Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,5,Mod(323,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.323");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.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: | \(39.0738460457\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.5443747577856.29 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 24x^{6} + 180x^{4} + 488x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.3 | ||
Root | \(-3.56118i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.323 |
Dual form | 378.5.b.a.323.6 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.82843i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | − 3.12468i | − 0.124987i | −0.998045 | − | 0.0624936i | \(-0.980095\pi\) | ||||
0.998045 | − | 0.0624936i | \(-0.0199053\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.5203 | 0.377964 | ||||||||
\(8\) | 22.6274i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.83793 | −0.0883793 | ||||||||
\(11\) | 141.266i | 1.16749i | 0.811938 | + | 0.583744i | \(0.198413\pi\) | ||||
−0.811938 | + | 0.583744i | \(0.801587\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −237.623 | −1.40606 | −0.703028 | − | 0.711162i | \(-0.748169\pi\) | ||||
−0.703028 | + | 0.711162i | \(0.748169\pi\) | |||||||
\(14\) | − 52.3832i | − 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | − 394.261i | − 1.36423i | −0.731247 | − | 0.682113i | \(-0.761061\pi\) | ||||
0.731247 | − | 0.682113i | \(-0.238939\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 535.891 | 1.48446 | 0.742232 | − | 0.670143i | \(-0.233767\pi\) | ||||
0.742232 | + | 0.670143i | \(0.233767\pi\) | |||||||
\(20\) | 24.9974i | 0.0624936i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 399.561 | 0.825539 | ||||||||
\(23\) | − 487.858i | − 0.922227i | −0.887341 | − | 0.461114i | \(-0.847450\pi\) | ||||
0.887341 | − | 0.461114i | \(-0.152550\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 615.236 | 0.984378 | ||||||||
\(26\) | 672.101i | 0.994232i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −148.162 | −0.188982 | ||||||||
\(29\) | 1201.77i | 1.42897i | 0.699649 | + | 0.714487i | \(0.253340\pi\) | ||||
−0.699649 | + | 0.714487i | \(0.746660\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 296.662 | 0.308701 | 0.154350 | − | 0.988016i | \(-0.450672\pi\) | ||||
0.154350 | + | 0.988016i | \(0.450672\pi\) | |||||||
\(32\) | − 181.019i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1115.14 | −0.964653 | ||||||||
\(35\) | − 57.8699i | − 0.0472407i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −380.977 | −0.278289 | −0.139144 | − | 0.990272i | \(-0.544435\pi\) | ||||
−0.139144 | + | 0.990272i | \(0.544435\pi\) | |||||||
\(38\) | − 1515.73i | − 1.04967i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 70.7034 | 0.0441896 | ||||||||
\(41\) | 73.6638i | 0.0438214i | 0.999760 | + | 0.0219107i | \(0.00697495\pi\) | ||||
−0.999760 | + | 0.0219107i | \(0.993025\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2912.26 | 1.57504 | 0.787522 | − | 0.616287i | \(-0.211364\pi\) | ||||
0.787522 | + | 0.616287i | \(0.211364\pi\) | |||||||
\(44\) | − 1130.13i | − 0.583744i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1379.87 | −0.652113 | ||||||||
\(47\) | − 2845.13i | − 1.28797i | −0.765037 | − | 0.643986i | \(-0.777279\pi\) | ||||
0.765037 | − | 0.643986i | \(-0.222721\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 343.000 | 0.142857 | ||||||||
\(50\) | − 1740.15i | − 0.696061i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1900.99 | 0.703028 | ||||||||
\(53\) | − 2125.45i | − 0.756657i | −0.925671 | − | 0.378328i | \(-0.876499\pi\) | ||||
0.925671 | − | 0.378328i | \(-0.123501\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 441.411 | 0.145921 | ||||||||
\(56\) | 419.066i | 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3399.11 | 1.01044 | ||||||||
\(59\) | − 5486.16i | − 1.57603i | −0.615656 | − | 0.788015i | \(-0.711109\pi\) | ||||
0.615656 | − | 0.788015i | \(-0.288891\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5032.38 | −1.35243 | −0.676214 | − | 0.736705i | \(-0.736381\pi\) | ||||
−0.676214 | + | 0.736705i | \(0.736381\pi\) | |||||||
\(62\) | − 839.086i | − 0.218284i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | 742.497i | 0.175739i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7342.60 | 1.63569 | 0.817844 | − | 0.575440i | \(-0.195169\pi\) | ||||
0.817844 | + | 0.575440i | \(0.195169\pi\) | |||||||
\(68\) | 3154.09i | 0.682113i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −163.681 | −0.0334042 | ||||||||
\(71\) | − 8600.64i | − 1.70614i | −0.521799 | − | 0.853068i | \(-0.674739\pi\) | ||||
0.521799 | − | 0.853068i | \(-0.325261\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2165.28 | 0.406320 | 0.203160 | − | 0.979146i | \(-0.434879\pi\) | ||||
0.203160 | + | 0.979146i | \(0.434879\pi\) | |||||||
\(74\) | 1077.57i | 0.196780i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4287.13 | −0.742232 | ||||||||
\(77\) | 2616.28i | 0.441269i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5796.36 | −0.928756 | −0.464378 | − | 0.885637i | \(-0.653722\pi\) | ||||
−0.464378 | + | 0.885637i | \(0.653722\pi\) | |||||||
\(80\) | − 199.979i | − 0.0312468i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 208.353 | 0.0309864 | ||||||||
\(83\) | − 2410.24i | − 0.349868i | −0.984580 | − | 0.174934i | \(-0.944029\pi\) | ||||
0.984580 | − | 0.174934i | \(-0.0559713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1231.94 | −0.170511 | ||||||||
\(86\) | − 8237.10i | − 1.11372i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3196.49 | −0.412769 | ||||||||
\(89\) | − 13791.5i | − 1.74113i | −0.492055 | − | 0.870564i | \(-0.663754\pi\) | ||||
0.492055 | − | 0.870564i | \(-0.336246\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4400.85 | −0.531439 | ||||||||
\(92\) | 3902.87i | 0.461114i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8047.25 | −0.910734 | ||||||||
\(95\) | − 1674.49i | − 0.185539i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10613.0 | 1.12797 | 0.563984 | − | 0.825786i | \(-0.309268\pi\) | ||||
0.563984 | + | 0.825786i | \(0.309268\pi\) | |||||||
\(98\) | − 970.151i | − 0.101015i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4921.89 | −0.492189 | ||||||||
\(101\) | 4424.36i | 0.433718i | 0.976203 | + | 0.216859i | \(0.0695812\pi\) | ||||
−0.976203 | + | 0.216859i | \(0.930419\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11498.7 | 1.08387 | 0.541933 | − | 0.840422i | \(-0.317693\pi\) | ||||
0.541933 | + | 0.840422i | \(0.317693\pi\) | |||||||
\(104\) | − 5376.81i | − 0.497116i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6011.68 | −0.535037 | ||||||||
\(107\) | 13254.7i | 1.15771i | 0.815429 | + | 0.578857i | \(0.196501\pi\) | ||||
−0.815429 | + | 0.578857i | \(0.803499\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7021.44 | 0.590981 | 0.295490 | − | 0.955346i | \(-0.404517\pi\) | ||||
0.295490 | + | 0.955346i | \(0.404517\pi\) | |||||||
\(110\) | − 1248.50i | − 0.103182i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1185.30 | 0.0944911 | ||||||||
\(113\) | − 16163.8i | − 1.26586i | −0.774208 | − | 0.632932i | \(-0.781851\pi\) | ||||
0.774208 | − | 0.632932i | \(-0.218149\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1524.40 | −0.115267 | ||||||||
\(116\) | − 9614.14i | − 0.714487i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15517.2 | −1.11442 | ||||||||
\(119\) | − 7301.82i | − 0.515629i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5315.10 | −0.363028 | ||||||||
\(122\) | 14233.7i | 0.956311i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2373.29 | −0.154350 | ||||||||
\(125\) | − 3875.34i | − 0.248022i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −29047.0 | −1.80092 | −0.900458 | − | 0.434942i | \(-0.856769\pi\) | ||||
−0.900458 | + | 0.434942i | \(0.856769\pi\) | |||||||
\(128\) | 1448.15i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2100.10 | 0.124266 | ||||||||
\(131\) | 33352.2i | 1.94349i | 0.236032 | + | 0.971745i | \(0.424153\pi\) | ||||
−0.236032 | + | 0.971745i | \(0.575847\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9924.85 | 0.561075 | ||||||||
\(134\) | − 20768.0i | − 1.15661i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8921.11 | 0.482326 | ||||||||
\(137\) | − 3627.12i | − 0.193251i | −0.995321 | − | 0.0966254i | \(-0.969195\pi\) | ||||
0.995321 | − | 0.0966254i | \(-0.0308049\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9107.22 | 0.471364 | 0.235682 | − | 0.971830i | \(-0.424268\pi\) | ||||
0.235682 | + | 0.971830i | \(0.424268\pi\) | |||||||
\(140\) | 462.959i | 0.0236204i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −24326.3 | −1.20642 | ||||||||
\(143\) | − 33568.1i | − 1.64155i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3755.14 | 0.178603 | ||||||||
\(146\) | − 6124.33i | − 0.287312i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3047.82 | 0.139144 | ||||||||
\(149\) | − 9668.97i | − 0.435520i | −0.976002 | − | 0.217760i | \(-0.930125\pi\) | ||||
0.976002 | − | 0.217760i | \(-0.0698749\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21411.0 | −0.939039 | −0.469520 | − | 0.882922i | \(-0.655573\pi\) | ||||
−0.469520 | + | 0.882922i | \(0.655573\pi\) | |||||||
\(152\) | 12125.8i | 0.524837i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7399.97 | 0.312024 | ||||||||
\(155\) | − 926.972i | − 0.0385836i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 26796.2 | 1.08711 | 0.543555 | − | 0.839374i | \(-0.317078\pi\) | ||||
0.543555 | + | 0.839374i | \(0.317078\pi\) | |||||||
\(158\) | 16394.6i | 0.656729i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −565.627 | −0.0220948 | ||||||||
\(161\) | − 9035.26i | − 0.348569i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 32250.2 | 1.21383 | 0.606914 | − | 0.794768i | \(-0.292407\pi\) | ||||
0.606914 | + | 0.794768i | \(0.292407\pi\) | |||||||
\(164\) | − 589.310i | − 0.0219107i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6817.20 | −0.247394 | ||||||||
\(167\) | 6114.20i | 0.219233i | 0.993974 | + | 0.109617i | \(0.0349623\pi\) | ||||
−0.993974 | + | 0.109617i | \(0.965038\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27903.9 | 0.976994 | ||||||||
\(170\) | 3484.45i | 0.120569i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −23298.0 | −0.787522 | ||||||||
\(173\) | 29551.1i | 0.987372i | 0.869640 | + | 0.493686i | \(0.164351\pi\) | ||||
−0.869640 | + | 0.493686i | \(0.835649\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11394.3 | 0.372060 | ||||||||
\(176\) | 9041.03i | 0.291872i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −39008.2 | −1.23116 | ||||||||
\(179\) | − 3311.38i | − 0.103348i | −0.998664 | − | 0.0516741i | \(-0.983544\pi\) | ||||
0.998664 | − | 0.0516741i | \(-0.0164557\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −38821.0 | −1.18497 | −0.592487 | − | 0.805580i | \(-0.701854\pi\) | ||||
−0.592487 | + | 0.805580i | \(0.701854\pi\) | |||||||
\(182\) | 12447.5i | 0.375784i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11039.0 | 0.326057 | ||||||||
\(185\) | 1190.43i | 0.0347825i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 55695.7 | 1.59272 | ||||||||
\(188\) | 22761.1i | 0.643986i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4736.17 | −0.131196 | ||||||||
\(191\) | 40870.6i | 1.12033i | 0.828382 | + | 0.560163i | \(0.189262\pi\) | ||||
−0.828382 | + | 0.560163i | \(0.810738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 38211.7 | 1.02585 | 0.512923 | − | 0.858435i | \(-0.328563\pi\) | ||||
0.512923 | + | 0.858435i | \(0.328563\pi\) | |||||||
\(194\) | − 30018.2i | − 0.797593i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2744.00 | −0.0714286 | ||||||||
\(197\) | 21225.2i | 0.546915i | 0.961884 | + | 0.273457i | \(0.0881673\pi\) | ||||
−0.961884 | + | 0.273457i | \(0.911833\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 44448.3 | 1.12240 | 0.561202 | − | 0.827679i | \(-0.310339\pi\) | ||||
0.561202 | + | 0.827679i | \(0.310339\pi\) | |||||||
\(200\) | 13921.2i | 0.348030i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12514.0 | 0.306685 | ||||||||
\(203\) | 22257.0i | 0.540102i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 230.176 | 0.00547712 | ||||||||
\(206\) | − 32523.3i | − 0.766409i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −15207.9 | −0.351514 | ||||||||
\(209\) | 75703.3i | 1.73309i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 902.367 | 0.0202683 | 0.0101342 | − | 0.999949i | \(-0.496774\pi\) | ||||
0.0101342 | + | 0.999949i | \(0.496774\pi\) | |||||||
\(212\) | 17003.6i | 0.378328i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 37489.9 | 0.818628 | ||||||||
\(215\) | − 9099.87i | − 0.196860i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5494.25 | 0.116678 | ||||||||
\(218\) | − 19859.6i | − 0.417886i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3531.29 | −0.0729605 | ||||||||
\(221\) | 93685.7i | 1.91818i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2439.54 | 0.0490566 | 0.0245283 | − | 0.999699i | \(-0.492192\pi\) | ||||
0.0245283 | + | 0.999699i | \(0.492192\pi\) | |||||||
\(224\) | − 3352.53i | − 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −45718.2 | −0.895101 | ||||||||
\(227\) | 3408.89i | 0.0661548i | 0.999453 | + | 0.0330774i | \(0.0105308\pi\) | ||||
−0.999453 | + | 0.0330774i | \(0.989469\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10788.1 | −0.205719 | −0.102860 | − | 0.994696i | \(-0.532799\pi\) | ||||
−0.102860 | + | 0.994696i | \(0.532799\pi\) | |||||||
\(230\) | 4311.66i | 0.0815058i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −27192.9 | −0.505219 | ||||||||
\(233\) | − 63204.8i | − 1.16423i | −0.813107 | − | 0.582114i | \(-0.802226\pi\) | ||||
0.813107 | − | 0.582114i | \(-0.197774\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8890.12 | −0.160980 | ||||||||
\(236\) | 43889.3i | 0.788015i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −20652.7 | −0.364604 | ||||||||
\(239\) | 42989.7i | 0.752607i | 0.926496 | + | 0.376304i | \(0.122805\pi\) | ||||
−0.926496 | + | 0.376304i | \(0.877195\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 37709.8 | 0.649262 | 0.324631 | − | 0.945841i | \(-0.394760\pi\) | ||||
0.324631 | + | 0.945841i | \(0.394760\pi\) | |||||||
\(242\) | 15033.4i | 0.256700i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 40259.1 | 0.676214 | ||||||||
\(245\) | − 1071.76i | − 0.0178553i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −127340. | −2.08724 | ||||||||
\(248\) | 6712.68i | 0.109142i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10961.1 | −0.175378 | ||||||||
\(251\) | − 113426.i | − 1.80038i | −0.435497 | − | 0.900190i | \(-0.643427\pi\) | ||||
0.435497 | − | 0.900190i | \(-0.356573\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 68917.8 | 1.07669 | ||||||||
\(254\) | 82157.3i | 1.27344i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 8447.17i | 0.127892i | 0.997953 | + | 0.0639462i | \(0.0203686\pi\) | ||||
−0.997953 | + | 0.0639462i | \(0.979631\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7055.80 | −0.105183 | ||||||||
\(260\) | − 5939.98i | − 0.0878695i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 94334.4 | 1.37426 | ||||||||
\(263\) | 115681.i | 1.67244i | 0.548391 | + | 0.836222i | \(0.315240\pi\) | ||||
−0.548391 | + | 0.836222i | \(0.684760\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6641.35 | −0.0945724 | ||||||||
\(266\) | − 28071.7i | − 0.396740i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −58740.8 | −0.817844 | ||||||||
\(269\) | 34096.2i | 0.471195i | 0.971851 | + | 0.235598i | \(0.0757048\pi\) | ||||
−0.971851 | + | 0.235598i | \(0.924295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 68752.9 | 0.936165 | 0.468083 | − | 0.883685i | \(-0.344945\pi\) | ||||
0.468083 | + | 0.883685i | \(0.344945\pi\) | |||||||
\(272\) | − 25232.7i | − 0.341056i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10259.1 | −0.136649 | ||||||||
\(275\) | 86912.0i | 1.14925i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 115701. | 1.50792 | 0.753958 | − | 0.656923i | \(-0.228142\pi\) | ||||
0.753958 | + | 0.656923i | \(0.228142\pi\) | |||||||
\(278\) | − 25759.1i | − 0.333304i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1309.45 | 0.0167021 | ||||||||
\(281\) | − 9710.36i | − 0.122977i | −0.998108 | − | 0.0614883i | \(-0.980415\pi\) | ||||
0.998108 | − | 0.0614883i | \(-0.0195847\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16971.5 | 0.211907 | 0.105954 | − | 0.994371i | \(-0.466210\pi\) | ||||
0.105954 | + | 0.994371i | \(0.466210\pi\) | |||||||
\(284\) | 68805.1i | 0.853068i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −94945.0 | −1.16075 | ||||||||
\(287\) | 1364.27i | 0.0165629i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −71920.8 | −0.861110 | ||||||||
\(290\) | − 10621.1i | − 0.126292i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −17322.2 | −0.203160 | ||||||||
\(293\) | − 46472.1i | − 0.541324i | −0.962674 | − | 0.270662i | \(-0.912757\pi\) | ||||
0.962674 | − | 0.270662i | \(-0.0872425\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17142.5 | −0.196983 | ||||||||
\(296\) | − 8620.53i | − 0.0983899i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −27348.0 | −0.307959 | ||||||||
\(299\) | 115927.i | 1.29670i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 53935.7 | 0.595311 | ||||||||
\(302\) | 60559.5i | 0.664001i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 34297.0 | 0.371116 | ||||||||
\(305\) | 15724.6i | 0.169036i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −104419. | −1.10790 | −0.553951 | − | 0.832549i | \(-0.686880\pi\) | ||||
−0.553951 | + | 0.832549i | \(0.686880\pi\) | |||||||
\(308\) | − 20930.3i | − 0.220635i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2621.87 | −0.0272828 | ||||||||
\(311\) | − 114779.i | − 1.18671i | −0.804943 | − | 0.593353i | \(-0.797804\pi\) | ||||
0.804943 | − | 0.593353i | \(-0.202196\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7552.66 | −0.0770924 | −0.0385462 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385462 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(314\) | − 75791.0i | − 0.768702i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 46370.9 | 0.464378 | ||||||||
\(317\) | − 95323.4i | − 0.948595i | −0.880365 | − | 0.474298i | \(-0.842702\pi\) | ||||
0.880365 | − | 0.474298i | \(-0.157298\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −169769. | −1.66831 | ||||||||
\(320\) | 1599.84i | 0.0156234i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −25555.6 | −0.246476 | ||||||||
\(323\) | − 211281.i | − 2.02514i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −146195. | −1.38409 | ||||||||
\(326\) | − 91217.3i | − 0.858306i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1666.82 | −0.0154932 | ||||||||
\(329\) | − 52692.6i | − 0.486808i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −66158.3 | −0.603849 | −0.301924 | − | 0.953332i | \(-0.597629\pi\) | ||||
−0.301924 | + | 0.953332i | \(0.597629\pi\) | |||||||
\(332\) | 19281.9i | 0.174934i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17293.6 | 0.155021 | ||||||||
\(335\) | − 22943.3i | − 0.204440i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −140142. | −1.23398 | −0.616990 | − | 0.786971i | \(-0.711648\pi\) | ||||
−0.616990 | + | 0.786971i | \(0.711648\pi\) | |||||||
\(338\) | − 78924.2i | − 0.690839i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9855.51 | 0.0852553 | ||||||||
\(341\) | 41908.2i | 0.360405i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6352.45 | 0.0539949 | ||||||||
\(344\) | 65896.8i | 0.556862i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 83583.0 | 0.698178 | ||||||||
\(347\) | − 28633.6i | − 0.237803i | −0.992906 | − | 0.118901i | \(-0.962063\pi\) | ||||
0.992906 | − | 0.118901i | \(-0.0379372\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 82009.8 | 0.673310 | 0.336655 | − | 0.941628i | \(-0.390704\pi\) | ||||
0.336655 | + | 0.941628i | \(0.390704\pi\) | |||||||
\(350\) | − 32228.1i | − 0.263086i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 25571.9 | 0.206385 | ||||||||
\(353\) | 58668.4i | 0.470820i | 0.971896 | + | 0.235410i | \(0.0756433\pi\) | ||||
−0.971896 | + | 0.235410i | \(0.924357\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26874.2 | −0.213245 | ||||||||
\(356\) | 110332.i | 0.870564i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9365.99 | −0.0730782 | ||||||||
\(359\) | 37840.3i | 0.293606i | 0.989166 | + | 0.146803i | \(0.0468984\pi\) | ||||
−0.989166 | + | 0.146803i | \(0.953102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 156859. | 1.20363 | ||||||||
\(362\) | 109802.i | 0.837904i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 35206.8 | 0.265720 | ||||||||
\(365\) | − 6765.80i | − 0.0507848i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 76141.5 | 0.565313 | 0.282657 | − | 0.959221i | \(-0.408784\pi\) | ||||
0.282657 | + | 0.959221i | \(0.408784\pi\) | |||||||
\(368\) | − 31222.9i | − 0.230557i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3367.05 | 0.0245950 | ||||||||
\(371\) | − 39363.9i | − 0.285989i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 85550.6 | 0.614901 | 0.307451 | − | 0.951564i | \(-0.400524\pi\) | ||||
0.307451 | + | 0.951564i | \(0.400524\pi\) | |||||||
\(374\) | − 157531.i | − 1.12622i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 64378.0 | 0.455367 | ||||||||
\(377\) | − 285568.i | − 2.00922i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −136931. | −0.953287 | −0.476644 | − | 0.879097i | \(-0.658147\pi\) | ||||
−0.476644 | + | 0.879097i | \(0.658147\pi\) | |||||||
\(380\) | 13395.9i | 0.0927695i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 115600. | 0.792190 | ||||||||
\(383\) | − 42414.5i | − 0.289146i | −0.989494 | − | 0.144573i | \(-0.953819\pi\) | ||||
0.989494 | − | 0.144573i | \(-0.0461808\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8175.05 | 0.0551530 | ||||||||
\(386\) | − 108079.i | − 0.725383i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −84904.4 | −0.563984 | ||||||||
\(389\) | 258455.i | 1.70799i | 0.520277 | + | 0.853997i | \(0.325829\pi\) | ||||
−0.520277 | + | 0.853997i | \(0.674171\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −192343. | −1.25813 | ||||||||
\(392\) | 7761.20i | 0.0505076i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 60034.0 | 0.386727 | ||||||||
\(395\) | 18111.8i | 0.116083i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 114157. | 0.724303 | 0.362152 | − | 0.932119i | \(-0.382042\pi\) | ||||
0.362152 | + | 0.932119i | \(0.382042\pi\) | |||||||
\(398\) | − 125719.i | − 0.793660i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 39375.1 | 0.246095 | ||||||||
\(401\) | 140116.i | 0.871362i | 0.900101 | + | 0.435681i | \(0.143492\pi\) | ||||
−0.900101 | + | 0.435681i | \(0.856508\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −70493.8 | −0.434051 | ||||||||
\(404\) | − 35394.9i | − 0.216859i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 62952.4 | 0.381909 | ||||||||
\(407\) | − 53819.1i | − 0.324899i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −165912. | −0.991817 | −0.495908 | − | 0.868375i | \(-0.665165\pi\) | ||||
−0.495908 | + | 0.868375i | \(0.665165\pi\) | |||||||
\(410\) | − 651.035i | − 0.00387291i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −91989.9 | −0.541933 | ||||||||
\(413\) | − 101605.i | − 0.595683i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7531.24 | −0.0437291 | ||||||||
\(416\) | 43014.4i | 0.248558i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 214121. | 1.22548 | ||||||||
\(419\) | − 130600.i | − 0.743903i | −0.928252 | − | 0.371952i | \(-0.878689\pi\) | ||||
0.928252 | − | 0.371952i | \(-0.121311\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −62110.0 | −0.350427 | −0.175213 | − | 0.984530i | \(-0.556062\pi\) | ||||
−0.175213 | + | 0.984530i | \(0.556062\pi\) | |||||||
\(422\) | − 2552.28i | − 0.0143319i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 48093.4 | 0.267519 | ||||||||
\(425\) | − 242564.i | − 1.34291i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −93201.1 | −0.511170 | ||||||||
\(428\) | − 106037.i | − 0.578857i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25738.3 | −0.139201 | ||||||||
\(431\) | 112404.i | 0.605100i | 0.953133 | + | 0.302550i | \(0.0978380\pi\) | ||||
−0.953133 | + | 0.302550i | \(0.902162\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 64860.0 | 0.345940 | 0.172970 | − | 0.984927i | \(-0.444664\pi\) | ||||
0.172970 | + | 0.984927i | \(0.444664\pi\) | |||||||
\(434\) | − 15540.1i | − 0.0825038i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −56171.5 | −0.295490 | ||||||||
\(437\) | − 261439.i | − 1.36901i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 146510. | 0.760218 | 0.380109 | − | 0.924942i | \(-0.375887\pi\) | ||||
0.380109 | + | 0.924942i | \(0.375887\pi\) | |||||||
\(440\) | 9987.99i | 0.0515909i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 264983. | 1.35636 | ||||||||
\(443\) | − 130291.i | − 0.663908i | −0.943296 | − | 0.331954i | \(-0.892292\pi\) | ||||
0.943296 | − | 0.331954i | \(-0.107708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −43094.0 | −0.217619 | ||||||||
\(446\) | − 6900.05i | − 0.0346883i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9482.37 | −0.0472456 | ||||||||
\(449\) | 93245.1i | 0.462523i | 0.972892 | + | 0.231262i | \(0.0742853\pi\) | ||||
−0.972892 | + | 0.231262i | \(0.925715\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10406.2 | −0.0511610 | ||||||||
\(452\) | 129311.i | 0.632932i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9641.80 | 0.0467785 | ||||||||
\(455\) | 13751.2i | 0.0664231i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −137893. | −0.660252 | −0.330126 | − | 0.943937i | \(-0.607091\pi\) | ||||
−0.330126 | + | 0.943937i | \(0.607091\pi\) | |||||||
\(458\) | 30513.4i | 0.145465i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12195.2 | 0.0576333 | ||||||||
\(461\) | − 324498.i | − 1.52690i | −0.645869 | − | 0.763448i | \(-0.723505\pi\) | ||||
0.645869 | − | 0.763448i | \(-0.276495\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −267434. | −1.24754 | −0.623770 | − | 0.781608i | \(-0.714400\pi\) | ||||
−0.623770 | + | 0.781608i | \(0.714400\pi\) | |||||||
\(464\) | 76913.1i | 0.357244i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −178770. | −0.823234 | ||||||||
\(467\) | 77333.7i | 0.354597i | 0.984157 | + | 0.177299i | \(0.0567358\pi\) | ||||
−0.984157 | + | 0.177299i | \(0.943264\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 135987. | 0.618232 | ||||||||
\(470\) | 25145.1i | 0.113830i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 124138. | 0.557211 | ||||||||
\(473\) | 411403.i | 1.83884i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 329700. | 1.46127 | ||||||||
\(476\) | 58414.5i | 0.257814i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 121593. | 0.532174 | ||||||||
\(479\) | − 291569.i | − 1.27078i | −0.772191 | − | 0.635390i | \(-0.780839\pi\) | ||||
0.772191 | − | 0.635390i | \(-0.219161\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 90529.1 | 0.391290 | ||||||||
\(482\) | − 106659.i | − 0.459098i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 42520.8 | 0.181514 | ||||||||
\(485\) | − 33162.4i | − 0.140981i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −98706.0 | −0.416184 | −0.208092 | − | 0.978109i | \(-0.566725\pi\) | ||||
−0.208092 | + | 0.978109i | \(0.566725\pi\) | |||||||
\(488\) | − 113870.i | − 0.478155i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3031.41 | −0.0126256 | ||||||||
\(491\) | 68699.3i | 0.284963i | 0.989797 | + | 0.142482i | \(0.0455082\pi\) | ||||
−0.989797 | + | 0.142482i | \(0.954492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 473810. | 1.94944 | ||||||||
\(494\) | 360173.i | 1.47590i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18986.3 | 0.0771752 | ||||||||
\(497\) | − 159286.i | − 0.644859i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −180484. | −0.724834 | −0.362417 | − | 0.932016i | \(-0.618048\pi\) | ||||
−0.362417 | + | 0.932016i | \(0.618048\pi\) | |||||||
\(500\) | 31002.7i | 0.124011i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −320817. | −1.27306 | ||||||||
\(503\) | 170691.i | 0.674645i | 0.941389 | + | 0.337323i | \(0.109521\pi\) | ||||
−0.941389 | + | 0.337323i | \(0.890479\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13824.7 | 0.0542092 | ||||||||
\(506\) | − 194929.i | − 0.761334i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 232376. | 0.900458 | ||||||||
\(509\) | − 87777.9i | − 0.338805i | −0.985547 | − | 0.169403i | \(-0.945816\pi\) | ||||
0.985547 | − | 0.169403i | \(-0.0541838\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40101.5 | 0.153574 | ||||||||
\(512\) | − 11585.2i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 23892.2 | 0.0904336 | ||||||||
\(515\) | − 35929.9i | − 0.135469i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 401921. | 1.50369 | ||||||||
\(518\) | 19956.8i | 0.0743758i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −16800.8 | −0.0621331 | ||||||||
\(521\) | − 433477.i | − 1.59695i | −0.602030 | − | 0.798473i | \(-0.705641\pi\) | ||||
0.602030 | − | 0.798473i | \(-0.294359\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −380650. | −1.39163 | −0.695813 | − | 0.718223i | \(-0.744956\pi\) | ||||
−0.695813 | + | 0.718223i | \(0.744956\pi\) | |||||||
\(524\) | − 266818.i | − 0.971745i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 327196. | 1.18260 | ||||||||
\(527\) | − 116962.i | − 0.421137i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41835.4 | 0.149497 | ||||||||
\(530\) | 18784.6i | 0.0668728i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −79398.8 | −0.280537 | ||||||||
\(533\) | − 17504.3i | − 0.0616154i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 41416.6 | 0.144699 | ||||||||
\(536\) | 166144.i | 0.578303i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 96438.5 | 0.333185 | ||||||||
\(539\) | 48454.3i | 0.166784i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −158944. | −0.543061 | −0.271531 | − | 0.962430i | \(-0.587530\pi\) | ||||
−0.271531 | + | 0.962430i | \(0.587530\pi\) | |||||||
\(542\) | − 194463.i | − 0.661969i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −71368.9 | −0.241163 | ||||||||
\(545\) | − 21939.8i | − 0.0738650i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −500492. | −1.67272 | −0.836358 | − | 0.548183i | \(-0.815320\pi\) | ||||
−0.836358 | + | 0.548183i | \(0.815320\pi\) | |||||||
\(548\) | 29017.0i | 0.0966254i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 245824. | 0.812642 | ||||||||
\(551\) | 644017.i | 2.12126i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −107350. | −0.351037 | ||||||||
\(554\) | − 327251.i | − 1.06626i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −72857.7 | −0.235682 | ||||||||
\(557\) | 411990.i | 1.32793i | 0.747762 | + | 0.663967i | \(0.231128\pi\) | ||||
−0.747762 | + | 0.663967i | \(0.768872\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −692020. | −2.21460 | ||||||||
\(560\) | − 3703.67i | − 0.0118102i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −27465.0 | −0.0869576 | ||||||||
\(563\) | − 237439.i | − 0.749091i | −0.927209 | − | 0.374545i | \(-0.877799\pi\) | ||||
0.927209 | − | 0.374545i | \(-0.122201\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −50506.7 | −0.158217 | ||||||||
\(566\) | − 48002.5i | − 0.149841i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 194610. | 0.603210 | ||||||||
\(569\) | 548677.i | 1.69470i | 0.531037 | + | 0.847349i | \(0.321803\pi\) | ||||
−0.531037 | + | 0.847349i | \(0.678197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 205016. | 0.628806 | 0.314403 | − | 0.949290i | \(-0.398196\pi\) | ||||
0.314403 | + | 0.949290i | \(0.398196\pi\) | |||||||
\(572\) | 268545.i | 0.820777i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3858.75 | 0.0117118 | ||||||||
\(575\) | − 300148.i | − 0.907820i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −292763. | −0.879356 | −0.439678 | − | 0.898155i | \(-0.644907\pi\) | ||||
−0.439678 | + | 0.898155i | \(0.644907\pi\) | |||||||
\(578\) | 203423.i | 0.608897i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −30041.1 | −0.0893017 | ||||||||
\(581\) | − 44638.3i | − 0.132238i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 300254. | 0.883388 | ||||||||
\(584\) | 48994.7i | 0.143656i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −131443. | −0.382774 | ||||||||
\(587\) | 75489.1i | 0.219083i | 0.993982 | + | 0.109541i | \(0.0349382\pi\) | ||||
−0.993982 | + | 0.109541i | \(0.965062\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 158978. | 0.458255 | ||||||||
\(590\) | 48486.3i | 0.139288i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24382.5 | −0.0695722 | ||||||||
\(593\) | 664448.i | 1.88952i | 0.327764 | + | 0.944760i | \(0.393705\pi\) | ||||
−0.327764 | + | 0.944760i | \(0.606295\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22815.8 | −0.0644470 | ||||||||
\(596\) | 77351.8i | 0.217760i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 327890. | 0.916908 | ||||||||
\(599\) | 521123.i | 1.45240i | 0.687483 | + | 0.726201i | \(0.258716\pi\) | ||||
−0.687483 | + | 0.726201i | \(0.741284\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 52148.0 | 0.144374 | 0.0721869 | − | 0.997391i | \(-0.477002\pi\) | ||||
0.0721869 | + | 0.997391i | \(0.477002\pi\) | |||||||
\(602\) | − 152553.i | − 0.420948i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 171288. | 0.469520 | ||||||||
\(605\) | 16608.0i | 0.0453739i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −342719. | −0.930168 | −0.465084 | − | 0.885267i | \(-0.653976\pi\) | ||||
−0.465084 | + | 0.885267i | \(0.653976\pi\) | |||||||
\(608\) | − 97006.7i | − 0.262419i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 44475.8 | 0.119527 | ||||||||
\(611\) | 676070.i | 1.81096i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −702183. | −1.86866 | −0.934328 | − | 0.356415i | \(-0.883999\pi\) | ||||
−0.934328 | + | 0.356415i | \(0.883999\pi\) | |||||||
\(614\) | 295340.i | 0.783405i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −59199.7 | −0.156012 | ||||||||
\(617\) | − 5722.23i | − 0.0150312i | −0.999972 | − | 0.00751562i | \(-0.997608\pi\) | ||||
0.999972 | − | 0.00751562i | \(-0.00239232\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −493596. | −1.28822 | −0.644110 | − | 0.764933i | \(-0.722772\pi\) | ||||
−0.644110 | + | 0.764933i | \(0.722772\pi\) | |||||||
\(620\) | 7415.78i | 0.0192918i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −324645. | −0.839127 | ||||||||
\(623\) | − 255422.i | − 0.658085i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 372414. | 0.953379 | ||||||||
\(626\) | 21362.2i | 0.0545126i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −214369. | −0.543555 | ||||||||
\(629\) | 150204.i | 0.379648i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 369529. | 0.928089 | 0.464045 | − | 0.885812i | \(-0.346398\pi\) | ||||
0.464045 | + | 0.885812i | \(0.346398\pi\) | |||||||
\(632\) | − 131157.i | − 0.328365i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −269615. | −0.670758 | ||||||||
\(635\) | 90762.5i | 0.225091i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −81504.9 | −0.200865 | ||||||||
\(638\) | 480179.i | 1.17967i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4525.02 | 0.0110474 | ||||||||
\(641\) | − 685619.i | − 1.66866i | −0.551269 | − | 0.834328i | \(-0.685856\pi\) | ||||
0.551269 | − | 0.834328i | \(-0.314144\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 90659.6 | 0.219276 | 0.109638 | − | 0.993972i | \(-0.465031\pi\) | ||||
0.109638 | + | 0.993972i | \(0.465031\pi\) | |||||||
\(644\) | 72282.1i | 0.174285i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −597593. | −1.43199 | ||||||||
\(647\) | 758270.i | 1.81140i | 0.423916 | + | 0.905702i | \(0.360655\pi\) | ||||
−0.423916 | + | 0.905702i | \(0.639345\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 775008. | 1.84000 | ||||||||
\(650\) | 413501.i | 0.978700i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −258001. | −0.606914 | ||||||||
\(653\) | − 261552.i | − 0.613383i | −0.951809 | − | 0.306692i | \(-0.900778\pi\) | ||||
0.951809 | − | 0.306692i | \(-0.0992220\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 104215. | 0.242911 | ||||||||
\(656\) | 4714.48i | 0.0109554i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −149037. | −0.344225 | ||||||||
\(659\) | − 517272.i | − 1.19110i | −0.803319 | − | 0.595549i | \(-0.796934\pi\) | ||||
0.803319 | − | 0.595549i | \(-0.203066\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −626741. | −1.43445 | −0.717224 | − | 0.696842i | \(-0.754588\pi\) | ||||
−0.717224 | + | 0.696842i | \(0.754588\pi\) | |||||||
\(662\) | 187124.i | 0.426985i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 54537.6 | 0.123697 | ||||||||
\(665\) | − 31012.0i | − 0.0701271i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 586292. | 1.31784 | ||||||||
\(668\) | − 48913.6i | − 0.109617i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −64893.4 | −0.144561 | ||||||||
\(671\) | − 710905.i | − 1.57894i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 742305. | 1.63890 | 0.819450 | − | 0.573151i | \(-0.194279\pi\) | ||||
0.819450 | + | 0.573151i | \(0.194279\pi\) | |||||||
\(674\) | 396381.i | 0.872555i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −223231. | −0.488497 | ||||||||
\(677\) | 604523.i | 1.31897i | 0.751717 | + | 0.659486i | \(0.229226\pi\) | ||||
−0.751717 | + | 0.659486i | \(0.770774\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 196556. | 0.426332 | ||||||||
\(680\) | − 27875.6i | − 0.0602846i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 118534. | 0.254845 | ||||||||
\(683\) | 720939.i | 1.54546i | 0.634737 | + | 0.772728i | \(0.281109\pi\) | ||||
−0.634737 | + | 0.772728i | \(0.718891\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11333.6 | −0.0241539 | ||||||||
\(686\) | − 17967.4i | − 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 186384. | 0.393761 | ||||||||
\(689\) | 505057.i | 1.06390i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −588601. | −1.23272 | −0.616360 | − | 0.787464i | \(-0.711393\pi\) | ||||
−0.616360 | + | 0.787464i | \(0.711393\pi\) | |||||||
\(692\) | − 236409.i | − 0.493686i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −80988.0 | −0.168152 | ||||||||
\(695\) | − 28457.1i | − 0.0589144i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29042.8 | 0.0597823 | ||||||||
\(698\) | − 231959.i | − 0.476102i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −91154.7 | −0.186030 | ||||||||
\(701\) | 154697.i | 0.314809i | 0.987534 | + | 0.157404i | \(0.0503126\pi\) | ||||
−0.987534 | + | 0.157404i | \(0.949687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −204162. | −0.413109 | ||||||||
\(704\) | − 72328.2i | − 0.145936i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 165939. | 0.332920 | ||||||||
\(707\) | 81940.3i | 0.163930i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 715382. | 1.42313 | 0.711567 | − | 0.702619i | \(-0.247986\pi\) | ||||
0.711567 | + | 0.702619i | \(0.247986\pi\) | |||||||
\(710\) | 76011.8i | 0.150787i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 312066. | 0.615582 | ||||||||
\(713\) | − 144729.i | − 0.284692i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −104890. | −0.205173 | ||||||||
\(716\) | 26491.0i | 0.0516741i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 107028. | 0.207611 | ||||||||
\(719\) | − 371799.i | − 0.719202i | −0.933106 | − | 0.359601i | \(-0.882913\pi\) | ||||
0.933106 | − | 0.359601i | \(-0.117087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 212960. | 0.409663 | ||||||||
\(722\) | − 443663.i | − 0.851097i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 310568. | 0.592487 | ||||||||
\(725\) | 739371.i | 1.40665i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 52138.1 | 0.0986476 | 0.0493238 | − | 0.998783i | \(-0.484293\pi\) | ||||
0.0493238 | + | 0.998783i | \(0.484293\pi\) | |||||||
\(728\) | − 99579.8i | − 0.187892i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19136.6 | −0.0359103 | ||||||||
\(731\) | − 1.14819e6i | − 2.14871i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 324955. | 0.604805 | 0.302403 | − | 0.953180i | \(-0.402211\pi\) | ||||
0.302403 | + | 0.953180i | \(0.402211\pi\) | |||||||
\(734\) | − 215361.i | − 0.399737i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −88311.8 | −0.163028 | ||||||||
\(737\) | 1.03726e6i | 1.90965i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −971247. | −1.77845 | −0.889224 | − | 0.457473i | \(-0.848755\pi\) | ||||
−0.889224 | + | 0.457473i | \(0.848755\pi\) | |||||||
\(740\) | − 9523.45i | − 0.0173913i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −111338. | −0.202225 | ||||||||
\(743\) | − 681732.i | − 1.23491i | −0.786605 | − | 0.617456i | \(-0.788163\pi\) | ||||
0.786605 | − | 0.617456i | \(-0.211837\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30212.4 | −0.0544344 | ||||||||
\(746\) | − 241974.i | − 0.434801i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −445566. | −0.796358 | ||||||||
\(749\) | 245480.i | 0.437575i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −317894. | −0.563641 | −0.281821 | − | 0.959467i | \(-0.590938\pi\) | ||||
−0.281821 | + | 0.959467i | \(0.590938\pi\) | |||||||
\(752\) | − 182088.i | − 0.321993i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −807709. | −1.42073 | ||||||||
\(755\) | 66902.6i | 0.117368i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −700233. | −1.22194 | −0.610971 | − | 0.791653i | \(-0.709221\pi\) | ||||
−0.610971 | + | 0.791653i | \(0.709221\pi\) | |||||||
\(758\) | 387300.i | 0.674076i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 37889.4 | 0.0655979 | ||||||||
\(761\) | − 305818.i | − 0.528072i | −0.964513 | − | 0.264036i | \(-0.914946\pi\) | ||||
0.964513 | − | 0.264036i | \(-0.0850538\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 130039. | 0.223370 | ||||||||
\(764\) | − 326965.i | − 0.560163i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −119966. | −0.204457 | ||||||||
\(767\) | 1.30364e6i | 2.21599i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 820424. | 1.38735 | 0.693675 | − | 0.720289i | \(-0.255991\pi\) | ||||
0.693675 | + | 0.720289i | \(0.255991\pi\) | |||||||
\(770\) | − 23122.5i | − 0.0389990i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −305694. | −0.512923 | ||||||||
\(773\) | − 483522.i | − 0.809202i | −0.914493 | − | 0.404601i | \(-0.867410\pi\) | ||||
0.914493 | − | 0.404601i | \(-0.132590\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 182517. | 0.303878 | ||||||||
\(776\) | 240146.i | 0.398797i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 731022. | 1.20773 | ||||||||
\(779\) | 39475.8i | 0.0650513i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.21498e6 | 1.99189 | ||||||||
\(782\) | 544030.i | 0.889629i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21952.0 | 0.0357143 | ||||||||
\(785\) | − 83729.4i | − 0.135875i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −185741. | −0.299888 | −0.149944 | − | 0.988695i | \(-0.547909\pi\) | ||||
−0.149944 | + | 0.988695i | \(0.547909\pi\) | |||||||
\(788\) | − 169802.i | − 0.273457i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 51227.8 | 0.0820827 | ||||||||
\(791\) | − 299358.i | − 0.478452i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.19581e6 | 1.90159 | ||||||||
\(794\) | − 322884.i | − 0.512160i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −355587. | −0.561202 | ||||||||
\(797\) | − 720505.i | − 1.13428i | −0.823621 | − | 0.567140i | \(-0.808050\pi\) | ||||
0.823621 | − | 0.567140i | \(-0.191950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.12172e6 | −1.75708 | ||||||||
\(800\) | − 111370.i | − 0.174015i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 396307. | 0.616146 | ||||||||
\(803\) | 305880.i | 0.474374i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28232.3 | −0.0435667 | ||||||||
\(806\) | 199386.i | 0.306920i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −100112. | −0.153343 | ||||||||
\(809\) | 686330.i | 1.04866i | 0.851514 | + | 0.524331i | \(0.175685\pi\) | ||||
−0.851514 | + | 0.524331i | \(0.824315\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.24830e6 | 1.89791 | 0.948955 | − | 0.315412i | \(-0.102143\pi\) | ||||
0.948955 | + | 0.315412i | \(0.102143\pi\) | |||||||
\(812\) | − 178056.i | − 0.270051i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −152224. | −0.229738 | ||||||||
\(815\) | − 100771.i | − 0.151713i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.56065e6 | 2.33810 | ||||||||
\(818\) | 469270.i | 0.701320i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1841.41 | −0.00273856 | ||||||||
\(821\) | − 842160.i | − 1.24942i | −0.780857 | − | 0.624710i | \(-0.785217\pi\) | ||||
0.780857 | − | 0.624710i | \(-0.214783\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −105260. | −0.155404 | −0.0777019 | − | 0.996977i | \(-0.524758\pi\) | ||||
−0.0777019 | + | 0.996977i | \(0.524758\pi\) | |||||||
\(824\) | 260187.i | 0.383204i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −287383. | −0.421212 | ||||||||
\(827\) | − 373318.i | − 0.545844i | −0.962036 | − | 0.272922i | \(-0.912010\pi\) | ||||
0.962036 | − | 0.272922i | \(-0.0879900\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 867025. | 1.26160 | 0.630801 | − | 0.775944i | \(-0.282726\pi\) | ||||
0.630801 | + | 0.775944i | \(0.282726\pi\) | |||||||
\(830\) | 21301.6i | 0.0309211i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 121663. | 0.175757 | ||||||||
\(833\) | − 135232.i | − 0.194889i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19104.9 | 0.0274014 | ||||||||
\(836\) | − 605626.i | − 0.866547i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −369394. | −0.526019 | ||||||||
\(839\) | − 686493.i | − 0.975242i | −0.873055 | − | 0.487621i | \(-0.837865\pi\) | ||||
0.873055 | − | 0.487621i | \(-0.162135\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −736964. | −1.04197 | ||||||||
\(842\) | 175674.i | 0.247789i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7218.94 | −0.0101342 | ||||||||
\(845\) | − 87190.8i | − 0.122112i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −98437.0 | −0.137212 | ||||||||
\(848\) | − 136029.i | − 0.189164i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −686074. | −0.949583 | ||||||||
\(851\) | 185863.i | 0.256645i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 974427. | 1.33922 | 0.669609 | − | 0.742714i | \(-0.266462\pi\) | ||||
0.669609 | + | 0.742714i | \(0.266462\pi\) | |||||||
\(854\) | 263612.i | 0.361452i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −299919. | −0.409314 | ||||||||
\(857\) | − 275668.i | − 0.375339i | −0.982232 | − | 0.187670i | \(-0.939907\pi\) | ||||
0.982232 | − | 0.187670i | \(-0.0600934\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 176529. | 0.239237 | 0.119619 | − | 0.992820i | \(-0.461833\pi\) | ||||
0.119619 | + | 0.992820i | \(0.461833\pi\) | |||||||
\(860\) | 72798.9i | 0.0984301i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 317927. | 0.427871 | ||||||||
\(863\) | − 856520.i | − 1.15005i | −0.818136 | − | 0.575024i | \(-0.804993\pi\) | ||||
0.818136 | − | 0.575024i | \(-0.195007\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 92337.6 | 0.123409 | ||||||||
\(866\) | − 183452.i | − 0.244617i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −43954.0 | −0.0583390 | ||||||||
\(869\) | − 818829.i | − 1.08431i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.74478e6 | −2.29987 | ||||||||
\(872\) | 158877.i | 0.208943i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −739461. | −0.968038 | ||||||||
\(875\) | − 71772.3i | − 0.0937434i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.00077e6 | 1.30118 | 0.650589 | − | 0.759430i | \(-0.274522\pi\) | ||||
0.650589 | + | 0.759430i | \(0.274522\pi\) | |||||||
\(878\) | − 414393.i | − 0.537555i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 28250.3 | 0.0364803 | ||||||||
\(881\) | − 775427.i | − 0.999055i | −0.866298 | − | 0.499527i | \(-0.833507\pi\) | ||||
0.866298 | − | 0.499527i | \(-0.166493\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 160327. | 0.205630 | 0.102815 | − | 0.994701i | \(-0.467215\pi\) | ||||
0.102815 | + | 0.994701i | \(0.467215\pi\) | |||||||
\(884\) | − 749485.i | − 0.959089i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −368519. | −0.469454 | ||||||||
\(887\) | − 183914.i | − 0.233759i | −0.993146 | − | 0.116879i | \(-0.962711\pi\) | ||||
0.993146 | − | 0.116879i | \(-0.0372891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −537958. | −0.680682 | ||||||||
\(890\) | 121888.i | 0.153880i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19516.3 | −0.0245283 | ||||||||
\(893\) | − 1.52468e6i | − 1.91195i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10347.0 | −0.0129172 | ||||||||
\(896\) | 26820.2i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 263737. | 0.327053 | ||||||||
\(899\) | 356518.i | 0.441126i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −837982. | −1.03225 | ||||||||
\(902\) | 29433.2i | 0.0361763i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 365745. | 0.447550 | ||||||||
\(905\) | 121303.i | 0.148107i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 184492. | 0.224266 | 0.112133 | − | 0.993693i | \(-0.464232\pi\) | ||||
0.112133 | + | 0.993693i | \(0.464232\pi\) | |||||||
\(908\) | − 27271.1i | − 0.0330774i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 38894.4 | 0.0469682 | ||||||||
\(911\) | 979147.i | 1.17981i | 0.807474 | + | 0.589904i | \(0.200834\pi\) | ||||
−0.807474 | + | 0.589904i | \(0.799166\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 340486. | 0.408467 | ||||||||
\(914\) | 390020.i | 0.466868i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 86304.9 | 0.102860 | ||||||||
\(917\) | 617692.i | 0.734570i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.32373e6 | 1.56736 | 0.783679 | − | 0.621166i | \(-0.213341\pi\) | ||||
0.783679 | + | 0.621166i | \(0.213341\pi\) | |||||||
\(920\) | − 34493.2i | − 0.0407529i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −917818. | −1.07968 | ||||||||
\(923\) | 2.04371e6i | 2.39892i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −234391. | −0.273941 | ||||||||
\(926\) | 756417.i | 0.882143i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 217543. | 0.252609 | ||||||||
\(929\) | 1.15956e6i | 1.34358i | 0.740743 | + | 0.671789i | \(0.234474\pi\) | ||||
−0.740743 | + | 0.671789i | \(0.765526\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 183811. | 0.212066 | ||||||||
\(932\) | 505638.i | 0.582114i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 218733. | 0.250738 | ||||||||
\(935\) | − 174031.i | − 0.199069i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.49483e6 | −1.70260 | −0.851300 | − | 0.524679i | \(-0.824185\pi\) | ||||
−0.851300 | + | 0.524679i | \(0.824185\pi\) | |||||||
\(938\) | − 384629.i | − 0.437156i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 71121.0 | 0.0804900 | ||||||||
\(941\) | − 1.18590e6i | − 1.33927i | −0.742689 | − | 0.669637i | \(-0.766450\pi\) | ||||
0.742689 | − | 0.669637i | \(-0.233550\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35937.5 | 0.0404133 | ||||||||
\(944\) | − 351114.i | − 0.394007i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.16362e6 | 1.30026 | ||||||||
\(947\) | − 865824.i | − 0.965450i | −0.875772 | − | 0.482725i | \(-0.839647\pi\) | ||||
0.875772 | − | 0.482725i | \(-0.160353\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −514521. | −0.571309 | ||||||||
\(950\) | − 932532.i | − 1.03328i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 165221. | 0.182302 | ||||||||
\(953\) | − 388687.i | − 0.427971i | −0.976837 | − | 0.213986i | \(-0.931355\pi\) | ||||
0.976837 | − | 0.213986i | \(-0.0686446\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 127708. | 0.140026 | ||||||||
\(956\) | − 343917.i | − 0.376304i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −824682. | −0.898577 | ||||||||
\(959\) | − 67175.3i | − 0.0730419i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −835513. | −0.904704 | ||||||||
\(962\) | − 256055.i | − 0.276683i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −301678. | −0.324631 | ||||||||
\(965\) | − 119399.i | − 0.128218i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 192495. | 0.205858 | 0.102929 | − | 0.994689i | \(-0.467179\pi\) | ||||
0.102929 | + | 0.994689i | \(0.467179\pi\) | |||||||
\(968\) | − 120267.i | − 0.128350i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −93797.3 | −0.0996889 | ||||||||
\(971\) | − 453950.i | − 0.481470i | −0.970591 | − | 0.240735i | \(-0.922612\pi\) | ||||
0.970591 | − | 0.240735i | \(-0.0773885\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 168668. | 0.178159 | ||||||||
\(974\) | 279183.i | 0.294287i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −322073. | −0.338107 | ||||||||
\(977\) | − 727881.i | − 0.762555i | −0.924461 | − | 0.381278i | \(-0.875484\pi\) | ||||
0.924461 | − | 0.381278i | \(-0.124516\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.94827e6 | 2.03275 | ||||||||
\(980\) | 8574.12i | 0.00892765i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 194311. | 0.201500 | ||||||||
\(983\) | − 662759.i | − 0.685881i | −0.939357 | − | 0.342941i | \(-0.888577\pi\) | ||||
0.939357 | − | 0.342941i | \(-0.111423\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 66322.0 | 0.0683573 | ||||||||
\(986\) | − 1.34014e6i | − 1.37846i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.01872e6 | 1.04362 | ||||||||
\(989\) | − 1.42077e6i | − 1.45255i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.16764e6 | −1.18894 | −0.594472 | − | 0.804116i | \(-0.702639\pi\) | ||||
−0.594472 | + | 0.804116i | \(0.702639\pi\) | |||||||
\(992\) | − 53701.5i | − 0.0545711i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −450529. | −0.455984 | ||||||||
\(995\) | − 138887.i | − 0.140286i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.12634e6 | 1.13313 | 0.566563 | − | 0.824019i | \(-0.308273\pi\) | ||||
0.566563 | + | 0.824019i | \(0.308273\pi\) | |||||||
\(998\) | 510487.i | 0.512535i | ||||||||
\(999\) | 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 | 378.5.b.a.323.3 | ✓ | 8 | |
3.2 | odd | 2 | inner | 378.5.b.a.323.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.5.b.a.323.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
378.5.b.a.323.6 | yes | 8 | 3.2 | odd | 2 | inner |