Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(604,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.604");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 363) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 604.1 | ||
Root | \(-1.93185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.g.604.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.93185i | − 0.965926i | −0.875641 | − | 0.482963i | \(-0.839561\pi\) | ||||
0.875641 | − | 0.482963i | \(-0.160439\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.267949 | 0.0669873 | ||||||||
\(5\) | −3.19615 | −0.639230 | −0.319615 | − | 0.947547i | \(-0.603554\pi\) | ||||
−0.319615 | + | 0.947547i | \(0.603554\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.7632i | 1.96617i | 0.183147 | + | 0.983086i | \(0.441372\pi\) | ||||
−0.183147 | + | 0.983086i | \(0.558628\pi\) | |||||||
\(8\) | − 8.24504i | − 1.03063i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.17449i | 0.617449i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 13.6245i | − 1.04804i | −0.851706 | − | 0.524019i | \(-0.824432\pi\) | ||||
0.851706 | − | 0.524019i | \(-0.175568\pi\) | |||||||
\(14\) | 26.5885 | 1.89918 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −14.8564 | −0.928525 | ||||||||
\(17\) | 19.6603i | 1.15649i | 0.815864 | + | 0.578244i | \(0.196262\pi\) | ||||
−0.815864 | + | 0.578244i | \(0.803738\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 3.58630i | − 0.188753i | −0.995537 | − | 0.0943764i | \(-0.969914\pi\) | ||||
0.995537 | − | 0.0943764i | \(-0.0300857\pi\) | |||||||
\(20\) | −0.856406 | −0.0428203 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −10.0526 | −0.437068 | −0.218534 | − | 0.975829i | \(-0.570127\pi\) | ||||
−0.218534 | + | 0.975829i | \(0.570127\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.7846 | −0.591384 | ||||||||
\(26\) | −26.3205 | −1.01233 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.68784i | 0.131708i | ||||||||
\(29\) | − 47.6400i | − 1.64276i | −0.570384 | − | 0.821378i | \(-0.693205\pi\) | ||||
0.570384 | − | 0.821378i | \(-0.306795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.67949 | −0.0864352 | −0.0432176 | − | 0.999066i | \(-0.513761\pi\) | ||||
−0.0432176 | + | 0.999066i | \(0.513761\pi\) | |||||||
\(32\) | − 4.27981i | − 0.133744i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 37.9808 | 1.11708 | ||||||||
\(35\) | − 43.9893i | − 1.25684i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.87564 | 0.0506931 | 0.0253465 | − | 0.999679i | \(-0.491931\pi\) | ||||
0.0253465 | + | 0.999679i | \(0.491931\pi\) | |||||||
\(38\) | −6.92820 | −0.182321 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 26.3524i | 0.658810i | ||||||||
\(41\) | 62.2626i | 1.51860i | 0.650741 | + | 0.759300i | \(0.274458\pi\) | ||||
−0.650741 | + | 0.759300i | \(0.725542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.92996i | − 0.0681387i | −0.999419 | − | 0.0340693i | \(-0.989153\pi\) | ||||
0.999419 | − | 0.0340693i | \(-0.0108467\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 19.4201i | 0.422175i | ||||||||
\(47\) | −62.8897 | −1.33808 | −0.669040 | − | 0.743227i | \(-0.733294\pi\) | ||||
−0.669040 | + | 0.743227i | \(0.733294\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −140.426 | −2.86583 | ||||||||
\(50\) | 28.5617i | 0.571233i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 3.65067i | − 0.0702053i | ||||||||
\(53\) | −14.2154 | −0.268215 | −0.134107 | − | 0.990967i | \(-0.542817\pi\) | ||||
−0.134107 | + | 0.990967i | \(0.542817\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 113.478 | 2.02640 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −92.0333 | −1.58678 | ||||||||
\(59\) | −103.909 | −1.76117 | −0.880584 | − | 0.473889i | \(-0.842850\pi\) | ||||
−0.880584 | + | 0.473889i | \(0.842850\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 51.6424i | 0.846596i | 0.905991 | + | 0.423298i | \(0.139128\pi\) | ||||
−0.905991 | + | 0.423298i | \(0.860872\pi\) | |||||||
\(62\) | 5.17638i | 0.0834900i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −67.6936 | −1.05771 | ||||||||
\(65\) | 43.5460i | 0.669938i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.0910 | −0.240165 | −0.120082 | − | 0.992764i | \(-0.538316\pi\) | ||||
−0.120082 | + | 0.992764i | \(0.538316\pi\) | |||||||
\(68\) | 5.26796i | 0.0774700i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −84.9808 | −1.21401 | ||||||||
\(71\) | −54.6936 | −0.770332 | −0.385166 | − | 0.922847i | \(-0.625856\pi\) | ||||
−0.385166 | + | 0.922847i | \(0.625856\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 85.4348i | − 1.17034i | −0.810911 | − | 0.585170i | \(-0.801028\pi\) | ||||
0.810911 | − | 0.585170i | \(-0.198972\pi\) | |||||||
\(74\) | − 3.62347i | − 0.0489658i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 0.960947i | − 0.0126440i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 8.83701i | − 0.111861i | −0.998435 | − | 0.0559305i | \(-0.982187\pi\) | ||||
0.998435 | − | 0.0559305i | \(-0.0178125\pi\) | |||||||
\(80\) | 47.4833 | 0.593542 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 120.282 | 1.46685 | ||||||||
\(83\) | 56.0137i | 0.674864i | 0.941350 | + | 0.337432i | \(0.109558\pi\) | ||||
−0.941350 | + | 0.337432i | \(0.890442\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 62.8373i | − 0.739262i | ||||||||
\(86\) | −5.66025 | −0.0658169 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −44.1628 | −0.496212 | −0.248106 | − | 0.968733i | \(-0.579808\pi\) | ||||
−0.248106 | + | 0.968733i | \(0.579808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 187.517 | 2.06062 | ||||||||
\(92\) | −2.69358 | −0.0292780 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 121.494i | 1.29249i | ||||||||
\(95\) | 11.4624i | 0.120656i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 78.2295 | 0.806489 | 0.403245 | − | 0.915092i | \(-0.367882\pi\) | ||||
0.403245 | + | 0.915092i | \(0.367882\pi\) | |||||||
\(98\) | 271.281i | 2.76818i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.96152 | −0.0396152 | ||||||||
\(101\) | 20.6783i | 0.204736i | 0.994747 | + | 0.102368i | \(0.0326419\pi\) | ||||
−0.994747 | + | 0.102368i | \(0.967358\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −122.799 | −1.19222 | −0.596110 | − | 0.802903i | \(-0.703288\pi\) | ||||
−0.596110 | + | 0.802903i | \(0.703288\pi\) | |||||||
\(104\) | −112.335 | −1.08014 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 27.4620i | 0.259076i | ||||||||
\(107\) | − 14.4467i | − 0.135016i | −0.997719 | − | 0.0675081i | \(-0.978495\pi\) | ||||
0.997719 | − | 0.0675081i | \(-0.0215049\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 107.490i | 0.986149i | 0.869987 | + | 0.493074i | \(0.164127\pi\) | ||||
−0.869987 | + | 0.493074i | \(0.835873\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 204.472i | − 1.82564i | ||||||||
\(113\) | 127.785 | 1.13084 | 0.565419 | − | 0.824804i | \(-0.308715\pi\) | ||||
0.565419 | + | 0.824804i | \(0.308715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 32.1295 | 0.279387 | ||||||||
\(116\) | − 12.7651i | − 0.110044i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 200.737i | 1.70116i | ||||||||
\(119\) | −270.588 | −2.27385 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 99.7654 | 0.817749 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.717968 | −0.00579006 | ||||||||
\(125\) | 127.158 | 1.01726 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 162.553i | − 1.27994i | −0.768398 | − | 0.639972i | \(-0.778946\pi\) | ||||
0.768398 | − | 0.639972i | \(-0.221054\pi\) | |||||||
\(128\) | 113.655i | 0.887928i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 84.1244 | 0.647110 | ||||||||
\(131\) | 29.0893i | 0.222055i | 0.993817 | + | 0.111028i | \(0.0354142\pi\) | ||||
−0.993817 | + | 0.111028i | \(0.964586\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 49.3590 | 0.371120 | ||||||||
\(134\) | 31.0855i | 0.231981i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 162.100 | 1.19191 | ||||||||
\(137\) | −52.0666 | −0.380048 | −0.190024 | − | 0.981779i | \(-0.560857\pi\) | ||||
−0.190024 | + | 0.981779i | \(0.560857\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 163.913i | − 1.17923i | −0.807685 | − | 0.589614i | \(-0.799280\pi\) | ||||
0.807685 | − | 0.589614i | \(-0.200720\pi\) | |||||||
\(140\) | − 11.7869i | − 0.0841921i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 105.660i | 0.744084i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 152.265i | 1.05010i | ||||||||
\(146\) | −165.047 | −1.13046 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.502577 | 0.00339579 | ||||||||
\(149\) | 170.602i | 1.14498i | 0.819911 | + | 0.572491i | \(0.194023\pi\) | ||||
−0.819911 | + | 0.572491i | \(0.805977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 40.1528i | 0.265912i | 0.991122 | + | 0.132956i | \(0.0424470\pi\) | ||||
−0.991122 | + | 0.132956i | \(0.957553\pi\) | |||||||
\(152\) | −29.5692 | −0.194534 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.56406 | 0.0552520 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 97.9615 | 0.623959 | 0.311979 | − | 0.950089i | \(-0.399008\pi\) | ||||
0.311979 | + | 0.950089i | \(0.399008\pi\) | |||||||
\(158\) | −17.0718 | −0.108049 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.6789i | 0.0854932i | ||||||||
\(161\) | − 138.355i | − 0.859350i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −225.478 | −1.38330 | −0.691651 | − | 0.722232i | \(-0.743116\pi\) | ||||
−0.691651 | + | 0.722232i | \(0.743116\pi\) | |||||||
\(164\) | 16.6832i | 0.101727i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 108.210 | 0.651869 | ||||||||
\(167\) | 36.7768i | 0.220221i | 0.993919 | + | 0.110110i | \(0.0351204\pi\) | ||||
−0.993919 | + | 0.110110i | \(0.964880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16.6269 | −0.0983842 | ||||||||
\(170\) | −121.392 | −0.714072 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 0.785081i | − 0.00456443i | ||||||||
\(173\) | 242.371i | 1.40099i | 0.713659 | + | 0.700493i | \(0.247037\pi\) | ||||
−0.713659 | + | 0.700493i | \(0.752963\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 203.484i | − 1.16276i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 85.3160i | 0.479304i | ||||||||
\(179\) | −9.32051 | −0.0520699 | −0.0260349 | − | 0.999661i | \(-0.508288\pi\) | ||||
−0.0260349 | + | 0.999661i | \(0.508288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 231.186 | 1.27727 | 0.638635 | − | 0.769510i | \(-0.279499\pi\) | ||||
0.638635 | + | 0.769510i | \(0.279499\pi\) | |||||||
\(182\) | − 362.254i | − 1.99041i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 82.8838i | 0.450455i | ||||||||
\(185\) | −5.99485 | −0.0324046 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −16.8513 | −0.0896343 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 22.1436 | 0.116545 | ||||||||
\(191\) | −244.133 | −1.27818 | −0.639092 | − | 0.769130i | \(-0.720690\pi\) | ||||
−0.639092 | + | 0.769130i | \(0.720690\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.7888i | 0.0559004i | 0.999609 | + | 0.0279502i | \(0.00889799\pi\) | ||||
−0.999609 | + | 0.0279502i | \(0.991102\pi\) | |||||||
\(194\) | − 151.128i | − 0.779009i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −37.6269 | −0.191974 | ||||||||
\(197\) | − 109.967i | − 0.558208i | −0.960261 | − | 0.279104i | \(-0.909963\pi\) | ||||
0.960261 | − | 0.279104i | \(-0.0900373\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −28.5218 | −0.143326 | −0.0716629 | − | 0.997429i | \(-0.522831\pi\) | ||||
−0.0716629 | + | 0.997429i | \(0.522831\pi\) | |||||||
\(200\) | 121.900i | 0.609499i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 39.9474 | 0.197760 | ||||||||
\(203\) | 655.678 | 3.22994 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 199.001i | − 0.970735i | ||||||||
\(206\) | 237.229i | 1.15160i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 202.411i | 0.973130i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 172.101i | 0.815643i | 0.913062 | + | 0.407822i | \(0.133711\pi\) | ||||
−0.913062 | + | 0.407822i | \(0.866289\pi\) | |||||||
\(212\) | −3.80900 | −0.0179670 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −27.9090 | −0.130416 | ||||||||
\(215\) | 9.36461i | 0.0435563i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 36.8784i | − 0.169946i | ||||||||
\(218\) | 207.655 | 0.952546 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 267.862 | 1.21204 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −146.603 | −0.657410 | −0.328705 | − | 0.944433i | \(-0.606612\pi\) | ||||
−0.328705 | + | 0.944433i | \(0.606612\pi\) | |||||||
\(224\) | 58.9038 | 0.262963 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 246.861i | − 1.09230i | ||||||||
\(227\) | 68.7616i | 0.302914i | 0.988464 | + | 0.151457i | \(0.0483966\pi\) | ||||
−0.988464 | + | 0.151457i | \(0.951603\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −252.755 | −1.10373 | −0.551867 | − | 0.833932i | \(-0.686084\pi\) | ||||
−0.551867 | + | 0.833932i | \(0.686084\pi\) | |||||||
\(230\) | − 62.0694i | − 0.269867i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −392.794 | −1.69308 | ||||||||
\(233\) | − 282.853i | − 1.21396i | −0.794717 | − | 0.606980i | \(-0.792381\pi\) | ||||
0.794717 | − | 0.606980i | \(-0.207619\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 201.005 | 0.855341 | ||||||||
\(236\) | −27.8423 | −0.117976 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 522.737i | 2.19637i | ||||||||
\(239\) | − 360.434i | − 1.50809i | −0.656822 | − | 0.754046i | \(-0.728100\pi\) | ||||
0.656822 | − | 0.754046i | \(-0.271900\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 111.282i | 0.461752i | 0.972983 | + | 0.230876i | \(0.0741592\pi\) | ||||
−0.972983 | + | 0.230876i | \(0.925841\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.8375i | 0.0567112i | ||||||||
\(245\) | 448.822 | 1.83193 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −48.8616 | −0.197820 | ||||||||
\(248\) | 22.0925i | 0.0890828i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 245.650i | − 0.982599i | ||||||||
\(251\) | 366.406 | 1.45979 | 0.729893 | − | 0.683561i | \(-0.239570\pi\) | ||||
0.729893 | + | 0.683561i | \(0.239570\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −314.028 | −1.23633 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −51.2102 | −0.200040 | ||||||||
\(257\) | 47.5500 | 0.185019 | 0.0925097 | − | 0.995712i | \(-0.470511\pi\) | ||||
0.0925097 | + | 0.995712i | \(0.470511\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.8149i | 0.0996713i | ||||||||
\(260\) | 11.6681i | 0.0448773i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 56.1962 | 0.214489 | ||||||||
\(263\) | − 63.4637i | − 0.241307i | −0.992695 | − | 0.120654i | \(-0.961501\pi\) | ||||
0.992695 | − | 0.120654i | \(-0.0384990\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 45.4346 | 0.171451 | ||||||||
\(266\) | − 95.3542i | − 0.358475i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.31158 | −0.0160880 | ||||||||
\(269\) | −145.172 | −0.539672 | −0.269836 | − | 0.962906i | \(-0.586969\pi\) | ||||
−0.269836 | + | 0.962906i | \(0.586969\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 315.890i | 1.16565i | 0.812599 | + | 0.582823i | \(0.198052\pi\) | ||||
−0.812599 | + | 0.582823i | \(0.801948\pi\) | |||||||
\(272\) | − 292.081i | − 1.07383i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 100.585i | 0.367099i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 319.073i | 1.15189i | 0.817489 | + | 0.575944i | \(0.195365\pi\) | ||||
−0.817489 | + | 0.575944i | \(0.804635\pi\) | |||||||
\(278\) | −316.655 | −1.13905 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −362.694 | −1.29533 | ||||||||
\(281\) | 365.935i | 1.30226i | 0.758966 | + | 0.651130i | \(0.225705\pi\) | ||||
−0.758966 | + | 0.651130i | \(0.774295\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 231.978i | − 0.819711i | −0.912151 | − | 0.409855i | \(-0.865579\pi\) | ||||
0.912151 | − | 0.409855i | \(-0.134421\pi\) | |||||||
\(284\) | −14.6551 | −0.0516025 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −856.932 | −2.98583 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −97.5270 | −0.337464 | ||||||||
\(290\) | 294.153 | 1.01432 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 22.8922i | − 0.0783979i | ||||||||
\(293\) | − 151.128i | − 0.515794i | −0.966172 | − | 0.257897i | \(-0.916970\pi\) | ||||
0.966172 | − | 0.257897i | \(-0.0830296\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 332.109 | 1.12579 | ||||||||
\(296\) | − 15.4648i | − 0.0522458i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 329.578 | 1.10597 | ||||||||
\(299\) | 136.961i | 0.458064i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 40.3257 | 0.133972 | ||||||||
\(302\) | 77.5692 | 0.256852 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 53.2796i | 0.175262i | ||||||||
\(305\) | − 165.057i | − 0.541170i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 396.582i | − 1.29180i | −0.763423 | − | 0.645899i | \(-0.776483\pi\) | ||||
0.763423 | − | 0.645899i | \(-0.223517\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 16.5445i | − 0.0533694i | ||||||||
\(311\) | 219.951 | 0.707239 | 0.353619 | − | 0.935389i | \(-0.384951\pi\) | ||||
0.353619 | + | 0.935389i | \(0.384951\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.6410 | −0.101090 | −0.0505448 | − | 0.998722i | \(-0.516096\pi\) | ||||
−0.0505448 | + | 0.998722i | \(0.516096\pi\) | |||||||
\(314\) | − 189.247i | − 0.602698i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − 2.36787i | − 0.00749326i | ||||||||
\(317\) | 307.990 | 0.971576 | 0.485788 | − | 0.874077i | \(-0.338533\pi\) | ||||
0.485788 | + | 0.874077i | \(0.338533\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 216.359 | 0.676122 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −267.282 | −0.830068 | ||||||||
\(323\) | 70.5077 | 0.218290 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 201.433i | 0.619793i | ||||||||
\(326\) | 435.590i | 1.33617i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 513.358 | 1.56511 | ||||||||
\(329\) | − 865.564i | − 2.63089i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −152.515 | −0.460771 | −0.230386 | − | 0.973099i | \(-0.573999\pi\) | ||||
−0.230386 | + | 0.973099i | \(0.573999\pi\) | |||||||
\(332\) | 15.0088i | 0.0452073i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 71.0474 | 0.212717 | ||||||||
\(335\) | 51.4294 | 0.153521 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 404.069i | − 1.19902i | −0.800368 | − | 0.599509i | \(-0.795363\pi\) | ||||
0.800368 | − | 0.599509i | \(-0.204637\pi\) | |||||||
\(338\) | 32.1208i | 0.0950319i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 16.8372i | − 0.0495212i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1258.31i | − 3.66854i | ||||||||
\(344\) | −24.1577 | −0.0702258 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 468.224 | 1.35325 | ||||||||
\(347\) | − 66.6240i | − 0.192000i | −0.995381 | − | 0.0960000i | \(-0.969395\pi\) | ||||
0.995381 | − | 0.0960000i | \(-0.0306049\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.5147i | 0.104627i | 0.998631 | + | 0.0523134i | \(0.0166595\pi\) | ||||
−0.998631 | + | 0.0523134i | \(0.983341\pi\) | |||||||
\(350\) | −393.100 | −1.12314 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 329.196 | 0.932567 | 0.466284 | − | 0.884635i | \(-0.345593\pi\) | ||||
0.466284 | + | 0.884635i | \(0.345593\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 174.809 | 0.492420 | ||||||||
\(356\) | −11.8334 | −0.0332399 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.0058i | 0.0502956i | ||||||||
\(359\) | − 618.017i | − 1.72149i | −0.509032 | − | 0.860747i | \(-0.669997\pi\) | ||||
0.509032 | − | 0.860747i | \(-0.330003\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 348.138 | 0.964372 | ||||||||
\(362\) | − 446.617i | − 1.23375i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 50.2449 | 0.138036 | ||||||||
\(365\) | 273.063i | 0.748117i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −180.809 | −0.492668 | −0.246334 | − | 0.969185i | \(-0.579226\pi\) | ||||
−0.246334 | + | 0.969185i | \(0.579226\pi\) | |||||||
\(368\) | 149.345 | 0.405829 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.5812i | 0.0313004i | ||||||||
\(371\) | − 195.649i | − 0.527356i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 343.842i | − 0.921829i | −0.887444 | − | 0.460915i | \(-0.847521\pi\) | ||||
0.887444 | − | 0.460915i | \(-0.152479\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 518.529i | 1.37907i | ||||||||
\(377\) | −649.070 | −1.72167 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −353.611 | −0.933012 | −0.466506 | − | 0.884518i | \(-0.654487\pi\) | ||||
−0.466506 | + | 0.884518i | \(0.654487\pi\) | |||||||
\(380\) | 3.07133i | 0.00808245i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 471.629i | 1.23463i | ||||||||
\(383\) | 158.070 | 0.412716 | 0.206358 | − | 0.978477i | \(-0.433839\pi\) | ||||
0.206358 | + | 0.978477i | \(0.433839\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.8423 | 0.0539957 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 20.9615 | 0.0540245 | ||||||||
\(389\) | 407.242 | 1.04690 | 0.523448 | − | 0.852058i | \(-0.324646\pi\) | ||||
0.523448 | + | 0.852058i | \(0.324646\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 197.636i | − 0.505463i | ||||||||
\(392\) | 1157.82i | 2.95361i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −212.440 | −0.539187 | ||||||||
\(395\) | 28.2444i | 0.0715049i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.07180 | 0.0102564 | 0.00512821 | − | 0.999987i | \(-0.498368\pi\) | ||||
0.00512821 | + | 0.999987i | \(0.498368\pi\) | |||||||
\(398\) | 55.0999i | 0.138442i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 219.646 | 0.549115 | ||||||||
\(401\) | −433.862 | −1.08195 | −0.540975 | − | 0.841039i | \(-0.681944\pi\) | ||||
−0.540975 | + | 0.841039i | \(0.681944\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.5067i | 0.0905874i | ||||||||
\(404\) | 5.54074i | 0.0137147i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − 1266.67i | − 3.11988i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 105.088i | 0.256938i | 0.991713 | + | 0.128469i | \(0.0410064\pi\) | ||||
−0.991713 | + | 0.128469i | \(0.958994\pi\) | |||||||
\(410\) | −384.440 | −0.937658 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −32.9038 | −0.0798636 | ||||||||
\(413\) | − 1430.12i | − 3.46276i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 179.028i | − 0.431394i | ||||||||
\(416\) | −58.3102 | −0.140169 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −72.6757 | −0.173450 | −0.0867252 | − | 0.996232i | \(-0.527640\pi\) | ||||
−0.0867252 | + | 0.996232i | \(0.527640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −343.172 | −0.815135 | −0.407567 | − | 0.913175i | \(-0.633623\pi\) | ||||
−0.407567 | + | 0.913175i | \(0.633623\pi\) | |||||||
\(422\) | 332.473 | 0.787851 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 117.207i | 0.276430i | ||||||||
\(425\) | − 290.670i | − 0.683929i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −710.764 | −1.66455 | ||||||||
\(428\) | − 3.87099i | − 0.00904438i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.0910 | 0.0420722 | ||||||||
\(431\) | − 409.946i | − 0.951151i | −0.879675 | − | 0.475575i | \(-0.842240\pi\) | ||||
0.879675 | − | 0.475575i | \(-0.157760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −573.158 | −1.32369 | −0.661845 | − | 0.749641i | \(-0.730226\pi\) | ||||
−0.661845 | + | 0.749641i | \(0.730226\pi\) | |||||||
\(434\) | −71.2436 | −0.164156 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 28.8019i | 0.0660594i | ||||||||
\(437\) | 36.0515i | 0.0824977i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 146.143i | − 0.332899i | −0.986050 | − | 0.166449i | \(-0.946770\pi\) | ||||
0.986050 | − | 0.166449i | \(-0.0532302\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 517.469i | − 1.17074i | ||||||||
\(443\) | −470.788 | −1.06273 | −0.531364 | − | 0.847144i | \(-0.678320\pi\) | ||||
−0.531364 | + | 0.847144i | \(0.678320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 141.151 | 0.317194 | ||||||||
\(446\) | 283.214i | 0.635010i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 931.680i | − 2.07964i | ||||||||
\(449\) | 271.722 | 0.605171 | 0.302585 | − | 0.953122i | \(-0.402150\pi\) | ||||
0.302585 | + | 0.953122i | \(0.402150\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 34.2398 | 0.0757517 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 132.837 | 0.292593 | ||||||||
\(455\) | −599.332 | −1.31721 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 731.035i | 1.59964i | 0.600241 | + | 0.799819i | \(0.295071\pi\) | ||||
−0.600241 | + | 0.799819i | \(0.704929\pi\) | |||||||
\(458\) | 488.285i | 1.06613i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.60908 | 0.0187154 | ||||||||
\(461\) | 271.180i | 0.588243i | 0.955768 | + | 0.294121i | \(0.0950270\pi\) | ||||
−0.955768 | + | 0.294121i | \(0.904973\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −755.381 | −1.63149 | −0.815746 | − | 0.578411i | \(-0.803673\pi\) | ||||
−0.815746 | + | 0.578411i | \(0.803673\pi\) | |||||||
\(464\) | 707.758i | 1.52534i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −546.429 | −1.17260 | ||||||||
\(467\) | −173.919 | −0.372418 | −0.186209 | − | 0.982510i | \(-0.559620\pi\) | ||||
−0.186209 | + | 0.982510i | \(0.559620\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 221.464i | − 0.472205i | ||||||||
\(470\) | − 388.312i | − 0.826196i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 856.734i | 1.81511i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 53.0221i | 0.111625i | ||||||||
\(476\) | −72.5040 | −0.152319 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −696.305 | −1.45671 | ||||||||
\(479\) | 458.787i | 0.957802i | 0.877869 | + | 0.478901i | \(0.158965\pi\) | ||||
−0.877869 | + | 0.478901i | \(0.841035\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 25.5547i | − 0.0531283i | ||||||||
\(482\) | 214.981 | 0.446018 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −250.033 | −0.515533 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 483.734 | 0.993295 | 0.496647 | − | 0.867952i | \(-0.334564\pi\) | ||||
0.496647 | + | 0.867952i | \(0.334564\pi\) | |||||||
\(488\) | 425.794 | 0.872528 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − 867.057i | − 1.76950i | ||||||||
\(491\) | 676.366i | 1.37753i | 0.724986 | + | 0.688763i | \(0.241846\pi\) | ||||
−0.724986 | + | 0.688763i | \(0.758154\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 936.615 | 1.89983 | ||||||||
\(494\) | 94.3933i | 0.191080i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 39.8076 | 0.0802573 | ||||||||
\(497\) | − 752.759i | − 1.51460i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 851.486 | 1.70638 | 0.853192 | − | 0.521597i | \(-0.174663\pi\) | ||||
0.853192 | + | 0.521597i | \(0.174663\pi\) | |||||||
\(500\) | 34.0718 | 0.0681436 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 707.843i | − 1.41005i | ||||||||
\(503\) | 224.969i | 0.447254i | 0.974675 | + | 0.223627i | \(0.0717898\pi\) | ||||
−0.974675 | + | 0.223627i | \(0.928210\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 66.0911i | − 0.130873i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 43.5559i | − 0.0857400i | ||||||||
\(509\) | 845.520 | 1.66114 | 0.830570 | − | 0.556914i | \(-0.188015\pi\) | ||||
0.830570 | + | 0.556914i | \(0.188015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1175.86 | 2.30109 | ||||||||
\(512\) | 553.549i | 1.08115i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 91.8595i | − 0.178715i | ||||||||
\(515\) | 392.483 | 0.762104 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 49.8705 | 0.0962751 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 359.038 | 0.690459 | ||||||||
\(521\) | −272.841 | −0.523687 | −0.261844 | − | 0.965110i | \(-0.584330\pi\) | ||||
−0.261844 | + | 0.965110i | \(0.584330\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 371.713i | 0.710733i | 0.934727 | + | 0.355366i | \(0.115644\pi\) | ||||
−0.934727 | + | 0.355366i | \(0.884356\pi\) | |||||||
\(524\) | 7.79445i | 0.0148749i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −122.603 | −0.233085 | ||||||||
\(527\) | − 52.6796i | − 0.0999613i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −427.946 | −0.808972 | ||||||||
\(530\) | − 87.7728i | − 0.165609i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.2257 | 0.0248603 | ||||||||
\(533\) | 848.296 | 1.59155 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 46.1740i | 0.0863065i | ||||||||
\(536\) | 132.671i | 0.247521i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 280.450i | 0.521283i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 202.644i | − 0.374573i | −0.982305 | − | 0.187287i | \(-0.940031\pi\) | ||||
0.982305 | − | 0.187287i | \(-0.0599693\pi\) | |||||||
\(542\) | 610.252 | 1.12593 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 84.1422 | 0.154673 | ||||||||
\(545\) | − 343.555i | − 0.630376i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 835.947i | 1.52824i | 0.645075 | + | 0.764120i | \(0.276826\pi\) | ||||
−0.645075 | + | 0.764120i | \(0.723174\pi\) | |||||||
\(548\) | −13.9512 | −0.0254584 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −170.851 | −0.310075 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 121.626 | 0.219938 | ||||||||
\(554\) | 616.401 | 1.11264 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 43.9203i | − 0.0789933i | ||||||||
\(557\) | − 840.516i | − 1.50901i | −0.656297 | − | 0.754503i | \(-0.727878\pi\) | ||||
0.656297 | − | 0.754503i | \(-0.272122\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −39.9193 | −0.0714119 | ||||||||
\(560\) | 653.523i | 1.16700i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 706.932 | 1.25789 | ||||||||
\(563\) | 519.631i | 0.922968i | 0.887149 | + | 0.461484i | \(0.152683\pi\) | ||||
−0.887149 | + | 0.461484i | \(0.847317\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −408.419 | −0.722866 | ||||||||
\(566\) | −448.147 | −0.791780 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 450.951i | 0.793928i | ||||||||
\(569\) | − 46.7089i | − 0.0820894i | −0.999157 | − | 0.0410447i | \(-0.986931\pi\) | ||||
0.999157 | − | 0.0410447i | \(-0.0130686\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 318.501i | 0.557795i | 0.960321 | + | 0.278897i | \(0.0899689\pi\) | ||||
−0.960321 | + | 0.278897i | \(0.910031\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1655.47i | 2.88409i | ||||||||
\(575\) | 148.623 | 0.258475 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −219.963 | −0.381218 | −0.190609 | − | 0.981666i | \(-0.561046\pi\) | ||||
−0.190609 | + | 0.981666i | \(0.561046\pi\) | |||||||
\(578\) | 188.408i | 0.325965i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 40.7992i | 0.0703434i | ||||||||
\(581\) | −770.928 | −1.32690 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −704.414 | −1.20619 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −291.956 | −0.498219 | ||||||||
\(587\) | −147.674 | −0.251575 | −0.125787 | − | 0.992057i | \(-0.540146\pi\) | ||||
−0.125787 | + | 0.992057i | \(0.540146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.60947i | 0.0163149i | ||||||||
\(590\) | − 641.585i | − 1.08743i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −27.8653 | −0.0470698 | ||||||||
\(593\) | 446.800i | 0.753457i | 0.926324 | + | 0.376728i | \(0.122951\pi\) | ||||
−0.926324 | + | 0.376728i | \(0.877049\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 864.842 | 1.45352 | ||||||||
\(596\) | 45.7127i | 0.0766992i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 264.588 | 0.442456 | ||||||||
\(599\) | 353.205 | 0.589658 | 0.294829 | − | 0.955550i | \(-0.404737\pi\) | ||||
0.294829 | + | 0.955550i | \(0.404737\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1152.51i | 1.91765i | 0.284005 | + | 0.958823i | \(0.408337\pi\) | ||||
−0.284005 | + | 0.958823i | \(0.591663\pi\) | |||||||
\(602\) | − 77.9032i | − 0.129407i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.7589i | 0.0178128i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 249.462i | 0.410975i | 0.978660 | + | 0.205487i | \(0.0658780\pi\) | ||||
−0.978660 | + | 0.205487i | \(0.934122\pi\) | |||||||
\(608\) | −15.3487 | −0.0252445 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −318.865 | −0.522730 | ||||||||
\(611\) | 856.841i | 1.40236i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 320.244i | 0.522421i | 0.965282 | + | 0.261210i | \(0.0841217\pi\) | ||||
−0.965282 | + | 0.261210i | \(0.915878\pi\) | |||||||
\(614\) | −766.137 | −1.24778 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1036.56 | 1.67999 | 0.839997 | − | 0.542591i | \(-0.182557\pi\) | ||||
0.839997 | + | 0.542591i | \(0.182557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −701.542 | −1.13335 | −0.566674 | − | 0.823942i | \(-0.691770\pi\) | ||||
−0.566674 | + | 0.823942i | \(0.691770\pi\) | |||||||
\(620\) | 2.29473 | 0.00370118 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 424.913i | − 0.683140i | ||||||||
\(623\) | − 607.822i | − 0.975637i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −36.8001 | −0.0588801 | ||||||||
\(626\) | 61.1257i | 0.0976450i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 26.2487 | 0.0417973 | ||||||||
\(629\) | 36.8757i | 0.0586259i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1199.17 | 1.90043 | 0.950214 | − | 0.311597i | \(-0.100864\pi\) | ||||
0.950214 | + | 0.311597i | \(0.100864\pi\) | |||||||
\(632\) | −72.8616 | −0.115287 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − 594.990i | − 0.938471i | ||||||||
\(635\) | 519.544i | 0.818179i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1913.23i | 3.00350i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 363.258i | − 0.567590i | ||||||||
\(641\) | 739.327 | 1.15340 | 0.576698 | − | 0.816958i | \(-0.304341\pi\) | ||||
0.576698 | + | 0.816958i | \(0.304341\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 410.087 | 0.637772 | 0.318886 | − | 0.947793i | \(-0.396691\pi\) | ||||
0.318886 | + | 0.947793i | \(0.396691\pi\) | |||||||
\(644\) | − 37.0722i | − 0.0575655i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − 136.210i | − 0.210852i | ||||||||
\(647\) | 352.115 | 0.544228 | 0.272114 | − | 0.962265i | \(-0.412277\pi\) | ||||
0.272114 | + | 0.962265i | \(0.412277\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 389.138 | 0.598675 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −60.4167 | −0.0926636 | ||||||||
\(653\) | −864.574 | −1.32400 | −0.662002 | − | 0.749502i | \(-0.730293\pi\) | ||||
−0.662002 | + | 0.749502i | \(0.730293\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 92.9737i | − 0.141945i | ||||||||
\(656\) | − 924.998i | − 1.41006i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1672.14 | −2.54125 | ||||||||
\(659\) | − 985.279i | − 1.49511i | −0.664199 | − | 0.747556i | \(-0.731227\pi\) | ||||
0.664199 | − | 0.747556i | \(-0.268773\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −529.651 | −0.801288 | −0.400644 | − | 0.916234i | \(-0.631214\pi\) | ||||
−0.400644 | + | 0.916234i | \(0.631214\pi\) | |||||||
\(662\) | 294.637i | 0.445071i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 461.836 | 0.695536 | ||||||||
\(665\) | −157.759 | −0.237231 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 478.903i | 0.717996i | ||||||||
\(668\) | 9.85433i | 0.0147520i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 99.3540i | − 0.148290i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 535.126i | 0.795135i | 0.917573 | + | 0.397567i | \(0.130145\pi\) | ||||
−0.917573 | + | 0.397567i | \(0.869855\pi\) | |||||||
\(674\) | −780.601 | −1.15816 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.45517 | −0.00659049 | ||||||||
\(677\) | − 740.764i | − 1.09419i | −0.837072 | − | 0.547093i | \(-0.815734\pi\) | ||||
0.837072 | − | 0.547093i | \(-0.184266\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1076.69i | 1.58570i | ||||||||
\(680\) | −518.096 | −0.761906 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 376.722 | 0.551569 | 0.275785 | − | 0.961219i | \(-0.411062\pi\) | ||||
0.275785 | + | 0.961219i | \(0.411062\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 166.413 | 0.242939 | ||||||||
\(686\) | −2430.87 | −3.54354 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 43.5287i | 0.0632685i | ||||||||
\(689\) | 193.678i | 0.281099i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 336.404 | 0.486836 | 0.243418 | − | 0.969921i | \(-0.421731\pi\) | ||||
0.243418 | + | 0.969921i | \(0.421731\pi\) | |||||||
\(692\) | 64.9430i | 0.0938483i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −128.708 | −0.185458 | ||||||||
\(695\) | 523.890i | 0.753799i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1224.10 | −1.75624 | ||||||||
\(698\) | 70.5411 | 0.101062 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − 54.5232i | − 0.0778903i | ||||||||
\(701\) | 842.500i | 1.20185i | 0.799304 | + | 0.600927i | \(0.205202\pi\) | ||||
−0.799304 | + | 0.600927i | \(0.794798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 6.72663i | − 0.00956846i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 635.958i | − 0.900791i | ||||||||
\(707\) | −284.600 | −0.402546 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 318.882 | 0.449763 | 0.224882 | − | 0.974386i | \(-0.427800\pi\) | ||||
0.224882 | + | 0.974386i | \(0.427800\pi\) | |||||||
\(710\) | − 337.705i | − 0.475641i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 364.125i | 0.511411i | ||||||||
\(713\) | 26.9358 | 0.0377781 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.49742 | −0.00348802 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1193.92 | −1.66284 | ||||||||
\(719\) | 548.788 | 0.763266 | 0.381633 | − | 0.924314i | \(-0.375362\pi\) | ||||
0.381633 | + | 0.924314i | \(0.375362\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 1690.10i | − 2.34411i | ||||||||
\(722\) | − 672.552i | − 0.931512i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 61.9461 | 0.0855609 | ||||||||
\(725\) | 704.338i | 0.971501i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 897.699 | 1.23480 | 0.617399 | − | 0.786650i | \(-0.288186\pi\) | ||||
0.617399 | + | 0.786650i | \(0.288186\pi\) | |||||||
\(728\) | − 1546.08i | − 2.12374i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 527.517 | 0.722626 | ||||||||
\(731\) | 57.6039 | 0.0788015 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 198.000i | − 0.270123i | −0.990837 | − | 0.135061i | \(-0.956877\pi\) | ||||
0.990837 | − | 0.135061i | \(-0.0431231\pi\) | |||||||
\(734\) | 349.296i | 0.475880i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 43.0230i | 0.0584552i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 560.286i | − 0.758168i | −0.925362 | − | 0.379084i | \(-0.876239\pi\) | ||||
0.925362 | − | 0.379084i | \(-0.123761\pi\) | |||||||
\(740\) | −1.60631 | −0.00217069 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −377.965 | −0.509387 | ||||||||
\(743\) | 1007.49i | 1.35598i | 0.735071 | + | 0.677990i | \(0.237149\pi\) | ||||
−0.735071 | + | 0.677990i | \(0.762851\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 545.271i | − 0.731907i | ||||||||
\(746\) | −664.252 | −0.890419 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 198.833 | 0.265465 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1181.32 | 1.57300 | 0.786501 | − | 0.617589i | \(-0.211891\pi\) | ||||
0.786501 | + | 0.617589i | \(0.211891\pi\) | |||||||
\(752\) | 934.315 | 1.24244 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1253.91i | 1.66301i | ||||||||
\(755\) | − 128.334i | − 0.169979i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1244.66 | −1.64420 | −0.822101 | − | 0.569341i | \(-0.807198\pi\) | ||||
−0.822101 | + | 0.569341i | \(0.807198\pi\) | |||||||
\(758\) | 683.125i | 0.901220i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 94.5077 | 0.124352 | ||||||||
\(761\) | − 1191.43i | − 1.56562i | −0.622263 | − | 0.782808i | \(-0.713787\pi\) | ||||
0.622263 | − | 0.782808i | \(-0.286213\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1479.41 | −1.93894 | ||||||||
\(764\) | −65.4153 | −0.0856221 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 305.369i | − 0.398654i | ||||||||
\(767\) | 1415.71i | 1.84577i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 823.778i | − 1.07123i | −0.844461 | − | 0.535617i | \(-0.820079\pi\) | ||||
0.844461 | − | 0.535617i | \(-0.179921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.89085i | 0.00374462i | ||||||||
\(773\) | 1439.82 | 1.86264 | 0.931318 | − | 0.364207i | \(-0.118660\pi\) | ||||
0.931318 | + | 0.364207i | \(0.118660\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.6152 | 0.0511164 | ||||||||
\(776\) | − 645.006i | − 0.831193i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 786.731i | − 1.01122i | ||||||||
\(779\) | 223.292 | 0.286640 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −381.804 | −0.488240 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2086.22 | 2.66100 | ||||||||
\(785\) | −313.100 | −0.398853 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 638.284i | 0.811034i | 0.914088 | + | 0.405517i | \(0.132908\pi\) | ||||
−0.914088 | + | 0.405517i | \(0.867092\pi\) | |||||||
\(788\) | − 29.4655i | − 0.0373928i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 54.5641 | 0.0690684 | ||||||||
\(791\) | 1758.72i | 2.22342i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 703.601 | 0.887265 | ||||||||
\(794\) | − 7.86611i | − 0.00990694i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.64240 | −0.00960100 | ||||||||
\(797\) | 255.590 | 0.320690 | 0.160345 | − | 0.987061i | \(-0.448739\pi\) | ||||
0.160345 | + | 0.987061i | \(0.448739\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1236.43i | − 1.54747i | ||||||||
\(800\) | 63.2753i | 0.0790941i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 838.156i | 1.04508i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 442.205i | 0.549323i | ||||||||
\(806\) | 70.5256 | 0.0875007 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 170.494 | 0.211007 | ||||||||
\(809\) | 356.384i | 0.440524i | 0.975441 | + | 0.220262i | \(0.0706912\pi\) | ||||
−0.975441 | + | 0.220262i | \(0.929309\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 166.748i | 0.205608i | 0.994702 | + | 0.102804i | \(0.0327815\pi\) | ||||
−0.994702 | + | 0.102804i | \(0.967218\pi\) | |||||||
\(812\) | 175.688 | 0.216365 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 720.663 | 0.884249 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.5077 | −0.0128614 | ||||||||
\(818\) | 203.014 | 0.248183 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − 53.3221i | − 0.0650269i | ||||||||
\(821\) | 1028.61i | 1.25287i | 0.779472 | + | 0.626437i | \(0.215487\pi\) | ||||
−0.779472 | + | 0.626437i | \(0.784513\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −445.570 | −0.541398 | −0.270699 | − | 0.962664i | \(-0.587255\pi\) | ||||
−0.270699 | + | 0.962664i | \(0.587255\pi\) | |||||||
\(824\) | 1012.48i | 1.22874i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2762.78 | −3.34477 | ||||||||
\(827\) | 954.877i | 1.15463i | 0.816522 | + | 0.577314i | \(0.195899\pi\) | ||||
−0.816522 | + | 0.577314i | \(0.804101\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1098.95 | 1.32563 | 0.662817 | − | 0.748781i | \(-0.269361\pi\) | ||||
0.662817 | + | 0.748781i | \(0.269361\pi\) | |||||||
\(830\) | −345.856 | −0.416694 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 922.291i | 1.10852i | ||||||||
\(833\) | − 2760.81i | − 3.31430i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 117.544i | − 0.140772i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 140.399i | 0.167540i | ||||||||
\(839\) | −952.974 | −1.13585 | −0.567923 | − | 0.823082i | \(-0.692253\pi\) | ||||
−0.567923 | + | 0.823082i | \(0.692253\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1428.57 | −1.69865 | ||||||||
\(842\) | 662.957i | 0.787360i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 46.1142i | 0.0546377i | ||||||||
\(845\) | 53.1422 | 0.0628902 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 211.190 | 0.249044 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −561.531 | −0.660624 | ||||||||
\(851\) | −18.8550 | −0.0221563 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 376.647i | − 0.441556i | −0.975324 | − | 0.220778i | \(-0.929140\pi\) | ||||
0.975324 | − | 0.220778i | \(-0.0708597\pi\) | |||||||
\(854\) | 1373.09i | 1.60783i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −119.114 | −0.139152 | ||||||||
\(857\) | − 552.323i | − 0.644484i | −0.946657 | − | 0.322242i | \(-0.895563\pi\) | ||||
0.946657 | − | 0.322242i | \(-0.104437\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1556.85 | 1.81240 | 0.906200 | − | 0.422849i | \(-0.138970\pi\) | ||||
0.906200 | + | 0.422849i | \(0.138970\pi\) | |||||||
\(860\) | 2.50924i | 0.00291772i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −791.955 | −0.918741 | ||||||||
\(863\) | −201.173 | −0.233109 | −0.116555 | − | 0.993184i | \(-0.537185\pi\) | ||||
−0.116555 | + | 0.993184i | \(0.537185\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 774.654i | − 0.895554i | ||||||||
\(866\) | 1107.26i | 1.27859i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 9.88153i | − 0.0113843i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 219.232i | 0.251702i | ||||||||
\(872\) | 886.261 | 1.01635 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 69.6462 | 0.0796867 | ||||||||
\(875\) | 1750.10i | 2.00011i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 696.933i | − 0.794678i | −0.917672 | − | 0.397339i | \(-0.869934\pi\) | ||||
0.917672 | − | 0.397339i | \(-0.130066\pi\) | |||||||
\(878\) | −282.326 | −0.321555 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 159.841 | 0.181431 | 0.0907156 | − | 0.995877i | \(-0.471085\pi\) | ||||
0.0907156 | + | 0.995877i | \(0.471085\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −185.864 | −0.210491 | −0.105246 | − | 0.994446i | \(-0.533563\pi\) | ||||
−0.105246 | + | 0.994446i | \(0.533563\pi\) | |||||||
\(884\) | 71.7733 | 0.0811915 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 909.493i | 1.02652i | ||||||||
\(887\) | 1061.32i | 1.19652i | 0.801301 | + | 0.598262i | \(0.204142\pi\) | ||||
−0.801301 | + | 0.598262i | \(0.795858\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2237.25 | 2.51659 | ||||||||
\(890\) | − 272.683i | − 0.306385i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −39.2820 | −0.0440382 | ||||||||
\(893\) | 225.542i | 0.252566i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.7898 | 0.0332847 | ||||||||
\(896\) | −1564.25 | −1.74582 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 524.926i | − 0.584550i | ||||||||
\(899\) | 127.651i | 0.141992i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 279.479i | − 0.310187i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 1053.59i | − 1.16548i | ||||||||
\(905\) | −738.905 | −0.816470 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −974.991 | −1.07496 | −0.537481 | − | 0.843276i | \(-0.680624\pi\) | ||||
−0.537481 | + | 0.843276i | \(0.680624\pi\) | |||||||
\(908\) | 18.4246i | 0.0202914i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1157.82i | 1.27233i | ||||||||
\(911\) | −1106.62 | −1.21473 | −0.607366 | − | 0.794422i | \(-0.707774\pi\) | ||||
−0.607366 | + | 0.794422i | \(0.707774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1412.25 | 1.54513 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −67.7255 | −0.0739362 | ||||||||
\(917\) | −400.361 | −0.436599 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 865.081i | 0.941329i | 0.882312 | + | 0.470665i | \(0.155986\pi\) | ||||
−0.882312 | + | 0.470665i | \(0.844014\pi\) | |||||||
\(920\) | − 264.909i | − 0.287945i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 523.879 | 0.568199 | ||||||||
\(923\) | 745.172i | 0.807337i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.7307 | −0.0299791 | ||||||||
\(926\) | 1459.28i | 1.57590i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −203.890 | −0.219709 | ||||||||
\(929\) | −1520.93 | −1.63717 | −0.818583 | − | 0.574388i | \(-0.805240\pi\) | ||||
−0.818583 | + | 0.574388i | \(0.805240\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 503.609i | 0.540933i | ||||||||
\(932\) | − 75.7901i | − 0.0813199i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 335.986i | 0.359728i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 835.522i | − 0.891699i | −0.895108 | − | 0.445849i | \(-0.852902\pi\) | ||||
0.895108 | − | 0.445849i | \(-0.147098\pi\) | |||||||
\(938\) | −427.836 | −0.456115 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 53.8592 | 0.0572970 | ||||||||
\(941\) | − 860.626i | − 0.914586i | −0.889316 | − | 0.457293i | \(-0.848819\pi\) | ||||
0.889316 | − | 0.457293i | \(-0.151181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 625.898i | − 0.663731i | ||||||||
\(944\) | 1543.71 | 1.63529 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1268.54 | −1.33954 | −0.669768 | − | 0.742571i | \(-0.733606\pi\) | ||||
−0.669768 | + | 0.742571i | \(0.733606\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1164.01 | −1.22656 | ||||||||
\(950\) | 102.431 | 0.107822 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2231.01i | 2.34350i | ||||||||
\(953\) | 290.553i | 0.304882i | 0.988313 | + | 0.152441i | \(0.0487135\pi\) | ||||
−0.988313 | + | 0.152441i | \(0.951287\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 780.287 | 0.817055 | ||||||||
\(956\) | − 96.5780i | − 0.101023i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 886.309 | 0.925166 | ||||||||
\(959\) | − 716.604i | − 0.747240i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −953.820 | −0.992529 | ||||||||
\(962\) | −49.3679 | −0.0513180 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 29.8180i | 0.0309315i | ||||||||
\(965\) | − 34.4826i | − 0.0357333i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1253.94i | − 1.29673i | −0.761330 | − | 0.648365i | \(-0.775453\pi\) | ||||
0.761330 | − | 0.648365i | \(-0.224547\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 483.027i | 0.497966i | ||||||||
\(971\) | −516.837 | −0.532273 | −0.266137 | − | 0.963935i | \(-0.585747\pi\) | ||||
−0.266137 | + | 0.963935i | \(0.585747\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2255.96 | 2.31856 | ||||||||
\(974\) | − 934.503i | − 0.959449i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 767.220i | − 0.786086i | ||||||||
\(977\) | −106.061 | −0.108558 | −0.0542792 | − | 0.998526i | \(-0.517286\pi\) | ||||
−0.0542792 | + | 0.998526i | \(0.517286\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 120.261 | 0.122716 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1306.64 | 1.33059 | ||||||||
\(983\) | 1625.88 | 1.65400 | 0.826998 | − | 0.562204i | \(-0.190046\pi\) | ||||
0.826998 | + | 0.562204i | \(0.190046\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 351.471i | 0.356823i | ||||||||
\(986\) | − 1809.40i | − 1.83509i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.0924 | −0.0132514 | ||||||||
\(989\) | 29.4536i | 0.0297812i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −458.638 | −0.462803 | −0.231402 | − | 0.972858i | \(-0.574331\pi\) | ||||
−0.231402 | + | 0.972858i | \(0.574331\pi\) | |||||||
\(992\) | 11.4677i | 0.0115602i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1454.22 | −1.46300 | ||||||||
\(995\) | 91.1601 | 0.0916182 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 140.671i | − 0.141095i | −0.997508 | − | 0.0705474i | \(-0.977525\pi\) | ||||
0.997508 | − | 0.0705474i | \(-0.0224746\pi\) | |||||||
\(998\) | − 1644.94i | − 1.64824i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1089.3.c.g.604.1 | 4 | ||
3.2 | odd | 2 | 363.3.c.c.241.4 | yes | 4 | ||
11.10 | odd | 2 | inner | 1089.3.c.g.604.4 | 4 | ||
33.2 | even | 10 | 363.3.g.b.40.1 | 16 | |||
33.5 | odd | 10 | 363.3.g.b.118.1 | 16 | |||
33.8 | even | 10 | 363.3.g.b.112.1 | 16 | |||
33.14 | odd | 10 | 363.3.g.b.112.4 | 16 | |||
33.17 | even | 10 | 363.3.g.b.118.4 | 16 | |||
33.20 | odd | 10 | 363.3.g.b.40.4 | 16 | |||
33.26 | odd | 10 | 363.3.g.b.94.1 | 16 | |||
33.29 | even | 10 | 363.3.g.b.94.4 | 16 | |||
33.32 | even | 2 | 363.3.c.c.241.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.3.c.c.241.1 | ✓ | 4 | 33.32 | even | 2 | ||
363.3.c.c.241.4 | yes | 4 | 3.2 | odd | 2 | ||
363.3.g.b.40.1 | 16 | 33.2 | even | 10 | |||
363.3.g.b.40.4 | 16 | 33.20 | odd | 10 | |||
363.3.g.b.94.1 | 16 | 33.26 | odd | 10 | |||
363.3.g.b.94.4 | 16 | 33.29 | even | 10 | |||
363.3.g.b.112.1 | 16 | 33.8 | even | 10 | |||
363.3.g.b.112.4 | 16 | 33.14 | odd | 10 | |||
363.3.g.b.118.1 | 16 | 33.5 | odd | 10 | |||
363.3.g.b.118.4 | 16 | 33.17 | even | 10 | |||
1089.3.c.g.604.1 | 4 | 1.1 | even | 1 | trivial | ||
1089.3.c.g.604.4 | 4 | 11.10 | odd | 2 | inner |