Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7616,2,Mod(1,7616)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7616, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7616.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7616 = 2^{6} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7616.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: | \(60.8140661794\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + x + 11 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 952) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.10522\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7616.1 |
$q$-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 | ||||||||
\(3\) | 2.10522 | 1.21545 | 0.607724 | − | 0.794148i | \(-0.292083\pi\) | ||||
0.607724 | + | 0.794148i | \(0.292083\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.40632 | 1.52335 | 0.761675 | − | 0.647959i | \(-0.224377\pi\) | ||||
0.761675 | + | 0.647959i | \(0.224377\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.43195 | 0.477315 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.23607 | 0.372689 | 0.186344 | − | 0.982485i | \(-0.440336\pi\) | ||||
0.186344 | + | 0.982485i | \(0.440336\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.47214 | 1.79505 | 0.897524 | − | 0.440966i | \(-0.145364\pi\) | ||||
0.897524 | + | 0.440966i | \(0.145364\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.17104 | 1.85155 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.21044 | 0.507109 | 0.253555 | − | 0.967321i | \(-0.418400\pi\) | ||||
0.253555 | + | 0.967321i | \(0.418400\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.10522 | −0.459396 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.39781 | 0.291463 | 0.145731 | − | 0.989324i | \(-0.453446\pi\) | ||||
0.145731 | + | 0.989324i | \(0.453446\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.60299 | 1.32060 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.30110 | −0.635296 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.633874 | 0.117708 | 0.0588538 | − | 0.998267i | \(-0.481255\pi\) | ||||
0.0588538 | + | 0.998267i | \(0.481255\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.965861 | 0.173474 | 0.0867368 | − | 0.996231i | \(-0.472356\pi\) | ||||
0.0867368 | + | 0.996231i | \(0.472356\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.60219 | 0.452984 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.40632 | −0.575772 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.31040 | 1.36622 | 0.683110 | − | 0.730315i | \(-0.260627\pi\) | ||||
0.683110 | + | 0.730315i | \(0.260627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.6253 | 2.18179 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.60299 | −0.875039 | −0.437520 | − | 0.899209i | \(-0.644143\pi\) | ||||
−0.437520 | + | 0.899209i | \(0.644143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.0796 | −1.68962 | −0.844811 | − | 0.535065i | \(-0.820287\pi\) | ||||
−0.844811 | + | 0.535065i | \(0.820287\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.87766 | 0.727119 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.67652 | 1.11974 | 0.559868 | − | 0.828582i | \(-0.310852\pi\) | ||||
0.559868 | + | 0.828582i | \(0.310852\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.10522 | 0.294790 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.7167 | −1.60941 | −0.804707 | − | 0.593672i | \(-0.797678\pi\) | ||||
−0.804707 | + | 0.593672i | \(0.797678\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.21044 | 0.567735 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.65345 | 0.616365 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.602193 | 0.0783989 | 0.0391995 | − | 0.999231i | \(-0.487519\pi\) | ||||
0.0391995 | + | 0.999231i | \(0.487519\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.84352 | 1.26033 | 0.630167 | − | 0.776460i | \(-0.282986\pi\) | ||||
0.630167 | + | 0.776460i | \(0.282986\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.43195 | −0.180408 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22.0461 | 2.73449 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.30636 | −0.648275 | −0.324137 | − | 0.946010i | \(-0.605074\pi\) | ||||
−0.324137 | + | 0.946010i | \(0.605074\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.94269 | 0.354258 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.33603 | −0.395914 | −0.197957 | − | 0.980211i | \(-0.563431\pi\) | ||||
−0.197957 | + | 0.980211i | \(0.563431\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0239 | 1.64137 | 0.820684 | − | 0.571382i | \(-0.193592\pi\) | ||||
0.820684 | + | 0.571382i | \(0.193592\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.9007 | 1.60512 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.23607 | −0.140863 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.323477 | −0.0363940 | −0.0181970 | − | 0.999834i | \(-0.505793\pi\) | ||||
−0.0181970 | + | 0.999834i | \(0.505793\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2454 | −1.24949 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.8870 | −1.52429 | −0.762146 | − | 0.647405i | \(-0.775854\pi\) | ||||
−0.762146 | + | 0.647405i | \(0.775854\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.40632 | 0.369467 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.33444 | 0.143067 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7509 | −1.56359 | −0.781794 | − | 0.623537i | \(-0.785695\pi\) | ||||
−0.781794 | + | 0.623537i | \(0.785695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.47214 | −0.678464 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.03335 | 0.210848 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.52945 | 0.772505 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.90855 | −0.599922 | −0.299961 | − | 0.953951i | \(-0.596974\pi\) | ||||
−0.299961 | + | 0.953951i | \(0.596974\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.76998 | 0.177890 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.08485 | −0.505961 | −0.252981 | − | 0.967471i | \(-0.581411\pi\) | ||||
−0.252981 | + | 0.967471i | \(0.581411\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.28477 | −0.520724 | −0.260362 | − | 0.965511i | \(-0.583842\pi\) | ||||
−0.260362 | + | 0.965511i | \(0.583842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.17104 | −0.699822 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.25309 | 0.894530 | 0.447265 | − | 0.894402i | \(-0.352398\pi\) | ||||
0.447265 | + | 0.894402i | \(0.352398\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.1000 | 1.54210 | 0.771048 | − | 0.636777i | \(-0.219733\pi\) | ||||
0.771048 | + | 0.636777i | \(0.219733\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.4952 | 1.66057 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5509 | 0.992548 | 0.496274 | − | 0.868166i | \(-0.334701\pi\) | ||||
0.496274 | + | 0.868166i | \(0.334701\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.76137 | 0.444000 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.26775 | 0.856804 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.00000 | −0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47214 | −0.861103 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.7955 | −1.06357 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.46027 | 0.488382 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.9272 | −1.59078 | −0.795389 | − | 0.606100i | \(-0.792733\pi\) | ||||
−0.795389 | + | 0.606100i | \(0.792733\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −23.3250 | −2.05365 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.49777 | −0.130860 | −0.0654302 | − | 0.997857i | \(-0.520842\pi\) | ||||
−0.0654302 | + | 0.997857i | \(0.520842\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.21044 | −0.191669 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.2446 | −0.967779 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.6030 | 1.16218 | 0.581091 | − | 0.813839i | \(-0.302626\pi\) | ||||
0.581091 | + | 0.813839i | \(0.302626\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.28073 | 0.532724 | 0.266362 | − | 0.963873i | \(-0.414178\pi\) | ||||
0.266362 | + | 0.963873i | \(0.414178\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.1608 | 1.36098 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.00000 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.15918 | 0.179310 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.10522 | 0.173636 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.7004 | −1.77776 | −0.888882 | − | 0.458136i | \(-0.848517\pi\) | ||||
−0.888882 | + | 0.458136i | \(0.848517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.60745 | 0.374949 | 0.187475 | − | 0.982269i | \(-0.439970\pi\) | ||||
0.187475 | + | 0.982269i | \(0.439970\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.43195 | 0.115766 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.29003 | 0.264261 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.53391 | 0.361846 | 0.180923 | − | 0.983497i | \(-0.442092\pi\) | ||||
0.180923 | + | 0.983497i | \(0.442092\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −24.6662 | −1.95616 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.39781 | −0.110163 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.2421 | 0.958877 | 0.479438 | − | 0.877576i | \(-0.340840\pi\) | ||||
0.479438 | + | 0.877576i | \(0.340840\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.86389 | 0.690053 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.34129 | 0.103792 | 0.0518959 | − | 0.998652i | \(-0.483474\pi\) | ||||
0.0518959 | + | 0.998652i | \(0.483474\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.8885 | 2.22220 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.16523 | 0.242051 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.83300 | −0.139361 | −0.0696803 | − | 0.997569i | \(-0.522198\pi\) | ||||
−0.0696803 | + | 0.997569i | \(0.522198\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.60299 | −0.499139 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.26775 | 0.0952898 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.2343 | −1.51238 | −0.756191 | − | 0.654351i | \(-0.772942\pi\) | ||||
−0.756191 | + | 0.654351i | \(0.772942\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.03010 | 0.448214 | 0.224107 | − | 0.974565i | \(-0.428054\pi\) | ||||
0.224107 | + | 0.974565i | \(0.428054\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.7228 | 1.53187 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 28.3078 | 2.08123 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.23607 | 0.0903902 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.30110 | 0.240119 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.9146 | −0.789753 | −0.394876 | − | 0.918734i | \(-0.629213\pi\) | ||||
−0.394876 | + | 0.918734i | \(0.629213\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.1717 | −1.38001 | −0.690006 | − | 0.723804i | \(-0.742392\pi\) | ||||
−0.690006 | + | 0.723804i | \(0.742392\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 46.4119 | 3.32363 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.89557 | −0.206301 | −0.103151 | − | 0.994666i | \(-0.532892\pi\) | ||||
−0.103151 | + | 0.994666i | \(0.532892\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.1830 | 1.85607 | 0.928033 | − | 0.372498i | \(-0.121499\pi\) | ||||
0.928033 | + | 0.372498i | \(0.121499\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.1710 | −0.787944 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.633874 | −0.0444893 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.0855 | −1.33299 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00158 | 0.139120 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.73225 | 0.188994 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.11048 | 0.145291 | 0.0726456 | − | 0.997358i | \(-0.476856\pi\) | ||||
0.0726456 | + | 0.997358i | \(0.476856\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.02307 | −0.481213 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −37.7406 | −2.57389 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.965861 | −0.0655669 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 29.5233 | 1.99500 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.47214 | 0.435363 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.8126 | −1.25979 | −0.629893 | − | 0.776682i | \(-0.716901\pi\) | ||||
−0.629893 | + | 0.776682i | \(0.716901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.45512 | 0.630341 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.3737 | 1.15313 | 0.576565 | − | 0.817051i | \(-0.304393\pi\) | ||||
0.576565 | + | 0.817051i | \(0.304393\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.71523 | 0.179428 | 0.0897138 | − | 0.995968i | \(-0.471405\pi\) | ||||
0.0897138 | + | 0.995968i | \(0.471405\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.60219 | −0.171212 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.715233 | 0.0468565 | 0.0234282 | − | 0.999726i | \(-0.492542\pi\) | ||||
0.0234282 | + | 0.999726i | \(0.492542\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.1487 | 1.70575 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.680990 | −0.0442351 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.60745 | 0.556770 | 0.278385 | − | 0.960470i | \(-0.410201\pi\) | ||||
0.278385 | + | 0.960470i | \(0.410201\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.31241 | 0.406618 | 0.203309 | − | 0.979115i | \(-0.434830\pi\) | ||||
0.203309 | + | 0.979115i | \(0.434830\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.7707 | −0.883389 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.40632 | 0.217622 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.3063 | 0.910285 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −29.2351 | −1.85270 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.5711 | 1.67715 | 0.838577 | − | 0.544783i | \(-0.183388\pi\) | ||||
0.838577 | + | 0.544783i | \(0.183388\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.72778 | 0.108625 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.17104 | 0.449068 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.75085 | 0.421107 | 0.210553 | − | 0.977582i | \(-0.432473\pi\) | ||||
0.210553 | + | 0.977582i | \(0.432473\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.31040 | −0.516383 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.907674 | 0.0561836 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.20439 | 0.0742657 | 0.0371328 | − | 0.999310i | \(-0.488178\pi\) | ||||
0.0371328 | + | 0.999310i | \(0.488178\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −39.9108 | −2.45170 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −31.0538 | −1.90046 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.0673 | −1.10158 | −0.550791 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550791 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.7464 | 1.19951 | 0.599754 | − | 0.800185i | \(-0.295265\pi\) | ||||
0.599754 | + | 0.800185i | \(0.295265\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.6253 | −0.824638 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.16174 | 0.492171 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.99744 | 0.480519 | 0.240260 | − | 0.970709i | \(-0.422767\pi\) | ||||
0.240260 | + | 0.970709i | \(0.422767\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.38306 | 0.0828016 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.07890 | 0.183672 | 0.0918359 | − | 0.995774i | \(-0.470726\pi\) | ||||
0.0918359 | + | 0.995774i | \(0.470726\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.6927 | −1.70560 | −0.852801 | − | 0.522236i | \(-0.825098\pi\) | ||||
−0.852801 | + | 0.522236i | \(0.825098\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.8511 | 0.938940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.60299 | 0.330734 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.4388 | −0.729175 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.14866 | 0.125526 | 0.0627630 | − | 0.998028i | \(-0.480009\pi\) | ||||
0.0627630 | + | 0.998028i | \(0.480009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.05126 | 0.119429 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.08038 | −0.236768 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.04679 | 0.523190 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.0796 | 0.638617 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.7047 | −0.614970 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 33.5301 | 1.91993 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0291 | −0.914830 | −0.457415 | − | 0.889253i | \(-0.651225\pi\) | ||||
−0.457415 | + | 0.889253i | \(0.651225\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.1256 | −0.632913 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.4505 | 1.95351 | 0.976756 | − | 0.214356i | \(-0.0687652\pi\) | ||||
0.976756 | + | 0.214356i | \(0.0687652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.5585 | 1.84031 | 0.920157 | − | 0.391551i | \(-0.128061\pi\) | ||||
0.920157 | + | 0.391551i | \(0.128061\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.87766 | −0.274825 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.82571 | −0.158708 | −0.0793539 | − | 0.996847i | \(-0.525286\pi\) | ||||
−0.0793539 | + | 0.996847i | \(0.525286\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.783512 | 0.0438682 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.4798 | 1.08725 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.21044 | 0.122992 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 42.7354 | 2.37053 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 33.8939 | 1.87434 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.67652 | −0.423220 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.5822 | −0.911439 | −0.455720 | − | 0.890123i | \(-0.650618\pi\) | ||||
−0.455720 | + | 0.890123i | \(0.650618\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.9000 | 0.652118 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.0751 | −0.987549 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.7553 | 0.858247 | 0.429123 | − | 0.903246i | \(-0.358823\pi\) | ||||
0.429123 | + | 0.903246i | \(0.358823\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.2120 | 1.20639 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.19387 | 0.0646516 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.0237 | 0.539659 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.6630 | 0.679785 | 0.339893 | − | 0.940464i | \(-0.389609\pi\) | ||||
0.339893 | + | 0.940464i | \(0.389609\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.1547 | 1.34650 | 0.673250 | − | 0.739415i | \(-0.264898\pi\) | ||||
0.673250 | + | 0.739415i | \(0.264898\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.3651 | −1.14039 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.5801 | 1.52116 | 0.760581 | − | 0.649243i | \(-0.224914\pi\) | ||||
0.760581 | + | 0.649243i | \(0.224914\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.3636 | −0.603115 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.10522 | −0.111420 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.4038 | −1.34076 | −0.670379 | − | 0.742018i | \(-0.733869\pi\) | ||||
−0.670379 | + | 0.742018i | \(0.733869\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.1140 | −0.742840 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.9409 | −1.04663 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 47.7697 | 2.50038 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.87073 | −0.254250 | −0.127125 | − | 0.991887i | \(-0.540575\pi\) | ||||
−0.127125 | + | 0.991887i | \(0.540575\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.02317 | −0.417670 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.7167 | 0.608301 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.2388 | −1.20326 | −0.601629 | − | 0.798776i | \(-0.705481\pi\) | ||||
−0.601629 | + | 0.798776i | \(0.705481\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.4951 | 0.593603 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.10252 | 0.211291 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.8658 | −0.814971 | −0.407486 | − | 0.913212i | \(-0.633594\pi\) | ||||
−0.407486 | + | 0.913212i | \(0.633594\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.7406 | −1.93351 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.06828 | −0.105684 | −0.0528421 | − | 0.998603i | \(-0.516828\pi\) | ||||
−0.0528421 | + | 0.998603i | \(0.516828\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.21044 | −0.214584 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.8654 | −0.806482 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.51679 | −0.178308 | −0.0891542 | − | 0.996018i | \(-0.528416\pi\) | ||||
−0.0891542 | + | 0.996018i | \(0.528416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.39781 | 0.0706901 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.15313 | −0.159054 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.10187 | −0.0554408 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.47459 | −0.274762 | −0.137381 | − | 0.990518i | \(-0.543868\pi\) | ||||
−0.137381 | + | 0.990518i | \(0.543868\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.65345 | −0.232964 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.76137 | −0.337647 | −0.168823 | − | 0.985646i | \(-0.553997\pi\) | ||||
−0.168823 | + | 0.985646i | \(0.553997\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.25118 | 0.311393 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −38.3053 | −1.90340 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.2722 | 0.509175 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.6378 | −0.723793 | −0.361897 | − | 0.932218i | \(-0.617871\pi\) | ||||
−0.361897 | + | 0.932218i | \(0.617871\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.6373 | 1.41257 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.602193 | −0.0296320 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −47.3034 | −2.32203 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.2223 | 0.647499 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.5736 | −1.44476 | −0.722382 | − | 0.691494i | \(-0.756953\pi\) | ||||
−0.722382 | + | 0.691494i | \(0.756953\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0223 | −0.585930 | −0.292965 | − | 0.956123i | \(-0.594642\pi\) | ||||
−0.292965 | + | 0.956123i | \(0.594642\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.9924 | 0.534467 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.60299 | 0.320292 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.84352 | −0.476361 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.8417 | 0.813127 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.1034 | −0.534834 | −0.267417 | − | 0.963581i | \(-0.586170\pi\) | ||||
−0.267417 | + | 0.963581i | \(0.586170\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.2165 | 0.827372 | 0.413686 | − | 0.910420i | \(-0.364241\pi\) | ||||
0.413686 | + | 0.910420i | \(0.364241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.54554 | 0.217942 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.08976 | 0.147803 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.1681 | 1.20121 | 0.600603 | − | 0.799548i | \(-0.294927\pi\) | ||||
0.600603 | + | 0.799548i | \(0.294927\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.43195 | 0.0681879 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.1531 | −1.48013 | −0.740065 | − | 0.672536i | \(-0.765205\pi\) | ||||
−0.740065 | + | 0.672536i | \(0.765205\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −50.2461 | −2.38189 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −45.6841 | −2.16078 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.7444 | 0.507057 | 0.253529 | − | 0.967328i | \(-0.418409\pi\) | ||||
0.253529 | + | 0.967328i | \(0.418409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.92567 | −0.326117 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.69969 | 0.455731 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.0461 | −1.03354 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.0863 | −1.40738 | −0.703690 | − | 0.710508i | \(-0.748465\pi\) | ||||
−0.703690 | + | 0.710508i | \(0.748465\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.30110 | −0.154082 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.29082 | −0.386142 | −0.193071 | − | 0.981185i | \(-0.561845\pi\) | ||||
−0.193071 | + | 0.981185i | \(0.561845\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.2795 | 0.524203 | 0.262102 | − | 0.965040i | \(-0.415584\pi\) | ||||
0.262102 | + | 0.965040i | \(0.415584\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.92622 | 0.321196 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −38.2582 | −1.77038 | −0.885188 | − | 0.465233i | \(-0.845971\pi\) | ||||
−0.885188 | + | 0.465233i | \(0.845971\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.30636 | 0.245025 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.54488 | 0.439805 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.6951 | −0.629702 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.5955 | 0.669687 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.7777 | −0.768198 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.0812 | −1.51152 | −0.755759 | − | 0.654850i | \(-0.772732\pi\) | ||||
−0.755759 | + | 0.654850i | \(0.772732\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 53.7860 | 2.45243 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.94269 | −0.133897 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.1264 | −0.913892 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.3757 | −1.14988 | −0.574941 | − | 0.818195i | \(-0.694975\pi\) | ||||
−0.574941 | + | 0.818195i | \(0.694975\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.7723 | 1.16547 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.4505 | −1.37421 | −0.687107 | − | 0.726556i | \(-0.741120\pi\) | ||||
−0.687107 | + | 0.726556i | \(0.741120\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.633874 | 0.0285483 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.02912 | 0.270989 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.33603 | 0.149641 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.9016 | −0.532790 | −0.266395 | − | 0.963864i | \(-0.585833\pi\) | ||||
−0.266395 | + | 0.963864i | \(0.585833\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.82370 | 0.126154 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.90567 | 0.397084 | 0.198542 | − | 0.980092i | \(-0.436379\pi\) | ||||
0.198542 | + | 0.980092i | \(0.436379\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.3206 | −0.770756 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 60.8167 | 2.70096 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.1838 | 1.20490 | 0.602451 | − | 0.798156i | \(-0.294191\pi\) | ||||
0.602451 | + | 0.798156i | \(0.294191\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0239 | −0.620379 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.29687 | −0.322165 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.0016 | −0.793245 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.48870 | 0.417313 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.85887 | −0.169386 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.10981 | 0.311487 | 0.155743 | − | 0.987798i | \(-0.450223\pi\) | ||||
0.155743 | + | 0.987798i | \(0.450223\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.4581 | 1.33184 | 0.665919 | − | 0.746024i | \(-0.268039\pi\) | ||||
0.665919 | + | 0.746024i | \(0.268039\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.9007 | −0.606678 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.965861 | 0.0420735 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0461 | −0.915049 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.862309 | 0.0374210 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.2633 | −1.57074 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.5189 | 1.36268 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −42.5976 | −1.83822 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.23607 | 0.0532412 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.88794 | 0.0811688 | 0.0405844 | − | 0.999176i | \(-0.487078\pi\) | ||||
0.0405844 | + | 0.999176i | \(0.487078\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.6947 | 0.544781 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 54.8415 | 2.34915 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.8844 | −0.593654 | −0.296827 | − | 0.954931i | \(-0.595928\pi\) | ||||
−0.296827 | + | 0.954931i | \(0.595928\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.0954 | 0.601577 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.40114 | 0.0596906 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.323477 | 0.0137556 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 59.5942 | 2.52963 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.5183 | 0.784644 | 0.392322 | − | 0.919828i | \(-0.371672\pi\) | ||||
0.392322 | + | 0.919828i | \(0.371672\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −71.7086 | −3.03295 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.60219 | 0.109865 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.1932 | 1.52536 | 0.762681 | − | 0.646775i | \(-0.223883\pi\) | ||||
0.762681 | + | 0.646775i | \(0.223883\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 35.9398 | 1.51200 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.2454 | 0.472261 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.9137 | 1.21213 | 0.606063 | − | 0.795417i | \(-0.292748\pi\) | ||||
0.606063 | + | 0.795417i | \(0.292748\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.1214 | −0.632813 | −0.316406 | − | 0.948624i | \(-0.602476\pi\) | ||||
−0.316406 | + | 0.948624i | \(0.602476\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.9776 | −0.959904 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.22970 | 0.384905 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.1608 | −0.756042 | −0.378021 | − | 0.925797i | \(-0.623395\pi\) | ||||
−0.378021 | + | 0.925797i | \(0.623395\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −40.3607 | −1.67733 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.8870 | 0.576128 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.4827 | −0.599810 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 31.5689 | 1.30521 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45.0538 | −1.85957 | −0.929784 | − | 0.368105i | \(-0.880007\pi\) | ||||
−0.929784 | + | 0.368105i | \(0.880007\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.13497 | 0.0879701 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.09581 | −0.250748 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.43139 | 0.264106 | 0.132053 | − | 0.991243i | \(-0.457843\pi\) | ||||
0.132053 | + | 0.991243i | \(0.457843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.40632 | −0.139645 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 55.1210 | 2.25595 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.0655 | −1.67789 | −0.838946 | − | 0.544215i | \(-0.816828\pi\) | ||||
−0.838946 | + | 0.544215i | \(0.816828\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.2626 | 1.60156 | 0.800778 | − | 0.598961i | \(-0.204420\pi\) | ||||
0.800778 | + | 0.598961i | \(0.204420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.59841 | −0.309431 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −32.2651 | −1.31176 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.9954 | −0.486879 | −0.243440 | − | 0.969916i | \(-0.578276\pi\) | ||||
−0.243440 | + | 0.969916i | \(0.578276\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.33444 | −0.0540744 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 49.6835 | 2.00998 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.0774 | −1.13404 | −0.567018 | − | 0.823706i | \(-0.691903\pi\) | ||||
−0.567018 | + | 0.823706i | \(0.691903\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −40.1792 | −1.62018 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.08688 | −0.245049 | −0.122524 | − | 0.992466i | \(-0.539099\pi\) | ||||
−0.122524 | + | 0.992466i | \(0.539099\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.24659 | −0.130491 | −0.0652456 | − | 0.997869i | \(-0.520783\pi\) | ||||
−0.0652456 | + | 0.997869i | \(0.520783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.61429 | −0.185165 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.7509 | 0.590980 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.4155 | −0.576621 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.75199 | 0.229712 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.31040 | 0.331357 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.53093 | −0.259992 | −0.129996 | − | 0.991515i | \(-0.541496\pi\) | ||||
−0.129996 | + | 0.991515i | \(0.541496\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.44302 | 0.176594 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −61.0655 | −2.42331 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.47214 | 0.256435 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.77701 | −0.188976 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.98745 | −0.275988 | −0.137994 | − | 0.990433i | \(-0.544065\pi\) | ||||
−0.137994 | + | 0.990433i | \(0.544065\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.1348 | −0.833475 | −0.416737 | − | 0.909027i | \(-0.636827\pi\) | ||||
−0.416737 | + | 0.909027i | \(0.636827\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −79.4522 | −3.12843 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.2892 | 1.34805 | 0.674024 | − | 0.738709i | \(-0.264564\pi\) | ||||
0.674024 | + | 0.738709i | \(0.264564\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.744352 | 0.0292184 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.03335 | −0.0796932 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.4234 | −0.799231 | −0.399615 | − | 0.916683i | \(-0.630856\pi\) | ||||
−0.399615 | + | 0.916683i | \(0.630856\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.10187 | −0.199346 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.0814 | 0.783450 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.16578 | 0.357048 | 0.178524 | − | 0.983936i | \(-0.442868\pi\) | ||||
0.178524 | + | 0.983936i | \(0.442868\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.1919 | −1.29102 | −0.645508 | − | 0.763754i | \(-0.723354\pi\) | ||||
−0.645508 | + | 0.763754i | \(0.723354\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.6253 | 0.529161 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.52945 | −0.291979 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.886034 | 0.0343074 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −39.6047 | −1.53121 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.1673 | 0.469712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.8277 | 1.72798 | 0.863990 | − | 0.503509i | \(-0.167958\pi\) | ||||
0.863990 | + | 0.503509i | \(0.167958\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.7971 | −0.838970 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.9276 | 0.689013 | 0.344506 | − | 0.938784i | \(-0.388046\pi\) | ||||
0.344506 | + | 0.938784i | \(0.388046\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.90855 | 0.226749 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.5753 | 1.40157 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.3742 | 1.35356 | 0.676778 | − | 0.736187i | \(-0.263376\pi\) | ||||
0.676778 | + | 0.736187i | \(0.263376\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 46.3361 | 1.77041 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.71616 | 0.218085 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −75.8322 | −2.88898 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.6537 | 1.24221 | 0.621103 | − | 0.783729i | \(-0.286685\pi\) | ||||
0.621103 | + | 0.783729i | \(0.286685\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.76998 | −0.0672361 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.3941 | 0.811526 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.60299 | −0.212228 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.50572 | 0.0569516 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.3696 | 0.467194 | 0.233597 | − | 0.972334i | \(-0.424950\pi\) | ||||
0.233597 | + | 0.972334i | \(0.424950\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.3696 | 0.692823 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 55.0486 | 2.07325 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.08485 | 0.191235 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.9482 | −0.786727 | −0.393363 | − | 0.919383i | \(-0.628689\pi\) | ||||
−0.393363 | + | 0.919383i | \(0.628689\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.463202 | −0.0173714 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.35009 | 0.0505611 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.2505 | 1.01911 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.1206 | 0.676725 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.0239 | −1.04511 | −0.522557 | − | 0.852604i | \(-0.675022\pi\) | ||||
−0.522557 | + | 0.852604i | \(0.675022\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.28477 | 0.196815 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.2890 | 0.494223 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.18546 | 0.155444 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.9844 | −0.889531 | −0.444765 | − | 0.895647i | \(-0.646713\pi\) | ||||
−0.444765 | + | 0.895647i | \(0.646713\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.74583 | 0.175772 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.0796 | −0.409793 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.0864 | 1.14820 | 0.574102 | − | 0.818784i | \(-0.305351\pi\) | ||||
0.574102 | + | 0.818784i | \(0.305351\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.17104 | 0.264508 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.55902 | −0.241604 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.0841 | 0.444519 | 0.222260 | − | 0.974988i | \(-0.428657\pi\) | ||||
0.222260 | + | 0.974988i | \(0.428657\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.1178 | 1.10640 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 52.8588 | 1.93920 | 0.969600 | − | 0.244695i | \(-0.0786879\pi\) | ||||
0.969600 | + | 0.244695i | \(0.0786879\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −73.9184 | −2.70816 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.8854 | −0.727568 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.25309 | −0.338100 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.6499 | 1.11843 | 0.559216 | − | 0.829022i | \(-0.311102\pi\) | ||||
0.559216 | + | 0.829022i | \(0.311102\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 55.9380 | 2.03849 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.6944 | 0.571179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.57276 | 0.129854 | 0.0649271 | − | 0.997890i | \(-0.479319\pi\) | ||||
0.0649271 | + | 0.997890i | \(0.479319\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.63736 | 0.132028 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.64537 | −0.168395 | −0.0841973 | − | 0.996449i | \(-0.526833\pi\) | ||||
−0.0841973 | + | 0.996449i | \(0.526833\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.1000 | −0.582858 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.87766 | 0.176352 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.89748 | 0.140730 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.1361 | −0.473700 | −0.236850 | − | 0.971546i | \(-0.576115\pi\) | ||||
−0.236850 | + | 0.971546i | \(0.576115\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.2120 | 0.511833 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.0372 | 1.58391 | 0.791954 | − | 0.610581i | \(-0.209064\pi\) | ||||
0.791954 | + | 0.610581i | \(0.209064\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.37756 | 0.229089 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.4952 | −0.627637 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.3850 | −0.443740 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.12356 | −0.147552 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.09248 | −0.0747792 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.4439 | 0.551218 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.3178 | −1.40153 | −0.700765 | − | 0.713393i | \(-0.747158\pi\) | ||||
−0.700765 | + | 0.713393i | \(0.747158\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.53550 | 0.0902661 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.5509 | −0.375148 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 63.7086 | 2.26236 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −84.0210 | −2.97992 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.5987 | 1.15470 | 0.577352 | − | 0.816496i | \(-0.304086\pi\) | ||||
0.577352 | + | 0.816496i | \(0.304086\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.67652 | 0.271576 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21.1224 | −0.746324 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.3344 | 0.611719 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.76137 | −0.167816 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38.0356 | −1.33892 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −56.0461 | −1.97048 | −0.985239 | − | 0.171187i | \(-0.945240\pi\) | ||||
−0.985239 | + | 0.171187i | \(0.945240\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.39490 | −0.329900 | −0.164950 | − | 0.986302i | \(-0.552746\pi\) | ||||
−0.164950 | + | 0.986302i | \(0.552746\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 41.5705 | 1.45794 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41.7005 | 1.46071 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.4907 | −0.856822 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.26775 | −0.323841 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.40016 | 0.258267 | 0.129134 | − | 0.991627i | \(-0.458780\pi\) | ||||
0.129134 | + | 0.991627i | \(0.458780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.2675 | −1.36878 | −0.684390 | − | 0.729116i | \(-0.739932\pi\) | ||||
−0.684390 | + | 0.729116i | \(0.739932\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.1822 | 0.598209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.5052 | −1.06077 | −0.530385 | − | 0.847757i | \(-0.677953\pi\) | ||||
−0.530385 | + | 0.847757i | \(0.677953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.0461 | 1.59925 | 0.799624 | − | 0.600501i | \(-0.205032\pi\) | ||||
0.799624 | + | 0.600501i | \(0.205032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.8364 | 0.584047 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.00000 | 0.0346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.56885 | 0.158111 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.18840 | −0.110207 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.1903 | 1.49110 | 0.745548 | − | 0.666452i | \(-0.232188\pi\) | ||||
0.745548 | + | 0.666452i | \(0.232188\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5982 | −0.986145 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.48176 | 0.223244 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 98.4035 | 3.38518 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.47214 | 0.325466 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −60.4043 | −2.07307 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.6163 | 0.398203 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.9186 | −1.09287 | −0.546437 | − | 0.837500i | \(-0.684016\pi\) | ||||
−0.546437 | + | 0.837500i | \(0.684016\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.7818 | 0.368728 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.6363 | 0.397490 | 0.198745 | − | 0.980051i | \(-0.436314\pi\) | ||||
0.198745 | + | 0.980051i | \(0.436314\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.9205 | −1.53267 | −0.766335 | − | 0.642442i | \(-0.777922\pi\) | ||||
−0.766335 | + | 0.642442i | \(0.777922\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.7955 | 0.401990 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.2676 | 0.757999 | 0.379000 | − | 0.925397i | \(-0.376268\pi\) | ||||
0.379000 | + | 0.925397i | \(0.376268\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.24379 | −0.212295 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.10522 | 0.0714970 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.399840 | −0.0135636 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.3435 | −1.16368 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.46072 | −0.286352 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.46027 | −0.184591 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.2095 | −0.614890 | −0.307445 | − | 0.951566i | \(-0.599474\pi\) | ||||
−0.307445 | + | 0.951566i | \(0.599474\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.52340 | 0.152570 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.7548 | 1.06985 | 0.534923 | − | 0.844901i | \(-0.320341\pi\) | ||||
0.534923 | + | 0.844901i | \(0.320341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.7644 | 1.94393 | 0.971964 | − | 0.235130i | \(-0.0755515\pi\) | ||||
0.971964 | + | 0.235130i | \(0.0755515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.31835 | 0.145160 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.9442 | 0.736813 | 0.368407 | − | 0.929665i | \(-0.379903\pi\) | ||||
0.368407 | + | 0.929665i | \(0.379903\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.9272 | 0.601257 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.9000 | −0.465669 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.9685 | 0.567828 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −68.9244 | −2.30389 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.0455 | 0.635910 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.612234 | 0.0204192 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.7167 | −0.390340 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.3250 | 0.776206 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.5404 | 0.682786 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.0883 | 0.334978 | 0.167489 | − | 0.985874i | \(-0.446434\pi\) | ||||
0.167489 | + | 0.985874i | \(0.446434\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.28123 | −0.241503 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.3155 | −1.76642 | −0.883210 | − | 0.468977i | \(-0.844623\pi\) | ||||
−0.883210 | + | 0.468977i | \(0.844623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.1652 | −0.568086 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 70.5883 | 2.33358 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.49777 | 0.0494606 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.3247 | 0.472529 | 0.236264 | − | 0.971689i | \(-0.424077\pi\) | ||||
0.236264 | + | 0.971689i | \(0.424077\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.7448 | −1.11193 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.5912 | −0.710684 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 54.8734 | 1.80423 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.56750 | −0.248549 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.0091 | 0.984567 | 0.492284 | − | 0.870435i | \(-0.336162\pi\) | ||||
0.492284 | + | 0.870435i | \(0.336162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.21044 | 0.0724442 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 72.5259 | 2.37439 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.21044 | 0.137696 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.1807 | −1.47599 | −0.737994 | − | 0.674807i | \(-0.764227\pi\) | ||||
−0.737994 | + | 0.674807i | \(0.764227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 68.5427 | 2.23681 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.4598 | 1.22116 | 0.610578 | − | 0.791956i | \(-0.290937\pi\) | ||||
0.610578 | + | 0.791956i | \(0.290937\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.83189 | −0.255041 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.2446 | 0.365786 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.33347 | 0.0433318 | 0.0216659 | − | 0.999765i | \(-0.493103\pi\) | ||||
0.0216659 | + | 0.999765i | \(0.493103\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 90.7643 | 2.94633 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.94874 | −0.192901 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.14271 | 0.134196 | 0.0670978 | − | 0.997746i | \(-0.478626\pi\) | ||||
0.0670978 | + | 0.997746i | \(0.478626\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37.1786 | −1.20307 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.64946 | 0.0533196 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.6030 | −0.439263 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0671 | −0.969907 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.2499 | 0.426973 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −65.3050 | −2.10224 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.9265 | 0.769423 | 0.384712 | − | 0.923037i | \(-0.374301\pi\) | ||||
0.384712 | + | 0.923037i | \(0.374301\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.65345 | 0.149490 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.7634 | −1.34025 | −0.670126 | − | 0.742248i | \(-0.733760\pi\) | ||||
−0.670126 | + | 0.742248i | \(0.733760\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.28073 | −0.201351 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 89.9674 | 2.88126 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.4143 | −1.13300 | −0.566501 | − | 0.824061i | \(-0.691703\pi\) | ||||
−0.566501 | + | 0.824061i | \(0.691703\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.2331 | −0.582731 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.0543 | 0.736066 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.7062 | −1.45780 | −0.728901 | − | 0.684620i | \(-0.759968\pi\) | ||||
−0.728901 | + | 0.684620i | \(0.759968\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.86324 | −0.314269 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.1608 | −0.514403 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.4871 | −0.492462 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.3586 | 0.424351 | 0.212176 | − | 0.977232i | \(-0.431945\pi\) | ||||
0.212176 | + | 0.977232i | \(0.431945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.9091 | −1.10781 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 89.1877 | 2.82744 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.8346 | 1.00821 | 0.504106 | − | 0.863642i | \(-0.331822\pi\) | ||||
0.504106 | + | 0.863642i | \(0.331822\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.4334 | −0.867955 |
(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 | 7616.2.a.bj.1.4 | 4 | ||
4.3 | odd | 2 | 7616.2.a.bp.1.1 | 4 | |||
8.3 | odd | 2 | 1904.2.a.q.1.4 | 4 | |||
8.5 | even | 2 | 952.2.a.g.1.1 | ✓ | 4 | ||
24.5 | odd | 2 | 8568.2.a.bj.1.4 | 4 | |||
56.13 | odd | 2 | 6664.2.a.o.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
952.2.a.g.1.1 | ✓ | 4 | 8.5 | even | 2 | ||
1904.2.a.q.1.4 | 4 | 8.3 | odd | 2 | |||
6664.2.a.o.1.4 | 4 | 56.13 | odd | 2 | |||
7616.2.a.bj.1.4 | 4 | 1.1 | even | 1 | trivial | ||
7616.2.a.bp.1.1 | 4 | 4.3 | odd | 2 | |||
8568.2.a.bj.1.4 | 4 | 24.5 | odd | 2 |