Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,5,Mod(8,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, 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("21.8");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17076922476\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 82x^{6} + 2017x^{4} + 13020x^{2} + 756 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 3^{3}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 8.1 | ||
Root | \(-6.02741i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.8 |
Dual form | 21.5.b.a.8.8 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 6.02741i | − | 1.50685i | −0.657533 | − | 0.753426i | \(-0.728400\pi\) | ||
0.657533 | − | 0.753426i | \(-0.271600\pi\) | |||||||
\(3\) | −8.92230 | + | 1.18010i | −0.991366 | + | 0.131122i | ||||
\(4\) | −20.3296 | −1.27060 | ||||||||
\(5\) | − | 15.7540i | − | 0.630159i | −0.949065 | − | 0.315079i | \(-0.897969\pi\) | ||
0.949065 | − | 0.315079i | \(-0.102031\pi\) | |||||||
\(6\) | 7.11292 | + | 53.7783i | 0.197581 | + | 1.49384i | ||||
\(7\) | −18.5203 | −0.377964 | ||||||||
\(8\) | 26.0965i | 0.407757i | ||||||||
\(9\) | 78.2147 | − | 21.0583i | 0.965614 | − | 0.259980i | ||||
\(10\) | −94.9556 | −0.949556 | ||||||||
\(11\) | − | 196.340i | − | 1.62264i | −0.584600 | − | 0.811322i | \(-0.698748\pi\) | ||
0.584600 | − | 0.811322i | \(-0.301252\pi\) | |||||||
\(12\) | 181.387 | − | 23.9909i | 1.25963 | − | 0.166604i | ||||
\(13\) | 151.709 | 0.897684 | 0.448842 | − | 0.893611i | \(-0.351837\pi\) | ||||
0.448842 | + | 0.893611i | \(0.351837\pi\) | |||||||
\(14\) | 111.629i | 0.569536i | ||||||||
\(15\) | 18.5912 | + | 140.562i | 0.0826276 | + | 0.624718i | ||||
\(16\) | −167.980 | −0.656173 | ||||||||
\(17\) | 421.337i | 1.45791i | 0.684560 | + | 0.728956i | \(0.259994\pi\) | ||||
−0.684560 | + | 0.728956i | \(0.740006\pi\) | |||||||
\(18\) | −126.927 | − | 471.432i | −0.391751 | − | 1.45504i | ||||
\(19\) | 196.481 | 0.544268 | 0.272134 | − | 0.962259i | \(-0.412271\pi\) | ||||
0.272134 | + | 0.962259i | \(0.412271\pi\) | |||||||
\(20\) | 320.272i | 0.800681i | ||||||||
\(21\) | 165.243 | − | 21.8557i | 0.374701 | − | 0.0495594i | ||||
\(22\) | −1183.42 | −2.44508 | ||||||||
\(23\) | − | 143.456i | − | 0.271183i | −0.990765 | − | 0.135591i | \(-0.956707\pi\) | ||
0.990765 | − | 0.135591i | \(-0.0432935\pi\) | |||||||
\(24\) | −30.7963 | − | 232.840i | −0.0534659 | − | 0.404237i | ||||
\(25\) | 376.813 | 0.602900 | ||||||||
\(26\) | − | 914.409i | − | 1.35268i | ||||||
\(27\) | −673.004 | + | 280.190i | −0.923188 | + | 0.384348i | ||||
\(28\) | 376.510 | 0.480242 | ||||||||
\(29\) | − | 753.566i | − | 0.896035i | −0.894025 | − | 0.448018i | \(-0.852130\pi\) | ||
0.894025 | − | 0.448018i | \(-0.147870\pi\) | |||||||
\(30\) | 847.222 | − | 112.057i | 0.941357 | − | 0.124507i | ||||
\(31\) | −635.323 | −0.661107 | −0.330553 | − | 0.943787i | \(-0.607235\pi\) | ||||
−0.330553 | + | 0.943787i | \(0.607235\pi\) | |||||||
\(32\) | 1430.03i | 1.39651i | ||||||||
\(33\) | 231.700 | + | 1751.80i | 0.212764 | + | 1.60863i | ||||
\(34\) | 2539.57 | 2.19686 | ||||||||
\(35\) | 291.768i | 0.238178i | ||||||||
\(36\) | −1590.08 | + | 428.108i | −1.22691 | + | 0.330331i | ||||
\(37\) | 1336.52 | 0.976276 | 0.488138 | − | 0.872767i | \(-0.337676\pi\) | ||||
0.488138 | + | 0.872767i | \(0.337676\pi\) | |||||||
\(38\) | − | 1184.27i | − | 0.820131i | ||||||
\(39\) | −1353.59 | + | 179.031i | −0.889933 | + | 0.117706i | ||||
\(40\) | 411.123 | 0.256952 | ||||||||
\(41\) | − | 2846.73i | − | 1.69347i | −0.532012 | − | 0.846737i | \(-0.678564\pi\) | ||
0.532012 | − | 0.846737i | \(-0.321436\pi\) | |||||||
\(42\) | −131.733 | − | 995.988i | −0.0746787 | − | 0.564619i | ||||
\(43\) | 99.0370 | 0.0535624 | 0.0267812 | − | 0.999641i | \(-0.491474\pi\) | ||||
0.0267812 | + | 0.999641i | \(0.491474\pi\) | |||||||
\(44\) | 3991.52i | 2.06173i | ||||||||
\(45\) | −331.752 | − | 1232.19i | −0.163828 | − | 0.608490i | ||||
\(46\) | −864.666 | −0.408632 | ||||||||
\(47\) | − | 512.989i | − | 0.232227i | −0.993236 | − | 0.116113i | \(-0.962956\pi\) | ||
0.993236 | − | 0.116113i | \(-0.0370436\pi\) | |||||||
\(48\) | 1498.77 | − | 198.233i | 0.650507 | − | 0.0860386i | ||||
\(49\) | 343.000 | 0.142857 | ||||||||
\(50\) | − | 2271.20i | − | 0.908481i | ||||||
\(51\) | −497.218 | − | 3759.29i | −0.191164 | − | 1.44532i | ||||
\(52\) | −3084.18 | −1.14060 | ||||||||
\(53\) | 4252.16i | 1.51376i | 0.653553 | + | 0.756881i | \(0.273278\pi\) | ||||
−0.653553 | + | 0.756881i | \(0.726722\pi\) | |||||||
\(54\) | 1688.82 | + | 4056.47i | 0.579156 | + | 1.39111i | ||||
\(55\) | −3093.13 | −1.02252 | ||||||||
\(56\) | − | 483.313i | − | 0.154118i | ||||||
\(57\) | −1753.06 | + | 231.866i | −0.539569 | + | 0.0713654i | ||||
\(58\) | −4542.05 | −1.35019 | ||||||||
\(59\) | 2893.09i | 0.831110i | 0.909568 | + | 0.415555i | \(0.136413\pi\) | ||||
−0.909568 | + | 0.415555i | \(0.863587\pi\) | |||||||
\(60\) | −377.952 | − | 2857.56i | −0.104987 | − | 0.793768i | ||||
\(61\) | 2661.40 | 0.715238 | 0.357619 | − | 0.933868i | \(-0.383589\pi\) | ||||
0.357619 | + | 0.933868i | \(0.383589\pi\) | |||||||
\(62\) | 3829.35i | 0.996190i | ||||||||
\(63\) | −1448.56 | + | 390.006i | −0.364968 | + | 0.0982630i | ||||
\(64\) | 5931.68 | 1.44816 | ||||||||
\(65\) | − | 2390.01i | − | 0.565683i | ||||||
\(66\) | 10558.8 | − | 1396.55i | 2.42397 | − | 0.320604i | ||||
\(67\) | 2567.47 | 0.571947 | 0.285974 | − | 0.958237i | \(-0.407683\pi\) | ||||
0.285974 | + | 0.958237i | \(0.407683\pi\) | |||||||
\(68\) | − | 8565.62i | − | 1.85243i | ||||||
\(69\) | 169.292 | + | 1279.95i | 0.0355580 | + | 0.268842i | ||||
\(70\) | 1758.60 | 0.358898 | ||||||||
\(71\) | 1769.31i | 0.350983i | 0.984481 | + | 0.175492i | \(0.0561515\pi\) | ||||
−0.984481 | + | 0.175492i | \(0.943849\pi\) | |||||||
\(72\) | 549.548 | + | 2041.13i | 0.106009 | + | 0.393736i | ||||
\(73\) | −3531.14 | −0.662628 | −0.331314 | − | 0.943521i | \(-0.607492\pi\) | ||||
−0.331314 | + | 0.943521i | \(0.607492\pi\) | |||||||
\(74\) | − | 8055.76i | − | 1.47110i | ||||||
\(75\) | −3362.03 | + | 444.675i | −0.597695 | + | 0.0790534i | ||||
\(76\) | −3994.38 | −0.691548 | ||||||||
\(77\) | 3636.27i | 0.613302i | ||||||||
\(78\) | 1079.09 | + | 8158.63i | 0.177365 | + | 1.34100i | ||||
\(79\) | 2251.95 | 0.360832 | 0.180416 | − | 0.983590i | \(-0.442256\pi\) | ||||
0.180416 | + | 0.983590i | \(0.442256\pi\) | |||||||
\(80\) | 2646.35i | 0.413493i | ||||||||
\(81\) | 5674.09 | − | 3294.15i | 0.864821 | − | 0.502080i | ||||
\(82\) | −17158.4 | −2.55181 | ||||||||
\(83\) | − | 2063.23i | − | 0.299496i | −0.988724 | − | 0.149748i | \(-0.952154\pi\) | ||
0.988724 | − | 0.149748i | \(-0.0478463\pi\) | |||||||
\(84\) | −3359.33 | + | 444.318i | −0.476096 | + | 0.0629703i | ||||
\(85\) | 6637.72 | 0.918716 | ||||||||
\(86\) | − | 596.936i | − | 0.0807107i | ||||||
\(87\) | 889.280 | + | 6723.54i | 0.117490 | + | 0.888299i | ||||
\(88\) | 5123.78 | 0.661645 | ||||||||
\(89\) | 3069.01i | 0.387453i | 0.981056 | + | 0.193726i | \(0.0620574\pi\) | ||||
−0.981056 | + | 0.193726i | \(0.937943\pi\) | |||||||
\(90\) | −7426.92 | + | 1999.61i | −0.916904 | + | 0.246865i | ||||
\(91\) | −2809.68 | −0.339293 | ||||||||
\(92\) | 2916.40i | 0.344566i | ||||||||
\(93\) | 5668.54 | − | 749.743i | 0.655399 | − | 0.0866855i | ||||
\(94\) | −3091.99 | −0.349931 | ||||||||
\(95\) | − | 3095.35i | − | 0.342975i | ||||||
\(96\) | −1687.57 | − | 12759.1i | −0.183113 | − | 1.38445i | ||||
\(97\) | 3416.07 | 0.363064 | 0.181532 | − | 0.983385i | \(-0.441894\pi\) | ||||
0.181532 | + | 0.983385i | \(0.441894\pi\) | |||||||
\(98\) | − | 2067.40i | − | 0.215265i | ||||||
\(99\) | −4134.59 | − | 15356.7i | −0.421854 | − | 1.56685i | ||||
\(100\) | −7660.46 | −0.766046 | ||||||||
\(101\) | 868.123i | 0.0851017i | 0.999094 | + | 0.0425509i | \(0.0135484\pi\) | ||||
−0.999094 | + | 0.0425509i | \(0.986452\pi\) | |||||||
\(102\) | −22658.8 | + | 2996.93i | −2.17789 | + | 0.288056i | ||||
\(103\) | 2420.92 | 0.228195 | 0.114098 | − | 0.993470i | \(-0.463602\pi\) | ||||
0.114098 | + | 0.993470i | \(0.463602\pi\) | |||||||
\(104\) | 3959.06i | 0.366037i | ||||||||
\(105\) | −344.314 | − | 2603.24i | −0.0312303 | − | 0.236121i | ||||
\(106\) | 25629.5 | 2.28102 | ||||||||
\(107\) | − | 5171.46i | − | 0.451695i | −0.974163 | − | 0.225848i | \(-0.927485\pi\) | ||
0.974163 | − | 0.225848i | \(-0.0725152\pi\) | |||||||
\(108\) | 13681.9 | − | 5696.16i | 1.17300 | − | 0.488353i | ||||
\(109\) | 18184.1 | 1.53052 | 0.765258 | − | 0.643723i | \(-0.222611\pi\) | ||||
0.765258 | + | 0.643723i | \(0.222611\pi\) | |||||||
\(110\) | 18643.6i | 1.54079i | ||||||||
\(111\) | −11924.8 | + | 1577.22i | −0.967847 | + | 0.128011i | ||||
\(112\) | 3111.04 | 0.248010 | ||||||||
\(113\) | 8272.19i | 0.647834i | 0.946086 | + | 0.323917i | \(0.105000\pi\) | ||||
−0.946086 | + | 0.323917i | \(0.895000\pi\) | |||||||
\(114\) | 1397.55 | + | 10566.4i | 0.107537 | + | 0.813050i | ||||
\(115\) | −2260.00 | −0.170888 | ||||||||
\(116\) | 15319.7i | 1.13850i | ||||||||
\(117\) | 11865.8 | − | 3194.73i | 0.866816 | − | 0.233379i | ||||
\(118\) | 17437.9 | 1.25236 | ||||||||
\(119\) | − | 7803.26i | − | 0.551039i | ||||||
\(120\) | −3668.16 | + | 485.164i | −0.254733 | + | 0.0336920i | ||||
\(121\) | −23908.4 | −1.63297 | ||||||||
\(122\) | − | 16041.3i | − | 1.07776i | ||||||
\(123\) | 3359.42 | + | 25399.4i | 0.222051 | + | 1.67885i | ||||
\(124\) | 12915.9 | 0.840003 | ||||||||
\(125\) | − | 15782.5i | − | 1.01008i | ||||||
\(126\) | 2350.72 | + | 8731.04i | 0.148068 | + | 0.549952i | ||||
\(127\) | −23527.3 | −1.45870 | −0.729348 | − | 0.684143i | \(-0.760176\pi\) | ||||
−0.729348 | + | 0.684143i | \(0.760176\pi\) | |||||||
\(128\) | − | 12872.2i | − | 0.785656i | ||||||
\(129\) | −883.637 | + | 116.873i | −0.0531000 | + | 0.00702321i | ||||
\(130\) | −14405.6 | −0.852400 | ||||||||
\(131\) | 19736.1i | 1.15005i | 0.818134 | + | 0.575027i | \(0.195008\pi\) | ||||
−0.818134 | + | 0.575027i | \(0.804992\pi\) | |||||||
\(132\) | −4710.38 | − | 35613.5i | −0.270339 | − | 2.04393i | ||||
\(133\) | −3638.87 | −0.205714 | ||||||||
\(134\) | − | 15475.2i | − | 0.861840i | ||||||
\(135\) | 4414.10 | + | 10602.5i | 0.242200 | + | 0.581755i | ||||
\(136\) | −10995.4 | −0.594474 | ||||||||
\(137\) | − | 13653.6i | − | 0.727457i | −0.931505 | − | 0.363728i | \(-0.881504\pi\) | ||
0.931505 | − | 0.363728i | \(-0.118496\pi\) | |||||||
\(138\) | 7714.81 | − | 1020.39i | 0.405104 | − | 0.0535806i | ||||
\(139\) | 6654.45 | 0.344416 | 0.172208 | − | 0.985061i | \(-0.444910\pi\) | ||||
0.172208 | + | 0.985061i | \(0.444910\pi\) | |||||||
\(140\) | − | 5931.53i | − | 0.302629i | ||||||
\(141\) | 605.376 | + | 4577.04i | 0.0304500 | + | 0.230222i | ||||
\(142\) | 10664.3 | 0.528880 | ||||||||
\(143\) | − | 29786.4i | − | 1.45662i | ||||||
\(144\) | −13138.5 | + | 3537.38i | −0.633609 | + | 0.170591i | ||||
\(145\) | −11871.6 | −0.564644 | ||||||||
\(146\) | 21283.6i | 0.998482i | ||||||||
\(147\) | −3060.35 | + | 404.773i | −0.141624 | + | 0.0187317i | ||||
\(148\) | −27171.0 | −1.24046 | ||||||||
\(149\) | 25398.8i | 1.14404i | 0.820239 | + | 0.572020i | \(0.193840\pi\) | ||||
−0.820239 | + | 0.572020i | \(0.806160\pi\) | |||||||
\(150\) | 2680.24 | + | 20264.3i | 0.119122 | + | 0.900638i | ||||
\(151\) | −2253.44 | −0.0988307 | −0.0494154 | − | 0.998778i | \(-0.515736\pi\) | ||||
−0.0494154 | + | 0.998778i | \(0.515736\pi\) | |||||||
\(152\) | 5127.45i | 0.221929i | ||||||||
\(153\) | 8872.65 | + | 32954.7i | 0.379027 | + | 1.40778i | ||||
\(154\) | 21917.3 | 0.924155 | ||||||||
\(155\) | 10008.9i | 0.416602i | ||||||||
\(156\) | 27518.0 | − | 3639.63i | 1.13075 | − | 0.149557i | ||||
\(157\) | −41471.1 | −1.68246 | −0.841232 | − | 0.540674i | \(-0.818169\pi\) | ||||
−0.841232 | + | 0.540674i | \(0.818169\pi\) | |||||||
\(158\) | − | 13573.4i | − | 0.543720i | ||||||
\(159\) | −5017.96 | − | 37939.0i | −0.198487 | − | 1.50069i | ||||
\(160\) | 22528.6 | 0.880024 | ||||||||
\(161\) | 2656.84i | 0.102498i | ||||||||
\(162\) | −19855.2 | − | 34200.1i | −0.756560 | − | 1.30316i | ||||
\(163\) | 43022.4 | 1.61927 | 0.809635 | − | 0.586934i | \(-0.199665\pi\) | ||||
0.809635 | + | 0.586934i | \(0.199665\pi\) | |||||||
\(164\) | 57873.0i | 2.15173i | ||||||||
\(165\) | 27597.8 | − | 3650.20i | 1.01369 | − | 0.134075i | ||||
\(166\) | −12435.9 | −0.451296 | ||||||||
\(167\) | 13076.2i | 0.468867i | 0.972132 | + | 0.234433i | \(0.0753234\pi\) | ||||
−0.972132 | + | 0.234433i | \(0.924677\pi\) | |||||||
\(168\) | 570.356 | + | 4312.26i | 0.0202082 | + | 0.152787i | ||||
\(169\) | −5545.52 | −0.194164 | ||||||||
\(170\) | − | 40008.2i | − | 1.38437i | ||||||
\(171\) | 15367.7 | − | 4137.56i | 0.525553 | − | 0.141498i | ||||
\(172\) | −2013.38 | −0.0680566 | ||||||||
\(173\) | − | 20091.4i | − | 0.671303i | −0.941986 | − | 0.335652i | \(-0.891043\pi\) | ||
0.941986 | − | 0.335652i | \(-0.108957\pi\) | |||||||
\(174\) | 40525.5 | − | 5360.06i | 1.33854 | − | 0.177040i | ||||
\(175\) | −6978.67 | −0.227875 | ||||||||
\(176\) | 32981.2i | 1.06473i | ||||||||
\(177\) | −3414.13 | − | 25813.1i | −0.108977 | − | 0.823935i | ||||
\(178\) | 18498.2 | 0.583834 | ||||||||
\(179\) | − | 40066.7i | − | 1.25048i | −0.780431 | − | 0.625242i | \(-0.785000\pi\) | ||
0.780431 | − | 0.625242i | \(-0.215000\pi\) | |||||||
\(180\) | 6744.40 | + | 25050.0i | 0.208161 | + | 0.773149i | ||||
\(181\) | −63926.2 | −1.95129 | −0.975645 | − | 0.219354i | \(-0.929605\pi\) | ||||
−0.975645 | + | 0.219354i | \(0.929605\pi\) | |||||||
\(182\) | 16935.1i | 0.511264i | ||||||||
\(183\) | −23745.8 | + | 3140.71i | −0.709063 | + | 0.0937834i | ||||
\(184\) | 3743.69 | 0.110577 | ||||||||
\(185\) | − | 21055.5i | − | 0.615209i | ||||||
\(186\) | −4519.01 | − | 34166.6i | −0.130622 | − | 0.987589i | ||||
\(187\) | 82725.2 | 2.36567 | ||||||||
\(188\) | 10428.9i | 0.295068i | ||||||||
\(189\) | 12464.2 | − | 5189.19i | 0.348932 | − | 0.145270i | ||||
\(190\) | −18656.9 | −0.516812 | ||||||||
\(191\) | 57708.3i | 1.58187i | 0.611899 | + | 0.790936i | \(0.290406\pi\) | ||||
−0.611899 | + | 0.790936i | \(0.709594\pi\) | |||||||
\(192\) | −52924.2 | + | 6999.95i | −1.43566 | + | 0.189886i | ||||
\(193\) | −2395.62 | −0.0643137 | −0.0321568 | − | 0.999483i | \(-0.510238\pi\) | ||||
−0.0321568 | + | 0.999483i | \(0.510238\pi\) | |||||||
\(194\) | − | 20590.0i | − | 0.547084i | ||||||
\(195\) | 2820.44 | + | 21324.4i | 0.0741734 | + | 0.560799i | ||||
\(196\) | −6973.06 | −0.181515 | ||||||||
\(197\) | 2034.61i | 0.0524263i | 0.999656 | + | 0.0262132i | \(0.00834487\pi\) | ||||
−0.999656 | + | 0.0262132i | \(0.991655\pi\) | |||||||
\(198\) | −92560.9 | + | 24920.9i | −2.36101 | + | 0.635672i | ||||
\(199\) | 25978.9 | 0.656016 | 0.328008 | − | 0.944675i | \(-0.393623\pi\) | ||||
0.328008 | + | 0.944675i | \(0.393623\pi\) | |||||||
\(200\) | 9833.47i | 0.245837i | ||||||||
\(201\) | −22907.7 | + | 3029.87i | −0.567009 | + | 0.0749948i | ||||
\(202\) | 5232.53 | 0.128236 | ||||||||
\(203\) | 13956.2i | 0.338670i | ||||||||
\(204\) | 10108.3 | + | 76425.0i | 0.242894 | + | 1.83643i | ||||
\(205\) | −44847.3 | −1.06716 | ||||||||
\(206\) | − | 14591.9i | − | 0.343856i | ||||||
\(207\) | −3020.94 | − | 11220.4i | −0.0705020 | − | 0.261858i | ||||
\(208\) | −25484.0 | −0.589035 | ||||||||
\(209\) | − | 38577.0i | − | 0.883153i | ||||||
\(210\) | −15690.8 | + | 2075.32i | −0.355800 | + | 0.0470594i | ||||
\(211\) | 60437.2 | 1.35750 | 0.678749 | − | 0.734370i | \(-0.262522\pi\) | ||||
0.678749 | + | 0.734370i | \(0.262522\pi\) | |||||||
\(212\) | − | 86444.8i | − | 1.92339i | ||||||
\(213\) | −2087.95 | − | 15786.3i | −0.0460216 | − | 0.347953i | ||||
\(214\) | −31170.5 | −0.680638 | ||||||||
\(215\) | − | 1560.22i | − | 0.0337528i | ||||||
\(216\) | −7311.96 | − | 17563.0i | −0.156721 | − | 0.376437i | ||||
\(217\) | 11766.4 | 0.249875 | ||||||||
\(218\) | − | 109603.i | − | 2.30626i | ||||||
\(219\) | 31505.9 | − | 4167.09i | 0.656907 | − | 0.0868850i | ||||
\(220\) | 62882.2 | 1.29922 | ||||||||
\(221\) | 63920.4i | 1.30874i | ||||||||
\(222\) | 9506.58 | + | 71875.9i | 0.192894 | + | 1.45840i | ||||
\(223\) | 11036.5 | 0.221933 | 0.110966 | − | 0.993824i | \(-0.464605\pi\) | ||||
0.110966 | + | 0.993824i | \(0.464605\pi\) | |||||||
\(224\) | − | 26484.5i | − | 0.527832i | ||||||
\(225\) | 29472.3 | − | 7935.05i | 0.582169 | − | 0.156742i | ||||
\(226\) | 49859.8 | 0.976189 | ||||||||
\(227\) | 73080.6i | 1.41824i | 0.705087 | + | 0.709121i | \(0.250908\pi\) | ||||
−0.705087 | + | 0.709121i | \(0.749092\pi\) | |||||||
\(228\) | 35639.0 | − | 4713.75i | 0.685577 | − | 0.0906770i | ||||
\(229\) | 15706.6 | 0.299509 | 0.149755 | − | 0.988723i | \(-0.452152\pi\) | ||||
0.149755 | + | 0.988723i | \(0.452152\pi\) | |||||||
\(230\) | 13621.9i | 0.257503i | ||||||||
\(231\) | −4291.15 | − | 32443.8i | −0.0804173 | − | 0.608007i | ||||
\(232\) | 19665.4 | 0.365365 | ||||||||
\(233\) | 58490.4i | 1.07739i | 0.842501 | + | 0.538694i | \(0.181082\pi\) | ||||
−0.842501 | + | 0.538694i | \(0.818918\pi\) | |||||||
\(234\) | −19255.9 | − | 71520.3i | −0.351668 | − | 1.30616i | ||||
\(235\) | −8081.61 | −0.146340 | ||||||||
\(236\) | − | 58815.6i | − | 1.05601i | ||||||
\(237\) | −20092.6 | + | 2657.52i | −0.357716 | + | 0.0473129i | ||||
\(238\) | −47033.4 | −0.830334 | ||||||||
\(239\) | 13382.2i | 0.234277i | 0.993116 | + | 0.117139i | \(0.0373722\pi\) | ||||
−0.993116 | + | 0.117139i | \(0.962628\pi\) | |||||||
\(240\) | −3122.95 | − | 23611.6i | −0.0542179 | − | 0.409923i | ||||
\(241\) | −310.843 | −0.00535189 | −0.00267595 | − | 0.999996i | \(-0.500852\pi\) | ||||
−0.00267595 | + | 0.999996i | \(0.500852\pi\) | |||||||
\(242\) | 144105.i | 2.46065i | ||||||||
\(243\) | −46738.5 | + | 36087.3i | −0.791521 | + | 0.611142i | ||||
\(244\) | −54105.3 | −0.908783 | ||||||||
\(245\) | − | 5403.61i | − | 0.0900227i | ||||||
\(246\) | 153092. | − | 20248.6i | 2.52978 | − | 0.334599i | ||||
\(247\) | 29807.8 | 0.488580 | ||||||||
\(248\) | − | 16579.7i | − | 0.269571i | ||||||
\(249\) | 2434.81 | + | 18408.7i | 0.0392705 | + | 0.296910i | ||||
\(250\) | −95127.7 | −1.52204 | ||||||||
\(251\) | − | 82720.9i | − | 1.31301i | −0.754322 | − | 0.656505i | \(-0.772034\pi\) | ||
0.754322 | − | 0.656505i | \(-0.227966\pi\) | |||||||
\(252\) | 29448.6 | − | 7928.68i | 0.463729 | − | 0.124853i | ||||
\(253\) | −28166.1 | −0.440033 | ||||||||
\(254\) | 141809.i | 2.19804i | ||||||||
\(255\) | −59223.7 | + | 7833.15i | −0.910784 | + | 0.120464i | ||||
\(256\) | 17320.9 | 0.264297 | ||||||||
\(257\) | 10849.5i | 0.164265i | 0.996621 | + | 0.0821324i | \(0.0261730\pi\) | ||||
−0.996621 | + | 0.0821324i | \(0.973827\pi\) | |||||||
\(258\) | 704.442 | + | 5326.04i | 0.0105829 | + | 0.0800138i | ||||
\(259\) | −24752.7 | −0.368998 | ||||||||
\(260\) | 48588.0i | 0.718758i | ||||||||
\(261\) | −15868.8 | − | 58940.0i | −0.232951 | − | 0.865224i | ||||
\(262\) | 118957. | 1.73296 | ||||||||
\(263\) | − | 40082.3i | − | 0.579484i | −0.957105 | − | 0.289742i | \(-0.906431\pi\) | ||
0.957105 | − | 0.289742i | \(-0.0935695\pi\) | |||||||
\(264\) | −45715.8 | + | 6046.55i | −0.655932 | + | 0.0867561i | ||||
\(265\) | 66988.3 | 0.953910 | ||||||||
\(266\) | 21933.0i | 0.309980i | ||||||||
\(267\) | −3621.73 | − | 27382.7i | −0.0508036 | − | 0.384108i | ||||
\(268\) | −52195.8 | −0.726717 | ||||||||
\(269\) | − | 75313.8i | − | 1.04081i | −0.853921 | − | 0.520403i | \(-0.825782\pi\) | ||
0.853921 | − | 0.520403i | \(-0.174218\pi\) | |||||||
\(270\) | 63905.5 | − | 26605.6i | 0.876618 | − | 0.364960i | ||||
\(271\) | −113072. | −1.53963 | −0.769814 | − | 0.638268i | \(-0.779651\pi\) | ||||
−0.769814 | + | 0.638268i | \(0.779651\pi\) | |||||||
\(272\) | − | 70776.2i | − | 0.956642i | ||||||
\(273\) | 25068.8 | − | 3315.70i | 0.336363 | − | 0.0444887i | ||||
\(274\) | −82296.0 | −1.09617 | ||||||||
\(275\) | − | 73983.4i | − | 0.978292i | ||||||
\(276\) | −3441.64 | − | 26021.0i | −0.0451801 | − | 0.341591i | ||||
\(277\) | −52989.5 | −0.690606 | −0.345303 | − | 0.938491i | \(-0.612224\pi\) | ||||
−0.345303 | + | 0.938491i | \(0.612224\pi\) | |||||||
\(278\) | − | 40109.1i | − | 0.518983i | ||||||
\(279\) | −49691.7 | + | 13378.9i | −0.638374 | + | 0.171874i | ||||
\(280\) | −7614.10 | −0.0971186 | ||||||||
\(281\) | − | 48221.1i | − | 0.610695i | −0.952241 | − | 0.305347i | \(-0.901227\pi\) | ||
0.952241 | − | 0.305347i | \(-0.0987726\pi\) | |||||||
\(282\) | 27587.7 | − | 3648.85i | 0.346910 | − | 0.0458836i | ||||
\(283\) | 63901.6 | 0.797882 | 0.398941 | − | 0.916977i | \(-0.369378\pi\) | ||||
0.398941 | + | 0.916977i | \(0.369378\pi\) | |||||||
\(284\) | − | 35969.4i | − | 0.445960i | ||||||
\(285\) | 3652.81 | + | 27617.6i | 0.0449715 | + | 0.340014i | ||||
\(286\) | −179535. | −2.19491 | ||||||||
\(287\) | 52722.2i | 0.640073i | ||||||||
\(288\) | 30114.0 | + | 111849.i | 0.363065 | + | 1.34849i | ||||
\(289\) | −94003.5 | −1.12551 | ||||||||
\(290\) | 71555.2i | 0.850835i | ||||||||
\(291\) | −30479.2 | + | 4031.29i | −0.359930 | + | 0.0476056i | ||||
\(292\) | 71786.9 | 0.841937 | ||||||||
\(293\) | 76356.1i | 0.889423i | 0.895674 | + | 0.444711i | \(0.146694\pi\) | ||||
−0.895674 | + | 0.444711i | \(0.853306\pi\) | |||||||
\(294\) | 2439.73 | + | 18446.0i | 0.0282259 | + | 0.213406i | ||||
\(295\) | 45577.7 | 0.523731 | ||||||||
\(296\) | 34878.5i | 0.398083i | ||||||||
\(297\) | 55012.4 | + | 132138.i | 0.623660 | + | 1.49801i | ||||
\(298\) | 153089. | 1.72390 | ||||||||
\(299\) | − | 21763.5i | − | 0.243436i | ||||||
\(300\) | 68348.9 | − | 9040.09i | 0.759432 | − | 0.100445i | ||||
\(301\) | −1834.19 | −0.0202447 | ||||||||
\(302\) | 13582.4i | 0.148923i | ||||||||
\(303\) | −1024.47 | − | 7745.65i | −0.0111587 | − | 0.0843670i | ||||
\(304\) | −33004.9 | −0.357134 | ||||||||
\(305\) | − | 41927.6i | − | 0.450713i | ||||||
\(306\) | 198632. | − | 53479.1i | 2.12132 | − | 0.571138i | ||||
\(307\) | 88506.5 | 0.939071 | 0.469535 | − | 0.882914i | \(-0.344421\pi\) | ||||
0.469535 | + | 0.882914i | \(0.344421\pi\) | |||||||
\(308\) | − | 73924.0i | − | 0.779263i | ||||||
\(309\) | −21600.2 | + | 2856.92i | −0.226225 | + | 0.0299214i | ||||
\(310\) | 60327.5 | 0.627757 | ||||||||
\(311\) | − | 23502.0i | − | 0.242987i | −0.992592 | − | 0.121494i | \(-0.961232\pi\) | ||
0.992592 | − | 0.121494i | \(-0.0387684\pi\) | |||||||
\(312\) | −4672.07 | − | 35323.9i | −0.0479954 | − | 0.362877i | ||||
\(313\) | 158727. | 1.62018 | 0.810089 | − | 0.586307i | \(-0.199419\pi\) | ||||
0.810089 | + | 0.586307i | \(0.199419\pi\) | |||||||
\(314\) | 249963.i | 2.53522i | ||||||||
\(315\) | 6144.14 | + | 22820.5i | 0.0619213 | + | 0.229988i | ||||
\(316\) | −45781.3 | −0.458473 | ||||||||
\(317\) | − | 173185.i | − | 1.72342i | −0.507403 | − | 0.861709i | \(-0.669394\pi\) | ||
0.507403 | − | 0.861709i | \(-0.330606\pi\) | |||||||
\(318\) | −228674. | + | 30245.3i | −2.26132 | + | 0.299091i | ||||
\(319\) | −147955. | −1.45395 | ||||||||
\(320\) | − | 93447.4i | − | 0.912573i | ||||||
\(321\) | 6102.82 | + | 46141.3i | 0.0592271 | + | 0.447796i | ||||
\(322\) | 16013.8 | 0.154449 | ||||||||
\(323\) | 82784.5i | 0.793494i | ||||||||
\(324\) | −115352. | + | 66968.8i | −1.09884 | + | 0.637944i | ||||
\(325\) | 57165.7 | 0.541214 | ||||||||
\(326\) | − | 259313.i | − | 2.44000i | ||||||
\(327\) | −162244. | + | 21459.0i | −1.51730 | + | 0.200684i | ||||
\(328\) | 74289.5 | 0.690526 | ||||||||
\(329\) | 9500.68i | 0.0877734i | ||||||||
\(330\) | −22001.2 | − | 166343.i | −0.202031 | − | 1.52749i | ||||
\(331\) | 84106.5 | 0.767668 | 0.383834 | − | 0.923402i | \(-0.374603\pi\) | ||||
0.383834 | + | 0.923402i | \(0.374603\pi\) | |||||||
\(332\) | 41944.7i | 0.380540i | ||||||||
\(333\) | 104536. | − | 28144.9i | 0.942706 | − | 0.253812i | ||||
\(334\) | 78815.7 | 0.706512 | ||||||||
\(335\) | − | 40447.9i | − | 0.360418i | ||||||
\(336\) | −27757.6 | + | 3671.32i | −0.245869 | + | 0.0325195i | ||||
\(337\) | 3077.59 | 0.0270989 | 0.0135494 | − | 0.999908i | \(-0.495687\pi\) | ||||
0.0135494 | + | 0.999908i | \(0.495687\pi\) | |||||||
\(338\) | 33425.1i | 0.292576i | ||||||||
\(339\) | −9761.98 | − | 73806.9i | −0.0849451 | − | 0.642240i | ||||
\(340\) | −134942. | −1.16732 | ||||||||
\(341\) | 124739.i | 1.07274i | ||||||||
\(342\) | −24938.7 | − | 92627.3i | −0.213217 | − | 0.791930i | ||||
\(343\) | −6352.45 | −0.0539949 | ||||||||
\(344\) | 2584.51i | 0.0218405i | ||||||||
\(345\) | 20164.4 | − | 2667.02i | 0.169413 | − | 0.0224072i | ||||
\(346\) | −121099. | −1.01155 | ||||||||
\(347\) | 102480.i | 0.851101i | 0.904935 | + | 0.425551i | \(0.139920\pi\) | ||||
−0.904935 | + | 0.425551i | \(0.860080\pi\) | |||||||
\(348\) | −18078.7 | − | 136687.i | −0.149283 | − | 1.12867i | ||||
\(349\) | 81452.0 | 0.668730 | 0.334365 | − | 0.942444i | \(-0.391478\pi\) | ||||
0.334365 | + | 0.942444i | \(0.391478\pi\) | |||||||
\(350\) | 42063.3i | 0.343374i | ||||||||
\(351\) | −102100. | + | 42507.2i | −0.828731 | + | 0.345023i | ||||
\(352\) | 280772. | 2.26604 | ||||||||
\(353\) | 198402.i | 1.59220i | 0.605167 | + | 0.796099i | \(0.293106\pi\) | ||||
−0.605167 | + | 0.796099i | \(0.706894\pi\) | |||||||
\(354\) | −155586. | + | 20578.4i | −1.24155 | + | 0.164212i | ||||
\(355\) | 27873.6 | 0.221175 | ||||||||
\(356\) | − | 62391.9i | − | 0.492298i | ||||||
\(357\) | 9208.61 | + | 69623.0i | 0.0722533 | + | 0.546281i | ||||
\(358\) | −241498. | −1.88429 | ||||||||
\(359\) | − | 20290.7i | − | 0.157437i | −0.996897 | − | 0.0787186i | \(-0.974917\pi\) | ||
0.996897 | − | 0.0787186i | \(-0.0250829\pi\) | |||||||
\(360\) | 32155.8 | − | 8657.56i | 0.248116 | − | 0.0668022i | ||||
\(361\) | −91716.4 | −0.703773 | ||||||||
\(362\) | 385309.i | 2.94031i | ||||||||
\(363\) | 213318. | − | 28214.2i | 1.61888 | − | 0.214119i | ||||
\(364\) | 57119.8 | 0.431106 | ||||||||
\(365\) | 55629.5i | 0.417561i | ||||||||
\(366\) | 18930.3 | + | 143126.i | 0.141318 | + | 1.06845i | ||||
\(367\) | −196750. | −1.46077 | −0.730385 | − | 0.683036i | \(-0.760659\pi\) | ||||
−0.730385 | + | 0.683036i | \(0.760659\pi\) | |||||||
\(368\) | 24097.7i | 0.177943i | ||||||||
\(369\) | −59947.4 | − | 222656.i | −0.440269 | − | 1.63524i | ||||
\(370\) | −126910. | −0.927028 | ||||||||
\(371\) | − | 78751.1i | − | 0.572148i | ||||||
\(372\) | −115239. | + | 15242.0i | −0.832751 | + | 0.110143i | ||||
\(373\) | −144072. | −1.03553 | −0.517765 | − | 0.855523i | \(-0.673236\pi\) | ||||
−0.517765 | + | 0.855523i | \(0.673236\pi\) | |||||||
\(374\) | − | 498618.i | − | 3.56472i | ||||||
\(375\) | 18624.9 | + | 140816.i | 0.132444 | + | 1.00136i | ||||
\(376\) | 13387.2 | 0.0946921 | ||||||||
\(377\) | − | 114322.i | − | 0.804356i | ||||||
\(378\) | −31277.3 | − | 75126.9i | −0.218900 | − | 0.525789i | ||||
\(379\) | 134879. | 0.939004 | 0.469502 | − | 0.882931i | \(-0.344433\pi\) | ||||
0.469502 | + | 0.882931i | \(0.344433\pi\) | |||||||
\(380\) | 62927.3i | 0.435785i | ||||||||
\(381\) | 209918. | − | 27764.5i | 1.44610 | − | 0.191267i | ||||
\(382\) | 347831. | 2.38365 | ||||||||
\(383\) | − | 10393.5i | − | 0.0708540i | −0.999372 | − | 0.0354270i | \(-0.988721\pi\) | ||
0.999372 | − | 0.0354270i | \(-0.0112791\pi\) | |||||||
\(384\) | 15190.4 | + | 114849.i | 0.103017 | + | 0.778873i | ||||
\(385\) | 57285.6 | 0.386477 | ||||||||
\(386\) | 14439.4i | 0.0969112i | ||||||||
\(387\) | 7746.15 | − | 2085.55i | 0.0517207 | − | 0.0139251i | ||||
\(388\) | −69447.5 | −0.461310 | ||||||||
\(389\) | − | 22075.3i | − | 0.145884i | −0.997336 | − | 0.0729421i | \(-0.976761\pi\) | ||
0.997336 | − | 0.0729421i | \(-0.0232388\pi\) | |||||||
\(390\) | 128531. | − | 17000.0i | 0.845041 | − | 0.111768i | ||||
\(391\) | 60443.2 | 0.395361 | ||||||||
\(392\) | 8951.08i | 0.0582510i | ||||||||
\(393\) | −23290.5 | − | 176091.i | −0.150797 | − | 1.14012i | ||||
\(394\) | 12263.4 | 0.0789987 | ||||||||
\(395\) | − | 35477.1i | − | 0.227381i | ||||||
\(396\) | 84054.8 | + | 312196.i | 0.536009 | + | 1.99084i | ||||
\(397\) | 39063.7 | 0.247852 | 0.123926 | − | 0.992291i | \(-0.460452\pi\) | ||||
0.123926 | + | 0.992291i | \(0.460452\pi\) | |||||||
\(398\) | − | 156585.i | − | 0.988518i | ||||||
\(399\) | 32467.1 | − | 4294.22i | 0.203938 | − | 0.0269736i | ||||
\(400\) | −63297.0 | −0.395607 | ||||||||
\(401\) | − | 42017.8i | − | 0.261303i | −0.991428 | − | 0.130652i | \(-0.958293\pi\) | ||
0.991428 | − | 0.130652i | \(-0.0417069\pi\) | |||||||
\(402\) | 18262.2 | + | 138074.i | 0.113006 | + | 0.854399i | ||||
\(403\) | −96384.0 | −0.593465 | ||||||||
\(404\) | − | 17648.6i | − | 0.108130i | ||||||
\(405\) | −51895.9 | − | 89389.4i | −0.316390 | − | 0.544975i | ||||
\(406\) | 84119.9 | 0.510325 | ||||||||
\(407\) | − | 262413.i | − | 1.58415i | ||||||
\(408\) | 98104.1 | − | 12975.6i | 0.589341 | − | 0.0779485i | ||||
\(409\) | 279559. | 1.67120 | 0.835598 | − | 0.549342i | \(-0.185122\pi\) | ||||
0.835598 | + | 0.549342i | \(0.185122\pi\) | |||||||
\(410\) | 270313.i | 1.60805i | ||||||||
\(411\) | 16112.6 | + | 121822.i | 0.0953855 | + | 0.721176i | ||||
\(412\) | −49216.5 | −0.289945 | ||||||||
\(413\) | − | 53580.9i | − | 0.314130i | ||||||
\(414\) | −67629.6 | + | 18208.4i | −0.394581 | + | 0.106236i | ||||
\(415\) | −32504.0 | −0.188730 | ||||||||
\(416\) | 216947.i | 1.25363i | ||||||||
\(417\) | −59373.0 | + | 7852.90i | −0.341442 | + | 0.0451604i | ||||
\(418\) | −232519. | −1.33078 | ||||||||
\(419\) | 230293.i | 1.31175i | 0.754868 | + | 0.655876i | \(0.227701\pi\) | ||||
−0.754868 | + | 0.655876i | \(0.772299\pi\) | |||||||
\(420\) | 6999.77 | + | 52922.8i | 0.0396813 | + | 0.300016i | ||||
\(421\) | −50251.7 | −0.283522 | −0.141761 | − | 0.989901i | \(-0.545276\pi\) | ||||
−0.141761 | + | 0.989901i | \(0.545276\pi\) | |||||||
\(422\) | − | 364279.i | − | 2.04555i | ||||||
\(423\) | −10802.7 | − | 40123.3i | −0.0603742 | − | 0.224241i | ||||
\(424\) | −110966. | −0.617247 | ||||||||
\(425\) | 158765.i | 0.878975i | ||||||||
\(426\) | −95150.3 | + | 12584.9i | −0.524314 | + | 0.0693477i | ||||
\(427\) | −49289.8 | −0.270335 | ||||||||
\(428\) | 105134.i | 0.573925i | ||||||||
\(429\) | 35150.9 | + | 265763.i | 0.190995 | + | 1.44405i | ||||
\(430\) | −9404.11 | −0.0508605 | ||||||||
\(431\) | − | 89839.7i | − | 0.483631i | −0.970322 | − | 0.241815i | \(-0.922257\pi\) | ||
0.970322 | − | 0.241815i | \(-0.0777428\pi\) | |||||||
\(432\) | 113051. | − | 47066.3i | 0.605771 | − | 0.252199i | ||||
\(433\) | −204051. | −1.08833 | −0.544167 | − | 0.838977i | \(-0.683154\pi\) | ||||
−0.544167 | + | 0.838977i | \(0.683154\pi\) | |||||||
\(434\) | − | 70920.6i | − | 0.376524i | ||||||
\(435\) | 105922. | − | 14009.7i | 0.559769 | − | 0.0740372i | ||||
\(436\) | −369675. | −1.94468 | ||||||||
\(437\) | − | 28186.3i | − | 0.147596i | ||||||
\(438\) | −25116.8 | − | 189899.i | −0.130923 | − | 0.989862i | ||||
\(439\) | −195110. | −1.01239 | −0.506197 | − | 0.862418i | \(-0.668949\pi\) | ||||
−0.506197 | + | 0.862418i | \(0.668949\pi\) | |||||||
\(440\) | − | 80719.8i | − | 0.416941i | ||||||
\(441\) | 26827.7 | − | 7223.01i | 0.137945 | − | 0.0371399i | ||||
\(442\) | 385274. | 1.97208 | ||||||||
\(443\) | 302752.i | 1.54269i | 0.636416 | + | 0.771346i | \(0.280416\pi\) | ||||
−0.636416 | + | 0.771346i | \(0.719584\pi\) | |||||||
\(444\) | 242428. | − | 32064.4i | 1.22975 | − | 0.162651i | ||||
\(445\) | 48349.1 | 0.244157 | ||||||||
\(446\) | − | 66521.5i | − | 0.334420i | ||||||
\(447\) | −29973.1 | − | 226616.i | −0.150009 | − | 1.13416i | ||||
\(448\) | −109856. | −0.547354 | ||||||||
\(449\) | 162997.i | 0.808512i | 0.914646 | + | 0.404256i | \(0.132470\pi\) | ||||
−0.914646 | + | 0.404256i | \(0.867530\pi\) | |||||||
\(450\) | −47827.8 | − | 177642.i | −0.236187 | − | 0.877242i | ||||
\(451\) | −558927. | −2.74790 | ||||||||
\(452\) | − | 168171.i | − | 0.823139i | ||||||
\(453\) | 20105.9 | − | 2659.28i | 0.0979774 | − | 0.0129589i | ||||
\(454\) | 440486. | 2.13708 | ||||||||
\(455\) | 44263.6i | 0.213808i | ||||||||
\(456\) | −6050.88 | − | 45748.6i | −0.0290997 | − | 0.220013i | ||||
\(457\) | −156346. | −0.748607 | −0.374304 | − | 0.927306i | \(-0.622118\pi\) | ||||
−0.374304 | + | 0.927306i | \(0.622118\pi\) | |||||||
\(458\) | − | 94669.9i | − | 0.451316i | ||||||
\(459\) | −118054. | − | 283561.i | −0.560346 | − | 1.34593i | ||||
\(460\) | 45944.9 | 0.217131 | ||||||||
\(461\) | 140167.i | 0.659543i | 0.944061 | + | 0.329772i | \(0.106972\pi\) | ||||
−0.944061 | + | 0.329772i | \(0.893028\pi\) | |||||||
\(462\) | −195552. | + | 25864.5i | −0.916176 | + | 0.121177i | ||||
\(463\) | 46832.0 | 0.218464 | 0.109232 | − | 0.994016i | \(-0.465161\pi\) | ||||
0.109232 | + | 0.994016i | \(0.465161\pi\) | |||||||
\(464\) | 126584.i | 0.587954i | ||||||||
\(465\) | −11811.4 | − | 89302.0i | −0.0546256 | − | 0.413005i | ||||
\(466\) | 352545. | 1.62347 | ||||||||
\(467\) | − | 364198.i | − | 1.66995i | −0.550285 | − | 0.834977i | \(-0.685481\pi\) | ||
0.550285 | − | 0.834977i | \(-0.314519\pi\) | |||||||
\(468\) | −241228. | + | 64947.7i | −1.10138 | + | 0.296532i | ||||
\(469\) | −47550.2 | −0.216176 | ||||||||
\(470\) | 48711.1i | 0.220512i | ||||||||
\(471\) | 370017. | − | 48939.9i | 1.66794 | − | 0.220608i | ||||
\(472\) | −75499.5 | −0.338891 | ||||||||
\(473\) | − | 19444.9i | − | 0.0869128i | ||||||
\(474\) | 16018.0 | + | 121106.i | 0.0712936 | + | 0.539026i | ||||
\(475\) | 74036.4 | 0.328139 | ||||||||
\(476\) | 158637.i | 0.700151i | ||||||||
\(477\) | 89543.4 | + | 332581.i | 0.393547 | + | 1.46171i | ||||
\(478\) | 80659.7 | 0.353021 | ||||||||
\(479\) | 139602.i | 0.608445i | 0.952601 | + | 0.304223i | \(0.0983967\pi\) | ||||
−0.952601 | + | 0.304223i | \(0.901603\pi\) | |||||||
\(480\) | −201007. | + | 26585.9i | −0.872426 | + | 0.115390i | ||||
\(481\) | 202762. | 0.876387 | ||||||||
\(482\) | 1873.58i | 0.00806451i | ||||||||
\(483\) | −3135.33 | − | 23705.1i | −0.0134397 | − | 0.101613i | ||||
\(484\) | 486048. | 2.07486 | ||||||||
\(485\) | − | 53816.7i | − | 0.228788i | ||||||
\(486\) | 217513. | + | 281712.i | 0.920900 | + | 1.19270i | ||||
\(487\) | −122130. | −0.514950 | −0.257475 | − | 0.966285i | \(-0.582891\pi\) | ||||
−0.257475 | + | 0.966285i | \(0.582891\pi\) | |||||||
\(488\) | 69453.1i | 0.291643i | ||||||||
\(489\) | −383858. | + | 50770.6i | −1.60529 | + | 0.212322i | ||||
\(490\) | −32569.8 | −0.135651 | ||||||||
\(491\) | 239214.i | 0.992257i | 0.868249 | + | 0.496129i | \(0.165246\pi\) | ||||
−0.868249 | + | 0.496129i | \(0.834754\pi\) | |||||||
\(492\) | −68295.7 | − | 516360.i | −0.282139 | − | 2.13315i | ||||
\(493\) | 317505. | 1.30634 | ||||||||
\(494\) | − | 179664.i | − | 0.736218i | ||||||
\(495\) | −241929. | + | 65136.2i | −0.987363 | + | 0.265835i | ||||
\(496\) | 106722. | 0.433800 | ||||||||
\(497\) | − | 32768.0i | − | 0.132659i | ||||||
\(498\) | 110957. | − | 14675.6i | 0.447400 | − | 0.0591748i | ||||
\(499\) | 28578.8 | 0.114774 | 0.0573869 | − | 0.998352i | \(-0.481723\pi\) | ||||
0.0573869 | + | 0.998352i | \(0.481723\pi\) | |||||||
\(500\) | 320853.i | 1.28341i | ||||||||
\(501\) | −15431.2 | − | 116670.i | −0.0614787 | − | 0.464818i | ||||
\(502\) | −498593. | −1.97851 | ||||||||
\(503\) | 394825.i | 1.56052i | 0.625457 | + | 0.780258i | \(0.284912\pi\) | ||||
−0.625457 | + | 0.780258i | \(0.715088\pi\) | |||||||
\(504\) | −10177.8 | − | 37802.2i | −0.0400675 | − | 0.148818i | ||||
\(505\) | 13676.4 | 0.0536276 | ||||||||
\(506\) | 169769.i | 0.663065i | ||||||||
\(507\) | 49478.8 | − | 6544.25i | 0.192488 | − | 0.0254591i | ||||
\(508\) | 478301. | 1.85342 | ||||||||
\(509\) | − | 370203.i | − | 1.42891i | −0.699681 | − | 0.714455i | \(-0.746675\pi\) | ||
0.699681 | − | 0.714455i | \(-0.253325\pi\) | |||||||
\(510\) | 47213.6 | + | 356965.i | 0.181521 | + | 1.37242i | ||||
\(511\) | 65397.7 | 0.250450 | ||||||||
\(512\) | − | 310355.i | − | 1.18391i | ||||||
\(513\) | −132232. | + | 55051.9i | −0.502462 | + | 0.209188i | ||||
\(514\) | 65394.5 | 0.247523 | ||||||||
\(515\) | − | 38139.1i | − | 0.143799i | ||||||
\(516\) | 17964.0 | − | 2375.99i | 0.0674690 | − | 0.00892370i | ||||
\(517\) | −100720. | −0.376821 | ||||||||
\(518\) | 149195.i | 0.556025i | ||||||||
\(519\) | 23709.8 | + | 179262.i | 0.0880226 | + | 0.665508i | ||||
\(520\) | 62370.8 | 0.230661 | ||||||||
\(521\) | − | 319934.i | − | 1.17865i | −0.807896 | − | 0.589325i | \(-0.799394\pi\) | ||
0.807896 | − | 0.589325i | \(-0.200606\pi\) | |||||||
\(522\) | −355255. | + | 95648.0i | −1.30376 | + | 0.351022i | ||||
\(523\) | 365694. | 1.33695 | 0.668474 | − | 0.743736i | \(-0.266948\pi\) | ||||
0.668474 | + | 0.743736i | \(0.266948\pi\) | |||||||
\(524\) | − | 401227.i | − | 1.46126i | ||||||
\(525\) | 62265.7 | − | 8235.50i | 0.225907 | − | 0.0298794i | ||||
\(526\) | −241592. | −0.873196 | ||||||||
\(527\) | − | 267685.i | − | 0.963835i | ||||||
\(528\) | −38921.0 | − | 294268.i | −0.139610 | − | 1.05554i | ||||
\(529\) | 259261. | 0.926460 | ||||||||
\(530\) | − | 403766.i | − | 1.43740i | ||||||
\(531\) | 60923.8 | + | 226283.i | 0.216072 | + | 0.802532i | ||||
\(532\) | 73976.9 | 0.261380 | ||||||||
\(533\) | − | 431873.i | − | 1.52020i | ||||||
\(534\) | −165046. | + | 21829.7i | −0.578793 | + | 0.0765534i | ||||
\(535\) | −81471.0 | −0.284640 | ||||||||
\(536\) | 67001.9i | 0.233216i | ||||||||
\(537\) | 47282.6 | + | 357487.i | 0.163966 | + | 1.23969i | ||||
\(538\) | −453947. | −1.56834 | ||||||||
\(539\) | − | 67344.6i | − | 0.231806i | ||||||
\(540\) | −89737.0 | − | 215545.i | −0.307740 | − | 0.739179i | ||||
\(541\) | −398244. | −1.36068 | −0.680339 | − | 0.732898i | \(-0.738167\pi\) | ||||
−0.680339 | + | 0.732898i | \(0.738167\pi\) | |||||||
\(542\) | 681530.i | 2.31999i | ||||||||
\(543\) | 570369. | − | 75439.1i | 1.93444 | − | 0.255857i | ||||
\(544\) | −602523. | −2.03599 | ||||||||
\(545\) | − | 286471.i | − | 0.964468i | ||||||
\(546\) | −19985.0 | − | 151100.i | −0.0670378 | − | 0.506849i | ||||
\(547\) | 310182. | 1.03667 | 0.518336 | − | 0.855177i | \(-0.326552\pi\) | ||||
0.518336 | + | 0.855177i | \(0.326552\pi\) | |||||||
\(548\) | 277573.i | 0.924308i | ||||||||
\(549\) | 208161. | − | 56044.7i | 0.690644 | − | 0.185947i | ||||
\(550\) | −445928. | −1.47414 | ||||||||
\(551\) | − | 148061.i | − | 0.487683i | ||||||
\(552\) | −33402.3 | + | 4417.91i | −0.109622 | + | 0.0144990i | ||||
\(553\) | −41706.7 | −0.136382 | ||||||||
\(554\) | 319389.i | 1.04064i | ||||||||
\(555\) | 24847.5 | + | 187864.i | 0.0806673 | + | 0.609897i | ||||
\(556\) | −135283. | −0.437615 | ||||||||
\(557\) | 446126.i | 1.43796i | 0.695030 | + | 0.718980i | \(0.255391\pi\) | ||||
−0.695030 | + | 0.718980i | \(0.744609\pi\) | |||||||
\(558\) | 80639.8 | + | 299512.i | 0.258989 | + | 0.961935i | ||||
\(559\) | 15024.8 | 0.0480821 | ||||||||
\(560\) | − | 49011.2i | − | 0.156286i | ||||||
\(561\) | −738099. | + | 97623.7i | −2.34525 | + | 0.310191i | ||||
\(562\) | −290648. | −0.920226 | ||||||||
\(563\) | − | 489563.i | − | 1.54451i | −0.635310 | − | 0.772257i | \(-0.719128\pi\) | ||
0.635310 | − | 0.772257i | \(-0.280872\pi\) | |||||||
\(564\) | −12307.1 | − | 93049.5i | −0.0386898 | − | 0.292520i | ||||
\(565\) | 130320. | 0.408238 | ||||||||
\(566\) | − | 385161.i | − | 1.20229i | ||||||
\(567\) | −105086. | + | 61008.4i | −0.326872 | + | 0.189768i | ||||
\(568\) | −46172.6 | −0.143116 | ||||||||
\(569\) | 444748.i | 1.37369i | 0.726803 | + | 0.686846i | \(0.241005\pi\) | ||||
−0.726803 | + | 0.686846i | \(0.758995\pi\) | |||||||
\(570\) | 166463. | − | 22017.0i | 0.512350 | − | 0.0677654i | ||||
\(571\) | 48894.3 | 0.149964 | 0.0749818 | − | 0.997185i | \(-0.476110\pi\) | ||||
0.0749818 | + | 0.997185i | \(0.476110\pi\) | |||||||
\(572\) | 605547.i | 1.85079i | ||||||||
\(573\) | −68101.4 | − | 514890.i | −0.207418 | − | 1.56821i | ||||
\(574\) | 317778. | 0.964495 | ||||||||
\(575\) | − | 54055.9i | − | 0.163496i | ||||||
\(576\) | 463945. | − | 124911.i | 1.39837 | − | 0.376493i | ||||
\(577\) | −80474.7 | −0.241717 | −0.120859 | − | 0.992670i | \(-0.538565\pi\) | ||||
−0.120859 | + | 0.992670i | \(0.538565\pi\) | |||||||
\(578\) | 566598.i | 1.69597i | ||||||||
\(579\) | 21374.4 | − | 2827.06i | 0.0637584 | − | 0.00843293i | ||||
\(580\) | 241346. | 0.717438 | ||||||||
\(581\) | 38211.5i | 0.113199i | ||||||||
\(582\) | 24298.2 | + | 183710.i | 0.0717347 | + | 0.542360i | ||||
\(583\) | 834868. | 2.45630 | ||||||||
\(584\) | − | 92150.4i | − | 0.270191i | ||||||
\(585\) | −50329.7 | − | 186934.i | −0.147066 | − | 0.546232i | ||||
\(586\) | 460229. | 1.34023 | ||||||||
\(587\) | 54845.0i | 0.159170i | 0.996828 | + | 0.0795849i | \(0.0253595\pi\) | ||||
−0.996828 | + | 0.0795849i | \(0.974641\pi\) | |||||||
\(588\) | 62215.7 | − | 8228.89i | 0.179947 | − | 0.0238005i | ||||
\(589\) | −124829. | −0.359819 | ||||||||
\(590\) | − | 274715.i | − | 0.789185i | ||||||
\(591\) | −2401.04 | − | 18153.4i | −0.00687424 | − | 0.0519737i | ||||
\(592\) | −224509. | −0.640605 | ||||||||
\(593\) | 192797.i | 0.548265i | 0.961692 | + | 0.274133i | \(0.0883907\pi\) | ||||
−0.961692 | + | 0.274133i | \(0.911609\pi\) | |||||||
\(594\) | 796447. | − | 331582.i | 2.25727 | − | 0.939763i | ||||
\(595\) | −122932. | −0.347242 | ||||||||
\(596\) | − | 516349.i | − | 1.45362i | ||||||
\(597\) | −231791. | + | 30657.6i | −0.650352 | + | 0.0860180i | ||||
\(598\) | −131177. | −0.366823 | ||||||||
\(599\) | 466565.i | 1.30035i | 0.759786 | + | 0.650173i | \(0.225304\pi\) | ||||
−0.759786 | + | 0.650173i | \(0.774696\pi\) | |||||||
\(600\) | −11604.4 | − | 87737.2i | −0.0322346 | − | 0.243714i | ||||
\(601\) | 125070. | 0.346261 | 0.173130 | − | 0.984899i | \(-0.444612\pi\) | ||||
0.173130 | + | 0.984899i | \(0.444612\pi\) | |||||||
\(602\) | 11055.4i | 0.0305058i | ||||||||
\(603\) | 200814. | − | 54066.7i | 0.552280 | − | 0.148695i | ||||
\(604\) | 45811.6 | 0.125575 | ||||||||
\(605\) | 376652.i | 1.02903i | ||||||||
\(606\) | −46686.2 | + | 6174.89i | −0.127129 | + | 0.0168145i | ||||
\(607\) | −385152. | −1.04533 | −0.522667 | − | 0.852537i | \(-0.675063\pi\) | ||||
−0.522667 | + | 0.852537i | \(0.675063\pi\) | |||||||
\(608\) | 280973.i | 0.760076i | ||||||||
\(609\) | −16469.7 | − | 124522.i | −0.0444070 | − | 0.335746i | ||||
\(610\) | −252715. | −0.679158 | ||||||||
\(611\) | − | 77824.8i | − | 0.208466i | ||||||
\(612\) | −180378. | − | 669958.i | −0.481593 | − | 1.78873i | ||||
\(613\) | −135252. | −0.359933 | −0.179967 | − | 0.983673i | \(-0.557599\pi\) | ||||
−0.179967 | + | 0.983673i | \(0.557599\pi\) | |||||||
\(614\) | − | 533464.i | − | 1.41504i | ||||||
\(615\) | 400141. | − | 52924.1i | 1.05794 | − | 0.139928i | ||||
\(616\) | −94893.7 | −0.250078 | ||||||||
\(617\) | − | 378025.i | − | 0.993003i | −0.868036 | − | 0.496502i | \(-0.834618\pi\) | ||
0.868036 | − | 0.496502i | \(-0.165382\pi\) | |||||||
\(618\) | 17219.8 | + | 130193.i | 0.0450871 | + | 0.340888i | ||||
\(619\) | −286244. | −0.747059 | −0.373529 | − | 0.927618i | \(-0.621853\pi\) | ||||
−0.373529 | + | 0.927618i | \(0.621853\pi\) | |||||||
\(620\) | − | 203476.i | − | 0.529335i | ||||||
\(621\) | 40194.8 | + | 96546.3i | 0.104229 | + | 0.250353i | ||||
\(622\) | −141656. | −0.366146 | ||||||||
\(623\) | − | 56838.9i | − | 0.146443i | ||||||
\(624\) | 227376. | − | 30073.6i | 0.583950 | − | 0.0772354i | ||||
\(625\) | −13129.4 | −0.0336112 | ||||||||
\(626\) | − | 956713.i | − | 2.44137i | ||||||
\(627\) | 45524.6 | + | 344195.i | 0.115801 | + | 0.875528i | ||||
\(628\) | 843091. | 2.13774 | ||||||||
\(629\) | 563125.i | 1.42332i | ||||||||
\(630\) | 137549. | − | 37033.2i | 0.346557 | − | 0.0933062i | ||||
\(631\) | −104005. | −0.261214 | −0.130607 | − | 0.991434i | \(-0.541693\pi\) | ||||
−0.130607 | + | 0.991434i | \(0.541693\pi\) | |||||||
\(632\) | 58767.9i | 0.147132i | ||||||||
\(633\) | −539238. | + | 71321.7i | −1.34578 | + | 0.177998i | ||||
\(634\) | −1.04385e6 | −2.59694 | ||||||||
\(635\) | 370648.i | 0.919210i | ||||||||
\(636\) | 102013. | + | 771286.i | 0.252198 | + | 1.90678i | ||||
\(637\) | 52036.0 | 0.128241 | ||||||||
\(638\) | 891785.i | 2.19088i | ||||||||
\(639\) | 37258.7 | + | 138386.i | 0.0912485 | + | 0.338914i | ||||
\(640\) | −202788. | −0.495088 | ||||||||
\(641\) | − | 313789.i | − | 0.763699i | −0.924224 | − | 0.381850i | \(-0.875287\pi\) | ||
0.924224 | − | 0.381850i | \(-0.124713\pi\) | |||||||
\(642\) | 278112. | − | 36784.2i | 0.674761 | − | 0.0892465i | ||||
\(643\) | −17439.4 | −0.0421803 | −0.0210902 | − | 0.999778i | \(-0.506714\pi\) | ||||
−0.0210902 | + | 0.999778i | \(0.506714\pi\) | |||||||
\(644\) | − | 54012.5i | − | 0.130234i | ||||||
\(645\) | 1841.22 | + | 13920.8i | 0.00442573 | + | 0.0334614i | ||||
\(646\) | 498976. | 1.19568 | ||||||||
\(647\) | 470170.i | 1.12317i | 0.827419 | + | 0.561586i | \(0.189808\pi\) | ||||
−0.827419 | + | 0.561586i | \(0.810192\pi\) | |||||||
\(648\) | 85965.5 | + | 148074.i | 0.204727 | + | 0.352637i | ||||
\(649\) | 568030. | 1.34860 | ||||||||
\(650\) | − | 344561.i | − | 0.815529i | ||||||
\(651\) | −104983. | + | 13885.4i | −0.247717 | + | 0.0327641i | ||||
\(652\) | −874629. | −2.05745 | ||||||||
\(653\) | − | 426505.i | − | 1.00022i | −0.865961 | − | 0.500112i | \(-0.833292\pi\) | ||
0.865961 | − | 0.500112i | \(-0.166708\pi\) | |||||||
\(654\) | 129342. | + | 977908.i | 0.302401 | + | 2.28635i | ||||
\(655\) | 310921. | 0.724716 | ||||||||
\(656\) | 478194.i | 1.11121i | ||||||||
\(657\) | −276188. | + | 74360.1i | −0.639843 | + | 0.172270i | ||||
\(658\) | 57264.5 | 0.132262 | ||||||||
\(659\) | − | 201868.i | − | 0.464833i | −0.972616 | − | 0.232416i | \(-0.925337\pi\) | ||
0.972616 | − | 0.232416i | \(-0.0746632\pi\) | |||||||
\(660\) | −561054. | + | 74207.1i | −1.28800 | + | 0.170356i | ||||
\(661\) | −64778.0 | −0.148260 | −0.0741301 | − | 0.997249i | \(-0.523618\pi\) | ||||
−0.0741301 | + | 0.997249i | \(0.523618\pi\) | |||||||
\(662\) | − | 506944.i | − | 1.15676i | ||||||
\(663\) | −75432.2 | − | 570316.i | −0.171605 | − | 1.29744i | ||||
\(664\) | 53843.0 | 0.122122 | ||||||||
\(665\) | 57326.7i | 0.129632i | ||||||||
\(666\) | −169641. | − | 630079.i | −0.382457 | − | 1.42052i | ||||
\(667\) | −108103. | −0.242989 | ||||||||
\(668\) | − | 265835.i | − | 0.595743i | ||||||
\(669\) | −98470.9 | + | 13024.1i | −0.220017 | + | 0.0291002i | ||||
\(670\) | −243796. | −0.543096 | ||||||||
\(671\) | − | 522539.i | − | 1.16058i | ||||||
\(672\) | 31254.3 | + | 236302.i | 0.0692103 | + | 0.523275i | ||||
\(673\) | −417567. | −0.921925 | −0.460963 | − | 0.887420i | \(-0.652496\pi\) | ||||
−0.460963 | + | 0.887420i | \(0.652496\pi\) | |||||||
\(674\) | − | 18549.9i | − | 0.0408340i | ||||||
\(675\) | −253596. | + | 105579.i | −0.556590 | + | 0.231724i | ||||
\(676\) | 112738. | 0.246705 | ||||||||
\(677\) | − | 291796.i | − | 0.636652i | −0.947981 | − | 0.318326i | \(-0.896879\pi\) | ||
0.947981 | − | 0.318326i | \(-0.103121\pi\) | |||||||
\(678\) | −444864. | + | 58839.4i | −0.967761 | + | 0.128000i | ||||
\(679\) | −63266.5 | −0.137225 | ||||||||
\(680\) | 173221.i | 0.374613i | ||||||||
\(681\) | −86242.2 | − | 652047.i | −0.185963 | − | 1.40600i | ||||
\(682\) | 751855. | 1.61646 | ||||||||
\(683\) | − | 493655.i | − | 1.05823i | −0.848549 | − | 0.529117i | \(-0.822523\pi\) | ||
0.848549 | − | 0.529117i | \(-0.177477\pi\) | |||||||
\(684\) | −312419. | + | 84115.0i | −0.667768 | + | 0.179788i | ||||
\(685\) | −215099. | −0.458413 | ||||||||
\(686\) | 38288.8i | 0.0813623i | ||||||||
\(687\) | −140139. | + | 18535.3i | −0.296923 | + | 0.0392722i | ||||
\(688\) | −16636.2 | −0.0351462 | ||||||||
\(689\) | 645089.i | 1.35888i | ||||||||
\(690\) | −16075.2 | − | 121539.i | −0.0337643 | − | 0.255280i | ||||
\(691\) | −56687.4 | −0.118722 | −0.0593609 | − | 0.998237i | \(-0.518906\pi\) | ||||
−0.0593609 | + | 0.998237i | \(0.518906\pi\) | |||||||
\(692\) | 408452.i | 0.852959i | ||||||||
\(693\) | 76573.8 | + | 284410.i | 0.159446 | + | 0.592213i | ||||
\(694\) | 617690. | 1.28248 | ||||||||
\(695\) | − | 104834.i | − | 0.217036i | ||||||
\(696\) | −175460. | + | 23207.1i | −0.362210 | + | 0.0479073i | ||||
\(697\) | 1.19943e6 | 2.46894 | ||||||||
\(698\) | − | 490944.i | − | 1.00768i | ||||||
\(699\) | −69024.3 | − | 521868.i | −0.141269 | − | 1.06809i | ||||
\(700\) | 141874. | 0.289538 | ||||||||
\(701\) | 441765.i | 0.898992i | 0.893282 | + | 0.449496i | \(0.148396\pi\) | ||||
−0.893282 | + | 0.449496i | \(0.851604\pi\) | |||||||
\(702\) | 256208. | + | 615401.i | 0.519899 | + | 1.24877i | ||||
\(703\) | 262601. | 0.531355 | ||||||||
\(704\) | − | 1.16463e6i | − | 2.34985i | ||||||
\(705\) | 72106.5 | − | 9537.08i | 0.145076 | − | 0.0191883i | ||||
\(706\) | 1.19585e6 | 2.39921 | ||||||||
\(707\) | − | 16077.9i | − | 0.0321654i | ||||||
\(708\) | 69408.0 | + | 524770.i | 0.138466 | + | 1.04689i | ||||
\(709\) | −590139. | −1.17398 | −0.586992 | − | 0.809593i | \(-0.699688\pi\) | ||||
−0.586992 | + | 0.809593i | \(0.699688\pi\) | |||||||
\(710\) | − | 168005.i | − | 0.333278i | ||||||
\(711\) | 176136. | − | 47422.4i | 0.348424 | − | 0.0938089i | ||||
\(712\) | −80090.4 | −0.157987 | ||||||||
\(713\) | 91140.8i | 0.179281i | ||||||||
\(714\) | 419646. | − | 55504.0i | 0.823165 | − | 0.108875i | ||||
\(715\) | −469255. | −0.917902 | ||||||||
\(716\) | 814542.i | 1.58887i | ||||||||
\(717\) | −15792.2 | − | 119400.i | −0.0307189 | − | 0.232255i | ||||
\(718\) | −122300. | −0.237234 | ||||||||
\(719\) | 918202.i | 1.77615i | 0.459695 | + | 0.888077i | \(0.347959\pi\) | ||||
−0.459695 | + | 0.888077i | \(0.652041\pi\) | |||||||
\(720\) | 55727.8 | + | 206984.i | 0.107500 | + | 0.399274i | ||||
\(721\) | −44836.1 | −0.0862497 | ||||||||
\(722\) | 552812.i | 1.06048i | ||||||||
\(723\) | 2773.44 | − | 366.825i | 0.00530569 | − | 0.000701750i | ||||
\(724\) | 1.29960e6 | 2.47931 | ||||||||
\(725\) | − | 283953.i | − | 0.540220i | ||||||
\(726\) | −170058. | − | 1.28575e6i | −0.322645 | − | 2.43940i | ||||
\(727\) | −242969. | −0.459708 | −0.229854 | − | 0.973225i | \(-0.573825\pi\) | ||||
−0.229854 | + | 0.973225i | \(0.573825\pi\) | |||||||
\(728\) | − | 73322.7i | − | 0.138349i | ||||||
\(729\) | 374428. | − | 377138.i | 0.704553 | − | 0.709651i | ||||
\(730\) | 335302. | 0.629202 | ||||||||
\(731\) | 41727.9i | 0.0780893i | ||||||||
\(732\) | 482744. | − | 63849.5i | 0.900937 | − | 0.119161i | ||||
\(733\) | −145455. | −0.270721 | −0.135361 | − | 0.990796i | \(-0.543219\pi\) | ||||
−0.135361 | + | 0.990796i | \(0.543219\pi\) | |||||||
\(734\) | 1.18589e6i | 2.20116i | ||||||||
\(735\) | 6376.78 | + | 48212.6i | 0.0118039 | + | 0.0892454i | ||||
\(736\) | 205146. | 0.378710 | ||||||||
\(737\) | − | 504097.i | − | 0.928067i | ||||||
\(738\) | −1.34204e6 | + | 361327.i | −2.46407 | + | 0.663419i | ||||
\(739\) | −971847. | −1.77955 | −0.889773 | − | 0.456404i | \(-0.849137\pi\) | ||||
−0.889773 | + | 0.456404i | \(0.849137\pi\) | |||||||
\(740\) | 428051.i | 0.781685i | ||||||||
\(741\) | −265954. | + | 35176.1i | −0.484362 | + | 0.0640636i | ||||
\(742\) | −474665. | −0.862143 | ||||||||
\(743\) | − | 26014.8i | − | 0.0471241i | −0.999722 | − | 0.0235620i | \(-0.992499\pi\) | ||
0.999722 | − | 0.0235620i | \(-0.00750072\pi\) | |||||||
\(744\) | 19565.6 | + | 147929.i | 0.0353466 | + | 0.267244i | ||||
\(745\) | 400133. | 0.720927 | ||||||||
\(746\) | 868381.i | 1.56039i | ||||||||
\(747\) | −43448.2 | − | 161375.i | −0.0778629 | − | 0.289198i | ||||
\(748\) | −1.68177e6 | −3.00583 | ||||||||
\(749\) | 95776.8i | 0.170725i | ||||||||
\(750\) | 848757. | − | 112260.i | 1.50890 | − | 0.199573i | ||||
\(751\) | 424520. | 0.752694 | 0.376347 | − | 0.926479i | \(-0.377180\pi\) | ||||
0.376347 | + | 0.926479i | \(0.377180\pi\) | |||||||
\(752\) | 86171.9i | 0.152381i | ||||||||
\(753\) | 97618.7 | + | 738061.i | 0.172164 | + | 1.30167i | ||||
\(754\) | −689067. | −1.21205 | ||||||||
\(755\) | 35500.6i | 0.0622790i | ||||||||
\(756\) | −253393. | + | 105494.i | −0.443354 | + | 0.184580i | ||||
\(757\) | 241891. | 0.422112 | 0.211056 | − | 0.977474i | \(-0.432310\pi\) | ||||
0.211056 | + | 0.977474i | \(0.432310\pi\) | |||||||
\(758\) | − | 812974.i | − | 1.41494i | ||||||
\(759\) | 251306. | − | 33238.7i | 0.436234 | − | 0.0576980i | ||||
\(760\) | 80777.6 | 0.139850 | ||||||||
\(761\) | − | 57363.8i | − | 0.0990531i | −0.998773 | − | 0.0495266i | \(-0.984229\pi\) | ||
0.998773 | − | 0.0495266i | \(-0.0157712\pi\) | |||||||
\(762\) | −167348. | − | 1.26526e6i | −0.288211 | − | 2.17906i | ||||
\(763\) | −336774. | −0.578481 | ||||||||
\(764\) | − | 1.17319e6i | − | 2.00993i | ||||||
\(765\) | 519168. | − | 139779.i | 0.887125 | − | 0.238847i | ||||
\(766\) | −62645.8 | −0.106766 | ||||||||
\(767\) | 438907.i | 0.746074i | ||||||||
\(768\) | −154543. | + | 20440.4i | −0.262015 | + | 0.0346551i | ||||
\(769\) | 919966. | 1.55568 | 0.777838 | − | 0.628465i | \(-0.216316\pi\) | ||||
0.777838 | + | 0.628465i | \(0.216316\pi\) | |||||||
\(770\) | − | 345284.i | − | 0.582364i | ||||||
\(771\) | −12803.5 | − | 96802.7i | −0.0215387 | − | 0.162847i | ||||
\(772\) | 48702.1 | 0.0817171 | ||||||||
\(773\) | − | 620899.i | − | 1.03911i | −0.854437 | − | 0.519556i | \(-0.826097\pi\) | ||
0.854437 | − | 0.519556i | \(-0.173903\pi\) | |||||||
\(774\) | −12570.5 | − | 46689.2i | −0.0209831 | − | 0.0779354i | ||||
\(775\) | −239398. | −0.398581 | ||||||||
\(776\) | 89147.3i | 0.148042i | ||||||||
\(777\) | 220851. | − | 29210.6i | 0.365812 | − | 0.0483837i | ||||
\(778\) | −133057. | −0.219826 | ||||||||
\(779\) | − | 559327.i | − | 0.921703i | ||||||
\(780\) | −57338.6 | − | 433517.i | −0.0942449 | − | 0.712552i | ||||
\(781\) | 347386. | 0.569521 | ||||||||
\(782\) | − | 364316.i | − | 0.595750i | ||||||
\(783\) | 211141. | + | 507153.i | 0.344389 | + | 0.827209i | ||||
\(784\) | −57617.2 | −0.0937389 | ||||||||
\(785\) | 653334.i | 1.06022i | ||||||||
\(786\) | −1.06137e6 | + | 140381.i | −1.71800 | + | 0.227229i | ||||
\(787\) | −559334. | −0.903071 | −0.451536 | − | 0.892253i | \(-0.649124\pi\) | ||||
−0.451536 | + | 0.892253i | \(0.649124\pi\) | |||||||
\(788\) | − | 41363.0i | − | 0.0666130i | ||||||
\(789\) | 47301.0 | + | 357626.i | 0.0759830 | + | 0.574481i | ||||
\(790\) | −213835. | −0.342630 | ||||||||
\(791\) | − | 153203.i | − | 0.244858i | ||||||
\(792\) | 400755. | − | 107898.i | 0.638893 | − | 0.172014i | ||||
\(793\) | 403757. | 0.642058 | ||||||||
\(794\) | − | 235453.i | − | 0.373476i | ||||||
\(795\) | −597690. | + | 79052.7i | −0.945674 | + | 0.125078i | ||||
\(796\) | −528141. | −0.833535 | ||||||||
\(797\) | − | 280663.i | − | 0.441843i | −0.975292 | − | 0.220922i | \(-0.929093\pi\) | ||
0.975292 | − | 0.220922i | \(-0.0709065\pi\) | |||||||
\(798\) | −25883.0 | − | 195692.i | −0.0406452 | − | 0.307304i | ||||
\(799\) | 216141. | 0.338566 | ||||||||
\(800\) | 538853.i | 0.841957i | ||||||||
\(801\) | 64628.4 | + | 240042.i | 0.100730 | + | 0.374130i | ||||
\(802\) | −253258. | −0.393745 | ||||||||
\(803\) | 693305.i | 1.07521i | ||||||||
\(804\) | 465706. | − | 61596.0i | 0.720443 | − | 0.0952885i | ||||
\(805\) | 41855.7 | 0.0645897 | ||||||||
\(806\) | 580946.i | 0.894263i | ||||||||
\(807\) | 88877.5 | + | 671972.i | 0.136472 | + | 1.03182i | ||||
\(808\) | −22654.9 | −0.0347008 | ||||||||
\(809\) | 572672.i | 0.875002i | 0.899218 | + | 0.437501i | \(0.144136\pi\) | ||||
−0.899218 | + | 0.437501i | \(0.855864\pi\) | |||||||
\(810\) | −538787. | + | 312797.i | −0.821196 | + | 0.476753i | ||||
\(811\) | −980201. | −1.49030 | −0.745149 | − | 0.666898i | \(-0.767622\pi\) | ||||
−0.745149 | + | 0.666898i | \(0.767622\pi\) | |||||||
\(812\) | − | 283725.i | − | 0.430314i | ||||||
\(813\) | 1.00886e6 | − | 133436.i | 1.52634 | − | 0.201879i | ||||
\(814\) | −1.58167e6 | −2.38708 | ||||||||
\(815\) | − | 677773.i | − | 1.02040i | ||||||
\(816\) | 83522.8 | + | 631486.i | 0.125437 | + | 0.948383i | ||||
\(817\) | 19458.8 | 0.0291523 | ||||||||
\(818\) | − | 1.68502e6i | − | 2.51824i | ||||||
\(819\) | −219759. | + | 59167.2i | −0.327626 | + | 0.0882091i | ||||
\(820\) | 911728. | 1.35593 | ||||||||
\(821\) | 263704.i | 0.391228i | 0.980681 | + | 0.195614i | \(0.0626700\pi\) | ||||
−0.980681 | + | 0.195614i | \(0.937330\pi\) | |||||||
\(822\) | 734270. | − | 97117.3i | 1.08671 | − | 0.143732i | ||||
\(823\) | −148647. | −0.219461 | −0.109730 | − | 0.993961i | \(-0.534999\pi\) | ||||
−0.109730 | + | 0.993961i | \(0.534999\pi\) | |||||||
\(824\) | 63177.5i | 0.0930482i | ||||||||
\(825\) | 87307.5 | + | 660101.i | 0.128276 | + | 0.969846i | ||||
\(826\) | −322954. | −0.473348 | ||||||||
\(827\) | − | 30591.1i | − | 0.0447285i | −0.999750 | − | 0.0223642i | \(-0.992881\pi\) | ||
0.999750 | − | 0.0223642i | \(-0.00711935\pi\) | |||||||
\(828\) | 61414.6 | + | 228106.i | 0.0895800 | + | 0.332717i | ||||
\(829\) | 285462. | 0.415374 | 0.207687 | − | 0.978195i | \(-0.433407\pi\) | ||||
0.207687 | + | 0.978195i | \(0.433407\pi\) | |||||||
\(830\) | 195915.i | 0.284388i | ||||||||
\(831\) | 472788. | − | 62532.7i | 0.684643 | − | 0.0905535i | ||||
\(832\) | 899886. | 1.29999 | ||||||||
\(833\) | 144518.i | 0.208273i | ||||||||
\(834\) | 47332.6 | + | 357865.i | 0.0680500 | + | 0.514502i | ||||
\(835\) | 206002. | 0.295460 | ||||||||
\(836\) | 784256.i | 1.12214i | ||||||||
\(837\) | 427575. | − | 178011.i | 0.610326 | − | 0.254095i | ||||
\(838\) | 1.38807e6 | 1.97662 | ||||||||
\(839\) | − | 1.03015e6i | − | 1.46345i | −0.681602 | − | 0.731723i | \(-0.738716\pi\) | ||
0.681602 | − | 0.731723i | \(-0.261284\pi\) | |||||||
\(840\) | 67935.2 | − | 8985.37i | 0.0962801 | − | 0.0127344i | ||||
\(841\) | 139420. | 0.197121 | ||||||||
\(842\) | 302887.i | 0.427225i | ||||||||
\(843\) | 56905.5 | + | 430243.i | 0.0800754 | + | 0.605422i | ||||
\(844\) | −1.22867e6 | −1.72484 | ||||||||
\(845\) | 87363.9i | 0.122354i | ||||||||
\(846\) | −241839. | + | 65112.2i | −0.337898 | + | 0.0909750i | ||||
\(847\) | 442789. | 0.617206 | ||||||||
\(848\) | − | 714278.i | − | 0.993289i | ||||||
\(849\) | −570149. | + | 75410.1i | −0.790994 | + | 0.104620i | ||||
\(850\) | 956941. | 1.32449 | ||||||||
\(851\) | − | 191732.i | − | 0.264749i | ||||||
\(852\) | 42447.3 | + | 320929.i | 0.0584751 | + | 0.442110i | ||||
\(853\) | −1.02297e6 | −1.40593 | −0.702967 | − | 0.711223i | \(-0.748142\pi\) | ||||
−0.702967 | + | 0.711223i | \(0.748142\pi\) | |||||||
\(854\) | 297090.i | 0.407354i | ||||||||
\(855\) | −65182.9 | − | 242102.i | −0.0891665 | − | 0.331181i | ||||
\(856\) | 134957. | 0.184182 | ||||||||
\(857\) | − | 838435.i | − | 1.14158i | −0.821095 | − | 0.570792i | \(-0.806636\pi\) | ||
0.821095 | − | 0.570792i | \(-0.193364\pi\) | |||||||
\(858\) | 1.60186e6 | − | 211869.i | 2.17596 | − | 0.287801i | ||||
\(859\) | 272504. | 0.369306 | 0.184653 | − | 0.982804i | \(-0.440884\pi\) | ||||
0.184653 | + | 0.982804i | \(0.440884\pi\) | |||||||
\(860\) | 31718.8i | 0.0428864i | ||||||||
\(861\) | −62217.3 | − | 470403.i | −0.0839275 | − | 0.634547i | ||||
\(862\) | −541501. | −0.728760 | ||||||||
\(863\) | 600703.i | 0.806563i | 0.915076 | + | 0.403281i | \(0.132130\pi\) | ||||
−0.915076 | + | 0.403281i | \(0.867870\pi\) | |||||||
\(864\) | −400679. | − | 962415.i | −0.536747 | − | 1.28924i | ||||
\(865\) | −316520. | −0.423028 | ||||||||
\(866\) | 1.22990e6i | 1.63996i | ||||||||
\(867\) | 838727. | − | 110933.i | 1.11579 | − | 0.147579i | ||||
\(868\) | −239206. | −0.317491 | ||||||||
\(869\) | − | 442148.i | − | 0.585501i | ||||||
\(870\) | −84442.1 | − | 638437.i | −0.111563 | − | 0.843489i | ||||
\(871\) | 389507. | 0.513428 | ||||||||
\(872\) | 474540.i | 0.624079i | ||||||||
\(873\) | 267187. | − | 71936.8i | 0.350580 | − | 0.0943893i | ||||
\(874\) | −169890. | −0.222405 | ||||||||
\(875\) | 292296.i | 0.381775i | ||||||||
\(876\) | −640504. | + | 84715.5i | −0.834667 | + | 0.110396i | ||||
\(877\) | −446820. | −0.580943 | −0.290472 | − | 0.956884i | \(-0.593812\pi\) | ||||
−0.290472 | + | 0.956884i | \(0.593812\pi\) | |||||||
\(878\) | 1.17600e6i | 1.52553i | ||||||||
\(879\) | −90107.5 | − | 681271.i | −0.116623 | − | 0.881744i | ||||
\(880\) | 519585. | 0.670952 | ||||||||
\(881\) | − | 437687.i | − | 0.563913i | −0.959427 | − | 0.281956i | \(-0.909017\pi\) | ||
0.959427 | − | 0.281956i | \(-0.0909833\pi\) | |||||||
\(882\) | −43536.0 | − | 161701.i | −0.0559644 | − | 0.207862i | ||||
\(883\) | −80288.7 | −0.102975 | −0.0514876 | − | 0.998674i | \(-0.516396\pi\) | ||||
−0.0514876 | + | 0.998674i | \(0.516396\pi\) | |||||||
\(884\) | − | 1.29948e6i | − | 1.66289i | ||||||
\(885\) | −406658. | + | 53786.1i | −0.519210 | + | 0.0686726i | ||||
\(886\) | 1.82481e6 | 2.32461 | ||||||||
\(887\) | − | 1.44826e6i | − | 1.84076i | −0.391022 | − | 0.920381i | \(-0.627878\pi\) | ||
0.391022 | − | 0.920381i | \(-0.372122\pi\) | |||||||
\(888\) | −41160.0 | − | 311196.i | −0.0521974 | − | 0.394646i | ||||
\(889\) | 435732. | 0.551335 | ||||||||
\(890\) | − | 291420.i | − | 0.367908i | ||||||
\(891\) | −646772. | − | 1.11405e6i | −0.814697 | − | 1.40330i | ||||
\(892\) | −224368. | −0.281988 | ||||||||
\(893\) | − | 100792.i | − | 0.126393i | ||||||
\(894\) | −1.36591e6 | + | 180660.i | −1.70902 | + | 0.226041i | ||||
\(895\) | −631210. | −0.788003 | ||||||||
\(896\) | 238396.i | 0.296950i | ||||||||
\(897\) | 25683.0 | + | 194180.i | 0.0319198 | + | 0.241335i | ||||
\(898\) | 982448. | 1.21831 | ||||||||
\(899\) | 478758.i | 0.592375i | ||||||||
\(900\) | −599161. | + | 161317.i | −0.739705 | + | 0.199156i | ||||
\(901\) | −1.79159e6 | −2.20693 | ||||||||
\(902\) | 3.36888e6i | 4.14069i | ||||||||
\(903\) | 16365.2 | − | 2164.52i | 0.0200699 | − | 0.00265452i | ||||
\(904\) | −215875. | −0.264159 | ||||||||
\(905\) | 1.00709e6i | 1.22962i | ||||||||
\(906\) | −16028.5 | − | 121186.i | −0.0195271 | − | 0.147637i | ||||
\(907\) | −903376. | −1.09813 | −0.549065 | − | 0.835779i | \(-0.685016\pi\) | ||||
−0.549065 | + | 0.835779i | \(0.685016\pi\) | |||||||
\(908\) | − | 1.48570e6i | − | 1.80202i | ||||||
\(909\) | 18281.2 | + | 67900.0i | 0.0221247 | + | 0.0821754i | ||||
\(910\) | 266795. | 0.322177 | ||||||||
\(911\) | 1.15959e6i | 1.39723i | 0.715499 | + | 0.698614i | \(0.246200\pi\) | ||||
−0.715499 | + | 0.698614i | \(0.753800\pi\) | |||||||
\(912\) | 294479. | − | 38948.9i | 0.354050 | − | 0.0468280i | ||||
\(913\) | −405094. | −0.485976 | ||||||||
\(914\) | 942360.i | 1.12804i | ||||||||
\(915\) | 49478.6 | + | 374091.i | 0.0590984 | + | 0.446822i | ||||
\(916\) | −319309. | −0.380557 | ||||||||
\(917\) | − | 365517.i | − | 0.434680i | ||||||
\(918\) | −1.70914e6 | + | 711561.i | −2.02811 | + | 0.844358i | ||||
\(919\) | 1.39808e6 | 1.65539 | 0.827697 | − | 0.561176i | \(-0.189651\pi\) | ||||
0.827697 | + | 0.561176i | \(0.189651\pi\) | |||||||
\(920\) | − | 58977.9i | − | 0.0696809i | ||||||
\(921\) | −789681. | + | 104446.i | −0.930963 | + | 0.123133i | ||||
\(922\) | 844842. | 0.993834 | ||||||||
\(923\) | 268419.i | 0.315072i | ||||||||
\(924\) | 87237.4 | + | 659571.i | 0.102178 | + | 0.772535i | ||||
\(925\) | 503618. | 0.588597 | ||||||||
\(926\) | − | 282276.i | − | 0.329194i | ||||||
\(927\) | 189352. | − | 50980.7i | 0.220349 | − | 0.0593261i | ||||
\(928\) | 1.07762e6 | 1.25132 | ||||||||
\(929\) | − | 1.23771e6i | − | 1.43413i | −0.697006 | − | 0.717066i | \(-0.745485\pi\) | ||
0.697006 | − | 0.717066i | \(-0.254515\pi\) | |||||||
\(930\) | −538260. | + | 71192.3i | −0.622338 | + | 0.0823127i | ||||
\(931\) | 67392.9 | 0.0777525 | ||||||||
\(932\) | − | 1.18909e6i | − | 1.36893i | ||||||
\(933\) | 27734.6 | + | 209691.i | 0.0318609 | + | 0.240889i | ||||
\(934\) | −2.19517e6 | −2.51637 | ||||||||
\(935\) | − | 1.30325e6i | − | 1.49075i | ||||||
\(936\) | 83371.2 | + | 309656.i | 0.0951621 | + | 0.353450i | ||||
\(937\) | 1.41105e6 | 1.60718 | 0.803589 | − | 0.595185i | \(-0.202921\pi\) | ||||
0.803589 | + | 0.595185i | \(0.202921\pi\) | |||||||
\(938\) | 286605.i | 0.325745i | ||||||||
\(939\) | −1.41621e6 | + | 187313.i | −1.60619 | + | 0.212441i | ||||
\(940\) | 164296. | 0.185939 | ||||||||
\(941\) | 1.68557e6i | 1.90356i | 0.306775 | + | 0.951782i | \(0.400750\pi\) | ||||
−0.306775 | + | 0.951782i | \(0.599250\pi\) | |||||||
\(942\) | −294980. | − | 2.23024e6i | −0.332423 | − | 2.51334i | ||||
\(943\) | −408380. | −0.459241 | ||||||||
\(944\) | − | 485983.i | − | 0.545352i | ||||||
\(945\) | −81750.3 | − | 196361.i | −0.0915431 | − | 0.219883i | ||||
\(946\) | −117202. | −0.130965 | ||||||||
\(947\) | 1.28636e6i | 1.43437i | 0.696883 | + | 0.717185i | \(0.254570\pi\) | ||||
−0.696883 | + | 0.717185i | \(0.745430\pi\) | |||||||
\(948\) | 408475. | − | 54026.4i | 0.454515 | − | 0.0601159i | ||||
\(949\) | −535705. | −0.594830 | ||||||||
\(950\) | − | 446247.i | − | 0.494457i | ||||||
\(951\) | 204375. | + | 1.54520e6i | 0.225978 | + | 1.70854i | ||||
\(952\) | 203637. | 0.224690 | ||||||||
\(953\) | − | 261159.i | − | 0.287553i | −0.989610 | − | 0.143777i | \(-0.954075\pi\) | ||
0.989610 | − | 0.143777i | \(-0.0459247\pi\) | |||||||
\(954\) | 2.00460e6 | − | 539715.i | 2.20258 | − | 0.593017i | ||||
\(955\) | 909134. | 0.996830 | ||||||||
\(956\) | − | 272054.i | − | 0.297673i | ||||||
\(957\) | 1.32010e6 | − | 174601.i | 1.44139 | − | 0.190644i | ||||
\(958\) | 841440. | 0.916837 | ||||||||
\(959\) | 252869.i | 0.274953i | ||||||||
\(960\) | 110277. | + | 833766.i | 0.119658 | + | 0.904694i | ||||
\(961\) | −519885. | −0.562938 | ||||||||
\(962\) | − | 1.22213e6i | − | 1.32059i | ||||||
\(963\) | −108902. | − | 404484.i | −0.117432 | − | 0.436163i | ||||
\(964\) | 6319.33 | 0.00680013 | ||||||||
\(965\) | 37740.5i | 0.0405278i | ||||||||
\(966\) | −142880. | + | 18897.9i | −0.153115 | + | 0.0202516i | ||||
\(967\) | −522045. | −0.558284 | −0.279142 | − | 0.960250i | \(-0.590050\pi\) | ||||
−0.279142 | + | 0.960250i | \(0.590050\pi\) | |||||||
\(968\) | − | 623924.i | − | 0.665857i | ||||||
\(969\) | −97693.7 | − | 738628.i | −0.104044 | − | 0.786644i | ||||
\(970\) | −324375. | −0.344750 | ||||||||
\(971\) | − | 527907.i | − | 0.559911i | −0.960013 | − | 0.279956i | \(-0.909680\pi\) | ||
0.960013 | − | 0.279956i | \(-0.0903198\pi\) | |||||||
\(972\) | 950177. | − | 733642.i | 1.00571 | − | 0.776518i | ||||
\(973\) | −123242. | −0.130177 | ||||||||
\(974\) | 736129.i | 0.775954i | ||||||||
\(975\) | −510049. | + | 67461.1i | −0.536541 | + | 0.0709649i | ||||
\(976\) | −447063. | −0.469320 | ||||||||
\(977\) | − | 730919.i | − | 0.765737i | −0.923803 | − | 0.382869i | \(-0.874936\pi\) | ||
0.923803 | − | 0.382869i | \(-0.125064\pi\) | |||||||
\(978\) | 306015. | + | 2.31367e6i | 0.319937 | + | 2.41893i | ||||
\(979\) | 602570. | 0.628698 | ||||||||
\(980\) | 109853.i | 0.114383i | ||||||||
\(981\) | 1.42226e6 | − | 382926.i | 1.47789 | − | 0.397903i | ||||
\(982\) | 1.44184e6 | 1.49518 | ||||||||
\(983\) | − | 163325.i | − | 0.169023i | −0.996423 | − | 0.0845115i | \(-0.973067\pi\) | ||
0.996423 | − | 0.0845115i | \(-0.0269330\pi\) | |||||||
\(984\) | −662833. | + | 87668.8i | −0.684564 | + | 0.0905430i | ||||
\(985\) | 32053.2 | 0.0330369 | ||||||||
\(986\) | − | 1.91373e6i | − | 1.96846i | ||||||
\(987\) | −11211.7 | − | 84767.9i | −0.0115090 | − | 0.0870156i | ||||
\(988\) | −605981. | −0.620791 | ||||||||
\(989\) | − | 14207.4i | − | 0.0145252i | ||||||
\(990\) | 392603. | + | 1.45820e6i | 0.400574 | + | 1.48781i | ||||
\(991\) | 1.24036e6 | 1.26299 | 0.631494 | − | 0.775381i | \(-0.282442\pi\) | ||||
0.631494 | + | 0.775381i | \(0.282442\pi\) | |||||||
\(992\) | − | 908530.i | − | 0.923243i | ||||||
\(993\) | −750423. | + | 99253.8i | −0.761040 | + | 0.100658i | ||||
\(994\) | −197506. | −0.199898 | ||||||||
\(995\) | − | 409270.i | − | 0.413394i | ||||||
\(996\) | −49498.8 | − | 374243.i | −0.0498972 | − | 0.377255i | ||||
\(997\) | −881732. | −0.887046 | −0.443523 | − | 0.896263i | \(-0.646272\pi\) | ||||
−0.443523 | + | 0.896263i | \(0.646272\pi\) | |||||||
\(998\) | − | 172256.i | − | 0.172947i | ||||||
\(999\) | −899485. | + | 374480.i | −0.901286 | + | 0.375230i |
(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 | 21.5.b.a.8.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 21.5.b.a.8.8 | yes | 8 | |
4.3 | odd | 2 | 336.5.d.b.113.7 | 8 | |||
7.2 | even | 3 | 147.5.h.e.116.1 | 16 | |||
7.3 | odd | 6 | 147.5.h.c.128.8 | 16 | |||
7.4 | even | 3 | 147.5.h.e.128.8 | 16 | |||
7.5 | odd | 6 | 147.5.h.c.116.1 | 16 | |||
7.6 | odd | 2 | 147.5.b.e.50.1 | 8 | |||
12.11 | even | 2 | 336.5.d.b.113.8 | 8 | |||
21.2 | odd | 6 | 147.5.h.e.116.8 | 16 | |||
21.5 | even | 6 | 147.5.h.c.116.8 | 16 | |||
21.11 | odd | 6 | 147.5.h.e.128.1 | 16 | |||
21.17 | even | 6 | 147.5.h.c.128.1 | 16 | |||
21.20 | even | 2 | 147.5.b.e.50.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.5.b.a.8.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
21.5.b.a.8.8 | yes | 8 | 3.2 | odd | 2 | inner | |
147.5.b.e.50.1 | 8 | 7.6 | odd | 2 | |||
147.5.b.e.50.8 | 8 | 21.20 | even | 2 | |||
147.5.h.c.116.1 | 16 | 7.5 | odd | 6 | |||
147.5.h.c.116.8 | 16 | 21.5 | even | 6 | |||
147.5.h.c.128.1 | 16 | 21.17 | even | 6 | |||
147.5.h.c.128.8 | 16 | 7.3 | odd | 6 | |||
147.5.h.e.116.1 | 16 | 7.2 | even | 3 | |||
147.5.h.e.116.8 | 16 | 21.2 | odd | 6 | |||
147.5.h.e.128.1 | 16 | 21.11 | odd | 6 | |||
147.5.h.e.128.8 | 16 | 7.4 | even | 3 | |||
336.5.d.b.113.7 | 8 | 4.3 | odd | 2 | |||
336.5.d.b.113.8 | 8 | 12.11 | even | 2 |