Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(949,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.949");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bc (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1549.3 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1549 |
Dual form | 2100.2.bc.f.949.3 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.358719 | + | 2.62132i | −0.135583 | + | 0.990766i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.12132 | − | 3.67423i | −0.639602 | − | 1.10782i | −0.985520 | − | 0.169559i | \(-0.945766\pi\) |
0.345918 | − | 0.938265i | \(-0.387568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.24264i | − | 1.45405i | −0.686613 | − | 0.727023i | \(-0.740903\pi\) | ||
0.686613 | − | 0.727023i | \(-0.259097\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.67423 | − | 2.12132i | 0.891133 | − | 0.514496i | 0.0168199 | − | 0.999859i | \(-0.494646\pi\) |
0.874313 | + | 0.485363i | \(0.161312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | + | 6.06218i | −0.802955 | + | 1.39076i | 0.114708 | + | 0.993399i | \(0.463407\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | + | 2.44949i | 0.218218 | + | 0.534522i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.67423 | − | 2.12132i | −0.766131 | − | 0.442326i | 0.0653618 | − | 0.997862i | \(-0.479180\pi\) |
−0.831493 | + | 0.555536i | \(0.812513\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.2426 | 1.90201 | 0.951005 | − | 0.309175i | \(-0.100053\pi\) | ||||
0.951005 | + | 0.309175i | \(0.100053\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.74264 | − | 6.48244i | −0.672198 | − | 1.16428i | −0.977279 | − | 0.211955i | \(-0.932017\pi\) |
0.305081 | − | 0.952326i | \(-0.401316\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.67423 | − | 2.12132i | −0.639602 | − | 0.369274i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.54026 | − | 2.62132i | −0.746414 | − | 0.430942i | 0.0779826 | − | 0.996955i | \(-0.475152\pi\) |
−0.824397 | + | 0.566012i | \(0.808485\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.62132 | − | 4.54026i | −0.419747 | − | 0.727023i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24264 | 0.662589 | 0.331295 | − | 0.943527i | \(-0.392515\pi\) | ||||
0.331295 | + | 0.943527i | \(0.392515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.24264i | − | 0.799495i | −0.916625 | − | 0.399748i | \(-0.869098\pi\) | ||
0.916625 | − | 0.399748i | \(-0.130902\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.19615 | − | 3.00000i | −0.757937 | − | 0.437595i | 0.0706177 | − | 0.997503i | \(-0.477503\pi\) |
−0.828554 | + | 0.559908i | \(0.810836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.74264 | − | 1.88064i | −0.963234 | − | 0.268662i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.12132 | − | 3.67423i | 0.297044 | − | 0.514496i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.34847 | + | 4.24264i | −1.00939 | + | 0.582772i | −0.911013 | − | 0.412378i | \(-0.864698\pi\) |
−0.0983769 | + | 0.995149i | \(0.531365\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.00000i | 0.927173i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.878680 | − | 1.52192i | −0.114394 | − | 0.198137i | 0.803143 | − | 0.595786i | \(-0.203159\pi\) |
−0.917537 | + | 0.397649i | \(0.869826\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.24264 | − | 10.8126i | 0.799288 | − | 1.38441i | −0.120792 | − | 0.992678i | \(-0.538543\pi\) |
0.920080 | − | 0.391730i | \(-0.128123\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.09077 | + | 1.62132i | 0.263412 | + | 0.204267i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.80821 | + | 1.62132i | −0.343077 | + | 0.198076i | −0.661632 | − | 0.749829i | \(-0.730136\pi\) |
0.318555 | + | 0.947904i | \(0.396803\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.24264 | −0.510754 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7279 | 1.51053 | 0.755263 | − | 0.655422i | \(-0.227509\pi\) | ||||
0.755263 | + | 0.655422i | \(0.227509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.655892 | − | 0.378680i | 0.0767664 | − | 0.0443211i | −0.461125 | − | 0.887335i | \(-0.652554\pi\) |
0.537892 | + | 0.843014i | \(0.319221\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.3923 | − | 4.24264i | 1.18431 | − | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.50000 | − | 9.52628i | 0.618798 | − | 1.07179i | −0.370907 | − | 0.928670i | \(-0.620953\pi\) |
0.989705 | − | 0.143120i | \(-0.0457135\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.75736i | − | 0.192895i | −0.995338 | − | 0.0964476i | \(-0.969252\pi\) | ||
0.995338 | − | 0.0964476i | \(-0.0307480\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.87039 | − | 5.12132i | 0.951005 | − | 0.549063i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.878680 | + | 1.52192i | −0.0931399 | + | 0.161323i | −0.908831 | − | 0.417165i | \(-0.863024\pi\) |
0.815691 | + | 0.578488i | \(0.196357\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.7426 | + | 1.88064i | 1.44062 | + | 0.197144i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.48244 | − | 3.74264i | −0.672198 | − | 0.388094i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 16.4853i | − | 1.67383i | −0.547335 | − | 0.836913i | \(-0.684358\pi\) | ||
0.547335 | − | 0.836913i | \(-0.315642\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.24264 | −0.426401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.12132 | + | 14.0665i | 0.808102 | + | 1.39967i | 0.914177 | + | 0.405315i | \(0.132838\pi\) |
−0.106076 | + | 0.994358i | \(0.533829\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.58410 | + | 4.37868i | 0.747283 | + | 0.431444i | 0.824711 | − | 0.565554i | \(-0.191338\pi\) |
−0.0774283 | + | 0.996998i | \(0.524671\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.0227 | − | 6.36396i | −1.06561 | − | 0.615227i | −0.138628 | − | 0.990345i | \(-0.544269\pi\) |
−0.926977 | + | 0.375117i | \(0.877602\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.74264 | + | 6.48244i | 0.358480 | + | 0.620906i | 0.987707 | − | 0.156316i | \(-0.0499618\pi\) |
−0.629227 | + | 0.777221i | \(0.716628\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.24264 | −0.497609 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 18.0000i | − | 1.69330i | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||
0.532152 | − | 0.846649i | \(-0.321383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.54026 | − | 2.62132i | −0.419747 | − | 0.242341i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.24264 | + | 10.3923i | 0.388922 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.50000 | + | 6.06218i | −0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.67423 | − | 2.12132i | 0.331295 | − | 0.191273i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2426i | 0.997623i | 0.866710 | + | 0.498812i | \(0.166230\pi\) | ||||
−0.866710 | + | 0.498812i | \(0.833770\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.62132 | − | 4.54026i | −0.230794 | − | 0.399748i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.24264 | − | 2.15232i | 0.108570 | − | 0.188049i | −0.806621 | − | 0.591069i | \(-0.798706\pi\) |
0.915191 | + | 0.403020i | \(0.132039\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.6354 | − | 11.3492i | −1.26905 | − | 0.984104i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.67423 | − | 2.12132i | 0.313911 | − | 0.181237i | −0.334764 | − | 0.942302i | \(-0.608657\pi\) |
0.648675 | + | 0.761065i | \(0.275323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.48528 | −0.125980 | −0.0629900 | − | 0.998014i | \(-0.520064\pi\) | ||||
−0.0629900 | + | 0.998014i | \(0.520064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.2627 | + | 11.1213i | −1.61083 | + | 0.930012i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.77962 | + | 1.74264i | −0.559173 | + | 0.143731i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | + | 10.3923i | −0.491539 | + | 0.851371i | −0.999953 | − | 0.00974235i | \(-0.996899\pi\) |
0.508413 | + | 0.861113i | \(0.330232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.75736 | − | 4.77589i | −0.224391 | − | 0.388656i | 0.731746 | − | 0.681578i | \(-0.238706\pi\) |
−0.956136 | + | 0.292922i | \(0.905373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.24264i | − | 0.342997i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.08052 | + | 5.24264i | −0.724704 | + | 0.418408i | −0.816482 | − | 0.577371i | \(-0.804079\pi\) |
0.0917773 | + | 0.995780i | \(0.470745\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.24264 | + | 7.34847i | −0.336463 | + | 0.582772i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.87868 | − | 8.87039i | 0.542116 | − | 0.699084i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.92820 | − | 4.00000i | −0.542659 | − | 0.313304i | 0.203497 | − | 0.979076i | \(-0.434769\pi\) |
−0.746156 | + | 0.665771i | \(0.768103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.72792i | 0.520622i | 0.965525 | + | 0.260311i | \(0.0838251\pi\) | ||||
−0.965525 | + | 0.260311i | \(0.916175\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.4853 | −1.11425 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.50000 | + | 6.06218i | 0.267652 | + | 0.463586i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.04384 | + | 1.75736i | 0.231419 | + | 0.133610i | 0.611226 | − | 0.791456i | \(-0.290677\pi\) |
−0.379808 | + | 0.925065i | \(0.624010\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.52192 | − | 0.878680i | −0.114394 | − | 0.0660456i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.00000 | − | 5.19615i | −0.224231 | − | 0.388379i | 0.731858 | − | 0.681457i | \(-0.238654\pi\) |
−0.956088 | + | 0.293079i | \(0.905320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0000 | −0.966282 | −0.483141 | − | 0.875542i | \(-0.660504\pi\) | ||||
−0.483141 | + | 0.875542i | \(0.660504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 12.4853i | − | 0.922939i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.5885 | − | 9.00000i | −1.13994 | − | 0.658145i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.62132 | + | 0.358719i | 0.190673 | + | 0.0260930i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | + | 5.19615i | −0.217072 | + | 0.375980i | −0.953912 | − | 0.300088i | \(-0.902984\pi\) |
0.736839 | + | 0.676068i | \(0.236317\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.2005 | − | 7.62132i | 0.950194 | − | 0.548595i | 0.0570527 | − | 0.998371i | \(-0.481830\pi\) |
0.893141 | + | 0.449777i | \(0.148496\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.75736i | 0.552689i | 0.961059 | + | 0.276344i | \(0.0891231\pi\) | ||||
−0.961059 | + | 0.276344i | \(0.910877\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.24264 | − | 5.61642i | −0.229865 | − | 0.398137i | 0.727903 | − | 0.685680i | \(-0.240495\pi\) |
−0.957768 | + | 0.287543i | \(0.907162\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.62132 | + | 2.80821i | −0.114359 | + | 0.198076i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.67423 | + | 26.8492i | −0.257881 | + | 1.88445i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.67423 | + | 2.12132i | −0.255377 | + | 0.147442i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.6985 | 2.05429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.51472 | 0.379649 | 0.189824 | − | 0.981818i | \(-0.439208\pi\) | ||||
0.189824 | + | 0.981818i | \(0.439208\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.0227 | − | 6.36396i | 0.755263 | − | 0.436051i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.3351 | − | 7.48528i | 1.24467 | − | 0.508134i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.378680 | − | 0.655892i | 0.0255888 | − | 0.0443211i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.1213 | − | 19.2627i | −0.748101 | − | 1.29575i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.4853i | − | 1.63966i | −0.572610 | − | 0.819828i | \(-0.694069\pi\) | ||
0.572610 | − | 0.819828i | \(-0.305931\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.5673 | + | 13.6066i | −1.56422 | + | 0.903102i | −0.567396 | + | 0.823445i | \(0.692049\pi\) |
−0.996822 | + | 0.0796568i | \(0.974618\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.50000 | + | 6.06218i | −0.231287 | + | 0.400600i | −0.958187 | − | 0.286143i | \(-0.907627\pi\) |
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.87868 | − | 8.87039i | 0.452584 | − | 0.583629i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.15232 | + | 1.24264i | 0.141003 | + | 0.0814081i | 0.568842 | − | 0.822447i | \(-0.307392\pi\) |
−0.427839 | + | 0.903855i | \(0.640725\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 11.0000i | − | 0.714527i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.9706 | 1.48584 | 0.742921 | − | 0.669379i | \(-0.233440\pi\) | ||||
0.742921 | + | 0.669379i | \(0.233440\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | + | 3.46410i | 0.128831 | + | 0.223142i | 0.923224 | − | 0.384262i | \(-0.125544\pi\) |
−0.794393 | + | 0.607404i | \(0.792211\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.7818 | + | 18.3492i | 2.02223 | + | 1.16753i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.878680 | − | 1.52192i | −0.0556841 | − | 0.0964476i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.72792 | 0.424663 | 0.212331 | − | 0.977198i | \(-0.431894\pi\) | ||||
0.212331 | + | 0.977198i | \(0.431894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000i | 1.13165i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.52192 | + | 0.878680i | 0.0949346 | + | 0.0548105i | 0.546716 | − | 0.837318i | \(-0.315878\pi\) |
−0.451781 | + | 0.892129i | \(0.649211\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.50000 | − | 10.9612i | 0.528164 | − | 0.681093i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.12132 | − | 8.87039i | 0.317002 | − | 0.549063i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.34847 | − | 4.24264i | 0.453126 | − | 0.261612i | −0.256023 | − | 0.966671i | \(-0.582412\pi\) |
0.709150 | + | 0.705058i | \(0.249079\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.75736i | 0.107549i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.24264 | + | 12.5446i | 0.441592 | + | 0.764859i | 0.997808 | − | 0.0661785i | \(-0.0210807\pi\) |
−0.556216 | + | 0.831038i | \(0.687747\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.7279 | + | 23.7775i | −0.833912 | + | 1.44438i | 0.0610014 | + | 0.998138i | \(0.480571\pi\) |
−0.894913 | + | 0.446240i | \(0.852763\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.8418 | − | 5.24264i | 0.777221 | − | 0.317299i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.69258 | − | 3.86396i | 0.402118 | − | 0.232163i | −0.285279 | − | 0.958444i | \(-0.592086\pi\) |
0.687397 | + | 0.726281i | \(0.258753\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.48528 | −0.448132 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.97056 | −0.296519 | −0.148259 | − | 0.988948i | \(-0.547367\pi\) | ||||
−0.148259 | + | 0.988948i | \(0.547367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.49642 | + | 0.863961i | −0.0889532 | + | 0.0513572i | −0.543817 | − | 0.839204i | \(-0.683021\pi\) |
0.454864 | + | 0.890561i | \(0.349688\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.52192 | + | 11.1213i | −0.0898360 | + | 0.656471i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.24264 | − | 14.2767i | −0.483192 | − | 0.836913i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.9706i | 1.69248i | 0.532803 | + | 0.846239i | \(0.321139\pi\) | ||||
−0.532803 | + | 0.846239i | \(0.678861\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.67423 | + | 2.12132i | −0.213201 | + | 0.123091i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.1213 | + | 19.2627i | −0.643163 | + | 1.11399i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.7426 | + | 1.88064i | 0.792113 | + | 0.108398i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.0665 | + | 8.12132i | 0.808102 | + | 0.466558i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.24264i | 0.299213i | 0.988746 | + | 0.149607i | \(0.0478007\pi\) | ||||
−0.988746 | + | 0.149607i | \(0.952199\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.75736 | 0.498189 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.6066 | + | 18.3712i | 0.601445 | + | 1.04173i | 0.992602 | + | 0.121410i | \(0.0387415\pi\) |
−0.391157 | + | 0.920324i | \(0.627925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.49642 | + | 0.863961i | 0.0845829 | + | 0.0488340i | 0.541695 | − | 0.840575i | \(-0.317783\pi\) |
−0.457112 | + | 0.889409i | \(0.651116\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.630399 | + | 0.363961i | 0.0354067 | + | 0.0204421i | 0.517599 | − | 0.855623i | \(-0.326826\pi\) |
−0.482192 | + | 0.876065i | \(0.660159\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.7279 | − | 37.6339i | −1.21653 | − | 2.10709i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.7279 | −0.710403 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.6985i | 1.65247i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.48244 | + | 3.74264i | 0.358480 | + | 0.206969i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.72792 | − | 12.5446i | 0.536318 | − | 0.691607i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50000 | + | 14.7224i | −0.467202 | + | 0.809218i | −0.999298 | − | 0.0374662i | \(-0.988071\pi\) |
0.532096 | + | 0.846684i | \(0.321405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.54026 | + | 2.62132i | −0.248805 | + | 0.143647i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 11.7279i | − | 0.638861i | −0.947610 | − | 0.319430i | \(-0.896508\pi\) | ||
0.947610 | − | 0.319430i | \(-0.103492\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.00000 | − | 15.5885i | −0.488813 | − | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.8787 | + | 27.5027i | −0.859879 | + | 1.48935i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.34847 | − | 17.0000i | 0.396780 | − | 0.917914i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7846 | − | 12.0000i | 1.11578 | − | 0.644194i | 0.175457 | − | 0.984487i | \(-0.443860\pi\) |
0.940319 | + | 0.340293i | \(0.110526\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.24264 | −0.279831 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.52192 | + | 0.878680i | −0.0810035 | + | 0.0467674i | −0.539955 | − | 0.841694i | \(-0.681559\pi\) |
0.458951 | + | 0.888462i | \(0.348225\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.87039 | + | 6.87868i | 0.469471 | + | 0.364058i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.12132 | − | 8.87039i | 0.270293 | − | 0.468161i | −0.698644 | − | 0.715470i | \(-0.746213\pi\) |
0.968937 | + | 0.247309i | \(0.0795461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000i | 0.367405i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.89588 | + | 5.13604i | −0.464361 | + | 0.268099i | −0.713876 | − | 0.700272i | \(-0.753062\pi\) |
0.249515 | + | 0.968371i | \(0.419729\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.12132 | − | 3.67423i | 0.110432 | − | 0.191273i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.48528 | − | 20.7846i | −0.440534 | − | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.69258 | + | 3.86396i | 0.346528 | + | 0.200068i | 0.663155 | − | 0.748482i | \(-0.269217\pi\) |
−0.316627 | + | 0.948550i | \(0.602550\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 53.6985i | − | 2.76561i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.4558 | −1.56441 | −0.782206 | − | 0.623020i | \(-0.785905\pi\) | ||||
−0.782206 | + | 0.623020i | \(0.785905\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.62132 | + | 9.73641i | 0.287989 | + | 0.498812i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.0454 | + | 12.7279i | 1.12647 | + | 0.650366i | 0.943044 | − | 0.332668i | \(-0.107949\pi\) |
0.183424 | + | 0.983034i | \(0.441282\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.54026 | − | 2.62132i | −0.230794 | − | 0.133249i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.6066 | + | 18.3712i | 0.537776 | + | 0.931455i | 0.999023 | + | 0.0441839i | \(0.0140687\pi\) |
−0.461247 | + | 0.887272i | \(0.652598\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.48528i | − | 0.125366i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.9326 | − | 8.62132i | −0.749444 | − | 0.432692i | 0.0760490 | − | 0.997104i | \(-0.475769\pi\) |
−0.825493 | + | 0.564412i | \(0.809103\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.3492 | − | 2.51104i | −0.918611 | − | 0.125709i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.2426 | − | 17.7408i | 0.511493 | − | 0.885932i | −0.488418 | − | 0.872610i | \(-0.662426\pi\) |
0.999911 | − | 0.0133223i | \(-0.00424074\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.9851 | + | 19.6213i | −1.69292 | + | 0.977408i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.2426i | 1.10253i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.50000 | + | 14.7224i | 0.420298 | + | 0.727977i | 0.995968 | − | 0.0897044i | \(-0.0285922\pi\) |
−0.575670 | + | 0.817682i | \(0.695259\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.12132 | − | 3.67423i | 0.104637 | − | 0.181237i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.30463 | − | 1.75736i | 0.211817 | − | 0.0864740i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.28629 | + | 0.742641i | −0.0629900 | + | 0.0363673i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.48528 | −0.121414 | −0.0607070 | − | 0.998156i | \(-0.519336\pi\) | ||||
−0.0607070 | + | 0.998156i | \(0.519336\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5147 | 0.707404 | 0.353702 | − | 0.935358i | \(-0.384923\pi\) | ||||
0.353702 | + | 0.935358i | \(0.384923\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.19615 | + | 3.00000i | −0.252646 | + | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.1039 | + | 20.2426i | 1.26325 | + | 0.979610i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.1213 | + | 19.2627i | −0.536942 | + | 0.930012i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.7279 | + | 27.2416i | 0.757587 | + | 1.31218i | 0.944078 | + | 0.329723i | \(0.106955\pi\) |
−0.186490 | + | 0.982457i | \(0.559711\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.7574i | 1.18976i | 0.803814 | + | 0.594881i | \(0.202801\pi\) | ||||
−0.803814 | + | 0.594881i | \(0.797199\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.7196 | − | 14.8492i | 1.23034 | − | 0.710336i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.00000 | + | 8.66025i | −0.238637 | + | 0.413331i | −0.960323 | − | 0.278889i | \(-0.910034\pi\) |
0.721686 | + | 0.692220i | \(0.243367\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | + | 4.89898i | −0.238095 | + | 0.233285i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.04384 | − | 1.75736i | −0.144617 | − | 0.0834947i | 0.425946 | − | 0.904749i | \(-0.359941\pi\) |
−0.570563 | + | 0.821254i | \(0.693275\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0000i | 0.567581i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | − | 15.5885i | −0.423793 | − | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.77589 | − | 2.75736i | −0.224391 | − | 0.129552i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.84489 | − | 5.10660i | −0.413747 | − | 0.238877i | 0.278652 | − | 0.960392i | \(-0.410113\pi\) |
−0.692398 | + | 0.721516i | \(0.743446\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.12132 | − | 3.67423i | −0.0990148 | − | 0.171499i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.72792 | −0.313351 | −0.156675 | − | 0.987650i | \(-0.550078\pi\) | ||||
−0.156675 | + | 0.987650i | \(0.550078\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.7279i | 1.66042i | 0.557453 | + | 0.830209i | \(0.311779\pi\) | ||||
−0.557453 | + | 0.830209i | \(0.688221\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.8931 | + | 11.4853i | 0.920542 | + | 0.531475i | 0.883808 | − | 0.467850i | \(-0.154971\pi\) |
0.0367344 | + | 0.999325i | \(0.488304\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.24264 | − | 7.94282i | −0.149731 | − | 0.366765i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.24264 | + | 9.08052i | −0.241568 | + | 0.418408i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.2627 | + | 11.1213i | −0.885700 | + | 0.511359i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.48528i | 0.388514i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.00000 | + | 10.3923i | 0.274147 | + | 0.474837i | 0.969920 | − | 0.243426i | \(-0.0782712\pi\) |
−0.695773 | + | 0.718262i | \(0.744938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.7426 | + | 23.8030i | −0.626610 | + | 1.08532i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.52192 | − | 11.1213i | 0.0692497 | − | 0.506038i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.6279 | − | 6.13604i | 0.481598 | − | 0.278050i | −0.239484 | − | 0.970900i | \(-0.576978\pi\) |
0.721082 | + | 0.692850i | \(0.243645\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.00000 | −0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.4853 | 1.46604 | 0.733020 | − | 0.680207i | \(-0.238110\pi\) | ||||
0.733020 | + | 0.680207i | \(0.238110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.6339 | − | 21.7279i | 1.69494 | − | 0.978576i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.56575 | + | 33.3640i | −0.204802 | + | 1.49658i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.25736 | − | 2.17781i | 0.0562871 | − | 0.0974922i | −0.836509 | − | 0.547953i | \(-0.815407\pi\) |
0.892796 | + | 0.450461i | \(0.148740\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.36396 | + | 5.82655i | 0.150291 | + | 0.260311i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 9.51472i | − | 0.424240i | −0.977244 | − | 0.212120i | \(-0.931963\pi\) | ||
0.977244 | − | 0.212120i | \(-0.0680368\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.5446 | + | 7.24264i | −0.557126 | + | 0.321657i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.7279 | − | 27.2416i | 0.697128 | − | 1.20746i | −0.272330 | − | 0.962204i | \(-0.587794\pi\) |
0.969458 | − | 0.245257i | \(-0.0788724\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.757359 | + | 1.85514i | 0.0335036 | + | 0.0820667i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.06218 | + | 3.50000i | 0.267652 | + | 0.154529i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.4558i | 1.11955i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.51472 | 0.154279 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.7279 | − | 32.4377i | −0.820485 | − | 1.42112i | −0.905321 | − | 0.424727i | \(-0.860370\pi\) |
0.0848363 | − | 0.996395i | \(-0.472963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.80821 | − | 1.62132i | −0.122794 | − | 0.0708954i | 0.437345 | − | 0.899294i | \(-0.355919\pi\) |
−0.560139 | + | 0.828399i | \(0.689252\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.5027 | − | 15.8787i | −1.19804 | − | 0.691686i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.50000 | − | 4.33013i | −0.108696 | − | 0.188266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.75736 | −0.0762629 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 22.2426i | − | 0.963436i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.19615 | − | 3.00000i | −0.224231 | − | 0.129460i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.39340 | + | 28.7635i | 0.318456 | + | 1.23893i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.4706 | + | 23.3317i | −0.579145 | + | 1.00311i | 0.416433 | + | 0.909166i | \(0.363280\pi\) |
−0.995578 | + | 0.0939417i | \(0.970053\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.2583 | + | 6.50000i | −0.483141 | + | 0.278942i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.4558i | 0.746358i | 0.927759 | + | 0.373179i | \(0.121732\pi\) | ||||
−0.927759 | + | 0.373179i | \(0.878268\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.24264 | − | 10.8126i | −0.266429 | − | 0.461469i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.8492 | + | 62.0927i | −1.52723 | + | 2.64524i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.9985 | + | 17.8345i | 0.977995 | + | 0.758401i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.9808 | − | 15.0000i | 1.10084 | − | 0.635570i | 0.164399 | − | 0.986394i | \(-0.447432\pi\) |
0.936442 | + | 0.350824i | \(0.114098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.4853 | −1.16250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0000 | −0.759961 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.19615 | + | 3.00000i | −0.218992 | + | 0.126435i | −0.605483 | − | 0.795858i | \(-0.707020\pi\) |
0.386492 | + | 0.922293i | \(0.373687\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.44949 | − | 1.00000i | 0.102869 | − | 0.0419961i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.84924 | − | 15.3273i | 0.370980 | − | 0.642555i | −0.618737 | − | 0.785598i | \(-0.712355\pi\) |
0.989717 | + | 0.143043i | \(0.0456887\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.4706 | − | 33.7240i | −0.814818 | − | 1.41131i | −0.909459 | − | 0.415794i | \(-0.863504\pi\) |
0.0946410 | − | 0.995511i | \(-0.469830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.00000i | 0.250654i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.3967 | + | 10.6213i | −0.765863 | + | 0.442171i | −0.831397 | − | 0.555679i | \(-0.812458\pi\) |
0.0655337 | + | 0.997850i | \(0.479125\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.62132 | − | 13.2005i | 0.316731 | − | 0.548595i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.60660 | + | 0.630399i | 0.191114 | + | 0.0261534i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.1769 | + | 18.0000i | 1.29122 | + | 0.745484i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 2.78680i | − | 0.115023i | −0.998345 | − | 0.0575117i | \(-0.981683\pi\) | ||
0.998345 | − | 0.0575117i | \(-0.0183167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 52.3970 | 2.15898 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.87868 | + | 6.71807i | 0.159548 | + | 0.276344i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.9596 | + | 19.6066i | 1.39455 | + | 0.805147i | 0.993815 | − | 0.111045i | \(-0.0354199\pi\) |
0.400740 | + | 0.916192i | \(0.368753\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.61642 | − | 3.24264i | −0.229865 | − | 0.132712i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.75736 | − | 13.4361i | −0.316957 | − | 0.548986i | 0.662894 | − | 0.748713i | \(-0.269328\pi\) |
−0.979852 | + | 0.199727i | \(0.935994\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.4853 | 0.550076 | 0.275038 | − | 0.961433i | \(-0.411310\pi\) | ||||
0.275038 | + | 0.961433i | \(0.411310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.24264i | 0.132051i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.9764 | − | 10.3787i | −0.729640 | − | 0.421258i | 0.0886507 | − | 0.996063i | \(-0.471745\pi\) |
−0.818290 | + | 0.574805i | \(0.805078\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.2426 | + | 25.0892i | 0.415053 | + | 1.01667i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.7279 | + | 27.2416i | −0.636284 | + | 1.10208i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.3659 | − | 22.7279i | 1.58997 | − | 0.917972i | 0.596665 | − | 0.802491i | \(-0.296492\pi\) |
0.993310 | − | 0.115482i | \(-0.0368411\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.51472i | 0.383048i | 0.981488 | + | 0.191524i | \(0.0613430\pi\) | ||||
−0.981488 | + | 0.191524i | \(0.938657\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.9853 | + | 19.0271i | 0.441536 | + | 0.764762i | 0.997804 | − | 0.0662407i | \(-0.0211005\pi\) |
−0.556268 | + | 0.831003i | \(0.687767\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.12132 | + | 3.67423i | −0.0851257 | + | 0.147442i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.67423 | − | 2.84924i | −0.147205 | − | 0.114152i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25.7196 | − | 14.8492i | 1.02714 | − | 0.593022i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.2426 | −0.886872 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.77589 | − | 2.75736i | 0.189824 | − | 0.109595i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.85951 | + | 35.3492i | −0.390648 | + | 1.40059i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.36396 | − | 11.0227i | 0.251754 | − | 0.436051i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.8787 | − | 22.3065i | −0.508677 | − | 0.881055i | −0.999950 | − | 0.0100488i | \(-0.996801\pi\) |
0.491272 | − | 0.871006i | \(-0.336532\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.72792i | 0.225887i | 0.993601 | + | 0.112944i | \(0.0360279\pi\) | ||||
−0.993601 | + | 0.112944i | \(0.963972\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.52192 | + | 0.878680i | −0.0598328 | + | 0.0345445i | −0.529618 | − | 0.848236i | \(-0.677665\pi\) |
0.469785 | + | 0.882781i | \(0.344331\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.72792 | + | 6.45695i | −0.146334 | + | 0.253457i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.1360 | − | 15.6500i | 0.475649 | − | 0.613372i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.52192 | − | 0.878680i | −0.0595572 | − | 0.0343854i | 0.469926 | − | 0.882706i | \(-0.344281\pi\) |
−0.529483 | + | 0.848321i | \(0.677614\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.757359i | − | 0.0295474i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.02944 | −0.273828 | −0.136914 | − | 0.990583i | \(-0.543718\pi\) | ||||
−0.136914 | + | 0.990583i | \(0.543718\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.9853 | + | 31.1514i | 0.699546 | + | 1.21165i | 0.968624 | + | 0.248531i | \(0.0799479\pi\) |
−0.269077 | + | 0.963119i | \(0.586719\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.2627 | − | 11.1213i | −0.748101 | − | 0.431916i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.6339 | − | 21.7279i | −1.45719 | − | 0.841309i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.2426 | − | 21.2049i | −0.473328 | − | 0.819828i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −52.9706 | −2.04491 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.27208i | 0.164677i | 0.996604 | + | 0.0823383i | \(0.0262388\pi\) | ||||
−0.996604 | + | 0.0823383i | \(0.973761\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.0227 | − | 6.36396i | −0.423637 | − | 0.244587i | 0.272995 | − | 0.962015i | \(-0.411986\pi\) |
−0.696632 | + | 0.717428i | \(0.745319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 43.2132 | + | 5.91359i | 1.65837 | + | 0.226943i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.6066 | + | 23.5673i | −0.521406 | + | 0.903102i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.97887 | + | 4.60660i | −0.305303 | + | 0.176267i | −0.644823 | − | 0.764332i | \(-0.723069\pi\) |
0.339520 | + | 0.940599i | \(0.389735\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.00000i | 0.267067i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.2426 | + | 38.5254i | 0.847377 | + | 1.46770i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.4706 | − | 35.4561i | 0.778737 | − | 1.34881i | −0.153933 | − | 0.988081i | \(-0.549194\pi\) |
0.932670 | − | 0.360731i | \(-0.117473\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.52192 | − | 11.1213i | 0.0578129 | − | 0.422464i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.5885 | − | 9.00000i | 0.590455 | − | 0.340899i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.48528 | 0.0940020 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.2132 | 1.93430 | 0.967148 | − | 0.254214i | \(-0.0818167\pi\) | ||||
0.967148 | + | 0.254214i | \(0.0818167\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.7818 | − | 18.3492i | 1.19867 | − | 0.692055i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −39.7862 | + | 16.2426i | −1.49631 | + | 0.610867i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.75736 | + | 16.9002i | −0.366445 | + | 0.634702i | −0.989007 | − | 0.147869i | \(-0.952759\pi\) |
0.622562 | + | 0.782571i | \(0.286092\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.50000 | − | 9.52628i | −0.206266 | − | 0.357263i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.7574i | 1.18932i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.8931 | − | 11.4853i | 0.742921 | − | 0.428926i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.75736 | − | 8.23999i | 0.177420 | − | 0.307300i | −0.763576 | − | 0.645718i | \(-0.776558\pi\) |
0.940996 | + | 0.338418i | \(0.109892\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.1985 | + | 18.3096i | −0.528779 | + | 0.681886i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.46410 | + | 2.00000i | 0.128831 | + | 0.0743808i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.24264i | − | 0.342791i | −0.985202 | − | 0.171395i | \(-0.945172\pi\) | ||
0.985202 | − | 0.171395i | \(-0.0548275\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.1213 | − | 19.2627i | −0.411337 | − | 0.712456i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.2898 | − | 22.1066i | −1.41426 | − | 0.816526i | −0.418478 | − | 0.908227i | \(-0.637436\pi\) |
−0.995787 | + | 0.0917010i | \(0.970770\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.9142 | + | 6.87868i | 0.438866 | + | 0.253379i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.742641 | + | 1.28629i | 0.0273185 | + | 0.0473170i | 0.879361 | − | 0.476155i | \(-0.157970\pi\) |
−0.852043 | + | 0.523472i | \(0.824637\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.6985 | 1.34815 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 27.2132i | − | 0.998356i | −0.866500 | − | 0.499178i | \(-0.833635\pi\) | ||
0.866500 | − | 0.499178i | \(-0.166365\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.52192 | − | 0.878680i | −0.0556841 | − | 0.0321492i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.6360 | − | 26.6112i | 0.754024 | − | 0.972351i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.4706 | − | 19.8676i | 0.418567 | − | 0.724979i | −0.577229 | − | 0.816582i | \(-0.695866\pi\) |
0.995796 | + | 0.0916035i | \(0.0291992\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.82655 | − | 3.36396i | 0.212331 | − | 0.122590i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 42.9706i | − | 1.56179i | −0.624661 | − | 0.780896i | \(-0.714763\pi\) | ||
0.624661 | − | 0.780896i | \(-0.285237\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.00000 | + | 15.5885i | 0.326679 | + | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.8787 | + | 32.6988i | −0.684352 | + | 1.18533i | 0.289288 | + | 0.957242i | \(0.406581\pi\) |
−0.973640 | + | 0.228090i | \(0.926752\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.3351 | + | 7.48528i | −0.663776 | + | 0.270985i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.97887 | + | 4.60660i | −0.288100 | + | 0.166335i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.00000 | −0.180305 | −0.0901523 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901523 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.75736 | 0.0632897 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −41.3081 | + | 23.8492i | −1.48575 | + | 0.857798i | −0.999868 | − | 0.0162275i | \(-0.994834\pi\) |
−0.485881 | + | 0.874025i | \(0.661501\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.88064 | − | 13.7426i | 0.0674675 | − | 0.493014i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.8492 | + | 25.7196i | −0.532029 | + | 0.921502i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0000 | − | 46.7654i | −0.966136 | − | 1.67340i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 10.2426i | − | 0.366042i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.97204 | + | 5.75736i | −0.355465 | + | 0.205228i | −0.667090 | − | 0.744978i | \(-0.732460\pi\) |
0.311625 | + | 0.950205i | \(0.399127\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.24264 | − | 7.34847i | 0.151042 | − | 0.261612i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 47.1838 | + | 6.45695i | 1.67766 | + | 0.229583i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.6864 | − | 32.7279i | −2.01299 | − | 1.16220i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.2426i | 1.42547i | 0.701435 | + | 0.712734i | \(0.252543\pi\) | ||||
−0.701435 | + | 0.712734i | \(0.747457\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.4558 | −0.900563 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.878680 | + | 1.52192i | 0.0310466 | + | 0.0537743i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.78272 | − | 1.60660i | −0.0981999 | − | 0.0566957i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.5446 | + | 7.24264i | 0.441592 | + | 0.254953i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.9706 | − | 34.5900i | −0.702128 | − | 1.21612i | −0.967718 | − | 0.252035i | \(-0.918900\pi\) |
0.265591 | − | 0.964086i | \(-0.414433\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −55.9411 | −1.96436 | −0.982179 | − | 0.187946i | \(-0.939817\pi\) | ||||
−0.982179 | + | 0.187946i | \(0.939817\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.4558i | 0.962918i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.7818 | + | 18.3492i | 1.11191 | + | 0.641959i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.50000 | − | 10.9612i | 0.297014 | − | 0.383014i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.8492 | − | 46.5043i | 0.937045 | − | 1.62301i | 0.166099 | − | 0.986109i | \(-0.446883\pi\) |
0.770946 | − | 0.636901i | \(-0.219784\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.35562 | + | 2.51472i | −0.151827 | + | 0.0876576i | −0.573989 | − | 0.818863i | \(-0.694605\pi\) |
0.422162 | + | 0.906521i | \(0.361271\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.45584i | 0.259265i | 0.991562 | + | 0.129633i | \(0.0413798\pi\) | ||||
−0.991562 | + | 0.129633i | \(0.958620\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.50000 | + | 9.52628i | 0.191023 | + | 0.330861i | 0.945589 | − | 0.325362i | \(-0.105486\pi\) |
−0.754567 | + | 0.656223i | \(0.772153\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.86396 | − | 6.69258i | 0.134039 | − | 0.232163i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.7635 | + | 7.39340i | −0.996595 | + | 0.256166i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.48244 | + | 3.74264i | −0.224066 | + | 0.129365i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.2426 | −1.18219 | −0.591094 | − | 0.806603i | \(-0.701304\pi\) | ||||
−0.591094 | + | 0.806603i | \(0.701304\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 75.9117 | 2.61764 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.30463 | + | 2.48528i | −0.148259 | + | 0.0855976i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.6354 | − | 11.3492i | −0.502878 | − | 0.389965i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.863961 | + | 1.49642i | −0.0296511 | + | 0.0513572i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.1213 | + | 19.2627i | 0.381234 | + | 0.660317i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 0.272078i | − | 0.00931577i | −0.999989 | − | 0.00465789i | \(-0.998517\pi\) | ||
0.999989 | − | 0.00465789i | \(-0.00148266\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.67423 | − | 2.12132i | 0.125509 | − | 0.0724629i | −0.435931 | − | 0.899980i | \(-0.643581\pi\) |
0.561440 | + | 0.827517i | \(0.310247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0000 | + | 19.0526i | −0.375315 | + | 0.650065i | −0.990374 | − | 0.138416i | \(-0.955799\pi\) |
0.615059 | + | 0.788481i | \(0.289132\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.24264 | + | 10.3923i | 0.144589 | + | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.3292 | + | 19.2426i | 1.13454 | + | 0.655027i | 0.945073 | − | 0.326860i | \(-0.105991\pi\) |
0.189467 | + | 0.981887i | \(0.439324\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1.00000i | − | 0.0339618i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −46.6690 | −1.58314 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.50000 | + | 14.7224i | 0.288012 | + | 0.498851i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.2767 | − | 8.24264i | −0.483192 | − | 0.278971i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.66025 | − | 5.00000i | −0.292436 | − | 0.168838i | 0.346604 | − | 0.938012i | \(-0.387335\pi\) |
−0.639040 | + | 0.769174i | \(0.720668\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.4853 | + | 25.0892i | 0.488576 | + | 0.846239i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.02944 | 0.236828 | 0.118414 | − | 0.992964i | \(-0.462219\pi\) | ||||
0.118414 | + | 0.992964i | \(0.462219\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 19.7279i | − | 0.663897i | −0.943297 | − | 0.331949i | \(-0.892294\pi\) | ||
0.943297 | − | 0.331949i | \(-0.107706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.5673 | − | 13.6066i | −0.791313 | − | 0.456865i | 0.0491114 | − | 0.998793i | \(-0.484361\pi\) |
−0.840425 | + | 0.541928i | \(0.817694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.4706 | − | 4.03295i | −0.988411 | − | 0.135261i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.12132 | + | 3.67423i | −0.0710669 | + | 0.123091i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.3731 | − | 21.0000i | 1.21718 | − | 0.702738i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.2426i | 0.742660i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.3345 | − | 66.3973i | −1.27853 | − | 2.21448i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | + | 31.1769i | −0.599667 | + | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.8418 | − | 5.24264i | 0.427348 | − | 0.174464i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.2618 | − | 27.8640i | 1.60251 | − | 0.925208i | 0.611523 | − | 0.791227i | \(-0.290557\pi\) |
0.990984 | − | 0.133981i | \(-0.0427760\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.2426 | 0.538734 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.78680 | 0.291120 | 0.145560 | − | 0.989349i | \(-0.453502\pi\) | ||||
0.145560 | + | 0.989349i | \(0.453502\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.45695 | + | 3.72792i | −0.213694 | + | 0.123376i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.19615 | + | 4.02944i | 0.171592 | + | 0.133064i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.0147186 | − | 0.0254934i | 0.000485523 | − | 0.000840950i | −0.865783 | − | 0.500420i | \(-0.833179\pi\) |
0.866268 | + | 0.499579i | \(0.166512\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.62132 | + | 4.54026i | 0.0863754 | + | 0.149607i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 66.7279i | − | 2.19638i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.58410 | − | 4.37868i | 0.249094 | − | 0.143815i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.63604 | − | 9.76191i | 0.184912 | − | 0.320278i | −0.758635 | − | 0.651516i | \(-0.774133\pi\) |
0.943547 | + | 0.331239i | \(0.107467\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.0000 | − | 34.2929i | 1.14708 | − | 1.12390i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.3712 | + | 10.6066i | 0.601445 | + | 0.347245i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 40.6985i | − | 1.32956i | −0.747039 | − | 0.664781i | \(-0.768525\pi\) | ||
0.747039 | − | 0.664781i | \(-0.231475\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.72792 | 0.0563886 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.84924 | − | 10.1312i | −0.190680 | − | 0.330267i | 0.754796 | − | 0.655960i | \(-0.227736\pi\) |
−0.945476 | + | 0.325693i | \(0.894403\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.5885 | − | 9.00000i | −0.507630 | − | 0.293080i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.9596 | + | 19.6066i | 1.10354 | + | 0.637129i | 0.937148 | − | 0.348931i | \(-0.113455\pi\) |
0.166391 | + | 0.986060i | \(0.446789\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.98528 | − | 3.43861i | −0.0644450 | − | 0.111622i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.727922 | 0.0236045 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 44.4853i | − | 1.44102i | −0.693445 | − | 0.720510i | \(-0.743908\pi\) | ||
0.693445 | − | 0.720510i | \(-0.256092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −37.6339 | − | 21.7279i | −1.21653 | − | 0.702364i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.24264 | + | 10.3923i | 0.137002 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.5147 | + | 21.6761i | −0.403701 | + | 0.699230i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.0227 | + | 6.36396i | −0.355202 | + | 0.205076i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.7574i | 0.860459i | 0.902720 | + | 0.430229i | \(0.141567\pi\) | ||||
−0.902720 | + | 0.430229i | \(0.858433\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.8492 | + | 25.7196i | 0.477026 | + | 0.826234i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.51472 | + | 16.4800i | −0.305342 | + | 0.528868i | −0.977337 | − | 0.211688i | \(-0.932104\pi\) |
0.671996 | + | 0.740555i | \(0.265437\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.532799 | − | 3.89340i | 0.0170808 | − | 0.124817i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.3519 | − | 25.6066i | 1.41894 | − | 0.819228i | 0.422738 | − | 0.906252i | \(-0.361069\pi\) |
0.996206 | + | 0.0870242i | \(0.0277358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.45584 | 0.238290 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.48528 | 0.238987 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.3273 | − | 8.84924i | 0.488866 | − | 0.282247i | −0.235238 | − | 0.971938i | \(-0.575587\pi\) |
0.724104 | + | 0.689691i | \(0.242254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.15232 | − | 15.7279i | 0.0685090 | − | 0.500625i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.1213 | + | 19.2627i | −0.353637 | + | 0.612518i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.4706 | + | 45.8484i | 0.840865 | + | 1.45642i | 0.889164 | + | 0.457588i | \(0.151287\pi\) |
−0.0482991 | + | 0.998833i | \(0.515380\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.0000i | 0.539479i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.235626 | − | 0.136039i | 0.00746236 | − | 0.00430840i | −0.496264 | − | 0.868172i | \(-0.665295\pi\) |
0.503727 | + | 0.863863i | \(0.331962\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.62132 | + | 4.54026i | −0.0829349 | + | 0.143647i |
(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 | 2100.2.bc.f.1549.3 | 8 | ||
5.2 | odd | 4 | 420.2.q.d.121.1 | ✓ | 4 | ||
5.3 | odd | 4 | 2100.2.q.k.1801.2 | 4 | |||
5.4 | even | 2 | inner | 2100.2.bc.f.1549.2 | 8 | ||
7.4 | even | 3 | inner | 2100.2.bc.f.949.2 | 8 | ||
15.2 | even | 4 | 1260.2.s.e.541.1 | 4 | |||
20.7 | even | 4 | 1680.2.bg.t.961.2 | 4 | |||
35.2 | odd | 12 | 2940.2.a.r.1.2 | 2 | |||
35.4 | even | 6 | inner | 2100.2.bc.f.949.3 | 8 | ||
35.12 | even | 12 | 2940.2.a.p.1.2 | 2 | |||
35.17 | even | 12 | 2940.2.q.q.361.1 | 4 | |||
35.18 | odd | 12 | 2100.2.q.k.1201.2 | 4 | |||
35.27 | even | 4 | 2940.2.q.q.961.1 | 4 | |||
35.32 | odd | 12 | 420.2.q.d.361.1 | yes | 4 | ||
105.2 | even | 12 | 8820.2.a.bk.1.1 | 2 | |||
105.32 | even | 12 | 1260.2.s.e.361.1 | 4 | |||
105.47 | odd | 12 | 8820.2.a.bf.1.1 | 2 | |||
140.67 | even | 12 | 1680.2.bg.t.1201.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.q.d.121.1 | ✓ | 4 | 5.2 | odd | 4 | ||
420.2.q.d.361.1 | yes | 4 | 35.32 | odd | 12 | ||
1260.2.s.e.361.1 | 4 | 105.32 | even | 12 | |||
1260.2.s.e.541.1 | 4 | 15.2 | even | 4 | |||
1680.2.bg.t.961.2 | 4 | 20.7 | even | 4 | |||
1680.2.bg.t.1201.2 | 4 | 140.67 | even | 12 | |||
2100.2.q.k.1201.2 | 4 | 35.18 | odd | 12 | |||
2100.2.q.k.1801.2 | 4 | 5.3 | odd | 4 | |||
2100.2.bc.f.949.2 | 8 | 7.4 | even | 3 | inner | ||
2100.2.bc.f.949.3 | 8 | 35.4 | even | 6 | inner | ||
2100.2.bc.f.1549.2 | 8 | 5.4 | even | 2 | inner | ||
2100.2.bc.f.1549.3 | 8 | 1.1 | even | 1 | trivial | ||
2940.2.a.p.1.2 | 2 | 35.12 | even | 12 | |||
2940.2.a.r.1.2 | 2 | 35.2 | odd | 12 | |||
2940.2.q.q.361.1 | 4 | 35.17 | even | 12 | |||
2940.2.q.q.961.1 | 4 | 35.27 | even | 4 | |||
8820.2.a.bf.1.1 | 2 | 105.47 | odd | 12 | |||
8820.2.a.bk.1.1 | 2 | 105.2 | even | 12 |