Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 93 x^{16} + 3429 x^{14} + 64261 x^{12} + 647217 x^{10} + 3386277 x^{8} + 8232133 x^{6} + \cdots + 69312 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 21.3 | ||
Root | \(5.44868i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.21 |
Dual form | 76.3.j.a.29.3 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 2.23630 | − | 2.66512i | 0.745434 | − | 0.888374i | −0.251400 | − | 0.967883i | \(-0.580891\pi\) |
0.996834 | + | 0.0795096i | \(0.0253354\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.62283 | − | 0.590661i | 0.324565 | − | 0.118132i | −0.174599 | − | 0.984640i | \(-0.555863\pi\) |
0.499164 | + | 0.866508i | \(0.333641\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.87959 | − | 3.25555i | −0.268513 | − | 0.465078i | 0.699965 | − | 0.714177i | \(-0.253199\pi\) |
−0.968478 | + | 0.249099i | \(0.919866\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.538989 | − | 3.05676i | −0.0598877 | − | 0.339640i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.58396 | − | 4.47556i | 0.234906 | − | 0.406869i | −0.724339 | − | 0.689444i | \(-0.757855\pi\) |
0.959245 | + | 0.282575i | \(0.0911885\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.02160 | + | 3.60100i | 0.232431 | + | 0.277000i | 0.869635 | − | 0.493694i | \(-0.164354\pi\) |
−0.637205 | + | 0.770695i | \(0.719909\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.05495 | − | 5.64593i | 0.136997 | − | 0.376395i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.43654 | + | 13.8183i | −0.143326 | + | 0.812843i | 0.825370 | + | 0.564593i | \(0.190967\pi\) |
−0.968696 | + | 0.248250i | \(0.920144\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.2978 | + | 15.9673i | 0.541990 | + | 0.840385i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.8798 | − | 2.27105i | −0.613322 | − | 0.108145i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −11.1854 | − | 4.07116i | −0.486323 | − | 0.177007i | 0.0872094 | − | 0.996190i | \(-0.472205\pi\) |
−0.573532 | + | 0.819183i | \(0.694427\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −16.8664 | + | 14.1526i | −0.674657 | + | 0.566104i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.7647 | + | 10.2564i | 0.657951 | + | 0.379868i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −52.5255 | + | 9.26166i | −1.81122 | + | 0.319367i | −0.973837 | − | 0.227246i | \(-0.927028\pi\) |
−0.837385 | + | 0.546613i | \(0.815917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.93716 | − | 2.85047i | 0.159263 | − | 0.0919506i | −0.418250 | − | 0.908332i | \(-0.637356\pi\) |
0.577513 | + | 0.816381i | \(0.304023\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.14938 | − | 16.8953i | −0.186345 | − | 0.511978i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.97317 | − | 4.17299i | −0.142091 | − | 0.119228i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 35.7995i | 0.967555i | 0.875191 | + | 0.483778i | \(0.160736\pi\) | ||||
−0.875191 | + | 0.483778i | \(0.839264\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.3543 | 0.419341 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.8339 | − | 14.1031i | 0.288633 | − | 0.343979i | −0.602171 | − | 0.798367i | \(-0.705698\pi\) |
0.890804 | + | 0.454388i | \(0.150142\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 72.4831 | − | 26.3817i | 1.68565 | − | 0.613528i | 0.691587 | − | 0.722294i | \(-0.256912\pi\) |
0.994067 | + | 0.108766i | \(0.0346898\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.68020 | − | 4.64223i | −0.0595599 | − | 0.103161i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.56111 | − | 37.2099i | −0.139598 | − | 0.791699i | −0.971547 | − | 0.236847i | \(-0.923886\pi\) |
0.831949 | − | 0.554852i | \(-0.187225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.4343 | − | 30.1971i | 0.355802 | − | 0.616266i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 31.3787 | + | 37.3956i | 0.615268 | + | 0.733248i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 16.1770 | − | 44.4460i | 0.305227 | − | 0.838603i | −0.688344 | − | 0.725385i | \(-0.741662\pi\) |
0.993570 | − | 0.113218i | \(-0.0361159\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.54979 | − | 8.78930i | 0.0281780 | − | 0.159806i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 65.5838 | + | 8.26284i | 1.15059 | + | 0.144962i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −86.2842 | − | 15.2142i | −1.46244 | − | 0.257868i | −0.614905 | − | 0.788601i | \(-0.710806\pi\) |
−0.847539 | + | 0.530733i | \(0.821917\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −19.7588 | − | 7.19161i | −0.323915 | − | 0.117895i | 0.174945 | − | 0.984578i | \(-0.444025\pi\) |
−0.498859 | + | 0.866683i | \(0.666248\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.93835 | + | 7.50016i | −0.141879 | + | 0.119050i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.03050 | + | 4.05906i | 0.108162 | + | 0.0624471i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −46.1336 | + | 8.13459i | −0.688560 | + | 0.121412i | −0.506972 | − | 0.861963i | \(-0.669235\pi\) |
−0.181589 | + | 0.983375i | \(0.558124\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −35.8641 | + | 20.7062i | −0.519770 | + | 0.300089i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −30.2932 | − | 83.2298i | −0.426665 | − | 1.17225i | −0.947825 | − | 0.318792i | \(-0.896723\pi\) |
0.521160 | − | 0.853459i | \(-0.325499\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 57.7624 | + | 48.4684i | 0.791266 | + | 0.663951i | 0.946059 | − | 0.323996i | \(-0.105026\pi\) |
−0.154792 | + | 0.987947i | \(0.549471\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 76.6006i | 1.02134i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −19.4272 | −0.252301 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.5650 | + | 12.5908i | −0.133734 | + | 0.159378i | −0.828755 | − | 0.559611i | \(-0.810950\pi\) |
0.695021 | + | 0.718989i | \(0.255395\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 93.3124 | − | 33.9629i | 1.15200 | − | 0.419295i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.5572 | − | 30.4100i | −0.211533 | − | 0.366386i | 0.740662 | − | 0.671878i | \(-0.234512\pi\) |
−0.952194 | + | 0.305493i | \(0.901179\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.20785 | + | 23.8639i | 0.0495042 | + | 0.280752i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −92.7794 | + | 160.699i | −1.06643 | + | 1.84711i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.1327 | + | 21.6097i | 0.203738 | + | 0.242805i | 0.858232 | − | 0.513262i | \(-0.171563\pi\) |
−0.654495 | + | 0.756067i | \(0.727119\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.04386 | − | 16.6054i | 0.0664160 | − | 0.182477i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.44413 | − | 19.5326i | 0.0370337 | − | 0.210028i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 26.1428 | + | 19.8297i | 0.275188 | + | 0.208734i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 39.0070 | + | 6.87798i | 0.402134 | + | 0.0709070i | 0.371057 | − | 0.928610i | \(-0.378995\pi\) |
0.0310764 | + | 0.999517i | \(0.490106\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.0734 | − | 5.48628i | −0.152257 | − | 0.0554170i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −108.963 | + | 91.4309i | −1.07884 | + | 0.905257i | −0.995824 | − | 0.0912913i | \(-0.970901\pi\) |
−0.0830187 | + | 0.996548i | \(0.526456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −65.8869 | − | 38.0398i | −0.639678 | − | 0.369318i | 0.144812 | − | 0.989459i | \(-0.453742\pi\) |
−0.784491 | + | 0.620141i | \(0.787075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −22.2430 | + | 3.92205i | −0.211838 | + | 0.0373528i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −91.1219 | + | 52.6092i | −0.851606 | + | 0.491675i | −0.861193 | − | 0.508279i | \(-0.830282\pi\) |
0.00958612 | + | 0.999954i | \(0.496949\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −57.2122 | − | 157.189i | −0.524882 | − | 1.44210i | −0.865025 | − | 0.501729i | \(-0.832698\pi\) |
0.340142 | − | 0.940374i | \(-0.389525\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 95.4101 | + | 80.0586i | 0.859551 | + | 0.721249i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 121.409i | − | 1.07441i | −0.843451 | − | 0.537207i | \(-0.819480\pi\) | ||
0.843451 | − | 0.537207i | \(-0.180520\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.5567 | −0.178754 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.37879 | − | 11.1772i | 0.0801606 | − | 0.0955317i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 49.5659 | − | 18.0405i | 0.416520 | − | 0.151601i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 47.1463 | + | 81.6597i | 0.389638 | + | 0.674874i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.1223 | − | 63.0777i | −0.0904253 | − | 0.512827i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −40.5991 | + | 70.3197i | −0.324793 | + | 0.562558i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 142.132 | + | 169.387i | 1.11915 | + | 1.33375i | 0.936537 | + | 0.350567i | \(0.114011\pi\) |
0.182614 | + | 0.983185i | \(0.441544\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 91.7837 | − | 252.174i | 0.711502 | − | 1.95484i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 28.1211 | − | 159.483i | 0.214665 | − | 1.21742i | −0.666823 | − | 0.745217i | \(-0.732346\pi\) |
0.881487 | − | 0.472208i | \(-0.156543\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 32.6267 | − | 63.5370i | 0.245313 | − | 0.477722i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 34.8871 | + | 6.15153i | 0.258423 | + | 0.0455669i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 165.933 | + | 60.3948i | 1.21119 | + | 0.440838i | 0.867117 | − | 0.498104i | \(-0.165970\pi\) |
0.344075 | + | 0.938942i | \(0.388192\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 78.7451 | − | 66.0750i | 0.566512 | − | 0.475360i | −0.313975 | − | 0.949431i | \(-0.601661\pi\) |
0.880486 | + | 0.474072i | \(0.157216\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −113.841 | − | 65.7264i | −0.807386 | − | 0.466145i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.9242 | − | 4.21848i | 0.167302 | − | 0.0294999i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −79.7692 | + | 46.0548i | −0.550133 | + | 0.317619i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −41.4905 | − | 113.994i | −0.282248 | − | 0.775471i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 203.127 | + | 170.444i | 1.36327 | + | 1.14392i | 0.974959 | + | 0.222387i | \(0.0713848\pi\) |
0.388308 | + | 0.921530i | \(0.373060\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 81.7629i | − | 0.541476i | −0.962653 | − | 0.270738i | \(-0.912732\pi\) | ||
0.962653 | − | 0.270738i | \(-0.0872677\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 43.5526 | 0.284658 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.32849 | − | 7.54200i | 0.0408290 | − | 0.0486581i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −71.7181 | + | 26.1033i | −0.456803 | + | 0.166263i | −0.560165 | − | 0.828381i | \(-0.689262\pi\) |
0.103362 | + | 0.994644i | \(0.467040\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −82.2772 | − | 142.508i | −0.517467 | − | 0.896278i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.77017 | + | 44.0668i | 0.0482619 | + | 0.273707i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −157.116 | + | 272.133i | −0.963903 | + | 1.66953i | −0.251370 | + | 0.967891i | \(0.580881\pi\) |
−0.712533 | + | 0.701638i | \(0.752452\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −19.9588 | − | 23.7859i | −0.120962 | − | 0.144157i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −25.8348 | + | 70.9804i | −0.154699 | + | 0.425032i | −0.992696 | − | 0.120643i | \(-0.961504\pi\) |
0.837997 | + | 0.545675i | \(0.183727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.5094 | − | 144.671i | 0.150943 | − | 0.856041i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 43.2579 | − | 40.0841i | 0.252970 | − | 0.234410i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −28.4830 | − | 5.02233i | −0.164642 | − | 0.0290308i | 0.0907195 | − | 0.995876i | \(-0.471083\pi\) |
−0.255361 | + | 0.966846i | \(0.582194\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 77.7765 | + | 28.3083i | 0.444437 | + | 0.161762i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −233.505 | + | 195.934i | −1.31924 | + | 1.10697i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −152.955 | − | 88.3085i | −0.854496 | − | 0.493344i | 0.00766916 | − | 0.999971i | \(-0.497559\pi\) |
−0.862165 | + | 0.506627i | \(0.830892\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −198.928 | + | 35.0764i | −1.09905 | + | 0.193792i | −0.693626 | − | 0.720335i | \(-0.743988\pi\) |
−0.405426 | + | 0.914128i | \(0.632877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −63.3532 | + | 36.5770i | −0.346192 | + | 0.199874i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.1454 | + | 58.0965i | 0.114299 | + | 0.314035i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 55.5488 | + | 46.6110i | 0.297052 | + | 0.249257i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 77.1116i | − | 0.407998i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 35.5679 | 0.186219 | 0.0931097 | − | 0.995656i | \(-0.470319\pi\) | ||||
0.0931097 | + | 0.995656i | \(0.470319\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.5263 | + | 30.4210i | −0.132260 | + | 0.157622i | −0.828110 | − | 0.560566i | \(-0.810584\pi\) |
0.695849 | + | 0.718188i | \(0.255028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 26.5402 | − | 9.65985i | 0.136104 | − | 0.0495377i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 172.127 | + | 298.132i | 0.873739 | + | 1.51336i | 0.858100 | + | 0.513483i | \(0.171645\pi\) |
0.0156396 | + | 0.999878i | \(0.495022\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.9894 | − | 73.6666i | −0.0652735 | − | 0.370184i | −0.999894 | − | 0.0145385i | \(-0.995372\pi\) |
0.934621 | − | 0.355646i | \(-0.115739\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −81.4889 | + | 141.143i | −0.405417 | + | 0.702203i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 128.878 | + | 153.591i | 0.634868 | + | 0.756606i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.8743 | − | 29.8768i | 0.0530452 | − | 0.145740i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.41574 | + | 36.3855i | −0.0309939 | + | 0.175775i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 98.0718 | − | 4.82945i | 0.469243 | − | 0.0231074i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.9068 | − | 2.09948i | −0.0564301 | − | 0.00995015i | 0.145362 | − | 0.989379i | \(-0.453565\pi\) |
−0.201792 | + | 0.979428i | \(0.564676\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −289.562 | − | 105.392i | −1.35945 | − | 0.494798i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 102.045 | − | 85.6259i | 0.474628 | − | 0.398260i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.5597 | − | 10.7154i | −0.0855284 | − | 0.0493799i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 258.349 | − | 45.5538i | 1.17967 | − | 0.208008i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −57.1221 | + | 32.9794i | −0.258471 | + | 0.149228i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −77.1612 | − | 211.999i | −0.346014 | − | 0.950667i | −0.983612 | − | 0.180297i | \(-0.942294\pi\) |
0.637598 | − | 0.770369i | \(-0.279928\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 52.3520 | + | 43.9285i | 0.232675 | + | 0.195238i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 99.1388i | 0.436735i | 0.975867 | + | 0.218367i | \(0.0700731\pi\) | ||||
−0.975867 | + | 0.218367i | \(0.929927\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −73.3690 | −0.320389 | −0.160194 | − | 0.987086i | \(-0.551212\pi\) | ||||
−0.160194 | + | 0.987086i | \(0.551212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −43.4450 | + | 51.7758i | −0.188074 | + | 0.224138i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 96.3134 | − | 35.0552i | 0.413362 | − | 0.150452i | −0.126964 | − | 0.991907i | \(-0.540523\pi\) |
0.540326 | + | 0.841456i | \(0.318301\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −32.6260 | − | 56.5098i | −0.138834 | − | 0.240467i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.92965 | + | 56.3139i | 0.0418973 | + | 0.237611i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 103.142 | − | 178.648i | 0.431558 | − | 0.747481i | −0.565449 | − | 0.824783i | \(-0.691297\pi\) |
0.997008 | + | 0.0773020i | \(0.0246306\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −201.345 | − | 239.954i | −0.835457 | − | 0.995659i | −0.999957 | − | 0.00928168i | \(-0.997046\pi\) |
0.164500 | − | 0.986377i | \(-0.447399\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 55.0170 | − | 151.158i | 0.226407 | − | 0.622049i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.4566 | − | 59.3023i | 0.0426800 | − | 0.242050i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.3825 | + | 85.3292i | −0.106812 | + | 0.345462i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −120.310 | − | 21.2138i | −0.483171 | − | 0.0851961i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 197.035 | + | 71.7149i | 0.785001 | + | 0.285717i | 0.703256 | − | 0.710937i | \(-0.251729\pi\) |
0.0817443 | + | 0.996653i | \(0.473951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −47.1235 | + | 39.5413i | −0.186259 | + | 0.156290i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 73.0103 | + | 42.1525i | 0.286315 | + | 0.165304i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −150.440 | + | 26.5267i | −0.585371 | + | 0.103217i | −0.458487 | − | 0.888701i | \(-0.651609\pi\) |
−0.126884 | + | 0.991918i | \(0.540497\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 116.547 | − | 67.2885i | 0.449989 | − | 0.259801i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 56.6213 | + | 155.566i | 0.216940 | + | 0.596038i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −123.404 | − | 103.548i | −0.469216 | − | 0.393719i | 0.377293 | − | 0.926094i | \(-0.376855\pi\) |
−0.846508 | + | 0.532375i | \(0.821299\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 81.6832i | − | 0.308239i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 98.1424 | 0.367575 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 278.090 | − | 331.415i | 1.03379 | − | 1.23203i | 0.0615377 | − | 0.998105i | \(-0.480400\pi\) |
0.972255 | − | 0.233922i | \(-0.0751560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 301.996 | − | 109.918i | 1.11438 | − | 0.405600i | 0.281779 | − | 0.959479i | \(-0.409075\pi\) |
0.832597 | + | 0.553879i | \(0.186853\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −30.7394 | − | 53.2422i | −0.112599 | − | 0.195026i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.7586 | + | 112.056i | 0.0718494 | + | 0.407478i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 187.838 | − | 325.345i | 0.678115 | − | 1.17453i | −0.297433 | − | 0.954743i | \(-0.596131\pi\) |
0.975548 | − | 0.219787i | \(-0.0705361\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.3743 | − | 13.5553i | −0.0407680 | − | 0.0485854i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −78.1955 | + | 214.840i | −0.278276 | + | 0.764556i | 0.719283 | + | 0.694718i | \(0.244471\pi\) |
−0.997558 | + | 0.0698386i | \(0.977752\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.5662 | + | 122.308i | −0.0762058 | + | 0.432184i | 0.922704 | + | 0.385508i | \(0.125974\pi\) |
−0.998910 | + | 0.0466759i | \(0.985137\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 111.312 | − | 25.3286i | 0.390568 | − | 0.0888724i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −68.1564 | − | 12.0178i | −0.237479 | − | 0.0418739i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 86.5617 | + | 31.5059i | 0.299521 | + | 0.109017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 105.562 | − | 88.5770i | 0.362756 | − | 0.304388i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 351.093 | + | 202.704i | 1.19827 | + | 0.691821i | 0.960169 | − | 0.279419i | \(-0.0901419\pi\) |
0.238100 | + | 0.971241i | \(0.423475\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −149.011 | + | 26.2746i | −0.505121 | + | 0.0890665i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 91.8066 | − | 53.0046i | 0.309113 | − | 0.178467i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.1376 | − | 52.5802i | −0.0640054 | − | 0.175853i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −222.125 | − | 186.385i | −0.737958 | − | 0.619221i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 494.867i | 1.63322i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −36.3129 | −0.119059 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −256.739 | + | 305.969i | −0.836283 | + | 0.996643i | 0.163666 | + | 0.986516i | \(0.447668\pi\) |
−0.999949 | + | 0.0101272i | \(0.996776\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −248.724 | + | 90.5280i | −0.804931 | + | 0.292971i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −236.487 | − | 409.607i | −0.760407 | − | 1.31706i | −0.942641 | − | 0.333808i | \(-0.891666\pi\) |
0.182234 | − | 0.983255i | \(-0.441667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −47.1130 | − | 267.191i | −0.150521 | − | 0.853646i | −0.962767 | − | 0.270332i | \(-0.912867\pi\) |
0.812246 | − | 0.583314i | \(-0.198244\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.0753 | + | 17.4510i | −0.0319852 | + | 0.0554000i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 174.153 | + | 207.547i | 0.549378 | + | 0.654724i | 0.967263 | − | 0.253777i | \(-0.0816728\pi\) |
−0.417885 | + | 0.908500i | \(0.637228\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −94.2728 | + | 259.013i | −0.295526 | + | 0.811951i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −63.5661 | + | 360.501i | −0.198025 | + | 1.12306i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −245.733 | + | 103.393i | −0.760782 | + | 0.320103i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −101.927 | − | 17.9725i | −0.313622 | − | 0.0553000i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −546.872 | − | 199.045i | −1.67239 | − | 0.608701i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −108.806 | + | 91.2993i | −0.330718 | + | 0.277506i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 237.042 | + | 136.856i | 0.716139 | + | 0.413463i | 0.813330 | − | 0.581803i | \(-0.197652\pi\) |
−0.0971909 | + | 0.995266i | \(0.530986\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 109.431 | − | 19.2956i | 0.328621 | − | 0.0579447i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −70.0620 | + | 40.4503i | −0.209140 | + | 0.120747i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 123.097 | + | 338.206i | 0.365272 | + | 1.00358i | 0.977136 | + | 0.212614i | \(0.0681978\pi\) |
−0.611864 | + | 0.790963i | \(0.709580\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −323.569 | − | 271.507i | −0.954480 | − | 0.800904i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 29.4620i | − | 0.0863990i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −315.277 | −0.919175 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −45.9710 | + | 54.7861i | −0.133249 | + | 0.158800i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −143.155 | + | 52.1043i | −0.412552 | + | 0.150156i | −0.539954 | − | 0.841695i | \(-0.681558\pi\) |
0.127402 | + | 0.991851i | \(0.459336\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 162.592 | + | 281.617i | 0.465879 | + | 0.806927i | 0.999241 | − | 0.0389607i | \(-0.0124047\pi\) |
−0.533361 | + | 0.845888i | \(0.679071\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.7443 | + | 94.9614i | 0.0477045 | + | 0.270545i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 303.741 | − | 526.095i | 0.860456 | − | 1.49035i | −0.0110341 | − | 0.999939i | \(-0.503512\pi\) |
0.871490 | − | 0.490414i | \(-0.163154\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −98.3212 | − | 117.175i | −0.276961 | − | 0.330069i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 62.7642 | − | 172.443i | 0.175810 | − | 0.483034i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −58.4549 | + | 331.514i | −0.162827 | + | 0.923438i | 0.788449 | + | 0.615100i | \(0.210884\pi\) |
−0.951277 | + | 0.308339i | \(0.900227\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −148.910 | + | 328.857i | −0.412494 | + | 0.910960i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 323.066 | + | 56.9653i | 0.889990 | + | 0.156929i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 122.367 | + | 44.5379i | 0.335252 | + | 0.122022i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 335.139 | − | 281.215i | 0.913186 | − | 0.766254i | −0.0595366 | − | 0.998226i | \(-0.518962\pi\) |
0.972722 | + | 0.231972i | \(0.0745178\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −49.4883 | − | 28.5721i | −0.134115 | − | 0.0774311i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −175.102 | + | 30.8752i | −0.471973 | + | 0.0832216i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 467.732 | − | 270.045i | 1.25397 | − | 0.723981i | 0.282076 | − | 0.959392i | \(-0.408977\pi\) |
0.971896 | + | 0.235411i | \(0.0756436\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 96.6187 | + | 265.458i | 0.257650 | + | 0.707887i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −192.062 | − | 161.159i | −0.509448 | − | 0.427478i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 333.773i | 0.880668i | 0.897834 | + | 0.440334i | \(0.145140\pi\) | ||||
−0.897834 | + | 0.440334i | \(0.854860\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 769.286 | 2.01912 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.9067 | + | 16.5733i | −0.0363099 | + | 0.0432724i | −0.783894 | − | 0.620895i | \(-0.786769\pi\) |
0.747584 | + | 0.664167i | \(0.231214\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.5270 | + | 11.4749i | −0.0818882 | + | 0.0298049i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −119.710 | − | 207.344i | −0.309329 | − | 0.535773i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.22122 | − | 18.2685i | −0.00828078 | − | 0.0469626i | 0.980387 | − | 0.197080i | \(-0.0631459\pi\) |
−0.988668 | + | 0.150117i | \(0.952035\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 83.5105 | − | 144.644i | 0.213582 | − | 0.369934i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −362.153 | − | 431.597i | −0.921509 | − | 1.09821i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.70821 | + | 26.6731i | −0.0245777 | + | 0.0675268i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.77687 | + | 55.4474i | −0.0246269 | + | 0.139666i | −0.994642 | − | 0.103378i | \(-0.967035\pi\) |
0.970015 | + | 0.243044i | \(0.0781460\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −96.3707 | − | 229.042i | −0.241531 | − | 0.574040i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.0196 | − | 6.52756i | −0.0923183 | − | 0.0162782i | 0.127298 | − | 0.991864i | \(-0.459369\pi\) |
−0.219616 | + | 0.975586i | \(0.570481\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.1827 | + | 9.16574i | 0.0624880 | + | 0.0227438i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 131.369 | − | 110.232i | 0.324369 | − | 0.272178i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 160.223 | + | 92.5048i | 0.393668 | + | 0.227284i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.2294 | + | 2.33270i | −0.0323457 | + | 0.00570342i | −0.189798 | − | 0.981823i | \(-0.560783\pi\) |
0.157452 | + | 0.987527i | \(0.449672\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 532.037 | − | 307.171i | 1.29449 | − | 0.747376i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 112.648 | + | 309.499i | 0.272756 | + | 0.749392i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −46.4543 | − | 38.9798i | −0.111938 | − | 0.0939273i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 357.629i | − | 0.857623i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −784.559 | −1.87245 | −0.936227 | − | 0.351395i | \(-0.885708\pi\) | ||||
−0.936227 | + | 0.351395i | \(0.885708\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 349.429 | − | 416.434i | 0.829998 | − | 0.989153i | −0.169995 | − | 0.985445i | \(-0.554375\pi\) |
0.999993 | − | 0.00370830i | \(-0.00118039\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −110.205 | + | 40.1115i | −0.260533 | + | 0.0948261i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −154.470 | − | 267.549i | −0.363458 | − | 0.629528i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.7258 | + | 77.8430i | 0.0321448 | + | 0.182302i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 42.2590 | − | 73.1947i | 0.0985057 | − | 0.170617i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −222.339 | − | 264.974i | −0.515868 | − | 0.614788i | 0.443730 | − | 0.896160i | \(-0.353655\pi\) |
−0.959599 | + | 0.281373i | \(0.909210\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −185.662 | + | 510.102i | −0.428781 | + | 1.17807i | 0.517773 | + | 0.855518i | \(0.326761\pi\) |
−0.946553 | + | 0.322547i | \(0.895461\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −55.6465 | + | 315.587i | −0.127923 | + | 0.725488i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −50.1798 | − | 220.525i | −0.114828 | − | 0.504635i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 496.329 | + | 87.5162i | 1.13059 | + | 0.199354i | 0.707486 | − | 0.706727i | \(-0.249829\pi\) |
0.423104 | + | 0.906081i | \(0.360940\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −101.702 | − | 37.0165i | −0.230617 | − | 0.0839377i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 308.416 | − | 258.791i | 0.696198 | − | 0.584179i | −0.224491 | − | 0.974476i | \(-0.572072\pi\) |
0.920689 | + | 0.390297i | \(0.127628\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 42.1901 | + | 24.3585i | 0.0948093 | + | 0.0547382i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 908.505 | − | 160.194i | 2.03245 | − | 0.358376i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −411.423 | + | 237.535i | −0.916309 | + | 0.529031i | −0.882456 | − | 0.470396i | \(-0.844111\pi\) |
−0.0338533 | + | 0.999427i | \(0.510778\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.5409 | − | 89.4055i | −0.0721528 | − | 0.198238i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −217.908 | − | 182.846i | −0.481033 | − | 0.403635i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 30.5175i | − | 0.0670714i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 169.918 | 0.371813 | 0.185906 | − | 0.982567i | \(-0.440478\pi\) | ||||
0.185906 | + | 0.982567i | \(0.440478\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −185.011 | + | 220.488i | −0.403075 | + | 0.480366i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −647.342 | + | 235.613i | −1.40421 | + | 0.511091i | −0.929426 | − | 0.369010i | \(-0.879697\pi\) |
−0.474786 | + | 0.880101i | \(0.657475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 324.936 | + | 562.805i | 0.701805 | + | 1.21556i | 0.967832 | + | 0.251596i | \(0.0809554\pi\) |
−0.266028 | + | 0.963965i | \(0.585711\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.94793 | − | 33.7324i | −0.0127913 | − | 0.0725428i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 368.835 | − | 638.841i | 0.789797 | − | 1.36797i | −0.136294 | − | 0.990668i | \(-0.543519\pi\) |
0.926091 | − | 0.377300i | \(-0.123147\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 113.195 | + | 134.900i | 0.241353 | + | 0.287634i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −90.8150 | + | 249.512i | −0.192813 | + | 0.529750i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 69.2210 | − | 392.572i | 0.146345 | − | 0.829962i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −399.666 | − | 123.571i | −0.841403 | − | 0.260149i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −144.580 | − | 25.4933i | −0.303103 | − | 0.0534452i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 356.818 | + | 129.871i | 0.744923 | + | 0.271130i | 0.686468 | − | 0.727160i | \(-0.259160\pi\) |
0.0584553 | + | 0.998290i | \(0.481383\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −128.914 | + | 108.172i | −0.268013 | + | 0.224890i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 134.820 | + | 77.8382i | 0.279130 | + | 0.161156i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 67.3641 | − | 11.8781i | 0.138895 | − | 0.0244910i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −92.9634 | + | 53.6724i | −0.190890 | + | 0.110210i | −0.592399 | − | 0.805645i | \(-0.701819\pi\) |
0.401509 | + | 0.915855i | \(0.368486\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 373.909 | + | 1027.31i | 0.764640 | + | 2.10083i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 91.7009 | + | 76.9462i | 0.186763 | + | 0.156713i | 0.731376 | − | 0.681975i | \(-0.238879\pi\) |
−0.544612 | + | 0.838688i | \(0.683323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 748.381i | − | 1.51801i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −27.7021 | −0.0559639 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −214.020 | + | 255.059i | −0.430623 | + | 0.513197i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −419.529 | + | 152.696i | −0.840740 | + | 0.306004i | −0.726259 | − | 0.687421i | \(-0.758743\pi\) |
−0.114481 | + | 0.993425i | \(0.536520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 131.397 | + | 227.586i | 0.262270 | + | 0.454264i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.3025 | + | 171.854i | 0.0602435 | + | 0.341658i | 1.00000 | 0.000186740i | \(-5.94411e-5\pi\) | |
−0.939756 | + | 0.341845i | \(0.888948\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −122.824 | + | 212.737i | −0.243215 | + | 0.421261i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −328.519 | − | 391.514i | −0.647966 | − | 0.772216i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −331.344 | + | 910.361i | −0.650971 | + | 1.78853i | −0.0368442 | + | 0.999321i | \(0.511731\pi\) |
−0.614127 | + | 0.789207i | \(0.710492\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 49.2215 | − | 279.149i | 0.0963239 | − | 0.546280i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.1694 | + | 389.273i | 0.0373672 | + | 0.758817i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −129.392 | − | 22.8152i | −0.251246 | − | 0.0443014i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −183.489 | − | 66.7844i | −0.354910 | − | 0.129177i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −77.0818 | + | 64.6793i | −0.148520 | + | 0.124623i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −847.732 | − | 489.438i | −1.62713 | − | 0.939421i | −0.984945 | − | 0.172867i | \(-0.944697\pi\) |
−0.642180 | − | 0.766554i | \(-0.721970\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 467.583 | − | 82.4475i | 0.894040 | − | 0.157643i | 0.292292 | − | 0.956329i | \(-0.405582\pi\) |
0.601748 | + | 0.798686i | \(0.294471\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 249.377 | − | 143.978i | 0.475003 | − | 0.274243i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.3591 | + | 75.1686i | 0.0519148 | + | 0.142635i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −296.698 | − | 248.959i | −0.560866 | − | 0.470622i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 271.951i | 0.512148i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 86.5428 | 0.162369 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −116.801 | + | 139.198i | −0.218319 | + | 0.260183i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −577.406 | + | 210.159i | −1.07524 | + | 0.391357i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −90.0991 | − | 156.056i | −0.167160 | − | 0.289529i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 174.061 | + | 987.148i | 0.321739 | + | 1.82467i | 0.531665 | + | 0.846955i | \(0.321567\pi\) |
−0.209926 | + | 0.977717i | \(0.567322\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −351.381 | + | 608.610i | −0.647110 | + | 1.12083i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −185.691 | − | 221.298i | −0.340717 | − | 0.406051i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 190.375 | − | 523.051i | 0.348035 | − | 0.956218i | −0.634954 | − | 0.772550i | \(-0.718981\pi\) |
0.982988 | − | 0.183667i | \(-0.0587969\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.3333 | + | 64.2741i | −0.0206435 | + | 0.117075i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −688.781 | − | 743.316i | −1.25006 | − | 1.34903i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 60.8479 | + | 10.7291i | 0.110032 | + | 0.0194017i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 202.122 | + | 73.5662i | 0.364183 | + | 0.132552i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 441.858 | − | 370.763i | 0.793282 | − | 0.665642i | −0.153274 | − | 0.988184i | \(-0.548982\pi\) |
0.946555 | + | 0.322541i | \(0.104537\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 314.015 | + | 181.297i | 0.561745 | + | 0.324324i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 248.448 | − | 43.8080i | 0.442866 | − | 0.0780892i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −217.337 | + | 125.479i | −0.386033 | + | 0.222876i | −0.680440 | − | 0.732804i | \(-0.738211\pi\) |
0.294407 | + | 0.955680i | \(0.404878\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −71.7114 | − | 197.025i | −0.126923 | − | 0.348717i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −285.957 | − | 239.946i | −0.504333 | − | 0.423186i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 336.315i | − | 0.591063i | −0.955333 | − | 0.295532i | \(-0.904503\pi\) | ||
0.955333 | − | 0.295532i | \(-0.0954967\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.08871 | 0.0141659 | 0.00708294 | − | 0.999975i | \(-0.497745\pi\) | ||||
0.00708294 | + | 0.999975i | \(0.497745\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 79.5406 | − | 94.7928i | 0.138814 | − | 0.165432i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 246.276 | − | 89.6370i | 0.428306 | − | 0.155891i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 282.888 | + | 489.976i | 0.490274 | + | 0.849179i | 0.999937 | − | 0.0111946i | \(-0.00356343\pi\) |
−0.509663 | + | 0.860374i | \(0.670230\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 23.9913 | + | 136.061i | 0.0414357 | + | 0.234993i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −66.0008 | + | 114.317i | −0.113599 | + | 0.196759i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −157.120 | − | 187.248i | −0.269502 | − | 0.321180i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.61822 | − | 23.6784i | 0.0147320 | − | 0.0404758i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 52.0032 | − | 294.925i | 0.0885915 | − | 0.502427i | −0.907932 | − | 0.419117i | \(-0.862340\pi\) |
0.996524 | − | 0.0833102i | \(-0.0265492\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 96.3562 | + | 49.4796i | 0.163593 | + | 0.0840061i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1179.49 | + | 207.975i | 1.99574 | + | 0.351904i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 744.241 | + | 270.882i | 1.25504 | + | 0.456799i | 0.882103 | − | 0.471056i | \(-0.156127\pi\) |
0.372941 | + | 0.927855i | \(0.378349\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 69.7811 | − | 58.5533i | 0.117279 | − | 0.0984089i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −225.379 | − | 130.123i | −0.377519 | − | 0.217961i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 682.243 | − | 120.298i | 1.13897 | − | 0.200831i | 0.427815 | − | 0.903866i | \(-0.359283\pi\) |
0.711155 | + | 0.703035i | \(0.248172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 582.555 | − | 336.338i | 0.969309 | − | 0.559631i | 0.0702836 | − | 0.997527i | \(-0.477610\pi\) |
0.899026 | + | 0.437896i | \(0.144276\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 49.7310 | + | 136.635i | 0.0824726 | + | 0.226592i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 124.743 | + | 104.672i | 0.206187 | + | 0.173012i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 655.314i | − | 1.07960i | −0.841795 | − | 0.539798i | \(-0.818501\pi\) | ||
0.841795 | − | 0.539798i | \(-0.181499\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 697.549 | 1.14540 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 114.168 | − | 136.060i | 0.186854 | − | 0.222684i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −744.718 | + | 271.055i | −1.21487 | + | 0.442178i | −0.868392 | − | 0.495879i | \(-0.834846\pi\) |
−0.346482 | + | 0.938057i | \(0.612624\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −55.3071 | − | 95.7948i | −0.0899303 | − | 0.155764i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −143.509 | − | 813.879i | −0.232591 | − | 1.31909i | −0.847628 | − | 0.530592i | \(-0.821970\pi\) |
0.615036 | − | 0.788499i | \(-0.289141\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 117.442 | − | 203.416i | 0.189729 | − | 0.328621i | −0.755431 | − | 0.655229i | \(-0.772572\pi\) |
0.945160 | + | 0.326608i | \(0.105906\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −156.950 | − | 187.046i | −0.252737 | − | 0.301201i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.2693 | − | 99.6490i | 0.0582171 | − | 0.159950i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 71.2325 | − | 403.979i | 0.113972 | − | 0.646367i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 206.447 | − | 272.173i | 0.329262 | − | 0.434088i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −494.690 | − | 87.2272i | −0.786470 | − | 0.138676i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −259.957 | − | 94.6165i | −0.411976 | − | 0.149947i | 0.127714 | − | 0.991811i | \(-0.459236\pi\) |
−0.539689 | + | 0.841864i | \(0.681458\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.2225 | + | 27.0379i | −0.0509044 | + | 0.0427138i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 330.706 | + | 190.933i | 0.520797 | + | 0.300682i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 161.419 | − | 28.4625i | 0.253405 | − | 0.0446821i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −238.086 | + | 137.459i | −0.372592 | + | 0.215116i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 176.948 | + | 486.162i | 0.276050 | + | 0.758442i | 0.997800 | + | 0.0662886i | \(0.0211158\pi\) |
−0.721750 | + | 0.692154i | \(0.756662\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 198.821 | + | 166.830i | 0.309208 | + | 0.259456i | 0.784165 | − | 0.620553i | \(-0.213092\pi\) |
−0.474957 | + | 0.880009i | \(0.657536\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 463.447i | − | 0.718523i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −922.026 | −1.42508 | −0.712539 | − | 0.701632i | \(-0.752455\pi\) | ||||
−0.712539 | + | 0.701632i | \(0.752455\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −291.048 | + | 346.857i | −0.448455 | + | 0.534448i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −70.0629 | + | 25.5008i | −0.107624 | + | 0.0391718i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −54.7347 | − | 94.8034i | −0.0838204 | − | 0.145181i | 0.821068 | − | 0.570831i | \(-0.193379\pi\) |
−0.904888 | + | 0.425650i | \(0.860046\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −48.5644 | − | 275.423i | −0.0741442 | − | 0.420493i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 117.023 | − | 202.690i | 0.178117 | − | 0.308508i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 396.936 | + | 473.050i | 0.602330 | + | 0.717829i | 0.977925 | − | 0.208954i | \(-0.0670061\pi\) |
−0.375595 | + | 0.926784i | \(0.622562\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −107.714 | + | 295.941i | −0.162956 | + | 0.447717i | −0.994117 | − | 0.108315i | \(-0.965455\pi\) |
0.831161 | + | 0.556032i | \(0.187677\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −39.8480 | + | 225.989i | −0.0601026 | + | 0.340859i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.4186 | − | 122.381i | 0.0231859 | − | 0.184031i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 625.225 | + | 110.244i | 0.937370 | + | 0.165284i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −737.558 | − | 268.449i | −1.10248 | − | 0.401269i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −83.2425 | + | 69.8488i | −0.124057 | + | 0.104097i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −520.089 | − | 300.274i | −0.772793 | − | 0.446172i | 0.0610773 | − | 0.998133i | \(-0.480546\pi\) |
−0.833870 | + | 0.551961i | \(0.813880\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −444.782 | + | 78.4270i | −0.658936 | + | 0.116188i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −473.739 | + | 273.513i | −0.699762 | + | 0.404008i | −0.807259 | − | 0.590198i | \(-0.799050\pi\) |
0.107497 | + | 0.994205i | \(0.465716\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −50.9255 | − | 139.917i | −0.0750008 | − | 0.206063i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 264.217 | + | 221.704i | 0.387984 | + | 0.325557i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 970.166i | 1.42045i | 0.703976 | + | 0.710224i | \(0.251406\pi\) | ||||
−0.703976 | + | 0.710224i | \(0.748594\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 304.954 | 0.445188 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −164.075 | + | 195.537i | −0.238829 | + | 0.284625i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 208.930 | − | 76.0444i | 0.303237 | − | 0.110369i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −372.204 | − | 644.676i | −0.538646 | − | 0.932961i | −0.998977 | − | 0.0452145i | \(-0.985603\pi\) |
0.460332 | − | 0.887747i | \(-0.347730\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.4710 | + | 59.3843i | 0.0151097 | + | 0.0856916i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 88.7618 | − | 153.740i | 0.127715 | − | 0.221209i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 166.048 | + | 197.888i | 0.238232 | + | 0.283914i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 121.959 | − | 335.081i | 0.174477 | − | 0.479372i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −94.2397 | + | 534.460i | −0.134436 | + | 0.762425i | 0.840815 | + | 0.541323i | \(0.182076\pi\) |
−0.975251 | + | 0.221102i | \(0.929035\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −571.623 | + | 368.657i | −0.813119 | + | 0.524405i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −223.567 | − | 39.4209i | −0.317116 | − | 0.0559162i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 502.464 | + | 182.882i | 0.710698 | + | 0.258673i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 126.356 | − | 106.025i | 0.178217 | − | 0.149542i | −0.549315 | − | 0.835615i | \(-0.685111\pi\) |
0.727533 | + | 0.686073i | \(0.240667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 44.1816 | + | 25.5083i | 0.0621401 | + | 0.0358766i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −66.8290 | + | 11.7837i | −0.0937292 | + | 0.0165270i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.3331 | − | 20.9769i | 0.0508156 | − | 0.0293384i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −245.461 | − | 674.398i | −0.342344 | − | 0.940583i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 812.523 | + | 681.788i | 1.13007 | + | 0.948245i | 0.999069 | − | 0.0431372i | \(-0.0137353\pi\) |
0.131005 | + | 0.991382i | \(0.458180\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 285.997i | 0.396667i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1089.77 | −1.50729 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 754.840 | − | 899.583i | 1.04116 | − | 1.24080i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 562.409 | − | 204.700i | 0.773603 | − | 0.281568i | 0.0751003 | − | 0.997176i | \(-0.476072\pi\) |
0.698503 | + | 0.715608i | \(0.253850\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 167.035 | + | 289.313i | 0.229129 | + | 0.396862i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 187.943 | + | 1065.88i | 0.257104 | + | 1.45811i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −364.997 | + | 632.193i | −0.497949 | + | 0.862474i | −0.999997 | − | 0.00236619i | \(-0.999247\pi\) |
0.502048 | + | 0.864840i | \(0.332580\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −134.664 | − | 160.486i | −0.183216 | − | 0.218348i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −82.8006 | + | 227.493i | −0.112348 | + | 0.308674i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −104.267 | + | 591.327i | −0.141092 | + | 0.800172i | 0.829330 | + | 0.558758i | \(0.188722\pi\) |
−0.970422 | + | 0.241413i | \(0.922389\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 168.414 | + | 261.134i | 0.227279 | + | 0.352408i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −473.851 | − | 83.5527i | −0.637753 | − | 0.112453i | −0.154583 | − | 0.987980i | \(-0.549404\pi\) |
−0.483170 | + | 0.875527i | \(0.660515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 430.314 | + | 156.621i | 0.577602 | + | 0.210230i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −83.4929 | + | 70.0589i | −0.111771 | + | 0.0937870i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 342.544 | + | 197.768i | 0.457335 | + | 0.264042i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1264.86 | + | 223.029i | −1.68423 | + | 0.296975i | −0.932144 | − | 0.362088i | \(-0.882064\pi\) |
−0.752087 | + | 0.659063i | \(0.770953\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 631.759 | − | 364.746i | 0.838989 | − | 0.484391i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −48.2941 | − | 132.687i | −0.0639657 | − | 0.175744i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −861.349 | − | 722.757i | −1.13784 | − | 0.954765i | −0.138479 | − | 0.990365i | \(-0.544221\pi\) |
−0.999366 | + | 0.0356002i | \(0.988666\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 214.016i | 0.281971i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 464.910 | 0.610920 | 0.305460 | − | 0.952205i | \(-0.401190\pi\) | ||||
0.305460 | + | 0.952205i | \(0.401190\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −404.201 | + | 481.708i | −0.529753 | + | 0.631335i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 70.6783 | − | 25.7248i | 0.0923900 | − | 0.0336272i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −205.930 | − | 356.681i | −0.268487 | − | 0.465034i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −90.2830 | − | 512.020i | −0.117403 | − | 0.665826i | −0.985532 | − | 0.169488i | \(-0.945789\pi\) |
0.868129 | − | 0.496338i | \(-0.165322\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −265.733 | + | 460.263i | −0.344660 | + | 0.596969i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 670.945 | + | 799.601i | 0.867975 | + | 1.03441i | 0.999073 | + | 0.0430433i | \(0.0137053\pi\) |
−0.131098 | + | 0.991369i | \(0.541850\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.9306 | + | 117.951i | −0.0553943 | + | 0.152195i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 81.3025 | − | 461.089i | 0.104636 | − | 0.593423i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 347.053 | + | 43.7248i | 0.445511 | + | 0.0561294i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −450.776 | − | 79.4841i | −0.577179 | − | 0.101772i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1028.09 | − | 374.194i | −1.31301 | − | 0.477898i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −100.968 | + | 84.7221i | −0.128622 | + | 0.107926i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −265.038 | − | 153.020i | −0.336770 | − | 0.194434i | 0.322073 | − | 0.946715i | \(-0.395620\pi\) |
−0.658843 | + | 0.752281i | \(0.728954\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −551.936 | + | 97.3212i | −0.699538 | + | 0.123348i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −395.252 | + | 228.199i | −0.499686 | + | 0.288494i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.8061 | − | 92.8816i | −0.0426307 | − | 0.117127i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −217.696 | − | 182.668i | −0.273831 | − | 0.229772i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 629.223i | 0.789489i | 0.918791 | + | 0.394745i | \(0.129167\pi\) | ||||
−0.918791 | + | 0.394745i | \(0.870833\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 530.165 | 0.663535 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 56.2822 | − | 67.0746i | 0.0702650 | − | 0.0837385i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 366.179 | − | 133.278i | 0.456014 | − | 0.165976i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.6382 | + | 66.9233i | 0.0479977 | + | 0.0831345i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −261.367 | − | 1482.29i | −0.323875 | − | 1.83679i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 508.334 | − | 880.460i | 0.628349 | − | 1.08833i | −0.359534 | − | 0.933132i | \(-0.617064\pi\) |
0.987883 | − | 0.155200i | \(-0.0496022\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −469.178 | − | 559.145i | −0.578518 | − | 0.689451i | 0.394838 | − | 0.918751i | \(-0.370801\pi\) |
−0.973356 | + | 0.229300i | \(0.926356\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 382.411 | − | 1050.66i | 0.470370 | − | 1.29233i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −94.2340 | + | 534.428i | −0.115625 | + | 0.655739i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1167.66 | + | 885.687i | 1.42921 | + | 1.08407i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −54.0162 | − | 9.52451i | −0.0659538 | − | 0.0116294i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 286.345 | + | 104.221i | 0.348776 | + | 0.126944i | 0.510467 | − | 0.859897i | \(-0.329473\pi\) |
−0.161691 | + | 0.986841i | \(0.551695\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −319.242 | + | 267.876i | −0.387901 | + | 0.325488i | −0.815795 | − | 0.578341i | \(-0.803700\pi\) |
0.427894 | + | 0.903829i | \(0.359256\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 342.830 | + | 197.933i | 0.415552 | + | 0.239919i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 367.526 | − | 64.8048i | 0.444409 | − | 0.0783613i | 0.0530342 | − | 0.998593i | \(-0.483111\pi\) |
0.391375 | + | 0.920231i | \(0.372000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −370.307 | + | 213.797i | −0.446691 | + | 0.257897i | −0.706432 | − | 0.707781i | \(-0.749696\pi\) |
0.259741 | + | 0.965678i | \(0.416363\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −447.021 | − | 1228.18i | −0.537931 | − | 1.47795i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 374.793 | + | 314.489i | 0.449932 | + | 0.377538i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 130.448i | 0.156226i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 116.943 | 0.139716 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 121.054 | − | 144.266i | 0.144284 | − | 0.171950i | −0.689063 | − | 0.724702i | \(-0.741978\pi\) |
0.833346 | + | 0.552751i | \(0.186422\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1882.86 | − | 685.306i | 2.23884 | − | 0.814871i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 397.707 | + | 688.848i | 0.471775 | + | 0.817139i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −44.0541 | − | 249.843i | −0.0521351 | − | 0.295673i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 177.231 | − | 306.974i | 0.209246 | − | 0.362425i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 277.737 | + | 330.995i | 0.327135 | + | 0.389864i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 145.746 | − | 400.433i | 0.171264 | − | 0.470544i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 69.5191 | − | 394.262i | 0.0814995 | − | 0.462206i | −0.916558 | − | 0.399902i | \(-0.869044\pi\) |
0.998057 | − | 0.0623041i | \(-0.0198449\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 46.5239 | − | 90.6004i | 0.0544139 | − | 0.105965i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −419.466 | − | 73.9631i | −0.489458 | − | 0.0863047i | −0.0765282 | − | 0.997067i | \(-0.524384\pi\) |
−0.412930 | + | 0.910763i | \(0.635495\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −652.245 | − | 237.398i | −0.759307 | − | 0.276365i | −0.0667903 | − | 0.997767i | \(-0.521276\pi\) |
−0.692517 | + | 0.721402i | \(0.743498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −184.447 | + | 154.770i | −0.214224 | + | 0.179756i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1067.21 | + | 616.154i | 1.23663 | + | 0.713968i | 0.968404 | − | 0.249388i | \(-0.0802295\pi\) |
0.268225 | + | 0.963356i | \(0.413563\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49.1895 | + | 8.67344i | −0.0568665 | + | 0.0100271i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 277.545 | − | 160.241i | 0.320121 | − | 0.184822i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.0515 | + | 79.8184i | 0.0334310 | + | 0.0918509i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −168.690 | − | 141.548i | −0.193674 | − | 0.162511i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 122.942i | − | 0.140827i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 305.239 | 0.348844 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −66.5831 | + | 79.3507i | −0.0759215 | + | 0.0904797i | −0.802668 | − | 0.596426i | \(-0.796587\pi\) |
0.726747 | + | 0.686906i | \(0.241031\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1325.38 | − | 482.399i | 1.50783 | − | 0.548804i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −786.786 | − | 1362.75i | −0.893060 | − | 1.54683i | −0.836187 | − | 0.548444i | \(-0.815220\pi\) |
−0.0568725 | − | 0.998381i | \(-0.518113\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.3265 | + | 228.703i | 0.0456699 | + | 0.259007i | 0.999091 | − | 0.0426369i | \(-0.0135759\pi\) |
−0.953421 | + | 0.301644i | \(0.902465\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −263.208 | + | 455.890i | −0.297410 | + | 0.515130i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1113.80 | + | 1327.37i | 1.25569 | + | 1.49647i | 0.792062 | + | 0.610440i | \(0.209008\pi\) |
0.463626 | + | 0.886031i | \(0.346548\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 284.295 | − | 781.095i | 0.319792 | − | 0.878622i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 89.1128 | − | 505.384i | 0.100014 | − | 0.567210i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 526.577 | − | 487.943i | 0.589672 | − | 0.546409i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −300.380 | − | 52.9650i | −0.335620 | − | 0.0591788i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −182.930 | − | 66.5811i | −0.203935 | − | 0.0742264i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −232.926 | + | 195.448i | −0.259095 | + | 0.217407i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 574.753 | + | 331.834i | 0.637906 | + | 0.368295i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −993.479 | + | 175.177i | −1.10020 | + | 0.193995i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −302.108 | + | 174.422i | −0.333821 | + | 0.192732i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −360.985 | − | 991.799i | −0.397999 | − | 1.09349i | −0.963257 | − | 0.268580i | \(-0.913446\pi\) |
0.565258 | − | 0.824914i | \(-0.308777\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 338.212 | + | 283.794i | 0.372071 | + | 0.312205i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 765.235i | 0.839995i | 0.907525 | + | 0.419997i | \(0.137969\pi\) | ||||
−0.907525 | + | 0.419997i | \(0.862031\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −181.469 | −0.198761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −81.2066 | + | 96.7783i | −0.0887504 | + | 0.105769i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −572.059 | + | 208.212i | −0.623838 | + | 0.227058i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −70.5236 | − | 122.151i | −0.0767395 | − | 0.132917i | 0.825102 | − | 0.564984i | \(-0.191118\pi\) |
−0.901841 | + | 0.432067i | \(0.857784\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 241.300 | + | 1368.48i | 0.261998 | + | 1.48586i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 208.177 | − | 360.573i | 0.225544 | − | 0.390653i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −506.657 | − | 603.810i | −0.547737 | − | 0.652768i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −80.7662 | + | 221.903i | −0.0871265 | + | 0.239378i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 76.8896 | − | 436.063i | 0.0827660 | − | 0.469389i | −0.915050 | − | 0.403340i | \(-0.867849\pi\) |
0.997816 | − | 0.0660497i | \(-0.0210396\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 661.701 | − | 32.5848i | 0.710742 | − | 0.0349998i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1620.51 | − | 285.739i | −1.73688 | − | 0.306258i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 117.677 | + | 42.8311i | 0.125858 | + | 0.0458086i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1288.21 | + | 1080.94i | −1.37482 | + | 1.15361i | −0.403739 | + | 0.914874i | \(0.632290\pi\) |
−0.971084 | + | 0.238739i | \(0.923266\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −817.456 | − | 471.958i | −0.870560 | − | 0.502618i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1623.23 | + | 286.219i | −1.72501 | + | 0.304165i | −0.946316 | − | 0.323243i | \(-0.895227\pi\) |
−0.778690 | + | 0.627408i | \(0.784116\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −189.784 | + | 109.572i | −0.201255 | + | 0.116195i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −45.5468 | − | 125.139i | −0.0481977 | − | 0.132422i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 559.654 | + | 469.605i | 0.590975 | + | 0.495887i | 0.888531 | − | 0.458817i | \(-0.151727\pi\) |
−0.297555 | + | 0.954705i | \(0.596171\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 354.455i | 0.373504i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 942.597 | 0.991164 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 817.829 | − | 974.651i | 0.858163 | − | 1.02272i | −0.141301 | − | 0.989967i | \(-0.545128\pi\) |
0.999464 | − | 0.0327519i | \(-0.0104271\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 57.7206 | − | 21.0086i | 0.0604404 | − | 0.0219985i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 479.477 | + | 830.479i | 0.501021 | + | 0.867794i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −115.269 | − | 653.721i | −0.120197 | − | 0.681670i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −464.250 | + | 804.104i | −0.483090 | + | 0.836737i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 209.928 | + | 250.182i | 0.217993 | + | 0.259794i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.4562 | + | 64.4454i | −0.0243070 | + | 0.0667828i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −128.633 | + | 729.513i | −0.133023 | + | 0.754409i | 0.843194 | + | 0.537610i | \(0.180673\pi\) |
−0.976216 | + | 0.216799i | \(0.930438\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −273.977 | + | 886.126i | −0.282742 | + | 0.914475i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1006.39 | − | 177.454i | −1.03645 | − | 0.182754i | −0.370563 | − | 0.928807i | \(-0.620835\pi\) |
−0.665886 | + | 0.746053i | \(0.731946\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −363.119 | − | 132.164i | −0.373195 | − | 0.135832i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −275.839 | + | 231.456i | −0.282912 | + | 0.237391i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1153.54 | − | 665.998i | −1.18070 | − | 0.681677i | −0.224523 | − | 0.974469i | \(-0.572082\pi\) |
−0.956176 | + | 0.292792i | \(0.905416\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 143.569 | − | 25.3152i | 0.146649 | − | 0.0258582i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −449.653 | + | 259.607i | −0.458362 | + | 0.264635i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 397.788 | + | 1092.91i | 0.404667 | + | 1.11181i | 0.959955 | + | 0.280156i | \(0.0903861\pi\) |
−0.555287 | + | 0.831659i | \(0.687392\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 455.427 | + | 382.148i | 0.462362 | + | 0.387968i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 494.155i | 0.500663i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −918.159 | −0.928371 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 146.942 | − | 175.119i | 0.148277 | − | 0.176709i | −0.686794 | − | 0.726852i | \(-0.740982\pi\) |
0.835070 | + | 0.550143i | \(0.185427\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 894.836 | − | 325.694i | 0.901144 | − | 0.327990i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −64.5916 | − | 111.876i | −0.0649162 | − | 0.112438i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −78.4445 | − | 444.881i | −0.0786805 | − | 0.446219i | −0.998542 | − | 0.0539765i | \(-0.982810\pi\) |
0.919862 | − | 0.392243i | \(-0.128301\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −367.176 | + | 635.967i | −0.367543 | + | 0.636604i |
(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 | 76.3.j.a.21.3 | ✓ | 18 | |
4.3 | odd | 2 | 304.3.z.b.97.1 | 18 | |||
19.3 | odd | 18 | 1444.3.c.c.721.15 | 18 | |||
19.10 | odd | 18 | inner | 76.3.j.a.29.3 | yes | 18 | |
19.16 | even | 9 | 1444.3.c.c.721.4 | 18 | |||
76.67 | even | 18 | 304.3.z.b.257.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.j.a.21.3 | ✓ | 18 | 1.1 | even | 1 | trivial | |
76.3.j.a.29.3 | yes | 18 | 19.10 | odd | 18 | inner | |
304.3.z.b.97.1 | 18 | 4.3 | odd | 2 | |||
304.3.z.b.257.1 | 18 | 76.67 | even | 18 | |||
1444.3.c.c.721.4 | 18 | 19.16 | even | 9 | |||
1444.3.c.c.721.15 | 18 | 19.3 | odd | 18 |