Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1677830643\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.470117.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 8x^{2} + 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.78088\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.78088 | 1.60554 | 0.802771 | − | 0.596287i | \(-0.203358\pi\) | ||||
0.802771 | + | 0.596287i | \(0.203358\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.592821 | 0.265117 | 0.132559 | − | 0.991175i | \(-0.457681\pi\) | ||||
0.132559 | + | 0.991175i | \(0.457681\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.73330 | 1.57777 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.21318 | −0.667298 | −0.333649 | − | 0.942697i | \(-0.608280\pi\) | ||||
−0.333649 | + | 0.942697i | \(0.608280\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.00816 | −1.38901 | −0.694507 | − | 0.719486i | \(-0.744378\pi\) | ||||
−0.694507 | + | 0.719486i | \(0.744378\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.64856 | 0.425657 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.32612 | −1.04924 | −0.524619 | − | 0.851337i | \(-0.675792\pi\) | ||||
−0.524619 | + | 0.851337i | \(0.675792\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.38471 | 0.547091 | 0.273546 | − | 0.961859i | \(-0.411804\pi\) | ||||
0.273546 | + | 0.961859i | \(0.411804\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.67368 | 0.348986 | 0.174493 | − | 0.984658i | \(-0.444171\pi\) | ||||
0.174493 | + | 0.984658i | \(0.444171\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.64856 | −0.929713 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.82010 | 0.927629 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.27244 | −0.236287 | −0.118143 | − | 0.992997i | \(-0.537694\pi\) | ||||
−0.118143 | + | 0.992997i | \(0.537694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.49766 | −0.448593 | −0.224296 | − | 0.974521i | \(-0.572008\pi\) | ||||
−0.224296 | + | 0.974521i | \(0.572008\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.15458 | −1.07138 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.24526 | −0.697917 | −0.348958 | − | 0.937138i | \(-0.613465\pi\) | ||||
−0.348958 | + | 0.937138i | \(0.613465\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.9271 | −2.23012 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.15665 | −1.24388 | −0.621939 | − | 0.783066i | \(-0.713655\pi\) | ||||
−0.621939 | + | 0.783066i | \(0.713655\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.80600 | 0.418293 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.65958 | −0.242074 | −0.121037 | − | 0.992648i | \(-0.538622\pi\) | ||||
−0.121037 | + | 0.992648i | \(0.538622\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.0304 | −1.68460 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.60486 | −1.04461 | −0.522304 | − | 0.852759i | \(-0.674927\pi\) | ||||
−0.522304 | + | 0.852759i | \(0.674927\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.31202 | −0.176912 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.63161 | 0.878378 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.12638 | 0.797586 | 0.398793 | − | 0.917041i | \(-0.369429\pi\) | ||||
0.398793 | + | 0.917041i | \(0.369429\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.08395 | −0.650933 | −0.325467 | − | 0.945554i | \(-0.605521\pi\) | ||||
−0.325467 | + | 0.945554i | \(0.605521\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.96894 | −0.368252 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.0092 | −1.71149 | −0.855747 | − | 0.517394i | \(-0.826902\pi\) | ||||
−0.855747 | + | 0.517394i | \(0.826902\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.65431 | 0.560313 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.62939 | −0.312051 | −0.156026 | − | 0.987753i | \(-0.549868\pi\) | ||||
−0.156026 | + | 0.987753i | \(0.549868\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.2577 | 1.90282 | 0.951410 | − | 0.307926i | \(-0.0996348\pi\) | ||||
0.951410 | + | 0.307926i | \(0.0996348\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.9271 | −1.49269 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.77561 | 0.537298 | 0.268649 | − | 0.963238i | \(-0.413423\pi\) | ||||
0.268649 | + | 0.963238i | \(0.413423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.795771 | −0.0884190 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.0170 | −1.20927 | −0.604636 | − | 0.796502i | \(-0.706681\pi\) | ||||
−0.604636 | + | 0.796502i | \(0.706681\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.56461 | −0.278171 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.53851 | −0.379368 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.37164 | −0.675392 | −0.337696 | − | 0.941255i | \(-0.609648\pi\) | ||||
−0.337696 | + | 0.941255i | \(0.609648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.94569 | −0.720235 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.41371 | 0.145043 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.9608 | 1.21444 | 0.607219 | − | 0.794535i | \(-0.292285\pi\) | ||||
0.607219 | + | 0.794535i | \(0.292285\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.4756 | −1.05284 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.3506 | 1.82595 | 0.912977 | − | 0.408011i | \(-0.133778\pi\) | ||||
0.912977 | + | 0.408011i | \(0.133778\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.0362 | 1.58009 | 0.790045 | − | 0.613048i | \(-0.210057\pi\) | ||||
0.790045 | + | 0.613048i | \(0.210057\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.5723 | −1.02207 | −0.511034 | − | 0.859561i | \(-0.670737\pi\) | ||||
−0.511034 | + | 0.859561i | \(0.670737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.49481 | 0.717872 | 0.358936 | − | 0.933362i | \(-0.383140\pi\) | ||||
0.358936 | + | 0.933362i | \(0.383140\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.8056 | −1.12053 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.3907 | 1.16562 | 0.582809 | − | 0.812609i | \(-0.301953\pi\) | ||||
0.582809 | + | 0.812609i | \(0.301953\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.992192 | 0.0925224 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −23.7051 | −2.19154 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.10185 | −0.554713 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.78088 | −0.250744 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.71987 | −0.511601 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.60383 | −0.585995 | −0.292998 | − | 0.956113i | \(-0.594653\pi\) | ||||
−0.292998 | + | 0.956113i | \(0.594653\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.6827 | −1.99710 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3120 | −0.988336 | −0.494168 | − | 0.869367i | \(-0.664527\pi\) | ||||
−0.494168 | + | 0.869367i | \(0.664527\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.85746 | 0.245931 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.12052 | −0.266604 | −0.133302 | − | 0.991075i | \(-0.542558\pi\) | ||||
−0.133302 | + | 0.991075i | \(0.542558\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.85393 | −0.242067 | −0.121034 | − | 0.992648i | \(-0.538621\pi\) | ||||
−0.121034 | + | 0.992648i | \(0.538621\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.61509 | −0.388660 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.0840 | 0.926886 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.754330 | −0.0626437 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.0502334 | 0.00411528 | 0.00205764 | − | 0.999998i | \(-0.499345\pi\) | ||||
0.00205764 | + | 0.999998i | \(0.499345\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.6578 | 1.11145 | 0.555726 | − | 0.831366i | \(-0.312440\pi\) | ||||
0.555726 | + | 0.831366i | \(0.312440\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20.4768 | −1.65545 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.48066 | −0.118930 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.22014 | 0.416613 | 0.208306 | − | 0.978064i | \(-0.433205\pi\) | ||||
0.208306 | + | 0.978064i | \(0.433205\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.1482 | −1.67716 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.97366 | −0.781197 | −0.390599 | − | 0.920561i | \(-0.627732\pi\) | ||||
−0.390599 | + | 0.920561i | \(0.627732\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.64856 | −0.284040 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.9041 | −0.998545 | −0.499273 | − | 0.866445i | \(-0.666399\pi\) | ||||
−0.499273 | + | 0.866445i | \(0.666399\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0817 | 0.929360 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.2876 | 0.863182 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.327578 | 0.0249053 | 0.0124526 | − | 0.999922i | \(-0.496036\pi\) | ||||
0.0124526 | + | 0.999922i | \(0.496036\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.0367 | 1.28056 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.70431 | −0.351616 | −0.175808 | − | 0.984424i | \(-0.556254\pi\) | ||||
−0.175808 | + | 0.984424i | \(0.556254\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.993451 | 0.0738426 | 0.0369213 | − | 0.999318i | \(-0.488245\pi\) | ||||
0.0369213 | + | 0.999318i | \(0.488245\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.1379 | −1.04510 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.51668 | −0.185030 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.57447 | 0.700155 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.5734 | −1.05449 | −0.527247 | − | 0.849712i | \(-0.676776\pi\) | ||||
−0.527247 | + | 0.849712i | \(0.676776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.7510 | 0.773875 | 0.386938 | − | 0.922106i | \(-0.373533\pi\) | ||||
0.386938 | + | 0.922106i | \(0.373533\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.25627 | −0.591244 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.9790 | −1.20970 | −0.604851 | − | 0.796339i | \(-0.706767\pi\) | ||||
−0.604851 | + | 0.796339i | \(0.706767\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9681 | −0.777506 | −0.388753 | − | 0.921342i | \(-0.627094\pi\) | ||||
−0.388753 | + | 0.921342i | \(0.627094\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −38.9579 | −2.74788 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.592821 | −0.0414044 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.92203 | 0.550619 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.27780 | −0.365073 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.54912 | −0.588545 | −0.294273 | − | 0.955721i | \(-0.595077\pi\) | ||||
−0.294273 | + | 0.955721i | \(0.595077\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.31202 | −0.501011 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.83543 | −0.329774 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 45.2108 | 3.05506 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.6659 | 1.45741 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.25505 | 0.418869 | 0.209435 | − | 0.977823i | \(-0.432838\pi\) | ||||
0.209435 | + | 0.977823i | \(0.432838\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −22.0030 | −1.46687 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.4817 | 1.29305 | 0.646523 | − | 0.762895i | \(-0.276222\pi\) | ||||
0.646523 | + | 0.762895i | \(0.276222\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.8356 | −1.70727 | −0.853633 | − | 0.520875i | \(-0.825606\pi\) | ||||
−0.853633 | + | 0.520875i | \(0.825606\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.3055 | 1.00270 | 0.501348 | − | 0.865246i | \(-0.332838\pi\) | ||||
0.501348 | + | 0.865246i | \(0.332838\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.983831 | −0.0641781 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.2804 | 0.862655 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2062 | 0.983607 | 0.491804 | − | 0.870706i | \(-0.336338\pi\) | ||||
0.491804 | + | 0.870706i | \(0.336338\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.4744 | −0.739128 | −0.369564 | − | 0.929205i | \(-0.620493\pi\) | ||||
−0.369564 | + | 0.929205i | \(0.620493\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.6732 | −1.06959 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.9430 | −0.759917 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.6370 | −1.94154 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.21160 | 0.518312 | 0.259156 | − | 0.965835i | \(-0.416556\pi\) | ||||
0.259156 | + | 0.965835i | \(0.416556\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.70415 | −0.232878 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.13189 | −0.446616 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.7648 | −0.921001 | −0.460500 | − | 0.887659i | \(-0.652330\pi\) | ||||
−0.460500 | + | 0.887659i | \(0.652330\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.02285 | −0.372805 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.4721 | 1.01571 | 0.507857 | − | 0.861441i | \(-0.330438\pi\) | ||||
0.507857 | + | 0.861441i | \(0.330438\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.50832 | −0.276944 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.7188 | −1.08437 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.4540 | 0.637389 | 0.318694 | − | 0.947858i | \(-0.396756\pi\) | ||||
0.318694 | + | 0.947858i | \(0.396756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.4555 | 1.78930 | 0.894648 | − | 0.446771i | \(-0.147426\pi\) | ||||
0.894648 | + | 0.446771i | \(0.147426\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.2881 | 0.620396 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.5127 | −0.871985 | −0.435993 | − | 0.899950i | \(-0.643603\pi\) | ||||
−0.435993 | + | 0.899950i | \(0.643603\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.8222 | −0.707775 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.7868 | 0.703143 | 0.351571 | − | 0.936161i | \(-0.385647\pi\) | ||||
0.351571 | + | 0.936161i | \(0.385647\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.22160 | 0.429280 | 0.214640 | − | 0.976693i | \(-0.431142\pi\) | ||||
0.214640 | + | 0.976693i | \(0.431142\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.93135 | 0.232873 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.71532 | 0.100901 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33.2616 | 1.94983 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.0496 | 1.58026 | 0.790129 | − | 0.612941i | \(-0.210014\pi\) | ||||
0.790129 | + | 0.612941i | \(0.210014\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.63184 | 0.211454 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.6677 | −0.619005 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.38206 | −0.484747 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 51.0309 | 2.93165 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.01387 | −0.172574 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.45012 | 0.253982 | 0.126991 | − | 0.991904i | \(-0.459468\pi\) | ||||
0.126991 | + | 0.991904i | \(0.459468\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 44.5947 | 2.53690 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.67308 | −0.491805 | −0.245903 | − | 0.969295i | \(-0.579084\pi\) | ||||
−0.245903 | + | 0.969295i | \(0.579084\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.28722 | −0.185805 | −0.0929023 | − | 0.995675i | \(-0.529614\pi\) | ||||
−0.0929023 | + | 0.995675i | \(0.529614\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.27116 | 0.127561 | 0.0637806 | − | 0.997964i | \(-0.479684\pi\) | ||||
0.0637806 | + | 0.997964i | \(0.479684\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.81614 | 0.157674 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.4004 | −1.64097 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.3166 | −0.574029 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.2808 | 1.29138 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.8422 | 1.15257 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.94977 | −0.327029 | −0.163514 | − | 0.986541i | \(-0.552283\pi\) | ||||
−0.163514 | + | 0.986541i | \(0.552283\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.0941 | −1.10115 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.30494 | −0.453747 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.3739 | −1.43668 | −0.718338 | − | 0.695695i | \(-0.755097\pi\) | ||||
−0.718338 | + | 0.695695i | \(0.755097\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 34.4571 | 1.87145 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.52776 | 0.299345 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.75917 | 0.148549 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.52887 | −0.457854 | −0.228927 | − | 0.973444i | \(-0.573522\pi\) | ||||
−0.228927 | + | 0.973444i | \(0.573522\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.92722 | 0.531392 | 0.265696 | − | 0.964057i | \(-0.414398\pi\) | ||||
0.265696 | + | 0.964057i | \(0.414398\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.1398 | −1.28849 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.9113 | 1.59202 | 0.796010 | − | 0.605284i | \(-0.206940\pi\) | ||||
0.796010 | + | 0.605284i | \(0.206940\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.55876 | −0.0827302 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.51710 | −0.0800692 | −0.0400346 | − | 0.999198i | \(-0.512747\pi\) | ||||
−0.0400346 | + | 0.999198i | \(0.512747\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.3131 | −0.700691 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.9685 | −0.890616 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.63790 | 0.504471 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.5791 | 0.604424 | 0.302212 | − | 0.953241i | \(-0.402275\pi\) | ||||
0.302212 | + | 0.953241i | \(0.402275\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.73330 | −0.246406 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.21111 | 0.321599 | 0.160800 | − | 0.986987i | \(-0.448593\pi\) | ||||
0.160800 | + | 0.986987i | \(0.448593\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.9063 | −0.821396 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.37260 | 0.328206 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.1641 | −1.08713 | −0.543564 | − | 0.839367i | \(-0.682926\pi\) | ||||
−0.543564 | + | 0.839367i | \(0.682926\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.3645 | −0.940841 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.18271 | 0.111531 | 0.0557655 | − | 0.998444i | \(-0.482240\pi\) | ||||
0.0557655 | + | 0.998444i | \(0.482240\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −38.6079 | −1.96255 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.1345 | −1.37578 | −0.687888 | − | 0.725817i | \(-0.741462\pi\) | ||||
−0.687888 | + | 0.725817i | \(0.741462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.24054 | −0.366170 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −31.4574 | −1.58681 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.83108 | 0.142447 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.6475 | 0.835514 | 0.417757 | − | 0.908559i | \(-0.362816\pi\) | ||||
0.417757 | + | 0.908559i | \(0.362816\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.8927 | −0.643829 | −0.321914 | − | 0.946769i | \(-0.604326\pi\) | ||||
−0.321914 | + | 0.946769i | \(0.604326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.5087 | 0.623102 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.471749 | −0.0234414 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.39551 | 0.465718 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.53906 | −0.323336 | −0.161668 | − | 0.986845i | \(-0.551687\pi\) | ||||
−0.161668 | + | 0.986845i | \(0.551687\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.67779 | −0.428044 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.53110 | −0.320599 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.93645 | −0.388650 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.74856 | −0.280836 | −0.140418 | − | 0.990092i | \(-0.544845\pi\) | ||||
−0.140418 | + | 0.990092i | \(0.544845\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.88749 | −0.335676 | −0.167838 | − | 0.985815i | \(-0.553679\pi\) | ||||
−0.167838 | + | 0.985815i | \(0.553679\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.85528 | −0.381937 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.1102 | 0.975490 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 30.8231 | 1.48816 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.7117 | 1.72017 | 0.860086 | − | 0.510148i | \(-0.170410\pi\) | ||||
0.860086 | + | 0.510148i | \(0.170410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.5183 | 0.937988 | 0.468994 | − | 0.883201i | \(-0.344617\pi\) | ||||
0.468994 | + | 0.883201i | \(0.344617\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.09770 | −0.100577 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.99125 | 0.190927 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.16465 | 0.0555859 | 0.0277930 | − | 0.999614i | \(-0.491152\pi\) | ||||
0.0277930 | + | 0.999614i | \(0.491152\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.7880 | 0.845134 | 0.422567 | − | 0.906332i | \(-0.361129\pi\) | ||||
0.422567 | + | 0.906332i | \(0.361129\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.77724 | −0.179058 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.139693 | 0.00660726 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.6447 | −1.16305 | −0.581527 | − | 0.813527i | \(-0.697545\pi\) | ||||
−0.581527 | + | 0.813527i | \(0.697545\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.21318 | 0.104214 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 37.9806 | 1.78448 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.39264 | −0.252257 | −0.126128 | − | 0.992014i | \(-0.540255\pi\) | ||||
−0.126128 | + | 0.992014i | \(0.540255\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20.8523 | −0.973304 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.1343 | −1.49665 | −0.748323 | − | 0.663335i | \(-0.769141\pi\) | ||||
−0.748323 | + | 0.663335i | \(0.769141\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.34660 | −0.294951 | −0.147476 | − | 0.989066i | \(-0.547115\pi\) | ||||
−0.147476 | + | 0.989066i | \(0.547115\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.11755 | −0.190947 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.03372 | 0.232933 | 0.116466 | − | 0.993195i | \(-0.462843\pi\) | ||||
0.116466 | + | 0.993195i | \(0.462843\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.5166 | 0.668890 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.0521 | 0.830037 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.0855 | −0.508638 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.9961 | −1.64815 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.6160 | −1.62734 | −0.813668 | − | 0.581329i | \(-0.802533\pi\) | ||||
−0.813668 | + | 0.581329i | \(0.802533\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.2610 | 0.969416 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.09062 | 0.321969 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.4713 | 0.519815 | 0.259908 | − | 0.965633i | \(-0.416308\pi\) | ||||
0.259908 | + | 0.965633i | \(0.416308\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −27.7356 | −1.25425 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.0829 | 1.89917 | 0.949587 | − | 0.313504i | \(-0.101503\pi\) | ||||
0.949587 | + | 0.313504i | \(0.101503\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.50474 | 0.247921 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.21017 | −0.279126 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −42.8986 | −1.92040 | −0.960202 | − | 0.279306i | \(-0.909896\pi\) | ||||
−0.960202 | + | 0.279306i | \(0.909896\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.8846 | −1.60321 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.1067 | −1.11945 | −0.559727 | − | 0.828677i | \(-0.689094\pi\) | ||||
−0.559727 | + | 0.828677i | \(0.689094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.8786 | 0.484092 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.5977 | 1.49213 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.0937 | 0.491721 | 0.245861 | − | 0.969305i | \(-0.420929\pi\) | ||||
0.245861 | + | 0.969305i | \(0.420929\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.4946 | 0.507498 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.50657 | 0.418910 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.67294 | 0.161536 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.910955 | 0.0399865 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.1255 | −1.71412 | −0.857060 | − | 0.515216i | \(-0.827712\pi\) | ||||
−0.857060 | + | 0.515216i | \(0.827712\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.7377 | −0.994250 | −0.497125 | − | 0.867679i | \(-0.665611\pi\) | ||||
−0.497125 | + | 0.867679i | \(0.665611\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.8052 | 0.470681 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.1988 | −0.878208 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.9980 | 1.25840 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.00816 | 0.216928 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.26750 | −0.270968 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.0821 | −0.564535 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.82913 | 0.379594 | 0.189797 | − | 0.981823i | \(-0.439217\pi\) | ||||
0.189797 | + | 0.981823i | \(0.439217\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.76267 | 0.118557 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.44308 | 0.190320 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.3632 | −1.42651 | −0.713253 | − | 0.700907i | \(-0.752779\pi\) | ||||
−0.713253 | + | 0.700907i | \(0.752779\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.0639 | −1.02702 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.03441 | −0.129270 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.99858 | −0.297073 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.8730 | 0.714933 | 0.357467 | − | 0.933926i | \(-0.383641\pi\) | ||||
0.357467 | + | 0.933926i | \(0.383641\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.8498 | 1.72776 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.6255 | 1.12413 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.6024 | 0.994723 | 0.497362 | − | 0.867543i | \(-0.334302\pi\) | ||||
0.497362 | + | 0.867543i | \(0.334302\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.34546 | 0.309026 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.4601 | 0.731964 | 0.365982 | − | 0.930622i | \(-0.380733\pi\) | ||||
0.365982 | + | 0.930622i | \(0.380733\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.4898 | 1.06672 | 0.533358 | − | 0.845890i | \(-0.320930\pi\) | ||||
0.533358 | + | 0.845890i | \(0.320930\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −40.5269 | −1.69304 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.78021 | −0.324457 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.6392 | 0.651067 | 0.325533 | − | 0.945531i | \(-0.394456\pi\) | ||||
0.325533 | + | 0.945531i | \(0.394456\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.8973 | 1.24249 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.8309 | 0.697065 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.0529 | −0.581016 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.5500 | −1.83878 | −0.919388 | − | 0.393351i | \(-0.871316\pi\) | ||||
−0.919388 | + | 0.393351i | \(0.871316\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.95620 | −0.245421 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −47.2165 | −1.94223 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.3296 | 1.45081 | 0.725407 | − | 0.688320i | \(-0.241651\pi\) | ||||
0.725407 | + | 0.688320i | \(0.241651\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −30.5009 | −1.24832 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.87532 | 0.321777 | 0.160888 | − | 0.986973i | \(-0.448564\pi\) | ||||
0.160888 | + | 0.986973i | \(0.448564\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.51170 | −0.102454 | −0.0512272 | − | 0.998687i | \(-0.516313\pi\) | ||||
−0.0512272 | + | 0.998687i | \(0.516313\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −66.3097 | −2.70034 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.61730 | −0.147064 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.6137 | 0.552563 | 0.276281 | − | 0.961077i | \(-0.410898\pi\) | ||||
0.276281 | + | 0.961077i | \(0.410898\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.31143 | 0.336244 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.1790 | −1.01697 | −0.508486 | − | 0.861070i | \(-0.669795\pi\) | ||||
−0.508486 | + | 0.861070i | \(0.669795\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.64856 | −0.0664765 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.129305 | −0.00520562 | −0.00260281 | − | 0.999997i | \(-0.500829\pi\) | ||||
−0.00260281 | + | 0.999997i | \(0.500829\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.9871 | −1.36606 | −0.683029 | − | 0.730392i | \(-0.739338\pi\) | ||||
−0.683029 | + | 0.730392i | \(0.739338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.06731 | 0.323730 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.8520 | 0.794079 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.6769 | −0.586140 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.3655 | 0.732281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.20584 | −0.366479 | −0.183239 | − | 0.983068i | \(-0.558658\pi\) | ||||
−0.183239 | + | 0.983068i | \(0.558658\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.7741 | −0.944935 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.91489 | −0.155358 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.4457 | −0.492344 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.1014 | 0.754462 | 0.377231 | − | 0.926119i | \(-0.376876\pi\) | ||||
0.377231 | + | 0.926119i | \(0.376876\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.6674 | −1.48546 | −0.742728 | − | 0.669593i | \(-0.766469\pi\) | ||||
−0.742728 | + | 0.669593i | \(0.766469\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.4468 | −0.529465 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.4110 | 1.70666 | 0.853331 | − | 0.521369i | \(-0.174578\pi\) | ||||
0.853331 | + | 0.521369i | \(0.174578\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.5588 | −0.532228 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.9271 | −0.466744 | −0.233372 | − | 0.972387i | \(-0.574976\pi\) | ||||
−0.233372 | + | 0.972387i | \(0.574976\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.70600 | −0.262025 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 76.9526 | 3.00221 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.7327 | −0.807632 | −0.403816 | − | 0.914840i | \(-0.632316\pi\) | ||||
−0.403816 | + | 0.914840i | \(0.632316\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.4832 | 0.952288 | 0.476144 | − | 0.879367i | \(-0.342034\pi\) | ||||
0.476144 | + | 0.879367i | \(0.342034\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 60.2503 | 2.33993 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.12966 | −0.0824609 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.3946 | 0.672512 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.2517 | 0.434366 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.1195 | 1.12247 | 0.561237 | − | 0.827655i | \(-0.310325\pi\) | ||||
0.561237 | + | 0.827655i | \(0.310325\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.4065 | −0.862428 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.4949 | 1.05671 | 0.528357 | − | 0.849022i | \(-0.322808\pi\) | ||||
0.528357 | + | 0.849022i | \(0.322808\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 54.1763 | 2.07604 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.3060 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.84991 | −0.0706813 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −71.8458 | −2.74109 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.0864 | 1.45097 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.51216 | 0.0955669 | 0.0477835 | − | 0.998858i | \(-0.484784\pi\) | ||||
0.0477835 | + | 0.998858i | \(0.484784\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.69187 | −0.0641763 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.32612 | 0.163864 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 42.5627 | 1.60987 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.69744 | −0.366267 | −0.183134 | − | 0.983088i | \(-0.558624\pi\) | ||||
−0.183134 | + | 0.983088i | \(0.558624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.1237 | −0.381824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.73592 | −0.103041 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.7425 | 1.00433 | 0.502167 | − | 0.864770i | \(-0.332536\pi\) | ||||
0.502167 | + | 0.864770i | \(0.332536\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.6044 | 0.847731 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.18028 | −0.156553 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.57079 | 0.245734 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 42.2866 | 1.57922 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.6483 | −0.471701 | −0.235850 | − | 0.971789i | \(-0.575788\pi\) | ||||
−0.235850 | + | 0.971789i | \(0.575788\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −31.9088 | −1.18670 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.91503 | 0.219679 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.5407 | 1.28105 | 0.640523 | − | 0.767939i | \(-0.278718\pi\) | ||||
0.640523 | + | 0.767939i | \(0.278718\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.9790 | −1.62885 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.2866 | 1.30512 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.1244 | −0.484759 | −0.242379 | − | 0.970182i | \(-0.577928\pi\) | ||||
−0.242379 | + | 0.970182i | \(0.577928\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.0048 | 1.14208 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.7457 | 1.94028 | 0.970142 | − | 0.242539i | \(-0.0779802\pi\) | ||||
0.970142 | + | 0.242539i | \(0.0779802\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33.2122 | −1.22008 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.10219 | −0.297241 | −0.148620 | − | 0.988894i | \(-0.547483\pi\) | ||||
−0.148620 | + | 0.988894i | \(0.547483\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.0297794 | 0.00109103 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −52.1467 | −1.90795 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −53.2853 | −1.94441 | −0.972204 | − | 0.234137i | \(-0.924774\pi\) | ||||
−0.972204 | + | 0.234137i | \(0.924774\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.8355 | 0.832172 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.09660 | 0.294665 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.0792 | 0.875174 | 0.437587 | − | 0.899176i | \(-0.355833\pi\) | ||||
0.437587 | + | 0.899176i | \(0.355833\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.3008 | −0.373896 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.2174 | −1.05913 | −0.529565 | − | 0.848269i | \(-0.677645\pi\) | ||||
−0.529565 | + | 0.848269i | \(0.677645\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.1391 | −0.438890 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −30.6819 | −1.10786 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.5367 | 1.49785 | 0.748926 | − | 0.662653i | \(-0.230570\pi\) | ||||
0.748926 | + | 0.662653i | \(0.230570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.0591 | −1.47871 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.4847 | −1.31226 | −0.656131 | − | 0.754647i | \(-0.727808\pi\) | ||||
−0.656131 | + | 0.754647i | \(0.727808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.6105 | 0.417062 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.38471 | −0.0854413 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.81930 | 0.208231 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.13330 | −0.219186 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.09461 | 0.110451 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.1940 | −1.14759 | −0.573797 | − | 0.818998i | \(-0.694530\pi\) | ||||
−0.573797 | + | 0.818998i | \(0.694530\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 45.8070 | 1.63077 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.4612 | 0.904155 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.5371 | −0.444645 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.2909 | 1.14380 | 0.571901 | − | 0.820323i | \(-0.306206\pi\) | ||||
0.571901 | + | 0.820323i | \(0.306206\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.17953 | 0.253994 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.1589 | −1.06561 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −35.9812 | −1.26975 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.0712 | 1.02335 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.3729 | −0.716275 | −0.358137 | − | 0.933669i | \(-0.616588\pi\) | ||||
−0.358137 | + | 0.933669i | \(0.616588\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.1851 | −0.638563 | −0.319282 | − | 0.947660i | \(-0.603442\pi\) | ||||
−0.319282 | + | 0.947660i | \(0.603442\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 81.9124 | 2.87279 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.91259 | −0.207109 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.4513 | −0.680514 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.3250 | −1.58185 | −0.790927 | − | 0.611911i | \(-0.790401\pi\) | ||||
−0.790927 | + | 0.611911i | \(0.790401\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.9058 | 1.25160 | 0.625798 | − | 0.779985i | \(-0.284773\pi\) | ||||
0.625798 | + | 0.779985i | \(0.284773\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 28.6100 | 0.996071 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.1662 | −1.39671 | −0.698357 | − | 0.715749i | \(-0.746085\pi\) | ||||
−0.698357 | + | 0.715749i | \(0.746085\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.09462 | −0.176943 | −0.0884717 | − | 0.996079i | \(-0.528198\pi\) | ||||
−0.0884717 | + | 0.996079i | \(0.528198\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.3582 | −1.40001 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.64979 | −0.264732 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.0390 | −0.416128 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.0941 | −0.624677 | −0.312338 | − | 0.949971i | \(-0.601112\pi\) | ||||
−0.312338 | + | 0.949971i | \(0.601112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3809 | −0.944169 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.7778 | 1.12893 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.16227 | 0.246390 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.0824 | 0.689227 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.10521 | −0.243563 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.5790 | −1.56060 | −0.780298 | − | 0.625408i | \(-0.784933\pi\) | ||||
−0.780298 | + | 0.625408i | \(0.784933\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.69151 | 0.228845 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −53.4497 | −1.82581 | −0.912904 | − | 0.408174i | \(-0.866166\pi\) | ||||
−0.912904 | + | 0.408174i | \(0.866166\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.28760 | 0.112171 | 0.0560857 | − | 0.998426i | \(-0.482138\pi\) | ||||
0.0560857 | + | 0.998426i | \(0.482138\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.87675 | −0.0638853 | −0.0319426 | − | 0.999490i | \(-0.510169\pi\) | ||||
−0.0319426 | + | 0.999490i | \(0.510169\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.194195 | 0.00660283 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.77010 | 0.162001 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.5693 | −0.358538 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 70.1603 | 2.37729 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 56.6141 | 1.91610 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.69488 | −0.192302 | −0.0961512 | − | 0.995367i | \(-0.530653\pi\) | ||||
−0.0961512 | + | 0.995367i | \(0.530653\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 75.2218 | 2.53717 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.468017 | 0.0157679 | 0.00788395 | − | 0.999969i | \(-0.497490\pi\) | ||||
0.00788395 | + | 0.999969i | \(0.497490\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.3412 | 1.49220 | 0.746100 | − | 0.665834i | \(-0.231924\pi\) | ||||
0.746100 | + | 0.665834i | \(0.231924\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.0997 | 0.339498 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 52.6344 | 1.76729 | 0.883645 | − | 0.468158i | \(-0.155082\pi\) | ||||
0.883645 | + | 0.468158i | \(0.155082\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.76118 | 0.0590018 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.95762 | −0.132437 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.78881 | −0.0932196 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.3095 | −0.778282 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.17813 | 0.105996 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.8995 | 1.09604 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.588938 | 0.0195770 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.81824 | −0.259600 | −0.129800 | − | 0.991540i | \(-0.541434\pi\) | ||||
−0.129800 | + | 0.991540i | \(0.541434\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 86.8589 | 2.88093 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.22863 | 0.173232 | 0.0866162 | − | 0.996242i | \(-0.472395\pi\) | ||||
0.0866162 | + | 0.996242i | \(0.472395\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.3826 | 0.806945 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.38122 | −0.277074 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.0843 | −0.596547 | −0.298273 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298273 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.3753 | 0.407779 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.1684 | 0.433443 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.7344 | 0.648862 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 75.9040 | 2.49301 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.3901 | −1.32515 | −0.662577 | − | 0.748994i | \(-0.730537\pi\) | ||||
−0.662577 | + | 0.748994i | \(0.730537\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.1188 | −0.789614 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.67594 | 0.185623 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.45124 | −0.0474099 | −0.0237049 | − | 0.999719i | \(-0.507546\pi\) | ||||
−0.0237049 | + | 0.999719i | \(0.507546\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.14136 | −0.298317 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.03771 | −0.0338282 | −0.0169141 | − | 0.999857i | \(-0.505384\pi\) | ||||
−0.0169141 | + | 0.999857i | \(0.505384\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.67368 | −0.0545025 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.0133 | 1.65771 | 0.828854 | − | 0.559465i | \(-0.188993\pi\) | ||||
0.828854 | + | 0.559465i | \(0.188993\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −81.4212 | −2.64305 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.31584 | 0.204805 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.39299 | 0.304269 | 0.152134 | − | 0.988360i | \(-0.451385\pi\) | ||||
0.152134 | + | 0.988360i | \(0.451385\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.63941 | −0.279565 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.83135 | 0.253152 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.7617 | −0.798765 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −50.0421 | −1.61258 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.37343 | 0.205168 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.1155 | 0.711187 | 0.355594 | − | 0.934641i | \(-0.384279\pi\) | ||||
0.355594 | + | 0.934641i | \(0.384279\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.6891 | −0.921628 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.0253 | −0.931468 | −0.465734 | − | 0.884925i | \(-0.654210\pi\) | ||||
−0.465734 | + | 0.884925i | \(0.654210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 64.7410 | 2.07337 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.4228 | 0.621391 | 0.310695 | − | 0.950510i | \(-0.399438\pi\) | ||||
0.310695 | + | 0.950510i | \(0.399438\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.1016 | 0.450688 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.4752 | 1.13264 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.4311 | −1.25766 | −0.628828 | − | 0.777545i | \(-0.716465\pi\) | ||||
−0.628828 | + | 0.777545i | \(0.716465\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0655 | −0.320713 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.6516 | −0.434096 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.3793 | −0.774435 | −0.387218 | − | 0.921988i | \(-0.626564\pi\) | ||||
−0.387218 | + | 0.921988i | \(0.626564\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.5456 | −0.525059 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.50210 | −0.206130 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.3658 | 1.46842 | 0.734210 | − | 0.678923i | \(-0.237553\pi\) | ||||
0.734210 | + | 0.678923i | \(0.237553\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.4626 | −0.647408 |
(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 | 8036.2.a.l.1.5 | 5 | ||
7.6 | odd | 2 | 1148.2.a.c.1.1 | ✓ | 5 | ||
28.27 | even | 2 | 4592.2.a.be.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.a.c.1.1 | ✓ | 5 | 7.6 | odd | 2 | ||
4592.2.a.be.1.5 | 5 | 28.27 | even | 2 | |||
8036.2.a.l.1.5 | 5 | 1.1 | even | 1 | trivial |