Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3680,2,Mod(1,3680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3680, 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("3680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3680 = 2^{5} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3680.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: | \(29.3849479438\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.876604.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 9x^{3} + 8x^{2} + 18x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.63675\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3680.1 |
$q$-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 | ||||||||
\(3\) | −0.706809 | −0.408076 | −0.204038 | − | 0.978963i | \(-0.565407\pi\) | ||||
−0.204038 | + | 0.978963i | \(0.565407\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.21261 | −1.97018 | −0.985090 | − | 0.172041i | \(-0.944964\pi\) | ||||
−0.985090 | + | 0.172041i | \(0.944964\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.50042 | −0.833474 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.73273 | −1.42697 | −0.713485 | − | 0.700670i | \(-0.752884\pi\) | ||||
−0.713485 | + | 0.700670i | \(0.752884\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.250999 | −0.0696145 | −0.0348073 | − | 0.999394i | \(-0.511082\pi\) | ||||
−0.0348073 | + | 0.999394i | \(0.511082\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.706809 | −0.182497 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.11467 | −0.512884 | −0.256442 | − | 0.966560i | \(-0.582550\pi\) | ||||
−0.256442 | + | 0.966560i | \(0.582550\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.84398 | −1.34070 | −0.670350 | − | 0.742045i | \(-0.733856\pi\) | ||||
−0.670350 | + | 0.742045i | \(0.733856\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.68431 | 0.803983 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.88775 | 0.748197 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.19011 | −1.14947 | −0.574737 | − | 0.818338i | \(-0.694896\pi\) | ||||
−0.574737 | + | 0.818338i | \(0.694896\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.60888 | 0.648173 | 0.324087 | − | 0.946027i | \(-0.394943\pi\) | ||||
0.324087 | + | 0.946027i | \(0.394943\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.34513 | 0.582313 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.21261 | −0.881091 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.8474 | 1.78330 | 0.891651 | − | 0.452724i | \(-0.149548\pi\) | ||||
0.891651 | + | 0.452724i | \(0.149548\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.177408 | 0.0284080 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.02054 | 0.159382 | 0.0796909 | − | 0.996820i | \(-0.474607\pi\) | ||||
0.0796909 | + | 0.996820i | \(0.474607\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.6670 | −1.77921 | −0.889603 | − | 0.456734i | \(-0.849019\pi\) | ||||
−0.889603 | + | 0.456734i | \(0.849019\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.50042 | −0.372741 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.134372 | −0.0196002 | −0.00980011 | − | 0.999952i | \(-0.503120\pi\) | ||||
−0.00980011 | + | 0.999952i | \(0.503120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20.1713 | 2.88161 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.49467 | 0.209296 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.78309 | −1.34381 | −0.671905 | − | 0.740637i | \(-0.734524\pi\) | ||||
−0.671905 | + | 0.740637i | \(0.734524\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.73273 | −0.638161 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.13057 | 0.547108 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3695 | 1.34999 | 0.674995 | − | 0.737822i | \(-0.264146\pi\) | ||||
0.674995 | + | 0.737822i | \(0.264146\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.05036 | 0.134485 | 0.0672426 | − | 0.997737i | \(-0.478580\pi\) | ||||
0.0672426 | + | 0.997737i | \(0.478580\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.0337 | 1.64209 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.250999 | −0.0311326 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.2602 | 1.37565 | 0.687825 | − | 0.725877i | \(-0.258566\pi\) | ||||
0.687825 | + | 0.725877i | \(0.258566\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.706809 | 0.0850898 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4582 | −1.24116 | −0.620582 | − | 0.784142i | \(-0.713103\pi\) | ||||
−0.620582 | + | 0.784142i | \(0.713103\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.98568 | −0.817612 | −0.408806 | − | 0.912621i | \(-0.634055\pi\) | ||||
−0.408806 | + | 0.912621i | \(0.634055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.706809 | −0.0816152 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 24.6698 | 2.81139 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.07590 | 0.683593 | 0.341796 | − | 0.939774i | \(-0.388965\pi\) | ||||
0.341796 | + | 0.939774i | \(0.388965\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.75337 | 0.528153 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.6987 | 1.94269 | 0.971343 | − | 0.237684i | \(-0.0763882\pi\) | ||||
0.971343 | + | 0.237684i | \(0.0763882\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.11467 | −0.229369 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.37522 | 0.469073 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.300413 | 0.0318438 | 0.0159219 | − | 0.999873i | \(-0.494932\pi\) | ||||
0.0159219 | + | 0.999873i | \(0.494932\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.30836 | 0.137153 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.55079 | −0.264504 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.84398 | −0.599579 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.307515 | 0.0312234 | 0.0156117 | − | 0.999878i | \(-0.495030\pi\) | ||||
0.0156117 | + | 0.999878i | \(0.495030\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.8338 | 1.18934 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.12937 | 0.211881 | 0.105940 | − | 0.994372i | \(-0.466215\pi\) | ||||
0.105940 | + | 0.994372i | \(0.466215\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4734 | −1.22904 | −0.614520 | − | 0.788901i | \(-0.710650\pi\) | ||||
−0.614520 | + | 0.788901i | \(0.710650\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.68431 | 0.359552 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.33381 | −0.322291 | −0.161146 | − | 0.986931i | \(-0.551519\pi\) | ||||
−0.161146 | + | 0.986931i | \(0.551519\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.67046 | −0.830479 | −0.415240 | − | 0.909712i | \(-0.636302\pi\) | ||||
−0.415240 | + | 0.909712i | \(0.636302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.66704 | −0.727723 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.49258 | 0.234483 | 0.117241 | − | 0.993103i | \(-0.462595\pi\) | ||||
0.117241 | + | 0.993103i | \(0.462595\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.627603 | 0.0580219 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.0230 | 1.01047 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3987 | 1.03624 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.721328 | −0.0650399 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.54715 | −0.226023 | −0.113011 | − | 0.993594i | \(-0.536050\pi\) | ||||
−0.113011 | + | 0.993594i | \(0.536050\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.24636 | 0.726052 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3878 | −0.907585 | −0.453793 | − | 0.891107i | \(-0.649929\pi\) | ||||
−0.453793 | + | 0.891107i | \(0.649929\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30.4623 | 2.64142 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.88775 | 0.334604 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.14830 | −0.183541 | −0.0917706 | − | 0.995780i | \(-0.529253\pi\) | ||||
−0.0917706 | + | 0.995780i | \(0.529253\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.69753 | 0.313620 | 0.156810 | − | 0.987629i | \(-0.449879\pi\) | ||||
0.156810 | + | 0.987629i | \(0.449879\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0949755 | 0.00799838 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.18791 | 0.0993379 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.19011 | −0.514061 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.2572 | −1.17592 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.33265 | −0.682638 | −0.341319 | − | 0.939948i | \(-0.610874\pi\) | ||||
−0.341319 | + | 0.939948i | \(0.610874\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.1453 | −1.23251 | −0.616255 | − | 0.787547i | \(-0.711351\pi\) | ||||
−0.616255 | + | 0.787547i | \(0.711351\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.28758 | 0.427475 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.60888 | 0.289872 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.97518 | −0.157636 | −0.0788181 | − | 0.996889i | \(-0.525115\pi\) | ||||
−0.0788181 | + | 0.996889i | \(0.525115\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.91477 | 0.548377 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.21261 | 0.410811 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7337 | 1.23236 | 0.616178 | − | 0.787607i | \(-0.288680\pi\) | ||||
0.616178 | + | 0.787607i | \(0.288680\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.34513 | 0.260418 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.2115 | 1.56401 | 0.782005 | − | 0.623273i | \(-0.214197\pi\) | ||||
0.782005 | + | 0.623273i | \(0.214197\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9370 | −0.995154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.6124 | 1.11744 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.579282 | −0.0440420 | −0.0220210 | − | 0.999758i | \(-0.507010\pi\) | ||||
−0.0220210 | + | 0.999758i | \(0.507010\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.21261 | −0.394036 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.32923 | −0.550899 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.22178 | −0.465038 | −0.232519 | − | 0.972592i | \(-0.574697\pi\) | ||||
−0.232519 | + | 0.972592i | \(0.574697\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1175 | −0.826355 | −0.413178 | − | 0.910651i | \(-0.635581\pi\) | ||||
−0.413178 | + | 0.910651i | \(0.635581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.742406 | −0.0548802 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.8474 | 0.797517 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0082 | 0.731870 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −20.2653 | −1.47408 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.2812 | −1.75692 | −0.878462 | − | 0.477812i | \(-0.841430\pi\) | ||||
−0.878462 | + | 0.477812i | \(0.841430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.1931 | −1.30957 | −0.654785 | − | 0.755815i | \(-0.727241\pi\) | ||||
−0.654785 | + | 0.755815i | \(0.727241\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.177408 | 0.0127045 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.7099 | 1.97425 | 0.987125 | − | 0.159950i | \(-0.0511334\pi\) | ||||
0.987125 | + | 0.159950i | \(0.0511334\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.9434 | −1.13020 | −0.565098 | − | 0.825024i | \(-0.691162\pi\) | ||||
−0.565098 | + | 0.825024i | \(0.691162\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.95879 | −0.561370 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 32.2666 | 2.26467 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.02054 | 0.0712777 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.50042 | 0.173791 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.6579 | 1.91314 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.00559 | 0.413442 | 0.206721 | − | 0.978400i | \(-0.433721\pi\) | ||||
0.206721 | + | 0.978400i | \(0.433721\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.39197 | 0.506489 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.6670 | −0.795685 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.8117 | −1.27702 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.93754 | 0.333648 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.530781 | 0.0357042 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.90571 | 0.194581 | 0.0972903 | − | 0.995256i | \(-0.468982\pi\) | ||||
0.0972903 | + | 0.995256i | \(0.468982\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.50042 | −0.166695 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8063 | 0.717240 | 0.358620 | − | 0.933484i | \(-0.383247\pi\) | ||||
0.358620 | + | 0.933484i | \(0.383247\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.6384 | 1.56207 | 0.781034 | − | 0.624488i | \(-0.214692\pi\) | ||||
0.781034 | + | 0.624488i | \(0.214692\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.4368 | −1.14726 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.4845 | 0.883400 | 0.441700 | − | 0.897163i | \(-0.354375\pi\) | ||||
0.441700 | + | 0.897163i | \(0.354375\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.134372 | −0.00876548 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.29450 | −0.278958 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.6295 | −1.39910 | −0.699548 | − | 0.714586i | \(-0.746615\pi\) | ||||
−0.699548 | + | 0.714586i | \(0.746615\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.0901 | −0.972037 | −0.486018 | − | 0.873949i | \(-0.661551\pi\) | ||||
−0.486018 | + | 0.873949i | \(0.661551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.0230 | −0.963723 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.1713 | 1.28869 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.46683 | 0.0933322 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.5096 | −0.792763 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.91589 | 0.184049 | 0.0920245 | − | 0.995757i | \(-0.470666\pi\) | ||||
0.0920245 | + | 0.995757i | \(0.470666\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.73273 | 0.297544 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.49467 | 0.0935998 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.5613 | 0.970688 | 0.485344 | − | 0.874323i | \(-0.338694\pi\) | ||||
0.485344 | + | 0.874323i | \(0.338694\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −56.5432 | −3.51342 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.4779 | 0.958057 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.342206 | 0.0211013 | 0.0105507 | − | 0.999944i | \(-0.496642\pi\) | ||||
0.0105507 | + | 0.999944i | \(0.496642\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.78309 | −0.600970 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.212335 | −0.0129947 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.5603 | −0.887759 | −0.443880 | − | 0.896086i | \(-0.646398\pi\) | ||||
−0.443880 | + | 0.896086i | \(0.646398\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.17019 | −0.0710837 | −0.0355419 | − | 0.999368i | \(-0.511316\pi\) | ||||
−0.0355419 | + | 0.999368i | \(0.511316\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.924758 | −0.0559689 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.73273 | −0.285394 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.3954 | 1.46578 | 0.732888 | − | 0.680349i | \(-0.238172\pi\) | ||||
0.732888 | + | 0.680349i | \(0.238172\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.02371 | −0.540236 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.83106 | 0.168887 | 0.0844434 | − | 0.996428i | \(-0.473089\pi\) | ||||
0.0844434 | + | 0.996428i | \(0.473089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.81964 | 0.405385 | 0.202693 | − | 0.979242i | \(-0.435031\pi\) | ||||
0.202693 | + | 0.979242i | \(0.435031\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.13057 | 0.244674 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.31968 | −0.314011 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.5282 | −0.736950 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.217354 | −0.0127415 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −29.0172 | −1.69520 | −0.847601 | − | 0.530634i | \(-0.821954\pi\) | ||||
−0.847601 | + | 0.530634i | \(0.821954\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.3695 | 0.603734 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.3996 | −1.06765 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.250999 | 0.0145156 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 60.8157 | 3.50536 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.50506 | −0.0864634 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.05036 | 0.0601437 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.24320 | 0.527538 | 0.263769 | − | 0.964586i | \(-0.415034\pi\) | ||||
0.263769 | + | 0.964586i | \(0.415034\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.81630 | 0.501542 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.2166 | 0.806151 | 0.403075 | − | 0.915167i | \(-0.367941\pi\) | ||||
0.403075 | + | 0.915167i | \(0.367941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.45918 | 0.195524 | 0.0977622 | − | 0.995210i | \(-0.468832\pi\) | ||||
0.0977622 | + | 0.995210i | \(0.468832\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.0337 | 0.734366 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.9776 | 0.897393 | 0.448696 | − | 0.893684i | \(-0.351888\pi\) | ||||
0.448696 | + | 0.893684i | \(0.351888\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.2961 | 1.64027 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.35636 | 0.131519 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.3581 | 0.687623 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.250999 | −0.0139229 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.12835 | 0.338899 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.700430 | 0.0386159 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.63455 | 0.474598 | 0.237299 | − | 0.971437i | \(-0.423738\pi\) | ||||
0.237299 | + | 0.971437i | \(0.423738\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −27.1231 | −1.48634 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.2602 | 0.615209 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.9718 | 1.74161 | 0.870807 | − | 0.491624i | \(-0.163597\pi\) | ||||
0.870807 | + | 0.491624i | \(0.163597\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.76178 | −0.0956867 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.0798 | −0.924924 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −68.6566 | −3.70711 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.706809 | 0.0380533 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.3122 | −0.660955 | −0.330477 | − | 0.943814i | \(-0.607210\pi\) | ||||
−0.330477 | + | 0.943814i | \(0.607210\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.5094 | −0.562557 | −0.281279 | − | 0.959626i | \(-0.590759\pi\) | ||||
−0.281279 | + | 0.959626i | \(0.590759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.975819 | −0.0520854 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.1250 | −0.592127 | −0.296063 | − | 0.955168i | \(-0.595674\pi\) | ||||
−0.296063 | + | 0.955168i | \(0.595674\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.4582 | −0.555065 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.79112 | −0.412350 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.2718 | −1.28101 | −0.640507 | − | 0.767952i | \(-0.721276\pi\) | ||||
−0.640507 | + | 0.767952i | \(0.721276\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.1521 | 0.797477 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.05669 | −0.422867 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.98568 | −0.365647 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.78708 | 0.458682 | 0.229341 | − | 0.973346i | \(-0.426343\pi\) | ||||
0.229341 | + | 0.973346i | \(0.426343\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.55178 | −0.132841 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 50.9954 | 2.64755 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.53233 | 0.338231 | 0.169116 | − | 0.985596i | \(-0.445909\pi\) | ||||
0.169116 | + | 0.985596i | \(0.445909\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.706809 | −0.0364994 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.55371 | 0.0800202 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.4920 | 1.00124 | 0.500620 | − | 0.865667i | \(-0.333106\pi\) | ||||
0.500620 | + | 0.865667i | \(0.333106\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.80034 | 0.0922345 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.0604 | 1.33163 | 0.665813 | − | 0.746118i | \(-0.268085\pi\) | ||||
0.665813 | + | 0.746118i | \(0.268085\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 24.6698 | 1.25729 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 29.1725 | 1.48292 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.4470 | −0.732490 | −0.366245 | − | 0.930518i | \(-0.619357\pi\) | ||||
−0.366245 | + | 0.930518i | \(0.619357\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.11467 | 0.106944 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.34218 | 0.370364 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.07590 | 0.305712 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.9996 | 1.05394 | 0.526970 | − | 0.849884i | \(-0.323328\pi\) | ||||
0.526970 | + | 0.849884i | \(0.323328\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −21.5310 | −1.07790 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.2831 | −1.41239 | −0.706195 | − | 0.708018i | \(-0.749590\pi\) | ||||
−0.706195 | + | 0.708018i | \(0.749590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.905824 | −0.0451223 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.75337 | 0.236197 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −51.3378 | −2.54472 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.0734 | 1.14091 | 0.570454 | − | 0.821329i | \(-0.306767\pi\) | ||||
0.570454 | + | 0.821329i | \(0.306767\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.51843 | 0.0748988 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −54.0520 | −2.65972 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.6987 | 0.868795 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.61344 | −0.127981 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.4805 | 1.34251 | 0.671254 | − | 0.741227i | \(-0.265756\pi\) | ||||
0.671254 | + | 0.741227i | \(0.265756\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.9524 | −0.533787 | −0.266893 | − | 0.963726i | \(-0.585997\pi\) | ||||
−0.266893 | + | 0.963726i | \(0.585997\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.335987 | 0.0163363 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.11467 | −0.102577 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.47513 | −0.264960 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.839624 | −0.0405374 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.7335 | 0.661521 | 0.330760 | − | 0.943715i | \(-0.392695\pi\) | ||||
0.330760 | + | 0.943715i | \(0.392695\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.5907 | 1.71038 | 0.855190 | − | 0.518315i | \(-0.173441\pi\) | ||||
0.855190 | + | 0.518315i | \(0.173441\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.37522 | 0.209776 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.84398 | 0.279555 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.1827 | 1.53600 | 0.767999 | − | 0.640451i | \(-0.221252\pi\) | ||||
0.767999 | + | 0.640451i | \(0.221252\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −50.4366 | −2.40174 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.5678 | 1.54734 | 0.773670 | − | 0.633588i | \(-0.218419\pi\) | ||||
0.773670 | + | 0.633588i | \(0.218419\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.300413 | 0.0142410 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.88959 | 0.278568 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.9995 | −0.802257 | −0.401128 | − | 0.916022i | \(-0.631382\pi\) | ||||
−0.401128 | + | 0.916022i | \(0.631382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.82994 | −0.227433 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.7049 | 0.502958 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.30836 | 0.0613368 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.0768 | 0.752040 | 0.376020 | − | 0.926611i | \(-0.377292\pi\) | ||||
0.376020 | + | 0.926611i | \(0.377292\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.22131 | −0.383738 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.2977 | 0.665910 | 0.332955 | − | 0.942943i | \(-0.391954\pi\) | ||||
0.332955 | + | 0.942943i | \(0.391954\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.5700 | −1.51365 | −0.756827 | − | 0.653615i | \(-0.773252\pi\) | ||||
−0.756827 | + | 0.653615i | \(0.773252\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.55079 | −0.118290 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.31563 | −0.199704 | −0.0998518 | − | 0.995002i | \(-0.531837\pi\) | ||||
−0.0998518 | + | 0.995002i | \(0.531837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −58.6948 | −2.71028 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.39607 | 0.0643276 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 55.2169 | 2.53887 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.84398 | −0.268140 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.4618 | 1.12003 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.0248 | −0.869265 | −0.434632 | − | 0.900608i | \(-0.643122\pi\) | ||||
−0.434632 | + | 0.900608i | \(0.643122\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.72268 | −0.124144 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.68431 | −0.167642 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.307515 | 0.0139635 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.21675 | 0.191079 | 0.0955396 | − | 0.995426i | \(-0.469542\pi\) | ||||
0.0955396 | + | 0.995426i | \(0.469542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.1207 | −0.502895 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.6441 | 1.60860 | 0.804299 | − | 0.594225i | \(-0.202541\pi\) | ||||
0.804299 | + | 0.594225i | \(0.202541\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.0901 | 0.589547 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.8338 | 0.531890 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 54.5146 | 2.44531 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.5025 | −0.738754 | −0.369377 | − | 0.929280i | \(-0.620429\pi\) | ||||
−0.369377 | + | 0.929280i | \(0.620429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.2856 | −0.638235 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.4530 | −1.00113 | −0.500564 | − | 0.865699i | \(-0.666874\pi\) | ||||
−0.500564 | + | 0.865699i | \(0.666874\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.12937 | 0.0947559 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.14398 | 0.406099 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.8789 | 0.570848 | 0.285424 | − | 0.958401i | \(-0.407866\pi\) | ||||
0.285424 | + | 0.958401i | \(0.407866\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.4136 | 1.61084 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −22.7199 | −1.00311 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.4734 | −0.549643 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.635947 | 0.0279689 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.409441 | 0.0179725 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.6355 | 0.904058 | 0.452029 | − | 0.892003i | \(-0.350700\pi\) | ||||
0.452029 | + | 0.892003i | \(0.350700\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.6823 | −0.729467 | −0.364734 | − | 0.931112i | \(-0.618840\pi\) | ||||
−0.364734 | + | 0.931112i | \(0.618840\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.68431 | 0.160797 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.63160 | −0.332438 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.9281 | −1.12518 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.256155 | −0.0110953 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.33381 | −0.144133 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.39761 | 0.189771 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −95.4650 | −4.11197 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.1313 | −0.908506 | −0.454253 | − | 0.890873i | \(-0.650094\pi\) | ||||
−0.454253 | + | 0.890873i | \(0.650094\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.85792 | 0.337216 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.67046 | −0.371402 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.7265 | −0.928959 | −0.464480 | − | 0.885584i | \(-0.653759\pi\) | ||||
−0.464480 | + | 0.885584i | \(0.653759\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.62635 | −0.112090 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.1749 | 1.54110 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.6713 | −1.34680 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.66704 | −0.325448 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.8821 | −1.90172 | −0.950858 | − | 0.309628i | \(-0.899795\pi\) | ||||
−0.950858 | + | 0.309628i | \(0.899795\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.92841 | 0.123859 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.07386 | −0.298659 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.5584 | 0.824287 | 0.412143 | − | 0.911119i | \(-0.364780\pi\) | ||||
0.412143 | + | 0.911119i | \(0.364780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.49258 | 0.104864 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −24.7775 | −1.04056 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.5392 | −0.861047 | −0.430524 | − | 0.902579i | \(-0.641671\pi\) | ||||
−0.430524 | + | 0.902579i | \(0.641671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.8879 | 0.539340 | 0.269670 | − | 0.962953i | \(-0.413085\pi\) | ||||
0.269670 | + | 0.962953i | \(0.413085\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.1621 | 0.716959 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.2883 | 0.761351 | 0.380675 | − | 0.924709i | \(-0.375692\pi\) | ||||
0.380675 | + | 0.924709i | \(0.375692\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.8591 | 0.534404 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −92.2564 | −3.82744 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 46.3007 | 1.91758 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.627603 | 0.0259482 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.1035 | 1.73780 | 0.868898 | − | 0.494991i | \(-0.164829\pi\) | ||||
0.868898 | + | 0.494991i | \(0.164829\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.0902 | −0.869006 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.5856 | −0.805644 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.5902 | 1.42045 | 0.710225 | − | 0.703975i | \(-0.248593\pi\) | ||||
0.710225 | + | 0.703975i | \(0.248593\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.0230 | 0.451897 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.2689 | 0.461206 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.4714 | 0.427849 | 0.213925 | − | 0.976850i | \(-0.431375\pi\) | ||||
0.213925 | + | 0.976850i | \(0.431375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.2450 | −1.68242 | −0.841210 | − | 0.540708i | \(-0.818156\pi\) | ||||
−0.841210 | + | 0.540708i | \(0.818156\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.1552 | −1.14657 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.3987 | 0.463423 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.5933 | 0.714091 | 0.357045 | − | 0.934087i | \(-0.383784\pi\) | ||||
0.357045 | + | 0.934087i | \(0.383784\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.8063 | −0.924159 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0337273 | 0.00136446 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.8066 | 0.840370 | 0.420185 | − | 0.907439i | \(-0.361965\pi\) | ||||
0.420185 | + | 0.907439i | \(0.361965\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.721328 | −0.0290867 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.4765 | −1.42823 | −0.714115 | − | 0.700028i | \(-0.753171\pi\) | ||||
−0.714115 | + | 0.700028i | \(0.753171\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.2405 | 0.813533 | 0.406766 | − | 0.913532i | \(-0.366656\pi\) | ||||
0.406766 | + | 0.913532i | \(0.366656\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.88775 | −0.156010 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.56594 | −0.0627379 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.5489 | −0.780707 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.9387 | −0.914626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.40468 | −0.294776 | −0.147388 | − | 0.989079i | \(-0.547087\pi\) | ||||
−0.147388 | + | 0.989079i | \(0.547087\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.24480 | −0.168716 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.54715 | −0.101080 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.06296 | −0.200602 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.1500 | 1.03448 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.0313 | 0.633200 | 0.316600 | − | 0.948559i | \(-0.397459\pi\) | ||||
0.316600 | + | 0.948559i | \(0.397459\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.77825 | −0.149000 | −0.0744998 | − | 0.997221i | \(-0.523736\pi\) | ||||
−0.0744998 | + | 0.997221i | \(0.523736\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.24636 | 0.324700 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.1818 | −1.69765 | −0.848826 | − | 0.528672i | \(-0.822690\pi\) | ||||
−0.848826 | + | 0.528672i | \(0.822690\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −49.0759 | −1.92640 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.2962 | 0.521121 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.8519 | −1.16819 | −0.584097 | − | 0.811684i | \(-0.698551\pi\) | ||||
−0.584097 | + | 0.811684i | \(0.698551\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.3878 | −0.405885 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.4671 | 0.681458 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.9212 | −0.620202 | −0.310101 | − | 0.950704i | \(-0.600363\pi\) | ||||
−0.310101 | + | 0.950704i | \(0.600363\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.1121 | −1.05454 | −0.527269 | − | 0.849699i | \(-0.676784\pi\) | ||||
−0.527269 | + | 0.849699i | \(0.676784\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.375160 | −0.0145700 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.4623 | 1.18128 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.19011 | 0.239682 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.05378 | −0.0794037 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.97108 | −0.191907 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.6258 | −1.37327 | −0.686637 | − | 0.727001i | \(-0.740914\pi\) | ||||
−0.686637 | + | 0.727001i | \(0.740914\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.88775 | 0.149639 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48.4246 | −1.86111 | −0.930554 | − | 0.366154i | \(-0.880674\pi\) | ||||
−0.930554 | + | 0.366154i | \(0.880674\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.60295 | −0.0615156 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.63800 | −0.292689 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.8433 | 0.567965 | 0.283982 | − | 0.958829i | \(-0.408344\pi\) | ||||
0.283982 | + | 0.958829i | \(0.408344\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.14830 | −0.0820821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.7078 | −0.637443 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.45554 | 0.0935488 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.3369 | 0.925820 | 0.462910 | − | 0.886405i | \(-0.346805\pi\) | ||||
0.462910 | + | 0.886405i | \(0.346805\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −61.6850 | −2.34322 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.69753 | 0.140255 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.15811 | −0.0817443 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.53098 | −0.360495 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.0235 | 0.718509 | 0.359255 | − | 0.933240i | \(-0.383031\pi\) | ||||
0.359255 | + | 0.933240i | \(0.383031\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −63.3919 | −2.39087 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.0949755 | 0.00357698 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.0996 | −0.417443 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.7681 | −0.404405 | −0.202202 | − | 0.979344i | \(-0.564810\pi\) | ||||
−0.202202 | + | 0.979344i | \(0.564810\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.1923 | −0.569757 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.60888 | −0.135154 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.18791 | 0.0444253 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.2879 | 0.570937 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.3605 | 0.647436 | 0.323718 | − | 0.946154i | \(-0.395067\pi\) | ||||
0.323718 | + | 0.946154i | \(0.395067\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 65.0189 | 2.42143 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.6658 | 0.396665 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.19011 | −0.229895 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.28344 | −0.158864 | −0.0794321 | − | 0.996840i | \(-0.525311\pi\) | ||||
−0.0794321 | + | 0.996840i | \(0.525311\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.64176 | −0.134880 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.6720 | 0.912526 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.7449 | −1.09865 | −0.549327 | − | 0.835607i | \(-0.685116\pi\) | ||||
−0.549327 | + | 0.835607i | \(0.685116\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.2572 | −0.525885 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −53.2913 | −1.96301 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.9696 | 0.734592 | 0.367296 | − | 0.930104i | \(-0.380284\pi\) | ||||
0.367296 | + | 0.930104i | \(0.380284\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.03677 | −0.0380867 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.3943 | −0.454703 | −0.227351 | − | 0.973813i | \(-0.573007\pi\) | ||||
−0.227351 | + | 0.973813i | \(0.573007\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.33265 | −0.305285 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −44.2542 | −1.61918 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.3778 | 0.634972 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.0772 | 1.27999 | 0.639993 | − | 0.768381i | \(-0.278937\pi\) | ||||
0.639993 | + | 0.768381i | \(0.278937\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.06097 | −0.0751060 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.1453 | −0.551195 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.91074 | −0.105793 | −0.0528963 | − | 0.998600i | \(-0.516845\pi\) | ||||
−0.0528963 | + | 0.998600i | \(0.516845\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.34513 | −0.121421 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.6494 | 0.748542 | 0.374271 | − | 0.927319i | \(-0.377893\pi\) | ||||
0.374271 | + | 0.927319i | \(0.377893\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 45.1957 | 1.63619 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.28758 | 0.191173 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.60272 | −0.0939790 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.0441 | −1.11948 | −0.559739 | − | 0.828669i | \(-0.689099\pi\) | ||||
−0.559739 | + | 0.828669i | \(0.689099\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.9989 | −0.396115 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.64944 | −0.0593262 | −0.0296631 | − | 0.999560i | \(-0.509443\pi\) | ||||
−0.0296631 | + | 0.999560i | \(0.509443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.60888 | 0.129635 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 39.9652 | 1.43374 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.96402 | −0.213683 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.4959 | 1.77110 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.0656 | −0.860034 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.97518 | −0.0704971 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.0488 | −0.821600 | −0.410800 | − | 0.911725i | \(-0.634751\pi\) | ||||
−0.410800 | + | 0.911725i | \(0.634751\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.241874 | −0.00861095 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.9929 | −0.461973 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.263640 | −0.00936213 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.91477 | 0.245242 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.69319 | 0.272507 | 0.136253 | − | 0.990674i | \(-0.456494\pi\) | ||||
0.136253 | + | 0.990674i | \(0.456494\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.284154 | 0.0100526 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.751160 | −0.0265409 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.0613 | 1.16671 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.21261 | 0.183720 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.2914 | 0.362273 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.02914 | −0.282290 | −0.141145 | − | 0.989989i | \(-0.545078\pi\) | ||||
−0.141145 | + | 0.989989i | \(0.545078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.5287 | −0.369712 | −0.184856 | − | 0.982766i | \(-0.559182\pi\) | ||||
−0.184856 | + | 0.982766i | \(0.559182\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.827098 | 0.0290076 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.7337 | 0.551127 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 68.1819 | 2.38538 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.27145 | −0.114314 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.5562 | −0.612715 | −0.306357 | − | 0.951917i | \(-0.599110\pi\) | ||||
−0.306357 | + | 0.951917i | \(0.599110\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.7749 | 0.933316 | 0.466658 | − | 0.884438i | \(-0.345458\pi\) | ||||
0.466658 | + | 0.884438i | \(0.345458\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.34513 | 0.116463 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.8652 | −0.412592 | −0.206296 | − | 0.978490i | \(-0.566141\pi\) | ||||
−0.206296 | + | 0.978490i | \(0.566141\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.0687 | 1.70423 | 0.852113 | − | 0.523358i | \(-0.175321\pi\) | ||||
0.852113 | + | 0.523358i | \(0.175321\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.2429 | −0.598149 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −42.6556 | −1.47793 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.2115 | 0.699446 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.0304 | 0.484961 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.1610 | −0.626989 | −0.313494 | − | 0.949590i | \(-0.601500\pi\) | ||||
−0.313494 | + | 0.949590i | \(0.601500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.31748 | 0.321292 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.00102 | −0.0689186 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.9370 | −0.445046 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −59.4169 | −2.04159 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.82018 | −0.165428 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.8474 | −0.371844 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.3535 | −1.21048 | −0.605241 | − | 0.796042i | \(-0.706923\pi\) | ||||
−0.605241 | + | 0.796042i | \(0.706923\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.6124 | 0.499734 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.2249 | −0.895827 | −0.447913 | − | 0.894077i | \(-0.647833\pi\) | ||||
−0.447913 | + | 0.894077i | \(0.647833\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.7616 | 1.18605 | 0.593026 | − | 0.805184i | \(-0.297933\pi\) | ||||
0.593026 | + | 0.805184i | \(0.297933\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.76000 | 0.128140 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.7005 | 0.636571 | 0.318286 | − | 0.947995i | \(-0.396893\pi\) | ||||
0.318286 | + | 0.947995i | \(0.396893\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.579282 | −0.0196962 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.85501 | 0.300732 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.7556 | −0.975466 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.82629 | −0.0957652 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.768916 | −0.0260239 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.21261 | −0.176218 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.1856 | 0.749155 | 0.374577 | − | 0.927196i | \(-0.377788\pi\) | ||||
0.374577 | + | 0.927196i | \(0.377788\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.5096 | 0.691772 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.8580 | −1.17440 | −0.587198 | − | 0.809443i | \(-0.699769\pi\) | ||||
−0.587198 | + | 0.809443i | \(0.699769\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.7441 | −1.43845 | −0.719227 | − | 0.694775i | \(-0.755504\pi\) | ||||
−0.719227 | + | 0.694775i | \(0.755504\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.32923 | −0.246369 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −47.9301 | −1.60934 | −0.804668 | − | 0.593725i | \(-0.797657\pi\) | ||||
−0.804668 | + | 0.593725i | \(0.797657\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.2773 | 0.445305 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.4964 | −0.753658 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.785269 | 0.0262780 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.22178 | −0.207971 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.177408 | −0.00592348 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.3394 | −0.745059 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.6880 | 0.689219 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −42.9850 | −1.43045 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.1175 | −0.369557 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.88310 | −0.162141 | −0.0810704 | − | 0.996708i | \(-0.525834\pi\) | ||||
−0.0810704 | + | 0.996708i | \(0.525834\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.32433 | −0.176597 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.83697 | −0.0939930 | −0.0469965 | − | 0.998895i | \(-0.514965\pi\) | ||||
−0.0469965 | + | 0.998895i | \(0.514965\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −83.7631 | −2.77215 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.742406 | −0.0245432 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 54.1475 | 1.78811 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.2430 | 0.436847 | 0.218424 | − | 0.975854i | \(-0.429909\pi\) | ||||
0.218424 | + | 0.975854i | \(0.429909\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.53318 | −0.215275 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.62500 | 0.0864030 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.8474 | 0.356660 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.1887 | 1.02437 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −57.7862 | −1.89590 | −0.947952 | − | 0.318413i | \(-0.896850\pi\) | ||||
−0.947952 | + | 0.318413i | \(0.896850\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −117.880 | −3.86337 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.0484 | −0.328971 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.0082 | 0.327302 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.8345 | −0.876646 | −0.438323 | − | 0.898818i | \(-0.644427\pi\) | ||||
−0.438323 | + | 0.898818i | \(0.644427\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.44498 | −0.0797888 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.8892 | −0.452776 | −0.226388 | − | 0.974037i | \(-0.572692\pi\) | ||||
−0.226388 | + | 0.974037i | \(0.572692\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.02054 | −0.0332334 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −20.2653 | −0.659230 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.4571 | −0.502289 | −0.251144 | − | 0.967950i | \(-0.580807\pi\) | ||||
−0.251144 | + | 0.967950i | \(0.580807\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.75340 | 0.0569177 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.2931 | −0.366205 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.9863 | 1.52203 | 0.761017 | − | 0.648731i | \(-0.224700\pi\) | ||||
0.761017 | + | 0.648731i | \(0.224700\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.2812 | −0.785721 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.7067 | −0.669354 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.1982 | 0.361609 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.9760 | −0.579871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.33593 | 0.268621 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.1931 | −0.585658 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.0807 | 0.356331 | 0.178165 | − | 0.984001i | \(-0.442984\pi\) | ||||
0.178165 | + | 0.984001i | \(0.442984\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.73481 | −0.280603 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.3401 | 0.909478 | 0.454739 | − | 0.890625i | \(-0.349733\pi\) | ||||
0.454739 | + | 0.890625i | \(0.349733\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.2738 | −0.617888 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.177408 | 0.00568161 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.9491 | −0.382286 | −0.191143 | − | 0.981562i | \(-0.561219\pi\) | ||||
−0.191143 | + | 0.981562i | \(0.561219\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.42177 | −0.0454401 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.6798 | 0.692183 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.9566 | 1.65716 | 0.828579 | − | 0.559873i | \(-0.189150\pi\) | ||||
0.828579 | + | 0.559873i | \(0.189150\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.7099 | 0.882912 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.495070 | −0.0157582 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.6670 | 0.370990 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.7230 | 1.29361 | 0.646804 | − | 0.762656i | \(-0.276105\pi\) | ||||
0.646804 | + | 0.762656i | \(0.276105\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.10298 | −0.193672 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.9434 | −0.505439 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.4242 | −0.456820 | −0.228410 | − | 0.973565i | \(-0.573353\pi\) | ||||
−0.228410 | + | 0.973565i | \(0.573353\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 42.1719 | 1.33426 |
(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 | 3680.2.a.ba.1.2 | yes | 5 | |
4.3 | odd | 2 | 3680.2.a.x.1.4 | ✓ | 5 | ||
8.3 | odd | 2 | 7360.2.a.cq.1.2 | 5 | |||
8.5 | even | 2 | 7360.2.a.cl.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3680.2.a.x.1.4 | ✓ | 5 | 4.3 | odd | 2 | ||
3680.2.a.ba.1.2 | yes | 5 | 1.1 | even | 1 | trivial | |
7360.2.a.cl.1.4 | 5 | 8.5 | even | 2 | |||
7360.2.a.cq.1.2 | 5 | 8.3 | odd | 2 |