Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(235,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.235");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.c (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: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | no (minimal twist has level 177) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.5 | ||
Character | \(\chi\) | \(=\) | 531.235 |
Dual form | 531.5.c.d.235.36 |
$q$-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 \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 6.70986i | − | 1.67747i | −0.544544 | − | 0.838733i | \(-0.683297\pi\) | ||
0.544544 | − | 0.838733i | \(-0.316703\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −29.0222 | −1.81389 | ||||||||
\(5\) | 41.0870 | 1.64348 | 0.821739 | − | 0.569864i | \(-0.193004\pi\) | ||||
0.821739 | + | 0.569864i | \(0.193004\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.70931 | −0.136925 | −0.0684623 | − | 0.997654i | \(-0.521809\pi\) | ||||
−0.0684623 | + | 0.997654i | \(0.521809\pi\) | |||||||
\(8\) | 87.3773i | 1.36527i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 275.688i | − | 2.75688i | ||||||
\(11\) | 21.2822i | 0.175886i | 0.996126 | + | 0.0879430i | \(0.0280293\pi\) | ||||
−0.996126 | + | 0.0879430i | \(0.971971\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 73.2439i | − | 0.433396i | −0.976239 | − | 0.216698i | \(-0.930471\pi\) | ||
0.976239 | − | 0.216698i | \(-0.0695286\pi\) | |||||||
\(14\) | 45.0185i | 0.229686i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 121.934 | 0.476304 | ||||||||
\(17\) | −76.4439 | −0.264512 | −0.132256 | − | 0.991216i | \(-0.542222\pi\) | ||||
−0.132256 | + | 0.991216i | \(0.542222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 439.767 | 1.21819 | 0.609095 | − | 0.793097i | \(-0.291533\pi\) | ||||
0.609095 | + | 0.793097i | \(0.291533\pi\) | |||||||
\(20\) | −1192.43 | −2.98109 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 142.801 | 0.295043 | ||||||||
\(23\) | 164.608i | 0.311169i | 0.987823 | + | 0.155584i | \(0.0497260\pi\) | ||||
−0.987823 | + | 0.155584i | \(0.950274\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1063.14 | 1.70102 | ||||||||
\(26\) | −491.456 | −0.727006 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 194.719 | 0.248366 | ||||||||
\(29\) | 788.819 | 0.937954 | 0.468977 | − | 0.883211i | \(-0.344623\pi\) | ||||
0.468977 | + | 0.883211i | \(0.344623\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 754.698i | − | 0.785325i | −0.919683 | − | 0.392663i | \(-0.871554\pi\) | ||
0.919683 | − | 0.392663i | \(-0.128446\pi\) | |||||||
\(32\) | 579.878i | 0.566287i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 512.928i | 0.443709i | ||||||||
\(35\) | −275.665 | −0.225033 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1700.99i | − | 1.24251i | −0.783610 | − | 0.621253i | \(-0.786624\pi\) | ||
0.783610 | − | 0.621253i | \(-0.213376\pi\) | |||||||
\(38\) | − | 2950.77i | − | 2.04347i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3590.07i | 2.24379i | ||||||||
\(41\) | −72.3910 | −0.0430643 | −0.0215321 | − | 0.999768i | \(-0.506854\pi\) | ||||
−0.0215321 | + | 0.999768i | \(0.506854\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2692.60i | − | 1.45625i | −0.685447 | − | 0.728123i | \(-0.740393\pi\) | ||
0.685447 | − | 0.728123i | \(-0.259607\pi\) | |||||||
\(44\) | − | 617.657i | − | 0.319038i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1104.50 | 0.521975 | ||||||||
\(47\) | − | 2903.21i | − | 1.31426i | −0.753775 | − | 0.657132i | \(-0.771769\pi\) | ||
0.753775 | − | 0.657132i | \(-0.228231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2355.99 | −0.981252 | ||||||||
\(50\) | − | 7133.51i | − | 2.85340i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2125.70i | 0.786131i | ||||||||
\(53\) | −1176.18 | −0.418719 | −0.209360 | − | 0.977839i | \(-0.567138\pi\) | ||||
−0.209360 | + | 0.977839i | \(0.567138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 874.422i | 0.289065i | ||||||||
\(56\) | − | 586.241i | − | 0.186939i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 5292.86i | − | 1.57338i | ||||||
\(59\) | 3479.47 | − | 103.350i | 0.999559 | − | 0.0296897i | ||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2041.78i | − | 0.548718i | −0.961627 | − | 0.274359i | \(-0.911534\pi\) | ||
0.961627 | − | 0.274359i | \(-0.0884657\pi\) | |||||||
\(62\) | −5063.92 | −1.31736 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5841.84 | 1.42623 | ||||||||
\(65\) | − | 3009.37i | − | 0.712276i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 796.587i | − | 0.177453i | −0.996056 | − | 0.0887266i | \(-0.971720\pi\) | ||
0.996056 | − | 0.0887266i | \(-0.0282797\pi\) | |||||||
\(68\) | 2218.57 | 0.479795 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1849.67i | 0.377484i | ||||||||
\(71\) | 4861.25 | 0.964343 | 0.482171 | − | 0.876077i | \(-0.339848\pi\) | ||||
0.482171 | + | 0.876077i | \(0.339848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1824.82i | − | 0.342433i | −0.985233 | − | 0.171216i | \(-0.945230\pi\) | ||
0.985233 | − | 0.171216i | \(-0.0547697\pi\) | |||||||
\(74\) | −11413.4 | −2.08426 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12763.0 | −2.20966 | ||||||||
\(77\) | − | 142.789i | − | 0.0240831i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7086.59 | −1.13549 | −0.567745 | − | 0.823204i | \(-0.692184\pi\) | ||||
−0.567745 | + | 0.823204i | \(0.692184\pi\) | |||||||
\(80\) | 5009.89 | 0.782795 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 485.734i | 0.0722388i | ||||||||
\(83\) | 4425.07i | 0.642338i | 0.947022 | + | 0.321169i | \(0.104076\pi\) | ||||
−0.947022 | + | 0.321169i | \(0.895924\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3140.85 | −0.434719 | ||||||||
\(86\) | −18067.0 | −2.44280 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1859.58 | −0.240132 | ||||||||
\(89\) | 8041.54i | 1.01522i | 0.861588 | + | 0.507609i | \(0.169471\pi\) | ||||
−0.861588 | + | 0.507609i | \(0.830529\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 491.415i | 0.0593425i | ||||||||
\(92\) | − | 4777.30i | − | 0.564425i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −19480.1 | −2.20463 | ||||||||
\(95\) | 18068.7 | 2.00207 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2354.04i | 0.250190i | 0.992145 | + | 0.125095i | \(0.0399235\pi\) | ||||
−0.992145 | + | 0.125095i | \(0.960076\pi\) | |||||||
\(98\) | 15808.3i | 1.64602i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −30854.6 | −3.08546 | ||||||||
\(101\) | − | 15071.0i | − | 1.47741i | −0.674032 | − | 0.738703i | \(-0.735439\pi\) | ||
0.674032 | − | 0.738703i | \(-0.264561\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13089.2i | − | 1.23378i | −0.787048 | − | 0.616892i | \(-0.788392\pi\) | ||
0.787048 | − | 0.616892i | \(-0.211608\pi\) | |||||||
\(104\) | 6399.85 | 0.591702 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7892.02i | 0.702387i | ||||||||
\(107\) | 264.977 | 0.0231441 | 0.0115721 | − | 0.999933i | \(-0.496316\pi\) | ||||
0.0115721 | + | 0.999933i | \(0.496316\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13760.9i | − | 1.15823i | −0.815247 | − | 0.579113i | \(-0.803399\pi\) | ||
0.815247 | − | 0.579113i | \(-0.196601\pi\) | |||||||
\(110\) | 5867.25 | 0.484896 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −818.091 | −0.0652177 | ||||||||
\(113\) | 8838.66i | 0.692197i | 0.938198 | + | 0.346098i | \(0.112494\pi\) | ||||
−0.938198 | + | 0.346098i | \(0.887506\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6763.25i | 0.511399i | ||||||||
\(116\) | −22893.3 | −1.70134 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −693.464 | − | 23346.7i | −0.0498035 | − | 1.67673i | ||||
\(119\) | 512.886 | 0.0362182 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14188.1 | 0.969064 | ||||||||
\(122\) | −13700.1 | −0.920456 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 21903.0i | 1.42449i | ||||||||
\(125\) | 18001.8 | 1.15211 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12508.4 | −0.775524 | −0.387762 | − | 0.921759i | \(-0.626752\pi\) | ||||
−0.387762 | + | 0.921759i | \(0.626752\pi\) | |||||||
\(128\) | − | 29919.9i | − | 1.82616i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −20192.4 | −1.19482 | ||||||||
\(131\) | 30033.4i | 1.75010i | 0.484036 | + | 0.875048i | \(0.339170\pi\) | ||||
−0.484036 | + | 0.875048i | \(0.660830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2950.53 | −0.166800 | ||||||||
\(134\) | −5344.99 | −0.297672 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 6679.46i | − | 0.361130i | ||||||
\(137\) | −30546.6 | −1.62750 | −0.813751 | − | 0.581213i | \(-0.802578\pi\) | ||||
−0.813751 | + | 0.581213i | \(0.802578\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13641.7 | 0.706056 | 0.353028 | − | 0.935613i | \(-0.385152\pi\) | ||||
0.353028 | + | 0.935613i | \(0.385152\pi\) | |||||||
\(140\) | 8000.41 | 0.408184 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 32618.3i | − | 1.61765i | ||||||
\(143\) | 1558.79 | 0.0762283 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 32410.2 | 1.54151 | ||||||||
\(146\) | −12244.3 | −0.574419 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 49366.5i | 2.25377i | ||||||||
\(149\) | − | 18026.1i | − | 0.811949i | −0.913884 | − | 0.405975i | \(-0.866932\pi\) | ||
0.913884 | − | 0.405975i | \(-0.133068\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 39094.7i | 1.71460i | 0.514814 | + | 0.857302i | \(0.327861\pi\) | ||||
−0.514814 | + | 0.857302i | \(0.672139\pi\) | |||||||
\(152\) | 38425.6i | 1.66316i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −958.094 | −0.0403986 | ||||||||
\(155\) | − | 31008.2i | − | 1.29067i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 27675.1i | 1.12277i | 0.827556 | + | 0.561383i | \(0.189731\pi\) | ||||
−0.827556 | + | 0.561383i | \(0.810269\pi\) | |||||||
\(158\) | 47550.1i | 1.90475i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 23825.4i | 0.930680i | ||||||||
\(161\) | − | 1104.41i | − | 0.0426067i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −28910.4 | −1.08813 | −0.544063 | − | 0.839044i | \(-0.683115\pi\) | ||||
−0.544063 | + | 0.839044i | \(0.683115\pi\) | |||||||
\(164\) | 2100.95 | 0.0781138 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 29691.6 | 1.07750 | ||||||||
\(167\) | 44721.0 | 1.60354 | 0.801768 | − | 0.597635i | \(-0.203893\pi\) | ||||
0.801768 | + | 0.597635i | \(0.203893\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23196.3 | 0.812168 | ||||||||
\(170\) | 21074.6i | 0.729227i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 78145.2i | 2.64147i | ||||||||
\(173\) | 37239.4i | 1.24426i | 0.782914 | + | 0.622129i | \(0.213732\pi\) | ||||
−0.782914 | + | 0.622129i | \(0.786268\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7132.92 | −0.232912 | ||||||||
\(176\) | 2595.02i | 0.0837752i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 53957.6 | 1.70299 | ||||||||
\(179\) | − | 23586.9i | − | 0.736147i | −0.929797 | − | 0.368073i | \(-0.880017\pi\) | ||
0.929797 | − | 0.368073i | \(-0.119983\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1350.22 | −0.0412144 | −0.0206072 | − | 0.999788i | \(-0.506560\pi\) | ||||
−0.0206072 | + | 0.999788i | \(0.506560\pi\) | |||||||
\(182\) | 3297.33 | 0.0995450 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14383.0 | −0.424829 | ||||||||
\(185\) | − | 69888.5i | − | 2.04203i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1626.90i | − | 0.0465239i | ||||||
\(188\) | 84257.6i | 2.38393i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 121238.i | − | 3.35840i | ||||||
\(191\) | 34964.8i | 0.958438i | 0.877695 | + | 0.479219i | \(0.159080\pi\) | ||||
−0.877695 | + | 0.479219i | \(0.840920\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −28062.0 | −0.753362 | −0.376681 | − | 0.926343i | \(-0.622935\pi\) | ||||
−0.376681 | + | 0.926343i | \(0.622935\pi\) | |||||||
\(194\) | 15795.3 | 0.419685 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 68375.9 | 1.77988 | ||||||||
\(197\) | 8658.99 | 0.223118 | 0.111559 | − | 0.993758i | \(-0.464416\pi\) | ||||
0.111559 | + | 0.993758i | \(0.464416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −31291.6 | −0.790173 | −0.395087 | − | 0.918644i | \(-0.629285\pi\) | ||||
−0.395087 | + | 0.918644i | \(0.629285\pi\) | |||||||
\(200\) | 92894.1i | 2.32235i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −101124. | −2.47830 | ||||||||
\(203\) | −5292.43 | −0.128429 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2974.33 | −0.0707752 | ||||||||
\(206\) | −87826.8 | −2.06963 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 8930.90i | − | 0.206428i | ||||||
\(209\) | 9359.21i | 0.214263i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1277.25i | − | 0.0286888i | −0.999897 | − | 0.0143444i | \(-0.995434\pi\) | ||
0.999897 | − | 0.0143444i | \(-0.00456612\pi\) | |||||||
\(212\) | 34135.4 | 0.759510 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 1777.96i | − | 0.0388235i | ||||||
\(215\) | − | 110631.i | − | 2.39331i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5063.50i | 0.107530i | ||||||||
\(218\) | −92333.7 | −1.94288 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 25377.7i | − | 0.524332i | ||||||
\(221\) | 5599.05i | 0.114638i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18556.2 | 0.373146 | 0.186573 | − | 0.982441i | \(-0.440262\pi\) | ||||
0.186573 | + | 0.982441i | \(0.440262\pi\) | |||||||
\(224\) | − | 3890.58i | − | 0.0775386i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 59306.2 | 1.16114 | ||||||||
\(227\) | − | 61320.0i | − | 1.19001i | −0.803722 | − | 0.595005i | \(-0.797150\pi\) | ||
0.803722 | − | 0.595005i | \(-0.202850\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 86222.5i | − | 1.64418i | −0.569356 | − | 0.822091i | \(-0.692807\pi\) | ||
0.569356 | − | 0.822091i | \(-0.307193\pi\) | |||||||
\(230\) | 45380.5 | 0.857854 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 68924.9i | 1.28056i | ||||||||
\(233\) | − | 40899.5i | − | 0.753367i | −0.926342 | − | 0.376683i | \(-0.877064\pi\) | ||
0.926342 | − | 0.376683i | \(-0.122936\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 119284.i | − | 2.15997i | ||||||
\(236\) | −100982. | + | 2999.45i | −1.81309 | + | 0.0538539i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 3441.39i | − | 0.0607547i | ||||||
\(239\) | −4438.81 | −0.0777089 | −0.0388544 | − | 0.999245i | \(-0.512371\pi\) | ||||
−0.0388544 | + | 0.999245i | \(0.512371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −65511.7 | −1.12794 | −0.563968 | − | 0.825797i | \(-0.690726\pi\) | ||||
−0.563968 | + | 0.825797i | \(0.690726\pi\) | |||||||
\(242\) | − | 95199.9i | − | 1.62557i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 59257.0i | 0.995314i | ||||||||
\(245\) | −96800.3 | −1.61267 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 32210.2i | − | 0.527959i | ||||||
\(248\) | 65943.4 | 1.07218 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 120789.i | − | 1.93263i | ||||||
\(251\) | 26481.1 | 0.420328 | 0.210164 | − | 0.977666i | \(-0.432600\pi\) | ||||
0.210164 | + | 0.977666i | \(0.432600\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3503.23 | −0.0547302 | ||||||||
\(254\) | 83929.8i | 1.30091i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −107289. | −1.63710 | ||||||||
\(257\) | 73530.4 | 1.11327 | 0.556635 | − | 0.830757i | \(-0.312092\pi\) | ||||
0.556635 | + | 0.830757i | \(0.312092\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11412.5i | 0.170130i | ||||||||
\(260\) | 87338.5i | 1.29199i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 201520. | 2.93573 | ||||||||
\(263\) | 58037.1 | 0.839062 | 0.419531 | − | 0.907741i | \(-0.362194\pi\) | ||||
0.419531 | + | 0.907741i | \(0.362194\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −48325.8 | −0.688156 | ||||||||
\(266\) | 19797.6i | 0.279802i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 23118.7i | 0.321880i | ||||||||
\(269\) | − | 119064.i | − | 1.64542i | −0.568464 | − | 0.822708i | \(-0.692462\pi\) | ||
0.568464 | − | 0.822708i | \(-0.307538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 95279.2 | 1.29736 | 0.648679 | − | 0.761062i | \(-0.275322\pi\) | ||||
0.648679 | + | 0.761062i | \(0.275322\pi\) | |||||||
\(272\) | −9321.10 | −0.125988 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 204963.i | 2.73008i | ||||||||
\(275\) | 22625.9i | 0.299186i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −70994.3 | −0.925260 | −0.462630 | − | 0.886551i | \(-0.653094\pi\) | ||||
−0.462630 | + | 0.886551i | \(0.653094\pi\) | |||||||
\(278\) | − | 91534.0i | − | 1.18438i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 24086.9i | − | 0.307230i | ||||||
\(281\) | −89157.2 | −1.12913 | −0.564565 | − | 0.825389i | \(-0.690956\pi\) | ||||
−0.564565 | + | 0.825389i | \(0.690956\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 121771.i | 1.52044i | 0.649664 | + | 0.760222i | \(0.274910\pi\) | ||||
−0.649664 | + | 0.760222i | \(0.725090\pi\) | |||||||
\(284\) | −141084. | −1.74921 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 10459.3i | − | 0.127870i | ||||||
\(287\) | 485.693 | 0.00589656 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −77677.3 | −0.930034 | ||||||||
\(290\) | − | 217468.i | − | 2.58582i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 52960.5i | 0.621135i | ||||||||
\(293\) | 14072.9 | 0.163927 | 0.0819633 | − | 0.996635i | \(-0.473881\pi\) | ||||
0.0819633 | + | 0.996635i | \(0.473881\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 142961. | − | 4246.34i | 1.64275 | − | 0.0487944i | ||||
\(296\) | 148628. | 1.69636 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −120953. | −1.36202 | ||||||||
\(299\) | 12056.5 | 0.134859 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18065.5i | 0.199396i | ||||||||
\(302\) | 262320. | 2.87619 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 53622.4 | 0.580229 | ||||||||
\(305\) | − | 83890.6i | − | 0.901807i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 84061.4 | 0.891908 | 0.445954 | − | 0.895056i | \(-0.352865\pi\) | ||||
0.445954 | + | 0.895056i | \(0.352865\pi\) | |||||||
\(308\) | 4144.05i | 0.0436841i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −208061. | −2.16505 | ||||||||
\(311\) | 27808.7 | 0.287514 | 0.143757 | − | 0.989613i | \(-0.454082\pi\) | ||||
0.143757 | + | 0.989613i | \(0.454082\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3675.80i | 0.0375200i | 0.999824 | + | 0.0187600i | \(0.00597184\pi\) | ||||
−0.999824 | + | 0.0187600i | \(0.994028\pi\) | |||||||
\(314\) | 185696. | 1.88340 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 205669. | 2.05965 | ||||||||
\(317\) | −30461.2 | −0.303129 | −0.151565 | − | 0.988447i | \(-0.548431\pi\) | ||||
−0.151565 | + | 0.988447i | \(0.548431\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16787.8i | 0.164973i | ||||||||
\(320\) | 240023. | 2.34398 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7410.42 | −0.0714712 | ||||||||
\(323\) | −33617.5 | −0.322226 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 77868.4i | − | 0.737215i | ||||||
\(326\) | 193985.i | 1.82529i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6325.33i | − | 0.0587943i | ||||||
\(329\) | 19478.5i | 0.179955i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 206607. | 1.88577 | 0.942884 | − | 0.333120i | \(-0.108102\pi\) | ||||
0.942884 | + | 0.333120i | \(0.108102\pi\) | |||||||
\(332\) | − | 128425.i | − | 1.16513i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 300072.i | − | 2.68988i | ||||||
\(335\) | − | 32729.4i | − | 0.291641i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 145823.i | 1.28401i | 0.766702 | + | 0.642004i | \(0.221897\pi\) | ||||
−0.766702 | + | 0.642004i | \(0.778103\pi\) | |||||||
\(338\) | − | 155644.i | − | 1.36238i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 91154.4 | 0.788533 | ||||||||
\(341\) | 16061.6 | 0.138128 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 31916.1 | 0.271282 | ||||||||
\(344\) | 235272. | 1.98817 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 249871. | 2.08720 | ||||||||
\(347\) | 32401.9i | 0.269098i | 0.990907 | + | 0.134549i | \(0.0429586\pi\) | ||||
−0.990907 | + | 0.134549i | \(0.957041\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 165183.i | − | 1.35617i | −0.734982 | − | 0.678086i | \(-0.762809\pi\) | ||
0.734982 | − | 0.678086i | \(-0.237191\pi\) | |||||||
\(350\) | 47860.9i | 0.390701i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12341.1 | −0.0996020 | ||||||||
\(353\) | 193446.i | 1.55242i | 0.630472 | + | 0.776212i | \(0.282861\pi\) | ||||
−0.630472 | + | 0.776212i | \(0.717139\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 199734. | 1.58488 | ||||||||
\(356\) | − | 233383.i | − | 1.84149i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −158265. | −1.23486 | ||||||||
\(359\) | 94638.7 | 0.734311 | 0.367155 | − | 0.930160i | \(-0.380332\pi\) | ||||
0.367155 | + | 0.930160i | \(0.380332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 63073.9 | 0.483989 | ||||||||
\(362\) | 9059.82i | 0.0691357i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 14262.0i | − | 0.107641i | ||||||
\(365\) | − | 74976.5i | − | 0.562781i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 250626.i | − | 1.86078i | −0.366576 | − | 0.930388i | \(-0.619470\pi\) | ||
0.366576 | − | 0.930388i | \(-0.380530\pi\) | |||||||
\(368\) | 20071.3i | 0.148211i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −468942. | −3.42544 | ||||||||
\(371\) | 7891.37 | 0.0573330 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 65456.3 | 0.470472 | 0.235236 | − | 0.971938i | \(-0.424414\pi\) | ||||
0.235236 | + | 0.971938i | \(0.424414\pi\) | |||||||
\(374\) | −10916.2 | −0.0780423 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 253675. | 1.79433 | ||||||||
\(377\) | − | 57776.1i | − | 0.406505i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 60322.5 | 0.419953 | 0.209977 | − | 0.977706i | \(-0.432661\pi\) | ||||
0.209977 | + | 0.977706i | \(0.432661\pi\) | |||||||
\(380\) | −524393. | −3.63153 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 234609. | 1.60775 | ||||||||
\(383\) | 53450.5 | 0.364380 | 0.182190 | − | 0.983263i | \(-0.441681\pi\) | ||||
0.182190 | + | 0.983263i | \(0.441681\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 5866.76i | − | 0.0395801i | ||||||
\(386\) | 188292.i | 1.26374i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 68319.4i | − | 0.453817i | ||||||
\(389\) | −49209.3 | −0.325198 | −0.162599 | − | 0.986692i | \(-0.551988\pi\) | ||||
−0.162599 | + | 0.986692i | \(0.551988\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12583.3i | − | 0.0823078i | ||||||
\(392\) | − | 205860.i | − | 1.33967i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 58100.6i | − | 0.374273i | ||||||
\(395\) | −291167. | −1.86615 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 75598.4i | 0.479658i | 0.970815 | + | 0.239829i | \(0.0770914\pi\) | ||||
−0.970815 | + | 0.239829i | \(0.922909\pi\) | |||||||
\(398\) | 209963.i | 1.32549i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 129633. | 0.810203 | ||||||||
\(401\) | 289441.i | 1.80000i | 0.435893 | + | 0.899999i | \(0.356433\pi\) | ||||
−0.435893 | + | 0.899999i | \(0.643567\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −55277.0 | −0.340357 | ||||||||
\(404\) | 437394.i | 2.67985i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 35511.4i | 0.215435i | ||||||||
\(407\) | 36200.9 | 0.218540 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 157956.i | − | 0.944256i | −0.881530 | − | 0.472128i | \(-0.843486\pi\) | ||
0.881530 | − | 0.472128i | \(-0.156514\pi\) | |||||||
\(410\) | 19957.3i | 0.118723i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 379878.i | 2.23795i | ||||||||
\(413\) | −23344.8 | + | 693.407i | −0.136864 | + | 0.00406526i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 181813.i | 1.05567i | ||||||||
\(416\) | 42472.5 | 0.245426 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 62799.0 | 0.359418 | ||||||||
\(419\) | 280260.i | 1.59637i | 0.602412 | + | 0.798185i | \(0.294206\pi\) | ||||
−0.602412 | + | 0.798185i | \(0.705794\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 123028.i | 0.694126i | 0.937842 | + | 0.347063i | \(0.112821\pi\) | ||||
−0.937842 | + | 0.347063i | \(0.887179\pi\) | |||||||
\(422\) | −8570.20 | −0.0481245 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 102772.i | − | 0.571665i | ||||||
\(425\) | −81270.4 | −0.449940 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13698.9i | 0.0751331i | ||||||||
\(428\) | −7690.23 | −0.0419809 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −742317. | −4.01469 | ||||||||
\(431\) | 118678.i | 0.638877i | 0.947607 | + | 0.319438i | \(0.103494\pi\) | ||||
−0.947607 | + | 0.319438i | \(0.896506\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −336890. | −1.79685 | −0.898425 | − | 0.439127i | \(-0.855288\pi\) | ||||
−0.898425 | + | 0.439127i | \(0.855288\pi\) | |||||||
\(434\) | 33975.4 | 0.180378 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 399372.i | 2.10089i | ||||||||
\(437\) | 72389.3i | 0.379063i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 333202. | 1.72893 | 0.864466 | − | 0.502691i | \(-0.167657\pi\) | ||||
0.864466 | + | 0.502691i | \(0.167657\pi\) | |||||||
\(440\) | −76404.6 | −0.394652 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 37568.8 | 0.192302 | ||||||||
\(443\) | 79729.2i | 0.406265i | 0.979151 | + | 0.203133i | \(0.0651123\pi\) | ||||
−0.979151 | + | 0.203133i | \(0.934888\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 330403.i | 1.66849i | ||||||||
\(446\) | − | 124509.i | − | 0.625940i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −39194.7 | −0.195286 | ||||||||
\(449\) | 278079. | 1.37935 | 0.689676 | − | 0.724118i | \(-0.257753\pi\) | ||||
0.689676 | + | 0.724118i | \(0.257753\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1540.64i | − | 0.00757440i | ||||||
\(452\) | − | 256518.i | − | 1.25557i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −411449. | −1.99620 | ||||||||
\(455\) | 20190.8i | 0.0975282i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 175865.i | 0.842067i | 0.907045 | + | 0.421033i | \(0.138332\pi\) | ||||
−0.907045 | + | 0.421033i | \(0.861668\pi\) | |||||||
\(458\) | −578541. | −2.75806 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 196285.i | − | 0.927621i | ||||||
\(461\) | 158569. | 0.746134 | 0.373067 | − | 0.927804i | \(-0.378306\pi\) | ||||
0.373067 | + | 0.927804i | \(0.378306\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 77926.4i | − | 0.363515i | −0.983343 | − | 0.181758i | \(-0.941821\pi\) | ||
0.983343 | − | 0.181758i | \(-0.0581786\pi\) | |||||||
\(464\) | 96183.7 | 0.446751 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −274430. | −1.26375 | ||||||||
\(467\) | − | 408542.i | − | 1.87328i | −0.350291 | − | 0.936641i | \(-0.613917\pi\) | ||
0.350291 | − | 0.936641i | \(-0.386083\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5344.55i | 0.0242977i | ||||||||
\(470\) | −800380. | −3.62327 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9030.44 | + | 304026.i | 0.0405345 | + | 1.36467i | ||||
\(473\) | 57304.5 | 0.256133 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 467533. | 2.07217 | ||||||||
\(476\) | −14885.1 | −0.0656957 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 29783.8i | 0.130354i | ||||||||
\(479\) | 161846. | 0.705393 | 0.352697 | − | 0.935738i | \(-0.385265\pi\) | ||||
0.352697 | + | 0.935738i | \(0.385265\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −124587. | −0.538497 | ||||||||
\(482\) | 439574.i | 1.89207i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −411769. | −1.75777 | ||||||||
\(485\) | 96720.2i | 0.411182i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −156630. | −0.660414 | −0.330207 | − | 0.943909i | \(-0.607119\pi\) | ||||
−0.330207 | + | 0.943909i | \(0.607119\pi\) | |||||||
\(488\) | 178405. | 0.749149 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 649516.i | 2.70519i | ||||||||
\(491\) | −289340. | −1.20018 | −0.600089 | − | 0.799933i | \(-0.704868\pi\) | ||||
−0.600089 | + | 0.799933i | \(0.704868\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −60300.4 | −0.248100 | ||||||||
\(494\) | −216126. | −0.885632 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 92023.2i | − | 0.374054i | ||||||
\(497\) | −32615.6 | −0.132042 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 366469. | 1.47176 | 0.735878 | − | 0.677114i | \(-0.236769\pi\) | ||||
0.735878 | + | 0.677114i | \(0.236769\pi\) | |||||||
\(500\) | −522452. | −2.08981 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 177684.i | − | 0.705085i | ||||||
\(503\) | 160477.i | 0.634274i | 0.948380 | + | 0.317137i | \(0.102722\pi\) | ||||
−0.948380 | + | 0.317137i | \(0.897278\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 619222.i | − | 2.42808i | ||||||
\(506\) | 23506.2i | 0.0918081i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 363022. | 1.40671 | ||||||||
\(509\) | 244953.i | 0.945468i | 0.881205 | + | 0.472734i | \(0.156733\pi\) | ||||
−0.881205 | + | 0.472734i | \(0.843267\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12243.3i | 0.0468875i | ||||||||
\(512\) | 241175.i | 0.920008i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 493379.i | − | 1.86747i | ||||||
\(515\) | − | 537796.i | − | 2.02770i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 61786.8 | 0.231161 | ||||||||
\(518\) | 76576.1 | 0.285387 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 262950. | 0.972450 | ||||||||
\(521\) | 366691. | 1.35090 | 0.675452 | − | 0.737404i | \(-0.263948\pi\) | ||||
0.675452 | + | 0.737404i | \(0.263948\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 97476.4 | 0.356366 | 0.178183 | − | 0.983997i | \(-0.442978\pi\) | ||||
0.178183 | + | 0.983997i | \(0.442978\pi\) | |||||||
\(524\) | − | 871636.i | − | 3.17448i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 389421.i | − | 1.40750i | ||||||
\(527\) | 57692.0i | 0.207728i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 252745. | 0.903174 | ||||||||
\(530\) | 324259.i | 1.15436i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 85631.0 | 0.302557 | ||||||||
\(533\) | 5302.20i | 0.0186639i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10887.1 | 0.0380369 | ||||||||
\(536\) | 69603.6 | 0.242272 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −798903. | −2.76013 | ||||||||
\(539\) | − | 50140.6i | − | 0.172589i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 321027.i | − | 1.09685i | −0.836199 | − | 0.548425i | \(-0.815227\pi\) | ||
0.836199 | − | 0.548425i | \(-0.184773\pi\) | |||||||
\(542\) | − | 639310.i | − | 2.17627i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 44328.1i | − | 0.149790i | ||||||
\(545\) | − | 565393.i | − | 1.90352i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −82148.9 | −0.274554 | −0.137277 | − | 0.990533i | \(-0.543835\pi\) | ||||
−0.137277 | + | 0.990533i | \(0.543835\pi\) | |||||||
\(548\) | 886530. | 2.95211 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 151817. | 0.501874 | ||||||||
\(551\) | 346896. | 1.14261 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 47546.1 | 0.155477 | ||||||||
\(554\) | 476362.i | 1.55209i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −395913. | −1.28071 | ||||||||
\(557\) | 92439.5 | 0.297953 | 0.148976 | − | 0.988841i | \(-0.452402\pi\) | ||||
0.148976 | + | 0.988841i | \(0.452402\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −197216. | −0.631131 | ||||||||
\(560\) | −33612.9 | −0.107184 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 598232.i | 1.89408i | ||||||||
\(563\) | 332807.i | 1.04997i | 0.851112 | + | 0.524984i | \(0.175929\pi\) | ||||
−0.851112 | + | 0.524984i | \(0.824071\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 363154.i | 1.13761i | ||||||||
\(566\) | 817065. | 2.55049 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 424763.i | 1.31659i | ||||||||
\(569\) | 71655.2i | 0.221321i | 0.993858 | + | 0.110661i | \(0.0352966\pi\) | ||||
−0.993858 | + | 0.110661i | \(0.964703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 235330.i | 0.721780i | 0.932608 | + | 0.360890i | \(0.117527\pi\) | ||||
−0.932608 | + | 0.360890i | \(0.882473\pi\) | |||||||
\(572\) | −45239.6 | −0.138270 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 3258.94i | − | 0.00989127i | ||||||
\(575\) | 175001.i | 0.529305i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 582269. | 1.74893 | 0.874465 | − | 0.485089i | \(-0.161213\pi\) | ||||
0.874465 | + | 0.485089i | \(0.161213\pi\) | |||||||
\(578\) | 521204.i | 1.56010i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −940615. | −2.79612 | ||||||||
\(581\) | − | 29689.1i | − | 0.0879519i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 25031.8i | − | 0.0736469i | ||||||
\(584\) | 159448. | 0.467513 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 94427.4i | − | 0.274981i | ||||||
\(587\) | 535088.i | 1.55292i | 0.630166 | + | 0.776460i | \(0.282987\pi\) | ||||
−0.630166 | + | 0.776460i | \(0.717013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 331891.i | − | 0.956676i | ||||||
\(590\) | −28492.3 | − | 959246.i | −0.0818510 | − | 2.75566i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 207408.i | − | 0.591810i | ||||||
\(593\) | −439880. | −1.25091 | −0.625453 | − | 0.780262i | \(-0.715086\pi\) | ||||
−0.625453 | + | 0.780262i | \(0.715086\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21072.9 | 0.0595238 | ||||||||
\(596\) | 523157.i | 1.47279i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 80897.7i | − | 0.226222i | ||||||
\(599\) | 177415. | 0.494465 | 0.247233 | − | 0.968956i | \(-0.420479\pi\) | ||||
0.247233 | + | 0.968956i | \(0.420479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 602513.i | 1.66808i | 0.551703 | + | 0.834041i | \(0.313978\pi\) | ||||
−0.551703 | + | 0.834041i | \(0.686022\pi\) | |||||||
\(602\) | 121217. | 0.334480 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 1.13461e6i | − | 3.11010i | ||||||
\(605\) | 582945. | 1.59264 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −235674. | −0.639639 | −0.319820 | − | 0.947478i | \(-0.603622\pi\) | ||||
−0.319820 | + | 0.947478i | \(0.603622\pi\) | |||||||
\(608\) | 255011.i | 0.689846i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −562894. | −1.51275 | ||||||||
\(611\) | −212642. | −0.569597 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3306.79i | 0.00880006i | 0.999990 | + | 0.00440003i | \(0.00140058\pi\) | ||||
−0.999990 | + | 0.00440003i | \(0.998599\pi\) | |||||||
\(614\) | − | 564040.i | − | 1.49614i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12476.5 | 0.0328800 | ||||||||
\(617\) | −194814. | −0.511740 | −0.255870 | − | 0.966711i | \(-0.582362\pi\) | ||||
−0.255870 | + | 0.966711i | \(0.582362\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −346456. | −0.904206 | −0.452103 | − | 0.891966i | \(-0.649326\pi\) | ||||
−0.452103 | + | 0.891966i | \(0.649326\pi\) | |||||||
\(620\) | 899928.i | 2.34112i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 186592.i | − | 0.482295i | ||||||
\(623\) | − | 53953.2i | − | 0.139008i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 75176.8 | 0.192453 | ||||||||
\(626\) | 24664.1 | 0.0629385 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 803192.i | − | 2.03657i | ||||||
\(629\) | 130030.i | 0.328657i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 694008. | 1.74303 | 0.871517 | − | 0.490365i | \(-0.163136\pi\) | ||||
0.871517 | + | 0.490365i | \(0.163136\pi\) | |||||||
\(632\) | − | 619207.i | − | 1.55025i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 204390.i | 0.508489i | ||||||||
\(635\) | −513933. | −1.27456 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 172561.i | 0.425270i | ||||||||
\(638\) | 112644. | 0.276736 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 1.22932e6i | − | 3.00126i | ||||||
\(641\) | 97669.8 | 0.237708 | 0.118854 | − | 0.992912i | \(-0.462078\pi\) | ||||
0.118854 | + | 0.992912i | \(0.462078\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −128561. | −0.310947 | −0.155474 | − | 0.987840i | \(-0.549690\pi\) | ||||
−0.155474 | + | 0.987840i | \(0.549690\pi\) | |||||||
\(644\) | 32052.3i | 0.0772837i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 225569.i | 0.540523i | ||||||||
\(647\) | 280631. | 0.670390 | 0.335195 | − | 0.942149i | \(-0.391198\pi\) | ||||
0.335195 | + | 0.942149i | \(0.391198\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2199.52 | + | 74050.7i | 0.00522201 | + | 0.175809i | ||||
\(650\) | −522486. | −1.23665 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 839044. | 1.97374 | ||||||||
\(653\) | −380413. | −0.892132 | −0.446066 | − | 0.895000i | \(-0.647175\pi\) | ||||
−0.446066 | + | 0.895000i | \(0.647175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.23398e6i | 2.87625i | ||||||||
\(656\) | −8826.91 | −0.0205117 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 130698. | 0.301869 | ||||||||
\(659\) | − | 59943.3i | − | 0.138029i | −0.997616 | − | 0.0690145i | \(-0.978015\pi\) | ||
0.997616 | − | 0.0690145i | \(-0.0219855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −87318.8 | −0.199850 | −0.0999252 | − | 0.994995i | \(-0.531860\pi\) | ||||
−0.0999252 | + | 0.994995i | \(0.531860\pi\) | |||||||
\(662\) | − | 1.38630e6i | − | 3.16331i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −386650. | −0.876965 | ||||||||
\(665\) | −121228. | −0.274133 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 129846.i | 0.291862i | ||||||||
\(668\) | −1.29790e6 | −2.90864 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −219609. | −0.489217 | ||||||||
\(671\) | 43453.6 | 0.0965119 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 598287.i | 1.32093i | 0.750857 | + | 0.660465i | \(0.229641\pi\) | ||||
−0.750857 | + | 0.660465i | \(0.770359\pi\) | |||||||
\(674\) | 978455. | 2.15388 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −673209. | −1.47318 | ||||||||
\(677\) | −874864. | −1.90881 | −0.954406 | − | 0.298512i | \(-0.903510\pi\) | ||||
−0.954406 | + | 0.298512i | \(0.903510\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 15794.0i | − | 0.0342572i | ||||||
\(680\) | − | 274439.i | − | 0.593509i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 107771.i | − | 0.231705i | ||||||
\(683\) | − | 742238.i | − | 1.59112i | −0.605878 | − | 0.795558i | \(-0.707178\pi\) | ||
0.605878 | − | 0.795558i | \(-0.292822\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.25507e6 | −2.67477 | ||||||||
\(686\) | − | 214152.i | − | 0.455066i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 328319.i | − | 0.693616i | ||||||
\(689\) | 86148.1i | 0.181471i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 339025.i | − | 0.710028i | −0.934861 | − | 0.355014i | \(-0.884476\pi\) | ||
0.934861 | − | 0.355014i | \(-0.115524\pi\) | |||||||
\(692\) | − | 1.08077e6i | − | 2.25695i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 217412. | 0.451403 | ||||||||
\(695\) | 560496. | 1.16039 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5533.85 | 0.0113910 | ||||||||
\(698\) | −1.10836e6 | −2.27493 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 207013. | 0.422476 | ||||||||
\(701\) | − | 288735.i | − | 0.587576i | −0.955871 | − | 0.293788i | \(-0.905084\pi\) | ||
0.955871 | − | 0.293788i | \(-0.0949159\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 748039.i | − | 1.51361i | ||||||
\(704\) | 124327.i | 0.250854i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.29800e6 | 2.60414 | ||||||||
\(707\) | 101116.i | 0.202293i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −65496.9 | −0.130295 | −0.0651476 | − | 0.997876i | \(-0.520752\pi\) | ||||
−0.0651476 | + | 0.997876i | \(0.520752\pi\) | |||||||
\(710\) | − | 1.34019e6i | − | 2.65858i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −702648. | −1.38605 | ||||||||
\(713\) | 124229. | 0.244369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 64046.0 | 0.125279 | ||||||||
\(716\) | 684544.i | 1.33529i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 635013.i | − | 1.23178i | ||||||
\(719\) | − | 616651.i | − | 1.19284i | −0.802673 | − | 0.596420i | \(-0.796589\pi\) | ||
0.802673 | − | 0.596420i | \(-0.203411\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 87819.5i | 0.168935i | ||||||||
\(722\) | − | 423217.i | − | 0.811875i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 39186.5 | 0.0747583 | ||||||||
\(725\) | 838624. | 1.59548 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 79727.7 | 0.150848 | 0.0754241 | − | 0.997152i | \(-0.475969\pi\) | ||||
0.0754241 | + | 0.997152i | \(0.475969\pi\) | |||||||
\(728\) | −42938.5 | −0.0810186 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −503082. | −0.944045 | ||||||||
\(731\) | 205833.i | 0.385194i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −797529. | −1.48436 | −0.742179 | − | 0.670202i | \(-0.766207\pi\) | ||||
−0.742179 | + | 0.670202i | \(0.766207\pi\) | |||||||
\(734\) | −1.68167e6 | −3.12139 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −95452.7 | −0.176211 | ||||||||
\(737\) | 16953.1 | 0.0312115 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 924588.i | 1.69301i | 0.532381 | + | 0.846505i | \(0.321297\pi\) | ||||
−0.532381 | + | 0.846505i | \(0.678703\pi\) | |||||||
\(740\) | 2.02832e6i | 3.70402i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 52950.0i | − | 0.0961741i | ||||||
\(743\) | −671065. | −1.21559 | −0.607795 | − | 0.794094i | \(-0.707946\pi\) | ||||
−0.607795 | + | 0.794094i | \(0.707946\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 740637.i | − | 1.33442i | ||||||
\(746\) | − | 439202.i | − | 0.789200i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 47216.1i | 0.0843893i | ||||||||
\(749\) | −1777.81 | −0.00316900 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 405680.i | 0.719289i | 0.933089 | + | 0.359645i | \(0.117102\pi\) | ||||
−0.933089 | + | 0.359645i | \(0.882898\pi\) | |||||||
\(752\) | − | 354000.i | − | 0.625989i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −387670. | −0.681898 | ||||||||
\(755\) | 1.60628e6i | 2.81791i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −843491. | −1.47193 | −0.735967 | − | 0.677017i | \(-0.763272\pi\) | ||||
−0.735967 | + | 0.677017i | \(0.763272\pi\) | |||||||
\(758\) | − | 404755.i | − | 0.704457i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.57879e6i | 2.73337i | ||||||||
\(761\) | 953711. | 1.64682 | 0.823412 | − | 0.567444i | \(-0.192068\pi\) | ||||
0.823412 | + | 0.567444i | \(0.192068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 92326.0i | 0.158590i | ||||||||
\(764\) | − | 1.01476e6i | − | 1.73850i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 358645.i | − | 0.611234i | ||||||
\(767\) | −7569.75 | − | 254849.i | −0.0128674 | − | 0.433205i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 551211.i | 0.932106i | 0.884757 | + | 0.466053i | \(0.154324\pi\) | ||||
−0.884757 | + | 0.466053i | \(0.845676\pi\) | |||||||
\(770\) | −39365.2 | −0.0663943 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 814421. | 1.36651 | ||||||||
\(773\) | − | 98128.0i | − | 0.164223i | −0.996623 | − | 0.0821115i | \(-0.973834\pi\) | ||
0.996623 | − | 0.0821115i | \(-0.0261664\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 802348.i | − | 1.33586i | ||||||
\(776\) | −205689. | −0.341577 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 330187.i | 0.545508i | ||||||||
\(779\) | −31835.2 | −0.0524605 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 103458.i | 0.169614i | ||||||||
\(782\) | −84432.2 | −0.138068 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −287274. | −0.467374 | ||||||||
\(785\) | 1.13708e6i | 1.84524i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 975267. | 1.57461 | 0.787307 | − | 0.616561i | \(-0.211475\pi\) | ||||
0.787307 | + | 0.616561i | \(0.211475\pi\) | |||||||
\(788\) | −251303. | −0.404712 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.95369e6i | 3.13041i | ||||||||
\(791\) | − | 59301.3i | − | 0.0947788i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −149548. | −0.237812 | ||||||||
\(794\) | 507255. | 0.804610 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 908153. | 1.43329 | ||||||||
\(797\) | 838974.i | 1.32078i | 0.750921 | + | 0.660392i | \(0.229610\pi\) | ||||
−0.750921 | + | 0.660392i | \(0.770390\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 221933.i | 0.347638i | ||||||||
\(800\) | 616490.i | 0.963266i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.94211e6 | 3.01943 | ||||||||
\(803\) | 38836.3 | 0.0602292 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 45376.7i | − | 0.0700231i | ||||||
\(806\) | 370901.i | 0.570936i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.31686e6 | 2.01706 | ||||||||
\(809\) | 620319.i | 0.947804i | 0.880578 | + | 0.473902i | \(0.157155\pi\) | ||||
−0.880578 | + | 0.473902i | \(0.842845\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.20442e6i | − | 1.83120i | −0.402093 | − | 0.915599i | \(-0.631717\pi\) | ||
0.402093 | − | 0.915599i | \(-0.368283\pi\) | |||||||
\(812\) | 153598. | 0.232956 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 242903.i | − | 0.366592i | ||||||
\(815\) | −1.18784e6 | −1.78831 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.18412e6i | − | 1.77399i | ||||||
\(818\) | −1.05986e6 | −1.58396 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 86321.6 | 0.128378 | ||||||||
\(821\) | 254507.i | 0.377584i | 0.982017 | + | 0.188792i | \(0.0604571\pi\) | ||||
−0.982017 | + | 0.188792i | \(0.939543\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 272405.i | 0.402175i | 0.979573 | + | 0.201088i | \(0.0644476\pi\) | ||||
−0.979573 | + | 0.201088i | \(0.935552\pi\) | |||||||
\(824\) | 1.14370e6 | 1.68445 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4652.66 | + | 156640.i | 0.00681932 | + | 0.229585i | ||||
\(827\) | −460578. | −0.673430 | −0.336715 | − | 0.941607i | \(-0.609316\pi\) | ||||
−0.336715 | + | 0.941607i | \(0.609316\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −106117. | −0.154411 | −0.0772053 | − | 0.997015i | \(-0.524600\pi\) | ||||
−0.0772053 | + | 0.997015i | \(0.524600\pi\) | |||||||
\(830\) | 1.21994e6 | 1.77085 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 427879.i | − | 0.618122i | ||||||
\(833\) | 180101. | 0.259553 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.83745e6 | 2.63538 | ||||||||
\(836\) | − | 271625.i | − | 0.388649i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.88051e6 | 2.67786 | ||||||||
\(839\) | 1.07945e6i | 1.53348i | 0.641957 | + | 0.766741i | \(0.278123\pi\) | ||||
−0.641957 | + | 0.766741i | \(0.721877\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −85045.7 | −0.120243 | ||||||||
\(842\) | 825498. | 1.16437 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 37068.8i | 0.0520383i | ||||||||
\(845\) | 953067. | 1.33478 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −95192.1 | −0.132689 | ||||||||
\(848\) | −143416. | −0.199438 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 545313.i | 0.754759i | ||||||||
\(851\) | 279997. | 0.386629 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −694278. | −0.954191 | −0.477096 | − | 0.878851i | \(-0.658311\pi\) | ||||
−0.477096 | + | 0.878851i | \(0.658311\pi\) | |||||||
\(854\) | 91917.9 | 0.126033 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23153.0i | 0.0315980i | ||||||||
\(857\) | − | 565662.i | − | 0.770186i | −0.922878 | − | 0.385093i | \(-0.874169\pi\) | ||
0.922878 | − | 0.385093i | \(-0.125831\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 918130.i | − | 1.24428i | −0.782906 | − | 0.622139i | \(-0.786264\pi\) | ||
0.782906 | − | 0.622139i | \(-0.213736\pi\) | |||||||
\(860\) | 3.21075e6i | 4.34120i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 796316. | 1.07169 | ||||||||
\(863\) | 930295.i | 1.24911i | 0.780982 | + | 0.624553i | \(0.214719\pi\) | ||||
−0.780982 | + | 0.624553i | \(0.785281\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.53005e6i | 2.04491i | ||||||||
\(866\) | 2.26048e6i | 3.01415i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 146954.i | − | 0.195048i | ||||||
\(869\) | − | 150818.i | − | 0.199717i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −58345.1 | −0.0769074 | ||||||||
\(872\) | 1.20239e6 | 1.58129 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 485722. | 0.635865 | ||||||||
\(875\) | −120779. | −0.157753 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −313247. | −0.407275 | −0.203638 | − | 0.979046i | \(-0.565276\pi\) | ||||
−0.203638 | + | 0.979046i | \(0.565276\pi\) | |||||||
\(878\) | − | 2.23574e6i | − | 2.90022i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 106622.i | 0.137683i | ||||||||
\(881\) | − | 185355.i | − | 0.238810i | −0.992846 | − | 0.119405i | \(-0.961901\pi\) | ||
0.992846 | − | 0.119405i | \(-0.0380988\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −613135. | −0.786384 | −0.393192 | − | 0.919456i | \(-0.628629\pi\) | ||||
−0.393192 | + | 0.919456i | \(0.628629\pi\) | |||||||
\(884\) | − | 162497.i | − | 0.207941i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 534972. | 0.681496 | ||||||||
\(887\) | − | 673956.i | − | 0.856612i | −0.903634 | − | 0.428306i | \(-0.859111\pi\) | ||
0.903634 | − | 0.428306i | \(-0.140889\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 83922.9 | 0.106188 | ||||||||
\(890\) | 2.21695e6 | 2.79883 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −538542. | −0.676846 | ||||||||
\(893\) | − | 1.27674e6i | − | 1.60103i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 969113.i | − | 1.20984i | ||||||
\(896\) | 200742.i | 0.250047i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 1.86587e6i | − | 2.31382i | ||||||
\(899\) | − | 595320.i | − | 0.736599i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 89912.0 | 0.110756 | ||||||||
\(902\) | −10337.5 | −0.0127058 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −772298. | −0.945036 | ||||||||
\(905\) | −55476.6 | −0.0677349 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.07679e6 | 1.30894 | 0.654468 | − | 0.756090i | \(-0.272893\pi\) | ||||
0.654468 | + | 0.756090i | \(0.272893\pi\) | |||||||
\(908\) | 1.77964e6i | 2.15855i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 135477. | 0.163600 | ||||||||
\(911\) | −288010. | −0.347033 | −0.173516 | − | 0.984831i | \(-0.555513\pi\) | ||||
−0.173516 | + | 0.984831i | \(0.555513\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −94175.3 | −0.112978 | ||||||||
\(914\) | 1.18003e6 | 1.41254 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.50237e6i | 2.98236i | ||||||||
\(917\) | − | 201503.i | − | 0.239631i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 90535.9i | 0.107199i | 0.998563 | + | 0.0535994i | \(0.0170694\pi\) | ||||
−0.998563 | + | 0.0535994i | \(0.982931\pi\) | |||||||
\(920\) | −590955. | −0.698198 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1.06398e6i | − | 1.25161i | ||||||
\(923\) | − | 356057.i | − | 0.417942i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.80839e6i | − | 2.11353i | ||||||
\(926\) | −522875. | −0.609784 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 457419.i | 0.531151i | ||||||||
\(929\) | 922758.i | 1.06919i | 0.845107 | + | 0.534597i | \(0.179537\pi\) | ||||
−0.845107 | + | 0.534597i | \(0.820463\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.03608e6 | −1.19535 | ||||||||
\(932\) | 1.18700e6i | 1.36652i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.74126e6 | −3.14237 | ||||||||
\(935\) | − | 66844.2i | − | 0.0764611i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.63873e6i | − | 1.86650i | −0.359226 | − | 0.933251i | \(-0.616959\pi\) | ||
0.359226 | − | 0.933251i | \(-0.383041\pi\) | |||||||
\(938\) | 35861.2 | 0.0407586 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.46189e6i | 3.91794i | ||||||||
\(941\) | − | 432139.i | − | 0.488028i | −0.969772 | − | 0.244014i | \(-0.921536\pi\) | ||
0.969772 | − | 0.244014i | \(-0.0784642\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 11916.2i | − | 0.0134002i | ||||||
\(944\) | 424264. | − | 12601.9i | 0.476094 | − | 0.0141413i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 384505.i | − | 0.429655i | ||||||
\(947\) | 1.68549e6 | 1.87943 | 0.939716 | − | 0.341956i | \(-0.111089\pi\) | ||||
0.939716 | + | 0.341956i | \(0.111089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −133657. | −0.148409 | ||||||||
\(950\) | − | 3.13708e6i | − | 3.47599i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 44814.5i | 0.0494476i | ||||||||
\(953\) | 1.30178e6 | 1.43335 | 0.716677 | − | 0.697405i | \(-0.245662\pi\) | ||||
0.716677 | + | 0.697405i | \(0.245662\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.43660e6i | 1.57517i | ||||||||
\(956\) | 128824. | 0.140955 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 1.08596e6i | − | 1.18327i | ||||||
\(959\) | 204946. | 0.222845 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 353952. | 0.383264 | ||||||||
\(962\) | 835962.i | 0.903309i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.90129e6 | 2.04595 | ||||||||
\(965\) | −1.15298e6 | −1.23813 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.16546e6i | 1.24636i | 0.782077 | + | 0.623182i | \(0.214160\pi\) | ||||
−0.782077 | + | 0.623182i | \(0.785840\pi\) | |||||||
\(968\) | 1.23971e6i | 1.32303i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 648979. | 0.689743 | ||||||||
\(971\) | −158501. | −0.168110 | −0.0840550 | − | 0.996461i | \(-0.526787\pi\) | ||||
−0.0840550 | + | 0.996461i | \(0.526787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −91526.4 | −0.0966764 | ||||||||
\(974\) | 1.05096e6i | 1.10782i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 248962.i | − | 0.261357i | ||||||
\(977\) | − | 510200.i | − | 0.534504i | −0.963627 | − | 0.267252i | \(-0.913884\pi\) | ||
0.963627 | − | 0.267252i | \(-0.0861157\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −171142. | −0.178563 | ||||||||
\(980\) | 2.80936e6 | 2.92520 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.94143e6i | 2.01326i | ||||||||
\(983\) | − | 853370.i | − | 0.883141i | −0.897226 | − | 0.441571i | \(-0.854421\pi\) | ||
0.897226 | − | 0.441571i | \(-0.145579\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 355772. | 0.366690 | ||||||||
\(986\) | 404607.i | 0.416179i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 934812.i | 0.957658i | ||||||||
\(989\) | 443224. | 0.453138 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 609956.i | 0.621086i | 0.950559 | + | 0.310543i | \(0.100511\pi\) | ||||
−0.950559 | + | 0.310543i | \(0.899489\pi\) | |||||||
\(992\) | 437632. | 0.444719 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 218846.i | 0.221496i | ||||||||
\(995\) | −1.28568e6 | −1.29863 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 712553. | 0.716847 | 0.358424 | − | 0.933559i | \(-0.383314\pi\) | ||||
0.358424 | + | 0.933559i | \(0.383314\pi\) | |||||||
\(998\) | − | 2.45896e6i | − | 2.46882i | ||||||
\(999\) | 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 | 531.5.c.d.235.5 | 40 | ||
3.2 | odd | 2 | 177.5.c.a.58.36 | yes | 40 | ||
59.58 | odd | 2 | inner | 531.5.c.d.235.36 | 40 | ||
177.176 | even | 2 | 177.5.c.a.58.5 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.5 | ✓ | 40 | 177.176 | even | 2 | ||
177.5.c.a.58.36 | yes | 40 | 3.2 | odd | 2 | ||
531.5.c.d.235.5 | 40 | 1.1 | even | 1 | trivial | ||
531.5.c.d.235.36 | 40 | 59.58 | odd | 2 | inner |