Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3724,2,Mod(1,3724)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3724, 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("3724.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3724 = 2^{2} \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3724.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(29.7362897127\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.733.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 532) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.51820\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3724.1 |
$q$-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 | ||||||||
\(3\) | 2.51820 | 1.45388 | 0.726941 | − | 0.686700i | \(-0.240941\pi\) | ||||
0.726941 | + | 0.686700i | \(0.240941\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.85952 | 1.27882 | 0.639409 | − | 0.768867i | \(-0.279179\pi\) | ||||
0.639409 | + | 0.768867i | \(0.279179\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.34132 | 1.11377 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.34132 | −0.705936 | −0.352968 | − | 0.935635i | \(-0.614828\pi\) | ||||
−0.352968 | + | 0.935635i | \(0.614828\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.859523 | 0.238389 | 0.119194 | − | 0.992871i | \(-0.461969\pi\) | ||||
0.119194 | + | 0.992871i | \(0.461969\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.20085 | 1.85925 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.34132 | −1.05293 | −0.526463 | − | 0.850198i | \(-0.676482\pi\) | ||||
−0.526463 | + | 0.850198i | \(0.676482\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.85952 | 1.01328 | 0.506640 | − | 0.862158i | \(-0.330887\pi\) | ||||
0.506640 | + | 0.862158i | \(0.330887\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.17687 | 0.635375 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.859523 | 0.165415 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.37772 | 1.74140 | 0.870700 | − | 0.491815i | \(-0.163666\pi\) | ||||
0.870700 | + | 0.491815i | \(0.163666\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.37772 | 1.32508 | 0.662539 | − | 0.749027i | \(-0.269479\pi\) | ||||
0.662539 | + | 0.749027i | \(0.269479\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.89592 | −1.02635 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.17687 | 0.357876 | 0.178938 | − | 0.983860i | \(-0.442734\pi\) | ||||
0.178938 | + | 0.983860i | \(0.442734\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.16445 | 0.346589 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.69507 | −1.04559 | −0.522797 | − | 0.852457i | \(-0.675112\pi\) | ||||
−0.522797 | + | 0.852457i | \(0.675112\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.353748 | 0.0539461 | 0.0269730 | − | 0.999636i | \(-0.491413\pi\) | ||||
0.0269730 | + | 0.999636i | \(0.491413\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.55460 | 1.42432 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.54217 | −0.808409 | −0.404204 | − | 0.914669i | \(-0.632452\pi\) | ||||
−0.404204 | + | 0.914669i | \(0.632452\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.9323 | −1.53083 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.55460 | 1.31242 | 0.656212 | − | 0.754576i | \(-0.272158\pi\) | ||||
0.656212 | + | 0.754576i | \(0.272158\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.69507 | −0.902763 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.51820 | 0.333544 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.5786 | 1.89797 | 0.948984 | − | 0.315324i | \(-0.102113\pi\) | ||||
0.948984 | + | 0.315324i | \(0.102113\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9323 | 1.65581 | 0.827907 | − | 0.560866i | \(-0.189532\pi\) | ||||
0.827907 | + | 0.560866i | \(0.189532\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.45783 | 0.304856 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.34132 | −0.530377 | −0.265189 | − | 0.964197i | \(-0.585434\pi\) | ||||
−0.265189 | + | 0.964197i | \(0.585434\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.2372 | 1.47319 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.89592 | 0.937073 | 0.468537 | − | 0.883444i | \(-0.344781\pi\) | ||||
0.468537 | + | 0.883444i | \(0.344781\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.23725 | −0.261850 | −0.130925 | − | 0.991392i | \(-0.541795\pi\) | ||||
−0.130925 | + | 0.991392i | \(0.541795\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.00000 | 0.923760 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.36530 | 0.828661 | 0.414330 | − | 0.910127i | \(-0.364016\pi\) | ||||
0.414330 | + | 0.910127i | \(0.364016\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.85952 | −0.873280 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.83555 | 0.201478 | 0.100739 | − | 0.994913i | \(-0.467879\pi\) | ||||
0.100739 | + | 0.994913i | \(0.467879\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.4141 | −1.34650 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 23.6150 | 2.53179 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.31735 | 0.351638 | 0.175819 | − | 0.984422i | \(-0.443743\pi\) | ||||
0.175819 | + | 0.984422i | \(0.443743\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.5786 | 1.92651 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.85952 | 0.293381 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.2248 | −1.85045 | −0.925225 | − | 0.379418i | \(-0.876124\pi\) | ||||
−0.925225 | + | 0.379418i | \(0.876124\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.82313 | −0.786254 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.18842 | −0.715275 | −0.357637 | − | 0.933860i | \(-0.616418\pi\) | ||||
−0.357637 | + | 0.933860i | \(0.616418\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.21327 | −0.513679 | −0.256839 | − | 0.966454i | \(-0.582681\pi\) | ||||
−0.256839 | + | 0.966454i | \(0.582681\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.89592 | −0.376633 | −0.188316 | − | 0.982108i | \(-0.560303\pi\) | ||||
−0.188316 | + | 0.982108i | \(0.560303\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.578570 | 0.0554170 | 0.0277085 | − | 0.999616i | \(-0.491179\pi\) | ||||
0.0277085 | + | 0.999616i | \(0.491179\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.48180 | 0.520310 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.51820 | 0.425036 | 0.212518 | − | 0.977157i | \(-0.431834\pi\) | ||||
0.212518 | + | 0.977157i | \(0.431834\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.8959 | 1.29580 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.87195 | 0.265512 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.51820 | −0.501654 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.8595 | −1.52017 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.21327 | −0.466289 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.4017 | −1.10047 | −0.550236 | − | 0.835009i | \(-0.685462\pi\) | ||||
−0.550236 | + | 0.835009i | \(0.685462\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.890808 | 0.0784313 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.98758 | 0.173655 | 0.0868277 | − | 0.996223i | \(-0.472327\pi\) | ||||
0.0868277 | + | 0.996223i | \(0.472327\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.45783 | 0.211536 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.4381 | −1.14809 | −0.574047 | − | 0.818822i | \(-0.694627\pi\) | ||||
−0.574047 | + | 0.818822i | \(0.694627\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6150 | −0.985169 | −0.492584 | − | 0.870265i | \(-0.663948\pi\) | ||||
−0.492584 | + | 0.870265i | \(0.663948\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.9563 | −1.17533 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.01242 | −0.168287 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 26.8158 | 2.22693 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.10408 | 0.336219 | 0.168110 | − | 0.985768i | \(-0.446234\pi\) | ||||
0.168110 | + | 0.985768i | \(0.446234\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7794 | 0.958595 | 0.479298 | − | 0.877652i | \(-0.340891\pi\) | ||||
0.479298 | + | 0.877652i | \(0.340891\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.5058 | −1.17272 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.0968 | 1.69453 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.8158 | −1.34205 | −0.671024 | − | 0.741436i | \(-0.734145\pi\) | ||||
−0.671024 | + | 0.741436i | \(0.734145\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24.0604 | 1.90811 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.2736 | 1.03967 | 0.519836 | − | 0.854266i | \(-0.325993\pi\) | ||||
0.519836 | + | 0.854266i | \(0.325993\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16.8595 | −1.31251 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.2497 | −1.10267 | −0.551336 | − | 0.834283i | \(-0.685882\pi\) | ||||
−0.551336 | + | 0.834283i | \(0.685882\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2612 | −0.943171 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.34132 | 0.255517 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.6826 | −1.57247 | −0.786236 | − | 0.617926i | \(-0.787973\pi\) | ||||
−0.786236 | + | 0.617926i | \(0.787973\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 36.7117 | 2.75942 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.0604 | 1.05092 | 0.525461 | − | 0.850818i | \(-0.323893\pi\) | ||||
0.525461 | + | 0.850818i | \(0.323893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.02397 | −0.522088 | −0.261044 | − | 0.965327i | \(-0.584067\pi\) | ||||
−0.261044 | + | 0.965327i | \(0.584067\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 32.5661 | 2.40736 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.22482 | 0.457658 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.1645 | 0.743298 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.6753 | −1.13423 | −0.567114 | − | 0.823639i | \(-0.691940\pi\) | ||||
−0.567114 | + | 0.823639i | \(0.691940\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.670226 | −0.0482439 | −0.0241220 | − | 0.999709i | \(-0.507679\pi\) | ||||
−0.0241220 | + | 0.999709i | \(0.507679\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.18930 | 0.443225 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.9811 | −1.70859 | −0.854293 | − | 0.519792i | \(-0.826009\pi\) | ||||
−0.854293 | + | 0.519792i | \(0.826009\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.9803 | −1.20370 | −0.601850 | − | 0.798609i | \(-0.705569\pi\) | ||||
−0.601850 | + | 0.798609i | \(0.705569\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.9323 | −0.771106 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.1447 | −1.33713 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.2372 | 1.12857 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.34132 | −0.161953 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.8471 | 0.884431 | 0.442215 | − | 0.896909i | \(-0.354193\pi\) | ||||
0.442215 | + | 0.896909i | \(0.354193\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.8835 | 1.36239 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.01155 | 0.0689872 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.63383 | −0.380699 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.73147 | −0.251006 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.53062 | −0.571253 | −0.285626 | − | 0.958341i | \(-0.592202\pi\) | ||||
−0.285626 | + | 0.958341i | \(0.592202\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.6150 | 0.707665 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.4985 | −1.82514 | −0.912569 | − | 0.408924i | \(-0.865904\pi\) | ||||
−0.912569 | + | 0.408924i | \(0.865904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.4381 | 1.68100 | 0.840498 | − | 0.541814i | \(-0.182262\pi\) | ||||
0.840498 | + | 0.541814i | \(0.182262\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.6587 | 1.02583 | 0.512917 | − | 0.858438i | \(-0.328565\pi\) | ||||
0.512917 | + | 0.858438i | \(0.328565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.8480 | −1.03381 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.5473 | 1.20478 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.0051 | −1.09997 | −0.549985 | − | 0.835175i | \(-0.685366\pi\) | ||||
−0.549985 | + | 0.835175i | \(0.685366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.40170 | −0.154707 | −0.0773534 | − | 0.997004i | \(-0.524647\pi\) | ||||
−0.0773534 | + | 0.997004i | \(0.524647\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.3704 | −1.43506 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.859523 | 0.0546902 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.62228 | 0.292925 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.77942 | −0.364794 | −0.182397 | − | 0.983225i | \(-0.558386\pi\) | ||||
−0.182397 | + | 0.983225i | \(0.558386\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.3777 | −0.715311 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −31.2612 | −1.95765 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.49335 | −0.155531 | −0.0777655 | − | 0.996972i | \(-0.524779\pi\) | ||||
−0.0777655 | + | 0.996972i | \(0.524779\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 31.3340 | 1.93953 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.72636 | 0.414765 | 0.207382 | − | 0.978260i | \(-0.433506\pi\) | ||||
0.207382 | + | 0.978260i | \(0.433506\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.3216 | 1.67835 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.35375 | 0.511241 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.1893 | −0.621252 | −0.310626 | − | 0.950532i | \(-0.600539\pi\) | ||||
−0.310626 | + | 0.950532i | \(0.600539\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.1083 | −1.34298 | −0.671492 | − | 0.741011i | \(-0.734346\pi\) | ||||
−0.671492 | + | 0.741011i | \(0.734346\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.43809 | −0.448534 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.31735 | −0.559825 | −0.279913 | − | 0.960025i | \(-0.590306\pi\) | ||||
−0.279913 | + | 0.960025i | \(0.590306\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.6514 | 1.47584 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.9323 | −0.771477 | −0.385739 | − | 0.922608i | \(-0.626053\pi\) | ||||
−0.385739 | + | 0.922608i | \(0.626053\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.9083 | −1.18343 | −0.591714 | − | 0.806148i | \(-0.701549\pi\) | ||||
−0.591714 | + | 0.806148i | \(0.701549\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.20085 | 0.426541 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.84710 | 0.108653 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −45.8937 | −2.69034 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.1769 | −1.17875 | −0.589373 | − | 0.807861i | \(-0.700625\pi\) | ||||
−0.589373 | + | 0.807861i | \(0.700625\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.6878 | 2.42716 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.01242 | −0.116773 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.17687 | 0.241555 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.1019 | −1.03993 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.9803 | 2.11748 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.5713 | 1.68772 | 0.843860 | − | 0.536563i | \(-0.180278\pi\) | ||||
0.843860 | + | 0.536563i | \(0.180278\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.1281 | −0.746829 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.7794 | 1.00818 | 0.504089 | − | 0.863652i | \(-0.331828\pi\) | ||||
0.504089 | + | 0.863652i | \(0.331828\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.0479 | −1.35927 | −0.679635 | − | 0.733550i | \(-0.737862\pi\) | ||||
−0.679635 | + | 0.733550i | \(0.737862\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.5109 | 0.871178 | 0.435589 | − | 0.900146i | \(-0.356540\pi\) | ||||
0.435589 | + | 0.900146i | \(0.356540\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.9563 | −1.22932 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.81070 | −0.547580 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.34132 | −0.241558 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.73060 | 0.151466 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.45695 | 0.0805698 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.8835 | 1.64255 | 0.821273 | − | 0.570536i | \(-0.193264\pi\) | ||||
0.821273 | + | 0.570536i | \(0.193264\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.27364 | 0.398593 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.4141 | −0.678256 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.8771 | −1.84540 | −0.922701 | − | 0.385518i | \(-0.874023\pi\) | ||||
−0.922701 | + | 0.385518i | \(0.874023\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.3777 | 0.617953 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.2736 | −0.935420 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 34.9927 | 1.88394 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.2124 | −1.08506 | −0.542529 | − | 0.840037i | \(-0.682533\pi\) | ||||
−0.542529 | + | 0.840037i | \(0.682533\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.77431 | 0.148505 | 0.0742526 | − | 0.997239i | \(-0.476343\pi\) | ||||
0.0742526 | + | 0.997239i | \(0.476343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.738780 | 0.0394332 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.3049 | 1.02750 | 0.513749 | − | 0.857941i | \(-0.328256\pi\) | ||||
0.513749 | + | 0.857941i | \(0.328256\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.5786 | 1.19835 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.5349 | 1.50601 | 0.753006 | − | 0.658013i | \(-0.228603\pi\) | ||||
0.753006 | + | 0.658013i | \(0.228603\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.8959 | −0.729347 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.39746 | −0.334858 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.94387 | 0.205868 | 0.102934 | − | 0.994688i | \(-0.467177\pi\) | ||||
0.102934 | + | 0.994688i | \(0.467177\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.3704 | −1.16456 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.3216 | 0.896878 | 0.448439 | − | 0.893813i | \(-0.351980\pi\) | ||||
0.448439 | + | 0.893813i | \(0.351980\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.1281 | −0.677930 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.06037 | 0.415130 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.2248 | −0.833413 | −0.416707 | − | 0.909041i | \(-0.636816\pi\) | ||||
−0.416707 | + | 0.909041i | \(0.636816\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −31.2299 | −1.59996 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.65136 | 0.237674 | 0.118837 | − | 0.992914i | \(-0.462083\pi\) | ||||
0.118837 | + | 0.992914i | \(0.462083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.18199 | 0.0600838 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.6587 | 0.591118 | 0.295559 | − | 0.955324i | \(-0.404494\pi\) | ||||
0.295559 | + | 0.955324i | \(0.404494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.0968 | −1.06691 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.00511 | 0.252475 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.0612 | 1.05971 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.9126 | 1.70202 | 0.851012 | − | 0.525146i | \(-0.175989\pi\) | ||||
0.851012 | + | 0.525146i | \(0.175989\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.69507 | 0.234461 | 0.117230 | − | 0.993105i | \(-0.462598\pi\) | ||||
0.117230 | + | 0.993105i | \(0.462598\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.34132 | 0.315884 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.4745 | −1.11677 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.09677 | −0.252637 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.7628 | 0.581631 | 0.290815 | − | 0.956779i | \(-0.406073\pi\) | ||||
0.290815 | + | 0.956779i | \(0.406073\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −33.8398 | −1.66919 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.24880 | 0.257653 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.2488 | −1.43232 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.7606 | 1.55160 | 0.775802 | − | 0.630976i | \(-0.217345\pi\) | ||||
0.775802 | + | 0.630976i | \(0.217345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.8116 | 0.624398 | 0.312199 | − | 0.950017i | \(-0.398934\pi\) | ||||
0.312199 | + | 0.950017i | \(0.398934\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −18.5182 | −0.900386 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.7918 | −0.669003 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.06768 | −0.244670 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.4381 | 1.03264 | 0.516318 | − | 0.856397i | \(-0.327302\pi\) | ||||
0.516318 | + | 0.856397i | \(0.327302\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.176874 | 0.00850002 | 0.00425001 | − | 0.999991i | \(-0.498647\pi\) | ||||
0.00425001 | + | 0.999991i | \(0.498647\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 67.5276 | 3.23770 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.85952 | 0.232463 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.14559 | 0.197858 | 0.0989291 | − | 0.995094i | \(-0.468458\pi\) | ||||
0.0989291 | + | 0.995094i | \(0.468458\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.6753 | 0.744758 | 0.372379 | − | 0.928081i | \(-0.378542\pi\) | ||||
0.372379 | + | 0.928081i | \(0.378542\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.48604 | 0.449682 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.3349 | 0.488823 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.00731 | −0.141924 | −0.0709619 | − | 0.997479i | \(-0.522607\pi\) | ||||
−0.0709619 | + | 0.997479i | \(0.522607\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.6753 | 0.738123 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 29.6629 | 1.39369 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.7117 | −1.06241 | −0.531205 | − | 0.847243i | \(-0.678261\pi\) | ||||
−0.531205 | + | 0.847243i | \(0.678261\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.73147 | −0.174170 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.0406 | 1.81830 | 0.909152 | − | 0.416465i | \(-0.136731\pi\) | ||||
0.909152 | + | 0.416465i | \(0.136731\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.2497 | −1.21993 | −0.609963 | − | 0.792430i | \(-0.708816\pi\) | ||||
−0.609963 | + | 0.792430i | \(0.708816\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 53.1259 | 2.46365 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.63894 | −0.307214 | −0.153607 | − | 0.988132i | \(-0.549089\pi\) | ||||
−0.153607 | + | 0.988132i | \(0.549089\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −42.3456 | −1.95118 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.828239 | −0.0380825 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.17687 | 0.145765 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.9250 | 1.46175 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.0603715 | −0.00275844 | −0.00137922 | − | 0.999999i | \(-0.500439\pi\) | ||||
−0.00137922 | + | 0.999999i | \(0.500439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.87107 | 0.0853136 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −52.1143 | −2.36639 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.6034 | 1.29614 | 0.648072 | − | 0.761579i | \(-0.275575\pi\) | ||||
0.648072 | + | 0.761579i | \(0.275575\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 33.4257 | 1.51156 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.73060 | −0.303748 | −0.151874 | − | 0.988400i | \(-0.548531\pi\) | ||||
−0.151874 | + | 0.988400i | \(0.548531\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −40.7117 | −1.83356 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −22.3704 | −1.00548 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.5546 | −1.77071 | −0.885353 | − | 0.464919i | \(-0.846084\pi\) | ||||
−0.885353 | + | 0.464919i | \(0.846084\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.8835 | −1.60316 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.8531 | −1.28650 | −0.643248 | − | 0.765658i | \(-0.722413\pi\) | ||||
−0.643248 | + | 0.765658i | \(0.722413\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.5555 | −0.914706 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −30.8762 | −1.37126 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.4496 | −1.43831 | −0.719153 | − | 0.694852i | \(-0.755470\pi\) | ||||
−0.719153 | + | 0.694852i | \(0.755470\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.859523 | 0.0379489 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.9075 | −0.656902 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.9760 | 0.570685 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −52.0830 | −2.28619 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.88437 | 0.389231 | 0.194616 | − | 0.980880i | \(-0.437654\pi\) | ||||
0.194616 | + | 0.980880i | \(0.437654\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.0531 | 1.35786 | 0.678928 | − | 0.734205i | \(-0.262445\pi\) | ||||
0.678928 | + | 0.734205i | \(0.262445\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.0291 | −1.39521 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.614968 | 0.0267377 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 48.7117 | 2.11391 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.75457 | −0.249258 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.1405 | −0.481645 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 35.4068 | 1.52792 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.1687 | −1.72699 | −0.863493 | − | 0.504360i | \(-0.831728\pi\) | ||||
−0.863493 | + | 0.504360i | \(0.831728\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.6878 | −0.759055 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.65443 | 0.0708682 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.6638 | −0.541464 | −0.270732 | − | 0.962655i | \(-0.587266\pi\) | ||||
−0.270732 | + | 0.962655i | \(0.587266\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 43.2111 | 1.84420 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.37772 | 0.399504 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.6753 | 0.665381 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.7679 | 1.30368 | 0.651838 | − | 0.758358i | \(-0.273998\pi\) | ||||
0.651838 | + | 0.758358i | \(0.273998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.304055 | 0.0128601 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.5961 | 1.08067 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.2976 | 1.36118 | 0.680591 | − | 0.732663i | \(-0.261723\pi\) | ||||
0.680591 | + | 0.732663i | \(0.261723\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.9199 | 0.543544 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.4912 | −1.36210 | −0.681050 | − | 0.732237i | \(-0.738476\pi\) | ||||
−0.681050 | + | 0.732237i | \(0.738476\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.9687 | 1.00306 | 0.501530 | − | 0.865140i | \(-0.332771\pi\) | ||||
0.501530 | + | 0.865140i | \(0.332771\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −39.4736 | −1.64903 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.4381 | 0.643813 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.0655 | 1.12675 | 0.563375 | − | 0.826201i | \(-0.309502\pi\) | ||||
0.563375 | + | 0.826201i | \(0.309502\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.68776 | −0.0701410 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.3704 | −0.926488 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.21240 | 0.339541 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.15714 | −0.377956 | −0.188978 | − | 0.981981i | \(-0.560517\pi\) | ||||
−0.188978 | + | 0.981981i | \(0.560517\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.37772 | 0.303994 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −60.3893 | −2.48408 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.6034 | 0.517560 | 0.258780 | − | 0.965936i | \(-0.416679\pi\) | ||||
0.258780 | + | 0.965936i | \(0.416679\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −42.7597 | −1.75004 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.7002 | 1.54039 | 0.770194 | − | 0.637810i | \(-0.220159\pi\) | ||||
0.770194 | + | 0.637810i | \(0.220159\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.0291 | −0.817004 | −0.408502 | − | 0.912758i | \(-0.633949\pi\) | ||||
−0.408502 | + | 0.912758i | \(0.633949\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.5058 | −0.590721 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.7794 | −0.641525 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.8480 | 0.805604 | 0.402802 | − | 0.915287i | \(-0.368036\pi\) | ||||
0.402802 | + | 0.915287i | \(0.368036\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.76363 | −0.192716 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.1498 | 1.21774 | 0.608870 | − | 0.793270i | \(-0.291623\pi\) | ||||
0.608870 | + | 0.793270i | \(0.291623\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −48.2102 | −1.94402 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.6702 | 0.671118 | 0.335559 | − | 0.942019i | \(-0.391075\pi\) | ||||
0.335559 | + | 0.942019i | \(0.391075\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.823999 | 0.0331193 | 0.0165596 | − | 0.999863i | \(-0.494729\pi\) | ||||
0.0165596 | + | 0.999863i | \(0.494729\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.17687 | 0.167612 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7918 | −1.23167 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.89592 | −0.235460 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.45052 | −0.376817 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.6762 | 1.61929 | 0.809647 | − | 0.586917i | \(-0.199658\pi\) | ||||
0.809647 | + | 0.586917i | \(0.199658\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.3516 | 1.28586 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −35.4629 | −1.40730 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.3828 | 1.04369 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.8407 | −0.507176 | −0.253588 | − | 0.967312i | \(-0.581611\pi\) | ||||
−0.253588 | + | 0.967312i | \(0.581611\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.3820 | 1.71082 | 0.855409 | − | 0.517953i | \(-0.173306\pi\) | ||||
0.855409 | + | 0.517953i | \(0.173306\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.54729 | 0.100299 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.0531 | −1.37808 | −0.689039 | − | 0.724724i | \(-0.741967\pi\) | ||||
−0.689039 | + | 0.724724i | \(0.741967\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34.1332 | −1.33984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.8085 | 1.87089 | 0.935446 | − | 0.353470i | \(-0.114999\pi\) | ||||
0.935446 | + | 0.353470i | \(0.114999\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.68352 | 0.222074 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.47536 | −0.291642 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.6325 | 1.58282 | 0.791409 | − | 0.611287i | \(-0.209348\pi\) | ||||
0.791409 | + | 0.611287i | \(0.209348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.4265 | 1.02787 | 0.513937 | − | 0.857828i | \(-0.328187\pi\) | ||||
0.513937 | + | 0.857828i | \(0.328187\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.39658 | −0.364933 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.5713 | 1.76453 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.4818 | −0.830534 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.2788 | −1.16890 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.4077 | −1.48051 | −0.740254 | − | 0.672328i | \(-0.765295\pi\) | ||||
−0.740254 | + | 0.672328i | \(0.765295\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.73060 | 0.105101 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.3944 | 0.822253 | 0.411127 | − | 0.911578i | \(-0.365135\pi\) | ||||
0.411127 | + | 0.911578i | \(0.365135\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −69.2466 | −2.65354 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.6265 | 1.32495 | 0.662473 | − | 0.749085i | \(-0.269507\pi\) | ||||
0.662473 | + | 0.749085i | \(0.269507\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.4265 | −1.46820 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 64.0582 | 2.44397 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.21240 | 0.312867 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.8895 | −1.74572 | −0.872859 | − | 0.487972i | \(-0.837737\pi\) | ||||
−0.872859 | + | 0.487972i | \(0.837737\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.2133 | −1.25985 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.0655 | 1.10093 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 39.4317 | 1.49144 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0843 | −0.494189 | −0.247094 | − | 0.968991i | \(-0.579476\pi\) | ||||
−0.247094 | + | 0.968991i | \(0.579476\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.17687 | 0.0821024 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −39.9083 | −1.50304 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.8085 | 1.64526 | 0.822631 | − | 0.568575i | \(-0.192505\pi\) | ||||
0.822631 | + | 0.568575i | \(0.192505\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.6099 | 0.922942 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35.8522 | 1.34268 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.75457 | −0.215209 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −42.8223 | −1.59923 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 46.2184 | 1.72365 | 0.861827 | − | 0.507202i | \(-0.169320\pi\) | ||||
0.861827 | + | 0.507202i | \(0.169320\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.04795 | −0.224926 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.7918 | 1.10644 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.8085 | −1.55059 | −0.775296 | − | 0.631598i | \(-0.782399\pi\) | ||||
−0.775296 | + | 0.631598i | \(0.782399\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −32.7546 | −1.21313 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.53574 | −0.0568012 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.30405 | 0.0851022 | 0.0425511 | − | 0.999094i | \(-0.486451\pi\) | ||||
0.0425511 | + | 0.999094i | \(0.486451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.1645 | 0.374412 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.1405 | 0.556951 | 0.278476 | − | 0.960443i | \(-0.410171\pi\) | ||||
0.278476 | + | 0.960443i | \(0.410171\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.16445 | 0.0795131 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −51.2714 | −1.88097 | −0.940483 | − | 0.339839i | \(-0.889627\pi\) | ||||
−0.940483 | + | 0.339839i | \(0.889627\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.7357 | 0.429963 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.13317 | 0.224401 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.57770 | 0.276514 | 0.138257 | − | 0.990396i | \(-0.455850\pi\) | ||||
0.138257 | + | 0.990396i | \(0.455850\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.5537 | −0.530367 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.6835 | 1.22587 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.5109 | 1.29067 | 0.645333 | − | 0.763902i | \(-0.276719\pi\) | ||||
0.645333 | + | 0.763902i | \(0.276719\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.6514 | −1.03998 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.2861 | −1.20662 | −0.603309 | − | 0.797507i | \(-0.706152\pi\) | ||||
−0.603309 | + | 0.797507i | \(0.706152\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −41.4796 | −1.49970 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.5306 | 0.452455 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.6680 | −1.89926 | −0.949629 | − | 0.313377i | \(-0.898540\pi\) | ||||
−0.949629 | + | 0.313377i | \(0.898540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.27876 | −0.226124 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.62141 | 0.130253 | 0.0651264 | − | 0.997877i | \(-0.479255\pi\) | ||||
0.0651264 | + | 0.997877i | \(0.479255\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.4381 | 0.841921 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.69507 | −0.239876 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.4869 | −0.661514 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.06037 | 0.288054 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.0852 | −1.71624 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.85441 | −0.279979 | −0.139990 | − | 0.990153i | \(-0.544707\pi\) | ||||
−0.139990 | + | 0.990153i | \(0.544707\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.9383 | 0.603020 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.1156 | 0.394728 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 68.8012 | 2.44013 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.0355 | −0.709695 | −0.354847 | − | 0.934924i | \(-0.615467\pi\) | ||||
−0.354847 | + | 0.934924i | \(0.615467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0604 | 0.851195 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.0843 | 0.391646 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.23812 | 0.184849 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.6587 | −0.903228 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.4942 | 0.755697 | 0.377848 | − | 0.925867i | \(-0.376664\pi\) | ||||
0.377848 | + | 0.925867i | \(0.376664\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.15714 | 0.0406327 | 0.0203163 | − | 0.999794i | \(-0.493533\pi\) | ||||
0.0203163 | + | 0.999794i | \(0.493533\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −55.6731 | −1.95254 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37.9563 | 1.32955 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.353748 | 0.0123761 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.6463 | −0.895060 | −0.447530 | − | 0.894269i | \(-0.647696\pi\) | ||||
−0.447530 | + | 0.894269i | \(0.647696\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.8398 | 0.482425 | 0.241212 | − | 0.970472i | \(-0.422455\pi\) | ||||
0.241212 | + | 0.970472i | \(0.422455\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.7306 | −0.652116 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.23812 | 0.251694 | 0.125847 | − | 0.992050i | \(-0.459835\pi\) | ||||
0.125847 | + | 0.992050i | \(0.459835\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −56.2415 | −1.95335 | −0.976674 | − | 0.214729i | \(-0.931113\pi\) | ||||
−0.976674 | + | 0.214729i | \(0.931113\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.4629 | −0.813920 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −40.7473 | −1.41012 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.34132 | 0.219188 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.9272 | 0.757011 | 0.378506 | − | 0.925599i | \(-0.376438\pi\) | ||||
0.378506 | + | 0.925599i | \(0.376438\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.9417 | 2.03247 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.5661 | −1.12164 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −35.0612 | −1.20614 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −50.1332 | −1.72057 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.5786 | 0.362629 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.2008 | −0.725903 | −0.362952 | − | 0.931808i | \(-0.618231\pi\) | ||||
−0.362952 | + | 0.931808i | \(0.618231\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.55460 | 0.326760 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.0240 | −1.19640 | −0.598198 | − | 0.801348i | \(-0.704116\pi\) | ||||
−0.598198 | + | 0.801348i | \(0.704116\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.6441 | 1.48912 | 0.744558 | − | 0.667558i | \(-0.232660\pi\) | ||||
0.744558 | + | 0.667558i | \(0.232660\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.32159 | −0.181149 | −0.0905745 | − | 0.995890i | \(-0.528870\pi\) | ||||
−0.0905745 | + | 0.995890i | \(0.528870\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −59.1425 | −2.01091 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.65136 | 0.157969 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.2446 | −0.584981 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.73147 | −0.126436 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −60.8950 | −2.06099 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.6942 | −0.529955 | −0.264978 | − | 0.964255i | \(-0.585365\pi\) | ||||
−0.264978 | + | 0.964255i | \(0.585365\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −50.8094 | −1.71376 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.7743 | 0.767286 | 0.383643 | − | 0.923482i | \(-0.374669\pi\) | ||||
0.383643 | + | 0.923482i | \(0.374669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.4548 | 1.39506 | 0.697532 | − | 0.716554i | \(-0.254282\pi\) | ||||
0.697532 | + | 0.716554i | \(0.254282\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 104.978 | 3.52880 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.0415 | 1.00870 | 0.504348 | − | 0.863501i | \(-0.331733\pi\) | ||||
0.504348 | + | 0.863501i | \(0.331733\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.4017 | 0.616480 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.54217 | −0.185462 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 40.2060 | 1.34394 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.5182 | 0.351192 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 69.1862 | 2.30749 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −41.4796 | −1.38189 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.0852 | −0.667655 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.9323 | −0.827864 | −0.413932 | − | 0.910308i | \(-0.635845\pi\) | ||||
−0.413932 | + | 0.910308i | \(0.635845\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.0189 | −0.796655 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.8034 | −1.15309 | −0.576544 | − | 0.817066i | \(-0.695599\pi\) | ||||
−0.576544 | + | 0.817066i | \(0.695599\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.29762 | −0.142230 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 93.1237 | 3.07857 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.10408 | −0.0694072 | −0.0347036 | − | 0.999398i | \(-0.511049\pi\) | ||||
−0.0347036 | + | 0.999398i | \(0.511049\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 74.4663 | 2.45375 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.78673 | 0.223388 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.91565 | 0.227385 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.4192 | −0.572123 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.2985 | −0.501927 | −0.250964 | − | 0.967997i | \(-0.580747\pi\) | ||||
−0.250964 | + | 0.967997i | \(0.580747\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 44.7721 | 1.46577 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.0655 | 0.950543 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.8522 | −1.36725 | −0.683626 | − | 0.729832i | \(-0.739598\pi\) | ||||
−0.683626 | + | 0.729832i | \(0.739598\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −60.5575 | −1.97622 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.7918 | −0.514799 | −0.257400 | − | 0.966305i | \(-0.582866\pi\) | ||||
−0.257400 | + | 0.966305i | \(0.582866\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.5349 | −1.05948 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.1383 | 0.491928 | 0.245964 | − | 0.969279i | \(-0.420896\pi\) | ||||
0.245964 | + | 0.969279i | \(0.420896\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.92296 | −0.0624221 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39.0595 | 1.26659 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.5961 | 0.634780 | 0.317390 | − | 0.948295i | \(-0.397194\pi\) | ||||
0.317390 | + | 0.948295i | \(0.397194\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44.8240 | −1.45047 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −55.2903 | −1.78728 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.4308 | 0.755832 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.0175 | −0.419484 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.91653 | −0.0616952 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.0852 | −0.388634 | −0.194317 | − | 0.980939i | \(-0.562249\pi\) | ||||
−0.194317 | + | 0.980939i | \(0.562249\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.9323 | −0.351197 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.3589 | −0.557072 | −0.278536 | − | 0.960426i | \(-0.589849\pi\) | ||||
−0.278536 | + | 0.960426i | \(0.589849\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.87619 | 0.220214 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.9969 | −1.31161 | −0.655804 | − | 0.754931i | \(-0.727670\pi\) | ||||
−0.655804 | + | 0.754931i | \(0.727670\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.76699 | −0.248234 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.93319 | 0.0617220 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −54.1126 | −1.72592 | −0.862961 | − | 0.505270i | \(-0.831393\pi\) | ||||
−0.862961 | + | 0.505270i | \(0.831393\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −68.5746 | −2.18497 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.71905 | 0.0546625 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.9241 | −0.855273 | −0.427637 | − | 0.903951i | \(-0.640654\pi\) | ||||
−0.427637 | + | 0.903951i | \(0.640654\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 75.2526 | 2.38807 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.5555 | −1.53931 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.7845 | −0.784934 | −0.392467 | − | 0.919766i | \(-0.628378\pi\) | ||||
−0.392467 | + | 0.919766i | \(0.628378\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.87107 | 0.0591982 |
(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 | 3724.2.a.i.1.3 | 3 | ||
7.6 | odd | 2 | 532.2.a.e.1.1 | ✓ | 3 | ||
21.20 | even | 2 | 4788.2.a.o.1.3 | 3 | |||
28.27 | even | 2 | 2128.2.a.r.1.3 | 3 | |||
56.13 | odd | 2 | 8512.2.a.bn.1.3 | 3 | |||
56.27 | even | 2 | 8512.2.a.bl.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
532.2.a.e.1.1 | ✓ | 3 | 7.6 | odd | 2 | ||
2128.2.a.r.1.3 | 3 | 28.27 | even | 2 | |||
3724.2.a.i.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4788.2.a.o.1.3 | 3 | 21.20 | even | 2 | |||
8512.2.a.bl.1.1 | 3 | 56.27 | even | 2 | |||
8512.2.a.bn.1.3 | 3 | 56.13 | odd | 2 |