Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [840,2,Mod(121,840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(840, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("840.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 840.bg (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.70743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.29428272.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 6x^{4} - 4x^{3} - 42x^{2} + 343 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(-0.0741344 - 2.64471i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 840.121 |
Dual form | 840.2.bg.j.361.2 |
$q$-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 \(\left(\mathbb{Z}/840\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(281\) | \(337\) | \(421\) | \(631\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0741344 | + | 2.64471i | −0.0280202 | + | 0.999607i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.08078 | − | 5.33606i | −0.928889 | − | 1.60888i | −0.785184 | − | 0.619262i | \(-0.787432\pi\) |
−0.143705 | − | 0.989621i | \(-0.545902\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50664 | 0.695217 | 0.347609 | − | 0.937640i | \(-0.386994\pi\) | ||||
0.347609 | + | 0.937640i | \(0.386994\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.90159 | − | 5.02570i | −0.703739 | − | 1.21891i | −0.967145 | − | 0.254226i | \(-0.918179\pi\) |
0.263406 | − | 0.964685i | \(-0.415154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.32746 | − | 1.25815i | 0.507892 | − | 0.274552i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.425866 | − | 0.737621i | 0.0887991 | − | 0.153805i | −0.818205 | − | 0.574927i | \(-0.805030\pi\) |
0.907004 | + | 0.421122i | \(0.138364\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.50664 | 1.02256 | 0.511279 | − | 0.859415i | \(-0.329172\pi\) | ||||
0.511279 | + | 0.859415i | \(0.329172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.67919 | − | 6.37254i | −0.660801 | − | 1.14454i | −0.980405 | − | 0.196990i | \(-0.936883\pi\) |
0.319604 | − | 0.947551i | \(-0.396450\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.08078 | + | 5.33606i | −0.536294 | + | 0.928889i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.25332 | + | 1.38656i | 0.380881 | + | 0.234371i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.90823 | − | 8.50131i | 0.806908 | − | 1.39761i | −0.108087 | − | 0.994141i | \(-0.534472\pi\) |
0.914995 | − | 0.403465i | \(-0.132194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.25332 | − | 2.17082i | −0.200692 | − | 0.347609i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.14827 | −0.491677 | −0.245838 | − | 0.969311i | \(-0.579063\pi\) | ||||
−0.245838 | + | 0.969311i | \(0.579063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.16155 | −1.09213 | −0.546063 | − | 0.837744i | \(-0.683874\pi\) | ||||
−0.546063 | + | 0.837744i | \(0.683874\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.17919 | − | 2.04241i | 0.172002 | − | 0.297916i | −0.767118 | − | 0.641506i | \(-0.778310\pi\) |
0.939120 | + | 0.343590i | \(0.111643\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.98901 | − | 0.392129i | −0.998430 | − | 0.0560184i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.90159 | + | 5.02570i | −0.406304 | + | 0.703739i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.672545 | + | 1.16488i | 0.0923811 | + | 0.160009i | 0.908513 | − | 0.417857i | \(-0.137219\pi\) |
−0.816131 | + | 0.577866i | \(0.803886\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.16155 | −0.830824 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.24668 | − | 5.62341i | −0.422682 | − | 0.732106i | 0.573519 | − | 0.819192i | \(-0.305578\pi\) |
−0.996201 | + | 0.0870861i | \(0.972244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.25332 | − | 1.38656i | −0.283892 | − | 0.174690i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.25332 | − | 2.17082i | 0.155455 | − | 0.269257i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.58078 | + | 6.20209i | 0.437461 | + | 0.757705i | 0.997493 | − | 0.0707658i | \(-0.0225443\pi\) |
−0.560031 | + | 0.828471i | \(0.689211\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.851731 | −0.102536 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.1130 | −1.79358 | −0.896792 | − | 0.442453i | \(-0.854108\pi\) | ||||
−0.896792 | + | 0.442453i | \(0.854108\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.92587 | − | 5.06775i | −0.342447 | − | 0.593135i | 0.642440 | − | 0.766336i | \(-0.277922\pi\) |
−0.984886 | + | 0.173201i | \(0.944589\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.3407 | − | 7.75218i | 1.63428 | − | 0.883443i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.33410 | + | 10.9710i | −0.712642 | + | 1.23433i | 0.251220 | + | 0.967930i | \(0.419168\pi\) |
−0.963862 | + | 0.266402i | \(0.914165\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.50664 | 0.604432 | 0.302216 | − | 0.953239i | \(-0.402274\pi\) | ||||
0.302216 | + | 0.953239i | \(0.402274\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.80318 | −0.629443 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.75332 | − | 4.76889i | −0.295187 | − | 0.511279i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.40823 | − | 9.36733i | 0.573271 | − | 0.992935i | −0.422956 | − | 0.906150i | \(-0.639007\pi\) |
0.996227 | − | 0.0867848i | \(-0.0276593\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.185828 | + | 6.62935i | −0.0194801 | + | 0.694944i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.67919 | + | 6.37254i | −0.381514 | + | 0.660801i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.500000 | + | 0.866025i | 0.0512989 | + | 0.0888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.16155 | 0.619259 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.09841 | − | 1.90250i | −0.109296 | − | 0.189306i | 0.806189 | − | 0.591658i | \(-0.201526\pi\) |
−0.915485 | + | 0.402352i | \(0.868193\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.08742 | − | 8.81167i | 0.501278 | − | 0.868239i | −0.498721 | − | 0.866763i | \(-0.666197\pi\) |
0.999999 | − | 0.00147659i | \(-0.000470015\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0741344 | − | 2.64471i | 0.00723478 | − | 0.258098i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.55650 | − | 9.62414i | 0.537167 | − | 0.930401i | −0.461888 | − | 0.886938i | \(-0.652828\pi\) |
0.999055 | − | 0.0434625i | \(-0.0138389\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.33410 | + | 5.77483i | 0.319349 | + | 0.553128i | 0.980352 | − | 0.197255i | \(-0.0632026\pi\) |
−0.661004 | + | 0.750383i | \(0.729869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.81646 | −0.931737 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.6196 | 1.93973 | 0.969866 | − | 0.243637i | \(-0.0783406\pi\) | ||||
0.969866 | + | 0.243637i | \(0.0783406\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.425866 | − | 0.737621i | −0.0397122 | − | 0.0687835i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.25332 | + | 2.17082i | −0.115870 | + | 0.200692i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.5066 | − | 7.30129i | 1.23815 | − | 0.669308i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.4824 | + | 23.3521i | −1.22567 | + | 2.12292i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.57413 | + | 2.72648i | 0.141935 | + | 0.245838i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.11300 | 0.719912 | 0.359956 | − | 0.932969i | \(-0.382792\pi\) | ||||
0.359956 | + | 0.932969i | \(0.382792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.58078 | + | 6.20209i | 0.315270 | + | 0.546063i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.32746 | + | 4.03127i | −0.203351 | + | 0.352214i | −0.949606 | − | 0.313446i | \(-0.898516\pi\) |
0.746255 | + | 0.665660i | \(0.231850\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.25332 | − | 1.38656i | −0.195388 | − | 0.120230i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.500000 | − | 0.866025i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.7666 | + | 18.6483i | 0.919853 | + | 1.59323i | 0.799636 | + | 0.600485i | \(0.205026\pi\) |
0.120217 | + | 0.992748i | \(0.461641\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.9647 | 1.43893 | 0.719465 | − | 0.694529i | \(-0.244387\pi\) | ||||
0.719465 | + | 0.694529i | \(0.244387\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.35837 | −0.198611 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.72240 | − | 13.3756i | −0.645780 | − | 1.11852i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.75332 | − | 4.76889i | 0.228651 | − | 0.396035i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.15491 | + | 6.24872i | 0.260213 | + | 0.515386i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.0133 | + | 19.0756i | −0.902243 | + | 1.56273i | −0.0776680 | + | 0.996979i | \(0.524747\pi\) |
−0.824575 | + | 0.565752i | \(0.808586\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.30982 | + | 7.46483i | 0.350728 | + | 0.607479i | 0.986377 | − | 0.164499i | \(-0.0526007\pi\) |
−0.635649 | + | 0.771978i | \(0.719267\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.80318 | 0.469159 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.35837 | −0.591039 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.03092 | + | 3.51765i | 0.162085 | + | 0.280739i | 0.935616 | − | 0.353019i | \(-0.114845\pi\) |
−0.773531 | + | 0.633758i | \(0.781511\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.672545 | − | 1.16488i | 0.0533363 | − | 0.0923811i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.91922 | + | 1.18098i | 0.151256 | + | 0.0930739i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | + | 6.92820i | −0.313304 | + | 0.542659i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) |
0.665771 | + | 0.746156i | \(0.268103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.08078 | + | 5.33606i | 0.239838 | + | 0.415412i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.47137 | −0.732917 | −0.366458 | − | 0.930434i | \(-0.619430\pi\) | ||||
−0.366458 | + | 0.930434i | \(0.619430\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.71675 | −0.516673 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.500000 | − | 0.866025i | −0.0382360 | − | 0.0662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.03092 | + | 1.78560i | −0.0783792 | + | 0.135757i | −0.902551 | − | 0.430583i | \(-0.858308\pi\) |
0.824172 | + | 0.566340i | \(0.191641\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.32746 | − | 1.25815i | 0.175939 | − | 0.0951075i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.24668 | + | 5.62341i | −0.244035 | + | 0.422682i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.524276 | + | 0.908072i | 0.0391862 | + | 0.0678725i | 0.884953 | − | 0.465680i | \(-0.154190\pi\) |
−0.845767 | + | 0.533552i | \(0.820857\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.37166 | −0.324943 | −0.162471 | − | 0.986713i | \(-0.551947\pi\) | ||||
−0.162471 | + | 0.986713i | \(0.551947\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.90823 | − | 8.50131i | −0.360860 | − | 0.625029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.8783 | + | 30.9661i | −1.30739 | + | 2.26447i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.0741344 | + | 2.64471i | −0.00539249 | + | 0.192375i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.0133 | − | 17.3435i | 0.724536 | − | 1.25493i | −0.234629 | − | 0.972085i | \(-0.575388\pi\) |
0.959165 | − | 0.282848i | \(-0.0912791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.08742 | − | 7.07962i | −0.294219 | − | 0.509602i | 0.680584 | − | 0.732670i | \(-0.261726\pi\) |
−0.974803 | + | 0.223068i | \(0.928393\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.50664 | −0.179504 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.17484 | 0.653680 | 0.326840 | − | 0.945080i | \(-0.394016\pi\) | ||||
0.326840 | + | 0.945080i | \(0.394016\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.35837 | + | 2.35277i | 0.0962925 | + | 0.166784i | 0.910147 | − | 0.414285i | \(-0.135968\pi\) |
−0.813855 | + | 0.581068i | \(0.802635\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.58078 | − | 6.20209i | 0.252568 | − | 0.437461i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.408232 | + | 14.5635i | −0.0286523 | + | 1.02216i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.57413 | + | 2.72648i | −0.109942 | + | 0.190426i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.425866 | + | 0.737621i | 0.0295997 | + | 0.0512682i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.16155 | 0.426204 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.95145 | 0.203186 | 0.101593 | − | 0.994826i | \(-0.467606\pi\) | ||||
0.101593 | + | 0.994826i | \(0.467606\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.55650 | + | 13.0882i | 0.517763 | + | 0.896792i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.58078 | + | 6.20209i | −0.244207 | + | 0.422979i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.1263 | − | 9.25797i | 1.16261 | − | 0.628472i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.92587 | + | 5.06775i | −0.197712 | + | 0.342447i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.27325 | − | 12.5976i | −0.489252 | − | 0.847408i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.0133 | 1.54108 | 0.770542 | − | 0.637390i | \(-0.219986\pi\) | ||||
0.770542 | + | 0.637390i | \(0.219986\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.55650 | + | 7.89209i | 0.302426 | + | 0.523816i | 0.976685 | − | 0.214678i | \(-0.0688703\pi\) |
−0.674259 | + | 0.738495i | \(0.735537\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.67919 | − | 16.7648i | 0.639619 | − | 1.10785i | −0.345898 | − | 0.938272i | \(-0.612426\pi\) |
0.985516 | − | 0.169580i | \(-0.0542411\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.8840 | − | 8.54335i | −0.913497 | − | 0.562111i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.50664 | + | 11.2698i | −0.426264 | + | 0.738311i | −0.996538 | − | 0.0831436i | \(-0.973504\pi\) |
0.570273 | + | 0.821455i | \(0.306837\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.17919 | − | 2.04241i | −0.0769216 | − | 0.133232i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.6682 | 0.822888 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.02657 | 0.260457 | 0.130229 | − | 0.991484i | \(-0.458429\pi\) | ||||
0.130229 | + | 0.991484i | \(0.458429\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.67254 | − | 11.5572i | −0.429816 | − | 0.744464i | 0.567040 | − | 0.823690i | \(-0.308088\pi\) |
−0.996857 | + | 0.0792263i | \(0.974755\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.83410 | + | 5.85659i | −0.244951 | + | 0.374164i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.25332 | + | 2.17082i | −0.0797469 | + | 0.138126i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.75332 | − | 4.76889i | −0.174485 | − | 0.302216i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.7945 | 1.88061 | 0.940305 | − | 0.340332i | \(-0.110539\pi\) | ||||
0.940305 | + | 0.340332i | \(0.110539\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.24799 | −0.329938 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.90159 | + | 5.02570i | 0.181705 | + | 0.314722i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.06314 | − | 7.03757i | 0.253452 | − | 0.438992i | −0.711022 | − | 0.703170i | \(-0.751767\pi\) |
0.964474 | + | 0.264178i | \(0.0851007\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.1196 | + | 13.6111i | 1.37445 | + | 0.845753i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.75332 | + | 4.76889i | −0.170426 | + | 0.295187i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.50664 | + | 9.53778i | 0.339554 | + | 0.588125i | 0.984349 | − | 0.176231i | \(-0.0563905\pi\) |
−0.644795 | + | 0.764356i | \(0.723057\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.34509 | 0.0826282 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.8165 | −0.661957 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.85173 | − | 3.20729i | −0.112902 | − | 0.195552i | 0.804037 | − | 0.594579i | \(-0.202681\pi\) |
−0.916939 | + | 0.399027i | \(0.869348\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6549 | + | 23.6510i | −0.829477 | + | 1.43670i | 0.0689725 | + | 0.997619i | \(0.478028\pi\) |
−0.898449 | + | 0.439077i | \(0.855305\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.83410 | − | 3.15374i | 0.353096 | − | 0.190873i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.08078 | + | 5.33606i | −0.185778 | + | 0.321777i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.74233 | − | 6.48190i | −0.224855 | − | 0.389460i | 0.731421 | − | 0.681926i | \(-0.238857\pi\) |
−0.956276 | + | 0.292466i | \(0.905524\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.35837 | 0.440534 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.2878 | −1.44889 | −0.724445 | − | 0.689332i | \(-0.757904\pi\) | ||||
−0.724445 | + | 0.689332i | \(0.757904\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.5808 | − | 21.7905i | −0.747850 | − | 1.29531i | −0.948852 | − | 0.315723i | \(-0.897753\pi\) |
0.201002 | − | 0.979591i | \(-0.435580\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.500000 | − | 0.866025i | 0.0296174 | − | 0.0512989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.233395 | − | 8.32627i | 0.0137769 | − | 0.491484i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.33845 | + | 14.4426i | −0.490497 | + | 0.849566i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.00000 | − | 6.92820i | −0.234484 | − | 0.406138i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.6682 | −1.49955 | −0.749776 | − | 0.661692i | \(-0.769839\pi\) | ||||
−0.749776 | + | 0.661692i | \(0.769839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.49336 | −0.378058 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.08078 | − | 5.33606i | −0.178765 | − | 0.309630i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.06749 | − | 1.84895i | 0.0617347 | − | 0.106928i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.530918 | − | 18.9402i | 0.0306016 | − | 1.09170i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.09841 | + | 1.90250i | −0.0631020 | + | 0.109296i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.0644 | 1.77294 | 0.886471 | − | 0.462784i | \(-0.153150\pi\) | ||||
0.886471 | + | 0.462784i | \(0.153150\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.1748 | −0.578826 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.4215 | − | 23.2467i | −0.761064 | − | 1.31820i | −0.942302 | − | 0.334763i | \(-0.891344\pi\) |
0.181238 | − | 0.983439i | \(-0.441990\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.03887 | + | 15.6558i | −0.510907 | + | 0.884917i | 0.489013 | + | 0.872276i | \(0.337357\pi\) |
−0.999920 | + | 0.0126404i | \(0.995976\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.32746 | + | 1.25815i | −0.131137 | + | 0.0708889i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.75332 | − | 13.4291i | 0.435470 | − | 0.754256i | −0.561864 | − | 0.827230i | \(-0.689916\pi\) |
0.997334 | + | 0.0729737i | \(0.0232489\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.9647 | − | 29.3838i | −0.949843 | − | 1.64518i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.1130 | −0.620267 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.80318 | 0.322898 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.25332 | − | 2.17082i | −0.0695217 | − | 0.120415i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.33410 | − | 5.77483i | 0.184376 | − | 0.319349i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.31417 | + | 3.27002i | 0.292980 | + | 0.180282i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3650 | + | 17.9527i | −0.569713 | + | 0.986771i | 0.426881 | + | 0.904308i | \(0.359612\pi\) |
−0.996594 | + | 0.0824638i | \(0.973721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.90823 | + | 8.50131i | 0.268969 | + | 0.465869i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.16155 | 0.391277 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.7546 | −1.51189 | −0.755945 | − | 0.654635i | \(-0.772823\pi\) | ||||
−0.755945 | + | 0.654635i | \(0.772823\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.3098 | − | 17.8571i | −0.559953 | − | 0.969866i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.6695 | + | 39.2647i | −1.22762 | + | 2.12630i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.55519 | − | 18.4548i | 0.0839725 | − | 0.996468i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.425866 | + | 0.737621i | −0.0229278 | + | 0.0397122i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.9647 | + | 24.1876i | 0.749666 | + | 1.29846i | 0.947983 | + | 0.318322i | \(0.103119\pi\) |
−0.198317 | + | 0.980138i | \(0.563547\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.71675 | 0.359539 | 0.179770 | − | 0.983709i | \(-0.442465\pi\) | ||||
0.179770 | + | 0.983709i | \(0.442465\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.50664 | 0.133795 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.74004 | − | 6.47793i | −0.199062 | − | 0.344786i | 0.749162 | − | 0.662386i | \(-0.230456\pi\) |
−0.948225 | + | 0.317601i | \(0.897123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.55650 | + | 13.0882i | −0.401057 | + | 0.694652i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −13.0764 | − | 8.04645i | −0.692078 | − | 0.425863i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.7666 | − | 27.3086i | 0.832130 | − | 1.44129i | −0.0642167 | − | 0.997936i | \(-0.520455\pi\) |
0.896346 | − | 0.443355i | \(-0.146212\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.9647 | 1.41528 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.85173 | −0.306294 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0565 | + | 27.8107i | 0.838143 | + | 1.45171i | 0.891446 | + | 0.453127i | \(0.149692\pi\) |
−0.0533034 | + | 0.998578i | \(0.516975\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.57413 | − | 2.72648i | 0.0819462 | − | 0.141935i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.13064 | + | 1.69233i | −0.162534 | + | 0.0878614i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.79088 | − | 16.9583i | 0.506953 | − | 0.878068i | −0.493015 | − | 0.870021i | \(-0.664105\pi\) |
0.999968 | − | 0.00804684i | \(-0.00256142\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.8032 | 0.710900 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0266 | 1.18280 | 0.591398 | − | 0.806380i | \(-0.298576\pi\) | ||||
0.591398 | + | 0.806380i | \(0.298576\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.05650 | − | 7.02607i | −0.207821 | − | 0.359956i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.637277 | − | 1.10380i | 0.0325633 | − | 0.0564014i | −0.849284 | − | 0.527936i | \(-0.822966\pi\) |
0.881848 | + | 0.471534i | \(0.156300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.456783 | − | 16.2955i | 0.0232798 | − | 0.830497i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.58078 | − | 6.20209i | 0.182021 | − | 0.315270i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.0631 | + | 22.6260i | 0.662328 | + | 1.14719i | 0.980002 | + | 0.198985i | \(0.0637646\pi\) |
−0.317675 | + | 0.948200i | \(0.602902\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.94275 | −0.249966 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.65491 | 0.234809 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.33410 | + | 10.9710i | 0.318703 | + | 0.552010i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.7423 | − | 27.2665i | 0.790085 | − | 1.36847i | −0.135829 | − | 0.990732i | \(-0.543370\pi\) |
0.925914 | − | 0.377735i | \(-0.123297\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0741344 | + | 2.64471i | −0.00371136 | + | 0.132401i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.34074 | − | 14.4466i | 0.416517 | − | 0.721428i | −0.579070 | − | 0.815278i | \(-0.696584\pi\) |
0.995586 | + | 0.0938501i | \(0.0299174\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.22240 | − | 15.9737i | −0.459401 | − | 0.795705i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −60.4847 | −2.99811 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.03756 | − | 12.1894i | −0.347985 | − | 0.602728i | 0.637906 | − | 0.770114i | \(-0.279801\pi\) |
−0.985891 | + | 0.167386i | \(0.946467\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.7666 | − | 18.6483i | 0.531077 | − | 0.919853i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.1130 | − | 8.16964i | 0.743662 | − | 0.402002i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.75332 | − | 4.76889i | 0.135155 | − | 0.234096i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.48237 | − | 14.6919i | −0.415383 | − | 0.719465i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.5844 | −1.59185 | −0.795925 | − | 0.605395i | \(-0.793015\pi\) | ||||
−0.795925 | + | 0.605395i | \(0.793015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5711 | 0.710152 | 0.355076 | − | 0.934838i | \(-0.384455\pi\) | ||||
0.355076 | + | 0.934838i | \(0.384455\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.17919 | + | 2.04241i | 0.0573340 | + | 0.0993054i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.90159 | + | 5.02570i | −0.140748 | + | 0.243782i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.72240 | + | 13.3756i | −0.372841 | + | 0.645780i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.148269 | − | 0.256809i | −0.00714186 | − | 0.0123701i | 0.862432 | − | 0.506172i | \(-0.168940\pi\) |
−0.869574 | + | 0.493802i | \(0.835607\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.0910 | −1.59025 | −0.795126 | − | 0.606444i | \(-0.792596\pi\) | ||||
−0.795126 | + | 0.606444i | \(0.792596\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.50664 | −0.264023 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.425866 | + | 0.737621i | 0.0203719 | + | 0.0352852i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.4714 | − | 25.0652i | 0.690681 | − | 1.19629i | −0.280934 | − | 0.959727i | \(-0.590644\pi\) |
0.971615 | − | 0.236568i | \(-0.0760225\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.83410 | − | 5.85659i | 0.182576 | − | 0.278885i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.50664 | + | 9.53778i | −0.261628 | + | 0.453154i | −0.966675 | − | 0.256007i | \(-0.917593\pi\) |
0.705046 | + | 0.709161i | \(0.250926\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.40823 | − | 9.36733i | −0.256375 | − | 0.444054i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.0266 | 1.04182 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.9780 | −0.801242 | −0.400621 | − | 0.916244i | \(-0.631206\pi\) | ||||
−0.400621 | + | 0.916244i | \(0.631206\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.69911 | + | 16.7994i | 0.456713 | + | 0.791051i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.30982 | − | 7.46483i | 0.202493 | − | 0.350728i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.64827 | + | 3.47561i | 0.264795 | + | 0.162939i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.1007 | + | 19.2270i | −0.519269 | + | 0.899400i | 0.480480 | + | 0.877006i | \(0.340462\pi\) |
−0.999749 | + | 0.0223947i | \(0.992871\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.90159 | − | 5.02570i | −0.135435 | − | 0.234580i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.5066 | −1.56056 | −0.780280 | − | 0.625430i | \(-0.784923\pi\) | ||||
−0.780280 | + | 0.625430i | \(0.784923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.59046 | 0.0739150 | 0.0369575 | − | 0.999317i | \(-0.488233\pi\) | ||||
0.0369575 | + | 0.999317i | \(0.488233\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.67919 | + | 6.37254i | 0.170618 | + | 0.295519i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.668195 | − | 1.15735i | 0.0309204 | − | 0.0535556i | −0.850151 | − | 0.526539i | \(-0.823490\pi\) |
0.881071 | + | 0.472983i | \(0.156823\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.6682 | + | 9.01034i | −0.769666 | + | 0.416059i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.03092 | − | 3.51765i | 0.0935797 | − | 0.162085i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.0631 | + | 38.2145i | 1.01446 | + | 1.75710i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.34509 | −0.0615874 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.6549 | − | 21.9189i | −0.578218 | − | 1.00150i | −0.995684 | − | 0.0928099i | \(-0.970415\pi\) |
0.417466 | − | 0.908692i | \(-0.362918\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.3032 | − | 21.3097i | 0.560977 | − | 0.971640i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0631426 | − | 2.25258i | 0.00287309 | − | 0.102496i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.00000 | − | 6.92820i | 0.181631 | − | 0.314594i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.2357 | − | 29.8531i | −0.781024 | − | 1.35277i | −0.931346 | − | 0.364135i | \(-0.881365\pi\) |
0.150322 | − | 0.988637i | \(-0.451969\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.6329 | 0.976280 | 0.488140 | − | 0.872765i | \(-0.337675\pi\) | ||||
0.488140 | + | 0.872765i | \(0.337675\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.9780 | − | 27.6747i | −0.719614 | − | 1.24641i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.08078 | − | 5.33606i | 0.138471 | − | 0.239838i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.12039 | − | 39.9695i | 0.0502565 | − | 1.79288i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.0023 | − | 25.9847i | 0.671595 | − | 1.16324i | −0.305857 | − | 0.952077i | \(-0.598943\pi\) |
0.977452 | − | 0.211159i | \(-0.0677237\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.73569 | + | 8.20245i | 0.211575 | + | 0.366458i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.2965 | 0.904978 | 0.452489 | − | 0.891770i | \(-0.350536\pi\) | ||||
0.452489 | + | 0.891770i | \(0.350536\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.19682 | −0.0977572 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.35837 | + | 5.81687i | 0.149151 | + | 0.258336i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.49336 | − | 6.05067i | 0.154840 | − | 0.268191i | −0.778161 | − | 0.628065i | \(-0.783847\pi\) |
0.933001 | + | 0.359874i | \(0.117180\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.6196 | − | 7.36238i | 0.602498 | − | 0.325692i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.500000 | + | 0.866025i | −0.0220755 | + | 0.0382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.08742 | − | 8.81167i | −0.224178 | − | 0.388288i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.5312 | −0.639083 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.06184 | 0.0905045 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.6858 | − | 27.1687i | −0.687209 | − | 1.19028i | −0.972737 | − | 0.231910i | \(-0.925502\pi\) |
0.285529 | − | 0.958370i | \(-0.407831\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.0608505 | + | 0.105396i | −0.00266081 | + | 0.00460866i | −0.867353 | − | 0.497694i | \(-0.834180\pi\) |
0.864692 | + | 0.502303i | \(0.167514\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.25332 | − | 1.38656i | −0.0983430 | − | 0.0605144i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.3510 | + | 36.9810i | −0.930063 | + | 1.61092i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1373 | + | 19.2903i | 0.484229 | + | 0.838710i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.49336 | 0.281788 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.89158 | −0.341822 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.55650 | − | 9.62414i | −0.240228 | − | 0.416088i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.524276 | − | 0.908072i | 0.0226242 | − | 0.0391862i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.4391 | + | 38.5018i | 0.837303 | + | 1.65839i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.33410 | + | 9.23893i | −0.229331 | + | 0.397213i | −0.957610 | − | 0.288068i | \(-0.906987\pi\) |
0.728279 | + | 0.685281i | \(0.240320\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.18583 | + | 3.78597i | 0.0938029 | + | 0.162471i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.66819 | 0.285634 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.6329 | 0.753930 | 0.376965 | − | 0.926228i | \(-0.376968\pi\) | ||||
0.376965 | + | 0.926228i | \(0.376968\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.75332 | + | 4.76889i | −0.117295 | + | 0.203162i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.5455 | − | 17.5652i | −1.21388 | − | 0.746948i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.90823 | + | 8.50131i | −0.208343 | + | 0.360860i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.86936 | + | 3.23783i | 0.0792075 | + | 0.137191i | 0.902908 | − | 0.429833i | \(-0.141428\pi\) |
−0.823701 | + | 0.567025i | \(0.808094\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.9514 | −0.759265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.7566 | 1.50964 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.7167 | − | 20.2940i | −0.493802 | − | 0.855290i | 0.506173 | − | 0.862432i | \(-0.331060\pi\) |
−0.999974 | + | 0.00714214i | \(0.997727\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3098 | − | 17.8571i | 0.433737 | − | 0.751255i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.32746 | − | 1.25815i | 0.0977439 | − | 0.0528375i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.5741 | + | 20.0470i | −0.485213 | + | 0.840413i | −0.999856 | − | 0.0169913i | \(-0.994591\pi\) |
0.514643 | + | 0.857405i | \(0.327925\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.33410 | + | 4.04278i | 0.0976789 | + | 0.169185i | 0.910724 | − | 0.413017i | \(-0.135525\pi\) |
−0.813045 | + | 0.582201i | \(0.802192\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.0266 | −0.836622 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.851731 | −0.0355196 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.3840 | + | 28.3778i | 0.682073 | + | 1.18139i | 0.974347 | + | 0.225051i | \(0.0722547\pi\) |
−0.292274 | + | 0.956335i | \(0.594412\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.08742 | + | 7.07962i | −0.169867 | + | 0.294219i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.408232 | + | 14.5635i | −0.0169363 | + | 0.604195i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.14392 | − | 7.17748i | 0.171624 | − | 0.297261i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.25332 | + | 2.17082i | 0.0518184 | + | 0.0897522i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.1529 | −1.49219 | −0.746094 | − | 0.665841i | \(-0.768073\pi\) | ||||
−0.746094 | + | 0.665841i | \(0.768073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.35837 | 0.303196 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.58742 | − | 7.94564i | −0.188701 | − | 0.326840i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.5565 | + | 21.7485i | −0.515634 | + | 0.893104i | 0.484202 | + | 0.874956i | \(0.339110\pi\) |
−0.999835 | + | 0.0181473i | \(0.994223\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.430215 | − | 15.3477i | 0.0176371 | − | 0.629196i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.35837 | − | 2.35277i | 0.0555945 | − | 0.0962925i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.555193 | − | 0.961623i | −0.0226846 | − | 0.0392909i | 0.854460 | − | 0.519517i | \(-0.173888\pi\) |
−0.877145 | + | 0.480226i | \(0.840555\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.8809 | 1.70836 | 0.854179 | − | 0.519979i | \(-0.174060\pi\) | ||||
0.854179 | + | 0.519979i | \(0.174060\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.16155 | −0.291641 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.4824 | + | 23.3521i | 0.548136 | + | 0.949400i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.2048 | + | 17.6752i | −0.414199 | + | 0.717413i | −0.995344 | − | 0.0963865i | \(-0.969272\pi\) |
0.581145 | + | 0.813800i | \(0.302605\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.8165 | − | 6.92820i | 0.519349 | − | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.95580 | − | 5.11959i | 0.119579 | − | 0.207117i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.47572 | − | 4.28808i | −0.0999936 | − | 0.173194i | 0.811688 | − | 0.584091i | \(-0.198549\pi\) |
−0.911682 | + | 0.410897i | \(0.865216\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.14827 | 0.126950 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.6769 | −0.550611 | −0.275306 | − | 0.961357i | \(-0.588779\pi\) | ||||
−0.275306 | + | 0.961357i | \(0.588779\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.30318 | + | 9.18538i | 0.213153 | + | 0.369191i | 0.952700 | − | 0.303914i | \(-0.0982935\pi\) |
−0.739547 | + | 0.673105i | \(0.764960\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.425866 | − | 0.737621i | 0.0170894 | − | 0.0295997i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.3730 | + | 14.9977i | 0.976482 | + | 0.600869i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.08078 | − | 5.33606i | −0.123034 | − | 0.213102i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −56.9667 | −2.27141 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.3364 | −0.769770 | −0.384885 | − | 0.922965i | \(-0.625759\pi\) | ||||
−0.384885 | + | 0.922965i | \(0.625759\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.47572 | − | 2.55603i | −0.0586548 | − | 0.101593i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.05650 | − | 7.02607i | 0.160977 | − | 0.278821i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.5189 | − | 0.982926i | −0.694126 | − | 0.0389449i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.55650 | − | 13.0882i | 0.298931 | − | 0.517763i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.42587 | + | 9.39787i | 0.214309 | + | 0.371194i | 0.953059 | − | 0.302786i | \(-0.0979168\pi\) |
−0.738750 | + | 0.673980i | \(0.764583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.3876 | −1.08006 | −0.540030 | − | 0.841646i | \(-0.681587\pi\) | ||||
−0.540030 | + | 0.841646i | \(0.681587\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.16155 | 0.281986 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.574134 | + | 0.994430i | 0.0225716 | + | 0.0390951i | 0.877091 | − | 0.480325i | \(-0.159481\pi\) |
−0.854519 | + | 0.519420i | \(0.826148\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.0046 | + | 34.6490i | −0.785249 | + | 1.36009i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.5808 | − | 10.2028i | −0.649852 | − | 0.399880i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.2643 | − | 19.5104i | 0.440807 | − | 0.763499i | −0.556943 | − | 0.830551i | \(-0.688026\pi\) |
0.997750 | + | 0.0670513i | \(0.0213591\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.32746 | + | 4.03127i | 0.0909412 | + | 0.157515i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.85173 | 0.228298 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.0531 | −0.936977 | −0.468489 | − | 0.883470i | \(-0.655201\pi\) | ||||
−0.468489 | + | 0.883470i | \(0.655201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.84074 | + | 13.5806i | 0.304969 | + | 0.528223i | 0.977255 | − | 0.212070i | \(-0.0680204\pi\) |
−0.672285 | + | 0.740292i | \(0.734687\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.27325 | + | 12.5976i | −0.282469 | + | 0.489252i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.32746 | + | 1.25815i | −0.0902548 | + | 0.0487891i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.34509 | − | 4.06181i | 0.0908022 | − | 0.157274i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.5066 | − | 19.9301i | −0.444872 | − | 0.770542i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.7812 | 0.993792 | 0.496896 | − | 0.867810i | \(-0.334473\pi\) | ||||
0.496896 | + | 0.867810i | \(0.334473\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.5874 | + | 25.2661i | −0.560640 | + | 0.971057i | 0.436801 | + | 0.899558i | \(0.356112\pi\) |
−0.997441 | + | 0.0714987i | \(0.977222\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.593075 | + | 21.1577i | −0.0227601 | + | 0.811958i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.55650 | − | 7.89209i | 0.174605 | − | 0.302426i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.70477 | + | 4.68480i | 0.103495 | + | 0.179259i | 0.913122 | − | 0.407686i | \(-0.133664\pi\) |
−0.809627 | + | 0.586944i | \(0.800331\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.5332 | 0.822742 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.3584 | −0.738568 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.68583 | + | 2.91994i | 0.0642250 | + | 0.111241i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.43381 | − | 11.1437i | 0.244754 | − | 0.423926i | −0.717309 | − | 0.696756i | \(-0.754626\pi\) |
0.962062 | + | 0.272830i | \(0.0879595\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.456783 | + | 16.2955i | −0.0173518 | + | 0.619016i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.48237 | − | 14.6919i | 0.321754 | − | 0.557295i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.13498 | + | 15.8223i | 0.346012 | + | 0.599311i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.0133 | 0.492208 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.81646 | −0.106376 | −0.0531882 | − | 0.998585i | \(-0.516938\pi\) | ||||
−0.0531882 | + | 0.998585i | \(0.516938\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.90823 | + | 8.50131i | 0.185117 | + | 0.320633i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.17919 | + | 2.04241i | −0.0444107 | + | 0.0769216i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.11300 | − | 2.76394i | 0.192294 | − | 0.103949i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.70346 | + | 9.87869i | −0.214198 | + | 0.371002i | −0.953024 | − | 0.302894i | \(-0.902047\pi\) |
0.738826 | + | 0.673896i | \(0.235380\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.33410 | − | 10.9710i | −0.237547 | − | 0.411444i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.26736 | −0.234714 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.4448 | −0.577603 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.01328 | − | 3.48711i | −0.0751875 | − | 0.130229i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.1130 | + | 31.3726i | −0.675501 | + | 1.17000i | 0.300821 | + | 0.953681i | \(0.402739\pi\) |
−0.976322 | + | 0.216321i | \(0.930594\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.9272 | + | 14.1080i | 0.853853 | + | 0.525410i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.67254 | + | 11.5572i | −0.248155 | + | 0.429816i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.75332 | − | 4.76889i | −0.102256 | − | 0.177112i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.3523 | 1.83038 | 0.915188 | − | 0.403028i | \(-0.132042\pi\) | ||||
0.915188 | + | 0.403028i | \(0.132042\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.7799 | + | 35.9918i | 0.768572 | + | 1.33121i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.9215 | − | 41.4333i | 0.883561 | − | 1.53037i | 0.0362076 | − | 0.999344i | \(-0.488472\pi\) |
0.847354 | − | 0.531029i | \(-0.178194\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.98901 | + | 0.392129i | 0.257793 | + | 0.0144639i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.0631 | − | 38.2145i | 0.812706 | − | 1.40765i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.316464 | + | 0.548131i | 0.0116413 | + | 0.0201633i | 0.871787 | − | 0.489884i | \(-0.162961\pi\) |
−0.860146 | + | 0.510048i | \(0.829628\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.50664 | 0.0920838 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.8078 | 0.910109 | 0.455054 | − | 0.890464i | \(-0.349620\pi\) | ||||
0.455054 | + | 0.890464i | \(0.349620\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.0133 | + | 19.0756i | 0.403496 | + | 0.698875i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.75332 | + | 4.76889i | −0.100739 | + | 0.174485i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.0412 | + | 15.4088i | 0.914984 | + | 0.563026i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.15056 | − | 3.72488i | 0.0784751 | − | 0.135923i | −0.824117 | − | 0.566419i | \(-0.808328\pi\) |
0.902592 | + | 0.430497i | \(0.141662\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.8972 | − | 25.8028i | −0.542886 | − | 0.940305i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.61964 | 0.313701 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.02657 | −0.146348 | −0.0731740 | − | 0.997319i | \(-0.523313\pi\) | ||||
−0.0731740 | + | 0.997319i | \(0.523313\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.62399 | + | 4.54489i | 0.0952449 | + | 0.164969i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.6871 | − | 20.2427i | 0.423658 | − | 0.733798i | −0.572636 | − | 0.819810i | \(-0.694079\pi\) |
0.996294 | + | 0.0860121i | \(0.0274124\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.5199 | + | 8.38962i | −0.561859 | + | 0.303724i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.90159 | − | 5.02570i | 0.104907 | − | 0.181705i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.13826 | − | 14.0959i | −0.293856 | − | 0.508973i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.88961 | 0.140263 | 0.0701315 | − | 0.997538i | \(-0.477658\pi\) | ||||
0.0701315 | + | 0.997538i | \(0.477658\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.12629 | −0.292661 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.0588 | + | 39.9390i | 0.829367 | + | 1.43651i | 0.898535 | + | 0.438901i | \(0.144632\pi\) |
−0.0691683 | + | 0.997605i | \(0.522035\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.67919 | + | 6.37254i | −0.132160 | + | 0.228908i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.727738 | − | 25.9617i | 0.0261075 | − | 0.931372i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.57413 | − | 2.72648i | 0.0563992 | − | 0.0976863i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 46.5598 | + | 80.6439i | 1.66604 | + | 2.88567i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.50664 | 0.196791 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.06184 | 0.144973 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.47137 | − | 2.54850i | −0.0524488 | − | 0.0908440i | 0.838609 | − | 0.544734i | \(-0.183369\pi\) |
−0.891058 | + | 0.453890i | \(0.850036\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.50664 | − | 9.53778i | 0.196042 | − | 0.339554i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.52863 | + | 54.5330i | −0.0543517 | + | 1.93897i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.672545 | − | 1.16488i | −0.0238527 | − | 0.0413141i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.5465 | 0.444420 | 0.222210 | − | 0.974999i | \(-0.428673\pi\) | ||||
0.222210 | + | 0.974999i | \(0.428673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.6861 | −0.484178 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.40823 | + | 9.36733i | 0.191090 | + | 0.330978i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.0279 | + | 31.2252i | −0.636190 | + | 1.10191i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.98237 | − | 1.07161i | 0.0698692 | − | 0.0377692i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.85173 | + | 3.20729i | −0.0651840 | + | 0.112902i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.1925 | − | 17.6539i | −0.358348 | − | 0.620677i | 0.629337 | − | 0.777133i | \(-0.283327\pi\) |
−0.987685 | + | 0.156455i | \(0.949993\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.6109 | 1.35581 | 0.677907 | − | 0.735148i | \(-0.262887\pi\) | ||||
0.677907 | + | 0.735148i | \(0.262887\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.3098 | 0.957797 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.00000 | + | 6.92820i | 0.140114 | + | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.58078 | − | 6.20209i | 0.125276 | − | 0.216984i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.64827 | − | 3.47561i | −0.197366 | − | 0.121447i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.7533 | − | 23.8215i | 0.479994 | − | 0.831374i | −0.519742 | − | 0.854323i | \(-0.673972\pi\) |
0.999737 | + | 0.0229486i | \(0.00730542\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.1616 | − | 33.1888i | −0.667930 | − | 1.15689i | −0.978482 | − | 0.206332i | \(-0.933847\pi\) |
0.310552 | − | 0.950556i | \(-0.399486\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.16155 | 0.214518 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.0133 | −0.452516 | −0.226258 | − | 0.974067i | \(-0.572649\pi\) | ||||
−0.226258 | + | 0.974067i | \(0.572649\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.4471 | − | 19.8270i | −0.397574 | − | 0.688619i | 0.595852 | − | 0.803094i | \(-0.296815\pi\) |
−0.993426 | + | 0.114476i | \(0.963481\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.74233 | + | 6.48190i | −0.129820 | + | 0.224855i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.3085 | + | 36.2625i | 0.634352 | + | 1.25642i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.73569 | + | 8.20245i | −0.163885 | + | 0.283858i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.67919 | − | 6.37254i | −0.127171 | − | 0.220267i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.1396 | 0.522676 | 0.261338 | − | 0.965247i | \(-0.415836\pi\) | ||||
0.261338 | + | 0.965247i | \(0.415836\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.32311 | 0.0456243 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.1439 | + | 21.0339i | 0.418259 | + | 0.724445i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.35837 | + | 5.81687i | −0.115532 | + | 0.200107i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −60.7602 | − | 37.3882i | −2.08775 | − | 1.28467i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.5808 | + | 21.7905i | −0.431771 | + | 0.747850i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.18049 | − | 7.24083i | −0.143305 | − | 0.248212i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.55061 | −0.0873312 | −0.0436656 | − | 0.999046i | \(-0.513904\pi\) | ||||
−0.0436656 | + | 0.999046i | \(0.513904\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.06314 | + | 15.6978i | 0.309591 | + | 0.536227i | 0.978273 | − | 0.207321i | \(-0.0664745\pi\) |
−0.668682 | + | 0.743549i | \(0.733141\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.8650 | − | 22.2829i | 0.438949 | − | 0.760281i | −0.558660 | − | 0.829397i | \(-0.688684\pi\) |
0.997609 | + | 0.0691154i | \(0.0220177\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.32746 | + | 3.96101i | −0.249719 | + | 0.134991i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.73438 | + | 6.46814i | −0.127120 | + | 0.220178i | −0.922560 | − | 0.385855i | \(-0.873907\pi\) |
0.795440 | + | 0.606033i | \(0.207240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.03092 | + | 1.78560i | 0.0350523 | + | 0.0607123i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.6769 | 0.566377 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 78.0558 | 2.64786 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.97572 | + | 15.5464i | 0.304131 | + | 0.526770i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.00000 | + | 6.92820i | −0.135379 | + | 0.234484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.0741344 | − | 2.64471i | 0.00250620 | − | 0.0894076i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.1306 | − | 41.7955i | 0.814834 | − | 1.41133i | −0.0946136 | − | 0.995514i | \(-0.530162\pi\) |
0.909447 | − | 0.415819i | \(-0.136505\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.8341 | + | 22.2293i | 0.432883 | + | 0.749776i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.2347 | −0.546961 | −0.273481 | − | 0.961878i | \(-0.588175\pi\) | ||||
−0.273481 | + | 0.961878i | \(0.588175\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8252 | 0.667170 | 0.333585 | − | 0.942720i | \(-0.391742\pi\) | ||||
0.333585 | + | 0.942720i | \(0.391742\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.24668 | + | 5.62341i | 0.109136 | + | 0.189029i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.8663 | + | 30.9454i | −0.599892 | + | 1.03904i | 0.392944 | + | 0.919562i | \(0.371457\pi\) |
−0.992836 | + | 0.119482i | \(0.961877\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.601453 | + | 21.4566i | −0.0201721 | + | 0.719630i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.08078 | + | 5.33606i | −0.103210 | + | 0.178765i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.17919 | + | 2.04241i | 0.0394600 | + | 0.0683467i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.04855 | 0.0350492 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.13498 | −0.0712851 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.2600 | − | 35.0913i | −0.675708 | − | 1.17036i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.90290 | − | 6.76002i | 0.130024 | − | 0.225209i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.6682 | + | 9.01034i | −0.554683 | + | 0.299845i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.18583 | + | 3.78597i | −0.0726594 | + | 0.125850i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.60276 | − | 4.50811i | −0.0864232 | − | 0.149689i | 0.819574 | − | 0.572974i | \(-0.194210\pi\) |
−0.905997 | + | 0.423285i | \(0.860877\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.19682 | 0.0728639 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.4361 | 1.24031 | 0.620157 | − | 0.784478i | \(-0.287069\pi\) | ||||
0.620157 | + | 0.784478i | \(0.287069\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.9647 | − | 29.3838i | −0.561451 | − | 0.972461i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.4890 | − | 6.45431i | −0.346378 | − | 0.213140i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.8055 | + | 39.5002i | −0.752283 | + | 1.30299i | 0.194431 | + | 0.980916i | \(0.437714\pi\) |
−0.946714 | + | 0.322076i | \(0.895619\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.5322 | − | 26.9026i | −0.511804 | − | 0.886471i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −37.8829 | −1.24693 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.81646 | −0.322763 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.08742 | + | 8.81167i | 0.167093 | + | 0.289413i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.9458 | − | 32.8151i | 0.621591 | − | 1.07663i | −0.367598 | − | 0.929985i | \(-0.619820\pi\) |
0.989189 | − | 0.146643i | \(-0.0468468\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.83410 | − | 5.85659i | 0.125657 | − | 0.191942i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.4215 | + | 23.2467i | −0.439401 | + | 0.761064i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.8783 | + | 30.9661i | 0.584683 | + | 1.01270i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.6083 | −1.16327 | −0.581637 | − | 0.813449i | \(-0.697587\pi\) | ||||
−0.581637 | + | 0.813449i | \(0.697587\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.0777 | 0.589945 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.71805 | − | 11.6360i | −0.219002 | − | 0.379323i | 0.735501 | − | 0.677524i | \(-0.236947\pi\) |
−0.954503 | + | 0.298201i | \(0.903614\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.34074 | + | 2.32223i | −0.0436605 | + | 0.0756222i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.25332 | + | 1.38656i | 0.0733005 | + | 0.0451048i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.3218 | − | 24.8061i | 0.465396 | − | 0.806089i | −0.533823 | − | 0.845596i | \(-0.679245\pi\) |
0.999219 | + | 0.0395066i | \(0.0125786\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.33410 | − | 12.7030i | −0.238075 | − | 0.412358i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.5066 | −0.502837 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.2791 | −0.851265 | −0.425632 | − | 0.904896i | \(-0.639948\pi\) | ||||
−0.425632 | + | 0.904896i | \(0.639948\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0133 | − | 17.3435i | −0.324022 | − | 0.561223i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.9647 | + | 29.3838i | −0.548392 | + | 0.949843i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −50.1176 | + | 27.0921i | −1.61838 | + | 0.874849i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.5728 | + | 20.0447i | −0.373317 | + | 0.646604i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.55650 | + | 9.62414i | 0.179056 | + | 0.310134i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.17484 | −0.263157 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.4581 | −0.882993 | −0.441496 | − | 0.897263i | \(-0.645552\pi\) | ||||
−0.441496 | + | 0.897263i | \(0.645552\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.90159 | − | 5.02570i | −0.0932125 | − | 0.161449i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.7370 | − | 42.8457i | 0.793848 | − | 1.37498i | −0.129720 | − | 0.991551i | \(-0.541408\pi\) |
0.923568 | − | 0.383434i | \(-0.125259\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.25767 | + | 44.8668i | −0.0403191 | + | 1.43836i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.25332 | + | 2.17082i | −0.0401384 | + | 0.0695217i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.11169 | + | 8.85371i | 0.163538 | + | 0.283255i | 0.936135 | − | 0.351641i | \(-0.114376\pi\) |
−0.772597 | + | 0.634896i | \(0.781043\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −66.6462 | −2.13002 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.66819 | −0.212899 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.57413 | + | 6.19058i | 0.113997 | + | 0.197449i | 0.917378 | − | 0.398016i | \(-0.130301\pi\) |
−0.803381 | + | 0.595465i | \(0.796968\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.58742 | − | 7.94564i | 0.146167 | − | 0.253169i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.174837 | − | 6.23722i | 0.00556511 | − | 0.198533i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.04986 | + | 5.28251i | −0.0969799 | + | 0.167974i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.0376 | − | 36.4381i | −0.668280 | − | 1.15750i | −0.978385 | − | 0.206793i | \(-0.933697\pi\) |
0.310105 | − | 0.950702i | \(-0.399636\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.7300 | 0.657848 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.71675 | 0.0861266 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.7290 | + | 35.9038i | 0.656495 | + | 1.13708i | 0.981517 | + | 0.191377i | \(0.0612952\pi\) |
−0.325021 | + | 0.945707i | \(0.605371\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.90823 | − | 8.50131i | 0.155290 | − | 0.268969i |
(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 | 840.2.bg.j.121.2 | ✓ | 6 | |
3.2 | odd | 2 | 2520.2.bi.n.1801.2 | 6 | |||
4.3 | odd | 2 | 1680.2.bg.v.961.2 | 6 | |||
7.2 | even | 3 | 5880.2.a.bv.1.3 | 3 | |||
7.4 | even | 3 | inner | 840.2.bg.j.361.2 | yes | 6 | |
7.5 | odd | 6 | 5880.2.a.bu.1.3 | 3 | |||
21.11 | odd | 6 | 2520.2.bi.n.361.2 | 6 | |||
28.11 | odd | 6 | 1680.2.bg.v.1201.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.bg.j.121.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
840.2.bg.j.361.2 | yes | 6 | 7.4 | even | 3 | inner | |
1680.2.bg.v.961.2 | 6 | 4.3 | odd | 2 | |||
1680.2.bg.v.1201.2 | 6 | 28.11 | odd | 6 | |||
2520.2.bi.n.361.2 | 6 | 21.11 | odd | 6 | |||
2520.2.bi.n.1801.2 | 6 | 3.2 | odd | 2 | |||
5880.2.a.bu.1.3 | 3 | 7.5 | odd | 6 | |||
5880.2.a.bv.1.3 | 3 | 7.2 | even | 3 |