Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9408,2,Mod(1,9408)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9408, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9408.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9408.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: | \(75.1232582216\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1176) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9408.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.41421 | −1.52688 | −0.763441 | − | 0.645877i | \(-0.776492\pi\) | ||||
−0.763441 | + | 0.645877i | \(0.776492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.82843 | 1.45583 | 0.727913 | − | 0.685670i | \(-0.240491\pi\) | ||||
0.727913 | + | 0.685670i | \(0.240491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41421 | −0.392232 | −0.196116 | − | 0.980581i | \(-0.562833\pi\) | ||||
−0.196116 | + | 0.980581i | \(0.562833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.41421 | −0.881546 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.24264 | −1.51406 | −0.757031 | − | 0.653379i | \(-0.773351\pi\) | ||||
−0.757031 | + | 0.653379i | \(0.773351\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.17157 | 0.268777 | 0.134389 | − | 0.990929i | \(-0.457093\pi\) | ||||
0.134389 | + | 0.990929i | \(0.457093\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.828427 | 0.172739 | 0.0863695 | − | 0.996263i | \(-0.472473\pi\) | ||||
0.0863695 | + | 0.996263i | \(0.472473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.48528 | 1.57568 | 0.787839 | − | 0.615882i | \(-0.211200\pi\) | ||||
0.787839 | + | 0.615882i | \(0.211200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.8284 | −1.94484 | −0.972421 | − | 0.233231i | \(-0.925070\pi\) | ||||
−0.972421 | + | 0.233231i | \(0.925070\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.82843 | 0.840521 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.65685 | 1.58758 | 0.793789 | − | 0.608194i | \(-0.208106\pi\) | ||||
0.793789 | + | 0.608194i | \(0.208106\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.41421 | −0.226455 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.41421 | −0.533211 | −0.266605 | − | 0.963806i | \(-0.585902\pi\) | ||||
−0.266605 | + | 0.963806i | \(0.585902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.41421 | −0.508961 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.17157 | −0.170891 | −0.0854457 | − | 0.996343i | \(-0.527231\pi\) | ||||
−0.0854457 | + | 0.996343i | \(0.527231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.24264 | −0.874145 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.31371 | −1.27934 | −0.639668 | − | 0.768651i | \(-0.720928\pi\) | ||||
−0.639668 | + | 0.768651i | \(0.720928\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.4853 | −2.22287 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.17157 | 0.155179 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.8284 | 1.40974 | 0.704871 | − | 0.709336i | \(-0.251005\pi\) | ||||
0.704871 | + | 0.709336i | \(0.251005\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.89949 | 0.755353 | 0.377676 | − | 0.925938i | \(-0.376723\pi\) | ||||
0.377676 | + | 0.925938i | \(0.376723\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.82843 | 0.598893 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.828427 | 0.0997309 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.82843 | −0.573029 | −0.286514 | − | 0.958076i | \(-0.592497\pi\) | ||||
−0.286514 | + | 0.958076i | \(0.592497\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.07107 | 0.359441 | 0.179721 | − | 0.983718i | \(-0.442481\pi\) | ||||
0.179721 | + | 0.983718i | \(0.442481\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.65685 | 0.768667 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6569 | 1.53652 | 0.768258 | − | 0.640140i | \(-0.221124\pi\) | ||||
0.768258 | + | 0.640140i | \(0.221124\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.31371 | −0.802784 | −0.401392 | − | 0.915906i | \(-0.631473\pi\) | ||||
−0.401392 | + | 0.915906i | \(0.631473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.3137 | 2.31180 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.48528 | 0.909718 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.7279 | 1.56116 | 0.780578 | − | 0.625058i | \(-0.214925\pi\) | ||||
0.780578 | + | 0.625058i | \(0.214925\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.8284 | −1.12286 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00000 | −0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.2426 | −1.64919 | −0.824595 | − | 0.565723i | \(-0.808597\pi\) | ||||
−0.824595 | + | 0.565723i | \(0.808597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.82843 | 0.485275 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.585786 | −0.0582879 | −0.0291440 | − | 0.999575i | \(-0.509278\pi\) | ||||
−0.0291440 | + | 0.999575i | \(0.509278\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.17157 | −0.509570 | −0.254785 | − | 0.966998i | \(-0.582005\pi\) | ||||
−0.254785 | + | 0.966998i | \(0.582005\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.48528 | −0.240261 | −0.120131 | − | 0.992758i | \(-0.538331\pi\) | ||||
−0.120131 | + | 0.992758i | \(0.538331\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3137 | −1.08366 | −0.541828 | − | 0.840489i | \(-0.682268\pi\) | ||||
−0.541828 | + | 0.840489i | \(0.682268\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.65685 | 0.916588 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.82843 | −0.263752 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.41421 | −0.130744 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.41421 | −0.307849 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.31371 | −0.648987 | −0.324493 | − | 0.945888i | \(-0.605194\pi\) | ||||
−0.324493 | + | 0.945888i | \(0.605194\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.3137 | 1.33796 | 0.668982 | − | 0.743278i | \(-0.266730\pi\) | ||||
0.668982 | + | 0.743278i | \(0.266730\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.41421 | −0.293849 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.4853 | −1.06669 | −0.533345 | − | 0.845898i | \(-0.679065\pi\) | ||||
−0.533345 | + | 0.845898i | \(0.679065\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.65685 | 0.819084 | 0.409542 | − | 0.912291i | \(-0.365689\pi\) | ||||
0.409542 | + | 0.912291i | \(0.365689\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.17157 | −0.0986642 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.82843 | −0.571022 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −28.9706 | −2.40587 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.65685 | 0.134833 | 0.0674164 | − | 0.997725i | \(-0.478524\pi\) | ||||
0.0674164 | + | 0.997725i | \(0.478524\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.24264 | −0.504688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 36.9706 | 2.96955 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.89949 | −0.470831 | −0.235415 | − | 0.971895i | \(-0.575645\pi\) | ||||
−0.235415 | + | 0.971895i | \(0.575645\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.31371 | −0.738625 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.34315 | −0.183529 | −0.0917647 | − | 0.995781i | \(-0.529251\pi\) | ||||
−0.0917647 | + | 0.995781i | \(0.529251\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16.4853 | −1.28338 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.82843 | −0.528400 | −0.264200 | − | 0.964468i | \(-0.585108\pi\) | ||||
−0.264200 | + | 0.964468i | \(0.585108\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.17157 | 0.0895924 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.585786 | 0.0445365 | 0.0222683 | − | 0.999752i | \(-0.492911\pi\) | ||||
0.0222683 | + | 0.999752i | \(0.492911\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.8284 | 0.813914 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.7990 | −1.62933 | −0.814667 | − | 0.579930i | \(-0.803080\pi\) | ||||
−0.814667 | + | 0.579930i | \(0.803080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.89949 | −0.735824 | −0.367912 | − | 0.929861i | \(-0.619927\pi\) | ||||
−0.367912 | + | 0.929861i | \(0.619927\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.89949 | 0.436103 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −32.9706 | −2.42404 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −30.1421 | −2.20421 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.8284 | −1.50709 | −0.753546 | − | 0.657395i | \(-0.771658\pi\) | ||||
−0.753546 | + | 0.657395i | \(0.771658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.6274 | −1.48479 | −0.742397 | − | 0.669960i | \(-0.766311\pi\) | ||||
−0.742397 | + | 0.669960i | \(0.766311\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.82843 | 0.345771 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.65685 | 0.401004 | 0.200502 | − | 0.979693i | \(-0.435743\pi\) | ||||
0.200502 | + | 0.979693i | \(0.435743\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.6569 | 0.814150 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.828427 | 0.0575797 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.65685 | 0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.6569 | −1.76629 | −0.883145 | − | 0.469099i | \(-0.844579\pi\) | ||||
−0.883145 | + | 0.469099i | \(0.844579\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.82843 | −0.330838 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.3137 | 1.86278 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.07107 | 0.207524 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.82843 | 0.593864 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.34315 | 0.156909 | 0.0784543 | − | 0.996918i | \(-0.475002\pi\) | ||||
0.0784543 | + | 0.996918i | \(0.475002\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.65685 | 0.443790 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.7990 | 1.31411 | 0.657053 | − | 0.753845i | \(-0.271803\pi\) | ||||
0.657053 | + | 0.753845i | \(0.271803\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.928932 | −0.0613856 | −0.0306928 | − | 0.999529i | \(-0.509771\pi\) | ||||
−0.0306928 | + | 0.999529i | \(0.509771\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.5147 | −0.754354 | −0.377177 | − | 0.926141i | \(-0.623105\pi\) | ||||
−0.377177 | + | 0.926141i | \(0.623105\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | 0.260931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.6569 | 0.887108 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.82843 | 0.571063 | 0.285532 | − | 0.958369i | \(-0.407830\pi\) | ||||
0.285532 | + | 0.958369i | \(0.407830\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.10051 | −0.135305 | −0.0676527 | − | 0.997709i | \(-0.521551\pi\) | ||||
−0.0676527 | + | 0.997709i | \(0.521551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.65685 | −0.105423 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.31371 | −0.463487 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.48528 | −0.535586 | −0.267793 | − | 0.963476i | \(-0.586294\pi\) | ||||
−0.267793 | + | 0.963476i | \(0.586294\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.3137 | 1.33472 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.7574 | −1.35719 | −0.678593 | − | 0.734514i | \(-0.737410\pi\) | ||||
−0.678593 | + | 0.734514i | \(0.737410\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.48528 | 0.525226 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.1716 | −1.18217 | −0.591085 | − | 0.806609i | \(-0.701300\pi\) | ||||
−0.591085 | + | 0.806609i | \(0.701300\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 31.7990 | 1.95340 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.7279 | 0.901334 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.0416 | 1.10002 | 0.550009 | − | 0.835159i | \(-0.314624\pi\) | ||||
0.550009 | + | 0.835159i | \(0.314624\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.8284 | 1.14375 | 0.571873 | − | 0.820342i | \(-0.306217\pi\) | ||||
0.571873 | + | 0.820342i | \(0.306217\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 32.1421 | 1.93824 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.00000 | 0.360505 | 0.180253 | − | 0.983620i | \(-0.442309\pi\) | ||||
0.180253 | + | 0.983620i | \(0.442309\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.8284 | −0.648281 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.48528 | 0.267569 | 0.133785 | − | 0.991010i | \(-0.457287\pi\) | ||||
0.133785 | + | 0.991010i | \(0.457287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.17157 | −0.545193 | −0.272597 | − | 0.962128i | \(-0.587882\pi\) | ||||
−0.272597 | + | 0.962128i | \(0.587882\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.9706 | 1.29239 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.2426 | −0.952160 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.0711 | 0.763620 | 0.381810 | − | 0.924241i | \(-0.375301\pi\) | ||||
0.381810 | + | 0.924241i | \(0.375301\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.9706 | −2.15251 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.82843 | 0.280174 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.17157 | −0.0677538 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.585786 | −0.0336526 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.1421 | −1.15334 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.4853 | −1.62574 | −0.812870 | − | 0.582445i | \(-0.802096\pi\) | ||||
−0.812870 | + | 0.582445i | \(0.802096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.17157 | −0.294201 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.14214 | −0.121469 | −0.0607347 | − | 0.998154i | \(-0.519344\pi\) | ||||
−0.0607347 | + | 0.998154i | \(0.519344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.5858 | −0.824437 | −0.412219 | − | 0.911085i | \(-0.635246\pi\) | ||||
−0.412219 | + | 0.911085i | \(0.635246\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.31371 | 0.0737852 | 0.0368926 | − | 0.999319i | \(-0.488254\pi\) | ||||
0.0368926 | + | 0.999319i | \(0.488254\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 40.9706 | 2.29391 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.48528 | −0.138715 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.31371 | −0.406946 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.41421 | −0.522207 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.3137 | −0.625650 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.3137 | −1.72116 | −0.860579 | − | 0.509318i | \(-0.829898\pi\) | ||||
−0.860579 | + | 0.509318i | \(0.829898\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.65685 | 0.529192 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.3137 | 1.49231 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.9706 | 0.924445 | 0.462223 | − | 0.886764i | \(-0.347052\pi\) | ||||
0.462223 | + | 0.886764i | \(0.347052\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −52.2843 | −2.83135 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.82843 | −0.152277 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.1421 | 1.29602 | 0.648009 | − | 0.761633i | \(-0.275602\pi\) | ||||
0.648009 | + | 0.761633i | \(0.275602\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.38478 | 0.341769 | 0.170885 | − | 0.985291i | \(-0.445337\pi\) | ||||
0.170885 | + | 0.985291i | \(0.445337\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.41421 | −0.0754851 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.89949 | 0.207549 | 0.103775 | − | 0.994601i | \(-0.466908\pi\) | ||||
0.103775 | + | 0.994601i | \(0.466908\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.4853 | 0.874948 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.4558 | −0.815728 | −0.407864 | − | 0.913043i | \(-0.633726\pi\) | ||||
−0.407864 | + | 0.913043i | \(0.633726\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6274 | −0.927759 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.3137 | 0.646302 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.4853 | −0.548825 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.41421 | −0.177737 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −37.3137 | −1.93203 | −0.966015 | − | 0.258485i | \(-0.916777\pi\) | ||||
−0.966015 | + | 0.258485i | \(0.916777\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.65685 | −0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.3137 | −1.19754 | −0.598772 | − | 0.800919i | \(-0.704345\pi\) | ||||
−0.598772 | + | 0.800919i | \(0.704345\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.31371 | −0.374693 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.97056 | 0.458374 | 0.229187 | − | 0.973382i | \(-0.426393\pi\) | ||||
0.229187 | + | 0.973382i | \(0.426393\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.1421 | −0.717035 | −0.358517 | − | 0.933523i | \(-0.616718\pi\) | ||||
−0.358517 | + | 0.933523i | \(0.616718\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.17157 | −0.261538 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.3137 | 0.772474 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −46.6274 | −2.34608 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.7279 | −1.64257 | −0.821284 | − | 0.570520i | \(-0.806742\pi\) | ||||
−0.821284 | + | 0.570520i | \(0.806742\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.48528 | 0.223984 | 0.111992 | − | 0.993709i | \(-0.464277\pi\) | ||||
0.111992 | + | 0.993709i | \(0.464277\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.3137 | 0.762830 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.41421 | −0.169654 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 46.6274 | 2.31124 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.75736 | 0.383577 | 0.191788 | − | 0.981436i | \(-0.438571\pi\) | ||||
0.191788 | + | 0.981436i | \(0.438571\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.4853 | −0.615854 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.9706 | 1.22576 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.65685 | 0.472898 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.17157 | 0.252648 | 0.126324 | − | 0.991989i | \(-0.459682\pi\) | ||||
0.126324 | + | 0.991989i | \(0.459682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.3137 | −1.42866 | −0.714331 | − | 0.699808i | \(-0.753269\pi\) | ||||
−0.714331 | + | 0.699808i | \(0.753269\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.17157 | −0.0569638 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −41.5563 | −2.01578 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.82843 | −0.329680 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.5147 | 0.650981 | 0.325491 | − | 0.945545i | \(-0.394471\pi\) | ||||
0.325491 | + | 0.945545i | \(0.394471\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.3848 | −0.499061 | −0.249530 | − | 0.968367i | \(-0.580276\pi\) | ||||
−0.249530 | + | 0.968367i | \(0.580276\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −28.9706 | −1.38903 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.970563 | 0.0464283 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.3137 | −0.921793 | −0.460897 | − | 0.887454i | \(-0.652472\pi\) | ||||
−0.460897 | + | 0.887454i | \(0.652472\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.5147 | 1.02220 | 0.511098 | − | 0.859523i | \(-0.329239\pi\) | ||||
0.511098 | + | 0.859523i | \(0.329239\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −50.2843 | −2.38370 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0000 | 0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.4853 | −0.776262 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.65685 | 0.0778458 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.6274 | −1.15202 | −0.576011 | − | 0.817442i | \(-0.695391\pi\) | ||||
−0.576011 | + | 0.817442i | \(0.695391\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.24264 | −0.291382 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.75736 | −0.454446 | −0.227223 | − | 0.973843i | \(-0.572965\pi\) | ||||
−0.227223 | + | 0.973843i | \(0.572965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9706 | 0.602793 | 0.301397 | − | 0.953499i | \(-0.402547\pi\) | ||||
0.301397 | + | 0.953499i | \(0.402547\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 36.9706 | 1.71447 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.17157 | −0.239312 | −0.119656 | − | 0.992815i | \(-0.538179\pi\) | ||||
−0.119656 | + | 0.992815i | \(0.538179\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.89949 | −0.271834 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −38.6274 | −1.77609 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.79899 | 0.357842 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.31371 | −0.426445 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.1127 | −0.873281 | −0.436641 | − | 0.899636i | \(-0.643832\pi\) | ||||
−0.436641 | + | 0.899636i | \(0.643832\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.6569 | −0.622699 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 55.4558 | 2.51812 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.9706 | −0.587752 | −0.293876 | − | 0.955844i | \(-0.594945\pi\) | ||||
−0.293876 | + | 0.955844i | \(0.594945\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.34315 | −0.105961 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.14214 | −0.186932 | −0.0934660 | − | 0.995622i | \(-0.529795\pi\) | ||||
−0.0934660 | + | 0.995622i | \(0.529795\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −52.9706 | −2.38567 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.4853 | −0.740958 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.2843 | 1.26618 | 0.633089 | − | 0.774079i | \(-0.281787\pi\) | ||||
0.633089 | + | 0.774079i | \(0.281787\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.82843 | −0.305072 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.6274 | −1.36561 | −0.682805 | − | 0.730601i | \(-0.739240\pi\) | ||||
−0.682805 | + | 0.730601i | \(0.739240\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.0000 | −0.488527 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.9289 | −1.01631 | −0.508154 | − | 0.861267i | \(-0.669672\pi\) | ||||
−0.508154 | + | 0.861267i | \(0.669672\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.17157 | 0.0517262 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.6569 | 0.778054 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.65685 | −0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.585786 | 0.0257132 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.27208 | 0.230974 | 0.115487 | − | 0.993309i | \(-0.463157\pi\) | ||||
0.115487 | + | 0.993309i | \(0.463157\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.65685 | −0.0724492 | −0.0362246 | − | 0.999344i | \(-0.511533\pi\) | ||||
−0.0362246 | + | 0.999344i | \(0.511533\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 67.5980 | 2.94461 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.8284 | 0.469914 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.82843 | 0.209142 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.48528 | 0.366851 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.7990 | −0.940696 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.62742 | 0.370922 | 0.185461 | − | 0.982652i | \(-0.440622\pi\) | ||||
0.185461 | + | 0.982652i | \(0.440622\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.89949 | −0.424828 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38.6274 | 1.65462 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.97056 | −0.212526 | −0.106263 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106263 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.89949 | 0.251784 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.94113 | 0.423506 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −32.9706 | −1.39952 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.9411 | −1.86185 | −0.930923 | − | 0.365216i | \(-0.880995\pi\) | ||||
−0.930923 | + | 0.365216i | \(0.880995\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.3137 | 0.478519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −30.1421 | −1.27260 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.8284 | 1.13068 | 0.565342 | − | 0.824857i | \(-0.308744\pi\) | ||||
0.565342 | + | 0.824857i | \(0.308744\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.4853 | −0.861822 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.82843 | 0.286263 | 0.143131 | − | 0.989704i | \(-0.454283\pi\) | ||||
0.143131 | + | 0.989704i | \(0.454283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.2843 | 1.68584 | 0.842922 | − | 0.538036i | \(-0.180833\pi\) | ||||
0.842922 | + | 0.538036i | \(0.180833\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.8284 | −0.870120 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.51472 | 0.229980 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.41421 | −0.391919 | −0.195959 | − | 0.980612i | \(-0.562782\pi\) | ||||
−0.195959 | + | 0.980612i | \(0.562782\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.6274 | −0.857246 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −44.9706 | −1.86249 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.82843 | 0.199631 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.8284 | −1.10733 | −0.553664 | − | 0.832740i | \(-0.686771\pi\) | ||||
−0.553664 | + | 0.832740i | \(0.686771\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.6863 | −0.522730 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.00000 | −0.0822690 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.0711 | 1.19381 | 0.596903 | − | 0.802314i | \(-0.296398\pi\) | ||||
0.596903 | + | 0.802314i | \(0.296398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.65685 | 0.231520 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.1421 | −0.659550 | −0.329775 | − | 0.944060i | \(-0.606973\pi\) | ||||
−0.329775 | + | 0.944060i | \(0.606973\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.2426 | −0.499388 | −0.249694 | − | 0.968325i | \(-0.580330\pi\) | ||||
−0.249694 | + | 0.968325i | \(0.580330\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.00000 | −0.325785 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −42.0416 | −1.70924 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.5980 | −1.28252 | −0.641261 | − | 0.767323i | \(-0.721588\pi\) | ||||
−0.641261 | + | 0.767323i | \(0.721588\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.65685 | 0.0670291 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.34315 | 0.0946388 | 0.0473194 | − | 0.998880i | \(-0.484932\pi\) | ||||
0.0473194 | + | 0.998880i | \(0.484932\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.6569 | 0.470050 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.4558 | 0.863780 | 0.431890 | − | 0.901926i | \(-0.357847\pi\) | ||||
0.431890 | + | 0.901926i | \(0.357847\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.2843 | −1.61916 | −0.809581 | − | 0.587008i | \(-0.800306\pi\) | ||||
−0.809581 | + | 0.587008i | \(0.800306\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.828427 | 0.0332436 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.65685 | 0.225913 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −60.2843 | −2.40369 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.28427 | 0.329792 | 0.164896 | − | 0.986311i | \(-0.447271\pi\) | ||||
0.164896 | + | 0.986311i | \(0.447271\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.6569 | −1.01977 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.9706 | 0.990927 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.82843 | −0.191010 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.1716 | 0.994217 | 0.497109 | − | 0.867688i | \(-0.334395\pi\) | ||||
0.497109 | + | 0.867688i | \(0.334395\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.5147 | 0.769585 | 0.384793 | − | 0.923003i | \(-0.374273\pi\) | ||||
0.384793 | + | 0.923003i | \(0.374273\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.3137 | 1.07548 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.8284 | −0.582966 | −0.291483 | − | 0.956576i | \(-0.594149\pi\) | ||||
−0.291483 | + | 0.956576i | \(0.594149\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 52.2843 | 2.05234 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.82843 | −0.110685 | −0.0553425 | − | 0.998467i | \(-0.517625\pi\) | ||||
−0.0553425 | + | 0.998467i | \(0.517625\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −52.2843 | −2.04292 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.07107 | 0.119814 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.5147 | 0.993912 | 0.496956 | − | 0.867776i | \(-0.334451\pi\) | ||||
0.496956 | + | 0.867776i | \(0.334451\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.3553 | 0.908417 | 0.454209 | − | 0.890895i | \(-0.349922\pi\) | ||||
0.454209 | + | 0.890895i | \(0.349922\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.82843 | 0.342868 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.02944 | 0.272181 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.34315 | 0.0905912 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.4853 | 1.09966 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.3137 | 0.590300 | 0.295150 | − | 0.955451i | \(-0.404630\pi\) | ||||
0.295150 | + | 0.955451i | \(0.404630\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.65685 | 0.256222 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.55635 | 0.0598154 | 0.0299077 | − | 0.999553i | \(-0.490479\pi\) | ||||
0.0299077 | + | 0.999553i | \(0.490479\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.7990 | 0.758699 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.1421 | 0.464606 | 0.232303 | − | 0.972643i | \(-0.425374\pi\) | ||||
0.232303 | + | 0.972643i | \(0.425374\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42.6274 | 1.62871 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.928932 | −0.0354410 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.1716 | 0.501797 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0000 | 1.06517 | 0.532585 | − | 0.846376i | \(-0.321221\pi\) | ||||
0.532585 | + | 0.846376i | \(0.321221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −32.9706 | −1.25064 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.3137 | 0.807314 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.5147 | −0.435527 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.8284 | 0.408984 | 0.204492 | − | 0.978868i | \(-0.434446\pi\) | ||||
0.204492 | + | 0.978868i | \(0.434446\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.3137 | 0.426705 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.00000 | 0.150649 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.00000 | 0.300446 | 0.150223 | − | 0.988652i | \(-0.452001\pi\) | ||||
0.150223 | + | 0.988652i | \(0.452001\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.6569 | 0.512172 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.97056 | −0.335950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.3137 | 0.871883 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.82843 | 0.329704 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.3137 | 1.01863 | 0.509315 | − | 0.860580i | \(-0.329899\pi\) | ||||
0.509315 | + | 0.860580i | \(0.329899\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.10051 | −0.0781186 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 56.4853 | 2.09781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.4558 | 0.944105 | 0.472052 | − | 0.881570i | \(-0.343513\pi\) | ||||
0.472052 | + | 0.881570i | \(0.343513\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.9411 | 1.84714 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.2426 | −0.747679 | −0.373839 | − | 0.927493i | \(-0.621959\pi\) | ||||
−0.373839 | + | 0.927493i | \(0.621959\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38.6274 | −1.42286 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.2843 | −1.33474 | −0.667369 | − | 0.744727i | \(-0.732580\pi\) | ||||
−0.667369 | + | 0.744727i | \(0.732580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.65685 | −0.0608661 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.8284 | 0.617375 | 0.308688 | − | 0.951163i | \(-0.400110\pi\) | ||||
0.308688 | + | 0.951163i | \(0.400110\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.1421 | −1.25087 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.31371 | −0.267595 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.3431 | −0.669351 | −0.334675 | − | 0.942333i | \(-0.608627\pi\) | ||||
−0.334675 | + | 0.942333i | \(0.608627\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.48528 | −0.309221 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.65685 | −0.205874 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.3137 | −0.411204 | −0.205602 | − | 0.978636i | \(-0.565915\pi\) | ||||
−0.205602 | + | 0.978636i | \(0.565915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.2426 | −0.661295 | −0.330648 | − | 0.943754i | \(-0.607267\pi\) | ||||
−0.330648 | + | 0.943754i | \(0.607267\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.3137 | 0.770599 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.3137 | −0.552946 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.928932 | 0.0334982 | 0.0167491 | − | 0.999860i | \(-0.494668\pi\) | ||||
0.0167491 | + | 0.999860i | \(0.494668\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.7574 | −0.783572 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.585786 | 0.0210693 | 0.0105346 | − | 0.999945i | \(-0.496647\pi\) | ||||
0.0105346 | + | 0.999945i | \(0.496647\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −72.0833 | −2.58931 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.00000 | −0.143315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.3137 | −0.834230 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.48528 | 0.303239 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.1421 | 0.718904 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.6274 | 1.23433 | 0.617167 | − | 0.786832i | \(-0.288280\pi\) | ||||
0.617167 | + | 0.786832i | \(0.288280\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.1716 | −0.682526 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.34315 | −0.296274 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 31.7990 | 1.12779 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.786797 | 0.0278698 | 0.0139349 | − | 0.999903i | \(-0.495564\pi\) | ||||
0.0139349 | + | 0.999903i | \(0.495564\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.31371 | 0.258740 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.7279 | 0.520386 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.8284 | 0.523284 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0416 | 0.635095 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.9706 | 0.455458 | 0.227729 | − | 0.973725i | \(-0.426870\pi\) | ||||
0.227729 | + | 0.973725i | \(0.426870\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.8284 | 0.660342 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.00000 | 0.280228 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.37258 | −0.327905 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.0000 | −0.349002 | −0.174501 | − | 0.984657i | \(-0.555831\pi\) | ||||
−0.174501 | + | 0.984657i | \(0.555831\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.6569 | 0.476048 | 0.238024 | − | 0.971259i | \(-0.423500\pi\) | ||||
0.238024 | + | 0.971259i | \(0.423500\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 32.1421 | 1.11905 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.4558 | 1.09383 | 0.546913 | − | 0.837189i | \(-0.315803\pi\) | ||||
0.546913 | + | 0.837189i | \(0.315803\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.7279 | −0.997762 | −0.498881 | − | 0.866671i | \(-0.666256\pi\) | ||||
−0.498881 | + | 0.866671i | \(0.666256\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.00000 | 0.208138 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.3137 | 0.806804 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.8284 | −0.374285 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −54.8284 | −1.89289 | −0.946444 | − | 0.322869i | \(-0.895353\pi\) | ||||
−0.946444 | + | 0.322869i | \(0.895353\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000 | 1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.48528 | 0.154481 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.5563 | 1.29198 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.17157 | −0.314768 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00000 | 0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.0416 | 0.412298 | 0.206149 | − | 0.978521i | \(-0.433907\pi\) | ||||
0.206149 | + | 0.978521i | \(0.433907\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.6985 | 0.536250 | 0.268125 | − | 0.963384i | \(-0.413596\pi\) | ||||
0.268125 | + | 0.963384i | \(0.413596\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.1716 | −1.13180 | −0.565900 | − | 0.824474i | \(-0.691471\pi\) | ||||
−0.565900 | + | 0.824474i | \(0.691471\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.4853 | 1.58238 | 0.791189 | − | 0.611572i | \(-0.209463\pi\) | ||||
0.791189 | + | 0.611572i | \(0.209463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.00000 | −0.0680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.9706 | 0.746159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 65.9411 | 2.23690 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.3137 | 0.383350 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.2426 | −0.549730 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.2843 | 1.22523 | 0.612616 | − | 0.790380i | \(-0.290117\pi\) | ||||
0.612616 | + | 0.790380i | \(0.290117\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.0711 | 0.440876 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.9289 | −0.368205 | −0.184103 | − | 0.982907i | \(-0.558938\pi\) | ||||
−0.184103 | + | 0.982907i | \(0.558938\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.6569 | 0.998033 | 0.499016 | − | 0.866593i | \(-0.333695\pi\) | ||||
0.499016 | + | 0.866593i | \(0.333695\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −36.9706 | −1.24275 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.4558 | 0.989030 | 0.494515 | − | 0.869169i | \(-0.335346\pi\) | ||||
0.494515 | + | 0.869169i | \(0.335346\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.82843 | 0.161758 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.37258 | −0.0459317 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 74.4264 | 2.48780 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.17157 | −0.0391177 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −91.8823 | −3.06444 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.1421 | 1.93700 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.7990 | 1.12352 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.9706 | −1.36041 | −0.680203 | − | 0.733024i | \(-0.738108\pi\) | ||||
−0.680203 | + | 0.733024i | \(0.738108\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.585786 | −0.0194293 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.5147 | 1.24292 | 0.621459 | − | 0.783447i | \(-0.286540\pi\) | ||||
0.621459 | + | 0.783447i | \(0.286540\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.3137 | −1.16871 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.1421 | −0.665878 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.2548 | −1.36087 | −0.680436 | − | 0.732808i | \(-0.738209\pi\) | ||||
−0.680436 | + | 0.732808i | \(0.738209\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.4853 | −0.938622 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.82843 | 0.224760 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 64.2843 | 2.11365 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.17157 | −0.169857 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.12994 | 0.233926 | 0.116963 | − | 0.993136i | \(-0.462684\pi\) | ||||
0.116963 | + | 0.993136i | \(0.462684\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.14214 | −0.0701304 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 102.912 | 3.36557 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.8995 | −0.846100 | −0.423050 | − | 0.906106i | \(-0.639040\pi\) | ||||
−0.423050 | + | 0.906106i | \(0.639040\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.5858 | −0.475989 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.1005 | 0.785654 | 0.392827 | − | 0.919612i | \(-0.371497\pi\) | ||||
0.392827 | + | 0.919612i | \(0.371497\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.82843 | −0.0921063 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.14214 | −0.264584 | −0.132292 | − | 0.991211i | \(-0.542234\pi\) | ||||
−0.132292 | + | 0.991211i | \(0.542234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.34315 | −0.140984 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.31371 | 0.0425999 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.6274 | −1.70477 | −0.852385 | − | 0.522915i | \(-0.824844\pi\) | ||||
−0.852385 | + | 0.522915i | \(0.824844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 71.1127 | 2.30115 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 40.9706 | 1.32439 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 86.2548 | 2.78241 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.48528 | −0.0800871 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 70.4264 | 2.26711 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.6274 | −0.341755 | −0.170877 | − | 0.985292i | \(-0.554660\pi\) | ||||
−0.170877 | + | 0.985292i | \(0.554660\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.31371 | −0.234950 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.2548 | 1.06720 | 0.533599 | − | 0.845737i | \(-0.320839\pi\) | ||||
0.533599 | + | 0.845737i | \(0.320839\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.41421 | −0.301496 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.1421 | 1.60419 | 0.802095 | − | 0.597197i | \(-0.203719\pi\) | ||||
0.802095 | + | 0.597197i | \(0.203719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 71.1127 | 2.27277 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.3137 | −0.361219 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.6274 | −0.976863 | −0.488431 | − | 0.872602i | \(-0.662431\pi\) | ||||
−0.488431 | + | 0.872602i | \(0.662431\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.82843 | 0.217572 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.62742 | −0.210740 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.686292 | −0.0218008 | −0.0109004 | − | 0.999941i | \(-0.503470\pi\) | ||||
−0.0109004 | + | 0.999941i | \(0.503470\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −31.3137 | −0.993711 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.3137 | −0.612286 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.4142 | 1.18492 | 0.592460 | − | 0.805600i | \(-0.298157\pi\) | ||||
0.592460 | + | 0.805600i | \(0.298157\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.65685 | 0.305529 |
(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 | 9408.2.a.du.1.1 | 2 | ||
4.3 | odd | 2 | 9408.2.a.dg.1.1 | 2 | |||
7.6 | odd | 2 | 9408.2.a.ds.1.2 | 2 | |||
8.3 | odd | 2 | 1176.2.a.o.1.2 | yes | 2 | ||
8.5 | even | 2 | 2352.2.a.bb.1.2 | 2 | |||
24.5 | odd | 2 | 7056.2.a.cg.1.1 | 2 | |||
24.11 | even | 2 | 3528.2.a.bb.1.1 | 2 | |||
28.27 | even | 2 | 9408.2.a.ee.1.2 | 2 | |||
56.3 | even | 6 | 1176.2.q.o.961.2 | 4 | |||
56.5 | odd | 6 | 2352.2.q.bc.1537.2 | 4 | |||
56.11 | odd | 6 | 1176.2.q.k.961.1 | 4 | |||
56.13 | odd | 2 | 2352.2.a.bd.1.1 | 2 | |||
56.19 | even | 6 | 1176.2.q.o.361.2 | 4 | |||
56.27 | even | 2 | 1176.2.a.j.1.1 | ✓ | 2 | ||
56.37 | even | 6 | 2352.2.q.be.1537.1 | 4 | |||
56.45 | odd | 6 | 2352.2.q.bc.961.2 | 4 | |||
56.51 | odd | 6 | 1176.2.q.k.361.1 | 4 | |||
56.53 | even | 6 | 2352.2.q.be.961.1 | 4 | |||
168.11 | even | 6 | 3528.2.s.bm.3313.2 | 4 | |||
168.59 | odd | 6 | 3528.2.s.bd.3313.1 | 4 | |||
168.83 | odd | 2 | 3528.2.a.bl.1.2 | 2 | |||
168.107 | even | 6 | 3528.2.s.bm.361.2 | 4 | |||
168.125 | even | 2 | 7056.2.a.cx.1.2 | 2 | |||
168.131 | odd | 6 | 3528.2.s.bd.361.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.2.a.j.1.1 | ✓ | 2 | 56.27 | even | 2 | ||
1176.2.a.o.1.2 | yes | 2 | 8.3 | odd | 2 | ||
1176.2.q.k.361.1 | 4 | 56.51 | odd | 6 | |||
1176.2.q.k.961.1 | 4 | 56.11 | odd | 6 | |||
1176.2.q.o.361.2 | 4 | 56.19 | even | 6 | |||
1176.2.q.o.961.2 | 4 | 56.3 | even | 6 | |||
2352.2.a.bb.1.2 | 2 | 8.5 | even | 2 | |||
2352.2.a.bd.1.1 | 2 | 56.13 | odd | 2 | |||
2352.2.q.bc.961.2 | 4 | 56.45 | odd | 6 | |||
2352.2.q.bc.1537.2 | 4 | 56.5 | odd | 6 | |||
2352.2.q.be.961.1 | 4 | 56.53 | even | 6 | |||
2352.2.q.be.1537.1 | 4 | 56.37 | even | 6 | |||
3528.2.a.bb.1.1 | 2 | 24.11 | even | 2 | |||
3528.2.a.bl.1.2 | 2 | 168.83 | odd | 2 | |||
3528.2.s.bd.361.1 | 4 | 168.131 | odd | 6 | |||
3528.2.s.bd.3313.1 | 4 | 168.59 | odd | 6 | |||
3528.2.s.bm.361.2 | 4 | 168.107 | even | 6 | |||
3528.2.s.bm.3313.2 | 4 | 168.11 | even | 6 | |||
7056.2.a.cg.1.1 | 2 | 24.5 | odd | 2 | |||
7056.2.a.cx.1.2 | 2 | 168.125 | even | 2 | |||
9408.2.a.dg.1.1 | 2 | 4.3 | odd | 2 | |||
9408.2.a.ds.1.2 | 2 | 7.6 | odd | 2 | |||
9408.2.a.du.1.1 | 2 | 1.1 | even | 1 | trivial | ||
9408.2.a.ee.1.2 | 2 | 28.27 | even | 2 |