Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,5,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, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.97");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
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: | \(10.1302563822\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.97 |
Dual form | 98.5.b.b.97.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82843 | −0.707107 | ||||||||
\(3\) | 4.60181i | 0.511312i | 0.966768 | + | 0.255656i | \(0.0822914\pi\) | ||||
−0.966768 | + | 0.255656i | \(0.917709\pi\) | |||||||
\(4\) | 8.00000 | 0.500000 | ||||||||
\(5\) | − 5.79050i | − 0.231620i | −0.993271 | − | 0.115810i | \(-0.963054\pi\) | ||||
0.993271 | − | 0.115810i | \(-0.0369464\pi\) | |||||||
\(6\) | − 13.0159i | − 0.361552i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −22.6274 | −0.353553 | ||||||||
\(9\) | 59.8234 | 0.738560 | ||||||||
\(10\) | 16.3780i | 0.163780i | ||||||||
\(11\) | 10.0294 | 0.0828879 | 0.0414440 | − | 0.999141i | \(-0.486804\pi\) | ||||
0.0414440 | + | 0.999141i | \(0.486804\pi\) | |||||||
\(12\) | 36.8145i | 0.255656i | ||||||||
\(13\) | − 190.220i | − 1.12556i | −0.826607 | − | 0.562780i | \(-0.809732\pi\) | ||||
0.826607 | − | 0.562780i | \(-0.190268\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 26.6468 | 0.118430 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 421.771i | 1.45942i | 0.683759 | + | 0.729708i | \(0.260344\pi\) | ||||
−0.683759 | + | 0.729708i | \(0.739656\pi\) | |||||||
\(18\) | −169.206 | −0.522241 | ||||||||
\(19\) | 432.248i | 1.19736i | 0.800987 | + | 0.598681i | \(0.204308\pi\) | ||||
−0.800987 | + | 0.598681i | \(0.795692\pi\) | |||||||
\(20\) | − 46.3240i | − 0.115810i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −28.3675 | −0.0586106 | ||||||||
\(23\) | 921.823 | 1.74258 | 0.871288 | − | 0.490772i | \(-0.163285\pi\) | ||||
0.871288 | + | 0.490772i | \(0.163285\pi\) | |||||||
\(24\) | − 104.127i | − 0.180776i | ||||||||
\(25\) | 591.470 | 0.946352 | ||||||||
\(26\) | 538.022i | 0.795891i | ||||||||
\(27\) | 648.042i | 0.888946i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 877.882 | 1.04386 | 0.521928 | − | 0.852990i | \(-0.325213\pi\) | ||||
0.521928 | + | 0.852990i | \(0.325213\pi\) | |||||||
\(30\) | −75.3684 | −0.0837427 | ||||||||
\(31\) | 724.200i | 0.753590i | 0.926297 | + | 0.376795i | \(0.122974\pi\) | ||||
−0.926297 | + | 0.376795i | \(0.877026\pi\) | |||||||
\(32\) | −181.019 | −0.176777 | ||||||||
\(33\) | 46.1535i | 0.0423816i | ||||||||
\(34\) | − 1192.95i | − 1.03196i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 478.587 | 0.369280 | ||||||||
\(37\) | −540.675 | −0.394942 | −0.197471 | − | 0.980309i | \(-0.563273\pi\) | ||||
−0.197471 | + | 0.980309i | \(0.563273\pi\) | |||||||
\(38\) | − 1222.58i | − 0.846663i | ||||||||
\(39\) | 875.354 | 0.575512 | ||||||||
\(40\) | 131.024i | 0.0818900i | ||||||||
\(41\) | 894.280i | 0.531993i | 0.963974 | + | 0.265996i | \(0.0857009\pi\) | ||||
−0.963974 | + | 0.265996i | \(0.914299\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1246.82 | −0.674322 | −0.337161 | − | 0.941447i | \(-0.609467\pi\) | ||||
−0.337161 | + | 0.941447i | \(0.609467\pi\) | |||||||
\(44\) | 80.2355 | 0.0414440 | ||||||||
\(45\) | − 346.407i | − 0.171065i | ||||||||
\(46\) | −2607.31 | −1.23219 | ||||||||
\(47\) | − 1750.73i | − 0.792543i | −0.918133 | − | 0.396271i | \(-0.870304\pi\) | ||||
0.918133 | − | 0.396271i | \(-0.129696\pi\) | |||||||
\(48\) | 294.516i | 0.127828i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1672.93 | −0.669172 | ||||||||
\(51\) | −1940.91 | −0.746216 | ||||||||
\(52\) | − 1521.76i | − 0.562780i | ||||||||
\(53\) | 812.203 | 0.289143 | 0.144571 | − | 0.989494i | \(-0.453820\pi\) | ||||
0.144571 | + | 0.989494i | \(0.453820\pi\) | |||||||
\(54\) | − 1832.94i | − 0.628580i | ||||||||
\(55\) | − 58.0754i | − 0.0191985i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1989.12 | −0.612226 | ||||||||
\(58\) | −2483.03 | −0.738117 | ||||||||
\(59\) | 2854.51i | 0.820025i | 0.912080 | + | 0.410012i | \(0.134476\pi\) | ||||
−0.912080 | + | 0.410012i | \(0.865524\pi\) | |||||||
\(60\) | 213.174 | 0.0592150 | ||||||||
\(61\) | − 5834.20i | − 1.56791i | −0.620816 | − | 0.783956i | \(-0.713199\pi\) | ||||
0.620816 | − | 0.783956i | \(-0.286801\pi\) | |||||||
\(62\) | − 2048.35i | − 0.532868i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | −1101.47 | −0.260702 | ||||||||
\(66\) | − 130.542i | − 0.0299683i | ||||||||
\(67\) | −2203.79 | −0.490930 | −0.245465 | − | 0.969405i | \(-0.578941\pi\) | ||||
−0.245465 | + | 0.969405i | \(0.578941\pi\) | |||||||
\(68\) | 3374.17i | 0.729708i | ||||||||
\(69\) | 4242.05i | 0.891000i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3408.24 | 0.676103 | 0.338052 | − | 0.941128i | \(-0.390232\pi\) | ||||
0.338052 | + | 0.941128i | \(0.390232\pi\) | |||||||
\(72\) | −1353.65 | −0.261120 | ||||||||
\(73\) | − 9395.66i | − 1.76312i | −0.472074 | − | 0.881559i | \(-0.656494\pi\) | ||||
0.472074 | − | 0.881559i | \(-0.343506\pi\) | |||||||
\(74\) | 1529.26 | 0.279266 | ||||||||
\(75\) | 2721.83i | 0.483881i | ||||||||
\(76\) | 3457.98i | 0.598681i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2475.88 | −0.406949 | ||||||||
\(79\) | 2352.23 | 0.376900 | 0.188450 | − | 0.982083i | \(-0.439654\pi\) | ||||
0.188450 | + | 0.982083i | \(0.439654\pi\) | |||||||
\(80\) | − 370.592i | − 0.0579050i | ||||||||
\(81\) | 1863.53 | 0.284031 | ||||||||
\(82\) | − 2529.41i | − 0.376176i | ||||||||
\(83\) | − 3750.16i | − 0.544370i | −0.962245 | − | 0.272185i | \(-0.912254\pi\) | ||||
0.962245 | − | 0.272185i | \(-0.0877462\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2442.26 | 0.338030 | ||||||||
\(86\) | 3526.54 | 0.476817 | ||||||||
\(87\) | 4039.84i | 0.533736i | ||||||||
\(88\) | −226.940 | −0.0293053 | ||||||||
\(89\) | 6363.96i | 0.803429i | 0.915765 | + | 0.401714i | \(0.131586\pi\) | ||||
−0.915765 | + | 0.401714i | \(0.868414\pi\) | |||||||
\(90\) | 979.787i | 0.120961i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7374.58 | 0.871288 | ||||||||
\(93\) | −3332.63 | −0.385319 | ||||||||
\(94\) | 4951.81i | 0.560413i | ||||||||
\(95\) | 2502.93 | 0.277333 | ||||||||
\(96\) | − 833.016i | − 0.0903880i | ||||||||
\(97\) | − 6370.47i | − 0.677062i | −0.940955 | − | 0.338531i | \(-0.890070\pi\) | ||||
0.940955 | − | 0.338531i | \(-0.109930\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 599.995 | 0.0612177 | ||||||||
\(100\) | 4731.76 | 0.473176 | ||||||||
\(101\) | 9110.83i | 0.893131i | 0.894751 | + | 0.446566i | \(0.147353\pi\) | ||||
−0.894751 | + | 0.446566i | \(0.852647\pi\) | |||||||
\(102\) | 5489.72 | 0.527655 | ||||||||
\(103\) | 16111.8i | 1.51869i | 0.650686 | + | 0.759347i | \(0.274482\pi\) | ||||
−0.650686 | + | 0.759347i | \(0.725518\pi\) | |||||||
\(104\) | 4304.18i | 0.397946i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2297.26 | −0.204455 | ||||||||
\(107\) | 20551.4 | 1.79504 | 0.897518 | − | 0.440977i | \(-0.145368\pi\) | ||||
0.897518 | + | 0.440977i | \(0.145368\pi\) | |||||||
\(108\) | 5184.34i | 0.444473i | ||||||||
\(109\) | −14257.7 | −1.20005 | −0.600023 | − | 0.799983i | \(-0.704842\pi\) | ||||
−0.600023 | + | 0.799983i | \(0.704842\pi\) | |||||||
\(110\) | 164.262i | 0.0135754i | ||||||||
\(111\) | − 2488.08i | − 0.201938i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10304.7 | −0.807010 | −0.403505 | − | 0.914978i | \(-0.632208\pi\) | ||||
−0.403505 | + | 0.914978i | \(0.632208\pi\) | |||||||
\(114\) | 5626.08 | 0.432909 | ||||||||
\(115\) | − 5337.81i | − 0.403615i | ||||||||
\(116\) | 7023.06 | 0.521928 | ||||||||
\(117\) | − 11379.6i | − 0.831294i | ||||||||
\(118\) | − 8073.76i | − 0.579845i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −602.947 | −0.0418713 | ||||||||
\(121\) | −14540.4 | −0.993130 | ||||||||
\(122\) | 16501.6i | 1.10868i | ||||||||
\(123\) | −4115.30 | −0.272014 | ||||||||
\(124\) | 5793.60i | 0.376795i | ||||||||
\(125\) | − 7043.97i | − 0.450814i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2116.70 | −0.131236 | −0.0656179 | − | 0.997845i | \(-0.520902\pi\) | ||||
−0.0656179 | + | 0.997845i | \(0.520902\pi\) | |||||||
\(128\) | −1448.15 | −0.0883883 | ||||||||
\(129\) | − 5737.63i | − 0.344789i | ||||||||
\(130\) | 3115.42 | 0.184344 | ||||||||
\(131\) | 6057.15i | 0.352960i | 0.984304 | + | 0.176480i | \(0.0564711\pi\) | ||||
−0.984304 | + | 0.176480i | \(0.943529\pi\) | |||||||
\(132\) | 369.228i | 0.0211908i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6233.25 | 0.347140 | ||||||||
\(135\) | 3752.49 | 0.205898 | ||||||||
\(136\) | − 9543.59i | − 0.515981i | ||||||||
\(137\) | 2860.25 | 0.152392 | 0.0761962 | − | 0.997093i | \(-0.475722\pi\) | ||||
0.0761962 | + | 0.997093i | \(0.475722\pi\) | |||||||
\(138\) | − 11998.3i | − 0.630032i | ||||||||
\(139\) | − 16966.2i | − 0.878124i | −0.898457 | − | 0.439062i | \(-0.855311\pi\) | ||||
0.898457 | − | 0.439062i | \(-0.144689\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8056.51 | 0.405237 | ||||||||
\(142\) | −9639.95 | −0.478077 | ||||||||
\(143\) | − 1907.80i | − 0.0932953i | ||||||||
\(144\) | 3828.70 | 0.184640 | ||||||||
\(145\) | − 5083.38i | − 0.241778i | ||||||||
\(146\) | 26574.9i | 1.24671i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4325.40 | −0.197471 | ||||||||
\(149\) | −14910.1 | −0.671596 | −0.335798 | − | 0.941934i | \(-0.609006\pi\) | ||||
−0.335798 | + | 0.941934i | \(0.609006\pi\) | |||||||
\(150\) | − 7698.50i | − 0.342156i | ||||||||
\(151\) | −2161.45 | −0.0947961 | −0.0473981 | − | 0.998876i | \(-0.515093\pi\) | ||||
−0.0473981 | + | 0.998876i | \(0.515093\pi\) | |||||||
\(152\) | − 9780.65i | − 0.423332i | ||||||||
\(153\) | 25231.8i | 1.07787i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4193.48 | 0.174546 | ||||||||
\(156\) | 7002.83 | 0.287756 | ||||||||
\(157\) | − 41553.7i | − 1.68582i | −0.538056 | − | 0.842909i | \(-0.680841\pi\) | ||||
0.538056 | − | 0.842909i | \(-0.319159\pi\) | |||||||
\(158\) | −6653.11 | −0.266508 | ||||||||
\(159\) | 3737.60i | 0.147842i | ||||||||
\(160\) | 1048.19i | 0.0409450i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5270.86 | −0.200841 | ||||||||
\(163\) | −11765.1 | −0.442814 | −0.221407 | − | 0.975182i | \(-0.571065\pi\) | ||||
−0.221407 | + | 0.975182i | \(0.571065\pi\) | |||||||
\(164\) | 7154.24i | 0.265996i | ||||||||
\(165\) | 267.252 | 0.00981642 | ||||||||
\(166\) | 10607.1i | 0.384927i | ||||||||
\(167\) | 13600.3i | 0.487660i | 0.969818 | + | 0.243830i | \(0.0784038\pi\) | ||||
−0.969818 | + | 0.243830i | \(0.921596\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7622.52 | −0.266886 | ||||||||
\(170\) | −6907.77 | −0.239023 | ||||||||
\(171\) | 25858.5i | 0.884324i | ||||||||
\(172\) | −9974.57 | −0.337161 | ||||||||
\(173\) | − 45153.1i | − 1.50867i | −0.656487 | − | 0.754337i | \(-0.727958\pi\) | ||||
0.656487 | − | 0.754337i | \(-0.272042\pi\) | |||||||
\(174\) | − 11426.4i | − 0.377408i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 641.884 | 0.0207220 | ||||||||
\(177\) | −13135.9 | −0.419288 | ||||||||
\(178\) | − 18000.0i | − 0.568110i | ||||||||
\(179\) | 19852.4 | 0.619593 | 0.309797 | − | 0.950803i | \(-0.399739\pi\) | ||||
0.309797 | + | 0.950803i | \(0.399739\pi\) | |||||||
\(180\) | − 2771.26i | − 0.0855326i | ||||||||
\(181\) | 21398.5i | 0.653170i | 0.945168 | + | 0.326585i | \(0.105898\pi\) | ||||
−0.945168 | + | 0.326585i | \(0.894102\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26847.9 | 0.801692 | ||||||||
\(184\) | −20858.5 | −0.616094 | ||||||||
\(185\) | 3130.78i | 0.0914764i | ||||||||
\(186\) | 9426.09 | 0.272462 | ||||||||
\(187\) | 4230.13i | 0.120968i | ||||||||
\(188\) | − 14005.8i | − 0.396271i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7079.36 | −0.196104 | ||||||||
\(191\) | 11625.9 | 0.318683 | 0.159341 | − | 0.987224i | \(-0.449063\pi\) | ||||
0.159341 | + | 0.987224i | \(0.449063\pi\) | |||||||
\(192\) | 2356.12i | 0.0639140i | ||||||||
\(193\) | −52546.9 | −1.41069 | −0.705347 | − | 0.708862i | \(-0.749209\pi\) | ||||
−0.705347 | + | 0.708862i | \(0.749209\pi\) | |||||||
\(194\) | 18018.4i | 0.478755i | ||||||||
\(195\) | − 5068.74i | − 0.133300i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −54811.7 | −1.41235 | −0.706173 | − | 0.708039i | \(-0.749580\pi\) | ||||
−0.706173 | + | 0.708039i | \(0.749580\pi\) | |||||||
\(198\) | −1697.04 | −0.0432875 | ||||||||
\(199\) | 5972.87i | 0.150826i | 0.997152 | + | 0.0754131i | \(0.0240276\pi\) | ||||
−0.997152 | + | 0.0754131i | \(0.975972\pi\) | |||||||
\(200\) | −13383.4 | −0.334586 | ||||||||
\(201\) | − 10141.4i | − 0.251019i | ||||||||
\(202\) | − 25769.3i | − 0.631539i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −15527.3 | −0.373108 | ||||||||
\(205\) | 5178.33 | 0.123220 | ||||||||
\(206\) | − 45571.1i | − 1.07388i | ||||||||
\(207\) | 55146.5 | 1.28700 | ||||||||
\(208\) | − 12174.1i | − 0.281390i | ||||||||
\(209\) | 4335.20i | 0.0992469i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3042.82 | 0.0683457 | 0.0341729 | − | 0.999416i | \(-0.489120\pi\) | ||||
0.0341729 | + | 0.999416i | \(0.489120\pi\) | |||||||
\(212\) | 6497.62 | 0.144571 | ||||||||
\(213\) | 15684.0i | 0.345700i | ||||||||
\(214\) | −58128.1 | −1.26928 | ||||||||
\(215\) | 7219.71i | 0.156186i | ||||||||
\(216\) | − 14663.5i | − 0.314290i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 40327.0 | 0.848560 | ||||||||
\(219\) | 43237.0 | 0.901503 | ||||||||
\(220\) | − 464.604i | − 0.00959925i | ||||||||
\(221\) | 80229.2 | 1.64266 | ||||||||
\(222\) | 7037.36i | 0.142792i | ||||||||
\(223\) | − 42104.7i | − 0.846683i | −0.905970 | − | 0.423341i | \(-0.860857\pi\) | ||||
0.905970 | − | 0.423341i | \(-0.139143\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 35383.7 | 0.698938 | ||||||||
\(226\) | 29146.1 | 0.570642 | ||||||||
\(227\) | 92189.5i | 1.78908i | 0.446989 | + | 0.894540i | \(0.352496\pi\) | ||||
−0.446989 | + | 0.894540i | \(0.647504\pi\) | |||||||
\(228\) | −15913.0 | −0.306113 | ||||||||
\(229\) | 23963.1i | 0.456953i | 0.973549 | + | 0.228477i | \(0.0733745\pi\) | ||||
−0.973549 | + | 0.228477i | \(0.926626\pi\) | |||||||
\(230\) | 15097.6i | 0.285399i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19864.2 | −0.369059 | ||||||||
\(233\) | −35348.1 | −0.651110 | −0.325555 | − | 0.945523i | \(-0.605551\pi\) | ||||
−0.325555 | + | 0.945523i | \(0.605551\pi\) | |||||||
\(234\) | 32186.3i | 0.587814i | ||||||||
\(235\) | −10137.6 | −0.183569 | ||||||||
\(236\) | 22836.0i | 0.410012i | ||||||||
\(237\) | 10824.5i | 0.192713i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14393.5 | 0.251983 | 0.125992 | − | 0.992031i | \(-0.459789\pi\) | ||||
0.125992 | + | 0.992031i | \(0.459789\pi\) | |||||||
\(240\) | 1705.39 | 0.0296075 | ||||||||
\(241\) | 7499.94i | 0.129129i | 0.997914 | + | 0.0645645i | \(0.0205658\pi\) | ||||
−0.997914 | + | 0.0645645i | \(0.979434\pi\) | |||||||
\(242\) | 41126.5 | 0.702249 | ||||||||
\(243\) | 61067.0i | 1.03418i | ||||||||
\(244\) | − 46673.6i | − 0.783956i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11639.8 | 0.192343 | ||||||||
\(247\) | 82222.1 | 1.34770 | ||||||||
\(248\) | − 16386.8i | − 0.266434i | ||||||||
\(249\) | 17257.5 | 0.278343 | ||||||||
\(250\) | 19923.4i | 0.318774i | ||||||||
\(251\) | 45414.9i | 0.720860i | 0.932786 | + | 0.360430i | \(0.117370\pi\) | ||||
−0.932786 | + | 0.360430i | \(0.882630\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9245.36 | 0.144438 | ||||||||
\(254\) | 5986.94 | 0.0927977 | ||||||||
\(255\) | 11238.8i | 0.172839i | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | − 51727.9i | − 0.783175i | −0.920141 | − | 0.391588i | \(-0.871926\pi\) | ||||
0.920141 | − | 0.391588i | \(-0.128074\pi\) | |||||||
\(258\) | 16228.5i | 0.243802i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8811.73 | −0.130351 | ||||||||
\(261\) | 52517.9 | 0.770950 | ||||||||
\(262\) | − 17132.2i | − 0.249580i | ||||||||
\(263\) | −89833.9 | −1.29876 | −0.649380 | − | 0.760464i | \(-0.724971\pi\) | ||||
−0.649380 | + | 0.760464i | \(0.724971\pi\) | |||||||
\(264\) | − 1044.34i | − 0.0149841i | ||||||||
\(265\) | − 4703.06i | − 0.0669713i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −29285.7 | −0.410803 | ||||||||
\(268\) | −17630.3 | −0.245465 | ||||||||
\(269\) | − 23763.8i | − 0.328406i | −0.986427 | − | 0.164203i | \(-0.947495\pi\) | ||||
0.986427 | − | 0.164203i | \(-0.0525052\pi\) | |||||||
\(270\) | −10613.6 | −0.145592 | ||||||||
\(271\) | 110819.i | 1.50895i | 0.656331 | + | 0.754473i | \(0.272108\pi\) | ||||
−0.656331 | + | 0.754473i | \(0.727892\pi\) | |||||||
\(272\) | 26993.4i | 0.364854i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8090.01 | −0.107758 | ||||||||
\(275\) | 5932.11 | 0.0784412 | ||||||||
\(276\) | 33936.4i | 0.445500i | ||||||||
\(277\) | −7122.38 | −0.0928252 | −0.0464126 | − | 0.998922i | \(-0.514779\pi\) | ||||
−0.0464126 | + | 0.998922i | \(0.514779\pi\) | |||||||
\(278\) | 47987.7i | 0.620927i | ||||||||
\(279\) | 43324.1i | 0.556571i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 90209.2 | 1.14245 | 0.571226 | − | 0.820792i | \(-0.306468\pi\) | ||||
0.571226 | + | 0.820792i | \(0.306468\pi\) | |||||||
\(282\) | −22787.2 | −0.286546 | ||||||||
\(283\) | − 72449.3i | − 0.904610i | −0.891863 | − | 0.452305i | \(-0.850602\pi\) | ||||
0.891863 | − | 0.452305i | \(-0.149398\pi\) | |||||||
\(284\) | 27265.9 | 0.338052 | ||||||||
\(285\) | 11518.0i | 0.141804i | ||||||||
\(286\) | 5396.06i | 0.0659698i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −10829.2 | −0.130560 | ||||||||
\(289\) | −94369.9 | −1.12989 | ||||||||
\(290\) | 14378.0i | 0.170963i | ||||||||
\(291\) | 29315.7 | 0.346190 | ||||||||
\(292\) | − 75165.2i | − 0.881559i | ||||||||
\(293\) | − 89167.8i | − 1.03866i | −0.854574 | − | 0.519329i | \(-0.826182\pi\) | ||||
0.854574 | − | 0.519329i | \(-0.173818\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16529.0 | 0.189934 | ||||||||
\(296\) | 12234.1 | 0.139633 | ||||||||
\(297\) | 6499.50i | 0.0736829i | ||||||||
\(298\) | 42172.2 | 0.474890 | ||||||||
\(299\) | − 175349.i | − 1.96137i | ||||||||
\(300\) | 21774.6i | 0.241941i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6113.49 | 0.0670310 | ||||||||
\(303\) | −41926.3 | −0.456668 | ||||||||
\(304\) | 27663.9i | 0.299341i | ||||||||
\(305\) | −33782.9 | −0.363160 | ||||||||
\(306\) | − 71366.2i | − 0.762167i | ||||||||
\(307\) | − 113110.i | − 1.20012i | −0.799954 | − | 0.600061i | \(-0.795143\pi\) | ||||
0.799954 | − | 0.600061i | \(-0.204857\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −74143.5 | −0.776526 | ||||||||
\(310\) | −11860.9 | −0.123423 | ||||||||
\(311\) | − 65344.2i | − 0.675595i | −0.941219 | − | 0.337797i | \(-0.890318\pi\) | ||||
0.941219 | − | 0.337797i | \(-0.109682\pi\) | |||||||
\(312\) | −19807.0 | −0.203474 | ||||||||
\(313\) | − 1958.86i | − 0.0199947i | −0.999950 | − | 0.00999734i | \(-0.996818\pi\) | ||||
0.999950 | − | 0.00999734i | \(-0.00318231\pi\) | |||||||
\(314\) | 117532.i | 1.19205i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18817.8 | 0.188450 | ||||||||
\(317\) | −86151.2 | −0.857320 | −0.428660 | − | 0.903466i | \(-0.641014\pi\) | ||||
−0.428660 | + | 0.903466i | \(0.641014\pi\) | |||||||
\(318\) | − 10571.5i | − 0.104540i | ||||||||
\(319\) | 8804.66 | 0.0865230 | ||||||||
\(320\) | − 2964.74i | − 0.0289525i | ||||||||
\(321\) | 94573.5i | 0.917824i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −182310. | −1.74745 | ||||||||
\(324\) | 14908.2 | 0.142016 | ||||||||
\(325\) | − 112509.i | − 1.06518i | ||||||||
\(326\) | 33276.8 | 0.313117 | ||||||||
\(327\) | − 65611.3i | − 0.613597i | ||||||||
\(328\) | − 20235.2i | − 0.188088i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −755.903 | −0.00694125 | ||||||||
\(331\) | −90622.3 | −0.827140 | −0.413570 | − | 0.910472i | \(-0.635718\pi\) | ||||
−0.413570 | + | 0.910472i | \(0.635718\pi\) | |||||||
\(332\) | − 30001.3i | − 0.272185i | ||||||||
\(333\) | −32345.0 | −0.291688 | ||||||||
\(334\) | − 38467.6i | − 0.344827i | ||||||||
\(335\) | 12761.0i | 0.113709i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26197.5 | −0.230675 | −0.115338 | − | 0.993326i | \(-0.536795\pi\) | ||||
−0.115338 | + | 0.993326i | \(0.536795\pi\) | |||||||
\(338\) | 21559.7 | 0.188717 | ||||||||
\(339\) | − 47420.3i | − 0.412634i | ||||||||
\(340\) | 19538.1 | 0.169015 | ||||||||
\(341\) | 7263.32i | 0.0624635i | ||||||||
\(342\) | − 73139.0i | − 0.625312i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 28212.3 | 0.238409 | ||||||||
\(345\) | 24563.6 | 0.206373 | ||||||||
\(346\) | 127712.i | 1.06679i | ||||||||
\(347\) | −160661. | −1.33429 | −0.667146 | − | 0.744927i | \(-0.732484\pi\) | ||||
−0.667146 | + | 0.744927i | \(0.732484\pi\) | |||||||
\(348\) | 32318.8i | 0.266868i | ||||||||
\(349\) | 18120.2i | 0.148769i | 0.997230 | + | 0.0743845i | \(0.0236992\pi\) | ||||
−0.997230 | + | 0.0743845i | \(0.976301\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 123270. | 1.00056 | ||||||||
\(352\) | −1815.52 | −0.0146527 | ||||||||
\(353\) | − 13229.5i | − 0.106168i | −0.998590 | − | 0.0530839i | \(-0.983095\pi\) | ||||
0.998590 | − | 0.0530839i | \(-0.0169051\pi\) | |||||||
\(354\) | 37153.9 | 0.296482 | ||||||||
\(355\) | − 19735.4i | − 0.156599i | ||||||||
\(356\) | 50911.7i | 0.401714i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −56151.0 | −0.438119 | ||||||||
\(359\) | −107735. | −0.835924 | −0.417962 | − | 0.908464i | \(-0.637256\pi\) | ||||
−0.417962 | + | 0.908464i | \(0.637256\pi\) | |||||||
\(360\) | 7838.30i | 0.0604807i | ||||||||
\(361\) | −56517.2 | −0.433677 | ||||||||
\(362\) | − 60524.1i | − 0.461861i | ||||||||
\(363\) | − 66912.2i | − 0.507799i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −54405.5 | −0.408373 | ||||||||
\(366\) | −75937.3 | −0.566882 | ||||||||
\(367\) | 70427.2i | 0.522887i | 0.965219 | + | 0.261444i | \(0.0841986\pi\) | ||||
−0.965219 | + | 0.261444i | \(0.915801\pi\) | |||||||
\(368\) | 58996.6 | 0.435644 | ||||||||
\(369\) | 53498.9i | 0.392909i | ||||||||
\(370\) | − 8855.18i | − 0.0646836i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −26661.0 | −0.192660 | ||||||||
\(373\) | 191053. | 1.37321 | 0.686605 | − | 0.727030i | \(-0.259100\pi\) | ||||
0.686605 | + | 0.727030i | \(0.259100\pi\) | |||||||
\(374\) | − 11964.6i | − 0.0855372i | ||||||||
\(375\) | 32415.0 | 0.230507 | ||||||||
\(376\) | 39614.4i | 0.280206i | ||||||||
\(377\) | − 166990.i | − 1.17492i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 74979.5 | 0.521992 | 0.260996 | − | 0.965340i | \(-0.415949\pi\) | ||||
0.260996 | + | 0.965340i | \(0.415949\pi\) | |||||||
\(380\) | 20023.4 | 0.138667 | ||||||||
\(381\) | − 9740.65i | − 0.0671024i | ||||||||
\(382\) | −32882.9 | −0.225343 | ||||||||
\(383\) | 128637.i | 0.876936i | 0.898747 | + | 0.438468i | \(0.144479\pi\) | ||||
−0.898747 | + | 0.438468i | \(0.855521\pi\) | |||||||
\(384\) | − 6664.13i | − 0.0451940i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 148625. | 0.997511 | ||||||||
\(387\) | −74589.0 | −0.498027 | ||||||||
\(388\) | − 50963.8i | − 0.338531i | ||||||||
\(389\) | 26308.0 | 0.173856 | 0.0869278 | − | 0.996215i | \(-0.472295\pi\) | ||||
0.0869278 | + | 0.996215i | \(0.472295\pi\) | |||||||
\(390\) | 14336.6i | 0.0942574i | ||||||||
\(391\) | 388798.i | 2.54314i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27873.8 | −0.180473 | ||||||||
\(394\) | 155031. | 0.998679 | ||||||||
\(395\) | − 13620.6i | − 0.0872975i | ||||||||
\(396\) | 4799.96 | 0.0306089 | ||||||||
\(397\) | 88026.3i | 0.558511i | 0.960217 | + | 0.279255i | \(0.0900876\pi\) | ||||
−0.960217 | + | 0.279255i | \(0.909912\pi\) | |||||||
\(398\) | − 16893.8i | − 0.106650i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 37854.1 | 0.236588 | ||||||||
\(401\) | 264600. | 1.64551 | 0.822755 | − | 0.568397i | \(-0.192436\pi\) | ||||
0.822755 | + | 0.568397i | \(0.192436\pi\) | |||||||
\(402\) | 28684.2i | 0.177497i | ||||||||
\(403\) | 137757. | 0.848211 | ||||||||
\(404\) | 72886.6i | 0.446566i | ||||||||
\(405\) | − 10790.8i | − 0.0657873i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5422.67 | −0.0327359 | ||||||||
\(408\) | 43917.8 | 0.263827 | ||||||||
\(409\) | 140171.i | 0.837937i | 0.908001 | + | 0.418968i | \(0.137608\pi\) | ||||
−0.908001 | + | 0.418968i | \(0.862392\pi\) | |||||||
\(410\) | −14646.5 | −0.0871298 | ||||||||
\(411\) | 13162.3i | 0.0779200i | ||||||||
\(412\) | 128895.i | 0.759347i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −155978. | −0.910044 | ||||||||
\(415\) | −21715.3 | −0.126087 | ||||||||
\(416\) | 34433.4i | 0.198973i | ||||||||
\(417\) | 78075.3 | 0.448995 | ||||||||
\(418\) | − 12261.8i | − 0.0701781i | ||||||||
\(419\) | − 319409.i | − 1.81936i | −0.415306 | − | 0.909682i | \(-0.636325\pi\) | ||||
0.415306 | − | 0.909682i | \(-0.363675\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 315726. | 1.78134 | 0.890670 | − | 0.454651i | \(-0.150236\pi\) | ||||
0.890670 | + | 0.454651i | \(0.150236\pi\) | |||||||
\(422\) | −8606.40 | −0.0483277 | ||||||||
\(423\) | − 104734.i | − 0.585341i | ||||||||
\(424\) | −18378.0 | −0.102227 | ||||||||
\(425\) | 249465.i | 1.38112i | ||||||||
\(426\) | − 44361.2i | − 0.244447i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 164411. | 0.897518 | ||||||||
\(429\) | 8779.31 | 0.0477030 | ||||||||
\(430\) | − 20420.4i | − 0.110440i | ||||||||
\(431\) | 168531. | 0.907245 | 0.453623 | − | 0.891194i | \(-0.350131\pi\) | ||||
0.453623 | + | 0.891194i | \(0.350131\pi\) | |||||||
\(432\) | 41474.7i | 0.222237i | ||||||||
\(433\) | − 17104.3i | − 0.0912284i | −0.998959 | − | 0.0456142i | \(-0.985476\pi\) | ||||
0.998959 | − | 0.0456142i | \(-0.0145245\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23392.7 | 0.123624 | ||||||||
\(436\) | −114062. | −0.600023 | ||||||||
\(437\) | 398456.i | 2.08649i | ||||||||
\(438\) | −122293. | −0.637459 | ||||||||
\(439\) | − 221981.i | − 1.15183i | −0.817511 | − | 0.575913i | \(-0.804647\pi\) | ||||
0.817511 | − | 0.575913i | \(-0.195353\pi\) | |||||||
\(440\) | 1314.10i | 0.00678769i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −226922. | −1.16154 | ||||||||
\(443\) | 34230.7 | 0.174425 | 0.0872124 | − | 0.996190i | \(-0.472204\pi\) | ||||
0.0872124 | + | 0.996190i | \(0.472204\pi\) | |||||||
\(444\) | − 19904.7i | − 0.100969i | ||||||||
\(445\) | 36850.5 | 0.186090 | ||||||||
\(446\) | 119090.i | 0.598695i | ||||||||
\(447\) | − 68613.4i | − 0.343395i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −187206. | −0.928598 | −0.464299 | − | 0.885679i | \(-0.653694\pi\) | ||||
−0.464299 | + | 0.885679i | \(0.653694\pi\) | |||||||
\(450\) | −100080. | −0.494224 | ||||||||
\(451\) | 8969.13i | 0.0440958i | ||||||||
\(452\) | −82437.6 | −0.403505 | ||||||||
\(453\) | − 9946.56i | − 0.0484704i | ||||||||
\(454\) | − 260751.i | − 1.26507i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 45008.7 | 0.216454 | ||||||||
\(457\) | 147845. | 0.707904 | 0.353952 | − | 0.935264i | \(-0.384838\pi\) | ||||
0.353952 | + | 0.935264i | \(0.384838\pi\) | |||||||
\(458\) | − 67777.9i | − 0.323115i | ||||||||
\(459\) | −273325. | −1.29734 | ||||||||
\(460\) | − 42702.5i | − 0.201808i | ||||||||
\(461\) | 73979.5i | 0.348105i | 0.984736 | + | 0.174052i | \(0.0556862\pi\) | ||||
−0.984736 | + | 0.174052i | \(0.944314\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −66987.3 | −0.312486 | −0.156243 | − | 0.987719i | \(-0.549938\pi\) | ||||
−0.156243 | + | 0.987719i | \(0.549938\pi\) | |||||||
\(464\) | 56184.5 | 0.260964 | ||||||||
\(465\) | 19297.6i | 0.0892476i | ||||||||
\(466\) | 99979.6 | 0.460405 | ||||||||
\(467\) | − 232034.i | − 1.06394i | −0.846763 | − | 0.531970i | \(-0.821452\pi\) | ||||
0.846763 | − | 0.531970i | \(-0.178548\pi\) | |||||||
\(468\) | − 91036.7i | − 0.415647i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 28673.4 | 0.129803 | ||||||||
\(471\) | 191222. | 0.861979 | ||||||||
\(472\) | − 64590.1i | − 0.289922i | ||||||||
\(473\) | −12504.9 | −0.0558931 | ||||||||
\(474\) | − 30616.3i | − 0.136269i | ||||||||
\(475\) | 255662.i | 1.13313i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 48588.7 | 0.213549 | ||||||||
\(478\) | −40711.1 | −0.178179 | ||||||||
\(479\) | − 220049.i | − 0.959065i | −0.877524 | − | 0.479532i | \(-0.840806\pi\) | ||||
0.877524 | − | 0.479532i | \(-0.159194\pi\) | |||||||
\(480\) | −4823.58 | −0.0209357 | ||||||||
\(481\) | 102847.i | 0.444531i | ||||||||
\(482\) | − 21213.0i | − 0.0913079i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −116323. | −0.496565 | ||||||||
\(485\) | −36888.2 | −0.156821 | ||||||||
\(486\) | − 172724.i | − 0.731272i | ||||||||
\(487\) | 139656. | 0.588847 | 0.294423 | − | 0.955675i | \(-0.404872\pi\) | ||||
0.294423 | + | 0.955675i | \(0.404872\pi\) | |||||||
\(488\) | 132013.i | 0.554341i | ||||||||
\(489\) | − 54140.8i | − 0.226416i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −284872. | −1.18164 | −0.590821 | − | 0.806802i | \(-0.701196\pi\) | ||||
−0.590821 | + | 0.806802i | \(0.701196\pi\) | |||||||
\(492\) | −32922.4 | −0.136007 | ||||||||
\(493\) | 370265.i | 1.52342i | ||||||||
\(494\) | −232559. | −0.952970 | ||||||||
\(495\) | − 3474.27i | − 0.0141792i | ||||||||
\(496\) | 46348.8i | 0.188397i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −48811.6 | −0.196818 | ||||||||
\(499\) | −313573. | −1.25933 | −0.629663 | − | 0.776869i | \(-0.716807\pi\) | ||||
−0.629663 | + | 0.776869i | \(0.716807\pi\) | |||||||
\(500\) | − 56351.7i | − 0.225407i | ||||||||
\(501\) | −62586.1 | −0.249346 | ||||||||
\(502\) | − 128453.i | − 0.509725i | ||||||||
\(503\) | 192865.i | 0.762285i | 0.924516 | + | 0.381143i | \(0.124469\pi\) | ||||
−0.924516 | + | 0.381143i | \(0.875531\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 52756.2 | 0.206867 | ||||||||
\(506\) | −26149.8 | −0.102133 | ||||||||
\(507\) | − 35077.4i | − 0.136462i | ||||||||
\(508\) | −16933.6 | −0.0656179 | ||||||||
\(509\) | − 173256.i | − 0.668734i | −0.942443 | − | 0.334367i | \(-0.891477\pi\) | ||||
0.942443 | − | 0.334367i | \(-0.108523\pi\) | |||||||
\(510\) | − 31788.2i | − 0.122215i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11585.2 | −0.0441942 | ||||||||
\(513\) | −280115. | −1.06439 | ||||||||
\(514\) | 146309.i | 0.553789i | ||||||||
\(515\) | 93295.5 | 0.351760 | ||||||||
\(516\) | − 45901.0i | − 0.172394i | ||||||||
\(517\) | − 17558.8i | − 0.0656922i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 207786. | 0.771403 | ||||||||
\(520\) | 24923.3 | 0.0921721 | ||||||||
\(521\) | − 168311.i | − 0.620064i | −0.950726 | − | 0.310032i | \(-0.899660\pi\) | ||||
0.950726 | − | 0.310032i | \(-0.100340\pi\) | |||||||
\(522\) | −148543. | −0.545144 | ||||||||
\(523\) | − 452722.i | − 1.65512i | −0.561380 | − | 0.827558i | \(-0.689729\pi\) | ||||
0.561380 | − | 0.827558i | \(-0.310271\pi\) | |||||||
\(524\) | 48457.2i | 0.176480i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 254089. | 0.918362 | ||||||||
\(527\) | −305447. | −1.09980 | ||||||||
\(528\) | 2953.83i | 0.0105954i | ||||||||
\(529\) | 569916. | 2.03657 | ||||||||
\(530\) | 13302.3i | 0.0473558i | ||||||||
\(531\) | 170766.i | 0.605638i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 170110. | 0.598790 | ||||||||
\(534\) | 82832.5 | 0.290481 | ||||||||
\(535\) | − 119003.i | − 0.415766i | ||||||||
\(536\) | 49866.0 | 0.173570 | ||||||||
\(537\) | 91356.8i | 0.316805i | ||||||||
\(538\) | 67214.1i | 0.232218i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 30019.9 | 0.102949 | ||||||||
\(541\) | −14472.4 | −0.0494477 | −0.0247238 | − | 0.999694i | \(-0.507871\pi\) | ||||
−0.0247238 | + | 0.999694i | \(0.507871\pi\) | |||||||
\(542\) | − 313442.i | − 1.06699i | ||||||||
\(543\) | −98471.7 | −0.333973 | ||||||||
\(544\) | − 76348.7i | − 0.257991i | ||||||||
\(545\) | 82559.4i | 0.277954i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −370524. | −1.23835 | −0.619173 | − | 0.785255i | \(-0.712532\pi\) | ||||
−0.619173 | + | 0.785255i | \(0.712532\pi\) | |||||||
\(548\) | 22882.0 | 0.0761962 | ||||||||
\(549\) | − 349022.i | − 1.15800i | ||||||||
\(550\) | −16778.5 | −0.0554663 | ||||||||
\(551\) | 379463.i | 1.24987i | ||||||||
\(552\) | − 95986.6i | − 0.315016i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 20145.1 | 0.0656373 | ||||||||
\(555\) | −14407.2 | −0.0467730 | ||||||||
\(556\) | − 135730.i | − 0.439062i | ||||||||
\(557\) | −437281. | −1.40945 | −0.704727 | − | 0.709479i | \(-0.748930\pi\) | ||||
−0.704727 | + | 0.709479i | \(0.748930\pi\) | |||||||
\(558\) | − 122539.i | − 0.393555i | ||||||||
\(559\) | 237170.i | 0.758990i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19466.2 | −0.0618523 | ||||||||
\(562\) | −255150. | −0.807836 | ||||||||
\(563\) | − 4062.71i | − 0.0128174i | −0.999979 | − | 0.00640869i | \(-0.997960\pi\) | ||||
0.999979 | − | 0.00640869i | \(-0.00203996\pi\) | |||||||
\(564\) | 64452.1 | 0.202618 | ||||||||
\(565\) | 59669.4i | 0.186919i | ||||||||
\(566\) | 204918.i | 0.639656i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −77119.6 | −0.239039 | ||||||||
\(569\) | 433364. | 1.33853 | 0.669266 | − | 0.743023i | \(-0.266609\pi\) | ||||
0.669266 | + | 0.743023i | \(0.266609\pi\) | |||||||
\(570\) | − 32577.8i | − 0.100270i | ||||||||
\(571\) | 47636.6 | 0.146106 | 0.0730530 | − | 0.997328i | \(-0.476726\pi\) | ||||
0.0730530 | + | 0.997328i | \(0.476726\pi\) | |||||||
\(572\) | − 15262.4i | − 0.0466477i | ||||||||
\(573\) | 53500.0i | 0.162946i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 545230. | 1.64909 | ||||||||
\(576\) | 30629.6 | 0.0923200 | ||||||||
\(577\) | 24131.0i | 0.0724809i | 0.999343 | + | 0.0362404i | \(0.0115382\pi\) | ||||
−0.999343 | + | 0.0362404i | \(0.988462\pi\) | |||||||
\(578\) | 266918. | 0.798956 | ||||||||
\(579\) | − 241811.i | − 0.721304i | ||||||||
\(580\) | − 40667.0i | − 0.120889i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −82917.3 | −0.244793 | ||||||||
\(583\) | 8145.93 | 0.0239665 | ||||||||
\(584\) | 212599.i | 0.623356i | ||||||||
\(585\) | −65893.5 | −0.192544 | ||||||||
\(586\) | 252205.i | 0.734442i | ||||||||
\(587\) | − 680260.i | − 1.97423i | −0.160003 | − | 0.987117i | \(-0.551150\pi\) | ||||
0.160003 | − | 0.987117i | \(-0.448850\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −313034. | −0.902320 | ||||||||
\(590\) | −46751.1 | −0.134304 | ||||||||
\(591\) | − 252233.i | − 0.722149i | ||||||||
\(592\) | −34603.2 | −0.0987354 | ||||||||
\(593\) | − 352622.i | − 1.00277i | −0.865225 | − | 0.501383i | \(-0.832825\pi\) | ||||
0.865225 | − | 0.501383i | \(-0.167175\pi\) | |||||||
\(594\) | − 18383.4i | − 0.0521017i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −119281. | −0.335798 | ||||||||
\(597\) | −27486.0 | −0.0771193 | ||||||||
\(598\) | 495961.i | 1.38690i | ||||||||
\(599\) | −382596. | −1.06632 | −0.533159 | − | 0.846015i | \(-0.678995\pi\) | ||||
−0.533159 | + | 0.846015i | \(0.678995\pi\) | |||||||
\(600\) | − 61588.0i | − 0.171078i | ||||||||
\(601\) | − 8474.87i | − 0.0234630i | −0.999931 | − | 0.0117315i | \(-0.996266\pi\) | ||||
0.999931 | − | 0.0117315i | \(-0.00373434\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −131838. | −0.362582 | ||||||||
\(604\) | −17291.6 | −0.0473981 | ||||||||
\(605\) | 84196.2i | 0.230029i | ||||||||
\(606\) | 118585. | 0.322913 | ||||||||
\(607\) | 222052.i | 0.602668i | 0.953519 | + | 0.301334i | \(0.0974319\pi\) | ||||
−0.953519 | + | 0.301334i | \(0.902568\pi\) | |||||||
\(608\) | − 78245.2i | − 0.211666i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 95552.6 | 0.256793 | ||||||||
\(611\) | −333023. | −0.892055 | ||||||||
\(612\) | 201854.i | 0.538933i | ||||||||
\(613\) | 13140.4 | 0.0349694 | 0.0174847 | − | 0.999847i | \(-0.494434\pi\) | ||||
0.0174847 | + | 0.999847i | \(0.494434\pi\) | |||||||
\(614\) | 319924.i | 0.848615i | ||||||||
\(615\) | 23829.7i | 0.0630039i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −235797. | −0.619394 | −0.309697 | − | 0.950835i | \(-0.600228\pi\) | ||||
−0.309697 | + | 0.950835i | \(0.600228\pi\) | |||||||
\(618\) | 209710. | 0.549087 | ||||||||
\(619\) | 617960.i | 1.61279i | 0.591374 | + | 0.806397i | \(0.298586\pi\) | ||||
−0.591374 | + | 0.806397i | \(0.701414\pi\) | |||||||
\(620\) | 33547.8 | 0.0872732 | ||||||||
\(621\) | 597380.i | 1.54906i | ||||||||
\(622\) | 184821.i | 0.477718i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 56022.7 | 0.143878 | ||||||||
\(625\) | 328881. | 0.841935 | ||||||||
\(626\) | 5540.49i | 0.0141384i | ||||||||
\(627\) | −19949.8 | −0.0507461 | ||||||||
\(628\) | − 332430.i | − 0.842909i | ||||||||
\(629\) | − 228041.i | − 0.576384i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 453628. | 1.13931 | 0.569653 | − | 0.821885i | \(-0.307077\pi\) | ||||
0.569653 | + | 0.821885i | \(0.307077\pi\) | |||||||
\(632\) | −53224.9 | −0.133254 | ||||||||
\(633\) | 14002.5i | 0.0349460i | ||||||||
\(634\) | 243672. | 0.606217 | ||||||||
\(635\) | 12256.8i | 0.0303968i | ||||||||
\(636\) | 29900.8i | 0.0739211i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −24903.4 | −0.0611810 | ||||||||
\(639\) | 203892. | 0.499343 | ||||||||
\(640\) | 8385.54i | 0.0204725i | ||||||||
\(641\) | −144938. | −0.352750 | −0.176375 | − | 0.984323i | \(-0.556437\pi\) | ||||
−0.176375 | + | 0.984323i | \(0.556437\pi\) | |||||||
\(642\) | − 267494.i | − 0.648999i | ||||||||
\(643\) | − 238775.i | − 0.577520i | −0.957401 | − | 0.288760i | \(-0.906757\pi\) | ||||
0.957401 | − | 0.288760i | \(-0.0932430\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33223.7 | −0.0798599 | ||||||||
\(646\) | 515650. | 1.23563 | ||||||||
\(647\) | 33276.6i | 0.0794933i | 0.999210 | + | 0.0397466i | \(0.0126551\pi\) | ||||
−0.999210 | + | 0.0397466i | \(0.987345\pi\) | |||||||
\(648\) | −42166.9 | −0.100420 | ||||||||
\(649\) | 28629.1i | 0.0679701i | ||||||||
\(650\) | 318224.i | 0.753193i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −94121.0 | −0.221407 | ||||||||
\(653\) | 77564.4 | 0.181901 | 0.0909507 | − | 0.995855i | \(-0.471009\pi\) | ||||
0.0909507 | + | 0.995855i | \(0.471009\pi\) | |||||||
\(654\) | 185577.i | 0.433879i | ||||||||
\(655\) | 35073.9 | 0.0817526 | ||||||||
\(656\) | 57233.9i | 0.132998i | ||||||||
\(657\) | − 562080.i | − 1.30217i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −762599. | −1.75600 | −0.878001 | − | 0.478658i | \(-0.841123\pi\) | ||||
−0.878001 | + | 0.478658i | \(0.841123\pi\) | |||||||
\(660\) | 2138.02 | 0.00490821 | ||||||||
\(661\) | − 499668.i | − 1.14361i | −0.820389 | − | 0.571805i | \(-0.806243\pi\) | ||||
0.820389 | − | 0.571805i | \(-0.193757\pi\) | |||||||
\(662\) | 256318. | 0.584876 | ||||||||
\(663\) | 369199.i | 0.839912i | ||||||||
\(664\) | 84856.5i | 0.192464i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 91485.5 | 0.206255 | ||||||||
\(667\) | 809252. | 1.81900 | ||||||||
\(668\) | 108803.i | 0.243830i | ||||||||
\(669\) | 193758. | 0.432919 | ||||||||
\(670\) | − 36093.6i | − 0.0804046i | ||||||||
\(671\) | − 58513.8i | − 0.129961i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 601790. | 1.32866 | 0.664332 | − | 0.747438i | \(-0.268716\pi\) | ||||
0.664332 | + | 0.747438i | \(0.268716\pi\) | |||||||
\(674\) | 74097.8 | 0.163112 | ||||||||
\(675\) | 383297.i | 0.841256i | ||||||||
\(676\) | −60980.2 | −0.133443 | ||||||||
\(677\) | 161904.i | 0.353248i | 0.984278 | + | 0.176624i | \(0.0565177\pi\) | ||||
−0.984278 | + | 0.176624i | \(0.943482\pi\) | |||||||
\(678\) | 134125.i | 0.291776i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −55262.1 | −0.119512 | ||||||||
\(681\) | −424238. | −0.914777 | ||||||||
\(682\) | − 20543.8i | − 0.0441683i | ||||||||
\(683\) | −13434.3 | −0.0287987 | −0.0143994 | − | 0.999896i | \(-0.504584\pi\) | ||||
−0.0143994 | + | 0.999896i | \(0.504584\pi\) | |||||||
\(684\) | 206868.i | 0.442162i | ||||||||
\(685\) | − 16562.3i | − 0.0352971i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −110274. | −0.233646 | ||||||||
\(688\) | −79796.5 | −0.168580 | ||||||||
\(689\) | − 154497.i | − 0.325448i | ||||||||
\(690\) | −69476.3 | −0.145928 | ||||||||
\(691\) | 246175.i | 0.515571i | 0.966202 | + | 0.257785i | \(0.0829927\pi\) | ||||
−0.966202 | + | 0.257785i | \(0.917007\pi\) | |||||||
\(692\) | − 361225.i | − 0.754337i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 454417. | 0.943487 | ||||||||
\(695\) | −98242.9 | −0.203391 | ||||||||
\(696\) | − 91411.2i | − 0.188704i | ||||||||
\(697\) | −377182. | −0.776399 | ||||||||
\(698\) | − 51251.7i | − 0.105196i | ||||||||
\(699\) | − 162665.i | − 0.332920i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 750473. | 1.52721 | 0.763605 | − | 0.645683i | \(-0.223427\pi\) | ||||
0.763605 | + | 0.645683i | \(0.223427\pi\) | |||||||
\(702\) | −348661. | −0.707505 | ||||||||
\(703\) | − 233706.i | − 0.472889i | ||||||||
\(704\) | 5135.07 | 0.0103610 | ||||||||
\(705\) | − 46651.2i | − 0.0938609i | ||||||||
\(706\) | 37418.6i | 0.0750720i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −105087. | −0.209644 | ||||||||
\(709\) | −595336. | −1.18432 | −0.592161 | − | 0.805820i | \(-0.701725\pi\) | ||||
−0.592161 | + | 0.805820i | \(0.701725\pi\) | |||||||
\(710\) | 55820.1i | 0.110732i | ||||||||
\(711\) | 140718. | 0.278363 | ||||||||
\(712\) | − 144000.i | − 0.284055i | ||||||||
\(713\) | 667584.i | 1.31319i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11047.1 | −0.0216091 | ||||||||
\(716\) | 158819. | 0.309797 | ||||||||
\(717\) | 66236.3i | 0.128842i | ||||||||
\(718\) | 304720. | 0.591088 | ||||||||
\(719\) | 26728.2i | 0.0517026i | 0.999666 | + | 0.0258513i | \(0.00822964\pi\) | ||||
−0.999666 | + | 0.0258513i | \(0.991770\pi\) | |||||||
\(720\) | − 22170.1i | − 0.0427663i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 159855. | 0.306656 | ||||||||
\(723\) | −34513.3 | −0.0660252 | ||||||||
\(724\) | 171188.i | 0.326585i | ||||||||
\(725\) | 519241. | 0.987855 | ||||||||
\(726\) | 189256.i | 0.359068i | ||||||||
\(727\) | 514869.i | 0.974154i | 0.873359 | + | 0.487077i | \(0.161937\pi\) | ||||
−0.873359 | + | 0.487077i | \(0.838063\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −130073. | −0.244755 | ||||||||
\(730\) | 153882. | 0.288764 | ||||||||
\(731\) | − 525873.i | − 0.984116i | ||||||||
\(732\) | 214783. | 0.400846 | ||||||||
\(733\) | − 241789.i | − 0.450016i | −0.974357 | − | 0.225008i | \(-0.927759\pi\) | ||||
0.974357 | − | 0.225008i | \(-0.0722409\pi\) | |||||||
\(734\) | − 199198.i | − 0.369737i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −166868. | −0.308047 | ||||||||
\(737\) | −22102.7 | −0.0406922 | ||||||||
\(738\) | − 151318.i | − 0.277828i | ||||||||
\(739\) | −671522. | −1.22962 | −0.614811 | − | 0.788675i | \(-0.710768\pi\) | ||||
−0.614811 | + | 0.788675i | \(0.710768\pi\) | |||||||
\(740\) | 25046.2i | 0.0457382i | ||||||||
\(741\) | 378370.i | 0.689097i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −134542. | −0.243714 | −0.121857 | − | 0.992548i | \(-0.538885\pi\) | ||||
−0.121857 | + | 0.992548i | \(0.538885\pi\) | |||||||
\(744\) | 75408.7 | 0.136231 | ||||||||
\(745\) | 86337.0i | 0.155555i | ||||||||
\(746\) | −540381. | −0.971006 | ||||||||
\(747\) | − 224347.i | − 0.402050i | ||||||||
\(748\) | 33841.0i | 0.0604840i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −91683.4 | −0.162993 | ||||||||
\(751\) | 446561. | 0.791774 | 0.395887 | − | 0.918299i | \(-0.370437\pi\) | ||||
0.395887 | + | 0.918299i | \(0.370437\pi\) | |||||||
\(752\) | − 112047.i | − 0.198136i | ||||||||
\(753\) | −208991. | −0.368584 | ||||||||
\(754\) | 472320.i | 0.830795i | ||||||||
\(755\) | 12515.9i | 0.0219567i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −939360. | −1.63923 | −0.819616 | − | 0.572913i | \(-0.805813\pi\) | ||||
−0.819616 | + | 0.572913i | \(0.805813\pi\) | |||||||
\(758\) | −212074. | −0.369104 | ||||||||
\(759\) | 42545.4i | 0.0738531i | ||||||||
\(760\) | −56634.9 | −0.0980520 | ||||||||
\(761\) | − 991448.i | − 1.71199i | −0.516986 | − | 0.855994i | \(-0.672946\pi\) | ||||
0.516986 | − | 0.855994i | \(-0.327054\pi\) | |||||||
\(762\) | 27550.7i | 0.0474486i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 93007.0 | 0.159341 | ||||||||
\(765\) | 146105. | 0.249655 | ||||||||
\(766\) | − 363840.i | − 0.620087i | ||||||||
\(767\) | 542983. | 0.922987 | ||||||||
\(768\) | 18849.0i | 0.0319570i | ||||||||
\(769\) | − 180922.i | − 0.305942i | −0.988231 | − | 0.152971i | \(-0.951116\pi\) | ||||
0.988231 | − | 0.152971i | \(-0.0488841\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 238042. | 0.400447 | ||||||||
\(772\) | −420375. | −0.705347 | ||||||||
\(773\) | − 19270.4i | − 0.0322502i | −0.999870 | − | 0.0161251i | \(-0.994867\pi\) | ||||
0.999870 | − | 0.0161251i | \(-0.00513300\pi\) | |||||||
\(774\) | 210970. | 0.352158 | ||||||||
\(775\) | 428342.i | 0.713161i | ||||||||
\(776\) | 144147.i | 0.239377i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −74410.3 | −0.122935 | ||||||||
\(779\) | −386551. | −0.636988 | ||||||||
\(780\) | − 40549.9i | − 0.0666501i | ||||||||
\(781\) | 34182.7 | 0.0560408 | ||||||||
\(782\) | − 1.09969e6i | − 1.79827i | ||||||||
\(783\) | 568905.i | 0.927931i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −240617. | −0.390469 | ||||||||
\(786\) | 78839.0 | 0.127613 | ||||||||
\(787\) | 278163.i | 0.449107i | 0.974462 | + | 0.224553i | \(0.0720923\pi\) | ||||
−0.974462 | + | 0.224553i | \(0.927908\pi\) | |||||||
\(788\) | −438494. | −0.706173 | ||||||||
\(789\) | − 413398.i | − 0.664071i | ||||||||
\(790\) | 38524.8i | 0.0617286i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −13576.3 | −0.0216437 | ||||||||
\(793\) | −1.10978e6 | −1.76478 | ||||||||
\(794\) | − 248976.i | − 0.394927i | ||||||||
\(795\) | 21642.6 | 0.0342432 | ||||||||
\(796\) | 47783.0i | 0.0754131i | ||||||||
\(797\) | − 60214.6i | − 0.0947950i | −0.998876 | − | 0.0473975i | \(-0.984907\pi\) | ||||
0.998876 | − | 0.0473975i | \(-0.0150927\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 738406. | 1.15665 | ||||||||
\(800\) | −107068. | −0.167293 | ||||||||
\(801\) | 380713.i | 0.593380i | ||||||||
\(802\) | −748400. | −1.16355 | ||||||||
\(803\) | − 94233.1i | − 0.146141i | ||||||||
\(804\) | − 81131.2i | − 0.125509i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −389636. | −0.599775 | ||||||||
\(807\) | 109356. | 0.167918 | ||||||||
\(808\) | − 206155.i | − 0.315770i | ||||||||
\(809\) | 70473.9 | 0.107679 | 0.0538395 | − | 0.998550i | \(-0.482854\pi\) | ||||
0.0538395 | + | 0.998550i | \(0.482854\pi\) | |||||||
\(810\) | 30520.9i | 0.0465187i | ||||||||
\(811\) | − 1.08434e6i | − 1.64863i | −0.566133 | − | 0.824314i | \(-0.691561\pi\) | ||||
0.566133 | − | 0.824314i | \(-0.308439\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −509966. | −0.771542 | ||||||||
\(814\) | 15337.6 | 0.0231478 | ||||||||
\(815\) | 68125.9i | 0.102565i | ||||||||
\(816\) | −124218. | −0.186554 | ||||||||
\(817\) | − 538936.i | − 0.807408i | ||||||||
\(818\) | − 396463.i | − 0.592511i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 41426.6 | 0.0616101 | ||||||||
\(821\) | −647690. | −0.960906 | −0.480453 | − | 0.877020i | \(-0.659528\pi\) | ||||
−0.480453 | + | 0.877020i | \(0.659528\pi\) | |||||||
\(822\) | − 37228.7i | − 0.0550978i | ||||||||
\(823\) | 1.07902e6 | 1.59306 | 0.796529 | − | 0.604600i | \(-0.206667\pi\) | ||||
0.796529 | + | 0.604600i | \(0.206667\pi\) | |||||||
\(824\) | − 364569.i | − 0.536940i | ||||||||
\(825\) | 27298.4i | 0.0401079i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9026.16 | 0.0131975 | 0.00659875 | − | 0.999978i | \(-0.497900\pi\) | ||||
0.00659875 | + | 0.999978i | \(0.497900\pi\) | |||||||
\(828\) | 441172. | 0.643499 | ||||||||
\(829\) | − 756024.i | − 1.10009i | −0.835136 | − | 0.550043i | \(-0.814611\pi\) | ||||
0.835136 | − | 0.550043i | \(-0.185389\pi\) | |||||||
\(830\) | 61420.2 | 0.0891569 | ||||||||
\(831\) | − 32775.8i | − 0.0474626i | ||||||||
\(832\) | − 97392.5i | − 0.140695i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −220830. | −0.317487 | ||||||||
\(835\) | 78752.7 | 0.112952 | ||||||||
\(836\) | 34681.6i | 0.0496234i | ||||||||
\(837\) | −469312. | −0.669901 | ||||||||
\(838\) | 903426.i | 1.28648i | ||||||||
\(839\) | 654438.i | 0.929704i | 0.885388 | + | 0.464852i | \(0.153893\pi\) | ||||
−0.885388 | + | 0.464852i | \(0.846107\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 63396.2 | 0.0896337 | ||||||||
\(842\) | −893009. | −1.25960 | ||||||||
\(843\) | 415125.i | 0.584150i | ||||||||
\(844\) | 24342.6 | 0.0341729 | ||||||||
\(845\) | 44138.2i | 0.0618160i | ||||||||
\(846\) | 296234.i | 0.413898i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 51981.0 | 0.0722857 | ||||||||
\(849\) | 333398. | 0.462538 | ||||||||
\(850\) | − 705594.i | − 0.976600i | ||||||||
\(851\) | −498407. | −0.688216 | ||||||||
\(852\) | 125472.i | 0.172850i | ||||||||
\(853\) | − 123790.i | − 0.170133i | −0.996375 | − | 0.0850664i | \(-0.972890\pi\) | ||||
0.996375 | − | 0.0850664i | \(-0.0271102\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 149734. | 0.204827 | ||||||||
\(856\) | −465025. | −0.634641 | ||||||||
\(857\) | − 173232.i | − 0.235866i | −0.993022 | − | 0.117933i | \(-0.962373\pi\) | ||||
0.993022 | − | 0.117933i | \(-0.0376268\pi\) | |||||||
\(858\) | −24831.6 | −0.0337311 | ||||||||
\(859\) | − 267312.i | − 0.362270i | −0.983458 | − | 0.181135i | \(-0.942023\pi\) | ||||
0.983458 | − | 0.181135i | \(-0.0579770\pi\) | |||||||
\(860\) | 57757.7i | 0.0780932i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −476677. | −0.641519 | ||||||||
\(863\) | 1.23904e6 | 1.66366 | 0.831830 | − | 0.555030i | \(-0.187293\pi\) | ||||
0.831830 | + | 0.555030i | \(0.187293\pi\) | |||||||
\(864\) | − 117308.i | − 0.157145i | ||||||||
\(865\) | −261459. | −0.349439 | ||||||||
\(866\) | 48378.4i | 0.0645083i | ||||||||
\(867\) | − 434272.i | − 0.577728i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23591.6 | 0.0312404 | ||||||||
\(870\) | −66164.6 | −0.0874152 | ||||||||
\(871\) | 419204.i | 0.552572i | ||||||||
\(872\) | 322616. | 0.424280 | ||||||||
\(873\) | − 381103.i | − 0.500051i | ||||||||
\(874\) | − 1.12700e6i | − 1.47537i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 345896. | 0.450752 | ||||||||
\(877\) | 697922. | 0.907419 | 0.453710 | − | 0.891150i | \(-0.350100\pi\) | ||||
0.453710 | + | 0.891150i | \(0.350100\pi\) | |||||||
\(878\) | 627857.i | 0.814464i | ||||||||
\(879\) | 410333. | 0.531078 | ||||||||
\(880\) | − 3716.83i | − 0.00479962i | ||||||||
\(881\) | 1.44660e6i | 1.86378i | 0.362735 | + | 0.931892i | \(0.381843\pi\) | ||||
−0.362735 | + | 0.931892i | \(0.618157\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −539049. | −0.691364 | −0.345682 | − | 0.938352i | \(-0.612352\pi\) | ||||
−0.345682 | + | 0.938352i | \(0.612352\pi\) | |||||||
\(884\) | 641833. | 0.821330 | ||||||||
\(885\) | 76063.3i | 0.0971155i | ||||||||
\(886\) | −96819.1 | −0.123337 | ||||||||
\(887\) | 983274.i | 1.24976i | 0.780720 | + | 0.624881i | \(0.214853\pi\) | ||||
−0.780720 | + | 0.624881i | \(0.785147\pi\) | |||||||
\(888\) | 56298.9i | 0.0713960i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −104229. | −0.131586 | ||||||||
\(891\) | 18690.2 | 0.0235428 | ||||||||
\(892\) | − 336838.i | − 0.423341i | ||||||||
\(893\) | 756748. | 0.948961 | ||||||||
\(894\) | 194068.i | 0.242817i | ||||||||
\(895\) | − 114955.i | − 0.143510i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 806921. | 1.00287 | ||||||||
\(898\) | 529499. | 0.656618 | ||||||||
\(899\) | 635762.i | 0.786639i | ||||||||
\(900\) | 283070. | 0.349469 | ||||||||
\(901\) | 342564.i | 0.421980i | ||||||||
\(902\) | − 25368.5i | − 0.0311804i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 233169. | 0.285321 | ||||||||
\(905\) | 123908. | 0.151287 | ||||||||
\(906\) | 28133.1i | 0.0342737i | ||||||||
\(907\) | 293081. | 0.356266 | 0.178133 | − | 0.984006i | \(-0.442994\pi\) | ||||
0.178133 | + | 0.984006i | \(0.442994\pi\) | |||||||
\(908\) | 737516.i | 0.894540i | ||||||||
\(909\) | 545041.i | 0.659631i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.39546e6 | 1.68143 | 0.840716 | − | 0.541477i | \(-0.182135\pi\) | ||||
0.840716 | + | 0.541477i | \(0.182135\pi\) | |||||||
\(912\) | −127304. | −0.153056 | ||||||||
\(913\) | − 37612.0i | − 0.0451217i | ||||||||
\(914\) | −418169. | −0.500564 | ||||||||
\(915\) | − 155463.i | − 0.185688i | ||||||||
\(916\) | 191705.i | 0.228477i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 773081. | 0.917360 | ||||||||
\(919\) | −860318. | −1.01866 | −0.509328 | − | 0.860572i | \(-0.670106\pi\) | ||||
−0.509328 | + | 0.860572i | \(0.670106\pi\) | |||||||
\(920\) | 120781.i | 0.142700i | ||||||||
\(921\) | 520512. | 0.613637 | ||||||||
\(922\) | − 209246.i | − 0.246147i | ||||||||
\(923\) | − 648314.i | − 0.760995i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −319793. | −0.373754 | ||||||||
\(926\) | 189469. | 0.220961 | ||||||||
\(927\) | 963864.i | 1.12165i | ||||||||
\(928\) | −158914. | −0.184529 | ||||||||
\(929\) | 1.08037e6i | 1.25182i | 0.779894 | + | 0.625911i | \(0.215273\pi\) | ||||
−0.779894 | + | 0.625911i | \(0.784727\pi\) | |||||||
\(930\) | − 54581.8i | − 0.0631076i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −282785. | −0.325555 | ||||||||
\(933\) | 300701. | 0.345440 | ||||||||
\(934\) | 656290.i | 0.752319i | ||||||||
\(935\) | 24494.5 | 0.0280186 | ||||||||
\(936\) | 257491.i | 0.293907i | ||||||||
\(937\) | − 659462.i | − 0.751122i | −0.926798 | − | 0.375561i | \(-0.877450\pi\) | ||||
0.926798 | − | 0.375561i | \(-0.122550\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9014.29 | 0.0102235 | ||||||||
\(940\) | −81100.7 | −0.0917844 | ||||||||
\(941\) | 890694.i | 1.00589i | 0.864319 | + | 0.502944i | \(0.167750\pi\) | ||||
−0.864319 | + | 0.502944i | \(0.832250\pi\) | |||||||
\(942\) | −540858. | −0.609511 | ||||||||
\(943\) | 824368.i | 0.927038i | ||||||||
\(944\) | 182688.i | 0.205006i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35369.2 | 0.0395224 | ||||||||
\(947\) | 1.52254e6 | 1.69773 | 0.848863 | − | 0.528613i | \(-0.177288\pi\) | ||||
0.848863 | + | 0.528613i | \(0.177288\pi\) | |||||||
\(948\) | 86596.1i | 0.0963566i | ||||||||
\(949\) | −1.78724e6 | −1.98450 | ||||||||
\(950\) | − 723121.i | − 0.801242i | ||||||||
\(951\) | − 396451.i | − 0.438358i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −464150. | −0.511061 | −0.255530 | − | 0.966801i | \(-0.582250\pi\) | ||||
−0.255530 | + | 0.966801i | \(0.582250\pi\) | |||||||
\(954\) | −137430. | −0.151002 | ||||||||
\(955\) | − 67319.6i | − 0.0738133i | ||||||||
\(956\) | 115148. | 0.125992 | ||||||||
\(957\) | 40517.4i | 0.0442402i | ||||||||
\(958\) | 622392.i | 0.678161i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13643.1 | 0.0148038 | ||||||||
\(961\) | 399056. | 0.432103 | ||||||||
\(962\) | − 290895.i | − 0.314331i | ||||||||
\(963\) | 1.22945e6 | 1.32574 | ||||||||
\(964\) | 59999.5i | 0.0645645i | ||||||||
\(965\) | 304273.i | 0.326745i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 61596.4 | 0.0658723 | 0.0329361 | − | 0.999457i | \(-0.489514\pi\) | ||||
0.0329361 | + | 0.999457i | \(0.489514\pi\) | |||||||
\(968\) | 329012. | 0.351124 | ||||||||
\(969\) | − 838954.i | − 0.893492i | ||||||||
\(970\) | 104336. | 0.110889 | ||||||||
\(971\) | 772298.i | 0.819118i | 0.912284 | + | 0.409559i | \(0.134317\pi\) | ||||
−0.912284 | + | 0.409559i | \(0.865683\pi\) | |||||||
\(972\) | 488536.i | 0.517088i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −395007. | −0.416378 | ||||||||
\(975\) | 517746. | 0.544637 | ||||||||
\(976\) | − 373389.i | − 0.391978i | ||||||||
\(977\) | 1.00334e6 | 1.05114 | 0.525570 | − | 0.850750i | \(-0.323852\pi\) | ||||
0.525570 | + | 0.850750i | \(0.323852\pi\) | |||||||
\(978\) | 153133.i | 0.160100i | ||||||||
\(979\) | 63826.9i | 0.0665945i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −852946. | −0.886306 | ||||||||
\(982\) | 805739. | 0.835548 | ||||||||
\(983\) | − 523081.i | − 0.541330i | −0.962674 | − | 0.270665i | \(-0.912756\pi\) | ||||
0.962674 | − | 0.270665i | \(-0.0872435\pi\) | |||||||
\(984\) | 93118.7 | 0.0961716 | ||||||||
\(985\) | 317387.i | 0.327127i | ||||||||
\(986\) | − 1.04727e6i | − 1.07722i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 657776. | 0.673852 | ||||||||
\(989\) | −1.14935e6 | −1.17506 | ||||||||
\(990\) | 9826.72i | 0.0100262i | ||||||||
\(991\) | −1.67549e6 | −1.70606 | −0.853029 | − | 0.521863i | \(-0.825237\pi\) | ||||
−0.853029 | + | 0.521863i | \(0.825237\pi\) | |||||||
\(992\) | − 131094.i | − 0.133217i | ||||||||
\(993\) | − 417026.i | − 0.422926i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34585.9 | 0.0349344 | ||||||||
\(996\) | 138060. | 0.139171 | ||||||||
\(997\) | − 656503.i | − 0.660460i | −0.943901 | − | 0.330230i | \(-0.892874\pi\) | ||||
0.943901 | − | 0.330230i | \(-0.107126\pi\) | |||||||
\(998\) | 886919. | 0.890477 | ||||||||
\(999\) | − 350380.i | − 0.351082i |
(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 | 98.5.b.b.97.2 | 4 | ||
3.2 | odd | 2 | 882.5.c.b.685.4 | 4 | |||
4.3 | odd | 2 | 784.5.c.b.97.2 | 4 | |||
7.2 | even | 3 | 98.5.d.a.31.2 | 4 | |||
7.3 | odd | 6 | 98.5.d.a.19.2 | 4 | |||
7.4 | even | 3 | 14.5.d.a.5.2 | yes | 4 | ||
7.5 | odd | 6 | 14.5.d.a.3.2 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 98.5.b.b.97.1 | 4 | ||
21.5 | even | 6 | 126.5.n.a.73.1 | 4 | |||
21.11 | odd | 6 | 126.5.n.a.19.1 | 4 | |||
21.20 | even | 2 | 882.5.c.b.685.3 | 4 | |||
28.11 | odd | 6 | 112.5.s.b.33.1 | 4 | |||
28.19 | even | 6 | 112.5.s.b.17.1 | 4 | |||
28.27 | even | 2 | 784.5.c.b.97.3 | 4 | |||
35.4 | even | 6 | 350.5.k.a.201.1 | 4 | |||
35.12 | even | 12 | 350.5.i.a.199.1 | 8 | |||
35.18 | odd | 12 | 350.5.i.a.299.1 | 8 | |||
35.19 | odd | 6 | 350.5.k.a.101.1 | 4 | |||
35.32 | odd | 12 | 350.5.i.a.299.4 | 8 | |||
35.33 | even | 12 | 350.5.i.a.199.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.5.d.a.3.2 | ✓ | 4 | 7.5 | odd | 6 | ||
14.5.d.a.5.2 | yes | 4 | 7.4 | even | 3 | ||
98.5.b.b.97.1 | 4 | 7.6 | odd | 2 | inner | ||
98.5.b.b.97.2 | 4 | 1.1 | even | 1 | trivial | ||
98.5.d.a.19.2 | 4 | 7.3 | odd | 6 | |||
98.5.d.a.31.2 | 4 | 7.2 | even | 3 | |||
112.5.s.b.17.1 | 4 | 28.19 | even | 6 | |||
112.5.s.b.33.1 | 4 | 28.11 | odd | 6 | |||
126.5.n.a.19.1 | 4 | 21.11 | odd | 6 | |||
126.5.n.a.73.1 | 4 | 21.5 | even | 6 | |||
350.5.i.a.199.1 | 8 | 35.12 | even | 12 | |||
350.5.i.a.199.4 | 8 | 35.33 | even | 12 | |||
350.5.i.a.299.1 | 8 | 35.18 | odd | 12 | |||
350.5.i.a.299.4 | 8 | 35.32 | odd | 12 | |||
350.5.k.a.101.1 | 4 | 35.19 | odd | 6 | |||
350.5.k.a.201.1 | 4 | 35.4 | even | 6 | |||
784.5.c.b.97.2 | 4 | 4.3 | odd | 2 | |||
784.5.c.b.97.3 | 4 | 28.27 | even | 2 | |||
882.5.c.b.685.3 | 4 | 21.20 | even | 2 | |||
882.5.c.b.685.4 | 4 | 3.2 | odd | 2 |