Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,6,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.a (trivial) |
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: | yes |
Analytic conductor: | \(87.5695656179\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 546.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 24.0000 | 0.429325 | 0.214663 | − | 0.976688i | \(-0.431135\pi\) | ||||
0.214663 | + | 0.976688i | \(0.431135\pi\) | |||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 96.0000 | 0.303579 | ||||||||
\(11\) | 374.000 | 0.931944 | 0.465972 | − | 0.884799i | \(-0.345705\pi\) | ||||
0.465972 | + | 0.884799i | \(0.345705\pi\) | |||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | −169.000 | −0.277350 | ||||||||
\(14\) | 196.000 | 0.267261 | ||||||||
\(15\) | 216.000 | 0.247871 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1786.00 | 1.49885 | 0.749427 | − | 0.662087i | \(-0.230329\pi\) | ||||
0.749427 | + | 0.662087i | \(0.230329\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | 584.000 | 0.371132 | 0.185566 | − | 0.982632i | \(-0.440588\pi\) | ||||
0.185566 | + | 0.982632i | \(0.440588\pi\) | |||||||
\(20\) | 384.000 | 0.214663 | ||||||||
\(21\) | 441.000 | 0.218218 | ||||||||
\(22\) | 1496.00 | 0.658984 | ||||||||
\(23\) | −884.000 | −0.348444 | −0.174222 | − | 0.984706i | \(-0.555741\pi\) | ||||
−0.174222 | + | 0.984706i | \(0.555741\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | −2549.00 | −0.815680 | ||||||||
\(26\) | −676.000 | −0.196116 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 784.000 | 0.188982 | ||||||||
\(29\) | −5878.00 | −1.29788 | −0.648940 | − | 0.760840i | \(-0.724787\pi\) | ||||
−0.648940 | + | 0.760840i | \(0.724787\pi\) | |||||||
\(30\) | 864.000 | 0.175271 | ||||||||
\(31\) | 6196.00 | 1.15800 | 0.578998 | − | 0.815329i | \(-0.303444\pi\) | ||||
0.578998 | + | 0.815329i | \(0.303444\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 3366.00 | 0.538058 | ||||||||
\(34\) | 7144.00 | 1.05985 | ||||||||
\(35\) | 1176.00 | 0.162270 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −2690.00 | −0.323034 | −0.161517 | − | 0.986870i | \(-0.551639\pi\) | ||||
−0.161517 | + | 0.986870i | \(0.551639\pi\) | |||||||
\(38\) | 2336.00 | 0.262430 | ||||||||
\(39\) | −1521.00 | −0.160128 | ||||||||
\(40\) | 1536.00 | 0.151789 | ||||||||
\(41\) | 1848.00 | 0.171689 | 0.0858445 | − | 0.996309i | \(-0.472641\pi\) | ||||
0.0858445 | + | 0.996309i | \(0.472641\pi\) | |||||||
\(42\) | 1764.00 | 0.154303 | ||||||||
\(43\) | 22164.0 | 1.82800 | 0.914002 | − | 0.405710i | \(-0.132976\pi\) | ||||
0.914002 | + | 0.405710i | \(0.132976\pi\) | |||||||
\(44\) | 5984.00 | 0.465972 | ||||||||
\(45\) | 1944.00 | 0.143108 | ||||||||
\(46\) | −3536.00 | −0.246387 | ||||||||
\(47\) | −4190.00 | −0.276675 | −0.138337 | − | 0.990385i | \(-0.544176\pi\) | ||||
−0.138337 | + | 0.990385i | \(0.544176\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | −10196.0 | −0.576773 | ||||||||
\(51\) | 16074.0 | 0.865363 | ||||||||
\(52\) | −2704.00 | −0.138675 | ||||||||
\(53\) | −1082.00 | −0.0529100 | −0.0264550 | − | 0.999650i | \(-0.508422\pi\) | ||||
−0.0264550 | + | 0.999650i | \(0.508422\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 8976.00 | 0.400107 | ||||||||
\(56\) | 3136.00 | 0.133631 | ||||||||
\(57\) | 5256.00 | 0.214273 | ||||||||
\(58\) | −23512.0 | −0.917740 | ||||||||
\(59\) | −14286.0 | −0.534294 | −0.267147 | − | 0.963656i | \(-0.586081\pi\) | ||||
−0.267147 | + | 0.963656i | \(0.586081\pi\) | |||||||
\(60\) | 3456.00 | 0.123935 | ||||||||
\(61\) | −8390.00 | −0.288694 | −0.144347 | − | 0.989527i | \(-0.546108\pi\) | ||||
−0.144347 | + | 0.989527i | \(0.546108\pi\) | |||||||
\(62\) | 24784.0 | 0.818827 | ||||||||
\(63\) | 3969.00 | 0.125988 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −4056.00 | −0.119073 | ||||||||
\(66\) | 13464.0 | 0.380465 | ||||||||
\(67\) | −21508.0 | −0.585346 | −0.292673 | − | 0.956213i | \(-0.594545\pi\) | ||||
−0.292673 | + | 0.956213i | \(0.594545\pi\) | |||||||
\(68\) | 28576.0 | 0.749427 | ||||||||
\(69\) | −7956.00 | −0.201174 | ||||||||
\(70\) | 4704.00 | 0.114742 | ||||||||
\(71\) | 19266.0 | 0.453571 | 0.226786 | − | 0.973945i | \(-0.427178\pi\) | ||||
0.226786 | + | 0.973945i | \(0.427178\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | 71926.0 | 1.57972 | 0.789858 | − | 0.613290i | \(-0.210154\pi\) | ||||
0.789858 | + | 0.613290i | \(0.210154\pi\) | |||||||
\(74\) | −10760.0 | −0.228419 | ||||||||
\(75\) | −22941.0 | −0.470933 | ||||||||
\(76\) | 9344.00 | 0.185566 | ||||||||
\(77\) | 18326.0 | 0.352242 | ||||||||
\(78\) | −6084.00 | −0.113228 | ||||||||
\(79\) | −7184.00 | −0.129509 | −0.0647543 | − | 0.997901i | \(-0.520626\pi\) | ||||
−0.0647543 | + | 0.997901i | \(0.520626\pi\) | |||||||
\(80\) | 6144.00 | 0.107331 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 7392.00 | 0.121402 | ||||||||
\(83\) | 99134.0 | 1.57953 | 0.789764 | − | 0.613411i | \(-0.210203\pi\) | ||||
0.789764 | + | 0.613411i | \(0.210203\pi\) | |||||||
\(84\) | 7056.00 | 0.109109 | ||||||||
\(85\) | 42864.0 | 0.643495 | ||||||||
\(86\) | 88656.0 | 1.29259 | ||||||||
\(87\) | −52902.0 | −0.749331 | ||||||||
\(88\) | 23936.0 | 0.329492 | ||||||||
\(89\) | −19940.0 | −0.266840 | −0.133420 | − | 0.991060i | \(-0.542596\pi\) | ||||
−0.133420 | + | 0.991060i | \(0.542596\pi\) | |||||||
\(90\) | 7776.00 | 0.101193 | ||||||||
\(91\) | −8281.00 | −0.104828 | ||||||||
\(92\) | −14144.0 | −0.174222 | ||||||||
\(93\) | 55764.0 | 0.668569 | ||||||||
\(94\) | −16760.0 | −0.195639 | ||||||||
\(95\) | 14016.0 | 0.159336 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | −42322.0 | −0.456706 | −0.228353 | − | 0.973578i | \(-0.573334\pi\) | ||||
−0.228353 | + | 0.973578i | \(0.573334\pi\) | |||||||
\(98\) | 9604.00 | 0.101015 | ||||||||
\(99\) | 30294.0 | 0.310648 | ||||||||
\(100\) | −40784.0 | −0.407840 | ||||||||
\(101\) | −162462. | −1.58470 | −0.792352 | − | 0.610064i | \(-0.791144\pi\) | ||||
−0.792352 | + | 0.610064i | \(0.791144\pi\) | |||||||
\(102\) | 64296.0 | 0.611904 | ||||||||
\(103\) | −120600. | −1.12009 | −0.560047 | − | 0.828461i | \(-0.689217\pi\) | ||||
−0.560047 | + | 0.828461i | \(0.689217\pi\) | |||||||
\(104\) | −10816.0 | −0.0980581 | ||||||||
\(105\) | 10584.0 | 0.0936864 | ||||||||
\(106\) | −4328.00 | −0.0374130 | ||||||||
\(107\) | 42992.0 | 0.363018 | 0.181509 | − | 0.983389i | \(-0.441902\pi\) | ||||
0.181509 | + | 0.983389i | \(0.441902\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | 204522. | 1.64882 | 0.824411 | − | 0.565992i | \(-0.191507\pi\) | ||||
0.824411 | + | 0.565992i | \(0.191507\pi\) | |||||||
\(110\) | 35904.0 | 0.282918 | ||||||||
\(111\) | −24210.0 | −0.186504 | ||||||||
\(112\) | 12544.0 | 0.0944911 | ||||||||
\(113\) | 79046.0 | 0.582350 | 0.291175 | − | 0.956670i | \(-0.405954\pi\) | ||||
0.291175 | + | 0.956670i | \(0.405954\pi\) | |||||||
\(114\) | 21024.0 | 0.151514 | ||||||||
\(115\) | −21216.0 | −0.149596 | ||||||||
\(116\) | −94048.0 | −0.648940 | ||||||||
\(117\) | −13689.0 | −0.0924500 | ||||||||
\(118\) | −57144.0 | −0.377803 | ||||||||
\(119\) | 87514.0 | 0.566513 | ||||||||
\(120\) | 13824.0 | 0.0876356 | ||||||||
\(121\) | −21175.0 | −0.131480 | ||||||||
\(122\) | −33560.0 | −0.204137 | ||||||||
\(123\) | 16632.0 | 0.0991247 | ||||||||
\(124\) | 99136.0 | 0.578998 | ||||||||
\(125\) | −136176. | −0.779517 | ||||||||
\(126\) | 15876.0 | 0.0890871 | ||||||||
\(127\) | 125904. | 0.692676 | 0.346338 | − | 0.938110i | \(-0.387425\pi\) | ||||
0.346338 | + | 0.938110i | \(0.387425\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 199476. | 1.05540 | ||||||||
\(130\) | −16224.0 | −0.0841976 | ||||||||
\(131\) | 159568. | 0.812396 | 0.406198 | − | 0.913785i | \(-0.366854\pi\) | ||||
0.406198 | + | 0.913785i | \(0.366854\pi\) | |||||||
\(132\) | 53856.0 | 0.269029 | ||||||||
\(133\) | 28616.0 | 0.140275 | ||||||||
\(134\) | −86032.0 | −0.413902 | ||||||||
\(135\) | 17496.0 | 0.0826236 | ||||||||
\(136\) | 114304. | 0.529925 | ||||||||
\(137\) | −1824.00 | −0.00830278 | −0.00415139 | − | 0.999991i | \(-0.501321\pi\) | ||||
−0.00415139 | + | 0.999991i | \(0.501321\pi\) | |||||||
\(138\) | −31824.0 | −0.142252 | ||||||||
\(139\) | 135268. | 0.593824 | 0.296912 | − | 0.954905i | \(-0.404043\pi\) | ||||
0.296912 | + | 0.954905i | \(0.404043\pi\) | |||||||
\(140\) | 18816.0 | 0.0811348 | ||||||||
\(141\) | −37710.0 | −0.159738 | ||||||||
\(142\) | 77064.0 | 0.320723 | ||||||||
\(143\) | −63206.0 | −0.258475 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −141072. | −0.557212 | ||||||||
\(146\) | 287704. | 1.11703 | ||||||||
\(147\) | 21609.0 | 0.0824786 | ||||||||
\(148\) | −43040.0 | −0.161517 | ||||||||
\(149\) | −138700. | −0.511812 | −0.255906 | − | 0.966702i | \(-0.582374\pi\) | ||||
−0.255906 | + | 0.966702i | \(0.582374\pi\) | |||||||
\(150\) | −91764.0 | −0.333000 | ||||||||
\(151\) | −206196. | −0.735932 | −0.367966 | − | 0.929839i | \(-0.619946\pi\) | ||||
−0.367966 | + | 0.929839i | \(0.619946\pi\) | |||||||
\(152\) | 37376.0 | 0.131215 | ||||||||
\(153\) | 144666. | 0.499618 | ||||||||
\(154\) | 73304.0 | 0.249073 | ||||||||
\(155\) | 148704. | 0.497157 | ||||||||
\(156\) | −24336.0 | −0.0800641 | ||||||||
\(157\) | −40802.0 | −0.132109 | −0.0660545 | − | 0.997816i | \(-0.521041\pi\) | ||||
−0.0660545 | + | 0.997816i | \(0.521041\pi\) | |||||||
\(158\) | −28736.0 | −0.0915764 | ||||||||
\(159\) | −9738.00 | −0.0305476 | ||||||||
\(160\) | 24576.0 | 0.0758947 | ||||||||
\(161\) | −43316.0 | −0.131699 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | −76904.0 | −0.226715 | −0.113357 | − | 0.993554i | \(-0.536161\pi\) | ||||
−0.113357 | + | 0.993554i | \(0.536161\pi\) | |||||||
\(164\) | 29568.0 | 0.0858445 | ||||||||
\(165\) | 80784.0 | 0.231002 | ||||||||
\(166\) | 396536. | 1.11690 | ||||||||
\(167\) | 287434. | 0.797530 | 0.398765 | − | 0.917053i | \(-0.369439\pi\) | ||||
0.398765 | + | 0.917053i | \(0.369439\pi\) | |||||||
\(168\) | 28224.0 | 0.0771517 | ||||||||
\(169\) | 28561.0 | 0.0769231 | ||||||||
\(170\) | 171456. | 0.455020 | ||||||||
\(171\) | 47304.0 | 0.123711 | ||||||||
\(172\) | 354624. | 0.914002 | ||||||||
\(173\) | 113466. | 0.288238 | 0.144119 | − | 0.989560i | \(-0.453965\pi\) | ||||
0.144119 | + | 0.989560i | \(0.453965\pi\) | |||||||
\(174\) | −211608. | −0.529857 | ||||||||
\(175\) | −124901. | −0.308298 | ||||||||
\(176\) | 95744.0 | 0.232986 | ||||||||
\(177\) | −128574. | −0.308475 | ||||||||
\(178\) | −79760.0 | −0.188684 | ||||||||
\(179\) | 87524.0 | 0.204171 | 0.102086 | − | 0.994776i | \(-0.467448\pi\) | ||||
0.102086 | + | 0.994776i | \(0.467448\pi\) | |||||||
\(180\) | 31104.0 | 0.0715542 | ||||||||
\(181\) | −320810. | −0.727866 | −0.363933 | − | 0.931425i | \(-0.618566\pi\) | ||||
−0.363933 | + | 0.931425i | \(0.618566\pi\) | |||||||
\(182\) | −33124.0 | −0.0741249 | ||||||||
\(183\) | −75510.0 | −0.166677 | ||||||||
\(184\) | −56576.0 | −0.123193 | ||||||||
\(185\) | −64560.0 | −0.138687 | ||||||||
\(186\) | 223056. | 0.472750 | ||||||||
\(187\) | 667964. | 1.39685 | ||||||||
\(188\) | −67040.0 | −0.138337 | ||||||||
\(189\) | 35721.0 | 0.0727393 | ||||||||
\(190\) | 56064.0 | 0.112668 | ||||||||
\(191\) | −609128. | −1.20816 | −0.604081 | − | 0.796923i | \(-0.706460\pi\) | ||||
−0.604081 | + | 0.796923i | \(0.706460\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | −16118.0 | −0.0311471 | −0.0155736 | − | 0.999879i | \(-0.504957\pi\) | ||||
−0.0155736 | + | 0.999879i | \(0.504957\pi\) | |||||||
\(194\) | −169288. | −0.322940 | ||||||||
\(195\) | −36504.0 | −0.0687470 | ||||||||
\(196\) | 38416.0 | 0.0714286 | ||||||||
\(197\) | −267048. | −0.490257 | −0.245128 | − | 0.969491i | \(-0.578830\pi\) | ||||
−0.245128 | + | 0.969491i | \(0.578830\pi\) | |||||||
\(198\) | 121176. | 0.219661 | ||||||||
\(199\) | 227872. | 0.407904 | 0.203952 | − | 0.978981i | \(-0.434621\pi\) | ||||
0.203952 | + | 0.978981i | \(0.434621\pi\) | |||||||
\(200\) | −163136. | −0.288386 | ||||||||
\(201\) | −193572. | −0.337950 | ||||||||
\(202\) | −649848. | −1.12056 | ||||||||
\(203\) | −288022. | −0.490553 | ||||||||
\(204\) | 257184. | 0.432682 | ||||||||
\(205\) | 44352.0 | 0.0737104 | ||||||||
\(206\) | −482400. | −0.792026 | ||||||||
\(207\) | −71604.0 | −0.116148 | ||||||||
\(208\) | −43264.0 | −0.0693375 | ||||||||
\(209\) | 218416. | 0.345875 | ||||||||
\(210\) | 42336.0 | 0.0662463 | ||||||||
\(211\) | −341948. | −0.528754 | −0.264377 | − | 0.964419i | \(-0.585166\pi\) | ||||
−0.264377 | + | 0.964419i | \(0.585166\pi\) | |||||||
\(212\) | −17312.0 | −0.0264550 | ||||||||
\(213\) | 173394. | 0.261870 | ||||||||
\(214\) | 171968. | 0.256693 | ||||||||
\(215\) | 531936. | 0.784808 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | 303604. | 0.437681 | ||||||||
\(218\) | 818088. | 1.16589 | ||||||||
\(219\) | 647334. | 0.912049 | ||||||||
\(220\) | 143616. | 0.200053 | ||||||||
\(221\) | −301834. | −0.415707 | ||||||||
\(222\) | −96840.0 | −0.131878 | ||||||||
\(223\) | 316596. | 0.426327 | 0.213164 | − | 0.977016i | \(-0.431623\pi\) | ||||
0.213164 | + | 0.977016i | \(0.431623\pi\) | |||||||
\(224\) | 50176.0 | 0.0668153 | ||||||||
\(225\) | −206469. | −0.271893 | ||||||||
\(226\) | 316184. | 0.411783 | ||||||||
\(227\) | 984474. | 1.26806 | 0.634030 | − | 0.773309i | \(-0.281400\pi\) | ||||
0.634030 | + | 0.773309i | \(0.281400\pi\) | |||||||
\(228\) | 84096.0 | 0.107137 | ||||||||
\(229\) | −51734.0 | −0.0651910 | −0.0325955 | − | 0.999469i | \(-0.510377\pi\) | ||||
−0.0325955 | + | 0.999469i | \(0.510377\pi\) | |||||||
\(230\) | −84864.0 | −0.105780 | ||||||||
\(231\) | 164934. | 0.203367 | ||||||||
\(232\) | −376192. | −0.458870 | ||||||||
\(233\) | 739926. | 0.892891 | 0.446446 | − | 0.894811i | \(-0.352690\pi\) | ||||
0.446446 | + | 0.894811i | \(0.352690\pi\) | |||||||
\(234\) | −54756.0 | −0.0653720 | ||||||||
\(235\) | −100560. | −0.118783 | ||||||||
\(236\) | −228576. | −0.267147 | ||||||||
\(237\) | −64656.0 | −0.0747718 | ||||||||
\(238\) | 350056. | 0.400585 | ||||||||
\(239\) | −142014. | −0.160819 | −0.0804093 | − | 0.996762i | \(-0.525623\pi\) | ||||
−0.0804093 | + | 0.996762i | \(0.525623\pi\) | |||||||
\(240\) | 55296.0 | 0.0619677 | ||||||||
\(241\) | −174810. | −0.193876 | −0.0969379 | − | 0.995290i | \(-0.530905\pi\) | ||||
−0.0969379 | + | 0.995290i | \(0.530905\pi\) | |||||||
\(242\) | −84700.0 | −0.0929705 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −134240. | −0.144347 | ||||||||
\(245\) | 57624.0 | 0.0613322 | ||||||||
\(246\) | 66528.0 | 0.0700917 | ||||||||
\(247\) | −98696.0 | −0.102934 | ||||||||
\(248\) | 396544. | 0.409414 | ||||||||
\(249\) | 892206. | 0.911941 | ||||||||
\(250\) | −544704. | −0.551202 | ||||||||
\(251\) | −428960. | −0.429766 | −0.214883 | − | 0.976640i | \(-0.568937\pi\) | ||||
−0.214883 | + | 0.976640i | \(0.568937\pi\) | |||||||
\(252\) | 63504.0 | 0.0629941 | ||||||||
\(253\) | −330616. | −0.324730 | ||||||||
\(254\) | 503616. | 0.489796 | ||||||||
\(255\) | 385776. | 0.371522 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.57731e6 | −1.48965 | −0.744827 | − | 0.667258i | \(-0.767468\pi\) | ||||
−0.744827 | + | 0.667258i | \(0.767468\pi\) | |||||||
\(258\) | 797904. | 0.746279 | ||||||||
\(259\) | −131810. | −0.122095 | ||||||||
\(260\) | −64896.0 | −0.0595367 | ||||||||
\(261\) | −476118. | −0.432627 | ||||||||
\(262\) | 638272. | 0.574450 | ||||||||
\(263\) | −1.02049e6 | −0.909746 | −0.454873 | − | 0.890556i | \(-0.650315\pi\) | ||||
−0.454873 | + | 0.890556i | \(0.650315\pi\) | |||||||
\(264\) | 215424. | 0.190232 | ||||||||
\(265\) | −25968.0 | −0.0227156 | ||||||||
\(266\) | 114464. | 0.0991893 | ||||||||
\(267\) | −179460. | −0.154060 | ||||||||
\(268\) | −344128. | −0.292673 | ||||||||
\(269\) | 575954. | 0.485296 | 0.242648 | − | 0.970114i | \(-0.421984\pi\) | ||||
0.242648 | + | 0.970114i | \(0.421984\pi\) | |||||||
\(270\) | 69984.0 | 0.0584237 | ||||||||
\(271\) | −1.11443e6 | −0.921787 | −0.460893 | − | 0.887456i | \(-0.652471\pi\) | ||||
−0.460893 | + | 0.887456i | \(0.652471\pi\) | |||||||
\(272\) | 457216. | 0.374713 | ||||||||
\(273\) | −74529.0 | −0.0605228 | ||||||||
\(274\) | −7296.00 | −0.00587095 | ||||||||
\(275\) | −953326. | −0.760168 | ||||||||
\(276\) | −127296. | −0.100587 | ||||||||
\(277\) | 218942. | 0.171447 | 0.0857235 | − | 0.996319i | \(-0.472680\pi\) | ||||
0.0857235 | + | 0.996319i | \(0.472680\pi\) | |||||||
\(278\) | 541072. | 0.419897 | ||||||||
\(279\) | 501876. | 0.385999 | ||||||||
\(280\) | 75264.0 | 0.0573710 | ||||||||
\(281\) | 480496. | 0.363015 | 0.181507 | − | 0.983390i | \(-0.441902\pi\) | ||||
0.181507 | + | 0.983390i | \(0.441902\pi\) | |||||||
\(282\) | −150840. | −0.112952 | ||||||||
\(283\) | −1.31389e6 | −0.975200 | −0.487600 | − | 0.873067i | \(-0.662127\pi\) | ||||
−0.487600 | + | 0.873067i | \(0.662127\pi\) | |||||||
\(284\) | 308256. | 0.226786 | ||||||||
\(285\) | 126144. | 0.0919929 | ||||||||
\(286\) | −252824. | −0.182769 | ||||||||
\(287\) | 90552.0 | 0.0648923 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | 1.76994e6 | 1.24656 | ||||||||
\(290\) | −564288. | −0.394009 | ||||||||
\(291\) | −380898. | −0.263679 | ||||||||
\(292\) | 1.15082e6 | 0.789858 | ||||||||
\(293\) | 502236. | 0.341774 | 0.170887 | − | 0.985291i | \(-0.445337\pi\) | ||||
0.170887 | + | 0.985291i | \(0.445337\pi\) | |||||||
\(294\) | 86436.0 | 0.0583212 | ||||||||
\(295\) | −342864. | −0.229386 | ||||||||
\(296\) | −172160. | −0.114210 | ||||||||
\(297\) | 272646. | 0.179353 | ||||||||
\(298\) | −554800. | −0.361906 | ||||||||
\(299\) | 149396. | 0.0966409 | ||||||||
\(300\) | −367056. | −0.235467 | ||||||||
\(301\) | 1.08604e6 | 0.690920 | ||||||||
\(302\) | −824784. | −0.520383 | ||||||||
\(303\) | −1.46216e6 | −0.914930 | ||||||||
\(304\) | 149504. | 0.0927831 | ||||||||
\(305\) | −201360. | −0.123943 | ||||||||
\(306\) | 578664. | 0.353283 | ||||||||
\(307\) | 355796. | 0.215454 | 0.107727 | − | 0.994180i | \(-0.465643\pi\) | ||||
0.107727 | + | 0.994180i | \(0.465643\pi\) | |||||||
\(308\) | 293216. | 0.176121 | ||||||||
\(309\) | −1.08540e6 | −0.646686 | ||||||||
\(310\) | 594816. | 0.351543 | ||||||||
\(311\) | −1.93790e6 | −1.13614 | −0.568068 | − | 0.822982i | \(-0.692309\pi\) | ||||
−0.568068 | + | 0.822982i | \(0.692309\pi\) | |||||||
\(312\) | −97344.0 | −0.0566139 | ||||||||
\(313\) | −2.71943e6 | −1.56898 | −0.784490 | − | 0.620141i | \(-0.787075\pi\) | ||||
−0.784490 | + | 0.620141i | \(0.787075\pi\) | |||||||
\(314\) | −163208. | −0.0934152 | ||||||||
\(315\) | 95256.0 | 0.0540899 | ||||||||
\(316\) | −114944. | −0.0647543 | ||||||||
\(317\) | −1.32195e6 | −0.738869 | −0.369435 | − | 0.929257i | \(-0.620449\pi\) | ||||
−0.369435 | + | 0.929257i | \(0.620449\pi\) | |||||||
\(318\) | −38952.0 | −0.0216004 | ||||||||
\(319\) | −2.19837e6 | −1.20955 | ||||||||
\(320\) | 98304.0 | 0.0536656 | ||||||||
\(321\) | 386928. | 0.209589 | ||||||||
\(322\) | −173264. | −0.0931255 | ||||||||
\(323\) | 1.04302e6 | 0.556273 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 430781. | 0.226229 | ||||||||
\(326\) | −307616. | −0.160312 | ||||||||
\(327\) | 1.84070e6 | 0.951948 | ||||||||
\(328\) | 118272. | 0.0607012 | ||||||||
\(329\) | −205310. | −0.104573 | ||||||||
\(330\) | 323136. | 0.163343 | ||||||||
\(331\) | −1.68150e6 | −0.843581 | −0.421791 | − | 0.906693i | \(-0.638598\pi\) | ||||
−0.421791 | + | 0.906693i | \(0.638598\pi\) | |||||||
\(332\) | 1.58614e6 | 0.789764 | ||||||||
\(333\) | −217890. | −0.107678 | ||||||||
\(334\) | 1.14974e6 | 0.563939 | ||||||||
\(335\) | −516192. | −0.251304 | ||||||||
\(336\) | 112896. | 0.0545545 | ||||||||
\(337\) | 2.19209e6 | 1.05144 | 0.525720 | − | 0.850658i | \(-0.323796\pi\) | ||||
0.525720 | + | 0.850658i | \(0.323796\pi\) | |||||||
\(338\) | 114244. | 0.0543928 | ||||||||
\(339\) | 711414. | 0.336220 | ||||||||
\(340\) | 685824. | 0.321748 | ||||||||
\(341\) | 2.31730e6 | 1.07919 | ||||||||
\(342\) | 189216. | 0.0874767 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 1.41850e6 | 0.646297 | ||||||||
\(345\) | −190944. | −0.0863691 | ||||||||
\(346\) | 453864. | 0.203815 | ||||||||
\(347\) | −15628.0 | −0.00696754 | −0.00348377 | − | 0.999994i | \(-0.501109\pi\) | ||||
−0.00348377 | + | 0.999994i | \(0.501109\pi\) | |||||||
\(348\) | −846432. | −0.374666 | ||||||||
\(349\) | 525182. | 0.230806 | 0.115403 | − | 0.993319i | \(-0.463184\pi\) | ||||
0.115403 | + | 0.993319i | \(0.463184\pi\) | |||||||
\(350\) | −499604. | −0.218000 | ||||||||
\(351\) | −123201. | −0.0533761 | ||||||||
\(352\) | 382976. | 0.164746 | ||||||||
\(353\) | −4.58393e6 | −1.95795 | −0.978974 | − | 0.203986i | \(-0.934610\pi\) | ||||
−0.978974 | + | 0.203986i | \(0.934610\pi\) | |||||||
\(354\) | −514296. | −0.218125 | ||||||||
\(355\) | 462384. | 0.194730 | ||||||||
\(356\) | −319040. | −0.133420 | ||||||||
\(357\) | 787626. | 0.327077 | ||||||||
\(358\) | 350096. | 0.144371 | ||||||||
\(359\) | 1.22984e6 | 0.503632 | 0.251816 | − | 0.967775i | \(-0.418972\pi\) | ||||
0.251816 | + | 0.967775i | \(0.418972\pi\) | |||||||
\(360\) | 124416. | 0.0505964 | ||||||||
\(361\) | −2.13504e6 | −0.862261 | ||||||||
\(362\) | −1.28324e6 | −0.514679 | ||||||||
\(363\) | −190575. | −0.0759101 | ||||||||
\(364\) | −132496. | −0.0524142 | ||||||||
\(365\) | 1.72622e6 | 0.678211 | ||||||||
\(366\) | −302040. | −0.117859 | ||||||||
\(367\) | −3.37209e6 | −1.30687 | −0.653437 | − | 0.756981i | \(-0.726674\pi\) | ||||
−0.653437 | + | 0.756981i | \(0.726674\pi\) | |||||||
\(368\) | −226304. | −0.0871109 | ||||||||
\(369\) | 149688. | 0.0572296 | ||||||||
\(370\) | −258240. | −0.0980662 | ||||||||
\(371\) | −53018.0 | −0.0199981 | ||||||||
\(372\) | 892224. | 0.334285 | ||||||||
\(373\) | −2.92194e6 | −1.08743 | −0.543713 | − | 0.839271i | \(-0.682982\pi\) | ||||
−0.543713 | + | 0.839271i | \(0.682982\pi\) | |||||||
\(374\) | 2.67186e6 | 0.987720 | ||||||||
\(375\) | −1.22558e6 | −0.450054 | ||||||||
\(376\) | −268160. | −0.0978193 | ||||||||
\(377\) | 993382. | 0.359967 | ||||||||
\(378\) | 142884. | 0.0514344 | ||||||||
\(379\) | 862640. | 0.308483 | 0.154242 | − | 0.988033i | \(-0.450707\pi\) | ||||
0.154242 | + | 0.988033i | \(0.450707\pi\) | |||||||
\(380\) | 224256. | 0.0796682 | ||||||||
\(381\) | 1.13314e6 | 0.399917 | ||||||||
\(382\) | −2.43651e6 | −0.854299 | ||||||||
\(383\) | −208506. | −0.0726309 | −0.0363155 | − | 0.999340i | \(-0.511562\pi\) | ||||
−0.0363155 | + | 0.999340i | \(0.511562\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | 439824. | 0.151226 | ||||||||
\(386\) | −64472.0 | −0.0220243 | ||||||||
\(387\) | 1.79528e6 | 0.609334 | ||||||||
\(388\) | −677152. | −0.228353 | ||||||||
\(389\) | −2.89455e6 | −0.969854 | −0.484927 | − | 0.874555i | \(-0.661154\pi\) | ||||
−0.484927 | + | 0.874555i | \(0.661154\pi\) | |||||||
\(390\) | −146016. | −0.0486115 | ||||||||
\(391\) | −1.57882e6 | −0.522266 | ||||||||
\(392\) | 153664. | 0.0505076 | ||||||||
\(393\) | 1.43611e6 | 0.469037 | ||||||||
\(394\) | −1.06819e6 | −0.346664 | ||||||||
\(395\) | −172416. | −0.0556013 | ||||||||
\(396\) | 484704. | 0.155324 | ||||||||
\(397\) | −2.58856e6 | −0.824294 | −0.412147 | − | 0.911117i | \(-0.635221\pi\) | ||||
−0.412147 | + | 0.911117i | \(0.635221\pi\) | |||||||
\(398\) | 911488. | 0.288432 | ||||||||
\(399\) | 257544. | 0.0809877 | ||||||||
\(400\) | −652544. | −0.203920 | ||||||||
\(401\) | 4.23658e6 | 1.31569 | 0.657846 | − | 0.753152i | \(-0.271468\pi\) | ||||
0.657846 | + | 0.753152i | \(0.271468\pi\) | |||||||
\(402\) | −774288. | −0.238967 | ||||||||
\(403\) | −1.04712e6 | −0.321170 | ||||||||
\(404\) | −2.59939e6 | −0.792352 | ||||||||
\(405\) | 157464. | 0.0477028 | ||||||||
\(406\) | −1.15209e6 | −0.346873 | ||||||||
\(407\) | −1.00606e6 | −0.301049 | ||||||||
\(408\) | 1.02874e6 | 0.305952 | ||||||||
\(409\) | −4.39615e6 | −1.29946 | −0.649731 | − | 0.760164i | \(-0.725119\pi\) | ||||
−0.649731 | + | 0.760164i | \(0.725119\pi\) | |||||||
\(410\) | 177408. | 0.0521211 | ||||||||
\(411\) | −16416.0 | −0.00479361 | ||||||||
\(412\) | −1.92960e6 | −0.560047 | ||||||||
\(413\) | −700014. | −0.201944 | ||||||||
\(414\) | −286416. | −0.0821290 | ||||||||
\(415\) | 2.37922e6 | 0.678131 | ||||||||
\(416\) | −173056. | −0.0490290 | ||||||||
\(417\) | 1.21741e6 | 0.342845 | ||||||||
\(418\) | 873664. | 0.244570 | ||||||||
\(419\) | −4.06963e6 | −1.13245 | −0.566226 | − | 0.824250i | \(-0.691597\pi\) | ||||
−0.566226 | + | 0.824250i | \(0.691597\pi\) | |||||||
\(420\) | 169344. | 0.0468432 | ||||||||
\(421\) | −1.05229e6 | −0.289356 | −0.144678 | − | 0.989479i | \(-0.546215\pi\) | ||||
−0.144678 | + | 0.989479i | \(0.546215\pi\) | |||||||
\(422\) | −1.36779e6 | −0.373886 | ||||||||
\(423\) | −339390. | −0.0922249 | ||||||||
\(424\) | −69248.0 | −0.0187065 | ||||||||
\(425\) | −4.55251e6 | −1.22258 | ||||||||
\(426\) | 693576. | 0.185170 | ||||||||
\(427\) | −411110. | −0.109116 | ||||||||
\(428\) | 687872. | 0.181509 | ||||||||
\(429\) | −568854. | −0.149230 | ||||||||
\(430\) | 2.12774e6 | 0.554943 | ||||||||
\(431\) | −7746.00 | −0.00200856 | −0.00100428 | − | 0.999999i | \(-0.500320\pi\) | ||||
−0.00100428 | + | 0.999999i | \(0.500320\pi\) | |||||||
\(432\) | 186624. | 0.0481125 | ||||||||
\(433\) | −739858. | −0.189639 | −0.0948197 | − | 0.995494i | \(-0.530227\pi\) | ||||
−0.0948197 | + | 0.995494i | \(0.530227\pi\) | |||||||
\(434\) | 1.21442e6 | 0.309488 | ||||||||
\(435\) | −1.26965e6 | −0.321707 | ||||||||
\(436\) | 3.27235e6 | 0.824411 | ||||||||
\(437\) | −516256. | −0.129319 | ||||||||
\(438\) | 2.58934e6 | 0.644916 | ||||||||
\(439\) | −599792. | −0.148539 | −0.0742693 | − | 0.997238i | \(-0.523662\pi\) | ||||
−0.0742693 | + | 0.997238i | \(0.523662\pi\) | |||||||
\(440\) | 574464. | 0.141459 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | −1.20734e6 | −0.293949 | ||||||||
\(443\) | 6.68431e6 | 1.61826 | 0.809128 | − | 0.587632i | \(-0.199940\pi\) | ||||
0.809128 | + | 0.587632i | \(0.199940\pi\) | |||||||
\(444\) | −387360. | −0.0932518 | ||||||||
\(445\) | −478560. | −0.114561 | ||||||||
\(446\) | 1.26638e6 | 0.301459 | ||||||||
\(447\) | −1.24830e6 | −0.295495 | ||||||||
\(448\) | 200704. | 0.0472456 | ||||||||
\(449\) | −4.51972e6 | −1.05802 | −0.529012 | − | 0.848615i | \(-0.677437\pi\) | ||||
−0.529012 | + | 0.848615i | \(0.677437\pi\) | |||||||
\(450\) | −825876. | −0.192258 | ||||||||
\(451\) | 691152. | 0.160005 | ||||||||
\(452\) | 1.26474e6 | 0.291175 | ||||||||
\(453\) | −1.85576e6 | −0.424891 | ||||||||
\(454\) | 3.93790e6 | 0.896653 | ||||||||
\(455\) | −198744. | −0.0450055 | ||||||||
\(456\) | 336384. | 0.0757571 | ||||||||
\(457\) | −6.03042e6 | −1.35069 | −0.675347 | − | 0.737500i | \(-0.736006\pi\) | ||||
−0.675347 | + | 0.737500i | \(0.736006\pi\) | |||||||
\(458\) | −206936. | −0.0460970 | ||||||||
\(459\) | 1.30199e6 | 0.288454 | ||||||||
\(460\) | −339456. | −0.0747978 | ||||||||
\(461\) | −8.98766e6 | −1.96967 | −0.984837 | − | 0.173480i | \(-0.944499\pi\) | ||||
−0.984837 | + | 0.173480i | \(0.944499\pi\) | |||||||
\(462\) | 659736. | 0.143802 | ||||||||
\(463\) | 1.40153e6 | 0.303843 | 0.151922 | − | 0.988393i | \(-0.451454\pi\) | ||||
0.151922 | + | 0.988393i | \(0.451454\pi\) | |||||||
\(464\) | −1.50477e6 | −0.324470 | ||||||||
\(465\) | 1.33834e6 | 0.287034 | ||||||||
\(466\) | 2.95970e6 | 0.631369 | ||||||||
\(467\) | −5.62831e6 | −1.19422 | −0.597112 | − | 0.802158i | \(-0.703685\pi\) | ||||
−0.597112 | + | 0.802158i | \(0.703685\pi\) | |||||||
\(468\) | −219024. | −0.0462250 | ||||||||
\(469\) | −1.05389e6 | −0.221240 | ||||||||
\(470\) | −402240. | −0.0839925 | ||||||||
\(471\) | −367218. | −0.0762732 | ||||||||
\(472\) | −914304. | −0.188902 | ||||||||
\(473\) | 8.28934e6 | 1.70360 | ||||||||
\(474\) | −258624. | −0.0528717 | ||||||||
\(475\) | −1.48862e6 | −0.302725 | ||||||||
\(476\) | 1.40022e6 | 0.283257 | ||||||||
\(477\) | −87642.0 | −0.0176367 | ||||||||
\(478\) | −568056. | −0.113716 | ||||||||
\(479\) | 3.70610e6 | 0.738038 | 0.369019 | − | 0.929422i | \(-0.379694\pi\) | ||||
0.369019 | + | 0.929422i | \(0.379694\pi\) | |||||||
\(480\) | 221184. | 0.0438178 | ||||||||
\(481\) | 454610. | 0.0895935 | ||||||||
\(482\) | −699240. | −0.137091 | ||||||||
\(483\) | −389844. | −0.0760367 | ||||||||
\(484\) | −338800. | −0.0657400 | ||||||||
\(485\) | −1.01573e6 | −0.196075 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | −6.22468e6 | −1.18931 | −0.594655 | − | 0.803981i | \(-0.702711\pi\) | ||||
−0.594655 | + | 0.803981i | \(0.702711\pi\) | |||||||
\(488\) | −536960. | −0.102069 | ||||||||
\(489\) | −692136. | −0.130894 | ||||||||
\(490\) | 230496. | 0.0433684 | ||||||||
\(491\) | 4.55595e6 | 0.852855 | 0.426428 | − | 0.904522i | \(-0.359772\pi\) | ||||
0.426428 | + | 0.904522i | \(0.359772\pi\) | |||||||
\(492\) | 266112. | 0.0495623 | ||||||||
\(493\) | −1.04981e7 | −1.94533 | ||||||||
\(494\) | −394784. | −0.0727850 | ||||||||
\(495\) | 727056. | 0.133369 | ||||||||
\(496\) | 1.58618e6 | 0.289499 | ||||||||
\(497\) | 944034. | 0.171434 | ||||||||
\(498\) | 3.56882e6 | 0.644840 | ||||||||
\(499\) | −2.44377e6 | −0.439349 | −0.219674 | − | 0.975573i | \(-0.570499\pi\) | ||||
−0.219674 | + | 0.975573i | \(0.570499\pi\) | |||||||
\(500\) | −2.17882e6 | −0.389758 | ||||||||
\(501\) | 2.58691e6 | 0.460454 | ||||||||
\(502\) | −1.71584e6 | −0.303891 | ||||||||
\(503\) | −2.06452e6 | −0.363831 | −0.181916 | − | 0.983314i | \(-0.558230\pi\) | ||||
−0.181916 | + | 0.983314i | \(0.558230\pi\) | |||||||
\(504\) | 254016. | 0.0445435 | ||||||||
\(505\) | −3.89909e6 | −0.680353 | ||||||||
\(506\) | −1.32246e6 | −0.229619 | ||||||||
\(507\) | 257049. | 0.0444116 | ||||||||
\(508\) | 2.01446e6 | 0.346338 | ||||||||
\(509\) | −2.26445e6 | −0.387407 | −0.193704 | − | 0.981060i | \(-0.562050\pi\) | ||||
−0.193704 | + | 0.981060i | \(0.562050\pi\) | |||||||
\(510\) | 1.54310e6 | 0.262706 | ||||||||
\(511\) | 3.52437e6 | 0.597076 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 425736. | 0.0714245 | ||||||||
\(514\) | −6.30926e6 | −1.05334 | ||||||||
\(515\) | −2.89440e6 | −0.480884 | ||||||||
\(516\) | 3.19162e6 | 0.527699 | ||||||||
\(517\) | −1.56706e6 | −0.257845 | ||||||||
\(518\) | −527240. | −0.0863344 | ||||||||
\(519\) | 1.02119e6 | 0.166414 | ||||||||
\(520\) | −259584. | −0.0420988 | ||||||||
\(521\) | 1.13926e7 | 1.83877 | 0.919383 | − | 0.393363i | \(-0.128688\pi\) | ||||
0.919383 | + | 0.393363i | \(0.128688\pi\) | |||||||
\(522\) | −1.90447e6 | −0.305913 | ||||||||
\(523\) | −8.15304e6 | −1.30336 | −0.651682 | − | 0.758493i | \(-0.725936\pi\) | ||||
−0.651682 | + | 0.758493i | \(0.725936\pi\) | |||||||
\(524\) | 2.55309e6 | 0.406198 | ||||||||
\(525\) | −1.12411e6 | −0.177996 | ||||||||
\(526\) | −4.08197e6 | −0.643288 | ||||||||
\(527\) | 1.10661e7 | 1.73567 | ||||||||
\(528\) | 861696. | 0.134515 | ||||||||
\(529\) | −5.65489e6 | −0.878587 | ||||||||
\(530\) | −103872. | −0.0160623 | ||||||||
\(531\) | −1.15717e6 | −0.178098 | ||||||||
\(532\) | 457856. | 0.0701374 | ||||||||
\(533\) | −312312. | −0.0476179 | ||||||||
\(534\) | −717840. | −0.108937 | ||||||||
\(535\) | 1.03181e6 | 0.155853 | ||||||||
\(536\) | −1.37651e6 | −0.206951 | ||||||||
\(537\) | 787716. | 0.117878 | ||||||||
\(538\) | 2.30382e6 | 0.343156 | ||||||||
\(539\) | 897974. | 0.133135 | ||||||||
\(540\) | 279936. | 0.0413118 | ||||||||
\(541\) | −5.17796e6 | −0.760616 | −0.380308 | − | 0.924860i | \(-0.624182\pi\) | ||||
−0.380308 | + | 0.924860i | \(0.624182\pi\) | |||||||
\(542\) | −4.45773e6 | −0.651801 | ||||||||
\(543\) | −2.88729e6 | −0.420234 | ||||||||
\(544\) | 1.82886e6 | 0.264962 | ||||||||
\(545\) | 4.90853e6 | 0.707881 | ||||||||
\(546\) | −298116. | −0.0427960 | ||||||||
\(547\) | 3.97011e6 | 0.567328 | 0.283664 | − | 0.958924i | \(-0.408450\pi\) | ||||
0.283664 | + | 0.958924i | \(0.408450\pi\) | |||||||
\(548\) | −29184.0 | −0.00415139 | ||||||||
\(549\) | −679590. | −0.0962312 | ||||||||
\(550\) | −3.81330e6 | −0.537520 | ||||||||
\(551\) | −3.43275e6 | −0.481685 | ||||||||
\(552\) | −509184. | −0.0711258 | ||||||||
\(553\) | −352016. | −0.0489496 | ||||||||
\(554\) | 875768. | 0.121231 | ||||||||
\(555\) | −581040. | −0.0800707 | ||||||||
\(556\) | 2.16429e6 | 0.296912 | ||||||||
\(557\) | 204396. | 0.0279148 | 0.0139574 | − | 0.999903i | \(-0.495557\pi\) | ||||
0.0139574 | + | 0.999903i | \(0.495557\pi\) | |||||||
\(558\) | 2.00750e6 | 0.272942 | ||||||||
\(559\) | −3.74572e6 | −0.506997 | ||||||||
\(560\) | 301056. | 0.0405674 | ||||||||
\(561\) | 6.01168e6 | 0.806470 | ||||||||
\(562\) | 1.92198e6 | 0.256690 | ||||||||
\(563\) | 1.07479e7 | 1.42907 | 0.714537 | − | 0.699598i | \(-0.246638\pi\) | ||||
0.714537 | + | 0.699598i | \(0.246638\pi\) | |||||||
\(564\) | −603360. | −0.0798691 | ||||||||
\(565\) | 1.89710e6 | 0.250017 | ||||||||
\(566\) | −5.25557e6 | −0.689570 | ||||||||
\(567\) | 321489. | 0.0419961 | ||||||||
\(568\) | 1.23302e6 | 0.160362 | ||||||||
\(569\) | 1.39894e7 | 1.81142 | 0.905709 | − | 0.423899i | \(-0.139339\pi\) | ||||
0.905709 | + | 0.423899i | \(0.139339\pi\) | |||||||
\(570\) | 504576. | 0.0650488 | ||||||||
\(571\) | −1.23318e7 | −1.58284 | −0.791420 | − | 0.611273i | \(-0.790658\pi\) | ||||
−0.791420 | + | 0.611273i | \(0.790658\pi\) | |||||||
\(572\) | −1.01130e6 | −0.129237 | ||||||||
\(573\) | −5.48215e6 | −0.697533 | ||||||||
\(574\) | 362208. | 0.0458858 | ||||||||
\(575\) | 2.25332e6 | 0.284219 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −1.00343e7 | −1.25472 | −0.627358 | − | 0.778731i | \(-0.715864\pi\) | ||||
−0.627358 | + | 0.778731i | \(0.715864\pi\) | |||||||
\(578\) | 7.07976e6 | 0.881452 | ||||||||
\(579\) | −145062. | −0.0179828 | ||||||||
\(580\) | −2.25715e6 | −0.278606 | ||||||||
\(581\) | 4.85757e6 | 0.597006 | ||||||||
\(582\) | −1.52359e6 | −0.186449 | ||||||||
\(583\) | −404668. | −0.0493091 | ||||||||
\(584\) | 4.60326e6 | 0.558514 | ||||||||
\(585\) | −328536. | −0.0396911 | ||||||||
\(586\) | 2.00894e6 | 0.241671 | ||||||||
\(587\) | 1.13866e6 | 0.136395 | 0.0681977 | − | 0.997672i | \(-0.478275\pi\) | ||||
0.0681977 | + | 0.997672i | \(0.478275\pi\) | |||||||
\(588\) | 345744. | 0.0412393 | ||||||||
\(589\) | 3.61846e6 | 0.429770 | ||||||||
\(590\) | −1.37146e6 | −0.162200 | ||||||||
\(591\) | −2.40343e6 | −0.283050 | ||||||||
\(592\) | −688640. | −0.0807585 | ||||||||
\(593\) | 4.92581e6 | 0.575229 | 0.287615 | − | 0.957746i | \(-0.407138\pi\) | ||||
0.287615 | + | 0.957746i | \(0.407138\pi\) | |||||||
\(594\) | 1.09058e6 | 0.126822 | ||||||||
\(595\) | 2.10034e6 | 0.243218 | ||||||||
\(596\) | −2.21920e6 | −0.255906 | ||||||||
\(597\) | 2.05085e6 | 0.235504 | ||||||||
\(598\) | 597584. | 0.0683354 | ||||||||
\(599\) | −1.08550e7 | −1.23613 | −0.618066 | − | 0.786127i | \(-0.712083\pi\) | ||||
−0.618066 | + | 0.786127i | \(0.712083\pi\) | |||||||
\(600\) | −1.46822e6 | −0.166500 | ||||||||
\(601\) | −1.20410e7 | −1.35981 | −0.679905 | − | 0.733300i | \(-0.737979\pi\) | ||||
−0.679905 | + | 0.733300i | \(0.737979\pi\) | |||||||
\(602\) | 4.34414e6 | 0.488554 | ||||||||
\(603\) | −1.74215e6 | −0.195115 | ||||||||
\(604\) | −3.29914e6 | −0.367966 | ||||||||
\(605\) | −508200. | −0.0564477 | ||||||||
\(606\) | −5.84863e6 | −0.646953 | ||||||||
\(607\) | −1.39099e7 | −1.53233 | −0.766166 | − | 0.642642i | \(-0.777838\pi\) | ||||
−0.766166 | + | 0.642642i | \(0.777838\pi\) | |||||||
\(608\) | 598016. | 0.0656076 | ||||||||
\(609\) | −2.59220e6 | −0.283221 | ||||||||
\(610\) | −805440. | −0.0876413 | ||||||||
\(611\) | 708110. | 0.0767357 | ||||||||
\(612\) | 2.31466e6 | 0.249809 | ||||||||
\(613\) | 4.47612e6 | 0.481117 | 0.240558 | − | 0.970635i | \(-0.422669\pi\) | ||||
0.240558 | + | 0.970635i | \(0.422669\pi\) | |||||||
\(614\) | 1.42318e6 | 0.152349 | ||||||||
\(615\) | 399168. | 0.0425567 | ||||||||
\(616\) | 1.17286e6 | 0.124536 | ||||||||
\(617\) | 7.73177e6 | 0.817647 | 0.408824 | − | 0.912613i | \(-0.365939\pi\) | ||||
0.408824 | + | 0.912613i | \(0.365939\pi\) | |||||||
\(618\) | −4.34160e6 | −0.457276 | ||||||||
\(619\) | 1.29248e7 | 1.35580 | 0.677901 | − | 0.735153i | \(-0.262890\pi\) | ||||
0.677901 | + | 0.735153i | \(0.262890\pi\) | |||||||
\(620\) | 2.37926e6 | 0.248578 | ||||||||
\(621\) | −644436. | −0.0670580 | ||||||||
\(622\) | −7.75160e6 | −0.803370 | ||||||||
\(623\) | −977060. | −0.100856 | ||||||||
\(624\) | −389376. | −0.0400320 | ||||||||
\(625\) | 4.69740e6 | 0.481014 | ||||||||
\(626\) | −1.08777e7 | −1.10944 | ||||||||
\(627\) | 1.96574e6 | 0.199691 | ||||||||
\(628\) | −652832. | −0.0660545 | ||||||||
\(629\) | −4.80434e6 | −0.484180 | ||||||||
\(630\) | 381024. | 0.0382473 | ||||||||
\(631\) | 1.33124e7 | 1.33102 | 0.665509 | − | 0.746390i | \(-0.268215\pi\) | ||||
0.665509 | + | 0.746390i | \(0.268215\pi\) | |||||||
\(632\) | −459776. | −0.0457882 | ||||||||
\(633\) | −3.07753e6 | −0.305276 | ||||||||
\(634\) | −5.28781e6 | −0.522459 | ||||||||
\(635\) | 3.02170e6 | 0.297383 | ||||||||
\(636\) | −155808. | −0.0152738 | ||||||||
\(637\) | −405769. | −0.0396214 | ||||||||
\(638\) | −8.79349e6 | −0.855282 | ||||||||
\(639\) | 1.56055e6 | 0.151190 | ||||||||
\(640\) | 393216. | 0.0379473 | ||||||||
\(641\) | 1.03522e7 | 0.995150 | 0.497575 | − | 0.867421i | \(-0.334224\pi\) | ||||
0.497575 | + | 0.867421i | \(0.334224\pi\) | |||||||
\(642\) | 1.54771e6 | 0.148201 | ||||||||
\(643\) | −6.11730e6 | −0.583489 | −0.291744 | − | 0.956496i | \(-0.594236\pi\) | ||||
−0.291744 | + | 0.956496i | \(0.594236\pi\) | |||||||
\(644\) | −693056. | −0.0658497 | ||||||||
\(645\) | 4.78742e6 | 0.453109 | ||||||||
\(646\) | 4.17210e6 | 0.393344 | ||||||||
\(647\) | 1.14021e7 | 1.07084 | 0.535420 | − | 0.844586i | \(-0.320153\pi\) | ||||
0.535420 | + | 0.844586i | \(0.320153\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | −5.34296e6 | −0.497933 | ||||||||
\(650\) | 1.72312e6 | 0.159968 | ||||||||
\(651\) | 2.73244e6 | 0.252696 | ||||||||
\(652\) | −1.23046e6 | −0.113357 | ||||||||
\(653\) | −2.63309e6 | −0.241648 | −0.120824 | − | 0.992674i | \(-0.538554\pi\) | ||||
−0.120824 | + | 0.992674i | \(0.538554\pi\) | |||||||
\(654\) | 7.36279e6 | 0.673129 | ||||||||
\(655\) | 3.82963e6 | 0.348782 | ||||||||
\(656\) | 473088. | 0.0429222 | ||||||||
\(657\) | 5.82601e6 | 0.526572 | ||||||||
\(658\) | −821240. | −0.0739444 | ||||||||
\(659\) | 2.71632e6 | 0.243651 | 0.121825 | − | 0.992552i | \(-0.461125\pi\) | ||||
0.121825 | + | 0.992552i | \(0.461125\pi\) | |||||||
\(660\) | 1.29254e6 | 0.115501 | ||||||||
\(661\) | 2.14041e7 | 1.90543 | 0.952714 | − | 0.303868i | \(-0.0982783\pi\) | ||||
0.952714 | + | 0.303868i | \(0.0982783\pi\) | |||||||
\(662\) | −6.72600e6 | −0.596502 | ||||||||
\(663\) | −2.71651e6 | −0.240009 | ||||||||
\(664\) | 6.34458e6 | 0.558448 | ||||||||
\(665\) | 686784. | 0.0602235 | ||||||||
\(666\) | −871560. | −0.0761398 | ||||||||
\(667\) | 5.19615e6 | 0.452238 | ||||||||
\(668\) | 4.59894e6 | 0.398765 | ||||||||
\(669\) | 2.84936e6 | 0.246140 | ||||||||
\(670\) | −2.06477e6 | −0.177699 | ||||||||
\(671\) | −3.13786e6 | −0.269046 | ||||||||
\(672\) | 451584. | 0.0385758 | ||||||||
\(673\) | −8.01013e6 | −0.681713 | −0.340857 | − | 0.940115i | \(-0.610717\pi\) | ||||
−0.340857 | + | 0.940115i | \(0.610717\pi\) | |||||||
\(674\) | 8.76838e6 | 0.743480 | ||||||||
\(675\) | −1.85822e6 | −0.156978 | ||||||||
\(676\) | 456976. | 0.0384615 | ||||||||
\(677\) | 7.94655e6 | 0.666357 | 0.333178 | − | 0.942864i | \(-0.391879\pi\) | ||||
0.333178 | + | 0.942864i | \(0.391879\pi\) | |||||||
\(678\) | 2.84566e6 | 0.237743 | ||||||||
\(679\) | −2.07378e6 | −0.172619 | ||||||||
\(680\) | 2.74330e6 | 0.227510 | ||||||||
\(681\) | 8.86027e6 | 0.732114 | ||||||||
\(682\) | 9.26922e6 | 0.763101 | ||||||||
\(683\) | 1.11470e7 | 0.914333 | 0.457166 | − | 0.889381i | \(-0.348864\pi\) | ||||
0.457166 | + | 0.889381i | \(0.348864\pi\) | |||||||
\(684\) | 756864. | 0.0618554 | ||||||||
\(685\) | −43776.0 | −0.00356459 | ||||||||
\(686\) | 470596. | 0.0381802 | ||||||||
\(687\) | −465606. | −0.0376380 | ||||||||
\(688\) | 5.67398e6 | 0.457001 | ||||||||
\(689\) | 182858. | 0.0146746 | ||||||||
\(690\) | −763776. | −0.0610722 | ||||||||
\(691\) | −2.45717e7 | −1.95768 | −0.978838 | − | 0.204637i | \(-0.934399\pi\) | ||||
−0.978838 | + | 0.204637i | \(0.934399\pi\) | |||||||
\(692\) | 1.81546e6 | 0.144119 | ||||||||
\(693\) | 1.48441e6 | 0.117414 | ||||||||
\(694\) | −62512.0 | −0.00492680 | ||||||||
\(695\) | 3.24643e6 | 0.254944 | ||||||||
\(696\) | −3.38573e6 | −0.264929 | ||||||||
\(697\) | 3.30053e6 | 0.257337 | ||||||||
\(698\) | 2.10073e6 | 0.163204 | ||||||||
\(699\) | 6.65933e6 | 0.515511 | ||||||||
\(700\) | −1.99842e6 | −0.154149 | ||||||||
\(701\) | 359214. | 0.0276095 | 0.0138047 | − | 0.999905i | \(-0.495606\pi\) | ||||
0.0138047 | + | 0.999905i | \(0.495606\pi\) | |||||||
\(702\) | −492804. | −0.0377426 | ||||||||
\(703\) | −1.57096e6 | −0.119888 | ||||||||
\(704\) | 1.53190e6 | 0.116493 | ||||||||
\(705\) | −905040. | −0.0685796 | ||||||||
\(706\) | −1.83357e7 | −1.38448 | ||||||||
\(707\) | −7.96064e6 | −0.598962 | ||||||||
\(708\) | −2.05718e6 | −0.154238 | ||||||||
\(709\) | 2.20095e7 | 1.64435 | 0.822177 | − | 0.569232i | \(-0.192759\pi\) | ||||
0.822177 | + | 0.569232i | \(0.192759\pi\) | |||||||
\(710\) | 1.84954e6 | 0.137695 | ||||||||
\(711\) | −581904. | −0.0431695 | ||||||||
\(712\) | −1.27616e6 | −0.0943420 | ||||||||
\(713\) | −5.47726e6 | −0.403497 | ||||||||
\(714\) | 3.15050e6 | 0.231278 | ||||||||
\(715\) | −1.51694e6 | −0.110970 | ||||||||
\(716\) | 1.40038e6 | 0.102086 | ||||||||
\(717\) | −1.27813e6 | −0.0928487 | ||||||||
\(718\) | 4.91937e6 | 0.356122 | ||||||||
\(719\) | 7.60177e6 | 0.548394 | 0.274197 | − | 0.961674i | \(-0.411588\pi\) | ||||
0.274197 | + | 0.961674i | \(0.411588\pi\) | |||||||
\(720\) | 497664. | 0.0357771 | ||||||||
\(721\) | −5.90940e6 | −0.423356 | ||||||||
\(722\) | −8.54017e6 | −0.609710 | ||||||||
\(723\) | −1.57329e6 | −0.111934 | ||||||||
\(724\) | −5.13296e6 | −0.363933 | ||||||||
\(725\) | 1.49830e7 | 1.05865 | ||||||||
\(726\) | −762300. | −0.0536765 | ||||||||
\(727\) | −9.43667e6 | −0.662190 | −0.331095 | − | 0.943597i | \(-0.607418\pi\) | ||||
−0.331095 | + | 0.943597i | \(0.607418\pi\) | |||||||
\(728\) | −529984. | −0.0370625 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 6.90490e6 | 0.479568 | ||||||||
\(731\) | 3.95849e7 | 2.73991 | ||||||||
\(732\) | −1.20816e6 | −0.0833387 | ||||||||
\(733\) | 5.03323e6 | 0.346009 | 0.173004 | − | 0.984921i | \(-0.444653\pi\) | ||||
0.173004 | + | 0.984921i | \(0.444653\pi\) | |||||||
\(734\) | −1.34884e7 | −0.924100 | ||||||||
\(735\) | 518616. | 0.0354101 | ||||||||
\(736\) | −905216. | −0.0615967 | ||||||||
\(737\) | −8.04399e6 | −0.545510 | ||||||||
\(738\) | 598752. | 0.0404675 | ||||||||
\(739\) | −5.53779e6 | −0.373014 | −0.186507 | − | 0.982454i | \(-0.559717\pi\) | ||||
−0.186507 | + | 0.982454i | \(0.559717\pi\) | |||||||
\(740\) | −1.03296e6 | −0.0693433 | ||||||||
\(741\) | −888264. | −0.0594287 | ||||||||
\(742\) | −212072. | −0.0141408 | ||||||||
\(743\) | 1.59329e7 | 1.05882 | 0.529411 | − | 0.848366i | \(-0.322413\pi\) | ||||
0.529411 | + | 0.848366i | \(0.322413\pi\) | |||||||
\(744\) | 3.56890e6 | 0.236375 | ||||||||
\(745\) | −3.32880e6 | −0.219734 | ||||||||
\(746\) | −1.16878e7 | −0.768926 | ||||||||
\(747\) | 8.02985e6 | 0.526509 | ||||||||
\(748\) | 1.06874e7 | 0.698424 | ||||||||
\(749\) | 2.10661e6 | 0.137208 | ||||||||
\(750\) | −4.90234e6 | −0.318236 | ||||||||
\(751\) | 1.76926e7 | 1.14470 | 0.572351 | − | 0.820009i | \(-0.306032\pi\) | ||||
0.572351 | + | 0.820009i | \(0.306032\pi\) | |||||||
\(752\) | −1.07264e6 | −0.0691687 | ||||||||
\(753\) | −3.86064e6 | −0.248126 | ||||||||
\(754\) | 3.97353e6 | 0.254535 | ||||||||
\(755\) | −4.94870e6 | −0.315954 | ||||||||
\(756\) | 571536. | 0.0363696 | ||||||||
\(757\) | 8.76182e6 | 0.555718 | 0.277859 | − | 0.960622i | \(-0.410375\pi\) | ||||
0.277859 | + | 0.960622i | \(0.410375\pi\) | |||||||
\(758\) | 3.45056e6 | 0.218131 | ||||||||
\(759\) | −2.97554e6 | −0.187483 | ||||||||
\(760\) | 897024. | 0.0563339 | ||||||||
\(761\) | 7.26804e6 | 0.454942 | 0.227471 | − | 0.973785i | \(-0.426954\pi\) | ||||
0.227471 | + | 0.973785i | \(0.426954\pi\) | |||||||
\(762\) | 4.53254e6 | 0.282784 | ||||||||
\(763\) | 1.00216e7 | 0.623196 | ||||||||
\(764\) | −9.74605e6 | −0.604081 | ||||||||
\(765\) | 3.47198e6 | 0.214498 | ||||||||
\(766\) | −834024. | −0.0513578 | ||||||||
\(767\) | 2.41433e6 | 0.148187 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | −4.01863e6 | −0.245054 | −0.122527 | − | 0.992465i | \(-0.539100\pi\) | ||||
−0.122527 | + | 0.992465i | \(0.539100\pi\) | |||||||
\(770\) | 1.75930e6 | 0.106933 | ||||||||
\(771\) | −1.41958e7 | −0.860052 | ||||||||
\(772\) | −257888. | −0.0155736 | ||||||||
\(773\) | 1.77194e7 | 1.06660 | 0.533298 | − | 0.845927i | \(-0.320952\pi\) | ||||
0.533298 | + | 0.845927i | \(0.320952\pi\) | |||||||
\(774\) | 7.18114e6 | 0.430865 | ||||||||
\(775\) | −1.57936e7 | −0.944554 | ||||||||
\(776\) | −2.70861e6 | −0.161470 | ||||||||
\(777\) | −1.18629e6 | −0.0704918 | ||||||||
\(778\) | −1.15782e7 | −0.685790 | ||||||||
\(779\) | 1.07923e6 | 0.0637193 | ||||||||
\(780\) | −584064. | −0.0343735 | ||||||||
\(781\) | 7.20548e6 | 0.422703 | ||||||||
\(782\) | −6.31530e6 | −0.369298 | ||||||||
\(783\) | −4.28506e6 | −0.249777 | ||||||||
\(784\) | 614656. | 0.0357143 | ||||||||
\(785\) | −979248. | −0.0567177 | ||||||||
\(786\) | 5.74445e6 | 0.331659 | ||||||||
\(787\) | 6.58989e6 | 0.379264 | 0.189632 | − | 0.981855i | \(-0.439271\pi\) | ||||
0.189632 | + | 0.981855i | \(0.439271\pi\) | |||||||
\(788\) | −4.27277e6 | −0.245128 | ||||||||
\(789\) | −9.18443e6 | −0.525242 | ||||||||
\(790\) | −689664. | −0.0393160 | ||||||||
\(791\) | 3.87325e6 | 0.220107 | ||||||||
\(792\) | 1.93882e6 | 0.109831 | ||||||||
\(793\) | 1.41791e6 | 0.0800692 | ||||||||
\(794\) | −1.03542e7 | −0.582864 | ||||||||
\(795\) | −233712. | −0.0131148 | ||||||||
\(796\) | 3.64595e6 | 0.203952 | ||||||||
\(797\) | 3.97198e6 | 0.221494 | 0.110747 | − | 0.993849i | \(-0.464676\pi\) | ||||
0.110747 | + | 0.993849i | \(0.464676\pi\) | |||||||
\(798\) | 1.03018e6 | 0.0572670 | ||||||||
\(799\) | −7.48334e6 | −0.414695 | ||||||||
\(800\) | −2.61018e6 | −0.144193 | ||||||||
\(801\) | −1.61514e6 | −0.0889465 | ||||||||
\(802\) | 1.69463e7 | 0.930335 | ||||||||
\(803\) | 2.69003e7 | 1.47221 | ||||||||
\(804\) | −3.09715e6 | −0.168975 | ||||||||
\(805\) | −1.03958e6 | −0.0565418 | ||||||||
\(806\) | −4.18850e6 | −0.227102 | ||||||||
\(807\) | 5.18359e6 | 0.280186 | ||||||||
\(808\) | −1.03976e7 | −0.560278 | ||||||||
\(809\) | 3.61744e7 | 1.94326 | 0.971628 | − | 0.236513i | \(-0.0760045\pi\) | ||||
0.971628 | + | 0.236513i | \(0.0760045\pi\) | |||||||
\(810\) | 629856. | 0.0337310 | ||||||||
\(811\) | −1.61022e7 | −0.859672 | −0.429836 | − | 0.902907i | \(-0.641429\pi\) | ||||
−0.429836 | + | 0.902907i | \(0.641429\pi\) | |||||||
\(812\) | −4.60835e6 | −0.245276 | ||||||||
\(813\) | −1.00299e7 | −0.532194 | ||||||||
\(814\) | −4.02424e6 | −0.212874 | ||||||||
\(815\) | −1.84570e6 | −0.0973344 | ||||||||
\(816\) | 4.11494e6 | 0.216341 | ||||||||
\(817\) | 1.29438e7 | 0.678431 | ||||||||
\(818\) | −1.75846e7 | −0.918859 | ||||||||
\(819\) | −670761. | −0.0349428 | ||||||||
\(820\) | 709632. | 0.0368552 | ||||||||
\(821\) | 2.33984e7 | 1.21151 | 0.605756 | − | 0.795650i | \(-0.292871\pi\) | ||||
0.605756 | + | 0.795650i | \(0.292871\pi\) | |||||||
\(822\) | −65664.0 | −0.00338959 | ||||||||
\(823\) | 3.45541e7 | 1.77828 | 0.889140 | − | 0.457636i | \(-0.151304\pi\) | ||||
0.889140 | + | 0.457636i | \(0.151304\pi\) | |||||||
\(824\) | −7.71840e6 | −0.396013 | ||||||||
\(825\) | −8.57993e6 | −0.438883 | ||||||||
\(826\) | −2.80006e6 | −0.142796 | ||||||||
\(827\) | −2.16044e7 | −1.09845 | −0.549224 | − | 0.835675i | \(-0.685076\pi\) | ||||
−0.549224 | + | 0.835675i | \(0.685076\pi\) | |||||||
\(828\) | −1.14566e6 | −0.0580740 | ||||||||
\(829\) | 1.26865e7 | 0.641145 | 0.320572 | − | 0.947224i | \(-0.396125\pi\) | ||||
0.320572 | + | 0.947224i | \(0.396125\pi\) | |||||||
\(830\) | 9.51686e6 | 0.479511 | ||||||||
\(831\) | 1.97048e6 | 0.0989849 | ||||||||
\(832\) | −692224. | −0.0346688 | ||||||||
\(833\) | 4.28819e6 | 0.214122 | ||||||||
\(834\) | 4.86965e6 | 0.242428 | ||||||||
\(835\) | 6.89842e6 | 0.342400 | ||||||||
\(836\) | 3.49466e6 | 0.172937 | ||||||||
\(837\) | 4.51688e6 | 0.222856 | ||||||||
\(838\) | −1.62785e7 | −0.800765 | ||||||||
\(839\) | −322154. | −0.0158001 | −0.00790003 | − | 0.999969i | \(-0.502515\pi\) | ||||
−0.00790003 | + | 0.999969i | \(0.502515\pi\) | |||||||
\(840\) | 677376. | 0.0331231 | ||||||||
\(841\) | 1.40397e7 | 0.684493 | ||||||||
\(842\) | −4.20918e6 | −0.204605 | ||||||||
\(843\) | 4.32446e6 | 0.209587 | ||||||||
\(844\) | −5.47117e6 | −0.264377 | ||||||||
\(845\) | 685464. | 0.0330250 | ||||||||
\(846\) | −1.35756e6 | −0.0652128 | ||||||||
\(847\) | −1.03758e6 | −0.0496948 | ||||||||
\(848\) | −276992. | −0.0132275 | ||||||||
\(849\) | −1.18250e7 | −0.563032 | ||||||||
\(850\) | −1.82101e7 | −0.864498 | ||||||||
\(851\) | 2.37796e6 | 0.112559 | ||||||||
\(852\) | 2.77430e6 | 0.130935 | ||||||||
\(853\) | 2.80762e7 | 1.32119 | 0.660595 | − | 0.750742i | \(-0.270304\pi\) | ||||
0.660595 | + | 0.750742i | \(0.270304\pi\) | |||||||
\(854\) | −1.64444e6 | −0.0771566 | ||||||||
\(855\) | 1.13530e6 | 0.0531121 | ||||||||
\(856\) | 2.75149e6 | 0.128346 | ||||||||
\(857\) | 2.46095e7 | 1.14459 | 0.572296 | − | 0.820047i | \(-0.306053\pi\) | ||||
0.572296 | + | 0.820047i | \(0.306053\pi\) | |||||||
\(858\) | −2.27542e6 | −0.105522 | ||||||||
\(859\) | −1.82440e7 | −0.843599 | −0.421800 | − | 0.906689i | \(-0.638601\pi\) | ||||
−0.421800 | + | 0.906689i | \(0.638601\pi\) | |||||||
\(860\) | 8.51098e6 | 0.392404 | ||||||||
\(861\) | 814968. | 0.0374656 | ||||||||
\(862\) | −30984.0 | −0.00142026 | ||||||||
\(863\) | −1.15851e7 | −0.529506 | −0.264753 | − | 0.964316i | \(-0.585290\pi\) | ||||
−0.264753 | + | 0.964316i | \(0.585290\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 2.72318e6 | 0.123748 | ||||||||
\(866\) | −2.95943e6 | −0.134095 | ||||||||
\(867\) | 1.59295e7 | 0.719703 | ||||||||
\(868\) | 4.85766e6 | 0.218841 | ||||||||
\(869\) | −2.68682e6 | −0.120695 | ||||||||
\(870\) | −5.07859e6 | −0.227481 | ||||||||
\(871\) | 3.63485e6 | 0.162346 | ||||||||
\(872\) | 1.30894e7 | 0.582947 | ||||||||
\(873\) | −3.42808e6 | −0.152235 | ||||||||
\(874\) | −2.06502e6 | −0.0914422 | ||||||||
\(875\) | −6.67262e6 | −0.294630 | ||||||||
\(876\) | 1.03573e7 | 0.456024 | ||||||||
\(877\) | 3.16646e7 | 1.39019 | 0.695097 | − | 0.718916i | \(-0.255361\pi\) | ||||
0.695097 | + | 0.718916i | \(0.255361\pi\) | |||||||
\(878\) | −2.39917e6 | −0.105033 | ||||||||
\(879\) | 4.52012e6 | 0.197323 | ||||||||
\(880\) | 2.29786e6 | 0.100027 | ||||||||
\(881\) | −2.68256e7 | −1.16442 | −0.582210 | − | 0.813038i | \(-0.697812\pi\) | ||||
−0.582210 | + | 0.813038i | \(0.697812\pi\) | |||||||
\(882\) | 777924. | 0.0336718 | ||||||||
\(883\) | −4.51779e7 | −1.94995 | −0.974977 | − | 0.222307i | \(-0.928641\pi\) | ||||
−0.974977 | + | 0.222307i | \(0.928641\pi\) | |||||||
\(884\) | −4.82934e6 | −0.207854 | ||||||||
\(885\) | −3.08578e6 | −0.132436 | ||||||||
\(886\) | 2.67372e7 | 1.14428 | ||||||||
\(887\) | 7.09987e6 | 0.302999 | 0.151500 | − | 0.988457i | \(-0.451590\pi\) | ||||
0.151500 | + | 0.988457i | \(0.451590\pi\) | |||||||
\(888\) | −1.54944e6 | −0.0659390 | ||||||||
\(889\) | 6.16930e6 | 0.261807 | ||||||||
\(890\) | −1.91424e6 | −0.0810068 | ||||||||
\(891\) | 2.45381e6 | 0.103549 | ||||||||
\(892\) | 5.06554e6 | 0.213164 | ||||||||
\(893\) | −2.44696e6 | −0.102683 | ||||||||
\(894\) | −4.99320e6 | −0.208947 | ||||||||
\(895\) | 2.10058e6 | 0.0876558 | ||||||||
\(896\) | 802816. | 0.0334077 | ||||||||
\(897\) | 1.34456e6 | 0.0557957 | ||||||||
\(898\) | −1.80789e7 | −0.748136 | ||||||||
\(899\) | −3.64201e7 | −1.50294 | ||||||||
\(900\) | −3.30350e6 | −0.135947 | ||||||||
\(901\) | −1.93245e6 | −0.0793043 | ||||||||
\(902\) | 2.76461e6 | 0.113140 | ||||||||
\(903\) | 9.77432e6 | 0.398903 | ||||||||
\(904\) | 5.05894e6 | 0.205892 | ||||||||
\(905\) | −7.69944e6 | −0.312491 | ||||||||
\(906\) | −7.42306e6 | −0.300443 | ||||||||
\(907\) | 1.22356e7 | 0.493864 | 0.246932 | − | 0.969033i | \(-0.420578\pi\) | ||||
0.246932 | + | 0.969033i | \(0.420578\pi\) | |||||||
\(908\) | 1.57516e7 | 0.634030 | ||||||||
\(909\) | −1.31594e7 | −0.528235 | ||||||||
\(910\) | −794976. | −0.0318237 | ||||||||
\(911\) | −6.85780e6 | −0.273772 | −0.136886 | − | 0.990587i | \(-0.543709\pi\) | ||||
−0.136886 | + | 0.990587i | \(0.543709\pi\) | |||||||
\(912\) | 1.34554e6 | 0.0535683 | ||||||||
\(913\) | 3.70761e7 | 1.47203 | ||||||||
\(914\) | −2.41217e7 | −0.955085 | ||||||||
\(915\) | −1.81224e6 | −0.0715588 | ||||||||
\(916\) | −827744. | −0.0325955 | ||||||||
\(917\) | 7.81883e6 | 0.307057 | ||||||||
\(918\) | 5.20798e6 | 0.203968 | ||||||||
\(919\) | 4.74950e7 | 1.85506 | 0.927532 | − | 0.373743i | \(-0.121926\pi\) | ||||
0.927532 | + | 0.373743i | \(0.121926\pi\) | |||||||
\(920\) | −1.35782e6 | −0.0528900 | ||||||||
\(921\) | 3.20216e6 | 0.124393 | ||||||||
\(922\) | −3.59507e7 | −1.39277 | ||||||||
\(923\) | −3.25595e6 | −0.125798 | ||||||||
\(924\) | 2.63894e6 | 0.101683 | ||||||||
\(925\) | 6.85681e6 | 0.263492 | ||||||||
\(926\) | 5.60611e6 | 0.214849 | ||||||||
\(927\) | −9.76860e6 | −0.373364 | ||||||||
\(928\) | −6.01907e6 | −0.229435 | ||||||||
\(929\) | −9.27974e6 | −0.352774 | −0.176387 | − | 0.984321i | \(-0.556441\pi\) | ||||
−0.176387 | + | 0.984321i | \(0.556441\pi\) | |||||||
\(930\) | 5.35334e6 | 0.202963 | ||||||||
\(931\) | 1.40218e6 | 0.0530189 | ||||||||
\(932\) | 1.18388e7 | 0.446446 | ||||||||
\(933\) | −1.74411e7 | −0.655949 | ||||||||
\(934\) | −2.25132e7 | −0.844444 | ||||||||
\(935\) | 1.60311e7 | 0.599702 | ||||||||
\(936\) | −876096. | −0.0326860 | ||||||||
\(937\) | 4.88738e7 | 1.81856 | 0.909279 | − | 0.416188i | \(-0.136634\pi\) | ||||
0.909279 | + | 0.416188i | \(0.136634\pi\) | |||||||
\(938\) | −4.21557e6 | −0.156440 | ||||||||
\(939\) | −2.44749e7 | −0.905852 | ||||||||
\(940\) | −1.60896e6 | −0.0593917 | ||||||||
\(941\) | −3.95399e7 | −1.45567 | −0.727833 | − | 0.685754i | \(-0.759473\pi\) | ||||
−0.727833 | + | 0.685754i | \(0.759473\pi\) | |||||||
\(942\) | −1.46887e6 | −0.0539333 | ||||||||
\(943\) | −1.63363e6 | −0.0598239 | ||||||||
\(944\) | −3.65722e6 | −0.133574 | ||||||||
\(945\) | 857304. | 0.0312288 | ||||||||
\(946\) | 3.31573e7 | 1.20463 | ||||||||
\(947\) | −2.22841e7 | −0.807459 | −0.403729 | − | 0.914878i | \(-0.632286\pi\) | ||||
−0.403729 | + | 0.914878i | \(0.632286\pi\) | |||||||
\(948\) | −1.03450e6 | −0.0373859 | ||||||||
\(949\) | −1.21555e7 | −0.438134 | ||||||||
\(950\) | −5.95446e6 | −0.214059 | ||||||||
\(951\) | −1.18976e7 | −0.426586 | ||||||||
\(952\) | 5.60090e6 | 0.200293 | ||||||||
\(953\) | −4.94948e7 | −1.76534 | −0.882668 | − | 0.469998i | \(-0.844255\pi\) | ||||
−0.882668 | + | 0.469998i | \(0.844255\pi\) | |||||||
\(954\) | −350568. | −0.0124710 | ||||||||
\(955\) | −1.46191e7 | −0.518694 | ||||||||
\(956\) | −2.27222e6 | −0.0804093 | ||||||||
\(957\) | −1.97853e7 | −0.698335 | ||||||||
\(958\) | 1.48244e7 | 0.521872 | ||||||||
\(959\) | −89376.0 | −0.00313816 | ||||||||
\(960\) | 884736. | 0.0309839 | ||||||||
\(961\) | 9.76126e6 | 0.340955 | ||||||||
\(962\) | 1.81844e6 | 0.0633521 | ||||||||
\(963\) | 3.48235e6 | 0.121006 | ||||||||
\(964\) | −2.79696e6 | −0.0969379 | ||||||||
\(965\) | −386832. | −0.0133722 | ||||||||
\(966\) | −1.55938e6 | −0.0537660 | ||||||||
\(967\) | −1.82132e7 | −0.626353 | −0.313177 | − | 0.949695i | \(-0.601393\pi\) | ||||
−0.313177 | + | 0.949695i | \(0.601393\pi\) | |||||||
\(968\) | −1.35520e6 | −0.0464852 | ||||||||
\(969\) | 9.38722e6 | 0.321164 | ||||||||
\(970\) | −4.06291e6 | −0.138646 | ||||||||
\(971\) | 7.90048e6 | 0.268909 | 0.134454 | − | 0.990920i | \(-0.457072\pi\) | ||||
0.134454 | + | 0.990920i | \(0.457072\pi\) | |||||||
\(972\) | 944784. | 0.0320750 | ||||||||
\(973\) | 6.62813e6 | 0.224445 | ||||||||
\(974\) | −2.48987e7 | −0.840969 | ||||||||
\(975\) | 3.87703e6 | 0.130613 | ||||||||
\(976\) | −2.14784e6 | −0.0721734 | ||||||||
\(977\) | 1.11208e7 | 0.372733 | 0.186367 | − | 0.982480i | \(-0.440329\pi\) | ||||
0.186367 | + | 0.982480i | \(0.440329\pi\) | |||||||
\(978\) | −2.76854e6 | −0.0925559 | ||||||||
\(979\) | −7.45756e6 | −0.248680 | ||||||||
\(980\) | 921984. | 0.0306661 | ||||||||
\(981\) | 1.65663e7 | 0.549607 | ||||||||
\(982\) | 1.82238e7 | 0.603060 | ||||||||
\(983\) | −2.35770e7 | −0.778224 | −0.389112 | − | 0.921191i | \(-0.627218\pi\) | ||||
−0.389112 | + | 0.921191i | \(0.627218\pi\) | |||||||
\(984\) | 1.06445e6 | 0.0350459 | ||||||||
\(985\) | −6.40915e6 | −0.210480 | ||||||||
\(986\) | −4.19924e7 | −1.37556 | ||||||||
\(987\) | −1.84779e6 | −0.0603754 | ||||||||
\(988\) | −1.57914e6 | −0.0514668 | ||||||||
\(989\) | −1.95930e7 | −0.636956 | ||||||||
\(990\) | 2.90822e6 | 0.0943061 | ||||||||
\(991\) | −5.11700e7 | −1.65513 | −0.827564 | − | 0.561371i | \(-0.810274\pi\) | ||||
−0.827564 | + | 0.561371i | \(0.810274\pi\) | |||||||
\(992\) | 6.34470e6 | 0.204707 | ||||||||
\(993\) | −1.51335e7 | −0.487042 | ||||||||
\(994\) | 3.77614e6 | 0.121222 | ||||||||
\(995\) | 5.46893e6 | 0.175124 | ||||||||
\(996\) | 1.42753e7 | 0.455971 | ||||||||
\(997\) | −4.57099e7 | −1.45637 | −0.728186 | − | 0.685380i | \(-0.759636\pi\) | ||||
−0.728186 | + | 0.685380i | \(0.759636\pi\) | |||||||
\(998\) | −9.77509e6 | −0.310666 | ||||||||
\(999\) | −1.96101e6 | −0.0621679 |
(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 | 546.6.a.i.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.6.a.i.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial |