Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.21913473024.16 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 11x^{6} - 2x^{5} + 51x^{4} + 162x^{2} + 112x + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.3 | ||
Root | \(1.09199 + 1.89138i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.961 |
Dual form | 1960.2.q.y.361.3 |
$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.09199 | + | 1.89138i | 0.630461 | + | 1.09199i | 0.987458 | + | 0.157884i | \(0.0504673\pi\) |
−0.356997 | + | 0.934105i | \(0.616199\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.884883 | + | 1.53266i | −0.294961 | + | 0.510887i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.79910 | − | 3.11613i | −0.542448 | − | 0.939547i | −0.998763 | − | 0.0497290i | \(-0.984164\pi\) |
0.456315 | − | 0.889818i | \(-0.349169\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.85838 | −1.62482 | −0.812411 | − | 0.583085i | \(-0.801845\pi\) | ||||
−0.812411 | + | 0.583085i | \(0.801845\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.18398 | 0.563901 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.18060 | − | 5.50897i | −0.771410 | − | 1.33612i | −0.936791 | − | 0.349891i | \(-0.886219\pi\) |
0.165381 | − | 0.986230i | \(-0.447115\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.25141 | − | 3.89956i | 0.516510 | − | 0.894621i | −0.483307 | − | 0.875451i | \(-0.660564\pi\) |
0.999816 | − | 0.0191698i | \(-0.00610231\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.31407 | + | 2.27604i | −0.274003 | + | 0.474587i | −0.969883 | − | 0.243571i | \(-0.921681\pi\) |
0.695880 | + | 0.718158i | \(0.255015\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.68681 | 0.517076 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.05866 | 0.382284 | 0.191142 | − | 0.981562i | \(-0.438781\pi\) | ||||
0.191142 | + | 0.981562i | \(0.438781\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.31407 | − | 5.74014i | −0.595225 | − | 1.03096i | −0.993515 | − | 0.113700i | \(-0.963730\pi\) |
0.398290 | − | 0.917259i | \(-0.369604\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.92919 | − | 6.80556i | 0.683984 | − | 1.18470i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.95852 | − | 5.12431i | 0.486378 | − | 0.842431i | −0.513500 | − | 0.858090i | \(-0.671651\pi\) |
0.999877 | + | 0.0156589i | \(0.00498458\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.39729 | − | 11.0804i | −1.02439 | − | 1.77429i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.22348 | −1.12812 | −0.564059 | − | 0.825734i | \(-0.690761\pi\) | ||||
−0.564059 | + | 0.825734i | \(0.690761\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.34880 | −0.815684 | −0.407842 | − | 0.913052i | \(-0.633719\pi\) | ||||
−0.407842 | + | 0.913052i | \(0.633719\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.884883 | + | 1.53266i | 0.131911 | + | 0.228476i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.15942 | − | 2.00818i | 0.169119 | − | 0.292923i | −0.768991 | − | 0.639259i | \(-0.779241\pi\) |
0.938110 | + | 0.346336i | \(0.112574\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.94637 | − | 12.0315i | 0.972686 | − | 1.68474i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.05389 | + | 3.55744i | 0.282123 | + | 0.488651i | 0.971907 | − | 0.235363i | \(-0.0756280\pi\) |
−0.689784 | + | 0.724015i | \(0.742295\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.59819 | −0.485180 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.83408 | 1.30256 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.53553 | − | 4.39167i | −0.330098 | − | 0.571747i | 0.652432 | − | 0.757847i | \(-0.273749\pi\) |
−0.982531 | + | 0.186100i | \(0.940415\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.68681 | + | 6.38574i | −0.472047 | + | 0.817610i | −0.999488 | − | 0.0319818i | \(-0.989818\pi\) |
0.527441 | + | 0.849591i | \(0.323151\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.92919 | + | 5.07351i | −0.363321 | + | 0.629291i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.69833 | − | 2.94160i | −0.207485 | − | 0.359374i | 0.743437 | − | 0.668806i | \(-0.233194\pi\) |
−0.950921 | + | 0.309432i | \(0.899861\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.73981 | −0.690992 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.7224 | 1.98459 | 0.992293 | − | 0.123917i | \(-0.0395457\pi\) | ||||
0.992293 | + | 0.123917i | \(0.0395457\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.35919 | + | 12.7465i | 0.861328 | + | 1.49186i | 0.870648 | + | 0.491907i | \(0.163700\pi\) |
−0.00932043 | + | 0.999957i | \(0.502967\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.09199 | − | 1.89138i | 0.126092 | − | 0.218398i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.62752 | − | 2.81895i | 0.183111 | − | 0.317157i | −0.759828 | − | 0.650125i | \(-0.774717\pi\) |
0.942938 | + | 0.332968i | \(0.108050\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.58861 | + | 9.67976i | 0.620957 | + | 1.07553i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.6936 | −1.17377 | −0.586885 | − | 0.809670i | \(-0.699646\pi\) | ||||
−0.586885 | + | 0.809670i | \(0.699646\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.36121 | −0.689970 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.24804 | + | 3.89371i | 0.241015 | + | 0.417450i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.57701 | − | 9.65967i | 0.591162 | − | 1.02392i | −0.402914 | − | 0.915238i | \(-0.632003\pi\) |
0.994076 | − | 0.108685i | \(-0.0346641\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.23787 | − | 12.5364i | 0.750532 | − | 1.29996i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.25141 | − | 3.89956i | −0.230990 | − | 0.400087i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.1896 | −1.74534 | −0.872671 | − | 0.488308i | \(-0.837614\pi\) | ||||
−0.872671 | + | 0.488308i | \(0.837614\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.36796 | 0.640004 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.72065 | + | 2.98026i | 0.171212 | + | 0.296547i | 0.938844 | − | 0.344344i | \(-0.111899\pi\) |
−0.767632 | + | 0.640891i | \(0.778565\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.98785 | + | 10.3713i | −0.590000 | + | 1.02191i | 0.404231 | + | 0.914657i | \(0.367539\pi\) |
−0.994232 | + | 0.107254i | \(0.965794\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.33801 | − | 9.24570i | 0.516045 | − | 0.893815i | −0.483782 | − | 0.875189i | \(-0.660737\pi\) |
0.999827 | − | 0.0186269i | \(-0.00592946\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.16706 | + | 7.21755i | 0.399131 | + | 0.691316i | 0.993619 | − | 0.112789i | \(-0.0359784\pi\) |
−0.594487 | + | 0.804105i | \(0.702645\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.9227 | 1.22657 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.1542 | −1.14337 | −0.571684 | − | 0.820474i | \(-0.693710\pi\) | ||||
−0.571684 | + | 0.820474i | \(0.693710\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.31407 | + | 2.27604i | 0.122538 | + | 0.212242i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.18398 | − | 8.97892i | 0.479259 | − | 0.830101i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.973496 | + | 1.68614i | −0.0884996 | + | 0.153286i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.88797 | − | 13.6624i | −0.711234 | − | 1.23189i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.82453 | −0.871786 | −0.435893 | − | 0.899998i | \(-0.643567\pi\) | ||||
−0.435893 | + | 0.899998i | \(0.643567\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.84083 | − | 10.1166i | −0.514257 | − | 0.890719i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.47687 | − | 4.29007i | 0.216405 | − | 0.374825i | −0.737301 | − | 0.675564i | \(-0.763900\pi\) |
0.953706 | + | 0.300739i | \(0.0972334\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.34340 | − | 2.32684i | 0.115622 | − | 0.200263i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.65685 | + | 9.79796i | 0.483298 | + | 0.837096i | 0.999816 | − | 0.0191800i | \(-0.00610555\pi\) |
−0.516518 | + | 0.856276i | \(0.672772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.70311 | −0.738188 | −0.369094 | − | 0.929392i | \(-0.620332\pi\) | ||||
−0.369094 | + | 0.929392i | \(0.620332\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.06431 | 0.426492 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.5398 | + | 18.2554i | 0.881381 | + | 1.52660i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.02933 | − | 1.78285i | 0.0854813 | − | 0.148058i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.22634 | − | 5.58818i | 0.264312 | − | 0.457802i | −0.703071 | − | 0.711119i | \(-0.748189\pi\) |
0.967383 | + | 0.253318i | \(0.0815218\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.01303 | + | 3.48667i | 0.163818 | + | 0.283741i | 0.936235 | − | 0.351375i | \(-0.114286\pi\) |
−0.772417 | + | 0.635116i | \(0.780952\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.2578 | 0.910143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.62814 | −0.532385 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.76301 | + | 13.4459i | 0.619556 | + | 1.07310i | 0.989567 | + | 0.144075i | \(0.0460206\pi\) |
−0.370011 | + | 0.929027i | \(0.620646\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.48565 | + | 7.76937i | −0.355735 | + | 0.616151i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.4805 | − | 21.6169i | 0.977549 | − | 1.69316i | 0.306294 | − | 0.951937i | \(-0.400911\pi\) |
0.671254 | − | 0.741227i | \(-0.265756\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.92919 | − | 6.80556i | −0.305887 | − | 0.529812i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.0739 | 1.24384 | 0.621919 | − | 0.783082i | \(-0.286353\pi\) | ||||
0.621919 | + | 0.783082i | \(0.286353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.3206 | 1.64005 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.98447 | + | 6.90131i | 0.304700 | + | 0.527757i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.0178027 | + | 0.0308352i | −0.00135351 | + | 0.00234436i | −0.866701 | − | 0.498827i | \(-0.833764\pi\) |
0.865348 | + | 0.501172i | \(0.167098\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.53755 | − | 9.59132i | 0.416228 | − | 0.720928i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.22634 | + | 3.85613i | 0.166404 | + | 0.288221i | 0.937153 | − | 0.348918i | \(-0.113451\pi\) |
−0.770749 | + | 0.637139i | \(0.780118\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.7377 | 1.69008 | 0.845039 | − | 0.534705i | \(-0.179577\pi\) | ||||
0.845039 | + | 0.534705i | \(0.179577\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.1038 | −1.19043 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.95852 | − | 5.12431i | −0.217515 | − | 0.376747i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.4444 | + | 19.8223i | −0.836899 | + | 1.44955i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.7760 | − | 22.1288i | 0.924442 | − | 1.60118i | 0.131985 | − | 0.991252i | \(-0.457865\pi\) |
0.792456 | − | 0.609929i | \(-0.208802\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5452 | − | 18.2648i | −0.759059 | − | 1.31473i | −0.943331 | − | 0.331854i | \(-0.892326\pi\) |
0.184272 | − | 0.982875i | \(-0.441007\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.7946 | −0.916239 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.4622 | 1.17288 | 0.586442 | − | 0.809991i | \(-0.300528\pi\) | ||||
0.586442 | + | 0.809991i | \(0.300528\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.9709 | − | 22.4663i | −0.919485 | − | 1.59259i | −0.800199 | − | 0.599734i | \(-0.795273\pi\) |
−0.119285 | − | 0.992860i | \(-0.538060\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.70913 | − | 6.42440i | 0.261622 | − | 0.453142i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.61174 | + | 6.25572i | −0.252255 | + | 0.436918i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.32560 | − | 4.02806i | −0.161640 | − | 0.279969i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.2020 | −1.12072 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.84877 | 0.609174 | 0.304587 | − | 0.952484i | \(-0.401481\pi\) | ||||
0.304587 | + | 0.952484i | \(0.401481\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.2607 | + | 31.6285i | 1.25120 | + | 2.16715i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.67440 | + | 4.63220i | −0.182393 | + | 0.315913i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.0723 | + | 27.8381i | −1.08607 | + | 1.88112i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.6332 | + | 32.2736i | 1.25340 | + | 2.17096i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.06042 | −0.271906 | −0.135953 | − | 0.990715i | \(-0.543410\pi\) | ||||
−0.135953 | + | 0.990715i | \(0.543410\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.76977 | 0.117984 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.98032 | − | 10.3582i | −0.396928 | − | 0.687499i | 0.596417 | − | 0.802674i | \(-0.296590\pi\) |
−0.993345 | + | 0.115175i | \(0.963257\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.65208 | − | 9.78969i | 0.373500 | − | 0.646921i | −0.616601 | − | 0.787276i | \(-0.711491\pi\) |
0.990101 | + | 0.140355i | \(0.0448243\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.6530 | + | 18.4515i | −0.697898 | + | 1.20880i | 0.271295 | + | 0.962496i | \(0.412548\pi\) |
−0.969194 | + | 0.246299i | \(0.920785\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.15942 | − | 2.00818i | −0.0756325 | − | 0.130999i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.10896 | 0.461776 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.5361 | −1.45774 | −0.728871 | − | 0.684651i | \(-0.759955\pi\) | ||||
−0.728871 | + | 0.684651i | \(0.759955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.42386 | − | 11.1265i | −0.413798 | − | 0.716718i | 0.581504 | − | 0.813544i | \(-0.302465\pi\) |
−0.995301 | + | 0.0968253i | \(0.969131\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.17521 | + | 14.1599i | −0.524440 | + | 0.908356i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.1896 | + | 22.8451i | −0.839236 | + | 1.45360i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.6773 | − | 20.2256i | −0.740016 | − | 1.28175i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.7361 | −1.49821 | −0.749103 | − | 0.662453i | \(-0.769515\pi\) | ||||
−0.749103 | + | 0.662453i | \(0.769515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.45657 | 0.594530 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.94637 | − | 12.0315i | −0.434999 | − | 0.753440i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.60697 | − | 11.4436i | 0.412131 | − | 0.713832i | −0.582991 | − | 0.812478i | \(-0.698118\pi\) |
0.995123 | + | 0.0986462i | \(0.0314512\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.82167 | + | 3.15523i | −0.112759 | + | 0.195304i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.4266 | + | 24.9876i | 0.889584 | + | 1.54080i | 0.840368 | + | 0.542016i | \(0.182339\pi\) |
0.0492151 | + | 0.998788i | \(0.484328\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.10777 | 0.252338 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.3602 | 1.49082 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.28536 | + | 2.22631i | 0.0783700 | + | 0.135741i | 0.902547 | − | 0.430592i | \(-0.141695\pi\) |
−0.824177 | + | 0.566333i | \(0.808362\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.37361 | − | 5.84327i | 0.204932 | − | 0.354953i | −0.745179 | − | 0.666865i | \(-0.767636\pi\) |
0.950111 | + | 0.311911i | \(0.100969\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.79910 | + | 3.11613i | −0.108490 | + | 0.187909i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.62727 | + | 2.81851i | 0.0977730 | + | 0.169348i | 0.910763 | − | 0.412931i | \(-0.135495\pi\) |
−0.812990 | + | 0.582278i | \(0.802161\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.7303 | 0.702273 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.55422 | −0.152372 | −0.0761860 | − | 0.997094i | \(-0.524274\pi\) | ||||
−0.0761860 | + | 0.997094i | \(0.524274\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.25681 | − | 10.8371i | −0.371929 | − | 0.644199i | 0.617933 | − | 0.786230i | \(-0.287970\pi\) |
−0.989862 | + | 0.142031i | \(0.954637\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.91704 | − | 8.51656i | 0.291260 | − | 0.504478i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.7325 | + | 20.3212i | −0.690145 | + | 1.19537i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.7709 | − | 32.5122i | −1.10037 | − | 1.90590i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.6574 | 1.49892 | 0.749460 | − | 0.662050i | \(-0.230313\pi\) | ||||
0.749460 | + | 0.662050i | \(0.230313\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.07107 | −0.295249 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.83382 | − | 8.37243i | −0.280487 | − | 0.485818i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.69833 | − | 13.3339i | 0.445206 | − | 0.771120i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.75787 | + | 6.50883i | −0.215884 | + | 0.373922i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.68681 | + | 6.38574i | 0.211106 | + | 0.365646i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.9391 | 0.681398 | 0.340699 | − | 0.940172i | \(-0.389336\pi\) | ||||
0.340699 | + | 0.940172i | \(0.389336\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −26.1547 | −1.48789 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.24939 | + | 7.36017i | 0.240961 | + | 0.417357i | 0.960988 | − | 0.276589i | \(-0.0892041\pi\) |
−0.720027 | + | 0.693946i | \(0.755871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.878058 | + | 1.52084i | −0.0496308 | + | 0.0859631i | −0.889774 | − | 0.456402i | \(-0.849138\pi\) |
0.840143 | + | 0.542365i | \(0.182471\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.98245 | + | 5.16576i | −0.167511 | + | 0.290138i | −0.937544 | − | 0.347866i | \(-0.886906\pi\) |
0.770033 | + | 0.638004i | \(0.220240\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.70373 | − | 6.41505i | −0.207369 | − | 0.359174i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.3162 | 1.30138 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.6434 | −1.59376 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.92919 | + | 5.07351i | 0.162482 | + | 0.281427i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.10076 | + | 15.7630i | −0.503273 | + | 0.871695i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.05191 | − | 12.2143i | 0.387608 | − | 0.671357i | −0.604519 | − | 0.796590i | \(-0.706635\pi\) |
0.992127 | + | 0.125234i | \(0.0399681\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.23589 | + | 9.06882i | 0.286925 | + | 0.496968i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.39667 | −0.185580 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.8876 | −1.24677 | −0.623384 | − | 0.781916i | \(-0.714242\pi\) | ||||
−0.623384 | + | 0.781916i | \(0.714242\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.2722 | − | 22.9882i | −0.720849 | − | 1.24855i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.9247 | + | 20.6541i | −0.645757 | + | 1.11848i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.86991 | + | 4.97082i | −0.154511 | + | 0.267620i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.8293 | + | 20.4890i | 0.635030 | + | 1.09990i | 0.986509 | + | 0.163709i | \(0.0523458\pi\) |
−0.351478 | + | 0.936196i | \(0.614321\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.7912 | −1.48763 | −0.743814 | − | 0.668386i | \(-0.766985\pi\) | ||||
−0.743814 | + | 0.668386i | \(0.766985\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.7403 | −0.840157 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.5840 | + | 18.3321i | 0.563331 | + | 0.975717i | 0.997203 | + | 0.0747430i | \(0.0238136\pi\) |
−0.433872 | + | 0.900974i | \(0.642853\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.36121 | − | 14.4820i | 0.443767 | − | 0.768627i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.1421 | + | 31.4231i | −0.957505 | + | 1.65845i | −0.228977 | + | 0.973432i | \(0.573538\pi\) |
−0.728528 | + | 0.685016i | \(0.759795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.637724 | − | 1.10457i | −0.0335644 | − | 0.0581353i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.25219 | −0.223182 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.7184 | 0.770395 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.5793 | − | 26.9841i | −0.813232 | − | 1.40856i | −0.910590 | − | 0.413310i | \(-0.864372\pi\) |
0.0973579 | − | 0.995249i | \(-0.468961\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.39194 | − | 11.0712i | 0.332751 | − | 0.576341i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.33639 | − | 5.77880i | 0.172752 | − | 0.299215i | −0.766629 | − | 0.642090i | \(-0.778067\pi\) |
0.939381 | + | 0.342875i | \(0.111401\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.09199 | − | 1.89138i | −0.0563901 | − | 0.0976705i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0604 | −0.621143 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.3984 | 1.09916 | 0.549582 | − | 0.835440i | \(-0.314787\pi\) | ||||
0.549582 | + | 0.835440i | \(0.314787\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.7283 | − | 18.5819i | −0.549627 | − | 0.951981i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.81726 | − | 3.14759i | 0.0928578 | − | 0.160834i | −0.815855 | − | 0.578257i | \(-0.803733\pi\) |
0.908713 | + | 0.417422i | \(0.137066\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.73306 | − | 8.19790i | 0.240595 | − | 0.416723i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.9476 | − | 18.9618i | −0.555066 | − | 0.961403i | −0.997898 | − | 0.0647981i | \(-0.979360\pi\) |
0.442832 | − | 0.896604i | \(-0.353974\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.7182 | 0.845474 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.8189 | 0.545740 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.62752 | − | 2.81895i | −0.0818896 | − | 0.141837i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.98785 | + | 15.5674i | −0.451087 | + | 0.781306i | −0.998454 | − | 0.0555869i | \(-0.982297\pi\) |
0.547367 | + | 0.836893i | \(0.315630\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.8172 | + | 23.9320i | −0.689996 | + | 1.19511i | 0.281843 | + | 0.959461i | \(0.409054\pi\) |
−0.971839 | + | 0.235647i | \(0.924279\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.4151 | + | 33.6279i | 0.967135 | + | 1.67513i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.1772 | 0.555401 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.2907 | −1.05534 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.9630 | − | 34.5770i | −0.987108 | − | 1.70972i | −0.632164 | − | 0.774834i | \(-0.717833\pi\) |
−0.354944 | − | 0.934887i | \(-0.615500\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.3545 | + | 21.3985i | −0.609400 | + | 1.05551i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.34678 | + | 9.26089i | −0.262463 | + | 0.454599i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.50371 | − | 16.4609i | −0.465398 | − | 0.806094i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.89384 | −0.141373 | −0.0706867 | − | 0.997499i | \(-0.522519\pi\) | ||||
−0.0706867 | + | 0.997499i | \(0.522519\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.5744 | −1.63632 | −0.818158 | − | 0.574993i | \(-0.805005\pi\) | ||||
−0.818158 | + | 0.574993i | \(0.805005\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.05191 | + | 3.55401i | 0.0997672 | + | 0.172802i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.18060 | + | 5.50897i | −0.154282 | + | 0.267224i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −23.0187 | + | 39.8695i | −1.11135 | + | 1.92492i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.165441 | − | 0.286552i | −0.00796902 | − | 0.0138027i | 0.862013 | − | 0.506885i | \(-0.169203\pi\) |
−0.869982 | + | 0.493083i | \(0.835870\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.573752 | 0.0275727 | 0.0137864 | − | 0.999905i | \(-0.495612\pi\) | ||||
0.0137864 | + | 0.999905i | \(0.495612\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.49607 | 0.215570 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.91704 | + | 10.2486i | 0.283050 | + | 0.490258i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.7582 | + | 23.8300i | −0.656645 | + | 1.13734i | 0.324834 | + | 0.945771i | \(0.394692\pi\) |
−0.981479 | + | 0.191571i | \(0.938642\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.85838 | − | 17.0752i | 0.468386 | − | 0.811268i | −0.530961 | − | 0.847396i | \(-0.678169\pi\) |
0.999347 | + | 0.0361281i | \(0.0115024\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.57701 | − | 9.65967i | −0.264376 | − | 0.457912i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.0925 | 0.666553 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.6751 | 1.54203 | 0.771016 | − | 0.636816i | \(-0.219749\pi\) | ||||
0.771016 | + | 0.636816i | \(0.219749\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.9957 | + | 22.5093i | 0.611945 | + | 1.05992i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.39641 | + | 7.61481i | −0.206561 | + | 0.357775i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.87556 | + | 3.24857i | −0.0877350 | + | 0.151962i | −0.906553 | − | 0.422091i | \(-0.861296\pi\) |
0.818818 | + | 0.574053i | \(0.194630\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.54566 | − | 14.8015i | −0.398877 | − | 0.690876i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.77983 | −0.408917 | −0.204459 | − | 0.978875i | \(-0.565543\pi\) | ||||
−0.204459 | + | 0.978875i | \(0.565543\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.78203 | −0.222240 | −0.111120 | − | 0.993807i | \(-0.535444\pi\) | ||||
−0.111120 | + | 0.993807i | \(0.535444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.23787 | − | 12.5364i | −0.335648 | − | 0.581359i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.9599 | − | 18.9831i | 0.507165 | − | 0.878435i | −0.492801 | − | 0.870142i | \(-0.664027\pi\) |
0.999966 | − | 0.00829277i | \(-0.00263970\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.9543 | + | 29.3656i | −0.781211 | + | 1.35310i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.62301 | + | 16.6675i | 0.442466 | + | 0.766374i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.50283 | −0.206604 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.26980 | −0.332861 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.54431 | + | 4.40687i | 0.116252 | + | 0.201355i | 0.918280 | − | 0.395932i | \(-0.129579\pi\) |
−0.802027 | + | 0.597287i | \(0.796245\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.3321 | + | 30.0201i | −0.790277 | + | 1.36880i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.59482 | + | 14.8867i | −0.390271 | + | 0.675968i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.02518 | − | 6.97181i | −0.182398 | − | 0.315923i | 0.760299 | − | 0.649574i | \(-0.225053\pi\) |
−0.942697 | + | 0.333651i | \(0.891719\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 54.5143 | 2.46522 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.8081 | 0.578021 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.54778 | − | 11.3411i | −0.294897 | − | 0.510777i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.18398 | − | 5.51481i | 0.143109 | − | 0.247872i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.2642 | − | 24.7063i | 0.638552 | − | 1.10601i | −0.347198 | − | 0.937792i | \(-0.612867\pi\) |
0.985751 | − | 0.168213i | \(-0.0537997\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.5526 | + | 30.4019i | 0.784191 | + | 1.35826i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.56948 | 0.292919 | 0.146459 | − | 0.989217i | \(-0.453212\pi\) | ||||
0.146459 | + | 0.989217i | \(0.453212\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.44131 | 0.153136 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.2819 | + | 40.3254i | 1.03398 | + | 1.79091i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.0787 | − | 20.9209i | 0.535379 | − | 0.927304i | −0.463766 | − | 0.885958i | \(-0.653502\pi\) |
0.999145 | − | 0.0413458i | \(-0.0131645\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.04911 | − | 10.4774i | 0.267075 | − | 0.462587i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.98785 | + | 10.3713i | 0.263856 | + | 0.457012i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.34366 | −0.366954 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.0777615 | −0.00341335 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.4315 | + | 18.0679i | 0.457012 | + | 0.791568i | 0.998801 | − | 0.0489461i | \(-0.0155863\pi\) |
−0.541789 | + | 0.840514i | \(0.682253\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.43539 | + | 11.1464i | −0.281400 | + | 0.487399i | −0.971730 | − | 0.236096i | \(-0.924132\pi\) |
0.690330 | + | 0.723495i | \(0.257465\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.0815 | + | 36.5142i | −0.918324 | + | 1.59058i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.04643 | + | 13.9368i | 0.349845 | + | 0.605949i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.97460 | 0.389465 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.3179 | 1.83299 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.33801 | − | 9.24570i | −0.230782 | − | 0.399726i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.86228 | + | 8.42171i | −0.209823 | + | 0.363424i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.2681 | − | 21.2489i | 0.527446 | − | 0.913563i | −0.472043 | − | 0.881576i | \(-0.656483\pi\) |
0.999488 | − | 0.0319870i | \(-0.0101835\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.8293 | + | 43.0056i | 1.06553 | + | 1.84555i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.33411 | 0.356994 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.5781 | −1.17916 | −0.589578 | − | 0.807711i | \(-0.700706\pi\) | ||||
−0.589578 | + | 0.807711i | \(0.700706\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.52478 | − | 11.3013i | −0.278471 | − | 0.482326i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.63490 | − | 8.02788i | 0.197453 | − | 0.341999i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.46135 | − | 11.1914i | 0.274269 | − | 0.475048i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.30130 | + | 5.71802i | 0.139881 | + | 0.242280i | 0.927451 | − | 0.373944i | \(-0.121995\pi\) |
−0.787571 | + | 0.616224i | \(0.788661\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.3353 | 1.32534 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −49.9888 | −2.11053 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.987331 | − | 1.71011i | −0.0416110 | − | 0.0720724i | 0.844470 | − | 0.535603i | \(-0.179916\pi\) |
−0.886081 | + | 0.463531i | \(0.846582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.07709 | + | 10.5258i | −0.255665 | + | 0.442825i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.86403 | − | 10.1568i | 0.245833 | − | 0.425795i | −0.716532 | − | 0.697554i | \(-0.754272\pi\) |
0.962365 | + | 0.271758i | \(0.0876052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.84987 | − | 4.93612i | −0.119263 | − | 0.206570i | 0.800213 | − | 0.599716i | \(-0.204720\pi\) |
−0.919476 | + | 0.393146i | \(0.871387\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 55.8052 | 2.33130 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.62814 | 0.109601 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.6671 | + | 20.2081i | 0.485709 | + | 0.841272i | 0.999865 | − | 0.0164241i | \(-0.00522820\pi\) |
−0.514156 | + | 0.857697i | \(0.671895\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 23.0305 | − | 39.8899i | 0.957114 | − | 1.65777i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.39028 | − | 12.8003i | 0.306074 | − | 0.530136i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.18398 | − | 8.97892i | −0.214331 | − | 0.371232i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.8470 | 0.942997 | 0.471498 | − | 0.881867i | \(-0.343713\pi\) | ||||
0.471498 | + | 0.881867i | \(0.343713\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.8454 | −1.22976 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.9766 | + | 31.1364i | 0.739458 | + | 1.28078i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.24051 | + | 12.5409i | −0.297332 | + | 0.514994i | −0.975525 | − | 0.219890i | \(-0.929430\pi\) |
0.678193 | + | 0.734884i | \(0.262763\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28.3282 | − | 49.0659i | 1.15940 | − | 2.00814i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.56762 | + | 2.71520i | 0.0640512 | + | 0.110940i | 0.896273 | − | 0.443503i | \(-0.146265\pi\) |
−0.832222 | + | 0.554443i | \(0.812931\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.2118 | −1.31395 | −0.656973 | − | 0.753914i | \(-0.728164\pi\) | ||||
−0.656973 | + | 0.753914i | \(0.728164\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.01131 | 0.244799 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.973496 | + | 1.68614i | 0.0395782 | + | 0.0685515i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.57929 | − | 9.66362i | 0.226456 | − | 0.392234i | −0.730299 | − | 0.683128i | \(-0.760619\pi\) |
0.956755 | + | 0.290894i | \(0.0939526\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.79234 | + | 11.7647i | −0.274789 | + | 0.475948i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.76852 | − | 6.52727i | −0.152209 | − | 0.263634i | 0.779830 | − | 0.625991i | \(-0.215305\pi\) |
−0.932039 | + | 0.362357i | \(0.881972\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.7759 | −0.636147 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.7728 | −0.916797 | −0.458399 | − | 0.888747i | \(-0.651577\pi\) | ||||
−0.458399 | + | 0.888747i | \(0.651577\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.482383 | − | 0.835512i | −0.0193886 | − | 0.0335821i | 0.856168 | − | 0.516697i | \(-0.172839\pi\) |
−0.875557 | + | 0.483115i | \(0.839505\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.53066 | + | 6.11528i | −0.141680 | + | 0.245398i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.6925 | − | 30.6442i | −0.706569 | − | 1.22381i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.6395 | −1.50079 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.90059 | 0.274708 | 0.137354 | − | 0.990522i | \(-0.456140\pi\) | ||||
0.137354 | + | 0.990522i | \(0.456140\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.66277 | + | 16.7364i | 0.384060 | + | 0.665212i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.91227 | + | 8.50829i | −0.194937 | + | 0.337641i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.7974 | + | 25.6298i | −0.585375 | + | 1.01390i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.07217 | + | 1.85705i | 0.0423481 | + | 0.0733490i | 0.886423 | − | 0.462877i | \(-0.153183\pi\) |
−0.844074 | + | 0.536226i | \(0.819849\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.4980 | 1.08441 | 0.542207 | − | 0.840245i | \(-0.317589\pi\) | ||||
0.542207 | + | 0.840245i | \(0.317589\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.6817 | −0.459965 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.4741 | + | 26.8020i | 0.608350 | + | 1.05369i | 0.991512 | + | 0.130013i | \(0.0415018\pi\) |
−0.383162 | + | 0.923681i | \(0.625165\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.12334 | + | 15.8021i | −0.358122 | + | 0.620286i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.7224 | − | 34.1602i | 0.771798 | − | 1.33679i | −0.164779 | − | 0.986330i | \(-0.552691\pi\) |
0.936577 | − | 0.350462i | \(-0.113975\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.47687 | − | 4.29007i | −0.0967794 | − | 0.167627i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26.0481 | −1.01623 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.80237 | 0.342892 | 0.171446 | − | 0.985194i | \(-0.445156\pi\) | ||||
0.171446 | + | 0.985194i | \(0.445156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0548 | + | 24.3436i | 0.546667 | + | 0.946855i | 0.998500 | + | 0.0547525i | \(0.0174370\pi\) |
−0.451833 | + | 0.892103i | \(0.649230\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −40.6945 | + | 70.4849i | −1.58044 | + | 2.73741i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.70523 | + | 4.68560i | −0.104747 | + | 0.181427i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.43393 | − | 7.67980i | −0.171426 | − | 0.296918i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.5317 | 1.02424 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.7933 | −0.570241 | −0.285121 | − | 0.958492i | \(-0.592034\pi\) | ||||
−0.285121 | + | 0.958492i | \(0.592034\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.34340 | − | 2.32684i | −0.0517076 | − | 0.0895602i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.35581 | + | 2.34833i | −0.0521080 | + | 0.0902537i | −0.890903 | − | 0.454194i | \(-0.849927\pi\) |
0.838795 | + | 0.544448i | \(0.183261\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.0609 | − | 22.6221i | 0.500495 | − | 0.866882i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.813164 | + | 1.40844i | 0.0311149 | + | 0.0538925i | 0.881164 | − | 0.472812i | \(-0.156761\pi\) |
−0.850049 | + | 0.526704i | \(0.823428\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.3137 | 0.432275 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.6880 | 0.941908 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0324 | − | 20.8408i | −0.458400 | − | 0.793971i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.4410 | − | 44.0652i | 0.967823 | − | 1.67632i | 0.265992 | − | 0.963975i | \(-0.414301\pi\) |
0.701831 | − | 0.712343i | \(-0.252366\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.35155 | + | 7.53711i | −0.165064 | + | 0.285899i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.9750 | + | 39.7939i | 0.870241 | + | 1.50730i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −46.5317 | −1.75999 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.93106 | 0.299552 | 0.149776 | − | 0.988720i | \(-0.452145\pi\) | ||||
0.149776 | + | 0.988720i | \(0.452145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.3217 | − | 23.0739i | −0.502438 | − | 0.870247i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.53216 | − | 4.38583i | 0.0953666 | − | 0.165180i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.74609 | + | 15.1487i | −0.328466 | + | 0.568920i | −0.982208 | − | 0.187798i | \(-0.939865\pi\) |
0.653741 | + | 0.756718i | \(0.273198\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.88034 | + | 4.98889i | 0.108021 | + | 0.187098i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.4197 | 0.652374 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.0796 | 0.788332 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.6092 | − | 42.6245i | −0.919049 | − | 1.59184i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.06468 | − | 15.7005i | 0.338055 | − | 0.585529i | −0.646011 | − | 0.763328i | \(-0.723564\pi\) |
0.984067 | + | 0.177798i | \(0.0568975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.0296 | − | 24.3000i | 0.521766 | − | 0.903725i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.02933 | − | 1.78285i | −0.0382284 | − | 0.0662135i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.42538 | −0.0899523 | −0.0449761 | − | 0.998988i | \(-0.514321\pi\) | ||||
−0.0449761 | + | 0.998988i | \(0.514321\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.17729 | −0.0806402 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.0124 | + | 29.4664i | 0.629227 | + | 1.08985i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.88293 | + | 17.1177i | −0.365035 | + | 0.632258i | −0.988782 | − | 0.149368i | \(-0.952276\pi\) |
0.623747 | + | 0.781626i | \(0.285609\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.11093 | + | 10.5844i | −0.225099 | + | 0.389883i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.9533 | − | 34.5601i | −0.733993 | − | 1.27131i | −0.955164 | − | 0.296078i | \(-0.904321\pi\) |
0.221171 | − | 0.975235i | \(-0.429012\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −57.6118 | −2.11642 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.0921 | 1.21403 | 0.607016 | − | 0.794689i | \(-0.292366\pi\) | ||||
0.607016 | + | 0.794689i | \(0.292366\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.22634 | − | 5.58818i | −0.118204 | − | 0.204735i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.46255 | − | 16.3896i | 0.346217 | − | 0.599665i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.49266 | − | 6.04946i | 0.127449 | − | 0.220748i | −0.795239 | − | 0.606296i | \(-0.792654\pi\) |
0.922688 | + | 0.385549i | \(0.125988\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.9195 | − | 44.8939i | −0.944560 | − | 1.63603i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.02606 | 0.146523 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.4796 | −0.889725 | −0.444863 | − | 0.895599i | \(-0.646747\pi\) | ||||
−0.444863 | + | 0.895599i | \(0.646747\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.3265 | + | 17.8860i | 0.374827 | + | 0.649220i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.69756 | − | 8.13641i | 0.170286 | − | 0.294945i | −0.768234 | − | 0.640170i | \(-0.778864\pi\) |
0.938520 | + | 0.345225i | \(0.112197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.62892 | − | 9.74958i | 0.203514 | − | 0.352497i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.8541 | + | 25.7281i | 0.536351 | + | 0.928987i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.7183 | −1.07167 | −0.535835 | − | 0.844323i | \(-0.680003\pi\) | ||||
−0.535835 | + | 0.844323i | \(0.680003\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.8590 | 1.03933 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.1054 | − | 33.0915i | −0.687173 | − | 1.19022i | −0.972749 | − | 0.231862i | \(-0.925518\pi\) |
0.285576 | − | 0.958356i | \(-0.407815\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.31407 | + | 5.74014i | −0.119045 | + | 0.206192i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.2630 | + | 28.1684i | −0.582684 | + | 1.00924i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.0852 | − | 52.1091i | −1.07653 | − | 1.86461i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.53122 | 0.197670 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.5260 | 0.554148 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.4057 | + | 21.4873i | 0.442215 | + | 0.765940i | 0.997854 | − | 0.0654847i | \(-0.0208594\pi\) |
−0.555638 | + | 0.831424i | \(0.687526\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31.5074 | + | 54.5725i | −1.12169 | + | 1.94283i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.5987 | − | 37.4101i | 0.766993 | − | 1.32847i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.48565 | + | 7.76937i | 0.159089 | + | 0.275551i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.9296 | 0.812210 | 0.406105 | − | 0.913826i | \(-0.366887\pi\) | ||||
0.406105 | + | 0.913826i | \(0.366887\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.7507 | −0.521841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.87001 | + | 17.0954i | 0.348740 | + | 0.604035i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.4798 | − | 45.8643i | 0.934451 | − | 1.61852i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.80721 | + | 4.86222i | −0.0988183 | + | 0.171158i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.1360 | + | 29.6804i | 0.602470 | + | 1.04351i | 0.992446 | + | 0.122683i | \(0.0391499\pi\) |
−0.389976 | + | 0.920825i | \(0.627517\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.5925 | 1.32005 | 0.660025 | − | 0.751244i | \(-0.270546\pi\) | ||||
0.660025 | + | 0.751244i | \(0.270546\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.7358 | 0.516807 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.4805 | − | 21.6169i | −0.437173 | − | 0.757206i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0424 | + | 20.8580i | −0.421309 | + | 0.729728i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.6321 | + | 27.0757i | −0.545565 | + | 0.944947i | 0.453006 | + | 0.891508i | \(0.350352\pi\) |
−0.998571 | + | 0.0534393i | \(0.982982\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.22260 | + | 15.9740i | 0.321480 | + | 0.556819i | 0.980794 | − | 0.195049i | \(-0.0624865\pi\) |
−0.659314 | + | 0.751868i | \(0.729153\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.85838 | −0.273594 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.5931 | 0.507450 | 0.253725 | − | 0.967276i | \(-0.418344\pi\) | ||||
0.253725 | + | 0.967276i | \(0.418344\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.05285 | + | 10.4838i | 0.210224 | + | 0.364119i | 0.951785 | − | 0.306767i | \(-0.0992473\pi\) |
−0.741561 | + | 0.670886i | \(0.765914\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.55392 | + | 6.15556i | −0.123284 | + | 0.213534i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.03696 | − | 13.9204i | 0.278131 | − | 0.481736i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.90427 | − | 15.4226i | −0.307777 | − | 0.533085i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.8245 | −0.477276 | −0.238638 | − | 0.971109i | \(-0.576701\pi\) | ||||
−0.238638 | + | 0.971109i | \(0.576701\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.7619 | −0.853859 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.78918 | − | 4.83101i | −0.0960645 | − | 0.166389i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.6603 | − | 18.4642i | 0.366726 | − | 0.635187i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.6647 | − | 23.6680i | 0.468973 | − | 0.812285i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.77542 | + | 13.4674i | 0.266538 | + | 0.461657i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.7912 | 0.540680 | 0.270340 | − | 0.962765i | \(-0.412864\pi\) | ||||
0.270340 | + | 0.962765i | \(0.412864\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.96895 | 0.272532 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.74183 | − | 11.6772i | −0.230297 | − | 0.398886i | 0.727599 | − | 0.686003i | \(-0.240636\pi\) |
−0.957895 | + | 0.287117i | \(0.907303\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.9150 | − | 20.6374i | 0.406535 | − | 0.704140i | −0.587964 | − | 0.808887i | \(-0.700070\pi\) |
0.994499 | + | 0.104748i | \(0.0334035\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.17796 | + | 2.04029i | −0.0400983 | + | 0.0694523i | −0.885378 | − | 0.464872i | \(-0.846100\pi\) |
0.845280 | + | 0.534324i | \(0.179434\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0178027 | + | 0.0308352i | 0.000605310 | + | 0.00104843i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −51.2469 | −1.74044 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.7123 | −0.397312 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.94948 | + | 17.2330i | 0.337125 | + | 0.583918i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.2108 | − | 26.3459i | 0.514808 | − | 0.891674i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.1446 | + | 22.7672i | −0.443862 | + | 0.768792i | −0.997972 | − | 0.0636515i | \(-0.979725\pi\) |
0.554110 | + | 0.832444i | \(0.313059\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.0176 | + | 48.5279i | 0.945010 | + | 1.63680i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.2476 | −1.55812 | −0.779061 | − | 0.626948i | \(-0.784304\pi\) | ||||
−0.779061 | + | 0.626948i | \(0.784304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.1184 | 1.35009 | 0.675045 | − | 0.737777i | \(-0.264124\pi\) | ||||
0.675045 | + | 0.737777i | \(0.264124\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.53755 | − | 9.59132i | −0.186143 | − | 0.322409i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.3843 | − | 28.3784i | 0.550130 | − | 0.952853i | −0.448135 | − | 0.893966i | \(-0.647912\pi\) |
0.998265 | − | 0.0588866i | \(-0.0187551\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.1089 | − | 34.8297i | 0.673674 | − | 1.16684i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.22068 | − | 9.04249i | −0.174704 | − | 0.302595i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.45268 | 0.148837 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.6260 | 1.12274 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.82255 | − | 11.8170i | −0.227545 | − | 0.394119i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.0652 | − | 22.6296i | 0.435265 | − | 0.753901i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.3688 | − | 19.6914i | 0.377913 | − | 0.654564i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.74355 | − | 4.75197i | −0.0910980 | − | 0.157786i | 0.816875 | − | 0.576814i | \(-0.195704\pi\) |
−0.907973 | + | 0.419028i | \(0.862371\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.09031 | −0.202003 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.3276 | −1.26985 | −0.634924 | − | 0.772574i | \(-0.718969\pi\) | ||||
−0.634924 | + | 0.772574i | \(0.718969\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.2387 | + | 33.3225i | 0.636710 | + | 1.10281i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.05191 | + | 13.9463i | −0.266188 | + | 0.461051i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.3047 | − | 33.4368i | 0.636804 | − | 1.10298i | −0.349326 | − | 0.937001i | \(-0.613589\pi\) |
0.986130 | − | 0.165976i | \(-0.0530773\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.0373 | + | 22.5813i | 0.429594 | + | 0.744079i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −97.9662 | −3.22460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.91704 | −0.194551 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.5971 | − | 18.3547i | −0.348054 | − | 0.602848i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.6694 | − | 34.0683i | 0.645331 | − | 1.11775i | −0.338894 | − | 0.940824i | \(-0.610053\pi\) |
0.984225 | − | 0.176921i | \(-0.0566138\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.28059 | + | 16.0744i | −0.303833 | + | 0.526254i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.4444 | + | 19.8223i | 0.374273 | + | 0.648259i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.4619 | 0.603124 | 0.301562 | − | 0.953447i | \(-0.402492\pi\) | ||||
0.301562 | + | 0.953447i | \(0.402492\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.83532 | −0.125161 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.8002 | − | 32.5630i | −0.612870 | − | 1.06152i | −0.990754 | − | 0.135669i | \(-0.956682\pi\) |
0.377884 | − | 0.925853i | \(-0.376652\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.49218 | − | 16.4409i | 0.309108 | − | 0.535390i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.7107 | − | 34.1400i | 0.640513 | − | 1.10940i | −0.344805 | − | 0.938674i | \(-0.612055\pi\) |
0.985318 | − | 0.170727i | \(-0.0546116\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43.1129 | − | 74.6737i | −1.39950 | − | 2.42401i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.0272 | −0.422437 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.4541 | 0.792148 | 0.396074 | − | 0.918219i | \(-0.370372\pi\) | ||||
0.396074 | + | 0.918219i | \(0.370372\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.7760 | − | 22.1288i | −0.413423 | − | 0.716070i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.08887 | − | 14.0103i | 0.261476 | − | 0.452890i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.46615 | + | 11.1997i | −0.208586 | + | 0.361281i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.44702 | + | 16.3627i | 0.304426 | + | 0.527281i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.0904 | −0.678923 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.5757 | 0.725986 | 0.362993 | − | 0.931792i | \(-0.381755\pi\) | ||||
0.362993 | + | 0.931792i | \(0.381755\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31.2783 | − | 54.1756i | −1.00480 | − | 1.74037i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.5818 | − | 30.4526i | 0.564226 | − | 0.977269i | −0.432895 | − | 0.901444i | \(-0.642508\pi\) |
0.997121 | − | 0.0758244i | \(-0.0241588\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.39729 | + | 11.0804i | −0.204877 | + | 0.354858i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.2455 | − | 22.9419i | −0.423761 | − | 0.733976i | 0.572543 | − | 0.819875i | \(-0.305957\pi\) |
−0.996304 | + | 0.0858992i | \(0.972624\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.1343 | −1.28270 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.7494 | −0.470913 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.6690 | + | 23.6754i | 0.435974 | + | 0.755128i | 0.997375 | − | 0.0724156i | \(-0.0230708\pi\) |
−0.561401 | + | 0.827544i | \(0.689737\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.23111 | − | 14.2567i | 0.262265 | − | 0.454256i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.02871 | − | 12.1741i | 0.223500 | − | 0.387113i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.9950 | − | 51.9529i | −0.952823 | − | 1.65034i | −0.739274 | − | 0.673405i | \(-0.764831\pi\) |
−0.213549 | − | 0.976932i | \(-0.568502\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.8024 | 0.977486 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.9419 | −0.822412 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.2322 | − | 19.4548i | −0.355729 | − | 0.616140i | 0.631514 | − | 0.775365i | \(-0.282434\pi\) |
−0.987242 | + | 0.159224i | \(0.949101\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.94897 | − | 13.7680i | 0.251494 | − | 0.435601i |
(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 | 1960.2.q.y.961.3 | 8 | ||
7.2 | even | 3 | 1960.2.a.x.1.2 | ✓ | 4 | ||
7.3 | odd | 6 | 1960.2.q.x.361.2 | 8 | |||
7.4 | even | 3 | inner | 1960.2.q.y.361.3 | 8 | ||
7.5 | odd | 6 | 1960.2.a.y.1.3 | yes | 4 | ||
7.6 | odd | 2 | 1960.2.q.x.961.2 | 8 | |||
28.19 | even | 6 | 3920.2.a.cd.1.2 | 4 | |||
28.23 | odd | 6 | 3920.2.a.ce.1.3 | 4 | |||
35.9 | even | 6 | 9800.2.a.cs.1.3 | 4 | |||
35.19 | odd | 6 | 9800.2.a.cl.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.a.x.1.2 | ✓ | 4 | 7.2 | even | 3 | ||
1960.2.a.y.1.3 | yes | 4 | 7.5 | odd | 6 | ||
1960.2.q.x.361.2 | 8 | 7.3 | odd | 6 | |||
1960.2.q.x.961.2 | 8 | 7.6 | odd | 2 | |||
1960.2.q.y.361.3 | 8 | 7.4 | even | 3 | inner | ||
1960.2.q.y.961.3 | 8 | 1.1 | even | 1 | trivial | ||
3920.2.a.cd.1.2 | 4 | 28.19 | even | 6 | |||
3920.2.a.ce.1.3 | 4 | 28.23 | odd | 6 | |||
9800.2.a.cl.1.2 | 4 | 35.19 | odd | 6 | |||
9800.2.a.cs.1.3 | 4 | 35.9 | even | 6 |