Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.37 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.18 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.20926 | + | 0.345224i | 0.988010 | + | 0.154389i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.0620642i | − | 0.0234581i | −0.999931 | − | 0.0117290i | \(-0.996266\pi\) | ||
0.999931 | − | 0.0117290i | \(-0.00373355\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.73721 | 1.12681 | 0.563405 | − | 0.826181i | \(-0.309491\pi\) | ||||
0.563405 | + | 0.826181i | \(0.309491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.61751i | − | 1.00332i | −0.865066 | − | 0.501659i | \(-0.832723\pi\) | ||
0.865066 | − | 0.501659i | \(-0.167277\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.345224 | + | 2.20926i | −0.0891364 | + | 0.570428i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.75776i | − | 1.39646i | −0.715873 | − | 0.698231i | \(-0.753971\pi\) | ||
0.715873 | − | 0.698231i | \(-0.246029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.84485 | −1.11148 | −0.555742 | − | 0.831355i | \(-0.687566\pi\) | ||||
−0.555742 | + | 0.831355i | \(0.687566\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0620642 | 0.0135435 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.34603i | 0.697696i | 0.937179 | + | 0.348848i | \(0.113427\pi\) | ||||
−0.937179 | + | 0.348848i | \(0.886573\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.76164 | + | 1.52538i | 0.952328 | + | 0.305075i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.90056 | −0.910012 | −0.455006 | − | 0.890488i | \(-0.650363\pi\) | ||||
−0.455006 | + | 0.890488i | \(0.650363\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.28015 | 1.66676 | 0.833382 | − | 0.552697i | \(-0.186401\pi\) | ||||
0.833382 | + | 0.552697i | \(0.186401\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.73721i | 0.650564i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0214260 | − | 0.137116i | 0.00362166 | − | 0.0231768i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.35286i | 0.551207i | 0.961271 | + | 0.275604i | \(0.0888778\pi\) | ||||
−0.961271 | + | 0.275604i | \(0.911122\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.61751 | 0.579265 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.38987 | 1.46645 | 0.733226 | − | 0.679985i | \(-0.238014\pi\) | ||||
0.733226 | + | 0.679985i | \(0.238014\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.89223i | − | 0.441061i | −0.975380 | − | 0.220530i | \(-0.929221\pi\) | ||
0.975380 | − | 0.220530i | \(-0.0707788\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.20926 | − | 0.345224i | −0.329337 | − | 0.0514629i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.5191i | − | 1.53436i | −0.641429 | − | 0.767182i | \(-0.721658\pi\) | ||
0.641429 | − | 0.767182i | \(-0.278342\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99615 | 0.999450 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.75776 | 0.806248 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.91099i | − | 1.36138i | −0.732572 | − | 0.680689i | \(-0.761680\pi\) | ||
0.732572 | − | 0.680689i | \(-0.238320\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.25646 | + | 1.29017i | 1.11330 | + | 0.173967i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.84485i | − | 0.641716i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.42481 | −1.22701 | −0.613503 | − | 0.789692i | \(-0.710240\pi\) | ||||
−0.613503 | + | 0.789692i | \(0.710240\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.5713 | −1.48156 | −0.740779 | − | 0.671749i | \(-0.765544\pi\) | ||||
−0.740779 | + | 0.671749i | \(0.765544\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0620642i | 0.00781935i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.24885 | − | 7.99201i | 0.154901 | − | 0.991287i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000i | 0.122169i | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.34603 | −0.402815 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.9803 | 1.77784 | 0.888920 | − | 0.458062i | \(-0.151456\pi\) | ||||
0.888920 | + | 0.458062i | \(0.151456\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.5508i | − | 1.23488i | −0.786618 | − | 0.617441i | \(-0.788170\pi\) | ||
0.786618 | − | 0.617441i | \(-0.211830\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.52538 | + | 4.76164i | −0.176135 | + | 0.549827i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.231947i | − | 0.0264328i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4258 | 1.51052 | 0.755262 | − | 0.655423i | \(-0.227510\pi\) | ||||
0.755262 | + | 0.655423i | \(0.227510\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.66914i | 0.402740i | 0.979515 | + | 0.201370i | \(0.0645394\pi\) | ||||
−0.979515 | + | 0.201370i | \(0.935461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.98772 | − | 12.7204i | 0.215598 | − | 1.37972i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 4.90056i | − | 0.525395i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.66849 | −0.600859 | −0.300429 | − | 0.953804i | \(-0.597130\pi\) | ||||
−0.300429 | + | 0.953804i | \(0.597130\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.224518 | −0.0235359 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.28015i | 0.962307i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.7035 | − | 1.67256i | −1.09816 | − | 0.171601i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.89298i | 0.293737i | 0.989156 | + | 0.146869i | \(0.0469194\pi\) | ||||
−0.989156 | + | 0.146869i | \(0.953081\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.73721 | −0.375604 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.57914 | −0.256634 | −0.128317 | − | 0.991733i | \(-0.540958\pi\) | ||||
−0.128317 | + | 0.991733i | \(0.540958\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.1600i | 1.59229i | 0.605105 | + | 0.796146i | \(0.293131\pi\) | ||||
−0.605105 | + | 0.796146i | \(0.706869\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.137116 | + | 0.0214260i | 0.0133811 | + | 0.00209097i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.20665i | − | 0.600019i | −0.953936 | − | 0.300010i | \(-0.903010\pi\) | ||
0.953936 | − | 0.300010i | \(-0.0969899\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.56692 | −0.437431 | −0.218716 | − | 0.975789i | \(-0.570187\pi\) | ||||
−0.218716 | + | 0.975789i | \(0.570187\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.35286 | −0.318240 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 7.46157i | − | 0.701925i | −0.936390 | − | 0.350963i | \(-0.885854\pi\) | ||
0.936390 | − | 0.350963i | \(-0.114146\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.15513 | + | 7.39225i | −0.107716 | + | 0.689331i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.61751i | 0.334439i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.357351 | −0.0327583 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.96672 | 0.269702 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.38987i | 0.846656i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.99310 | + | 5.01378i | 0.893810 | + | 0.448446i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.69867i | 0.416940i | 0.978029 | + | 0.208470i | \(0.0668483\pi\) | ||||
−0.978029 | + | 0.208470i | \(0.933152\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.89223 | 0.254647 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.24849 | 0.283822 | 0.141911 | − | 0.989879i | \(-0.454675\pi\) | ||||
0.141911 | + | 0.989879i | \(0.454675\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.300692i | 0.0260733i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.345224 | − | 2.20926i | 0.0297121 | − | 0.190143i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.5204i | 1.24056i | 0.784381 | + | 0.620280i | \(0.212981\pi\) | ||||
−0.784381 | + | 0.620280i | \(0.787019\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.51459 | 0.467741 | 0.233871 | − | 0.972268i | \(-0.424861\pi\) | ||||
0.233871 | + | 0.972268i | \(0.424861\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.5191 | 0.885866 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 13.5194i | − | 1.13055i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.8266 | − | 1.69179i | −0.899101 | − | 0.140496i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.99615i | 0.577033i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.7886 | 1.12961 | 0.564803 | − | 0.825226i | \(-0.308952\pi\) | ||||
0.564803 | + | 0.825226i | \(0.308952\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.495460 | 0.0403199 | 0.0201600 | − | 0.999797i | \(-0.493582\pi\) | ||||
0.0201600 | + | 0.999797i | \(0.493582\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.75776i | 0.465487i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.5023 | + | 3.20373i | 1.64678 | + | 0.257330i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.7674i | − | 1.41799i | −0.705211 | − | 0.708997i | \(-0.749148\pi\) | ||
0.705211 | − | 0.708997i | \(-0.250852\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.91099 | 0.785993 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.207669 | 0.0163666 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.8769i | − | 1.32190i | −0.750430 | − | 0.660950i | \(-0.770153\pi\) | ||
0.750430 | − | 0.660950i | \(-0.229847\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.29017 | + | 8.25646i | −0.100440 | + | 0.642764i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.9078i | 1.38575i | 0.721060 | + | 0.692873i | \(0.243655\pi\) | ||||
−0.721060 | + | 0.692873i | \(0.756345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0863858 | −0.00664506 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.84485 | 0.370495 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.43227i | 0.565065i | 0.959258 | + | 0.282533i | \(0.0911746\pi\) | ||||
−0.959258 | + | 0.282533i | \(0.908825\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0946713 | − | 0.295527i | 0.00715648 | − | 0.0223398i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 9.42481i | − | 0.708412i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.78910 | −0.656928 | −0.328464 | − | 0.944516i | \(-0.606531\pi\) | ||||
−0.328464 | + | 0.944516i | \(0.606531\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2064 | −1.05595 | −0.527977 | − | 0.849259i | \(-0.677049\pi\) | ||||
−0.527977 | + | 0.849259i | \(0.677049\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 11.5713i | − | 0.855378i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.15749 | + | 7.40734i | −0.0851003 | + | 0.544599i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 21.5179i | − | 1.57355i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.0620642 | −0.00451450 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.33664 | 0.241431 | 0.120716 | − | 0.992687i | \(-0.461481\pi\) | ||||
0.120716 | + | 0.992687i | \(0.461481\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.227371i | 0.0163665i | 0.999967 | + | 0.00818327i | \(0.00260484\pi\) | ||||
−0.999967 | + | 0.00818327i | \(0.997395\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.99201 | + | 1.24885i | 0.572320 | + | 0.0894321i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.8648i | 1.27282i | 0.771353 | + | 0.636408i | \(0.219580\pi\) | ||||
−0.771353 | + | 0.636408i | \(0.780420\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.02003 | −0.497637 | −0.248818 | − | 0.968550i | \(-0.580042\pi\) | ||||
−0.248818 | + | 0.968550i | \(0.580042\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.304149i | 0.0213471i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.7447 | + | 3.24161i | 1.44887 | + | 0.226404i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 3.34603i | − | 0.232565i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.1062 | −1.25243 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4786 | 1.06559 | 0.532795 | − | 0.846244i | \(-0.321142\pi\) | ||||
0.532795 | + | 0.846244i | \(0.321142\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.9803i | 1.02644i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.998466 | − | 6.38968i | 0.0680948 | − | 0.435773i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.575965i | − | 0.0390991i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5508 | 0.712959 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.8288 | −1.40109 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.6955i | − | 0.984081i | −0.870572 | − | 0.492040i | \(-0.836251\pi\) | ||
0.870572 | − | 0.492040i | \(-0.163749\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.76164 | − | 1.52538i | −0.317443 | − | 0.101692i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.83025i | − | 0.121478i | −0.998154 | − | 0.0607390i | \(-0.980654\pi\) | ||
0.998154 | − | 0.0607390i | \(-0.0193457\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.5339 | 1.29084 | 0.645418 | − | 0.763830i | \(-0.276683\pi\) | ||||
0.645418 | + | 0.763830i | \(0.276683\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.231947 | 0.0152610 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.91720i | 0.256624i | 0.991734 | + | 0.128312i | \(0.0409559\pi\) | ||||
−0.991734 | + | 0.128312i | \(0.959044\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.63144 | − | 23.2394i | 0.236889 | − | 1.51597i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.4258i | 0.872101i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.408885 | −0.0264486 | −0.0132243 | − | 0.999913i | \(-0.504210\pi\) | ||||
−0.0132243 | + | 0.999913i | \(0.504210\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.711176 | −0.0458109 | −0.0229054 | − | 0.999738i | \(-0.507292\pi\) | ||||
−0.0229054 | + | 0.999738i | \(0.507292\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.4563 | + | 2.41524i | 0.987466 | + | 0.154304i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.5263i | 1.11517i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.66914 | −0.232522 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.8243 | 1.18818 | 0.594091 | − | 0.804398i | \(-0.297512\pi\) | ||||
0.594091 | + | 0.804398i | \(0.297512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.5048i | 0.786172i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.7204 | + | 1.98772i | 0.796581 | + | 0.124476i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.3805i | 1.83271i | 0.400370 | + | 0.916354i | \(0.368882\pi\) | ||||
−0.400370 | + | 0.916354i | \(0.631118\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.208093 | 0.0129303 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.90056 | 0.303337 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 17.9546i | − | 1.10713i | −0.832806 | − | 0.553565i | \(-0.813267\pi\) | ||
0.832806 | − | 0.553565i | \(-0.186733\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.42151 | − | 21.8959i | 0.210182 | − | 1.34506i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.66849i | − | 0.346906i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.37091 | 0.205528 | 0.102764 | − | 0.994706i | \(-0.467231\pi\) | ||||
0.102764 | + | 0.994706i | \(0.467231\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.707519 | 0.0429787 | 0.0214893 | − | 0.999769i | \(-0.493159\pi\) | ||||
0.0214893 | + | 0.999769i | \(0.493159\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 0.224518i | − | 0.0135884i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.7952 | + | 5.70065i | 1.07309 | + | 0.343762i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 31.4894i | − | 1.89202i | −0.324145 | − | 0.946008i | \(-0.605076\pi\) | ||
0.324145 | − | 0.946008i | \(-0.394924\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.28015 | −0.555588 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.98185 | 0.237537 | 0.118769 | − | 0.992922i | \(-0.462105\pi\) | ||||
0.118769 | + | 0.992922i | \(0.462105\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.7478i | 1.70888i | 0.519553 | + | 0.854438i | \(0.326099\pi\) | ||||
−0.519553 | + | 0.854438i | \(0.673901\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.67256 | − | 10.7035i | 0.0990738 | − | 0.634022i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.582775i | − | 0.0344001i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1518 | −0.950106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.89298 | −0.169589 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.4818i | 1.31340i | 0.754151 | + | 0.656701i | \(0.228049\pi\) | ||||
−0.754151 | + | 0.656701i | \(0.771951\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.8218 | − | 3.25367i | −1.21229 | − | 0.189436i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.73721i | − | 0.216855i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.1043 | 0.700011 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.179504 | −0.0103464 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.57914i | − | 0.148168i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −25.5641 | − | 3.99470i | −1.46379 | − | 0.228736i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.9009i | − | 0.907511i | −0.891126 | − | 0.453755i | \(-0.850084\pi\) | ||
0.891126 | − | 0.453755i | \(-0.149916\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.1600 | −0.919310 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.41108 | −0.476948 | −0.238474 | − | 0.971149i | \(-0.576647\pi\) | ||||
−0.238474 | + | 0.971149i | \(0.576647\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0588i | 1.13379i | 0.823790 | + | 0.566895i | \(0.191855\pi\) | ||||
−0.823790 | + | 0.566895i | \(0.808145\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0214260 | + | 0.137116i | −0.00120722 | + | 0.00772560i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 14.2660i | − | 0.801259i | −0.916240 | − | 0.400629i | \(-0.868791\pi\) | ||
0.916240 | − | 0.400629i | \(-0.131209\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.3144 | −1.02541 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.20665 | 0.346421 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.8955i | 1.55215i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.51807 | − | 17.2253i | 0.306087 | − | 0.955487i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 4.56692i | − | 0.252551i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.652858 | −0.0359932 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.8860 | −1.25793 | −0.628963 | − | 0.777435i | \(-0.716520\pi\) | ||||
−0.628963 | + | 0.777435i | \(0.716520\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3.35286i | − | 0.183736i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.345224 | + | 2.20926i | −0.0188616 | + | 0.120705i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4698i | 0.897166i | 0.893741 | + | 0.448583i | \(0.148071\pi\) | ||||
−0.893741 | + | 0.448583i | \(0.851929\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.46157 | 0.405257 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 34.6819 | 1.87813 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 0.868659i | − | 0.0469032i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.39225 | − | 1.15513i | −0.397985 | − | 0.0621901i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 7.63004i | − | 0.409602i | −0.978804 | − | 0.204801i | \(-0.934345\pi\) | ||
0.978804 | − | 0.204801i | \(-0.0656547\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.9413 | −1.92389 | −0.961946 | − | 0.273240i | \(-0.911905\pi\) | ||||
−0.961946 | + | 0.273240i | \(0.911905\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.61751 | −0.193088 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 3.59182i | − | 0.191173i | −0.995421 | − | 0.0955865i | \(-0.969527\pi\) | ||
0.995421 | − | 0.0955865i | \(-0.0304727\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.0955 | + | 5.17157i | 1.75652 | + | 0.274479i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 0.357351i | − | 0.0189130i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.5358 | 1.13662 | 0.568309 | − | 0.822815i | \(-0.307598\pi\) | ||||
0.568309 | + | 0.822815i | \(0.307598\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.47256 | 0.235398 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.96672i | 0.155713i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.64240 | − | 23.3095i | 0.190652 | − | 1.22008i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.57129i | 0.447418i | 0.974656 | + | 0.223709i | \(0.0718165\pi\) | ||||
−0.974656 | + | 0.223709i | \(0.928183\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.38987 | −0.488817 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.615117 | −0.0319353 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.42610i | − | 0.229175i | −0.993413 | − | 0.114587i | \(-0.963445\pi\) | ||
0.993413 | − | 0.114587i | \(-0.0365546\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.01378 | + | 9.99310i | −0.258911 | + | 0.516041i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.7278i | 0.913030i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.6306 | 1.62475 | 0.812377 | − | 0.583133i | \(-0.198173\pi\) | ||||
0.812377 | + | 0.583133i | \(0.198173\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.69867 | −0.240720 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 38.3554i | 1.95987i | 0.199313 | + | 0.979936i | \(0.436129\pi\) | ||||
−0.199313 | + | 0.979936i | \(0.563871\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0800735 | − | 0.512430i | 0.00408093 | − | 0.0261159i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.89223i | 0.147020i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.83638 | −0.346618 | −0.173309 | − | 0.984867i | \(-0.555446\pi\) | ||||
−0.173309 | + | 0.984867i | \(0.555446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.2657 | 0.974306 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.24849i | 0.163865i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.6611 | + | 4.63492i | 1.49241 | + | 0.233208i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.2569i | 0.765722i | 0.923806 | + | 0.382861i | \(0.125061\pi\) | ||||
−0.923806 | + | 0.382861i | \(0.874939\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.300692 | −0.0150534 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.50327 | 0.0750696 | 0.0375348 | − | 0.999295i | \(-0.488049\pi\) | ||||
0.0375348 | + | 0.999295i | \(0.488049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 33.5711i | − | 1.67229i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.20926 | + | 0.345224i | 0.109779 | + | 0.0171543i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.5304i | 0.621106i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.59665 | −0.227290 | −0.113645 | − | 0.993521i | \(-0.536253\pi\) | ||||
−0.113645 | + | 0.993521i | \(0.536253\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.5204 | −0.716237 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.584943i | 0.0287832i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.26667 | + | 8.10607i | −0.0621786 | + | 0.397912i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.51459i | 0.270051i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.1376 | −0.495255 | −0.247628 | − | 0.968855i | \(-0.579651\pi\) | ||||
−0.247628 | + | 0.968855i | \(0.579651\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.20988 | 0.107703 | 0.0538514 | − | 0.998549i | \(-0.482850\pi\) | ||||
0.0538514 | + | 0.998549i | \(0.482850\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.5191i | 0.511455i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.78276 | − | 27.4164i | 0.426026 | − | 1.32989i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.718166i | 0.0347545i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.5194 | 0.652722 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.6797 | 1.18878 | 0.594389 | − | 0.804177i | \(-0.297394\pi\) | ||||
0.594389 | + | 0.804177i | \(0.297394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 34.3378i | − | 1.65017i | −0.565009 | − | 0.825085i | \(-0.691127\pi\) | ||
0.565009 | − | 0.825085i | \(-0.308873\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.69179 | − | 10.8266i | 0.0811152 | − | 0.519096i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 16.2110i | − | 0.775479i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.7048 | 1.51319 | 0.756593 | − | 0.653886i | \(-0.226862\pi\) | ||||
0.756593 | + | 0.653886i | \(0.226862\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.99615 | −0.333150 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.5075i | 1.21190i | 0.795503 | + | 0.605949i | \(0.207207\pi\) | ||||
−0.795503 | + | 0.605949i | \(0.792793\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.5232 | − | 1.95690i | −0.593655 | − | 0.0927659i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.7886i | 0.652178i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.1343 | −1.04458 | −0.522291 | − | 0.852767i | \(-0.674923\pi\) | ||||
−0.522291 | + | 0.852767i | \(0.674923\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.0919 | 1.65241 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.495460i | 0.0232787i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.496018 | − | 0.0775089i | −0.0232537 | − | 0.00363367i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 8.10869i | − | 0.379308i | −0.981851 | − | 0.189654i | \(-0.939263\pi\) | ||
0.981851 | − | 0.189654i | \(-0.0607367\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.75776 | −0.268749 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.3960 | −1.36911 | −0.684553 | − | 0.728963i | \(-0.740003\pi\) | ||||
−0.684553 | + | 0.728963i | \(0.740003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.79537i | 0.362281i | 0.983457 | + | 0.181141i | \(0.0579790\pi\) | ||||
−0.983457 | + | 0.181141i | \(0.942021\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.20373 | + | 20.5023i | −0.148569 | + | 0.950769i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 32.2930i | − | 1.49434i | −0.664631 | − | 0.747172i | \(-0.731411\pi\) | ||
0.664631 | − | 0.747172i | \(-0.268589\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0620642 | 0.00286586 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.7674 | 0.818679 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10.8089i | − | 0.496992i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.0694 | − | 7.39022i | −1.05850 | − | 0.339087i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.91099i | 0.453793i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.14877 | −0.418018 | −0.209009 | − | 0.977914i | \(-0.567024\pi\) | ||||
−0.209009 | + | 0.977914i | \(0.567024\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.1290 | 0.553036 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.207669i | 0.00944926i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.998724 | + | 6.39133i | −0.0453497 | + | 0.290215i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.6778i | 0.529171i | 0.964362 | + | 0.264586i | \(0.0852351\pi\) | ||||
−0.964362 | + | 0.264586i | \(0.914765\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.8769 | 0.763200 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.3324 | 1.68479 | 0.842394 | − | 0.538862i | \(-0.181145\pi\) | ||||
0.842394 | + | 0.538862i | \(0.181145\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.2163i | 1.27080i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.25646 | − | 1.29017i | −0.371100 | − | 0.0579890i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 0.929743i | − | 0.0417047i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.59494 | −0.160931 | −0.0804657 | − | 0.996757i | \(-0.525641\pi\) | ||||
−0.0804657 | + | 0.996757i | \(0.525641\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.9078 | −0.800061 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.80672i | 0.125146i | 0.998040 | + | 0.0625728i | \(0.0199305\pi\) | ||||
−0.998040 | + | 0.0625728i | \(0.980069\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.69799 | − | 0.890381i | −0.253557 | − | 0.0396214i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 0.0863858i | − | 0.00383653i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.1919 | −0.806342 | −0.403171 | − | 0.915125i | \(-0.632092\pi\) | ||||
−0.403171 | + | 0.915125i | \(0.632092\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.654828 | −0.0289679 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.84485i | 0.213905i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.57881 | + | 35.7016i | −0.245832 | + | 1.57320i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 39.3120i | − | 1.72894i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.43227 | −0.326241 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.4963 | −1.29226 | −0.646129 | − | 0.763229i | \(-0.723613\pi\) | ||||
−0.646129 | + | 0.763229i | \(0.723613\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 13.5787i | − | 0.593754i | −0.954916 | − | 0.296877i | \(-0.904055\pi\) | ||
0.954916 | − | 0.296877i | \(-0.0959452\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.295527 | + | 0.0946713i | 0.0128979 | + | 0.00413179i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 53.4329i | − | 2.32757i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.8041 | 0.513220 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.42481 | 0.409002 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 33.9680i | − | 1.47132i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.14268 | − | 13.7121i | 0.0926362 | − | 0.592825i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 8.78910i | − | 0.379278i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.1461 | 1.12619 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.9413 | 0.599384 | 0.299692 | − | 0.954036i | \(-0.403116\pi\) | ||||
0.299692 | + | 0.954036i | \(0.403116\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 14.2064i | − | 0.609655i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0895 | − | 1.57661i | −0.432187 | − | 0.0675345i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 34.5930i | − | 1.47909i | −0.673107 | − | 0.739545i | \(-0.735041\pi\) | ||
0.673107 | − | 0.739545i | \(-0.264959\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.5713 | 0.493853 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.7425 | 1.01146 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 0.833263i | − | 0.0354339i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.40734 | − | 1.15749i | −0.314424 | − | 0.0491327i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.13485i | 0.0480852i | 0.999711 | + | 0.0240426i | \(0.00765373\pi\) | ||||
−0.999711 | + | 0.0240426i | \(0.992346\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.4627 | −0.442524 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.5179 | 0.908489 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.2026i | 1.35718i | 0.734518 | + | 0.678589i | \(0.237408\pi\) | ||||
−0.734518 | + | 0.678589i | \(0.762592\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.57591 | − | 16.4845i | 0.108369 | − | 0.693509i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.0620642i | − | 0.00260645i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.597888 | 0.0250648 | 0.0125324 | − | 0.999921i | \(-0.496011\pi\) | ||||
0.0125324 | + | 0.999921i | \(0.496011\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.09387 | 0.129474 | 0.0647372 | − | 0.997902i | \(-0.479379\pi\) | ||||
0.0647372 | + | 0.997902i | \(0.479379\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.33664i | 0.139390i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.10396 | + | 15.9326i | −0.212850 | + | 0.664436i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.4178i | 1.01653i | 0.861202 | + | 0.508263i | \(0.169712\pi\) | ||||
−0.861202 | + | 0.508263i | \(0.830288\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.227371 | −0.00944922 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.227722 | 0.00944750 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 37.0394i | − | 1.53402i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.24885 | + | 7.99201i | −0.0516336 | + | 0.330429i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.4585i | 1.05079i | 0.850860 | + | 0.525393i | \(0.176082\pi\) | ||||
−0.850860 | + | 0.525393i | \(0.823918\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44.9609 | −1.85258 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.8648 | −0.734860 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.5909i | 1.62580i | 0.582401 | + | 0.812901i | \(0.302113\pi\) | ||||
−0.582401 | + | 0.812901i | \(0.697887\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.789480 | − | 0.123366i | −0.0323655 | − | 0.00505751i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 7.02003i | − | 0.287311i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0181 | 0.981353 | 0.490677 | − | 0.871342i | \(-0.336750\pi\) | ||||
0.490677 | + | 0.871342i | \(0.336750\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.0711 | −0.451598 | −0.225799 | − | 0.974174i | \(-0.572499\pi\) | ||||
−0.225799 | + | 0.974174i | \(0.572499\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.00000i | − | 0.0407231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.55426 | + | 1.02418i | 0.266469 | + | 0.0416390i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 17.3591i | − | 0.704585i | −0.935890 | − | 0.352292i | \(-0.885402\pi\) | ||
0.935890 | − | 0.352292i | \(-0.114598\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.304149 | −0.0123248 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −38.0529 | −1.53945 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 48.6986i | − | 1.96692i | −0.181133 | − | 0.983459i | \(-0.557976\pi\) | ||
0.181133 | − | 0.983459i | \(-0.442024\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.24161 | + | 20.7447i | −0.130714 | + | 0.836505i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.53591i | 0.102092i | 0.998696 | + | 0.0510458i | \(0.0162555\pi\) | ||||
−0.998696 | + | 0.0510458i | \(0.983745\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −49.0882 | −1.97302 | −0.986510 | − | 0.163702i | \(-0.947656\pi\) | ||||
−0.986510 | + | 0.163702i | \(0.947656\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.34603 | 0.134272 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.351810i | 0.0140950i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3464 | + | 14.5266i | 0.813858 | + | 0.581064i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 18.1062i | − | 0.723092i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.3050 | 0.769740 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.9294 | −0.514712 | −0.257356 | − | 0.966317i | \(-0.582851\pi\) | ||||
−0.257356 | + | 0.966317i | \(0.582851\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.4786i | 0.615219i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.62209 | + | 10.3806i | −0.0643708 | + | 0.411941i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 25.3086i | − | 1.00276i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.9803 | −0.592613 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −44.5813 | −1.76086 | −0.880428 | − | 0.474179i | \(-0.842745\pi\) | ||||
−0.880428 | + | 0.474179i | \(0.842745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.4654i | 1.67467i | 0.546689 | + | 0.837336i | \(0.315888\pi\) | ||||
−0.546689 | + | 0.837336i | \(0.684112\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.38968 | + | 0.998466i | 0.251593 | + | 0.0393146i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.5954i | 1.47803i | 0.673691 | + | 0.739013i | \(0.264708\pi\) | ||||
−0.673691 | + | 0.739013i | \(0.735292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.2225 | −1.38260 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.575965 | 0.0225739 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 3.15354i | − | 0.123408i | −0.998095 | − | 0.0617039i | \(-0.980347\pi\) | ||
0.998095 | − | 0.0617039i | \(-0.0196534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.17676 | + | 1.12146i | 0.280419 | + | 0.0438190i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.5508i | 0.411627i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.3854 | −1.49528 | −0.747641 | − | 0.664103i | \(-0.768814\pi\) | ||||
−0.747641 | + | 0.664103i | \(0.768814\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.1892 | −0.979746 | −0.489873 | − | 0.871794i | \(-0.662957\pi\) | ||||
−0.489873 | + | 0.871794i | \(0.662957\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 20.8288i | − | 0.808922i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.103806 | + | 0.664305i | −0.00402542 | + | 0.0257607i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 16.3975i | − | 0.634912i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.6955 | 0.568159 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −43.2445 | −1.66944 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 16.8789i | − | 0.650634i | −0.945605 | − | 0.325317i | \(-0.894529\pi\) | ||
0.945605 | − | 0.325317i | \(-0.105471\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.52538 | − | 4.76164i | 0.0587118 | − | 0.183276i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.6539i | 1.44716i | 0.690242 | + | 0.723579i | \(0.257504\pi\) | ||||
−0.690242 | + | 0.723579i | \(0.742496\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.179550 | 0.00689050 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.83025 | 0.0701354 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.7551i | 1.78903i | 0.447034 | + | 0.894517i | \(0.352480\pi\) | ||||
−0.447034 | + | 0.894517i | \(0.647520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.01278 | + | 32.0792i | −0.191528 | + | 1.22568i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.5339i | 0.745265i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.8531 | −1.36589 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.97821 | −0.189380 | −0.0946899 | − | 0.995507i | \(-0.530186\pi\) | ||||
−0.0946899 | + | 0.995507i | \(0.530186\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.231947i | 0.00881093i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.1831 | + | 1.90377i | 0.462133 | + | 0.0722140i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 54.0646i | − | 2.04784i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.91720 | −0.148162 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.2085 | 0.649958 | 0.324979 | − | 0.945721i | \(-0.394643\pi\) | ||||
0.324979 | + | 0.945721i | \(0.394643\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 16.2441i | − | 0.612659i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.2394 | + | 3.63144i | 0.875245 | + | 0.136768i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.160072i | 0.00602014i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.1539 | −1.05734 | −0.528671 | − | 0.848827i | \(-0.677309\pi\) | ||||
−0.528671 | + | 0.848827i | \(0.677309\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.4258 | −0.503508 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.0517i | 1.16290i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.66722 | − | 29.8678i | 0.174544 | − | 1.11699i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 0.408885i | − | 0.0152701i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.0589 | −1.27018 | −0.635091 | − | 0.772437i | \(-0.719038\pi\) | ||||
−0.635091 | + | 0.772437i | \(0.719038\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.00296 | 0.0373521 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 0.711176i | − | 0.0264489i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.3347 | − | 7.47521i | −0.866630 | − | 0.277622i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.65868i | 0.209869i | 0.994479 | + | 0.104934i | \(0.0334633\pi\) | ||||
−0.994479 | + | 0.104934i | \(0.966537\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.6528 | −0.615925 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 51.5641i | − | 1.90456i | −0.305222 | − | 0.952281i | \(-0.598731\pi\) | ||
0.305222 | − | 0.952281i | \(-0.401269\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.41524 | + | 15.4563i | −0.0890874 | + | 0.570114i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.73721i | 0.137662i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.6118 | −0.868574 | −0.434287 | − | 0.900775i | \(-0.643000\pi\) | ||||
−0.434287 | + | 0.900775i | \(0.643000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.5263 | −0.643845 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 42.7648i | − | 1.56889i | −0.620199 | − | 0.784444i | \(-0.712948\pi\) | ||
0.620199 | − | 0.784444i | \(-0.287052\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.4625 | + | 4.76015i | 1.11606 | + | 0.174398i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 3.66914i | − | 0.134247i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.385210 | −0.0140753 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −52.9184 | −1.93102 | −0.965510 | − | 0.260365i | \(-0.916157\pi\) | ||||
−0.965510 | + | 0.260365i | \(0.916157\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.8243i | 0.685997i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.09460 | + | 0.171044i | 0.0398365 | + | 0.00622495i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 20.1352i | − | 0.731827i | −0.930649 | − | 0.365913i | \(-0.880757\pi\) | ||
0.930649 | − | 0.365913i | \(-0.119243\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.5048 | −0.453896 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0948 | 1.52594 | 0.762968 | − | 0.646436i | \(-0.223741\pi\) | ||||
0.762968 | + | 0.646436i | \(0.223741\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.283442i | 0.0102613i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.98772 | + | 12.7204i | −0.0718660 | + | 0.459906i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.0944i | 1.23108i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.9154 | −0.573925 | −0.286963 | − | 0.957942i | \(-0.592646\pi\) | ||||
−0.286963 | + | 0.957942i | \(0.592646\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −29.3805 | −1.05811 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 35.2489i | − | 1.26782i | −0.773409 | − | 0.633908i | \(-0.781450\pi\) | ||
0.773409 | − | 0.633908i | \(-0.218550\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.1888 | + | 14.1557i | 1.58731 | + | 0.508489i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.208093i | 0.00746529i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −45.4925 | −1.62994 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 55.9847 | 2.00329 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.90056i | 0.175132i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.13374 | − | 39.2528i | 0.218922 | − | 1.40099i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.42686i | 0.193447i | 0.995311 | + | 0.0967233i | \(0.0308362\pi\) | ||||
−0.995311 | + | 0.0967233i | \(0.969164\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.9546 | 0.639202 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.463096 | −0.0164658 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.8595i | 1.48647i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21.8959 | + | 3.42151i | 0.776569 | + | 0.121348i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.0568i | 1.20635i | 0.797608 | + | 0.603176i | \(0.206098\pi\) | ||||
−0.797608 | + | 0.603176i | \(0.793902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60.5663 | −2.14268 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.66849 | 0.200286 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 39.4306i | − | 1.39148i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.458794 | + | 0.0716922i | 0.0161704 | + | 0.00252682i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.37091i | 0.118662i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.0641 | −0.986680 | −0.493340 | − | 0.869837i | \(-0.664224\pi\) | ||||
−0.493340 | + | 0.869837i | \(0.664224\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.14104 | −0.0400674 | −0.0200337 | − | 0.999799i | \(-0.506377\pi\) | ||||
−0.0200337 | + | 0.999799i | \(0.506377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.707519i | 0.0248138i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.82631 | − | 37.2854i | 0.204087 | − | 1.30605i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.0124i | 0.490232i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.224518 | 0.00784529 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.70896 | 0.0596431 | 0.0298216 | − | 0.999555i | \(-0.490506\pi\) | ||||
0.0298216 | + | 0.999555i | \(0.490506\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.83491i | − | 0.0639609i | −0.999488 | − | 0.0319805i | \(-0.989819\pi\) | ||
0.999488 | − | 0.0319805i | \(-0.0101814\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.70065 | + | 17.7952i | −0.198471 | + | 0.619551i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.5761i | 0.645953i | 0.946407 | + | 0.322976i | \(0.104683\pi\) | ||||
−0.946407 | + | 0.322976i | \(0.895317\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.3189 | −1.40033 | −0.700166 | − | 0.713980i | \(-0.746891\pi\) | ||||
−0.700166 | + | 0.713980i | \(0.746891\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.4894 | 1.09236 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 40.2821i | − | 1.39569i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.18219 | + | 39.5629i | −0.213944 | + | 1.36913i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 9.28015i | − | 0.320769i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.2970 | 0.355492 | 0.177746 | − | 0.984076i | \(-0.443119\pi\) | ||||
0.177746 | + | 0.984076i | \(0.443119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.98448 | −0.171879 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.98185i | 0.137142i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.190848 | − | 0.0298224i | −0.00656539 | − | 0.00102592i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 0.184127i | − | 0.00632669i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.7478 | −0.986620 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.2188 | −0.384575 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.7501i | − | 0.676231i | −0.941105 | − | 0.338115i | \(-0.890211\pi\) | ||
0.941105 | − | 0.338115i | \(-0.109789\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.7035 | + | 1.67256i | 0.366053 | + | 0.0572003i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.84604i | 0.131378i | 0.997840 | + | 0.0656891i | \(0.0209246\pi\) | ||||
−0.997840 | + | 0.0656891i | \(0.979075\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.54184 | 0.257324 | 0.128662 | − | 0.991688i | \(-0.458932\pi\) | ||||
0.128662 | + | 0.991688i | \(0.458932\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.582775 | 0.0198609 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 41.6569i | − | 1.41802i | −0.705200 | − | 0.709009i | \(-0.749143\pi\) | ||
0.705200 | − | 0.709009i | \(-0.250857\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.56580 | + | 16.4198i | −0.0872398 | + | 0.558290i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.1518i | − | 0.548544i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.1751 | 1.70207 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.61751 | 0.122575 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.89298i | − | 0.0979124i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.311176 | − | 0.620213i | 0.0105197 | − | 0.0209670i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 56.5554i | 1.90974i | 0.297021 | + | 0.954871i | \(0.404007\pi\) | ||||
−0.297021 | + | 0.954871i | \(0.595993\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.4818 | −0.758294 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.7594 | −0.598329 | −0.299164 | − | 0.954202i | \(-0.596708\pi\) | ||||
−0.299164 | + | 0.954202i | \(0.596708\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 0.958905i | − | 0.0322697i | −0.999870 | − | 0.0161349i | \(-0.994864\pi\) | ||
0.999870 | − | 0.0161349i | \(-0.00513611\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.25367 | − | 20.8218i | 0.109371 | − | 0.699918i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 36.1188i | − | 1.21275i | −0.795178 | − | 0.606376i | \(-0.792623\pi\) | ||
0.795178 | − | 0.606376i | \(-0.207377\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.291619 | 0.00978060 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.73721 | 0.125201 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 50.9633i | 1.70542i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.4174 | − | 3.03421i | −0.649052 | − | 0.101422i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.1043i | 0.404151i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45.4780 | −1.51678 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −57.0651 | −1.90111 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 0.179504i | − | 0.00597351i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.3856 | − | 4.90439i | −1.04329 | − | 0.163027i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 31.9767i | − | 1.06177i | −0.847445 | − | 0.530884i | \(-0.821860\pi\) | ||
0.847445 | − | 0.530884i | \(-0.178140\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.57914 | 0.0855447 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.1020 | 0.334695 | 0.167347 | − | 0.985898i | \(-0.446480\pi\) | ||||
0.167347 | + | 0.985898i | \(0.446480\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.7123i | 0.453812i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.99470 | − | 25.5641i | 0.132061 | − | 0.845122i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 0.201615i | − | 0.00665791i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.33952 | 0.308082 | 0.154041 | − | 0.988064i | \(-0.450771\pi\) | ||||
0.154041 | + | 0.988064i | \(0.450771\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.9009 | 0.523952 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 54.1916i | − | 1.78374i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.11438 | + | 15.9651i | −0.168160 | + | 0.524930i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 16.1600i | − | 0.530764i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.1802 | −1.12142 | −0.560708 | − | 0.828014i | \(-0.689471\pi\) | ||||
−0.560708 | + | 0.828014i | \(0.689471\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.8953 | −1.11087 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 8.41108i | − | 0.275366i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.42851 | − | 47.5387i | 0.242938 | − | 1.55468i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.9382i | 0.553347i | 0.960964 | + | 0.276674i | \(0.0892321\pi\) | ||||
−0.960964 | + | 0.276674i | \(0.910768\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.0588 | −0.654594 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.04918 | 0.132000 | 0.0659998 | − | 0.997820i | \(-0.478976\pi\) | ||||
0.0659998 | + | 0.997820i | \(0.478976\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.4188i | 1.02314i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.137116 | − | 0.0214260i | −0.00446038 | − | 0.000696989i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.8592i | 1.68520i | 0.538541 | + | 0.842599i | \(0.318976\pi\) | ||||
−0.538541 | + | 0.842599i | \(0.681024\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.1677 | −1.23898 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.2660 | 0.462607 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 5.66405i | − | 0.183476i | −0.995783 | − | 0.0917382i | \(-0.970758\pi\) | ||
0.995783 | − | 0.0917382i | \(-0.0292423\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.37151 | + | 1.15189i | 0.238536 | + | 0.0372743i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 18.3144i | − | 0.592021i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.901195 | 0.0291011 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.1213 | 1.77810 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.20665i | 0.200006i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.0784940 | + | 0.502322i | −0.00252681 | + | 0.0161703i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.7751i | 0.378663i | 0.981913 | + | 0.189331i | \(0.0606320\pi\) | ||||
−0.981913 | + | 0.189331i | \(0.939368\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −27.8955 | −0.896132 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.8593 | 0.380581 | 0.190291 | − | 0.981728i | \(-0.439057\pi\) | ||||
0.190291 | + | 0.981728i | \(0.439057\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 0.342258i | − | 0.0109723i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.2253 | + | 5.51807i | 0.551651 | + | 0.176720i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.9862i | 0.767387i | 0.923461 | + | 0.383693i | \(0.125348\pi\) | ||||
−0.923461 | + | 0.383693i | \(0.874652\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.1843 | −0.677054 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.56692 | 0.145810 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.3508i | 1.31888i | 0.751755 | + | 0.659442i | \(0.229208\pi\) | ||||
−0.751755 | + | 0.659442i | \(0.770792\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.16736 | + | 39.4680i | −0.196508 | + | 1.25755i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 0.652858i | − | 0.0207807i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.67750 | 0.307726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.05926 | 0.0654145 | 0.0327073 | − | 0.999465i | \(-0.489587\pi\) | ||||
0.0327073 | + | 0.999465i | \(0.489587\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 22.8860i | − | 0.726264i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.5091 | − | 2.42348i | −0.491670 | − | 0.0768296i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 39.1206i | − | 1.23896i | −0.785012 | − | 0.619480i | \(-0.787343\pi\) | ||
0.785012 | − | 0.619480i | \(-0.212657\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.35286 | 0.106080 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4020.2.g.c.1609.37 | yes | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.18 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.18 | ✓ | 38 | 5.4 | even | 2 | inner | |
4020.2.g.c.1609.37 | yes | 38 | 1.1 | even | 1 | trivial |