Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,4,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, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
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: | \(32.2150428631\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 9.00000 | 0.804984 | 0.402492 | − | 0.915423i | \(-0.368144\pi\) | ||||
0.402492 | + | 0.915423i | \(0.368144\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 18.0000 | 0.569210 | ||||||||
\(11\) | 62.0000 | 1.69943 | 0.849714 | − | 0.527244i | \(-0.176775\pi\) | ||||
0.849714 | + | 0.527244i | \(0.176775\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | 27.0000 | 0.464758 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −16.0000 | −0.228269 | −0.114134 | − | 0.993465i | \(-0.536409\pi\) | ||||
−0.114134 | + | 0.993465i | \(0.536409\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 79.0000 | 0.953886 | 0.476943 | − | 0.878934i | \(-0.341745\pi\) | ||||
0.476943 | + | 0.878934i | \(0.341745\pi\) | |||||||
\(20\) | 36.0000 | 0.402492 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 124.000 | 1.20168 | ||||||||
\(23\) | −155.000 | −1.40521 | −0.702603 | − | 0.711582i | \(-0.747979\pi\) | ||||
−0.702603 | + | 0.711582i | \(0.747979\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | −44.0000 | −0.352000 | ||||||||
\(26\) | −26.0000 | −0.196116 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | 51.0000 | 0.326568 | 0.163284 | − | 0.986579i | \(-0.447791\pi\) | ||||
0.163284 | + | 0.986579i | \(0.447791\pi\) | |||||||
\(30\) | 54.0000 | 0.328634 | ||||||||
\(31\) | 243.000 | 1.40787 | 0.703937 | − | 0.710263i | \(-0.251424\pi\) | ||||
0.703937 | + | 0.710263i | \(0.251424\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 186.000 | 0.981165 | ||||||||
\(34\) | −32.0000 | −0.161410 | ||||||||
\(35\) | −63.0000 | −0.304256 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 412.000 | 1.83060 | 0.915302 | − | 0.402767i | \(-0.131952\pi\) | ||||
0.915302 | + | 0.402767i | \(0.131952\pi\) | |||||||
\(38\) | 158.000 | 0.674500 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 72.0000 | 0.284605 | ||||||||
\(41\) | −406.000 | −1.54650 | −0.773251 | − | 0.634101i | \(-0.781371\pi\) | ||||
−0.773251 | + | 0.634101i | \(0.781371\pi\) | |||||||
\(42\) | −42.0000 | −0.154303 | ||||||||
\(43\) | −103.000 | −0.365287 | −0.182644 | − | 0.983179i | \(-0.558465\pi\) | ||||
−0.182644 | + | 0.983179i | \(0.558465\pi\) | |||||||
\(44\) | 248.000 | 0.849714 | ||||||||
\(45\) | 81.0000 | 0.268328 | ||||||||
\(46\) | −310.000 | −0.993631 | ||||||||
\(47\) | 429.000 | 1.33141 | 0.665703 | − | 0.746217i | \(-0.268132\pi\) | ||||
0.665703 | + | 0.746217i | \(0.268132\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −88.0000 | −0.248902 | ||||||||
\(51\) | −48.0000 | −0.131791 | ||||||||
\(52\) | −52.0000 | −0.138675 | ||||||||
\(53\) | −169.000 | −0.437999 | −0.218999 | − | 0.975725i | \(-0.570279\pi\) | ||||
−0.218999 | + | 0.975725i | \(0.570279\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 558.000 | 1.36801 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | 237.000 | 0.550727 | ||||||||
\(58\) | 102.000 | 0.230918 | ||||||||
\(59\) | 320.000 | 0.706109 | 0.353055 | − | 0.935603i | \(-0.385143\pi\) | ||||
0.353055 | + | 0.935603i | \(0.385143\pi\) | |||||||
\(60\) | 108.000 | 0.232379 | ||||||||
\(61\) | −614.000 | −1.28876 | −0.644382 | − | 0.764703i | \(-0.722885\pi\) | ||||
−0.644382 | + | 0.764703i | \(0.722885\pi\) | |||||||
\(62\) | 486.000 | 0.995517 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −117.000 | −0.223263 | ||||||||
\(66\) | 372.000 | 0.693788 | ||||||||
\(67\) | 258.000 | 0.470444 | 0.235222 | − | 0.971942i | \(-0.424418\pi\) | ||||
0.235222 | + | 0.971942i | \(0.424418\pi\) | |||||||
\(68\) | −64.0000 | −0.114134 | ||||||||
\(69\) | −465.000 | −0.811296 | ||||||||
\(70\) | −126.000 | −0.215141 | ||||||||
\(71\) | −264.000 | −0.441282 | −0.220641 | − | 0.975355i | \(-0.570815\pi\) | ||||
−0.220641 | + | 0.975355i | \(0.570815\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | −121.000 | −0.194000 | −0.0969999 | − | 0.995284i | \(-0.530925\pi\) | ||||
−0.0969999 | + | 0.995284i | \(0.530925\pi\) | |||||||
\(74\) | 824.000 | 1.29443 | ||||||||
\(75\) | −132.000 | −0.203227 | ||||||||
\(76\) | 316.000 | 0.476943 | ||||||||
\(77\) | −434.000 | −0.642323 | ||||||||
\(78\) | −78.0000 | −0.113228 | ||||||||
\(79\) | −967.000 | −1.37716 | −0.688582 | − | 0.725158i | \(-0.741767\pi\) | ||||
−0.688582 | + | 0.725158i | \(0.741767\pi\) | |||||||
\(80\) | 144.000 | 0.201246 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −812.000 | −1.09354 | ||||||||
\(83\) | −679.000 | −0.897951 | −0.448975 | − | 0.893544i | \(-0.648211\pi\) | ||||
−0.448975 | + | 0.893544i | \(0.648211\pi\) | |||||||
\(84\) | −84.0000 | −0.109109 | ||||||||
\(85\) | −144.000 | −0.183753 | ||||||||
\(86\) | −206.000 | −0.258297 | ||||||||
\(87\) | 153.000 | 0.188544 | ||||||||
\(88\) | 496.000 | 0.600838 | ||||||||
\(89\) | 1059.00 | 1.26128 | 0.630639 | − | 0.776076i | \(-0.282793\pi\) | ||||
0.630639 | + | 0.776076i | \(0.282793\pi\) | |||||||
\(90\) | 162.000 | 0.189737 | ||||||||
\(91\) | 91.0000 | 0.104828 | ||||||||
\(92\) | −620.000 | −0.702603 | ||||||||
\(93\) | 729.000 | 0.812836 | ||||||||
\(94\) | 858.000 | 0.941446 | ||||||||
\(95\) | 711.000 | 0.767864 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | −21.0000 | −0.0219817 | −0.0109909 | − | 0.999940i | \(-0.503499\pi\) | ||||
−0.0109909 | + | 0.999940i | \(0.503499\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | 558.000 | 0.566476 | ||||||||
\(100\) | −176.000 | −0.176000 | ||||||||
\(101\) | 894.000 | 0.880756 | 0.440378 | − | 0.897813i | \(-0.354844\pi\) | ||||
0.440378 | + | 0.897813i | \(0.354844\pi\) | |||||||
\(102\) | −96.0000 | −0.0931904 | ||||||||
\(103\) | 128.000 | 0.122449 | 0.0612243 | − | 0.998124i | \(-0.480499\pi\) | ||||
0.0612243 | + | 0.998124i | \(0.480499\pi\) | |||||||
\(104\) | −104.000 | −0.0980581 | ||||||||
\(105\) | −189.000 | −0.175662 | ||||||||
\(106\) | −338.000 | −0.309712 | ||||||||
\(107\) | −708.000 | −0.639672 | −0.319836 | − | 0.947473i | \(-0.603628\pi\) | ||||
−0.319836 | + | 0.947473i | \(0.603628\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 1238.00 | 1.08788 | 0.543940 | − | 0.839124i | \(-0.316932\pi\) | ||||
0.543940 | + | 0.839124i | \(0.316932\pi\) | |||||||
\(110\) | 1116.00 | 0.967331 | ||||||||
\(111\) | 1236.00 | 1.05690 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | 1073.00 | 0.893269 | 0.446634 | − | 0.894717i | \(-0.352623\pi\) | ||||
0.446634 | + | 0.894717i | \(0.352623\pi\) | |||||||
\(114\) | 474.000 | 0.389423 | ||||||||
\(115\) | −1395.00 | −1.13117 | ||||||||
\(116\) | 204.000 | 0.163284 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 640.000 | 0.499295 | ||||||||
\(119\) | 112.000 | 0.0862775 | ||||||||
\(120\) | 216.000 | 0.164317 | ||||||||
\(121\) | 2513.00 | 1.88805 | ||||||||
\(122\) | −1228.00 | −0.911294 | ||||||||
\(123\) | −1218.00 | −0.892873 | ||||||||
\(124\) | 972.000 | 0.703937 | ||||||||
\(125\) | −1521.00 | −1.08834 | ||||||||
\(126\) | −126.000 | −0.0890871 | ||||||||
\(127\) | −1748.00 | −1.22134 | −0.610669 | − | 0.791886i | \(-0.709099\pi\) | ||||
−0.610669 | + | 0.791886i | \(0.709099\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −309.000 | −0.210899 | ||||||||
\(130\) | −234.000 | −0.157870 | ||||||||
\(131\) | −936.000 | −0.624265 | −0.312132 | − | 0.950039i | \(-0.601043\pi\) | ||||
−0.312132 | + | 0.950039i | \(0.601043\pi\) | |||||||
\(132\) | 744.000 | 0.490582 | ||||||||
\(133\) | −553.000 | −0.360535 | ||||||||
\(134\) | 516.000 | 0.332654 | ||||||||
\(135\) | 243.000 | 0.154919 | ||||||||
\(136\) | −128.000 | −0.0807052 | ||||||||
\(137\) | −1128.00 | −0.703442 | −0.351721 | − | 0.936105i | \(-0.614403\pi\) | ||||
−0.351721 | + | 0.936105i | \(0.614403\pi\) | |||||||
\(138\) | −930.000 | −0.573673 | ||||||||
\(139\) | −854.000 | −0.521118 | −0.260559 | − | 0.965458i | \(-0.583907\pi\) | ||||
−0.260559 | + | 0.965458i | \(0.583907\pi\) | |||||||
\(140\) | −252.000 | −0.152128 | ||||||||
\(141\) | 1287.00 | 0.768688 | ||||||||
\(142\) | −528.000 | −0.312034 | ||||||||
\(143\) | −806.000 | −0.471336 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 459.000 | 0.262882 | ||||||||
\(146\) | −242.000 | −0.137179 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 1648.00 | 0.915302 | ||||||||
\(149\) | −442.000 | −0.243020 | −0.121510 | − | 0.992590i | \(-0.538774\pi\) | ||||
−0.121510 | + | 0.992590i | \(0.538774\pi\) | |||||||
\(150\) | −264.000 | −0.143703 | ||||||||
\(151\) | −1016.00 | −0.547556 | −0.273778 | − | 0.961793i | \(-0.588273\pi\) | ||||
−0.273778 | + | 0.961793i | \(0.588273\pi\) | |||||||
\(152\) | 632.000 | 0.337250 | ||||||||
\(153\) | −144.000 | −0.0760896 | ||||||||
\(154\) | −868.000 | −0.454191 | ||||||||
\(155\) | 2187.00 | 1.13332 | ||||||||
\(156\) | −156.000 | −0.0800641 | ||||||||
\(157\) | −3880.00 | −1.97234 | −0.986171 | − | 0.165731i | \(-0.947002\pi\) | ||||
−0.986171 | + | 0.165731i | \(0.947002\pi\) | |||||||
\(158\) | −1934.00 | −0.973802 | ||||||||
\(159\) | −507.000 | −0.252879 | ||||||||
\(160\) | 288.000 | 0.142302 | ||||||||
\(161\) | 1085.00 | 0.531118 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | −1604.00 | −0.770767 | −0.385383 | − | 0.922757i | \(-0.625931\pi\) | ||||
−0.385383 | + | 0.922757i | \(0.625931\pi\) | |||||||
\(164\) | −1624.00 | −0.773251 | ||||||||
\(165\) | 1674.00 | 0.789823 | ||||||||
\(166\) | −1358.00 | −0.634947 | ||||||||
\(167\) | 959.000 | 0.444369 | 0.222185 | − | 0.975005i | \(-0.428681\pi\) | ||||
0.222185 | + | 0.975005i | \(0.428681\pi\) | |||||||
\(168\) | −168.000 | −0.0771517 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | −288.000 | −0.129933 | ||||||||
\(171\) | 711.000 | 0.317962 | ||||||||
\(172\) | −412.000 | −0.182644 | ||||||||
\(173\) | −488.000 | −0.214462 | −0.107231 | − | 0.994234i | \(-0.534198\pi\) | ||||
−0.107231 | + | 0.994234i | \(0.534198\pi\) | |||||||
\(174\) | 306.000 | 0.133321 | ||||||||
\(175\) | 308.000 | 0.133043 | ||||||||
\(176\) | 992.000 | 0.424857 | ||||||||
\(177\) | 960.000 | 0.407672 | ||||||||
\(178\) | 2118.00 | 0.891858 | ||||||||
\(179\) | 2533.00 | 1.05768 | 0.528842 | − | 0.848721i | \(-0.322627\pi\) | ||||
0.528842 | + | 0.848721i | \(0.322627\pi\) | |||||||
\(180\) | 324.000 | 0.134164 | ||||||||
\(181\) | −3626.00 | −1.48905 | −0.744526 | − | 0.667593i | \(-0.767325\pi\) | ||||
−0.744526 | + | 0.667593i | \(0.767325\pi\) | |||||||
\(182\) | 182.000 | 0.0741249 | ||||||||
\(183\) | −1842.00 | −0.744069 | ||||||||
\(184\) | −1240.00 | −0.496815 | ||||||||
\(185\) | 3708.00 | 1.47361 | ||||||||
\(186\) | 1458.00 | 0.574762 | ||||||||
\(187\) | −992.000 | −0.387926 | ||||||||
\(188\) | 1716.00 | 0.665703 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 1422.00 | 0.542962 | ||||||||
\(191\) | −4992.00 | −1.89114 | −0.945572 | − | 0.325413i | \(-0.894497\pi\) | ||||
−0.945572 | + | 0.325413i | \(0.894497\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | −470.000 | −0.175292 | −0.0876460 | − | 0.996152i | \(-0.527934\pi\) | ||||
−0.0876460 | + | 0.996152i | \(0.527934\pi\) | |||||||
\(194\) | −42.0000 | −0.0155434 | ||||||||
\(195\) | −351.000 | −0.128901 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −3190.00 | −1.15370 | −0.576848 | − | 0.816852i | \(-0.695717\pi\) | ||||
−0.576848 | + | 0.816852i | \(0.695717\pi\) | |||||||
\(198\) | 1116.00 | 0.400559 | ||||||||
\(199\) | 1944.00 | 0.692495 | 0.346248 | − | 0.938143i | \(-0.387456\pi\) | ||||
0.346248 | + | 0.938143i | \(0.387456\pi\) | |||||||
\(200\) | −352.000 | −0.124451 | ||||||||
\(201\) | 774.000 | 0.271611 | ||||||||
\(202\) | 1788.00 | 0.622788 | ||||||||
\(203\) | −357.000 | −0.123431 | ||||||||
\(204\) | −192.000 | −0.0658955 | ||||||||
\(205\) | −3654.00 | −1.24491 | ||||||||
\(206\) | 256.000 | 0.0865843 | ||||||||
\(207\) | −1395.00 | −0.468402 | ||||||||
\(208\) | −208.000 | −0.0693375 | ||||||||
\(209\) | 4898.00 | 1.62106 | ||||||||
\(210\) | −378.000 | −0.124212 | ||||||||
\(211\) | −1139.00 | −0.371621 | −0.185810 | − | 0.982586i | \(-0.559491\pi\) | ||||
−0.185810 | + | 0.982586i | \(0.559491\pi\) | |||||||
\(212\) | −676.000 | −0.218999 | ||||||||
\(213\) | −792.000 | −0.254774 | ||||||||
\(214\) | −1416.00 | −0.452317 | ||||||||
\(215\) | −927.000 | −0.294051 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | −1701.00 | −0.532126 | ||||||||
\(218\) | 2476.00 | 0.769247 | ||||||||
\(219\) | −363.000 | −0.112006 | ||||||||
\(220\) | 2232.00 | 0.684006 | ||||||||
\(221\) | 208.000 | 0.0633104 | ||||||||
\(222\) | 2472.00 | 0.747341 | ||||||||
\(223\) | 833.000 | 0.250143 | 0.125071 | − | 0.992148i | \(-0.460084\pi\) | ||||
0.125071 | + | 0.992148i | \(0.460084\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | −396.000 | −0.117333 | ||||||||
\(226\) | 2146.00 | 0.631636 | ||||||||
\(227\) | −3516.00 | −1.02804 | −0.514020 | − | 0.857778i | \(-0.671844\pi\) | ||||
−0.514020 | + | 0.857778i | \(0.671844\pi\) | |||||||
\(228\) | 948.000 | 0.275363 | ||||||||
\(229\) | 3222.00 | 0.929763 | 0.464882 | − | 0.885373i | \(-0.346097\pi\) | ||||
0.464882 | + | 0.885373i | \(0.346097\pi\) | |||||||
\(230\) | −2790.00 | −0.799857 | ||||||||
\(231\) | −1302.00 | −0.370846 | ||||||||
\(232\) | 408.000 | 0.115459 | ||||||||
\(233\) | −477.000 | −0.134117 | −0.0670586 | − | 0.997749i | \(-0.521361\pi\) | ||||
−0.0670586 | + | 0.997749i | \(0.521361\pi\) | |||||||
\(234\) | −234.000 | −0.0653720 | ||||||||
\(235\) | 3861.00 | 1.07176 | ||||||||
\(236\) | 1280.00 | 0.353055 | ||||||||
\(237\) | −2901.00 | −0.795106 | ||||||||
\(238\) | 224.000 | 0.0610074 | ||||||||
\(239\) | −6368.00 | −1.72348 | −0.861740 | − | 0.507350i | \(-0.830625\pi\) | ||||
−0.861740 | + | 0.507350i | \(0.830625\pi\) | |||||||
\(240\) | 432.000 | 0.116190 | ||||||||
\(241\) | 747.000 | 0.199662 | 0.0998309 | − | 0.995004i | \(-0.468170\pi\) | ||||
0.0998309 | + | 0.995004i | \(0.468170\pi\) | |||||||
\(242\) | 5026.00 | 1.33506 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −2456.00 | −0.644382 | ||||||||
\(245\) | 441.000 | 0.114998 | ||||||||
\(246\) | −2436.00 | −0.631356 | ||||||||
\(247\) | −1027.00 | −0.264561 | ||||||||
\(248\) | 1944.00 | 0.497759 | ||||||||
\(249\) | −2037.00 | −0.518432 | ||||||||
\(250\) | −3042.00 | −0.769572 | ||||||||
\(251\) | 7518.00 | 1.89057 | 0.945283 | − | 0.326252i | \(-0.105786\pi\) | ||||
0.945283 | + | 0.326252i | \(0.105786\pi\) | |||||||
\(252\) | −252.000 | −0.0629941 | ||||||||
\(253\) | −9610.00 | −2.38805 | ||||||||
\(254\) | −3496.00 | −0.863616 | ||||||||
\(255\) | −432.000 | −0.106090 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 1094.00 | 0.265532 | 0.132766 | − | 0.991147i | \(-0.457614\pi\) | ||||
0.132766 | + | 0.991147i | \(0.457614\pi\) | |||||||
\(258\) | −618.000 | −0.149128 | ||||||||
\(259\) | −2884.00 | −0.691904 | ||||||||
\(260\) | −468.000 | −0.111631 | ||||||||
\(261\) | 459.000 | 0.108856 | ||||||||
\(262\) | −1872.00 | −0.441422 | ||||||||
\(263\) | −1289.00 | −0.302217 | −0.151109 | − | 0.988517i | \(-0.548284\pi\) | ||||
−0.151109 | + | 0.988517i | \(0.548284\pi\) | |||||||
\(264\) | 1488.00 | 0.346894 | ||||||||
\(265\) | −1521.00 | −0.352582 | ||||||||
\(266\) | −1106.00 | −0.254937 | ||||||||
\(267\) | 3177.00 | 0.728199 | ||||||||
\(268\) | 1032.00 | 0.235222 | ||||||||
\(269\) | −2060.00 | −0.466916 | −0.233458 | − | 0.972367i | \(-0.575004\pi\) | ||||
−0.233458 | + | 0.972367i | \(0.575004\pi\) | |||||||
\(270\) | 486.000 | 0.109545 | ||||||||
\(271\) | 576.000 | 0.129113 | 0.0645563 | − | 0.997914i | \(-0.479437\pi\) | ||||
0.0645563 | + | 0.997914i | \(0.479437\pi\) | |||||||
\(272\) | −256.000 | −0.0570672 | ||||||||
\(273\) | 273.000 | 0.0605228 | ||||||||
\(274\) | −2256.00 | −0.497409 | ||||||||
\(275\) | −2728.00 | −0.598199 | ||||||||
\(276\) | −1860.00 | −0.405648 | ||||||||
\(277\) | −5699.00 | −1.23617 | −0.618086 | − | 0.786110i | \(-0.712092\pi\) | ||||
−0.618086 | + | 0.786110i | \(0.712092\pi\) | |||||||
\(278\) | −1708.00 | −0.368486 | ||||||||
\(279\) | 2187.00 | 0.469291 | ||||||||
\(280\) | −504.000 | −0.107571 | ||||||||
\(281\) | 4062.00 | 0.862344 | 0.431172 | − | 0.902270i | \(-0.358100\pi\) | ||||
0.431172 | + | 0.902270i | \(0.358100\pi\) | |||||||
\(282\) | 2574.00 | 0.543544 | ||||||||
\(283\) | −772.000 | −0.162158 | −0.0810789 | − | 0.996708i | \(-0.525837\pi\) | ||||
−0.0810789 | + | 0.996708i | \(0.525837\pi\) | |||||||
\(284\) | −1056.00 | −0.220641 | ||||||||
\(285\) | 2133.00 | 0.443326 | ||||||||
\(286\) | −1612.00 | −0.333285 | ||||||||
\(287\) | 2842.00 | 0.584522 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −4657.00 | −0.947893 | ||||||||
\(290\) | 918.000 | 0.185886 | ||||||||
\(291\) | −63.0000 | −0.0126912 | ||||||||
\(292\) | −484.000 | −0.0969999 | ||||||||
\(293\) | 7833.00 | 1.56180 | 0.780902 | − | 0.624653i | \(-0.214760\pi\) | ||||
0.780902 | + | 0.624653i | \(0.214760\pi\) | |||||||
\(294\) | 294.000 | 0.0583212 | ||||||||
\(295\) | 2880.00 | 0.568407 | ||||||||
\(296\) | 3296.00 | 0.647217 | ||||||||
\(297\) | 1674.00 | 0.327055 | ||||||||
\(298\) | −884.000 | −0.171841 | ||||||||
\(299\) | 2015.00 | 0.389734 | ||||||||
\(300\) | −528.000 | −0.101614 | ||||||||
\(301\) | 721.000 | 0.138066 | ||||||||
\(302\) | −2032.00 | −0.387180 | ||||||||
\(303\) | 2682.00 | 0.508505 | ||||||||
\(304\) | 1264.00 | 0.238472 | ||||||||
\(305\) | −5526.00 | −1.03744 | ||||||||
\(306\) | −288.000 | −0.0538035 | ||||||||
\(307\) | −2891.00 | −0.537453 | −0.268727 | − | 0.963217i | \(-0.586603\pi\) | ||||
−0.268727 | + | 0.963217i | \(0.586603\pi\) | |||||||
\(308\) | −1736.00 | −0.321162 | ||||||||
\(309\) | 384.000 | 0.0706958 | ||||||||
\(310\) | 4374.00 | 0.801376 | ||||||||
\(311\) | −3530.00 | −0.643627 | −0.321813 | − | 0.946803i | \(-0.604292\pi\) | ||||
−0.321813 | + | 0.946803i | \(0.604292\pi\) | |||||||
\(312\) | −312.000 | −0.0566139 | ||||||||
\(313\) | 5490.00 | 0.991416 | 0.495708 | − | 0.868489i | \(-0.334909\pi\) | ||||
0.495708 | + | 0.868489i | \(0.334909\pi\) | |||||||
\(314\) | −7760.00 | −1.39466 | ||||||||
\(315\) | −567.000 | −0.101419 | ||||||||
\(316\) | −3868.00 | −0.688582 | ||||||||
\(317\) | −5636.00 | −0.998578 | −0.499289 | − | 0.866435i | \(-0.666405\pi\) | ||||
−0.499289 | + | 0.866435i | \(0.666405\pi\) | |||||||
\(318\) | −1014.00 | −0.178812 | ||||||||
\(319\) | 3162.00 | 0.554978 | ||||||||
\(320\) | 576.000 | 0.100623 | ||||||||
\(321\) | −2124.00 | −0.369315 | ||||||||
\(322\) | 2170.00 | 0.375557 | ||||||||
\(323\) | −1264.00 | −0.217743 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 572.000 | 0.0976272 | ||||||||
\(326\) | −3208.00 | −0.545014 | ||||||||
\(327\) | 3714.00 | 0.628088 | ||||||||
\(328\) | −3248.00 | −0.546771 | ||||||||
\(329\) | −3003.00 | −0.503224 | ||||||||
\(330\) | 3348.00 | 0.558489 | ||||||||
\(331\) | −9962.00 | −1.65426 | −0.827131 | − | 0.562008i | \(-0.810029\pi\) | ||||
−0.827131 | + | 0.562008i | \(0.810029\pi\) | |||||||
\(332\) | −2716.00 | −0.448975 | ||||||||
\(333\) | 3708.00 | 0.610202 | ||||||||
\(334\) | 1918.00 | 0.314216 | ||||||||
\(335\) | 2322.00 | 0.378700 | ||||||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | −11415.0 | −1.84515 | −0.922574 | − | 0.385821i | \(-0.873918\pi\) | ||||
−0.922574 | + | 0.385821i | \(0.873918\pi\) | |||||||
\(338\) | 338.000 | 0.0543928 | ||||||||
\(339\) | 3219.00 | 0.515729 | ||||||||
\(340\) | −576.000 | −0.0918764 | ||||||||
\(341\) | 15066.0 | 2.39258 | ||||||||
\(342\) | 1422.00 | 0.224833 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −824.000 | −0.129149 | ||||||||
\(345\) | −4185.00 | −0.653081 | ||||||||
\(346\) | −976.000 | −0.151648 | ||||||||
\(347\) | 4864.00 | 0.752488 | 0.376244 | − | 0.926521i | \(-0.377216\pi\) | ||||
0.376244 | + | 0.926521i | \(0.377216\pi\) | |||||||
\(348\) | 612.000 | 0.0942720 | ||||||||
\(349\) | −469.000 | −0.0719341 | −0.0359670 | − | 0.999353i | \(-0.511451\pi\) | ||||
−0.0359670 | + | 0.999353i | \(0.511451\pi\) | |||||||
\(350\) | 616.000 | 0.0940760 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | 1984.00 | 0.300419 | ||||||||
\(353\) | 4198.00 | 0.632966 | 0.316483 | − | 0.948598i | \(-0.397498\pi\) | ||||
0.316483 | + | 0.948598i | \(0.397498\pi\) | |||||||
\(354\) | 1920.00 | 0.288268 | ||||||||
\(355\) | −2376.00 | −0.355225 | ||||||||
\(356\) | 4236.00 | 0.630639 | ||||||||
\(357\) | 336.000 | 0.0498123 | ||||||||
\(358\) | 5066.00 | 0.747895 | ||||||||
\(359\) | 3408.00 | 0.501023 | 0.250512 | − | 0.968114i | \(-0.419401\pi\) | ||||
0.250512 | + | 0.968114i | \(0.419401\pi\) | |||||||
\(360\) | 648.000 | 0.0948683 | ||||||||
\(361\) | −618.000 | −0.0901006 | ||||||||
\(362\) | −7252.00 | −1.05292 | ||||||||
\(363\) | 7539.00 | 1.09007 | ||||||||
\(364\) | 364.000 | 0.0524142 | ||||||||
\(365\) | −1089.00 | −0.156167 | ||||||||
\(366\) | −3684.00 | −0.526136 | ||||||||
\(367\) | −8290.00 | −1.17911 | −0.589557 | − | 0.807727i | \(-0.700697\pi\) | ||||
−0.589557 | + | 0.807727i | \(0.700697\pi\) | |||||||
\(368\) | −2480.00 | −0.351301 | ||||||||
\(369\) | −3654.00 | −0.515500 | ||||||||
\(370\) | 7416.00 | 1.04200 | ||||||||
\(371\) | 1183.00 | 0.165548 | ||||||||
\(372\) | 2916.00 | 0.406418 | ||||||||
\(373\) | −9906.00 | −1.37510 | −0.687551 | − | 0.726136i | \(-0.741314\pi\) | ||||
−0.687551 | + | 0.726136i | \(0.741314\pi\) | |||||||
\(374\) | −1984.00 | −0.274305 | ||||||||
\(375\) | −4563.00 | −0.628353 | ||||||||
\(376\) | 3432.00 | 0.470723 | ||||||||
\(377\) | −663.000 | −0.0905736 | ||||||||
\(378\) | −378.000 | −0.0514344 | ||||||||
\(379\) | −9238.00 | −1.25204 | −0.626021 | − | 0.779806i | \(-0.715318\pi\) | ||||
−0.626021 | + | 0.779806i | \(0.715318\pi\) | |||||||
\(380\) | 2844.00 | 0.383932 | ||||||||
\(381\) | −5244.00 | −0.705140 | ||||||||
\(382\) | −9984.00 | −1.33724 | ||||||||
\(383\) | 4972.00 | 0.663335 | 0.331668 | − | 0.943396i | \(-0.392389\pi\) | ||||
0.331668 | + | 0.943396i | \(0.392389\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | −3906.00 | −0.517060 | ||||||||
\(386\) | −940.000 | −0.123950 | ||||||||
\(387\) | −927.000 | −0.121762 | ||||||||
\(388\) | −84.0000 | −0.0109909 | ||||||||
\(389\) | 7454.00 | 0.971550 | 0.485775 | − | 0.874084i | \(-0.338538\pi\) | ||||
0.485775 | + | 0.874084i | \(0.338538\pi\) | |||||||
\(390\) | −702.000 | −0.0911465 | ||||||||
\(391\) | 2480.00 | 0.320765 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | −2808.00 | −0.360419 | ||||||||
\(394\) | −6380.00 | −0.815786 | ||||||||
\(395\) | −8703.00 | −1.10860 | ||||||||
\(396\) | 2232.00 | 0.283238 | ||||||||
\(397\) | 7219.00 | 0.912623 | 0.456311 | − | 0.889820i | \(-0.349170\pi\) | ||||
0.456311 | + | 0.889820i | \(0.349170\pi\) | |||||||
\(398\) | 3888.00 | 0.489668 | ||||||||
\(399\) | −1659.00 | −0.208155 | ||||||||
\(400\) | −704.000 | −0.0880000 | ||||||||
\(401\) | 10772.0 | 1.34147 | 0.670733 | − | 0.741699i | \(-0.265980\pi\) | ||||
0.670733 | + | 0.741699i | \(0.265980\pi\) | |||||||
\(402\) | 1548.00 | 0.192058 | ||||||||
\(403\) | −3159.00 | −0.390474 | ||||||||
\(404\) | 3576.00 | 0.440378 | ||||||||
\(405\) | 729.000 | 0.0894427 | ||||||||
\(406\) | −714.000 | −0.0872789 | ||||||||
\(407\) | 25544.0 | 3.11098 | ||||||||
\(408\) | −384.000 | −0.0465952 | ||||||||
\(409\) | 13151.0 | 1.58991 | 0.794957 | − | 0.606665i | \(-0.207493\pi\) | ||||
0.794957 | + | 0.606665i | \(0.207493\pi\) | |||||||
\(410\) | −7308.00 | −0.880284 | ||||||||
\(411\) | −3384.00 | −0.406132 | ||||||||
\(412\) | 512.000 | 0.0612243 | ||||||||
\(413\) | −2240.00 | −0.266884 | ||||||||
\(414\) | −2790.00 | −0.331210 | ||||||||
\(415\) | −6111.00 | −0.722837 | ||||||||
\(416\) | −416.000 | −0.0490290 | ||||||||
\(417\) | −2562.00 | −0.300867 | ||||||||
\(418\) | 9796.00 | 1.14626 | ||||||||
\(419\) | 6034.00 | 0.703533 | 0.351766 | − | 0.936088i | \(-0.385581\pi\) | ||||
0.351766 | + | 0.936088i | \(0.385581\pi\) | |||||||
\(420\) | −756.000 | −0.0878310 | ||||||||
\(421\) | 8864.00 | 1.02614 | 0.513070 | − | 0.858347i | \(-0.328508\pi\) | ||||
0.513070 | + | 0.858347i | \(0.328508\pi\) | |||||||
\(422\) | −2278.00 | −0.262776 | ||||||||
\(423\) | 3861.00 | 0.443802 | ||||||||
\(424\) | −1352.00 | −0.154856 | ||||||||
\(425\) | 704.000 | 0.0803506 | ||||||||
\(426\) | −1584.00 | −0.180153 | ||||||||
\(427\) | 4298.00 | 0.487107 | ||||||||
\(428\) | −2832.00 | −0.319836 | ||||||||
\(429\) | −2418.00 | −0.272126 | ||||||||
\(430\) | −1854.00 | −0.207925 | ||||||||
\(431\) | −134.000 | −0.0149758 | −0.00748788 | − | 0.999972i | \(-0.502383\pi\) | ||||
−0.00748788 | + | 0.999972i | \(0.502383\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 12376.0 | 1.37356 | 0.686781 | − | 0.726864i | \(-0.259023\pi\) | ||||
0.686781 | + | 0.726864i | \(0.259023\pi\) | |||||||
\(434\) | −3402.00 | −0.376270 | ||||||||
\(435\) | 1377.00 | 0.151775 | ||||||||
\(436\) | 4952.00 | 0.543940 | ||||||||
\(437\) | −12245.0 | −1.34041 | ||||||||
\(438\) | −726.000 | −0.0792000 | ||||||||
\(439\) | 14198.0 | 1.54358 | 0.771792 | − | 0.635875i | \(-0.219361\pi\) | ||||
0.771792 | + | 0.635875i | \(0.219361\pi\) | |||||||
\(440\) | 4464.00 | 0.483666 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 416.000 | 0.0447672 | ||||||||
\(443\) | 7657.00 | 0.821208 | 0.410604 | − | 0.911814i | \(-0.365318\pi\) | ||||
0.410604 | + | 0.911814i | \(0.365318\pi\) | |||||||
\(444\) | 4944.00 | 0.528450 | ||||||||
\(445\) | 9531.00 | 1.01531 | ||||||||
\(446\) | 1666.00 | 0.176878 | ||||||||
\(447\) | −1326.00 | −0.140308 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | 15500.0 | 1.62915 | 0.814577 | − | 0.580055i | \(-0.196969\pi\) | ||||
0.814577 | + | 0.580055i | \(0.196969\pi\) | |||||||
\(450\) | −792.000 | −0.0829672 | ||||||||
\(451\) | −25172.0 | −2.62817 | ||||||||
\(452\) | 4292.00 | 0.446634 | ||||||||
\(453\) | −3048.00 | −0.316131 | ||||||||
\(454\) | −7032.00 | −0.726934 | ||||||||
\(455\) | 819.000 | 0.0843853 | ||||||||
\(456\) | 1896.00 | 0.194711 | ||||||||
\(457\) | 10184.0 | 1.04242 | 0.521212 | − | 0.853427i | \(-0.325480\pi\) | ||||
0.521212 | + | 0.853427i | \(0.325480\pi\) | |||||||
\(458\) | 6444.00 | 0.657442 | ||||||||
\(459\) | −432.000 | −0.0439304 | ||||||||
\(460\) | −5580.00 | −0.565584 | ||||||||
\(461\) | 19250.0 | 1.94482 | 0.972410 | − | 0.233279i | \(-0.0749455\pi\) | ||||
0.972410 | + | 0.233279i | \(0.0749455\pi\) | |||||||
\(462\) | −2604.00 | −0.262227 | ||||||||
\(463\) | −15622.0 | −1.56807 | −0.784034 | − | 0.620717i | \(-0.786841\pi\) | ||||
−0.784034 | + | 0.620717i | \(0.786841\pi\) | |||||||
\(464\) | 816.000 | 0.0816419 | ||||||||
\(465\) | 6561.00 | 0.654321 | ||||||||
\(466\) | −954.000 | −0.0948352 | ||||||||
\(467\) | −15594.0 | −1.54519 | −0.772596 | − | 0.634898i | \(-0.781042\pi\) | ||||
−0.772596 | + | 0.634898i | \(0.781042\pi\) | |||||||
\(468\) | −468.000 | −0.0462250 | ||||||||
\(469\) | −1806.00 | −0.177811 | ||||||||
\(470\) | 7722.00 | 0.757850 | ||||||||
\(471\) | −11640.0 | −1.13873 | ||||||||
\(472\) | 2560.00 | 0.249647 | ||||||||
\(473\) | −6386.00 | −0.620779 | ||||||||
\(474\) | −5802.00 | −0.562225 | ||||||||
\(475\) | −3476.00 | −0.335768 | ||||||||
\(476\) | 448.000 | 0.0431388 | ||||||||
\(477\) | −1521.00 | −0.146000 | ||||||||
\(478\) | −12736.0 | −1.21868 | ||||||||
\(479\) | 3239.00 | 0.308964 | 0.154482 | − | 0.987996i | \(-0.450629\pi\) | ||||
0.154482 | + | 0.987996i | \(0.450629\pi\) | |||||||
\(480\) | 864.000 | 0.0821584 | ||||||||
\(481\) | −5356.00 | −0.507718 | ||||||||
\(482\) | 1494.00 | 0.141182 | ||||||||
\(483\) | 3255.00 | 0.306641 | ||||||||
\(484\) | 10052.0 | 0.944027 | ||||||||
\(485\) | −189.000 | −0.0176949 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 1798.00 | 0.167300 | 0.0836501 | − | 0.996495i | \(-0.473342\pi\) | ||||
0.0836501 | + | 0.996495i | \(0.473342\pi\) | |||||||
\(488\) | −4912.00 | −0.455647 | ||||||||
\(489\) | −4812.00 | −0.445002 | ||||||||
\(490\) | 882.000 | 0.0813157 | ||||||||
\(491\) | 13708.0 | 1.25995 | 0.629973 | − | 0.776617i | \(-0.283066\pi\) | ||||
0.629973 | + | 0.776617i | \(0.283066\pi\) | |||||||
\(492\) | −4872.00 | −0.446436 | ||||||||
\(493\) | −816.000 | −0.0745452 | ||||||||
\(494\) | −2054.00 | −0.187073 | ||||||||
\(495\) | 5022.00 | 0.456004 | ||||||||
\(496\) | 3888.00 | 0.351968 | ||||||||
\(497\) | 1848.00 | 0.166789 | ||||||||
\(498\) | −4074.00 | −0.366587 | ||||||||
\(499\) | −11936.0 | −1.07080 | −0.535400 | − | 0.844599i | \(-0.679839\pi\) | ||||
−0.535400 | + | 0.844599i | \(0.679839\pi\) | |||||||
\(500\) | −6084.00 | −0.544170 | ||||||||
\(501\) | 2877.00 | 0.256557 | ||||||||
\(502\) | 15036.0 | 1.33683 | ||||||||
\(503\) | 2562.00 | 0.227105 | 0.113553 | − | 0.993532i | \(-0.463777\pi\) | ||||
0.113553 | + | 0.993532i | \(0.463777\pi\) | |||||||
\(504\) | −504.000 | −0.0445435 | ||||||||
\(505\) | 8046.00 | 0.708995 | ||||||||
\(506\) | −19220.0 | −1.68860 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | −6992.00 | −0.610669 | ||||||||
\(509\) | −8055.00 | −0.701437 | −0.350719 | − | 0.936481i | \(-0.614063\pi\) | ||||
−0.350719 | + | 0.936481i | \(0.614063\pi\) | |||||||
\(510\) | −864.000 | −0.0750168 | ||||||||
\(511\) | 847.000 | 0.0733250 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 2133.00 | 0.183576 | ||||||||
\(514\) | 2188.00 | 0.187760 | ||||||||
\(515\) | 1152.00 | 0.0985693 | ||||||||
\(516\) | −1236.00 | −0.105449 | ||||||||
\(517\) | 26598.0 | 2.26263 | ||||||||
\(518\) | −5768.00 | −0.489250 | ||||||||
\(519\) | −1464.00 | −0.123820 | ||||||||
\(520\) | −936.000 | −0.0789352 | ||||||||
\(521\) | −5980.00 | −0.502857 | −0.251429 | − | 0.967876i | \(-0.580900\pi\) | ||||
−0.251429 | + | 0.967876i | \(0.580900\pi\) | |||||||
\(522\) | 918.000 | 0.0769727 | ||||||||
\(523\) | 19238.0 | 1.60845 | 0.804225 | − | 0.594325i | \(-0.202581\pi\) | ||||
0.804225 | + | 0.594325i | \(0.202581\pi\) | |||||||
\(524\) | −3744.00 | −0.312132 | ||||||||
\(525\) | 924.000 | 0.0768127 | ||||||||
\(526\) | −2578.00 | −0.213700 | ||||||||
\(527\) | −3888.00 | −0.321374 | ||||||||
\(528\) | 2976.00 | 0.245291 | ||||||||
\(529\) | 11858.0 | 0.974603 | ||||||||
\(530\) | −3042.00 | −0.249313 | ||||||||
\(531\) | 2880.00 | 0.235370 | ||||||||
\(532\) | −2212.00 | −0.180268 | ||||||||
\(533\) | 5278.00 | 0.428922 | ||||||||
\(534\) | 6354.00 | 0.514915 | ||||||||
\(535\) | −6372.00 | −0.514926 | ||||||||
\(536\) | 2064.00 | 0.166327 | ||||||||
\(537\) | 7599.00 | 0.610654 | ||||||||
\(538\) | −4120.00 | −0.330160 | ||||||||
\(539\) | 3038.00 | 0.242775 | ||||||||
\(540\) | 972.000 | 0.0774597 | ||||||||
\(541\) | 13012.0 | 1.03407 | 0.517033 | − | 0.855966i | \(-0.327036\pi\) | ||||
0.517033 | + | 0.855966i | \(0.327036\pi\) | |||||||
\(542\) | 1152.00 | 0.0912964 | ||||||||
\(543\) | −10878.0 | −0.859705 | ||||||||
\(544\) | −512.000 | −0.0403526 | ||||||||
\(545\) | 11142.0 | 0.875726 | ||||||||
\(546\) | 546.000 | 0.0427960 | ||||||||
\(547\) | 18055.0 | 1.41129 | 0.705645 | − | 0.708565i | \(-0.250657\pi\) | ||||
0.705645 | + | 0.708565i | \(0.250657\pi\) | |||||||
\(548\) | −4512.00 | −0.351721 | ||||||||
\(549\) | −5526.00 | −0.429588 | ||||||||
\(550\) | −5456.00 | −0.422990 | ||||||||
\(551\) | 4029.00 | 0.311508 | ||||||||
\(552\) | −3720.00 | −0.286836 | ||||||||
\(553\) | 6769.00 | 0.520519 | ||||||||
\(554\) | −11398.0 | −0.874106 | ||||||||
\(555\) | 11124.0 | 0.850788 | ||||||||
\(556\) | −3416.00 | −0.260559 | ||||||||
\(557\) | −19608.0 | −1.49159 | −0.745797 | − | 0.666174i | \(-0.767931\pi\) | ||||
−0.745797 | + | 0.666174i | \(0.767931\pi\) | |||||||
\(558\) | 4374.00 | 0.331839 | ||||||||
\(559\) | 1339.00 | 0.101312 | ||||||||
\(560\) | −1008.00 | −0.0760639 | ||||||||
\(561\) | −2976.00 | −0.223969 | ||||||||
\(562\) | 8124.00 | 0.609769 | ||||||||
\(563\) | −13512.0 | −1.01148 | −0.505740 | − | 0.862686i | \(-0.668780\pi\) | ||||
−0.505740 | + | 0.862686i | \(0.668780\pi\) | |||||||
\(564\) | 5148.00 | 0.384344 | ||||||||
\(565\) | 9657.00 | 0.719067 | ||||||||
\(566\) | −1544.00 | −0.114663 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | −2112.00 | −0.156017 | ||||||||
\(569\) | −4061.00 | −0.299202 | −0.149601 | − | 0.988746i | \(-0.547799\pi\) | ||||
−0.149601 | + | 0.988746i | \(0.547799\pi\) | |||||||
\(570\) | 4266.00 | 0.313479 | ||||||||
\(571\) | −2255.00 | −0.165269 | −0.0826347 | − | 0.996580i | \(-0.526333\pi\) | ||||
−0.0826347 | + | 0.996580i | \(0.526333\pi\) | |||||||
\(572\) | −3224.00 | −0.235668 | ||||||||
\(573\) | −14976.0 | −1.09185 | ||||||||
\(574\) | 5684.00 | 0.413320 | ||||||||
\(575\) | 6820.00 | 0.494632 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −254.000 | −0.0183261 | −0.00916305 | − | 0.999958i | \(-0.502917\pi\) | ||||
−0.00916305 | + | 0.999958i | \(0.502917\pi\) | |||||||
\(578\) | −9314.00 | −0.670262 | ||||||||
\(579\) | −1410.00 | −0.101205 | ||||||||
\(580\) | 1836.00 | 0.131441 | ||||||||
\(581\) | 4753.00 | 0.339394 | ||||||||
\(582\) | −126.000 | −0.00897400 | ||||||||
\(583\) | −10478.0 | −0.744347 | ||||||||
\(584\) | −968.000 | −0.0685893 | ||||||||
\(585\) | −1053.00 | −0.0744208 | ||||||||
\(586\) | 15666.0 | 1.10436 | ||||||||
\(587\) | 15057.0 | 1.05872 | 0.529360 | − | 0.848397i | \(-0.322432\pi\) | ||||
0.529360 | + | 0.848397i | \(0.322432\pi\) | |||||||
\(588\) | 588.000 | 0.0412393 | ||||||||
\(589\) | 19197.0 | 1.34295 | ||||||||
\(590\) | 5760.00 | 0.401924 | ||||||||
\(591\) | −9570.00 | −0.666087 | ||||||||
\(592\) | 6592.00 | 0.457651 | ||||||||
\(593\) | 19917.0 | 1.37925 | 0.689623 | − | 0.724168i | \(-0.257776\pi\) | ||||
0.689623 | + | 0.724168i | \(0.257776\pi\) | |||||||
\(594\) | 3348.00 | 0.231263 | ||||||||
\(595\) | 1008.00 | 0.0694521 | ||||||||
\(596\) | −1768.00 | −0.121510 | ||||||||
\(597\) | 5832.00 | 0.399812 | ||||||||
\(598\) | 4030.00 | 0.275584 | ||||||||
\(599\) | −15107.0 | −1.03048 | −0.515238 | − | 0.857047i | \(-0.672297\pi\) | ||||
−0.515238 | + | 0.857047i | \(0.672297\pi\) | |||||||
\(600\) | −1056.00 | −0.0718517 | ||||||||
\(601\) | 23674.0 | 1.60679 | 0.803397 | − | 0.595444i | \(-0.203024\pi\) | ||||
0.803397 | + | 0.595444i | \(0.203024\pi\) | |||||||
\(602\) | 1442.00 | 0.0976271 | ||||||||
\(603\) | 2322.00 | 0.156815 | ||||||||
\(604\) | −4064.00 | −0.273778 | ||||||||
\(605\) | 22617.0 | 1.51985 | ||||||||
\(606\) | 5364.00 | 0.359567 | ||||||||
\(607\) | 23746.0 | 1.58784 | 0.793921 | − | 0.608021i | \(-0.208036\pi\) | ||||
0.793921 | + | 0.608021i | \(0.208036\pi\) | |||||||
\(608\) | 2528.00 | 0.168625 | ||||||||
\(609\) | −1071.00 | −0.0712629 | ||||||||
\(610\) | −11052.0 | −0.733578 | ||||||||
\(611\) | −5577.00 | −0.369266 | ||||||||
\(612\) | −576.000 | −0.0380448 | ||||||||
\(613\) | −19216.0 | −1.26611 | −0.633056 | − | 0.774106i | \(-0.718200\pi\) | ||||
−0.633056 | + | 0.774106i | \(0.718200\pi\) | |||||||
\(614\) | −5782.00 | −0.380037 | ||||||||
\(615\) | −10962.0 | −0.718749 | ||||||||
\(616\) | −3472.00 | −0.227096 | ||||||||
\(617\) | 20862.0 | 1.36122 | 0.680610 | − | 0.732646i | \(-0.261715\pi\) | ||||
0.680610 | + | 0.732646i | \(0.261715\pi\) | |||||||
\(618\) | 768.000 | 0.0499895 | ||||||||
\(619\) | 124.000 | 0.00805167 | 0.00402583 | − | 0.999992i | \(-0.498719\pi\) | ||||
0.00402583 | + | 0.999992i | \(0.498719\pi\) | |||||||
\(620\) | 8748.00 | 0.566658 | ||||||||
\(621\) | −4185.00 | −0.270432 | ||||||||
\(622\) | −7060.00 | −0.455113 | ||||||||
\(623\) | −7413.00 | −0.476718 | ||||||||
\(624\) | −624.000 | −0.0400320 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | 10980.0 | 0.701037 | ||||||||
\(627\) | 14694.0 | 0.935920 | ||||||||
\(628\) | −15520.0 | −0.986171 | ||||||||
\(629\) | −6592.00 | −0.417870 | ||||||||
\(630\) | −1134.00 | −0.0717137 | ||||||||
\(631\) | 23942.0 | 1.51048 | 0.755242 | − | 0.655446i | \(-0.227519\pi\) | ||||
0.755242 | + | 0.655446i | \(0.227519\pi\) | |||||||
\(632\) | −7736.00 | −0.486901 | ||||||||
\(633\) | −3417.00 | −0.214555 | ||||||||
\(634\) | −11272.0 | −0.706101 | ||||||||
\(635\) | −15732.0 | −0.983158 | ||||||||
\(636\) | −2028.00 | −0.126439 | ||||||||
\(637\) | −637.000 | −0.0396214 | ||||||||
\(638\) | 6324.00 | 0.392429 | ||||||||
\(639\) | −2376.00 | −0.147094 | ||||||||
\(640\) | 1152.00 | 0.0711512 | ||||||||
\(641\) | −15723.0 | −0.968832 | −0.484416 | − | 0.874838i | \(-0.660968\pi\) | ||||
−0.484416 | + | 0.874838i | \(0.660968\pi\) | |||||||
\(642\) | −4248.00 | −0.261145 | ||||||||
\(643\) | −5544.00 | −0.340022 | −0.170011 | − | 0.985442i | \(-0.554380\pi\) | ||||
−0.170011 | + | 0.985442i | \(0.554380\pi\) | |||||||
\(644\) | 4340.00 | 0.265559 | ||||||||
\(645\) | −2781.00 | −0.169770 | ||||||||
\(646\) | −2528.00 | −0.153967 | ||||||||
\(647\) | −6078.00 | −0.369321 | −0.184661 | − | 0.982802i | \(-0.559119\pi\) | ||||
−0.184661 | + | 0.982802i | \(0.559119\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | 19840.0 | 1.19998 | ||||||||
\(650\) | 1144.00 | 0.0690329 | ||||||||
\(651\) | −5103.00 | −0.307223 | ||||||||
\(652\) | −6416.00 | −0.385383 | ||||||||
\(653\) | 30778.0 | 1.84447 | 0.922233 | − | 0.386635i | \(-0.126363\pi\) | ||||
0.922233 | + | 0.386635i | \(0.126363\pi\) | |||||||
\(654\) | 7428.00 | 0.444125 | ||||||||
\(655\) | −8424.00 | −0.502524 | ||||||||
\(656\) | −6496.00 | −0.386625 | ||||||||
\(657\) | −1089.00 | −0.0646666 | ||||||||
\(658\) | −6006.00 | −0.355833 | ||||||||
\(659\) | −11205.0 | −0.662344 | −0.331172 | − | 0.943570i | \(-0.607444\pi\) | ||||
−0.331172 | + | 0.943570i | \(0.607444\pi\) | |||||||
\(660\) | 6696.00 | 0.394911 | ||||||||
\(661\) | −20785.0 | −1.22306 | −0.611530 | − | 0.791221i | \(-0.709446\pi\) | ||||
−0.611530 | + | 0.791221i | \(0.709446\pi\) | |||||||
\(662\) | −19924.0 | −1.16974 | ||||||||
\(663\) | 624.000 | 0.0365523 | ||||||||
\(664\) | −5432.00 | −0.317474 | ||||||||
\(665\) | −4977.00 | −0.290225 | ||||||||
\(666\) | 7416.00 | 0.431478 | ||||||||
\(667\) | −7905.00 | −0.458895 | ||||||||
\(668\) | 3836.00 | 0.222185 | ||||||||
\(669\) | 2499.00 | 0.144420 | ||||||||
\(670\) | 4644.00 | 0.267781 | ||||||||
\(671\) | −38068.0 | −2.19016 | ||||||||
\(672\) | −672.000 | −0.0385758 | ||||||||
\(673\) | 1297.00 | 0.0742878 | 0.0371439 | − | 0.999310i | \(-0.488174\pi\) | ||||
0.0371439 | + | 0.999310i | \(0.488174\pi\) | |||||||
\(674\) | −22830.0 | −1.30472 | ||||||||
\(675\) | −1188.00 | −0.0677424 | ||||||||
\(676\) | 676.000 | 0.0384615 | ||||||||
\(677\) | 7310.00 | 0.414987 | 0.207493 | − | 0.978236i | \(-0.433469\pi\) | ||||
0.207493 | + | 0.978236i | \(0.433469\pi\) | |||||||
\(678\) | 6438.00 | 0.364675 | ||||||||
\(679\) | 147.000 | 0.00830831 | ||||||||
\(680\) | −1152.00 | −0.0649664 | ||||||||
\(681\) | −10548.0 | −0.593539 | ||||||||
\(682\) | 30132.0 | 1.69181 | ||||||||
\(683\) | −26384.0 | −1.47812 | −0.739060 | − | 0.673640i | \(-0.764730\pi\) | ||||
−0.739060 | + | 0.673640i | \(0.764730\pi\) | |||||||
\(684\) | 2844.00 | 0.158981 | ||||||||
\(685\) | −10152.0 | −0.566260 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | 9666.00 | 0.536799 | ||||||||
\(688\) | −1648.00 | −0.0913218 | ||||||||
\(689\) | 2197.00 | 0.121479 | ||||||||
\(690\) | −8370.00 | −0.461798 | ||||||||
\(691\) | −27823.0 | −1.53175 | −0.765873 | − | 0.642992i | \(-0.777693\pi\) | ||||
−0.765873 | + | 0.642992i | \(0.777693\pi\) | |||||||
\(692\) | −1952.00 | −0.107231 | ||||||||
\(693\) | −3906.00 | −0.214108 | ||||||||
\(694\) | 9728.00 | 0.532089 | ||||||||
\(695\) | −7686.00 | −0.419492 | ||||||||
\(696\) | 1224.00 | 0.0666603 | ||||||||
\(697\) | 6496.00 | 0.353018 | ||||||||
\(698\) | −938.000 | −0.0508651 | ||||||||
\(699\) | −1431.00 | −0.0774326 | ||||||||
\(700\) | 1232.00 | 0.0665217 | ||||||||
\(701\) | 24117.0 | 1.29941 | 0.649705 | − | 0.760186i | \(-0.274892\pi\) | ||||
0.649705 | + | 0.760186i | \(0.274892\pi\) | |||||||
\(702\) | −702.000 | −0.0377426 | ||||||||
\(703\) | 32548.0 | 1.74619 | ||||||||
\(704\) | 3968.00 | 0.212428 | ||||||||
\(705\) | 11583.0 | 0.618782 | ||||||||
\(706\) | 8396.00 | 0.447575 | ||||||||
\(707\) | −6258.00 | −0.332894 | ||||||||
\(708\) | 3840.00 | 0.203836 | ||||||||
\(709\) | 28286.0 | 1.49831 | 0.749156 | − | 0.662394i | \(-0.230459\pi\) | ||||
0.749156 | + | 0.662394i | \(0.230459\pi\) | |||||||
\(710\) | −4752.00 | −0.251182 | ||||||||
\(711\) | −8703.00 | −0.459055 | ||||||||
\(712\) | 8472.00 | 0.445929 | ||||||||
\(713\) | −37665.0 | −1.97835 | ||||||||
\(714\) | 672.000 | 0.0352226 | ||||||||
\(715\) | −7254.00 | −0.379418 | ||||||||
\(716\) | 10132.0 | 0.528842 | ||||||||
\(717\) | −19104.0 | −0.995052 | ||||||||
\(718\) | 6816.00 | 0.354277 | ||||||||
\(719\) | −26346.0 | −1.36654 | −0.683268 | − | 0.730167i | \(-0.739442\pi\) | ||||
−0.683268 | + | 0.730167i | \(0.739442\pi\) | |||||||
\(720\) | 1296.00 | 0.0670820 | ||||||||
\(721\) | −896.000 | −0.0462813 | ||||||||
\(722\) | −1236.00 | −0.0637107 | ||||||||
\(723\) | 2241.00 | 0.115275 | ||||||||
\(724\) | −14504.0 | −0.744526 | ||||||||
\(725\) | −2244.00 | −0.114952 | ||||||||
\(726\) | 15078.0 | 0.770795 | ||||||||
\(727\) | −22862.0 | −1.16631 | −0.583153 | − | 0.812362i | \(-0.698181\pi\) | ||||
−0.583153 | + | 0.812362i | \(0.698181\pi\) | |||||||
\(728\) | 728.000 | 0.0370625 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −2178.00 | −0.110427 | ||||||||
\(731\) | 1648.00 | 0.0833837 | ||||||||
\(732\) | −7368.00 | −0.372034 | ||||||||
\(733\) | 18587.0 | 0.936598 | 0.468299 | − | 0.883570i | \(-0.344867\pi\) | ||||
0.468299 | + | 0.883570i | \(0.344867\pi\) | |||||||
\(734\) | −16580.0 | −0.833759 | ||||||||
\(735\) | 1323.00 | 0.0663940 | ||||||||
\(736\) | −4960.00 | −0.248408 | ||||||||
\(737\) | 15996.0 | 0.799485 | ||||||||
\(738\) | −7308.00 | −0.364514 | ||||||||
\(739\) | 5102.00 | 0.253965 | 0.126982 | − | 0.991905i | \(-0.459471\pi\) | ||||
0.126982 | + | 0.991905i | \(0.459471\pi\) | |||||||
\(740\) | 14832.0 | 0.736804 | ||||||||
\(741\) | −3081.00 | −0.152744 | ||||||||
\(742\) | 2366.00 | 0.117060 | ||||||||
\(743\) | 27428.0 | 1.35429 | 0.677144 | − | 0.735851i | \(-0.263217\pi\) | ||||
0.677144 | + | 0.735851i | \(0.263217\pi\) | |||||||
\(744\) | 5832.00 | 0.287381 | ||||||||
\(745\) | −3978.00 | −0.195628 | ||||||||
\(746\) | −19812.0 | −0.972344 | ||||||||
\(747\) | −6111.00 | −0.299317 | ||||||||
\(748\) | −3968.00 | −0.193963 | ||||||||
\(749\) | 4956.00 | 0.241773 | ||||||||
\(750\) | −9126.00 | −0.444313 | ||||||||
\(751\) | 125.000 | 0.00607365 | 0.00303683 | − | 0.999995i | \(-0.499033\pi\) | ||||
0.00303683 | + | 0.999995i | \(0.499033\pi\) | |||||||
\(752\) | 6864.00 | 0.332851 | ||||||||
\(753\) | 22554.0 | 1.09152 | ||||||||
\(754\) | −1326.00 | −0.0640452 | ||||||||
\(755\) | −9144.00 | −0.440774 | ||||||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | −27907.0 | −1.33989 | −0.669945 | − | 0.742410i | \(-0.733682\pi\) | ||||
−0.669945 | + | 0.742410i | \(0.733682\pi\) | |||||||
\(758\) | −18476.0 | −0.885328 | ||||||||
\(759\) | −28830.0 | −1.37874 | ||||||||
\(760\) | 5688.00 | 0.271481 | ||||||||
\(761\) | 7793.00 | 0.371217 | 0.185608 | − | 0.982624i | \(-0.440574\pi\) | ||||
0.185608 | + | 0.982624i | \(0.440574\pi\) | |||||||
\(762\) | −10488.0 | −0.498609 | ||||||||
\(763\) | −8666.00 | −0.411180 | ||||||||
\(764\) | −19968.0 | −0.945572 | ||||||||
\(765\) | −1296.00 | −0.0612510 | ||||||||
\(766\) | 9944.00 | 0.469049 | ||||||||
\(767\) | −4160.00 | −0.195839 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | 29393.0 | 1.37833 | 0.689167 | − | 0.724603i | \(-0.257977\pi\) | ||||
0.689167 | + | 0.724603i | \(0.257977\pi\) | |||||||
\(770\) | −7812.00 | −0.365617 | ||||||||
\(771\) | 3282.00 | 0.153305 | ||||||||
\(772\) | −1880.00 | −0.0876460 | ||||||||
\(773\) | 20326.0 | 0.945764 | 0.472882 | − | 0.881126i | \(-0.343214\pi\) | ||||
0.472882 | + | 0.881126i | \(0.343214\pi\) | |||||||
\(774\) | −1854.00 | −0.0860990 | ||||||||
\(775\) | −10692.0 | −0.495572 | ||||||||
\(776\) | −168.000 | −0.00777171 | ||||||||
\(777\) | −8652.00 | −0.399471 | ||||||||
\(778\) | 14908.0 | 0.686989 | ||||||||
\(779\) | −32074.0 | −1.47519 | ||||||||
\(780\) | −1404.00 | −0.0644503 | ||||||||
\(781\) | −16368.0 | −0.749927 | ||||||||
\(782\) | 4960.00 | 0.226815 | ||||||||
\(783\) | 1377.00 | 0.0628480 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −34920.0 | −1.58770 | ||||||||
\(786\) | −5616.00 | −0.254855 | ||||||||
\(787\) | 16679.0 | 0.755454 | 0.377727 | − | 0.925917i | \(-0.376706\pi\) | ||||
0.377727 | + | 0.925917i | \(0.376706\pi\) | |||||||
\(788\) | −12760.0 | −0.576848 | ||||||||
\(789\) | −3867.00 | −0.174485 | ||||||||
\(790\) | −17406.0 | −0.783896 | ||||||||
\(791\) | −7511.00 | −0.337624 | ||||||||
\(792\) | 4464.00 | 0.200279 | ||||||||
\(793\) | 7982.00 | 0.357439 | ||||||||
\(794\) | 14438.0 | 0.645322 | ||||||||
\(795\) | −4563.00 | −0.203563 | ||||||||
\(796\) | 7776.00 | 0.346248 | ||||||||
\(797\) | −9282.00 | −0.412529 | −0.206264 | − | 0.978496i | \(-0.566131\pi\) | ||||
−0.206264 | + | 0.978496i | \(0.566131\pi\) | |||||||
\(798\) | −3318.00 | −0.147188 | ||||||||
\(799\) | −6864.00 | −0.303918 | ||||||||
\(800\) | −1408.00 | −0.0622254 | ||||||||
\(801\) | 9531.00 | 0.420426 | ||||||||
\(802\) | 21544.0 | 0.948560 | ||||||||
\(803\) | −7502.00 | −0.329688 | ||||||||
\(804\) | 3096.00 | 0.135805 | ||||||||
\(805\) | 9765.00 | 0.427542 | ||||||||
\(806\) | −6318.00 | −0.276107 | ||||||||
\(807\) | −6180.00 | −0.269574 | ||||||||
\(808\) | 7152.00 | 0.311394 | ||||||||
\(809\) | −883.000 | −0.0383741 | −0.0191870 | − | 0.999816i | \(-0.506108\pi\) | ||||
−0.0191870 | + | 0.999816i | \(0.506108\pi\) | |||||||
\(810\) | 1458.00 | 0.0632456 | ||||||||
\(811\) | −12684.0 | −0.549193 | −0.274596 | − | 0.961560i | \(-0.588544\pi\) | ||||
−0.274596 | + | 0.961560i | \(0.588544\pi\) | |||||||
\(812\) | −1428.00 | −0.0617155 | ||||||||
\(813\) | 1728.00 | 0.0745432 | ||||||||
\(814\) | 51088.0 | 2.19980 | ||||||||
\(815\) | −14436.0 | −0.620455 | ||||||||
\(816\) | −768.000 | −0.0329478 | ||||||||
\(817\) | −8137.00 | −0.348443 | ||||||||
\(818\) | 26302.0 | 1.12424 | ||||||||
\(819\) | 819.000 | 0.0349428 | ||||||||
\(820\) | −14616.0 | −0.622455 | ||||||||
\(821\) | −34126.0 | −1.45068 | −0.725338 | − | 0.688393i | \(-0.758317\pi\) | ||||
−0.725338 | + | 0.688393i | \(0.758317\pi\) | |||||||
\(822\) | −6768.00 | −0.287179 | ||||||||
\(823\) | −7568.00 | −0.320539 | −0.160270 | − | 0.987073i | \(-0.551236\pi\) | ||||
−0.160270 | + | 0.987073i | \(0.551236\pi\) | |||||||
\(824\) | 1024.00 | 0.0432921 | ||||||||
\(825\) | −8184.00 | −0.345370 | ||||||||
\(826\) | −4480.00 | −0.188716 | ||||||||
\(827\) | 32076.0 | 1.34872 | 0.674360 | − | 0.738403i | \(-0.264420\pi\) | ||||
0.674360 | + | 0.738403i | \(0.264420\pi\) | |||||||
\(828\) | −5580.00 | −0.234201 | ||||||||
\(829\) | −22598.0 | −0.946756 | −0.473378 | − | 0.880859i | \(-0.656966\pi\) | ||||
−0.473378 | + | 0.880859i | \(0.656966\pi\) | |||||||
\(830\) | −12222.0 | −0.511123 | ||||||||
\(831\) | −17097.0 | −0.713704 | ||||||||
\(832\) | −832.000 | −0.0346688 | ||||||||
\(833\) | −784.000 | −0.0326098 | ||||||||
\(834\) | −5124.00 | −0.212745 | ||||||||
\(835\) | 8631.00 | 0.357710 | ||||||||
\(836\) | 19592.0 | 0.810530 | ||||||||
\(837\) | 6561.00 | 0.270945 | ||||||||
\(838\) | 12068.0 | 0.497473 | ||||||||
\(839\) | 25480.0 | 1.04847 | 0.524236 | − | 0.851573i | \(-0.324351\pi\) | ||||
0.524236 | + | 0.851573i | \(0.324351\pi\) | |||||||
\(840\) | −1512.00 | −0.0621059 | ||||||||
\(841\) | −21788.0 | −0.893354 | ||||||||
\(842\) | 17728.0 | 0.725591 | ||||||||
\(843\) | 12186.0 | 0.497874 | ||||||||
\(844\) | −4556.00 | −0.185810 | ||||||||
\(845\) | 1521.00 | 0.0619219 | ||||||||
\(846\) | 7722.00 | 0.313815 | ||||||||
\(847\) | −17591.0 | −0.713617 | ||||||||
\(848\) | −2704.00 | −0.109500 | ||||||||
\(849\) | −2316.00 | −0.0936218 | ||||||||
\(850\) | 1408.00 | 0.0568165 | ||||||||
\(851\) | −63860.0 | −2.57238 | ||||||||
\(852\) | −3168.00 | −0.127387 | ||||||||
\(853\) | −22939.0 | −0.920770 | −0.460385 | − | 0.887719i | \(-0.652289\pi\) | ||||
−0.460385 | + | 0.887719i | \(0.652289\pi\) | |||||||
\(854\) | 8596.00 | 0.344437 | ||||||||
\(855\) | 6399.00 | 0.255955 | ||||||||
\(856\) | −5664.00 | −0.226158 | ||||||||
\(857\) | −38782.0 | −1.54582 | −0.772910 | − | 0.634516i | \(-0.781200\pi\) | ||||
−0.772910 | + | 0.634516i | \(0.781200\pi\) | |||||||
\(858\) | −4836.00 | −0.192422 | ||||||||
\(859\) | −13970.0 | −0.554890 | −0.277445 | − | 0.960742i | \(-0.589488\pi\) | ||||
−0.277445 | + | 0.960742i | \(0.589488\pi\) | |||||||
\(860\) | −3708.00 | −0.147025 | ||||||||
\(861\) | 8526.00 | 0.337474 | ||||||||
\(862\) | −268.000 | −0.0105895 | ||||||||
\(863\) | −22212.0 | −0.876136 | −0.438068 | − | 0.898942i | \(-0.644337\pi\) | ||||
−0.438068 | + | 0.898942i | \(0.644337\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | −4392.00 | −0.172639 | ||||||||
\(866\) | 24752.0 | 0.971255 | ||||||||
\(867\) | −13971.0 | −0.547266 | ||||||||
\(868\) | −6804.00 | −0.266063 | ||||||||
\(869\) | −59954.0 | −2.34039 | ||||||||
\(870\) | 2754.00 | 0.107321 | ||||||||
\(871\) | −3354.00 | −0.130478 | ||||||||
\(872\) | 9904.00 | 0.384624 | ||||||||
\(873\) | −189.000 | −0.00732724 | ||||||||
\(874\) | −24490.0 | −0.947811 | ||||||||
\(875\) | 10647.0 | 0.411353 | ||||||||
\(876\) | −1452.00 | −0.0560029 | ||||||||
\(877\) | −24816.0 | −0.955504 | −0.477752 | − | 0.878495i | \(-0.658548\pi\) | ||||
−0.477752 | + | 0.878495i | \(0.658548\pi\) | |||||||
\(878\) | 28396.0 | 1.09148 | ||||||||
\(879\) | 23499.0 | 0.901708 | ||||||||
\(880\) | 8928.00 | 0.342003 | ||||||||
\(881\) | 7490.00 | 0.286430 | 0.143215 | − | 0.989692i | \(-0.454256\pi\) | ||||
0.143215 | + | 0.989692i | \(0.454256\pi\) | |||||||
\(882\) | 882.000 | 0.0336718 | ||||||||
\(883\) | 6092.00 | 0.232177 | 0.116088 | − | 0.993239i | \(-0.462964\pi\) | ||||
0.116088 | + | 0.993239i | \(0.462964\pi\) | |||||||
\(884\) | 832.000 | 0.0316552 | ||||||||
\(885\) | 8640.00 | 0.328170 | ||||||||
\(886\) | 15314.0 | 0.580682 | ||||||||
\(887\) | −6480.00 | −0.245295 | −0.122648 | − | 0.992450i | \(-0.539139\pi\) | ||||
−0.122648 | + | 0.992450i | \(0.539139\pi\) | |||||||
\(888\) | 9888.00 | 0.373671 | ||||||||
\(889\) | 12236.0 | 0.461622 | ||||||||
\(890\) | 19062.0 | 0.717932 | ||||||||
\(891\) | 5022.00 | 0.188825 | ||||||||
\(892\) | 3332.00 | 0.125071 | ||||||||
\(893\) | 33891.0 | 1.27001 | ||||||||
\(894\) | −2652.00 | −0.0992127 | ||||||||
\(895\) | 22797.0 | 0.851419 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | 6045.00 | 0.225013 | ||||||||
\(898\) | 31000.0 | 1.15199 | ||||||||
\(899\) | 12393.0 | 0.459766 | ||||||||
\(900\) | −1584.00 | −0.0586667 | ||||||||
\(901\) | 2704.00 | 0.0999815 | ||||||||
\(902\) | −50344.0 | −1.85839 | ||||||||
\(903\) | 2163.00 | 0.0797122 | ||||||||
\(904\) | 8584.00 | 0.315818 | ||||||||
\(905\) | −32634.0 | −1.19866 | ||||||||
\(906\) | −6096.00 | −0.223539 | ||||||||
\(907\) | −12111.0 | −0.443373 | −0.221686 | − | 0.975118i | \(-0.571156\pi\) | ||||
−0.221686 | + | 0.975118i | \(0.571156\pi\) | |||||||
\(908\) | −14064.0 | −0.514020 | ||||||||
\(909\) | 8046.00 | 0.293585 | ||||||||
\(910\) | 1638.00 | 0.0596694 | ||||||||
\(911\) | 7191.00 | 0.261524 | 0.130762 | − | 0.991414i | \(-0.458258\pi\) | ||||
0.130762 | + | 0.991414i | \(0.458258\pi\) | |||||||
\(912\) | 3792.00 | 0.137682 | ||||||||
\(913\) | −42098.0 | −1.52600 | ||||||||
\(914\) | 20368.0 | 0.737105 | ||||||||
\(915\) | −16578.0 | −0.598964 | ||||||||
\(916\) | 12888.0 | 0.464882 | ||||||||
\(917\) | 6552.00 | 0.235950 | ||||||||
\(918\) | −864.000 | −0.0310635 | ||||||||
\(919\) | −12272.0 | −0.440496 | −0.220248 | − | 0.975444i | \(-0.570687\pi\) | ||||
−0.220248 | + | 0.975444i | \(0.570687\pi\) | |||||||
\(920\) | −11160.0 | −0.399929 | ||||||||
\(921\) | −8673.00 | −0.310299 | ||||||||
\(922\) | 38500.0 | 1.37520 | ||||||||
\(923\) | 3432.00 | 0.122390 | ||||||||
\(924\) | −5208.00 | −0.185423 | ||||||||
\(925\) | −18128.0 | −0.644373 | ||||||||
\(926\) | −31244.0 | −1.10879 | ||||||||
\(927\) | 1152.00 | 0.0408162 | ||||||||
\(928\) | 1632.00 | 0.0577296 | ||||||||
\(929\) | 3285.00 | 0.116014 | 0.0580072 | − | 0.998316i | \(-0.481525\pi\) | ||||
0.0580072 | + | 0.998316i | \(0.481525\pi\) | |||||||
\(930\) | 13122.0 | 0.462675 | ||||||||
\(931\) | 3871.00 | 0.136269 | ||||||||
\(932\) | −1908.00 | −0.0670586 | ||||||||
\(933\) | −10590.0 | −0.371598 | ||||||||
\(934\) | −31188.0 | −1.09262 | ||||||||
\(935\) | −8928.00 | −0.312275 | ||||||||
\(936\) | −936.000 | −0.0326860 | ||||||||
\(937\) | −5068.00 | −0.176696 | −0.0883481 | − | 0.996090i | \(-0.528159\pi\) | ||||
−0.0883481 | + | 0.996090i | \(0.528159\pi\) | |||||||
\(938\) | −3612.00 | −0.125731 | ||||||||
\(939\) | 16470.0 | 0.572394 | ||||||||
\(940\) | 15444.0 | 0.535881 | ||||||||
\(941\) | 13571.0 | 0.470140 | 0.235070 | − | 0.971978i | \(-0.424468\pi\) | ||||
0.235070 | + | 0.971978i | \(0.424468\pi\) | |||||||
\(942\) | −23280.0 | −0.805205 | ||||||||
\(943\) | 62930.0 | 2.17315 | ||||||||
\(944\) | 5120.00 | 0.176527 | ||||||||
\(945\) | −1701.00 | −0.0585540 | ||||||||
\(946\) | −12772.0 | −0.438957 | ||||||||
\(947\) | −17662.0 | −0.606059 | −0.303030 | − | 0.952981i | \(-0.597998\pi\) | ||||
−0.303030 | + | 0.952981i | \(0.597998\pi\) | |||||||
\(948\) | −11604.0 | −0.397553 | ||||||||
\(949\) | 1573.00 | 0.0538058 | ||||||||
\(950\) | −6952.00 | −0.237424 | ||||||||
\(951\) | −16908.0 | −0.576529 | ||||||||
\(952\) | 896.000 | 0.0305037 | ||||||||
\(953\) | 37893.0 | 1.28801 | 0.644006 | − | 0.765021i | \(-0.277271\pi\) | ||||
0.644006 | + | 0.765021i | \(0.277271\pi\) | |||||||
\(954\) | −3042.00 | −0.103237 | ||||||||
\(955\) | −44928.0 | −1.52234 | ||||||||
\(956\) | −25472.0 | −0.861740 | ||||||||
\(957\) | 9486.00 | 0.320417 | ||||||||
\(958\) | 6478.00 | 0.218470 | ||||||||
\(959\) | 7896.00 | 0.265876 | ||||||||
\(960\) | 1728.00 | 0.0580948 | ||||||||
\(961\) | 29258.0 | 0.982109 | ||||||||
\(962\) | −10712.0 | −0.359011 | ||||||||
\(963\) | −6372.00 | −0.213224 | ||||||||
\(964\) | 2988.00 | 0.0998309 | ||||||||
\(965\) | −4230.00 | −0.141107 | ||||||||
\(966\) | 6510.00 | 0.216828 | ||||||||
\(967\) | −48914.0 | −1.62665 | −0.813324 | − | 0.581811i | \(-0.802344\pi\) | ||||
−0.813324 | + | 0.581811i | \(0.802344\pi\) | |||||||
\(968\) | 20104.0 | 0.667528 | ||||||||
\(969\) | −3792.00 | −0.125714 | ||||||||
\(970\) | −378.000 | −0.0125122 | ||||||||
\(971\) | 31110.0 | 1.02818 | 0.514092 | − | 0.857735i | \(-0.328129\pi\) | ||||
0.514092 | + | 0.857735i | \(0.328129\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 5978.00 | 0.196964 | ||||||||
\(974\) | 3596.00 | 0.118299 | ||||||||
\(975\) | 1716.00 | 0.0563651 | ||||||||
\(976\) | −9824.00 | −0.322191 | ||||||||
\(977\) | 22294.0 | 0.730039 | 0.365020 | − | 0.931000i | \(-0.381062\pi\) | ||||
0.365020 | + | 0.931000i | \(0.381062\pi\) | |||||||
\(978\) | −9624.00 | −0.314664 | ||||||||
\(979\) | 65658.0 | 2.14345 | ||||||||
\(980\) | 1764.00 | 0.0574989 | ||||||||
\(981\) | 11142.0 | 0.362627 | ||||||||
\(982\) | 27416.0 | 0.890916 | ||||||||
\(983\) | −317.000 | −0.0102856 | −0.00514279 | − | 0.999987i | \(-0.501637\pi\) | ||||
−0.00514279 | + | 0.999987i | \(0.501637\pi\) | |||||||
\(984\) | −9744.00 | −0.315678 | ||||||||
\(985\) | −28710.0 | −0.928707 | ||||||||
\(986\) | −1632.00 | −0.0527114 | ||||||||
\(987\) | −9009.00 | −0.290537 | ||||||||
\(988\) | −4108.00 | −0.132280 | ||||||||
\(989\) | 15965.0 | 0.513304 | ||||||||
\(990\) | 10044.0 | 0.322444 | ||||||||
\(991\) | 40564.0 | 1.30026 | 0.650130 | − | 0.759823i | \(-0.274714\pi\) | ||||
0.650130 | + | 0.759823i | \(0.274714\pi\) | |||||||
\(992\) | 7776.00 | 0.248879 | ||||||||
\(993\) | −29886.0 | −0.955089 | ||||||||
\(994\) | 3696.00 | 0.117938 | ||||||||
\(995\) | 17496.0 | 0.557448 | ||||||||
\(996\) | −8148.00 | −0.259216 | ||||||||
\(997\) | −57528.0 | −1.82741 | −0.913706 | − | 0.406376i | \(-0.866792\pi\) | ||||
−0.913706 | + | 0.406376i | \(0.866792\pi\) | |||||||
\(998\) | −23872.0 | −0.757169 | ||||||||
\(999\) | 11124.0 | 0.352300 |
(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 | 546.4.a.e.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 1638.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.4.a.e.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
1638.4.a.b.1.1 | 1 | 3.2 | odd | 2 |