Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,5,Mod(323,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.323");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(39.0738460457\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 92x^{6} + 2949x^{4} + 37548x^{2} + 142884 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(5.12618i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.323 |
Dual form | 378.5.b.b.323.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.82843i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | − 28.1791i | − 1.12717i | −0.826060 | − | 0.563583i | \(-0.809423\pi\) | ||||
0.826060 | − | 0.563583i | \(-0.190577\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.5203 | −0.377964 | ||||||||
\(8\) | 22.6274i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −79.7026 | −0.797026 | ||||||||
\(11\) | 168.507i | 1.39262i | 0.717740 | + | 0.696311i | \(0.245177\pi\) | ||||
−0.717740 | + | 0.696311i | \(0.754823\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 319.388 | 1.88987 | 0.944934 | − | 0.327261i | \(-0.106126\pi\) | ||||
0.944934 | + | 0.327261i | \(0.106126\pi\) | |||||||
\(14\) | 52.3832i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 39.1240i | 0.135377i | 0.997706 | + | 0.0676886i | \(0.0215624\pi\) | ||||
−0.997706 | + | 0.0676886i | \(0.978438\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 457.590 | 1.26756 | 0.633782 | − | 0.773512i | \(-0.281502\pi\) | ||||
0.633782 | + | 0.773512i | \(0.281502\pi\) | |||||||
\(20\) | 225.433i | 0.563583i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 476.611 | 0.984733 | ||||||||
\(23\) | − 435.106i | − 0.822506i | −0.911521 | − | 0.411253i | \(-0.865091\pi\) | ||||
0.911521 | − | 0.411253i | \(-0.134909\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −169.064 | −0.270502 | ||||||||
\(26\) | − 903.365i | − 1.33634i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 148.162 | 0.188982 | ||||||||
\(29\) | 135.719i | 0.161378i | 0.996739 | + | 0.0806890i | \(0.0257121\pi\) | ||||
−0.996739 | + | 0.0806890i | \(0.974288\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −267.371 | −0.278222 | −0.139111 | − | 0.990277i | \(-0.544424\pi\) | ||||
−0.139111 | + | 0.990277i | \(0.544424\pi\) | |||||||
\(32\) | − 181.019i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 110.659 | 0.0957261 | ||||||||
\(35\) | 521.885i | 0.426028i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 812.186 | 0.593270 | 0.296635 | − | 0.954991i | \(-0.404136\pi\) | ||||
0.296635 | + | 0.954991i | \(0.404136\pi\) | |||||||
\(38\) | − 1294.26i | − 0.896303i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 637.621 | 0.398513 | ||||||||
\(41\) | 737.686i | 0.438837i | 0.975631 | + | 0.219419i | \(0.0704161\pi\) | ||||
−0.975631 | + | 0.219419i | \(0.929584\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2092.00 | −1.13142 | −0.565710 | − | 0.824604i | \(-0.691398\pi\) | ||||
−0.565710 | + | 0.824604i | \(0.691398\pi\) | |||||||
\(44\) | − 1348.06i | − 0.696311i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1230.66 | −0.581599 | ||||||||
\(47\) | − 2962.37i | − 1.34105i | −0.741889 | − | 0.670523i | \(-0.766070\pi\) | ||||
0.741889 | − | 0.670523i | \(-0.233930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 343.000 | 0.142857 | ||||||||
\(50\) | 478.184i | 0.191274i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2555.10 | −0.944934 | ||||||||
\(53\) | 3190.68i | 1.13588i | 0.823071 | + | 0.567939i | \(0.192259\pi\) | ||||
−0.823071 | + | 0.567939i | \(0.807741\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4748.39 | 1.56972 | ||||||||
\(56\) | − 419.066i | − 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 383.871 | 0.114111 | ||||||||
\(59\) | − 5620.52i | − 1.61463i | −0.590122 | − | 0.807314i | \(-0.700920\pi\) | ||||
0.590122 | − | 0.807314i | \(-0.299080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4862.90 | 1.30688 | 0.653439 | − | 0.756979i | \(-0.273325\pi\) | ||||
0.653439 | + | 0.756979i | \(0.273325\pi\) | |||||||
\(62\) | 756.240i | 0.196733i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − 9000.07i | − 2.13019i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2008.97 | −0.447533 | −0.223766 | − | 0.974643i | \(-0.571835\pi\) | ||||
−0.223766 | + | 0.974643i | \(0.571835\pi\) | |||||||
\(68\) | − 312.992i | − 0.0676886i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1476.11 | 0.301248 | ||||||||
\(71\) | − 4306.53i | − 0.854302i | −0.904180 | − | 0.427151i | \(-0.859517\pi\) | ||||
0.904180 | − | 0.427151i | \(-0.140483\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6314.60 | 1.18495 | 0.592475 | − | 0.805589i | \(-0.298151\pi\) | ||||
0.592475 | + | 0.805589i | \(0.298151\pi\) | |||||||
\(74\) | − 2297.21i | − 0.419505i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3660.72 | −0.633782 | ||||||||
\(77\) | − 3120.80i | − 0.526362i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3703.76 | −0.593457 | −0.296728 | − | 0.954962i | \(-0.595896\pi\) | ||||
−0.296728 | + | 0.954962i | \(0.595896\pi\) | |||||||
\(80\) | − 1803.46i | − 0.281791i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2086.49 | 0.310305 | ||||||||
\(83\) | − 9033.39i | − 1.31128i | −0.755075 | − | 0.655639i | \(-0.772399\pi\) | ||||
0.755075 | − | 0.655639i | \(-0.227601\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1102.48 | 0.152592 | ||||||||
\(86\) | 5917.06i | 0.800035i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3812.88 | −0.492366 | ||||||||
\(89\) | 3711.45i | 0.468559i | 0.972169 | + | 0.234279i | \(0.0752730\pi\) | ||||
−0.972169 | + | 0.234279i | \(0.924727\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5915.14 | −0.714303 | ||||||||
\(92\) | 3480.84i | 0.411253i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8378.85 | −0.948263 | ||||||||
\(95\) | − 12894.5i | − 1.42875i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13748.8 | 1.46124 | 0.730620 | − | 0.682784i | \(-0.239231\pi\) | ||||
0.730620 | + | 0.682784i | \(0.239231\pi\) | |||||||
\(98\) | − 970.151i | − 0.101015i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1352.51 | 0.135251 | ||||||||
\(101\) | 17899.9i | 1.75472i | 0.479835 | + | 0.877359i | \(0.340697\pi\) | ||||
−0.479835 | + | 0.877359i | \(0.659303\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3979.89 | 0.375143 | 0.187571 | − | 0.982251i | \(-0.439938\pi\) | ||||
0.187571 | + | 0.982251i | \(0.439938\pi\) | |||||||
\(104\) | 7226.92i | 0.668169i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9024.61 | 0.803187 | ||||||||
\(107\) | − 8914.65i | − 0.778640i | −0.921103 | − | 0.389320i | \(-0.872710\pi\) | ||||
0.921103 | − | 0.389320i | \(-0.127290\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13486.3 | −1.13511 | −0.567557 | − | 0.823334i | \(-0.692111\pi\) | ||||
−0.567557 | + | 0.823334i | \(0.692111\pi\) | |||||||
\(110\) | − 13430.5i | − 1.10996i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1185.30 | −0.0944911 | ||||||||
\(113\) | − 4042.36i | − 0.316576i | −0.987393 | − | 0.158288i | \(-0.949403\pi\) | ||||
0.987393 | − | 0.158288i | \(-0.0505974\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12260.9 | −0.927100 | ||||||||
\(116\) | − 1085.75i | − 0.0806890i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15897.2 | −1.14171 | ||||||||
\(119\) | − 724.586i | − 0.0511677i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13753.7 | −0.939397 | ||||||||
\(122\) | − 13754.3i | − 0.924103i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2138.97 | 0.139111 | ||||||||
\(125\) | − 12847.9i | − 0.822265i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18650.2 | 1.15631 | 0.578157 | − | 0.815926i | \(-0.303772\pi\) | ||||
0.578157 | + | 0.815926i | \(0.303772\pi\) | |||||||
\(128\) | 1448.15i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −25456.0 | −1.50627 | ||||||||
\(131\) | − 14164.3i | − 0.825375i | −0.910873 | − | 0.412688i | \(-0.864590\pi\) | ||||
0.910873 | − | 0.412688i | \(-0.135410\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8474.69 | −0.479094 | ||||||||
\(134\) | 5682.24i | 0.316453i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −885.275 | −0.0478630 | ||||||||
\(137\) | − 27896.5i | − 1.48631i | −0.669120 | − | 0.743154i | \(-0.733329\pi\) | ||||
0.669120 | − | 0.743154i | \(-0.266671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6374.52 | 0.329927 | 0.164963 | − | 0.986300i | \(-0.447249\pi\) | ||||
0.164963 | + | 0.986300i | \(0.447249\pi\) | |||||||
\(140\) | − 4175.08i | − 0.213014i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12180.7 | −0.604082 | ||||||||
\(143\) | 53819.2i | 2.63187i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3824.44 | 0.181900 | ||||||||
\(146\) | − 17860.4i | − 0.837887i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6497.49 | −0.296635 | ||||||||
\(149\) | 32359.8i | 1.45758i | 0.684736 | + | 0.728791i | \(0.259918\pi\) | ||||
−0.684736 | + | 0.728791i | \(0.740082\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19569.8 | 0.858288 | 0.429144 | − | 0.903236i | \(-0.358815\pi\) | ||||
0.429144 | + | 0.903236i | \(0.358815\pi\) | |||||||
\(152\) | 10354.1i | 0.448151i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8826.95 | −0.372194 | ||||||||
\(155\) | 7534.29i | 0.313602i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −29337.2 | −1.19020 | −0.595100 | − | 0.803652i | \(-0.702888\pi\) | ||||
−0.595100 | + | 0.803652i | \(0.702888\pi\) | |||||||
\(158\) | 10475.8i | 0.419637i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5100.97 | −0.199257 | ||||||||
\(161\) | 8058.27i | 0.310878i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 39562.6 | 1.48905 | 0.744526 | − | 0.667593i | \(-0.232675\pi\) | ||||
0.744526 | + | 0.667593i | \(0.232675\pi\) | |||||||
\(164\) | − 5901.49i | − 0.219419i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25550.3 | −0.927214 | ||||||||
\(167\) | − 26576.6i | − 0.952943i | −0.879190 | − | 0.476471i | \(-0.841916\pi\) | ||||
0.879190 | − | 0.476471i | \(-0.158084\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 73447.5 | 2.57160 | ||||||||
\(170\) | − 3118.28i | − 0.107899i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 16736.0 | 0.565710 | ||||||||
\(173\) | − 2650.12i | − 0.0885468i | −0.999019 | − | 0.0442734i | \(-0.985903\pi\) | ||||
0.999019 | − | 0.0442734i | \(-0.0140973\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3131.10 | 0.102240 | ||||||||
\(176\) | 10784.5i | 0.348156i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10497.6 | 0.331321 | ||||||||
\(179\) | 28123.7i | 0.877741i | 0.898550 | + | 0.438871i | \(0.144621\pi\) | ||||
−0.898550 | + | 0.438871i | \(0.855379\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6956.01 | 0.212326 | 0.106163 | − | 0.994349i | \(-0.466143\pi\) | ||||
0.106163 | + | 0.994349i | \(0.466143\pi\) | |||||||
\(182\) | 16730.6i | 0.505089i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9845.31 | 0.290800 | ||||||||
\(185\) | − 22886.7i | − 0.668713i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6592.68 | −0.188529 | ||||||||
\(188\) | 23699.0i | 0.670523i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −36471.1 | −1.01028 | ||||||||
\(191\) | − 35193.7i | − 0.964713i | −0.875975 | − | 0.482356i | \(-0.839781\pi\) | ||||
0.875975 | − | 0.482356i | \(-0.160219\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 37582.9 | 1.00897 | 0.504483 | − | 0.863422i | \(-0.331683\pi\) | ||||
0.504483 | + | 0.863422i | \(0.331683\pi\) | |||||||
\(194\) | − 38887.5i | − 1.03325i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2744.00 | −0.0714286 | ||||||||
\(197\) | 40590.7i | 1.04591i | 0.852361 | + | 0.522954i | \(0.175170\pi\) | ||||
−0.852361 | + | 0.522954i | \(0.824830\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 71304.5 | 1.80057 | 0.900286 | − | 0.435298i | \(-0.143357\pi\) | ||||
0.900286 | + | 0.435298i | \(0.143357\pi\) | |||||||
\(200\) | − 3825.47i | − 0.0956368i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 50628.5 | 1.24077 | ||||||||
\(203\) | − 2513.55i | − 0.0609951i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20787.3 | 0.494642 | ||||||||
\(206\) | − 11256.8i | − 0.265266i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20440.8 | 0.472467 | ||||||||
\(209\) | 77107.3i | 1.76524i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −58607.1 | −1.31639 | −0.658196 | − | 0.752847i | \(-0.728680\pi\) | ||||
−0.658196 | + | 0.752847i | \(0.728680\pi\) | |||||||
\(212\) | − 25525.5i | − 0.567939i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −25214.4 | −0.550582 | ||||||||
\(215\) | 58950.6i | 1.27530i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4951.79 | 0.105158 | ||||||||
\(218\) | 38145.0i | 0.802646i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −37987.1 | −0.784858 | ||||||||
\(221\) | 12495.7i | 0.255845i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −31333.8 | −0.630091 | −0.315045 | − | 0.949077i | \(-0.602020\pi\) | ||||
−0.315045 | + | 0.949077i | \(0.602020\pi\) | |||||||
\(224\) | 3352.53i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11433.5 | −0.223853 | ||||||||
\(227\) | 3437.19i | 0.0667040i | 0.999444 | + | 0.0333520i | \(0.0106182\pi\) | ||||
−0.999444 | + | 0.0333520i | \(0.989382\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 67814.1 | 1.29315 | 0.646576 | − | 0.762850i | \(-0.276201\pi\) | ||||
0.646576 | + | 0.762850i | \(0.276201\pi\) | |||||||
\(230\) | 34679.1i | 0.655559i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3070.97 | −0.0570557 | ||||||||
\(233\) | 62389.0i | 1.14920i | 0.818434 | + | 0.574601i | \(0.194843\pi\) | ||||
−0.818434 | + | 0.574601i | \(0.805157\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −83477.0 | −1.51158 | ||||||||
\(236\) | 44964.2i | 0.807314i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2049.44 | −0.0361811 | ||||||||
\(239\) | 93904.5i | 1.64396i | 0.569518 | + | 0.821979i | \(0.307130\pi\) | ||||
−0.569518 | + | 0.821979i | \(0.692870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −107318. | −1.84773 | −0.923864 | − | 0.382722i | \(-0.874987\pi\) | ||||
−0.923864 | + | 0.382722i | \(0.874987\pi\) | |||||||
\(242\) | 38901.4i | 0.664254i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −38903.2 | −0.653439 | ||||||||
\(245\) | − 9665.44i | − 0.161024i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 146149. | 2.39553 | ||||||||
\(248\) | − 6049.92i | − 0.0983663i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −36339.3 | −0.581429 | ||||||||
\(251\) | 56349.2i | 0.894417i | 0.894430 | + | 0.447209i | \(0.147582\pi\) | ||||
−0.894430 | + | 0.447209i | \(0.852418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 73318.5 | 1.14544 | ||||||||
\(254\) | − 52750.7i | − 0.817638i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | − 34716.3i | − 0.525614i | −0.964848 | − | 0.262807i | \(-0.915352\pi\) | ||||
0.964848 | − | 0.262807i | \(-0.0846482\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15041.9 | −0.224235 | ||||||||
\(260\) | 72000.6i | 1.06510i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −40062.6 | −0.583628 | ||||||||
\(263\) | − 104358.i | − 1.50874i | −0.656449 | − | 0.754371i | \(-0.727942\pi\) | ||||
0.656449 | − | 0.754371i | \(-0.272058\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 89910.7 | 1.28032 | ||||||||
\(266\) | 23970.0i | 0.338771i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16071.8 | 0.223766 | ||||||||
\(269\) | 81356.1i | 1.12431i | 0.827032 | + | 0.562155i | \(0.190027\pi\) | ||||
−0.827032 | + | 0.562155i | \(0.809973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −125208. | −1.70488 | −0.852439 | − | 0.522827i | \(-0.824878\pi\) | ||||
−0.852439 | + | 0.522827i | \(0.824878\pi\) | |||||||
\(272\) | 2503.94i | 0.0338443i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −78903.3 | −1.05098 | ||||||||
\(275\) | − 28488.4i | − 0.376707i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3328.93 | 0.0433855 | 0.0216928 | − | 0.999765i | \(-0.493094\pi\) | ||||
0.0216928 | + | 0.999765i | \(0.493094\pi\) | |||||||
\(278\) | − 18029.9i | − 0.233294i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11808.9 | −0.150624 | ||||||||
\(281\) | − 151897.i | − 1.92370i | −0.273584 | − | 0.961848i | \(-0.588209\pi\) | ||||
0.273584 | − | 0.961848i | \(-0.411791\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4034.61 | 0.0503765 | 0.0251883 | − | 0.999683i | \(-0.491981\pi\) | ||||
0.0251883 | + | 0.999683i | \(0.491981\pi\) | |||||||
\(284\) | 34452.3i | 0.427151i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 152224. | 1.86101 | ||||||||
\(287\) | − 13662.1i | − 0.165865i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 81990.3 | 0.981673 | ||||||||
\(290\) | − 10817.1i | − 0.128622i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −50516.8 | −0.592475 | ||||||||
\(293\) | 39529.1i | 0.460449i | 0.973138 | + | 0.230225i | \(0.0739461\pi\) | ||||
−0.973138 | + | 0.230225i | \(0.926054\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −158381. | −1.81995 | ||||||||
\(296\) | 18377.7i | 0.209752i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 91527.3 | 1.03067 | ||||||||
\(299\) | − 138967.i | − 1.55443i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38744.3 | 0.427637 | ||||||||
\(302\) | − 55351.8i | − 0.606902i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 29285.8 | 0.316891 | ||||||||
\(305\) | − 137032.i | − 1.47307i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −87173.0 | −0.924922 | −0.462461 | − | 0.886640i | \(-0.653034\pi\) | ||||
−0.462461 | + | 0.886640i | \(0.653034\pi\) | |||||||
\(308\) | 24966.4i | 0.263181i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 21310.2 | 0.221750 | ||||||||
\(311\) | 130723.i | 1.35154i | 0.737110 | + | 0.675772i | \(0.236190\pi\) | ||||
−0.737110 | + | 0.675772i | \(0.763810\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −129850. | −1.32542 | −0.662711 | − | 0.748876i | \(-0.730594\pi\) | ||||
−0.662711 | + | 0.748876i | \(0.730594\pi\) | |||||||
\(314\) | 82978.2i | 0.841598i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 29630.1 | 0.296728 | ||||||||
\(317\) | 80859.0i | 0.804656i | 0.915496 | + | 0.402328i | \(0.131799\pi\) | ||||
−0.915496 | + | 0.402328i | \(0.868201\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22869.6 | −0.224739 | ||||||||
\(320\) | 14427.7i | 0.140896i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 22792.2 | 0.219824 | ||||||||
\(323\) | 17902.8i | 0.171599i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −53996.8 | −0.511213 | ||||||||
\(326\) | − 111900.i | − 1.05292i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −16691.9 | −0.155152 | ||||||||
\(329\) | 54863.9i | 0.506868i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 44166.4 | 0.403122 | 0.201561 | − | 0.979476i | \(-0.435399\pi\) | ||||
0.201561 | + | 0.979476i | \(0.435399\pi\) | |||||||
\(332\) | 72267.1i | 0.655639i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −75170.0 | −0.673832 | ||||||||
\(335\) | 56611.2i | 0.504443i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19903.7 | −0.175256 | −0.0876280 | − | 0.996153i | \(-0.527929\pi\) | ||||
−0.0876280 | + | 0.996153i | \(0.527929\pi\) | |||||||
\(338\) | − 207741.i | − 1.81840i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8819.84 | −0.0762962 | ||||||||
\(341\) | − 45054.0i | − 0.387458i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6352.45 | −0.0539949 | ||||||||
\(344\) | − 47336.5i | − 0.400017i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7495.66 | −0.0626120 | ||||||||
\(347\) | − 151074.i | − 1.25467i | −0.778749 | − | 0.627335i | \(-0.784146\pi\) | ||||
0.778749 | − | 0.627335i | \(-0.215854\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −67141.3 | −0.551237 | −0.275619 | − | 0.961267i | \(-0.588883\pi\) | ||||
−0.275619 | + | 0.961267i | \(0.588883\pi\) | |||||||
\(350\) | − 8856.09i | − 0.0722946i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 30503.1 | 0.246183 | ||||||||
\(353\) | 48713.4i | 0.390930i | 0.980711 | + | 0.195465i | \(0.0626216\pi\) | ||||
−0.980711 | + | 0.195465i | \(0.937378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −121354. | −0.962939 | ||||||||
\(356\) | − 29691.6i | − 0.234279i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 79545.9 | 0.620657 | ||||||||
\(359\) | 149704.i | 1.16157i | 0.814057 | + | 0.580784i | \(0.197254\pi\) | ||||
−0.814057 | + | 0.580784i | \(0.802746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 79067.9 | 0.606716 | ||||||||
\(362\) | − 19674.6i | − 0.150137i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 47321.1 | 0.357152 | ||||||||
\(365\) | − 177940.i | − 1.33564i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 170863. | 1.26857 | 0.634286 | − | 0.773098i | \(-0.281294\pi\) | ||||
0.634286 | + | 0.773098i | \(0.281294\pi\) | |||||||
\(368\) | − 27846.8i | − 0.205626i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −64733.4 | −0.472851 | ||||||||
\(371\) | − 59092.3i | − 0.429322i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 75344.3 | 0.541542 | 0.270771 | − | 0.962644i | \(-0.412721\pi\) | ||||
0.270771 | + | 0.962644i | \(0.412721\pi\) | |||||||
\(374\) | 18646.9i | 0.133310i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 67030.8 | 0.474131 | ||||||||
\(377\) | 43346.9i | 0.304983i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 213599. | 1.48703 | 0.743515 | − | 0.668719i | \(-0.233157\pi\) | ||||
0.743515 | + | 0.668719i | \(0.233157\pi\) | |||||||
\(380\) | 103156.i | 0.714377i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −99542.8 | −0.682155 | ||||||||
\(383\) | 37077.1i | 0.252760i | 0.991982 | + | 0.126380i | \(0.0403359\pi\) | ||||
−0.991982 | + | 0.126380i | \(0.959664\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −87941.4 | −0.593297 | ||||||||
\(386\) | − 106301.i | − 0.713446i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −109991. | −0.730620 | ||||||||
\(389\) | − 152168.i | − 1.00560i | −0.864403 | − | 0.502799i | \(-0.832303\pi\) | ||||
0.864403 | − | 0.502799i | \(-0.167697\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17023.1 | 0.111348 | ||||||||
\(392\) | 7761.20i | 0.0505076i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 114808. | 0.739569 | ||||||||
\(395\) | 104369.i | 0.668924i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −273698. | −1.73656 | −0.868281 | − | 0.496073i | \(-0.834775\pi\) | ||||
−0.868281 | + | 0.496073i | \(0.834775\pi\) | |||||||
\(398\) | − 201680.i | − 1.27320i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10820.1 | −0.0676254 | ||||||||
\(401\) | − 206734.i | − 1.28565i | −0.766014 | − | 0.642824i | \(-0.777763\pi\) | ||||
0.766014 | − | 0.642824i | \(-0.222237\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −85395.1 | −0.525803 | ||||||||
\(404\) | − 143199.i | − 0.877359i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7109.39 | −0.0431301 | ||||||||
\(407\) | 136859.i | 0.826200i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18110.7 | −0.108265 | −0.0541327 | − | 0.998534i | \(-0.517239\pi\) | ||||
−0.0541327 | + | 0.998534i | \(0.517239\pi\) | |||||||
\(410\) | − 58795.5i | − 0.349765i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −31839.1 | −0.187571 | ||||||||
\(413\) | 104094.i | 0.610272i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −254553. | −1.47803 | ||||||||
\(416\) | − 57815.4i | − 0.334085i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 218092. | 1.24821 | ||||||||
\(419\) | − 31032.7i | − 0.176763i | −0.996087 | − | 0.0883816i | \(-0.971830\pi\) | ||||
0.996087 | − | 0.0883816i | \(-0.0281695\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 104982. | 0.592314 | 0.296157 | − | 0.955139i | \(-0.404295\pi\) | ||||
0.296157 | + | 0.955139i | \(0.404295\pi\) | |||||||
\(422\) | 165766.i | 0.930830i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −72196.9 | −0.401594 | ||||||||
\(425\) | − 6614.44i | − 0.0366197i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −90062.1 | −0.493954 | ||||||||
\(428\) | 71317.2i | 0.389320i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 166738. | 0.901771 | ||||||||
\(431\) | − 279476.i | − 1.50449i | −0.658882 | − | 0.752246i | \(-0.728971\pi\) | ||||
0.658882 | − | 0.752246i | \(-0.271029\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 147044. | 0.784280 | 0.392140 | − | 0.919905i | \(-0.371735\pi\) | ||||
0.392140 | + | 0.919905i | \(0.371735\pi\) | |||||||
\(434\) | − 14005.8i | − 0.0743580i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 107890. | 0.567557 | ||||||||
\(437\) | − 199100.i | − 1.04258i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −191301. | −0.992631 | −0.496316 | − | 0.868142i | \(-0.665314\pi\) | ||||
−0.496316 | + | 0.868142i | \(0.665314\pi\) | |||||||
\(440\) | 107444.i | 0.554978i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35343.2 | 0.180910 | ||||||||
\(443\) | − 268170.i | − 1.36648i | −0.730195 | − | 0.683239i | \(-0.760571\pi\) | ||||
0.730195 | − | 0.683239i | \(-0.239429\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 104586. | 0.528143 | ||||||||
\(446\) | 88625.3i | 0.445541i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9482.37 | 0.0472456 | ||||||||
\(449\) | − 71968.8i | − 0.356986i | −0.983941 | − | 0.178493i | \(-0.942878\pi\) | ||||
0.983941 | − | 0.178493i | \(-0.0571222\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −124305. | −0.611135 | ||||||||
\(452\) | 32338.9i | 0.158288i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9721.85 | 0.0471669 | ||||||||
\(455\) | 166684.i | 0.805138i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −261174. | −1.25054 | −0.625270 | − | 0.780408i | \(-0.715011\pi\) | ||||
−0.625270 | + | 0.780408i | \(0.715011\pi\) | |||||||
\(458\) | − 191807.i | − 0.914396i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 98087.2 | 0.463550 | ||||||||
\(461\) | 148535.i | 0.698917i | 0.936952 | + | 0.349458i | \(0.113634\pi\) | ||||
−0.936952 | + | 0.349458i | \(0.886366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −179727. | −0.838401 | −0.419200 | − | 0.907894i | \(-0.637689\pi\) | ||||
−0.419200 | + | 0.907894i | \(0.637689\pi\) | |||||||
\(464\) | 8686.01i | 0.0403445i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 176463. | 0.812609 | ||||||||
\(467\) | − 86089.6i | − 0.394745i | −0.980329 | − | 0.197373i | \(-0.936759\pi\) | ||||
0.980329 | − | 0.197373i | \(-0.0632409\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 37206.7 | 0.169152 | ||||||||
\(470\) | 236109.i | 1.06885i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 127178. | 0.570857 | ||||||||
\(473\) | − 352517.i | − 1.57564i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −77361.8 | −0.342878 | ||||||||
\(476\) | 5796.69i | 0.0255839i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 265602. | 1.16245 | ||||||||
\(479\) | − 100240.i | − 0.436890i | −0.975849 | − | 0.218445i | \(-0.929902\pi\) | ||||
0.975849 | − | 0.218445i | \(-0.0700984\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 259402. | 1.12120 | ||||||||
\(482\) | 303541.i | 1.30654i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 110030. | 0.469698 | ||||||||
\(485\) | − 387430.i | − 1.64706i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −79918.4 | −0.336968 | −0.168484 | − | 0.985704i | \(-0.553887\pi\) | ||||
−0.168484 | + | 0.985704i | \(0.553887\pi\) | |||||||
\(488\) | 110035.i | 0.462051i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −27338.0 | −0.113861 | ||||||||
\(491\) | 376135.i | 1.56020i | 0.625654 | + | 0.780101i | \(0.284832\pi\) | ||||
−0.625654 | + | 0.780101i | \(0.715168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5309.86 | −0.0218469 | ||||||||
\(494\) | − 413371.i | − 1.69389i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17111.8 | −0.0695555 | ||||||||
\(497\) | 79758.1i | 0.322896i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 104632. | 0.420205 | 0.210103 | − | 0.977679i | \(-0.432620\pi\) | ||||
0.210103 | + | 0.977679i | \(0.432620\pi\) | |||||||
\(500\) | 102783.i | 0.411133i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 159380. | 0.632449 | ||||||||
\(503\) | 8060.64i | 0.0318591i | 0.999873 | + | 0.0159295i | \(0.00507075\pi\) | ||||
−0.999873 | + | 0.0159295i | \(0.994929\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 504403. | 1.97786 | ||||||||
\(506\) | − 207376.i | − 0.809948i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −149202. | −0.578157 | ||||||||
\(509\) | − 383177.i | − 1.47898i | −0.673165 | − | 0.739492i | \(-0.735066\pi\) | ||||
0.673165 | − | 0.739492i | \(-0.264934\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −116948. | −0.447869 | ||||||||
\(512\) | − 11585.2i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −98192.4 | −0.371665 | ||||||||
\(515\) | − 112150.i | − 0.422848i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 499181. | 1.86757 | ||||||||
\(518\) | 42544.9i | 0.158558i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 203648. | 0.753137 | ||||||||
\(521\) | 165297.i | 0.608962i | 0.952518 | + | 0.304481i | \(0.0984831\pi\) | ||||
−0.952518 | + | 0.304481i | \(0.901517\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 346312. | 1.26609 | 0.633044 | − | 0.774116i | \(-0.281805\pi\) | ||||
0.633044 | + | 0.774116i | \(0.281805\pi\) | |||||||
\(524\) | 113314.i | 0.412688i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −295169. | −1.06684 | ||||||||
\(527\) | − 10460.6i | − 0.0376649i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 90524.2 | 0.323484 | ||||||||
\(530\) | − 254306.i | − 0.905325i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 67797.5 | 0.239547 | ||||||||
\(533\) | 235608.i | 0.829345i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −251207. | −0.877656 | ||||||||
\(536\) | − 45457.9i | − 0.158227i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 230110. | 0.795007 | ||||||||
\(539\) | 57798.0i | 0.198946i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 138669. | 0.473787 | 0.236894 | − | 0.971536i | \(-0.423871\pi\) | ||||
0.236894 | + | 0.971536i | \(0.423871\pi\) | |||||||
\(542\) | 354142.i | 1.20553i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7082.20 | 0.0239315 | ||||||||
\(545\) | 380032.i | 1.27946i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −284471. | −0.950742 | −0.475371 | − | 0.879785i | \(-0.657686\pi\) | ||||
−0.475371 | + | 0.879785i | \(0.657686\pi\) | |||||||
\(548\) | 223172.i | 0.743154i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −80577.5 | −0.266372 | ||||||||
\(551\) | 62103.6i | 0.204557i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 68594.6 | 0.224305 | ||||||||
\(554\) | − 9415.63i | − 0.0306782i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −50996.2 | −0.164963 | ||||||||
\(557\) | 37910.6i | 0.122194i | 0.998132 | + | 0.0610971i | \(0.0194599\pi\) | ||||
−0.998132 | + | 0.0610971i | \(0.980540\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −668158. | −2.13823 | ||||||||
\(560\) | 33400.6i | 0.106507i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −429629. | −1.36026 | ||||||||
\(563\) | − 164337.i | − 0.518465i | −0.965815 | − | 0.259233i | \(-0.916530\pi\) | ||||
0.965815 | − | 0.259233i | \(-0.0834696\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −113910. | −0.356833 | ||||||||
\(566\) | − 11411.6i | − 0.0356216i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 97445.7 | 0.302041 | ||||||||
\(569\) | 394027.i | 1.21703i | 0.793542 | + | 0.608516i | \(0.208235\pi\) | ||||
−0.793542 | + | 0.608516i | \(0.791765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −269585. | −0.826844 | −0.413422 | − | 0.910540i | \(-0.635667\pi\) | ||||
−0.413422 | + | 0.910540i | \(0.635667\pi\) | |||||||
\(572\) | − 430553.i | − 1.31594i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −38642.3 | −0.117284 | ||||||||
\(575\) | 73560.5i | 0.222489i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11879.8 | 0.0356826 | 0.0178413 | − | 0.999841i | \(-0.494321\pi\) | ||||
0.0178413 | + | 0.999841i | \(0.494321\pi\) | |||||||
\(578\) | − 231904.i | − 0.694148i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −30595.5 | −0.0909498 | ||||||||
\(581\) | 167301.i | 0.495616i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −537653. | −1.58185 | ||||||||
\(584\) | 142883.i | 0.418943i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 111805. | 0.325587 | ||||||||
\(587\) | 433502.i | 1.25810i | 0.777365 | + | 0.629050i | \(0.216556\pi\) | ||||
−0.777365 | + | 0.629050i | \(0.783444\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −122347. | −0.352664 | ||||||||
\(590\) | 447970.i | 1.28690i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 51979.9 | 0.148317 | ||||||||
\(593\) | 65763.0i | 0.187013i | 0.995619 | + | 0.0935066i | \(0.0298076\pi\) | ||||
−0.995619 | + | 0.0935066i | \(0.970192\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20418.2 | −0.0576745 | ||||||||
\(596\) | − 258878.i | − 0.728791i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −393059. | −1.09915 | ||||||||
\(599\) | 232771.i | 0.648746i | 0.945929 | + | 0.324373i | \(0.105153\pi\) | ||||
−0.945929 | + | 0.324373i | \(0.894847\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −98549.6 | −0.272839 | −0.136419 | − | 0.990651i | \(-0.543559\pi\) | ||||
−0.136419 | + | 0.990651i | \(0.543559\pi\) | |||||||
\(602\) | − 109585.i | − 0.302385i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −156559. | −0.429144 | ||||||||
\(605\) | 387568.i | 1.05886i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 58943.3 | 0.159977 | 0.0799884 | − | 0.996796i | \(-0.474512\pi\) | ||||
0.0799884 | + | 0.996796i | \(0.474512\pi\) | |||||||
\(608\) | − 82832.7i | − 0.224076i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −387586. | −1.04162 | ||||||||
\(611\) | − 946145.i | − 2.53440i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 127556. | 0.339453 | 0.169727 | − | 0.985491i | \(-0.445712\pi\) | ||||
0.169727 | + | 0.985491i | \(0.445712\pi\) | |||||||
\(614\) | 246562.i | 0.654019i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 70615.6 | 0.186097 | ||||||||
\(617\) | 183225.i | 0.481299i | 0.970612 | + | 0.240649i | \(0.0773604\pi\) | ||||
−0.970612 | + | 0.240649i | \(0.922640\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −171376. | −0.447268 | −0.223634 | − | 0.974673i | \(-0.571792\pi\) | ||||
−0.223634 | + | 0.974673i | \(0.571792\pi\) | |||||||
\(620\) | − 60274.3i | − 0.156801i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 369740. | 0.955686 | ||||||||
\(623\) | − 68737.1i | − 0.177099i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −467707. | −1.19733 | ||||||||
\(626\) | 367272.i | 0.937214i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 234698. | 0.595100 | ||||||||
\(629\) | 31776.0i | 0.0803151i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −195310. | −0.490530 | −0.245265 | − | 0.969456i | \(-0.578875\pi\) | ||||
−0.245265 | + | 0.969456i | \(0.578875\pi\) | |||||||
\(632\) | − 83806.6i | − 0.209819i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 228704. | 0.568977 | ||||||||
\(635\) | − 525546.i | − 1.30336i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 109550. | 0.269981 | ||||||||
\(638\) | 64685.0i | 0.158914i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 40807.7 | 0.0996283 | ||||||||
\(641\) | 10697.3i | 0.0260351i | 0.999915 | + | 0.0130175i | \(0.00414373\pi\) | ||||
−0.999915 | + | 0.0130175i | \(0.995856\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −171673. | −0.415221 | −0.207611 | − | 0.978212i | \(-0.566569\pi\) | ||||
−0.207611 | + | 0.978212i | \(0.566569\pi\) | |||||||
\(644\) | − 64466.1i | − 0.155439i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 50636.6 | 0.121339 | ||||||||
\(647\) | 814856.i | 1.94658i | 0.229580 | + | 0.973290i | \(0.426265\pi\) | ||||
−0.229580 | + | 0.973290i | \(0.573735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 947099. | 2.24857 | ||||||||
\(650\) | 152726.i | 0.361482i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −316501. | −0.744526 | ||||||||
\(653\) | 741201.i | 1.73824i | 0.494601 | + | 0.869120i | \(0.335314\pi\) | ||||
−0.494601 | + | 0.869120i | \(0.664686\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −399137. | −0.930334 | ||||||||
\(656\) | 47211.9i | 0.109709i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 155178. | 0.358410 | ||||||||
\(659\) | 548473.i | 1.26294i | 0.775398 | + | 0.631472i | \(0.217549\pi\) | ||||
−0.775398 | + | 0.631472i | \(0.782451\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 426168. | 0.975389 | 0.487695 | − | 0.873014i | \(-0.337838\pi\) | ||||
0.487695 | + | 0.873014i | \(0.337838\pi\) | |||||||
\(662\) | − 124922.i | − 0.285050i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 204402. | 0.463607 | ||||||||
\(665\) | 238809.i | 0.540018i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 59052.0 | 0.132734 | ||||||||
\(668\) | 212613.i | 0.476471i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 160121. | 0.356695 | ||||||||
\(671\) | 819433.i | 1.81999i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 332282. | 0.733630 | 0.366815 | − | 0.930294i | \(-0.380448\pi\) | ||||
0.366815 | + | 0.930294i | \(0.380448\pi\) | |||||||
\(674\) | 56296.0i | 0.123925i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −587580. | −1.28580 | ||||||||
\(677\) | 371163.i | 0.809818i | 0.914357 | + | 0.404909i | \(0.132697\pi\) | ||||
−0.914357 | + | 0.404909i | \(0.867303\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −254632. | −0.552297 | ||||||||
\(680\) | 24946.3i | 0.0539496i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −127432. | −0.273974 | ||||||||
\(683\) | − 688730.i | − 1.47641i | −0.674575 | − | 0.738206i | \(-0.735673\pi\) | ||||
0.674575 | − | 0.738206i | \(-0.264327\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −786100. | −1.67532 | ||||||||
\(686\) | 17967.4i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −133888. | −0.282855 | ||||||||
\(689\) | 1.01906e6i | 2.14666i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28665.8 | 0.0600354 | 0.0300177 | − | 0.999549i | \(-0.490444\pi\) | ||||
0.0300177 | + | 0.999549i | \(0.490444\pi\) | |||||||
\(692\) | 21200.9i | 0.0442734i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −427301. | −0.887186 | ||||||||
\(695\) | − 179628.i | − 0.371882i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28861.2 | −0.0594085 | ||||||||
\(698\) | 189904.i | 0.389784i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −25048.8 | −0.0511200 | ||||||||
\(701\) | − 347036.i | − 0.706218i | −0.935582 | − | 0.353109i | \(-0.885124\pi\) | ||||
0.935582 | − | 0.353109i | \(-0.114876\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 371648. | 0.752007 | ||||||||
\(704\) | − 86275.7i | − 0.174078i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 137782. | 0.276429 | ||||||||
\(707\) | − 331510.i | − 0.663221i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 117651. | 0.234047 | 0.117024 | − | 0.993129i | \(-0.462665\pi\) | ||||
0.117024 | + | 0.993129i | \(0.462665\pi\) | |||||||
\(710\) | 343242.i | 0.680901i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −83980.6 | −0.165661 | ||||||||
\(713\) | 116335.i | 0.228839i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.51658e6 | 2.96656 | ||||||||
\(716\) | − 224990.i | − 0.438871i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 423427. | 0.821353 | ||||||||
\(719\) | − 376532.i | − 0.728356i | −0.931329 | − | 0.364178i | \(-0.881350\pi\) | ||||
0.931329 | − | 0.364178i | \(-0.118650\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −73708.6 | −0.141791 | ||||||||
\(722\) | − 223638.i | − 0.429013i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −55648.0 | −0.106163 | ||||||||
\(725\) | − 22945.1i | − 0.0436530i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 618700. | 1.17061 | 0.585304 | − | 0.810814i | \(-0.300975\pi\) | ||||
0.585304 | + | 0.810814i | \(0.300975\pi\) | |||||||
\(728\) | − 133844.i | − 0.252544i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −503290. | −0.944437 | ||||||||
\(731\) | − 81847.2i | − 0.153168i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −454163. | −0.845287 | −0.422643 | − | 0.906296i | \(-0.638898\pi\) | ||||
−0.422643 | + | 0.906296i | \(0.638898\pi\) | |||||||
\(734\) | − 483273.i | − 0.897016i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −78762.5 | −0.145400 | ||||||||
\(737\) | − 338527.i | − 0.623244i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 200302. | 0.366771 | 0.183386 | − | 0.983041i | \(-0.441294\pi\) | ||||
0.183386 | + | 0.983041i | \(0.441294\pi\) | |||||||
\(740\) | 183094.i | 0.334356i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −167138. | −0.303576 | ||||||||
\(743\) | 854018.i | 1.54700i | 0.633799 | + | 0.773498i | \(0.281495\pi\) | ||||
−0.633799 | + | 0.773498i | \(0.718505\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 911871. | 1.64294 | ||||||||
\(746\) | − 213106.i | − 0.382928i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 52741.4 | 0.0942646 | ||||||||
\(749\) | 165102.i | 0.294298i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −692616. | −1.22804 | −0.614020 | − | 0.789290i | \(-0.710449\pi\) | ||||
−0.614020 | + | 0.789290i | \(0.710449\pi\) | |||||||
\(752\) | − 189592.i | − 0.335261i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 122604. | 0.215656 | ||||||||
\(755\) | − 551461.i | − 0.967433i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 154839. | 0.270202 | 0.135101 | − | 0.990832i | \(-0.456864\pi\) | ||||
0.135101 | + | 0.990832i | \(0.456864\pi\) | |||||||
\(758\) | − 604148.i | − 1.05149i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 291769. | 0.505141 | ||||||||
\(761\) | − 913167.i | − 1.57682i | −0.615153 | − | 0.788408i | \(-0.710906\pi\) | ||||
0.615153 | − | 0.788408i | \(-0.289094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 249769. | 0.429032 | ||||||||
\(764\) | 281549.i | 0.482356i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 104870. | 0.178728 | ||||||||
\(767\) | − 1.79513e6i | − 3.05144i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.00329e6 | −1.69657 | −0.848286 | − | 0.529538i | \(-0.822365\pi\) | ||||
−0.848286 | + | 0.529538i | \(0.822365\pi\) | |||||||
\(770\) | 248736.i | 0.419524i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −300664. | −0.504483 | ||||||||
\(773\) | − 474439.i | − 0.794001i | −0.917818 | − | 0.397001i | \(-0.870051\pi\) | ||||
0.917818 | − | 0.397001i | \(-0.129949\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45202.8 | 0.0752595 | ||||||||
\(776\) | 311100.i | 0.516627i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −430397. | −0.711066 | ||||||||
\(779\) | 337558.i | 0.556254i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 725682. | 1.18972 | ||||||||
\(782\) | − 48148.5i | − 0.0787353i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21952.0 | 0.0357143 | ||||||||
\(785\) | 826698.i | 1.34155i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 590744. | 0.953783 | 0.476892 | − | 0.878962i | \(-0.341763\pi\) | ||||
0.476892 | + | 0.878962i | \(0.341763\pi\) | |||||||
\(788\) | − 324725.i | − 0.522954i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 295200. | 0.473000 | ||||||||
\(791\) | 74865.5i | 0.119654i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.55315e6 | 2.46983 | ||||||||
\(794\) | 774134.i | 1.22793i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −570436. | −0.900286 | ||||||||
\(797\) | 600262.i | 0.944984i | 0.881335 | + | 0.472492i | \(0.156645\pi\) | ||||
−0.881335 | + | 0.472492i | \(0.843355\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 115900. | 0.181547 | ||||||||
\(800\) | 30603.8i | 0.0478184i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −584731. | −0.909091 | ||||||||
\(803\) | 1.06406e6i | 1.65019i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 227075. | 0.350411 | ||||||||
\(806\) | 241534.i | 0.371799i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −405028. | −0.620386 | ||||||||
\(809\) | 649360.i | 0.992176i | 0.868272 | + | 0.496088i | \(0.165231\pi\) | ||||
−0.868272 | + | 0.496088i | \(0.834769\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.13293e6 | −1.72250 | −0.861251 | − | 0.508179i | \(-0.830319\pi\) | ||||
−0.861251 | + | 0.508179i | \(0.830319\pi\) | |||||||
\(812\) | 20108.4i | 0.0304976i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 387096. | 0.584212 | ||||||||
\(815\) | − 1.11484e6i | − 1.67841i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −957277. | −1.43415 | ||||||||
\(818\) | 51224.9i | 0.0765552i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −166299. | −0.247321 | ||||||||
\(821\) | − 463203.i | − 0.687204i | −0.939115 | − | 0.343602i | \(-0.888353\pi\) | ||||
0.939115 | − | 0.343602i | \(-0.111647\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.00476e6 | 1.48341 | 0.741705 | − | 0.670726i | \(-0.234017\pi\) | ||||
0.741705 | + | 0.670726i | \(0.234017\pi\) | |||||||
\(824\) | 90054.6i | 0.132633i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 294421. | 0.431528 | ||||||||
\(827\) | − 57967.0i | − 0.0847559i | −0.999102 | − | 0.0423779i | \(-0.986507\pi\) | ||||
0.999102 | − | 0.0423779i | \(-0.0134934\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.08695e6 | 1.58162 | 0.790809 | − | 0.612063i | \(-0.209660\pi\) | ||||
0.790809 | + | 0.612063i | \(0.209660\pi\) | |||||||
\(830\) | 719985.i | 1.04512i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −163527. | −0.236234 | ||||||||
\(833\) | 13419.5i | 0.0193396i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −748906. | −1.07412 | ||||||||
\(836\) | − 616858.i | − 0.882618i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −87773.8 | −0.124990 | ||||||||
\(839\) | 1.04936e6i | 1.49073i | 0.666655 | + | 0.745367i | \(0.267726\pi\) | ||||
−0.666655 | + | 0.745367i | \(0.732274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 688861. | 0.973957 | ||||||||
\(842\) | − 296935.i | − 0.418829i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 468857. | 0.658196 | ||||||||
\(845\) | − 2.06969e6i | − 2.89862i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 254722. | 0.355059 | ||||||||
\(848\) | 204204.i | 0.283970i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18708.5 | −0.0258941 | ||||||||
\(851\) | − 353387.i | − 0.487968i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 731878. | 1.00587 | 0.502933 | − | 0.864325i | \(-0.332254\pi\) | ||||
0.502933 | + | 0.864325i | \(0.332254\pi\) | |||||||
\(854\) | 254734.i | 0.349278i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 201715. | 0.275291 | ||||||||
\(857\) | − 704349.i | − 0.959017i | −0.877537 | − | 0.479509i | \(-0.840815\pi\) | ||||
0.877537 | − | 0.479509i | \(-0.159185\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.16702e6 | −1.58159 | −0.790793 | − | 0.612084i | \(-0.790331\pi\) | ||||
−0.790793 | + | 0.612084i | \(0.790331\pi\) | |||||||
\(860\) | − 471605.i | − 0.637649i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −790477. | −1.06384 | ||||||||
\(863\) | − 126671.i | − 0.170081i | −0.996377 | − | 0.0850405i | \(-0.972898\pi\) | ||||
0.996377 | − | 0.0850405i | \(-0.0271020\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −74678.0 | −0.0998069 | ||||||||
\(866\) | − 415903.i | − 0.554570i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −39614.3 | −0.0525790 | ||||||||
\(869\) | − 624111.i | − 0.826461i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −641642. | −0.845778 | ||||||||
\(872\) | − 305160.i | − 0.401323i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −563140. | −0.737214 | ||||||||
\(875\) | 237946.i | 0.310787i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −891593. | −1.15922 | −0.579612 | − | 0.814892i | \(-0.696796\pi\) | ||||
−0.579612 | + | 0.814892i | \(0.696796\pi\) | |||||||
\(878\) | 541081.i | 0.701896i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 303897. | 0.392429 | ||||||||
\(881\) | − 494760.i | − 0.637445i | −0.947848 | − | 0.318723i | \(-0.896746\pi\) | ||||
0.947848 | − | 0.318723i | \(-0.103254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −104454. | −0.133969 | −0.0669847 | − | 0.997754i | \(-0.521338\pi\) | ||||
−0.0669847 | + | 0.997754i | \(0.521338\pi\) | |||||||
\(884\) | − 99965.8i | − 0.127922i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −758499. | −0.966246 | ||||||||
\(887\) | 176125.i | 0.223859i | 0.993716 | + | 0.111929i | \(0.0357031\pi\) | ||||
−0.993716 | + | 0.111929i | \(0.964297\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −345406. | −0.437046 | ||||||||
\(890\) | − 295813.i | − 0.373454i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 250670. | 0.315045 | ||||||||
\(893\) | − 1.35555e6i | − 1.69986i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 792502. | 0.989360 | ||||||||
\(896\) | − 26820.2i | − 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −203559. | −0.252427 | ||||||||
\(899\) | − 36287.3i | − 0.0448989i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −124832. | −0.153772 | ||||||||
\(902\) | 351589.i | 0.432138i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 91468.1 | 0.111926 | ||||||||
\(905\) | − 196014.i | − 0.239326i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 734712. | 0.893105 | 0.446553 | − | 0.894757i | \(-0.352652\pi\) | ||||
0.446553 | + | 0.894757i | \(0.352652\pi\) | |||||||
\(908\) | − 27497.5i | − 0.0333520i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 471452. | 0.569318 | ||||||||
\(911\) | 628633.i | 0.757462i | 0.925507 | + | 0.378731i | \(0.123639\pi\) | ||||
−0.925507 | + | 0.378731i | \(0.876361\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.52219e6 | 1.82611 | ||||||||
\(914\) | 738712.i | 0.884266i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −542513. | −0.646576 | ||||||||
\(917\) | 262326.i | 0.311963i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.34955e6 | −1.59793 | −0.798965 | − | 0.601377i | \(-0.794619\pi\) | ||||
−0.798965 | + | 0.601377i | \(0.794619\pi\) | |||||||
\(920\) | − 277432.i | − 0.327779i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 420119. | 0.494209 | ||||||||
\(923\) | − 1.37545e6i | − 1.61452i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −137311. | −0.160480 | ||||||||
\(926\) | 508345.i | 0.592839i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 24567.7 | 0.0285279 | ||||||||
\(929\) | − 1.52629e6i | − 1.76851i | −0.467007 | − | 0.884254i | \(-0.654668\pi\) | ||||
0.467007 | − | 0.884254i | \(-0.345332\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 156953. | 0.181080 | ||||||||
\(932\) | − 499112.i | − 0.574601i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −243498. | −0.279127 | ||||||||
\(935\) | 185776.i | 0.212504i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 542424. | 0.617817 | 0.308908 | − | 0.951092i | \(-0.400036\pi\) | ||||
0.308908 | + | 0.951092i | \(0.400036\pi\) | |||||||
\(938\) | − 105237.i | − 0.119608i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 667816. | 0.755790 | ||||||||
\(941\) | 620071.i | 0.700265i | 0.936700 | + | 0.350132i | \(0.113863\pi\) | ||||
−0.936700 | + | 0.350132i | \(0.886137\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 320971. | 0.360946 | ||||||||
\(944\) | − 359713.i | − 0.403657i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −997067. | −1.11415 | ||||||||
\(947\) | 620123.i | 0.691477i | 0.938331 | + | 0.345738i | \(0.112372\pi\) | ||||
−0.938331 | + | 0.345738i | \(0.887628\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.01681e6 | 2.23940 | ||||||||
\(950\) | 218812.i | 0.242451i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16395.5 | 0.0180905 | ||||||||
\(953\) | 568767.i | 0.626251i | 0.949712 | + | 0.313126i | \(0.101376\pi\) | ||||
−0.949712 | + | 0.313126i | \(0.898624\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −991727. | −1.08739 | ||||||||
\(956\) | − 751236.i | − 0.821979i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −283523. | −0.308928 | ||||||||
\(959\) | 516651.i | 0.561772i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −852034. | −0.922593 | ||||||||
\(962\) | − 733700.i | − 0.792809i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 858543. | 0.923864 | ||||||||
\(965\) | − 1.05905e6i | − 1.13727i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 747986. | 0.799909 | 0.399954 | − | 0.916535i | \(-0.369026\pi\) | ||||
0.399954 | + | 0.916535i | \(0.369026\pi\) | |||||||
\(968\) | − 311211.i | − 0.332127i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.09582e6 | −1.16465 | ||||||||
\(971\) | 1.50806e6i | 1.59949i | 0.600343 | + | 0.799743i | \(0.295031\pi\) | ||||
−0.600343 | + | 0.799743i | \(0.704969\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −118058. | −0.124701 | ||||||||
\(974\) | 226043.i | 0.238272i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 311225. | 0.326720 | ||||||||
\(977\) | 1.24528e6i | 1.30460i | 0.757960 | + | 0.652301i | \(0.226196\pi\) | ||||
−0.757960 | + | 0.652301i | \(0.773804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −625407. | −0.652525 | ||||||||
\(980\) | 77323.5i | 0.0805118i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.06387e6 | 1.10323 | ||||||||
\(983\) | − 753418.i | − 0.779703i | −0.920878 | − | 0.389851i | \(-0.872526\pi\) | ||||
0.920878 | − | 0.389851i | \(-0.127474\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.14381e6 | 1.17891 | ||||||||
\(986\) | 15018.6i | 0.0154481i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.16919e6 | −1.19776 | ||||||||
\(989\) | 910239.i | 0.930599i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −77288.4 | −0.0786986 | −0.0393493 | − | 0.999226i | \(-0.512528\pi\) | ||||
−0.0393493 | + | 0.999226i | \(0.512528\pi\) | |||||||
\(992\) | 48399.4i | 0.0491832i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 225590. | 0.228322 | ||||||||
\(995\) | − 2.00930e6i | − 2.02954i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.32860e6 | 1.33661 | 0.668305 | − | 0.743888i | \(-0.267020\pi\) | ||||
0.668305 | + | 0.743888i | \(0.267020\pi\) | |||||||
\(998\) | − 295943.i | − 0.297130i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 378.5.b.b.323.2 | ✓ | 8 | |
3.2 | odd | 2 | inner | 378.5.b.b.323.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.5.b.b.323.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
378.5.b.b.323.7 | yes | 8 | 3.2 | odd | 2 | inner |