Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(369,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("920.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.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: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} + \cdots + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.5 | ||
Root | \(0.416087 - 0.416087i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 920.369 |
Dual form | 920.2.e.b.369.10 |
$q$-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 \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(281\) | \(461\) | \(737\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.40334i | − | 0.810221i | −0.914268 | − | 0.405110i | \(-0.867233\pi\) | ||
0.914268 | − | 0.405110i | \(-0.132767\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.466981 | − | 2.18676i | 0.208840 | − | 0.977950i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.57117i | − | 0.593846i | −0.954901 | − | 0.296923i | \(-0.904040\pi\) | ||
0.954901 | − | 0.296923i | \(-0.0959605\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.03063 | 0.343543 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.35401 | 1.31278 | 0.656391 | − | 0.754421i | \(-0.272082\pi\) | ||||
0.656391 | + | 0.754421i | \(0.272082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.964590i | 0.267529i | 0.991013 | + | 0.133765i | \(0.0427066\pi\) | ||||
−0.991013 | + | 0.133765i | \(0.957293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.06878 | − | 0.655335i | −0.792355 | − | 0.169207i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.300242i | 0.0728193i | 0.999337 | + | 0.0364096i | \(0.0115921\pi\) | ||||
−0.999337 | + | 0.0364096i | \(0.988408\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.62443 | 1.97858 | 0.989290 | − | 0.145963i | \(-0.0466280\pi\) | ||||
0.989290 | + | 0.145963i | \(0.0466280\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.20489 | −0.481146 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.56386 | − | 2.04235i | −0.912772 | − | 0.408471i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.65635i | − | 1.08857i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.76644 | −0.885106 | −0.442553 | − | 0.896742i | \(-0.645927\pi\) | ||||
−0.442553 | + | 0.896742i | \(0.645927\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.59148 | −1.00426 | −0.502129 | − | 0.864792i | \(-0.667450\pi\) | ||||
−0.502129 | + | 0.864792i | \(0.667450\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 6.11017i | − | 1.06364i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.43577 | − | 0.733706i | −0.580752 | − | 0.124019i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.38462i | 0.720827i | 0.932793 | + | 0.360413i | \(0.117364\pi\) | ||||
−0.932793 | + | 0.360413i | \(0.882636\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.35365 | 0.216758 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.62014 | −1.03389 | −0.516946 | − | 0.856018i | \(-0.672931\pi\) | ||||
−0.516946 | + | 0.856018i | \(0.672931\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.72988i | − | 0.263804i | −0.991263 | − | 0.131902i | \(-0.957892\pi\) | ||
0.991263 | − | 0.131902i | \(-0.0421085\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.481284 | − | 2.25374i | 0.0717455 | − | 0.335967i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.687333i | 0.100258i | 0.998743 | + | 0.0501289i | \(0.0159632\pi\) | ||||
−0.998743 | + | 0.0501289i | \(0.984037\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.53143 | 0.647347 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.421342 | 0.0589997 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.05208i | 1.10604i | 0.833168 | + | 0.553019i | \(0.186524\pi\) | ||||
−0.833168 | + | 0.553019i | \(0.813476\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.03324 | − | 9.52118i | 0.274162 | − | 1.28384i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12.1030i | − | 1.60309i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.74620 | −0.748091 | −0.374046 | − | 0.927410i | \(-0.622030\pi\) | ||||
−0.374046 | + | 0.927410i | \(0.622030\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.6547 | −1.74831 | −0.874153 | − | 0.485651i | \(-0.838583\pi\) | ||||
−0.874153 | + | 0.485651i | \(0.838583\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.61929i | − | 0.204011i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.10933 | + | 0.450445i | 0.261630 | + | 0.0558708i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.49053i | − | 0.792945i | −0.918047 | − | 0.396472i | \(-0.870234\pi\) | ||
0.918047 | − | 0.396472i | \(-0.129766\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.40334 | −0.168943 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.89977 | 1.17489 | 0.587443 | − | 0.809265i | \(-0.300134\pi\) | ||||
0.587443 | + | 0.809265i | \(0.300134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.35994i | 0.744375i | 0.928158 | + | 0.372187i | \(0.121392\pi\) | ||||
−0.928158 | + | 0.372187i | \(0.878608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.86612 | + | 6.40466i | −0.330951 | + | 0.739546i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 6.84088i | − | 0.779591i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.95266 | 0.782236 | 0.391118 | − | 0.920341i | \(-0.372088\pi\) | ||||
0.391118 | + | 0.920341i | \(0.372088\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.84592 | −0.538436 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 0.185320i | − | 0.0203415i | −0.999948 | − | 0.0101707i | \(-0.996762\pi\) | ||
0.999948 | − | 0.0101707i | \(-0.00323750\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.656557 | + | 0.140207i | 0.0712136 | + | 0.0152076i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.68895i | 0.717131i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.64878 | 0.174770 | 0.0873852 | − | 0.996175i | \(-0.472149\pi\) | ||||
0.0873852 | + | 0.996175i | \(0.472149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.51553 | 0.158871 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.84676i | 0.813671i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.02744 | − | 18.8596i | 0.413207 | − | 1.93495i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.21689i | 0.935834i | 0.883773 | + | 0.467917i | \(0.154995\pi\) | ||||
−0.883773 | + | 0.467917i | \(0.845005\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.48736 | 0.450997 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.719780 | −0.0716208 | −0.0358104 | − | 0.999359i | \(-0.511401\pi\) | ||||
−0.0358104 | + | 0.999359i | \(0.511401\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.16137i | 0.902696i | 0.892348 | + | 0.451348i | \(0.149057\pi\) | ||||
−0.892348 | + | 0.451348i | \(0.850943\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.02964 | + | 4.82157i | −0.100483 | + | 0.470537i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.7486i | 1.23245i | 0.787570 | + | 0.616226i | \(0.211339\pi\) | ||||
−0.787570 | + | 0.616226i | \(0.788661\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.38019 | 0.323763 | 0.161882 | − | 0.986810i | \(-0.448244\pi\) | ||||
0.161882 | + | 0.986810i | \(0.448244\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.15312 | 0.584029 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 15.8547i | − | 1.49148i | −0.666237 | − | 0.745741i | \(-0.732096\pi\) | ||
0.666237 | − | 0.745741i | \(-0.267904\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.18676 | − | 0.466981i | −0.203917 | − | 0.0435462i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.994133i | 0.0919076i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.471730 | 0.0432434 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.95739 | 0.723399 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.29032i | 0.837680i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.59737 | + | 9.02633i | −0.590087 | + | 0.807340i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.2222i | − | 1.35075i | −0.737473 | − | 0.675377i | \(-0.763981\pi\) | ||
0.737473 | − | 0.675377i | \(-0.236019\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.42762 | −0.213740 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.8695 | −1.12441 | −0.562207 | − | 0.826997i | \(-0.690047\pi\) | ||||
−0.562207 | + | 0.826997i | \(0.690047\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 13.5504i | − | 1.17497i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.3691 | − | 2.64141i | −1.06456 | − | 0.227336i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 16.7433i | − | 1.43048i | −0.698881 | − | 0.715238i | \(-0.746318\pi\) | ||
0.698881 | − | 0.715238i | \(-0.253682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.8293 | 1.00335 | 0.501676 | − | 0.865056i | \(-0.332717\pi\) | ||||
0.501676 | + | 0.865056i | \(0.332717\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.964565 | 0.0812310 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.19983i | 0.351208i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.22584 | + | 10.4231i | −0.184846 | + | 0.865589i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 6.35915i | − | 0.524494i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.46021 | −0.119625 | −0.0598125 | − | 0.998210i | \(-0.519050\pi\) | ||||
−0.0598125 | + | 0.998210i | \(0.519050\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.7897 | 1.44771 | 0.723854 | − | 0.689953i | \(-0.242369\pi\) | ||||
0.723854 | + | 0.689953i | \(0.242369\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.309437i | 0.0250165i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.61111 | + | 12.2272i | −0.209730 | + | 0.982115i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0359i | 1.59904i | 0.600642 | + | 0.799518i | \(0.294912\pi\) | ||||
−0.600642 | + | 0.799518i | \(0.705088\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.2998 | 0.896135 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.57117 | −0.123825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.9076i | 1.79426i | 0.441766 | + | 0.897130i | \(0.354352\pi\) | ||||
−0.441766 | + | 0.897130i | \(0.645648\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.3615 | − | 2.85333i | −1.04019 | − | 0.222132i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.826887i | 0.0639864i | 0.999488 | + | 0.0319932i | \(0.0101855\pi\) | ||||
−0.999488 | + | 0.0319932i | \(0.989815\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0696 | 0.928428 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.88858 | 0.679727 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 8.03904i | − | 0.611197i | −0.952160 | − | 0.305599i | \(-0.901143\pi\) | ||
0.952160 | − | 0.305599i | \(-0.0988565\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.20888 | + | 7.17059i | −0.242569 | + | 0.542046i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.06389i | 0.606119i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.6941 | 1.62149 | 0.810747 | − | 0.585397i | \(-0.199061\pi\) | ||||
0.810747 | + | 0.585397i | \(0.199061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.9499 | −1.11122 | −0.555609 | − | 0.831444i | \(-0.687515\pi\) | ||||
−0.555609 | + | 0.831444i | \(0.687515\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.1622i | 1.41651i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.58812 | + | 2.04753i | 0.704932 | + | 0.150538i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.30725i | 0.0955959i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.88709 | −0.646441 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.86406 | −0.569024 | −0.284512 | − | 0.958673i | \(-0.591831\pi\) | ||||
−0.284512 | + | 0.958673i | \(0.591831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.1864i | 1.09314i | 0.837413 | + | 0.546571i | \(0.184067\pi\) | ||||
−0.837413 | + | 0.546571i | \(0.815933\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.632129 | − | 2.96011i | 0.0452677 | − | 0.211978i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.2911i | 0.875707i | 0.899046 | + | 0.437853i | \(0.144261\pi\) | ||||
−0.899046 | + | 0.437853i | \(0.855739\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.37123 | 0.309869 | 0.154934 | − | 0.987925i | \(-0.450483\pi\) | ||||
0.154934 | + | 0.987925i | \(0.450483\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.10845 | −0.642460 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.48888i | 0.525617i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.09148 | + | 14.4767i | −0.215918 | + | 1.01109i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.03063i | − | 0.0716336i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 37.5508 | 2.59745 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.93960 | −0.615427 | −0.307714 | − | 0.951479i | \(-0.599564\pi\) | ||||
−0.307714 | + | 0.951479i | \(0.599564\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 13.8928i | − | 0.951917i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.78284 | − | 0.807822i | −0.257987 | − | 0.0550930i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.78516i | 0.596375i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.92518 | 0.603108 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.289610 | −0.0194813 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.9586i | 0.800806i | 0.916339 | + | 0.400403i | \(0.131130\pi\) | ||||
−0.916339 | + | 0.400403i | \(0.868870\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.70364 | − | 2.10491i | −0.313576 | − | 0.140327i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.85445i | 0.123084i | 0.998104 | + | 0.0615419i | \(0.0196018\pi\) | ||||
−0.998104 | + | 0.0615419i | \(0.980398\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.5190 | 1.09161 | 0.545804 | − | 0.837913i | \(-0.316224\pi\) | ||||
0.545804 | + | 0.837913i | \(0.316224\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.60011 | −0.631641 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 24.5906i | − | 1.61099i | −0.592606 | − | 0.805493i | \(-0.701901\pi\) | ||
0.592606 | − | 0.805493i | \(-0.298099\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.50303 | + | 0.320972i | 0.0980472 | + | 0.0209379i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 9.75697i | − | 0.633783i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.1169 | −1.75405 | −0.877025 | − | 0.480446i | \(-0.840475\pi\) | ||||
−0.877025 | + | 0.480446i | \(0.840475\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.8855 | −0.830030 | −0.415015 | − | 0.909815i | \(-0.636224\pi\) | ||||
−0.415015 | + | 0.909815i | \(0.636224\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 10.1686i | − | 0.652314i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.11609 | − | 9.90915i | 0.135192 | − | 0.633073i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.31904i | 0.529328i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.260067 | −0.0164811 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.4610 | −0.786533 | −0.393267 | − | 0.919424i | \(-0.628655\pi\) | ||||
−0.393267 | + | 0.919424i | \(0.628655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.35401i | − | 0.273734i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.196759 | − | 0.921374i | 0.0123215 | − | 0.0576987i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.5073i | 0.842564i | 0.906930 | + | 0.421282i | \(0.138420\pi\) | ||||
−0.906930 | + | 0.421282i | \(0.861580\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.88898 | 0.428060 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.91243 | −0.304072 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 27.2579i | − | 1.68080i | −0.541969 | − | 0.840399i | \(-0.682321\pi\) | ||
0.541969 | − | 0.840399i | \(-0.317679\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.6080 | + | 3.76017i | 1.08165 | + | 0.230985i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2.31380i | − | 0.141603i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.8409 | 1.08778 | 0.543889 | − | 0.839157i | \(-0.316951\pi\) | ||||
0.543889 | + | 0.839157i | \(0.316951\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.31906 | 0.140873 | 0.0704364 | − | 0.997516i | \(-0.477561\pi\) | ||||
0.0704364 | + | 0.997516i | \(0.477561\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 2.12681i | − | 0.128721i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.8711 | − | 8.89242i | −1.19827 | − | 0.536233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.0762i | 1.92727i | 0.267215 | + | 0.963637i | \(0.413897\pi\) | ||||
−0.267215 | + | 0.963637i | \(0.586103\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.76273 | −0.345006 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9448 | 0.772221 | 0.386110 | − | 0.922453i | \(-0.373818\pi\) | ||||
0.386110 | + | 0.922453i | \(0.373818\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.6070i | 1.34385i | 0.740621 | + | 0.671923i | \(0.234532\pi\) | ||||
−0.740621 | + | 0.671923i | \(0.765468\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −26.4665 | − | 5.65189i | −1.56774 | − | 0.334789i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.4014i | 0.613972i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9099 | 0.994697 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.9345 | 0.758232 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5.61612i | − | 0.328097i | −0.986452 | − | 0.164049i | \(-0.947545\pi\) | ||
0.986452 | − | 0.164049i | \(-0.0524554\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.68336 | + | 12.5656i | −0.156232 | + | 0.731596i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 24.6278i | − | 1.42905i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.964590 | 0.0557837 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.71794 | −0.156659 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.01010i | 0.0580286i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.37649 | + | 29.8596i | −0.365117 | + | 1.70976i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.42467i | 0.138383i | 0.997603 | + | 0.0691915i | \(0.0220419\pi\) | ||||
−0.997603 | + | 0.0691915i | \(0.977958\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.8565 | 0.731383 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.57886 | 0.202938 | 0.101469 | − | 0.994839i | \(-0.467646\pi\) | ||||
0.101469 | + | 0.994839i | \(0.467646\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.51000i | 0.311443i | 0.987801 | + | 0.155722i | \(0.0497703\pi\) | ||||
−0.987801 | + | 0.155722i | \(0.950230\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.54100 | − | 0.756178i | −0.199513 | − | 0.0426058i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.88368i | 0.330461i | 0.986255 | + | 0.165230i | \(0.0528367\pi\) | ||||
−0.986255 | + | 0.165230i | \(0.947163\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.7531 | −1.16195 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.8906 | 0.998558 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.58941i | 0.144079i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.97003 | − | 4.40225i | 0.109278 | − | 0.244193i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 4.74356i | − | 0.262320i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.07992 | 0.0595377 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.6138 | −1.02311 | −0.511553 | − | 0.859252i | \(-0.670930\pi\) | ||||
−0.511553 | + | 0.859252i | \(0.670930\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.51891i | 0.247635i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.1933 | − | 3.03096i | −0.775460 | − | 0.165599i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.9571i | 1.63187i | 0.578146 | + | 0.815933i | \(0.303776\pi\) | ||||
−0.578146 | + | 0.815933i | \(0.696224\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −22.2495 | −1.20843 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.3453 | −1.31837 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.1178i | − | 0.978270i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.655335 | + | 3.06878i | −0.0352820 | + | 0.165217i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 26.7363i | − | 1.43528i | −0.696415 | − | 0.717640i | \(-0.745222\pi\) | ||
0.696415 | − | 0.717640i | \(-0.254778\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.7392 | −1.53837 | −0.769186 | − | 0.639025i | \(-0.779338\pi\) | ||||
−0.769186 | + | 0.639025i | \(0.779338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.45606 | 0.291223 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.662874i | 0.0352812i | 0.999844 | + | 0.0176406i | \(0.00561547\pi\) | ||||
−0.999844 | + | 0.0176406i | \(0.994385\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.62300 | − | 21.6484i | 0.245364 | − | 1.14898i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 0.661999i | − | 0.0350367i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.0576 | 0.847485 | 0.423743 | − | 0.905783i | \(-0.360716\pi\) | ||||
0.423743 | + | 0.905783i | \(0.360716\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 55.3808 | 2.91478 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 11.1669i | − | 0.586113i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.9077 | + | 2.96997i | 0.727961 | + | 0.155455i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 27.5855i | − | 1.43995i | −0.693999 | − | 0.719976i | \(-0.744153\pi\) | ||
0.693999 | − | 0.719976i | \(-0.255847\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.82290 | −0.355186 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.6512 | 0.656817 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 33.1014i | − | 1.71393i | −0.515376 | − | 0.856964i | \(-0.672348\pi\) | ||
0.515376 | − | 0.856964i | \(-0.327652\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.6670 | + | 9.25838i | 0.654123 | + | 0.478101i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.59766i | − | 0.236791i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.17121 | −0.111527 | −0.0557637 | − | 0.998444i | \(-0.517759\pi\) | ||||
−0.0557637 | + | 0.998444i | \(0.517759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.3620 | −1.09441 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 5.52673i | − | 0.282403i | −0.989981 | − | 0.141201i | \(-0.954903\pi\) | ||
0.989981 | − | 0.141201i | \(-0.0450965\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.9594 | − | 3.19456i | −0.762401 | − | 0.162810i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 1.78286i | − | 0.0906281i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.1036 | −0.867185 | −0.433593 | − | 0.901109i | \(-0.642754\pi\) | ||||
−0.433593 | + | 0.901109i | \(0.642754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.300242 | 0.0151839 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.0603i | 0.911023i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.24676 | − | 15.2038i | 0.163362 | − | 0.764987i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 12.7419i | − | 0.639497i | −0.947503 | − | 0.319748i | \(-0.896402\pi\) | ||
0.947503 | − | 0.319748i | \(-0.103598\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.0159 | −0.951987 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1997 | 0.709098 | 0.354549 | − | 0.935038i | \(-0.384634\pi\) | ||||
0.354549 | + | 0.935038i | \(0.384634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5.39348i | − | 0.268668i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.26295 | + | 10.5969i | −0.112447 | + | 0.526563i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.0907i | 0.946289i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.0235143 | 0.00116271 | 0.000581354 | − | 1.00000i | \(-0.499815\pi\) | ||||
0.000581354 | 1.00000i | \(0.499815\pi\) | ||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.4966 | −1.15900 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.02825i | 0.444251i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.405250 | − | 0.0865407i | −0.0198929 | − | 0.00424812i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 16.6006i | − | 0.812936i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.2763 | 0.990562 | 0.495281 | − | 0.868733i | \(-0.335065\pi\) | ||||
0.495281 | + | 0.868733i | \(0.335065\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5320 | 0.610771 | 0.305386 | − | 0.952229i | \(-0.401215\pi\) | ||||
0.305386 | + | 0.952229i | \(0.401215\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.708385i | 0.0344429i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.613199 | − | 1.37026i | 0.0297445 | − | 0.0664673i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.4539i | 1.03822i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.89380 | 0.284556 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.8635 | −1.10130 | −0.550648 | − | 0.834737i | \(-0.685619\pi\) | ||||
−0.550648 | + | 0.834737i | \(0.685619\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 23.7997i | − | 1.14374i | −0.820343 | − | 0.571871i | \(-0.806218\pi\) | ||
0.820343 | − | 0.571871i | \(-0.193782\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.6271 | + | 3.12361i | 0.701318 | + | 0.149766i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 8.62443i | − | 0.412562i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.66686 | −0.222737 | −0.111368 | − | 0.993779i | \(-0.535523\pi\) | ||||
−0.111368 | + | 0.993779i | \(0.535523\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.67022 | 0.222391 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 13.6616i | − | 0.649082i | −0.945872 | − | 0.324541i | \(-0.894790\pi\) | ||
0.945872 | − | 0.324541i | \(-0.105210\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.769949 | − | 3.60549i | 0.0364991 | − | 0.170917i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.04917i | 0.0969226i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.8921 | 1.22192 | 0.610961 | − | 0.791661i | \(-0.290783\pi\) | ||||
0.610961 | + | 0.791661i | \(0.290783\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.8241 | −1.35727 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 24.9651i | − | 1.17296i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.707725 | − | 3.31411i | 0.0331787 | − | 0.155368i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 12.6856i | − | 0.593405i | −0.954970 | − | 0.296703i | \(-0.904113\pi\) | ||
0.954970 | − | 0.296703i | \(-0.0958870\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.69827 | 0.0792686 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.5769 | 1.23781 | 0.618904 | − | 0.785466i | \(-0.287577\pi\) | ||||
0.618904 | + | 0.785466i | \(0.287577\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.6461i | 0.680664i | 0.940305 | + | 0.340332i | \(0.110539\pi\) | ||||
−0.940305 | + | 0.340332i | \(0.889461\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.1590 | + | 3.66429i | 0.795730 | + | 0.169927i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 12.7601i | − | 0.590467i | −0.955425 | − | 0.295233i | \(-0.904603\pi\) | ||
0.955425 | − | 0.295233i | \(-0.0953974\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.1977 | −0.470887 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.1172 | 1.29557 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.53192i | − | 0.346318i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −39.3607 | − | 17.6141i | −1.80599 | − | 0.808192i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.29870i | 0.379971i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2315 | −0.467488 | −0.233744 | − | 0.972298i | \(-0.575098\pi\) | ||||
−0.233744 | + | 0.972298i | \(0.575098\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.22936 | −0.192842 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.20489i | 0.100326i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.1552 | + | 4.30411i | 0.915198 | + | 0.195440i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.8299i | 0.989207i | 0.869119 | + | 0.494603i | \(0.164687\pi\) | ||||
−0.869119 | + | 0.494603i | \(0.835313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.1472 | 1.45375 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.1315 | −1.72085 | −0.860426 | − | 0.509575i | \(-0.829802\pi\) | ||||
−0.860426 | + | 0.509575i | \(0.829802\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.43108i | − | 0.0644527i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.09551 | − | 9.81279i | 0.0941863 | − | 0.441052i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 15.5542i | − | 0.697702i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.36523 | −0.284947 | −0.142474 | − | 0.989799i | \(-0.545506\pi\) | ||||
−0.142474 | + | 0.989799i | \(0.545506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.16041 | 0.0518431 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 21.3160i | − | 0.950433i | −0.879869 | − | 0.475217i | \(-0.842370\pi\) | ||
0.879869 | − | 0.475217i | \(-0.157630\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.336123 | + | 1.57399i | −0.0149573 | + | 0.0700415i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 16.9377i | − | 0.752232i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.5122 | 1.13081 | 0.565405 | − | 0.824814i | \(-0.308720\pi\) | ||||
0.565405 | + | 0.824814i | \(0.308720\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.99254 | 0.442044 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 48.7828i | − | 2.15381i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.0337 | + | 4.27818i | 0.882792 | + | 0.188519i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.99266i | 0.131617i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.2815 | −0.495205 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.7247 | −1.78418 | −0.892091 | − | 0.451856i | \(-0.850762\pi\) | ||||
−0.892091 | + | 0.451856i | \(0.850762\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.3437i | 1.02075i | 0.859953 | + | 0.510374i | \(0.170493\pi\) | ||||
−0.859953 | + | 0.510374i | \(0.829507\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.0628 | + | 4.50316i | 0.439177 | + | 0.196534i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.67879i | − | 0.0731294i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.92219 | −0.257001 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6.38571i | − | 0.276596i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.8781 | + | 5.95334i | 1.20528 | + | 0.257385i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 30.4443i | − | 1.31377i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.7299 | 0.849826 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.23303 | 0.0530123 | 0.0265061 | − | 0.999649i | \(-0.491562\pi\) | ||||
0.0265061 | + | 0.999649i | \(0.491562\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.9798i | 0.900331i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.57848 | − | 7.39166i | 0.0676148 | − | 0.316624i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.56470i | 0.0669018i | 0.999440 | + | 0.0334509i | \(0.0106497\pi\) | ||||
−0.999440 | + | 0.0334509i | \(0.989350\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.0729 | −0.600618 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −41.1078 | −1.75125 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 10.9238i | − | 0.464528i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.87339 | − | 13.4554i | 0.121969 | − | 0.571151i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 22.4857i | − | 0.952749i | −0.879242 | − | 0.476375i | \(-0.841951\pi\) | ||
0.879242 | − | 0.476375i | \(-0.158049\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.66863 | 0.0705753 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.83453 | 0.0774537 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.68774i | 0.324000i | 0.986791 | + | 0.162000i | \(0.0517944\pi\) | ||||
−0.986791 | + | 0.162000i | \(0.948206\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.6704 | − | 7.40382i | −1.45859 | − | 0.311481i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.61376i | 0.319748i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.1828 | −1.18149 | −0.590743 | − | 0.806860i | \(-0.701165\pi\) | ||||
−0.590743 | + | 0.806860i | \(0.701165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.1444 | 1.30335 | 0.651676 | − | 0.758497i | \(-0.274066\pi\) | ||||
0.651676 | + | 0.758497i | \(0.274066\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.0360i | 0.461035i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.04235 | + | 4.56386i | −0.0851720 | + | 0.190326i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.20837i | 0.0503051i | 0.999684 | + | 0.0251525i | \(0.00800714\pi\) | ||||
−0.999684 | + | 0.0251525i | \(0.991993\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.3118 | 0.885687 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.291168 | −0.0120797 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.0588i | 1.45199i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.17393 | + | 0.464241i | 0.0898810 | + | 0.0191940i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.4162i | 0.553746i | 0.960906 | + | 0.276873i | \(0.0892982\pi\) | ||||
−0.960906 | + | 0.276873i | \(0.910702\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.2233 | −1.98701 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.2487 | 0.709516 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 5.37465i | − | 0.220711i | −0.993892 | − | 0.110355i | \(-0.964801\pi\) | ||
0.993892 | − | 0.110355i | \(-0.0351989\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.220289 | − | 1.03156i | 0.00903097 | − | 0.0422899i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 6.13434i | − | 0.251062i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.7001 | 0.764064 | 0.382032 | − | 0.924149i | \(-0.375224\pi\) | ||||
0.382032 | + | 0.924149i | \(0.375224\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.4418 | 0.752255 | 0.376128 | − | 0.926568i | \(-0.377255\pi\) | ||||
0.376128 | + | 0.926568i | \(0.377255\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 6.68932i | − | 0.272410i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.71595 | − | 17.4009i | 0.151075 | − | 0.707448i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.6501i | 0.635218i | 0.948222 | + | 0.317609i | \(0.102880\pi\) | ||||
−0.948222 | + | 0.317609i | \(0.897120\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.5095 | 0.425865 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.662995 | −0.0268219 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.18552i | 0.0882725i | 0.999026 | + | 0.0441363i | \(0.0140536\pi\) | ||||
−0.999026 | + | 0.0441363i | \(0.985946\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20.3157 | + | 4.33840i | 0.819209 | + | 0.174941i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 4.07539i | − | 0.164069i | −0.996629 | − | 0.0820346i | \(-0.973858\pi\) | ||
0.996629 | − | 0.0820346i | \(-0.0261418\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.0289543 | 0.00116377 | 0.000581885 | − | 1.00000i | \(-0.499815\pi\) | ||||
0.000581885 | 1.00000i | \(0.499815\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.65635 | −0.226982 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.59051i | − | 0.103787i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.6576 | + | 18.6420i | 0.666304 | + | 0.745681i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 52.6967i | − | 2.10450i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.31644 | −0.0524901 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.3679 | 1.32836 | 0.664178 | − | 0.747575i | \(-0.268782\pi\) | ||||
0.664178 | + | 0.747575i | \(0.268782\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.5453i | 0.498632i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33.2874 | − | 7.10849i | −1.32097 | − | 0.282092i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.37097i | 0.173184i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.2030 | 0.403624 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.56295 | 0.0617327 | 0.0308663 | − | 0.999524i | \(-0.490173\pi\) | ||||
0.0308663 | + | 0.999524i | \(0.490173\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 33.3037i | − | 1.31337i | −0.754166 | − | 0.656684i | \(-0.771958\pi\) | ||
0.754166 | − | 0.656684i | \(-0.228042\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.13365 | + | 5.30862i | −0.0446375 | + | 0.209027i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.54230i | − | 0.0606343i | −0.999540 | − | 0.0303171i | \(-0.990348\pi\) | ||
0.999540 | − | 0.0303171i | \(-0.00965172\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.0190 | −0.982081 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.3286 | 0.483195 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 13.1195i | − | 0.513407i | −0.966490 | − | 0.256703i | \(-0.917364\pi\) | ||
0.966490 | − | 0.256703i | \(-0.0826364\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.00981 | + | 28.1425i | −0.234823 | + | 1.09962i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.55473i | 0.255724i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.38016 | −0.287490 | −0.143745 | − | 0.989615i | \(-0.545915\pi\) | ||||
−0.143745 | + | 0.989615i | \(0.545915\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.0266 | −0.973421 | −0.486710 | − | 0.873563i | \(-0.661803\pi\) | ||||
−0.486710 | + | 0.873563i | \(0.661803\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.406422i | 0.0157841i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −29.6316 | − | 6.32780i | −1.14906 | − | 0.245381i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.76644i | 0.184557i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.7820 | 0.648830 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −59.4527 | −2.29515 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.2500i | 1.35879i | 0.733773 | + | 0.679395i | \(0.237757\pi\) | ||||
−0.733773 | + | 0.679395i | \(0.762243\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.5523 | + | 25.8148i | −0.444647 | + | 0.993612i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.04850i | 0.232463i | 0.993222 | + | 0.116231i | \(0.0370814\pi\) | ||||
−0.993222 | + | 0.116231i | \(0.962919\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.4813 | 0.555741 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.60242 | 0.0997251 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.9347i | 1.26021i | 0.776510 | + | 0.630105i | \(0.216988\pi\) | ||||
−0.776510 | + | 0.630105i | \(0.783012\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.6136 | − | 7.81880i | −1.39893 | − | 0.298741i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 23.1819i | − | 0.884443i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.76696 | −0.295897 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.7152 | 0.445668 | 0.222834 | − | 0.974856i | \(-0.428469\pi\) | ||||
0.222834 | + | 0.974856i | \(0.428469\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 7.05040i | − | 0.267823i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.52408 | − | 25.8680i | 0.209540 | − | 0.981228i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.98764i | − | 0.0752872i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −34.5091 | −1.30525 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.8861 | 1.65756 | 0.828779 | − | 0.559577i | \(-0.189036\pi\) | ||||
0.828779 | + | 0.559577i | \(0.189036\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.8148i | 1.42621i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.450433 | − | 2.10927i | 0.0169643 | − | 0.0794398i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.13090i | 0.0425317i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.2394 | −1.13567 | −0.567833 | − | 0.823144i | \(-0.692218\pi\) | ||||
−0.567833 | + | 0.823144i | \(0.692218\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.16561 | 0.268731 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.59148i | 0.209402i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.18403 | + | 1.96124i | 0.343463 | + | 0.0733463i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 38.0544i | 1.42117i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.5338 | −1.02684 | −0.513419 | − | 0.858138i | \(-0.671621\pi\) | ||||
−0.513419 | + | 0.858138i | \(0.671621\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3941 | 0.536063 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.0828i | 0.672507i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.7534 | + | 9.73475i | 0.807899 | + | 0.361540i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 33.7995i | − | 1.25356i | −0.779198 | − | 0.626778i | \(-0.784373\pi\) | ||
0.779198 | − | 0.626778i | \(-0.215627\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.8078 | −1.06695 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.519382 | 0.0192100 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.3133i | 1.78449i | 0.451550 | + | 0.892246i | \(0.350871\pi\) | ||||
−0.451550 | + | 0.892246i | \(0.649129\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.9059 | − | 2.96960i | −0.512928 | − | 0.109535i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 28.2598i | − | 1.04096i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.7004 | 0.835048 | 0.417524 | − | 0.908666i | \(-0.362898\pi\) | ||||
0.417524 | + | 0.908666i | \(0.362898\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.6745 | 0.428872 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.9953i | 0.770242i | 0.922866 | + | 0.385121i | \(0.125840\pi\) | ||||
−0.922866 | + | 0.385121i | \(0.874160\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.681890 | + | 3.19313i | −0.0249825 | + | 0.116987i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 0.190995i | − | 0.00698816i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.0302 | 0.731887 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.3909 | −0.780565 | −0.390283 | − | 0.920695i | \(-0.627623\pi\) | ||||
−0.390283 | + | 0.920695i | \(0.627623\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.4871i | 0.637266i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.30747 | − | 38.9019i | 0.302340 | − | 1.41579i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 54.7364i | 1.98943i | 0.102676 | + | 0.994715i | \(0.467260\pi\) | ||||
−0.102676 | + | 0.994715i | \(0.532740\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.11017 | −0.221785 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.87321 | 0.285404 | 0.142702 | − | 0.989766i | \(-0.454421\pi\) | ||||
0.142702 | + | 0.989766i | \(0.454421\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 5.31084i | − | 0.192265i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.676666 | + | 0.144501i | 0.0244649 | + | 0.00522446i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 5.54272i | − | 0.200136i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.7134 | −1.17968 | −0.589838 | − | 0.807522i | \(-0.700808\pi\) | ||||
−0.589838 | + | 0.807522i | \(0.700808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.9554 | 0.682663 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.88974i | 0.103937i | 0.998649 | + | 0.0519684i | \(0.0165495\pi\) | ||||
−0.998649 | + | 0.0519684i | \(0.983450\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.5187 | + | 11.4198i | 0.916659 | + | 0.410210i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 9.66760i | − | 0.346823i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −57.0949 | −2.04564 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.1037 | 1.54237 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.9607i | 0.963496i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43.8137 | + | 9.35637i | 1.56378 | + | 0.333943i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.4472i | 1.65566i | 0.560976 | + | 0.827832i | \(0.310426\pi\) | ||||
−0.560976 | + | 0.827832i | \(0.689574\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38.2523 | −1.36182 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.9104 | −0.885710 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 13.1712i | − | 0.467723i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.27681 | − | 24.7101i | 0.187149 | − | 0.876375i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.6713i | 1.61776i | 0.587974 | + | 0.808880i | \(0.299926\pi\) | ||||
−0.587974 | + | 0.808880i | \(0.700074\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.206366 | −0.00730070 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.69928 | 0.0600411 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.6912i | 0.977202i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.733706 | + | 3.43577i | −0.0258597 | + | 0.121095i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 25.0369i | − | 0.881340i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.7080 | −1.32574 | −0.662872 | − | 0.748733i | \(-0.730663\pi\) | ||||
−0.662872 | + | 0.748733i | \(0.730663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.02541 | 0.316925 | 0.158462 | − | 0.987365i | \(-0.449346\pi\) | ||||
0.158462 | + | 0.987365i | \(0.449346\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 3.25444i | − | 0.114138i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 50.0934 | + | 10.6974i | 1.75470 | + | 0.374714i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.9192i | − | 0.521958i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.56195 | 0.0545790 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.2481 | −1.19527 | −0.597634 | − | 0.801769i | \(-0.703892\pi\) | ||||
−0.597634 | + | 0.801769i | \(0.703892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 10.1842i | − | 0.354999i | −0.984121 | − | 0.177499i | \(-0.943199\pi\) | ||
0.984121 | − | 0.177499i | \(-0.0568008\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.4791 | + | 27.8859i | −0.434467 | + | 0.970864i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.0710i | 1.18477i | 0.805656 | + | 0.592383i | \(0.201813\pi\) | ||||
−0.805656 | + | 0.592383i | \(0.798187\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.5131 | 0.851376 | 0.425688 | − | 0.904870i | \(-0.360032\pi\) | ||||
0.425688 | + | 0.904870i | \(0.360032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 45.0140 | 1.56152 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.36052i | 0.0471393i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.80820 | + | 0.386140i | 0.0625755 | + | 0.0133629i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.6274i | 1.09320i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.2362 | −0.664107 | −0.332053 | − | 0.943261i | \(-0.607741\pi\) | ||||
−0.332053 | + | 0.943261i | \(0.607741\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.28105 | −0.216588 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 18.1660i | − | 0.625669i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.63626 | − | 26.3933i | 0.193893 | − | 0.907956i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 12.5024i | − | 0.429588i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.7254 | 1.08881 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.38462 | 0.150303 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 34.8964i | − | 1.19483i | −0.801932 | − | 0.597415i | \(-0.796195\pi\) | ||
0.801932 | − | 0.597415i | \(-0.203805\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.15080 | − | 19.4372i | 0.141954 | − | 0.664738i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.9040i | 1.43141i | 0.698401 | + | 0.715706i | \(0.253895\pi\) | ||||
−0.698401 | + | 0.715706i | \(0.746105\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.1286 | 0.652658 | 0.326329 | − | 0.945256i | \(-0.394188\pi\) | ||||
0.326329 | + | 0.945256i | \(0.394188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.5967 | 0.497453 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.509621i | 0.0173477i | 0.999962 | + | 0.00867385i | \(0.00276101\pi\) | ||||
−0.999962 | + | 0.00867385i | \(0.997239\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.5795 | − | 3.75408i | −0.597720 | − | 0.127643i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 23.7303i | − | 0.805924i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.2719 | 1.02691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.26070 | 0.212136 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.49919i | 0.321499i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.1819 | + | 10.3656i | 0.479435 | + | 0.350421i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.6710i | 0.529171i | 0.964362 | + | 0.264586i | \(0.0852352\pi\) | ||||
−0.964362 | + | 0.264586i | \(0.914765\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.88135 | −0.265831 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.00846 | −0.0676667 | −0.0338333 | − | 0.999427i | \(-0.510772\pi\) | ||||
−0.0338333 | + | 0.999427i | \(0.510772\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 16.7848i | − | 0.564854i | −0.959289 | − | 0.282427i | \(-0.908861\pi\) | ||
0.959289 | − | 0.282427i | \(-0.0911394\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.6338 | + | 3.76568i | 0.592754 | + | 0.126582i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 51.7294i | − | 1.73690i | −0.495774 | − | 0.868452i | \(-0.665116\pi\) | ||
0.495774 | − | 0.868452i | \(-0.334884\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.9167 | −0.802140 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.0992 | −0.706849 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.92786i | 0.198368i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.1307 | − | 47.4399i | 0.338633 | − | 1.58574i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1.35365i | − | 0.0451971i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.6514 | 0.888875 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.41757 | −0.0805409 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.81420i | 0.126929i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.98132 | + | 32.6919i | −0.232067 | + | 1.08672i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.0849i | 0.965747i | 0.875690 | + | 0.482874i | \(0.160407\pi\) | ||||
−0.875690 | + | 0.482874i | \(0.839593\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.741825 | −0.0246048 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.3517 | 0.873070 | 0.436535 | − | 0.899687i | \(-0.356205\pi\) | ||||
0.436535 | + | 0.899687i | \(0.356205\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 0.806883i | − | 0.0267039i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 41.9033 | + | 8.94840i | 1.38528 | + | 0.295825i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.2202i | 0.667728i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.0148 | 1.51789 | 0.758945 | − | 0.651155i | \(-0.225715\pi\) | ||||
0.758945 | + | 0.651155i | \(0.225715\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.40264 | 0.112121 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.54922i | 0.314316i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.95494 | − | 20.0108i | 0.294436 | − | 0.657950i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.44196i | 0.310115i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.1770 | −0.858838 | −0.429419 | − | 0.903105i | \(-0.641282\pi\) | ||||
−0.429419 | + | 0.903105i | \(0.641282\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39.0810 | 1.28083 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 5.02237i | − | 0.164425i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.85865 | + | 0.610463i | 0.0934880 | + | 0.0199643i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 44.4429i | − | 1.45189i | −0.687754 | − | 0.725944i | \(-0.741403\pi\) | ||
0.687754 | − | 0.725944i | \(-0.258597\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.73242 | 0.252338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.07346 | 0.230588 | 0.115294 | − | 0.993331i | \(-0.463219\pi\) | ||||
0.115294 | + | 0.993331i | \(0.463219\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.62014i | 0.215581i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.15010 | + | 19.4340i | −0.135003 | + | 0.632186i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 14.4533i | − | 0.469670i | −0.972035 | − | 0.234835i | \(-0.924545\pi\) | ||
0.972035 | − | 0.234835i | \(-0.0754549\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.13473 | −0.199142 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.25683 | 0.267746 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.3773i | 1.04880i | 0.851471 | + | 0.524402i | \(0.175711\pi\) | ||||
−0.851471 | + | 0.524402i | \(0.824289\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.67237 | + | 17.1968i | −0.118835 | + | 0.556476i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.1237i | 0.941437i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.3065 | −0.849482 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.264608 | 0.00853575 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.1390i | 0.423400i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33.2091 | + | 7.09177i | 1.06904 | + | 0.228292i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 25.8993i | − | 0.832865i | −0.909167 | − | 0.416433i | \(-0.863280\pi\) | ||
0.909167 | − | 0.416433i | \(-0.136720\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.63383 | 0.116736 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.2153 | −0.809197 | −0.404599 | − | 0.914494i | \(-0.632589\pi\) | ||||
−0.404599 | + | 0.914494i | \(0.632589\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 18.5859i | − | 0.595837i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.17787 | − | 2.76463i | −0.197850 | − | 0.0885391i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 5.64235i | − | 0.180515i | −0.995918 | − | 0.0902573i | \(-0.971231\pi\) | ||
0.995918 | − | 0.0902573i | \(-0.0287690\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.17880 | 0.229436 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.48371 | 0.111226 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.0322i | 1.18114i | 0.806986 | + | 0.590571i | \(0.201097\pi\) | ||||
−0.806986 | + | 0.590571i | \(0.798903\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.8778 | + | 5.73972i | 0.856397 | + | 0.182883i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.51549i | − | 0.0482387i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.72988 | −0.0550070 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.14822 | 0.227071 | 0.113535 | − | 0.993534i | \(-0.463782\pi\) | ||||
0.113535 | + | 0.993534i | \(0.463782\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.1215i | 0.828942i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.04128 | − | 9.55885i | 0.0647130 | − | 0.303036i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.96521i | 0.157250i | 0.996904 | + | 0.0786249i | \(0.0250529\pi\) | ||||
−0.996904 | + | 0.0786249i | \(0.974947\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.8010 | 0.784667 |
(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 | 920.2.e.b.369.5 | ✓ | 14 | |
4.3 | odd | 2 | 1840.2.e.g.369.10 | 14 | |||
5.2 | odd | 4 | 4600.2.a.bi.1.2 | 7 | |||
5.3 | odd | 4 | 4600.2.a.bh.1.6 | 7 | |||
5.4 | even | 2 | inner | 920.2.e.b.369.10 | yes | 14 | |
20.3 | even | 4 | 9200.2.a.dc.1.2 | 7 | |||
20.7 | even | 4 | 9200.2.a.cz.1.6 | 7 | |||
20.19 | odd | 2 | 1840.2.e.g.369.5 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.5 | ✓ | 14 | 1.1 | even | 1 | trivial | |
920.2.e.b.369.10 | yes | 14 | 5.4 | even | 2 | inner | |
1840.2.e.g.369.5 | 14 | 20.19 | odd | 2 | |||
1840.2.e.g.369.10 | 14 | 4.3 | odd | 2 | |||
4600.2.a.bh.1.6 | 7 | 5.3 | odd | 4 | |||
4600.2.a.bi.1.2 | 7 | 5.2 | odd | 4 | |||
9200.2.a.cz.1.6 | 7 | 20.7 | even | 4 | |||
9200.2.a.dc.1.2 | 7 | 20.3 | even | 4 |