Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(119,177)]
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([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.119");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 119.28 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.5.b.a.119.51 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.68814i | − | 0.672036i | −0.941856 | − | 0.336018i | \(-0.890920\pi\) | ||
0.941856 | − | 0.336018i | \(-0.109080\pi\) | |||||||
\(3\) | 6.36775 | + | 6.36017i | 0.707528 | + | 0.706685i | ||||
\(4\) | 8.77388 | 0.548368 | ||||||||
\(5\) | 40.9357i | 1.63743i | 0.574201 | + | 0.818714i | \(0.305313\pi\) | ||||
−0.574201 | + | 0.818714i | \(0.694687\pi\) | |||||||
\(6\) | 17.0970 | − | 17.1174i | 0.474918 | − | 0.475484i | ||||
\(7\) | 27.0431 | 0.551900 | 0.275950 | − | 0.961172i | \(-0.411008\pi\) | ||||
0.275950 | + | 0.961172i | \(0.411008\pi\) | |||||||
\(8\) | − | 66.5958i | − | 1.04056i | ||||||
\(9\) | 0.0965568 | + | 80.9999i | 0.00119206 | + | 0.999999i | ||||
\(10\) | 110.041 | 1.10041 | ||||||||
\(11\) | − | 103.074i | − | 0.851854i | −0.904758 | − | 0.425927i | \(-0.859948\pi\) | ||
0.904758 | − | 0.425927i | \(-0.140052\pi\) | |||||||
\(12\) | 55.8699 | + | 55.8034i | 0.387986 | + | 0.387523i | ||||
\(13\) | 118.814 | 0.703040 | 0.351520 | − | 0.936180i | \(-0.385665\pi\) | ||||
0.351520 | + | 0.936180i | \(0.385665\pi\) | |||||||
\(14\) | − | 72.6957i | − | 0.370897i | ||||||
\(15\) | −260.358 | + | 260.669i | −1.15715 | + | 1.15853i | ||||
\(16\) | −38.6368 | −0.150925 | ||||||||
\(17\) | 49.6376i | 0.171756i | 0.996306 | + | 0.0858782i | \(0.0273696\pi\) | ||||
−0.996306 | + | 0.0858782i | \(0.972630\pi\) | |||||||
\(18\) | 217.739 | − | 0.259559i | 0.672035 | − | 0.000801107i | ||||
\(19\) | 76.7031 | 0.212474 | 0.106237 | − | 0.994341i | \(-0.466120\pi\) | ||||
0.106237 | + | 0.994341i | \(0.466120\pi\) | |||||||
\(20\) | 359.165i | 0.897913i | ||||||||
\(21\) | 172.204 | + | 171.999i | 0.390485 | + | 0.390019i | ||||
\(22\) | −277.078 | −0.572476 | ||||||||
\(23\) | 924.844i | 1.74829i | 0.485668 | + | 0.874143i | \(0.338576\pi\) | ||||
−0.485668 | + | 0.874143i | \(0.661424\pi\) | |||||||
\(24\) | 423.560 | − | 424.065i | 0.735347 | − | 0.736225i | ||||
\(25\) | −1050.73 | −1.68117 | ||||||||
\(26\) | − | 319.388i | − | 0.472468i | ||||||
\(27\) | −514.558 | + | 516.402i | −0.705841 | + | 0.708370i | ||||
\(28\) | 237.273 | 0.302644 | ||||||||
\(29\) | 183.370i | 0.218039i | 0.994040 | + | 0.109019i | \(0.0347710\pi\) | ||||
−0.994040 | + | 0.109019i | \(0.965229\pi\) | |||||||
\(30\) | 700.714 | + | 699.880i | 0.778571 | + | 0.777644i | ||||
\(31\) | −755.744 | −0.786414 | −0.393207 | − | 0.919450i | \(-0.628634\pi\) | ||||
−0.393207 | + | 0.919450i | \(0.628634\pi\) | |||||||
\(32\) | − | 961.671i | − | 0.939132i | ||||||
\(33\) | 655.570 | − | 656.352i | 0.601992 | − | 0.602710i | ||||
\(34\) | 133.433 | 0.115426 | ||||||||
\(35\) | 1107.03i | 0.903697i | ||||||||
\(36\) | 0.847178 | + | 710.684i | 0.000653687 | + | 0.548367i | ||||
\(37\) | −41.7055 | −0.0304642 | −0.0152321 | − | 0.999884i | \(-0.504849\pi\) | ||||
−0.0152321 | + | 0.999884i | \(0.504849\pi\) | |||||||
\(38\) | − | 206.189i | − | 0.142790i | ||||||
\(39\) | 756.576 | + | 755.675i | 0.497420 | + | 0.496828i | ||||
\(40\) | 2726.14 | 1.70384 | ||||||||
\(41\) | 1404.41i | 0.835462i | 0.908571 | + | 0.417731i | \(0.137175\pi\) | ||||
−0.908571 | + | 0.417731i | \(0.862825\pi\) | |||||||
\(42\) | 462.357 | − | 462.908i | 0.262107 | − | 0.262420i | ||||
\(43\) | 2258.06 | 1.22124 | 0.610618 | − | 0.791926i | \(-0.290921\pi\) | ||||
0.610618 | + | 0.791926i | \(0.290921\pi\) | |||||||
\(44\) | − | 904.362i | − | 0.467129i | ||||||
\(45\) | −3315.79 | + | 3.95262i | −1.63743 | + | 0.00195191i | ||||
\(46\) | 2486.11 | 1.17491 | ||||||||
\(47\) | − | 4238.13i | − | 1.91857i | −0.282433 | − | 0.959287i | \(-0.591141\pi\) | ||
0.282433 | − | 0.959287i | \(-0.408859\pi\) | |||||||
\(48\) | −246.030 | − | 245.736i | −0.106784 | − | 0.106656i | ||||
\(49\) | −1669.67 | −0.695406 | ||||||||
\(50\) | 2824.52i | 1.12981i | ||||||||
\(51\) | −315.703 | + | 316.080i | −0.121378 | + | 0.121522i | ||||
\(52\) | 1042.46 | 0.385524 | ||||||||
\(53\) | 416.398i | 0.148237i | 0.997249 | + | 0.0741185i | \(0.0236143\pi\) | ||||
−0.997249 | + | 0.0741185i | \(0.976386\pi\) | |||||||
\(54\) | 1388.16 | + | 1383.21i | 0.476050 | + | 0.474351i | ||||
\(55\) | 4219.42 | 1.39485 | ||||||||
\(56\) | − | 1800.96i | − | 0.574284i | ||||||
\(57\) | 488.426 | + | 487.845i | 0.150331 | + | 0.150152i | ||||
\(58\) | 492.926 | 0.146530 | ||||||||
\(59\) | − | 453.188i | − | 0.130189i | ||||||
\(60\) | −2284.35 | + | 2287.08i | −0.634542 | + | 0.635299i | ||||
\(61\) | 3032.63 | 0.815005 | 0.407503 | − | 0.913204i | \(-0.366400\pi\) | ||||
0.407503 | + | 0.913204i | \(0.366400\pi\) | |||||||
\(62\) | 2031.55i | 0.528498i | ||||||||
\(63\) | 2.61119 | + | 2190.49i | 0.000657897 | + | 0.551900i | ||||
\(64\) | −3203.30 | −0.782055 | ||||||||
\(65\) | 4863.72i | 1.15118i | ||||||||
\(66\) | −1764.37 | − | 1762.27i | −0.405043 | − | 0.404560i | ||||
\(67\) | 954.878 | 0.212715 | 0.106358 | − | 0.994328i | \(-0.466081\pi\) | ||||
0.106358 | + | 0.994328i | \(0.466081\pi\) | |||||||
\(68\) | 435.515i | 0.0941857i | ||||||||
\(69\) | −5882.16 | + | 5889.18i | −1.23549 | + | 1.23696i | ||||
\(70\) | 2975.85 | 0.607317 | ||||||||
\(71\) | − | 6293.85i | − | 1.24853i | −0.781212 | − | 0.624266i | \(-0.785398\pi\) | ||
0.781212 | − | 0.624266i | \(-0.214602\pi\) | |||||||
\(72\) | 5394.25 | − | 6.43027i | 1.04056 | − | 0.00124041i | ||||
\(73\) | 5846.79 | 1.09716 | 0.548582 | − | 0.836097i | \(-0.315168\pi\) | ||||
0.548582 | + | 0.836097i | \(0.315168\pi\) | |||||||
\(74\) | 112.110i | 0.0204731i | ||||||||
\(75\) | −6690.81 | − | 6682.83i | −1.18948 | − | 1.18806i | ||||
\(76\) | 672.984 | 0.116514 | ||||||||
\(77\) | − | 2787.45i | − | 0.470138i | ||||||
\(78\) | 2031.36 | − | 2033.79i | 0.333886 | − | 0.334284i | ||||
\(79\) | 585.429 | 0.0938037 | 0.0469019 | − | 0.998900i | \(-0.485065\pi\) | ||||
0.0469019 | + | 0.998900i | \(0.485065\pi\) | |||||||
\(80\) | − | 1581.62i | − | 0.247129i | ||||||
\(81\) | −6560.98 | + | 15.6422i | −0.999997 | + | 0.00238412i | ||||
\(82\) | 3775.26 | 0.561461 | ||||||||
\(83\) | − | 12230.0i | − | 1.77529i | −0.460528 | − | 0.887645i | \(-0.652340\pi\) | ||
0.460528 | − | 0.887645i | \(-0.347660\pi\) | |||||||
\(84\) | 1510.90 | + | 1509.10i | 0.214129 | + | 0.213874i | ||||
\(85\) | −2031.95 | −0.281239 | ||||||||
\(86\) | − | 6070.00i | − | 0.820714i | ||||||
\(87\) | −1166.27 | + | 1167.66i | −0.154085 | + | 0.154268i | ||||
\(88\) | −6864.31 | −0.886404 | ||||||||
\(89\) | − | 4079.55i | − | 0.515029i | −0.966274 | − | 0.257515i | \(-0.917096\pi\) | ||
0.966274 | − | 0.257515i | \(-0.0829036\pi\) | |||||||
\(90\) | 10.6252 | + | 8913.32i | 0.00131175 | + | 1.10041i | ||||
\(91\) | 3213.09 | 0.388007 | ||||||||
\(92\) | 8114.47i | 0.958704i | ||||||||
\(93\) | −4812.39 | − | 4806.66i | −0.556410 | − | 0.555747i | ||||
\(94\) | −11392.7 | −1.28935 | ||||||||
\(95\) | 3139.90i | 0.347911i | ||||||||
\(96\) | 6116.39 | − | 6123.68i | 0.663670 | − | 0.664462i | ||||
\(97\) | −16180.1 | −1.71964 | −0.859822 | − | 0.510594i | \(-0.829425\pi\) | ||||
−0.859822 | + | 0.510594i | \(0.829425\pi\) | |||||||
\(98\) | 4488.32i | 0.467338i | ||||||||
\(99\) | 8349.01 | − | 9.95252i | 0.851853 | − | 0.00101546i | ||||
\(100\) | −9219.01 | −0.921901 | ||||||||
\(101\) | − | 2742.03i | − | 0.268800i | −0.990927 | − | 0.134400i | \(-0.957089\pi\) | ||
0.990927 | − | 0.134400i | \(-0.0429107\pi\) | |||||||
\(102\) | 849.668 | + | 848.656i | 0.0816675 | + | 0.0815702i | ||||
\(103\) | −7324.02 | −0.690359 | −0.345180 | − | 0.938537i | \(-0.612182\pi\) | ||||
−0.345180 | + | 0.938537i | \(0.612182\pi\) | |||||||
\(104\) | − | 7912.49i | − | 0.731554i | ||||||
\(105\) | −7040.89 | + | 7049.28i | −0.638629 | + | 0.639391i | ||||
\(106\) | 1119.34 | 0.0996206 | ||||||||
\(107\) | − | 3760.73i | − | 0.328476i | −0.986421 | − | 0.164238i | \(-0.947483\pi\) | ||
0.986421 | − | 0.164238i | \(-0.0525166\pi\) | |||||||
\(108\) | −4514.68 | + | 4530.85i | −0.387061 | + | 0.388447i | ||||
\(109\) | 107.989 | 0.00908921 | 0.00454461 | − | 0.999990i | \(-0.498553\pi\) | ||||
0.00454461 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(110\) | − | 11342.4i | − | 0.937389i | ||||||
\(111\) | −265.571 | − | 265.254i | −0.0215543 | − | 0.0215286i | ||||
\(112\) | −1044.86 | −0.0832955 | ||||||||
\(113\) | 9200.74i | 0.720553i | 0.932846 | + | 0.360277i | \(0.117318\pi\) | ||||
−0.932846 | + | 0.360277i | \(0.882682\pi\) | |||||||
\(114\) | 1311.40 | − | 1312.96i | 0.100908 | − | 0.101028i | ||||
\(115\) | −37859.1 | −2.86269 | ||||||||
\(116\) | 1608.87i | 0.119565i | ||||||||
\(117\) | 11.4723 | + | 9623.90i | 0.000838065 | + | 0.703039i | ||||
\(118\) | −1218.23 | −0.0874916 | ||||||||
\(119\) | 1342.35i | 0.0947923i | ||||||||
\(120\) | 17359.4 | + | 17338.7i | 1.20552 | + | 1.20408i | ||||
\(121\) | 4016.69 | 0.274345 | ||||||||
\(122\) | − | 8152.15i | − | 0.547713i | ||||||
\(123\) | −8932.30 | + | 8942.95i | −0.590409 | + | 0.591113i | ||||
\(124\) | −6630.81 | −0.431244 | ||||||||
\(125\) | − | 17427.7i | − | 1.11537i | ||||||
\(126\) | 5888.35 | − | 7.01927i | 0.370896 | − | 0.000442131i | ||||
\(127\) | 23490.3 | 1.45640 | 0.728201 | − | 0.685363i | \(-0.240357\pi\) | ||||
0.728201 | + | 0.685363i | \(0.240357\pi\) | |||||||
\(128\) | − | 6775.81i | − | 0.413563i | ||||||
\(129\) | 14378.8 | + | 14361.7i | 0.864058 | + | 0.863029i | ||||
\(130\) | 13074.4 | 0.773632 | ||||||||
\(131\) | − | 24755.6i | − | 1.44255i | −0.692648 | − | 0.721275i | \(-0.743556\pi\) | ||
0.692648 | − | 0.721275i | \(-0.256444\pi\) | |||||||
\(132\) | 5751.89 | − | 5758.75i | 0.330113 | − | 0.330507i | ||||
\(133\) | 2074.29 | 0.117264 | ||||||||
\(134\) | − | 2566.85i | − | 0.142952i | ||||||
\(135\) | −21139.3 | − | 21063.8i | −1.15991 | − | 1.15576i | ||||
\(136\) | 3305.65 | 0.178723 | ||||||||
\(137\) | 24333.7i | 1.29649i | 0.761434 | + | 0.648243i | \(0.224496\pi\) | ||||
−0.761434 | + | 0.648243i | \(0.775504\pi\) | |||||||
\(138\) | 15830.9 | + | 15812.1i | 0.831283 | + | 0.830292i | ||||
\(139\) | −13893.6 | −0.719095 | −0.359547 | − | 0.933127i | \(-0.617069\pi\) | ||||
−0.359547 | + | 0.933127i | \(0.617069\pi\) | |||||||
\(140\) | 9712.94i | 0.495558i | ||||||||
\(141\) | 26955.2 | − | 26987.4i | 1.35583 | − | 1.35745i | ||||
\(142\) | −16918.8 | −0.839058 | ||||||||
\(143\) | − | 12246.6i | − | 0.598887i | ||||||
\(144\) | −3.73064 | − | 3129.58i | −0.000179912 | − | 0.150925i | ||||
\(145\) | −7506.40 | −0.357023 | ||||||||
\(146\) | − | 15717.0i | − | 0.737333i | ||||||
\(147\) | −10632.1 | − | 10619.4i | −0.492020 | − | 0.491433i | ||||
\(148\) | −365.920 | −0.0167056 | ||||||||
\(149\) | − | 30511.7i | − | 1.37434i | −0.726496 | − | 0.687171i | \(-0.758853\pi\) | ||
0.726496 | − | 0.687171i | \(-0.241147\pi\) | |||||||
\(150\) | −17964.4 | + | 17985.8i | −0.798419 | + | 0.799371i | ||||
\(151\) | 37570.7 | 1.64776 | 0.823882 | − | 0.566761i | \(-0.191804\pi\) | ||||
0.823882 | + | 0.566761i | \(0.191804\pi\) | |||||||
\(152\) | − | 5108.10i | − | 0.221092i | ||||||
\(153\) | −4020.64 | + | 4.79285i | −0.171756 | + | 0.000204744i | ||||
\(154\) | −7493.06 | −0.315950 | ||||||||
\(155\) | − | 30936.9i | − | 1.28770i | ||||||
\(156\) | 6638.11 | + | 6630.20i | 0.272769 | + | 0.272444i | ||||
\(157\) | 13046.6 | 0.529293 | 0.264647 | − | 0.964345i | \(-0.414745\pi\) | ||||
0.264647 | + | 0.964345i | \(0.414745\pi\) | |||||||
\(158\) | − | 1573.72i | − | 0.0630395i | ||||||
\(159\) | −2648.36 | + | 2651.52i | −0.104757 | + | 0.104882i | ||||
\(160\) | 39366.7 | 1.53776 | ||||||||
\(161\) | 25010.6i | 0.964879i | ||||||||
\(162\) | 42.0485 | + | 17636.9i | 0.00160221 | + | 0.672034i | ||||
\(163\) | 44429.9 | 1.67225 | 0.836124 | − | 0.548541i | \(-0.184816\pi\) | ||||
0.836124 | + | 0.548541i | \(0.184816\pi\) | |||||||
\(164\) | 12322.2i | 0.458141i | ||||||||
\(165\) | 26868.2 | + | 26836.2i | 0.986895 | + | 0.985720i | ||||
\(166\) | −32875.9 | −1.19306 | ||||||||
\(167\) | 15168.7i | 0.543895i | 0.962312 | + | 0.271948i | \(0.0876677\pi\) | ||||
−0.962312 | + | 0.271948i | \(0.912332\pi\) | |||||||
\(168\) | 11454.4 | − | 11468.0i | 0.405838 | − | 0.406322i | ||||
\(169\) | −14444.3 | −0.505735 | ||||||||
\(170\) | 5462.17i | 0.189003i | ||||||||
\(171\) | 7.40621 | + | 6212.95i | 0.000253282 | + | 0.212474i | ||||
\(172\) | 19812.0 | 0.669686 | ||||||||
\(173\) | − | 18323.9i | − | 0.612245i | −0.951992 | − | 0.306122i | \(-0.900968\pi\) | ||
0.951992 | − | 0.306122i | \(-0.0990317\pi\) | |||||||
\(174\) | 3138.83 | + | 3135.09i | 0.103674 | + | 0.103550i | ||||
\(175\) | −28415.1 | −0.927839 | ||||||||
\(176\) | 3982.46i | 0.128566i | ||||||||
\(177\) | 2882.35 | − | 2885.79i | 0.0920026 | − | 0.0921123i | ||||
\(178\) | −10966.4 | −0.346118 | ||||||||
\(179\) | 30093.5i | 0.939218i | 0.882875 | + | 0.469609i | \(0.155605\pi\) | ||||
−0.882875 | + | 0.469609i | \(0.844395\pi\) | |||||||
\(180\) | −29092.4 | + | 34.6798i | −0.897912 | + | 0.00107037i | ||||
\(181\) | 28153.2 | 0.859351 | 0.429675 | − | 0.902983i | \(-0.358628\pi\) | ||||
0.429675 | + | 0.902983i | \(0.358628\pi\) | |||||||
\(182\) | − | 8637.25i | − | 0.260755i | ||||||
\(183\) | 19311.1 | + | 19288.1i | 0.576639 | + | 0.575952i | ||||
\(184\) | 61590.7 | 1.81919 | ||||||||
\(185\) | − | 1707.25i | − | 0.0498830i | ||||||
\(186\) | −12921.0 | + | 12936.4i | −0.373482 | + | 0.373927i | ||||
\(187\) | 5116.36 | 0.146311 | ||||||||
\(188\) | − | 37184.9i | − | 1.05208i | ||||||
\(189\) | −13915.2 | + | 13965.1i | −0.389554 | + | 0.390949i | ||||
\(190\) | 8440.49 | 0.233809 | ||||||||
\(191\) | 37672.9i | 1.03267i | 0.856386 | + | 0.516336i | \(0.172704\pi\) | ||||
−0.856386 | + | 0.516336i | \(0.827296\pi\) | |||||||
\(192\) | −20397.8 | − | 20373.5i | −0.553326 | − | 0.552667i | ||||
\(193\) | −24338.6 | −0.653402 | −0.326701 | − | 0.945128i | \(-0.605937\pi\) | ||||
−0.326701 | + | 0.945128i | \(0.605937\pi\) | |||||||
\(194\) | 43494.5i | 1.15566i | ||||||||
\(195\) | −30934.1 | + | 30971.0i | −0.813520 | + | 0.814490i | ||||
\(196\) | −14649.5 | −0.381339 | ||||||||
\(197\) | − | 34199.6i | − | 0.881229i | −0.897696 | − | 0.440614i | \(-0.854761\pi\) | ||
0.897696 | − | 0.440614i | \(-0.145239\pi\) | |||||||
\(198\) | −26.7538 | − | 22443.3i | −0.000682426 | − | 0.572476i | ||||
\(199\) | 27858.0 | 0.703466 | 0.351733 | − | 0.936100i | \(-0.385592\pi\) | ||||
0.351733 | + | 0.936100i | \(0.385592\pi\) | |||||||
\(200\) | 69974.3i | 1.74936i | ||||||||
\(201\) | 6080.43 | + | 6073.18i | 0.150502 | + | 0.150323i | ||||
\(202\) | −7370.97 | −0.180643 | ||||||||
\(203\) | 4958.90i | 0.120335i | ||||||||
\(204\) | −2769.95 | + | 2773.25i | −0.0665596 | + | 0.0666390i | ||||
\(205\) | −57490.6 | −1.36801 | ||||||||
\(206\) | 19688.0i | 0.463946i | ||||||||
\(207\) | −74912.3 | + | 89.2999i | −1.74829 | + | 0.00208406i | ||||
\(208\) | −4590.58 | −0.106106 | ||||||||
\(209\) | − | 7906.12i | − | 0.180997i | ||||||
\(210\) | 18949.5 | + | 18926.9i | 0.429694 | + | 0.429182i | ||||
\(211\) | −88085.2 | −1.97851 | −0.989255 | − | 0.146202i | \(-0.953295\pi\) | ||||
−0.989255 | + | 0.146202i | \(0.953295\pi\) | |||||||
\(212\) | 3653.43i | 0.0812884i | ||||||||
\(213\) | 40029.9 | − | 40077.7i | 0.882319 | − | 0.883372i | ||||
\(214\) | −10109.4 | −0.220748 | ||||||||
\(215\) | 92435.5i | 1.99969i | ||||||||
\(216\) | 34390.2 | + | 34267.4i | 0.737101 | + | 0.734469i | ||||
\(217\) | −20437.6 | −0.434022 | ||||||||
\(218\) | − | 290.290i | − | 0.00610828i | ||||||
\(219\) | 37230.9 | + | 37186.5i | 0.776274 | + | 0.775349i | ||||
\(220\) | 37020.7 | 0.764891 | ||||||||
\(221\) | 5897.63i | 0.120752i | ||||||||
\(222\) | −713.041 | + | 713.892i | −0.0144680 | + | 0.0144853i | ||||
\(223\) | −5907.75 | −0.118799 | −0.0593994 | − | 0.998234i | \(-0.518919\pi\) | ||||
−0.0593994 | + | 0.998234i | \(0.518919\pi\) | |||||||
\(224\) | − | 26006.6i | − | 0.518307i | ||||||
\(225\) | −101.455 | − | 85109.3i | −0.00200406 | − | 1.68117i | ||||
\(226\) | 24732.9 | 0.484238 | ||||||||
\(227\) | 12182.5i | 0.236420i | 0.992989 | + | 0.118210i | \(0.0377156\pi\) | ||||
−0.992989 | + | 0.118210i | \(0.962284\pi\) | |||||||
\(228\) | 4285.40 | + | 4280.29i | 0.0824369 | + | 0.0823386i | ||||
\(229\) | −28702.6 | −0.547332 | −0.273666 | − | 0.961825i | \(-0.588236\pi\) | ||||
−0.273666 | + | 0.961825i | \(0.588236\pi\) | |||||||
\(230\) | 101771.i | 1.92383i | ||||||||
\(231\) | 17728.6 | − | 17749.8i | 0.332240 | − | 0.332636i | ||||
\(232\) | 12211.7 | 0.226882 | ||||||||
\(233\) | − | 50516.8i | − | 0.930516i | −0.885175 | − | 0.465258i | \(-0.845962\pi\) | ||
0.885175 | − | 0.465258i | \(-0.154038\pi\) | |||||||
\(234\) | 25870.4 | − | 30.8391i | 0.472467 | − | 0.000563210i | ||||
\(235\) | 173491. | 3.14153 | ||||||||
\(236\) | − | 3976.22i | − | 0.0713914i | ||||||
\(237\) | 3727.87 | + | 3723.43i | 0.0663688 | + | 0.0662897i | ||||
\(238\) | 3608.44 | 0.0637039 | ||||||||
\(239\) | − | 112466.i | − | 1.96890i | −0.175663 | − | 0.984450i | \(-0.556207\pi\) | ||
0.175663 | − | 0.984450i | \(-0.443793\pi\) | |||||||
\(240\) | 10059.4 | − | 10071.4i | 0.174642 | − | 0.174851i | ||||
\(241\) | −46239.5 | −0.796122 | −0.398061 | − | 0.917359i | \(-0.630317\pi\) | ||||
−0.398061 | + | 0.917359i | \(0.630317\pi\) | |||||||
\(242\) | − | 10797.4i | − | 0.184370i | ||||||
\(243\) | −41878.2 | − | 41629.3i | −0.709211 | − | 0.704996i | ||||
\(244\) | 26608.0 | 0.446923 | ||||||||
\(245\) | − | 68349.2i | − | 1.13868i | ||||||
\(246\) | 24039.9 | + | 24011.3i | 0.397249 | + | 0.396776i | ||||
\(247\) | 9113.38 | 0.149378 | ||||||||
\(248\) | 50329.3i | 0.818310i | ||||||||
\(249\) | 77784.7 | − | 77877.4i | 1.25457 | − | 1.25607i | ||||
\(250\) | −46848.1 | −0.749569 | ||||||||
\(251\) | − | 75727.7i | − | 1.20201i | −0.799246 | − | 0.601004i | \(-0.794768\pi\) | ||
0.799246 | − | 0.601004i | \(-0.205232\pi\) | |||||||
\(252\) | 22.9103 | + | 19219.1i | 0.000360770 | + | 0.302644i | ||||
\(253\) | 95327.6 | 1.48928 | ||||||||
\(254\) | − | 63145.4i | − | 0.978755i | ||||||
\(255\) | −12939.0 | − | 12923.5i | −0.198984 | − | 0.198747i | ||||
\(256\) | −69467.1 | −1.05998 | ||||||||
\(257\) | 1522.24i | 0.0230472i | 0.999934 | + | 0.0115236i | \(0.00366816\pi\) | ||||
−0.999934 | + | 0.0115236i | \(0.996332\pi\) | |||||||
\(258\) | 38606.2 | − | 38652.3i | 0.579986 | − | 0.580678i | ||||
\(259\) | −1127.85 | −0.0168132 | ||||||||
\(260\) | 42673.7i | 0.631268i | ||||||||
\(261\) | −14853.0 | + | 17.7057i | −0.218038 | + | 0.000259915i | ||||
\(262\) | −66546.6 | −0.969446 | ||||||||
\(263\) | 26666.8i | 0.385530i | 0.981245 | + | 0.192765i | \(0.0617456\pi\) | ||||
−0.981245 | + | 0.192765i | \(0.938254\pi\) | |||||||
\(264\) | −43710.2 | − | 43658.2i | −0.627156 | − | 0.626408i | ||||
\(265\) | −17045.5 | −0.242728 | ||||||||
\(266\) | − | 5575.99i | − | 0.0788059i | ||||||
\(267\) | 25946.6 | − | 25977.6i | 0.363964 | − | 0.364398i | ||||
\(268\) | 8377.99 | 0.116646 | ||||||||
\(269\) | 123702.i | 1.70952i | 0.519027 | + | 0.854758i | \(0.326294\pi\) | ||||
−0.519027 | + | 0.854758i | \(0.673706\pi\) | |||||||
\(270\) | −56622.5 | + | 56825.4i | −0.776715 | + | 0.779498i | ||||
\(271\) | −75081.3 | −1.02233 | −0.511167 | − | 0.859481i | \(-0.670787\pi\) | ||||
−0.511167 | + | 0.859481i | \(0.670787\pi\) | |||||||
\(272\) | − | 1917.84i | − | 0.0259223i | ||||||
\(273\) | 20460.2 | + | 20435.8i | 0.274526 | + | 0.274199i | ||||
\(274\) | 65412.6 | 0.871284 | ||||||||
\(275\) | 108304.i | 1.43211i | ||||||||
\(276\) | −51609.4 | + | 51670.9i | −0.677502 | + | 0.678310i | ||||
\(277\) | −135889. | −1.77103 | −0.885514 | − | 0.464612i | \(-0.846194\pi\) | ||||
−0.885514 | + | 0.464612i | \(0.846194\pi\) | |||||||
\(278\) | 37348.1i | 0.483258i | ||||||||
\(279\) | −72.9722 | − | 61215.2i | −0.000937452 | − | 0.786413i | ||||
\(280\) | 73723.4 | 0.940349 | ||||||||
\(281\) | 69801.6i | 0.884000i | 0.897015 | + | 0.442000i | \(0.145731\pi\) | ||||
−0.897015 | + | 0.442000i | \(0.854269\pi\) | |||||||
\(282\) | −72545.9 | − | 72459.5i | −0.912252 | − | 0.911165i | ||||
\(283\) | −42484.7 | −0.530469 | −0.265234 | − | 0.964184i | \(-0.585449\pi\) | ||||
−0.265234 | + | 0.964184i | \(0.585449\pi\) | |||||||
\(284\) | − | 55221.5i | − | 0.684655i | ||||||
\(285\) | −19970.3 | + | 19994.1i | −0.245864 | + | 0.246157i | ||||
\(286\) | −32920.7 | −0.402473 | ||||||||
\(287\) | 37979.7i | 0.461092i | ||||||||
\(288\) | 77895.3 | − | 92.8559i | 0.939131 | − | 0.00111950i | ||||
\(289\) | 81057.1 | 0.970500 | ||||||||
\(290\) | 20178.3i | 0.239932i | ||||||||
\(291\) | −103031. | − | 102908.i | −1.21670 | − | 1.21525i | ||||
\(292\) | 51299.0 | 0.601649 | ||||||||
\(293\) | − | 154913.i | − | 1.80448i | −0.431229 | − | 0.902242i | \(-0.641920\pi\) | ||
0.431229 | − | 0.902242i | \(-0.358080\pi\) | |||||||
\(294\) | −28546.4 | + | 28580.5i | −0.330261 | + | 0.330655i | ||||
\(295\) | 18551.6 | 0.213175 | ||||||||
\(296\) | 2777.41i | 0.0316998i | ||||||||
\(297\) | 53227.7 | + | 53037.7i | 0.603428 | + | 0.601274i | ||||
\(298\) | −82020.0 | −0.923607 | ||||||||
\(299\) | 109884.i | 1.22911i | ||||||||
\(300\) | −58704.4 | − | 58634.4i | −0.652271 | − | 0.651494i | ||||
\(301\) | 61065.0 | 0.674000 | ||||||||
\(302\) | − | 100995.i | − | 1.10736i | ||||||
\(303\) | 17439.8 | − | 17460.6i | 0.189957 | − | 0.190184i | ||||
\(304\) | −2963.56 | −0.0320676 | ||||||||
\(305\) | 124143.i | 1.33451i | ||||||||
\(306\) | 12.8839 | + | 10808.1i | 0.000137595 | + | 0.115426i | ||||
\(307\) | −85430.9 | −0.906439 | −0.453219 | − | 0.891399i | \(-0.649725\pi\) | ||||
−0.453219 | + | 0.891399i | \(0.649725\pi\) | |||||||
\(308\) | − | 24456.7i | − | 0.257809i | ||||||
\(309\) | −46637.6 | − | 46582.0i | −0.488449 | − | 0.487867i | ||||
\(310\) | −83162.8 | −0.865378 | ||||||||
\(311\) | − | 7709.13i | − | 0.0797048i | −0.999206 | − | 0.0398524i | \(-0.987311\pi\) | ||
0.999206 | − | 0.0398524i | \(-0.0126888\pi\) | |||||||
\(312\) | 50324.7 | − | 50384.8i | 0.516978 | − | 0.517595i | ||||
\(313\) | 88993.3 | 0.908382 | 0.454191 | − | 0.890904i | \(-0.349928\pi\) | ||||
0.454191 | + | 0.890904i | \(0.349928\pi\) | |||||||
\(314\) | − | 35071.0i | − | 0.355704i | ||||||
\(315\) | −89669.2 | + | 106.891i | −0.903696 | + | 0.00107726i | ||||
\(316\) | 5136.49 | 0.0514389 | ||||||||
\(317\) | − | 54169.2i | − | 0.539056i | −0.962993 | − | 0.269528i | \(-0.913132\pi\) | ||
0.962993 | − | 0.269528i | \(-0.0868677\pi\) | |||||||
\(318\) | 7127.66 | + | 7119.17i | 0.0704844 | + | 0.0704004i | ||||
\(319\) | 18900.8 | 0.185737 | ||||||||
\(320\) | − | 131129.i | − | 1.28056i | ||||||
\(321\) | 23918.8 | − | 23947.4i | 0.232129 | − | 0.232406i | ||||
\(322\) | 67232.2 | 0.648433 | ||||||||
\(323\) | 3807.36i | 0.0364938i | ||||||||
\(324\) | −57565.3 | + | 137.243i | −0.548366 | + | 0.00130737i | ||||
\(325\) | −124841. | −1.18193 | ||||||||
\(326\) | − | 119434.i | − | 1.12381i | ||||||
\(327\) | 687.647 | + | 686.828i | 0.00643087 | + | 0.00642321i | ||||
\(328\) | 93527.9 | 0.869348 | ||||||||
\(329\) | − | 114612.i | − | 1.05886i | ||||||
\(330\) | 72139.6 | − | 72225.6i | 0.662439 | − | 0.663229i | ||||
\(331\) | 127337. | 1.16225 | 0.581125 | − | 0.813814i | \(-0.302613\pi\) | ||||
0.581125 | + | 0.813814i | \(0.302613\pi\) | |||||||
\(332\) | − | 107304.i | − | 0.973512i | ||||||
\(333\) | −4.02695 | − | 3378.15i | −3.63152e−5 | − | 0.0304642i | ||||
\(334\) | 40775.6 | 0.365517 | ||||||||
\(335\) | 39088.6i | 0.348306i | ||||||||
\(336\) | −6653.40 | − | 6645.47i | −0.0589339 | − | 0.0588637i | ||||
\(337\) | 35955.2 | 0.316594 | 0.158297 | − | 0.987392i | \(-0.449400\pi\) | ||||
0.158297 | + | 0.987392i | \(0.449400\pi\) | |||||||
\(338\) | 38828.4i | 0.339872i | ||||||||
\(339\) | −58518.3 | + | 58588.1i | −0.509204 | + | 0.509812i | ||||
\(340\) | −17828.1 | −0.154222 | ||||||||
\(341\) | 77897.7i | 0.669909i | ||||||||
\(342\) | 16701.3 | − | 19.9089i | 0.142790 | − | 0.000170214i | ||||
\(343\) | −110084. | −0.935695 | ||||||||
\(344\) | − | 150377.i | − | 1.27077i | ||||||
\(345\) | −241078. | − | 240790.i | −2.02544 | − | 2.02302i | ||||
\(346\) | −49257.2 | −0.411450 | ||||||||
\(347\) | 192952.i | 1.60247i | 0.598351 | + | 0.801234i | \(0.295823\pi\) | ||||
−0.598351 | + | 0.801234i | \(0.704177\pi\) | |||||||
\(348\) | −10232.7 | + | 10244.9i | −0.0844950 | + | 0.0845958i | ||||
\(349\) | −8373.26 | −0.0687454 | −0.0343727 | − | 0.999409i | \(-0.510943\pi\) | ||||
−0.0343727 | + | 0.999409i | \(0.510943\pi\) | |||||||
\(350\) | 76383.8i | 0.623541i | ||||||||
\(351\) | −61136.6 | + | 61355.6i | −0.496234 | + | 0.498012i | ||||
\(352\) | −99123.5 | −0.800003 | ||||||||
\(353\) | 90515.6i | 0.726397i | 0.931712 | + | 0.363198i | \(0.118315\pi\) | ||||
−0.931712 | + | 0.363198i | \(0.881685\pi\) | |||||||
\(354\) | −7757.41 | − | 7748.17i | −0.0619028 | − | 0.0618290i | ||||
\(355\) | 257643. | 2.04438 | ||||||||
\(356\) | − | 35793.5i | − | 0.282426i | ||||||
\(357\) | −8537.60 | + | 8547.78i | −0.0669883 | + | 0.0670683i | ||||
\(358\) | 80895.6 | 0.631188 | ||||||||
\(359\) | − | 33358.3i | − | 0.258830i | −0.991591 | − | 0.129415i | \(-0.958690\pi\) | ||
0.991591 | − | 0.129415i | \(-0.0413100\pi\) | |||||||
\(360\) | 263.228 | + | 220818.i | 0.00203108 | + | 1.70384i | ||||
\(361\) | −124438. | −0.954855 | ||||||||
\(362\) | − | 75679.8i | − | 0.577514i | ||||||
\(363\) | 25577.3 | + | 25546.8i | 0.194107 | + | 0.193876i | ||||
\(364\) | 28191.3 | 0.212771 | ||||||||
\(365\) | 239342.i | 1.79653i | ||||||||
\(366\) | 51849.1 | − | 51910.9i | 0.387060 | − | 0.387522i | ||||
\(367\) | −173393. | −1.28736 | −0.643678 | − | 0.765297i | \(-0.722592\pi\) | ||||
−0.643678 | + | 0.765297i | \(0.722592\pi\) | |||||||
\(368\) | − | 35733.0i | − | 0.263860i | ||||||
\(369\) | −113757. | + | 135.606i | −0.835462 | + | 0.000995921i | ||||
\(370\) | −4589.32 | −0.0335232 | ||||||||
\(371\) | 11260.7i | 0.0818120i | ||||||||
\(372\) | −42223.3 | − | 42173.0i | −0.305117 | − | 0.304754i | ||||
\(373\) | 212006. | 1.52381 | 0.761906 | − | 0.647688i | \(-0.224264\pi\) | ||||
0.761906 | + | 0.647688i | \(0.224264\pi\) | |||||||
\(374\) | − | 13753.5i | − | 0.0983265i | ||||||
\(375\) | 110843. | − | 110975.i | 0.788216 | − | 0.789156i | ||||
\(376\) | −282241. | −1.99639 | ||||||||
\(377\) | 21786.9i | 0.153290i | ||||||||
\(378\) | 37540.2 | + | 37406.2i | 0.262732 | + | 0.261794i | ||||
\(379\) | 127813. | 0.889807 | 0.444904 | − | 0.895578i | \(-0.353238\pi\) | ||||
0.444904 | + | 0.895578i | \(0.353238\pi\) | |||||||
\(380\) | 27549.1i | 0.190783i | ||||||||
\(381\) | 149581. | + | 149402.i | 1.03045 | + | 1.02922i | ||||
\(382\) | 101270. | 0.693993 | ||||||||
\(383\) | 60318.9i | 0.411202i | 0.978636 | + | 0.205601i | \(0.0659150\pi\) | ||||
−0.978636 | + | 0.205601i | \(0.934085\pi\) | |||||||
\(384\) | 43095.3 | − | 43146.7i | 0.292259 | − | 0.292607i | ||||
\(385\) | 114106. | 0.769817 | ||||||||
\(386\) | 65425.6i | 0.439110i | ||||||||
\(387\) | 218.031 | + | 182903.i | 0.00145578 | + | 1.22123i | ||||
\(388\) | −141963. | −0.942997 | ||||||||
\(389\) | 215748.i | 1.42576i | 0.701284 | + | 0.712882i | \(0.252611\pi\) | ||||
−0.701284 | + | 0.712882i | \(0.747389\pi\) | |||||||
\(390\) | 83254.5 | + | 83155.3i | 0.547367 | + | 0.546714i | ||||
\(391\) | −45907.0 | −0.300279 | ||||||||
\(392\) | 111193.i | 0.723611i | ||||||||
\(393\) | 157450. | − | 157638.i | 1.01943 | − | 1.02065i | ||||
\(394\) | −91933.4 | −0.592217 | ||||||||
\(395\) | 23965.0i | 0.153597i | ||||||||
\(396\) | 73253.3 | − | 87.3223i | 0.467129 | − | 0.000556846i | ||||
\(397\) | −269182. | −1.70791 | −0.853954 | − | 0.520349i | \(-0.825802\pi\) | ||||
−0.853954 | + | 0.520349i | \(0.825802\pi\) | |||||||
\(398\) | − | 74886.2i | − | 0.472755i | ||||||
\(399\) | 13208.6 | + | 13192.8i | 0.0829678 | + | 0.0828690i | ||||
\(400\) | 40596.9 | 0.253731 | ||||||||
\(401\) | 79912.1i | 0.496963i | 0.968637 | + | 0.248481i | \(0.0799315\pi\) | ||||
−0.968637 | + | 0.248481i | \(0.920069\pi\) | |||||||
\(402\) | 16325.6 | − | 16345.1i | 0.101022 | − | 0.101143i | ||||
\(403\) | −89792.7 | −0.552880 | ||||||||
\(404\) | − | 24058.3i | − | 0.147401i | ||||||
\(405\) | −640.324 | − | 268578.i | −0.00390382 | − | 1.63742i | ||||
\(406\) | 13330.2 | 0.0808697 | ||||||||
\(407\) | 4298.77i | 0.0259511i | ||||||||
\(408\) | 21049.6 | + | 21024.5i | 0.126451 | + | 0.126301i | ||||
\(409\) | 56708.3 | 0.339000 | 0.169500 | − | 0.985530i | \(-0.445785\pi\) | ||||
0.169500 | + | 0.985530i | \(0.445785\pi\) | |||||||
\(410\) | 154543.i | 0.919352i | ||||||||
\(411\) | −154767. | + | 154951.i | −0.916207 | + | 0.917300i | ||||
\(412\) | −64260.1 | −0.378571 | ||||||||
\(413\) | − | 12255.6i | − | 0.0718512i | ||||||
\(414\) | 240.051 | + | 201375.i | 0.00140056 | + | 1.17491i | ||||
\(415\) | 500643. | 2.90691 | ||||||||
\(416\) | − | 114260.i | − | 0.660247i | ||||||
\(417\) | −88471.2 | − | 88365.8i | −0.508780 | − | 0.508174i | ||||
\(418\) | −21252.8 | −0.121636 | ||||||||
\(419\) | 265845.i | 1.51426i | 0.653265 | + | 0.757129i | \(0.273399\pi\) | ||||
−0.653265 | + | 0.757129i | \(0.726601\pi\) | |||||||
\(420\) | −61775.9 | + | 61849.6i | −0.350204 | + | 0.350621i | ||||
\(421\) | −154820. | −0.873498 | −0.436749 | − | 0.899583i | \(-0.643870\pi\) | ||||
−0.436749 | + | 0.899583i | \(0.643870\pi\) | |||||||
\(422\) | 236786.i | 1.32963i | ||||||||
\(423\) | 343288. | − | 409.220i | 1.91857 | − | 0.00228705i | ||||
\(424\) | 27730.3 | 0.154249 | ||||||||
\(425\) | − | 52155.8i | − | 0.288752i | ||||||
\(426\) | −107735. | − | 107606.i | −0.593657 | − | 0.592950i | ||||
\(427\) | 82011.8 | 0.449801 | ||||||||
\(428\) | − | 32996.2i | − | 0.180126i | ||||||
\(429\) | 77890.7 | − | 77983.6i | 0.423225 | − | 0.423729i | ||||
\(430\) | 248480. | 1.34386 | ||||||||
\(431\) | − | 73453.6i | − | 0.395420i | −0.980261 | − | 0.197710i | \(-0.936650\pi\) | ||
0.980261 | − | 0.197710i | \(-0.0633504\pi\) | |||||||
\(432\) | 19880.9 | − | 19952.1i | 0.106529 | − | 0.106911i | ||||
\(433\) | 198727. | 1.05994 | 0.529971 | − | 0.848016i | \(-0.322203\pi\) | ||||
0.529971 | + | 0.848016i | \(0.322203\pi\) | |||||||
\(434\) | 54939.3i | 0.291678i | ||||||||
\(435\) | −47798.9 | − | 47741.9i | −0.252603 | − | 0.252303i | ||||
\(436\) | 947.482 | 0.00498423 | ||||||||
\(437\) | 70938.4i | 0.371465i | ||||||||
\(438\) | 99962.7 | − | 100082.i | 0.521063 | − | 0.521684i | ||||
\(439\) | 106016. | 0.550100 | 0.275050 | − | 0.961430i | \(-0.411306\pi\) | ||||
0.275050 | + | 0.961430i | \(0.411306\pi\) | |||||||
\(440\) | − | 280995.i | − | 1.45142i | ||||||
\(441\) | −161.218 | − | 135243.i | −0.000828966 | − | 0.695406i | ||||
\(442\) | 15853.7 | 0.0811494 | ||||||||
\(443\) | − | 214472.i | − | 1.09286i | −0.837505 | − | 0.546429i | \(-0.815987\pi\) | ||
0.837505 | − | 0.546429i | \(-0.184013\pi\) | |||||||
\(444\) | −2330.09 | − | 2327.31i | −0.0118197 | − | 0.0118056i | ||||
\(445\) | 166999. | 0.843324 | ||||||||
\(446\) | 15880.9i | 0.0798371i | ||||||||
\(447\) | 194060. | − | 194291.i | 0.971227 | − | 0.972385i | ||||
\(448\) | −86627.1 | −0.431616 | ||||||||
\(449\) | 81179.4i | 0.402673i | 0.979522 | + | 0.201337i | \(0.0645285\pi\) | ||||
−0.979522 | + | 0.201337i | \(0.935471\pi\) | |||||||
\(450\) | −228786. | + | 272.727i | −1.12981 | + | 0.00134680i | ||||
\(451\) | 144759. | 0.711692 | ||||||||
\(452\) | 80726.3i | 0.395128i | ||||||||
\(453\) | 239241. | + | 238956.i | 1.16584 | + | 1.16445i | ||||
\(454\) | 32748.3 | 0.158883 | ||||||||
\(455\) | 131530.i | 0.635335i | ||||||||
\(456\) | 32488.4 | − | 32527.1i | 0.156242 | − | 0.156429i | ||||
\(457\) | −188136. | −0.900822 | −0.450411 | − | 0.892821i | \(-0.648723\pi\) | ||||
−0.450411 | + | 0.892821i | \(0.648723\pi\) | |||||||
\(458\) | 77156.8i | 0.367827i | ||||||||
\(459\) | −25632.9 | − | 25541.4i | −0.121667 | − | 0.121233i | ||||
\(460\) | −332172. | −1.56981 | ||||||||
\(461\) | 312198.i | 1.46902i | 0.678596 | + | 0.734512i | \(0.262589\pi\) | ||||
−0.678596 | + | 0.734512i | \(0.737411\pi\) | |||||||
\(462\) | −47714.0 | − | 47657.1i | −0.223543 | − | 0.223277i | ||||
\(463\) | −294194. | −1.37237 | −0.686187 | − | 0.727425i | \(-0.740717\pi\) | ||||
−0.686187 | + | 0.727425i | \(0.740717\pi\) | |||||||
\(464\) | − | 7084.84i | − | 0.0329075i | ||||||
\(465\) | 196764. | − | 196999.i | 0.909996 | − | 0.911081i | ||||
\(466\) | −135796. | −0.625340 | ||||||||
\(467\) | 205884.i | 0.944039i | 0.881588 | + | 0.472019i | \(0.156475\pi\) | ||||
−0.881588 | + | 0.472019i | \(0.843525\pi\) | |||||||
\(468\) | 100.656 | + | 84439.0i | 0.000459568 | + | 0.385524i | ||||
\(469\) | 25822.9 | 0.117397 | ||||||||
\(470\) | − | 466368.i | − | 2.11122i | ||||||
\(471\) | 83077.2 | + | 82978.3i | 0.374490 | + | 0.374044i | ||||
\(472\) | −30180.4 | −0.135469 | ||||||||
\(473\) | − | 232748.i | − | 1.04031i | ||||||
\(474\) | 10009.1 | − | 10021.0i | 0.0445491 | − | 0.0446022i | ||||
\(475\) | −80594.5 | −0.357205 | ||||||||
\(476\) | 11777.7i | 0.0519811i | ||||||||
\(477\) | −33728.2 | + | 40.2060i | −0.148237 | + | 0.000176707i | ||||
\(478\) | −302324. | −1.32317 | ||||||||
\(479\) | 162807.i | 0.709583i | 0.934945 | + | 0.354791i | \(0.115448\pi\) | ||||
−0.934945 | + | 0.354791i | \(0.884552\pi\) | |||||||
\(480\) | 250677. | + | 250379.i | 1.08801 | + | 1.08671i | ||||
\(481\) | −4955.19 | −0.0214176 | ||||||||
\(482\) | 124299.i | 0.535022i | ||||||||
\(483\) | −159072. | + | 159262.i | −0.681866 | + | 0.682679i | ||||
\(484\) | 35242.0 | 0.150442 | ||||||||
\(485\) | − | 662345.i | − | 2.81579i | ||||||
\(486\) | −111906. | + | 112575.i | −0.473783 | + | 0.476615i | ||||
\(487\) | 247232. | 1.04243 | 0.521216 | − | 0.853425i | \(-0.325479\pi\) | ||||
0.521216 | + | 0.853425i | \(0.325479\pi\) | |||||||
\(488\) | − | 201961.i | − | 0.848061i | ||||||
\(489\) | 282919. | + | 282582.i | 1.18316 | + | 1.18175i | ||||
\(490\) | −183732. | −0.765233 | ||||||||
\(491\) | 287137.i | 1.19104i | 0.803340 | + | 0.595520i | \(0.203054\pi\) | ||||
−0.803340 | + | 0.595520i | \(0.796946\pi\) | |||||||
\(492\) | −78370.9 | + | 78464.4i | −0.323761 | + | 0.324147i | ||||
\(493\) | −9102.07 | −0.0374495 | ||||||||
\(494\) | − | 24498.1i | − | 0.100387i | ||||||
\(495\) | 407.414 | + | 341773.i | 0.00166274 | + | 1.39485i | ||||
\(496\) | 29199.5 | 0.118689 | ||||||||
\(497\) | − | 170205.i | − | 0.689065i | ||||||
\(498\) | −209346. | − | 209096.i | −0.844123 | − | 0.843117i | ||||
\(499\) | 60111.9 | 0.241412 | 0.120706 | − | 0.992688i | \(-0.461484\pi\) | ||||
0.120706 | + | 0.992688i | \(0.461484\pi\) | |||||||
\(500\) | − | 152908.i | − | 0.611633i | ||||||
\(501\) | −96475.4 | + | 96590.5i | −0.384363 | + | 0.384821i | ||||
\(502\) | −203567. | −0.807792 | ||||||||
\(503\) | 113543.i | 0.448771i | 0.974500 | + | 0.224386i | \(0.0720375\pi\) | ||||
−0.974500 | + | 0.224386i | \(0.927962\pi\) | |||||||
\(504\) | 145877. | − | 173.894i | 0.574284 | − | 0.000684581i | ||||
\(505\) | 112247. | 0.440141 | ||||||||
\(506\) | − | 256254.i | − | 1.00085i | ||||||
\(507\) | −91977.8 | − | 91868.2i | −0.357822 | − | 0.357396i | ||||
\(508\) | 206101. | 0.798644 | ||||||||
\(509\) | − | 134798.i | − | 0.520293i | −0.965569 | − | 0.260146i | \(-0.916229\pi\) | ||
0.965569 | − | 0.260146i | \(-0.0837708\pi\) | |||||||
\(510\) | −34740.3 | + | 34781.8i | −0.133565 | + | 0.133725i | ||||
\(511\) | 158115. | 0.605525 | ||||||||
\(512\) | 78324.6i | 0.298785i | ||||||||
\(513\) | −39468.2 | + | 39609.6i | −0.149973 | + | 0.150510i | ||||
\(514\) | 4092.01 | 0.0154885 | ||||||||
\(515\) | − | 299814.i | − | 1.13041i | ||||||
\(516\) | 126158. | + | 126008.i | 0.473822 | + | 0.473257i | ||||
\(517\) | −436842. | −1.63434 | ||||||||
\(518\) | 3031.81i | 0.0112991i | ||||||||
\(519\) | 116543. | − | 116682.i | 0.432664 | − | 0.433180i | ||||
\(520\) | 323903. | 1.19787 | ||||||||
\(521\) | − | 371391.i | − | 1.36822i | −0.729379 | − | 0.684110i | \(-0.760191\pi\) | ||
0.729379 | − | 0.684110i | \(-0.239809\pi\) | |||||||
\(522\) | 47.5954 | + | 39927.0i | 0.000174672 | + | 0.146530i | ||||
\(523\) | −357941. | −1.30860 | −0.654302 | − | 0.756234i | \(-0.727037\pi\) | ||||
−0.654302 | + | 0.756234i | \(0.727037\pi\) | |||||||
\(524\) | − | 217203.i | − | 0.791048i | ||||||
\(525\) | −180940. | − | 180725.i | −0.656472 | − | 0.655690i | ||||
\(526\) | 71684.1 | 0.259090 | ||||||||
\(527\) | − | 37513.3i | − | 0.135072i | ||||||
\(528\) | −25329.1 | + | 25359.3i | −0.0908557 | + | 0.0909640i | ||||
\(529\) | −575495. | −2.05651 | ||||||||
\(530\) | 45820.9i | 0.163122i | ||||||||
\(531\) | 36708.2 | − | 43.7583i | 0.130189 | − | 0.000155193i | ||||
\(532\) | 18199.6 | 0.0643040 | ||||||||
\(533\) | 166863.i | 0.587363i | ||||||||
\(534\) | −69831.4 | − | 69748.2i | −0.244888 | − | 0.244597i | ||||
\(535\) | 153948. | 0.537857 | ||||||||
\(536\) | − | 63590.8i | − | 0.221343i | ||||||
\(537\) | −191400. | + | 191628.i | −0.663731 | + | 0.664523i | ||||
\(538\) | 332529. | 1.14886 | ||||||||
\(539\) | 172100.i | 0.592385i | ||||||||
\(540\) | −185474. | − | 184811.i | −0.636055 | − | 0.633784i | ||||
\(541\) | 10655.7 | 0.0364071 | 0.0182036 | − | 0.999834i | \(-0.494205\pi\) | ||||
0.0182036 | + | 0.999834i | \(0.494205\pi\) | |||||||
\(542\) | 201829.i | 0.687046i | ||||||||
\(543\) | 179273. | + | 179059.i | 0.608015 | + | 0.607290i | ||||
\(544\) | 47735.0 | 0.161302 | ||||||||
\(545\) | 4420.60i | 0.0148829i | ||||||||
\(546\) | 54934.3 | − | 54999.9i | 0.184272 | − | 0.184491i | ||||
\(547\) | −55656.0 | −0.186011 | −0.0930053 | − | 0.995666i | \(-0.529647\pi\) | ||||
−0.0930053 | + | 0.995666i | \(0.529647\pi\) | |||||||
\(548\) | 213501.i | 0.710951i | ||||||||
\(549\) | 292.821 | + | 245643.i | 0.000971534 | + | 0.815004i | ||||
\(550\) | 291135. | 0.962431 | ||||||||
\(551\) | 14065.1i | 0.0463275i | ||||||||
\(552\) | 392194. | + | 391727.i | 1.28713 | + | 1.28560i | ||||
\(553\) | 15831.8 | 0.0517703 | ||||||||
\(554\) | 365290.i | 1.19019i | ||||||||
\(555\) | 10858.4 | − | 10871.3i | 0.0352516 | − | 0.0352936i | ||||
\(556\) | −121901. | −0.394328 | ||||||||
\(557\) | − | 83749.7i | − | 0.269943i | −0.990849 | − | 0.134972i | \(-0.956906\pi\) | ||
0.990849 | − | 0.134972i | \(-0.0430944\pi\) | |||||||
\(558\) | −164555. | + | 196.160i | −0.528498 | + | 0.000630001i | ||||
\(559\) | 268289. | 0.858577 | ||||||||
\(560\) | − | 42772.0i | − | 0.136390i | ||||||
\(561\) | 32579.7 | + | 32540.9i | 0.103519 | + | 0.103396i | ||||
\(562\) | 187637. | 0.594080 | ||||||||
\(563\) | 97847.0i | 0.308696i | 0.988017 | + | 0.154348i | \(0.0493277\pi\) | ||||
−0.988017 | + | 0.154348i | \(0.950672\pi\) | |||||||
\(564\) | 236502. | − | 236784.i | 0.743492 | − | 0.744379i | ||||
\(565\) | −376639. | −1.17985 | ||||||||
\(566\) | 114205.i | 0.356494i | ||||||||
\(567\) | −177429. | + | 423.013i | −0.551898 | + | 0.00131579i | ||||
\(568\) | −419144. | −1.29917 | ||||||||
\(569\) | − | 241508.i | − | 0.745944i | −0.927843 | − | 0.372972i | \(-0.878339\pi\) | ||
0.927843 | − | 0.372972i | \(-0.121661\pi\) | |||||||
\(570\) | 53747.0 | + | 53682.9i | 0.165426 | + | 0.165229i | ||||
\(571\) | 624773. | 1.91624 | 0.958120 | − | 0.286366i | \(-0.0924473\pi\) | ||||
0.958120 | + | 0.286366i | \(0.0924473\pi\) | |||||||
\(572\) | − | 107451.i | − | 0.328410i | ||||||
\(573\) | −239606. | + | 239892.i | −0.729774 | + | 0.730644i | ||||
\(574\) | 102095. | 0.309870 | ||||||||
\(575\) | − | 971763.i | − | 2.93917i | ||||||
\(576\) | −309.300 | − | 259467.i | −0.000932256 | − | 0.782055i | ||||
\(577\) | −217020. | −0.651852 | −0.325926 | − | 0.945395i | \(-0.605676\pi\) | ||||
−0.325926 | + | 0.945395i | \(0.605676\pi\) | |||||||
\(578\) | − | 217893.i | − | 0.652211i | ||||||
\(579\) | −154982. | − | 154797.i | −0.462300 | − | 0.461750i | ||||
\(580\) | −65860.3 | −0.195780 | ||||||||
\(581\) | − | 330736.i | − | 0.979782i | ||||||
\(582\) | −276632. | + | 276962.i | −0.816689 | + | 0.817663i | ||||
\(583\) | 42919.9 | 0.126276 | ||||||||
\(584\) | − | 389371.i | − | 1.14166i | ||||||
\(585\) | −393961. | + | 469.626i | −1.15118 | + | 0.00137227i | ||||
\(586\) | −416429. | −1.21268 | ||||||||
\(587\) | 593750.i | 1.72317i | 0.507615 | + | 0.861584i | \(0.330527\pi\) | ||||
−0.507615 | + | 0.861584i | \(0.669473\pi\) | |||||||
\(588\) | −93284.4 | − | 93173.3i | −0.269808 | − | 0.269486i | ||||
\(589\) | −57967.9 | −0.167092 | ||||||||
\(590\) | − | 49869.2i | − | 0.143261i | ||||||
\(591\) | 217515. | − | 217775.i | 0.622751 | − | 0.623494i | ||||
\(592\) | 1611.37 | 0.00459781 | ||||||||
\(593\) | − | 352380.i | − | 1.00208i | −0.865425 | − | 0.501039i | \(-0.832951\pi\) | ||
0.865425 | − | 0.501039i | \(-0.167049\pi\) | |||||||
\(594\) | 142573. | − | 143084.i | 0.404077 | − | 0.405525i | ||||
\(595\) | −54950.2 | −0.155216 | ||||||||
\(596\) | − | 267707.i | − | 0.753644i | ||||||
\(597\) | 177393. | + | 177181.i | 0.497722 | + | 0.497129i | ||||
\(598\) | 295384. | 0.826009 | ||||||||
\(599\) | 457318.i | 1.27457i | 0.770627 | + | 0.637286i | \(0.219943\pi\) | ||||
−0.770627 | + | 0.637286i | \(0.780057\pi\) | |||||||
\(600\) | −445048. | + | 445579.i | −1.23625 | + | 1.23772i | ||||
\(601\) | 169949. | 0.470511 | 0.235255 | − | 0.971934i | \(-0.424407\pi\) | ||||
0.235255 | + | 0.971934i | \(0.424407\pi\) | |||||||
\(602\) | − | 164152.i | − | 0.452952i | ||||||
\(603\) | 92.2000 | + | 77345.1i | 0.000253569 | + | 0.212715i | ||||
\(604\) | 329641. | 0.903581 | ||||||||
\(605\) | 164426.i | 0.449221i | ||||||||
\(606\) | −46936.5 | − | 46880.6i | −0.127810 | − | 0.127658i | ||||
\(607\) | −77491.0 | −0.210317 | −0.105158 | − | 0.994455i | \(-0.533535\pi\) | ||||
−0.105158 | + | 0.994455i | \(0.533535\pi\) | |||||||
\(608\) | − | 73763.1i | − | 0.199541i | ||||||
\(609\) | −31539.5 | + | 31577.1i | −0.0850393 | + | 0.0851407i | ||||
\(610\) | 333714. | 0.896840 | ||||||||
\(611\) | − | 503548.i | − | 1.34883i | ||||||
\(612\) | −35276.7 | + | 42.0519i | −0.0941856 | + | 0.000112275i | ||||
\(613\) | −523471. | −1.39307 | −0.696533 | − | 0.717525i | \(-0.745275\pi\) | ||||
−0.696533 | + | 0.717525i | \(0.745275\pi\) | |||||||
\(614\) | 229651.i | 0.609159i | ||||||||
\(615\) | −366086. | − | 365650.i | −0.967906 | − | 0.966752i | ||||
\(616\) | −185632. | −0.489206 | ||||||||
\(617\) | 518426.i | 1.36181i | 0.732372 | + | 0.680905i | \(0.238413\pi\) | ||||
−0.732372 | + | 0.680905i | \(0.761587\pi\) | |||||||
\(618\) | −125219. | + | 125368.i | −0.327864 | + | 0.328255i | ||||
\(619\) | 699994. | 1.82689 | 0.913447 | − | 0.406958i | \(-0.133411\pi\) | ||||
0.913447 | + | 0.406958i | \(0.133411\pi\) | |||||||
\(620\) | − | 271437.i | − | 0.706131i | ||||||
\(621\) | −477591. | − | 475886.i | −1.23843 | − | 1.23401i | ||||
\(622\) | −20723.2 | −0.0535645 | ||||||||
\(623\) | − | 110324.i | − | 0.284245i | ||||||
\(624\) | −29231.7 | − | 29196.9i | −0.0750731 | − | 0.0749837i | ||||
\(625\) | 56706.1 | 0.145168 | ||||||||
\(626\) | − | 239227.i | − | 0.610465i | ||||||
\(627\) | 50284.2 | − | 50344.2i | 0.127908 | − | 0.128060i | ||||
\(628\) | 114469. | 0.290247 | ||||||||
\(629\) | − | 2070.16i | − | 0.00523243i | ||||||
\(630\) | 287.339 | + | 241044.i | 0.000723957 | + | 0.607316i | ||||
\(631\) | 178942. | 0.449422 | 0.224711 | − | 0.974425i | \(-0.427856\pi\) | ||||
0.224711 | + | 0.974425i | \(0.427856\pi\) | |||||||
\(632\) | − | 38987.1i | − | 0.0976083i | ||||||
\(633\) | −560905. | − | 560237.i | −1.39985 | − | 1.39818i | ||||
\(634\) | −145615. | −0.362265 | ||||||||
\(635\) | 961593.i | 2.38476i | ||||||||
\(636\) | −23236.4 | + | 23264.1i | −0.0574453 | + | 0.0575138i | ||||
\(637\) | −198380. | −0.488898 | ||||||||
\(638\) | − | 50808.0i | − | 0.124822i | ||||||
\(639\) | 509801. | − | 607.714i | 1.24853 | − | 0.00148832i | ||||
\(640\) | 277373. | 0.677179 | ||||||||
\(641\) | 57985.0i | 0.141124i | 0.997507 | + | 0.0705618i | \(0.0224792\pi\) | ||||
−0.997507 | + | 0.0705618i | \(0.977521\pi\) | |||||||
\(642\) | −64374.0 | − | 64297.3i | −0.156185 | − | 0.155999i | ||||
\(643\) | −358015. | −0.865922 | −0.432961 | − | 0.901413i | \(-0.642531\pi\) | ||||
−0.432961 | + | 0.901413i | \(0.642531\pi\) | |||||||
\(644\) | 219440.i | 0.529109i | ||||||||
\(645\) | −587905. | + | 588606.i | −1.41315 | + | 1.41483i | ||||
\(646\) | 10234.7 | 0.0245251 | ||||||||
\(647\) | − | 779724.i | − | 1.86265i | −0.364183 | − | 0.931327i | \(-0.618652\pi\) | ||
0.364183 | − | 0.931327i | \(-0.381348\pi\) | |||||||
\(648\) | 1041.70 | + | 436934.i | 0.00248081 | + | 1.04056i | ||||
\(649\) | −46712.0 | −0.110902 | ||||||||
\(650\) | 335592.i | 0.794300i | ||||||||
\(651\) | −130142. | − | 129987.i | −0.307083 | − | 0.306717i | ||||
\(652\) | 389823. | 0.917007 | ||||||||
\(653\) | − | 479973.i | − | 1.12562i | −0.826588 | − | 0.562808i | \(-0.809721\pi\) | ||
0.826588 | − | 0.562808i | \(-0.190279\pi\) | |||||||
\(654\) | 1846.29 | − | 1848.49i | 0.00431663 | − | 0.00432178i | ||||
\(655\) | 1.01339e6 | 2.36207 | ||||||||
\(656\) | − | 54262.0i | − | 0.126092i | ||||||
\(657\) | 564.547 | + | 473589.i | 0.00130788 | + | 1.09716i | ||||
\(658\) | −308094. | −0.711592 | ||||||||
\(659\) | 22445.0i | 0.0516832i | 0.999666 | + | 0.0258416i | \(0.00822656\pi\) | ||||
−0.999666 | + | 0.0258416i | \(0.991773\pi\) | |||||||
\(660\) | 235739. | + | 235458.i | 0.541182 | + | 0.540537i | ||||
\(661\) | −415383. | −0.950705 | −0.475352 | − | 0.879795i | \(-0.657679\pi\) | ||||
−0.475352 | + | 0.879795i | \(0.657679\pi\) | |||||||
\(662\) | − | 342301.i | − | 0.781073i | ||||||
\(663\) | −37509.9 | + | 37554.6i | −0.0853333 | + | 0.0854351i | ||||
\(664\) | −814464. | −1.84729 | ||||||||
\(665\) | 84912.5i | 0.192012i | ||||||||
\(666\) | −9080.94 | + | 10.8250i | −0.0204730 | + | 2.44051e-5i | ||||
\(667\) | −169589. | −0.381194 | ||||||||
\(668\) | 133088.i | 0.298255i | ||||||||
\(669\) | −37619.1 | − | 37574.3i | −0.0840535 | − | 0.0839534i | ||||
\(670\) | 105076. | 0.234074 | ||||||||
\(671\) | − | 312587.i | − | 0.694265i | ||||||
\(672\) | 165406. | − | 165603.i | 0.366280 | − | 0.366717i | ||||
\(673\) | −481165. | −1.06234 | −0.531170 | − | 0.847265i | \(-0.678247\pi\) | ||||
−0.531170 | + | 0.847265i | \(0.678247\pi\) | |||||||
\(674\) | − | 96652.8i | − | 0.212762i | ||||||
\(675\) | 540663. | − | 542600.i | 1.18664 | − | 1.19089i | ||||
\(676\) | −126733. | −0.277329 | ||||||||
\(677\) | 327961.i | 0.715559i | 0.933806 | + | 0.357780i | \(0.116466\pi\) | ||||
−0.933806 | + | 0.357780i | \(0.883534\pi\) | |||||||
\(678\) | 157493. | + | 157305.i | 0.342612 | + | 0.342203i | ||||
\(679\) | −437561. | −0.949071 | ||||||||
\(680\) | 135319.i | 0.292646i | ||||||||
\(681\) | −77482.7 | + | 77575.1i | −0.167075 | + | 0.167274i | ||||
\(682\) | 209400. | 0.450203 | ||||||||
\(683\) | 692561.i | 1.48462i | 0.670055 | + | 0.742312i | \(0.266271\pi\) | ||||
−0.670055 | + | 0.742312i | \(0.733729\pi\) | |||||||
\(684\) | 64.9812 | + | 54511.7i | 0.000138891 | + | 0.116514i | ||||
\(685\) | −996119. | −2.12290 | ||||||||
\(686\) | 295920.i | 0.628820i | ||||||||
\(687\) | −182771. | − | 182553.i | −0.387253 | − | 0.386791i | ||||
\(688\) | −87244.3 | −0.184315 | ||||||||
\(689\) | 49473.8i | 0.104217i | ||||||||
\(690\) | −647279. | + | 648051.i | −1.35954 | + | 1.36117i | ||||
\(691\) | −40721.0 | −0.0852830 | −0.0426415 | − | 0.999090i | \(-0.513577\pi\) | ||||
−0.0426415 | + | 0.999090i | \(0.513577\pi\) | |||||||
\(692\) | − | 160772.i | − | 0.335735i | ||||||
\(693\) | 225783. | − | 269.147i | 0.470138 | − | 0.000560432i | ||||
\(694\) | 518681. | 1.07692 | ||||||||
\(695\) | − | 568746.i | − | 1.17747i | ||||||
\(696\) | 77761.0 | + | 77668.4i | 0.160525 | + | 0.160334i | ||||
\(697\) | −69711.7 | −0.143496 | ||||||||
\(698\) | 22508.5i | 0.0461994i | ||||||||
\(699\) | 321295. | − | 321678.i | 0.657582 | − | 0.658366i | ||||
\(700\) | −249310. | −0.508797 | ||||||||
\(701\) | − | 149272.i | − | 0.303768i | −0.988398 | − | 0.151884i | \(-0.951466\pi\) | ||
0.988398 | − | 0.151884i | \(-0.0485341\pi\) | |||||||
\(702\) | 164933. | + | 164344.i | 0.334682 | + | 0.333487i | ||||
\(703\) | −3198.94 | −0.00647286 | ||||||||
\(704\) | 330178.i | 0.666197i | ||||||||
\(705\) | 1.10475e6 | + | 1.10343e6i | 2.22272 | + | 2.22007i | ||||
\(706\) | 243319. | 0.488165 | ||||||||
\(707\) | − | 74153.0i | − | 0.148351i | ||||||
\(708\) | 25289.4 | − | 25319.6i | 0.0504513 | − | 0.0505114i | ||||
\(709\) | 480678. | 0.956230 | 0.478115 | − | 0.878297i | \(-0.341320\pi\) | ||||
0.478115 | + | 0.878297i | \(0.341320\pi\) | |||||||
\(710\) | − | 692582.i | − | 1.37390i | ||||||
\(711\) | 56.5271 | + | 47419.7i | 0.000111820 | + | 0.0938036i | ||||
\(712\) | −271681. | −0.535918 | ||||||||
\(713\) | − | 698945.i | − | 1.37488i | ||||||
\(714\) | 22977.7 | + | 22950.3i | 0.0450723 | + | 0.0450186i | ||||
\(715\) | 501325. | 0.980634 | ||||||||
\(716\) | 264037.i | 0.515037i | ||||||||
\(717\) | 715300. | − | 716153.i | 1.39139 | − | 1.39305i | ||||
\(718\) | −89671.9 | −0.173943 | ||||||||
\(719\) | − | 185672.i | − | 0.359161i | −0.983743 | − | 0.179581i | \(-0.942526\pi\) | ||
0.983743 | − | 0.179581i | \(-0.0574741\pi\) | |||||||
\(720\) | 128111. | − | 152.717i | 0.247129 | − | 0.000294592i | ||||
\(721\) | −198064. | −0.381009 | ||||||||
\(722\) | 334506.i | 0.641697i | ||||||||
\(723\) | −294442. | − | 294091.i | −0.563278 | − | 0.562607i | ||||
\(724\) | 247013. | 0.471240 | ||||||||
\(725\) | − | 192673.i | − | 0.366560i | ||||||
\(726\) | 68673.5 | − | 68755.4i | 0.130291 | − | 0.130447i | ||||
\(727\) | −624321. | −1.18124 | −0.590621 | − | 0.806949i | \(-0.701117\pi\) | ||||
−0.590621 | + | 0.806949i | \(0.701117\pi\) | |||||||
\(728\) | − | 213978.i | − | 0.403745i | ||||||
\(729\) | −1900.52 | − | 531438.i | −0.00357617 | − | 0.999994i | ||||
\(730\) | 643387. | 1.20733 | ||||||||
\(731\) | 112085.i | 0.209755i | ||||||||
\(732\) | 169433. | + | 169231.i | 0.316210 | + | 0.315834i | ||||
\(733\) | −625420. | −1.16403 | −0.582014 | − | 0.813178i | \(-0.697735\pi\) | ||||
−0.582014 | + | 0.813178i | \(0.697735\pi\) | |||||||
\(734\) | 466104.i | 0.865149i | ||||||||
\(735\) | 434712. | − | 435231.i | 0.804687 | − | 0.805647i | ||||
\(736\) | 889395. | 1.64187 | ||||||||
\(737\) | − | 98423.4i | − | 0.181202i | ||||||
\(738\) | 364.527 | + | 305796.i | 0.000669294 | + | 0.561460i | ||||
\(739\) | 203495. | 0.372619 | 0.186310 | − | 0.982491i | \(-0.440347\pi\) | ||||
0.186310 | + | 0.982491i | \(0.440347\pi\) | |||||||
\(740\) | − | 14979.2i | − | 0.0273542i | ||||||
\(741\) | 58031.8 | + | 57962.6i | 0.105689 | + | 0.105563i | ||||
\(742\) | 30270.3 | 0.0549806 | ||||||||
\(743\) | 406447.i | 0.736251i | 0.929776 | + | 0.368125i | \(0.120000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(744\) | −320103. | + | 320485.i | −0.578287 | + | 0.578977i | ||||
\(745\) | 1.24902e6 | 2.25039 | ||||||||
\(746\) | − | 569904.i | − | 1.02406i | ||||||
\(747\) | 990627. | − | 1180.89i | 1.77529 | − | 0.00211625i | ||||
\(748\) | 44890.4 | 0.0802324 | ||||||||
\(749\) | − | 101702.i | − | 0.181286i | ||||||
\(750\) | −298317. | − | 297962.i | −0.530341 | − | 0.529709i | ||||
\(751\) | 305223. | 0.541175 | 0.270587 | − | 0.962695i | \(-0.412782\pi\) | ||||
0.270587 | + | 0.962695i | \(0.412782\pi\) | |||||||
\(752\) | 163748.i | 0.289561i | ||||||||
\(753\) | 481641. | − | 482215.i | 0.849441 | − | 0.850454i | ||||
\(754\) | 58566.4 | 0.103016 | ||||||||
\(755\) | 1.53798e6i | 2.69810i | ||||||||
\(756\) | −122091. | + | 122528.i | −0.213619 | + | 0.214384i | ||||
\(757\) | 316129. | 0.551662 | 0.275831 | − | 0.961206i | \(-0.411047\pi\) | ||||
0.275831 | + | 0.961206i | \(0.411047\pi\) | |||||||
\(758\) | − | 343579.i | − | 0.597982i | ||||||
\(759\) | 607023. | + | 606299.i | 1.05371 | + | 1.05246i | ||||
\(760\) | 209104. | 0.362022 | ||||||||
\(761\) | 539926.i | 0.932319i | 0.884701 | + | 0.466160i | \(0.154363\pi\) | ||||
−0.884701 | + | 0.466160i | \(0.845637\pi\) | |||||||
\(762\) | 401615. | − | 402094.i | 0.691672 | − | 0.692497i | ||||
\(763\) | 2920.35 | 0.00501633 | ||||||||
\(764\) | 330538.i | 0.566284i | ||||||||
\(765\) | −196.199 | − | 164588.i | −0.000335253 | − | 0.281239i | ||||
\(766\) | 162146. | 0.276343 | ||||||||
\(767\) | − | 53844.9i | − | 0.0915280i | ||||||
\(768\) | −442349. | − | 441822.i | −0.749969 | − | 0.749075i | ||||
\(769\) | 175981. | 0.297586 | 0.148793 | − | 0.988868i | \(-0.452461\pi\) | ||||
0.148793 | + | 0.988868i | \(0.452461\pi\) | |||||||
\(770\) | − | 306734.i | − | 0.517345i | ||||||
\(771\) | −9681.73 | + | 9693.28i | −0.0162871 | + | 0.0163065i | ||||
\(772\) | −213544. | −0.358305 | ||||||||
\(773\) | 64980.9i | 0.108749i | 0.998521 | + | 0.0543747i | \(0.0173165\pi\) | ||||
−0.998521 | + | 0.0543747i | \(0.982683\pi\) | |||||||
\(774\) | 491670. | − | 586.100i | 0.820713 | − | 0.000978340i | ||||
\(775\) | 794084. | 1.32210 | ||||||||
\(776\) | 1.07753e6i | 1.78939i | ||||||||
\(777\) | −7181.85 | − | 7173.29i | −0.0118958 | − | 0.0118816i | ||||
\(778\) | 579962. | 0.958165 | ||||||||
\(779\) | 107723.i | 0.177514i | ||||||||
\(780\) | −271412. | + | 271736.i | −0.446108 | + | 0.446640i | ||||
\(781\) | −648734. | −1.06357 | ||||||||
\(782\) | 123405.i | 0.201799i | ||||||||
\(783\) | −94692.8 | − | 94354.8i | −0.154452 | − | 0.153901i | ||||
\(784\) | 64510.7 | 0.104954 | ||||||||
\(785\) | 534070.i | 0.866680i | ||||||||
\(786\) | −423753. | − | 423248.i | −0.685910 | − | 0.685093i | ||||
\(787\) | 87675.0 | 0.141555 | 0.0707777 | − | 0.997492i | \(-0.477452\pi\) | ||||
0.0707777 | + | 0.997492i | \(0.477452\pi\) | |||||||
\(788\) | − | 300063.i | − | 0.483237i | ||||||
\(789\) | −169605. | + | 169807.i | −0.272449 | + | 0.272774i | ||||
\(790\) | 64421.2 | 0.103223 | ||||||||
\(791\) | 248817.i | 0.397673i | ||||||||
\(792\) | −662.796 | − | 556009.i | −0.00105665 | − | 0.886403i | ||||
\(793\) | 360318. | 0.572981 | ||||||||
\(794\) | 723599.i | 1.14777i | ||||||||
\(795\) | −108542. | − | 108412.i | −0.171737 | − | 0.171532i | ||||
\(796\) | 244423. | 0.385758 | ||||||||
\(797\) | − | 1.12602e6i | − | 1.77268i | −0.463036 | − | 0.886339i | \(-0.653240\pi\) | ||
0.463036 | − | 0.886339i | \(-0.346760\pi\) | |||||||
\(798\) | 35464.2 | − | 35506.5i | 0.0556909 | − | 0.0557574i | ||||
\(799\) | 210371. | 0.329527 | ||||||||
\(800\) | 1.01046e6i | 1.57884i | ||||||||
\(801\) | 330443. | − | 393.908i | 0.515029 | − | 0.000613946i | ||||
\(802\) | 214815. | 0.333977 | ||||||||
\(803\) | − | 602653.i | − | 0.934623i | ||||||
\(804\) | 53349.0 | + | 53285.4i | 0.0825304 | + | 0.0824321i | ||||
\(805\) | −1.02383e6 | −1.57992 | ||||||||
\(806\) | 241376.i | 0.371555i | ||||||||
\(807\) | −786767. | + | 787705.i | −1.20809 | + | 1.20953i | ||||
\(808\) | −182608. | −0.279702 | ||||||||
\(809\) | 224415.i | 0.342890i | 0.985194 | + | 0.171445i | \(0.0548435\pi\) | ||||
−0.985194 | + | 0.171445i | \(0.945156\pi\) | |||||||
\(810\) | −721977. | + | 1721.28i | −1.10041 | + | 0.00262351i | ||||
\(811\) | −1.22110e6 | −1.85657 | −0.928283 | − | 0.371875i | \(-0.878715\pi\) | ||||
−0.928283 | + | 0.371875i | \(0.878715\pi\) | |||||||
\(812\) | 43508.8i | 0.0659881i | ||||||||
\(813\) | −478099. | − | 477530.i | −0.723331 | − | 0.722469i | ||||
\(814\) | 11555.7 | 0.0174401 | ||||||||
\(815\) | 1.81877e6i | 2.73819i | ||||||||
\(816\) | 12197.8 | − | 12212.3i | 0.0183189 | − | 0.0183408i | ||||
\(817\) | 173201. | 0.259481 | ||||||||
\(818\) | − | 152440.i | − | 0.227820i | ||||||
\(819\) | 310.246 | + | 260260.i | 0.000462528 | + | 0.388007i | ||||
\(820\) | −504416. | −0.750173 | ||||||||
\(821\) | 484305.i | 0.718510i | 0.933239 | + | 0.359255i | \(0.116969\pi\) | ||||
−0.933239 | + | 0.359255i | \(0.883031\pi\) | |||||||
\(822\) | 416531. | + | 416035.i | 0.616458 | + | 0.615724i | ||||
\(823\) | −435559. | −0.643053 | −0.321527 | − | 0.946901i | \(-0.604196\pi\) | ||||
−0.321527 | + | 0.946901i | \(0.604196\pi\) | |||||||
\(824\) | 487749.i | 0.718359i | ||||||||
\(825\) | −688828. | + | 689650.i | −1.01205 | + | 1.01326i | ||||
\(826\) | −32944.8 | −0.0482866 | ||||||||
\(827\) | 1.28768e6i | 1.88276i | 0.337346 | + | 0.941381i | \(0.390471\pi\) | ||||
−0.337346 | + | 0.941381i | \(0.609529\pi\) | |||||||
\(828\) | −657272. | + | 783.507i | −0.958703 | + | 0.00114283i | ||||
\(829\) | 250804. | 0.364943 | 0.182471 | − | 0.983211i | \(-0.441590\pi\) | ||||
0.182471 | + | 0.983211i | \(0.441590\pi\) | |||||||
\(830\) | − | 1.34580e6i | − | 1.95355i | ||||||
\(831\) | −865309. | − | 864278.i | −1.25305 | − | 1.25156i | ||||
\(832\) | −380596. | −0.549816 | ||||||||
\(833\) | − | 82878.5i | − | 0.119441i | ||||||
\(834\) | −237540. | + | 237823.i | −0.341511 | + | 0.341918i | ||||
\(835\) | −620941. | −0.890589 | ||||||||
\(836\) | − | 69367.4i | − | 0.0992528i | ||||||
\(837\) | 388874. | − | 390267.i | 0.555083 | − | 0.557072i | ||||
\(838\) | 714629. | 1.01764 | ||||||||
\(839\) | − | 402394.i | − | 0.571646i | −0.958282 | − | 0.285823i | \(-0.907733\pi\) | ||
0.958282 | − | 0.285823i | \(-0.0922669\pi\) | |||||||
\(840\) | 469452. | + | 468893.i | 0.665324 | + | 0.664531i | ||||
\(841\) | 673656. | 0.952459 | ||||||||
\(842\) | 416177.i | 0.587022i | ||||||||
\(843\) | −443950. | + | 444479.i | −0.624710 | + | 0.625455i | ||||
\(844\) | −772850. | −1.08495 | ||||||||
\(845\) | − | 591288.i | − | 0.828105i | ||||||
\(846\) | −1100.04 | − | 922808.i | −0.00153698 | − | 1.28935i | ||||
\(847\) | 108624. | 0.151411 | ||||||||
\(848\) | − | 16088.3i | − | 0.0223727i | ||||||
\(849\) | −270532. | − | 270210.i | −0.375322 | − | 0.374875i | ||||
\(850\) | −140202. | −0.194052 | ||||||||
\(851\) | − | 38571.1i | − | 0.0532602i | ||||||
\(852\) | 351218. | − | 351637.i | 0.483835 | − | 0.484412i | ||||
\(853\) | −882553. | −1.21295 | −0.606475 | − | 0.795103i | \(-0.707417\pi\) | ||||
−0.606475 | + | 0.795103i | \(0.707417\pi\) | |||||||
\(854\) | − | 220460.i | − | 0.302283i | ||||||
\(855\) | −254331. | + | 303.178i | −0.347911 | + | 0.000414731i | ||||
\(856\) | −250448. | −0.341799 | ||||||||
\(857\) | − | 1.10133e6i | − | 1.49954i | −0.661701 | − | 0.749768i | \(-0.730165\pi\) | ||
0.661701 | − | 0.749768i | \(-0.269835\pi\) | |||||||
\(858\) | −209631. | − | 209381.i | −0.284761 | − | 0.284422i | ||||
\(859\) | −190437. | −0.258086 | −0.129043 | − | 0.991639i | \(-0.541191\pi\) | ||||
−0.129043 | + | 0.991639i | \(0.541191\pi\) | |||||||
\(860\) | 811018.i | 1.09656i | ||||||||
\(861\) | −241557. | + | 241845.i | −0.325847 | + | 0.326235i | ||||
\(862\) | −197454. | −0.265736 | ||||||||
\(863\) | − | 1.26740e6i | − | 1.70173i | −0.525383 | − | 0.850866i | \(-0.676078\pi\) | ||
0.525383 | − | 0.850866i | \(-0.323922\pi\) | |||||||
\(864\) | 496609. | + | 494836.i | 0.665253 | + | 0.662878i | ||||
\(865\) | 750101. | 1.00251 | ||||||||
\(866\) | − | 534207.i | − | 0.712318i | ||||||
\(867\) | 516152. | + | 515537.i | 0.686656 | + | 0.685838i | ||||
\(868\) | −179318. | −0.238004 | ||||||||
\(869\) | − | 60342.7i | − | 0.0799070i | ||||||
\(870\) | −128337. | + | 128490.i | −0.169556 | + | 0.169759i | ||||
\(871\) | 113453. | 0.149547 | ||||||||
\(872\) | − | 7191.60i | − | 0.00945786i | ||||||
\(873\) | −1562.30 | − | 1.31059e6i | −0.00204992 | − | 1.71964i | ||||
\(874\) | 190693. | 0.249638 | ||||||||
\(875\) | − | 471298.i | − | 0.615573i | ||||||
\(876\) | 326660. | + | 326270.i | 0.425684 | + | 0.425177i | ||||
\(877\) | 219156. | 0.284940 | 0.142470 | − | 0.989799i | \(-0.454496\pi\) | ||||
0.142470 | + | 0.989799i | \(0.454496\pi\) | |||||||
\(878\) | − | 284986.i | − | 0.369687i | ||||||
\(879\) | 985274. | − | 986449.i | 1.27520 | − | 1.27672i | ||||
\(880\) | −163025. | −0.210518 | ||||||||
\(881\) | 158303.i | 0.203956i | 0.994787 | + | 0.101978i | \(0.0325172\pi\) | ||||
−0.994787 | + | 0.101978i | \(0.967483\pi\) | |||||||
\(882\) | −363553. | + | 433.377i | −0.467338 | + | 0.000557095i | ||||
\(883\) | 523888. | 0.671920 | 0.335960 | − | 0.941876i | \(-0.390939\pi\) | ||||
0.335960 | + | 0.941876i | \(0.390939\pi\) | |||||||
\(884\) | 51745.1i | 0.0662163i | ||||||||
\(885\) | 118132. | + | 117991.i | 0.150827 | + | 0.150648i | ||||
\(886\) | −576533. | −0.734440 | ||||||||
\(887\) | 342381.i | 0.435173i | 0.976041 | + | 0.217587i | \(0.0698185\pi\) | ||||
−0.976041 | + | 0.217587i | \(0.930182\pi\) | |||||||
\(888\) | −17664.8 | + | 17685.9i | −0.0224018 | + | 0.0224285i | ||||
\(889\) | 635251. | 0.803789 | ||||||||
\(890\) | − | 448918.i | − | 0.566744i | ||||||
\(891\) | 1612.31 | + | 676269.i | 0.00203092 | + | 0.851851i | ||||
\(892\) | −51833.9 | −0.0651455 | ||||||||
\(893\) | − | 325078.i | − | 0.407647i | ||||||
\(894\) | −522283. | − | 521661.i | −0.653478 | − | 0.652699i | ||||
\(895\) | −1.23190e6 | −1.53790 | ||||||||
\(896\) | − | 183239.i | − | 0.228245i | ||||||
\(897\) | −698881. | + | 699715.i | −0.868597 | + | 0.869633i | ||||
\(898\) | 218222. | 0.270611 | ||||||||
\(899\) | − | 138581.i | − | 0.171468i | ||||||
\(900\) | −890.158 | − | 746739.i | −0.00109896 | − | 0.921900i | ||||
\(901\) | −20669.0 | −0.0254607 | ||||||||
\(902\) | − | 389132.i | − | 0.478282i | ||||||
\(903\) | 388847. | + | 388384.i | 0.476874 | + | 0.476306i | ||||
\(904\) | 612730. | 0.749778 | ||||||||
\(905\) | 1.15247e6i | 1.40713i | ||||||||
\(906\) | 642347. | − | 643114.i | 0.782553 | − | 0.783486i | ||||
\(907\) | −1.04119e6 | −1.26566 | −0.632831 | − | 0.774290i | \(-0.718107\pi\) | ||||
−0.632831 | + | 0.774290i | \(0.718107\pi\) | |||||||
\(908\) | 106888.i | 0.129645i | ||||||||
\(909\) | 222104. | − | 264.762i | 0.268800 | − | 0.000320426i | ||||
\(910\) | 353572. | 0.426968 | ||||||||
\(911\) | 1.00350e6i | 1.20915i | 0.796547 | + | 0.604577i | \(0.206658\pi\) | ||||
−0.796547 | + | 0.604577i | \(0.793342\pi\) | |||||||
\(912\) | −18871.2 | − | 18848.7i | −0.0226887 | − | 0.0226617i | ||||
\(913\) | −1.26060e6 | −1.51229 | ||||||||
\(914\) | 505736.i | 0.605385i | ||||||||
\(915\) | −789570. | + | 790512.i | −0.943080 | + | 0.944205i | ||||
\(916\) | −251833. | −0.300139 | ||||||||
\(917\) | − | 669468.i | − | 0.796144i | ||||||
\(918\) | −68659.1 | + | 68905.0i | −0.0814728 | + | 0.0817647i | ||||
\(919\) | 806292. | 0.954688 | 0.477344 | − | 0.878717i | \(-0.341600\pi\) | ||||
0.477344 | + | 0.878717i | \(0.341600\pi\) | |||||||
\(920\) | 2.52126e6i | 2.97880i | ||||||||
\(921\) | −544003. | − | 543355.i | −0.641331 | − | 0.640567i | ||||
\(922\) | 839234. | 0.987237 | ||||||||
\(923\) | − | 747796.i | − | 0.877767i | ||||||
\(924\) | 155549. | − | 155735.i | 0.182189 | − | 0.182407i | ||||
\(925\) | 43821.4 | 0.0512156 | ||||||||
\(926\) | 790837.i | 0.922284i | ||||||||
\(927\) | −707.184 | − | 593245.i | −0.000822949 | − | 0.690359i | ||||
\(928\) | 176342. | 0.204767 | ||||||||
\(929\) | 119797.i | 0.138808i | 0.997589 | + | 0.0694040i | \(0.0221097\pi\) | ||||
−0.997589 | + | 0.0694040i | \(0.977890\pi\) | |||||||
\(930\) | −529560. | − | 528929.i | −0.612279 | − | 0.611550i | ||||
\(931\) | −128069. | −0.147756 | ||||||||
\(932\) | − | 443228.i | − | 0.510265i | ||||||
\(933\) | 49031.3 | − | 49089.8i | 0.0563262 | − | 0.0563934i | ||||
\(934\) | 553447. | 0.634428 | ||||||||
\(935\) | 209442.i | 0.239574i | ||||||||
\(936\) | 640911. | − | 764.005i | 0.731553 | − | 0.000872056i | ||||
\(937\) | 252847. | 0.287991 | 0.143996 | − | 0.989578i | \(-0.454005\pi\) | ||||
0.143996 | + | 0.989578i | \(0.454005\pi\) | |||||||
\(938\) | − | 69415.6i | − | 0.0788953i | ||||||
\(939\) | 566687. | + | 566012.i | 0.642706 | + | 0.641940i | ||||
\(940\) | 1.52219e6 | 1.72271 | ||||||||
\(941\) | − | 354100.i | − | 0.399896i | −0.979807 | − | 0.199948i | \(-0.935923\pi\) | ||
0.979807 | − | 0.199948i | \(-0.0640773\pi\) | |||||||
\(942\) | 223057. | − | 223324.i | 0.251371 | − | 0.251671i | ||||
\(943\) | −1.29886e6 | −1.46063 | ||||||||
\(944\) | 17509.7i | 0.0196488i | ||||||||
\(945\) | −571671. | − | 569631.i | −0.640152 | − | 0.637866i | ||||
\(946\) | −625661. | −0.699128 | ||||||||
\(947\) | 230565.i | 0.257095i | 0.991703 | + | 0.128547i | \(0.0410314\pi\) | ||||
−0.991703 | + | 0.128547i | \(0.958969\pi\) | |||||||
\(948\) | 32707.9 | + | 32668.9i | 0.0363945 | + | 0.0363511i | ||||
\(949\) | 694678. | 0.771350 | ||||||||
\(950\) | 216649.i | 0.240055i | ||||||||
\(951\) | 344525. | − | 344936.i | 0.380943 | − | 0.381397i | ||||
\(952\) | 89395.1 | 0.0986370 | ||||||||
\(953\) | − | 1.56135e6i | − | 1.71915i | −0.511008 | − | 0.859576i | \(-0.670728\pi\) | ||
0.511008 | − | 0.859576i | \(-0.329272\pi\) | |||||||
\(954\) | 108.080 | + | 90666.2i | 0.000118754 | + | 0.0996205i | ||||
\(955\) | −1.54217e6 | −1.69093 | ||||||||
\(956\) | − | 986760.i | − | 1.07968i | ||||||
\(957\) | 120355. | + | 120212.i | 0.131414 | + | 0.131258i | ||||
\(958\) | 437650. | 0.476865 | ||||||||
\(959\) | 658059.i | 0.715530i | ||||||||
\(960\) | 834004. | − | 834999.i | 0.904952 | − | 0.906032i | ||||
\(961\) | −352373. | −0.381553 | ||||||||
\(962\) | 13320.3i | 0.0143934i | ||||||||
\(963\) | 304619. | − | 363.124i | 0.328476 | − | 0.000391563i | ||||
\(964\) | −405700. | −0.436567 | ||||||||
\(965\) | − | 996317.i | − | 1.06990i | ||||||
\(966\) | 428118. | + | 427608.i | 0.458785 | + | 0.458238i | ||||
\(967\) | −855705. | −0.915105 | −0.457553 | − | 0.889183i | \(-0.651274\pi\) | ||||
−0.457553 | + | 0.889183i | \(0.651274\pi\) | |||||||
\(968\) | − | 267494.i | − | 0.285472i | ||||||
\(969\) | −24215.4 | + | 24244.3i | −0.0257896 | + | 0.0258204i | ||||
\(970\) | −1.78048e6 | −1.89231 | ||||||||
\(971\) | − | 1.66911e6i | − | 1.77030i | −0.465306 | − | 0.885150i | \(-0.654056\pi\) | ||
0.465306 | − | 0.885150i | \(-0.345944\pi\) | |||||||
\(972\) | −367434. | − | 365251.i | −0.388908 | − | 0.386597i | ||||
\(973\) | −375727. | −0.396868 | ||||||||
\(974\) | − | 664596.i | − | 0.700552i | ||||||
\(975\) | −794959. | − | 794012.i | −0.836249 | − | 0.835253i | ||||
\(976\) | −117171. | −0.123005 | ||||||||
\(977\) | − | 1.31255e6i | − | 1.37508i | −0.726147 | − | 0.687540i | \(-0.758691\pi\) | ||
0.726147 | − | 0.687540i | \(-0.241309\pi\) | |||||||
\(978\) | 759621. | − | 760527.i | 0.794180 | − | 0.795127i | ||||
\(979\) | −420496. | −0.438730 | ||||||||
\(980\) | − | 599688.i | − | 0.624415i | ||||||
\(981\) | 10.4271 | + | 8747.10i | 1.08349e−5 | + | 0.00908920i | ||||
\(982\) | 771866. | 0.800422 | ||||||||
\(983\) | 1.68444e6i | 1.74321i | 0.490210 | + | 0.871605i | \(0.336920\pi\) | ||||
−0.490210 | + | 0.871605i | \(0.663080\pi\) | |||||||
\(984\) | 595563. | + | 594853.i | 0.615088 | + | 0.614355i | ||||
\(985\) | 1.39999e6 | 1.44295 | ||||||||
\(986\) | 24467.7i | 0.0251674i | ||||||||
\(987\) | 728952. | − | 729822.i | 0.748281 | − | 0.749174i | ||||
\(988\) | 79959.7 | 0.0819139 | ||||||||
\(989\) | 2.08836e6i | 2.13507i | ||||||||
\(990\) | 918734. | − | 1095.19i | 0.937388 | − | 0.00111742i | ||||
\(991\) | −76820.4 | −0.0782220 | −0.0391110 | − | 0.999235i | \(-0.512453\pi\) | ||||
−0.0391110 | + | 0.999235i | \(0.512453\pi\) | |||||||
\(992\) | 726777.i | 0.738546i | ||||||||
\(993\) | 810852. | + | 809886.i | 0.822324 | + | 0.821345i | ||||
\(994\) | −457536. | −0.463076 | ||||||||
\(995\) | 1.14039e6i | 1.15188i | ||||||||
\(996\) | 682474. | − | 683288.i | 0.687966 | − | 0.688787i | ||||
\(997\) | −549557. | −0.552870 | −0.276435 | − | 0.961033i | \(-0.589153\pi\) | ||||
−0.276435 | + | 0.961033i | \(0.589153\pi\) | |||||||
\(998\) | − | 161589.i | − | 0.162238i | ||||||
\(999\) | 21459.9 | − | 21536.8i | 0.0215029 | − | 0.0215800i |
(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.b.a.119.28 | ✓ | 78 | |
3.2 | odd | 2 | inner | 177.5.b.a.119.51 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.b.a.119.28 | ✓ | 78 | 1.1 | even | 1 | trivial | |
177.5.b.a.119.51 | yes | 78 | 3.2 | odd | 2 | inner |