Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(1268,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1268");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.m (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: | \(12.5764383184\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1268.2 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1268 |
Dual form | 1575.2.m.a.1457.2 |
$q$-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 \(\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(1226\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | − | 1.36603i | −0.965926 | − | 0.965926i | 0.0335125 | − | 0.999438i | \(-0.489331\pi\) |
−0.999438 | + | 0.0335125i | \(0.989331\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.73205i | 0.866025i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | −0.366025 | + | 0.366025i | −0.129410 | + | 0.129410i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.44949i | 0.738549i | 0.929320 | + | 0.369274i | \(0.120394\pi\) | ||||
−0.929320 | + | 0.369274i | \(0.879606\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.03528 | − | 1.03528i | −0.287134 | − | 0.287134i | 0.548812 | − | 0.835946i | \(-0.315080\pi\) |
−0.835946 | + | 0.548812i | \(0.815080\pi\) | |||||||
\(14\) | −1.93185 | −0.516309 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.46410 | 1.11603 | ||||||||
\(17\) | −2.00000 | − | 2.00000i | −0.485071 | − | 0.485071i | 0.421676 | − | 0.906747i | \(-0.361442\pi\) |
−0.906747 | + | 0.421676i | \(0.861442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.34607 | − | 3.34607i | 0.713384 | − | 0.713384i | ||||
\(23\) | −0.464102 | + | 0.464102i | −0.0967719 | + | 0.0967719i | −0.753835 | − | 0.657063i | \(-0.771798\pi\) |
0.657063 | + | 0.753835i | \(0.271798\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.82843i | 0.554700i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.22474 | + | 1.22474i | 0.231455 | + | 0.231455i | ||||
\(29\) | −3.48477 | −0.647105 | −0.323552 | − | 0.946210i | \(-0.604877\pi\) | ||||
−0.323552 | + | 0.946210i | \(0.604877\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.92820 | 1.60355 | 0.801776 | − | 0.597624i | \(-0.203889\pi\) | ||||
0.801776 | + | 0.597624i | \(0.203889\pi\) | |||||||
\(32\) | −5.36603 | − | 5.36603i | −0.948588 | − | 0.948588i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.46410i | 0.937086i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.27792 | − | 5.27792i | 0.867684 | − | 0.867684i | −0.124531 | − | 0.992216i | \(-0.539743\pi\) |
0.992216 | + | 0.124531i | \(0.0397428\pi\) | |||||||
\(38\) | 2.73205 | − | 2.73205i | 0.443197 | − | 0.443197i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.72741i | 1.20682i | 0.797432 | + | 0.603409i | \(0.206191\pi\) | ||||
−0.797432 | + | 0.603409i | \(0.793809\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.82843 | + | 2.82843i | 0.431331 | + | 0.431331i | 0.889081 | − | 0.457750i | \(-0.151344\pi\) |
−0.457750 | + | 0.889081i | \(0.651344\pi\) | |||||||
\(44\) | −4.24264 | −0.639602 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.26795 | 0.186949 | ||||||||
\(47\) | −0.535898 | − | 0.535898i | −0.0781688 | − | 0.0781688i | 0.666941 | − | 0.745110i | \(-0.267603\pi\) |
−0.745110 | + | 0.666941i | \(0.767603\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.79315 | − | 1.79315i | 0.248665 | − | 0.248665i | ||||
\(53\) | 5.73205 | − | 5.73205i | 0.787358 | − | 0.787358i | −0.193703 | − | 0.981060i | \(-0.562050\pi\) |
0.981060 | + | 0.193703i | \(0.0620497\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.517638i | 0.0691723i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.76028 | + | 4.76028i | 0.625055 | + | 0.625055i | ||||
\(59\) | 6.96953 | 0.907356 | 0.453678 | − | 0.891166i | \(-0.350112\pi\) | ||||
0.453678 | + | 0.891166i | \(0.350112\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92820 | 0.630992 | 0.315496 | − | 0.948927i | \(-0.397829\pi\) | ||||
0.315496 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(62\) | −12.1962 | − | 12.1962i | −1.54891 | − | 1.54891i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.73205i | 0.716506i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.48477 | + | 3.48477i | −0.425732 | + | 0.425732i | −0.887172 | − | 0.461440i | \(-0.847333\pi\) |
0.461440 | + | 0.887172i | \(0.347333\pi\) | |||||||
\(68\) | 3.46410 | − | 3.46410i | 0.420084 | − | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1769i | 1.20778i | 0.797069 | + | 0.603888i | \(0.206382\pi\) | ||||
−0.797069 | + | 0.603888i | \(0.793618\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.86370 | + | 3.86370i | 0.452212 | + | 0.452212i | 0.896088 | − | 0.443876i | \(-0.146397\pi\) |
−0.443876 | + | 0.896088i | \(0.646397\pi\) | |||||||
\(74\) | −14.4195 | −1.67624 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.46410 | −0.397360 | ||||||||
\(77\) | 1.73205 | + | 1.73205i | 0.197386 | + | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.00000i | − | 0.450035i | −0.974355 | − | 0.225018i | \(-0.927756\pi\) | ||
0.974355 | − | 0.225018i | \(-0.0722440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.5558 | − | 10.5558i | 1.16570 | − | 1.16570i | ||||
\(83\) | 11.4641 | − | 11.4641i | 1.25835 | − | 1.25835i | 0.306468 | − | 0.951881i | \(-0.400853\pi\) |
0.951881 | − | 0.306468i | \(-0.0991471\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 7.72741i | − | 0.833268i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.896575 | − | 0.896575i | −0.0955753 | − | 0.0955753i | ||||
\(89\) | 14.1421 | 1.49906 | 0.749532 | − | 0.661968i | \(-0.230279\pi\) | ||||
0.749532 | + | 0.661968i | \(0.230279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.46410 | −0.153480 | ||||||||
\(92\) | −0.803848 | − | 0.803848i | −0.0838069 | − | 0.0838069i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.46410i | 0.151011i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.6617 | + | 13.6617i | −1.38713 | + | 1.38713i | −0.555847 | + | 0.831285i | \(0.687606\pi\) |
−0.831285 | + | 0.555847i | \(0.812394\pi\) | |||||||
\(98\) | −1.36603 | + | 1.36603i | −0.137989 | + | 0.137989i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 17.5254i | − | 1.74384i | −0.489649 | − | 0.871920i | \(-0.662875\pi\) | ||
0.489649 | − | 0.871920i | \(-0.337125\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.48528 | + | 8.48528i | 0.836080 | + | 0.836080i | 0.988340 | − | 0.152261i | \(-0.0486553\pi\) |
−0.152261 | + | 0.988340i | \(0.548655\pi\) | |||||||
\(104\) | 0.757875 | 0.0743157 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.6603 | −1.52106 | ||||||||
\(107\) | 5.92820 | + | 5.92820i | 0.573101 | + | 0.573101i | 0.932994 | − | 0.359893i | \(-0.117187\pi\) |
−0.359893 | + | 0.932994i | \(0.617187\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.9282i | − | 1.42986i | −0.699195 | − | 0.714931i | \(-0.746458\pi\) | ||
0.699195 | − | 0.714931i | \(-0.253542\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.15660 | − | 3.15660i | 0.298270 | − | 0.298270i | ||||
\(113\) | 3.73205 | − | 3.73205i | 0.351082 | − | 0.351082i | −0.509430 | − | 0.860512i | \(-0.670144\pi\) |
0.860512 | + | 0.509430i | \(0.170144\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 6.03579i | − | 0.560409i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.52056 | − | 9.52056i | −0.876438 | − | 0.876438i | ||||
\(119\) | −2.82843 | −0.259281 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | −6.73205 | − | 6.73205i | −0.609491 | − | 0.609491i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.4641i | 1.38872i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0406 | − | 14.0406i | 1.24590 | − | 1.24590i | 0.288388 | − | 0.957514i | \(-0.406881\pi\) |
0.957514 | − | 0.288388i | \(-0.0931193\pi\) | |||||||
\(128\) | −2.90192 | + | 2.90192i | −0.256496 | + | 0.256496i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.58630i | 0.313337i | 0.987651 | + | 0.156668i | \(0.0500754\pi\) | ||||
−0.987651 | + | 0.156668i | \(0.949925\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.41421 | + | 1.41421i | 0.122628 | + | 0.122628i | ||||
\(134\) | 9.52056 | 0.822451 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.46410 | 0.125546 | ||||||||
\(137\) | −3.19615 | − | 3.19615i | −0.273066 | − | 0.273066i | 0.557267 | − | 0.830333i | \(-0.311850\pi\) |
−0.830333 | + | 0.557267i | \(0.811850\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.8564i | − | 1.34492i | −0.740132 | − | 0.672461i | \(-0.765237\pi\) | ||
0.740132 | − | 0.672461i | \(-0.234763\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.9019 | − | 13.9019i | 1.16662 | − | 1.16662i | ||||
\(143\) | 2.53590 | − | 2.53590i | 0.212062 | − | 0.212062i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 10.5558i | − | 0.873607i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.14162 | + | 9.14162i | 0.751437 | + | 0.751437i | ||||
\(149\) | 10.4543 | 0.856449 | 0.428225 | − | 0.903672i | \(-0.359139\pi\) | ||||
0.428225 | + | 0.903672i | \(0.359139\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.3923 | −0.845714 | −0.422857 | − | 0.906196i | \(-0.638973\pi\) | ||||
−0.422857 | + | 0.906196i | \(0.638973\pi\) | |||||||
\(152\) | −0.732051 | − | 0.732051i | −0.0593772 | − | 0.0593772i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 4.73205i | − | 0.381320i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.3490 | + | 12.3490i | −0.985556 | + | 0.985556i | −0.999897 | − | 0.0143409i | \(-0.995435\pi\) |
0.0143409 | + | 0.999897i | \(0.495435\pi\) | |||||||
\(158\) | −5.46410 | + | 5.46410i | −0.434701 | + | 0.434701i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.656339i | 0.0517267i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2122 | + | 11.2122i | 0.878205 | + | 0.878205i | 0.993349 | − | 0.115144i | \(-0.0367329\pi\) |
−0.115144 | + | 0.993349i | \(0.536733\pi\) | |||||||
\(164\) | −13.3843 | −1.04514 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −31.3205 | −2.43094 | ||||||||
\(167\) | −10.9282 | − | 10.9282i | −0.845650 | − | 0.845650i | 0.143937 | − | 0.989587i | \(-0.454024\pi\) |
−0.989587 | + | 0.143937i | \(0.954024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 10.8564i | − | 0.835108i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.89898 | + | 4.89898i | −0.373544 | + | 0.373544i | ||||
\(173\) | −6.39230 | + | 6.39230i | −0.485998 | + | 0.485998i | −0.907041 | − | 0.421043i | \(-0.861664\pi\) |
0.421043 | + | 0.907041i | \(0.361664\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.9348i | 0.824239i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −19.3185 | − | 19.3185i | −1.44798 | − | 1.44798i | ||||
\(179\) | −3.96524 | −0.296376 | −0.148188 | − | 0.988959i | \(-0.547344\pi\) | ||||
−0.148188 | + | 0.988959i | \(0.547344\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 2.00000 | + | 2.00000i | 0.148250 | + | 0.148250i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 0.339746i | − | 0.0250464i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.89898 | − | 4.89898i | 0.358249 | − | 0.358249i | ||||
\(188\) | 0.928203 | − | 0.928203i | 0.0676962 | − | 0.0676962i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 21.4906i | − | 1.55501i | −0.628879 | − | 0.777503i | \(-0.716486\pi\) | ||
0.628879 | − | 0.777503i | \(-0.283514\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.59059 | − | 6.59059i | −0.474401 | − | 0.474401i | 0.428934 | − | 0.903336i | \(-0.358889\pi\) |
−0.903336 | + | 0.428934i | \(0.858889\pi\) | |||||||
\(194\) | 37.3244 | 2.67973 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.73205 | 0.123718 | ||||||||
\(197\) | 13.7321 | + | 13.7321i | 0.978368 | + | 0.978368i | 0.999771 | − | 0.0214028i | \(-0.00681325\pi\) |
−0.0214028 | + | 0.999771i | \(0.506813\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 7.07180i | − | 0.501306i | −0.968077 | − | 0.250653i | \(-0.919355\pi\) | ||
0.968077 | − | 0.250653i | \(-0.0806454\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −23.9401 | + | 23.9401i | −1.68442 | + | 1.68442i | ||||
\(203\) | −2.46410 | + | 2.46410i | −0.172946 | + | 0.172946i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 23.1822i | − | 1.61518i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.62158 | − | 4.62158i | −0.320449 | − | 0.320449i | ||||
\(209\) | −4.89898 | −0.338869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.46410 | −0.513850 | −0.256925 | − | 0.966431i | \(-0.582709\pi\) | ||||
−0.256925 | + | 0.966431i | \(0.582709\pi\) | |||||||
\(212\) | 9.92820 | + | 9.92820i | 0.681872 | + | 0.681872i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 16.1962i | − | 1.10715i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.31319 | − | 6.31319i | 0.428567 | − | 0.428567i | ||||
\(218\) | −20.3923 | + | 20.3923i | −1.38114 | + | 1.38114i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.14110i | 0.278561i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.5254 | − | 17.5254i | −1.17359 | − | 1.17359i | −0.981349 | − | 0.192237i | \(-0.938426\pi\) |
−0.192237 | − | 0.981349i | \(-0.561574\pi\) | |||||||
\(224\) | −7.58871 | −0.507042 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.1962 | −0.678238 | ||||||||
\(227\) | −4.39230 | − | 4.39230i | −0.291528 | − | 0.291528i | 0.546156 | − | 0.837683i | \(-0.316091\pi\) |
−0.837683 | + | 0.546156i | \(0.816091\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.0718i | 0.731645i | 0.930685 | + | 0.365822i | \(0.119212\pi\) | ||||
−0.930685 | + | 0.365822i | \(0.880788\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.27551 | − | 1.27551i | 0.0837415 | − | 0.0837415i | ||||
\(233\) | −3.73205 | + | 3.73205i | −0.244495 | + | 0.244495i | −0.818707 | − | 0.574212i | \(-0.805309\pi\) |
0.574212 | + | 0.818707i | \(0.305309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.0716i | 0.785793i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.86370 | + | 3.86370i | 0.250447 | + | 0.250447i | ||||
\(239\) | 22.2485 | 1.43913 | 0.719567 | − | 0.694423i | \(-0.244340\pi\) | ||||
0.719567 | + | 0.694423i | \(0.244340\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.928203 | −0.0597908 | −0.0298954 | − | 0.999553i | \(-0.509517\pi\) | ||||
−0.0298954 | + | 0.999553i | \(0.509517\pi\) | |||||||
\(242\) | −6.83013 | − | 6.83013i | −0.439057 | − | 0.439057i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.53590i | 0.546455i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.07055 | − | 2.07055i | 0.131746 | − | 0.131746i | ||||
\(248\) | −3.26795 | + | 3.26795i | −0.207515 | + | 0.207515i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.1421i | 0.892644i | 0.894873 | + | 0.446322i | \(0.147266\pi\) | ||||
−0.894873 | + | 0.446322i | \(0.852734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.13681 | − | 1.13681i | −0.0714708 | − | 0.0714708i | ||||
\(254\) | −38.3596 | −2.40690 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.3923 | 1.21202 | ||||||||
\(257\) | 21.4641 | + | 21.4641i | 1.33889 | + | 1.33889i | 0.897133 | + | 0.441761i | \(0.145646\pi\) |
0.441761 | + | 0.897133i | \(0.354354\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 7.46410i | − | 0.463797i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.89898 | − | 4.89898i | 0.302660 | − | 0.302660i | ||||
\(263\) | 13.3923 | − | 13.3923i | 0.825805 | − | 0.825805i | −0.161129 | − | 0.986933i | \(-0.551513\pi\) |
0.986933 | + | 0.161129i | \(0.0515134\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 3.86370i | − | 0.236899i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.03579 | − | 6.03579i | −0.368695 | − | 0.368695i | ||||
\(269\) | −0.757875 | −0.0462084 | −0.0231042 | − | 0.999733i | \(-0.507355\pi\) | ||||
−0.0231042 | + | 0.999733i | \(0.507355\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.85641 | 0.234260 | 0.117130 | − | 0.993117i | \(-0.462631\pi\) | ||||
0.117130 | + | 0.993117i | \(0.462631\pi\) | |||||||
\(272\) | −8.92820 | − | 8.92820i | −0.541352 | − | 0.541352i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.73205i | 0.527522i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.0716 | + | 12.0716i | −0.725311 | + | 0.725311i | −0.969682 | − | 0.244371i | \(-0.921419\pi\) |
0.244371 | + | 0.969682i | \(0.421419\pi\) | |||||||
\(278\) | −21.6603 | + | 21.6603i | −1.29910 | + | 1.29910i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.41421i | − | 0.0843649i | −0.999110 | − | 0.0421825i | \(-0.986569\pi\) | ||
0.999110 | − | 0.0421825i | \(-0.0134311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.0411 | + | 19.0411i | 1.13188 | + | 1.13188i | 0.989865 | + | 0.142012i | \(0.0453571\pi\) |
0.142012 | + | 0.989865i | \(0.454643\pi\) | |||||||
\(284\) | −17.6269 | −1.04596 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.92820 | −0.409673 | ||||||||
\(287\) | 5.46410 | + | 5.46410i | 0.322536 | + | 0.322536i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 9.00000i | − | 0.529412i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.69213 | + | 6.69213i | −0.391627 | + | 0.391627i | ||||
\(293\) | 12.3923 | − | 12.3923i | 0.723966 | − | 0.723966i | −0.245444 | − | 0.969411i | \(-0.578934\pi\) |
0.969411 | + | 0.245444i | \(0.0789339\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.86370i | 0.224573i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.2808 | − | 14.2808i | −0.827267 | − | 0.827267i | ||||
\(299\) | 0.960947 | 0.0555730 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 14.1962 | + | 14.1962i | 0.816897 | + | 0.816897i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.92820i | 0.512068i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.2832 | + | 18.2832i | −1.04348 | + | 1.04348i | −0.0444689 | + | 0.999011i | \(0.514160\pi\) |
−0.999011 | + | 0.0444689i | \(0.985840\pi\) | |||||||
\(308\) | −3.00000 | + | 3.00000i | −0.170941 | + | 0.170941i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.8685i | 0.673002i | 0.941683 | + | 0.336501i | \(0.109243\pi\) | ||||
−0.941683 | + | 0.336501i | \(0.890757\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.17638 | + | 5.17638i | 0.292586 | + | 0.292586i | 0.838101 | − | 0.545515i | \(-0.183666\pi\) |
−0.545515 | + | 0.838101i | \(0.683666\pi\) | |||||||
\(314\) | 33.7381 | 1.90395 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.92820 | 0.389742 | ||||||||
\(317\) | 17.7321 | + | 17.7321i | 0.995931 | + | 0.995931i | 0.999992 | − | 0.00406056i | \(-0.00129252\pi\) |
−0.00406056 | + | 0.999992i | \(0.501293\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.53590i | − | 0.477919i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.896575 | − | 0.896575i | 0.0499642 | − | 0.0499642i | ||||
\(323\) | 4.00000 | − | 4.00000i | 0.222566 | − | 0.222566i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 30.6322i | − | 1.69656i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.82843 | − | 2.82843i | −0.156174 | − | 0.156174i | ||||
\(329\) | −0.757875 | −0.0417830 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.4641 | 1.28970 | 0.644852 | − | 0.764308i | \(-0.276919\pi\) | ||||
0.644852 | + | 0.764308i | \(0.276919\pi\) | |||||||
\(332\) | 19.8564 | + | 19.8564i | 1.08976 | + | 1.08976i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 29.8564i | 1.63367i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.933740 | − | 0.933740i | 0.0508641 | − | 0.0508641i | −0.681217 | − | 0.732081i | \(-0.738549\pi\) |
0.732081 | + | 0.681217i | \(0.238549\pi\) | |||||||
\(338\) | −14.8301 | + | 14.8301i | −0.806653 | + | 0.806653i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.8695i | 1.18430i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | −2.07055 | −0.111637 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.4641 | 0.938876 | ||||||||
\(347\) | 1.00000 | + | 1.00000i | 0.0536828 | + | 0.0536828i | 0.733439 | − | 0.679756i | \(-0.237914\pi\) |
−0.679756 | + | 0.733439i | \(0.737914\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.7128i | 1.37638i | 0.725533 | + | 0.688188i | \(0.241593\pi\) | ||||
−0.725533 | + | 0.688188i | \(0.758407\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.1440 | − | 13.1440i | 0.700579 | − | 0.700579i | ||||
\(353\) | −5.07180 | + | 5.07180i | −0.269945 | + | 0.269945i | −0.829078 | − | 0.559133i | \(-0.811134\pi\) |
0.559133 | + | 0.829078i | \(0.311134\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 24.4949i | 1.29823i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.41662 | + | 5.41662i | 0.286277 | + | 0.286277i | ||||
\(359\) | −16.5916 | −0.875672 | −0.437836 | − | 0.899055i | \(-0.644255\pi\) | ||||
−0.437836 | + | 0.899055i | \(0.644255\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 8.19615 | + | 8.19615i | 0.430780 | + | 0.430780i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 2.53590i | − | 0.132917i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.6969 | + | 14.6969i | −0.767174 | + | 0.767174i | −0.977608 | − | 0.210434i | \(-0.932512\pi\) |
0.210434 | + | 0.977608i | \(0.432512\pi\) | |||||||
\(368\) | −2.07180 | + | 2.07180i | −0.108000 | + | 0.108000i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 8.10634i | − | 0.420860i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.7990 | + | 19.7990i | 1.02515 | + | 1.02515i | 0.999675 | + | 0.0254774i | \(0.00811060\pi\) |
0.0254774 | + | 0.999675i | \(0.491889\pi\) | |||||||
\(374\) | −13.3843 | −0.692084 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.392305 | 0.0202316 | ||||||||
\(377\) | 3.60770 | + | 3.60770i | 0.185806 | + | 0.185806i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.3923i | 1.76661i | 0.468795 | + | 0.883307i | \(0.344688\pi\) | ||||
−0.468795 | + | 0.883307i | \(0.655312\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −29.3567 | + | 29.3567i | −1.50202 | + | 1.50202i | ||||
\(383\) | 19.8564 | − | 19.8564i | 1.01461 | − | 1.01461i | 0.0147234 | − | 0.999892i | \(-0.495313\pi\) |
0.999892 | − | 0.0147234i | \(-0.00468676\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.0058i | 0.916473i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −23.6627 | − | 23.6627i | −1.20129 | − | 1.20129i | ||||
\(389\) | −24.7995 | −1.25738 | −0.628692 | − | 0.777654i | \(-0.716410\pi\) | ||||
−0.628692 | + | 0.777654i | \(0.716410\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.85641 | 0.0938825 | ||||||||
\(392\) | 0.366025 | + | 0.366025i | 0.0184871 | + | 0.0184871i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 37.5167i | − | 1.89006i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.86370 | + | 3.86370i | −0.193914 | + | 0.193914i | −0.797385 | − | 0.603471i | \(-0.793784\pi\) |
0.603471 | + | 0.797385i | \(0.293784\pi\) | |||||||
\(398\) | −9.66025 | + | 9.66025i | −0.484225 | + | 0.484225i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.92996i | − | 0.146315i | −0.997320 | − | 0.0731577i | \(-0.976692\pi\) | ||
0.997320 | − | 0.0731577i | \(-0.0233076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.24316 | − | 9.24316i | −0.460434 | − | 0.460434i | ||||
\(404\) | 30.3548 | 1.51021 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.73205 | 0.334106 | ||||||||
\(407\) | 12.9282 | + | 12.9282i | 0.640827 | + | 0.640827i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.92820i | − | 0.243684i | −0.992550 | − | 0.121842i | \(-0.961120\pi\) | ||
0.992550 | − | 0.121842i | \(-0.0388801\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.6969 | + | 14.6969i | −0.724066 | + | 0.724066i | ||||
\(413\) | 4.92820 | − | 4.92820i | 0.242501 | − | 0.242501i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 11.1106i | 0.544744i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.69213 | + | 6.69213i | 0.327323 | + | 0.327323i | ||||
\(419\) | 5.65685 | 0.276355 | 0.138178 | − | 0.990407i | \(-0.455875\pi\) | ||||
0.138178 | + | 0.990407i | \(0.455875\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.7128 | 1.25317 | 0.626583 | − | 0.779355i | \(-0.284453\pi\) | ||||
0.626583 | + | 0.779355i | \(0.284453\pi\) | |||||||
\(422\) | 10.1962 | + | 10.1962i | 0.496341 | + | 0.496341i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.19615i | 0.203783i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.48477 | − | 3.48477i | 0.168640 | − | 0.168640i | ||||
\(428\) | −10.2679 | + | 10.2679i | −0.496320 | + | 0.496320i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.378937i | 0.0182528i | 0.999958 | + | 0.00912639i | \(0.00290506\pi\) | ||||
−0.999958 | + | 0.00912639i | \(0.997095\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.1774 | − | 15.1774i | −0.729380 | − | 0.729380i | 0.241116 | − | 0.970496i | \(-0.422486\pi\) |
−0.970496 | + | 0.241116i | \(0.922486\pi\) | |||||||
\(434\) | −17.2480 | −0.827929 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 25.8564 | 1.23830 | ||||||||
\(437\) | −0.928203 | − | 0.928203i | −0.0444020 | − | 0.0444020i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1436i | 0.579582i | 0.957090 | + | 0.289791i | \(0.0935858\pi\) | ||||
−0.957090 | + | 0.289791i | \(0.906414\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.65685 | − | 5.65685i | 0.269069 | − | 0.269069i | ||||
\(443\) | −1.92820 | + | 1.92820i | −0.0916117 | + | 0.0916117i | −0.751427 | − | 0.659816i | \(-0.770634\pi\) |
0.659816 | + | 0.751427i | \(0.270634\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 47.8802i | 2.26719i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.05317 | + | 4.05317i | 0.191494 | + | 0.191494i | ||||
\(449\) | 2.92996 | 0.138274 | 0.0691368 | − | 0.997607i | \(-0.477976\pi\) | ||||
0.0691368 | + | 0.997607i | \(0.477976\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.9282 | −0.891294 | ||||||||
\(452\) | 6.46410 | + | 6.46410i | 0.304046 | + | 0.304046i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.0000i | 0.563188i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.79367 | + | 6.79367i | −0.317794 | + | 0.317794i | −0.847919 | − | 0.530125i | \(-0.822145\pi\) |
0.530125 | + | 0.847919i | \(0.322145\pi\) | |||||||
\(458\) | 15.1244 | − | 15.1244i | 0.706715 | − | 0.706715i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.203072i | 0.00945800i | 0.999989 | + | 0.00472900i | \(0.00150529\pi\) | ||||
−0.999989 | + | 0.00472900i | \(0.998495\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.75839 | + | 5.75839i | 0.267615 | + | 0.267615i | 0.828139 | − | 0.560523i | \(-0.189400\pi\) |
−0.560523 | + | 0.828139i | \(0.689400\pi\) | |||||||
\(464\) | −15.5563 | −0.722185 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.1962 | 0.472328 | ||||||||
\(467\) | −13.4641 | − | 13.4641i | −0.623044 | − | 0.623044i | 0.323264 | − | 0.946309i | \(-0.395220\pi\) |
−0.946309 | + | 0.323264i | \(0.895220\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.92820i | 0.227563i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.55103 | + | 2.55103i | −0.117420 | + | 0.117420i | ||||
\(473\) | −6.92820 | + | 6.92820i | −0.318559 | + | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 4.89898i | − | 0.224544i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −30.3920 | − | 30.3920i | −1.39010 | − | 1.39010i | ||||
\(479\) | −40.1528 | −1.83463 | −0.917314 | − | 0.398165i | \(-0.869647\pi\) | ||||
−0.917314 | + | 0.398165i | \(0.869647\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.9282 | −0.498283 | ||||||||
\(482\) | 1.26795 | + | 1.26795i | 0.0577535 | + | 0.0577535i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.66025i | 0.393648i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.24316 | − | 9.24316i | 0.418847 | − | 0.418847i | −0.465959 | − | 0.884806i | \(-0.654291\pi\) |
0.884806 | + | 0.465959i | \(0.154291\pi\) | |||||||
\(488\) | −1.80385 | + | 1.80385i | −0.0816563 | + | 0.0816563i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21.2875i | − | 0.960693i | −0.877079 | − | 0.480346i | \(-0.840511\pi\) | ||
0.877079 | − | 0.480346i | \(-0.159489\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.96953 | + | 6.96953i | 0.313892 | + | 0.313892i | ||||
\(494\) | −5.65685 | −0.254514 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 39.8564 | 1.78961 | ||||||||
\(497\) | 7.19615 | + | 7.19615i | 0.322792 | + | 0.322792i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3205i | 0.775372i | 0.921791 | + | 0.387686i | \(0.126726\pi\) | ||||
−0.921791 | + | 0.387686i | \(0.873274\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 19.3185 | − | 19.3185i | 0.862228 | − | 0.862228i | ||||
\(503\) | −0.928203 | + | 0.928203i | −0.0413865 | + | 0.0413865i | −0.727497 | − | 0.686111i | \(-0.759317\pi\) |
0.686111 | + | 0.727497i | \(0.259317\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.10583i | 0.138071i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 24.3190 | + | 24.3190i | 1.07898 | + | 1.07898i | ||||
\(509\) | 29.0421 | 1.28727 | 0.643635 | − | 0.765332i | \(-0.277425\pi\) | ||||
0.643635 | + | 0.765332i | \(0.277425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.46410 | 0.241718 | ||||||||
\(512\) | −20.6865 | − | 20.6865i | −0.914224 | − | 0.914224i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 58.6410i | − | 2.58654i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.31268 | − | 1.31268i | 0.0577315 | − | 0.0577315i | ||||
\(518\) | −10.1962 | + | 10.1962i | −0.447993 | + | 0.447993i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.9497i | 1.75023i | 0.483916 | + | 0.875114i | \(0.339214\pi\) | ||||
−0.483916 | + | 0.875114i | \(0.660786\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.82843 | + | 2.82843i | 0.123678 | + | 0.123678i | 0.766237 | − | 0.642558i | \(-0.222127\pi\) |
−0.642558 | + | 0.766237i | \(0.722127\pi\) | |||||||
\(524\) | −6.21166 | −0.271357 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −36.5885 | −1.59533 | ||||||||
\(527\) | −17.8564 | − | 17.8564i | −0.777837 | − | 0.777837i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.5692i | 0.981270i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.44949 | + | 2.44949i | −0.106199 | + | 0.106199i | ||||
\(533\) | 8.00000 | − | 8.00000i | 0.346518 | − | 0.346518i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 2.55103i | − | 0.110188i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.03528 | + | 1.03528i | 0.0446339 | + | 0.0446339i | ||||
\(539\) | 2.44949 | 0.105507 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.8564 | −0.681720 | −0.340860 | − | 0.940114i | \(-0.610718\pi\) | ||||
−0.340860 | + | 0.940114i | \(0.610718\pi\) | |||||||
\(542\) | −5.26795 | − | 5.26795i | −0.226278 | − | 0.226278i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.4641i | 0.920266i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.7985 | − | 14.7985i | 0.632737 | − | 0.632737i | −0.316017 | − | 0.948754i | \(-0.602346\pi\) |
0.948754 | + | 0.316017i | \(0.102346\pi\) | |||||||
\(548\) | 5.53590 | − | 5.53590i | 0.236482 | − | 0.236482i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.96953i | − | 0.296912i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.82843 | − | 2.82843i | −0.120277 | − | 0.120277i | ||||
\(554\) | 32.9802 | 1.40119 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.4641 | 1.16474 | ||||||||
\(557\) | 17.7321 | + | 17.7321i | 0.751331 | + | 0.751331i | 0.974728 | − | 0.223397i | \(-0.0717145\pi\) |
−0.223397 | + | 0.974728i | \(0.571714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.85641i | − | 0.247700i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.93185 | + | 1.93185i | −0.0814902 | + | 0.0814902i | ||||
\(563\) | −18.7846 | + | 18.7846i | −0.791677 | + | 0.791677i | −0.981767 | − | 0.190090i | \(-0.939122\pi\) |
0.190090 | + | 0.981767i | \(0.439122\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 52.0213i | − | 2.18662i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.72500 | − | 3.72500i | −0.156298 | − | 0.156298i | ||||
\(569\) | −9.89949 | −0.415008 | −0.207504 | − | 0.978234i | \(-0.566534\pi\) | ||||
−0.207504 | + | 0.978234i | \(0.566534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.85641 | 0.412478 | 0.206239 | − | 0.978502i | \(-0.433878\pi\) | ||||
0.206239 | + | 0.978502i | \(0.433878\pi\) | |||||||
\(572\) | 4.39230 | + | 4.39230i | 0.183651 | + | 0.183651i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 14.9282i | − | 0.623091i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.6617 | + | 13.6617i | −0.568742 | + | 0.568742i | −0.931776 | − | 0.363034i | \(-0.881741\pi\) |
0.363034 | + | 0.931776i | \(0.381741\pi\) | |||||||
\(578\) | −12.2942 | + | 12.2942i | −0.511372 | + | 0.511372i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 16.2127i | − | 0.672616i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.0406 | + | 14.0406i | 0.581502 | + | 0.581502i | ||||
\(584\) | −2.82843 | −0.117041 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −33.8564 | −1.39860 | ||||||||
\(587\) | −14.0000 | − | 14.0000i | −0.577842 | − | 0.577842i | 0.356466 | − | 0.934308i | \(-0.383981\pi\) |
−0.934308 | + | 0.356466i | \(0.883981\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8564i | 0.735760i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 23.5612 | − | 23.5612i | 0.968358 | − | 0.968358i | ||||
\(593\) | −21.8564 | + | 21.8564i | −0.897535 | + | 0.897535i | −0.995218 | − | 0.0976826i | \(-0.968857\pi\) |
0.0976826 | + | 0.995218i | \(0.468857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.1074i | 0.741707i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.31268 | − | 1.31268i | −0.0536794 | − | 0.0536794i | ||||
\(599\) | −7.55154 | −0.308548 | −0.154274 | − | 0.988028i | \(-0.549304\pi\) | ||||
−0.154274 | + | 0.988028i | \(0.549304\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.7846 | −1.90838 | −0.954192 | − | 0.299195i | \(-0.903282\pi\) | ||||
−0.954192 | + | 0.299195i | \(0.903282\pi\) | |||||||
\(602\) | −5.46410 | − | 5.46410i | −0.222700 | − | 0.222700i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 18.0000i | − | 0.732410i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.82843 | + | 2.82843i | −0.114802 | + | 0.114802i | −0.762174 | − | 0.647372i | \(-0.775868\pi\) |
0.647372 | + | 0.762174i | \(0.275868\pi\) | |||||||
\(608\) | 10.7321 | − | 10.7321i | 0.435242 | − | 0.435242i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.10961i | 0.0448898i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.3538 | − | 20.3538i | −0.822082 | − | 0.822082i | 0.164324 | − | 0.986406i | \(-0.447456\pi\) |
−0.986406 | + | 0.164324i | \(0.947456\pi\) | |||||||
\(614\) | 49.9507 | 2.01585 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.26795 | −0.0510871 | ||||||||
\(617\) | 9.05256 | + | 9.05256i | 0.364442 | + | 0.364442i | 0.865445 | − | 0.501003i | \(-0.167036\pi\) |
−0.501003 | + | 0.865445i | \(0.667036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 12.9282i | − | 0.519628i | −0.965659 | − | 0.259814i | \(-0.916339\pi\) | ||
0.965659 | − | 0.259814i | \(-0.0836613\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.2127 | − | 16.2127i | 0.650070 | − | 0.650070i | ||||
\(623\) | 10.0000 | − | 10.0000i | 0.400642 | − | 0.400642i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 14.1421i | − | 0.565233i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.3891 | − | 21.3891i | −0.853517 | − | 0.853517i | ||||
\(629\) | −21.1117 | −0.841777 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.85641 | −0.0739024 | −0.0369512 | − | 0.999317i | \(-0.511765\pi\) | ||||
−0.0369512 | + | 0.999317i | \(0.511765\pi\) | |||||||
\(632\) | 1.46410 | + | 1.46410i | 0.0582388 | + | 0.0582388i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 48.4449i | − | 1.92399i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.03528 | + | 1.03528i | −0.0410191 | + | 0.0410191i | ||||
\(638\) | −11.6603 | + | 11.6603i | −0.461634 | + | 0.461634i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 44.9502i | − | 1.77543i | −0.460396 | − | 0.887714i | \(-0.652293\pi\) | ||
0.460396 | − | 0.887714i | \(-0.347707\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.7284 | + | 17.7284i | 0.699141 | + | 0.699141i | 0.964225 | − | 0.265084i | \(-0.0853997\pi\) |
−0.265084 | + | 0.964225i | \(0.585400\pi\) | |||||||
\(644\) | −1.13681 | −0.0447967 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.9282 | −0.429964 | ||||||||
\(647\) | −20.0000 | − | 20.0000i | −0.786281 | − | 0.786281i | 0.194601 | − | 0.980882i | \(-0.437659\pi\) |
−0.980882 | + | 0.194601i | \(0.937659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.0718i | 0.670127i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.4201 | + | 19.4201i | −0.760548 | + | 0.760548i | ||||
\(653\) | −20.6603 | + | 20.6603i | −0.808498 | + | 0.808498i | −0.984407 | − | 0.175908i | \(-0.943714\pi\) |
0.175908 | + | 0.984407i | \(0.443714\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 34.4959i | 1.34684i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.03528 | + | 1.03528i | 0.0403593 | + | 0.0403593i | ||||
\(659\) | 20.1779 | 0.786020 | 0.393010 | − | 0.919534i | \(-0.371434\pi\) | ||||
0.393010 | + | 0.919534i | \(0.371434\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.7846 | −0.886219 | −0.443109 | − | 0.896468i | \(-0.646125\pi\) | ||||
−0.443109 | + | 0.896468i | \(0.646125\pi\) | |||||||
\(662\) | −32.0526 | − | 32.0526i | −1.24576 | − | 1.24576i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.39230i | 0.325685i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.61729 | − | 1.61729i | 0.0626215 | − | 0.0626215i | ||||
\(668\) | 18.9282 | − | 18.9282i | 0.732354 | − | 0.732354i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0716i | 0.466018i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.3896 | − | 26.3896i | −1.01724 | − | 1.01724i | −0.999849 | − | 0.0173950i | \(-0.994463\pi\) |
−0.0173950 | − | 0.999849i | \(-0.505537\pi\) | |||||||
\(674\) | −2.55103 | −0.0982618 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.8038 | 0.723225 | ||||||||
\(677\) | −7.32051 | − | 7.32051i | −0.281350 | − | 0.281350i | 0.552297 | − | 0.833647i | \(-0.313751\pi\) |
−0.833647 | + | 0.552297i | \(0.813751\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.3205i | 0.741453i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 29.8744 | − | 29.8744i | 1.14395 | − | 1.14395i | ||||
\(683\) | 32.8564 | − | 32.8564i | 1.25722 | − | 1.25722i | 0.304799 | − | 0.952417i | \(-0.401411\pi\) |
0.952417 | − | 0.304799i | \(-0.0985892\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.93185i | 0.0737584i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.6264 | + | 12.6264i | 0.481376 | + | 0.481376i | ||||
\(689\) | −11.8685 | −0.452154 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.7846 | −1.17110 | −0.585551 | − | 0.810636i | \(-0.699122\pi\) | ||||
−0.585551 | + | 0.810636i | \(0.699122\pi\) | |||||||
\(692\) | −11.0718 | − | 11.0718i | −0.420887 | − | 0.420887i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 2.73205i | − | 0.103707i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.4548 | − | 15.4548i | 0.585393 | − | 0.585393i | ||||
\(698\) | 35.1244 | − | 35.1244i | 1.32948 | − | 1.32948i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.4249i | − | 1.03582i | −0.855434 | − | 0.517911i | \(-0.826710\pi\) | ||
0.855434 | − | 0.517911i | \(-0.173290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.5558 | + | 10.5558i | 0.398121 | + | 0.398121i | ||||
\(704\) | −14.0406 | −0.529175 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.8564 | 0.521493 | ||||||||
\(707\) | −12.3923 | − | 12.3923i | −0.466061 | − | 0.466061i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 16.7846i | − | 0.630359i | −0.949032 | − | 0.315180i | \(-0.897935\pi\) | ||
0.949032 | − | 0.315180i | \(-0.102065\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.17638 | + | 5.17638i | −0.193993 | + | 0.193993i | ||||
\(713\) | −4.14359 | + | 4.14359i | −0.155179 | + | 0.155179i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 6.86800i | − | 0.256669i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.6646 | + | 22.6646i | 0.845835 | + | 0.845835i | ||||
\(719\) | 10.0010 | 0.372976 | 0.186488 | − | 0.982457i | \(-0.440290\pi\) | ||||
0.186488 | + | 0.982457i | \(0.440290\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | −20.4904 | − | 20.4904i | −0.762573 | − | 0.762573i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 10.3923i | − | 0.386227i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.9096 | − | 30.9096i | 1.14637 | − | 1.14637i | 0.159114 | − | 0.987260i | \(-0.449136\pi\) |
0.987260 | − | 0.159114i | \(-0.0508639\pi\) | |||||||
\(728\) | 0.535898 | − | 0.535898i | 0.0198617 | − | 0.0198617i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 11.3137i | − | 0.418453i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.8647 | + | 13.8647i | 0.512106 | + | 0.512106i | 0.915171 | − | 0.403065i | \(-0.132055\pi\) |
−0.403065 | + | 0.915171i | \(0.632055\pi\) | |||||||
\(734\) | 40.1528 | 1.48207 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.98076 | 0.183593 | ||||||||
\(737\) | −8.53590 | − | 8.53590i | −0.314424 | − | 0.314424i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 17.8564i | − | 0.656859i | −0.944529 | − | 0.328429i | \(-0.893481\pi\) | ||
0.944529 | − | 0.328429i | \(-0.106519\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.0735 | + | 11.0735i | −0.406520 | + | 0.406520i | ||||
\(743\) | 29.3923 | − | 29.3923i | 1.07830 | − | 1.07830i | 0.0816370 | − | 0.996662i | \(-0.473985\pi\) |
0.996662 | − | 0.0816370i | \(-0.0260148\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 54.0918i | − | 1.98044i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.48528 | + | 8.48528i | 0.310253 | + | 0.310253i | ||||
\(749\) | 8.38375 | 0.306335 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.1051 | −0.952589 | −0.476295 | − | 0.879286i | \(-0.658020\pi\) | ||||
−0.476295 | + | 0.879286i | \(0.658020\pi\) | |||||||
\(752\) | −2.39230 | − | 2.39230i | −0.0872384 | − | 0.0872384i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 9.85641i | − | 0.358949i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.3886 | + | 16.3886i | −0.595652 | + | 0.595652i | −0.939153 | − | 0.343500i | \(-0.888387\pi\) |
0.343500 | + | 0.939153i | \(0.388387\pi\) | |||||||
\(758\) | 46.9808 | − | 46.9808i | 1.70642 | − | 1.70642i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 32.2223i | − | 1.16806i | −0.811733 | − | 0.584029i | \(-0.801476\pi\) | ||
0.811733 | − | 0.584029i | \(-0.198524\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.5558 | − | 10.5558i | −0.382147 | − | 0.382147i | ||||
\(764\) | 37.2228 | 1.34667 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −54.2487 | −1.96009 | ||||||||
\(767\) | −7.21539 | − | 7.21539i | −0.260533 | − | 0.260533i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 30.7846i | − | 1.11012i | −0.831810 | − | 0.555061i | \(-0.812695\pi\) | ||
0.831810 | − | 0.555061i | \(-0.187305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.4152 | − | 11.4152i | 0.410844 | − | 0.410844i | ||||
\(773\) | −13.3205 | + | 13.3205i | −0.479105 | + | 0.479105i | −0.904845 | − | 0.425740i | \(-0.860014\pi\) |
0.425740 | + | 0.904845i | \(0.360014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 10.0010i | − | 0.359016i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.8768 | + | 33.8768i | 1.21454 | + | 1.21454i | ||||
\(779\) | −15.4548 | −0.553726 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.9282 | −0.892001 | ||||||||
\(782\) | −2.53590 | − | 2.53590i | −0.0906835 | − | 0.0906835i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 4.46410i | − | 0.159432i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.2127 | − | 16.2127i | 0.577920 | − | 0.577920i | −0.356410 | − | 0.934330i | \(-0.615999\pi\) |
0.934330 | + | 0.356410i | \(0.115999\pi\) | |||||||
\(788\) | −23.7846 | + | 23.7846i | −0.847292 | + | 0.847292i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.27792i | − | 0.187661i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.10205 | − | 5.10205i | −0.181179 | − | 0.181179i | ||||
\(794\) | 10.5558 | 0.374613 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.2487 | 0.434144 | ||||||||
\(797\) | 35.1769 | + | 35.1769i | 1.24603 | + | 1.24603i | 0.957458 | + | 0.288572i | \(0.0931805\pi\) |
0.288572 | + | 0.957458i | \(0.406820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.14359i | 0.0758349i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.00240 | + | 4.00240i | −0.141330 | + | 0.141330i | ||||
\(803\) | −9.46410 | + | 9.46410i | −0.333981 | + | 0.333981i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25.2528i | 0.889491i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.41473 | + | 6.41473i | 0.225669 | + | 0.225669i | ||||
\(809\) | −24.0416 | −0.845259 | −0.422629 | − | 0.906303i | \(-0.638893\pi\) | ||||
−0.422629 | + | 0.906303i | \(0.638893\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.0718 | −0.388783 | −0.194392 | − | 0.980924i | \(-0.562273\pi\) | ||||
−0.194392 | + | 0.980924i | \(0.562273\pi\) | |||||||
\(812\) | −4.26795 | − | 4.26795i | −0.149776 | − | 0.149776i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 35.3205i | − | 1.23798i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.65685 | + | 5.65685i | −0.197908 | + | 0.197908i | ||||
\(818\) | −6.73205 | + | 6.73205i | −0.235381 | + | 0.235381i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2.17209i | − | 0.0758064i | −0.999281 | − | 0.0379032i | \(-0.987932\pi\) | ||
0.999281 | − | 0.0379032i | \(-0.0120679\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.5563 | + | 15.5563i | 0.542260 | + | 0.542260i | 0.924191 | − | 0.381931i | \(-0.124741\pi\) |
−0.381931 | + | 0.924191i | \(0.624741\pi\) | |||||||
\(824\) | −6.21166 | −0.216393 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.4641 | −0.468476 | ||||||||
\(827\) | −21.0000 | − | 21.0000i | −0.730242 | − | 0.730242i | 0.240426 | − | 0.970667i | \(-0.422713\pi\) |
−0.970667 | + | 0.240426i | \(0.922713\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.7846i | 0.374565i | 0.982306 | + | 0.187282i | \(0.0599680\pi\) | ||||
−0.982306 | + | 0.187282i | \(0.940032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.93426 | − | 5.93426i | 0.205733 | − | 0.205733i | ||||
\(833\) | −2.00000 | + | 2.00000i | −0.0692959 | + | 0.0692959i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 8.48528i | − | 0.293470i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.72741 | − | 7.72741i | −0.266939 | − | 0.266939i | ||||
\(839\) | 13.1812 | 0.455065 | 0.227533 | − | 0.973770i | \(-0.426934\pi\) | ||||
0.227533 | + | 0.973770i | \(0.426934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.8564 | −0.581255 | ||||||||
\(842\) | −35.1244 | − | 35.1244i | −1.21047 | − | 1.21047i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 12.9282i | − | 0.445007i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.53553 | − | 3.53553i | 0.121482 | − | 0.121482i | ||||
\(848\) | 25.5885 | − | 25.5885i | 0.878711 | − | 0.878711i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.89898i | 0.167935i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.24693 | + | 7.24693i | 0.248130 | + | 0.248130i | 0.820203 | − | 0.572073i | \(-0.193860\pi\) |
−0.572073 | + | 0.820203i | \(0.693860\pi\) | |||||||
\(854\) | −9.52056 | −0.325787 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.33975 | −0.148329 | ||||||||
\(857\) | 10.3923 | + | 10.3923i | 0.354994 | + | 0.354994i | 0.861964 | − | 0.506970i | \(-0.169234\pi\) |
−0.506970 | + | 0.861964i | \(0.669234\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.7846i | 0.777401i | 0.921364 | + | 0.388700i | \(0.127076\pi\) | ||||
−0.921364 | + | 0.388700i | \(0.872924\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.517638 | − | 0.517638i | 0.0176308 | − | 0.0176308i | ||||
\(863\) | 25.2487 | − | 25.2487i | 0.859476 | − | 0.859476i | −0.131800 | − | 0.991276i | \(-0.542076\pi\) |
0.991276 | + | 0.131800i | \(0.0420757\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 41.4655i | 1.40905i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.9348 | + | 10.9348i | 0.371150 | + | 0.371150i | ||||
\(869\) | 9.79796 | 0.332373 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.21539 | 0.244484 | ||||||||
\(872\) | 5.46410 | + | 5.46410i | 0.185038 | + | 0.185038i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.53590i | 0.0857780i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.6675 | + | 31.6675i | −1.06934 | + | 1.06934i | −0.0719255 | + | 0.997410i | \(0.522914\pi\) |
−0.997410 | + | 0.0719255i | \(0.977086\pi\) | |||||||
\(878\) | 16.5885 | − | 16.5885i | 0.559833 | − | 0.559833i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.9411i | 1.14351i | 0.820426 | + | 0.571753i | \(0.193736\pi\) | ||||
−0.820426 | + | 0.571753i | \(0.806264\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.4949 | − | 24.4949i | −0.824319 | − | 0.824319i | 0.162405 | − | 0.986724i | \(-0.448075\pi\) |
−0.986724 | + | 0.162405i | \(0.948075\pi\) | |||||||
\(884\) | −7.17260 | −0.241241 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.26795 | 0.176980 | ||||||||
\(887\) | −6.67949 | − | 6.67949i | −0.224275 | − | 0.224275i | 0.586021 | − | 0.810296i | \(-0.300694\pi\) |
−0.810296 | + | 0.586021i | \(0.800694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 19.8564i | − | 0.665962i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 30.3548 | − | 30.3548i | 1.01635 | − | 1.01635i | ||||
\(893\) | 1.07180 | − | 1.07180i | 0.0358663 | − | 0.0358663i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.10394i | 0.137103i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.00240 | − | 4.00240i | −0.133562 | − | 0.133562i | ||||
\(899\) | −31.1127 | −1.03767 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.9282 | −0.763849 | ||||||||
\(902\) | 25.8564 | + | 25.8564i | 0.860924 | + | 0.860924i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.73205i | 0.0908667i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.8695 | − | 21.8695i | 0.726166 | − | 0.726166i | −0.243688 | − | 0.969854i | \(-0.578357\pi\) |
0.969854 | + | 0.243688i | \(0.0783571\pi\) | |||||||
\(908\) | 7.60770 | − | 7.60770i | 0.252470 | − | 0.252470i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.0464i | − | 1.06175i | −0.847451 | − | 0.530873i | \(-0.821864\pi\) | ||
0.847451 | − | 0.530873i | \(-0.178136\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.0812 | + | 28.0812i | 0.929352 | + | 0.929352i | ||||
\(914\) | 18.5606 | 0.613931 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.1769 | −0.633623 | ||||||||
\(917\) | 2.53590 | + | 2.53590i | 0.0837427 | + | 0.0837427i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.1769i | 0.368692i | 0.982861 | + | 0.184346i | \(0.0590168\pi\) | ||||
−0.982861 | + | 0.184346i | \(0.940983\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.277401 | − | 0.277401i | 0.00913573 | − | 0.00913573i | ||||
\(923\) | 10.5359 | − | 10.5359i | 0.346793 | − | 0.346793i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 15.7322i | − | 0.516993i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 18.6993 | + | 18.6993i | 0.613836 | + | 0.613836i | ||||
\(929\) | 4.34418 | 0.142528 | 0.0712639 | − | 0.997457i | \(-0.477297\pi\) | ||||
0.0712639 | + | 0.997457i | \(0.477297\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | 0.0655474 | ||||||||
\(932\) | −6.46410 | − | 6.46410i | −0.211739 | − | 0.211739i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 36.7846i | 1.20363i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.0470 | − | 37.0470i | 1.21027 | − | 1.21027i | 0.239334 | − | 0.970937i | \(-0.423071\pi\) |
0.970937 | − | 0.239334i | \(-0.0769291\pi\) | |||||||
\(938\) | 6.73205 | − | 6.73205i | 0.219809 | − | 0.219809i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.51575i | 0.0494120i | 0.999695 | + | 0.0247060i | \(0.00786497\pi\) | ||||
−0.999695 | + | 0.0247060i | \(0.992135\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.58630 | − | 3.58630i | −0.116786 | − | 0.116786i | ||||
\(944\) | 31.1127 | 1.01263 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.9282 | 0.615409 | ||||||||
\(947\) | −31.0000 | − | 31.0000i | −1.00736 | − | 1.00736i | −0.999973 | − | 0.00739197i | \(-0.997647\pi\) |
−0.00739197 | − | 0.999973i | \(-0.502353\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 8.00000i | − | 0.259691i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.03528 | − | 1.03528i | 0.0335535 | − | 0.0335535i | ||||
\(953\) | −21.3397 | + | 21.3397i | −0.691262 | + | 0.691262i | −0.962510 | − | 0.271247i | \(-0.912564\pi\) |
0.271247 | + | 0.962510i | \(0.412564\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 38.5355i | 1.24633i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 54.8497 | + | 54.8497i | 1.77211 | + | 1.77211i | ||||
\(959\) | −4.52004 | −0.145960 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.7128 | 1.57138 | ||||||||
\(962\) | 14.9282 | + | 14.9282i | 0.481305 | + | 0.481305i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1.60770i | − | 0.0517804i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.34469 | − | 9.34469i | 0.300505 | − | 0.300505i | −0.540706 | − | 0.841211i | \(-0.681843\pi\) |
0.841211 | + | 0.540706i | \(0.181843\pi\) | |||||||
\(968\) | −1.83013 | + | 1.83013i | −0.0588225 | + | 0.0588225i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.757875i | 0.0243214i | 0.999926 | + | 0.0121607i | \(0.00387096\pi\) | ||||
−0.999926 | + | 0.0121607i | \(0.996129\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.2122 | − | 11.2122i | −0.359446 | − | 0.359446i | ||||
\(974\) | −25.2528 | −0.809151 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.0000 | 0.704203 | ||||||||
\(977\) | 12.2679 | + | 12.2679i | 0.392486 | + | 0.392486i | 0.875573 | − | 0.483086i | \(-0.160484\pi\) |
−0.483086 | + | 0.875573i | \(0.660484\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.6410i | 1.10713i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −29.0793 | + | 29.0793i | −0.927958 | + | 0.927958i | ||||
\(983\) | −11.3205 | + | 11.3205i | −0.361068 | + | 0.361068i | −0.864206 | − | 0.503138i | \(-0.832179\pi\) |
0.503138 | + | 0.864206i | \(0.332179\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 19.0411i | − | 0.606393i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.58630 | + | 3.58630i | 0.114095 | + | 0.114095i | ||||
\(989\) | −2.62536 | −0.0834814 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.3205 | 0.677268 | 0.338634 | − | 0.940918i | \(-0.390035\pi\) | ||||
0.338634 | + | 0.940918i | \(0.390035\pi\) | |||||||
\(992\) | −47.9090 | − | 47.9090i | −1.52111 | − | 1.52111i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 19.6603i | − | 0.623585i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.5617 | + | 28.5617i | −0.904557 | + | 0.904557i | −0.995826 | − | 0.0912690i | \(-0.970908\pi\) |
0.0912690 | + | 0.995826i | \(0.470908\pi\) | |||||||
\(998\) | 23.6603 | − | 23.6603i | 0.748952 | − | 0.748952i | ||||
\(999\) | 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 | 1575.2.m.a.1268.2 | yes | 8 | |
3.2 | odd | 2 | 1575.2.m.b.1268.4 | yes | 8 | ||
5.2 | odd | 4 | 1575.2.m.b.1457.4 | yes | 8 | ||
5.3 | odd | 4 | inner | 1575.2.m.a.1457.1 | yes | 8 | |
5.4 | even | 2 | 1575.2.m.b.1268.3 | yes | 8 | ||
15.2 | even | 4 | inner | 1575.2.m.a.1457.2 | yes | 8 | |
15.8 | even | 4 | 1575.2.m.b.1457.3 | yes | 8 | ||
15.14 | odd | 2 | inner | 1575.2.m.a.1268.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1575.2.m.a.1268.1 | ✓ | 8 | 15.14 | odd | 2 | inner | |
1575.2.m.a.1268.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1575.2.m.a.1457.1 | yes | 8 | 5.3 | odd | 4 | inner | |
1575.2.m.a.1457.2 | yes | 8 | 15.2 | even | 4 | inner | |
1575.2.m.b.1268.3 | yes | 8 | 5.4 | even | 2 | ||
1575.2.m.b.1268.4 | yes | 8 | 3.2 | odd | 2 | ||
1575.2.m.b.1457.3 | yes | 8 | 15.8 | even | 4 | ||
1575.2.m.b.1457.4 | yes | 8 | 5.2 | odd | 4 |