Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,4,Mod(1,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("490.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.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: | \(28.9109359028\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 490.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.192450 | 0.0962250 | − | 0.995360i | \(-0.469323\pi\) | ||||
0.0962250 | + | 0.995360i | \(0.469323\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −2.00000 | −0.136083 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −26.0000 | −0.962963 | ||||||||
\(10\) | −10.0000 | −0.316228 | ||||||||
\(11\) | −2.00000 | −0.0548202 | −0.0274101 | − | 0.999624i | \(-0.508726\pi\) | ||||
−0.0274101 | + | 0.999624i | \(0.508726\pi\) | |||||||
\(12\) | 4.00000 | 0.0962250 | ||||||||
\(13\) | 8.00000 | 0.170677 | 0.0853385 | − | 0.996352i | \(-0.472803\pi\) | ||||
0.0853385 | + | 0.996352i | \(0.472803\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.00000 | 0.0860663 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 52.0000 | 0.741874 | 0.370937 | − | 0.928658i | \(-0.379037\pi\) | ||||
0.370937 | + | 0.928658i | \(0.379037\pi\) | |||||||
\(18\) | 52.0000 | 0.680918 | ||||||||
\(19\) | −26.0000 | −0.313937 | −0.156969 | − | 0.987604i | \(-0.550172\pi\) | ||||
−0.156969 | + | 0.987604i | \(0.550172\pi\) | |||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.0387638 | ||||||||
\(23\) | 67.0000 | 0.607412 | 0.303706 | − | 0.952766i | \(-0.401776\pi\) | ||||
0.303706 | + | 0.952766i | \(0.401776\pi\) | |||||||
\(24\) | −8.00000 | −0.0680414 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −16.0000 | −0.120687 | ||||||||
\(27\) | −53.0000 | −0.377772 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 69.0000 | 0.441827 | 0.220913 | − | 0.975293i | \(-0.429096\pi\) | ||||
0.220913 | + | 0.975293i | \(0.429096\pi\) | |||||||
\(30\) | −10.0000 | −0.0608581 | ||||||||
\(31\) | 332.000 | 1.92351 | 0.961757 | − | 0.273903i | \(-0.0883146\pi\) | ||||
0.961757 | + | 0.273903i | \(0.0883146\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −2.00000 | −0.0105502 | ||||||||
\(34\) | −104.000 | −0.524584 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −104.000 | −0.481481 | ||||||||
\(37\) | 196.000 | 0.870870 | 0.435435 | − | 0.900220i | \(-0.356595\pi\) | ||||
0.435435 | + | 0.900220i | \(0.356595\pi\) | |||||||
\(38\) | 52.0000 | 0.221987 | ||||||||
\(39\) | 8.00000 | 0.0328468 | ||||||||
\(40\) | −40.0000 | −0.158114 | ||||||||
\(41\) | −353.000 | −1.34462 | −0.672309 | − | 0.740271i | \(-0.734697\pi\) | ||||
−0.672309 | + | 0.740271i | \(0.734697\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −369.000 | −1.30865 | −0.654325 | − | 0.756213i | \(-0.727047\pi\) | ||||
−0.654325 | + | 0.756213i | \(0.727047\pi\) | |||||||
\(44\) | −8.00000 | −0.0274101 | ||||||||
\(45\) | −130.000 | −0.430650 | ||||||||
\(46\) | −134.000 | −0.429505 | ||||||||
\(47\) | −88.0000 | −0.273109 | −0.136554 | − | 0.990633i | \(-0.543603\pi\) | ||||
−0.136554 | + | 0.990633i | \(0.543603\pi\) | |||||||
\(48\) | 16.0000 | 0.0481125 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | 52.0000 | 0.142774 | ||||||||
\(52\) | 32.0000 | 0.0853385 | ||||||||
\(53\) | 582.000 | 1.50837 | 0.754187 | − | 0.656659i | \(-0.228031\pi\) | ||||
0.754187 | + | 0.656659i | \(0.228031\pi\) | |||||||
\(54\) | 106.000 | 0.267125 | ||||||||
\(55\) | −10.0000 | −0.0245164 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −26.0000 | −0.0604173 | ||||||||
\(58\) | −138.000 | −0.312419 | ||||||||
\(59\) | 350.000 | 0.772307 | 0.386154 | − | 0.922435i | \(-0.373803\pi\) | ||||
0.386154 | + | 0.922435i | \(0.373803\pi\) | |||||||
\(60\) | 20.0000 | 0.0430331 | ||||||||
\(61\) | 467.000 | 0.980217 | 0.490108 | − | 0.871662i | \(-0.336957\pi\) | ||||
0.490108 | + | 0.871662i | \(0.336957\pi\) | |||||||
\(62\) | −664.000 | −1.36013 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 40.0000 | 0.0763291 | ||||||||
\(66\) | 4.00000 | 0.00746009 | ||||||||
\(67\) | 291.000 | 0.530617 | 0.265308 | − | 0.964164i | \(-0.414526\pi\) | ||||
0.265308 | + | 0.964164i | \(0.414526\pi\) | |||||||
\(68\) | 208.000 | 0.370937 | ||||||||
\(69\) | 67.0000 | 0.116896 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 770.000 | 1.28707 | 0.643537 | − | 0.765415i | \(-0.277466\pi\) | ||||
0.643537 | + | 0.765415i | \(0.277466\pi\) | |||||||
\(72\) | 208.000 | 0.340459 | ||||||||
\(73\) | −628.000 | −1.00687 | −0.503437 | − | 0.864032i | \(-0.667931\pi\) | ||||
−0.503437 | + | 0.864032i | \(0.667931\pi\) | |||||||
\(74\) | −392.000 | −0.615798 | ||||||||
\(75\) | 25.0000 | 0.0384900 | ||||||||
\(76\) | −104.000 | −0.156969 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −16.0000 | −0.0232262 | ||||||||
\(79\) | 1170.00 | 1.66627 | 0.833135 | − | 0.553070i | \(-0.186544\pi\) | ||||
0.833135 | + | 0.553070i | \(0.186544\pi\) | |||||||
\(80\) | 80.0000 | 0.111803 | ||||||||
\(81\) | 649.000 | 0.890261 | ||||||||
\(82\) | 706.000 | 0.950789 | ||||||||
\(83\) | −525.000 | −0.694292 | −0.347146 | − | 0.937811i | \(-0.612849\pi\) | ||||
−0.347146 | + | 0.937811i | \(0.612849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 260.000 | 0.331776 | ||||||||
\(86\) | 738.000 | 0.925356 | ||||||||
\(87\) | 69.0000 | 0.0850296 | ||||||||
\(88\) | 16.0000 | 0.0193819 | ||||||||
\(89\) | −89.0000 | −0.106000 | −0.0529999 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0529999 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(90\) | 260.000 | 0.304516 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 268.000 | 0.303706 | ||||||||
\(93\) | 332.000 | 0.370181 | ||||||||
\(94\) | 176.000 | 0.193117 | ||||||||
\(95\) | −130.000 | −0.140397 | ||||||||
\(96\) | −32.0000 | −0.0340207 | ||||||||
\(97\) | 290.000 | 0.303557 | 0.151779 | − | 0.988415i | \(-0.451500\pi\) | ||||
0.151779 | + | 0.988415i | \(0.451500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 52.0000 | 0.0527899 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 1233.00 | 1.21473 | 0.607367 | − | 0.794422i | \(-0.292226\pi\) | ||||
0.607367 | + | 0.794422i | \(0.292226\pi\) | |||||||
\(102\) | −104.000 | −0.100956 | ||||||||
\(103\) | −1553.00 | −1.48565 | −0.742823 | − | 0.669487i | \(-0.766514\pi\) | ||||
−0.742823 | + | 0.669487i | \(0.766514\pi\) | |||||||
\(104\) | −64.0000 | −0.0603434 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1164.00 | −1.06658 | ||||||||
\(107\) | 1831.00 | 1.65429 | 0.827147 | − | 0.561986i | \(-0.189962\pi\) | ||||
0.827147 | + | 0.561986i | \(0.189962\pi\) | |||||||
\(108\) | −212.000 | −0.188886 | ||||||||
\(109\) | 811.000 | 0.712658 | 0.356329 | − | 0.934361i | \(-0.384028\pi\) | ||||
0.356329 | + | 0.934361i | \(0.384028\pi\) | |||||||
\(110\) | 20.0000 | 0.0173357 | ||||||||
\(111\) | 196.000 | 0.167599 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2170.00 | 1.80652 | 0.903259 | − | 0.429097i | \(-0.141168\pi\) | ||||
0.903259 | + | 0.429097i | \(0.141168\pi\) | |||||||
\(114\) | 52.0000 | 0.0427215 | ||||||||
\(115\) | 335.000 | 0.271643 | ||||||||
\(116\) | 276.000 | 0.220913 | ||||||||
\(117\) | −208.000 | −0.164356 | ||||||||
\(118\) | −700.000 | −0.546104 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −40.0000 | −0.0304290 | ||||||||
\(121\) | −1327.00 | −0.996995 | ||||||||
\(122\) | −934.000 | −0.693118 | ||||||||
\(123\) | −353.000 | −0.258772 | ||||||||
\(124\) | 1328.00 | 0.961757 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 48.0000 | 0.0335379 | 0.0167689 | − | 0.999859i | \(-0.494662\pi\) | ||||
0.0167689 | + | 0.999859i | \(0.494662\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −369.000 | −0.251850 | ||||||||
\(130\) | −80.0000 | −0.0539728 | ||||||||
\(131\) | 792.000 | 0.528224 | 0.264112 | − | 0.964492i | \(-0.414921\pi\) | ||||
0.264112 | + | 0.964492i | \(0.414921\pi\) | |||||||
\(132\) | −8.00000 | −0.00527508 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −582.000 | −0.375203 | ||||||||
\(135\) | −265.000 | −0.168945 | ||||||||
\(136\) | −416.000 | −0.262292 | ||||||||
\(137\) | 1084.00 | 0.676003 | 0.338001 | − | 0.941146i | \(-0.390249\pi\) | ||||
0.338001 | + | 0.941146i | \(0.390249\pi\) | |||||||
\(138\) | −134.000 | −0.0826582 | ||||||||
\(139\) | 46.0000 | 0.0280696 | 0.0140348 | − | 0.999902i | \(-0.495532\pi\) | ||||
0.0140348 | + | 0.999902i | \(0.495532\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −88.0000 | −0.0525598 | ||||||||
\(142\) | −1540.00 | −0.910098 | ||||||||
\(143\) | −16.0000 | −0.00935655 | ||||||||
\(144\) | −416.000 | −0.240741 | ||||||||
\(145\) | 345.000 | 0.197591 | ||||||||
\(146\) | 1256.00 | 0.711968 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 784.000 | 0.435435 | ||||||||
\(149\) | −369.000 | −0.202884 | −0.101442 | − | 0.994841i | \(-0.532346\pi\) | ||||
−0.101442 | + | 0.994841i | \(0.532346\pi\) | |||||||
\(150\) | −50.0000 | −0.0272166 | ||||||||
\(151\) | 2480.00 | 1.33655 | 0.668277 | − | 0.743913i | \(-0.267032\pi\) | ||||
0.668277 | + | 0.743913i | \(0.267032\pi\) | |||||||
\(152\) | 208.000 | 0.110994 | ||||||||
\(153\) | −1352.00 | −0.714397 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1660.00 | 0.860222 | ||||||||
\(156\) | 32.0000 | 0.0164234 | ||||||||
\(157\) | −1226.00 | −0.623219 | −0.311610 | − | 0.950210i | \(-0.600868\pi\) | ||||
−0.311610 | + | 0.950210i | \(0.600868\pi\) | |||||||
\(158\) | −2340.00 | −1.17823 | ||||||||
\(159\) | 582.000 | 0.290287 | ||||||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1298.00 | −0.629509 | ||||||||
\(163\) | −660.000 | −0.317148 | −0.158574 | − | 0.987347i | \(-0.550690\pi\) | ||||
−0.158574 | + | 0.987347i | \(0.550690\pi\) | |||||||
\(164\) | −1412.00 | −0.672309 | ||||||||
\(165\) | −10.0000 | −0.00471818 | ||||||||
\(166\) | 1050.00 | 0.490939 | ||||||||
\(167\) | 949.000 | 0.439735 | 0.219868 | − | 0.975530i | \(-0.429437\pi\) | ||||
0.219868 | + | 0.975530i | \(0.429437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2133.00 | −0.970869 | ||||||||
\(170\) | −520.000 | −0.234601 | ||||||||
\(171\) | 676.000 | 0.302310 | ||||||||
\(172\) | −1476.00 | −0.654325 | ||||||||
\(173\) | −3392.00 | −1.49069 | −0.745344 | − | 0.666680i | \(-0.767715\pi\) | ||||
−0.745344 | + | 0.666680i | \(0.767715\pi\) | |||||||
\(174\) | −138.000 | −0.0601250 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −32.0000 | −0.0137051 | ||||||||
\(177\) | 350.000 | 0.148631 | ||||||||
\(178\) | 178.000 | 0.0749532 | ||||||||
\(179\) | 268.000 | 0.111906 | 0.0559532 | − | 0.998433i | \(-0.482180\pi\) | ||||
0.0559532 | + | 0.998433i | \(0.482180\pi\) | |||||||
\(180\) | −520.000 | −0.215325 | ||||||||
\(181\) | 4093.00 | 1.68083 | 0.840415 | − | 0.541943i | \(-0.182311\pi\) | ||||
0.840415 | + | 0.541943i | \(0.182311\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 467.000 | 0.188643 | ||||||||
\(184\) | −536.000 | −0.214752 | ||||||||
\(185\) | 980.000 | 0.389465 | ||||||||
\(186\) | −664.000 | −0.261757 | ||||||||
\(187\) | −104.000 | −0.0406697 | ||||||||
\(188\) | −352.000 | −0.136554 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 260.000 | 0.0992757 | ||||||||
\(191\) | −1978.00 | −0.749335 | −0.374668 | − | 0.927159i | \(-0.622243\pi\) | ||||
−0.374668 | + | 0.927159i | \(0.622243\pi\) | |||||||
\(192\) | 64.0000 | 0.0240563 | ||||||||
\(193\) | −3998.00 | −1.49110 | −0.745550 | − | 0.666450i | \(-0.767813\pi\) | ||||
−0.745550 | + | 0.666450i | \(0.767813\pi\) | |||||||
\(194\) | −580.000 | −0.214647 | ||||||||
\(195\) | 40.0000 | 0.0146895 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3030.00 | −1.09583 | −0.547915 | − | 0.836534i | \(-0.684578\pi\) | ||||
−0.547915 | + | 0.836534i | \(0.684578\pi\) | |||||||
\(198\) | −104.000 | −0.0373281 | ||||||||
\(199\) | −356.000 | −0.126815 | −0.0634075 | − | 0.997988i | \(-0.520197\pi\) | ||||
−0.0634075 | + | 0.997988i | \(0.520197\pi\) | |||||||
\(200\) | −200.000 | −0.0707107 | ||||||||
\(201\) | 291.000 | 0.102117 | ||||||||
\(202\) | −2466.00 | −0.858946 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 208.000 | 0.0713868 | ||||||||
\(205\) | −1765.00 | −0.601331 | ||||||||
\(206\) | 3106.00 | 1.05051 | ||||||||
\(207\) | −1742.00 | −0.584915 | ||||||||
\(208\) | 128.000 | 0.0426692 | ||||||||
\(209\) | 52.0000 | 0.0172101 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2602.00 | −0.848953 | −0.424476 | − | 0.905439i | \(-0.639542\pi\) | ||||
−0.424476 | + | 0.905439i | \(0.639542\pi\) | |||||||
\(212\) | 2328.00 | 0.754187 | ||||||||
\(213\) | 770.000 | 0.247697 | ||||||||
\(214\) | −3662.00 | −1.16976 | ||||||||
\(215\) | −1845.00 | −0.585246 | ||||||||
\(216\) | 424.000 | 0.133563 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1622.00 | −0.503925 | ||||||||
\(219\) | −628.000 | −0.193773 | ||||||||
\(220\) | −40.0000 | −0.0122582 | ||||||||
\(221\) | 416.000 | 0.126621 | ||||||||
\(222\) | −392.000 | −0.118510 | ||||||||
\(223\) | 3156.00 | 0.947719 | 0.473860 | − | 0.880600i | \(-0.342860\pi\) | ||||
0.473860 | + | 0.880600i | \(0.342860\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −650.000 | −0.192593 | ||||||||
\(226\) | −4340.00 | −1.27740 | ||||||||
\(227\) | −4236.00 | −1.23856 | −0.619280 | − | 0.785170i | \(-0.712575\pi\) | ||||
−0.619280 | + | 0.785170i | \(0.712575\pi\) | |||||||
\(228\) | −104.000 | −0.0302086 | ||||||||
\(229\) | −6334.00 | −1.82778 | −0.913892 | − | 0.405958i | \(-0.866938\pi\) | ||||
−0.913892 | + | 0.405958i | \(0.866938\pi\) | |||||||
\(230\) | −670.000 | −0.192080 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −552.000 | −0.156209 | ||||||||
\(233\) | −4688.00 | −1.31812 | −0.659058 | − | 0.752092i | \(-0.729045\pi\) | ||||
−0.659058 | + | 0.752092i | \(0.729045\pi\) | |||||||
\(234\) | 416.000 | 0.116217 | ||||||||
\(235\) | −440.000 | −0.122138 | ||||||||
\(236\) | 1400.00 | 0.386154 | ||||||||
\(237\) | 1170.00 | 0.320674 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1856.00 | 0.502321 | 0.251160 | − | 0.967945i | \(-0.419188\pi\) | ||||
0.251160 | + | 0.967945i | \(0.419188\pi\) | |||||||
\(240\) | 80.0000 | 0.0215166 | ||||||||
\(241\) | 4806.00 | 1.28457 | 0.642286 | − | 0.766465i | \(-0.277986\pi\) | ||||
0.642286 | + | 0.766465i | \(0.277986\pi\) | |||||||
\(242\) | 2654.00 | 0.704982 | ||||||||
\(243\) | 2080.00 | 0.549103 | ||||||||
\(244\) | 1868.00 | 0.490108 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 706.000 | 0.182979 | ||||||||
\(247\) | −208.000 | −0.0535819 | ||||||||
\(248\) | −2656.00 | −0.680065 | ||||||||
\(249\) | −525.000 | −0.133617 | ||||||||
\(250\) | −250.000 | −0.0632456 | ||||||||
\(251\) | 3200.00 | 0.804710 | 0.402355 | − | 0.915484i | \(-0.368192\pi\) | ||||
0.402355 | + | 0.915484i | \(0.368192\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −134.000 | −0.0332984 | ||||||||
\(254\) | −96.0000 | −0.0237149 | ||||||||
\(255\) | 260.000 | 0.0638503 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 1120.00 | 0.271843 | 0.135922 | − | 0.990720i | \(-0.456600\pi\) | ||||
0.135922 | + | 0.990720i | \(0.456600\pi\) | |||||||
\(258\) | 738.000 | 0.178085 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 160.000 | 0.0381645 | ||||||||
\(261\) | −1794.00 | −0.425463 | ||||||||
\(262\) | −1584.00 | −0.373511 | ||||||||
\(263\) | 6405.00 | 1.50171 | 0.750854 | − | 0.660468i | \(-0.229642\pi\) | ||||
0.750854 | + | 0.660468i | \(0.229642\pi\) | |||||||
\(264\) | 16.0000 | 0.00373005 | ||||||||
\(265\) | 2910.00 | 0.674566 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −89.0000 | −0.0203997 | ||||||||
\(268\) | 1164.00 | 0.265308 | ||||||||
\(269\) | −4935.00 | −1.11856 | −0.559279 | − | 0.828979i | \(-0.688922\pi\) | ||||
−0.559279 | + | 0.828979i | \(0.688922\pi\) | |||||||
\(270\) | 530.000 | 0.119462 | ||||||||
\(271\) | 1446.00 | 0.324126 | 0.162063 | − | 0.986780i | \(-0.448185\pi\) | ||||
0.162063 | + | 0.986780i | \(0.448185\pi\) | |||||||
\(272\) | 832.000 | 0.185468 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2168.00 | −0.478006 | ||||||||
\(275\) | −50.0000 | −0.0109640 | ||||||||
\(276\) | 268.000 | 0.0584482 | ||||||||
\(277\) | −8020.00 | −1.73962 | −0.869811 | − | 0.493386i | \(-0.835759\pi\) | ||||
−0.869811 | + | 0.493386i | \(0.835759\pi\) | |||||||
\(278\) | −92.0000 | −0.0198482 | ||||||||
\(279\) | −8632.00 | −1.85227 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4978.00 | 1.05681 | 0.528403 | − | 0.848994i | \(-0.322791\pi\) | ||||
0.528403 | + | 0.848994i | \(0.322791\pi\) | |||||||
\(282\) | 176.000 | 0.0371654 | ||||||||
\(283\) | −5852.00 | −1.22921 | −0.614603 | − | 0.788837i | \(-0.710684\pi\) | ||||
−0.614603 | + | 0.788837i | \(0.710684\pi\) | |||||||
\(284\) | 3080.00 | 0.643537 | ||||||||
\(285\) | −130.000 | −0.0270194 | ||||||||
\(286\) | 32.0000 | 0.00661608 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 832.000 | 0.170229 | ||||||||
\(289\) | −2209.00 | −0.449623 | ||||||||
\(290\) | −690.000 | −0.139718 | ||||||||
\(291\) | 290.000 | 0.0584196 | ||||||||
\(292\) | −2512.00 | −0.503437 | ||||||||
\(293\) | 3012.00 | 0.600556 | 0.300278 | − | 0.953852i | \(-0.402921\pi\) | ||||
0.300278 | + | 0.953852i | \(0.402921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1750.00 | 0.345386 | ||||||||
\(296\) | −1568.00 | −0.307899 | ||||||||
\(297\) | 106.000 | 0.0207096 | ||||||||
\(298\) | 738.000 | 0.143460 | ||||||||
\(299\) | 536.000 | 0.103671 | ||||||||
\(300\) | 100.000 | 0.0192450 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4960.00 | −0.945086 | ||||||||
\(303\) | 1233.00 | 0.233776 | ||||||||
\(304\) | −416.000 | −0.0784843 | ||||||||
\(305\) | 2335.00 | 0.438366 | ||||||||
\(306\) | 2704.00 | 0.505155 | ||||||||
\(307\) | −9443.00 | −1.75551 | −0.877753 | − | 0.479113i | \(-0.840958\pi\) | ||||
−0.877753 | + | 0.479113i | \(0.840958\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1553.00 | −0.285913 | ||||||||
\(310\) | −3320.00 | −0.608269 | ||||||||
\(311\) | 9994.00 | 1.82221 | 0.911106 | − | 0.412173i | \(-0.135230\pi\) | ||||
0.911106 | + | 0.412173i | \(0.135230\pi\) | |||||||
\(312\) | −64.0000 | −0.0116131 | ||||||||
\(313\) | −1456.00 | −0.262933 | −0.131466 | − | 0.991321i | \(-0.541969\pi\) | ||||
−0.131466 | + | 0.991321i | \(0.541969\pi\) | |||||||
\(314\) | 2452.00 | 0.440683 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4680.00 | 0.833135 | ||||||||
\(317\) | 6872.00 | 1.21757 | 0.608785 | − | 0.793335i | \(-0.291657\pi\) | ||||
0.608785 | + | 0.793335i | \(0.291657\pi\) | |||||||
\(318\) | −1164.00 | −0.205264 | ||||||||
\(319\) | −138.000 | −0.0242211 | ||||||||
\(320\) | 320.000 | 0.0559017 | ||||||||
\(321\) | 1831.00 | 0.318369 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1352.00 | −0.232902 | ||||||||
\(324\) | 2596.00 | 0.445130 | ||||||||
\(325\) | 200.000 | 0.0341354 | ||||||||
\(326\) | 1320.00 | 0.224258 | ||||||||
\(327\) | 811.000 | 0.137151 | ||||||||
\(328\) | 2824.00 | 0.475394 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 20.0000 | 0.00333625 | ||||||||
\(331\) | −392.000 | −0.0650945 | −0.0325472 | − | 0.999470i | \(-0.510362\pi\) | ||||
−0.0325472 | + | 0.999470i | \(0.510362\pi\) | |||||||
\(332\) | −2100.00 | −0.347146 | ||||||||
\(333\) | −5096.00 | −0.838616 | ||||||||
\(334\) | −1898.00 | −0.310940 | ||||||||
\(335\) | 1455.00 | 0.237299 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3926.00 | 0.634608 | 0.317304 | − | 0.948324i | \(-0.397222\pi\) | ||||
0.317304 | + | 0.948324i | \(0.397222\pi\) | |||||||
\(338\) | 4266.00 | 0.686508 | ||||||||
\(339\) | 2170.00 | 0.347664 | ||||||||
\(340\) | 1040.00 | 0.165888 | ||||||||
\(341\) | −664.000 | −0.105448 | ||||||||
\(342\) | −1352.00 | −0.213765 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2952.00 | 0.462678 | ||||||||
\(345\) | 335.000 | 0.0522777 | ||||||||
\(346\) | 6784.00 | 1.05408 | ||||||||
\(347\) | −1785.00 | −0.276149 | −0.138075 | − | 0.990422i | \(-0.544091\pi\) | ||||
−0.138075 | + | 0.990422i | \(0.544091\pi\) | |||||||
\(348\) | 276.000 | 0.0425148 | ||||||||
\(349\) | 1591.00 | 0.244024 | 0.122012 | − | 0.992529i | \(-0.461065\pi\) | ||||
0.122012 | + | 0.992529i | \(0.461065\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −424.000 | −0.0644771 | ||||||||
\(352\) | 64.0000 | 0.00969094 | ||||||||
\(353\) | −1686.00 | −0.254212 | −0.127106 | − | 0.991889i | \(-0.540569\pi\) | ||||
−0.127106 | + | 0.991889i | \(0.540569\pi\) | |||||||
\(354\) | −700.000 | −0.105098 | ||||||||
\(355\) | 3850.00 | 0.575597 | ||||||||
\(356\) | −356.000 | −0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −536.000 | −0.0791298 | ||||||||
\(359\) | 7372.00 | 1.08379 | 0.541893 | − | 0.840447i | \(-0.317708\pi\) | ||||
0.541893 | + | 0.840447i | \(0.317708\pi\) | |||||||
\(360\) | 1040.00 | 0.152258 | ||||||||
\(361\) | −6183.00 | −0.901443 | ||||||||
\(362\) | −8186.00 | −1.18853 | ||||||||
\(363\) | −1327.00 | −0.191872 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3140.00 | −0.450288 | ||||||||
\(366\) | −934.000 | −0.133391 | ||||||||
\(367\) | −6637.00 | −0.944002 | −0.472001 | − | 0.881598i | \(-0.656468\pi\) | ||||
−0.472001 | + | 0.881598i | \(0.656468\pi\) | |||||||
\(368\) | 1072.00 | 0.151853 | ||||||||
\(369\) | 9178.00 | 1.29482 | ||||||||
\(370\) | −1960.00 | −0.275393 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1328.00 | 0.185090 | ||||||||
\(373\) | 3476.00 | 0.482521 | 0.241261 | − | 0.970460i | \(-0.422439\pi\) | ||||
0.241261 | + | 0.970460i | \(0.422439\pi\) | |||||||
\(374\) | 208.000 | 0.0287578 | ||||||||
\(375\) | 125.000 | 0.0172133 | ||||||||
\(376\) | 704.000 | 0.0965586 | ||||||||
\(377\) | 552.000 | 0.0754097 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2378.00 | −0.322295 | −0.161147 | − | 0.986930i | \(-0.551519\pi\) | ||||
−0.161147 | + | 0.986930i | \(0.551519\pi\) | |||||||
\(380\) | −520.000 | −0.0701985 | ||||||||
\(381\) | 48.0000 | 0.00645437 | ||||||||
\(382\) | 3956.00 | 0.529860 | ||||||||
\(383\) | 2457.00 | 0.327799 | 0.163899 | − | 0.986477i | \(-0.447593\pi\) | ||||
0.163899 | + | 0.986477i | \(0.447593\pi\) | |||||||
\(384\) | −128.000 | −0.0170103 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7996.00 | 1.05437 | ||||||||
\(387\) | 9594.00 | 1.26018 | ||||||||
\(388\) | 1160.00 | 0.151779 | ||||||||
\(389\) | 8562.00 | 1.11597 | 0.557983 | − | 0.829853i | \(-0.311575\pi\) | ||||
0.557983 | + | 0.829853i | \(0.311575\pi\) | |||||||
\(390\) | −80.0000 | −0.0103871 | ||||||||
\(391\) | 3484.00 | 0.450623 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 792.000 | 0.101657 | ||||||||
\(394\) | 6060.00 | 0.774869 | ||||||||
\(395\) | 5850.00 | 0.745178 | ||||||||
\(396\) | 208.000 | 0.0263949 | ||||||||
\(397\) | 9842.00 | 1.24422 | 0.622111 | − | 0.782929i | \(-0.286275\pi\) | ||||
0.622111 | + | 0.782929i | \(0.286275\pi\) | |||||||
\(398\) | 712.000 | 0.0896717 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | −8097.00 | −1.00834 | −0.504171 | − | 0.863604i | \(-0.668202\pi\) | ||||
−0.504171 | + | 0.863604i | \(0.668202\pi\) | |||||||
\(402\) | −582.000 | −0.0722078 | ||||||||
\(403\) | 2656.00 | 0.328300 | ||||||||
\(404\) | 4932.00 | 0.607367 | ||||||||
\(405\) | 3245.00 | 0.398137 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −392.000 | −0.0477413 | ||||||||
\(408\) | −416.000 | −0.0504781 | ||||||||
\(409\) | −15259.0 | −1.84477 | −0.922383 | − | 0.386277i | \(-0.873761\pi\) | ||||
−0.922383 | + | 0.386277i | \(0.873761\pi\) | |||||||
\(410\) | 3530.00 | 0.425206 | ||||||||
\(411\) | 1084.00 | 0.130097 | ||||||||
\(412\) | −6212.00 | −0.742823 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3484.00 | 0.413597 | ||||||||
\(415\) | −2625.00 | −0.310497 | ||||||||
\(416\) | −256.000 | −0.0301717 | ||||||||
\(417\) | 46.0000 | 0.00540199 | ||||||||
\(418\) | −104.000 | −0.0121694 | ||||||||
\(419\) | −16224.0 | −1.89163 | −0.945817 | − | 0.324701i | \(-0.894736\pi\) | ||||
−0.945817 | + | 0.324701i | \(0.894736\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2977.00 | 0.344632 | 0.172316 | − | 0.985042i | \(-0.444875\pi\) | ||||
0.172316 | + | 0.985042i | \(0.444875\pi\) | |||||||
\(422\) | 5204.00 | 0.600300 | ||||||||
\(423\) | 2288.00 | 0.262994 | ||||||||
\(424\) | −4656.00 | −0.533291 | ||||||||
\(425\) | 1300.00 | 0.148375 | ||||||||
\(426\) | −1540.00 | −0.175148 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7324.00 | 0.827147 | ||||||||
\(429\) | −16.0000 | −0.00180067 | ||||||||
\(430\) | 3690.00 | 0.413832 | ||||||||
\(431\) | 14202.0 | 1.58721 | 0.793604 | − | 0.608435i | \(-0.208202\pi\) | ||||
0.793604 | + | 0.608435i | \(0.208202\pi\) | |||||||
\(432\) | −848.000 | −0.0944431 | ||||||||
\(433\) | −14310.0 | −1.58821 | −0.794105 | − | 0.607781i | \(-0.792060\pi\) | ||||
−0.794105 | + | 0.607781i | \(0.792060\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 345.000 | 0.0380264 | ||||||||
\(436\) | 3244.00 | 0.356329 | ||||||||
\(437\) | −1742.00 | −0.190689 | ||||||||
\(438\) | 1256.00 | 0.137018 | ||||||||
\(439\) | 2356.00 | 0.256141 | 0.128070 | − | 0.991765i | \(-0.459122\pi\) | ||||
0.128070 | + | 0.991765i | \(0.459122\pi\) | |||||||
\(440\) | 80.0000 | 0.00866784 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −832.000 | −0.0895344 | ||||||||
\(443\) | 8291.00 | 0.889204 | 0.444602 | − | 0.895728i | \(-0.353345\pi\) | ||||
0.444602 | + | 0.895728i | \(0.353345\pi\) | |||||||
\(444\) | 784.000 | 0.0837995 | ||||||||
\(445\) | −445.000 | −0.0474045 | ||||||||
\(446\) | −6312.00 | −0.670139 | ||||||||
\(447\) | −369.000 | −0.0390450 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3521.00 | −0.370081 | −0.185040 | − | 0.982731i | \(-0.559242\pi\) | ||||
−0.185040 | + | 0.982731i | \(0.559242\pi\) | |||||||
\(450\) | 1300.00 | 0.136184 | ||||||||
\(451\) | 706.000 | 0.0737123 | ||||||||
\(452\) | 8680.00 | 0.903259 | ||||||||
\(453\) | 2480.00 | 0.257220 | ||||||||
\(454\) | 8472.00 | 0.875794 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 208.000 | 0.0213607 | ||||||||
\(457\) | −5432.00 | −0.556014 | −0.278007 | − | 0.960579i | \(-0.589674\pi\) | ||||
−0.278007 | + | 0.960579i | \(0.589674\pi\) | |||||||
\(458\) | 12668.0 | 1.29244 | ||||||||
\(459\) | −2756.00 | −0.280259 | ||||||||
\(460\) | 1340.00 | 0.135821 | ||||||||
\(461\) | 5350.00 | 0.540508 | 0.270254 | − | 0.962789i | \(-0.412892\pi\) | ||||
0.270254 | + | 0.962789i | \(0.412892\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10123.0 | −1.01610 | −0.508052 | − | 0.861327i | \(-0.669634\pi\) | ||||
−0.508052 | + | 0.861327i | \(0.669634\pi\) | |||||||
\(464\) | 1104.00 | 0.110457 | ||||||||
\(465\) | 1660.00 | 0.165550 | ||||||||
\(466\) | 9376.00 | 0.932049 | ||||||||
\(467\) | −6463.00 | −0.640411 | −0.320206 | − | 0.947348i | \(-0.603752\pi\) | ||||
−0.320206 | + | 0.947348i | \(0.603752\pi\) | |||||||
\(468\) | −832.000 | −0.0821778 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 880.000 | 0.0863646 | ||||||||
\(471\) | −1226.00 | −0.119939 | ||||||||
\(472\) | −2800.00 | −0.273052 | ||||||||
\(473\) | 738.000 | 0.0717405 | ||||||||
\(474\) | −2340.00 | −0.226751 | ||||||||
\(475\) | −650.000 | −0.0627875 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15132.0 | −1.45251 | ||||||||
\(478\) | −3712.00 | −0.355194 | ||||||||
\(479\) | 17640.0 | 1.68266 | 0.841328 | − | 0.540525i | \(-0.181774\pi\) | ||||
0.841328 | + | 0.540525i | \(0.181774\pi\) | |||||||
\(480\) | −160.000 | −0.0152145 | ||||||||
\(481\) | 1568.00 | 0.148638 | ||||||||
\(482\) | −9612.00 | −0.908329 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5308.00 | −0.498497 | ||||||||
\(485\) | 1450.00 | 0.135755 | ||||||||
\(486\) | −4160.00 | −0.388275 | ||||||||
\(487\) | −10032.0 | −0.933456 | −0.466728 | − | 0.884401i | \(-0.654567\pi\) | ||||
−0.466728 | + | 0.884401i | \(0.654567\pi\) | |||||||
\(488\) | −3736.00 | −0.346559 | ||||||||
\(489\) | −660.000 | −0.0610352 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5916.00 | 0.543758 | 0.271879 | − | 0.962331i | \(-0.412355\pi\) | ||||
0.271879 | + | 0.962331i | \(0.412355\pi\) | |||||||
\(492\) | −1412.00 | −0.129386 | ||||||||
\(493\) | 3588.00 | 0.327780 | ||||||||
\(494\) | 416.000 | 0.0378881 | ||||||||
\(495\) | 260.000 | 0.0236083 | ||||||||
\(496\) | 5312.00 | 0.480879 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1050.00 | 0.0944812 | ||||||||
\(499\) | 13894.0 | 1.24645 | 0.623227 | − | 0.782041i | \(-0.285821\pi\) | ||||
0.623227 | + | 0.782041i | \(0.285821\pi\) | |||||||
\(500\) | 500.000 | 0.0447214 | ||||||||
\(501\) | 949.000 | 0.0846271 | ||||||||
\(502\) | −6400.00 | −0.569016 | ||||||||
\(503\) | −18427.0 | −1.63344 | −0.816719 | − | 0.577036i | \(-0.804209\pi\) | ||||
−0.816719 | + | 0.577036i | \(0.804209\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6165.00 | 0.543245 | ||||||||
\(506\) | 268.000 | 0.0235456 | ||||||||
\(507\) | −2133.00 | −0.186844 | ||||||||
\(508\) | 192.000 | 0.0167689 | ||||||||
\(509\) | −18557.0 | −1.61596 | −0.807981 | − | 0.589209i | \(-0.799440\pi\) | ||||
−0.807981 | + | 0.589209i | \(0.799440\pi\) | |||||||
\(510\) | −520.000 | −0.0451490 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 1378.00 | 0.118597 | ||||||||
\(514\) | −2240.00 | −0.192222 | ||||||||
\(515\) | −7765.00 | −0.664402 | ||||||||
\(516\) | −1476.00 | −0.125925 | ||||||||
\(517\) | 176.000 | 0.0149719 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3392.00 | −0.286883 | ||||||||
\(520\) | −320.000 | −0.0269864 | ||||||||
\(521\) | 9930.00 | 0.835012 | 0.417506 | − | 0.908674i | \(-0.362904\pi\) | ||||
0.417506 | + | 0.908674i | \(0.362904\pi\) | |||||||
\(522\) | 3588.00 | 0.300848 | ||||||||
\(523\) | 7924.00 | 0.662509 | 0.331255 | − | 0.943541i | \(-0.392528\pi\) | ||||
0.331255 | + | 0.943541i | \(0.392528\pi\) | |||||||
\(524\) | 3168.00 | 0.264112 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12810.0 | −1.06187 | ||||||||
\(527\) | 17264.0 | 1.42701 | ||||||||
\(528\) | −32.0000 | −0.00263754 | ||||||||
\(529\) | −7678.00 | −0.631051 | ||||||||
\(530\) | −5820.00 | −0.476990 | ||||||||
\(531\) | −9100.00 | −0.743703 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2824.00 | −0.229495 | ||||||||
\(534\) | 178.000 | 0.0144247 | ||||||||
\(535\) | 9155.00 | 0.739823 | ||||||||
\(536\) | −2328.00 | −0.187601 | ||||||||
\(537\) | 268.000 | 0.0215364 | ||||||||
\(538\) | 9870.00 | 0.790940 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1060.00 | −0.0844725 | ||||||||
\(541\) | −23497.0 | −1.86731 | −0.933655 | − | 0.358173i | \(-0.883400\pi\) | ||||
−0.933655 | + | 0.358173i | \(0.883400\pi\) | |||||||
\(542\) | −2892.00 | −0.229192 | ||||||||
\(543\) | 4093.00 | 0.323476 | ||||||||
\(544\) | −1664.00 | −0.131146 | ||||||||
\(545\) | 4055.00 | 0.318710 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11131.0 | 0.870068 | 0.435034 | − | 0.900414i | \(-0.356736\pi\) | ||||
0.435034 | + | 0.900414i | \(0.356736\pi\) | |||||||
\(548\) | 4336.00 | 0.338001 | ||||||||
\(549\) | −12142.0 | −0.943912 | ||||||||
\(550\) | 100.000 | 0.00775275 | ||||||||
\(551\) | −1794.00 | −0.138706 | ||||||||
\(552\) | −536.000 | −0.0413291 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 16040.0 | 1.23010 | ||||||||
\(555\) | 980.000 | 0.0749526 | ||||||||
\(556\) | 184.000 | 0.0140348 | ||||||||
\(557\) | −11978.0 | −0.911174 | −0.455587 | − | 0.890191i | \(-0.650571\pi\) | ||||
−0.455587 | + | 0.890191i | \(0.650571\pi\) | |||||||
\(558\) | 17264.0 | 1.30976 | ||||||||
\(559\) | −2952.00 | −0.223357 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −104.000 | −0.00782689 | ||||||||
\(562\) | −9956.00 | −0.747275 | ||||||||
\(563\) | 10059.0 | 0.752995 | 0.376498 | − | 0.926418i | \(-0.377128\pi\) | ||||
0.376498 | + | 0.926418i | \(0.377128\pi\) | |||||||
\(564\) | −352.000 | −0.0262799 | ||||||||
\(565\) | 10850.0 | 0.807899 | ||||||||
\(566\) | 11704.0 | 0.869180 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6160.00 | −0.455049 | ||||||||
\(569\) | −15666.0 | −1.15422 | −0.577111 | − | 0.816665i | \(-0.695820\pi\) | ||||
−0.577111 | + | 0.816665i | \(0.695820\pi\) | |||||||
\(570\) | 260.000 | 0.0191056 | ||||||||
\(571\) | 2530.00 | 0.185424 | 0.0927121 | − | 0.995693i | \(-0.470446\pi\) | ||||
0.0927121 | + | 0.995693i | \(0.470446\pi\) | |||||||
\(572\) | −64.0000 | −0.00467828 | ||||||||
\(573\) | −1978.00 | −0.144210 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1675.00 | 0.121482 | ||||||||
\(576\) | −1664.00 | −0.120370 | ||||||||
\(577\) | −12818.0 | −0.924819 | −0.462409 | − | 0.886667i | \(-0.653015\pi\) | ||||
−0.462409 | + | 0.886667i | \(0.653015\pi\) | |||||||
\(578\) | 4418.00 | 0.317932 | ||||||||
\(579\) | −3998.00 | −0.286962 | ||||||||
\(580\) | 1380.00 | 0.0987955 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −580.000 | −0.0413089 | ||||||||
\(583\) | −1164.00 | −0.0826895 | ||||||||
\(584\) | 5024.00 | 0.355984 | ||||||||
\(585\) | −1040.00 | −0.0735021 | ||||||||
\(586\) | −6024.00 | −0.424657 | ||||||||
\(587\) | 15228.0 | 1.07074 | 0.535372 | − | 0.844616i | \(-0.320171\pi\) | ||||
0.535372 | + | 0.844616i | \(0.320171\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8632.00 | −0.603863 | ||||||||
\(590\) | −3500.00 | −0.244225 | ||||||||
\(591\) | −3030.00 | −0.210893 | ||||||||
\(592\) | 3136.00 | 0.217718 | ||||||||
\(593\) | 2598.00 | 0.179911 | 0.0899554 | − | 0.995946i | \(-0.471328\pi\) | ||||
0.0899554 | + | 0.995946i | \(0.471328\pi\) | |||||||
\(594\) | −212.000 | −0.0146439 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1476.00 | −0.101442 | ||||||||
\(597\) | −356.000 | −0.0244055 | ||||||||
\(598\) | −1072.00 | −0.0733066 | ||||||||
\(599\) | −2548.00 | −0.173804 | −0.0869019 | − | 0.996217i | \(-0.527697\pi\) | ||||
−0.0869019 | + | 0.996217i | \(0.527697\pi\) | |||||||
\(600\) | −200.000 | −0.0136083 | ||||||||
\(601\) | −1706.00 | −0.115789 | −0.0578945 | − | 0.998323i | \(-0.518439\pi\) | ||||
−0.0578945 | + | 0.998323i | \(0.518439\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7566.00 | −0.510964 | ||||||||
\(604\) | 9920.00 | 0.668277 | ||||||||
\(605\) | −6635.00 | −0.445870 | ||||||||
\(606\) | −2466.00 | −0.165304 | ||||||||
\(607\) | 12567.0 | 0.840328 | 0.420164 | − | 0.907448i | \(-0.361973\pi\) | ||||
0.420164 | + | 0.907448i | \(0.361973\pi\) | |||||||
\(608\) | 832.000 | 0.0554968 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4670.00 | −0.309972 | ||||||||
\(611\) | −704.000 | −0.0466134 | ||||||||
\(612\) | −5408.00 | −0.357198 | ||||||||
\(613\) | −9628.00 | −0.634374 | −0.317187 | − | 0.948363i | \(-0.602738\pi\) | ||||
−0.317187 | + | 0.948363i | \(0.602738\pi\) | |||||||
\(614\) | 18886.0 | 1.24133 | ||||||||
\(615\) | −1765.00 | −0.115726 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4316.00 | −0.281614 | −0.140807 | − | 0.990037i | \(-0.544970\pi\) | ||||
−0.140807 | + | 0.990037i | \(0.544970\pi\) | |||||||
\(618\) | 3106.00 | 0.202171 | ||||||||
\(619\) | −16402.0 | −1.06503 | −0.532514 | − | 0.846421i | \(-0.678753\pi\) | ||||
−0.532514 | + | 0.846421i | \(0.678753\pi\) | |||||||
\(620\) | 6640.00 | 0.430111 | ||||||||
\(621\) | −3551.00 | −0.229463 | ||||||||
\(622\) | −19988.0 | −1.28850 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 128.000 | 0.00821170 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 2912.00 | 0.185922 | ||||||||
\(627\) | 52.0000 | 0.00331209 | ||||||||
\(628\) | −4904.00 | −0.311610 | ||||||||
\(629\) | 10192.0 | 0.646076 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8490.00 | 0.535628 | 0.267814 | − | 0.963471i | \(-0.413699\pi\) | ||||
0.267814 | + | 0.963471i | \(0.413699\pi\) | |||||||
\(632\) | −9360.00 | −0.589115 | ||||||||
\(633\) | −2602.00 | −0.163381 | ||||||||
\(634\) | −13744.0 | −0.860953 | ||||||||
\(635\) | 240.000 | 0.0149986 | ||||||||
\(636\) | 2328.00 | 0.145143 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 276.000 | 0.0171269 | ||||||||
\(639\) | −20020.0 | −1.23940 | ||||||||
\(640\) | −640.000 | −0.0395285 | ||||||||
\(641\) | −123.000 | −0.00757911 | −0.00378955 | − | 0.999993i | \(-0.501206\pi\) | ||||
−0.00378955 | + | 0.999993i | \(0.501206\pi\) | |||||||
\(642\) | −3662.00 | −0.225121 | ||||||||
\(643\) | 23924.0 | 1.46729 | 0.733647 | − | 0.679530i | \(-0.237816\pi\) | ||||
0.733647 | + | 0.679530i | \(0.237816\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1845.00 | −0.112631 | ||||||||
\(646\) | 2704.00 | 0.164686 | ||||||||
\(647\) | −181.000 | −0.0109982 | −0.00549911 | − | 0.999985i | \(-0.501750\pi\) | ||||
−0.00549911 | + | 0.999985i | \(0.501750\pi\) | |||||||
\(648\) | −5192.00 | −0.314755 | ||||||||
\(649\) | −700.000 | −0.0423381 | ||||||||
\(650\) | −400.000 | −0.0241374 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2640.00 | −0.158574 | ||||||||
\(653\) | −17812.0 | −1.06744 | −0.533719 | − | 0.845662i | \(-0.679206\pi\) | ||||
−0.533719 | + | 0.845662i | \(0.679206\pi\) | |||||||
\(654\) | −1622.00 | −0.0969805 | ||||||||
\(655\) | 3960.00 | 0.236229 | ||||||||
\(656\) | −5648.00 | −0.336154 | ||||||||
\(657\) | 16328.0 | 0.969583 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15334.0 | 0.906416 | 0.453208 | − | 0.891405i | \(-0.350280\pi\) | ||||
0.453208 | + | 0.891405i | \(0.350280\pi\) | |||||||
\(660\) | −40.0000 | −0.00235909 | ||||||||
\(661\) | −1337.00 | −0.0786736 | −0.0393368 | − | 0.999226i | \(-0.512525\pi\) | ||||
−0.0393368 | + | 0.999226i | \(0.512525\pi\) | |||||||
\(662\) | 784.000 | 0.0460287 | ||||||||
\(663\) | 416.000 | 0.0243682 | ||||||||
\(664\) | 4200.00 | 0.245469 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10192.0 | 0.592991 | ||||||||
\(667\) | 4623.00 | 0.268371 | ||||||||
\(668\) | 3796.00 | 0.219868 | ||||||||
\(669\) | 3156.00 | 0.182389 | ||||||||
\(670\) | −2910.00 | −0.167796 | ||||||||
\(671\) | −934.000 | −0.0537357 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15112.0 | −0.865564 | −0.432782 | − | 0.901499i | \(-0.642468\pi\) | ||||
−0.432782 | + | 0.901499i | \(0.642468\pi\) | |||||||
\(674\) | −7852.00 | −0.448736 | ||||||||
\(675\) | −1325.00 | −0.0755545 | ||||||||
\(676\) | −8532.00 | −0.485435 | ||||||||
\(677\) | −25392.0 | −1.44150 | −0.720749 | − | 0.693196i | \(-0.756202\pi\) | ||||
−0.720749 | + | 0.693196i | \(0.756202\pi\) | |||||||
\(678\) | −4340.00 | −0.245836 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2080.00 | −0.117301 | ||||||||
\(681\) | −4236.00 | −0.238361 | ||||||||
\(682\) | 1328.00 | 0.0745627 | ||||||||
\(683\) | 29231.0 | 1.63762 | 0.818809 | − | 0.574066i | \(-0.194635\pi\) | ||||
0.818809 | + | 0.574066i | \(0.194635\pi\) | |||||||
\(684\) | 2704.00 | 0.151155 | ||||||||
\(685\) | 5420.00 | 0.302318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6334.00 | −0.351757 | ||||||||
\(688\) | −5904.00 | −0.327163 | ||||||||
\(689\) | 4656.00 | 0.257445 | ||||||||
\(690\) | −670.000 | −0.0369659 | ||||||||
\(691\) | 7538.00 | 0.414991 | 0.207496 | − | 0.978236i | \(-0.433469\pi\) | ||||
0.207496 | + | 0.978236i | \(0.433469\pi\) | |||||||
\(692\) | −13568.0 | −0.745344 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3570.00 | 0.195267 | ||||||||
\(695\) | 230.000 | 0.0125531 | ||||||||
\(696\) | −552.000 | −0.0300625 | ||||||||
\(697\) | −18356.0 | −0.997537 | ||||||||
\(698\) | −3182.00 | −0.172551 | ||||||||
\(699\) | −4688.00 | −0.253672 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22125.0 | 1.19208 | 0.596041 | − | 0.802954i | \(-0.296739\pi\) | ||||
0.596041 | + | 0.802954i | \(0.296739\pi\) | |||||||
\(702\) | 848.000 | 0.0455922 | ||||||||
\(703\) | −5096.00 | −0.273399 | ||||||||
\(704\) | −128.000 | −0.00685253 | ||||||||
\(705\) | −440.000 | −0.0235055 | ||||||||
\(706\) | 3372.00 | 0.179755 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1400.00 | 0.0743153 | ||||||||
\(709\) | −4439.00 | −0.235134 | −0.117567 | − | 0.993065i | \(-0.537510\pi\) | ||||
−0.117567 | + | 0.993065i | \(0.537510\pi\) | |||||||
\(710\) | −7700.00 | −0.407008 | ||||||||
\(711\) | −30420.0 | −1.60456 | ||||||||
\(712\) | 712.000 | 0.0374766 | ||||||||
\(713\) | 22244.0 | 1.16837 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −80.0000 | −0.00418438 | ||||||||
\(716\) | 1072.00 | 0.0559532 | ||||||||
\(717\) | 1856.00 | 0.0966717 | ||||||||
\(718\) | −14744.0 | −0.766353 | ||||||||
\(719\) | −13650.0 | −0.708010 | −0.354005 | − | 0.935244i | \(-0.615180\pi\) | ||||
−0.354005 | + | 0.935244i | \(0.615180\pi\) | |||||||
\(720\) | −2080.00 | −0.107663 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12366.0 | 0.637417 | ||||||||
\(723\) | 4806.00 | 0.247216 | ||||||||
\(724\) | 16372.0 | 0.840415 | ||||||||
\(725\) | 1725.00 | 0.0883654 | ||||||||
\(726\) | 2654.00 | 0.135674 | ||||||||
\(727\) | 11397.0 | 0.581419 | 0.290709 | − | 0.956811i | \(-0.406109\pi\) | ||||
0.290709 | + | 0.956811i | \(0.406109\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15443.0 | −0.784586 | ||||||||
\(730\) | 6280.00 | 0.318402 | ||||||||
\(731\) | −19188.0 | −0.970853 | ||||||||
\(732\) | 1868.00 | 0.0943214 | ||||||||
\(733\) | −16686.0 | −0.840807 | −0.420403 | − | 0.907337i | \(-0.638111\pi\) | ||||
−0.420403 | + | 0.907337i | \(0.638111\pi\) | |||||||
\(734\) | 13274.0 | 0.667510 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2144.00 | −0.107376 | ||||||||
\(737\) | −582.000 | −0.0290885 | ||||||||
\(738\) | −18356.0 | −0.915574 | ||||||||
\(739\) | 22470.0 | 1.11850 | 0.559251 | − | 0.828999i | \(-0.311089\pi\) | ||||
0.559251 | + | 0.828999i | \(0.311089\pi\) | |||||||
\(740\) | 3920.00 | 0.194733 | ||||||||
\(741\) | −208.000 | −0.0103118 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5625.00 | 0.277741 | 0.138870 | − | 0.990311i | \(-0.455653\pi\) | ||||
0.138870 | + | 0.990311i | \(0.455653\pi\) | |||||||
\(744\) | −2656.00 | −0.130879 | ||||||||
\(745\) | −1845.00 | −0.0907323 | ||||||||
\(746\) | −6952.00 | −0.341194 | ||||||||
\(747\) | 13650.0 | 0.668577 | ||||||||
\(748\) | −416.000 | −0.0203348 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −250.000 | −0.0121716 | ||||||||
\(751\) | 17620.0 | 0.856142 | 0.428071 | − | 0.903745i | \(-0.359193\pi\) | ||||
0.428071 | + | 0.903745i | \(0.359193\pi\) | |||||||
\(752\) | −1408.00 | −0.0682772 | ||||||||
\(753\) | 3200.00 | 0.154867 | ||||||||
\(754\) | −1104.00 | −0.0533227 | ||||||||
\(755\) | 12400.0 | 0.597725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39056.0 | 1.87518 | 0.937592 | − | 0.347737i | \(-0.113050\pi\) | ||||
0.937592 | + | 0.347737i | \(0.113050\pi\) | |||||||
\(758\) | 4756.00 | 0.227897 | ||||||||
\(759\) | −134.000 | −0.00640829 | ||||||||
\(760\) | 1040.00 | 0.0496378 | ||||||||
\(761\) | −29738.0 | −1.41656 | −0.708280 | − | 0.705932i | \(-0.750528\pi\) | ||||
−0.708280 | + | 0.705932i | \(0.750528\pi\) | |||||||
\(762\) | −96.0000 | −0.00456393 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7912.00 | −0.374668 | ||||||||
\(765\) | −6760.00 | −0.319488 | ||||||||
\(766\) | −4914.00 | −0.231789 | ||||||||
\(767\) | 2800.00 | 0.131815 | ||||||||
\(768\) | 256.000 | 0.0120281 | ||||||||
\(769\) | 1118.00 | 0.0524267 | 0.0262133 | − | 0.999656i | \(-0.491655\pi\) | ||||
0.0262133 | + | 0.999656i | \(0.491655\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1120.00 | 0.0523162 | ||||||||
\(772\) | −15992.0 | −0.745550 | ||||||||
\(773\) | −13432.0 | −0.624988 | −0.312494 | − | 0.949920i | \(-0.601164\pi\) | ||||
−0.312494 | + | 0.949920i | \(0.601164\pi\) | |||||||
\(774\) | −19188.0 | −0.891083 | ||||||||
\(775\) | 8300.00 | 0.384703 | ||||||||
\(776\) | −2320.00 | −0.107324 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17124.0 | −0.789107 | ||||||||
\(779\) | 9178.00 | 0.422126 | ||||||||
\(780\) | 160.000 | 0.00734477 | ||||||||
\(781\) | −1540.00 | −0.0705577 | ||||||||
\(782\) | −6968.00 | −0.318638 | ||||||||
\(783\) | −3657.00 | −0.166910 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6130.00 | −0.278712 | ||||||||
\(786\) | −1584.00 | −0.0718822 | ||||||||
\(787\) | 9349.00 | 0.423451 | 0.211725 | − | 0.977329i | \(-0.432092\pi\) | ||||
0.211725 | + | 0.977329i | \(0.432092\pi\) | |||||||
\(788\) | −12120.0 | −0.547915 | ||||||||
\(789\) | 6405.00 | 0.289004 | ||||||||
\(790\) | −11700.0 | −0.526921 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −416.000 | −0.0186640 | ||||||||
\(793\) | 3736.00 | 0.167300 | ||||||||
\(794\) | −19684.0 | −0.879797 | ||||||||
\(795\) | 2910.00 | 0.129820 | ||||||||
\(796\) | −1424.00 | −0.0634075 | ||||||||
\(797\) | 28008.0 | 1.24479 | 0.622393 | − | 0.782705i | \(-0.286161\pi\) | ||||
0.622393 | + | 0.782705i | \(0.286161\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4576.00 | −0.202612 | ||||||||
\(800\) | −800.000 | −0.0353553 | ||||||||
\(801\) | 2314.00 | 0.102074 | ||||||||
\(802\) | 16194.0 | 0.713005 | ||||||||
\(803\) | 1256.00 | 0.0551971 | ||||||||
\(804\) | 1164.00 | 0.0510586 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5312.00 | −0.232143 | ||||||||
\(807\) | −4935.00 | −0.215267 | ||||||||
\(808\) | −9864.00 | −0.429473 | ||||||||
\(809\) | 19669.0 | 0.854790 | 0.427395 | − | 0.904065i | \(-0.359431\pi\) | ||||
0.427395 | + | 0.904065i | \(0.359431\pi\) | |||||||
\(810\) | −6490.00 | −0.281525 | ||||||||
\(811\) | −31860.0 | −1.37948 | −0.689739 | − | 0.724059i | \(-0.742275\pi\) | ||||
−0.689739 | + | 0.724059i | \(0.742275\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1446.00 | 0.0623781 | ||||||||
\(814\) | 784.000 | 0.0337582 | ||||||||
\(815\) | −3300.00 | −0.141833 | ||||||||
\(816\) | 832.000 | 0.0356934 | ||||||||
\(817\) | 9594.00 | 0.410834 | ||||||||
\(818\) | 30518.0 | 1.30445 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7060.00 | −0.300666 | ||||||||
\(821\) | 2230.00 | 0.0947960 | 0.0473980 | − | 0.998876i | \(-0.484907\pi\) | ||||
0.0473980 | + | 0.998876i | \(0.484907\pi\) | |||||||
\(822\) | −2168.00 | −0.0919923 | ||||||||
\(823\) | 14803.0 | 0.626975 | 0.313487 | − | 0.949592i | \(-0.398503\pi\) | ||||
0.313487 | + | 0.949592i | \(0.398503\pi\) | |||||||
\(824\) | 12424.0 | 0.525256 | ||||||||
\(825\) | −50.0000 | −0.00211003 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13257.0 | 0.557426 | 0.278713 | − | 0.960374i | \(-0.410092\pi\) | ||||
0.278713 | + | 0.960374i | \(0.410092\pi\) | |||||||
\(828\) | −6968.00 | −0.292457 | ||||||||
\(829\) | 21574.0 | 0.903855 | 0.451928 | − | 0.892055i | \(-0.350737\pi\) | ||||
0.451928 | + | 0.892055i | \(0.350737\pi\) | |||||||
\(830\) | 5250.00 | 0.219554 | ||||||||
\(831\) | −8020.00 | −0.334790 | ||||||||
\(832\) | 512.000 | 0.0213346 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −92.0000 | −0.00381978 | ||||||||
\(835\) | 4745.00 | 0.196656 | ||||||||
\(836\) | 208.000 | 0.00860506 | ||||||||
\(837\) | −17596.0 | −0.726651 | ||||||||
\(838\) | 32448.0 | 1.33759 | ||||||||
\(839\) | −12990.0 | −0.534523 | −0.267261 | − | 0.963624i | \(-0.586119\pi\) | ||||
−0.267261 | + | 0.963624i | \(0.586119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19628.0 | −0.804789 | ||||||||
\(842\) | −5954.00 | −0.243692 | ||||||||
\(843\) | 4978.00 | 0.203382 | ||||||||
\(844\) | −10408.0 | −0.424476 | ||||||||
\(845\) | −10665.0 | −0.434186 | ||||||||
\(846\) | −4576.00 | −0.185965 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9312.00 | 0.377094 | ||||||||
\(849\) | −5852.00 | −0.236561 | ||||||||
\(850\) | −2600.00 | −0.104917 | ||||||||
\(851\) | 13132.0 | 0.528977 | ||||||||
\(852\) | 3080.00 | 0.123849 | ||||||||
\(853\) | −24838.0 | −0.996995 | −0.498498 | − | 0.866891i | \(-0.666115\pi\) | ||||
−0.498498 | + | 0.866891i | \(0.666115\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3380.00 | 0.135197 | ||||||||
\(856\) | −14648.0 | −0.584881 | ||||||||
\(857\) | 17026.0 | 0.678643 | 0.339322 | − | 0.940670i | \(-0.389803\pi\) | ||||
0.339322 | + | 0.940670i | \(0.389803\pi\) | |||||||
\(858\) | 32.0000 | 0.00127327 | ||||||||
\(859\) | −6728.00 | −0.267237 | −0.133618 | − | 0.991033i | \(-0.542660\pi\) | ||||
−0.133618 | + | 0.991033i | \(0.542660\pi\) | |||||||
\(860\) | −7380.00 | −0.292623 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28404.0 | −1.12232 | ||||||||
\(863\) | −30099.0 | −1.18723 | −0.593616 | − | 0.804748i | \(-0.702300\pi\) | ||||
−0.593616 | + | 0.804748i | \(0.702300\pi\) | |||||||
\(864\) | 1696.00 | 0.0667814 | ||||||||
\(865\) | −16960.0 | −0.666656 | ||||||||
\(866\) | 28620.0 | 1.12303 | ||||||||
\(867\) | −2209.00 | −0.0865301 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2340.00 | −0.0913453 | ||||||||
\(870\) | −690.000 | −0.0268887 | ||||||||
\(871\) | 2328.00 | 0.0905640 | ||||||||
\(872\) | −6488.00 | −0.251963 | ||||||||
\(873\) | −7540.00 | −0.292314 | ||||||||
\(874\) | 3484.00 | 0.134838 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2512.00 | −0.0968865 | ||||||||
\(877\) | −5626.00 | −0.216621 | −0.108310 | − | 0.994117i | \(-0.534544\pi\) | ||||
−0.108310 | + | 0.994117i | \(0.534544\pi\) | |||||||
\(878\) | −4712.00 | −0.181119 | ||||||||
\(879\) | 3012.00 | 0.115577 | ||||||||
\(880\) | −160.000 | −0.00612909 | ||||||||
\(881\) | 15927.0 | 0.609074 | 0.304537 | − | 0.952500i | \(-0.401498\pi\) | ||||
0.304537 | + | 0.952500i | \(0.401498\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39124.0 | 1.49108 | 0.745542 | − | 0.666458i | \(-0.232191\pi\) | ||||
0.745542 | + | 0.666458i | \(0.232191\pi\) | |||||||
\(884\) | 1664.00 | 0.0633104 | ||||||||
\(885\) | 1750.00 | 0.0664696 | ||||||||
\(886\) | −16582.0 | −0.628762 | ||||||||
\(887\) | 25331.0 | 0.958886 | 0.479443 | − | 0.877573i | \(-0.340839\pi\) | ||||
0.479443 | + | 0.877573i | \(0.340839\pi\) | |||||||
\(888\) | −1568.00 | −0.0592552 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 890.000 | 0.0335201 | ||||||||
\(891\) | −1298.00 | −0.0488043 | ||||||||
\(892\) | 12624.0 | 0.473860 | ||||||||
\(893\) | 2288.00 | 0.0857391 | ||||||||
\(894\) | 738.000 | 0.0276090 | ||||||||
\(895\) | 1340.00 | 0.0500461 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 536.000 | 0.0199515 | ||||||||
\(898\) | 7042.00 | 0.261687 | ||||||||
\(899\) | 22908.0 | 0.849860 | ||||||||
\(900\) | −2600.00 | −0.0962963 | ||||||||
\(901\) | 30264.0 | 1.11902 | ||||||||
\(902\) | −1412.00 | −0.0521225 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17360.0 | −0.638700 | ||||||||
\(905\) | 20465.0 | 0.751690 | ||||||||
\(906\) | −4960.00 | −0.181882 | ||||||||
\(907\) | 26385.0 | 0.965931 | 0.482966 | − | 0.875639i | \(-0.339560\pi\) | ||||
0.482966 | + | 0.875639i | \(0.339560\pi\) | |||||||
\(908\) | −16944.0 | −0.619280 | ||||||||
\(909\) | −32058.0 | −1.16974 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40770.0 | −1.48273 | −0.741367 | − | 0.671100i | \(-0.765822\pi\) | ||||
−0.741367 | + | 0.671100i | \(0.765822\pi\) | |||||||
\(912\) | −416.000 | −0.0151043 | ||||||||
\(913\) | 1050.00 | 0.0380613 | ||||||||
\(914\) | 10864.0 | 0.393161 | ||||||||
\(915\) | 2335.00 | 0.0843636 | ||||||||
\(916\) | −25336.0 | −0.913892 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5512.00 | 0.198173 | ||||||||
\(919\) | −14618.0 | −0.524704 | −0.262352 | − | 0.964972i | \(-0.584498\pi\) | ||||
−0.262352 | + | 0.964972i | \(0.584498\pi\) | |||||||
\(920\) | −2680.00 | −0.0960402 | ||||||||
\(921\) | −9443.00 | −0.337847 | ||||||||
\(922\) | −10700.0 | −0.382197 | ||||||||
\(923\) | 6160.00 | 0.219674 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4900.00 | 0.174174 | ||||||||
\(926\) | 20246.0 | 0.718493 | ||||||||
\(927\) | 40378.0 | 1.43062 | ||||||||
\(928\) | −2208.00 | −0.0781047 | ||||||||
\(929\) | −41323.0 | −1.45938 | −0.729690 | − | 0.683778i | \(-0.760336\pi\) | ||||
−0.729690 | + | 0.683778i | \(0.760336\pi\) | |||||||
\(930\) | −3320.00 | −0.117061 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18752.0 | −0.659058 | ||||||||
\(933\) | 9994.00 | 0.350685 | ||||||||
\(934\) | 12926.0 | 0.452839 | ||||||||
\(935\) | −520.000 | −0.0181880 | ||||||||
\(936\) | 1664.00 | 0.0581085 | ||||||||
\(937\) | 22620.0 | 0.788648 | 0.394324 | − | 0.918971i | \(-0.370979\pi\) | ||||
0.394324 | + | 0.918971i | \(0.370979\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1456.00 | −0.0506015 | ||||||||
\(940\) | −1760.00 | −0.0610690 | ||||||||
\(941\) | −51978.0 | −1.80067 | −0.900337 | − | 0.435193i | \(-0.856680\pi\) | ||||
−0.900337 | + | 0.435193i | \(0.856680\pi\) | |||||||
\(942\) | 2452.00 | 0.0848094 | ||||||||
\(943\) | −23651.0 | −0.816737 | ||||||||
\(944\) | 5600.00 | 0.193077 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1476.00 | −0.0507282 | ||||||||
\(947\) | 9987.00 | 0.342697 | 0.171348 | − | 0.985210i | \(-0.445188\pi\) | ||||
0.171348 | + | 0.985210i | \(0.445188\pi\) | |||||||
\(948\) | 4680.00 | 0.160337 | ||||||||
\(949\) | −5024.00 | −0.171850 | ||||||||
\(950\) | 1300.00 | 0.0443974 | ||||||||
\(951\) | 6872.00 | 0.234322 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6588.00 | 0.223931 | 0.111966 | − | 0.993712i | \(-0.464285\pi\) | ||||
0.111966 | + | 0.993712i | \(0.464285\pi\) | |||||||
\(954\) | 30264.0 | 1.02708 | ||||||||
\(955\) | −9890.00 | −0.335113 | ||||||||
\(956\) | 7424.00 | 0.251160 | ||||||||
\(957\) | −138.000 | −0.00466134 | ||||||||
\(958\) | −35280.0 | −1.18982 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 320.000 | 0.0107583 | ||||||||
\(961\) | 80433.0 | 2.69991 | ||||||||
\(962\) | −3136.00 | −0.105103 | ||||||||
\(963\) | −47606.0 | −1.59302 | ||||||||
\(964\) | 19224.0 | 0.642286 | ||||||||
\(965\) | −19990.0 | −0.666840 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4091.00 | −0.136047 | −0.0680236 | − | 0.997684i | \(-0.521669\pi\) | ||||
−0.0680236 | + | 0.997684i | \(0.521669\pi\) | |||||||
\(968\) | 10616.0 | 0.352491 | ||||||||
\(969\) | −1352.00 | −0.0448220 | ||||||||
\(970\) | −2900.00 | −0.0959932 | ||||||||
\(971\) | −23640.0 | −0.781301 | −0.390651 | − | 0.920539i | \(-0.627750\pi\) | ||||
−0.390651 | + | 0.920539i | \(0.627750\pi\) | |||||||
\(972\) | 8320.00 | 0.274552 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 20064.0 | 0.660053 | ||||||||
\(975\) | 200.000 | 0.00656936 | ||||||||
\(976\) | 7472.00 | 0.245054 | ||||||||
\(977\) | 36666.0 | 1.20066 | 0.600332 | − | 0.799751i | \(-0.295035\pi\) | ||||
0.600332 | + | 0.799751i | \(0.295035\pi\) | |||||||
\(978\) | 1320.00 | 0.0431584 | ||||||||
\(979\) | 178.000 | 0.00581093 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21086.0 | −0.686263 | ||||||||
\(982\) | −11832.0 | −0.384495 | ||||||||
\(983\) | 41071.0 | 1.33262 | 0.666308 | − | 0.745677i | \(-0.267874\pi\) | ||||
0.666308 | + | 0.745677i | \(0.267874\pi\) | |||||||
\(984\) | 2824.00 | 0.0914897 | ||||||||
\(985\) | −15150.0 | −0.490070 | ||||||||
\(986\) | −7176.00 | −0.231775 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −832.000 | −0.0267909 | ||||||||
\(989\) | −24723.0 | −0.794889 | ||||||||
\(990\) | −520.000 | −0.0166936 | ||||||||
\(991\) | 31984.0 | 1.02523 | 0.512616 | − | 0.858618i | \(-0.328676\pi\) | ||||
0.512616 | + | 0.858618i | \(0.328676\pi\) | |||||||
\(992\) | −10624.0 | −0.340033 | ||||||||
\(993\) | −392.000 | −0.0125274 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1780.00 | −0.0567134 | ||||||||
\(996\) | −2100.00 | −0.0668083 | ||||||||
\(997\) | 43894.0 | 1.39432 | 0.697160 | − | 0.716916i | \(-0.254447\pi\) | ||||
0.697160 | + | 0.716916i | \(0.254447\pi\) | |||||||
\(998\) | −27788.0 | −0.881377 | ||||||||
\(999\) | −10388.0 | −0.328991 |
(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 | 490.4.a.e.1.1 | 1 | ||
5.4 | even | 2 | 2450.4.a.be.1.1 | 1 | |||
7.2 | even | 3 | 490.4.e.m.361.1 | 2 | |||
7.3 | odd | 6 | 70.4.e.c.51.1 | yes | 2 | ||
7.4 | even | 3 | 490.4.e.m.471.1 | 2 | |||
7.5 | odd | 6 | 70.4.e.c.11.1 | ✓ | 2 | ||
7.6 | odd | 2 | 490.4.a.c.1.1 | 1 | |||
21.5 | even | 6 | 630.4.k.b.361.1 | 2 | |||
21.17 | even | 6 | 630.4.k.b.541.1 | 2 | |||
28.3 | even | 6 | 560.4.q.d.401.1 | 2 | |||
28.19 | even | 6 | 560.4.q.d.81.1 | 2 | |||
35.3 | even | 12 | 350.4.j.e.149.1 | 4 | |||
35.12 | even | 12 | 350.4.j.e.249.1 | 4 | |||
35.17 | even | 12 | 350.4.j.e.149.2 | 4 | |||
35.19 | odd | 6 | 350.4.e.a.151.1 | 2 | |||
35.24 | odd | 6 | 350.4.e.a.51.1 | 2 | |||
35.33 | even | 12 | 350.4.j.e.249.2 | 4 | |||
35.34 | odd | 2 | 2450.4.a.bg.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.4.e.c.11.1 | ✓ | 2 | 7.5 | odd | 6 | ||
70.4.e.c.51.1 | yes | 2 | 7.3 | odd | 6 | ||
350.4.e.a.51.1 | 2 | 35.24 | odd | 6 | |||
350.4.e.a.151.1 | 2 | 35.19 | odd | 6 | |||
350.4.j.e.149.1 | 4 | 35.3 | even | 12 | |||
350.4.j.e.149.2 | 4 | 35.17 | even | 12 | |||
350.4.j.e.249.1 | 4 | 35.12 | even | 12 | |||
350.4.j.e.249.2 | 4 | 35.33 | even | 12 | |||
490.4.a.c.1.1 | 1 | 7.6 | odd | 2 | |||
490.4.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
490.4.e.m.361.1 | 2 | 7.2 | even | 3 | |||
490.4.e.m.471.1 | 2 | 7.4 | even | 3 | |||
560.4.q.d.81.1 | 2 | 28.19 | even | 6 | |||
560.4.q.d.401.1 | 2 | 28.3 | even | 6 | |||
630.4.k.b.361.1 | 2 | 21.5 | even | 6 | |||
630.4.k.b.541.1 | 2 | 21.17 | even | 6 | |||
2450.4.a.be.1.1 | 1 | 5.4 | even | 2 | |||
2450.4.a.bg.1.1 | 1 | 35.34 | odd | 2 |