Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(881,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.f (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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + x^{14} - 4 x^{13} + 10 x^{12} - 32 x^{11} + 71 x^{10} - 70 x^{9} + 74 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.11 | ||
Root | \(-1.49826 + 0.869033i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.881 |
Dual form | 1680.2.f.l.881.12 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0.869033 | − | 1.49826i | 0.501737 | − | 0.865020i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.807952 | + | 2.51937i | 0.305377 | + | 0.952231i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.48956 | − | 2.60407i | −0.496521 | − | 0.868025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.541366i | − | 0.163228i | −0.996664 | − | 0.0816139i | \(-0.973993\pi\) | ||
0.996664 | − | 0.0816139i | \(-0.0260075\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.85348i | 1.62346i | 0.584030 | + | 0.811732i | \(0.301475\pi\) | ||||
−0.584030 | + | 0.811732i | \(0.698525\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.869033 | − | 1.49826i | 0.224383 | − | 0.386849i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.22086 | 1.50878 | 0.754390 | − | 0.656426i | \(-0.227933\pi\) | ||||
0.754390 | + | 0.656426i | \(0.227933\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.74951i | − | 1.31903i | −0.751692 | − | 0.659515i | \(-0.770762\pi\) | ||
0.751692 | − | 0.659515i | \(-0.229238\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.47680 | + | 0.978892i | 0.976919 | + | 0.213612i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.55465i | 1.36674i | 0.730072 | + | 0.683370i | \(0.239486\pi\) | ||||
−0.730072 | + | 0.683370i | \(0.760514\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19606 | − | 0.0312759i | −0.999982 | − | 0.00601904i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.28395i | 0.981206i | 0.871383 | + | 0.490603i | \(0.163223\pi\) | ||||
−0.871383 | + | 0.490603i | \(0.836777\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.99125i | − | 1.61488i | −0.589952 | − | 0.807438i | \(-0.700853\pi\) | ||
0.589952 | − | 0.807438i | \(-0.299147\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.811106 | − | 0.470465i | −0.141195 | − | 0.0818974i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.807952 | + | 2.51937i | 0.136569 | + | 0.425851i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.33408 | 1.20572 | 0.602858 | − | 0.797849i | \(-0.294029\pi\) | ||||
0.602858 | + | 0.797849i | \(0.294029\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.77004 | + | 5.08687i | 1.40433 | + | 0.814551i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.16593 | 0.806783 | 0.403392 | − | 0.915027i | \(-0.367831\pi\) | ||||
0.403392 | + | 0.915027i | \(0.367831\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.48280 | 0.378623 | 0.189311 | − | 0.981917i | \(-0.439374\pi\) | ||||
0.189311 | + | 0.981917i | \(0.439374\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.48956 | − | 2.60407i | −0.222051 | − | 0.388192i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.09597 | 0.305728 | 0.152864 | − | 0.988247i | \(-0.451150\pi\) | ||||
0.152864 | + | 0.988247i | \(0.451150\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.69443 | + | 4.07106i | −0.813489 | + | 0.581580i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.40614 | − | 9.32047i | 0.757010 | − | 1.30513i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.75661i | 1.34017i | 0.742283 | + | 0.670086i | \(0.233743\pi\) | ||||
−0.742283 | + | 0.670086i | \(0.766257\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.541366i | − | 0.0729977i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.61426 | − | 4.99652i | −1.14099 | − | 0.661805i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.76727 | 1.27159 | 0.635795 | − | 0.771858i | \(-0.280672\pi\) | ||||
0.635795 | + | 0.771858i | \(0.280672\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.433188i | − | 0.0554640i | −0.999615 | − | 0.0277320i | \(-0.991171\pi\) | ||
0.999615 | − | 0.0277320i | \(-0.00882850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.35712 | − | 5.85672i | 0.674934 | − | 0.737878i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.85348i | 0.726035i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.26790 | 1.01008 | 0.505042 | − | 0.863095i | \(-0.331477\pi\) | ||||
0.505042 | + | 0.863095i | \(0.331477\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.82057 | + | 5.69621i | 1.18226 | + | 0.685743i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.25045i | − | 0.623114i | −0.950228 | − | 0.311557i | \(-0.899150\pi\) | ||
0.950228 | − | 0.311557i | \(-0.100850\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.42155i | − | 1.10271i | −0.834271 | − | 0.551354i | \(-0.814111\pi\) | ||
0.834271 | − | 0.551354i | \(-0.185889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.869033 | − | 1.49826i | 0.100347 | − | 0.173004i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.36390 | − | 0.437398i | 0.155431 | − | 0.0498461i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.3885 | −1.95635 | −0.978177 | − | 0.207772i | \(-0.933379\pi\) | ||||
−0.978177 | + | 0.207772i | \(0.933379\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.56241 | + | 7.75786i | −0.506934 | + | 0.861985i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.8593 | −1.63102 | −0.815510 | − | 0.578742i | \(-0.803544\pi\) | ||||
−0.815510 | + | 0.578742i | \(0.803544\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.22086 | 0.674747 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.91673 | + | 4.59193i | 0.848763 | + | 0.492307i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.12418 | 0.755162 | 0.377581 | − | 0.925977i | \(-0.376756\pi\) | ||||
0.377581 | + | 0.925977i | \(0.376756\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.7471 | + | 4.72933i | −1.54591 | + | 0.495769i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.4712 | − | 7.81370i | −1.39690 | − | 0.810243i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 5.74951i | − | 0.589888i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.24620i | − | 0.329602i | −0.986327 | − | 0.164801i | \(-0.947302\pi\) | ||
0.986327 | − | 0.164801i | \(-0.0526982\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.40976 | + | 0.806398i | −0.141686 | + | 0.0810460i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.9842 | −1.49098 | −0.745492 | − | 0.666515i | \(-0.767785\pi\) | ||||
−0.745492 | + | 0.666515i | \(0.767785\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.0115i | − | 1.28206i | −0.767515 | − | 0.641031i | \(-0.778507\pi\) | ||
0.767515 | − | 0.641031i | \(-0.221493\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.47680 | + | 0.978892i | 0.436891 | + | 0.0955301i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.1046i | 1.17019i | 0.810963 | + | 0.585097i | \(0.198943\pi\) | ||||
−0.810963 | + | 0.585097i | \(0.801057\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.41160 | −0.135207 | −0.0676033 | − | 0.997712i | \(-0.521535\pi\) | ||||
−0.0676033 | + | 0.997712i | \(0.521535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.37356 | − | 10.9884i | 0.604952 | − | 1.04297i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.79738i | − | 0.827588i | −0.910371 | − | 0.413794i | \(-0.864203\pi\) | ||
0.910371 | − | 0.413794i | \(-0.135797\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.55465i | 0.611225i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.2429 | − | 8.71913i | 1.40921 | − | 0.806084i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.02616 | + | 15.6726i | 0.460747 | + | 1.43671i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7069 | 0.973357 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.48937 | − | 7.73991i | 0.404793 | − | 0.697884i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.861929 | −0.0764839 | −0.0382419 | − | 0.999269i | \(-0.512176\pi\) | ||||
−0.0382419 | + | 0.999269i | \(0.512176\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.15763 | − | 3.71987i | 0.189969 | − | 0.327517i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.94338 | 0.868757 | 0.434378 | − | 0.900730i | \(-0.356968\pi\) | ||||
0.434378 | + | 0.900730i | \(0.356968\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.4851 | − | 4.64533i | 1.25602 | − | 0.402802i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.19606 | − | 0.0312759i | −0.447205 | − | 0.00269180i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 12.4338i | − | 1.06229i | −0.847280 | − | 0.531147i | \(-0.821761\pi\) | ||
0.847280 | − | 0.531147i | \(-0.178239\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.11832i | 0.434130i | 0.976157 | + | 0.217065i | \(0.0696484\pi\) | ||||
−0.976157 | + | 0.217065i | \(0.930352\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.82146 | − | 3.14030i | 0.153395 | − | 0.264461i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.16887 | 0.264995 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.28395i | 0.438808i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.15086 | + | 12.0696i | 0.0949210 | + | 0.995485i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.74937i | 0.307161i | 0.988136 | + | 0.153580i | \(0.0490804\pi\) | ||||
−0.988136 | + | 0.153580i | \(0.950920\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.33203 | 0.271156 | 0.135578 | − | 0.990767i | \(-0.456711\pi\) | ||||
0.135578 | + | 0.990767i | \(0.456711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.26636 | − | 16.1996i | −0.749141 | − | 1.30966i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.99125i | − | 0.722195i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.75551i | − | 0.219914i | −0.993936 | − | 0.109957i | \(-0.964929\pi\) | ||
0.993936 | − | 0.109957i | \(-0.0350713\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.6179 | + | 8.47881i | 1.15928 | + | 0.672414i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.5136 | + | 5.29585i | −1.30145 | + | 0.417371i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.6131 | −0.909611 | −0.454806 | − | 0.890591i | \(-0.650291\pi\) | ||||
−0.454806 | + | 0.890591i | \(0.650291\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.811106 | − | 0.470465i | −0.0631445 | − | 0.0366256i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.85657 | 0.607960 | 0.303980 | − | 0.952678i | \(-0.401684\pi\) | ||||
0.303980 | + | 0.952678i | \(0.401684\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.2633 | −1.63564 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.9722 | + | 8.56426i | −1.14495 | + | 0.654925i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.82479 | 0.442850 | 0.221425 | − | 0.975177i | \(-0.428929\pi\) | ||||
0.221425 | + | 0.975177i | \(0.428929\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.807952 | + | 2.51937i | 0.0610755 | + | 0.190446i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.48808 | − | 14.6339i | 0.638003 | − | 1.09995i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.5161i | 0.786011i | 0.919536 | + | 0.393005i | \(0.128565\pi\) | ||||
−0.919536 | + | 0.393005i | \(0.871435\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.28411i | − | 0.169777i | −0.996390 | − | 0.0848883i | \(-0.972947\pi\) | ||
0.996390 | − | 0.0848883i | \(-0.0270533\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.649028 | − | 0.376454i | −0.0479775 | − | 0.0278283i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.33408 | 0.539212 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.36776i | − | 0.246275i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.11937 | − | 13.1161i | −0.299640 | − | 0.954052i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.26399i | − | 0.308531i | −0.988029 | − | 0.154266i | \(-0.950699\pi\) | ||
0.988029 | − | 0.154266i | \(-0.0493012\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.02782 | −0.577855 | −0.288928 | − | 0.957351i | \(-0.593299\pi\) | ||||
−0.288928 | + | 0.957351i | \(0.593299\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.77004 | + | 5.08687i | 0.628035 | + | 0.364278i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 11.3017i | − | 0.805210i | −0.915374 | − | 0.402605i | \(-0.868105\pi\) | ||
0.915374 | − | 0.402605i | \(-0.131895\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 8.86775i | − | 0.628618i | −0.949321 | − | 0.314309i | \(-0.898227\pi\) | ||
0.949321 | − | 0.314309i | \(-0.101773\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.18508 | − | 12.3875i | 0.506796 | − | 0.873744i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.3122 | + | 4.26918i | −0.934335 | + | 0.299638i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.16593 | 0.360804 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.0688 | − | 9.76357i | 1.18636 | − | 0.678615i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.11259 | −0.215302 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.5275 | −1.48201 | −0.741006 | − | 0.671499i | \(-0.765651\pi\) | ||||
−0.741006 | + | 0.671499i | \(0.765651\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.86654 | − | 4.56282i | −0.539006 | − | 0.312639i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.48280 | 0.169325 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.6523 | − | 7.26450i | 1.53774 | − | 0.493147i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.1159 | − | 8.18764i | −0.953865 | − | 0.553269i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36.4137i | 2.44945i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.9108i | 0.730640i | 0.930882 | + | 0.365320i | \(0.119040\pi\) | ||||
−0.930882 | + | 0.365320i | \(0.880960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.48956 | − | 2.60407i | −0.0993042 | − | 0.173605i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.4610 | −1.29167 | −0.645835 | − | 0.763477i | \(-0.723491\pi\) | ||||
−0.645835 | + | 0.763477i | \(0.723491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 18.8113i | − | 1.24308i | −0.783381 | − | 0.621542i | \(-0.786507\pi\) | ||
0.783381 | − | 0.621542i | \(-0.213493\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.529938 | − | 2.42359i | 0.0348674 | − | 0.159460i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.01806i | 0.459769i | 0.973218 | + | 0.229884i | \(0.0738348\pi\) | ||||
−0.973218 | + | 0.229884i | \(0.926165\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.09597 | 0.136726 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.1111 | + | 26.0524i | −0.981575 | + | 1.69229i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.60528i | 0.556629i | 0.960490 | + | 0.278315i | \(0.0897758\pi\) | ||||
−0.960490 | + | 0.278315i | \(0.910224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.4188i | 0.799967i | 0.916522 | + | 0.399984i | \(0.130984\pi\) | ||||
−0.916522 | + | 0.399984i | \(0.869016\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.65841 | + | 13.5775i | 0.491287 | + | 0.870998i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.69443 | + | 4.07106i | −0.363804 | + | 0.260090i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.6547 | 2.14140 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.9132 | + | 22.2631i | −0.818343 | + | 1.41087i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.77791 | 0.490938 | 0.245469 | − | 0.969405i | \(-0.421058\pi\) | ||||
0.245469 | + | 0.969405i | \(0.421058\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.54846 | 0.223090 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.40614 | − | 9.32047i | 0.338545 | − | 0.583670i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.1332 | −1.50539 | −0.752694 | − | 0.658371i | \(-0.771246\pi\) | ||||
−0.752694 | + | 0.658371i | \(0.771246\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.92559 | + | 18.4772i | 0.368198 | + | 1.14812i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.7598 | − | 7.87078i | 0.851711 | − | 0.487189i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.7824i | 0.664874i | 0.943125 | + | 0.332437i | \(0.107871\pi\) | ||||
−0.943125 | + | 0.332437i | \(0.892129\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.75661i | 0.599343i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.19115 | − | 10.6739i | 0.378892 | − | 0.653230i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.23229 | −0.258047 | −0.129024 | − | 0.991642i | \(-0.541184\pi\) | ||||
−0.129024 | + | 0.991642i | \(0.541184\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.11109i | 0.128240i | 0.997942 | + | 0.0641199i | \(0.0204240\pi\) | ||||
−0.997942 | + | 0.0641199i | \(0.979576\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.72993 | + | 26.2049i | −0.346791 | + | 1.58599i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 0.541366i | − | 0.0326456i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.9024 | −0.655062 | −0.327531 | − | 0.944840i | \(-0.606217\pi\) | ||||
−0.327531 | + | 0.944840i | \(0.606217\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.4139 | + | 13.3930i | −1.40175 | + | 0.801820i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.6151i | 1.28945i | 0.764415 | + | 0.644724i | \(0.223028\pi\) | ||||
−0.764415 | + | 0.644724i | \(0.776972\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.9033i | 0.826463i | 0.910626 | + | 0.413231i | \(0.135600\pi\) | ||||
−0.910626 | + | 0.413231i | \(0.864400\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.61426 | − | 4.99652i | −0.510265 | − | 0.295968i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.17383 | + | 13.0149i | 0.246373 | + | 0.768244i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.6991 | 1.27642 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.86366 | − | 2.82106i | −0.285113 | − | 0.165373i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.86654 | 0.225885 | 0.112943 | − | 0.993602i | \(-0.463972\pi\) | ||||
0.112943 | + | 0.993602i | \(0.463972\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.76727 | 0.568672 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.0169317 | + | 2.81297i | −0.000982476 | + | 0.163225i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −38.3676 | −2.21885 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00598 | + | 6.25508i | 0.115623 | + | 0.360537i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.0218 | + | 22.4502i | −0.748081 | + | 1.28973i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 0.433188i | − | 0.0248043i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.12531i | − | 0.292517i | −0.989246 | − | 0.146258i | \(-0.953277\pi\) | ||
0.989246 | − | 0.146258i | \(-0.0467231\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.4946 | − | 11.3074i | −1.10901 | − | 0.643257i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.8443 | 1.06856 | 0.534280 | − | 0.845307i | \(-0.320583\pi\) | ||||
0.534280 | + | 0.845307i | \(0.320583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.36435i | 0.529304i | 0.964344 | + | 0.264652i | \(0.0852571\pi\) | ||||
−0.964344 | + | 0.264652i | \(0.914743\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.35712 | − | 5.85672i | 0.301840 | − | 0.329989i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 19.1203i | − | 1.07390i | −0.843613 | − | 0.536952i | \(-0.819576\pi\) | ||
0.843613 | − | 0.536952i | \(-0.180424\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.86055 | 0.160160 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.1358 | + | 10.5193i | 1.01224 | + | 0.587129i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 35.7669i | − | 1.99013i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.85348i | 0.324693i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.22673 | + | 2.11494i | −0.0678381 | + | 0.116956i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.69344 | + | 5.28051i | 0.0933624 | + | 0.291124i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.94896 | −0.436915 | −0.218457 | − | 0.975847i | \(-0.570102\pi\) | ||||
−0.218457 | + | 0.975847i | \(0.570102\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.9246 | − | 19.0985i | −0.598663 | − | 1.04659i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.26790 | 0.451724 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.34820 | −0.291335 | −0.145667 | − | 0.989334i | \(-0.546533\pi\) | ||||
−0.145667 | + | 0.989334i | \(0.546533\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.1808 | − | 7.64521i | −0.715880 | − | 0.415231i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.86755 | −0.263593 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.8573 | − | 11.0571i | −0.802220 | − | 0.597029i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.82057 | + | 5.69621i | 0.528722 | + | 0.306674i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.49471i | 0.402337i | 0.979557 | + | 0.201169i | \(0.0644739\pi\) | ||||
−0.979557 | + | 0.201169i | \(0.935526\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 25.1595i | − | 1.34676i | −0.739297 | − | 0.673379i | \(-0.764842\pi\) | ||
0.739297 | − | 0.673379i | \(-0.235158\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.183073 | − | 30.4150i | 0.00977170 | − | 1.62343i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.26591 | 0.386726 | 0.193363 | − | 0.981127i | \(-0.438061\pi\) | ||||
0.193363 | + | 0.981127i | \(0.438061\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 5.25045i | − | 0.278665i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27.8496 | + | 6.08955i | 1.47396 | + | 0.322293i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.72746i | 0.302284i | 0.988512 | + | 0.151142i | \(0.0482950\pi\) | ||||
−0.988512 | + | 0.151142i | \(0.951705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.0569 | −0.739838 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.30467 | − | 16.0417i | 0.488369 | − | 0.841973i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 9.42155i | − | 0.493146i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13.2019i | − | 0.689132i | −0.938762 | − | 0.344566i | \(-0.888026\pi\) | ||
0.938762 | − | 0.344566i | \(-0.111974\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.69498 | − | 13.4525i | −0.400585 | − | 0.700308i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.5805 | + | 7.88287i | −1.27615 | + | 0.409258i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −37.5328 | −1.94338 | −0.971688 | − | 0.236266i | \(-0.924076\pi\) | ||||
−0.971688 | + | 0.236266i | \(0.924076\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.869033 | − | 1.49826i | 0.0448767 | − | 0.0773698i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −30.9295 | −1.59295 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.85408 | −0.352070 | −0.176035 | − | 0.984384i | \(-0.556327\pi\) | ||||
−0.176035 | + | 0.984384i | \(0.556327\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.749045 | + | 1.29139i | −0.0383748 | + | 0.0661601i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.8927 | −1.01647 | −0.508234 | − | 0.861219i | \(-0.669702\pi\) | ||||
−0.508234 | + | 0.861219i | \(0.669702\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.36390 | − | 0.437398i | 0.0695107 | − | 0.0222918i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.69828 | − | 6.46539i | −0.187994 | − | 0.328654i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.4577i | 1.29076i | 0.763864 | + | 0.645378i | \(0.223300\pi\) | ||||
−0.763864 | + | 0.645378i | \(0.776700\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.7756i | 2.06211i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.64112 | − | 14.8978i | 0.435887 | − | 0.751492i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.3885 | −0.874908 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.3280i | 1.42174i | 0.703322 | + | 0.710871i | \(0.251699\pi\) | ||||
−0.703322 | + | 0.710871i | \(0.748301\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.62815 | − | 25.7394i | 0.281760 | − | 1.28858i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 37.1327i | − | 1.85432i | −0.374666 | − | 0.927160i | \(-0.622243\pi\) | ||
0.374666 | − | 0.927160i | \(-0.377757\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 52.6301 | 2.62169 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.56241 | + | 7.75786i | −0.226708 | + | 0.385491i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.97042i | − | 0.196806i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.94224i | 0.491612i | 0.969319 | + | 0.245806i | \(0.0790527\pi\) | ||||
−0.969319 | + | 0.245806i | \(0.920947\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.6291 | − | 10.8054i | −0.918906 | − | 0.532992i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.89149 | + | 24.6073i | 0.388315 | + | 1.21085i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.8593 | −0.729415 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.66857 | + | 4.44799i | 0.375531 | + | 0.217819i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.7361 | −0.671052 | −0.335526 | − | 0.942031i | \(-0.608914\pi\) | ||||
−0.335526 | + | 0.942031i | \(0.608914\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.8838 | −1.16402 | −0.582012 | − | 0.813181i | \(-0.697734\pi\) | ||||
−0.582012 | + | 0.813181i | \(0.697734\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.12207 | − | 5.45805i | −0.151800 | − | 0.265379i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.22086 | 0.301756 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.09136 | − | 0.349995i | 0.0528146 | − | 0.0169374i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.75386 | − | 4.74780i | 0.132957 | − | 0.229226i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.2319i | 0.541022i | 0.962717 | + | 0.270511i | \(0.0871927\pi\) | ||||
−0.962717 | + | 0.270511i | \(0.912807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.14457i | − | 0.247232i | −0.992330 | − | 0.123616i | \(-0.960551\pi\) | ||
0.992330 | − | 0.123616i | \(-0.0394492\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.91673 | + | 4.59193i | 0.379578 | + | 0.220166i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 37.6861 | 1.80277 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 39.7058i | − | 1.89506i | −0.319672 | − | 0.947528i | \(-0.603573\pi\) | ||
0.319672 | − | 0.947528i | \(-0.396427\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.0835 | + | 8.76461i | 0.908740 | + | 0.417363i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.7817i | 0.654789i | 0.944888 | + | 0.327395i | \(0.106171\pi\) | ||||
−0.944888 | + | 0.327395i | \(0.893829\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.12418 | 0.337719 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.61753 | + | 3.25833i | 0.265700 | + | 0.154114i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 40.7969i | − | 1.92532i | −0.270707 | − | 0.962662i | \(-0.587257\pi\) | ||
0.270707 | − | 0.962662i | \(-0.412743\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.79666i | − | 0.131689i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.89564 | − | 4.99224i | 0.136049 | − | 0.234556i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.7471 | + | 4.72933i | −0.691353 | + | 0.221715i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.4973 | 0.491044 | 0.245522 | − | 0.969391i | \(-0.421041\pi\) | ||||
0.245522 | + | 0.969391i | \(0.421041\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −32.3240 | − | 0.194563i | −1.50875 | − | 0.00908142i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.7172 | −1.84982 | −0.924908 | − | 0.380192i | \(-0.875858\pi\) | ||||
−0.924908 | + | 0.380192i | \(0.875858\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.3647 | −1.64353 | −0.821767 | − | 0.569823i | \(-0.807012\pi\) | ||||
−0.821767 | + | 0.569823i | \(0.807012\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.4712 | − | 7.81370i | −0.624713 | − | 0.362351i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.44968 | 0.437279 | 0.218640 | − | 0.975806i | \(-0.429838\pi\) | ||||
0.218640 | + | 0.975806i | \(0.429838\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.68007 | + | 20.8299i | 0.308457 | + | 0.961834i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.12847 | − | 2.39463i | −0.190230 | − | 0.110339i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.34410i | − | 0.0618018i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.74951i | − | 0.263806i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.4069 | − | 14.5331i | 1.16330 | − | 0.665424i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.2364 | 0.696168 | 0.348084 | − | 0.937463i | \(-0.386832\pi\) | ||||
0.348084 | + | 0.937463i | \(0.386832\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42.9299i | 1.95744i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.41630 | + | 29.3439i | −0.291952 | + | 1.33519i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 3.24620i | − | 0.147403i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.3328 | 1.10263 | 0.551313 | − | 0.834299i | \(-0.314127\pi\) | ||||
0.551313 | + | 0.834299i | \(0.314127\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.0922 | + | 17.3995i | −0.456385 | + | 0.786832i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.14825i | − | 0.0969494i | −0.998824 | − | 0.0484747i | \(-0.984564\pi\) | ||
0.998824 | − | 0.0484747i | \(-0.0154360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.8707i | 1.48042i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.40976 | + | 0.806398i | −0.0633638 | + | 0.0362449i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.2278 | − | 4.24211i | 0.593348 | − | 0.190285i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.22753 | −0.278783 | −0.139391 | − | 0.990237i | \(-0.544515\pi\) | ||||
−0.139391 | + | 0.990237i | \(0.544515\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.82762 | − | 11.7712i | 0.305036 | − | 0.525898i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.1213 | −0.852575 | −0.426288 | − | 0.904588i | \(-0.640179\pi\) | ||||
−0.426288 | + | 0.904588i | \(0.640179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.9842 | −0.666788 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.4785 | + | 31.8579i | −0.820658 | + | 1.41486i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.3463 | −1.43372 | −0.716861 | − | 0.697216i | \(-0.754422\pi\) | ||||
−0.716861 | + | 0.697216i | \(0.754422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.7363 | − | 7.61216i | 1.05003 | − | 0.336742i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.179821 | + | 29.8748i | −0.00793929 | + | 1.31901i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 13.0115i | − | 0.573355i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.13468i | − | 0.0499033i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.06193 | − | 8.72704i | 0.222194 | − | 0.383075i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.3045 | 1.02099 | 0.510494 | − | 0.859881i | \(-0.329463\pi\) | ||||
0.510494 | + | 0.859881i | \(0.329463\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.56564i | 0.374549i | 0.982308 | + | 0.187275i | \(0.0599654\pi\) | ||||
−0.982308 | + | 0.187275i | \(0.940035\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.47680 | + | 0.978892i | 0.195384 | + | 0.0427223i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 55.9333i | − | 2.43649i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.9635 | −0.867978 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.5490 | − | 25.4347i | −0.631371 | − | 1.10377i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.2387i | 1.30978i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.1046i | 0.523326i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.7559 | + | 9.13884i | 0.679915 | + | 0.394370i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.20393 | + | 3.08277i | 0.0949300 | + | 0.132784i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.3978 | −0.533021 | −0.266511 | − | 0.963832i | \(-0.585871\pi\) | ||||
−0.266511 | + | 0.963832i | \(0.585871\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.42219 | − | 1.98497i | −0.146860 | − | 0.0851831i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.41160 | −0.0604662 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.9082 | 0.722944 | 0.361472 | − | 0.932383i | \(-0.382274\pi\) | ||||
0.361472 | + | 0.932383i | \(0.382274\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.12805 | + | 0.645260i | −0.0481441 | + | 0.0275390i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.3802 | 1.29424 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.0490 | − | 43.8079i | −0.597426 | − | 1.86290i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.37356 | − | 10.9884i | 0.270543 | − | 0.466430i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 45.7000i | 1.93637i | 0.250235 | + | 0.968185i | \(0.419492\pi\) | ||||
−0.250235 | + | 0.968185i | \(0.580508\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.5330i | 0.614681i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.04578 | − | 2.92670i | −0.213033 | − | 0.123565i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.39076 | −0.100759 | −0.0503793 | − | 0.998730i | \(-0.516043\pi\) | ||||
−0.0503793 | + | 0.998730i | \(0.516043\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 8.79738i | − | 0.370108i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.2311 | − | 5.22640i | −0.975615 | − | 0.219488i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.3765i | 0.896151i | 0.893996 | + | 0.448075i | \(0.147890\pi\) | ||||
−0.893996 | + | 0.448075i | \(0.852110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.2563 | 0.429214 | 0.214607 | − | 0.976701i | \(-0.431153\pi\) | ||||
0.214607 | + | 0.976701i | \(0.431153\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.38856 | − | 3.70555i | −0.266886 | − | 0.154801i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.55465i | 0.273348i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 15.6181i | − | 0.650189i | −0.945682 | − | 0.325094i | \(-0.894604\pi\) | ||
0.945682 | − | 0.325094i | \(-0.105396\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.97645 | + | 12.0278i | −0.289931 | + | 0.499857i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0056 | − | 37.4361i | −0.498077 | − | 1.55311i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.28189 | 0.218754 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.2429 | − | 8.71913i | 0.630216 | − | 0.360492i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.1826 | 1.41087 | 0.705433 | − | 0.708777i | \(-0.250753\pi\) | ||||
0.705433 | + | 0.708777i | \(0.250753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −51.6953 | −2.13007 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.9328 | − | 9.82152i | −0.696524 | − | 0.404004i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.3917 | 0.549932 | 0.274966 | − | 0.961454i | \(-0.411333\pi\) | ||||
0.274966 | + | 0.961454i | \(0.411333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.02616 | + | 15.6726i | 0.206052 | + | 0.642516i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.2862 | − | 7.70637i | −0.543767 | − | 0.315401i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 13.1768i | − | 0.538388i | −0.963086 | − | 0.269194i | \(-0.913243\pi\) | ||
0.963086 | − | 0.269194i | \(-0.0867572\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.11187i | − | 0.126936i | −0.997984 | − | 0.0634678i | \(-0.979784\pi\) | ||
0.997984 | − | 0.0634678i | \(-0.0202160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.3156 | − | 21.5302i | −0.501528 | − | 0.876778i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.7069 | 0.435298 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.97466i | 0.283093i | 0.989932 | + | 0.141546i | \(0.0452075\pi\) | ||||
−0.989932 | + | 0.141546i | \(0.954793\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.17242 | + | 23.6552i | −0.209597 | + | 0.958558i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.2687i | 0.496338i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.1829 | 1.05752 | 0.528759 | − | 0.848772i | \(-0.322658\pi\) | ||||
0.528759 | + | 0.848772i | \(0.322658\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.48937 | − | 7.73991i | 0.181029 | − | 0.312103i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 15.1290i | − | 0.609070i | −0.952501 | − | 0.304535i | \(-0.901499\pi\) | ||
0.952501 | − | 0.304535i | \(-0.0985010\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8.76028i | − | 0.352105i | −0.984381 | − | 0.176053i | \(-0.943667\pi\) | ||
0.984381 | − | 0.176053i | \(-0.0563329\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.205002 | − | 34.0584i | 0.00822647 | − | 1.36672i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.75600 | + | 17.9484i | 0.230609 | + | 0.719089i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.70494 | + | 4.66347i | −0.108025 | + | 0.186241i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 45.6243 | 1.81916 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.79895 | −0.191043 | −0.0955215 | − | 0.995427i | \(-0.530452\pi\) | ||||
−0.0955215 | + | 0.995427i | \(0.530452\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.7081 | + | 32.2537i | −0.743579 | + | 1.28197i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.861929 | −0.0342046 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.8299 | − | 33.3322i | −0.944174 | − | 1.32067i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.6726 | + | 7.82087i | −0.540878 | + | 0.309389i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 0.836584i | − | 0.0330431i | −0.999864 | − | 0.0165215i | \(-0.994741\pi\) | ||
0.999864 | − | 0.0165215i | \(-0.00525921\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.91098i | 0.351415i | 0.984442 | + | 0.175707i | \(0.0562212\pi\) | ||||
−0.984442 | + | 0.175707i | \(0.943779\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.15763 | − | 3.71987i | 0.0849567 | − | 0.146470i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.8709 | 1.01709 | 0.508544 | − | 0.861036i | \(-0.330184\pi\) | ||||
0.508544 | + | 0.861036i | \(0.330184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 5.28766i | − | 0.207559i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.80146 | − | 40.2521i | 0.344957 | − | 1.57760i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 18.2837i | − | 0.715495i | −0.933818 | − | 0.357747i | \(-0.883545\pi\) | ||
0.933818 | − | 0.357747i | \(-0.116455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.94338 | 0.388520 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.5344 | + | 14.0340i | −0.957178 | + | 0.547518i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.66460i | 0.376479i | 0.982123 | + | 0.188240i | \(0.0602782\pi\) | ||||
−0.982123 | + | 0.188240i | \(0.939722\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 19.6253i | − | 0.763336i | −0.924299 | − | 0.381668i | \(-0.875350\pi\) | ||
0.924299 | − | 0.381668i | \(-0.124650\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 54.5572 | + | 31.6447i | 2.11883 | + | 1.22898i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.4851 | − | 4.64533i | 0.561710 | − | 0.180138i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34.6345 | −1.34105 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.3472 | + | 9.48184i | 0.632019 | + | 0.366589i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.234513 | −0.00905327 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.8787 | −0.457889 | −0.228945 | − | 0.973439i | \(-0.573527\pi\) | ||||
−0.228945 | + | 0.973439i | \(0.573527\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.19606 | − | 0.0312759i | −0.199996 | − | 0.00120381i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.7301 | −1.25792 | −0.628961 | − | 0.777437i | \(-0.716519\pi\) | ||||
−0.628961 | + | 0.777437i | \(0.716519\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.17838 | − | 2.62278i | 0.313858 | − | 0.100653i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.9122 | + | 29.1576i | −0.648078 | + | 1.11732i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 18.9837i | − | 0.726391i | −0.931713 | − | 0.363196i | \(-0.881686\pi\) | ||
0.931713 | − | 0.363196i | \(-0.118314\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 12.4338i | − | 0.475072i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.1842 | − | 16.3476i | −1.07529 | − | 0.623701i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −57.1101 | −2.17572 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.8425i | 0.983095i | 0.870851 | + | 0.491547i | \(0.163569\pi\) | ||||
−0.870851 | + | 0.491547i | \(0.836431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.17063 | − | 2.90016i | −0.120442 | − | 0.110168i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.11832i | 0.194149i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.1366 | 1.21726 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.5149 | + | 6.09893i | 0.397709 | + | 0.230683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 34.9210i | − | 1.31895i | −0.751727 | − | 0.659475i | \(-0.770779\pi\) | ||
0.751727 | − | 0.659475i | \(-0.229221\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 42.1674i | − | 1.59037i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.82146 | − | 3.14030i | 0.0686003 | − | 0.118271i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.1065 | − | 37.7507i | −0.455313 | − | 1.41976i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.52065 | −0.0946648 | −0.0473324 | − | 0.998879i | \(-0.515072\pi\) | ||||
−0.0473324 | + | 0.998879i | \(0.515072\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.9012 | + | 45.2808i | 0.971371 | + | 1.69816i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 58.9345 | 2.20712 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.16887 | 0.118509 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.8929 | + | 7.47827i | 0.481496 | + | 0.279281i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.1230 | −0.825049 | −0.412524 | − | 0.910947i | \(-0.635353\pi\) | ||||
−0.412524 | + | 0.910947i | \(0.635353\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.7808 | − | 10.5127i | 1.22082 | − | 0.391512i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.6066 | + | 10.7924i | 0.691988 | + | 0.401373i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.28395i | 0.196241i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 15.2639i | − | 0.566107i | −0.959104 | − | 0.283054i | \(-0.908653\pi\) | ||
0.959104 | − | 0.283054i | \(-0.0913474\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.9980 | + | 0.325022i | 0.999928 | + | 0.0120379i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.4451 | 0.571259 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.2260i | 0.673191i | 0.941649 | + | 0.336596i | \(0.109276\pi\) | ||||
−0.941649 | + | 0.336596i | \(0.890724\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.15086 | + | 12.0696i | 0.0424499 | + | 0.445194i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.47596i | − | 0.164874i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.67453 | −0.135170 | −0.0675849 | − | 0.997714i | \(-0.521529\pi\) | ||||
−0.0675849 | + | 0.997714i | \(0.521529\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.2470 | − | 50.4234i | 1.07442 | − | 1.85235i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.79110i | 0.0657090i | 0.999460 | + | 0.0328545i | \(0.0104598\pi\) | ||||
−0.999460 | + | 0.0328545i | \(0.989540\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.74937i | 0.137366i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.1339 | + | 38.6947i | 0.809836 | + | 1.41577i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.4959 | + | 9.77992i | −1.11430 | + | 0.357351i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.0699 | 1.42568 | 0.712840 | − | 0.701327i | \(-0.247409\pi\) | ||||
0.712840 | + | 0.701327i | \(0.247409\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.75926 | − | 11.6533i | 0.246321 | − | 0.424671i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.33203 | 0.121265 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.9534 | 1.56117 | 0.780583 | − | 0.625052i | \(-0.214922\pi\) | ||||
0.780583 | + | 0.625052i | \(0.214922\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.08373 | − | 5.31652i | 0.111932 | − | 0.192977i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.0235 | 0.689603 | 0.344801 | − | 0.938676i | \(-0.387946\pi\) | ||||
0.344801 | + | 0.938676i | \(0.387946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.14050 | − | 3.55633i | −0.0412890 | − | 0.128748i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.26636 | − | 16.1996i | −0.335026 | − | 0.585697i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 57.1725i | 2.06438i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 48.9415i | − | 1.76488i | −0.470429 | − | 0.882438i | \(-0.655901\pi\) | ||
0.470429 | − | 0.882438i | \(-0.344099\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.9725 | + | 36.1578i | −0.755308 | + | 1.30219i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.2306 | 0.511840 | 0.255920 | − | 0.966698i | \(-0.417622\pi\) | ||||
0.255920 | + | 0.966698i | \(0.417622\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 8.99125i | − | 0.322975i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.8332 | + | 7.17927i | 1.17789 | + | 0.257555i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 29.7016i | − | 1.06417i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.84241 | −0.101710 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.165260 | − | 27.4557i | 0.00590592 | − | 0.981188i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.75551i | − | 0.0983484i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.6962i | 1.41502i | 0.706705 | + | 0.707508i | \(0.250181\pi\) | ||||
−0.706705 | + | 0.707508i | \(0.749819\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.1549 | + | 9.37030i | 0.575130 | + | 0.333592i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.1638 | − | 7.10786i | 0.788055 | − | 0.252726i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.53566 | 0.0900438 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.6179 | + | 8.47881i | 0.518444 | + | 0.300713i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.31625 | 0.152890 | 0.0764448 | − | 0.997074i | \(-0.475643\pi\) | ||||
0.0764448 | + | 0.997074i | \(0.475643\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.0387 | 0.461276 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.6119 | − | 18.5519i | −0.374954 | − | 0.655499i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.10050 | −0.179993 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.5136 | + | 5.29585i | −0.582027 | + | 0.186654i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.67800 | + | 6.34107i | −0.129472 | + | 0.223216i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 24.0182i | − | 0.844434i | −0.906495 | − | 0.422217i | \(-0.861252\pi\) | ||
0.906495 | − | 0.422217i | \(-0.138748\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12.3193i | − | 0.432589i | −0.976328 | − | 0.216294i | \(-0.930603\pi\) | ||
0.976328 | − | 0.216294i | \(-0.0693971\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.16297 | + | 1.83461i | 0.110930 | + | 0.0643426i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.6131 | −0.406791 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.2749i | − | 0.499415i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 34.2822 | + | 31.3578i | 1.19792 | + | 1.09573i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 7.25501i | − | 0.253202i | −0.991954 | − | 0.126601i | \(-0.959593\pi\) | ||
0.991954 | − | 0.126601i | \(-0.0404067\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −53.1582 | −1.85298 | −0.926489 | − | 0.376321i | \(-0.877189\pi\) | ||||
−0.926489 | + | 0.376321i | \(0.877189\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.811106 | − | 0.470465i | −0.0282391 | − | 0.0163795i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 41.3798i | − | 1.43892i | −0.694536 | − | 0.719458i | \(-0.744390\pi\) | ||
0.694536 | − | 0.719458i | \(-0.255610\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.37838i | − | 0.0478730i | −0.999713 | − | 0.0239365i | \(-0.992380\pi\) | ||
0.999713 | − | 0.0239365i | \(-0.00761996\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.47455 | + | 16.3346i | −0.328668 | + | 0.566642i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35.4242 | + | 25.3255i | −1.22738 | + | 0.877476i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.85657 | 0.271888 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.281209 | + | 46.7191i | −0.00972001 | + | 1.61485i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.647037 | 0.0223382 | 0.0111691 | − | 0.999938i | \(-0.496445\pi\) | ||||
0.0111691 | + | 0.999938i | \(0.496445\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.07983 | 0.0372357 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.3850 | + | 18.7842i | 1.11540 | + | 0.646963i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.2633 | −0.731478 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.65068 | + | 26.9747i | 0.297241 | + | 0.926861i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.8307 | + | 12.0824i | 0.714907 | + | 0.414667i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.0724i | 1.64790i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 43.9133i | − | 1.50356i | −0.659412 | − | 0.751782i | \(-0.729195\pi\) | ||
0.659412 | − | 0.751782i | \(-0.270805\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.9722 | + | 8.56426i | −0.512037 | + | 0.292892i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.6363 | 0.944039 | 0.472019 | − | 0.881588i | \(-0.343525\pi\) | ||||
0.472019 | + | 0.881588i | \(0.343525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 43.0054i | − | 1.46733i | −0.679513 | − | 0.733663i | \(-0.737809\pi\) | ||
0.679513 | − | 0.733663i | \(-0.262191\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.1269 | + | 5.05689i | 0.788161 | + | 0.172338i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.18506i | 0.176501i | 0.996098 | + | 0.0882507i | \(0.0281277\pi\) | ||||
−0.996098 | + | 0.0882507i | \(0.971872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.82479 | 0.198049 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.8573 | − | 32.5109i | 0.640426 | − | 1.10413i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.41351i | 0.319332i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.3960i | 1.63984i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.45336 | + | 4.83542i | −0.286103 | + | 0.163654i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.807952 | + | 2.51937i | 0.0273138 | + | 0.0851702i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.8853 | 1.07669 | 0.538346 | − | 0.842724i | \(-0.319049\pi\) | ||||
0.538346 | + | 0.842724i | \(0.319049\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.36015 | − | 5.79307i | 0.113335 | − | 0.195396i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.8971 | 0.771422 | 0.385711 | − | 0.922620i | \(-0.373956\pi\) | ||||
0.385711 | + | 0.922620i | \(0.373956\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.815622 | −0.0274479 | −0.0137239 | − | 0.999906i | \(-0.504369\pi\) | ||||
−0.0137239 | + | 0.999906i | \(0.504369\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.48808 | − | 14.6339i | 0.285324 | − | 0.491913i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.9931 | −1.00707 | −0.503535 | − | 0.863975i | \(-0.667967\pi\) | ||||
−0.503535 | + | 0.863975i | \(0.667967\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.696398 | − | 2.17152i | −0.0233564 | − | 0.0728303i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.19984 | + | 2.46993i | 0.140700 | + | 0.0827458i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 12.0508i | − | 0.403264i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.5161i | 0.351515i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −33.3427 | + | 57.4845i | −1.11328 | + | 1.91935i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 47.5094 | 1.58453 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 60.6945i | 2.02203i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.1150 | + | 2.43039i | 0.369884 | + | 0.0808783i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.28411i | − | 0.0759264i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.0918 | −1.13200 | −0.566000 | − | 0.824405i | \(-0.691510\pi\) | ||||
−0.566000 | + | 0.824405i | \(0.691510\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.3199 | + | 39.0200i | 0.740305 | + | 1.29421i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.3838i | 0.476558i | 0.971197 | + | 0.238279i | \(0.0765832\pi\) | ||||
−0.971197 | + | 0.238279i | \(0.923417\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.04432i | 0.266228i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.649028 | − | 0.376454i | −0.0214562 | − | 0.0124452i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.03377 | + | 25.0510i | 0.265299 | + | 0.827258i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.0149 | −1.05608 | −0.528038 | − | 0.849221i | \(-0.677072\pi\) | ||||
−0.528038 | + | 0.849221i | \(0.677072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.67904 | − | 4.45406i | −0.253033 | − | 0.146766i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.7334 | 1.01160 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.33408 | 0.241143 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −33.8829 | + | 19.3814i | −1.11286 | + | 0.636570i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.3260 | −0.634064 | −0.317032 | − | 0.948415i | \(-0.602686\pi\) | ||||
−0.317032 | + | 0.948415i | \(0.602686\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.4066 | + | 32.7402i | 0.767121 | + | 1.07302i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.3763 | − | 28.2336i | 0.536136 | − | 0.924327i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 3.36776i | − | 0.110138i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.81494i | − | 0.255303i | −0.991819 | − | 0.127651i | \(-0.959256\pi\) | ||
0.991819 | − | 0.127651i | \(-0.0407439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0302 | + | 8.13793i | 0.457859 | + | 0.265571i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.16553 | −0.168391 | −0.0841957 | − | 0.996449i | \(-0.526832\pi\) | ||||
−0.0841957 | + | 0.996449i | \(0.526832\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.8609i | 1.10266i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.11937 | − | 13.1161i | −0.134003 | − | 0.426665i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.58998i | 0.279137i | 0.990212 | + | 0.139568i | \(0.0445715\pi\) | ||||
−0.990212 | + | 0.139568i | \(0.955428\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 55.1489 | 1.79021 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.6472 | − | 16.6162i | −0.928949 | − | 0.538817i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 55.0367i | − | 1.78281i | −0.453205 | − | 0.891406i | \(-0.649719\pi\) | ||
0.453205 | − | 0.891406i | \(-0.350281\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4.26399i | − | 0.137979i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.48591 | − | 4.28585i | 0.0803582 | − | 0.138542i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.3254 | − | 10.0459i | 1.01155 | − | 0.324400i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −49.8426 | −1.60783 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.5212 | − | 18.0305i | 1.01576 | − | 0.581026i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.02782 | −0.258425 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.3877 | 1.42741 | 0.713707 | − | 0.700445i | \(-0.247015\pi\) | ||||
0.713707 | + | 0.700445i | \(0.247015\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −53.5882 | − | 31.0827i | −1.72150 | − | 0.998519i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.7190 | −0.408172 | −0.204086 | − | 0.978953i | \(-0.565422\pi\) | ||||
−0.204086 | + | 0.978953i | \(0.565422\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.8949 | + | 4.13536i | −0.413392 | + | 0.132573i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.77004 | + | 5.08687i | 0.280866 | + | 0.162910i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 33.1021i | − | 1.05903i | −0.848300 | − | 0.529516i | \(-0.822374\pi\) | ||
0.848300 | − | 0.529516i | \(-0.177626\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.85679i | − | 0.123263i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.10266 | + | 3.67590i | 0.0671329 | + | 0.117363i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.7287 | 1.07578 | 0.537889 | − | 0.843016i | \(-0.319222\pi\) | ||||
0.537889 | + | 0.843016i | \(0.319222\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 11.3017i | − | 0.360101i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.38322 | + | 2.05172i | 0.298671 | + | 0.0653071i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.2739i | 0.517479i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.4912 | −0.777990 | −0.388995 | − | 0.921240i | \(-0.627178\pi\) | ||||
−0.388995 | + | 0.921240i | \(0.627178\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.90791 | + | 11.9096i | −0.219216 | + | 0.377940i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 8.86775i | − | 0.281127i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 43.8446i | − | 1.38857i | −0.719700 | − | 0.694286i | \(-0.755720\pi\) | ||
0.719700 | − | 0.694286i | \(-0.244280\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −38.1083 | − | 0.229380i | −1.20569 | − | 0.00725726i |
(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 | 1680.2.f.l.881.11 | 16 | ||
3.2 | odd | 2 | 1680.2.f.k.881.5 | 16 | |||
4.3 | odd | 2 | 840.2.f.b.41.6 | yes | 16 | ||
7.6 | odd | 2 | 1680.2.f.k.881.6 | 16 | |||
12.11 | even | 2 | 840.2.f.a.41.12 | yes | 16 | ||
21.20 | even | 2 | inner | 1680.2.f.l.881.12 | 16 | ||
28.27 | even | 2 | 840.2.f.a.41.11 | ✓ | 16 | ||
84.83 | odd | 2 | 840.2.f.b.41.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.f.a.41.11 | ✓ | 16 | 28.27 | even | 2 | ||
840.2.f.a.41.12 | yes | 16 | 12.11 | even | 2 | ||
840.2.f.b.41.5 | yes | 16 | 84.83 | odd | 2 | ||
840.2.f.b.41.6 | yes | 16 | 4.3 | odd | 2 | ||
1680.2.f.k.881.5 | 16 | 3.2 | odd | 2 | |||
1680.2.f.k.881.6 | 16 | 7.6 | odd | 2 | |||
1680.2.f.l.881.11 | 16 | 1.1 | even | 1 | trivial | ||
1680.2.f.l.881.12 | 16 | 21.20 | even | 2 | inner |