Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | ||||||||
\(3\) | −1.70544 | −0.984639 | −0.492319 | − | 0.870415i | \(-0.663851\pi\) | ||||
−0.492319 | + | 0.870415i | \(0.663851\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.03894 | −0.392681 | −0.196340 | − | 0.980536i | \(-0.562906\pi\) | ||||
−0.196340 | + | 0.980536i | \(0.562906\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0914601 | −0.0304867 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.24754 | 0.376146 | 0.188073 | − | 0.982155i | \(-0.439776\pi\) | ||||
0.188073 | + | 0.982155i | \(0.439776\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47261 | −1.24048 | −0.620239 | − | 0.784413i | \(-0.712965\pi\) | ||||
−0.620239 | + | 0.784413i | \(0.712965\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.70544 | −0.440344 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.95732 | 0.717254 | 0.358627 | − | 0.933481i | \(-0.383245\pi\) | ||||
0.358627 | + | 0.933481i | \(0.383245\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.264785 | 0.0607459 | 0.0303729 | − | 0.999539i | \(-0.490331\pi\) | ||||
0.0303729 | + | 0.999539i | \(0.490331\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.77185 | 0.386649 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.16188 | −0.242268 | −0.121134 | − | 0.992636i | \(-0.538653\pi\) | ||||
−0.121134 | + | 0.992636i | \(0.538653\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.27231 | 1.01466 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.37291 | −0.440638 | −0.220319 | − | 0.975428i | \(-0.570710\pi\) | ||||
−0.220319 | + | 0.975428i | \(0.570710\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.78592 | −0.679972 | −0.339986 | − | 0.940431i | \(-0.610422\pi\) | ||||
−0.339986 | + | 0.940431i | \(0.610422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.12760 | −0.370368 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.03894 | −0.175612 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.8644 | 1.78610 | 0.893048 | − | 0.449962i | \(-0.148562\pi\) | ||||
0.893048 | + | 0.449962i | \(0.148562\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.62779 | 1.22142 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.50826 | −0.547897 | −0.273949 | − | 0.961744i | \(-0.588330\pi\) | ||||
−0.273949 | + | 0.961744i | \(0.588330\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.37679 | −0.819953 | −0.409977 | − | 0.912096i | \(-0.634463\pi\) | ||||
−0.409977 | + | 0.912096i | \(0.634463\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.0914601 | −0.0136341 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.48532 | −1.09185 | −0.545923 | − | 0.837835i | \(-0.683821\pi\) | ||||
−0.545923 | + | 0.837835i | \(0.683821\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.92061 | −0.845802 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.04354 | −0.706236 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.25982 | 0.173049 | 0.0865247 | − | 0.996250i | \(-0.472424\pi\) | ||||
0.0865247 | + | 0.996250i | \(0.472424\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.24754 | 0.168218 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.451576 | −0.0598128 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.9858 | 1.69061 | 0.845306 | − | 0.534283i | \(-0.179418\pi\) | ||||
0.845306 | + | 0.534283i | \(0.179418\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.329725 | 0.0422170 | 0.0211085 | − | 0.999777i | \(-0.493280\pi\) | ||||
0.0211085 | + | 0.999777i | \(0.493280\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0950212 | 0.0119715 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.47261 | −0.554759 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.42358 | −0.418257 | −0.209129 | − | 0.977888i | \(-0.567063\pi\) | ||||
−0.209129 | + | 0.977888i | \(0.567063\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.98152 | 0.238546 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.9478 | −1.65530 | −0.827652 | − | 0.561242i | \(-0.810324\pi\) | ||||
−0.827652 | + | 0.561242i | \(0.810324\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.47463 | −0.289634 | −0.144817 | − | 0.989458i | \(-0.546259\pi\) | ||||
−0.144817 | + | 0.989458i | \(0.546259\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.70544 | −0.196928 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.29611 | −0.147705 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.30359 | −0.371683 | −0.185841 | − | 0.982580i | \(-0.559501\pi\) | ||||
−0.185841 | + | 0.982580i | \(0.559501\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.71725 | −0.968584 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.25472 | 1.01584 | 0.507919 | − | 0.861405i | \(-0.330415\pi\) | ||||
0.507919 | + | 0.861405i | \(0.330415\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.95732 | 0.320766 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.04686 | 0.433869 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.23642 | 0.343060 | 0.171530 | − | 0.985179i | \(-0.445129\pi\) | ||||
0.171530 | + | 0.985179i | \(0.445129\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.64675 | 0.487112 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.45668 | 0.669527 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.264785 | 0.0271664 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.95948 | 0.300490 | 0.150245 | − | 0.988649i | \(-0.451994\pi\) | ||||
0.150245 | + | 0.988649i | \(0.451994\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.114100 | −0.0114675 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.92384 | −0.489941 | −0.244970 | − | 0.969531i | \(-0.578778\pi\) | ||||
−0.244970 | + | 0.969531i | \(0.578778\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.31224 | 0.720497 | 0.360248 | − | 0.932856i | \(-0.382692\pi\) | ||||
0.360248 | + | 0.932856i | \(0.382692\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.77185 | 0.172915 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.63925 | −0.545167 | −0.272583 | − | 0.962132i | \(-0.587878\pi\) | ||||
−0.272583 | + | 0.962132i | \(0.587878\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.5663 | 1.20363 | 0.601817 | − | 0.798634i | \(-0.294443\pi\) | ||||
0.601817 | + | 0.798634i | \(0.294443\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.5286 | −1.75866 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.7634 | 1.10660 | 0.553302 | − | 0.832981i | \(-0.313367\pi\) | ||||
0.553302 | + | 0.832981i | \(0.313367\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.16188 | −0.108346 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.409065 | 0.0378181 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.07246 | −0.281652 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.44365 | −0.858514 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.98313 | 0.539481 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.74501 | 0.864730 | 0.432365 | − | 0.901699i | \(-0.357679\pi\) | ||||
0.432365 | + | 0.901699i | \(0.357679\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.16982 | 0.807358 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.8121 | −1.11940 | −0.559701 | − | 0.828695i | \(-0.689084\pi\) | ||||
−0.559701 | + | 0.828695i | \(0.689084\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.275095 | −0.0238537 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.27231 | 0.453768 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.22995 | 0.532260 | 0.266130 | − | 0.963937i | \(-0.414255\pi\) | ||||
0.266130 | + | 0.963937i | \(0.414255\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.47158 | −0.209636 | −0.104818 | − | 0.994491i | \(-0.533426\pi\) | ||||
−0.104818 | + | 0.994491i | \(0.533426\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.7658 | 1.07507 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.57974 | −0.466601 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.37291 | −0.197059 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.0973 | 0.832809 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.1788 | 0.915802 | 0.457901 | − | 0.889003i | \(-0.348601\pi\) | ||||
0.457901 | + | 0.889003i | \(0.348601\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.434658 | 0.0353720 | 0.0176860 | − | 0.999844i | \(-0.494370\pi\) | ||||
0.0176860 | + | 0.999844i | \(0.494370\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.270476 | −0.0218667 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.78592 | −0.304093 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.53918 | 0.442075 | 0.221037 | − | 0.975265i | \(-0.429056\pi\) | ||||
0.221037 | + | 0.975265i | \(0.429056\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.14855 | −0.170391 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.20711 | 0.0951340 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.4778 | 0.977338 | 0.488669 | − | 0.872469i | \(-0.337483\pi\) | ||||
0.488669 | + | 0.872469i | \(0.337483\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.12760 | −0.165634 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.42245 | −0.187455 | −0.0937274 | − | 0.995598i | \(-0.529878\pi\) | ||||
−0.0937274 | + | 0.995598i | \(0.529878\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00423 | 0.538787 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0242173 | −0.00185194 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8848 | −1.05564 | −0.527820 | − | 0.849356i | \(-0.676991\pi\) | ||||
−0.527820 | + | 0.849356i | \(0.676991\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.03894 | −0.0785361 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22.1466 | −1.66464 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.17120 | −0.162283 | −0.0811416 | − | 0.996703i | \(-0.525857\pi\) | ||||
−0.0811416 | + | 0.996703i | \(0.525857\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.8637 | 1.84810 | 0.924052 | − | 0.382266i | \(-0.124856\pi\) | ||||
0.924052 | + | 0.382266i | \(0.124856\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.562328 | −0.0415684 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.8644 | 0.798766 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.68936 | 0.269792 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.47759 | −0.398436 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.42202 | −0.175251 | −0.0876257 | − | 0.996153i | \(-0.527928\pi\) | ||||
−0.0876257 | + | 0.996153i | \(0.527928\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.47117 | −0.177878 | −0.0889392 | − | 0.996037i | \(-0.528348\pi\) | ||||
−0.0889392 | + | 0.996037i | \(0.528348\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.62779 | 0.546237 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.77386 | −0.411371 | −0.205685 | − | 0.978618i | \(-0.565942\pi\) | ||||
−0.205685 | + | 0.978618i | \(0.565942\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.83937 | −0.343054 | −0.171527 | − | 0.985179i | \(-0.554870\pi\) | ||||
−0.171527 | + | 0.985179i | \(0.554870\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.83873 | 0.411832 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.46530 | 0.173030 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.50826 | −0.245027 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.106265 | 0.00738596 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.330329 | 0.0228493 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.3400 | −1.67564 | −0.837819 | − | 0.545949i | \(-0.816169\pi\) | ||||
−0.837819 | + | 0.545949i | \(0.816169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 23.7873 | 1.62988 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.37679 | −0.366694 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.93333 | 0.267012 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.22034 | 0.285184 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.2269 | −0.889739 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.8137 | 1.46076 | 0.730378 | − | 0.683043i | \(-0.239344\pi\) | ||||
0.730378 | + | 0.683043i | \(0.239344\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.0914601 | −0.00609734 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.91508 | 0.591715 | 0.295857 | − | 0.955232i | \(-0.404395\pi\) | ||||
0.295857 | + | 0.955232i | \(0.404395\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.2510 | −1.13998 | −0.569990 | − | 0.821651i | \(-0.693053\pi\) | ||||
−0.569990 | + | 0.821651i | \(0.693053\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.21044 | 0.145436 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.77959 | 0.182097 | 0.0910485 | − | 0.995846i | \(-0.470978\pi\) | ||||
0.0910485 | + | 0.995846i | \(0.470978\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.48532 | −0.488288 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.63408 | 0.365973 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.3462 | 1.44545 | 0.722726 | − | 0.691134i | \(-0.242889\pi\) | ||||
0.722726 | + | 0.691134i | \(0.242889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.3969 | 1.37829 | 0.689146 | − | 0.724622i | \(-0.257986\pi\) | ||||
0.689146 | + | 0.724622i | \(0.257986\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.950147 | −0.0609520 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.92061 | −0.378254 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.18428 | −0.0753540 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.7834 | −1.00023 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0744 | −0.951485 | −0.475743 | − | 0.879585i | \(-0.657821\pi\) | ||||
−0.475743 | + | 0.879585i | \(0.657821\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.44948 | −0.0911282 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.04354 | −0.315838 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.8220 | 0.737435 | 0.368717 | − | 0.929542i | \(-0.379797\pi\) | ||||
0.368717 | + | 0.929542i | \(0.379797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.2874 | −0.701365 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.217027 | 0.0134336 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.2808 | 0.757269 | 0.378635 | − | 0.925546i | \(-0.376394\pi\) | ||||
0.378635 | + | 0.925546i | \(0.376394\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.25982 | 0.0773900 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.51954 | −0.337790 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.37062 | 0.0835684 | 0.0417842 | − | 0.999127i | \(-0.486696\pi\) | ||||
0.0417842 | + | 0.999127i | \(0.486696\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.8644 | 1.26742 | 0.633712 | − | 0.773569i | \(-0.281530\pi\) | ||||
0.633712 | + | 0.773569i | \(0.281530\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.92478 | −0.479629 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.24754 | 0.0752292 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.90537 | 0.294735 | 0.147368 | − | 0.989082i | \(-0.452920\pi\) | ||||
0.147368 | + | 0.989082i | \(0.452920\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.346261 | 0.0207301 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.2408 | 1.08816 | 0.544079 | − | 0.839034i | \(-0.316879\pi\) | ||||
0.544079 | + | 0.839034i | \(0.316879\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.82060 | −0.286555 | −0.143278 | − | 0.989683i | \(-0.545764\pi\) | ||||
−0.143278 | + | 0.989683i | \(0.545764\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.451576 | −0.0267491 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.64485 | 0.215149 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.25429 | −0.485546 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.04723 | −0.295874 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.1770 | 0.945071 | 0.472536 | − | 0.881312i | \(-0.343339\pi\) | ||||
0.472536 | + | 0.881312i | \(0.343339\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.9858 | 0.756064 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.57740 | 0.381659 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.19662 | 0.300528 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.58614 | 0.321980 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.39734 | 0.482414 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.329725 | 0.0188800 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.3626 | −1.96118 | −0.980589 | − | 0.196073i | \(-0.937181\pi\) | ||||
−0.980589 | + | 0.196073i | \(0.937181\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.4706 | −0.709429 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.5692 | −1.84683 | −0.923416 | − | 0.383801i | \(-0.874615\pi\) | ||||
−0.923416 | + | 0.383801i | \(0.874615\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.45798 | 0.308503 | 0.154252 | − | 0.988032i | \(-0.450703\pi\) | ||||
0.154252 | + | 0.988032i | \(0.450703\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0950212 | 0.00535384 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.29720 | 0.241355 | 0.120677 | − | 0.992692i | \(-0.461493\pi\) | ||||
0.120677 | + | 0.992692i | \(0.461493\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.96029 | −0.165744 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.61743 | 0.536792 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.783053 | 0.0435703 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.47261 | −0.248096 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.4312 | −1.18515 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.77677 | 0.428747 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.7563 | 0.701149 | 0.350575 | − | 0.936535i | \(-0.385986\pi\) | ||||
0.350575 | + | 0.936535i | \(0.385986\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.993659 | −0.0544522 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.42358 | −0.187050 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.9831 | 0.598286 | 0.299143 | − | 0.954208i | \(-0.403299\pi\) | ||||
0.299143 | + | 0.954208i | \(0.403299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.0618 | −1.08961 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.72307 | −0.255769 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.4237 | 0.724811 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.98152 | 0.106681 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.2286 | 1.56907 | 0.784537 | − | 0.620082i | \(-0.212901\pi\) | ||||
0.784537 | + | 0.620082i | \(0.212901\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.9388 | 0.799656 | 0.399828 | − | 0.916590i | \(-0.369070\pi\) | ||||
0.399828 | + | 0.916590i | \(0.369070\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.5810 | −1.25866 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.70996 | −0.197461 | −0.0987307 | − | 0.995114i | \(-0.531478\pi\) | ||||
−0.0987307 | + | 0.995114i | \(0.531478\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.9478 | −0.740274 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.23991 | 0.277325 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.5876 | −1.66713 | −0.833564 | − | 0.552423i | \(-0.813703\pi\) | ||||
−0.833564 | + | 0.552423i | \(0.813703\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9299 | −0.996310 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.1056 | 0.845326 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.47463 | −0.129528 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.7342 | 1.55211 | 0.776056 | − | 0.630664i | \(-0.217217\pi\) | ||||
0.776056 | + | 0.630664i | \(0.217217\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.320866 | 0.0167036 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.30887 | −0.0679531 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.4303 | 1.36851 | 0.684255 | − | 0.729243i | \(-0.260128\pi\) | ||||
0.684255 | + | 0.729243i | \(0.260128\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.70544 | −0.0880688 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.6131 | 0.546602 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7764 | 0.759011 | 0.379505 | − | 0.925190i | \(-0.376094\pi\) | ||||
0.379505 | + | 0.925190i | \(0.376094\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.6196 | −0.851447 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.5329 | 0.691498 | 0.345749 | − | 0.938327i | \(-0.387625\pi\) | ||||
0.345749 | + | 0.938327i | \(0.387625\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.29611 | −0.0660558 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.491762 | 0.0249977 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.65637 | 0.438895 | 0.219448 | − | 0.975624i | \(-0.429575\pi\) | ||||
0.219448 | + | 0.975624i | \(0.429575\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.43604 | −0.173768 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.8504 | 1.10221 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.30359 | −0.166222 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.6287 | 0.985139 | 0.492569 | − | 0.870273i | \(-0.336058\pi\) | ||||
0.492569 | + | 0.870273i | \(0.336058\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.469159 | 0.0234873 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.9330 | 0.843491 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.71725 | −0.433164 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.5537 | 0.671833 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.5314 | 1.11411 | 0.557054 | − | 0.830476i | \(-0.311932\pi\) | ||||
0.557054 | + | 0.830476i | \(0.311932\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.6248 | −0.524084 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.4914 | −0.663870 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.25472 | 0.454296 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.21513 | 0.206416 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.9477 | −1.80501 | −0.902507 | − | 0.430675i | \(-0.858276\pi\) | ||||
−0.902507 | + | 0.430675i | \(0.858276\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.4356 | 1.77576 | 0.887881 | − | 0.460073i | \(-0.152177\pi\) | ||||
0.887881 | + | 0.460073i | \(0.152177\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.684608 | 0.0332868 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.95732 | 0.143451 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.342563 | −0.0165778 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.51594 | 0.459434 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.85860 | −0.282199 | −0.141100 | − | 0.989995i | \(-0.545064\pi\) | ||||
−0.141100 | + | 0.989995i | \(0.545064\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0506 | 0.867455 | 0.433728 | − | 0.901044i | \(-0.357198\pi\) | ||||
0.433728 | + | 0.901044i | \(0.357198\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.04686 | 0.194032 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.307648 | −0.0147168 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.26849 | 0.203724 | 0.101862 | − | 0.994799i | \(-0.467520\pi\) | ||||
0.101862 | + | 0.994799i | \(0.467520\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.541500 | 0.0257857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.0788 | −1.33406 | −0.667031 | − | 0.745030i | \(-0.732435\pi\) | ||||
−0.667031 | + | 0.745030i | \(0.732435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.23642 | 0.153421 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.0648 | −0.901734 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.09066 | 0.193050 | 0.0965250 | − | 0.995331i | \(-0.469227\pi\) | ||||
0.0965250 | + | 0.995331i | \(0.469227\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.37667 | −0.206090 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.741285 | −0.0348286 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.64675 | 0.217843 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.2733 | 1.36935 | 0.684674 | − | 0.728849i | \(-0.259945\pi\) | ||||
0.684674 | + | 0.728849i | \(0.259945\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.5919 | 0.727767 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.5121 | 0.955342 | 0.477671 | − | 0.878539i | \(-0.341481\pi\) | ||||
0.477671 | + | 0.878539i | \(0.341481\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.94546 | 0.369257 | 0.184628 | − | 0.982808i | \(-0.440892\pi\) | ||||
0.184628 | + | 0.982808i | \(0.440892\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.45668 | 0.299421 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.1027 | −1.11534 | −0.557671 | − | 0.830062i | \(-0.688305\pi\) | ||||
−0.557671 | + | 0.830062i | \(0.688305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.55688 | 0.164242 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.44677 | −0.435284 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.70774 | −0.308422 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.264785 | 0.0121492 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.115223 | −0.00527571 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.0509 | 1.82997 | 0.914986 | − | 0.403485i | \(-0.132201\pi\) | ||||
0.914986 | + | 0.403485i | \(0.132201\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.5922 | −2.21561 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.05867 | −0.0936726 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.95948 | 0.134383 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.5151 | 0.838998 | 0.419499 | − | 0.907756i | \(-0.362206\pi\) | ||||
0.419499 | + | 0.907756i | \(0.362206\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.2802 | −0.962325 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.4837 | 0.698771 | 0.349385 | − | 0.936979i | \(-0.386390\pi\) | ||||
0.349385 | + | 0.936979i | \(0.386390\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.01744 | −0.316050 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.114100 | −0.00512840 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.4909 | 0.650006 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.3315 | −1.26829 | −0.634146 | − | 0.773213i | \(-0.718648\pi\) | ||||
−0.634146 | + | 0.773213i | \(0.718648\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.13135 | 0.184575 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.97020 | 0.221610 | 0.110805 | − | 0.993842i | \(-0.464657\pi\) | ||||
0.110805 | + | 0.993842i | \(0.464657\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.92384 | −0.219108 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.9453 | −0.530511 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.98686 | 0.221039 | 0.110519 | − | 0.993874i | \(-0.464749\pi\) | ||||
0.110519 | + | 0.993874i | \(0.464749\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.57098 | 0.113734 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.39603 | 0.0616363 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.31224 | 0.322216 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.33821 | −0.410694 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.6797 | 1.03942 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.2374 | 0.755184 | 0.377592 | − | 0.925972i | \(-0.376752\pi\) | ||||
0.377592 | + | 0.925972i | \(0.376752\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.1672 | −0.794398 | −0.397199 | − | 0.917733i | \(-0.630018\pi\) | ||||
−0.397199 | + | 0.917733i | \(0.630018\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.77185 | 0.0773297 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.1962 | −0.487713 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6500 | −0.941306 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.18769 | −0.0515412 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.6911 | 0.679655 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.63925 | −0.243806 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.70286 | 0.159790 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.38618 | −0.318145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.6109 | 0.542183 | 0.271092 | − | 0.962554i | \(-0.412615\pi\) | ||||
0.271092 | + | 0.962554i | \(0.412615\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −42.4037 | −1.81972 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.5663 | 0.538282 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.86168 | −0.336141 | −0.168071 | − | 0.985775i | \(-0.553754\pi\) | ||||
−0.168071 | + | 0.985775i | \(0.553754\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0301567 | −0.00128706 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.628311 | −0.0267670 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.43221 | 0.145953 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.5286 | −0.786496 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.1398 | 1.14995 | 0.574974 | − | 0.818172i | \(-0.305012\pi\) | ||||
0.574974 | + | 0.818172i | \(0.305012\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0483 | 1.01713 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.29199 | −0.265648 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.8505 | −1.34234 | −0.671168 | − | 0.741305i | \(-0.734207\pi\) | ||||
−0.671168 | + | 0.741305i | \(0.734207\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.7634 | 0.494889 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.05667 | 0.380344 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.4465 | 1.69560 | 0.847802 | − | 0.530313i | \(-0.177926\pi\) | ||||
0.847802 | + | 0.530313i | \(0.177926\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 47.0510 | 1.96902 | 0.984511 | − | 0.175324i | \(-0.0560974\pi\) | ||||
0.984511 | + | 0.175324i | \(0.0560974\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.13062 | 0.172559 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.16188 | −0.0484536 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.7884 | −0.490758 | −0.245379 | − | 0.969427i | \(-0.578912\pi\) | ||||
−0.245379 | + | 0.969427i | \(0.578912\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.21444 | 0.175146 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.61506 | −0.398900 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.57167 | 0.0650919 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.409065 | 0.0169128 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.0190257 | 0.000785275 0 | 0.000392637 | − | 1.00000i | \(-0.499875\pi\) | ||||
0.000392637 | 1.00000i | \(0.499875\pi\) | ||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.00246 | −0.0413055 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.84700 | 0.405052 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.6448 | 1.54589 | 0.772944 | − | 0.634475i | \(-0.218784\pi\) | ||||
0.772944 | + | 0.634475i | \(0.218784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.07246 | −0.125959 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.25327 | 0.337784 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.9824 | −0.693881 | −0.346940 | − | 0.937887i | \(-0.612779\pi\) | ||||
−0.346940 | + | 0.937887i | \(0.612779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.46937 | −0.100728 | −0.0503638 | − | 0.998731i | \(-0.516038\pi\) | ||||
−0.0503638 | + | 0.998731i | \(0.516038\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.313121 | 0.0127513 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.44365 | −0.383939 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.34548 | −0.338733 | −0.169366 | − | 0.985553i | \(-0.554172\pi\) | ||||
−0.169366 | + | 0.985553i | \(0.554172\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.20443 | −0.170372 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.4789 | 1.35441 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.7942 | 0.557143 | 0.278571 | − | 0.960416i | \(-0.410139\pi\) | ||||
0.278571 | + | 0.960416i | \(0.410139\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.98313 | 0.241263 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.8627 | −1.40352 | −0.701760 | − | 0.712414i | \(-0.747602\pi\) | ||||
−0.701760 | + | 0.712414i | \(0.747602\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.5689 | 1.42964 | 0.714818 | − | 0.699311i | \(-0.246510\pi\) | ||||
0.714818 | + | 0.699311i | \(0.246510\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.12578 | −0.245819 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.36244 | −0.134713 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.563358 | −0.0224983 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.1294 | 1.28108 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.6299 | 1.37860 | 0.689298 | − | 0.724478i | \(-0.257919\pi\) | ||||
0.689298 | + | 0.724478i | \(0.257919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 41.5106 | 1.64990 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.74501 | 0.386719 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.4806 | 1.04920 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.27567 | 0.0504648 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.4660 | −0.650367 | −0.325183 | − | 0.945651i | \(-0.605426\pi\) | ||||
−0.325183 | + | 0.945651i | \(0.605426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.6618 | 0.499332 | 0.249666 | − | 0.968332i | \(-0.419679\pi\) | ||||
0.249666 | + | 0.968332i | \(0.419679\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.16982 | 0.361061 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.9919 | 1.37567 | 0.687837 | − | 0.725865i | \(-0.258560\pi\) | ||||
0.687837 | + | 0.725865i | \(0.258560\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.2003 | 0.635917 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.70807 | −0.262910 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.0998 | 1.41269 | 0.706347 | − | 0.707865i | \(-0.250342\pi\) | ||||
0.706347 | + | 0.707865i | \(0.250342\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.8121 | −0.500611 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.226330 | 0.00882997 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.541141 | 0.0210798 | 0.0105399 | − | 0.999944i | \(-0.496645\pi\) | ||||
0.0105399 | + | 0.999944i | \(0.496645\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.65857 | −0.297884 | −0.148942 | − | 0.988846i | \(-0.547587\pi\) | ||||
−0.148942 | + | 0.988846i | \(0.547587\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.5578 | 0.876071 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.275095 | −0.0106677 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.75703 | 0.106753 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −37.2021 | −1.43832 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.411344 | 0.0158797 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.9836 | 1.38707 | 0.693533 | − | 0.720425i | \(-0.256053\pi\) | ||||
0.693533 | + | 0.720425i | \(0.256053\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.27231 | 0.202931 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.18804 | 0.199393 | 0.0996963 | − | 0.995018i | \(-0.468213\pi\) | ||||
0.0996963 | + | 0.995018i | \(0.468213\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.07471 | −0.117997 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.2042 | −0.582625 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.89639 | 0.149091 | 0.0745456 | − | 0.997218i | \(-0.476249\pi\) | ||||
0.0745456 | + | 0.997218i | \(0.476249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.22995 | 0.238034 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.4207 | 1.12247 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.63467 | −0.214664 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.7879 | −0.981017 | −0.490509 | − | 0.871436i | \(-0.663189\pi\) | ||||
−0.490509 | + | 0.871436i | \(0.663189\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.118542 | 0.00450305 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.47158 | −0.0937522 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.3750 | −0.392982 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.74044 | −0.179300 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.5620 | −0.587770 | −0.293885 | − | 0.955841i | \(-0.594948\pi\) | ||||
−0.293885 | + | 0.955841i | \(0.594948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.87673 | 0.108498 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.7658 | 0.480788 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.11555 | 0.192390 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.2090 | 0.834075 | 0.417038 | − | 0.908889i | \(-0.363068\pi\) | ||||
0.417038 | + | 0.908889i | \(0.363068\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.302147 | 0.0113314 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.39878 | 0.164735 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.57974 | −0.208670 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −38.1101 | −1.42325 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.3486 | 0.423230 | 0.211615 | − | 0.977353i | \(-0.432128\pi\) | ||||
0.211615 | + | 0.977353i | \(0.432128\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.59695 | −0.282925 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36.4911 | −1.35712 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.37291 | −0.0881276 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.9526 | 0.406211 | 0.203105 | − | 0.979157i | \(-0.434897\pi\) | ||||
0.203105 | + | 0.979157i | \(0.434897\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.7722 | 1.02860 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.9009 | −0.588115 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.49978 | 0.277011 | 0.138505 | − | 0.990362i | \(-0.455770\pi\) | ||||
0.138505 | + | 0.990362i | \(0.455770\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.0973 | 0.372444 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.27104 | −0.157326 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.1186 | −0.592934 | −0.296467 | − | 0.955043i | \(-0.595808\pi\) | ||||
−0.296467 | + | 0.955043i | \(0.595808\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.01972 | 0.0741964 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5604 | 0.827659 | 0.413830 | − | 0.910354i | \(-0.364191\pi\) | ||||
0.413830 | + | 0.910354i | \(0.364191\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.1788 | 0.409559 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.846438 | −0.0309695 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.85882 | 0.214077 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.9217 | −1.05537 | −0.527684 | − | 0.849441i | \(-0.676940\pi\) | ||||
−0.527684 | + | 0.849441i | \(0.676940\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.7085 | 0.936869 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.434658 | 0.0158188 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.0020 | 1.27217 | 0.636085 | − | 0.771619i | \(-0.280553\pi\) | ||||
0.636085 | + | 0.771619i | \(0.280553\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.47201 | 0.0897284 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.27185 | −0.263604 | −0.131802 | − | 0.991276i | \(-0.542076\pi\) | ||||
−0.131802 | + | 0.991276i | \(0.542076\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.0556 | −0.472644 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.270476 | −0.00977910 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −58.0806 | −2.09717 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.1027 | 1.01341 | 0.506704 | − | 0.862120i | \(-0.330864\pi\) | ||||
0.506704 | + | 0.862120i | \(0.330864\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.1617 | −0.726107 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.65665 | −0.167488 | −0.0837440 | − | 0.996487i | \(-0.526688\pi\) | ||||
−0.0837440 | + | 0.996487i | \(0.526688\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.78592 | −0.135994 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.2500 | 0.690591 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.928934 | −0.0332825 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.4004 | −0.622636 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.5107 | −0.447097 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.53918 | 0.197702 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.8416 | −1.24197 | −0.620985 | − | 0.783823i | \(-0.713267\pi\) | ||||
−0.620985 | + | 0.783823i | \(0.713267\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.9443 | −0.745636 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.2214 | −0.434542 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.47473 | −0.0523692 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.14855 | −0.0762012 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.9674 | −0.742704 | −0.371352 | − | 0.928492i | \(-0.621106\pi\) | ||||
−0.371352 | + | 0.928492i | \(0.621106\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.1365 | −0.783131 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.296004 | −0.0104588 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.08719 | −0.108945 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.20711 | 0.0425452 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.33752 | −0.0822847 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.6343 | 1.70989 | 0.854946 | − | 0.518717i | \(-0.173590\pi\) | ||||
0.854946 | + | 0.518717i | \(0.173590\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.7943 | −0.589727 | −0.294864 | − | 0.955539i | \(-0.595274\pi\) | ||||
−0.294864 | + | 0.955539i | \(0.595274\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −35.5831 | −1.24796 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.4778 | 0.437079 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.42370 | −0.0498088 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.424993 | −0.0148504 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.0295 | 0.838636 | 0.419318 | − | 0.907839i | \(-0.362269\pi\) | ||||
0.419318 | + | 0.907839i | \(0.362269\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.2743 | −0.706717 | −0.353359 | − | 0.935488i | \(-0.614960\pi\) | ||||
−0.353359 | + | 0.935488i | \(0.614960\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.12760 | −0.0740736 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.3412 | −1.08984 | −0.544920 | − | 0.838488i | \(-0.683440\pi\) | ||||
−0.544920 | + | 0.838488i | \(0.683440\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.81916 | −0.306302 | −0.153151 | − | 0.988203i | \(-0.548942\pi\) | ||||
−0.153151 | + | 0.988203i | \(0.548942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.36584 | −0.290208 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.5091 | −0.606655 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.42245 | −0.0838323 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.9606 | −0.689938 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.3130 | 0.701284 | 0.350642 | − | 0.936510i | \(-0.385963\pi\) | ||||
0.350642 | + | 0.936510i | \(0.385963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.3693 | −0.805838 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −31.1087 | −1.07144 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.00423 | 0.240953 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.81135 | 0.337122 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.22127 | 0.282153 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.6231 | −0.432714 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.3454 | −1.44988 | −0.724940 | − | 0.688812i | \(-0.758133\pi\) | ||||
−0.724940 | + | 0.688812i | \(0.758133\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0242173 | −0.000828214 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.2312 | −0.520287 | −0.260143 | − | 0.965570i | \(-0.583770\pi\) | ||||
−0.260143 | + | 0.965570i | \(0.583770\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.3949 | 0.491147 | 0.245573 | − | 0.969378i | \(-0.421024\pi\) | ||||
0.245573 | + | 0.969378i | \(0.421024\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.21609 | −0.211844 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.7061 | −0.670804 | −0.335402 | − | 0.942075i | \(-0.608872\pi\) | ||||
−0.335402 | + | 0.942075i | \(0.608872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.8848 | −0.472097 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.0772 | 0.478088 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.12134 | −0.139807 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.3124 | 0.518839 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.270675 | −0.00916095 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.03894 | −0.0351224 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.8570 | −0.771826 | −0.385913 | − | 0.922535i | \(-0.626114\pi\) | ||||
−0.385913 | + | 0.922535i | \(0.626114\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.5890 | −0.930554 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.6516 | −1.50435 | −0.752175 | − | 0.658964i | \(-0.770995\pi\) | ||||
−0.752175 | + | 0.658964i | \(0.770995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.86586 | −0.298360 | −0.149180 | − | 0.988810i | \(-0.547663\pi\) | ||||
−0.149180 | + | 0.988810i | \(0.547663\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22.1466 | −0.744450 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.1170 | 1.48130 | 0.740652 | − | 0.671889i | \(-0.234517\pi\) | ||||
0.740652 | + | 0.671889i | \(0.234517\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.1244 | −0.339563 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.8751 | −0.364329 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.98200 | −0.0663252 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.17120 | −0.0725753 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.86255 | −0.295912 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.98365 | 0.299622 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.72568 | 0.124120 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.52685 | −0.317034 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.8637 | 0.826498 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.91674 | −0.0636442 | −0.0318221 | − | 0.999494i | \(-0.510131\pi\) | ||||
−0.0318221 | + | 0.999494i | \(0.510131\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.450335 | 0.0149367 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.0610 | 1.09536 | 0.547680 | − | 0.836688i | \(-0.315511\pi\) | ||||
0.547680 | + | 0.836688i | \(0.315511\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.5456 | 0.382103 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.562328 | −0.0185900 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.3110 | 0.439567 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.7397 | −1.54180 | −0.770900 | − | 0.636956i | \(-0.780193\pi\) | ||||
−0.770900 | + | 0.636956i | \(0.780193\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 58.6035 | 1.93105 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 62.3832 | 2.05337 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.8644 | 0.357219 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.668779 | −0.0219656 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.2846 | −0.960797 | −0.480398 | − | 0.877050i | \(-0.659508\pi\) | ||||
−0.480398 | + | 0.877050i | \(0.659508\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.56769 | −0.0513790 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 55.5450 | 1.81846 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.68936 | 0.120655 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.84570 | 0.321645 | 0.160822 | − | 0.986983i | \(-0.448585\pi\) | ||||
0.160822 | + | 0.986983i | \(0.448585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.30828 | −0.303764 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.1728 | 1.30959 | 0.654797 | − | 0.755804i | \(-0.272754\pi\) | ||||
0.654797 | + | 0.755804i | \(0.272754\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.07616 | 0.132738 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.47759 | −0.178186 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.9735 | 1.26647 | 0.633235 | − | 0.773960i | \(-0.281727\pi\) | ||||
0.633235 | + | 0.773960i | \(0.281727\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.0681 | 0.359284 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.32864 | −0.237647 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.0204 | −0.389380 | −0.194690 | − | 0.980865i | \(-0.562370\pi\) | ||||
−0.194690 | + | 0.980865i | \(0.562370\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.42202 | −0.0783748 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.04861 | 0.163198 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.47252 | −0.209008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.6668 | −0.537638 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.515767 | 0.0166203 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.47117 | −0.0795497 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.3940 | −1.00956 | −0.504781 | − | 0.863248i | \(-0.668427\pi\) | ||||
−0.504781 | + | 0.863248i | \(0.668427\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.33545 | −0.0429010 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.3196 | −0.491629 | −0.245815 | − | 0.969317i | \(-0.579055\pi\) | ||||
−0.245815 | + | 0.969317i | \(0.579055\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.56781 | 0.0823201 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.62779 | 0.244285 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.8928 | 1.05233 | 0.526167 | − | 0.850381i | \(-0.323629\pi\) | ||||
0.526167 | + | 0.850381i | \(0.323629\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.03756 | 0.129041 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.14932 | −0.0366949 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.6876 | 1.17015 | 0.585077 | − | 0.810978i | \(-0.301064\pi\) | ||||
0.585077 | + | 0.810978i | \(0.301064\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.77386 | −0.183971 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.2628 | −0.422161 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.24717 | 0.198649 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.0692 | −1.08224 | −0.541121 | − | 0.840944i | \(-0.682000\pi\) | ||||
−0.541121 | + | 0.840944i | \(0.682000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.7551 | −0.690378 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.83937 | −0.153418 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.9353 | −0.726369 | −0.363184 | − | 0.931717i | \(-0.618310\pi\) | ||||
−0.363184 | + | 0.931717i | \(0.618310\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 57.2805 | 1.81227 |
(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 | 8020.2.a.f.1.10 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.f.1.10 | ✓ | 37 | 1.1 | even | 1 | trivial |