Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,4,Mod(1,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.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: | \(94.4030560092\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1600.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.00000 | 0.769800 | 0.384900 | − | 0.922958i | \(-0.374236\pi\) | ||||
0.384900 | + | 0.922958i | \(0.374236\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.0000 | −0.863919 | −0.431959 | − | 0.901893i | \(-0.642178\pi\) | ||||
−0.431959 | + | 0.901893i | \(0.642178\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.0000 | −0.407407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −36.0000 | −0.986764 | −0.493382 | − | 0.869813i | \(-0.664240\pi\) | ||||
−0.493382 | + | 0.869813i | \(0.664240\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −42.0000 | −0.896054 | −0.448027 | − | 0.894020i | \(-0.647873\pi\) | ||||
−0.448027 | + | 0.894020i | \(0.647873\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 110.000 | 1.56935 | 0.784674 | − | 0.619909i | \(-0.212830\pi\) | ||||
0.784674 | + | 0.619909i | \(0.212830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 116.000 | 1.40064 | 0.700322 | − | 0.713827i | \(-0.253040\pi\) | ||||
0.700322 | + | 0.713827i | \(0.253040\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −64.0000 | −0.665045 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −16.0000 | −0.145054 | −0.0725268 | − | 0.997366i | \(-0.523106\pi\) | ||||
−0.0725268 | + | 0.997366i | \(0.523106\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −152.000 | −1.08342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −198.000 | −1.26785 | −0.633925 | − | 0.773394i | \(-0.718557\pi\) | ||||
−0.633925 | + | 0.773394i | \(0.718557\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 240.000 | 1.39049 | 0.695246 | − | 0.718772i | \(-0.255295\pi\) | ||||
0.695246 | + | 0.718772i | \(0.255295\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −144.000 | −0.759612 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −258.000 | −1.14635 | −0.573175 | − | 0.819433i | \(-0.694288\pi\) | ||||
−0.573175 | + | 0.819433i | \(0.694288\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −168.000 | −0.689783 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 442.000 | 1.68363 | 0.841815 | − | 0.539767i | \(-0.181488\pi\) | ||||
0.841815 | + | 0.539767i | \(0.181488\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −292.000 | −1.03557 | −0.517786 | − | 0.855510i | \(-0.673244\pi\) | ||||
−0.517786 | + | 0.855510i | \(0.673244\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −392.000 | −1.21658 | −0.608288 | − | 0.793716i | \(-0.708143\pi\) | ||||
−0.608288 | + | 0.793716i | \(0.708143\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −87.0000 | −0.253644 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 440.000 | 1.20808 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 142.000 | 0.368023 | 0.184011 | − | 0.982924i | \(-0.441092\pi\) | ||||
0.184011 | + | 0.982924i | \(0.441092\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 464.000 | 1.07822 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 348.000 | 0.767894 | 0.383947 | − | 0.923355i | \(-0.374565\pi\) | ||||
0.383947 | + | 0.923355i | \(0.374565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 570.000 | 1.19641 | 0.598205 | − | 0.801343i | \(-0.295881\pi\) | ||||
0.598205 | + | 0.801343i | \(0.295881\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 176.000 | 0.351967 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 692.000 | 1.26181 | 0.630905 | − | 0.775860i | \(-0.282684\pi\) | ||||
0.630905 | + | 0.775860i | \(0.282684\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −64.0000 | −0.111662 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 168.000 | 0.280816 | 0.140408 | − | 0.990094i | \(-0.455159\pi\) | ||||
0.140408 | + | 0.990094i | \(0.455159\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 134.000 | 0.214843 | 0.107421 | − | 0.994214i | \(-0.465741\pi\) | ||||
0.107421 | + | 0.994214i | \(0.465741\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 576.000 | 0.852484 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 784.000 | 1.11654 | 0.558271 | − | 0.829658i | \(-0.311465\pi\) | ||||
0.558271 | + | 0.829658i | \(0.311465\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −311.000 | −0.426612 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 564.000 | 0.745868 | 0.372934 | − | 0.927858i | \(-0.378352\pi\) | ||||
0.372934 | + | 0.927858i | \(0.378352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −792.000 | −0.975992 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1034.00 | 1.23150 | 0.615752 | − | 0.787940i | \(-0.288852\pi\) | ||||
0.615752 | + | 0.787940i | \(0.288852\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 672.000 | 0.774118 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 960.000 | 1.07040 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 382.000 | 0.399858 | 0.199929 | − | 0.979810i | \(-0.435929\pi\) | ||||
0.199929 | + | 0.979810i | \(0.435929\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 396.000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 674.000 | 0.664015 | 0.332007 | − | 0.943277i | \(-0.392274\pi\) | ||||
0.332007 | + | 0.943277i | \(0.392274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 992.000 | 0.948977 | 0.474489 | − | 0.880262i | \(-0.342633\pi\) | ||||
0.474489 | + | 0.880262i | \(0.342633\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −500.000 | −0.451746 | −0.225873 | − | 0.974157i | \(-0.572523\pi\) | ||||
−0.225873 | + | 0.974157i | \(0.572523\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1046.00 | −0.919162 | −0.459581 | − | 0.888136i | \(-0.652000\pi\) | ||||
−0.459581 | + | 0.888136i | \(0.652000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1032.00 | −0.882460 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 558.000 | 0.464533 | 0.232266 | − | 0.972652i | \(-0.425386\pi\) | ||||
0.232266 | + | 0.972652i | \(0.425386\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 462.000 | 0.365059 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1760.00 | −1.35579 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.0000 | −0.0262960 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1768.00 | 1.29606 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 328.000 | 0.229176 | 0.114588 | − | 0.993413i | \(-0.463445\pi\) | ||||
0.114588 | + | 0.993413i | \(0.463445\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1168.00 | −0.797183 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 212.000 | 0.141393 | 0.0706967 | − | 0.997498i | \(-0.477478\pi\) | ||||
0.0706967 | + | 0.997498i | \(0.477478\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1856.00 | −1.21004 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1434.00 | −0.894269 | −0.447135 | − | 0.894467i | \(-0.647556\pi\) | ||||
−0.447135 | + | 0.894467i | \(0.647556\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2196.00 | −1.34002 | −0.670008 | − | 0.742354i | \(-0.733709\pi\) | ||||
−0.670008 | + | 0.742354i | \(0.733709\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1568.00 | −0.936521 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1512.00 | 0.884194 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −348.000 | −0.195255 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2418.00 | 1.32946 | 0.664732 | − | 0.747081i | \(-0.268546\pi\) | ||||
0.664732 | + | 0.747081i | \(0.268546\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3672.00 | 1.97896 | 0.989481 | − | 0.144666i | \(-0.0462108\pi\) | ||||
0.989481 | + | 0.144666i | \(0.0462108\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1210.00 | −0.639364 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 358.000 | 0.181984 | 0.0909921 | − | 0.995852i | \(-0.470996\pi\) | ||||
0.0909921 | + | 0.995852i | \(0.470996\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 568.000 | 0.283304 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 256.000 | 0.125314 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2564.00 | 1.23207 | 0.616037 | − | 0.787717i | \(-0.288737\pi\) | ||||
0.616037 | + | 0.787717i | \(0.288737\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3056.00 | 1.41605 | 0.708025 | − | 0.706187i | \(-0.249586\pi\) | ||||
0.708025 | + | 0.706187i | \(0.249586\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −433.000 | −0.197087 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1276.00 | −0.570633 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −234.000 | −0.102836 | −0.0514182 | − | 0.998677i | \(-0.516374\pi\) | ||||
−0.0514182 | + | 0.998677i | \(0.516374\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1392.00 | 0.591125 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −524.000 | −0.218802 | −0.109401 | − | 0.993998i | \(-0.534893\pi\) | ||||
−0.109401 | + | 0.993998i | \(0.534893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1138.00 | 0.467331 | 0.233665 | − | 0.972317i | \(-0.424928\pi\) | ||||
0.233665 | + | 0.972317i | \(0.424928\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2280.00 | 0.920997 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3960.00 | −1.54858 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2432.00 | 0.935989 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1520.00 | 0.575829 | 0.287915 | − | 0.957656i | \(-0.407038\pi\) | ||||
0.287915 | + | 0.957656i | \(0.407038\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2142.00 | 0.798884 | 0.399442 | − | 0.916759i | \(-0.369204\pi\) | ||||
0.399442 | + | 0.916759i | \(0.369204\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2306.00 | −0.833988 | −0.416994 | − | 0.908909i | \(-0.636916\pi\) | ||||
−0.416994 | + | 0.908909i | \(0.636916\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3288.00 | 1.17126 | 0.585628 | − | 0.810580i | \(-0.300848\pi\) | ||||
0.585628 | + | 0.810580i | \(0.300848\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2768.00 | 0.971342 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3168.00 | 1.09532 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 176.000 | 0.0590959 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4176.00 | −1.38211 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3876.00 | 1.26462 | 0.632310 | − | 0.774715i | \(-0.282107\pi\) | ||||
0.632310 | + | 0.774715i | \(0.282107\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 672.000 | 0.216172 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3840.00 | −1.20127 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 536.000 | 0.165386 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4620.00 | −1.40622 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5688.00 | 1.70806 | 0.854028 | − | 0.520226i | \(-0.174152\pi\) | ||||
0.854028 | + | 0.520226i | \(0.174152\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2796.00 | −0.817520 | −0.408760 | − | 0.912642i | \(-0.634039\pi\) | ||||
−0.408760 | + | 0.912642i | \(0.634039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4446.00 | −1.28297 | −0.641485 | − | 0.767136i | \(-0.721681\pi\) | ||||
−0.641485 | + | 0.767136i | \(0.721681\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2304.00 | 0.656243 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2522.00 | −0.709106 | −0.354553 | − | 0.935036i | \(-0.615367\pi\) | ||||
−0.354553 | + | 0.935036i | \(0.615367\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3136.00 | 0.859515 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 816.000 | 0.220848 | 0.110424 | − | 0.993885i | \(-0.464779\pi\) | ||||
0.110424 | + | 0.993885i | \(0.464779\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5422.00 | −1.44922 | −0.724609 | − | 0.689160i | \(-0.757980\pi\) | ||||
−0.724609 | + | 0.689160i | \(0.757980\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2860.00 | 0.755017 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4872.00 | −1.25505 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2256.00 | 0.574169 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5900.00 | 1.48368 | 0.741842 | − | 0.670575i | \(-0.233952\pi\) | ||||
0.741842 | + | 0.670575i | \(0.233952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 576.000 | 0.143134 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5250.00 | −1.27426 | −0.637132 | − | 0.770754i | \(-0.719880\pi\) | ||||
−0.637132 | + | 0.770754i | \(0.719880\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4128.00 | 0.990353 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2178.00 | 0.516532 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6240.00 | −1.46302 | −0.731511 | − | 0.681829i | \(-0.761185\pi\) | ||||
−0.731511 | + | 0.681829i | \(0.761185\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4136.00 | 0.948012 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 714.000 | 0.161834 | 0.0809170 | − | 0.996721i | \(-0.474215\pi\) | ||||
0.0809170 | + | 0.996721i | \(0.474215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2144.00 | 0.480586 | 0.240293 | − | 0.970700i | \(-0.422757\pi\) | ||||
0.240293 | + | 0.970700i | \(0.422757\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2688.00 | 0.595916 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4466.00 | −0.968722 | −0.484361 | − | 0.874868i | \(-0.660948\pi\) | ||||
−0.484361 | + | 0.874868i | \(0.660948\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2640.00 | −0.566497 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5302.00 | −1.12559 | −0.562795 | − | 0.826596i | \(-0.690274\pi\) | ||||
−0.562795 | + | 0.826596i | \(0.690274\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6932.00 | −1.45606 | −0.728029 | − | 0.685546i | \(-0.759564\pi\) | ||||
−0.728029 | + | 0.685546i | \(0.759564\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7072.00 | −1.45452 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7187.00 | 1.46285 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1528.00 | 0.307811 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4034.00 | −0.804330 | −0.402165 | − | 0.915567i | \(-0.631742\pi\) | ||||
−0.402165 | + | 0.915567i | \(0.631742\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5472.00 | 1.06908 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 672.000 | 0.129976 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4672.00 | 0.894650 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2696.00 | 0.511159 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3836.00 | −0.713134 | −0.356567 | − | 0.934270i | \(-0.616053\pi\) | ||||
−0.356567 | + | 0.934270i | \(0.616053\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3968.00 | 0.730523 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 664.000 | 0.121067 | 0.0605337 | − | 0.998166i | \(-0.480720\pi\) | ||||
0.0605337 | + | 0.998166i | \(0.480720\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2986.00 | −0.539229 | −0.269615 | − | 0.962968i | \(-0.586896\pi\) | ||||
−0.269615 | + | 0.962968i | \(0.586896\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2726.00 | 0.482989 | 0.241494 | − | 0.970402i | \(-0.422362\pi\) | ||||
0.241494 | + | 0.970402i | \(0.422362\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7128.00 | 1.25107 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2000.00 | −0.347754 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12760.0 | 2.19810 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4184.00 | −0.707571 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6272.00 | 1.05102 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9212.00 | 1.52972 | 0.764860 | − | 0.644197i | \(-0.222808\pi\) | ||||
0.764860 | + | 0.644197i | \(0.222808\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2838.00 | 0.467031 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3278.00 | 0.529864 | 0.264932 | − | 0.964267i | \(-0.414651\pi\) | ||||
0.264932 | + | 0.964267i | \(0.414651\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2232.00 | 0.357598 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8640.00 | −1.37209 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6880.00 | 1.08305 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4956.00 | 0.766721 | 0.383360 | − | 0.923599i | \(-0.374767\pi\) | ||||
0.383360 | + | 0.923599i | \(0.374767\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4678.00 | −0.717500 | −0.358750 | − | 0.933434i | \(-0.616797\pi\) | ||||
−0.358750 | + | 0.933434i | \(0.616797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6384.00 | 0.970805 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1890.00 | −0.284970 | −0.142485 | − | 0.989797i | \(-0.545509\pi\) | ||||
−0.142485 | + | 0.989797i | \(0.545509\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7040.00 | −1.04369 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6472.00 | −0.951474 | −0.475737 | − | 0.879588i | \(-0.657819\pi\) | ||||
−0.475737 | + | 0.879588i | \(0.657819\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6597.00 | 0.961802 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −140.000 | −0.0202427 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1960.00 | −0.278777 | −0.139389 | − | 0.990238i | \(-0.544514\pi\) | ||||
−0.139389 | + | 0.990238i | \(0.544514\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4862.00 | −0.685923 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2272.00 | −0.317942 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8750.00 | 1.21463 | 0.607316 | − | 0.794460i | \(-0.292246\pi\) | ||||
0.607316 | + | 0.794460i | \(0.292246\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8316.00 | 1.13606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 380.000 | 0.0515021 | 0.0257510 | − | 0.999668i | \(-0.491802\pi\) | ||||
0.0257510 | + | 0.999668i | \(0.491802\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1312.00 | 0.176419 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9688.00 | 1.29252 | 0.646258 | − | 0.763119i | \(-0.276333\pi\) | ||||
0.646258 | + | 0.763119i | \(0.276333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3212.00 | 0.421900 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3870.00 | −0.504413 | −0.252207 | − | 0.967673i | \(-0.581156\pi\) | ||||
−0.252207 | + | 0.967673i | \(0.581156\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1760.00 | −0.227639 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 848.000 | 0.108845 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1622.00 | 0.205053 | 0.102526 | − | 0.994730i | \(-0.467307\pi\) | ||||
0.102526 | + | 0.994730i | \(0.467307\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7424.00 | −0.931491 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9906.00 | 1.23362 | 0.616811 | − | 0.787112i | \(-0.288424\pi\) | ||||
0.616811 | + | 0.787112i | \(0.288424\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10080.0 | −1.24596 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9288.00 | 1.13118 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4214.00 | −0.509459 | −0.254730 | − | 0.967012i | \(-0.581986\pi\) | ||||
−0.254730 | + | 0.967012i | \(0.581986\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5736.00 | −0.688409 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5568.00 | −0.663398 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8784.00 | −1.03155 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7012.00 | 0.817562 | 0.408781 | − | 0.912632i | \(-0.365954\pi\) | ||||
0.408781 | + | 0.912632i | \(0.365954\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1602.00 | 0.185455 | 0.0927277 | − | 0.995692i | \(-0.470441\pi\) | ||||
0.0927277 | + | 0.995692i | \(0.470441\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4312.00 | 0.495642 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9120.00 | −1.03360 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6048.00 | 0.680653 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3584.00 | −0.400546 | −0.200273 | − | 0.979740i | \(-0.564183\pi\) | ||||
−0.200273 | + | 0.979740i | \(0.564183\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3470.00 | 0.385121 | 0.192561 | − | 0.981285i | \(-0.438321\pi\) | ||||
0.192561 | + | 0.981285i | \(0.438321\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1856.00 | −0.203168 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3416.00 | −0.371382 | −0.185691 | − | 0.982608i | \(-0.559452\pi\) | ||||
−0.185691 | + | 0.982608i | \(0.559452\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 957.000 | 0.103337 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9708.00 | 1.04118 | 0.520588 | − | 0.853808i | \(-0.325713\pi\) | ||||
0.520588 | + | 0.853808i | \(0.325713\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9672.00 | 1.02342 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10366.0 | −1.08954 | −0.544768 | − | 0.838587i | \(-0.683382\pi\) | ||||
−0.544768 | + | 0.838587i | \(0.683382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15912.0 | −1.66135 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14688.0 | 1.52340 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16742.0 | 1.71369 | 0.856847 | − | 0.515572i | \(-0.172420\pi\) | ||||
0.856847 | + | 0.515572i | \(0.172420\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16720.0 | −1.70027 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1258.00 | 0.127095 | 0.0635476 | − | 0.997979i | \(-0.479759\pi\) | ||||
0.0635476 | + | 0.997979i | \(0.479759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13528.0 | −1.35788 | −0.678941 | − | 0.734193i | \(-0.737561\pi\) | ||||
−0.678941 | + | 0.734193i | \(0.737561\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6916.00 | 0.685298 | 0.342649 | − | 0.939463i | \(-0.388676\pi\) | ||||
0.342649 | + | 0.939463i | \(0.388676\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11072.0 | −1.09010 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1432.00 | 0.140091 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10512.0 | 1.02187 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1562.00 | −0.149935 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1728.00 | 0.164832 | 0.0824158 | − | 0.996598i | \(-0.473736\pi\) | ||||
0.0824158 | + | 0.996598i | \(0.473736\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10836.0 | 1.02719 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1024.00 | 0.0964671 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16656.0 | −1.54981 | −0.774903 | − | 0.632080i | \(-0.782201\pi\) | ||||
−0.774903 | + | 0.632080i | \(0.782201\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10256.0 | 0.948451 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1084.00 | 0.0996339 | 0.0498169 | − | 0.998758i | \(-0.484136\pi\) | ||||
0.0498169 | + | 0.998758i | \(0.484136\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21780.0 | −1.98970 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2688.00 | −0.242602 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5804.00 | −0.520687 | −0.260343 | − | 0.965516i | \(-0.583836\pi\) | ||||
−0.260343 | + | 0.965516i | \(0.583836\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12224.0 | 1.09008 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10512.0 | −0.931823 | −0.465911 | − | 0.884831i | \(-0.654273\pi\) | ||||
−0.465911 | + | 0.884831i | \(0.654273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1732.00 | −0.151718 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4314.00 | 0.375667 | 0.187834 | − | 0.982201i | \(-0.439853\pi\) | ||||
0.187834 | + | 0.982201i | \(0.439853\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2144.00 | −0.185607 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17632.0 | −1.51749 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14112.0 | 1.20047 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −936.000 | −0.0791635 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1190.00 | −0.100067 | −0.0500334 | − | 0.998748i | \(-0.515933\pi\) | ||||
−0.0500334 | + | 0.998748i | \(0.515933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3780.00 | −0.316038 | −0.158019 | − | 0.987436i | \(-0.550511\pi\) | ||||
−0.158019 | + | 0.987436i | \(0.550511\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26400.0 | 2.18217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11911.0 | −0.978959 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3828.00 | −0.312846 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18564.0 | −1.50862 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2096.00 | −0.168434 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3132.00 | 0.250287 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11002.0 | 0.874331 | 0.437165 | − | 0.899381i | \(-0.355982\pi\) | ||||
0.437165 | + | 0.899381i | \(0.355982\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4552.00 | 0.359751 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5908.00 | 0.461806 | 0.230903 | − | 0.972977i | \(-0.425832\pi\) | ||||
0.230903 | + | 0.972977i | \(0.425832\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6270.00 | −0.487426 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22968.0 | −1.77581 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12544.0 | −0.964602 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14806.0 | 1.12630 | 0.563151 | − | 0.826354i | \(-0.309589\pi\) | ||||
0.563151 | + | 0.826354i | \(0.309589\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12264.0 | 0.927928 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15840.0 | −1.19210 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −684.000 | −0.0512028 | −0.0256014 | − | 0.999672i | \(-0.508150\pi\) | ||||
−0.0256014 | + | 0.999672i | \(0.508150\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4976.00 | 0.368558 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2582.00 | −0.190234 | −0.0951169 | − | 0.995466i | \(-0.530323\pi\) | ||||
−0.0951169 | + | 0.995466i | \(0.530323\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2540.00 | 0.186157 | 0.0930785 | − | 0.995659i | \(-0.470329\pi\) | ||||
0.0930785 | + | 0.995659i | \(0.470329\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6080.00 | 0.443273 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22786.0 | −1.64401 | −0.822005 | − | 0.569480i | \(-0.807144\pi\) | ||||
−0.822005 | + | 0.569480i | \(0.807144\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8568.00 | 0.614981 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9024.00 | −0.644369 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5112.00 | −0.363152 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7884.00 | 0.554357 | 0.277178 | − | 0.960818i | \(-0.410601\pi\) | ||||
0.277178 | + | 0.960818i | \(0.410601\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27840.0 | 1.94758 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9224.00 | −0.642005 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21902.0 | 1.51671 | 0.758354 | − | 0.651843i | \(-0.226004\pi\) | ||||
0.758354 | + | 0.651843i | \(0.226004\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13152.0 | 0.901634 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15080.0 | 1.02863 | 0.514317 | − | 0.857600i | \(-0.328045\pi\) | ||||
0.514317 | + | 0.857600i | \(0.328045\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19702.0 | −1.33721 | −0.668603 | − | 0.743619i | \(-0.733108\pi\) | ||||
−0.668603 | + | 0.743619i | \(0.733108\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7612.00 | −0.514071 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7320.00 | −0.489472 | −0.244736 | − | 0.969590i | \(-0.578701\pi\) | ||||
−0.244736 | + | 0.969590i | \(0.578701\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12672.0 | 0.843178 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16464.0 | 1.09012 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24350.0 | 1.60438 | 0.802192 | − | 0.597066i | \(-0.203667\pi\) | ||||
0.802192 | + | 0.597066i | \(0.203667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19546.0 | −1.27535 | −0.637676 | − | 0.770305i | \(-0.720104\pi\) | ||||
−0.637676 | + | 0.770305i | \(0.720104\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3476.00 | −0.225706 | −0.112853 | − | 0.993612i | \(-0.535999\pi\) | ||||
−0.112853 | + | 0.993612i | \(0.535999\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2432.00 | 0.157154 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16544.0 | −1.06392 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16704.0 | −1.06394 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28380.0 | −1.79902 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21880.0 | 1.38039 | 0.690197 | − | 0.723621i | \(-0.257524\pi\) | ||||
0.690197 | + | 0.723621i | \(0.257524\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15504.0 | 0.973505 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3654.00 | 0.227279 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1848.00 | −0.114406 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20994.0 | 1.29362 | 0.646812 | − | 0.762649i | \(-0.276102\pi\) | ||||
0.646812 | + | 0.762649i | \(0.276102\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18204.0 | −1.11648 | −0.558239 | − | 0.829680i | \(-0.688523\pi\) | ||||
−0.558239 | + | 0.829680i | \(0.688523\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2064.00 | 0.125416 | 0.0627080 | − | 0.998032i | \(-0.480026\pi\) | ||||
0.0627080 | + | 0.998032i | \(0.480026\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12528.0 | −0.757730 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15360.0 | −0.924740 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9942.00 | 0.595805 | 0.297902 | − | 0.954596i | \(-0.403713\pi\) | ||||
0.297902 | + | 0.954596i | \(0.403713\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1474.00 | −0.0875285 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24236.0 | −1.43263 | −0.716313 | − | 0.697779i | \(-0.754172\pi\) | ||||
−0.716313 | + | 0.697779i | \(0.754172\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17614.0 | −1.03647 | −0.518234 | − | 0.855239i | \(-0.673410\pi\) | ||||
−0.518234 | + | 0.855239i | \(0.673410\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18480.0 | −1.08251 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3168.00 | 0.183906 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22752.0 | 1.31486 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20520.0 | −1.18057 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13058.0 | −0.747918 | −0.373959 | − | 0.927445i | \(-0.622000\pi\) | ||||
−0.373959 | + | 0.927445i | \(0.622000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33186.0 | −1.88396 | −0.941980 | − | 0.335668i | \(-0.891038\pi\) | ||||
−0.941980 | + | 0.335668i | \(0.891038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6112.00 | −0.345445 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11184.0 | −0.629327 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31716.0 | −1.77684 | −0.888418 | − | 0.459035i | \(-0.848195\pi\) | ||||
−0.888418 | + | 0.459035i | \(0.848195\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17784.0 | −0.987630 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5964.00 | −0.329768 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2084.00 | 0.114731 | 0.0573655 | − | 0.998353i | \(-0.481730\pi\) | ||||
0.0573655 | + | 0.998353i | \(0.481730\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6336.00 | −0.347308 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48620.0 | 2.64220 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10088.0 | −0.545870 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7418.00 | 0.399678 | 0.199839 | − | 0.979829i | \(-0.435958\pi\) | ||||
0.199839 | + | 0.979829i | \(0.435958\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29928.0 | −1.60563 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10784.0 | −0.573655 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18242.0 | 0.966280 | 0.483140 | − | 0.875543i | \(-0.339496\pi\) | ||||
0.483140 | + | 0.875543i | \(0.339496\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8624.00 | −0.454888 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3840.00 | −0.201696 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3264.00 | 0.170009 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3024.00 | 0.156851 | 0.0784257 | − | 0.996920i | \(-0.475011\pi\) | ||||
0.0784257 | + | 0.996920i | \(0.475011\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15872.0 | −0.819839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21688.0 | −1.11561 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26176.0 | 1.33537 | 0.667685 | − | 0.744444i | \(-0.267285\pi\) | ||||
0.667685 | + | 0.744444i | \(0.267285\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19837.0 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32120.0 | −1.62517 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17818.0 | −0.897848 | −0.448924 | − | 0.893570i | \(-0.648193\pi\) | ||||
−0.448924 | + | 0.893570i | \(0.648193\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24912.0 | −1.24511 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22052.0 | 1.09769 | 0.548847 | − | 0.835923i | \(-0.315067\pi\) | ||||
0.548847 | + | 0.835923i | \(0.315067\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19488.0 | −0.966140 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15840.0 | −0.782117 | −0.391059 | − | 0.920366i | \(-0.627891\pi\) | ||||
−0.391059 | + | 0.920366i | \(0.627891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6204.00 | −0.303872 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8000.00 | 0.390272 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21024.0 | 1.02154 | 0.510770 | − | 0.859717i | \(-0.329360\pi\) | ||||
0.510770 | + | 0.859717i | \(0.329360\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23600.0 | 1.14214 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38034.0 | −1.82612 | −0.913058 | − | 0.407831i | \(-0.866285\pi\) | ||||
−0.913058 | + | 0.407831i | \(0.866285\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2304.00 | 0.110184 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37802.0 | 1.80069 | 0.900343 | − | 0.435182i | \(-0.143316\pi\) | ||||
0.900343 | + | 0.435182i | \(0.143316\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16736.0 | 0.794081 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14616.0 | −0.688075 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15042.0 | 0.705369 | 0.352684 | − | 0.935742i | \(-0.385269\pi\) | ||||
0.352684 | + | 0.935742i | \(0.385269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21000.0 | −0.980929 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5950.00 | 0.276852 | 0.138426 | − | 0.990373i | \(-0.455796\pi\) | ||||
0.138426 | + | 0.990373i | \(0.455796\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16512.0 | 0.762374 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 51272.0 | 2.35816 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6048.00 | −0.277099 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30096.0 | 1.37362 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23364.0 | 1.05824 | 0.529121 | − | 0.848546i | \(-0.322522\pi\) | ||||
0.529121 | + | 0.848546i | \(0.322522\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24960.0 | −1.12624 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8928.00 | −0.401319 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23940.0 | −1.07205 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19846.0 | 0.882034 | 0.441017 | − | 0.897499i | \(-0.354618\pi\) | ||||
0.441017 | + | 0.897499i | \(0.354618\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43120.0 | −1.90923 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11374.0 | −0.501724 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4824.00 | −0.211999 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2856.00 | 0.124580 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24762.0 | 1.07613 | 0.538063 | − | 0.842905i | \(-0.319156\pi\) | ||||
0.538063 | + | 0.842905i | \(0.319156\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16644.0 | −0.720653 | −0.360327 | − | 0.932826i | \(-0.617335\pi\) | ||||
−0.360327 | + | 0.932826i | \(0.617335\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8576.00 | 0.369955 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33872.0 | −1.45047 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7392.00 | −0.315381 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3182.00 | −0.135265 | −0.0676325 | − | 0.997710i | \(-0.521545\pi\) | ||||
−0.0676325 | + | 0.997710i | \(0.521545\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7504.00 | 0.317829 | 0.158914 | − | 0.987292i | \(-0.449201\pi\) | ||||
0.158914 | + | 0.987292i | \(0.449201\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12604.0 | 0.529969 | 0.264984 | − | 0.964253i | \(-0.414633\pi\) | ||||
0.264984 | + | 0.964253i | \(0.414633\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12230.0 | −0.512383 | −0.256191 | − | 0.966626i | \(-0.582468\pi\) | ||||
−0.256191 | + | 0.966626i | \(0.582468\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17864.0 | −0.745722 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9570.00 | −0.398056 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −36480.0 | −1.50649 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9656.00 | 0.397333 | 0.198666 | − | 0.980067i | \(-0.436339\pi\) | ||||
0.198666 | + | 0.980067i | \(0.436339\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14815.0 | 0.607446 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21208.0 | −0.866480 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 560.000 | 0.0227176 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27728.0 | −1.12087 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4128.00 | 0.166282 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5806.00 | 0.233052 | 0.116526 | − | 0.993188i | \(-0.462824\pi\) | ||||
0.116526 | + | 0.993188i | \(0.462824\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39094.0 | 1.55826 | 0.779128 | − | 0.626865i | \(-0.215662\pi\) | ||||
0.779128 | + | 0.626865i | \(0.215662\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18876.0 | 0.749756 | 0.374878 | − | 0.927074i | \(-0.377685\pi\) | ||||
0.374878 | + | 0.927074i | \(0.377685\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28288.0 | −1.11969 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32296.0 | −1.27389 | −0.636946 | − | 0.770909i | \(-0.719803\pi\) | ||||
−0.636946 | + | 0.770909i | \(0.719803\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28748.0 | 1.12611 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28224.0 | −1.10176 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29064.0 | −1.13065 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4202.00 | −0.162905 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9578.00 | −0.368787 | −0.184393 | − | 0.982853i | \(-0.559032\pi\) | ||||
−0.184393 | + | 0.982853i | \(0.559032\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16136.0 | −0.619174 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41710.0 | −1.59506 | −0.797529 | − | 0.603281i | \(-0.793860\pi\) | ||||
−0.797529 | + | 0.603281i | \(0.793860\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2260.00 | 0.0861326 | 0.0430663 | − | 0.999072i | \(-0.486287\pi\) | ||||
0.0430663 | + | 0.999072i | \(0.486287\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33696.0 | 1.27554 | 0.637768 | − | 0.770228i | \(-0.279858\pi\) | ||||
0.637768 | + | 0.770228i | \(0.279858\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5248.00 | −0.197989 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11196.0 | 0.420965 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −45472.0 | −1.70399 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2688.00 | 0.100055 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −47520.0 | −1.76294 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15620.0 | 0.577556 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18688.0 | 0.688702 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7756.00 | 0.283940 | 0.141970 | − | 0.989871i | \(-0.454656\pi\) | ||||
0.141970 | + | 0.989871i | \(0.454656\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7414.00 | −0.270525 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5312.00 | −0.193188 | −0.0965941 | − | 0.995324i | \(-0.530795\pi\) | ||||
−0.0965941 | + | 0.995324i | \(0.530795\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20304.0 | −0.735996 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3392.00 | −0.122152 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23576.0 | −0.846246 | −0.423123 | − | 0.906072i | \(-0.639066\pi\) | ||||
−0.423123 | + | 0.906072i | \(0.639066\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15344.0 | −0.548971 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7056.00 | −0.251626 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10912.0 | −0.386620 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19038.0 | −0.672354 | −0.336177 | − | 0.941799i | \(-0.609134\pi\) | ||||
−0.336177 | + | 0.941799i | \(0.609134\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10092.0 | −0.355265 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2656.00 | 0.0931978 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20570.0 | −0.717175 | −0.358587 | − | 0.933496i | \(-0.616741\pi\) | ||||
−0.358587 | + | 0.933496i | \(0.616741\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11944.0 | −0.415099 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21386.0 | 0.740875 | 0.370438 | − | 0.928857i | \(-0.379208\pi\) | ||||
0.370438 | + | 0.928857i | \(0.379208\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7072.00 | −0.244216 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38020.0 | 1.30463 | 0.652315 | − | 0.757948i | \(-0.273798\pi\) | ||||
0.652315 | + | 0.757948i | \(0.273798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5628.00 | −0.192511 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10904.0 | 0.371805 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20202.0 | −0.686681 | −0.343340 | − | 0.939211i | \(-0.611558\pi\) | ||||
−0.343340 | + | 0.939211i | \(0.611558\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28512.0 | 0.963074 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22944.0 | 0.772576 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27809.0 | 0.933470 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5500.00 | 0.184045 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29840.0 | −0.992337 | −0.496168 | − | 0.868226i | \(-0.665260\pi\) | ||||
−0.496168 | + | 0.868226i | \(0.665260\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 51040.0 | 1.69210 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12476.0 | 0.412332 | 0.206166 | − | 0.978517i | \(-0.433901\pi\) | ||||
0.206166 | + | 0.978517i | \(0.433901\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35136.0 | 1.15767 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36974.0 | 1.21075 | 0.605375 | − | 0.795940i | \(-0.293023\pi\) | ||||
0.605375 | + | 0.795940i | \(0.293023\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37224.0 | −1.21520 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11506.0 | 0.374473 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16368.0 | 0.531087 | 0.265543 | − | 0.964099i | \(-0.414449\pi\) | ||||
0.265543 | + | 0.964099i | \(0.414449\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 25088.0 | 0.809078 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4672.00 | 0.150213 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49552.0 | −1.58837 | −0.794183 | − | 0.607678i | \(-0.792101\pi\) | ||||
−0.794183 | + | 0.607678i | \(0.792101\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 36848.0 | 1.17758 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24414.0 | 0.775526 | 0.387763 | − | 0.921759i | \(-0.373248\pi\) | ||||
0.387763 | + | 0.921759i | \(0.373248\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 39216.0 | 1.24198 |
(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 | 1600.4.a.bk.1.1 | 1 | ||
4.3 | odd | 2 | 1600.4.a.q.1.1 | 1 | |||
5.4 | even | 2 | 320.4.a.e.1.1 | 1 | |||
8.3 | odd | 2 | 400.4.a.p.1.1 | 1 | |||
8.5 | even | 2 | 200.4.a.d.1.1 | 1 | |||
20.19 | odd | 2 | 320.4.a.j.1.1 | 1 | |||
24.5 | odd | 2 | 1800.4.a.h.1.1 | 1 | |||
40.3 | even | 4 | 400.4.c.h.49.2 | 2 | |||
40.13 | odd | 4 | 200.4.c.f.49.1 | 2 | |||
40.19 | odd | 2 | 80.4.a.b.1.1 | 1 | |||
40.27 | even | 4 | 400.4.c.h.49.1 | 2 | |||
40.29 | even | 2 | 40.4.a.b.1.1 | ✓ | 1 | ||
40.37 | odd | 4 | 200.4.c.f.49.2 | 2 | |||
80.19 | odd | 4 | 1280.4.d.m.641.2 | 2 | |||
80.29 | even | 4 | 1280.4.d.d.641.1 | 2 | |||
80.59 | odd | 4 | 1280.4.d.m.641.1 | 2 | |||
80.69 | even | 4 | 1280.4.d.d.641.2 | 2 | |||
120.29 | odd | 2 | 360.4.a.f.1.1 | 1 | |||
120.53 | even | 4 | 1800.4.f.d.649.2 | 2 | |||
120.59 | even | 2 | 720.4.a.d.1.1 | 1 | |||
120.77 | even | 4 | 1800.4.f.d.649.1 | 2 | |||
280.69 | odd | 2 | 1960.4.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.4.a.b.1.1 | ✓ | 1 | 40.29 | even | 2 | ||
80.4.a.b.1.1 | 1 | 40.19 | odd | 2 | |||
200.4.a.d.1.1 | 1 | 8.5 | even | 2 | |||
200.4.c.f.49.1 | 2 | 40.13 | odd | 4 | |||
200.4.c.f.49.2 | 2 | 40.37 | odd | 4 | |||
320.4.a.e.1.1 | 1 | 5.4 | even | 2 | |||
320.4.a.j.1.1 | 1 | 20.19 | odd | 2 | |||
360.4.a.f.1.1 | 1 | 120.29 | odd | 2 | |||
400.4.a.p.1.1 | 1 | 8.3 | odd | 2 | |||
400.4.c.h.49.1 | 2 | 40.27 | even | 4 | |||
400.4.c.h.49.2 | 2 | 40.3 | even | 4 | |||
720.4.a.d.1.1 | 1 | 120.59 | even | 2 | |||
1280.4.d.d.641.1 | 2 | 80.29 | even | 4 | |||
1280.4.d.d.641.2 | 2 | 80.69 | even | 4 | |||
1280.4.d.m.641.1 | 2 | 80.59 | odd | 4 | |||
1280.4.d.m.641.2 | 2 | 80.19 | odd | 4 | |||
1600.4.a.q.1.1 | 1 | 4.3 | odd | 2 | |||
1600.4.a.bk.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1800.4.a.h.1.1 | 1 | 24.5 | odd | 2 | |||
1800.4.f.d.649.1 | 2 | 120.77 | even | 4 | |||
1800.4.f.d.649.2 | 2 | 120.53 | even | 4 | |||
1960.4.a.e.1.1 | 1 | 280.69 | odd | 2 |