Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(2431,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 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("4560.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.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: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.9821011968.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 20x^{4} + 118x^{2} + 192 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.1 | ||
Root | \(-3.24237i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.2431 |
Dual form | 4560.2.d.e.2431.6 |
$q$-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 \(\left(\mathbb{Z}/4560\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(1711\) | \(1921\) | \(2737\) | \(3041\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.24237i | − | 1.22550i | −0.790276 | − | 0.612751i | \(-0.790063\pi\) | ||
0.790276 | − | 0.612751i | \(-0.209937\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.82288i | − | 1.75566i | −0.478970 | − | 0.877832i | \(-0.658990\pi\) | ||
0.478970 | − | 0.877832i | \(-0.341010\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.24237i | − | 0.899272i | −0.893212 | − | 0.449636i | \(-0.851554\pi\) | ||
0.893212 | − | 0.449636i | \(-0.148446\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.51298 | −1.09456 | −0.547279 | − | 0.836950i | \(-0.684336\pi\) | ||||
−0.547279 | + | 0.836950i | \(0.684336\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.51298 | − | 2.58050i | −0.805932 | − | 0.592008i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.24237i | 0.707544i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.56750i | − | 1.16090i | −0.814295 | − | 0.580452i | \(-0.802876\pi\) | ||
0.814295 | − | 0.580452i | \(-0.197124\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.82288i | − | 1.08128i | −0.841254 | − | 0.540640i | \(-0.818182\pi\) | ||
0.841254 | − | 0.540640i | \(-0.181818\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.85398 | −1.41062 | −0.705308 | − | 0.708901i | \(-0.749191\pi\) | ||||
−0.705308 | + | 0.708901i | \(0.749191\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.82288i | 1.01363i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.24237i | 0.548061i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.255376i | 0.0419836i | 0.999780 | + | 0.0209918i | \(0.00668239\pi\) | ||||
−0.999780 | + | 0.0209918i | \(0.993318\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.24237i | 0.519195i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.661868i | − | 0.103366i | −0.998664 | − | 0.0516832i | \(-0.983541\pi\) | ||
0.998664 | − | 0.0516832i | \(-0.0164586\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.255376i | 0.0389445i | 0.999810 | + | 0.0194723i | \(0.00619860\pi\) | ||||
−0.999810 | + | 0.0194723i | \(0.993801\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.406492i | 0.0592930i | 0.999560 | + | 0.0296465i | \(0.00943815\pi\) | ||||
−0.999560 | + | 0.0296465i | \(0.990562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.51298 | −0.501854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.51298 | 0.631943 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.56750i | 0.764755i | 0.924006 | + | 0.382377i | \(0.124895\pi\) | ||||
−0.924006 | + | 0.382377i | \(0.875105\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.82288i | 0.785156i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.51298 | + | 2.58050i | 0.465305 | + | 0.341796i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.02595 | 1.17508 | 0.587539 | − | 0.809196i | \(-0.300097\pi\) | ||||
0.587539 | + | 0.809196i | \(0.300097\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.85398 | −0.749525 | −0.374762 | − | 0.927121i | \(-0.622276\pi\) | ||||
−0.374762 | + | 0.927121i | \(0.622276\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 3.24237i | − | 0.408500i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.24237i | 0.402167i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3670 | 1.26652 | 0.633262 | − | 0.773937i | \(-0.281715\pi\) | ||||
0.633262 | + | 0.773937i | \(0.281715\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.56750i | 0.670248i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.02595 | 1.07118 | 0.535592 | − | 0.844477i | \(-0.320089\pi\) | ||||
0.535592 | + | 0.844477i | \(0.320089\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.68495 | −0.665373 | −0.332687 | − | 0.943037i | \(-0.607955\pi\) | ||||
−0.332687 | + | 0.943037i | \(0.607955\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.8799 | −2.15157 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.65900 | 0.524178 | 0.262089 | − | 0.965044i | \(-0.415589\pi\) | ||||
0.262089 | + | 0.965044i | \(0.415589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.07825i | − | 0.667175i | −0.942719 | − | 0.333587i | \(-0.891741\pi\) | ||
0.942719 | − | 0.333587i | \(-0.108259\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.51298 | 0.489501 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.82288i | 0.624278i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.64886i | − | 0.386779i | −0.981122 | − | 0.193389i | \(-0.938052\pi\) | ||
0.981122 | − | 0.193389i | \(-0.0619481\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.5130 | −1.10206 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.85398 | 0.814419 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.51298 | + | 2.58050i | 0.360424 | + | 0.264754i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0536i | 1.32540i | 0.748887 | + | 0.662698i | \(0.230589\pi\) | ||||
−0.748887 | + | 0.662698i | \(0.769411\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.82288i | − | 0.585221i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.7080 | 1.36399 | 0.681996 | − | 0.731356i | \(-0.261112\pi\) | ||||
0.681996 | + | 0.731356i | \(0.261112\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.02595 | −0.495222 | −0.247611 | − | 0.968860i | \(-0.579645\pi\) | ||||
−0.247611 | + | 0.968860i | \(0.579645\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 3.24237i | − | 0.316423i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.3929 | 1.68144 | 0.840718 | − | 0.541474i | \(-0.182133\pi\) | ||||
0.840718 | + | 0.541474i | \(0.182133\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.65025i | − | 0.445414i | −0.974885 | − | 0.222707i | \(-0.928511\pi\) | ||
0.974885 | − | 0.222707i | \(-0.0714893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.255376i | − | 0.0242392i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2393i | 1.05730i | 0.848840 | + | 0.528650i | \(0.177302\pi\) | ||||
−0.848840 | + | 0.528650i | \(0.822698\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.56750i | 0.519172i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 3.24237i | − | 0.299757i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.6327i | 1.34138i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −22.9059 | −2.08235 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.661868i | 0.0596787i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.68495 | −0.681929 | −0.340965 | − | 0.940076i | \(-0.610754\pi\) | ||||
−0.340965 | + | 0.940076i | \(0.610754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 0.255376i | − | 0.0224846i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.00139i | − | 0.0874919i | −0.999043 | − | 0.0437460i | \(-0.986071\pi\) | ||
0.999043 | − | 0.0437460i | \(-0.0139292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.36695 | + | 11.3904i | −0.725507 | + | 0.987671i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.68495 | −0.314827 | −0.157413 | − | 0.987533i | \(-0.550315\pi\) | ||||
−0.157413 | + | 0.987533i | \(0.550315\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.32374i | − | 0.112278i | −0.998423 | − | 0.0561389i | \(-0.982121\pi\) | ||
0.998423 | − | 0.0561389i | \(-0.0178790\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 0.406492i | − | 0.0342328i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.8799 | −1.57882 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.82288i | 0.483564i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.51298 | 0.289745 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.0260 | 1.23097 | 0.615487 | − | 0.788147i | \(-0.288959\pi\) | ||||
0.615487 | + | 0.788147i | \(0.288959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.2209 | 1.80831 | 0.904157 | − | 0.427201i | \(-0.140500\pi\) | ||||
0.904157 | + | 0.427201i | \(0.140500\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.51298 | −0.364852 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.85398 | 0.630847 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.36695 | −0.348521 | −0.174260 | − | 0.984700i | \(-0.555753\pi\) | ||||
−0.174260 | + | 0.984700i | \(0.555753\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 5.56750i | − | 0.441531i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.0519 | −1.42269 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.56889i | 0.514515i | 0.966343 | + | 0.257258i | \(0.0828189\pi\) | ||||
−0.966343 | + | 0.257258i | \(0.917181\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 5.82288i | − | 0.453310i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.48702 | −0.115069 | −0.0575347 | − | 0.998344i | \(-0.518324\pi\) | ||||
−0.0575347 | + | 0.998344i | \(0.518324\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.48702 | 0.191310 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.51298 | − | 2.58050i | −0.268644 | − | 0.197336i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.4003i | 1.24689i | 0.781868 | + | 0.623445i | \(0.214267\pi\) | ||||
−0.781868 | + | 0.623445i | \(0.785733\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.24237i | − | 0.245100i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.02595 | −0.678432 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 24.6152i | − | 1.82964i | −0.403866 | − | 0.914818i | \(-0.632334\pi\) | ||
0.403866 | − | 0.914818i | \(-0.367666\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.85398 | 0.432738 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 0.255376i | − | 0.0187756i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26.2785i | 1.92167i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.24237i | 0.235848i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.17262i | 0.0848479i | 0.999100 | + | 0.0424239i | \(0.0135080\pi\) | ||||
−0.999100 | + | 0.0424239i | \(0.986492\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 17.5356i | − | 1.26224i | −0.775685 | − | 0.631120i | \(-0.782596\pi\) | ||
0.775685 | − | 0.631120i | \(-0.217404\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 3.24237i | − | 0.232191i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.48702 | 0.533428 | 0.266714 | − | 0.963776i | \(-0.414062\pi\) | ||||
0.266714 | + | 0.963776i | \(0.414062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.510752i | 0.0362063i | 0.999836 | + | 0.0181031i | \(0.00576272\pi\) | ||||
−0.999836 | + | 0.0181031i | \(0.994237\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.3670 | −0.731228 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.8799 | −1.32511 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.661868i | 0.0462269i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 5.56750i | − | 0.386968i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.0260 | + | 20.4556i | −1.03937 | + | 1.41495i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.3670 | −1.26443 | −0.632217 | − | 0.774792i | \(-0.717855\pi\) | ||||
−0.632217 | + | 0.774792i | \(0.717855\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.02595 | −0.618448 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 0.255376i | − | 0.0174165i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.4655i | 1.72871i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.68495 | 0.384153 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.6327i | 0.984305i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.0779 | −1.54541 | −0.772704 | − | 0.634767i | \(-0.781096\pi\) | ||||
−0.772704 | + | 0.634767i | \(0.781096\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.85693 | 0.587855 | 0.293927 | − | 0.955828i | \(-0.405038\pi\) | ||||
0.293927 | + | 0.955828i | \(0.405038\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.5130 | −1.35554 | −0.677768 | − | 0.735276i | \(-0.737053\pi\) | ||||
−0.677768 | + | 0.735276i | \(0.737053\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.8799 | 1.24221 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.7858 | −1.88582 | −0.942911 | − | 0.333046i | \(-0.891924\pi\) | ||||
−0.942911 | + | 0.333046i | \(0.891924\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 0.406492i | − | 0.0265166i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.65900 | −0.302635 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.6166i | − | 1.65700i | −0.559988 | − | 0.828501i | \(-0.689194\pi\) | ||
0.559988 | − | 0.828501i | \(-0.310806\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.4785i | 1.44797i | 0.689816 | + | 0.723984i | \(0.257691\pi\) | ||||
−0.689816 | + | 0.723984i | \(0.742309\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.51298 | 0.224436 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.36695 | + | 11.3904i | −0.532376 | + | 0.724752i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.07825i | 0.385194i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 15.8054i | − | 0.997626i | −0.866710 | − | 0.498813i | \(-0.833769\pi\) | ||
0.866710 | − | 0.498813i | \(-0.166231\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.4189 | −2.03816 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.51298 | −0.282614 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 18.0262i | − | 1.12445i | −0.826986 | − | 0.562223i | \(-0.809946\pi\) | ||
0.826986 | − | 0.562223i | \(-0.190054\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.828025 | 0.0514510 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 5.82288i | − | 0.360427i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 18.0262i | − | 1.11155i | −0.831334 | − | 0.555773i | \(-0.812423\pi\) | ||
0.831334 | − | 0.555773i | \(-0.187577\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.56750i | − | 0.342009i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.64886i | 0.223307i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.34663i | − | 0.204048i | −0.994782 | − | 0.102024i | \(-0.967468\pi\) | ||
0.994782 | − | 0.102024i | \(-0.0325318\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.83727i | 0.233098i | 0.993185 | + | 0.116549i | \(0.0371831\pi\) | ||||
−0.993185 | + | 0.116549i | \(0.962817\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.5130 | 0.636274 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 5.82288i | − | 0.351133i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.7080 | 1.30430 | 0.652152 | − | 0.758088i | \(-0.273866\pi\) | ||||
0.652152 | + | 0.758088i | \(0.273866\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.85398 | −0.470205 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.8081i | 1.06235i | 0.847264 | + | 0.531173i | \(0.178248\pi\) | ||||
−0.847264 | + | 0.531173i | \(0.821752\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.8881i | 0.885007i | 0.896767 | + | 0.442504i | \(0.145910\pi\) | ||||
−0.896767 | + | 0.442504i | \(0.854090\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.51298 | − | 2.58050i | −0.208091 | − | 0.152856i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.14602 | −0.126676 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.36695 | 0.198056 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 13.0536i | − | 0.765218i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.2133i | 1.00561i | 0.864400 | + | 0.502804i | \(0.167698\pi\) | ||||
−0.864400 | + | 0.502804i | \(0.832302\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.02595 | −0.525511 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.82288i | 0.337878i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.0519 | −1.04397 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.828025 | 0.0477265 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.7080 | −0.787501 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.85398 | 0.335198 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.97405 | 0.398030 | 0.199015 | − | 0.979996i | \(-0.436226\pi\) | ||||
0.199015 | + | 0.979996i | \(0.436226\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.02595 | 0.285916 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 9.83138i | − | 0.557486i | −0.960366 | − | 0.278743i | \(-0.910082\pi\) | ||
0.960366 | − | 0.278743i | \(-0.0899178\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.7109 | −0.831509 | −0.415755 | − | 0.909477i | \(-0.636483\pi\) | ||||
−0.415755 | + | 0.909477i | \(0.636483\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.24237i | 0.182687i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 25.5325i | − | 1.43405i | −0.697049 | − | 0.717024i | \(-0.745504\pi\) | ||
0.697049 | − | 0.717024i | \(-0.254496\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −33.9059 | −1.89836 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.3929 | −0.970777 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.8540 | + | 11.6458i | 0.882139 | + | 0.647987i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.24237i | − | 0.179854i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.65025i | 0.257160i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.31800 | 0.0726636 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.53893 | −0.194517 | −0.0972585 | − | 0.995259i | \(-0.531007\pi\) | ||||
−0.0972585 | + | 0.995259i | \(0.531007\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.255376i | 0.0139945i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.3670 | −0.566407 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.8231i | 1.62457i | 0.583262 | + | 0.812284i | \(0.301776\pi\) | ||||
−0.583262 | + | 0.812284i | \(0.698224\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 11.2393i | − | 0.610433i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 45.7327i | 2.47657i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 11.3062i | − | 0.610479i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 5.56750i | − | 0.299744i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.56472i | 0.191364i | 0.995412 | + | 0.0956820i | \(0.0305032\pi\) | ||||
−0.995412 | + | 0.0956820i | \(0.969497\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.4189 | 1.52123 | 0.760613 | − | 0.649205i | \(-0.224898\pi\) | ||||
0.760613 | + | 0.649205i | \(0.224898\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.24237i | 0.173065i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0519 | −0.641458 | −0.320729 | − | 0.947171i | \(-0.603928\pi\) | ||||
−0.320729 | + | 0.947171i | \(0.603928\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.02595 | −0.479048 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 14.6327i | − | 0.774447i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.0884i | 1.85189i | 0.377654 | + | 0.925947i | \(0.376731\pi\) | ||||
−0.377654 | + | 0.925947i | \(0.623269\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.68200 | + | 18.1305i | 0.299053 | + | 0.954237i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.9059 | 1.20225 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.68495 | 0.297564 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 32.1683i | − | 1.67917i | −0.543225 | − | 0.839587i | \(-0.682797\pi\) | ||
0.543225 | − | 0.839587i | \(-0.317203\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 0.661868i | − | 0.0344555i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.0519 | 0.937208 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.42939i | 0.125789i | 0.998020 | + | 0.0628945i | \(0.0200332\pi\) | ||||
−0.998020 | + | 0.0628945i | \(0.979967\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.8799 | −0.972366 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.53893 | −0.181783 | −0.0908913 | − | 0.995861i | \(-0.528972\pi\) | ||||
−0.0908913 | + | 0.995861i | \(0.528972\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.68495 | 0.393712 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.0000 | 1.22634 | 0.613171 | − | 0.789950i | \(-0.289894\pi\) | ||||
0.613171 | + | 0.789950i | \(0.289894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.8799 | 0.962210 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.255376i | 0.0129815i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.0779 | 1.06869 | 0.534345 | − | 0.845267i | \(-0.320558\pi\) | ||||
0.534345 | + | 0.845267i | \(0.320558\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.1260i | 1.27068i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.00139i | 0.0505135i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.65900 | −0.234420 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.36695 | − | 11.3904i | 0.418872 | − | 0.570232i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 14.1421i | − | 0.706223i | −0.935581 | − | 0.353112i | \(-0.885124\pi\) | ||
0.935581 | − | 0.353112i | \(-0.114876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.4655i | 1.26853i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.48702 | 0.0737090 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.6412i | − | 0.921750i | −0.887465 | − | 0.460875i | \(-0.847536\pi\) | ||
0.887465 | − | 0.460875i | \(-0.152464\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.68495 | 0.181765 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 29.2655i | − | 1.44006i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.07825i | 0.298370i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.32374i | 0.0648237i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6.63586i | − | 0.324183i | −0.986776 | − | 0.162091i | \(-0.948176\pi\) | ||
0.986776 | − | 0.162091i | \(-0.0518240\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.1565i | − | 0.592472i | −0.955115 | − | 0.296236i | \(-0.904269\pi\) | ||
0.955115 | − | 0.296236i | \(-0.0957314\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.406492i | 0.0197643i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.51298 | −0.218911 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.9808i | 0.918544i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.8799 | 0.911532 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.02595 | 0.434765 | 0.217382 | − | 0.976087i | \(-0.430248\pi\) | ||||
0.217382 | + | 0.976087i | \(0.430248\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.8881i | 0.715478i | 0.933822 | + | 0.357739i | \(0.116452\pi\) | ||||
−0.933822 | + | 0.357739i | \(0.883548\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 5.82288i | − | 0.279186i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.3670 | + | 19.5585i | −0.687265 | + | 0.935610i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.51298 | −0.167285 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.0200i | 1.61634i | 0.588950 | + | 0.808170i | \(0.299542\pi\) | ||||
−0.588950 | + | 0.808170i | \(0.700458\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.64886i | 0.172973i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.0260 | −0.710703 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 30.6064i | − | 1.44441i | −0.691681 | − | 0.722203i | \(-0.743130\pi\) | ||
0.691681 | − | 0.722203i | \(-0.256870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.85398 | −0.181477 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.2209 | −1.04403 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.5130 | 0.492856 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.3670 | 0.578502 | 0.289251 | − | 0.957253i | \(-0.406594\pi\) | ||||
0.289251 | + | 0.957253i | \(0.406594\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.51298 | 0.210648 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.4159 | 1.55633 | 0.778167 | − | 0.628057i | \(-0.216150\pi\) | ||||
0.778167 | + | 0.628057i | \(0.216150\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0621i | 0.792945i | 0.918047 | + | 0.396472i | \(0.129766\pi\) | ||||
−0.918047 | + | 0.396472i | \(0.870234\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.85398 | −0.364219 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 27.0245i | − | 1.25055i | −0.780406 | − | 0.625273i | \(-0.784988\pi\) | ||
0.780406 | − | 0.625273i | \(-0.215012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 33.6135i | − | 1.55213i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.36695 | 0.201219 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.48702 | 0.0683734 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.51298 | − | 2.58050i | −0.161186 | − | 0.118402i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.56750i | 0.254918i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 21.7794i | − | 0.995124i | −0.867428 | − | 0.497562i | \(-0.834229\pi\) | ||
0.867428 | − | 0.497562i | \(-0.165771\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.828025 | 0.0377547 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.0519 | 0.821390 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 13.0536i | − | 0.592735i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.3929 | −0.697519 | −0.348760 | − | 0.937212i | \(-0.613397\pi\) | ||||
−0.348760 | + | 0.937212i | \(0.613397\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6.56889i | − | 0.297055i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 17.4686i | − | 0.788348i | −0.919036 | − | 0.394174i | \(-0.871031\pi\) | ||
0.919036 | − | 0.394174i | \(-0.128969\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.2785i | 1.18352i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.82288i | 0.261719i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 29.2655i | − | 1.31274i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 5.67176i | − | 0.253903i | −0.991909 | − | 0.126951i | \(-0.959481\pi\) | ||
0.991909 | − | 0.126951i | \(-0.0405192\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.48702 | 0.0664353 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.0262i | 0.803750i | 0.915695 | + | 0.401875i | \(0.131641\pi\) | ||||
−0.915695 | + | 0.401875i | \(0.868359\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.7080 | −0.609996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.48702 | −0.110453 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 14.3104i | − | 0.634297i | −0.948376 | − | 0.317149i | \(-0.897275\pi\) | ||
0.948376 | − | 0.317149i | \(-0.102725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.4327i | 0.815416i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.51298 | + | 2.58050i | 0.155102 | + | 0.113932i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.02595 | 0.221470 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.36695 | 0.104098 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 16.4003i | − | 0.719892i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6.29634i | − | 0.275848i | −0.990443 | − | 0.137924i | \(-0.955957\pi\) | ||
0.990443 | − | 0.137924i | \(-0.0440429\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.7628 | −1.52007 | −0.760036 | − | 0.649881i | \(-0.774819\pi\) | ||||
−0.760036 | + | 0.649881i | \(0.774819\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.24237i | 0.141509i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.4448 | 1.54400 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.99705 | −0.347698 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.02595 | 0.391693 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.14602 | −0.0929546 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.3929 | −0.751961 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.4556i | 0.881086i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.4159 | −1.52265 | −0.761324 | − | 0.648371i | \(-0.775451\pi\) | ||||
−0.761324 | + | 0.648371i | \(0.775451\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.6152i | 1.05634i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.65025i | 0.199195i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7080 | −0.671624 | −0.335812 | − | 0.941929i | \(-0.609011\pi\) | ||||
−0.335812 | + | 0.941929i | \(0.609011\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.85398 | −0.249842 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0260 | + | 20.4556i | −0.640127 | + | 0.871439i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15.1062i | − | 0.642381i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.255376i | 0.0108401i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.99705 | −0.296475 | −0.148237 | − | 0.988952i | \(-0.547360\pi\) | ||||
−0.148237 | + | 0.988952i | \(0.547360\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.828025 | 0.0350217 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 26.2785i | − | 1.10948i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.19498 | −0.387522 | −0.193761 | − | 0.981049i | \(-0.562069\pi\) | ||||
−0.193761 | + | 0.981049i | \(0.562069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 11.2393i | − | 0.472839i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3.24237i | − | 0.136167i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.6099i | 0.528632i | 0.964436 | + | 0.264316i | \(0.0851463\pi\) | ||||
−0.964436 | + | 0.264316i | \(0.914854\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 32.4237i | − | 1.35689i | −0.734651 | − | 0.678445i | \(-0.762654\pi\) | ||
0.734651 | − | 0.678445i | \(-0.237346\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.17262i | − | 0.0489869i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.56750i | − | 0.232181i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.3929 | 0.890598 | 0.445299 | − | 0.895382i | \(-0.353097\pi\) | ||||
0.445299 | + | 0.895382i | \(0.353097\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.5356i | 0.728755i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.7080 | −0.817624 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.4189 | 1.34265 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.24237i | 0.134056i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 37.6890i | − | 1.55559i | −0.628517 | − | 0.777795i | \(-0.716338\pi\) | ||
0.628517 | − | 0.777795i | \(-0.283662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.5908 | + | 20.2672i | 1.13686 | + | 0.835096i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.48702 | −0.307975 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.4189 | −1.33128 | −0.665641 | − | 0.746272i | \(-0.731842\pi\) | ||||
−0.665641 | + | 0.746272i | \(0.731842\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 14.6327i | − | 0.599884i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 0.510752i | − | 0.0209037i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.29205 | −0.175368 | −0.0876841 | − | 0.996148i | \(-0.527947\pi\) | ||||
−0.0876841 | + | 0.996148i | \(0.527947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.0983i | 1.63564i | 0.575473 | + | 0.817821i | \(0.304818\pi\) | ||||
−0.575473 | + | 0.817821i | \(0.695182\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.3670 | 0.422175 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.9059 | 0.931256 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.7369 | −1.04463 | −0.522313 | − | 0.852754i | \(-0.674931\pi\) | ||||
−0.522313 | + | 0.852754i | \(0.674931\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.8799 | 0.765053 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.31800 | 0.0533205 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.0749 | 1.29549 | 0.647747 | − | 0.761856i | \(-0.275712\pi\) | ||||
0.647747 | + | 0.761856i | \(0.275712\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 0.661868i | − | 0.0266891i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.5389 | 0.545057 | 0.272528 | − | 0.962148i | \(-0.412140\pi\) | ||||
0.272528 | + | 0.962148i | \(0.412140\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 21.2887i | − | 0.855666i | −0.903858 | − | 0.427833i | \(-0.859277\pi\) | ||
0.903858 | − | 0.427833i | \(-0.140723\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.56750i | 0.223416i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.8310 | −0.473998 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.0260 | − | 20.4556i | 0.600079 | − | 0.816919i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.15251i | − | 0.0459535i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.4005i | 1.60832i | 0.594414 | + | 0.804159i | \(0.297384\pi\) | ||||
−0.594414 | + | 0.804159i | \(0.702616\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.3670 | 0.730021 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.68495 | 0.304968 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.3904i | 0.451303i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.02595 | 0.357061 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.4528i | 0.728843i | 0.931234 | + | 0.364422i | \(0.118733\pi\) | ||||
−0.931234 | + | 0.364422i | \(0.881267\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.7141i | 0.501396i | 0.968065 | + | 0.250698i | \(0.0806600\pi\) | ||||
−0.968065 | + | 0.250698i | \(0.919340\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.255376i | 0.0100554i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.72573i | 0.343044i | 0.985180 | + | 0.171522i | \(0.0548684\pi\) | ||||
−0.985180 | + | 0.171522i | \(0.945132\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 52.5570i | − | 2.06304i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 25.4655i | − | 0.998072i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.8829 | −0.465013 | −0.232506 | − | 0.972595i | \(-0.574693\pi\) | ||||
−0.232506 | + | 0.972595i | \(0.574693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.00139i | 0.0391276i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.68495 | −0.221791 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.3180 | −0.518796 | −0.259398 | − | 0.965771i | \(-0.583524\pi\) | ||||
−0.259398 | + | 0.965771i | \(0.583524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 15.7853i | − | 0.613975i | −0.951714 | − | 0.306988i | \(-0.900679\pi\) | ||
0.951714 | − | 0.306988i | \(-0.0993210\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 14.6327i | − | 0.568289i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.36695 | − | 11.3904i | 0.324457 | − | 0.441700i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.4189 | −1.25526 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.0779 | 0.892241 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.0870i | 1.31591i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.1378i | 1.73994i | 0.493109 | + | 0.869968i | \(0.335861\pi\) | ||||
−0.493109 | + | 0.869968i | \(0.664139\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.54599i | 0.174717i | 0.996177 | + | 0.0873584i | \(0.0278425\pi\) | ||||
−0.996177 | + | 0.0873584i | \(0.972157\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.3247 | 1.62427 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.85693 | −0.339398 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.7569 | 1.02382 | 0.511912 | − | 0.859038i | \(-0.328937\pi\) | ||||
0.511912 | + | 0.859038i | \(0.328937\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.68495 | 0.140795 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.5130 | 0.782619 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.0519 | 0.687723 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 11.4372i | − | 0.435093i | −0.976050 | − | 0.217546i | \(-0.930195\pi\) | ||
0.976050 | − | 0.217546i | \(-0.0698053\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.8799 | −0.717189 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.32374i | 0.0502122i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.98700i | 0.113141i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.7858 | 1.08878 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.0779 | 0.796100 | 0.398050 | − | 0.917364i | \(-0.369687\pi\) | ||||
0.398050 | + | 0.917364i | \(0.369687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.658999 | − | 0.897131i | 0.0248546 | − | 0.0338359i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.406492i | 0.0153094i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 44.4463i | − | 1.67157i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.9578 | 1.42553 | 0.712767 | − | 0.701401i | \(-0.247442\pi\) | ||||
0.712767 | + | 0.701401i | \(0.247442\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.65900 | 0.174726 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 43.7270i | 1.63759i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.8799 | 0.706069 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.6166i | 0.956671i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 17.9421i | − | 0.669127i | −0.942373 | − | 0.334563i | \(-0.891411\pi\) | ||
0.942373 | − | 0.334563i | \(-0.108589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.2960i | 0.606895i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 22.4785i | − | 0.835985i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 5.82288i | − | 0.216256i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.89263i | − | 0.292721i | −0.989231 | − | 0.146361i | \(-0.953244\pi\) | ||
0.989231 | − | 0.146361i | \(-0.0467560\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.15251i | − | 0.0426270i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.6850 | 0.948695 | 0.474348 | − | 0.880338i | \(-0.342684\pi\) | ||||
0.474348 | + | 0.880338i | \(0.342684\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.51298 | −0.129578 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 60.3655i | − | 2.22359i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.5045i | 0.607129i | 0.952811 | + | 0.303564i | \(0.0981768\pi\) | ||||
−0.952811 | + | 0.303564i | \(0.901823\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.36695 | − | 11.3904i | 0.307368 | − | 0.418436i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.6820 | −1.27236 | −0.636180 | − | 0.771541i | \(-0.719486\pi\) | ||||
−0.636180 | + | 0.771541i | \(0.719486\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.0260 | −0.550508 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 6.07825i | − | 0.222392i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 56.3943i | − | 2.06060i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.2728 | 1.46958 | 0.734788 | − | 0.678297i | \(-0.237282\pi\) | ||||
0.734788 | + | 0.678297i | \(0.237282\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.8054i | 0.575980i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.2209 | −0.808702 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.7080 | −1.07975 | −0.539877 | − | 0.841744i | \(-0.681529\pi\) | ||||
−0.539877 | + | 0.841744i | \(0.681529\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 32.4189 | 1.17673 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −52.4478 | −1.90123 | −0.950615 | − | 0.310373i | \(-0.899546\pi\) | ||||
−0.950615 | + | 0.310373i | \(0.899546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.0779 | −0.545855 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.51298 | 0.163167 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 29.2655i | − | 1.05672i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.7858 | 1.39865 | 0.699326 | − | 0.714803i | \(-0.253484\pi\) | ||||
0.699326 | + | 0.714803i | \(0.253484\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0262i | 0.649199i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 44.4760i | − | 1.59969i | −0.600207 | − | 0.799845i | \(-0.704915\pi\) | ||
0.600207 | − | 0.799845i | \(-0.295085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.85398 | −0.282123 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.828025 | −0.0297052 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.70795 | + | 2.32513i | −0.0611938 | + | 0.0833063i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 52.5570i | − | 1.88064i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.82288i | 0.208093i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.36695 | 0.155863 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.3410 | 0.475555 | 0.237778 | − | 0.971320i | \(-0.423581\pi\) | ||||
0.237778 | + | 0.971320i | \(0.423581\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.0262i | 0.641751i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.4419 | 1.29572 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.9808i | 0.674027i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.56750i | 0.197459i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.5602i | 0.374062i | 0.982354 | + | 0.187031i | \(0.0598865\pi\) | ||||
−0.982354 | + | 0.187031i | \(0.940114\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.83449i | − | 0.0648996i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.64886i | − | 0.128926i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.1028i | 1.16817i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.0519 | 0.636246 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.34663i | 0.117807i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.8118 | 1.75129 | 0.875644 | − | 0.482957i | \(-0.160437\pi\) | ||||
0.875644 | + | 0.482957i | \(0.160437\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.1038 | −1.12732 | −0.563659 | − | 0.826008i | \(-0.690607\pi\) | ||||
−0.563659 | + | 0.826008i | \(0.690607\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 3.83727i | − | 0.134579i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 6.56889i | − | 0.230098i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.658999 | − | 0.897131i | 0.0230555 | − | 0.0313866i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.5130 | −0.367353 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.6820 | −0.582206 | −0.291103 | − | 0.956692i | \(-0.594022\pi\) | ||||
−0.291103 | + | 0.956692i | \(0.594022\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 29.2186i | − | 1.01850i | −0.860619 | − | 0.509249i | \(-0.829923\pi\) | ||
0.860619 | − | 0.509249i | \(-0.170077\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.82288i | 0.202727i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.82507 | −0.0634641 | −0.0317320 | − | 0.999496i | \(-0.510102\pi\) | ||||
−0.0317320 | + | 0.999496i | \(0.510102\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 45.2593i | − | 1.57192i | −0.618278 | − | 0.785960i | \(-0.712169\pi\) | ||
0.618278 | − | 0.785960i | \(-0.287831\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.7080 | −0.753041 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.8540 | 0.549308 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.48702 | 0.0514606 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.85398 | 0.271473 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 55.7080 | 1.92325 | 0.961626 | − | 0.274363i | \(-0.0884671\pi\) | ||||
0.961626 | + | 0.274363i | \(0.0884671\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.90588 | −0.169168 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 17.8081i | − | 0.613345i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.48702 | −0.0855562 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 74.2694i | 2.55193i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 14.8881i | − | 0.510959i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.42181 | 0.0487389 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.7599 | −0.402650 | −0.201325 | − | 0.979525i | \(-0.564525\pi\) | ||||
−0.201325 | + | 0.979525i | \(0.564525\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.51298 | + | 2.58050i | 0.120141 | + | 0.0882514i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.5065i | 1.07624i | 0.842868 | + | 0.538120i | \(0.180865\pi\) | ||||
−0.842868 | + | 0.538120i | \(0.819135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.0650i | 1.74231i | 0.491004 | + | 0.871157i | \(0.336630\pi\) | ||||
−0.491004 | + | 0.871157i | \(0.663370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.14602 | 0.0731363 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.7109 | 1.45390 | 0.726948 | − | 0.686692i | \(-0.240938\pi\) | ||||
0.726948 | + | 0.686692i | \(0.240938\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 16.4003i | − | 0.557626i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.36695 | −0.114348 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 27.1288i | − | 0.920281i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 33.6135i | − | 1.13895i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.0536i | 0.441799i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.24237i | 0.109612i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.27688i | 0.0431172i | 0.999768 | + | 0.0215586i | \(0.00686285\pi\) | ||||
−0.999768 | + | 0.0215586i | \(0.993137\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 17.2133i | − | 0.580589i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.3180 | 0.650840 | 0.325420 | − | 0.945570i | \(-0.394494\pi\) | ||||
0.325420 | + | 0.945570i | \(0.394494\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 6.40060i | − | 0.215397i | −0.994184 | − | 0.107699i | \(-0.965652\pi\) | ||
0.994184 | − | 0.107699i | \(-0.0343482\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.02595 | 0.303404 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.4218 | 0.853581 | 0.426790 | − | 0.904351i | \(-0.359644\pi\) | ||||
0.426790 | + | 0.904351i | \(0.359644\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.9175i | 0.835705i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 5.82288i | − | 0.195074i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.04895 | − | 1.42800i | 0.0351019 | − | 0.0477861i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.0519 | 0.602736 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 45.7327i | 1.52527i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 25.1260i | − | 0.837068i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.828025 | −0.0275549 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.6152i | 0.818238i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −54.4708 | −1.80867 | −0.904336 | − | 0.426821i | \(-0.859633\pi\) | ||||
−0.904336 | + | 0.426821i | \(0.859633\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.7080 | 0.454664 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.4938 | −1.40788 | −0.703941 | − | 0.710259i | \(-0.748578\pi\) | ||||
−0.703941 | + | 0.710259i | \(0.748578\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.3929 | −1.17133 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.85398 | −0.193527 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.24688 | −0.107221 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.0220i | 1.61709i | 0.588438 | + | 0.808543i | \(0.299743\pi\) | ||||
−0.588438 | + | 0.808543i | \(0.700257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.97405 | −0.229803 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 29.2655i | − | 0.963285i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.255376i | 0.00839672i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.02595 | −0.165074 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.1557 | 1.18623 | 0.593115 | − | 0.805118i | \(-0.297898\pi\) | ||||
0.593115 | + | 0.805118i | \(0.297898\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.3410 | + | 9.06525i | 0.404460 | + | 0.297101i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.83138i | 0.321865i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 26.2785i | − | 0.859399i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.7599 | −1.56025 | −0.780123 | − | 0.625626i | \(-0.784844\pi\) | ||||
−0.780123 | + | 0.625626i | \(0.784844\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.7109 | 0.480072 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 38.7946i | − | 1.26467i | −0.774695 | − | 0.632335i | \(-0.782097\pi\) | ||
0.774695 | − | 0.632335i | \(-0.217903\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.68495 | −0.119999 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 3.24237i | − | 0.105474i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.5297i | 0.764613i | 0.924036 | + | 0.382306i | \(0.124870\pi\) | ||||
−0.924036 | + | 0.382306i | \(0.875130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.4327i | 0.598352i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.5325i | 0.827948i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31.8087i | − | 1.03039i | −0.857074 | − | 0.515193i | \(-0.827720\pi\) | ||
0.857074 | − | 0.515193i | \(-0.172280\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.17262i | − | 0.0379451i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.9059 | 1.09602 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.9480i | 0.385820i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.6850 | 0.989837 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.3929 | 0.560479 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.5356i | 0.564491i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 44.9666i | − | 1.44603i | −0.690833 | − | 0.723014i | \(-0.742756\pi\) | ||
0.690833 | − | 0.723014i | \(-0.257244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.8540 | − | 11.6458i | −0.509303 | − | 0.374115i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.4218 | −1.58602 | −0.793011 | − | 0.609208i | \(-0.791488\pi\) | ||||
−0.793011 | + | 0.609208i | \(0.791488\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.29205 | −0.137597 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.24237i | 0.103839i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.7025i | 0.534360i | 0.963647 | + | 0.267180i | \(0.0860919\pi\) | ||||
−0.963647 | + | 0.267180i | \(0.913908\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.2469 | −0.679053 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 4.65025i | − | 0.148471i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.2469 | −1.63452 | −0.817261 | − | 0.576268i | \(-0.804508\pi\) | ||||
−0.817261 | + | 0.576268i | \(0.804508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.48702 | −0.238556 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.31800 | −0.0419524 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.42181 | 0.0452108 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.0260 | 1.11264 | 0.556318 | − | 0.830969i | \(-0.312214\pi\) | ||||
0.556318 | + | 0.830969i | \(0.312214\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.53893 | 0.112304 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 0.510752i | − | 0.0161919i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0490 | 0.349924 | 0.174962 | − | 0.984575i | \(-0.444020\pi\) | ||||
0.174962 | + | 0.984575i | \(0.444020\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 0.255376i | − | 0.00807975i |
(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 | 4560.2.d.e.2431.1 | ✓ | 6 | |
4.3 | odd | 2 | 4560.2.d.g.2431.6 | yes | 6 | ||
19.18 | odd | 2 | 4560.2.d.g.2431.1 | yes | 6 | ||
76.75 | even | 2 | inner | 4560.2.d.e.2431.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4560.2.d.e.2431.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
4560.2.d.e.2431.6 | yes | 6 | 76.75 | even | 2 | inner | |
4560.2.d.g.2431.1 | yes | 6 | 19.18 | odd | 2 | ||
4560.2.d.g.2431.6 | yes | 6 | 4.3 | odd | 2 |