Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(129,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.12745506816.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 16x^{6} + 79x^{4} + 120x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.1 | ||
Root | \(0.281155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.129 |
Dual form | 260.2.d.a.129.7 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.09557i | − | 1.78723i | −0.448834 | − | 0.893615i | \(-0.648161\pi\) | ||
0.448834 | − | 0.893615i | \(-0.351839\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.73205 | + | 1.41421i | −0.774597 | + | 0.632456i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.37780 | −1.65465 | −0.827327 | − | 0.561721i | \(-0.810140\pi\) | ||||
−0.827327 | + | 0.561721i | \(0.810140\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.58258 | −2.19419 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.53326i | − | 0.763808i | −0.924202 | − | 0.381904i | \(-0.875269\pi\) | ||
0.924202 | − | 0.381904i | \(-0.124731\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64575 | + | 2.44949i | 0.733799 | + | 0.679366i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.37780 | + | 5.36169i | 1.13034 | + | 1.38438i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.29217i | − | 0.313397i | −0.987647 | − | 0.156698i | \(-0.949915\pi\) | ||
0.987647 | − | 0.156698i | \(-0.0500850\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.36169i | − | 1.23006i | −0.788505 | − | 0.615028i | \(-0.789145\pi\) | ||
0.788505 | − | 0.615028i | \(-0.210855\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.5518i | 2.95725i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.80341i | − | 0.376036i | −0.982166 | − | 0.188018i | \(-0.939794\pi\) | ||
0.982166 | − | 0.188018i | \(-0.0602064\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | − | 4.89898i | 0.200000 | − | 0.979796i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.0901i | 2.13430i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.58258 | −1.40805 | −0.704024 | − | 0.710176i | \(-0.748615\pi\) | ||||
−0.704024 | + | 0.710176i | \(0.748615\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.12359i | − | 0.561013i | −0.959852 | − | 0.280507i | \(-0.909498\pi\) | ||
0.959852 | − | 0.280507i | \(-0.0905025\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.84190 | −1.36510 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.58258 | − | 6.19115i | 1.28169 | − | 1.04649i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.55040 | 0.419283 | 0.209642 | − | 0.977778i | \(-0.432770\pi\) | ||||
0.209642 | + | 0.977778i | \(0.432770\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.58258 | − | 8.19012i | 1.21418 | − | 1.31147i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.89495i | − | 1.23298i | −0.787361 | − | 0.616492i | \(-0.788553\pi\) | ||
0.787361 | − | 0.616492i | \(-0.211447\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.38774i | 0.669124i | 0.942374 | + | 0.334562i | \(0.108588\pi\) | ||||
−0.942374 | + | 0.334562i | \(0.891412\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.4014 | − | 9.30917i | 1.69961 | − | 1.38773i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.20520 | −0.905122 | −0.452561 | − | 0.891733i | \(-0.649490\pi\) | ||||
−0.452561 | + | 0.891733i | \(0.649490\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.1652 | 1.73788 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.19115i | − | 0.850419i | −0.905095 | − | 0.425210i | \(-0.860200\pi\) | ||
0.905095 | − | 0.425210i | \(-0.139800\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.58258 | + | 4.38774i | 0.483074 | + | 0.591643i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.5975 | −2.19839 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.4282i | 1.35764i | 0.734305 | + | 0.678819i | \(0.237508\pi\) | ||||
−0.734305 | + | 0.678819i | \(0.762492\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.58258 | 0.458702 | 0.229351 | − | 0.973344i | \(-0.426340\pi\) | ||||
0.229351 | + | 0.973344i | \(0.426340\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 28.8172 | 3.63063 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.04668 | − | 0.500983i | −0.998067 | − | 0.0621393i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.55040 | 0.311581 | 0.155791 | − | 0.987790i | \(-0.450208\pi\) | ||||
0.155791 | + | 0.987790i | \(0.450208\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.58258 | −0.672063 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.295164i | − | 0.0350295i | −0.999847 | − | 0.0175147i | \(-0.994425\pi\) | ||
0.999847 | − | 0.0175147i | \(-0.00557540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.55040 | 0.298502 | 0.149251 | − | 0.988799i | \(-0.452314\pi\) | ||||
0.149251 | + | 0.988799i | \(0.452314\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −15.1652 | − | 3.09557i | −1.75112 | − | 0.357446i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.0901i | 1.26384i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1652 | 1.25618 | 0.628089 | − | 0.778142i | \(-0.283837\pi\) | ||||
0.628089 | + | 0.778142i | \(0.283837\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 14.5826 | 1.62029 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.723000 | −0.0793596 | −0.0396798 | − | 0.999212i | \(-0.512634\pi\) | ||||
−0.0396798 | + | 0.999212i | \(0.512634\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.82740 | + | 2.23810i | 0.198209 | + | 0.242756i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 23.4724i | 2.51651i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.3137i | 1.19925i | 0.800281 | + | 0.599625i | \(0.204684\pi\) | ||||
−0.800281 | + | 0.599625i | \(0.795316\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.5826 | − | 10.7234i | −1.21418 | − | 1.12412i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.66930 | −1.00266 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.58258 | + | 9.28672i | 0.777956 | + | 0.952797i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2197 | 1.24072 | 0.620362 | − | 0.784316i | \(-0.286986\pi\) | ||||
0.620362 | + | 0.784316i | \(0.286986\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.6754i | 1.67594i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.16515 | −0.911967 | −0.455983 | − | 0.889988i | \(-0.650712\pi\) | ||||
−0.455983 | + | 0.889988i | \(0.650712\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.28672i | − | 0.915048i | −0.889197 | − | 0.457524i | \(-0.848736\pi\) | ||
0.889197 | − | 0.457524i | \(-0.151264\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −19.1652 | − | 23.4724i | −1.87033 | − | 2.29067i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.5789i | − | 1.02270i | −0.859373 | − | 0.511350i | \(-0.829146\pi\) | ||
0.859373 | − | 0.511350i | \(-0.170854\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.48528i | − | 0.812743i | −0.913708 | − | 0.406371i | \(-0.866794\pi\) | ||
0.913708 | − | 0.406371i | \(-0.133206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 7.89495i | − | 0.749356i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.0901i | − | 1.04327i | −0.853168 | − | 0.521636i | \(-0.825322\pi\) | ||
0.853168 | − | 0.521636i | \(-0.174678\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.55040 | + | 3.12359i | 0.237826 | + | 0.291276i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.4159 | − | 16.1240i | −1.61010 | − | 1.49066i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.65685i | 0.518563i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.58258 | 0.416598 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −24.4394 | −2.20363 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.19615 | + | 9.89949i | 0.464758 | + | 0.885438i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.511238i | 0.0453651i | 0.999743 | + | 0.0226825i | \(0.00722069\pi\) | ||||
−0.999743 | + | 0.0226825i | \(0.992779\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.5826 | 1.19588 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.16515 | −0.276541 | −0.138270 | − | 0.990395i | \(-0.544154\pi\) | ||||
−0.138270 | + | 0.990395i | \(0.544154\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.4724i | 2.03532i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.6838 | − | 19.2087i | −1.34985 | − | 1.65322i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3923 | −0.887875 | −0.443937 | − | 0.896058i | \(-0.646419\pi\) | ||||
−0.443937 | + | 0.896058i | \(0.646419\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.16515 | −0.607740 | −0.303870 | − | 0.952713i | \(-0.598279\pi\) | ||||
−0.303870 | + | 0.952713i | \(0.598279\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.2087i | 1.61766i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.20520 | − | 6.70239i | 0.518905 | − | 0.560482i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.1334 | − | 10.7234i | 1.09067 | − | 0.890528i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 37.6581i | − | 3.10599i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.82843i | 0.231714i | 0.993266 | + | 0.115857i | \(0.0369614\pi\) | ||||
−0.993266 | + | 0.115857i | \(0.963039\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16.0851i | − | 1.30898i | −0.756069 | − | 0.654492i | \(-0.772882\pi\) | ||
0.756069 | − | 0.654492i | \(-0.227118\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.50579i | 0.687652i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.41742 | + | 5.41022i | 0.354816 | + | 0.434559i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.4499i | 1.79170i | 0.444356 | + | 0.895850i | \(0.353433\pi\) | ||||
−0.444356 | + | 0.895850i | \(0.646567\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.1652 | −1.51990 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.89495i | 0.622210i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3060 | −0.885555 | −0.442777 | − | 0.896632i | \(-0.646007\pi\) | ||||
−0.442777 | + | 0.896632i | \(0.646007\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.5826 | − | 11.0901i | 1.05740 | − | 0.863365i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.723000 | 0.0559474 | 0.0279737 | − | 0.999609i | \(-0.491095\pi\) | ||||
0.0279737 | + | 0.999609i | \(0.491095\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | + | 12.9615i | 0.0769231 | + | 0.997037i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 35.2937i | 2.69898i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.60681i | 0.274221i | 0.990556 | + | 0.137110i | \(0.0437815\pi\) | ||||
−0.990556 | + | 0.137110i | \(0.956218\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.37780 | + | 21.4468i | −0.330931 | + | 1.62122i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 32.2813 | 2.42641 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.5826 | −1.75288 | −0.876440 | − | 0.481512i | \(-0.840088\pi\) | ||||
−0.876440 | + | 0.481512i | \(0.840088\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 11.0901i | − | 0.819806i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.41742 | + | 3.60681i | −0.324775 | + | 0.265178i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.27340 | −0.239375 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 48.5504i | − | 3.53152i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.190700 | −0.0137269 | −0.00686346 | − | 0.999976i | \(-0.502185\pi\) | ||||
−0.00686346 | + | 0.999976i | \(0.502185\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.55083 | + | 24.9091i | −0.111057 | + | 1.78378i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.8027 | 1.62463 | 0.812313 | − | 0.583222i | \(-0.198208\pi\) | ||||
0.812313 | + | 0.583222i | \(0.198208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 7.89495i | − | 0.556867i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 33.1950 | 2.32983 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1652 | + | 13.6745i | 0.779808 | + | 0.955066i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.8711i | 0.825095i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.5826 | −0.939526 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.913701 | −0.0626057 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.20520 | − | 7.59979i | −0.423191 | − | 0.518301i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.6745i | 0.928283i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 7.89495i | − | 0.533492i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.16515 | − | 3.41875i | 0.212911 | − | 0.229970i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.55040 | 0.170787 | 0.0853937 | − | 0.996347i | \(-0.472785\pi\) | ||||
0.0853937 | + | 0.996347i | \(0.472785\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.58258 | + | 32.2479i | −0.438838 | + | 2.14986i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.9898 | −1.79138 | −0.895688 | − | 0.444682i | \(-0.853317\pi\) | ||||
−0.895688 | + | 0.444682i | \(0.853317\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.7234i | − | 0.708621i | −0.935128 | − | 0.354310i | \(-0.884716\pi\) | ||
0.935128 | − | 0.354310i | \(-0.115284\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 34.3303 | 2.25877 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.3823i | 0.811191i | 0.914053 | + | 0.405596i | \(0.132936\pi\) | ||||
−0.914053 | + | 0.405596i | \(0.867064\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.7477 | − | 8.77548i | 0.701104 | − | 0.572449i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 34.5625i | − | 2.24508i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 30.2272i | − | 1.95524i | −0.210389 | − | 0.977618i | \(-0.567473\pi\) | ||
0.210389 | − | 0.977618i | \(-0.432527\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.7325i | − | 0.949001i | −0.880255 | − | 0.474501i | \(-0.842629\pi\) | ||
0.880255 | − | 0.474501i | \(-0.157371\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 11.8711i | − | 0.761529i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −21.0707 | + | 17.2041i | −1.34616 | + | 1.09913i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.1334 | − | 14.1857i | 0.835659 | − | 0.902614i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.23810i | 0.141834i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.1652 | −0.957216 | −0.478608 | − | 0.878029i | \(-0.658858\pi\) | ||||
−0.478608 | + | 0.878029i | \(0.658858\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.56850 | −0.287219 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.92820 | − | 5.65685i | 0.433861 | − | 0.354246i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 7.21362i | − | 0.449973i | −0.974362 | − | 0.224987i | \(-0.927766\pi\) | ||
0.974362 | − | 0.224987i | \(-0.0722339\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.1652 | −0.693769 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 49.9129 | 3.08953 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.5003i | − | 1.01745i | −0.860928 | − | 0.508727i | \(-0.830116\pi\) | ||
0.860928 | − | 0.508727i | \(-0.169884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.75560 | + | 10.7234i | 0.537852 | + | 0.658732i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.0224 | 2.14334 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.16515 | 0.558809 | 0.279405 | − | 0.960173i | \(-0.409863\pi\) | ||||
0.279405 | + | 0.960173i | \(0.409863\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.3323i | 1.35659i | 0.734791 | + | 0.678294i | \(0.237280\pi\) | ||||
−0.734791 | + | 0.678294i | \(0.762720\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −33.1950 | + | 35.8547i | −2.00905 | + | 2.17003i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.4104 | − | 2.53326i | −0.748376 | − | 0.152762i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 28.3714i | − | 1.70467i | −0.522994 | − | 0.852336i | \(-0.675185\pi\) | ||
0.522994 | − | 0.852336i | \(-0.324815\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.5613i | 1.23097i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.3712i | − | 0.738001i | −0.929429 | − | 0.369001i | \(-0.879700\pi\) | ||
0.929429 | − | 0.369001i | \(-0.120300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.38774i | 0.260824i | 0.991460 | + | 0.130412i | \(0.0416300\pi\) | ||||
−0.991460 | + | 0.130412i | \(0.958370\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 28.7477 | − | 23.4724i | 1.70287 | − | 1.39039i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.5625i | 2.04016i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.3303 | 0.901783 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 37.8270i | − | 2.21746i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.20520 | 0.362512 | 0.181256 | − | 0.983436i | \(-0.441984\pi\) | ||||
0.181256 | + | 0.983436i | \(0.441984\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.7477 | − | 18.0622i | −0.858646 | − | 1.05162i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.0942 | 1.63019 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.41742 | − | 4.77136i | 0.255466 | − | 0.275935i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 19.2087i | − | 1.10717i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 28.3714i | 1.62989i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.20520 | + | 5.06653i | −0.355309 | + | 0.290108i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.03260 | 0.458445 | 0.229222 | − | 0.973374i | \(-0.426382\pi\) | ||||
0.229222 | + | 0.973374i | \(0.426382\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −28.7477 | −1.63540 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.33030 | 0.358959 | 0.179479 | − | 0.983762i | \(-0.442559\pi\) | ||||
0.179479 | + | 0.983762i | \(0.442559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.87650i | − | 0.219113i | −0.993981 | − | 0.109556i | \(-0.965057\pi\) | ||
0.993981 | − | 0.109556i | \(-0.0349430\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −49.9129 | + | 40.7537i | −2.81227 | + | 2.29621i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.0616 | 1.12677 | 0.563386 | − | 0.826194i | \(-0.309498\pi\) | ||||
0.563386 | + | 0.826194i | \(0.309498\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.2087i | 1.07548i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −32.7477 | −1.82780 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.92820 | −0.385496 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.6458 | − | 10.5120i | 0.812400 | − | 0.583100i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −26.2668 | −1.45256 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.1652 | 1.49766 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.5704i | 1.35051i | 0.737585 | + | 0.675254i | \(0.235966\pi\) | ||||
−0.737585 | + | 0.675254i | \(0.764034\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.7882 | −0.919988 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.41742 | + | 3.60681i | −0.241350 | + | 0.197061i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 23.4724i | − | 1.27862i | −0.768947 | − | 0.639312i | \(-0.779219\pi\) | ||
0.768947 | − | 0.639312i | \(-0.220781\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −34.3303 | −1.86457 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.91288 | −0.428506 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −22.6120 | −1.22093 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.66930 | − | 7.89495i | 0.520578 | − | 0.425050i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.07310i | 0.111290i | 0.998451 | + | 0.0556448i | \(0.0177215\pi\) | ||||
−0.998451 | + | 0.0556448i | \(0.982279\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.1701i | 1.72203i | 0.508581 | + | 0.861014i | \(0.330170\pi\) | ||||
−0.508581 | + | 0.861014i | \(0.669830\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.1652 | + | 29.3417i | −1.44997 | + | 1.56614i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.20520 | 0.330270 | 0.165135 | − | 0.986271i | \(-0.447194\pi\) | ||||
0.165135 | + | 0.986271i | \(0.447194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.417424 | + | 0.511238i | 0.0221546 | + | 0.0271337i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.5112 | 0.926791 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 21.7419i | − | 1.14749i | −0.819032 | − | 0.573747i | \(-0.805489\pi\) | ||
0.819032 | − | 0.573747i | \(-0.194511\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.74773 | −0.513038 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 14.1857i | − | 0.744556i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.41742 | + | 3.60681i | −0.231219 | + | 0.188789i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 9.28672i | − | 0.484763i | −0.970181 | − | 0.242381i | \(-0.922071\pi\) | ||
0.970181 | − | 0.242381i | \(-0.0779285\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 51.9691i | 2.70541i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.1036i | 1.40715i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.6969i | 0.760979i | 0.924785 | + | 0.380489i | \(0.124244\pi\) | ||||
−0.924785 | + | 0.380489i | \(0.875756\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 30.6446 | − | 16.0851i | 1.58248 | − | 0.830630i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.0616 | − | 18.5734i | −1.03323 | − | 0.956581i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.35261i | − | 0.0694789i | −0.999396 | − | 0.0347394i | \(-0.988940\pi\) | ||
0.999396 | − | 0.0347394i | \(-0.0110601\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.58258 | 0.0810778 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.6156 | 0.951213 | 0.475607 | − | 0.879658i | \(-0.342229\pi\) | ||||
0.475607 | + | 0.879658i | \(0.342229\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.6838 | − | 19.2087i | −0.799321 | − | 0.978964i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 28.8826i | − | 1.46819i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.0000 | 0.912636 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.33030 | −0.117848 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.79796i | 0.494242i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.3386 | + | 15.7899i | −0.973031 | + | 0.794477i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.1624 | −1.26287 | −0.631433 | − | 0.775431i | \(-0.717533\pi\) | ||||
−0.631433 | + | 0.775431i | \(0.717533\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 72.6606 | 3.63758 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 22.6274i | − | 1.12996i | −0.825105 | − | 0.564980i | \(-0.808884\pi\) | ||
0.825105 | − | 0.564980i | \(-0.191116\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.65120 | − | 8.26424i | 0.381134 | − | 0.411671i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −25.2578 | + | 20.6229i | −1.25507 | + | 1.02476i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6.46084i | − | 0.320252i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.71430i | − | 0.332001i | −0.986126 | − | 0.166000i | \(-0.946915\pi\) | ||
0.986126 | − | 0.166000i | \(-0.0530853\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.1701i | 1.58684i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 45.6527i | − | 2.24642i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.25227 | − | 1.02248i | 0.0614717 | − | 0.0501914i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.1803i | 1.08617i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.4955 | 1.63636 | 0.818180 | − | 0.574962i | \(-0.194983\pi\) | ||||
0.818180 | + | 0.574962i | \(0.194983\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 17.4377i | − | 0.849861i | −0.905226 | − | 0.424930i | \(-0.860299\pi\) | ||
0.905226 | − | 0.424930i | \(-0.139701\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 40.8462 | 1.98601 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.33030 | − | 1.29217i | −0.307065 | − | 0.0626793i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.6838 | −0.758993 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.7477 | − | 19.2087i | −1.00171 | − | 0.927403i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 30.2272i | − | 1.45599i | −0.685581 | − | 0.727997i | \(-0.740452\pi\) | ||
0.685581 | − | 0.727997i | \(-0.259548\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.79796i | − | 0.470860i | −0.971891 | − | 0.235430i | \(-0.924350\pi\) | ||
0.971891 | − | 0.235430i | \(-0.0756498\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −33.1950 | − | 40.6554i | −1.59158 | − | 1.94928i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.66930 | −0.462546 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.4955 | −1.78956 | −0.894780 | − | 0.446507i | \(-0.852668\pi\) | ||||
−0.894780 | + | 0.446507i | \(0.852668\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −80.0780 | −3.81324 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 25.2758i | − | 1.20089i | −0.799666 | − | 0.600445i | \(-0.794990\pi\) | ||
0.799666 | − | 0.600445i | \(-0.205010\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.0000 | − | 19.5959i | −0.758473 | − | 0.928936i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.75560 | 0.414126 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.9986i | 1.65168i | 0.563901 | + | 0.825842i | \(0.309300\pi\) | ||||
−0.563901 | + | 0.825842i | \(0.690700\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.0000 | −0.941763 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −49.7925 | −2.33946 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 35.2268 | + | 2.19321i | 1.65146 | + | 0.102819i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.63670 | −0.0765616 | −0.0382808 | − | 0.999267i | \(-0.512188\pi\) | ||||
−0.0382808 | + | 0.999267i | \(0.512188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.3303 | 0.668881 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.590327i | 0.0274943i | 0.999906 | + | 0.0137471i | \(0.00437599\pi\) | ||||
−0.999906 | + | 0.0137471i | \(0.995624\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.0188 | −1.81336 | −0.906679 | − | 0.421821i | \(-0.861391\pi\) | ||||
−0.906679 | + | 0.421821i | \(0.861391\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.7477 | − | 13.6745i | 0.776657 | − | 0.634138i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.4670i | 1.45612i | 0.685515 | + | 0.728059i | \(0.259577\pi\) | ||||
−0.685515 | + | 0.728059i | \(0.740423\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.1652 | −0.515559 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 69.4955 | 3.20218 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.1153 | 0.511082 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.2668 | − | 5.36169i | −1.20520 | − | 0.246011i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 40.7537i | 1.86598i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 0.295164i | − | 0.0134864i | −0.999977 | − | 0.00674318i | \(-0.997854\pi\) | ||
0.999977 | − | 0.00674318i | \(-0.00214644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.74773 | + | 6.24718i | 0.307670 | + | 0.284847i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.4394 | 1.11203 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.1652 | + | 17.2813i | −0.961060 | + | 0.784702i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.47860 | 0.429517 | 0.214758 | − | 0.976667i | \(-0.431104\pi\) | ||||
0.214758 | + | 0.976667i | \(0.431104\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 34.9986i | 1.58269i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.3303 | 1.36879 | 0.684394 | − | 0.729113i | \(-0.260067\pi\) | ||||
0.684394 | + | 0.729113i | \(0.260067\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.79796i | 0.441278i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −23.5826 | − | 28.8826i | −1.05996 | − | 1.29818i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.29217i | 0.0579616i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.885491i | − | 0.0396400i | −0.999804 | − | 0.0198200i | \(-0.993691\pi\) | ||
0.999804 | − | 0.0198200i | \(-0.00630932\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 2.23810i | − | 0.0999909i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.94960i | 0.265280i | 0.991164 | + | 0.132640i | \(0.0423453\pi\) | ||||
−0.991164 | + | 0.132640i | \(0.957655\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.8745 | − | 12.9615i | 0.706406 | − | 0.576778i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 40.1232 | − | 3.09557i | 1.78193 | − | 0.137479i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 11.9040i | − | 0.527637i | −0.964572 | − | 0.263819i | \(-0.915018\pi\) | ||
0.964572 | − | 0.263819i | \(-0.0849820\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.1652 | −0.493917 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 59.4618 | 2.62530 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.1334 | + | 16.0851i | 0.578727 | + | 0.708793i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.7194i | 0.691339i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.1652 | 0.490096 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.5826 | 1.38366 | 0.691829 | − | 0.722061i | \(-0.256805\pi\) | ||||
0.691829 | + | 0.722061i | \(0.256805\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.53371i | 0.0670647i | 0.999438 | + | 0.0335323i | \(0.0106757\pi\) | ||||
−0.999438 | + | 0.0335323i | \(0.989324\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 66.3900 | + | 13.5518i | 2.89750 | + | 0.591449i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.03620 | −0.175820 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.7477 | 0.858597 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 68.6445i | − | 2.97892i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.3386 | − | 20.8881i | 0.837648 | − | 0.904763i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.9608 | + | 18.3232i | 0.646812 | + | 0.792180i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 30.8175i | − | 1.32741i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.6758i | 0.845928i | 0.906147 | + | 0.422964i | \(0.139010\pi\) | ||||
−0.906147 | + | 0.422964i | \(0.860990\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 73.0016i | 3.13280i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.0000 | + | 14.6969i | 0.514024 | + | 0.629548i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 15.2082i | − | 0.650255i | −0.945670 | − | 0.325127i | \(-0.894593\pi\) | ||
0.945670 | − | 0.325127i | \(-0.105407\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.5826 | −1.00648 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40.6554i | 1.73198i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −48.8788 | −2.07854 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.1652 | + | 13.6745i | 0.473934 | + | 0.580449i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.65120 | −0.324192 | −0.162096 | − | 0.986775i | \(-0.551825\pi\) | ||||
−0.162096 | + | 0.986775i | \(0.551825\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.7477 | + | 11.6089i | −0.454580 | + | 0.491003i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.1331i | 0.427818i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.5230i | 1.03352i | 0.856129 | + | 0.516761i | \(0.172863\pi\) | ||||
−0.856129 | + | 0.516761i | \(0.827137\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.6838 | + | 19.2087i | 0.659823 | + | 0.808115i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −63.8396 | −2.68101 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.5826 | −0.820944 | −0.410472 | − | 0.911873i | \(-0.634636\pi\) | ||||
−0.410472 | + | 0.911873i | \(0.634636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.4955 | 0.732162 | 0.366081 | − | 0.930583i | \(-0.380699\pi\) | ||||
0.366081 | + | 0.930583i | \(0.380699\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37.1469i | 1.55183i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.83485 | − | 1.80341i | −0.368439 | − | 0.0752072i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.2704 | −0.927129 | −0.463565 | − | 0.886063i | \(-0.653430\pi\) | ||||
−0.463565 | + | 0.886063i | \(0.653430\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.590327i | 0.0245332i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.16515 | 0.131313 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.6838 | −0.649557 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 52.9679 | + | 3.29776i | 2.18995 | + | 0.136346i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.9898 | 1.11399 | 0.556994 | − | 0.830516i | \(-0.311954\pi\) | ||||
0.556994 | + | 0.830516i | \(0.311954\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.7477 | −0.690078 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 70.5875i | − | 2.90358i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.8745 | 0.651888 | 0.325944 | − | 0.945389i | \(-0.394318\pi\) | ||||
0.325944 | + | 0.945389i | \(0.394318\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.00000 | − | 9.79796i | −0.327968 | − | 0.401677i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.3823i | 0.506774i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.66970 | −0.231658 | −0.115829 | − | 0.993269i | \(-0.536952\pi\) | ||||
−0.115829 | + | 0.993269i | \(0.536952\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.66970 | 0.312853 | 0.156427 | − | 0.987690i | \(-0.450002\pi\) | ||||
0.156427 | + | 0.987690i | \(0.450002\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.7882 | −0.683669 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.93725 | + | 6.48074i | −0.322695 | + | 0.263480i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 21.9387i | − | 0.890465i | −0.895415 | − | 0.445232i | \(-0.853121\pi\) | ||
0.895415 | − | 0.445232i | \(-0.146879\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 102.758i | − | 4.16395i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.4174 | − | 15.1996i | −0.664178 | − | 0.614909i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.7019 | 0.714973 | 0.357487 | − | 0.933918i | \(-0.383634\pi\) | ||||
0.357487 | + | 0.933918i | \(0.383634\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 42.3303 | − | 34.5625i | 1.70692 | − | 1.39370i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.2131 | −1.41763 | −0.708813 | − | 0.705396i | \(-0.750769\pi\) | ||||
−0.708813 | + | 0.705396i | \(0.750769\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 39.3028i | − | 1.57971i | −0.613291 | − | 0.789857i | \(-0.710155\pi\) | ||
0.613291 | − | 0.789857i | \(-0.289845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.0000 | 0.802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 49.5292i | − | 1.98434i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | − | 9.79796i | −0.920000 | − | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 42.0459i | 1.67915i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 3.29555i | − | 0.131402i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.8175i | 1.22683i | 0.789762 | + | 0.613413i | \(0.210204\pi\) | ||||
−0.789762 | + | 0.613413i | \(0.789796\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 61.9115i | − | 2.46076i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.723000 | − | 0.885491i | −0.0286914 | − | 0.0351396i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.1860 | + | 29.7984i | 1.27525 | + | 1.18066i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.94294i | 0.0768614i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.3303 | 0.487018 | 0.243509 | − | 0.969899i | \(-0.421702\pi\) | ||||
0.243509 | + | 0.969899i | \(0.421702\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.7454 | 1.40966 | 0.704831 | − | 0.709375i | \(-0.251023\pi\) | ||||
0.704831 | + | 0.709375i | \(0.251023\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.5257 | + | 19.2087i | −0.926324 | + | 0.756340i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.4895i | 1.27729i | 0.769501 | + | 0.638646i | \(0.220505\pi\) | ||||
−0.769501 | + | 0.638646i | \(0.779495\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.4174 | 1.03697 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 42.3303 | 1.65906 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.6302i | 1.74651i | 0.487259 | + | 0.873257i | \(0.337997\pi\) | ||||
−0.487259 | + | 0.873257i | \(0.662003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.48220 | − | 4.47620i | 0.214207 | − | 0.174900i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.7882 | −0.654970 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.4955 | −1.30480 | −0.652399 | − | 0.757876i | \(-0.726237\pi\) | ||||
−0.652399 | + | 0.757876i | \(0.726237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.48528i | 0.330039i | 0.986290 | + | 0.165020i | \(0.0527687\pi\) | ||||
−0.986290 | + | 0.165020i | \(0.947231\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.5830 | − | 9.79796i | −0.411010 | − | 0.380521i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −33.1950 | − | 40.6554i | −1.28725 | − | 1.57655i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.6745i | 0.529477i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 7.89495i | − | 0.305237i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 9.07561i | − | 0.350360i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 23.4724i | − | 0.904795i | −0.891816 | − | 0.452398i | \(-0.850569\pi\) | ||
0.891816 | − | 0.452398i | \(-0.149431\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 54.3303 | + | 11.0901i | 2.09117 | + | 0.426859i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 23.7421i | − | 0.912483i | −0.889856 | − | 0.456242i | \(-0.849195\pi\) | ||
0.889856 | − | 0.456242i | \(-0.150805\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −53.4955 | −2.05297 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 83.5490i | 3.20160i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.9898 | 1.03274 | 0.516368 | − | 0.856367i | \(-0.327284\pi\) | ||||
0.516368 | + | 0.856367i | \(0.327284\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | − | 14.6969i | 0.687745 | − | 0.561541i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.1950 | −1.26647 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.1652 | − | 16.3802i | 0.577746 | − | 0.624037i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0942i | 0.764418i | 0.924076 | + | 0.382209i | \(0.124836\pi\) | ||||
−0.924076 | + | 0.382209i | \(0.875164\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 73.0016i | − | 2.77310i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.4104 | − | 10.1331i | 0.470754 | − | 0.384369i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.2016 | −0.386413 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38.3303 | 1.44979 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.8348 | −0.560304 | −0.280152 | − | 0.959956i | \(-0.590385\pi\) | ||||
−0.280152 | + | 0.959956i | \(0.590385\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 13.6745i | − | 0.515742i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.1652 | − | 33.2704i | −1.02310 | − | 1.25303i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 40.1232 | 1.50899 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.1996i | 0.570832i | 0.958404 | + | 0.285416i | \(0.0921318\pi\) | ||||
−0.958404 | + | 0.285416i | \(0.907868\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −73.4955 | −2.75629 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.63310 | −0.210961 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.26912 | + | 20.3844i | −0.0474625 | + | 0.762332i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −93.5705 | −3.49446 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.4955 | −1.24917 | −0.624585 | − | 0.780957i | \(-0.714732\pi\) | ||||
−0.624585 | + | 0.780957i | \(0.714732\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.6554i | 1.51409i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −45.6054 | −1.69608 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.58258 | + | 37.1469i | −0.281610 | + | 1.37960i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.2082i | 0.564040i | 0.959409 | + | 0.282020i | \(0.0910045\pi\) | ||||
−0.959409 | + | 0.282020i | \(0.908996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.00000 | 0.259259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.66970 | 0.209701 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.0043 | 1.21904 | 0.609521 | − | 0.792770i | \(-0.291362\pi\) | ||||
0.609521 | + | 0.792770i | \(0.291362\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 53.2566 | + | 65.2258i | 1.96440 | + | 2.40589i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 6.46084i | − | 0.237988i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.5228i | 1.23315i | 0.787294 | + | 0.616577i | \(0.211481\pi\) | ||||
−0.787294 | + | 0.616577i | \(0.788519\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −43.9129 | − | 40.6554i | −1.61318 | − | 1.49351i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.6156 | 0.682940 | 0.341470 | − | 0.939893i | \(-0.389075\pi\) | ||||
0.341470 | + | 0.939893i | \(0.389075\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.00000 | − | 4.89898i | −0.146549 | − | 0.179485i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.75920 | 0.174130 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46.3123i | 1.69221i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.83485 | 0.176426 | 0.0882131 | − | 0.996102i | \(-0.471884\pi\) | ||||
0.0882131 | + | 0.996102i | \(0.471884\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 46.9448i | 1.71077i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.7477 | + | 27.8602i | 0.827875 | + | 1.01394i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 26.3264i | − | 0.956851i | −0.878128 | − | 0.478426i | \(-0.841208\pi\) | ||
0.878128 | − | 0.478426i | \(-0.158792\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.1421i | 0.513327i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.3137i | 0.410122i | 0.978749 | + | 0.205061i | \(0.0657392\pi\) | ||||
−0.978749 | + | 0.205061i | \(0.934261\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 37.1469i | 1.34481i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.0290 | − | 14.7325i | −0.434910 | − | 0.532653i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.5438 | + | 27.5905i | −0.922334 | + | 0.996234i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 42.8935i | − | 1.54678i | −0.633930 | − | 0.773390i | \(-0.718559\pi\) | ||
0.633930 | − | 0.773390i | \(-0.281441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.3303 | −0.804206 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.20520 | 0.223186 | 0.111593 | − | 0.993754i | \(-0.464405\pi\) | ||||
0.111593 | + | 0.993754i | \(0.464405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.3024 | − | 3.12359i | −0.549679 | − | 0.112203i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 34.5625i | 1.23992i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −42.3303 | −1.51664 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.747727 | −0.0267558 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 84.0917i | − | 3.00519i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −31.7490 | − | 38.8844i | −1.13317 | − | 1.38785i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.03260 | 0.286331 | 0.143166 | − | 0.989699i | \(-0.454272\pi\) | ||||
0.143166 | + | 0.989699i | \(0.454272\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −51.0780 | −1.81843 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.5504i | 1.72625i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.47860 | + | 8.77548i | 0.336595 | + | 0.311627i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.1950 | − | 27.1036i | 1.17731 | − | 0.961266i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.8322i | 1.23382i | 0.787033 | + | 0.616911i | \(0.211616\pi\) | ||||
−0.787033 | + | 0.616911i | \(0.788384\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.01816i | 0.283662i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 74.4733i | − | 2.63139i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 6.46084i | − | 0.227998i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.1652 | − | 13.6745i | −0.393520 | − | 0.481961i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 28.3714i | − | 0.998721i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.7477 | −0.799767 | −0.399884 | − | 0.916566i | \(-0.630950\pi\) | ||||
−0.399884 | + | 0.916566i | \(0.630950\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.0760i | 0.424045i | 0.977265 | + | 0.212023i | \(0.0680051\pi\) | ||||
−0.977265 | + | 0.212023i | \(0.931995\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 69.1311 | 2.42453 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.5826 | − | 15.9891i | 0.685948 | − | 0.560074i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.5257 | 0.823060 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 76.2432 | + | 70.5875i | 2.66415 | + | 2.46653i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.7990i | 0.690990i | 0.938421 | + | 0.345495i | \(0.112289\pi\) | ||||
−0.938421 | + | 0.345495i | \(0.887711\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.7031i | 1.38396i | 0.721916 | + | 0.691981i | \(0.243262\pi\) | ||||
−0.721916 | + | 0.691981i | \(0.756738\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.84190 | + | 38.4173i | −0.273020 | + | 1.33752i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.4720 | −1.12916 | −0.564581 | − | 0.825377i | \(-0.690962\pi\) | ||||
−0.564581 | + | 0.825377i | \(0.690962\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.2432 | 1.39770 | 0.698852 | − | 0.715267i | \(-0.253695\pi\) | ||||
0.698852 | + | 0.715267i | \(0.253695\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −87.8258 | −3.04664 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 15.7194i | − | 0.544645i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.25227 | + | 1.02248i | −0.0433367 | + | 0.0353843i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.6410 | 1.19737 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 0.762282i | − | 0.0263169i | −0.999913 | − | 0.0131585i | \(-0.995811\pi\) | ||
0.999913 | − | 0.0131585i | \(-0.00418859\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.4955 | 0.982602 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −38.2958 | −1.31898 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.0624 | − | 21.0357i | −0.690166 | − | 0.723651i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0616 | −0.689325 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.5826 | 0.466153 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.59941i | − | 0.157666i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.0188 | −1.33598 | −0.667989 | − | 0.744171i | \(-0.732845\pi\) | ||||
−0.667989 | + | 0.744171i | \(0.732845\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −49.9129 | − | 61.1305i | −1.70698 | − | 2.09062i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 44.3605i | − | 1.51533i | −0.652646 | − | 0.757663i | \(-0.726341\pi\) | ||
0.652646 | − | 0.757663i | \(-0.273659\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | −0.136478 | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 106.991 | 3.64624 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.20520 | 0.211228 | 0.105614 | − | 0.994407i | \(-0.466319\pi\) | ||||
0.105614 | + | 0.994407i | \(0.466319\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.10080 | − | 6.24718i | −0.173432 | − | 0.212411i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 47.4561i | − | 1.61169i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 28.2843i | − | 0.959478i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.74773 | + | 6.24718i | 0.228638 | + | 0.211678i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −80.4371 | −2.72238 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22.7477 | − | 43.3380i | −0.769014 | − | 1.46509i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.5939 | 0.695407 | 0.347703 | − | 0.937605i | \(-0.386962\pi\) | ||||
0.347703 | + | 0.937605i | \(0.386962\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 19.2087i | − | 0.647892i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.41742 | 0.148827 | 0.0744134 | − | 0.997227i | \(-0.476292\pi\) | ||||
0.0744134 | + | 0.997227i | \(0.476292\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.7367i | 1.06802i | 0.845477 | + | 0.534012i | \(0.179316\pi\) | ||||
−0.845477 | + | 0.534012i | \(0.820684\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −55.9129 | + | 45.6527i | −1.87949 | + | 1.53460i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.2425i | 1.35121i | 0.737264 | + | 0.675605i | \(0.236117\pi\) | ||||
−0.737264 | + | 0.675605i | \(0.763883\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2.23810i | − | 0.0750635i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 36.9415i | − | 1.23759i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.2704i | 1.11335i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.7701 | − | 13.6745i | −0.493160 | − | 0.456577i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.6849i | 0.789934i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.00000 | −0.266519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −59.4618 | −1.97877 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 40.8462 | − | 33.3508i | 1.35777 | − | 1.10862i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 39.7031i | − | 1.31832i | −0.752003 | − | 0.659159i | \(-0.770912\pi\) | ||
0.752003 | − | 0.659159i | \(-0.229088\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 60.3303 | 2.00103 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.6697 | 0.585423 | 0.292712 | − | 0.956201i | \(-0.405442\pi\) | ||||
0.292712 | + | 0.956201i | \(0.405442\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.83155i | 0.0606155i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.6838 | + | 19.2087i | 0.518491 | + | 0.635019i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.8564 | 0.457579 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.6697 | 0.450922 | 0.225461 | − | 0.974252i | \(-0.427611\pi\) | ||||
0.225461 | + | 0.974252i | \(0.427611\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 24.8655i | − | 0.819347i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.723000 | − | 0.780929i | 0.0237978 | − | 0.0257046i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.55040 | − | 12.4944i | 0.0838567 | − | 0.410812i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 61.1305i | 2.00779i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.9510i | 1.44198i | 0.692943 | + | 0.720992i | \(0.256314\pi\) | ||||
−0.692943 | + | 0.720992i | \(0.743686\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 65.2258i | − | 2.13769i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 19.5959i | − | 0.641542i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.66970 | − | 4.62929i | 0.185419 | − | 0.151394i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.75301i | − | 0.253280i | −0.991949 | − | 0.126640i | \(-0.959581\pi\) | ||
0.991949 | − | 0.126640i | \(-0.0404192\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.0000 | −0.391605 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 20.8564i | − | 0.679900i | −0.940443 | − | 0.339950i | \(-0.889590\pi\) | ||
0.940443 | − | 0.339950i | \(-0.110410\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.2378 | −0.463647 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 68.6606 | + | 84.0917i | 2.23353 | + | 2.73550i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.3640 | −1.14918 | −0.574588 | − | 0.818443i | \(-0.694838\pi\) | ||||
−0.574588 | + | 0.818443i | \(0.694838\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.74773 | + | 6.24718i | 0.219040 | + | 0.202792i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 62.1022i | − | 2.01380i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 52.1135i | − | 1.68812i | −0.536247 | − | 0.844061i | \(-0.680158\pi\) | ||
0.536247 | − | 0.844061i | \(-0.319842\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.7846 | − | 16.9706i | 0.672574 | − | 0.549155i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 59.4618 | 1.92213 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.4955 | 1.46912 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.2432 | 0.685264 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 69.6363i | 2.24400i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.330303 | − | 0.269691i | 0.0106328 | − | 0.00868166i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.5010 | −1.43106 | −0.715528 | − | 0.698584i | \(-0.753814\pi\) | ||||
−0.715528 | + | 0.698584i | \(0.753814\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.4468i | 0.688969i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.6606 | 1.56159 | 0.780797 | − | 0.624785i | \(-0.214814\pi\) | ||||
0.780797 | + | 0.624785i | \(0.214814\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.3676 | 1.00560 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −32.5406 | − | 45.3370i | −1.04213 | − | 1.45195i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 58.7388 | 1.87922 | 0.939611 | − | 0.342245i | \(-0.111187\pi\) | ||||
0.939611 | + | 0.342245i | \(0.111187\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.6606 | 0.915997 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 55.8550i | 1.78331i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 58.7388 | 1.87348 | 0.936739 | − | 0.350029i | \(-0.113828\pi\) | ||||
0.936739 | + | 0.350029i | \(0.113828\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −39.4955 | + | 32.2479i | −1.25843 | + | 1.02750i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 84.0917i | − | 2.67667i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.91288 | 0.251615 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4955 | −0.809890 | −0.404945 | − | 0.914341i | \(-0.632709\pi\) | ||||
−0.404945 | + | 0.914341i | \(0.632709\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 76.0593 | 2.41367 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.92820 | − | 5.65685i | 0.219639 | − | 0.179334i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 30.4164i | − | 0.963296i | −0.876365 | − | 0.481648i | \(-0.840038\pi\) | ||
0.876365 | − | 0.481648i | \(-0.159962\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.2843i | 0.894875i |
(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 | 260.2.d.a.129.1 | ✓ | 8 | |
3.2 | odd | 2 | 2340.2.j.d.649.5 | 8 | |||
4.3 | odd | 2 | 1040.2.f.e.129.7 | 8 | |||
5.2 | odd | 4 | 1300.2.f.f.701.1 | 8 | |||
5.3 | odd | 4 | 1300.2.f.f.701.8 | 8 | |||
5.4 | even | 2 | inner | 260.2.d.a.129.8 | yes | 8 | |
13.5 | odd | 4 | 3380.2.c.d.2029.2 | 8 | |||
13.8 | odd | 4 | 3380.2.c.d.2029.1 | 8 | |||
13.12 | even | 2 | inner | 260.2.d.a.129.2 | yes | 8 | |
15.14 | odd | 2 | 2340.2.j.d.649.2 | 8 | |||
20.19 | odd | 2 | 1040.2.f.e.129.2 | 8 | |||
39.38 | odd | 2 | 2340.2.j.d.649.4 | 8 | |||
52.51 | odd | 2 | 1040.2.f.e.129.8 | 8 | |||
65.12 | odd | 4 | 1300.2.f.f.701.2 | 8 | |||
65.34 | odd | 4 | 3380.2.c.d.2029.7 | 8 | |||
65.38 | odd | 4 | 1300.2.f.f.701.7 | 8 | |||
65.44 | odd | 4 | 3380.2.c.d.2029.8 | 8 | |||
65.64 | even | 2 | inner | 260.2.d.a.129.7 | yes | 8 | |
195.194 | odd | 2 | 2340.2.j.d.649.7 | 8 | |||
260.259 | odd | 2 | 1040.2.f.e.129.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.d.a.129.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
260.2.d.a.129.2 | yes | 8 | 13.12 | even | 2 | inner | |
260.2.d.a.129.7 | yes | 8 | 65.64 | even | 2 | inner | |
260.2.d.a.129.8 | yes | 8 | 5.4 | even | 2 | inner | |
1040.2.f.e.129.1 | 8 | 260.259 | odd | 2 | |||
1040.2.f.e.129.2 | 8 | 20.19 | odd | 2 | |||
1040.2.f.e.129.7 | 8 | 4.3 | odd | 2 | |||
1040.2.f.e.129.8 | 8 | 52.51 | odd | 2 | |||
1300.2.f.f.701.1 | 8 | 5.2 | odd | 4 | |||
1300.2.f.f.701.2 | 8 | 65.12 | odd | 4 | |||
1300.2.f.f.701.7 | 8 | 65.38 | odd | 4 | |||
1300.2.f.f.701.8 | 8 | 5.3 | odd | 4 | |||
2340.2.j.d.649.2 | 8 | 15.14 | odd | 2 | |||
2340.2.j.d.649.4 | 8 | 39.38 | odd | 2 | |||
2340.2.j.d.649.5 | 8 | 3.2 | odd | 2 | |||
2340.2.j.d.649.7 | 8 | 195.194 | odd | 2 | |||
3380.2.c.d.2029.1 | 8 | 13.8 | odd | 4 | |||
3380.2.c.d.2029.2 | 8 | 13.5 | odd | 4 | |||
3380.2.c.d.2029.7 | 8 | 65.34 | odd | 4 | |||
3380.2.c.d.2029.8 | 8 | 65.44 | odd | 4 |