Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,3,Mod(97,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.67030659073\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.4 | ||
Root | \(0.765367i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.97 |
Dual form | 98.3.b.a.97.3 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 5.22625i | 1.74208i | 0.491209 | + | 0.871042i | \(0.336555\pi\) | ||||
−0.491209 | + | 0.871042i | \(0.663445\pi\) | |||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − 1.21371i | − 0.242742i | −0.992607 | − | 0.121371i | \(-0.961271\pi\) | ||||
0.992607 | − | 0.121371i | \(-0.0387290\pi\) | |||||||
\(6\) | 7.39104i | 1.23184i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −18.3137 | −2.03486 | ||||||||
\(10\) | − 1.71644i | − 0.171644i | ||||||||
\(11\) | 6.34315 | 0.576650 | 0.288325 | − | 0.957533i | \(-0.406902\pi\) | ||||
0.288325 | + | 0.957533i | \(0.406902\pi\) | |||||||
\(12\) | 10.4525i | 0.871042i | ||||||||
\(13\) | 8.15640i | 0.627416i | 0.949520 | + | 0.313708i | \(0.101571\pi\) | ||||
−0.949520 | + | 0.313708i | \(0.898429\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.34315 | 0.422876 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 6.88830i | − 0.405194i | −0.979262 | − | 0.202597i | \(-0.935062\pi\) | ||||
0.979262 | − | 0.202597i | \(-0.0649382\pi\) | |||||||
\(18\) | −25.8995 | −1.43886 | ||||||||
\(19\) | − 30.4608i | − 1.60320i | −0.597860 | − | 0.801601i | \(-0.703982\pi\) | ||||
0.597860 | − | 0.801601i | \(-0.296018\pi\) | |||||||
\(20\) | − 2.42742i | − 0.121371i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.97056 | 0.407753 | ||||||||
\(23\) | 36.9706 | 1.60742 | 0.803708 | − | 0.595024i | \(-0.202857\pi\) | ||||
0.803708 | + | 0.595024i | \(0.202857\pi\) | |||||||
\(24\) | 14.7821i | 0.615920i | ||||||||
\(25\) | 23.5269 | 0.941076 | ||||||||
\(26\) | 11.5349i | 0.443650i | ||||||||
\(27\) | − 48.6758i | − 1.80281i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −34.3848 | −1.18568 | −0.592841 | − | 0.805320i | \(-0.701994\pi\) | ||||
−0.592841 | + | 0.805320i | \(0.701994\pi\) | |||||||
\(30\) | 8.97056 | 0.299019 | ||||||||
\(31\) | − 17.8435i | − 0.575598i | −0.957691 | − | 0.287799i | \(-0.907076\pi\) | ||||
0.957691 | − | 0.287799i | \(-0.0929235\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 33.1509i | 1.00457i | ||||||||
\(34\) | − 9.74153i | − 0.286516i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −36.6274 | −1.01743 | ||||||||
\(37\) | −36.2426 | −0.979531 | −0.489765 | − | 0.871854i | \(-0.662918\pi\) | ||||
−0.489765 | + | 0.871854i | \(0.662918\pi\) | |||||||
\(38\) | − 43.0781i | − 1.13363i | ||||||||
\(39\) | −42.6274 | −1.09301 | ||||||||
\(40\) | − 3.43289i | − 0.0858221i | ||||||||
\(41\) | 14.0936i | 0.343747i | 0.985119 | + | 0.171874i | \(0.0549820\pi\) | ||||
−0.985119 | + | 0.171874i | \(0.945018\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −32.6863 | −0.760146 | −0.380073 | − | 0.924956i | \(-0.624101\pi\) | ||||
−0.380073 | + | 0.924956i | \(0.624101\pi\) | |||||||
\(44\) | 12.6863 | 0.288325 | ||||||||
\(45\) | 22.2275i | 0.493944i | ||||||||
\(46\) | 52.2843 | 1.13661 | ||||||||
\(47\) | 36.4299i | 0.775105i | 0.921848 | + | 0.387552i | \(0.126679\pi\) | ||||
−0.921848 | + | 0.387552i | \(0.873321\pi\) | |||||||
\(48\) | 20.9050i | 0.435521i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 33.2721 | 0.665442 | ||||||||
\(51\) | 36.0000 | 0.705882 | ||||||||
\(52\) | 16.3128i | 0.313708i | ||||||||
\(53\) | −46.6274 | −0.879763 | −0.439881 | − | 0.898056i | \(-0.644979\pi\) | ||||
−0.439881 | + | 0.898056i | \(0.644979\pi\) | |||||||
\(54\) | − 68.8380i | − 1.27478i | ||||||||
\(55\) | − 7.69873i | − 0.139977i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 159.196 | 2.79291 | ||||||||
\(58\) | −48.6274 | −0.838404 | ||||||||
\(59\) | 1.94721i | 0.0330036i | 0.999864 | + | 0.0165018i | \(0.00525293\pi\) | ||||
−0.999864 | + | 0.0165018i | \(0.994747\pi\) | |||||||
\(60\) | 12.6863 | 0.211438 | ||||||||
\(61\) | − 78.4800i | − 1.28656i | −0.765632 | − | 0.643279i | \(-0.777574\pi\) | ||||
0.765632 | − | 0.643279i | \(-0.222426\pi\) | |||||||
\(62\) | − 25.2346i | − 0.407009i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 9.89949 | 0.152300 | ||||||||
\(66\) | 46.8824i | 0.710340i | ||||||||
\(67\) | 30.0589 | 0.448640 | 0.224320 | − | 0.974516i | \(-0.427984\pi\) | ||||
0.224320 | + | 0.974516i | \(0.427984\pi\) | |||||||
\(68\) | − 13.7766i | − 0.202597i | ||||||||
\(69\) | 193.217i | 2.80025i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −48.5685 | −0.684064 | −0.342032 | − | 0.939688i | \(-0.611115\pi\) | ||||
−0.342032 | + | 0.939688i | \(0.611115\pi\) | |||||||
\(72\) | −51.7990 | −0.719430 | ||||||||
\(73\) | 70.5769i | 0.966807i | 0.875398 | + | 0.483404i | \(0.160600\pi\) | ||||
−0.875398 | + | 0.483404i | \(0.839400\pi\) | |||||||
\(74\) | −51.2548 | −0.692633 | ||||||||
\(75\) | 122.958i | 1.63943i | ||||||||
\(76\) | − 60.9217i | − 0.801601i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −60.2843 | −0.772875 | ||||||||
\(79\) | −76.2843 | −0.965624 | −0.482812 | − | 0.875724i | \(-0.660384\pi\) | ||||
−0.482812 | + | 0.875724i | \(0.660384\pi\) | |||||||
\(80\) | − 4.85483i | − 0.0606854i | ||||||||
\(81\) | 89.5685 | 1.10578 | ||||||||
\(82\) | 19.9314i | 0.243066i | ||||||||
\(83\) | 30.9861i | 0.373326i | 0.982424 | + | 0.186663i | \(0.0597673\pi\) | ||||
−0.982424 | + | 0.186663i | \(0.940233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.36039 | −0.0983575 | ||||||||
\(86\) | −46.2254 | −0.537505 | ||||||||
\(87\) | − 179.704i | − 2.06556i | ||||||||
\(88\) | 17.9411 | 0.203876 | ||||||||
\(89\) | 66.0166i | 0.741759i | 0.928681 | + | 0.370880i | \(0.120944\pi\) | ||||
−0.928681 | + | 0.370880i | \(0.879056\pi\) | |||||||
\(90\) | 31.4344i | 0.349271i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 73.9411 | 0.803708 | ||||||||
\(93\) | 93.2548 | 1.00274 | ||||||||
\(94\) | 51.5197i | 0.548082i | ||||||||
\(95\) | −36.9706 | −0.389164 | ||||||||
\(96\) | 29.5641i | 0.307960i | ||||||||
\(97\) | − 155.791i | − 1.60610i | −0.595914 | − | 0.803049i | \(-0.703210\pi\) | ||||
0.595914 | − | 0.803049i | \(-0.296790\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −116.167 | −1.17340 | ||||||||
\(100\) | 47.0538 | 0.470538 | ||||||||
\(101\) | 187.027i | 1.85175i | 0.377828 | + | 0.925876i | \(0.376671\pi\) | ||||
−0.377828 | + | 0.925876i | \(0.623329\pi\) | |||||||
\(102\) | 50.9117 | 0.499134 | ||||||||
\(103\) | − 141.173i | − 1.37061i | −0.728258 | − | 0.685304i | \(-0.759670\pi\) | ||||
0.728258 | − | 0.685304i | \(-0.240330\pi\) | |||||||
\(104\) | 23.0698i | 0.221825i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −65.9411 | −0.622086 | ||||||||
\(107\) | 67.4802 | 0.630656 | 0.315328 | − | 0.948983i | \(-0.397885\pi\) | ||||
0.315328 | + | 0.948983i | \(0.397885\pi\) | |||||||
\(108\) | − 97.3516i | − 0.901403i | ||||||||
\(109\) | −93.6152 | −0.858855 | −0.429428 | − | 0.903101i | \(-0.641285\pi\) | ||||
−0.429428 | + | 0.903101i | \(0.641285\pi\) | |||||||
\(110\) | − 10.8876i | − 0.0989786i | ||||||||
\(111\) | − 189.413i | − 1.70642i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 65.9411 | 0.583550 | 0.291775 | − | 0.956487i | \(-0.405754\pi\) | ||||
0.291775 | + | 0.956487i | \(0.405754\pi\) | |||||||
\(114\) | 225.137 | 1.97489 | ||||||||
\(115\) | − 44.8715i | − 0.390187i | ||||||||
\(116\) | −68.7696 | −0.592841 | ||||||||
\(117\) | − 149.374i | − 1.27670i | ||||||||
\(118\) | 2.75377i | 0.0233371i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 17.9411 | 0.149509 | ||||||||
\(121\) | −80.7645 | −0.667475 | ||||||||
\(122\) | − 110.988i | − 0.909734i | ||||||||
\(123\) | −73.6569 | −0.598836 | ||||||||
\(124\) | − 35.6871i | − 0.287799i | ||||||||
\(125\) | − 58.8975i | − 0.471180i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 33.6569 | 0.265015 | 0.132507 | − | 0.991182i | \(-0.457697\pi\) | ||||
0.132507 | + | 0.991182i | \(0.457697\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | − 170.827i | − 1.32424i | ||||||||
\(130\) | 14.0000 | 0.107692 | ||||||||
\(131\) | 119.153i | 0.909567i | 0.890602 | + | 0.454783i | \(0.150283\pi\) | ||||
−0.890602 | + | 0.454783i | \(0.849717\pi\) | |||||||
\(132\) | 66.3018i | 0.502286i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 42.5097 | 0.317236 | ||||||||
\(135\) | −59.0782 | −0.437616 | ||||||||
\(136\) | − 19.4831i | − 0.143258i | ||||||||
\(137\) | 107.924 | 0.787766 | 0.393883 | − | 0.919161i | \(-0.371132\pi\) | ||||
0.393883 | + | 0.919161i | \(0.371132\pi\) | |||||||
\(138\) | 273.251i | 1.98008i | ||||||||
\(139\) | − 45.4605i | − 0.327054i | −0.986539 | − | 0.163527i | \(-0.947713\pi\) | ||||
0.986539 | − | 0.163527i | \(-0.0522870\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −190.392 | −1.35030 | ||||||||
\(142\) | −68.6863 | −0.483706 | ||||||||
\(143\) | 51.7373i | 0.361799i | ||||||||
\(144\) | −73.2548 | −0.508714 | ||||||||
\(145\) | 41.7331i | 0.287814i | ||||||||
\(146\) | 99.8109i | 0.683636i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −72.4853 | −0.489765 | ||||||||
\(149\) | −184.000 | −1.23490 | −0.617450 | − | 0.786610i | \(-0.711834\pi\) | ||||
−0.617450 | + | 0.786610i | \(0.711834\pi\) | |||||||
\(150\) | 173.888i | 1.15926i | ||||||||
\(151\) | 159.716 | 1.05772 | 0.528860 | − | 0.848709i | \(-0.322620\pi\) | ||||
0.528860 | + | 0.848709i | \(0.322620\pi\) | |||||||
\(152\) | − 86.1562i | − 0.566817i | ||||||||
\(153\) | 126.150i | 0.824512i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.6569 | −0.139722 | ||||||||
\(156\) | −85.2548 | −0.546505 | ||||||||
\(157\) | − 168.998i | − 1.07642i | −0.842811 | − | 0.538209i | \(-0.819101\pi\) | ||||
0.842811 | − | 0.538209i | \(-0.180899\pi\) | |||||||
\(158\) | −107.882 | −0.682799 | ||||||||
\(159\) | − 243.687i | − 1.53262i | ||||||||
\(160\) | − 6.86577i | − 0.0429111i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 126.669 | 0.781908 | ||||||||
\(163\) | 135.078 | 0.828701 | 0.414350 | − | 0.910117i | \(-0.364009\pi\) | ||||
0.414350 | + | 0.910117i | \(0.364009\pi\) | |||||||
\(164\) | 28.1873i | 0.171874i | ||||||||
\(165\) | 40.2355 | 0.243852 | ||||||||
\(166\) | 43.8210i | 0.263982i | ||||||||
\(167\) | 238.614i | 1.42883i | 0.699723 | + | 0.714414i | \(0.253307\pi\) | ||||
−0.699723 | + | 0.714414i | \(0.746693\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 102.473 | 0.606350 | ||||||||
\(170\) | −11.8234 | −0.0695493 | ||||||||
\(171\) | 557.851i | 3.26228i | ||||||||
\(172\) | −65.3726 | −0.380073 | ||||||||
\(173\) | 58.2409i | 0.336653i | 0.985731 | + | 0.168326i | \(0.0538363\pi\) | ||||
−0.985731 | + | 0.168326i | \(0.946164\pi\) | |||||||
\(174\) | − 254.139i | − 1.46057i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 25.3726 | 0.144162 | ||||||||
\(177\) | −10.1766 | −0.0574950 | ||||||||
\(178\) | 93.3616i | 0.524503i | ||||||||
\(179\) | 321.872 | 1.79817 | 0.899084 | − | 0.437776i | \(-0.144234\pi\) | ||||
0.899084 | + | 0.437776i | \(0.144234\pi\) | |||||||
\(180\) | 44.4550i | 0.246972i | ||||||||
\(181\) | 113.891i | 0.629234i | 0.949219 | + | 0.314617i | \(0.101876\pi\) | ||||
−0.949219 | + | 0.314617i | \(0.898124\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 410.156 | 2.24129 | ||||||||
\(184\) | 104.569 | 0.568307 | ||||||||
\(185\) | 43.9880i | 0.237773i | ||||||||
\(186\) | 131.882 | 0.709044 | ||||||||
\(187\) | − 43.6935i | − 0.233655i | ||||||||
\(188\) | 72.8598i | 0.387552i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −52.2843 | −0.275180 | ||||||||
\(191\) | 89.2061 | 0.467047 | 0.233524 | − | 0.972351i | \(-0.424974\pi\) | ||||
0.233524 | + | 0.972351i | \(0.424974\pi\) | |||||||
\(192\) | 41.8100i | 0.217760i | ||||||||
\(193\) | −140.451 | −0.727724 | −0.363862 | − | 0.931453i | \(-0.618542\pi\) | ||||
−0.363862 | + | 0.931453i | \(0.618542\pi\) | |||||||
\(194\) | − 220.322i | − 1.13568i | ||||||||
\(195\) | 51.7373i | 0.265319i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −140.510 | −0.713247 | −0.356624 | − | 0.934248i | \(-0.616072\pi\) | ||||
−0.356624 | + | 0.934248i | \(0.616072\pi\) | |||||||
\(198\) | −164.284 | −0.829719 | ||||||||
\(199\) | − 222.872i | − 1.11996i | −0.828507 | − | 0.559979i | \(-0.810809\pi\) | ||||
0.828507 | − | 0.559979i | \(-0.189191\pi\) | |||||||
\(200\) | 66.5442 | 0.332721 | ||||||||
\(201\) | 157.095i | 0.781568i | ||||||||
\(202\) | 264.496i | 1.30939i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 72.0000 | 0.352941 | ||||||||
\(205\) | 17.1056 | 0.0834417 | ||||||||
\(206\) | − 199.648i | − 0.969166i | ||||||||
\(207\) | −677.068 | −3.27086 | ||||||||
\(208\) | 32.6256i | 0.156854i | ||||||||
\(209\) | − 193.217i | − 0.924486i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.2843 | 0.0961340 | 0.0480670 | − | 0.998844i | \(-0.484694\pi\) | ||||
0.0480670 | + | 0.998844i | \(0.484694\pi\) | |||||||
\(212\) | −93.2548 | −0.439881 | ||||||||
\(213\) | − 253.831i | − 1.19170i | ||||||||
\(214\) | 95.4315 | 0.445941 | ||||||||
\(215\) | 39.6716i | 0.184519i | ||||||||
\(216\) | − 137.676i | − 0.637388i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −132.392 | −0.607302 | ||||||||
\(219\) | −368.853 | −1.68426 | ||||||||
\(220\) | − 15.3975i | − 0.0699884i | ||||||||
\(221\) | 56.1838 | 0.254225 | ||||||||
\(222\) | − 267.871i | − 1.20662i | ||||||||
\(223\) | 140.737i | 0.631109i | 0.948907 | + | 0.315555i | \(0.102191\pi\) | ||||
−0.948907 | + | 0.315555i | \(0.897809\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −430.865 | −1.91496 | ||||||||
\(226\) | 93.2548 | 0.412632 | ||||||||
\(227\) | − 10.2085i | − 0.0449715i | −0.999747 | − | 0.0224858i | \(-0.992842\pi\) | ||||
0.999747 | − | 0.0224858i | \(-0.00715804\pi\) | |||||||
\(228\) | 318.392 | 1.39646 | ||||||||
\(229\) | 431.995i | 1.88644i | 0.332168 | + | 0.943220i | \(0.392220\pi\) | ||||
−0.332168 | + | 0.943220i | \(0.607780\pi\) | |||||||
\(230\) | − 63.4579i | − 0.275904i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −97.2548 | −0.419202 | ||||||||
\(233\) | 144.610 | 0.620645 | 0.310322 | − | 0.950631i | \(-0.399563\pi\) | ||||
0.310322 | + | 0.950631i | \(0.399563\pi\) | |||||||
\(234\) | − 211.247i | − 0.902764i | ||||||||
\(235\) | 44.2153 | 0.188150 | ||||||||
\(236\) | 3.89443i | 0.0165018i | ||||||||
\(237\) | − 398.681i | − 1.68220i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 213.470 | 0.893180 | 0.446590 | − | 0.894739i | \(-0.352638\pi\) | ||||
0.446590 | + | 0.894739i | \(0.352638\pi\) | |||||||
\(240\) | 25.3726 | 0.105719 | ||||||||
\(241\) | 65.4012i | 0.271374i | 0.990752 | + | 0.135687i | \(0.0433242\pi\) | ||||
−0.990752 | + | 0.135687i | \(0.956676\pi\) | |||||||
\(242\) | −114.218 | −0.471976 | ||||||||
\(243\) | 30.0257i | 0.123562i | ||||||||
\(244\) | − 156.960i | − 0.643279i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −104.167 | −0.423441 | ||||||||
\(247\) | 248.451 | 1.00587 | ||||||||
\(248\) | − 50.4692i | − 0.203505i | ||||||||
\(249\) | −161.941 | −0.650366 | ||||||||
\(250\) | − 83.2937i | − 0.333175i | ||||||||
\(251\) | − 74.8070i | − 0.298036i | −0.988834 | − | 0.149018i | \(-0.952389\pi\) | ||||
0.988834 | − | 0.149018i | \(-0.0476112\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 234.510 | 0.926916 | ||||||||
\(254\) | 47.5980 | 0.187394 | ||||||||
\(255\) | − 43.6935i | − 0.171347i | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 429.222i | − 1.67013i | −0.550154 | − | 0.835063i | \(-0.685431\pi\) | ||||
0.550154 | − | 0.835063i | \(-0.314569\pi\) | |||||||
\(258\) | − 241.586i | − 0.936378i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 19.7990 | 0.0761500 | ||||||||
\(261\) | 629.713 | 2.41269 | ||||||||
\(262\) | 168.508i | 0.643161i | ||||||||
\(263\) | 113.539 | 0.431708 | 0.215854 | − | 0.976426i | \(-0.430747\pi\) | ||||
0.215854 | + | 0.976426i | \(0.430747\pi\) | |||||||
\(264\) | 93.7648i | 0.355170i | ||||||||
\(265\) | 56.5921i | 0.213555i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −345.019 | −1.29221 | ||||||||
\(268\) | 60.1177 | 0.224320 | ||||||||
\(269\) | 11.2629i | 0.0418696i | 0.999781 | + | 0.0209348i | \(0.00666425\pi\) | ||||
−0.999781 | + | 0.0209348i | \(0.993336\pi\) | |||||||
\(270\) | −83.5492 | −0.309442 | ||||||||
\(271\) | 283.358i | 1.04560i | 0.852455 | + | 0.522801i | \(0.175113\pi\) | ||||
−0.852455 | + | 0.522801i | \(0.824887\pi\) | |||||||
\(272\) | − 27.5532i | − 0.101299i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 152.627 | 0.557034 | ||||||||
\(275\) | 149.235 | 0.542671 | ||||||||
\(276\) | 386.435i | 1.40013i | ||||||||
\(277\) | −217.765 | −0.786153 | −0.393077 | − | 0.919506i | \(-0.628589\pi\) | ||||
−0.393077 | + | 0.919506i | \(0.628589\pi\) | |||||||
\(278\) | − 64.2908i | − 0.231262i | ||||||||
\(279\) | 326.781i | 1.17126i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −317.782 | −1.13090 | −0.565448 | − | 0.824784i | \(-0.691297\pi\) | ||||
−0.565448 | + | 0.824784i | \(0.691297\pi\) | |||||||
\(282\) | −269.255 | −0.954804 | ||||||||
\(283\) | 240.164i | 0.848635i | 0.905514 | + | 0.424317i | \(0.139486\pi\) | ||||
−0.905514 | + | 0.424317i | \(0.860514\pi\) | |||||||
\(284\) | −97.1371 | −0.342032 | ||||||||
\(285\) | − 193.217i | − 0.677956i | ||||||||
\(286\) | 73.1675i | 0.255831i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −103.598 | −0.359715 | ||||||||
\(289\) | 241.551 | 0.835818 | ||||||||
\(290\) | 59.0195i | 0.203516i | ||||||||
\(291\) | 814.205 | 2.79796 | ||||||||
\(292\) | 141.154i | 0.483404i | ||||||||
\(293\) | − 437.887i | − 1.49450i | −0.664546 | − | 0.747248i | \(-0.731375\pi\) | ||||
0.664546 | − | 0.747248i | \(-0.268625\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.36335 | 0.00801135 | ||||||||
\(296\) | −102.510 | −0.346316 | ||||||||
\(297\) | − 308.758i | − 1.03959i | ||||||||
\(298\) | −260.215 | −0.873206 | ||||||||
\(299\) | 301.547i | 1.00852i | ||||||||
\(300\) | 245.915i | 0.819717i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 225.872 | 0.747921 | ||||||||
\(303\) | −977.450 | −3.22591 | ||||||||
\(304\) | − 121.843i | − 0.400800i | ||||||||
\(305\) | −95.2519 | −0.312301 | ||||||||
\(306\) | 178.404i | 0.583018i | ||||||||
\(307\) | 476.947i | 1.55357i | 0.629764 | + | 0.776787i | \(0.283152\pi\) | ||||
−0.629764 | + | 0.776787i | \(0.716848\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 737.803 | 2.38771 | ||||||||
\(310\) | −30.6274 | −0.0987981 | ||||||||
\(311\) | − 330.586i | − 1.06298i | −0.847066 | − | 0.531488i | \(-0.821633\pi\) | ||||
0.847066 | − | 0.531488i | \(-0.178367\pi\) | |||||||
\(312\) | −120.569 | −0.386438 | ||||||||
\(313\) | − 162.421i | − 0.518917i | −0.965754 | − | 0.259458i | \(-0.916456\pi\) | ||||
0.965754 | − | 0.259458i | \(-0.0835440\pi\) | |||||||
\(314\) | − 238.999i | − 0.761143i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −152.569 | −0.482812 | ||||||||
\(317\) | −434.548 | −1.37081 | −0.685407 | − | 0.728160i | \(-0.740376\pi\) | ||||
−0.685407 | + | 0.728160i | \(0.740376\pi\) | |||||||
\(318\) | − 344.625i | − 1.08373i | ||||||||
\(319\) | −218.108 | −0.683723 | ||||||||
\(320\) | − 9.70967i | − 0.0303427i | ||||||||
\(321\) | 352.669i | 1.09866i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −209.823 | −0.649608 | ||||||||
\(324\) | 179.137 | 0.552892 | ||||||||
\(325\) | 191.895i | 0.590446i | ||||||||
\(326\) | 191.029 | 0.585980 | ||||||||
\(327\) | − 489.257i | − 1.49620i | ||||||||
\(328\) | 39.8628i | 0.121533i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 56.9016 | 0.172429 | ||||||||
\(331\) | −460.666 | −1.39174 | −0.695870 | − | 0.718168i | \(-0.744981\pi\) | ||||
−0.695870 | + | 0.718168i | \(0.744981\pi\) | |||||||
\(332\) | 61.9722i | 0.186663i | ||||||||
\(333\) | 663.737 | 1.99320 | ||||||||
\(334\) | 337.451i | 1.01033i | ||||||||
\(335\) | − 36.4827i | − 0.108904i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −61.8650 | −0.183576 | −0.0917878 | − | 0.995779i | \(-0.529258\pi\) | ||||
−0.0917878 | + | 0.995779i | \(0.529258\pi\) | |||||||
\(338\) | 144.919 | 0.428754 | ||||||||
\(339\) | 344.625i | 1.01659i | ||||||||
\(340\) | −16.7208 | −0.0491788 | ||||||||
\(341\) | − 113.184i | − 0.331918i | ||||||||
\(342\) | 788.920i | 2.30678i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −92.4508 | −0.268752 | ||||||||
\(345\) | 234.510 | 0.679738 | ||||||||
\(346\) | 82.3651i | 0.238049i | ||||||||
\(347\) | −536.950 | −1.54741 | −0.773704 | − | 0.633548i | \(-0.781598\pi\) | ||||
−0.773704 | + | 0.633548i | \(0.781598\pi\) | |||||||
\(348\) | − 359.407i | − 1.03278i | ||||||||
\(349\) | − 86.8633i | − 0.248892i | −0.992226 | − | 0.124446i | \(-0.960285\pi\) | ||||
0.992226 | − | 0.124446i | \(-0.0397154\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 397.019 | 1.13111 | ||||||||
\(352\) | 35.8823 | 0.101938 | ||||||||
\(353\) | 575.197i | 1.62945i | 0.579845 | + | 0.814727i | \(0.303113\pi\) | ||||
−0.579845 | + | 0.814727i | \(0.696887\pi\) | |||||||
\(354\) | −14.3919 | −0.0406551 | ||||||||
\(355\) | 58.9480i | 0.166051i | ||||||||
\(356\) | 132.033i | 0.370880i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 455.196 | 1.27150 | ||||||||
\(359\) | −50.0589 | −0.139440 | −0.0697199 | − | 0.997567i | \(-0.522211\pi\) | ||||
−0.0697199 | + | 0.997567i | \(0.522211\pi\) | |||||||
\(360\) | 62.8689i | 0.174636i | ||||||||
\(361\) | −566.862 | −1.57025 | ||||||||
\(362\) | 161.067i | 0.444935i | ||||||||
\(363\) | − 422.096i | − 1.16280i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 85.6598 | 0.234684 | ||||||||
\(366\) | 580.049 | 1.58483 | ||||||||
\(367\) | − 141.788i | − 0.386343i | −0.981165 | − | 0.193172i | \(-0.938123\pi\) | ||||
0.981165 | − | 0.193172i | \(-0.0618774\pi\) | |||||||
\(368\) | 147.882 | 0.401854 | ||||||||
\(369\) | − 258.107i | − 0.699476i | ||||||||
\(370\) | 62.2084i | 0.168131i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 186.510 | 0.501370 | ||||||||
\(373\) | 62.1564 | 0.166639 | 0.0833196 | − | 0.996523i | \(-0.473448\pi\) | ||||
0.0833196 | + | 0.996523i | \(0.473448\pi\) | |||||||
\(374\) | − 61.7919i | − 0.165219i | ||||||||
\(375\) | 307.813 | 0.820835 | ||||||||
\(376\) | 103.039i | 0.274041i | ||||||||
\(377\) | − 280.456i | − 0.743915i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 103.245 | 0.272414 | 0.136207 | − | 0.990680i | \(-0.456509\pi\) | ||||
0.136207 | + | 0.990680i | \(0.456509\pi\) | |||||||
\(380\) | −73.9411 | −0.194582 | ||||||||
\(381\) | 175.899i | 0.461678i | ||||||||
\(382\) | 126.156 | 0.330252 | ||||||||
\(383\) | − 355.077i | − 0.927095i | −0.886072 | − | 0.463548i | \(-0.846576\pi\) | ||||
0.886072 | − | 0.463548i | \(-0.153424\pi\) | |||||||
\(384\) | 59.1283i | 0.153980i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −198.627 | −0.514579 | ||||||||
\(387\) | 598.607 | 1.54679 | ||||||||
\(388\) | − 311.583i | − 0.803049i | ||||||||
\(389\) | 404.909 | 1.04090 | 0.520448 | − | 0.853893i | \(-0.325765\pi\) | ||||
0.520448 | + | 0.853893i | \(0.325765\pi\) | |||||||
\(390\) | 73.1675i | 0.187609i | ||||||||
\(391\) | − 254.664i | − 0.651316i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −622.725 | −1.58454 | ||||||||
\(394\) | −198.711 | −0.504342 | ||||||||
\(395\) | 92.5869i | 0.234397i | ||||||||
\(396\) | −232.333 | −0.586700 | ||||||||
\(397\) | 540.926i | 1.36254i | 0.732035 | + | 0.681268i | \(0.238571\pi\) | ||||
−0.732035 | + | 0.681268i | \(0.761429\pi\) | |||||||
\(398\) | − 315.188i | − 0.791930i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 94.1076 | 0.235269 | ||||||||
\(401\) | −467.688 | −1.16631 | −0.583153 | − | 0.812363i | \(-0.698181\pi\) | ||||
−0.583153 | + | 0.812363i | \(0.698181\pi\) | |||||||
\(402\) | 222.166i | 0.552652i | ||||||||
\(403\) | 145.539 | 0.361139 | ||||||||
\(404\) | 374.054i | 0.925876i | ||||||||
\(405\) | − 108.710i | − 0.268420i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −229.892 | −0.564846 | ||||||||
\(408\) | 101.823 | 0.249567 | ||||||||
\(409\) | − 96.2280i | − 0.235276i | −0.993057 | − | 0.117638i | \(-0.962468\pi\) | ||||
0.993057 | − | 0.117638i | \(-0.0375323\pi\) | |||||||
\(410\) | 24.1909 | 0.0590022 | ||||||||
\(411\) | 564.037i | 1.37235i | ||||||||
\(412\) | − 282.345i | − 0.685304i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −957.519 | −2.31285 | ||||||||
\(415\) | 37.6081 | 0.0906219 | ||||||||
\(416\) | 46.1396i | 0.110912i | ||||||||
\(417\) | 237.588 | 0.569755 | ||||||||
\(418\) | − 273.251i | − 0.653710i | ||||||||
\(419\) | 433.126i | 1.03371i | 0.856072 | + | 0.516857i | \(0.172898\pi\) | ||||
−0.856072 | + | 0.516857i | \(0.827102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −516.627 | −1.22714 | −0.613572 | − | 0.789639i | \(-0.710268\pi\) | ||||
−0.613572 | + | 0.789639i | \(0.710268\pi\) | |||||||
\(422\) | 28.6863 | 0.0679770 | ||||||||
\(423\) | − 667.167i | − 1.57723i | ||||||||
\(424\) | −131.882 | −0.311043 | ||||||||
\(425\) | − 162.060i | − 0.381319i | ||||||||
\(426\) | − 358.972i | − 0.842657i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 134.960 | 0.315328 | ||||||||
\(429\) | −270.392 | −0.630284 | ||||||||
\(430\) | 56.1042i | 0.130475i | ||||||||
\(431\) | −366.745 | −0.850917 | −0.425458 | − | 0.904978i | \(-0.639887\pi\) | ||||
−0.425458 | + | 0.904978i | \(0.639887\pi\) | |||||||
\(432\) | − 194.703i | − 0.450702i | ||||||||
\(433\) | 449.480i | 1.03806i | 0.854756 | + | 0.519030i | \(0.173707\pi\) | ||||
−0.854756 | + | 0.519030i | \(0.826293\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −218.108 | −0.501397 | ||||||||
\(436\) | −187.230 | −0.429428 | ||||||||
\(437\) | − 1126.15i | − 2.57701i | ||||||||
\(438\) | −521.637 | −1.19095 | ||||||||
\(439\) | − 661.824i | − 1.50757i | −0.657120 | − | 0.753786i | \(-0.728226\pi\) | ||||
0.657120 | − | 0.753786i | \(-0.271774\pi\) | |||||||
\(440\) | − 21.7753i | − 0.0494893i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 79.4558 | 0.179764 | ||||||||
\(443\) | 787.647 | 1.77798 | 0.888992 | − | 0.457923i | \(-0.151406\pi\) | ||||
0.888992 | + | 0.457923i | \(0.151406\pi\) | |||||||
\(444\) | − 378.826i | − 0.853212i | ||||||||
\(445\) | 80.1249 | 0.180056 | ||||||||
\(446\) | 199.033i | 0.446262i | ||||||||
\(447\) | − 961.630i | − 2.15130i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 281.373 | 0.626665 | 0.313332 | − | 0.949643i | \(-0.398555\pi\) | ||||
0.313332 | + | 0.949643i | \(0.398555\pi\) | |||||||
\(450\) | −609.335 | −1.35408 | ||||||||
\(451\) | 89.3979i | 0.198222i | ||||||||
\(452\) | 131.882 | 0.291775 | ||||||||
\(453\) | 834.715i | 1.84264i | ||||||||
\(454\) | − 14.4371i | − 0.0317997i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 450.274 | 0.987443 | ||||||||
\(457\) | 397.117 | 0.868965 | 0.434482 | − | 0.900680i | \(-0.356931\pi\) | ||||
0.434482 | + | 0.900680i | \(0.356931\pi\) | |||||||
\(458\) | 610.933i | 1.33391i | ||||||||
\(459\) | −335.294 | −0.730487 | ||||||||
\(460\) | − 89.7430i | − 0.195093i | ||||||||
\(461\) | 433.589i | 0.940541i | 0.882522 | + | 0.470270i | \(0.155844\pi\) | ||||
−0.882522 | + | 0.470270i | \(0.844156\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −107.813 | −0.232858 | −0.116429 | − | 0.993199i | \(-0.537145\pi\) | ||||
−0.116429 | + | 0.993199i | \(0.537145\pi\) | |||||||
\(464\) | −137.539 | −0.296420 | ||||||||
\(465\) | − 113.184i | − 0.243407i | ||||||||
\(466\) | 204.510 | 0.438862 | ||||||||
\(467\) | 163.372i | 0.349833i | 0.984583 | + | 0.174917i | \(0.0559656\pi\) | ||||
−0.984583 | + | 0.174917i | \(0.944034\pi\) | |||||||
\(468\) | − 298.748i | − 0.638350i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 62.5299 | 0.133042 | ||||||||
\(471\) | 883.225 | 1.87521 | ||||||||
\(472\) | 5.50755i | 0.0116685i | ||||||||
\(473\) | −207.334 | −0.438338 | ||||||||
\(474\) | − 563.820i | − 1.18949i | ||||||||
\(475\) | − 716.649i | − 1.50874i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 853.921 | 1.79019 | ||||||||
\(478\) | 301.892 | 0.631574 | ||||||||
\(479\) | 599.724i | 1.25203i | 0.779809 | + | 0.626017i | \(0.215316\pi\) | ||||
−0.779809 | + | 0.626017i | \(0.784684\pi\) | |||||||
\(480\) | 35.8823 | 0.0747547 | ||||||||
\(481\) | − 295.610i | − 0.614573i | ||||||||
\(482\) | 92.4913i | 0.191891i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −161.529 | −0.333738 | ||||||||
\(485\) | −189.085 | −0.389867 | ||||||||
\(486\) | 42.4627i | 0.0873719i | ||||||||
\(487\) | 453.608 | 0.931433 | 0.465717 | − | 0.884934i | \(-0.345797\pi\) | ||||
0.465717 | + | 0.884934i | \(0.345797\pi\) | |||||||
\(488\) | − 221.975i | − 0.454867i | ||||||||
\(489\) | 705.953i | 1.44367i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 507.578 | 1.03376 | 0.516882 | − | 0.856057i | \(-0.327093\pi\) | ||||
0.516882 | + | 0.856057i | \(0.327093\pi\) | |||||||
\(492\) | −147.314 | −0.299418 | ||||||||
\(493\) | 236.853i | 0.480431i | ||||||||
\(494\) | 351.362 | 0.711260 | ||||||||
\(495\) | 140.992i | 0.284833i | ||||||||
\(496\) | − 71.3742i | − 0.143900i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −229.019 | −0.459878 | ||||||||
\(499\) | 303.598 | 0.608413 | 0.304206 | − | 0.952606i | \(-0.401609\pi\) | ||||
0.304206 | + | 0.952606i | \(0.401609\pi\) | |||||||
\(500\) | − 117.795i | − 0.235590i | ||||||||
\(501\) | −1247.06 | −2.48914 | ||||||||
\(502\) | − 105.793i | − 0.210743i | ||||||||
\(503\) | 884.733i | 1.75891i | 0.475979 | + | 0.879456i | \(0.342094\pi\) | ||||
−0.475979 | + | 0.879456i | \(0.657906\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 226.996 | 0.449497 | ||||||||
\(506\) | 331.647 | 0.655428 | ||||||||
\(507\) | 535.550i | 1.05631i | ||||||||
\(508\) | 67.3137 | 0.132507 | ||||||||
\(509\) | − 646.067i | − 1.26929i | −0.772805 | − | 0.634643i | \(-0.781147\pi\) | ||||
0.772805 | − | 0.634643i | \(-0.218853\pi\) | |||||||
\(510\) | − 61.7919i | − 0.121161i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −1482.70 | −2.89026 | ||||||||
\(514\) | − 607.012i | − 1.18096i | ||||||||
\(515\) | −171.342 | −0.332703 | ||||||||
\(516\) | − 341.654i | − 0.662119i | ||||||||
\(517\) | 231.080i | 0.446964i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −304.382 | −0.586477 | ||||||||
\(520\) | 28.0000 | 0.0538462 | ||||||||
\(521\) | 53.1872i | 0.102087i | 0.998696 | + | 0.0510434i | \(0.0162547\pi\) | ||||
−0.998696 | + | 0.0510434i | \(0.983745\pi\) | |||||||
\(522\) | 890.548 | 1.70603 | ||||||||
\(523\) | − 283.947i | − 0.542920i | −0.962450 | − | 0.271460i | \(-0.912494\pi\) | ||||
0.962450 | − | 0.271460i | \(-0.0875065\pi\) | |||||||
\(524\) | 238.307i | 0.454783i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 160.569 | 0.305263 | ||||||||
\(527\) | −122.912 | −0.233229 | ||||||||
\(528\) | 132.604i | 0.251143i | ||||||||
\(529\) | 837.823 | 1.58379 | ||||||||
\(530\) | 80.0333i | 0.151006i | ||||||||
\(531\) | − 35.6607i | − 0.0671576i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −114.953 | −0.215672 | ||||||||
\(534\) | −487.931 | −0.913729 | ||||||||
\(535\) | − 81.9013i | − 0.153087i | ||||||||
\(536\) | 85.0193 | 0.158618 | ||||||||
\(537\) | 1682.18i | 3.13256i | ||||||||
\(538\) | 15.9282i | 0.0296063i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −118.156 | −0.218808 | ||||||||
\(541\) | −678.392 | −1.25396 | −0.626980 | − | 0.779036i | \(-0.715709\pi\) | ||||
−0.626980 | + | 0.779036i | \(0.715709\pi\) | |||||||
\(542\) | 400.729i | 0.739353i | ||||||||
\(543\) | −595.225 | −1.09618 | ||||||||
\(544\) | − 38.9661i | − 0.0716289i | ||||||||
\(545\) | 113.622i | 0.208480i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −517.470 | −0.946015 | −0.473007 | − | 0.881058i | \(-0.656832\pi\) | ||||
−0.473007 | + | 0.881058i | \(0.656832\pi\) | |||||||
\(548\) | 215.848 | 0.393883 | ||||||||
\(549\) | 1437.26i | 2.61796i | ||||||||
\(550\) | 211.050 | 0.383727 | ||||||||
\(551\) | 1047.39i | 1.90089i | ||||||||
\(552\) | 546.502i | 0.990039i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −307.966 | −0.555894 | ||||||||
\(555\) | −229.892 | −0.414220 | ||||||||
\(556\) | − 90.9209i | − 0.163527i | ||||||||
\(557\) | 583.373 | 1.04735 | 0.523674 | − | 0.851919i | \(-0.324561\pi\) | ||||
0.523674 | + | 0.851919i | \(0.324561\pi\) | |||||||
\(558\) | 462.139i | 0.828206i | ||||||||
\(559\) | − 266.603i | − 0.476928i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 228.353 | 0.407047 | ||||||||
\(562\) | −449.411 | −0.799664 | ||||||||
\(563\) | − 1047.67i | − 1.86087i | −0.366456 | − | 0.930435i | \(-0.619429\pi\) | ||||
0.366456 | − | 0.930435i | \(-0.380571\pi\) | |||||||
\(564\) | −380.784 | −0.675149 | ||||||||
\(565\) | − 80.0333i | − 0.141652i | ||||||||
\(566\) | 339.643i | 0.600075i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −137.373 | −0.241853 | ||||||||
\(569\) | 334.336 | 0.587585 | 0.293793 | − | 0.955869i | \(-0.405082\pi\) | ||||
0.293793 | + | 0.955869i | \(0.405082\pi\) | |||||||
\(570\) | − 273.251i | − 0.479387i | ||||||||
\(571\) | 413.401 | 0.723995 | 0.361998 | − | 0.932179i | \(-0.382095\pi\) | ||||
0.361998 | + | 0.932179i | \(0.382095\pi\) | |||||||
\(572\) | 103.475i | 0.180899i | ||||||||
\(573\) | 466.213i | 0.813636i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 869.803 | 1.51270 | ||||||||
\(576\) | −146.510 | −0.254357 | ||||||||
\(577\) | 398.531i | 0.690695i | 0.938475 | + | 0.345347i | \(0.112239\pi\) | ||||
−0.938475 | + | 0.345347i | \(0.887761\pi\) | |||||||
\(578\) | 341.605 | 0.591012 | ||||||||
\(579\) | − 734.031i | − 1.26776i | ||||||||
\(580\) | 83.4662i | 0.143907i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1151.46 | 1.97845 | ||||||||
\(583\) | −295.765 | −0.507315 | ||||||||
\(584\) | 199.622i | 0.341818i | ||||||||
\(585\) | −181.296 | −0.309908 | ||||||||
\(586\) | − 619.266i | − 1.05677i | ||||||||
\(587\) | − 236.810i | − 0.403424i | −0.979445 | − | 0.201712i | \(-0.935349\pi\) | ||||
0.979445 | − | 0.201712i | \(-0.0646505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −543.529 | −0.922800 | ||||||||
\(590\) | 3.34228 | 0.00566488 | ||||||||
\(591\) | − 734.339i | − 1.24254i | ||||||||
\(592\) | −144.971 | −0.244883 | ||||||||
\(593\) | − 597.691i | − 1.00791i | −0.863730 | − | 0.503955i | \(-0.831878\pi\) | ||||
0.863730 | − | 0.503955i | \(-0.168122\pi\) | |||||||
\(594\) | − 436.649i | − 0.735100i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −368.000 | −0.617450 | ||||||||
\(597\) | 1164.78 | 1.95106 | ||||||||
\(598\) | 426.452i | 0.713130i | ||||||||
\(599\) | −821.754 | −1.37188 | −0.685939 | − | 0.727659i | \(-0.740608\pi\) | ||||
−0.685939 | + | 0.727659i | \(0.740608\pi\) | |||||||
\(600\) | 347.777i | 0.579628i | ||||||||
\(601\) | − 130.321i | − 0.216840i | −0.994105 | − | 0.108420i | \(-0.965421\pi\) | ||||
0.994105 | − | 0.108420i | \(-0.0345791\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −550.489 | −0.912918 | ||||||||
\(604\) | 319.431 | 0.528860 | ||||||||
\(605\) | 98.0246i | 0.162024i | ||||||||
\(606\) | −1382.32 | −2.28106 | ||||||||
\(607\) | − 46.0121i | − 0.0758025i | −0.999281 | − | 0.0379013i | \(-0.987933\pi\) | ||||
0.999281 | − | 0.0379013i | \(-0.0120672\pi\) | |||||||
\(608\) | − 172.312i | − 0.283409i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −134.706 | −0.220830 | ||||||||
\(611\) | −297.137 | −0.486313 | ||||||||
\(612\) | 252.301i | 0.412256i | ||||||||
\(613\) | 513.360 | 0.837454 | 0.418727 | − | 0.908112i | \(-0.362476\pi\) | ||||
0.418727 | + | 0.908112i | \(0.362476\pi\) | |||||||
\(614\) | 674.505i | 1.09854i | ||||||||
\(615\) | 89.3979i | 0.145363i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1018.23 | 1.65030 | 0.825148 | − | 0.564917i | \(-0.191092\pi\) | ||||
0.825148 | + | 0.564917i | \(0.191092\pi\) | |||||||
\(618\) | 1043.41 | 1.68837 | ||||||||
\(619\) | − 62.7414i | − 0.101359i | −0.998715 | − | 0.0506797i | \(-0.983861\pi\) | ||||
0.998715 | − | 0.0506797i | \(-0.0161388\pi\) | |||||||
\(620\) | −43.3137 | −0.0698608 | ||||||||
\(621\) | − 1799.57i | − 2.89786i | ||||||||
\(622\) | − 467.519i | − 0.751638i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −170.510 | −0.273253 | ||||||||
\(625\) | 516.688 | 0.826701 | ||||||||
\(626\) | − 229.698i | − 0.366930i | ||||||||
\(627\) | 1009.80 | 1.61053 | ||||||||
\(628\) | − 337.995i | − 0.538209i | ||||||||
\(629\) | 249.650i | 0.396900i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −264.735 | −0.419548 | −0.209774 | − | 0.977750i | \(-0.567273\pi\) | ||||
−0.209774 | + | 0.977750i | \(0.567273\pi\) | |||||||
\(632\) | −215.765 | −0.341400 | ||||||||
\(633\) | 106.011i | 0.167473i | ||||||||
\(634\) | −614.544 | −0.969313 | ||||||||
\(635\) | − 40.8496i | − 0.0643301i | ||||||||
\(636\) | − 487.373i | − 0.766310i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −308.451 | −0.483465 | ||||||||
\(639\) | 889.470 | 1.39197 | ||||||||
\(640\) | − 13.7315i | − 0.0214555i | ||||||||
\(641\) | 422.350 | 0.658893 | 0.329446 | − | 0.944174i | \(-0.393138\pi\) | ||||
0.329446 | + | 0.944174i | \(0.393138\pi\) | |||||||
\(642\) | 498.749i | 0.776867i | ||||||||
\(643\) | − 827.350i | − 1.28670i | −0.765571 | − | 0.643351i | \(-0.777543\pi\) | ||||
0.765571 | − | 0.643351i | \(-0.222457\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −207.334 | −0.321448 | ||||||||
\(646\) | −296.735 | −0.459342 | ||||||||
\(647\) | − 336.979i | − 0.520833i | −0.965496 | − | 0.260417i | \(-0.916140\pi\) | ||||
0.965496 | − | 0.260417i | \(-0.0838599\pi\) | |||||||
\(648\) | 253.338 | 0.390954 | ||||||||
\(649\) | 12.3515i | 0.0190315i | ||||||||
\(650\) | 271.380i | 0.417508i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 270.156 | 0.414350 | ||||||||
\(653\) | −47.7776 | −0.0731663 | −0.0365831 | − | 0.999331i | \(-0.511647\pi\) | ||||
−0.0365831 | + | 0.999331i | \(0.511647\pi\) | |||||||
\(654\) | − 691.914i | − 1.05797i | ||||||||
\(655\) | 144.617 | 0.220790 | ||||||||
\(656\) | 56.3745i | 0.0859368i | ||||||||
\(657\) | − 1292.53i | − 1.96731i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −557.803 | −0.846439 | −0.423219 | − | 0.906027i | \(-0.639100\pi\) | ||||
−0.423219 | + | 0.906027i | \(0.639100\pi\) | |||||||
\(660\) | 80.4710 | 0.121926 | ||||||||
\(661\) | − 950.853i | − 1.43851i | −0.694748 | − | 0.719253i | \(-0.744484\pi\) | ||||
0.694748 | − | 0.719253i | \(-0.255516\pi\) | |||||||
\(662\) | −651.480 | −0.984109 | ||||||||
\(663\) | 293.631i | 0.442882i | ||||||||
\(664\) | 87.6419i | 0.131991i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 938.666 | 1.40941 | ||||||||
\(667\) | −1271.22 | −1.90588 | ||||||||
\(668\) | 477.228i | 0.714414i | ||||||||
\(669\) | −735.529 | −1.09945 | ||||||||
\(670\) | − 51.5943i | − 0.0770065i | ||||||||
\(671\) | − 497.810i | − 0.741893i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 753.747 | 1.11998 | 0.559991 | − | 0.828499i | \(-0.310805\pi\) | ||||
0.559991 | + | 0.828499i | \(0.310805\pi\) | |||||||
\(674\) | −87.4903 | −0.129808 | ||||||||
\(675\) | − 1145.19i | − 1.69658i | ||||||||
\(676\) | 204.946 | 0.303175 | ||||||||
\(677\) | 254.029i | 0.375227i | 0.982243 | + | 0.187614i | \(0.0600753\pi\) | ||||
−0.982243 | + | 0.187614i | \(0.939925\pi\) | |||||||
\(678\) | 487.373i | 0.718840i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −23.6468 | −0.0347746 | ||||||||
\(681\) | 53.3524 | 0.0783442 | ||||||||
\(682\) | − 160.067i | − 0.234702i | ||||||||
\(683\) | −792.500 | −1.16032 | −0.580161 | − | 0.814502i | \(-0.697010\pi\) | ||||
−0.580161 | + | 0.814502i | \(0.697010\pi\) | |||||||
\(684\) | 1115.70i | 1.63114i | ||||||||
\(685\) | − 130.988i | − 0.191224i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2257.71 | −3.28634 | ||||||||
\(688\) | −130.745 | −0.190037 | ||||||||
\(689\) | − 380.312i | − 0.551977i | ||||||||
\(690\) | 331.647 | 0.480647 | ||||||||
\(691\) | − 55.0054i | − 0.0796025i | −0.999208 | − | 0.0398013i | \(-0.987328\pi\) | ||||
0.999208 | − | 0.0398013i | \(-0.0126725\pi\) | |||||||
\(692\) | 116.482i | 0.168326i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −759.362 | −1.09418 | ||||||||
\(695\) | −55.1758 | −0.0793896 | ||||||||
\(696\) | − 508.278i | − 0.730285i | ||||||||
\(697\) | 97.0812 | 0.139284 | ||||||||
\(698\) | − 122.843i | − 0.175993i | ||||||||
\(699\) | 755.769i | 1.08121i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −829.894 | −1.18387 | −0.591936 | − | 0.805985i | \(-0.701636\pi\) | ||||
−0.591936 | + | 0.805985i | \(0.701636\pi\) | |||||||
\(702\) | 561.470 | 0.799815 | ||||||||
\(703\) | 1103.98i | 1.57039i | ||||||||
\(704\) | 50.7452 | 0.0720812 | ||||||||
\(705\) | 231.080i | 0.327773i | ||||||||
\(706\) | 813.451i | 1.15220i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −20.3532 | −0.0287475 | ||||||||
\(709\) | −302.503 | −0.426661 | −0.213330 | − | 0.976980i | \(-0.568431\pi\) | ||||
−0.213330 | + | 0.976980i | \(0.568431\pi\) | |||||||
\(710\) | 83.3651i | 0.117416i | ||||||||
\(711\) | 1397.05 | 1.96491 | ||||||||
\(712\) | 186.723i | 0.262252i | ||||||||
\(713\) | − 659.686i | − 0.925225i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 62.7939 | 0.0878237 | ||||||||
\(716\) | 643.744 | 0.899084 | ||||||||
\(717\) | 1115.65i | 1.55600i | ||||||||
\(718\) | −70.7939 | −0.0985988 | ||||||||
\(719\) | 1241.26i | 1.72637i | 0.504889 | + | 0.863184i | \(0.331533\pi\) | ||||
−0.504889 | + | 0.863184i | \(0.668467\pi\) | |||||||
\(720\) | 88.9100i | 0.123486i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −801.664 | −1.11034 | ||||||||
\(723\) | −341.803 | −0.472757 | ||||||||
\(724\) | 227.783i | 0.314617i | ||||||||
\(725\) | −808.968 | −1.11582 | ||||||||
\(726\) | − 596.933i | − 0.822222i | ||||||||
\(727\) | − 546.321i | − 0.751474i | −0.926726 | − | 0.375737i | \(-0.877390\pi\) | ||||
0.926726 | − | 0.375737i | \(-0.122610\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 649.195 | 0.890528 | ||||||||
\(730\) | 121.141 | 0.165947 | ||||||||
\(731\) | 225.153i | 0.308007i | ||||||||
\(732\) | 820.313 | 1.12065 | ||||||||
\(733\) | − 406.633i | − 0.554751i | −0.960762 | − | 0.277376i | \(-0.910535\pi\) | ||||
0.960762 | − | 0.277376i | \(-0.0894647\pi\) | |||||||
\(734\) | − 200.518i | − 0.273186i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 209.137 | 0.284154 | ||||||||
\(737\) | 190.668 | 0.258708 | ||||||||
\(738\) | − 365.018i | − 0.494604i | ||||||||
\(739\) | −382.412 | −0.517472 | −0.258736 | − | 0.965948i | \(-0.583306\pi\) | ||||
−0.258736 | + | 0.965948i | \(0.583306\pi\) | |||||||
\(740\) | 87.9760i | 0.118886i | ||||||||
\(741\) | 1298.47i | 1.75232i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1015.04 | 1.36613 | 0.683067 | − | 0.730356i | \(-0.260646\pi\) | ||||
0.683067 | + | 0.730356i | \(0.260646\pi\) | |||||||
\(744\) | 263.765 | 0.354522 | ||||||||
\(745\) | 223.322i | 0.299762i | ||||||||
\(746\) | 87.9025 | 0.117832 | ||||||||
\(747\) | − 567.470i | − 0.759666i | ||||||||
\(748\) | − 87.3870i | − 0.116828i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 435.314 | 0.580418 | ||||||||
\(751\) | −761.961 | −1.01460 | −0.507298 | − | 0.861771i | \(-0.669356\pi\) | ||||
−0.507298 | + | 0.861771i | \(0.669356\pi\) | |||||||
\(752\) | 145.720i | 0.193776i | ||||||||
\(753\) | 390.960 | 0.519204 | ||||||||
\(754\) | − 396.625i | − 0.526028i | ||||||||
\(755\) | − 193.848i | − 0.256753i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 223.307 | 0.294989 | 0.147494 | − | 0.989063i | \(-0.452879\pi\) | ||||
0.147494 | + | 0.989063i | \(0.452879\pi\) | |||||||
\(758\) | 146.010 | 0.192625 | ||||||||
\(759\) | 1225.61i | 1.61476i | ||||||||
\(760\) | −104.569 | −0.137590 | ||||||||
\(761\) | − 817.907i | − 1.07478i | −0.843334 | − | 0.537389i | \(-0.819411\pi\) | ||||
0.843334 | − | 0.537389i | \(-0.180589\pi\) | |||||||
\(762\) | 248.759i | 0.326455i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 178.412 | 0.233524 | ||||||||
\(765\) | 153.110 | 0.200143 | ||||||||
\(766\) | − 502.155i | − 0.655555i | ||||||||
\(767\) | −15.8823 | −0.0207070 | ||||||||
\(768\) | 83.6200i | 0.108880i | ||||||||
\(769\) | − 726.318i | − 0.944496i | −0.881466 | − | 0.472248i | \(-0.843443\pi\) | ||||
0.881466 | − | 0.472248i | \(-0.156557\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2243.22 | 2.90950 | ||||||||
\(772\) | −280.902 | −0.363862 | ||||||||
\(773\) | 466.557i | 0.603566i | 0.953377 | + | 0.301783i | \(0.0975819\pi\) | ||||
−0.953377 | + | 0.301783i | \(0.902418\pi\) | |||||||
\(774\) | 846.558 | 1.09374 | ||||||||
\(775\) | − 419.803i | − 0.541682i | ||||||||
\(776\) | − 440.645i | − 0.567841i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 572.627 | 0.736025 | ||||||||
\(779\) | 429.304 | 0.551096 | ||||||||
\(780\) | 103.475i | 0.132660i | ||||||||
\(781\) | −308.077 | −0.394465 | ||||||||
\(782\) | − 360.150i | − 0.460550i | ||||||||
\(783\) | 1673.71i | 2.13756i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −205.114 | −0.261292 | ||||||||
\(786\) | −880.666 | −1.12044 | ||||||||
\(787\) | 723.552i | 0.919380i | 0.888079 | + | 0.459690i | \(0.152040\pi\) | ||||
−0.888079 | + | 0.459690i | \(0.847960\pi\) | |||||||
\(788\) | −281.019 | −0.356624 | ||||||||
\(789\) | 593.384i | 0.752071i | ||||||||
\(790\) | 130.938i | 0.165744i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −328.569 | −0.414859 | ||||||||
\(793\) | 640.115 | 0.807207 | ||||||||
\(794\) | 764.985i | 0.963458i | ||||||||
\(795\) | −295.765 | −0.372031 | ||||||||
\(796\) | − 445.743i | − 0.559979i | ||||||||
\(797\) | − 296.985i | − 0.372628i | −0.982490 | − | 0.186314i | \(-0.940346\pi\) | ||||
0.982490 | − | 0.186314i | \(-0.0596542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 250.940 | 0.314068 | ||||||||
\(800\) | 133.088 | 0.166360 | ||||||||
\(801\) | − 1209.01i | − 1.50937i | ||||||||
\(802\) | −661.411 | −0.824702 | ||||||||
\(803\) | 447.680i | 0.557509i | ||||||||
\(804\) | 314.190i | 0.390784i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 205.823 | 0.255364 | ||||||||
\(807\) | −58.8629 | −0.0729404 | ||||||||
\(808\) | 528.992i | 0.654693i | ||||||||
\(809\) | 1176.18 | 1.45386 | 0.726932 | − | 0.686709i | \(-0.240945\pi\) | ||||
0.726932 | + | 0.686709i | \(0.240945\pi\) | |||||||
\(810\) | − 153.739i | − 0.189802i | ||||||||
\(811\) | 907.076i | 1.11847i | 0.829011 | + | 0.559233i | \(0.188904\pi\) | ||||
−0.829011 | + | 0.559233i | \(0.811096\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1480.90 | −1.82153 | ||||||||
\(814\) | −325.117 | −0.399406 | ||||||||
\(815\) | − 163.946i | − 0.201160i | ||||||||
\(816\) | 144.000 | 0.176471 | ||||||||
\(817\) | 995.652i | 1.21867i | ||||||||
\(818\) | − 136.087i | − 0.166365i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 34.2111 | 0.0417209 | ||||||||
\(821\) | −584.156 | −0.711518 | −0.355759 | − | 0.934578i | \(-0.615778\pi\) | ||||
−0.355759 | + | 0.934578i | \(0.615778\pi\) | |||||||
\(822\) | 797.669i | 0.970401i | ||||||||
\(823\) | −220.077 | −0.267409 | −0.133704 | − | 0.991021i | \(-0.542687\pi\) | ||||
−0.133704 | + | 0.991021i | \(0.542687\pi\) | |||||||
\(824\) | − 399.296i | − 0.484583i | ||||||||
\(825\) | 779.938i | 0.945379i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −69.2548 | −0.0837422 | −0.0418711 | − | 0.999123i | \(-0.513332\pi\) | ||||
−0.0418711 | + | 0.999123i | \(0.513332\pi\) | |||||||
\(828\) | −1354.14 | −1.63543 | ||||||||
\(829\) | − 844.672i | − 1.01890i | −0.860499 | − | 0.509452i | \(-0.829848\pi\) | ||||
0.860499 | − | 0.509452i | \(-0.170152\pi\) | |||||||
\(830\) | 53.1859 | 0.0640793 | ||||||||
\(831\) | − 1138.09i | − 1.36955i | ||||||||
\(832\) | 65.2512i | 0.0784270i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 336.000 | 0.402878 | ||||||||
\(835\) | 289.608 | 0.346836 | ||||||||
\(836\) | − 386.435i | − 0.462243i | ||||||||
\(837\) | −868.548 | −1.03769 | ||||||||
\(838\) | 612.533i | 0.730946i | ||||||||
\(839\) | 428.770i | 0.511049i | 0.966803 | + | 0.255525i | \(0.0822482\pi\) | ||||
−0.966803 | + | 0.255525i | \(0.917752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 341.313 | 0.405842 | ||||||||
\(842\) | −730.621 | −0.867721 | ||||||||
\(843\) | − 1660.81i | − 1.97012i | ||||||||
\(844\) | 40.5685 | 0.0480670 | ||||||||
\(845\) | − 124.372i | − 0.147186i | ||||||||
\(846\) | − 943.516i | − 1.11527i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −186.510 | −0.219941 | ||||||||
\(849\) | −1255.16 | −1.47839 | ||||||||
\(850\) | − 229.188i | − 0.269633i | ||||||||
\(851\) | −1339.91 | −1.57451 | ||||||||
\(852\) | − 507.663i | − 0.595848i | ||||||||
\(853\) | 1386.09i | 1.62496i | 0.582989 | + | 0.812480i | \(0.301883\pi\) | ||||
−0.582989 | + | 0.812480i | \(0.698117\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 677.068 | 0.791893 | ||||||||
\(856\) | 190.863 | 0.222971 | ||||||||
\(857\) | − 326.586i | − 0.381081i | −0.981679 | − | 0.190540i | \(-0.938976\pi\) | ||||
0.981679 | − | 0.190540i | \(-0.0610240\pi\) | |||||||
\(858\) | −382.392 | −0.445678 | ||||||||
\(859\) | 360.882i | 0.420118i | 0.977689 | + | 0.210059i | \(0.0673657\pi\) | ||||
−0.977689 | + | 0.210059i | \(0.932634\pi\) | |||||||
\(860\) | 79.3433i | 0.0922596i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −518.656 | −0.601689 | ||||||||
\(863\) | 690.705 | 0.800353 | 0.400177 | − | 0.916438i | \(-0.368949\pi\) | ||||
0.400177 | + | 0.916438i | \(0.368949\pi\) | |||||||
\(864\) | − 275.352i | − 0.318694i | ||||||||
\(865\) | 70.6875 | 0.0817197 | ||||||||
\(866\) | 635.661i | 0.734020i | ||||||||
\(867\) | 1262.41i | 1.45606i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −483.882 | −0.556827 | ||||||||
\(870\) | −308.451 | −0.354541 | ||||||||
\(871\) | 245.172i | 0.281484i | ||||||||
\(872\) | −264.784 | −0.303651 | ||||||||
\(873\) | 2853.12i | 3.26818i | ||||||||
\(874\) | − 1592.62i | − 1.82222i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −737.706 | −0.842130 | ||||||||
\(877\) | 617.150 | 0.703706 | 0.351853 | − | 0.936055i | \(-0.385552\pi\) | ||||
0.351853 | + | 0.936055i | \(0.385552\pi\) | |||||||
\(878\) | − 935.961i | − 1.06601i | ||||||||
\(879\) | 2288.51 | 2.60354 | ||||||||
\(880\) | − 30.7949i | − 0.0349942i | ||||||||
\(881\) | − 1015.48i | − 1.15264i | −0.817224 | − | 0.576320i | \(-0.804488\pi\) | ||||
0.817224 | − | 0.576320i | \(-0.195512\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1266.30 | 1.43409 | 0.717046 | − | 0.697026i | \(-0.245494\pi\) | ||||
0.717046 | + | 0.697026i | \(0.245494\pi\) | |||||||
\(884\) | 112.368 | 0.127113 | ||||||||
\(885\) | 12.3515i | 0.0139564i | ||||||||
\(886\) | 1113.90 | 1.25722 | ||||||||
\(887\) | − 893.482i | − 1.00731i | −0.863905 | − | 0.503654i | \(-0.831989\pi\) | ||||
0.863905 | − | 0.503654i | \(-0.168011\pi\) | |||||||
\(888\) | − 535.741i | − 0.603312i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 113.314 | 0.127319 | ||||||||
\(891\) | 568.146 | 0.637650 | ||||||||
\(892\) | 281.475i | 0.315555i | ||||||||
\(893\) | 1109.69 | 1.24265 | ||||||||
\(894\) | − 1359.95i | − 1.52120i | ||||||||
\(895\) | − 390.659i | − 0.436490i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1575.96 | −1.75692 | ||||||||
\(898\) | 397.921 | 0.443119 | ||||||||
\(899\) | 613.546i | 0.682476i | ||||||||
\(900\) | −861.730 | −0.957478 | ||||||||
\(901\) | 321.184i | 0.356475i | ||||||||
\(902\) | 126.428i | 0.140164i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 186.510 | 0.206316 | ||||||||
\(905\) | 138.231 | 0.152741 | ||||||||
\(906\) | 1180.46i | 1.30294i | ||||||||
\(907\) | −337.706 | −0.372333 | −0.186166 | − | 0.982518i | \(-0.559606\pi\) | ||||
−0.186166 | + | 0.982518i | \(0.559606\pi\) | |||||||
\(908\) | − 20.4171i | − 0.0224858i | ||||||||
\(909\) | − 3425.16i | − 3.76805i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −482.461 | −0.529595 | −0.264797 | − | 0.964304i | \(-0.585305\pi\) | ||||
−0.264797 | + | 0.964304i | \(0.585305\pi\) | |||||||
\(912\) | 636.784 | 0.698228 | ||||||||
\(913\) | 196.549i | 0.215279i | ||||||||
\(914\) | 561.608 | 0.614451 | ||||||||
\(915\) | − 497.810i | − 0.544055i | ||||||||
\(916\) | 863.990i | 0.943220i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −474.177 | −0.516532 | ||||||||
\(919\) | 658.940 | 0.717019 | 0.358509 | − | 0.933526i | \(-0.383285\pi\) | ||||
0.358509 | + | 0.933526i | \(0.383285\pi\) | |||||||
\(920\) | − 126.916i | − 0.137952i | ||||||||
\(921\) | −2492.65 | −2.70646 | ||||||||
\(922\) | 613.188i | 0.665063i | ||||||||
\(923\) | − 396.145i | − 0.429192i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −852.677 | −0.921813 | ||||||||
\(926\) | −152.471 | −0.164656 | ||||||||
\(927\) | 2585.39i | 2.78899i | ||||||||
\(928\) | −194.510 | −0.209601 | ||||||||
\(929\) | − 595.770i | − 0.641303i | −0.947197 | − | 0.320651i | \(-0.896098\pi\) | ||||
0.947197 | − | 0.320651i | \(-0.103902\pi\) | |||||||
\(930\) | − 160.067i | − 0.172115i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 289.220 | 0.310322 | ||||||||
\(933\) | 1727.72 | 1.85179 | ||||||||
\(934\) | 231.043i | 0.247369i | ||||||||
\(935\) | −53.0312 | −0.0567178 | ||||||||
\(936\) | − 422.493i | − 0.451382i | ||||||||
\(937\) | 1397.12i | 1.49106i | 0.666473 | + | 0.745529i | \(0.267803\pi\) | ||||
−0.666473 | + | 0.745529i | \(0.732197\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 848.853 | 0.903997 | ||||||||
\(940\) | 88.4306 | 0.0940751 | ||||||||
\(941\) | − 1863.58i | − 1.98043i | −0.139550 | − | 0.990215i | \(-0.544566\pi\) | ||||
0.139550 | − | 0.990215i | \(-0.455434\pi\) | |||||||
\(942\) | 1249.07 | 1.32597 | ||||||||
\(943\) | 521.049i | 0.552544i | ||||||||
\(944\) | 7.78885i | 0.00825090i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −293.214 | −0.309952 | ||||||||
\(947\) | 390.412 | 0.412262 | 0.206131 | − | 0.978524i | \(-0.433913\pi\) | ||||
0.206131 | + | 0.978524i | \(0.433913\pi\) | |||||||
\(948\) | − 797.362i | − 0.841099i | ||||||||
\(949\) | −575.654 | −0.606590 | ||||||||
\(950\) | − 1013.50i | − 1.06684i | ||||||||
\(951\) | − 2271.06i | − 2.38807i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −232.432 | −0.243895 | −0.121948 | − | 0.992537i | \(-0.538914\pi\) | ||||
−0.121948 | + | 0.992537i | \(0.538914\pi\) | |||||||
\(954\) | 1207.63 | 1.26586 | ||||||||
\(955\) | − 108.270i | − 0.113372i | ||||||||
\(956\) | 426.940 | 0.446590 | ||||||||
\(957\) | − 1139.89i | − 1.19110i | ||||||||
\(958\) | 848.138i | 0.885322i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 50.7452 | 0.0528595 | ||||||||
\(961\) | 642.608 | 0.668687 | ||||||||
\(962\) | − 418.055i | − 0.434569i | ||||||||
\(963\) | −1235.81 | −1.28330 | ||||||||
\(964\) | 130.802i | 0.135687i | ||||||||
\(965\) | 170.466i | 0.176649i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1734.97 | −1.79418 | −0.897088 | − | 0.441851i | \(-0.854322\pi\) | ||||
−0.897088 | + | 0.441851i | \(0.854322\pi\) | |||||||
\(968\) | −228.437 | −0.235988 | ||||||||
\(969\) | − 1096.59i | − 1.13167i | ||||||||
\(970\) | −267.407 | −0.275677 | ||||||||
\(971\) | 113.158i | 0.116537i | 0.998301 | + | 0.0582687i | \(0.0185580\pi\) | ||||
−0.998301 | + | 0.0582687i | \(0.981442\pi\) | |||||||
\(972\) | 60.0514i | 0.0617812i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 641.499 | 0.658623 | ||||||||
\(975\) | −1002.89 | −1.02861 | ||||||||
\(976\) | − 313.920i | − 0.321639i | ||||||||
\(977\) | 484.409 | 0.495813 | 0.247906 | − | 0.968784i | \(-0.420257\pi\) | ||||
0.247906 | + | 0.968784i | \(0.420257\pi\) | |||||||
\(978\) | 998.368i | 1.02083i | ||||||||
\(979\) | 418.753i | 0.427735i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1714.44 | 1.74765 | ||||||||
\(982\) | 717.823 | 0.730981 | ||||||||
\(983\) | 1786.00i | 1.81689i | 0.418003 | + | 0.908446i | \(0.362730\pi\) | ||||
−0.418003 | + | 0.908446i | \(0.637270\pi\) | |||||||
\(984\) | −208.333 | −0.211721 | ||||||||
\(985\) | 170.538i | 0.173135i | ||||||||
\(986\) | 334.960i | 0.339716i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 496.902 | 0.502937 | ||||||||
\(989\) | −1208.43 | −1.22187 | ||||||||
\(990\) | 199.393i | 0.201407i | ||||||||
\(991\) | 321.568 | 0.324488 | 0.162244 | − | 0.986751i | \(-0.448127\pi\) | ||||
0.162244 | + | 0.986751i | \(0.448127\pi\) | |||||||
\(992\) | − 100.938i | − 0.101752i | ||||||||
\(993\) | − 2407.56i | − 2.42453i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −270.501 | −0.271861 | ||||||||
\(996\) | −323.882 | −0.325183 | ||||||||
\(997\) | − 785.969i | − 0.788334i | −0.919039 | − | 0.394167i | \(-0.871033\pi\) | ||||
0.919039 | − | 0.394167i | \(-0.128967\pi\) | |||||||
\(998\) | 429.352 | 0.430213 | ||||||||
\(999\) | 1764.14i | 1.76590i |
(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 | 98.3.b.a.97.4 | yes | 4 | |
3.2 | odd | 2 | 882.3.c.a.685.2 | 4 | |||
4.3 | odd | 2 | 784.3.c.b.97.1 | 4 | |||
7.2 | even | 3 | 98.3.d.b.31.1 | 8 | |||
7.3 | odd | 6 | 98.3.d.b.19.1 | 8 | |||
7.4 | even | 3 | 98.3.d.b.19.2 | 8 | |||
7.5 | odd | 6 | 98.3.d.b.31.2 | 8 | |||
7.6 | odd | 2 | inner | 98.3.b.a.97.3 | ✓ | 4 | |
21.2 | odd | 6 | 882.3.n.j.325.4 | 8 | |||
21.5 | even | 6 | 882.3.n.j.325.3 | 8 | |||
21.11 | odd | 6 | 882.3.n.j.19.3 | 8 | |||
21.17 | even | 6 | 882.3.n.j.19.4 | 8 | |||
21.20 | even | 2 | 882.3.c.a.685.1 | 4 | |||
28.3 | even | 6 | 784.3.s.j.705.4 | 8 | |||
28.11 | odd | 6 | 784.3.s.j.705.1 | 8 | |||
28.19 | even | 6 | 784.3.s.j.129.1 | 8 | |||
28.23 | odd | 6 | 784.3.s.j.129.4 | 8 | |||
28.27 | even | 2 | 784.3.c.b.97.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.3.b.a.97.3 | ✓ | 4 | 7.6 | odd | 2 | inner | |
98.3.b.a.97.4 | yes | 4 | 1.1 | even | 1 | trivial | |
98.3.d.b.19.1 | 8 | 7.3 | odd | 6 | |||
98.3.d.b.19.2 | 8 | 7.4 | even | 3 | |||
98.3.d.b.31.1 | 8 | 7.2 | even | 3 | |||
98.3.d.b.31.2 | 8 | 7.5 | odd | 6 | |||
784.3.c.b.97.1 | 4 | 4.3 | odd | 2 | |||
784.3.c.b.97.4 | 4 | 28.27 | even | 2 | |||
784.3.s.j.129.1 | 8 | 28.19 | even | 6 | |||
784.3.s.j.129.4 | 8 | 28.23 | odd | 6 | |||
784.3.s.j.705.1 | 8 | 28.11 | odd | 6 | |||
784.3.s.j.705.4 | 8 | 28.3 | even | 6 | |||
882.3.c.a.685.1 | 4 | 21.20 | even | 2 | |||
882.3.c.a.685.2 | 4 | 3.2 | odd | 2 | |||
882.3.n.j.19.3 | 8 | 21.11 | odd | 6 | |||
882.3.n.j.19.4 | 8 | 21.17 | even | 6 | |||
882.3.n.j.325.3 | 8 | 21.5 | even | 6 | |||
882.3.n.j.325.4 | 8 | 21.2 | odd | 6 |