Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(737,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 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("1380.737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.r (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.5 | ||
Character | \(\chi\) | \(=\) | 1380.737 |
Dual form | 1380.2.r.c.1013.5 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.53876 | + | 0.795128i | −0.888401 | + | 0.459067i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.56652 | − | 1.59562i | 0.700570 | − | 0.713583i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.769646 | + | 0.769646i | 0.290899 | + | 0.290899i | 0.837435 | − | 0.546537i | \(-0.184054\pi\) |
−0.546537 | + | 0.837435i | \(0.684054\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.73554 | − | 2.44702i | 0.578514 | − | 0.815672i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.12034i | 0.639307i | 0.947534 | + | 0.319654i | \(0.103567\pi\) | ||||
−0.947534 | + | 0.319654i | \(0.896433\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.53512 | − | 3.53512i | 0.980465 | − | 0.980465i | −0.0193482 | − | 0.999813i | \(-0.506159\pi\) |
0.999813 | + | 0.0193482i | \(0.00615911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.14178 | + | 3.70086i | −0.294805 | + | 0.955557i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.63046 | + | 1.63046i | −0.395444 | + | 0.395444i | −0.876623 | − | 0.481179i | \(-0.840209\pi\) |
0.481179 | + | 0.876623i | \(0.340209\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.93859i | − | 0.903574i | −0.892126 | − | 0.451787i | \(-0.850787\pi\) | ||
0.892126 | − | 0.451787i | \(-0.149213\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.79626 | − | 0.572331i | −0.391977 | − | 0.124893i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.707107 | + | 0.707107i | 0.147442 | + | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0920108 | − | 4.99915i | −0.0184022 | − | 0.999831i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.724887 | + | 5.14534i | −0.139505 | + | 0.990221i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.04476 | −0.194008 | −0.0970038 | − | 0.995284i | \(-0.530926\pi\) | ||||
−0.0970038 | + | 0.995284i | \(0.530926\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.661930 | −0.118886 | −0.0594430 | − | 0.998232i | \(-0.518932\pi\) | ||||
−0.0594430 | + | 0.998232i | \(0.518932\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.68594 | − | 3.26269i | −0.293485 | − | 0.567961i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.43373 | − | 0.0223949i | 0.411376 | − | 0.00378542i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.26541 | + | 2.26541i | 0.372431 | + | 0.372431i | 0.868362 | − | 0.495931i | \(-0.165173\pi\) |
−0.495931 | + | 0.868362i | \(0.665173\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.62881 | + | 8.25055i | −0.420947 | + | 1.32115i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.31675i | − | 0.830337i | −0.909745 | − | 0.415168i | \(-0.863723\pi\) | ||
0.909745 | − | 0.415168i | \(-0.136277\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.28783 | − | 1.28783i | 0.196392 | − | 0.196392i | −0.602059 | − | 0.798451i | \(-0.705653\pi\) |
0.798451 | + | 0.602059i | \(0.205653\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.18574 | − | 6.60258i | −0.176760 | − | 0.984254i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.204904 | + | 0.204904i | −0.0298882 | + | 0.0298882i | −0.721893 | − | 0.692005i | \(-0.756728\pi\) |
0.692005 | + | 0.721893i | \(0.256728\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.81529i | − | 0.830756i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.21245 | − | 3.80530i | 0.169778 | − | 0.532849i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.488959 | − | 0.488959i | −0.0671636 | − | 0.0671636i | 0.672727 | − | 0.739891i | \(-0.265123\pi\) |
−0.739891 | + | 0.672727i | \(0.765123\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.38326 | + | 3.32156i | 0.456199 | + | 0.447880i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.13168 | + | 6.06053i | 0.414801 | + | 0.802736i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.286614 | −0.0373140 | −0.0186570 | − | 0.999826i | \(-0.505939\pi\) | ||||
−0.0186570 | + | 0.999826i | \(0.505939\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92347 | 0.630386 | 0.315193 | − | 0.949028i | \(-0.397931\pi\) | ||||
0.315193 | + | 0.949028i | \(0.397931\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.21909 | − | 0.547582i | 0.405567 | − | 0.0689889i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.102863 | − | 11.1785i | −0.0127586 | − | 1.38653i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.93068 | + | 1.93068i | 0.235871 | + | 0.235871i | 0.815138 | − | 0.579267i | \(-0.196661\pi\) |
−0.579267 | + | 0.815138i | \(0.696661\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.65031 | − | 0.525825i | −0.198673 | − | 0.0633019i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.5645i | − | 1.60981i | −0.593401 | − | 0.804907i | \(-0.702215\pi\) | ||
0.593401 | − | 0.804907i | \(-0.297785\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.71007 | − | 8.71007i | 1.01944 | − | 1.01944i | 0.0196298 | − | 0.999807i | \(-0.493751\pi\) |
0.999807 | − | 0.0196298i | \(-0.00624877\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.11655 | + | 7.61932i | 0.475338 | + | 0.879803i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.63191 | + | 1.63191i | −0.185974 | + | 0.185974i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.33841i | 0.488110i | 0.969761 | + | 0.244055i | \(0.0784777\pi\) | ||||
−0.969761 | + | 0.244055i | \(0.921522\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.97578 | − | 8.49381i | −0.330642 | − | 0.943756i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.5210 | + | 12.5210i | 1.37435 | + | 1.37435i | 0.853873 | + | 0.520482i | \(0.174248\pi\) |
0.520482 | + | 0.853873i | \(0.325752\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0474424 | + | 5.15574i | 0.00514585 | + | 0.559219i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.60764 | − | 0.830720i | 0.172357 | − | 0.0890626i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.39452 | 0.465818 | 0.232909 | − | 0.972499i | \(-0.425176\pi\) | ||||
0.232909 | + | 0.972499i | \(0.425176\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.44157 | 0.570432 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.01855 | − | 0.526319i | 0.105619 | − | 0.0545767i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.28449 | − | 6.16989i | −0.644775 | − | 0.633017i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.43748 | + | 7.43748i | 0.755161 | + | 0.755161i | 0.975438 | − | 0.220276i | \(-0.0706958\pi\) |
−0.220276 | + | 0.975438i | \(0.570696\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.18851 | + | 3.67994i | 0.521465 | + | 0.369848i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.81667i | 0.976795i | 0.872621 | + | 0.488397i | \(0.162418\pi\) | ||||
−0.872621 | + | 0.488397i | \(0.837582\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.88737 | − | 9.88737i | 0.974232 | − | 0.974232i | −0.0254446 | − | 0.999676i | \(-0.508100\pi\) |
0.999676 | + | 0.0254446i | \(0.00810013\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.72711 | + | 1.96959i | −0.363729 | + | 0.192212i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.08163 | + | 1.08163i | −0.104565 | + | 0.104565i | −0.757454 | − | 0.652889i | \(-0.773557\pi\) |
0.652889 | + | 0.757454i | \(0.273557\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.1672i | − | 1.16540i | −0.812686 | − | 0.582702i | \(-0.801995\pi\) | ||
0.812686 | − | 0.582702i | \(-0.198005\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.28720 | − | 1.68462i | −0.501839 | − | 0.159897i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.79146 | + | 5.79146i | 0.544815 | + | 0.544815i | 0.924936 | − | 0.380122i | \(-0.124118\pi\) |
−0.380122 | + | 0.924936i | \(0.624118\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.23597 | − | 0.0205751i | 0.208506 | − | 0.00191864i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.51514 | − | 14.7858i | −0.232525 | − | 1.36695i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.50975 | −0.230068 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.50415 | 0.591286 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.22750 | + | 8.18118i | 0.381181 | + | 0.737673i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.12089 | − | 7.68447i | −0.726354 | − | 0.687320i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.61722 | + | 1.61722i | 0.143505 | + | 0.143505i | 0.775209 | − | 0.631705i | \(-0.217644\pi\) |
−0.631705 | + | 0.775209i | \(0.717644\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.957665 | + | 3.00564i | −0.0843177 | + | 0.264632i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 21.8392i | − | 1.90810i | −0.299642 | − | 0.954052i | \(-0.596867\pi\) | ||
0.299642 | − | 0.954052i | \(-0.403133\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.03132 | − | 3.03132i | 0.262849 | − | 0.262849i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.07446 | + | 9.21694i | 0.608873 | + | 0.793268i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.6170 | + | 13.6170i | −1.16338 | + | 1.16338i | −0.179645 | + | 0.983732i | \(0.557495\pi\) |
−0.983732 | + | 0.179645i | \(0.942505\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.56281i | − | 0.217375i | −0.994076 | − | 0.108688i | \(-0.965335\pi\) | ||
0.994076 | − | 0.108688i | \(-0.0346648\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.152372 | − | 0.478221i | 0.0128320 | − | 0.0402735i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.49565 | + | 7.49565i | 0.626818 | + | 0.626818i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.63665 | + | 1.66705i | −0.135916 | + | 0.138441i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.62390 | + | 8.94832i | 0.381373 | + | 0.738045i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.66617 | −0.382268 | −0.191134 | − | 0.981564i | \(-0.561216\pi\) | ||||
−0.191134 | + | 0.981564i | \(0.561216\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.8647 | 1.29105 | 0.645527 | − | 0.763738i | \(-0.276638\pi\) | ||||
0.645527 | + | 0.763738i | \(0.276638\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.16003 | + | 6.81949i | 0.0937826 | + | 0.551323i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.03693 | + | 1.05619i | −0.0832881 | + | 0.0848351i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.96043 | − | 5.96043i | −0.475694 | − | 0.475694i | 0.428057 | − | 0.903752i | \(-0.359198\pi\) |
−0.903752 | + | 0.428057i | \(0.859198\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.14117 | + | 0.363604i | 0.0905009 | + | 0.0288356i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.08844i | 0.0857814i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.40360 | + | 1.40360i | −0.109939 | + | 0.109939i | −0.759936 | − | 0.649998i | \(-0.774770\pi\) |
0.649998 | + | 0.759936i | \(0.274770\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.84708 | − | 2.42095i | −0.610895 | − | 0.188471i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.10670 | − | 4.10670i | 0.317786 | − | 0.317786i | −0.530130 | − | 0.847916i | \(-0.677857\pi\) |
0.847916 | + | 0.530130i | \(0.177857\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.9941i | − | 0.922622i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.63779 | − | 6.83559i | −0.737020 | − | 0.522731i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.90766 | + | 6.90766i | 0.525180 | + | 0.525180i | 0.919131 | − | 0.393951i | \(-0.128892\pi\) |
−0.393951 | + | 0.919131i | \(0.628892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.77676 | − | 3.91839i | 0.285496 | − | 0.296203i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.441030 | − | 0.227895i | 0.0331498 | − | 0.0171296i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.17936 | −0.237637 | −0.118818 | − | 0.992916i | \(-0.537911\pi\) | ||||
−0.118818 | + | 0.992916i | \(0.537911\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.3431 | −1.21477 | −0.607387 | − | 0.794406i | \(-0.707782\pi\) | ||||
−0.607387 | + | 0.794406i | \(0.707782\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.57603 | + | 3.91479i | −0.560036 | + | 0.289390i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.16354 | − | 0.0659179i | 0.526674 | − | 0.00484638i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.45713 | − | 3.45713i | −0.252810 | − | 0.252810i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.51800 | + | 3.40218i | −0.328636 | + | 0.247472i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.34094i | − | 0.169385i | −0.996407 | − | 0.0846923i | \(-0.973009\pi\) | ||
0.996407 | − | 0.0846923i | \(-0.0269907\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.9377 | − | 14.9377i | 1.07524 | − | 1.07524i | 0.0783090 | − | 0.996929i | \(-0.475048\pi\) |
0.996929 | − | 0.0783090i | \(-0.0249521\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.04665 | + | 17.1193i | 0.647844 | + | 1.22594i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.1550 | + | 19.1550i | −1.36473 | + | 1.36473i | −0.496961 | + | 0.867773i | \(0.665551\pi\) |
−0.867773 | + | 0.496961i | \(0.834449\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.1982i | 1.21915i | 0.792730 | + | 0.609573i | \(0.208659\pi\) | ||||
−0.792730 | + | 0.609573i | \(0.791341\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.50600 | − | 1.43571i | −0.317828 | − | 0.101267i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.804097 | − | 0.804097i | −0.0564366 | − | 0.0564366i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.48352 | − | 8.32881i | −0.592514 | − | 0.581709i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.95752 | − | 0.503088i | 0.205562 | − | 0.0349670i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.35115 | 0.577661 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.0643 | −1.45013 | −0.725065 | − | 0.688681i | \(-0.758190\pi\) | ||||
−0.725065 | + | 0.688681i | \(0.758190\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.7855 | + | 20.8725i | 0.739013 | + | 1.43016i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.0374727 | − | 4.07229i | −0.00255562 | − | 0.277728i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.509451 | − | 0.509451i | −0.0345838 | − | 0.0345838i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.47706 | + | 20.3283i | −0.437679 | + | 1.37366i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.5277i | 0.775438i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.9227 | + | 18.9227i | −1.26716 | + | 1.26716i | −0.319610 | + | 0.947549i | \(0.603552\pi\) |
−0.947549 | + | 0.319610i | \(0.896448\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.3927 | − | 8.45109i | −0.826180 | − | 0.563406i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.93255 | + | 3.93255i | −0.261013 | + | 0.261013i | −0.825465 | − | 0.564453i | \(-0.809087\pi\) |
0.564453 | + | 0.825465i | \(0.309087\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.3913i | − | 0.884920i | −0.896788 | − | 0.442460i | \(-0.854106\pi\) | ||
0.896788 | − | 0.442460i | \(-0.145894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.21354 | − | 3.80869i | 0.0798448 | − | 0.250594i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.28261 | − | 6.28261i | −0.411588 | − | 0.411588i | 0.470704 | − | 0.882291i | \(-0.344000\pi\) |
−0.882291 | + | 0.470704i | \(0.844000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.00596220 | + | 0.647934i | 0.000388931 | + | 0.0422666i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.44959 | − | 6.67576i | −0.224075 | − | 0.433637i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.0871 | −1.29933 | −0.649664 | − | 0.760221i | \(-0.725091\pi\) | ||||
−0.649664 | + | 0.760221i | \(0.725091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.89303 | −0.444019 | −0.222010 | − | 0.975044i | \(-0.571262\pi\) | ||||
−0.222010 | + | 0.975044i | \(0.571262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.3327 | + | 10.7038i | 0.726991 | + | 0.686647i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.27900 | − | 9.10979i | −0.592813 | − | 0.582003i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.9234 | − | 13.9234i | −0.885922 | − | 0.885922i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −29.2225 | − | 9.31095i | −1.85190 | − | 0.590057i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.26055i | 0.205804i | 0.994692 | + | 0.102902i | \(0.0328128\pi\) | ||||
−0.994692 | + | 0.102902i | \(0.967187\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.49931 | + | 1.49931i | −0.0942607 | + | 0.0942607i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.17248 | − | 7.89571i | −0.261291 | − | 0.494448i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.1328 | − | 10.1328i | 0.632067 | − | 0.632067i | −0.316519 | − | 0.948586i | \(-0.602514\pi\) |
0.948586 | + | 0.316519i | \(0.102514\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.48712i | 0.216679i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.81323 | + | 2.55655i | −0.112236 | + | 0.158247i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.16925 | − | 3.16925i | −0.195424 | − | 0.195424i | 0.602611 | − | 0.798035i | \(-0.294127\pi\) |
−0.798035 | + | 0.602611i | \(0.794127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.54616 | + | 0.0142275i | −0.0949797 | + | 0.000873990i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.76209 | + | 3.49420i | −0.413833 | + | 0.213842i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.6487 | −1.19801 | −0.599003 | − | 0.800747i | \(-0.704436\pi\) | ||||
−0.599003 | + | 0.800747i | \(0.704436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.83702 | 0.172337 | 0.0861684 | − | 0.996281i | \(-0.472538\pi\) | ||||
0.0861684 | + | 0.996281i | \(0.472538\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.37326 | + | 4.32675i | −0.506772 | + | 0.261867i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.5999 | − | 0.195094i | 0.639199 | − | 0.0117646i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0664 | − | 14.0664i | −0.845167 | − | 0.845167i | 0.144359 | − | 0.989525i | \(-0.453888\pi\) |
−0.989525 | + | 0.144359i | \(0.953888\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.14881 | + | 1.61975i | −0.0687773 | + | 0.0969721i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.4661i | 1.10159i | 0.834640 | + | 0.550796i | \(0.185676\pi\) | ||||
−0.834640 | + | 0.550796i | \(0.814324\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.79021 | + | 3.79021i | −0.225304 | + | 0.225304i | −0.810728 | − | 0.585423i | \(-0.800928\pi\) |
0.585423 | + | 0.810728i | \(0.300928\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.5762 | + | 4.49698i | 0.863417 | + | 0.266378i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.09201 | − | 4.09201i | 0.241544 | − | 0.241544i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.6832i | 0.687248i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.3582 | − | 5.53072i | −1.01756 | − | 0.324217i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.15261 | + | 8.15261i | 0.476280 | + | 0.476280i | 0.903940 | − | 0.427660i | \(-0.140662\pi\) |
−0.427660 | + | 0.903940i | \(0.640662\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.448988 | + | 0.457328i | −0.0261411 | + | 0.0266267i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.9099 | − | 1.53701i | −0.633056 | − | 0.0891863i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.99941 | 0.289123 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.98234 | 0.114260 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.80551 | − | 15.1055i | −0.448415 | − | 0.867786i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.71273 | − | 7.85600i | 0.441630 | − | 0.449833i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.78701 | + | 2.78701i | 0.159063 | + | 0.159063i | 0.782151 | − | 0.623088i | \(-0.214122\pi\) |
−0.623088 | + | 0.782151i | \(0.714122\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.35253 | + | 23.0760i | −0.418271 | + | 1.31275i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.2686i | 0.979210i | 0.871944 | + | 0.489605i | \(0.162859\pi\) | ||||
−0.871944 | + | 0.489605i | \(0.837141\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.96358 | − | 8.96358i | 0.506652 | − | 0.506652i | −0.406845 | − | 0.913497i | \(-0.633371\pi\) |
0.913497 | + | 0.406845i | \(0.133371\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.16904 | − | 5.99425i | 0.234899 | − | 0.337737i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.525557 | + | 0.525557i | −0.0295182 | + | 0.0295182i | −0.721712 | − | 0.692194i | \(-0.756644\pi\) |
0.692194 | + | 0.721712i | \(0.256644\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.21525i | − | 0.124030i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.804330 | − | 2.52440i | 0.0448933 | − | 0.140898i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.42170 | + | 6.42170i | 0.357313 | + | 0.357313i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.9979 | − | 17.3473i | −0.998341 | − | 0.962256i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.67446 | + | 18.7223i | 0.534999 | + | 1.03535i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.315406 | −0.0173889 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.1031 | −1.92944 | −0.964720 | − | 0.263278i | \(-0.915196\pi\) | ||||
−0.964720 | + | 0.263278i | \(0.915196\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.47520 | − | 1.61178i | 0.519238 | − | 0.0883248i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.10510 | − | 0.0561783i | 0.333557 | − | 0.00306935i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.2986 | + | 24.2986i | 1.32363 | + | 1.32363i | 0.910814 | + | 0.412817i | \(0.135455\pi\) |
0.412817 | + | 0.910814i | \(0.364545\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.5166 | − | 4.30669i | −0.734121 | − | 0.233908i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.40352i | − | 0.0760047i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.86323 | − | 9.86323i | 0.532565 | − | 0.532565i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.42426 | + | 1.80954i | −0.184356 | + | 0.0974226i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0302 | + | 15.0302i | −0.806865 | + | 0.806865i | −0.984158 | − | 0.177293i | \(-0.943266\pi\) |
0.177293 | + | 0.984158i | \(0.443266\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.66694i | 0.249815i | 0.992168 | + | 0.124908i | \(0.0398635\pi\) | ||||
−0.992168 | + | 0.124908i | \(0.960137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.6268 | + | 20.7519i | 0.834098 | + | 1.10766i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.42229 | + | 7.42229i | 0.395049 | + | 0.395049i | 0.876482 | − | 0.481434i | \(-0.159884\pi\) |
−0.481434 | + | 0.876482i | \(0.659884\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.6438 | − | 21.2492i | −1.14874 | − | 1.12779i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.86189 | − | 1.99557i | 0.204393 | − | 0.105617i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.7363 | 1.14720 | 0.573599 | − | 0.819136i | \(-0.305547\pi\) | ||||
0.573599 | + | 0.819136i | \(0.305547\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.48753 | 0.183554 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.0083 | + | 5.17163i | −0.525300 | + | 0.271440i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.253442 | − | 27.5425i | −0.0132658 | − | 1.44164i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.54200 | − | 3.54200i | −0.184891 | − | 0.184891i | 0.608592 | − | 0.793483i | \(-0.291735\pi\) |
−0.793483 | + | 0.608592i | \(0.791735\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.0102 | − | 9.22745i | −0.677283 | − | 0.480362i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 0.752650i | − | 0.0390756i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.88620 | + | 7.88620i | −0.408332 | + | 0.408332i | −0.881157 | − | 0.472825i | \(-0.843234\pi\) |
0.472825 | + | 0.881157i | \(0.343234\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.6062 | + | 5.36739i | 0.960821 | + | 0.277171i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.69336 | + | 3.69336i | −0.190218 | + | 0.190218i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 11.8176i | − | 0.607031i | −0.952826 | − | 0.303516i | \(-0.901840\pi\) | ||
0.952826 | − | 0.303516i | \(-0.0981605\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.77440 | − | 1.20261i | −0.193368 | − | 0.0616115i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.3566 | − | 19.3566i | −0.989074 | − | 0.989074i | 0.0108666 | − | 0.999941i | \(-0.496541\pi\) |
−0.999941 | + | 0.0108666i | \(0.996541\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0474847 | + | 5.16034i | 0.00242005 | + | 0.262995i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.916254 | − | 5.38641i | −0.0465758 | − | 0.273807i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.0231 | 0.558894 | 0.279447 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279447 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.30582 | −0.116610 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.3650 | + | 33.6053i | 0.875948 | + | 1.69516i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.92246 | + | 6.79622i | 0.348307 | + | 0.341955i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.53780 | + | 5.53780i | 0.277934 | + | 0.277934i | 0.832284 | − | 0.554350i | \(-0.187033\pi\) |
−0.554350 | + | 0.832284i | \(0.687033\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.25417 | + | 7.07474i | −0.112850 | + | 0.354180i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 12.0757i | − | 0.603030i | −0.953461 | − | 0.301515i | \(-0.902508\pi\) | ||
0.953461 | − | 0.301515i | \(-0.0974924\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.34000 | + | 2.34000i | −0.116564 | + | 0.116564i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.2145 | − | 8.55753i | −0.905087 | − | 0.425227i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.80344 | + | 4.80344i | −0.238098 | + | 0.238098i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.6986i | 1.56740i | 0.621142 | + | 0.783698i | \(0.286669\pi\) | ||||
−0.621142 | + | 0.783698i | \(0.713331\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.1260 | − | 31.7804i | 0.499477 | − | 1.56761i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.220591 | − | 0.220591i | −0.0108546 | − | 0.0108546i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 39.5931 | − | 0.364330i | 1.94355 | − | 0.0178843i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.03776 | + | 3.94355i | 0.0997898 | + | 0.193116i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.9071 | 1.16794 | 0.583968 | − | 0.811776i | \(-0.301499\pi\) | ||||
0.583968 | + | 0.811776i | \(0.301499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.08958 | −0.0531030 | −0.0265515 | − | 0.999647i | \(-0.508453\pi\) | ||||
−0.0265515 | + | 0.999647i | \(0.508453\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.145783 | + | 0.857021i | 0.00708823 | + | 0.0416698i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.30093 | + | 8.00089i | 0.402654 | + | 0.388100i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.78933 | + | 3.78933i | 0.183379 | + | 0.183379i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.4940 | − | 5.57398i | −0.844618 | − | 0.269114i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 13.0880i | − | 0.630426i | −0.949021 | − | 0.315213i | \(-0.897924\pi\) | ||
0.949021 | − | 0.315213i | \(-0.102076\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.2741 | + | 13.2741i | −0.637912 | + | 0.637912i | −0.950040 | − | 0.312128i | \(-0.898958\pi\) |
0.312128 | + | 0.950040i | \(0.398958\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.19288 | − | 3.86652i | 0.0571944 | − | 0.185385i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.78500 | − | 2.78500i | 0.133225 | − | 0.133225i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.4167i | 0.688074i | 0.938956 | + | 0.344037i | \(0.111794\pi\) | ||||
−0.938956 | + | 0.344037i | \(0.888206\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.2301 | − | 10.0927i | −0.677624 | − | 0.480604i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.7602 | + | 21.7602i | 1.03386 | + | 1.03386i | 0.999406 | + | 0.0344525i | \(0.0109687\pi\) |
0.0344525 | + | 0.999406i | \(0.489031\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.88411 | − | 7.01198i | 0.326338 | − | 0.332400i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.18010 | − | 3.71020i | 0.339607 | − | 0.175487i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.2206 | 1.85093 | 0.925467 | − | 0.378827i | \(-0.123672\pi\) | ||||
0.925467 | + | 0.378827i | \(0.123672\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.2733 | 0.530840 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.4120 | + | 12.6145i | −1.14697 | + | 0.592681i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.52435 | − | 8.68269i | 0.399628 | − | 0.407051i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.6764 | − | 20.6764i | −0.967202 | − | 0.967202i | 0.0322771 | − | 0.999479i | \(-0.489724\pi\) |
−0.999479 | + | 0.0322771i | \(0.989724\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.20736 | − | 9.57116i | −0.336411 | − | 0.446743i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.1416i | 1.49699i | 0.663143 | + | 0.748493i | \(0.269222\pi\) | ||||
−0.663143 | + | 0.748493i | \(0.730778\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.9312 | − | 13.9312i | 0.647436 | − | 0.647436i | −0.304937 | − | 0.952373i | \(-0.598635\pi\) |
0.952373 | + | 0.304937i | \(0.0986354\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.755775 | − | 2.44971i | 0.0350482 | − | 0.113602i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.16367 | + | 6.16367i | −0.285221 | + | 0.285221i | −0.835187 | − | 0.549966i | \(-0.814641\pi\) |
0.549966 | + | 0.835187i | \(0.314641\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.97189i | 0.137229i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.9110 | + | 4.43235i | 0.640983 | + | 0.204232i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.73063 | + | 2.73063i | 0.125555 | + | 0.125555i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.6896 | + | 0.362393i | −0.903421 | + | 0.0166277i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.04510 | + | 0.347881i | −0.0936386 | + | 0.0159284i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.2812 | −0.880979 | −0.440489 | − | 0.897758i | \(-0.645195\pi\) | ||||
−0.440489 | + | 0.897758i | \(0.645195\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0169 | 0.730310 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.865452 | − | 1.67485i | −0.0393794 | − | 0.0762083i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.5184 | − | 0.216413i | 1.06791 | − | 0.00982680i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.8022 | + | 14.8022i | 0.670752 | + | 0.670752i | 0.957889 | − | 0.287137i | \(-0.0927037\pi\) |
−0.287137 | + | 0.957889i | \(0.592704\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.04376 | − | 3.27585i | 0.0472005 | − | 0.148139i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.44013i | − | 0.200380i | −0.994968 | − | 0.100190i | \(-0.968055\pi\) | ||
0.994968 | − | 0.100190i | \(-0.0319451\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.70344 | − | 1.70344i | 0.0767192 | − | 0.0767192i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.9997 | − | 2.51418i | 0.629241 | − | 0.113004i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.4399 | − | 10.4399i | 0.468293 | − | 0.468293i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.94637i | 0.0871317i | 0.999051 | + | 0.0435658i | \(0.0138718\pi\) | ||||
−0.999051 | + | 0.0435658i | \(0.986128\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.05386 | + | 9.58457i | −0.136436 | + | 0.428207i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.4060 | − | 17.4060i | −0.776093 | − | 0.776093i | 0.203071 | − | 0.979164i | \(-0.434908\pi\) |
−0.979164 | + | 0.203071i | \(0.934908\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.6637 | + | 15.3780i | 0.697024 | + | 0.684314i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.53683 | + | 18.4560i | 0.423545 | + | 0.819658i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.50231 | −0.288210 | −0.144105 | − | 0.989562i | \(-0.546030\pi\) | ||||
−0.144105 | + | 0.989562i | \(0.546030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.4073 | 0.593106 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.2654 | + | 2.85503i | 0.894738 | + | 0.126053i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.287699 | − | 31.2653i | −0.0126775 | − | 1.37771i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.434465 | − | 0.434465i | −0.0191078 | − | 0.0191078i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.1217 | − | 5.13674i | −0.707664 | − | 0.225478i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 17.6022i | − | 0.771167i | −0.922673 | − | 0.385584i | \(-0.874000\pi\) | ||
0.922673 | − | 0.385584i | \(-0.126000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.02681 | + | 5.02681i | −0.219807 | + | 0.219807i | −0.808417 | − | 0.588610i | \(-0.799675\pi\) |
0.588610 | + | 0.808417i | \(0.299675\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.69589 | + | 9.03246i | −0.117658 | + | 0.394209i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.07925 | − | 1.07925i | 0.0470128 | − | 0.0470128i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.497432 | + | 0.701350i | −0.0215867 | + | 0.0304360i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.7953 | − | 18.7953i | −0.814116 | − | 0.814116i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0314728 | + | 3.42026i | 0.00136069 | + | 0.147871i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.89227 | − | 2.52800i | 0.211117 | − | 0.109091i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.3304 | 0.531108 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.4650 | 1.56775 | 0.783875 | − | 0.620918i | \(-0.213240\pi\) | ||||
0.783875 | + | 0.620918i | \(0.213240\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.1481 | − | 12.9949i | 1.07921 | − | 0.557663i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.4142 | − | 19.0602i | −0.831613 | − | 0.816448i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.82950 | + | 9.82950i | 0.420279 | + | 0.420279i | 0.885300 | − | 0.465021i | \(-0.153953\pi\) |
−0.465021 | + | 0.885300i | \(0.653953\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.54490 | − | 12.0478i | 0.364687 | − | 0.514188i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.11489i | 0.175300i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.33904 | + | 3.33904i | −0.141990 | + | 0.141990i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.9705 | + | 5.79736i | −0.465673 | + | 0.246084i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.2811 | + | 23.2811i | −0.986454 | + | 0.986454i | −0.999909 | − | 0.0134559i | \(-0.995717\pi\) |
0.0134559 | + | 0.999909i | \(0.495717\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.10523i | − | 0.385110i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.06854 | + | 2.57082i | 0.340654 | + | 0.108540i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.5149 | + | 15.5149i | 0.653877 | + | 0.653877i | 0.953924 | − | 0.300048i | \(-0.0970026\pi\) |
−0.300048 | + | 0.953924i | \(0.597003\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.3134 | − | 0.168518i | 0.770452 | − | 0.00708959i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.24692 | − | 8.82752i | 0.178354 | − | 0.370721i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.39226 | −0.267977 | −0.133989 | − | 0.990983i | \(-0.542779\pi\) | ||||
−0.133989 | + | 0.990983i | \(0.542779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.6929 | −0.991519 | −0.495759 | − | 0.868460i | \(-0.665110\pi\) | ||||
−0.495759 | + | 0.868460i | \(0.665110\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.86135 | + | 3.60214i | 0.0777590 | + | 0.150482i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.46987 | − | 3.60000i | 0.144704 | − | 0.150130i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.36275 | + | 6.36275i | 0.264885 | + | 0.264885i | 0.827035 | − | 0.562150i | \(-0.190026\pi\) |
−0.562150 | + | 0.827035i | \(0.690026\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.1081 | + | 34.8628i | −0.461636 | + | 1.44885i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.2734i | 0.799596i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.03676 | − | 1.03676i | 0.0429382 | − | 0.0429382i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27.5326 | − | 19.1491i | −1.13833 | − | 0.791719i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.9023 | + | 23.9023i | −0.986553 | + | 0.986553i | −0.999911 | − | 0.0133579i | \(-0.995748\pi\) |
0.0133579 | + | 0.999911i | \(0.495748\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.60707i | 0.107422i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.2442 | − | 44.7055i | 0.585927 | − | 1.83894i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.7761 | − | 24.7761i | −1.01743 | − | 1.01743i | −0.999845 | − | 0.0175869i | \(-0.994402\pi\) |
−0.0175869 | − | 0.999845i | \(-0.505598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.93158 | + | 4.00461i | −0.161179 | + | 0.164173i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.6747 | − | 26.4638i | −0.559670 | − | 1.08309i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.6005 | −1.12773 | −0.563864 | − | 0.825868i | \(-0.690686\pi\) | ||||
−0.563864 | + | 0.825868i | \(0.690686\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.94916 | 0.405835 | 0.202917 | − | 0.979196i | \(-0.434958\pi\) | ||||
0.202917 | + | 0.979196i | \(0.434958\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.07520 | − | 1.37363i | 0.328848 | − | 0.0559386i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.1889 | − | 10.3782i | 0.414238 | − | 0.421932i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.0925441 | + | 0.0925441i | 0.00375625 | + | 0.00375625i | 0.708982 | − | 0.705226i | \(-0.249155\pi\) |
−0.705226 | + | 0.708982i | \(0.749155\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.87667 | + | 0.597950i | 0.0760465 | + | 0.0242301i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.44872i | 0.0586087i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0136 | − | 11.0136i | 0.444834 | − | 0.444834i | −0.448799 | − | 0.893633i | \(-0.648148\pi\) |
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.6765 | + | 6.07053i | 0.793435 | + | 0.244787i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.1932 | − | 23.1932i | 0.933722 | − | 0.933722i | −0.0642143 | − | 0.997936i | \(-0.520454\pi\) |
0.997936 | + | 0.0642143i | \(0.0204541\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 19.8708i | − | 0.798675i | −0.916804 | − | 0.399338i | \(-0.869240\pi\) | ||
0.916804 | − | 0.399338i | \(-0.130760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.15088 | + | 3.12573i | −0.166569 | + | 0.125431i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.38222 | + | 3.38222i | 0.135506 | + | 0.135506i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9831 | + | 0.919953i | −0.999323 | + | 0.0367981i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.8504 | + | 6.64023i | −0.513195 | + | 0.265185i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.38730 | −0.294551 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.9354 | −0.594567 | −0.297284 | − | 0.954789i | \(-0.596081\pi\) | ||||
−0.297284 | + | 0.954789i | \(0.596081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.4129 | − | 16.7488i | 1.28830 | − | 0.665707i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.11387 | − | 0.0470571i | 0.202938 | − | 0.00186741i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.5577 | − | 20.5577i | −0.814527 | − | 0.814527i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −33.1926 | − | 23.5418i | −1.31308 | − | 0.931300i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 2.26909i | − | 0.0896238i | −0.998995 | − | 0.0448119i | \(-0.985731\pi\) | ||
0.998995 | − | 0.0448119i | \(-0.0142688\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.5042 | + | 29.5042i | −1.16353 | + | 1.16353i | −0.179835 | + | 0.983697i | \(0.557556\pi\) |
−0.983697 | + | 0.179835i | \(0.942444\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.29566 | + | 6.23647i | 0.129766 | + | 0.245561i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.6539 | + | 27.6539i | −1.08719 | + | 1.08719i | −0.0913696 | + | 0.995817i | \(0.529124\pi\) |
−0.995817 | + | 0.0913696i | \(0.970876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.607720i | − | 0.0238551i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.18900 | + | 0.378843i | 0.0466006 | + | 0.0148480i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.1124 | − | 29.1124i | −1.13926 | − | 1.13926i | −0.988583 | − | 0.150674i | \(-0.951856\pi\) |
−0.150674 | − | 0.988583i | \(-0.548144\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34.8471 | − | 34.2117i | −1.36159 | − | 1.33676i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.19699 | − | 36.4304i | −0.241767 | − | 1.42129i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.0210 | −1.20841 | −0.604204 | − | 0.796830i | \(-0.706509\pi\) | ||||
−0.604204 | + | 0.796830i | \(0.706509\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.2767 | 0.788671 | 0.394335 | − | 0.918967i | \(-0.370975\pi\) | ||||
0.394335 | + | 0.918967i | \(0.370975\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.16601 | − | 17.7383i | −0.355978 | − | 0.688900i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0882041 | − | 9.58546i | −0.00342041 | − | 0.371708i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.738759 | − | 0.738759i | −0.0286049 | − | 0.0286049i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.0715 | − | 44.1635i | 0.544035 | − | 1.70746i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.4394i | 0.403010i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.338766 | − | 0.338766i | 0.0130585 | − | 0.0130585i | −0.700547 | − | 0.713606i | \(-0.747061\pi\) |
0.713606 | + | 0.700547i | \(0.247061\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.7890 | + | 3.15040i | 0.992621 | + | 0.121259i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.1120 | − | 12.1120i | 0.465501 | − | 0.465501i | −0.434952 | − | 0.900453i | \(-0.643235\pi\) |
0.900453 | + | 0.434952i | \(0.143235\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.4484i | 0.439351i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.92436 | − | 9.17812i | 0.112062 | − | 0.351706i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.6497 | − | 19.6497i | −0.751877 | − | 0.751877i | 0.222953 | − | 0.974829i | \(-0.428430\pi\) |
−0.974829 | + | 0.222953i | \(0.928430\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.396221 | + | 43.0588i | 0.0151388 | + | 1.64519i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.6478 | + | 20.6059i | 0.406238 | + | 0.786164i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.45705 | −0.131703 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.8202 | −0.449661 | −0.224831 | − | 0.974398i | \(-0.572183\pi\) | ||||
−0.224831 | + | 0.974398i | \(0.572183\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.16106 | + | 6.82557i | 0.0441051 | + | 0.259282i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.08928 | − | 4.01471i | −0.155115 | − | 0.152287i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.66874 | + | 8.66874i | 0.328352 | + | 0.328352i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.6629 | + | 4.67193i | 0.554602 | + | 0.176709i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.9281i | 1.20591i | 0.797776 | + | 0.602953i | \(0.206009\pi\) | ||||
−0.797776 | + | 0.602953i | \(0.793991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.92250 | − | 8.92250i | 0.336519 | − | 0.336519i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.524365 | − | 0.992273i | −0.0197487 | − | 0.0373711i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.55536 | + | 7.55536i | −0.284148 | + | 0.284148i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 27.1129i | − | 1.01825i | −0.860694 | − | 0.509123i | \(-0.829970\pi\) | ||
0.860694 | − | 0.509123i | \(-0.170030\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.6162 | + | 7.52950i | 0.398137 | + | 0.282378i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.468055 | − | 0.468055i | −0.0175288 | − | 0.0175288i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.7023 | − | 0.218106i | 0.886417 | − | 0.00815669i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 30.9092 | − | 15.9718i | 1.15433 | − | 0.596479i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.5274 | 1.39954 | 0.699768 | − | 0.714370i | \(-0.253287\pi\) | ||||
0.699768 | + | 0.714370i | \(0.253287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.2195 | 0.566806 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.6067 | − | 5.48084i | 0.394467 | − | 0.203835i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.0961295 | + | 5.22293i | 0.00357016 | + | 0.193975i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.4537 | − | 21.4537i | −0.795675 | − | 0.795675i | 0.186735 | − | 0.982410i | \(-0.440209\pi\) |
−0.982410 | + | 0.186735i | \(0.940209\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.9491 | − | 7.45958i | −0.961077 | − | 0.276281i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.19949i | 0.155324i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.4671 | + | 17.4671i | −0.645164 | + | 0.645164i | −0.951820 | − | 0.306657i | \(-0.900790\pi\) |
0.306657 | + | 0.951820i | \(0.400790\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.5216 | + | 6.63975i | 0.793835 | + | 0.244911i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.09371 | + | 4.09371i | −0.150794 | + | 0.150794i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.3324i | 1.74115i | 0.492035 | + | 0.870575i | \(0.336253\pi\) | ||||
−0.492035 | + | 0.870575i | \(0.663747\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.4955 | + | 10.3538i | 1.19375 | + | 0.380357i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.2979 | + | 21.2979i | 0.781345 | + | 0.781345i | 0.980058 | − | 0.198713i | \(-0.0636761\pi\) |
−0.198713 | + | 0.980058i | \(0.563676\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.30966 | + | 7.44544i | −0.267805 | + | 0.272780i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 52.3697 | − | 8.90833i | 1.91611 | − | 0.325939i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.66494 | −0.0608356 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.520366 | 0.0189884 | 0.00949422 | − | 0.999955i | \(-0.496978\pi\) | ||||
0.00949422 | + | 0.999955i | \(0.496978\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.59255 | − | 5.01719i | −0.0944779 | − | 0.182837i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.8525 | − | 25.3141i | 0.904474 | − | 0.921274i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.0141 | + | 27.0141i | 0.981843 | + | 0.981843i | 0.999838 | − | 0.0179948i | \(-0.00572822\pi\) |
−0.0179948 | + | 0.999838i | \(0.505728\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.11493 | − | 3.49921i | 0.0404693 | − | 0.127013i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.2267i | 1.05947i | 0.848165 | + | 0.529733i | \(0.177708\pi\) | ||||
−0.848165 | + | 0.529733i | \(0.822292\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.36442 | − | 9.36442i | 0.339015 | − | 0.339015i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.6985 | + | 8.83192i | 0.459116 | + | 0.319319i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.01321 | + | 1.01321i | −0.0365851 | + | 0.0365851i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.7070i | 1.28763i | 0.765183 | + | 0.643813i | \(0.222649\pi\) | ||||
−0.765183 | + | 0.643813i | \(0.777351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.53505 | + | 23.6488i | −0.271368 | + | 0.851691i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.1187 | + | 30.1187i | 1.08329 | + | 1.08329i | 0.996200 | + | 0.0870940i | \(0.0277581\pi\) |
0.0870940 | + | 0.996200i | \(0.472242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0609047 | + | 3.30909i | 0.00218776 | + | 0.118866i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.77271 | − | 5.36583i | −0.0994703 | − | 0.192498i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.9405 | −0.750271 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.7614 | 1.02917 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.757335 | − | 5.37566i | 0.0270650 | − | 0.192111i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.8477 | + | 0.173434i | −0.672705 | + | 0.00619014i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.4014 | − | 21.4014i | −0.762878 | − | 0.762878i | 0.213964 | − | 0.976842i | \(-0.431363\pi\) |
−0.976842 | + | 0.213964i | \(0.931363\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.39666 | + | 2.35675i | 0.263328 | + | 0.0839024i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.91474i | 0.316972i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.4050 | − | 17.4050i | 0.618071 | − | 0.618071i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.36785 | − | 1.25129i | 0.0839789 | − | 0.0443785i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.786685 | + | 0.786685i | −0.0278658 | + | 0.0278658i | −0.720902 | − | 0.693037i | \(-0.756272\pi\) |
0.693037 | + | 0.720902i | \(0.256272\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.668173i | − | 0.0236383i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.62687 | − | 10.7535i | 0.269482 | − | 0.379955i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.4683 | + | 18.4683i | 0.651733 | + | 0.651733i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.73674 | + | 1.70507i | 0.0612121 | + | 0.0600959i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.2346 | − | 15.6233i | 1.06431 | − | 0.549965i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.42050 | −0.225733 | −0.112866 | − | 0.993610i | \(-0.536003\pi\) | ||||
−0.112866 | + | 0.993610i | \(0.536003\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.4432 | 0.717859 | 0.358930 | − | 0.933365i | \(-0.383142\pi\) | ||||
0.358930 | + | 0.933365i | \(0.383142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.36549 | + | 2.25580i | −0.153104 | + | 0.0791142i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.0408416 | + | 4.43840i | 0.00143062 | + | 0.155470i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.07222 | − | 5.07222i | −0.177454 | − | 0.177454i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.44408 | − | 13.3156i | 0.330003 | − | 0.465285i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 46.2281i | − | 1.61337i | −0.590981 | − | 0.806686i | \(-0.701259\pi\) | ||
0.590981 | − | 0.806686i | \(-0.298741\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.1291 | − | 28.1291i | 0.980520 | − | 0.980520i | −0.0192940 | − | 0.999814i | \(-0.506142\pi\) |
0.999814 | + | 0.0192940i | \(0.00614184\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.1556 | + | 8.72849i | −0.562464 | + | 0.303887i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.6229 | + | 11.6229i | −0.404168 | + | 0.404168i | −0.879699 | − | 0.475531i | \(-0.842256\pi\) |
0.475531 | + | 0.879699i | \(0.342256\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.1278i | 1.28950i | 0.764393 | + | 0.644751i | \(0.223039\pi\) | ||||
−0.764393 | + | 0.644751i | \(0.776961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.8293 | + | 10.4602i | 1.13884 | + | 0.362859i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.48159 | + | 9.48159i | 0.328517 | + | 0.328517i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.119495 | − | 12.9860i | −0.00413530 | − | 0.449399i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.479824 | − | 3.40585i | 0.0165852 | − | 0.117724i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.5834 | 1.67729 | 0.838643 | − | 0.544682i | \(-0.183349\pi\) | ||||
0.838643 | + | 0.544682i | \(0.183349\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9085 | −0.962361 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.6829 | − | 28.4148i | −0.505705 | − | 0.978656i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.1380 | − | 18.7890i | −0.658367 | − | 0.646361i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.00589 | + | 5.00589i | 0.172004 | + | 0.172004i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.81851 | − | 8.84590i | 0.0967309 | − | 0.303591i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.20377i | 0.109824i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.19911 | − | 2.19911i | 0.0752962 | − | 0.0752962i | −0.668456 | − | 0.743752i | \(-0.733044\pi\) |
0.743752 | + | 0.668456i | \(0.233044\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −26.0048 | + | 4.67015i | −0.889346 | + | 0.159716i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.8471 | − | 14.8471i | 0.507169 | − | 0.507169i | −0.406488 | − | 0.913656i | \(-0.633247\pi\) |
0.913656 | + | 0.406488i | \(0.133247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.455728i | 0.0155492i | 0.999970 | + | 0.00777462i | \(0.00247476\pi\) | ||||
−0.999970 | + | 0.00777462i | \(0.997525\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.04294 | + | 9.55029i | −0.103703 | + | 0.325473i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.62428 | − | 3.62428i | −0.123372 | − | 0.123372i | 0.642725 | − | 0.766097i | \(-0.277804\pi\) |
−0.766097 | + | 0.642725i | \(0.777804\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.8430 | − | 0.200997i | 0.742685 | − | 0.00683409i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.28965 | − | 17.9776i | −0.315493 | − | 0.610552i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.19892 | −0.312052 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.6504 | 0.462526 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.1077 | − | 5.29157i | 1.05284 | − | 0.179092i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.335885 | − | 12.1645i | −0.0113550 | − | 0.411236i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.70945 | + | 4.70945i | 0.159027 | + | 0.159027i | 0.782135 | − | 0.623109i | \(-0.214131\pi\) |
−0.623109 | + | 0.782135i | \(0.714131\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.0272 | − | 6.06251i | −0.641773 | − | 0.204483i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.4607i | 0.588266i | 0.955764 | + | 0.294133i | \(0.0950309\pi\) | ||||
−0.955764 | + | 0.294133i | \(0.904969\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.5302 | + | 17.5302i | −0.589938 | + | 0.589938i | −0.937615 | − | 0.347676i | \(-0.886971\pi\) |
0.347676 | + | 0.937615i | \(0.386971\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.327249 | − | 1.06072i | 0.0110004 | − | 0.0356557i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.8924 | − | 10.8924i | 0.365732 | − | 0.365732i | −0.500186 | − | 0.865918i | \(-0.666735\pi\) |
0.865918 | + | 0.500186i | \(0.166735\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.48937i | 0.0834907i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.0098 | − | 6.30967i | 0.603350 | − | 0.211382i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.807030 | + | 0.807030i | 0.0270062 | + | 0.0270062i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.98055 | + | 5.07306i | −0.166481 | + | 0.169574i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.69287 | + | 3.97517i | −0.256858 | + | 0.132727i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.691560 | 0.0230648 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.59445 | 0.0531189 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.05034 | + | 1.57621i | −0.101509 | + | 0.0524531i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.6019 | + | 26.0774i | −0.851035 | + | 0.866842i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.4788 | − | 12.4788i | −0.414352 | − | 0.414352i | 0.468899 | − | 0.883252i | \(-0.344651\pi\) |
−0.883252 | + | 0.468899i | \(0.844651\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.0215 | + | 17.0372i | 0.796744 | + | 0.565090i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 11.4011i | − | 0.377736i | −0.982002 | − | 0.188868i | \(-0.939518\pi\) | ||
0.982002 | − | 0.188868i | \(-0.0604819\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.5487 | + | 26.5487i | −0.878635 | + | 0.878635i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.62150 | + | 18.2211i | −0.185841 | + | 0.602370i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.8085 | − | 16.8085i | 0.555065 | − | 0.555065i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 41.7932i | − | 1.37863i | −0.724461 | − | 0.689316i | \(-0.757911\pi\) | ||
0.724461 | − | 0.689316i | \(-0.242089\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.50456 | − | 2.07250i | −0.214332 | − | 0.0682912i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −47.9522 | − | 47.9522i | −1.57837 | − | 1.57837i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.1167 | − | 11.5336i | 0.365514 | − | 0.379221i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.03460 | − | 41.3545i | −0.231047 | − | 1.35826i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.4189 | 0.669922 | 0.334961 | − | 0.942232i | \(-0.391277\pi\) | ||||
0.334961 | + | 0.942232i | \(0.391277\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.9040 | −0.750649 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.7307 | − | 26.5721i | −0.449523 | − | 0.869932i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.9319 | + | 0.100594i | −0.357512 | + | 0.00328978i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.2594 | + | 17.2594i | 0.563839 | + | 0.563839i | 0.930396 | − | 0.366557i | \(-0.119463\pi\) |
−0.366557 | + | 0.930396i | \(0.619463\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.66558 | + | 20.9200i | −0.217523 | + | 0.682697i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.2803i | 1.47609i | 0.674749 | + | 0.738047i | \(0.264252\pi\) | ||||
−0.674749 | + | 0.738047i | \(0.735748\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.75951 | − | 3.75951i | 0.122426 | − | 0.122426i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.64895 | + | 12.5386i | −0.0536404 | + | 0.407881i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.1761 | + | 22.1761i | −0.720628 | + | 0.720628i | −0.968733 | − | 0.248105i | \(-0.920192\pi\) |
0.248105 | + | 0.968733i | \(0.420192\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 61.5822i | − | 1.99904i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.390819 | − | 1.22659i | 0.0126732 | − | 0.0397749i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.0491 | − | 35.0491i | −1.13535 | − | 1.13535i | −0.989273 | − | 0.146077i | \(-0.953335\pi\) |
−0.146077 | − | 0.989273i | \(-0.546665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.73526 | − | 3.66714i | −0.120870 | − | 0.118666i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.76141 | + | 3.40874i | 0.0569383 | + | 0.110189i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.9605 | −0.676849 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5618 | −0.985866 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.769550 | + | 4.52398i | 0.0247984 | + | 0.145783i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.434651 | − | 47.2351i | −0.0139919 | − | 1.52055i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.54533 | − | 2.54533i | −0.0818523 | − | 0.0818523i | 0.664995 | − | 0.746848i | \(-0.268434\pi\) |
−0.746848 | + | 0.664995i | \(0.768434\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.9875 | − | 4.77536i | −0.481468 | − | 0.153407i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 53.6724i | − | 1.72243i | −0.508242 | − | 0.861214i | \(-0.669704\pi\) | ||
0.508242 | − | 0.861214i | \(-0.330296\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.97246 | − | 1.97246i | 0.0632341 | − | 0.0632341i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 41.4876 | + | 12.3827i | 1.32867 | + | 0.396564i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.97649 | + | 2.97649i | −0.0952264 | + | 0.0952264i | −0.753115 | − | 0.657889i | \(-0.771450\pi\) |
0.657889 | + | 0.753115i | \(0.271450\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.31787i | 0.297801i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.7733 | − | 21.1167i | −0.950588 | − | 0.674203i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.1628 | + | 28.1628i | 0.898254 | + | 0.898254i | 0.995282 | − | 0.0970278i | \(-0.0309336\pi\) |
−0.0970278 | + | 0.995282i | \(0.530934\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.557363 | + | 60.5707i | 0.0177591 | + | 1.92994i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.485333 | − | 0.250788i | 0.0154483 | − | 0.00798268i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.82126 | 0.0579128 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.52755 | 0.270886 | 0.135443 | − | 0.990785i | \(-0.456754\pi\) | ||||
0.135443 | + | 0.990785i | \(0.456754\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 54.0151 | − | 27.9114i | 1.71412 | − | 0.885743i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.4417 | + | 26.9413i | 0.869962 | + | 0.854097i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.7830 | + | 39.7830i | 1.25994 | + | 1.25994i | 0.951121 | + | 0.308818i | \(0.0999335\pi\) |
0.308818 | + | 0.951121i | \(0.400066\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.2985 | + | 10.0141i | −0.420745 | + | 0.316833i |
(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 | 1380.2.r.c.737.5 | ✓ | 80 | |
3.2 | odd | 2 | inner | 1380.2.r.c.737.14 | yes | 80 | |
5.3 | odd | 4 | inner | 1380.2.r.c.1013.14 | yes | 80 | |
15.8 | even | 4 | inner | 1380.2.r.c.1013.5 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.r.c.737.5 | ✓ | 80 | 1.1 | even | 1 | trivial | |
1380.2.r.c.737.14 | yes | 80 | 3.2 | odd | 2 | inner | |
1380.2.r.c.1013.5 | yes | 80 | 15.8 | even | 4 | inner | |
1380.2.r.c.1013.14 | yes | 80 | 5.3 | odd | 4 | inner |