Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.78641 | 1.26318 | 0.631590 | − | 0.775302i | \(-0.282402\pi\) | ||||
0.631590 | + | 0.775302i | \(0.282402\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.19125 | 0.595626 | ||||||||
\(5\) | 0.326188 | 0.145876 | 0.0729378 | − | 0.997336i | \(-0.476763\pi\) | ||||
0.0729378 | + | 0.997336i | \(0.476763\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.17242 | 0.443134 | 0.221567 | − | 0.975145i | \(-0.428883\pi\) | ||||
0.221567 | + | 0.975145i | \(0.428883\pi\) | |||||||
\(8\) | −1.44475 | −0.510797 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.582705 | 0.184267 | ||||||||
\(11\) | −0.852209 | −0.256951 | −0.128475 | − | 0.991713i | \(-0.541008\pi\) | ||||
−0.128475 | + | 0.991713i | \(0.541008\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.22671 | 0.894929 | 0.447464 | − | 0.894302i | \(-0.352327\pi\) | ||||
0.447464 | + | 0.894302i | \(0.352327\pi\) | |||||||
\(14\) | 2.09442 | 0.559758 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.96342 | −1.24086 | ||||||||
\(17\) | −5.35744 | −1.29937 | −0.649685 | − | 0.760203i | \(-0.725099\pi\) | ||||
−0.649685 | + | 0.760203i | \(0.725099\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.49277 | −0.342466 | −0.171233 | − | 0.985231i | \(-0.554775\pi\) | ||||
−0.171233 | + | 0.985231i | \(0.554775\pi\) | |||||||
\(20\) | 0.388572 | 0.0868874 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.52239 | −0.324575 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.89360 | −0.978720 | ||||||||
\(26\) | 5.76422 | 1.13046 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.39665 | 0.263942 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.352535 | 0.0633171 | 0.0316586 | − | 0.999499i | \(-0.489921\pi\) | ||||
0.0316586 | + | 0.999499i | \(0.489921\pi\) | |||||||
\(32\) | −5.97719 | −1.05663 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.57057 | −1.64134 | ||||||||
\(35\) | 0.382430 | 0.0646424 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.9308 | −1.79702 | −0.898509 | − | 0.438955i | \(-0.855349\pi\) | ||||
−0.898509 | + | 0.438955i | \(0.855349\pi\) | |||||||
\(38\) | −2.66670 | −0.432596 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.471261 | −0.0745129 | ||||||||
\(41\) | 11.6880 | 1.82535 | 0.912677 | − | 0.408682i | \(-0.134012\pi\) | ||||
0.912677 | + | 0.408682i | \(0.134012\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.16001 | −0.481897 | −0.240948 | − | 0.970538i | \(-0.577458\pi\) | ||||
−0.240948 | + | 0.970538i | \(0.577458\pi\) | |||||||
\(44\) | −1.01520 | −0.153047 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.78641 | −0.263391 | ||||||||
\(47\) | −1.44410 | −0.210643 | −0.105322 | − | 0.994438i | \(-0.533587\pi\) | ||||
−0.105322 | + | 0.994438i | \(0.533587\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.62543 | −0.803632 | ||||||||
\(50\) | −8.74197 | −1.23630 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.84383 | 0.533043 | ||||||||
\(53\) | −6.05996 | −0.832400 | −0.416200 | − | 0.909273i | \(-0.636638\pi\) | ||||
−0.416200 | + | 0.909273i | \(0.636638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.277980 | −0.0374828 | ||||||||
\(56\) | −1.69386 | −0.226352 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.78641 | −0.234567 | ||||||||
\(59\) | −1.56212 | −0.203370 | −0.101685 | − | 0.994817i | \(-0.532423\pi\) | ||||
−0.101685 | + | 0.994817i | \(0.532423\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.48678 | −0.830546 | −0.415273 | − | 0.909697i | \(-0.636314\pi\) | ||||
−0.415273 | + | 0.909697i | \(0.636314\pi\) | |||||||
\(62\) | 0.629771 | 0.0799810 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.750853 | −0.0938566 | ||||||||
\(65\) | 1.05251 | 0.130548 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.67740 | −0.815774 | −0.407887 | − | 0.913032i | \(-0.633734\pi\) | ||||
−0.407887 | + | 0.913032i | \(0.633734\pi\) | |||||||
\(68\) | −6.38206 | −0.773939 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.683176 | 0.0816551 | ||||||||
\(71\) | 13.6764 | 1.62309 | 0.811545 | − | 0.584291i | \(-0.198627\pi\) | ||||
0.811545 | + | 0.584291i | \(0.198627\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6053 | 1.47534 | 0.737669 | − | 0.675162i | \(-0.235926\pi\) | ||||
0.737669 | + | 0.675162i | \(0.235926\pi\) | |||||||
\(74\) | −19.5269 | −2.26996 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.77827 | −0.203982 | ||||||||
\(77\) | −0.999148 | −0.113864 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.9954 | −1.79962 | −0.899809 | − | 0.436284i | \(-0.856294\pi\) | ||||
−0.899809 | + | 0.436284i | \(0.856294\pi\) | |||||||
\(80\) | −1.61901 | −0.181011 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 20.8795 | 2.30575 | ||||||||
\(83\) | 4.84681 | 0.532006 | 0.266003 | − | 0.963972i | \(-0.414297\pi\) | ||||
0.266003 | + | 0.963972i | \(0.414297\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.74753 | −0.189546 | ||||||||
\(86\) | −5.64507 | −0.608723 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.23123 | 0.131250 | ||||||||
\(89\) | 7.47777 | 0.792642 | 0.396321 | − | 0.918112i | \(-0.370287\pi\) | ||||
0.396321 | + | 0.918112i | \(0.370287\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.78307 | 0.396573 | ||||||||
\(92\) | −1.19125 | −0.124197 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.57975 | −0.266081 | ||||||||
\(95\) | −0.486925 | −0.0499574 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.68119 | 0.373769 | 0.186884 | − | 0.982382i | \(-0.440161\pi\) | ||||
0.186884 | + | 0.982382i | \(0.440161\pi\) | |||||||
\(98\) | −10.0493 | −1.01513 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.82951 | −0.582951 | ||||||||
\(101\) | −9.80422 | −0.975556 | −0.487778 | − | 0.872968i | \(-0.662192\pi\) | ||||
−0.487778 | + | 0.872968i | \(0.662192\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.857878 | −0.0845292 | −0.0422646 | − | 0.999106i | \(-0.513457\pi\) | ||||
−0.0422646 | + | 0.999106i | \(0.513457\pi\) | |||||||
\(104\) | −4.66180 | −0.457127 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.8256 | −1.05147 | ||||||||
\(107\) | −12.8882 | −1.24595 | −0.622977 | − | 0.782240i | \(-0.714077\pi\) | ||||
−0.622977 | + | 0.782240i | \(0.714077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.06867 | −0.389708 | −0.194854 | − | 0.980832i | \(-0.562423\pi\) | ||||
−0.194854 | + | 0.980832i | \(0.562423\pi\) | |||||||
\(110\) | −0.496586 | −0.0473476 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.81923 | −0.549865 | ||||||||
\(113\) | 5.77823 | 0.543570 | 0.271785 | − | 0.962358i | \(-0.412386\pi\) | ||||
0.271785 | + | 0.962358i | \(0.412386\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.326188 | −0.0304172 | ||||||||
\(116\) | −1.19125 | −0.110605 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.79057 | −0.256893 | ||||||||
\(119\) | −6.28118 | −0.575795 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2737 | −0.933976 | ||||||||
\(122\) | −11.5880 | −1.04913 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.419958 | 0.0377133 | ||||||||
\(125\) | −3.22717 | −0.288647 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.81622 | 0.161164 | 0.0805818 | − | 0.996748i | \(-0.474322\pi\) | ||||
0.0805818 | + | 0.996748i | \(0.474322\pi\) | |||||||
\(128\) | 10.6131 | 0.938070 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.88022 | 0.164906 | ||||||||
\(131\) | 3.89276 | 0.340112 | 0.170056 | − | 0.985434i | \(-0.445605\pi\) | ||||
0.170056 | + | 0.985434i | \(0.445605\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.75016 | −0.151758 | ||||||||
\(134\) | −11.9286 | −1.03047 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.74018 | 0.663715 | ||||||||
\(137\) | −3.15056 | −0.269171 | −0.134585 | − | 0.990902i | \(-0.542970\pi\) | ||||
−0.134585 | + | 0.990902i | \(0.542970\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.43304 | −0.121549 | −0.0607743 | − | 0.998152i | \(-0.519357\pi\) | ||||
−0.0607743 | + | 0.998152i | \(0.519357\pi\) | |||||||
\(140\) | 0.455570 | 0.0385027 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 24.4316 | 2.05026 | ||||||||
\(143\) | −2.74983 | −0.229952 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.326188 | −0.0270884 | ||||||||
\(146\) | 22.5182 | 1.86362 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.0214 | −1.07035 | ||||||||
\(149\) | 0.913677 | 0.0748513 | 0.0374257 | − | 0.999299i | \(-0.488084\pi\) | ||||
0.0374257 | + | 0.999299i | \(0.488084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.4830 | −1.34137 | −0.670684 | − | 0.741743i | \(-0.733999\pi\) | ||||
−0.670684 | + | 0.741743i | \(0.733999\pi\) | |||||||
\(152\) | 2.15669 | 0.174931 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.78489 | −0.143830 | ||||||||
\(155\) | 0.114993 | 0.00923643 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.94251 | 0.314647 | 0.157323 | − | 0.987547i | \(-0.449713\pi\) | ||||
0.157323 | + | 0.987547i | \(0.449713\pi\) | |||||||
\(158\) | −28.5742 | −2.27324 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.94969 | −0.154136 | ||||||||
\(161\) | −1.17242 | −0.0923998 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.76256 | −0.764663 | −0.382331 | − | 0.924025i | \(-0.624879\pi\) | ||||
−0.382331 | + | 0.924025i | \(0.624879\pi\) | |||||||
\(164\) | 13.9233 | 1.08723 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.65837 | 0.672020 | ||||||||
\(167\) | −21.4326 | −1.65851 | −0.829254 | − | 0.558872i | \(-0.811234\pi\) | ||||
−0.829254 | + | 0.558872i | \(0.811234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.58834 | −0.199103 | ||||||||
\(170\) | −3.12180 | −0.239432 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.76437 | −0.287030 | ||||||||
\(173\) | 13.4151 | 1.01993 | 0.509967 | − | 0.860194i | \(-0.329658\pi\) | ||||
0.509967 | + | 0.860194i | \(0.329658\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.73737 | −0.433704 | ||||||||
\(176\) | 4.22987 | 0.318839 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.3583 | 1.00125 | ||||||||
\(179\) | −0.550115 | −0.0411175 | −0.0205588 | − | 0.999789i | \(-0.506545\pi\) | ||||
−0.0205588 | + | 0.999789i | \(0.506545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.93736 | 0.589979 | 0.294990 | − | 0.955500i | \(-0.404684\pi\) | ||||
0.294990 | + | 0.955500i | \(0.404684\pi\) | |||||||
\(182\) | 6.75810 | 0.500944 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.44475 | 0.106509 | ||||||||
\(185\) | −3.56551 | −0.262141 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.56566 | 0.333874 | ||||||||
\(188\) | −1.72029 | −0.125465 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.869846 | −0.0631052 | ||||||||
\(191\) | −1.69390 | −0.122566 | −0.0612831 | − | 0.998120i | \(-0.519519\pi\) | ||||
−0.0612831 | + | 0.998120i | \(0.519519\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.47769 | −0.178348 | −0.0891741 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891741 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(194\) | 6.57611 | 0.472138 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.70130 | −0.478664 | ||||||||
\(197\) | −0.544234 | −0.0387751 | −0.0193875 | − | 0.999812i | \(-0.506172\pi\) | ||||
−0.0193875 | + | 0.999812i | \(0.506172\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.56260 | 0.465211 | 0.232605 | − | 0.972571i | \(-0.425275\pi\) | ||||
0.232605 | + | 0.972571i | \(0.425275\pi\) | |||||||
\(200\) | 7.07005 | 0.499928 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −17.5143 | −1.23230 | ||||||||
\(203\) | −1.17242 | −0.0822879 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.81247 | 0.266275 | ||||||||
\(206\) | −1.53252 | −0.106776 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −16.0155 | −1.11048 | ||||||||
\(209\) | 1.27215 | 0.0879968 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.71720 | −0.531274 | −0.265637 | − | 0.964073i | \(-0.585582\pi\) | ||||
−0.265637 | + | 0.964073i | \(0.585582\pi\) | |||||||
\(212\) | −7.21894 | −0.495799 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23.0237 | −1.57387 | ||||||||
\(215\) | −1.03076 | −0.0702970 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.413320 | 0.0280580 | ||||||||
\(218\) | −7.26830 | −0.492272 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.331145 | −0.0223258 | ||||||||
\(221\) | −17.2869 | −1.16284 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6536 | 0.780386 | 0.390193 | − | 0.920733i | \(-0.372408\pi\) | ||||
0.390193 | + | 0.920733i | \(0.372408\pi\) | |||||||
\(224\) | −7.00779 | −0.468228 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.3223 | 0.686627 | ||||||||
\(227\) | −18.0449 | −1.19769 | −0.598843 | − | 0.800867i | \(-0.704372\pi\) | ||||
−0.598843 | + | 0.800867i | \(0.704372\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.11185 | 0.469964 | 0.234982 | − | 0.972000i | \(-0.424497\pi\) | ||||
0.234982 | + | 0.972000i | \(0.424497\pi\) | |||||||
\(230\) | −0.582705 | −0.0384224 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.44475 | 0.0948527 | ||||||||
\(233\) | 5.44024 | 0.356402 | 0.178201 | − | 0.983994i | \(-0.442972\pi\) | ||||
0.178201 | + | 0.983994i | \(0.442972\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.471048 | −0.0307278 | ||||||||
\(236\) | −1.86087 | −0.121133 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.2207 | −0.727333 | ||||||||
\(239\) | 5.34393 | 0.345670 | 0.172835 | − | 0.984951i | \(-0.444707\pi\) | ||||
0.172835 | + | 0.984951i | \(0.444707\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.78763 | 0.308398 | 0.154199 | − | 0.988040i | \(-0.450720\pi\) | ||||
0.154199 | + | 0.988040i | \(0.450720\pi\) | |||||||
\(242\) | −18.3531 | −1.17978 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.72739 | −0.494695 | ||||||||
\(245\) | −1.83495 | −0.117230 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.81675 | −0.306482 | ||||||||
\(248\) | −0.509326 | −0.0323422 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.76505 | −0.364614 | ||||||||
\(251\) | 11.8178 | 0.745934 | 0.372967 | − | 0.927845i | \(-0.378340\pi\) | ||||
0.372967 | + | 0.927845i | \(0.378340\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.852209 | 0.0535779 | ||||||||
\(254\) | 3.24451 | 0.203579 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.4609 | 1.27881 | ||||||||
\(257\) | 8.04832 | 0.502041 | 0.251020 | − | 0.967982i | \(-0.419234\pi\) | ||||
0.251020 | + | 0.967982i | \(0.419234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.8155 | −0.796319 | ||||||||
\(260\) | 1.25381 | 0.0777580 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.95406 | 0.429623 | ||||||||
\(263\) | 8.69157 | 0.535945 | 0.267973 | − | 0.963427i | \(-0.413646\pi\) | ||||
0.267973 | + | 0.963427i | \(0.413646\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.97669 | −0.121427 | ||||||||
\(266\) | −3.12650 | −0.191698 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.95446 | −0.485896 | ||||||||
\(269\) | −13.3150 | −0.811829 | −0.405915 | − | 0.913911i | \(-0.633047\pi\) | ||||
−0.405915 | + | 0.913911i | \(0.633047\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.6543 | 0.950932 | 0.475466 | − | 0.879734i | \(-0.342279\pi\) | ||||
0.475466 | + | 0.879734i | \(0.342279\pi\) | |||||||
\(272\) | 26.5912 | 1.61233 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.62819 | −0.340011 | ||||||||
\(275\) | 4.17037 | 0.251483 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.8305 | −1.07133 | −0.535664 | − | 0.844431i | \(-0.679939\pi\) | ||||
−0.535664 | + | 0.844431i | \(0.679939\pi\) | |||||||
\(278\) | −2.55999 | −0.153538 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.552517 | −0.0330192 | ||||||||
\(281\) | −2.21112 | −0.131904 | −0.0659522 | − | 0.997823i | \(-0.521008\pi\) | ||||
−0.0659522 | + | 0.997823i | \(0.521008\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.97755 | 0.474216 | 0.237108 | − | 0.971483i | \(-0.423800\pi\) | ||||
0.237108 | + | 0.971483i | \(0.423800\pi\) | |||||||
\(284\) | 16.2920 | 0.966754 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.91232 | −0.290472 | ||||||||
\(287\) | 13.7032 | 0.808876 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.7022 | 0.688363 | ||||||||
\(290\) | −0.582705 | −0.0342176 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.0161 | 0.878750 | ||||||||
\(293\) | −10.3091 | −0.602267 | −0.301133 | − | 0.953582i | \(-0.597365\pi\) | ||||
−0.301133 | + | 0.953582i | \(0.597365\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.509543 | −0.0296667 | ||||||||
\(296\) | 15.7924 | 0.917912 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.63220 | 0.0945508 | ||||||||
\(299\) | −3.22671 | −0.186606 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.70486 | −0.213545 | ||||||||
\(302\) | −29.4454 | −1.69439 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.40926 | 0.424950 | ||||||||
\(305\) | −2.11591 | −0.121157 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.75282 | −0.214185 | −0.107092 | − | 0.994249i | \(-0.534154\pi\) | ||||
−0.107092 | + | 0.994249i | \(0.534154\pi\) | |||||||
\(308\) | −1.19024 | −0.0678201 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.205424 | 0.0116673 | ||||||||
\(311\) | 1.70068 | 0.0964367 | 0.0482184 | − | 0.998837i | \(-0.484646\pi\) | ||||
0.0482184 | + | 0.998837i | \(0.484646\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.4550 | −1.60837 | −0.804186 | − | 0.594378i | \(-0.797398\pi\) | ||||
−0.804186 | + | 0.594378i | \(0.797398\pi\) | |||||||
\(314\) | 7.04294 | 0.397456 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.0545 | −1.07190 | ||||||||
\(317\) | −4.71662 | −0.264912 | −0.132456 | − | 0.991189i | \(-0.542286\pi\) | ||||
−0.132456 | + | 0.991189i | \(0.542286\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.852209 | 0.0477145 | ||||||||
\(320\) | −0.244919 | −0.0136914 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.09442 | −0.116718 | ||||||||
\(323\) | 7.99744 | 0.444990 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.7902 | −0.875885 | ||||||||
\(326\) | −17.4399 | −0.965908 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −16.8862 | −0.932386 | ||||||||
\(329\) | −1.69309 | −0.0933432 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.172157 | −0.00946260 | −0.00473130 | − | 0.999989i | \(-0.501506\pi\) | ||||
−0.00473130 | + | 0.999989i | \(0.501506\pi\) | |||||||
\(332\) | 5.77377 | 0.316877 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −38.2874 | −2.09500 | ||||||||
\(335\) | −2.17809 | −0.119002 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.30625 | 0.289050 | 0.144525 | − | 0.989501i | \(-0.453835\pi\) | ||||
0.144525 | + | 0.989501i | \(0.453835\pi\) | |||||||
\(338\) | −4.62382 | −0.251503 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.08175 | −0.112899 | ||||||||
\(341\) | −0.300433 | −0.0162694 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.8023 | −0.799251 | ||||||||
\(344\) | 4.56543 | 0.246152 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23.9649 | 1.28836 | ||||||||
\(347\) | 6.97399 | 0.374383 | 0.187192 | − | 0.982323i | \(-0.440061\pi\) | ||||
0.187192 | + | 0.982323i | \(0.440061\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.2958 | −0.872291 | −0.436146 | − | 0.899876i | \(-0.643657\pi\) | ||||
−0.436146 | + | 0.899876i | \(0.643657\pi\) | |||||||
\(350\) | −10.2493 | −0.547847 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.09381 | 0.271501 | ||||||||
\(353\) | −1.29005 | −0.0686623 | −0.0343311 | − | 0.999411i | \(-0.510930\pi\) | ||||
−0.0343311 | + | 0.999411i | \(0.510930\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.46107 | 0.236769 | ||||||||
\(356\) | 8.90791 | 0.472118 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.982729 | −0.0519389 | ||||||||
\(359\) | 30.4439 | 1.60677 | 0.803385 | − | 0.595460i | \(-0.203030\pi\) | ||||
0.803385 | + | 0.595460i | \(0.203030\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7716 | −0.882717 | ||||||||
\(362\) | 14.1794 | 0.745250 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.50659 | 0.236209 | ||||||||
\(365\) | 4.11170 | 0.215216 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.3547 | −1.06251 | −0.531253 | − | 0.847213i | \(-0.678279\pi\) | ||||
−0.531253 | + | 0.847213i | \(0.678279\pi\) | |||||||
\(368\) | 4.96342 | 0.258736 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.36945 | −0.331132 | ||||||||
\(371\) | −7.10483 | −0.368864 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.7681 | −1.23067 | −0.615334 | − | 0.788266i | \(-0.710979\pi\) | ||||
−0.615334 | + | 0.788266i | \(0.710979\pi\) | |||||||
\(374\) | 8.15613 | 0.421743 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.08637 | 0.107596 | ||||||||
\(377\) | −3.22671 | −0.166184 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.60685 | 0.288005 | 0.144002 | − | 0.989577i | \(-0.454003\pi\) | ||||
0.144002 | + | 0.989577i | \(0.454003\pi\) | |||||||
\(380\) | −0.580050 | −0.0297559 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.02600 | −0.154823 | ||||||||
\(383\) | −34.5495 | −1.76540 | −0.882699 | − | 0.469938i | \(-0.844276\pi\) | ||||
−0.882699 | + | 0.469938i | \(0.844276\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.325910 | −0.0166099 | ||||||||
\(386\) | −4.42617 | −0.225286 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.38523 | 0.222626 | ||||||||
\(389\) | 12.1605 | 0.616560 | 0.308280 | − | 0.951296i | \(-0.400247\pi\) | ||||
0.308280 | + | 0.951296i | \(0.400247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.35744 | 0.270937 | ||||||||
\(392\) | 8.12735 | 0.410493 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.972224 | −0.0489800 | ||||||||
\(395\) | −5.21749 | −0.262520 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.8664 | 0.746122 | 0.373061 | − | 0.927807i | \(-0.378308\pi\) | ||||
0.373061 | + | 0.927807i | \(0.378308\pi\) | |||||||
\(398\) | 11.7235 | 0.587645 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24.2890 | 1.21445 | ||||||||
\(401\) | 11.9695 | 0.597728 | 0.298864 | − | 0.954296i | \(-0.403392\pi\) | ||||
0.298864 | + | 0.954296i | \(0.403392\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.13753 | 0.0566643 | ||||||||
\(404\) | −11.6793 | −0.581067 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.09442 | −0.103944 | ||||||||
\(407\) | 9.31535 | 0.461745 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.9672 | 1.82791 | 0.913954 | − | 0.405817i | \(-0.133013\pi\) | ||||
0.913954 | + | 0.405817i | \(0.133013\pi\) | |||||||
\(410\) | 6.81063 | 0.336353 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.02195 | −0.0503478 | ||||||||
\(413\) | −1.83146 | −0.0901202 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.58097 | 0.0776068 | ||||||||
\(416\) | −19.2867 | −0.945607 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.27259 | 0.111156 | ||||||||
\(419\) | 18.3400 | 0.895969 | 0.447984 | − | 0.894041i | \(-0.352142\pi\) | ||||
0.447984 | + | 0.894041i | \(0.352142\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.09440 | −0.297023 | −0.148512 | − | 0.988911i | \(-0.547448\pi\) | ||||
−0.148512 | + | 0.988911i | \(0.547448\pi\) | |||||||
\(422\) | −13.7861 | −0.671095 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.75515 | 0.425187 | ||||||||
\(425\) | 26.2172 | 1.27172 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.60524 | −0.368043 | ||||||||
\(428\) | −15.3532 | −0.742123 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.84135 | −0.0887979 | ||||||||
\(431\) | 7.49900 | 0.361214 | 0.180607 | − | 0.983555i | \(-0.442194\pi\) | ||||
0.180607 | + | 0.983555i | \(0.442194\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.7396 | 0.804453 | 0.402226 | − | 0.915540i | \(-0.368237\pi\) | ||||
0.402226 | + | 0.915540i | \(0.368237\pi\) | |||||||
\(434\) | 0.738357 | 0.0354423 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.84681 | −0.232120 | ||||||||
\(437\) | 1.49277 | 0.0714090 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.9913 | 1.43141 | 0.715704 | − | 0.698404i | \(-0.246106\pi\) | ||||
0.715704 | + | 0.698404i | \(0.246106\pi\) | |||||||
\(440\) | 0.401613 | 0.0191461 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −30.8815 | −1.46888 | ||||||||
\(443\) | −27.1617 | −1.29049 | −0.645245 | − | 0.763976i | \(-0.723245\pi\) | ||||
−0.645245 | + | 0.763976i | \(0.723245\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.43916 | 0.115627 | ||||||||
\(446\) | 20.8182 | 0.985768 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.880317 | −0.0415910 | ||||||||
\(449\) | −21.8977 | −1.03342 | −0.516708 | − | 0.856161i | \(-0.672843\pi\) | ||||
−0.516708 | + | 0.856161i | \(0.672843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.96059 | −0.469026 | ||||||||
\(452\) | 6.88333 | 0.323764 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −32.2356 | −1.51289 | ||||||||
\(455\) | 1.23399 | 0.0578504 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.7853 | 1.01908 | 0.509538 | − | 0.860448i | \(-0.329817\pi\) | ||||
0.509538 | + | 0.860448i | \(0.329817\pi\) | |||||||
\(458\) | 12.7047 | 0.593650 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.388572 | −0.0181173 | ||||||||
\(461\) | 18.0738 | 0.841781 | 0.420890 | − | 0.907111i | \(-0.361718\pi\) | ||||
0.420890 | + | 0.907111i | \(0.361718\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.22965 | −0.382464 | −0.191232 | − | 0.981545i | \(-0.561248\pi\) | ||||
−0.191232 | + | 0.981545i | \(0.561248\pi\) | |||||||
\(464\) | 4.96342 | 0.230421 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.71848 | 0.450200 | ||||||||
\(467\) | −25.0014 | −1.15693 | −0.578463 | − | 0.815708i | \(-0.696347\pi\) | ||||
−0.578463 | + | 0.815708i | \(0.696347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.82873 | −0.361497 | ||||||||
\(470\) | −0.841483 | −0.0388147 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.25687 | 0.103881 | ||||||||
\(473\) | 2.69299 | 0.123824 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.30504 | 0.335178 | ||||||||
\(476\) | −7.48247 | −0.342959 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.54644 | 0.436644 | ||||||||
\(479\) | 2.60344 | 0.118954 | 0.0594772 | − | 0.998230i | \(-0.481057\pi\) | ||||
0.0594772 | + | 0.998230i | \(0.481057\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −35.2706 | −1.60820 | ||||||||
\(482\) | 8.55265 | 0.389563 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.2386 | −0.556301 | ||||||||
\(485\) | 1.20076 | 0.0545238 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.77061 | 0.261491 | 0.130746 | − | 0.991416i | \(-0.458263\pi\) | ||||
0.130746 | + | 0.991416i | \(0.458263\pi\) | |||||||
\(488\) | 9.37179 | 0.424241 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.27796 | −0.148083 | ||||||||
\(491\) | 26.5293 | 1.19725 | 0.598625 | − | 0.801030i | \(-0.295714\pi\) | ||||
0.598625 | + | 0.801030i | \(0.295714\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.35744 | 0.241287 | ||||||||
\(494\) | −8.60468 | −0.387143 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.74978 | −0.0785674 | ||||||||
\(497\) | 16.0345 | 0.719246 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.1318 | 1.70701 | 0.853507 | − | 0.521081i | \(-0.174471\pi\) | ||||
0.853507 | + | 0.521081i | \(0.174471\pi\) | |||||||
\(500\) | −3.84438 | −0.171926 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.1114 | 0.942250 | ||||||||
\(503\) | 9.14152 | 0.407600 | 0.203800 | − | 0.979013i | \(-0.434671\pi\) | ||||
0.203800 | + | 0.979013i | \(0.434671\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.19802 | −0.142310 | ||||||||
\(506\) | 1.52239 | 0.0676786 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.16358 | 0.0959932 | ||||||||
\(509\) | 36.4615 | 1.61613 | 0.808063 | − | 0.589096i | \(-0.200516\pi\) | ||||
0.808063 | + | 0.589096i | \(0.200516\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.7787 | 0.653773 | ||||||||
\(512\) | 15.3255 | 0.677297 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.3776 | 0.634168 | ||||||||
\(515\) | −0.279829 | −0.0123308 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.23067 | 0.0541250 | ||||||||
\(518\) | −22.8938 | −1.00590 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.52062 | −0.0666837 | ||||||||
\(521\) | −2.69985 | −0.118282 | −0.0591412 | − | 0.998250i | \(-0.518836\pi\) | ||||
−0.0591412 | + | 0.998250i | \(0.518836\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.0986 | 1.40358 | 0.701788 | − | 0.712386i | \(-0.252386\pi\) | ||||
0.701788 | + | 0.712386i | \(0.252386\pi\) | |||||||
\(524\) | 4.63726 | 0.202580 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.5267 | 0.676996 | ||||||||
\(527\) | −1.88868 | −0.0822724 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −3.53117 | −0.153384 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.08488 | −0.0903911 | ||||||||
\(533\) | 37.7137 | 1.63356 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.20399 | −0.181754 | ||||||||
\(536\) | 9.64719 | 0.416695 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −23.7860 | −1.02549 | ||||||||
\(539\) | 4.79404 | 0.206494 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.4359 | −0.663641 | −0.331821 | − | 0.943342i | \(-0.607663\pi\) | ||||
−0.331821 | + | 0.943342i | \(0.607663\pi\) | |||||||
\(542\) | 27.9650 | 1.20120 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.0224 | 1.37295 | ||||||||
\(545\) | −1.32715 | −0.0568489 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.05171 | −0.215996 | −0.107998 | − | 0.994151i | \(-0.534444\pi\) | ||||
−0.107998 | + | 0.994151i | \(0.534444\pi\) | |||||||
\(548\) | −3.75312 | −0.160325 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.44998 | 0.317668 | ||||||||
\(551\) | 1.49277 | 0.0635943 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.7533 | −0.797472 | ||||||||
\(554\) | −31.8525 | −1.35328 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.70711 | −0.0723975 | ||||||||
\(557\) | −10.4714 | −0.443688 | −0.221844 | − | 0.975082i | \(-0.571208\pi\) | ||||
−0.221844 | + | 0.975082i | \(0.571208\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.1964 | −0.431263 | ||||||||
\(560\) | −1.89816 | −0.0802119 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.94996 | −0.166619 | ||||||||
\(563\) | 15.1161 | 0.637069 | 0.318535 | − | 0.947911i | \(-0.396809\pi\) | ||||
0.318535 | + | 0.947911i | \(0.396809\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.88479 | 0.0792936 | ||||||||
\(566\) | 14.2512 | 0.599021 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19.7590 | −0.829070 | ||||||||
\(569\) | 34.2755 | 1.43691 | 0.718453 | − | 0.695576i | \(-0.244851\pi\) | ||||
0.718453 | + | 0.695576i | \(0.244851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.8728 | −1.66862 | −0.834312 | − | 0.551293i | \(-0.814135\pi\) | ||||
−0.834312 | + | 0.551293i | \(0.814135\pi\) | |||||||
\(572\) | −3.27574 | −0.136966 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.4796 | 1.02176 | ||||||||
\(575\) | 4.89360 | 0.204077 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.0528 | −1.25111 | −0.625556 | − | 0.780179i | \(-0.715128\pi\) | ||||
−0.625556 | + | 0.780179i | \(0.715128\pi\) | |||||||
\(578\) | 20.9048 | 0.869527 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.388572 | −0.0161346 | ||||||||
\(581\) | 5.68250 | 0.235750 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.16435 | 0.213886 | ||||||||
\(584\) | −18.2115 | −0.753599 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.4163 | −0.760772 | ||||||||
\(587\) | 11.6696 | 0.481656 | 0.240828 | − | 0.970568i | \(-0.422581\pi\) | ||||
0.240828 | + | 0.970568i | \(0.422581\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.526255 | −0.0216839 | ||||||||
\(590\) | −0.910252 | −0.0374745 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 54.2543 | 2.22984 | ||||||||
\(593\) | 32.5160 | 1.33527 | 0.667635 | − | 0.744489i | \(-0.267307\pi\) | ||||
0.667635 | + | 0.744489i | \(0.267307\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.04885 | −0.0839945 | ||||||||
\(596\) | 1.08842 | 0.0445834 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.76422 | −0.235717 | ||||||||
\(599\) | 30.3911 | 1.24175 | 0.620874 | − | 0.783911i | \(-0.286778\pi\) | ||||
0.620874 | + | 0.783911i | \(0.286778\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.2479 | −1.43779 | −0.718896 | − | 0.695118i | \(-0.755352\pi\) | ||||
−0.718896 | + | 0.695118i | \(0.755352\pi\) | |||||||
\(602\) | −6.61840 | −0.269746 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.6354 | −0.798954 | ||||||||
\(605\) | −3.35117 | −0.136244 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.10437 | −0.0854139 | −0.0427070 | − | 0.999088i | \(-0.513598\pi\) | ||||
−0.0427070 | + | 0.999088i | \(0.513598\pi\) | |||||||
\(608\) | 8.92259 | 0.361859 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.77987 | −0.153043 | ||||||||
\(611\) | −4.65969 | −0.188511 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.4130 | −0.662914 | −0.331457 | − | 0.943470i | \(-0.607540\pi\) | ||||
−0.331457 | + | 0.943470i | \(0.607540\pi\) | |||||||
\(614\) | −6.70406 | −0.270554 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.44352 | 0.0581612 | ||||||||
\(617\) | −7.81267 | −0.314526 | −0.157263 | − | 0.987557i | \(-0.550267\pi\) | ||||
−0.157263 | + | 0.987557i | \(0.550267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.8878 | −1.12091 | −0.560453 | − | 0.828186i | \(-0.689373\pi\) | ||||
−0.560453 | + | 0.828186i | \(0.689373\pi\) | |||||||
\(620\) | 0.136985 | 0.00550146 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.03811 | 0.121817 | ||||||||
\(623\) | 8.76710 | 0.351246 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4153 | 0.936614 | ||||||||
\(626\) | −50.8322 | −2.03166 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.69653 | 0.187412 | ||||||||
\(629\) | 58.5613 | 2.33499 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.5765 | 0.779330 | 0.389665 | − | 0.920957i | \(-0.372591\pi\) | ||||
0.389665 | + | 0.920957i | \(0.372591\pi\) | |||||||
\(632\) | 23.1093 | 0.919240 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.42581 | −0.334632 | ||||||||
\(635\) | 0.592429 | 0.0235098 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.1516 | −0.719194 | ||||||||
\(638\) | 1.52239 | 0.0602721 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.46185 | 0.136842 | ||||||||
\(641\) | 9.47844 | 0.374376 | 0.187188 | − | 0.982324i | \(-0.440063\pi\) | ||||
0.187188 | + | 0.982324i | \(0.440063\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.98714 | −0.196674 | −0.0983368 | − | 0.995153i | \(-0.531352\pi\) | ||||
−0.0983368 | + | 0.995153i | \(0.531352\pi\) | |||||||
\(644\) | −1.39665 | −0.0550357 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.2867 | 0.562103 | ||||||||
\(647\) | 10.2381 | 0.402501 | 0.201251 | − | 0.979540i | \(-0.435499\pi\) | ||||
0.201251 | + | 0.979540i | \(0.435499\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.33125 | 0.0522561 | ||||||||
\(650\) | −28.2078 | −1.10640 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.6297 | −0.455453 | ||||||||
\(653\) | −29.3913 | −1.15017 | −0.575086 | − | 0.818093i | \(-0.695031\pi\) | ||||
−0.575086 | + | 0.818093i | \(0.695031\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.26977 | 0.0496141 | ||||||||
\(656\) | −58.0123 | −2.26500 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.02455 | −0.117909 | ||||||||
\(659\) | 37.1953 | 1.44892 | 0.724462 | − | 0.689315i | \(-0.242088\pi\) | ||||
0.724462 | + | 0.689315i | \(0.242088\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.87718 | 0.306387 | 0.153193 | − | 0.988196i | \(-0.451044\pi\) | ||||
0.153193 | + | 0.988196i | \(0.451044\pi\) | |||||||
\(662\) | −0.307542 | −0.0119530 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.00244 | −0.271747 | ||||||||
\(665\) | −0.570881 | −0.0221378 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −25.5317 | −0.987850 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.89095 | −0.150321 | ||||||||
\(671\) | 5.52809 | 0.213409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.46069 | 0.326136 | 0.163068 | − | 0.986615i | \(-0.447861\pi\) | ||||
0.163068 | + | 0.986615i | \(0.447861\pi\) | |||||||
\(674\) | 9.47913 | 0.365122 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.08336 | −0.118591 | ||||||||
\(677\) | 0.648694 | 0.0249313 | 0.0124657 | − | 0.999922i | \(-0.496032\pi\) | ||||
0.0124657 | + | 0.999922i | \(0.496032\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.31591 | 0.165630 | ||||||||
\(680\) | 2.52475 | 0.0968198 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.536696 | −0.0205512 | ||||||||
\(683\) | −15.5457 | −0.594838 | −0.297419 | − | 0.954747i | \(-0.596126\pi\) | ||||
−0.297419 | + | 0.954747i | \(0.596126\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.02768 | −0.0392655 | ||||||||
\(686\) | −26.4430 | −1.00960 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.6845 | 0.597965 | ||||||||
\(689\) | −19.5537 | −0.744938 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.1134 | −0.651023 | −0.325511 | − | 0.945538i | \(-0.605536\pi\) | ||||
−0.325511 | + | 0.945538i | \(0.605536\pi\) | |||||||
\(692\) | 15.9808 | 0.607499 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.4584 | 0.472914 | ||||||||
\(695\) | −0.467439 | −0.0177310 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −62.6176 | −2.37181 | ||||||||
\(698\) | −29.1109 | −1.10186 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.83465 | −0.258326 | ||||||||
\(701\) | −16.8345 | −0.635829 | −0.317915 | − | 0.948119i | \(-0.602983\pi\) | ||||
−0.317915 | + | 0.948119i | \(0.602983\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3173 | 0.615417 | ||||||||
\(704\) | 0.639884 | 0.0241165 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.30455 | −0.0867329 | ||||||||
\(707\) | −11.4947 | −0.432302 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.6600 | −1.15146 | −0.575730 | − | 0.817640i | \(-0.695282\pi\) | ||||
−0.575730 | + | 0.817640i | \(0.695282\pi\) | |||||||
\(710\) | 7.96930 | 0.299082 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.8035 | −0.404879 | ||||||||
\(713\) | −0.352535 | −0.0132025 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.896962 | −0.0335445 | ||||||||
\(716\) | −0.655326 | −0.0244907 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 54.3853 | 2.02964 | ||||||||
\(719\) | −26.6976 | −0.995654 | −0.497827 | − | 0.867276i | \(-0.665868\pi\) | ||||
−0.497827 | + | 0.867276i | \(0.665868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.00579 | −0.0374577 | ||||||||
\(722\) | −29.9610 | −1.11503 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.45539 | 0.351407 | ||||||||
\(725\) | 4.89360 | 0.181744 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.0018 | 1.66903 | 0.834513 | − | 0.550989i | \(-0.185749\pi\) | ||||
0.834513 | + | 0.550989i | \(0.185749\pi\) | |||||||
\(728\) | −5.46560 | −0.202569 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.34517 | 0.271857 | ||||||||
\(731\) | 16.9296 | 0.626163 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.8424 | −0.769833 | −0.384917 | − | 0.922951i | \(-0.625770\pi\) | ||||
−0.384917 | + | 0.922951i | \(0.625770\pi\) | |||||||
\(734\) | −36.3618 | −1.34214 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.97719 | 0.220322 | ||||||||
\(737\) | 5.69054 | 0.209614 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.5125 | 1.04885 | 0.524425 | − | 0.851457i | \(-0.324280\pi\) | ||||
0.524425 | + | 0.851457i | \(0.324280\pi\) | |||||||
\(740\) | −4.24742 | −0.156138 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.6921 | −0.465943 | ||||||||
\(743\) | 22.4337 | 0.823013 | 0.411506 | − | 0.911407i | \(-0.365003\pi\) | ||||
0.411506 | + | 0.911407i | \(0.365003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.298030 | 0.0109190 | ||||||||
\(746\) | −42.4596 | −1.55456 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.43885 | 0.198864 | ||||||||
\(749\) | −15.1105 | −0.552124 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.21818 | 0.299886 | 0.149943 | − | 0.988695i | \(-0.452091\pi\) | ||||
0.149943 | + | 0.988695i | \(0.452091\pi\) | |||||||
\(752\) | 7.16767 | 0.261378 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.76422 | −0.209921 | ||||||||
\(755\) | −5.37656 | −0.195673 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.6868 | −0.570145 | −0.285073 | − | 0.958506i | \(-0.592018\pi\) | ||||
−0.285073 | + | 0.958506i | \(0.592018\pi\) | |||||||
\(758\) | 10.0161 | 0.363802 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.703486 | 0.0255181 | ||||||||
\(761\) | 16.0488 | 0.581768 | 0.290884 | − | 0.956758i | \(-0.406051\pi\) | ||||
0.290884 | + | 0.956758i | \(0.406051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.77020 | −0.172693 | ||||||||
\(764\) | −2.01786 | −0.0730037 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −61.7196 | −2.23002 | ||||||||
\(767\) | −5.04049 | −0.182002 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.81368 | −0.137525 | −0.0687624 | − | 0.997633i | \(-0.521905\pi\) | ||||
−0.0687624 | + | 0.997633i | \(0.521905\pi\) | |||||||
\(770\) | −0.582208 | −0.0209813 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.95156 | −0.106229 | ||||||||
\(773\) | −9.76179 | −0.351107 | −0.175554 | − | 0.984470i | \(-0.556172\pi\) | ||||
−0.175554 | + | 0.984470i | \(0.556172\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.72517 | −0.0619698 | ||||||||
\(776\) | −5.31842 | −0.190920 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.7236 | 0.778827 | ||||||||
\(779\) | −17.4475 | −0.625121 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.6551 | −0.417054 | ||||||||
\(782\) | 9.57057 | 0.342243 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 27.9214 | 0.997192 | ||||||||
\(785\) | 1.28600 | 0.0458993 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.60016 | −0.342209 | −0.171104 | − | 0.985253i | \(-0.554734\pi\) | ||||
−0.171104 | + | 0.985253i | \(0.554734\pi\) | |||||||
\(788\) | −0.648320 | −0.0230955 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.32057 | −0.331611 | ||||||||
\(791\) | 6.77452 | 0.240874 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.9309 | −0.743280 | ||||||||
\(794\) | 26.5574 | 0.942487 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.81772 | 0.277092 | ||||||||
\(797\) | 44.4356 | 1.57399 | 0.786994 | − | 0.616960i | \(-0.211636\pi\) | ||||
0.786994 | + | 0.616960i | \(0.211636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.73667 | 0.273704 | ||||||||
\(800\) | 29.2500 | 1.03414 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.3824 | 0.755039 | ||||||||
\(803\) | −10.7423 | −0.379089 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.382430 | −0.0134789 | ||||||||
\(806\) | 2.03209 | 0.0715773 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.1647 | 0.498311 | ||||||||
\(809\) | −14.6055 | −0.513501 | −0.256751 | − | 0.966478i | \(-0.582652\pi\) | ||||
−0.256751 | + | 0.966478i | \(0.582652\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.6349 | 0.689474 | 0.344737 | − | 0.938699i | \(-0.387968\pi\) | ||||
0.344737 | + | 0.938699i | \(0.387968\pi\) | |||||||
\(812\) | −1.39665 | −0.0490128 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 16.6410 | 0.583267 | ||||||||
\(815\) | −3.18443 | −0.111546 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.71718 | 0.165033 | ||||||||
\(818\) | 66.0384 | 2.30898 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.54162 | 0.158600 | ||||||||
\(821\) | −32.1373 | −1.12160 | −0.560800 | − | 0.827952i | \(-0.689506\pi\) | ||||
−0.560800 | + | 0.827952i | \(0.689506\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.5635 | 1.06538 | 0.532689 | − | 0.846311i | \(-0.321182\pi\) | ||||
0.532689 | + | 0.846311i | \(0.321182\pi\) | |||||||
\(824\) | 1.23942 | 0.0431773 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.27173 | −0.113838 | ||||||||
\(827\) | 45.4056 | 1.57891 | 0.789453 | − | 0.613811i | \(-0.210364\pi\) | ||||
0.789453 | + | 0.613811i | \(0.210364\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.3167 | −0.948747 | −0.474374 | − | 0.880324i | \(-0.657325\pi\) | ||||
−0.474374 | + | 0.880324i | \(0.657325\pi\) | |||||||
\(830\) | 2.82426 | 0.0980314 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.42279 | −0.0839950 | ||||||||
\(833\) | 30.1379 | 1.04422 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.99107 | −0.241936 | ||||||||
\(836\) | 1.51546 | 0.0524132 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 32.7628 | 1.13177 | ||||||||
\(839\) | 5.77471 | 0.199365 | 0.0996826 | − | 0.995019i | \(-0.468217\pi\) | ||||
0.0996826 | + | 0.995019i | \(0.468217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −10.8871 | −0.375194 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.19313 | −0.316441 | ||||||||
\(845\) | −0.844284 | −0.0290443 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.0452 | −0.413877 | ||||||||
\(848\) | 30.0781 | 1.03289 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 46.8346 | 1.60641 | ||||||||
\(851\) | 10.9308 | 0.374704 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.09579 | −0.0717585 | −0.0358792 | − | 0.999356i | \(-0.511423\pi\) | ||||
−0.0358792 | + | 0.999356i | \(0.511423\pi\) | |||||||
\(854\) | −13.5861 | −0.464905 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.6203 | 0.636430 | ||||||||
\(857\) | 52.3317 | 1.78762 | 0.893809 | − | 0.448449i | \(-0.148023\pi\) | ||||
0.893809 | + | 0.448449i | \(0.148023\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.34901 | −0.0460277 | −0.0230139 | − | 0.999735i | \(-0.507326\pi\) | ||||
−0.0230139 | + | 0.999735i | \(0.507326\pi\) | |||||||
\(860\) | −1.22789 | −0.0418708 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.3963 | 0.456279 | ||||||||
\(863\) | −0.664000 | −0.0226028 | −0.0113014 | − | 0.999936i | \(-0.503597\pi\) | ||||
−0.0113014 | + | 0.999936i | \(0.503597\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.37585 | 0.148783 | ||||||||
\(866\) | 29.9037 | 1.01617 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.492368 | 0.0167121 | ||||||||
\(869\) | 13.6314 | 0.462413 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.5460 | −0.730059 | ||||||||
\(872\) | 5.87822 | 0.199062 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.66670 | 0.0902025 | ||||||||
\(875\) | −3.78361 | −0.127909 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.2825 | 0.482285 | 0.241143 | − | 0.970490i | \(-0.422478\pi\) | ||||
0.241143 | + | 0.970490i | \(0.422478\pi\) | |||||||
\(878\) | 53.5767 | 1.80813 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.37973 | 0.0465108 | ||||||||
\(881\) | −45.7708 | −1.54206 | −0.771028 | − | 0.636801i | \(-0.780257\pi\) | ||||
−0.771028 | + | 0.636801i | \(0.780257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.0494 | −1.24681 | −0.623406 | − | 0.781898i | \(-0.714252\pi\) | ||||
−0.623406 | + | 0.781898i | \(0.714252\pi\) | |||||||
\(884\) | −20.5931 | −0.692620 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −48.5218 | −1.63012 | ||||||||
\(887\) | 0.840415 | 0.0282184 | 0.0141092 | − | 0.999900i | \(-0.495509\pi\) | ||||
0.0141092 | + | 0.999900i | \(0.495509\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.12938 | 0.0714170 | ||||||||
\(890\) | 4.35733 | 0.146058 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.8824 | 0.464818 | ||||||||
\(893\) | 2.15571 | 0.0721381 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.179441 | −0.00599804 | ||||||||
\(896\) | 12.4430 | 0.415691 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −39.1182 | −1.30539 | ||||||||
\(899\) | −0.352535 | −0.0117577 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.4659 | 1.08160 | ||||||||
\(902\) | −17.7937 | −0.592464 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.34811 | −0.277654 | ||||||||
\(905\) | 2.58907 | 0.0860636 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.7632 | −0.423794 | −0.211897 | − | 0.977292i | \(-0.567964\pi\) | ||||
−0.211897 | + | 0.977292i | \(0.567964\pi\) | |||||||
\(908\) | −21.4961 | −0.713373 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.20441 | 0.0730755 | ||||||||
\(911\) | −0.499026 | −0.0165335 | −0.00826674 | − | 0.999966i | \(-0.502631\pi\) | ||||
−0.00826674 | + | 0.999966i | \(0.502631\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.13049 | −0.136699 | ||||||||
\(914\) | 38.9175 | 1.28728 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.47201 | 0.279923 | ||||||||
\(917\) | 4.56396 | 0.150715 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.62310 | −0.185489 | −0.0927445 | − | 0.995690i | \(-0.529564\pi\) | ||||
−0.0927445 | + | 0.995690i | \(0.529564\pi\) | |||||||
\(920\) | 0.471261 | 0.0155370 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.2872 | 1.06332 | ||||||||
\(923\) | 44.1298 | 1.45255 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 53.4911 | 1.75878 | ||||||||
\(926\) | −14.7015 | −0.483121 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.97719 | 0.196211 | ||||||||
\(929\) | −3.39932 | −0.111528 | −0.0557641 | − | 0.998444i | \(-0.517759\pi\) | ||||
−0.0557641 | + | 0.998444i | \(0.517759\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.39749 | 0.275217 | ||||||||
\(932\) | 6.48069 | 0.212282 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −44.6627 | −1.46141 | ||||||||
\(935\) | 1.48926 | 0.0487041 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.5379 | 1.12830 | 0.564152 | − | 0.825671i | \(-0.309203\pi\) | ||||
0.564152 | + | 0.825671i | \(0.309203\pi\) | |||||||
\(938\) | −13.9853 | −0.456636 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.561136 | −0.0183023 | ||||||||
\(941\) | −0.850674 | −0.0277312 | −0.0138656 | − | 0.999904i | \(-0.504414\pi\) | ||||
−0.0138656 | + | 0.999904i | \(0.504414\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.6880 | −0.380613 | ||||||||
\(944\) | 7.75344 | 0.252353 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.81077 | 0.156412 | ||||||||
\(947\) | 48.6038 | 1.57941 | 0.789706 | − | 0.613485i | \(-0.210233\pi\) | ||||
0.789706 | + | 0.613485i | \(0.210233\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.6737 | 1.32032 | ||||||||
\(950\) | 13.0498 | 0.423391 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.07476 | 0.294115 | ||||||||
\(953\) | −45.2493 | −1.46577 | −0.732885 | − | 0.680353i | \(-0.761827\pi\) | ||||
−0.732885 | + | 0.680353i | \(0.761827\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.552530 | −0.0178794 | ||||||||
\(956\) | 6.36597 | 0.205890 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.65081 | 0.150261 | ||||||||
\(959\) | −3.69379 | −0.119279 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8757 | −0.995991 | ||||||||
\(962\) | −63.0077 | −2.03145 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.70327 | 0.183690 | ||||||||
\(965\) | −0.808193 | −0.0260167 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.1176 | −0.872043 | −0.436021 | − | 0.899936i | \(-0.643613\pi\) | ||||
−0.436021 | + | 0.899936i | \(0.643613\pi\) | |||||||
\(968\) | 14.8430 | 0.477073 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.14505 | 0.0688734 | ||||||||
\(971\) | −40.2983 | −1.29323 | −0.646617 | − | 0.762815i | \(-0.723817\pi\) | ||||
−0.646617 | + | 0.762815i | \(0.723817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.68012 | −0.0538623 | ||||||||
\(974\) | 10.3087 | 0.330311 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.1966 | 1.03059 | ||||||||
\(977\) | −43.0726 | −1.37801 | −0.689007 | − | 0.724755i | \(-0.741953\pi\) | ||||
−0.689007 | + | 0.724755i | \(0.741953\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.37262 | −0.203670 | ||||||||
\(980\) | −2.18588 | −0.0698255 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 47.3921 | 1.51234 | ||||||||
\(983\) | 24.0627 | 0.767481 | 0.383740 | − | 0.923441i | \(-0.374636\pi\) | ||||
0.383740 | + | 0.923441i | \(0.374636\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.177523 | −0.00565634 | ||||||||
\(986\) | 9.57057 | 0.304789 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.73796 | −0.182549 | ||||||||
\(989\) | 3.16001 | 0.100482 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.202445 | 0.00643088 | 0.00321544 | − | 0.999995i | \(-0.498976\pi\) | ||||
0.00321544 | + | 0.999995i | \(0.498976\pi\) | |||||||
\(992\) | −2.10717 | −0.0669026 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 28.6442 | 0.908537 | ||||||||
\(995\) | 2.14064 | 0.0678629 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.0857 | −0.477770 | −0.238885 | − | 0.971048i | \(-0.576782\pi\) | ||||
−0.238885 | + | 0.971048i | \(0.576782\pi\) | |||||||
\(998\) | 68.1190 | 2.15627 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.u.1.17 | yes | 22 | |
3.2 | odd | 2 | 6003.2.a.t.1.6 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.t.1.6 | ✓ | 22 | 3.2 | odd | 2 | ||
6003.2.a.u.1.17 | yes | 22 | 1.1 | even | 1 | trivial |