Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(865,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.s (of order \(3\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1297.3 | ||
Root | \(0.500000 + 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.1297 |
Dual form | 1512.2.s.l.865.3 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.23025 | − | 2.13086i | 0.550186 | − | 0.952949i | −0.448075 | − | 0.893996i | \(-0.647890\pi\) |
0.998261 | − | 0.0589535i | \(-0.0187764\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0665372 | − | 2.64491i | −0.0251487 | − | 0.999684i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.433463 | + | 0.750780i | 0.130694 | + | 0.226369i | 0.923944 | − | 0.382527i | \(-0.124946\pi\) |
−0.793250 | + | 0.608896i | \(0.791613\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.46050 | −0.405071 | −0.202536 | − | 0.979275i | \(-0.564918\pi\) | ||||
−0.202536 | + | 0.979275i | \(0.564918\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.933463 | − | 1.61680i | −0.226398 | − | 0.392133i | 0.730340 | − | 0.683084i | \(-0.239362\pi\) |
−0.956738 | + | 0.290951i | \(0.906028\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.29679 | − | 2.24611i | 0.297504 | − | 0.515292i | −0.678060 | − | 0.735006i | \(-0.737179\pi\) |
0.975564 | + | 0.219714i | \(0.0705125\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.796790 | − | 1.38008i | 0.166142 | − | 0.287767i | −0.770918 | − | 0.636934i | \(-0.780202\pi\) |
0.937060 | + | 0.349168i | \(0.113536\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.527042 | − | 0.912864i | −0.105408 | − | 0.182573i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.78794 | 1.07479 | 0.537396 | − | 0.843330i | \(-0.319408\pi\) | ||||
0.537396 | + | 0.843330i | \(0.319408\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.78434 | − | 8.28671i | −0.859292 | − | 1.48834i | −0.872605 | − | 0.488426i | \(-0.837571\pi\) |
0.0133129 | − | 0.999911i | \(-0.495762\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.71780 | − | 3.11213i | −0.966485 | − | 0.526046i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.66012 | − | 2.87541i | 0.272921 | − | 0.472714i | −0.696687 | − | 0.717375i | \(-0.745343\pi\) |
0.969609 | + | 0.244661i | \(0.0786767\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.78074 | 0.434278 | 0.217139 | − | 0.976141i | \(-0.430327\pi\) | ||||
0.217139 | + | 0.976141i | \(0.430327\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.7089 | −1.63310 | −0.816549 | − | 0.577276i | \(-0.804116\pi\) | ||||
−0.816549 | + | 0.577276i | \(0.804116\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.74484 | + | 11.6824i | −0.983836 | + | 1.70405i | −0.336839 | + | 0.941562i | \(0.609358\pi\) |
−0.646998 | + | 0.762492i | \(0.723976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99115 | + | 0.351971i | −0.998735 | + | 0.0502815i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.32383 | + | 5.75705i | 0.456563 | + | 0.790791i | 0.998777 | − | 0.0494499i | \(-0.0157468\pi\) |
−0.542213 | + | 0.840241i | \(0.682413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.13307 | 0.287624 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.21780 | − | 5.57339i | −0.418922 | − | 0.725594i | 0.576909 | − | 0.816808i | \(-0.304259\pi\) |
−0.995831 | + | 0.0912142i | \(0.970925\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.09358 | − | 5.35824i | 0.396092 | − | 0.686052i | −0.597148 | − | 0.802131i | \(-0.703699\pi\) |
0.993240 | + | 0.116079i | \(0.0370327\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.79679 | + | 3.11213i | −0.222864 | + | 0.386012i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.850874 | − | 1.47376i | −0.103951 | − | 0.180048i | 0.809358 | − | 0.587315i | \(-0.199815\pi\) |
−0.913309 | + | 0.407267i | \(0.866482\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.14027 | 0.135325 | 0.0676627 | − | 0.997708i | \(-0.478446\pi\) | ||||
0.0676627 | + | 0.997708i | \(0.478446\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.08113 | − | 8.80077i | −0.594701 | − | 1.03005i | −0.993589 | − | 0.113053i | \(-0.963937\pi\) |
0.398888 | − | 0.917000i | \(-0.369396\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.95691 | − | 1.19643i | 0.223010 | − | 0.136345i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.39037 | − | 5.87229i | 0.381446 | − | 0.660684i | −0.609823 | − | 0.792538i | \(-0.708759\pi\) |
0.991269 | + | 0.131853i | \(0.0420928\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.75583 | −1.07084 | −0.535421 | − | 0.844585i | \(-0.679847\pi\) | ||||
−0.535421 | + | 0.844585i | \(0.679847\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.59358 | −0.498244 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.96050 | + | 8.59185i | −0.525812 | + | 0.910734i | 0.473735 | + | 0.880667i | \(0.342905\pi\) |
−0.999548 | + | 0.0300667i | \(0.990428\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0971780 | + | 3.86291i | 0.0101870 | + | 0.404943i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.19076 | − | 5.52655i | −0.327365 | − | 0.567012i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.81284 | 0.285601 | 0.142800 | − | 0.989752i | \(-0.454389\pi\) | ||||
0.142800 | + | 0.989752i | \(0.454389\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.176168 | − | 0.305132i | −0.0175294 | − | 0.0303618i | 0.857128 | − | 0.515104i | \(-0.172247\pi\) |
−0.874657 | + | 0.484742i | \(0.838913\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.09358 | − | 8.82234i | 0.501885 | − | 0.869291i | −0.498112 | − | 0.867113i | \(-0.665973\pi\) |
0.999998 | − | 0.00217831i | \(-0.000693378\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.83628 | − | 3.18054i | 0.177520 | − | 0.307474i | −0.763510 | − | 0.645796i | \(-0.776526\pi\) |
0.941031 | + | 0.338321i | \(0.109859\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.97509 | − | 6.88506i | −0.380745 | − | 0.659470i | 0.610424 | − | 0.792075i | \(-0.290999\pi\) |
−0.991169 | + | 0.132605i | \(0.957666\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.4035 | 1.73126 | 0.865628 | − | 0.500688i | \(-0.166920\pi\) | ||||
0.865628 | + | 0.500688i | \(0.166920\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.96050 | − | 3.39569i | −0.182818 | − | 0.316650i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.21420 | + | 2.57651i | −0.386315 | + | 0.236188i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.12422 | − | 8.87541i | 0.465838 | − | 0.806855i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.70895 | 0.868394 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.24844 | 0.110781 | 0.0553906 | − | 0.998465i | \(-0.482360\pi\) | ||||
0.0553906 | + | 0.998465i | \(0.482360\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.84728 | − | 8.39573i | 0.423508 | − | 0.733538i | −0.572771 | − | 0.819715i | \(-0.694132\pi\) |
0.996280 | + | 0.0861770i | \(0.0274651\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.02704 | − | 3.28045i | −0.522611 | − | 0.284451i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.51459 | + | 4.35540i | 0.214836 | + | 0.372107i | 0.953222 | − | 0.302272i | \(-0.0977450\pi\) |
−0.738386 | + | 0.674378i | \(0.764412\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.80564 | 0.237972 | 0.118986 | − | 0.992896i | \(-0.462036\pi\) | ||||
0.118986 | + | 0.992896i | \(0.462036\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.633074 | − | 1.09652i | −0.0529403 | − | 0.0916954i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.12062 | − | 12.3333i | 0.591335 | − | 1.02422i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.19289 | − | 15.9226i | 0.753111 | − | 1.30443i | −0.193197 | − | 0.981160i | \(-0.561886\pi\) |
0.946308 | − | 0.323267i | \(-0.104781\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.39397 | + | 12.8067i | 0.601713 | + | 1.04220i | 0.992562 | + | 0.121742i | \(0.0388480\pi\) |
−0.390849 | + | 0.920455i | \(0.627819\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.5438 | −1.89108 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.07227 | + | 13.9816i | 0.644237 | + | 1.11585i | 0.984477 | + | 0.175513i | \(0.0561585\pi\) |
−0.340240 | + | 0.940339i | \(0.610508\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.70321 | − | 2.01561i | −0.291854 | − | 0.158853i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.40496 | + | 16.2899i | −0.736653 | + | 1.27592i | 0.217341 | + | 0.976096i | \(0.430262\pi\) |
−0.953994 | + | 0.299825i | \(0.903072\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.3025 | 1.02938 | 0.514690 | − | 0.857376i | \(-0.327907\pi\) | ||||
0.514690 | + | 0.857376i | \(0.327907\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8669 | −0.835917 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.379379 | − | 0.657103i | 0.0288436 | − | 0.0499586i | −0.851243 | − | 0.524771i | \(-0.824151\pi\) |
0.880087 | + | 0.474813i | \(0.157484\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.37938 | + | 1.45472i | −0.179864 | + | 0.109967i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.550486 | − | 0.953469i | −0.0411452 | − | 0.0712656i | 0.844719 | − | 0.535209i | \(-0.179767\pi\) |
−0.885865 | + | 0.463944i | \(0.846434\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2235 | −1.05723 | −0.528613 | − | 0.848863i | \(-0.677288\pi\) | ||||
−0.528613 | + | 0.848863i | \(0.677288\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.08472 | − | 7.07495i | −0.300315 | − | 0.520161i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.809243 | − | 1.40165i | 0.0591777 | − | 0.102499i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.80778 | + | 3.13117i | −0.130806 | + | 0.226563i | −0.923988 | − | 0.382422i | \(-0.875090\pi\) |
0.793181 | + | 0.608986i | \(0.208423\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.9050 | + | 20.6200i | 0.856938 | + | 1.48426i | 0.874836 | + | 0.484420i | \(0.160969\pi\) |
−0.0178981 | + | 0.999840i | \(0.505697\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.8348 | 1.34193 | 0.670963 | − | 0.741491i | \(-0.265881\pi\) | ||||
0.670963 | + | 0.741491i | \(0.265881\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.64027 | − | 11.5013i | −0.470716 | − | 0.815305i | 0.528723 | − | 0.848795i | \(-0.322671\pi\) |
−0.999439 | + | 0.0334899i | \(0.989338\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.385113 | − | 15.3086i | −0.0270296 | − | 1.07445i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.42101 | − | 5.92536i | 0.238934 | − | 0.413845i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.24844 | 0.155528 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.86693 | −0.541581 | −0.270791 | − | 0.962638i | \(-0.587285\pi\) | ||||
−0.270791 | + | 0.962638i | \(0.587285\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.1747 | + | 22.8193i | −0.898507 | + | 1.55626i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.5993 | + | 13.2055i | −1.46626 | + | 0.896450i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.36333 | + | 2.36135i | 0.0917073 | + | 0.158842i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.0364 | 1.00691 | 0.503455 | − | 0.864021i | \(-0.332062\pi\) | ||||
0.503455 | + | 0.864021i | \(0.332062\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.38298 | + | 2.39539i | 0.0917914 | + | 0.158987i | 0.908265 | − | 0.418395i | \(-0.137407\pi\) |
−0.816474 | + | 0.577383i | \(0.804074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.30399 | − | 12.6509i | 0.482661 | − | 0.835993i | −0.517141 | − | 0.855900i | \(-0.673004\pi\) |
0.999802 | + | 0.0199069i | \(0.00633698\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.68716 | + | 6.38635i | −0.241554 | + | 0.418383i | −0.961157 | − | 0.276002i | \(-0.910990\pi\) |
0.719603 | + | 0.694385i | \(0.244324\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.5957 | + | 28.7446i | 1.08259 | + | 1.87509i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.9531 | −0.837867 | −0.418934 | − | 0.908017i | \(-0.637596\pi\) | ||||
−0.418934 | + | 0.908017i | \(0.637596\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.98968 | + | 13.8385i | 0.514661 | + | 0.891419i | 0.999855 | + | 0.0170123i | \(0.00541545\pi\) |
−0.485195 | + | 0.874406i | \(0.661251\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.85087 | + | 15.3302i | −0.501574 | + | 0.979408i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.89397 | + | 3.28045i | −0.120510 | + | 0.208730i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.5510 | −0.729090 | −0.364545 | − | 0.931186i | \(-0.618776\pi\) | ||||
−0.364545 | + | 0.931186i | \(0.618776\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.38151 | 0.0868551 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.0687 | − | 22.6356i | 0.815201 | − | 1.41197i | −0.0939817 | − | 0.995574i | \(-0.529960\pi\) |
0.909183 | − | 0.416396i | \(-0.136707\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.71566 | − | 4.19954i | −0.479428 | − | 0.260947i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.5993 | + | 18.3586i | 0.653582 | + | 1.13204i | 0.982247 | + | 0.187590i | \(0.0600677\pi\) |
−0.328666 | + | 0.944446i | \(0.606599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.3566 | 1.00478 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.05195 | − | 3.55408i | −0.125109 | − | 0.216696i | 0.796666 | − | 0.604419i | \(-0.206595\pi\) |
−0.921776 | + | 0.387723i | \(0.873262\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.710602 | + | 1.23080i | −0.0431660 | + | 0.0747657i | −0.886801 | − | 0.462151i | \(-0.847078\pi\) |
0.843635 | + | 0.536917i | \(0.180411\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.456906 | − | 0.791385i | 0.0275525 | − | 0.0477223i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0811 | + | 22.6572i | 0.785969 | + | 1.36134i | 0.928419 | + | 0.371536i | \(0.121169\pi\) |
−0.142450 | + | 0.989802i | \(0.545498\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.111094 | 0.00662728 | 0.00331364 | − | 0.999995i | \(-0.498945\pi\) | ||||
0.00331364 | + | 0.999995i | \(0.498945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.66012 | − | 9.80361i | −0.336459 | − | 0.582764i | 0.647305 | − | 0.762231i | \(-0.275896\pi\) |
−0.983764 | + | 0.179467i | \(0.942563\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.185023 | − | 7.35481i | −0.0109215 | − | 0.434141i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.75729 | − | 11.7040i | 0.397488 | − | 0.688469i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.5290 | −0.790372 | −0.395186 | − | 0.918601i | \(-0.629320\pi\) | ||||
−0.395186 | + | 0.918601i | \(0.629320\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.8348 | −0.921939 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.16372 | + | 2.01561i | −0.0672994 | + | 0.116566i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.712544 | + | 28.3242i | 0.0410703 | + | 1.63258i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.61177 | − | 13.1840i | −0.435849 | − | 0.754912i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.0187 | 1.48496 | 0.742482 | − | 0.669866i | \(-0.233649\pi\) | ||||
0.742482 | + | 0.669866i | \(0.233649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.5687 | + | 30.4298i | 0.996228 | + | 1.72552i | 0.573262 | + | 0.819372i | \(0.305678\pi\) |
0.422966 | + | 0.906146i | \(0.360989\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.1768 | + | 21.0909i | −0.688276 | + | 1.19213i | 0.284119 | + | 0.958789i | \(0.408299\pi\) |
−0.972395 | + | 0.233340i | \(0.925035\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.6264 | + | 30.5297i | −0.989995 | + | 1.71472i | −0.372798 | + | 0.927913i | \(0.621602\pi\) |
−0.617197 | + | 0.786809i | \(0.711732\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.50885 | + | 4.34546i | 0.140469 | + | 0.243299i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.84202 | −0.269417 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.769748 | + | 1.33324i | 0.0426979 | + | 0.0739550i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 31.3478 | + | 17.0622i | 1.72826 | + | 0.940670i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.96410 | − | 15.5263i | 0.492712 | − | 0.853402i | −0.507253 | − | 0.861797i | \(-0.669339\pi\) |
0.999965 | + | 0.00839547i | \(0.00267239\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.18716 | −0.228769 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.5801 | 1.01212 | 0.506062 | − | 0.862497i | \(-0.331101\pi\) | ||||
0.506062 | + | 0.862497i | \(0.331101\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.14766 | − | 7.18396i | 0.224609 | − | 0.389033i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.39610 | + | 18.4676i | 0.0753825 | + | 0.997155i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.8171 | − | 29.1281i | −0.902790 | − | 1.56368i | −0.823857 | − | 0.566798i | \(-0.808182\pi\) |
−0.0789333 | − | 0.996880i | \(-0.525151\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.1301 | 1.39871 | 0.699357 | − | 0.714772i | \(-0.253470\pi\) | ||||
0.699357 | + | 0.714772i | \(0.253470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.61177 | + | 11.4519i | 0.351909 | + | 0.609524i | 0.986584 | − | 0.163255i | \(-0.0521994\pi\) |
−0.634675 | + | 0.772779i | \(0.718866\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.40282 | − | 2.42976i | 0.0744541 | − | 0.128958i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.97296 | − | 3.41726i | 0.104129 | − | 0.180356i | −0.809253 | − | 0.587460i | \(-0.800128\pi\) |
0.913382 | + | 0.407104i | \(0.133461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.13667 | + | 10.6290i | 0.322983 | + | 0.559423i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.0043 | −1.30878 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.97509 | + | 17.2774i | 0.520696 | + | 0.901871i | 0.999710 | + | 0.0240645i | \(0.00766071\pi\) |
−0.479015 | + | 0.877807i | \(0.659006\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.0057 | − | 9.17431i | 0.779059 | − | 0.476306i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4035 | + | 28.4117i | −0.849341 | + | 1.47110i | 0.0324567 | + | 0.999473i | \(0.489667\pi\) |
−0.881797 | + | 0.471628i | \(0.843666\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.45331 | −0.435367 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.51886 | 0.334851 | 0.167426 | − | 0.985885i | \(-0.446455\pi\) | ||||
0.167426 | + | 0.985885i | \(0.446455\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.1460 | − | 24.5016i | 0.722827 | − | 1.25197i | −0.237035 | − | 0.971501i | \(-0.576176\pi\) |
0.959862 | − | 0.280472i | \(-0.0904911\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.141929 | − | 5.64180i | −0.00723337 | − | 0.287533i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.86546 | − | 13.6234i | −0.398795 | − | 0.690733i | 0.594783 | − | 0.803887i | \(-0.297238\pi\) |
−0.993578 | + | 0.113154i | \(0.963905\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.97509 | −0.150457 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.34202 | − | 14.4488i | −0.419733 | − | 0.726998i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.7448 | − | 27.2709i | 0.790211 | − | 1.36869i | −0.135625 | − | 0.990760i | \(-0.543304\pi\) |
0.925836 | − | 0.377925i | \(-0.123362\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.17111 | − | 2.02842i | 0.0584823 | − | 0.101294i | −0.835302 | − | 0.549791i | \(-0.814707\pi\) |
0.893784 | + | 0.448497i | \(0.148041\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.98755 | + | 12.1028i | 0.348075 | + | 0.602883i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.87839 | 0.142677 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.13142 | − | 10.6199i | −0.303179 | − | 0.525122i | 0.673675 | − | 0.739028i | \(-0.264715\pi\) |
−0.976854 | + | 0.213906i | \(0.931381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.5270 | + | 8.88164i | −0.714829 | + | 0.437037i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0021 | + | 20.7883i | −0.589162 | + | 1.02046i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.3743 | 0.653378 | 0.326689 | − | 0.945132i | \(-0.394067\pi\) | ||||
0.326689 | + | 0.945132i | \(0.394067\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0905 | −1.66147 | −0.830734 | − | 0.556670i | \(-0.812079\pi\) | ||||
−0.830734 | + | 0.556670i | \(0.812079\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.983948 | + | 1.70425i | −0.0477285 | + | 0.0826682i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.3779 | − | 7.82573i | −0.695796 | − | 0.378714i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.3370 | + | 35.2246i | 0.979597 | + | 1.69671i | 0.663846 | + | 0.747869i | \(0.268923\pi\) |
0.315751 | + | 0.948842i | \(0.397744\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.43560 | −0.117047 | −0.0585237 | − | 0.998286i | \(-0.518639\pi\) | ||||
−0.0585237 | + | 0.998286i | \(0.518639\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.06654 | − | 3.57935i | −0.0988559 | − | 0.171223i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.55408 | − | 16.5482i | 0.455992 | − | 0.789801i | −0.542753 | − | 0.839892i | \(-0.682618\pi\) |
0.998745 | + | 0.0500918i | \(0.0159514\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.3224 | − | 30.0032i | 0.823011 | − | 1.42550i | −0.0804197 | − | 0.996761i | \(-0.525626\pi\) |
0.903430 | − | 0.428735i | \(-0.141041\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.2053 | + | 21.1403i | 0.578589 | + | 1.00215i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.9167 | 0.892736 | 0.446368 | − | 0.894849i | \(-0.352717\pi\) | ||||
0.446368 | + | 0.894849i | \(0.352717\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.20535 | + | 2.08772i | 0.0567575 | + | 0.0983070i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.35087 | + | 4.54528i | 0.391495 | + | 0.213086i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.11702 | + | 7.13089i | −0.192586 | + | 0.333569i | −0.946107 | − | 0.323855i | \(-0.895021\pi\) |
0.753520 | + | 0.657425i | \(0.228354\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.78074 | −0.222661 | −0.111331 | − | 0.993783i | \(-0.535511\pi\) | ||||
−0.111331 | + | 0.993783i | \(0.535511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.2163 | −1.12543 | −0.562714 | − | 0.826651i | \(-0.690243\pi\) | ||||
−0.562714 | + | 0.826651i | \(0.690243\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.05622 | − | 3.56148i | 0.0951505 | − | 0.164806i | −0.814521 | − | 0.580134i | \(-0.803000\pi\) |
0.909671 | + | 0.415329i | \(0.136333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.84135 | + | 2.34855i | −0.177377 | + | 0.108446i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.64193 | − | 8.04006i | −0.213436 | − | 0.369682i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.73385 | −0.125438 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.2917 | + | 19.5578i | 0.515932 | + | 0.893621i | 0.999829 | + | 0.0184957i | \(0.00588771\pi\) |
−0.483897 | + | 0.875125i | \(0.660779\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.42461 | + | 4.19954i | −0.110553 | + | 0.191483i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.46050 | − | 5.99377i | 0.157133 | − | 0.272163i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.0957 | + | 36.5389i | 0.955938 | + | 1.65573i | 0.732207 | + | 0.681083i | \(0.238491\pi\) |
0.223731 | + | 0.974651i | \(0.428176\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.2911 | −0.780334 | −0.390167 | − | 0.920744i | \(-0.627583\pi\) | ||||
−0.390167 | + | 0.920744i | \(0.627583\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.40282 | − | 9.35796i | −0.243331 | − | 0.421461i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.0758705 | − | 3.01592i | −0.00340326 | − | 0.135283i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.49494 | − | 16.4457i | 0.425052 | − | 0.736211i | −0.571373 | − | 0.820690i | \(-0.693589\pi\) |
0.996425 | + | 0.0844788i | \(0.0269225\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.8961 | 0.797948 | 0.398974 | − | 0.916962i | \(-0.369366\pi\) | ||||
0.398974 | + | 0.916962i | \(0.369366\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.866926 | −0.0385777 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.5125 | − | 21.6722i | 0.554605 | − | 0.960604i | −0.443329 | − | 0.896359i | \(-0.646203\pi\) |
0.997934 | − | 0.0642448i | \(-0.0204639\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.9392 | + | 14.0247i | −1.01477 | + | 0.620417i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.5328 | − | 21.7074i | −0.552260 | − | 0.956543i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.6946 | −0.514326 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.8078 | − | 30.8440i | −0.780173 | − | 1.35130i | −0.931841 | − | 0.362868i | \(-0.881798\pi\) |
0.151668 | − | 0.988432i | \(-0.451536\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.47656 | − | 16.4139i | 0.414381 | − | 0.717729i | −0.580982 | − | 0.813916i | \(-0.697331\pi\) |
0.995363 | + | 0.0961874i | \(0.0306648\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.93200 | + | 15.4707i | −0.389084 | + | 0.673913i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.2303 | + | 17.7193i | 0.444794 | + | 0.770405i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.06128 | −0.175914 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.51819 | − | 7.82573i | −0.195338 | − | 0.338336i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.29465 | − | 5.09624i | −0.141911 | − | 0.219511i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.66012 | − | 14.9998i | 0.372327 | − | 0.644890i | −0.617596 | − | 0.786496i | \(-0.711893\pi\) |
0.989923 | + | 0.141606i | \(0.0452265\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.5615 | −0.837922 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.06128 | −0.259162 | −0.129581 | − | 0.991569i | \(-0.541363\pi\) | ||||
−0.129581 | + | 0.991569i | \(0.541363\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.50573 | − | 13.0003i | 0.319755 | − | 0.553832i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.7573 | − | 8.57651i | −0.670068 | − | 0.364710i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.16372 | + | 14.1400i | 0.345908 | + | 0.599130i | 0.985518 | − | 0.169569i | \(-0.0542377\pi\) |
−0.639611 | + | 0.768699i | \(0.720904\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.6405 | 0.661521 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.5826 | + | 21.7937i | 0.530293 | + | 0.918494i | 0.999375 | + | 0.0353399i | \(0.0112514\pi\) |
−0.469082 | + | 0.883154i | \(0.655415\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.6409 | − | 39.2153i | 0.952512 | − | 1.64980i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.1929 | + | 29.7790i | −0.720764 | + | 1.24840i | 0.239931 | + | 0.970790i | \(0.422875\pi\) |
−0.960694 | + | 0.277609i | \(0.910458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.28580 | + | 7.42322i | 0.179355 | + | 0.310652i | 0.941660 | − | 0.336566i | \(-0.109266\pi\) |
−0.762305 | + | 0.647218i | \(0.775932\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.67977 | −0.0700511 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7199 | − | 23.7636i | −0.571168 | − | 0.989293i | −0.996446 | − | 0.0842299i | \(-0.973157\pi\) |
0.425278 | − | 0.905063i | \(-0.360176\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.649126 | + | 25.8033i | 0.0269303 | + | 1.07050i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.88151 | + | 4.99093i | −0.119340 | + | 0.206703i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.8276 | 0.488178 | 0.244089 | − | 0.969753i | \(-0.421511\pi\) | ||||
0.244089 | + | 0.969753i | \(0.421511\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.8171 | −1.02257 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.9964 | + | 19.0463i | −0.451568 | + | 0.782139i | −0.998484 | − | 0.0550489i | \(-0.982469\pi\) |
0.546916 | + | 0.837188i | \(0.315802\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.305644 | + | 12.1496i | 0.0125302 | + | 0.498086i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.3640 | + | 23.1471i | 0.546038 | + | 0.945766i | 0.998541 | + | 0.0540029i | \(0.0171980\pi\) |
−0.452503 | + | 0.891763i | \(0.649469\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.20914 | −0.0901127 | −0.0450563 | − | 0.998984i | \(-0.514347\pi\) | ||||
−0.0450563 | + | 0.998984i | \(0.514347\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.6082 | − | 21.8380i | −0.512595 | − | 0.887840i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.66012 | − | 14.9998i | 0.351503 | − | 0.608822i | −0.635010 | − | 0.772504i | \(-0.719004\pi\) |
0.986513 | + | 0.163683i | \(0.0523373\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.85087 | − | 17.0622i | 0.398524 | − | 0.690263i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.18570 | − | 14.1780i | −0.330617 | − | 0.572646i | 0.652016 | − | 0.758205i | \(-0.273924\pi\) |
−0.982633 | + | 0.185560i | \(0.940590\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.6198 | −0.709348 | −0.354674 | − | 0.934990i | \(-0.615408\pi\) | ||||
−0.354674 | + | 0.934990i | \(0.615408\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.26236 | + | 3.91852i | 0.0909318 | + | 0.157498i | 0.907903 | − | 0.419179i | \(-0.137682\pi\) |
−0.816972 | + | 0.576678i | \(0.804349\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.0548 | + | 12.5484i | 0.923669 | + | 0.502742i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5797 | − | 25.2527i | 0.583187 | − | 1.01011i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.19863 | −0.247155 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.99280 | −0.198760 | −0.0993802 | − | 0.995050i | \(-0.531686\pi\) | ||||
−0.0993802 | + | 0.995050i | \(0.531686\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.53590 | − | 2.66025i | 0.0609502 | − | 0.105569i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.2106 | − | 0.514055i | 0.404559 | − | 0.0203676i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.3602 | − | 36.9970i | −0.843677 | − | 1.46129i | −0.886765 | − | 0.462221i | \(-0.847053\pi\) |
0.0430873 | − | 0.999071i | \(-0.486281\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.8200 | 0.663318 | 0.331659 | − | 0.943399i | \(-0.392392\pi\) | ||||
0.331659 | + | 0.943399i | \(0.392392\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.5548 | + | 40.7980i | 0.926033 | + | 1.60394i | 0.789891 | + | 0.613247i | \(0.210137\pi\) |
0.136142 | + | 0.990689i | \(0.456530\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.78959 | − | 4.83172i | 0.109501 | − | 0.189661i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.6967 | + | 37.5798i | −0.849057 | + | 1.47061i | 0.0329939 | + | 0.999456i | \(0.489496\pi\) |
−0.882051 | + | 0.471154i | \(0.843838\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.9267 | − | 20.6577i | −0.466016 | − | 0.807164i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.1049 | −1.21167 | −0.605837 | − | 0.795589i | \(-0.707161\pi\) | ||||
−0.605837 | + | 0.795589i | \(0.707161\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.74484 | + | 3.02215i | 0.0678665 | + | 0.117548i | 0.897962 | − | 0.440073i | \(-0.145047\pi\) |
−0.830095 | + | 0.557621i | \(0.811714\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.4050 | + | 8.80700i | −0.558600 | + | 0.341521i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.61177 | − | 7.98781i | 0.178568 | − | 0.309289i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.36381 | 0.207067 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.25175 | −0.0867988 | −0.0433994 | − | 0.999058i | \(-0.513819\pi\) | ||||
−0.0433994 | + | 0.999058i | \(0.513819\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.6623 | − | 34.0560i | 0.755682 | − | 1.30888i | −0.189353 | − | 0.981909i | \(-0.560639\pi\) |
0.945035 | − | 0.326970i | \(-0.106028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.187159 | − | 7.43972i | −0.00718249 | − | 0.285510i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.24338 | − | 5.61770i | −0.124104 | − | 0.214955i | 0.797278 | − | 0.603612i | \(-0.206272\pi\) |
−0.921383 | + | 0.388657i | \(0.872939\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.3743 | 0.472798 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.85447 | − | 8.40819i | −0.184941 | − | 0.320327i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.7843 | − | 18.6790i | 0.410256 | − | 0.710583i | −0.584662 | − | 0.811277i | \(-0.698773\pi\) |
0.994917 | + | 0.100694i | \(0.0321062\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.45165 | − | 5.97843i | 0.130929 | − | 0.226775i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.59572 | − | 4.49591i | −0.0983197 | − | 0.170295i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.6329 | 0.817063 | 0.408531 | − | 0.912744i | \(-0.366041\pi\) | ||||
0.408531 | + | 0.912744i | \(0.366041\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.30564 | − | 7.45759i | −0.162390 | − | 0.281268i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.795327 | + | 0.486253i | −0.0299114 | + | 0.0182874i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.8370 | − | 18.7702i | 0.406991 | − | 0.704928i | −0.587560 | − | 0.809180i | \(-0.699912\pi\) |
0.994551 | + | 0.104252i | \(0.0332449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.2484 | −0.571059 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.11537 | −0.116508 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.8669 | + | 32.6785i | −0.703618 | + | 1.21870i | 0.263571 | + | 0.964640i | \(0.415100\pi\) |
−0.967188 | + | 0.254061i | \(0.918234\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.6732 | − | 12.8851i | −0.881638 | − | 0.479865i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.05049 | − | 5.28360i | −0.113292 | − | 0.196228i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.6414 | −1.35896 | −0.679478 | − | 0.733696i | \(-0.737794\pi\) | ||||
−0.679478 | + | 0.733696i | \(0.737794\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.99640 | + | 17.3143i | 0.369730 | + | 0.640392i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.69289 | + | 9.86038i | −0.210272 | + | 0.364201i | −0.951800 | − | 0.306721i | \(-0.900768\pi\) |
0.741528 | + | 0.670922i | \(0.234102\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.737644 | − | 1.27764i | 0.0271715 | − | 0.0470624i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0349 | − | 27.7733i | −0.589854 | − | 1.02166i | −0.994251 | − | 0.107073i | \(-0.965852\pi\) |
0.404397 | − | 0.914583i | \(-0.367481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.7516 | −0.944733 | −0.472367 | − | 0.881402i | \(-0.656600\pi\) | ||||
−0.472367 | + | 0.881402i | \(0.656600\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.6192 | − | 39.1775i | −0.828702 | − | 1.43535i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.53443 | − | 4.64519i | −0.311841 | − | 0.169732i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.64766 | − | 13.2461i | 0.279067 | − | 0.483359i | −0.692086 | − | 0.721815i | \(-0.743308\pi\) |
0.971153 | + | 0.238456i | \(0.0766414\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36.3858 | 1.32421 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.2891 | −1.35529 | −0.677647 | − | 0.735387i | \(-0.737000\pi\) | ||||
−0.677647 | + | 0.735387i | \(0.737000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.1431 | + | 31.4247i | −0.657686 | + | 1.13915i | 0.323527 | + | 0.946219i | \(0.395131\pi\) |
−0.981213 | + | 0.192927i | \(0.938202\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.9459 | + | 10.9719i | −0.649686 | + | 0.397209i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.69961 | + | 8.13997i | 0.169693 | + | 0.293917i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.0908 | 1.15723 | 0.578613 | − | 0.815602i | \(-0.303594\pi\) | ||||
0.578613 | + | 0.815602i | \(0.303594\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.7178 | − | 32.4202i | −0.673232 | − | 1.16607i | −0.976982 | − | 0.213321i | \(-0.931572\pi\) |
0.303750 | − | 0.952752i | \(-0.401761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.04309 | + | 8.73489i | −0.181153 | + | 0.313767i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.60603 | − | 6.24583i | 0.129200 | − | 0.223780i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.494265 | + | 0.856093i | 0.0176862 | + | 0.0306334i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.7237 | 1.41780 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.4751 | − | 25.0716i | −0.515981 | − | 0.893706i | −0.999828 | − | 0.0185531i | \(-0.994094\pi\) |
0.483847 | − | 0.875153i | \(-0.339239\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.22452 | − | 48.6757i | −0.0435388 | − | 1.73071i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.51819 | + | 7.82573i | −0.160446 | + | 0.277900i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.9941 | −1.34582 | −0.672911 | − | 0.739724i | \(-0.734956\pi\) | ||||
−0.672911 | + | 0.739724i | \(0.734956\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.1842 | 0.890954 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.40496 | − | 7.62961i | 0.155448 | − | 0.269243i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.85087 | + | 5.41131i | −0.311952 | + | 0.190724i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.47869 | + | 2.56117i | 0.0519881 | + | 0.0900460i | 0.890848 | − | 0.454301i | \(-0.150111\pi\) |
−0.838860 | + | 0.544347i | \(0.816778\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.7204 | −1.14897 | −0.574485 | − | 0.818515i | \(-0.694797\pi\) | ||||
−0.574485 | + | 0.818515i | \(0.694797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.1409 | + | 40.0813i | 0.810592 | + | 1.40399i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.8872 | + | 24.0534i | −0.485853 | + | 0.841523i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.1572 | − | 27.9851i | 0.563890 | − | 0.976686i | −0.433262 | − | 0.901268i | \(-0.642638\pi\) |
0.997152 | − | 0.0754180i | \(-0.0240291\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.41021 | − | 4.17461i | −0.0840148 | − | 0.145518i | 0.820956 | − | 0.570991i | \(-0.193441\pi\) |
−0.904971 | + | 0.425473i | \(0.860108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.2383 | 0.981943 | 0.490971 | − | 0.871176i | \(-0.336642\pi\) | ||||
0.490971 | + | 0.871176i | \(0.336642\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.85301 | − | 3.20951i | −0.0643577 | − | 0.111471i | 0.832051 | − | 0.554699i | \(-0.187167\pi\) |
−0.896409 | + | 0.443228i | \(0.853833\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.09504 | + | 10.9748i | 0.245829 | + | 0.380253i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.3655 | − | 28.3458i | 0.566350 | − | 0.980947i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.9430 | 0.377794 | 0.188897 | − | 0.981997i | \(-0.439509\pi\) | ||||
0.188897 | + | 0.981997i | \(0.439509\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.50019 | 0.155179 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.3691 | + | 23.1559i | −0.459910 | + | 0.796587i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.8157 | − | 12.9626i | −0.818315 | − | 0.445399i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.64553 | − | 4.58219i | −0.0906875 | − | 0.157075i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.4064 | 0.835660 | 0.417830 | − | 0.908525i | \(-0.362791\pi\) | ||||
0.417830 | + | 0.908525i | \(0.362791\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.15292 | − | 7.19307i | −0.141861 | − | 0.245710i | 0.786336 | − | 0.617799i | \(-0.211975\pi\) |
−0.928197 | + | 0.372088i | \(0.878642\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.3946 | − | 31.8605i | 0.627617 | − | 1.08706i | −0.360411 | − | 0.932793i | \(-0.617364\pi\) |
0.988029 | − | 0.154271i | \(-0.0493030\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.1190 | − | 41.7753i | 0.821019 | − | 1.42205i | −0.0839050 | − | 0.996474i | \(-0.526739\pi\) |
0.904924 | − | 0.425573i | \(-0.139927\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.933463 | − | 1.61680i | −0.0317387 | − | 0.0549730i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.87839 | 0.199411 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.24271 | + | 2.15243i | 0.0421075 | + | 0.0729323i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.646006 | − | 25.6793i | −0.0218390 | − | 0.868120i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.6840 | + | 21.9694i | −0.428310 | + | 0.741854i | −0.996723 | − | 0.0808891i | \(-0.974224\pi\) |
0.568414 | + | 0.822743i | \(0.307557\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.8636 | −0.669222 | −0.334611 | − | 0.942356i | \(-0.608605\pi\) | ||||
−0.334611 | + | 0.942356i | \(0.608605\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.6519 | −1.46900 | −0.734502 | − | 0.678606i | \(-0.762584\pi\) | ||||
−0.734502 | + | 0.678606i | \(0.762584\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.13735 | + | 8.89815i | −0.172495 | + | 0.298770i | −0.939292 | − | 0.343120i | \(-0.888516\pi\) |
0.766796 | + | 0.641890i | \(0.221850\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0830678 | − | 3.30202i | −0.00278600 | − | 0.110746i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.4933 | + | 30.2993i | 0.585390 | + | 1.01393i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.70895 | −0.0905500 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.6914 | − | 47.9630i | −0.923561 | − | 1.59965i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.20535 | − | 10.7480i | 0.206730 | − | 0.358067i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.4985 | + | 30.3084i | −0.581671 | + | 1.00748i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.78074 | − | 4.81638i | −0.0923329 | − | 0.159925i | 0.816159 | − | 0.577827i | \(-0.196099\pi\) |
−0.908492 | + | 0.417901i | \(0.862766\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.9908 | 0.960509 | 0.480255 | − | 0.877129i | \(-0.340544\pi\) | ||||
0.480255 | + | 0.877129i | \(0.340544\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.22879 | − | 7.32448i | −0.139953 | − | 0.242405i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.5285 | − | 12.2620i | −0.743957 | − | 0.404927i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.2132 | − | 41.9385i | 0.798720 | − | 1.38342i | −0.121729 | − | 0.992563i | \(-0.538844\pi\) |
0.920450 | − | 0.390861i | \(-0.127823\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.66537 | −0.0548164 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.49981 | −0.115073 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.3838 | − | 31.8418i | 0.603154 | − | 1.04469i | −0.389186 | − | 0.921159i | \(-0.627244\pi\) |
0.992340 | − | 0.123535i | \(-0.0394231\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.27548 | + | 16.1593i | −0.271218 | + | 0.529599i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.99115 | − | 3.44877i | −0.0651174 | − | 0.112787i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.6477 | −0.576524 | −0.288262 | − | 0.957552i | \(-0.593077\pi\) | ||||
−0.288262 | + | 0.957552i | \(0.593077\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.879573 | − | 1.52347i | −0.0286733 | − | 0.0496636i | 0.851333 | − | 0.524626i | \(-0.175795\pi\) |
−0.880006 | + | 0.474963i | \(0.842462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.21566 | − | 3.83764i | 0.0721519 | − | 0.124971i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.6139 | − | 33.9723i | 0.637366 | − | 1.10395i | −0.348642 | − | 0.937256i | \(-0.613357\pi\) |
0.986009 | − | 0.166695i | \(-0.0533095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.42101 | + | 12.8536i | 0.240896 | + | 0.417244i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.4313 | 1.21252 | 0.606260 | − | 0.795267i | \(-0.292669\pi\) | ||||
0.606260 | + | 0.795267i | \(0.292669\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.44805 | + | 7.70425i | 0.143936 | + | 0.249304i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.3523 | − | 6.94067i | 0.366586 | − | 0.224126i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2798 | + | 52.4461i | −0.976766 | + | 1.69181i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 58.5844 | 1.88590 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.31731 | 0.235309 | 0.117654 | − | 0.993055i | \(-0.462463\pi\) | ||||
0.117654 | + | 0.993055i | \(0.462463\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.0775 | + | 38.2394i | −0.708502 | + | 1.22716i | 0.256911 | + | 0.966435i | \(0.417295\pi\) |
−0.965413 | + | 0.260726i | \(0.916038\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.186680 | − | 7.42069i | −0.00598468 | − | 0.237896i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.57685 | − | 2.73119i | −0.0504480 | − | 0.0873786i | 0.839699 | − | 0.543053i | \(-0.182732\pi\) |
−0.890147 | + | 0.455674i | \(0.849398\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.60078 | −0.274882 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.3338 | − | 35.2192i | −0.648549 | − | 1.12332i | −0.983470 | − | 0.181073i | \(-0.942043\pi\) |
0.334921 | − | 0.942246i | \(-0.391290\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.1716 | − | 40.1344i | 0.738308 | − | 1.27879i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.53278 | + | 14.7792i | −0.271327 | + | 0.469951i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.50360 | + | 9.53251i | 0.174828 | + | 0.302810i | 0.940102 | − | 0.340894i | \(-0.110730\pi\) |
−0.765274 | + | 0.643705i | \(0.777397\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.6768 | −1.03593 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.8368 | − | 39.5544i | −0.723248 | − | 1.25270i | −0.959691 | − | 0.281056i | \(-0.909315\pi\) |
0.236444 | − | 0.971645i | \(-0.424018\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1512.2.s.l.1297.3 | yes | 6 | |
3.2 | odd | 2 | 1512.2.s.k.1297.1 | yes | 6 | ||
7.4 | even | 3 | inner | 1512.2.s.l.865.3 | yes | 6 | |
21.11 | odd | 6 | 1512.2.s.k.865.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.k.865.1 | ✓ | 6 | 21.11 | odd | 6 | ||
1512.2.s.k.1297.1 | yes | 6 | 3.2 | odd | 2 | ||
1512.2.s.l.865.3 | yes | 6 | 7.4 | even | 3 | inner | |
1512.2.s.l.1297.3 | yes | 6 | 1.1 | even | 1 | trivial |