Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 24x^{10} + 188x^{8} + 530x^{6} + 508x^{4} + 80x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 460) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.12 | ||
Root | \(-3.16223i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.f.369.1 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.21923i | 1.85862i | 0.369298 | + | 0.929311i | \(0.379598\pi\) | ||||
−0.369298 | + | 0.929311i | \(0.620402\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.59013 | + | 1.57210i | 0.711126 | + | 0.703065i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.43185i | 0.919152i | 0.888138 | + | 0.459576i | \(0.151999\pi\) | ||||
−0.888138 | + | 0.459576i | \(0.848001\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.36343 | −2.45448 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.884969 | 0.266828 | 0.133414 | − | 0.991060i | \(-0.457406\pi\) | ||||
0.133414 | + | 0.991060i | \(0.457406\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.10522i | − | 1.41593i | −0.706245 | − | 0.707967i | \(-0.749612\pi\) | ||
0.706245 | − | 0.707967i | \(-0.250388\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.06095 | + | 5.11898i | −1.30673 | + | 1.32171i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.366626i | 0.0889198i | 0.999011 | + | 0.0444599i | \(0.0141567\pi\) | ||||
−0.999011 | + | 0.0444599i | \(0.985843\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.79847 | −0.642014 | −0.321007 | − | 0.947077i | \(-0.604021\pi\) | ||||
−0.321007 | + | 0.947077i | \(0.604021\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.82867 | −1.70836 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0570016 | + | 4.99968i | 0.0114003 | + | 0.999935i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 14.0469i | − | 2.70332i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.02431 | −1.49008 | −0.745038 | − | 0.667022i | \(-0.767569\pi\) | ||||
−0.745038 | + | 0.667022i | \(0.767569\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.24179 | −1.30066 | −0.650332 | − | 0.759650i | \(-0.725370\pi\) | ||||
−0.650332 | + | 0.759650i | \(0.725370\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.84892i | 0.495933i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.82311 | + | 3.86694i | −0.646223 | + | 0.653633i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.10036i | − | 0.509697i | −0.966981 | − | 0.254848i | \(-0.917974\pi\) | ||
0.966981 | − | 0.254848i | \(-0.0820256\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.4349 | 2.63169 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.47185 | −0.542212 | −0.271106 | − | 0.962550i | \(-0.587389\pi\) | ||||
−0.271106 | + | 0.962550i | \(0.587389\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.56841i | 1.30667i | 0.757069 | + | 0.653335i | \(0.226631\pi\) | ||||
−0.757069 | + | 0.653335i | \(0.773369\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.7088 | − | 11.5760i | −1.74544 | − | 1.72566i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.25528i | − | 0.766561i | −0.923632 | − | 0.383281i | \(-0.874794\pi\) | ||
0.923632 | − | 0.383281i | \(-0.125206\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.08612 | 0.155160 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.18025 | −0.165268 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.6413i | 1.59905i | 0.600632 | + | 0.799526i | \(0.294916\pi\) | ||||
−0.600632 | + | 0.799526i | \(0.705084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.40721 | + | 1.39126i | 0.189749 | + | 0.187598i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 9.00892i | − | 1.19326i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.33209 | −1.21493 | −0.607467 | − | 0.794345i | \(-0.707814\pi\) | ||||
−0.607467 | + | 0.794345i | \(0.707814\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.46699 | 0.699976 | 0.349988 | − | 0.936754i | \(-0.386186\pi\) | ||||
0.349988 | + | 0.936754i | \(0.386186\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 17.9067i | − | 2.25604i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.02592 | − | 8.11795i | 0.995493 | − | 1.00691i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.49020i | − | 0.182057i | −0.995848 | − | 0.0910285i | \(-0.970985\pi\) | ||
0.995848 | − | 0.0910285i | \(-0.0290154\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.21923 | −0.387549 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.29949 | −0.984969 | −0.492484 | − | 0.870321i | \(-0.663911\pi\) | ||||
−0.492484 | + | 0.870321i | \(0.663911\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2409i | 1.19860i | 0.800523 | + | 0.599302i | \(0.204555\pi\) | ||||
−0.800523 | + | 0.599302i | \(0.795445\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16.0951 | + | 0.183501i | −1.85850 | + | 0.0211889i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.15211i | 0.245256i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.06522 | 0.682391 | 0.341195 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341195 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23.1298 | 2.56998 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.2520i | 1.78389i | 0.452148 | + | 0.891943i | \(0.350658\pi\) | ||||
−0.452148 | + | 0.891943i | \(0.649342\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.576373 | + | 0.582981i | −0.0625164 | + | 0.0632332i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 25.8321i | − | 2.76949i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.6033 | 1.86594 | 0.932972 | − | 0.359949i | \(-0.117206\pi\) | ||||
0.932972 | + | 0.359949i | \(0.117206\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.4151 | 1.30146 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 23.3130i | − | 2.41744i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.44992 | − | 4.39948i | −0.456553 | − | 0.451377i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.55618i | − | 0.665679i | −0.942984 | − | 0.332839i | \(-0.891993\pi\) | ||
0.942984 | − | 0.332839i | \(-0.108007\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.51641 | −0.654924 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4912 | 1.34243 | 0.671213 | − | 0.741265i | \(-0.265774\pi\) | ||||
0.671213 | + | 0.741265i | \(0.265774\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.5460i | 1.23619i | 0.786103 | + | 0.618096i | \(0.212096\pi\) | ||||
−0.786103 | + | 0.618096i | \(0.787904\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.4486 | − | 12.3075i | −1.21486 | − | 1.20108i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.46269i | − | 0.141404i | −0.997497 | − | 0.0707020i | \(-0.977476\pi\) | ||
0.997497 | − | 0.0707020i | \(-0.0225239\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.2173 | 1.84069 | 0.920343 | − | 0.391113i | \(-0.127910\pi\) | ||||
0.920343 | + | 0.391113i | \(0.127910\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.98078 | 0.947334 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.834901i | 0.0785409i | 0.999229 | + | 0.0392705i | \(0.0125034\pi\) | ||||
−0.999229 | + | 0.0392705i | \(0.987497\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.57210 | + | 1.59013i | −0.146599 | + | 0.148280i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 37.5920i | 3.47538i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.891578 | −0.0817308 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2168 | −0.928803 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 11.1767i | − | 1.00777i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.76935 | + | 8.03973i | −0.694912 | + | 0.719095i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.87453i | − | 0.698751i | −0.936983 | − | 0.349376i | \(-0.886394\pi\) | ||
0.936983 | − | 0.349376i | \(-0.113606\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −27.5837 | −2.42861 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.8740 | 1.12481 | 0.562403 | − | 0.826863i | \(-0.309877\pi\) | ||||
0.562403 | + | 0.826863i | \(0.309877\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.80546i | − | 0.590108i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 22.0831 | − | 22.3363i | 1.90061 | − | 1.92240i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.26675i | 0.279097i | 0.990215 | + | 0.139549i | \(0.0445651\pi\) | ||||
−0.990215 | + | 0.139549i | \(0.955435\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.5578 | −1.06514 | −0.532570 | − | 0.846386i | \(-0.678774\pi\) | ||||
−0.532570 | + | 0.846386i | \(0.678774\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.9179 | 1.42475 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.51797i | − | 0.377811i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.7597 | − | 12.6150i | −1.05963 | − | 1.04762i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.49647i | 0.288384i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.188265 | 0.0154233 | 0.00771164 | − | 0.999970i | \(-0.497545\pi\) | ||||
0.00771164 | + | 0.999970i | \(0.497545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.6708 | 1.51941 | 0.759704 | − | 0.650269i | \(-0.225344\pi\) | ||||
0.759704 | + | 0.650269i | \(0.225344\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.69962i | − | 0.218252i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.5154 | − | 11.3848i | −0.924936 | − | 0.914451i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0277i | 1.59839i | 0.601074 | + | 0.799193i | \(0.294740\pi\) | ||||
−0.601074 | + | 0.799193i | \(0.705260\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −37.4759 | −2.97203 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.43185 | −0.191656 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.35607i | 0.262867i | 0.991325 | + | 0.131434i | \(0.0419580\pi\) | ||||
−0.991325 | + | 0.131434i | \(0.958042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.47878 | + | 4.53014i | −0.348673 | + | 0.352671i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.57745i | 0.199449i | 0.995015 | + | 0.0997246i | \(0.0317962\pi\) | ||||
−0.995015 | + | 0.0997246i | \(0.968204\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0633 | −1.00487 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.6064 | 1.57581 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.4182i | 1.47634i | 0.674615 | + | 0.738170i | \(0.264310\pi\) | ||||
−0.674615 | + | 0.738170i | \(0.735690\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.1584 | + | 0.138619i | −0.919092 | + | 0.0104786i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 30.0421i | − | 2.25810i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.3628 | −1.52199 | −0.760993 | − | 0.648760i | \(-0.775288\pi\) | ||||
−0.760993 | + | 0.648760i | \(0.775288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.5629 | −1.67709 | −0.838543 | − | 0.544835i | \(-0.816592\pi\) | ||||
−0.838543 | + | 0.544835i | \(0.816592\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.5995i | 1.30099i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.87408 | − | 4.92997i | 0.358350 | − | 0.362459i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.324453i | 0.0237263i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 34.1598 | 2.48476 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.6554 | 1.20514 | 0.602571 | − | 0.798065i | \(-0.294143\pi\) | ||||
0.602571 | + | 0.798065i | \(0.294143\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 14.5214i | − | 1.04527i | −0.852556 | − | 0.522636i | \(-0.824949\pi\) | ||
0.852556 | − | 0.522636i | \(-0.175051\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 26.1335 | + | 25.8373i | 1.87146 | + | 1.85025i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 13.3479i | − | 0.950995i | −0.879717 | − | 0.475498i | \(-0.842268\pi\) | ||
0.879717 | − | 0.475498i | \(-0.157732\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7856 | 1.33168 | 0.665838 | − | 0.746097i | \(-0.268074\pi\) | ||||
0.665838 | + | 0.746097i | \(0.268074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.79730 | 0.338375 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 19.5139i | − | 1.36961i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.52068 | − | 5.45810i | −0.385581 | − | 0.381210i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 7.36343i | − | 0.511794i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.47656 | −0.171307 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.1078 | −1.17775 | −0.588874 | − | 0.808225i | \(-0.700429\pi\) | ||||
−0.588874 | + | 0.808225i | \(0.700429\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 26.7180i | − | 1.83068i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.4704 | + | 13.6249i | −0.918674 | + | 0.929207i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 17.6109i | − | 1.19551i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −32.9677 | −2.22775 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.87171 | 0.125905 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.5184i | − | 0.905262i | −0.891698 | − | 0.452631i | \(-0.850485\pi\) | ||
0.891698 | − | 0.452631i | \(-0.149515\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.419727 | − | 36.8147i | −0.0279818 | − | 2.45432i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 8.29581i | − | 0.550612i | −0.961357 | − | 0.275306i | \(-0.911221\pi\) | ||
0.961357 | − | 0.275306i | \(-0.0887792\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.22318 | 0.411239 | 0.205620 | − | 0.978632i | \(-0.434079\pi\) | ||||
0.205620 | + | 0.978632i | \(0.434079\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.92813 | −0.455838 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.6347i | 0.893242i | 0.894723 | + | 0.446621i | \(0.147373\pi\) | ||||
−0.894723 | + | 0.446621i | \(0.852627\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.26183 | − | 8.35656i | 0.538942 | − | 0.545122i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.5253i | 1.26831i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.5281 | 0.745693 | 0.372847 | − | 0.927893i | \(-0.378382\pi\) | ||||
0.372847 | + | 0.927893i | \(0.378382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.5952 | −1.13341 | −0.566704 | − | 0.823921i | \(-0.691782\pi\) | ||||
−0.566704 | + | 0.823921i | \(0.691782\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 32.3195i | 2.07329i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.72707 | + | 1.70749i | 0.110338 | + | 0.109087i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.2868i | 0.909049i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −52.3188 | −3.31557 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.5471 | −0.791968 | −0.395984 | − | 0.918257i | \(-0.629596\pi\) | ||||
−0.395984 | + | 0.918257i | \(0.629596\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.884969i | 0.0556375i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.87675 | − | 1.85547i | −0.117527 | − | 0.116194i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.88072i | 0.304451i | 0.988346 | + | 0.152225i | \(0.0486439\pi\) | ||||
−0.988346 | + | 0.152225i | \(0.951356\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.53961 | 0.468489 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 59.0864 | 3.65736 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 11.6045i | − | 0.715566i | −0.933805 | − | 0.357783i | \(-0.883533\pi\) | ||
0.933805 | − | 0.357783i | \(-0.116467\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.3012 | + | 18.5111i | −1.12424 | + | 1.13713i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 56.6690i | 3.46808i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.04327 | 0.368465 | 0.184232 | − | 0.982883i | \(-0.441020\pi\) | ||||
0.184232 | + | 0.982883i | \(0.441020\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.93401 | −0.238974 | −0.119487 | − | 0.992836i | \(-0.538125\pi\) | ||||
−0.119487 | + | 0.992836i | \(0.538125\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 39.9671i | 2.41892i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0504447 | + | 4.42456i | 0.00304193 | + | 0.266811i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.92174i | 0.475971i | 0.971269 | + | 0.237986i | \(0.0764871\pi\) | ||||
−0.971269 | + | 0.237986i | \(0.923513\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 53.3244 | 3.19245 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00419 | −0.358180 | −0.179090 | − | 0.983833i | \(-0.557315\pi\) | ||||
−0.179090 | + | 0.983833i | \(0.557315\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.65299i | 0.454923i | 0.973787 | + | 0.227461i | \(0.0730426\pi\) | ||||
−0.973787 | + | 0.227461i | \(0.926957\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.1629 | − | 14.3253i | 0.838940 | − | 0.848559i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 8.44301i | − | 0.498375i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8656 | 0.992093 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.1058 | 1.23725 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.5480i | 0.791485i | 0.918361 | + | 0.395743i | \(0.129513\pi\) | ||||
−0.918361 | + | 0.395743i | \(0.870487\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.8392 | − | 14.6710i | −0.863971 | − | 0.854177i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 12.4310i | − | 0.721323i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.10522 | 0.295243 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.8371 | −1.20103 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 43.4313i | 2.49506i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.69320 | + | 8.59466i | 0.497771 | + | 0.492129i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.0870i | − | 0.575697i | −0.957676 | − | 0.287848i | \(-0.907060\pi\) | ||
0.957676 | − | 0.287848i | \(-0.0929399\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −40.3883 | −2.29761 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.2481 | 1.60180 | 0.800902 | − | 0.598795i | \(-0.204354\pi\) | ||||
0.800902 | + | 0.598795i | \(0.204354\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.4504i | 0.816786i | 0.912806 | + | 0.408393i | \(0.133911\pi\) | ||||
−0.912806 | + | 0.408393i | \(0.866089\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 28.1512 | − | 28.4740i | 1.58614 | − | 1.60433i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.7835i | 0.830324i | 0.909748 | + | 0.415162i | \(0.136275\pi\) | ||||
−0.909748 | + | 0.415162i | \(0.863725\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.10127 | −0.397595 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.70875 | 0.262817 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.02599i | − | 0.0570877i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.5245 | − | 0.291006i | 1.41584 | − | 0.0161421i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 61.8649i | 3.42114i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.7800 | 0.704586 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.1494 | 1.10751 | 0.553757 | − | 0.832679i | \(-0.313194\pi\) | ||||
0.553757 | + | 0.832679i | \(0.313194\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.8293i | 1.25104i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.34275 | − | 2.36961i | 0.127998 | − | 0.129465i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.0660i | 1.31096i | 0.755214 | + | 0.655479i | \(0.227533\pi\) | ||||
−0.755214 | + | 0.655479i | \(0.772467\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.68774 | −0.145978 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.40876 | −0.347054 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.6642i | 1.06177i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.11898 | − | 5.06095i | −0.275597 | − | 0.272472i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.3788i | 1.41609i | 0.706168 | + | 0.708045i | \(0.250422\pi\) | ||||
−0.706168 | + | 0.708045i | \(0.749578\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.535518 | −0.0286656 | −0.0143328 | − | 0.999897i | \(-0.504562\pi\) | ||||
−0.0143328 | + | 0.999897i | \(0.504562\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −71.7124 | −3.82773 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.27606i | 0.280816i | 0.990094 | + | 0.140408i | \(0.0448415\pi\) | ||||
−0.990094 | + | 0.140408i | \(0.955159\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.1972 | − | 13.0476i | −0.700437 | − | 0.692497i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 2.87019i | − | 0.151907i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.4351 | 1.07852 | 0.539261 | − | 0.842139i | \(-0.318704\pi\) | ||||
0.539261 | + | 0.842139i | \(0.318704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.1685 | −0.587818 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 32.8903i | − | 1.72629i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.0997 | + | 16.2843i | −0.842696 | + | 0.852359i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 12.4382i | − | 0.649268i | −0.945840 | − | 0.324634i | \(-0.894759\pi\) | ||
0.945840 | − | 0.324634i | \(-0.105241\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 25.5647 | 1.33085 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.3098 | −1.46977 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.99999i | − | 0.155334i | −0.996979 | − | 0.0776669i | \(-0.975253\pi\) | ||
0.996979 | − | 0.0776669i | \(-0.0247471\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.8817 | − | 25.0113i | −1.33653 | − | 1.29158i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40.9659i | 2.10985i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.02165 | −0.155212 | −0.0776059 | − | 0.996984i | \(-0.524728\pi\) | ||||
−0.0776059 | + | 0.996984i | \(0.524728\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.3499 | 1.29871 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.15719i | 0.416813i | 0.978042 | + | 0.208406i | \(0.0668277\pi\) | ||||
−0.978042 | + | 0.208406i | \(0.933172\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.38333 | + | 3.42213i | −0.172431 | + | 0.174408i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 63.0929i | − | 3.20719i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.7789 | −0.597214 | −0.298607 | − | 0.954376i | \(-0.596522\pi\) | ||||
−0.298607 | + | 0.954376i | \(0.596522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.366626 | −0.0185411 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 41.4443i | 2.09059i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.64447 | + | 9.53514i | 0.485266 | + | 0.479765i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.7004i | − | 0.838167i | −0.907948 | − | 0.419083i | \(-0.862351\pi\) | ||
0.907948 | − | 0.419083i | \(-0.137649\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.9083 | 1.09679 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.99936 | 0.499344 | 0.249672 | − | 0.968330i | \(-0.419677\pi\) | ||||
0.249672 | + | 0.968330i | \(0.419677\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.9710i | 1.84165i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 36.7793 | + | 36.3624i | 1.82758 | + | 1.80686i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.74373i | − | 0.136002i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.20305 | −0.108934 | −0.0544668 | − | 0.998516i | \(-0.517346\pi\) | ||||
−0.0544668 | + | 0.998516i | \(0.517346\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.5164 | −0.518736 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 22.6942i | − | 1.11671i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.5497 | + | 25.8427i | −1.25419 | + | 1.26857i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 40.4264i | − | 1.97969i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.12814 | 0.201673 | 0.100836 | − | 0.994903i | \(-0.467848\pi\) | ||||
0.100836 | + | 0.994903i | \(0.467848\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7354 | −0.766899 | −0.383449 | − | 0.923562i | \(-0.625264\pi\) | ||||
−0.383449 | + | 0.923562i | \(0.625264\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 38.6969i | 1.88151i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.83301 | + | 0.0208983i | −0.0889140 | + | 0.00101372i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.2949i | 0.643385i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.5444 | 0.702209 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.35158 | 0.0651034 | 0.0325517 | − | 0.999470i | \(-0.489637\pi\) | ||||
0.0325517 | + | 0.999470i | \(0.489637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 39.4114i | − | 1.89399i | −0.321244 | − | 0.946996i | \(-0.604101\pi\) | ||
0.321244 | − | 0.946996i | \(-0.395899\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 40.6106 | − | 41.0763i | 1.94713 | − | 1.96946i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.79847i | − | 0.133869i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1059 | 0.482326 | 0.241163 | − | 0.970485i | \(-0.422471\pi\) | ||||
0.241163 | + | 0.970485i | \(0.422471\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.99756 | −0.380836 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.25526i | 0.297197i | 0.988898 | + | 0.148598i | \(0.0474761\pi\) | ||||
−0.988898 | + | 0.148598i | \(0.952524\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.9914 | + | 27.6741i | 1.32692 | + | 1.31188i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.606068i | 0.0286660i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.28779 | −0.107968 | −0.0539839 | − | 0.998542i | \(-0.517192\pi\) | ||||
−0.0539839 | + | 0.998542i | \(0.517192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.07248 | −0.144677 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 60.1055i | 2.82400i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.7416 | + | 19.5178i | 0.925501 | + | 0.915010i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 14.3062i | − | 0.669217i | −0.942357 | − | 0.334609i | \(-0.891396\pi\) | ||
0.942357 | − | 0.334609i | \(-0.108604\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.14995 | 0.240379 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.38995 | −0.111311 | −0.0556556 | − | 0.998450i | \(-0.517725\pi\) | ||||
−0.0556556 | + | 0.998450i | \(0.517725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 9.52232i | − | 0.442540i | −0.975213 | − | 0.221270i | \(-0.928980\pi\) | ||
0.975213 | − | 0.221270i | \(-0.0710202\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 36.6503 | − | 37.0706i | 1.69962 | − | 1.71911i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.14501i | 0.284357i | 0.989841 | + | 0.142178i | \(0.0454107\pi\) | ||||
−0.989841 | + | 0.142178i | \(0.954589\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.62394 | 0.167338 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −64.4738 | −2.97080 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.58278i | 0.348657i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.159518 | − | 13.9915i | −0.00731917 | − | 0.641972i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 85.7197i | − | 3.92483i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.40986 | −0.0644180 | −0.0322090 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322090 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.8281 | −0.721697 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 7.82867i | − | 0.356217i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.3070 | − | 10.4251i | 0.468015 | − | 0.473382i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 31.2993i | − | 1.41831i | −0.705054 | − | 0.709154i | \(-0.749077\pi\) | ||
0.705054 | − | 0.709154i | \(-0.250923\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.8039 | −0.488571 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.9254 | 1.17000 | 0.584999 | − | 0.811034i | \(-0.301095\pi\) | ||||
0.584999 | + | 0.811034i | \(0.301095\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.94192i | − | 0.132497i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.3619 | − | 10.2444i | −0.465733 | − | 0.460454i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 20.1831i | − | 0.905336i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.04562 | −0.360172 | −0.180086 | − | 0.983651i | \(-0.557638\pi\) | ||||
−0.180086 | + | 0.983651i | \(0.557638\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.29740 | −0.370701 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5.50490i | − | 0.245451i | −0.992441 | − | 0.122726i | \(-0.960836\pi\) | ||
0.992441 | − | 0.122726i | \(-0.0391635\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.4527 | + | 21.2095i | 0.954634 | + | 0.943812i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 42.0538i | − | 1.86767i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.26586 | 0.366378 | 0.183189 | − | 0.983078i | \(-0.441358\pi\) | ||||
0.183189 | + | 0.983078i | \(0.441358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.9043 | −1.10170 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 39.3098i | 1.73557i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.7235 | + | 19.9497i | −0.869122 | + | 0.879088i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.65076i | − | 0.204540i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −62.5116 | −2.74396 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.9776 | 0.524747 | 0.262374 | − | 0.964966i | \(-0.415495\pi\) | ||||
0.262374 | + | 0.964966i | \(0.415495\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 0.711546i | − | 0.0311137i | −0.999879 | − | 0.0155569i | \(-0.995048\pi\) | ||
0.999879 | − | 0.0155569i | \(-0.00495210\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.446247 | − | 39.1408i | −0.0194758 | − | 1.70824i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.65503i | − | 0.115655i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 68.7162 | 2.98203 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.7246i | 0.767737i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.29950 | − | 2.32587i | 0.0994161 | − | 0.100556i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 65.5524i | − | 2.82880i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.961182 | 0.0414011 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.9533 | 1.50276 | 0.751381 | − | 0.659869i | \(-0.229388\pi\) | ||||
0.751381 | + | 0.659869i | \(0.229388\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 72.6351i | − | 3.11707i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.5580 | + | 30.2115i | 1.30896 | + | 1.29412i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 17.8478i | − | 0.763118i | −0.924345 | − | 0.381559i | \(-0.875387\pi\) | ||
0.924345 | − | 0.381559i | \(-0.124613\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −40.2558 | −1.71808 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.4558 | 0.956650 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.7497i | 0.627221i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.8707 | + | 15.6908i | 0.673674 | + | 0.666037i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.29661i | 0.139682i | 0.997558 | + | 0.0698410i | \(0.0222492\pi\) | ||||
−0.997558 | + | 0.0698410i | \(0.977751\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.7437 | 1.85016 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.04449 | −0.0440983 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.44153i | 0.187188i | 0.995610 | + | 0.0935941i | \(0.0298356\pi\) | ||||
−0.995610 | + | 0.0935941i | \(0.970164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.31255 | + | 1.32760i | −0.0552193 | + | 0.0558525i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 56.2481i | 2.36220i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00088 | 0.251570 | 0.125785 | − | 0.992058i | \(-0.459855\pi\) | ||||
0.125785 | + | 0.992058i | \(0.459855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.1609 | −0.760008 | −0.380004 | − | 0.924985i | \(-0.624077\pi\) | ||||
−0.380004 | + | 0.924985i | \(0.624077\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 53.6175i | 2.23990i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.99968 | + | 0.0570016i | −0.208501 | + | 0.00237713i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 10.0474i | − | 0.418279i | −0.977886 | − | 0.209140i | \(-0.932934\pi\) | ||
0.977886 | − | 0.209140i | \(-0.0670663\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 46.7476 | 1.94277 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.5223 | −1.63966 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.3022i | 0.426672i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −59.0983 | + | 59.7759i | −2.44341 | + | 2.47143i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.3593i | 1.74836i | 0.485605 | + | 0.874178i | \(0.338599\pi\) | ||||
−0.485605 | + | 0.874178i | \(0.661401\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.2660 | 0.835044 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 42.9698 | 1.76754 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 19.6741i | − | 0.807917i | −0.914777 | − | 0.403958i | \(-0.867634\pi\) | ||
0.914777 | − | 0.403958i | \(-0.132366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.41772 | − | 1.40165i | −0.0581209 | − | 0.0574620i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 60.4751i | 2.47508i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.2740 | −0.746655 | −0.373328 | − | 0.927700i | \(-0.621783\pi\) | ||||
−0.373328 | + | 0.927700i | \(0.621783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.17793 | −0.333585 | −0.166792 | − | 0.985992i | \(-0.553341\pi\) | ||||
−0.166792 | + | 0.985992i | \(0.553341\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.9730i | 0.446855i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.2460 | − | 16.0619i | −0.660496 | − | 0.653008i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 21.7927i | − | 0.884538i | −0.896883 | − | 0.442269i | \(-0.854174\pi\) | ||
0.896883 | − | 0.442269i | \(-0.145826\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 62.8197 | 2.54558 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.8294 | −1.08540 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.2379i | 0.615455i | 0.951475 | + | 0.307727i | \(0.0995685\pi\) | ||||
−0.951475 | + | 0.307727i | \(0.900432\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.5709 | − | 17.7723i | 0.708525 | − | 0.716649i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.2945i | 0.817024i | 0.912753 | + | 0.408512i | \(0.133952\pi\) | ||||
−0.912753 | + | 0.408512i | \(0.866048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.08510 | 0.0838073 | 0.0419037 | − | 0.999122i | \(-0.486658\pi\) | ||||
0.0419037 | + | 0.999122i | \(0.486658\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.0469 | 0.563681 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 42.8085i | 1.71509i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9935 | + | 0.569979i | −0.999740 | + | 0.0227992i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 7.97262i | − | 0.318396i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.13667 | 0.0453221 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.0512 | −1.55461 | −0.777303 | − | 0.629127i | \(-0.783413\pi\) | ||||
−0.777303 | + | 0.629127i | \(0.783413\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 55.0738i | − | 2.18899i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.3795 | − | 12.5215i | 0.491267 | − | 0.496900i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 5.54488i | − | 0.219696i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 61.1127 | 2.41758 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.8361 | −0.862475 | −0.431238 | − | 0.902238i | \(-0.641923\pi\) | ||||
−0.431238 | + | 0.902238i | \(0.641923\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 16.3727i | − | 0.645676i | −0.946454 | − | 0.322838i | \(-0.895363\pi\) | ||
0.946454 | − | 0.322838i | \(-0.104637\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −43.8615 | − | 43.3643i | −1.72705 | − | 1.70747i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.9991i | 0.825560i | 0.910831 | + | 0.412780i | \(0.135442\pi\) | ||||
−0.910831 | + | 0.412780i | \(0.864558\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.25861 | −0.324179 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 56.6936 | 2.22200 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.2756i | 0.910846i | 0.890275 | + | 0.455423i | \(0.150512\pi\) | ||||
−0.890275 | + | 0.455423i | \(0.849488\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.4713 | + | 20.2392i | 0.799878 | + | 0.790811i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 75.4080i | − | 2.94195i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.09639 | −0.0816637 | −0.0408318 | − | 0.999166i | \(-0.513001\pi\) | ||||
−0.0408318 | + | 0.999166i | \(0.513001\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.3184 | −1.21814 | −0.609072 | − | 0.793115i | \(-0.708458\pi\) | ||||
−0.609072 | + | 0.793115i | \(0.708458\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.02545i | 0.234009i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.6989 | − | 10.8215i | 0.414884 | − | 0.419641i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8.02431i | − | 0.310703i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 43.5190 | 1.68254 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.83812 | 0.186773 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 44.3377i | − | 1.70909i | −0.519377 | − | 0.854545i | \(-0.673836\pi\) | ||
0.519377 | − | 0.854545i | \(-0.326164\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 70.2298 | − | 0.800695i | 2.70315 | − | 0.0308188i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.03772i | 0.116749i | 0.998295 | + | 0.0583746i | \(0.0185918\pi\) | ||||
−0.998295 | + | 0.0583746i | \(0.981408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.9436 | 0.611860 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.7061 | 1.02338 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 22.6750i | − | 0.867635i | −0.901001 | − | 0.433817i | \(-0.857166\pi\) | ||
0.901001 | − | 0.433817i | \(-0.142834\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.13566 | + | 5.19454i | −0.196223 | + | 0.198473i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.0338i | 0.764338i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 59.4313 | 2.26415 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.2394 | 0.693860 | 0.346930 | − | 0.937891i | \(-0.387224\pi\) | ||||
0.346930 | + | 0.937891i | \(0.387224\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 15.8469i | − | 0.601974i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.9685 | − | 19.7421i | −0.757448 | − | 0.748862i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.27287i | − | 0.0482134i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −43.8934 | −1.66020 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.4315 | 0.658378 | 0.329189 | − | 0.944264i | \(-0.393225\pi\) | ||||
0.329189 | + | 0.944264i | \(0.393225\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.67629i | 0.327232i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 26.9017 | + | 26.5967i | 1.01318 | + | 1.00169i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 32.8086i | 1.23389i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.4207 | 1.21758 | 0.608792 | − | 0.793330i | \(-0.291654\pi\) | ||||
0.608792 | + | 0.793330i | \(0.291654\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −44.6608 | −1.67491 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7.24179i | − | 0.271207i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.10270 | − | 7.18414i | 0.265626 | − | 0.268671i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 37.1117i | 1.38596i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.494269 | 0.0184331 | 0.00921656 | − | 0.999958i | \(-0.497066\pi\) | ||||
0.00921656 | + | 0.999958i | \(0.497066\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.5099 | −1.13625 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 56.6430i | − | 2.10658i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.457399 | − | 40.1189i | −0.0169874 | − | 1.48998i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.25774i | 0.157911i | 0.996878 | + | 0.0789555i | \(0.0251585\pi\) | ||||
−0.996878 | + | 0.0789555i | \(0.974842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.6543 | −1.28349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.14140 | −0.116189 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 14.8525i | − | 0.548589i | −0.961646 | − | 0.274295i | \(-0.911556\pi\) | ||
0.961646 | − | 0.274295i | \(-0.0884443\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.49680 | + | 5.55982i | −0.202752 | + | 0.205077i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.31878i | − | 0.0485780i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.1389 | −1.55010 | −0.775052 | − | 0.631898i | \(-0.782276\pi\) | ||||
−0.775052 | + | 0.631898i | \(0.782276\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −45.9926 | −1.68958 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.97014i | 0.145650i | 0.997345 | + | 0.0728252i | \(0.0232015\pi\) | ||||
−0.997345 | + | 0.0728252i | \(0.976798\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.299365 | + | 0.295971i | 0.0109679 | + | 0.0108436i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 119.670i | − | 4.37851i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.55705 | 0.129972 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.5382 | −1.88066 | −0.940328 | − | 0.340269i | \(-0.889482\pi\) | ||||
−0.940328 | + | 0.340269i | \(0.889482\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 40.3921i | − | 1.47197i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.6889 | + | 29.3524i | 1.08049 | + | 1.06824i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 39.9808i | − | 1.45313i | −0.687099 | − | 0.726564i | \(-0.741116\pi\) | ||
0.687099 | − | 0.726564i | \(-0.258884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.84892 | −0.103409 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.6683 | −0.749226 | −0.374613 | − | 0.927181i | \(-0.622224\pi\) | ||||
−0.374613 | + | 0.927181i | \(0.622224\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.7336i | 1.69187i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.24408 | − | 4.29274i | 0.153445 | − | 0.155204i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47.6424i | 1.72027i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.0670558 | 0.00241809 | 0.00120905 | − | 0.999999i | \(-0.499615\pi\) | ||||
0.00120905 | + | 0.999999i | \(0.499615\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.7121 | −0.565859 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 21.2074i | − | 0.762778i | −0.924415 | − | 0.381389i | \(-0.875446\pi\) | ||
0.924415 | − | 0.381389i | \(-0.124554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.412794 | − | 36.2066i | −0.0148280 | − | 1.30058i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.2717i | 0.870744i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.71588 | 0.348108 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.34480 | −0.262817 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 112.716i | 4.02816i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −31.4856 | + | 31.8466i | −1.12377 | + | 1.13665i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 19.1047i | − | 0.681010i | −0.940243 | − | 0.340505i | \(-0.889402\pi\) | ||
0.940243 | − | 0.340505i | \(-0.110598\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 37.3577 | 1.32997 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.03035 | −0.0721910 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 27.9102i | − | 0.991121i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −59.5914 | − | 58.9159i | −2.11349 | − | 2.08953i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 51.0751i | − | 1.80917i | −0.426290 | − | 0.904587i | \(-0.640180\pi\) | ||
0.426290 | − | 0.904587i | \(-0.359820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.92672 | 0.0681625 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −129.621 | −4.57992 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.06286i | 0.319822i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.86694 | − | 3.82311i | −0.136292 | − | 0.134747i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.4547i | 0.684837i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.02800 | 0.176775 | 0.0883876 | − | 0.996086i | \(-0.471829\pi\) | ||||
0.0883876 | + | 0.996086i | \(0.471829\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.3571 | −1.80339 | −0.901696 | − | 0.432371i | \(-0.857677\pi\) | ||||
−0.901696 | + | 0.432371i | \(0.857677\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 12.6645i | − | 0.444162i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.27607 | + | 5.33657i | −0.184813 | + | 0.186932i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 23.9785i | − | 0.838900i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −91.4179 | −3.19440 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.7483 | 0.479818 | 0.239909 | − | 0.970795i | \(-0.422882\pi\) | ||||
0.239909 | + | 0.970795i | \(0.422882\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9.07220i | − | 0.316237i | −0.987420 | − | 0.158119i | \(-0.949457\pi\) | ||
0.987420 | − | 0.158119i | \(-0.0505428\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.2437 | + | 0.162393i | −0.495901 | + | 0.00565380i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.2010i | 1.67611i | 0.545583 | + | 0.838057i | \(0.316308\pi\) | ||||
−0.545583 | + | 0.838057i | \(0.683692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.0601 | −1.42608 | −0.713038 | − | 0.701125i | \(-0.752681\pi\) | ||||
−0.713038 | + | 0.701125i | \(0.752681\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.5019 | −0.884651 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.398199i | 0.0137968i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.05201 | + | 4.09847i | −0.140226 | + | 0.141834i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 101.724i | 3.51611i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.3970 | 1.01490 | 0.507449 | − | 0.861682i | \(-0.330588\pi\) | ||||
0.507449 | + | 0.861682i | \(0.330588\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.3895 | 1.22033 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 19.3288i | − | 0.665721i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.7723 | − | 20.5368i | −0.714590 | − | 0.706489i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 24.8458i | − | 0.853711i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24.6367 | −0.845530 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.10036 | 0.106279 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.39913i | 0.0479053i | 0.999713 | + | 0.0239527i | \(0.00762510\pi\) | ||||
−0.999713 | + | 0.0239527i | \(0.992375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32.7667 | + | 32.3953i | 1.12060 | + | 1.10789i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 3.68808i | − | 0.125982i | −0.998014 | − | 0.0629912i | \(-0.979936\pi\) | ||
0.998014 | − | 0.0629912i | \(-0.0200640\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.0281 | 0.546871 | 0.273435 | − | 0.961890i | \(-0.411840\pi\) | ||||
0.273435 | + | 0.961890i | \(0.411840\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.1800 | 0.926291 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 35.0979i | − | 1.19475i | −0.801963 | − | 0.597374i | \(-0.796211\pi\) | ||
0.801963 | − | 0.597374i | \(-0.203789\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.5274 | + | 30.8774i | −1.03796 | + | 1.04986i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 54.2942i | 1.84393i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.36753 | 0.182081 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.60781 | −0.257781 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 48.2759i | 1.63389i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.5514 | − | 18.8939i | −0.660957 | − | 0.638729i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.2491i | 1.79809i | 0.437853 | + | 0.899046i | \(0.355739\pi\) | ||||
−0.437853 | + | 0.899046i | \(0.644261\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −43.6142 | −1.47107 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.8449 | 1.37610 | 0.688050 | − | 0.725663i | \(-0.258467\pi\) | ||||
0.688050 | + | 0.725663i | \(0.258467\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 14.9288i | − | 0.502393i | −0.967936 | − | 0.251196i | \(-0.919176\pi\) | ||
0.967936 | − | 0.251196i | \(-0.0808240\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 47.2292 | − | 47.7708i | 1.58759 | − | 1.60580i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 34.9975i | − | 1.17510i | −0.809188 | − | 0.587550i | \(-0.800092\pi\) | ||
0.809188 | − | 0.587550i | \(-0.199908\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.1496 | 0.642259 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.4692 | 0.685742 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.7068i | 0.492143i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.3794 | − | 32.0123i | −1.08232 | − | 1.07005i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.4349i | 0.548745i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.1104 | 1.93809 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.26799 | −0.142187 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 67.0793i | − | 2.23226i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −35.8778 | − | 35.4711i | −1.19262 | − | 1.17910i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.3920i | 0.544288i | 0.962257 | + | 0.272144i | \(0.0877327\pi\) | ||||
−0.962257 | + | 0.272144i | \(0.912267\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −99.3416 | −3.29495 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.1111 | 1.46147 | 0.730733 | − | 0.682663i | \(-0.239178\pi\) | ||||
0.730733 | + | 0.682663i | \(0.239178\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.3825i | 0.475991i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27.6682 | + | 27.9854i | −0.914681 | + | 0.925169i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.3076i | 1.03387i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.5629 | 0.942203 | 0.471101 | − | 0.882079i | \(-0.343857\pi\) | ||||
0.471101 | + | 0.882079i | \(0.343857\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.4724 | 1.07000 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42.3708i | 1.39465i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.5008 | − | 0.176726i | 0.509664 | − | 0.00581071i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 92.3813i | − | 3.03420i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.2273 | −0.532400 | −0.266200 | − | 0.963918i | \(-0.585768\pi\) | ||||
−0.266200 | + | 0.963918i | \(0.585768\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.03948 | −0.0996148 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 90.9372i | 2.97715i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.510072 | + | 0.515920i | −0.0166811 | + | 0.0168724i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 5.65418i | − | 0.184714i | −0.995726 | − | 0.0923571i | \(-0.970560\pi\) | ||
0.995726 | − | 0.0923571i | \(-0.0294401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −46.5192 | −1.51810 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.6246 | −0.835338 | −0.417669 | − | 0.908599i | \(-0.637153\pi\) | ||||
−0.417669 | + | 0.908599i | \(0.637153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.47185i | − | 0.113059i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 54.3185 | + | 53.7027i | 1.76698 | + | 1.74695i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 0.248718i | − | 0.00808223i | −0.999992 | − | 0.00404112i | \(-0.998714\pi\) | ||
0.999992 | − | 0.00404112i | \(-0.00128633\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 52.2820 | 1.69715 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47.5914 | −1.54326 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.1737i | 1.26896i | 0.772939 | + | 0.634481i | \(0.218786\pi\) | ||||
−0.772939 | + | 0.634481i | \(0.781214\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.4842 | + | 26.1840i | 0.857008 | + | 0.847293i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 22.8606i | − | 0.738978i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.94423 | −0.256533 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.4435 | 0.691726 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.7704i | 0.347073i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.8291 | − | 23.0908i | 0.734894 | − | 0.743320i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.04114i | − | 0.0656386i | −0.999461 | − | 0.0328193i | \(-0.989551\pi\) | ||
0.999461 | − | 0.0328193i | \(-0.0104486\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.30290 | 0.106105 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.6713 | 0.438734 | 0.219367 | − | 0.975642i | \(-0.429601\pi\) | ||||
0.219367 | + | 0.975642i | \(0.429601\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 30.5387i | − | 0.979025i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.936815 | + | 82.1691i | 0.0300021 | + | 2.63152i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.8777i | 1.46776i | 0.679281 | + | 0.733878i | \(0.262292\pi\) | ||||
−0.679281 | + | 0.733878i | \(0.737708\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.5784 | 0.497887 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −141.505 | −4.51792 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 59.6356i | − | 1.90208i | −0.309070 | − | 0.951039i | \(-0.600018\pi\) | ||
0.309070 | − | 0.951039i | \(-0.399982\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.9842 | − | 21.2248i | 0.668611 | − | 0.676277i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 41.1418i | 1.30956i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.56841 | −0.272460 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.3396 | 1.34496 | 0.672480 | − | 0.740115i | \(-0.265229\pi\) | ||||
0.672480 | + | 0.740115i | \(0.265229\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 64.8656i | 2.05845i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.8715 | + | 29.5328i | 0.946989 | + | 0.936254i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 7.02379i | − | 0.222446i | −0.993795 | − | 0.111223i | \(-0.964523\pi\) | ||
0.993795 | − | 0.111223i | \(-0.0354767\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −43.5504 | −1.37787 |
(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 | 1840.2.e.f.369.12 | 12 | ||
4.3 | odd | 2 | 460.2.c.a.369.1 | ✓ | 12 | ||
5.2 | odd | 4 | 9200.2.a.cy.1.6 | 6 | |||
5.3 | odd | 4 | 9200.2.a.cx.1.1 | 6 | |||
5.4 | even | 2 | inner | 1840.2.e.f.369.1 | 12 | ||
12.11 | even | 2 | 4140.2.f.b.829.3 | 12 | |||
20.3 | even | 4 | 2300.2.a.o.1.6 | 6 | |||
20.7 | even | 4 | 2300.2.a.n.1.1 | 6 | |||
20.19 | odd | 2 | 460.2.c.a.369.12 | yes | 12 | ||
60.59 | even | 2 | 4140.2.f.b.829.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.c.a.369.1 | ✓ | 12 | 4.3 | odd | 2 | ||
460.2.c.a.369.12 | yes | 12 | 20.19 | odd | 2 | ||
1840.2.e.f.369.1 | 12 | 5.4 | even | 2 | inner | ||
1840.2.e.f.369.12 | 12 | 1.1 | even | 1 | trivial | ||
2300.2.a.n.1.1 | 6 | 20.7 | even | 4 | |||
2300.2.a.o.1.6 | 6 | 20.3 | even | 4 | |||
4140.2.f.b.829.3 | 12 | 12.11 | even | 2 | |||
4140.2.f.b.829.4 | 12 | 60.59 | even | 2 | |||
9200.2.a.cx.1.1 | 6 | 5.3 | odd | 4 | |||
9200.2.a.cy.1.6 | 6 | 5.2 | odd | 4 |