Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 30 x^{10} - 53 x^{9} + 798 x^{8} - 1096 x^{7} + 4060 x^{6} - 915 x^{5} + 10392 x^{4} + \cdots + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 841.4 | ||
Root | \(-0.818190 + 1.41715i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.841 |
Dual form | 4020.2.q.j.3781.4 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.22030 | − | 2.11362i | 0.461229 | − | 0.798871i | −0.537794 | − | 0.843076i | \(-0.680742\pi\) |
0.999022 | + | 0.0442049i | \(0.0140755\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.39089 | + | 2.40909i | −0.419368 | + | 0.726367i | −0.995876 | − | 0.0907246i | \(-0.971082\pi\) |
0.576508 | + | 0.817092i | \(0.304415\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.87422 | + | 6.71035i | 0.939637 | + | 1.62750i | 0.766148 | + | 0.642664i | \(0.222171\pi\) |
0.173489 | + | 0.984836i | \(0.444496\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.64240 | − | 6.30882i | −0.835623 | − | 1.44734i | −0.893522 | − | 0.449019i | \(-0.851773\pi\) |
0.0578987 | − | 0.998322i | \(-0.481560\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.22030 | − | 2.11362i | 0.266290 | − | 0.461229i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.334853 | + | 0.579982i | 0.0698216 | + | 0.120935i | 0.898823 | − | 0.438312i | \(-0.144424\pi\) |
−0.829001 | + | 0.559247i | \(0.811090\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.34001 | + | 7.51712i | −0.805920 | + | 1.39589i | 0.109748 | + | 0.993959i | \(0.464996\pi\) |
−0.915668 | + | 0.401935i | \(0.868338\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.47181 | − | 4.28129i | 0.443950 | − | 0.768943i | −0.554029 | − | 0.832498i | \(-0.686910\pi\) |
0.997978 | + | 0.0635543i | \(0.0202436\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.39089 | + | 2.40909i | −0.242122 | + | 0.419368i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.22030 | + | 2.11362i | −0.206268 | + | 0.357266i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.86878 | + | 8.43298i | 0.800423 | + | 1.38637i | 0.919338 | + | 0.393468i | \(0.128725\pi\) |
−0.118916 | + | 0.992904i | \(0.537942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | + | 0.866025i | 0.0800641 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.30666 | + | 3.99525i | −0.360240 | + | 0.623953i | −0.988000 | − | 0.154453i | \(-0.950638\pi\) |
0.627760 | + | 0.778407i | \(0.283972\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.28479 | 0.653425 | 0.326713 | − | 0.945124i | \(-0.394059\pi\) | ||||
0.326713 | + | 0.945124i | \(0.394059\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.96028 | − | 5.12735i | 0.431801 | − | 0.747901i | −0.565228 | − | 0.824935i | \(-0.691212\pi\) |
0.997028 | + | 0.0770342i | \(0.0245451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.521754 | + | 0.903704i | 0.0745363 | + | 0.129101i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.87422 | + | 6.71035i | 0.542500 | + | 0.939637i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.94361 | 0.541697 | 0.270848 | − | 0.962622i | \(-0.412696\pi\) | ||||
0.270848 | + | 0.962622i | \(0.412696\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.39089 | − | 2.40909i | 0.187547 | − | 0.324841i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.64240 | − | 6.30882i | −0.482447 | − | 0.835623i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.583616 | −0.0759804 | −0.0379902 | − | 0.999278i | \(-0.512096\pi\) | ||||
−0.0379902 | + | 0.999278i | \(0.512096\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.949983 | + | 1.64542i | 0.121633 | + | 0.210674i | 0.920412 | − | 0.390950i | \(-0.127854\pi\) |
−0.798779 | + | 0.601625i | \(0.794520\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.22030 | − | 2.11362i | 0.153743 | − | 0.266290i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.500000 | − | 0.866025i | −0.0620174 | − | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.58812 | − | 7.35700i | 0.438359 | − | 0.898800i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.334853 | + | 0.579982i | 0.0403115 | + | 0.0698216i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.74756 | + | 3.02687i | −0.207398 | + | 0.359223i | −0.950894 | − | 0.309517i | \(-0.899833\pi\) |
0.743496 | + | 0.668740i | \(0.233166\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.24155 | + | 3.88247i | 0.262353 | + | 0.454409i | 0.966867 | − | 0.255282i | \(-0.0821682\pi\) |
−0.704514 | + | 0.709690i | \(0.748835\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.39459 | + | 5.87960i | 0.386849 | + | 0.670043i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.89911 | + | 5.02141i | −0.326175 | + | 0.564952i | −0.981750 | − | 0.190179i | \(-0.939093\pi\) |
0.655574 | + | 0.755131i | \(0.272427\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.02703 | + | 6.97501i | 0.442023 | + | 0.765607i | 0.997840 | − | 0.0656982i | \(-0.0209275\pi\) |
−0.555816 | + | 0.831305i | \(0.687594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.87422 | − | 6.71035i | −0.420219 | − | 0.727840i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.34001 | + | 7.51712i | −0.465298 | + | 0.805920i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.596874 | 0.0632685 | 0.0316342 | − | 0.999500i | \(-0.489929\pi\) | ||||
0.0316342 | + | 0.999500i | \(0.489929\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.44059 | 0.255844 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.47181 | − | 4.28129i | 0.256314 | − | 0.443950i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.64240 | + | 6.30882i | 0.373702 | + | 0.647271i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.689324 | + | 1.19394i | 0.0699902 | + | 0.121227i | 0.898897 | − | 0.438161i | \(-0.144370\pi\) |
−0.828907 | + | 0.559387i | \(0.811037\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.39089 | + | 2.40909i | −0.139789 | + | 0.242122i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.79513 | − | 3.10925i | 0.178622 | − | 0.309382i | −0.762787 | − | 0.646650i | \(-0.776169\pi\) |
0.941409 | + | 0.337268i | \(0.109503\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.89146 | + | 10.2043i | −0.580503 | + | 1.00546i | 0.414917 | + | 0.909859i | \(0.363811\pi\) |
−0.995420 | + | 0.0956012i | \(0.969523\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.22030 | + | 2.11362i | −0.119089 | + | 0.206268i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.20720 | 0.213378 | 0.106689 | − | 0.994292i | \(-0.465975\pi\) | ||||
0.106689 | + | 0.994292i | \(0.465975\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.5691 | −1.39547 | −0.697734 | − | 0.716357i | \(-0.745808\pi\) | ||||
−0.697734 | + | 0.716357i | \(0.745808\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.86878 | + | 8.43298i | 0.462124 | + | 0.800423i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.47181 | − | 6.01335i | 0.326600 | − | 0.565688i | −0.655235 | − | 0.755425i | \(-0.727430\pi\) |
0.981835 | + | 0.189737i | \(0.0607636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.334853 | − | 0.579982i | −0.0312252 | − | 0.0540836i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.500000 | + | 0.866025i | 0.0462250 | + | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.9108 | 1.73355 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.63087 | + | 2.82474i | 0.148261 | + | 0.256795i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.30666 | + | 3.99525i | −0.207984 | + | 0.360240i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.83179 | − | 4.90481i | 0.251281 | − | 0.435231i | −0.712598 | − | 0.701573i | \(-0.752482\pi\) |
0.963879 | + | 0.266342i | \(0.0858149\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.28479 | 0.377255 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.69628 | 0.322946 | 0.161473 | − | 0.986877i | \(-0.448376\pi\) | ||||
0.161473 | + | 0.986877i | \(0.448376\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.7792 | −1.54165 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.7025 | 1.42699 | 0.713494 | − | 0.700661i | \(-0.247112\pi\) | ||||
0.713494 | + | 0.700661i | \(0.247112\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.7732 | 1.33786 | 0.668932 | − | 0.743324i | \(-0.266752\pi\) | ||||
0.668932 | + | 0.743324i | \(0.266752\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.96028 | − | 5.12735i | 0.249300 | − | 0.431801i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.78177 | −0.232624 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.34001 | − | 7.51712i | 0.360418 | − | 0.624263i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.521754 | + | 0.903704i | 0.0430335 | + | 0.0745363i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.6059 | 1.85194 | 0.925972 | − | 0.377591i | \(-0.123248\pi\) | ||||
0.925972 | + | 0.377591i | \(0.123248\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9860 | − | 20.7603i | −0.975405 | − | 1.68945i | −0.678591 | − | 0.734516i | \(-0.737409\pi\) |
−0.296814 | − | 0.954935i | \(-0.595924\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.87422 | + | 6.71035i | 0.313212 | + | 0.542500i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.47181 | + | 4.28129i | −0.198540 | + | 0.343882i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2026 | + | 17.6715i | 0.814259 | + | 1.41034i | 0.909859 | + | 0.414918i | \(0.136190\pi\) |
−0.0955996 | + | 0.995420i | \(0.530477\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.94361 | 0.312749 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.63448 | 0.128815 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.34522 | + | 10.9902i | −0.496996 | + | 0.860822i | −0.999994 | − | 0.00346570i | \(-0.998897\pi\) |
0.502998 | + | 0.864287i | \(0.332230\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.39089 | − | 2.40909i | 0.108280 | − | 0.187547i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.5026 | − | 19.9231i | 0.890098 | − | 1.54170i | 0.0503416 | − | 0.998732i | \(-0.483969\pi\) |
0.839757 | − | 0.542963i | \(-0.182698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.64240 | − | 6.30882i | −0.278541 | − | 0.482447i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.0548381 | − | 0.0949824i | −0.00416927 | − | 0.00722138i | 0.863933 | − | 0.503606i | \(-0.167994\pi\) |
−0.868103 | + | 0.496385i | \(0.834660\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.22030 | − | 2.11362i | 0.0922457 | − | 0.159774i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.583616 | −0.0438673 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.76914 | −0.132232 | −0.0661158 | − | 0.997812i | \(-0.521061\pi\) | ||||
−0.0661158 | + | 0.997812i | \(0.521061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.11125 | + | 1.92475i | −0.0825988 | + | 0.143065i | −0.904365 | − | 0.426759i | \(-0.859655\pi\) |
0.821767 | + | 0.569824i | \(0.192989\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.949983 | + | 1.64542i | 0.0702248 | + | 0.121633i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.86878 | − | 8.43298i | −0.357960 | − | 0.620005i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.5544 | −1.57622 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.22030 | − | 2.11362i | 0.0887635 | − | 0.153743i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.43628 | + | 11.1480i | 0.465713 | + | 0.806638i | 0.999233 | − | 0.0391491i | \(-0.0124647\pi\) |
−0.533521 | + | 0.845787i | \(0.679131\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1758 | 1.02040 | 0.510198 | − | 0.860057i | \(-0.329572\pi\) | ||||
0.510198 | + | 0.860057i | \(0.329572\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.500000 | − | 0.866025i | −0.0358057 | − | 0.0620174i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.97300 | + | 5.14939i | −0.211818 | + | 0.366879i | −0.952283 | − | 0.305215i | \(-0.901272\pi\) |
0.740466 | + | 0.672094i | \(0.234605\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.54607 | − | 6.14197i | −0.251374 | − | 0.435392i | 0.712530 | − | 0.701641i | \(-0.247549\pi\) |
−0.963904 | + | 0.266249i | \(0.914216\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.58812 | − | 7.35700i | 0.253087 | − | 0.518922i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.5922 | + | 18.3462i | 0.743427 | + | 1.28765i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.30666 | − | 3.99525i | 0.161104 | − | 0.279040i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.334853 | + | 0.579982i | 0.0232739 | + | 0.0403115i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.2647 | 1.40174 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.71424 | + | 15.0935i | 0.599913 | + | 1.03908i | 0.992833 | + | 0.119507i | \(0.0381314\pi\) |
−0.392921 | + | 0.919572i | \(0.628535\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.74756 | + | 3.02687i | −0.119741 | + | 0.207398i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.28479 | −0.292221 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.03267 | − | 10.4489i | −0.409525 | − | 0.709317i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.24155 | + | 3.88247i | 0.151470 | + | 0.262353i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.87422 | + | 6.71035i | −0.260609 | + | 0.451387i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.1265 | −1.81653 | −0.908263 | − | 0.418399i | \(-0.862591\pi\) | ||||
−0.908263 | + | 0.418399i | \(0.862591\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.3924 | + | 19.7322i | −0.756141 | + | 1.30967i | 0.188664 | + | 0.982042i | \(0.439584\pi\) |
−0.944805 | + | 0.327633i | \(0.893749\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.63810 | − | 8.03342i | −0.306494 | − | 0.530863i | 0.671099 | − | 0.741368i | \(-0.265823\pi\) |
−0.977593 | + | 0.210505i | \(0.932489\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.39459 | + | 5.87960i | 0.223348 | + | 0.386849i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.23603 | − | 7.33702i | 0.277512 | − | 0.480664i | −0.693254 | − | 0.720693i | \(-0.743824\pi\) |
0.970766 | + | 0.240029i | \(0.0771569\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.96028 | + | 5.12735i | −0.193107 | + | 0.334471i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.89911 | + | 5.02141i | −0.188317 | + | 0.326175i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.874507 | − | 1.51469i | 0.0565672 | − | 0.0979772i | −0.836355 | − | 0.548188i | \(-0.815318\pi\) |
0.892922 | + | 0.450211i | \(0.148651\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.12424 | 0.587744 | 0.293872 | − | 0.955845i | \(-0.405056\pi\) | ||||
0.293872 | + | 0.955845i | \(0.405056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.521754 | − | 0.903704i | −0.0333336 | − | 0.0577355i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.64240 | − | 6.30882i | 0.231760 | − | 0.401420i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.02703 | + | 6.97501i | 0.255202 | + | 0.442023i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.55127 | + | 6.15098i | 0.224154 | + | 0.388246i | 0.956065 | − | 0.293154i | \(-0.0947048\pi\) |
−0.731911 | + | 0.681400i | \(0.761371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.86297 | −0.117124 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.87422 | − | 6.71035i | −0.242613 | − | 0.420219i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.8699 | + | 22.2912i | −0.802799 | + | 1.39049i | 0.114967 | + | 0.993369i | \(0.463324\pi\) |
−0.917767 | + | 0.397120i | \(0.870010\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.7654 | 1.47671 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.34001 | + | 7.51712i | −0.268640 | + | 0.465298i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.0417 | −0.989171 | −0.494585 | − | 0.869129i | \(-0.664680\pi\) | ||||
−0.494585 | + | 0.869129i | \(0.664680\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.94361 | −0.242254 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.596874 | 0.0365281 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.59445 | 0.584984 | 0.292492 | − | 0.956268i | \(-0.405515\pi\) | ||||
0.292492 | + | 0.956268i | \(0.405515\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5032 | 0.759513 | 0.379756 | − | 0.925087i | \(-0.376008\pi\) | ||||
0.379756 | + | 0.925087i | \(0.376008\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.44059 | 0.147711 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.39089 | + | 2.40909i | −0.0838736 | + | 0.145273i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.8143 | 1.49095 | 0.745474 | − | 0.666535i | \(-0.232223\pi\) | ||||
0.745474 | + | 0.666535i | \(0.232223\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.47181 | − | 4.28129i | 0.147983 | − | 0.256314i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.54113 | − | 13.0616i | −0.449866 | − | 0.779191i | 0.548511 | − | 0.836143i | \(-0.315195\pi\) |
−0.998377 | + | 0.0569525i | \(0.981862\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.28294 | −0.551814 | −0.275907 | − | 0.961184i | \(-0.588978\pi\) | ||||
−0.275907 | + | 0.961184i | \(0.588978\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.64240 | + | 6.30882i | 0.215757 | + | 0.373702i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.62962 | + | 9.75078i | 0.332306 | + | 0.575570i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −21.5192 | + | 37.2724i | −1.26584 | + | 2.19249i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.689324 | + | 1.19394i | 0.0404089 | + | 0.0699902i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.1448 | −1.58582 | −0.792909 | − | 0.609340i | \(-0.791434\pi\) | ||||
−0.792909 | + | 0.609340i | \(0.791434\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.583616 | 0.0339795 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.39089 | + | 2.40909i | −0.0807074 | + | 0.139789i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.334853 | + | 0.579982i | −0.0193650 | + | 0.0335412i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.22872 | − | 9.05641i | 0.301378 | − | 0.522003i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.79513 | − | 3.10925i | 0.103127 | − | 0.178622i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.949983 | − | 1.64542i | −0.0543959 | − | 0.0942164i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.08212 | + | 8.80248i | 0.290052 | + | 0.502384i | 0.973822 | − | 0.227313i | \(-0.0729942\pi\) |
−0.683770 | + | 0.729698i | \(0.739661\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.89146 | + | 10.2043i | −0.335154 | + | 0.580503i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.6823 | −1.11608 | −0.558041 | − | 0.829813i | \(-0.688447\pi\) | ||||
−0.558041 | + | 0.829813i | \(0.688447\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.5586 | −0.596805 | −0.298403 | − | 0.954440i | \(-0.596454\pi\) | ||||
−0.298403 | + | 0.954440i | \(0.596454\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.22030 | + | 2.11362i | −0.0687559 | + | 0.119089i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.5394 | + | 25.1830i | 0.816613 | + | 1.41442i | 0.908164 | + | 0.418615i | \(0.137484\pi\) |
−0.0915502 | + | 0.995800i | \(0.529182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0729 | − | 20.9109i | −0.675955 | − | 1.17079i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.20720 | 0.123194 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.2229 | − | 48.8835i | 1.57037 | − | 2.71995i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.500000 | + | 0.866025i | 0.0277350 | + | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.5691 | −0.805673 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.22483 | − | 12.5138i | −0.398318 | − | 0.689906i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5362 | + | 25.1775i | −0.798984 | + | 1.38388i | 0.121294 | + | 0.992617i | \(0.461295\pi\) |
−0.920278 | + | 0.391264i | \(0.872038\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.86878 | + | 8.43298i | 0.266808 | + | 0.462124i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.58812 | + | 7.35700i | −0.196040 | + | 0.401956i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.80364 | + | 8.32015i | 0.261671 | + | 0.453227i | 0.966686 | − | 0.255965i | \(-0.0823932\pi\) |
−0.705015 | + | 0.709192i | \(0.749060\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.47181 | − | 6.01335i | 0.188563 | − | 0.326600i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.87601 | + | 11.9096i | 0.372357 | + | 0.644941i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.6309 | 1.05997 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.334853 | − | 0.579982i | −0.0180279 | − | 0.0312252i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.0651 | + | 27.8256i | −0.862419 | + | 1.49375i | 0.00716792 | + | 0.999974i | \(0.497718\pi\) |
−0.869587 | + | 0.493780i | \(0.835615\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.8362 | −0.740635 | −0.370317 | − | 0.928905i | \(-0.620751\pi\) | ||||
−0.370317 | + | 0.928905i | \(0.620751\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.500000 | + | 0.866025i | 0.0266880 | + | 0.0462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.6118 | − | 28.7724i | −0.884156 | − | 1.53140i | −0.846678 | − | 0.532105i | \(-0.821401\pi\) |
−0.0374778 | − | 0.999297i | \(-0.511932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.74756 | − | 3.02687i | 0.0927510 | − | 0.160649i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.9108 | 1.00087 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.5139 | 1.55768 | 0.778841 | − | 0.627221i | \(-0.215808\pi\) | ||||
0.778841 | + | 0.627221i | \(0.215808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0341 | + | 29.5040i | −0.896532 | + | 1.55284i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.63087 | + | 2.82474i | 0.0855983 | + | 0.148261i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.24155 | − | 3.88247i | −0.117328 | − | 0.203218i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.3563 | − | 30.0619i | 0.905989 | − | 1.56922i | 0.0864056 | − | 0.996260i | \(-0.472462\pi\) |
0.819584 | − | 0.572959i | \(-0.194205\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.30666 | + | 3.99525i | −0.120080 | + | 0.207984i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.81238 | − | 8.33528i | 0.249846 | − | 0.432746i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.8739 | − | 30.9585i | 0.925475 | − | 1.60297i | 0.134681 | − | 0.990889i | \(-0.456999\pi\) |
0.790795 | − | 0.612081i | \(-0.209668\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.68003 | −0.447044 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.30785 | + | 10.9255i | 0.324013 | + | 0.561206i | 0.981312 | − | 0.192423i | \(-0.0616346\pi\) |
−0.657299 | + | 0.753630i | \(0.728301\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.83179 | − | 4.90481i | 0.145077 | − | 0.251281i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.75633 | − | 15.1664i | −0.447427 | − | 0.774967i | 0.550790 | − | 0.834644i | \(-0.314326\pi\) |
−0.998218 | + | 0.0596766i | \(0.980993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.39459 | − | 5.87960i | −0.173004 | − | 0.299652i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.28479 | 0.217808 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.46758 | − | 14.6663i | −0.429323 | − | 0.743610i | 0.567490 | − | 0.823380i | \(-0.307915\pi\) |
−0.996813 | + | 0.0797707i | \(0.974581\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.59459 | + | 4.49396i | −0.131214 | + | 0.227269i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.69628 | 0.186453 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.89911 | − | 5.02141i | 0.145870 | − | 0.252654i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.4197 | −1.32597 | −0.662984 | − | 0.748633i | \(-0.730710\pi\) | ||||
−0.662984 | + | 0.748633i | \(0.730710\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.7792 | −0.890074 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.12171 | 0.305704 | 0.152852 | − | 0.988249i | \(-0.451154\pi\) | ||||
0.152852 | + | 0.988249i | \(0.451154\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.94361 | 0.246259 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.0877 | −1.34269 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.62655 | + | 11.4775i | −0.327662 | + | 0.567527i | −0.982047 | − | 0.188634i | \(-0.939594\pi\) |
0.654386 | + | 0.756161i | \(0.272927\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.7025 | 0.823872 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.712185 | + | 1.23354i | −0.0350443 | + | 0.0606985i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.02703 | − | 6.97501i | −0.197679 | − | 0.342390i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.7732 | 0.772416 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.15432 | + | 8.92755i | 0.251805 | + | 0.436139i | 0.964023 | − | 0.265819i | \(-0.0856425\pi\) |
−0.712218 | + | 0.701959i | \(0.752309\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.37700 | + | 4.11709i | 0.115848 | + | 0.200655i | 0.918118 | − | 0.396306i | \(-0.129708\pi\) |
−0.802270 | + | 0.596961i | \(0.796375\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.96028 | − | 5.12735i | 0.143934 | − | 0.249300i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.87422 | + | 6.71035i | 0.187927 | + | 0.325500i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.63704 | 0.224402 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.78177 | −0.134305 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.47031 | − | 7.74280i | 0.215327 | − | 0.372957i | −0.738047 | − | 0.674750i | \(-0.764252\pi\) |
0.953374 | + | 0.301792i | \(0.0975849\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.91121 | − | 10.2385i | 0.284075 | − | 0.492032i | −0.688310 | − | 0.725417i | \(-0.741647\pi\) |
0.972384 | + | 0.233385i | \(0.0749803\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.34001 | − | 7.51712i | 0.208088 | − | 0.360418i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.43933 | − | 4.22505i | 0.116689 | − | 0.202112i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.68006 | − | 2.90996i | −0.0801851 | − | 0.138885i | 0.823144 | − | 0.567832i | \(-0.192218\pi\) |
−0.903329 | + | 0.428948i | \(0.858884\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.521754 | + | 0.903704i | 0.0248454 | + | 0.0430335i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.0105 | + | 19.0707i | −0.523124 | + | 0.906077i | 0.476514 | + | 0.879167i | \(0.341900\pi\) |
−0.999638 | + | 0.0269101i | \(0.991433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.596874 | −0.0282945 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.6059 | 1.06922 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.64777 | − | 4.58607i | 0.124956 | − | 0.216430i | −0.796760 | − | 0.604296i | \(-0.793454\pi\) |
0.921716 | + | 0.387866i | \(0.126788\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.41661 | − | 11.1139i | −0.302146 | − | 0.523332i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.9860 | − | 20.7603i | −0.563151 | − | 0.975405i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.44059 | −0.114417 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.96596 | − | 5.13720i | 0.138742 | − | 0.240308i | −0.788279 | − | 0.615318i | \(-0.789028\pi\) |
0.927021 | + | 0.375010i | \(0.122361\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.87422 | + | 6.71035i | 0.180833 | + | 0.313212i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.68430 | 0.0784456 | 0.0392228 | − | 0.999230i | \(-0.487512\pi\) | ||||
0.0392228 | + | 0.999230i | \(0.487512\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.2082 | − | 19.4131i | −0.520887 | − | 0.902203i | −0.999705 | − | 0.0242885i | \(-0.992268\pi\) |
0.478818 | − | 0.877914i | \(-0.341065\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.47181 | + | 4.28129i | −0.114627 | + | 0.198540i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.282154 | + | 0.488706i | 0.0130565 | + | 0.0226146i | 0.872480 | − | 0.488650i | \(-0.162511\pi\) |
−0.859423 | + | 0.511265i | \(0.829177\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.1713 | − | 16.5616i | −0.515842 | − | 0.764745i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.2026 | + | 17.6715i | 0.470113 | + | 0.814259i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.95967 | + | 10.3224i | −0.274026 | + | 0.474626i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.64240 | − | 6.30882i | −0.167125 | − | 0.289468i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.94361 | 0.180566 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.72662 | + | 8.18675i | 0.215965 | + | 0.374062i | 0.953571 | − | 0.301169i | \(-0.0973770\pi\) |
−0.737606 | + | 0.675232i | \(0.764044\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.86878 | + | 8.43298i | −0.221997 | + | 0.384511i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.63448 | 0.0743714 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.689324 | − | 1.19394i | −0.0313006 | − | 0.0542142i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.52143 | − | 2.63519i | −0.0689424 | − | 0.119412i | 0.829494 | − | 0.558516i | \(-0.188629\pi\) |
−0.898436 | + | 0.439104i | \(0.855296\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.34522 | + | 10.9902i | −0.286941 | + | 0.496996i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.3197 | 0.736496 | 0.368248 | − | 0.929728i | \(-0.379958\pi\) | ||||
0.368248 | + | 0.929728i | \(0.379958\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −67.2567 | −3.02909 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.39089 | − | 2.40909i | 0.0625157 | − | 0.108280i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.26509 | + | 7.38735i | 0.191315 | + | 0.331368i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.173542 | − | 0.300584i | −0.00776881 | − | 0.0134560i | 0.862115 | − | 0.506713i | \(-0.169140\pi\) |
−0.869884 | + | 0.493257i | \(0.835806\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.5026 | − | 19.9231i | 0.513898 | − | 0.890098i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.3851 | − | 26.6478i | 0.685987 | − | 1.18816i | −0.287138 | − | 0.957889i | \(-0.592704\pi\) |
0.973125 | − | 0.230275i | \(-0.0739627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.79513 | + | 3.10925i | −0.0798822 | + | 0.138360i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | − | 10.3923i | 0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.3865 | −0.637669 | −0.318834 | − | 0.947810i | \(-0.603291\pi\) | ||||
−0.318834 | + | 0.947810i | \(0.603291\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.9414 | 0.484019 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.64240 | − | 6.30882i | −0.160816 | − | 0.278541i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.89146 | − | 10.2043i | 0.259609 | − | 0.449656i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.23482 | + | 14.2631i | 0.362167 | + | 0.627292i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.0548381 | − | 0.0949824i | −0.00240713 | − | 0.00416927i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −43.5339 | −1.90726 | −0.953628 | − | 0.300987i | \(-0.902684\pi\) | ||||
−0.953628 | + | 0.300987i | \(0.902684\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.5682 | − | 21.7688i | −0.549569 | − | 0.951882i | −0.998304 | − | 0.0582168i | \(-0.981459\pi\) |
0.448735 | − | 0.893665i | \(-0.351875\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.22030 | − | 2.11362i | 0.0532581 | − | 0.0922457i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 38.3053 | 1.66861 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2757 | − | 19.5302i | 0.490250 | − | 0.849138i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.583616 | −0.0253268 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.61332 | −0.199825 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.20720 | −0.0954256 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.76914 | −0.0763440 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.90280 | −0.125033 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.5488 | −1.57136 | −0.785679 | − | 0.618635i | \(-0.787686\pi\) | ||||
−0.785679 | + | 0.618635i | \(0.787686\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.11125 | + | 1.92475i | −0.0476884 | + | 0.0825988i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.5691 | 0.624072 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.81993 | + | 4.88427i | −0.120572 | + | 0.208836i | −0.919993 | − | 0.391934i | \(-0.871806\pi\) |
0.799422 | + | 0.600770i | \(0.205139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.949983 | + | 1.64542i | 0.0405443 | + | 0.0702248i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 63.2322 | 2.69378 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.07555 | + | 12.2552i | 0.300883 | + | 0.521144i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.86878 | − | 8.43298i | −0.206668 | − | 0.357960i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.31325 | − | 4.00666i | 0.0980154 | − | 0.169768i | −0.812848 | − | 0.582476i | \(-0.802084\pi\) |
0.910863 | + | 0.412709i | \(0.135417\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.14240 | + | 3.71074i | 0.0906138 | + | 0.156948i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.5544 | −0.910029 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.2239 | −1.35808 | −0.679039 | − | 0.734103i | \(-0.737603\pi\) | ||||
−0.679039 | + | 0.734103i | \(0.737603\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.47181 | + | 6.01335i | −0.146060 | + | 0.252983i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.22030 | − | 2.11362i | 0.0512476 | − | 0.0887635i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.66605 | + | 2.88568i | −0.0698444 | + | 0.120974i | −0.898833 | − | 0.438292i | \(-0.855584\pi\) |
0.828988 | + | 0.559266i | \(0.188917\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.3842 | − | 26.6462i | 0.643809 | − | 1.11511i | −0.340766 | − | 0.940148i | \(-0.610686\pi\) |
0.984575 | − | 0.174962i | \(-0.0559804\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.43628 | + | 11.1480i | 0.268879 | + | 0.465713i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.334853 | + | 0.579982i | 0.0139643 | + | 0.0241869i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.4490 | − | 19.8303i | 0.476629 | − | 0.825545i | −0.523013 | − | 0.852325i | \(-0.675192\pi\) |
0.999641 | + | 0.0267797i | \(0.00852527\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.1758 | 0.589125 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.6567 | 0.815496 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.48512 | + | 9.50051i | −0.227170 | + | 0.393471i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.500000 | − | 0.866025i | −0.0206725 | − | 0.0358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.84220 | + | 4.92284i | 0.117310 | + | 0.203187i | 0.918701 | − | 0.394954i | \(-0.129239\pi\) |
−0.801391 | + | 0.598141i | \(0.795906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.0132 | −1.48390 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.97300 | + | 5.14939i | −0.122293 | + | 0.211818i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.86947 | − | 15.3624i | −0.364226 | − | 0.630857i | 0.624426 | − | 0.781084i | \(-0.285333\pi\) |
−0.988652 | + | 0.150227i | \(0.952000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.9108 | −0.775267 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.54607 | − | 6.14197i | −0.145131 | − | 0.251374i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.1500 | + | 26.2406i | −0.619013 | + | 1.07216i | 0.370654 | + | 0.928771i | \(0.379134\pi\) |
−0.989666 | + | 0.143390i | \(0.954200\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.112939 | + | 0.195615i | 0.00460686 | + | 0.00797932i | 0.868320 | − | 0.496005i | \(-0.165200\pi\) |
−0.863713 | + | 0.503984i | \(0.831867\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.58812 | − | 7.35700i | 0.146120 | − | 0.299600i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.63087 | − | 2.82474i | −0.0663042 | − | 0.114842i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.976639 | + | 1.69159i | −0.0396406 | + | 0.0686595i | −0.885165 | − | 0.465277i | \(-0.845955\pi\) |
0.845524 | + | 0.533937i | \(0.179288\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.5922 | + | 18.3462i | 0.429218 | + | 0.743427i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.92055 | 0.239520 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.1722 | − | 28.0111i | −0.653189 | − | 1.13136i | −0.982345 | − | 0.187081i | \(-0.940097\pi\) |
0.329155 | − | 0.944276i | \(-0.393236\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.30666 | − | 3.99525i | 0.0930135 | − | 0.161104i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4424 | 0.661945 | 0.330972 | − | 0.943640i | \(-0.392623\pi\) | ||||
0.330972 | + | 0.943640i | \(0.392623\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.29238 | − | 12.6308i | −0.293105 | − | 0.507673i | 0.681437 | − | 0.731877i | \(-0.261355\pi\) |
−0.974542 | + | 0.224203i | \(0.928022\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.334853 | + | 0.579982i | 0.0134372 | + | 0.0232739i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.728363 | − | 1.26156i | 0.0291812 | − | 0.0505434i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.2647 | 0.809292 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.7255 | + | 65.3425i | −1.50421 | + | 2.60537i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.41419 | + | 7.64560i | 0.175726 | + | 0.304367i | 0.940412 | − | 0.340036i | \(-0.110439\pi\) |
−0.764686 | + | 0.644403i | \(0.777106\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.71424 | + | 15.0935i | 0.346360 | + | 0.599913i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.83179 | + | 4.90481i | −0.112376 | + | 0.194641i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.521754 | + | 0.903704i | −0.0206726 | + | 0.0358061i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.74756 | + | 3.02687i | −0.0691325 | + | 0.119741i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.596262 | + | 1.03276i | −0.0235509 | + | 0.0407914i | −0.877561 | − | 0.479466i | \(-0.840831\pi\) |
0.854010 | + | 0.520257i | \(0.174164\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.75194 | −0.0690898 | −0.0345449 | − | 0.999403i | \(-0.510998\pi\) | ||||
−0.0345449 | + | 0.999403i | \(0.510998\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.28479 | −0.168714 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.66307 | + | 4.61257i | 0.104696 | + | 0.181339i | 0.913614 | − | 0.406583i | \(-0.133280\pi\) |
−0.808918 | + | 0.587922i | \(0.799946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.811744 | − | 1.40598i | 0.0318637 | − | 0.0551896i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.03267 | − | 10.4489i | −0.236439 | − | 0.409525i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.32354 | + | 14.4168i | 0.325725 | + | 0.564173i | 0.981659 | − | 0.190646i | \(-0.0610582\pi\) |
−0.655933 | + | 0.754819i | \(0.727725\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.69628 | −0.144426 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.24155 | + | 3.88247i | 0.0874510 | + | 0.151470i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.14489 | + | 14.1074i | −0.317280 | + | 0.549545i | −0.979919 | − | 0.199394i | \(-0.936103\pi\) |
0.662640 | + | 0.748938i | \(0.269436\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.7204 | −1.03930 | −0.519652 | − | 0.854378i | \(-0.673938\pi\) | ||||
−0.519652 | + | 0.854378i | \(0.673938\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.87422 | + | 6.71035i | −0.150462 | + | 0.260609i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.7792 | 0.689448 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.81306 | −0.225083 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.1265 | −1.04877 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.28528 | −0.204036 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.7222 | 1.10716 | 0.553579 | − | 0.832796i | \(-0.313262\pi\) | ||||
0.553579 | + | 0.832796i | \(0.313262\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.4324 | − | 33.6579i | 0.746848 | − | 1.29358i | −0.202479 | − | 0.979287i | \(-0.564900\pi\) |
0.949327 | − | 0.314292i | \(-0.101767\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.36472 | 0.129126 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.3924 | + | 19.7322i | −0.436558 | + | 0.756141i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.7268 | − | 42.8281i | −0.946144 | − | 1.63877i | −0.753443 | − | 0.657513i | \(-0.771609\pi\) |
−0.192701 | − | 0.981257i | \(-0.561725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.7025 | −0.638168 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.63810 | − | 8.03342i | −0.176954 | − | 0.306494i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.97181 | + | 3.41527i | 0.0751199 | + | 0.130111i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.2305 | − | 19.4519i | 0.427230 | − | 0.739984i | −0.569396 | − | 0.822063i | \(-0.692823\pi\) |
0.996626 | + | 0.0820796i | \(0.0261562\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.39459 | + | 5.87960i | 0.128950 | + | 0.223348i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.7732 | −0.598311 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35.7461 | −1.35398 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.23603 | − | 7.33702i | 0.160221 | − | 0.277512i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.9923 | − | 38.0917i | 0.830636 | − | 1.43870i | −0.0668980 | − | 0.997760i | \(-0.521310\pi\) |
0.897534 | − | 0.440945i | \(-0.145356\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.4681 | − | 61.4325i | 1.33770 | − | 2.31697i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.96028 | + | 5.12735i | −0.111490 | + | 0.193107i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.38118 | − | 7.58842i | −0.164771 | − | 0.285392i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.44843 | − | 16.3652i | −0.354843 | − | 0.614607i | 0.632248 | − | 0.774766i | \(-0.282132\pi\) |
−0.987091 | + | 0.160160i | \(0.948799\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.89911 | + | 5.02141i | −0.108725 | + | 0.188317i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.31077 | 0.123989 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.78177 | 0.104032 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.874507 | − | 1.51469i | 0.0326591 | − | 0.0565672i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.80093 | − | 11.7795i | −0.253632 | − | 0.439303i | 0.710891 | − | 0.703302i | \(-0.248292\pi\) |
−0.964523 | + | 0.263999i | \(0.914958\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3787 | + | 24.9046i | 0.535489 | + | 0.927494i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.12424 | 0.339334 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.34001 | + | 7.51712i | −0.161184 | + | 0.279179i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.45300 | − | 14.6410i | −0.313505 | − | 0.543006i | 0.665614 | − | 0.746296i | \(-0.268170\pi\) |
−0.979118 | + | 0.203290i | \(0.934836\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.6003 | + | 28.7525i | 0.613983 | + | 1.06345i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.78996 | + | 4.83236i | −0.103050 | + | 0.178487i | −0.912940 | − | 0.408094i | \(-0.866193\pi\) |
0.809890 | + | 0.586582i | \(0.199527\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.521754 | − | 0.903704i | −0.0192452 | − | 0.0333336i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.7330 | + | 18.8768i | 0.469025 | + | 0.695338i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.0394 | + | 29.5131i | 0.626804 | + | 1.08566i | 0.988189 | + | 0.153240i | \(0.0489708\pi\) |
−0.361385 | + | 0.932417i | \(0.617696\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.64240 | − | 6.30882i | 0.133807 | − | 0.231760i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.41801 | + | 2.45606i | 0.0520216 | + | 0.0901040i | 0.890864 | − | 0.454271i | \(-0.150100\pi\) |
−0.838842 | + | 0.544375i | \(0.816767\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.6059 | −0.828215 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.02703 | + | 6.97501i | 0.147341 | + | 0.255202i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.69344 | − | 4.66517i | 0.0984161 | − | 0.170462i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.3321 | 1.87314 | 0.936568 | − | 0.350487i | \(-0.113984\pi\) | ||||
0.936568 | + | 0.350487i | \(0.113984\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.55127 | + | 6.15098i | 0.129415 | + | 0.224154i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.9860 | + | 20.7603i | 0.436215 | + | 0.755546i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.68615 | − | 4.65256i | 0.0976300 | − | 0.169100i | −0.813073 | − | 0.582161i | \(-0.802207\pi\) |
0.910703 | + | 0.413061i | \(0.135541\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.86297 | −0.0676215 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.1411 | 0.766365 | 0.383183 | − | 0.923673i | \(-0.374828\pi\) | ||||
0.383183 | + | 0.923673i | \(0.374828\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.7786 | + | 30.7935i | −0.643629 | + | 1.11480i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.87422 | − | 6.71035i | −0.140073 | − | 0.242613i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.291808 | − | 0.505426i | −0.0105366 | − | 0.0182499i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.0729 | + | 22.6429i | −0.471421 | + | 0.816525i | −0.999465 | − | 0.0326914i | \(-0.989592\pi\) |
0.528044 | + | 0.849217i | \(0.322925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.8699 | + | 22.2912i | −0.463497 | + | 0.802799i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.81636 | − | 11.8063i | 0.245168 | − | 0.424643i | −0.717011 | − | 0.697062i | \(-0.754490\pi\) |
0.962179 | + | 0.272419i | \(0.0878237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.47181 | − | 4.28129i | 0.0887899 | − | 0.153789i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23.7654 | 0.852580 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.6071 | 1.20410 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.86133 | − | 8.42006i | −0.173952 | − | 0.301294i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.34001 | + | 7.51712i | −0.155099 | + | 0.268640i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.2026 | − | 17.6715i | −0.364148 | − | 0.630722i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.31724 | − | 2.28152i | −0.0469544 | − | 0.0813274i | 0.841593 | − | 0.540112i | \(-0.181618\pi\) |
−0.888547 | + | 0.458785i | \(0.848285\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.0417 | −0.571098 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.47327 | − | 14.6761i | −0.301275 | − | 0.521823i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.949983 | + | 1.64542i | −0.0337349 | + | 0.0584306i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.94361 | −0.139866 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.24567 | + | 10.8178i | −0.221233 | + | 0.383186i | −0.955183 | − | 0.296017i | \(-0.904341\pi\) |
0.733950 | + | 0.679204i | \(0.237675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.8751 | 1.62294 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.596874 | 0.0210895 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.4709 | −0.440090 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.63448 | −0.0576078 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.59445 | 0.337741 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.30833 | 0.221789 | 0.110894 | − | 0.993832i | \(-0.464628\pi\) | ||||
0.110894 | + | 0.993832i | \(0.464628\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.06701 | + | 1.84811i | −0.0374677 | + | 0.0648960i | −0.884151 | − | 0.467201i | \(-0.845262\pi\) |
0.846683 | + | 0.532097i | \(0.178596\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.5032 | 0.438505 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.34522 | − | 10.9902i | 0.222263 | − | 0.384971i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.6069 | − | 27.0320i | −0.546017 | − | 0.945730i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.44059 | 0.0852812 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.53897 | − | 16.5220i | −0.332912 | − | 0.576621i | 0.650169 | − | 0.759789i | \(-0.274698\pi\) |
−0.983082 | + | 0.183168i | \(0.941365\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.44047 | + | 7.69112i | 0.154785 | + | 0.268095i | 0.932981 | − | 0.359926i | \(-0.117198\pi\) |
−0.778196 | + | 0.628022i | \(0.783865\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.39089 | + | 2.40909i | −0.0484245 | + | 0.0838736i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.4919 | − | 26.8328i | −0.538706 | − | 0.933066i | −0.998974 | − | 0.0452863i | \(-0.985580\pi\) |
0.460268 | − | 0.887780i | \(-0.347753\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.7142 | −1.13621 | −0.568105 | − | 0.822956i | \(-0.692323\pi\) | ||||
−0.568105 | + | 0.822956i | \(0.692323\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.8143 | 0.860799 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.04278 | + | 7.00231i | −0.140074 | + | 0.242616i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.5026 | + | 19.9231i | −0.398064 | + | 0.689467i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.47181 | − | 4.28129i | 0.0854381 | − | 0.147983i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.4014 | + | 26.6761i | −0.531717 | + | 0.920961i | 0.467597 | + | 0.883942i | \(0.345120\pi\) |
−0.999315 | + | 0.0370195i | \(0.988214\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.1714 | − | 40.1341i | −0.799015 | − | 1.38393i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.54113 | − | 13.0616i | −0.259730 | − | 0.449866i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.00000 | + | 10.3923i | −0.206406 | + | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.96056 | 0.273528 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.28294 | −0.318590 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.26065 | + | 5.64761i | −0.111774 | + | 0.193598i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.63151 | − | 2.82586i | −0.0558619 | − | 0.0967556i | 0.836742 | − | 0.547597i | \(-0.184457\pi\) |
−0.892604 | + | 0.450841i | \(0.851124\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.64240 | + | 6.30882i | 0.124567 | + | 0.215757i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.2395 | 0.588889 | 0.294444 | − | 0.955669i | \(-0.404865\pi\) | ||||
0.294444 | + | 0.955669i | \(0.404865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.2000 | − | 26.3272i | 0.518618 | − | 0.898272i | −0.481148 | − | 0.876639i | \(-0.659780\pi\) |
0.999766 | − | 0.0216329i | \(-0.00688651\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.62962 | + | 9.75078i | 0.191857 | + | 0.332306i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.1827 | −0.721068 | −0.360534 | − | 0.932746i | \(-0.617406\pi\) | ||||
−0.360534 | + | 0.932746i | \(0.617406\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0548381 | + | 0.0949824i | 0.00186455 | + | 0.00322950i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.5192 | + | 37.2724i | −0.730831 | + | 1.26584i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.06467 | − | 13.9684i | −0.273575 | − | 0.473846i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.16541 | − | 0.571092i | 0.276674 | − | 0.0193507i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.689324 | + | 1.19394i | 0.0233301 | + | 0.0404089i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.22030 | + | 2.11362i | −0.0412535 | + | 0.0714532i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.25138 | + | 3.89950i | 0.0760237 | + | 0.131677i | 0.901531 | − | 0.432715i | \(-0.142444\pi\) |
−0.825507 | + | 0.564391i | \(0.809111\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.1448 | −0.915572 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.6781 | + | 20.2271i | 0.393446 | + | 0.681469i | 0.992902 | − | 0.118939i | \(-0.0379494\pi\) |
−0.599455 | + | 0.800408i | \(0.704616\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.52174 | − | 11.2960i | 0.219474 | − | 0.380140i | −0.735173 | − | 0.677879i | \(-0.762899\pi\) |
0.954647 | + | 0.297739i | \(0.0962325\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.583616 | 0.0196180 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.0844 | + | 31.3232i | 0.607216 | + | 1.05173i | 0.991697 | + | 0.128597i | \(0.0410472\pi\) |
−0.384481 | + | 0.923133i | \(0.625619\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.91125 | − | 11.9706i | −0.231796 | − | 0.401482i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.39089 | + | 2.40909i | −0.0465965 | + | 0.0807074i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −43.1300 | −1.44329 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.76914 | 0.0591358 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.334853 | + | 0.579982i | −0.0111804 | + | 0.0193650i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.4553 | + | 37.1618i | 0.715576 | + | 1.23941i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.2784 | + | 26.4630i | 0.508999 | + | 0.881612i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.22872 | − | 9.05641i | 0.174001 | − | 0.301378i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.11125 | − | 1.92475i | 0.0369393 | − | 0.0639807i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.4403 | + | 38.8678i | −0.745119 | + | 1.29058i | 0.205020 | + | 0.978758i | \(0.434274\pi\) |
−0.950139 | + | 0.311826i | \(0.899059\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.79513 | − | 3.10925i | 0.0595407 | − | 0.103127i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.5285 | −1.07772 | −0.538859 | − | 0.842396i | \(-0.681144\pi\) | ||||
−0.538859 | + | 0.842396i | \(0.681144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.4045 | −0.741482 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.949983 | − | 1.64542i | −0.0314055 | − | 0.0543959i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.51056 | − | 7.81252i | 0.148952 | − | 0.257992i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.0584 | − | 41.6703i | −0.793612 | − | 1.37458i | −0.923717 | − | 0.383076i | \(-0.874865\pi\) |
0.130104 | − | 0.991500i | \(-0.458469\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.08212 | + | 8.80248i | 0.167461 | + | 0.290052i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.49513 | −0.115043 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.86878 | + | 8.43298i | 0.160085 | + | 0.277275i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.89146 | + | 10.2043i | −0.193501 | + | 0.335154i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.7251 | 0.417496 | 0.208748 | − | 0.977969i | \(-0.433061\pi\) | ||||
0.208748 | + | 0.977969i | \(0.433061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.80087 | − | 6.58330i | 0.124568 | − | 0.215759i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.6823 | −0.644370 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.5544 | 0.704905 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.3990 | −1.71180 | −0.855900 | − | 0.517142i | \(-0.826996\pi\) | ||||
−0.855900 | + | 0.517142i | \(0.826996\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.5586 | −0.344566 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.413413 | −0.0134769 | −0.00673844 | − | 0.999977i | \(-0.502145\pi\) | ||||
−0.00673844 | + | 0.999977i | \(0.502145\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.08957 | −0.100610 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.22030 | + | 2.11362i | −0.0396962 | + | 0.0687559i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.9156 | −1.03712 | −0.518559 | − | 0.855042i | \(-0.673531\pi\) | ||||
−0.518559 | + | 0.855042i | \(0.673531\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.24155 | + | 3.88247i | −0.0727637 | + | 0.126030i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.5394 | + | 25.1830i | 0.471472 | + | 0.816613i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.8755 | −0.902975 | −0.451487 | − | 0.892278i | \(-0.649106\pi\) | ||||
−0.451487 | + | 0.892278i | \(0.649106\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.43628 | − | 11.1480i | −0.208273 | − | 0.360739i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.0729 | − | 20.9109i | −0.390263 | − | 0.675955i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.3820 | − | 35.3026i | 0.658168 | − | 1.13998i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.28034 | + | 5.68172i | 0.105818 | + | 0.183281i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.20720 | 0.0711260 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.1758 | −0.456335 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.0919 | + | 43.4604i | −0.806900 | + | 1.39759i | 0.108100 | + | 0.994140i | \(0.465523\pi\) |
−0.915001 | + | 0.403452i | \(0.867810\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.2229 | − | 48.8835i | 0.906651 | − | 1.57037i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.8290 | + | 49.9333i | −0.925166 | + | 1.60244i | −0.133873 | + | 0.990999i | \(0.542741\pi\) |
−0.791293 | + | 0.611437i | \(0.790592\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.2479 | − | 33.3384i | 0.617061 | − | 1.06878i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.500000 | + | 0.866025i | 0.0160128 | + | 0.0277350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.3630 | − | 38.7339i | −0.715456 | − | 1.23921i | −0.962783 | − | 0.270274i | \(-0.912886\pi\) |
0.247328 | − | 0.968932i | \(-0.420448\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.830184 | + | 1.43792i | −0.0265328 | + | 0.0459561i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.5691 | −0.465156 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.04840 | −0.0972287 | −0.0486144 | − | 0.998818i | \(-0.515481\pi\) | ||||
−0.0486144 | + | 0.998818i | \(0.515481\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.97300 | − | 5.14939i | 0.0947277 | − | 0.164073i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.22483 | − | 12.5138i | −0.229969 | − | 0.398318i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.43478 | + | 2.48510i | 0.0456232 | + | 0.0790217i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.2961 | −0.390599 | −0.195299 | − | 0.980744i | \(-0.562568\pi\) | ||||
−0.195299 | + | 0.980744i | \(0.562568\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.5362 | + | 25.1775i | −0.461294 | + | 0.798984i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.54607 | + | 6.14197i | 0.112418 | + | 0.194713i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.9271 | 0.504417 | 0.252209 | − | 0.967673i | \(-0.418843\pi\) | ||||
0.252209 | + | 0.967673i | \(0.418843\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.86878 | + | 8.43298i | 0.154041 | + | 0.266808i |
(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 | 4020.2.q.j.841.4 | ✓ | 12 | |
67.29 | even | 3 | inner | 4020.2.q.j.3781.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.j.841.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
4020.2.q.j.3781.4 | yes | 12 | 67.29 | even | 3 | inner |