Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(649,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.6525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{401})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 201x^{2} + 10000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(9.51249i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.649 |
Dual form | 1350.4.c.u.649.4 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 29.5375i | − 1.59487i | −0.603402 | − | 0.797437i | \(-0.706189\pi\) | ||||
0.603402 | − | 0.797437i | \(-0.293811\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −46.5375 | −1.27560 | −0.637799 | − | 0.770203i | \(-0.720155\pi\) | ||||
−0.637799 | + | 0.770203i | \(0.720155\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 92.0750i | − 1.96438i | −0.187879 | − | 0.982192i | \(-0.560161\pi\) | ||||
0.187879 | − | 0.982192i | \(-0.439839\pi\) | |||||||
\(14\) | −59.0750 | −1.12775 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 4.53748i | 0.0647353i | 0.999476 | + | 0.0323676i | \(0.0103047\pi\) | ||||
−0.999476 | + | 0.0323676i | \(0.989695\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −87.5375 | −1.05697 | −0.528486 | − | 0.848942i | \(-0.677240\pi\) | ||||
−0.528486 | + | 0.848942i | \(0.677240\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 93.0750i | 0.901984i | ||||||||
\(23\) | 160.687i | 1.45677i | 0.685170 | + | 0.728383i | \(0.259728\pi\) | ||||
−0.685170 | + | 0.728383i | \(0.740272\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −184.150 | −1.38903 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 118.150i | 0.797437i | ||||||||
\(29\) | −241.762 | −1.54807 | −0.774037 | − | 0.633141i | \(-0.781766\pi\) | ||||
−0.774037 | + | 0.633141i | \(0.781766\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.68738 | −0.0155699 | −0.00778497 | − | 0.999970i | \(-0.502478\pi\) | ||||
−0.00778497 | + | 0.999970i | \(0.502478\pi\) | |||||||
\(32\) | − 32.0000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.07495 | 0.0457748 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 20.6124i | − 0.0915855i | −0.998951 | − | 0.0457927i | \(-0.985419\pi\) | ||||
0.998951 | − | 0.0457927i | \(-0.0145814\pi\) | |||||||
\(38\) | 175.075i | 0.747392i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 501.225 | 1.90922 | 0.954612 | − | 0.297853i | \(-0.0962704\pi\) | ||||
0.954612 | + | 0.297853i | \(0.0962704\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 294.687i | − 1.04510i | −0.852608 | − | 0.522551i | \(-0.824980\pi\) | ||||
0.852608 | − | 0.522551i | \(-0.175020\pi\) | |||||||
\(44\) | 186.150 | 0.637799 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 321.375 | 1.03009 | ||||||||
\(47\) | − 478.987i | − 1.48654i | −0.668991 | − | 0.743271i | \(-0.733273\pi\) | ||||
0.668991 | − | 0.743271i | \(-0.266727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −529.463 | −1.54362 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 368.300i | 0.982192i | ||||||||
\(53\) | − 243.075i | − 0.629979i | −0.949095 | − | 0.314990i | \(-0.897999\pi\) | ||||
0.949095 | − | 0.314990i | \(-0.102001\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 236.300 | 0.563873 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 483.525i | 1.09465i | ||||||||
\(59\) | −383.700 | −0.846670 | −0.423335 | − | 0.905973i | \(-0.639141\pi\) | ||||
−0.423335 | + | 0.905973i | \(0.639141\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 132.612 | 0.278349 | 0.139174 | − | 0.990268i | \(-0.455555\pi\) | ||||
0.139174 | + | 0.990268i | \(0.455555\pi\) | |||||||
\(62\) | 5.37477i | 0.0110096i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 582.612i | 1.06235i | 0.847262 | + | 0.531175i | \(0.178249\pi\) | ||||
−0.847262 | + | 0.531175i | \(0.821751\pi\) | |||||||
\(68\) | − 18.1499i | − 0.0323676i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 566.775 | 0.947378 | 0.473689 | − | 0.880692i | \(-0.342922\pi\) | ||||
0.473689 | + | 0.880692i | \(0.342922\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 839.388i | 1.34579i | 0.739737 | + | 0.672896i | \(0.234950\pi\) | ||||
−0.739737 | + | 0.672896i | \(0.765050\pi\) | |||||||
\(74\) | −41.2249 | −0.0647607 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 350.150 | 0.528486 | ||||||||
\(77\) | 1374.60i | 2.03442i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −451.775 | −0.643401 | −0.321700 | − | 0.946841i | \(-0.604254\pi\) | ||||
−0.321700 | + | 0.946841i | \(0.604254\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 1002.45i | − 1.35003i | ||||||||
\(83\) | − 301.049i | − 0.398126i | −0.979987 | − | 0.199063i | \(-0.936210\pi\) | ||||
0.979987 | − | 0.199063i | \(-0.0637898\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −589.375 | −0.738999 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 372.300i | − 0.450992i | ||||||||
\(89\) | 739.349 | 0.880571 | 0.440286 | − | 0.897858i | \(-0.354877\pi\) | ||||
0.440286 | + | 0.897858i | \(0.354877\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2719.66 | −3.13295 | ||||||||
\(92\) | − 642.750i | − 0.728383i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −957.974 | −1.05114 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1146.14i | − 1.19972i | −0.800106 | − | 0.599859i | \(-0.795223\pi\) | ||||
0.800106 | − | 0.599859i | \(-0.204777\pi\) | |||||||
\(98\) | 1058.93i | 1.09151i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 511.463 | 0.503885 | 0.251943 | − | 0.967742i | \(-0.418931\pi\) | ||||
0.251943 | + | 0.967742i | \(0.418931\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 421.512i | − 0.403231i | −0.979465 | − | 0.201616i | \(-0.935381\pi\) | ||||
0.979465 | − | 0.201616i | \(-0.0646191\pi\) | |||||||
\(104\) | 736.600 | 0.694515 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −486.150 | −0.445463 | ||||||||
\(107\) | 1639.50i | 1.48127i | 0.671905 | + | 0.740637i | \(0.265476\pi\) | ||||
−0.671905 | + | 0.740637i | \(0.734524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 690.475 | 0.606748 | 0.303374 | − | 0.952872i | \(-0.401887\pi\) | ||||
0.303374 | + | 0.952872i | \(0.401887\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 472.600i | − 0.398718i | ||||||||
\(113\) | 970.238i | 0.807719i | 0.914821 | + | 0.403860i | \(0.132332\pi\) | ||||
−0.914821 | + | 0.403860i | \(0.867668\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 967.049 | 0.774037 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 767.400i | 0.598686i | ||||||||
\(119\) | 134.026 | 0.103245 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 834.737 | 0.627150 | ||||||||
\(122\) | − 265.225i | − 0.196822i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.7495 | 0.00778497 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 805.024i | 0.562475i | 0.959638 | + | 0.281237i | \(0.0907448\pi\) | ||||
−0.959638 | + | 0.281237i | \(0.909255\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −214.687 | −0.143186 | −0.0715928 | − | 0.997434i | \(-0.522808\pi\) | ||||
−0.0715928 | + | 0.997434i | \(0.522808\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2585.64i | 1.68574i | ||||||||
\(134\) | 1165.22 | 0.751195 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −36.2998 | −0.0228874 | ||||||||
\(137\) | − 367.799i | − 0.229366i | −0.993402 | − | 0.114683i | \(-0.963415\pi\) | ||||
0.993402 | − | 0.114683i | \(-0.0365853\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1427.31 | 0.870956 | 0.435478 | − | 0.900199i | \(-0.356579\pi\) | ||||
0.435478 | + | 0.900199i | \(0.356579\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 1133.55i | − 0.669897i | ||||||||
\(143\) | 4284.94i | 2.50576i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1678.78 | 0.951619 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 82.4497i | 0.0457927i | ||||||||
\(149\) | −1757.74 | −0.966439 | −0.483219 | − | 0.875499i | \(-0.660533\pi\) | ||||
−0.483219 | + | 0.875499i | \(0.660533\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −537.775 | −0.289825 | −0.144912 | − | 0.989445i | \(-0.546290\pi\) | ||||
−0.144912 | + | 0.989445i | \(0.546290\pi\) | |||||||
\(152\) | − 700.300i | − 0.373696i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2749.20 | 1.43855 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 671.788i | 0.341494i | 0.985315 | + | 0.170747i | \(0.0546180\pi\) | ||||
−0.985315 | + | 0.170747i | \(0.945382\pi\) | |||||||
\(158\) | 903.550i | 0.454953i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4746.30 | 2.32336 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2501.42i | 1.20200i | 0.799248 | + | 0.601002i | \(0.205232\pi\) | ||||
−0.799248 | + | 0.601002i | \(0.794768\pi\) | |||||||
\(164\) | −2004.90 | −0.954612 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −602.099 | −0.281518 | ||||||||
\(167\) | − 751.649i | − 0.348289i | −0.984720 | − | 0.174145i | \(-0.944284\pi\) | ||||
0.984720 | − | 0.174145i | \(-0.0557161\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6280.80 | −2.85881 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1178.75i | 0.522551i | ||||||||
\(173\) | 2374.27i | 1.04343i | 0.853121 | + | 0.521713i | \(0.174707\pi\) | ||||
−0.853121 | + | 0.521713i | \(0.825293\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −744.600 | −0.318899 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 1478.70i | − 0.622658i | ||||||||
\(179\) | −2424.52 | −1.01239 | −0.506194 | − | 0.862420i | \(-0.668948\pi\) | ||||
−0.506194 | + | 0.862420i | \(0.668948\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1179.46 | 0.484357 | 0.242179 | − | 0.970232i | \(-0.422138\pi\) | ||||
0.242179 | + | 0.970232i | \(0.422138\pi\) | |||||||
\(182\) | 5439.32i | 2.21533i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1285.50 | −0.515045 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 211.163i | − 0.0825762i | ||||||||
\(188\) | 1915.95i | 0.743271i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 344.475 | 0.130499 | 0.0652496 | − | 0.997869i | \(-0.479216\pi\) | ||||
0.0652496 | + | 0.997869i | \(0.479216\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 1941.84i | − 0.724231i | −0.932133 | − | 0.362115i | \(-0.882055\pi\) | ||||
0.932133 | − | 0.362115i | \(-0.117945\pi\) | |||||||
\(194\) | −2292.27 | −0.848328 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2117.85 | 0.771811 | ||||||||
\(197\) | 1780.95i | 0.644099i | 0.946723 | + | 0.322049i | \(0.104372\pi\) | ||||
−0.946723 | + | 0.322049i | \(0.895628\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 808.375 | 0.287961 | 0.143980 | − | 0.989581i | \(-0.454010\pi\) | ||||
0.143980 | + | 0.989581i | \(0.454010\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 1022.93i | − 0.356301i | ||||||||
\(203\) | 7141.05i | 2.46898i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −843.024 | −0.285127 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 1473.20i | − 0.491096i | ||||||||
\(209\) | 4073.77 | 1.34827 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1223.04 | 0.399039 | 0.199520 | − | 0.979894i | \(-0.436062\pi\) | ||||
0.199520 | + | 0.979894i | \(0.436062\pi\) | |||||||
\(212\) | 972.300i | 0.314990i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3279.00 | 1.04742 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 79.3785i | 0.0248321i | ||||||||
\(218\) | − 1380.95i | − 0.429036i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 417.788 | 0.127165 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1061.00i | − 0.318610i | −0.987229 | − | 0.159305i | \(-0.949075\pi\) | ||||
0.987229 | − | 0.159305i | \(-0.0509253\pi\) | |||||||
\(224\) | −945.199 | −0.281937 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1940.48 | 0.571144 | ||||||||
\(227\) | 3573.07i | 1.04473i | 0.852723 | + | 0.522364i | \(0.174950\pi\) | ||||
−0.852723 | + | 0.522364i | \(0.825050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1001.82 | −0.289094 | −0.144547 | − | 0.989498i | \(-0.546172\pi\) | ||||
−0.144547 | + | 0.989498i | \(0.546172\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 1934.10i | − 0.547327i | ||||||||
\(233\) | − 6082.42i | − 1.71018i | −0.518477 | − | 0.855091i | \(-0.673501\pi\) | ||||
0.518477 | − | 0.855091i | \(-0.326499\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1534.80 | 0.423335 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 268.051i | − 0.0730050i | ||||||||
\(239\) | 212.399 | 0.0574850 | 0.0287425 | − | 0.999587i | \(-0.490850\pi\) | ||||
0.0287425 | + | 0.999587i | \(0.490850\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2944.45 | −0.787006 | −0.393503 | − | 0.919323i | \(-0.628737\pi\) | ||||
−0.393503 | + | 0.919323i | \(0.628737\pi\) | |||||||
\(242\) | − 1669.47i | − 0.443462i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −530.450 | −0.139174 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8060.01i | 2.07630i | ||||||||
\(248\) | − 21.4991i | − 0.00550481i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1130.36 | 0.284254 | 0.142127 | − | 0.989848i | \(-0.454606\pi\) | ||||
0.142127 | + | 0.989848i | \(0.454606\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 7477.99i | − 1.85825i | ||||||||
\(254\) | 1610.05 | 0.397730 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 1218.34i | 0.295711i | 0.989009 | + | 0.147856i | \(0.0472371\pi\) | ||||
−0.989009 | + | 0.147856i | \(0.952763\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −608.839 | −0.146067 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 429.375i | 0.101248i | ||||||||
\(263\) | 6937.50i | 1.62656i | 0.581875 | + | 0.813279i | \(0.302319\pi\) | ||||
−0.581875 | + | 0.813279i | \(0.697681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5171.27 | 1.19200 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 2330.45i | − 0.531175i | ||||||||
\(269\) | −515.214 | −0.116778 | −0.0583888 | − | 0.998294i | \(-0.518596\pi\) | ||||
−0.0583888 | + | 0.998294i | \(0.518596\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −652.411 | −0.146240 | −0.0731202 | − | 0.997323i | \(-0.523296\pi\) | ||||
−0.0731202 | + | 0.997323i | \(0.523296\pi\) | |||||||
\(272\) | 72.5996i | 0.0161838i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −735.598 | −0.162186 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2938.85i | 0.637467i | 0.947844 | + | 0.318733i | \(0.103257\pi\) | ||||
−0.947844 | + | 0.318733i | \(0.896743\pi\) | |||||||
\(278\) | − 2854.62i | − 0.615859i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5351.77 | 1.13616 | 0.568078 | − | 0.822974i | \(-0.307687\pi\) | ||||
0.568078 | + | 0.822974i | \(0.307687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1479.95i | − 0.310862i | −0.987847 | − | 0.155431i | \(-0.950323\pi\) | ||||
0.987847 | − | 0.155431i | \(-0.0496766\pi\) | |||||||
\(284\) | −2267.10 | −0.473689 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8569.87 | 1.77184 | ||||||||
\(287\) | − 14804.9i | − 3.04497i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4892.41 | 0.995809 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 3357.55i | − 0.672896i | ||||||||
\(293\) | 5178.90i | 1.03261i | 0.856405 | + | 0.516305i | \(0.172693\pi\) | ||||
−0.856405 | + | 0.516305i | \(0.827307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 164.899 | 0.0323804 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3515.47i | 0.683376i | ||||||||
\(299\) | 14795.3 | 2.86165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8704.32 | −1.66681 | ||||||||
\(302\) | 1075.55i | 0.204937i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1400.60 | −0.264243 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10306.0i | 1.91594i | 0.286868 | + | 0.957970i | \(0.407386\pi\) | ||||
−0.286868 | + | 0.957970i | \(0.592614\pi\) | |||||||
\(308\) | − 5498.40i | − 1.01721i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2062.65 | 0.376084 | 0.188042 | − | 0.982161i | \(-0.439786\pi\) | ||||
0.188042 | + | 0.982161i | \(0.439786\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 9247.96i | − 1.67005i | −0.550212 | − | 0.835025i | \(-0.685453\pi\) | ||||
0.550212 | − | 0.835025i | \(-0.314547\pi\) | |||||||
\(314\) | 1343.58 | 0.241473 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1807.10 | 0.321700 | ||||||||
\(317\) | 610.347i | 0.108140i | 0.998537 | + | 0.0540702i | \(0.0172195\pi\) | ||||
−0.998537 | + | 0.0540702i | \(0.982781\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11251.0 | 1.97472 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 9492.60i | − 1.64286i | ||||||||
\(323\) | − 397.199i | − 0.0684234i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5002.85 | 0.849945 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4009.80i | 0.675013i | ||||||||
\(329\) | −14148.1 | −2.37085 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2089.26 | −0.346937 | −0.173469 | − | 0.984839i | \(-0.555498\pi\) | ||||
−0.173469 | + | 0.984839i | \(0.555498\pi\) | |||||||
\(332\) | 1204.20i | 0.199063i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1503.30 | −0.246278 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 9426.36i | − 1.52370i | −0.647754 | − | 0.761849i | \(-0.724292\pi\) | ||||
0.647754 | − | 0.761849i | \(-0.275708\pi\) | |||||||
\(338\) | 12561.6i | 2.02148i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 125.064 | 0.0198610 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5507.63i | 0.867009i | ||||||||
\(344\) | 2357.50 | 0.369500 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4748.55 | 0.737814 | ||||||||
\(347\) | 1221.22i | 0.188930i | 0.995528 | + | 0.0944651i | \(0.0301141\pi\) | ||||
−0.995528 | + | 0.0944651i | \(0.969886\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4188.29 | 0.642389 | 0.321195 | − | 0.947013i | \(-0.395916\pi\) | ||||
0.321195 | + | 0.947013i | \(0.395916\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1489.20i | 0.225496i | ||||||||
\(353\) | − 4469.36i | − 0.673882i | −0.941526 | − | 0.336941i | \(-0.890608\pi\) | ||||
0.941526 | − | 0.336941i | \(-0.109392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2957.40 | −0.440286 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4849.05i | 0.715866i | ||||||||
\(359\) | −643.572 | −0.0946140 | −0.0473070 | − | 0.998880i | \(-0.515064\pi\) | ||||
−0.0473070 | + | 0.998880i | \(0.515064\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 803.810 | 0.117191 | ||||||||
\(362\) | − 2358.92i | − 0.342492i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10878.6 | 1.56647 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 5934.74i | − 0.844116i | −0.906569 | − | 0.422058i | \(-0.861308\pi\) | ||||
0.906569 | − | 0.422058i | \(-0.138692\pi\) | |||||||
\(368\) | 2571.00i | 0.364192i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7179.82 | −1.00474 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6187.83i | 0.858964i | 0.903075 | + | 0.429482i | \(0.141304\pi\) | ||||
−0.903075 | + | 0.429482i | \(0.858696\pi\) | |||||||
\(374\) | −422.325 | −0.0583902 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3831.90 | 0.525572 | ||||||||
\(377\) | 22260.3i | 3.04101i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10428.5 | −1.41340 | −0.706699 | − | 0.707515i | \(-0.749816\pi\) | ||||
−0.706699 | + | 0.707515i | \(0.749816\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 688.951i | − 0.0922769i | ||||||||
\(383\) | − 10246.7i | − 1.36705i | −0.729926 | − | 0.683526i | \(-0.760446\pi\) | ||||
0.729926 | − | 0.683526i | \(-0.239554\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3883.67 | −0.512108 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4584.55i | 0.599859i | ||||||||
\(389\) | −8508.48 | −1.10899 | −0.554495 | − | 0.832187i | \(-0.687088\pi\) | ||||
−0.554495 | + | 0.832187i | \(0.687088\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −729.115 | −0.0943042 | ||||||||
\(392\) | − 4235.70i | − 0.545753i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3561.90 | 0.455447 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3775.96i | 0.477356i | 0.971099 | + | 0.238678i | \(0.0767140\pi\) | ||||
−0.971099 | + | 0.238678i | \(0.923286\pi\) | |||||||
\(398\) | − 1616.75i | − 0.203619i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7556.02 | −0.940971 | −0.470486 | − | 0.882408i | \(-0.655921\pi\) | ||||
−0.470486 | + | 0.882408i | \(0.655921\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 247.441i | 0.0305854i | ||||||||
\(404\) | −2045.85 | −0.251943 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14282.1 | 1.74583 | ||||||||
\(407\) | 959.250i | 0.116826i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8963.22 | −1.08362 | −0.541812 | − | 0.840499i | \(-0.682262\pi\) | ||||
−0.541812 | + | 0.840499i | \(0.682262\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1686.05i | 0.201616i | ||||||||
\(413\) | 11333.5i | 1.35033i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2946.40 | −0.347257 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 8147.55i | − 0.953372i | ||||||||
\(419\) | −14153.8 | −1.65026 | −0.825130 | − | 0.564943i | \(-0.808898\pi\) | ||||
−0.825130 | + | 0.564943i | \(0.808898\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14727.3 | −1.70490 | −0.852451 | − | 0.522807i | \(-0.824885\pi\) | ||||
−0.852451 | + | 0.522807i | \(0.824885\pi\) | |||||||
\(422\) | − 2446.07i | − 0.282163i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1944.60 | 0.222731 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3917.04i | − 0.443931i | ||||||||
\(428\) | − 6558.00i | − 0.740637i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3048.98 | −0.340752 | −0.170376 | − | 0.985379i | \(-0.554498\pi\) | ||||
−0.170376 | + | 0.985379i | \(0.554498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 17218.4i | − 1.91100i | −0.294990 | − | 0.955500i | \(-0.595316\pi\) | ||||
0.294990 | − | 0.955500i | \(-0.404684\pi\) | |||||||
\(434\) | 158.757 | 0.0175589 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2761.90 | −0.303374 | ||||||||
\(437\) | − 14066.2i | − 1.53976i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1667.91 | −0.181332 | −0.0906660 | − | 0.995881i | \(-0.528900\pi\) | ||||
−0.0906660 | + | 0.995881i | \(0.528900\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 835.576i | − 0.0899192i | ||||||||
\(443\) | − 9223.20i | − 0.989182i | −0.869126 | − | 0.494591i | \(-0.835318\pi\) | ||||
0.869126 | − | 0.494591i | \(-0.164682\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2122.00 | −0.225291 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1890.40i | 0.199359i | ||||||||
\(449\) | −2636.18 | −0.277080 | −0.138540 | − | 0.990357i | \(-0.544241\pi\) | ||||
−0.138540 | + | 0.990357i | \(0.544241\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23325.7 | −2.43540 | ||||||||
\(452\) | − 3880.95i | − 0.403860i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7146.14 | 0.738734 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 3859.67i | − 0.395072i | −0.980296 | − | 0.197536i | \(-0.936706\pi\) | ||||
0.980296 | − | 0.197536i | \(-0.0632940\pi\) | |||||||
\(458\) | 2003.65i | 0.204420i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6615.07 | 0.668318 | 0.334159 | − | 0.942517i | \(-0.391548\pi\) | ||||
0.334159 | + | 0.942517i | \(0.391548\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17571.7i | 1.76377i | 0.471460 | + | 0.881887i | \(0.343727\pi\) | ||||
−0.471460 | + | 0.881887i | \(0.656273\pi\) | |||||||
\(464\) | −3868.20 | −0.387018 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12164.8 | −1.20928 | ||||||||
\(467\) | 10076.8i | 0.998502i | 0.866457 | + | 0.499251i | \(0.166391\pi\) | ||||
−0.866457 | + | 0.499251i | \(0.833609\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17208.9 | 1.69431 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 3069.60i | − 0.299343i | ||||||||
\(473\) | 13714.0i | 1.33313i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −536.102 | −0.0516223 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 424.797i | − 0.0406480i | ||||||||
\(479\) | 17945.8 | 1.71182 | 0.855912 | − | 0.517122i | \(-0.172997\pi\) | ||||
0.855912 | + | 0.517122i | \(0.172997\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1897.89 | −0.179909 | ||||||||
\(482\) | 5888.90i | 0.556498i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3338.95 | −0.313575 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17356.9i | 1.61502i | 0.589853 | + | 0.807511i | \(0.299186\pi\) | ||||
−0.589853 | + | 0.807511i | \(0.700814\pi\) | |||||||
\(488\) | 1060.90i | 0.0984112i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8393.17 | −0.771443 | −0.385722 | − | 0.922615i | \(-0.626047\pi\) | ||||
−0.385722 | + | 0.922615i | \(0.626047\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1096.99i | − 0.100215i | ||||||||
\(494\) | 16120.0 | 1.46817 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −42.9981 | −0.00389249 | ||||||||
\(497\) | − 16741.1i | − 1.51095i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16421.1 | −1.47317 | −0.736585 | − | 0.676345i | \(-0.763563\pi\) | ||||
−0.736585 | + | 0.676345i | \(0.763563\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 2260.72i | − 0.200998i | ||||||||
\(503\) | − 16014.9i | − 1.41962i | −0.704395 | − | 0.709808i | \(-0.748782\pi\) | ||||
0.704395 | − | 0.709808i | \(-0.251218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14956.0 | −1.31398 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 3220.09i | − 0.281237i | ||||||||
\(509\) | 13695.9 | 1.19265 | 0.596327 | − | 0.802741i | \(-0.296626\pi\) | ||||
0.596327 | + | 0.802741i | \(0.296626\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24793.4 | 2.14637 | ||||||||
\(512\) | − 512.000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2436.67 | 0.209099 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22290.9i | 1.89623i | ||||||||
\(518\) | 1217.68i | 0.103285i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5887.12 | 0.495047 | 0.247523 | − | 0.968882i | \(-0.420383\pi\) | ||||
0.247523 | + | 0.968882i | \(0.420383\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8544.57i | − 0.714394i | −0.934029 | − | 0.357197i | \(-0.883733\pi\) | ||||
0.934029 | − | 0.357197i | \(-0.116267\pi\) | |||||||
\(524\) | 858.750 | 0.0715928 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13875.0 | 1.15015 | ||||||||
\(527\) | − 12.1939i | − 0.00100792i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13653.4 | −1.12217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 10342.5i | − 0.842869i | ||||||||
\(533\) | − 46150.3i | − 3.75045i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4660.90 | −0.375597 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1030.43i | 0.0825742i | ||||||||
\(539\) | 24639.8 | 1.96904 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10236.5 | 0.813499 | 0.406749 | − | 0.913540i | \(-0.366662\pi\) | ||||
0.406749 | + | 0.913540i | \(0.366662\pi\) | |||||||
\(542\) | 1304.82i | 0.103408i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 145.199 | 0.0114437 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 4785.31i | − 0.374050i | −0.982355 | − | 0.187025i | \(-0.940115\pi\) | ||||
0.982355 | − | 0.187025i | \(-0.0598845\pi\) | |||||||
\(548\) | 1471.20i | 0.114683i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21163.3 | 1.63627 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13344.3i | 1.02614i | ||||||||
\(554\) | 5877.70 | 0.450757 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5709.24 | −0.435478 | ||||||||
\(557\) | − 2031.75i | − 0.154557i | −0.997010 | − | 0.0772783i | \(-0.975377\pi\) | ||||
0.997010 | − | 0.0772783i | \(-0.0246230\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27133.3 | −2.05298 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 10703.5i | − 0.803384i | ||||||||
\(563\) | 12162.4i | 0.910449i | 0.890377 | + | 0.455224i | \(0.150441\pi\) | ||||
−0.890377 | + | 0.455224i | \(0.849559\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2959.90 | −0.219812 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4534.20i | 0.334949i | ||||||||
\(569\) | 144.753 | 0.0106650 | 0.00533249 | − | 0.999986i | \(-0.498303\pi\) | ||||
0.00533249 | + | 0.999986i | \(0.498303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7479.28 | −0.548158 | −0.274079 | − | 0.961707i | \(-0.588373\pi\) | ||||
−0.274079 | + | 0.961707i | \(0.588373\pi\) | |||||||
\(572\) | − 17139.7i | − 1.25288i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −29609.8 | −2.15312 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 6562.94i | − 0.473516i | −0.971569 | − | 0.236758i | \(-0.923915\pi\) | ||||
0.971569 | − | 0.236758i | \(-0.0760848\pi\) | |||||||
\(578\) | − 9784.82i | − 0.704144i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8892.24 | −0.634961 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11312.1i | 0.803601i | ||||||||
\(584\) | −6715.10 | −0.475810 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10357.8 | 0.730165 | ||||||||
\(587\) | − 4227.89i | − 0.297281i | −0.988891 | − | 0.148640i | \(-0.952510\pi\) | ||||
0.988891 | − | 0.148640i | \(-0.0474897\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 235.247 | 0.0164570 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 329.799i | − 0.0228964i | ||||||||
\(593\) | − 28746.9i | − 1.99071i | −0.0962641 | − | 0.995356i | \(-0.530689\pi\) | ||||
0.0962641 | − | 0.995356i | \(-0.469311\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7030.95 | 0.483219 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 29590.6i | − 2.02349i | ||||||||
\(599\) | −21714.9 | −1.48121 | −0.740607 | − | 0.671939i | \(-0.765462\pi\) | ||||
−0.740607 | + | 0.671939i | \(0.765462\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6055.82 | 0.411018 | 0.205509 | − | 0.978655i | \(-0.434115\pi\) | ||||
0.205509 | + | 0.978655i | \(0.434115\pi\) | |||||||
\(602\) | 17408.6i | 1.17861i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2151.10 | 0.144912 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18260.0i | 1.22100i | 0.792015 | + | 0.610502i | \(0.209032\pi\) | ||||
−0.792015 | + | 0.610502i | \(0.790968\pi\) | |||||||
\(608\) | 2801.20i | 0.186848i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −44102.7 | −2.92014 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16207.4i | 1.06788i | 0.845521 | + | 0.533941i | \(0.179290\pi\) | ||||
−0.845521 | + | 0.533941i | \(0.820710\pi\) | |||||||
\(614\) | 20612.0 | 1.35477 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10996.8 | −0.719275 | ||||||||
\(617\) | 14003.1i | 0.913686i | 0.889547 | + | 0.456843i | \(0.151020\pi\) | ||||
−0.889547 | + | 0.456843i | \(0.848980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 269.684 | 0.0175113 | 0.00875565 | − | 0.999962i | \(-0.497213\pi\) | ||||
0.00875565 | + | 0.999962i | \(0.497213\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 4125.29i | − 0.265931i | ||||||||
\(623\) | − 21838.5i | − 1.40440i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18495.9 | −1.18090 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 2687.15i | − 0.170747i | ||||||||
\(629\) | 93.5284 | 0.00592881 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21240.2 | −1.34003 | −0.670016 | − | 0.742347i | \(-0.733713\pi\) | ||||
−0.670016 | + | 0.742347i | \(0.733713\pi\) | |||||||
\(632\) | − 3614.20i | − 0.227477i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1220.69 | 0.0764668 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 48750.2i | 3.03227i | ||||||||
\(638\) | − 22502.0i | − 1.39634i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19210.9 | −1.18375 | −0.591875 | − | 0.806030i | \(-0.701612\pi\) | ||||
−0.591875 | + | 0.806030i | \(0.701612\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 7731.07i | − 0.474158i | −0.971490 | − | 0.237079i | \(-0.923810\pi\) | ||||
0.971490 | − | 0.237079i | \(-0.0761901\pi\) | |||||||
\(644\) | −18985.2 | −1.16168 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −794.399 | −0.0483826 | ||||||||
\(647\) | − 23347.4i | − 1.41867i | −0.704870 | − | 0.709337i | \(-0.748995\pi\) | ||||
0.704870 | − | 0.709337i | \(-0.251005\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17856.4 | 1.08001 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 10005.7i | − 0.601002i | ||||||||
\(653\) | 7667.71i | 0.459511i | 0.973248 | + | 0.229755i | \(0.0737926\pi\) | ||||
−0.973248 | + | 0.229755i | \(0.926207\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8019.60 | 0.477306 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 28296.1i | 1.67644i | ||||||||
\(659\) | −14673.6 | −0.867378 | −0.433689 | − | 0.901063i | \(-0.642788\pi\) | ||||
−0.433689 | + | 0.901063i | \(0.642788\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25446.9 | 1.49738 | 0.748691 | − | 0.662919i | \(-0.230683\pi\) | ||||
0.748691 | + | 0.662919i | \(0.230683\pi\) | |||||||
\(662\) | 4178.53i | 0.245322i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2408.39 | 0.140759 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 38848.2i | − 2.25518i | ||||||||
\(668\) | 3006.60i | 0.174145i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6171.45 | −0.355061 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12239.5i | 0.701035i | 0.936556 | + | 0.350518i | \(0.113994\pi\) | ||||
−0.936556 | + | 0.350518i | \(0.886006\pi\) | |||||||
\(674\) | −18852.7 | −1.07742 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25123.2 | 1.42940 | ||||||||
\(677\) | 10457.5i | 0.593672i | 0.954929 | + | 0.296836i | \(0.0959314\pi\) | ||||
−0.954929 | + | 0.296836i | \(0.904069\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33854.0 | −1.91340 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 250.128i | − 0.0140438i | ||||||||
\(683\) | 304.720i | 0.0170714i | 0.999964 | + | 0.00853572i | \(0.00271704\pi\) | ||||
−0.999964 | + | 0.00853572i | \(0.997283\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11015.3 | 0.613068 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 4715.00i | − 0.261276i | ||||||||
\(689\) | −22381.1 | −1.23752 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14937.8 | −0.822373 | −0.411186 | − | 0.911551i | \(-0.634885\pi\) | ||||
−0.411186 | + | 0.911551i | \(0.634885\pi\) | |||||||
\(692\) | − 9497.10i | − 0.521713i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2442.45 | 0.133594 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2274.30i | 0.123594i | ||||||||
\(698\) | − 8376.57i | − 0.454238i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13752.9 | −0.741000 | −0.370500 | − | 0.928832i | \(-0.620814\pi\) | ||||
−0.370500 | + | 0.928832i | \(0.620814\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1804.36i | 0.0968033i | ||||||||
\(704\) | 2978.40 | 0.159450 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8938.73 | −0.476506 | ||||||||
\(707\) | − 15107.3i | − 0.803634i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31225.5 | 1.65402 | 0.827008 | − | 0.562190i | \(-0.190041\pi\) | ||||
0.827008 | + | 0.562190i | \(0.190041\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5914.79i | 0.311329i | ||||||||
\(713\) | − 431.829i | − 0.0226818i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9698.09 | 0.506194 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1287.14i | 0.0669022i | ||||||||
\(719\) | 13945.5 | 0.723337 | 0.361669 | − | 0.932307i | \(-0.382207\pi\) | ||||
0.361669 | + | 0.932307i | \(0.382207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12450.4 | −0.643103 | ||||||||
\(722\) | − 1607.62i | − 0.0828662i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4717.84 | −0.242179 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 37585.1i | − 1.91741i | −0.284407 | − | 0.958704i | \(-0.591797\pi\) | ||||
0.284407 | − | 0.958704i | \(-0.408203\pi\) | |||||||
\(728\) | − 21757.3i | − 1.10766i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1337.14 | 0.0676550 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2848.70i | − 0.143546i | −0.997421 | − | 0.0717729i | \(-0.977134\pi\) | ||||
0.997421 | − | 0.0717729i | \(-0.0228657\pi\) | |||||||
\(734\) | −11869.5 | −0.596880 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5142.00 | 0.257522 | ||||||||
\(737\) | − 27113.3i | − 1.35513i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1828.99 | −0.0910428 | −0.0455214 | − | 0.998963i | \(-0.514495\pi\) | ||||
−0.0455214 | + | 0.998963i | \(0.514495\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14359.6i | 0.710457i | ||||||||
\(743\) | 32798.9i | 1.61948i | 0.586789 | + | 0.809740i | \(0.300392\pi\) | ||||
−0.586789 | + | 0.809740i | \(0.699608\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12375.7 | 0.607379 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 844.651i | 0.0412881i | ||||||||
\(749\) | 48426.7 | 2.36245 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16225.2 | −0.788371 | −0.394186 | − | 0.919031i | \(-0.628973\pi\) | ||||
−0.394186 | + | 0.919031i | \(0.628973\pi\) | |||||||
\(752\) | − 7663.80i | − 0.371635i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 44520.5 | 2.15032 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 14461.0i | − 0.694312i | −0.937807 | − | 0.347156i | \(-0.887147\pi\) | ||||
0.937807 | − | 0.347156i | \(-0.112853\pi\) | |||||||
\(758\) | 20857.1i | 0.999423i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22060.5 | −1.05084 | −0.525422 | − | 0.850842i | \(-0.676093\pi\) | ||||
−0.525422 | + | 0.850842i | \(0.676093\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 20394.9i | − 0.967687i | ||||||||
\(764\) | −1377.90 | −0.0652496 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20493.4 | −0.966652 | ||||||||
\(767\) | 35329.2i | 1.66318i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1675.74 | 0.0785810 | 0.0392905 | − | 0.999228i | \(-0.487490\pi\) | ||||
0.0392905 | + | 0.999228i | \(0.487490\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7767.35i | 0.362115i | ||||||||
\(773\) | 10878.6i | 0.506179i | 0.967443 | + | 0.253089i | \(0.0814467\pi\) | ||||
−0.967443 | + | 0.253089i | \(0.918553\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9169.10 | 0.424164 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17017.0i | 0.784174i | ||||||||
\(779\) | −43876.0 | −2.01800 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26376.3 | −1.20847 | ||||||||
\(782\) | 1458.23i | 0.0666831i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8471.40 | −0.385906 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 27293.2i | − 1.23621i | −0.786096 | − | 0.618105i | \(-0.787901\pi\) | ||||
0.786096 | − | 0.618105i | \(-0.212099\pi\) | |||||||
\(788\) | − 7123.80i | − 0.322049i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28658.4 | 1.28821 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 12210.3i | − 0.546784i | ||||||||
\(794\) | 7551.93 | 0.337541 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3233.50 | −0.143980 | ||||||||
\(797\) | − 38925.4i | − 1.73000i | −0.501772 | − | 0.865000i | \(-0.667318\pi\) | ||||
0.501772 | − | 0.865000i | \(-0.332682\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2173.39 | 0.0962317 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15112.0i | 0.665367i | ||||||||
\(803\) | − 39063.0i | − 1.71669i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 494.881 | 0.0216271 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4091.70i | 0.178150i | ||||||||
\(809\) | −22806.9 | −0.991159 | −0.495579 | − | 0.868563i | \(-0.665044\pi\) | ||||
−0.495579 | + | 0.868563i | \(0.665044\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42523.0 | −1.84117 | −0.920583 | − | 0.390547i | \(-0.872286\pi\) | ||||
−0.920583 | + | 0.390547i | \(0.872286\pi\) | |||||||
\(812\) | − 28564.2i | − 1.23449i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1918.50 | 0.0826086 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25796.2i | 1.10464i | ||||||||
\(818\) | 17926.4i | 0.766238i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32644.4 | −1.38770 | −0.693848 | − | 0.720122i | \(-0.744086\pi\) | ||||
−0.693848 | + | 0.720122i | \(0.744086\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 4471.81i | − 0.189402i | −0.995506 | − | 0.0947008i | \(-0.969811\pi\) | ||||
0.995506 | − | 0.0947008i | \(-0.0301894\pi\) | |||||||
\(824\) | 3372.09 | 0.142564 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 22667.1 | 0.954828 | ||||||||
\(827\) | − 29667.5i | − 1.24745i | −0.781644 | − | 0.623725i | \(-0.785619\pi\) | ||||
0.781644 | − | 0.623725i | \(-0.214381\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5130.74 | −0.214955 | −0.107478 | − | 0.994207i | \(-0.534277\pi\) | ||||
−0.107478 | + | 0.994207i | \(0.534277\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5892.80i | 0.245548i | ||||||||
\(833\) | − 2402.42i | − 0.0999268i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −16295.1 | −0.674136 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 28307.6i | 1.16691i | ||||||||
\(839\) | 24205.9 | 0.996042 | 0.498021 | − | 0.867165i | \(-0.334060\pi\) | ||||
0.498021 | + | 0.867165i | \(0.334060\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34060.0 | 1.39653 | ||||||||
\(842\) | 29454.6i | 1.20555i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4892.15 | −0.199520 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 24656.0i | − 1.00023i | ||||||||
\(848\) | − 3889.20i | − 0.157495i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3312.16 | 0.133419 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 21843.2i | − 0.876784i | −0.898784 | − | 0.438392i | \(-0.855548\pi\) | ||||
0.898784 | − | 0.438392i | \(-0.144452\pi\) | |||||||
\(854\) | −7834.07 | −0.313907 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13116.0 | −0.523710 | ||||||||
\(857\) | − 2770.50i | − 0.110430i | −0.998474 | − | 0.0552151i | \(-0.982416\pi\) | ||||
0.998474 | − | 0.0552151i | \(-0.0175844\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18439.6 | 0.732421 | 0.366211 | − | 0.930532i | \(-0.380655\pi\) | ||||
0.366211 | + | 0.930532i | \(0.380655\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6097.95i | 0.240948i | ||||||||
\(863\) | 22073.1i | 0.870659i | 0.900271 | + | 0.435329i | \(0.143368\pi\) | ||||
−0.900271 | + | 0.435329i | \(0.856632\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −34436.8 | −1.35128 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 317.514i | − 0.0124160i | ||||||||
\(869\) | 21024.5 | 0.820721 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53644.0 | 2.08686 | ||||||||
\(872\) | 5523.80i | 0.214518i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −28132.3 | −1.08878 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 8446.67i | − 0.325227i | −0.986690 | − | 0.162613i | \(-0.948008\pi\) | ||||
0.986690 | − | 0.162613i | \(-0.0519923\pi\) | |||||||
\(878\) | 3335.81i | 0.128221i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16665.8 | 0.637325 | 0.318663 | − | 0.947868i | \(-0.396766\pi\) | ||||
0.318663 | + | 0.947868i | \(0.396766\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 37742.6i | − 1.43844i | −0.694784 | − | 0.719219i | \(-0.744500\pi\) | ||||
0.694784 | − | 0.719219i | \(-0.255500\pi\) | |||||||
\(884\) | −1671.15 | −0.0635825 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18446.4 | −0.699457 | ||||||||
\(887\) | 19447.2i | 0.736158i | 0.929795 | + | 0.368079i | \(0.119984\pi\) | ||||
−0.929795 | + | 0.368079i | \(0.880016\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23778.4 | 0.897076 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4244.01i | 0.159305i | ||||||||
\(893\) | 41929.3i | 1.57123i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3780.80 | 0.140968 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5272.35i | 0.195925i | ||||||||
\(899\) | 649.708 | 0.0241034 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1102.95 | 0.0407819 | ||||||||
\(902\) | 46651.5i | 1.72209i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7761.90 | −0.285572 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15428.9i | 0.564838i | 0.959291 | + | 0.282419i | \(0.0911369\pi\) | ||||
−0.959291 | + | 0.282419i | \(0.908863\pi\) | |||||||
\(908\) | − 14292.3i | − 0.522364i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −688.190 | −0.0250283 | −0.0125141 | − | 0.999922i | \(-0.503983\pi\) | ||||
−0.0125141 | + | 0.999922i | \(0.503983\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14010.1i | 0.507849i | ||||||||
\(914\) | −7719.35 | −0.279358 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4007.30 | 0.144547 | ||||||||
\(917\) | 6341.32i | 0.228363i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6809.05 | −0.244407 | −0.122203 | − | 0.992505i | \(-0.538996\pi\) | ||||
−0.122203 | + | 0.992505i | \(0.538996\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 13230.1i | − 0.472572i | ||||||||
\(923\) | − 52185.8i | − 1.86101i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 35143.5 | 1.24718 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7736.39i | 0.273663i | ||||||||
\(929\) | 47682.2 | 1.68396 | 0.841982 | − | 0.539506i | \(-0.181389\pi\) | ||||
0.841982 | + | 0.539506i | \(0.181389\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 46347.8 | 1.63157 | ||||||||
\(932\) | 24329.7i | 0.855091i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20153.7 | 0.706048 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 30516.3i | − 1.06395i | −0.846759 | − | 0.531977i | \(-0.821449\pi\) | ||||
0.846759 | − | 0.531977i | \(-0.178551\pi\) | |||||||
\(938\) | − 34417.8i | − 1.19806i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31348.8 | −1.08602 | −0.543009 | − | 0.839727i | \(-0.682715\pi\) | ||||
−0.543009 | + | 0.839727i | \(0.682715\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 80540.5i | 2.78129i | ||||||||
\(944\) | −6139.20 | −0.211667 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27428.0 | 0.942666 | ||||||||
\(947\) | 34598.6i | 1.18723i | 0.804750 | + | 0.593614i | \(0.202299\pi\) | ||||
−0.804750 | + | 0.593614i | \(0.797701\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 77286.6 | 2.64365 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1072.20i | 0.0365025i | ||||||||
\(953\) | − 26766.7i | − 0.909820i | −0.890537 | − | 0.454910i | \(-0.849671\pi\) | ||||
0.890537 | − | 0.454910i | \(-0.150329\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −849.594 | −0.0287425 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 35891.5i | − 1.21044i | ||||||||
\(959\) | −10863.9 | −0.365810 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29783.8 | −0.999758 | ||||||||
\(962\) | 3795.78i | 0.127215i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11777.8 | 0.393503 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8764.26i | 0.291458i | 0.989325 | + | 0.145729i | \(0.0465527\pi\) | ||||
−0.989325 | + | 0.145729i | \(0.953447\pi\) | |||||||
\(968\) | 6677.89i | 0.221731i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35417.3 | 1.17054 | 0.585270 | − | 0.810838i | \(-0.300988\pi\) | ||||
0.585270 | + | 0.810838i | \(0.300988\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 42159.2i | − 1.38907i | ||||||||
\(974\) | 34713.8 | 1.14199 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2121.80 | 0.0695872 | ||||||||
\(977\) | 26629.0i | 0.871993i | 0.899948 | + | 0.435997i | \(0.143604\pi\) | ||||
−0.899948 | + | 0.435997i | \(0.856396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34407.4 | −1.12326 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16786.3i | 0.545493i | ||||||||
\(983\) | 16809.2i | 0.545402i | 0.962099 | + | 0.272701i | \(0.0879169\pi\) | ||||
−0.962099 | + | 0.272701i | \(0.912083\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2193.98 | −0.0708627 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 32240.0i | − 1.03815i | ||||||||
\(989\) | 47352.5 | 1.52247 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53758.7 | 1.72321 | 0.861606 | − | 0.507578i | \(-0.169459\pi\) | ||||
0.861606 | + | 0.507578i | \(0.169459\pi\) | |||||||
\(992\) | 85.9963i | 0.00275240i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −33482.2 | −1.06840 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41575.1i | 1.32066i | 0.750976 | + | 0.660330i | \(0.229583\pi\) | ||||
−0.750976 | + | 0.660330i | \(0.770417\pi\) | |||||||
\(998\) | 32842.3i | 1.04169i | ||||||||
\(999\) | 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 | 1350.4.c.u.649.1 | 4 | ||
3.2 | odd | 2 | 1350.4.c.bb.649.3 | 4 | |||
5.2 | odd | 4 | 1350.4.a.bm.1.2 | 2 | |||
5.3 | odd | 4 | 270.4.a.m.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 1350.4.c.u.649.4 | 4 | ||
15.2 | even | 4 | 1350.4.a.bf.1.2 | 2 | |||
15.8 | even | 4 | 270.4.a.n.1.1 | yes | 2 | ||
15.14 | odd | 2 | 1350.4.c.bb.649.2 | 4 | |||
20.3 | even | 4 | 2160.4.a.w.1.2 | 2 | |||
45.13 | odd | 12 | 810.4.e.bd.541.2 | 4 | |||
45.23 | even | 12 | 810.4.e.z.541.2 | 4 | |||
45.38 | even | 12 | 810.4.e.z.271.2 | 4 | |||
45.43 | odd | 12 | 810.4.e.bd.271.2 | 4 | |||
60.23 | odd | 4 | 2160.4.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.4.a.m.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
270.4.a.n.1.1 | yes | 2 | 15.8 | even | 4 | ||
810.4.e.z.271.2 | 4 | 45.38 | even | 12 | |||
810.4.e.z.541.2 | 4 | 45.23 | even | 12 | |||
810.4.e.bd.271.2 | 4 | 45.43 | odd | 12 | |||
810.4.e.bd.541.2 | 4 | 45.13 | odd | 12 | |||
1350.4.a.bf.1.2 | 2 | 15.2 | even | 4 | |||
1350.4.a.bm.1.2 | 2 | 5.2 | odd | 4 | |||
1350.4.c.u.649.1 | 4 | 1.1 | even | 1 | trivial | ||
1350.4.c.u.649.4 | 4 | 5.4 | even | 2 | inner | ||
1350.4.c.bb.649.2 | 4 | 15.14 | odd | 2 | |||
1350.4.c.bb.649.3 | 4 | 3.2 | odd | 2 | |||
2160.4.a.w.1.2 | 2 | 20.3 | even | 4 | |||
2160.4.a.bb.1.2 | 2 | 60.23 | odd | 4 |