) | ||||
−0.0766503 | + | 0.997058i | \(0.524422\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.467910i | 0.0183671i | ||||||||
\(650\) | 3.06345 | − | 5.30606i | 0.120159 | − | 0.208121i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.56837 | − | 2.71650i | −0.0614222 | − | 0.106386i | ||||
\(653\) | −20.0302 | + | 11.5644i | −0.783843 | + | 0.452552i | −0.837790 | − | 0.545992i | \(-0.816153\pi\) |
0.0539477 | + | 0.998544i | \(0.482820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.9618 | + | 32.8428i | −0.740898 | + | 1.28327i | ||||
\(656\) | −7.63782 | −0.298207 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.2312 | + | 16.2993i | 1.09973 | + | 0.634930i | 0.936150 | − | 0.351600i | \(-0.114362\pi\) |
0.163580 | + | 0.986530i | \(0.447696\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.4612 | − | 25.0924i | 1.69045 | − | 0.975979i | 0.736292 | − | 0.676664i | \(-0.236575\pi\) |
0.954154 | − | 0.299315i | \(-0.0967583\pi\) | |||||||
\(662\) | −16.0535 | + | 9.26852i | −0.623939 | + | 0.360231i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.32052 | + | 0.762403i | 0.0512461 | + | 0.0295870i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 83.2234 | 3.22242 | ||||||||
\(668\) | 3.19575 | − | 5.53520i | 0.123647 | − | 0.214163i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −20.9707 | + | 12.1074i | −0.810169 | + | 0.467751i | ||||
\(671\) | 1.49162 | + | 2.58357i | 0.0575835 | + | 0.0997375i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.02645 | + | 15.6343i | −0.347944 | + | 0.602657i | −0.985884 | − | 0.167429i | \(-0.946453\pi\) |
0.637940 | + | 0.770086i | \(0.279787\pi\) | |||||||
\(674\) | 9.41461i | 0.362637i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.85942 | −0.225362 | ||||||||
\(677\) | −10.1509 | + | 17.5819i | −0.390131 | + | 0.675726i | −0.992466 | − | 0.122517i | \(-0.960903\pi\) |
0.602336 | + | 0.798243i | \(0.294237\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 13.7219 | − | 7.92232i | 0.526209 | − | 0.303807i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.24142 | − | 0.716737i | −0.0475366 | − | 0.0274453i | ||||
\(683\) | − | 20.0741i | − | 0.768113i | −0.923310 | − | 0.384056i | \(-0.874527\pi\) | ||
0.923310 | − | 0.384056i | \(-0.125473\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.3004i | 1.11951i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.69219 | + | 4.66301i | 0.102639 | + | 0.177776i | ||||
\(689\) | 0.292811 | + | 0.507164i | 0.0111552 | + | 0.0193214i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.3874 | − | 12.3480i | −0.813616 | − | 0.469742i | 0.0345939 | − | 0.999401i | \(-0.488986\pi\) |
−0.848210 | + | 0.529660i | \(0.822320\pi\) | |||||||
\(692\) | 0.293533 | 0.0111585 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.2427 | −0.426767 | ||||||||
\(695\) | 52.8239 | + | 30.4979i | 2.00372 | + | 1.15685i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.4065 | − | 38.8091i | −0.848705 | − | 1.47000i | ||||
\(698\) | −0.513552 | − | 0.889499i | −0.0194382 | − | 0.0336680i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.1616i | − | 0.799263i | −0.916676 | − | 0.399632i | \(-0.869138\pi\) | ||
0.916676 | − | 0.399632i | \(-0.130862\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.1641i | 0.421063i | ||||||||
\(704\) | −0.205998 | − | 0.118933i | −0.00776383 | − | 0.00448245i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.3291 | + | 12.3144i | −0.802733 | + | 0.463458i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.4861 | + | 18.1624i | −0.393812 | + | 0.682103i | −0.992949 | − | 0.118544i | \(-0.962177\pi\) |
0.599137 | + | 0.800647i | \(0.295511\pi\) | |||||||
\(710\) | 6.06296 | 0.227539 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 13.5277i | − | 0.506972i | ||||||
\(713\) | 24.4344 | − | 42.3217i | 0.915077 | − | 1.58496i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.858256 | − | 1.48654i | −0.0320970 | − | 0.0555936i | ||||
\(716\) | −19.9833 | + | 11.5374i | −0.746810 | + | 0.431171i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.26168 | + | 9.11350i | −0.196364 | + | 0.340113i | ||||
\(719\) | −22.7726 | −0.849273 | −0.424637 | − | 0.905364i | \(-0.639598\pi\) | ||||
−0.424637 | + | 0.905364i | \(0.639598\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.3037 | + | 8.83560i | 0.569545 | + | 0.328827i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.45493 | + | 5.45881i | −0.351390 | + | 0.202875i | ||||
\(725\) | 20.3787 | − | 11.7657i | 0.756846 | − | 0.436965i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.4847 | − | 8.94010i | −0.574296 | − | 0.331570i | 0.184567 | − | 0.982820i | \(-0.440912\pi\) |
−0.758863 | + | 0.651250i | \(0.774245\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.5959 | −0.725279 | ||||||||
\(731\) | −15.7957 | + | 27.3590i | −0.584226 | + | 1.01191i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.8378 | − | 10.8760i | 0.695790 | − | 0.401715i | −0.109987 | − | 0.993933i | \(-0.535081\pi\) |
0.805778 | + | 0.592218i | \(0.201748\pi\) | |||||||
\(734\) | −3.46567 | − | 6.00271i | −0.127920 | − | 0.221564i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.05456 | − | 7.02271i | 0.149453 | − | 0.258861i | ||||
\(737\) | 2.13288i | 0.0785655i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.5207 | −0.975578 | −0.487789 | − | 0.872961i | \(-0.662197\pi\) | ||||
−0.487789 | + | 0.872961i | \(0.662197\pi\) | |||||||
\(740\) | −13.0771 | + | 22.6503i | −0.480725 | + | 0.832641i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.53406 | − | 0.885688i | 0.0562791 | − | 0.0324927i | −0.471596 | − | 0.881814i | \(-0.656322\pi\) |
0.527876 | + | 0.849322i | \(0.322989\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.637746 | − | 0.368203i | −0.0233652 | − | 0.0134899i | ||||
\(746\) | − | 1.90047i | − | 0.0695813i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.39561i | − | 0.0510287i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.9293 | + | 34.5186i | 0.727231 | + | 1.25960i | 0.958049 | + | 0.286605i | \(0.0925266\pi\) |
−0.230818 | + | 0.972997i | \(0.574140\pi\) | |||||||
\(752\) | −0.221142 | − | 0.383029i | −0.00806421 | − | 0.0139676i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 23.7503 | + | 13.7122i | 0.864934 | + | 0.499370i | ||||
\(755\) | −50.8859 | −1.85193 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.2462 | −1.35374 | −0.676869 | − | 0.736104i | \(-0.736663\pi\) | ||||
−0.676869 | + | 0.736104i | \(0.736663\pi\) | |||||||
\(758\) | 32.4460 | + | 18.7327i | 1.17849 | + | 0.680403i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.55650 | − | 2.69593i | −0.0564601 | − | 0.0977918i | ||||
\(761\) | 21.6642 | + | 37.5235i | 0.785327 | + | 1.36023i | 0.928804 | + | 0.370573i | \(0.120839\pi\) |
−0.143477 | + | 0.989654i | \(0.545828\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 12.8698i | − | 0.465613i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.48131i | 0.0535218i | ||||||||
\(767\) | −4.55227 | − | 2.62825i | −0.164373 | − | 0.0949007i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.2010 | − | 10.5084i | 0.656345 | − | 0.378941i | −0.134538 | − | 0.990908i | \(-0.542955\pi\) |
0.790883 | + | 0.611967i | \(0.209622\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.11771 | + | 8.86414i | −0.184190 | + | 0.319027i | ||||
\(773\) | −3.08047 | −0.110797 | −0.0553984 | − | 0.998464i | \(-0.517643\pi\) | ||||
−0.0553984 | + | 0.998464i | \(0.517643\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 13.8176i | − | 0.496343i | ||||||
\(776\) | −0.795057 | + | 1.37708i | −0.0285409 | + | 0.0494343i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.35131 | − | 11.0008i | −0.227706 | − | 0.394398i | ||||
\(779\) | −7.62483 | + | 4.40220i | −0.273188 | + | 0.157725i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.267016 | − | 0.462486i | 0.00955459 | − | 0.0165490i | ||||
\(782\) | 47.5782 | 1.70139 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.62386 | + | 4.40164i | 0.272107 | + | 0.157101i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.0182 | + | 17.9083i | −1.10568 | + | 0.638363i | −0.937707 | − | 0.347428i | \(-0.887055\pi\) |
−0.167971 | + | 0.985792i | \(0.553722\pi\) | |||||||
\(788\) | −3.36943 | + | 1.94534i | −0.120031 | + | 0.0692999i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 25.4262 | + | 14.6798i | 0.904624 | + | 0.522285i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.5139 | −1.19011 | ||||||||
\(794\) | −9.67431 | + | 16.7564i | −0.343328 | + | 0.594662i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.01914 | + | 1.16575i | −0.0715665 | + | 0.0413189i | ||||
\(797\) | −11.0878 | − | 19.2046i | −0.392749 | − | 0.680261i | 0.600062 | − | 0.799953i | \(-0.295142\pi\) |
−0.992811 | + | 0.119693i | \(0.961809\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.29749 | − | 2.24732i | 0.0459019 | − | 0.0795045i | ||||
\(800\) | − | 2.29284i | − | 0.0810643i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.8991 | 0.384860 | ||||||||
\(803\) | −0.863017 | + | 1.49479i | −0.0304552 | + | 0.0527500i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.9462 | − | 8.05184i | 0.491234 | − | 0.283614i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.2298 | − | 6.48353i | −0.395063 | − | 0.228090i | ||||
\(809\) | − | 3.15819i | − | 0.111036i | −0.998458 | − | 0.0555180i | \(-0.982319\pi\) | ||
0.998458 | − | 0.0555180i | \(-0.0176810\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.8867i | 1.11969i | 0.828596 | + | 0.559847i | \(0.189140\pi\) | ||||
−0.828596 | + | 0.559847i | \(0.810860\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.15185 | + | 1.99506i | 0.0403723 | + | 0.0699269i | ||||
\(815\) | −4.23543 | − | 7.33599i | −0.148361 | − | 0.256968i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.37523 | + | 3.10339i | 0.188055 | + | 0.108574i | ||||
\(818\) | 20.5180 | 0.717396 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.6261 | −0.720296 | ||||||||
\(821\) | −23.1617 | − | 13.3724i | −0.808348 | − | 0.466700i | 0.0380341 | − | 0.999276i | \(-0.487890\pi\) |
−0.846382 | + | 0.532577i | \(0.821224\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0895 | + | 26.1358i | 0.525988 | + | 0.911038i | 0.999542 | + | 0.0302730i | \(0.00963766\pi\) |
−0.473554 | + | 0.880765i | \(0.657029\pi\) | |||||||
\(824\) | −9.22402 | − | 15.9765i | −0.321334 | − | 0.556567i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.9486i | 0.832773i | 0.909188 | + | 0.416387i | \(0.136704\pi\) | ||||
−0.909188 | + | 0.416387i | \(0.863296\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.0860i | 0.871273i | 0.900123 | + | 0.435636i | \(0.143477\pi\) | ||||
−0.900123 | + | 0.435636i | \(0.856523\pi\) | |||||||
\(830\) | 3.56610 | + | 2.05889i | 0.123781 | + | 0.0714651i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.31418 | − | 1.33609i | 0.0802298 | − | 0.0463207i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.63021 | − | 14.9480i | 0.298661 | − | 0.517296i | ||||
\(836\) | −0.274196 | −0.00948328 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 5.46173i | − | 0.188672i | ||||||
\(839\) | 24.0987 | − | 41.7402i | 0.831980 | − | 1.44103i | −0.0644863 | − | 0.997919i | \(-0.520541\pi\) |
0.896466 | − | 0.443113i | \(-0.146126\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.1638 | + | 66.1017i | 1.31599 | + | 2.27937i | ||||
\(842\) | 24.7265 | − | 14.2759i | 0.852132 | − | 0.491979i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.48854 | − | 12.9705i | 0.257766 | − | 0.446464i | ||||
\(845\) | −15.8235 | −0.544345 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.189794 | + | 0.109577i | 0.00651754 | + | 0.00376290i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.6504 | − | 6.72633i | 0.399604 | − | 0.230711i | ||||
\(851\) | −68.0141 | + | 39.2680i | −2.33149 | + | 1.34609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.64492 | − | 1.52704i | −0.0905602 | − | 0.0522850i | 0.454036 | − | 0.890983i | \(-0.349984\pi\) |
−0.544596 | + | 0.838698i | \(0.683317\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.65158 | 0.158988 | ||||||||
\(857\) | −13.9460 | + | 24.1552i | −0.476386 | + | 0.825125i | −0.999634 | − | 0.0270556i | \(-0.991387\pi\) |
0.523248 | + | 0.852181i | \(0.324720\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.3959 | − | 15.8170i | 0.934734 | − | 0.539669i | 0.0464286 | − | 0.998922i | \(-0.485216\pi\) |
0.888306 | + | 0.459252i | \(0.151883\pi\) | |||||||
\(860\) | 7.27034 | + | 12.5926i | 0.247916 | + | 0.429404i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.77819 | − | 8.27607i | 0.162746 | − | 0.281884i | ||||
\(863\) | − | 31.1120i | − | 1.05906i | −0.848290 | − | 0.529532i | \(-0.822367\pi\) | ||
0.848290 | − | 0.529532i | \(-0.177633\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.792694 | 0.0269524 | ||||||||
\(866\) | 9.85611 | − | 17.0713i | 0.334924 | − | 0.580106i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.23957 | − | 1.29302i | 0.0759722 | − | 0.0438626i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.7506 | − | 11.9804i | −0.703108 | − | 0.405940i | ||||
\(872\) | 10.0651i | 0.340849i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 9.34769i | − | 0.316190i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.94066 | − | 10.2895i | −0.200602 | − | 0.347452i | 0.748121 | − | 0.663563i | \(-0.230956\pi\) |
−0.948722 | + | 0.316110i | \(0.897623\pi\) | |||||||
\(878\) | 12.1822 | + | 21.1001i | 0.411129 | + | 0.712096i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.556302 | − | 0.321181i | −0.0187529 | − | 0.0108270i | ||||
\(881\) | −37.0866 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.53904 | −0.253709 | −0.126854 | − | 0.991921i | \(-0.540488\pi\) | ||||
−0.126854 | + | 0.991921i | \(0.540488\pi\) | |||||||
\(884\) | 13.5779 | + | 7.83918i | 0.456673 | + | 0.263660i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.7483 | + | 32.4731i | 0.629863 | + | 1.09095i | ||||
\(887\) | 26.4500 | + | 45.8127i | 0.888103 | + | 1.53824i | 0.842115 | + | 0.539298i | \(0.181310\pi\) |
0.0459884 | + | 0.998942i | \(0.485356\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 36.5319i | − | 1.22455i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 20.2670i | − | 0.678590i | ||||||
\(893\) | −0.441531 | − | 0.254918i | −0.0147753 | − | 0.00853051i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −53.9654 | + | 31.1569i | −1.80386 | + | 1.04146i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.3499 | + | 19.6585i | −0.378749 | + | 0.656013i | ||||
\(899\) | 61.8486 | 2.06276 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.28583i | 0.0428373i | ||||||||
\(902\) | −0.908388 | + | 1.57337i | −0.0302460 | + | 0.0523876i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.81290 | + | 8.33618i | 0.160075 | + | 0.277257i | ||||
\(905\) | −25.5333 | + | 14.7417i | −0.848755 | + | 0.490029i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.1097 | − | 45.2233i | 0.866958 | − | 1.50162i | 0.00186910 | − | 0.999998i | \(-0.499405\pi\) |
0.865089 | − | 0.501618i | \(-0.167262\pi\) | |||||||
\(908\) | 10.3097 | 0.342139 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.52440 | + | 4.34421i | 0.249295 | + | 0.143930i | 0.619441 | − | 0.785043i | \(-0.287359\pi\) |
−0.370147 | + | 0.928973i | \(0.620693\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.314106 | − | 0.181349i | 0.0103954 | − | 0.00600179i | ||||
\(914\) | −34.4878 | + | 19.9116i | −1.14076 | + | 0.658616i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.57314 | + | 4.37235i | 0.250224 | + | 0.144467i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.6927 | −0.913498 | −0.456749 | − | 0.889596i | \(-0.650986\pi\) | ||||
−0.456749 | + | 0.889596i | \(0.650986\pi\) | |||||||
\(920\) | 10.9495 | − | 18.9650i | 0.360993 | − | 0.625258i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.51299 | − | 4.33763i | 0.247427 | − | 0.142852i | ||||
\(923\) | 2.99967 | + | 5.19557i | 0.0987352 | + | 0.171014i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.1030 | + | 19.2309i | −0.365063 | + | 0.632308i | ||||
\(926\) | 14.1321i | 0.464409i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.2629 | 0.336897 | ||||||||
\(929\) | −16.9599 | + | 29.3753i | −0.556435 | + | 0.963774i | 0.441355 | + | 0.897332i | \(0.354498\pi\) |
−0.997790 | + | 0.0664412i | \(0.978836\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −13.5112 | + | 7.80068i | −0.442573 | + | 0.255520i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.3113 | − | 12.3041i | −0.697329 | − | 0.402603i | ||||
\(935\) | − | 3.76889i | − | 0.123256i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.54431i | 0.181125i | 0.995891 | + | 0.0905623i | \(0.0288664\pi\) | ||||
−0.995891 | + | 0.0905623i | \(0.971134\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.597199 | − | 1.03438i | −0.0194785 | − | 0.0337377i | ||||
\(941\) | 3.55887 | + | 6.16415i | 0.116016 | + | 0.200946i | 0.918185 | − | 0.396151i | \(-0.129654\pi\) |
−0.802169 | + | 0.597096i | \(0.796321\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −53.6382 | − | 30.9680i | −1.74670 | − | 1.00846i | ||||
\(944\) | −1.96712 | −0.0640242 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.28076 | 0.0416411 | ||||||||
\(947\) | 1.06457 | + | 0.614627i | 0.0345937 | + | 0.0199727i | 0.517197 | − | 0.855866i | \(-0.326975\pi\) |
−0.482603 | + | 0.875839i | \(0.660309\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.69515 | − | 16.7925i | −0.314718 | − | 0.545108i | ||||
\(950\) | −1.32152 | − | 2.28894i | −0.0428759 | − | 0.0742632i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0059i | 0.777628i | 0.921316 | + | 0.388814i | \(0.127115\pi\) | ||||
−0.921316 | + | 0.388814i | \(0.872885\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 34.7552i | − | 1.12465i | ||||||
\(956\) | 19.2977 | + | 11.1415i | 0.624133 | + | 0.360343i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.5779 | − | 14.7674i | 0.826385 | − | 0.477114i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.65878 | − | 4.60514i | 0.0857670 | − | 0.148553i | ||||
\(962\) | −25.8798 | −0.834399 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.656523i | 0.0211452i | ||||||||
\(965\) | −13.8205 | + | 23.9378i | −0.444898 | + | 0.770586i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.7378 | − | 32.4549i | −0.602568 | − | 1.04368i | −0.992431 | − | 0.122805i | \(-0.960811\pi\) |
0.389863 | − | 0.920873i | \(-0.372522\pi\) | |||||||
\(968\) | 9.47728 | − | 5.47171i | 0.304611 | − | 0.175867i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.14707 | + | 3.71884i | −0.0689384 | + | 0.119405i | ||||
\(971\) | −29.7244 | −0.953902 | −0.476951 | − | 0.878930i | \(-0.658258\pi\) | ||||
−0.476951 | + | 0.878930i | \(0.658258\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.941315 | + | 0.543468i | 0.0301617 | + | 0.0174139i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.8615 | + | 6.27087i | −0.347667 | + | 0.200726i | ||||
\(977\) | 35.9649 | − | 20.7644i | 1.15062 | − | 0.664310i | 0.201581 | − | 0.979472i | \(-0.435392\pi\) |
0.949038 | + | 0.315161i | \(0.102059\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.78668 | − | 1.60889i | −0.0890626 | − | 0.0514203i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.8931 | 0.347614 | ||||||||
\(983\) | 6.25746 | − | 10.8382i | 0.199582 | − | 0.345686i | −0.748811 | − | 0.662784i | \(-0.769375\pi\) |
0.948393 | + | 0.317098i | \(0.102708\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.09923 | + | 5.25345i | −0.289926 | + | 0.167389i | ||||
\(986\) | 30.1075 | + | 52.1478i | 0.958819 | + | 1.66072i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.54016 | − | 2.66764i | 0.0489991 | − | 0.0848690i | ||||
\(989\) | 43.6627i | 1.38839i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.2038 | −1.65831 | −0.829154 | − | 0.559020i | \(-0.811178\pi\) | ||||
−0.829154 | + | 0.559020i | \(0.811178\pi\) | |||||||
\(992\) | 3.01320 | − | 5.21902i | 0.0956693 | − | 0.165704i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.45274 | + | 3.14814i | −0.172863 | + | 0.0998027i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.92399 | + | 3.99757i | 0.219285 | + | 0.126604i | 0.605619 | − | 0.795755i | \(-0.292926\pi\) |
−0.386334 | + | 0.922359i | \(0.626259\pi\) | |||||||
\(998\) | − | 40.0684i | − | 1.26834i | ||||||
\(999\) | 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 | 2646.2.m.c.1763.14 | 48 | ||
3.2 | odd | 2 | 882.2.m.c.587.7 | yes | 48 | ||
7.2 | even | 3 | 2646.2.l.c.521.18 | 48 | |||
7.3 | odd | 6 | 2646.2.t.c.1979.10 | 48 | |||
7.4 | even | 3 | 2646.2.t.c.1979.9 | 48 | |||
7.5 | odd | 6 | 2646.2.l.c.521.17 | 48 | |||
7.6 | odd | 2 | inner | 2646.2.m.c.1763.13 | 48 | ||
9.4 | even | 3 | 882.2.m.c.293.6 | ✓ | 48 | ||
9.5 | odd | 6 | inner | 2646.2.m.c.881.13 | 48 | ||
21.2 | odd | 6 | 882.2.l.c.227.15 | 48 | |||
21.5 | even | 6 | 882.2.l.c.227.22 | 48 | |||
21.11 | odd | 6 | 882.2.t.c.803.23 | 48 | |||
21.17 | even | 6 | 882.2.t.c.803.14 | 48 | |||
21.20 | even | 2 | 882.2.m.c.587.6 | yes | 48 | ||
63.4 | even | 3 | 882.2.l.c.509.10 | 48 | |||
63.5 | even | 6 | 2646.2.t.c.2285.9 | 48 | |||
63.13 | odd | 6 | 882.2.m.c.293.7 | yes | 48 | ||
63.23 | odd | 6 | 2646.2.t.c.2285.10 | 48 | |||
63.31 | odd | 6 | 882.2.l.c.509.3 | 48 | |||
63.32 | odd | 6 | 2646.2.l.c.1097.17 | 48 | |||
63.40 | odd | 6 | 882.2.t.c.815.23 | 48 | |||
63.41 | even | 6 | inner | 2646.2.m.c.881.14 | 48 | ||
63.58 | even | 3 | 882.2.t.c.815.14 | 48 | |||
63.59 | even | 6 | 2646.2.l.c.1097.18 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.l.c.227.15 | 48 | 21.2 | odd | 6 | |||
882.2.l.c.227.22 | 48 | 21.5 | even | 6 | |||
882.2.l.c.509.3 | 48 | 63.31 | odd | 6 | |||
882.2.l.c.509.10 | 48 | 63.4 | even | 3 | |||
882.2.m.c.293.6 | ✓ | 48 | 9.4 | even | 3 | ||
882.2.m.c.293.7 | yes | 48 | 63.13 | odd | 6 | ||
882.2.m.c.587.6 | yes | 48 | 21.20 | even | 2 | ||
882.2.m.c.587.7 | yes | 48 | 3.2 | odd | 2 | ||
882.2.t.c.803.14 | 48 | 21.17 | even | 6 | |||
882.2.t.c.803.23 | 48 | 21.11 | odd | 6 | |||
882.2.t.c.815.14 | 48 | 63.58 | even | 3 | |||
882.2.t.c.815.23 | 48 | 63.40 | odd | 6 | |||
2646.2.l.c.521.17 | 48 | 7.5 | odd | 6 | |||
2646.2.l.c.521.18 | 48 | 7.2 | even | 3 | |||
2646.2.l.c.1097.17 | 48 | 63.32 | odd | 6 | |||
2646.2.l.c.1097.18 | 48 | 63.59 | even | 6 | |||
2646.2.m.c.881.13 | 48 | 9.5 | odd | 6 | inner | ||
2646.2.m.c.881.14 | 48 | 63.41 | even | 6 | inner | ||
2646.2.m.c.1763.13 | 48 | 7.6 | odd | 2 | inner | ||
2646.2.m.c.1763.14 | 48 | 1.1 | even | 1 | trivial | ||
2646.2.t.c.1979.9 | 48 | 7.4 | even | 3 | |||
2646.2.t.c.1979.10 | 48 | 7.3 | odd | 6 | |||
2646.2.t.c.2285.9 | 48 | 63.5 | even | 6 | |||
2646.2.t.c.2285.10 | 48 | 63.23 | odd | 6 |