Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,5,Mod(26,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, 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("27.26");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.79098900326\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} + 6 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 26.2 | ||
Root | \(2.44949i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.26 |
Dual form | 27.5.b.b.26.1 |
$q$-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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.34847i | 1.83712i | 0.395285 | + | 0.918559i | \(0.370646\pi\) | ||||
−0.395285 | + | 0.918559i | \(0.629354\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −38.0000 | −2.37500 | ||||||||
\(5\) | 14.6969i | 0.587878i | 0.955824 | + | 0.293939i | \(0.0949662\pi\) | ||||
−0.955824 | + | 0.293939i | \(0.905034\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.0000 | 0.346939 | 0.173469 | − | 0.984839i | \(-0.444502\pi\) | ||||
0.173469 | + | 0.984839i | \(0.444502\pi\) | |||||||
\(8\) | − 161.666i | − 2.52604i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −108.000 | −1.08000 | ||||||||
\(11\) | 161.666i | 1.33609i | 0.744123 | + | 0.668043i | \(0.232868\pi\) | ||||
−0.744123 | + | 0.668043i | \(0.767132\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 95.0000 | 0.562130 | 0.281065 | − | 0.959689i | \(-0.409312\pi\) | ||||
0.281065 | + | 0.959689i | \(0.409312\pi\) | |||||||
\(14\) | 124.924i | 0.637367i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 580.000 | 2.26562 | ||||||||
\(17\) | 308.636i | 1.06794i | 0.845502 | + | 0.533972i | \(0.179301\pi\) | ||||
−0.845502 | + | 0.533972i | \(0.820699\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 209.000 | 0.578947 | 0.289474 | − | 0.957186i | \(-0.406520\pi\) | ||||
0.289474 | + | 0.957186i | \(0.406520\pi\) | |||||||
\(20\) | − 558.484i | − 1.39621i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1188.00 | −2.45455 | ||||||||
\(23\) | − 867.119i | − 1.63917i | −0.572960 | − | 0.819584i | \(-0.694205\pi\) | ||||
0.572960 | − | 0.819584i | \(-0.305795\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 409.000 | 0.654400 | ||||||||
\(26\) | 698.105i | 1.03270i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −646.000 | −0.823980 | ||||||||
\(29\) | − 323.333i | − 0.384462i | −0.981350 | − | 0.192231i | \(-0.938428\pi\) | ||||
0.981350 | − | 0.192231i | \(-0.0615723\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 950.000 | 0.988554 | 0.494277 | − | 0.869305i | \(-0.335433\pi\) | ||||
0.494277 | + | 0.869305i | \(0.335433\pi\) | |||||||
\(32\) | 1675.45i | 1.63618i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2268.00 | −1.96194 | ||||||||
\(35\) | 249.848i | 0.203958i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1177.00 | −0.859752 | −0.429876 | − | 0.902888i | \(-0.641443\pi\) | ||||
−0.429876 | + | 0.902888i | \(0.641443\pi\) | |||||||
\(38\) | 1535.83i | 1.06359i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2376.00 | 1.48500 | ||||||||
\(41\) | − 2145.75i | − 1.27647i | −0.769840 | − | 0.638237i | \(-0.779664\pi\) | ||||
0.769840 | − | 0.638237i | \(-0.220336\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1430.00 | 0.773391 | 0.386696 | − | 0.922207i | \(-0.373616\pi\) | ||||
0.386696 | + | 0.922207i | \(0.373616\pi\) | |||||||
\(44\) | − 6143.32i | − 3.17320i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6372.00 | 3.01134 | ||||||||
\(47\) | 1572.57i | 0.711893i | 0.934506 | + | 0.355947i | \(0.115842\pi\) | ||||
−0.934506 | + | 0.355947i | \(0.884158\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2112.00 | −0.879633 | ||||||||
\(50\) | 3005.52i | 1.20221i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3610.00 | −1.33506 | ||||||||
\(53\) | 2909.99i | 1.03595i | 0.855395 | + | 0.517977i | \(0.173315\pi\) | ||||
−0.855395 | + | 0.517977i | \(0.826685\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2376.00 | −0.785455 | ||||||||
\(56\) | − 2748.33i | − 0.876380i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2376.00 | 0.706302 | ||||||||
\(59\) | 2131.06i | 0.612197i | 0.952000 | + | 0.306098i | \(0.0990236\pi\) | ||||
−0.952000 | + | 0.306098i | \(0.900976\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1441.00 | −0.387261 | −0.193631 | − | 0.981074i | \(-0.562026\pi\) | ||||
−0.193631 | + | 0.981074i | \(0.562026\pi\) | |||||||
\(62\) | 6981.05i | 1.81609i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3032.00 | −0.740234 | ||||||||
\(65\) | 1396.21i | 0.330464i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3497.00 | 0.779015 | 0.389508 | − | 0.921023i | \(-0.372645\pi\) | ||||
0.389508 | + | 0.921023i | \(0.372645\pi\) | |||||||
\(68\) | − 11728.2i | − 2.53637i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1836.00 | −0.374694 | ||||||||
\(71\) | − 1940.00i | − 0.384843i | −0.981312 | − | 0.192422i | \(-0.938366\pi\) | ||||
0.981312 | − | 0.192422i | \(-0.0616342\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9025.00 | −1.69356 | −0.846782 | − | 0.531940i | \(-0.821463\pi\) | ||||
−0.846782 | + | 0.531940i | \(0.821463\pi\) | |||||||
\(74\) | − 8649.15i | − 1.57946i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7942.00 | −1.37500 | ||||||||
\(77\) | 2748.33i | 0.463540i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5273.00 | 0.844897 | 0.422448 | − | 0.906387i | \(-0.361171\pi\) | ||||
0.422448 | + | 0.906387i | \(0.361171\pi\) | |||||||
\(80\) | 8524.22i | 1.33191i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 15768.0 | 2.34503 | ||||||||
\(83\) | − 6143.32i | − 0.891758i | −0.895093 | − | 0.445879i | \(-0.852891\pi\) | ||||
0.895093 | − | 0.445879i | \(-0.147109\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4536.00 | −0.627820 | ||||||||
\(86\) | 10508.3i | 1.42081i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 26136.0 | 3.37500 | ||||||||
\(89\) | − 11155.0i | − 1.40828i | −0.710062 | − | 0.704139i | \(-0.751333\pi\) | ||||
0.710062 | − | 0.704139i | \(-0.248667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1615.00 | 0.195025 | ||||||||
\(92\) | 32950.5i | 3.89302i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −11556.0 | −1.30783 | ||||||||
\(95\) | 3071.66i | 0.340350i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2809.00 | −0.298544 | −0.149272 | − | 0.988796i | \(-0.547693\pi\) | ||||
−0.149272 | + | 0.988796i | \(0.547693\pi\) | |||||||
\(98\) | − 15520.0i | − 1.61599i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −15542.0 | −1.55420 | ||||||||
\(101\) | − 6231.50i | − 0.610872i | −0.952213 | − | 0.305436i | \(-0.901198\pi\) | ||||
0.952213 | − | 0.305436i | \(-0.0988021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16385.0 | 1.54444 | 0.772222 | − | 0.635353i | \(-0.219145\pi\) | ||||
0.772222 | + | 0.635353i | \(0.219145\pi\) | |||||||
\(104\) | − 15358.3i | − 1.41996i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −21384.0 | −1.90317 | ||||||||
\(107\) | − 7274.98i | − 0.635425i | −0.948187 | − | 0.317713i | \(-0.897085\pi\) | ||||
0.948187 | − | 0.317713i | \(-0.102915\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1946.00 | 0.163791 | 0.0818955 | − | 0.996641i | \(-0.473903\pi\) | ||||
0.0818955 | + | 0.996641i | \(0.473903\pi\) | |||||||
\(110\) | − 17460.0i | − 1.44297i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9860.00 | 0.786033 | ||||||||
\(113\) | 15358.3i | 1.20278i | 0.798956 | + | 0.601390i | \(0.205386\pi\) | ||||
−0.798956 | + | 0.601390i | \(0.794614\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12744.0 | 0.963629 | ||||||||
\(116\) | 12286.6i | 0.913098i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15660.0 | −1.12468 | ||||||||
\(119\) | 5246.81i | 0.370511i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11495.0 | −0.785124 | ||||||||
\(122\) | − 10589.1i | − 0.711445i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −36100.0 | −2.34781 | ||||||||
\(125\) | 15196.6i | 0.972585i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6878.00 | 0.426437 | 0.213218 | − | 0.977005i | \(-0.431605\pi\) | ||||
0.213218 | + | 0.977005i | \(0.431605\pi\) | |||||||
\(128\) | 4526.66i | 0.276285i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10260.0 | −0.607101 | ||||||||
\(131\) | 6143.32i | 0.357981i | 0.983851 | + | 0.178991i | \(0.0572832\pi\) | ||||
−0.983851 | + | 0.178991i | \(0.942717\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3553.00 | 0.200859 | ||||||||
\(134\) | 25697.6i | 1.43114i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 49896.0 | 2.69766 | ||||||||
\(137\) | 1925.30i | 0.102579i | 0.998684 | + | 0.0512893i | \(0.0163331\pi\) | ||||
−0.998684 | + | 0.0512893i | \(0.983667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10049.0 | 0.520108 | 0.260054 | − | 0.965594i | \(-0.416260\pi\) | ||||
0.260054 | + | 0.965594i | \(0.416260\pi\) | |||||||
\(140\) | − 9494.22i | − 0.484399i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14256.0 | 0.707003 | ||||||||
\(143\) | 15358.3i | 0.751054i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4752.00 | 0.226017 | ||||||||
\(146\) | − 66319.9i | − 3.11127i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 44726.0 | 2.04191 | ||||||||
\(149\) | − 25690.2i | − 1.15717i | −0.815623 | − | 0.578583i | \(-0.803606\pi\) | ||||
0.815623 | − | 0.578583i | \(-0.196394\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13015.0 | −0.570808 | −0.285404 | − | 0.958407i | \(-0.592128\pi\) | ||||
−0.285404 | + | 0.958407i | \(0.592128\pi\) | |||||||
\(152\) | − 33788.3i | − 1.46244i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −20196.0 | −0.851577 | ||||||||
\(155\) | 13962.1i | 0.581148i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18742.0 | −0.760355 | −0.380178 | − | 0.924913i | \(-0.624137\pi\) | ||||
−0.380178 | + | 0.924913i | \(0.624137\pi\) | |||||||
\(158\) | 38748.5i | 1.55217i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −24624.0 | −0.961875 | ||||||||
\(161\) | − 14741.0i | − 0.568691i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13471.0 | −0.507019 | −0.253510 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253510 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(164\) | 81538.6i | 3.03163i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 45144.0 | 1.63826 | ||||||||
\(167\) | − 42841.6i | − 1.53615i | −0.640362 | − | 0.768073i | \(-0.721216\pi\) | ||||
0.640362 | − | 0.768073i | \(-0.278784\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19536.0 | −0.684010 | ||||||||
\(170\) | − 33332.7i | − 1.15338i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −54340.0 | −1.83680 | ||||||||
\(173\) | 13256.6i | 0.442936i | 0.975168 | + | 0.221468i | \(0.0710849\pi\) | ||||
−0.975168 | + | 0.221468i | \(0.928915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6953.00 | 0.227037 | ||||||||
\(176\) | 93766.5i | 3.02707i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 81972.0 | 2.58717 | ||||||||
\(179\) | 21340.0i | 0.666020i | 0.942923 | + | 0.333010i | \(0.108064\pi\) | ||||
−0.942923 | + | 0.333010i | \(0.891936\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 57071.0 | 1.74204 | 0.871020 | − | 0.491247i | \(-0.163459\pi\) | ||||
0.871020 | + | 0.491247i | \(0.163459\pi\) | |||||||
\(182\) | 11867.8i | 0.358283i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −140184. | −4.14060 | ||||||||
\(185\) | − 17298.3i | − 0.505429i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −49896.0 | −1.42686 | ||||||||
\(188\) | − 59757.8i | − 1.69075i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −22572.0 | −0.625263 | ||||||||
\(191\) | − 41195.5i | − 1.12923i | −0.825354 | − | 0.564616i | \(-0.809024\pi\) | ||||
0.825354 | − | 0.564616i | \(-0.190976\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −59449.0 | −1.59599 | −0.797995 | − | 0.602665i | \(-0.794106\pi\) | ||||
−0.797995 | + | 0.602665i | \(0.794106\pi\) | |||||||
\(194\) | − 20641.9i | − 0.548460i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 80256.0 | 2.08913 | ||||||||
\(197\) | − 19620.4i | − 0.505563i | −0.967523 | − | 0.252782i | \(-0.918655\pi\) | ||||
0.967523 | − | 0.252782i | \(-0.0813455\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17215.0 | −0.434711 | −0.217356 | − | 0.976092i | \(-0.569743\pi\) | ||||
−0.217356 | + | 0.976092i | \(0.569743\pi\) | |||||||
\(200\) | − 66121.5i | − 1.65304i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 45792.0 | 1.12224 | ||||||||
\(203\) | − 5496.65i | − 0.133385i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31536.0 | 0.750410 | ||||||||
\(206\) | 120405.i | 2.83732i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 55100.0 | 1.27358 | ||||||||
\(209\) | 33788.3i | 0.773523i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20273.0 | 0.455358 | 0.227679 | − | 0.973736i | \(-0.426886\pi\) | ||||
0.227679 | + | 0.973736i | \(0.426886\pi\) | |||||||
\(212\) | − 110580.i | − 2.46039i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 53460.0 | 1.16735 | ||||||||
\(215\) | 21016.6i | 0.454659i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16150.0 | 0.342968 | ||||||||
\(218\) | 14300.1i | 0.300903i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 90288.0 | 1.86545 | ||||||||
\(221\) | 29320.4i | 0.600323i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −47962.0 | −0.964467 | −0.482234 | − | 0.876043i | \(-0.660174\pi\) | ||||
−0.482234 | + | 0.876043i | \(0.660174\pi\) | |||||||
\(224\) | 28482.7i | 0.567655i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −112860. | −2.20965 | ||||||||
\(227\) | − 1293.33i | − 0.0250991i | −0.999921 | − | 0.0125495i | \(-0.996005\pi\) | ||||
0.999921 | − | 0.0125495i | \(-0.00399475\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24530.0 | 0.467764 | 0.233882 | − | 0.972265i | \(-0.424857\pi\) | ||||
0.233882 | + | 0.972265i | \(0.424857\pi\) | |||||||
\(230\) | 93648.9i | 1.77030i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −52272.0 | −0.971165 | ||||||||
\(233\) | 102820.i | 1.89393i | 0.321331 | + | 0.946967i | \(0.395870\pi\) | ||||
−0.321331 | + | 0.946967i | \(0.604130\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23112.0 | −0.418506 | ||||||||
\(236\) | − 80980.1i | − 1.45397i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −38556.0 | −0.680672 | ||||||||
\(239\) | 73073.2i | 1.27927i | 0.768679 | + | 0.639635i | \(0.220914\pi\) | ||||
−0.768679 | + | 0.639635i | \(0.779086\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 38807.0 | 0.668153 | 0.334077 | − | 0.942546i | \(-0.391576\pi\) | ||||
0.334077 | + | 0.942546i | \(0.391576\pi\) | |||||||
\(242\) | − 84470.7i | − 1.44236i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 54758.0 | 0.919746 | ||||||||
\(245\) | − 31039.9i | − 0.517117i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19855.0 | 0.325444 | ||||||||
\(248\) | − 153583.i | − 2.49712i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −111672. | −1.78675 | ||||||||
\(251\) | − 106788.i | − 1.69502i | −0.530779 | − | 0.847510i | \(-0.678101\pi\) | ||||
0.530779 | − | 0.847510i | \(-0.321899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 140184. | 2.19007 | ||||||||
\(254\) | 50542.8i | 0.783415i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −81776.0 | −1.24780 | ||||||||
\(257\) | − 17489.4i | − 0.264794i | −0.991197 | − | 0.132397i | \(-0.957733\pi\) | ||||
0.991197 | − | 0.132397i | \(-0.0422673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20009.0 | −0.298281 | ||||||||
\(260\) | − 53055.9i | − 0.784851i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −45144.0 | −0.657654 | ||||||||
\(263\) | 90591.9i | 1.30972i | 0.755751 | + | 0.654859i | \(0.227272\pi\) | ||||
−0.755751 | + | 0.654859i | \(0.772728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −42768.0 | −0.609014 | ||||||||
\(266\) | 26109.1i | 0.369002i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −132886. | −1.85016 | ||||||||
\(269\) | − 121558.i | − 1.67989i | −0.542673 | − | 0.839944i | \(-0.682588\pi\) | ||||
0.542673 | − | 0.839944i | \(-0.317412\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −73519.0 | −1.00106 | −0.500531 | − | 0.865719i | \(-0.666862\pi\) | ||||
−0.500531 | + | 0.865719i | \(0.666862\pi\) | |||||||
\(272\) | 179009.i | 2.41956i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14148.0 | −0.188449 | ||||||||
\(275\) | 66121.5i | 0.874334i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 139850. | 1.82265 | 0.911324 | − | 0.411689i | \(-0.135061\pi\) | ||||
0.911324 | + | 0.411689i | \(0.135061\pi\) | |||||||
\(278\) | 73844.8i | 0.955499i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 40392.0 | 0.515204 | ||||||||
\(281\) | − 120603.i | − 1.52738i | −0.645586 | − | 0.763688i | \(-0.723387\pi\) | ||||
0.645586 | − | 0.763688i | \(-0.276613\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 52934.0 | 0.660940 | 0.330470 | − | 0.943817i | \(-0.392793\pi\) | ||||
0.330470 | + | 0.943817i | \(0.392793\pi\) | |||||||
\(284\) | 73719.8i | 0.914003i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −112860. | −1.37977 | ||||||||
\(287\) | − 36477.8i | − 0.442858i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11735.0 | −0.140504 | ||||||||
\(290\) | 34919.9i | 0.415219i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 342950. | 4.02221 | ||||||||
\(293\) | 89078.1i | 1.03761i | 0.854891 | + | 0.518807i | \(0.173624\pi\) | ||||
−0.854891 | + | 0.518807i | \(0.826376\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31320.0 | −0.359897 | ||||||||
\(296\) | 190281.i | 2.17176i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 188784. | 2.12585 | ||||||||
\(299\) | − 82376.3i | − 0.921425i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24310.0 | 0.268319 | ||||||||
\(302\) | − 95640.3i | − 1.04864i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 121220. | 1.31168 | ||||||||
\(305\) | − 21178.3i | − 0.227662i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −135178. | −1.43426 | −0.717132 | − | 0.696937i | \(-0.754546\pi\) | ||||
−0.717132 | + | 0.696937i | \(0.754546\pi\) | |||||||
\(308\) | − 104436.i | − 1.10091i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −102600. | −1.06764 | ||||||||
\(311\) | − 160211.i | − 1.65643i | −0.560412 | − | 0.828214i | \(-0.689357\pi\) | ||||
0.560412 | − | 0.828214i | \(-0.310643\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −62857.0 | −0.641601 | −0.320800 | − | 0.947147i | \(-0.603952\pi\) | ||||
−0.320800 | + | 0.947147i | \(0.603952\pi\) | |||||||
\(314\) | − 137725.i | − 1.39686i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −200374. | −2.00663 | ||||||||
\(317\) | 49058.4i | 0.488197i | 0.969751 | + | 0.244098i | \(0.0784919\pi\) | ||||
−0.969751 | + | 0.244098i | \(0.921508\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 52272.0 | 0.513674 | ||||||||
\(320\) | − 44561.1i | − 0.435167i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 108324. | 1.04475 | ||||||||
\(323\) | 64504.9i | 0.618283i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38855.0 | 0.367858 | ||||||||
\(326\) | − 98991.2i | − 0.931454i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −346896. | −3.22442 | ||||||||
\(329\) | 26733.7i | 0.246983i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 81665.0 | 0.745384 | 0.372692 | − | 0.927955i | \(-0.378435\pi\) | ||||
0.372692 | + | 0.927955i | \(0.378435\pi\) | |||||||
\(332\) | 233446.i | 2.11793i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 314820. | 2.82208 | ||||||||
\(335\) | 51395.2i | 0.457966i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −145705. | −1.28296 | −0.641482 | − | 0.767138i | \(-0.721680\pi\) | ||||
−0.641482 | + | 0.767138i | \(0.721680\pi\) | |||||||
\(338\) | − 143560.i | − 1.25661i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 172368. | 1.49107 | ||||||||
\(341\) | 153583.i | 1.32079i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −76721.0 | −0.652118 | ||||||||
\(344\) | − 231183.i | − 1.95361i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −97416.0 | −0.813726 | ||||||||
\(347\) | 105877.i | 0.879309i | 0.898167 | + | 0.439655i | \(0.144899\pi\) | ||||
−0.898167 | + | 0.439655i | \(0.855101\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 40535.0 | 0.332797 | 0.166398 | − | 0.986059i | \(-0.446786\pi\) | ||||
0.166398 | + | 0.986059i | \(0.446786\pi\) | |||||||
\(350\) | 51093.9i | 0.417093i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −270864. | −2.18608 | ||||||||
\(353\) | 8406.65i | 0.0674642i | 0.999431 | + | 0.0337321i | \(0.0107393\pi\) | ||||
−0.999431 | + | 0.0337321i | \(0.989261\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28512.0 | 0.226241 | ||||||||
\(356\) | 423889.i | 3.34466i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −156816. | −1.22356 | ||||||||
\(359\) | 19267.7i | 0.149500i | 0.997202 | + | 0.0747499i | \(0.0238158\pi\) | ||||
−0.997202 | + | 0.0747499i | \(0.976184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −86640.0 | −0.664820 | ||||||||
\(362\) | 419384.i | 3.20033i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −61370.0 | −0.463184 | ||||||||
\(365\) | − 132640.i | − 0.995608i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −119719. | −0.888855 | −0.444428 | − | 0.895815i | \(-0.646593\pi\) | ||||
−0.444428 | + | 0.895815i | \(0.646593\pi\) | |||||||
\(368\) | − 502929.i | − 3.71374i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 127116. | 0.928532 | ||||||||
\(371\) | 49469.9i | 0.359412i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1319.00 | 0.00948041 | 0.00474021 | − | 0.999989i | \(-0.498491\pi\) | ||||
0.00474021 | + | 0.999989i | \(0.498491\pi\) | |||||||
\(374\) | − 366659.i | − 2.62132i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 254232. | 1.79827 | ||||||||
\(377\) | − 30716.6i | − 0.216118i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −164887. | −1.14791 | −0.573955 | − | 0.818887i | \(-0.694592\pi\) | ||||
−0.573955 | + | 0.818887i | \(0.694592\pi\) | |||||||
\(380\) | − 116723.i | − 0.808332i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 302724. | 2.07453 | ||||||||
\(383\) | 29511.5i | 0.201184i | 0.994928 | + | 0.100592i | \(0.0320736\pi\) | ||||
−0.994928 | + | 0.100592i | \(0.967926\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −40392.0 | −0.272505 | ||||||||
\(386\) | − 436859.i | − 2.93202i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 106742. | 0.709042 | ||||||||
\(389\) | 168941.i | 1.11644i | 0.829692 | + | 0.558222i | \(0.188516\pi\) | ||||
−0.829692 | + | 0.558222i | \(0.811484\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 267624. | 1.75054 | ||||||||
\(392\) | 341439.i | 2.22199i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 144180. | 0.928779 | ||||||||
\(395\) | 77497.0i | 0.496696i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21242.0 | 0.134777 | 0.0673883 | − | 0.997727i | \(-0.478533\pi\) | ||||
0.0673883 | + | 0.997727i | \(0.478533\pi\) | |||||||
\(398\) | − 126504.i | − 0.798616i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 237220. | 1.48263 | ||||||||
\(401\) | − 109463.i | − 0.680735i | −0.940293 | − | 0.340367i | \(-0.889449\pi\) | ||||
0.940293 | − | 0.340367i | \(-0.110551\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 90250.0 | 0.555696 | ||||||||
\(404\) | 236797.i | 1.45082i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 40392.0 | 0.245044 | ||||||||
\(407\) | − 190281.i | − 1.14870i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −302665. | −1.80932 | −0.904660 | − | 0.426133i | \(-0.859875\pi\) | ||||
−0.904660 | + | 0.426133i | \(0.859875\pi\) | |||||||
\(410\) | 231741.i | 1.37859i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −622630. | −3.66805 | ||||||||
\(413\) | 36228.0i | 0.212395i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 90288.0 | 0.524244 | ||||||||
\(416\) | 159168.i | 0.919748i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −248292. | −1.42105 | ||||||||
\(419\) | − 299626.i | − 1.70668i | −0.521355 | − | 0.853340i | \(-0.674573\pi\) | ||||
0.521355 | − | 0.853340i | \(-0.325427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 195479. | 1.10290 | 0.551450 | − | 0.834208i | \(-0.314075\pi\) | ||||
0.551450 | + | 0.834208i | \(0.314075\pi\) | |||||||
\(422\) | 148976.i | 0.836546i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 470448. | 2.61686 | ||||||||
\(425\) | 126232.i | 0.698862i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24497.0 | −0.134356 | ||||||||
\(428\) | 276449.i | 1.50914i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −154440. | −0.835262 | ||||||||
\(431\) | 36374.9i | 0.195816i | 0.995195 | + | 0.0979079i | \(0.0312150\pi\) | ||||
−0.995195 | + | 0.0979079i | \(0.968785\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −173014. | −0.922795 | −0.461398 | − | 0.887193i | \(-0.652652\pi\) | ||||
−0.461398 | + | 0.887193i | \(0.652652\pi\) | |||||||
\(434\) | 118678.i | 0.630072i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −73948.0 | −0.389003 | ||||||||
\(437\) | − 181228.i | − 0.948991i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 115334. | 0.598451 | 0.299225 | − | 0.954182i | \(-0.403272\pi\) | ||||
0.299225 | + | 0.954182i | \(0.403272\pi\) | |||||||
\(440\) | 384119.i | 1.98409i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −215460. | −1.10286 | ||||||||
\(443\) | − 9494.22i | − 0.0483784i | −0.999707 | − | 0.0241892i | \(-0.992300\pi\) | ||||
0.999707 | − | 0.0241892i | \(-0.00770042\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 163944. | 0.827895 | ||||||||
\(446\) | − 352447.i | − 1.77184i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −51544.0 | −0.256816 | ||||||||
\(449\) | − 165296.i | − 0.819919i | −0.912104 | − | 0.409959i | \(-0.865543\pi\) | ||||
0.912104 | − | 0.409959i | \(-0.134457\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 346896. | 1.70548 | ||||||||
\(452\) | − 583615.i | − 2.85660i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9504.00 | 0.0461100 | ||||||||
\(455\) | 23735.6i | 0.114651i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −255574. | −1.22373 | −0.611863 | − | 0.790964i | \(-0.709580\pi\) | ||||
−0.611863 | + | 0.790964i | \(0.709580\pi\) | |||||||
\(458\) | 180258.i | 0.859337i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −484272. | −2.28862 | ||||||||
\(461\) | − 234578.i | − 1.10379i | −0.833915 | − | 0.551893i | \(-0.813906\pi\) | ||||
0.833915 | − | 0.551893i | \(-0.186094\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 155849. | 0.727013 | 0.363506 | − | 0.931592i | \(-0.381579\pi\) | ||||
0.363506 | + | 0.931592i | \(0.381579\pi\) | |||||||
\(464\) | − 187533.i | − 0.871047i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −755568. | −3.47938 | ||||||||
\(467\) | 52864.9i | 0.242401i | 0.992628 | + | 0.121200i | \(0.0386743\pi\) | ||||
−0.992628 | + | 0.121200i | \(0.961326\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 59449.0 | 0.270271 | ||||||||
\(470\) | − 169838.i | − 0.768845i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 344520. | 1.54643 | ||||||||
\(473\) | 231183.i | 1.03332i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 85481.0 | 0.378863 | ||||||||
\(476\) | − 199379.i | − 0.879964i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −536976. | −2.35017 | ||||||||
\(479\) | 87152.8i | 0.379849i | 0.981799 | + | 0.189924i | \(0.0608243\pi\) | ||||
−0.981799 | + | 0.189924i | \(0.939176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −111815. | −0.483292 | ||||||||
\(482\) | 285172.i | 1.22748i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 436810. | 1.86467 | ||||||||
\(485\) | − 41283.7i | − 0.175507i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 109001. | 0.459592 | 0.229796 | − | 0.973239i | \(-0.426194\pi\) | ||||
0.229796 | + | 0.973239i | \(0.426194\pi\) | |||||||
\(488\) | 232961.i | 0.978237i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 228096. | 0.950004 | ||||||||
\(491\) | 191281.i | 0.793429i | 0.917942 | + | 0.396714i | \(0.129850\pi\) | ||||
−0.917942 | + | 0.396714i | \(0.870150\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 99792.0 | 0.410584 | ||||||||
\(494\) | 145904.i | 0.597878i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 551000. | 2.23969 | ||||||||
\(497\) | − 32979.9i | − 0.133517i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43214.0 | 0.173550 | 0.0867748 | − | 0.996228i | \(-0.472344\pi\) | ||||
0.0867748 | + | 0.996228i | \(0.472344\pi\) | |||||||
\(500\) | − 577472.i | − 2.30989i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 784728. | 3.11395 | ||||||||
\(503\) | 80465.7i | 0.318035i | 0.987276 | + | 0.159018i | \(0.0508326\pi\) | ||||
−0.987276 | + | 0.159018i | \(0.949167\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 91584.0 | 0.359118 | ||||||||
\(506\) | 1.03014e6i | 4.02341i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −261364. | −1.01279 | ||||||||
\(509\) | 493567.i | 1.90507i | 0.304430 | + | 0.952535i | \(0.401534\pi\) | ||||
−0.304430 | + | 0.952535i | \(0.598466\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −153425. | −0.587563 | ||||||||
\(512\) | − 528502.i | − 2.01607i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 128520. | 0.486457 | ||||||||
\(515\) | 240809.i | 0.907944i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −254232. | −0.951150 | ||||||||
\(518\) | − 147036.i | − 0.547978i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 225720. | 0.834763 | ||||||||
\(521\) | − 101365.i | − 0.373432i | −0.982414 | − | 0.186716i | \(-0.940216\pi\) | ||||
0.982414 | − | 0.186716i | \(-0.0597844\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38945.0 | 0.142380 | 0.0711899 | − | 0.997463i | \(-0.477320\pi\) | ||||
0.0711899 | + | 0.997463i | \(0.477320\pi\) | |||||||
\(524\) | − 233446.i | − 0.850206i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −665712. | −2.40611 | ||||||||
\(527\) | 293204.i | 1.05572i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −472055. | −1.68687 | ||||||||
\(530\) | − 314279.i | − 1.11883i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −135014. | −0.477041 | ||||||||
\(533\) | − 203847.i | − 0.717545i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 106920. | 0.373552 | ||||||||
\(536\) | − 565347.i | − 1.96782i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 893268. | 3.08615 | ||||||||
\(539\) | − 341439.i | − 1.17527i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 55271.0 | 0.188844 | 0.0944219 | − | 0.995532i | \(-0.469900\pi\) | ||||
0.0944219 | + | 0.995532i | \(0.469900\pi\) | |||||||
\(542\) | − 540252.i | − 1.83907i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −517104. | −1.74735 | ||||||||
\(545\) | 28600.2i | 0.0962890i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 297449. | 0.994118 | 0.497059 | − | 0.867717i | \(-0.334413\pi\) | ||||
0.497059 | + | 0.867717i | \(0.334413\pi\) | |||||||
\(548\) | − 73161.4i | − 0.243624i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −485892. | −1.60625 | ||||||||
\(551\) | − 67576.5i | − 0.222583i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 89641.0 | 0.293127 | ||||||||
\(554\) | 1.02768e6i | 3.34842i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −381862. | −1.23526 | ||||||||
\(557\) | 175437.i | 0.565473i | 0.959198 | + | 0.282736i | \(0.0912422\pi\) | ||||
−0.959198 | + | 0.282736i | \(0.908758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 135850. | 0.434746 | ||||||||
\(560\) | 144912.i | 0.462091i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 886248. | 2.80597 | ||||||||
\(563\) | − 324538.i | − 1.02388i | −0.859022 | − | 0.511939i | \(-0.828927\pi\) | ||||
0.859022 | − | 0.511939i | \(-0.171073\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −225720. | −0.707087 | ||||||||
\(566\) | 388984.i | 1.21422i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −313632. | −0.972129 | ||||||||
\(569\) | 137901.i | 0.425936i | 0.977059 | + | 0.212968i | \(0.0683130\pi\) | ||||
−0.977059 | + | 0.212968i | \(0.931687\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −412015. | −1.26369 | −0.631845 | − | 0.775094i | \(-0.717702\pi\) | ||||
−0.631845 | + | 0.775094i | \(0.717702\pi\) | |||||||
\(572\) | − 583615.i | − 1.78375i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 268056. | 0.813583 | ||||||||
\(575\) | − 354652.i | − 1.07267i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −108097. | −0.324685 | −0.162342 | − | 0.986734i | \(-0.551905\pi\) | ||||
−0.162342 | + | 0.986734i | \(0.551905\pi\) | |||||||
\(578\) | − 86234.3i | − 0.258122i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −180576. | −0.536790 | ||||||||
\(581\) | − 104436.i | − 0.309385i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −470448. | −1.38412 | ||||||||
\(584\) | 1.45904e6i | 4.27800i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −654588. | −1.90622 | ||||||||
\(587\) | − 380430.i | − 1.10408i | −0.833819 | − | 0.552038i | \(-0.813850\pi\) | ||||
0.833819 | − | 0.552038i | \(-0.186150\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 198550. | 0.572320 | ||||||||
\(590\) | − 230154.i | − 0.661172i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −682660. | −1.94787 | ||||||||
\(593\) | 185975.i | 0.528866i | 0.964404 | + | 0.264433i | \(0.0851847\pi\) | ||||
−0.964404 | + | 0.264433i | \(0.914815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −77112.0 | −0.217815 | ||||||||
\(596\) | 976229.i | 2.74827i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 605340. | 1.69277 | ||||||||
\(599\) | 237179.i | 0.661033i | 0.943800 | + | 0.330516i | \(0.107223\pi\) | ||||
−0.943800 | + | 0.330516i | \(0.892777\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 198170. | 0.548642 | 0.274321 | − | 0.961638i | \(-0.411547\pi\) | ||||
0.274321 | + | 0.961638i | \(0.411547\pi\) | |||||||
\(602\) | 178641.i | 0.492934i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 494570. | 1.35567 | ||||||||
\(605\) | − 168941.i | − 0.461557i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −432175. | −1.17296 | −0.586479 | − | 0.809965i | \(-0.699486\pi\) | ||||
−0.586479 | + | 0.809965i | \(0.699486\pi\) | |||||||
\(608\) | 350169.i | 0.947264i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 155628. | 0.418242 | ||||||||
\(611\) | 149394.i | 0.400177i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 107831. | 0.286961 | 0.143480 | − | 0.989653i | \(-0.454171\pi\) | ||||
0.143480 | + | 0.989653i | \(0.454171\pi\) | |||||||
\(614\) | − 993351.i | − 2.63491i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 444312. | 1.17092 | ||||||||
\(617\) | − 329961.i | − 0.866747i | −0.901214 | − | 0.433373i | \(-0.857323\pi\) | ||||
0.901214 | − | 0.433373i | \(-0.142677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 63593.0 | 0.165969 | 0.0829847 | − | 0.996551i | \(-0.473555\pi\) | ||||
0.0829847 | + | 0.996551i | \(0.473555\pi\) | |||||||
\(620\) | − 530559.i | − 1.38023i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.17731e6 | 3.04305 | ||||||||
\(623\) | − 189635.i | − 0.488587i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 32281.0 | 0.0826394 | ||||||||
\(626\) | − 461903.i | − 1.17870i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 712196. | 1.80584 | ||||||||
\(629\) | − 363264.i | − 0.918166i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 530777. | 1.33307 | 0.666536 | − | 0.745473i | \(-0.267776\pi\) | ||||
0.666536 | + | 0.745473i | \(0.267776\pi\) | |||||||
\(632\) | − 852467.i | − 2.13424i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −360504. | −0.896874 | ||||||||
\(635\) | 101086.i | 0.250693i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −200640. | −0.494469 | ||||||||
\(638\) | 384119.i | 0.943680i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −66528.0 | −0.162422 | ||||||||
\(641\) | 419686.i | 1.02143i | 0.859750 | + | 0.510715i | \(0.170619\pi\) | ||||
−0.859750 | + | 0.510715i | \(0.829381\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −494266. | −1.19547 | −0.597735 | − | 0.801694i | \(-0.703933\pi\) | ||||
−0.597735 | + | 0.801694i | \(0.703933\pi\) | |||||||
\(644\) | 560159.i | 1.35064i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −474012. | −1.13586 | ||||||||
\(647\) | 91268.0i | 0.218027i | 0.994040 | + | 0.109013i | \(0.0347691\pi\) | ||||
−0.994040 | + | 0.109013i | \(0.965231\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −344520. | −0.817947 | ||||||||
\(650\) | 285525.i | 0.675798i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 511898. | 1.20417 | ||||||||
\(653\) | − 595608.i | − 1.39680i | −0.715708 | − | 0.698400i | \(-0.753896\pi\) | ||||
0.715708 | − | 0.698400i | \(-0.246104\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −90288.0 | −0.210449 | ||||||||
\(656\) | − 1.24454e6i | − 2.89201i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −196452. | −0.453737 | ||||||||
\(659\) | 452930.i | 1.04294i | 0.853269 | + | 0.521471i | \(0.174617\pi\) | ||||
−0.853269 | + | 0.521471i | \(0.825383\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 804695. | 1.84174 | 0.920870 | − | 0.389869i | \(-0.127480\pi\) | ||||
0.920870 | + | 0.389869i | \(0.127480\pi\) | |||||||
\(662\) | 600113.i | 1.36936i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −993168. | −2.25261 | ||||||||
\(665\) | 52218.2i | 0.118081i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −280368. | −0.630198 | ||||||||
\(668\) | 1.62798e6i | 3.64835i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −377676. | −0.841337 | ||||||||
\(671\) | − 232961.i | − 0.517414i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 308807. | 0.681800 | 0.340900 | − | 0.940100i | \(-0.389268\pi\) | ||||
0.340900 | + | 0.940100i | \(0.389268\pi\) | |||||||
\(674\) | − 1.07071e6i | − 2.35696i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 742368. | 1.62452 | ||||||||
\(677\) | 510381.i | 1.11357i | 0.830657 | + | 0.556784i | \(0.187965\pi\) | ||||
−0.830657 | + | 0.556784i | \(0.812035\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −47753.0 | −0.103576 | ||||||||
\(680\) | 733318.i | 1.58590i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.12860e6 | −2.42645 | ||||||||
\(683\) | 796633.i | 1.70772i | 0.520502 | + | 0.853860i | \(0.325745\pi\) | ||||
−0.520502 | + | 0.853860i | \(0.674255\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28296.0 | −0.0603037 | ||||||||
\(686\) | − 563782.i | − 1.19802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 829400. | 1.75221 | ||||||||
\(689\) | 276449.i | 0.582341i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 759590. | 1.59083 | 0.795414 | − | 0.606067i | \(-0.207254\pi\) | ||||
0.795414 | + | 0.606067i | \(0.207254\pi\) | |||||||
\(692\) | − 503752.i | − 1.05197i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −778032. | −1.61539 | ||||||||
\(695\) | 147690.i | 0.305760i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 662256. | 1.36320 | ||||||||
\(698\) | 297870.i | 0.611387i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −264214. | −0.539212 | ||||||||
\(701\) | 650913.i | 1.32461i | 0.749236 | + | 0.662303i | \(0.230421\pi\) | ||||
−0.749236 | + | 0.662303i | \(0.769579\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −245993. | −0.497751 | ||||||||
\(704\) | − 490172.i | − 0.989016i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −61776.0 | −0.123940 | ||||||||
\(707\) | − 105936.i | − 0.211935i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 183455. | 0.364953 | 0.182477 | − | 0.983210i | \(-0.441589\pi\) | ||||
0.182477 | + | 0.983210i | \(0.441589\pi\) | |||||||
\(710\) | 209520.i | 0.415631i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.80338e6 | −3.55736 | ||||||||
\(713\) | − 823763.i | − 1.62040i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −225720. | −0.441528 | ||||||||
\(716\) | − 810918.i | − 1.58180i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −141588. | −0.274649 | ||||||||
\(719\) | − 412249.i | − 0.797447i | −0.917071 | − | 0.398724i | \(-0.869453\pi\) | ||||
0.917071 | − | 0.398724i | \(-0.130547\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 278545. | 0.535827 | ||||||||
\(722\) | − 636671.i | − 1.22135i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.16870e6 | −4.13735 | ||||||||
\(725\) | − 132243.i | − 0.251592i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −446842. | −0.845445 | −0.422722 | − | 0.906259i | \(-0.638925\pi\) | ||||
−0.422722 | + | 0.906259i | \(0.638925\pi\) | |||||||
\(728\) | − 261091.i | − 0.492640i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 974700. | 1.82905 | ||||||||
\(731\) | 441349.i | 0.825938i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 204314. | 0.380268 | 0.190134 | − | 0.981758i | \(-0.439108\pi\) | ||||
0.190134 | + | 0.981758i | \(0.439108\pi\) | |||||||
\(734\) | − 879751.i | − 1.63293i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.45282e6 | 2.68198 | ||||||||
\(737\) | 565347.i | 1.04083i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 140870. | 0.257946 | 0.128973 | − | 0.991648i | \(-0.458832\pi\) | ||||
0.128973 | + | 0.991648i | \(0.458832\pi\) | |||||||
\(740\) | 657335.i | 1.20039i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −363528. | −0.660283 | ||||||||
\(743\) | − 284547.i | − 0.515439i | −0.966220 | − | 0.257719i | \(-0.917029\pi\) | ||||
0.966220 | − | 0.257719i | \(-0.0829710\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 377568. | 0.680272 | ||||||||
\(746\) | 9692.63i | 0.0174166i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.89605e6 | 3.38880 | ||||||||
\(749\) | − 123675.i | − 0.220454i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −315823. | −0.559969 | −0.279984 | − | 0.960005i | \(-0.590329\pi\) | ||||
−0.279984 | + | 0.960005i | \(0.590329\pi\) | |||||||
\(752\) | 912092.i | 1.61288i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 225720. | 0.397034 | ||||||||
\(755\) | − 191281.i | − 0.335565i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −436561. | −0.761821 | −0.380911 | − | 0.924612i | \(-0.624389\pi\) | ||||
−0.380911 | + | 0.924612i | \(0.624389\pi\) | |||||||
\(758\) | − 1.21167e6i | − 2.10885i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 496584. | 0.859737 | ||||||||
\(761\) | 120118.i | 0.207414i | 0.994608 | + | 0.103707i | \(0.0330705\pi\) | ||||
−0.994608 | + | 0.103707i | \(0.966929\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33082.0 | 0.0568254 | ||||||||
\(764\) | 1.56543e6i | 2.68193i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −216864. | −0.369598 | ||||||||
\(767\) | 202450.i | 0.344134i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 697775. | 1.17995 | 0.589974 | − | 0.807422i | \(-0.299138\pi\) | ||||
0.589974 | + | 0.807422i | \(0.299138\pi\) | |||||||
\(770\) | − 296819.i | − 0.500623i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.25906e6 | 3.79047 | ||||||||
\(773\) | − 679969.i | − 1.13797i | −0.822349 | − | 0.568984i | \(-0.807337\pi\) | ||||
0.822349 | − | 0.568984i | \(-0.192663\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 388550. | 0.646909 | ||||||||
\(776\) | 454121.i | 0.754133i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.24146e6 | −2.05104 | ||||||||
\(779\) | − 448462.i | − 0.739011i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 313632. | 0.514184 | ||||||||
\(782\) | 1.96663e6i | 3.21594i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.22496e6 | −1.99292 | ||||||||
\(785\) | − 275450.i | − 0.446996i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −765823. | −1.23646 | −0.618228 | − | 0.785999i | \(-0.712149\pi\) | ||||
−0.618228 | + | 0.785999i | \(0.712149\pi\) | |||||||
\(788\) | 745576.i | 1.20071i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −569484. | −0.912488 | ||||||||
\(791\) | 261091.i | 0.417291i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −136895. | −0.217691 | ||||||||
\(794\) | 156096.i | 0.247600i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 654170. | 1.03244 | ||||||||
\(797\) | 621916.i | 0.979072i | 0.871983 | + | 0.489536i | \(0.162834\pi\) | ||||
−0.871983 | + | 0.489536i | \(0.837166\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −485352. | −0.760262 | ||||||||
\(800\) | 685259.i | 1.07072i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 804384. | 1.25059 | ||||||||
\(803\) | − 1.45904e6i | − 2.26275i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 216648. | 0.334320 | ||||||||
\(806\) | 663199.i | 1.02088i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.00742e6 | −1.54308 | ||||||||
\(809\) | − 611099.i | − 0.933715i | −0.884333 | − | 0.466857i | \(-0.845386\pi\) | ||||
0.884333 | − | 0.466857i | \(-0.154614\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.19631e6 | −1.81888 | −0.909439 | − | 0.415838i | \(-0.863488\pi\) | ||||
−0.909439 | + | 0.415838i | \(0.863488\pi\) | |||||||
\(812\) | 208873.i | 0.316789i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.39828e6 | 2.11030 | ||||||||
\(815\) | − 197982.i | − 0.298065i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 298870. | 0.447753 | ||||||||
\(818\) | − 2.22412e6i | − 3.32393i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.19837e6 | −1.78222 | ||||||||
\(821\) | 635863.i | 0.943360i | 0.881770 | + | 0.471680i | \(0.156352\pi\) | ||||
−0.881770 | + | 0.471680i | \(0.843648\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 573089. | 0.846101 | 0.423051 | − | 0.906106i | \(-0.360959\pi\) | ||||
0.423051 | + | 0.906106i | \(0.360959\pi\) | |||||||
\(824\) | − 2.64890e6i | − 3.90132i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −266220. | −0.390194 | ||||||||
\(827\) | − 702852.i | − 1.02767i | −0.857890 | − | 0.513834i | \(-0.828225\pi\) | ||||
0.857890 | − | 0.513834i | \(-0.171775\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −590281. | −0.858914 | −0.429457 | − | 0.903087i | \(-0.641295\pi\) | ||||
−0.429457 | + | 0.903087i | \(0.641295\pi\) | |||||||
\(830\) | 663479.i | 0.963099i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −288040. | −0.416108 | ||||||||
\(833\) | − 651839.i | − 0.939399i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 629640. | 0.903066 | ||||||||
\(836\) | − 1.28395e6i | − 1.83712i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.20180e6 | 3.13537 | ||||||||
\(839\) | 617124.i | 0.876696i | 0.898805 | + | 0.438348i | \(0.144436\pi\) | ||||
−0.898805 | + | 0.438348i | \(0.855564\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 602737. | 0.852189 | ||||||||
\(842\) | 1.43647e6i | 2.02616i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −770374. | −1.08148 | ||||||||
\(845\) | − 287119.i | − 0.402114i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −195415. | −0.272390 | ||||||||
\(848\) | 1.68780e6i | 2.34708i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −927612. | −1.28389 | ||||||||
\(851\) | 1.02060e6i | 1.40928i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.07179e6 | −1.47303 | −0.736517 | − | 0.676419i | \(-0.763531\pi\) | ||||
−0.736517 | + | 0.676419i | \(0.763531\pi\) | |||||||
\(854\) | − 180015.i | − 0.246828i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.17612e6 | −1.60511 | ||||||||
\(857\) | − 78187.7i | − 0.106458i | −0.998582 | − | 0.0532288i | \(-0.983049\pi\) | ||||
0.998582 | − | 0.0532288i | \(-0.0169513\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.19862e6 | −1.62440 | −0.812201 | − | 0.583378i | \(-0.801731\pi\) | ||||
−0.812201 | + | 0.583378i | \(0.801731\pi\) | |||||||
\(860\) | − 798632.i | − 1.07982i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −267300. | −0.359736 | ||||||||
\(863\) | 705673.i | 0.947507i | 0.880658 | + | 0.473753i | \(0.157101\pi\) | ||||
−0.880658 | + | 0.473753i | \(0.842899\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −194832. | −0.260392 | ||||||||
\(866\) | − 1.27139e6i | − 1.69528i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −613700. | −0.814548 | ||||||||
\(869\) | 852467.i | 1.12885i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 332215. | 0.437908 | ||||||||
\(872\) | − 314603.i | − 0.413742i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.33175e6 | 1.74341 | ||||||||
\(875\) | 258343.i | 0.337427i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −639265. | −0.831154 | −0.415577 | − | 0.909558i | \(-0.636420\pi\) | ||||
−0.415577 | + | 0.909558i | \(0.636420\pi\) | |||||||
\(878\) | 847528.i | 1.09942i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.37808e6 | −1.77955 | ||||||||
\(881\) | − 230110.i | − 0.296472i | −0.988952 | − | 0.148236i | \(-0.952640\pi\) | ||||
0.988952 | − | 0.148236i | \(-0.0473595\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 711929. | 0.913094 | 0.456547 | − | 0.889699i | \(-0.349086\pi\) | ||||
0.456547 | + | 0.889699i | \(0.349086\pi\) | |||||||
\(884\) | − 1.11417e6i | − 1.42577i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 69768.0 | 0.0888769 | ||||||||
\(887\) | 1.11353e6i | 1.41532i | 0.706554 | + | 0.707659i | \(0.250249\pi\) | ||||
−0.706554 | + | 0.707659i | \(0.749751\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 116926. | 0.147947 | ||||||||
\(890\) | 1.20474e6i | 1.52094i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.82256e6 | 2.29061 | ||||||||
\(893\) | 328668.i | 0.412149i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −313632. | −0.391538 | ||||||||
\(896\) | 76953.2i | 0.0958541i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.21468e6 | 1.50629 | ||||||||
\(899\) | − 307166.i | − 0.380061i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −898128. | −1.10634 | ||||||||
\(902\) | 2.54915e6i | 3.13316i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.48292e6 | 3.03827 | ||||||||
\(905\) | 838769.i | 1.02411i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 762641. | 0.927055 | 0.463528 | − | 0.886082i | \(-0.346583\pi\) | ||||
0.463528 | + | 0.886082i | \(0.346583\pi\) | |||||||
\(908\) | 49146.6i | 0.0596103i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −174420. | −0.210627 | ||||||||
\(911\) | − 927641.i | − 1.11775i | −0.829253 | − | 0.558873i | \(-0.811234\pi\) | ||||
0.829253 | − | 0.558873i | \(-0.188766\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 993168. | 1.19146 | ||||||||
\(914\) | − 1.87808e6i | − 2.24813i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −932140. | −1.11094 | ||||||||
\(917\) | 104436.i | 0.124198i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 615062. | 0.728262 | 0.364131 | − | 0.931348i | \(-0.381366\pi\) | ||||
0.364131 | + | 0.931348i | \(0.381366\pi\) | |||||||
\(920\) | − 2.06028e6i | − 2.43416i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.72379e6 | 2.02779 | ||||||||
\(923\) | − 184300.i | − 0.216332i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −481393. | −0.562621 | ||||||||
\(926\) | 1.14525e6i | 1.33561i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 541728. | 0.629050 | ||||||||
\(929\) | 324626.i | 0.376142i | 0.982155 | + | 0.188071i | \(0.0602235\pi\) | ||||
−0.982155 | + | 0.188071i | \(0.939776\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −441408. | −0.509261 | ||||||||
\(932\) | − 3.90715e6i | − 4.49809i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −388476. | −0.445318 | ||||||||
\(935\) | − 733318.i | − 0.838821i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −176425. | −0.200947 | −0.100473 | − | 0.994940i | \(-0.532036\pi\) | ||||
−0.100473 | + | 0.994940i | \(0.532036\pi\) | |||||||
\(938\) | 436859.i | 0.496519i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 878256. | 0.993952 | ||||||||
\(941\) | 10508.3i | 0.0118673i | 0.999982 | + | 0.00593367i | \(0.00188876\pi\) | ||||
−0.999982 | + | 0.00593367i | \(0.998111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.86062e6 | −2.09235 | ||||||||
\(944\) | 1.23601e6i | 1.38701i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.69884e6 | −1.89832 | ||||||||
\(947\) | 123351.i | 0.137545i | 0.997632 | + | 0.0687724i | \(0.0219082\pi\) | ||||
−0.997632 | + | 0.0687724i | \(0.978092\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −857375. | −0.952003 | ||||||||
\(950\) | 628154.i | 0.696016i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 848232. | 0.935924 | ||||||||
\(953\) | 1.01158e6i | 1.11381i | 0.830575 | + | 0.556907i | \(0.188012\pi\) | ||||
−0.830575 | + | 0.556907i | \(0.811988\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 605448. | 0.663850 | ||||||||
\(956\) | − 2.77678e6i | − 3.03827i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −640440. | −0.697826 | ||||||||
\(959\) | 32730.1i | 0.0355885i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21021.0 | −0.0227618 | ||||||||
\(962\) | − 821669.i | − 0.887865i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.47467e6 | −1.58686 | ||||||||
\(965\) | − 873718.i | − 0.938246i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.59902e6 | 1.71002 | 0.855008 | − | 0.518615i | \(-0.173552\pi\) | ||||
0.855008 | + | 0.518615i | \(0.173552\pi\) | |||||||
\(968\) | 1.85835e6i | 1.98325i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 303372. | 0.322427 | ||||||||
\(971\) | 1.21148e6i | 1.28493i | 0.766316 | + | 0.642464i | \(0.222088\pi\) | ||||
−0.766316 | + | 0.642464i | \(0.777912\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 170833. | 0.180446 | ||||||||
\(974\) | 800990.i | 0.844325i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −835780. | −0.877389 | ||||||||
\(977\) | − 1.10353e6i | − 1.15610i | −0.816000 | − | 0.578052i | \(-0.803813\pi\) | ||||
0.816000 | − | 0.578052i | \(-0.196187\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.80338e6 | 1.88158 | ||||||||
\(980\) | 1.17952e6i | 1.22815i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.40562e6 | −1.45762 | ||||||||
\(983\) | − 881566.i | − 0.912322i | −0.889897 | − | 0.456161i | \(-0.849224\pi\) | ||||
0.889897 | − | 0.456161i | \(-0.150776\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 288360. | 0.297209 | ||||||||
\(986\) | 733318.i | 0.754291i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −754490. | −0.772929 | ||||||||
\(989\) | − 1.23998e6i | − 1.26772i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 750377. | 0.764068 | 0.382034 | − | 0.924148i | \(-0.375224\pi\) | ||||
0.382034 | + | 0.924148i | \(0.375224\pi\) | |||||||
\(992\) | 1.59168e6i | 1.61745i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 242352. | 0.245287 | ||||||||
\(995\) | − 253008.i | − 0.255557i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −208918. | −0.210177 | −0.105089 | − | 0.994463i | \(-0.533513\pi\) | ||||
−0.105089 | + | 0.994463i | \(0.533513\pi\) | |||||||
\(998\) | 317557.i | 0.318831i | ||||||||
\(999\) | 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 | 27.5.b.b.26.2 | yes | 2 | |
3.2 | odd | 2 | inner | 27.5.b.b.26.1 | ✓ | 2 | |
4.3 | odd | 2 | 432.5.e.c.161.2 | 2 | |||
5.2 | odd | 4 | 675.5.d.g.674.2 | 4 | |||
5.3 | odd | 4 | 675.5.d.g.674.3 | 4 | |||
5.4 | even | 2 | 675.5.c.d.26.1 | 2 | |||
9.2 | odd | 6 | 81.5.d.d.53.1 | 4 | |||
9.4 | even | 3 | 81.5.d.d.26.1 | 4 | |||
9.5 | odd | 6 | 81.5.d.d.26.2 | 4 | |||
9.7 | even | 3 | 81.5.d.d.53.2 | 4 | |||
12.11 | even | 2 | 432.5.e.c.161.1 | 2 | |||
15.2 | even | 4 | 675.5.d.g.674.4 | 4 | |||
15.8 | even | 4 | 675.5.d.g.674.1 | 4 | |||
15.14 | odd | 2 | 675.5.c.d.26.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.5.b.b.26.1 | ✓ | 2 | 3.2 | odd | 2 | inner | |
27.5.b.b.26.2 | yes | 2 | 1.1 | even | 1 | trivial | |
81.5.d.d.26.1 | 4 | 9.4 | even | 3 | |||
81.5.d.d.26.2 | 4 | 9.5 | odd | 6 | |||
81.5.d.d.53.1 | 4 | 9.2 | odd | 6 | |||
81.5.d.d.53.2 | 4 | 9.7 | even | 3 | |||
432.5.e.c.161.1 | 2 | 12.11 | even | 2 | |||
432.5.e.c.161.2 | 2 | 4.3 | odd | 2 | |||
675.5.c.d.26.1 | 2 | 5.4 | even | 2 | |||
675.5.c.d.26.2 | 2 | 15.14 | odd | 2 | |||
675.5.d.g.674.1 | 4 | 15.8 | even | 4 | |||
675.5.d.g.674.2 | 4 | 5.2 | odd | 4 | |||
675.5.d.g.674.3 | 4 | 5.3 | odd | 4 | |||
675.5.d.g.674.4 | 4 | 15.2 | even | 4 |