Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.58");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.5 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.36 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | \(-0.316703\pi\) | |||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | −29.0222 | −1.81389 | ||||||||
\(5\) | −41.0870 | −1.64348 | −0.821739 | − | 0.569864i | \(-0.806996\pi\) | ||||
−0.821739 | + | 0.569864i | \(0.806996\pi\) | |||||||
\(6\) | − | 34.8655i | − | 0.968485i | ||||||
\(7\) | −6.70931 | −0.136925 | −0.0684623 | − | 0.997654i | \(-0.521809\pi\) | ||||
−0.0684623 | + | 0.997654i | \(0.521809\pi\) | |||||||
\(8\) | 87.3773i | 1.36527i | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 275.688i | 2.75688i | ||||||||
\(11\) | 21.2822i | 0.175886i | 0.996126 | + | 0.0879430i | \(0.0280293\pi\) | ||||
−0.996126 | + | 0.0879430i | \(0.971971\pi\) | |||||||
\(12\) | −150.804 | −1.04725 | ||||||||
\(13\) | 73.2439i | 0.433396i | 0.976239 | + | 0.216698i | \(0.0695286\pi\) | ||||
−0.976239 | + | 0.216698i | \(0.930471\pi\) | |||||||
\(14\) | 45.0185i | 0.229686i | ||||||||
\(15\) | −213.494 | −0.948863 | ||||||||
\(16\) | 121.934 | 0.476304 | ||||||||
\(17\) | 76.4439 | 0.264512 | 0.132256 | − | 0.991216i | \(-0.457778\pi\) | ||||
0.132256 | + | 0.991216i | \(0.457778\pi\) | |||||||
\(18\) | − | 181.166i | − | 0.559155i | ||||||
\(19\) | 439.767 | 1.21819 | 0.609095 | − | 0.793097i | \(-0.291533\pi\) | ||||
0.609095 | + | 0.793097i | \(0.291533\pi\) | |||||||
\(20\) | 1192.43 | 2.98109 | ||||||||
\(21\) | −34.8626 | −0.0790535 | ||||||||
\(22\) | 142.801 | 0.295043 | ||||||||
\(23\) | 164.608i | 0.311169i | 0.987823 | + | 0.155584i | \(0.0497260\pi\) | ||||
−0.987823 | + | 0.155584i | \(0.950274\pi\) | |||||||
\(24\) | 454.026i | 0.788239i | ||||||||
\(25\) | 1063.14 | 1.70102 | ||||||||
\(26\) | 491.456 | 0.727006 | ||||||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | 194.719 | 0.248366 | ||||||||
\(29\) | −788.819 | −0.937954 | −0.468977 | − | 0.883211i | \(-0.655377\pi\) | ||||
−0.468977 | + | 0.883211i | \(0.655377\pi\) | |||||||
\(30\) | 1432.52i | 1.59168i | ||||||||
\(31\) | 754.698i | 0.785325i | 0.919683 | + | 0.392663i | \(0.128446\pi\) | ||||
−0.919683 | + | 0.392663i | \(0.871554\pi\) | |||||||
\(32\) | 579.878i | 0.566287i | ||||||||
\(33\) | 110.586i | 0.101548i | ||||||||
\(34\) | − | 512.928i | − | 0.443709i | ||||||
\(35\) | 275.665 | 0.225033 | ||||||||
\(36\) | −783.600 | −0.604630 | ||||||||
\(37\) | 1700.99i | 1.24251i | 0.783610 | + | 0.621253i | \(0.213376\pi\) | ||||
−0.783610 | + | 0.621253i | \(0.786624\pi\) | |||||||
\(38\) | − | 2950.77i | − | 2.04347i | ||||||
\(39\) | 380.586i | 0.250221i | ||||||||
\(40\) | − | 3590.07i | − | 2.24379i | ||||||
\(41\) | 72.3910 | 0.0430643 | 0.0215321 | − | 0.999768i | \(-0.493146\pi\) | ||||
0.0215321 | + | 0.999768i | \(0.493146\pi\) | |||||||
\(42\) | 233.923i | 0.132609i | ||||||||
\(43\) | 2692.60i | 1.45625i | 0.685447 | + | 0.728123i | \(0.259607\pi\) | ||||
−0.685447 | + | 0.728123i | \(0.740393\pi\) | |||||||
\(44\) | − | 617.657i | − | 0.319038i | ||||||
\(45\) | −1109.35 | −0.547826 | ||||||||
\(46\) | 1104.50 | 0.521975 | ||||||||
\(47\) | − | 2903.21i | − | 1.31426i | −0.753775 | − | 0.657132i | \(-0.771769\pi\) | ||
0.753775 | − | 0.657132i | \(-0.228231\pi\) | |||||||
\(48\) | 633.587 | 0.274994 | ||||||||
\(49\) | −2355.99 | −0.981252 | ||||||||
\(50\) | − | 7133.51i | − | 2.85340i | ||||||
\(51\) | 397.214 | 0.152716 | ||||||||
\(52\) | − | 2125.70i | − | 0.786131i | ||||||
\(53\) | 1176.18 | 0.418719 | 0.209360 | − | 0.977839i | \(-0.432862\pi\) | ||||
0.209360 | + | 0.977839i | \(0.432862\pi\) | |||||||
\(54\) | − | 941.367i | − | 0.322828i | ||||||
\(55\) | − | 874.422i | − | 0.289065i | ||||||
\(56\) | − | 586.241i | − | 0.186939i | ||||||
\(57\) | 2285.10 | 0.703323 | ||||||||
\(58\) | 5292.86i | 1.57338i | ||||||||
\(59\) | −3479.47 | − | 103.350i | −0.999559 | − | 0.0296897i | ||||
\(60\) | 6196.07 | 1.72113 | ||||||||
\(61\) | 2041.78i | 0.548718i | 0.961627 | + | 0.274359i | \(0.0884657\pi\) | ||||
−0.961627 | + | 0.274359i | \(0.911534\pi\) | |||||||
\(62\) | 5063.92 | 1.31736 | ||||||||
\(63\) | −181.151 | −0.0456415 | ||||||||
\(64\) | 5841.84 | 1.42623 | ||||||||
\(65\) | − | 3009.37i | − | 0.712276i | ||||||
\(66\) | 742.014 | 0.170343 | ||||||||
\(67\) | 796.587i | 0.177453i | 0.996056 | + | 0.0887266i | \(0.0282797\pi\) | ||||
−0.996056 | + | 0.0887266i | \(0.971720\pi\) | |||||||
\(68\) | −2218.57 | −0.479795 | ||||||||
\(69\) | 855.330i | 0.179653i | ||||||||
\(70\) | − | 1849.67i | − | 0.377484i | ||||||
\(71\) | −4861.25 | −0.964343 | −0.482171 | − | 0.876077i | \(-0.660152\pi\) | ||||
−0.482171 | + | 0.876077i | \(0.660152\pi\) | |||||||
\(72\) | 2359.19i | 0.455090i | ||||||||
\(73\) | 1824.82i | 0.342433i | 0.985233 | + | 0.171216i | \(0.0547697\pi\) | ||||
−0.985233 | + | 0.171216i | \(0.945230\pi\) | |||||||
\(74\) | 11413.4 | 2.08426 | ||||||||
\(75\) | 5524.23 | 0.982085 | ||||||||
\(76\) | −12763.0 | −2.20966 | ||||||||
\(77\) | − | 142.789i | − | 0.0240831i | ||||||
\(78\) | 2553.68 | 0.419737 | ||||||||
\(79\) | −7086.59 | −1.13549 | −0.567745 | − | 0.823204i | \(-0.692184\pi\) | ||||
−0.567745 | + | 0.823204i | \(0.692184\pi\) | |||||||
\(80\) | −5009.89 | −0.782795 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | − | 485.734i | − | 0.0722388i | ||||||
\(83\) | 4425.07i | 0.642338i | 0.947022 | + | 0.321169i | \(0.104076\pi\) | ||||
−0.947022 | + | 0.321169i | \(0.895924\pi\) | |||||||
\(84\) | 1011.79 | 0.143394 | ||||||||
\(85\) | −3140.85 | −0.434719 | ||||||||
\(86\) | 18067.0 | 2.44280 | ||||||||
\(87\) | −4098.82 | −0.541528 | ||||||||
\(88\) | −1859.58 | −0.240132 | ||||||||
\(89\) | 8041.54i | 1.01522i | 0.861588 | + | 0.507609i | \(0.169471\pi\) | ||||
−0.861588 | + | 0.507609i | \(0.830529\pi\) | |||||||
\(90\) | 7443.57i | 0.918959i | ||||||||
\(91\) | − | 491.415i | − | 0.0593425i | ||||||
\(92\) | − | 4777.30i | − | 0.564425i | ||||||
\(93\) | 3921.52i | 0.453408i | ||||||||
\(94\) | −19480.1 | −2.20463 | ||||||||
\(95\) | −18068.7 | −2.00207 | ||||||||
\(96\) | 3013.13i | 0.326946i | ||||||||
\(97\) | − | 2354.04i | − | 0.250190i | −0.992145 | − | 0.125095i | \(-0.960076\pi\) | ||
0.992145 | − | 0.125095i | \(-0.0399235\pi\) | |||||||
\(98\) | 15808.3i | 1.64602i | ||||||||
\(99\) | 574.620i | 0.0586287i | ||||||||
\(100\) | −30854.6 | −3.08546 | ||||||||
\(101\) | − | 15071.0i | − | 1.47741i | −0.674032 | − | 0.738703i | \(-0.735439\pi\) | ||
0.674032 | − | 0.738703i | \(-0.264561\pi\) | |||||||
\(102\) | − | 2665.25i | − | 0.256176i | ||||||
\(103\) | 13089.2i | 1.23378i | 0.787048 | + | 0.616892i | \(0.211608\pi\) | ||||
−0.787048 | + | 0.616892i | \(0.788392\pi\) | |||||||
\(104\) | −6399.85 | −0.591702 | ||||||||
\(105\) | 1432.40 | 0.129923 | ||||||||
\(106\) | − | 7892.02i | − | 0.702387i | ||||||
\(107\) | −264.977 | −0.0231441 | −0.0115721 | − | 0.999933i | \(-0.503684\pi\) | ||||
−0.0115721 | + | 0.999933i | \(0.503684\pi\) | |||||||
\(108\) | −4071.70 | −0.349083 | ||||||||
\(109\) | 13760.9i | 1.15823i | 0.815247 | + | 0.579113i | \(0.196601\pi\) | ||||
−0.815247 | + | 0.579113i | \(0.803399\pi\) | |||||||
\(110\) | −5867.25 | −0.484896 | ||||||||
\(111\) | 8838.61i | 0.717361i | ||||||||
\(112\) | −818.091 | −0.0652177 | ||||||||
\(113\) | 8838.66i | 0.692197i | 0.938198 | + | 0.346098i | \(0.112494\pi\) | ||||
−0.938198 | + | 0.346098i | \(0.887506\pi\) | |||||||
\(114\) | − | 15332.7i | − | 1.17980i | ||||||
\(115\) | − | 6763.25i | − | 0.511399i | ||||||
\(116\) | 22893.3 | 1.70134 | ||||||||
\(117\) | 1977.58i | 0.144465i | ||||||||
\(118\) | −693.464 | + | 23346.7i | −0.0498035 | + | 1.67673i | ||||
\(119\) | −512.886 | −0.0362182 | ||||||||
\(120\) | − | 18654.5i | − | 1.29545i | ||||||
\(121\) | 14188.1 | 0.969064 | ||||||||
\(122\) | 13700.1 | 0.920456 | ||||||||
\(123\) | 376.155 | 0.0248632 | ||||||||
\(124\) | − | 21903.0i | − | 1.42449i | ||||||
\(125\) | −18001.8 | −1.15211 | ||||||||
\(126\) | 1215.50i | 0.0765621i | ||||||||
\(127\) | −12508.4 | −0.775524 | −0.387762 | − | 0.921759i | \(-0.626752\pi\) | ||||
−0.387762 | + | 0.921759i | \(0.626752\pi\) | |||||||
\(128\) | − | 29919.9i | − | 1.82616i | ||||||
\(129\) | 13991.2i | 0.840764i | ||||||||
\(130\) | −20192.4 | −1.19482 | ||||||||
\(131\) | 30033.4i | 1.75010i | 0.484036 | + | 0.875048i | \(0.339170\pi\) | ||||
−0.484036 | + | 0.875048i | \(0.660830\pi\) | |||||||
\(132\) | − | 3209.44i | − | 0.184197i | ||||||
\(133\) | −2950.53 | −0.166800 | ||||||||
\(134\) | 5344.99 | 0.297672 | ||||||||
\(135\) | −5764.34 | −0.316288 | ||||||||
\(136\) | 6679.46i | 0.361130i | ||||||||
\(137\) | 30546.6 | 1.62750 | 0.813751 | − | 0.581213i | \(-0.197422\pi\) | ||||
0.813751 | + | 0.581213i | \(0.197422\pi\) | |||||||
\(138\) | 5739.14 | 0.301362 | ||||||||
\(139\) | 13641.7 | 0.706056 | 0.353028 | − | 0.935613i | \(-0.385152\pi\) | ||||
0.353028 | + | 0.935613i | \(0.385152\pi\) | |||||||
\(140\) | −8000.41 | −0.408184 | ||||||||
\(141\) | − | 15085.5i | − | 0.758791i | ||||||
\(142\) | 32618.3i | 1.61765i | ||||||||
\(143\) | −1558.79 | −0.0762283 | ||||||||
\(144\) | 3292.21 | 0.158768 | ||||||||
\(145\) | 32410.2 | 1.54151 | ||||||||
\(146\) | 12244.3 | 0.574419 | ||||||||
\(147\) | −12242.1 | −0.566526 | ||||||||
\(148\) | − | 49366.5i | − | 2.25377i | ||||||
\(149\) | − | 18026.1i | − | 0.811949i | −0.913884 | − | 0.405975i | \(-0.866932\pi\) | ||
0.913884 | − | 0.405975i | \(-0.133068\pi\) | |||||||
\(150\) | − | 37066.8i | − | 1.64741i | ||||||
\(151\) | − | 39094.7i | − | 1.71460i | −0.514814 | − | 0.857302i | \(-0.672139\pi\) | ||
0.514814 | − | 0.857302i | \(-0.327861\pi\) | |||||||
\(152\) | 38425.6i | 1.66316i | ||||||||
\(153\) | 2063.99 | 0.0881706 | ||||||||
\(154\) | −958.094 | −0.0403986 | ||||||||
\(155\) | − | 31008.2i | − | 1.29067i | ||||||
\(156\) | − | 11045.5i | − | 0.453873i | ||||||
\(157\) | − | 27675.1i | − | 1.12277i | −0.827556 | − | 0.561383i | \(-0.810269\pi\) | ||
0.827556 | − | 0.561383i | \(-0.189731\pi\) | |||||||
\(158\) | 47550.1i | 1.90475i | ||||||||
\(159\) | 6111.62 | 0.241748 | ||||||||
\(160\) | − | 23825.4i | − | 0.930680i | ||||||
\(161\) | − | 1104.41i | − | 0.0426067i | ||||||
\(162\) | − | 4891.49i | − | 0.186385i | ||||||
\(163\) | −28910.4 | −1.08813 | −0.544063 | − | 0.839044i | \(-0.683115\pi\) | ||||
−0.544063 | + | 0.839044i | \(0.683115\pi\) | |||||||
\(164\) | −2100.95 | −0.0781138 | ||||||||
\(165\) | − | 4543.63i | − | 0.166892i | ||||||
\(166\) | 29691.6 | 1.07750 | ||||||||
\(167\) | −44721.0 | −1.60354 | −0.801768 | − | 0.597635i | \(-0.796107\pi\) | ||||
−0.801768 | + | 0.597635i | \(0.796107\pi\) | |||||||
\(168\) | − | 3046.20i | − | 0.107929i | ||||||
\(169\) | 23196.3 | 0.812168 | ||||||||
\(170\) | 21074.6i | 0.729227i | ||||||||
\(171\) | 11873.7 | 0.406064 | ||||||||
\(172\) | − | 78145.2i | − | 2.64147i | ||||||
\(173\) | 37239.4i | 1.24426i | 0.782914 | + | 0.622129i | \(0.213732\pi\) | ||||
−0.782914 | + | 0.622129i | \(0.786268\pi\) | |||||||
\(174\) | 27502.5i | 0.908394i | ||||||||
\(175\) | −7132.92 | −0.232912 | ||||||||
\(176\) | 2595.02i | 0.0837752i | ||||||||
\(177\) | −18079.8 | − | 537.022i | −0.577096 | − | 0.0171414i | ||||
\(178\) | 53957.6 | 1.70299 | ||||||||
\(179\) | − | 23586.9i | − | 0.736147i | −0.929797 | − | 0.368073i | \(-0.880017\pi\) | ||
0.929797 | − | 0.368073i | \(-0.119983\pi\) | |||||||
\(180\) | 32195.7 | 0.993696 | ||||||||
\(181\) | −1350.22 | −0.0412144 | −0.0206072 | − | 0.999788i | \(-0.506560\pi\) | ||||
−0.0206072 | + | 0.999788i | \(0.506560\pi\) | |||||||
\(182\) | −3297.33 | −0.0995450 | ||||||||
\(183\) | 10609.4i | 0.316803i | ||||||||
\(184\) | −14383.0 | −0.424829 | ||||||||
\(185\) | − | 69888.5i | − | 2.04203i | ||||||
\(186\) | 26312.9 | 0.760576 | ||||||||
\(187\) | 1626.90i | 0.0465239i | ||||||||
\(188\) | 84257.6i | 2.38393i | ||||||||
\(189\) | −941.290 | −0.0263512 | ||||||||
\(190\) | 121238.i | 3.35840i | ||||||||
\(191\) | 34964.8i | 0.958438i | 0.877695 | + | 0.479219i | \(0.159080\pi\) | ||||
−0.877695 | + | 0.479219i | \(0.840920\pi\) | |||||||
\(192\) | 30355.1 | 0.823435 | ||||||||
\(193\) | −28062.0 | −0.753362 | −0.376681 | − | 0.926343i | \(-0.622935\pi\) | ||||
−0.376681 | + | 0.926343i | \(0.622935\pi\) | |||||||
\(194\) | −15795.3 | −0.419685 | ||||||||
\(195\) | − | 15637.1i | − | 0.411233i | ||||||
\(196\) | 68375.9 | 1.77988 | ||||||||
\(197\) | −8658.99 | −0.223118 | −0.111559 | − | 0.993758i | \(-0.535584\pi\) | ||||
−0.111559 | + | 0.993758i | \(0.535584\pi\) | |||||||
\(198\) | 3855.62 | 0.0983476 | ||||||||
\(199\) | −31291.6 | −0.790173 | −0.395087 | − | 0.918644i | \(-0.629285\pi\) | ||||
−0.395087 | + | 0.918644i | \(0.629285\pi\) | |||||||
\(200\) | 92894.1i | 2.32235i | ||||||||
\(201\) | 4139.19i | 0.102453i | ||||||||
\(202\) | −101124. | −2.47830 | ||||||||
\(203\) | 5292.43 | 0.128429 | ||||||||
\(204\) | −11528.0 | −0.277010 | ||||||||
\(205\) | −2974.33 | −0.0707752 | ||||||||
\(206\) | 87826.8 | 2.06963 | ||||||||
\(207\) | 4444.42i | 0.103723i | ||||||||
\(208\) | 8930.90i | 0.206428i | ||||||||
\(209\) | 9359.21i | 0.214263i | ||||||||
\(210\) | − | 9611.19i | − | 0.217941i | ||||||
\(211\) | 1277.25i | 0.0286888i | 0.999897 | + | 0.0143444i | \(0.00456612\pi\) | ||||
−0.999897 | + | 0.0143444i | \(0.995434\pi\) | |||||||
\(212\) | −34135.4 | −0.759510 | ||||||||
\(213\) | −25259.8 | −0.556764 | ||||||||
\(214\) | 1777.96i | 0.0388235i | ||||||||
\(215\) | − | 110631.i | − | 2.39331i | ||||||
\(216\) | 12258.7i | 0.262746i | ||||||||
\(217\) | − | 5063.50i | − | 0.107530i | ||||||
\(218\) | 92333.7 | 1.94288 | ||||||||
\(219\) | 9482.07i | 0.197704i | ||||||||
\(220\) | 25377.7i | 0.524332i | ||||||||
\(221\) | 5599.05i | 0.114638i | ||||||||
\(222\) | 59305.8 | 1.20335 | ||||||||
\(223\) | 18556.2 | 0.373146 | 0.186573 | − | 0.982441i | \(-0.440262\pi\) | ||||
0.186573 | + | 0.982441i | \(0.440262\pi\) | |||||||
\(224\) | − | 3890.58i | − | 0.0775386i | ||||||
\(225\) | 28704.7 | 0.567007 | ||||||||
\(226\) | 59306.2 | 1.16114 | ||||||||
\(227\) | − | 61320.0i | − | 1.19001i | −0.803722 | − | 0.595005i | \(-0.797150\pi\) | ||
0.803722 | − | 0.595005i | \(-0.202850\pi\) | |||||||
\(228\) | −66318.6 | −1.27575 | ||||||||
\(229\) | 86222.5i | 1.64418i | 0.569356 | + | 0.822091i | \(0.307193\pi\) | ||||
−0.569356 | + | 0.822091i | \(0.692807\pi\) | |||||||
\(230\) | −45380.5 | −0.857854 | ||||||||
\(231\) | − | 741.953i | − | 0.0139044i | ||||||
\(232\) | − | 68924.9i | − | 1.28056i | ||||||
\(233\) | − | 40899.5i | − | 0.753367i | −0.926342 | − | 0.376683i | \(-0.877064\pi\) | ||
0.926342 | − | 0.376683i | \(-0.122936\pi\) | |||||||
\(234\) | 13269.3 | 0.242335 | ||||||||
\(235\) | 119284.i | 2.15997i | ||||||||
\(236\) | 100982. | + | 2999.45i | 1.81309 | + | 0.0538539i | ||||
\(237\) | −36823.0 | −0.655576 | ||||||||
\(238\) | 3441.39i | 0.0607547i | ||||||||
\(239\) | 4438.81 | 0.0777089 | 0.0388544 | − | 0.999245i | \(-0.487629\pi\) | ||||
0.0388544 | + | 0.999245i | \(0.487629\pi\) | |||||||
\(240\) | −26032.1 | −0.451947 | ||||||||
\(241\) | −65511.7 | −1.12794 | −0.563968 | − | 0.825797i | \(-0.690726\pi\) | ||||
−0.563968 | + | 0.825797i | \(0.690726\pi\) | |||||||
\(242\) | − | 95199.9i | − | 1.62557i | ||||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | − | 59257.0i | − | 0.995314i | ||||||
\(245\) | 96800.3 | 1.61267 | ||||||||
\(246\) | − | 2523.95i | − | 0.0417071i | ||||||
\(247\) | 32210.2i | 0.527959i | ||||||||
\(248\) | −65943.4 | −1.07218 | ||||||||
\(249\) | 22993.3i | 0.370854i | ||||||||
\(250\) | 120789.i | 1.93263i | ||||||||
\(251\) | −26481.1 | −0.420328 | −0.210164 | − | 0.977666i | \(-0.567400\pi\) | ||||
−0.210164 | + | 0.977666i | \(0.567400\pi\) | |||||||
\(252\) | 5257.41 | 0.0827887 | ||||||||
\(253\) | −3503.23 | −0.0547302 | ||||||||
\(254\) | 83929.8i | 1.30091i | ||||||||
\(255\) | −16320.3 | −0.250985 | ||||||||
\(256\) | −107289. | −1.63710 | ||||||||
\(257\) | −73530.4 | −1.11327 | −0.556635 | − | 0.830757i | \(-0.687908\pi\) | ||||
−0.556635 | + | 0.830757i | \(0.687908\pi\) | |||||||
\(258\) | 93878.7 | 1.41035 | ||||||||
\(259\) | − | 11412.5i | − | 0.170130i | ||||||
\(260\) | 87338.5i | 1.29199i | ||||||||
\(261\) | −21298.1 | −0.312651 | ||||||||
\(262\) | 201520. | 2.93573 | ||||||||
\(263\) | −58037.1 | −0.839062 | −0.419531 | − | 0.907741i | \(-0.637806\pi\) | ||||
−0.419531 | + | 0.907741i | \(0.637806\pi\) | |||||||
\(264\) | −9662.67 | −0.138640 | ||||||||
\(265\) | −48325.8 | −0.688156 | ||||||||
\(266\) | 19797.6i | 0.279802i | ||||||||
\(267\) | 41785.1i | 0.586136i | ||||||||
\(268\) | − | 23118.7i | − | 0.321880i | ||||||
\(269\) | − | 119064.i | − | 1.64542i | −0.568464 | − | 0.822708i | \(-0.692462\pi\) | ||
0.568464 | − | 0.822708i | \(-0.307538\pi\) | |||||||
\(270\) | 38677.9i | 0.530561i | ||||||||
\(271\) | 95279.2 | 1.29736 | 0.648679 | − | 0.761062i | \(-0.275322\pi\) | ||||
0.648679 | + | 0.761062i | \(0.275322\pi\) | |||||||
\(272\) | 9321.10 | 0.125988 | ||||||||
\(273\) | − | 2553.47i | − | 0.0342614i | ||||||
\(274\) | − | 204963.i | − | 2.73008i | ||||||
\(275\) | 22625.9i | 0.299186i | ||||||||
\(276\) | − | 24823.6i | − | 0.325871i | ||||||
\(277\) | −70994.3 | −0.925260 | −0.462630 | − | 0.886551i | \(-0.653094\pi\) | ||||
−0.462630 | + | 0.886551i | \(0.653094\pi\) | |||||||
\(278\) | − | 91534.0i | − | 1.18438i | ||||||
\(279\) | 20376.8i | 0.261775i | ||||||||
\(280\) | 24086.9i | 0.307230i | ||||||||
\(281\) | 89157.2 | 1.12913 | 0.564565 | − | 0.825389i | \(-0.309044\pi\) | ||||
0.564565 | + | 0.825389i | \(0.309044\pi\) | |||||||
\(282\) | −101222. | −1.27285 | ||||||||
\(283\) | − | 121771.i | − | 1.52044i | −0.649664 | − | 0.760222i | \(-0.725090\pi\) | ||
0.649664 | − | 0.760222i | \(-0.274910\pi\) | |||||||
\(284\) | 141084. | 1.74921 | ||||||||
\(285\) | −93887.6 | −1.15590 | ||||||||
\(286\) | 10459.3i | 0.127870i | ||||||||
\(287\) | −485.693 | −0.00589656 | ||||||||
\(288\) | 15656.7i | 0.188762i | ||||||||
\(289\) | −77677.3 | −0.930034 | ||||||||
\(290\) | − | 217468.i | − | 2.58582i | ||||||
\(291\) | − | 12231.9i | − | 0.144447i | ||||||
\(292\) | − | 52960.5i | − | 0.621135i | ||||||
\(293\) | −14072.9 | −0.163927 | −0.0819633 | − | 0.996635i | \(-0.526119\pi\) | ||||
−0.0819633 | + | 0.996635i | \(0.526119\pi\) | |||||||
\(294\) | 82142.5i | 0.950327i | ||||||||
\(295\) | 142961. | + | 4246.34i | 1.64275 | + | 0.0487944i | ||||
\(296\) | −148628. | −1.69636 | ||||||||
\(297\) | 2985.81i | 0.0338493i | ||||||||
\(298\) | −120953. | −1.36202 | ||||||||
\(299\) | −12056.5 | −0.134859 | ||||||||
\(300\) | −160325. | −1.78139 | ||||||||
\(301\) | − | 18065.5i | − | 0.199396i | ||||||
\(302\) | −262320. | −2.87619 | ||||||||
\(303\) | − | 78311.3i | − | 0.852980i | ||||||
\(304\) | 53622.4 | 0.580229 | ||||||||
\(305\) | − | 83890.6i | − | 0.901807i | ||||||
\(306\) | − | 13849.1i | − | 0.147903i | ||||||
\(307\) | 84061.4 | 0.891908 | 0.445954 | − | 0.895056i | \(-0.352865\pi\) | ||||
0.445954 | + | 0.895056i | \(0.352865\pi\) | |||||||
\(308\) | 4144.05i | 0.0436841i | ||||||||
\(309\) | 68013.5i | 0.712325i | ||||||||
\(310\) | −208061. | −2.16505 | ||||||||
\(311\) | −27808.7 | −0.287514 | −0.143757 | − | 0.989613i | \(-0.545918\pi\) | ||||
−0.143757 | + | 0.989613i | \(0.545918\pi\) | |||||||
\(312\) | −33254.6 | −0.341619 | ||||||||
\(313\) | − | 3675.80i | − | 0.0375200i | −0.999824 | − | 0.0187600i | \(-0.994028\pi\) | ||
0.999824 | − | 0.0187600i | \(-0.00597184\pi\) | |||||||
\(314\) | −185696. | −1.88340 | ||||||||
\(315\) | 7442.96 | 0.0750109 | ||||||||
\(316\) | 205669. | 2.05965 | ||||||||
\(317\) | 30461.2 | 0.303129 | 0.151565 | − | 0.988447i | \(-0.451569\pi\) | ||||
0.151565 | + | 0.988447i | \(0.451569\pi\) | |||||||
\(318\) | − | 41008.1i | − | 0.405523i | ||||||
\(319\) | − | 16787.8i | − | 0.164973i | ||||||
\(320\) | −240023. | −2.34398 | ||||||||
\(321\) | −1376.86 | −0.0133623 | ||||||||
\(322\) | −7410.42 | −0.0714712 | ||||||||
\(323\) | 33617.5 | 0.322226 | ||||||||
\(324\) | −21157.2 | −0.201543 | ||||||||
\(325\) | 77868.4i | 0.737215i | ||||||||
\(326\) | 193985.i | 1.82529i | ||||||||
\(327\) | 71503.7i | 0.668703i | ||||||||
\(328\) | 6325.33i | 0.0587943i | ||||||||
\(329\) | 19478.5i | 0.179955i | ||||||||
\(330\) | −30487.1 | −0.279955 | ||||||||
\(331\) | 206607. | 1.88577 | 0.942884 | − | 0.333120i | \(-0.108102\pi\) | ||||
0.942884 | + | 0.333120i | \(0.108102\pi\) | |||||||
\(332\) | − | 128425.i | − | 1.16513i | ||||||
\(333\) | 45926.7i | 0.414169i | ||||||||
\(334\) | 300072.i | 2.68988i | ||||||||
\(335\) | − | 32729.4i | − | 0.291641i | ||||||
\(336\) | −4250.93 | −0.0376535 | ||||||||
\(337\) | − | 145823.i | − | 1.28401i | −0.766702 | − | 0.642004i | \(-0.778103\pi\) | ||
0.766702 | − | 0.642004i | \(-0.221897\pi\) | |||||||
\(338\) | − | 155644.i | − | 1.36238i | ||||||
\(339\) | 45927.0i | 0.399640i | ||||||||
\(340\) | 91154.4 | 0.788533 | ||||||||
\(341\) | −16061.6 | −0.138128 | ||||||||
\(342\) | − | 79670.9i | − | 0.681158i | ||||||
\(343\) | 31916.1 | 0.271282 | ||||||||
\(344\) | −235272. | −1.98817 | ||||||||
\(345\) | − | 35142.9i | − | 0.295256i | ||||||
\(346\) | 249871. | 2.08720 | ||||||||
\(347\) | 32401.9i | 0.269098i | 0.990907 | + | 0.134549i | \(0.0429586\pi\) | ||||
−0.990907 | + | 0.134549i | \(0.957041\pi\) | |||||||
\(348\) | 118957. | 0.982271 | ||||||||
\(349\) | 165183.i | 1.35617i | 0.734982 | + | 0.678086i | \(0.237191\pi\) | ||||
−0.734982 | + | 0.678086i | \(0.762809\pi\) | |||||||
\(350\) | 47860.9i | 0.390701i | ||||||||
\(351\) | 10275.8i | 0.0834070i | ||||||||
\(352\) | −12341.1 | −0.0996020 | ||||||||
\(353\) | 193446.i | 1.55242i | 0.630472 | + | 0.776212i | \(0.282861\pi\) | ||||
−0.630472 | + | 0.776212i | \(0.717139\pi\) | |||||||
\(354\) | −3603.34 | + | 121313.i | −0.0287541 | + | 0.968058i | ||||
\(355\) | 199734. | 1.58488 | ||||||||
\(356\) | − | 233383.i | − | 1.84149i | ||||||
\(357\) | −2665.03 | −0.0209106 | ||||||||
\(358\) | −158265. | −1.23486 | ||||||||
\(359\) | −94638.7 | −0.734311 | −0.367155 | − | 0.930160i | \(-0.619668\pi\) | ||||
−0.367155 | + | 0.930160i | \(0.619668\pi\) | |||||||
\(360\) | − | 96931.8i | − | 0.747931i | ||||||
\(361\) | 63073.9 | 0.483989 | ||||||||
\(362\) | 9059.82i | 0.0691357i | ||||||||
\(363\) | 73723.4 | 0.559489 | ||||||||
\(364\) | 14262.0i | 0.107641i | ||||||||
\(365\) | − | 74976.5i | − | 0.562781i | ||||||
\(366\) | 71187.6 | 0.531425 | ||||||||
\(367\) | 250626.i | 1.86078i | 0.366576 | + | 0.930388i | \(0.380530\pi\) | ||||
−0.366576 | + | 0.930388i | \(0.619470\pi\) | |||||||
\(368\) | 20071.3i | 0.148211i | ||||||||
\(369\) | 1954.56 | 0.0143548 | ||||||||
\(370\) | −468942. | −3.42544 | ||||||||
\(371\) | −7891.37 | −0.0573330 | ||||||||
\(372\) | − | 113811.i | − | 0.822431i | ||||||
\(373\) | 65456.3 | 0.470472 | 0.235236 | − | 0.971938i | \(-0.424414\pi\) | ||||
0.235236 | + | 0.971938i | \(0.424414\pi\) | |||||||
\(374\) | 10916.2 | 0.0780423 | ||||||||
\(375\) | −93540.0 | −0.665173 | ||||||||
\(376\) | 253675. | 1.79433 | ||||||||
\(377\) | − | 57776.1i | − | 0.406505i | ||||||
\(378\) | 6315.92i | 0.0442031i | ||||||||
\(379\) | 60322.5 | 0.419953 | 0.209977 | − | 0.977706i | \(-0.432661\pi\) | ||||
0.209977 | + | 0.977706i | \(0.432661\pi\) | |||||||
\(380\) | 524393. | 3.63153 | ||||||||
\(381\) | −64995.7 | −0.447749 | ||||||||
\(382\) | 234609. | 1.60775 | ||||||||
\(383\) | −53450.5 | −0.364380 | −0.182190 | − | 0.983263i | \(-0.558319\pi\) | ||||
−0.182190 | + | 0.983263i | \(0.558319\pi\) | |||||||
\(384\) | − | 155468.i | − | 1.05434i | ||||||
\(385\) | 5866.76i | 0.0395801i | ||||||||
\(386\) | 188292.i | 1.26374i | ||||||||
\(387\) | 72700.2i | 0.485415i | ||||||||
\(388\) | 68319.4i | 0.453817i | ||||||||
\(389\) | 49209.3 | 0.325198 | 0.162599 | − | 0.986692i | \(-0.448012\pi\) | ||||
0.162599 | + | 0.986692i | \(0.448012\pi\) | |||||||
\(390\) | −104923. | −0.689829 | ||||||||
\(391\) | 12583.3i | 0.0823078i | ||||||||
\(392\) | − | 205860.i | − | 1.33967i | ||||||
\(393\) | 156058.i | 1.01042i | ||||||||
\(394\) | 58100.6i | 0.374273i | ||||||||
\(395\) | 291167. | 1.86615 | ||||||||
\(396\) | − | 16676.7i | − | 0.106346i | ||||||
\(397\) | − | 75598.4i | − | 0.479658i | −0.970815 | − | 0.239829i | \(-0.922909\pi\) | ||
0.970815 | − | 0.239829i | \(-0.0770914\pi\) | |||||||
\(398\) | 209963.i | 1.32549i | ||||||||
\(399\) | −15331.4 | −0.0963022 | ||||||||
\(400\) | 129633. | 0.810203 | ||||||||
\(401\) | 289441.i | 1.80000i | 0.435893 | + | 0.899999i | \(0.356433\pi\) | ||||
−0.435893 | + | 0.899999i | \(0.643567\pi\) | |||||||
\(402\) | 27773.4 | 0.171861 | ||||||||
\(403\) | −55277.0 | −0.340357 | ||||||||
\(404\) | 437394.i | 2.67985i | ||||||||
\(405\) | −29952.4 | −0.182609 | ||||||||
\(406\) | − | 35511.4i | − | 0.215435i | ||||||
\(407\) | −36200.9 | −0.218540 | ||||||||
\(408\) | 34707.5i | 0.208498i | ||||||||
\(409\) | 157956.i | 0.944256i | 0.881530 | + | 0.472128i | \(0.156514\pi\) | ||||
−0.881530 | + | 0.472128i | \(0.843486\pi\) | |||||||
\(410\) | 19957.3i | 0.118723i | ||||||||
\(411\) | 158725. | 0.939639 | ||||||||
\(412\) | − | 379878.i | − | 2.23795i | ||||||
\(413\) | 23344.8 | + | 693.407i | 0.136864 | + | 0.00406526i | ||||
\(414\) | 29821.5 | 0.173992 | ||||||||
\(415\) | − | 181813.i | − | 1.05567i | ||||||
\(416\) | −42472.5 | −0.245426 | ||||||||
\(417\) | 70884.4 | 0.407642 | ||||||||
\(418\) | 62799.0 | 0.359418 | ||||||||
\(419\) | 280260.i | 1.59637i | 0.602412 | + | 0.798185i | \(0.294206\pi\) | ||||
−0.602412 | + | 0.798185i | \(0.705794\pi\) | |||||||
\(420\) | −41571.4 | −0.235665 | ||||||||
\(421\) | − | 123028.i | − | 0.694126i | −0.937842 | − | 0.347063i | \(-0.887179\pi\) | ||
0.937842 | − | 0.347063i | \(-0.112821\pi\) | |||||||
\(422\) | 8570.20 | 0.0481245 | ||||||||
\(423\) | − | 78386.7i | − | 0.438088i | ||||||
\(424\) | 102772.i | 0.571665i | ||||||||
\(425\) | 81270.4 | 0.449940 | ||||||||
\(426\) | 169490.i | 0.933951i | ||||||||
\(427\) | − | 13698.9i | − | 0.0751331i | ||||||
\(428\) | 7690.23 | 0.0419809 | ||||||||
\(429\) | −8099.72 | −0.0440104 | ||||||||
\(430\) | −742317. | −4.01469 | ||||||||
\(431\) | 118678.i | 0.638877i | 0.947607 | + | 0.319438i | \(0.103494\pi\) | ||||
−0.947607 | + | 0.319438i | \(0.896506\pi\) | |||||||
\(432\) | 17106.8 | 0.0916647 | ||||||||
\(433\) | −336890. | −1.79685 | −0.898425 | − | 0.439127i | \(-0.855288\pi\) | ||||
−0.898425 | + | 0.439127i | \(0.855288\pi\) | |||||||
\(434\) | −33975.4 | −0.180378 | ||||||||
\(435\) | 168408. | 0.889989 | ||||||||
\(436\) | − | 399372.i | − | 2.10089i | ||||||
\(437\) | 72389.3i | 0.379063i | ||||||||
\(438\) | 63623.3 | 0.331641 | ||||||||
\(439\) | 333202. | 1.72893 | 0.864466 | − | 0.502691i | \(-0.167657\pi\) | ||||
0.864466 | + | 0.502691i | \(0.167657\pi\) | |||||||
\(440\) | 76404.6 | 0.394652 | ||||||||
\(441\) | −63611.6 | −0.327084 | ||||||||
\(442\) | 37568.8 | 0.192302 | ||||||||
\(443\) | 79729.2i | 0.406265i | 0.979151 | + | 0.203133i | \(0.0651123\pi\) | ||||
−0.979151 | + | 0.203133i | \(0.934888\pi\) | |||||||
\(444\) | − | 256516.i | − | 1.30121i | ||||||
\(445\) | − | 330403.i | − | 1.66849i | ||||||
\(446\) | − | 124509.i | − | 0.625940i | ||||||
\(447\) | − | 93666.3i | − | 0.468779i | ||||||
\(448\) | −39194.7 | −0.195286 | ||||||||
\(449\) | −278079. | −1.37935 | −0.689676 | − | 0.724118i | \(-0.742247\pi\) | ||||
−0.689676 | + | 0.724118i | \(0.742247\pi\) | |||||||
\(450\) | − | 192605.i | − | 0.951135i | ||||||
\(451\) | 1540.64i | 0.00757440i | ||||||||
\(452\) | − | 256518.i | − | 1.25557i | ||||||
\(453\) | − | 203142.i | − | 0.989927i | ||||||
\(454\) | −411449. | −1.99620 | ||||||||
\(455\) | 20190.8i | 0.0975282i | ||||||||
\(456\) | 199665.i | 0.960226i | ||||||||
\(457\) | − | 175865.i | − | 0.842067i | −0.907045 | − | 0.421033i | \(-0.861668\pi\) | ||
0.907045 | − | 0.421033i | \(-0.138332\pi\) | |||||||
\(458\) | 578541. | 2.75806 | ||||||||
\(459\) | 10724.8 | 0.0509053 | ||||||||
\(460\) | 196285.i | 0.927621i | ||||||||
\(461\) | −158569. | −0.746134 | −0.373067 | − | 0.927804i | \(-0.621694\pi\) | ||||
−0.373067 | + | 0.927804i | \(0.621694\pi\) | |||||||
\(462\) | −4978.40 | −0.0233242 | ||||||||
\(463\) | 77926.4i | 0.363515i | 0.983343 | + | 0.181758i | \(0.0581786\pi\) | ||||
−0.983343 | + | 0.181758i | \(0.941821\pi\) | |||||||
\(464\) | −96183.7 | −0.446751 | ||||||||
\(465\) | − | 161124.i | − | 0.745166i | ||||||
\(466\) | −274430. | −1.26375 | ||||||||
\(467\) | − | 408542.i | − | 1.87328i | −0.350291 | − | 0.936641i | \(-0.613917\pi\) | ||
0.350291 | − | 0.936641i | \(-0.386083\pi\) | |||||||
\(468\) | − | 57393.9i | − | 0.262044i | ||||||
\(469\) | − | 5344.55i | − | 0.0242977i | ||||||
\(470\) | 800380. | 3.62327 | ||||||||
\(471\) | − | 143804.i | − | 0.648230i | ||||||
\(472\) | 9030.44 | − | 304026.i | 0.0405345 | − | 1.36467i | ||||
\(473\) | −57304.5 | −0.256133 | ||||||||
\(474\) | 247077.i | 1.09971i | ||||||||
\(475\) | 467533. | 2.07217 | ||||||||
\(476\) | 14885.1 | 0.0656957 | ||||||||
\(477\) | 31756.9 | 0.139573 | ||||||||
\(478\) | − | 29783.8i | − | 0.130354i | ||||||
\(479\) | −161846. | −0.705393 | −0.352697 | − | 0.935738i | \(-0.614735\pi\) | ||||
−0.352697 | + | 0.935738i | \(0.614735\pi\) | |||||||
\(480\) | − | 123801.i | − | 0.537329i | ||||||
\(481\) | −124587. | −0.538497 | ||||||||
\(482\) | 439574.i | 1.89207i | ||||||||
\(483\) | − | 5738.67i | − | 0.0245990i | ||||||
\(484\) | −411769. | −1.75777 | ||||||||
\(485\) | 96720.2i | 0.411182i | ||||||||
\(486\) | − | 25416.9i | − | 0.107609i | ||||||
\(487\) | −156630. | −0.660414 | −0.330207 | − | 0.943909i | \(-0.607119\pi\) | ||||
−0.330207 | + | 0.943909i | \(0.607119\pi\) | |||||||
\(488\) | −178405. | −0.749149 | ||||||||
\(489\) | −150223. | −0.628230 | ||||||||
\(490\) | − | 649516.i | − | 2.70519i | ||||||
\(491\) | 289340. | 1.20018 | 0.600089 | − | 0.799933i | \(-0.295132\pi\) | ||||
0.600089 | + | 0.799933i | \(0.295132\pi\) | |||||||
\(492\) | −10916.8 | −0.0450990 | ||||||||
\(493\) | −60300.4 | −0.248100 | ||||||||
\(494\) | 216126. | 0.885632 | ||||||||
\(495\) | − | 23609.4i | − | 0.0963550i | ||||||
\(496\) | 92023.2i | 0.374054i | ||||||||
\(497\) | 32615.6 | 0.132042 | ||||||||
\(498\) | 154282. | 0.622095 | ||||||||
\(499\) | 366469. | 1.47176 | 0.735878 | − | 0.677114i | \(-0.236769\pi\) | ||||
0.735878 | + | 0.677114i | \(0.236769\pi\) | |||||||
\(500\) | 522452. | 2.08981 | ||||||||
\(501\) | −232377. | −0.925802 | ||||||||
\(502\) | 177684.i | 0.705085i | ||||||||
\(503\) | 160477.i | 0.634274i | 0.948380 | + | 0.317137i | \(0.102722\pi\) | ||||
−0.948380 | + | 0.317137i | \(0.897278\pi\) | |||||||
\(504\) | − | 15828.5i | − | 0.0623130i | ||||||
\(505\) | 619222.i | 2.42808i | ||||||||
\(506\) | 23506.2i | 0.0918081i | ||||||||
\(507\) | 120532. | 0.468906 | ||||||||
\(508\) | 363022. | 1.40671 | ||||||||
\(509\) | 244953.i | 0.945468i | 0.881205 | + | 0.472734i | \(0.156733\pi\) | ||||
−0.881205 | + | 0.472734i | \(0.843267\pi\) | |||||||
\(510\) | 109507.i | 0.421019i | ||||||||
\(511\) | − | 12243.3i | − | 0.0468875i | ||||||
\(512\) | 241175.i | 0.920008i | ||||||||
\(513\) | 61697.6 | 0.234441 | ||||||||
\(514\) | 493379.i | 1.86747i | ||||||||
\(515\) | − | 537796.i | − | 2.02770i | ||||||
\(516\) | − | 406054.i | − | 1.52505i | ||||||
\(517\) | 61786.8 | 0.231161 | ||||||||
\(518\) | −76576.1 | −0.285387 | ||||||||
\(519\) | 193502.i | 0.718373i | ||||||||
\(520\) | 262950. | 0.972450 | ||||||||
\(521\) | −366691. | −1.35090 | −0.675452 | − | 0.737404i | \(-0.736052\pi\) | ||||
−0.675452 | + | 0.737404i | \(0.736052\pi\) | |||||||
\(522\) | 142907.i | 0.524461i | ||||||||
\(523\) | 97476.4 | 0.356366 | 0.178183 | − | 0.983997i | \(-0.442978\pi\) | ||||
0.178183 | + | 0.983997i | \(0.442978\pi\) | |||||||
\(524\) | − | 871636.i | − | 3.17448i | ||||||
\(525\) | −37063.7 | −0.134472 | ||||||||
\(526\) | 389421.i | 1.40750i | ||||||||
\(527\) | 57692.0i | 0.207728i | ||||||||
\(528\) | 13484.1i | 0.0483677i | ||||||||
\(529\) | 252745. | 0.903174 | ||||||||
\(530\) | 324259.i | 1.15436i | ||||||||
\(531\) | −93945.6 | − | 2790.45i | −0.333186 | − | 0.00989658i | ||||
\(532\) | 85631.0 | 0.302557 | ||||||||
\(533\) | 5302.20i | 0.0186639i | ||||||||
\(534\) | 280372. | 0.983223 | ||||||||
\(535\) | 10887.1 | 0.0380369 | ||||||||
\(536\) | −69603.6 | −0.242272 | ||||||||
\(537\) | − | 122561.i | − | 0.425015i | ||||||
\(538\) | −798903. | −2.76013 | ||||||||
\(539\) | − | 50140.6i | − | 0.172589i | ||||||
\(540\) | 167294. | 0.573711 | ||||||||
\(541\) | 321027.i | 1.09685i | 0.836199 | + | 0.548425i | \(0.184773\pi\) | ||||
−0.836199 | + | 0.548425i | \(0.815227\pi\) | |||||||
\(542\) | − | 639310.i | − | 2.17627i | ||||||
\(543\) | −7015.97 | −0.0237951 | ||||||||
\(544\) | 44328.1i | 0.149790i | ||||||||
\(545\) | − | 565393.i | − | 1.90352i | ||||||
\(546\) | −17133.4 | −0.0574723 | ||||||||
\(547\) | −82148.9 | −0.274554 | −0.137277 | − | 0.990533i | \(-0.543835\pi\) | ||||
−0.137277 | + | 0.990533i | \(0.543835\pi\) | |||||||
\(548\) | −886530. | −2.95211 | ||||||||
\(549\) | 55128.1i | 0.182906i | ||||||||
\(550\) | 151817. | 0.501874 | ||||||||
\(551\) | −346896. | −1.14261 | ||||||||
\(552\) | −74736.4 | −0.245275 | ||||||||
\(553\) | 47546.1 | 0.155477 | ||||||||
\(554\) | 476362.i | 1.55209i | ||||||||
\(555\) | − | 363151.i | − | 1.17897i | ||||||
\(556\) | −395913. | −1.28071 | ||||||||
\(557\) | −92439.5 | −0.297953 | −0.148976 | − | 0.988841i | \(-0.547598\pi\) | ||||
−0.148976 | + | 0.988841i | \(0.547598\pi\) | |||||||
\(558\) | 136726. | 0.439119 | ||||||||
\(559\) | −197216. | −0.631131 | ||||||||
\(560\) | 33612.9 | 0.107184 | ||||||||
\(561\) | 8453.60i | 0.0268606i | ||||||||
\(562\) | − | 598232.i | − | 1.89408i | ||||||
\(563\) | 332807.i | 1.04997i | 0.851112 | + | 0.524984i | \(0.175929\pi\) | ||||
−0.851112 | + | 0.524984i | \(0.824071\pi\) | |||||||
\(564\) | 437815.i | 1.37636i | ||||||||
\(565\) | − | 363154.i | − | 1.13761i | ||||||
\(566\) | −817065. | −2.55049 | ||||||||
\(567\) | −4891.08 | −0.0152138 | ||||||||
\(568\) | − | 424763.i | − | 1.31659i | ||||||
\(569\) | 71655.2i | 0.221321i | 0.993858 | + | 0.110661i | \(0.0352966\pi\) | ||||
−0.993858 | + | 0.110661i | \(0.964703\pi\) | |||||||
\(570\) | 629973.i | 1.93897i | ||||||||
\(571\) | − | 235330.i | − | 0.721780i | −0.932608 | − | 0.360890i | \(-0.882473\pi\) | ||
0.932608 | − | 0.360890i | \(-0.117527\pi\) | |||||||
\(572\) | 45239.6 | 0.138270 | ||||||||
\(573\) | 181682.i | 0.553354i | ||||||||
\(574\) | 3258.94i | 0.00989127i | ||||||||
\(575\) | 175001.i | 0.529305i | ||||||||
\(576\) | 157730. | 0.475410 | ||||||||
\(577\) | 582269. | 1.74893 | 0.874465 | − | 0.485089i | \(-0.161213\pi\) | ||||
0.874465 | + | 0.485089i | \(0.161213\pi\) | |||||||
\(578\) | 521204.i | 1.56010i | ||||||||
\(579\) | −145814. | −0.434954 | ||||||||
\(580\) | −940615. | −2.79612 | ||||||||
\(581\) | − | 29689.1i | − | 0.0879519i | ||||||
\(582\) | −82074.6 | −0.242305 | ||||||||
\(583\) | 25031.8i | 0.0736469i | ||||||||
\(584\) | −159448. | −0.467513 | ||||||||
\(585\) | − | 81252.9i | − | 0.237425i | ||||||
\(586\) | 94427.4i | 0.274981i | ||||||||
\(587\) | 535088.i | 1.55292i | 0.630166 | + | 0.776460i | \(0.282987\pi\) | ||||
−0.630166 | + | 0.776460i | \(0.717013\pi\) | |||||||
\(588\) | 355292. | 1.02762 | ||||||||
\(589\) | 331891.i | 0.956676i | ||||||||
\(590\) | 28492.3 | − | 959246.i | 0.0818510 | − | 2.75566i | ||||
\(591\) | −44993.4 | −0.128817 | ||||||||
\(592\) | 207408.i | 0.591810i | ||||||||
\(593\) | 439880. | 1.25091 | 0.625453 | − | 0.780262i | \(-0.284914\pi\) | ||||
0.625453 | + | 0.780262i | \(0.284914\pi\) | |||||||
\(594\) | 20034.4 | 0.0567810 | ||||||||
\(595\) | 21072.9 | 0.0595238 | ||||||||
\(596\) | 523157.i | 1.47279i | ||||||||
\(597\) | −162596. | −0.456207 | ||||||||
\(598\) | 80897.7i | 0.226222i | ||||||||
\(599\) | −177415. | −0.494465 | −0.247233 | − | 0.968956i | \(-0.579521\pi\) | ||||
−0.247233 | + | 0.968956i | \(0.579521\pi\) | |||||||
\(600\) | 482692.i | 1.34081i | ||||||||
\(601\) | − | 602513.i | − | 1.66808i | −0.551703 | − | 0.834041i | \(-0.686022\pi\) | ||
0.551703 | − | 0.834041i | \(-0.313978\pi\) | |||||||
\(602\) | −121217. | −0.334480 | ||||||||
\(603\) | 21507.9i | 0.0591511i | ||||||||
\(604\) | 1.13461e6i | 3.11010i | ||||||||
\(605\) | −582945. | −1.59264 | ||||||||
\(606\) | −525458. | −1.43084 | ||||||||
\(607\) | −235674. | −0.639639 | −0.319820 | − | 0.947478i | \(-0.603622\pi\) | ||||
−0.319820 | + | 0.947478i | \(0.603622\pi\) | |||||||
\(608\) | 255011.i | 0.689846i | ||||||||
\(609\) | 27500.3 | 0.0741485 | ||||||||
\(610\) | −562894. | −1.51275 | ||||||||
\(611\) | 212642. | 0.569597 | ||||||||
\(612\) | −59901.4 | −0.159932 | ||||||||
\(613\) | − | 3306.79i | − | 0.00880006i | −0.999990 | − | 0.00440003i | \(-0.998599\pi\) | ||
0.999990 | − | 0.00440003i | \(-0.00140058\pi\) | |||||||
\(614\) | − | 564040.i | − | 1.49614i | ||||||
\(615\) | −15455.1 | −0.0408621 | ||||||||
\(616\) | 12476.5 | 0.0328800 | ||||||||
\(617\) | 194814. | 0.511740 | 0.255870 | − | 0.966711i | \(-0.417638\pi\) | ||||
0.255870 | + | 0.966711i | \(0.417638\pi\) | |||||||
\(618\) | 456361. | 1.19490 | ||||||||
\(619\) | −346456. | −0.904206 | −0.452103 | − | 0.891966i | \(-0.649326\pi\) | ||||
−0.452103 | + | 0.891966i | \(0.649326\pi\) | |||||||
\(620\) | 899928.i | 2.34112i | ||||||||
\(621\) | 23093.9i | 0.0598844i | ||||||||
\(622\) | 186592.i | 0.482295i | ||||||||
\(623\) | − | 53953.2i | − | 0.139008i | ||||||
\(624\) | 46406.3i | 0.119181i | ||||||||
\(625\) | 75176.8 | 0.192453 | ||||||||
\(626\) | −24664.1 | −0.0629385 | ||||||||
\(627\) | 48631.9i | 0.123705i | ||||||||
\(628\) | 803192.i | 2.03657i | ||||||||
\(629\) | 130030.i | 0.328657i | ||||||||
\(630\) | − | 49941.2i | − | 0.125828i | ||||||
\(631\) | 694008. | 1.74303 | 0.871517 | − | 0.490365i | \(-0.163136\pi\) | ||||
0.871517 | + | 0.490365i | \(0.163136\pi\) | |||||||
\(632\) | − | 619207.i | − | 1.55025i | ||||||
\(633\) | 6636.81i | 0.0165635i | ||||||||
\(634\) | − | 204390.i | − | 0.508489i | ||||||
\(635\) | 513933. | 1.27456 | ||||||||
\(636\) | −177373. | −0.438503 | ||||||||
\(637\) | − | 172561.i | − | 0.425270i | ||||||
\(638\) | −112644. | −0.276736 | ||||||||
\(639\) | −131254. | −0.321448 | ||||||||
\(640\) | 1.22932e6i | 3.00126i | ||||||||
\(641\) | −97669.8 | −0.237708 | −0.118854 | − | 0.992912i | \(-0.537922\pi\) | ||||
−0.118854 | + | 0.992912i | \(0.537922\pi\) | |||||||
\(642\) | 9238.55i | 0.0224147i | ||||||||
\(643\) | −128561. | −0.310947 | −0.155474 | − | 0.987840i | \(-0.549690\pi\) | ||||
−0.155474 | + | 0.987840i | \(0.549690\pi\) | |||||||
\(644\) | 32052.3i | 0.0772837i | ||||||||
\(645\) | − | 574854.i | − | 1.38178i | ||||||
\(646\) | − | 225569.i | − | 0.540523i | ||||||
\(647\) | −280631. | −0.670390 | −0.335195 | − | 0.942149i | \(-0.608802\pi\) | ||||
−0.335195 | + | 0.942149i | \(0.608802\pi\) | |||||||
\(648\) | 63698.0i | 0.151697i | ||||||||
\(649\) | 2199.52 | − | 74050.7i | 0.00522201 | − | 0.175809i | ||||
\(650\) | 522486. | 1.23665 | ||||||||
\(651\) | − | 26310.7i | − | 0.0620827i | ||||||
\(652\) | 839044. | 1.97374 | ||||||||
\(653\) | 380413. | 0.892132 | 0.446066 | − | 0.895000i | \(-0.352825\pi\) | ||||
0.446066 | + | 0.895000i | \(0.352825\pi\) | |||||||
\(654\) | 479780. | 1.12173 | ||||||||
\(655\) | − | 1.23398e6i | − | 2.87625i | ||||||
\(656\) | 8826.91 | 0.0205117 | ||||||||
\(657\) | 49270.3i | 0.114144i | ||||||||
\(658\) | 130698. | 0.301869 | ||||||||
\(659\) | − | 59943.3i | − | 0.138029i | −0.997616 | − | 0.0690145i | \(-0.978015\pi\) | ||
0.997616 | − | 0.0690145i | \(-0.0219855\pi\) | |||||||
\(660\) | 131866.i | 0.302723i | ||||||||
\(661\) | −87318.8 | −0.199850 | −0.0999252 | − | 0.994995i | \(-0.531860\pi\) | ||||
−0.0999252 | + | 0.994995i | \(0.531860\pi\) | |||||||
\(662\) | − | 1.38630e6i | − | 3.16331i | ||||||
\(663\) | 29093.5i | 0.0661864i | ||||||||
\(664\) | −386650. | −0.876965 | ||||||||
\(665\) | 121228. | 0.274133 | ||||||||
\(666\) | 308162. | 0.694753 | ||||||||
\(667\) | − | 129846.i | − | 0.291862i | ||||||
\(668\) | 1.29790e6 | 2.90864 | ||||||||
\(669\) | 96420.8 | 0.215436 | ||||||||
\(670\) | −219609. | −0.489217 | ||||||||
\(671\) | −43453.6 | −0.0965119 | ||||||||
\(672\) | − | 20216.0i | − | 0.0447669i | ||||||
\(673\) | − | 598287.i | − | 1.32093i | −0.750857 | − | 0.660465i | \(-0.770359\pi\) | ||
0.750857 | − | 0.660465i | \(-0.229641\pi\) | |||||||
\(674\) | −978455. | −2.15388 | ||||||||
\(675\) | 149154. | 0.327362 | ||||||||
\(676\) | −673209. | −1.47318 | ||||||||
\(677\) | 874864. | 1.90881 | 0.954406 | − | 0.298512i | \(-0.0964902\pi\) | ||||
0.954406 | + | 0.298512i | \(0.0964902\pi\) | |||||||
\(678\) | 308164. | 0.670382 | ||||||||
\(679\) | 15794.0i | 0.0342572i | ||||||||
\(680\) | − | 274439.i | − | 0.593509i | ||||||
\(681\) | − | 318628.i | − | 0.687053i | ||||||
\(682\) | 107771.i | 0.231705i | ||||||||
\(683\) | − | 742238.i | − | 1.59112i | −0.605878 | − | 0.795558i | \(-0.707178\pi\) | ||
0.605878 | − | 0.795558i | \(-0.292822\pi\) | |||||||
\(684\) | −344601. | −0.736554 | ||||||||
\(685\) | −1.25507e6 | −2.67477 | ||||||||
\(686\) | − | 214152.i | − | 0.455066i | ||||||
\(687\) | 448025.i | 0.949269i | ||||||||
\(688\) | 328319.i | 0.693616i | ||||||||
\(689\) | 86148.1i | 0.181471i | ||||||||
\(690\) | −235804. | −0.495282 | ||||||||
\(691\) | 339025.i | 0.710028i | 0.934861 | + | 0.355014i | \(0.115524\pi\) | ||||
−0.934861 | + | 0.355014i | \(0.884476\pi\) | |||||||
\(692\) | − | 1.08077e6i | − | 2.25695i | ||||||
\(693\) | − | 3855.30i | − | 0.00802771i | ||||||
\(694\) | 217412. | 0.451403 | ||||||||
\(695\) | −560496. | −1.16039 | ||||||||
\(696\) | − | 358144.i | − | 0.739332i | ||||||
\(697\) | 5533.85 | 0.0113910 | ||||||||
\(698\) | 1.10836e6 | 2.27493 | ||||||||
\(699\) | − | 212520.i | − | 0.434957i | ||||||
\(700\) | 207013. | 0.422476 | ||||||||
\(701\) | − | 288735.i | − | 0.587576i | −0.955871 | − | 0.293788i | \(-0.905084\pi\) | ||
0.955871 | − | 0.293788i | \(-0.0949159\pi\) | |||||||
\(702\) | 68949.4 | 0.139912 | ||||||||
\(703\) | 748039.i | 1.51361i | ||||||||
\(704\) | 124327.i | 0.250854i | ||||||||
\(705\) | 619818.i | 1.24706i | ||||||||
\(706\) | 1.29800e6 | 2.60414 | ||||||||
\(707\) | 101116.i | 0.202293i | ||||||||
\(708\) | 524717. | + | 15585.6i | 1.04679 | + | 0.0310925i | ||||
\(709\) | −65496.9 | −0.130295 | −0.0651476 | − | 0.997876i | \(-0.520752\pi\) | ||||
−0.0651476 | + | 0.997876i | \(0.520752\pi\) | |||||||
\(710\) | − | 1.34019e6i | − | 2.65858i | ||||||
\(711\) | −191338. | −0.378497 | ||||||||
\(712\) | −702648. | −1.38605 | ||||||||
\(713\) | −124229. | −0.244369 | ||||||||
\(714\) | 17882.0i | 0.0350768i | ||||||||
\(715\) | 64046.0 | 0.125279 | ||||||||
\(716\) | 684544.i | 1.33529i | ||||||||
\(717\) | 23064.7 | 0.0448652 | ||||||||
\(718\) | 635013.i | 1.23178i | ||||||||
\(719\) | − | 616651.i | − | 1.19284i | −0.802673 | − | 0.596420i | \(-0.796589\pi\) | ||
0.802673 | − | 0.596420i | \(-0.203411\pi\) | |||||||
\(720\) | −135267. | −0.260932 | ||||||||
\(721\) | − | 87819.5i | − | 0.168935i | ||||||
\(722\) | − | 423217.i | − | 0.811875i | ||||||
\(723\) | −340409. | −0.651214 | ||||||||
\(724\) | 39186.5 | 0.0747583 | ||||||||
\(725\) | −838624. | −1.59548 | ||||||||
\(726\) | − | 494673.i | − | 0.938524i | ||||||
\(727\) | 79727.7 | 0.150848 | 0.0754241 | − | 0.997152i | \(-0.475969\pi\) | ||||
0.0754241 | + | 0.997152i | \(0.475969\pi\) | |||||||
\(728\) | 42938.5 | 0.0810186 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | −503082. | −0.944045 | ||||||||
\(731\) | 205833.i | 0.385194i | ||||||||
\(732\) | − | 307909.i | − | 0.574645i | ||||||
\(733\) | −797529. | −1.48436 | −0.742179 | − | 0.670202i | \(-0.766207\pi\) | ||||
−0.742179 | + | 0.670202i | \(0.766207\pi\) | |||||||
\(734\) | 1.68167e6 | 3.12139 | ||||||||
\(735\) | 502989. | 0.931073 | ||||||||
\(736\) | −95452.7 | −0.176211 | ||||||||
\(737\) | −16953.1 | −0.0312115 | ||||||||
\(738\) | − | 13114.8i | − | 0.0240796i | ||||||
\(739\) | − | 924588.i | − | 1.69301i | −0.532381 | − | 0.846505i | \(-0.678703\pi\) | ||
0.532381 | − | 0.846505i | \(-0.321297\pi\) | |||||||
\(740\) | 2.02832e6i | 3.70402i | ||||||||
\(741\) | 167369.i | 0.304817i | ||||||||
\(742\) | 52950.0i | 0.0961741i | ||||||||
\(743\) | 671065. | 1.21559 | 0.607795 | − | 0.794094i | \(-0.292054\pi\) | ||||
0.607795 | + | 0.794094i | \(0.292054\pi\) | |||||||
\(744\) | −342652. | −0.619024 | ||||||||
\(745\) | 740637.i | 1.33442i | ||||||||
\(746\) | − | 439202.i | − | 0.789200i | ||||||
\(747\) | 119477.i | 0.214113i | ||||||||
\(748\) | − | 47216.1i | − | 0.0843893i | ||||||
\(749\) | 1777.81 | 0.00316900 | ||||||||
\(750\) | 627640.i | 1.11580i | ||||||||
\(751\) | − | 405680.i | − | 0.719289i | −0.933089 | − | 0.359645i | \(-0.882898\pi\) | ||
0.933089 | − | 0.359645i | \(-0.117102\pi\) | |||||||
\(752\) | − | 354000.i | − | 0.625989i | ||||||
\(753\) | −137600. | −0.242676 | ||||||||
\(754\) | −387670. | −0.681898 | ||||||||
\(755\) | 1.60628e6i | 2.81791i | ||||||||
\(756\) | 27318.3 | 0.0477981 | ||||||||
\(757\) | −843491. | −1.47193 | −0.735967 | − | 0.677017i | \(-0.763272\pi\) | ||||
−0.735967 | + | 0.677017i | \(0.763272\pi\) | |||||||
\(758\) | − | 404755.i | − | 0.704457i | ||||||
\(759\) | −18203.3 | −0.0315985 | ||||||||
\(760\) | − | 1.57879e6i | − | 2.73337i | ||||||
\(761\) | −953711. | −1.64682 | −0.823412 | − | 0.567444i | \(-0.807932\pi\) | ||||
−0.823412 | + | 0.567444i | \(0.807932\pi\) | |||||||
\(762\) | 436112.i | 0.751084i | ||||||||
\(763\) | − | 92326.0i | − | 0.158590i | ||||||
\(764\) | − | 1.01476e6i | − | 1.73850i | ||||||
\(765\) | −84802.9 | −0.144906 | ||||||||
\(766\) | 358645.i | 0.611234i | ||||||||
\(767\) | 7569.75 | − | 254849.i | 0.0128674 | − | 0.433205i | ||||
\(768\) | −557489. | −0.945178 | ||||||||
\(769\) | − | 551211.i | − | 0.932106i | −0.884757 | − | 0.466053i | \(-0.845676\pi\) | ||
0.884757 | − | 0.466053i | \(-0.154324\pi\) | |||||||
\(770\) | 39365.2 | 0.0663943 | ||||||||
\(771\) | −382075. | −0.642747 | ||||||||
\(772\) | 814421. | 1.36651 | ||||||||
\(773\) | − | 98128.0i | − | 0.164223i | −0.996623 | − | 0.0821115i | \(-0.973834\pi\) | ||
0.996623 | − | 0.0821115i | \(-0.0261664\pi\) | |||||||
\(774\) | 487808. | 0.814267 | ||||||||
\(775\) | 802348.i | 1.33586i | ||||||||
\(776\) | 205689. | 0.341577 | ||||||||
\(777\) | − | 59300.9i | − | 0.0982244i | ||||||
\(778\) | − | 330187.i | − | 0.545508i | ||||||
\(779\) | 31835.2 | 0.0524605 | ||||||||
\(780\) | 453824.i | 0.745931i | ||||||||
\(781\) | − | 103458.i | − | 0.169614i | ||||||
\(782\) | 84432.2 | 0.138068 | ||||||||
\(783\) | −110668. | −0.180509 | ||||||||
\(784\) | −287274. | −0.467374 | ||||||||
\(785\) | 1.13708e6i | 1.84524i | ||||||||
\(786\) | 1.04713e6 | 1.69494 | ||||||||
\(787\) | 975267. | 1.57461 | 0.787307 | − | 0.616561i | \(-0.211475\pi\) | ||||
0.787307 | + | 0.616561i | \(0.211475\pi\) | |||||||
\(788\) | 251303. | 0.404712 | ||||||||
\(789\) | −301570. | −0.484433 | ||||||||
\(790\) | − | 1.95369e6i | − | 3.13041i | ||||||
\(791\) | − | 59301.3i | − | 0.0947788i | ||||||
\(792\) | −50208.7 | −0.0800440 | ||||||||
\(793\) | −149548. | −0.237812 | ||||||||
\(794\) | −507255. | −0.804610 | ||||||||
\(795\) | −251108. | −0.397307 | ||||||||
\(796\) | 908153. | 1.43329 | ||||||||
\(797\) | 838974.i | 1.32078i | 0.750921 | + | 0.660392i | \(0.229610\pi\) | ||||
−0.750921 | + | 0.660392i | \(0.770390\pi\) | |||||||
\(798\) | 102872.i | 0.161544i | ||||||||
\(799\) | − | 221933.i | − | 0.347638i | ||||||
\(800\) | 616490.i | 0.963266i | ||||||||
\(801\) | 217122.i | 0.338406i | ||||||||
\(802\) | 1.94211e6 | 3.01943 | ||||||||
\(803\) | −38836.3 | −0.0602292 | ||||||||
\(804\) | − | 120128.i | − | 0.185838i | ||||||
\(805\) | 45376.7i | 0.0700231i | ||||||||
\(806\) | 370901.i | 0.570936i | ||||||||
\(807\) | − | 618675.i | − | 0.949982i | ||||||
\(808\) | 1.31686e6 | 2.01706 | ||||||||
\(809\) | 620319.i | 0.947804i | 0.880578 | + | 0.473902i | \(0.157155\pi\) | ||||
−0.880578 | + | 0.473902i | \(0.842845\pi\) | |||||||
\(810\) | 200976.i | 0.306320i | ||||||||
\(811\) | 1.20442e6i | 1.83120i | 0.402093 | + | 0.915599i | \(0.368283\pi\) | ||||
−0.402093 | + | 0.915599i | \(0.631717\pi\) | |||||||
\(812\) | −153598. | −0.232956 | ||||||||
\(813\) | 495085. | 0.749030 | ||||||||
\(814\) | 242903.i | 0.366592i | ||||||||
\(815\) | 1.18784e6 | 1.78831 | ||||||||
\(816\) | 48433.8 | 0.0727392 | ||||||||
\(817\) | 1.18412e6i | 1.77399i | ||||||||
\(818\) | 1.05986e6 | 1.58396 | ||||||||
\(819\) | − | 13268.2i | − | 0.0197808i | ||||||
\(820\) | 86321.6 | 0.128378 | ||||||||
\(821\) | 254507.i | 0.377584i | 0.982017 | + | 0.188792i | \(0.0604571\pi\) | ||||
−0.982017 | + | 0.188792i | \(0.939543\pi\) | |||||||
\(822\) | − | 1.06502e6i | − | 1.57621i | ||||||
\(823\) | − | 272405.i | − | 0.402175i | −0.979573 | − | 0.201088i | \(-0.935552\pi\) | ||
0.979573 | − | 0.201088i | \(-0.0644476\pi\) | |||||||
\(824\) | −1.14370e6 | −1.68445 | ||||||||
\(825\) | 117568.i | 0.172735i | ||||||||
\(826\) | 4652.66 | − | 156640.i | 0.00681932 | − | 0.229585i | ||||
\(827\) | 460578. | 0.673430 | 0.336715 | − | 0.941607i | \(-0.390684\pi\) | ||||
0.336715 | + | 0.941607i | \(0.390684\pi\) | |||||||
\(828\) | − | 128987.i | − | 0.188142i | ||||||
\(829\) | −106117. | −0.154411 | −0.0772053 | − | 0.997015i | \(-0.524600\pi\) | ||||
−0.0772053 | + | 0.997015i | \(0.524600\pi\) | |||||||
\(830\) | −1.21994e6 | −1.77085 | ||||||||
\(831\) | −368897. | −0.534199 | ||||||||
\(832\) | 427879.i | 0.618122i | ||||||||
\(833\) | −180101. | −0.259553 | ||||||||
\(834\) | − | 475624.i | − | 0.683805i | ||||||
\(835\) | 1.83745e6 | 2.63538 | ||||||||
\(836\) | − | 271625.i | − | 0.388649i | ||||||
\(837\) | 105881.i | 0.151136i | ||||||||
\(838\) | 1.88051e6 | 2.67786 | ||||||||
\(839\) | 1.07945e6i | 1.53348i | 0.641957 | + | 0.766741i | \(0.278123\pi\) | ||||
−0.641957 | + | 0.766741i | \(0.721877\pi\) | |||||||
\(840\) | 125159.i | 0.177380i | ||||||||
\(841\) | −85045.7 | −0.120243 | ||||||||
\(842\) | −825498. | −1.16437 | ||||||||
\(843\) | 463274. | 0.651903 | ||||||||
\(844\) | − | 37068.8i | − | 0.0520383i | ||||||
\(845\) | −953067. | −1.33478 | ||||||||
\(846\) | −525964. | −0.734878 | ||||||||
\(847\) | −95192.1 | −0.132689 | ||||||||
\(848\) | 143416. | 0.199438 | ||||||||
\(849\) | − | 632740.i | − | 0.877829i | ||||||
\(850\) | − | 545313.i | − | 0.754759i | ||||||
\(851\) | −279997. | −0.386629 | ||||||||
\(852\) | 733096. | 1.00991 | ||||||||
\(853\) | −694278. | −0.954191 | −0.477096 | − | 0.878851i | \(-0.658311\pi\) | ||||
−0.477096 | + | 0.878851i | \(0.658311\pi\) | |||||||
\(854\) | −91917.9 | −0.126033 | ||||||||
\(855\) | −487855. | −0.667357 | ||||||||
\(856\) | − | 23153.0i | − | 0.0315980i | ||||||
\(857\) | − | 565662.i | − | 0.770186i | −0.922878 | − | 0.385093i | \(-0.874169\pi\) | ||
0.922878 | − | 0.385093i | \(-0.125831\pi\) | |||||||
\(858\) | 54348.0i | 0.0738259i | ||||||||
\(859\) | 918130.i | 1.24428i | 0.782906 | + | 0.622139i | \(0.213736\pi\) | ||||
−0.782906 | + | 0.622139i | \(0.786264\pi\) | |||||||
\(860\) | 3.21075e6i | 4.34120i | ||||||||
\(861\) | −2523.74 | −0.00340438 | ||||||||
\(862\) | 796316. | 1.07169 | ||||||||
\(863\) | 930295.i | 1.24911i | 0.780982 | + | 0.624553i | \(0.214719\pi\) | ||||
−0.780982 | + | 0.624553i | \(0.785281\pi\) | |||||||
\(864\) | 81354.6i | 0.108982i | ||||||||
\(865\) | − | 1.53005e6i | − | 2.04491i | ||||||
\(866\) | 2.26048e6i | 3.01415i | ||||||||
\(867\) | −403623. | −0.536955 | ||||||||
\(868\) | 146954.i | 0.195048i | ||||||||
\(869\) | − | 150818.i | − | 0.199717i | ||||||
\(870\) | − | 1.13000e6i | − | 1.49293i | ||||||
\(871\) | −58345.1 | −0.0769074 | ||||||||
\(872\) | −1.20239e6 | −1.58129 | ||||||||
\(873\) | − | 63559.0i | − | 0.0833966i | ||||||
\(874\) | 485722. | 0.635865 | ||||||||
\(875\) | 120779. | 0.157753 | ||||||||
\(876\) | − | 275191.i | − | 0.358613i | ||||||
\(877\) | −313247. | −0.407275 | −0.203638 | − | 0.979046i | \(-0.565276\pi\) | ||||
−0.203638 | + | 0.979046i | \(0.565276\pi\) | |||||||
\(878\) | − | 2.23574e6i | − | 2.90022i | ||||||
\(879\) | −73125.1 | −0.0946431 | ||||||||
\(880\) | − | 106622.i | − | 0.137683i | ||||||
\(881\) | − | 185355.i | − | 0.238810i | −0.992846 | − | 0.119405i | \(-0.961901\pi\) | ||
0.992846 | − | 0.119405i | \(-0.0380988\pi\) | |||||||
\(882\) | 426825.i | 0.548672i | ||||||||
\(883\) | −613135. | −0.786384 | −0.393192 | − | 0.919456i | \(-0.628629\pi\) | ||||
−0.393192 | + | 0.919456i | \(0.628629\pi\) | |||||||
\(884\) | − | 162497.i | − | 0.207941i | ||||||
\(885\) | 742845. | + | 22064.6i | 0.948444 | + | 0.0281715i | ||||
\(886\) | 534972. | 0.681496 | ||||||||
\(887\) | − | 673956.i | − | 0.856612i | −0.903634 | − | 0.428306i | \(-0.859111\pi\) | ||
0.903634 | − | 0.428306i | \(-0.140889\pi\) | |||||||
\(888\) | −772293. | −0.979392 | ||||||||
\(889\) | 83922.9 | 0.106188 | ||||||||
\(890\) | −2.21695e6 | −2.79883 | ||||||||
\(891\) | 15514.7i | 0.0195429i | ||||||||
\(892\) | −538542. | −0.676846 | ||||||||
\(893\) | − | 1.27674e6i | − | 1.60103i | ||||||
\(894\) | −628488. | −0.786361 | ||||||||
\(895\) | 969113.i | 1.20984i | ||||||||
\(896\) | 200742.i | 0.250047i | ||||||||
\(897\) | −62647.6 | −0.0778610 | ||||||||
\(898\) | 1.86587e6i | 2.31382i | ||||||||
\(899\) | − | 595320.i | − | 0.736599i | ||||||
\(900\) | −833075. | −1.02849 | ||||||||
\(901\) | 89912.0 | 0.110756 | ||||||||
\(902\) | 10337.5 | 0.0127058 | ||||||||
\(903\) | − | 93870.9i | − | 0.115121i | ||||||
\(904\) | −772298. | −0.945036 | ||||||||
\(905\) | 55476.6 | 0.0677349 | ||||||||
\(906\) | −1.36305e6 | −1.66057 | ||||||||
\(907\) | 1.07679e6 | 1.30894 | 0.654468 | − | 0.756090i | \(-0.272893\pi\) | ||||
0.654468 | + | 0.756090i | \(0.272893\pi\) | |||||||
\(908\) | 1.77964e6i | 2.15855i | ||||||||
\(909\) | − | 406917.i | − | 0.492468i | ||||||
\(910\) | 135477. | 0.163600 | ||||||||
\(911\) | 288010. | 0.347033 | 0.173516 | − | 0.984831i | \(-0.444487\pi\) | ||||
0.173516 | + | 0.984831i | \(0.444487\pi\) | |||||||
\(912\) | 278630. | 0.334995 | ||||||||
\(913\) | −94175.3 | −0.112978 | ||||||||
\(914\) | −1.18003e6 | −1.41254 | ||||||||
\(915\) | − | 435908.i | − | 0.520658i | ||||||
\(916\) | − | 2.50237e6i | − | 2.98236i | ||||||
\(917\) | − | 201503.i | − | 0.239631i | ||||||
\(918\) | − | 71961.8i | − | 0.0853919i | ||||||
\(919\) | − | 90535.9i | − | 0.107199i | −0.998563 | − | 0.0535994i | \(-0.982931\pi\) | ||
0.998563 | − | 0.0535994i | \(-0.0170694\pi\) | |||||||
\(920\) | 590955. | 0.698198 | ||||||||
\(921\) | 436796. | 0.514943 | ||||||||
\(922\) | 1.06398e6i | 1.25161i | ||||||||
\(923\) | − | 356057.i | − | 0.417942i | ||||||
\(924\) | 21533.1i | 0.0252210i | ||||||||
\(925\) | 1.80839e6i | 2.11353i | ||||||||
\(926\) | 522875. | 0.609784 | ||||||||
\(927\) | 353409.i | 0.411261i | ||||||||
\(928\) | − | 457419.i | − | 0.531151i | ||||||
\(929\) | 922758.i | 1.06919i | 0.845107 | + | 0.534597i | \(0.179537\pi\) | ||||
−0.845107 | + | 0.534597i | \(0.820463\pi\) | |||||||
\(930\) | −1.08112e6 | −1.24999 | ||||||||
\(931\) | −1.03608e6 | −1.19535 | ||||||||
\(932\) | 1.18700e6i | 1.36652i | ||||||||
\(933\) | −144498. | −0.165997 | ||||||||
\(934\) | −2.74126e6 | −3.14237 | ||||||||
\(935\) | − | 66844.2i | − | 0.0764611i | ||||||
\(936\) | −172796. | −0.197234 | ||||||||
\(937\) | 1.63873e6i | 1.86650i | 0.359226 | + | 0.933251i | \(0.383041\pi\) | ||||
−0.359226 | + | 0.933251i | \(0.616959\pi\) | |||||||
\(938\) | −35861.2 | −0.0407586 | ||||||||
\(939\) | − | 19100.0i | − | 0.0216622i | ||||||
\(940\) | − | 3.46189e6i | − | 3.91794i | ||||||
\(941\) | − | 432139.i | − | 0.488028i | −0.969772 | − | 0.244014i | \(-0.921536\pi\) | ||
0.969772 | − | 0.244014i | \(-0.0784642\pi\) | |||||||
\(942\) | −964904. | −1.08738 | ||||||||
\(943\) | 11916.2i | 0.0134002i | ||||||||
\(944\) | −424264. | − | 12601.9i | −0.476094 | − | 0.0141413i | ||||
\(945\) | 38674.7 | 0.0433076 | ||||||||
\(946\) | 384505.i | 0.429655i | ||||||||
\(947\) | −1.68549e6 | −1.87943 | −0.939716 | − | 0.341956i | \(-0.888911\pi\) | ||||
−0.939716 | + | 0.341956i | \(0.888911\pi\) | |||||||
\(948\) | 1.06869e6 | 1.18914 | ||||||||
\(949\) | −133657. | −0.148409 | ||||||||
\(950\) | − | 3.13708e6i | − | 3.47599i | ||||||
\(951\) | 158281. | 0.175012 | ||||||||
\(952\) | − | 44814.5i | − | 0.0494476i | ||||||
\(953\) | −1.30178e6 | −1.43335 | −0.716677 | − | 0.697405i | \(-0.754338\pi\) | ||||
−0.716677 | + | 0.697405i | \(0.754338\pi\) | |||||||
\(954\) | − | 213085.i | − | 0.234129i | ||||||
\(955\) | − | 1.43660e6i | − | 1.57517i | ||||||
\(956\) | −128824. | −0.140955 | ||||||||
\(957\) | − | 87232.0i | − | 0.0952472i | ||||||
\(958\) | 1.08596e6i | 1.18327i | ||||||||
\(959\) | −204946. | −0.222845 | ||||||||
\(960\) | −1.24720e6 | −1.35330 | ||||||||
\(961\) | 353952. | 0.383264 | ||||||||
\(962\) | 835962.i | 0.903309i | ||||||||
\(963\) | −7154.38 | −0.00771471 | ||||||||
\(964\) | 1.90129e6 | 2.04595 | ||||||||
\(965\) | 1.15298e6 | 1.23813 | ||||||||
\(966\) | −38505.7 | −0.0412639 | ||||||||
\(967\) | − | 1.16546e6i | − | 1.24636i | −0.782077 | − | 0.623182i | \(-0.785840\pi\) | ||
0.782077 | − | 0.623182i | \(-0.214160\pi\) | |||||||
\(968\) | 1.23971e6i | 1.32303i | ||||||||
\(969\) | 174682. | 0.186037 | ||||||||
\(970\) | 648979. | 0.689743 | ||||||||
\(971\) | 158501. | 0.168110 | 0.0840550 | − | 0.996461i | \(-0.473213\pi\) | ||||
0.0840550 | + | 0.996461i | \(0.473213\pi\) | |||||||
\(972\) | −109936. | −0.116361 | ||||||||
\(973\) | −91526.4 | −0.0966764 | ||||||||
\(974\) | 1.05096e6i | 1.10782i | ||||||||
\(975\) | 404616.i | 0.425631i | ||||||||
\(976\) | 248962.i | 0.261357i | ||||||||
\(977\) | − | 510200.i | − | 0.534504i | −0.963627 | − | 0.267252i | \(-0.913884\pi\) | ||
0.963627 | − | 0.267252i | \(-0.0861157\pi\) | |||||||
\(978\) | 1.00797e6i | 1.05383i | ||||||||
\(979\) | −171142. | −0.178563 | ||||||||
\(980\) | −2.80936e6 | −2.92520 | ||||||||
\(981\) | 371544.i | 0.386076i | ||||||||
\(982\) | − | 1.94143e6i | − | 2.01326i | ||||||
\(983\) | − | 853370.i | − | 0.883141i | −0.897226 | − | 0.441571i | \(-0.854421\pi\) | ||
0.897226 | − | 0.441571i | \(-0.145579\pi\) | |||||||
\(984\) | 32867.4i | 0.0339449i | ||||||||
\(985\) | 355772. | 0.366690 | ||||||||
\(986\) | 404607.i | 0.416179i | ||||||||
\(987\) | 101213.i | 0.103897i | ||||||||
\(988\) | − | 934812.i | − | 0.957658i | ||||||
\(989\) | −443224. | −0.453138 | ||||||||
\(990\) | −158416. | −0.161632 | ||||||||
\(991\) | − | 609956.i | − | 0.621086i | −0.950559 | − | 0.310543i | \(-0.899489\pi\) | ||
0.950559 | − | 0.310543i | \(-0.100511\pi\) | |||||||
\(992\) | −437632. | −0.444719 | ||||||||
\(993\) | 1.07356e6 | 1.08875 | ||||||||
\(994\) | − | 218846.i | − | 0.221496i | ||||||
\(995\) | 1.28568e6 | 1.29863 | ||||||||
\(996\) | − | 667318.i | − | 0.672688i | ||||||
\(997\) | 712553. | 0.716847 | 0.358424 | − | 0.933559i | \(-0.383314\pi\) | ||||
0.358424 | + | 0.933559i | \(0.383314\pi\) | |||||||
\(998\) | − | 2.45896e6i | − | 2.46882i | ||||||
\(999\) | 238642.i | 0.239120i |
(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 | 177.5.c.a.58.5 | ✓ | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.36 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.36 | yes | 40 | |
177.176 | even | 2 | 531.5.c.d.235.5 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.5 | ✓ | 40 | 1.1 | even | 1 | trivial | |
177.5.c.a.58.36 | yes | 40 | 59.58 | odd | 2 | inner | |
531.5.c.d.235.5 | 40 | 177.176 | even | 2 | |||
531.5.c.d.235.36 | 40 | 3.2 | odd | 2 |