Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("825.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), not 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.3 | ||
Root | \(-1.75233 - 1.75233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.2.c.f.199.4 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.36333i | − 0.964019i | −0.876166 | − | 0.482009i | \(-0.839907\pi\) | ||||
0.876166 | − | 0.482009i | \(-0.160093\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0.141336 | 0.0706681 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.36333 | 0.556576 | ||||||||
\(7\) | − 2.50466i | − 0.946674i | −0.880881 | − | 0.473337i | \(-0.843049\pi\) | ||||
0.880881 | − | 0.473337i | \(-0.156951\pi\) | |||||||
\(8\) | − 2.91934i | − 1.03214i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.141336i | 0.0408002i | ||||||||
\(13\) | 1.14134i | 0.316550i | 0.987395 | + | 0.158275i | \(0.0505932\pi\) | ||||
−0.987395 | + | 0.158275i | \(0.949407\pi\) | |||||||
\(14\) | −3.41468 | −0.912612 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.69735 | −0.924338 | ||||||||
\(17\) | − 7.64600i | − 1.85443i | −0.374533 | − | 0.927214i | \(-0.622197\pi\) | ||||
0.374533 | − | 0.927214i | \(-0.377803\pi\) | |||||||
\(18\) | 1.36333i | 0.321340i | ||||||||
\(19\) | −1.77801 | −0.407903 | −0.203951 | − | 0.978981i | \(-0.565378\pi\) | ||||
−0.203951 | + | 0.978981i | \(0.565378\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.50466 | 0.546563 | ||||||||
\(22\) | − 1.36333i | − 0.290663i | ||||||||
\(23\) | 1.41468i | 0.294981i | 0.989063 | + | 0.147491i | \(0.0471196\pi\) | ||||
−0.989063 | + | 0.147491i | \(0.952880\pi\) | |||||||
\(24\) | 2.91934 | 0.595909 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.55602 | 0.305160 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 0.354000i | − 0.0668996i | ||||||||
\(29\) | 0.726656 | 0.134937 | 0.0674684 | − | 0.997721i | \(-0.478508\pi\) | ||||
0.0674684 | + | 0.997721i | \(0.478508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.85866 | 0.513431 | 0.256716 | − | 0.966487i | \(-0.417360\pi\) | ||||
0.256716 | + | 0.966487i | \(0.417360\pi\) | |||||||
\(32\) | − 0.797984i | − 0.141065i | ||||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | −10.4240 | −1.78770 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.141336 | −0.0235560 | ||||||||
\(37\) | 8.42401i | 1.38490i | 0.721467 | + | 0.692449i | \(0.243468\pi\) | ||||
−0.721467 | + | 0.692449i | \(0.756532\pi\) | |||||||
\(38\) | 2.42401i | 0.393226i | ||||||||
\(39\) | −1.14134 | −0.182760 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.636672 | 0.0994314 | 0.0497157 | − | 0.998763i | \(-0.484168\pi\) | ||||
0.0497157 | + | 0.998763i | \(0.484168\pi\) | |||||||
\(42\) | − 3.41468i | − 0.526897i | ||||||||
\(43\) | − 12.6974i | − 1.93633i | −0.250317 | − | 0.968164i | \(-0.580535\pi\) | ||||
0.250317 | − | 0.968164i | \(-0.419465\pi\) | |||||||
\(44\) | 0.141336 | 0.0213072 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.92867 | 0.284367 | ||||||||
\(47\) | − 6.14134i | − 0.895806i | −0.894082 | − | 0.447903i | \(-0.852171\pi\) | ||||
0.894082 | − | 0.447903i | \(-0.147829\pi\) | |||||||
\(48\) | − 3.69735i | − 0.533667i | ||||||||
\(49\) | 0.726656 | 0.103808 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.64600 | 1.07065 | ||||||||
\(52\) | 0.161312i | 0.0223700i | ||||||||
\(53\) | − 12.0187i | − 1.65089i | −0.564483 | − | 0.825445i | \(-0.690924\pi\) | ||||
0.564483 | − | 0.825445i | \(-0.309076\pi\) | |||||||
\(54\) | −1.36333 | −0.185525 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.31198 | −0.977104 | ||||||||
\(57\) | − 1.77801i | − 0.235503i | ||||||||
\(58\) | − 0.990671i | − 0.130082i | ||||||||
\(59\) | 3.41468 | 0.444553 | 0.222277 | − | 0.974984i | \(-0.428651\pi\) | ||||
0.222277 | + | 0.974984i | \(0.428651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.59465 | 0.588285 | 0.294142 | − | 0.955762i | \(-0.404966\pi\) | ||||
0.294142 | + | 0.955762i | \(0.404966\pi\) | |||||||
\(62\) | − 3.89730i | − 0.494957i | ||||||||
\(63\) | 2.50466i | 0.315558i | ||||||||
\(64\) | −8.48262 | −1.06033 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.36333 | 0.167814 | ||||||||
\(67\) | 9.32131i | 1.13878i | 0.822068 | + | 0.569389i | \(0.192820\pi\) | ||||
−0.822068 | + | 0.569389i | \(0.807180\pi\) | |||||||
\(68\) | − 1.08066i | − 0.131049i | ||||||||
\(69\) | −1.41468 | −0.170307 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.85866 | 0.695295 | 0.347648 | − | 0.937625i | \(-0.386981\pi\) | ||||
0.347648 | + | 0.937625i | \(0.386981\pi\) | |||||||
\(72\) | 2.91934i | 0.344048i | ||||||||
\(73\) | 7.55602i | 0.884365i | 0.896925 | + | 0.442182i | \(0.145796\pi\) | ||||
−0.896925 | + | 0.442182i | \(0.854204\pi\) | |||||||
\(74\) | 11.4847 | 1.33507 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.251297 | −0.0288257 | ||||||||
\(77\) | − 2.50466i | − 0.285433i | ||||||||
\(78\) | 1.55602i | 0.176184i | ||||||||
\(79\) | −6.91934 | −0.778487 | −0.389244 | − | 0.921135i | \(-0.627264\pi\) | ||||
−0.389244 | + | 0.921135i | \(0.627264\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 0.867993i | − 0.0958537i | ||||||||
\(83\) | − 6.17997i | − 0.678340i | −0.940725 | − | 0.339170i | \(-0.889854\pi\) | ||||
0.940725 | − | 0.339170i | \(-0.110146\pi\) | |||||||
\(84\) | 0.354000 | 0.0386245 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −17.3107 | −1.86666 | ||||||||
\(87\) | 0.726656i | 0.0779058i | ||||||||
\(88\) | − 2.91934i | − 0.311203i | ||||||||
\(89\) | −3.45331 | −0.366050 | −0.183025 | − | 0.983108i | \(-0.558589\pi\) | ||||
−0.183025 | + | 0.983108i | \(0.558589\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.85866 | 0.299669 | ||||||||
\(92\) | 0.199945i | 0.0208457i | ||||||||
\(93\) | 2.85866i | 0.296430i | ||||||||
\(94\) | −8.37266 | −0.863574 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.797984 | 0.0814439 | ||||||||
\(97\) | 19.4626i | 1.97613i | 0.154032 | + | 0.988066i | \(0.450774\pi\) | ||||
−0.154032 | + | 0.988066i | \(0.549226\pi\) | |||||||
\(98\) | − 0.990671i | − 0.100073i | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.37266 | −0.833111 | −0.416555 | − | 0.909110i | \(-0.636763\pi\) | ||||
−0.416555 | + | 0.909110i | \(0.636763\pi\) | |||||||
\(102\) | − 10.4240i | − 1.03213i | ||||||||
\(103\) | 2.54669i | 0.250933i | 0.992098 | + | 0.125466i | \(0.0400427\pi\) | ||||
−0.992098 | + | 0.125466i | \(0.959957\pi\) | |||||||
\(104\) | 3.33195 | 0.326725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.3854 | −1.59149 | ||||||||
\(107\) | 14.5653i | 1.40808i | 0.710158 | + | 0.704042i | \(0.248624\pi\) | ||||
−0.710158 | + | 0.704042i | \(0.751376\pi\) | |||||||
\(108\) | − 0.141336i | − 0.0136001i | ||||||||
\(109\) | −2.41468 | −0.231284 | −0.115642 | − | 0.993291i | \(-0.536893\pi\) | ||||
−0.115642 | + | 0.993291i | \(0.536893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.42401 | −0.799571 | ||||||||
\(112\) | 9.26063i | 0.875047i | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −2.42401 | −0.227029 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.102703 | 0.00953572 | ||||||||
\(117\) | − 1.14134i | − 0.105517i | ||||||||
\(118\) | − 4.65533i | − 0.428558i | ||||||||
\(119\) | −19.1507 | −1.75554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − 6.26401i | − 0.567117i | ||||||||
\(123\) | 0.636672i | 0.0574068i | ||||||||
\(124\) | 0.404032 | 0.0362832 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.41468 | 0.304204 | ||||||||
\(127\) | 15.2020i | 1.34896i | 0.738293 | + | 0.674480i | \(0.235632\pi\) | ||||
−0.738293 | + | 0.674480i | \(0.764368\pi\) | |||||||
\(128\) | 9.96862i | 0.881110i | ||||||||
\(129\) | 12.6974 | 1.11794 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.7453 | 1.63779 | 0.818893 | − | 0.573946i | \(-0.194588\pi\) | ||||
0.818893 | + | 0.573946i | \(0.194588\pi\) | |||||||
\(132\) | 0.141336i | 0.0123017i | ||||||||
\(133\) | 4.45331i | 0.386151i | ||||||||
\(134\) | 12.7080 | 1.09780 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −22.3213 | −1.91404 | ||||||||
\(137\) | − 8.74531i | − 0.747163i | −0.927597 | − | 0.373581i | \(-0.878130\pi\) | ||||
0.927597 | − | 0.373581i | \(-0.121870\pi\) | |||||||
\(138\) | 1.92867i | 0.164180i | ||||||||
\(139\) | 22.3013 | 1.89157 | 0.945787 | − | 0.324787i | \(-0.105293\pi\) | ||||
0.945787 | + | 0.324787i | \(0.105293\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.14134 | 0.517194 | ||||||||
\(142\) | − 7.98728i | − 0.670278i | ||||||||
\(143\) | 1.14134i | 0.0954433i | ||||||||
\(144\) | 3.69735 | 0.308113 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.3013 | 0.852544 | ||||||||
\(147\) | 0.726656i | 0.0599336i | ||||||||
\(148\) | 1.19062i | 0.0978681i | ||||||||
\(149\) | 15.9287 | 1.30493 | 0.652464 | − | 0.757820i | \(-0.273735\pi\) | ||||
0.652464 | + | 0.757820i | \(0.273735\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.88665 | −0.804564 | −0.402282 | − | 0.915516i | \(-0.631783\pi\) | ||||
−0.402282 | + | 0.915516i | \(0.631783\pi\) | |||||||
\(152\) | 5.19062i | 0.421015i | ||||||||
\(153\) | 7.64600i | 0.618143i | ||||||||
\(154\) | −3.41468 | −0.275163 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.161312 | −0.0129153 | ||||||||
\(157\) | 0.132007i | 0.0105353i | 0.999986 | + | 0.00526767i | \(0.00167676\pi\) | ||||
−0.999986 | + | 0.00526767i | \(0.998323\pi\) | |||||||
\(158\) | 9.43334i | 0.750476i | ||||||||
\(159\) | 12.0187 | 0.953142 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.54330 | 0.279251 | ||||||||
\(162\) | − 1.36333i | − 0.107113i | ||||||||
\(163\) | − 4.31198i | − 0.337740i | −0.985638 | − | 0.168870i | \(-0.945988\pi\) | ||||
0.985638 | − | 0.168870i | \(-0.0540118\pi\) | |||||||
\(164\) | 0.0899847 | 0.00702663 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.42533 | −0.653932 | ||||||||
\(167\) | 11.2920i | 0.873801i | 0.899510 | + | 0.436901i | \(0.143924\pi\) | ||||
−0.899510 | + | 0.436901i | \(0.856076\pi\) | |||||||
\(168\) | − 7.31198i | − 0.564131i | ||||||||
\(169\) | 11.6974 | 0.899796 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.77801 | 0.135968 | ||||||||
\(172\) | − 1.79459i | − 0.136837i | ||||||||
\(173\) | 21.6460i | 1.64571i | 0.568248 | + | 0.822857i | \(0.307621\pi\) | ||||
−0.568248 | + | 0.822857i | \(0.692379\pi\) | |||||||
\(174\) | 0.990671 | 0.0751026 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.69735 | −0.278698 | ||||||||
\(177\) | 3.41468i | 0.256663i | ||||||||
\(178\) | 4.70800i | 0.352879i | ||||||||
\(179\) | −16.1413 | −1.20646 | −0.603230 | − | 0.797567i | \(-0.706120\pi\) | ||||
−0.603230 | + | 0.797567i | \(0.706120\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7546 | 1.54268 | 0.771340 | − | 0.636423i | \(-0.219587\pi\) | ||||
0.771340 | + | 0.636423i | \(0.219587\pi\) | |||||||
\(182\) | − 3.89730i | − 0.288887i | ||||||||
\(183\) | 4.59465i | 0.339646i | ||||||||
\(184\) | 4.12994 | 0.304463 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.89730 | 0.285764 | ||||||||
\(187\) | − 7.64600i | − 0.559131i | ||||||||
\(188\) | − 0.867993i | − 0.0633049i | ||||||||
\(189\) | −2.50466 | −0.182188 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.31198 | 0.239646 | 0.119823 | − | 0.992795i | \(-0.461767\pi\) | ||||
0.119823 | + | 0.992795i | \(0.461767\pi\) | |||||||
\(192\) | − 8.48262i | − 0.612180i | ||||||||
\(193\) | − 2.13201i | − 0.153465i | −0.997052 | − | 0.0767326i | \(-0.975551\pi\) | ||||
0.997052 | − | 0.0767326i | \(-0.0244488\pi\) | |||||||
\(194\) | 26.5340 | 1.90503 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.102703 | 0.00733591 | ||||||||
\(197\) | − 17.9287i | − 1.27737i | −0.769470 | − | 0.638683i | \(-0.779480\pi\) | ||||
0.769470 | − | 0.638683i | \(-0.220520\pi\) | |||||||
\(198\) | 1.36333i | 0.0968875i | ||||||||
\(199\) | −15.1600 | −1.07466 | −0.537332 | − | 0.843371i | \(-0.680568\pi\) | ||||
−0.537332 | + | 0.843371i | \(0.680568\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.32131 | −0.657474 | ||||||||
\(202\) | 11.4147i | 0.803134i | ||||||||
\(203\) | − 1.82003i | − 0.127741i | ||||||||
\(204\) | 1.08066 | 0.0756611 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.47197 | 0.241904 | ||||||||
\(207\) | − 1.41468i | − 0.0983270i | ||||||||
\(208\) | − 4.21992i | − 0.292599i | ||||||||
\(209\) | −1.77801 | −0.122987 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.3213 | −0.917076 | −0.458538 | − | 0.888675i | \(-0.651627\pi\) | ||||
−0.458538 | + | 0.888675i | \(0.651627\pi\) | |||||||
\(212\) | − 1.69867i | − 0.116665i | ||||||||
\(213\) | 5.85866i | 0.401429i | ||||||||
\(214\) | 19.8573 | 1.35742 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.91934 | −0.198636 | ||||||||
\(217\) | − 7.15999i | − 0.486052i | ||||||||
\(218\) | 3.29200i | 0.222962i | ||||||||
\(219\) | −7.55602 | −0.510588 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.72666 | 0.587018 | ||||||||
\(222\) | 11.4847i | 0.770802i | ||||||||
\(223\) | − 12.2534i | − 0.820546i | −0.911963 | − | 0.410273i | \(-0.865433\pi\) | ||||
0.911963 | − | 0.410273i | \(-0.134567\pi\) | |||||||
\(224\) | −1.99868 | −0.133543 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.17997 | 0.544123 | ||||||||
\(227\) | − 8.74531i | − 0.580447i | −0.956959 | − | 0.290223i | \(-0.906270\pi\) | ||||
0.956959 | − | 0.290223i | \(-0.0937296\pi\) | |||||||
\(228\) | − 0.251297i | − 0.0166425i | ||||||||
\(229\) | 11.4626 | 0.757473 | 0.378736 | − | 0.925505i | \(-0.376359\pi\) | ||||
0.378736 | + | 0.925505i | \(0.376359\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.50466 | 0.164795 | ||||||||
\(232\) | − 2.12136i | − 0.139274i | ||||||||
\(233\) | 7.48469i | 0.490338i | 0.969480 | + | 0.245169i | \(0.0788435\pi\) | ||||
−0.969480 | + | 0.245169i | \(0.921157\pi\) | |||||||
\(234\) | −1.55602 | −0.101720 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.482618 | 0.0314157 | ||||||||
\(237\) | − 6.91934i | − 0.449460i | ||||||||
\(238\) | 26.1086i | 1.69237i | ||||||||
\(239\) | −12.9066 | −0.834860 | −0.417430 | − | 0.908709i | \(-0.637069\pi\) | ||||
−0.417430 | + | 0.908709i | \(0.637069\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.8773 | −1.08716 | −0.543582 | − | 0.839356i | \(-0.682932\pi\) | ||||
−0.543582 | + | 0.839356i | \(0.682932\pi\) | |||||||
\(242\) | − 1.36333i | − 0.0876381i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0.649390 | 0.0415729 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.867993 | 0.0553412 | ||||||||
\(247\) | − 2.02930i | − 0.129122i | ||||||||
\(248\) | − 8.34542i | − 0.529935i | ||||||||
\(249\) | 6.17997 | 0.391640 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.28267 | 0.144081 | 0.0720405 | − | 0.997402i | \(-0.477049\pi\) | ||||
0.0720405 | + | 0.997402i | \(0.477049\pi\) | |||||||
\(252\) | 0.354000i | 0.0222999i | ||||||||
\(253\) | 1.41468i | 0.0889401i | ||||||||
\(254\) | 20.7253 | 1.30042 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.37473 | −0.210920 | ||||||||
\(257\) | 26.8667i | 1.67590i | 0.545749 | + | 0.837949i | \(0.316245\pi\) | ||||
−0.545749 | + | 0.837949i | \(0.683755\pi\) | |||||||
\(258\) | − 17.3107i | − 1.07771i | ||||||||
\(259\) | 21.0993 | 1.31105 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.726656 | −0.0449789 | ||||||||
\(262\) | − 25.5560i | − 1.57886i | ||||||||
\(263\) | 12.0187i | 0.741102i | 0.928812 | + | 0.370551i | \(0.120831\pi\) | ||||
−0.928812 | + | 0.370551i | \(0.879169\pi\) | |||||||
\(264\) | 2.91934 | 0.179673 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.07133 | 0.372257 | ||||||||
\(267\) | − 3.45331i | − 0.211339i | ||||||||
\(268\) | 1.31744i | 0.0804753i | ||||||||
\(269\) | 14.3854 | 0.877092 | 0.438546 | − | 0.898709i | \(-0.355494\pi\) | ||||
0.438546 | + | 0.898709i | \(0.355494\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.6553 | 1.74069 | 0.870344 | − | 0.492445i | \(-0.163897\pi\) | ||||
0.870344 | + | 0.492445i | \(0.163897\pi\) | |||||||
\(272\) | 28.2700i | 1.71412i | ||||||||
\(273\) | 2.85866i | 0.173014i | ||||||||
\(274\) | −11.9227 | −0.720279 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.199945 | −0.0120353 | ||||||||
\(277\) | 29.1600i | 1.75205i | 0.482262 | + | 0.876027i | \(0.339815\pi\) | ||||
−0.482262 | + | 0.876027i | \(0.660185\pi\) | |||||||
\(278\) | − 30.4040i | − 1.82351i | ||||||||
\(279\) | −2.85866 | −0.171144 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.36333 | −0.319949 | −0.159975 | − | 0.987121i | \(-0.551141\pi\) | ||||
−0.159975 | + | 0.987121i | \(0.551141\pi\) | |||||||
\(282\) | − 8.37266i | − 0.498584i | ||||||||
\(283\) | − 10.0420i | − 0.596936i | −0.954420 | − | 0.298468i | \(-0.903524\pi\) | ||||
0.954420 | − | 0.298468i | \(-0.0964757\pi\) | |||||||
\(284\) | 0.828041 | 0.0491352 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.55602 | 0.0920091 | ||||||||
\(287\) | − 1.59465i | − 0.0941292i | ||||||||
\(288\) | 0.797984i | 0.0470216i | ||||||||
\(289\) | −41.4613 | −2.43890 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.4626 | −1.14092 | ||||||||
\(292\) | 1.06794i | 0.0624963i | ||||||||
\(293\) | 20.3540i | 1.18909i | 0.804061 | + | 0.594547i | \(0.202668\pi\) | ||||
−0.804061 | + | 0.594547i | \(0.797332\pi\) | |||||||
\(294\) | 0.990671 | 0.0577771 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 24.5926 | 1.42941 | ||||||||
\(297\) | − 1.00000i | − 0.0580259i | ||||||||
\(298\) | − 21.7160i | − 1.25797i | ||||||||
\(299\) | −1.61462 | −0.0933762 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.8026 | −1.83307 | ||||||||
\(302\) | 13.4787i | 0.775615i | ||||||||
\(303\) | − 8.37266i | − 0.480997i | ||||||||
\(304\) | 6.57392 | 0.377040 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.4240 | 0.595901 | ||||||||
\(307\) | − 25.6226i | − 1.46236i | −0.682184 | − | 0.731181i | \(-0.738970\pi\) | ||||
0.682184 | − | 0.731181i | \(-0.261030\pi\) | |||||||
\(308\) | − 0.354000i | − 0.0201710i | ||||||||
\(309\) | −2.54669 | −0.144876 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.9414 | 0.677134 | 0.338567 | − | 0.940942i | \(-0.390058\pi\) | ||||
0.338567 | + | 0.940942i | \(0.390058\pi\) | |||||||
\(312\) | 3.33195i | 0.188635i | ||||||||
\(313\) | 17.1986i | 0.972124i | 0.873924 | + | 0.486062i | \(0.161567\pi\) | ||||
−0.873924 | + | 0.486062i | \(0.838433\pi\) | |||||||
\(314\) | 0.179969 | 0.0101563 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.977953 | −0.0550142 | ||||||||
\(317\) | 22.7453i | 1.27750i | 0.769413 | + | 0.638752i | \(0.220549\pi\) | ||||
−0.769413 | + | 0.638752i | \(0.779451\pi\) | |||||||
\(318\) | − 16.3854i | − 0.918846i | ||||||||
\(319\) | 0.726656 | 0.0406850 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.5653 | −0.812958 | ||||||||
\(322\) | − 4.83068i | − 0.269203i | ||||||||
\(323\) | 13.5946i | 0.756427i | ||||||||
\(324\) | 0.141336 | 0.00785201 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.87864 | −0.325588 | ||||||||
\(327\) | − 2.41468i | − 0.133532i | ||||||||
\(328\) | − 1.85866i | − 0.102628i | ||||||||
\(329\) | −15.3820 | −0.848036 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.2733 | 1.38915 | 0.694574 | − | 0.719421i | \(-0.255593\pi\) | ||||
0.694574 | + | 0.719421i | \(0.255593\pi\) | |||||||
\(332\) | − 0.873453i | − 0.0479370i | ||||||||
\(333\) | − 8.42401i | − 0.461633i | ||||||||
\(334\) | 15.3947 | 0.842361 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −9.26063 | −0.505209 | ||||||||
\(337\) | 17.6880i | 0.963528i | 0.876301 | + | 0.481764i | \(0.160004\pi\) | ||||
−0.876301 | + | 0.481764i | \(0.839996\pi\) | |||||||
\(338\) | − 15.9473i | − 0.867420i | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.85866 | 0.154805 | ||||||||
\(342\) | − 2.42401i | − 0.131075i | ||||||||
\(343\) | − 19.3527i | − 1.04495i | ||||||||
\(344\) | −37.0679 | −1.99857 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.5106 | 1.58650 | ||||||||
\(347\) | − 20.1027i | − 1.07917i | −0.841931 | − | 0.539585i | \(-0.818581\pi\) | ||||
0.841931 | − | 0.539585i | \(-0.181419\pi\) | |||||||
\(348\) | 0.102703i | 0.00550545i | ||||||||
\(349\) | 10.9907 | 0.588317 | 0.294159 | − | 0.955757i | \(-0.404961\pi\) | ||||
0.294159 | + | 0.955757i | \(0.404961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.14134 | 0.0609200 | ||||||||
\(352\) | − 0.797984i | − 0.0425327i | ||||||||
\(353\) | 16.7267i | 0.890270i | 0.895463 | + | 0.445135i | \(0.146844\pi\) | ||||
−0.895463 | + | 0.445135i | \(0.853156\pi\) | |||||||
\(354\) | 4.65533 | 0.247428 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.488078 | −0.0258681 | ||||||||
\(357\) | − 19.1507i | − 1.01356i | ||||||||
\(358\) | 22.0059i | 1.16305i | ||||||||
\(359\) | 13.5933 | 0.717429 | 0.358714 | − | 0.933447i | \(-0.383215\pi\) | ||||
0.358714 | + | 0.933447i | \(0.383215\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8387 | −0.833615 | ||||||||
\(362\) | − 28.2954i | − 1.48717i | ||||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | 0.404032 | 0.0211771 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.26401 | 0.327425 | ||||||||
\(367\) | − 28.9987i | − 1.51372i | −0.653578 | − | 0.756859i | \(-0.726733\pi\) | ||||
0.653578 | − | 0.756859i | \(-0.273267\pi\) | |||||||
\(368\) | − 5.23057i | − 0.272662i | ||||||||
\(369\) | −0.636672 | −0.0331438 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −30.1027 | −1.56285 | ||||||||
\(372\) | 0.404032i | 0.0209481i | ||||||||
\(373\) | − 17.8867i | − 0.926136i | −0.886323 | − | 0.463068i | \(-0.846749\pi\) | ||||
0.886323 | − | 0.463068i | \(-0.153251\pi\) | |||||||
\(374\) | −10.4240 | −0.539013 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.9287 | −0.924601 | ||||||||
\(377\) | 0.829359i | 0.0427142i | ||||||||
\(378\) | 3.41468i | 0.175632i | ||||||||
\(379\) | −23.7839 | −1.22170 | −0.610850 | − | 0.791747i | \(-0.709172\pi\) | ||||
−0.610850 | + | 0.791747i | \(0.709172\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.2020 | −0.778823 | ||||||||
\(382\) | − 4.51531i | − 0.231023i | ||||||||
\(383\) | − 31.7360i | − 1.62163i | −0.585300 | − | 0.810817i | \(-0.699023\pi\) | ||||
0.585300 | − | 0.810817i | \(-0.300977\pi\) | |||||||
\(384\) | −9.96862 | −0.508709 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.90663 | −0.147943 | ||||||||
\(387\) | 12.6974i | 0.645443i | ||||||||
\(388\) | 2.75077i | 0.139649i | ||||||||
\(389\) | −25.7546 | −1.30581 | −0.652906 | − | 0.757439i | \(-0.726450\pi\) | ||||
−0.652906 | + | 0.757439i | \(0.726450\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.8166 | 0.547021 | ||||||||
\(392\) | − 2.12136i | − 0.107145i | ||||||||
\(393\) | 18.7453i | 0.945576i | ||||||||
\(394\) | −24.4427 | −1.23140 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.141336 | −0.00710241 | ||||||||
\(397\) | 3.03863i | 0.152505i | 0.997089 | + | 0.0762523i | \(0.0242954\pi\) | ||||
−0.997089 | + | 0.0762523i | \(0.975705\pi\) | |||||||
\(398\) | 20.6680i | 1.03600i | ||||||||
\(399\) | −4.45331 | −0.222945 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.1800 | −0.907864 | −0.453932 | − | 0.891036i | \(-0.649979\pi\) | ||||
−0.453932 | + | 0.891036i | \(0.649979\pi\) | |||||||
\(402\) | 12.7080i | 0.633817i | ||||||||
\(403\) | 3.26270i | 0.162526i | ||||||||
\(404\) | −1.18336 | −0.0588743 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.48130 | −0.123145 | ||||||||
\(407\) | 8.42401i | 0.417563i | ||||||||
\(408\) | − 22.3213i | − 1.10507i | ||||||||
\(409\) | 20.5946 | 1.01834 | 0.509170 | − | 0.860666i | \(-0.329952\pi\) | ||||
0.509170 | + | 0.860666i | \(0.329952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.74531 | 0.431375 | ||||||||
\(412\) | 0.359939i | 0.0177329i | ||||||||
\(413\) | − 8.55263i | − 0.420847i | ||||||||
\(414\) | −1.92867 | −0.0947891 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.910768 | 0.0446541 | ||||||||
\(417\) | 22.3013i | 1.09210i | ||||||||
\(418\) | 2.42401i | 0.118562i | ||||||||
\(419\) | −32.7253 | −1.59874 | −0.799369 | − | 0.600841i | \(-0.794833\pi\) | ||||
−0.799369 | + | 0.600841i | \(0.794833\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.5640 | 1.58707 | 0.793537 | − | 0.608522i | \(-0.208237\pi\) | ||||
0.793537 | + | 0.608522i | \(0.208237\pi\) | |||||||
\(422\) | 18.1613i | 0.884079i | ||||||||
\(423\) | 6.14134i | 0.298602i | ||||||||
\(424\) | −35.0866 | −1.70396 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.98728 | 0.386985 | ||||||||
\(427\) | − 11.5081i | − 0.556914i | ||||||||
\(428\) | 2.05861i | 0.0995066i | ||||||||
\(429\) | −1.14134 | −0.0551042 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.82003 | 0.0876678 | 0.0438339 | − | 0.999039i | \(-0.486043\pi\) | ||||
0.0438339 | + | 0.999039i | \(0.486043\pi\) | |||||||
\(432\) | 3.69735i | 0.177889i | ||||||||
\(433\) | − 29.8280i | − 1.43344i | −0.697359 | − | 0.716722i | \(-0.745642\pi\) | ||||
0.697359 | − | 0.716722i | \(-0.254358\pi\) | |||||||
\(434\) | −9.76142 | −0.468563 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.341281 | −0.0163444 | ||||||||
\(437\) | − 2.51531i | − 0.120324i | ||||||||
\(438\) | 10.3013i | 0.492217i | ||||||||
\(439\) | −18.2220 | −0.869688 | −0.434844 | − | 0.900506i | \(-0.643197\pi\) | ||||
−0.434844 | + | 0.900506i | \(0.643197\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.726656 | −0.0346027 | ||||||||
\(442\) | − 11.8973i | − 0.565897i | ||||||||
\(443\) | − 22.2627i | − 1.05773i | −0.848705 | − | 0.528866i | \(-0.822617\pi\) | ||||
0.848705 | − | 0.528866i | \(-0.177383\pi\) | |||||||
\(444\) | −1.19062 | −0.0565042 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.7054 | −0.791022 | ||||||||
\(447\) | 15.9287i | 0.753400i | ||||||||
\(448\) | 21.2461i | 1.00378i | ||||||||
\(449\) | −25.8760 | −1.22116 | −0.610582 | − | 0.791953i | \(-0.709064\pi\) | ||||
−0.610582 | + | 0.791953i | \(0.709064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.636672 | 0.0299797 | ||||||||
\(452\) | 0.848017i | 0.0398874i | ||||||||
\(453\) | − 9.88665i | − 0.464515i | ||||||||
\(454\) | −11.9227 | −0.559562 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.19062 | −0.243073 | ||||||||
\(457\) | 10.4626i | 0.489422i | 0.969596 | + | 0.244711i | \(0.0786930\pi\) | ||||
−0.969596 | + | 0.244711i | \(0.921307\pi\) | |||||||
\(458\) | − 15.6273i | − 0.730218i | ||||||||
\(459\) | −7.64600 | −0.356885 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.8387 | 0.551383 | 0.275691 | − | 0.961246i | \(-0.411093\pi\) | ||||
0.275691 | + | 0.961246i | \(0.411093\pi\) | |||||||
\(462\) | − 3.41468i | − 0.158865i | ||||||||
\(463\) | 27.7546i | 1.28987i | 0.764238 | + | 0.644934i | \(0.223115\pi\) | ||||
−0.764238 | + | 0.644934i | \(0.776885\pi\) | |||||||
\(464\) | −2.68670 | −0.124727 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.2041 | 0.472695 | ||||||||
\(467\) | − 20.8294i | − 0.963868i | −0.876208 | − | 0.481934i | \(-0.839935\pi\) | ||||
0.876208 | − | 0.481934i | \(-0.160065\pi\) | |||||||
\(468\) | − 0.161312i | − 0.00745665i | ||||||||
\(469\) | 23.3467 | 1.07805 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.132007 | −0.00608258 | ||||||||
\(472\) | − 9.96862i | − 0.458843i | ||||||||
\(473\) | − 12.6974i | − 0.583825i | ||||||||
\(474\) | −9.43334 | −0.433288 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.70668 | −0.124061 | ||||||||
\(477\) | 12.0187i | 0.550297i | ||||||||
\(478\) | 17.5960i | 0.804821i | ||||||||
\(479\) | −2.64939 | −0.121054 | −0.0605269 | − | 0.998167i | \(-0.519278\pi\) | ||||
−0.0605269 | + | 0.998167i | \(0.519278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.61462 | −0.438389 | ||||||||
\(482\) | 23.0093i | 1.04805i | ||||||||
\(483\) | 3.54330i | 0.161226i | ||||||||
\(484\) | 0.141336 | 0.00642437 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.36333 | 0.0618418 | ||||||||
\(487\) | − 40.5360i | − 1.83686i | −0.395580 | − | 0.918432i | \(-0.629456\pi\) | ||||
0.395580 | − | 0.918432i | \(-0.370544\pi\) | |||||||
\(488\) | − 13.4134i | − 0.607194i | ||||||||
\(489\) | 4.31198 | 0.194994 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.1214 | −0.727547 | −0.363773 | − | 0.931487i | \(-0.618512\pi\) | ||||
−0.363773 | + | 0.931487i | \(0.618512\pi\) | |||||||
\(492\) | 0.0899847i | 0.00405682i | ||||||||
\(493\) | − 5.55602i | − 0.250230i | ||||||||
\(494\) | −2.76661 | −0.124476 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.5695 | −0.474584 | ||||||||
\(497\) | − 14.6740i | − 0.658218i | ||||||||
\(498\) | − 8.42533i | − 0.377548i | ||||||||
\(499\) | 28.0666 | 1.25643 | 0.628217 | − | 0.778038i | \(-0.283785\pi\) | ||||
0.628217 | + | 0.778038i | \(0.283785\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.2920 | −0.504489 | ||||||||
\(502\) | − 3.11203i | − 0.138897i | ||||||||
\(503\) | 0.906626i | 0.0404245i | 0.999796 | + | 0.0202122i | \(0.00643419\pi\) | ||||
−0.999796 | + | 0.0202122i | \(0.993566\pi\) | |||||||
\(504\) | 7.31198 | 0.325701 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.92867 | 0.0857400 | ||||||||
\(507\) | 11.6974i | 0.519498i | ||||||||
\(508\) | 2.14859i | 0.0953284i | ||||||||
\(509\) | 14.3013 | 0.633895 | 0.316948 | − | 0.948443i | \(-0.397342\pi\) | ||||
0.316948 | + | 0.948443i | \(0.397342\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.9253 | 0.837205 | ||||||||
\(512\) | 24.5381i | 1.08444i | ||||||||
\(513\) | 1.77801i | 0.0785010i | ||||||||
\(514\) | 36.6281 | 1.61560 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.79459 | 0.0790026 | ||||||||
\(517\) | − 6.14134i | − 0.270096i | ||||||||
\(518\) | − 28.7653i | − 1.26387i | ||||||||
\(519\) | −21.6460 | −0.950154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.1214 | 0.881533 | 0.440766 | − | 0.897622i | \(-0.354707\pi\) | ||||
0.440766 | + | 0.897622i | \(0.354707\pi\) | |||||||
\(522\) | 0.990671i | 0.0433605i | ||||||||
\(523\) | − 12.8459i | − 0.561714i | −0.959750 | − | 0.280857i | \(-0.909381\pi\) | ||||
0.959750 | − | 0.280857i | \(-0.0906187\pi\) | |||||||
\(524\) | 2.64939 | 0.115739 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.3854 | 0.714436 | ||||||||
\(527\) | − 21.8573i | − 0.952121i | ||||||||
\(528\) | − 3.69735i | − 0.160907i | ||||||||
\(529\) | 20.9987 | 0.912986 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.41468 | −0.148184 | ||||||||
\(532\) | 0.629414i | 0.0272886i | ||||||||
\(533\) | 0.726656i | 0.0314750i | ||||||||
\(534\) | −4.70800 | −0.203735 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 27.2121 | 1.17538 | ||||||||
\(537\) | − 16.1413i | − 0.696550i | ||||||||
\(538\) | − 19.6120i | − 0.845533i | ||||||||
\(539\) | 0.726656 | 0.0312993 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.6040 | 0.756854 | 0.378427 | − | 0.925631i | \(-0.376465\pi\) | ||||
0.378427 | + | 0.925631i | \(0.376465\pi\) | |||||||
\(542\) | − 39.0666i | − 1.67805i | ||||||||
\(543\) | 20.7546i | 0.890667i | ||||||||
\(544\) | −6.10138 | −0.261595 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.89730 | 0.166789 | ||||||||
\(547\) | − 19.9873i | − 0.854594i | −0.904111 | − | 0.427297i | \(-0.859466\pi\) | ||||
0.904111 | − | 0.427297i | \(-0.140534\pi\) | |||||||
\(548\) | − 1.23603i | − 0.0528005i | ||||||||
\(549\) | −4.59465 | −0.196095 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.29200 | −0.0550411 | ||||||||
\(552\) | 4.12994i | 0.175782i | ||||||||
\(553\) | 17.3306i | 0.736974i | ||||||||
\(554\) | 39.7546 | 1.68901 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.15198 | 0.133674 | ||||||||
\(557\) | 41.5933i | 1.76237i | 0.472775 | + | 0.881183i | \(0.343252\pi\) | ||||
−0.472775 | + | 0.881183i | \(0.656748\pi\) | |||||||
\(558\) | 3.89730i | 0.164986i | ||||||||
\(559\) | 14.4919 | 0.612944 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.64600 | 0.322814 | ||||||||
\(562\) | 7.31198i | 0.308437i | ||||||||
\(563\) | 2.28267i | 0.0962032i | 0.998842 | + | 0.0481016i | \(0.0153171\pi\) | ||||
−0.998842 | + | 0.0481016i | \(0.984683\pi\) | |||||||
\(564\) | 0.867993 | 0.0365491 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.6906 | −0.575458 | ||||||||
\(567\) | − 2.50466i | − 0.105186i | ||||||||
\(568\) | − 17.1035i | − 0.717645i | ||||||||
\(569\) | 2.37266 | 0.0994670 | 0.0497335 | − | 0.998763i | \(-0.484163\pi\) | ||||
0.0497335 | + | 0.998763i | \(0.484163\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.9053 | −1.33520 | −0.667598 | − | 0.744522i | \(-0.732677\pi\) | ||||
−0.667598 | + | 0.744522i | \(0.732677\pi\) | |||||||
\(572\) | 0.161312i | 0.00674479i | ||||||||
\(573\) | 3.31198i | 0.138360i | ||||||||
\(574\) | −2.17403 | −0.0907423 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.48262 | 0.353442 | ||||||||
\(577\) | − 3.28267i | − 0.136659i | −0.997663 | − | 0.0683297i | \(-0.978233\pi\) | ||||
0.997663 | − | 0.0683297i | \(-0.0217670\pi\) | |||||||
\(578\) | 56.5254i | 2.35115i | ||||||||
\(579\) | 2.13201 | 0.0886032 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.4787 | −0.642167 | ||||||||
\(582\) | 26.5340i | 1.09987i | ||||||||
\(583\) | − 12.0187i | − 0.497762i | ||||||||
\(584\) | 22.0586 | 0.912792 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.7492 | 1.14631 | ||||||||
\(587\) | − 26.3400i | − 1.08717i | −0.839355 | − | 0.543583i | \(-0.817067\pi\) | ||||
0.839355 | − | 0.543583i | \(-0.182933\pi\) | |||||||
\(588\) | 0.102703i | 0.00423539i | ||||||||
\(589\) | −5.08273 | −0.209430 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.9287 | 0.737487 | ||||||||
\(592\) | − 31.1465i | − 1.28011i | ||||||||
\(593\) | − 32.9694i | − 1.35389i | −0.736034 | − | 0.676945i | \(-0.763303\pi\) | ||||
0.736034 | − | 0.676945i | \(-0.236697\pi\) | |||||||
\(594\) | −1.36333 | −0.0559380 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.25130 | 0.0922167 | ||||||||
\(597\) | − 15.1600i | − 0.620457i | ||||||||
\(598\) | 2.20126i | 0.0900164i | ||||||||
\(599\) | −24.5454 | −1.00290 | −0.501448 | − | 0.865188i | \(-0.667199\pi\) | ||||
−0.501448 | + | 0.865188i | \(0.667199\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.70668 | −0.395944 | −0.197972 | − | 0.980208i | \(-0.563435\pi\) | ||||
−0.197972 | + | 0.980208i | \(0.563435\pi\) | |||||||
\(602\) | 43.3574i | 1.76712i | ||||||||
\(603\) | − 9.32131i | − 0.379593i | ||||||||
\(604\) | −1.39734 | −0.0568570 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.4147 | −0.463690 | ||||||||
\(607\) | − 1.73599i | − 0.0704615i | −0.999379 | − | 0.0352307i | \(-0.988783\pi\) | ||||
0.999379 | − | 0.0352307i | \(-0.0112166\pi\) | |||||||
\(608\) | 1.41882i | 0.0575408i | ||||||||
\(609\) | 1.82003 | 0.0737514 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.00933 | 0.283567 | ||||||||
\(612\) | 1.08066i | 0.0436829i | ||||||||
\(613\) | 12.0187i | 0.485429i | 0.970098 | + | 0.242715i | \(0.0780378\pi\) | ||||
−0.970098 | + | 0.242715i | \(0.921962\pi\) | |||||||
\(614\) | −34.9321 | −1.40974 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.31198 | −0.294608 | ||||||||
\(617\) | − 42.1587i | − 1.69724i | −0.528999 | − | 0.848622i | \(-0.677433\pi\) | ||||
0.528999 | − | 0.848622i | \(-0.322567\pi\) | |||||||
\(618\) | 3.47197i | 0.139663i | ||||||||
\(619\) | −9.03863 | −0.363293 | −0.181647 | − | 0.983364i | \(-0.558143\pi\) | ||||
−0.181647 | + | 0.983364i | \(0.558143\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.41468 | 0.0567691 | ||||||||
\(622\) | − 16.2800i | − 0.652770i | ||||||||
\(623\) | 8.64939i | 0.346530i | ||||||||
\(624\) | 4.21992 | 0.168932 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23.4474 | 0.937146 | ||||||||
\(627\) | − 1.77801i | − 0.0710068i | ||||||||
\(628\) | 0.0186574i | 0 0.000744512i | ||||||||
\(629\) | 64.4100 | 2.56819 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9614 | 0.436365 | 0.218183 | − | 0.975908i | \(-0.429987\pi\) | ||||
0.218183 | + | 0.975908i | \(0.429987\pi\) | |||||||
\(632\) | 20.1999i | 0.803511i | ||||||||
\(633\) | − 13.3213i | − 0.529474i | ||||||||
\(634\) | 31.0093 | 1.23154 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.69867 | 0.0673567 | ||||||||
\(637\) | 0.829359i | 0.0328604i | ||||||||
\(638\) | − 0.990671i | − 0.0392211i | ||||||||
\(639\) | −5.85866 | −0.231765 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −44.1587 | −1.74416 | −0.872081 | − | 0.489361i | \(-0.837230\pi\) | ||||
−0.872081 | + | 0.489361i | \(0.837230\pi\) | |||||||
\(642\) | 19.8573i | 0.783707i | ||||||||
\(643\) | 22.5840i | 0.890626i | 0.895375 | + | 0.445313i | \(0.146908\pi\) | ||||
−0.895375 | + | 0.445313i | \(0.853092\pi\) | |||||||
\(644\) | 0.500796 | 0.0197341 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.5340 | 0.729209 | ||||||||
\(647\) | 13.3561i | 0.525081i | 0.964921 | + | 0.262541i | \(0.0845604\pi\) | ||||
−0.964921 | + | 0.262541i | \(0.915440\pi\) | |||||||
\(648\) | − 2.91934i | − 0.114683i | ||||||||
\(649\) | 3.41468 | 0.134038 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.15999 | 0.280622 | ||||||||
\(652\) | − 0.609438i | − 0.0238674i | ||||||||
\(653\) | 37.5933i | 1.47114i | 0.677448 | + | 0.735570i | \(0.263086\pi\) | ||||
−0.677448 | + | 0.735570i | \(0.736914\pi\) | |||||||
\(654\) | −3.29200 | −0.128727 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.35400 | −0.0919082 | ||||||||
\(657\) | − 7.55602i | − 0.294788i | ||||||||
\(658\) | 20.9707i | 0.817523i | ||||||||
\(659\) | −7.00933 | −0.273045 | −0.136522 | − | 0.990637i | \(-0.543593\pi\) | ||||
−0.136522 | + | 0.990637i | \(0.543593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.6226 | 1.03550 | 0.517750 | − | 0.855532i | \(-0.326770\pi\) | ||||
0.517750 | + | 0.855532i | \(0.326770\pi\) | |||||||
\(662\) | − 34.4559i | − 1.33917i | ||||||||
\(663\) | 8.72666i | 0.338915i | ||||||||
\(664\) | −18.0415 | −0.700144 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11.4847 | −0.445023 | ||||||||
\(667\) | 1.02799i | 0.0398038i | ||||||||
\(668\) | 1.59597i | 0.0617498i | ||||||||
\(669\) | 12.2534 | 0.473743 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.59465 | 0.177374 | ||||||||
\(672\) | − 1.99868i | − 0.0771008i | ||||||||
\(673\) | 35.6960i | 1.37598i | 0.725720 | + | 0.687990i | \(0.241507\pi\) | ||||
−0.725720 | + | 0.687990i | \(0.758493\pi\) | |||||||
\(674\) | 24.1146 | 0.928859 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.65326 | 0.0635869 | ||||||||
\(677\) | − 33.2920i | − 1.27952i | −0.768577 | − | 0.639758i | \(-0.779035\pi\) | ||||
0.768577 | − | 0.639758i | \(-0.220965\pi\) | |||||||
\(678\) | 8.17997i | 0.314150i | ||||||||
\(679\) | 48.7474 | 1.87075 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.74531 | 0.335121 | ||||||||
\(682\) | − 3.89730i | − 0.149235i | ||||||||
\(683\) | − 36.1787i | − 1.38434i | −0.721736 | − | 0.692169i | \(-0.756655\pi\) | ||||
0.721736 | − | 0.692169i | \(-0.243345\pi\) | |||||||
\(684\) | 0.251297 | 0.00960857 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.3841 | −1.00735 | ||||||||
\(687\) | 11.4626i | 0.437327i | ||||||||
\(688\) | 46.9466i | 1.78982i | ||||||||
\(689\) | 13.7173 | 0.522589 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.3293 | 1.34399 | 0.671995 | − | 0.740555i | \(-0.265438\pi\) | ||||
0.671995 | + | 0.740555i | \(0.265438\pi\) | |||||||
\(692\) | 3.05936i | 0.116299i | ||||||||
\(693\) | 2.50466i | 0.0951443i | ||||||||
\(694\) | −27.4066 | −1.04034 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.12136 | 0.0804100 | ||||||||
\(697\) | − 4.86799i | − 0.184388i | ||||||||
\(698\) | − 14.9839i | − 0.567149i | ||||||||
\(699\) | −7.48469 | −0.283097 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.4006 | −1.86584 | −0.932918 | − | 0.360088i | \(-0.882747\pi\) | ||||
−0.932918 | + | 0.360088i | \(0.882747\pi\) | |||||||
\(702\) | − 1.55602i | − 0.0587280i | ||||||||
\(703\) | − 14.9780i | − 0.564904i | ||||||||
\(704\) | −8.48262 | −0.319701 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.8039 | 0.858237 | ||||||||
\(707\) | 20.9707i | 0.788684i | ||||||||
\(708\) | 0.482618i | 0.0181379i | ||||||||
\(709\) | 11.1027 | 0.416971 | 0.208485 | − | 0.978025i | \(-0.433147\pi\) | ||||
0.208485 | + | 0.978025i | \(0.433147\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.91934 | 0.259496 | ||||||||
\(712\) | 10.0814i | 0.377817i | ||||||||
\(713\) | 4.04409i | 0.151452i | ||||||||
\(714\) | −26.1086 | −0.977091 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.28135 | −0.0852582 | ||||||||
\(717\) | − 12.9066i | − 0.482007i | ||||||||
\(718\) | − 18.5322i | − 0.691614i | ||||||||
\(719\) | 43.9787 | 1.64013 | 0.820064 | − | 0.572271i | \(-0.193938\pi\) | ||||
0.820064 | + | 0.572271i | \(0.193938\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.37860 | 0.237551 | ||||||||
\(722\) | 21.5933i | 0.803621i | ||||||||
\(723\) | − 16.8773i | − 0.627674i | ||||||||
\(724\) | 2.93338 | 0.109018 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.36333 | 0.0505979 | ||||||||
\(727\) | 44.1880i | 1.63884i | 0.573193 | + | 0.819421i | \(0.305705\pi\) | ||||
−0.573193 | + | 0.819421i | \(0.694295\pi\) | |||||||
\(728\) | − 8.34542i | − 0.309302i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −97.0840 | −3.59078 | ||||||||
\(732\) | 0.649390i | 0.0240021i | ||||||||
\(733\) | − 47.3879i | − 1.75031i | −0.483840 | − | 0.875156i | \(-0.660758\pi\) | ||||
0.483840 | − | 0.875156i | \(-0.339242\pi\) | |||||||
\(734\) | −39.5347 | −1.45925 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.12889 | 0.0416115 | ||||||||
\(737\) | 9.32131i | 0.343355i | ||||||||
\(738\) | 0.867993i | 0.0319512i | ||||||||
\(739\) | 13.0407 | 0.479710 | 0.239855 | − | 0.970809i | \(-0.422900\pi\) | ||||
0.239855 | + | 0.970809i | \(0.422900\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.02930 | 0.0745484 | ||||||||
\(742\) | 41.0399i | 1.50662i | ||||||||
\(743\) | − 14.1800i | − 0.520213i | −0.965580 | − | 0.260106i | \(-0.916242\pi\) | ||||
0.965580 | − | 0.260106i | \(-0.0837576\pi\) | |||||||
\(744\) | 8.34542 | 0.305958 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −24.3854 | −0.892812 | ||||||||
\(747\) | 6.17997i | 0.226113i | ||||||||
\(748\) | − 1.08066i | − 0.0395127i | ||||||||
\(749\) | 36.4813 | 1.33300 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.1120 | 0.697408 | 0.348704 | − | 0.937233i | \(-0.386622\pi\) | ||||
0.348704 | + | 0.937233i | \(0.386622\pi\) | |||||||
\(752\) | 22.7067i | 0.828027i | ||||||||
\(753\) | 2.28267i | 0.0831852i | ||||||||
\(754\) | 1.13069 | 0.0411773 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.354000 | −0.0128748 | ||||||||
\(757\) | − 24.7347i | − 0.898997i | −0.893281 | − | 0.449498i | \(-0.851603\pi\) | ||||
0.893281 | − | 0.449498i | \(-0.148397\pi\) | |||||||
\(758\) | 32.4253i | 1.17774i | ||||||||
\(759\) | −1.41468 | −0.0513496 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.82003 | −0.355976 | −0.177988 | − | 0.984033i | \(-0.556959\pi\) | ||||
−0.177988 | + | 0.984033i | \(0.556959\pi\) | |||||||
\(762\) | 20.7253i | 0.750800i | ||||||||
\(763\) | 6.04796i | 0.218951i | ||||||||
\(764\) | 0.468102 | 0.0169353 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −43.2666 | −1.56328 | ||||||||
\(767\) | 3.89730i | 0.140723i | ||||||||
\(768\) | − 3.37473i | − 0.121775i | ||||||||
\(769\) | 15.3026 | 0.551828 | 0.275914 | − | 0.961182i | \(-0.411020\pi\) | ||||
0.275914 | + | 0.961182i | \(0.411020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.8667 | −0.967580 | ||||||||
\(772\) | − 0.301330i | − 0.0108451i | ||||||||
\(773\) | 5.36927i | 0.193119i | 0.995327 | + | 0.0965596i | \(0.0307838\pi\) | ||||
−0.995327 | + | 0.0965596i | \(0.969216\pi\) | |||||||
\(774\) | 17.3107 | 0.622219 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 56.8181 | 2.03965 | ||||||||
\(777\) | 21.0993i | 0.756934i | ||||||||
\(778\) | 35.1120i | 1.25883i | ||||||||
\(779\) | −1.13201 | −0.0405584 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.85866 | 0.209639 | ||||||||
\(782\) | − 14.7466i | − 0.527338i | ||||||||
\(783\) | − 0.726656i | − 0.0259686i | ||||||||
\(784\) | −2.68670 | −0.0959537 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 25.5560 | 0.911553 | ||||||||
\(787\) | − 15.4767i | − 0.551684i | −0.961203 | − | 0.275842i | \(-0.911043\pi\) | ||||
0.961203 | − | 0.275842i | \(-0.0889567\pi\) | |||||||
\(788\) | − 2.53397i | − 0.0902689i | ||||||||
\(789\) | −12.0187 | −0.427876 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.0280 | 0.534334 | ||||||||
\(792\) | 2.91934i | 0.103734i | ||||||||
\(793\) | 5.24404i | 0.186221i | ||||||||
\(794\) | 4.14265 | 0.147017 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.14265 | −0.0759444 | ||||||||
\(797\) | 43.6774i | 1.54713i | 0.633716 | + | 0.773566i | \(0.281529\pi\) | ||||
−0.633716 | + | 0.773566i | \(0.718471\pi\) | |||||||
\(798\) | 6.07133i | 0.214923i | ||||||||
\(799\) | −46.9567 | −1.66121 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.45331 | 0.122017 | ||||||||
\(802\) | 24.7853i | 0.875198i | ||||||||
\(803\) | 7.55602i | 0.266646i | ||||||||
\(804\) | −1.31744 | −0.0464624 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.44813 | 0.156679 | ||||||||
\(807\) | 14.3854i | 0.506389i | ||||||||
\(808\) | 24.4427i | 0.859890i | ||||||||
\(809\) | 26.9966 | 0.949150 | 0.474575 | − | 0.880215i | \(-0.342602\pi\) | ||||
0.474575 | + | 0.880215i | \(0.342602\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.2220 | −0.499402 | −0.249701 | − | 0.968323i | \(-0.580332\pi\) | ||||
−0.249701 | + | 0.968323i | \(0.580332\pi\) | |||||||
\(812\) | − 0.257236i | − 0.00902722i | ||||||||
\(813\) | 28.6553i | 1.00499i | ||||||||
\(814\) | 11.4847 | 0.402538 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −28.2700 | −0.989646 | ||||||||
\(817\) | 22.5760i | 0.789834i | ||||||||
\(818\) | − 28.0773i | − 0.981699i | ||||||||
\(819\) | −2.85866 | −0.0998898 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.7801 | 0.829930 | 0.414965 | − | 0.909837i | \(-0.363794\pi\) | ||||
0.414965 | + | 0.909837i | \(0.363794\pi\) | |||||||
\(822\) | − 11.9227i | − 0.415853i | ||||||||
\(823\) | − 1.84934i | − 0.0644638i | −0.999480 | − | 0.0322319i | \(-0.989738\pi\) | ||||
0.999480 | − | 0.0322319i | \(-0.0102615\pi\) | |||||||
\(824\) | 7.43466 | 0.258998 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.6600 | −0.405705 | ||||||||
\(827\) | − 15.6987i | − 0.545896i | −0.962029 | − | 0.272948i | \(-0.912001\pi\) | ||||
0.962029 | − | 0.272948i | \(-0.0879987\pi\) | |||||||
\(828\) | − 0.199945i | − 0.00694858i | ||||||||
\(829\) | 4.34128 | 0.150779 | 0.0753895 | − | 0.997154i | \(-0.475980\pi\) | ||||
0.0753895 | + | 0.997154i | \(0.475980\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.1600 | −1.01155 | ||||||||
\(832\) | − 9.68152i | − 0.335646i | ||||||||
\(833\) | − 5.55602i | − 0.192505i | ||||||||
\(834\) | 30.4040 | 1.05281 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.251297 | −0.00869128 | ||||||||
\(837\) | − 2.85866i | − 0.0988099i | ||||||||
\(838\) | 44.6154i | 1.54121i | ||||||||
\(839\) | −28.3013 | −0.977070 | −0.488535 | − | 0.872544i | \(-0.662469\pi\) | ||||
−0.488535 | + | 0.872544i | \(0.662469\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4720 | −0.981792 | ||||||||
\(842\) | − 44.3955i | − 1.52997i | ||||||||
\(843\) | − 5.36333i | − 0.184723i | ||||||||
\(844\) | −1.88278 | −0.0648080 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.37266 | 0.287858 | ||||||||
\(847\) | − 2.50466i | − 0.0860613i | ||||||||
\(848\) | 44.4372i | 1.52598i | ||||||||
\(849\) | 10.0420 | 0.344641 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.9173 | −0.408519 | ||||||||
\(852\) | 0.828041i | 0.0283682i | ||||||||
\(853\) | − 35.7653i | − 1.22458i | −0.790633 | − | 0.612290i | \(-0.790248\pi\) | ||||
0.790633 | − | 0.612290i | \(-0.209752\pi\) | |||||||
\(854\) | −15.6893 | −0.536875 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 42.5213 | 1.45335 | ||||||||
\(857\) | 24.7513i | 0.845487i | 0.906249 | + | 0.422743i | \(0.138933\pi\) | ||||
−0.906249 | + | 0.422743i | \(0.861067\pi\) | |||||||
\(858\) | 1.55602i | 0.0531215i | ||||||||
\(859\) | 10.8039 | 0.368625 | 0.184313 | − | 0.982868i | \(-0.440994\pi\) | ||||
0.184313 | + | 0.982868i | \(0.440994\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.59465 | 0.0543455 | ||||||||
\(862\) | − 2.48130i | − 0.0845134i | ||||||||
\(863\) | − 16.6027i | − 0.565161i | −0.959244 | − | 0.282581i | \(-0.908810\pi\) | ||||
0.959244 | − | 0.282581i | \(-0.0911904\pi\) | |||||||
\(864\) | −0.797984 | −0.0271480 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −40.6654 | −1.38187 | ||||||||
\(867\) | − 41.4613i | − 1.40810i | ||||||||
\(868\) | − 1.01197i | − 0.0343484i | ||||||||
\(869\) | −6.91934 | −0.234723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.6387 | −0.360480 | ||||||||
\(872\) | 7.04928i | 0.238719i | ||||||||
\(873\) | − 19.4626i | − 0.658711i | ||||||||
\(874\) | −3.42920 | −0.115994 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.06794 | −0.0360823 | ||||||||
\(877\) | 11.1600i | 0.376846i | 0.982088 | + | 0.188423i | \(0.0603376\pi\) | ||||
−0.982088 | + | 0.188423i | \(0.939662\pi\) | |||||||
\(878\) | 24.8426i | 0.838396i | ||||||||
\(879\) | −20.3540 | −0.686523 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.5254 | 1.83701 | 0.918504 | − | 0.395413i | \(-0.129398\pi\) | ||||
0.918504 | + | 0.395413i | \(0.129398\pi\) | |||||||
\(882\) | 0.990671i | 0.0333576i | ||||||||
\(883\) | 12.7746i | 0.429900i | 0.976625 | + | 0.214950i | \(0.0689589\pi\) | ||||
−0.976625 | + | 0.214950i | \(0.931041\pi\) | |||||||
\(884\) | 1.23339 | 0.0414835 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.3514 | −1.01967 | ||||||||
\(887\) | 47.1053i | 1.58164i | 0.612049 | + | 0.790820i | \(0.290345\pi\) | ||||
−0.612049 | + | 0.790820i | \(0.709655\pi\) | |||||||
\(888\) | 24.5926i | 0.825273i | ||||||||
\(889\) | 38.0759 | 1.27703 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | − 1.73184i | − 0.0579864i | ||||||||
\(893\) | 10.9193i | 0.365402i | ||||||||
\(894\) | 21.7160 | 0.726292 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 24.9681 | 0.834124 | ||||||||
\(897\) | − 1.61462i | − 0.0539108i | ||||||||
\(898\) | 35.2775i | 1.17722i | ||||||||
\(899\) | 2.07727 | 0.0692807 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −91.8947 | −3.06146 | ||||||||
\(902\) | − 0.867993i | − 0.0289010i | ||||||||
\(903\) | − 31.8026i | − 1.05832i | ||||||||
\(904\) | 17.5161 | 0.582576 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.4787 | −0.447801 | ||||||||
\(907\) | 24.7826i | 0.822894i | 0.911434 | + | 0.411447i | \(0.134976\pi\) | ||||
−0.911434 | + | 0.411447i | \(0.865024\pi\) | |||||||
\(908\) | − 1.23603i | − 0.0410191i | ||||||||
\(909\) | 8.37266 | 0.277704 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.08273 | −0.201530 | −0.100765 | − | 0.994910i | \(-0.532129\pi\) | ||||
−0.100765 | + | 0.994910i | \(0.532129\pi\) | |||||||
\(912\) | 6.57392i | 0.217684i | ||||||||
\(913\) | − 6.17997i | − 0.204527i | ||||||||
\(914\) | 14.2640 | 0.471812 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.62009 | 0.0535291 | ||||||||
\(917\) | − 46.9507i | − 1.55045i | ||||||||
\(918\) | 10.4240i | 0.344044i | ||||||||
\(919\) | −17.9953 | −0.593610 | −0.296805 | − | 0.954938i | \(-0.595921\pi\) | ||||
−0.296805 | + | 0.954938i | \(0.595921\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.6226 | 0.844295 | ||||||||
\(922\) | − 16.1400i | − 0.531543i | ||||||||
\(923\) | 6.68670i | 0.220096i | ||||||||
\(924\) | 0.354000 | 0.0116457 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 37.8387 | 1.24346 | ||||||||
\(927\) | − 2.54669i | − 0.0836442i | ||||||||
\(928\) | − 0.579860i | − 0.0190348i | ||||||||
\(929\) | 16.7453 | 0.549396 | 0.274698 | − | 0.961531i | \(-0.411422\pi\) | ||||
0.274698 | + | 0.961531i | \(0.411422\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.29200 | −0.0423436 | ||||||||
\(932\) | 1.05786i | 0.0346513i | ||||||||
\(933\) | 11.9414i | 0.390944i | ||||||||
\(934\) | −28.3973 | −0.929187 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.33195 | −0.108908 | ||||||||
\(937\) | 31.5853i | 1.03185i | 0.856635 | + | 0.515924i | \(0.172551\pi\) | ||||
−0.856635 | + | 0.515924i | \(0.827449\pi\) | |||||||
\(938\) | − 31.8293i | − 1.03926i | ||||||||
\(939\) | −17.1986 | −0.561256 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.8421 | −0.483838 | −0.241919 | − | 0.970296i | \(-0.577777\pi\) | ||||
−0.241919 | + | 0.970296i | \(0.577777\pi\) | |||||||
\(942\) | 0.179969i | 0.00586372i | ||||||||
\(943\) | 0.900687i | 0.0293304i | ||||||||
\(944\) | −12.6253 | −0.410918 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.3107 | −0.562818 | ||||||||
\(947\) | − 2.68802i | − 0.0873490i | −0.999046 | − | 0.0436745i | \(-0.986094\pi\) | ||||
0.999046 | − | 0.0436745i | \(-0.0139065\pi\) | |||||||
\(948\) | − 0.977953i | − 0.0317624i | ||||||||
\(949\) | −8.62395 | −0.279945 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.7453 | −0.737567 | ||||||||
\(952\) | 55.9074i | 1.81197i | ||||||||
\(953\) | 14.2700i | 0.462249i | 0.972924 | + | 0.231125i | \(0.0742405\pi\) | ||||
−0.972924 | + | 0.231125i | \(0.925760\pi\) | |||||||
\(954\) | 16.3854 | 0.530496 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.82417 | −0.0589980 | ||||||||
\(957\) | 0.726656i | 0.0234895i | ||||||||
\(958\) | 3.61199i | 0.116698i | ||||||||
\(959\) | −21.9041 | −0.707320 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.8280 | −0.736388 | ||||||||
\(962\) | 13.1079i | 0.422615i | ||||||||
\(963\) | − 14.5653i | − 0.469362i | ||||||||
\(964\) | −2.38538 | −0.0768278 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.83068 | 0.155425 | ||||||||
\(967\) | − 10.0586i | − 0.323463i | −0.986835 | − | 0.161732i | \(-0.948292\pi\) | ||||
0.986835 | − | 0.161732i | \(-0.0517079\pi\) | |||||||
\(968\) | − 2.91934i | − 0.0938313i | ||||||||
\(969\) | −13.5946 | −0.436723 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.4520 | −0.431695 | −0.215848 | − | 0.976427i | \(-0.569251\pi\) | ||||
−0.215848 | + | 0.976427i | \(0.569251\pi\) | |||||||
\(972\) | 0.141336i | 0.00453336i | ||||||||
\(973\) | − 55.8573i | − 1.79070i | ||||||||
\(974\) | −55.2639 | −1.77077 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.9880 | −0.543774 | ||||||||
\(977\) | 32.8294i | 1.05030i | 0.851008 | + | 0.525152i | \(0.175992\pi\) | ||||
−0.851008 | + | 0.525152i | \(0.824008\pi\) | |||||||
\(978\) | − 5.87864i | − 0.187978i | ||||||||
\(979\) | −3.45331 | −0.110368 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.41468 | 0.0770948 | ||||||||
\(982\) | 21.9787i | 0.701369i | ||||||||
\(983\) | 43.7746i | 1.39619i | 0.716003 | + | 0.698097i | \(0.245969\pi\) | ||||
−0.716003 | + | 0.698097i | \(0.754031\pi\) | |||||||
\(984\) | 1.85866 | 0.0592520 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.57467 | −0.241227 | ||||||||
\(987\) | − 15.3820i | − 0.489614i | ||||||||
\(988\) | − 0.286814i | − 0.00912477i | ||||||||
\(989\) | 17.9627 | 0.571180 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.1507 | 1.33896 | 0.669480 | − | 0.742830i | \(-0.266517\pi\) | ||||
0.669480 | + | 0.742830i | \(0.266517\pi\) | |||||||
\(992\) | − 2.28117i | − 0.0724271i | ||||||||
\(993\) | 25.2733i | 0.802025i | ||||||||
\(994\) | −20.0055 | −0.634535 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.873453 | 0.0276764 | ||||||||
\(997\) | 17.4347i | 0.552161i | 0.961135 | + | 0.276081i | \(0.0890357\pi\) | ||||
−0.961135 | + | 0.276081i | \(0.910964\pi\) | |||||||
\(998\) | − 38.2640i | − 1.21123i | ||||||||
\(999\) | 8.42401 | 0.266524 |
(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 | 825.2.c.f.199.3 | 6 | ||
3.2 | odd | 2 | 2475.2.c.q.199.4 | 6 | |||
5.2 | odd | 4 | 825.2.a.m.1.2 | yes | 3 | ||
5.3 | odd | 4 | 825.2.a.i.1.2 | ✓ | 3 | ||
5.4 | even | 2 | inner | 825.2.c.f.199.4 | 6 | ||
15.2 | even | 4 | 2475.2.a.z.1.2 | 3 | |||
15.8 | even | 4 | 2475.2.a.bd.1.2 | 3 | |||
15.14 | odd | 2 | 2475.2.c.q.199.3 | 6 | |||
55.32 | even | 4 | 9075.2.a.cd.1.2 | 3 | |||
55.43 | even | 4 | 9075.2.a.cj.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.a.i.1.2 | ✓ | 3 | 5.3 | odd | 4 | ||
825.2.a.m.1.2 | yes | 3 | 5.2 | odd | 4 | ||
825.2.c.f.199.3 | 6 | 1.1 | even | 1 | trivial | ||
825.2.c.f.199.4 | 6 | 5.4 | even | 2 | inner | ||
2475.2.a.z.1.2 | 3 | 15.2 | even | 4 | |||
2475.2.a.bd.1.2 | 3 | 15.8 | even | 4 | |||
2475.2.c.q.199.3 | 6 | 15.14 | odd | 2 | |||
2475.2.c.q.199.4 | 6 | 3.2 | odd | 2 | |||
9075.2.a.cd.1.2 | 3 | 55.32 | even | 4 | |||
9075.2.a.cj.1.2 | 3 | 55.43 | even | 4 |