Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2520,2,Mod(361,2520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2520.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2520.bi (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: | \(20.1223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 29x^{8} + 247x^{6} + 855x^{4} + 1212x^{2} + 588 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(1.05780i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2520.361 |
Dual form | 2520.2.bi.r.1801.1 |
$q$-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 \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(1081\) | \(1261\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.62478 | − | 0.332488i | −0.992072 | − | 0.125668i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41608 | + | 2.45273i | −0.426965 | + | 0.739525i | −0.996602 | − | 0.0823715i | \(-0.973751\pi\) |
0.569637 | + | 0.821897i | \(0.307084\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.08882 | −0.301985 | −0.150993 | − | 0.988535i | \(-0.548247\pi\) | ||||
−0.150993 | + | 0.988535i | \(0.548247\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.23314 | + | 3.86791i | −0.541616 | + | 0.938106i | 0.457196 | + | 0.889366i | \(0.348854\pi\) |
−0.998811 | + | 0.0487401i | \(0.984479\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.06886 | + | 3.58337i | 0.474628 | + | 0.822080i | 0.999578 | − | 0.0290530i | \(-0.00924915\pi\) |
−0.524950 | + | 0.851133i | \(0.675916\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.69363 | − | 6.39756i | −0.770176 | − | 1.33398i | −0.937466 | − | 0.348076i | \(-0.886835\pi\) |
0.167290 | − | 0.985908i | \(-0.446498\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.17054 | 1.70293 | 0.851463 | − | 0.524414i | \(-0.175716\pi\) | ||||
0.851463 | + | 0.524414i | \(0.175716\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.37788 | − | 9.31476i | 0.965896 | − | 1.67298i | 0.258708 | − | 0.965956i | \(-0.416703\pi\) |
0.707188 | − | 0.707026i | \(-0.249963\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.02445 | + | 2.43937i | 0.173163 | + | 0.412328i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0244456 | + | 0.0423411i | 0.00401884 | + | 0.00696083i | 0.868028 | − | 0.496516i | \(-0.165387\pi\) |
−0.864009 | + | 0.503476i | \(0.832054\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.66694 | 1.50972 | 0.754861 | − | 0.655884i | \(-0.227704\pi\) | ||||
0.754861 | + | 0.655884i | \(0.227704\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.20962 | 0.946958 | 0.473479 | − | 0.880805i | \(-0.342998\pi\) | ||||
0.473479 | + | 0.880805i | \(0.342998\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.371671 | − | 0.643754i | −0.0542138 | − | 0.0939011i | 0.837645 | − | 0.546215i | \(-0.183932\pi\) |
−0.891859 | + | 0.452314i | \(0.850599\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.77890 | + | 1.74541i | 0.968415 | + | 0.249344i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.46049 | + | 5.99375i | −0.475335 | + | 0.823305i | −0.999601 | − | 0.0282498i | \(-0.991007\pi\) |
0.524265 | + | 0.851555i | \(0.324340\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.83217 | 0.381889 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.75311 | + | 3.03647i | −0.228235 | + | 0.395314i | −0.957285 | − | 0.289146i | \(-0.906629\pi\) |
0.729050 | + | 0.684460i | \(0.239962\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.68070 | − | 6.37515i | −0.471265 | − | 0.816255i | 0.528195 | − | 0.849123i | \(-0.322869\pi\) |
−0.999460 | + | 0.0328685i | \(0.989536\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.544411 | + | 0.942948i | 0.0675259 | + | 0.116958i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.87433 | − | 11.9067i | 0.839833 | − | 1.45463i | −0.0502009 | − | 0.998739i | \(-0.515986\pi\) |
0.890034 | − | 0.455894i | \(-0.150681\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.50621 | −0.890823 | −0.445412 | − | 0.895326i | \(-0.646943\pi\) | ||||
−0.445412 | + | 0.895326i | \(0.646943\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.97691 | − | 8.62026i | 0.582503 | − | 1.00892i | −0.412679 | − | 0.910877i | \(-0.635407\pi\) |
0.995182 | − | 0.0980481i | \(-0.0312599\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.53240 | − | 5.96703i | 0.516515 | − | 0.680006i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.73001 | − | 15.1208i | −0.982203 | − | 1.70123i | −0.653760 | − | 0.756702i | \(-0.726809\pi\) |
−0.328443 | − | 0.944524i | \(-0.606524\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.5319 | −1.37556 | −0.687779 | − | 0.725920i | \(-0.741414\pi\) | ||||
−0.687779 | + | 0.725920i | \(0.741414\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.46628 | 0.484436 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.33572 | − | 2.31353i | −0.141586 | − | 0.245234i | 0.786508 | − | 0.617580i | \(-0.211887\pi\) |
−0.928094 | + | 0.372346i | \(0.878553\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.85792 | + | 0.362020i | 0.299591 | + | 0.0379500i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.06886 | − | 3.58337i | 0.212260 | − | 0.367646i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.9725 | 1.41869 | 0.709346 | − | 0.704861i | \(-0.248991\pi\) | ||||
0.709346 | + | 0.704861i | \(0.248991\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.95377 | − | 8.58018i | 0.492918 | − | 0.853759i | −0.507048 | − | 0.861918i | \(-0.669263\pi\) |
0.999967 | + | 0.00815809i | \(0.00259683\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.24252 | + | 12.5444i | 0.713627 | + | 1.23604i | 0.963487 | + | 0.267756i | \(0.0862822\pi\) |
−0.249859 | + | 0.968282i | \(0.580384\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.23314 | − | 2.13586i | −0.119212 | − | 0.206481i | 0.800244 | − | 0.599675i | \(-0.204704\pi\) |
−0.919456 | + | 0.393194i | \(0.871370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.64119 | − | 9.77083i | 0.540328 | − | 0.935876i | −0.458557 | − | 0.888665i | \(-0.651633\pi\) |
0.998885 | − | 0.0472106i | \(-0.0150332\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.49911 | −0.799529 | −0.399764 | − | 0.916618i | \(-0.630908\pi\) | ||||
−0.399764 | + | 0.916618i | \(0.630908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.69363 | + | 6.39756i | −0.344433 | + | 0.596576i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.14752 | − | 9.40991i | 0.655212 | − | 0.862605i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.48942 | + | 2.57975i | 0.135402 | + | 0.234523i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.85094 | 0.785394 | 0.392697 | − | 0.919668i | \(-0.371542\pi\) | ||||
0.392697 | + | 0.919668i | \(0.371542\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.16919 | − | 5.48919i | −0.276893 | − | 0.479593i | 0.693718 | − | 0.720247i | \(-0.255972\pi\) |
−0.970611 | + | 0.240654i | \(0.922638\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.23886 | − | 10.0934i | −0.367556 | − | 0.875209i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.72693 | + | 2.99113i | −0.147542 | + | 0.255549i | −0.930318 | − | 0.366753i | \(-0.880469\pi\) |
0.782777 | + | 0.622303i | \(0.213803\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.7158 | 1.33300 | 0.666500 | − | 0.745505i | \(-0.267792\pi\) | ||||
0.666500 | + | 0.745505i | \(0.267792\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.54186 | − | 2.67058i | 0.128937 | − | 0.223326i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.58527 | − | 7.94192i | −0.380786 | − | 0.659541i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.4362 | + | 19.8080i | 0.936887 | + | 1.62274i | 0.771235 | + | 0.636551i | \(0.219639\pi\) |
0.165652 | + | 0.986184i | \(0.447027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.40102 | + | 14.5510i | −0.683666 | + | 1.18414i | 0.290189 | + | 0.956969i | \(0.406282\pi\) |
−0.973854 | + | 0.227174i | \(0.927051\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.7558 | −0.863924 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.03147 | − | 3.51862i | 0.162129 | − | 0.280816i | −0.773503 | − | 0.633793i | \(-0.781497\pi\) |
0.935632 | + | 0.352977i | \(0.114831\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.56785 | + | 18.0203i | 0.596430 | + | 1.42020i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.32857 | − | 9.22935i | −0.417365 | − | 0.722898i | 0.578308 | − | 0.815818i | \(-0.303713\pi\) |
−0.995674 | + | 0.0929203i | \(0.970380\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.38727 | 0.726409 | 0.363204 | − | 0.931710i | \(-0.381683\pi\) | ||||
0.363204 | + | 0.931710i | \(0.381683\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8145 | −0.908805 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.71005 | − | 15.0862i | −0.662213 | − | 1.14699i | −0.980033 | − | 0.198835i | \(-0.936284\pi\) |
0.317820 | − | 0.948151i | \(-0.397049\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.60033 | − | 2.10688i | 0.120974 | − | 0.159265i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.12030 | + | 1.94041i | −0.0837349 | + | 0.145033i | −0.904851 | − | 0.425727i | \(-0.860018\pi\) |
0.821117 | + | 0.570761i | \(0.193352\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.6432 | 1.68305 | 0.841527 | − | 0.540215i | \(-0.181657\pi\) | ||||
0.841527 | + | 0.540215i | \(0.181657\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.0244456 | − | 0.0423411i | 0.00179728 | − | 0.00311298i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.32462 | − | 10.9546i | −0.462502 | − | 0.801077i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.71583 | + | 15.0963i | 0.630655 | + | 1.09233i | 0.987418 | + | 0.158132i | \(0.0505472\pi\) |
−0.356762 | + | 0.934195i | \(0.616119\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.99297 | + | 6.91603i | −0.287420 | + | 0.497827i | −0.973193 | − | 0.229989i | \(-0.926131\pi\) |
0.685773 | + | 0.727816i | \(0.259464\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.4457 | 1.59919 | 0.799596 | − | 0.600539i | \(-0.205047\pi\) | ||||
0.799596 | + | 0.600539i | \(0.205047\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.89742 | − | 8.48258i | 0.347169 | − | 0.601314i | −0.638576 | − | 0.769558i | \(-0.720476\pi\) |
0.985745 | + | 0.168244i | \(0.0538097\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −24.0706 | − | 3.04909i | −1.68943 | − | 0.214004i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.83347 | − | 8.37182i | −0.337584 | − | 0.584713i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.7187 | −0.810599 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.31451 | −0.159337 | −0.0796687 | − | 0.996821i | \(-0.525386\pi\) | ||||
−0.0796687 | + | 0.996821i | \(0.525386\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.10481 | − | 5.37769i | −0.211746 | − | 0.366755i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.2128 | + | 22.6611i | −1.16848 | + | 1.53834i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.43149 | − | 4.21147i | 0.163560 | − | 0.283294i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.67854 | 0.246333 | 0.123167 | − | 0.992386i | \(-0.460695\pi\) | ||||
0.123167 | + | 0.992386i | \(0.460695\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.312151 | − | 0.540662i | 0.0207182 | − | 0.0358850i | −0.855480 | − | 0.517835i | \(-0.826738\pi\) |
0.876199 | + | 0.481950i | \(0.160071\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.17012 | + | 14.1511i | 0.539896 | + | 0.935128i | 0.998909 | + | 0.0466983i | \(0.0148699\pi\) |
−0.459013 | + | 0.888430i | \(0.651797\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.18661 | − | 8.98346i | −0.339786 | − | 0.588526i | 0.644606 | − | 0.764515i | \(-0.277021\pi\) |
−0.984392 | + | 0.175988i | \(0.943688\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.371671 | + | 0.643754i | −0.0242452 | + | 0.0419939i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.3287 | −0.862159 | −0.431080 | − | 0.902314i | \(-0.641867\pi\) | ||||
−0.431080 | + | 0.902314i | \(0.641867\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.31798 | − | 10.9431i | 0.406977 | − | 0.704905i | −0.587572 | − | 0.809172i | \(-0.699916\pi\) |
0.994549 | + | 0.104267i | \(0.0332495\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.87788 | − | 6.74341i | −0.119973 | − | 0.430821i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.25262 | − | 3.90165i | −0.143331 | − | 0.248256i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.5764 | 1.17253 | 0.586265 | − | 0.810120i | \(-0.300598\pi\) | ||||
0.586265 | + | 0.810120i | \(0.300598\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.9220 | 1.31535 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.3247 | + | 23.0790i | 0.831170 | + | 1.43963i | 0.897111 | + | 0.441805i | \(0.145662\pi\) |
−0.0659410 | + | 0.997824i | \(0.521005\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0500864 | − | 0.119264i | −0.00311222 | − | 0.00741069i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.65798 | + | 4.60376i | −0.163898 | + | 0.283880i | −0.936263 | − | 0.351299i | \(-0.885740\pi\) |
0.772365 | + | 0.635179i | \(0.219074\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.92099 | 0.425153 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.70687 | − | 13.3487i | 0.469896 | − | 0.813884i | −0.529511 | − | 0.848303i | \(-0.677625\pi\) |
0.999408 | + | 0.0344187i | \(0.0109580\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.710817 | + | 1.23117i | 0.0431791 | + | 0.0747883i | 0.886807 | − | 0.462140i | \(-0.152918\pi\) |
−0.843628 | + | 0.536928i | \(0.819585\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.41608 | − | 2.45273i | −0.0853930 | − | 0.147905i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.64114 | + | 9.77074i | −0.338943 | + | 0.587067i | −0.984234 | − | 0.176870i | \(-0.943403\pi\) |
0.645291 | + | 0.763937i | \(0.276736\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.2388 | 1.26700 | 0.633500 | − | 0.773742i | \(-0.281617\pi\) | ||||
0.633500 | + | 0.773742i | \(0.281617\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.67846 | − | 4.63923i | 0.159218 | − | 0.275774i | −0.775369 | − | 0.631509i | \(-0.782436\pi\) |
0.934587 | + | 0.355735i | \(0.115769\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.3736 | − | 3.21414i | −1.49775 | − | 0.189725i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.47382 | − | 2.55274i | −0.0866955 | − | 0.150161i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.9585 | 1.10757 | 0.553785 | − | 0.832660i | \(-0.313183\pi\) | ||||
0.553785 | + | 0.832660i | \(0.313183\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.50621 | 0.204139 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.02171 | + | 6.96581i | 0.232582 | + | 0.402843i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.2989 | − | 2.06462i | −0.939451 | − | 0.119003i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.68070 | + | 6.37515i | −0.210756 | + | 0.365040i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.1572 | −1.32165 | −0.660825 | − | 0.750540i | \(-0.729794\pi\) | ||||
−0.660825 | + | 0.750540i | \(0.729794\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.46362 | + | 7.73122i | −0.253109 | + | 0.438397i | −0.964380 | − | 0.264520i | \(-0.914786\pi\) |
0.711271 | + | 0.702917i | \(0.248120\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.77625 | − | 3.07655i | −0.100399 | − | 0.173897i | 0.811450 | − | 0.584422i | \(-0.198679\pi\) |
−0.911849 | + | 0.410525i | \(0.865345\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.49876 | + | 9.52413i | 0.308841 | + | 0.534928i | 0.978109 | − | 0.208093i | \(-0.0667256\pi\) |
−0.669268 | + | 0.743021i | \(0.733392\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.9862 | + | 22.4928i | −0.727090 | + | 1.25936i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.4802 | −1.02826 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.544411 | − | 0.942948i | 0.0301985 | − | 0.0523053i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.761514 | + | 1.81329i | 0.0419836 | + | 0.0999697i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.950215 | + | 1.64582i | 0.0522285 | + | 0.0904625i | 0.890958 | − | 0.454086i | \(-0.150034\pi\) |
−0.838729 | + | 0.544549i | \(0.816701\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.7487 | −0.751170 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.3951 | 1.16546 | 0.582732 | − | 0.812664i | \(-0.301984\pi\) | ||||
0.582732 | + | 0.812664i | \(0.301984\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.2311 | + | 26.3810i | 0.824808 | + | 1.42861i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.2128 | − | 6.83522i | −0.929403 | − | 0.369067i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.54353 | − | 4.40553i | 0.136544 | − | 0.236501i | −0.789642 | − | 0.613568i | \(-0.789734\pi\) |
0.926186 | + | 0.377066i | \(0.123067\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.41924 | −0.236557 | −0.118278 | − | 0.992980i | \(-0.537738\pi\) | ||||
−0.118278 | + | 0.992980i | \(0.537738\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.46663 | + | 11.2005i | −0.344184 | + | 0.596144i | −0.985205 | − | 0.171379i | \(-0.945178\pi\) |
0.641021 | + | 0.767523i | \(0.278511\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.75311 | + | 6.50057i | 0.199194 | + | 0.345014i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.5507 | − | 23.4704i | −0.715176 | − | 1.23872i | −0.962892 | − | 0.269889i | \(-0.913013\pi\) |
0.247715 | − | 0.968833i | \(-0.420320\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.939662 | − | 1.62754i | 0.0494559 | − | 0.0856601i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.95382 | −0.521007 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.55337 | − | 14.8149i | 0.446482 | − | 0.773330i | −0.551672 | − | 0.834061i | \(-0.686010\pi\) |
0.998154 | + | 0.0607312i | \(0.0193432\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.0759 | − | 14.5817i | 0.575031 | − | 0.757043i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0680 | − | 24.3666i | −0.728415 | − | 1.26165i | −0.957553 | − | 0.288258i | \(-0.906924\pi\) |
0.229137 | − | 0.973394i | \(-0.426410\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.98509 | −0.514258 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.47949 | −0.0759960 | −0.0379980 | − | 0.999278i | \(-0.512098\pi\) | ||||
−0.0379980 | + | 0.999278i | \(0.512098\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.05468 | − | 3.55880i | −0.104989 | − | 0.181846i | 0.808745 | − | 0.588160i | \(-0.200147\pi\) |
−0.913734 | + | 0.406314i | \(0.866814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.43380 | − | 0.941660i | −0.378862 | − | 0.0479914i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.391713 | + | 0.678466i | −0.0198606 | + | 0.0343996i | −0.875785 | − | 0.482702i | \(-0.839656\pi\) |
0.855924 | + | 0.517101i | \(0.172989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.9936 | 1.66856 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.73001 | + | 15.1208i | −0.439255 | + | 0.760811i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.0097 | + | 20.8015i | 0.602751 | + | 1.04400i | 0.992403 | + | 0.123033i | \(0.0392622\pi\) |
−0.389651 | + | 0.920963i | \(0.627404\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.64257 | − | 13.2373i | −0.381652 | − | 0.661040i | 0.609647 | − | 0.792673i | \(-0.291311\pi\) |
−0.991299 | + | 0.131633i | \(0.957978\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.85556 | + | 10.1421i | −0.291686 | + | 0.505215i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.138468 | −0.00686361 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.799763 | − | 1.38523i | 0.0395458 | − | 0.0684953i | −0.845575 | − | 0.533857i | \(-0.820742\pi\) |
0.885121 | + | 0.465361i | \(0.154076\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.61110 | − | 7.38716i | 0.276104 | − | 0.363498i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.26597 | + | 10.8530i | 0.307584 | + | 0.532751i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.416537 | 0.0203492 | 0.0101746 | − | 0.999948i | \(-0.496761\pi\) | ||||
0.0101746 | + | 0.999948i | \(0.496761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.1154 | −1.71142 | −0.855709 | − | 0.517457i | \(-0.826879\pi\) | ||||
−0.855709 | + | 0.517457i | \(0.826879\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.23314 | − | 3.86791i | −0.108323 | − | 0.187621i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.54135 | + | 17.9571i | 0.364951 | + | 0.869007i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.5292 | − | 26.8974i | 0.748017 | − | 1.29560i | −0.200756 | − | 0.979641i | \(-0.564340\pi\) |
0.948772 | − | 0.315961i | \(-0.102327\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.62276 | −0.174099 | −0.0870494 | − | 0.996204i | \(-0.527744\pi\) | ||||
−0.0870494 | + | 0.996204i | \(0.527744\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.2832 | − | 26.4713i | 0.731095 | − | 1.26629i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.94631 | − | 3.37111i | −0.0928925 | − | 0.160894i | 0.815835 | − | 0.578285i | \(-0.196278\pi\) |
−0.908727 | + | 0.417391i | \(0.862945\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.2585 | − | 19.5003i | −0.534908 | − | 0.926488i | −0.999168 | − | 0.0407889i | \(-0.987013\pi\) |
0.464260 | − | 0.885699i | \(-0.346320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.33572 | + | 2.31353i | −0.0633191 | + | 0.109672i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.40582 | 0.349502 | 0.174751 | − | 0.984613i | \(-0.444088\pi\) | ||||
0.174751 | + | 0.984613i | \(0.444088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.6892 | + | 23.7104i | −0.644599 | + | 1.11648i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.11544 | − | 2.65604i | −0.0522926 | − | 0.124517i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.6107 | − | 21.8424i | −0.589905 | − | 1.02174i | −0.994244 | − | 0.107136i | \(-0.965832\pi\) |
0.404340 | − | 0.914609i | \(-0.367501\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.2593 | 1.45589 | 0.727946 | − | 0.685634i | \(-0.240475\pi\) | ||||
0.727946 | + | 0.685634i | \(0.240475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.2062 | −0.799641 | −0.399821 | − | 0.916593i | \(-0.630928\pi\) | ||||
−0.399821 | + | 0.916593i | \(0.630928\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.38456 | + | 2.39813i | 0.0640698 | + | 0.110972i | 0.896281 | − | 0.443487i | \(-0.146259\pi\) |
−0.832211 | + | 0.554459i | \(0.812925\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.0024 | + | 28.9668i | −1.01598 | + | 1.33756i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.79334 | + | 15.2305i | −0.404318 | + | 0.700300i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.13771 | −0.189851 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.5969 | + | 23.5505i | −0.621258 | + | 1.07605i | 0.367994 | + | 0.929828i | \(0.380045\pi\) |
−0.989252 | + | 0.146222i | \(0.953289\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0266169 | − | 0.0461019i | −0.00121363 | − | 0.00210207i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.98624 | − | 12.1005i | −0.317229 | − | 0.549457i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.07229 | + | 1.85725i | −0.0485899 | + | 0.0841601i | −0.889297 | − | 0.457329i | \(-0.848806\pi\) |
0.840708 | + | 0.541489i | \(0.182139\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.9253 | 1.03460 | 0.517302 | − | 0.855803i | \(-0.326937\pi\) | ||||
0.517302 | + | 0.855803i | \(0.326937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.4791 | + | 35.4708i | −0.922332 | + | 1.59753i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.7021 | + | 2.49572i | 0.883761 | + | 0.111948i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.34505 | − | 14.4541i | −0.373576 | − | 0.647053i | 0.616537 | − | 0.787326i | \(-0.288535\pi\) |
−0.990113 | + | 0.140274i | \(0.955202\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −42.1562 | −1.87965 | −0.939825 | − | 0.341656i | \(-0.889012\pi\) | ||||
−0.939825 | + | 0.341656i | \(0.889012\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.90753 | −0.440879 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.3712 | − | 24.8917i | −0.636992 | − | 1.10330i | −0.986089 | − | 0.166217i | \(-0.946845\pi\) |
0.349097 | − | 0.937087i | \(-0.386488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.9294 | + | 20.9715i | −0.704675 | + | 0.927724i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.24252 | − | 12.5444i | 0.319144 | − | 0.552773i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.10527 | 0.0925897 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.6053 | + | 35.6895i | −0.902737 | + | 1.56359i | −0.0788096 | + | 0.996890i | \(0.525112\pi\) |
−0.823927 | + | 0.566696i | \(0.808221\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.57589 | + | 13.1218i | 0.331270 | + | 0.573777i | 0.982761 | − | 0.184879i | \(-0.0591895\pi\) |
−0.651491 | + | 0.758656i | \(0.725856\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.0191 | + | 41.6023i | 1.04629 | + | 1.81223i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7859 | + | 27.3419i | −0.686342 | + | 1.18878i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.5256 | −0.455914 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.23314 | + | 2.13586i | −0.0533133 | + | 0.0923413i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.8805 | + | 14.1552i | −0.597876 | + | 0.609706i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.4197 | − | 33.6359i | −0.834917 | − | 1.44612i | −0.894098 | − | 0.447871i | \(-0.852182\pi\) |
0.0591814 | − | 0.998247i | \(-0.481151\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.2824 | −0.483284 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.2415 | −1.07925 | −0.539625 | − | 0.841906i | \(-0.681434\pi\) | ||||
−0.539625 | + | 0.841906i | \(0.681434\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.9725 | + | 32.8614i | 0.808257 | + | 1.39994i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.8868 | + | 42.5914i | 0.760626 | + | 1.81117i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.58475 | − | 7.94103i | 0.194262 | − | 0.336472i | −0.752396 | − | 0.658711i | \(-0.771102\pi\) |
0.946658 | + | 0.322239i | \(0.104435\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.76118 | −0.285967 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.69021 | − | 13.3198i | 0.324104 | − | 0.561364i | −0.657227 | − | 0.753693i | \(-0.728271\pi\) |
0.981331 | + | 0.192329i | \(0.0616041\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.24955 | + | 7.36044i | 0.178780 | + | 0.309656i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.03413 | + | 13.9155i | 0.336808 | + | 0.583369i | 0.983831 | − | 0.179102i | \(-0.0573192\pi\) |
−0.647022 | + | 0.762471i | \(0.723986\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.6200 | + | 33.9829i | −0.821073 | + | 1.42214i | 0.0838115 | + | 0.996482i | \(0.473291\pi\) |
−0.904884 | + | 0.425658i | \(0.860043\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.38727 | 0.308070 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.0351 | + | 19.1133i | −0.459396 | + | 0.795696i | −0.998929 | − | 0.0462677i | \(-0.985267\pi\) |
0.539534 | + | 0.841964i | \(0.318601\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 32.8935 | + | 4.16671i | 1.36465 | + | 0.172864i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.80069 | − | 16.9753i | −0.405903 | − | 0.703045i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.6421 | 0.975815 | 0.487908 | − | 0.872895i | \(-0.337760\pi\) | ||||
0.487908 | + | 0.872895i | \(0.337760\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.5043 | 1.83377 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.2120 | − | 26.3479i | −0.624681 | − | 1.08198i | −0.988602 | − | 0.150550i | \(-0.951896\pi\) |
0.363921 | − | 0.931430i | \(-0.381438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.7230 | − | 1.48498i | −0.480596 | − | 0.0608783i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.3685 | − | 19.6908i | 0.464504 | − | 0.804545i | −0.534675 | − | 0.845058i | \(-0.679566\pi\) |
0.999179 | + | 0.0405131i | \(0.0128992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.5185 | −0.429058 | −0.214529 | − | 0.976718i | \(-0.568822\pi\) | ||||
−0.214529 | + | 0.976718i | \(0.568822\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.48942 | − | 2.57975i | 0.0605535 | − | 0.104882i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.60311 | + | 14.9010i | 0.349190 | + | 0.604814i | 0.986106 | − | 0.166119i | \(-0.0531236\pi\) |
−0.636916 | + | 0.770933i | \(0.719790\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.404684 | + | 0.700934i | 0.0163718 | + | 0.0283567i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.4449 | + | 25.0193i | −0.583425 | + | 1.01052i | 0.411645 | + | 0.911344i | \(0.364954\pi\) |
−0.995070 | + | 0.0991770i | \(0.968379\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.7125 | −1.27670 | −0.638349 | − | 0.769747i | \(-0.720382\pi\) | ||||
−0.638349 | + | 0.769747i | \(0.720382\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.70701 | − | 15.0810i | 0.349964 | − | 0.606156i | −0.636278 | − | 0.771460i | \(-0.719527\pi\) |
0.986243 | + | 0.165303i | \(0.0528604\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.73674 | + | 6.51661i | 0.109645 | + | 0.261082i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.218362 | −0.00870666 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.02512 | −0.279666 | −0.139833 | − | 0.990175i | \(-0.544657\pi\) | ||||
−0.139833 | + | 0.990175i | \(0.544657\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.42547 | − | 7.66514i | −0.175619 | − | 0.304182i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.38102 | − | 1.90044i | −0.292447 | − | 0.0752983i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.7864 | + | 22.1468i | −0.505034 | + | 0.874744i | 0.494949 | + | 0.868922i | \(0.335187\pi\) |
−0.999983 | + | 0.00582234i | \(0.998147\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.5232 | 1.59808 | 0.799039 | − | 0.601279i | \(-0.205342\pi\) | ||||
0.799039 | + | 0.601279i | \(0.205342\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.4893 | − | 26.8283i | 0.608948 | − | 1.05473i | −0.382466 | − | 0.923970i | \(-0.624925\pi\) |
0.991414 | − | 0.130760i | \(-0.0417417\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.96508 | − | 8.59978i | −0.194897 | − | 0.337571i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.4724 | − | 25.0670i | −0.566349 | − | 0.980946i | −0.996923 | − | 0.0783902i | \(-0.975022\pi\) |
0.430573 | − | 0.902556i | \(-0.358311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.16919 | + | 5.48919i | −0.123830 | + | 0.214481i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.18836 | −0.357928 | −0.178964 | − | 0.983856i | \(-0.557275\pi\) | ||||
−0.178964 | + | 0.983856i | \(0.557275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.11457 | − | 14.0549i | 0.315620 | − | 0.546670i | −0.663949 | − | 0.747778i | \(-0.731121\pi\) |
0.979569 | + | 0.201108i | \(0.0644541\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.62171 | + | 8.71766i | −0.256779 | + | 0.338057i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.8726 | − | 58.6691i | −1.31155 | − | 2.27168i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.8487 | 0.804854 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.68822 | −0.142171 | −0.0710853 | − | 0.997470i | \(-0.522646\pi\) | ||||
−0.0710853 | + | 0.997470i | \(0.522646\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.9857 | − | 22.4919i | −0.499082 | − | 0.864436i | 0.500917 | − | 0.865495i | \(-0.332996\pi\) |
−0.999999 | + | 0.00105961i | \(0.999663\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.6747 | − | 4.64568i | −1.40744 | − | 0.178285i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.0050 | − | 27.7214i | 0.612413 | − | 1.06073i | −0.378419 | − | 0.925634i | \(-0.623532\pi\) |
0.990832 | − | 0.135096i | \(-0.0431344\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.45386 | 0.131965 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.76786 | − | 6.52613i | 0.143544 | − | 0.248626i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.8191 | + | 23.9354i | 0.525705 | + | 0.910547i | 0.999552 | + | 0.0299401i | \(0.00953166\pi\) |
−0.473847 | + | 0.880607i | \(0.657135\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.85792 | − | 13.6103i | −0.298068 | − | 0.516268i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.5876 | + | 37.3909i | −0.817690 | + | 1.41628i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.7157 | 1.27342 | 0.636712 | − | 0.771102i | \(-0.280294\pi\) | ||||
0.636712 | + | 0.771102i | \(0.280294\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.101149 | + | 0.175195i | −0.00381491 | + | 0.00660761i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.8553 | + | 20.8740i | −0.596301 | + | 0.785047i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.26863 | + | 3.92937i | 0.0852000 | + | 0.147571i | 0.905476 | − | 0.424397i | \(-0.139514\pi\) |
−0.820276 | + | 0.571967i | \(0.806180\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −79.4557 | −2.97564 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.08373 | −0.115325 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.18661 | + | 15.9117i | 0.342603 | + | 0.593405i | 0.984915 | − | 0.173038i | \(-0.0553582\pi\) |
−0.642313 | + | 0.766443i | \(0.722025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.8391 | − | 35.3344i | −0.552639 | − | 1.31592i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.58527 | + | 7.94192i | −0.170293 | + | 0.294956i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.7650 | 0.658866 | 0.329433 | − | 0.944179i | \(-0.393142\pi\) | ||||
0.329433 | + | 0.944179i | \(0.393142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.8670 | + | 24.0183i | −0.512888 | + | 0.888348i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.11096 | + | 10.5845i | 0.225713 | + | 0.390947i | 0.956533 | − | 0.291623i | \(-0.0941954\pi\) |
−0.730820 | + | 0.682570i | \(0.760862\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.4692 | + | 33.7217i | 0.717159 | + | 1.24216i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.02182 | − | 10.4301i | 0.221516 | − | 0.383677i | −0.733752 | − | 0.679417i | \(-0.762233\pi\) |
0.955269 | + | 0.295740i | \(0.0955661\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.7408 | −1.71475 | −0.857376 | − | 0.514690i | \(-0.827907\pi\) | ||||
−0.857376 | + | 0.514690i | \(0.827907\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.4362 | − | 19.8080i | 0.418988 | − | 0.725709i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.52657 | + | 6.01616i | 0.0923188 | + | 0.219826i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.4924 | + | 18.1734i | 0.382874 | + | 0.663157i | 0.991472 | − | 0.130322i | \(-0.0416010\pi\) |
−0.608598 | + | 0.793479i | \(0.708268\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.8020 | 0.611489 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.3254 | −1.35661 | −0.678307 | − | 0.734778i | \(-0.737286\pi\) | ||||
−0.678307 | + | 0.734778i | \(0.737286\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.1880 | − | 36.6987i | −0.768065 | − | 1.33033i | −0.938611 | − | 0.344977i | \(-0.887887\pi\) |
0.170546 | − | 0.985350i | \(-0.445447\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.0555 | + | 23.7706i | −0.653655 | + | 0.860554i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.90882 | − | 3.30617i | 0.0689235 | − | 0.119379i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.14491 | −0.257652 | −0.128826 | − | 0.991667i | \(-0.541121\pi\) | ||||
−0.128826 | + | 0.991667i | \(0.541121\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.60566 | + | 7.97724i | −0.165654 | + | 0.286921i | −0.936887 | − | 0.349631i | \(-0.886307\pi\) |
0.771233 | + | 0.636553i | \(0.219640\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.37788 | + | 9.31476i | 0.193179 | + | 0.334596i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.9995 | + | 34.6402i | 0.716557 | + | 1.24111i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.6294 | − | 18.4107i | 0.380350 | − | 0.658786i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.06295 | −0.145013 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.5089 | − | 33.7904i | 0.695418 | − | 1.20450i | −0.274622 | − | 0.961552i | \(-0.588553\pi\) |
0.970040 | − | 0.242947i | \(-0.0781140\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.3083 | + | 2.82585i | 0.793190 | + | 0.100476i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00763 | + | 6.94141i | 0.142315 | + | 0.246497i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.4359 | −0.546769 | −0.273384 | − | 0.961905i | \(-0.588143\pi\) | ||||
−0.273384 | + | 0.961905i | \(0.588143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.31998 | 0.117452 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.0954 | + | 24.4140i | 0.497417 | + | 0.861551i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.8221 | − | 15.5641i | 0.416673 | − | 0.548562i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.6194 | + | 35.7139i | −0.724940 | + | 1.25563i | 0.234059 | + | 0.972222i | \(0.424799\pi\) |
−0.958999 | + | 0.283410i | \(0.908534\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.1064 | 1.05718 | 0.528590 | − | 0.848877i | \(-0.322721\pi\) | ||||
0.528590 | + | 0.848877i | \(0.322721\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.32857 | + | 9.22935i | −0.186651 | + | 0.323290i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.8468 | + | 22.2513i | 0.449453 | + | 0.778476i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.8978 | − | 34.4640i | −0.694437 | − | 1.20280i | −0.970370 | − | 0.241623i | \(-0.922320\pi\) |
0.275933 | − | 0.961177i | \(-0.411013\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.61410 | − | 6.25981i | 0.125980 | − | 0.218203i | −0.796136 | − | 0.605118i | \(-0.793126\pi\) |
0.922116 | + | 0.386915i | \(0.126459\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.0639 | 1.21929 | 0.609645 | − | 0.792675i | \(-0.291312\pi\) | ||||
0.609645 | + | 0.792675i | \(0.291312\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.88889 | − | 11.9319i | 0.239261 | − | 0.414412i | −0.721241 | − | 0.692684i | \(-0.756428\pi\) |
0.960502 | + | 0.278272i | \(0.0897615\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.8893 | + | 22.3225i | −0.758420 | + | 0.773427i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.69363 | − | 8.12961i | −0.162430 | − | 0.281337i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.7017 | 1.05994 | 0.529970 | − | 0.848016i | \(-0.322203\pi\) | ||||
0.529970 | + | 0.848016i | \(0.322203\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55.0988 | 1.89996 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.90723 | + | 10.2316i | 0.203215 | + | 0.351979i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.05166 | − | 7.26648i | −0.104856 | − | 0.249679i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.180586 | − | 0.312785i | 0.00619042 | − | 0.0107221i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.4895 | 0.461873 | 0.230937 | − | 0.972969i | \(-0.425821\pi\) | ||||
0.230937 | + | 0.972969i | \(0.425821\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.5086 | − | 40.7180i | 0.803037 | − | 1.39090i | −0.114571 | − | 0.993415i | \(-0.536549\pi\) |
0.917608 | − | 0.397486i | \(-0.130117\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.94631 | + | 3.37111i | 0.0664074 | + | 0.115021i | 0.897317 | − | 0.441386i | \(-0.145513\pi\) |
−0.830910 | + | 0.556407i | \(0.812180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.3113 | + | 24.7880i | 0.487163 | + | 0.843792i | 0.999891 | − | 0.0147595i | \(-0.00469826\pi\) |
−0.512728 | + | 0.858551i | \(0.671365\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.71005 | + | 15.0862i | −0.296150 | + | 0.512948i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 49.4497 | 1.67747 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.48493 | + | 12.9643i | −0.253617 | + | 0.439278i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.62478 | − | 0.332488i | −0.0887336 | − | 0.0112401i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.9392 | + | 46.6601i | 0.909673 | + | 1.57560i | 0.814519 | + | 0.580137i | \(0.197001\pi\) |
0.0951545 | + | 0.995463i | \(0.469665\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.97237 | 0.167523 | 0.0837616 | − | 0.996486i | \(-0.473307\pi\) | ||||
0.0837616 | + | 0.996486i | \(0.473307\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.8864 | −0.635577 | −0.317789 | − | 0.948162i | \(-0.602940\pi\) | ||||
−0.317789 | + | 0.948162i | \(0.602940\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.3735 | + | 28.3597i | 0.549767 | + | 0.952225i | 0.998290 | + | 0.0584533i | \(0.0186169\pi\) |
−0.448523 | + | 0.893771i | \(0.648050\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.2317 | − | 2.94283i | −0.779167 | − | 0.0986992i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.53787 | − | 2.66367i | 0.0514629 | − | 0.0891363i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.24059 | 0.0748948 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 49.3181 | − | 85.4214i | 1.64485 | − | 2.84896i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.4555 | − | 26.7698i | −0.514898 | − | 0.891830i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.3216 | − | 19.6096i | −0.376342 | − | 0.651844i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.5818 | + | 25.2563i | −0.484179 | + | 0.838623i | −0.999835 | − | 0.0181731i | \(-0.994215\pi\) |
0.515656 | + | 0.856796i | \(0.327548\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.1370 | −0.435249 | −0.217624 | − | 0.976033i | \(-0.569831\pi\) | ||||
−0.217624 | + | 0.976033i | \(0.569831\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.7463 | − | 30.7374i | 0.587315 | − | 1.01726i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.49332 | + | 15.4616i | 0.214428 | + | 0.510588i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00939 | + | 6.94446i | 0.132257 | + | 0.229077i | 0.924546 | − | 0.381069i | \(-0.124444\pi\) |
−0.792289 | + | 0.610146i | \(0.791111\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.17293 | 0.269015 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0488912 | −0.00160753 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.9186 | + | 18.9117i | 0.358229 | + | 0.620471i | 0.987665 | − | 0.156581i | \(-0.0500473\pi\) |
−0.629436 | + | 0.777052i | \(0.716714\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.77014 | + | 27.9023i | 0.254656 | + | 0.914461i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.32462 | + | 10.9546i | −0.206837 | + | 0.358253i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.2895 | 1.31620 | 0.658100 | − | 0.752930i | \(-0.271360\pi\) | ||||
0.658100 | + | 0.752930i | \(0.271360\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.29400 | − | 14.3656i | 0.270377 | − | 0.468306i | −0.698582 | − | 0.715530i | \(-0.746185\pi\) |
0.968958 | + | 0.247224i | \(0.0795184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.7061 | − | 61.8448i | −1.16275 | − | 2.01395i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.8050 | − | 29.1071i | −0.546089 | − | 0.945854i | −0.998537 | − | 0.0540637i | \(-0.982783\pi\) |
0.452448 | − | 0.891791i | \(-0.350551\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.41897 | + | 9.38593i | −0.175907 | + | 0.304680i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.344657 | 0.0111645 | 0.00558227 | − | 0.999984i | \(-0.498223\pi\) | ||||
0.00558227 | + | 0.999984i | \(0.498223\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.71583 | − | 15.0963i | 0.282038 | − | 0.488504i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.52732 | − | 7.27686i | 0.178486 | − | 0.234982i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −42.3432 | − | 73.3406i | −1.36591 | − | 2.36583i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.98594 | 0.257077 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.1298 | 0.711645 | 0.355823 | − | 0.934554i | \(-0.384201\pi\) | ||||
0.355823 | + | 0.934554i | \(0.384201\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.9215 | + | 20.6486i | 0.382579 | + | 0.662646i | 0.991430 | − | 0.130638i | \(-0.0417027\pi\) |
−0.608851 | + | 0.793284i | \(0.708369\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −41.2505 | − | 5.22532i | −1.32243 | − | 0.167516i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.3485 | + | 49.1011i | −0.906950 | + | 1.57088i | −0.0886720 | + | 0.996061i | \(0.528262\pi\) |
−0.818278 | + | 0.574823i | \(0.805071\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.56595 | 0.241809 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.81978 | + | 10.0802i | −0.185622 | + | 0.321507i | −0.943786 | − | 0.330557i | \(-0.892763\pi\) |
0.758164 | + | 0.652064i | \(0.226097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.2229 | − | 19.4386i | −0.357590 | − | 0.619364i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.9361 | − | 39.7264i | −0.729324 | − | 1.26323i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.3065 | + | 47.2962i | −0.867419 | + | 1.50241i | −0.00279476 | + | 0.999996i | \(0.500890\pi\) |
−0.864625 | + | 0.502418i | \(0.832444\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.79484 | −0.310517 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.727355 | + | 1.25981i | −0.0230355 | + | 0.0398987i | −0.877313 | − | 0.479918i | \(-0.840666\pi\) |
0.854278 | + | 0.519817i | \(0.174000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2520.2.bi.r.361.1 | ✓ | 10 | |
3.2 | odd | 2 | 2520.2.bi.s.361.1 | yes | 10 | ||
7.2 | even | 3 | inner | 2520.2.bi.r.1801.1 | yes | 10 | |
21.2 | odd | 6 | 2520.2.bi.s.1801.1 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2520.2.bi.r.361.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
2520.2.bi.r.1801.1 | yes | 10 | 7.2 | even | 3 | inner | |
2520.2.bi.s.361.1 | yes | 10 | 3.2 | odd | 2 | ||
2520.2.bi.s.1801.1 | yes | 10 | 21.2 | odd | 6 |