Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1079,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1764.1079");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.e (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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{12} - 10x^{10} + 4x^{8} - 40x^{6} + 16x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1079.10 | ||
Root | \(0.545545 + 1.30475i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1079 |
Dual form | 1764.2.e.i.1079.9 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.545545 | + | 1.30475i | 0.385759 | + | 0.922600i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.40476 | + | 1.42360i | −0.702381 | + | 0.711802i | ||||
\(5\) | 0.698240i | 0.312262i | 0.987736 | + | 0.156131i | \(0.0499023\pi\) | ||||
−0.987736 | + | 0.156131i | \(0.950098\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.62381 | − | 1.05623i | −0.927657 | − | 0.373433i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.911031 | + | 0.380921i | −0.288093 | + | 0.120458i | ||||
\(11\) | 2.55198 | 0.769452 | 0.384726 | − | 0.923031i | \(-0.374296\pi\) | ||||
0.384726 | + | 0.923031i | \(0.374296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.88088 | 0.521661 | 0.260831 | − | 0.965385i | \(-0.416004\pi\) | ||||
0.260831 | + | 0.965385i | \(0.416004\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.0532920 | − | 3.99964i | −0.0133230 | − | 0.999911i | ||||
\(17\) | 3.97326i | 0.963658i | 0.876265 | + | 0.481829i | \(0.160027\pi\) | ||||
−0.876265 | + | 0.481829i | \(0.839973\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.05819i | 1.61926i | 0.586941 | + | 0.809630i | \(0.300332\pi\) | ||||
−0.586941 | + | 0.809630i | \(0.699668\pi\) | |||||||
\(20\) | −0.994017 | − | 0.980861i | −0.222269 | − | 0.219327i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.39222 | + | 3.32971i | 0.296823 | + | 0.709896i | ||||
\(23\) | −4.02656 | −0.839595 | −0.419798 | − | 0.907618i | \(-0.637899\pi\) | ||||
−0.419798 | + | 0.907618i | \(0.637899\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.51246 | 0.902492 | ||||||||
\(26\) | 1.02610 | + | 2.45408i | 0.201235 | + | 0.481285i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.86081i | − | 0.345544i | −0.984962 | − | 0.172772i | \(-0.944728\pi\) | ||
0.984962 | − | 0.172772i | \(-0.0552724\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.941102i | − | 0.169027i | −0.996422 | − | 0.0845134i | \(-0.973066\pi\) | ||
0.996422 | − | 0.0845134i | \(-0.0269336\pi\) | |||||||
\(32\) | 5.18948 | − | 2.25152i | 0.917378 | − | 0.398016i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.18413 | + | 2.16759i | −0.889071 | + | 0.371739i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.49992 | −1.23298 | −0.616490 | − | 0.787363i | \(-0.711446\pi\) | ||||
−0.616490 | + | 0.787363i | \(0.711446\pi\) | |||||||
\(38\) | −9.20919 | + | 3.85056i | −1.49393 | + | 0.624643i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.737500 | − | 1.83205i | 0.116609 | − | 0.289673i | ||||
\(41\) | 10.6065i | 1.65646i | 0.560392 | + | 0.828228i | \(0.310651\pi\) | ||||
−0.560392 | + | 0.828228i | \(0.689349\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.97212i | 0.605743i | 0.953031 | + | 0.302871i | \(0.0979452\pi\) | ||||
−0.953031 | + | 0.302871i | \(0.902055\pi\) | |||||||
\(44\) | −3.58493 | + | 3.63301i | −0.540448 | + | 0.547697i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.19667 | − | 5.25366i | −0.323881 | − | 0.774610i | ||||
\(47\) | −8.90438 | −1.29884 | −0.649418 | − | 0.760431i | \(-0.724988\pi\) | ||||
−0.649418 | + | 0.760431i | \(0.724988\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.46175 | + | 5.88765i | 0.348144 | + | 0.832639i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.64218 | + | 2.67762i | −0.366405 | + | 0.371319i | ||||
\(53\) | 0.529774i | 0.0727701i | 0.999338 | + | 0.0363850i | \(0.0115843\pi\) | ||||
−0.999338 | + | 0.0363850i | \(0.988416\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.78190i | 0.240271i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.42790 | − | 1.01516i | 0.318799 | − | 0.133297i | ||||
\(59\) | −13.3007 | −1.73161 | −0.865804 | − | 0.500383i | \(-0.833193\pi\) | ||||
−0.865804 | + | 0.500383i | \(0.833193\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3683 | 1.32752 | 0.663760 | − | 0.747946i | \(-0.268960\pi\) | ||||
0.663760 | + | 0.747946i | \(0.268960\pi\) | |||||||
\(62\) | 1.22791 | − | 0.513413i | 0.155944 | − | 0.0652036i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.76877 | + | 5.54268i | 0.721096 | + | 0.692835i | ||||
\(65\) | 1.31330i | 0.162895i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.72300i | 0.332667i | 0.986070 | + | 0.166334i | \(0.0531929\pi\) | ||||
−0.986070 | + | 0.166334i | \(0.946807\pi\) | |||||||
\(68\) | −5.65635 | − | 5.58149i | −0.685933 | − | 0.676855i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.51310 | 0.416928 | 0.208464 | − | 0.978030i | \(-0.433154\pi\) | ||||
0.208464 | + | 0.978030i | \(0.433154\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.75071 | −0.321946 | −0.160973 | − | 0.986959i | \(-0.551463\pi\) | ||||
−0.160973 | + | 0.986959i | \(0.551463\pi\) | |||||||
\(74\) | −4.09155 | − | 9.78555i | −0.475632 | − | 1.13755i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.0481 | − | 9.91507i | −1.15259 | − | 1.13734i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.5338i | − | 1.52267i | −0.648358 | − | 0.761335i | \(-0.724544\pi\) | ||
0.648358 | − | 0.761335i | \(-0.275456\pi\) | |||||||
\(80\) | 2.79271 | − | 0.0372106i | 0.312235 | − | 0.00416027i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.8389 | + | 5.78632i | −1.52825 | + | 0.638992i | ||||
\(83\) | −17.1516 | −1.88264 | −0.941319 | − | 0.337520i | \(-0.890412\pi\) | ||||
−0.941319 | + | 0.337520i | \(0.890412\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.77429 | −0.300914 | ||||||||
\(86\) | −5.18264 | + | 2.16697i | −0.558858 | + | 0.233670i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.69592 | − | 2.69547i | −0.713788 | − | 0.287338i | ||||
\(89\) | 11.8700i | 1.25821i | 0.777319 | + | 0.629107i | \(0.216579\pi\) | ||||
−0.777319 | + | 0.629107i | \(0.783421\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.65635 | − | 5.73222i | 0.589715 | − | 0.597625i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.85774 | − | 11.6180i | −0.501038 | − | 1.19831i | ||||
\(95\) | −4.92831 | −0.505634 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.8682 | 1.10350 | 0.551748 | − | 0.834011i | \(-0.313961\pi\) | ||||
0.551748 | + | 0.834011i | \(0.313961\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.33893 | + | 6.42395i | −0.633893 | + | 0.642395i | ||||
\(101\) | 10.6065i | 1.05539i | 0.849435 | + | 0.527693i | \(0.176943\pi\) | ||||
−0.849435 | + | 0.527693i | \(0.823057\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.2756i | − | 1.30808i | −0.756459 | − | 0.654041i | \(-0.773072\pi\) | ||
0.756459 | − | 0.654041i | \(-0.226928\pi\) | |||||||
\(104\) | −4.93507 | − | 1.98663i | −0.483923 | − | 0.194805i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.691224 | + | 0.289016i | −0.0671377 | + | 0.0280717i | ||||
\(107\) | 9.61198 | 0.929225 | 0.464613 | − | 0.885514i | \(-0.346194\pi\) | ||||
0.464613 | + | 0.885514i | \(0.346194\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.2241 | 1.36242 | 0.681209 | − | 0.732089i | \(-0.261455\pi\) | ||||
0.681209 | + | 0.732089i | \(0.261455\pi\) | |||||||
\(110\) | −2.32494 | + | 0.972105i | −0.221674 | + | 0.0926866i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.1039i | − | 1.13864i | −0.822117 | − | 0.569319i | \(-0.807207\pi\) | ||
0.822117 | − | 0.569319i | \(-0.192793\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.81150i | − | 0.262174i | ||||||
\(116\) | 2.64906 | + | 2.61400i | 0.245959 | + | 0.242703i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.25615 | − | 17.3542i | −0.667983 | − | 1.59758i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.48738 | −0.407944 | ||||||||
\(122\) | 5.65635 | + | 13.5280i | 0.512102 | + | 1.22477i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.33976 | + | 1.32202i | 0.120314 | + | 0.118721i | ||||
\(125\) | 6.64198i | 0.594077i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.582584i | − | 0.0516960i | −0.999666 | − | 0.0258480i | \(-0.991771\pi\) | ||
0.999666 | − | 0.0258480i | \(-0.00822859\pi\) | |||||||
\(128\) | −4.08470 | + | 10.5506i | −0.361040 | + | 0.932550i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.71354 | + | 0.716466i | −0.150287 | + | 0.0628382i | ||||
\(131\) | 10.8924 | 0.951674 | 0.475837 | − | 0.879533i | \(-0.342145\pi\) | ||||
0.475837 | + | 0.879533i | \(0.342145\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.55284 | + | 1.48552i | −0.306919 | + | 0.128329i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.19667 | − | 10.4251i | 0.359861 | − | 0.893945i | ||||
\(137\) | 13.3019i | 1.13646i | 0.822870 | + | 0.568230i | \(0.192372\pi\) | ||||
−0.822870 | + | 0.568230i | \(0.807628\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.840795i | 0.0713153i | 0.999364 | + | 0.0356577i | \(0.0113526\pi\) | ||||
−0.999364 | + | 0.0356577i | \(0.988647\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.91655 | + | 4.58373i | 0.160834 | + | 0.384658i | ||||
\(143\) | 4.79997 | 0.401393 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.29929 | 0.107900 | ||||||||
\(146\) | −1.50063 | − | 3.58899i | −0.124193 | − | 0.297027i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.5356 | − | 10.6769i | 0.866021 | − | 0.877637i | ||||
\(149\) | 5.65685i | 0.463428i | 0.972784 | + | 0.231714i | \(0.0744333\pi\) | ||||
−0.972784 | + | 0.231714i | \(0.925567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.9829i | 1.38205i | 0.722830 | + | 0.691026i | \(0.242841\pi\) | ||||
−0.722830 | + | 0.691026i | \(0.757159\pi\) | |||||||
\(152\) | 7.45505 | − | 18.5194i | 0.604684 | − | 1.50212i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.657115 | 0.0527807 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.97492 | −0.157616 | −0.0788079 | − | 0.996890i | \(-0.525111\pi\) | ||||
−0.0788079 | + | 0.996890i | \(0.525111\pi\) | |||||||
\(158\) | 17.6583 | − | 7.38329i | 1.40482 | − | 0.587383i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.57210 | + | 3.62350i | 0.124286 | + | 0.286463i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.81150i | 0.220214i | 0.993920 | + | 0.110107i | \(0.0351194\pi\) | ||||
−0.993920 | + | 0.110107i | \(0.964881\pi\) | |||||||
\(164\) | −15.0994 | − | 14.8996i | −1.17907 | − | 1.16346i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.35699 | − | 22.3787i | −0.726243 | − | 1.73692i | ||||
\(167\) | 2.40833 | 0.186362 | 0.0931810 | − | 0.995649i | \(-0.470296\pi\) | ||||
0.0931810 | + | 0.995649i | \(0.470296\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.46230 | −0.727869 | ||||||||
\(170\) | −1.51350 | − | 3.61977i | −0.116080 | − | 0.277623i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.65472 | − | 5.57988i | −0.431169 | − | 0.425462i | ||||
\(173\) | 4.68026i | 0.355834i | 0.984046 | + | 0.177917i | \(0.0569358\pi\) | ||||
−0.984046 | + | 0.177917i | \(0.943064\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.136000 | − | 10.2070i | −0.0102514 | − | 0.769384i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.4874 | + | 6.47560i | −1.16083 | + | 0.485367i | ||||
\(179\) | −13.1909 | −0.985933 | −0.492966 | − | 0.870048i | \(-0.664087\pi\) | ||||
−0.492966 | + | 0.870048i | \(0.664087\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6801 | 1.31415 | 0.657075 | − | 0.753825i | \(-0.271793\pi\) | ||||
0.657075 | + | 0.753825i | \(0.271793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.5649 | + | 4.25296i | 0.778857 | + | 0.313532i | ||||
\(185\) | − | 5.23675i | − | 0.385013i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.1397i | 0.741489i | ||||||||
\(188\) | 12.5085 | − | 12.6763i | 0.912278 | − | 0.924514i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.68862 | − | 6.43023i | −0.195053 | − | 0.466498i | ||||
\(191\) | −21.2440 | −1.53716 | −0.768581 | − | 0.639753i | \(-0.779037\pi\) | ||||
−0.768581 | + | 0.639753i | \(0.779037\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.16763 | 0.299993 | 0.149996 | − | 0.988687i | \(-0.452074\pi\) | ||||
0.149996 | + | 0.988687i | \(0.452074\pi\) | |||||||
\(194\) | 5.92908 | + | 14.1803i | 0.425683 | + | 1.01809i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.04744i | 0.573356i | 0.958027 | + | 0.286678i | \(0.0925510\pi\) | ||||
−0.958027 | + | 0.286678i | \(0.907449\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.52369i | − | 0.108011i | −0.998541 | − | 0.0540056i | \(-0.982801\pi\) | ||
0.998541 | − | 0.0540056i | \(-0.0171989\pi\) | |||||||
\(200\) | −11.8398 | − | 4.76618i | −0.837203 | − | 0.337020i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.8389 | + | 5.78632i | −0.973698 | + | 0.407124i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.40588 | −0.517249 | ||||||||
\(206\) | 17.3214 | − | 7.24243i | 1.20684 | − | 0.504604i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.100236 | − | 7.52284i | −0.00695009 | − | 0.521615i | ||||
\(209\) | 18.0124i | 1.24594i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 19.2878i | − | 1.32783i | −0.747809 | − | 0.663914i | \(-0.768894\pi\) | ||
0.747809 | − | 0.663914i | \(-0.231106\pi\) | |||||||
\(212\) | −0.754188 | − | 0.744206i | −0.0517979 | − | 0.0511123i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.24377 | + | 12.5413i | 0.358457 | + | 0.857303i | ||||
\(215\) | −2.77349 | −0.189151 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.75986 | + | 18.5589i | 0.525564 | + | 1.25697i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.53671 | − | 2.50314i | −0.171025 | − | 0.168762i | ||||
\(221\) | 7.47322i | 0.502703i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.1390i | 1.21468i | 0.794443 | + | 0.607338i | \(0.207763\pi\) | ||||
−0.794443 | + | 0.607338i | \(0.792237\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.7926 | − | 6.60321i | 1.05051 | − | 0.439239i | ||||
\(227\) | 9.57818 | 0.635726 | 0.317863 | − | 0.948137i | \(-0.397035\pi\) | ||||
0.317863 | + | 0.948137i | \(0.397035\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.84326 | 0.320052 | 0.160026 | − | 0.987113i | \(-0.448842\pi\) | ||||
0.160026 | + | 0.987113i | \(0.448842\pi\) | |||||||
\(230\) | 3.66832 | − | 1.53380i | 0.241882 | − | 0.101136i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.96544 | + | 4.88242i | −0.129037 | + | 0.320546i | ||||
\(233\) | − | 21.6331i | − | 1.41723i | −0.705595 | − | 0.708615i | \(-0.749320\pi\) | ||
0.705595 | − | 0.708615i | \(-0.250680\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 6.21739i | − | 0.405578i | ||||||
\(236\) | 18.6844 | − | 18.9350i | 1.21625 | − | 1.23256i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.5549 | 1.32958 | 0.664792 | − | 0.747028i | \(-0.268520\pi\) | ||||
0.664792 | + | 0.747028i | \(0.268520\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7506 | 0.692504 | 0.346252 | − | 0.938142i | \(-0.387454\pi\) | ||||
0.346252 | + | 0.938142i | \(0.387454\pi\) | |||||||
\(242\) | −2.44807 | − | 5.85493i | −0.157368 | − | 0.376369i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.5649 | + | 14.7603i | −0.932424 | + | 0.944930i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.2756i | 0.844705i | ||||||||
\(248\) | −0.994017 | + | 2.46927i | −0.0631201 | + | 0.156799i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.66615 | + | 3.62350i | −0.548095 | + | 0.229170i | ||||
\(251\) | 19.4316 | 1.22651 | 0.613257 | − | 0.789884i | \(-0.289859\pi\) | ||||
0.613257 | + | 0.789884i | \(0.289859\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.2757 | −0.646028 | ||||||||
\(254\) | 0.760128 | − | 0.317826i | 0.0476947 | − | 0.0199422i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.9943 | + | 0.426298i | −0.999645 | + | 0.0266436i | ||||
\(257\) | − | 8.73670i | − | 0.544980i | −0.962159 | − | 0.272490i | \(-0.912153\pi\) | ||
0.962159 | − | 0.272490i | \(-0.0878472\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.86962 | − | 1.84488i | −0.115949 | − | 0.114414i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.94230 | + | 14.2119i | 0.367117 | + | 0.878015i | ||||
\(263\) | 21.8079 | 1.34474 | 0.672368 | − | 0.740217i | \(-0.265277\pi\) | ||||
0.672368 | + | 0.740217i | \(0.265277\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.369910 | −0.0227234 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.87647 | − | 3.82516i | −0.236793 | − | 0.233659i | ||||
\(269\) | − | 14.7040i | − | 0.896519i | −0.893904 | − | 0.448259i | \(-0.852044\pi\) | ||
0.893904 | − | 0.448259i | \(-0.147956\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.18779i | 0.315136i | 0.987508 | + | 0.157568i | \(0.0503653\pi\) | ||||
−0.987508 | + | 0.157568i | \(0.949635\pi\) | |||||||
\(272\) | 15.8916 | − | 0.211743i | 0.963573 | − | 0.0128388i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.3557 | + | 7.25680i | −1.04850 | + | 0.438399i | ||||
\(275\) | 11.5157 | 0.694424 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.7255 | 1.42553 | 0.712763 | − | 0.701405i | \(-0.247444\pi\) | ||||
0.712763 | + | 0.701405i | \(0.247444\pi\) | |||||||
\(278\) | −1.09703 | + | 0.458692i | −0.0657955 | + | 0.0275105i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4.12400i | − | 0.246017i | −0.992406 | − | 0.123009i | \(-0.960746\pi\) | ||
0.992406 | − | 0.123009i | \(-0.0392542\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7.05819i | − | 0.419566i | −0.977748 | − | 0.209783i | \(-0.932724\pi\) | ||
0.977748 | − | 0.209783i | \(-0.0672757\pi\) | |||||||
\(284\) | −4.93507 | + | 5.00126i | −0.292842 | + | 0.296770i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.61860 | + | 6.26277i | 0.154841 | + | 0.370325i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.21317 | 0.0713628 | ||||||||
\(290\) | 0.708823 | + | 1.69526i | 0.0416235 | + | 0.0995489i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.86409 | − | 3.91592i | 0.226129 | − | 0.229162i | ||||
\(293\) | − | 15.9675i | − | 0.932830i | −0.884566 | − | 0.466415i | \(-0.845545\pi\) | ||
0.884566 | − | 0.466415i | \(-0.154455\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.28711i | − | 0.540716i | ||||||
\(296\) | 19.6784 | + | 7.92162i | 1.14378 | + | 0.460435i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.38080 | + | 3.08607i | −0.427558 | + | 0.178771i | ||||
\(299\) | −7.57346 | −0.437984 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −22.1585 | + | 9.26495i | −1.27508 | + | 0.533138i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 28.2302 | − | 0.376145i | 1.61912 | − | 0.0215734i | ||||
\(305\) | 7.23953i | 0.414534i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.53450i | − | 0.315871i | −0.987449 | − | 0.157935i | \(-0.949516\pi\) | ||
0.987449 | − | 0.157935i | \(-0.0504838\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.358486 | + | 0.857373i | 0.0203606 | + | 0.0486955i | ||||
\(311\) | 10.4888 | 0.594766 | 0.297383 | − | 0.954758i | \(-0.403886\pi\) | ||||
0.297383 | + | 0.954758i | \(0.403886\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.26317 | 0.127922 | 0.0639609 | − | 0.997952i | \(-0.479627\pi\) | ||||
0.0639609 | + | 0.997952i | \(0.479627\pi\) | |||||||
\(314\) | −1.07741 | − | 2.57678i | −0.0608017 | − | 0.145416i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.2668 | + | 19.0117i | 1.08384 | + | 1.06949i | ||||
\(317\) | − | 9.50588i | − | 0.533903i | −0.963710 | − | 0.266952i | \(-0.913984\pi\) | ||
0.963710 | − | 0.266952i | \(-0.0860164\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.74876i | − | 0.265879i | ||||||
\(320\) | −3.87012 | + | 4.02799i | −0.216346 | + | 0.225171i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.0441 | −1.56041 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.48738 | 0.470795 | ||||||||
\(326\) | −3.66832 | + | 1.53380i | −0.203169 | + | 0.0849494i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.2029 | − | 27.8294i | 0.618574 | − | 1.53662i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.94110i | 0.546412i | 0.961956 | + | 0.273206i | \(0.0880841\pi\) | ||||
−0.961956 | + | 0.273206i | \(0.911916\pi\) | |||||||
\(332\) | 24.0940 | − | 24.4171i | 1.32233 | − | 1.34006i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.31385 | + | 3.14227i | 0.0718907 | + | 0.171937i | ||||
\(335\) | −1.90131 | −0.103879 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.6441 | 0.579822 | 0.289911 | − | 0.957054i | \(-0.406374\pi\) | ||||
0.289911 | + | 0.957054i | \(0.406374\pi\) | |||||||
\(338\) | −5.16211 | − | 12.3460i | −0.280782 | − | 0.671532i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.89722 | − | 3.94949i | 0.211356 | − | 0.214191i | ||||
\(341\) | − | 2.40168i | − | 0.130058i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.19546 | − | 10.4221i | 0.226204 | − | 0.561922i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.10658 | + | 2.55329i | −0.328292 | + | 0.137266i | ||||
\(347\) | −17.5488 | −0.942069 | −0.471035 | − | 0.882115i | \(-0.656119\pi\) | ||||
−0.471035 | + | 0.882115i | \(0.656119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.0703 | 1.55610 | 0.778049 | − | 0.628204i | \(-0.216210\pi\) | ||||
0.778049 | + | 0.628204i | \(0.216210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.2435 | − | 5.74584i | 0.705879 | − | 0.306254i | ||||
\(353\) | 11.2462i | 0.598572i | 0.954163 | + | 0.299286i | \(0.0967485\pi\) | ||||
−0.954163 | + | 0.299286i | \(0.903251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.45299i | 0.130191i | ||||||||
\(356\) | −16.8981 | − | 16.6745i | −0.895599 | − | 0.883745i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.19622 | − | 17.2108i | −0.380332 | − | 0.909621i | ||||
\(359\) | 29.0436 | 1.53286 | 0.766431 | − | 0.642326i | \(-0.222031\pi\) | ||||
0.766431 | + | 0.642326i | \(0.222031\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −30.8180 | −1.62200 | ||||||||
\(362\) | 9.64529 | + | 23.0682i | 0.506945 | + | 1.21244i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.92065i | − | 0.100532i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.0864i | 1.25730i | 0.777689 | + | 0.628649i | \(0.216392\pi\) | ||||
−0.777689 | + | 0.628649i | \(0.783608\pi\) | |||||||
\(368\) | 0.214583 | + | 16.1048i | 0.0111859 | + | 0.839521i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.83266 | − | 2.85688i | 0.355213 | − | 0.148522i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.3947 | 0.693550 | 0.346775 | − | 0.937948i | \(-0.387277\pi\) | ||||
0.346775 | + | 0.937948i | \(0.387277\pi\) | |||||||
\(374\) | −13.2298 | + | 5.53167i | −0.684097 | + | 0.286036i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 23.3634 | + | 9.40504i | 1.20488 | + | 0.485028i | ||||
\(377\) | − | 3.49996i | − | 0.180257i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.9558i | 0.665493i | 0.943016 | + | 0.332746i | \(0.107975\pi\) | ||||
−0.943016 | + | 0.332746i | \(0.892025\pi\) | |||||||
\(380\) | 6.92310 | − | 7.01596i | 0.355147 | − | 0.359911i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.5896 | − | 27.7182i | −0.592973 | − | 1.41819i | ||||
\(383\) | −2.53349 | −0.129455 | −0.0647277 | − | 0.997903i | \(-0.520618\pi\) | ||||
−0.0647277 | + | 0.997903i | \(0.520618\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.27363 | + | 5.43773i | 0.115725 | + | 0.276773i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.2672 | + | 15.4720i | −0.775075 | + | 0.785471i | ||||
\(389\) | − | 15.3047i | − | 0.775979i | −0.921664 | − | 0.387990i | \(-0.873170\pi\) | ||
0.921664 | − | 0.387990i | \(-0.126830\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15.9986i | − | 0.809083i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.4999 | + | 4.39024i | −0.528978 | + | 0.221177i | ||||
\(395\) | 9.44984 | 0.475473 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.1066 | 0.657801 | 0.328900 | − | 0.944365i | \(-0.393322\pi\) | ||||
0.328900 | + | 0.944365i | \(0.393322\pi\) | |||||||
\(398\) | 1.98803 | − | 0.831239i | 0.0996511 | − | 0.0416663i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.240478 | − | 18.0482i | −0.0120239 | − | 0.902412i | ||||
\(401\) | 1.16046i | 0.0579505i | 0.999580 | + | 0.0289753i | \(0.00922440\pi\) | ||||
−0.999580 | + | 0.0289753i | \(0.990776\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.77010i | − | 0.0881748i | ||||||
\(404\) | −15.0994 | − | 14.8996i | −0.751225 | − | 0.741282i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.1397 | −0.948718 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.18809 | 0.355428 | 0.177714 | − | 0.984082i | \(-0.443130\pi\) | ||||
0.177714 | + | 0.984082i | \(0.443130\pi\) | |||||||
\(410\) | −4.04024 | − | 9.66284i | −0.199533 | − | 0.477214i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18.8992 | + | 18.6490i | 0.931095 | + | 0.918771i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11.9760i | − | 0.587877i | ||||||
\(416\) | 9.76076 | − | 4.23483i | 0.478561 | − | 0.207630i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.5017 | + | 9.82656i | −1.14951 | + | 0.480633i | ||||
\(419\) | −16.1127 | −0.787155 | −0.393578 | − | 0.919291i | \(-0.628763\pi\) | ||||
−0.393578 | + | 0.919291i | \(0.628763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.49992 | 0.268050 | 0.134025 | − | 0.990978i | \(-0.457210\pi\) | ||||
0.134025 | + | 0.990978i | \(0.457210\pi\) | |||||||
\(422\) | 25.1658 | − | 10.5224i | 1.22505 | − | 0.512221i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.559562 | − | 1.39003i | 0.0271747 | − | 0.0675057i | ||||
\(425\) | 17.9292i | 0.869694i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −13.5025 | + | 13.6836i | −0.652670 | + | 0.661424i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.51307 | − | 3.61872i | −0.0729665 | − | 0.174510i | ||||
\(431\) | −13.4106 | −0.645965 | −0.322983 | − | 0.946405i | \(-0.604686\pi\) | ||||
−0.322983 | + | 0.946405i | \(0.604686\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.6801 | −1.52245 | −0.761224 | − | 0.648489i | \(-0.775401\pi\) | ||||
−0.761224 | + | 0.648489i | \(0.775401\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.9814 | + | 20.2494i | −0.956936 | + | 0.969771i | ||||
\(437\) | − | 28.4202i | − | 1.35952i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.4812i | 0.929786i | 0.885367 | + | 0.464893i | \(0.153907\pi\) | ||||
−0.885367 | + | 0.464893i | \(0.846093\pi\) | |||||||
\(440\) | 1.88209 | − | 4.67536i | 0.0897250 | − | 0.222889i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.75071 | + | 4.07698i | −0.463794 | + | 0.193922i | ||||
\(443\) | 6.88254 | 0.326999 | 0.163500 | − | 0.986543i | \(-0.447722\pi\) | ||||
0.163500 | + | 0.986543i | \(0.447722\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.28809 | −0.392893 | ||||||||
\(446\) | −23.6669 | + | 9.89564i | −1.12066 | + | 0.468572i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.3255i | 0.912025i | 0.889973 | + | 0.456012i | \(0.150723\pi\) | ||||
−0.889973 | + | 0.456012i | \(0.849277\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.0676i | 1.27456i | ||||||||
\(452\) | 17.2311 | + | 17.0031i | 0.810484 | + | 0.799757i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.22533 | + | 12.4972i | 0.245237 | + | 0.586521i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.83699 | 0.226265 | 0.113132 | − | 0.993580i | \(-0.463912\pi\) | ||||
0.113132 | + | 0.993580i | \(0.463912\pi\) | |||||||
\(458\) | 2.64222 | + | 6.31926i | 0.123463 | + | 0.295279i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.00247 | + | 3.94949i | 0.186616 | + | 0.184146i | ||||
\(461\) | − | 26.3490i | − | 1.22720i | −0.789618 | − | 0.613599i | \(-0.789721\pi\) | ||
0.789618 | − | 0.613599i | \(-0.210279\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.1024i | 1.77077i | 0.464858 | + | 0.885385i | \(0.346105\pi\) | ||||
−0.464858 | + | 0.885385i | \(0.653895\pi\) | |||||||
\(464\) | −7.44258 | + | 0.0991663i | −0.345513 | + | 0.00460368i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.2258 | − | 11.8018i | 1.30754 | − | 0.546709i | ||||
\(467\) | 6.38439 | 0.295435 | 0.147717 | − | 0.989030i | \(-0.452807\pi\) | ||||
0.147717 | + | 0.989030i | \(0.452807\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.11216 | − | 3.39187i | 0.374186 | − | 0.156455i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 34.8986 | + | 14.0486i | 1.60634 | + | 0.646639i | ||||
\(473\) | 10.1368i | 0.466090i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.8498i | 1.46137i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.2136 | + | 26.8190i | 0.512899 | + | 1.22667i | ||||
\(479\) | −21.0410 | −0.961387 | −0.480693 | − | 0.876889i | \(-0.659615\pi\) | ||||
−0.480693 | + | 0.876889i | \(0.659615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.1064 | −0.643198 | ||||||||
\(482\) | 5.86491 | + | 14.0268i | 0.267139 | + | 0.638904i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.30370 | − | 6.38825i | 0.286532 | − | 0.290375i | ||||
\(485\) | 7.58860i | 0.344581i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.7836i | − | 0.715224i | −0.933870 | − | 0.357612i | \(-0.883591\pi\) | ||
0.933870 | − | 0.357612i | \(-0.116409\pi\) | |||||||
\(488\) | −27.2044 | − | 10.9512i | −1.23148 | − | 0.495739i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.8204 | 0.849351 | 0.424675 | − | 0.905346i | \(-0.360388\pi\) | ||||
0.424675 | + | 0.905346i | \(0.360388\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.39349 | 0.332986 | ||||||||
\(494\) | −17.3214 | + | 7.24243i | −0.779325 | + | 0.325852i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.76407 | + | 0.0501532i | −0.169012 | + | 0.00225194i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.05889i | − | 0.360766i | −0.983596 | − | 0.180383i | \(-0.942266\pi\) | ||
0.983596 | − | 0.180383i | \(-0.0577337\pi\) | |||||||
\(500\) | −9.45555 | − | 9.33040i | −0.422865 | − | 0.417268i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.6008 | + | 25.3535i | 0.473138 | + | 1.13158i | ||||
\(503\) | 0.823898 | 0.0367358 | 0.0183679 | − | 0.999831i | \(-0.494153\pi\) | ||||
0.0183679 | + | 0.999831i | \(0.494153\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.40588 | −0.329557 | ||||||||
\(506\) | −5.60586 | − | 13.4073i | −0.249211 | − | 0.596025i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.829368 | + | 0.818391i | 0.0367973 | + | 0.0363102i | ||||
\(509\) | − | 39.1011i | − | 1.73313i | −0.499067 | − | 0.866563i | \(-0.666324\pi\) | ||
0.499067 | − | 0.866563i | \(-0.333676\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −9.28184 | − | 20.6361i | −0.410203 | − | 0.911994i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.3992 | − | 4.76626i | 0.502799 | − | 0.210231i | ||||
\(515\) | 9.26954 | 0.408465 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.7238 | −0.999392 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.38715 | − | 3.44586i | 0.0608304 | − | 0.151111i | ||||
\(521\) | − | 0.523131i | − | 0.0229188i | −0.999934 | − | 0.0114594i | \(-0.996352\pi\) | ||
0.999934 | − | 0.0114594i | \(-0.00364772\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 37.5317i | − | 1.64115i | −0.571542 | − | 0.820573i | \(-0.693655\pi\) | ||
0.571542 | − | 0.820573i | \(-0.306345\pi\) | |||||||
\(524\) | −15.3012 | + | 15.5065i | −0.668438 | + | 0.677403i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.8972 | + | 28.4540i | 0.518743 | + | 1.24065i | ||||
\(527\) | 3.73925 | 0.162884 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.78683 | −0.295080 | ||||||||
\(530\) | −0.201802 | − | 0.482641i | −0.00876573 | − | 0.0209646i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.9495i | 0.864109i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.71147i | 0.290162i | ||||||||
\(536\) | 2.87610 | − | 7.14463i | 0.124229 | − | 0.308601i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.1851 | − | 8.02169i | 0.827128 | − | 0.345840i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.3541 | 0.961076 | 0.480538 | − | 0.876974i | \(-0.340441\pi\) | ||||
0.480538 | + | 0.876974i | \(0.340441\pi\) | |||||||
\(542\) | −6.76878 | + | 2.83017i | −0.290744 | + | 0.121566i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.94588 | + | 20.6192i | 0.383552 | + | 0.884039i | ||||
\(545\) | 9.93181i | 0.425432i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.09960i | − | 0.346314i | −0.984894 | − | 0.173157i | \(-0.944603\pi\) | ||
0.984894 | − | 0.173157i | \(-0.0553968\pi\) | |||||||
\(548\) | −18.9367 | − | 18.6860i | −0.808934 | − | 0.798227i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.28235 | + | 15.0252i | 0.267880 | + | 0.640676i | ||||
\(551\) | 13.1340 | 0.559525 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.9433 | + | 30.9559i | 0.549909 | + | 1.31519i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.19696 | − | 1.18112i | −0.0507624 | − | 0.0500905i | ||||
\(557\) | − | 31.5924i | − | 1.33861i | −0.742986 | − | 0.669307i | \(-0.766591\pi\) | ||
0.742986 | − | 0.669307i | \(-0.233409\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.47107i | 0.315992i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.38080 | − | 2.24983i | 0.226975 | − | 0.0949032i | ||||
\(563\) | 8.35892 | 0.352286 | 0.176143 | − | 0.984365i | \(-0.443638\pi\) | ||||
0.176143 | + | 0.984365i | \(0.443638\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.45141 | 0.355554 | ||||||||
\(566\) | 9.20919 | − | 3.85056i | 0.387091 | − | 0.161851i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.21771 | − | 3.71063i | −0.386766 | − | 0.155695i | ||||
\(569\) | − | 13.0294i | − | 0.546220i | −0.961983 | − | 0.273110i | \(-0.911948\pi\) | ||
0.961983 | − | 0.273110i | \(-0.0880524\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 14.3864i | − | 0.602052i | −0.953616 | − | 0.301026i | \(-0.902671\pi\) | ||
0.953616 | − | 0.301026i | \(-0.0973290\pi\) | |||||||
\(572\) | −6.74281 | + | 6.83325i | −0.281931 | + | 0.285712i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.1697 | −0.757728 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.7616 | −1.07247 | −0.536235 | − | 0.844069i | \(-0.680154\pi\) | ||||
−0.536235 | + | 0.844069i | \(0.680154\pi\) | |||||||
\(578\) | 0.661838 | + | 1.58288i | 0.0275288 | + | 0.0658393i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.82520 | + | 1.84968i | −0.0757871 | + | 0.0768037i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.35197i | 0.0559931i | ||||||||
\(584\) | 7.21734 | + | 2.90537i | 0.298656 | + | 0.120225i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.8336 | − | 8.71098i | 0.860629 | − | 0.359847i | ||||
\(587\) | 33.3927 | 1.37826 | 0.689131 | − | 0.724637i | \(-0.257992\pi\) | ||||
0.689131 | + | 0.724637i | \(0.257992\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.64247 | 0.273698 | ||||||||
\(590\) | 12.1174 | − | 5.06654i | 0.498865 | − | 0.208586i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.399686 | + | 29.9970i | 0.0164270 | + | 1.23287i | ||||
\(593\) | 29.5496i | 1.21346i | 0.794909 | + | 0.606729i | \(0.207519\pi\) | ||||
−0.794909 | + | 0.606729i | \(0.792481\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.05312 | − | 7.94653i | −0.329868 | − | 0.325503i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.13166 | − | 9.88149i | −0.168956 | − | 0.404084i | ||||
\(599\) | 5.99928 | 0.245124 | 0.122562 | − | 0.992461i | \(-0.460889\pi\) | ||||
0.122562 | + | 0.992461i | \(0.460889\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.44843 | −0.222246 | −0.111123 | − | 0.993807i | \(-0.535445\pi\) | ||||
−0.111123 | + | 0.993807i | \(0.535445\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24.1770 | − | 23.8570i | −0.983746 | − | 0.970726i | ||||
\(605\) | − | 3.13327i | − | 0.127386i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.34699i | 0.176439i | 0.996101 | + | 0.0882195i | \(0.0281177\pi\) | ||||
−0.996101 | + | 0.0882195i | \(0.971882\pi\) | |||||||
\(608\) | 15.8916 | + | 36.6283i | 0.644491 | + | 1.48547i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.44580 | + | 3.94949i | −0.382449 | + | 0.159910i | ||||
\(611\) | −16.7480 | −0.677553 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.9621 | −0.604312 | −0.302156 | − | 0.953258i | \(-0.597706\pi\) | ||||
−0.302156 | + | 0.953258i | \(0.597706\pi\) | |||||||
\(614\) | 7.22116 | − | 3.01932i | 0.291422 | − | 0.121850i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 21.4967i | − | 0.865425i | −0.901532 | − | 0.432713i | \(-0.857557\pi\) | ||
0.901532 | − | 0.432713i | \(-0.142443\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.3864i | − | 0.578238i | −0.957293 | − | 0.289119i | \(-0.906638\pi\) | ||
0.957293 | − | 0.289119i | \(-0.0933623\pi\) | |||||||
\(620\) | −0.923089 | + | 0.935471i | −0.0370722 | + | 0.0375694i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.72212 | + | 13.6853i | 0.229436 | + | 0.548731i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.9246 | 0.716984 | ||||||||
\(626\) | 1.23466 | + | 2.95288i | 0.0493470 | + | 0.118021i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.77429 | − | 2.81150i | 0.110706 | − | 0.112191i | ||||
\(629\) | − | 29.7992i | − | 1.18817i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 15.8983i | − | 0.632900i | −0.948609 | − | 0.316450i | \(-0.897509\pi\) | ||
0.948609 | − | 0.316450i | \(-0.102491\pi\) | |||||||
\(632\) | −14.2948 | + | 35.5101i | −0.568615 | + | 1.41252i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.4028 | − | 5.18588i | 0.492579 | − | 0.205958i | ||||
\(635\) | 0.406784 | 0.0161427 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.19596 | − | 2.59066i | 0.245300 | − | 0.102565i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.36685 | − | 2.85210i | −0.291200 | − | 0.112739i | ||||
\(641\) | − | 1.56599i | − | 0.0618528i | −0.999522 | − | 0.0309264i | \(-0.990154\pi\) | ||
0.999522 | − | 0.0309264i | \(-0.00984576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 33.5314i | − | 1.32235i | −0.750232 | − | 0.661174i | \(-0.770058\pi\) | ||
0.750232 | − | 0.661174i | \(-0.229942\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.2993 | − | 36.5906i | −0.601943 | − | 1.43964i | ||||
\(647\) | 17.3184 | 0.680857 | 0.340429 | − | 0.940270i | \(-0.389428\pi\) | ||||
0.340429 | + | 0.940270i | \(0.389428\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.9433 | −1.33239 | ||||||||
\(650\) | 4.63025 | + | 11.0739i | 0.181613 | + | 0.434356i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00247 | − | 3.94949i | −0.156749 | − | 0.154674i | ||||
\(653\) | 27.0948i | 1.06030i | 0.847904 | + | 0.530150i | \(0.177864\pi\) | ||||
−0.847904 | + | 0.530150i | \(0.822136\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.60552i | 0.297172i | ||||||||
\(656\) | 42.4222 | − | 0.565241i | 1.65631 | − | 0.0220690i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.9749 | 0.427521 | 0.213761 | − | 0.976886i | \(-0.431429\pi\) | ||||
0.213761 | + | 0.976886i | \(0.431429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.88072 | 0.112047 | 0.0560235 | − | 0.998429i | \(-0.482158\pi\) | ||||
0.0560235 | + | 0.998429i | \(0.482158\pi\) | |||||||
\(662\) | −12.9707 | + | 5.42332i | −0.504120 | + | 0.210783i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 45.0027 | + | 18.1160i | 1.74644 | + | 0.703038i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.49266i | 0.290117i | ||||||||
\(668\) | −3.38312 | + | 3.42850i | −0.130897 | + | 0.132653i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.03725 | − | 2.48074i | −0.0400724 | − | 0.0958392i | ||||
\(671\) | 26.4596 | 1.02146 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.09255 | 0.350492 | 0.175246 | − | 0.984525i | \(-0.443928\pi\) | ||||
0.175246 | + | 0.984525i | \(0.443928\pi\) | |||||||
\(674\) | 5.80685 | + | 13.8880i | 0.223671 | + | 0.534944i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.2923 | − | 13.4706i | 0.511241 | − | 0.518099i | ||||
\(677\) | − | 15.9675i | − | 0.613680i | −0.951761 | − | 0.306840i | \(-0.900728\pi\) | ||
0.951761 | − | 0.306840i | \(-0.0992717\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.27922 | + | 2.93028i | 0.279145 | + | 0.112371i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.13359 | − | 1.31022i | 0.119991 | − | 0.0501710i | ||||
\(683\) | 44.5539 | 1.70481 | 0.852404 | − | 0.522885i | \(-0.175144\pi\) | ||||
0.852404 | + | 0.522885i | \(0.175144\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.28793 | −0.354874 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.8871 | − | 0.211682i | 0.605689 | − | 0.00807031i | ||||
\(689\) | 0.996440i | 0.0379613i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.9926i | 0.532304i | 0.963931 | + | 0.266152i | \(0.0857523\pi\) | ||||
−0.963931 | + | 0.266152i | \(0.914248\pi\) | |||||||
\(692\) | −6.66283 | − | 6.57465i | −0.253283 | − | 0.249931i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.57366 | − | 22.8969i | −0.363411 | − | 0.869153i | ||||
\(695\) | −0.587077 | −0.0222691 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.1424 | −1.59626 | ||||||||
\(698\) | 15.8592 | + | 37.9296i | 0.600278 | + | 1.43566i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.4059i | 0.544104i | 0.962283 | + | 0.272052i | \(0.0877022\pi\) | ||||
−0.962283 | + | 0.272052i | \(0.912298\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 52.9359i | − | 1.99651i | ||||||
\(704\) | 14.7218 | + | 14.1448i | 0.554849 | + | 0.533103i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.6735 | + | 6.13528i | −0.552243 | + | 0.230904i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.1878 | −1.65951 | −0.829753 | − | 0.558130i | \(-0.811519\pi\) | ||||
−0.829753 | + | 0.558130i | \(0.811519\pi\) | |||||||
\(710\) | −3.20054 | + | 1.33821i | −0.120114 | + | 0.0502223i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.5374 | − | 31.1446i | 0.469858 | − | 1.16719i | ||||
\(713\) | 3.78940i | 0.141914i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.35153i | 0.125340i | ||||||||
\(716\) | 18.5300 | − | 18.7786i | 0.692500 | − | 0.701789i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.8446 | + | 37.8947i | 0.591315 | + | 1.41422i | ||||
\(719\) | −12.1366 | −0.452619 | −0.226309 | − | 0.974055i | \(-0.572666\pi\) | ||||
−0.226309 | + | 0.974055i | \(0.572666\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −16.8126 | − | 40.2099i | −0.625701 | − | 1.49646i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −24.8363 | + | 25.1694i | −0.923034 | + | 0.935415i | ||||
\(725\) | − | 8.39684i | − | 0.311851i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 27.8081i | − | 1.03134i | −0.856786 | − | 0.515672i | \(-0.827542\pi\) | ||
0.856786 | − | 0.515672i | \(-0.172458\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.50598 | − | 1.04780i | 0.0927505 | − | 0.0387809i | ||||
\(731\) | −15.7823 | −0.583729 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.6626 | −1.46497 | −0.732486 | − | 0.680782i | \(-0.761640\pi\) | ||||
−0.732486 | + | 0.680782i | \(0.761640\pi\) | |||||||
\(734\) | −31.4268 | + | 13.1402i | −1.15998 | + | 0.485014i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.8957 | + | 9.06587i | −0.770227 | + | 0.334173i | ||||
\(737\) | 6.94905i | 0.255971i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.6564i | 1.20129i | 0.799517 | + | 0.600643i | \(0.205089\pi\) | ||||
−0.799517 | + | 0.600643i | \(0.794911\pi\) | |||||||
\(740\) | 7.45505 | + | 7.35638i | 0.274053 | + | 0.270426i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.8538 | −1.24198 | −0.620988 | − | 0.783820i | \(-0.713268\pi\) | ||||
−0.620988 | + | 0.783820i | \(0.713268\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.94984 | −0.144711 | ||||||||
\(746\) | 7.30740 | + | 17.4767i | 0.267543 | + | 0.639869i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.4349 | − | 14.2439i | −0.527793 | − | 0.520807i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.7617i | 1.08602i | 0.839726 | + | 0.543010i | \(0.182715\pi\) | ||||
−0.839726 | + | 0.543010i | \(0.817285\pi\) | |||||||
\(752\) | 0.474532 | + | 35.6143i | 0.0173044 | + | 1.29872i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.56658 | − | 1.90938i | 0.166305 | − | 0.0695357i | ||||
\(755\) | −11.8582 | −0.431563 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.4183 | 0.778460 | 0.389230 | − | 0.921141i | \(-0.372741\pi\) | ||||
0.389230 | + | 0.921141i | \(0.372741\pi\) | |||||||
\(758\) | −16.9041 | + | 7.06795i | −0.613983 | + | 0.256720i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.9310 | + | 5.20541i | 0.469055 | + | 0.188820i | ||||
\(761\) | − | 43.7901i | − | 1.58739i | −0.608315 | − | 0.793696i | \(-0.708154\pi\) | ||
0.608315 | − | 0.793696i | \(-0.291846\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 29.8427 | − | 30.2430i | 1.07967 | − | 1.09415i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.38213 | − | 3.30558i | −0.0499385 | − | 0.119436i | ||||
\(767\) | −25.0170 | −0.903313 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −53.6687 | −1.93534 | −0.967672 | − | 0.252212i | \(-0.918842\pi\) | ||||
−0.967672 | + | 0.252212i | \(0.918842\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.85452 | + | 5.93305i | −0.210709 | + | 0.213535i | ||||
\(773\) | 43.5231i | 1.56542i | 0.622389 | + | 0.782708i | \(0.286162\pi\) | ||||
−0.622389 | + | 0.782708i | \(0.713838\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.24668i | − | 0.152545i | ||||||
\(776\) | −28.5161 | − | 11.4793i | −1.02367 | − | 0.412082i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.9689 | − | 8.34941i | 0.715918 | − | 0.299341i | ||||
\(779\) | −74.8626 | −2.68223 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.96537 | 0.320806 | ||||||||
\(782\) | 20.8742 | − | 8.72795i | 0.746460 | − | 0.312111i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.37897i | − | 0.0492175i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 11.3049i | − | 0.402975i | −0.979491 | − | 0.201488i | \(-0.935422\pi\) | ||
0.979491 | − | 0.201488i | \(-0.0645776\pi\) | |||||||
\(788\) | −11.4564 | − | 11.3047i | −0.408116 | − | 0.402714i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.15531 | + | 12.3297i | 0.183418 | + | 0.438671i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.5014 | 0.692516 | ||||||||
\(794\) | 7.15023 | + | 17.1009i | 0.253752 | + | 0.606887i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.16912 | + | 2.14041i | 0.0768826 | + | 0.0758650i | ||||
\(797\) | − | 52.0507i | − | 1.84373i | −0.387511 | − | 0.921865i | \(-0.626665\pi\) | ||
0.387511 | − | 0.921865i | \(-0.373335\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 35.3794i | − | 1.25163i | ||||||
\(800\) | 23.4173 | − | 10.1599i | 0.827927 | − | 0.359206i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.51411 | + | 0.633082i | −0.0534651 | + | 0.0223549i | ||||
\(803\) | −7.01976 | −0.247722 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.30954 | − | 0.965667i | 0.0813500 | − | 0.0340142i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.2029 | − | 27.8294i | 0.394115 | − | 0.979036i | ||||
\(809\) | 12.7602i | 0.448626i | 0.974517 | + | 0.224313i | \(0.0720138\pi\) | ||||
−0.974517 | + | 0.224313i | \(0.927986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 37.2617i | − | 1.30843i | −0.756307 | − | 0.654217i | \(-0.772998\pi\) | ||
0.756307 | − | 0.654217i | \(-0.227002\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.4416 | − | 24.9725i | −0.365976 | − | 0.875287i | ||||
\(815\) | −1.96310 | −0.0687646 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.0360 | −0.980854 | ||||||||
\(818\) | 3.92143 | + | 9.37868i | 0.137109 | + | 0.327918i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.4035 | − | 10.5430i | 0.363306 | − | 0.368179i | ||||
\(821\) | 39.4205i | 1.37579i | 0.725812 | + | 0.687893i | \(0.241464\pi\) | ||||
−0.725812 | + | 0.687893i | \(0.758536\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 49.8543i | − | 1.73781i | −0.494976 | − | 0.868907i | \(-0.664823\pi\) | ||
0.494976 | − | 0.868907i | \(-0.335177\pi\) | |||||||
\(824\) | −14.0220 | + | 34.8326i | −0.488480 | + | 1.21345i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.4688 | 1.68542 | 0.842712 | − | 0.538364i | \(-0.180957\pi\) | ||||
0.842712 | + | 0.538364i | \(0.180957\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.61739 | −0.299294 | −0.149647 | − | 0.988739i | \(-0.547814\pi\) | ||||
−0.149647 | + | 0.988739i | \(0.547814\pi\) | |||||||
\(830\) | 15.6257 | − | 6.53343i | 0.542375 | − | 0.226779i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10.8503 | + | 10.4251i | 0.376168 | + | 0.361425i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.68159i | 0.0581938i | ||||||||
\(836\) | −25.6425 | − | 25.3031i | −0.886864 | − | 0.875126i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.79019 | − | 21.0231i | −0.303652 | − | 0.726229i | ||||
\(839\) | −35.7594 | −1.23455 | −0.617275 | − | 0.786747i | \(-0.711763\pi\) | ||||
−0.617275 | + | 0.786747i | \(0.711763\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.5374 | 0.880599 | ||||||||
\(842\) | 3.00045 | + | 7.17604i | 0.103403 | + | 0.247303i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 27.4582 | + | 27.0948i | 0.945150 | + | 0.932640i | ||||
\(845\) | − | 6.60696i | − | 0.227286i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.11891 | − | 0.0282327i | 0.0727636 | − | 0.000969516i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −23.3932 | + | 9.78119i | −0.802379 | + | 0.335492i | ||||
\(851\) | 30.1989 | 1.03520 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.3666 | −0.457664 | −0.228832 | − | 0.973466i | \(-0.573491\pi\) | ||||
−0.228832 | + | 0.973466i | \(0.573491\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.2200 | − | 10.1524i | −0.862003 | − | 0.347003i | ||||
\(857\) | − | 9.93285i | − | 0.339300i | −0.985504 | − | 0.169650i | \(-0.945736\pi\) | ||
0.985504 | − | 0.169650i | \(-0.0542637\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 29.8791i | − | 1.01946i | −0.860334 | − | 0.509731i | \(-0.829745\pi\) | ||
0.860334 | − | 0.509731i | \(-0.170255\pi\) | |||||||
\(860\) | 3.89610 | − | 3.94835i | 0.132856 | − | 0.134638i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.31608 | − | 17.4975i | −0.249187 | − | 0.595968i | ||||
\(863\) | 3.56359 | 0.121306 | 0.0606530 | − | 0.998159i | \(-0.480682\pi\) | ||||
0.0606530 | + | 0.998159i | \(0.480682\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.26795 | −0.111113 | ||||||||
\(866\) | −17.2829 | − | 41.3347i | −0.587297 | − | 1.40461i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 34.5380i | − | 1.17162i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.12162i | 0.173540i | ||||||||
\(872\) | −37.3212 | − | 15.0238i | −1.26386 | − | 0.508771i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 37.0813 | − | 15.5045i | 1.25430 | − | 0.524448i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.69412 | −0.293580 | −0.146790 | − | 0.989168i | \(-0.546894\pi\) | ||||
−0.146790 | + | 0.989168i | \(0.546894\pi\) | |||||||
\(878\) | −25.4181 | + | 10.6279i | −0.857820 | + | 0.358673i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.12696 | − | 0.0949608i | 0.240250 | − | 0.00320113i | ||||
\(881\) | 48.2017i | 1.62396i | 0.583688 | + | 0.811978i | \(0.301609\pi\) | ||||
−0.583688 | + | 0.811978i | \(0.698391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.60661i | 0.222330i | 0.993802 | + | 0.111165i | \(0.0354582\pi\) | ||||
−0.993802 | + | 0.111165i | \(0.964542\pi\) | |||||||
\(884\) | −10.6389 | − | 10.4981i | −0.357825 | − | 0.353089i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.75474 | + | 8.98002i | 0.126143 | + | 0.301690i | ||||
\(887\) | 48.1193 | 1.61569 | 0.807844 | − | 0.589397i | \(-0.200635\pi\) | ||||
0.807844 | + | 0.589397i | \(0.200635\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.52153 | − | 10.8139i | −0.151562 | − | 0.362483i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.8227 | − | 25.4810i | −0.864609 | − | 0.853165i | ||||
\(893\) | − | 62.8488i | − | 2.10315i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 9.21040i | − | 0.307870i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25.2150 | + | 10.5429i | −0.841434 | + | 0.351821i | ||||
\(899\) | −1.75121 | −0.0584062 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.10493 | −0.0701255 | ||||||||
\(902\) | −35.3165 | + | 14.7666i | −1.17591 | + | 0.491674i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.7844 | + | 31.7583i | −0.425204 | + | 1.05627i | ||||
\(905\) | 12.3449i | 0.410360i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.03274i | 0.266723i | 0.991067 | + | 0.133361i | \(0.0425771\pi\) | ||||
−0.991067 | + | 0.133361i | \(0.957423\pi\) | |||||||
\(908\) | −13.4551 | + | 13.6355i | −0.446522 | + | 0.452511i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.0200 | 1.82289 | 0.911446 | − | 0.411419i | \(-0.134967\pi\) | ||||
0.911446 | + | 0.411419i | \(0.134967\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43.7707 | −1.44860 | ||||||||
\(914\) | 2.63880 | + | 6.31108i | 0.0872836 | + | 0.208752i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.80362 | + | 6.89488i | −0.224798 | + | 0.227813i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.0878i | 0.563674i | 0.959462 | + | 0.281837i | \(0.0909438\pi\) | ||||
−0.959462 | + | 0.281837i | \(0.909056\pi\) | |||||||
\(920\) | −2.96959 | + | 7.37686i | −0.0979044 | + | 0.243208i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 34.3790 | − | 14.3746i | 1.13221 | − | 0.473402i | ||||
\(923\) | 6.60771 | 0.217495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33.8431 | −1.11275 | ||||||||
\(926\) | −49.7143 | + | 20.7866i | −1.63371 | + | 0.683090i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.18965 | − | 9.65663i | −0.137532 | − | 0.316995i | ||||
\(929\) | 27.9950i | 0.918488i | 0.888310 | + | 0.459244i | \(0.151880\pi\) | ||||
−0.888310 | + | 0.459244i | \(0.848120\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 30.7969 | + | 30.3893i | 1.00879 | + | 0.995435i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.48297 | + | 8.33006i | 0.113966 | + | 0.272568i | ||||
\(935\) | −7.07995 | −0.231539 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.4480 | −1.64806 | −0.824031 | − | 0.566544i | \(-0.808280\pi\) | ||||
−0.824031 | + | 0.566544i | \(0.808280\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.85110 | + | 8.73395i | 0.288691 | + | 0.284870i | ||||
\(941\) | − | 23.1572i | − | 0.754903i | −0.926029 | − | 0.377451i | \(-0.876801\pi\) | ||
0.926029 | − | 0.377451i | \(-0.123199\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 42.7076i | − | 1.39075i | ||||||
\(944\) | 0.708823 | + | 53.1982i | 0.0230702 | + | 1.73145i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.2260 | + | 5.53007i | −0.430014 | + | 0.179798i | ||||
\(947\) | 14.5787 | 0.473745 | 0.236873 | − | 0.971541i | \(-0.423878\pi\) | ||||
0.236873 | + | 0.971541i | \(0.423878\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.17374 | −0.167947 | ||||||||
\(950\) | −41.5561 | + | 17.3755i | −1.34826 | + | 0.563736i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.8728i | 0.902889i | 0.892299 | + | 0.451444i | \(0.149091\pi\) | ||||
−0.892299 | + | 0.451444i | \(0.850909\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 14.8334i | − | 0.479998i | ||||||
\(956\) | −28.8747 | + | 29.2620i | −0.933875 | + | 0.946401i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.4788 | − | 27.4533i | −0.370863 | − | 0.886975i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.1143 | 0.971430 | ||||||||
\(962\) | −7.69569 | − | 18.4054i | −0.248119 | − | 0.593414i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.1020 | + | 15.3045i | −0.486401 | + | 0.492925i | ||||
\(965\) | 2.91001i | 0.0936764i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.2042i | 0.714038i | 0.934097 | + | 0.357019i | \(0.116207\pi\) | ||||
−0.934097 | + | 0.357019i | \(0.883793\pi\) | |||||||
\(968\) | 11.7740 | + | 4.73969i | 0.378432 | + | 0.152340i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.90125 | + | 4.13992i | −0.317910 | + | 0.132925i | ||||
\(971\) | −16.1859 | −0.519430 | −0.259715 | − | 0.965685i | \(-0.583629\pi\) | ||||
−0.259715 | + | 0.965685i | \(0.583629\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 20.5937 | − | 8.61068i | 0.659866 | − | 0.275904i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.552545 | − | 41.4694i | −0.0176865 | − | 1.32740i | ||||
\(977\) | 28.6168i | 0.915531i | 0.889073 | + | 0.457766i | \(0.151350\pi\) | ||||
−0.889073 | + | 0.457766i | \(0.848650\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.2920i | 0.968135i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.2674 | + | 24.5559i | 0.327644 | + | 0.783611i | ||||
\(983\) | −47.7843 | −1.52408 | −0.762041 | − | 0.647528i | \(-0.775803\pi\) | ||||
−0.762041 | + | 0.647528i | \(0.775803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.61904 | −0.179038 | ||||||||
\(986\) | 4.03348 | + | 9.64668i | 0.128452 | + | 0.307213i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.8992 | − | 18.6490i | −0.601262 | − | 0.593304i | ||||
\(989\) | − | 15.9940i | − | 0.508579i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 20.4708i | − | 0.650275i | −0.945667 | − | 0.325138i | \(-0.894589\pi\) | ||
0.945667 | − | 0.325138i | \(-0.105411\pi\) | |||||||
\(992\) | −2.11891 | − | 4.88382i | −0.0672754 | − | 0.155062i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.06390 | 0.0337278 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.3491 | −1.08785 | −0.543924 | − | 0.839134i | \(-0.683062\pi\) | ||||
−0.543924 | + | 0.839134i | \(0.683062\pi\) | |||||||
\(998\) | 10.5149 | − | 4.39649i | 0.332842 | − | 0.139168i | ||||
\(999\) | 0 | 0 |
(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 | 1764.2.e.i.1079.10 | 16 | ||
3.2 | odd | 2 | inner | 1764.2.e.i.1079.7 | 16 | ||
4.3 | odd | 2 | inner | 1764.2.e.i.1079.8 | 16 | ||
7.2 | even | 3 | 252.2.be.a.179.13 | yes | 32 | ||
7.4 | even | 3 | 252.2.be.a.107.2 | ✓ | 32 | ||
7.6 | odd | 2 | 1764.2.e.h.1079.10 | 16 | |||
12.11 | even | 2 | inner | 1764.2.e.i.1079.9 | 16 | ||
21.2 | odd | 6 | 252.2.be.a.179.4 | yes | 32 | ||
21.11 | odd | 6 | 252.2.be.a.107.15 | yes | 32 | ||
21.20 | even | 2 | 1764.2.e.h.1079.7 | 16 | |||
28.11 | odd | 6 | 252.2.be.a.107.4 | yes | 32 | ||
28.23 | odd | 6 | 252.2.be.a.179.15 | yes | 32 | ||
28.27 | even | 2 | 1764.2.e.h.1079.8 | 16 | |||
84.11 | even | 6 | 252.2.be.a.107.13 | yes | 32 | ||
84.23 | even | 6 | 252.2.be.a.179.2 | yes | 32 | ||
84.83 | odd | 2 | 1764.2.e.h.1079.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.be.a.107.2 | ✓ | 32 | 7.4 | even | 3 | ||
252.2.be.a.107.4 | yes | 32 | 28.11 | odd | 6 | ||
252.2.be.a.107.13 | yes | 32 | 84.11 | even | 6 | ||
252.2.be.a.107.15 | yes | 32 | 21.11 | odd | 6 | ||
252.2.be.a.179.2 | yes | 32 | 84.23 | even | 6 | ||
252.2.be.a.179.4 | yes | 32 | 21.2 | odd | 6 | ||
252.2.be.a.179.13 | yes | 32 | 7.2 | even | 3 | ||
252.2.be.a.179.15 | yes | 32 | 28.23 | odd | 6 | ||
1764.2.e.h.1079.7 | 16 | 21.20 | even | 2 | |||
1764.2.e.h.1079.8 | 16 | 28.27 | even | 2 | |||
1764.2.e.h.1079.9 | 16 | 84.83 | odd | 2 | |||
1764.2.e.h.1079.10 | 16 | 7.6 | odd | 2 | |||
1764.2.e.i.1079.7 | 16 | 3.2 | odd | 2 | inner | ||
1764.2.e.i.1079.8 | 16 | 4.3 | odd | 2 | inner | ||
1764.2.e.i.1079.9 | 16 | 12.11 | even | 2 | inner | ||
1764.2.e.i.1079.10 | 16 | 1.1 | even | 1 | trivial |